LMFDB - Embedded newform 294.2.m.b.151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,2,Mod(25,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("294.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.m (of order $21$, degree $12$, 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:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			151.2
Character	$\chi$	$=$	294.151
Dual form			294.2.m.b.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.826239 + 0.563320i) q^{2} +(-0.733052 - 0.680173i) q^{3} +(0.365341 + 0.930874i) q^{4} +(1.32658 - 0.409195i) q^{5} +(-0.222521 - 0.974928i) q^{6} +(0.662652 + 2.56142i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(0.0747301 + 0.997204i) q^{9} +O(q^{10})$	\(q+(0.826239 + 0.563320i) q^{2} +(-0.733052 - 0.680173i) q^{3} +(0.365341 + 0.930874i) q^{4} +(1.32658 - 0.409195i) q^{5} +(-0.222521 - 0.974928i) q^{6} +(0.662652 + 2.56142i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(0.0747301 + 0.997204i) q^{9} +(1.32658 + 0.409195i) q^{10} +(-0.0332300 + 0.443423i) q^{11} +(0.365341 - 0.930874i) q^{12} +(4.28893 - 2.06544i) q^{13} +(-0.895392 + 2.48963i) q^{14} +(-1.25077 - 0.602340i) q^{15} +(-0.733052 + 0.680173i) q^{16} +(3.16037 - 0.476348i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-0.185455 - 0.321218i) q^{19} +(0.865562 + 1.08538i) q^{20} +(1.25645 - 2.32837i) q^{21} +(-0.277245 + 0.347654i) q^{22} +(1.06554 + 0.160605i) q^{23} +(0.826239 - 0.563320i) q^{24} +(-2.53883 + 1.73094i) q^{25} +(4.70719 + 0.709494i) q^{26} +(0.623490 - 0.781831i) q^{27} +(-2.14227 + 1.55264i) q^{28} +(-5.07096 - 6.35878i) q^{29} +(-0.694126 - 1.20226i) q^{30} +(-3.49647 + 6.05606i) q^{31} +(-0.988831 + 0.149042i) q^{32} +(0.325964 - 0.302450i) q^{33} +(2.87955 + 1.38672i) q^{34} +(1.92718 + 3.12677i) q^{35} +(-0.900969 + 0.433884i) q^{36} +(-2.63457 + 6.71279i) q^{37} +(0.0277182 - 0.369874i) q^{38} +(-4.54887 - 1.40314i) q^{39} +(0.103744 + 1.38437i) q^{40} +(1.57356 - 6.89423i) q^{41} +(2.34975 - 1.21601i) q^{42} +(-1.62663 - 7.12672i) q^{43} +(-0.424911 + 0.131068i) q^{44} +(0.507186 + 1.29229i) q^{45} +(0.789921 + 0.732940i) q^{46} +(-7.91100 - 5.39363i) q^{47} +1.00000 q^{48} +(-6.12178 + 3.39467i) q^{49} -3.07275 q^{50} +(-2.64071 - 1.80041i) q^{51} +(3.48959 + 3.23787i) q^{52} +(-3.32320 - 8.46739i) q^{53} +(0.955573 - 0.294755i) q^{54} +(0.137364 + 0.601833i) q^{55} +(-2.64466 + 0.0760677i) q^{56} +(-0.0825354 + 0.361611i) q^{57} +(-0.607794 - 8.11044i) q^{58} +(5.05775 + 1.56011i) q^{59} +(0.103744 - 1.38437i) q^{60} +(4.36117 - 11.1121i) q^{61} +(-6.30042 + 3.03412i) q^{62} +(-2.50474 + 0.852215i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(4.84443 - 4.49498i) q^{65} +(0.439700 - 0.0662741i) q^{66} +(-5.63206 + 9.75501i) q^{67} +(1.59803 + 2.76787i) q^{68} +(-0.671859 - 0.842485i) q^{69} +(-0.169062 + 3.66908i) q^{70} +(-1.77085 + 2.22058i) q^{71} +(-0.988831 - 0.149042i) q^{72} +(1.42932 - 0.974494i) q^{73} +(-5.95823 + 4.06226i) q^{74} +(3.03843 + 0.457970i) q^{75} +(0.231259 - 0.289990i) q^{76} +(-1.15781 + 0.208719i) q^{77} +(-2.96803 - 3.72180i) q^{78} +(3.04058 + 5.26644i) q^{79} +(-0.694126 + 1.20226i) q^{80} +(-0.988831 + 0.149042i) q^{81} +(5.18380 - 4.80986i) q^{82} +(-2.21046 - 1.06450i) q^{83} +(2.62646 + 0.318948i) q^{84} +(3.99755 - 1.92512i) q^{85} +(2.67064 - 6.80468i) q^{86} +(-0.607794 + 8.11044i) q^{87} +(-0.424911 - 0.131068i) q^{88} +(-0.300925 - 4.01556i) q^{89} +(-0.308915 + 1.35345i) q^{90} +(8.13254 + 9.61711i) q^{91} +(0.239784 + 1.05056i) q^{92} +(6.68226 - 2.06121i) q^{93} +(-3.49804 - 8.91285i) q^{94} +(-0.377462 - 0.350233i) q^{95} +(0.826239 + 0.563320i) q^{96} +4.66404 q^{97} +(-6.97034 - 0.643719i) q^{98} -0.444667 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9} + q^{10} + 8 q^{11} + 2 q^{12} - 2 q^{13} + 5 q^{15} + 2 q^{16} + 9 q^{17} - 12 q^{18} - 4 q^{19} + 5 q^{20} + 14 q^{21} + 5 q^{22} - 38 q^{23} + 2 q^{24} - 19 q^{25} - 20 q^{26} - 4 q^{27} - 14 q^{28} - 14 q^{29} + 8 q^{30} + 4 q^{31} + 2 q^{32} - 6 q^{33} + 17 q^{34} + 42 q^{35} - 4 q^{36} + 7 q^{37} - 18 q^{38} - 6 q^{39} - 13 q^{40} + 2 q^{41} - 7 q^{42} + 4 q^{43} - 6 q^{44} - 13 q^{45} + 11 q^{46} - 8 q^{47} + 24 q^{48} - 42 q^{49} - 4 q^{50} - 40 q^{51} + 15 q^{52} - 10 q^{53} + 2 q^{54} + 33 q^{55} - 7 q^{56} + q^{57} - 28 q^{58} + 14 q^{59} - 13 q^{60} + 7 q^{61} - 8 q^{62} - 14 q^{63} - 4 q^{64} + 23 q^{65} + 8 q^{66} + 23 q^{67} + 9 q^{68} + 13 q^{69} + 28 q^{70} + 36 q^{71} + 2 q^{72} + 15 q^{73} - 14 q^{74} + 9 q^{75} + q^{76} - 28 q^{77} + 19 q^{78} + 38 q^{79} + 8 q^{80} + 2 q^{81} - q^{82} + 27 q^{83} - 47 q^{85} + 26 q^{86} - 28 q^{87} - 6 q^{88} - 121 q^{89} - 2 q^{90} + 21 q^{91} - q^{92} + 46 q^{93} - q^{94} + 44 q^{95} + 2 q^{96} + 14 q^{97} - 21 q^{98} - 44 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9 + q^10 + 8 * q^11 + 2 * q^12 - 2 * q^13 + 5 * q^15 + 2 * q^16 + 9 * q^17 - 12 * q^18 - 4 * q^19 + 5 * q^20 + 14 * q^21 + 5 * q^22 - 38 * q^23 + 2 * q^24 - 19 * q^25 - 20 * q^26 - 4 * q^27 - 14 * q^28 - 14 * q^29 + 8 * q^30 + 4 * q^31 + 2 * q^32 - 6 * q^33 + 17 * q^34 + 42 * q^35 - 4 * q^36 + 7 * q^37 - 18 * q^38 - 6 * q^39 - 13 * q^40 + 2 * q^41 - 7 * q^42 + 4 * q^43 - 6 * q^44 - 13 * q^45 + 11 * q^46 - 8 * q^47 + 24 * q^48 - 42 * q^49 - 4 * q^50 - 40 * q^51 + 15 * q^52 - 10 * q^53 + 2 * q^54 + 33 * q^55 - 7 * q^56 + q^57 - 28 * q^58 + 14 * q^59 - 13 * q^60 + 7 * q^61 - 8 * q^62 - 14 * q^63 - 4 * q^64 + 23 * q^65 + 8 * q^66 + 23 * q^67 + 9 * q^68 + 13 * q^69 + 28 * q^70 + 36 * q^71 + 2 * q^72 + 15 * q^73 - 14 * q^74 + 9 * q^75 + q^76 - 28 * q^77 + 19 * q^78 + 38 * q^79 + 8 * q^80 + 2 * q^81 - q^82 + 27 * q^83 - 47 * q^85 + 26 * q^86 - 28 * q^87 - 6 * q^88 - 121 * q^89 - 2 * q^90 + 21 * q^91 - q^92 + 46 * q^93 - q^94 + 44 * q^95 + 2 * q^96 + 14 * q^97 - 21 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{5}{21}\right)$

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 $

$2$	0.826239	+	0.563320i	0.584239	+	0.398327i
$2$	0.826239	+	0.563320i	0.584239	+	0.398327i
$3$	−0.733052	−	0.680173i	−0.423228	−	0.392698i
$3$	−0.733052	−	0.680173i	−0.423228	−	0.392698i
$4$	0.365341	+	0.930874i	0.182671	+	0.465437i
$5$	1.32658	−	0.409195i	0.593263	−	0.182997i	0.0164377	−	0.999865i	$-0.494767\pi$
$5$	1.32658	−	0.409195i	0.593263	−	0.182997i	0.576825	+	0.816867i	$0.304291\pi$
$6$	−0.222521	−	0.974928i	−0.0908438	−	0.398013i
$7$	0.662652	+	2.56142i	0.250459	+	0.968127i
$7$	0.662652	+	2.56142i	0.250459	+	0.968127i
$8$	−0.222521	+	0.974928i	−0.0786730	+	0.344689i
$9$	0.0747301	+	0.997204i	0.0249100	+	0.332401i
$10$	1.32658	+	0.409195i	0.419500	+	0.129399i
$11$	−0.0332300	+	0.443423i	−0.0100192	+	0.133697i	−0.999970	−	0.00771341i	$-0.997545\pi$
$11$	−0.0332300	+	0.443423i	−0.0100192	+	0.133697i	0.989951	+	0.141411i	$0.0451638\pi$
$12$	0.365341	−	0.930874i	0.105465	−	0.268720i
$13$	4.28893	−	2.06544i	1.18954	−	0.572850i	0.268861	−	0.963179i	$-0.413353\pi$
$13$	4.28893	−	2.06544i	1.18954	−	0.572850i	0.920676	+	0.390329i	$0.127639\pi$
$14$	−0.895392	+	2.48963i	−0.239304	+	0.665382i
$15$	−1.25077	−	0.602340i	−0.322948	−	0.155524i
$16$	−0.733052	+	0.680173i	−0.183263	+	0.170043i
$17$	3.16037	−	0.476348i	0.766501	−	0.115531i	0.245858	−	0.969306i	$-0.420930\pi$
$17$	3.16037	−	0.476348i	0.766501	−	0.115531i	0.520643	+	0.853774i	$0.325692\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−0.185455	−	0.321218i	−0.0425464	−	0.0736925i	0.843968	−	0.536393i	$-0.180214\pi$
$19$	−0.185455	−	0.321218i	−0.0425464	−	0.0736925i	−0.886514	+	0.462701i	$0.846880\pi$
$20$	0.865562	+	1.08538i	0.193545	+	0.242698i
$21$	1.25645	−	2.32837i	0.274180	−	0.508093i
$22$	−0.277245	+	0.347654i	−0.0591089	+	0.0741202i
$23$	1.06554	+	0.160605i	0.222181	+	0.0334884i	0.259189	−	0.965827i	$-0.416545\pi$
$23$	1.06554	+	0.160605i	0.222181	+	0.0334884i	−0.0370081	+	0.999315i	$0.511783\pi$
$24$	0.826239	−	0.563320i	0.168655	−	0.114987i
$25$	−2.53883	+	1.73094i	−0.507766	+	0.346189i
$26$	4.70719	+	0.709494i	0.923155	+	0.139143i
$27$	0.623490	−	0.781831i	0.119991	−	0.150464i
$28$	−2.14227	+	1.55264i	−0.404851	+	0.293421i
$29$	−5.07096	−	6.35878i	−0.941653	−	1.18080i	−0.983360	−	0.181666i	$-0.941851\pi$
$29$	−5.07096	−	6.35878i	−0.941653	−	1.18080i	0.0417071	−	0.999130i	$-0.486720\pi$
$30$	−0.694126	−	1.20226i	−0.126730	−	0.219502i
$31$	−3.49647	+	6.05606i	−0.627985	+	1.08770i	0.359971	+	0.932963i	$0.382787\pi$
$31$	−3.49647	+	6.05606i	−0.627985	+	1.08770i	−0.987956	+	0.154738i	$0.950547\pi$
$32$	−0.988831	+	0.149042i	−0.174802	+	0.0263472i
$33$	0.325964	−	0.302450i	0.0567430	−	0.0526498i
$34$	2.87955	+	1.38672i	0.493839	+	0.237820i
$35$	1.92718	+	3.12677i	0.325753	+	0.528521i
$36$	−0.900969	+	0.433884i	−0.150161	+	0.0723140i
$37$	−2.63457	+	6.71279i	−0.433121	+	1.10358i	0.533143	+	0.846025i	$0.321011\pi$
$37$	−2.63457	+	6.71279i	−0.433121	+	1.10358i	−0.966265	+	0.257550i	$0.917085\pi$
$38$	0.0277182	−	0.369874i	0.00449649	−	0.0600014i
$39$	−4.54887	−	1.40314i	−0.728402	−	0.224682i
$40$	0.103744	+	1.38437i	0.0164034	+	0.218888i
$41$	1.57356	−	6.89423i	0.245749	−	1.07670i	−0.689938	−	0.723868i	$-0.742362\pi$
$41$	1.57356	−	6.89423i	0.245749	−	1.07670i	0.935688	−	0.352830i	$-0.114780\pi$
$42$	2.34975	−	1.21601i	0.362574	−	0.187634i
$43$	−1.62663	−	7.12672i	−0.248058	−	1.08681i	−0.933469	−	0.358658i	$-0.883234\pi$
$43$	−1.62663	−	7.12672i	−0.248058	−	1.08681i	0.685411	−	0.728157i	$-0.259623\pi$
$44$	−0.424911	+	0.131068i	−0.0640578	+	0.0197592i
$45$	0.507186	+	1.29229i	0.0756068	+	0.192643i
$46$	0.789921	+	0.732940i	0.116468	+	0.108066i
$47$	−7.91100	−	5.39363i	−1.15394	−	0.786742i	−0.173746	−	0.984791i	$-0.555587\pi$
$47$	−7.91100	−	5.39363i	−1.15394	−	0.786742i	−0.980192	+	0.198049i	$0.936540\pi$
$48$	1.00000			0.144338
$49$	−6.12178	+	3.39467i	−0.874541	+	0.484952i
$50$	−3.07275			−0.434553
$51$	−2.64071	−	1.80041i	−0.369774	−	0.252107i
$52$	3.48959	+	3.23787i	0.483919	+	0.449011i
$53$	−3.32320	−	8.46739i	−0.456477	−	1.16308i	−0.955105	−	0.296269i	$-0.904258\pi$
$53$	−3.32320	−	8.46739i	−0.456477	−	1.16308i	0.498627	−	0.866816i	$-0.333838\pi$
$54$	0.955573	−	0.294755i	0.130037	−	0.0401111i
$55$	0.137364	+	0.601833i	0.0185222	+	0.0811511i
$56$	−2.64466	+	0.0760677i	−0.353407	+	0.0101650i
$57$	−0.0825354	+	0.361611i	−0.0109321	+	0.0478966i
$58$	−0.607794	−	8.11044i	−0.0798072	−	1.06495i
$59$	5.05775	+	1.56011i	0.658463	+	0.203109i	0.605939	−	0.795511i	$-0.292797\pi$
$59$	5.05775	+	1.56011i	0.658463	+	0.203109i	0.0525236	+	0.998620i	$0.483274\pi$
$60$	0.103744	−	1.38437i	0.0133933	−	0.178722i
$61$	4.36117	−	11.1121i	0.558391	−	1.42276i	−0.321193	−	0.947014i	$-0.604084\pi$
$61$	4.36117	−	11.1121i	0.558391	−	1.42276i	0.879584	−	0.475743i	$-0.157821\pi$
$62$	−6.30042	+	3.03412i	−0.800154	+	0.385334i
$63$	−2.50474	+	0.852215i	−0.315568	+	0.107369i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	4.84443	−	4.49498i	0.600878	−	0.557533i
$66$	0.439700	−	0.0662741i	0.0541233	−	0.00815778i
$67$	−5.63206	+	9.75501i	−0.688065	+	1.19176i	0.284398	+	0.958706i	$0.408206\pi$
$67$	−5.63206	+	9.75501i	−0.688065	+	1.19176i	−0.972463	+	0.233057i	$0.925127\pi$
$68$	1.59803	+	2.76787i	0.193790	+	0.335654i
$69$	−0.671859	−	0.842485i	−0.0808824	−	0.101423i
$70$	−0.169062	+	3.66908i	−0.0202068	+	0.438539i
$71$	−1.77085	+	2.22058i	−0.210162	+	0.263534i	−0.875729	−	0.482804i	$-0.839618\pi$
$71$	−1.77085	+	2.22058i	−0.210162	+	0.263534i	0.665567	+	0.746338i	$0.268190\pi$
$72$	−0.988831	−	0.149042i	−0.116535	−	0.0175648i
$73$	1.42932	−	0.974494i	0.167289	−	0.114056i	−0.476781	−	0.879022i	$-0.658197\pi$
$73$	1.42932	−	0.974494i	0.167289	−	0.114056i	0.644071	+	0.764966i	$0.277244\pi$
$74$	−5.95823	+	4.06226i	−0.692631	+	0.472228i
$75$	3.03843	+	0.457970i	0.350848	+	0.0528818i
$76$	0.231259	−	0.289990i	0.0265272	−	0.0332641i
$77$	−1.15781	+	0.208719i	−0.131945	+	0.0237858i
$78$	−2.96803	−	3.72180i	−0.336064	−	0.421411i
$79$	3.04058	+	5.26644i	0.342092	+	0.592521i	0.984821	−	0.173573i	$-0.0555312\pi$
$79$	3.04058	+	5.26644i	0.342092	+	0.592521i	−0.642729	+	0.766094i	$0.722198\pi$
$80$	−0.694126	+	1.20226i	−0.0776057	+	0.134417i
$81$	−0.988831	+	0.149042i	−0.109870	+	0.0165603i
$82$	5.18380	−	4.80986i	0.572455	−	0.531160i
$83$	−2.21046	−	1.06450i	−0.242629	−	0.116844i	0.308618	−	0.951186i	$-0.400134\pi$
$83$	−2.21046	−	1.06450i	−0.242629	−	0.116844i	−0.551247	+	0.834342i	$0.685848\pi$
$84$	2.62646	+	0.318948i	0.286570	+	0.0348000i
$85$	3.99755	−	1.92512i	0.433595	−	0.208808i
$86$	2.67064	−	6.80468i	0.287983	−	0.733768i
$87$	−0.607794	+	8.11044i	−0.0651623	+	0.869531i
$88$	−0.424911	−	0.131068i	−0.0452957	−	0.0139719i
$89$	−0.300925	−	4.01556i	−0.0318979	−	0.425648i	−0.990178	−	0.139816i	$-0.955349\pi$
$89$	−0.300925	−	4.01556i	−0.0318979	−	0.425648i	0.958280	−	0.285833i	$-0.0922701\pi$
$90$	−0.308915	+	1.35345i	−0.0325625	+	0.142666i
$91$	8.13254	+	9.61711i	0.852522	+	1.00815i
$92$	0.239784	+	1.05056i	0.0249992	+	0.109529i
$93$	6.68226	−	2.06121i	0.692918	−	0.213737i
$94$	−3.49804	−	8.91285i	−0.360795	−	0.919290i
$95$	−0.377462	−	0.350233i	−0.0387267	−	0.0359332i
$96$	0.826239	+	0.563320i	0.0843276	+	0.0574936i
$97$	4.66404			0.473562			0.236781	−	0.971563i	$-0.423908\pi$
$97$	4.66404			0.473562			0.236781	+	0.971563i	$0.423908\pi$
$98$	−6.97034	−	0.643719i	−0.704111	−	0.0650254i
$99$	−0.444667			−0.0446907
$100$	−2.53883	−	1.73094i	−0.253883	−	0.173094i
$101$	7.63962	+	7.08853i	0.760171	+	0.705335i	0.961687	−	0.274150i	$-0.0883964\pi$
$101$	7.63962	+	7.08853i	0.760171	+	0.705335i	−0.201516	+	0.979485i	$0.564587\pi$
$102$	−1.16765	−	2.97513i	−0.115615	−	0.294582i
$103$	−10.4732	+	3.23056i	−1.03196	+	0.318317i	−0.764070	−	0.645133i	$-0.776802\pi$
$103$	−10.4732	+	3.23056i	−1.03196	+	0.318317i	−0.267888	+	0.963450i	$0.586326\pi$
$104$	1.05928	+	4.64100i	0.103871	+	0.455088i
$105$	0.714022	−	3.60290i	0.0696814	−	0.351607i
$106$	2.02409	−	8.86811i	0.196597	−	0.861347i
$107$	−0.791602	−	10.5632i	−0.0765270	−	1.02118i	−0.894833	−	0.446400i	$-0.852706\pi$
$107$	−0.791602	−	10.5632i	−0.0765270	−	1.02118i	0.818306	−	0.574782i	$-0.194913\pi$
$108$	0.955573	+	0.294755i	0.0919500	+	0.0283628i
$109$	−0.679922	+	9.07293i	−0.0651247	+	0.869029i	0.864997	+	0.501777i	$0.167320\pi$
$109$	−0.679922	+	9.07293i	−0.0651247	+	0.869029i	−0.930122	+	0.367252i	$0.880299\pi$
$110$	−0.225529	+	0.574638i	−0.0215033	+	0.0547895i
$111$	6.49713	−	3.12885i	0.616681	−	0.296978i
$112$	−2.22797	−	1.42694i	−0.210523	−	0.134833i
$113$	3.66136	+	1.76322i	0.344432	+	0.165870i	0.598100	−	0.801422i	$-0.295923\pi$
$113$	3.66136	+	1.76322i	0.344432	+	0.165870i	−0.253668	+	0.967291i	$0.581637\pi$
$114$	−0.271897	+	0.252283i	−0.0254655	+	0.0236285i
$115$	1.47924	−	0.222960i	0.137940	−	0.0207911i
$116$	4.06659	−	7.04354i	0.377574	−	0.653977i
$117$	2.38018	+	4.12259i	0.220048	+	0.381134i
$118$	3.30007	+	4.13816i	0.303796	+	0.380948i
$119$	3.31435	+	7.77938i	0.303826	+	0.713135i
$120$	0.865562	−	1.08538i	0.0790146	−	0.0990812i
$121$	10.6816	+	1.61000i	0.971056	+	0.146363i
$122$	9.86303	−	6.72450i	0.892957	−	0.608808i
$123$	−5.84277	+	3.98353i	−0.526825	+	0.359183i
$124$	−6.91483	−	1.04224i	−0.620970	−	0.0935962i
$125$	−6.98747	+	8.76200i	−0.624978	+	0.783698i
$126$	−2.54958	−	0.706838i	−0.227135	−	0.0629702i
$127$	−4.47200	−	5.60771i	−0.396826	−	0.497604i	0.542774	−	0.839879i	$-0.317374\pi$
$127$	−4.47200	−	5.60771i	−0.396826	−	0.497604i	−0.939600	+	0.342275i	$0.888803\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−3.65500	+	6.33064i	−0.321805	+	0.557382i
$130$	6.53477	−	0.984958i	0.573137	−	0.0863865i
$131$	3.19810	−	2.96740i	0.279419	−	0.259263i	−0.527996	−	0.849247i	$-0.677056\pi$
$131$	3.19810	−	2.96740i	0.279419	−	0.259263i	0.807415	+	0.589984i	$0.200866\pi$
$132$	0.400631	+	0.192934i	0.0348704	+	0.0167927i
$133$	0.699883	−	0.687886i	0.0606876	−	0.0596473i
$134$	−10.1486	+	4.88732i	−0.876707	+	0.422200i
$135$	0.507186	−	1.29229i	0.0436516	−	0.111222i
$136$	−0.238842	+	3.18713i	−0.0204805	+	0.273294i
$137$	−19.8152	−	6.11217i	−1.69292	−	0.522198i	−0.709684	−	0.704520i	$-0.751162\pi$
$137$	−19.8152	−	6.11217i	−1.69292	−	0.522198i	−0.983239	+	0.182323i	$0.941638\pi$
$138$	−0.0805276	−	1.07457i	−0.00685496	−	0.0914731i
$139$	2.24908	−	9.85388i	0.190765	−	0.835795i	−0.785439	−	0.618939i	$-0.787563\pi$
$139$	2.24908	−	9.85388i	0.190765	−	0.835795i	0.976204	−	0.216856i	$-0.0695801\pi$
$140$	−2.20655	+	2.93630i	−0.186488	+	0.248163i
$141$	2.13057	+	9.33466i	0.179427	+	0.786120i
$142$	−2.71405	+	0.837172i	−0.227758	+	0.0702539i
$143$	0.773344	+	1.97045i	0.0646702	+	0.164777i
$144$	−0.733052	−	0.680173i	−0.0610877	−	0.0566811i
$145$	−9.32899	−	6.36040i	−0.774731	−	0.528203i
$146$	1.72991			0.143168
$147$	6.79654	+	1.67540i	0.560570	+	0.138185i
$148$	−7.21127			−0.592763
$149$	12.0465	+	8.21320i	0.986892	+	0.672851i	0.945272	−	0.326282i	$-0.105796\pi$
$149$	12.0465	+	8.21320i	0.986892	+	0.672851i	0.0416192	+	0.999134i	$0.486748\pi$
$150$	2.25249	+	2.09000i	0.183915	+	0.170648i
$151$	2.99153	+	7.62229i	0.243447	+	0.620293i	0.999411	−	0.0343202i	$-0.0109266\pi$
$151$	2.99153	+	7.62229i	0.243447	+	0.620293i	−0.755964	+	0.654614i	$0.772831\pi$
$152$	0.354432	−	0.109328i	0.0287483	−	0.00886766i
$153$	0.711191	+	3.11593i	0.0574964	+	0.251908i
$154$	−1.07421	−	0.479768i	−0.0865621	−	0.0386608i
$155$	−2.16023	+	9.46457i	−0.173514	+	0.760213i
$156$	−0.355742	−	4.74705i	−0.0284821	−	0.380068i
$157$	1.03923	+	0.320559i	0.0829394	+	0.0255834i	0.335947	−	0.941881i	$-0.390944\pi$
$157$	1.03923	+	0.320559i	0.0829394	+	0.0255834i	−0.253008	+	0.967464i	$0.581420\pi$
$158$	−0.454446	+	6.06416i	−0.0361538	+	0.482438i
$159$	−3.32320	+	8.46739i	−0.263547	+	0.671507i
$160$	−1.25077	+	0.602340i	−0.0988823	+	0.0476192i
$161$	0.294708	+	2.83573i	0.0232262	+	0.223487i
$162$	−0.900969	−	0.433884i	−0.0707868	−	0.0340891i
$163$	−1.64460	+	1.52597i	−0.128815	+	0.119523i	−0.741950	−	0.670455i	$-0.766099\pi$
$163$	−1.64460	+	1.52597i	−0.128815	+	0.119523i	0.613135	+	0.789978i	$0.289908\pi$
$164$	6.99254	−	1.05396i	0.546026	−	0.0823002i
$165$	0.308655	−	0.534606i	0.0240288	−	0.0416190i
$166$	−1.22671	−	2.12473i	−0.0952112	−	0.164911i
$167$	7.18289	+	9.00705i	0.555828	+	0.696987i	0.977780	−	0.209631i	$-0.0672264\pi$
$167$	7.18289	+	9.00705i	0.555828	+	0.696987i	−0.421952	+	0.906618i	$0.638655\pi$
$168$	1.99041	+	1.74306i	0.153563	+	0.134480i
$169$	6.02353	−	7.55327i	0.463349	−	0.581021i
$170$	4.38739	+	0.661292i	0.336497	+	0.0507188i
$171$	0.306461	−	0.208941i	0.0234356	−	0.0159782i
$172$	6.03980	−	4.11787i	0.460531	−	0.313984i
$173$	−11.3397	−	1.70919i	−0.862142	−	0.129947i	−0.296937	−	0.954897i	$-0.595965\pi$
$173$	−11.3397	−	1.70919i	−0.862142	−	0.129947i	−0.565205	+	0.824950i	$0.691203\pi$
$174$	−5.07096	+	6.35878i	−0.384428	+	0.482058i
$175$	−6.11604	−	5.35600i	−0.462329	−	0.404876i
$176$	−0.277245	−	0.347654i	−0.0208981	−	0.0262054i
$177$	−2.64645	−	4.58379i	−0.198919	−	0.344538i
$178$	2.01341	−	3.48733i	0.150911	−	0.261386i
$179$	3.61626	−	0.545063i	0.270292	−	0.0407400i	−0.0124977	−	0.999922i	$-0.503978\pi$
$179$	3.61626	−	0.545063i	0.270292	−	0.0407400i	0.282790	+	0.959182i	$0.408740\pi$
$180$	−1.01766	+	0.944252i	−0.0758520	+	0.0703804i
$181$	17.2500	+	8.30718i	1.28218	+	0.617468i	0.945951	−	0.324311i	$-0.105132\pi$
$181$	17.2500	+	8.30718i	1.28218	+	0.617468i	0.336234	+	0.941778i	$0.390847\pi$
$182$	1.30191	+	12.5273i	0.0965042	+	0.928582i
$183$	−10.7551	+	5.17939i	−0.795040	+	0.382871i
$184$	−0.393684	+	1.00309i	−0.0290228	+	0.0739488i
$185$	−0.748128	+	9.98308i	−0.0550035	+	0.733971i
$186$	6.68226	+	2.06121i	0.489967	+	0.151135i
$187$	0.106205	+	1.41721i	0.00776649	+	0.103637i
$188$	2.13057	−	9.33466i	0.155388	−	0.680800i
$189$	2.41576	+	1.07894i	0.175721	+	0.0784813i
$190$	−0.114580	−	0.502008i	−0.00831251	−	0.0364195i
$191$	15.4576	−	4.76803i	1.11847	−	0.345002i	0.320229	−	0.947340i	$-0.396240\pi$
$191$	15.4576	−	4.76803i	1.11847	−	0.345002i	0.798241	+	0.602338i	$0.205764\pi$
$192$	0.365341	+	0.930874i	0.0263662	+	0.0671800i
$193$	4.79168	+	4.44603i	0.344912	+	0.320032i	0.833539	−	0.552461i	$-0.186311\pi$
$193$	4.79168	+	4.44603i	0.344912	+	0.320032i	−0.488626	+	0.872493i	$0.662502\pi$
$194$	3.85361	+	2.62735i	0.276673	+	0.188633i
$195$	−6.60858			−0.473250
$196$	−5.39654	−	4.45840i	−0.385467	−	0.318457i
$197$	23.4191			1.66854			0.834270	−	0.551356i	$-0.185889\pi$
$197$	23.4191			1.66854			0.834270	+	0.551356i	$0.185889\pi$
$198$	−0.367401	−	0.250490i	−0.0261100	−	0.0178015i
$199$	−19.7221	−	18.2994i	−1.39806	−	1.29721i	−0.903839	−	0.427872i	$-0.859263\pi$
$199$	−19.7221	−	18.2994i	−1.39806	−	1.29721i	−0.494220	−	0.869337i	$-0.664546\pi$
$200$	−1.12260	−	2.86035i	−0.0793800	−	0.202257i
$201$	10.7637	−	3.32016i	0.759211	−	0.234186i
$202$	2.31904	+	10.1604i	0.163167	+	0.714881i
$203$	12.9272	−	17.2025i	0.907315	−	1.20738i
$204$	0.711191	−	3.11593i	0.0497933	−	0.218159i
$205$	−0.733630	−	9.78962i	−0.0512390	−	0.683737i
$206$	−10.4732	−	3.23056i	−0.729705	−	0.225084i
$207$	−0.0805276	+	1.07457i	−0.00559705	+	0.0746875i
$208$	−1.73915	+	4.43129i	−0.120589	+	0.307255i
$209$	0.148598	−	0.0715612i	0.0102788	−	0.00494999i
$210$	2.61954	−	2.57463i	0.180765	−	0.177667i
$211$	11.7051	+	5.63688i	0.805812	+	0.388059i	0.790988	−	0.611832i	$-0.209567\pi$
$211$	11.7051	+	5.63688i	0.805812	+	0.388059i	0.0148238	+	0.999890i	$0.495281\pi$
$212$	6.66796	−	6.18697i	0.457958	−	0.424923i
$213$	2.80851	−	0.423314i	0.192436	−	0.0290050i
$214$	5.29641	−	9.17364i	0.362055	−	0.627097i
$215$	−5.07406	−	8.78853i	−0.346048	−	0.599373i
$216$	0.623490	+	0.781831i	0.0424231	+	0.0531969i
$217$	−17.8291	−	4.94288i	−1.21032	−	0.335544i
$218$	−5.67274	+	7.11339i	−0.384206	+	0.481780i
$219$	−1.71059	−	0.257830i	−0.115591	−	0.0174225i
$220$	−0.510045	+	0.347743i	−0.0343872	+	0.0234448i
$221$	12.5707	−	8.57058i	0.845599	−	0.576519i
$222$	7.13073	+	1.07478i	0.478583	+	0.0721348i
$223$	12.8198	−	16.0755i	0.858478	−	1.07650i	−0.137814	−	0.990458i	$-0.544008\pi$
$223$	12.8198	−	16.0755i	0.858478	−	1.07650i	0.996292	−	0.0860387i	$-0.0274209\pi$
$224$	−1.03701	−	2.43405i	−0.0692882	−	0.162632i
$225$	−1.91583	−	2.40238i	−0.127722	−	0.160158i
$226$	2.03190	+	3.51936i	0.135160	+	0.234104i
$227$	−10.8928	+	18.8669i	−0.722982	+	1.25224i	0.236818	+	0.971554i	$0.423896\pi$
$227$	−10.8928	+	18.8669i	−0.722982	+	1.25224i	−0.959799	+	0.280687i	$0.909438\pi$
$228$	−0.366768	+	0.0552814i	−0.0242898	+	0.00366110i
$229$	5.95837	−	5.52856i	0.393740	−	0.365337i	−0.458315	−	0.888790i	$-0.651547\pi$
$229$	5.95837	−	5.52856i	0.393740	−	0.365337i	0.852055	+	0.523453i	$0.175356\pi$
$230$	1.34781	+	0.649069i	0.0888717	+	0.0427984i
$231$	0.990704	+	0.634512i	0.0651835	+	0.0417478i
$232$	7.32775	−	3.52886i	0.481090	−	0.231681i
$233$	−10.4561	+	26.6416i	−0.684999	+	1.74535i	−0.0185148	+	0.999829i	$0.505894\pi$
$233$	−10.4561	+	26.6416i	−0.684999	+	1.74535i	−0.666484	+	0.745519i	$0.732201\pi$
$234$	−0.355742	+	4.74705i	−0.0232556	+	0.310324i
$235$	−12.7016	−	3.91792i	−0.828561	−	0.255577i
$236$	0.395539	+	5.27810i	0.0257474	+	0.343575i
$237$	1.35319	−	5.92869i	0.0878989	−	0.385110i
$238$	−1.64383	+	8.29467i	−0.106554	+	0.537664i
$239$	1.58478	+	6.94339i	0.102511	+	0.449131i	0.999968	+	0.00802792i	$0.00255539\pi$
$239$	1.58478	+	6.94339i	0.102511	+	0.449131i	−0.897457	+	0.441103i	$0.854587\pi$
$240$	1.32658	−	0.409195i	0.0856302	−	0.0264134i
$241$	−7.91286	−	20.1616i	−0.509712	−	1.29873i	−0.921830	−	0.387595i	$-0.873306\pi$
$241$	−7.91286	−	20.1616i	−0.509712	−	1.29873i	0.412118	−	0.911131i	$-0.364789\pi$
$242$	7.91863	+	7.34741i	0.509029	+	0.472309i
$243$	0.826239	+	0.563320i	0.0530032	+	0.0361370i
$244$	11.9373			0.764205
$245$	−6.73194	+	7.00829i	−0.430088	+	0.447743i
$246$	−7.07153			−0.450864
$247$	−1.45886	−	0.994636i	−0.0928252	−	0.0632872i
$248$	−5.12619	−	4.75641i	−0.325513	−	0.302032i
$249$	0.896336	+	2.28383i	0.0568030	+	0.144732i
$250$	−10.7091	+	3.30333i	−0.677305	+	0.208921i
$251$	−0.598879	−	2.62386i	−0.0378009	−	0.165617i	0.952504	−	0.304525i	$-0.0984977\pi$
$251$	−0.598879	−	2.62386i	−0.0378009	−	0.165617i	−0.990305	+	0.138909i	$0.955641\pi$
$252$	−1.70839	−	2.02025i	−0.107618	−	0.127264i
$253$	−0.106624	+	0.467150i	−0.00670339	+	0.0293695i
$254$	−0.536004	−	7.15247i	−0.0336319	−	0.448786i
$255$	−4.23982	−	1.30781i	−0.265508	−	0.0818984i
$256$	0.0747301	−	0.997204i	0.00467063	−	0.0623252i
$257$	2.89655	−	7.38029i	0.180682	−	0.460370i	−0.811624	−	0.584180i	$-0.801416\pi$
$257$	2.89655	−	7.38029i	0.180682	−	0.460370i	0.992306	+	0.123810i	$0.0395114\pi$
$258$	−6.58608	+	3.17169i	−0.410031	+	0.197461i
$259$	−18.9401	−	2.30002i	−1.17688	−	0.142916i
$260$	5.95412	+	2.86736i	0.369259	+	0.177826i
$261$	5.96205	−	5.53197i	0.369041	−	0.342420i
$262$	4.31399	−	0.650230i	0.266519	−	0.0401713i
$263$	−5.22733	+	9.05401i	−0.322331	+	0.558294i	−0.980969	−	0.194166i	$-0.937800\pi$
$263$	−5.22733	+	9.05401i	−0.322331	+	0.558294i	0.658637	+	0.752460i	$0.271133\pi$
$264$	0.222333	+	0.385093i	0.0136837	+	0.0237008i
$265$	−7.87330	−	9.87280i	−0.483653	−	0.606481i
$266$	0.965771	−	0.174100i	0.0592152	−	0.0106747i
$267$	−2.51068	+	3.14829i	−0.153651	+	0.192672i
$268$	−11.1383	−	1.67883i	−0.680380	−	0.102551i
$269$	−13.0407	+	8.89101i	−0.795106	+	0.542094i	−0.891378	−	0.453261i	$-0.850261\pi$
$269$	−13.0407	+	8.89101i	−0.795106	+	0.542094i	0.0962715	+	0.995355i	$0.469308\pi$
$270$	1.14703	−	0.782031i	0.0698059	−	0.0475929i
$271$	−31.4031	−	4.73325i	−1.90760	−	0.287525i	−0.914482	−	0.404626i	$-0.867402\pi$
$271$	−31.4031	−	4.73325i	−1.90760	−	0.287525i	−0.993120	+	0.117102i	$0.962640\pi$
$272$	−1.99271	+	2.49878i	−0.120826	+	0.151511i
$273$	0.579719	−	12.5814i	0.0350862	−	0.761459i
$274$	−12.9289	−	16.2124i	−0.781066	−	0.979426i
$275$	−0.683176	−	1.18329i	−0.0411970	−	0.0713554i
$276$	0.538789	−	0.933211i	0.0324313	−	0.0561727i
$277$	11.6306	−	1.75303i	0.698814	−	0.105329i	0.209979	−	0.977706i	$-0.432660\pi$
$277$	11.6306	−	1.75303i	0.698814	−	0.105329i	0.488834	+	0.872377i	$0.337422\pi$
$278$	7.40917	−	6.87470i	0.444372	−	0.412317i
$279$	−6.30042	−	3.03412i	−0.377196	−	0.181648i
$280$	−3.47721	+	1.18309i	−0.207803	+	0.0707031i
$281$	−16.6703	+	8.02801i	−0.994469	+	0.478911i	−0.859058	−	0.511878i	$-0.828950\pi$
$281$	−16.6703	+	8.02801i	−0.994469	+	0.478911i	−0.135411	+	0.990789i	$0.543236\pi$
$282$	−3.49804	+	8.91285i	−0.208305	+	0.530753i
$283$	−0.461610	+	6.15976i	−0.0274399	+	0.366160i	0.966534	+	0.256540i	$0.0825824\pi$
$283$	−0.461610	+	6.15976i	−0.0274399	+	0.366160i	−0.993974	+	0.109620i	$0.965037\pi$
$284$	−2.71405	−	0.837172i	−0.161049	−	0.0496770i
$285$	0.0384799	+	0.513478i	0.00227935	+	0.0304158i
$286$	−0.471026	+	2.06370i	−0.0278524	+	0.122029i
$287$	18.7018	−	0.537915i	1.10393	−	0.0317521i
$288$	−0.222521	−	0.974928i	−0.0131122	−	0.0574482i
$289$	−6.48373	+	1.99997i	−0.381396	+	0.117645i
$290$	−4.12504	−	10.5104i	−0.242230	−	0.617193i
$291$	−3.41898	−	3.17235i	−0.200424	−	0.185967i
$292$	1.42932	+	0.974494i	0.0836446	+	0.0570279i
$293$	−27.4652			−1.60453			−0.802266	−	0.596966i	$-0.796373\pi$
$293$	−27.4652			−1.60453			−0.802266	+	0.596966i	$0.796373\pi$
$294$	4.67178	+	5.21291i	0.272464	+	0.304023i
$295$	7.34788			0.427810
$296$	−5.95823	−	4.06226i	−0.346315	−	0.236114i
$297$	0.325964	+	0.302450i	0.0189143	+	0.0175499i
$298$	5.32667	+	13.5721i	0.308565	+	0.786212i
$299$	4.90176	−	1.51199i	0.283476	−	0.0874409i
$300$	0.683752	+	2.99571i	0.0394764	+	0.172958i
$301$	17.1767	−	8.88902i	0.990046	−	0.512354i
$302$	−1.82207	+	7.98302i	−0.104849	+	0.459371i
$303$	−0.778812	−	10.3925i	−0.0447416	−	0.597035i
$304$	0.354432	+	0.109328i	0.0203281	+	0.00627038i
$305$	1.23842	−	16.5256i	0.0709119	−	0.946253i
$306$	−1.16765	+	2.97513i	−0.0667503	+	0.170077i
$307$	8.37009	−	4.03082i	0.477706	−	0.230051i	−0.179506	−	0.983757i	$-0.557450\pi$
$307$	8.37009	−	4.03082i	0.477706	−	0.230051i	0.657212	+	0.753706i	$0.271736\pi$
$308$	−0.617289	−	1.00153i	−0.0351733	−	0.0570672i
$309$	9.87476	+	4.75544i	0.561756	+	0.270527i
$310$	−7.11645	+	6.60310i	−0.404187	+	0.375031i
$311$	22.8623	−	3.44593i	1.29640	−	0.195401i	0.535647	−	0.844442i	$-0.320068\pi$
$311$	22.8623	−	3.44593i	1.29640	−	0.195401i	0.760753	+	0.649041i	$0.224830\pi$
$312$	2.38018	−	4.12259i	0.134751	−	0.233396i
$313$	0.785860	+	1.36115i	0.0444194	+	0.0769367i	0.887380	−	0.461038i	$-0.152523\pi$
$313$	0.785860	+	1.36115i	0.0444194	+	0.0769367i	−0.842961	+	0.537975i	$0.819190\pi$
$314$	0.678073	+	0.850276i	0.0382659	+	0.0479839i
$315$	−2.97401	+	2.15546i	−0.167566	+	0.121446i
$316$	−3.79154	+	4.75444i	−0.213291	+	0.267458i
$317$	−32.8940	−	4.95797i	−1.84751	−	0.278467i	−0.870579	−	0.492029i	$-0.836255\pi$
$317$	−32.8940	−	4.95797i	−1.84751	−	0.278467i	−0.976930	+	0.213562i	$0.931494\pi$
$318$	−7.51561	+	5.12406i	−0.421454	+	0.287343i
$319$	2.98814	−	2.03728i	0.167304	−	0.114066i
$320$	−1.37275	−	0.206908i	−0.0767389	−	0.0115665i
$321$	−6.60451	+	8.28179i	−0.368628	+	0.462245i
$322$	−1.35393	+	2.50901i	−0.0754514	+	0.139822i
$323$	−0.739119	−	0.926825i	−0.0411257	−	0.0515699i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−7.31370	+	12.6677i	−0.405691	+	0.702678i
$326$	−2.21844	+	0.334376i	−0.122868	+	0.0185194i
$327$	6.66958	−	6.18846i	0.368828	−	0.342223i
$328$	6.37123	+	3.06822i	0.351792	+	0.169414i
$329$	8.57313	−	23.8375i	0.472652	−	1.31421i
$330$	0.556177	−	0.267841i	0.0306165	−	0.0147441i
$331$	−8.50511	+	21.6707i	−0.467483	+	1.19113i	0.481681	+	0.876347i	$0.340026\pi$
$331$	−8.50511	+	21.6707i	−0.467483	+	1.19113i	−0.949164	+	0.314781i	$0.898069\pi$
$332$	0.183344	−	2.44656i	0.0100623	−	0.134273i
$333$	−6.89090	−	2.12556i	−0.377619	−	0.116480i
$334$	0.860925	+	11.4882i	0.0471077	+	0.628609i
$335$	−3.47966	+	15.2454i	−0.190114	+	0.832944i
$336$	0.662652	+	2.56142i	0.0361506	+	0.139737i
$337$	−0.531219	−	2.32742i	−0.0289373	−	0.126783i	0.958396	−	0.285441i	$-0.0921402\pi$
$337$	−0.531219	−	2.32742i	−0.0289373	−	0.126783i	−0.987333	+	0.158659i	$0.949283\pi$
$338$	9.23179	−	2.84763i	0.502143	−	0.154891i
$339$	−1.48467	−	3.78289i	−0.0806365	−	0.205458i
$340$	3.25251	+	3.01789i	0.176392	+	0.163668i
$341$	−2.56921	−	1.75166i	−0.139131	−	0.0948577i
$342$	0.370911			0.0200566
$343$	−12.7518	−	13.4310i	−0.688532	−	0.725206i
$344$	7.31000			0.394129
$345$	−1.23601	−	0.842700i	−0.0665447	−	0.0453694i
$346$	−8.40649	−	7.80008i	−0.451935	−	0.419335i
$347$	−8.72989	−	22.2434i	−0.468645	−	1.19409i	−0.948510	−	0.316746i	$-0.897410\pi$
$347$	−8.72989	−	22.2434i	−0.468645	−	1.19409i	0.479865	−	0.877342i	$-0.340685\pi$
$348$	−7.77185	+	2.39730i	−0.416615	+	0.128509i
$349$	1.94577	+	8.52500i	0.104155	+	0.456333i	0.999930	+	0.0118251i	$0.00376415\pi$
$349$	1.94577	+	8.52500i	0.104155	+	0.456333i	−0.895775	+	0.444507i	$0.853379\pi$
$350$	−2.03617	−	7.87062i	−0.108838	−	0.420703i
$351$	1.05928	−	4.64100i	0.0565401	−	0.247719i
$352$	−0.0332300	−	0.443423i	−0.00177116	−	0.0236345i
$353$	−16.4818	−	5.08397i	−0.877238	−	0.270592i	−0.176750	−	0.984256i	$-0.556558\pi$
$353$	−16.4818	−	5.08397i	−0.877238	−	0.270592i	−0.700489	+	0.713664i	$0.747035\pi$
$354$	0.395539	−	5.27810i	0.0210227	−	0.280528i
$355$	−1.44052	+	3.67039i	−0.0764551	+	0.194804i
$356$	3.62804	−	1.74717i	0.192286	−	0.0925999i
$357$	2.86173	−	7.95702i	0.151459	−	0.421130i
$358$	3.29494	+	1.58676i	0.174143	+	0.0838628i
$359$	−5.71637	+	5.30402i	−0.301698	+	0.279935i	−0.816465	−	0.577395i	$-0.804069\pi$
$359$	−5.71637	+	5.30402i	−0.301698	+	0.279935i	0.514766	+	0.857331i	$0.327879\pi$
$360$	−1.37275	+	0.206908i	−0.0723501	+	0.0109050i
$361$	9.43121	−	16.3353i	0.496380	−	0.859755i
$362$	9.57304	+	16.5810i	0.503148	+	0.871478i
$363$	−6.73511	−	8.44556i	−0.353501	−	0.443277i
$364$	−5.98116	+	11.0839i	−0.313498	+	0.580954i
$365$	1.49734	−	1.87761i	0.0783746	−	0.0982786i
$366$	−11.8039	−	1.77916i	−0.617002	−	0.0929980i
$367$	28.8184	−	19.6480i	1.50431	−	1.02562i	0.519009	−	0.854769i	$-0.326301\pi$
$367$	28.8184	−	19.6480i	1.50431	−	1.02562i	0.985297	−	0.170850i	$-0.0546514\pi$
$368$	−0.890337	+	0.607022i	−0.0464120	+	0.0316432i
$369$	6.99254	+	1.05396i	0.364017	+	0.0548668i
$370$	−6.24180	+	7.82697i	−0.324496	+	0.406905i
$371$	19.4864	−	14.1231i	1.01169	−	0.733233i
$372$	4.36003	+	5.46730i	0.226057	+	0.283466i
$373$	18.0716	+	31.3009i	0.935712	+	1.62070i	0.773360	+	0.633967i	$0.218575\pi$
$373$	18.0716	+	31.3009i	0.935712	+	1.62070i	0.162352	+	0.986733i	$0.448092\pi$
$374$	−0.710591	+	1.23078i	−0.0367438	+	0.0636421i
$375$	11.0819	−	1.67032i	0.572264	−	0.0862550i
$376$	7.01876	−	6.51246i	0.361965	−	0.335855i
$377$	−34.8827	−	16.7986i	−1.79655	−	0.865173i
$378$	1.38821	+	2.25231i	0.0714016	+	0.115846i
$379$	−7.62221	+	3.67066i	−0.391527	+	0.188549i	−0.619281	−	0.785169i	$-0.712576\pi$
$379$	−7.62221	+	3.67066i	−0.391527	+	0.188549i	0.227754	+	0.973719i	$0.426862\pi$
$380$	0.188121	−	0.479324i	0.00965039	−	0.0245888i
$381$	−0.536004	+	7.15247i	−0.0274603	+	0.366432i
$382$	15.4576	+	4.76803i	0.790878	+	0.243954i
$383$	1.47325	+	19.6591i	0.0752795	+	1.00453i	0.899117	+	0.437709i	$0.144210\pi$
$383$	1.47325	+	19.6591i	0.0752795	+	1.00453i	−0.823837	+	0.566826i	$0.808171\pi$
$384$	−0.222521	+	0.974928i	−0.0113555	+	0.0497516i
$385$	−1.45052	+	0.750654i	−0.0739255	+	0.0382569i
$386$	1.45453	+	6.37273i	0.0740338	+	0.324363i
$387$	6.98523	−	2.15466i	0.355079	−	0.109527i
$388$	1.70397	+	4.34163i	0.0865058	+	0.220413i
$389$	16.3671	+	15.1864i	0.829844	+	0.769983i	0.975651	−	0.219330i	$-0.0703872\pi$
$389$	16.3671	+	15.1864i	0.829844	+	0.769983i	−0.145806	+	0.989313i	$0.546578\pi$
$390$	−5.46026	−	3.72275i	−0.276491	−	0.188509i
$391$	3.44401			0.174171
$392$	−1.94733	−	6.72368i	−0.0983550	−	0.339597i
$393$	−4.36272			−0.220070
$394$	19.3497	+	13.1924i	0.974826	+	0.664625i
$395$	6.18856	+	5.74215i	0.311380	+	0.288919i
$396$	−0.162455	−	0.413929i	−0.00816367	−	0.0208007i
$397$	19.3985	−	5.98364i	0.973582	−	0.300310i	0.233149	−	0.972441i	$-0.425097\pi$
$397$	19.3985	−	5.98364i	0.973582	−	0.300310i	0.740432	+	0.672131i	$0.234621\pi$
$398$	−5.98671	−	26.2295i	−0.300087	−	1.31477i
$399$	−0.980932	+	0.0282143i	−0.0491080	+	0.00141248i
$400$	0.683752	−	2.99571i	0.0341876	−	0.149786i
$401$	−0.403865	−	5.38921i	−0.0201681	−	0.269124i	−0.998167	−	0.0605155i	$-0.980726\pi$
$401$	−0.403865	−	5.38921i	−0.0201681	−	0.269124i	0.977999	−	0.208609i	$-0.0668935\pi$
$402$	10.7637	+	3.32016i	0.536844	+	0.165594i
$403$	−2.48768	+	33.1958i	−0.123920	+	1.65360i
$404$	−3.80746	+	9.70125i	−0.189428	+	0.482655i
$405$	−1.25077	+	0.602340i	−0.0621514	+	0.0299305i
$406$	20.3715	−	6.93122i	1.01102	−	0.343991i
$407$	−2.88906	−	1.39130i	−0.143205	−	0.0689641i
$408$	2.34288	−	2.17387i	0.115990	−	0.107623i
$409$	2.06527	−	0.311289i	0.102121	−	0.0153923i	−0.0977829	−	0.995208i	$-0.531175\pi$
$409$	2.06527	−	0.311289i	0.102121	−	0.0153923i	0.199904	+	0.979816i	$0.435937\pi$
$410$	4.90853	−	8.50183i	0.242415	−	0.419875i
$411$	10.3682	+	17.9583i	0.511426	+	0.885816i
$412$	−6.83355	−	8.56900i	−0.336665	−	0.422164i
$413$	−0.644572	+	13.9889i	−0.0317173	+	0.688346i
$414$	−0.671859	+	0.842485i	−0.0330201	+	0.0414059i
$415$	−3.36793	−	0.507634i	−0.165325	−	0.0249188i
$416$	−3.93319	+	2.68160i	−0.192841	+	0.131476i
$417$	−8.35103	+	5.69364i	−0.408952	+	0.278819i
$418$	0.163090	+	0.0245818i	0.00797697	+	0.00120233i
$419$	14.3777	−	18.0291i	0.702397	−	0.880778i	−0.294803	−	0.955558i	$-0.595254\pi$
$419$	14.3777	−	18.0291i	0.702397	−	0.880778i	0.997200	+	0.0747802i	$0.0238255\pi$
$420$	3.61471	−	0.651624i	0.176380	−	0.0317960i
$421$	14.4922	+	18.1727i	0.706308	+	0.885683i	0.997477	−	0.0709892i	$-0.0226156\pi$
$421$	14.4922	+	18.1727i	0.706308	+	0.885683i	−0.291169	+	0.956672i	$0.594044\pi$
$422$	6.49584	+	11.2511i	0.316212	+	0.547696i
$423$	4.78736	−	8.29195i	0.232769	−	0.403168i
$424$	8.99457	−	1.35571i	0.436815	−	0.0658393i
$425$	−7.19909	+	6.67978i	−0.349207	+	0.324017i
$426$	2.55896	+	1.23233i	0.123982	+	0.0597065i
$427$	31.3527	+	3.80736i	1.51726	+	0.184251i
$428$	9.54379	−	4.59605i	0.461317	−	0.222158i
$429$	0.773344	−	1.97045i	0.0373374	−	0.0951341i
$430$	0.758370	−	10.1197i	0.0365719	−	0.488018i
$431$	20.2739	+	6.25368i	0.976562	+	0.301229i	0.741650	−	0.670787i	$-0.234044\pi$
$431$	20.2739	+	6.25368i	0.976562	+	0.301229i	0.234912	+	0.972017i	$0.424520\pi$
$432$	0.0747301	+	0.997204i	0.00359545	+	0.0479780i
$433$	−5.43812	+	23.8260i	−0.261339	+	1.14500i	0.658461	+	0.752615i	$0.271208\pi$
$433$	−5.43812	+	23.8260i	−0.261339	+	1.14500i	−0.919800	+	0.392387i	$0.871649\pi$
$434$	−11.9467	−	14.1275i	−0.573458	−	0.678141i
$435$	2.51247	+	11.0078i	0.120464	+	0.527785i
$436$	−8.69415	+	2.68179i	−0.416374	+	0.128435i
$437$	−0.146022	−	0.372057i	−0.00698516	−	0.0177979i
$438$	−1.26811	−	1.17664i	−0.0605929	−	0.0562220i
$439$	15.5304	+	10.5884i	0.741224	+	0.505358i	0.874083	−	0.485777i	$-0.161463\pi$
$439$	15.5304	+	10.5884i	0.741224	+	0.505358i	−0.132858	+	0.991135i	$0.542416\pi$
$440$	−0.617310			−0.0294291
$441$	−3.84266	−	5.85098i	−0.182984	−	0.278618i
$442$	15.2144			0.723675
$443$	−33.2104	−	22.6425i	−1.57788	−	1.07578i	−0.956286	−	0.292434i	$-0.905535\pi$
$443$	−33.2104	−	22.6425i	−1.57788	−	1.07578i	−0.621589	−	0.783343i	$-0.713513\pi$
$444$	5.28624	+	4.90491i	0.250874	+	0.232777i
$445$	−2.04235	−	5.20381i	−0.0968165	−	0.246684i
$446$	19.6479	−	6.06057i	0.930354	−	0.286976i
$447$	−3.24435	−	14.2144i	−0.153453	−	0.672320i
$448$	0.514331	−	2.59528i	0.0242999	−	0.122615i
$449$	0.626337	−	2.74416i	0.0295587	−	0.129505i	−0.957996	−	0.286782i	$-0.907414\pi$
$449$	0.626337	−	2.74416i	0.0295587	−	0.129505i	0.987555	+	0.157277i	$0.0502716\pi$
$450$	−0.229627	−	3.06416i	−0.0108247	−	0.144446i
$451$	3.00477	+	0.926850i	0.141489	+	0.0436436i
$452$	−0.303689	+	4.05244i	−0.0142843	+	0.190611i
$453$	2.99153	−	7.62229i	0.140554	−	0.358127i
$454$	−19.6282	+	9.45243i	−0.921196	+	0.443625i
$455$	14.7237	+	9.43004i	0.690258	+	0.442087i
$456$	−0.334179	−	0.160932i	−0.0156494	−	0.00753634i
$457$	−23.5259	+	21.8288i	−1.10050	+	1.02111i	−0.100839	+	0.994903i	$0.532153\pi$
$457$	−23.5259	+	21.8288i	−1.10050	+	1.02111i	−0.999657	+	0.0262077i	$0.991657\pi$
$458$	8.03738	−	1.21144i	0.375562	−	0.0566069i
$459$	1.59803	−	2.76787i	0.0745897	−	0.129193i
$460$	0.747976	+	1.29553i	0.0348746	+	0.0604045i
$461$	11.8498	+	14.8592i	0.551900	+	0.692061i	0.977037	−	0.213068i	$-0.0683456\pi$
$461$	11.8498	+	14.8592i	0.551900	+	0.692061i	−0.425137	+	0.905129i	$0.639774\pi$
$462$	0.461124	+	1.08234i	0.0214534	+	0.0503551i
$463$	9.95712	−	12.4858i	0.462747	−	0.580266i	−0.494632	−	0.869103i	$-0.664697\pi$
$463$	9.95712	−	12.4858i	0.462747	−	0.580266i	0.957378	+	0.288837i	$0.0932685\pi$
$464$	8.04234	+	1.21219i	0.373356	+	0.0562744i
$465$	8.02110	−	5.46869i	0.371970	−	0.253605i
$466$	−23.6469	+	16.1222i	−1.09542	+	0.746847i
$467$	2.87351	+	0.433111i	0.132970	+	0.0200420i	0.215190	−	0.976572i	$-0.430963\pi$
$467$	2.87351	+	0.433111i	0.132970	+	0.0200420i	−0.0822200	+	0.996614i	$0.526201\pi$
$468$	−2.96803	+	3.72180i	−0.137197	+	0.172040i
$469$	−28.7188	−	7.96191i	−1.32611	−	0.367647i
$470$	−8.28751	−	10.3922i	−0.382274	−	0.479357i
$471$	−0.543772	−	0.941841i	−0.0250557	−	0.0433977i
$472$	−2.64645	+	4.58379i	−0.121813	+	0.210986i
$473$	3.21421	−	0.484464i	0.147789	−	0.0222757i
$474$	4.45781	−	4.13624i	0.204754	−	0.189984i
$475$	1.02685	+	0.494505i	0.0471151	+	0.0226894i
$476$	−6.03075	+	5.92737i	−0.276419	+	0.271681i
$477$	8.19537	−	3.94668i	0.375240	−	0.180706i
$478$	−2.60194	+	6.62964i	−0.119010	+	0.303233i
$479$	0.296098	−	3.95115i	0.0135291	−	0.180533i	−0.986345	−	0.164690i	$-0.947338\pi$
$479$	0.296098	−	3.95115i	0.0135291	−	0.180533i	0.999874	−	0.0158431i	$-0.00504321\pi$
$480$	1.32658	+	0.409195i	0.0605497	+	0.0186771i
$481$	2.56535	+	34.2323i	0.116970	+	1.56086i
$482$	4.81954	−	21.1158i	0.219524	−	0.961799i
$483$	1.71275	−	2.27919i	0.0779329	−	0.103707i
$484$	2.40373	+	10.5314i	0.109261	+	0.478702i
$485$	6.18721	−	1.90850i	0.280947	−	0.0866606i
$486$	0.365341	+	0.930874i	0.0165722	+	0.0422253i
$487$	21.2183	+	19.6877i	0.961492	+	0.892134i	0.994223	−	0.107330i	$-0.0342302\pi$
$487$	21.2183	+	19.6877i	0.961492	+	0.892134i	−0.0327317	+	0.999464i	$0.510421\pi$
$488$	9.86303	+	6.72450i	0.446478	+	0.304404i
$489$	2.24350			0.101455
$490$	−9.51010	+	1.99828i	−0.429622	+	0.0902733i
$491$	17.5050			0.789990			0.394995	−	0.918683i	$-0.370746\pi$
$491$	17.5050			0.789990			0.394995	+	0.918683i	$0.370746\pi$
$492$	−5.84277	−	3.98353i	−0.263412	−	0.179592i
$493$	−19.0551	−	17.6805i	−0.858197	−	0.796291i
$494$	−0.645071	−	1.64361i	−0.0290231	−	0.0739497i
$495$	−0.589885	+	0.181955i	−0.0265133	+	0.00817828i
$496$	−1.55608	−	6.81761i	−0.0698699	−	0.306120i
$497$	−6.86131	−	3.06443i	−0.307772	−	0.137459i
$498$	−0.545938	+	2.39191i	−0.0244641	+	0.107184i
$499$	−1.68568	−	22.4938i	−0.0754613	−	1.00696i	−0.898499	−	0.438975i	$-0.855342\pi$
$499$	−1.68568	−	22.4938i	−0.0754613	−	1.00696i	0.823038	−	0.567986i	$-0.192277\pi$
$500$	−10.7091	−	3.30333i	−0.478927	−	0.147729i
$501$	0.860925	−	11.4882i	0.0384633	−	0.513257i
$502$	0.983256	−	2.50530i	0.0438849	−	0.111817i
$503$	−16.4430	+	7.91851i	−0.733155	+	0.353069i	−0.762924	−	0.646488i	$-0.776237\pi$
$503$	−16.4430	+	7.91851i	−0.733155	+	0.353069i	0.0297690	+	0.999557i	$0.490523\pi$
$504$	−0.273491	−	2.63158i	−0.0121822	−	0.117220i
$505$	13.0351	+	6.27739i	0.580056	+	0.279340i
$506$	−0.351252	+	0.325914i	−0.0156150	+	0.0144886i
$507$	−9.55309	+	1.43990i	−0.424268	+	0.0639481i
$508$	3.58626	−	6.21159i	0.159115	−	0.275595i
$509$	18.2145	+	31.5485i	0.807345	+	1.39836i	0.914697	+	0.404141i	$0.132429\pi$
$509$	18.2145	+	31.5485i	0.807345	+	1.39836i	−0.107352	+	0.994221i	$0.534237\pi$
$510$	−2.76639	−	3.46894i	−0.122498	−	0.153607i
$511$	3.44323	+	3.01534i	0.152320	+	0.133391i
$512$	0.623490	−	0.781831i	0.0275546	−	0.0345524i
$513$	−0.366768	−	0.0552814i	−0.0161932	−	0.00244073i
$514$	6.55071	−	4.46620i	0.288939	−	0.196995i
$515$	−12.5716	+	8.57118i	−0.553972	+	0.377691i
$516$	−7.22835	−	1.08950i	−0.318210	−	0.0479625i
$517$	2.65454	−	3.32869i	0.116747	−	0.146396i
$518$	−14.3534	−	12.5697i	−0.630652	−	0.552281i
$519$	7.15005	+	8.96588i	0.313852	+	0.393558i
$520$	3.30429	+	5.72320i	0.144903	+	0.250979i
$521$	−17.8968	+	30.9982i	−0.784075	+	1.35806i	0.145475	+	0.989362i	$0.453529\pi$
$521$	−17.8968	+	30.9982i	−0.784075	+	1.35806i	−0.929550	+	0.368696i	$0.879804\pi$
$522$	8.04234	−	1.21219i	0.352004	−	0.0530560i
$523$	−24.1756	+	22.4317i	−1.05713	+	0.980869i	−0.999847	−	0.0174894i	$-0.994433\pi$
$523$	−24.1756	+	22.4317i	−1.05713	+	0.980869i	−0.0572782	+	0.998358i	$0.518242\pi$
$524$	3.93067	+	1.89291i	0.171712	+	0.0826923i
$525$	0.840369	+	8.08619i	0.0366767	+	0.352910i
$526$	−9.41933	+	4.53611i	−0.410702	+	0.197784i
$527$	−8.16533	+	20.8049i	−0.355687	+	0.906276i
$528$	−0.0332300	+	0.443423i	−0.00144615	+	0.0192975i
$529$	−20.8686	−	6.43711i	−0.907330	−	0.279874i
$530$	−0.943676	−	12.5925i	−0.0409907	−	0.546982i
$531$	−1.17778	+	5.16020i	−0.0511113	+	0.223933i
$532$	0.896031	+	0.400190i	0.0388479	+	0.0173504i
$533$	−7.49072	−	32.8190i	−0.324459	−	1.42155i
$534$	−3.84792	+	1.18693i	−0.166516	+	0.0513633i
$535$	−5.37252	−	13.6890i	−0.232274	−	0.591826i
$536$	−8.25718	−	7.66154i	−0.356656	−	0.330928i
$537$	−3.02164	−	2.06012i	−0.130394	−	0.0889008i
$538$	−15.7832			−0.680463
$539$	−1.30185	−	2.82735i	−0.0560745	−	0.121782i
$540$	1.38825			0.0597409
$541$	31.3195	+	21.3533i	1.34653	+	0.918050i	0.999802	−	0.0199155i	$-0.00633971\pi$
$541$	31.3195	+	21.3533i	1.34653	+	0.918050i	0.346730	+	0.937965i	$0.387292\pi$
$542$	−23.2801	−	21.6008i	−0.999967	−	0.927833i
$543$	−6.99485	−	17.8226i	−0.300178	−	0.764841i
$544$	−3.05407	+	0.942056i	−0.130942	+	0.0403903i
$545$	2.81063	+	12.3142i	0.120394	+	0.527481i
$546$	7.56633	−	10.0686i	0.323809	−	0.430898i
$547$	3.29292	−	14.4272i	0.140795	−	0.616863i	−0.854456	−	0.519524i	$-0.826109\pi$
$547$	3.29292	−	14.4272i	0.140795	−	0.616863i	0.995251	−	0.0973399i	$-0.0310334\pi$
$548$	−1.54963	−	20.6784i	−0.0661971	−	0.883339i
$549$	11.4069	+	3.51857i	0.486836	+	0.150169i
$550$	0.102108	−	1.36253i	0.00435388	−	0.0580985i
$551$	−1.10212	+	2.80815i	−0.0469519	+	0.119631i
$552$	0.970865	−	0.467544i	0.0413228	−	0.0199000i
$553$	−11.4747	+	11.2780i	−0.487956	+	0.479591i
$554$	10.5972	+	5.10332i	0.450230	+	0.216819i
$555$	7.33864	−	6.80926i	0.311508	−	0.289037i
$556$	9.99440	−	1.50641i	0.423857	−	0.0638861i
$557$	2.72168	−	4.71409i	0.115321	−	0.199743i	−0.802587	−	0.596535i	$-0.796544\pi$
$557$	2.72168	−	4.71409i	0.115321	−	0.199743i	0.917908	+	0.396793i	$0.129877\pi$
$558$	−3.49647	−	6.05606i	−0.148017	−	0.256374i
$559$	−21.6963	−	27.2063i	−0.917656	−	1.15070i
$560$	−3.53947	−	0.981270i	−0.149570	−	0.0414662i
$561$	0.886093	−	1.11113i	0.0374109	−	0.0469118i
$562$	−18.2960	−	2.75768i	−0.771771	−	0.116326i
$563$	37.8849	−	25.8295i	1.59666	−	1.08858i	0.653152	−	0.757227i	$-0.273446\pi$
$563$	37.8849	−	25.8295i	1.59666	−	1.08858i	0.943506	−	0.331355i	$-0.107506\pi$
$564$	−7.91100	+	5.39363i	−0.333113	+	0.227113i
$565$	5.57858	+	0.840835i	0.234693	+	0.0353742i
$566$	−3.85131	+	4.82940i	−0.161883	+	0.202995i
$567$	−1.03701	−	2.43405i	−0.0435504	−	0.102221i
$568$	−1.77085	−	2.22058i	−0.0743034	−	0.0931735i
$569$	21.3765	+	37.0253i	0.896151	+	1.55218i	0.832373	+	0.554216i	$0.186982\pi$
$569$	21.3765	+	37.0253i	0.896151	+	1.55218i	0.0637783	+	0.997964i	$0.479685\pi$
$570$	−0.257459	+	0.445932i	−0.0107838	+	0.0186780i
$571$	22.7952	−	3.43583i	0.953950	−	0.143785i	0.346418	−	0.938080i	$-0.387398\pi$
$571$	22.7952	−	3.43583i	0.953950	−	0.143785i	0.607532	+	0.794295i	$0.292160\pi$
$572$	−1.55170	+	1.43977i	−0.0648800	+	0.0601998i
$573$	−14.5743	−	7.01861i	−0.608850	−	0.293206i
$574$	15.7551	+	10.0906i	0.657607	+	0.421175i
$575$	−2.98323	+	1.43665i	−0.124409	+	0.0599123i
$576$	0.365341	−	0.930874i	0.0152225	−	0.0387864i
$577$	1.82314	−	24.3281i	0.0758984	−	1.01279i	−0.821107	−	0.570774i	$-0.806643\pi$
$577$	1.82314	−	24.3281i	0.0758984	−	1.01279i	0.897006	−	0.442019i	$-0.145738\pi$
$578$	−6.48373	−	1.99997i	−0.269688	−	0.0831877i
$579$	−0.488482	−	6.51834i	−0.0203006	−	0.270893i
$580$	2.51247	−	11.0078i	0.104324	−	0.457075i
$581$	1.26187	−	6.36731i	0.0523512	−	0.264161i
$582$	−1.03785	−	4.54710i	−0.0430201	−	0.188484i
$583$	3.86507	−	1.19222i	0.160075	−	0.0493765i
$584$	0.632008	+	1.61033i	0.0261527	+	0.0666359i
$585$	4.84443	+	4.49498i	0.200293	+	0.185844i
$586$	−22.6928	−	15.4717i	−0.937431	−	0.639129i
$587$	−1.84658			−0.0762167			−0.0381083	−	0.999274i	$-0.512133\pi$
$587$	−1.84658			−0.0762167			−0.0381083	+	0.999274i	$0.512133\pi$
$588$	0.923467	+	6.93882i	0.0380831	+	0.286152i
$589$	2.59376			0.106874
$590$	6.07111	+	4.13921i	0.249943	+	0.170409i
$591$	−17.1674	−	15.9290i	−0.706172	−	0.655232i
$592$	−2.63457	−	6.71279i	−0.108280	−	0.275894i
$593$	−13.7089	+	4.22863i	−0.562956	+	0.173649i	−0.563155	−	0.826351i	$-0.690413\pi$
$593$	−13.7089	+	4.22863i	−0.562956	+	0.173649i	0.000199312		1.00000i	$0.499937\pi$
$594$	0.0989476	+	0.433518i	0.00405987	+	0.0177875i
$595$	7.58003	+	8.96373i	0.310751	+	0.367477i
$596$	−3.24435	+	14.2144i	−0.132894	+	0.582246i
$597$	2.01054	+	26.8288i	0.0822860	+	1.09803i
$598$	4.90176	+	1.51199i	0.200448	+	0.0618300i
$599$	−0.730298	+	9.74515i	−0.0298392	+	0.398176i	0.962209	+	0.272314i	$0.0877889\pi$
$599$	−0.730298	+	9.74515i	−0.0298392	+	0.398176i	−0.992048	+	0.125862i	$0.959830\pi$
$600$	−1.12260	+	2.86035i	−0.0458301	+	0.116773i
$601$	8.95344	−	4.31175i	0.365218	−	0.175880i	−0.242269	−	0.970209i	$-0.577892\pi$
$601$	8.95344	−	4.31175i	0.365218	−	0.175880i	0.607488	+	0.794329i	$0.292177\pi$
$602$	19.1994	+	2.33151i	0.782509	+	0.0950251i
$603$	−10.1486	−	4.88732i	−0.413284	−	0.199027i
$604$	−6.00246	+	5.56947i	−0.244237	+	0.226619i
$605$	14.8288	−	2.23508i	0.602876	−	0.0908689i
$606$	5.21083	−	9.02543i	0.211676	−	0.366633i
$607$	−16.9361	−	29.3343i	−0.687417	−	1.19064i	−0.972671	−	0.232189i	$-0.925411\pi$
$607$	−16.9361	−	29.3343i	−0.687417	−	1.19064i	0.285254	−	0.958452i	$-0.407922\pi$
$608$	0.231259	+	0.289990i	0.00937879	+	0.0117606i
$609$	−21.1770	+	3.81759i	−0.858137	+	0.154696i
$610$	10.3324	−	12.9565i	0.418348	−	0.524592i
$611$	−45.0700	−	6.79321i	−1.82334	−	0.274824i
$612$	−2.64071	+	1.80041i	−0.106744	+	0.0727771i
$613$	9.65496	−	6.58264i	0.389960	−	0.265870i	−0.352430	−	0.935838i	$-0.614645\pi$
$613$	9.65496	−	6.58264i	0.389960	−	0.265870i	0.742390	+	0.669968i	$0.233692\pi$
$614$	9.18633	+	1.38462i	0.370730	+	0.0558786i
$615$	−6.12084	+	7.67529i	−0.246816	+	0.309498i
$616$	0.0541517	−	1.17523i	0.00218184	−	0.0473514i
$617$	−21.3208	−	26.7355i	−0.858344	−	1.07633i	−0.996304	−	0.0858920i	$-0.972626\pi$
$617$	−21.3208	−	26.7355i	−0.858344	−	1.07633i	0.137960	−	0.990438i	$-0.455945\pi$
$618$	5.48008	+	9.49178i	0.220441	+	0.381815i
$619$	2.98334	−	5.16729i	0.119910	−	0.207691i	−0.799822	−	0.600238i	$-0.795073\pi$
$619$	2.98334	−	5.16729i	0.119910	−	0.207691i	0.919732	+	0.392547i	$0.128406\pi$
$620$	−9.59954	+	1.44690i	−0.385527	+	0.0581088i
$621$	0.789921	−	0.732940i	0.0316984	−	0.0294119i
$622$	20.8309	+	10.0316i	0.835241	+	0.402231i
$623$	10.0861	−	3.43171i	0.404093	−	0.137489i
$624$	4.28893	−	2.06544i	0.171695	−	0.0826838i
$625$	−0.0710284	+	0.180978i	−0.00284114	+	0.00723910i
$626$	−0.117455	+	1.56732i	−0.00469443	+	0.0626429i
$627$	−0.157604	−	0.0486145i	−0.00629411	−	0.00194147i
$628$	0.0812723	+	1.08450i	0.00324312	+	0.0432764i
$629$	−5.12859	+	22.4698i	−0.204490	+	0.895931i
$630$	−3.67145	+	0.105601i	−0.146274	+	0.00420725i
$631$	9.15703	+	40.1196i	0.364536	+	1.59714i	0.741530	+	0.670920i	$0.234101\pi$
$631$	9.15703	+	40.1196i	0.364536	+	1.59714i	−0.376994	+	0.926216i	$0.623042\pi$
$632$	−5.81099	+	1.79245i	−0.231149	+	0.0713000i
$633$	−4.74639	−	12.0936i	−0.188652	−	0.480678i
$634$	−24.3853	−	22.6263i	−0.968465	−	0.898605i
$635$	−8.22709	−	5.60914i	−0.326482	−	0.222592i
$636$	−9.09617			−0.360687
$637$	−19.2444	+	27.2037i	−0.762492	+	1.07785i
$638$	3.61656			0.143181
$639$	−2.34671	−	1.59996i	−0.0928343	−	0.0632934i
$640$	−1.01766	−	0.944252i	−0.0402266	−	0.0373248i
$641$	−9.56761	−	24.3779i	−0.377898	−	0.962868i	−0.985659	−	0.168748i	$-0.946027\pi$
$641$	−9.56761	−	24.3779i	−0.377898	−	0.962868i	0.607761	−	0.794120i	$-0.292068\pi$
$642$	−10.1222	+	3.12229i	−0.399491	+	0.123227i
$643$	−0.995152	−	4.36005i	−0.0392450	−	0.171943i	0.951507	−	0.307626i	$-0.0995345\pi$
$643$	−0.995152	−	4.36005i	−0.0392450	−	0.171943i	−0.990752	+	0.135682i	$0.956677\pi$
$644$	−2.53204	+	1.31035i	−0.0997764	+	0.0516348i
$645$	−2.25817	+	9.89369i	−0.0889154	+	0.389564i
$646$	−0.0885891	−	1.18214i	−0.00348549	−	0.0465107i
$647$	15.6588	+	4.83009i	0.615609	+	0.189890i	0.586849	−	0.809696i	$-0.300368\pi$
$647$	15.6588	+	4.83009i	0.615609	+	0.189890i	0.0287597	+	0.999586i	$0.490844\pi$
$648$	0.0747301	−	0.997204i	0.00293568	−	0.0391739i
$649$	−0.859858	+	2.19088i	−0.0337524	+	0.0859996i
$650$	−13.1788	+	6.34659i	−0.516916	+	0.248934i
$651$	9.70764	+	15.7502i	0.380472	+	0.617301i
$652$	−2.02132	−	0.973418i	−0.0791612	−	0.0381220i
$653$	16.5957	−	15.3986i	0.649440	−	0.602592i	−0.285080	−	0.958504i	$-0.592020\pi$
$653$	16.5957	−	15.3986i	0.649440	−	0.602592i	0.934520	+	0.355911i	$0.115830\pi$
$654$	8.99675	−	1.35604i	0.351801	−	0.0530254i
$655$	3.02828	−	5.24513i	0.118325	−	0.204944i
$656$	3.53576	+	6.12412i	0.138048	+	0.239107i
$657$	1.07858	+	1.35250i	0.0420795	+	0.0527660i
$658$	20.5116	−	14.8661i	0.799626	−	0.579540i
$659$	9.22107	−	11.5629i	0.359202	−	0.450425i	−0.569091	−	0.822275i	$-0.692705\pi$
$659$	9.22107	−	11.5629i	0.359202	−	0.450425i	0.928293	+	0.371849i	$0.121276\pi$
$660$	0.610415	+	0.0920053i	0.0237604	+	0.00358130i
$661$	−22.5030	+	15.3423i	−0.875265	+	0.596745i	−0.915443	−	0.402447i	$-0.868160\pi$
$661$	−22.5030	+	15.3423i	−0.875265	+	0.596745i	0.0401784	+	0.999193i	$0.487207\pi$
$662$	−19.2348	+	13.1140i	−0.747581	+	0.509692i
$663$	−15.0445	−	2.26759i	−0.584279	−	0.0880659i
$664$	1.52968	−	1.91816i	0.0593632	−	0.0744391i
$665$	0.646970	−	1.19892i	0.0250884	−	0.0464922i
$666$	−4.49616	−	5.63800i	−0.174223	−	0.218468i
$667$	−4.38207	−	7.58997i	−0.169675	−	0.293885i
$668$	−5.76023	+	9.97701i	−0.222870	+	0.386022i
$669$	−20.3317	+	3.06451i	−0.786069	+	0.118481i
$670$	−11.4631	+	10.6362i	−0.442856	+	0.410911i
$671$	4.78244	+	2.30310i	0.184624	+	0.0889102i
$672$	−0.895392	+	2.48963i	−0.0345405	+	0.0960397i
$673$	−1.54003	+	0.741640i	−0.0593638	+	0.0285881i	−0.463330	−	0.886186i	$-0.653346\pi$
$673$	−1.54003	+	0.741640i	−0.0593638	+	0.0285881i	0.403966	+	0.914774i	$0.367631\pi$
$674$	0.872170	−	2.22225i	0.0335947	−	0.0855980i
$675$	−0.229627	+	3.06416i	−0.00883835	+	0.117940i
$676$	9.23179	+	2.84763i	0.355069	+	0.109524i
$677$	1.60652	+	21.4375i	0.0617434	+	0.823909i	0.939007	+	0.343899i	$0.111748\pi$
$677$	1.60652	+	21.4375i	0.0617434	+	0.823909i	−0.877263	+	0.480010i	$0.840633\pi$
$678$	0.904282	−	3.96192i	0.0347287	−	0.152156i
$679$	3.09064	+	11.9466i	0.118608	+	0.458468i
$680$	0.987313	+	4.32570i	0.0378617	+	0.165883i
$681$	20.8178	−	6.42143i	0.797738	−	0.246070i
$682$	−1.13604	−	2.89458i	−0.0435011	−	0.110839i
$683$	19.6876	+	18.2674i	0.753324	+	0.698983i	0.960178	−	0.279389i	$-0.0901320\pi$
$683$	19.6876	+	18.2674i	0.753324	+	0.698983i	−0.206854	+	0.978372i	$0.566322\pi$
$684$	0.306461	+	0.208941i	0.0117178	+	0.00798908i
$685$	−28.7874			−1.09991
$686$	−2.97007	−	18.2806i	−0.113398	−	0.697955i
$687$	−8.12816			−0.310109
$688$	6.03980	+	4.11787i	0.230265	+	0.156992i
$689$	−31.7419	−	29.4522i	−1.20927	−	1.12204i
$690$	−0.546533	−	1.39254i	−0.0208061	−	0.0530132i
$691$	3.29365	−	1.01596i	0.125296	−	0.0386488i	−0.231473	−	0.972841i	$-0.574354\pi$
$691$	3.29365	−	1.01596i	0.125296	−	0.0386488i	0.356769	+	0.934193i	$0.383878\pi$
$692$	−2.55182	−	11.1803i	−0.0970058	−	0.425010i
$693$	−0.294659	−	1.13898i	−0.0111932	−	0.0432663i
$694$	5.31718	−	23.2961i	0.201837	−	0.884307i
$695$	−1.04857	−	13.9922i	−0.0397747	−	0.530756i
$696$	−7.77185	−	2.39730i	−0.294591	−	0.0908694i
$697$	1.68898	−	22.5378i	0.0639746	−	0.853682i
$698$	−3.19463	+	8.13978i	−0.120918	+	0.308095i
$699$	25.7857	−	12.4177i	0.975305	−	0.469682i
$700$	2.75132	−	7.65003i	0.103990	−	0.289144i
$701$	−24.2816	−	11.6934i	−0.917102	−	0.441653i	−0.0850663	−	0.996375i	$-0.527110\pi$
$701$	−24.2816	−	11.6934i	−0.917102	−	0.441653i	−0.832036	+	0.554722i	$0.812824\pi$
$702$	3.48959	−	3.23787i	0.131706	−	0.122205i
$703$	2.64486	−	0.398649i	0.0997530	−	0.0150353i
$704$	0.222333	−	0.385093i	0.00837950	−	0.0145137i
$705$	6.64606	+	11.5113i	0.250305	+	0.433541i
$706$	−10.7540	−	13.4851i	−0.404733	−	0.507519i
$707$	−13.0943	+	24.2655i	−0.492463	+	0.912599i
$708$	3.30007	−	4.13816i	0.124024	−	0.155521i
$709$	−46.7244	−	7.04257i	−1.75477	−	0.264489i	−0.808647	−	0.588294i	$-0.799800\pi$
$709$	−46.7244	−	7.04257i	−1.75477	−	0.264489i	−0.946124	+	0.323805i	$0.895038\pi$
$710$	−3.25782	+	2.22115i	−0.122264	+	0.0833581i
$711$	−5.02449	+	3.42564i	−0.188433	+	0.128472i
$712$	3.98184	+	0.600166i	0.149226	+	0.0224922i
$713$	−4.69827	+	5.89145i	−0.175952	+	0.220636i
$714$	6.84682	−	4.96233i	0.256236	−	0.185711i
$715$	1.83220	+	2.29750i	0.0685203	+	0.0859217i
$716$	1.82855	+	3.16715i	0.0683362	+	0.118362i
$717$	3.56098	−	6.16779i	0.132987	−	0.230340i
$718$	−7.71094	+	1.16224i	−0.287770	+	0.0433743i
$719$	31.3786	−	29.1151i	1.17022	−	1.08581i	0.175368	−	0.984503i	$-0.443889\pi$
$719$	31.3786	−	29.1151i	1.17022	−	1.08581i	0.994855	−	0.101305i	$-0.0323019\pi$
$720$	−1.25077	−	0.602340i	−0.0466135	−	0.0224479i
$721$	−15.2150	−	24.6856i	−0.566634	−	0.919341i
$722$	16.9945	−	8.18410i	0.632468	−	0.304581i
$723$	−7.91286	+	20.1616i	−0.294282	+	0.749820i
$724$	−1.43079	+	19.0926i	−0.0531749	+	0.709569i
$725$	23.8810	+	7.36631i	0.886917	+	0.273578i
$726$	−0.807255	−	10.7721i	−0.0299600	−	0.399789i
$727$	−5.59043	+	24.4933i	−0.207337	+	0.908405i	0.758993	+	0.651099i	$0.225692\pi$
$727$	−5.59043	+	24.4933i	−0.207337	+	0.908405i	−0.966330	+	0.257306i	$0.917165\pi$
$728$	−11.1856	+	5.78863i	−0.414568	+	0.214541i
$729$	−0.222521	−	0.974928i	−0.00824152	−	0.0361084i
$730$	2.29486	−	0.707871i	0.0849366	−	0.0261995i
$731$	−8.53554	−	21.7482i	−0.315698	−	0.804386i
$732$	−8.75063	−	8.11940i	−0.323433	−	0.300102i
$733$	30.3043	+	20.6611i	1.11932	+	0.763137i	0.974067	−	0.226258i	$-0.0726494\pi$
$733$	30.3043	+	20.6611i	1.11932	+	0.763137i	0.145249	+	0.989395i	$0.453602\pi$
$734$	34.8790			1.28741
$735$	9.70171	−	0.558558i	0.357853	−	0.0206027i
$736$	−1.07758			−0.0397201
$737$	−4.13844	−	2.82154i	−0.152442	−	0.103933i
$738$	5.18380	+	4.80986i	0.190818	+	0.177053i
$739$	−5.89603	−	15.0228i	−0.216889	−	0.552624i	0.780475	−	0.625187i	$-0.214977\pi$
$739$	−5.89603	−	15.0228i	−0.216889	−	0.552624i	−0.997364	+	0.0725630i	$0.976882\pi$
$740$	−9.56631	+	2.95082i	−0.351665	+	0.108474i
$741$	0.392898	+	1.72140i	0.0144335	+	0.0632372i
$742$	24.0563	−	0.691925i	0.883133	−	0.0254014i
$743$	−6.86194	+	30.0641i	−0.251740	+	1.10295i	0.678097	+	0.734973i	$0.262805\pi$
$743$	−6.86194	+	30.0641i	−0.251740	+	1.10295i	−0.929837	+	0.367973i	$0.880052\pi$
$744$	0.522583	+	6.97339i	0.0191588	+	0.255657i
$745$	19.3415	+	5.96605i	0.708616	+	0.218579i
$746$	−2.70098	+	36.0421i	−0.0988901	+	1.31960i
$747$	0.896336	−	2.28383i	0.0327952	−	0.0835608i
$748$	−1.28044	+	0.616628i	−0.0468176	+	0.0225462i
$749$	26.5323	−	9.02735i	0.969468	−	0.329852i
$750$	10.0972	+	4.86255i	0.368697	+	0.177555i
$751$	30.9216	−	28.6910i	1.12834	−	1.04695i	0.129882	−	0.991530i	$-0.458540\pi$
$751$	30.9216	−	28.6910i	1.12834	−	1.04695i	0.998463	−	0.0554213i	$-0.0176502\pi$
$752$	9.46777	−	1.42704i	0.345254	−	0.0520387i
$753$	−1.34567	+	2.33077i	−0.0490389	+	0.0849378i
$754$	−19.3584	−	33.5298i	−0.704992	−	1.22108i
$755$	7.08750	+	8.88744i	0.257940	+	0.323447i
$756$	−0.121781	+	2.64295i	−0.00442911	+	0.0961231i
$757$	18.4964	−	23.1938i	0.672264	−	0.842992i	−0.322352	−	0.946620i	$-0.604474\pi$
$757$	18.4964	−	23.1938i	0.672264	−	0.842992i	0.994616	+	0.103628i	$0.0330450\pi$
$758$	−8.36553	−	1.26090i	−0.303850	−	0.0457980i
$759$	0.395903	−	0.269922i	0.0143704	−	0.00979756i
$760$	0.425445	−	0.290064i	0.0154325	−	0.0105217i
$761$	1.31506	+	0.198213i	0.0476709	+	0.00718523i	0.172834	−	0.984951i	$-0.444707\pi$
$761$	1.31506	+	0.198213i	0.0476709	+	0.00718523i	−0.125164	+	0.992136i	$0.539946\pi$
$762$	−4.47200	+	5.60771i	−0.162003	+	0.203146i
$763$	−23.6902	+	4.27063i	−0.857642	+	0.154607i
$764$	10.0857	+	12.6471i	0.364888	+	0.457556i
$765$	2.21847	+	3.84251i	0.0802090	+	0.138926i
$766$	−9.85713	+	17.0730i	−0.356153	+	0.616874i
$767$	24.9147	−	3.75528i	0.899617	−	0.135595i
$768$	−0.733052	+	0.680173i	−0.0264517	+	0.0245436i
$769$	−3.24787	−	1.56409i	−0.117121	−	0.0564027i	0.374406	−	0.927265i	$-0.377847\pi$
$769$	−3.24787	−	1.56409i	−0.117121	−	0.0564027i	−0.491527	+	0.870862i	$0.663561\pi$
$770$	−1.62134	−	0.196890i	−0.0584289	−	0.00709541i
$771$	−7.14319	+	3.43998i	−0.257256	+	0.123888i
$772$	−2.38809	+	6.08476i	−0.0859493	+	0.218995i
$773$	−1.45211	+	19.3771i	−0.0522289	+	0.696947i	0.908220	+	0.418492i	$0.137441\pi$
$773$	−1.45211	+	19.3771i	−0.0522289	+	0.696947i	−0.960449	+	0.278455i	$0.910178\pi$
$774$	6.98523	+	2.15466i	0.251079	+	0.0774476i
$775$	−1.60577	−	21.4275i	−0.0576809	−	0.769698i
$776$	−1.03785	+	4.54710i	−0.0372565	+	0.163232i
$777$	12.3197	+	14.5686i	0.441965	+	0.522645i
$778$	4.96830	+	21.7675i	0.178122	+	0.780404i
$779$	−2.50638	+	0.773115i	−0.0898003	+	0.0276997i
$780$	−2.41439	−	6.15175i	−0.0864489	−	0.220268i
$781$	−0.925812	−	0.859028i	−0.0331281	−	0.0307384i
$782$	2.84557	+	1.94008i	0.101758	+	0.0693771i
$783$	−8.13318			−0.290656
$784$	2.17863	−	6.65234i	0.0778081	−	0.237583i
$785$	1.50979			0.0538866
$786$	−3.60465	−	2.45761i	−0.128574	−	0.0876600i
$787$	−6.71790	−	6.23330i	−0.239467	−	0.222193i	0.551305	−	0.834304i	$-0.314130\pi$
$787$	−6.71790	−	6.23330i	−0.239467	−	0.222193i	−0.790772	+	0.612111i	$0.790321\pi$
$788$	8.55595	+	21.8002i	0.304793	+	0.776600i
$789$	9.99020	−	3.08157i	0.355660	−	0.109707i
$790$	1.87856	+	8.23053i	0.0668363	+	0.292829i
$791$	−2.09014	+	10.5467i	−0.0743169	+	0.374997i
$792$	0.0989476	−	0.433518i	0.00351595	−	0.0154044i
$793$	−4.24659	−	56.6667i	−0.150801	−	2.01230i
$794$	19.3985	+	5.98364i	0.688426	+	0.212351i
$795$	−0.943676	+	12.5925i	−0.0334687	+	0.446609i
$796$	9.82915	−	25.0443i	0.348385	−	0.887670i
$797$	35.2978	−	16.9985i	1.25031	−	0.602118i	0.312716	−	0.949847i	$-0.398761\pi$
$797$	35.2978	−	16.9985i	1.25031	−	0.602118i	0.937595	+	0.347729i	$0.113047\pi$
$798$	−0.826378	−	0.529267i	−0.0292535	−	0.0187358i
$799$	−27.5709	−	13.2774i	−0.975388	−	0.469722i
$800$	2.25249	−	2.09000i	0.0796375	−	0.0738928i
$801$	3.98184	−	0.600166i	0.140691	−	0.0212058i
$802$	2.70216	−	4.68028i	0.0954166	−	0.165266i
$803$	0.384617	+	0.666176i	0.0135728	+	0.0235088i
$804$	7.02306	+	8.80664i	0.247684	+	0.310586i
$805$	1.55132	+	3.64122i	0.0546768	+	0.128336i
$806$	−20.7553	+	26.0263i	−0.731074	+	0.916737i
$807$	15.6069	+	2.35237i	0.549390	+	0.0828073i
$808$	−8.61078	+	5.87073i	−0.302926	+	0.206532i
$809$	7.89623	−	5.38356i	0.277617	−	0.189276i	−0.416505	−	0.909133i	$-0.636745\pi$
$809$	7.89623	−	5.38356i	0.277617	−	0.189276i	0.694122	+	0.719858i	$0.255793\pi$
$810$	−1.37275	−	0.206908i	−0.0482334	−	0.00727002i
$811$	22.7320	−	28.5050i	0.798228	−	1.00095i	−0.201542	−	0.979480i	$-0.564595\pi$
$811$	22.7320	−	28.5050i	0.798228	−	1.00095i	0.999770	−	0.0214662i	$-0.00683342\pi$
$812$	20.7362	+	5.74885i	0.727699	+	0.201745i
$813$	19.8007	+	24.8292i	0.694440	+	0.870800i
$814$	−1.60331	−	2.77701i	−0.0561959	−	0.0973341i
$815$	−1.55727	+	2.69728i	−0.0545489	+	0.0944815i
$816$	3.16037	−	0.476348i	0.110635	−	0.0166755i
$817$	−1.98756	+	1.84419i	−0.0695361	+	0.0645201i
$818$	1.88176	+	0.906208i	0.0657942	+	0.0316848i
$819$	−8.98247	+	8.82849i	−0.313873	+	0.308492i
$820$	8.84487	−	4.25947i	0.308876	−	0.148747i
$821$	−2.73467	+	6.96783i	−0.0954407	+	0.243179i	−0.970619	−	0.240622i	$-0.922649\pi$
$821$	−2.73467	+	6.96783i	−0.0954407	+	0.243179i	0.875178	+	0.483801i	$0.160744\pi$
$822$	−1.54963	+	20.6784i	−0.0540497	+	0.721243i
$823$	−14.9381	−	4.60781i	−0.520711	−	0.160618i	0.0232483	−	0.999730i	$-0.492599\pi$
$823$	−14.9381	−	4.60781i	−0.520711	−	0.160618i	−0.543959	+	0.839112i	$0.683075\pi$
$824$	−0.819054	−	10.9295i	−0.0285331	−	0.380748i
$825$	−0.304042	+	1.33209i	−0.0105854	+	0.0463776i
$826$	−8.41277	+	11.1950i	−0.292718	+	0.389525i
$827$	−10.4619	−	45.8365i	−0.363795	−	1.59389i	−0.743470	−	0.668770i	$-0.766821\pi$
$827$	−10.4619	−	45.8365i	−0.363795	−	1.59389i	0.379675	−	0.925120i	$-0.376036\pi$
$828$	−1.02971	+	0.317622i	−0.0357847	+	0.0110381i
$829$	0.544119	+	1.38639i	0.0188980	+	0.0481514i	0.940011	−	0.341143i	$-0.110814\pi$
$829$	0.544119	+	1.38639i	0.0188980	+	0.0481514i	−0.921113	+	0.389295i	$0.872719\pi$
$830$	−2.49675	−	2.31665i	−0.0866636	−	0.0804120i
$831$	−9.71818	−	6.62574i	−0.337120	−	0.229844i
$832$	−4.76036			−0.165036
$833$	−17.7300	+	13.6445i	−0.614309	+	0.472754i
$834$	−10.1073			−0.349987
$835$	13.2143	+	9.00935i	0.457299	+	0.311781i
$836$	0.120903	+	0.112182i	0.00418153	+	0.00387990i
$837$	2.55481	+	6.50954i	0.0883071	+	0.225003i
$838$	22.0356	−	6.79707i	0.761206	−	0.234801i
$839$	2.02063	+	8.85296i	0.0697599	+	0.305638i	0.997756	−	0.0669511i	$-0.0213272\pi$
$839$	2.02063	+	8.85296i	0.0697599	+	0.305638i	−0.927996	+	0.372589i	$0.878470\pi$
$840$	3.35368	+	1.49784i	0.115713	+	0.0516804i
$841$	−8.26636	+	36.2173i	−0.285047	+	1.24887i
$842$	1.73701	+	23.1787i	0.0598612	+	0.798792i
$843$	17.6807	+	5.45376i	0.608954	+	0.187837i
$844$	−0.970869	+	12.9553i	−0.0334187	+	0.445941i
$845$	4.89992	−	12.4848i	0.168562	−	0.429490i
$846$	8.62652	−	4.15431i	0.296586	−	0.142828i
$847$	2.95432	+	28.4270i	0.101512	+	0.976764i
$848$	8.19537	+	3.94668i	0.281430	+	0.135530i
$849$	4.52808	−	4.20145i	0.155403	−	0.144193i
$850$	−9.71103	+	1.46370i	−0.333085	+	0.0502045i
$851$	−3.88536	+	6.72964i	−0.133188	+	0.230689i
$852$	1.42011	+	2.45971i	0.0486523	+	0.0842683i
$853$	−1.29908	−	1.62900i	−0.0444797	−	0.0557757i	0.759094	−	0.650981i	$-0.225642\pi$
$853$	−1.29908	−	1.62900i	−0.0444797	−	0.0557757i	−0.803574	+	0.595205i	$0.797071\pi$
$854$	23.7601	+	20.8074i	0.813052	+	0.712014i
$855$	0.321046	−	0.402579i	0.0109795	−	0.0137679i
$856$	10.4745	+	1.57878i	0.358011	+	0.0539615i
$857$	−34.0171	+	23.1925i	−1.16200	+	0.792239i	−0.981524	−	0.191340i	$-0.938717\pi$
$857$	−34.0171	+	23.1925i	−1.16200	+	0.792239i	−0.180477	+	0.983579i	$0.557764\pi$
$858$	1.74896	−	1.19242i	0.0597085	−	0.0407086i
$859$	4.23335	+	0.638075i	0.144440	+	0.0217708i	0.220864	−	0.975305i	$-0.429112\pi$
$859$	4.23335	+	0.638075i	0.144440	+	0.0217708i	−0.0764242	+	0.997075i	$0.524350\pi$
$860$	6.32725	−	7.93412i	0.215758	−	0.270551i
$861$	−14.0752	−	12.3261i	−0.479683	−	0.420073i
$862$	13.2283	+	16.5878i	0.450557	+	0.564981i
$863$	−18.5400	−	32.1122i	−0.631108	−	1.09311i	−0.987325	−	0.158709i	$-0.949267\pi$
$863$	−18.5400	−	32.1122i	−0.631108	−	1.09311i	0.356217	−	0.934403i	$-0.384066\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−15.7424	+	2.37278i	−0.535257	+	0.0806770i
$866$	−17.9148	+	16.6225i	−0.608771	+	0.564857i
$867$	6.11324	+	2.94398i	0.207616	+	0.0999828i
$868$	−1.91250	−	18.4025i	−0.0649146	−	0.624620i
$869$	−2.43630	+	1.17326i	−0.0826458	+	0.0398001i
$870$	−4.12504	+	10.5104i	−0.139852	+	0.356337i
$871$	−4.00712	+	53.4713i	−0.135776	+	1.81180i
$872$	−8.69415	−	2.68179i	−0.294421	−	0.0908169i
$873$	0.348544	+	4.65100i	0.0117964	+	0.157413i
$874$	0.0889384	−	0.389665i	0.00300839	−	0.0131806i
$875$	−27.0735	−	12.0917i	−0.915250	−	0.408774i
$876$	−0.384941	−	1.68654i	−0.0130060	−	0.0569829i
$877$	21.5057	−	6.63364i	0.726197	−	0.224002i	0.0904513	−	0.995901i	$-0.471169\pi$
$877$	21.5057	−	6.63364i	0.726197	−	0.224002i	0.635745	+	0.771899i	$0.280693\pi$
$878$	6.86712	+	17.4971i	0.231754	+	0.590500i
$879$	20.1334	+	18.6811i	0.679083	+	0.630097i
$880$	−0.510045	−	0.347743i	−0.0171936	−	0.0117224i
$881$	34.8300			1.17345			0.586726	−	0.809786i	$-0.300417\pi$
$881$	34.8300			1.17345			0.586726	+	0.809786i	$0.300417\pi$
$882$	0.121025	−	6.99895i	0.00407512	−	0.235667i
$883$	−37.2634			−1.25401			−0.627007	−	0.779013i	$-0.715720\pi$
$883$	−37.2634			−1.25401			−0.627007	+	0.779013i	$0.715720\pi$
$884$	12.5707	+	8.57058i	0.422799	+	0.288260i
$885$	−5.38638	−	4.99783i	−0.181061	−	0.168000i
$886$	−14.6848	−	37.4162i	−0.493345	−	1.25702i
$887$	−20.9336	+	6.45715i	−0.702880	+	0.216810i	−0.625537	−	0.780195i	$-0.715120\pi$
$887$	−20.9336	+	6.45715i	−0.702880	+	0.216810i	−0.0773433	+	0.997005i	$0.524644\pi$
$888$	1.60466	+	7.03047i	0.0538488	+	0.235927i
$889$	11.4003	−	15.1706i	0.382355	−	0.508807i
$890$	1.24395	−	5.45008i	0.0416972	−	0.182687i
$891$	−0.0332300	−	0.443423i	−0.00111325	−	0.0148552i
$892$	19.6479	+	6.06057i	0.657860	+	0.202923i
$893$	−0.265394	+	3.54143i	−0.00888107	+	0.118510i
$894$	5.32667	−	13.5721i	0.178150	−	0.453920i
$895$	4.57421	−	2.20282i	0.152899	−	0.0736322i
$896$	1.88693	−	1.85459i	0.0630380	−	0.0619574i
$897$	−4.62166	−	2.22568i	−0.154313	−	0.0743132i
$898$	2.06334	−	1.91450i	0.0688547	−	0.0638878i
$899$	56.2396	−	8.47676i	1.87570	−	0.282716i
$900$	1.53638	−	2.66108i	0.0512126	−	0.0887028i
$901$	−14.5360	−	25.1770i	−0.484263	−	0.838769i
$902$	1.96055	+	2.45845i	0.0652791	+	0.0818574i
$903$	−18.6375	−	5.16699i	−0.620216	−	0.171947i
$904$	−2.53374	+	3.17721i	−0.0842710	+	0.105672i
$905$	26.2827	+	3.96149i	0.873668	+	0.131684i
$906$	6.76551	−	4.61265i	0.224769	−	0.153245i
$907$	−4.21704	+	2.87513i	−0.140025	+	0.0954671i	−0.631306	−	0.775534i	$-0.717481\pi$
$907$	−4.21704	+	2.87513i	−0.140025	+	0.0954671i	0.491282	+	0.871001i	$0.336529\pi$
$908$	−21.5423	−	3.24698i	−0.714907	−	0.107755i
$909$	−6.49780	+	8.14799i	−0.215518	+	0.270252i
$910$	6.85317	+	16.0856i	0.227180	+	0.533233i
$911$	20.9380	+	26.2554i	0.693707	+	0.869881i	0.996536	−	0.0831639i	$-0.0265025\pi$
$911$	20.9380	+	26.2554i	0.693707	+	0.869881i	−0.302829	+	0.953045i	$0.597931\pi$
$912$	−0.185455	−	0.321218i	−0.00614104	−	0.0106366i
$913$	0.545478	−	0.944795i	0.0180527	−	0.0312681i
$914$	−31.7346	+	4.78323i	−1.04969	+	0.158215i
$915$	−12.1481	+	11.2718i	−0.401604	+	0.372634i
$916$	7.32322	+	3.52668i	0.241966	+	0.116525i
$917$	9.72000	+	6.22533i	0.320983	+	0.205579i
$918$	2.87955	−	1.38672i	0.0950394	−	0.0457686i
$919$	15.2800	−	38.9328i	0.504040	−	1.28427i	−0.421913	−	0.906636i	$-0.638641\pi$
$919$	15.2800	−	38.9328i	0.504040	−	1.28427i	0.925953	−	0.377638i	$-0.123263\pi$
$920$	−0.111793	+	1.49177i	−0.00368569	+	0.0491822i
$921$	−8.87736	−	2.73830i	−0.292519	−	0.0902302i
$922$	1.42029	+	18.9525i	0.0467748	+	0.624166i
$923$	−3.00859	+	13.1815i	−0.0990291	+	0.433875i
$924$	−0.228706	+	1.15403i	−0.00752387	+	0.0379649i
$925$	−4.93072	−	21.6029i	−0.162121	−	0.710299i
$926$	15.2605	−	4.70724i	0.501491	−	0.154689i
$927$	−4.00420	−	10.2025i	−0.131515	−	0.335095i
$928$	5.96205	+	5.53197i	0.195714	+	0.181596i
$929$	11.7966	+	8.04279i	0.387034	+	0.263875i	0.741168	−	0.671319i	$-0.234272\pi$
$929$	11.7966	+	8.04279i	0.387034	+	0.263875i	−0.354134	+	0.935195i	$0.615224\pi$
$930$	9.70797			0.318337
$931$	2.22575	+	1.33687i	0.0729459	+	0.0438141i
$932$	−28.6200			−0.937478
$933$	−19.1031	−	13.0242i	−0.625406	−	0.426395i
$934$	2.13022	+	1.97656i	0.0697030	+	0.0646749i
$935$	0.720804	+	1.83658i	0.0235728	+	0.0600625i
$936$	−4.54887	+	1.40314i	−0.148684	+	0.0458631i
$937$	8.00682	+	35.0802i	0.261571	+	1.14602i	0.919547	+	0.392980i	$0.128556\pi$
$937$	8.00682	+	35.0802i	0.261571	+	1.14602i	−0.657976	+	0.753039i	$0.728587\pi$
$938$	−19.2435	−	22.7563i	−0.628322	−	0.743020i
$939$	0.349740	−	1.53231i	0.0114133	−	0.0500051i
$940$	−0.993322	−	13.2550i	−0.0323986	−	0.432329i
$941$	−42.0360	−	12.9664i	−1.37033	−	0.422692i	−0.479708	−	0.877428i	$-0.659257\pi$
$941$	−42.0360	−	12.9664i	−1.37033	−	0.422692i	−0.890626	+	0.454736i	$0.849734\pi$
$942$	0.0812723	−	1.08450i	0.00264799	−	0.0353350i
$943$	2.78395	−	7.09338i	0.0906577	−	0.230992i
$944$	−4.76874	+	2.29650i	−0.155209	+	0.0747448i
$945$	3.64619	+	0.442780i	0.118610	+	0.0144036i
$946$	2.92861	+	1.41034i	0.0952173	+	0.0458542i
$947$	−20.9246	+	19.4152i	−0.679957	+	0.630908i	−0.942576	−	0.333992i	$-0.891604\pi$
$947$	−20.9246	+	19.4152i	−0.679957	+	0.630908i	0.262619	+	0.964900i	$0.415414\pi$
$948$	6.01324	−	0.906350i	0.195301	−	0.0294369i
$949$	4.11750	−	7.13171i	0.133660	−	0.231505i
$950$	0.569859	+	0.987024i	0.0184887	+	0.0320233i
$951$	20.7407	+	26.0080i	0.672563	+	0.843368i
$952$	−8.32185	+	1.50018i	−0.269713	+	0.0486211i
$953$	9.99958	−	12.5391i	0.323918	−	0.406181i	−0.593034	−	0.805177i	$-0.702070\pi$
$953$	9.99958	−	12.5391i	0.323918	−	0.406181i	0.916952	+	0.398997i	$0.130642\pi$
$954$	8.99457	+	1.35571i	0.291210	+	0.0438929i
$955$	18.5546	−	12.6503i	0.600413	−	0.409355i
$956$	−5.88443	+	4.01194i	−0.190316	+	0.129755i
$957$	−3.57616	−	0.539020i	−0.115601	−	0.0174240i
$958$	2.47041	−	3.09780i	0.0798153	−	0.100085i
$959$	2.52529	−	54.8052i	0.0815459	−	1.76975i
$960$	0.865562	+	1.08538i	0.0279359	+	0.0350305i
$961$	−8.95060	−	15.5029i	−0.288729	−	0.500094i
$962$	−17.1641	+	29.7291i	−0.553393	+	0.958506i
$963$	10.4745	−	1.57878i	0.337536	−	0.0508754i
$964$	15.8771	−	14.7318i	0.511365	−	0.474478i
$965$	8.17582	+	3.93727i	0.263189	+	0.126745i
$966$	2.69906	−	0.918329i	0.0868407	−	0.0295467i
$967$	−52.7064	+	25.3821i	−1.69492	+	0.816232i	−0.700165	+	0.713982i	$0.746890\pi$
$967$	−52.7064	+	25.3821i	−1.69492	+	0.816232i	−0.994759	+	0.102250i	$0.967396\pi$
$968$	−3.94651	+	10.0556i	−0.126846	+	0.323198i
$969$	−0.0885891	+	1.18214i	−0.00284589	+	0.0379758i
$970$	6.18721	+	1.90850i	0.198659	+	0.0612783i
$971$	−3.58320	−	47.8145i	−0.114990	−	1.53444i	−0.694511	−	0.719482i	$-0.744379\pi$
$971$	−3.58320	−	47.8145i	−0.114990	−	1.53444i	0.579521	−	0.814957i	$-0.303240\pi$
$972$	−0.222521	+	0.974928i	−0.00713736	+	0.0312708i
$973$	26.7303	−	0.768838i	0.856935	−	0.0246478i
$974$	6.44089	+	28.2194i	0.206380	+	0.904208i
$975$	13.9775	−	4.31150i	0.447640	−	0.138079i
$976$	4.36117	+	11.1121i	0.139598	+	0.355689i
$977$	−8.59910	−	7.97880i	−0.275110	−	0.255264i	0.530536	−	0.847663i	$-0.321991\pi$
$977$	−8.59910	−	7.97880i	−0.275110	−	0.255264i	−0.805645	+	0.592398i	$0.798181\pi$
$978$	1.85367	+	1.26381i	0.0592737	+	0.0404122i
$979$	1.79059			0.0572276
$980$	−8.98328	−	3.70617i	−0.286960	−	0.118389i
$981$	−9.09837			−0.290489
$982$	14.4633	+	9.86092i	0.461543	+	0.314675i
$983$	22.1432	+	20.5459i	0.706259	+	0.655313i	0.949180	−	0.314733i	$-0.101915\pi$
$983$	22.1432	+	20.5459i	0.706259	+	0.655313i	−0.242921	+	0.970046i	$0.578106\pi$
$984$	−2.58352	−	6.58270i	−0.0823596	−	0.209849i
$985$	31.0672	−	9.58296i	0.989883	−	0.305339i
$986$	−5.78425	−	25.3424i	−0.184208	−	0.807068i
$987$	−22.4982	+	11.6429i	−0.716125	+	0.370599i
$988$	0.392898	−	1.72140i	0.0124998	−	0.0547650i
$989$	−0.588656	−	7.85507i	−0.0187182	−	0.249777i
$990$	−0.589885	−	0.181955i	−0.0187478	−	0.00578292i
$991$	−1.03923	+	13.8676i	−0.0330123	+	0.440519i	0.956068	+	0.293144i	$0.0947015\pi$
$991$	−1.03923	+	13.8676i	−0.0330123	+	0.440519i	−0.989081	+	0.147375i	$0.952918\pi$
$992$	2.55481	−	6.50954i	0.0811152	−	0.206678i
$993$	20.9745	−	10.1008i	0.665605	−	0.320539i
$994$	−3.94282	−	6.39707i	−0.125059	−	0.202903i
$995$	−33.6508	−	16.2054i	−1.06680	−	0.513745i
$996$	−1.79849	+	1.66875i	−0.0569872	+	0.0528764i
$997$	25.8863	−	3.90173i	0.819827	−	0.123569i	0.274281	−	0.961650i	$-0.411560\pi$
$997$	25.8863	−	3.90173i	0.819827	−	0.123569i	0.545546	+	0.838081i	$0.316322\pi$
$998$	11.2784	−	19.5348i	0.357013	−	0.618364i
$999$	3.60564	+	6.24515i	0.114077	+	0.197588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.m.b.151.2	yes	24
3.2	odd	2		882.2.z.a.739.1		24
49.37	even	21	inner	294.2.m.b.37.2	✓	24
147.86	odd	42		882.2.z.a.37.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.m.b.37.2	✓	24	49.37	even	21	inner
294.2.m.b.151.2	yes	24	1.1	even	1	trivial
882.2.z.a.37.1		24	147.86	odd	42
882.2.z.a.739.1		24	3.2	odd	2

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.m (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.826239 + 0.563320i) q^{2} +(-0.733052 - 0.680173i) q^{3} +(0.365341 + 0.930874i) q^{4} +(1.32658 - 0.409195i) q^{5} +(-0.222521 - 0.974928i) q^{6} +(0.662652 + 2.56142i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(0.0747301 + 0.997204i) q^{9} +O(q^{10})\)	\(q+(0.826239 + 0.563320i) q^{2} +(-0.733052 - 0.680173i) q^{3} +(0.365341 + 0.930874i) q^{4} +(1.32658 - 0.409195i) q^{5} +(-0.222521 - 0.974928i) q^{6} +(0.662652 + 2.56142i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(0.0747301 + 0.997204i) q^{9} +(1.32658 + 0.409195i) q^{10} +(-0.0332300 + 0.443423i) q^{11} +(0.365341 - 0.930874i) q^{12} +(4.28893 - 2.06544i) q^{13} +(-0.895392 + 2.48963i) q^{14} +(-1.25077 - 0.602340i) q^{15} +(-0.733052 + 0.680173i) q^{16} +(3.16037 - 0.476348i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-0.185455 - 0.321218i) q^{19} +(0.865562 + 1.08538i) q^{20} +(1.25645 - 2.32837i) q^{21} +(-0.277245 + 0.347654i) q^{22} +(1.06554 + 0.160605i) q^{23} +(0.826239 - 0.563320i) q^{24} +(-2.53883 + 1.73094i) q^{25} +(4.70719 + 0.709494i) q^{26} +(0.623490 - 0.781831i) q^{27} +(-2.14227 + 1.55264i) q^{28} +(-5.07096 - 6.35878i) q^{29} +(-0.694126 - 1.20226i) q^{30} +(-3.49647 + 6.05606i) q^{31} +(-0.988831 + 0.149042i) q^{32} +(0.325964 - 0.302450i) q^{33} +(2.87955 + 1.38672i) q^{34} +(1.92718 + 3.12677i) q^{35} +(-0.900969 + 0.433884i) q^{36} +(-2.63457 + 6.71279i) q^{37} +(0.0277182 - 0.369874i) q^{38} +(-4.54887 - 1.40314i) q^{39} +(0.103744 + 1.38437i) q^{40} +(1.57356 - 6.89423i) q^{41} +(2.34975 - 1.21601i) q^{42} +(-1.62663 - 7.12672i) q^{43} +(-0.424911 + 0.131068i) q^{44} +(0.507186 + 1.29229i) q^{45} +(0.789921 + 0.732940i) q^{46} +(-7.91100 - 5.39363i) q^{47} +1.00000 q^{48} +(-6.12178 + 3.39467i) q^{49} -3.07275 q^{50} +(-2.64071 - 1.80041i) q^{51} +(3.48959 + 3.23787i) q^{52} +(-3.32320 - 8.46739i) q^{53} +(0.955573 - 0.294755i) q^{54} +(0.137364 + 0.601833i) q^{55} +(-2.64466 + 0.0760677i) q^{56} +(-0.0825354 + 0.361611i) q^{57} +(-0.607794 - 8.11044i) q^{58} +(5.05775 + 1.56011i) q^{59} +(0.103744 - 1.38437i) q^{60} +(4.36117 - 11.1121i) q^{61} +(-6.30042 + 3.03412i) q^{62} +(-2.50474 + 0.852215i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(4.84443 - 4.49498i) q^{65} +(0.439700 - 0.0662741i) q^{66} +(-5.63206 + 9.75501i) q^{67} +(1.59803 + 2.76787i) q^{68} +(-0.671859 - 0.842485i) q^{69} +(-0.169062 + 3.66908i) q^{70} +(-1.77085 + 2.22058i) q^{71} +(-0.988831 - 0.149042i) q^{72} +(1.42932 - 0.974494i) q^{73} +(-5.95823 + 4.06226i) q^{74} +(3.03843 + 0.457970i) q^{75} +(0.231259 - 0.289990i) q^{76} +(-1.15781 + 0.208719i) q^{77} +(-2.96803 - 3.72180i) q^{78} +(3.04058 + 5.26644i) q^{79} +(-0.694126 + 1.20226i) q^{80} +(-0.988831 + 0.149042i) q^{81} +(5.18380 - 4.80986i) q^{82} +(-2.21046 - 1.06450i) q^{83} +(2.62646 + 0.318948i) q^{84} +(3.99755 - 1.92512i) q^{85} +(2.67064 - 6.80468i) q^{86} +(-0.607794 + 8.11044i) q^{87} +(-0.424911 - 0.131068i) q^{88} +(-0.300925 - 4.01556i) q^{89} +(-0.308915 + 1.35345i) q^{90} +(8.13254 + 9.61711i) q^{91} +(0.239784 + 1.05056i) q^{92} +(6.68226 - 2.06121i) q^{93} +(-3.49804 - 8.91285i) q^{94} +(-0.377462 - 0.350233i) q^{95} +(0.826239 + 0.563320i) q^{96} +4.66404 q^{97} +(-6.97034 - 0.643719i) q^{98} -0.444667 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9} + q^{10} + 8 q^{11} + 2 q^{12} - 2 q^{13} + 5 q^{15} + 2 q^{16} + 9 q^{17} - 12 q^{18} - 4 q^{19} + 5 q^{20} + 14 q^{21} + 5 q^{22} - 38 q^{23} + 2 q^{24} - 19 q^{25} - 20 q^{26} - 4 q^{27} - 14 q^{28} - 14 q^{29} + 8 q^{30} + 4 q^{31} + 2 q^{32} - 6 q^{33} + 17 q^{34} + 42 q^{35} - 4 q^{36} + 7 q^{37} - 18 q^{38} - 6 q^{39} - 13 q^{40} + 2 q^{41} - 7 q^{42} + 4 q^{43} - 6 q^{44} - 13 q^{45} + 11 q^{46} - 8 q^{47} + 24 q^{48} - 42 q^{49} - 4 q^{50} - 40 q^{51} + 15 q^{52} - 10 q^{53} + 2 q^{54} + 33 q^{55} - 7 q^{56} + q^{57} - 28 q^{58} + 14 q^{59} - 13 q^{60} + 7 q^{61} - 8 q^{62} - 14 q^{63} - 4 q^{64} + 23 q^{65} + 8 q^{66} + 23 q^{67} + 9 q^{68} + 13 q^{69} + 28 q^{70} + 36 q^{71} + 2 q^{72} + 15 q^{73} - 14 q^{74} + 9 q^{75} + q^{76} - 28 q^{77} + 19 q^{78} + 38 q^{79} + 8 q^{80} + 2 q^{81} - q^{82} + 27 q^{83} - 47 q^{85} + 26 q^{86} - 28 q^{87} - 6 q^{88} - 121 q^{89} - 2 q^{90} + 21 q^{91} - q^{92} + 46 q^{93} - q^{94} + 44 q^{95} + 2 q^{96} + 14 q^{97} - 21 q^{98} - 44 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9 + q^10 + 8 * q^11 + 2 * q^12 - 2 * q^13 + 5 * q^15 + 2 * q^16 + 9 * q^17 - 12 * q^18 - 4 * q^19 + 5 * q^20 + 14 * q^21 + 5 * q^22 - 38 * q^23 + 2 * q^24 - 19 * q^25 - 20 * q^26 - 4 * q^27 - 14 * q^28 - 14 * q^29 + 8 * q^30 + 4 * q^31 + 2 * q^32 - 6 * q^33 + 17 * q^34 + 42 * q^35 - 4 * q^36 + 7 * q^37 - 18 * q^38 - 6 * q^39 - 13 * q^40 + 2 * q^41 - 7 * q^42 + 4 * q^43 - 6 * q^44 - 13 * q^45 + 11 * q^46 - 8 * q^47 + 24 * q^48 - 42 * q^49 - 4 * q^50 - 40 * q^51 + 15 * q^52 - 10 * q^53 + 2 * q^54 + 33 * q^55 - 7 * q^56 + q^57 - 28 * q^58 + 14 * q^59 - 13 * q^60 + 7 * q^61 - 8 * q^62 - 14 * q^63 - 4 * q^64 + 23 * q^65 + 8 * q^66 + 23 * q^67 + 9 * q^68 + 13 * q^69 + 28 * q^70 + 36 * q^71 + 2 * q^72 + 15 * q^73 - 14 * q^74 + 9 * q^75 + q^76 - 28 * q^77 + 19 * q^78 + 38 * q^79 + 8 * q^80 + 2 * q^81 - q^82 + 27 * q^83 - 47 * q^85 + 26 * q^86 - 28 * q^87 - 6 * q^88 - 121 * q^89 - 2 * q^90 + 21 * q^91 - q^92 + 46 * q^93 - q^94 + 44 * q^95 + 2 * q^96 + 14 * q^97 - 21 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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