LMFDB - Embedded newform 294.2.m.b.37.2

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			37.2
Character	$\chi$	$=$	294.37
Dual form			294.2.m.b.151.2

$q$-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 $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{16}{21}\right)$

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	0.576825	−	0.816867i	$-0.304291\pi$
$5$	1.32658	+	0.409195i	0.593263	+	0.182997i	0.0164377	+	0.999865i	$0.494767\pi$
$6$	−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	0.989951	−	0.141411i	$-0.0451638\pi$
$11$	−0.0332300	−	0.443423i	−0.0100192	−	0.133697i	−0.999970	+	0.00771341i	$0.997545\pi$
$12$	0.365341	+	0.930874i	0.105465	+	0.268720i
$13$	4.28893	+	2.06544i	1.18954	+	0.572850i	0.920676	−	0.390329i	$-0.127639\pi$
$13$	4.28893	+	2.06544i	1.18954	+	0.572850i	0.268861	+	0.963179i	$0.413353\pi$
$14$	−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	0.520643	−	0.853774i	$-0.325692\pi$
$17$	3.16037	+	0.476348i	0.766501	+	0.115531i	0.245858	+	0.969306i	$0.420930\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−0.185455	+	0.321218i	−0.0425464	+	0.0736925i	−0.886514	−	0.462701i	$-0.846880\pi$
$19$	−0.185455	+	0.321218i	−0.0425464	+	0.0736925i	0.843968	+	0.536393i	$0.180214\pi$
$20$	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	−0.0370081	−	0.999315i	$-0.511783\pi$
$23$	1.06554	−	0.160605i	0.222181	−	0.0334884i	0.259189	+	0.965827i	$0.416545\pi$
$24$	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	0.0417071	+	0.999130i	$0.486720\pi$
$29$	−5.07096	+	6.35878i	−0.941653	+	1.18080i	−0.983360	+	0.181666i	$0.941851\pi$
$30$	−0.694126	+	1.20226i	−0.126730	+	0.219502i
$31$	−3.49647	−	6.05606i	−0.627985	−	1.08770i	−0.987956	−	0.154738i	$-0.950547\pi$
$31$	−3.49647	−	6.05606i	−0.627985	−	1.08770i	0.359971	−	0.932963i	$-0.382787\pi$
$32$	−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	−0.966265	−	0.257550i	$-0.917085\pi$
$37$	−2.63457	−	6.71279i	−0.433121	−	1.10358i	0.533143	−	0.846025i	$-0.321011\pi$
$38$	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	0.935688	+	0.352830i	$0.114780\pi$
$41$	1.57356	+	6.89423i	0.245749	+	1.07670i	−0.689938	+	0.723868i	$0.742362\pi$
$42$	2.34975	+	1.21601i	0.362574	+	0.187634i
$43$	−1.62663	+	7.12672i	−0.248058	+	1.08681i	0.685411	+	0.728157i	$0.259623\pi$
$43$	−1.62663	+	7.12672i	−0.248058	+	1.08681i	−0.933469	+	0.358658i	$0.883234\pi$
$44$	−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	−0.980192	−	0.198049i	$-0.936540\pi$
$47$	−7.91100	+	5.39363i	−1.15394	+	0.786742i	−0.173746	+	0.984791i	$0.555587\pi$
$48$	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	0.498627	+	0.866816i	$0.333838\pi$
$53$	−3.32320	+	8.46739i	−0.456477	+	1.16308i	−0.955105	+	0.296269i	$0.904258\pi$
$54$	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	0.0525236	−	0.998620i	$-0.483274\pi$
$59$	5.05775	−	1.56011i	0.658463	−	0.203109i	0.605939	+	0.795511i	$0.292797\pi$
$60$	0.103744	+	1.38437i	0.0133933	+	0.178722i
$61$	4.36117	+	11.1121i	0.558391	+	1.42276i	0.879584	+	0.475743i	$0.157821\pi$
$61$	4.36117	+	11.1121i	0.558391	+	1.42276i	−0.321193	+	0.947014i	$0.604084\pi$
$62$	−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	−0.972463	−	0.233057i	$-0.925127\pi$
$67$	−5.63206	−	9.75501i	−0.688065	−	1.19176i	0.284398	−	0.958706i	$-0.408206\pi$
$68$	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	0.665567	−	0.746338i	$-0.268190\pi$
$71$	−1.77085	−	2.22058i	−0.210162	−	0.263534i	−0.875729	+	0.482804i	$0.839618\pi$
$72$	−0.988831	+	0.149042i	−0.116535	+	0.0175648i
$73$	1.42932	+	0.974494i	0.167289	+	0.114056i	0.644071	−	0.764966i	$-0.277244\pi$
$73$	1.42932	+	0.974494i	0.167289	+	0.114056i	−0.476781	+	0.879022i	$0.658197\pi$
$74$	−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	−0.642729	−	0.766094i	$-0.722198\pi$
$79$	3.04058	−	5.26644i	0.342092	−	0.592521i	0.984821	+	0.173573i	$0.0555312\pi$
$80$	−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	−0.551247	−	0.834342i	$-0.685848\pi$
$83$	−2.21046	+	1.06450i	−0.242629	+	0.116844i	0.308618	+	0.951186i	$0.400134\pi$
$84$	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	0.958280	+	0.285833i	$0.0922701\pi$
$89$	−0.300925	+	4.01556i	−0.0318979	+	0.425648i	−0.990178	+	0.139816i	$0.955349\pi$
$90$	−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	−0.201516	−	0.979485i	$-0.564587\pi$
$101$	7.63962	−	7.08853i	0.760171	−	0.705335i	0.961687	+	0.274150i	$0.0883964\pi$
$102$	−1.16765	+	2.97513i	−0.115615	+	0.294582i
$103$	−10.4732	−	3.23056i	−1.03196	−	0.318317i	−0.267888	−	0.963450i	$-0.586326\pi$
$103$	−10.4732	−	3.23056i	−1.03196	−	0.318317i	−0.764070	+	0.645133i	$0.776802\pi$
$104$	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	0.818306	+	0.574782i	$0.194913\pi$
$107$	−0.791602	+	10.5632i	−0.0765270	+	1.02118i	−0.894833	+	0.446400i	$0.852706\pi$
$108$	0.955573	−	0.294755i	0.0919500	−	0.0283628i
$109$	−0.679922	−	9.07293i	−0.0651247	−	0.869029i	−0.930122	−	0.367252i	$-0.880299\pi$
$109$	−0.679922	−	9.07293i	−0.0651247	−	0.869029i	0.864997	−	0.501777i	$-0.167320\pi$
$110$	−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	−0.253668	−	0.967291i	$-0.581637\pi$
$113$	3.66136	−	1.76322i	0.344432	−	0.165870i	0.598100	+	0.801422i	$0.295923\pi$
$114$	−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	−0.939600	−	0.342275i	$-0.888803\pi$
$127$	−4.47200	+	5.60771i	−0.396826	+	0.497604i	0.542774	+	0.839879i	$0.317374\pi$
$128$	−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	0.807415	−	0.589984i	$-0.200866\pi$
$131$	3.19810	+	2.96740i	0.279419	+	0.259263i	−0.527996	+	0.849247i	$0.677056\pi$
$132$	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	−0.983239	−	0.182323i	$-0.941638\pi$
$137$	−19.8152	+	6.11217i	−1.69292	+	0.522198i	−0.709684	+	0.704520i	$0.751162\pi$
$138$	−0.0805276	+	1.07457i	−0.00685496	+	0.0914731i
$139$	2.24908	+	9.85388i	0.190765	+	0.835795i	0.976204	+	0.216856i	$0.0695801\pi$
$139$	2.24908	+	9.85388i	0.190765	+	0.835795i	−0.785439	+	0.618939i	$0.787563\pi$
$140$	−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	0.0416192	−	0.999134i	$-0.486748\pi$
$149$	12.0465	−	8.21320i	0.986892	−	0.672851i	0.945272	+	0.326282i	$0.105796\pi$
$150$	2.25249	−	2.09000i	0.183915	−	0.170648i
$151$	2.99153	−	7.62229i	0.243447	−	0.620293i	−0.755964	−	0.654614i	$-0.772831\pi$
$151$	2.99153	−	7.62229i	0.243447	−	0.620293i	0.999411	+	0.0343202i	$0.0109266\pi$
$152$	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	−0.253008	−	0.967464i	$-0.581420\pi$
$157$	1.03923	−	0.320559i	0.0829394	−	0.0255834i	0.335947	+	0.941881i	$0.390944\pi$
$158$	−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	0.613135	−	0.789978i	$-0.289908\pi$
$163$	−1.64460	−	1.52597i	−0.128815	−	0.119523i	−0.741950	+	0.670455i	$0.766099\pi$
$164$	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	−0.421952	−	0.906618i	$-0.638655\pi$
$167$	7.18289	−	9.00705i	0.555828	−	0.696987i	0.977780	+	0.209631i	$0.0672264\pi$
$168$	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	−0.565205	−	0.824950i	$-0.691203\pi$
$173$	−11.3397	+	1.70919i	−0.862142	+	0.129947i	−0.296937	+	0.954897i	$0.595965\pi$
$174$	−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	0.282790	−	0.959182i	$-0.408740\pi$
$179$	3.61626	+	0.545063i	0.270292	+	0.0407400i	−0.0124977	+	0.999922i	$0.503978\pi$
$180$	−1.01766	−	0.944252i	−0.0758520	−	0.0703804i
$181$	17.2500	−	8.30718i	1.28218	−	0.617468i	0.336234	−	0.941778i	$-0.390847\pi$
$181$	17.2500	−	8.30718i	1.28218	−	0.617468i	0.945951	+	0.324311i	$0.105132\pi$
$182$	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	0.798241	−	0.602338i	$-0.205764\pi$
$191$	15.4576	+	4.76803i	1.11847	+	0.345002i	0.320229	+	0.947340i	$0.396240\pi$
$192$	0.365341	−	0.930874i	0.0263662	−	0.0671800i
$193$	4.79168	−	4.44603i	0.344912	−	0.320032i	−0.488626	−	0.872493i	$-0.662502\pi$
$193$	4.79168	−	4.44603i	0.344912	−	0.320032i	0.833539	+	0.552461i	$0.186311\pi$
$194$	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	−0.494220	+	0.869337i	$0.664546\pi$
$199$	−19.7221	+	18.2994i	−1.39806	+	1.29721i	−0.903839	+	0.427872i	$0.859263\pi$
$200$	−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	0.0148238	−	0.999890i	$-0.495281\pi$
$211$	11.7051	−	5.63688i	0.805812	−	0.388059i	0.790988	+	0.611832i	$0.209567\pi$
$212$	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	0.996292	+	0.0860387i	$0.0274209\pi$
$223$	12.8198	+	16.0755i	0.858478	+	1.07650i	−0.137814	+	0.990458i	$0.544008\pi$
$224$	−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	−0.959799	−	0.280687i	$-0.909438\pi$
$227$	−10.8928	−	18.8669i	−0.722982	−	1.25224i	0.236818	−	0.971554i	$-0.423896\pi$
$228$	−0.366768	−	0.0552814i	−0.0242898	−	0.00366110i
$229$	5.95837	+	5.52856i	0.393740	+	0.365337i	0.852055	−	0.523453i	$-0.175356\pi$
$229$	5.95837	+	5.52856i	0.393740	+	0.365337i	−0.458315	+	0.888790i	$0.651547\pi$
$230$	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	−0.666484	−	0.745519i	$-0.732201\pi$
$233$	−10.4561	−	26.6416i	−0.684999	−	1.74535i	−0.0185148	−	0.999829i	$-0.505894\pi$
$234$	−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	−0.897457	−	0.441103i	$-0.854587\pi$
$239$	1.58478	−	6.94339i	0.102511	−	0.449131i	0.999968	−	0.00802792i	$-0.00255539\pi$
$240$	1.32658	+	0.409195i	0.0856302	+	0.0264134i
$241$	−7.91286	+	20.1616i	−0.509712	+	1.29873i	0.412118	+	0.911131i	$0.364789\pi$
$241$	−7.91286	+	20.1616i	−0.509712	+	1.29873i	−0.921830	+	0.387595i	$0.873306\pi$
$242$	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	−0.990305	−	0.138909i	$-0.955641\pi$
$251$	−0.598879	+	2.62386i	−0.0378009	+	0.165617i	0.952504	+	0.304525i	$0.0984977\pi$
$252$	−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	0.992306	−	0.123810i	$-0.0395114\pi$
$257$	2.89655	+	7.38029i	0.180682	+	0.460370i	−0.811624	+	0.584180i	$0.801416\pi$
$258$	−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	0.658637	−	0.752460i	$-0.271133\pi$
$263$	−5.22733	−	9.05401i	−0.322331	−	0.558294i	−0.980969	+	0.194166i	$0.937800\pi$
$264$	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	0.0962715	−	0.995355i	$-0.469308\pi$
$269$	−13.0407	−	8.89101i	−0.795106	−	0.542094i	−0.891378	+	0.453261i	$0.850261\pi$
$270$	1.14703	+	0.782031i	0.0698059	+	0.0475929i
$271$	−31.4031	+	4.73325i	−1.90760	+	0.287525i	−0.993120	−	0.117102i	$-0.962640\pi$
$271$	−31.4031	+	4.73325i	−1.90760	+	0.287525i	−0.914482	+	0.404626i	$0.867402\pi$
$272$	−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	0.488834	−	0.872377i	$-0.337422\pi$
$277$	11.6306	+	1.75303i	0.698814	+	0.105329i	0.209979	+	0.977706i	$0.432660\pi$
$278$	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	−0.135411	−	0.990789i	$-0.543236\pi$
$281$	−16.6703	−	8.02801i	−0.994469	−	0.478911i	−0.859058	+	0.511878i	$0.828950\pi$
$282$	−3.49804	−	8.91285i	−0.208305	−	0.530753i
$283$	−0.461610	−	6.15976i	−0.0274399	−	0.366160i	−0.993974	−	0.109620i	$-0.965037\pi$
$283$	−0.461610	−	6.15976i	−0.0274399	−	0.366160i	0.966534	−	0.256540i	$-0.0825824\pi$
$284$	−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	0.657212	−	0.753706i	$-0.271736\pi$
$307$	8.37009	+	4.03082i	0.477706	+	0.230051i	−0.179506	+	0.983757i	$0.557450\pi$
$308$	−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	0.760753	−	0.649041i	$-0.224830\pi$
$311$	22.8623	+	3.44593i	1.29640	+	0.195401i	0.535647	+	0.844442i	$0.320068\pi$
$312$	2.38018	+	4.12259i	0.134751	+	0.233396i
$313$	0.785860	−	1.36115i	0.0444194	−	0.0769367i	−0.842961	−	0.537975i	$-0.819190\pi$
$313$	0.785860	−	1.36115i	0.0444194	−	0.0769367i	0.887380	+	0.461038i	$0.152523\pi$
$314$	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	−0.976930	−	0.213562i	$-0.931494\pi$
$317$	−32.8940	+	4.95797i	−1.84751	+	0.278467i	−0.870579	+	0.492029i	$0.836255\pi$
$318$	−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	−0.949164	−	0.314781i	$-0.898069\pi$
$331$	−8.50511	−	21.6707i	−0.467483	−	1.19113i	0.481681	−	0.876347i	$-0.340026\pi$
$332$	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	−0.987333	−	0.158659i	$-0.949283\pi$
$337$	−0.531219	+	2.32742i	−0.0289373	+	0.126783i	0.958396	+	0.285441i	$0.0921402\pi$
$338$	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	0.479865	+	0.877342i	$0.340685\pi$
$347$	−8.72989	+	22.2434i	−0.468645	+	1.19409i	−0.948510	+	0.316746i	$0.897410\pi$
$348$	−7.77185	−	2.39730i	−0.416615	−	0.128509i
$349$	1.94577	−	8.52500i	0.104155	−	0.456333i	−0.895775	−	0.444507i	$-0.853379\pi$
$349$	1.94577	−	8.52500i	0.104155	−	0.456333i	0.999930	−	0.0118251i	$-0.00376415\pi$
$350$	−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	−0.700489	−	0.713664i	$-0.747035\pi$
$353$	−16.4818	+	5.08397i	−0.877238	+	0.270592i	−0.176750	+	0.984256i	$0.556558\pi$
$354$	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	0.514766	−	0.857331i	$-0.327879\pi$
$359$	−5.71637	−	5.30402i	−0.301698	−	0.279935i	−0.816465	+	0.577395i	$0.804069\pi$
$360$	−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	0.985297	+	0.170850i	$0.0546514\pi$
$367$	28.8184	+	19.6480i	1.50431	+	1.02562i	0.519009	+	0.854769i	$0.326301\pi$
$368$	−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	0.162352	−	0.986733i	$-0.448092\pi$
$373$	18.0716	−	31.3009i	0.935712	−	1.62070i	0.773360	−	0.633967i	$-0.218575\pi$
$374$	−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	0.227754	−	0.973719i	$-0.426862\pi$
$379$	−7.62221	−	3.67066i	−0.391527	−	0.188549i	−0.619281	+	0.785169i	$0.712576\pi$
$380$	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	−0.823837	−	0.566826i	$-0.808171\pi$
$383$	1.47325	−	19.6591i	0.0752795	−	1.00453i	0.899117	−	0.437709i	$-0.144210\pi$
$384$	−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	−0.145806	−	0.989313i	$-0.546578\pi$
$389$	16.3671	−	15.1864i	0.829844	−	0.769983i	0.975651	+	0.219330i	$0.0703872\pi$
$390$	−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	0.740432	−	0.672131i	$-0.234621\pi$
$397$	19.3985	+	5.98364i	0.973582	+	0.300310i	0.233149	+	0.972441i	$0.425097\pi$
$398$	−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	0.977999	+	0.208609i	$0.0668935\pi$
$401$	−0.403865	+	5.38921i	−0.0201681	+	0.269124i	−0.998167	+	0.0605155i	$0.980726\pi$
$402$	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	0.199904	−	0.979816i	$-0.435937\pi$
$409$	2.06527	+	0.311289i	0.102121	+	0.0153923i	−0.0977829	+	0.995208i	$0.531175\pi$
$410$	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	0.997200	−	0.0747802i	$-0.0238255\pi$
$419$	14.3777	+	18.0291i	0.702397	+	0.880778i	−0.294803	+	0.955558i	$0.595254\pi$
$420$	3.61471	+	0.651624i	0.176380	+	0.0317960i
$421$	14.4922	−	18.1727i	0.706308	−	0.885683i	−0.291169	−	0.956672i	$-0.594044\pi$
$421$	14.4922	−	18.1727i	0.706308	−	0.885683i	0.997477	+	0.0709892i	$0.0226156\pi$
$422$	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	0.234912	−	0.972017i	$-0.424520\pi$
$431$	20.2739	−	6.25368i	0.976562	−	0.301229i	0.741650	+	0.670787i	$0.234044\pi$
$432$	0.0747301	−	0.997204i	0.00359545	−	0.0479780i
$433$	−5.43812	−	23.8260i	−0.261339	−	1.14500i	−0.919800	−	0.392387i	$-0.871649\pi$
$433$	−5.43812	−	23.8260i	−0.261339	−	1.14500i	0.658461	−	0.752615i	$-0.271208\pi$
$434$	−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	−0.132858	−	0.991135i	$-0.542416\pi$
$439$	15.5304	−	10.5884i	0.741224	−	0.505358i	0.874083	+	0.485777i	$0.161463\pi$
$440$	−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	−0.621589	+	0.783343i	$0.713513\pi$
$443$	−33.2104	+	22.6425i	−1.57788	+	1.07578i	−0.956286	+	0.292434i	$0.905535\pi$
$444$	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	0.987555	−	0.157277i	$-0.0502716\pi$
$449$	0.626337	+	2.74416i	0.0295587	+	0.129505i	−0.957996	+	0.286782i	$0.907414\pi$
$450$	−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	−0.999657	−	0.0262077i	$-0.991657\pi$
$457$	−23.5259	−	21.8288i	−1.10050	−	1.02111i	−0.100839	−	0.994903i	$-0.532153\pi$
$458$	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	−0.425137	−	0.905129i	$-0.639774\pi$
$461$	11.8498	−	14.8592i	0.551900	−	0.692061i	0.977037	+	0.213068i	$0.0683456\pi$
$462$	0.461124	−	1.08234i	0.0214534	−	0.0503551i
$463$	9.95712	+	12.4858i	0.462747	+	0.580266i	0.957378	−	0.288837i	$-0.0932685\pi$
$463$	9.95712	+	12.4858i	0.462747	+	0.580266i	−0.494632	+	0.869103i	$0.664697\pi$
$464$	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	−0.0822200	−	0.996614i	$-0.526201\pi$
$467$	2.87351	−	0.433111i	0.132970	−	0.0200420i	0.215190	+	0.976572i	$0.430963\pi$
$468$	−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	0.999874	+	0.0158431i	$0.00504321\pi$
$479$	0.296098	+	3.95115i	0.0135291	+	0.180533i	−0.986345	+	0.164690i	$0.947338\pi$
$480$	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	−0.0327317	−	0.999464i	$-0.510421\pi$
$487$	21.2183	−	19.6877i	0.961492	−	0.892134i	0.994223	+	0.107330i	$0.0342302\pi$
$488$	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	0.823038	+	0.567986i	$0.192277\pi$
$499$	−1.68568	+	22.4938i	−0.0754613	+	1.00696i	−0.898499	+	0.438975i	$0.855342\pi$
$500$	−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	0.0297690	−	0.999557i	$-0.490523\pi$
$503$	−16.4430	−	7.91851i	−0.733155	−	0.353069i	−0.762924	+	0.646488i	$0.776237\pi$
$504$	−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	−0.107352	−	0.994221i	$-0.534237\pi$
$509$	18.2145	−	31.5485i	0.807345	−	1.39836i	0.914697	−	0.404141i	$-0.132429\pi$
$510$	−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	−0.929550	−	0.368696i	$-0.879804\pi$
$521$	−17.8968	−	30.9982i	−0.784075	−	1.35806i	0.145475	−	0.989362i	$-0.453529\pi$
$522$	8.04234	+	1.21219i	0.352004	+	0.0530560i
$523$	−24.1756	−	22.4317i	−1.05713	−	0.980869i	−0.0572782	−	0.998358i	$-0.518242\pi$
$523$	−24.1756	−	22.4317i	−1.05713	−	0.980869i	−0.999847	+	0.0174894i	$0.994433\pi$
$524$	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	0.346730	−	0.937965i	$-0.387292\pi$
$541$	31.3195	−	21.3533i	1.34653	−	0.918050i	0.999802	+	0.0199155i	$0.00633971\pi$
$542$	−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	0.995251	+	0.0973399i	$0.0310334\pi$
$547$	3.29292	+	14.4272i	0.140795	+	0.616863i	−0.854456	+	0.519524i	$0.826109\pi$
$548$	−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	0.917908	−	0.396793i	$-0.129877\pi$
$557$	2.72168	+	4.71409i	0.115321	+	0.199743i	−0.802587	+	0.596535i	$0.796544\pi$
$558$	−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	0.943506	+	0.331355i	$0.107506\pi$
$563$	37.8849	+	25.8295i	1.59666	+	1.08858i	0.653152	+	0.757227i	$0.273446\pi$
$564$	−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	0.0637783	−	0.997964i	$-0.479685\pi$
$569$	21.3765	−	37.0253i	0.896151	−	1.55218i	0.832373	−	0.554216i	$-0.186982\pi$
$570$	−0.257459	−	0.445932i	−0.0107838	−	0.0186780i
$571$	22.7952	+	3.43583i	0.953950	+	0.143785i	0.607532	−	0.794295i	$-0.292160\pi$
$571$	22.7952	+	3.43583i	0.953950	+	0.143785i	0.346418	+	0.938080i	$0.387398\pi$
$572$	−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	0.897006	+	0.442019i	$0.145738\pi$
$577$	1.82314	+	24.3281i	0.0758984	+	1.01279i	−0.821107	+	0.570774i	$0.806643\pi$
$578$	−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	0.000199312	−	1.00000i	$-0.499937\pi$
$593$	−13.7089	−	4.22863i	−0.562956	−	0.173649i	−0.563155	+	0.826351i	$0.690413\pi$
$594$	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	−0.992048	−	0.125862i	$-0.959830\pi$
$599$	−0.730298	−	9.74515i	−0.0298392	−	0.398176i	0.962209	−	0.272314i	$-0.0877889\pi$
$600$	−1.12260	−	2.86035i	−0.0458301	−	0.116773i
$601$	8.95344	+	4.31175i	0.365218	+	0.175880i	0.607488	−	0.794329i	$-0.292177\pi$
$601$	8.95344	+	4.31175i	0.365218	+	0.175880i	−0.242269	+	0.970209i	$0.577892\pi$
$602$	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	0.285254	+	0.958452i	$0.407922\pi$
$607$	−16.9361	+	29.3343i	−0.687417	+	1.19064i	−0.972671	+	0.232189i	$0.925411\pi$
$608$	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	0.742390	−	0.669968i	$-0.233692\pi$
$613$	9.65496	+	6.58264i	0.389960	+	0.265870i	−0.352430	+	0.935838i	$0.614645\pi$
$614$	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	0.137960	+	0.990438i	$0.455945\pi$
$617$	−21.3208	+	26.7355i	−0.858344	+	1.07633i	−0.996304	+	0.0858920i	$0.972626\pi$
$618$	5.48008	−	9.49178i	0.220441	−	0.381815i
$619$	2.98334	+	5.16729i	0.119910	+	0.207691i	0.919732	−	0.392547i	$-0.128406\pi$
$619$	2.98334	+	5.16729i	0.119910	+	0.207691i	−0.799822	+	0.600238i	$0.795073\pi$
$620$	−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	−0.376994	−	0.926216i	$-0.623042\pi$
$631$	9.15703	−	40.1196i	0.364536	−	1.59714i	0.741530	−	0.670920i	$-0.234101\pi$
$632$	−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	0.607761	+	0.794120i	$0.292068\pi$
$641$	−9.56761	+	24.3779i	−0.377898	+	0.962868i	−0.985659	+	0.168748i	$0.946027\pi$
$642$	−10.1222	−	3.12229i	−0.399491	−	0.123227i
$643$	−0.995152	+	4.36005i	−0.0392450	+	0.171943i	−0.990752	−	0.135682i	$-0.956677\pi$
$643$	−0.995152	+	4.36005i	−0.0392450	+	0.171943i	0.951507	+	0.307626i	$0.0995345\pi$
$644$	−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	0.0287597	−	0.999586i	$-0.490844\pi$
$647$	15.6588	−	4.83009i	0.615609	−	0.189890i	0.586849	+	0.809696i	$0.300368\pi$
$648$	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	0.934520	−	0.355911i	$-0.115830\pi$
$653$	16.5957	+	15.3986i	0.649440	+	0.602592i	−0.285080	+	0.958504i	$0.592020\pi$
$654$	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	0.928293	−	0.371849i	$-0.121276\pi$
$659$	9.22107	+	11.5629i	0.359202	+	0.450425i	−0.569091	+	0.822275i	$0.692705\pi$
$660$	0.610415	−	0.0920053i	0.0237604	−	0.00358130i
$661$	−22.5030	−	15.3423i	−0.875265	−	0.596745i	0.0401784	−	0.999193i	$-0.487207\pi$
$661$	−22.5030	−	15.3423i	−0.875265	−	0.596745i	−0.915443	+	0.402447i	$0.868160\pi$
$662$	−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	0.403966	−	0.914774i	$-0.367631\pi$
$673$	−1.54003	−	0.741640i	−0.0593638	−	0.0285881i	−0.463330	+	0.886186i	$0.653346\pi$
$674$	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	−0.877263	−	0.480010i	$-0.840633\pi$
$677$	1.60652	−	21.4375i	0.0617434	−	0.823909i	0.939007	−	0.343899i	$-0.111748\pi$
$678$	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	−0.206854	−	0.978372i	$-0.566322\pi$
$683$	19.6876	−	18.2674i	0.753324	−	0.698983i	0.960178	+	0.279389i	$0.0901320\pi$
$684$	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	0.356769	−	0.934193i	$-0.383878\pi$
$691$	3.29365	+	1.01596i	0.125296	+	0.0386488i	−0.231473	+	0.972841i	$0.574354\pi$
$692$	−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	−0.832036	−	0.554722i	$-0.812824\pi$
$701$	−24.2816	+	11.6934i	−0.917102	+	0.441653i	−0.0850663	+	0.996375i	$0.527110\pi$
$702$	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	−0.946124	−	0.323805i	$-0.895038\pi$
$709$	−46.7244	+	7.04257i	−1.75477	+	0.264489i	−0.808647	+	0.588294i	$0.799800\pi$
$710$	−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	0.994855	+	0.101305i	$0.0323019\pi$
$719$	31.3786	+	29.1151i	1.17022	+	1.08581i	0.175368	+	0.984503i	$0.443889\pi$
$720$	−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	−0.966330	−	0.257306i	$-0.917165\pi$
$727$	−5.59043	−	24.4933i	−0.207337	−	0.908405i	0.758993	−	0.651099i	$-0.225692\pi$
$728$	−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	0.145249	−	0.989395i	$-0.453602\pi$
$733$	30.3043	−	20.6611i	1.11932	−	0.763137i	0.974067	+	0.226258i	$0.0726494\pi$
$734$	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	−0.997364	−	0.0725630i	$-0.976882\pi$
$739$	−5.89603	+	15.0228i	−0.216889	+	0.552624i	0.780475	+	0.625187i	$0.214977\pi$
$740$	−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	−0.929837	−	0.367973i	$-0.880052\pi$
$743$	−6.86194	−	30.0641i	−0.251740	−	1.10295i	0.678097	−	0.734973i	$-0.262805\pi$
$744$	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	0.998463	+	0.0554213i	$0.0176502\pi$
$751$	30.9216	+	28.6910i	1.12834	+	1.04695i	0.129882	+	0.991530i	$0.458540\pi$
$752$	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	0.994616	−	0.103628i	$-0.0330450\pi$
$757$	18.4964	+	23.1938i	0.672264	+	0.842992i	−0.322352	+	0.946620i	$0.604474\pi$
$758$	−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	−0.125164	−	0.992136i	$-0.539946\pi$
$761$	1.31506	−	0.198213i	0.0476709	−	0.00718523i	0.172834	+	0.984951i	$0.444707\pi$
$762$	−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	−0.491527	−	0.870862i	$-0.663561\pi$
$769$	−3.24787	+	1.56409i	−0.117121	+	0.0564027i	0.374406	+	0.927265i	$0.377847\pi$
$770$	−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	−0.960449	−	0.278455i	$-0.910178\pi$
$773$	−1.45211	−	19.3771i	−0.0522289	−	0.696947i	0.908220	−	0.418492i	$-0.137441\pi$
$774$	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	−0.790772	−	0.612111i	$-0.790321\pi$
$787$	−6.71790	+	6.23330i	−0.239467	+	0.222193i	0.551305	+	0.834304i	$0.314130\pi$
$788$	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	0.937595	−	0.347729i	$-0.113047\pi$
$797$	35.2978	+	16.9985i	1.25031	+	0.602118i	0.312716	+	0.949847i	$0.398761\pi$
$798$	−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	0.694122	−	0.719858i	$-0.255793\pi$
$809$	7.89623	+	5.38356i	0.277617	+	0.189276i	−0.416505	+	0.909133i	$0.636745\pi$
$810$	−1.37275	+	0.206908i	−0.0482334	+	0.00727002i
$811$	22.7320	+	28.5050i	0.798228	+	1.00095i	0.999770	+	0.0214662i	$0.00683342\pi$
$811$	22.7320	+	28.5050i	0.798228	+	1.00095i	−0.201542	+	0.979480i	$0.564595\pi$
$812$	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	0.875178	−	0.483801i	$-0.160744\pi$
$821$	−2.73467	−	6.96783i	−0.0954407	−	0.243179i	−0.970619	+	0.240622i	$0.922649\pi$
$822$	−1.54963	−	20.6784i	−0.0540497	−	0.721243i
$823$	−14.9381	+	4.60781i	−0.520711	+	0.160618i	−0.543959	−	0.839112i	$-0.683075\pi$
$823$	−14.9381	+	4.60781i	−0.520711	+	0.160618i	0.0232483	+	0.999730i	$0.492599\pi$
$824$	−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	0.379675	+	0.925120i	$0.376036\pi$
$827$	−10.4619	+	45.8365i	−0.363795	+	1.59389i	−0.743470	+	0.668770i	$0.766821\pi$
$828$	−1.02971	−	0.317622i	−0.0357847	−	0.0110381i
$829$	0.544119	−	1.38639i	0.0188980	−	0.0481514i	−0.921113	−	0.389295i	$-0.872719\pi$
$829$	0.544119	−	1.38639i	0.0188980	−	0.0481514i	0.940011	+	0.341143i	$0.110814\pi$
$830$	−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	−0.927996	−	0.372589i	$-0.878470\pi$
$839$	2.02063	−	8.85296i	0.0697599	−	0.305638i	0.997756	+	0.0669511i	$0.0213272\pi$
$840$	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	−0.803574	−	0.595205i	$-0.797071\pi$
$853$	−1.29908	+	1.62900i	−0.0444797	+	0.0557757i	0.759094	+	0.650981i	$0.225642\pi$
$854$	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	−0.180477	−	0.983579i	$-0.557764\pi$
$857$	−34.0171	−	23.1925i	−1.16200	−	0.792239i	−0.981524	+	0.191340i	$0.938717\pi$
$858$	1.74896	+	1.19242i	0.0597085	+	0.0407086i
$859$	4.23335	−	0.638075i	0.144440	−	0.0217708i	−0.0764242	−	0.997075i	$-0.524350\pi$
$859$	4.23335	−	0.638075i	0.144440	−	0.0217708i	0.220864	+	0.975305i	$0.429112\pi$
$860$	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	0.356217	+	0.934403i	$0.384066\pi$
$863$	−18.5400	+	32.1122i	−0.631108	+	1.09311i	−0.987325	+	0.158709i	$0.949267\pi$
$864$	−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	0.635745	−	0.771899i	$-0.280693\pi$
$877$	21.5057	+	6.63364i	0.726197	+	0.224002i	0.0904513	+	0.995901i	$0.471169\pi$
$878$	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	−0.0773433	−	0.997005i	$-0.524644\pi$
$887$	−20.9336	−	6.45715i	−0.702880	−	0.216810i	−0.625537	+	0.780195i	$0.715120\pi$
$888$	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	0.491282	−	0.871001i	$-0.336529\pi$
$907$	−4.21704	−	2.87513i	−0.140025	−	0.0954671i	−0.631306	+	0.775534i	$0.717481\pi$
$908$	−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	−0.302829	−	0.953045i	$-0.597931\pi$
$911$	20.9380	−	26.2554i	0.693707	−	0.869881i	0.996536	+	0.0831639i	$0.0265025\pi$
$912$	−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	0.925953	+	0.377638i	$0.123263\pi$
$919$	15.2800	+	38.9328i	0.504040	+	1.28427i	−0.421913	+	0.906636i	$0.638641\pi$
$920$	−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	−0.354134	−	0.935195i	$-0.615224\pi$
$929$	11.7966	−	8.04279i	0.387034	−	0.263875i	0.741168	+	0.671319i	$0.234272\pi$
$930$	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	−0.657976	−	0.753039i	$-0.728587\pi$
$937$	8.00682	−	35.0802i	0.261571	−	1.14602i	0.919547	−	0.392980i	$-0.128556\pi$
$938$	−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	−0.890626	−	0.454736i	$-0.849734\pi$
$941$	−42.0360	+	12.9664i	−1.37033	+	0.422692i	−0.479708	+	0.877428i	$0.659257\pi$
$942$	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	0.262619	−	0.964900i	$-0.415414\pi$
$947$	−20.9246	−	19.4152i	−0.679957	−	0.630908i	−0.942576	+	0.333992i	$0.891604\pi$
$948$	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	0.916952	−	0.398997i	$-0.130642\pi$
$953$	9.99958	+	12.5391i	0.323918	+	0.406181i	−0.593034	+	0.805177i	$0.702070\pi$
$954$	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	−0.994759	−	0.102250i	$-0.967396\pi$
$967$	−52.7064	−	25.3821i	−1.69492	−	0.816232i	−0.700165	−	0.713982i	$-0.746890\pi$
$968$	−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	0.579521	+	0.814957i	$0.303240\pi$
$971$	−3.58320	+	47.8145i	−0.114990	+	1.53444i	−0.694511	+	0.719482i	$0.744379\pi$
$972$	−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	−0.805645	−	0.592398i	$-0.798181\pi$
$977$	−8.59910	+	7.97880i	−0.275110	+	0.255264i	0.530536	+	0.847663i	$0.321991\pi$
$978$	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	−0.242921	−	0.970046i	$-0.578106\pi$
$983$	22.1432	−	20.5459i	0.706259	−	0.655313i	0.949180	+	0.314733i	$0.101915\pi$
$984$	−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	−0.989081	−	0.147375i	$-0.952918\pi$
$991$	−1.03923	−	13.8676i	−0.0330123	−	0.440519i	0.956068	−	0.293144i	$-0.0947015\pi$
$992$	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	0.545546	−	0.838081i	$-0.316322\pi$
$997$	25.8863	+	3.90173i	0.819827	+	0.123569i	0.274281	+	0.961650i	$0.411560\pi$
$998$	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.37.2	✓	24
3.2	odd	2		882.2.z.a.37.1		24
49.4	even	21	inner	294.2.m.b.151.2	yes	24
147.53	odd	42		882.2.z.a.739.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.m.b.37.2	✓	24	1.1	even	1	trivial
294.2.m.b.151.2	yes	24	49.4	even	21	inner
882.2.z.a.37.1		24	3.2	odd	2
882.2.z.a.739.1		24	147.53	odd	42

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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