LMFDB - Embedded newform 432.3.bc.c.65.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,3,Mod(65,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 13]))

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

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

chi := DirichletCharacter("432.65");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	432.bc (of order $18$, degree $6$, 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:	$11.7711474204$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			65.1
Character	$\chi$	$=$	432.65
Dual form			432.3.bc.c.113.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.80846 + 1.05478i) q^{3} +(2.86430 - 7.86960i) q^{5} +(1.95208 - 11.0708i) q^{7} +(6.77487 - 5.92462i) q^{9} +O(q^{10})$	\(q+(-2.80846 + 1.05478i) q^{3} +(2.86430 - 7.86960i) q^{5} +(1.95208 - 11.0708i) q^{7} +(6.77487 - 5.92462i) q^{9} +(-0.538121 - 1.47848i) q^{11} +(-6.82419 + 5.72617i) q^{13} +(0.256445 + 25.1227i) q^{15} +(-16.9870 + 9.80744i) q^{17} +(-4.86486 + 8.42619i) q^{19} +(6.19496 + 33.1510i) q^{21} +(13.8255 - 2.43781i) q^{23} +(-34.5753 - 29.0121i) q^{25} +(-12.7778 + 23.7851i) q^{27} +(7.05122 - 8.40331i) q^{29} +(-8.04854 - 45.6456i) q^{31} +(3.07076 + 3.58464i) q^{33} +(-81.5316 - 47.0723i) q^{35} +(7.89337 + 13.6717i) q^{37} +(13.1256 - 23.2797i) q^{39} +(-6.59742 - 7.86250i) q^{41} +(-24.6205 + 8.96112i) q^{43} +(-27.2191 - 70.2854i) q^{45} +(42.2938 + 7.45754i) q^{47} +(-72.7075 - 26.4634i) q^{49} +(37.3625 - 45.4614i) q^{51} +41.5395i q^{53} -13.1764 q^{55} +(4.77497 - 28.7960i) q^{57} +(-20.6989 + 56.8698i) q^{59} +(13.2934 - 75.3906i) q^{61} +(-52.3653 - 86.5688i) q^{63} +(25.5162 + 70.1051i) q^{65} +(-2.09011 + 1.75381i) q^{67} +(-36.2569 + 21.4293i) q^{69} +(-65.1324 + 37.6042i) q^{71} +(33.0777 - 57.2922i) q^{73} +(127.705 + 45.0099i) q^{75} +(-17.4184 + 3.07133i) q^{77} +(-38.8113 - 32.5666i) q^{79} +(10.7977 - 80.2771i) q^{81} +(-21.4712 + 25.5884i) q^{83} +(28.5248 + 161.772i) q^{85} +(-10.9394 + 31.0378i) q^{87} +(-75.2876 - 43.4673i) q^{89} +(50.0720 + 86.7273i) q^{91} +(70.7501 + 119.704i) q^{93} +(52.3763 + 62.4197i) q^{95} +(132.434 - 48.2019i) q^{97} +(-12.4051 - 6.82832i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{5} - 12 q^{9}+O(q^{10}) $ 36 * q + 18 * q^5 - 12 * q^9	$ 36 q + 18 q^{5} - 12 q^{9} + 18 q^{11} + 18 q^{15} - 228 q^{21} + 180 q^{23} + 18 q^{25} - 54 q^{27} + 144 q^{29} + 90 q^{31} + 324 q^{33} - 486 q^{35} - 102 q^{39} - 90 q^{41} - 90 q^{43} - 378 q^{45} + 378 q^{47} + 72 q^{49} + 54 q^{51} + 72 q^{57} - 252 q^{59} - 144 q^{61} - 318 q^{63} + 18 q^{65} + 594 q^{67} - 522 q^{69} + 648 q^{71} + 126 q^{73} + 438 q^{75} - 342 q^{77} + 72 q^{79} + 324 q^{81} - 594 q^{83} + 360 q^{85} - 1062 q^{87} + 648 q^{89} + 198 q^{91} + 462 q^{93} - 252 q^{95} + 702 q^{97} - 126 q^{99}+O(q^{100}) $ 36 * q + 18 * q^5 - 12 * q^9 + 18 * q^11 + 18 * q^15 - 228 * q^21 + 180 * q^23 + 18 * q^25 - 54 * q^27 + 144 * q^29 + 90 * q^31 + 324 * q^33 - 486 * q^35 - 102 * q^39 - 90 * q^41 - 90 * q^43 - 378 * q^45 + 378 * q^47 + 72 * q^49 + 54 * q^51 + 72 * q^57 - 252 * q^59 - 144 * q^61 - 318 * q^63 + 18 * q^65 + 594 * q^67 - 522 * q^69 + 648 * q^71 + 126 * q^73 + 438 * q^75 - 342 * q^77 + 72 * q^79 + 324 * q^81 - 594 * q^83 + 360 * q^85 - 1062 * q^87 + 648 * q^89 + 198 * q^91 + 462 * q^93 - 252 * q^95 + 702 * q^97 - 126 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{13}{18}\right)$

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
$3$	−2.80846	+	1.05478i	−0.936153	+	0.351594i
$3$	−2.80846	+	1.05478i	−0.936153	+	0.351594i
$4$		0			0
$5$	2.86430	−	7.86960i	0.572860	−	1.57392i	−0.227103	−	0.973871i	$-0.572925\pi$
$5$	2.86430	−	7.86960i	0.572860	−	1.57392i	0.799963	−	0.600049i	$-0.204852\pi$
$6$		0			0
$7$	1.95208	−	11.0708i	0.278869	−	1.58155i	−0.447527	−	0.894270i	$-0.647695\pi$
$7$	1.95208	−	11.0708i	0.278869	−	1.58155i	0.726397	−	0.687276i	$-0.241194\pi$
$8$		0			0
$9$	6.77487	−	5.92462i	0.752763	−	0.658291i
$10$		0			0
$11$	−0.538121	−	1.47848i	−0.0489201	−	0.134407i	0.912826	−	0.408348i	$-0.133895\pi$
$11$	−0.538121	−	1.47848i	−0.0489201	−	0.134407i	−0.961747	+	0.273941i	$0.911673\pi$
$12$		0			0
$13$	−6.82419	+	5.72617i	−0.524937	+	0.440475i	−0.866349	−	0.499439i	$-0.833539\pi$
$13$	−6.82419	+	5.72617i	−0.524937	+	0.440475i	0.341412	+	0.939914i	$0.389095\pi$
$14$		0			0
$15$	0.256445	+	25.1227i	0.0170963	+	1.67484i
$16$		0			0
$17$	−16.9870	+	9.80744i	−0.999235	+	0.576909i	−0.908022	−	0.418923i	$-0.862408\pi$
$17$	−16.9870	+	9.80744i	−0.999235	+	0.576909i	−0.0912130	+	0.995831i	$0.529074\pi$
$18$		0			0
$19$	−4.86486	+	8.42619i	−0.256045	+	0.443484i	−0.965179	−	0.261591i	$-0.915753\pi$
$19$	−4.86486	+	8.42619i	−0.256045	+	0.443484i	0.709134	+	0.705074i	$0.249086\pi$
$20$		0			0
$21$	6.19496	+	33.1510i	0.294998	+	1.57862i
$22$		0			0
$23$	13.8255	−	2.43781i	0.601108	−	0.105992i	0.135190	−	0.990820i	$-0.456835\pi$
$23$	13.8255	−	2.43781i	0.601108	−	0.105992i	0.465918	+	0.884828i	$0.345724\pi$
$24$		0			0
$25$	−34.5753	−	29.0121i	−1.38301	−	1.16048i
$26$		0			0
$27$	−12.7778	+	23.7851i	−0.473250	+	0.880928i
$28$		0			0
$29$	7.05122	−	8.40331i	0.243145	−	0.289769i	−0.630646	−	0.776071i	$-0.717210\pi$
$29$	7.05122	−	8.40331i	0.243145	−	0.289769i	0.873791	+	0.486301i	$0.161654\pi$
$30$		0			0
$31$	−8.04854	−	45.6456i	−0.259630	−	1.47244i	−0.783901	−	0.620886i	$-0.786773\pi$
$31$	−8.04854	−	45.6456i	−0.259630	−	1.47244i	0.524271	−	0.851552i	$-0.324338\pi$
$32$		0			0
$33$	3.07076	+	3.58464i	0.0930534	+	0.108625i
$34$		0			0
$35$	−81.5316	−	47.0723i	−2.32947	−	1.34492i
$36$		0			0
$37$	7.89337	+	13.6717i	0.213334	+	0.369506i	0.952756	−	0.303737i	$-0.0982343\pi$
$37$	7.89337	+	13.6717i	0.213334	+	0.369506i	−0.739422	+	0.673243i	$0.764901\pi$
$38$		0			0
$39$	13.1256	−	23.2797i	0.336553	−	0.596916i
$40$		0			0
$41$	−6.59742	−	7.86250i	−0.160913	−	0.191768i	0.679564	−	0.733617i	$-0.262169\pi$
$41$	−6.59742	−	7.86250i	−0.160913	−	0.191768i	−0.840476	+	0.541848i	$0.817725\pi$
$42$		0			0
$43$	−24.6205	+	8.96112i	−0.572569	+	0.208398i	−0.612046	−	0.790822i	$-0.709653\pi$
$43$	−24.6205	+	8.96112i	−0.572569	+	0.208398i	0.0394765	+	0.999220i	$0.487431\pi$
$44$		0			0
$45$	−27.2191	−	70.2854i	−0.604870	−	1.56190i
$46$		0			0
$47$	42.2938	+	7.45754i	0.899868	+	0.158671i	0.604399	−	0.796682i	$-0.293413\pi$
$47$	42.2938	+	7.45754i	0.899868	+	0.158671i	0.295468	+	0.955352i	$0.404524\pi$
$48$		0			0
$49$	−72.7075	−	26.4634i	−1.48383	−	0.540069i
$50$		0			0
$51$	37.3625	−	45.4614i	0.732599	−	0.891399i
$52$		0			0
$53$			41.5395i			0.783764i	0.920016	+	0.391882i	$0.128176\pi$
$53$			41.5395i			0.783764i	−0.920016	+	0.391882i	$0.871824\pi$
$54$		0			0
$55$	−13.1764			−0.239570
$56$		0			0
$57$	4.77497	−	28.7960i	0.0837714	−	0.505192i
$58$		0			0
$59$	−20.6989	+	56.8698i	−0.350829	+	0.963895i	0.631275	+	0.775559i	$0.282532\pi$
$59$	−20.6989	+	56.8698i	−0.350829	+	0.963895i	−0.982105	+	0.188336i	$0.939690\pi$
$60$		0			0
$61$	13.2934	−	75.3906i	0.217924	−	1.23591i	−0.657835	−	0.753162i	$-0.728527\pi$
$61$	13.2934	−	75.3906i	0.217924	−	1.23591i	0.875759	−	0.482748i	$-0.160361\pi$
$62$		0			0
$63$	−52.3653	−	86.5688i	−0.831195	−	1.37411i
$64$		0			0
$65$	25.5162	+	70.1051i	0.392556	+	1.07854i
$66$		0			0
$67$	−2.09011	+	1.75381i	−0.0311956	+	0.0261762i	−0.658252	−	0.752798i	$-0.728704\pi$
$67$	−2.09011	+	1.75381i	−0.0311956	+	0.0261762i	0.627057	+	0.778974i	$0.284259\pi$
$68$		0			0
$69$	−36.2569	+	21.4293i	−0.525463	+	0.310570i
$70$		0			0
$71$	−65.1324	+	37.6042i	−0.917358	+	0.529637i	−0.882791	−	0.469765i	$-0.844338\pi$
$71$	−65.1324	+	37.6042i	−0.917358	+	0.529637i	−0.0345668	+	0.999402i	$0.511005\pi$
$72$		0			0
$73$	33.0777	−	57.2922i	0.453119	−	0.784825i	−0.545459	−	0.838138i	$-0.683645\pi$
$73$	33.0777	−	57.2922i	0.453119	−	0.784825i	0.998578	+	0.0533125i	$0.0169779\pi$
$74$		0			0
$75$	127.705	+	45.0099i	1.70273	+	0.600132i
$76$		0			0
$77$	−17.4184	+	3.07133i	−0.226213	+	0.0398875i
$78$		0			0
$79$	−38.8113	−	32.5666i	−0.491283	−	0.412235i	0.363203	−	0.931710i	$-0.381683\pi$
$79$	−38.8113	−	32.5666i	−0.491283	−	0.412235i	−0.854486	+	0.519475i	$0.826128\pi$
$80$		0			0
$81$	10.7977	−	80.2771i	0.133305	−	0.991075i
$82$		0			0
$83$	−21.4712	+	25.5884i	−0.258689	+	0.308294i	−0.879720	−	0.475492i	$-0.842270\pi$
$83$	−21.4712	+	25.5884i	−0.258689	+	0.308294i	0.621030	+	0.783787i	$0.286714\pi$
$84$		0			0
$85$	28.5248	+	161.772i	0.335586	+	1.90320i
$86$		0			0
$87$	−10.9394	+	31.0378i	−0.125740	+	0.356757i
$88$		0			0
$89$	−75.2876	−	43.4673i	−0.845928	−	0.488397i	0.0133471	−	0.999911i	$-0.495751\pi$
$89$	−75.2876	−	43.4673i	−0.845928	−	0.488397i	−0.859275	+	0.511514i	$0.829085\pi$
$90$		0			0
$91$	50.0720	+	86.7273i	0.550242	+	0.953047i
$92$		0			0
$93$	70.7501	+	119.704i	0.760754	+	1.28714i
$94$		0			0
$95$	52.3763	+	62.4197i	0.551330	+	0.657049i
$96$		0			0
$97$	132.434	−	48.2019i	1.36530	−	0.496927i	0.447608	−	0.894230i	$-0.352276\pi$
$97$	132.434	−	48.2019i	1.36530	−	0.496927i	0.917688	+	0.397303i	$0.130054\pi$
$98$		0			0
$99$	−12.4051	−	6.82832i	−0.125304	−	0.0689729i
$100$		0			0
$101$	−88.8791	−	15.6718i	−0.879991	−	0.155166i	−0.284642	−	0.958634i	$-0.591875\pi$
$101$	−88.8791	−	15.6718i	−0.879991	−	0.155166i	−0.595348	+	0.803468i	$0.702986\pi$
$102$		0			0
$103$	−19.7299	−	7.18111i	−0.191553	−	0.0697195i	0.244463	−	0.969659i	$-0.421388\pi$
$103$	−19.7299	−	7.18111i	−0.191553	−	0.0697195i	−0.436015	+	0.899939i	$0.643611\pi$
$104$		0			0
$105$	278.629	+	46.2025i	2.65361	+	0.440024i
$106$		0			0
$107$			21.8959i			0.204635i	0.994752	+	0.102317i	$0.0326257\pi$
$107$			21.8959i			0.204635i	−0.994752	+	0.102317i	$0.967374\pi$
$108$		0			0
$109$	−92.6448			−0.849953			−0.424976	−	0.905204i	$-0.639718\pi$
$109$	−92.6448			−0.849953			−0.424976	+	0.905204i	$0.639718\pi$
$110$		0			0
$111$	−36.5889	−	30.0707i	−0.329629	−	0.270907i
$112$		0			0
$113$	−52.9813	+	145.565i	−0.468861	+	1.28819i	0.449796	+	0.893131i	$0.351497\pi$
$113$	−52.9813	+	145.565i	−0.468861	+	1.28819i	−0.918657	+	0.395055i	$0.870726\pi$
$114$		0			0
$115$	20.4158	−	115.784i	0.177529	−	1.00681i
$116$		0			0
$117$	−12.3076	+	79.2248i	−0.105193	+	0.677135i
$118$		0			0
$119$	75.4164	+	207.205i	0.633752	+	1.74122i
$120$		0			0
$121$	90.7951	−	76.1861i	0.750372	−	0.629637i
$122$		0			0
$123$	26.8218	+	15.1227i	0.218063	+	0.122948i
$124$		0			0
$125$	−146.031	+	84.3111i	−1.16825	+	0.674489i
$126$		0			0
$127$	115.693	−	200.387i	0.910971	−	1.57785i	0.0982763	−	0.995159i	$-0.468667\pi$
$127$	115.693	−	200.387i	0.910971	−	1.57785i	0.812695	−	0.582689i	$-0.198000\pi$
$128$		0			0
$129$	59.6935	−	51.1362i	0.462741	−	0.396404i
$130$		0			0
$131$	69.0825	−	12.1811i	0.527347	−	0.0929856i	0.0963653	−	0.995346i	$-0.469278\pi$
$131$	69.0825	−	12.1811i	0.527347	−	0.0929856i	0.430982	+	0.902360i	$0.358167\pi$
$132$		0			0
$133$	83.7882	+	70.3067i	0.629987	+	0.528621i
$134$		0			0
$135$	150.580	+	168.683i	1.11540	+	1.24951i
$136$		0			0
$137$	136.898	−	163.149i	0.999257	−	1.19087i	0.0176713	−	0.999844i	$-0.494375\pi$
$137$	136.898	−	163.149i	0.999257	−	1.19087i	0.981585	−	0.191024i	$-0.0611808\pi$
$138$		0			0
$139$	−9.79795	−	55.5669i	−0.0704888	−	0.399762i	−0.999554	−	0.0298471i	$-0.990498\pi$
$139$	−9.79795	−	55.5669i	−0.0704888	−	0.399762i	0.929066	−	0.369915i	$-0.120613\pi$
$140$		0			0
$141$	−126.646	+	23.6665i	−0.898201	+	0.167848i
$142$		0			0
$143$	12.1382	+	7.00802i	0.0848829	+	0.0490071i
$144$		0			0
$145$	−45.9339	−	79.5599i	−0.316786	−	0.548689i
$146$		0			0
$147$	232.109	−	2.36931i	1.57897	−	0.0161177i
$148$		0			0
$149$	18.5161	+	22.0666i	0.124269	+	0.148098i	0.824592	−	0.565728i	$-0.191405\pi$
$149$	18.5161	+	22.0666i	0.124269	+	0.148098i	−0.700323	+	0.713826i	$0.746961\pi$
$150$		0			0
$151$	145.452	−	52.9400i	0.963255	−	0.350596i	0.187947	−	0.982179i	$-0.439817\pi$
$151$	145.452	−	52.9400i	0.963255	−	0.350596i	0.775308	+	0.631583i	$0.217595\pi$
$152$		0			0
$153$	−56.9793	+	167.086i	−0.372414	+	1.09206i
$154$		0			0
$155$	−382.266	−	67.4038i	−2.46623	−	0.434863i
$156$		0			0
$157$	−200.915	−	73.1270i	−1.27971	−	0.465777i	−0.389375	−	0.921080i	$-0.627309\pi$
$157$	−200.915	−	73.1270i	−1.27971	−	0.465777i	−0.890337	+	0.455303i	$0.849531\pi$
$158$		0			0
$159$	−43.8151	−	116.662i	−0.275567	−	0.733722i
$160$		0			0
$161$		−	157.818i		−	0.980238i
$162$		0			0
$163$	−147.201			−0.903076			−0.451538	−	0.892252i	$-0.649124\pi$
$163$	−147.201			−0.903076			−0.451538	+	0.892252i	$0.649124\pi$
$164$		0			0
$165$	37.0052	−	13.8982i	0.224274	−	0.0842314i
$166$		0			0
$167$	50.5448	−	138.871i	0.302664	−	0.831561i	−0.691371	−	0.722500i	$-0.742993\pi$
$167$	50.5448	−	138.871i	0.302664	−	0.831561i	0.994035	−	0.109062i	$-0.0347846\pi$
$168$		0			0
$169$	−15.5661	+	88.2796i	−0.0921070	+	0.522364i
$170$		0			0
$171$	16.9632	+	85.9088i	0.0991997	+	0.502391i
$172$		0			0
$173$	72.2331	+	198.459i	0.417532	+	1.14716i	0.953097	+	0.302666i	$0.0978766\pi$
$173$	72.2331	+	198.459i	0.417532	+	1.14716i	−0.535565	+	0.844494i	$0.679901\pi$
$174$		0			0
$175$	−388.682	+	326.143i	−2.22104	+	1.86367i
$176$		0			0
$177$	−1.85320	−	181.549i	−0.0104701	−	1.02570i
$178$		0			0
$179$	225.133	−	129.980i	1.25772	−	0.726147i	0.285092	−	0.958500i	$-0.407976\pi$
$179$	225.133	−	129.980i	1.25772	−	0.726147i	0.972632	+	0.232353i	$0.0746424\pi$
$180$		0			0
$181$	159.698	−	276.606i	0.882311	−	1.52821i	0.0335470	−	0.999437i	$-0.489320\pi$
$181$	159.698	−	276.606i	0.882311	−	1.52821i	0.848764	−	0.528771i	$-0.177347\pi$
$182$		0			0
$183$	42.1867	+	225.753i	0.230528	+	1.23362i
$184$		0			0
$185$	130.200	−	22.9578i	0.703783	−	0.124096i
$186$		0			0
$187$	23.6411	+	19.8373i	0.126423	+	0.106082i
$188$		0			0
$189$	238.377	+	187.891i	1.26125	+	0.994131i
$190$		0			0
$191$	25.0422	−	29.8442i	0.131111	−	0.156252i	−0.696495	−	0.717562i	$-0.745258\pi$
$191$	25.0422	−	29.8442i	0.131111	−	0.156252i	0.827606	+	0.561310i	$0.189702\pi$
$192$		0			0
$193$	−28.3760	−	160.928i	−0.147026	−	0.833825i	−0.965718	−	0.259593i	$-0.916412\pi$
$193$	−28.3760	−	160.928i	−0.147026	−	0.833825i	0.818692	−	0.574233i	$-0.194699\pi$
$194$		0			0
$195$	−145.607	−	169.973i	−0.746701	−	0.871657i
$196$		0			0
$197$	296.815	+	171.366i	1.50668	+	0.869880i	0.999970	+	0.00776089i	$0.00247039\pi$
$197$	296.815	+	171.366i	1.50668	+	0.869880i	0.506706	+	0.862119i	$0.330863\pi$
$198$		0			0
$199$	−98.8611	−	171.232i	−0.496789	−	0.860464i	0.503204	−	0.864168i	$-0.332155\pi$
$199$	−98.8611	−	171.232i	−0.496789	−	0.860464i	−0.999993	+	0.00370331i	$0.998821\pi$
$200$		0			0
$201$	4.02009	−	7.13010i	0.0200005	−	0.0354731i
$202$		0			0
$203$	−79.2670	−	94.4668i	−0.390478	−	0.465353i
$204$		0			0
$205$	−80.7718	+	29.3985i	−0.394009	+	0.143407i
$206$		0			0
$207$	79.2228	−	98.4266i	0.382719	−	0.475491i
$208$		0			0
$209$	15.0758	+	2.65827i	0.0721330	+	0.0127190i
$210$		0			0
$211$	214.619	+	78.1150i	1.01715	+	0.370213i	0.796176	−	0.605066i	$-0.206853\pi$
$211$	214.619	+	78.1150i	1.01715	+	0.370213i	0.220977	+	0.975279i	$0.429075\pi$
$212$		0			0
$213$	143.257	−	174.310i	0.672570	−	0.818359i
$214$		0			0
$215$			219.421i			1.02056i
$216$		0			0
$217$	−521.045			−2.40113
$218$		0			0
$219$	−32.4665	+	195.793i	−0.148249	+	0.894030i
$220$		0			0
$221$	59.7633	−	164.198i	0.270422	−	0.742979i
$222$		0			0
$223$	−67.0596	+	380.314i	−0.300716	+	1.70544i	0.342301	+	0.939590i	$0.388794\pi$
$223$	−67.0596	+	380.314i	−0.300716	+	1.70544i	−0.643016	+	0.765852i	$0.722317\pi$
$224$		0			0
$225$	−406.129	+	8.29216i	−1.80502	+	0.0368541i
$226$		0			0
$227$	63.6795	+	174.958i	0.280527	+	0.770740i	0.997300	+	0.0734342i	$0.0233959\pi$
$227$	63.6795	+	174.958i	0.280527	+	0.770740i	−0.716774	+	0.697306i	$0.754382\pi$
$228$		0			0
$229$	−236.706	+	198.620i	−1.03365	+	0.867336i	−0.991281	−	0.131766i	$-0.957935\pi$
$229$	−236.706	+	198.620i	−1.03365	+	0.867336i	−0.0423704	+	0.999102i	$0.513491\pi$
$230$		0			0
$231$	45.6793	−	26.9983i	0.197746	−	0.116876i
$232$		0			0
$233$	−17.8085	+	10.2818i	−0.0764315	+	0.0441277i	−0.537729	−	0.843118i	$-0.680718\pi$
$233$	−17.8085	+	10.2818i	−0.0764315	+	0.0441277i	0.461297	+	0.887246i	$0.347384\pi$
$234$		0			0
$235$	179.830	−	311.475i	0.765234	−	1.32542i
$236$		0			0
$237$	143.351	+	50.5243i	0.604855	+	0.213183i
$238$		0			0
$239$	101.144	−	17.8344i	0.423197	−	0.0746211i	0.0420061	−	0.999117i	$-0.486625\pi$
$239$	101.144	−	17.8344i	0.423197	−	0.0746211i	0.381191	+	0.924496i	$0.375514\pi$
$240$		0			0
$241$	294.337	+	246.978i	1.22131	+	1.02480i	0.998755	+	0.0498853i	$0.0158856\pi$
$241$	294.337	+	246.978i	1.22131	+	1.02480i	0.222559	+	0.974919i	$0.428559\pi$
$242$		0			0
$243$	54.3498	+	236.844i	0.223662	+	0.974667i
$244$		0			0
$245$	−416.512	+	496.380i	−1.70005	+	2.02604i
$246$		0			0
$247$	−15.0511	−	85.3589i	−0.0609355	−	0.345583i
$248$		0			0
$249$	33.3108	−	94.5114i	0.133778	−	0.379564i
$250$		0			0
$251$	−281.668	−	162.621i	−1.12218	−	0.647893i	−0.180227	−	0.983625i	$-0.557683\pi$
$251$	−281.668	−	162.621i	−1.12218	−	0.647893i	−0.941958	+	0.335732i	$0.891016\pi$
$252$		0			0
$253$	−11.0440	−	19.1288i	−0.0436523	−	0.0756080i
$254$		0			0
$255$	−250.745	−	424.243i	−0.983315	−	1.66370i
$256$		0			0
$257$	−21.5034	−	25.6267i	−0.0836708	−	0.0997150i	0.722585	−	0.691282i	$-0.242954\pi$
$257$	−21.5034	−	25.6267i	−0.0836708	−	0.0997150i	−0.806256	+	0.591567i	$0.798509\pi$
$258$		0			0
$259$	166.766	−	60.6977i	0.643883	−	0.234354i
$260$		0			0
$261$	−2.01536	−	98.7072i	−0.00772169	−	0.378188i
$262$		0			0
$263$	154.814	+	27.2979i	0.588646	+	0.103794i	0.460035	−	0.887901i	$-0.347837\pi$
$263$	154.814	+	27.2979i	0.588646	+	0.103794i	0.128611	+	0.991695i	$0.458948\pi$
$264$		0			0
$265$	326.899	+	118.982i	1.23358	+	0.448987i
$266$		0			0
$267$	257.290	+	42.6641i	0.963635	+	0.159791i
$268$		0			0
$269$		−	289.194i		−	1.07507i	−0.843241	−	0.537536i	$-0.819355\pi$
$269$		−	289.194i		−	1.07507i	0.843241	−	0.537536i	$-0.180645\pi$
$270$		0			0
$271$	−438.046			−1.61641			−0.808204	−	0.588903i	$-0.799560\pi$
$271$	−438.046			−1.61641			−0.808204	+	0.588903i	$0.799560\pi$
$272$		0			0
$273$	−232.104	−	190.755i	−0.850196	−	0.698736i
$274$		0			0
$275$	−24.2880	+	66.7308i	−0.0883201	+	0.242657i
$276$		0			0
$277$	2.95396	−	16.7527i	0.0106641	−	0.0604791i	−0.979011	−	0.203806i	$-0.934669\pi$
$277$	2.95396	−	16.7527i	0.0106641	−	0.0604791i	0.989675	+	0.143327i	$0.0457800\pi$
$278$		0			0
$279$	−324.960	−	261.558i	−1.16473	−	0.937484i
$280$		0			0
$281$	31.3851	+	86.2298i	0.111691	+	0.306867i	0.982927	−	0.183996i	$-0.0589035\pi$
$281$	31.3851	+	86.2298i	0.111691	+	0.306867i	−0.871236	+	0.490864i	$0.836681\pi$
$282$		0			0
$283$	335.404	−	281.438i	1.18517	−	0.994479i	0.185243	−	0.982693i	$-0.440693\pi$
$283$	335.404	−	281.438i	1.18517	−	0.994479i	0.999931	−	0.0117863i	$-0.00375180\pi$
$284$		0			0
$285$	−212.936	−	120.057i	−0.747143	−	0.421254i
$286$		0			0
$287$	−99.9231	+	57.6906i	−0.348164	+	0.201013i
$288$		0			0
$289$	47.8719	−	82.9166i	0.165647	−	0.286909i
$290$		0			0
$291$	−321.092	+	275.062i	−1.10341	+	0.945229i
$292$		0			0
$293$	254.746	−	44.9185i	0.869439	−	0.153305i	0.278905	−	0.960319i	$-0.410028\pi$
$293$	254.746	−	44.9185i	0.869439	−	0.153305i	0.590533	+	0.807013i	$0.298917\pi$
$294$		0			0
$295$	388.255	+	325.784i	1.31612	+	1.10435i
$296$		0			0
$297$	42.0416	+	6.09236i	0.141554	+	0.0205130i
$298$		0			0
$299$	−80.3884	+	95.8031i	−0.268857	+	0.320412i
$300$		0			0
$301$	51.1457	+	290.062i	0.169919	+	0.963661i
$302$		0			0
$303$	266.143	−	49.7345i	0.878361	−	0.164140i
$304$		0			0
$305$	−555.217	−	320.555i	−1.82038	−	1.05100i
$306$		0			0
$307$	−106.596	−	184.630i	−0.347219	−	0.601401i	0.638535	−	0.769592i	$-0.279541\pi$
$307$	−106.596	−	184.630i	−0.347219	−	0.601401i	−0.985754	+	0.168192i	$0.946207\pi$
$308$		0			0
$309$	62.9852	−	0.642935i	0.203835	−	0.00208070i
$310$		0			0
$311$	−299.915	−	357.425i	−0.964358	−	1.14928i	−0.988750	−	0.149575i	$-0.952210\pi$
$311$	−299.915	−	357.425i	−0.964358	−	1.14928i	0.0243925	−	0.999702i	$-0.492235\pi$
$312$		0			0
$313$	−88.7107	+	32.2881i	−0.283421	+	0.103157i	−0.479819	−	0.877367i	$-0.659298\pi$
$313$	−88.7107	+	32.2881i	−0.283421	+	0.103157i	0.196398	+	0.980524i	$0.437075\pi$
$314$		0			0
$315$	−831.251	+	164.135i	−2.63889	+	0.521064i
$316$		0			0
$317$	−250.991	−	44.2565i	−0.791769	−	0.139610i	−0.236885	−	0.971538i	$-0.576126\pi$
$317$	−250.991	−	44.2565i	−0.791769	−	0.139610i	−0.554884	+	0.831927i	$0.687238\pi$
$318$		0			0
$319$	−16.2185	−	5.90305i	−0.0508417	−	0.0185049i
$320$		0			0
$321$	−23.0954	−	61.4938i	−0.0719484	−	0.191569i
$322$		0			0
$323$		−	190.847i		−	0.590859i
$324$		0			0
$325$	402.076			1.23716
$326$		0			0
$327$	260.189	−	97.7201i	0.795685	−	0.298838i
$328$		0			0
$329$	165.122	−	453.669i	0.501891	−	1.37893i
$330$		0			0
$331$	63.9844	−	362.874i	0.193306	−	1.09629i	−0.721504	−	0.692410i	$-0.756549\pi$
$331$	63.9844	−	362.874i	0.193306	−	1.09629i	0.914810	−	0.403884i	$-0.132340\pi$
$332$		0			0
$333$	134.476	+	45.8589i	0.403833	+	0.137714i
$334$		0			0
$335$	7.81507	+	21.4717i	0.0233286	+	0.0640947i
$336$		0			0
$337$	150.868	−	126.593i	0.447679	−	0.375647i	−0.390895	−	0.920435i	$-0.627834\pi$
$337$	150.868	−	126.593i	0.447679	−	0.375647i	0.838574	+	0.544788i	$0.183390\pi$
$338$		0			0
$339$	−4.74350	−	464.697i	−0.0139926	−	1.37079i
$340$		0			0
$341$	−63.1548	+	36.4624i	−0.185205	+	0.106928i
$342$		0			0
$343$	−159.483	+	276.233i	−0.464966	+	0.805344i
$344$		0			0
$345$	64.7896	+	346.708i	0.187796	+	1.00495i
$346$		0			0
$347$	263.673	−	46.4927i	0.759864	−	0.133985i	0.219727	−	0.975561i	$-0.429483\pi$
$347$	263.673	−	46.4927i	0.759864	−	0.133985i	0.540137	+	0.841577i	$0.318372\pi$
$348$		0			0
$349$	−395.788	−	332.105i	−1.13406	−	0.951591i	−0.134834	−	0.990868i	$-0.543050\pi$
$349$	−395.788	−	332.105i	−1.13406	−	0.951591i	−0.999228	+	0.0392770i	$0.987495\pi$
$350$		0			0
$351$	−48.9995	−	235.481i	−0.139600	−	0.670887i
$352$		0			0
$353$	−186.396	+	222.139i	−0.528035	+	0.629288i	−0.962461	−	0.271420i	$-0.912507\pi$
$353$	−186.396	+	222.139i	−0.528035	+	0.629288i	0.434426	+	0.900708i	$0.356951\pi$
$354$		0			0
$355$	109.371	+	620.276i	0.308088	+	1.74726i
$356$		0			0
$357$	−430.360	−	502.378i	−1.20549	−	1.40722i
$358$		0			0
$359$	−35.8110	−	20.6755i	−0.0997520	−	0.0575918i	0.449294	−	0.893384i	$-0.351676\pi$
$359$	−35.8110	−	20.6755i	−0.0997520	−	0.0575918i	−0.549046	+	0.835792i	$0.685009\pi$
$360$		0			0
$361$	133.166	+	230.651i	0.368882	+	0.638922i
$362$		0			0
$363$	−174.634	+	309.734i	−0.481086	+	0.853263i
$364$		0			0
$365$	−356.123	−	424.410i	−0.975678	−	1.16277i
$366$		0			0
$367$	−152.544	+	55.5215i	−0.415651	+	0.151285i	−0.541376	−	0.840780i	$-0.682097\pi$
$367$	−152.544	+	55.5215i	−0.415651	+	0.151285i	0.125725	+	0.992065i	$0.459874\pi$
$368$		0			0
$369$	−91.2790	−	14.1802i	−0.247369	−	0.0384287i
$370$		0			0
$371$	459.876	+	81.0886i	1.23956	+	0.218568i
$372$		0			0
$373$	63.6401	+	23.1631i	0.170617	+	0.0620995i	0.425916	−	0.904763i	$-0.359952\pi$
$373$	63.6401	+	23.1631i	0.170617	+	0.0620995i	−0.255299	+	0.966862i	$0.582174\pi$
$374$		0			0
$375$	321.193	−	390.815i	0.856513	−	1.04217i
$376$		0			0
$377$			97.7223i			0.259210i
$378$		0			0
$379$	−122.431			−0.323038			−0.161519	−	0.986870i	$-0.551639\pi$
$379$	−122.431			−0.323038			−0.161519	+	0.986870i	$0.551639\pi$
$380$		0			0
$381$	−113.556	+	684.809i	−0.298046	+	1.79740i
$382$		0			0
$383$	20.6906	−	56.8471i	0.0540226	−	0.148426i	−0.909746	−	0.415165i	$-0.863724\pi$
$383$	20.6906	−	56.8471i	0.0540226	−	0.148426i	0.963769	+	0.266739i	$0.0859462\pi$
$384$		0			0
$385$	−25.7214	+	145.873i	−0.0668087	+	0.378891i
$386$		0			0
$387$	−113.709	+	206.577i	−0.293823	+	0.533792i
$388$		0			0
$389$	−82.3102	−	226.145i	−0.211594	−	0.581350i	0.787808	−	0.615921i	$-0.211216\pi$
$389$	−82.3102	−	226.145i	−0.211594	−	0.581350i	−0.999402	+	0.0345705i	$0.988994\pi$
$390$		0			0
$391$	−210.945	+	177.004i	−0.539501	+	0.452695i
$392$		0			0
$393$	−181.167	+	107.077i	−0.460984	+	0.272461i
$394$		0			0
$395$	−367.453	+	212.149i	−0.930261	+	0.537087i
$396$		0			0
$397$	14.3451	−	24.8464i	0.0361337	−	0.0625854i	−0.847393	−	0.530966i	$-0.821829\pi$
$397$	14.3451	−	24.8464i	0.0361337	−	0.0625854i	0.883527	+	0.468381i	$0.155162\pi$
$398$		0			0
$399$	−309.474	−	109.075i	−0.775624	−	0.273371i
$400$		0			0
$401$	697.035	−	122.906i	1.73824	−	0.306499i	0.787461	−	0.616365i	$-0.211395\pi$
$401$	697.035	−	122.906i	1.73824	−	0.306499i	0.950780	+	0.309866i	$0.100284\pi$
$402$		0			0
$403$	316.299	+	265.406i	0.784861	+	0.658577i
$404$		0			0
$405$	−600.821	−	314.912i	−1.48351	−	0.777559i
$406$		0			0
$407$	15.9657	−	19.0272i	0.0392278	−	0.0467499i
$408$		0			0
$409$	−13.6664	−	77.5062i	−0.0334143	−	0.189502i	0.963532	−	0.267593i	$-0.0862284\pi$
$409$	−13.6664	−	77.5062i	−0.0334143	−	0.189502i	−0.996946	+	0.0780917i	$0.975117\pi$
$410$		0			0
$411$	−212.386	+	602.594i	−0.516755	+	1.46617i
$412$		0			0
$413$	589.190	+	340.169i	1.42661	+	0.823653i
$414$		0			0
$415$	139.871	+	242.263i	0.337037	+	0.583766i
$416$		0			0
$417$	86.1281	+	145.723i	0.206542	+	0.349455i
$418$		0			0
$419$	−33.8949	−	40.3944i	−0.0808948	−	0.0964067i	0.724079	−	0.689717i	$-0.242265\pi$
$419$	−33.8949	−	40.3944i	−0.0808948	−	0.0964067i	−0.804974	+	0.593310i	$0.797821\pi$
$420$		0			0
$421$	664.624	−	241.903i	1.57868	−	0.574592i	0.603763	−	0.797164i	$-0.293667\pi$
$421$	664.624	−	241.903i	1.57868	−	0.574592i	0.974916	+	0.222572i	$0.0714452\pi$
$422$		0			0
$423$	330.718	−	200.051i	0.781839	−	0.472933i
$424$		0			0
$425$	871.865	+	153.733i	2.05145	+	0.361725i
$426$		0			0
$427$	−808.686	−	294.338i	−1.89388	−	0.689315i
$428$		0			0
$429$	−41.4817	−	6.87853i	−0.0966939	−	0.0160339i
$430$		0			0
$431$		−	279.279i		−	0.647978i	−0.946061	−	0.323989i	$-0.894976\pi$
$431$		−	279.279i		−	0.647978i	0.946061	−	0.323989i	$-0.105024\pi$
$432$		0			0
$433$	100.836			0.232877			0.116439	−	0.993198i	$-0.462852\pi$
$433$	100.836			0.232877			0.116439	+	0.993198i	$0.462852\pi$
$434$		0			0
$435$	212.922	+	174.990i	0.489475	+	0.402277i
$436$		0			0
$437$	−46.7177	+	128.356i	−0.106905	+	0.293720i
$438$		0			0
$439$	−17.2883	+	98.0470i	−0.0393812	+	0.223342i	−0.998146	−	0.0608574i	$-0.980617\pi$
$439$	−17.2883	+	98.0470i	−0.0393812	+	0.223342i	0.958765	+	0.284199i	$0.0917276\pi$
$440$		0			0
$441$	−649.370	+	251.479i	−1.47249	+	0.570246i
$442$		0			0
$443$	−117.281	−	322.226i	−0.264742	−	0.727373i	−0.998832	−	0.0483203i	$-0.984613\pi$
$443$	−117.281	−	322.226i	−0.264742	−	0.727373i	0.734090	−	0.679052i	$-0.237609\pi$
$444$		0			0
$445$	−557.716	+	467.980i	−1.25330	+	1.05164i
$446$		0			0
$447$	−75.2771	−	42.4427i	−0.168405	−	0.0949501i
$448$		0			0
$449$	−433.309	+	250.171i	−0.965053	+	0.557174i	−0.897725	−	0.440557i	$-0.854781\pi$
$449$	−433.309	+	250.171i	−0.965053	+	0.557174i	−0.0673285	+	0.997731i	$0.521448\pi$
$450$		0			0
$451$	−8.07431	+	13.9851i	−0.0179031	+	0.0310091i
$452$		0			0
$453$	−352.654	+	302.099i	−0.778486	+	0.666886i
$454$		0			0
$455$	825.931	−	145.634i	1.81523	−	0.320074i
$456$		0			0
$457$	88.1631	+	73.9776i	0.192917	+	0.161877i	0.734130	−	0.679009i	$-0.237590\pi$
$457$	88.1631	+	73.9776i	0.192917	+	0.161877i	−0.541213	+	0.840886i	$0.682035\pi$
$458$		0			0
$459$	−16.2150	−	529.354i	−0.0353268	−	1.15328i
$460$		0			0
$461$	371.972	−	443.299i	0.806880	−	0.961602i	−0.192928	−	0.981213i	$-0.561798\pi$
$461$	371.972	−	443.299i	0.806880	−	0.961602i	0.999808	+	0.0196109i	$0.00624274\pi$
$462$		0			0
$463$	138.386	+	784.826i	0.298890	+	1.69509i	0.650957	+	0.759114i	$0.274368\pi$
$463$	138.386	+	784.826i	0.298890	+	1.69509i	−0.352067	+	0.935975i	$0.614521\pi$
$464$		0			0
$465$	1144.67	−	213.906i	2.46166	−	0.460014i
$466$		0			0
$467$	−234.565	−	135.426i	−0.502281	−	0.289992i	0.227374	−	0.973807i	$-0.426986\pi$
$467$	−234.565	−	135.426i	−0.502281	−	0.289992i	−0.729655	+	0.683816i	$0.760319\pi$
$468$		0			0
$469$	15.3360	+	26.5628i	0.0326994	+	0.0566371i
$470$		0			0
$471$	641.393	−	6.54716i	1.36177	−	0.0139006i
$472$		0			0
$473$	26.4976	+	31.5786i	0.0560203	+	0.0667624i
$474$		0			0
$475$	412.665	−	150.198i	0.868769	−	0.316206i
$476$		0			0
$477$	246.106	+	281.425i	0.515945	+	0.589989i
$478$		0			0
$479$	785.792	+	138.556i	1.64048	+	0.289262i	0.916344	−	0.400391i	$-0.131126\pi$
$479$	785.792	+	138.556i	1.64048	+	0.289262i	0.724140	+	0.689653i	$0.242237\pi$
$480$		0			0
$481$	−132.152	−	48.0995i	−0.274745	−	0.0999990i
$482$		0			0
$483$	166.464	+	443.226i	0.344646	+	0.917652i
$484$		0			0
$485$		−	1180.26i		−	2.43354i
$486$		0			0
$487$	139.213			0.285859			0.142929	−	0.989733i	$-0.454348\pi$
$487$	139.213			0.285859			0.142929	+	0.989733i	$0.454348\pi$
$488$		0			0
$489$	413.409	−	155.265i	0.845417	−	0.317516i
$490$		0			0
$491$	73.6069	−	202.233i	0.149912	−	0.411881i	−0.841892	−	0.539646i	$-0.818558\pi$
$491$	73.6069	−	202.233i	0.149912	−	0.411881i	0.991804	+	0.127765i	$0.0407804\pi$
$492$		0			0
$493$	−37.3639	+	211.901i	−0.0757889	+	0.429820i
$494$		0			0
$495$	−89.2681	+	78.0649i	−0.180340	+	0.157707i
$496$		0			0
$497$	289.166	+	794.476i	0.581822	+	1.59854i
$498$		0			0
$499$	363.724	−	305.201i	0.728906	−	0.611624i	−0.200927	−	0.979606i	$-0.564396\pi$
$499$	363.724	−	305.201i	0.728906	−	0.611624i	0.929833	+	0.367982i	$0.119951\pi$
$500$		0			0
$501$	4.52535	+	443.326i	0.00903264	+	0.884883i
$502$		0			0
$503$	696.911	−	402.362i	1.38551	−	0.799924i	0.392704	−	0.919665i	$-0.371540\pi$
$503$	696.911	−	402.362i	1.38551	−	0.799924i	0.992805	+	0.119740i	$0.0382063\pi$
$504$		0			0
$505$	−377.907	+	654.554i	−0.748331	+	1.29615i
$506$		0			0
$507$	−49.3991	−	264.348i	−0.0974340	−	0.521397i
$508$		0			0
$509$	924.707	−	163.051i	1.81671	−	0.320336i	0.841275	−	0.540607i	$-0.181806\pi$
$509$	924.707	−	163.051i	1.81671	−	0.320336i	0.975439	+	0.220272i	$0.0706945\pi$
$510$		0			0
$511$	−569.702	−	478.036i	−1.11488	−	0.935492i
$512$		0			0
$513$	−138.255	−	223.379i	−0.269504	−	0.435436i
$514$		0			0
$515$	−113.025	+	134.698i	−0.219466	+	0.261549i
$516$		0			0
$517$	−11.7334	−	66.5434i	−0.0226952	−	0.128711i
$518$		0			0
$519$	−412.194	−	481.173i	−0.794208	−	0.927115i
$520$		0			0
$521$	−832.809	−	480.823i	−1.59848	−	0.922884i	−0.991780	−	0.127955i	$-0.959159\pi$
$521$	−832.809	−	480.823i	−1.59848	−	0.922884i	−0.606703	−	0.794929i	$-0.707508\pi$
$522$		0			0
$523$	19.2517	+	33.3450i	0.0368102	+	0.0637572i	0.883844	−	0.467783i	$-0.154947\pi$
$523$	19.2517	+	33.3450i	0.0368102	+	0.0637572i	−0.847033	+	0.531540i	$0.821614\pi$
$524$		0			0
$525$	747.587	−	1325.93i	1.42398	−	2.52559i
$526$		0			0
$527$	584.387	+	696.445i	1.10889	+	1.32153i
$528$		0			0
$529$	−311.896	+	113.521i	−0.589596	+	0.214595i
$530$		0			0
$531$	196.700	+	507.919i	0.370432	+	0.956533i
$532$		0			0
$533$	90.0441	+	15.8772i	0.168938	+	0.0297884i
$534$		0			0
$535$	172.312	+	62.7165i	0.322079	+	0.117227i
$536$		0			0
$537$	−495.174	+	602.510i	−0.922112	+	1.12199i
$538$		0			0
$539$			121.737i			0.225857i
$540$		0			0
$541$	−16.4860			−0.0304731			−0.0152366	−	0.999884i	$-0.504850\pi$
$541$	−16.4860			−0.0304731			−0.0152366	+	0.999884i	$0.504850\pi$
$542$		0			0
$543$	−156.747	+	945.282i	−0.288669	+	1.74085i
$544$		0			0
$545$	−265.363	+	729.078i	−0.486904	+	1.33776i
$546$		0			0
$547$	−8.02809	+	45.5295i	−0.0146766	+	0.0832350i	−0.991266	−	0.131876i	$-0.957900\pi$
$547$	−8.02809	+	45.5295i	−0.0146766	+	0.0832350i	0.976590	+	0.215111i	$0.0690112\pi$
$548$		0			0
$549$	−356.599	−	589.520i	−0.649544	−	1.07381i
$550$		0			0
$551$	36.5047	+	100.296i	0.0662517	+	0.182025i
$552$		0			0
$553$	−436.302	+	366.101i	−0.788972	+	0.662026i
$554$		0			0
$555$	−341.446	+	201.808i	−0.615217	+	0.363619i
$556$		0			0
$557$	62.2086	−	35.9161i	0.111685	−	0.0644814i	−0.443117	−	0.896464i	$-0.646127\pi$
$557$	62.2086	−	35.9161i	0.111685	−	0.0644814i	0.554802	+	0.831982i	$0.312794\pi$
$558$		0			0
$559$	116.702	−	202.133i	0.208769	−	0.361598i
$560$		0			0
$561$	−87.3191	−	30.7759i	−0.155649	−	0.0548590i
$562$		0			0
$563$	342.983	−	60.4772i	0.609206	−	0.107420i	0.139470	−	0.990226i	$-0.455460\pi$
$563$	342.983	−	60.4772i	0.609206	−	0.107420i	0.469736	+	0.882807i	$0.344349\pi$
$564$		0			0
$565$	993.784	+	833.884i	1.75891	+	1.47590i
$566$		0			0
$567$	−867.655	−	276.248i	−1.53026	−	0.487209i
$568$		0			0
$569$	218.985	−	260.976i	0.384859	−	0.458657i	−0.538483	−	0.842637i	$-0.681002\pi$
$569$	218.985	−	260.976i	0.384859	−	0.458657i	0.923342	+	0.383980i	$0.125447\pi$
$570$		0			0
$571$	93.4096	+	529.752i	0.163589	+	0.927762i	0.950507	+	0.310704i	$0.100565\pi$
$571$	93.4096	+	529.752i	0.163589	+	0.927762i	−0.786917	+	0.617058i	$0.788324\pi$
$572$		0			0
$573$	−38.8510	+	110.230i	−0.0678027	+	0.192374i
$574$		0			0
$575$	−548.746	−	316.819i	−0.954341	−	0.550989i
$576$		0			0
$577$	−146.659	−	254.021i	−0.254175	−	0.440244i	0.710496	−	0.703701i	$-0.248471\pi$
$577$	−146.659	−	254.021i	−0.254175	−	0.440244i	−0.964671	+	0.263457i	$0.915137\pi$
$578$		0			0
$579$	249.437	+	422.030i	0.430807	+	0.728894i
$580$		0			0
$581$	241.371	+	287.655i	0.415441	+	0.495103i
$582$		0			0
$583$	61.4151	−	22.3533i	0.105343	−	0.0383418i
$584$		0			0
$585$	588.215	+	323.779i	1.00550	+	0.553469i
$586$		0			0
$587$	−462.413	−	81.5359i	−0.787757	−	0.138903i	−0.234724	−	0.972062i	$-0.575419\pi$
$587$	−462.413	−	81.5359i	−0.787757	−	0.138903i	−0.553033	+	0.833159i	$0.686530\pi$
$588$		0			0
$589$	423.773	+	154.241i	0.719479	+	0.261869i
$590$		0			0
$591$	−1014.35	−	168.200i	−1.71632	−	0.284602i
$592$		0			0
$593$			880.585i			1.48497i	0.669864	+	0.742483i	$0.266352\pi$
$593$			880.585i			1.48497i	−0.669864	+	0.742483i	$0.733648\pi$
$594$		0			0
$595$	1846.64			3.10359
$596$		0			0
$597$	458.260	+	376.622i	0.767605	+	0.630858i
$598$		0			0
$599$	−117.916	+	323.972i	−0.196855	+	0.540855i	−0.998367	−	0.0571238i	$-0.981807\pi$
$599$	−117.916	+	323.972i	−0.196855	+	0.540855i	0.801512	+	0.597979i	$0.204029\pi$
$600$		0			0
$601$	108.241	−	613.865i	0.180102	−	1.02141i	−0.751987	−	0.659177i	$-0.770905\pi$
$601$	108.241	−	613.865i	0.180102	−	1.02141i	0.932089	−	0.362229i	$-0.117984\pi$
$602$		0			0
$603$	−3.76956	+	24.2649i	−0.00625134	+	0.0402403i
$604$		0			0
$605$	−339.490	−	932.741i	−0.561140	−	1.54172i
$606$		0			0
$607$	−725.795	+	609.015i	−1.19571	+	1.00332i	−0.195967	+	0.980610i	$0.562785\pi$
$607$	−725.795	+	609.015i	−1.19571	+	1.00332i	−0.999742	+	0.0227086i	$0.992771\pi$
$608$		0			0
$609$	322.260	+	181.696i	0.529162	+	0.298352i
$610$		0			0
$611$	−331.324	+	191.290i	−0.542265	+	0.313077i
$612$		0			0
$613$	352.677	−	610.854i	0.575329	−	0.996499i	−0.420677	−	0.907211i	$-0.638207\pi$
$613$	352.677	−	610.854i	0.575329	−	0.996499i	0.996006	−	0.0892887i	$-0.0284594\pi$
$614$		0			0
$615$	195.835	−	167.761i	0.318431	−	0.272782i
$616$		0			0
$617$	−876.465	+	154.544i	−1.42053	+	0.250477i	−0.830550	−	0.556943i	$-0.811974\pi$
$617$	−876.465	+	154.544i	−1.42053	+	0.250477i	−0.589976	+	0.807421i	$0.700863\pi$
$618$		0			0
$619$	376.539	+	315.954i	0.608303	+	0.510426i	0.894102	−	0.447863i	$-0.147815\pi$
$619$	376.539	+	315.954i	0.608303	+	0.510426i	−0.285800	+	0.958289i	$0.592259\pi$
$620$		0			0
$621$	−118.675	+	359.990i	−0.191104	+	0.579693i
$622$		0			0
$623$	−628.186	+	748.643i	−1.00832	+	1.20167i
$624$		0			0
$625$	49.2783	+	279.471i	0.0788452	+	0.447154i
$626$		0			0
$627$	−45.1437	+	8.43604i	−0.0719994	+	0.0134546i
$628$		0			0
$629$	−268.169	−	154.828i	−0.426342	−	0.246149i
$630$		0			0
$631$	−14.7611	−	25.5670i	−0.0233932	−	0.0405183i	0.854092	−	0.520122i	$-0.174114\pi$
$631$	−14.7611	−	25.5670i	−0.0233932	−	0.0405183i	−0.877485	+	0.479604i	$0.840780\pi$
$632$		0			0
$633$	−685.143	+	6.99375i	−1.08238	+	0.0110486i
$634$		0			0
$635$	−1245.58	−	1484.43i	−1.96155	−	2.33768i
$636$		0			0
$637$	647.704	−	235.745i	1.01680	−	0.370086i
$638$		0			0
$639$	−218.473	+	640.649i	−0.341898	+	1.00258i
$640$		0			0
$641$	−94.3541	−	16.6372i	−0.147198	−	0.0259550i	0.0995634	−	0.995031i	$-0.468255\pi$
$641$	−94.3541	−	16.6372i	−0.147198	−	0.0259550i	−0.246762	+	0.969076i	$0.579366\pi$
$642$		0			0
$643$	−537.766	−	195.731i	−0.836339	−	0.304402i	−0.111881	−	0.993722i	$-0.535687\pi$
$643$	−537.766	−	195.731i	−0.836339	−	0.304402i	−0.724458	+	0.689319i	$0.757910\pi$
$644$		0			0
$645$	−231.441	−	616.234i	−0.358823	−	0.955401i
$646$		0			0
$647$			419.943i			0.649061i	0.945875	+	0.324531i	$0.105206\pi$
$647$			419.943i			0.649061i	−0.945875	+	0.324531i	$0.894794\pi$
$648$		0			0
$649$	95.2192			0.146717
$650$		0			0
$651$	1463.33	−	549.589i	2.24782	−	0.844223i
$652$		0			0
$653$	−425.980	+	1170.37i	−0.652343	+	1.79230i	−0.0434334	+	0.999056i	$0.513830\pi$
$653$	−425.980	+	1170.37i	−0.652343	+	1.79230i	−0.608909	+	0.793240i	$0.708393\pi$
$654$		0			0
$655$	102.013	−	578.542i	0.155744	−	0.883270i
$656$		0			0
$657$	−115.338	−	584.120i	−0.175552	−	0.889072i
$658$		0			0
$659$	−159.051	−	436.990i	−0.241353	−	0.663111i	−0.999934	−	0.0115322i	$-0.996329\pi$
$659$	−159.051	−	436.990i	−0.241353	−	0.663111i	0.758581	−	0.651579i	$-0.225893\pi$
$660$		0			0
$661$	−250.507	+	210.201i	−0.378982	+	0.318004i	−0.812303	−	0.583236i	$-0.801786\pi$
$661$	−250.507	+	210.201i	−0.378982	+	0.318004i	0.433320	+	0.901240i	$0.357342\pi$
$662$		0			0
$663$	5.35069	+	524.181i	0.00807043	+	0.790620i
$664$		0			0
$665$	793.280	−	458.000i	1.19290	−	0.688722i
$666$		0			0
$667$	77.0009	−	133.369i	0.115444	−	0.199954i
$668$		0			0
$669$	−212.814	−	1138.83i	−0.318108	−	1.70228i
$670$		0			0
$671$	−118.617	+	20.9153i	−0.176776	+	0.0311704i
$672$		0			0
$673$	−221.219	−	185.625i	−0.328706	−	0.275817i	0.463466	−	0.886115i	$-0.346605\pi$
$673$	−221.219	−	185.625i	−0.328706	−	0.275817i	−0.792172	+	0.610297i	$0.791050\pi$
$674$		0			0
$675$	1131.85	−	451.666i	1.67681	−	0.669134i
$676$		0			0
$677$	110.656	−	131.875i	0.163450	−	0.194793i	−0.678102	−	0.734967i	$-0.737197\pi$
$677$	110.656	−	131.875i	0.163450	−	0.194793i	0.841553	+	0.540175i	$0.181642\pi$
$678$		0			0
$679$	−275.113	−	1560.24i	−0.405174	−	2.29786i
$680$		0			0
$681$	−363.384	−	424.194i	−0.533603	−	0.622899i
$682$		0			0
$683$	113.042	+	65.2651i	0.165509	+	0.0955565i	0.580466	−	0.814284i	$-0.302870\pi$
$683$	113.042	+	65.2651i	0.165509	+	0.0955565i	−0.414958	+	0.909841i	$0.636204\pi$
$684$		0			0
$685$	−891.799	−	1544.64i	−1.30190	−	2.25495i
$686$		0			0
$687$	455.278	−	807.489i	0.662705	−	1.17538i
$688$		0			0
$689$	−237.862	−	283.473i	−0.345228	−	0.411427i
$690$		0			0
$691$	259.558	−	94.4713i	0.375626	−	0.136717i	−0.147306	−	0.989091i	$-0.547060\pi$
$691$	259.558	−	94.4713i	0.375626	−	0.136717i	0.522932	+	0.852374i	$0.324838\pi$
$692$		0			0
$693$	−99.8110	+	124.005i	−0.144027	+	0.178940i
$694$		0			0
$695$	−465.354	−	82.0544i	−0.669574	−	0.118064i
$696$		0			0
$697$	189.181	+	68.8564i	0.271422	+	0.0987897i
$698$		0			0
$699$	39.1695	−	47.6600i	0.0560365	−	0.0681831i
$700$		0			0
$701$			865.652i			1.23488i	0.786617	+	0.617441i	$0.211830\pi$
$701$			865.652i			1.23488i	−0.786617	+	0.617441i	$0.788170\pi$
$702$		0			0
$703$	−153.601			−0.218493
$704$		0			0
$705$	−176.507	+	1064.44i	−0.250365	+	1.50985i
$706$		0			0
$707$	−346.999	+	953.372i	−0.490805	+	1.34847i
$708$		0			0
$709$	−19.7944	+	112.259i	−0.0279187	+	0.158335i	−0.995580	−	0.0939188i	$-0.970061\pi$
$709$	−19.7944	+	112.259i	−0.0279187	+	0.158335i	0.967661	+	0.252254i	$0.0811717\pi$
$710$		0			0
$711$	−455.886	+	9.30809i	−0.641190	+	0.0130915i
$712$		0			0
$713$	−222.550	−	611.451i	−0.312132	−	0.857575i
$714$		0			0
$715$	89.9179	−	75.4501i	0.125759	−	0.105525i
$716$		0			0
$717$	−265.248	+	156.772i	−0.369941	+	0.218650i
$718$		0			0
$719$	117.571	−	67.8798i	0.163521	−	0.0944086i	−0.416006	−	0.909362i	$-0.636571\pi$
$719$	117.571	−	67.8798i	0.163521	−	0.0944086i	0.579527	+	0.814953i	$0.303237\pi$
$720$		0			0
$721$	−118.015	+	204.408i	−0.163683	+	0.283507i
$722$		0			0
$723$	−1087.14	−	383.166i	−1.50365	−	0.529967i
$724$		0			0
$725$	−487.596	+	85.9763i	−0.672546	+	0.118588i
$726$		0			0
$727$	−76.0522	−	63.8154i	−0.104611	−	0.0877790i	0.588982	−	0.808146i	$-0.299529\pi$
$727$	−76.0522	−	63.8154i	−0.104611	−	0.0877790i	−0.693593	+	0.720367i	$0.743973\pi$
$728$		0			0
$729$	−402.458	−	607.839i	−0.552068	−	0.833799i
$730$		0			0
$731$	330.342	−	393.686i	0.451904	−	0.538559i
$732$		0			0
$733$	−132.435	−	751.078i	−0.180676	−	1.02466i	−0.931387	−	0.364032i	$-0.881400\pi$
$733$	−132.435	−	751.078i	−0.180676	−	1.02466i	0.750711	−	0.660631i	$-0.229711\pi$
$734$		0			0
$735$	646.185	−	1833.39i	0.879163	−	2.49441i
$736$		0			0
$737$	3.71769	+	2.14641i	0.00504436	+	0.00291236i
$738$		0			0
$739$	−436.285	−	755.668i	−0.590373	−	1.02256i	−0.994182	−	0.107712i	$-0.965647\pi$
$739$	−436.285	−	755.668i	−0.590373	−	1.02256i	0.403810	−	0.914843i	$-0.367686\pi$
$740$		0			0
$741$	132.305	+	223.851i	0.178550	+	0.302093i
$742$		0			0
$743$	515.245	+	614.045i	0.693466	+	0.826441i	0.991770	−	0.128030i	$-0.0408654\pi$
$743$	515.245	+	614.045i	0.693466	+	0.826441i	−0.298304	+	0.954471i	$0.596421\pi$
$744$		0			0
$745$	226.691	−	82.5088i	0.304283	−	0.110750i
$746$		0			0
$747$	6.13685	+	300.567i	0.00821533	+	0.402366i
$748$		0			0
$749$	242.406	+	42.7427i	0.323639	+	0.0570663i
$750$		0			0
$751$	814.474	+	296.444i	1.08452	+	0.394733i	0.821588	−	0.570082i	$-0.193089\pi$
$751$	814.474	+	296.444i	1.08452	+	0.394733i	0.262931	+	0.964815i	$0.415311\pi$
$752$		0			0
$753$	962.583	+	159.616i	1.27833	+	0.211974i
$754$		0			0
$755$		−	1296.28i		−	1.71693i
$756$		0			0
$757$	−305.290			−0.403289			−0.201644	−	0.979459i	$-0.564629\pi$
$757$	−305.290			−0.403289			−0.201644	+	0.979459i	$0.564629\pi$
$758$		0			0
$759$	51.1934	+	42.0734i	0.0674485	+	0.0554327i
$760$		0			0
$761$	210.316	−	577.838i	0.276367	−	0.759313i	−0.721399	−	0.692519i	$-0.756501\pi$
$761$	210.316	−	577.838i	0.276367	−	0.759313i	0.997767	−	0.0667941i	$-0.0212771\pi$
$762$		0			0
$763$	−180.851	+	1025.65i	−0.237026	+	1.34424i
$764$		0			0
$765$	1151.69	+	926.988i	1.50548	+	1.21175i
$766$		0			0
$767$	−184.393	−	506.616i	−0.240408	−	0.660516i
$768$		0			0
$769$	105.505	−	88.5291i	0.137198	−	0.115122i	−0.571606	−	0.820528i	$-0.693680\pi$
$769$	105.505	−	88.5291i	0.137198	−	0.115122i	0.708804	+	0.705406i	$0.249235\pi$
$770$		0			0
$771$	87.4220	+	49.2903i	0.113388	+	0.0639303i
$772$		0			0
$773$	−154.674	+	89.3010i	−0.200096	+	0.115525i	−0.596700	−	0.802464i	$-0.703522\pi$
$773$	−154.674	+	89.3010i	−0.200096	+	0.115525i	0.396604	+	0.917990i	$0.370188\pi$
$774$		0			0
$775$	−1045.99	+	1811.71i	−1.34967	+	2.33769i
$776$		0			0
$777$	−404.331	+	346.368i	−0.520375	+	0.445777i
$778$		0			0
$779$	98.3465	−	17.3411i	0.126247	−	0.0222608i
$780$		0			0
$781$	90.6461	+	76.0611i	0.116064	+	0.0973894i
$782$		0			0
$783$	109.775	+	275.089i	0.140197	+	0.351327i
$784$		0			0
$785$	−1150.96	+	1371.66i	−1.46619	+	1.74734i
$786$		0			0
$787$	108.344	+	614.451i	0.137668	+	0.780752i	0.972965	+	0.230953i	$0.0741844\pi$
$787$	108.344	+	614.451i	0.137668	+	0.780752i	−0.835297	+	0.549798i	$0.814705\pi$
$788$		0			0
$789$	−463.582	+	86.6300i	−0.587556	+	0.109797i
$790$		0			0
$791$	1508.10	+	870.702i	1.90658	+	1.10076i
$792$		0			0
$793$	340.983	+	590.599i	0.429991	+	0.744766i
$794$		0			0
$795$	−1043.58	+	10.6526i	−1.31268	+	0.0133995i
$796$		0			0
$797$	−487.894	−	581.449i	−0.612163	−	0.729547i	0.367539	−	0.930008i	$-0.380200\pi$
$797$	−487.894	−	581.449i	−0.612163	−	0.729547i	−0.979702	+	0.200461i	$0.935756\pi$
$798$		0			0
$799$	−791.584	+	288.113i	−0.990718	+	0.360592i
$800$		0			0
$801$	−767.591	+	151.565i	−0.958291	+	0.189220i
$802$		0			0
$803$	−102.505	−	18.0744i	−0.127653	−	0.0225086i
$804$		0			0
$805$	−1241.97	−	452.039i	−1.54282	−	0.561539i
$806$		0			0
$807$	305.037	+	812.190i	0.377989	+	1.00643i
$808$		0			0
$809$			1035.21i			1.27961i	0.768537	+	0.639805i	$0.220985\pi$
$809$			1035.21i			1.27961i	−0.768537	+	0.639805i	$0.779015\pi$
$810$		0			0
$811$	−1435.70			−1.77029			−0.885144	−	0.465318i	$-0.845940\pi$
$811$	−1435.70			−1.77029			−0.885144	+	0.465318i	$0.845940\pi$
$812$		0			0
$813$	1230.23	−	462.043i	1.51320	−	0.568319i
$814$		0			0
$815$	−421.629	+	1158.42i	−0.517336	+	1.42137i
$816$		0			0
$817$	44.2671	−	251.051i	0.0541825	−	0.307284i
$818$		0			0
$819$	853.058	+	290.909i	1.04158	+	0.355200i
$820$		0			0
$821$	−2.84183	−	7.80786i	−0.00346142	−	0.00951018i	0.937950	−	0.346771i	$-0.112722\pi$
$821$	−2.84183	−	7.80786i	−0.00346142	−	0.00951018i	−0.941411	+	0.337261i	$0.890500\pi$
$822$		0			0
$823$	518.097	−	434.735i	0.629522	−	0.528232i	−0.271258	−	0.962507i	$-0.587440\pi$
$823$	518.097	−	434.735i	0.629522	−	0.528232i	0.900781	+	0.434275i	$0.142995\pi$
$824$		0			0
$825$	−2.17454	−	213.029i	−0.00263581	−	0.258217i
$826$		0			0
$827$	−1123.27	+	648.518i	−1.35824	+	0.784181i	−0.989387	−	0.145305i	$-0.953584\pi$
$827$	−1123.27	+	648.518i	−1.35824	+	0.784181i	−0.368855	+	0.929487i	$0.620250\pi$
$828$		0			0
$829$	−367.050	+	635.750i	−0.442763	+	0.766888i	−0.997893	−	0.0648754i	$-0.979335\pi$
$829$	−367.050	+	635.750i	−0.442763	+	0.766888i	0.555130	+	0.831763i	$0.312668\pi$
$830$		0			0
$831$	9.37440	+	50.1651i	0.0112809	+	0.0603671i
$832$		0			0
$833$	1494.62	−	263.542i	1.79426	−	0.316377i
$834$		0			0
$835$	−948.082	−	795.535i	−1.13543	−	0.952737i
$836$		0			0
$837$	1188.52	+	391.813i	1.41998	+	0.468116i
$838$		0			0
$839$	−447.625	+	533.458i	−0.533522	+	0.635826i	−0.963722	−	0.266907i	$-0.913998\pi$
$839$	−447.625	+	533.458i	−0.533522	+	0.635826i	0.430201	+	0.902733i	$0.358443\pi$
$840$		0			0
$841$	125.142	+	709.716i	0.148802	+	0.843896i
$842$		0			0
$843$	−179.097	−	209.068i	−0.212452	−	0.248005i
$844$		0			0
$845$	650.139	+	375.358i	0.769396	+	0.444211i
$846$		0			0
$847$	−666.203	−	1153.90i	−0.786544	−	1.36233i
$848$		0			0
$849$	−645.113	+	1144.18i	−0.759851	+	1.34768i
$850$		0			0
$851$	142.459	+	169.776i	0.167401	+	0.199501i
$852$		0			0
$853$	−1214.78	+	442.144i	−1.42413	+	0.518340i	−0.935242	−	0.354009i	$-0.884818\pi$
$853$	−1214.78	+	442.144i	−1.42413	+	0.518340i	−0.488885	+	0.872348i	$0.662596\pi$
$854$		0			0
$855$	724.655	+	112.575i	0.847550	+	0.131667i
$856$		0			0
$857$	−169.817	−	29.9433i	−0.198153	−	0.0349397i	0.0736908	−	0.997281i	$-0.476522\pi$
$857$	−169.817	−	29.9433i	−0.198153	−	0.0349397i	−0.271844	+	0.962341i	$0.587633\pi$
$858$		0			0
$859$	−602.703	−	219.366i	−0.701633	−	0.255373i	−0.0335249	−	0.999438i	$-0.510673\pi$
$859$	−602.703	−	219.366i	−0.701633	−	0.255373i	−0.668108	+	0.744064i	$0.732896\pi$
$860$		0			0
$861$	219.779	−	267.419i	0.255260	−	0.310591i
$862$		0			0
$863$		−	222.895i		−	0.258280i	−0.991626	−	0.129140i	$-0.958778\pi$
$863$		−	222.895i		−	0.258280i	0.991626	−	0.129140i	$-0.0412216\pi$
$864$		0			0
$865$	1768.69			2.04473
$866$		0			0
$867$	−46.9874	+	283.362i	−0.0541953	+	0.326831i
$868$		0			0
$869$	−27.2637	+	74.9064i	−0.0313736	+	0.0861984i
$870$		0			0
$871$	4.22067	−	23.9366i	0.00484578	−	0.0274818i
$872$		0			0
$873$	611.643	−	1111.18i	0.700622	−	1.27283i
$874$		0			0
$875$	648.328	+	1781.27i	0.740947	+	2.03573i
$876$		0			0
$877$	685.259	−	575.001i	0.781368	−	0.655645i	−0.162225	−	0.986754i	$-0.551867\pi$
$877$	685.259	−	575.001i	0.781368	−	0.655645i	0.943593	+	0.331108i	$0.107423\pi$
$878$		0			0
$879$	−668.063	+	394.853i	−0.760026	+	0.449207i
$880$		0			0
$881$	600.708	−	346.819i	0.681847	−	0.393665i	−0.118703	−	0.992930i	$-0.537874\pi$
$881$	600.708	−	346.819i	0.681847	−	0.393665i	0.800551	+	0.599265i	$0.204540\pi$
$882$		0			0
$883$	357.452	−	619.125i	0.404815	−	0.701161i	−0.589485	−	0.807780i	$-0.700669\pi$
$883$	357.452	−	619.125i	0.404815	−	0.701161i	0.994300	+	0.106619i	$0.0340024\pi$
$884$		0			0
$885$	−1434.03	−	505.428i	−1.62037	−	0.571105i
$886$		0			0
$887$	1637.53	−	288.740i	1.84614	−	0.325524i	0.862553	−	0.505966i	$-0.168864\pi$
$887$	1637.53	−	288.740i	1.84614	−	0.325524i	0.983586	+	0.180442i	$0.0577529\pi$
$888$		0			0
$889$	−1992.60	−	1671.99i	−2.24140	−	1.88076i
$890$		0			0
$891$	−124.498	+	27.2346i	−0.139729	+	0.0305663i
$892$		0			0
$893$	−268.592	+	320.095i	−0.300775	+	0.358450i
$894$		0			0
$895$	−378.046	−	2144.01i	−0.422398	−	2.39554i
$896$		0			0
$897$	124.716	−	353.851i	0.139037	−	0.394483i
$898$		0			0
$899$	−440.326	−	254.222i	−0.489795	−	0.282783i
$900$		0			0
$901$	−407.396	−	705.631i	−0.452160	−	0.783164i
$902$		0			0
$903$	−449.593	−	760.679i	−0.497888	−	0.842391i
$904$		0			0
$905$	−1719.35	−	2049.04i	−1.89984	−	2.26414i
$906$		0			0
$907$	−22.6374	+	8.23933i	−0.0249585	+	0.00908416i	−0.354469	−	0.935068i	$-0.615338\pi$
$907$	−22.6374	+	8.23933i	−0.0249585	+	0.00908416i	0.329511	+	0.944152i	$0.393116\pi$
$908$		0			0
$909$	−694.993	+	420.400i	−0.764569	+	0.462487i
$910$		0			0
$911$	324.675	+	57.2490i	0.356394	+	0.0628419i	0.348979	−	0.937131i	$-0.386528\pi$
$911$	324.675	+	57.2490i	0.356394	+	0.0628419i	0.00741541	+	0.999973i	$0.497640\pi$
$912$		0			0
$913$	49.3860	+	17.9750i	0.0540920	+	0.0196879i
$914$		0			0
$915$	1897.42	+	314.632i	2.07368	+	0.343860i
$916$		0			0
$917$		−	788.579i		−	0.859955i
$918$		0			0
$919$	174.813			0.190220			0.0951102	−	0.995467i	$-0.469680\pi$
$919$	174.813			0.190220			0.0951102	+	0.995467i	$0.469680\pi$
$920$		0			0
$921$	494.115	+	406.090i	0.536499	+	0.440923i
$922$		0			0
$923$	229.148	−	629.578i	0.248264	−	0.682099i
$924$		0			0
$925$	123.730	−	701.707i	0.133762	−	0.758602i
$926$		0			0
$927$	−176.213	+	68.2413i	−0.190090	+	0.0736152i
$928$		0			0
$929$	−46.7382	−	128.412i	−0.0503102	−	0.138226i	0.911992	−	0.410207i	$-0.134544\pi$
$929$	−46.7382	−	128.412i	−0.0503102	−	0.138226i	−0.962303	+	0.271981i	$0.912321\pi$
$930$		0			0
$931$	576.698	−	483.907i	0.619439	−	0.519771i
$932$		0			0
$933$	1219.31	+	687.468i	1.30687	+	0.736836i
$934$		0			0
$935$	223.827	−	129.226i	0.239387	−	0.138210i
$936$		0			0
$937$	−288.732	+	500.099i	−0.308145	+	0.533723i	−0.977957	−	0.208808i	$-0.933042\pi$
$937$	−288.732	+	500.099i	−0.308145	+	0.533723i	0.669811	+	0.742531i	$0.266375\pi$
$938$		0			0
$939$	215.083	−	184.250i	0.229056	−	0.196220i
$940$		0			0
$941$	−1294.60	+	228.273i	−1.37577	+	0.242585i	−0.812150	−	0.583449i	$-0.801703\pi$
$941$	−1294.60	+	228.273i	−1.37577	+	0.242585i	−0.563620	+	0.826034i	$0.690592\pi$
$942$		0			0
$943$	−110.380	−	92.6197i	−0.117052	−	0.0982181i
$944$		0			0
$945$	2161.41	−	1337.76i	2.28720	−	1.41561i
$946$		0			0
$947$	395.028	−	470.776i	0.417136	−	0.497123i	−0.516029	−	0.856571i	$-0.672590\pi$
$947$	395.028	−	470.776i	0.417136	−	0.497123i	0.933165	+	0.359448i	$0.117035\pi$
$948$		0			0
$949$	102.337	+	580.381i	0.107837	+	0.611571i
$950$		0			0
$951$	751.578	−	140.448i	0.790303	−	0.147685i
$952$		0			0
$953$	684.011	+	394.914i	0.717745	+	0.414391i	0.813922	−	0.580974i	$-0.197328\pi$
$953$	684.011	+	394.914i	0.717745	+	0.414391i	−0.0961768	+	0.995364i	$0.530661\pi$
$954$		0			0
$955$	−163.133	−	282.555i	−0.170820	−	0.295869i
$956$		0			0
$957$	51.7754	−	0.528509i	0.0541018	−	0.000552256i
$958$		0			0
$959$	−1538.96	−	1834.06i	−1.60475	−	1.91247i
$960$		0			0
$961$	−1115.69	+	406.079i	−1.16097	+	0.422559i
$962$		0			0
$963$	129.725	+	148.342i	0.134709	+	0.154042i
$964$		0			0
$965$	−1347.72	−	237.639i	−1.39660	−	0.246258i
$966$		0			0
$967$	1642.98	+	597.996i	1.69905	+	0.618403i	0.995717	−	0.0924577i	$-0.0294723\pi$
$967$	1642.98	+	597.996i	1.69905	+	0.618403i	0.703333	+	0.710861i	$0.251695\pi$
$968$		0			0
$969$	201.302	+	535.987i	0.207742	+	0.553134i
$970$		0			0
$971$			1254.82i			1.29230i	0.763211	+	0.646149i	$0.223622\pi$
$971$			1254.82i			1.29230i	−0.763211	+	0.646149i	$0.776378\pi$
$972$		0			0
$973$	−634.298			−0.651899
$974$		0			0
$975$	−1129.21	+	424.103i	−1.15817	+	0.434977i
$976$		0			0
$977$	239.287	−	657.435i	0.244920	−	0.672912i	−0.754934	−	0.655801i	$-0.772331\pi$
$977$	239.287	−	657.435i	0.244920	−	0.672912i	0.999854	−	0.0171106i	$-0.00544673\pi$
$978$		0			0
$979$	−23.7515	+	134.702i	−0.0242610	+	0.137591i
$980$		0			0
$981$	−627.657	+	548.885i	−0.639813	+	0.559516i
$982$		0			0
$983$	−129.688	−	356.315i	−0.131931	−	0.362477i	0.856084	−	0.516837i	$-0.172891\pi$
$983$	−129.688	−	356.315i	−0.131931	−	0.362477i	−0.988015	+	0.154360i	$0.950668\pi$
$984$		0			0
$985$	2198.75	−	1844.97i	2.23224	−	1.87307i
$986$		0			0
$987$	14.7836	+	1448.28i	0.0149783	+	1.46735i
$988$		0			0
$989$	−318.545	+	183.912i	−0.322088	+	0.185957i
$990$		0			0
$991$	298.374	−	516.798i	0.301083	−	0.521492i	−0.675298	−	0.737545i	$-0.735985\pi$
$991$	298.374	−	516.798i	0.301083	−	0.521492i	0.976382	+	0.216053i	$0.0693184\pi$
$992$		0			0
$993$	203.055	+	1086.60i	0.204486	+	1.09426i
$994$		0			0
$995$	−1630.70	+	287.536i	−1.63889	+	0.288981i
$996$		0			0
$997$	865.580	+	726.308i	0.868185	+	0.728494i	0.963715	−	0.266933i	$-0.0860102\pi$
$997$	865.580	+	726.308i	0.868185	+	0.728494i	−0.0955301	+	0.995427i	$0.530455\pi$
$998$		0			0
$999$	−426.042	+	13.0504i	−0.426468	+	0.0130634i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.bc.c.65.1		36
4.3	odd	2		54.3.f.a.11.3	yes	36
12.11	even	2		162.3.f.a.35.4		36
27.5	odd	18	inner	432.3.bc.c.113.1		36
108.7	odd	18		1458.3.b.c.1457.36		36
108.47	even	18		1458.3.b.c.1457.1		36
108.59	even	18		54.3.f.a.5.3	✓	36
108.103	odd	18		162.3.f.a.125.4		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.3.f.a.5.3	✓	36	108.59	even	18
54.3.f.a.11.3	yes	36	4.3	odd	2
162.3.f.a.35.4		36	12.11	even	2
162.3.f.a.125.4		36	108.103	odd	18
432.3.bc.c.65.1		36	1.1	even	1	trivial
432.3.bc.c.113.1		36	27.5	odd	18	inner
1458.3.b.c.1457.1		36	108.47	even	18
1458.3.b.c.1457.36		36	108.7	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.bc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.80846 + 1.05478i) q^{3} +(2.86430 - 7.86960i) q^{5} +(1.95208 - 11.0708i) q^{7} +(6.77487 - 5.92462i) q^{9} +O(q^{10})\)	\(q+(-2.80846 + 1.05478i) q^{3} +(2.86430 - 7.86960i) q^{5} +(1.95208 - 11.0708i) q^{7} +(6.77487 - 5.92462i) q^{9} +(-0.538121 - 1.47848i) q^{11} +(-6.82419 + 5.72617i) q^{13} +(0.256445 + 25.1227i) q^{15} +(-16.9870 + 9.80744i) q^{17} +(-4.86486 + 8.42619i) q^{19} +(6.19496 + 33.1510i) q^{21} +(13.8255 - 2.43781i) q^{23} +(-34.5753 - 29.0121i) q^{25} +(-12.7778 + 23.7851i) q^{27} +(7.05122 - 8.40331i) q^{29} +(-8.04854 - 45.6456i) q^{31} +(3.07076 + 3.58464i) q^{33} +(-81.5316 - 47.0723i) q^{35} +(7.89337 + 13.6717i) q^{37} +(13.1256 - 23.2797i) q^{39} +(-6.59742 - 7.86250i) q^{41} +(-24.6205 + 8.96112i) q^{43} +(-27.2191 - 70.2854i) q^{45} +(42.2938 + 7.45754i) q^{47} +(-72.7075 - 26.4634i) q^{49} +(37.3625 - 45.4614i) q^{51} +41.5395i q^{53} -13.1764 q^{55} +(4.77497 - 28.7960i) q^{57} +(-20.6989 + 56.8698i) q^{59} +(13.2934 - 75.3906i) q^{61} +(-52.3653 - 86.5688i) q^{63} +(25.5162 + 70.1051i) q^{65} +(-2.09011 + 1.75381i) q^{67} +(-36.2569 + 21.4293i) q^{69} +(-65.1324 + 37.6042i) q^{71} +(33.0777 - 57.2922i) q^{73} +(127.705 + 45.0099i) q^{75} +(-17.4184 + 3.07133i) q^{77} +(-38.8113 - 32.5666i) q^{79} +(10.7977 - 80.2771i) q^{81} +(-21.4712 + 25.5884i) q^{83} +(28.5248 + 161.772i) q^{85} +(-10.9394 + 31.0378i) q^{87} +(-75.2876 - 43.4673i) q^{89} +(50.0720 + 86.7273i) q^{91} +(70.7501 + 119.704i) q^{93} +(52.3763 + 62.4197i) q^{95} +(132.434 - 48.2019i) q^{97} +(-12.4051 - 6.82832i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{5} - 12 q^{9}+O(q^{10}) \) 36 * q + 18 * q^5 - 12 * q^9	\( 36 q + 18 q^{5} - 12 q^{9} + 18 q^{11} + 18 q^{15} - 228 q^{21} + 180 q^{23} + 18 q^{25} - 54 q^{27} + 144 q^{29} + 90 q^{31} + 324 q^{33} - 486 q^{35} - 102 q^{39} - 90 q^{41} - 90 q^{43} - 378 q^{45} + 378 q^{47} + 72 q^{49} + 54 q^{51} + 72 q^{57} - 252 q^{59} - 144 q^{61} - 318 q^{63} + 18 q^{65} + 594 q^{67} - 522 q^{69} + 648 q^{71} + 126 q^{73} + 438 q^{75} - 342 q^{77} + 72 q^{79} + 324 q^{81} - 594 q^{83} + 360 q^{85} - 1062 q^{87} + 648 q^{89} + 198 q^{91} + 462 q^{93} - 252 q^{95} + 702 q^{97} - 126 q^{99}+O(q^{100}) \) 36 * q + 18 * q^5 - 12 * q^9 + 18 * q^11 + 18 * q^15 - 228 * q^21 + 180 * q^23 + 18 * q^25 - 54 * q^27 + 144 * q^29 + 90 * q^31 + 324 * q^33 - 486 * q^35 - 102 * q^39 - 90 * q^41 - 90 * q^43 - 378 * q^45 + 378 * q^47 + 72 * q^49 + 54 * q^51 + 72 * q^57 - 252 * q^59 - 144 * q^61 - 318 * q^63 + 18 * q^65 + 594 * q^67 - 522 * q^69 + 648 * q^71 + 126 * q^73 + 438 * q^75 - 342 * q^77 + 72 * q^79 + 324 * q^81 - 594 * q^83 + 360 * q^85 - 1062 * q^87 + 648 * q^89 + 198 * q^91 + 462 * q^93 - 252 * q^95 + 702 * q^97 - 126 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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