LMFDB - Embedded newform 750.3.f.b.193.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [750,3,Mod(193,750)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(750, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("750.193"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	750.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,-16,0,0,0,0,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$20.4360198270$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.6879707136000000000000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 21x^{12} + 86x^{8} + 36x^{4} + 1 $ x^16 + 21x^12 + 86x^8 + 36*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{8}\cdot 5^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			193.2
Root			$1.05097 + 1.05097i$ of defining polynomial
Character	$\chi$	$=$	750.193
Dual form			750.3.f.b.307.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +2.44949 q^{6} +(2.69401 - 2.69401i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +1.76982 q^{11} +(-2.44949 + 2.44949i) q^{12} +(-13.2862 - 13.2862i) q^{13} +5.38803i q^{14} -4.00000 q^{16} +(13.3785 - 13.3785i) q^{17} +(-3.00000 - 3.00000i) q^{18} +13.5088i q^{19} -6.59896 q^{21} +(-1.76982 + 1.76982i) q^{22} +(-3.45989 - 3.45989i) q^{23} -4.89898i q^{24} +26.5723 q^{26} +(3.67423 - 3.67423i) q^{27} +(-5.38803 - 5.38803i) q^{28} +7.20434i q^{29} +15.1996 q^{31} +(4.00000 - 4.00000i) q^{32} +(-2.16758 - 2.16758i) q^{33} +26.7570i q^{34} +6.00000 q^{36} +(-28.4468 + 28.4468i) q^{37} +(-13.5088 - 13.5088i) q^{38} +32.5443i q^{39} +20.6534 q^{41} +(6.59896 - 6.59896i) q^{42} +(-28.7921 - 28.7921i) q^{43} -3.53965i q^{44} +6.91979 q^{46} +(16.4532 - 16.4532i) q^{47} +(4.89898 + 4.89898i) q^{48} +34.4846i q^{49} -32.7705 q^{51} +(-26.5723 + 26.5723i) q^{52} +(-71.9184 - 71.9184i) q^{53} +7.34847i q^{54} +10.7761 q^{56} +(16.5448 - 16.5448i) q^{57} +(-7.20434 - 7.20434i) q^{58} -27.4099i q^{59} -78.6807 q^{61} +(-15.1996 + 15.1996i) q^{62} +(8.08204 + 8.08204i) q^{63} +8.00000i q^{64} +4.33516 q^{66} +(-32.0521 + 32.0521i) q^{67} +(-26.7570 - 26.7570i) q^{68} +8.47497i q^{69} -111.105 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-20.1117 - 20.1117i) q^{73} -56.8936i q^{74} +27.0176 q^{76} +(4.76793 - 4.76793i) q^{77} +(-32.5443 - 32.5443i) q^{78} -81.3451i q^{79} -9.00000 q^{81} +(-20.6534 + 20.6534i) q^{82} +(-42.2649 - 42.2649i) q^{83} +13.1979i q^{84} +57.5842 q^{86} +(8.82348 - 8.82348i) q^{87} +(3.53965 + 3.53965i) q^{88} -118.921i q^{89} -71.5862 q^{91} +(-6.91979 + 6.91979i) q^{92} +(-18.6157 - 18.6157i) q^{93} +32.9064i q^{94} -9.79796 q^{96} +(79.0793 - 79.0793i) q^{97} +(-34.4846 - 34.4846i) q^{98} +5.30947i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} + 24 q^{7} + 32 q^{8} - 24 q^{11} - 48 q^{13} - 64 q^{16} - 16 q^{17} - 48 q^{18} - 48 q^{21} + 24 q^{22} + 104 q^{23} + 96 q^{26} - 48 q^{28} + 200 q^{31} + 64 q^{32} - 48 q^{33} + 96 q^{36}+ \cdots - 224 q^{98}+O(q^{100}) $ 16 * q - 16 * q^2 + 24 * q^7 + 32 * q^8 - 24 * q^11 - 48 * q^13 - 64 * q^16 - 16 * q^17 - 48 * q^18 - 48 * q^21 + 24 * q^22 + 104 * q^23 + 96 * q^26 - 48 * q^28 + 200 * q^31 + 64 * q^32 - 48 * q^33 + 96 * q^36 - 128 * q^37 + 56 * q^38 - 192 * q^41 + 48 * q^42 + 88 * q^43 - 208 * q^46 + 16 * q^47 - 48 * q^51 - 96 * q^52 - 160 * q^53 + 96 * q^56 + 48 * q^57 + 24 * q^58 - 24 * q^61 - 200 * q^62 + 72 * q^63 + 96 * q^66 + 264 * q^67 + 32 * q^68 + 176 * q^71 - 96 * q^72 + 32 * q^73 - 112 * q^76 + 32 * q^77 + 96 * q^78 - 144 * q^81 + 192 * q^82 - 288 * q^83 - 176 * q^86 - 168 * q^87 - 48 * q^88 + 32 * q^91 + 208 * q^92 + 144 * q^93 - 48 * q^97 - 224 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$4$		−	2.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	2.44949			0.408248
$7$	2.69401	−	2.69401i	0.384859	−	0.384859i	−0.487990	−	0.872849i	$-0.662270\pi$
$7$	2.69401	−	2.69401i	0.384859	−	0.384859i	0.872849	+	0.487990i	$0.162270\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$			3.00000i			0.333333i
$10$		0			0
$11$	1.76982			0.160893			0.0804465	−	0.996759i	$-0.474365\pi$
$11$	1.76982			0.160893			0.0804465	+	0.996759i	$0.474365\pi$
$12$	−2.44949	+	2.44949i	−0.204124	+	0.204124i
$13$	−13.2862	−	13.2862i	−1.02201	−	1.02201i	−0.999752	−	0.0222595i	$-0.992914\pi$
$13$	−13.2862	−	13.2862i	−1.02201	−	1.02201i	−0.0222595	−	0.999752i	$-0.507086\pi$
$14$			5.38803i			0.384859i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	13.3785	−	13.3785i	0.786971	−	0.786971i	−0.194025	−	0.980997i	$-0.562154\pi$
$17$	13.3785	−	13.3785i	0.786971	−	0.786971i	0.980997	+	0.194025i	$0.0621544\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$			13.5088i			0.710989i	0.934678	+	0.355494i	$0.115687\pi$
$19$			13.5088i			0.710989i	−0.934678	+	0.355494i	$0.884313\pi$
$20$		0			0
$21$	−6.59896			−0.314236
$22$	−1.76982	+	1.76982i	−0.0804465	+	0.0804465i
$23$	−3.45989	−	3.45989i	−0.150430	−	0.150430i	0.627880	−	0.778310i	$-0.283923\pi$
$23$	−3.45989	−	3.45989i	−0.150430	−	0.150430i	−0.778310	+	0.627880i	$0.783923\pi$
$24$		−	4.89898i		−	0.204124i
$25$		0			0
$26$	26.5723			1.02201
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	−5.38803	−	5.38803i	−0.192430	−	0.192430i
$29$			7.20434i			0.248426i	0.992256	+	0.124213i	$0.0396405\pi$
$29$			7.20434i			0.248426i	−0.992256	+	0.124213i	$0.960359\pi$
$30$		0			0
$31$	15.1996			0.490311			0.245156	−	0.969484i	$-0.421161\pi$
$31$	15.1996			0.490311			0.245156	+	0.969484i	$0.421161\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	−2.16758	−	2.16758i	−0.0656843	−	0.0656843i
$34$			26.7570i			0.786971i
$35$		0			0
$36$	6.00000			0.166667
$37$	−28.4468	+	28.4468i	−0.768832	+	0.768832i	−0.977901	−	0.209069i	$-0.932957\pi$
$37$	−28.4468	+	28.4468i	−0.768832	+	0.768832i	0.209069	+	0.977901i	$0.432957\pi$
$38$	−13.5088	−	13.5088i	−0.355494	−	0.355494i
$39$			32.5443i			0.834469i
$40$		0			0
$41$	20.6534			0.503741			0.251871	−	0.967761i	$-0.418954\pi$
$41$	20.6534			0.503741			0.251871	+	0.967761i	$0.418954\pi$
$42$	6.59896	−	6.59896i	0.157118	−	0.157118i
$43$	−28.7921	−	28.7921i	−0.669583	−	0.669583i	0.288036	−	0.957620i	$-0.406998\pi$
$43$	−28.7921	−	28.7921i	−0.669583	−	0.669583i	−0.957620	+	0.288036i	$0.906998\pi$
$44$		−	3.53965i		−	0.0804465i
$45$		0			0
$46$	6.91979			0.150430
$47$	16.4532	−	16.4532i	0.350068	−	0.350068i	−0.510067	−	0.860135i	$-0.670379\pi$
$47$	16.4532	−	16.4532i	0.350068	−	0.350068i	0.860135	+	0.510067i	$0.170379\pi$
$48$	4.89898	+	4.89898i	0.102062	+	0.102062i
$49$			34.4846i			0.703767i
$50$		0			0
$51$	−32.7705			−0.642559
$52$	−26.5723	+	26.5723i	−0.511006	+	0.511006i
$53$	−71.9184	−	71.9184i	−1.35695	−	1.35695i	−0.877651	−	0.479300i	$-0.840890\pi$
$53$	−71.9184	−	71.9184i	−1.35695	−	1.35695i	−0.479300	−	0.877651i	$-0.659110\pi$
$54$			7.34847i			0.136083i
$55$		0			0
$56$	10.7761			0.192430
$57$	16.5448	−	16.5448i	0.290260	−	0.290260i
$58$	−7.20434	−	7.20434i	−0.124213	−	0.124213i
$59$		−	27.4099i		−	0.464575i	−0.972647	−	0.232287i	$-0.925379\pi$
$59$		−	27.4099i		−	0.464575i	0.972647	−	0.232287i	$-0.0746210\pi$
$60$		0			0
$61$	−78.6807			−1.28985			−0.644924	−	0.764247i	$-0.723111\pi$
$61$	−78.6807			−1.28985			−0.644924	+	0.764247i	$0.723111\pi$
$62$	−15.1996	+	15.1996i	−0.245156	+	0.245156i
$63$	8.08204	+	8.08204i	0.128286	+	0.128286i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	4.33516			0.0656843
$67$	−32.0521	+	32.0521i	−0.478389	+	0.478389i	−0.904616	−	0.426227i	$-0.859843\pi$
$67$	−32.0521	+	32.0521i	−0.478389	+	0.478389i	0.426227	+	0.904616i	$0.359843\pi$
$68$	−26.7570	−	26.7570i	−0.393486	−	0.393486i
$69$			8.47497i			0.122826i
$70$		0			0
$71$	−111.105			−1.56486			−0.782431	−	0.622737i	$-0.786021\pi$
$71$	−111.105			−1.56486			−0.782431	+	0.622737i	$0.786021\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	−20.1117	−	20.1117i	−0.275503	−	0.275503i	0.555808	−	0.831311i	$-0.312409\pi$
$73$	−20.1117	−	20.1117i	−0.275503	−	0.275503i	−0.831311	+	0.555808i	$0.812409\pi$
$74$		−	56.8936i		−	0.768832i
$75$		0			0
$76$	27.0176			0.355494
$77$	4.76793	−	4.76793i	0.0619212	−	0.0619212i
$78$	−32.5443	−	32.5443i	−0.417235	−	0.417235i
$79$		−	81.3451i		−	1.02968i	−0.857285	−	0.514842i	$-0.827851\pi$
$79$		−	81.3451i		−	1.02968i	0.857285	−	0.514842i	$-0.172149\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	−20.6534	+	20.6534i	−0.251871	+	0.251871i
$83$	−42.2649	−	42.2649i	−0.509216	−	0.509216i	0.405070	−	0.914286i	$-0.367247\pi$
$83$	−42.2649	−	42.2649i	−0.509216	−	0.509216i	−0.914286	+	0.405070i	$0.867247\pi$
$84$			13.1979i			0.157118i
$85$		0			0
$86$	57.5842			0.669583
$87$	8.82348	−	8.82348i	0.101419	−	0.101419i
$88$	3.53965	+	3.53965i	0.0402233	+	0.0402233i
$89$		−	118.921i		−	1.33619i	−0.744077	−	0.668094i	$-0.767110\pi$
$89$		−	118.921i		−	1.33619i	0.744077	−	0.668094i	$-0.232890\pi$
$90$		0			0
$91$	−71.5862			−0.786661
$92$	−6.91979	+	6.91979i	−0.0752151	+	0.0752151i
$93$	−18.6157	−	18.6157i	−0.200169	−	0.200169i
$94$			32.9064i			0.350068i
$95$		0			0
$96$	−9.79796			−0.102062
$97$	79.0793	−	79.0793i	0.815250	−	0.815250i	−0.170165	−	0.985416i	$-0.554430\pi$
$97$	79.0793	−	79.0793i	0.815250	−	0.815250i	0.985416	+	0.170165i	$0.0544301\pi$
$98$	−34.4846	−	34.4846i	−0.351883	−	0.351883i
$99$			5.30947i			0.0536310i
$100$		0			0
$101$	17.9862			0.178081			0.0890406	−	0.996028i	$-0.471620\pi$
$101$	17.9862			0.178081			0.0890406	+	0.996028i	$0.471620\pi$
$102$	32.7705	−	32.7705i	0.321280	−	0.321280i
$103$	−128.163	−	128.163i	−1.24430	−	1.24430i	−0.958199	−	0.286102i	$-0.907640\pi$
$103$	−128.163	−	128.163i	−1.24430	−	1.24430i	−0.286102	−	0.958199i	$-0.592360\pi$
$104$		−	53.1446i		−	0.511006i
$105$		0			0
$106$	143.837			1.35695
$107$	−30.0106	+	30.0106i	−0.280473	+	0.280473i	−0.833298	−	0.552825i	$-0.813550\pi$
$107$	−30.0106	+	30.0106i	−0.280473	+	0.280473i	0.552825	+	0.833298i	$0.313550\pi$
$108$	−7.34847	−	7.34847i	−0.0680414	−	0.0680414i
$109$			166.166i			1.52446i	0.647306	+	0.762230i	$0.275896\pi$
$109$			166.166i			1.52446i	−0.647306	+	0.762230i	$0.724104\pi$
$110$		0			0
$111$	69.6801			0.627749
$112$	−10.7761	+	10.7761i	−0.0962148	+	0.0962148i
$113$	111.876	+	111.876i	0.990057	+	0.990057i	0.999951	−	0.00989414i	$-0.00314946\pi$
$113$	111.876	+	111.876i	0.990057	+	0.990057i	−0.00989414	+	0.999951i	$0.503149\pi$
$114$			33.0896i			0.290260i
$115$		0			0
$116$	14.4087			0.124213
$117$	39.8585	−	39.8585i	0.340671	−	0.340671i
$118$	27.4099	+	27.4099i	0.232287	+	0.232287i
$119$		−	72.0838i		−	0.605746i
$120$		0			0
$121$	−117.868			−0.974113
$122$	78.6807	−	78.6807i	0.644924	−	0.644924i
$123$	−25.2951	−	25.2951i	−0.205651	−	0.205651i
$124$		−	30.3993i		−	0.245156i
$125$		0			0
$126$	−16.1641			−0.128286
$127$	−147.676	+	147.676i	−1.16280	+	1.16280i	−0.178945	+	0.983859i	$0.557268\pi$
$127$	−147.676	+	147.676i	−1.16280	+	1.16280i	−0.983859	+	0.178945i	$0.942732\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$			70.5259i			0.546712i
$130$		0			0
$131$	−58.6448			−0.447671			−0.223835	−	0.974627i	$-0.571858\pi$
$131$	−58.6448			−0.447671			−0.223835	+	0.974627i	$0.571858\pi$
$132$	−4.33516	+	4.33516i	−0.0328421	+	0.0328421i
$133$	36.3929	+	36.3929i	0.273631	+	0.273631i
$134$		−	64.1042i		−	0.478389i
$135$		0			0
$136$	53.5140			0.393486
$137$	25.5466	−	25.5466i	0.186472	−	0.186472i	−0.607697	−	0.794169i	$-0.707907\pi$
$137$	25.5466	−	25.5466i	0.186472	−	0.186472i	0.794169	+	0.607697i	$0.207907\pi$
$138$	−8.47497	−	8.47497i	−0.0614129	−	0.0614129i
$139$		−	151.520i		−	1.09007i	−0.838414	−	0.545034i	$-0.816517\pi$
$139$		−	151.520i		−	1.09007i	0.838414	−	0.545034i	$-0.183483\pi$
$140$		0			0
$141$	−40.3020			−0.285830
$142$	111.105	−	111.105i	0.782431	−	0.782431i
$143$	−23.5141	−	23.5141i	−0.164435	−	0.164435i
$144$		−	12.0000i		−	0.0833333i
$145$		0			0
$146$	40.2234			0.275503
$147$	42.2348	−	42.2348i	0.287312	−	0.287312i
$148$	56.8936	+	56.8936i	0.384416	+	0.384416i
$149$		−	254.435i		−	1.70762i	−0.520585	−	0.853810i	$-0.674286\pi$
$149$		−	254.435i		−	1.70762i	0.520585	−	0.853810i	$-0.325714\pi$
$150$		0			0
$151$	−66.3316			−0.439282			−0.219641	−	0.975581i	$-0.570489\pi$
$151$	−66.3316			−0.439282			−0.219641	+	0.975581i	$0.570489\pi$
$152$	−27.0176	+	27.0176i	−0.177747	+	0.177747i
$153$	40.1355	+	40.1355i	0.262324	+	0.262324i
$154$			9.53586i			0.0619212i
$155$		0			0
$156$	65.0886			0.417235
$157$	−133.327	+	133.327i	−0.849215	+	0.849215i	−0.990035	−	0.140820i	$-0.955026\pi$
$157$	−133.327	+	133.327i	−0.849215	+	0.849215i	0.140820	+	0.990035i	$0.455026\pi$
$158$	81.3451	+	81.3451i	0.514842	+	0.514842i
$159$			176.163i			1.10795i
$160$		0			0
$161$	−18.6420			−0.115789
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	−66.7032	−	66.7032i	−0.409222	−	0.409222i	0.472245	−	0.881467i	$-0.343444\pi$
$163$	−66.7032	−	66.7032i	−0.409222	−	0.409222i	−0.881467	+	0.472245i	$0.843444\pi$
$164$		−	41.3068i		−	0.251871i
$165$		0			0
$166$	84.5299			0.509216
$167$	80.4654	−	80.4654i	0.481829	−	0.481829i	−0.423886	−	0.905715i	$-0.639334\pi$
$167$	80.4654	−	80.4654i	0.481829	−	0.481829i	0.905715	+	0.423886i	$0.139334\pi$
$168$	−13.1979	−	13.1979i	−0.0785591	−	0.0785591i
$169$			184.044i			1.08902i
$170$		0			0
$171$	−40.5264			−0.236996
$172$	−57.5842	+	57.5842i	−0.334792	+	0.334792i
$173$	101.280	+	101.280i	0.585435	+	0.585435i	0.936392	−	0.350957i	$-0.114144\pi$
$173$	101.280	+	101.280i	0.585435	+	0.585435i	−0.350957	+	0.936392i	$0.614144\pi$
$174$			17.6470i			0.101419i
$175$		0			0
$176$	−7.07929			−0.0402233
$177$	−33.5701	+	33.5701i	−0.189662	+	0.189662i
$178$	118.921	+	118.921i	0.668094	+	0.668094i
$179$		−	301.797i		−	1.68601i	−0.537903	−	0.843007i	$-0.680783\pi$
$179$		−	301.797i		−	1.68601i	0.537903	−	0.843007i	$-0.319217\pi$
$180$		0			0
$181$	103.906			0.574065			0.287033	−	0.957921i	$-0.407331\pi$
$181$	103.906			0.574065			0.287033	+	0.957921i	$0.407331\pi$
$182$	71.5862	−	71.5862i	0.393331	−	0.393331i
$183$	96.3638	+	96.3638i	0.526578	+	0.526578i
$184$		−	13.8396i		−	0.0752151i
$185$		0			0
$186$	37.2314			0.200169
$187$	23.6776	−	23.6776i	0.126618	−	0.126618i
$188$	−32.9064	−	32.9064i	−0.175034	−	0.175034i
$189$		−	19.7969i		−	0.104745i
$190$		0			0
$191$	−93.2098			−0.488010			−0.244005	−	0.969774i	$-0.578461\pi$
$191$	−93.2098			−0.488010			−0.244005	+	0.969774i	$0.578461\pi$
$192$	9.79796	−	9.79796i	0.0510310	−	0.0510310i
$193$	69.1868	+	69.1868i	0.358481	+	0.358481i	0.863253	−	0.504772i	$-0.168423\pi$
$193$	69.1868	+	69.1868i	0.358481	+	0.358481i	−0.504772	+	0.863253i	$0.668423\pi$
$194$			158.159i			0.815250i
$195$		0			0
$196$	68.9691			0.351883
$197$	−66.9137	+	66.9137i	−0.339663	+	0.339663i	−0.856241	−	0.516577i	$-0.827206\pi$
$197$	−66.9137	+	66.9137i	−0.339663	+	0.339663i	0.516577	+	0.856241i	$0.327206\pi$
$198$	−5.30947	−	5.30947i	−0.0268155	−	0.0268155i
$199$			127.464i			0.640521i	0.947330	+	0.320260i	$0.103770\pi$
$199$			127.464i			0.640521i	−0.947330	+	0.320260i	$0.896230\pi$
$200$		0			0
$201$	78.5113			0.390603
$202$	−17.9862	+	17.9862i	−0.0890406	+	0.0890406i
$203$	19.4086	+	19.4086i	0.0956089	+	0.0956089i
$204$			65.5410i			0.321280i
$205$		0			0
$206$	256.326			1.24430
$207$	10.3797	−	10.3797i	0.0501434	−	0.0501434i
$208$	53.1446	+	53.1446i	0.255503	+	0.255503i
$209$			23.9082i			0.114393i
$210$		0			0
$211$	360.045			1.70638			0.853188	−	0.521604i	$-0.174666\pi$
$211$	360.045			1.70638			0.853188	+	0.521604i	$0.174666\pi$
$212$	−143.837	+	143.837i	−0.678476	+	0.678476i
$213$	136.076	+	136.076i	0.638852	+	0.638852i
$214$		−	60.0212i		−	0.280473i
$215$		0			0
$216$	14.6969			0.0680414
$217$	40.9481	−	40.9481i	0.188701	−	0.188701i
$218$	−166.166	−	166.166i	−0.762230	−	0.762230i
$219$			49.2634i			0.224947i
$220$		0			0
$221$	−355.498			−1.60859
$222$	−69.6801	+	69.6801i	−0.313875	+	0.313875i
$223$	120.228	+	120.228i	0.539138	+	0.539138i	0.923276	−	0.384138i	$-0.125501\pi$
$223$	120.228	+	120.228i	0.539138	+	0.539138i	−0.384138	+	0.923276i	$0.625501\pi$
$224$		−	21.5521i		−	0.0962148i
$225$		0			0
$226$	−223.753			−0.990057
$227$	11.7621	−	11.7621i	0.0518155	−	0.0518155i	−0.680724	−	0.732540i	$-0.738335\pi$
$227$	11.7621	−	11.7621i	0.0518155	−	0.0518155i	0.732540	+	0.680724i	$0.238335\pi$
$228$	−33.0896	−	33.0896i	−0.145130	−	0.145130i
$229$			406.576i			1.77544i	0.460384	+	0.887720i	$0.347712\pi$
$229$			406.576i			1.77544i	−0.460384	+	0.887720i	$0.652288\pi$
$230$		0			0
$231$	−11.6790			−0.0505584
$232$	−14.4087	+	14.4087i	−0.0621064	+	0.0621064i
$233$	135.112	+	135.112i	0.579881	+	0.579881i	0.934870	−	0.354990i	$-0.115516\pi$
$233$	135.112	+	135.112i	0.579881	+	0.579881i	−0.354990	+	0.934870i	$0.615516\pi$
$234$			79.7169i			0.340671i
$235$		0			0
$236$	−54.8198			−0.232287
$237$	−99.6269	+	99.6269i	−0.420367	+	0.420367i
$238$	72.0838	+	72.0838i	0.302873	+	0.302873i
$239$		−	462.095i		−	1.93345i	−0.255812	−	0.966726i	$-0.582343\pi$
$239$		−	462.095i		−	1.93345i	0.255812	−	0.966726i	$-0.417657\pi$
$240$		0			0
$241$	−146.704			−0.608730			−0.304365	−	0.952555i	$-0.598444\pi$
$241$	−146.704			−0.608730			−0.304365	+	0.952555i	$0.598444\pi$
$242$	117.868	−	117.868i	0.487057	−	0.487057i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$			157.361i			0.644924i
$245$		0			0
$246$	50.5902			0.205651
$247$	179.480	−	179.480i	0.726639	−	0.726639i
$248$	30.3993	+	30.3993i	0.122578	+	0.122578i
$249$			103.528i			0.415773i
$250$		0			0
$251$	−2.71232			−0.0108060			−0.00540302	−	0.999985i	$-0.501720\pi$
$251$	−2.71232			−0.0108060			−0.00540302	+	0.999985i	$0.501720\pi$
$252$	16.1641	−	16.1641i	0.0641432	−	0.0641432i
$253$	−6.12340	−	6.12340i	−0.0242032	−	0.0242032i
$254$		−	295.352i		−	1.16280i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−73.9734	+	73.9734i	−0.287834	+	0.287834i	−0.836223	−	0.548389i	$-0.815241\pi$
$257$	−73.9734	+	73.9734i	−0.287834	+	0.287834i	0.548389	+	0.836223i	$0.315241\pi$
$258$	−70.5259	−	70.5259i	−0.273356	−	0.273356i
$259$			153.272i			0.591784i
$260$		0			0
$261$	−21.6130			−0.0828085
$262$	58.6448	−	58.6448i	0.223835	−	0.223835i
$263$	243.803	+	243.803i	0.927007	+	0.927007i	0.997511	−	0.0705046i	$-0.0224609\pi$
$263$	243.803	+	243.803i	0.927007	+	0.927007i	−0.0705046	+	0.997511i	$0.522461\pi$
$264$		−	8.67033i		−	0.0328421i
$265$		0			0
$266$	−72.7857			−0.273631
$267$	−145.648	+	145.648i	−0.545497	+	0.545497i
$268$	64.1042	+	64.1042i	0.239195	+	0.239195i
$269$			475.591i			1.76800i	0.467491	+	0.883998i	$0.345158\pi$
$269$			475.591i			1.76800i	−0.467491	+	0.883998i	$0.654842\pi$
$270$		0			0
$271$	−299.402			−1.10480			−0.552402	−	0.833578i	$-0.686289\pi$
$271$	−299.402			−1.10480			−0.552402	+	0.833578i	$0.686289\pi$
$272$	−53.5140	+	53.5140i	−0.196743	+	0.196743i
$273$	87.6748	+	87.6748i	0.321153	+	0.321153i
$274$			51.0933i			0.186472i
$275$		0			0
$276$	16.9499			0.0614129
$277$	−0.773639	+	0.773639i	−0.00279292	+	0.00279292i	−0.708502	−	0.705709i	$-0.750629\pi$
$277$	−0.773639	+	0.773639i	−0.00279292	+	0.00279292i	0.705709	+	0.708502i	$0.250629\pi$
$278$	151.520	+	151.520i	0.545034	+	0.545034i
$279$			45.5989i			0.163437i
$280$		0			0
$281$	133.812			0.476198			0.238099	−	0.971241i	$-0.423476\pi$
$281$	133.812			0.476198			0.238099	+	0.971241i	$0.423476\pi$
$282$	40.3020	−	40.3020i	0.142915	−	0.142915i
$283$	−58.7282	−	58.7282i	−0.207520	−	0.207520i	0.595692	−	0.803213i	$-0.296878\pi$
$283$	−58.7282	−	58.7282i	−0.207520	−	0.207520i	−0.803213	+	0.595692i	$0.796878\pi$
$284$			222.210i			0.782431i
$285$		0			0
$286$	47.0283			0.164435
$287$	55.6405	−	55.6405i	0.193869	−	0.193869i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$		−	68.9690i		−	0.238647i
$290$		0			0
$291$	−193.704			−0.665649
$292$	−40.2234	+	40.2234i	−0.137751	+	0.137751i
$293$	264.851	+	264.851i	0.903929	+	0.903929i	0.995773	−	0.0918440i	$-0.0292761\pi$
$293$	264.851	+	264.851i	0.903929	+	0.903929i	−0.0918440	+	0.995773i	$0.529276\pi$
$294$			84.4696i			0.287312i
$295$		0			0
$296$	−113.787			−0.384416
$297$	6.50275	−	6.50275i	0.0218948	−	0.0218948i
$298$	254.435	+	254.435i	0.853810	+	0.853810i
$299$			91.9373i			0.307483i
$300$		0			0
$301$	−155.133			−0.515391
$302$	66.3316	−	66.3316i	0.219641	−	0.219641i
$303$	−22.0285	−	22.0285i	−0.0727013	−	0.0727013i
$304$		−	54.0352i		−	0.177747i
$305$		0			0
$306$	−80.2711			−0.262324
$307$	−62.5922	+	62.5922i	−0.203883	+	0.203883i	−0.801662	−	0.597778i	$-0.796050\pi$
$307$	−62.5922	+	62.5922i	−0.203883	+	0.203883i	0.597778	+	0.801662i	$0.296050\pi$
$308$	−9.53586	−	9.53586i	−0.0309606	−	0.0309606i
$309$			313.934i			1.01597i
$310$		0			0
$311$	411.007			1.32157			0.660783	−	0.750577i	$-0.270224\pi$
$311$	411.007			1.32157			0.660783	+	0.750577i	$0.270224\pi$
$312$	−65.0886	+	65.0886i	−0.208617	+	0.208617i
$313$	−192.692	−	192.692i	−0.615631	−	0.615631i	0.328777	−	0.944408i	$-0.393364\pi$
$313$	−192.692	−	192.692i	−0.615631	−	0.615631i	−0.944408	+	0.328777i	$0.893364\pi$
$314$		−	266.653i		−	0.849215i
$315$		0			0
$316$	−162.690			−0.514842
$317$	−182.555	+	182.555i	−0.575882	+	0.575882i	−0.933766	−	0.357884i	$-0.883498\pi$
$317$	−182.555	+	182.555i	−0.575882	+	0.575882i	0.357884	+	0.933766i	$0.383498\pi$
$318$	−176.163	−	176.163i	−0.553973	−	0.553973i
$319$			12.7504i			0.0399699i
$320$		0			0
$321$	73.5107			0.229005
$322$	18.6420	−	18.6420i	0.0578944	−	0.0578944i
$323$	180.727	+	180.727i	0.559528	+	0.559528i
$324$			18.0000i			0.0555556i
$325$		0			0
$326$	133.406			0.409222
$327$	203.511	−	203.511i	0.622359	−	0.622359i
$328$	41.3068	+	41.3068i	0.125935	+	0.125935i
$329$		−	88.6503i		−	0.269454i
$330$		0			0
$331$	263.961			0.797465			0.398733	−	0.917067i	$-0.369450\pi$
$331$	263.961			0.797465			0.398733	+	0.917067i	$0.369450\pi$
$332$	−84.5299	+	84.5299i	−0.254608	+	0.254608i
$333$	−85.3404	−	85.3404i	−0.256277	−	0.256277i
$334$			160.931i			0.481829i
$335$		0			0
$336$	26.3958			0.0785591
$337$	388.677	−	388.677i	1.15335	−	1.15335i	0.167467	−	0.985878i	$-0.446441\pi$
$337$	388.677	−	388.677i	1.15335	−	1.15335i	0.985878	−	0.167467i	$-0.0535589\pi$
$338$	−184.044	−	184.044i	−0.544508	−	0.544508i
$339$		−	274.040i		−	0.808378i
$340$		0			0
$341$	26.9007			0.0788876
$342$	40.5264	−	40.5264i	0.118498	−	0.118498i
$343$	224.909	+	224.909i	0.655710	+	0.655710i
$344$		−	115.168i		−	0.334792i
$345$		0			0
$346$	−202.561			−0.585435
$347$	84.8870	−	84.8870i	0.244631	−	0.244631i	−0.574132	−	0.818763i	$-0.694660\pi$
$347$	84.8870	−	84.8870i	0.244631	−	0.244631i	0.818763	+	0.574132i	$0.194660\pi$
$348$	−17.6470	−	17.6470i	−0.0507097	−	0.0507097i
$349$		−	176.263i		−	0.505050i	−0.967590	−	0.252525i	$-0.918739\pi$
$349$		−	176.263i		−	0.505050i	0.967590	−	0.252525i	$-0.0812610\pi$
$350$		0			0
$351$	−97.6329			−0.278156
$352$	7.07929	−	7.07929i	0.0201116	−	0.0201116i
$353$	−220.926	−	220.926i	−0.625853	−	0.625853i	0.321169	−	0.947022i	$-0.395924\pi$
$353$	−220.926	−	220.926i	−0.625853	−	0.625853i	−0.947022	+	0.321169i	$0.895924\pi$
$354$		−	67.1403i		−	0.189662i
$355$		0			0
$356$	−237.842			−0.668094
$357$	−88.2842	+	88.2842i	−0.247295	+	0.247295i
$358$	301.797	+	301.797i	0.843007	+	0.843007i
$359$		−	545.295i		−	1.51893i	−0.650550	−	0.759464i	$-0.725461\pi$
$359$		−	545.295i		−	1.51893i	0.650550	−	0.759464i	$-0.274539\pi$
$360$		0			0
$361$	178.513			0.494495
$362$	−103.906	+	103.906i	−0.287033	+	0.287033i
$363$	144.358	+	144.358i	0.397680	+	0.397680i
$364$			143.172i			0.393331i
$365$		0			0
$366$	−192.728			−0.526578
$367$	134.238	−	134.238i	0.365772	−	0.365772i	−0.500161	−	0.865933i	$-0.666726\pi$
$367$	134.238	−	134.238i	0.365772	−	0.365772i	0.865933	+	0.500161i	$0.166726\pi$
$368$	13.8396	+	13.8396i	0.0376075	+	0.0376075i
$369$			61.9601i			0.167914i
$370$		0			0
$371$	−387.498			−1.04447
$372$	−37.2314	+	37.2314i	−0.100084	+	0.100084i
$373$	−314.472	−	314.472i	−0.843089	−	0.843089i	0.146171	−	0.989259i	$-0.453305\pi$
$373$	−314.472	−	314.472i	−0.843089	−	0.843089i	−0.989259	+	0.146171i	$0.953305\pi$
$374$			47.3552i			0.126618i
$375$		0			0
$376$	65.8128			0.175034
$377$	95.7180	−	95.7180i	0.253894	−	0.253894i
$378$	19.7969	+	19.7969i	0.0523727	+	0.0523727i
$379$		−	146.881i		−	0.387548i	−0.981046	−	0.193774i	$-0.937927\pi$
$379$		−	146.881i		−	0.387548i	0.981046	−	0.193774i	$-0.0620729\pi$
$380$		0			0
$381$	361.731			0.949425
$382$	93.2098	−	93.2098i	0.244005	−	0.244005i
$383$	−60.5500	−	60.5500i	−0.158094	−	0.158094i	0.623628	−	0.781722i	$-0.285658\pi$
$383$	−60.5500	−	60.5500i	−0.158094	−	0.158094i	−0.781722	+	0.623628i	$0.785658\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	−138.374			−0.358481
$387$	86.3762	−	86.3762i	0.223194	−	0.223194i
$388$	−158.159	−	158.159i	−0.407625	−	0.407625i
$389$		−	148.935i		−	0.382867i	−0.981506	−	0.191433i	$-0.938686\pi$
$389$		−	148.935i		−	0.382867i	0.981506	−	0.191433i	$-0.0613136\pi$
$390$		0			0
$391$	−92.5764			−0.236768
$392$	−68.9691	+	68.9691i	−0.175942	+	0.175942i
$393$	71.8250	+	71.8250i	0.182761	+	0.182761i
$394$		−	133.827i		−	0.339663i
$395$		0			0
$396$	10.6189			0.0268155
$397$	418.388	−	418.388i	1.05387	−	1.05387i	0.0554109	−	0.998464i	$-0.482353\pi$
$397$	418.388	−	418.388i	1.05387	−	1.05387i	0.998464	−	0.0554109i	$-0.0176469\pi$
$398$	−127.464	−	127.464i	−0.320260	−	0.320260i
$399$		−	89.1440i		−	0.223418i
$400$		0			0
$401$	525.592			1.31070			0.655352	−	0.755324i	$-0.272520\pi$
$401$	525.592			1.31070			0.655352	+	0.755324i	$0.272520\pi$
$402$	−78.5113	+	78.5113i	−0.195302	+	0.195302i
$403$	−201.945	−	201.945i	−0.501104	−	0.501104i
$404$		−	35.9724i		−	0.0890406i
$405$		0			0
$406$	−38.8172			−0.0956089
$407$	−50.3458	+	50.3458i	−0.123700	+	0.123700i
$408$	−65.5410	−	65.5410i	−0.160640	−	0.160640i
$409$			289.417i			0.707620i	0.935317	+	0.353810i	$0.115114\pi$
$409$			289.417i			0.707620i	−0.935317	+	0.353810i	$0.884886\pi$
$410$		0			0
$411$	−62.5762			−0.152254
$412$	−256.326	+	256.326i	−0.622151	+	0.622151i
$413$	−73.8427	−	73.8427i	−0.178796	−	0.178796i
$414$			20.7594i			0.0501434i
$415$		0			0
$416$	−106.289			−0.255503
$417$	−185.573	+	185.573i	−0.445019	+	0.445019i
$418$	−23.9082	−	23.9082i	−0.0571966	−	0.0571966i
$419$			29.5402i			0.0705017i	0.999378	+	0.0352509i	$0.0112230\pi$
$419$			29.5402i			0.0705017i	−0.999378	+	0.0352509i	$0.988777\pi$
$420$		0			0
$421$	47.3975			0.112583			0.0562916	−	0.998414i	$-0.482072\pi$
$421$	47.3975			0.112583			0.0562916	+	0.998414i	$0.482072\pi$
$422$	−360.045	+	360.045i	−0.853188	+	0.853188i
$423$	49.3596	+	49.3596i	0.116689	+	0.116689i
$424$		−	287.674i		−	0.678476i
$425$		0			0
$426$	−272.151			−0.638852
$427$	−211.967	+	211.967i	−0.496410	+	0.496410i
$428$	60.0212	+	60.0212i	0.140237	+	0.140237i
$429$			57.5976i			0.134260i
$430$		0			0
$431$	685.640			1.59081			0.795406	−	0.606076i	$-0.207257\pi$
$431$	685.640			1.59081			0.795406	+	0.606076i	$0.207257\pi$
$432$	−14.6969	+	14.6969i	−0.0340207	+	0.0340207i
$433$	−268.308	−	268.308i	−0.619650	−	0.619650i	0.325792	−	0.945442i	$-0.394369\pi$
$433$	−268.308	−	268.308i	−0.619650	−	0.619650i	−0.945442	+	0.325792i	$0.894369\pi$
$434$			81.8961i			0.188701i
$435$		0			0
$436$	332.332			0.762230
$437$	46.7390	−	46.7390i	0.106954	−	0.106954i
$438$	−49.2634	−	49.2634i	−0.112474	−	0.112474i
$439$		−	758.142i		−	1.72698i	−0.504369	−	0.863488i	$-0.668275\pi$
$439$		−	758.142i		−	1.72698i	0.504369	−	0.863488i	$-0.331725\pi$
$440$		0			0
$441$	−103.454			−0.234589
$442$	355.498	−	355.498i	0.804294	−	0.804294i
$443$	−526.285	−	526.285i	−1.18800	−	1.18800i	−0.977619	−	0.210383i	$-0.932529\pi$
$443$	−526.285	−	526.285i	−1.18800	−	1.18800i	−0.210383	−	0.977619i	$-0.567471\pi$
$444$		−	139.360i		−	0.313875i
$445$		0			0
$446$	−240.456			−0.539138
$447$	−311.618	+	311.618i	−0.697133	+	0.697133i
$448$	21.5521	+	21.5521i	0.0481074	+	0.0481074i
$449$			482.572i			1.07477i	0.843337	+	0.537386i	$0.180588\pi$
$449$			482.572i			1.07477i	−0.843337	+	0.537386i	$0.819412\pi$
$450$		0			0
$451$	36.5528			0.0810484
$452$	223.753	−	223.753i	0.495028	−	0.495028i
$453$	81.2393	+	81.2393i	0.179336	+	0.179336i
$454$			23.5242i			0.0518155i
$455$		0			0
$456$	66.1793			0.145130
$457$	−268.634	+	268.634i	−0.587820	+	0.587820i	−0.937040	−	0.349221i	$-0.886446\pi$
$457$	−268.634	+	268.634i	−0.587820	+	0.587820i	0.349221	+	0.937040i	$0.386446\pi$
$458$	−406.576	−	406.576i	−0.887720	−	0.887720i
$459$		−	98.3116i		−	0.214186i
$460$		0			0
$461$	577.734			1.25322			0.626610	−	0.779333i	$-0.284442\pi$
$461$	577.734			1.25322			0.626610	+	0.779333i	$0.284442\pi$
$462$	11.6790	−	11.6790i	0.0252792	−	0.0252792i
$463$	−583.398	−	583.398i	−1.26004	−	1.26004i	−0.951073	−	0.308967i	$-0.900017\pi$
$463$	−583.398	−	583.398i	−1.26004	−	1.26004i	−0.308967	−	0.951073i	$-0.599983\pi$
$464$		−	28.8174i		−	0.0621064i
$465$		0			0
$466$	−270.224			−0.579881
$467$	−569.585	+	569.585i	−1.21967	+	1.21967i	−0.251919	+	0.967748i	$0.581062\pi$
$467$	−569.585	+	569.585i	−1.21967	+	1.21967i	−0.967748	+	0.251919i	$0.918938\pi$
$468$	−79.7169	−	79.7169i	−0.170335	−	0.170335i
$469$			172.698i			0.368225i
$470$		0			0
$471$	326.582			0.693381
$472$	54.8198	−	54.8198i	0.116144	−	0.116144i
$473$	−50.9569	−	50.9569i	−0.107731	−	0.107731i
$474$		−	199.254i		−	0.420367i
$475$		0			0
$476$	−144.168			−0.302873
$477$	215.755	−	215.755i	0.452317	−	0.452317i
$478$	462.095	+	462.095i	0.966726	+	0.966726i
$479$		−	335.883i		−	0.701217i	−0.936522	−	0.350609i	$-0.885975\pi$
$479$		−	335.883i		−	0.701217i	0.936522	−	0.350609i	$-0.114025\pi$
$480$		0			0
$481$	755.897			1.57151
$482$	146.704	−	146.704i	0.304365	−	0.304365i
$483$	22.8317	+	22.8317i	0.0472706	+	0.0472706i
$484$			235.735i			0.487057i
$485$		0			0
$486$	−22.0454			−0.0453609
$487$	281.468	−	281.468i	0.577964	−	0.577964i	−0.356378	−	0.934342i	$-0.615989\pi$
$487$	281.468	−	281.468i	0.577964	−	0.577964i	0.934342	+	0.356378i	$0.115989\pi$
$488$	−157.361	−	157.361i	−0.322462	−	0.322462i
$489$			163.389i			0.334129i
$490$		0			0
$491$	383.934			0.781943			0.390971	−	0.920403i	$-0.372139\pi$
$491$	383.934			0.781943			0.390971	+	0.920403i	$0.372139\pi$
$492$	−50.5902	+	50.5902i	−0.102826	+	0.102826i
$493$	96.3833	+	96.3833i	0.195504	+	0.195504i
$494$			358.960i			0.726639i
$495$		0			0
$496$	−60.7986			−0.122578
$497$	−299.319	+	299.319i	−0.602252	+	0.602252i
$498$	−103.528	−	103.528i	−0.207887	−	0.207887i
$499$		−	507.775i		−	1.01759i	−0.860889	−	0.508793i	$-0.830092\pi$
$499$		−	507.775i		−	1.01759i	0.860889	−	0.508793i	$-0.169908\pi$
$500$		0			0
$501$	−197.099			−0.393412
$502$	2.71232	−	2.71232i	0.00540302	−	0.00540302i
$503$	181.127	+	181.127i	0.360093	+	0.360093i	0.863847	−	0.503754i	$-0.168048\pi$
$503$	181.127	+	181.127i	0.360093	+	0.360093i	−0.503754	+	0.863847i	$0.668048\pi$
$504$			32.3282i			0.0641432i
$505$		0			0
$506$	12.2468			0.0242032
$507$	225.407	−	225.407i	0.444589	−	0.444589i
$508$	295.352	+	295.352i	0.581402	+	0.581402i
$509$			335.611i			0.659354i	0.944094	+	0.329677i	$0.106940\pi$
$509$			335.611i			0.659354i	−0.944094	+	0.329677i	$0.893060\pi$
$510$		0			0
$511$	−108.362			−0.212060
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	49.6345	+	49.6345i	0.0967533	+	0.0967533i
$514$		−	147.947i		−	0.287834i
$515$		0			0
$516$	141.052			0.273356
$517$	29.1193	−	29.1193i	0.0563235	−	0.0563235i
$518$	−153.272	−	153.272i	−0.295892	−	0.295892i
$519$		−	248.085i		−	0.478006i
$520$		0			0
$521$	−745.739			−1.43136			−0.715681	−	0.698428i	$-0.753883\pi$
$521$	−745.739			−1.43136			−0.715681	+	0.698428i	$0.753883\pi$
$522$	21.6130	−	21.6130i	0.0414043	−	0.0414043i
$523$	−689.743	−	689.743i	−1.31882	−	1.31882i	−0.914711	−	0.404110i	$-0.867581\pi$
$523$	−689.743	−	689.743i	−1.31882	−	1.31882i	−0.404110	−	0.914711i	$-0.632419\pi$
$524$			117.290i			0.223835i
$525$		0			0
$526$	−487.606			−0.927007
$527$	203.349	−	203.349i	0.385861	−	0.385861i
$528$	8.67033	+	8.67033i	0.0164211	+	0.0164211i
$529$		−	505.058i		−	0.954742i
$530$		0			0
$531$	82.2297			0.154858
$532$	72.7857	−	72.7857i	0.136815	−	0.136815i
$533$	−274.404	−	274.404i	−0.514829	−	0.514829i
$534$		−	291.295i		−	0.545497i
$535$		0			0
$536$	−128.208			−0.239195
$537$	−369.624	+	369.624i	−0.688312	+	0.688312i
$538$	−475.591	−	475.591i	−0.883998	−	0.883998i
$539$			61.0316i			0.113231i
$540$		0			0
$541$	−696.184			−1.28685			−0.643423	−	0.765511i	$-0.722486\pi$
$541$	−696.184			−1.28685			−0.643423	+	0.765511i	$0.722486\pi$
$542$	299.402	−	299.402i	0.552402	−	0.552402i
$543$	−127.258	−	127.258i	−0.234361	−	0.234361i
$544$		−	107.028i		−	0.196743i
$545$		0			0
$546$	−175.350			−0.321153
$547$	−650.591	+	650.591i	−1.18938	+	1.18938i	−0.212141	+	0.977239i	$0.568044\pi$
$547$	−650.591	+	650.591i	−1.18938	+	1.18938i	−0.977239	+	0.212141i	$0.931956\pi$
$548$	−51.0933	−	51.0933i	−0.0932359	−	0.0932359i
$549$		−	236.042i		−	0.429949i
$550$		0			0
$551$	−97.3219			−0.176628
$552$	−16.9499	+	16.9499i	−0.0307064	+	0.0307064i
$553$	−219.145	−	219.145i	−0.396283	−	0.396283i
$554$		−	1.54728i		−	0.00279292i
$555$		0			0
$556$	−303.039			−0.545034
$557$	582.001	−	582.001i	1.04488	−	1.04488i	0.0459407	−	0.998944i	$-0.485371\pi$
$557$	582.001	−	582.001i	1.04488	−	1.04488i	0.998944	−	0.0459407i	$-0.0146285\pi$
$558$	−45.5989	−	45.5989i	−0.0817185	−	0.0817185i
$559$			765.072i			1.36864i
$560$		0			0
$561$	−57.9980			−0.103383
$562$	−133.812	+	133.812i	−0.238099	+	0.238099i
$563$	619.402	+	619.402i	1.10018	+	1.10018i	0.994388	+	0.105793i	$0.0337381\pi$
$563$	619.402	+	619.402i	1.10018	+	1.10018i	0.105793	+	0.994388i	$0.466262\pi$
$564$			80.6039i			0.142915i
$565$		0			0
$566$	117.456			0.207520
$567$	−24.2461	+	24.2461i	−0.0427621	+	0.0427621i
$568$	−222.210	−	222.210i	−0.391216	−	0.391216i
$569$			925.011i			1.62568i	0.582488	+	0.812839i	$0.302079\pi$
$569$			925.011i			1.62568i	−0.582488	+	0.812839i	$0.697921\pi$
$570$		0			0
$571$	824.295			1.44360			0.721800	−	0.692102i	$-0.243315\pi$
$571$	824.295			1.44360			0.721800	+	0.692102i	$0.243315\pi$
$572$	−47.0283	+	47.0283i	−0.0822173	+	0.0822173i
$573$	114.158	+	114.158i	0.199229	+	0.199229i
$574$			111.281i			0.193869i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$	10.5780	−	10.5780i	0.0183328	−	0.0183328i	−0.697881	−	0.716214i	$-0.745874\pi$
$577$	10.5780	−	10.5780i	0.0183328	−	0.0183328i	0.716214	+	0.697881i	$0.245874\pi$
$578$	68.9690	+	68.9690i	0.119323	+	0.119323i
$579$		−	169.472i		−	0.292698i
$580$		0			0
$581$	−227.725			−0.391953
$582$	193.704	−	193.704i	0.332825	−	0.332825i
$583$	−127.283	−	127.283i	−0.218324	−	0.218324i
$584$		−	80.4468i		−	0.137751i
$585$		0			0
$586$	−529.703			−0.903929
$587$	371.049	−	371.049i	0.632110	−	0.632110i	−0.316487	−	0.948597i	$-0.602503\pi$
$587$	371.049	−	371.049i	0.632110	−	0.632110i	0.948597	+	0.316487i	$0.102503\pi$
$588$	−84.4696	−	84.4696i	−0.143656	−	0.143656i
$589$			205.329i			0.348606i
$590$		0			0
$591$	163.904			0.277334
$592$	113.787	−	113.787i	0.192208	−	0.192208i
$593$	44.5712	+	44.5712i	0.0751623	+	0.0751623i	0.743689	−	0.668526i	$-0.233075\pi$
$593$	44.5712	+	44.5712i	0.0751623	+	0.0751623i	−0.668526	+	0.743689i	$0.733075\pi$
$594$			13.0055i			0.0218948i
$595$		0			0
$596$	−508.871			−0.853810
$597$	156.110	−	156.110i	0.261492	−	0.261492i
$598$	−91.9373	−	91.9373i	−0.153741	−	0.153741i
$599$		−	93.3473i		−	0.155839i	−0.996960	−	0.0779193i	$-0.975172\pi$
$599$		−	93.3473i		−	0.155839i	0.996960	−	0.0779193i	$-0.0248276\pi$
$600$		0			0
$601$	963.008			1.60234			0.801171	−	0.598435i	$-0.204211\pi$
$601$	963.008			1.60234			0.801171	+	0.598435i	$0.204211\pi$
$602$	155.133	−	155.133i	0.257695	−	0.257695i
$603$	−96.1563	−	96.1563i	−0.159463	−	0.159463i
$604$			132.663i			0.219641i
$605$		0			0
$606$	44.0570			0.0727013
$607$	−392.925	+	392.925i	−0.647323	+	0.647323i	−0.952345	−	0.305023i	$-0.901336\pi$
$607$	−392.925	+	392.925i	−0.647323	+	0.647323i	0.305023	+	0.952345i	$0.401336\pi$
$608$	54.0352	+	54.0352i	0.0888736	+	0.0888736i
$609$		−	47.5412i		−	0.0780643i
$610$		0			0
$611$	−437.200			−0.715548
$612$	80.2711	−	80.2711i	0.131162	−	0.131162i
$613$	−216.267	−	216.267i	−0.352801	−	0.352801i	0.508350	−	0.861151i	$-0.330256\pi$
$613$	−216.267	−	216.267i	−0.352801	−	0.352801i	−0.861151	+	0.508350i	$0.830256\pi$
$614$		−	125.184i		−	0.203883i
$615$		0			0
$616$	19.0717			0.0309606
$617$	−642.181	+	642.181i	−1.04081	+	1.04081i	−0.0416816	+	0.999131i	$0.513272\pi$
$617$	−642.181	+	642.181i	−1.04081	+	1.04081i	−0.999131	+	0.0416816i	$0.986728\pi$
$618$	−313.934	−	313.934i	−0.507984	−	0.507984i
$619$		−	544.753i		−	0.880053i	−0.897985	−	0.440027i	$-0.854969\pi$
$619$		−	544.753i		−	0.880053i	0.897985	−	0.440027i	$-0.145031\pi$
$620$		0			0
$621$	−25.4249			−0.0409419
$622$	−411.007	+	411.007i	−0.660783	+	0.660783i
$623$	−320.374	−	320.374i	−0.514244	−	0.514244i
$624$		−	130.177i		−	0.208617i
$625$		0			0
$626$	385.385			0.615631
$627$	29.2814	−	29.2814i	0.0467008	−	0.0467008i
$628$	266.653	+	266.653i	0.424607	+	0.424607i
$629$			761.152i			1.21010i
$630$		0			0
$631$	−590.551			−0.935897			−0.467949	−	0.883756i	$-0.655007\pi$
$631$	−590.551			−0.935897			−0.467949	+	0.883756i	$0.655007\pi$
$632$	162.690	−	162.690i	0.257421	−	0.257421i
$633$	−440.964	−	440.964i	−0.696625	−	0.696625i
$634$		−	365.109i		−	0.575882i
$635$		0			0
$636$	352.327			0.553973
$637$	458.167	−	458.167i	0.719258	−	0.719258i
$638$	−12.7504	−	12.7504i	−0.0199850	−	0.0199850i
$639$		−	333.316i		−	0.521621i
$640$		0			0
$641$	789.374			1.23147			0.615736	−	0.787952i	$-0.288859\pi$
$641$	789.374			1.23147			0.615736	+	0.787952i	$0.288859\pi$
$642$	−73.5107	+	73.5107i	−0.114503	+	0.114503i
$643$	808.269	+	808.269i	1.25703	+	1.25703i	0.952505	+	0.304522i	$0.0984968\pi$
$643$	808.269	+	808.269i	1.25703	+	1.25703i	0.304522	+	0.952505i	$0.401503\pi$
$644$			37.2840i			0.0578944i
$645$		0			0
$646$	−361.455			−0.559528
$647$	667.540	−	667.540i	1.03175	−	1.03175i	0.0322677	−	0.999479i	$-0.489727\pi$
$647$	667.540	−	667.540i	1.03175	−	1.03175i	0.999479	−	0.0322677i	$-0.0102729\pi$
$648$	−18.0000	−	18.0000i	−0.0277778	−	0.0277778i
$649$		−	48.5107i		−	0.0747468i
$650$		0			0
$651$	−100.302			−0.154074
$652$	−133.406	+	133.406i	−0.204611	+	0.204611i
$653$	135.714	+	135.714i	0.207831	+	0.207831i	0.803345	−	0.595514i	$-0.203052\pi$
$653$	135.714	+	135.714i	0.207831	+	0.207831i	−0.595514	+	0.803345i	$0.703052\pi$
$654$			407.023i			0.622359i
$655$		0			0
$656$	−82.6135			−0.125935
$657$	60.3351	−	60.3351i	0.0918343	−	0.0918343i
$658$	88.6503	+	88.6503i	0.134727	+	0.134727i
$659$			262.431i			0.398226i	0.979977	+	0.199113i	$0.0638061\pi$
$659$			262.431i			0.398226i	−0.979977	+	0.199113i	$0.936194\pi$
$660$		0			0
$661$	361.983			0.547630			0.273815	−	0.961782i	$-0.411714\pi$
$661$	361.983			0.547630			0.273815	+	0.961782i	$0.411714\pi$
$662$	−263.961	+	263.961i	−0.398733	+	0.398733i
$663$	435.394	+	435.394i	0.656703	+	0.656703i
$664$		−	169.060i		−	0.254608i
$665$		0			0
$666$	170.681			0.256277
$667$	24.9263	−	24.9263i	0.0373707	−	0.0373707i
$668$	−160.931	−	160.931i	−0.240914	−	0.240914i
$669$		−	294.497i		−	0.440205i
$670$		0			0
$671$	−139.251			−0.207527
$672$	−26.3958	+	26.3958i	−0.0392795	+	0.0392795i
$673$	−650.086	−	650.086i	−0.965953	−	0.965953i	0.0334866	−	0.999439i	$-0.489339\pi$
$673$	−650.086	−	650.086i	−0.965953	−	0.965953i	−0.999439	+	0.0334866i	$0.989339\pi$
$674$			777.355i			1.15335i
$675$		0			0
$676$	368.087			0.544508
$677$	−121.450	+	121.450i	−0.179395	+	0.179395i	−0.791092	−	0.611697i	$-0.790487\pi$
$677$	−121.450	+	121.450i	−0.179395	+	0.179395i	0.611697	+	0.791092i	$0.290487\pi$
$678$	274.040	+	274.040i	0.404189	+	0.404189i
$679$		−	426.081i		−	0.627513i
$680$		0			0
$681$	−28.8112			−0.0423071
$682$	−26.9007	+	26.9007i	−0.0394438	+	0.0394438i
$683$	−531.607	−	531.607i	−0.778342	−	0.778342i	0.201207	−	0.979549i	$-0.435514\pi$
$683$	−531.607	−	531.607i	−0.778342	−	0.778342i	−0.979549	+	0.201207i	$0.935514\pi$
$684$			81.0527i			0.118498i
$685$		0			0
$686$	−449.817			−0.655710
$687$	497.951	−	497.951i	0.724820	−	0.724820i
$688$	115.168	+	115.168i	0.167396	+	0.167396i
$689$			1911.04i			2.77364i
$690$		0			0
$691$	376.676			0.545118			0.272559	−	0.962139i	$-0.412130\pi$
$691$	376.676			0.545118			0.272559	+	0.962139i	$0.412130\pi$
$692$	202.561	−	202.561i	0.292718	−	0.292718i
$693$	14.3038	+	14.3038i	0.0206404	+	0.0206404i
$694$			169.774i			0.244631i
$695$		0			0
$696$	35.2939			0.0507097
$697$	276.311	−	276.311i	0.396430	−	0.396430i
$698$	176.263	+	176.263i	0.252525	+	0.252525i
$699$		−	330.956i		−	0.473471i
$700$		0			0
$701$	−1042.39			−1.48700			−0.743500	−	0.668735i	$-0.766836\pi$
$701$	−1042.39			−1.48700			−0.743500	+	0.668735i	$0.766836\pi$
$702$	97.6329	−	97.6329i	0.139078	−	0.139078i
$703$	−384.282	−	384.282i	−0.546631	−	0.546631i
$704$			14.1586i			0.0201116i
$705$		0			0
$706$	441.852			0.625853
$707$	48.4551	−	48.4551i	0.0685362	−	0.0685362i
$708$	67.1403	+	67.1403i	0.0948309	+	0.0948309i
$709$			783.451i			1.10501i	0.833510	+	0.552504i	$0.186328\pi$
$709$			783.451i			1.10501i	−0.833510	+	0.552504i	$0.813672\pi$
$710$		0			0
$711$	244.035			0.343228
$712$	237.842	−	237.842i	0.334047	−	0.334047i
$713$	−52.5892	−	52.5892i	−0.0737576	−	0.0737576i
$714$		−	176.568i		−	0.247295i
$715$		0			0
$716$	−603.593			−0.843007
$717$	−565.949	+	565.949i	−0.789329	+	0.789329i
$718$	545.295	+	545.295i	0.759464	+	0.759464i
$719$			569.165i			0.791606i	0.918335	+	0.395803i	$0.129534\pi$
$719$			569.165i			0.791606i	−0.918335	+	0.395803i	$0.870466\pi$
$720$		0			0
$721$	−690.546			−0.957762
$722$	−178.513	+	178.513i	−0.247247	+	0.247247i
$723$	179.675	+	179.675i	0.248513	+	0.248513i
$724$		−	207.812i		−	0.287033i
$725$		0			0
$726$	−288.716			−0.397680
$727$	−824.929	+	824.929i	−1.13470	+	1.13470i	−0.145317	+	0.989385i	$0.546420\pi$
$727$	−824.929	+	824.929i	−1.13470	+	1.13470i	−0.989385	+	0.145317i	$0.953580\pi$
$728$	−143.172	−	143.172i	−0.196665	−	0.196665i
$729$		−	27.0000i		−	0.0370370i
$730$		0			0
$731$	−770.390			−1.05389
$732$	192.728	−	192.728i	0.263289	−	0.263289i
$733$	315.116	+	315.116i	0.429900	+	0.429900i	0.888594	−	0.458695i	$-0.151683\pi$
$733$	315.116	+	315.116i	0.429900	+	0.429900i	−0.458695	+	0.888594i	$0.651683\pi$
$734$			268.477i			0.365772i
$735$		0			0
$736$	−27.6791			−0.0376075
$737$	−56.7265	+	56.7265i	−0.0769695	+	0.0769695i
$738$	−61.9601	−	61.9601i	−0.0839568	−	0.0839568i
$739$		−	354.088i		−	0.479145i	−0.970879	−	0.239572i	$-0.922993\pi$
$739$		−	354.088i		−	0.479145i	0.970879	−	0.239572i	$-0.0770072\pi$
$740$		0			0
$741$	−439.634			−0.593298
$742$	387.498	−	387.498i	0.522235	−	0.522235i
$743$	731.870	+	731.870i	0.985020	+	0.985020i	0.999889	−	0.0148696i	$-0.00473331\pi$
$743$	731.870	+	731.870i	0.985020	+	0.985020i	−0.0148696	+	0.999889i	$0.504733\pi$
$744$		−	74.4628i		−	0.100084i
$745$		0			0
$746$	628.944			0.843089
$747$	126.795	−	126.795i	0.169739	−	0.169739i
$748$	−47.3552	−	47.3552i	−0.0633091	−	0.0633091i
$749$			161.698i			0.215885i
$750$		0			0
$751$	−55.6888			−0.0741529			−0.0370764	−	0.999312i	$-0.511805\pi$
$751$	−55.6888			−0.0741529			−0.0370764	+	0.999312i	$0.511805\pi$
$752$	−65.8128	+	65.8128i	−0.0875171	+	0.0875171i
$753$	3.32190	+	3.32190i	0.00441155	+	0.00441155i
$754$			191.436i			0.253894i
$755$		0			0
$756$	−39.5938			−0.0523727
$757$	−368.602	+	368.602i	−0.486925	+	0.486925i	−0.907335	−	0.420409i	$-0.861886\pi$
$757$	−368.602	+	368.602i	−0.486925	+	0.486925i	0.420409	+	0.907335i	$0.361886\pi$
$758$	146.881	+	146.881i	0.193774	+	0.193774i
$759$			14.9992i			0.0197618i
$760$		0			0
$761$	371.468			0.488131			0.244065	−	0.969759i	$-0.421519\pi$
$761$	371.468			0.488131			0.244065	+	0.969759i	$0.421519\pi$
$762$	−361.731	+	361.731i	−0.474713	+	0.474713i
$763$	447.654	+	447.654i	0.586703	+	0.586703i
$764$			186.420i			0.244005i
$765$		0			0
$766$	121.100			0.158094
$767$	−364.172	+	364.172i	−0.474801	+	0.474801i
$768$	−19.5959	−	19.5959i	−0.0255155	−	0.0255155i
$769$		−	19.8844i		−	0.0258575i	−0.999916	−	0.0129287i	$-0.995885\pi$
$769$		−	19.8844i		−	0.0258575i	0.999916	−	0.0129287i	$-0.00411546\pi$
$770$		0			0
$771$	181.197			0.235016
$772$	138.374	−	138.374i	0.179240	−	0.179240i
$773$	−556.637	−	556.637i	−0.720100	−	0.720100i	0.248525	−	0.968625i	$-0.420054\pi$
$773$	−556.637	−	556.637i	−0.720100	−	0.720100i	−0.968625	+	0.248525i	$0.920054\pi$
$774$			172.752i			0.223194i
$775$		0			0
$776$	316.317			0.407625
$777$	187.719	−	187.719i	0.241595	−	0.241595i
$778$	148.935	+	148.935i	0.191433	+	0.191433i
$779$			279.002i			0.358154i
$780$		0			0
$781$	−196.637			−0.251775
$782$	92.5764	−	92.5764i	0.118384	−	0.118384i
$783$	26.4704	+	26.4704i	0.0338064	+	0.0338064i
$784$		−	137.938i		−	0.175942i
$785$		0			0
$786$	−143.650			−0.182761
$787$	−405.252	+	405.252i	−0.514932	+	0.514932i	−0.916034	−	0.401101i	$-0.868628\pi$
$787$	−405.252	+	405.252i	−0.514932	+	0.514932i	0.401101	+	0.916034i	$0.368628\pi$
$788$	133.827	+	133.827i	0.169832	+	0.169832i
$789$		−	597.192i		−	0.756898i
$790$		0			0
$791$	602.793			0.762065
$792$	−10.6189	+	10.6189i	−0.0134078	+	0.0134078i
$793$	1045.36	+	1045.36i	1.31824	+	1.31824i
$794$			836.776i			1.05387i
$795$		0			0
$796$	254.927			0.320260
$797$	136.640	−	136.640i	0.171443	−	0.171443i	−0.616170	−	0.787613i	$-0.711317\pi$
$797$	136.640	−	136.640i	0.171443	−	0.171443i	0.787613	+	0.616170i	$0.211317\pi$
$798$	89.1440	+	89.1440i	0.111709	+	0.111709i
$799$		−	440.239i		−	0.550987i
$800$		0			0
$801$	356.762			0.445396
$802$	−525.592	+	525.592i	−0.655352	+	0.655352i
$803$	−35.5942	−	35.5942i	−0.0443265	−	0.0443265i
$804$		−	157.023i		−	0.195302i
$805$		0			0
$806$	403.890			0.501104
$807$	582.478	−	582.478i	0.721781	−	0.721781i
$808$	35.9724	+	35.9724i	0.0445203	+	0.0445203i
$809$		−	1028.37i		−	1.27116i	−0.772033	−	0.635582i	$-0.780760\pi$
$809$		−	1028.37i		−	1.27116i	0.772033	−	0.635582i	$-0.219240\pi$
$810$		0			0
$811$	−825.076			−1.01736			−0.508678	−	0.860957i	$-0.669866\pi$
$811$	−825.076			−1.01736			−0.508678	+	0.860957i	$0.669866\pi$
$812$	38.8172	−	38.8172i	0.0478044	−	0.0478044i
$813$	366.691	+	366.691i	0.451034	+	0.451034i
$814$		−	100.692i		−	0.123700i
$815$		0			0
$816$	131.082			0.160640
$817$	388.946	−	388.946i	0.476066	−	0.476066i
$818$	−289.417	−	289.417i	−0.353810	−	0.353810i
$819$		−	214.758i		−	0.262220i
$820$		0			0
$821$	323.031			0.393460			0.196730	−	0.980458i	$-0.436968\pi$
$821$	323.031			0.393460			0.196730	+	0.980458i	$0.436968\pi$
$822$	62.5762	−	62.5762i	0.0761268	−	0.0761268i
$823$	448.732	+	448.732i	0.545239	+	0.545239i	0.925060	−	0.379821i	$-0.124014\pi$
$823$	448.732	+	448.732i	0.545239	+	0.545239i	−0.379821	+	0.925060i	$0.624014\pi$
$824$		−	512.652i		−	0.622151i
$825$		0			0
$826$	147.685			0.178796
$827$	−17.9769	+	17.9769i	−0.0217374	+	0.0217374i	−0.717892	−	0.696155i	$-0.754893\pi$
$827$	−17.9769	+	17.9769i	−0.0217374	+	0.0217374i	0.696155	+	0.717892i	$0.254893\pi$
$828$	−20.7594	−	20.7594i	−0.0250717	−	0.0250717i
$829$			85.2213i			0.102800i	0.998678	+	0.0514001i	$0.0163684\pi$
$829$			85.2213i			0.102800i	−0.998678	+	0.0514001i	$0.983632\pi$
$830$		0			0
$831$	1.89502			0.00228041
$832$	106.289	−	106.289i	0.127751	−	0.127751i
$833$	461.352	+	461.352i	0.553844	+	0.553844i
$834$		−	371.146i		−	0.445019i
$835$		0			0
$836$	47.8163			0.0571966
$837$	55.8471	−	55.8471i	0.0667229	−	0.0667229i
$838$	−29.5402	−	29.5402i	−0.0352509	−	0.0352509i
$839$			536.490i			0.639440i	0.947512	+	0.319720i	$0.103589\pi$
$839$			536.490i			0.639440i	−0.947512	+	0.319720i	$0.896411\pi$
$840$		0			0
$841$	789.097			0.938285
$842$	−47.3975	+	47.3975i	−0.0562916	+	0.0562916i
$843$	−163.885	−	163.885i	−0.194407	−	0.194407i
$844$		−	720.090i		−	0.853188i
$845$		0			0
$846$	−98.7192			−0.116689
$847$	−317.537	+	317.537i	−0.374896	+	0.374896i
$848$	287.674	+	287.674i	0.339238	+	0.339238i
$849$			143.854i			0.169440i
$850$		0			0
$851$	196.846			0.231311
$852$	272.151	−	272.151i	0.319426	−	0.319426i
$853$	−328.915	−	328.915i	−0.385597	−	0.385597i	0.487516	−	0.873114i	$-0.337903\pi$
$853$	−328.915	−	328.915i	−0.385597	−	0.385597i	−0.873114	+	0.487516i	$0.837903\pi$
$854$		−	423.934i		−	0.496410i
$855$		0			0
$856$	−120.042			−0.140237
$857$	209.117	−	209.117i	0.244010	−	0.244010i	−0.574497	−	0.818507i	$-0.694802\pi$
$857$	209.117	−	209.117i	0.244010	−	0.244010i	0.818507	+	0.574497i	$0.194802\pi$
$858$	−57.5976	−	57.5976i	−0.0671301	−	0.0671301i
$859$		−	1488.84i		−	1.73323i	−0.498979	−	0.866614i	$-0.666292\pi$
$859$		−	1488.84i		−	1.73323i	0.498979	−	0.866614i	$-0.333708\pi$
$860$		0			0
$861$	−136.291			−0.158294
$862$	−685.640	+	685.640i	−0.795406	+	0.795406i
$863$	827.823	+	827.823i	0.959239	+	0.959239i	0.999201	−	0.0399626i	$-0.0127239\pi$
$863$	827.823	+	827.823i	0.959239	+	0.959239i	−0.0399626	+	0.999201i	$0.512724\pi$
$864$		−	29.3939i		−	0.0340207i
$865$		0			0
$866$	536.617			0.619650
$867$	−84.4694	+	84.4694i	−0.0974272	+	0.0974272i
$868$	−81.8961	−	81.8961i	−0.0943504	−	0.0943504i
$869$		−	143.966i		−	0.165669i
$870$		0			0
$871$	851.698			0.977839
$872$	−332.332	+	332.332i	−0.381115	+	0.381115i
$873$	237.238	+	237.238i	0.271750	+	0.271750i
$874$			93.4779i			0.106954i
$875$		0			0
$876$	98.5269			0.112474
$877$	−4.35746	+	4.35746i	−0.00496860	+	0.00496860i	−0.709587	−	0.704618i	$-0.751118\pi$
$877$	−4.35746	+	4.35746i	−0.00496860	+	0.00496860i	0.704618	+	0.709587i	$0.251118\pi$
$878$	758.142	+	758.142i	0.863488	+	0.863488i
$879$		−	648.751i		−	0.738055i
$880$		0			0
$881$	798.035			0.905829			0.452914	−	0.891554i	$-0.350384\pi$
$881$	798.035			0.905829			0.452914	+	0.891554i	$0.350384\pi$
$882$	103.454	−	103.454i	0.117294	−	0.117294i
$883$	1150.08	+	1150.08i	1.30247	+	1.30247i	0.926724	+	0.375744i	$0.122613\pi$
$883$	1150.08	+	1150.08i	1.30247	+	1.30247i	0.375744	+	0.926724i	$0.377387\pi$
$884$			710.996i			0.804294i
$885$		0			0
$886$	1052.57			1.18800
$887$	173.672	−	173.672i	0.195797	−	0.195797i	−0.602399	−	0.798195i	$-0.705788\pi$
$887$	173.672	−	173.672i	0.195797	−	0.195797i	0.798195	+	0.602399i	$0.205788\pi$
$888$	139.360	+	139.360i	0.156937	+	0.156937i
$889$			795.683i			0.895032i
$890$		0			0
$891$	−15.9284			−0.0178770
$892$	240.456	−	240.456i	0.269569	−	0.269569i
$893$	222.263	+	222.263i	0.248895	+	0.248895i
$894$		−	623.237i		−	0.697133i
$895$		0			0
$896$	−43.1042			−0.0481074
$897$	112.600	−	112.600i	0.125529	−	0.125529i
$898$	−482.572	−	482.572i	−0.537386	−	0.537386i
$899$			109.503i			0.121806i
$900$		0			0
$901$	−1924.32			−2.13576
$902$	−36.5528	+	36.5528i	−0.0405242	+	0.0405242i
$903$	189.998	+	189.998i	0.210407	+	0.210407i
$904$			447.506i			0.495028i
$905$		0			0
$906$	−162.479			−0.179336
$907$	−254.707	+	254.707i	−0.280824	+	0.280824i	−0.833438	−	0.552614i	$-0.813631\pi$
$907$	−254.707	+	254.707i	−0.280824	+	0.280824i	0.552614	+	0.833438i	$0.313631\pi$
$908$	−23.5242	−	23.5242i	−0.0259077	−	0.0259077i
$909$			53.9586i			0.0593604i
$910$		0			0
$911$	−734.298			−0.806035			−0.403017	−	0.915192i	$-0.632039\pi$
$911$	−734.298			−0.806035			−0.403017	+	0.915192i	$0.632039\pi$
$912$	−66.1793	+	66.1793i	−0.0725650	+	0.0725650i
$913$	−74.8015	−	74.8015i	−0.0819293	−	0.0819293i
$914$		−	537.267i		−	0.587820i
$915$		0			0
$916$	813.151			0.887720
$917$	−157.990	+	157.990i	−0.172290	+	0.172290i
$918$	98.3116	+	98.3116i	0.107093	+	0.107093i
$919$		−	479.433i		−	0.521689i	−0.965381	−	0.260845i	$-0.915999\pi$
$919$		−	479.433i		−	0.521689i	0.965381	−	0.260845i	$-0.0840011\pi$
$920$		0			0
$921$	153.319			0.166470
$922$	−577.734	+	577.734i	−0.626610	+	0.626610i
$923$	1476.16	+	1476.16i	1.59931	+	1.59931i
$924$			23.3580i			0.0252792i
$925$		0			0
$926$	1166.80			1.26004
$927$	384.489	−	384.489i	0.414767	−	0.414767i
$928$	28.8174	+	28.8174i	0.0310532	+	0.0310532i
$929$			79.1230i			0.0851701i	0.999093	+	0.0425850i	$0.0135593\pi$
$929$			79.1230i			0.0851701i	−0.999093	+	0.0425850i	$0.986441\pi$
$930$		0			0
$931$	−465.845			−0.500370
$932$	270.224	−	270.224i	0.289940	−	0.289940i
$933$	−503.379	−	503.379i	−0.539527	−	0.539527i
$934$		−	1139.17i		−	1.21967i
$935$		0			0
$936$	159.434			0.170335
$937$	−171.622	+	171.622i	−0.183161	+	0.183161i	−0.792732	−	0.609571i	$-0.791342\pi$
$937$	−171.622	+	171.622i	−0.183161	+	0.183161i	0.609571	+	0.792732i	$0.291342\pi$
$938$	−172.698	−	172.698i	−0.184113	−	0.184113i
$939$			471.998i			0.502660i
$940$		0			0
$941$	−890.001			−0.945803			−0.472902	−	0.881115i	$-0.656793\pi$
$941$	−890.001			−0.945803			−0.472902	+	0.881115i	$0.656793\pi$
$942$	−326.582	+	326.582i	−0.346691	+	0.346691i
$943$	−71.4585	−	71.4585i	−0.0757778	−	0.0757778i
$944$			109.640i			0.116144i
$945$		0			0
$946$	101.914			0.107731
$947$	212.637	−	212.637i	0.224538	−	0.224538i	−0.585868	−	0.810406i	$-0.699246\pi$
$947$	212.637	−	212.637i	0.224538	−	0.224538i	0.810406	+	0.585868i	$0.199246\pi$
$948$	199.254	+	199.254i	0.210183	+	0.210183i
$949$			534.414i			0.563134i
$950$		0			0
$951$	447.166			0.470206
$952$	144.168	−	144.168i	0.151437	−	0.151437i
$953$	149.539	+	149.539i	0.156914	+	0.156914i	0.781198	−	0.624284i	$-0.214609\pi$
$953$	149.539	+	149.539i	0.156914	+	0.156914i	−0.624284	+	0.781198i	$0.714609\pi$
$954$			431.511i			0.452317i
$955$		0			0
$956$	−924.191			−0.966726
$957$	15.6160	−	15.6160i	0.0163177	−	0.0163177i
$958$	335.883	+	335.883i	0.350609	+	0.350609i
$959$		−	137.646i		−	0.143531i
$960$		0			0
$961$	−729.971			−0.759595
$962$	−755.897	+	755.897i	−0.785756	+	0.785756i
$963$	−90.0318	−	90.0318i	−0.0934910	−	0.0934910i
$964$			293.408i			0.304365i
$965$		0			0
$966$	−45.6634			−0.0472706
$967$	438.543	−	438.543i	0.453509	−	0.453509i	−0.443009	−	0.896517i	$-0.646089\pi$
$967$	438.543	−	438.543i	0.453509	−	0.453509i	0.896517	+	0.443009i	$0.146089\pi$
$968$	−235.735	−	235.735i	−0.243528	−	0.243528i
$969$		−	442.690i		−	0.456852i
$970$		0			0
$971$	926.353			0.954020			0.477010	−	0.878898i	$-0.341721\pi$
$971$	926.353			0.954020			0.477010	+	0.878898i	$0.341721\pi$
$972$	22.0454	−	22.0454i	0.0226805	−	0.0226805i
$973$	−408.196	−	408.196i	−0.419523	−	0.419523i
$974$			562.936i			0.577964i
$975$		0			0
$976$	314.723			0.322462
$977$	665.771	−	665.771i	0.681444	−	0.681444i	−0.278881	−	0.960326i	$-0.589964\pi$
$977$	665.771	−	665.771i	0.681444	−	0.681444i	0.960326	+	0.278881i	$0.0899636\pi$
$978$	−163.389	−	163.389i	−0.167064	−	0.167064i
$979$		−	210.469i		−	0.214983i
$980$		0			0
$981$	−498.499			−0.508154
$982$	−383.934	+	383.934i	−0.390971	+	0.390971i
$983$	−577.101	−	577.101i	−0.587082	−	0.587082i	0.349758	−	0.936840i	$-0.386264\pi$
$983$	−577.101	−	577.101i	−0.587082	−	0.587082i	−0.936840	+	0.349758i	$0.886264\pi$
$984$		−	101.180i		−	0.102826i
$985$		0			0
$986$	−192.767			−0.195504
$987$	−108.574	+	108.574i	−0.110004	+	0.110004i
$988$	−358.960	−	358.960i	−0.363319	−	0.363319i
$989$			199.235i			0.201451i
$990$		0			0
$991$	−1264.50			−1.27599			−0.637994	−	0.770041i	$-0.720236\pi$
$991$	−1264.50			−1.27599			−0.637994	+	0.770041i	$0.720236\pi$
$992$	60.7986	−	60.7986i	0.0612889	−	0.0612889i
$993$	−323.285	−	323.285i	−0.325564	−	0.325564i
$994$		−	598.638i		−	0.602252i
$995$		0			0
$996$	207.055			0.207887
$997$	1255.30	−	1255.30i	1.25908	−	1.25908i	0.307544	−	0.951534i	$-0.400493\pi$
$997$	1255.30	−	1255.30i	1.25908	−	1.25908i	0.951534	−	0.307544i	$-0.0995070\pi$
$998$	507.775	+	507.775i	0.508793	+	0.508793i
$999$			209.040i			0.209250i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.3.f.b.193.2	✓	16
5.2	odd	4	inner	750.3.f.b.307.2	yes	16
5.3	odd	4		750.3.f.c.307.7	yes	16
5.4	even	2		750.3.f.c.193.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.3.f.b.193.2	✓	16	1.1	even	1	trivial
750.3.f.b.307.2	yes	16	5.2	odd	4	inner
750.3.f.c.193.7	yes	16	5.4	even	2
750.3.f.c.307.7	yes	16	5.3	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	750.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +2.44949 q^{6} +(2.69401 - 2.69401i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +1.76982 q^{11} +(-2.44949 + 2.44949i) q^{12} +(-13.2862 - 13.2862i) q^{13} +5.38803i q^{14} -4.00000 q^{16} +(13.3785 - 13.3785i) q^{17} +(-3.00000 - 3.00000i) q^{18} +13.5088i q^{19} -6.59896 q^{21} +(-1.76982 + 1.76982i) q^{22} +(-3.45989 - 3.45989i) q^{23} -4.89898i q^{24} +26.5723 q^{26} +(3.67423 - 3.67423i) q^{27} +(-5.38803 - 5.38803i) q^{28} +7.20434i q^{29} +15.1996 q^{31} +(4.00000 - 4.00000i) q^{32} +(-2.16758 - 2.16758i) q^{33} +26.7570i q^{34} +6.00000 q^{36} +(-28.4468 + 28.4468i) q^{37} +(-13.5088 - 13.5088i) q^{38} +32.5443i q^{39} +20.6534 q^{41} +(6.59896 - 6.59896i) q^{42} +(-28.7921 - 28.7921i) q^{43} -3.53965i q^{44} +6.91979 q^{46} +(16.4532 - 16.4532i) q^{47} +(4.89898 + 4.89898i) q^{48} +34.4846i q^{49} -32.7705 q^{51} +(-26.5723 + 26.5723i) q^{52} +(-71.9184 - 71.9184i) q^{53} +7.34847i q^{54} +10.7761 q^{56} +(16.5448 - 16.5448i) q^{57} +(-7.20434 - 7.20434i) q^{58} -27.4099i q^{59} -78.6807 q^{61} +(-15.1996 + 15.1996i) q^{62} +(8.08204 + 8.08204i) q^{63} +8.00000i q^{64} +4.33516 q^{66} +(-32.0521 + 32.0521i) q^{67} +(-26.7570 - 26.7570i) q^{68} +8.47497i q^{69} -111.105 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-20.1117 - 20.1117i) q^{73} -56.8936i q^{74} +27.0176 q^{76} +(4.76793 - 4.76793i) q^{77} +(-32.5443 - 32.5443i) q^{78} -81.3451i q^{79} -9.00000 q^{81} +(-20.6534 + 20.6534i) q^{82} +(-42.2649 - 42.2649i) q^{83} +13.1979i q^{84} +57.5842 q^{86} +(8.82348 - 8.82348i) q^{87} +(3.53965 + 3.53965i) q^{88} -118.921i q^{89} -71.5862 q^{91} +(-6.91979 + 6.91979i) q^{92} +(-18.6157 - 18.6157i) q^{93} +32.9064i q^{94} -9.79796 q^{96} +(79.0793 - 79.0793i) q^{97} +(-34.4846 - 34.4846i) q^{98} +5.30947i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + 24 q^{7} + 32 q^{8} - 24 q^{11} - 48 q^{13} - 64 q^{16} - 16 q^{17} - 48 q^{18} - 48 q^{21} + 24 q^{22} + 104 q^{23} + 96 q^{26} - 48 q^{28} + 200 q^{31} + 64 q^{32} - 48 q^{33} + 96 q^{36}+ \cdots - 224 q^{98}+O(q^{100}) \) 16 * q - 16 * q^2 + 24 * q^7 + 32 * q^8 - 24 * q^11 - 48 * q^13 - 64 * q^16 - 16 * q^17 - 48 * q^18 - 48 * q^21 + 24 * q^22 + 104 * q^23 + 96 * q^26 - 48 * q^28 + 200 * q^31 + 64 * q^32 - 48 * q^33 + 96 * q^36 - 128 * q^37 + 56 * q^38 - 192 * q^41 + 48 * q^42 + 88 * q^43 - 208 * q^46 + 16 * q^47 - 48 * q^51 - 96 * q^52 - 160 * q^53 + 96 * q^56 + 48 * q^57 + 24 * q^58 - 24 * q^61 - 200 * q^62 + 72 * q^63 + 96 * q^66 + 264 * q^67 + 32 * q^68 + 176 * q^71 - 96 * q^72 + 32 * q^73 - 112 * q^76 + 32 * q^77 + 96 * q^78 - 144 * q^81 + 192 * q^82 - 288 * q^83 - 176 * q^86 - 168 * q^87 - 48 * q^88 + 32 * q^91 + 208 * q^92 + 144 * q^93 - 48 * q^97 - 224 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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