LMFDB - Embedded newform 162.2.g.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$4$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			31.1
Character	$\chi$	$=$	162.31
Dual form			162.2.g.a.115.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.396080 - 0.918216i) q^{2} +(-1.62371 + 0.602974i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(-0.0263678 + 0.452718i) q^{5} +(1.19678 + 1.25209i) q^{6} +(4.03057 - 0.955263i) q^{7} +(0.939693 + 0.342020i) q^{8} +(2.27284 - 1.95811i) q^{9} +O(q^{10})$	\(q+(-0.396080 - 0.918216i) q^{2} +(-1.62371 + 0.602974i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(-0.0263678 + 0.452718i) q^{5} +(1.19678 + 1.25209i) q^{6} +(4.03057 - 0.955263i) q^{7} +(0.939693 + 0.342020i) q^{8} +(2.27284 - 1.95811i) q^{9} +(0.426137 - 0.155101i) q^{10} +(0.410794 - 0.270184i) q^{11} +(0.675668 - 1.59483i) q^{12} +(3.42955 - 0.400857i) q^{13} +(-2.47357 - 3.32258i) q^{14} +(-0.230164 - 0.750981i) q^{15} +(-0.0581448 - 0.998308i) q^{16} +(2.51871 + 2.11345i) q^{17} +(-2.69819 - 1.31140i) q^{18} +(-1.21368 + 1.01840i) q^{19} +(-0.311201 - 0.329854i) q^{20} +(-5.96847 + 3.98140i) q^{21} +(-0.410794 - 0.270184i) q^{22} +(-6.89877 - 1.63504i) q^{23} +(-1.73201 + 0.0112699i) q^{24} +(4.76193 + 0.556590i) q^{25} +(-1.72645 - 2.99029i) q^{26} +(-2.50975 + 4.54985i) q^{27} +(-2.07111 + 3.58727i) q^{28} +(2.14438 - 2.88040i) q^{29} +(-0.598400 + 0.508788i) q^{30} +(1.00695 + 3.36344i) q^{31} +(-0.893633 + 0.448799i) q^{32} +(-0.504095 + 0.686397i) q^{33} +(0.942994 - 3.14982i) q^{34} +(0.326188 + 1.84990i) q^{35} +(-0.135446 + 2.99694i) q^{36} +(-0.757807 + 4.29774i) q^{37} +(1.41582 + 0.711053i) q^{38} +(-5.32687 + 2.71880i) q^{39} +(-0.179617 + 0.416398i) q^{40} +(3.78165 - 8.76684i) q^{41} +(6.01977 + 3.90339i) q^{42} +(-11.3624 - 5.70639i) q^{43} +(-0.0853797 + 0.484212i) q^{44} +(0.826540 + 1.08059i) q^{45} +(1.23114 + 6.98217i) q^{46} +(-0.460706 + 1.53886i) q^{47} +(0.696364 + 1.58590i) q^{48} +(9.07756 - 4.55892i) q^{49} +(-1.37504 - 4.59294i) q^{50} +(-5.36401 - 1.91291i) q^{51} +(-2.06193 + 2.76965i) q^{52} +(-6.96808 + 12.0691i) q^{53} +(5.17181 + 0.502384i) q^{54} +(0.111485 + 0.193098i) q^{55} +(4.11422 + 0.480883i) q^{56} +(1.35659 - 2.38540i) q^{57} +(-3.49418 - 0.828136i) q^{58} +(1.26512 + 0.832083i) q^{59} +(0.704192 + 0.347939i) q^{60} +(-3.67663 - 3.89700i) q^{61} +(2.68954 - 2.25679i) q^{62} +(7.29036 - 10.0634i) q^{63} +(0.766044 + 0.642788i) q^{64} +(0.0910454 + 1.56319i) q^{65} +(0.829923 + 0.191001i) q^{66} +(-0.930994 - 1.25054i) q^{67} +(-3.26572 + 0.381707i) q^{68} +(12.1875 - 1.50496i) q^{69} +(1.56941 - 1.03222i) q^{70} +(4.24906 - 1.54653i) q^{71} +(2.80549 - 1.06266i) q^{72} +(-9.97468 - 3.63049i) q^{73} +(4.24640 - 1.00642i) q^{74} +(-8.06759 + 1.96758i) q^{75} +(0.0921215 - 1.58167i) q^{76} +(1.39764 - 1.48141i) q^{77} +(4.60631 + 3.81436i) q^{78} +(-5.14102 - 11.9182i) q^{79} +0.453486 q^{80} +(1.33165 - 8.90094i) q^{81} -9.54769 q^{82} +(2.70032 + 6.26005i) q^{83} +(1.19985 - 7.07351i) q^{84} +(-1.02321 + 1.08454i) q^{85} +(-0.739300 + 12.6933i) q^{86} +(-1.74504 + 5.96994i) q^{87} +(0.478429 - 0.113390i) q^{88} +(7.03445 + 2.56033i) q^{89} +(0.664839 - 1.18694i) q^{90} +(13.4401 - 4.89180i) q^{91} +(5.92351 - 3.89595i) q^{92} +(-3.66306 - 4.85408i) q^{93} +(1.59549 - 0.186486i) q^{94} +(-0.429045 - 0.576308i) q^{95} +(1.18038 - 1.26756i) q^{96} +(0.517706 + 8.88867i) q^{97} +(-7.78151 - 6.52946i) q^{98} +(0.404624 - 1.41846i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{6}+O(q^{10}) $ 72 * q + 9 * q^6	$ 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) $ 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{10}{27}\right)$

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 $

$2$	−0.396080	−	0.918216i	−0.280071	−	0.649277i
$2$	−0.396080	−	0.918216i	−0.280071	−	0.649277i
$3$	−1.62371	+	0.602974i	−0.937447	+	0.348127i
$3$	−1.62371	+	0.602974i	−0.937447	+	0.348127i
$4$	−0.686242	+	0.727374i	−0.343121	+	0.363687i
$5$	−0.0263678	+	0.452718i	−0.0117921	+	0.202462i	0.987266	+	0.159076i	$0.0508515\pi$
$5$	−0.0263678	+	0.452718i	−0.0117921	+	0.202462i	−0.999058	+	0.0433858i	$0.986186\pi$
$6$	1.19678	+	1.25209i	0.488582	+	0.511163i
$7$	4.03057	−	0.955263i	1.52341	−	0.361056i	0.618203	−	0.786019i	$-0.287861\pi$
$7$	4.03057	−	0.955263i	1.52341	−	0.361056i	0.905211	+	0.424963i	$0.139713\pi$
$8$	0.939693	+	0.342020i	0.332232	+	0.120922i
$9$	2.27284	−	1.95811i	0.757615	−	0.652702i
$10$	0.426137	−	0.155101i	0.134756	−	0.0490473i
$11$	0.410794	−	0.270184i	0.123859	−	0.0814634i	−0.486068	−	0.873921i	$-0.661569\pi$
$11$	0.410794	−	0.270184i	0.123859	−	0.0814634i	0.609927	+	0.792458i	$0.291199\pi$
$12$	0.675668	−	1.59483i	0.195048	−	0.460387i
$13$	3.42955	−	0.400857i	0.951185	−	0.111178i	0.373674	−	0.927560i	$-0.378098\pi$
$13$	3.42955	−	0.400857i	0.951185	−	0.111178i	0.577512	+	0.816383i	$0.304024\pi$
$14$	−2.47357	−	3.32258i	−0.661088	−	0.887996i
$15$	−0.230164	−	0.750981i	−0.0594280	−	0.193902i
$16$	−0.0581448	−	0.998308i	−0.0145362	−	0.249577i
$17$	2.51871	+	2.11345i	0.610878	+	0.512587i	0.894921	−	0.446224i	$-0.147232\pi$
$17$	2.51871	+	2.11345i	0.610878	+	0.512587i	−0.284043	+	0.958811i	$0.591676\pi$
$18$	−2.69819	−	1.31140i	−0.635970	−	0.309099i
$19$	−1.21368	+	1.01840i	−0.278437	+	0.233636i	−0.771302	−	0.636469i	$-0.780394\pi$
$19$	−1.21368	+	1.01840i	−0.278437	+	0.233636i	0.492865	+	0.870106i	$0.335950\pi$
$20$	−0.311201	−	0.329854i	−0.0695866	−	0.0737575i
$21$	−5.96847	+	3.98140i	−1.30243	+	0.868812i
$22$	−0.410794	−	0.270184i	−0.0875816	−	0.0576033i
$23$	−6.89877	−	1.63504i	−1.43849	−	0.340929i	−0.563923	−	0.825828i	$-0.690708\pi$
$23$	−6.89877	−	1.63504i	−1.43849	−	0.340929i	−0.874570	+	0.484898i	$0.838857\pi$
$24$	−1.73201	+	0.0112699i	−0.353546	+	0.00230046i
$25$	4.76193	+	0.556590i	0.952387	+	0.111318i
$26$	−1.72645	−	2.99029i	−0.338584	−	0.586445i
$27$	−2.50975	+	4.54985i	−0.483001	+	0.875620i
$28$	−2.07111	+	3.58727i	−0.391404	+	0.677931i
$29$	2.14438	−	2.88040i	0.398202	−	0.534878i	−0.557125	−	0.830428i	$-0.688096\pi$
$29$	2.14438	−	2.88040i	0.398202	−	0.534878i	0.955327	+	0.295551i	$0.0955031\pi$
$30$	−0.598400	+	0.508788i	−0.109252	+	0.0928916i
$31$	1.00695	+	3.36344i	0.180853	+	0.604092i	0.999554	+	0.0298715i	$0.00950979\pi$
$31$	1.00695	+	3.36344i	0.180853	+	0.604092i	−0.818700	+	0.574221i	$0.805305\pi$
$32$	−0.893633	+	0.448799i	−0.157973	+	0.0793372i
$33$	−0.504095	+	0.686397i	−0.0877518	+	0.119486i
$34$	0.942994	−	3.14982i	0.161722	−	0.540190i
$35$	0.326188	+	1.84990i	0.0551358	+	0.312691i
$36$	−0.135446	+	2.99694i	−0.0225744	+	0.499490i
$37$	−0.757807	+	4.29774i	−0.124583	+	0.706544i	0.856972	+	0.515363i	$0.172343\pi$
$37$	−0.757807	+	4.29774i	−0.124583	+	0.706544i	−0.981555	+	0.191181i	$0.938768\pi$
$38$	1.41582	+	0.711053i	0.229677	+	0.115348i
$39$	−5.32687	+	2.71880i	−0.852982	+	0.435357i
$40$	−0.179617	+	0.416398i	−0.0283999	+	0.0658383i
$41$	3.78165	−	8.76684i	0.590594	−	1.36915i	−0.316649	−	0.948543i	$-0.602558\pi$
$41$	3.78165	−	8.76684i	0.590594	−	1.36915i	0.907243	−	0.420608i	$-0.138183\pi$
$42$	6.01977	+	3.90339i	0.928871	+	0.602306i
$43$	−11.3624	−	5.70639i	−1.73274	−	0.870217i	−0.976378	−	0.216068i	$-0.930677\pi$
$43$	−11.3624	−	5.70639i	−1.73274	−	0.870217i	−0.756366	−	0.654149i	$-0.773027\pi$
$44$	−0.0853797	+	0.484212i	−0.0128715	+	0.0729977i
$45$	0.826540	+	1.08059i	0.123213	+	0.161085i
$46$	1.23114	+	6.98217i	0.181522	+	1.02946i
$47$	−0.460706	+	1.53886i	−0.0672009	+	0.224467i	−0.984993	−	0.172595i	$-0.944785\pi$
$47$	−0.460706	+	1.53886i	−0.0672009	+	0.224467i	0.917792	+	0.397061i	$0.129970\pi$
$48$	0.696364	+	1.58590i	0.100511	+	0.228905i
$49$	9.07756	−	4.55892i	1.29679	−	0.651274i
$50$	−1.37504	−	4.59294i	−0.194459	−	0.649539i
$51$	−5.36401	−	1.91291i	−0.751112	−	0.267861i
$52$	−2.06193	+	2.76965i	−0.285938	+	0.384081i
$53$	−6.96808	+	12.0691i	−0.957140	+	1.65782i	−0.227747	+	0.973720i	$0.573136\pi$
$53$	−6.96808	+	12.0691i	−0.957140	+	1.65782i	−0.729393	+	0.684095i	$0.760197\pi$
$54$	5.17181	+	0.502384i	0.703794	+	0.0683658i
$55$	0.111485	+	0.193098i	0.0150327	+	0.0260374i
$56$	4.11422	+	0.480883i	0.549786	+	0.0642607i
$57$	1.35659	−	2.38540i	0.179685	−	0.315953i
$58$	−3.49418	−	0.828136i	−0.458808	−	0.108740i
$59$	1.26512	+	0.832083i	0.164705	+	0.108328i	0.629185	−	0.777255i	$-0.283389\pi$
$59$	1.26512	+	0.832083i	0.164705	+	0.108328i	−0.464481	+	0.885583i	$0.653759\pi$
$60$	0.704192	+	0.347939i	0.0909108	+	0.0449188i
$61$	−3.67663	−	3.89700i	−0.470744	−	0.498959i	0.447879	−	0.894094i	$-0.352179\pi$
$61$	−3.67663	−	3.89700i	−0.470744	−	0.498959i	−0.918623	+	0.395135i	$0.870698\pi$
$62$	2.68954	−	2.25679i	0.341571	−	0.286613i
$63$	7.29036	−	10.0634i	0.918499	−	1.26788i
$64$	0.766044	+	0.642788i	0.0957556	+	0.0803485i
$65$	0.0910454	+	1.56319i	0.0112928	+	0.193890i
$66$	0.829923	+	0.191001i	0.102156	+	0.0235106i
$67$	−0.930994	−	1.25054i	−0.113739	−	0.152778i	0.741608	−	0.670833i	$-0.234063\pi$
$67$	−0.930994	−	1.25054i	−0.113739	−	0.152778i	−0.855347	+	0.518055i	$0.826656\pi$
$68$	−3.26572	+	0.381707i	−0.396026	+	0.0462888i
$69$	12.1875	−	1.50496i	1.46720	−	0.181175i
$70$	1.56941	−	1.03222i	0.187581	−	0.123374i
$71$	4.24906	−	1.54653i	0.504271	−	0.183539i	−0.0773433	−	0.997005i	$-0.524644\pi$
$71$	4.24906	−	1.54653i	0.504271	−	0.183539i	0.581614	+	0.813465i	$0.302422\pi$
$72$	2.80549	−	1.06266i	0.330630	−	0.125236i
$73$	−9.97468	−	3.63049i	−1.16745	−	0.424916i	−0.315695	−	0.948861i	$-0.602238\pi$
$73$	−9.97468	−	3.63049i	−1.16745	−	0.424916i	−0.851753	+	0.523944i	$0.824460\pi$
$74$	4.24640	−	1.00642i	0.493634	−	0.116993i
$75$	−8.06759	+	1.96758i	−0.931565	+	0.227197i
$76$	0.0921215	−	1.58167i	0.0105671	−	0.181429i
$77$	1.39764	−	1.48141i	0.159276	−	0.168822i
$78$	4.60631	+	3.81436i	0.521562	+	0.431891i
$79$	−5.14102	−	11.9182i	−0.578410	−	1.34090i	−0.916592	−	0.399824i	$-0.869071\pi$
$79$	−5.14102	−	11.9182i	−0.578410	−	1.34090i	0.338182	−	0.941081i	$-0.390188\pi$
$80$	0.453486			0.0507012
$81$	1.33165	−	8.90094i	0.147961	−	0.988993i
$82$	−9.54769			−1.05437
$83$	2.70032	+	6.26005i	0.296399	+	0.687129i	0.999718	−	0.0237446i	$-0.00755885\pi$
$83$	2.70032	+	6.26005i	0.296399	+	0.687129i	−0.703319	+	0.710874i	$0.748300\pi$
$84$	1.19985	−	7.07351i	0.130914	−	0.771783i
$85$	−1.02321	+	1.08454i	−0.110983	+	0.117635i
$86$	−0.739300	+	12.6933i	−0.0797208	+	1.36875i
$87$	−1.74504	+	5.96994i	−0.187088	+	0.640044i
$88$	0.478429	−	0.113390i	0.0510007	−	0.0120874i
$89$	7.03445	+	2.56033i	0.745650	+	0.271394i	0.686774	−	0.726871i	$-0.259026\pi$
$89$	7.03445	+	2.56033i	0.745650	+	0.271394i	0.0588760	+	0.998265i	$0.481248\pi$
$90$	0.664839	−	1.18694i	0.0700802	−	0.125115i
$91$	13.4401	−	4.89180i	1.40891	−	0.512800i
$92$	5.92351	−	3.89595i	0.617568	−	0.406181i
$93$	−3.66306	−	4.85408i	−0.379842	−	0.503345i
$94$	1.59549	−	0.186486i	0.164562	−	0.0192345i
$95$	−0.429045	−	0.576308i	−0.0440191	−	0.0591279i
$96$	1.18038	−	1.26756i	0.120472	−	0.129369i
$97$	0.517706	+	8.88867i	0.0525651	+	0.902508i	0.916782	+	0.399388i	$0.130777\pi$
$97$	0.517706	+	8.88867i	0.0525651	+	0.902508i	−0.864217	+	0.503119i	$0.832186\pi$
$98$	−7.78151	−	6.52946i	−0.786051	−	0.659575i
$99$	0.404624	−	1.41846i	0.0406662	−	0.142561i
$100$	−3.67269	+	3.08175i	−0.367269	+	0.308175i
$101$	−13.1326	−	13.9197i	−1.30674	−	1.38506i	−0.875796	−	0.482682i	$-0.839663\pi$
$101$	−13.1326	−	13.9197i	−1.30674	−	1.38506i	−0.430942	−	0.902380i	$-0.641819\pi$
$102$	0.368114	+	5.68298i	0.0364487	+	0.562699i
$103$	10.9773	+	7.21990i	1.08163	+	0.711398i	0.959668	−	0.281137i	$-0.0907114\pi$
$103$	10.9773	+	7.21990i	1.08163	+	0.711398i	0.121961	+	0.992535i	$0.461082\pi$
$104$	3.35982	+	0.796292i	0.329458	+	0.0780829i
$105$	−1.64508	−	2.80702i	−0.160543	−	0.273937i
$106$	13.8419	+	1.61789i	1.34445	+	0.157143i
$107$	7.54292	+	13.0647i	0.729202	+	1.26301i	0.957221	+	0.289358i	$0.0934419\pi$
$107$	7.54292	+	13.0647i	0.729202	+	1.26301i	−0.228019	+	0.973657i	$0.573225\pi$
$108$	−1.58715	−	4.94782i	−0.152724	−	0.476104i
$109$	−4.43112	+	7.67492i	−0.424424	+	0.735124i	−0.996366	−	0.0851698i	$-0.972857\pi$
$109$	−4.43112	+	7.67492i	−0.424424	+	0.735124i	0.571942	+	0.820294i	$0.306190\pi$
$110$	0.133149	−	0.178850i	0.0126952	−	0.0170527i
$111$	−1.36097	−	7.43520i	−0.129177	−	0.705718i
$112$	−1.18800	−	3.96821i	−0.112256	−	0.374961i
$113$	−6.24439	+	3.13605i	−0.587422	+	0.295015i	−0.717577	−	0.696479i	$-0.754749\pi$
$113$	−6.24439	+	3.13605i	−0.587422	+	0.295015i	0.130155	+	0.991494i	$0.458453\pi$
$114$	−2.72763	−	0.300837i	−0.255466	−	0.0281760i
$115$	0.922118	−	3.08009i	0.0859879	−	0.287220i
$116$	0.623566	+	3.53642i	0.0578967	+	0.328348i
$117$	7.00991	−	7.62650i	0.648066	−	0.705070i
$118$	0.262943	−	1.49123i	0.0242059	−	0.137278i
$119$	12.1708	+	6.11239i	1.11569	+	0.560322i
$120$	0.0405674	−	0.784412i	0.00370328	−	0.0716067i
$121$	−4.26112	+	9.87840i	−0.387375	+	0.898036i
$122$	−2.12205	+	4.91946i	−0.192121	+	0.445387i
$123$	−0.854106	+	16.5150i	−0.0770121	+	1.48911i
$124$	−3.13749	−	1.57571i	−0.281755	−	0.141503i
$125$	−0.771275	+	4.37412i	−0.0689850	+	0.391233i
$126$	−12.1280	−	2.70820i	−1.08045	−	0.241265i
$127$	−2.57651	−	14.6121i	−0.228629	−	1.29662i	−0.855625	−	0.517596i	$-0.826827\pi$
$127$	−2.57651	−	14.6121i	−0.228629	−	1.29662i	0.626996	−	0.779022i	$-0.284284\pi$
$128$	0.286803	−	0.957990i	0.0253501	−	0.0846751i
$129$	21.8899	+	2.41430i	1.92730	+	0.212567i
$130$	1.39928	−	0.702747i	0.122725	−	0.0616350i
$131$	1.58886	+	5.30717i	0.138819	+	0.463689i	0.998921	−	0.0464329i	$-0.0147854\pi$
$131$	1.58886	+	5.30717i	0.138819	+	0.463689i	−0.860102	+	0.510122i	$0.829600\pi$
$132$	−0.153336	−	0.837700i	−0.0133462	−	0.0729124i
$133$	−3.91898	+	5.26411i	−0.339819	+	0.456456i
$134$	−0.779520	+	1.35017i	−0.0673402	+	0.116637i
$135$	−1.99363	−	1.25618i	−0.171584	−	0.108115i
$136$	1.64397	+	2.84745i	0.140970	+	0.244167i
$137$	−12.1153	−	1.41608i	−1.03508	−	0.120984i	−0.418453	−	0.908239i	$-0.637427\pi$
$137$	−12.1153	−	1.41608i	−1.03508	−	0.120984i	−0.616627	+	0.787255i	$0.711501\pi$
$138$	−6.20908	−	10.5946i	−0.528552	−	0.901876i
$139$	−11.8956	−	2.81930i	−1.00897	−	0.239130i	−0.307284	−	0.951618i	$-0.599420\pi$
$139$	−11.8956	−	2.81930i	−1.00897	−	0.239130i	−0.701684	+	0.712488i	$0.747568\pi$
$140$	−1.56941	−	1.03222i	−0.132640	−	0.0872385i
$141$	−0.179844	−	2.77646i	−0.0151456	−	0.233820i
$142$	−3.10302	−	3.28900i	−0.260399	−	0.276007i
$143$	1.30053	−	1.09128i	0.108756	−	0.0912572i
$144$	−2.08695	−	2.15515i	−0.173912	−	0.179595i
$145$	1.24747	+	1.04675i	0.103597	+	0.0869280i
$146$	0.617198	+	10.5969i	0.0510796	+	0.877003i
$147$	−11.9904	+	12.8759i	−0.988949	+	1.06198i
$148$	−2.60602	−	3.50049i	−0.214214	−	0.287739i
$149$	8.73065	−	1.02047i	0.715243	−	0.0835999i	0.249315	−	0.968423i	$-0.419795\pi$
$149$	8.73065	−	1.02047i	0.715243	−	0.0835999i	0.465928	+	0.884823i	$0.345721\pi$
$150$	5.00208	+	6.62847i	0.408418	+	0.541212i
$151$	−17.3980	+	11.4429i	−1.41583	+	0.931206i	−0.416070	+	0.909333i	$0.636593\pi$
$151$	−17.3980	+	11.4429i	−1.41583	+	0.931206i	−0.999761	+	0.0218738i	$0.993037\pi$
$152$	−1.48880	+	0.541878i	−0.120757	+	0.0439521i
$153$	9.86301	−	0.128359i	0.797377	−	0.0103772i
$154$	−1.91383	−	0.696578i	−0.154221	−	0.0561318i
$155$	−1.54924	+	0.367178i	−0.124438	+	0.0294924i
$156$	1.67794	−	5.74038i	0.134342	−	0.459598i
$157$	−0.463643	+	7.96045i	−0.0370028	+	0.635313i	0.927920	+	0.372779i	$0.121595\pi$
$157$	−0.463643	+	7.96045i	−0.0370028	+	0.635313i	−0.964923	+	0.262534i	$0.915442\pi$
$158$	−8.90725	+	9.44113i	−0.708622	+	0.751096i
$159$	4.03678	−	23.7982i	0.320138	−	1.88732i
$160$	−0.179617	−	0.416398i	−0.0141999	−	0.0329191i
$161$	−29.3679			−2.31451
$162$	−8.70042	+	2.30274i	−0.683570	+	0.180921i
$163$	−15.4139			−1.20731			−0.603654	−	0.797246i	$-0.706289\pi$
$163$	−15.4139			−1.20731			−0.603654	+	0.797246i	$0.706289\pi$
$164$	3.78165	+	8.76684i	0.295297	+	0.684575i
$165$	−0.297453	−	0.246312i	−0.0231567	−	0.0191754i
$166$	4.67853	−	4.95896i	0.363125	−	0.384890i
$167$	−0.0546992	+	0.939149i	−0.00423275	+	0.0726735i	−0.999763	−	0.0217695i	$-0.993070\pi$
$167$	−0.0546992	+	0.939149i	−0.00423275	+	0.0726735i	0.995530	+	0.0944431i	$0.0301070\pi$
$168$	−6.97024	+	1.69995i	−0.537766	+	0.131154i
$169$	−1.04847	+	0.248493i	−0.0806518	+	0.0191148i
$170$	1.40112	+	0.509965i	0.107461	+	0.0391125i
$171$	−0.764374	+	4.69117i	−0.0584532	+	0.358743i
$172$	11.9480	−	4.34872i	0.911027	−	0.331587i
$173$	19.8541	−	13.0583i	1.50948	−	0.992802i	0.519059	−	0.854738i	$-0.326282\pi$
$173$	19.8541	−	13.0583i	1.50948	−	0.992802i	0.990423	−	0.138064i	$-0.0440880\pi$
$174$	6.17287	−	0.762250i	0.467964	−	0.0577860i
$175$	19.7250	−	2.30552i	1.49107	−	0.174281i
$176$	−0.293612	−	0.394389i	−0.0221318	−	0.0297282i
$177$	−2.55591	−	0.588223i	−0.192114	−	0.0442136i
$178$	−0.435267	−	7.47324i	−0.0326246	−	0.560143i
$179$	0.506391	+	0.424913i	0.0378495	+	0.0317595i	0.661516	−	0.749931i	$-0.269913\pi$
$179$	0.506391	+	0.424913i	0.0378495	+	0.0317595i	−0.623667	+	0.781690i	$0.714358\pi$
$180$	−1.35320	−	0.140342i	−0.100861	−	0.0104605i
$181$	5.70224	−	4.78475i	0.423845	−	0.355648i	−0.405779	−	0.913971i	$-0.633000\pi$
$181$	5.70224	−	4.78475i	0.423845	−	0.355648i	0.829623	+	0.558324i	$0.188555\pi$
$182$	−9.81509	−	10.4034i	−0.727543	−	0.771150i
$183$	8.31955	+	4.11067i	0.614999	+	0.303869i
$184$	−5.92351	−	3.89595i	−0.436687	−	0.287213i
$185$	−1.92568	−	0.456395i	−0.141579	−	0.0335548i
$186$	−3.00623	+	5.28608i	−0.220428	+	0.387594i
$187$	1.60569	+	0.187679i	0.117420	+	0.0137244i
$188$	−0.803174	−	1.39114i	−0.0585775	−	0.101459i
$189$	−5.76940	+	20.7360i	−0.419662	+	1.50832i
$190$	−0.359239	+	0.622220i	−0.0260619	+	0.0451406i
$191$	−4.57966	+	6.15155i	−0.331373	+	0.445111i	−0.936316	−	0.351157i	$-0.885788\pi$
$191$	−4.57966	+	6.15155i	−0.331373	+	0.445111i	0.604944	+	0.796268i	$0.293196\pi$
$192$	−1.63142	−	0.581793i	−0.117737	−	0.0419873i
$193$	0.195854	+	0.654198i	0.0140979	+	0.0470902i	0.964749	−	0.263171i	$-0.0847685\pi$
$193$	0.195854	+	0.654198i	0.0140979	+	0.0470902i	−0.950651	+	0.310262i	$0.899583\pi$
$194$	7.95667	−	3.99599i	0.571255	−	0.286895i
$195$	−1.09039	−	2.48326i	−0.0780847	−	0.177830i
$196$	−2.91336	+	9.73130i	−0.208097	+	0.695093i
$197$	−2.85750	−	16.2057i	−0.203588	−	1.15461i	−0.899646	−	0.436621i	$-0.856175\pi$
$197$	−2.85750	−	16.2057i	−0.203588	−	1.15461i	0.696057	−	0.717986i	$-0.254936\pi$
$198$	−1.46272	+	0.190293i	−0.103951	+	0.0135235i
$199$	1.44765	−	8.21001i	0.102621	−	0.581992i	−0.889523	−	0.456891i	$-0.848963\pi$
$199$	1.44765	−	8.21001i	0.102621	−	0.581992i	0.992144	−	0.125102i	$-0.0399258\pi$
$200$	4.28439	+	2.15170i	0.302952	+	0.152148i
$201$	2.26570	+	1.46915i	0.159810	+	0.103626i
$202$	−7.57975	+	17.5718i	−0.533309	+	1.23635i
$203$	5.89154	−	13.6581i	0.413505	−	0.958612i
$204$	5.07240	−	2.58892i	0.355139	−	0.181261i
$205$	3.86920	+	1.94318i	0.270236	+	0.135718i
$206$	2.28153	−	12.9392i	0.158962	−	0.901518i
$207$	−18.8814	+	9.79233i	−1.31235	+	0.680614i
$208$	−0.599589	−	3.40044i	−0.0415740	−	0.235778i
$209$	−0.223418	+	0.746268i	−0.0154541	+	0.0516204i
$210$	−1.92587	+	2.62234i	−0.132897	+	0.180958i
$211$	15.0179	−	7.54228i	1.03388	−	0.519232i	0.150850	−	0.988557i	$-0.451799\pi$
$211$	15.0179	−	7.54228i	1.03388	−	0.519232i	0.883026	+	0.469325i	$0.155503\pi$
$212$	−3.99694	−	13.3507i	−0.274511	−	0.916930i
$213$	−5.96671	+	5.07318i	−0.408832	+	0.347609i
$214$	9.00864	−	12.1007i	0.615818	−	0.827187i
$215$	2.88299	−	4.99349i	0.196618	−	0.340553i
$216$	−3.91453	+	3.41708i	−0.266350	+	0.232503i
$217$	7.27156	+	12.5947i	0.493625	+	0.854984i
$218$	8.80231	+	1.02884i	0.596168	+	0.0696820i
$219$	18.3850	−	0.119628i	1.24235	−	0.00808372i
$220$	−0.216960	−	0.0514206i	−0.0146275	−	0.00346677i
$221$	9.48524	+	6.23854i	0.638046	+	0.419650i
$222$	−6.28807	+	4.19459i	−0.422028	+	0.281523i
$223$	2.10737	+	2.23368i	0.141120	+	0.149578i	0.794078	−	0.607815i	$-0.207954\pi$
$223$	2.10737	+	2.23368i	0.141120	+	0.149578i	−0.652959	+	0.757394i	$0.726472\pi$
$224$	−3.17313	+	2.66257i	−0.212014	+	0.177901i
$225$	11.9130	−	8.05932i	0.794200	−	0.537288i
$226$	5.35285	+	4.49157i	0.356066	+	0.298775i
$227$	−0.880658	−	15.1203i	−0.0584513	−	1.00357i	−0.892261	−	0.451519i	$-0.850882\pi$
$227$	−0.880658	−	15.1203i	−0.0584513	−	1.00357i	0.833810	−	0.552051i	$-0.186155\pi$
$228$	0.804125	+	2.62371i	0.0532545	+	0.173759i
$229$	−4.18392	−	5.61998i	−0.276481	−	0.371379i	0.642093	−	0.766626i	$-0.278066\pi$
$229$	−4.18392	−	5.61998i	−0.276481	−	0.371379i	−0.918575	+	0.395248i	$0.870659\pi$
$230$	−3.19342	+	0.373257i	−0.210568	+	0.0246118i
$231$	−1.37610	+	3.24812i	−0.0905410	+	0.213710i
$232$	3.00022	−	1.97327i	0.196974	−	0.129552i
$233$	1.11036	−	0.404137i	0.0727419	−	0.0264759i	−0.305393	−	0.952226i	$-0.598788\pi$
$233$	1.11036	−	0.404137i	0.0727419	−	0.0264759i	0.378135	+	0.925751i	$0.376566\pi$
$234$	−9.77926	−	3.41591i	−0.639290	−	0.223305i
$235$	−0.684525	−	0.249147i	−0.0446535	−	0.0162525i
$236$	−1.47341	+	0.349205i	−0.0959110	+	0.0227313i
$237$	15.5339	+	16.2518i	1.00903	+	1.05567i
$238$	0.791899	−	13.5964i	0.0513312	−	0.881323i
$239$	4.81039	−	5.09872i	0.311159	−	0.329809i	−0.552855	−	0.833278i	$-0.686462\pi$
$239$	4.81039	−	5.09872i	0.311159	−	0.329809i	0.864013	+	0.503469i	$0.167943\pi$
$240$	−0.736328	+	0.273440i	−0.0475297	+	0.0176505i
$241$	10.5600	+	24.4808i	0.680228	+	1.57695i	0.810679	+	0.585491i	$0.199098\pi$
$241$	10.5600	+	24.4808i	0.680228	+	1.57695i	−0.130451	+	0.991455i	$0.541642\pi$
$242$	10.7582			0.691566
$243$	3.20483	+	15.2555i	0.205590	+	0.978638i
$244$	5.35763			0.342987
$245$	1.82455	+	4.22979i	0.116566	+	0.270231i
$246$	15.5026	−	5.75701i	0.988412	−	0.367053i
$247$	−3.75414	+	3.97915i	−0.238870	+	0.253188i
$248$	−0.204143	+	3.50500i	−0.0129631	+	0.222568i
$249$	−8.15917	−	8.53626i	−0.517067	−	0.540963i
$250$	4.32187	−	1.02430i	0.273339	−	0.0647826i
$251$	13.6058	+	4.95209i	0.858788	+	0.312573i	0.733618	−	0.679562i	$-0.237830\pi$
$251$	13.6058	+	4.95209i	0.858788	+	0.312573i	0.125170	+	0.992135i	$0.460052\pi$
$252$	2.31694	+	12.2088i	0.145954	+	0.769080i
$253$	−3.27574	+	1.19227i	−0.205944	+	0.0749574i
$254$	−12.3966	+	8.15337i	−0.777832	+	0.511588i
$255$	1.00745	−	2.37795i	0.0630887	−	0.148913i
$256$	−0.993238	+	0.116093i	−0.0620774	+	0.00725581i
$257$	−5.63628	−	7.57083i	−0.351581	−	0.472255i	0.590790	−	0.806826i	$-0.298816\pi$
$257$	−5.63628	−	7.57083i	−0.351581	−	0.472255i	−0.942371	+	0.334570i	$0.891409\pi$
$258$	−6.45332	−	21.0560i	−0.401766	−	1.31089i
$259$	1.05107	+	18.0462i	0.0653106	+	1.12134i
$260$	−1.19950	−	1.00650i	−0.0743899	−	0.0624206i
$261$	−0.766289	−	10.7456i	−0.0474321	−	0.665138i
$262$	4.24381	−	3.56098i	0.262183	−	0.219998i
$263$	−4.24595	−	4.50045i	−0.261817	−	0.277510i	0.583108	−	0.812395i	$-0.301836\pi$
$263$	−4.24595	−	4.50045i	−0.261817	−	0.277510i	−0.844925	+	0.534885i	$0.820355\pi$
$264$	−0.708456	+	0.472591i	−0.0436025	+	0.0290860i
$265$	−5.28016	−	3.47282i	−0.324358	−	0.213333i
$266$	6.38582	+	1.51347i	0.391540	+	0.0927966i
$267$	−12.9657	+	0.0843655i	−0.793488	+	0.00516308i
$268$	1.54850	+	0.180993i	0.0945895	+	0.0110559i
$269$	−8.31694	−	14.4054i	−0.507093	−	0.878310i	−0.999966	−	0.00820935i	$-0.997387\pi$
$269$	−8.31694	−	14.4054i	−0.507093	−	0.878310i	0.492874	−	0.870101i	$-0.335946\pi$
$270$	−0.363808	+	2.32813i	−0.0221406	+	0.141685i
$271$	11.7975	−	20.4338i	0.716646	−	1.24127i	−0.245675	−	0.969352i	$-0.579010\pi$
$271$	11.7975	−	20.4338i	0.716646	−	1.24127i	0.962321	−	0.271915i	$-0.0876571\pi$
$272$	1.96343	−	2.63734i	0.119050	−	0.159912i
$273$	−18.8732	+	16.0469i	−1.14226	+	0.971202i
$274$	3.49836	+	11.6853i	0.211344	+	0.705937i
$275$	2.10656	−	1.05795i	0.127030	−	0.0637969i
$276$	−7.26888	+	9.89760i	−0.437535	+	0.595766i
$277$	5.53320	−	18.4822i	0.332458	−	1.11049i	−0.614444	−	0.788961i	$-0.710619\pi$
$277$	5.53320	−	18.4822i	0.332458	−	1.11049i	0.946901	−	0.321525i	$-0.104195\pi$
$278$	2.12286	+	12.0394i	0.127321	+	0.722073i
$279$	8.87462	+	5.67287i	0.531309	+	0.339626i
$280$	−0.326188	+	1.84990i	−0.0194934	+	0.110553i
$281$	−27.9599	−	14.0420i	−1.66795	−	0.837676i	−0.995206	−	0.0978007i	$-0.968819\pi$
$281$	−27.9599	−	14.0420i	−1.66795	−	0.837676i	−0.672744	−	0.739875i	$-0.734884\pi$
$282$	−2.47816	+	1.26484i	−0.147572	+	0.0753198i
$283$	−9.50918	+	22.0448i	−0.565262	+	1.31043i	0.360655	+	0.932699i	$0.382553\pi$
$283$	−9.50918	+	22.0448i	−0.565262	+	1.31043i	−0.925917	+	0.377726i	$0.876706\pi$
$284$	−1.79098	+	4.15195i	−0.106275	+	0.246373i
$285$	1.04414	+	0.677052i	0.0618497	+	0.0401051i
$286$	−1.51714	−	0.761938i	−0.0897106	−	0.0450543i
$287$	6.86756	−	38.9478i	0.405379	−	2.29902i
$288$	−1.15229	+	2.76988i	−0.0678995	+	0.163217i
$289$	−1.07478	−	6.09537i	−0.0632222	−	0.358551i
$290$	0.467046	−	1.56004i	0.0274259	−	0.0916089i
$291$	−6.20024	−	14.1204i	−0.363464	−	0.827754i
$292$	9.48576	−	4.76393i	0.555112	−	0.278788i
$293$	3.99504	+	13.3443i	0.233392	+	0.779585i	0.991799	+	0.127804i	$0.0407928\pi$
$293$	3.99504	+	13.3443i	0.233392	+	0.779585i	−0.758407	+	0.651781i	$0.774022\pi$
$294$	16.5720	+	5.90988i	0.966498	+	0.344671i
$295$	−0.410058	+	0.550803i	−0.0238745	+	0.0320690i
$296$	−2.18202	+	3.77937i	−0.126827	+	0.219671i
$297$	0.198307	+	2.54715i	0.0115069	+	0.147800i
$298$	−4.39504	−	7.61244i	−0.254598	−	0.440977i
$299$	−24.3151	−	2.84203i	−1.40618	−	0.164359i
$300$	4.10515	−	7.21839i	0.237011	−	0.416754i
$301$	−51.2479	−	12.1460i	−2.95388	−	0.700083i
$302$	17.3980	+	11.4429i	1.00114	+	0.658462i
$303$	29.7166	+	14.6829i	1.70718	+	0.843511i
$304$	1.08724	+	1.15241i	0.0623577	+	0.0660953i
$305$	1.86119	−	1.56172i	0.106571	−	0.0894239i
$306$	−4.02440	−	9.00553i	−0.230060	−	0.514812i
$307$	3.51947	+	2.95319i	0.200867	+	0.168547i	0.737673	−	0.675159i	$-0.235925\pi$
$307$	3.51947	+	2.95319i	0.200867	+	0.168547i	−0.536806	+	0.843706i	$0.680369\pi$
$308$	0.118421	+	2.03321i	0.00674767	+	0.115853i
$309$	−22.1774	−	5.10396i	−1.26163	−	0.290354i
$310$	0.950773	+	1.27711i	0.0540003	+	0.0725350i
$311$	18.5411	−	2.16715i	1.05137	−	0.122888i	0.427185	−	0.904164i	$-0.359505\pi$
$311$	18.5411	−	2.16715i	1.05137	−	0.122888i	0.624185	+	0.781276i	$0.285431\pi$
$312$	−5.93551	+	0.732940i	−0.336032	+	0.0414946i
$313$	0.931466	−	0.612635i	0.0526496	−	0.0346282i	−0.522911	−	0.852387i	$-0.675154\pi$
$313$	0.931466	−	0.612635i	0.0526496	−	0.0346282i	0.575561	+	0.817759i	$0.304784\pi$
$314$	7.49305	−	2.72725i	0.422857	−	0.153908i
$315$	4.36368	+	3.56583i	0.245865	+	0.200912i
$316$	12.1970	+	4.43934i	0.686134	+	0.249732i
$317$	4.81934	−	1.14221i	0.270681	−	0.0641526i	−0.0930336	−	0.995663i	$-0.529656\pi$
$317$	4.81934	−	1.14221i	0.270681	−	0.0641526i	0.363715	+	0.931510i	$0.381508\pi$
$318$	−23.4508	+	5.71935i	−1.31505	+	0.320725i
$319$	0.102662	−	1.76263i	0.00574794	−	0.0986883i
$320$	−0.311201	+	0.329854i	−0.0173967	+	0.0184394i
$321$	−20.1252	−	16.6651i	−1.12328	−	0.930155i
$322$	11.6320	+	26.9661i	0.648227	+	1.50276i
$323$	−5.20925			−0.289850
$324$	5.56048	+	7.07680i	0.308915	+	0.393156i
$325$	16.5544			0.918272
$326$	6.10513	+	14.1533i	0.338132	+	0.783878i
$327$	2.56706	−	15.1337i	0.141959	−	0.836894i
$328$	6.55202	−	6.94474i	0.361775	−	0.383459i
$329$	−0.386887	+	6.64260i	−0.0213298	+	0.366218i
$330$	−0.108353	+	0.370685i	−0.00596462	+	0.0204055i
$331$	5.70926	−	1.35312i	0.313809	−	0.0743742i	−0.0706932	−	0.997498i	$-0.522521\pi$
$331$	5.70926	−	1.35312i	0.313809	−	0.0743742i	0.384503	+	0.923124i	$0.374373\pi$
$332$	−6.40647	−	2.33176i	−0.351600	−	0.127972i
$333$	6.69304	+	11.2520i	0.366777	+	0.616603i
$334$	0.884007	−	0.321752i	0.0483707	−	0.0176055i
$335$	0.590692	−	0.388504i	0.0322729	−	0.0212262i
$336$	4.32170	+	5.72687i	0.235768	+	0.312426i
$337$	16.5085	−	1.92957i	0.899276	−	0.105110i	0.346122	−	0.938189i	$-0.387498\pi$
$337$	16.5085	−	1.92957i	0.899276	−	0.105110i	0.553154	+	0.833079i	$0.313424\pi$
$338$	0.643449	+	0.864302i	0.0349990	+	0.0470118i
$339$	8.24809	−	8.85723i	0.447975	−	0.481058i
$340$	−0.0866961	−	1.48851i	−0.00470176	−	0.0807260i
$341$	1.32240	+	1.10962i	0.0716118	+	0.0600894i
$342$	4.61026	−	1.15622i	0.249294	−	0.0625211i
$343$	10.0209	−	8.40851i	0.541076	−	0.454017i
$344$	−8.72543	−	9.24841i	−0.470444	−	0.498641i
$345$	0.359964	+	5.55717i	0.0193798	+	0.299188i
$346$	−19.8541	−	13.0583i	−1.06737	−	0.702017i
$347$	−23.4517	−	5.55814i	−1.25895	−	0.298377i	−0.453616	−	0.891197i	$-0.649866\pi$
$347$	−23.4517	−	5.55814i	−1.25895	−	0.298377i	−0.805335	+	0.592820i	$0.798014\pi$
$348$	−3.14486	−	5.36611i	−0.168582	−	0.287654i
$349$	−7.82251	−	0.914321i	−0.418730	−	0.0489425i	−0.0958803	−	0.995393i	$-0.530567\pi$
$349$	−7.82251	−	0.914321i	−0.418730	−	0.0489425i	−0.322849	+	0.946450i	$0.604641\pi$
$350$	−9.92964	−	17.1986i	−0.530762	−	0.919306i
$351$	−6.78345	+	16.6100i	−0.362074	+	0.886576i
$352$	−0.245841	+	0.425809i	−0.0131034	+	0.0226957i
$353$	−13.5589	+	18.2128i	−0.721669	+	0.969370i	0.278291	+	0.960497i	$0.410232\pi$
$353$	−13.5589	+	18.2128i	−0.721669	+	0.969370i	−0.999961	+	0.00887357i	$0.997175\pi$
$354$	0.472227	+	2.57986i	0.0250986	+	0.137118i
$355$	0.588105	+	1.96441i	0.0312134	+	0.104260i
$356$	−6.68965	+	3.35967i	−0.354551	+	0.178062i
$357$	−23.4474	−	2.58607i	−1.24097	−	0.136869i
$358$	0.189590	−	0.633276i	0.0100202	−	0.0334697i
$359$	2.77757	+	15.7524i	0.146595	+	0.831380i	0.966073	+	0.258270i	$0.0831523\pi$
$359$	2.77757	+	15.7524i	0.146595	+	0.831380i	−0.819478	+	0.573110i	$0.805737\pi$
$360$	0.407110	+	1.29812i	0.0214566	+	0.0684167i
$361$	−2.86343	+	16.2393i	−0.150707	+	0.854702i
$362$	−6.65198	−	3.34075i	−0.349620	−	0.175586i
$363$	0.962399	−	18.6090i	0.0505128	−	0.976717i
$364$	−5.66500	+	13.1329i	−0.296927	+	0.688353i
$365$	1.90660	−	4.41999i	0.0997960	−	0.231353i
$366$	0.479276	−	9.26729i	0.0250522	−	0.484409i
$367$	10.6608	+	5.35405i	0.556489	+	0.279479i	0.704734	−	0.709472i	$-0.251066\pi$
$367$	10.6608	+	5.35405i	0.556489	+	0.279479i	−0.148246	+	0.988951i	$0.547363\pi$
$368$	−1.23114	+	6.98217i	−0.0641778	+	0.363971i
$369$	−8.57130	−	27.3305i	−0.446204	−	1.42277i
$370$	0.343655	+	1.94896i	0.0178658	+	0.101322i
$371$	−16.5562	+	55.3016i	−0.859556	+	2.87112i
$372$	6.04448	+	0.666660i	0.313391	+	0.0345647i
$373$	−5.20593	+	2.61451i	−0.269553	+	0.135374i	−0.578442	−	0.815724i	$-0.696339\pi$
$373$	−5.20593	+	2.61451i	−0.269553	+	0.135374i	0.308889	+	0.951098i	$0.400043\pi$
$374$	−0.463653	−	1.54871i	−0.0239749	−	0.0800818i
$375$	−1.38516	−	7.56735i	−0.0715291	−	0.390776i
$376$	−0.959245	+	1.28849i	−0.0494693	+	0.0664488i
$377$	6.19963	−	10.7381i	0.319297	−	0.553039i
$378$	21.3253	−	2.91554i	1.09685	−	0.149959i
$379$	0.698246	+	1.20940i	0.0358665	+	0.0621225i	0.883401	−	0.468617i	$-0.155248\pi$
$379$	0.698246	+	1.20940i	0.0358665	+	0.0621225i	−0.847535	+	0.530740i	$0.821914\pi$
$380$	0.713620	+	0.0834102i	0.0366079	+	0.00427885i
$381$	12.9942	+	22.1723i	0.665715	+	1.13592i
$382$	7.46237	+	1.76861i	0.381808	+	0.0904901i
$383$	1.34490	+	0.884552i	0.0687210	+	0.0451985i	0.583405	−	0.812182i	$-0.301720\pi$
$383$	1.34490	+	0.884552i	0.0687210	+	0.0451985i	−0.514684	+	0.857380i	$0.672091\pi$
$384$	0.111959	+	1.72843i	0.00571336	+	0.0882035i
$385$	0.633809	+	0.671799i	0.0323019	+	0.0342380i
$386$	0.523122	−	0.438951i	0.0266262	−	0.0223420i
$387$	−36.9986	+	9.27896i	−1.88074	+	0.471676i
$388$	−6.82066	−	5.72321i	−0.346266	−	0.290552i
$389$	0.690976	+	11.8636i	0.0350339	+	0.601508i	0.969445	+	0.245311i	$0.0788900\pi$
$389$	0.690976	+	11.8636i	0.0350339	+	0.601508i	−0.934411	+	0.356198i	$0.884073\pi$
$390$	−1.84829	+	1.98479i	−0.0935917	+	0.100504i
$391$	−13.9205	−	18.6984i	−0.703988	−	0.945620i
$392$	10.0894	−	1.17928i	0.509589	−	0.0595625i
$393$	−5.77993	−	7.65924i	−0.291559	−	0.386357i
$394$	−13.7485	+	9.04255i	−0.692641	+	0.455557i
$395$	5.53115	−	2.01318i	0.278303	−	0.101294i
$396$	0.754084	+	1.26772i	0.0378941	+	0.0637054i
$397$	0.564047	+	0.205296i	0.0283087	+	0.0103035i	0.356136	−	0.934434i	$-0.384094\pi$
$397$	0.564047	+	0.205296i	0.0283087	+	0.0103035i	−0.327827	+	0.944738i	$0.606316\pi$
$398$	−8.11195	+	1.92257i	−0.406615	+	0.0963696i
$399$	3.18916	−	10.9104i	0.159658	−	0.546204i
$400$	0.278767	−	4.78624i	0.0139383	−	0.239312i
$401$	−15.5638	+	16.4967i	−0.777218	+	0.823803i	−0.988117	−	0.153705i	$-0.950880\pi$
$401$	−15.5638	+	16.4967i	−0.777218	+	0.823803i	0.210898	+	0.977508i	$0.432361\pi$
$402$	0.451595	−	2.66231i	0.0225235	−	0.132784i
$403$	4.80164	+	11.1315i	0.239187	+	0.554497i
$404$	19.1369			0.952098
$405$	3.99451	+	0.837560i	0.198489	+	0.0416187i
$406$	−14.8746			−0.738216
$407$	0.849875	+	1.97023i	0.0421267	+	0.0976608i
$408$	−4.38627	−	3.63214i	−0.217153	−	0.179818i
$409$	5.29929	−	5.61692i	0.262033	−	0.277739i	−0.582978	−	0.812488i	$-0.698112\pi$
$409$	5.29929	−	5.61692i	0.262033	−	0.277739i	0.845011	+	0.534749i	$0.179594\pi$
$410$	0.251752	−	4.32241i	0.0124331	−	0.213469i
$411$	20.5256	−	5.00592i	1.01245	−	0.246924i
$412$	−12.7847	+	3.03002i	−0.629855	+	0.149278i
$413$	5.89402	+	2.14525i	0.290026	+	0.105561i
$414$	16.4700	+	13.4587i	0.809457	+	0.661458i
$415$	−2.90524	+	1.05742i	−0.142613	+	0.0519068i
$416$	−2.88485	+	1.89740i	−0.141441	+	0.0930275i
$417$	21.0149	−	2.59500i	1.02910	−	0.127078i
$418$	0.773727	−	0.0904357i	0.0378442	−	0.00442335i
$419$	14.9250	+	20.0477i	0.729132	+	0.979395i	0.999860	+	0.0167387i	$0.00532833\pi$
$419$	14.9250	+	20.0477i	0.729132	+	0.979395i	−0.270728	+	0.962656i	$0.587264\pi$
$420$	3.17067	+	0.729706i	0.154713	+	0.0356060i
$421$	−1.12197	−	19.2635i	−0.0546815	−	0.938845i	−0.908398	−	0.418107i	$-0.862694\pi$
$421$	−1.12197	−	19.2635i	−0.0546815	−	0.938845i	0.853716	−	0.520738i	$-0.174343\pi$
$422$	−12.8737	−	10.8023i	−0.626684	−	0.525850i
$423$	1.96615	+	4.39971i	0.0955973	+	0.213921i
$424$	−10.6757	+	8.95800i	−0.518459	+	0.435039i
$425$	10.8176	+	11.4660i	0.524732	+	0.556183i
$426$	7.02157	+	3.46934i	0.340196	+	0.168090i
$427$	−18.5416	−	12.1950i	−0.897289	−	0.590156i
$428$	−14.6792	−	3.47904i	−0.709546	−	0.168166i
$429$	−1.45367	+	2.55610i	−0.0701840	+	0.123410i
$430$	−5.72699	−	0.669390i	−0.276180	−	0.0322808i
$431$	9.43737	+	16.3460i	0.454582	+	0.787360i	0.998664	−	0.0516725i	$-0.0164552\pi$
$431$	9.43737	+	16.3460i	0.454582	+	0.787360i	−0.544082	+	0.839032i	$0.683122\pi$
$432$	4.68809	+	2.24095i	0.225556	+	0.107818i
$433$	−13.6554	+	23.6519i	−0.656237	+	1.13664i	0.325345	+	0.945595i	$0.394519\pi$
$433$	−13.6554	+	23.6519i	−0.656237	+	1.13664i	−0.981582	+	0.191040i	$0.938814\pi$
$434$	8.68454	−	11.6654i	0.416871	−	0.559956i
$435$	−2.65669	−	0.947425i	−0.127378	−	0.0454255i
$436$	−2.54172	−	8.48993i	−0.121726	−	0.406594i
$437$	10.0380	−	5.04128i	0.480183	−	0.241157i
$438$	−7.39179	−	16.8341i	−0.353193	−	0.804362i
$439$	5.80959	−	19.4054i	0.277277	−	0.926169i	−0.699989	−	0.714153i	$-0.746812\pi$
$439$	5.80959	−	19.4054i	0.277277	−	0.926169i	0.977266	−	0.212016i	$-0.0680028\pi$
$440$	0.0387185	+	0.219583i	0.00184583	+	0.0104682i
$441$	11.7050	−	28.1365i	0.557382	−	1.33983i
$442$	1.97142	−	11.1805i	0.0937707	−	0.531800i
$443$	21.3696	+	10.7322i	1.01530	+	0.509902i	0.877001	−	0.480489i	$-0.159541\pi$
$443$	21.3696	+	10.7322i	1.01530	+	0.509902i	0.138298	+	0.990391i	$0.455837\pi$
$444$	6.34212	+	4.11241i	0.300984	+	0.195166i
$445$	−1.34459	+	3.11712i	−0.0637398	+	0.147765i
$446$	1.21631	−	2.81973i	0.0575941	−	0.133518i
$447$	−13.5607	+	6.92129i	−0.641399	+	0.327366i
$448$	3.70163	+	1.85903i	0.174886	+	0.0878308i
$449$	−4.38377	+	24.8616i	−0.206883	+	1.17329i	0.687566	+	0.726122i	$0.258679\pi$
$449$	−4.38377	+	24.8616i	−0.206883	+	1.17329i	−0.894449	+	0.447170i	$0.852432\pi$
$450$	−12.1187	−	7.74657i	−0.571281	−	0.365177i
$451$	−0.815178	−	4.62311i	−0.0383852	−	0.217694i
$452$	2.00408	−	6.69409i	0.0942639	−	0.314863i
$453$	21.3495	−	29.0704i	1.00309	−	1.36585i
$454$	−13.5349	+	6.79749i	−0.635225	+	0.319022i
$455$	1.86022	+	6.21357i	0.0872086	+	0.291297i
$456$	2.09063	−	1.77756i	0.0979028	−	0.0832417i
$457$	7.63555	−	10.2563i	0.357176	−	0.479770i	−0.586825	−	0.809714i	$-0.699622\pi$
$457$	7.63555	−	10.2563i	0.357176	−	0.479770i	0.944001	+	0.329944i	$0.107030\pi$
$458$	−3.50319	+	6.06770i	−0.163693	+	0.283525i
$459$	−15.9372	+	6.15556i	−0.743886	+	0.287317i
$460$	1.60758	+	2.78441i	0.0749538	+	0.129824i
$461$	−3.90904	−	0.456902i	−0.182062	−	0.0212800i	0.0245731	−	0.999698i	$-0.492177\pi$
$461$	−3.90904	−	0.456902i	−0.182062	−	0.0212800i	−0.206635	+	0.978418i	$0.566251\pi$
$462$	3.52752	−	0.0229529i	0.164115	−	0.00106787i
$463$	3.43180	+	0.813353i	0.159489	+	0.0377997i	0.309585	−	0.950872i	$-0.399810\pi$
$463$	3.43180	+	0.813353i	0.159489	+	0.0377997i	−0.150095	+	0.988672i	$0.547958\pi$
$464$	−3.00022	−	1.97327i	−0.139282	−	0.0916069i
$465$	2.29412	−	1.53034i	0.106387	−	0.0709680i
$466$	−0.810875	−	0.859477i	−0.0375630	−	0.0398145i
$467$	7.89239	−	6.62250i	0.365216	−	0.306453i	−0.441650	−	0.897188i	$-0.645607\pi$
$467$	7.89239	−	6.62250i	0.365216	−	0.306453i	0.806866	+	0.590735i	$0.201162\pi$
$468$	0.736823	+	10.3324i	0.0340597	+	0.477617i
$469$	−4.94703	−	4.15105i	−0.228433	−	0.191678i
$470$	0.0423560	+	0.727224i	0.00195373	+	0.0335443i
$471$	−4.04712	−	13.2050i	−0.186482	−	0.608454i
$472$	0.904235	+	1.21460i	0.0416208	+	0.0559064i
$473$	−6.20937	+	0.725771i	−0.285507	+	0.0333710i
$474$	8.77000	−	20.7005i	0.402819	−	0.950804i
$475$	−6.34629	+	4.17402i	−0.291188	+	0.191517i
$476$	−12.7981	+	4.65812i	−0.586599	+	0.213504i
$477$	7.79515	+	41.0754i	0.356915	+	1.88071i
$478$	−6.58703	−	2.39748i	−0.301284	−	0.109658i
$479$	32.5559	−	7.71588i	1.48752	−	0.352548i	0.595059	−	0.803682i	$-0.297129\pi$
$479$	32.5559	−	7.71588i	1.48752	−	0.352548i	0.892456	+	0.451134i	$0.148980\pi$
$480$	0.542722	+	0.567804i	0.0247717	+	0.0259166i
$481$	−0.876159	+	15.0431i	−0.0399494	+	0.685905i
$482$	18.2961	−	19.3927i	0.833363	−	0.883313i
$483$	47.6848	−	17.7081i	2.16973	−	0.805745i
$484$	−4.26112	−	9.87840i	−0.193687	−	0.449018i
$485$	−4.03772			−0.183343
$486$	12.7384	−	8.98511i	0.577827	−	0.407573i
$487$	31.3487			1.42055			0.710274	−	0.703926i	$-0.248571\pi$
$487$	31.3487			1.42055			0.710274	+	0.703926i	$0.248571\pi$
$488$	−2.12205	−	4.91946i	−0.0960606	−	0.222693i
$489$	25.0276	−	9.29417i	1.13179	−	0.420297i
$490$	3.16119	−	3.35067i	0.142808	−	0.151368i
$491$	2.21120	−	37.9648i	0.0997899	−	1.71333i	−0.462694	−	0.886518i	$-0.653117\pi$
$491$	2.21120	−	37.9648i	0.0997899	−	1.71333i	0.562484	−	0.826808i	$-0.309846\pi$
$492$	−11.4265	−	11.9545i	−0.515145	−	0.538952i
$493$	11.4887	−	2.72287i	0.517424	−	0.122632i
$494$	5.14066	+	1.87105i	0.231289	+	0.0841824i
$495$	0.631496	+	0.220582i	0.0283836	+	0.00991444i
$496$	3.29921	−	1.20081i	0.148139	−	0.0539181i
$497$	15.6488	−	10.2924i	0.701944	−	0.461676i
$498$	−4.60644	+	10.8729i	−0.206420	+	0.487227i
$499$	24.4174	−	2.85398i	1.09307	−	0.127762i	0.449599	−	0.893231i	$-0.351567\pi$
$499$	24.4174	−	2.85398i	1.09307	−	0.127762i	0.643473	+	0.765469i	$0.277493\pi$
$500$	−2.65234	−	3.56271i	−0.118616	−	0.159329i
$501$	−0.477467	−	1.55788i	−0.0213316	−	0.0696011i
$502$	−0.841876	−	14.4545i	−0.0375748	−	0.645134i
$503$	0.752251	+	0.631213i	0.0335412	+	0.0281444i	0.659404	−	0.751789i	$-0.270809\pi$
$503$	0.752251	+	0.631213i	0.0335412	+	0.0281444i	−0.625863	+	0.779933i	$0.715253\pi$
$504$	10.2926	−	6.96310i	0.458469	−	0.310161i
$505$	6.64798	−	5.57832i	0.295831	−	0.248232i
$506$	2.39221	+	2.53560i	0.106347	+	0.112721i
$507$	1.55258	−	1.03568i	0.0689524	−	0.0459962i
$508$	12.3966	+	8.15337i	0.550010	+	0.361747i
$509$	23.7102	+	5.61942i	1.05094	+	0.249077i	0.719566	−	0.694424i	$-0.244341\pi$
$509$	23.7102	+	5.61942i	1.05094	+	0.249077i	0.331371	+	0.943501i	$0.392489\pi$
$510$	−2.58250	+	0.0168039i	−0.114355	+	0.000744087i
$511$	−43.6717	−	5.10449i	−1.93192	−	0.225810i
$512$	0.500000	+	0.866025i	0.0220971	+	0.0382733i
$513$	−1.58754	−	8.07798i	−0.0700914	−	0.356652i
$514$	−4.71924	+	8.17397i	−0.208157	+	0.360538i
$515$	−3.55803	+	4.77927i	−0.156786	+	0.210600i
$516$	−16.7779	+	14.2654i	−0.738605	+	0.627998i
$517$	0.226521	+	0.756632i	0.00996237	+	0.0332766i
$518$	16.1540	−	8.11286i	0.709768	−	0.356459i
$519$	−24.3635	+	33.1743i	−1.06944	+	1.45619i
$520$	−0.449088	+	1.50006i	−0.0196938	+	0.0657818i
$521$	−3.30567	−	18.7474i	−0.144824	−	0.821339i	−0.967508	−	0.252840i	$-0.918635\pi$
$521$	−3.30567	−	18.7474i	−0.144824	−	0.821339i	0.822684	−	0.568499i	$-0.192476\pi$
$522$	−9.56331	+	4.95975i	−0.418574	+	0.217082i
$523$	−0.638077	+	3.61871i	−0.0279012	+	0.158235i	−0.995575	−	0.0939692i	$-0.970044\pi$
$523$	−0.638077	+	3.61871i	−0.0279012	+	0.158235i	0.967674	+	0.252205i	$0.0811556\pi$
$524$	−4.95064	−	2.48630i	−0.216270	−	0.108615i
$525$	−30.6374	+	15.6372i	−1.33713	+	0.682461i
$526$	−2.45065	+	5.68124i	−0.106853	+	0.247714i
$527$	−4.57226	+	10.5997i	−0.199171	+	0.461730i
$528$	0.714546	+	0.463332i	0.0310966	+	0.0201639i
$529$	24.3661	+	12.2371i	1.05940	+	0.532049i
$530$	−1.09743	+	6.22384i	−0.0476694	+	0.270346i
$531$	4.50473	−	0.586044i	0.195489	−	0.0254321i
$532$	−1.13960	−	6.46302i	−0.0494081	−	0.280207i
$533$	9.45509	−	31.5822i	0.409545	−	1.36798i
$534$	5.21292	+	11.8719i	0.225585	+	0.513747i
$535$	−6.11353	+	3.07033i	−0.264311	+	0.132742i
$536$	−0.447138	−	1.49354i	−0.0193134	−	0.0645112i
$537$	−1.07844	−	0.384593i	−0.0465382	−	0.0165964i
$538$	−9.93306	+	13.3424i	−0.428245	+	0.575232i
$539$	2.49726	−	4.32538i	0.107565	−	0.186307i
$540$	2.28182	−	0.588070i	0.0981939	−	0.0253065i
$541$	4.39234	+	7.60776i	0.188842	+	0.327083i	0.944864	−	0.327462i	$-0.106193\pi$
$541$	4.39234	+	7.60776i	0.188842	+	0.327083i	−0.756023	+	0.654545i	$0.772860\pi$
$542$	−23.4354	−	2.73921i	−1.00664	−	0.117659i
$543$	−6.37369	+	11.2073i	−0.273521	+	0.480953i
$544$	−3.19932	−	0.758253i	−0.137170	−	0.0325098i
$545$	−3.35774	−	2.20842i	−0.143830	−	0.0945983i
$546$	22.2098	+	10.9738i	0.950491	+	0.469635i
$547$	9.31031	+	9.86835i	0.398080	+	0.421940i	0.895146	−	0.445772i	$-0.147071\pi$
$547$	9.31031	+	9.86835i	0.398080	+	0.421940i	−0.497066	+	0.867713i	$0.665589\pi$
$548$	9.34404	−	7.84058i	0.399158	−	0.334933i
$549$	−15.9871	−	1.65805i	−0.682314	−	0.0707637i
$550$	−1.80579	−	1.51524i	−0.0769993	−	0.0646101i
$551$	0.330806	+	5.67972i	0.0140928	+	0.241964i
$552$	11.9672	+	2.75416i	0.509358	+	0.117225i
$553$	−32.1063	−	43.1262i	−1.36530	−	1.83391i
$554$	−19.1622	+	2.23974i	−0.814124	+	0.0951575i
$555$	3.40194	−	0.420085i	0.144404	−	0.0178316i
$556$	10.2139	−	6.71780i	0.433166	−	0.284898i
$557$	−7.36649	+	2.68118i	−0.312128	+	0.113605i	−0.493334	−	0.869840i	$-0.664222\pi$
$557$	−7.36649	+	2.68118i	−0.312128	+	0.113605i	0.181206	+	0.983445i	$0.442000\pi$
$558$	1.69387	−	10.3957i	0.0717072	−	0.440086i
$559$	−41.2552	−	15.0157i	−1.74491	−	0.635095i
$560$	1.82781	−	0.433198i	0.0772389	−	0.0183060i
$561$	−2.72034	+	0.663456i	−0.114853	+	0.0280111i
$562$	−1.81923	+	31.2350i	−0.0767397	+	1.31757i
$563$	−27.8189	+	29.4863i	−1.17243	+	1.24270i	−0.208063	+	0.978115i	$0.566716\pi$
$563$	−27.8189	+	29.4863i	−1.17243	+	1.24270i	−0.964363	+	0.264583i	$0.914766\pi$
$564$	2.14294	+	1.77451i	0.0902340	+	0.0747202i
$565$	−1.25510	−	2.90964i	−0.0528023	−	0.122409i
$566$	24.0083			1.00914
$567$	−3.13544	−	37.1480i	−0.131676	−	1.56007i
$568$	4.52175			0.189729
$569$	4.42565	+	10.2598i	0.185533	+	0.430114i	0.985443	−	0.170006i	$-0.0543788\pi$
$569$	4.42565	+	10.2598i	0.185533	+	0.430114i	−0.799910	+	0.600120i	$0.795120\pi$
$570$	0.208116	−	1.22691i	0.00871702	−	0.0513898i
$571$	20.0446	−	21.2460i	0.838841	−	0.889119i	−0.156287	−	0.987712i	$-0.549952\pi$
$571$	20.0446	−	21.2460i	0.838841	−	0.889119i	0.995128	+	0.0985923i	$0.0314340\pi$
$572$	−0.0987140	+	1.69485i	−0.00412744	+	0.0708654i
$573$	3.72680	−	12.7497i	0.155689	−	0.532628i
$574$	−38.4826	+	9.12055i	−1.60623	+	0.380685i
$575$	−31.9414	−	11.6257i	−1.33205	−	0.484827i
$576$	2.99975	−	0.0390393i	0.124989	−	0.00162664i
$577$	−32.1041	+	11.6849i	−1.33651	+	0.486450i	−0.908712	−	0.417423i	$-0.862933\pi$
$577$	−32.1041	+	11.6849i	−1.33651	+	0.486450i	−0.427799	+	0.903874i	$0.640711\pi$
$578$	−5.17117	+	3.40113i	−0.215092	+	0.141468i
$579$	−0.712474	−	0.944131i	−0.0296094	−	0.0392368i
$580$	−1.61744	+	0.189052i	−0.0671607	+	0.00784996i
$581$	16.8638	+	22.6521i	0.699630	+	0.939766i
$582$	−10.5098	+	11.2860i	−0.435646	+	0.467819i
$583$	0.398418	+	6.84057i	0.0165008	+	0.283307i
$584$	−8.13143	−	6.82308i	−0.336481	−	0.282341i
$585$	3.26782	+	3.37461i	0.135108	+	0.139523i
$586$	10.6706	−	8.95373i	0.440800	−	0.369875i
$587$	−11.9255	−	12.6403i	−0.492218	−	0.521720i	0.432879	−	0.901452i	$-0.357498\pi$
$587$	−11.9255	−	12.6403i	−0.492218	−	0.521720i	−0.925097	+	0.379732i	$0.876016\pi$
$588$	−1.13728	−	17.5574i	−0.0469006	−	0.724057i
$589$	−4.64744	−	3.05667i	−0.191494	−	0.125948i
$590$	0.668172	+	0.158360i	0.0275082	+	0.00651956i
$591$	14.4113	+	24.5903i	0.592804	+	1.01151i
$592$	4.33453	+	0.506634i	0.178148	+	0.0208225i
$593$	17.0003	+	29.4453i	0.698117	+	1.20917i	0.969118	+	0.246595i	$0.0793119\pi$
$593$	17.0003	+	29.4453i	0.698117	+	1.20917i	−0.271001	+	0.962579i	$0.587355\pi$
$594$	2.26029	−	1.19096i	0.0927406	−	0.0488657i
$595$	−3.08811	+	5.34876i	−0.126600	+	0.219278i
$596$	−5.24908	+	7.05073i	−0.215011	+	0.288809i
$597$	2.59987	+	14.2035i	0.106406	+	0.581312i
$598$	7.02112	+	23.4522i	0.287115	+	0.959030i
$599$	−40.0687	+	20.1233i	−1.63716	+	0.822215i	−0.638551	+	0.769580i	$0.720466\pi$
$599$	−40.0687	+	20.1233i	−1.63716	+	0.822215i	−0.998614	+	0.0526354i	$0.983238\pi$
$600$	−8.25401	−	0.910355i	−0.336968	−	0.0371651i
$601$	−1.80155	+	6.01759i	−0.0734867	+	0.245463i	−0.986839	−	0.161709i	$-0.948300\pi$
$601$	−1.80155	+	6.01759i	−0.0734867	+	0.245463i	0.913352	+	0.407171i	$0.133485\pi$
$602$	9.14563	+	51.8675i	0.372748	+	2.11396i
$603$	−4.56470	−	1.01930i	−0.185889	−	0.0415092i
$604$	3.61601	−	20.5074i	0.147133	−	0.834435i
$605$	−4.35978	−	2.18956i	−0.177250	−	0.0890184i
$606$	1.71193	−	33.1019i	0.0695423	−	1.34467i
$607$	−12.9207	+	29.9535i	−0.524435	+	1.21578i	0.425963	+	0.904740i	$0.359935\pi$
$607$	−12.9207	+	29.9535i	−0.524435	+	1.21578i	−0.950398	+	0.311036i	$0.899324\pi$
$608$	0.627527	−	1.45477i	0.0254496	−	0.0589988i
$609$	−1.33064	+	25.7292i	−0.0539201	+	1.04260i
$610$	−2.17118	−	1.09041i	−0.0879083	−	0.0441492i
$611$	−0.963149	+	5.46229i	−0.0389648	+	0.220980i
$612$	−6.67504	+	7.26218i	−0.269823	+	0.293556i
$613$	−2.26497	−	12.8453i	−0.0914812	−	0.518816i	−0.995769	−	0.0918922i	$-0.970708\pi$
$613$	−2.26497	−	12.8453i	−0.0914812	−	0.518816i	0.904288	−	0.426923i	$-0.140403\pi$
$614$	1.31767	−	4.40133i	0.0531769	−	0.177623i
$615$	−7.45413	−	0.822135i	−0.300579	−	0.0331517i
$616$	1.82002	−	0.914050i	0.0733308	−	0.0368281i
$617$	−8.09312	−	27.0329i	−0.325817	−	1.08830i	−0.951352	−	0.308108i	$-0.900304\pi$
$617$	−8.09312	−	27.0329i	−0.325817	−	1.08830i	0.625535	−	0.780196i	$-0.284881\pi$
$618$	4.09747	+	22.3852i	0.164825	+	0.900465i
$619$	13.5221	−	18.1633i	0.543499	−	0.730045i	−0.442506	−	0.896766i	$-0.645910\pi$
$619$	13.5221	−	18.1633i	0.543499	−	0.730045i	0.986004	+	0.166720i	$0.0533177\pi$
$620$	0.796081	−	1.37885i	0.0319714	−	0.0553760i
$621$	24.7533	−	27.2849i	0.993318	−	1.09490i
$622$	−9.33367	−	16.1664i	−0.374246	−	0.648213i
$623$	30.7986	+	3.59985i	1.23392	+	0.144225i
$624$	3.02393	+	5.15978i	0.121054	+	0.206556i
$625$	21.3657	+	5.06376i	0.854627	+	0.202550i
$626$	−0.931466	−	0.612635i	−0.0372289	−	0.0244858i
$627$	−0.0872150	−	1.34644i	−0.00348303	−	0.0537715i
$628$	−5.47205	−	5.80003i	−0.218359	−	0.231447i
$629$	−10.9918	+	9.22318i	−0.438270	+	0.367752i
$630$	1.54584	−	5.41915i	0.0615877	−	0.215904i
$631$	14.8006	+	12.4192i	0.589204	+	0.494401i	0.887955	−	0.459930i	$-0.152126\pi$
$631$	14.8006	+	12.4192i	0.589204	+	0.494401i	−0.298751	+	0.954331i	$0.596570\pi$
$632$	−0.754705	−	12.9578i	−0.0300206	−	0.515433i
$633$	−19.8369	+	21.3019i	−0.788445	+	0.846673i
$634$	−2.95763	−	3.97279i	−0.117463	−	0.157780i
$635$	6.68312	−	0.781145i	0.265212	−	0.0309988i
$636$	14.5400	+	19.2676i	0.576548	+	0.764009i
$637$	29.3044	−	19.2738i	1.16108	−	0.763657i
$638$	−1.65914	+	0.603877i	−0.0656859	+	0.0239077i
$639$	6.62918	−	11.8351i	0.262246	−	0.468190i
$640$	0.426137	+	0.155101i	0.0168446	+	0.00613091i
$641$	15.2911	−	3.62407i	0.603964	−	0.143142i	0.0827529	−	0.996570i	$-0.473629\pi$
$641$	15.2911	−	3.62407i	0.603964	−	0.143142i	0.521211	+	0.853428i	$0.325481\pi$
$642$	−7.33098	+	25.0800i	−0.289331	+	0.989828i
$643$	−0.959312	+	16.4708i	−0.0378316	+	0.649543i	0.925088	+	0.379753i	$0.123991\pi$
$643$	−0.959312	+	16.4708i	−0.0378316	+	0.649543i	−0.962919	+	0.269790i	$0.913046\pi$
$644$	20.1535	−	21.3614i	0.794158	−	0.841758i
$645$	−1.67019	+	9.84632i	−0.0657636	+	0.387699i
$646$	2.06328	+	4.78321i	0.0811785	+	0.188193i
$647$	5.08722			0.199999			0.0999997	−	0.994987i	$-0.468116\pi$
$647$	5.08722			0.199999			0.0999997	+	0.994987i	$0.468116\pi$
$648$	4.29564	−	7.90870i	0.168749	−	0.310683i
$649$	0.744519			0.0292249
$650$	−6.55686	−	15.2005i	−0.257181	−	0.596213i
$651$	−19.4012	−	16.0655i	−0.760391	−	0.629658i
$652$	10.5777	−	11.2117i	0.414253	−	0.439082i
$653$	−1.27939	+	21.9662i	−0.0500662	+	0.859604i	0.876016	+	0.482282i	$0.160192\pi$
$653$	−1.27939	+	21.9662i	−0.0500662	+	0.859604i	−0.926082	+	0.377322i	$0.876845\pi$
$654$	−14.9127	+	3.63703i	−0.583134	+	0.142219i
$655$	−2.44455	+	0.579368i	−0.0955164	+	0.0226378i
$656$	−8.97189	−	3.26550i	−0.350294	−	0.127496i
$657$	−29.7798	+	11.2799i	−1.16182	+	0.440072i
$658$	6.25258	−	2.27575i	0.243751	−	0.0887181i
$659$	−15.0203	+	9.87901i	−0.585108	+	0.384831i	−0.807274	−	0.590177i	$-0.799058\pi$
$659$	−15.0203	+	9.87901i	−0.585108	+	0.384831i	0.222166	+	0.975009i	$0.428687\pi$
$660$	0.383285	−	0.0473296i	0.0149194	−	0.00184230i
$661$	17.1320	−	2.00244i	0.666357	−	0.0778859i	0.223812	−	0.974632i	$-0.428150\pi$
$661$	17.1320	−	2.00244i	0.666357	−	0.0778859i	0.442545	+	0.896746i	$0.354076\pi$
$662$	−3.50378	−	4.70639i	−0.136178	−	0.182919i
$663$	−19.1629	−	4.41021i	−0.744226	−	0.171278i
$664$	0.396409	+	6.80608i	0.0153837	+	0.264127i
$665$	−2.27982	−	1.91300i	−0.0884078	−	0.0741829i
$666$	7.68075	−	10.6023i	0.297623	−	0.410832i
$667$	−19.5032	+	16.3651i	−0.755166	+	0.633659i
$668$	−0.645575	−	0.684270i	−0.0249781	−	0.0264752i
$669$	−4.76859	−	2.35615i	−0.184364	−	0.0910940i
$670$	−0.590692	−	0.388504i	−0.0228204	−	0.0150092i
$671$	−2.56324	−	0.607499i	−0.0989528	−	0.0234522i
$672$	3.54677	−	6.23655i	0.136820	−	0.240580i
$673$	18.3189	+	2.14117i	0.706142	+	0.0825361i	0.461581	−	0.887098i	$-0.347282\pi$
$673$	18.3189	+	2.14117i	0.706142	+	0.0825361i	0.244561	+	0.969634i	$0.421356\pi$
$674$	−8.31045	−	14.3941i	−0.320106	−	0.554441i
$675$	−14.4836	+	20.2692i	−0.557476	+	0.780162i
$676$	0.538759	−	0.933158i	0.0207215	−	0.0358907i
$677$	27.4628	−	36.8889i	1.05548	−	1.41776i	0.152383	−	0.988322i	$-0.451305\pi$
$677$	27.4628	−	36.8889i	1.05548	−	1.41776i	0.903098	−	0.429435i	$-0.141287\pi$
$678$	−11.3998	−	4.06537i	−0.437805	−	0.156129i
$679$	10.5777	+	35.3319i	0.405934	+	1.35591i
$680$	−1.33244	+	0.669176i	−0.0510967	+	0.0256617i
$681$	10.5471	+	24.0199i	0.404165	+	0.920446i
$682$	0.495099	−	1.65374i	0.0189583	−	0.0633252i
$683$	−6.65071	−	37.7181i	−0.254482	−	1.44324i	−0.797398	−	0.603454i	$-0.793791\pi$
$683$	−6.65071	−	37.7181i	−0.254482	−	1.44324i	0.542915	−	0.839787i	$-0.317320\pi$
$684$	−2.88769	−	3.77526i	−0.110414	−	0.144351i
$685$	0.960538	−	5.44748i	0.0367003	−	0.208138i
$686$	−11.6899	−	5.87088i	−0.446322	−	0.224151i
$687$	10.1822	+	6.60240i	0.388474	+	0.251897i
$688$	−5.03608	+	11.6749i	−0.191999	+	0.445103i
$689$	−19.0594	+	44.1847i	−0.726106	+	1.68330i
$690$	4.96011	−	2.53161i	0.188828	−	0.0963767i
$691$	−8.11346	−	4.07473i	−0.308651	−	0.155010i	0.287731	−	0.957711i	$-0.407099\pi$
$691$	−8.11346	−	4.07473i	−0.308651	−	0.155010i	−0.596381	+	0.802701i	$0.703395\pi$
$692$	−4.12649	+	23.4025i	−0.156866	+	0.889630i
$693$	0.275858	−	6.10374i	0.0104790	−	0.231862i
$694$	4.18515	+	23.7352i	0.158866	+	0.900974i
$695$	1.59001	−	5.31100i	0.0603125	−	0.201458i
$696$	−3.68164	+	5.01307i	−0.139552	+	0.190020i
$697$	28.0532	−	14.0888i	1.06259	−	0.533653i
$698$	2.25880	+	7.54490i	0.0854967	+	0.285579i
$699$	−1.55921	+	1.32572i	−0.0589747	+	0.0501432i
$700$	−11.8591	+	15.9296i	−0.448233	+	0.602082i
$701$	−1.01115	+	1.75136i	−0.0381904	+	0.0661478i	−0.884489	−	0.466561i	$-0.845493\pi$
$701$	−1.01115	+	1.75136i	−0.0381904	+	0.0661478i	0.846298	+	0.532709i	$0.178826\pi$
$702$	17.9383	−	0.350205i	0.677039	−	0.0132176i
$703$	−3.45707	−	5.98782i	−0.130386	−	0.225835i
$704$	0.488357	+	0.0570808i	0.0184057	+	0.00215131i
$705$	1.26170	−	0.00820963i	0.0475182	−	0.000309193i
$706$	22.0937	+	5.23631i	0.831508	+	0.197071i
$707$	−66.2287	−	43.5593i	−2.49079	−	1.63822i
$708$	2.18183	−	1.45544i	0.0819982	−	0.0546987i
$709$	−11.6878	−	12.3883i	−0.438944	−	0.465253i	0.469700	−	0.882826i	$-0.344362\pi$
$709$	−11.6878	−	12.3883i	−0.438944	−	0.465253i	−0.908643	+	0.417573i	$0.862881\pi$
$710$	1.57081	−	1.31807i	0.0589516	−	0.0494662i
$711$	−35.0219	−	17.0216i	−1.31342	−	0.638360i
$712$	5.73454	+	4.81185i	0.214911	+	0.180332i
$713$	−1.44735	−	24.8500i	−0.0542037	−	0.930641i
$714$	6.91245	+	22.5540i	0.258692	+	0.844063i
$715$	0.459749	+	0.617550i	0.0171936	+	0.0230951i
$716$	−0.656577	+	0.0767429i	−0.0245374	+	0.00286802i
$717$	−4.73627	+	11.1794i	−0.176879	+	0.417501i
$718$	13.3640	−	8.78962i	0.498739	−	0.328026i
$719$	−19.3167	+	7.03071i	−0.720392	+	0.262201i	−0.676092	−	0.736817i	$-0.736328\pi$
$719$	−19.3167	+	7.03071i	−0.720392	+	0.262201i	−0.0442998	+	0.999018i	$0.514106\pi$
$720$	1.03070	−	0.887973i	0.0384120	−	0.0330928i
$721$	51.1418	+	18.6141i	1.90462	+	0.693225i
$722$	16.0454	−	3.80282i	0.597147	−	0.141526i
$723$	−31.9076	−	33.3822i	−1.18666	−	1.24150i
$724$	−0.432816	+	7.43116i	−0.0160855	+	0.276177i
$725$	11.8146	−	12.5228i	0.438783	−	0.465083i
$726$	−17.4682	+	6.48694i	−0.648307	+	0.240753i
$727$	−13.9089	−	32.2446i	−0.515854	−	1.19588i	−0.954767	−	0.297355i	$-0.903896\pi$
$727$	−13.9089	−	32.2446i	−0.515854	−	1.19588i	0.438913	−	0.898530i	$-0.355364\pi$
$728$	14.3027			0.530092
$729$	−14.4024	−	22.8380i	−0.533420	−	0.845850i
$730$	−4.81367			−0.178162
$731$	−16.5584	−	38.3866i	−0.612433	−	1.41978i
$732$	−8.69921	+	3.23051i	−0.321532	+	0.119403i
$733$	22.3949	−	23.7372i	0.827174	−	0.876753i	−0.166843	−	0.985984i	$-0.553357\pi$
$733$	22.3949	−	23.7372i	0.827174	−	0.876753i	0.994016	+	0.109230i	$0.0348387\pi$
$734$	0.693652	−	11.9095i	0.0256031	−	0.439589i
$735$	−5.51299	−	5.76777i	−0.203350	−	0.212748i
$736$	6.89877	−	1.63504i	0.254292	−	0.0602683i
$737$	−0.720323	−	0.262176i	−0.0265334	−	0.00965738i
$738$	−21.7004	+	18.6954i	−0.798803	+	0.688186i
$739$	−17.4640	+	6.35639i	−0.642425	+	0.233824i	−0.642630	−	0.766176i	$-0.722157\pi$
$739$	−17.4640	+	6.35639i	−0.642425	+	0.233824i	0.000205241		1.00000i	$0.499935\pi$
$740$	1.65345	−	1.08749i	0.0607822	−	0.0399771i
$741$	3.69629	−	8.72463i	0.135787	−	0.320507i
$742$	57.3364	−	6.70167i	2.10489	−	0.246026i
$743$	−30.0795	−	40.4037i	−1.10351	−	1.48227i	−0.858546	−	0.512736i	$-0.828632\pi$
$743$	−30.0795	−	40.4037i	−1.10351	−	1.48227i	−0.244962	−	0.969533i	$-0.578775\pi$
$744$	−1.78196	−	5.81419i	−0.0653297	−	0.213158i
$745$	0.231776	+	3.97943i	0.00849160	+	0.145795i
$746$	4.46265	+	3.74461i	0.163389	+	0.137100i
$747$	18.3952	+	8.94060i	0.673047	+	0.327120i
$748$	−1.23841	+	1.03915i	−0.0452806	+	0.0379949i
$749$	42.8826	+	45.4529i	1.56689	+	1.66081i
$750$	−6.39983	+	4.26914i	−0.233689	+	0.155887i
$751$	9.75132	+	6.41354i	0.355831	+	0.234033i	0.714820	−	0.699308i	$-0.246508\pi$
$751$	9.75132	+	6.41354i	0.355831	+	0.234033i	−0.358990	+	0.933341i	$0.616879\pi$
$752$	1.56305	+	0.370449i	0.0569985	+	0.0135089i
$753$	−25.0778	+	0.163177i	−0.913884	+	0.00594648i
$754$	−12.3154	−	1.43947i	−0.448501	−	0.0524223i
$755$	−4.72164	−	8.17813i	−0.171838	−	0.297633i
$756$	−11.1236	−	18.4264i	−0.404562	−	0.670162i
$757$	2.83432	−	4.90919i	0.103015	−	0.178428i	−0.809910	−	0.586554i	$-0.800484\pi$
$757$	2.83432	−	4.90919i	0.103015	−	0.178428i	0.912926	+	0.408126i	$0.133818\pi$
$758$	0.833927	−	1.12016i	0.0302896	−	0.0406860i
$759$	4.59992	−	3.91108i	0.166967	−	0.141963i
$760$	−0.206062	−	0.688294i	−0.00747465	−	0.0249671i
$761$	41.1067	−	20.6446i	1.49012	−	0.748365i	0.497252	−	0.867606i	$-0.334343\pi$
$761$	41.1067	−	20.6446i	1.49012	−	0.748365i	0.992865	+	0.119241i	$0.0380462\pi$
$762$	15.2122	−	20.7135i	0.551079	−	0.750371i
$763$	−10.5284	+	35.1672i	−0.381153	+	1.27314i
$764$	−1.33172	−	7.55258i	−0.0481800	−	0.273243i
$765$	−0.201956	+	4.46855i	−0.00730173	+	0.161561i
$766$	0.279524	−	1.58526i	0.0100996	−	0.0572777i
$767$	4.67234	+	2.34654i	0.168708	+	0.0847285i
$768$	1.54273	−	0.787398i	0.0556683	−	0.0284128i
$769$	4.70492	−	10.9072i	0.169664	−	0.393325i	−0.812077	−	0.583551i	$-0.801663\pi$
$769$	4.70492	−	10.9072i	0.169664	−	0.393325i	0.981740	+	0.190226i	$0.0609222\pi$
$770$	0.365817	−	0.848060i	0.0131831	−	0.0305620i
$771$	13.7167	+	8.89428i	0.493994	+	0.320320i
$772$	−0.610250	−	0.306479i	−0.0219634	−	0.0110304i
$773$	4.03063	−	22.8588i	0.144972	−	0.822175i	−0.822418	−	0.568883i	$-0.807376\pi$
$773$	4.03063	−	22.8588i	0.144972	−	0.822175i	0.967390	−	0.253292i	$-0.0815133\pi$
$774$	23.1745	+	30.2975i	0.832990	+	1.08902i
$775$	2.92296	+	16.5770i	0.104996	+	0.595462i
$776$	−2.55362	+	8.52968i	−0.0916696	+	0.306198i
$777$	−12.5880	−	28.6680i	−0.451594	−	1.02846i
$778$	10.6197	−	5.33340i	0.380733	−	0.191211i
$779$	4.33843	+	14.4914i	0.155440	+	0.519207i
$780$	2.55453	+	0.910995i	0.0914670	+	0.0326188i
$781$	1.32764	−	1.78333i	0.0475067	−	0.0638126i
$782$	−11.6556	+	20.1881i	−0.416803	+	0.721923i
$783$	7.72357	+	16.9857i	0.276018	+	0.607020i
$784$	−5.07902	−	8.79712i	−0.181394	−	0.314183i
$785$	−3.59162	−	0.419800i	−0.128190	−	0.0149833i
$786$	−4.74352	+	8.34089i	−0.169196	+	0.297510i
$787$	20.4219	+	4.84009i	0.727964	+	0.172531i	0.577856	−	0.816139i	$-0.303890\pi$
$787$	20.4219	+	4.84009i	0.727964	+	0.172531i	0.150108	+	0.988670i	$0.452038\pi$
$788$	13.7485	+	9.04255i	0.489771	+	0.322127i
$789$	9.60784	+	4.74721i	0.342048	+	0.169005i
$790$	−4.03931	−	4.28142i	−0.143712	−	0.152326i
$791$	−22.1727	+	18.6051i	−0.788370	+	0.661521i
$792$	0.865365	−	1.19453i	0.0307494	−	0.0424458i
$793$	−14.1713	−	11.8911i	−0.503238	−	0.422266i
$794$	−0.0349012	−	0.599231i	−0.00123860	−	0.0212659i
$795$	10.6674	+	2.45503i	0.378335	+	0.0870711i
$796$	4.97831	+	6.68703i	0.176452	+	0.237016i
$797$	−3.10388	+	0.362792i	−0.109945	+	0.0128507i	−0.170887	−	0.985291i	$-0.554663\pi$
$797$	−3.10388	+	0.362792i	−0.109945	+	0.0128507i	0.0609424	+	0.998141i	$0.480589\pi$
$798$	−11.2813	+	1.39306i	−0.399353	+	0.0493137i
$799$	−4.41270	+	2.90228i	−0.156110	+	0.102675i
$800$	−4.50522	+	1.63976i	−0.159283	+	0.0579744i
$801$	21.0016	−	7.95496i	0.742055	−	0.281075i
$802$	21.3120	+	7.75693i	0.752553	+	0.273907i
$803$	−5.07844	+	1.20361i	−0.179214	+	0.0424745i
$804$	−2.62344	+	0.639824i	−0.0925216	+	0.0225648i
$805$	0.774368	−	13.2954i	0.0272929	−	0.468601i
$806$	8.31924	−	8.81788i	0.293033	−	0.310597i
$807$	22.1903	+	18.3752i	0.781136	+	0.646837i
$808$	−7.57975	−	17.5718i	−0.266655	−	0.618175i
$809$	−37.8617			−1.33115			−0.665573	−	0.746333i	$-0.731813\pi$
$809$	−37.8617			−1.33115			−0.665573	+	0.746333i	$0.731813\pi$
$810$	−0.813083	−	3.99956i	−0.0285688	−	0.140530i
$811$	17.1067			0.600698			0.300349	−	0.953829i	$-0.402897\pi$
$811$	17.1067			0.600698			0.300349	+	0.953829i	$0.402897\pi$
$812$	5.89154	+	13.6581i	0.206753	+	0.479306i
$813$	−6.83458	+	40.2921i	−0.239699	+	1.41311i
$814$	1.47248	−	1.56074i	0.0516104	−	0.0547038i
$815$	0.406431	−	6.97815i	0.0142367	−	0.244434i
$816$	−1.59778	+	5.46616i	−0.0559335	+	0.191354i
$817$	19.6016	−	4.64567i	0.685775	−	0.162532i
$818$	−7.25649	−	2.64115i	−0.253717	−	0.0923455i
$819$	20.9686	−	37.4355i	0.732703	−	1.30810i
$820$	−4.06862	+	1.48086i	−0.142083	+	0.0517138i
$821$	8.36033	−	5.49868i	0.291778	−	0.191905i	−0.395178	−	0.918605i	$-0.629317\pi$
$821$	8.36033	−	5.49868i	0.291778	−	0.191905i	0.686956	+	0.726699i	$0.258947\pi$
$822$	−12.7263	−	16.8641i	−0.443880	−	0.588205i
$823$	19.7825	−	2.31225i	0.689576	−	0.0805998i	0.235914	−	0.971774i	$-0.424192\pi$
$823$	19.7825	−	2.31225i	0.689576	−	0.0805998i	0.453661	+	0.891174i	$0.350118\pi$
$824$	7.84596	+	10.5390i	0.273327	+	0.367142i
$825$	−2.78251	+	2.98800i	−0.0968746	+	0.104029i
$826$	−0.364701	−	6.26167i	−0.0126896	−	0.217871i
$827$	28.2510	+	23.7054i	0.982383	+	0.824317i	0.984447	−	0.175681i	$-0.0562126\pi$
$827$	28.2510	+	23.7054i	0.982383	+	0.824317i	−0.00206431	+	0.999998i	$0.500657\pi$
$828$	5.83453	−	20.4537i	0.202764	−	0.710817i
$829$	−27.8364	+	23.3575i	−0.966797	+	0.811239i	−0.982045	−	0.188645i	$-0.939591\pi$
$829$	−27.8364	+	23.3575i	−0.966797	+	0.811239i	0.0152484	+	0.999884i	$0.495146\pi$
$830$	2.12165	+	2.24882i	0.0736435	+	0.0780575i
$831$	2.15998	+	33.3460i	0.0749288	+	1.15676i
$832$	2.88485	+	1.89740i	0.100014	+	0.0657804i
$833$	32.4988	+	7.70236i	1.12602	+	0.266871i
$834$	−10.7063	−	18.2684i	−0.370730	−	0.632581i
$835$	−0.423728	−	0.0495267i	−0.0146637	−	0.00171394i
$836$	−0.389497	−	0.674629i	−0.0134710	−	0.0233325i
$837$	−17.8304	−	3.85992i	−0.616308	−	0.133418i
$838$	12.4967	−	21.6448i	0.431690	−	0.747708i
$839$	11.5943	−	15.5738i	0.400279	−	0.537667i	−0.555592	−	0.831455i	$-0.687508\pi$
$839$	11.5943	−	15.5738i	0.400279	−	0.537667i	0.955871	+	0.293787i	$0.0949158\pi$
$840$	−0.585810	−	3.20038i	−0.0202124	−	0.110424i
$841$	4.61894	+	15.4283i	0.159274	+	0.532011i
$842$	−17.2437	+	8.66009i	−0.594256	+	0.298447i
$843$	53.8657	+	5.94098i	1.85523	+	0.204618i
$844$	−4.81986	+	16.0995i	−0.165907	+	0.554166i
$845$	−0.0848512	−	0.481215i	−0.00291897	−	0.0165543i
$846$	3.26114	−	3.54798i	0.112120	−	0.121982i
$847$	−7.73830	+	43.8861i	−0.265891	+	1.50794i
$848$	12.4538	+	6.25454i	0.427666	+	0.214782i
$849$	2.14770	−	41.5280i	0.0737089	−	1.42524i
$850$	6.24363	−	14.4744i	0.214155	−	0.496467i
$851$	12.2549	−	28.4101i	0.420093	−	0.973884i
$852$	0.404502	−	7.82145i	0.0138580	−	0.267959i
$853$	−25.5898	−	12.8517i	−0.876180	−	0.440034i	−0.0469208	−	0.998899i	$-0.514941\pi$
$853$	−25.5898	−	12.8517i	−0.876180	−	0.440034i	−0.829259	+	0.558865i	$0.811237\pi$
$854$	−3.85369	+	21.8553i	−0.131870	+	0.747874i
$855$	−2.10363	−	0.469742i	−0.0719425	−	0.0160649i
$856$	2.61963	+	14.8567i	0.0895371	+	0.507790i
$857$	0.434909	−	1.45270i	0.0148562	−	0.0496232i	−0.950240	−	0.311519i	$-0.899162\pi$
$857$	0.434909	−	1.45270i	0.0148562	−	0.0496232i	0.965096	+	0.261895i	$0.0843476\pi$
$858$	2.92282	+	0.322366i	0.0997836	+	0.0110054i
$859$	−30.8682	+	15.5026i	−1.05321	+	0.528942i	−0.889201	−	0.457517i	$-0.848739\pi$
$859$	−30.8682	+	15.5026i	−1.05321	+	0.528942i	−0.164009	+	0.986459i	$0.552443\pi$
$860$	1.65370	+	5.52375i	0.0563908	+	0.188358i
$861$	12.3336	+	67.3808i	0.420329	+	2.29633i
$862$	11.2712	−	15.1399i	0.383899	−	0.515666i
$863$	28.9690	−	50.1758i	0.986117	−	1.70800i	0.349252	−	0.937029i	$-0.386436\pi$
$863$	28.9690	−	50.1758i	0.986117	−	1.70800i	0.636865	−	0.770975i	$-0.280231\pi$
$864$	0.200820	−	5.19227i	0.00683203	−	0.176645i
$865$	5.38821	+	9.33266i	0.183205	+	0.317320i
$866$	27.1261	+	3.17059i	0.921784	+	0.107741i
$867$	5.42047	+	9.24902i	0.184089	+	0.314113i
$868$	−14.1511	−	3.35387i	−0.480320	−	0.113838i
$869$	−5.33201	−	3.50692i	−0.180876	−	0.118964i
$870$	0.182319	+	2.81467i	0.00618121	+	0.0954262i
$871$	−3.69418	−	3.91560i	−0.125172	−	0.132675i
$872$	−6.78887	+	5.69653i	−0.229900	+	0.192909i
$873$	18.5816	+	19.1888i	0.628892	+	0.649444i
$874$	−8.60484	−	7.22032i	−0.291063	−	0.244231i
$875$	1.06975	+	18.3670i	0.0361643	+	0.620917i
$876$	−12.5296	+	13.4549i	−0.423335	+	0.454598i
$877$	−26.6632	−	35.8148i	−0.900351	−	1.20938i	−0.977196	−	0.212338i	$-0.931892\pi$
$877$	−26.6632	−	35.8148i	−0.900351	−	1.20938i	0.0768450	−	0.997043i	$-0.475515\pi$
$878$	−20.1194	+	2.35162i	−0.678997	+	0.0793634i
$879$	−14.5331	−	19.2584i	−0.490188	−	0.649570i
$880$	0.186289	−	0.122524i	0.00627981	−	0.00413030i
$881$	−17.3955	+	6.33143i	−0.586068	+	0.213311i	−0.617999	−	0.786179i	$-0.712057\pi$
$881$	−17.3955	+	6.33143i	−0.586068	+	0.213311i	0.0319309	+	0.999490i	$0.489834\pi$
$882$	−30.4715	+	0.396563i	−1.02603	+	0.0133530i
$883$	24.4598	+	8.90265i	0.823138	+	0.299598i	0.719040	−	0.694969i	$-0.244582\pi$
$883$	24.4598	+	8.90265i	0.823138	+	0.299598i	0.104099	+	0.994567i	$0.466804\pi$
$884$	−11.0469	+	2.61817i	−0.371548	+	0.0880585i
$885$	0.333693	−	1.14160i	0.0112170	−	0.0383744i
$886$	1.39043	−	23.8727i	0.0467123	−	0.802019i
$887$	−6.86898	+	7.28069i	−0.230638	+	0.244462i	−0.832349	−	0.554252i	$-0.813004\pi$
$887$	−6.86898	+	7.28069i	−0.230638	+	0.244462i	0.601711	+	0.798714i	$0.294486\pi$
$888$	1.26410	−	7.45228i	0.0424203	−	0.250082i
$889$	−24.3433	−	56.4340i	−0.816447	−	1.89274i
$890$	3.39475			0.113792
$891$	−1.85785	−	4.01624i	−0.0622405	−	0.134549i
$892$	−3.07088			−0.102821
$893$	−1.00803	−	2.33687i	−0.0337323	−	0.0782004i
$894$	11.7264	+	9.71027i	0.392188	+	0.324760i
$895$	−0.205718	+	0.218049i	−0.00687640	+	0.00728856i
$896$	0.240849	−	4.13522i	0.00804620	−	0.138148i
$897$	41.1942	−	10.0467i	1.37543	−	0.335451i
$898$	24.5646	−	5.82193i	0.819733	−	0.194280i
$899$	11.8474	+	4.31209i	0.395132	+	0.143816i
$900$	−2.31305	+	14.1958i	−0.0771018	+	0.473195i
$901$	−43.0580	+	15.6718i	−1.43447	+	0.522105i
$902$	−3.92213	+	2.57963i	−0.130593	+	0.0858922i
$903$	90.5353	−	11.1797i	3.01283	−	0.372036i
$904$	−6.94040	+	0.811216i	−0.230834	+	0.0269806i
$905$	2.01579	+	2.70768i	0.0670071	+	0.0900062i
$906$	−35.1490	−	8.08929i	−1.16775	−	0.268749i
$907$	−1.46237	−	25.1079i	−0.0485572	−	0.833695i	−0.931393	−	0.364014i	$-0.881406\pi$
$907$	−1.46237	−	25.1079i	−0.0485572	−	0.833695i	0.882836	−	0.469681i	$-0.155631\pi$
$908$	11.6025	+	9.73562i	0.385041	+	0.323088i
$909$	−57.1045	−	5.92238i	−1.89404	−	0.196433i
$910$	4.96861	−	4.16916i	0.164708	−	0.138206i
$911$	5.61336	+	5.94982i	0.185979	+	0.197126i	0.813654	−	0.581349i	$-0.197475\pi$
$911$	5.61336	+	5.94982i	0.185979	+	0.197126i	−0.627675	+	0.778475i	$0.715993\pi$
$912$	−2.46024	−	1.21560i	−0.0814666	−	0.0402525i
$913$	2.80064	+	1.84201i	0.0926876	+	0.0609616i
$914$	−12.4418	−	2.94876i	−0.411538	−	0.0975364i
$915$	−2.08034	+	3.65802i	−0.0687740	+	0.120931i
$916$	6.95901	+	0.813391i	0.229932	+	0.0268752i
$917$	11.4738	+	19.8731i	0.378897	+	0.656269i
$918$	11.9645	+	12.1957i	0.394889	+	0.402519i
$919$	16.6768	−	28.8850i	0.550116	−	0.952829i	−0.448149	−	0.893959i	$-0.647917\pi$
$919$	16.6768	−	28.8850i	0.550116	−	0.952829i	0.998266	−	0.0588706i	$-0.0187499\pi$
$920$	1.91996	−	2.57895i	0.0632992	−	0.0850256i
$921$	−7.49528	−	2.67296i	−0.246978	−	0.0880770i
$922$	1.12876	+	3.77032i	0.0371737	+	0.124169i
$923$	13.9524	−	7.00716i	0.459249	−	0.230644i
$924$	−1.41825	−	3.22993i	−0.0466572	−	0.106257i
$925$	−6.00070	+	20.0437i	−0.197302	+	0.659034i
$926$	−0.612435	−	3.47329i	−0.0201259	−	0.114139i
$927$	39.0871	−	5.08505i	1.28379	−	0.167015i
$928$	−0.623566	+	3.53642i	−0.0204696	+	0.116089i
$929$	−38.2557	−	19.2127i	−1.25513	−	0.630349i	−0.308055	−	0.951368i	$-0.599678\pi$
$929$	−38.2557	−	19.2127i	−1.25513	−	0.630349i	−0.947073	+	0.321020i	$0.895974\pi$
$930$	−2.31384	−	1.50036i	−0.0758738	−	0.0491987i
$931$	−6.37445	+	14.7776i	−0.208914	+	0.484317i
$932$	−0.468014	+	1.08498i	−0.0153303	+	0.0355397i
$933$	−28.7986	+	14.6986i	−0.942824	+	0.481211i
$934$	−9.20690	−	4.62388i	−0.301259	−	0.151298i
$935$	−0.127304	+	0.721978i	−0.00416329	+	0.0236112i
$936$	9.19558	−	4.76904i	0.300567	−	0.155881i
$937$	5.16278	+	29.2796i	0.168661	+	0.956521i	0.945209	+	0.326464i	$0.105857\pi$
$937$	5.16278	+	29.2796i	0.168661	+	0.956521i	−0.776549	+	0.630057i	$0.783032\pi$
$938$	−1.85214	+	6.18659i	−0.0604747	+	0.201999i
$939$	−1.14302	+	1.55639i	−0.0373012	+	0.0507908i
$940$	0.650972	−	0.326930i	0.0212324	−	0.0106633i
$941$	−12.5454	−	41.9046i	−0.408969	−	1.36605i	−0.876213	−	0.481924i	$-0.839938\pi$
$941$	−12.5454	−	41.9046i	−0.408969	−	1.36605i	0.467244	−	0.884128i	$-0.345247\pi$
$942$	−10.5221	+	8.94637i	−0.342827	+	0.291488i
$943$	−40.4228	+	54.2973i	−1.31635	+	1.76816i
$944$	0.757115	−	1.31136i	0.0246420	−	0.0426812i
$945$	−9.23544	−	3.15868i	−0.300429	−	0.102752i
$946$	3.12582	+	5.41408i	0.101629	+	0.176027i
$947$	27.3023	+	3.19118i	0.887205	+	0.103699i	0.547474	−	0.836823i	$-0.315590\pi$
$947$	27.3023	+	3.19118i	0.887205	+	0.103699i	0.339732	+	0.940522i	$0.389664\pi$
$948$	−22.4811	+	0.146281i	−0.730153	+	0.00475097i
$949$	−35.6639	−	8.45251i	−1.15770	−	0.274380i
$950$	6.34629	+	4.17402i	0.205901	+	0.135423i
$951$	−7.13648	+	4.76054i	−0.231416	+	0.154371i
$952$	9.34622	+	9.90641i	0.302913	+	0.321069i
$953$	−23.9157	+	20.0677i	−0.774707	+	0.650056i	−0.941910	−	0.335866i	$-0.890971\pi$
$953$	−23.9157	+	20.0677i	−0.774707	+	0.650056i	0.167203	+	0.985922i	$0.446526\pi$
$954$	34.6286	−	23.4268i	1.12114	−	0.758469i
$955$	−2.66417	−	2.23550i	−0.0862104	−	0.0723391i
$956$	0.407582	+	6.99791i	0.0131821	+	0.226329i
$957$	0.896128	+	2.92390i	0.0289677	+	0.0945161i
$958$	−19.9796	−	26.8372i	−0.645511	−	0.867071i
$959$	−50.1843	+	5.86571i	−1.62054	+	0.189414i
$960$	0.306406	−	0.723231i	0.00988920	−	0.0233422i
$961$	15.6013	−	10.2611i	0.503268	−	0.331005i
$962$	14.1598	−	5.15375i	0.456531	−	0.166164i
$963$	42.7260	+	14.9243i	1.37683	+	0.480927i
$964$	−25.0534	−	9.11868i	−0.806915	−	0.293693i
$965$	−0.301332	+	0.0714170i	−0.00970022	+	0.00229899i
$966$	−35.1468	−	36.7712i	−1.13083	−	1.18309i
$967$	−3.09166	+	53.0817i	−0.0994209	+	1.70699i	0.468135	+	0.883657i	$0.344926\pi$
$967$	−3.09166	+	53.0817i	−0.0994209	+	1.70699i	−0.567556	+	0.823335i	$0.692111\pi$
$968$	−7.38276	+	7.82527i	−0.237291	+	0.251514i
$969$	8.45829	−	3.14104i	0.271719	−	0.100905i
$970$	1.59926	+	3.70750i	0.0513491	+	0.119041i
$971$	−5.29990			−0.170082			−0.0850409	−	0.996377i	$-0.527102\pi$
$971$	−5.29990			−0.170082			−0.0850409	+	0.996377i	$0.527102\pi$
$972$	−13.2957	−	8.13782i	−0.426460	−	0.261021i
$973$	−50.6391			−1.62341
$974$	−12.4166	−	28.7849i	−0.397854	−	0.922328i
$975$	−26.8795	+	9.98187i	−0.860832	+	0.319676i
$976$	−3.67663	+	3.89700i	−0.117686	+	0.124740i
$977$	−0.711989	+	12.2244i	−0.0227786	+	0.391093i	0.967580	+	0.252565i	$0.0812741\pi$
$977$	−0.711989	+	12.2244i	−0.0227786	+	0.391093i	−0.990359	+	0.138528i	$0.955763\pi$
$978$	−18.4470	−	19.2995i	−0.589870	−	0.617131i
$979$	3.58147	−	0.848824i	0.114464	−	0.0271285i
$980$	−4.32872	−	1.57552i	−0.138276	−	0.0503283i
$981$	4.95706	+	26.1205i	0.158267	+	0.833963i
$982$	−35.7357	+	13.0067i	−1.14037	+	0.415061i
$983$	−39.8514	+	26.2107i	−1.27106	+	0.835990i	−0.992238	−	0.124352i	$-0.960315\pi$
$983$	−39.8514	+	26.2107i	−1.27106	+	0.835990i	−0.278823	+	0.960342i	$0.589944\pi$
$984$	−6.45106	+	15.2269i	−0.205652	+	0.485416i
$985$	7.41196	−	0.866334i	0.236165	−	0.0276037i
$986$	−7.05061	−	9.47062i	−0.224537	−	0.301606i
$987$	−3.37712	−	11.0189i	−0.107495	−	0.350736i
$988$	−0.318086	−	5.46132i	−0.0101197	−	0.173748i
$989$	69.0562	+	57.9450i	2.19586	+	1.84254i
$990$	−0.0475804	−	0.667218i	−0.00151220	−	0.0212056i
$991$	1.53472	−	1.28778i	0.0487520	−	0.0409078i	−0.618086	−	0.786110i	$-0.712092\pi$
$991$	1.53472	−	1.28778i	0.0487520	−	0.0409078i	0.666838	+	0.745203i	$0.267647\pi$
$992$	−2.40935	−	2.55377i	−0.0764971	−	0.0810821i
$993$	−8.45427	+	5.63961i	−0.268288	+	0.178967i
$994$	−15.6488	−	10.2924i	−0.496350	−	0.326454i
$995$	3.67865	+	0.871857i	0.116621	+	0.0276397i
$996$	11.8082	−	0.0768339i	0.374158	−	0.00243458i
$997$	40.5174	+	4.73581i	1.28320	+	0.149985i	0.730221	−	0.683211i	$-0.239417\pi$
$997$	40.5174	+	4.73581i	1.28320	+	0.149985i	0.552979	+	0.833195i	$0.313491\pi$
$998$	−12.2918	−	21.2900i	−0.389090	−	0.673924i
$999$	−17.6522	−	14.2341i	−0.558490	−	0.450348i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.g.a.31.1	✓	72
3.2	odd	2		486.2.g.a.145.2		72
81.34	even	27	inner	162.2.g.a.115.1	yes	72
81.47	odd	54		486.2.g.a.181.2		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.a.31.1	✓	72	1.1	even	1	trivial
162.2.g.a.115.1	yes	72	81.34	even	27	inner
486.2.g.a.145.2		72	3.2	odd	2
486.2.g.a.181.2		72	81.47	odd	54

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.396080 - 0.918216i) q^{2} +(-1.62371 + 0.602974i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(-0.0263678 + 0.452718i) q^{5} +(1.19678 + 1.25209i) q^{6} +(4.03057 - 0.955263i) q^{7} +(0.939693 + 0.342020i) q^{8} +(2.27284 - 1.95811i) q^{9} +O(q^{10})\)	\(q+(-0.396080 - 0.918216i) q^{2} +(-1.62371 + 0.602974i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(-0.0263678 + 0.452718i) q^{5} +(1.19678 + 1.25209i) q^{6} +(4.03057 - 0.955263i) q^{7} +(0.939693 + 0.342020i) q^{8} +(2.27284 - 1.95811i) q^{9} +(0.426137 - 0.155101i) q^{10} +(0.410794 - 0.270184i) q^{11} +(0.675668 - 1.59483i) q^{12} +(3.42955 - 0.400857i) q^{13} +(-2.47357 - 3.32258i) q^{14} +(-0.230164 - 0.750981i) q^{15} +(-0.0581448 - 0.998308i) q^{16} +(2.51871 + 2.11345i) q^{17} +(-2.69819 - 1.31140i) q^{18} +(-1.21368 + 1.01840i) q^{19} +(-0.311201 - 0.329854i) q^{20} +(-5.96847 + 3.98140i) q^{21} +(-0.410794 - 0.270184i) q^{22} +(-6.89877 - 1.63504i) q^{23} +(-1.73201 + 0.0112699i) q^{24} +(4.76193 + 0.556590i) q^{25} +(-1.72645 - 2.99029i) q^{26} +(-2.50975 + 4.54985i) q^{27} +(-2.07111 + 3.58727i) q^{28} +(2.14438 - 2.88040i) q^{29} +(-0.598400 + 0.508788i) q^{30} +(1.00695 + 3.36344i) q^{31} +(-0.893633 + 0.448799i) q^{32} +(-0.504095 + 0.686397i) q^{33} +(0.942994 - 3.14982i) q^{34} +(0.326188 + 1.84990i) q^{35} +(-0.135446 + 2.99694i) q^{36} +(-0.757807 + 4.29774i) q^{37} +(1.41582 + 0.711053i) q^{38} +(-5.32687 + 2.71880i) q^{39} +(-0.179617 + 0.416398i) q^{40} +(3.78165 - 8.76684i) q^{41} +(6.01977 + 3.90339i) q^{42} +(-11.3624 - 5.70639i) q^{43} +(-0.0853797 + 0.484212i) q^{44} +(0.826540 + 1.08059i) q^{45} +(1.23114 + 6.98217i) q^{46} +(-0.460706 + 1.53886i) q^{47} +(0.696364 + 1.58590i) q^{48} +(9.07756 - 4.55892i) q^{49} +(-1.37504 - 4.59294i) q^{50} +(-5.36401 - 1.91291i) q^{51} +(-2.06193 + 2.76965i) q^{52} +(-6.96808 + 12.0691i) q^{53} +(5.17181 + 0.502384i) q^{54} +(0.111485 + 0.193098i) q^{55} +(4.11422 + 0.480883i) q^{56} +(1.35659 - 2.38540i) q^{57} +(-3.49418 - 0.828136i) q^{58} +(1.26512 + 0.832083i) q^{59} +(0.704192 + 0.347939i) q^{60} +(-3.67663 - 3.89700i) q^{61} +(2.68954 - 2.25679i) q^{62} +(7.29036 - 10.0634i) q^{63} +(0.766044 + 0.642788i) q^{64} +(0.0910454 + 1.56319i) q^{65} +(0.829923 + 0.191001i) q^{66} +(-0.930994 - 1.25054i) q^{67} +(-3.26572 + 0.381707i) q^{68} +(12.1875 - 1.50496i) q^{69} +(1.56941 - 1.03222i) q^{70} +(4.24906 - 1.54653i) q^{71} +(2.80549 - 1.06266i) q^{72} +(-9.97468 - 3.63049i) q^{73} +(4.24640 - 1.00642i) q^{74} +(-8.06759 + 1.96758i) q^{75} +(0.0921215 - 1.58167i) q^{76} +(1.39764 - 1.48141i) q^{77} +(4.60631 + 3.81436i) q^{78} +(-5.14102 - 11.9182i) q^{79} +0.453486 q^{80} +(1.33165 - 8.90094i) q^{81} -9.54769 q^{82} +(2.70032 + 6.26005i) q^{83} +(1.19985 - 7.07351i) q^{84} +(-1.02321 + 1.08454i) q^{85} +(-0.739300 + 12.6933i) q^{86} +(-1.74504 + 5.96994i) q^{87} +(0.478429 - 0.113390i) q^{88} +(7.03445 + 2.56033i) q^{89} +(0.664839 - 1.18694i) q^{90} +(13.4401 - 4.89180i) q^{91} +(5.92351 - 3.89595i) q^{92} +(-3.66306 - 4.85408i) q^{93} +(1.59549 - 0.186486i) q^{94} +(-0.429045 - 0.576308i) q^{95} +(1.18038 - 1.26756i) q^{96} +(0.517706 + 8.88867i) q^{97} +(-7.78151 - 6.52946i) q^{98} +(0.404624 - 1.41846i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{6}+O(q^{10}) \) 72 * q + 9 * q^6	\( 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) \) 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more