LMFDB - Embedded newform 540.2.be.a.11.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [540,2,Mod(11,540)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(540, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("540.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.be (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$432$
Relative dimension:	$72$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.19
Character	$\chi$	$=$	540.11
Dual form			540.2.be.a.491.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.992140 - 1.00780i) q^{2} +(1.73090 - 0.0631559i) q^{3} +(-0.0313148 + 1.99975i) q^{4} +(-0.342020 + 0.939693i) q^{5} +(-1.78094 - 1.68174i) q^{6} +(3.02663 + 0.533676i) q^{7} +(2.04642 - 1.95248i) q^{8} +(2.99202 - 0.218633i) q^{9} +(1.28635 - 0.587620i) q^{10} +(-0.256231 + 0.0932606i) q^{11} +(0.0720935 + 3.46335i) q^{12} +(-0.913826 + 0.766791i) q^{13} +(-2.46500 - 3.57971i) q^{14} +(-0.532655 + 1.64811i) q^{15} +(-3.99804 - 0.125244i) q^{16} +(-5.70507 + 3.29383i) q^{17} +(-3.18884 - 2.79844i) q^{18} +(4.77468 + 2.75666i) q^{19} +(-1.86844 - 0.713383i) q^{20} +(5.27249 + 0.732590i) q^{21} +(0.348205 + 0.165702i) q^{22} +(0.175183 + 0.993514i) q^{23} +(3.41883 - 3.50879i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(1.67942 + 0.160188i) q^{26} +(5.16508 - 0.567395i) q^{27} +(-1.16200 + 6.03580i) q^{28} +(3.81345 - 4.54470i) q^{29} +(2.18943 - 1.09835i) q^{30} +(2.75489 - 0.485761i) q^{31} +(3.84040 + 4.15348i) q^{32} +(-0.437621 + 0.177607i) q^{33} +(8.97975 + 2.48163i) q^{34} +(-1.53666 + 2.66157i) q^{35} +(0.343518 + 5.99016i) q^{36} +(2.75776 + 4.77658i) q^{37} +(-1.95899 - 7.54691i) q^{38} +(-1.53331 + 1.38495i) q^{39} +(1.13481 + 2.59079i) q^{40} +(0.739225 + 0.880975i) q^{41} +(-4.49275 - 6.04044i) q^{42} +(-2.78321 - 7.64682i) q^{43} +(-0.178474 - 0.515320i) q^{44} +(-0.817884 + 2.88636i) q^{45} +(0.827455 - 1.16226i) q^{46} +(1.32789 - 7.53084i) q^{47} +(-6.92811 + 0.0357152i) q^{48} +(2.29781 + 0.836334i) q^{49} +(0.112223 + 1.40975i) q^{50} +(-9.66688 + 6.06159i) q^{51} +(-1.50478 - 1.85144i) q^{52} -4.57133i q^{53} +(-5.69631 - 4.64242i) q^{54} -0.272676i q^{55} +(7.23573 - 4.81730i) q^{56} +(8.43859 + 4.46996i) q^{57} +(-8.36362 + 0.665786i) q^{58} +(-11.7816 - 4.28815i) q^{59} +(-3.27914 - 1.11679i) q^{60} +(-2.35317 + 13.3455i) q^{61} +(-3.22279 - 2.29443i) q^{62} +(9.17241 + 0.935050i) q^{63} +(0.375655 - 7.99118i) q^{64} +(-0.408001 - 1.12097i) q^{65} +(0.613173 + 0.264822i) q^{66} +(-2.27211 - 2.70779i) q^{67} +(-6.40819 - 11.5119i) q^{68} +(0.365971 + 1.70861i) q^{69} +(4.20691 - 1.09201i) q^{70} +(3.88602 + 6.73079i) q^{71} +(5.69605 - 6.28927i) q^{72} +(4.34479 - 7.52539i) q^{73} +(2.07774 - 7.51830i) q^{74} +(-1.36654 - 1.06422i) q^{75} +(-5.66217 + 9.46186i) q^{76} +(-0.825287 + 0.145520i) q^{77} +(2.91701 + 0.171204i) q^{78} +(8.77467 - 10.4572i) q^{79} +(1.48510 - 3.71409i) q^{80} +(8.90440 - 1.30831i) q^{81} +(0.154429 - 1.61904i) q^{82} +(-3.86041 - 3.23927i) q^{83} +(-1.63011 + 10.5207i) q^{84} +(-1.14393 - 6.48757i) q^{85} +(-4.94511 + 10.3916i) q^{86} +(6.31368 - 8.10726i) q^{87} +(-0.342267 + 0.691136i) q^{88} +(9.53204 + 5.50333i) q^{89} +(3.72032 - 2.03941i) q^{90} +(-3.17503 + 1.83310i) q^{91} +(-1.99227 + 0.319212i) q^{92} +(4.73776 - 1.01479i) q^{93} +(-8.90702 + 6.13340i) q^{94} +(-4.22345 + 3.54390i) q^{95} +(6.90965 + 6.94670i) q^{96} +(-15.7222 + 5.72241i) q^{97} +(-1.43689 - 3.14549i) q^{98} +(-0.746260 + 0.335058i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) $ 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	−0.992140	−	1.00780i	−0.701549	−	0.712621i
$2$	−0.992140	−	1.00780i	−0.701549	−	0.712621i
$3$	1.73090	−	0.0631559i	0.999335	−	0.0364631i
$3$	1.73090	−	0.0631559i	0.999335	−	0.0364631i
$4$	−0.0313148	+	1.99975i	−0.0156574	+	0.999877i
$5$	−0.342020	+	0.939693i	−0.152956	+	0.420243i
$5$	−0.342020	+	0.939693i	−0.152956	+	0.420243i
$6$	−1.78094	−	1.68174i	−0.727067	−	0.686566i
$7$	3.02663	+	0.533676i	1.14396	+	0.201711i	0.713336	−	0.700822i	$-0.247183\pi$
$7$	3.02663	+	0.533676i	1.14396	+	0.201711i	0.430621	+	0.902533i	$0.358294\pi$
$8$	2.04642	−	1.95248i	0.723518	−	0.690305i
$9$	2.99202	−	0.218633i	0.997341	−	0.0728776i
$10$	1.28635	−	0.587620i	0.406780	−	0.185822i
$11$	−0.256231	+	0.0932606i	−0.0772567	+	0.0281191i	−0.380359	−	0.924839i	$-0.624200\pi$
$11$	−0.256231	+	0.0932606i	−0.0772567	+	0.0281191i	0.303103	+	0.952958i	$0.401977\pi$
$12$	0.0720935	+	3.46335i	0.0208116	+	0.999783i
$13$	−0.913826	+	0.766791i	−0.253450	+	0.212670i	−0.760656	−	0.649155i	$-0.775123\pi$
$13$	−0.913826	+	0.766791i	−0.253450	+	0.212670i	0.507206	+	0.861825i	$0.330678\pi$
$14$	−2.46500	−	3.57971i	−0.658799	−	0.956718i
$15$	−0.532655	+	1.64811i	−0.137531	+	0.425541i
$16$	−3.99804	−	0.125244i	−0.999510	−	0.0313110i
$17$	−5.70507	+	3.29383i	−1.38368	+	0.798870i	−0.992594	−	0.121482i	$-0.961235\pi$
$17$	−5.70507	+	3.29383i	−1.38368	+	0.798870i	−0.391090	+	0.920352i	$0.627902\pi$
$18$	−3.18884	−	2.79844i	−0.751618	−	0.659599i
$19$	4.77468	+	2.75666i	1.09539	+	0.632422i	0.935005	−	0.354633i	$-0.115394\pi$
$19$	4.77468	+	2.75666i	1.09539	+	0.632422i	0.160381	+	0.987055i	$0.448728\pi$
$20$	−1.86844	−	0.713383i	−0.417797	−	0.159517i
$21$	5.27249	+	0.732590i	1.15055	+	0.159864i
$22$	0.348205	+	0.165702i	0.0742376	+	0.0353278i
$23$	0.175183	+	0.993514i	0.0365283	+	0.207162i	0.997609	−	0.0691040i	$-0.0220140\pi$
$23$	0.175183	+	0.993514i	0.0365283	+	0.207162i	−0.961081	+	0.276266i	$0.910903\pi$
$24$	3.41883	−	3.50879i	0.697866	−	0.716228i
$25$	−0.766044	−	0.642788i	−0.153209	−	0.128558i
$26$	1.67942	+	0.160188i	0.329360	+	0.0314154i
$27$	5.16508	−	0.567395i	0.994020	−	0.109195i
$28$	−1.16200	+	6.03580i	−0.219597	+	1.14066i
$29$	3.81345	−	4.54470i	0.708141	−	0.843929i	−0.285281	−	0.958444i	$-0.592087\pi$
$29$	3.81345	−	4.54470i	0.708141	−	0.843929i	0.993422	+	0.114515i	$0.0365313\pi$
$30$	2.18943	−	1.09835i	0.399734	−	0.200531i
$31$	2.75489	−	0.485761i	0.494793	−	0.0872453i	0.0793167	−	0.996849i	$-0.474726\pi$
$31$	2.75489	−	0.485761i	0.494793	−	0.0872453i	0.415476	+	0.909604i	$0.363615\pi$
$32$	3.84040	+	4.15348i	0.678892	+	0.734238i
$33$	−0.437621	+	0.177607i	−0.0761800	+	0.0309174i
$34$	8.97975	+	2.48163i	1.54001	+	0.425595i
$35$	−1.53666	+	2.66157i	−0.259743	+	0.449888i
$36$	0.343518	+	5.99016i	0.0572529	+	0.998360i
$37$	2.75776	+	4.77658i	0.453373	+	0.785265i	0.998593	−	0.0530281i	$-0.0168873\pi$
$37$	2.75776	+	4.77658i	0.453373	+	0.785265i	−0.545220	+	0.838293i	$0.683554\pi$
$38$	−1.95899	−	7.54691i	−0.317791	−	1.22427i
$39$	−1.53331	+	1.38495i	−0.245527	+	0.221770i
$40$	1.13481	+	2.59079i	0.179430	+	0.409640i
$41$	0.739225	+	0.880975i	0.115448	+	0.137585i	0.820673	−	0.571398i	$-0.193599\pi$
$41$	0.739225	+	0.880975i	0.115448	+	0.137585i	−0.705226	+	0.708983i	$0.749154\pi$
$42$	−4.49275	−	6.04044i	−0.693246	−	0.932060i
$43$	−2.78321	−	7.64682i	−0.424436	−	1.16613i	−0.949143	−	0.314846i	$-0.898047\pi$
$43$	−2.78321	−	7.64682i	−0.424436	−	1.16613i	0.524707	−	0.851283i	$-0.324175\pi$
$44$	−0.178474	−	0.515320i	−0.0269060	−	0.0776875i
$45$	−0.817884	+	2.88636i	−0.121923	+	0.430273i
$46$	0.827455	−	1.16226i	0.122002	−	0.171365i
$47$	1.32789	−	7.53084i	0.193693	−	1.09849i	−0.720576	−	0.693376i	$-0.756122\pi$
$47$	1.32789	−	7.53084i	0.193693	−	1.09849i	0.914268	−	0.405109i	$-0.132766\pi$
$48$	−6.92811	+	0.0357152i	−0.999987	+	0.00515504i
$49$	2.29781	+	0.836334i	0.328258	+	0.119476i
$50$	0.112223	+	1.40975i	0.0158708	+	0.199369i
$51$	−9.66688	+	6.06159i	−1.35363	+	0.848792i
$52$	−1.50478	−	1.85144i	−0.208675	−	0.256749i
$53$		−	4.57133i		−	0.627920i	−0.949436	−	0.313960i	$-0.898344\pi$
$53$		−	4.57133i		−	0.627920i	0.949436	−	0.313960i	$-0.101656\pi$
$54$	−5.69631	−	4.64242i	−0.775169	−	0.631754i
$55$		−	0.272676i		−	0.0367676i
$56$	7.23573	−	4.81730i	0.966916	−	0.643739i
$57$	8.43859	+	4.46996i	1.11772	+	0.592060i
$58$	−8.36362	+	0.665786i	−1.09820	+	0.0874219i
$59$	−11.7816	−	4.28815i	−1.53383	−	0.558270i	−0.569277	−	0.822146i	$-0.692777\pi$
$59$	−11.7816	−	4.28815i	−1.53383	−	0.558270i	−0.964557	+	0.263876i	$0.914999\pi$
$60$	−3.27914	−	1.11679i	−0.423336	−	0.144177i
$61$	−2.35317	+	13.3455i	−0.301292	+	1.70871i	0.339171	+	0.940725i	$0.389854\pi$
$61$	−2.35317	+	13.3455i	−0.301292	+	1.70871i	−0.640463	+	0.767989i	$0.721258\pi$
$62$	−3.22279	−	2.29443i	−0.409294	−	0.291393i
$63$	9.17241	+	0.935050i	1.15562	+	0.117805i
$64$	0.375655	−	7.99118i	0.0469568	−	0.998897i
$65$	−0.408001	−	1.12097i	−0.0506063	−	0.139040i
$66$	0.613173	+	0.264822i	0.0754764	+	0.0325973i
$67$	−2.27211	−	2.70779i	−0.277582	−	0.330810i	0.609183	−	0.793030i	$-0.291497\pi$
$67$	−2.27211	−	2.70779i	−0.277582	−	0.330810i	−0.886765	+	0.462220i	$0.847053\pi$
$68$	−6.40819	−	11.5119i	−0.777107	−	1.39602i
$69$	0.365971	+	1.70861i	0.0440577	+	0.205692i
$70$	4.20691	−	1.09201i	0.502822	−	0.130520i
$71$	3.88602	+	6.73079i	0.461186	+	0.798798i	0.999020	−	0.0442528i	$-0.0140907\pi$
$71$	3.88602	+	6.73079i	0.461186	+	0.798798i	−0.537834	+	0.843051i	$0.680757\pi$
$72$	5.69605	−	6.28927i	0.671286	−	0.741198i
$73$	4.34479	−	7.52539i	0.508519	−	0.880780i	−0.491433	−	0.870916i	$-0.663527\pi$
$73$	4.34479	−	7.52539i	0.508519	−	0.880780i	0.999951	−	0.00986458i	$-0.00314004\pi$
$74$	2.07774	−	7.51830i	0.241533	−	0.873985i
$75$	−1.36654	−	1.06422i	−0.157795	−	0.122886i
$76$	−5.66217	+	9.46186i	−0.649495	+	1.08535i
$77$	−0.825287	+	0.145520i	−0.0940502	+	0.0165836i
$78$	2.91701	+	0.171204i	0.330287	+	0.0193851i
$79$	8.77467	−	10.4572i	0.987227	−	1.17653i	0.00293291	−	0.999996i	$-0.499066\pi$
$79$	8.77467	−	10.4572i	0.987227	−	1.17653i	0.984294	−	0.176536i	$-0.0564891\pi$
$80$	1.48510	−	3.71409i	0.166039	−	0.415248i
$81$	8.90440	−	1.30831i	0.989378	−	0.145368i
$82$	0.154429	−	1.61904i	0.0170539	−	0.178793i
$83$	−3.86041	−	3.23927i	−0.423736	−	0.355556i	0.405846	−	0.913941i	$-0.366977\pi$
$83$	−3.86041	−	3.23927i	−0.423736	−	0.355556i	−0.829582	+	0.558385i	$0.811421\pi$
$84$	−1.63011	+	10.5207i	−0.177859	+	1.14791i
$85$	−1.14393	−	6.48757i	−0.124077	−	0.703676i
$86$	−4.94511	+	10.3916i	−0.533245	+	1.12056i
$87$	6.31368	−	8.10726i	0.676898	−	0.869189i
$88$	−0.342267	+	0.691136i	−0.0364858	+	0.0736754i
$89$	9.53204	+	5.50333i	1.01039	+	0.583351i	0.911307	−	0.411727i	$-0.135074\pi$
$89$	9.53204	+	5.50333i	1.01039	+	0.583351i	0.0990872	+	0.995079i	$0.468408\pi$
$90$	3.72032	−	2.03941i	0.392157	−	0.214973i
$91$	−3.17503	+	1.83310i	−0.332833	+	0.192161i
$92$	−1.99227	+	0.319212i	−0.207709	+	0.0332802i
$93$	4.73776	−	1.01479i	0.491282	−	0.105229i
$94$	−8.90702	+	6.13340i	−0.918689	+	0.632612i
$95$	−4.22345	+	3.54390i	−0.433317	+	0.363596i
$96$	6.90965	+	6.94670i	0.705213	+	0.708995i
$97$	−15.7222	+	5.72241i	−1.59635	+	0.581022i	−0.978675	−	0.205415i	$-0.934146\pi$
$97$	−15.7222	+	5.72241i	−1.59635	+	0.581022i	−0.617671	+	0.786437i	$0.711924\pi$
$98$	−1.43689	−	3.14549i	−0.145148	−	0.317742i
$99$	−0.746260	+	0.335058i	−0.0750020	+	0.0336746i
$100$	1.30941	−	1.51177i	0.130941	−	0.151177i
$101$	−0.826436	−	0.145723i	−0.0822335	−	0.0145000i	0.132380	−	0.991199i	$-0.457738\pi$
$101$	−0.826436	−	0.145723i	−0.0822335	−	0.0145000i	−0.214613	+	0.976699i	$0.568849\pi$
$102$	15.6998	+	3.72832i	1.55451	+	0.369159i
$103$	0.226636	−	0.622678i	0.0223311	−	0.0613542i	−0.928026	−	0.372515i	$-0.878496\pi$
$103$	0.226636	−	0.622678i	0.0223311	−	0.0613542i	0.950357	+	0.311161i	$0.100718\pi$
$104$	−0.372927	+	3.35340i	−0.0365685	+	0.328828i
$105$	−2.49171	+	4.70396i	−0.243166	+	0.459059i
$106$	−4.60698	+	4.53540i	−0.447469	+	0.440517i
$107$	−13.5654			−1.31141			−0.655707	−	0.755016i	$-0.727629\pi$
$107$	−13.5654			−1.31141			−0.655707	+	0.755016i	$0.727629\pi$
$108$	0.972908	+	10.3467i	0.0936181	+	0.995608i
$109$	1.82045			0.174368			0.0871840	−	0.996192i	$-0.472213\pi$
$109$	1.82045			0.174368			0.0871840	+	0.996192i	$0.472213\pi$
$110$	−0.274802	+	0.270533i	−0.0262014	+	0.0257943i
$111$	5.07507	+	8.09361i	0.481704	+	0.768211i
$112$	−12.0337	−	2.51272i	−1.13708	−	0.237430i
$113$	6.06096	−	16.6524i	0.570168	−	1.56652i	−0.234073	−	0.972219i	$-0.575206\pi$
$113$	6.06096	−	16.6524i	0.570168	−	1.56652i	0.804241	−	0.594303i	$-0.202572\pi$
$114$	−3.86745	−	12.9392i	−0.362220	−	1.21187i
$115$	−0.993514	−	0.175183i	−0.0926457	−	0.0163359i
$116$	8.96886	+	7.76829i	0.832738	+	0.721268i
$117$	−2.56654	+	2.49405i	−0.237277	+	0.230575i
$118$	7.36741	+	16.1279i	0.678225	+	1.48470i
$119$	−19.0250	+	6.92452i	−1.74402	+	0.634770i
$120$	2.12787	+	4.41273i	0.194247	+	0.402825i
$121$	−8.36953	+	7.02287i	−0.760867	+	0.638443i
$122$	15.7842	−	10.8691i	1.42904	−	0.984039i
$123$	1.33516	+	1.47819i	0.120388	+	0.133284i
$124$	0.885135	+	5.52431i	0.0794874	+	0.496098i
$125$	0.866025	−	0.500000i	0.0774597	−	0.0447214i
$126$	−8.15798	−	10.1716i	−0.726771	−	0.906162i
$127$	−2.61481	−	1.50966i	−0.232027	−	0.133961i	0.379480	−	0.925200i	$-0.376103\pi$
$127$	−2.61481	−	1.50966i	−0.232027	−	0.133961i	−0.611507	+	0.791239i	$0.709436\pi$
$128$	−8.42620	+	7.54978i	−0.744777	+	0.667313i
$129$	−5.30040	−	13.0601i	−0.466674	−	1.14988i
$130$	−0.724921	+	1.52335i	−0.0635798	+	0.133606i
$131$	0.306184	+	1.73646i	0.0267514	+	0.151715i	0.995258	−	0.0972748i	$-0.0310126\pi$
$131$	0.306184	+	1.73646i	0.0267514	+	0.151715i	−0.968506	+	0.248990i	$0.919901\pi$
$132$	−0.341467	−	0.880696i	−0.0297209	−	0.0766547i
$133$	12.9800	+	10.8915i	1.12551	+	0.944414i
$134$	−0.474659	+	4.97634i	−0.0410043	+	0.429890i
$135$	−1.23338	+	5.04765i	−0.106153	+	0.434432i
$136$	−5.24384	+	17.8796i	−0.449656	+	1.53316i
$137$	−7.01129	+	8.35573i	−0.599015	+	0.713878i	−0.977312	−	0.211806i	$-0.932065\pi$
$137$	−7.01129	+	8.35573i	−0.599015	+	0.713878i	0.378297	+	0.925684i	$0.376510\pi$
$138$	1.35884	−	2.06400i	0.115672	−	0.175700i
$139$	−18.5220	+	3.26592i	−1.57101	+	0.277012i	−0.890243	−	0.455485i	$-0.849466\pi$
$139$	−18.5220	+	3.26592i	−1.57101	+	0.277012i	−0.680770	+	0.732497i	$0.738355\pi$
$140$	−5.27437	−	3.15629i	−0.445765	−	0.266755i
$141$	1.82283	−	13.1190i	0.153510	−	1.10482i
$142$	2.92780	−	10.5942i	0.245695	−	0.889047i
$143$	0.162640	−	0.281700i	0.0136006	−	0.0235569i
$144$	−11.9896	+	0.499370i	−0.999134	+	0.0416142i
$145$	2.96634	+	5.13785i	0.246341	+	0.426675i
$146$	−11.8947	+	3.08758i	−0.984413	+	0.255530i
$147$	4.03009	+	1.30249i	0.332396	+	0.107428i
$148$	−9.63835	+	5.36526i	−0.792267	+	0.441022i
$149$	−3.43705	−	4.09611i	−0.281574	−	0.335566i	0.606657	−	0.794963i	$-0.292510\pi$
$149$	−3.43705	−	4.09611i	−0.281574	−	0.335566i	−0.888231	+	0.459397i	$0.848066\pi$
$150$	0.283282	+	2.43305i	0.0231298	+	0.198658i
$151$	−5.57086	−	15.3058i	−0.453350	−	1.24557i	−0.930352	−	0.366667i	$-0.880499\pi$
$151$	−5.57086	−	15.3058i	−0.453350	−	1.24557i	0.477002	−	0.878902i	$-0.341724\pi$
$152$	15.1533	−	3.68118i	1.22910	−	0.298583i
$153$	−16.3496	+	11.1025i	−1.32178	+	0.897585i
$154$	0.965456	+	0.687347i	0.0777987	+	0.0553880i
$155$	−0.485761	+	2.75489i	−0.0390173	+	0.221278i
$156$	−2.72155	−	3.10962i	−0.217898	−	0.248969i
$157$	−16.5568	−	6.02617i	−1.32137	−	0.480941i	−0.417476	−	0.908688i	$-0.637085\pi$
$157$	−16.5568	−	6.02617i	−1.32137	−	0.480941i	−0.903898	+	0.427747i	$0.859307\pi$
$158$	−19.2445	+	1.53196i	−1.53101	+	0.121876i
$159$	−0.288706	−	7.91251i	−0.0228959	−	0.627503i
$160$	−5.21648	+	2.18822i	−0.412399	+	0.172994i
$161$			3.10049i			0.244353i
$162$	−10.1529	−	7.67581i	−0.797689	−	0.603069i
$163$		−	4.39155i		−	0.343973i	−0.985099	−	0.171986i	$-0.944982\pi$
$163$		−	4.39155i		−	0.343973i	0.985099	−	0.171986i	$-0.0550185\pi$
$164$	−1.78488	+	1.45068i	−0.139376	+	0.113279i
$165$	−0.0172211	−	0.471974i	−0.00134066	−	0.0367431i
$166$	0.565540	+	7.10433i	0.0438944	+	0.551403i
$167$	13.0785	+	4.76018i	1.01204	+	0.368354i	0.794218	−	0.607634i	$-0.207881\pi$
$167$	13.0785	+	4.76018i	1.01204	+	0.368354i	0.217827	+	0.975987i	$0.430103\pi$
$168$	12.2201	−	8.79524i	0.942800	−	0.678567i
$169$	−2.01032	+	11.4011i	−0.154640	+	0.877006i
$170$	−5.40322	+	7.58944i	−0.414408	+	0.582083i
$171$	14.8886	+	7.20409i	1.13856	+	0.550911i
$172$	15.3789	−	5.32629i	1.17263	−	0.406125i
$173$	2.37693	+	6.53056i	0.180715	+	0.496509i	0.996664	−	0.0816142i	$-0.0260075\pi$
$173$	2.37693	+	6.53056i	0.180715	+	0.496509i	−0.815949	+	0.578123i	$0.803785\pi$
$174$	−14.4345	+	1.68062i	−1.09428	+	0.127407i
$175$	−1.97549	−	2.35430i	−0.149333	−	0.177968i
$176$	1.03610	−	0.340768i	0.0780992	−	0.0256864i
$177$	−20.6636	−	6.67828i	−1.55317	−	0.501970i
$178$	−3.91088	−	15.0664i	−0.293133	−	1.12928i
$179$	8.03508	+	13.9172i	0.600570	+	1.04022i	0.992735	+	0.120323i	$0.0383931\pi$
$179$	8.03508	+	13.9172i	0.600570	+	1.04022i	−0.392165	+	0.919895i	$0.628274\pi$
$180$	−5.74640	−	1.72595i	−0.428311	−	0.128645i
$181$	3.13911	−	5.43710i	0.233328	−	0.404136i	−0.725457	−	0.688267i	$-0.758372\pi$
$181$	3.13911	−	5.43710i	0.233328	−	0.404136i	0.958785	+	0.284131i	$0.0917050\pi$
$182$	4.99747	+	1.38109i	0.370437	+	0.102373i
$183$	−3.23025	+	23.2483i	−0.238787	+	1.71856i
$184$	2.29831	+	1.69110i	0.169434	+	0.124670i
$185$	−5.43173	+	0.957760i	−0.399348	+	0.0704159i
$186$	−5.72322	−	3.76789i	−0.419647	−	0.276275i
$187$	1.15463	−	1.37604i	0.0844352	−	0.100626i
$188$	15.0182	+	2.89128i	1.09532	+	0.210868i
$189$	15.9356	+	1.03919i	1.15914	+	0.0755897i
$190$	7.76179	+	0.740344i	0.563099	+	0.0537102i
$191$	3.59370	+	3.01548i	0.260031	+	0.218192i	0.763478	−	0.645834i	$-0.223490\pi$
$191$	3.59370	+	3.01548i	0.260031	+	0.218192i	−0.503446	+	0.864027i	$0.667935\pi$
$192$	0.145531	−	13.8556i	0.0105028	−	0.999945i
$193$	−3.73527	−	21.1838i	−0.268871	−	1.52484i	−0.757781	−	0.652509i	$-0.773717\pi$
$193$	−3.73527	−	21.1838i	−0.268871	−	1.52484i	0.488910	−	0.872334i	$-0.337395\pi$
$194$	21.3656	+	10.1674i	1.53396	+	0.729974i
$195$	−0.777005	−	1.91453i	−0.0556425	−	0.137102i
$196$	−1.74442	+	4.56886i	−0.124601	+	0.326347i
$197$	−18.7167	−	10.8061i	−1.33351	−	0.769902i	−0.347674	−	0.937616i	$-0.613028\pi$
$197$	−18.7167	−	10.8061i	−1.33351	−	0.769902i	−0.985836	+	0.167714i	$0.946362\pi$
$198$	1.07807	+	0.419655i	0.0766148	+	0.0298236i
$199$	16.2157	−	9.36214i	1.14950	−	0.663664i	0.200735	−	0.979646i	$-0.435667\pi$
$199$	16.2157	−	9.36214i	1.14950	−	0.663664i	0.948765	+	0.315981i	$0.102334\pi$
$200$	−2.82268	+	0.180273i	−0.199593	+	0.0127472i
$201$	−4.10380	−	4.54342i	−0.289460	−	0.320468i
$202$	0.673081	+	0.977458i	0.0473578	+	0.0687737i
$203$	13.9673	−	11.7200i	0.980312	−	0.822579i
$204$	−11.8190	−	19.5212i	−0.827494	−	1.36676i
$205$	−1.08068	+	0.393334i	−0.0754776	+	0.0274716i
$206$	−0.852388	+	0.389380i	−0.0593887	+	0.0271294i
$207$	0.741367	+	2.93432i	0.0515286	+	0.203949i
$208$	3.74955	−	2.95121i	0.259984	−	0.204630i
$209$	−1.48051	−	0.261054i	−0.102409	−	0.0180575i
$210$	7.21276	−	2.15585i	0.497728	−	0.148768i
$211$	2.92370	−	8.03281i	0.201276	−	0.553002i	−0.797454	−	0.603380i	$-0.793820\pi$
$211$	2.92370	−	8.03281i	0.201276	−	0.553002i	0.998730	+	0.0503781i	$0.0160426\pi$
$212$	9.14153	+	0.143150i	0.627843	+	0.00983159i
$213$	7.15140	+	11.4049i	0.490006	+	0.781450i
$214$	13.4587	+	13.6712i	0.920021	+	0.934541i
$215$	8.13757			0.554978
$216$	9.46209	−	11.2458i	0.643814	−	0.765182i
$217$	8.59726			0.583620
$218$	−1.80615	−	1.83465i	−0.122328	−	0.124258i
$219$	7.04511	−	13.3001i	0.476065	−	0.898737i
$220$	0.545285	+	0.00853878i	0.0367631	+	0.000575685i
$221$	2.68777	−	7.38459i	0.180799	−	0.496741i
$222$	3.12154	−	13.1446i	0.209504	−	0.882211i
$223$	−3.63666	−	0.641241i	−0.243528	−	0.0429406i	0.0505515	−	0.998721i	$-0.483902\pi$
$223$	−3.63666	−	0.641241i	−0.243528	−	0.0429406i	−0.294080	+	0.955781i	$0.595013\pi$
$224$	9.40683	+	14.6205i	0.628520	+	0.976876i
$225$	−2.43256	−	1.75575i	−0.162170	−	0.117050i
$226$	−22.7955	+	10.4133i	−1.51634	+	0.692679i
$227$	−26.1565	+	9.52017i	−1.73606	+	0.631876i	−0.999032	−	0.0439813i	$-0.985996\pi$
$227$	−26.1565	+	9.52017i	−1.73606	+	0.631876i	−0.737033	+	0.675857i	$0.763774\pi$
$228$	−9.20307	+	16.7351i	−0.609488	+	1.10831i
$229$	7.38380	−	6.19575i	0.487936	−	0.409427i	−0.365350	−	0.930870i	$-0.619051\pi$
$229$	7.38380	−	6.19575i	0.487936	−	0.409427i	0.853286	+	0.521444i	$0.174606\pi$
$230$	0.809156	+	1.17507i	0.0533542	+	0.0774817i
$231$	−1.41930	+	0.304003i	−0.0933830	+	0.0200019i
$232$	−1.06950	−	16.7460i	−0.0702163	−	1.09943i
$233$	−3.70672	+	2.14008i	−0.242835	+	0.140201i	−0.616479	−	0.787371i	$-0.711442\pi$
$233$	−3.70672	+	2.14008i	−0.242835	+	0.140201i	0.373644	+	0.927572i	$0.378108\pi$
$234$	5.05987	+	0.112111i	0.330774	+	0.00732890i
$235$	6.62251	+	3.82351i	0.432005	+	0.249418i
$236$	8.94419	−	23.4260i	0.582217	−	1.52490i
$237$	14.5276	−	18.6546i	0.943671	−	1.21175i
$238$	25.8540	+	12.3032i	1.67586	+	0.797500i
$239$	0.526760	+	2.98740i	0.0340732	+	0.193239i	0.997093	−	0.0761909i	$-0.0242759\pi$
$239$	0.526760	+	2.98740i	0.0340732	+	0.193239i	−0.963020	+	0.269430i	$0.913165\pi$
$240$	2.33599	−	6.52251i	0.150788	−	0.421026i
$241$	−13.4458	−	11.2824i	−0.866123	−	0.726763i	0.0971551	−	0.995269i	$-0.469026\pi$
$241$	−13.4458	−	11.2824i	−0.866123	−	0.726763i	−0.963278	+	0.268506i	$0.913470\pi$
$242$	15.3814	+	1.46713i	0.988753	+	0.0943104i
$243$	15.3300	−	2.82692i	0.983419	−	0.181347i
$244$	−26.6140	−	5.12367i	−1.70379	−	0.328009i
$245$	−1.57179	+	1.87319i	−0.100418	+	0.119674i
$246$	0.165050	−	2.81215i	0.0105232	−	0.179296i
$247$	−6.47701	+	1.14207i	−0.412122	+	0.0726683i
$248$	4.68922	−	6.37293i	0.297766	−	0.404682i
$249$	−6.88657	−	5.36305i	−0.436418	−	0.339869i
$250$	−1.36312	−	0.376709i	−0.0862111	−	0.0238252i
$251$	−9.52285	+	16.4941i	−0.601077	+	1.04110i	0.391581	+	0.920143i	$0.371928\pi$
$251$	−9.52285	+	16.4941i	−0.601077	+	1.04110i	−0.992658	+	0.120952i	$0.961405\pi$
$252$	−2.15710	+	18.3133i	−0.135885	+	1.15363i
$253$	−0.137543	−	0.238232i	−0.00864727	−	0.0149775i
$254$	1.07283	+	4.13300i	0.0673151	+	0.259328i
$255$	−2.38976	−	11.1571i	−0.149653	−	0.698684i
$256$	15.9686	+	1.00146i	0.998039	+	0.0625912i
$257$	10.5401	+	12.5612i	0.657474	+	0.783547i	0.987021	−	0.160592i	$-0.0513404\pi$
$257$	10.5401	+	12.5612i	0.657474	+	0.783547i	−0.329547	+	0.944139i	$0.606896\pi$
$258$	−7.90319	+	18.2992i	−0.492031	+	1.13926i
$259$	5.79756	+	15.9287i	0.360243	+	0.989759i
$260$	2.25445	−	0.780799i	0.139815	−	0.0484231i
$261$	10.4163	−	14.4316i	0.644754	−	0.893293i
$262$	1.44622	−	2.03138i	0.0893478	−	0.125499i
$263$	0.345777	−	1.96100i	0.0213215	−	0.120920i	−0.972289	−	0.233781i	$-0.924890\pi$
$263$	0.345777	−	1.96100i	0.0213215	−	0.120920i	0.993611	+	0.112860i	$0.0360013\pi$
$264$	−0.548781	+	1.21790i	−0.0337751	+	0.0749568i
$265$	4.29564	+	1.56349i	0.263879	+	0.0960442i
$266$	−1.90153	−	23.8871i	−0.116591	−	1.46461i
$267$	16.8466	+	8.92370i	1.03099	+	0.546121i
$268$	5.48607	−	4.45887i	0.335115	−	0.272369i
$269$			2.72407i			0.166090i	0.996546	+	0.0830449i	$0.0264645\pi$
$269$			2.72407i			0.166090i	−0.996546	+	0.0830449i	$0.973536\pi$
$270$	6.31070	−	3.76497i	0.384057	−	0.229129i
$271$		−	7.00424i		−	0.425477i	−0.977109	−	0.212739i	$-0.931762\pi$
$271$		−	7.00424i		−	0.425477i	0.977109	−	0.212739i	$-0.0682383\pi$
$272$	23.2216	−	12.4543i	1.40802	−	0.755154i
$273$	−5.37988	+	3.37344i	−0.325605	+	0.204170i
$274$	15.3771	−	1.22409i	0.928963	−	0.0739501i
$275$	0.256231	+	0.0932606i	0.0154513	+	0.00562382i
$276$	−3.42826	+	0.678347i	−0.206357	+	0.0408317i
$277$	2.88194	−	16.3443i	0.173159	−	0.982034i	−0.767088	−	0.641542i	$-0.778295\pi$
$277$	2.88194	−	16.3443i	0.173159	−	0.982034i	0.940247	−	0.340492i	$-0.110594\pi$
$278$	21.6678	+	15.4262i	1.29955	+	0.925199i
$279$	8.13649	−	2.05572i	0.487119	−	0.123073i
$280$	2.05201	+	8.44698i	0.122631	+	0.504804i
$281$	6.78234	+	18.6343i	0.404600	+	1.11163i	0.959989	+	0.280039i	$0.0903475\pi$
$281$	6.78234	+	18.6343i	0.404600	+	1.11163i	−0.555388	+	0.831591i	$0.687430\pi$
$282$	−15.0298	+	11.1788i	−0.895011	+	0.665690i
$283$	2.78301	+	3.31666i	0.165433	+	0.197155i	0.842392	−	0.538866i	$-0.181147\pi$
$283$	2.78301	+	3.31666i	0.165433	+	0.197155i	−0.676959	+	0.736021i	$0.736703\pi$
$284$	−13.5816	+	7.56032i	−0.805921	+	0.448622i
$285$	−7.08655	+	6.40086i	−0.419771	+	0.379154i
$286$	−0.445258	+	0.115578i	−0.0263287	+	0.00683427i
$287$	1.76720	+	3.06089i	0.104315	+	0.180678i
$288$	12.3986	+	11.5877i	0.730597	+	0.682809i
$289$	13.1986	−	22.8606i	0.776387	−	1.34474i
$290$	2.23489	−	8.08695i	0.131237	−	0.474882i
$291$	−26.8521	+	10.8979i	−1.57410	+	0.638844i
$292$	14.9129	+	8.92416i	0.872710	+	0.522247i
$293$	−15.3971	+	2.71493i	−0.899509	+	0.158608i	−0.604236	−	0.796805i	$-0.706522\pi$
$293$	−15.3971	+	2.71493i	−0.899509	+	0.158608i	−0.295273	+	0.955413i	$0.595410\pi$
$294$	−2.68577	−	5.35377i	−0.156637	−	0.312238i
$295$	8.05909	−	9.60445i	0.469218	−	0.559193i
$296$	14.9697	+	4.39041i	0.870096	+	0.255188i
$297$	−1.27054	+	0.627083i	−0.0737242	+	0.0363870i
$298$	−0.718022	+	7.52777i	−0.0415939	+	0.436072i
$299$	−0.921905	−	0.773570i	−0.0533152	−	0.0447367i
$300$	2.17097	−	2.69942i	0.125341	−	0.155851i
$301$	−4.34283	−	24.6294i	−0.250316	−	1.41961i
$302$	−9.89810	+	20.7998i	−0.569572	+	1.19690i
$303$	−1.43968	−	0.200037i	−0.0827075	−	0.0114919i
$304$	−18.7441	−	11.6192i	−1.07505	−	0.666409i
$305$	−11.7358	−	6.77568i	−0.671991	−	0.387974i
$306$	27.4102	+	5.46181i	1.56694	+	0.312231i
$307$	18.8970	−	10.9102i	1.07851	−	0.622676i	0.148013	−	0.988985i	$-0.452712\pi$
$307$	18.8970	−	10.9102i	1.07851	−	0.622676i	0.930493	+	0.366310i	$0.119379\pi$
$308$	−0.265161	−	1.65493i	−0.0151090	−	0.0942984i
$309$	0.352958	−	1.09211i	0.0200791	−	0.0621277i
$310$	3.25832	−	2.24369i	0.185060	−	0.127433i
$311$	9.02296	−	7.57116i	0.511645	−	0.429321i	−0.350063	−	0.936726i	$-0.613840\pi$
$311$	9.02296	−	7.57116i	0.511645	−	0.429321i	0.861708	+	0.507405i	$0.169395\pi$
$312$	−0.433712	+	5.82795i	−0.0245541	+	0.329943i
$313$	4.97757	−	1.81169i	0.281349	−	0.102403i	−0.197492	−	0.980305i	$-0.563280\pi$
$313$	4.97757	−	1.81169i	0.281349	−	0.102403i	0.478840	+	0.877902i	$0.341057\pi$
$314$	10.3535	+	22.6647i	0.584280	+	1.27904i
$315$	−4.01581	+	8.29944i	−0.226265	+	0.467621i
$316$	20.6371	+	17.8746i	1.16093	+	1.00553i
$317$	12.5595	+	2.21457i	0.705409	+	0.124383i	0.514834	−	0.857290i	$-0.327854\pi$
$317$	12.5595	+	2.21457i	0.705409	+	0.124383i	0.190575	+	0.981673i	$0.438965\pi$
$318$	−7.68777	+	8.14127i	−0.431109	+	0.456540i
$319$	−0.553285	+	1.52014i	−0.0309780	+	0.0851114i
$320$	7.38077	+	3.08614i	0.412597	+	0.172521i
$321$	−23.4803	+	0.856732i	−1.31054	+	0.0478181i
$322$	3.12467	−	3.07612i	0.174131	−	0.171425i
$323$	−36.3199			−2.02089
$324$	2.33746	+	17.8476i	0.129859	+	0.991533i
$325$	1.19292			0.0661711
$326$	−4.42580	+	4.35703i	−0.245122	+	0.241314i
$327$	3.15102	−	0.114972i	0.174252	−	0.00635799i
$328$	3.23285	+	0.359521i	0.178504	+	0.0198512i
$329$	8.03805	−	22.0844i	0.443152	−	1.21755i
$330$	−0.458569	+	0.485620i	−0.0252434	+	0.0267325i
$331$	−12.5177	−	2.20721i	−0.688035	−	0.121319i	−0.181309	−	0.983426i	$-0.558033\pi$
$331$	−12.5177	−	2.20721i	−0.688035	−	0.121319i	−0.506726	+	0.862107i	$0.669145\pi$
$332$	6.59864	−	7.61845i	0.362147	−	0.418117i
$333$	9.29560	+	13.6887i	0.509395	+	0.750136i
$334$	−8.17840	−	17.9033i	−0.447502	−	0.979622i
$335$	3.32160	−	1.20896i	0.181478	−	0.0660527i
$336$	−20.9879	−	3.58927i	−1.14498	−	0.195811i
$337$	−19.5386	+	16.3948i	−1.06433	+	0.893083i	−0.994527	−	0.104477i	$-0.966683\pi$
$337$	−19.5386	+	16.3948i	−1.06433	+	0.893083i	−0.0698077	+	0.997560i	$0.522239\pi$
$338$	13.4845	−	9.28547i	0.733460	−	0.505063i
$339$	9.43922	−	29.2063i	0.512668	−	1.58627i
$340$	13.0094	−	2.08443i	0.705532	−	0.113044i
$341$	−0.660587	+	0.381390i	−0.0357728	+	0.0206534i
$342$	−7.51135	−	22.1522i	−0.406167	−	1.19786i
$343$	−12.1227	−	6.99905i	−0.654565	−	0.377913i
$344$	−20.6259	−	10.2144i	−1.11207	−	0.550725i
$345$	−1.73074	−	0.240478i	−0.0931797	−	0.0129469i
$346$	4.22324	−	8.87469i	0.227043	−	0.477106i
$347$	−6.07234	−	34.4379i	−0.325980	−	1.84873i	−0.502696	−	0.864463i	$-0.667658\pi$
$347$	−6.07234	−	34.4379i	−0.325980	−	1.84873i	0.176716	−	0.984262i	$-0.443453\pi$
$348$	16.0148	+	12.8797i	0.858484	+	0.690424i
$349$	−8.88587	−	7.45613i	−0.475650	−	0.399117i	0.373201	−	0.927751i	$-0.378260\pi$
$349$	−8.88587	−	7.45613i	−0.475650	−	0.399117i	−0.848850	+	0.528633i	$0.822705\pi$
$350$	−0.412693	+	4.32669i	−0.0220594	+	0.231271i
$351$	−4.28491	+	4.47904i	−0.228712	+	0.239073i
$352$	−1.37139	−	0.706093i	−0.0730951	−	0.0376349i
$353$	3.76355	−	4.48523i	0.200314	−	0.238725i	−0.656531	−	0.754299i	$-0.727977\pi$
$353$	3.76355	−	4.48523i	0.200314	−	0.238725i	0.856845	+	0.515574i	$0.172421\pi$
$354$	13.7708	+	27.4505i	0.731911	+	1.45898i
$355$	−7.65397	+	1.34960i	−0.406231	+	0.0716294i
$356$	−11.3038	+	18.8894i	−0.599100	+	1.00114i
$357$	−32.4930	+	13.1872i	−1.71971	+	0.697940i
$358$	6.05377	−	21.9055i	0.319952	−	1.15774i
$359$	14.3972	−	24.9366i	0.759853	−	1.31610i	−0.183073	−	0.983099i	$-0.558604\pi$
$359$	14.3972	−	24.9366i	0.759853	−	1.31610i	0.942925	−	0.333004i	$-0.108062\pi$
$360$	3.96182	+	7.50360i	0.208806	+	0.395474i
$361$	5.69838	+	9.86988i	0.299914	+	0.519467i
$362$	−8.59393	+	2.23077i	−0.451687	+	0.117247i
$363$	−14.0433	+	12.6845i	−0.737081	+	0.665762i
$364$	−3.56633	−	6.40668i	−0.186927	−	0.335801i
$365$	5.58555	+	6.65660i	0.292361	+	0.348422i
$366$	26.6345	−	19.8101i	1.39221	−	1.03549i
$367$	6.97284	+	19.1577i	0.363979	+	1.00002i	0.977609	+	0.210430i	$0.0674865\pi$
$367$	6.97284	+	19.1577i	0.363979	+	1.00002i	−0.613630	+	0.789594i	$0.710291\pi$
$368$	−0.575958	−	3.99405i	−0.0300239	−	0.208204i
$369$	2.40439	+	2.47428i	0.125168	+	0.128806i
$370$	6.35426	+	4.52385i	0.330342	+	0.235184i
$371$	2.43961	−	13.8357i	0.126658	−	0.718314i
$372$	1.88097	+	9.50613i	0.0975238	+	0.492870i
$373$	32.8761	+	11.9659i	1.70226	+	0.619573i	0.996080	−	0.0884577i	$-0.0281938\pi$
$373$	32.8761	+	11.9659i	1.70226	+	0.619573i	0.706182	+	0.708030i	$0.250416\pi$
$374$	−2.53233	+	0.201586i	−0.130944	+	0.0104238i
$375$	1.46742	−	0.920144i	0.0757775	−	0.0475160i
$376$	−11.9864	−	18.0039i	−0.618150	−	0.928481i
$377$			7.07719i			0.364494i
$378$	−14.7630	−	17.0909i	−0.759329	−	0.879059i
$379$			15.2723i			0.784484i	0.919862	+	0.392242i	$0.128300\pi$
$379$			15.2723i			0.784484i	−0.919862	+	0.392242i	$0.871700\pi$
$380$	−6.95467	−	8.55684i	−0.356767	−	0.438957i
$381$	−4.62132	−	2.44793i	−0.236757	−	0.125411i
$382$	−0.526468	−	6.61351i	−0.0269364	−	0.338376i
$383$	5.61350	+	2.04315i	0.286837	+	0.104400i	0.481432	−	0.876484i	$-0.340117\pi$
$383$	5.61350	+	2.04315i	0.286837	+	0.104400i	−0.194595	+	0.980884i	$0.562339\pi$
$384$	−14.1081	+	13.6001i	−0.719950	+	0.694026i
$385$	0.145520	−	0.825287i	0.00741641	−	0.0420605i
$386$	−17.6431	+	24.7817i	−0.898009	+	1.26136i
$387$	−9.99928	−	22.2709i	−0.508292	−	1.13210i
$388$	−10.9511	−	31.6197i	−0.555956	−	1.60525i
$389$	12.0950	+	33.2306i	0.613239	+	1.68486i	0.722953	+	0.690897i	$0.242784\pi$
$389$	12.0950	+	33.2306i	0.613239	+	1.68486i	−0.109714	+	0.993963i	$0.534994\pi$
$390$	−1.15856	+	2.68254i	−0.0586658	+	0.135836i
$391$	−4.27190	−	5.09105i	−0.216039	−	0.257465i
$392$	6.33520	−	2.77493i	0.319976	−	0.140155i
$393$	0.639642	+	2.98630i	0.0322657	+	0.150639i
$394$	7.67923	+	29.5838i	0.386874	+	1.49041i
$395$	6.82548	+	11.8221i	0.343427	+	0.594833i
$396$	−0.646666	−	1.50283i	−0.0324962	−	0.0755200i
$397$	−5.48428	+	9.49906i	−0.275248	+	0.476744i	−0.970198	−	0.242315i	$-0.922093\pi$
$397$	−5.48428	+	9.49906i	−0.275248	+	0.476744i	0.694949	+	0.719059i	$0.255427\pi$
$398$	−25.5234	−	7.05360i	−1.27937	−	0.353565i
$399$	23.1549	+	18.0324i	1.15920	+	0.902747i
$400$	2.98217	+	2.66583i	0.149109	+	0.133292i
$401$	32.4626	−	5.72403i	1.62110	−	0.285844i	0.711927	−	0.702254i	$-0.247823\pi$
$401$	32.4626	−	5.72403i	1.62110	−	0.285844i	0.909177	+	0.416409i	$0.136712\pi$
$402$	−0.507302	+	8.64352i	−0.0253019	+	0.431099i
$403$	−2.14501	+	2.55633i	−0.106851	+	0.127340i
$404$	0.317290	−	1.64811i	0.0157858	−	0.0819963i
$405$	−1.81608	+	8.81487i	−0.0902415	+	0.438014i
$406$	−25.6689	−	2.44838i	−1.27392	−	0.121511i
$407$	−1.15209	−	0.966719i	−0.0571070	−	0.0479185i
$408$	−7.94736	+	31.2789i	−0.393453	+	1.54854i
$409$	−2.62605	−	14.8931i	−0.129850	−	0.736415i	−0.978308	−	0.207154i	$-0.933580\pi$
$409$	−2.62605	−	14.8931i	−0.129850	−	0.736415i	0.848459	−	0.529262i	$-0.177531\pi$
$410$	1.46858	+	0.698861i	0.0725281	+	0.0345143i
$411$	−11.6081	+	14.9057i	−0.572587	+	0.735246i
$412$	1.23811	+	0.472716i	0.0609971	+	0.0232890i
$413$	−33.3700	−	19.2662i	−1.64203	−	0.948027i
$414$	2.22166	−	3.65840i	0.109189	−	0.179801i
$415$	4.36426	−	2.51971i	0.214233	−	0.123688i
$416$	−6.69430	−	0.850774i	−0.328215	−	0.0417126i
$417$	−31.8534	+	6.82275i	−1.55987	+	0.334112i
$418$	1.20578	+	1.75106i	0.0589768	+	0.0856470i
$419$	−5.20207	+	4.36506i	−0.254138	+	0.213247i	−0.760952	−	0.648809i	$-0.775268\pi$
$419$	−5.20207	+	4.36506i	−0.254138	+	0.213247i	0.506814	+	0.862056i	$0.330823\pi$
$420$	−9.32874	−	5.13011i	−0.455196	−	0.250324i
$421$	−20.9679	+	7.63170i	−1.02191	+	0.371946i	−0.797997	−	0.602662i	$-0.794107\pi$
$421$	−20.9679	+	7.63170i	−1.02191	+	0.371946i	−0.223918	+	0.974608i	$0.571885\pi$
$422$	−10.9962	+	5.02317i	−0.535286	+	0.244524i
$423$	2.32659	−	22.8228i	0.113123	−	1.10968i
$424$	−8.92542	−	9.35485i	−0.433457	−	0.454312i
$425$	6.48757	+	1.14393i	0.314693	+	0.0554889i
$426$	4.39864	−	18.5224i	0.213115	−	0.897414i
$427$	−14.2443	+	39.1360i	−0.689331	+	1.89392i
$428$	0.424797	−	27.1274i	0.0205333	−	1.31125i
$429$	0.263722	−	0.497866i	0.0127326	−	0.0240372i
$430$	−8.07361	−	8.20103i	−0.389344	−	0.395489i
$431$	20.2304			0.974464			0.487232	−	0.873273i	$-0.338007\pi$
$431$	20.2304			0.974464			0.487232	+	0.873273i	$0.338007\pi$
$432$	−20.7213	+	1.62157i	−0.996952	+	0.0780180i
$433$	19.8244			0.952700			0.476350	−	0.879256i	$-0.341959\pi$
$433$	19.8244			0.952700			0.476350	+	0.879256i	$0.341959\pi$
$434$	−8.52969	−	8.66430i	−0.409438	−	0.415900i
$435$	5.45892	+	8.70576i	0.261735	+	0.417409i
$436$	−0.0570072	+	3.64046i	−0.00273015	+	0.174347i
$437$	−1.90234	+	5.22663i	−0.0910012	+	0.250024i
$438$	−20.3935	+	6.09550i	−0.974441	+	0.291254i
$439$	16.6315	+	2.93258i	0.793778	+	0.139964i	0.555811	−	0.831309i	$-0.312408\pi$
$439$	16.6315	+	2.93258i	0.793778	+	0.139964i	0.237967	+	0.971273i	$0.423519\pi$
$440$	−0.532393	−	0.558008i	−0.0253809	−	0.0266020i
$441$	7.05794	+	1.99995i	0.336093	+	0.0952359i
$442$	−10.1088	+	4.61782i	−0.480828	+	0.219647i
$443$	−12.7959	+	4.65734i	−0.607953	+	0.221277i	−0.627607	−	0.778530i	$-0.715966\pi$
$443$	−12.7959	+	4.65734i	−0.607953	+	0.221277i	0.0196543	+	0.999807i	$0.493743\pi$
$444$	−16.3442	+	9.89545i	−0.775659	+	0.469617i
$445$	−8.43158	+	7.07494i	−0.399695	+	0.335384i
$446$	2.96183	+	4.30122i	0.140247	+	0.203668i
$447$	−6.20787	−	6.87288i	−0.293622	−	0.325076i
$448$	5.40166	−	23.9858i	0.255205	−	1.13322i
$449$	6.31238	−	3.64445i	0.297899	−	0.171992i	−0.343599	−	0.939116i	$-0.611646\pi$
$449$	6.31238	−	3.64445i	0.297899	−	0.171992i	0.641499	+	0.767124i	$0.278313\pi$
$450$	0.643993	+	4.19348i	0.0303581	+	0.197683i
$451$	−0.271573	−	0.156793i	−0.0127879	−	0.00738308i
$452$	33.1108	+	12.6419i	1.55740	+	0.594625i
$453$	−10.6093	−	26.1410i	−0.498466	−	1.22821i
$454$	35.5453	+	16.9151i	1.66822	+	0.793864i
$455$	−0.636630	−	3.61051i	−0.0298457	−	0.169263i
$456$	25.9964	−	7.32876i	1.21739	−	0.343201i
$457$	3.89038	+	3.26441i	0.181984	+	0.152703i	0.729229	−	0.684270i	$-0.239879\pi$
$457$	3.89038	+	3.26441i	0.181984	+	0.152703i	−0.547245	+	0.836973i	$0.684323\pi$
$458$	−13.5698	−	1.29433i	−0.634077	−	0.0604803i
$459$	−27.5983	+	20.2499i	−1.28818	+	0.945185i
$460$	0.381435	−	1.98130i	0.0177845	−	0.0923785i
$461$	−14.8616	+	17.7114i	−0.692174	+	0.824901i	−0.991617	−	0.129213i	$-0.958755\pi$
$461$	−14.8616	+	17.7114i	−0.692174	+	0.824901i	0.299443	+	0.954114i	$0.403199\pi$
$462$	1.71452	+	1.12875i	0.0797666	+	0.0525144i
$463$	13.1825	−	2.32443i	0.612643	−	0.108025i	0.141287	−	0.989969i	$-0.454876\pi$
$463$	13.1825	−	2.32443i	0.612643	−	0.108025i	0.471356	+	0.881943i	$0.343765\pi$
$464$	−15.8155	+	17.6923i	−0.734218	+	0.821343i
$465$	−0.666816	+	4.79911i	−0.0309229	+	0.222554i
$466$	5.83436	+	1.61237i	0.270271	+	0.0746917i
$467$	11.5598	−	20.0221i	0.534922	−	0.926512i	−0.464245	−	0.885707i	$-0.653674\pi$
$467$	11.5598	−	20.0221i	0.534922	−	0.926512i	0.999167	−	0.0408051i	$-0.0129923\pi$
$468$	−4.90712	−	5.21056i	−0.226832	−	0.240858i
$469$	−5.43174	−	9.40805i	−0.250814	−	0.434423i
$470$	−2.71713	−	10.4676i	−0.125332	−	0.482835i
$471$	−29.0387	−	9.38504i	−1.33803	−	0.432440i
$472$	−32.4826	+	14.2280i	−1.49513	+	0.654895i
$473$	1.42629	+	1.69979i	0.0655810	+	0.0781564i
$474$	−33.2135	+	3.86707i	−1.52555	+	0.177620i
$475$	−1.88567	−	5.18083i	−0.0865204	−	0.237713i
$476$	−13.2516	−	38.2621i	−0.607385	−	1.75374i
$477$	−0.999442	−	13.6775i	−0.0457613	−	0.626250i
$478$	2.48808	−	3.49479i	0.113802	−	0.159848i
$479$	1.65861	−	9.40642i	0.0757836	−	0.429790i	−0.923184	−	0.384359i	$-0.874423\pi$
$479$	1.65861	−	9.40642i	0.0757836	−	0.429790i	0.998967	−	0.0454316i	$-0.0144663\pi$
$480$	−8.89101	+	4.11704i	−0.405817	+	0.187916i
$481$	−6.18275	−	2.25034i	−0.281909	−	0.102607i
$482$	1.96978	+	24.7444i	0.0897210	+	1.12708i
$483$	0.195814	+	5.36663i	0.00890984	+	0.244190i
$484$	−13.7819	−	16.9569i	−0.626451	−	0.770770i
$485$		−	16.7312i		−	0.759724i
$486$	−18.0585	−	12.6448i	−0.819148	−	0.573582i
$487$			33.3240i			1.51005i	0.655693	+	0.755027i	$0.272376\pi$
$487$			33.3240i			1.51005i	−0.655693	+	0.755027i	$0.727624\pi$
$488$	21.2412	+	31.9049i	0.961544	+	1.44427i
$489$	−0.277352	−	7.60133i	−0.0125423	−	0.343744i
$490$	3.44724	−	0.274417i	0.155730	−	0.0123969i
$491$	30.9548	+	11.2666i	1.39697	+	0.508456i	0.927278	−	0.374373i	$-0.122142\pi$
$491$	30.9548	+	11.2666i	1.39697	+	0.508456i	0.469694	+	0.882829i	$0.344364\pi$
$492$	−2.99783	+	2.62371i	−0.135153	+	0.118286i
$493$	−6.78660	+	38.4887i	−0.305653	+	1.73344i
$494$	7.57708	+	5.39443i	0.340909	+	0.242707i
$495$	−0.0596159	−	0.815852i	−0.00267953	−	0.0366698i
$496$	−11.0750	+	1.59706i	−0.497282	+	0.0717101i
$497$	8.16948	+	22.4455i	0.366451	+	1.00682i
$498$	1.42757	+	12.2612i	0.0639711	+	0.549436i
$499$	−9.83733	−	11.7237i	−0.440380	−	0.524824i	0.499507	−	0.866310i	$-0.333514\pi$
$499$	−9.83733	−	11.7237i	−0.440380	−	0.524824i	−0.939887	+	0.341486i	$0.889070\pi$
$500$	0.972758	+	1.74750i	0.0435031	+	0.0781504i
$501$	22.9382	+	7.41341i	1.02480	+	0.331207i
$502$	26.0707	−	6.76731i	1.16359	−	0.302040i
$503$	2.71843	+	4.70847i	0.121209	+	0.209940i	0.920245	−	0.391343i	$-0.127990\pi$
$503$	2.71843	+	4.70847i	0.121209	+	0.209940i	−0.799036	+	0.601284i	$0.794656\pi$
$504$	20.5963	−	15.9954i	0.917430	−	0.712493i
$505$	0.419593	−	0.726756i	0.0186716	−	0.0323402i
$506$	−0.103627	+	0.374975i	−0.00460680	+	0.0166697i
$507$	−2.75961	+	19.8611i	−0.122559	+	0.882061i
$508$	3.10084	−	5.18171i	0.137577	−	0.229901i
$509$	34.5659	−	6.09490i	1.53211	−	0.270152i	0.656928	−	0.753953i	$-0.271856\pi$
$509$	34.5659	−	6.09490i	1.53211	−	0.270152i	0.875178	+	0.483802i	$0.160744\pi$
$510$	−8.87311	+	13.4778i	−0.392908	+	0.596807i
$511$	17.1662	−	20.4578i	0.759386	−	0.905001i
$512$	−14.8339	−	17.0867i	−0.655570	−	0.755135i
$513$	26.2257	+	11.5293i	1.15789	+	0.509029i
$514$	2.20190	−	23.0848i	0.0971217	−	1.01823i
$515$	0.507611	+	0.425937i	0.0223680	+	0.0187690i
$516$	26.2830	−	10.1905i	1.15704	−	0.448613i
$517$	0.362083	+	2.05348i	0.0159244	+	0.0903118i
$518$	10.3009	−	21.6462i	0.452595	−	0.951082i
$519$	4.52667	+	11.1536i	0.198699	+	0.489589i
$520$	−3.02362	−	1.49737i	−0.132594	−	0.0656639i
$521$	33.6617	+	19.4346i	1.47475	+	0.851445i	0.999595	−	0.0284602i	$-0.00906038\pi$
$521$	33.6617	+	19.4346i	1.47475	+	0.851445i	0.475150	+	0.879905i	$0.342394\pi$
$522$	−24.8786	+	3.82061i	−1.08891	+	0.167223i
$523$	−27.4450	+	15.8454i	−1.20009	+	0.692871i	−0.960575	−	0.278022i	$-0.910321\pi$
$523$	−27.4450	+	15.8454i	−1.20009	+	0.692871i	−0.239513	+	0.970893i	$0.576988\pi$
$524$	−3.48208	+	0.557917i	−0.152115	+	0.0243727i
$525$	−3.56806	−	3.95029i	−0.155723	−	0.172405i
$526$	−2.31935	+	1.59711i	−0.101128	+	0.0696374i
$527$	−14.1168	+	11.8454i	−0.614939	+	0.515995i
$528$	1.77187	−	0.655271i	0.0771107	−	0.0285170i
$529$	20.6565	−	7.51837i	0.898111	−	0.326886i
$530$	−2.68620	−	5.88034i	−0.116681	−	0.255426i
$531$	−36.1883	−	10.2544i	−1.57044	−	0.445003i
$532$	−22.1868	+	25.6158i	−0.961921	+	1.11058i
$533$	−1.35105	−	0.238226i	−0.0585204	−	0.0103187i
$534$	−7.72087	−	25.8315i	−0.334115	−	1.11784i
$535$	4.63963	−	12.7473i	0.200589	−	0.551113i
$536$	−9.93659	−	1.10503i	−0.429195	−	0.0477302i
$537$	14.7869	+	23.5818i	0.638100	+	1.01763i
$538$	2.74532	−	2.70266i	0.118359	−	0.116520i
$539$	−0.666767			−0.0287197
$540$	−10.0554	−	2.62453i	−0.432717	−	0.112942i
$541$	16.8889			0.726113			0.363056	−	0.931767i	$-0.381733\pi$
$541$	16.8889			0.726113			0.363056	+	0.931767i	$0.381733\pi$
$542$	−7.05886	+	6.94919i	−0.303204	+	0.298493i
$543$	5.09010	−	9.60932i	0.218437	−	0.412375i
$544$	−35.5906	−	11.0463i	−1.52593	−	0.473606i
$545$	−0.622632	+	1.71067i	−0.0266706	+	0.0732770i
$546$	8.73735	+	2.07491i	0.373924	+	0.0887980i
$547$	−23.5366	−	4.15013i	−1.00635	−	0.177447i	−0.353905	−	0.935282i	$-0.615146\pi$
$547$	−23.5366	−	4.15013i	−1.00635	−	0.177447i	−0.652447	+	0.757835i	$0.726257\pi$
$548$	−16.4899	−	14.2825i	−0.704412	−	0.610119i
$549$	−4.12297	+	40.4445i	−0.175964	+	1.72613i
$550$	−0.160230	−	0.350757i	−0.00683221	−	0.0149563i
$551$	30.7362	−	11.1871i	1.30941	−	0.476585i
$552$	4.08495	+	2.78198i	0.173867	+	0.118409i
$553$	32.1384	−	26.9673i	1.36666	−	1.14677i
$554$	−19.3310	+	13.3114i	−0.821298	+	0.565548i
$555$	−9.34128	+	2.00083i	−0.396515	+	0.0849305i
$556$	−5.95103	−	37.1417i	−0.252380	−	1.57516i
$557$	−4.07157	+	2.35072i	−0.172518	+	0.0996032i	−0.583773	−	0.811917i	$-0.698424\pi$
$557$	−4.07157	+	2.35072i	−0.172518	+	0.0996032i	0.411255	+	0.911520i	$0.365091\pi$
$558$	−10.1443	−	6.16038i	−0.429442	−	0.260790i
$559$	8.40689	+	4.85372i	0.355573	+	0.205290i
$560$	6.47697	−	10.4486i	0.273702	−	0.441534i
$561$	1.91165	−	2.45471i	0.0807100	−	0.103638i
$562$	12.0506	−	25.3231i	0.508324	−	1.06819i
$563$	3.78196	+	21.4486i	0.159391	+	0.903949i	0.954661	+	0.297694i	$0.0962176\pi$
$563$	3.78196	+	21.4486i	0.159391	+	0.903949i	−0.795271	+	0.606255i	$0.792671\pi$
$564$	26.1777	+	4.05602i	1.10228	+	0.170789i
$565$	13.5751	+	11.3909i	0.571110	+	0.479218i
$566$	0.581390	−	6.09531i	0.0244376	−	0.256205i
$567$	27.6485	+	0.792301i	1.16113	+	0.0332735i
$568$	21.0942	+	6.18663i	0.885091	+	0.259585i
$569$	−27.1745	+	32.3853i	−1.13921	+	1.35766i	−0.214622	+	0.976697i	$0.568852\pi$
$569$	−27.1745	+	32.3853i	−1.13921	+	1.35766i	−0.924590	+	0.380964i	$0.875592\pi$
$570$	13.4816	+	0.791258i	0.564683	+	0.0331422i
$571$	24.9545	−	4.40015i	1.04431	−	0.184140i	0.374926	−	0.927055i	$-0.377668\pi$
$571$	24.9545	−	4.40015i	1.04431	−	0.184140i	0.669387	+	0.742914i	$0.266557\pi$
$572$	0.558238	+	0.334061i	0.0233411	+	0.0139678i
$573$	6.41079	+	4.99252i	0.267814	+	0.208566i
$574$	1.33144	−	4.81782i	0.0555733	−	0.201092i
$575$	0.504420	−	0.873682i	0.0210358	−	0.0364350i
$576$	−0.623166	−	23.9919i	−0.0259653	−	0.999663i
$577$	10.9057	+	18.8892i	0.454010	+	0.786368i	0.998631	−	0.0523144i	$-0.0166598\pi$
$577$	10.9057	+	18.8892i	0.454010	+	0.786368i	−0.544621	+	0.838682i	$0.683326\pi$
$578$	−36.1337	+	9.37943i	−1.50297	+	0.390133i
$579$	−7.80326	−	36.4311i	−0.324293	−	1.51402i
$580$	−10.3673	+	5.77106i	−0.430480	+	0.239630i
$581$	−9.95531	−	11.8643i	−0.413016	−	0.492213i
$582$	37.6239	+	16.2493i	1.55956	+	0.673555i
$583$	0.426325	+	1.17132i	0.0176566	+	0.0485110i
$584$	−5.80191	−	23.8832i	−0.240085	−	0.988294i
$585$	−1.46583	−	3.26478i	−0.0606046	−	0.134982i
$586$	18.0122	+	12.8236i	0.744077	+	0.529738i
$587$	0.849185	−	4.81597i	0.0350496	−	0.198776i	−0.962255	−	0.272150i	$-0.912265\pi$
$587$	0.849185	−	4.81597i	0.0350496	−	0.198776i	0.997305	+	0.0733735i	$0.0233765\pi$
$588$	−2.73086	+	8.01841i	−0.112619	+	0.330674i
$589$	14.4928	+	5.27494i	0.597165	+	0.217350i
$590$	−17.6751	+	1.40703i	−0.727672	+	0.0579263i
$591$	−33.0792	−	17.5222i	−1.36070	−	0.720766i
$592$	−10.4274	−	19.4423i	−0.428563	−	0.799075i
$593$		−	19.8805i		−	0.816393i	−0.912894	−	0.408196i	$-0.866158\pi$
$593$		−	19.8805i		−	0.816393i	0.912894	−	0.408196i	$-0.133842\pi$
$594$	1.89253	+	0.658294i	0.0776513	+	0.0270101i
$595$		−	20.2459i		−	0.830003i
$596$	8.29885	−	6.74498i	0.339934	−	0.276285i
$597$	27.4765	−	17.2290i	1.12454	−	0.705137i
$598$	0.135057	+	1.69659i	0.00552287	+	0.0693785i
$599$	−43.4392	−	15.8106i	−1.77488	−	0.646003i	−0.999902	−	0.0140140i	$-0.995539\pi$
$599$	−43.4392	−	15.8106i	−1.77488	−	0.646003i	−0.774977	−	0.631989i	$-0.782239\pi$
$600$	−4.87438	+	0.490303i	−0.198996	+	0.0200165i
$601$	4.76329	−	27.0140i	0.194299	−	1.10192i	−0.719115	−	0.694891i	$-0.755453\pi$
$601$	4.76329	−	27.0140i	0.194299	−	1.10192i	0.913414	−	0.407032i	$-0.133436\pi$
$602$	−20.5128	+	28.8125i	−0.836038	+	1.17431i
$603$	−7.39021	−	7.60502i	−0.300953	−	0.309700i
$604$	30.7823	−	10.6611i	1.25252	−	0.433792i
$605$	−3.73679	−	10.2668i	−0.151922	−	0.417403i
$606$	1.22677	+	1.64937i	0.0498340	+	0.0670012i
$607$	26.7992	+	31.9381i	1.08775	+	1.29633i	0.952173	+	0.305559i	$0.0988432\pi$
$607$	26.7992	+	31.9381i	1.08775	+	1.29633i	0.135573	+	0.990767i	$0.456712\pi$
$608$	6.88692	+	30.4182i	0.279302	+	1.23362i
$609$	23.4358	−	21.1682i	0.949666	−	0.857778i
$610$	4.81506	+	18.5498i	0.194956	+	0.751058i
$611$	4.56112	+	7.90009i	0.184523	+	0.319604i
$612$	−21.6903	−	33.0428i	−0.876780	−	1.33568i
$613$	−9.36878	+	16.2272i	−0.378402	+	0.655411i	−0.990830	−	0.135115i	$-0.956859\pi$
$613$	−9.36878	+	16.2272i	−0.378402	+	0.655411i	0.612428	+	0.790526i	$0.290193\pi$
$614$	−29.7437	−	8.21991i	−1.20036	−	0.331728i
$615$	−1.84570	+	0.749072i	−0.0744258	+	0.0302055i
$616$	−1.40476	+	1.90915i	−0.0565993	+	0.0769219i
$617$	27.9467	−	4.92777i	1.12509	−	0.198384i	0.420018	−	0.907516i	$-0.362024\pi$
$617$	27.9467	−	4.92777i	1.12509	−	0.198384i	0.705076	+	0.709132i	$0.250913\pi$
$618$	−1.45081	+	0.727811i	−0.0583600	+	0.0292768i
$619$	−10.7091	+	12.7626i	−0.430434	+	0.512972i	−0.937048	−	0.349202i	$-0.886453\pi$
$619$	−10.7091	+	12.7626i	−0.430434	+	0.512972i	0.506613	+	0.862173i	$0.330897\pi$
$620$	−5.49389	−	1.05767i	−0.220640	−	0.0424771i
$621$	1.46855	+	5.03218i	0.0589309	+	0.201935i
$622$	−16.5822	−	1.58167i	−0.664887	−	0.0634191i
$623$	25.9129	+	21.7435i	1.03818	+	0.871136i
$624$	6.30370	−	5.34505i	0.252350	−	0.213973i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	−6.76426	−	3.21894i	−0.270354	−	0.128655i
$627$	−2.57910	−	0.358355i	−0.102999	−	0.0143113i
$628$	12.5693	−	32.9208i	0.501571	−	1.31368i
$629$	−31.4664	−	18.1672i	−1.25465	−	0.724372i
$630$	12.3484	−	4.18709i	0.491973	−	0.166818i
$631$	−12.7122	+	7.33940i	−0.506065	+	0.292177i	−0.731215	−	0.682147i	$-0.761046\pi$
$631$	−12.7122	+	7.33940i	−0.506065	+	0.292177i	0.225150	+	0.974324i	$0.427713\pi$
$632$	−2.46090	−	38.5322i	−0.0978894	−	1.53273i
$633$	4.55332	−	14.0886i	0.180978	−	0.559973i
$634$	−10.2289	−	14.8546i	−0.406241	−	0.589950i
$635$	2.31294	−	1.94078i	0.0917861	−	0.0770177i
$636$	15.8321	−	0.329563i	0.627784	−	0.0130680i
$637$	−2.74109	+	0.997676i	−0.108606	+	0.0395293i
$638$	2.08093	−	0.950591i	0.0823848	−	0.0376343i
$639$	13.0986	+	19.2891i	0.518174	+	0.763064i
$640$	−4.21255	−	10.5002i	−0.166516	−	0.415057i
$641$	−6.25663	−	1.10321i	−0.247122	−	0.0435743i	0.0487150	−	0.998813i	$-0.484487\pi$
$641$	−6.25663	−	1.10321i	−0.247122	−	0.0435743i	−0.295837	+	0.955238i	$0.595598\pi$
$642$	24.1591	+	22.8134i	0.953485	+	0.900372i
$643$	1.52794	−	4.19799i	0.0602562	−	0.165552i	−0.905912	−	0.423467i	$-0.860813\pi$
$643$	1.52794	−	4.19799i	0.0602562	−	0.165552i	0.966168	+	0.257914i	$0.0830352\pi$
$644$	−6.20021	−	0.0970911i	−0.244323	−	0.00382593i
$645$	14.0853	−	0.513935i	0.554609	−	0.0202362i
$646$	36.0344	+	36.6031i	1.41775	+	1.44013i
$647$	−45.2638			−1.77950			−0.889751	−	0.456446i	$-0.849122\pi$
$647$	−45.2638			−1.77950			−0.889751	+	0.456446i	$0.849122\pi$
$648$	15.6677	−	20.0630i	0.615485	−	0.788149i
$649$	3.41873			0.134197
$650$	−1.18354	−	1.20222i	−0.0464223	−	0.0471549i
$651$	14.8810	−	0.542967i	0.583232	−	0.0212806i
$652$	8.78202	+	0.137520i	0.343930	+	0.00538572i
$653$	1.09898	−	3.01943i	0.0430065	−	0.118159i	−0.916330	−	0.400423i	$-0.868863\pi$
$653$	1.09898	−	3.01943i	0.0430065	−	0.118159i	0.959337	+	0.282264i	$0.0910853\pi$
$654$	−3.24213	−	3.06153i	−0.126777	−	0.119715i
$655$	−1.73646	−	0.306184i	−0.0678490	−	0.0119636i
$656$	−2.84512	−	3.61475i	−0.111083	−	0.141132i
$657$	11.3544	−	23.4660i	0.442977	−	0.915498i
$658$	−30.2315	+	13.8101i	−1.17855	+	0.538372i
$659$	43.4386	−	15.8103i	1.69213	−	0.615884i	0.697236	−	0.716842i	$-0.254413\pi$
$659$	43.4386	−	15.8103i	1.69213	−	0.615884i	0.994891	+	0.100958i	$0.0321909\pi$
$660$	0.944372	−	0.0196581i	0.0367596	−	0.000765192i
$661$	−37.1574	+	31.1788i	−1.44526	+	1.21271i	−0.509305	+	0.860586i	$0.670098\pi$
$661$	−37.1574	+	31.1788i	−1.44526	+	1.21271i	−0.935952	+	0.352129i	$0.885458\pi$
$662$	10.1949	+	14.8052i	0.396236	+	0.575420i
$663$	4.18588	−	12.9517i	0.162566	−	0.503003i
$664$	−14.2246	+	0.908471i	−0.552023	+	0.0352555i
$665$	−14.6741	+	8.47210i	−0.569037	+	0.328534i
$666$	4.57291	−	22.9492i	0.177197	−	0.889263i
$667$	5.18328	+	2.99257i	0.200697	+	0.115873i
$668$	−9.92875	+	26.0047i	−0.384155	+	1.00615i
$669$	−6.33518	−	0.880246i	−0.244932	−	0.0340323i
$670$	−4.51388	−	2.14804i	−0.174387	−	0.0829861i
$671$	−0.641652	−	3.63899i	−0.0247707	−	0.140482i
$672$	17.2056	+	24.7126i	0.663722	+	0.953309i
$673$	−6.00741	−	5.04082i	−0.231569	−	0.194309i	0.519619	−	0.854398i	$-0.326074\pi$
$673$	−6.00741	−	5.04082i	−0.231569	−	0.194309i	−0.751187	+	0.660089i	$0.770518\pi$
$674$	35.9077	+	3.42499i	1.38311	+	0.131926i
$675$	−4.32140	−	2.88540i	−0.166331	−	0.111059i
$676$	−22.7364	−	4.37716i	−0.874477	−	0.168352i
$677$	4.91578	−	5.85840i	0.188929	−	0.225157i	−0.663263	−	0.748387i	$-0.730829\pi$
$677$	4.91578	−	5.85840i	0.188929	−	0.225157i	0.852191	+	0.523230i	$0.175273\pi$
$678$	−38.7991	+	19.4640i	−1.49007	+	0.747509i
$679$	−50.6391	+	8.92904i	−1.94335	+	0.342665i
$680$	−15.0078	−	11.0428i	−0.575523	−	0.423471i
$681$	−44.6729	+	18.1304i	−1.71187	+	0.694758i
$682$	1.03976	+	0.287346i	0.0398144	+	0.0110030i
$683$	4.24195	−	7.34727i	0.162314	−	0.281136i	−0.773384	−	0.633937i	$-0.781438\pi$
$683$	4.24195	−	7.34727i	0.162314	−	0.281136i	0.935698	+	0.352802i	$0.114771\pi$
$684$	−14.8727	+	29.5480i	−0.568670	+	1.12980i
$685$	−5.45382	−	9.44629i	−0.208380	−	0.360924i
$686$	4.97380	+	19.1613i	0.189901	+	0.731582i
$687$	12.3893	−	11.1905i	0.472682	−	0.426946i
$688$	10.1697	+	30.9208i	0.387715	+	1.17885i
$689$	3.50525	+	4.17740i	0.133540	+	0.159146i
$690$	1.47478	+	1.98282i	0.0561439	+	0.0754847i
$691$	−6.41699	−	17.6305i	−0.244114	−	0.670697i	−0.999874	−	0.0158490i	$-0.994955\pi$
$691$	−6.41699	−	17.6305i	−0.244114	−	0.670697i	0.755761	−	0.654848i	$-0.227267\pi$
$692$	−13.1339	+	4.54877i	−0.499278	+	0.172918i
$693$	−2.43746	+	0.615835i	−0.0925916	+	0.0233937i
$694$	−28.6819	+	40.2870i	−1.08875	+	1.52927i
$695$	3.26592	−	18.5220i	0.123884	−	0.702578i
$696$	−2.90881	−	28.9182i	−0.110258	−	1.09614i
$697$	−7.11911	−	2.59115i	−0.269656	−	0.0981466i
$698$	1.30176	+	16.3527i	0.0492722	+	0.618959i
$699$	−6.28080	+	3.93836i	−0.237562	+	0.148962i
$700$	4.76988	−	3.87677i	0.180284	−	0.146528i
$701$			7.55317i			0.285279i	0.989775	+	0.142640i	$0.0455590\pi$
$701$			7.55317i			0.285279i	−0.989775	+	0.142640i	$0.954441\pi$
$702$	8.76521	−	0.125508i	0.330821	−	0.00473700i
$703$			30.4088i			1.14689i
$704$	0.649007	+	2.08262i	0.0244604	+	0.0784918i
$705$	11.7044	+	6.19985i	0.440812	+	0.233500i
$706$	−8.25418	+	0.657074i	−0.310650	+	0.0247293i
$707$	−2.42354	−	0.882098i	−0.0911467	−	0.0331747i
$708$	14.0020	−	41.1130i	0.526227	−	1.54512i
$709$	−9.16532	+	51.9791i	−0.344211	+	1.95212i	−0.0411264	+	0.999154i	$0.513095\pi$
$709$	−9.16532	+	51.9791i	−0.344211	+	1.95212i	−0.303085	+	0.952964i	$0.598016\pi$
$710$	8.95394	+	6.37467i	0.336035	+	0.239237i
$711$	23.9677	−	33.2067i	0.898859	−	1.24535i
$712$	30.2517	−	7.34900i	1.13373	−	0.275415i
$713$	0.965221	+	2.65192i	0.0361478	+	0.0993153i
$714$	45.5276	+	19.6628i	1.70383	+	0.735862i
$715$	0.209085	+	0.249178i	0.00781935	+	0.00931874i
$716$	−28.0825	+	15.6324i	−1.04949	+	0.584210i
$717$	1.10044	+	5.13762i	0.0410967	+	0.191868i
$718$	−39.4151	+	10.2312i	−1.47096	+	0.381824i
$719$	12.8423	+	22.2436i	0.478938	+	0.829545i	0.999708	−	0.0241521i	$-0.00768860\pi$
$719$	12.8423	+	22.2436i	0.478938	+	0.829545i	−0.520770	+	0.853697i	$0.674355\pi$
$720$	3.63143	−	11.4373i	0.135335	−	0.426244i
$721$	1.01825	−	1.76366i	0.0379216	−	0.0656822i
$722$	4.29326	−	15.5351i	0.159778	−	0.578157i
$723$	−23.9859	−	18.6795i	−0.892047	−	0.694699i
$724$	10.7746	+	6.44771i	0.400433	+	0.239627i
$725$	−5.84255	+	1.03020i	−0.216987	+	0.0382606i
$726$	26.7163	+	1.56802i	0.991534	+	0.0581947i
$727$	−25.3160	+	30.1704i	−0.938918	+	1.11896i	0.0538060	+	0.998551i	$0.482865\pi$
$727$	−25.3160	+	30.1704i	−0.938918	+	1.11896i	−0.992724	+	0.120408i	$0.961580\pi$
$728$	−2.91834	+	9.95047i	−0.108161	+	0.368789i
$729$	26.3561	−	5.86128i	0.976153	−	0.217085i
$730$	1.16686	−	12.2334i	0.0431874	−	0.452778i
$731$	41.0657	+	34.4582i	1.51887	+	1.27448i
$732$	−46.3897	−	7.18773i	−1.71461	−	0.265666i
$733$	−6.15340	−	34.8977i	−0.227281	−	1.28898i	−0.858276	−	0.513188i	$-0.828464\pi$
$733$	−6.15340	−	34.8977i	−0.227281	−	1.28898i	0.630995	−	0.775787i	$-0.282647\pi$
$734$	12.3891	−	26.0343i	0.457289	−	0.960945i
$735$	−2.60231	+	3.34157i	−0.0959877	+	0.123256i
$736$	−3.45376	+	4.54311i	−0.127307	+	0.167461i
$737$	0.834716	+	0.481923i	0.0307471	+	0.0177519i
$738$	0.108080	−	4.87797i	0.00397849	−	0.179561i
$739$	−14.1041	+	8.14299i	−0.518827	+	0.299545i	−0.736455	−	0.676487i	$-0.763501\pi$
$739$	−14.1041	+	8.14299i	−0.518827	+	0.299545i	0.217628	+	0.976032i	$0.430168\pi$
$740$	−1.74519	−	10.8921i	−0.0641545	−	0.400402i
$741$	−11.1389	+	2.38587i	−0.409199	+	0.0876472i
$742$	−16.3640	+	11.2683i	−0.600742	+	0.413673i
$743$	18.6123	−	15.6176i	0.682819	−	0.572953i	−0.234010	−	0.972234i	$-0.575185\pi$
$743$	18.6123	−	15.6176i	0.682819	−	0.572953i	0.916828	+	0.399281i	$0.130740\pi$
$744$	7.71407	−	11.3271i	0.282812	−	0.415270i
$745$	5.02462	−	1.82881i	0.184088	−	0.0670025i
$746$	−20.5585	−	45.0044i	−0.752700	−	1.64773i
$747$	−12.2587	−	8.84796i	−0.448521	−	0.323730i
$748$	2.71559	+	2.35208i	0.0992916	+	0.0860004i
$749$	−41.0573	−	7.23951i	−1.50020	−	0.264526i
$750$	−2.38321	−	0.565956i	−0.0870226	−	0.0206658i
$751$	10.3259	−	28.3701i	0.376797	−	1.03524i	−0.595879	−	0.803074i	$-0.703196\pi$
$751$	10.3259	−	28.3701i	0.376797	−	1.03524i	0.972676	−	0.232167i	$-0.0745816\pi$
$752$	−6.25215	+	29.9423i	−0.227992	+	1.09188i
$753$	−15.4414	+	29.1510i	−0.562716	+	1.06232i
$754$	7.13238	−	7.02157i	0.259746	−	0.255710i
$755$	16.2881			0.592785
$756$	−2.57714	+	31.8347i	−0.0937296	+	1.15782i
$757$	37.5060			1.36318			0.681589	−	0.731735i	$-0.261289\pi$
$757$	37.5060			1.36318			0.681589	+	0.731735i	$0.261289\pi$
$758$	15.3914	−	15.1522i	0.559040	−	0.550354i
$759$	−0.253119	−	0.403668i	−0.00918764	−	0.0146522i
$760$	−1.72357	+	15.4985i	−0.0625203	+	0.562189i
$761$	1.85478	−	5.09595i	0.0672356	−	0.184728i	−0.901525	−	0.432728i	$-0.857551\pi$
$761$	1.85478	−	5.09595i	0.0672356	−	0.184728i	0.968760	+	0.248000i	$0.0797733\pi$
$762$	2.11798	+	7.08605i	0.0767262	+	0.256701i
$763$	5.50984	+	0.971533i	0.199469	+	0.0351718i
$764$	−6.14275	+	7.09210i	−0.222237	+	0.256583i
$765$	−4.84107	−	19.1609i	−0.175029	−	0.692762i
$766$	−3.51030	−	7.68437i	−0.126832	−	0.277648i
$767$	14.0545	−	5.11540i	0.507477	−	0.184707i
$768$	27.7033	+	0.724912i	0.999658	+	0.0261580i
$769$	−23.5830	+	19.7885i	−0.850423	+	0.713590i	−0.959883	−	0.280401i	$-0.909532\pi$
$769$	−23.5830	+	19.7885i	−0.850423	+	0.713590i	0.109460	+	0.993991i	$0.465088\pi$
$770$	−0.976100	+	0.672146i	−0.0351762	+	0.0242225i
$771$	19.0372	+	21.0765i	0.685607	+	0.759053i
$772$	42.4794	−	6.80627i	1.52887	−	0.244963i
$773$	−9.39419	+	5.42374i	−0.337886	+	0.195078i	−0.659337	−	0.751848i	$-0.729163\pi$
$773$	−9.39419	+	5.42374i	−0.337886	+	0.195078i	0.321451	+	0.946926i	$0.395829\pi$
$774$	−12.5239	+	32.1732i	−0.450163	+	1.15644i
$775$	−2.42261	−	1.39869i	−0.0870227	−	0.0502426i
$776$	−21.0013	+	42.4077i	−0.753902	+	1.52235i
$777$	11.0410	+	27.2048i	0.396093	+	0.975966i
$778$	21.4899	−	45.1587i	0.770449	−	1.61902i
$779$	1.10102	+	6.24417i	0.0394480	+	0.223720i
$780$	3.85291	−	1.49387i	0.137956	−	0.0534890i
$781$	−1.62344	−	1.36223i	−0.0580912	−	0.0487443i
$782$	−0.892428	+	9.35625i	−0.0319132	+	0.334579i
$783$	17.1182	−	25.6375i	0.611753	−	0.916208i
$784$	−9.08198	−	3.63148i	−0.324356	−	0.129696i
$785$	11.3255	−	13.4972i	0.404224	−	0.481736i
$786$	2.37497	−	3.60745i	0.0847123	−	0.128674i
$787$	2.51966	−	0.444283i	0.0898161	−	0.0158370i	−0.128560	−	0.991702i	$-0.541035\pi$
$787$	2.51966	−	0.444283i	0.0898161	−	0.0158370i	0.218376	+	0.975865i	$0.429924\pi$
$788$	22.1956	−	37.0904i	0.790687	−	1.32129i
$789$	0.474656	−	3.41613i	0.0168982	−	0.121617i
$790$	5.14243	−	18.6079i	0.182960	−	0.662038i
$791$	27.2312	−	47.1659i	0.968231	−	1.67703i
$792$	−0.872966	+	2.14273i	−0.0310195	+	0.0761385i
$793$	−8.08281	−	13.9998i	−0.287029	−	0.497149i
$794$	15.0143	−	3.89735i	0.532838	−	0.138312i
$795$	7.53407	+	2.43494i	0.267206	+	0.0863585i
$796$	18.2142	+	32.7206i	0.645585	+	1.15975i
$797$	−27.1379	−	32.3417i	−0.961273	−	1.14560i	−0.989286	−	0.145993i	$-0.953362\pi$
$797$	−27.1379	−	32.3417i	−0.961273	−	1.14560i	0.0280127	−	0.999608i	$-0.491082\pi$
$798$	−4.79998	−	41.2261i	−0.169917	−	1.45939i
$799$	17.2296	+	47.3378i	0.609538	+	1.67469i
$800$	−0.272111	−	5.65031i	−0.00962056	−	0.199768i
$801$	29.7233	+	14.3821i	1.05022	+	0.508165i
$802$	−37.9761	−	27.0367i	−1.34098	−	0.954699i
$803$	−0.411448	+	2.33344i	−0.0145197	+	0.0823452i
$804$	9.21423	−	8.06432i	0.324961	−	0.284407i
$805$	−2.91351	−	1.06043i	−0.102688	−	0.0373752i
$806$	4.70442	−	0.374495i	0.165706	−	0.0131910i
$807$	0.172041	+	4.71510i	0.00605614	+	0.165979i
$808$	−1.97575	+	1.31539i	−0.0695068	+	0.0462752i
$809$		−	13.3269i		−	0.468547i	−0.972171	−	0.234274i	$-0.924729\pi$
$809$		−	13.3269i		−	0.468547i	0.972171	−	0.234274i	$-0.0752712\pi$
$810$	10.6854	−	6.91535i	0.375447	−	0.242981i
$811$		−	42.3578i		−	1.48738i	−0.668523	−	0.743692i	$-0.733073\pi$
$811$		−	42.3578i		−	1.48738i	0.668523	−	0.743692i	$-0.266927\pi$
$812$	22.9997	+	28.2982i	0.807130	+	0.993071i
$813$	−0.442359	−	12.1236i	−0.0155142	−	0.425194i
$814$	0.168778	+	2.12020i	0.00591567	+	0.0743128i
$815$	4.12671	+	1.50200i	0.144552	+	0.0526127i
$816$	39.4077	−	23.0238i	1.37955	−	0.805993i
$817$	7.79074	−	44.1835i	0.272563	−	1.54578i
$818$	−12.4038	+	17.4226i	−0.433689	+	0.609165i
$819$	−9.09898	+	6.17885i	−0.317944	+	0.215907i
$820$	−0.752730	−	2.17340i	−0.0262865	−	0.0758985i
$821$	−2.21776	−	6.09325i	−0.0774004	−	0.212656i	0.894957	−	0.446152i	$-0.147206\pi$
$821$	−2.21776	−	6.09325i	−0.0774004	−	0.212656i	−0.972358	+	0.233496i	$0.924984\pi$
$822$	26.5389	−	3.08993i	0.925649	−	0.107774i
$823$	8.52559	+	10.1604i	0.297183	+	0.354169i	0.893887	−	0.448292i	$-0.147968\pi$
$823$	8.52559	+	10.1604i	0.297183	+	0.354169i	−0.596704	+	0.802462i	$0.703523\pi$
$824$	−0.751972	−	1.71676i	−0.0261962	−	0.0598062i
$825$	0.449401	+	0.145242i	0.0156461	+	0.00505668i
$826$	13.6913	+	52.7450i	0.476382	+	1.83523i
$827$	15.3189	+	26.5331i	0.532691	+	0.922648i	0.999271	+	0.0381689i	$0.0121525\pi$
$827$	15.3189	+	26.5331i	0.532691	+	0.922648i	−0.466580	+	0.884479i	$0.654514\pi$
$828$	−5.89113	+	1.39067i	−0.204731	+	0.0483290i
$829$	−23.6173	+	40.9063i	−0.820262	+	1.42073i	0.0852257	+	0.996362i	$0.472839\pi$
$829$	−23.6173	+	40.9063i	−0.820262	+	1.42073i	−0.905487	+	0.424373i	$0.860494\pi$
$830$	−6.86931	−	1.89839i	−0.238437	−	0.0658941i
$831$	3.95611	−	28.4723i	0.137236	−	0.987695i
$832$	5.78428	+	7.59060i	0.200534	+	0.263157i
$833$	−15.8639	+	2.79723i	−0.549652	+	0.0969184i
$834$	38.4790	+	25.3327i	1.33242	+	0.877199i
$835$	−8.94622	+	10.6617i	−0.309597	+	0.368963i
$836$	0.568406	−	2.95248i	0.0196587	−	0.102114i
$837$	13.9536	−	4.07211i	0.482307	−	0.140753i
$838$	9.56028	+	0.911890i	0.330255	+	0.0315007i
$839$	−12.5942	−	10.5678i	−0.434801	−	0.364841i	0.398959	−	0.916969i	$-0.369372\pi$
$839$	−12.5942	−	10.5678i	−0.434801	−	0.364841i	−0.833760	+	0.552128i	$0.813816\pi$
$840$	4.08530	+	14.4913i	0.140956	+	0.499996i
$841$	−1.07605	−	6.10257i	−0.0371051	−	0.210434i
$842$	28.4943	+	13.5597i	0.981980	+	0.467299i
$843$	12.9164	+	31.8258i	0.444865	+	1.09614i
$844$	15.9721	+	6.09824i	0.549782	+	0.209910i
$845$	−10.0259	−	5.78848i	−0.344903	−	0.199130i
$846$	−25.3090	+	20.2986i	−0.870143	+	0.697882i
$847$	−29.0794	+	16.7890i	−0.999179	+	0.576876i
$848$	−0.572531	+	18.2763i	−0.0196608	+	0.627612i
$849$	5.02658	+	5.56505i	0.172512	+	0.190992i
$850$	−5.28373	−	7.67311i	−0.181230	−	0.263185i
$851$	−4.26249	+	3.57665i	−0.146116	+	0.122606i
$852$	−23.0309	+	13.9439i	−0.789027	+	0.477710i
$853$	−24.8635	+	9.04957i	−0.851310	+	0.309851i	−0.730574	−	0.682833i	$-0.760748\pi$
$853$	−24.8635	+	9.04957i	−0.851310	+	0.309851i	−0.120736	+	0.992685i	$0.538525\pi$
$854$	53.5735	−	24.4730i	1.83325	−	0.837447i
$855$	−11.8619	+	11.5268i	−0.405667	+	0.394208i
$856$	−27.7604	+	26.4861i	−0.948831	+	0.905276i
$857$	35.7866	+	6.31014i	1.22245	+	0.215550i	0.747378	−	0.664399i	$-0.231312\pi$
$857$	35.7866	+	6.31014i	1.22245	+	0.215550i	0.475068	+	0.879949i	$0.342424\pi$
$858$	−0.763397	+	0.228175i	−0.0260620	+	0.00778975i
$859$	−1.78310	+	4.89902i	−0.0608385	+	0.167152i	−0.966388	−	0.257089i	$-0.917237\pi$
$859$	−1.78310	+	4.89902i	−0.0608385	+	0.167152i	0.905549	+	0.424241i	$0.139459\pi$
$860$	−0.254826	+	16.2731i	−0.00868951	+	0.554910i
$861$	3.25217	+	5.18648i	0.110833	+	0.176755i
$862$	−20.0714	−	20.3882i	−0.683634	−	0.694423i
$863$	−24.2545			−0.825633			−0.412816	−	0.910814i	$-0.635455\pi$
$863$	−24.2545			−0.825633			−0.412816	+	0.910814i	$0.635455\pi$
$864$	22.1926	+	19.2740i	0.755008	+	0.655715i
$865$	−6.94967			−0.236296
$866$	−19.6686	−	19.9790i	−0.668366	−	0.678914i
$867$	21.4016	−	40.4030i	0.726837	−	1.37216i
$868$	−0.269221	+	17.1924i	−0.00913797	+	0.583548i
$869$	−1.27310	+	3.49780i	−0.0431868	+	0.118655i
$870$	3.35764	−	14.1388i	0.113835	−	0.479351i
$871$	4.15262	+	0.732220i	0.140706	+	0.0248103i
$872$	3.72541	−	3.55440i	0.126158	−	0.120367i
$873$	−45.7900	+	20.5590i	−1.54976	+	0.695815i
$874$	7.15478	−	3.26838i	0.242014	−	0.110555i
$875$	2.88797	−	1.05114i	0.0976313	−	0.0355349i
$876$	26.3763	+	14.5050i	0.891172	+	0.490078i
$877$	−15.9893	+	13.4166i	−0.539920	+	0.453046i	−0.871510	−	0.490377i	$-0.836859\pi$
$877$	−15.9893	+	13.4166i	−0.539920	+	0.453046i	0.331591	+	0.943423i	$0.392415\pi$
$878$	−13.5453	−	19.6707i	−0.457133	−	0.663855i
$879$	−26.4794	+	5.67168i	−0.893127	+	0.191301i
$880$	−0.0341509	+	1.09017i	−0.00115123	+	0.0367496i
$881$	−3.11044	+	1.79581i	−0.104793	+	0.0605025i	−0.551481	−	0.834188i	$-0.685937\pi$
$881$	−3.11044	+	1.79581i	−0.104793	+	0.0605025i	0.446687	+	0.894690i	$0.352604\pi$
$882$	−4.98692	−	9.09722i	−0.167918	−	0.306319i
$883$	33.0789	+	19.0981i	1.11320	+	0.642704i	0.939655	−	0.342123i	$-0.111146\pi$
$883$	33.0789	+	19.0981i	1.11320	+	0.642704i	0.173540	+	0.984827i	$0.444479\pi$
$884$	14.6832	+	5.60613i	0.493849	+	0.188554i
$885$	13.3429	−	17.1333i	0.448516	−	0.575930i
$886$	17.3890	+	8.27498i	0.584195	+	0.278004i
$887$	3.08404	+	17.4905i	0.103552	+	0.587273i	0.991789	+	0.127887i	$0.0408195\pi$
$887$	3.08404	+	17.4905i	0.103552	+	0.587273i	−0.888237	+	0.459386i	$0.848069\pi$
$888$	26.1883	+	6.65394i	0.878822	+	0.223291i
$889$	−7.10839	−	5.96465i	−0.238408	−	0.200048i
$890$	15.4954	+	1.47800i	0.519408	+	0.0495428i
$891$	−2.15957	+	1.16566i	−0.0723484	+	0.0390511i
$892$	1.39620	−	7.25234i	0.0467484	−	0.242826i
$893$	27.1002	−	32.2968i	0.906874	−	1.08077i
$894$	−0.767401	+	13.0751i	−0.0256657	+	0.437298i
$895$	−15.8260	+	2.79055i	−0.529006	+	0.0932780i
$896$	−29.5321	+	18.3535i	−0.986598	+	0.613148i
$897$	−1.64458	−	1.28075i	−0.0549109	−	0.0427629i
$898$	−9.93563	−	2.74579i	−0.331556	−	0.0916283i
$899$	8.29801	−	14.3726i	0.276754	−	0.479352i
$900$	3.58725	−	4.80954i	0.119575	−	0.160318i
$901$	15.0572	+	26.0798i	0.501627	+	0.868843i
$902$	0.111423	+	0.429251i	0.00370998	+	0.0142925i
$903$	−9.07248	−	42.3567i	−0.301913	−	1.40954i
$904$	−20.1101	−	45.9116i	−0.668852	−	1.52700i
$905$	4.03556	+	4.80939i	0.134147	+	0.159870i
$906$	−15.8190	+	36.6275i	−0.525550	+	1.21687i
$907$	−2.18337	−	5.99875i	−0.0724975	−	0.199185i	0.898151	−	0.439686i	$-0.144910\pi$
$907$	−2.18337	−	5.99875i	−0.0724975	−	0.199185i	−0.970649	+	0.240501i	$0.922688\pi$
$908$	−18.2189	−	52.6046i	−0.604616	−	1.74575i
$909$	−2.50457	−	0.255320i	−0.0830715	−	0.00846844i
$910$	−3.00704	+	4.22373i	−0.0996824	+	0.140015i
$911$	−10.3439	+	58.6634i	−0.342710	+	1.94361i	−0.0118413	+	0.999930i	$0.503769\pi$
$911$	−10.3439	+	58.6634i	−0.342710	+	1.94361i	−0.330869	+	0.943677i	$0.607342\pi$
$912$	−33.1780	−	18.9279i	−1.09863	−	0.626767i
$913$	1.29126	+	0.469979i	0.0427343	+	0.0155540i
$914$	−0.569930	−	7.15947i	−0.0188516	−	0.236814i
$915$	−20.7414	−	10.9868i	−0.685691	−	0.363213i
$916$	12.1588	+	14.9598i	0.401737	+	0.494286i
$917$			5.41901i			0.178952i
$918$	47.7892	+	7.72273i	1.57728	+	0.254888i
$919$		−	21.3779i		−	0.705192i	−0.935776	−	0.352596i	$-0.885299\pi$
$919$		−	21.3779i		−	0.705192i	0.935776	−	0.352596i	$-0.114701\pi$
$920$	−2.37519	+	1.58132i	−0.0783076	+	0.0521345i
$921$	32.0197	−	20.0778i	1.05508	−	0.661587i
$922$	32.5943	−	2.59467i	1.07344	−	0.0854508i
$923$	−8.71226	−	3.17100i	−0.286768	−	0.104375i
$924$	−0.563486	−	2.84777i	−0.0185373	−	0.0936847i
$925$	0.957760	−	5.43173i	0.0314909	−	0.178594i
$926$	−15.4214	−	10.9791i	−0.506780	−	0.360797i
$927$	0.541963	−	1.91262i	0.0178004	−	0.0628185i
$928$	33.5215	−	1.61435i	1.10040	−	0.0529935i
$929$	−5.05086	−	13.8771i	−0.165713	−	0.455294i	0.828845	−	0.559479i	$-0.188999\pi$
$929$	−5.05086	−	13.8771i	−0.165713	−	0.455294i	−0.994558	+	0.104185i	$0.966777\pi$
$930$	5.49811	−	4.08938i	0.180290	−	0.134096i
$931$	8.66581	+	10.3275i	0.284010	+	0.338470i
$932$	−4.16355	−	7.47955i	−0.136382	−	0.245001i
$933$	15.1397	−	13.6748i	0.495650	−	0.447692i
$934$	−31.6471	+	8.21482i	−1.03553	+	0.268797i
$935$	0.898146	+	1.55564i	0.0293725	+	0.0508747i
$936$	−0.382643	+	10.1150i	−0.0125071	+	0.330619i
$937$	4.62381	−	8.00868i	0.151053	−	0.261632i	−0.780562	−	0.625079i	$-0.785067\pi$
$937$	4.62381	−	8.00868i	0.151053	−	0.261632i	0.931615	+	0.363447i	$0.118400\pi$
$938$	−4.09237	+	14.8082i	−0.133621	+	0.483505i
$939$	8.50125	−	3.45021i	0.277428	−	0.112593i
$940$	−7.85346	+	13.1237i	−0.256152	+	0.428047i
$941$	28.7829	−	5.07520i	0.938296	−	0.165447i	0.316470	−	0.948602i	$-0.397502\pi$
$941$	28.7829	−	5.07520i	0.938296	−	0.165447i	0.621826	+	0.783156i	$0.286391\pi$
$942$	19.3522	+	38.5764i	0.630530	+	1.25689i
$943$	−0.745761	+	0.888763i	−0.0242853	+	0.0289421i
$944$	46.5662	+	18.6198i	1.51560	+	0.606022i
$945$	−6.42680	+	14.6191i	−0.209064	+	0.475560i
$946$	0.297962	−	3.12385i	0.00968759	−	0.101565i
$947$	−25.1935	−	21.1398i	−0.818678	−	0.686953i	0.133984	−	0.990984i	$-0.457223\pi$
$947$	−25.1935	−	21.1398i	−0.818678	−	0.686953i	−0.952662	+	0.304031i	$0.901667\pi$
$948$	36.8497	+	29.6359i	1.19682	+	0.962528i
$949$	1.80002	+	10.2084i	0.0584312	+	0.331380i
$950$	−3.35038	+	7.04048i	−0.108701	+	0.228423i
$951$	21.8790	+	3.03999i	0.709475	+	0.0985786i
$952$	−25.4131	+	51.3163i	−0.823642	+	1.66317i
$953$	−19.6716	−	11.3574i	−0.637226	−	0.367902i	0.146319	−	0.989237i	$-0.453257\pi$
$953$	−19.6716	−	11.3574i	−0.637226	−	0.367902i	−0.783545	+	0.621335i	$0.786591\pi$
$954$	−12.7926	+	14.5773i	−0.414175	+	0.471956i
$955$	−4.06274	+	2.34562i	−0.131467	+	0.0759026i
$956$	−5.99057	+	0.959840i	−0.193749	+	0.0310435i
$957$	−0.861675	+	2.66615i	−0.0278540	+	0.0861844i
$958$	−11.1253	+	7.66095i	−0.359444	+	0.247514i
$959$	−25.6798	+	21.5479i	−0.829244	+	0.695819i
$960$	12.9703	+	4.87566i	0.418614	+	0.157361i
$961$	−21.7770	+	7.92619i	−0.702485	+	0.255683i
$962$	3.86627	+	8.46362i	0.124654	+	0.272878i
$963$	−40.5879	+	2.96583i	−1.30793	+	0.0955727i
$964$	22.9831	−	26.5351i	0.740236	−	0.854638i
$965$	21.1838	+	3.73527i	0.681930	+	0.120243i
$966$	5.21421	−	5.52179i	0.167764	−	0.177661i
$967$	13.3297	−	36.6229i	0.428653	−	1.17771i	−0.517978	−	0.855394i	$-0.673315\pi$
$967$	13.3297	−	36.6229i	0.428653	−	1.17771i	0.946631	−	0.322320i	$-0.104463\pi$
$968$	−3.41556	+	30.7131i	−0.109780	+	0.987155i
$969$	−62.8660	+	2.29381i	−2.01955	+	0.0736879i
$970$	−16.8617	+	16.5997i	−0.541396	+	0.532984i
$971$	−20.3150			−0.651939			−0.325970	−	0.945380i	$-0.605691\pi$
$971$	−20.3150			−0.651939			−0.325970	+	0.945380i	$0.605691\pi$
$972$	5.17308	+	30.7447i	0.165927	+	0.986138i
$973$	−57.8020			−1.85305
$974$	33.5839	−	33.0621i	1.07610	−	1.05938i
$975$	2.06482	−	0.0753396i	0.0661271	−	0.00241280i
$976$	11.0795	−	53.0610i	0.354646	−	1.69844i
$977$	−1.16220	+	3.19311i	−0.0371820	+	0.102157i	−0.956894	−	0.290436i	$-0.906200\pi$
$977$	−1.16220	+	3.19311i	−0.0371820	+	0.102157i	0.919712	+	0.392593i	$0.128422\pi$
$978$	−7.38543	+	7.82110i	−0.236160	+	0.250091i
$979$	−2.95565	−	0.521161i	−0.0944630	−	0.0166564i
$980$	−3.69670	−	3.20186i	−0.118087	−	0.102280i
$981$	5.44684	−	0.398011i	0.173904	−	0.0127075i
$982$	−19.3570	−	42.3743i	−0.617708	−	1.35222i
$983$	0.415565	−	0.151253i	0.0132545	−	0.00482423i	−0.335384	−	0.942081i	$-0.608866\pi$
$983$	0.415565	−	0.151253i	0.0132545	−	0.00482423i	0.348639	+	0.937257i	$0.386644\pi$
$984$	5.61844	+	0.418120i	0.179109	+	0.0133292i
$985$	16.5559	−	13.8920i	0.527514	−	0.442637i
$986$	45.5221	−	31.3467i	1.44972	−	0.998281i
$987$	12.5183	−	38.7335i	0.398462	−	1.23290i
$988$	−2.08104	−	12.9882i	−0.0662066	−	0.413210i
$989$	7.10965	−	4.10476i	0.226074	−	0.130524i
$990$	−0.763067	+	0.869520i	−0.0242519	+	0.0276352i
$991$	12.1798	+	7.03200i	0.386903	+	0.223379i	0.680818	−	0.732453i	$-0.261625\pi$
$991$	12.1798	+	7.03200i	0.386903	+	0.223379i	−0.293914	+	0.955832i	$0.594958\pi$
$992$	12.5975	+	9.57685i	0.399970	+	0.304065i
$993$	−21.8063	−	3.02989i	−0.692001	−	0.0961506i
$994$	14.5152	−	30.5022i	0.460395	−	0.967472i
$995$	3.25144	+	18.4398i	0.103077	+	0.584581i
$996$	10.9404	−	13.6035i	0.346661	−	0.431043i
$997$	25.8756	+	21.7122i	0.819490	+	0.687634i	0.952853	−	0.303434i	$-0.0981331\pi$
$997$	25.8756	+	21.7122i	0.819490	+	0.687634i	−0.133363	+	0.991067i	$0.542578\pi$
$998$	−2.05509	+	21.5456i	−0.0650526	+	0.682014i
$999$	16.9543	+	23.1067i	0.536409	+	0.731063i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.be.a.11.19	✓	432
4.3	odd	2	inner	540.2.be.a.11.58	yes	432
27.5	odd	18	inner	540.2.be.a.491.58	yes	432
108.59	even	18	inner	540.2.be.a.491.19	yes	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
540.2.be.a.11.19	✓	432	1.1	even	1	trivial
540.2.be.a.11.58	yes	432	4.3	odd	2	inner
540.2.be.a.491.19	yes	432	108.59	even	18	inner
540.2.be.a.491.58	yes	432	27.5	odd	18	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:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.992140 - 1.00780i) q^{2} +(1.73090 - 0.0631559i) q^{3} +(-0.0313148 + 1.99975i) q^{4} +(-0.342020 + 0.939693i) q^{5} +(-1.78094 - 1.68174i) q^{6} +(3.02663 + 0.533676i) q^{7} +(2.04642 - 1.95248i) q^{8} +(2.99202 - 0.218633i) q^{9} +(1.28635 - 0.587620i) q^{10} +(-0.256231 + 0.0932606i) q^{11} +(0.0720935 + 3.46335i) q^{12} +(-0.913826 + 0.766791i) q^{13} +(-2.46500 - 3.57971i) q^{14} +(-0.532655 + 1.64811i) q^{15} +(-3.99804 - 0.125244i) q^{16} +(-5.70507 + 3.29383i) q^{17} +(-3.18884 - 2.79844i) q^{18} +(4.77468 + 2.75666i) q^{19} +(-1.86844 - 0.713383i) q^{20} +(5.27249 + 0.732590i) q^{21} +(0.348205 + 0.165702i) q^{22} +(0.175183 + 0.993514i) q^{23} +(3.41883 - 3.50879i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(1.67942 + 0.160188i) q^{26} +(5.16508 - 0.567395i) q^{27} +(-1.16200 + 6.03580i) q^{28} +(3.81345 - 4.54470i) q^{29} +(2.18943 - 1.09835i) q^{30} +(2.75489 - 0.485761i) q^{31} +(3.84040 + 4.15348i) q^{32} +(-0.437621 + 0.177607i) q^{33} +(8.97975 + 2.48163i) q^{34} +(-1.53666 + 2.66157i) q^{35} +(0.343518 + 5.99016i) q^{36} +(2.75776 + 4.77658i) q^{37} +(-1.95899 - 7.54691i) q^{38} +(-1.53331 + 1.38495i) q^{39} +(1.13481 + 2.59079i) q^{40} +(0.739225 + 0.880975i) q^{41} +(-4.49275 - 6.04044i) q^{42} +(-2.78321 - 7.64682i) q^{43} +(-0.178474 - 0.515320i) q^{44} +(-0.817884 + 2.88636i) q^{45} +(0.827455 - 1.16226i) q^{46} +(1.32789 - 7.53084i) q^{47} +(-6.92811 + 0.0357152i) q^{48} +(2.29781 + 0.836334i) q^{49} +(0.112223 + 1.40975i) q^{50} +(-9.66688 + 6.06159i) q^{51} +(-1.50478 - 1.85144i) q^{52} -4.57133i q^{53} +(-5.69631 - 4.64242i) q^{54} -0.272676i q^{55} +(7.23573 - 4.81730i) q^{56} +(8.43859 + 4.46996i) q^{57} +(-8.36362 + 0.665786i) q^{58} +(-11.7816 - 4.28815i) q^{59} +(-3.27914 - 1.11679i) q^{60} +(-2.35317 + 13.3455i) q^{61} +(-3.22279 - 2.29443i) q^{62} +(9.17241 + 0.935050i) q^{63} +(0.375655 - 7.99118i) q^{64} +(-0.408001 - 1.12097i) q^{65} +(0.613173 + 0.264822i) q^{66} +(-2.27211 - 2.70779i) q^{67} +(-6.40819 - 11.5119i) q^{68} +(0.365971 + 1.70861i) q^{69} +(4.20691 - 1.09201i) q^{70} +(3.88602 + 6.73079i) q^{71} +(5.69605 - 6.28927i) q^{72} +(4.34479 - 7.52539i) q^{73} +(2.07774 - 7.51830i) q^{74} +(-1.36654 - 1.06422i) q^{75} +(-5.66217 + 9.46186i) q^{76} +(-0.825287 + 0.145520i) q^{77} +(2.91701 + 0.171204i) q^{78} +(8.77467 - 10.4572i) q^{79} +(1.48510 - 3.71409i) q^{80} +(8.90440 - 1.30831i) q^{81} +(0.154429 - 1.61904i) q^{82} +(-3.86041 - 3.23927i) q^{83} +(-1.63011 + 10.5207i) q^{84} +(-1.14393 - 6.48757i) q^{85} +(-4.94511 + 10.3916i) q^{86} +(6.31368 - 8.10726i) q^{87} +(-0.342267 + 0.691136i) q^{88} +(9.53204 + 5.50333i) q^{89} +(3.72032 - 2.03941i) q^{90} +(-3.17503 + 1.83310i) q^{91} +(-1.99227 + 0.319212i) q^{92} +(4.73776 - 1.01479i) q^{93} +(-8.90702 + 6.13340i) q^{94} +(-4.22345 + 3.54390i) q^{95} +(6.90965 + 6.94670i) q^{96} +(-15.7222 + 5.72241i) q^{97} +(-1.43689 - 3.14549i) q^{98} +(-0.746260 + 0.335058i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) \) 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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