LMFDB - Embedded newform 740.2.i.b.121.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(121,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("740.121"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0,0,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 13 x^{12} - 6 x^{11} + 130 x^{10} - 44 x^{9} + 466 x^{8} - 4 x^{7} + 1211 x^{6} - 162 x^{5} + \cdots + 81 $ x^14 + 13x^12 - 6x^11 + 130x^10 - 44x^9 + 466x^8 - 4x^7 + 1211x^6 - 162x^5 + 973x^4 - 577x^3 + 670x^2 - 225x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{37}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$1.32457 + 2.29422i$ of defining polynomial
Character	$\chi$	$=$	740.121
Dual form			740.2.i.b.581.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.32457 - 2.29422i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.42866 + 2.47451i) q^{7} +(-2.00895 + 3.47961i) q^{9} -3.18233 q^{11} +(-1.96014 - 3.39506i) q^{13} +(1.32457 - 2.29422i) q^{15} +(2.70441 - 4.68418i) q^{17} +(-3.80196 - 6.58519i) q^{19} +(3.78471 - 6.55531i) q^{21} -6.03949 q^{23} +(-0.500000 + 0.866025i) q^{25} +2.69657 q^{27} -8.38297 q^{29} -2.32739 q^{31} +(4.21521 + 7.30095i) q^{33} +(-1.42866 + 2.47451i) q^{35} +(6.06458 + 0.469912i) q^{37} +(-5.19268 + 8.99398i) q^{39} +(4.44408 + 7.69737i) q^{41} -5.71448 q^{43} -4.01791 q^{45} +7.03084 q^{47} +(-0.582133 + 1.00828i) q^{49} -14.3287 q^{51} +(-0.602178 + 1.04300i) q^{53} +(-1.59116 - 2.75598i) q^{55} +(-10.0719 + 17.4450i) q^{57} +(-0.0552032 + 0.0956147i) q^{59} +(-5.06848 - 8.77887i) q^{61} -11.4804 q^{63} +(1.96014 - 3.39506i) q^{65} +(2.26921 + 3.93039i) q^{67} +(7.99971 + 13.8559i) q^{69} +(-8.12072 - 14.0655i) q^{71} +4.59471 q^{73} +2.64913 q^{75} +(-4.54646 - 7.87470i) q^{77} +(-8.35973 - 14.4795i) q^{79} +(2.45507 + 4.25230i) q^{81} +(-2.05322 + 3.55628i) q^{83} +5.40883 q^{85} +(11.1038 + 19.2324i) q^{87} +(-0.267372 + 0.463102i) q^{89} +(5.60075 - 9.70078i) q^{91} +(3.08279 + 5.33955i) q^{93} +(3.80196 - 6.58519i) q^{95} +5.70522 q^{97} +(6.39315 - 11.0733i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 7 q^{5} - 2 q^{7} - 5 q^{9} - 10 q^{11} - 2 q^{13} - 5 q^{17} - 8 q^{19} + 9 q^{21} + 8 q^{23} - 7 q^{25} - 18 q^{27} - 4 q^{29} + 16 q^{31} - 7 q^{33} + 2 q^{35} + 4 q^{37} + 13 q^{39} + 9 q^{41}+ \cdots + 26 q^{99}+O(q^{100}) $ 14 * q + 7 * q^5 - 2 * q^7 - 5 * q^9 - 10 * q^11 - 2 * q^13 - 5 * q^17 - 8 * q^19 + 9 * q^21 + 8 * q^23 - 7 * q^25 - 18 * q^27 - 4 * q^29 + 16 * q^31 - 7 * q^33 + 2 * q^35 + 4 * q^37 + 13 * q^39 + 9 * q^41 + 22 * q^43 - 10 * q^45 + 36 * q^47 - 7 * q^49 - 62 * q^51 + 2 * q^53 - 5 * q^55 - 38 * q^57 + 12 * q^59 - 20 * q^61 - 38 * q^63 + 2 * q^65 + 12 * q^67 + q^69 - 13 * q^71 - 12 * q^73 - q^77 - 21 * q^79 - 11 * q^81 + 7 * q^83 - 10 * q^85 + 41 * q^87 + 16 * q^89 - 6 * q^91 - 3 * q^93 + 8 * q^95 - 6 * q^97 + 26 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.32457	−	2.29422i	−0.764739	−	1.32457i	−0.940384	−	0.340113i	$-0.889535\pi$
$3$	−1.32457	−	2.29422i	−0.764739	−	1.32457i	0.175646	−	0.984453i	$-0.443799\pi$
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	1.42866	+	2.47451i	0.539982	+	0.935277i	0.998904	+	0.0468003i	$0.0149024\pi$
$7$	1.42866	+	2.47451i	0.539982	+	0.935277i	−0.458922	+	0.888477i	$0.651764\pi$
$8$		0			0
$9$	−2.00895	+	3.47961i	−0.669651	+	1.15987i
$10$		0			0
$11$	−3.18233			−0.959508			−0.479754	−	0.877403i	$-0.659274\pi$
$11$	−3.18233			−0.959508			−0.479754	+	0.877403i	$0.659274\pi$
$12$		0			0
$13$	−1.96014	−	3.39506i	−0.543645	−	0.941622i	−0.998691	−	0.0511533i	$-0.983710\pi$
$13$	−1.96014	−	3.39506i	−0.543645	−	0.941622i	0.455045	−	0.890468i	$-0.349623\pi$
$14$		0			0
$15$	1.32457	−	2.29422i	0.342002	−	0.592364i
$16$		0			0
$17$	2.70441	−	4.68418i	0.655917	−	1.13608i	−0.325747	−	0.945457i	$-0.605616\pi$
$17$	2.70441	−	4.68418i	0.655917	−	1.13608i	0.981663	−	0.190624i	$-0.0610510\pi$
$18$		0			0
$19$	−3.80196	−	6.58519i	−0.872230	−	1.51075i	−0.859685	−	0.510825i	$-0.829340\pi$
$19$	−3.80196	−	6.58519i	−0.872230	−	1.51075i	−0.0125451	−	0.999921i	$-0.503993\pi$
$20$		0			0
$21$	3.78471	−	6.55531i	0.825891	−	1.43049i
$22$		0			0
$23$	−6.03949			−1.25932			−0.629661	−	0.776870i	$-0.716806\pi$
$23$	−6.03949			−1.25932			−0.629661	+	0.776870i	$0.716806\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	2.69657			0.518956
$28$		0			0
$29$	−8.38297			−1.55668			−0.778339	−	0.627844i	$-0.783938\pi$
$29$	−8.38297			−1.55668			−0.778339	+	0.627844i	$0.783938\pi$
$30$		0			0
$31$	−2.32739			−0.418012			−0.209006	−	0.977914i	$-0.567023\pi$
$31$	−2.32739			−0.418012			−0.209006	+	0.977914i	$0.567023\pi$
$32$		0			0
$33$	4.21521	+	7.30095i	0.733773	+	1.27093i
$34$		0			0
$35$	−1.42866	+	2.47451i	−0.241487	+	0.418269i
$36$		0			0
$37$	6.06458	+	0.469912i	0.997012	+	0.0772531i
$37$	6.06458	+	0.469912i	0.997012	+	0.0772531i
$38$		0			0
$39$	−5.19268	+	8.99398i	−0.831494	+	1.44019i
$40$		0			0
$41$	4.44408	+	7.69737i	0.694049	+	1.20213i	0.970500	+	0.241100i	$0.0775081\pi$
$41$	4.44408	+	7.69737i	0.694049	+	1.20213i	−0.276452	+	0.961028i	$0.589159\pi$
$42$		0			0
$43$	−5.71448			−0.871450			−0.435725	−	0.900080i	$-0.643508\pi$
$43$	−5.71448			−0.871450			−0.435725	+	0.900080i	$0.643508\pi$
$44$		0			0
$45$	−4.01791			−0.598954
$46$		0			0
$47$	7.03084			1.02555			0.512777	−	0.858522i	$-0.328617\pi$
$47$	7.03084			1.02555			0.512777	+	0.858522i	$0.328617\pi$
$48$		0			0
$49$	−0.582133	+	1.00828i	−0.0831619	+	0.144041i
$50$		0			0
$51$	−14.3287			−2.00642
$52$		0			0
$53$	−0.602178	+	1.04300i	−0.0827154	+	0.143267i	−0.904415	−	0.426653i	$-0.859693\pi$
$53$	−0.602178	+	1.04300i	−0.0827154	+	0.143267i	0.821700	+	0.569920i	$0.193026\pi$
$54$		0			0
$55$	−1.59116	−	2.75598i	−0.214552	−	0.371616i
$56$		0			0
$57$	−10.0719	+	17.4450i	−1.33406	+	2.31065i
$58$		0			0
$59$	−0.0552032	+	0.0956147i	−0.00718684	+	0.0124480i	−0.869596	−	0.493763i	$-0.835621\pi$
$59$	−0.0552032	+	0.0956147i	−0.00718684	+	0.0124480i	0.862410	+	0.506211i	$0.168954\pi$
$60$		0			0
$61$	−5.06848	−	8.77887i	−0.648953	−	1.12402i	−0.983373	−	0.181595i	$-0.941874\pi$
$61$	−5.06848	−	8.77887i	−0.648953	−	1.12402i	0.334421	−	0.942424i	$-0.391459\pi$
$62$		0			0
$63$	−11.4804			−1.44640
$64$		0			0
$65$	1.96014	−	3.39506i	0.243126	−	0.421106i
$66$		0			0
$67$	2.26921	+	3.93039i	0.277228	+	0.480173i	0.970695	−	0.240315i	$-0.0772509\pi$
$67$	2.26921	+	3.93039i	0.277228	+	0.480173i	−0.693467	+	0.720489i	$0.743918\pi$
$68$		0			0
$69$	7.99971	+	13.8559i	0.963052	+	1.66805i
$70$		0			0
$71$	−8.12072	−	14.0655i	−0.963752	−	1.66927i	−0.712932	−	0.701233i	$-0.752633\pi$
$71$	−8.12072	−	14.0655i	−0.963752	−	1.66927i	−0.250819	−	0.968034i	$-0.580700\pi$
$72$		0			0
$73$	4.59471			0.537771			0.268885	−	0.963172i	$-0.413345\pi$
$73$	4.59471			0.537771			0.268885	+	0.963172i	$0.413345\pi$
$74$		0			0
$75$	2.64913			0.305896
$76$		0			0
$77$	−4.54646	−	7.87470i	−0.518117	−	0.897406i
$78$		0			0
$79$	−8.35973	−	14.4795i	−0.940544	−	1.62907i	−0.764437	−	0.644698i	$-0.776983\pi$
$79$	−8.35973	−	14.4795i	−0.940544	−	1.62907i	−0.176106	−	0.984371i	$-0.556350\pi$
$80$		0			0
$81$	2.45507	+	4.25230i	0.272785	+	0.472478i
$82$		0			0
$83$	−2.05322	+	3.55628i	−0.225370	+	0.390353i	−0.956430	−	0.291960i	$-0.905692\pi$
$83$	−2.05322	+	3.55628i	−0.225370	+	0.390353i	0.731060	+	0.682313i	$0.239026\pi$
$84$		0			0
$85$	5.40883			0.586670
$86$		0			0
$87$	11.1038	+	19.2324i	1.19045	+	2.06192i
$88$		0			0
$89$	−0.267372	+	0.463102i	−0.0283414	+	0.0490887i	−0.879848	−	0.475255i	$-0.842356\pi$
$89$	−0.267372	+	0.463102i	−0.0283414	+	0.0490887i	0.851507	+	0.524344i	$0.175689\pi$
$90$		0			0
$91$	5.60075	−	9.70078i	0.587118	−	1.01692i
$92$		0			0
$93$	3.08279	+	5.33955i	0.319670	+	0.553685i
$94$		0			0
$95$	3.80196	−	6.58519i	0.390073	−	0.675626i
$96$		0			0
$97$	5.70522			0.579278			0.289639	−	0.957136i	$-0.406465\pi$
$97$	5.70522			0.579278			0.289639	+	0.957136i	$0.406465\pi$
$98$		0			0
$99$	6.39315	−	11.0733i	0.642536	−	1.11290i
$100$		0			0
$101$	−0.274826			−0.0273462			−0.0136731	−	0.999907i	$-0.504352\pi$
$101$	−0.274826			−0.0273462			−0.0136731	+	0.999907i	$0.504352\pi$
$102$		0			0
$103$	6.90720			0.680586			0.340293	−	0.940319i	$-0.389474\pi$
$103$	6.90720			0.680586			0.340293	+	0.940319i	$0.389474\pi$
$104$		0			0
$105$	7.56942			0.738699
$106$		0			0
$107$	1.54320	+	2.67291i	0.149187	+	0.258400i	0.930927	−	0.365205i	$-0.119001\pi$
$107$	1.54320	+	2.67291i	0.149187	+	0.258400i	−0.781740	+	0.623604i	$0.785668\pi$
$108$		0			0
$109$	4.01661	−	6.95698i	0.384722	−	0.666358i	−0.607009	−	0.794695i	$-0.707631\pi$
$109$	4.01661	−	6.95698i	0.384722	−	0.666358i	0.991731	+	0.128337i	$0.0409641\pi$
$110$		0			0
$111$	−6.95487	−	14.5359i	−0.660127	−	1.37969i
$112$		0			0
$113$	−7.06303	+	12.2335i	−0.664434	+	1.15083i	0.315005	+	0.949090i	$0.397994\pi$
$113$	−7.06303	+	12.2335i	−0.664434	+	1.15083i	−0.979439	+	0.201743i	$0.935340\pi$
$114$		0			0
$115$	−3.01975	−	5.23035i	−0.281593	−	0.487733i
$116$		0			0
$117$	15.7513			1.45621
$118$		0			0
$119$	15.4547			1.41673
$120$		0			0
$121$	−0.872790			−0.0793446
$122$		0			0
$123$	11.7730	−	20.3914i	1.06153	−	1.83863i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−0.0206138	+	0.0357042i	−0.00182918	+	0.00316824i	−0.866939	−	0.498415i	$-0.833916\pi$
$127$	−0.0206138	+	0.0357042i	−0.00182918	+	0.00316824i	0.865109	+	0.501583i	$0.167249\pi$
$128$		0			0
$129$	7.56921	+	13.1103i	0.666432	+	1.15429i
$130$		0			0
$131$	−9.88749	+	17.1256i	−0.863874	+	1.49627i	0.00428686	+	0.999991i	$0.498635\pi$
$131$	−9.88749	+	17.1256i	−0.863874	+	1.49627i	−0.868161	+	0.496283i	$0.834698\pi$
$132$		0			0
$133$	10.8634	−	18.8160i	0.941977	−	1.63155i
$134$		0			0
$135$	1.34829	+	2.33530i	0.116042	+	0.200991i
$136$		0			0
$137$	9.42871			0.805549			0.402775	−	0.915299i	$-0.368046\pi$
$137$	9.42871			0.805549			0.402775	+	0.915299i	$0.368046\pi$
$138$		0			0
$139$	−3.89890	+	6.75310i	−0.330701	+	0.572790i	−0.982649	−	0.185473i	$-0.940618\pi$
$139$	−3.89890	+	6.75310i	−0.330701	+	0.572790i	0.651949	+	0.758263i	$0.273952\pi$
$140$		0			0
$141$	−9.31282	−	16.1303i	−0.784281	−	1.35841i
$142$		0			0
$143$	6.23781	+	10.8042i	0.521632	+	0.903493i
$144$		0			0
$145$	−4.19148	−	7.25986i	−0.348084	−	0.602899i
$146$		0			0
$147$	3.08430			0.254389
$148$		0			0
$149$	−19.3579			−1.58586			−0.792932	−	0.609310i	$-0.791447\pi$
$149$	−19.3579			−1.58586			−0.792932	+	0.609310i	$0.791447\pi$
$150$		0			0
$151$	8.15183	+	14.1194i	0.663386	+	1.14902i	0.979720	+	0.200371i	$0.0642148\pi$
$151$	8.15183	+	14.1194i	0.663386	+	1.14902i	−0.316334	+	0.948648i	$0.602452\pi$
$152$		0			0
$153$	10.8661	+	18.8206i	0.878471	+	1.52156i
$154$		0			0
$155$	−1.16370	−	2.01558i	−0.0934704	−	0.161895i
$156$		0			0
$157$	−1.54496	+	2.67596i	−0.123302	+	0.213565i	−0.921068	−	0.389402i	$-0.872682\pi$
$157$	−1.54496	+	2.67596i	−0.123302	+	0.213565i	0.797766	+	0.602967i	$0.206015\pi$
$158$		0			0
$159$	3.19050			0.253023
$160$		0			0
$161$	−8.62838	−	14.9448i	−0.680011	−	1.17781i
$162$		0			0
$163$	7.70973	−	13.3536i	0.603872	−	1.04594i	−0.388356	−	0.921509i	$-0.626957\pi$
$163$	7.70973	−	13.3536i	0.603872	−	1.04594i	0.992229	−	0.124428i	$-0.0397097\pi$
$164$		0			0
$165$	−4.21521	+	7.30095i	−0.328153	+	0.568378i
$166$		0			0
$167$	−11.6590	−	20.1940i	−0.902202	−	1.56266i	−0.824629	−	0.565673i	$-0.808616\pi$
$167$	−11.6590	−	20.1940i	−0.902202	−	1.56266i	−0.0775729	−	0.996987i	$-0.524717\pi$
$168$		0			0
$169$	−1.18431	+	2.05129i	−0.0911008	+	0.157791i
$170$		0			0
$171$	30.5519			2.33636
$172$		0			0
$173$	9.95558	−	17.2436i	0.756909	−	1.31100i	−0.187511	−	0.982262i	$-0.560042\pi$
$173$	9.95558	−	17.2436i	0.756909	−	1.31100i	0.944420	−	0.328742i	$-0.106625\pi$
$174$		0			0
$175$	−2.85732			−0.215993
$176$		0			0
$177$	0.292481			0.0219842
$178$		0			0
$179$	24.0418			1.79697			0.898483	−	0.439009i	$-0.144670\pi$
$179$	24.0418			1.79697			0.898483	+	0.439009i	$0.144670\pi$
$180$		0			0
$181$	−4.99453	−	8.65078i	−0.371240	−	0.643007i	0.618516	−	0.785772i	$-0.287734\pi$
$181$	−4.99453	−	8.65078i	−0.371240	−	0.643007i	−0.989757	+	0.142765i	$0.954401\pi$
$182$		0			0
$183$	−13.4271	+	23.2564i	−0.992559	+	1.71916i
$184$		0			0
$185$	2.62534	+	5.48704i	0.193019	+	0.403415i
$186$		0			0
$187$	−8.60633	+	14.9066i	−0.629357	+	1.09008i
$188$		0			0
$189$	3.85249	+	6.67270i	0.280227	+	0.485368i
$190$		0			0
$191$	8.42398			0.609538			0.304769	−	0.952426i	$-0.401421\pi$
$191$	8.42398			0.609538			0.304769	+	0.952426i	$0.401421\pi$
$192$		0			0
$193$	16.6438			1.19805			0.599023	−	0.800732i	$-0.295556\pi$
$193$	16.6438			1.19805			0.599023	+	0.800732i	$0.295556\pi$
$194$		0			0
$195$	−10.3854			−0.743711
$196$		0			0
$197$	−2.80399	+	4.85665i	−0.199776	+	0.346022i	−0.948456	−	0.316910i	$-0.897355\pi$
$197$	−2.80399	+	4.85665i	−0.199776	+	0.346022i	0.748680	+	0.662932i	$0.230688\pi$
$198$		0			0
$199$	−10.3781			−0.735687			−0.367843	−	0.929888i	$-0.619904\pi$
$199$	−10.3781			−0.735687			−0.367843	+	0.929888i	$0.619904\pi$
$200$		0			0
$201$	6.01144	−	10.4121i	0.424014	−	0.734414i
$202$		0			0
$203$	−11.9764	−	20.7437i	−0.840579	−	1.45593i
$204$		0			0
$205$	−4.44408	+	7.69737i	−0.310388	+	0.537608i
$206$		0			0
$207$	12.1331	−	21.0151i	0.843306	−	1.46065i
$208$		0			0
$209$	12.0991	+	20.9562i	0.836911	+	1.44957i
$210$		0			0
$211$	22.8995			1.57647			0.788234	−	0.615376i	$-0.210996\pi$
$211$	22.8995			1.57647			0.788234	+	0.615376i	$0.210996\pi$
$212$		0			0
$213$	−21.5129	+	37.2614i	−1.47404	+	2.55311i
$214$		0			0
$215$	−2.85724	−	4.94889i	−0.194862	−	0.337511i
$216$		0			0
$217$	−3.32505	−	5.75916i	−0.225719	−	0.390957i
$218$		0			0
$219$	−6.08601	−	10.5413i	−0.411254	−	0.712313i
$220$		0			0
$221$	−21.2041			−1.42634
$222$		0			0
$223$	5.58618			0.374078			0.187039	−	0.982352i	$-0.440111\pi$
$223$	5.58618			0.374078			0.187039	+	0.982352i	$0.440111\pi$
$224$		0			0
$225$	−2.00895	−	3.47961i	−0.133930	−	0.231974i
$226$		0			0
$227$	6.82316	+	11.8181i	0.452869	+	0.784392i	0.998563	−	0.0535923i	$-0.0170671\pi$
$227$	6.82316	+	11.8181i	0.452869	+	0.784392i	−0.545694	+	0.837985i	$0.683734\pi$
$228$		0			0
$229$	7.22516	+	12.5144i	0.477452	+	0.826972i	0.999666	−	0.0258430i	$-0.00822700\pi$
$229$	7.22516	+	12.5144i	0.477452	+	0.826972i	−0.522214	+	0.852815i	$0.674894\pi$
$230$		0			0
$231$	−12.0442	+	20.8611i	−0.792449	+	1.37256i
$232$		0			0
$233$	−2.95979			−0.193903			−0.0969513	−	0.995289i	$-0.530909\pi$
$233$	−2.95979			−0.193903			−0.0969513	+	0.995289i	$0.530909\pi$
$234$		0			0
$235$	3.51542	+	6.08889i	0.229321	+	0.397195i
$236$		0			0
$237$	−22.1461	+	38.3581i	−1.43854	+	2.49163i
$238$		0			0
$239$	−1.81414	+	3.14218i	−0.117347	+	0.203251i	−0.918716	−	0.394920i	$-0.870772\pi$
$239$	−1.81414	+	3.14218i	−0.117347	+	0.203251i	0.801368	+	0.598171i	$0.204106\pi$
$240$		0			0
$241$	−5.36821	−	9.29802i	−0.345797	−	0.598938i	0.639701	−	0.768624i	$-0.279058\pi$
$241$	−5.36821	−	9.29802i	−0.345797	−	0.598938i	−0.985498	+	0.169686i	$0.945725\pi$
$242$		0			0
$243$	10.5487	−	18.2708i	0.676697	−	1.17207i
$244$		0			0
$245$	−1.16427			−0.0743822
$246$		0			0
$247$	−14.9048	+	25.8158i	−0.948368	+	1.64262i
$248$		0			0
$249$	10.8785			0.689397
$250$		0			0
$251$	0.340221			0.0214745			0.0107373	−	0.999942i	$-0.496582\pi$
$251$	0.340221			0.0214745			0.0107373	+	0.999942i	$0.496582\pi$
$252$		0			0
$253$	19.2196			1.20833
$254$		0			0
$255$	−7.16435	−	12.4090i	−0.448649	−	0.777083i
$256$		0			0
$257$	−0.287134	+	0.497331i	−0.0179109	+	0.0310227i	−0.874842	−	0.484408i	$-0.839035\pi$
$257$	−0.287134	+	0.497331i	−0.0179109	+	0.0310227i	0.856931	+	0.515431i	$0.172368\pi$
$258$		0			0
$259$	7.50142	+	15.6782i	0.466116	+	0.974197i
$260$		0			0
$261$	16.8410	−	29.1695i	1.04243	−	1.80554i
$262$		0			0
$263$	−1.21300	−	2.10098i	−0.0747969	−	0.129552i	0.826201	−	0.563375i	$-0.190498\pi$
$263$	−1.21300	−	2.10098i	−0.0747969	−	0.129552i	−0.900998	+	0.433823i	$0.857164\pi$
$264$		0			0
$265$	−1.20436			−0.0739829
$266$		0			0
$267$	1.41661			0.0866951
$268$		0			0
$269$	−2.07886			−0.126751			−0.0633753	−	0.997990i	$-0.520187\pi$
$269$	−2.07886			−0.126751			−0.0633753	+	0.997990i	$0.520187\pi$
$270$		0			0
$271$	3.45425	−	5.98294i	0.209831	−	0.363438i	−0.741830	−	0.670588i	$-0.766042\pi$
$271$	3.45425	−	5.98294i	0.209831	−	0.363438i	0.951661	+	0.307150i	$0.0993753\pi$
$272$		0			0
$273$	−29.6743			−1.79597
$274$		0			0
$275$	1.59116	−	2.75598i	0.0959508	−	0.166192i
$276$		0			0
$277$	−8.16291	−	14.1386i	−0.490461	−	0.849504i	0.509478	−	0.860484i	$-0.329838\pi$
$277$	−8.16291	−	14.1386i	−0.490461	−	0.849504i	−0.999940	+	0.0109793i	$0.996505\pi$
$278$		0			0
$279$	4.67563	−	8.09842i	0.279922	−	0.484840i
$280$		0			0
$281$	−5.24790	+	9.08963i	−0.313063	+	0.542242i	−0.979024	−	0.203745i	$-0.934689\pi$
$281$	−5.24790	+	9.08963i	−0.313063	+	0.542242i	0.665961	+	0.745987i	$0.268022\pi$
$282$		0			0
$283$	−4.05020	−	7.01515i	−0.240759	−	0.417007i	0.720172	−	0.693796i	$-0.244063\pi$
$283$	−4.05020	−	7.01515i	−0.240759	−	0.417007i	−0.960931	+	0.276789i	$0.910730\pi$
$284$		0			0
$285$	−20.1438			−1.19322
$286$		0			0
$287$	−12.6982	+	21.9938i	−0.749548	+	1.29826i
$288$		0			0
$289$	−6.12770	−	10.6135i	−0.360453	−	0.624323i
$290$		0			0
$291$	−7.55695	−	13.0890i	−0.442996	−	0.767292i
$292$		0			0
$293$	13.2142	+	22.8877i	0.771982	+	1.33711i	0.936475	+	0.350734i	$0.114068\pi$
$293$	13.2142	+	22.8877i	0.771982	+	1.33711i	−0.164493	+	0.986378i	$0.552599\pi$
$294$		0			0
$295$	−0.110406			−0.00642811
$296$		0			0
$297$	−8.58138			−0.497942
$298$		0			0
$299$	11.8383	+	20.5045i	0.684624	+	1.18580i
$300$		0			0
$301$	−8.16405	−	14.1405i	−0.470568	−	0.815047i
$302$		0			0
$303$	0.364025	+	0.630510i	0.0209127	+	0.0362219i
$304$		0			0
$305$	5.06848	−	8.77887i	0.290220	−	0.502677i
$306$		0			0
$307$	15.9446			0.910006			0.455003	−	0.890490i	$-0.349638\pi$
$307$	15.9446			0.910006			0.455003	+	0.890490i	$0.349638\pi$
$308$		0			0
$309$	−9.14904	−	15.8466i	−0.520471	−	0.901482i
$310$		0			0
$311$	−0.502333	+	0.870067i	−0.0284847	+	0.0493370i	−0.879916	−	0.475129i	$-0.842402\pi$
$311$	−0.502333	+	0.870067i	−0.0284847	+	0.0493370i	0.851432	+	0.524466i	$0.175735\pi$
$312$		0			0
$313$	12.6959	−	21.9899i	0.717612	−	1.24294i	−0.244331	−	0.969692i	$-0.578568\pi$
$313$	12.6959	−	21.9899i	0.717612	−	1.24294i	0.961943	−	0.273249i	$-0.0880982\pi$
$314$		0			0
$315$	−5.74022	−	9.94235i	−0.323425	−	0.560188i
$316$		0			0
$317$	0.485529	−	0.840961i	0.0272700	−	0.0472331i	−0.852068	−	0.523431i	$-0.824652\pi$
$317$	0.485529	−	0.840961i	0.0272700	−	0.0472331i	0.879338	+	0.476198i	$0.157985\pi$
$318$		0			0
$319$	26.6774			1.49365
$320$		0			0
$321$	4.08815	−	7.08089i	0.228178	−	0.395216i
$322$		0			0
$323$	−41.1283			−2.28844
$324$		0			0
$325$	3.92028			0.217458
$326$		0			0
$327$	−21.2811			−1.17685
$328$		0			0
$329$	10.0447	+	17.3979i	0.553781	+	0.959177i
$330$		0			0
$331$	−5.94158	+	10.2911i	−0.326579	+	0.565651i	−0.981831	−	0.189760i	$-0.939229\pi$
$331$	−5.94158	+	10.2911i	−0.326579	+	0.565651i	0.655252	+	0.755410i	$0.272562\pi$
$332$		0			0
$333$	−13.8186	+	20.1584i	−0.757254	+	1.10467i
$334$		0			0
$335$	−2.26921	+	3.93039i	−0.123980	+	0.214740i
$336$		0			0
$337$	−12.2011	−	21.1329i	−0.664634	−	1.15118i	−0.979384	−	0.202005i	$-0.935254\pi$
$337$	−12.2011	−	21.1329i	−0.664634	−	1.15118i	0.314750	−	0.949175i	$-0.398079\pi$
$338$		0			0
$339$	37.4218			2.03247
$340$		0			0
$341$	7.40653			0.401086
$342$		0			0
$343$	16.6745			0.900341
$344$		0			0
$345$	−7.99971	+	13.8559i	−0.430690	+	0.745977i
$346$		0			0
$347$	−21.4655			−1.15233			−0.576164	−	0.817334i	$-0.695451\pi$
$347$	−21.4655			−1.15233			−0.576164	+	0.817334i	$0.695451\pi$
$348$		0			0
$349$	16.4709	−	28.5285i	0.881668	−	1.52709i	0.0321829	−	0.999482i	$-0.489754\pi$
$349$	16.4709	−	28.5285i	0.881668	−	1.52709i	0.849485	−	0.527612i	$-0.176913\pi$
$350$		0			0
$351$	−5.28567	−	9.15505i	−0.282128	−	0.488660i
$352$		0			0
$353$	2.06067	−	3.56918i	0.109678	−	0.189968i	−0.805962	−	0.591968i	$-0.798351\pi$
$353$	2.06067	−	3.56918i	0.109678	−	0.189968i	0.915640	+	0.401999i	$0.131685\pi$
$354$		0			0
$355$	8.12072	−	14.0655i	0.431003	−	0.746519i
$356$		0			0
$357$	−20.4708	−	35.4565i	−1.08343	−	1.87656i
$358$		0			0
$359$	6.61660			0.349211			0.174606	−	0.984638i	$-0.444135\pi$
$359$	6.61660			0.349211			0.174606	+	0.984638i	$0.444135\pi$
$360$		0			0
$361$	−19.4098	+	33.6188i	−1.02157	+	1.76941i
$362$		0			0
$363$	1.15607	+	2.00237i	0.0606779	+	0.105097i
$364$		0			0
$365$	2.29736	+	3.97914i	0.120249	+	0.208278i
$366$		0			0
$367$	−11.1549	−	19.3208i	−0.582280	−	1.00854i	−0.995208	−	0.0977756i	$-0.968827\pi$
$367$	−11.1549	−	19.3208i	−0.582280	−	1.00854i	0.412928	−	0.910764i	$-0.364506\pi$
$368$		0			0
$369$	−35.7118			−1.85908
$370$		0			0
$371$	−3.44123			−0.178660
$372$		0			0
$373$	−8.15508	−	14.1250i	−0.422254	−	0.731366i	0.573905	−	0.818922i	$-0.305428\pi$
$373$	−8.15508	−	14.1250i	−0.422254	−	0.731366i	−0.996160	+	0.0875558i	$0.972094\pi$
$374$		0			0
$375$	1.32457	+	2.29422i	0.0684003	+	0.118473i
$376$		0			0
$377$	16.4318	+	28.4607i	0.846281	+	1.46580i
$378$		0			0
$379$	14.9604	−	25.9122i	0.768466	−	1.33102i	−0.169929	−	0.985456i	$-0.554354\pi$
$379$	14.9604	−	25.9122i	0.768466	−	1.33102i	0.938395	−	0.345565i	$-0.112313\pi$
$380$		0			0
$381$	0.109218			0.00559539
$382$		0			0
$383$	−10.7509	−	18.6210i	−0.549344	−	0.951491i	−0.998320	−	0.0579472i	$-0.981544\pi$
$383$	−10.7509	−	18.6210i	−0.549344	−	0.951491i	0.448976	−	0.893544i	$-0.351789\pi$
$384$		0			0
$385$	4.54646	−	7.87470i	0.231709	−	0.401332i
$386$		0			0
$387$	11.4801	−	19.8842i	0.583568	−	1.01077i
$388$		0			0
$389$	−3.00596	−	5.20647i	−0.152408	−	0.263978i	0.779704	−	0.626148i	$-0.215369\pi$
$389$	−3.00596	−	5.20647i	−0.152408	−	0.263978i	−0.932112	+	0.362170i	$0.882036\pi$
$390$		0			0
$391$	−16.3333	+	28.2901i	−0.826010	+	1.43069i
$392$		0			0
$393$	52.3866			2.64255
$394$		0			0
$395$	8.35973	−	14.4795i	0.420624	−	0.728542i
$396$		0			0
$397$	29.3716			1.47412			0.737060	−	0.675828i	$-0.236214\pi$
$397$	29.3716			1.47412			0.737060	+	0.675828i	$0.236214\pi$
$398$		0			0
$399$	−57.5573			−2.88147
$400$		0			0
$401$	−0.149782			−0.00747977			−0.00373989	−	0.999993i	$-0.501190\pi$
$401$	−0.149782			−0.00747977			−0.00373989	+	0.999993i	$0.501190\pi$
$402$		0			0
$403$	4.56202	+	7.90165i	0.227250	+	0.393609i
$404$		0			0
$405$	−2.45507	+	4.25230i	−0.121993	+	0.211299i
$406$		0			0
$407$	−19.2995	−	1.49541i	−0.956640	−	0.0741249i
$408$		0			0
$409$	−17.4680	+	30.2554i	−0.863737	+	1.49604i	0.00455971	+	0.999990i	$0.498549\pi$
$409$	−17.4680	+	30.2554i	−0.863737	+	1.49604i	−0.868296	+	0.496046i	$0.834785\pi$
$410$		0			0
$411$	−12.4890	−	21.6315i	−0.616035	−	1.06700i
$412$		0			0
$413$	−0.315466			−0.0155231
$414$		0			0
$415$	−4.10644			−0.201577
$416$		0			0
$417$	20.6574			1.01160
$418$		0			0
$419$	−6.20937	+	10.7549i	−0.303347	+	0.525413i	−0.976892	−	0.213733i	$-0.931438\pi$
$419$	−6.20937	+	10.7549i	−0.303347	+	0.525413i	0.673545	+	0.739147i	$0.264771\pi$
$420$		0			0
$421$	27.0203			1.31689			0.658443	−	0.752630i	$-0.271215\pi$
$421$	27.0203			1.31689			0.658443	+	0.752630i	$0.271215\pi$
$422$		0			0
$423$	−14.1246	+	24.4646i	−0.686764	+	1.18951i
$424$		0			0
$425$	2.70441	+	4.68418i	0.131183	+	0.227216i
$426$		0			0
$427$	14.4823	−	25.0840i	0.700846	−	1.21390i
$428$		0			0
$429$	16.5248	−	28.6218i	0.797825	−	1.38187i
$430$		0			0
$431$	12.1245	+	21.0002i	0.584016	+	1.01155i	0.994997	+	0.0999014i	$0.0318527\pi$
$431$	12.1245	+	21.0002i	0.584016	+	1.01155i	−0.410981	+	0.911644i	$0.634814\pi$
$432$		0			0
$433$	−31.0338			−1.49139			−0.745694	−	0.666288i	$-0.767882\pi$
$433$	−31.0338			−1.49139			−0.745694	+	0.666288i	$0.767882\pi$
$434$		0			0
$435$	−11.1038	+	19.2324i	−0.532387	+	0.922121i
$436$		0			0
$437$	22.9619	+	39.7712i	1.09842	+	1.90251i
$438$		0			0
$439$	−18.3899	−	31.8522i	−0.877700	−	1.52022i	−0.853858	−	0.520505i	$-0.825744\pi$
$439$	−18.3899	−	31.8522i	−0.877700	−	1.52022i	−0.0238416	−	0.999716i	$-0.507590\pi$
$440$		0			0
$441$	−2.33896	−	4.05119i	−0.111379	−	0.192914i
$442$		0			0
$443$	−19.5596			−0.929305			−0.464653	−	0.885493i	$-0.653821\pi$
$443$	−19.5596			−0.929305			−0.464653	+	0.885493i	$0.653821\pi$
$444$		0			0
$445$	−0.534744			−0.0253493
$446$		0			0
$447$	25.6409	+	44.4113i	1.21277	+	2.10058i
$448$		0			0
$449$	−9.98328	−	17.2916i	−0.471140	−	0.816039i	0.528315	−	0.849049i	$-0.322824\pi$
$449$	−9.98328	−	17.2916i	−0.471140	−	0.816039i	−0.999455	+	0.0330096i	$0.989491\pi$
$450$		0			0
$451$	−14.1425	−	24.4956i	−0.665945	−	1.15345i
$452$		0			0
$453$	21.5953	−	37.4041i	1.01463	−	1.75740i
$454$		0			0
$455$	11.2015			0.525134
$456$		0			0
$457$	−4.57675	−	7.92717i	−0.214092	−	0.370817i	0.738900	−	0.673816i	$-0.235346\pi$
$457$	−4.57675	−	7.92717i	−0.214092	−	0.370817i	−0.952991	+	0.302998i	$0.902012\pi$
$458$		0			0
$459$	7.29265	−	12.6312i	0.340392	−	0.589576i
$460$		0			0
$461$	3.03643	−	5.25924i	0.141420	−	0.244947i	−0.786611	−	0.617449i	$-0.788166\pi$
$461$	3.03643	−	5.25924i	0.141420	−	0.244947i	0.928032	+	0.372501i	$0.121500\pi$
$462$		0			0
$463$	1.12243	+	1.94410i	0.0521636	+	0.0903501i	0.890928	−	0.454144i	$-0.150055\pi$
$463$	1.12243	+	1.94410i	0.0521636	+	0.0903501i	−0.838765	+	0.544494i	$0.816722\pi$
$464$		0			0
$465$	−3.08279	+	5.33955i	−0.142961	+	0.247616i
$466$		0			0
$467$	−31.6080			−1.46264			−0.731322	−	0.682032i	$-0.761097\pi$
$467$	−31.6080			−1.46264			−0.731322	+	0.682032i	$0.761097\pi$
$468$		0			0
$469$	−6.48386	+	11.2304i	−0.299397	+	0.518570i
$470$		0			0
$471$	8.18563			0.377174
$472$		0			0
$473$	18.1854			0.836164
$474$		0			0
$475$	7.60392			0.348892
$476$		0			0
$477$	−2.41949	−	4.19069i	−0.110781	−	0.191878i
$478$		0			0
$479$	−11.0148	+	19.0783i	−0.503281	+	0.871708i	0.496712	+	0.867916i	$0.334541\pi$
$479$	−11.0148	+	19.0783i	−0.503281	+	0.871708i	−0.999993	+	0.00379279i	$0.998793\pi$
$480$		0			0
$481$	−10.2921	−	21.5108i	−0.469278	−	0.980806i
$482$		0			0
$483$	−22.8577	+	39.5907i	−1.04006	+	1.80144i
$484$		0			0
$485$	2.85261	+	4.94087i	0.129530	+	0.224353i
$486$		0			0
$487$	−15.8414			−0.717840			−0.358920	−	0.933368i	$-0.616855\pi$
$487$	−15.8414			−0.717840			−0.358920	+	0.933368i	$0.616855\pi$
$488$		0			0
$489$	−40.8482			−1.84722
$490$		0			0
$491$	−19.3703			−0.874169			−0.437084	−	0.899420i	$-0.643989\pi$
$491$	−19.3703			−0.874169			−0.437084	+	0.899420i	$0.643989\pi$
$492$		0			0
$493$	−22.6710	+	39.2674i	−1.02105	+	1.76851i
$494$		0			0
$495$	12.7863			0.574701
$496$		0			0
$497$	23.2035	−	40.1896i	1.04082	−	1.80275i
$498$		0			0
$499$	6.74686	+	11.6859i	0.302031	+	0.523133i	0.976596	−	0.215083i	$-0.0690021\pi$
$499$	6.74686	+	11.6859i	0.302031	+	0.523133i	−0.674565	+	0.738215i	$0.735669\pi$
$500$		0			0
$501$	−30.8863	+	53.4967i	−1.37990	+	2.39005i
$502$		0			0
$503$	−4.00779	+	6.94169i	−0.178698	+	0.309515i	−0.941435	−	0.337195i	$-0.890522\pi$
$503$	−4.00779	+	6.94169i	−0.178698	+	0.309515i	0.762737	+	0.646709i	$0.223855\pi$
$504$		0			0
$505$	−0.137413	−	0.238006i	−0.00611480	−	0.0105911i
$506$		0			0
$507$	6.27479			0.278673
$508$		0			0
$509$	−3.84003	+	6.65113i	−0.170206	+	0.294806i	−0.938492	−	0.345301i	$-0.887777\pi$
$509$	−3.84003	+	6.65113i	−0.170206	+	0.294806i	0.768286	+	0.640107i	$0.221110\pi$
$510$		0			0
$511$	6.56428	+	11.3697i	0.290387	+	0.502964i
$512$		0			0
$513$	−10.2523	−	17.7575i	−0.452649	−	0.784011i
$514$		0			0
$515$	3.45360	+	5.98181i	0.152184	+	0.263590i
$516$		0			0
$517$	−22.3744			−0.984027
$518$		0			0
$519$	−52.7473			−2.31535
$520$		0			0
$521$	−4.41405	−	7.64535i	−0.193383	−	0.334949i	0.752986	−	0.658036i	$-0.228613\pi$
$521$	−4.41405	−	7.64535i	−0.193383	−	0.334949i	−0.946369	+	0.323087i	$0.895279\pi$
$522$		0			0
$523$	21.0059	+	36.3833i	0.918523	+	1.59093i	0.801660	+	0.597781i	$0.203951\pi$
$523$	21.0059	+	36.3833i	0.918523	+	1.59093i	0.116863	+	0.993148i	$0.462716\pi$
$524$		0			0
$525$	3.78471	+	6.55531i	0.165178	+	0.286097i
$526$		0			0
$527$	−6.29423	+	10.9019i	−0.274181	+	0.474896i
$528$		0			0
$529$	13.4755			0.585890
$530$		0			0
$531$	−0.221801	−	0.384171i	−0.00962536	−	0.0166716i
$532$		0			0
$533$	17.4221	−	30.1759i	0.754633	−	1.30706i
$534$		0			0
$535$	−1.54320	+	2.67291i	−0.0667185	+	0.115560i
$536$		0			0
$537$	−31.8449	−	55.1570i	−1.37421	−	2.38020i
$538$		0			0
$539$	1.85254	−	3.20869i	0.0797945	−	0.138208i
$540$		0			0
$541$	31.8382			1.36883			0.684416	−	0.729092i	$-0.260057\pi$
$541$	31.8382			1.36883			0.684416	+	0.729092i	$0.260057\pi$
$542$		0			0
$543$	−13.2312	+	22.9171i	−0.567804	+	0.983465i
$544$		0			0
$545$	8.03323			0.344106
$546$		0			0
$547$	6.61448			0.282815			0.141407	−	0.989951i	$-0.454837\pi$
$547$	6.61448			0.282815			0.141407	+	0.989951i	$0.454837\pi$
$548$		0			0
$549$	40.7294			1.73829
$550$		0			0
$551$	31.8717	+	55.2035i	1.35778	+	2.35175i
$552$		0			0
$553$	23.8864	−	41.3725i	1.01575	−	1.75934i
$554$		0			0
$555$	9.11103	−	13.2910i	0.386742	−	0.564173i
$556$		0			0
$557$	−8.35829	+	14.4770i	−0.354152	+	0.613409i	−0.986972	−	0.160889i	$-0.948564\pi$
$557$	−8.35829	+	14.4770i	−0.354152	+	0.613409i	0.632821	+	0.774299i	$0.281897\pi$
$558$		0			0
$559$	11.2012	+	19.4010i	0.473760	+	0.820577i
$560$		0			0
$561$	45.5986			1.92518
$562$		0			0
$563$	29.6650			1.25023			0.625115	−	0.780533i	$-0.285052\pi$
$563$	29.6650			1.25023			0.625115	+	0.780533i	$0.285052\pi$
$564$		0			0
$565$	−14.1261			−0.594287
$566$		0			0
$567$	−7.01491	+	12.1502i	−0.294599	+	0.510260i
$568$		0			0
$569$	−5.54577			−0.232491			−0.116245	−	0.993221i	$-0.537086\pi$
$569$	−5.54577			−0.232491			−0.116245	+	0.993221i	$0.537086\pi$
$570$		0			0
$571$	−0.878312	+	1.52128i	−0.0367562	+	0.0636636i	−0.883818	−	0.467830i	$-0.845036\pi$
$571$	−0.878312	+	1.52128i	−0.0367562	+	0.0636636i	0.847062	+	0.531494i	$0.178369\pi$
$572$		0			0
$573$	−11.1581	−	19.3264i	−0.466137	−	0.807373i
$574$		0			0
$575$	3.01975	−	5.23035i	0.125932	−	0.218121i
$576$		0			0
$577$	−16.9894	+	29.4265i	−0.707277	+	1.22504i	0.258586	+	0.965988i	$0.416744\pi$
$577$	−16.9894	+	29.4265i	−0.707277	+	1.22504i	−0.965863	+	0.259052i	$0.916590\pi$
$578$		0			0
$579$	−22.0458	−	38.1845i	−0.916192	−	1.58689i
$580$		0			0
$581$	−11.7334			−0.486784
$582$		0			0
$583$	1.91633	−	3.31917i	0.0793661	−	0.137466i
$584$		0			0
$585$	7.87567	+	13.6411i	0.325619	+	0.563988i
$586$		0			0
$587$	7.98333	+	13.8275i	0.329507	+	0.570724i	0.982414	−	0.186715i	$-0.0597840\pi$
$587$	7.98333	+	13.8275i	0.329507	+	0.570724i	−0.652907	+	0.757438i	$0.726451\pi$
$588$		0			0
$589$	8.84866	+	15.3263i	0.364603	+	0.631510i
$590$		0			0
$591$	14.8563			0.611105
$592$		0			0
$593$	−22.1665			−0.910270			−0.455135	−	0.890423i	$-0.650409\pi$
$593$	−22.1665			−0.910270			−0.455135	+	0.890423i	$0.650409\pi$
$594$		0			0
$595$	7.72737	+	13.3842i	0.316791	+	0.548699i
$596$		0			0
$597$	13.7465	+	23.8097i	0.562608	+	0.974466i
$598$		0			0
$599$	5.63329	+	9.75715i	0.230170	+	0.398666i	0.957858	−	0.287242i	$-0.0927384\pi$
$599$	5.63329	+	9.75715i	0.230170	+	0.398666i	−0.727688	+	0.685908i	$0.759405\pi$
$600$		0			0
$601$	−16.9749	+	29.4013i	−0.692419	+	1.19930i	0.278624	+	0.960400i	$0.410122\pi$
$601$	−16.9749	+	29.4013i	−0.692419	+	1.19930i	−0.971043	+	0.238905i	$0.923212\pi$
$602$		0			0
$603$	−18.2350			−0.742585
$604$		0			0
$605$	−0.436395	−	0.755858i	−0.0177420	−	0.0307300i
$606$		0			0
$607$	13.5884	−	23.5357i	0.551535	−	0.955287i	−0.446629	−	0.894719i	$-0.647376\pi$
$607$	13.5884	−	23.5357i	0.551535	−	0.955287i	0.998164	−	0.0605674i	$-0.0192910\pi$
$608$		0			0
$609$	−31.7271	+	54.9529i	−1.28565	+	2.22681i
$610$		0			0
$611$	−13.7814	−	23.8702i	−0.557538	−	0.965684i
$612$		0			0
$613$	7.49915	−	12.9889i	0.302888	−	0.524617i	−0.673901	−	0.738822i	$-0.735383\pi$
$613$	7.49915	−	12.9889i	0.302888	−	0.524617i	0.976789	+	0.214205i	$0.0687159\pi$
$614$		0			0
$615$	23.5459			0.949463
$616$		0			0
$617$	19.2658	−	33.3694i	0.775614	−	1.34340i	−0.158835	−	0.987305i	$-0.550774\pi$
$617$	19.2658	−	33.3694i	0.775614	−	1.34340i	0.934449	−	0.356097i	$-0.115893\pi$
$618$		0			0
$619$	−20.3957			−0.819773			−0.409886	−	0.912137i	$-0.634432\pi$
$619$	−20.3957			−0.819773			−0.409886	+	0.912137i	$0.634432\pi$
$620$		0			0
$621$	−16.2859			−0.653532
$622$		0			0
$623$	−1.52793			−0.0612154
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	32.0521	−	55.5159i	1.28004	−	2.21709i
$628$		0			0
$629$	18.6023	−	27.1368i	0.741722	−	1.08201i
$630$		0			0
$631$	−3.98798	+	6.90739i	−0.158759	+	0.274979i	−0.934421	−	0.356169i	$-0.884083\pi$
$631$	−3.98798	+	6.90739i	−0.158759	+	0.274979i	0.775662	+	0.631148i	$0.217416\pi$
$632$		0			0
$633$	−30.3319	−	52.5365i	−1.20559	−	2.08814i
$634$		0			0
$635$	−0.0412277			−0.00163607
$636$		0			0
$637$	4.56425			0.180842
$638$		0			0
$639$	65.2566			2.58151
$640$		0			0
$641$	−4.77289	+	8.26690i	−0.188518	+	0.326523i	−0.944756	−	0.327773i	$-0.893702\pi$
$641$	−4.77289	+	8.26690i	−0.188518	+	0.326523i	0.756238	+	0.654296i	$0.227035\pi$
$642$		0			0
$643$	20.0135			0.789256			0.394628	−	0.918841i	$-0.370873\pi$
$643$	20.0135			0.789256			0.394628	+	0.918841i	$0.370873\pi$
$644$		0			0
$645$	−7.56921	+	13.1103i	−0.298037	+	0.516216i
$646$		0			0
$647$	−4.05706	−	7.02703i	−0.159499	−	0.276261i	0.775189	−	0.631730i	$-0.217655\pi$
$647$	−4.05706	−	7.02703i	−0.159499	−	0.276261i	−0.934688	+	0.355468i	$0.884321\pi$
$648$		0			0
$649$	0.175675	−	0.304277i	0.00689583	−	0.0119439i
$650$		0			0
$651$	−8.80851	+	15.2568i	−0.345233	+	0.597960i
$652$		0			0
$653$	4.15115	+	7.19000i	0.162447	+	0.281366i	0.935746	−	0.352675i	$-0.114728\pi$
$653$	4.15115	+	7.19000i	0.162447	+	0.281366i	−0.773299	+	0.634042i	$0.781395\pi$
$654$		0			0
$655$	−19.7750			−0.772672
$656$		0			0
$657$	−9.23057	+	15.9878i	−0.360119	+	0.623744i
$658$		0			0
$659$	−1.22269	−	2.11776i	−0.0476291	−	0.0824961i	0.841228	−	0.540681i	$-0.181833\pi$
$659$	−1.22269	−	2.11776i	−0.0476291	−	0.0824961i	−0.888857	+	0.458185i	$0.848500\pi$
$660$		0			0
$661$	−21.4618	−	37.1729i	−0.834768	−	1.44586i	−0.894219	−	0.447629i	$-0.852269\pi$
$661$	−21.4618	−	37.1729i	−0.834768	−	1.44586i	0.0594518	−	0.998231i	$-0.481065\pi$
$662$		0			0
$663$	28.0863	+	48.6469i	1.09078	+	1.88929i
$664$		0			0
$665$	21.7268			0.842530
$666$		0			0
$667$	50.6289			1.96036
$668$		0			0
$669$	−7.39927	−	12.8159i	−0.286072	−	0.495492i
$670$		0			0
$671$	16.1296	+	27.9372i	0.622675	+	1.07851i
$672$		0			0
$673$	−2.58162	−	4.47150i	−0.0995141	−	0.172364i	0.811970	−	0.583700i	$-0.198396\pi$
$673$	−2.58162	−	4.47150i	−0.0995141	−	0.172364i	−0.911484	+	0.411336i	$0.865062\pi$
$674$		0			0
$675$	−1.34829	+	2.33530i	−0.0518956	+	0.0898858i
$676$		0			0
$677$	17.7159			0.680877			0.340438	−	0.940267i	$-0.389425\pi$
$677$	17.7159			0.680877			0.340438	+	0.940267i	$0.389425\pi$
$678$		0			0
$679$	8.15082	+	14.1176i	0.312800	+	0.541785i
$680$		0			0
$681$	18.0755	−	31.3076i	0.692653	−	1.19971i
$682$		0			0
$683$	21.7698	−	37.7063i	0.832997	−	1.44279i	−0.0626537	−	0.998035i	$-0.519956\pi$
$683$	21.7698	−	37.7063i	0.832997	−	1.44279i	0.895651	−	0.444758i	$-0.146710\pi$
$684$		0			0
$685$	4.71436	+	8.16550i	0.180126	+	0.311988i
$686$		0			0
$687$	19.1404	−	33.1522i	0.730253	−	1.26483i
$688$		0			0
$689$	4.72141			0.179872
$690$		0			0
$691$	−0.385620	+	0.667913i	−0.0146697	+	0.0254086i	−0.873267	−	0.487242i	$-0.838003\pi$
$691$	−0.385620	+	0.667913i	−0.0146697	+	0.0254086i	0.858597	+	0.512651i	$0.171336\pi$
$692$		0			0
$693$	36.5345			1.38783
$694$		0			0
$695$	−7.79780			−0.295788
$696$		0			0
$697$	48.0745			1.82095
$698$		0			0
$699$	3.92045	+	6.79041i	0.148285	+	0.256837i
$700$		0			0
$701$	−5.62488	+	9.74257i	−0.212449	+	0.367972i	−0.952480	−	0.304600i	$-0.901477\pi$
$701$	−5.62488	+	9.74257i	−0.212449	+	0.367972i	0.740032	+	0.672572i	$0.234810\pi$
$702$		0			0
$703$	−19.9629	−	41.7230i	−0.752913	−	1.57361i
$704$		0			0
$705$	9.31282	−	16.1303i	0.350741	−	0.607501i
$706$		0			0
$707$	−0.392633	−	0.680060i	−0.0147665	−	0.0255763i
$708$		0			0
$709$	−48.3736			−1.81671			−0.908355	−	0.418200i	$-0.862661\pi$
$709$	−48.3736			−1.81671			−0.908355	+	0.418200i	$0.862661\pi$
$710$		0			0
$711$	67.1773			2.51935
$712$		0			0
$713$	14.0563			0.526412
$714$		0			0
$715$	−6.23781	+	10.8042i	−0.233281	+	0.404055i
$716$		0			0
$717$	9.61180			0.358959
$718$		0			0
$719$	4.38271	−	7.59107i	0.163447	−	0.283099i	−0.772655	−	0.634826i	$-0.781072\pi$
$719$	4.38271	−	7.59107i	0.163447	−	0.283099i	0.936103	+	0.351726i	$0.114405\pi$
$720$		0			0
$721$	9.86803	+	17.0919i	0.367505	+	0.636536i
$722$		0			0
$723$	−14.2211	+	24.6317i	−0.528889	+	0.916062i
$724$		0			0
$725$	4.19148	−	7.25986i	0.155668	−	0.269625i
$726$		0			0
$727$	−0.761626	−	1.31918i	−0.0282472	−	0.0489255i	0.851556	−	0.524263i	$-0.175659\pi$
$727$	−0.761626	−	1.31918i	−0.0282472	−	0.0489255i	−0.879803	+	0.475338i	$0.842326\pi$
$728$		0			0
$729$	−41.1592			−1.52442
$730$		0			0
$731$	−15.4543	+	26.7677i	−0.571599	+	0.990038i
$732$		0			0
$733$	−14.4720	−	25.0663i	−0.534536	−	0.925844i	−0.999186	−	0.0403493i	$-0.987153\pi$
$733$	−14.4720	−	25.0663i	−0.534536	−	0.925844i	0.464649	−	0.885495i	$-0.346180\pi$
$734$		0			0
$735$	1.54215	+	2.67108i	0.0568830	+	0.0985242i
$736$		0			0
$737$	−7.22137	−	12.5078i	−0.266003	−	0.460730i
$738$		0			0
$739$	−15.1118			−0.555898			−0.277949	−	0.960596i	$-0.589655\pi$
$739$	−15.1118			−0.555898			−0.277949	+	0.960596i	$0.589655\pi$
$740$		0			0
$741$	78.9694			2.90101
$742$		0			0
$743$	9.58709	+	16.6053i	0.351716	+	0.609190i	0.986550	−	0.163458i	$-0.0522649\pi$
$743$	9.58709	+	16.6053i	0.351716	+	0.609190i	−0.634834	+	0.772648i	$0.718932\pi$
$744$		0			0
$745$	−9.67897	−	16.7645i	−0.354610	−	0.614203i
$746$		0			0
$747$	−8.24965	−	14.2888i	−0.301839	−	0.522800i
$748$		0			0
$749$	−4.40942	+	7.63734i	−0.161117	+	0.279062i
$750$		0			0
$751$	28.4343			1.03758			0.518791	−	0.854901i	$-0.326382\pi$
$751$	28.4343			1.03758			0.518791	+	0.854901i	$0.326382\pi$
$752$		0			0
$753$	−0.450645	−	0.780540i	−0.0164224	−	0.0284444i
$754$		0			0
$755$	−8.15183	+	14.1194i	−0.296675	+	0.513857i
$756$		0			0
$757$	−9.25575	+	16.0314i	−0.336406	+	0.582672i	−0.983754	−	0.179522i	$-0.942545\pi$
$757$	−9.25575	+	16.0314i	−0.336406	+	0.582672i	0.647348	+	0.762195i	$0.275878\pi$
$758$		0			0
$759$	−25.4577	−	44.0940i	−0.924056	−	1.60051i
$760$		0			0
$761$	−1.57754	+	2.73237i	−0.0571857	+	0.0990485i	−0.893201	−	0.449658i	$-0.851546\pi$
$761$	−1.57754	+	2.73237i	−0.0571857	+	0.0990485i	0.836015	+	0.548706i	$0.184879\pi$
$762$		0			0
$763$	22.9535			0.830972
$764$		0			0
$765$	−10.8661	+	18.8206i	−0.392864	+	0.680461i
$766$		0			0
$767$	0.432824			0.0156284
$768$		0			0
$769$	−40.4676			−1.45930			−0.729650	−	0.683821i	$-0.760317\pi$
$769$	−40.4676			−1.45930			−0.729650	+	0.683821i	$0.760317\pi$
$770$		0			0
$771$	1.52131			0.0547888
$772$		0			0
$773$	−17.0506	−	29.5325i	−0.613267	−	1.06221i	−0.990686	−	0.136168i	$-0.956521\pi$
$773$	−17.0506	−	29.5325i	−0.613267	−	1.06221i	0.377418	−	0.926043i	$-0.376812\pi$
$774$		0			0
$775$	1.16370	−	2.01558i	0.0418012	−	0.0724018i
$776$		0			0
$777$	26.0331	−	37.9767i	0.933932	−	1.36241i
$778$		0			0
$779$	33.7924	−	58.5302i	1.21074	−	2.09706i
$780$		0			0
$781$	25.8428	+	44.7610i	0.924727	+	1.60167i
$782$		0			0
$783$	−22.6053			−0.807848
$784$		0			0
$785$	−3.08993			−0.110284
$786$		0			0
$787$	10.7200			0.382127			0.191064	−	0.981578i	$-0.438806\pi$
$787$	10.7200			0.382127			0.191064	+	0.981578i	$0.438806\pi$
$788$		0			0
$789$	−3.21340	+	5.56578i	−0.114400	+	0.198147i
$790$		0			0
$791$	−40.3626			−1.43513
$792$		0			0
$793$	−19.8699	+	34.4157i	−0.705600	+	1.22214i
$794$		0			0
$795$	1.59525	+	2.76305i	0.0565776	+	0.0979953i
$796$		0			0
$797$	−9.23112	+	15.9888i	−0.326983	+	0.566351i	−0.981912	−	0.189339i	$-0.939365\pi$
$797$	−9.23112	+	15.9888i	−0.326983	+	0.566351i	0.654929	+	0.755691i	$0.272699\pi$
$798$		0			0
$799$	19.0143	−	32.9337i	0.672678	−	1.16511i
$800$		0			0
$801$	−1.07428	−	1.86070i	−0.0379577	−	0.0657447i
$802$		0			0
$803$	−14.6219			−0.515995
$804$		0			0
$805$	8.62838	−	14.9448i	0.304110	−	0.526734i
$806$		0			0
$807$	2.75359	+	4.76936i	0.0969311	+	0.167890i
$808$		0			0
$809$	−24.6007	−	42.6097i	−0.864916	−	1.49808i	−0.867131	−	0.498080i	$-0.834038\pi$
$809$	−24.6007	−	42.6097i	−0.864916	−	1.49808i	0.00221527	−	0.999998i	$-0.499295\pi$
$810$		0			0
$811$	−0.175474	−	0.303929i	−0.00616171	−	0.0106724i	0.862928	−	0.505327i	$-0.168628\pi$
$811$	−0.175474	−	0.303929i	−0.00616171	−	0.0106724i	−0.869090	+	0.494654i	$0.835295\pi$
$812$		0			0
$813$	−18.3016			−0.641863
$814$		0			0
$815$	15.4195			0.540120
$816$		0			0
$817$	21.7262	+	37.6310i	0.760105	+	1.31654i
$818$		0			0
$819$	22.5033	+	38.9768i	0.786329	+	1.36196i
$820$		0			0
$821$	−19.2820	−	33.3974i	−0.672947	−	1.16558i	−0.977064	−	0.212944i	$-0.931695\pi$
$821$	−19.2820	−	33.3974i	−0.672947	−	1.16558i	0.304118	−	0.952634i	$-0.401638\pi$
$822$		0			0
$823$	−11.3138	+	19.5960i	−0.394374	+	0.683075i	−0.993021	−	0.117937i	$-0.962372\pi$
$823$	−11.3138	+	19.5960i	−0.394374	+	0.683075i	0.598647	+	0.801013i	$0.295705\pi$
$824$		0			0
$825$	−8.43041			−0.293509
$826$		0			0
$827$	−0.977232	−	1.69262i	−0.0339817	−	0.0588580i	0.848534	−	0.529140i	$-0.177485\pi$
$827$	−0.977232	−	1.69262i	−0.0339817	−	0.0588580i	−0.882516	+	0.470282i	$0.844152\pi$
$828$		0			0
$829$	−0.454577	+	0.787350i	−0.0157881	+	0.0273458i	−0.873812	−	0.486265i	$-0.838359\pi$
$829$	−0.454577	+	0.787350i	−0.0157881	+	0.0273458i	0.858023	+	0.513611i	$0.171692\pi$
$830$		0			0
$831$	−21.6246	+	37.4550i	−0.750150	+	1.29930i
$832$		0			0
$833$	3.14866	+	5.45363i	0.109095	+	0.188957i
$834$		0			0
$835$	11.6590	−	20.1940i	0.403477	−	0.698843i
$836$		0			0
$837$	−6.27599			−0.216930
$838$		0			0
$839$	7.37874	−	12.7804i	0.254742	−	0.441227i	−0.710083	−	0.704118i	$-0.751343\pi$
$839$	7.37874	−	12.7804i	0.254742	−	0.441227i	0.964826	+	0.262891i	$0.0846760\pi$
$840$		0			0
$841$	41.2742			1.42325
$842$		0			0
$843$	27.8048			0.957647
$844$		0			0
$845$	−2.36862			−0.0814831
$846$		0			0
$847$	−1.24692	−	2.15973i	−0.0428447	−	0.0742091i
$848$		0			0
$849$	−10.7295	+	18.5841i	−0.368236	+	0.637803i
$850$		0			0
$851$	−36.6270	−	2.83803i	−1.25556	−	0.0972864i
$852$		0			0
$853$	−20.4281	+	35.3826i	−0.699446	+	1.21148i	0.269213	+	0.963081i	$0.413237\pi$
$853$	−20.4281	+	35.3826i	−0.699446	+	1.21148i	−0.968659	+	0.248396i	$0.920097\pi$
$854$		0			0
$855$	15.2759	+	26.4587i	0.522426	+	0.904868i
$856$		0			0
$857$	11.0065			0.375974			0.187987	−	0.982172i	$-0.439804\pi$
$857$	11.0065			0.375974			0.187987	+	0.982172i	$0.439804\pi$
$858$		0			0
$859$	33.2969			1.13607			0.568037	−	0.823003i	$-0.307703\pi$
$859$	33.2969			1.13607			0.568037	+	0.823003i	$0.307703\pi$
$860$		0			0
$861$	67.2782			2.29283
$862$		0			0
$863$	−12.5419	+	21.7232i	−0.426931	+	0.739466i	−0.996599	−	0.0824093i	$-0.973739\pi$
$863$	−12.5419	+	21.7232i	−0.426931	+	0.739466i	0.569668	+	0.821875i	$0.307072\pi$
$864$		0			0
$865$	19.9112			0.677000
$866$		0			0
$867$	−16.2331	+	28.1166i	−0.551305	+	0.954888i
$868$		0			0
$869$	26.6034	+	46.0785i	0.902459	+	1.56310i
$870$		0			0
$871$	8.89595	−	15.4082i	0.301428	−	0.522088i
$872$		0			0
$873$	−11.4615	+	19.8520i	−0.387914	+	0.671887i
$874$		0			0
$875$	−1.42866	−	2.47451i	−0.0482975	−	0.0836537i
$876$		0			0
$877$	−47.3336			−1.59834			−0.799171	−	0.601104i	$-0.794728\pi$
$877$	−47.3336			−1.59834			−0.799171	+	0.601104i	$0.794728\pi$
$878$		0			0
$879$	35.0062	−	60.6325i	1.18073	−	2.04508i
$880$		0			0
$881$	14.3186	+	24.8006i	0.482406	+	0.835552i	0.999796	−	0.0201975i	$-0.00642951\pi$
$881$	14.3186	+	24.8006i	0.482406	+	0.835552i	−0.517390	+	0.855750i	$0.673096\pi$
$882$		0			0
$883$	21.3690	+	37.0123i	0.719126	+	1.24556i	0.961347	+	0.275341i	$0.0887908\pi$
$883$	21.3690	+	37.0123i	0.719126	+	1.24556i	−0.242221	+	0.970221i	$0.577876\pi$
$884$		0			0
$885$	0.146241	+	0.253296i	0.00491582	+	0.00851446i
$886$		0			0
$887$	−26.7417			−0.897897			−0.448948	−	0.893558i	$-0.648201\pi$
$887$	−26.7417			−0.897897			−0.448948	+	0.893558i	$0.648201\pi$
$888$		0			0
$889$	−0.117801			−0.00395091
$890$		0			0
$891$	−7.81284	−	13.5322i	−0.261740	−	0.453347i
$892$		0			0
$893$	−26.7310	−	46.2994i	−0.894519	−	1.54935i
$894$		0			0
$895$	12.0209	+	20.8208i	0.401814	+	0.695962i
$896$		0			0
$897$	31.3611	−	54.3191i	1.04712	−	1.81366i
$898$		0			0
$899$	19.5105			0.650711
$900$		0			0
$901$	3.25707	+	5.64142i	0.108509	+	0.187943i
$902$		0			0
$903$	−21.6277	+	37.4602i	−0.719723	+	1.24660i
$904$		0			0
$905$	4.99453	−	8.65078i	0.166024	−	0.287562i
$906$		0			0
$907$	4.66980	+	8.08832i	0.155058	+	0.268568i	0.933080	−	0.359668i	$-0.117110\pi$
$907$	4.66980	+	8.08832i	0.155058	+	0.268568i	−0.778022	+	0.628237i	$0.783777\pi$
$908$		0			0
$909$	0.552113	−	0.956287i	0.0183124	−	0.0317180i
$910$		0			0
$911$	22.6135			0.749219			0.374609	−	0.927183i	$-0.377777\pi$
$911$	22.6135			0.749219			0.374609	+	0.927183i	$0.377777\pi$
$912$		0			0
$913$	6.53402	−	11.3173i	0.216244	−	0.374546i
$914$		0			0
$915$	−26.8542			−0.887771
$916$		0			0
$917$	−56.5034			−1.86591
$918$		0			0
$919$	−24.5941			−0.811283			−0.405641	−	0.914032i	$-0.632952\pi$
$919$	−24.5941			−0.811283			−0.405641	+	0.914032i	$0.632952\pi$
$920$		0			0
$921$	−21.1197	−	36.5804i	−0.695917	−	1.20536i
$922$		0			0
$923$	−31.8355	+	55.1407i	−1.04788	+	1.81498i
$924$		0			0
$925$	−3.43925	+	5.01713i	−0.113082	+	0.164962i
$926$		0			0
$927$	−13.8762	+	24.0343i	−0.455755	+	0.789392i
$928$		0			0
$929$	−10.6533	−	18.4521i	−0.349524	−	0.605393i	0.636641	−	0.771160i	$-0.280323\pi$
$929$	−10.6533	−	18.4521i	−0.349524	−	0.605393i	−0.986165	+	0.165767i	$0.946990\pi$
$930$		0			0
$931$	8.85299			0.290145
$932$		0			0
$933$	2.66150			0.0871335
$934$		0			0
$935$	−17.2127			−0.562914
$936$		0			0
$937$	13.8037	−	23.9087i	0.450946	−	0.781062i	−0.547499	−	0.836807i	$-0.684420\pi$
$937$	13.8037	−	23.9087i	0.450946	−	0.781062i	0.998445	+	0.0557444i	$0.0177532\pi$
$938$		0			0
$939$	−67.2660			−2.19514
$940$		0			0
$941$	−14.2776	+	24.7294i	−0.465435	+	0.806157i	−0.999221	−	0.0394627i	$-0.987435\pi$
$941$	−14.2776	+	24.7294i	−0.465435	+	0.806157i	0.533786	+	0.845619i	$0.320769\pi$
$942$		0			0
$943$	−26.8400	−	46.4882i	−0.874030	−	1.51386i
$944$		0			0
$945$	−3.85249	+	6.67270i	−0.125321	+	0.217063i
$946$		0			0
$947$	4.89437	−	8.47730i	0.159046	−	0.275475i	−0.775479	−	0.631373i	$-0.782492\pi$
$947$	4.89437	−	8.47730i	0.159046	−	0.275475i	0.934525	+	0.355898i	$0.115825\pi$
$948$		0			0
$949$	−9.00629	−	15.5994i	−0.292357	−	0.506376i
$950$		0			0
$951$	−2.57246			−0.0834179
$952$		0			0
$953$	21.2457	−	36.7986i	0.688215	−	1.19202i	−0.284200	−	0.958765i	$-0.591728\pi$
$953$	21.2457	−	36.7986i	0.688215	−	1.19202i	0.972415	−	0.233258i	$-0.0749387\pi$
$954$		0			0
$955$	4.21199	+	7.29538i	0.136297	+	0.236073i
$956$		0			0
$957$	−35.3359	−	61.2036i	−1.14225	−	1.97843i
$958$		0			0
$959$	13.4704	+	23.3314i	0.434982	+	0.753412i
$960$		0			0
$961$	−25.5832			−0.825266
$962$		0			0
$963$	−12.4009			−0.399613
$964$		0			0
$965$	8.32189	+	14.4139i	0.267891	+	0.464001i
$966$		0			0
$967$	−9.28643	−	16.0846i	−0.298631	−	0.517245i	0.677192	−	0.735807i	$-0.263197\pi$
$967$	−9.28643	−	16.0846i	−0.298631	−	0.517245i	−0.975823	+	0.218562i	$0.929863\pi$
$968$		0			0
$969$	54.4772	+	94.3572i	1.75006	+	3.03119i
$970$		0			0
$971$	−7.22464	+	12.5134i	−0.231850	+	0.401575i	−0.958352	−	0.285588i	$-0.907811\pi$
$971$	−7.22464	+	12.5134i	−0.231850	+	0.401575i	0.726503	+	0.687163i	$0.241144\pi$
$972$		0			0
$973$	−22.2808			−0.714290
$974$		0			0
$975$	−5.19268	−	8.99398i	−0.166299	−	0.288038i
$976$		0			0
$977$	−0.757674	+	1.31233i	−0.0242402	+	0.0419852i	−0.877891	−	0.478860i	$-0.841050\pi$
$977$	−0.757674	+	1.31233i	−0.0242402	+	0.0419852i	0.853651	+	0.520846i	$0.174383\pi$
$978$		0			0
$979$	0.850866	−	1.47374i	0.0271938	−	0.0471010i
$980$		0			0
$981$	16.1384	+	27.9525i	0.515259	+	0.892455i
$982$		0			0
$983$	0.0864348	−	0.149710i	0.00275684	−	0.00477499i	−0.864644	−	0.502386i	$-0.832456\pi$
$983$	0.0864348	−	0.149710i	0.00275684	−	0.00477499i	0.867401	+	0.497611i	$0.165789\pi$
$984$		0			0
$985$	−5.60797			−0.178685
$986$		0			0
$987$	26.6097	−	46.0893i	0.846996	−	1.46704i
$988$		0			0
$989$	34.5126			1.09744
$990$		0			0
$991$	−14.2431			−0.452446			−0.226223	−	0.974076i	$-0.572638\pi$
$991$	−14.2431			−0.452446			−0.226223	+	0.974076i	$0.572638\pi$
$992$		0			0
$993$	31.4801			0.998990
$994$		0			0
$995$	−5.18907	−	8.98773i	−0.164505	−	0.284930i
$996$		0			0
$997$	−4.15271	+	7.19270i	−0.131518	+	0.227795i	−0.924262	−	0.381759i	$-0.875318\pi$
$997$	−4.15271	+	7.19270i	−0.131518	+	0.227795i	0.792744	+	0.609554i	$0.208652\pi$
$998$		0			0
$999$	16.3536	+	1.26715i	0.517405	+	0.0400910i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.i.b.121.1	✓	14
37.26	even	3	inner	740.2.i.b.581.1	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.i.b.121.1	✓	14	1.1	even	1	trivial
740.2.i.b.581.1	yes	14	37.26	even	3	inner

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:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32457 - 2.29422i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.42866 + 2.47451i) q^{7} +(-2.00895 + 3.47961i) q^{9} -3.18233 q^{11} +(-1.96014 - 3.39506i) q^{13} +(1.32457 - 2.29422i) q^{15} +(2.70441 - 4.68418i) q^{17} +(-3.80196 - 6.58519i) q^{19} +(3.78471 - 6.55531i) q^{21} -6.03949 q^{23} +(-0.500000 + 0.866025i) q^{25} +2.69657 q^{27} -8.38297 q^{29} -2.32739 q^{31} +(4.21521 + 7.30095i) q^{33} +(-1.42866 + 2.47451i) q^{35} +(6.06458 + 0.469912i) q^{37} +(-5.19268 + 8.99398i) q^{39} +(4.44408 + 7.69737i) q^{41} -5.71448 q^{43} -4.01791 q^{45} +7.03084 q^{47} +(-0.582133 + 1.00828i) q^{49} -14.3287 q^{51} +(-0.602178 + 1.04300i) q^{53} +(-1.59116 - 2.75598i) q^{55} +(-10.0719 + 17.4450i) q^{57} +(-0.0552032 + 0.0956147i) q^{59} +(-5.06848 - 8.77887i) q^{61} -11.4804 q^{63} +(1.96014 - 3.39506i) q^{65} +(2.26921 + 3.93039i) q^{67} +(7.99971 + 13.8559i) q^{69} +(-8.12072 - 14.0655i) q^{71} +4.59471 q^{73} +2.64913 q^{75} +(-4.54646 - 7.87470i) q^{77} +(-8.35973 - 14.4795i) q^{79} +(2.45507 + 4.25230i) q^{81} +(-2.05322 + 3.55628i) q^{83} +5.40883 q^{85} +(11.1038 + 19.2324i) q^{87} +(-0.267372 + 0.463102i) q^{89} +(5.60075 - 9.70078i) q^{91} +(3.08279 + 5.33955i) q^{93} +(3.80196 - 6.58519i) q^{95} +5.70522 q^{97} +(6.39315 - 11.0733i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 7 q^{5} - 2 q^{7} - 5 q^{9} - 10 q^{11} - 2 q^{13} - 5 q^{17} - 8 q^{19} + 9 q^{21} + 8 q^{23} - 7 q^{25} - 18 q^{27} - 4 q^{29} + 16 q^{31} - 7 q^{33} + 2 q^{35} + 4 q^{37} + 13 q^{39} + 9 q^{41}+ \cdots + 26 q^{99}+O(q^{100}) \) 14 * q + 7 * q^5 - 2 * q^7 - 5 * q^9 - 10 * q^11 - 2 * q^13 - 5 * q^17 - 8 * q^19 + 9 * q^21 + 8 * q^23 - 7 * q^25 - 18 * q^27 - 4 * q^29 + 16 * q^31 - 7 * q^33 + 2 * q^35 + 4 * q^37 + 13 * q^39 + 9 * q^41 + 22 * q^43 - 10 * q^45 + 36 * q^47 - 7 * q^49 - 62 * q^51 + 2 * q^53 - 5 * q^55 - 38 * q^57 + 12 * q^59 - 20 * q^61 - 38 * q^63 + 2 * q^65 + 12 * q^67 + q^69 - 13 * q^71 - 12 * q^73 - q^77 - 21 * q^79 - 11 * q^81 + 7 * q^83 - 10 * q^85 + 41 * q^87 + 16 * q^89 - 6 * q^91 - 3 * q^93 + 8 * q^95 - 6 * q^97 + 26 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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