LMFDB - Embedded newform 294.2.m.b.25.2

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			25.2
Character	$\chi$	$=$	294.25
Dual form			294.2.m.b.247.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.955573 - 0.294755i) q^{2} +(0.365341 + 0.930874i) q^{3} +(0.826239 - 0.563320i) q^{4} +(1.22261 + 0.184279i) q^{5} +(0.623490 + 0.781831i) q^{6} +(0.792174 - 2.52437i) q^{7} +(0.623490 - 0.781831i) q^{8} +(-0.733052 + 0.680173i) q^{9} +O(q^{10})$	\(q+(0.955573 - 0.294755i) q^{2} +(0.365341 + 0.930874i) q^{3} +(0.826239 - 0.563320i) q^{4} +(1.22261 + 0.184279i) q^{5} +(0.623490 + 0.781831i) q^{6} +(0.792174 - 2.52437i) q^{7} +(0.623490 - 0.781831i) q^{8} +(-0.733052 + 0.680173i) q^{9} +(1.22261 - 0.184279i) q^{10} +(-0.146661 - 0.136082i) q^{11} +(0.826239 + 0.563320i) q^{12} +(-0.348089 + 1.52508i) q^{13} +(0.0129079 - 2.64572i) q^{14} +(0.275130 + 1.20542i) q^{15} +(0.365341 - 0.930874i) q^{16} +(-0.278533 + 3.71677i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(0.160926 + 0.278731i) q^{19} +(1.11398 - 0.536464i) q^{20} +(2.63929 - 0.184843i) q^{21} +(-0.180256 - 0.0868069i) q^{22} +(0.0653076 + 0.871469i) q^{23} +(0.955573 + 0.294755i) q^{24} +(-3.31704 - 1.02317i) q^{25} +(0.116900 + 1.55993i) q^{26} +(-0.900969 - 0.433884i) q^{27} +(-0.767505 - 2.53198i) q^{28} +(1.09524 - 0.527439i) q^{29} +(0.618212 + 1.07077i) q^{30} +(-0.447415 + 0.774946i) q^{31} +(0.0747301 - 0.997204i) q^{32} +(0.0730936 - 0.186239i) q^{33} +(0.829378 + 3.63374i) q^{34} +(1.43371 - 2.94035i) q^{35} +(-0.222521 + 0.974928i) q^{36} +(-8.45644 - 5.76550i) q^{37} +(0.235934 + 0.218914i) q^{38} +(-1.54683 + 0.233147i) q^{39} +(0.906362 - 0.840981i) q^{40} +(-3.56811 + 4.47427i) q^{41} +(2.46755 - 0.954574i) q^{42} +(-3.05403 - 3.82963i) q^{43} +(-0.197835 - 0.0298188i) q^{44} +(-1.02158 + 0.696502i) q^{45} +(0.319276 + 0.813502i) q^{46} +(11.3959 - 3.51516i) q^{47} +1.00000 q^{48} +(-5.74492 - 3.99949i) q^{49} -3.47126 q^{50} +(-3.56160 + 1.09861i) q^{51} +(0.571503 + 1.45617i) q^{52} +(-10.0086 + 6.82374i) q^{53} +(-0.988831 - 0.149042i) q^{54} +(-0.154233 - 0.193402i) q^{55} +(-1.47972 - 2.19327i) q^{56} +(-0.200671 + 0.251633i) q^{57} +(0.891115 - 0.826834i) q^{58} +(-6.38087 + 0.961761i) q^{59} +(0.906362 + 0.840981i) q^{60} +(1.41254 + 0.963053i) q^{61} +(-0.199119 + 0.872395i) q^{62} +(1.13631 + 2.38931i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-0.706619 + 1.80044i) q^{65} +(0.0149512 - 0.199510i) q^{66} +(0.872419 - 1.51107i) q^{67} +(1.86360 + 3.22784i) q^{68} +(-0.787368 + 0.379176i) q^{69} +(0.503333 - 3.23231i) q^{70} +(9.28471 + 4.47128i) q^{71} +(0.0747301 + 0.997204i) q^{72} +(3.27703 + 1.01083i) q^{73} +(-9.78016 - 3.01678i) q^{74} +(-0.259407 - 3.46155i) q^{75} +(0.289978 + 0.139646i) q^{76} +(-0.459703 + 0.262428i) q^{77} +(-1.40938 + 0.678724i) q^{78} +(-6.88394 - 11.9233i) q^{79} +(0.618212 - 1.07077i) q^{80} +(0.0747301 - 0.997204i) q^{81} +(-2.09078 + 5.32721i) q^{82} +(1.72387 + 7.55276i) q^{83} +(2.07655 - 1.63949i) q^{84} +(-1.02546 + 4.49285i) q^{85} +(-4.04715 - 2.75930i) q^{86} +(0.891115 + 0.826834i) q^{87} +(-0.197835 + 0.0298188i) q^{88} +(5.99443 - 5.56202i) q^{89} +(-0.770897 + 0.966675i) q^{90} +(3.57412 + 2.08684i) q^{91} +(0.544876 + 0.683252i) q^{92} +(-0.884836 - 0.133368i) q^{93} +(9.85348 - 6.71799i) q^{94} +(0.145385 + 0.370436i) q^{95} +(0.955573 - 0.294755i) q^{96} -7.14944 q^{97} +(-6.66856 - 2.12845i) q^{98} +0.200070 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 $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{8}{21}\right)$

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 $

$2$	0.955573	−	0.294755i	0.675692	−	0.208423i
$2$	0.955573	−	0.294755i	0.675692	−	0.208423i
$3$	0.365341	+	0.930874i	0.210930	+	0.537440i
$3$	0.365341	+	0.930874i	0.210930	+	0.537440i
$4$	0.826239	−	0.563320i	0.413119	−	0.281660i
$5$	1.22261	+	0.184279i	0.546769	+	0.0824122i	0.416618	−	0.909082i	$-0.363215\pi$
$5$	1.22261	+	0.184279i	0.546769	+	0.0824122i	0.130152	+	0.991494i	$0.458454\pi$
$6$	0.623490	+	0.781831i	0.254539	+	0.319181i
$7$	0.792174	−	2.52437i	0.299414	−	0.954123i
$7$	0.792174	−	2.52437i	0.299414	−	0.954123i
$8$	0.623490	−	0.781831i	0.220437	−	0.276419i
$9$	−0.733052	+	0.680173i	−0.244351	+	0.226724i
$10$	1.22261	−	0.184279i	0.386624	−	0.0582742i
$11$	−0.146661	−	0.136082i	−0.0442201	−	0.0410302i	0.657753	−	0.753233i	$-0.271507\pi$
$11$	−0.146661	−	0.136082i	−0.0442201	−	0.0410302i	−0.701973	+	0.712203i	$0.747697\pi$
$12$	0.826239	+	0.563320i	0.238515	+	0.162616i
$13$	−0.348089	+	1.52508i	−0.0965426	+	0.422981i	−0.999984	−	0.00573171i	$-0.998176\pi$
$13$	−0.348089	+	1.52508i	−0.0965426	+	0.422981i	0.903441	+	0.428713i	$0.141033\pi$
$14$	0.0129079	−	2.64572i	0.00344977	−	0.707098i
$15$	0.275130	+	1.20542i	0.0710383	+	0.311239i
$16$	0.365341	−	0.930874i	0.0913353	−	0.232718i
$17$	−0.278533	+	3.71677i	−0.0675543	+	0.901449i	0.855752	+	0.517386i	$0.173095\pi$
$17$	−0.278533	+	3.71677i	−0.0675543	+	0.901449i	−0.923307	+	0.384064i	$0.874524\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	0.160926	+	0.278731i	0.0369189	+	0.0639453i	0.883894	−	0.467686i	$-0.154912\pi$
$19$	0.160926	+	0.278731i	0.0369189	+	0.0639453i	−0.846976	+	0.531632i	$0.821579\pi$
$20$	1.11398	−	0.536464i	0.249093	−	0.119957i
$21$	2.63929	−	0.184843i	0.575940	−	0.0403361i
$22$	−0.180256	−	0.0868069i	−0.0384308	−	0.0185073i
$23$	0.0653076	+	0.871469i	0.0136176	+	0.181714i	0.999865	+	0.0164376i	$0.00523250\pi$
$23$	0.0653076	+	0.871469i	0.0136176	+	0.181714i	−0.986247	+	0.165276i	$0.947148\pi$
$24$	0.955573	+	0.294755i	0.195055	+	0.0601666i
$25$	−3.31704	−	1.02317i	−0.663408	−	0.204634i
$26$	0.116900	+	1.55993i	0.0229260	+	0.305926i
$27$	−0.900969	−	0.433884i	−0.173392	−	0.0835010i
$28$	−0.767505	−	2.53198i	−0.145045	−	0.478500i
$29$	1.09524	−	0.527439i	0.203381	−	0.0979430i	−0.329421	−	0.944183i	$-0.606853\pi$
$29$	1.09524	−	0.527439i	0.203381	−	0.0979430i	0.532802	+	0.846240i	$0.321139\pi$
$30$	0.618212	+	1.07077i	0.112869	+	0.195496i
$31$	−0.447415	+	0.774946i	−0.0803582	+	0.139184i	−0.903404	−	0.428791i	$-0.858940\pi$
$31$	−0.447415	+	0.774946i	−0.0803582	+	0.139184i	0.823046	+	0.567975i	$0.192273\pi$
$32$	0.0747301	−	0.997204i	0.0132105	−	0.176282i
$33$	0.0730936	−	0.186239i	0.0127240	−	0.0324201i
$34$	0.829378	+	3.63374i	0.142237	+	0.623182i
$35$	1.43371	−	2.94035i	0.242342	−	0.497010i
$36$	−0.222521	+	0.974928i	−0.0370868	+	0.162488i
$37$	−8.45644	−	5.76550i	−1.39023	−	0.947843i	−0.999628	−	0.0272836i	$-0.991314\pi$
$37$	−8.45644	−	5.76550i	−1.39023	−	0.947843i	−0.390603	−	0.920559i	$-0.627733\pi$
$38$	0.235934	+	0.218914i	0.0382735	+	0.0355126i
$39$	−1.54683	+	0.233147i	−0.247691	+	0.0373334i
$40$	0.906362	−	0.840981i	0.143308	−	0.132971i
$41$	−3.56811	+	4.47427i	−0.557245	+	0.698763i	−0.978046	−	0.208390i	$-0.933178\pi$
$41$	−3.56811	+	4.47427i	−0.557245	+	0.698763i	0.420801	+	0.907153i	$0.361749\pi$
$42$	2.46755	−	0.954574i	0.380751	−	0.147294i
$43$	−3.05403	−	3.82963i	−0.465735	−	0.584014i	0.492386	−	0.870377i	$-0.336125\pi$
$43$	−3.05403	−	3.82963i	−0.465735	−	0.584014i	−0.958121	+	0.286363i	$0.907554\pi$
$44$	−0.197835	−	0.0298188i	−0.0298247	−	0.00449536i
$45$	−1.02158	+	0.696502i	−0.152288	+	0.103828i
$46$	0.319276	+	0.813502i	0.0470747	+	0.119944i
$47$	11.3959	−	3.51516i	1.66226	−	0.512739i	0.685681	−	0.727902i	$-0.259504\pi$
$47$	11.3959	−	3.51516i	1.66226	−	0.512739i	0.976578	+	0.215163i	$0.0690282\pi$
$48$	1.00000			0.144338
$49$	−5.74492	−	3.99949i	−0.820703	−	0.571355i
$50$	−3.47126			−0.490910
$51$	−3.56160	+	1.09861i	−0.498724	+	0.153836i
$52$	0.571503	+	1.45617i	0.0792532	+	0.201934i
$53$	−10.0086	+	6.82374i	−1.37479	+	0.937313i	−0.374838	+	0.927090i	$0.622302\pi$
$53$	−10.0086	+	6.82374i	−1.37479	+	0.937313i	−0.999948	+	0.0102231i	$0.996746\pi$
$54$	−0.988831	−	0.149042i	−0.134563	−	0.0202821i
$55$	−0.154233	−	0.193402i	−0.0207968	−	0.0260783i
$56$	−1.47972	−	2.19327i	−0.197736	−	0.293088i
$57$	−0.200671	+	0.251633i	−0.0265795	+	0.0333297i
$58$	0.891115	−	0.826834i	0.117009	−	0.108569i
$59$	−6.38087	+	0.961761i	−0.830718	+	0.125211i	−0.550615	−	0.834759i	$-0.685607\pi$
$59$	−6.38087	+	0.961761i	−0.830718	+	0.125211i	−0.280103	+	0.959970i	$0.590369\pi$
$60$	0.906362	+	0.840981i	0.117011	+	0.108570i
$61$	1.41254	+	0.963053i	0.180857	+	0.123306i	0.650365	−	0.759622i	$-0.274616\pi$
$61$	1.41254	+	0.963053i	0.180857	+	0.123306i	−0.469507	+	0.882929i	$0.655568\pi$
$62$	−0.199119	+	0.872395i	−0.0252881	+	0.110794i
$63$	1.13631	+	2.38931i	0.143161	+	0.301025i
$64$	−0.222521	−	0.974928i	−0.0278151	−	0.121866i
$65$	−0.706619	+	1.80044i	−0.0876453	+	0.223317i
$66$	0.0149512	−	0.199510i	0.00184037	−	0.0245580i
$67$	0.872419	−	1.51107i	0.106583	−	0.184607i	−0.807801	−	0.589455i	$-0.799342\pi$
$67$	0.872419	−	1.51107i	0.106583	−	0.184607i	0.914384	+	0.404848i	$0.132676\pi$
$68$	1.86360	+	3.22784i	0.225994	+	0.391434i
$69$	−0.787368	+	0.379176i	−0.0947880	+	0.0456475i
$70$	0.503333	−	3.23231i	0.0601598	−	0.386335i
$71$	9.28471	+	4.47128i	1.10189	+	0.530644i	0.894253	−	0.447562i	$-0.147708\pi$
$71$	9.28471	+	4.47128i	1.10189	+	0.530644i	0.207640	+	0.978205i	$0.433422\pi$
$72$	0.0747301	+	0.997204i	0.00880703	+	0.117522i
$73$	3.27703	+	1.01083i	0.383547	+	0.118309i	0.480532	−	0.876977i	$-0.340444\pi$
$73$	3.27703	+	1.01083i	0.383547	+	0.118309i	−0.0969846	+	0.995286i	$0.530920\pi$
$74$	−9.78016	−	3.01678i	−1.13692	−	0.350693i
$75$	−0.259407	−	3.46155i	−0.0299538	−	0.399706i
$76$	0.289978	+	0.139646i	0.0332627	+	0.0160185i
$77$	−0.459703	+	0.262428i	−0.0523880	+	0.0299064i
$78$	−1.40938	+	0.678724i	−0.159581	+	0.0768504i
$79$	−6.88394	−	11.9233i	−0.774504	−	1.34148i	−0.935073	−	0.354456i	$-0.884666\pi$
$79$	−6.88394	−	11.9233i	−0.774504	−	1.34148i	0.160568	−	0.987025i	$-0.448667\pi$
$80$	0.618212	−	1.07077i	0.0691182	−	0.119716i
$81$	0.0747301	−	0.997204i	0.00830334	−	0.110800i
$82$	−2.09078	+	5.32721i	−0.230887	+	0.588292i
$83$	1.72387	+	7.55276i	0.189219	+	0.829023i	0.977029	+	0.213105i	$0.0683576\pi$
$83$	1.72387	+	7.55276i	0.189219	+	0.829023i	−0.787810	+	0.615918i	$0.788785\pi$
$84$	2.07655	−	1.63949i	0.226571	−	0.178883i
$85$	−1.02546	+	4.49285i	−0.111227	+	0.487318i
$86$	−4.04715	−	2.75930i	−0.436416	−	0.297543i
$87$	0.891115	+	0.826834i	0.0955376	+	0.0886459i
$88$	−0.197835	+	0.0298188i	−0.0210893	+	0.00317870i
$89$	5.99443	−	5.56202i	0.635409	−	0.589573i	−0.295269	−	0.955414i	$-0.595409\pi$
$89$	5.99443	−	5.56202i	0.635409	−	0.589573i	0.930677	+	0.365841i	$0.119219\pi$
$90$	−0.770897	+	0.966675i	−0.0812597	+	0.101896i
$91$	3.57412	+	2.08684i	0.374670	+	0.218760i
$92$	0.544876	+	0.683252i	0.0568072	+	0.0712340i
$93$	−0.884836	−	0.133368i	−0.0917532	−	0.0138296i
$94$	9.85348	−	6.71799i	1.01631	−	0.692907i
$95$	0.145385	+	0.370436i	0.0149162	+	0.0380059i
$96$	0.955573	−	0.294755i	0.0975277	−	0.0300833i
$97$	−7.14944			−0.725916			−0.362958	−	0.931806i	$-0.618233\pi$
$97$	−7.14944			−0.725916			−0.362958	+	0.931806i	$0.618233\pi$
$98$	−6.66856	−	2.12845i	−0.673626	−	0.215006i
$99$	0.200070			0.0201077
$100$	−3.31704	+	1.02317i	−0.331704	+	0.102317i
$101$	3.14537	+	8.01427i	0.312976	+	0.797449i	0.997645	+	0.0685950i	$0.0218516\pi$
$101$	3.14537	+	8.01427i	0.312976	+	0.797449i	−0.684669	+	0.728854i	$0.740053\pi$
$102$	−3.07955	+	2.09960i	−0.304921	+	0.207892i
$103$	8.73030	+	1.31588i	0.860222	+	0.129658i	0.564315	−	0.825559i	$-0.309140\pi$
$103$	8.73030	+	1.31588i	0.860222	+	0.129658i	0.295907	+	0.955217i	$0.404378\pi$
$104$	0.975325	+	1.22302i	0.0956384	+	0.119927i
$105$	3.26089	+	0.260374i	0.318230	+	0.0254099i
$106$	−7.55261	+	9.47067i	−0.733574	+	0.919873i
$107$	0.864747	−	0.802368i	0.0835983	−	0.0775679i	−0.637267	−	0.770643i	$-0.719935\pi$
$107$	0.864747	−	0.802368i	0.0835983	−	0.0775679i	0.720865	+	0.693075i	$0.243745\pi$
$108$	−0.988831	+	0.149042i	−0.0951503	+	0.0143416i
$109$	8.48830	+	7.87599i	0.813032	+	0.754383i	0.972521	−	0.232816i	$-0.0747941\pi$
$109$	8.48830	+	7.87599i	0.813032	+	0.754383i	−0.159489	+	0.987200i	$0.550985\pi$
$110$	−0.204387	−	0.139349i	−0.0194876	−	0.0132864i
$111$	2.27747	−	9.97825i	0.216168	−	0.947094i
$112$	−2.06046	−	1.65967i	−0.194695	−	0.156824i
$113$	2.25325	+	9.87215i	0.211968	+	0.928694i	0.963228	+	0.268687i	$0.0865896\pi$
$113$	2.25325	+	9.87215i	0.211968	+	0.928694i	−0.751259	+	0.660007i	$0.770553\pi$
$114$	−0.117585	+	0.299603i	−0.0110129	+	0.0280604i
$115$	−0.0807478	+	1.07750i	−0.00752977	+	0.100478i
$116$	0.607812	−	1.05276i	0.0564339	−	0.0977464i
$117$	−0.782150	−	1.35472i	−0.0723098	−	0.125244i
$118$	−5.81390	+	2.79983i	−0.535213	+	0.257745i
$119$	9.16187	+	3.64745i	0.839867	+	0.334361i
$120$	1.11398	+	0.536464i	0.101692	+	0.0489722i
$121$	−0.819040	−	10.9293i	−0.0744582	−	0.993575i
$122$	1.63365	+	0.503914i	0.147904	+	0.0456222i
$123$	−5.46856	−	1.68683i	−0.493083	−	0.152096i
$124$	0.0668708	+	0.892329i	0.00600517	+	0.0801335i
$125$	−9.43680	−	4.54452i	−0.844053	−	0.406475i
$126$	1.79008	+	1.94823i	0.159473	+	0.173562i
$127$	1.61299	−	0.776774i	0.143130	−	0.0689276i	−0.360948	−	0.932586i	$-0.617547\pi$
$127$	1.61299	−	0.776774i	0.143130	−	0.0689276i	0.504078	+	0.863658i	$0.331833\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	2.44914	−	4.24204i	0.215635	−	0.373491i
$130$	−0.144538	+	1.92873i	−0.0126768	+	0.169161i
$131$	4.06212	−	10.3501i	0.354909	−	0.904293i	−0.636234	−	0.771496i	$-0.719509\pi$
$131$	4.06212	−	10.3501i	0.354909	−	0.904293i	0.991143	−	0.132797i	$-0.0423959\pi$
$132$	−0.0445197	−	0.195053i	−0.00387494	−	0.0169772i
$133$	0.831103	−	0.185433i	0.0720658	−	0.0160790i
$134$	0.388263	−	1.70109i	0.0335408	−	0.146952i
$135$	−1.02158	−	0.696502i	−0.0879237	−	0.0599453i
$136$	2.73223	+	2.53513i	0.234286	+	0.217386i
$137$	3.41983	−	0.515457i	0.292176	−	0.0440384i	−0.00131874	−	0.999999i	$-0.500420\pi$
$137$	3.41983	−	0.515457i	0.292176	−	0.0440384i	0.293495	+	0.955961i	$0.405182\pi$
$138$	−0.640623	+	0.594411i	−0.0545335	+	0.0505997i
$139$	−1.21870	+	1.52820i	−0.103369	+	0.129620i	−0.830825	−	0.556534i	$-0.812131\pi$
$139$	−1.21870	+	1.52820i	−0.103369	+	0.129620i	0.727456	+	0.686154i	$0.240702\pi$
$140$	−0.471770	−	3.23707i	−0.0398719	−	0.273582i
$141$	7.43555	+	9.32389i	0.626187	+	0.785213i
$142$	10.1902	+	1.53592i	0.855139	+	0.128891i
$143$	0.258587	−	0.176302i	0.0216241	−	0.0147431i
$144$	0.365341	+	0.930874i	0.0304451	+	0.0775728i
$145$	1.43625	−	0.443025i	0.119274	−	0.0367912i
$146$	3.42939			0.283818
$147$	1.62416	−	6.80897i	0.133959	−	0.561595i
$148$	−10.2349			−0.841301
$149$	−1.41169	+	0.435449i	−0.115650	+	0.0356734i	−0.352040	−	0.935985i	$-0.614512\pi$
$149$	−1.41169	+	0.435449i	−0.115650	+	0.0356734i	0.236390	+	0.971658i	$0.424036\pi$
$150$	−1.26819	−	3.23130i	−0.103548	−	0.263835i
$151$	3.80472	−	2.59401i	0.309623	−	0.211098i	−0.398532	−	0.917155i	$-0.630480\pi$
$151$	3.80472	−	2.59401i	0.309623	−	0.211098i	0.708155	+	0.706057i	$0.249528\pi$
$152$	0.318256	+	0.0479694i	0.0258140	+	0.00389083i
$153$	−2.32387	−	2.91404i	−0.187873	−	0.235586i
$154$	−0.361928	+	0.386268i	−0.0291650	+	0.0311264i
$155$	−0.689823	+	0.865010i	−0.0554079	+	0.0694793i
$156$	−1.14671	+	1.06399i	−0.0918105	+	0.0851877i
$157$	14.5690	−	2.19593i	1.16274	−	0.175254i	0.460806	−	0.887501i	$-0.347560\pi$
$157$	14.5690	−	2.19593i	1.16274	−	0.175254i	0.701929	+	0.712247i	$0.252322\pi$
$158$	−10.0926	−	9.36454i	−0.802922	−	0.745003i
$159$	−10.0086	−	6.82374i	−0.793733	−	0.541158i
$160$	0.275130	−	1.20542i	0.0217509	−	0.0952971i
$161$	2.25165	+	0.525494i	0.177455	+	0.0414148i
$162$	−0.222521	−	0.974928i	−0.0174829	−	0.0765976i
$163$	6.90529	−	17.5944i	0.540864	−	1.37810i	−0.355457	−	0.934693i	$-0.615675\pi$
$163$	6.90529	−	17.5944i	0.540864	−	1.37810i	0.896321	−	0.443406i	$-0.146230\pi$
$164$	−0.427666	+	5.70680i	−0.0333951	+	0.445626i
$165$	0.123685	−	0.214229i	0.00962889	−	0.0166777i
$166$	3.87350	+	6.70909i	0.300642	+	0.520726i
$167$	1.26278	−	0.608122i	0.0977167	−	0.0470579i	−0.384387	−	0.923172i	$-0.625587\pi$
$167$	1.26278	−	0.608122i	0.0977167	−	0.0470579i	0.482104	+	0.876114i	$0.339873\pi$
$168$	1.50105	−	2.17873i	0.115809	−	0.168092i
$169$	9.50790	+	4.57876i	0.731377	+	0.352212i
$170$	0.344385	+	4.59550i	0.0264131	+	0.352459i
$171$	−0.307552	−	0.0948673i	−0.0235191	−	0.00725468i
$172$	−4.68067	−	1.44379i	−0.356898	−	0.110088i
$173$	−0.804823	−	10.7396i	−0.0611895	−	0.816518i	−0.940397	−	0.340079i	$-0.889546\pi$
$173$	−0.804823	−	10.7396i	−0.0611895	−	0.816518i	0.879208	−	0.476439i	$-0.158073\pi$
$174$	1.09524	+	0.527439i	0.0830299	+	0.0399851i
$175$	−5.21054	+	7.56292i	−0.393880	+	0.571703i
$176$	−0.180256	+	0.0868069i	−0.0135873	+	0.00654332i
$177$	−3.22647	−	5.58841i	−0.242516	−	0.420051i
$178$	4.08868	−	7.08181i	0.306460	−	0.530804i
$179$	0.736131	−	9.82298i	0.0550210	−	0.734204i	−0.899663	−	0.436584i	$-0.856188\pi$
$179$	0.736131	−	9.82298i	0.0550210	−	0.734204i	0.954684	−	0.297620i	$-0.0961928\pi$
$180$	−0.451716	+	1.15095i	−0.0336689	+	0.0857870i
$181$	5.25185	+	23.0099i	0.390367	+	1.71031i	0.663366	+	0.748295i	$0.269127\pi$
$181$	5.25185	+	23.0099i	0.390367	+	1.71031i	−0.272999	+	0.962014i	$0.588016\pi$
$182$	4.03044	+	0.940632i	0.298756	+	0.0697243i
$183$	−0.380422	+	1.66674i	−0.0281216	+	0.123209i
$184$	0.722060	+	0.492292i	0.0532310	+	0.0362923i
$185$	−9.27650	−	8.60733i	−0.682021	−	0.632823i
$186$	−0.884836	+	0.133368i	−0.0648793	+	0.00977899i
$187$	0.546635	−	0.507203i	0.0399739	−	0.0370904i
$188$	7.43555	−	9.32389i	0.542293	−	0.680015i
$189$	−1.80901	+	1.93067i	−0.131586	+	0.140436i
$190$	0.248114	+	0.311125i	0.0180001	+	0.0225714i
$191$	22.7555	+	3.42983i	1.64653	+	0.248174i	0.905823	−	0.423656i	$-0.139254\pi$
$191$	22.7555	+	3.42983i	1.64653	+	0.248174i	0.740705	+	0.671831i	$0.234492\pi$
$192$	0.826239	−	0.563320i	0.0596286	−	0.0406541i
$193$	8.52000	+	21.7086i	0.613283	+	1.56262i	0.812685	+	0.582703i	$0.198005\pi$
$193$	8.52000	+	21.7086i	0.613283	+	1.56262i	−0.199402	+	0.979918i	$0.563900\pi$
$194$	−6.83181	+	2.10734i	−0.490496	+	0.151298i
$195$	−1.93414			−0.138506
$196$	−6.99967	−	0.0683012i	−0.499976	−	0.00487865i
$197$	5.50041			0.391888			0.195944	−	0.980615i	$-0.437223\pi$
$197$	5.50041			0.391888			0.195944	+	0.980615i	$0.437223\pi$
$198$	0.191181	−	0.0589715i	0.0135866	−	0.00419092i
$199$	7.37174	+	18.7829i	0.522569	+	1.33148i	0.911910	+	0.410390i	$0.134607\pi$
$199$	7.37174	+	18.7829i	0.522569	+	1.33148i	−0.389342	+	0.921093i	$0.627297\pi$
$200$	−2.86809	+	1.95543i	−0.202804	+	0.138270i
$201$	1.72535	+	0.260055i	0.121697	+	0.0183428i
$202$	5.36787	+	6.73110i	0.377682	+	0.473599i
$203$	−0.463834	−	3.18262i	−0.0325548	−	0.223376i
$204$	−2.32387	+	2.91404i	−0.162703	+	0.204023i
$205$	−5.18693	+	4.81277i	−0.362271	+	0.336139i
$206$	8.73030	−	1.31588i	0.608269	−	0.0916818i
$207$	−0.640623	−	0.594411i	−0.0445264	−	0.0413145i
$208$	1.29248	+	0.881201i	0.0896177	+	0.0611003i
$209$	0.0143287	−	0.0627782i	0.000991137	−	0.00434246i
$210$	3.19276	−	0.712358i	0.220322	−	0.0491573i
$211$	−0.0763003	−	0.334293i	−0.00525273	−	0.0230137i	0.972234	−	0.234012i	$-0.0751856\pi$
$211$	−0.0763003	−	0.334293i	−0.00525273	−	0.0230137i	−0.977486	+	0.210999i	$0.932328\pi$
$212$	−4.42554	+	11.2761i	−0.303947	+	0.774445i
$213$	−0.770113	+	10.2764i	−0.0527672	+	0.704130i
$214$	0.589827	−	1.02161i	0.0403197	−	0.0698358i
$215$	−3.02818	−	5.24496i	−0.206520	−	0.357703i
$216$	−0.900969	+	0.433884i	−0.0613032	+	0.0295220i
$217$	1.60182	+	1.74334i	0.108739	+	0.118345i
$218$	10.4327	+	5.02411i	0.706590	+	0.340276i
$219$	0.256279	+	3.41980i	0.0173177	+	0.231089i
$220$	−0.236381	−	0.0729138i	−0.0159368	−	0.00491585i
$221$	−5.57141	−	1.71855i	−0.374774	−	0.115602i
$222$	−0.764852	−	10.2062i	−0.0513335	−	0.684998i
$223$	−24.5594	−	11.8272i	−1.64462	−	0.792008i	−0.999613	−	0.0278325i	$-0.991140\pi$
$223$	−24.5594	−	11.8272i	−1.64462	−	0.792008i	−0.645009	−	0.764175i	$-0.723146\pi$
$224$	−2.45812	−	0.978606i	−0.164240	−	0.0653858i
$225$	3.12750	−	1.50612i	0.208500	−	0.100408i
$226$	5.06302	+	8.76940i	0.336787	+	0.583332i
$227$	−5.40827	+	9.36740i	−0.358960	+	0.621736i	−0.987787	−	0.155808i	$-0.950202\pi$
$227$	−5.40827	+	9.36740i	−0.358960	+	0.621736i	0.628828	+	0.777545i	$0.283535\pi$
$228$	−0.0240520	+	0.320951i	−0.00159288	+	0.0212555i
$229$	−9.09446	+	23.1723i	−0.600979	+	1.53127i	0.228972	+	0.973433i	$0.426464\pi$
$229$	−9.09446	+	23.1723i	−0.600979	+	1.53127i	−0.829951	+	0.557836i	$0.811632\pi$
$230$	0.240440	+	1.05343i	0.0158541	+	0.0694614i
$231$	−0.412235	−	0.332050i	−0.0271231	−	0.0218473i
$232$	0.270502	−	1.18515i	0.0177593	−	0.0778086i
$233$	−9.59232	−	6.53994i	−0.628414	−	0.428445i	0.206790	−	0.978385i	$-0.433698\pi$
$233$	−9.59232	−	6.53994i	−0.628414	−	0.428445i	−0.835204	+	0.549940i	$0.814651\pi$
$234$	−1.14671	−	1.06399i	−0.0749629	−	0.0695554i
$235$	14.5805	−	2.19766i	0.951128	−	0.143360i
$236$	−4.73034	+	4.38911i	−0.307919	+	0.285707i
$237$	8.58414	−	10.7642i	0.557600	−	0.699208i
$238$	9.82994	+	0.784897i	0.637180	+	0.0508773i
$239$	−15.5281	−	19.4717i	−1.00443	−	1.25952i	−0.965534	−	0.260275i	$-0.916187\pi$
$239$	−15.5281	−	19.4717i	−1.00443	−	1.25952i	−0.0388981	−	0.999243i	$-0.512385\pi$
$240$	1.22261	+	0.184279i	0.0789194	+	0.0118952i
$241$	19.3549	−	13.1960i	1.24676	−	0.850027i	0.253660	−	0.967293i	$-0.418365\pi$
$241$	19.3549	−	13.1960i	1.24676	−	0.850027i	0.993101	+	0.117266i	$0.0374130\pi$
$242$	−4.00413	−	10.2024i	−0.257395	−	0.655832i
$243$	0.955573	−	0.294755i	0.0613000	−	0.0189086i
$244$	1.70960			0.109446
$245$	−6.28679	−	5.94849i	−0.401649	−	0.380035i
$246$	−5.72280			−0.364873
$247$	−0.481104	+	0.148401i	−0.0306119	+	0.00944252i
$248$	0.326918	+	0.832974i	0.0207593	+	0.0528939i
$249$	−6.40086	+	4.36404i	−0.405638	+	0.276560i
$250$	−10.3571	−	1.56108i	−0.655039	−	0.0987312i
$251$	5.26138	+	6.59757i	0.332096	+	0.416435i	0.919643	−	0.392755i	$-0.128478\pi$
$251$	5.26138	+	6.59757i	0.332096	+	0.416435i	−0.587548	+	0.809190i	$0.699907\pi$
$252$	2.28481	+	1.33404i	0.143929	+	0.0840365i
$253$	0.109013	−	0.136698i	0.00685359	−	0.00859413i
$254$	1.31237	−	1.21770i	0.0823454	−	0.0764054i
$255$	−4.55692	+	0.686845i	−0.285365	+	0.0430119i
$256$	−0.733052	−	0.680173i	−0.0458157	−	0.0425108i
$257$	−21.9444	−	14.9615i	−1.36886	−	0.933271i	−0.999993	−	0.00378702i	$-0.998795\pi$
$257$	−21.9444	−	14.9615i	−1.36886	−	0.933271i	−0.368864	−	0.929484i	$-0.620253\pi$
$258$	1.08997	−	4.77547i	0.0678586	−	0.297308i
$259$	−21.2533	+	16.7799i	−1.32061	+	1.04265i
$260$	0.430386	+	1.88564i	0.0266914	+	0.116943i
$261$	−0.444117	+	1.13159i	−0.0274902	+	0.0700438i
$262$	0.830902	−	11.0876i	0.0513333	−	0.684995i
$263$	5.64742	−	9.78161i	0.348235	−	0.603160i	−0.637701	−	0.770284i	$-0.720115\pi$
$263$	5.64742	−	9.78161i	0.348235	−	0.603160i	0.985936	+	0.167124i	$0.0534479\pi$
$264$	−0.100035	−	0.173265i	−0.00615671	−	0.0106637i
$265$	−13.4941	+	6.49842i	−0.828937	+	0.399195i
$266$	0.739522	−	0.422166i	0.0453430	−	0.0258847i
$267$	7.36755	+	3.54803i	0.450887	+	0.217136i
$268$	−0.130392	−	1.73996i	−0.00796495	−	0.106285i
$269$	−10.3930	−	3.20582i	−0.633673	−	0.195462i	−0.0387552	−	0.999249i	$-0.512339\pi$
$269$	−10.3930	−	3.20582i	−0.633673	−	0.195462i	−0.594918	+	0.803786i	$0.702815\pi$
$270$	−1.18149	−	0.364442i	−0.0719033	−	0.0221792i
$271$	0.785991	+	10.4883i	0.0477456	+	0.637120i	0.968825	+	0.247746i	$0.0796898\pi$
$271$	0.785991	+	10.4883i	0.0477456	+	0.637120i	−0.921079	+	0.389375i	$0.872691\pi$
$272$	3.35808	+	1.61717i	0.203614	+	0.0980552i
$273$	−0.636807	+	4.08946i	−0.0385413	+	0.247506i
$274$	3.11597	−	1.50057i	0.188242	−	0.0906527i
$275$	0.347246	+	0.601449i	0.0209398	+	0.0362687i
$276$	−0.436956	+	0.756830i	−0.0263017	+	0.0455558i
$277$	0.0169602	−	0.226318i	0.00101904	−	0.0135981i	−0.996671	−	0.0815274i	$-0.974020\pi$
$277$	0.0169602	−	0.226318i	0.00101904	−	0.0135981i	0.997690	+	0.0679293i	$0.0216392\pi$
$278$	−0.714111	+	1.81953i	−0.0428296	+	0.109128i
$279$	−0.199119	−	0.872395i	−0.0119209	−	0.0522290i
$280$	−1.40495	−	2.95420i	−0.0839621	−	0.176547i
$281$	0.905759	−	3.96839i	0.0540331	−	0.236734i	−0.940699	−	0.339242i	$-0.889829\pi$
$281$	0.905759	−	3.96839i	0.0540331	−	0.236734i	0.994732	+	0.102508i	$0.0326866\pi$
$282$	9.85348	+	6.71799i	0.586766	+	0.400050i
$283$	−17.5010	−	16.2385i	−1.04032	−	0.965279i	−0.0408980	−	0.999163i	$-0.513022\pi$
$283$	−17.5010	−	16.2385i	−1.04032	−	0.965279i	−0.999426	+	0.0338839i	$0.989212\pi$
$284$	10.1902	−	1.53592i	0.604674	−	0.0911400i
$285$	−0.291714	+	0.270671i	−0.0172796	+	0.0160332i
$286$	0.195133	−	0.244689i	0.0115384	−	0.0144687i
$287$	8.46816	+	12.5516i	0.499860	+	0.740900i
$288$	0.623490	+	0.781831i	0.0367395	+	0.0460699i
$289$	3.07332	+	0.463229i	0.180784	+	0.0272487i
$290$	1.24186	−	0.846684i	0.0729244	−	0.0497190i
$291$	−2.61198	−	6.65523i	−0.153117	−	0.390136i
$292$	3.27703	−	1.01083i	0.191774	−	0.0591544i
$293$	−30.6201			−1.78885			−0.894424	−	0.447221i	$-0.852414\pi$
$293$	−30.6201			−1.78885			−0.894424	+	0.447221i	$0.852414\pi$
$294$	−0.454976	−	6.98520i	−0.0265347	−	0.407385i
$295$	−7.97857			−0.464530
$296$	−9.78016	+	3.01678i	−0.568460	+	0.175347i
$297$	0.0730936	+	0.186239i	0.00424132	+	0.0108067i
$298$	−1.22062	+	0.832207i	−0.0707088	+	0.0482085i
$299$	−1.35179	−	0.203750i	−0.0781761	−	0.0117832i
$300$	−2.16429	−	2.71394i	−0.124956	−	0.156689i
$301$	−12.0867	+	4.67578i	−0.696669	+	0.269507i
$302$	2.87109	−	3.60023i	0.165212	−	0.207170i
$303$	−6.31114	+	5.85588i	−0.362565	+	0.336412i
$304$	0.318256	−	0.0479694i	0.0182533	−	0.00275124i
$305$	1.54952	+	1.43774i	0.0887252	+	0.0823250i
$306$	−3.07955	−	2.09960i	−0.176046	−	0.120026i
$307$	0.698801	−	3.06165i	0.0398827	−	0.174737i	−0.951064	−	0.308994i	$-0.900008\pi$
$307$	0.698801	−	3.06165i	0.0398827	−	0.174737i	0.990947	+	0.134257i	$0.0428647\pi$
$308$	−0.231994	+	0.475788i	−0.0132191	+	0.0271105i
$309$	1.96462	+	8.60755i	0.111763	+	0.489667i
$310$	−0.404209	+	1.02991i	−0.0229576	+	0.0584949i
$311$	−0.486403	+	6.49060i	−0.0275814	+	0.368048i	0.966286	+	0.257471i	$0.0828891\pi$
$311$	−0.486403	+	6.49060i	−0.0275814	+	0.368048i	−0.993868	+	0.110577i	$0.964730\pi$
$312$	−0.782150	+	1.35472i	−0.0442805	+	0.0766961i
$313$	−5.53127	−	9.58044i	−0.312646	−	0.541519i	0.666288	−	0.745694i	$-0.267882\pi$
$313$	−5.53127	−	9.58044i	−0.312646	−	0.541519i	−0.978934	+	0.204176i	$0.934549\pi$
$314$	13.2745	−	6.39267i	0.749124	−	0.360759i
$315$	0.948961	+	3.13060i	0.0534679	+	0.176389i
$316$	−12.4044	−	5.97366i	−0.697804	−	0.336045i
$317$	1.93091	+	25.7662i	0.108451	+	1.44717i	0.740402	+	0.672165i	$0.234635\pi$
$317$	1.93091	+	25.7662i	0.108451	+	1.44717i	−0.631951	+	0.775008i	$0.717746\pi$
$318$	−11.5753	−	3.57050i	−0.649109	−	0.200224i
$319$	−0.232404	−	0.0716872i	−0.0130121	−	0.00401371i
$320$	−0.0923980	−	1.23297i	−0.00516521	−	0.0689249i
$321$	1.06283	+	0.511833i	0.0593215	+	0.0285677i
$322$	2.30651	−	0.161537i	0.128537	−	0.00900209i
$323$	−1.08080	+	0.520487i	−0.0601375	+	0.0289607i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	2.71504	−	4.70259i	0.150603	−	0.260853i
$326$	1.41247	−	18.8481i	0.0782294	−	1.04390i
$327$	−4.23043	+	10.7790i	−0.233943	+	0.596078i
$328$	1.27344	+	5.57932i	0.0703142	+	0.308066i
$329$	0.153935	−	31.5521i	0.00848673	−	1.73952i
$330$	0.0550451	−	0.241169i	0.00303014	−	0.0132759i
$331$	16.6584	+	11.3575i	0.915627	+	0.624264i	0.926752	−	0.375674i	$-0.122589\pi$
$331$	16.6584	+	11.3575i	0.915627	+	0.624264i	−0.0111245	+	0.999938i	$0.503541\pi$
$332$	5.67895	+	5.26929i	0.311673	+	0.289190i
$333$	10.1205	−	1.52543i	0.554603	−	0.0835929i
$334$	1.02743	−	0.953315i	0.0562185	−	0.0521631i
$335$	1.34509	−	1.68669i	0.0734901	−	0.0921537i
$336$	0.792174	−	2.52437i	0.0432166	−	0.137716i
$337$	−21.7630	−	27.2900i	−1.18551	−	1.48658i	−0.835200	−	0.549946i	$-0.814648\pi$
$337$	−21.7630	−	27.2900i	−1.18551	−	1.48658i	−0.350308	−	0.936635i	$-0.613923\pi$
$338$	10.4351	+	1.57284i	0.567595	+	0.0855511i
$339$	−8.36652	+	5.70420i	−0.454407	+	0.309809i
$340$	1.68363	+	4.28983i	0.0913078	+	0.232649i
$341$	0.171075	−	0.0527695i	0.00926421	−	0.00285763i
$342$	−0.321851			−0.0174037
$343$	−14.6472	+	11.3340i	−0.790873	+	0.611980i
$344$	−4.89829			−0.264098
$345$	−1.03252	+	0.318491i	−0.0555891	+	0.0171470i
$346$	−3.93462	−	10.0253i	−0.211527	−	0.538961i
$347$	−17.9640	+	12.2476i	−0.964356	+	0.657487i	−0.939625	−	0.342207i	$-0.888826\pi$
$347$	−17.9640	+	12.2476i	−0.964356	+	0.657487i	−0.0247317	+	0.999694i	$0.507873\pi$
$348$	1.20205	+	0.181179i	0.0644364	+	0.00971223i
$349$	9.95592	+	12.4843i	0.532928	+	0.668271i	0.973298	−	0.229546i	$-0.0737240\pi$
$349$	9.95592	+	12.4843i	0.532928	+	0.668271i	−0.440370	+	0.897817i	$0.645153\pi$
$350$	−2.74984	+	8.76275i	−0.146985	+	0.468389i
$351$	0.975325	−	1.22302i	0.0520590	−	0.0652799i
$352$	−0.146661	+	0.136082i	−0.00781708	+	0.00725319i
$353$	−14.5981	+	2.20032i	−0.776981	+	0.117111i	−0.525548	−	0.850764i	$-0.676140\pi$
$353$	−14.5981	+	2.20032i	−0.776981	+	0.117111i	−0.251433	+	0.967875i	$0.580902\pi$
$354$	−4.73034	−	4.38911i	−0.251415	−	0.233279i
$355$	10.5277	+	7.17763i	0.558750	+	0.380949i
$356$	1.81964	−	7.97234i	0.0964405	−	0.422533i
$357$	−0.0481101	+	9.86111i	−0.00254626	+	0.521905i
$358$	−2.19195	−	9.60355i	−0.115848	−	0.507563i
$359$	−4.14709	+	10.5666i	−0.218875	+	0.557684i	−0.997566	−	0.0697227i	$-0.977789\pi$
$359$	−4.14709	+	10.5666i	−0.218875	+	0.557684i	0.778691	+	0.627407i	$0.215884\pi$
$360$	−0.0923980	+	1.23297i	−0.00486980	+	0.0649830i
$361$	9.44821	−	16.3648i	0.497274	−	0.861304i
$362$	11.8008	+	20.4396i	0.620236	+	1.07428i
$363$	9.87459	−	4.75535i	0.518282	−	0.249591i
$364$	4.12863	−	0.289150i	0.216399	−	0.0151556i
$365$	3.82027	+	1.83974i	0.199962	+	0.0962966i
$366$	0.127759	+	1.70482i	0.00667806	+	0.0891125i
$367$	−8.27630	−	2.55290i	−0.432019	−	0.133260i	0.0711159	−	0.997468i	$-0.477344\pi$
$367$	−8.27630	−	2.55290i	−0.432019	−	0.133260i	−0.503135	+	0.864208i	$0.667820\pi$
$368$	0.835087	+	0.257590i	0.0435319	+	0.0134278i
$369$	−0.427666	−	5.70680i	−0.0222634	−	0.297084i
$370$	−11.4014	−	5.49064i	−0.592732	−	0.285445i
$371$	9.29713	+	30.6710i	0.482683	+	1.59236i
$372$	−0.806215	+	0.388253i	−0.0418003	+	0.0201300i
$373$	−9.67587	−	16.7591i	−0.500997	−	0.867753i	−0.999999	−	0.00115210i	$-0.999633\pi$
$373$	−9.67587	−	16.7591i	−0.500997	−	0.867753i	0.499002	−	0.866601i	$-0.333700\pi$
$374$	0.372849	−	0.645793i	0.0192796	−	0.0333932i
$375$	0.782727	−	10.4448i	0.0404199	−	0.539366i
$376$	4.35695	−	11.1013i	0.224692	−	0.572507i
$377$	0.423146	+	1.85392i	0.0217931	+	0.0954819i
$378$	−1.15956	+	2.37811i	−0.0596416	+	0.122317i
$379$	5.89346	−	25.8209i	0.302727	−	1.32633i	−0.563266	−	0.826275i	$-0.690456\pi$
$379$	5.89346	−	25.8209i	0.302727	−	1.32633i	0.865993	−	0.500056i	$-0.166687\pi$
$380$	0.328797	+	0.224170i	0.0168669	+	0.0114997i
$381$	1.31237	+	1.21770i	0.0672347	+	0.0623847i
$382$	22.7555	−	3.42983i	1.16427	−	0.175486i
$383$	−2.10871	+	1.95659i	−0.107750	+	0.0999773i	−0.732208	−	0.681081i	$-0.761510\pi$
$383$	−2.10871	+	1.95659i	−0.107750	+	0.0999773i	0.624458	+	0.781058i	$0.285320\pi$
$384$	0.623490	−	0.781831i	0.0318173	−	0.0398977i
$385$	−0.610399	+	0.236134i	−0.0311088	+	0.0120345i
$386$	14.5402	+	18.2328i	0.740077	+	0.928028i
$387$	4.84358	+	0.730052i	0.246213	+	0.0371106i
$388$	−5.90715	+	4.02742i	−0.299890	+	0.204462i
$389$	7.62995	+	19.4408i	0.386854	+	0.985688i	0.983130	+	0.182908i	$0.0585512\pi$
$389$	7.62995	+	19.4408i	0.386854	+	0.985688i	−0.596276	+	0.802780i	$0.703354\pi$
$390$	−1.84821	+	0.570097i	−0.0935876	+	0.0288680i
$391$	−3.25724			−0.164726
$392$	−6.70882	+	1.99792i	−0.338847	+	0.100910i
$393$	11.1187			0.560864
$394$	5.25604	−	1.62127i	0.264795	−	0.0816786i
$395$	−6.21918	−	15.8462i	−0.312921	−	0.797309i
$396$	0.165305	−	0.112703i	0.00830690	−	0.00566355i
$397$	28.5378	+	4.30138i	1.43227	+	0.215880i	0.818910	−	0.573923i	$-0.194579\pi$
$397$	28.5378	+	4.30138i	1.43227	+	0.215880i	0.613361	+	0.789803i	$0.289817\pi$
$398$	12.5806	+	15.7756i	0.630608	+	0.790757i
$399$	0.476250	+	0.705906i	0.0238423	+	0.0353395i
$400$	−2.16429	+	2.71394i	−0.108215	+	0.135697i
$401$	1.42567	−	1.32283i	0.0711948	−	0.0660591i	−0.643773	−	0.765217i	$-0.722632\pi$
$401$	1.42567	−	1.32283i	0.0711948	−	0.0660591i	0.714968	+	0.699158i	$0.246441\pi$
$402$	1.72535	−	0.260055i	0.0860526	−	0.0129703i
$403$	−1.02611	−	0.952094i	−0.0511144	−	0.0474272i
$404$	7.11342	+	4.84985i	0.353906	+	0.241289i
$405$	0.275130	−	1.20542i	0.0136713	−	0.0598980i
$406$	−1.38132	−	2.90450i	−0.0685537	−	0.144148i
$407$	0.455653	+	1.99634i	0.0225859	+	0.0989551i
$408$	−1.36170	+	3.46955i	−0.0674140	+	0.171768i
$409$	0.917737	−	12.2464i	0.0453792	−	0.605543i	−0.927439	−	0.373974i	$-0.877995\pi$
$409$	0.917737	−	12.2464i	0.0453792	−	0.605543i	0.972818	−	0.231569i	$-0.0743860\pi$
$410$	−3.53790	+	6.12783i	−0.174725	+	0.302632i
$411$	1.72923	+	2.99511i	0.0852966	+	0.147738i
$412$	7.95457	−	3.83072i	0.391894	−	0.188726i
$413$	−2.62691	+	16.8696i	−0.129262	+	0.830097i
$414$	−0.787368	−	0.379176i	−0.0386970	−	0.0186355i
$415$	0.715807	+	9.55178i	0.0351376	+	0.468878i
$416$	1.49480	+	0.461085i	0.0732887	+	0.0226066i
$417$	−1.86780	−	0.576141i	−0.0914668	−	0.0282138i
$418$	−0.00481207	−	0.0642126i	−0.000235366	−	0.00314074i
$419$	5.92625	+	2.85393i	0.289516	+	0.139424i	0.573005	−	0.819552i	$-0.305778\pi$
$419$	5.92625	+	2.85393i	0.289516	+	0.139424i	−0.283489	+	0.958976i	$0.591492\pi$
$420$	2.84095	−	1.62179i	0.138624	−	0.0791354i
$421$	16.9637	−	8.16927i	0.826759	−	0.398146i	0.0278602	−	0.999612i	$-0.491131\pi$
$421$	16.9637	−	8.16927i	0.826759	−	0.398146i	0.798899	+	0.601466i	$0.205416\pi$
$422$	−0.171445	−	0.296952i	−0.00834582	−	0.0144554i
$423$	−5.96285	+	10.3280i	−0.289924	+	0.502163i
$424$	−0.905239	+	12.0796i	−0.0439623	+	0.586636i
$425$	4.72680	−	12.0437i	0.229283	−	0.584205i
$426$	2.29313	+	10.0469i	0.111103	+	0.486773i
$427$	3.55008	−	2.80287i	0.171801	−	0.135640i
$428$	0.262498	−	1.15008i	0.0126883	−	0.0555911i
$429$	0.258587	+	0.176302i	0.0124847	+	0.00851192i
$430$	−4.43962	−	4.11937i	−0.214098	−	0.198653i
$431$	38.0758	−	5.73900i	1.83405	−	0.276438i	0.861264	−	0.508158i	$-0.169673\pi$
$431$	38.0758	−	5.73900i	1.83405	−	0.276438i	0.972782	+	0.231720i	$0.0744354\pi$
$432$	−0.733052	+	0.680173i	−0.0352690	+	0.0327248i
$433$	25.6836	−	32.2063i	1.23428	−	1.54773i	0.505828	−	0.862634i	$-0.331187\pi$
$433$	25.6836	−	32.2063i	1.23428	−	1.54773i	0.728449	−	0.685100i	$-0.240242\pi$
$434$	2.04452	+	1.19374i	0.0981399	+	0.0573013i
$435$	0.937121	+	1.17511i	0.0449315	+	0.0563423i
$436$	11.4501	+	1.72582i	0.548359	+	0.0826518i
$437$	−0.232396	+	0.158445i	−0.0111170	+	0.00757945i
$438$	1.25290	+	3.19233i	0.0598657	+	0.152535i
$439$	−30.5216	+	9.41467i	−1.45672	+	0.449338i	−0.919158	−	0.393888i	$-0.871130\pi$
$439$	−30.5216	+	9.41467i	−1.45672	+	0.449338i	−0.537559	+	0.843226i	$0.680654\pi$
$440$	−0.247371			−0.0117929
$441$	6.93167	−	0.975708i	0.330079	−	0.0464623i
$442$	−5.83044			−0.277326
$443$	20.4439	−	6.30612i	0.971321	−	0.299613i	0.231813	−	0.972760i	$-0.425534\pi$
$443$	20.4439	−	6.30612i	0.971321	−	0.299613i	0.739508	+	0.673148i	$0.235058\pi$
$444$	−3.73922	−	9.52737i	−0.177455	−	0.452149i
$445$	8.35384	−	5.69555i	0.396010	−	0.269995i
$446$	−26.9545	−	4.06273i	−1.27633	−	0.192376i
$447$	−0.921097	−	1.15502i	−0.0435664	−	0.0546305i
$448$	−2.63736	−	0.210587i	−0.124603	−	0.00994928i
$449$	8.69237	−	10.8999i	0.410218	−	0.514397i	−0.533206	−	0.845985i	$-0.679013\pi$
$449$	8.69237	−	10.8999i	0.410218	−	0.514397i	0.943424	+	0.331588i	$0.107584\pi$
$450$	2.54461	−	2.36105i	0.119954	−	0.111301i
$451$	1.13217	−	0.170647i	0.0533118	−	0.00803547i
$452$	7.42291	+	6.88745i	0.349144	+	0.323958i
$453$	3.80472	+	2.59401i	0.178761	+	0.121877i
$454$	−2.40691	+	10.5454i	−0.112962	+	0.494918i
$455$	3.98521	+	3.21003i	0.186829	+	0.150489i
$456$	0.0716186	+	0.313782i	0.00335385	+	0.0146942i
$457$	0.887669	−	2.26174i	0.0415234	−	0.105800i	−0.908608	−	0.417651i	$-0.862854\pi$
$457$	0.887669	−	2.26174i	0.0415234	−	0.105800i	0.950131	+	0.311851i	$0.100949\pi$
$458$	−1.86026	+	24.8235i	−0.0869243	+	1.15992i
$459$	1.86360	−	3.22784i	0.0869852	−	0.150663i
$460$	0.540263	+	0.935763i	0.0251899	+	0.0436302i
$461$	26.0547	−	12.5473i	1.21349	−	0.584385i	0.285997	−	0.958231i	$-0.407675\pi$
$461$	26.0547	−	12.5473i	1.21349	−	0.584385i	0.927491	+	0.373846i	$0.121961\pi$
$462$	−0.491794	−	0.195789i	−0.0228803	−	0.00910894i
$463$	−16.0398	−	7.72437i	−0.745434	−	0.358982i	0.0222997	−	0.999751i	$-0.492901\pi$
$463$	−16.0398	−	7.72437i	−0.745434	−	0.358982i	−0.767733	+	0.640769i	$0.778615\pi$
$464$	−0.0908437	−	1.21222i	−0.00421731	−	0.0562761i
$465$	−1.05724	−	0.326114i	−0.0490281	−	0.0151232i
$466$	−11.0938	−	3.42200i	−0.513912	−	0.158521i
$467$	2.99371	+	39.9483i	0.138532	+	1.84858i	0.443564	+	0.896243i	$0.353714\pi$
$467$	2.99371	+	39.9483i	0.138532	+	1.84858i	−0.305032	+	0.952342i	$0.598667\pi$
$468$	−1.40938	−	0.678724i	−0.0651488	−	0.0313740i
$469$	−3.12341	−	3.39934i	−0.144225	−	0.156967i
$470$	13.2850	−	6.39771i	0.612790	−	0.295104i
$471$	7.36680	+	12.7597i	0.339444	+	0.587934i
$472$	−3.22647	+	5.58841i	−0.148510	+	0.257227i
$473$	−0.0732353	+	0.977257i	−0.00336736	+	0.0449343i
$474$	5.02997	−	12.8162i	0.231034	−	0.588666i
$475$	−0.248607	−	1.08922i	−0.0114069	−	0.0499767i
$476$	9.62457	−	2.14740i	0.441142	−	0.0984259i
$477$	2.69549	−	11.8097i	0.123418	−	0.540730i
$478$	−20.5777	−	14.0296i	−0.941200	−	0.641699i
$479$	−5.48604	−	5.09030i	−0.250664	−	0.232582i	0.544826	−	0.838549i	$-0.316596\pi$
$479$	−5.48604	−	5.09030i	−0.250664	−	0.232582i	−0.795490	+	0.605967i	$0.792786\pi$
$480$	1.22261	−	0.184279i	0.0558044	−	0.00841116i
$481$	11.7364	−	10.8898i	0.535136	−	0.496534i
$482$	14.6055	−	18.3147i	0.665261	−	0.834211i
$483$	0.333450	+	2.28798i	0.0151725	+	0.104107i
$484$	−6.83343	−	8.56885i	−0.310610	−	0.389493i
$485$	−8.74101	−	1.31749i	−0.396909	−	0.0598243i
$486$	0.826239	−	0.563320i	0.0374790	−	0.0255527i
$487$	11.2028	+	28.5443i	0.507648	+	1.29347i	0.923348	+	0.383965i	$0.125442\pi$
$487$	11.2028	+	28.5443i	0.507648	+	1.29347i	−0.415700	+	0.909502i	$0.636463\pi$
$488$	1.63365	−	0.503914i	0.0739518	−	0.0228111i
$489$	18.9009			0.854730
$490$	−7.76084	−	3.83115i	−0.350599	−	0.173074i
$491$	−26.3046			−1.18711			−0.593555	−	0.804793i	$-0.702276\pi$
$491$	−26.3046			−1.18711			−0.593555	+	0.804793i	$0.702276\pi$
$492$	−5.46856	+	1.68683i	−0.246542	+	0.0760480i
$493$	1.65531	+	4.21766i	0.0745514	+	0.189954i
$494$	−0.415988	+	0.283616i	−0.0187162	+	0.0127605i
$495$	0.244608	+	0.0368687i	0.0109943	+	0.00165712i
$496$	0.557918	+	0.699607i	0.0250513	+	0.0314133i
$497$	18.6423	−	19.8960i	0.836221	−	0.892460i
$498$	−4.83017	+	6.05684i	−0.216445	+	0.271414i
$499$	4.51037	−	4.18501i	0.201912	−	0.187347i	−0.572736	−	0.819740i	$-0.694118\pi$
$499$	4.51037	−	4.18501i	0.201912	−	0.187347i	0.774647	+	0.632393i	$0.217927\pi$
$500$	−10.3571	+	1.56108i	−0.463182	+	0.0698135i
$501$	1.02743	+	0.953315i	0.0459022	+	0.0425910i
$502$	6.97230	+	4.75363i	0.311189	+	0.212165i
$503$	6.46930	−	28.3439i	0.288452	−	1.26379i	−0.598198	−	0.801349i	$-0.704116\pi$
$503$	6.46930	−	28.3439i	0.288452	−	1.26379i	0.886650	−	0.462442i	$-0.153027\pi$
$504$	2.57651	+	0.601312i	0.114767	+	0.0267846i
$505$	2.36871	+	10.3780i	0.105406	+	0.461814i
$506$	0.0638774	−	0.162757i	0.00283970	−	0.00723543i
$507$	−0.788624	+	10.5235i	−0.0350240	+	0.467363i
$508$	0.895141	−	1.55043i	0.0397155	−	0.0687892i
$509$	−10.6665	−	18.4749i	−0.472783	−	0.818884i	0.526732	−	0.850032i	$-0.323417\pi$
$509$	−10.6665	−	18.4749i	−0.472783	−	0.818884i	−0.999515	+	0.0311473i	$0.990084\pi$
$510$	−4.15201	+	1.99950i	−0.183854	+	0.0885395i
$511$	5.14769	−	7.47170i	0.227720	−	0.330528i
$512$	−0.900969	−	0.433884i	−0.0398176	−	0.0191751i
$513$	−0.0240520	−	0.320951i	−0.00106192	−	0.0141703i
$514$	−25.3795	−	7.82853i	−1.11944	−	0.345302i
$515$	10.4313	+	3.21763i	0.459658	+	0.141786i
$516$	−0.366049	−	4.88459i	−0.0161144	−	0.215032i
$517$	−2.14968	−	1.03523i	−0.0945430	−	0.0455295i
$518$	−15.3631	+	22.2990i	−0.675014	+	0.979760i
$519$	9.70319	−	4.67281i	0.425923	−	0.205114i
$520$	0.967068	+	1.67501i	0.0424087	+	0.0734541i
$521$	8.91288	−	15.4376i	0.390480	−	0.676332i	−0.602033	−	0.798472i	$-0.705642\pi$
$521$	8.91288	−	15.4376i	0.390480	−	0.676332i	0.992513	+	0.122140i	$0.0389756\pi$
$522$	−0.0908437	+	1.21222i	−0.00397612	+	0.0530576i
$523$	−9.03277	+	23.0151i	−0.394975	+	1.00638i	0.585663	+	0.810555i	$0.300834\pi$
$523$	−9.03277	+	23.0151i	−0.394975	+	1.00638i	−0.980639	+	0.195826i	$0.937261\pi$
$524$	−2.47414	−	10.8399i	−0.108083	−	0.473545i
$525$	−8.94374	−	2.08731i	−0.390337	−	0.0910977i
$526$	2.51334	−	11.0116i	0.109587	−	0.480131i
$527$	−2.75568	−	1.87879i	−0.120039	−	0.0818413i
$528$	−0.146661	−	0.136082i	−0.00638262	−	0.00592220i
$529$	21.9879	−	3.31415i	0.955996	−	0.144093i
$530$	−10.9792	+	10.1872i	−0.476905	+	0.442503i
$531$	4.02334	−	5.04511i	0.174598	−	0.218939i
$532$	0.582232	−	0.621388i	0.0252429	−	0.0269406i
$533$	−5.58159	−	6.99909i	−0.241766	−	0.303164i
$534$	8.08603	+	1.21877i	0.349917	+	0.0527415i
$535$	1.20511	−	0.821631i	0.0521015	−	0.0355222i
$536$	−0.637461	−	1.62422i	−0.0275341	−	0.0701558i
$537$	9.41289	−	2.90349i	0.406196	−	0.125295i
$538$	−10.8762			−0.468907
$539$	0.298300	+	1.36835i	0.0128487	+	0.0589390i
$540$	−1.23642			−0.0532072
$541$	−5.27250	+	1.62635i	−0.226682	+	0.0699222i	−0.406016	−	0.913866i	$-0.633082\pi$
$541$	−5.27250	+	1.62635i	−0.226682	+	0.0699222i	0.179333	+	0.983788i	$0.442606\pi$
$542$	3.84256	+	9.79068i	0.165052	+	0.420546i
$543$	−19.5006	+	13.2953i	−0.836849	+	0.570554i
$544$	3.68556	+	0.555509i	0.158017	+	0.0238173i
$545$	8.92653	+	11.1935i	0.382370	+	0.479477i
$546$	0.596875	+	4.09548i	0.0255439	+	0.175270i
$547$	3.17298	−	3.97879i	0.135667	−	0.170121i	−0.709357	−	0.704849i	$-0.751015\pi$
$547$	3.17298	−	3.97879i	0.135667	−	0.170121i	0.845024	+	0.534728i	$0.179586\pi$
$548$	2.53523	−	2.35235i	0.108300	−	0.100487i
$549$	−1.69051	+	0.254803i	−0.0721491	+	0.0108747i
$550$	0.509099	+	0.472375i	0.0217081	+	0.0201421i
$551$	0.323266	+	0.220399i	0.0137716	+	0.00938931i
$552$	−0.194464	+	0.852002i	−0.00827693	+	0.0362636i
$553$	−35.5522	+	7.93228i	−1.51184	+	0.337315i
$554$	−0.0505017	−	0.221262i	−0.00214561	−	0.00940053i
$555$	4.62325	−	11.7799i	0.196246	−	0.500027i
$556$	−0.146071	+	1.94918i	−0.00619478	+	0.0826636i
$557$	−22.3375	+	38.6897i	−0.946471	+	1.63934i	−0.193691	+	0.981063i	$0.562046\pi$
$557$	−22.3375	+	38.6897i	−0.946471	+	1.63934i	−0.752779	+	0.658273i	$0.771287\pi$
$558$	−0.447415	−	0.774946i	−0.0189406	−	0.0328061i
$559$	6.90357	−	3.32458i	0.291990	−	0.140615i
$560$	−2.21330	−	2.40884i	−0.0935291	−	0.101792i
$561$	0.671850	+	0.323546i	0.0283655	+	0.0136601i
$562$	−0.304185	−	4.05906i	−0.0128313	−	0.171221i
$563$	−38.5031	−	11.8766i	−1.62271	−	0.500540i	−0.655647	−	0.755068i	$-0.727604\pi$
$563$	−38.5031	−	11.8766i	−1.62271	−	0.500540i	−0.967066	+	0.254527i	$0.918080\pi$
$564$	11.3959	+	3.51516i	0.479853	+	0.148015i
$565$	0.935625	+	12.4851i	0.0393621	+	0.525250i
$566$	−21.5098	−	10.3586i	−0.904125	−	0.435404i
$567$	−2.45812	−	0.978606i	−0.103231	−	0.0410976i
$568$	9.28471	−	4.47128i	0.389578	−	0.187611i
$569$	3.24559	+	5.62154i	0.136062	+	0.235667i	0.926003	−	0.377517i	$-0.123222\pi$
$569$	3.24559	+	5.62154i	0.136062	+	0.235667i	−0.789940	+	0.613184i	$0.789889\pi$
$570$	−0.198972	+	0.344630i	−0.00833403	+	0.0144350i
$571$	1.79038	−	23.8909i	0.0749250	−	0.999804i	−0.825389	−	0.564564i	$-0.809044\pi$
$571$	1.79038	−	23.8909i	0.0749250	−	0.999804i	0.900314	−	0.435240i	$-0.143337\pi$
$572$	0.114340	−	0.291334i	0.00478081	−	0.0121813i
$573$	5.12076	+	22.4355i	0.213923	+	0.937258i
$574$	11.7916	+	9.49797i	0.492172	+	0.396438i
$575$	0.675034	−	2.95752i	0.0281509	−	0.123337i
$576$	0.826239	+	0.563320i	0.0344266	+	0.0234717i
$577$	−1.95440	−	1.81342i	−0.0813626	−	0.0754935i	0.638443	−	0.769669i	$-0.279579\pi$
$577$	−1.95440	−	1.81342i	−0.0813626	−	0.0754935i	−0.719806	+	0.694175i	$0.755769\pi$
$578$	3.07332	−	0.463229i	0.127833	−	0.0192678i
$579$	−17.0953	+	15.8621i	−0.710455	+	0.659206i
$580$	0.937121	−	1.17511i	0.0389118	−	0.0487939i
$581$	20.4316	+	1.63141i	0.847645	+	0.0676824i
$582$	−4.45761	−	5.58966i	−0.184774	−	0.231699i
$583$	2.39646	+	0.361208i	0.0992513	+	0.0149597i
$584$	2.83349	−	1.93184i	0.117251	−	0.0799403i
$585$	−0.706619	−	1.80044i	−0.0292151	−	0.0744389i
$586$	−29.2598	+	9.02544i	−1.20871	+	0.372838i
$587$	−23.8723			−0.985315			−0.492658	−	0.870223i	$-0.663974\pi$
$587$	−23.8723			−0.985315			−0.492658	+	0.870223i	$0.663974\pi$
$588$	−2.49369	−	6.54076i	−0.102838	−	0.269736i
$589$	−0.288002			−0.0118669
$590$	−7.62410	+	2.35172i	−0.313879	+	0.0968189i
$591$	2.00952	+	5.12018i	0.0826608	+	0.210616i
$592$	−8.45644	+	5.76550i	−0.347558	+	0.236961i
$593$	−17.1195	−	2.58035i	−0.703013	−	0.105962i	−0.212199	−	0.977226i	$-0.568062\pi$
$593$	−17.1195	−	2.58035i	−0.703013	−	0.105962i	−0.490814	+	0.871264i	$0.663301\pi$
$594$	0.124741	+	0.156421i	0.00511820	+	0.00641802i
$595$	10.5293	+	6.14777i	0.431658	+	0.252034i
$596$	−0.921097	+	1.15502i	−0.0377296	+	0.0473114i
$597$	−14.7913	+	13.7243i	−0.605367	+	0.561699i
$598$	−1.35179	+	0.203750i	−0.0552789	+	0.00833195i
$599$	16.0157	+	14.8604i	0.654383	+	0.607179i	0.935853	−	0.352391i	$-0.114631\pi$
$599$	16.0157	+	14.8604i	0.654383	+	0.607179i	−0.281470	+	0.959570i	$0.590822\pi$
$600$	−2.86809	−	1.95543i	−0.117089	−	0.0798301i
$601$	−0.316392	+	1.38621i	−0.0129059	+	0.0565445i	−0.980971	−	0.194155i	$-0.937803\pi$
$601$	−0.316392	+	1.38621i	−0.0129059	+	0.0565445i	0.968065	+	0.250700i	$0.0806606\pi$
$602$	−10.1716	+	8.03068i	−0.414562	+	0.327306i
$603$	0.388263	+	1.70109i	0.0158113	+	0.0692738i
$604$	1.68235	−	4.28655i	0.0684537	−	0.174417i
$605$	1.01268	−	13.5133i	0.0411713	−	0.549393i
$606$	−4.30470	+	7.45596i	−0.174867	+	0.302878i
$607$	−9.89623	−	17.1408i	−0.401676	−	0.695723i	0.592253	−	0.805752i	$-0.298239\pi$
$607$	−9.89623	−	17.1408i	−0.401676	−	0.695723i	−0.993928	+	0.110030i	$0.964905\pi$
$608$	0.289978	−	0.139646i	0.0117602	−	0.00566339i
$609$	2.79316	−	1.59451i	0.113184	−	0.0646128i
$610$	1.90446	+	0.917140i	0.0771094	+	0.0371339i
$611$	1.39412	+	18.6032i	0.0564000	+	0.752605i
$612$	−3.56160	−	1.09861i	−0.143969	−	0.0444086i
$613$	−34.4015	−	10.6115i	−1.38946	−	0.428592i	−0.492351	−	0.870397i	$-0.663862\pi$
$613$	−34.4015	−	10.6115i	−1.38946	−	0.428592i	−0.897112	+	0.441804i	$0.854339\pi$
$614$	−0.234681	−	3.13160i	−0.00947096	−	0.126381i
$615$	−6.37508	−	3.07008i	−0.257068	−	0.123797i
$616$	−0.0814459	+	0.523031i	−0.00328155	+	0.0210735i
$617$	−14.3940	+	6.93179i	−0.579481	+	0.279063i	−0.700576	−	0.713578i	$-0.747074\pi$
$617$	−14.3940	+	6.93179i	−0.579481	+	0.279063i	0.121095	+	0.992641i	$0.461359\pi$
$618$	4.41446	+	7.64606i	0.177575	+	0.307570i
$619$	−17.6613	+	30.5902i	−0.709867	+	1.22953i	0.255040	+	0.966931i	$0.417912\pi$
$619$	−17.6613	+	30.5902i	−0.709867	+	1.22953i	−0.964906	+	0.262595i	$0.915422\pi$
$620$	−0.0826806	+	1.10330i	−0.00332053	+	0.0443094i
$621$	0.319276	−	0.813502i	0.0128121	−	0.0326447i
$622$	1.44834	+	6.34561i	0.0580733	+	0.254436i
$623$	−9.29199	−	19.5383i	−0.372276	−	0.782785i
$624$	−0.348089	+	1.52508i	−0.0139347	+	0.0610520i
$625$	3.64034	+	2.48194i	0.145614	+	0.0992777i
$626$	−8.10942	−	7.52444i	−0.324117	−	0.300737i
$627$	0.0636734	−	0.00959722i	0.00254287	−	0.000383276i
$628$	10.8005	−	10.0214i	0.430986	−	0.399897i
$629$	23.7845	−	29.8248i	0.948348	−	1.18919i
$630$	1.82956	+	2.71181i	0.0728915	+	0.108041i
$631$	−10.1066	−	12.6733i	−0.402337	−	0.504514i	0.538850	−	0.842402i	$-0.318859\pi$
$631$	−10.1066	−	12.6733i	−0.402337	−	0.504514i	−0.941186	+	0.337888i	$0.890288\pi$
$632$	−13.6141	−	2.05200i	−0.541540	−	0.0816241i
$633$	0.283309	−	0.193157i	0.0112605	−	0.00767730i
$634$	9.43984	+	24.0523i	0.374904	+	0.955239i
$635$	2.11520	−	0.652454i	0.0839393	−	0.0258919i
$636$	−12.1134			−0.480329
$637$	8.09928	−	7.36928i	0.320905	−	0.291981i
$638$	−0.243209			−0.00962875
$639$	−9.84742	+	3.03753i	−0.389558	+	0.120163i
$640$	−0.451716	−	1.15095i	−0.0178556	−	0.0454954i
$641$	−21.3453	+	14.5530i	−0.843088	+	0.574808i	−0.906032	−	0.423209i	$-0.860904\pi$
$641$	−21.3453	+	14.5530i	−0.843088	+	0.574808i	0.0629437	+	0.998017i	$0.479951\pi$
$642$	1.16648	+	0.175818i	0.0460372	+	0.00693899i
$643$	2.47090	+	3.09841i	0.0974428	+	0.122189i	0.828162	−	0.560489i	$-0.189387\pi$
$643$	2.47090	+	3.09841i	0.0974428	+	0.122189i	−0.730719	+	0.682678i	$0.760815\pi$
$644$	2.15642	−	0.834215i	0.0849749	−	0.0328727i
$645$	3.77607	−	4.73505i	0.148683	−	0.186442i
$646$	−0.879370	+	0.815936i	−0.0345983	+	0.0321026i
$647$	11.5833	−	1.74590i	0.455386	−	0.0686383i	0.0826556	−	0.996578i	$-0.473660\pi$
$647$	11.5833	−	1.74590i	0.455386	−	0.0686383i	0.372730	+	0.927940i	$0.378422\pi$
$648$	−0.733052	−	0.680173i	−0.0287970	−	0.0267197i
$649$	1.06670	+	0.727267i	0.0418718	+	0.0285477i
$650$	1.20831	−	5.29394i	0.0473937	−	0.207645i
$651$	−1.03761	+	2.12801i	−0.0406673	+	0.0834032i
$652$	−4.20586	−	18.4271i	−0.164714	−	0.721659i
$653$	6.65824	−	16.9649i	0.260557	−	0.663888i	−0.739399	−	0.673267i	$-0.764890\pi$
$653$	6.65824	−	16.9649i	0.260557	−	0.663888i	0.999956	+	0.00937910i	$0.00298550\pi$
$654$	−0.865330	+	11.5470i	−0.0338371	+	0.451524i
$655$	6.87371	−	11.9056i	0.268578	−	0.465191i
$656$	2.86140	+	4.95609i	0.111719	+	0.193503i
$657$	−3.08977	+	1.48796i	−0.120544	+	0.0580507i
$658$	−9.15304	−	30.1957i	−0.356823	−	1.17715i
$659$	−6.56802	−	3.16299i	−0.255854	−	0.123213i	0.301561	−	0.953447i	$-0.402492\pi$
$659$	−6.56802	−	3.16299i	−0.255854	−	0.123213i	−0.557415	+	0.830234i	$0.688207\pi$
$660$	−0.0184860	−	0.246679i	−0.000719568	−	0.00960196i
$661$	21.5404	+	6.64433i	0.837824	+	0.258434i	0.683834	−	0.729638i	$-0.260311\pi$
$661$	21.5404	+	6.64433i	0.837824	+	0.258434i	0.153990	+	0.988072i	$0.450788\pi$
$662$	19.2660	+	5.94277i	0.748793	+	0.230972i
$663$	−0.435710	−	5.81414i	−0.0169216	−	0.225803i
$664$	6.97980	+	3.36129i	0.270869	+	0.130443i
$665$	1.05029	−	0.0735573i	0.0407285	−	0.00285243i
$666$	9.22129	−	4.44074i	0.357318	−	0.172075i
$667$	0.531174	+	0.920021i	0.0205672	+	0.0356234i
$668$	0.700789	−	1.21380i	0.0271144	−	0.0469634i
$669$	2.03706	−	27.1827i	0.0787573	−	1.05094i
$670$	0.788171	−	2.00823i	0.0304497	−	0.0775846i
$671$	−0.0761109	−	0.333464i	−0.00293823	−	0.0128732i
$672$	0.0129079	−	2.64572i	0.000497931	−	0.102061i
$673$	−1.11571	+	4.88826i	−0.0430075	+	0.188428i	−0.991869	−	0.127265i	$-0.959380\pi$
$673$	−1.11571	+	4.88826i	−0.0430075	+	0.188428i	0.948861	+	0.315694i	$0.102237\pi$
$674$	−28.8400	−	19.6628i	−1.11088	−	0.757383i
$675$	2.54461	+	2.36105i	0.0979422	+	0.0908770i
$676$	10.4351	−	1.57284i	0.401350	−	0.0604938i
$677$	−7.80911	+	7.24579i	−0.300128	+	0.278478i	−0.815832	−	0.578288i	$-0.803721\pi$
$677$	−7.80911	+	7.24579i	−0.300128	+	0.278478i	0.515704	+	0.856767i	$0.327530\pi$
$678$	−6.31348	+	7.91685i	−0.242468	+	0.304045i
$679$	−5.66360	+	18.0479i	−0.217349	+	0.692613i
$680$	2.87328	+	3.60298i	0.110185	+	0.138168i
$681$	−10.6957	−	1.61212i	−0.409861	−	0.0617767i
$682$	0.147920	−	0.100850i	0.00566416	−	0.00386176i
$683$	−3.00510	−	7.65688i	−0.114987	−	0.292982i	0.861781	−	0.507280i	$-0.169349\pi$
$683$	−3.00510	−	7.65688i	−0.114987	−	0.292982i	−0.976768	+	0.214298i	$0.931254\pi$
$684$	−0.307552	+	0.0948673i	−0.0117596	+	0.00362734i
$685$	4.27612			0.163382
$686$	−10.6557	+	15.1478i	−0.406836	+	0.578347i
$687$	−24.8931			−0.949730
$688$	−4.68067	+	1.44379i	−0.178449	+	0.0550442i
$689$	−6.92286	−	17.6392i	−0.263740	−	0.671999i
$690$	−0.892772	+	0.608682i	−0.0339873	+	0.0231721i
$691$	−7.22816	−	1.08947i	−0.274972	−	0.0414454i	0.0101085	−	0.999949i	$-0.496782\pi$
$691$	−7.22816	−	1.08947i	−0.274972	−	0.0414454i	−0.285081	+	0.958504i	$0.592020\pi$
$692$	−6.71481	−	8.42011i	−0.255259	−	0.320085i
$693$	0.158490	−	0.505050i	0.00602053	−	0.0191853i
$694$	−13.5558	+	16.9985i	−0.514572	+	0.645253i
$695$	−1.77162	+	1.64382i	−0.0672012	+	0.0623536i
$696$	1.20205	−	0.181179i	0.0455634	−	0.00686758i
$697$	−15.6360	−	14.5081i	−0.592255	−	0.549533i
$698$	13.1934	+	8.99513i	0.499379	+	0.340471i
$699$	2.58339	−	11.3185i	0.0977126	−	0.428107i
$700$	−0.0448065	+	9.18398i	−0.00169353	+	0.347122i
$701$	7.47755	+	32.7613i	0.282423	+	1.23738i	0.894676	+	0.446715i	$0.147406\pi$
$701$	7.47755	+	32.7613i	0.282423	+	1.23738i	−0.612253	+	0.790662i	$0.709737\pi$
$702$	0.571503	−	1.45617i	0.0215700	−	0.0549594i
$703$	0.246169	−	3.28489i	0.00928442	−	0.123892i
$704$	−0.100035	+	0.173265i	−0.00377020	+	0.00653018i
$705$	7.37261	+	12.7697i	0.277668	+	0.480936i
$706$	−13.3010	+	6.40544i	−0.500591	+	0.241072i
$707$	22.7227	−	1.59139i	0.854574	−	0.0598503i
$708$	−5.81390	−	2.79983i	−0.218500	−	0.105224i
$709$	2.06140	+	27.5075i	0.0774175	+	1.03306i	0.891709	+	0.452609i	$0.149507\pi$
$709$	2.06140	+	27.5075i	0.0774175	+	1.03306i	−0.814292	+	0.580456i	$0.802874\pi$
$710$	12.1756	+	3.75567i	0.456941	+	0.140948i
$711$	13.1562	+	4.05816i	0.493397	+	0.152193i
$712$	−0.611095	−	8.15450i	−0.0229018	−	0.305603i
$713$	−0.704561	−	0.339299i	−0.0263860	−	0.0127068i
$714$	2.86064	+	9.43719i	0.107057	+	0.353178i
$715$	0.348640	−	0.167896i	0.0130384	−	0.00627897i
$716$	−4.92526	−	8.53080i	−0.184066	−	0.318811i
$717$	12.4526	−	21.5686i	0.465051	−	0.805492i
$718$	−0.848282	+	11.3195i	−0.0316576	+	0.422442i
$719$	0.168364	−	0.428984i	0.00627891	−	0.0159984i	−0.927700	−	0.373327i	$-0.878217\pi$
$719$	0.168364	−	0.428984i	0.00627891	−	0.0159984i	0.933979	+	0.357328i	$0.116312\pi$
$720$	0.275130	+	1.20542i	0.0102535	+	0.0449235i
$721$	10.2377	−	20.9961i	0.381272	−	0.781937i
$722$	4.20485	−	18.4226i	0.156488	−	0.685620i
$723$	19.3549	+	13.1960i	0.719818	+	0.490763i
$724$	17.3012	+	16.0532i	0.642994	+	0.596611i
$725$	−4.17261	+	0.628920i	−0.154967	+	0.0233575i
$726$	8.03423	−	7.45467i	0.298178	−	0.276669i
$727$	12.0868	−	15.1564i	0.448276	−	0.562120i	−0.505428	−	0.862869i	$-0.668665\pi$
$727$	12.0868	−	15.1564i	0.448276	−	0.562120i	0.953703	+	0.300749i	$0.0972367\pi$
$728$	3.85998	−	1.49324i	0.143060	−	0.0553432i
$729$	0.623490	+	0.781831i	0.0230922	+	0.0289567i
$730$	4.19282	+	0.631965i	0.155183	+	0.0233901i
$731$	15.0845	−	10.2845i	0.557921	−	0.380384i
$732$	0.624588	+	1.59142i	0.0230854	+	0.0588207i
$733$	−13.7172	+	4.23120i	−0.506657	+	0.156283i	−0.537537	−	0.843240i	$-0.680645\pi$
$733$	−13.7172	+	4.23120i	−0.506657	+	0.156283i	0.0308803	+	0.999523i	$0.490169\pi$
$734$	−8.66108			−0.319686
$735$	3.24047	−	8.02544i	0.119527	−	0.296023i
$736$	0.873913			0.0322128
$737$	−0.333580	+	0.102896i	−0.0122876	+	0.00379021i
$738$	−2.09078	−	5.32721i	−0.0769625	−	0.196097i
$739$	−16.6827	+	11.3741i	−0.613683	+	0.418402i	−0.829875	−	0.557949i	$-0.811588\pi$
$739$	−16.6827	+	11.3741i	−0.613683	+	0.418402i	0.216193	+	0.976351i	$0.430636\pi$
$740$	−12.5133	−	1.88607i	−0.459997	−	0.0693334i
$741$	−0.313909	−	0.393630i	−0.0115317	−	0.0144604i
$742$	17.9245	+	26.5680i	0.658030	+	0.975343i
$743$	−32.2444	+	40.4332i	−1.18293	+	1.48335i	−0.344121	+	0.938925i	$0.611823\pi$
$743$	−32.2444	+	40.4332i	−1.18293	+	1.48335i	−0.838810	+	0.544424i	$0.816748\pi$
$744$	−0.655957	+	0.608639i	−0.0240486	+	0.0223138i
$745$	−1.80620	+	0.272240i	−0.0661740	+	0.00997412i
$746$	−14.1858	−	13.1625i	−0.519380	−	0.481914i
$747$	−6.40086	−	4.36404i	−0.234195	−	0.159672i
$748$	0.165933	−	0.727002i	0.00606712	−	0.0265818i
$749$	−1.34045	−	2.81856i	−0.0489789	−	0.102988i
$750$	−2.33070	−	10.2115i	−0.0851050	−	0.372870i
$751$	1.49463	−	3.80825i	0.0545398	−	0.138965i	−0.901007	−	0.433804i	$-0.857171\pi$
$751$	1.49463	−	3.80825i	0.0545398	−	0.138965i	0.955547	+	0.294839i	$0.0952661\pi$
$752$	0.891209	−	11.8924i	0.0324990	−	0.433670i
$753$	−4.21930	+	7.30805i	−0.153760	+	0.266320i
$754$	0.950800	+	1.64683i	0.0346261	+	0.0599741i
$755$	5.12972	−	2.47034i	0.186690	−	0.0899050i
$756$	−0.407088	+	2.61425i	−0.0148056	+	0.0950792i
$757$	10.1010	+	4.86436i	0.367125	+	0.176798i	0.608346	−	0.793672i	$-0.291833\pi$
$757$	10.1010	+	4.86436i	0.367125	+	0.176798i	−0.241220	+	0.970470i	$0.577548\pi$
$758$	−1.97922	−	26.4109i	−0.0718886	−	0.959287i
$759$	0.167075	+	0.0515360i	0.00606446	+	0.00187064i
$760$	0.380265	+	0.117296i	0.0137937	+	0.00425478i
$761$	−2.14168	−	28.5788i	−0.0776360	−	1.03598i	−0.890934	−	0.454133i	$-0.849949\pi$
$761$	−2.14168	−	28.5788i	−0.0776360	−	1.03598i	0.813298	−	0.581847i	$-0.197670\pi$
$762$	1.61299	+	0.776774i	0.0584324	+	0.0281396i
$763$	26.6062	−	15.1885i	0.963208	−	0.549860i
$764$	20.7335	−	9.98475i	0.750113	−	0.361236i
$765$	−2.30419	−	3.99098i	−0.0833083	−	0.144294i
$766$	−1.43831	+	2.49122i	−0.0519681	+	0.0900114i
$767$	0.754350	−	10.0661i	0.0272380	−	0.363466i
$768$	0.365341	−	0.930874i	0.0131831	−	0.0335900i
$769$	9.80471	+	42.9572i	0.353567	+	1.54908i	0.768877	+	0.639397i	$0.220816\pi$
$769$	9.80471	+	42.9572i	0.353567	+	1.54908i	−0.415310	+	0.909680i	$0.636327\pi$
$770$	−0.513679	+	0.405561i	−0.0185117	+	0.0146154i
$771$	5.91003	−	25.8935i	0.212845	−	0.932533i
$772$	19.2685	+	13.1370i	0.693487	+	0.472811i
$773$	33.0358	+	30.6527i	1.18822	+	1.10250i	0.992551	+	0.121832i	$0.0388769\pi$
$773$	33.0358	+	30.6527i	1.18822	+	1.10250i	0.195665	+	0.980671i	$0.437314\pi$
$774$	4.84358	−	0.730052i	0.174099	−	0.0262412i
$775$	2.27700	−	2.11274i	0.0817921	−	0.0758920i
$776$	−4.45761	+	5.58966i	−0.160019	+	0.200657i
$777$	−23.3847	−	13.6537i	−0.838921	−	0.489824i
$778$	13.0213	+	16.3281i	0.466835	+	0.585392i
$779$	−1.82132	−	0.274520i	−0.0652555	−	0.00983569i
$780$	−1.59806	+	1.08954i	−0.0572197	+	0.0390117i
$781$	−0.753248	−	1.91925i	−0.0269533	−	0.0686760i
$782$	−3.11253	+	0.960088i	−0.111304	+	0.0343327i
$783$	−1.21562			−0.0434428
$784$	−5.82187	+	3.88662i	−0.207924	+	0.138808i
$785$	18.2170			0.650191
$786$	10.6247	−	3.27729i	0.378971	−	0.116897i
$787$	6.14356	+	15.6535i	0.218994	+	0.557989i	0.997578	−	0.0695518i	$-0.0221569\pi$
$787$	6.14356	+	15.6535i	0.218994	+	0.557989i	−0.778584	+	0.627540i	$0.784062\pi$
$788$	4.54465	−	3.09849i	0.161896	−	0.110379i
$789$	11.1687	+	1.68341i	0.397616	+	0.0599309i
$790$	−10.6136	−	13.3091i	−0.377616	−	0.473515i
$791$	26.7060	+	2.13241i	0.949555	+	0.0758197i
$792$	0.124741	−	0.156421i	0.00443249	−	0.00555817i
$793$	−1.96042	+	1.81901i	−0.0696166	+	0.0645948i
$794$	28.5378	−	4.30138i	1.01277	−	0.152650i
$795$	−10.9792	−	10.1872i	−0.389391	−	0.361302i
$796$	16.6716	+	11.3665i	0.590909	+	0.402875i
$797$	−6.95528	+	30.4731i	−0.246369	+	1.07941i	0.688728	+	0.725020i	$0.258169\pi$
$797$	−6.95528	+	30.4731i	−0.246369	+	1.07941i	−0.935097	+	0.354392i	$0.884688\pi$
$798$	0.663161	+	0.534167i	0.0234757	+	0.0189093i
$799$	9.89092	+	43.3350i	0.349916	+	1.53308i
$800$	−1.26819	+	3.23130i	−0.0448374	+	0.114244i
$801$	−0.611095	+	8.15450i	−0.0215920	+	0.288125i
$802$	0.972424	−	1.68429i	0.0343375	−	0.0594743i
$803$	−0.343058	−	0.594194i	−0.0121063	−	0.0209687i
$804$	1.57204	−	0.757057i	0.0554417	−	0.0266993i
$805$	2.65606	+	1.05741i	0.0936137	+	0.0372688i
$806$	−1.26116	−	0.607343i	−0.0444225	−	0.0213927i
$807$	−0.812780	−	10.8458i	−0.0286112	−	0.381790i
$808$	8.22691	+	2.53767i	0.289422	+	0.0892748i
$809$	−25.7777	−	7.95136i	−0.906295	−	0.279555i	−0.193643	−	0.981072i	$-0.562030\pi$
$809$	−25.7777	−	7.95136i	−0.906295	−	0.279555i	−0.712653	+	0.701517i	$0.752506\pi$
$810$	−0.0923980	−	1.23297i	−0.00324654	−	0.0433220i
$811$	4.50517	+	2.16958i	0.158198	+	0.0761841i	0.511307	−	0.859398i	$-0.329161\pi$
$811$	4.50517	+	2.16958i	0.158198	+	0.0761841i	−0.353109	+	0.935582i	$0.614876\pi$
$812$	−2.17607	−	2.36831i	−0.0763651	−	0.0831115i
$813$	−9.47615	+	4.56347i	−0.332343	+	0.160048i
$814$	1.02384	+	1.77335i	0.0358857	+	0.0621558i
$815$	11.6848	−	20.2386i	0.409300	−	0.708928i
$816$	−0.278533	+	3.71677i	−0.00975062	+	0.130113i
$817$	0.575967	−	1.46754i	0.0201505	−	0.0513427i
$818$	−2.73271	−	11.9728i	−0.0955470	−	0.418619i
$819$	−4.03942	+	0.901261i	−0.141149	+	0.0314926i
$820$	−1.57452	+	6.89840i	−0.0549845	+	0.240903i
$821$	5.06963	+	3.45641i	0.176931	+	0.120630i	0.648547	−	0.761174i	$-0.275377\pi$
$821$	5.06963	+	3.45641i	0.176931	+	0.120630i	−0.471616	+	0.881804i	$0.656329\pi$
$822$	2.53523	+	2.35235i	0.0884263	+	0.0820477i
$823$	21.3641	−	3.22013i	0.744707	−	0.112247i	0.234282	−	0.972169i	$-0.424726\pi$
$823$	21.3641	−	3.22013i	0.744707	−	0.112247i	0.510425	+	0.859922i	$0.329488\pi$
$824$	6.47205	−	6.00518i	0.225465	−	0.209201i
$825$	−0.433009	+	0.542976i	−0.0150754	+	0.0189040i
$826$	2.46219	+	16.8944i	0.0856704	+	0.587831i
$827$	−30.4250	−	38.1518i	−1.05798	−	1.32667i	−0.942813	−	0.333322i	$-0.891830\pi$
$827$	−30.4250	−	38.1518i	−1.05798	−	1.32667i	−0.115169	−	0.993346i	$-0.536741\pi$
$828$	−0.864152	−	0.130250i	−0.0300313	−	0.00452650i
$829$	−0.602130	+	0.410525i	−0.0209128	+	0.0142581i	−0.573731	−	0.819044i	$-0.694505\pi$
$829$	−0.602130	+	0.410525i	−0.0209128	+	0.0142581i	0.552819	+	0.833302i	$0.313552\pi$
$830$	3.49944	+	8.91643i	0.121467	+	0.309494i
$831$	0.216870	−	0.0668954i	0.00752312	−	0.00232058i
$832$	1.56430			0.0542323
$833$	16.4653	−	20.2386i	0.570490	−	0.701225i
$834$	−1.95464			−0.0676838
$835$	1.65595	−	0.510794i	0.0573067	−	0.0176768i
$836$	−0.0235253	−	0.0599414i	−0.000813638	−	0.00207312i
$837$	0.739344	−	0.504076i	0.0255555	−	0.0174234i
$838$	6.50417	+	0.980346i	0.224683	+	0.0338655i
$839$	12.5271	+	15.7085i	0.432485	+	0.542319i	0.949545	−	0.313630i	$-0.101545\pi$
$839$	12.5271	+	15.7085i	0.432485	+	0.542319i	−0.517060	+	0.855949i	$0.672974\pi$
$840$	2.23670	−	2.38713i	0.0771735	−	0.0823637i
$841$	−17.1598	+	21.5178i	−0.591719	+	0.741992i
$842$	13.8021	−	12.8065i	0.475651	−	0.441340i
$843$	4.02498	−	0.606668i	0.138628	−	0.0208948i
$844$	−0.251356	−	0.233225i	−0.00865204	−	0.00802792i
$845$	10.7807	+	7.35016i	0.370868	+	0.252853i
$846$	−2.65372	+	11.6267i	−0.0912367	+	0.399734i
$847$	−28.2385	−	6.59037i	−0.970287	−	0.226448i
$848$	2.69549	+	11.8097i	0.0925636	+	0.405548i
$849$	8.72219	−	22.2238i	0.299345	−	0.762718i
$850$	0.966861	−	12.9019i	0.0331631	−	0.442530i
$851$	4.47219	−	7.74606i	0.153305	−	0.265531i
$852$	5.15263	+	8.92461i	0.176526	+	0.305752i
$853$	−0.800565	+	0.385532i	−0.0274108	+	0.0132003i	−0.447539	−	0.894264i	$-0.647699\pi$
$853$	−0.800565	+	0.385532i	−0.0274108	+	0.0132003i	0.420128	+	0.907465i	$0.361985\pi$
$854$	2.56620	−	3.72475i	0.0878136	−	0.127458i
$855$	−0.358535	−	0.172662i	−0.0122617	−	0.00590490i
$856$	−0.0881556	−	1.17636i	−0.00301310	−	0.0402070i
$857$	−0.730151	−	0.225222i	−0.0249415	−	0.00769343i	0.282259	−	0.959338i	$-0.408916\pi$
$857$	−0.730151	−	0.225222i	−0.0249415	−	0.00769343i	−0.307201	+	0.951645i	$0.599392\pi$
$858$	0.299064	+	0.0922491i	0.0102099	+	0.00314933i
$859$	2.54816	+	34.0028i	0.0869420	+	1.16016i	0.854595	+	0.519295i	$0.173805\pi$
$859$	2.54816	+	34.0028i	0.0869420	+	1.16016i	−0.767653	+	0.640865i	$0.778576\pi$
$860$	−5.45659	−	2.62775i	−0.186068	−	0.0896056i
$861$	−8.59023	+	12.4684i	−0.292754	+	0.424922i
$862$	34.6926	−	16.7071i	1.18163	−	0.569045i
$863$	−6.32765	−	10.9598i	−0.215396	−	0.373076i	0.737999	−	0.674801i	$-0.235771\pi$
$863$	−6.32765	−	10.9598i	−0.215396	−	0.373076i	−0.953395	+	0.301725i	$0.902437\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	0.995101	−	13.2787i	0.0338345	−	0.451490i
$866$	15.0496	−	38.3458i	0.511407	−	1.30304i
$867$	0.691603	+	3.03011i	0.0234881	+	0.102908i
$868$	2.30554	+	0.538073i	0.0782553	+	0.0182634i
$869$	−0.612942	+	2.68547i	−0.0207926	+	0.0910984i
$870$	1.24186	+	0.846684i	0.0421029	+	0.0287053i
$871$	2.00083	+	1.85650i	0.0677954	+	0.0629050i
$872$	11.4501	−	1.72582i	0.387748	−	0.0584436i
$873$	5.24091	−	4.86286i	0.177378	−	0.164583i
$874$	−0.175369	+	0.219906i	−0.00593194	+	0.00743842i
$875$	−18.9477	+	20.2220i	−0.640548	+	0.683627i
$876$	2.13819	+	2.68120i	0.0722427	+	0.0905895i
$877$	−52.2919	−	7.88173i	−1.76577	−	0.266147i	−0.815766	−	0.578382i	$-0.803684\pi$
$877$	−52.2919	−	7.88173i	−1.76577	−	0.266147i	−0.950005	+	0.312234i	$0.898923\pi$
$878$	−26.3906	+	17.9928i	−0.890640	+	0.607228i
$879$	−11.1868	−	28.5035i	−0.377321	−	0.961398i
$880$	−0.236381	+	0.0729138i	−0.00796839	+	0.00245792i
$881$	−36.9335			−1.24432			−0.622160	−	0.782890i	$-0.713745\pi$
$881$	−36.9335			−1.24432			−0.622160	+	0.782890i	$0.713745\pi$
$882$	6.33612	−	2.97550i	0.213348	−	0.100190i
$883$	20.6268			0.694147			0.347074	−	0.937838i	$-0.387175\pi$
$883$	20.6268			0.694147			0.347074	+	0.937838i	$0.387175\pi$
$884$	−5.57141	+	1.71855i	−0.187387	+	0.0578012i
$885$	−2.91490	−	7.42704i	−0.0979832	−	0.249657i
$886$	17.6769	−	12.0519i	0.593867	−	0.404892i
$887$	28.9406	+	4.36209i	0.971729	+	0.146465i	0.615675	−	0.788001i	$-0.288884\pi$
$887$	28.9406	+	4.36209i	0.971729	+	0.146465i	0.356055	+	0.934465i	$0.384122\pi$
$888$	−6.38133	−	8.00194i	−0.214144	−	0.268527i
$889$	−0.683101	−	4.68712i	−0.0229105	−	0.157201i
$890$	6.30391	−	7.90485i	0.211308	−	0.264971i
$891$	−0.146661	+	0.136082i	−0.00491334	+	0.00455891i
$892$	−26.9545	+	4.06273i	−0.902502	+	0.136030i
$893$	2.81367	+	2.61071i	0.0941560	+	0.0873640i
$894$	−1.22062	−	0.832207i	−0.0408238	−	0.0278332i
$895$	2.71018	−	11.8741i	0.0905912	−	0.396906i
$896$	−2.58226	+	0.576144i	−0.0862672	+	0.0192476i
$897$	−0.304200	−	1.33279i	−0.0101569	−	0.0445004i
$898$	5.09339	−	12.9778i	0.169969	−	0.433073i
$899$	−0.0812897	+	1.08474i	−0.00271116	+	0.0361780i
$900$	1.73563	−	3.00620i	0.0578543	−	0.100207i
$901$	−22.5746	−	39.1003i	−0.752068	−	1.30262i
$902$	1.03157	−	0.496779i	0.0343476	−	0.0165409i
$903$	−8.76834	−	9.54298i	−0.291792	−	0.317571i
$904$	9.12324	+	4.39352i	0.303434	+	0.146126i
$905$	2.18074	+	29.1000i	0.0724903	+	0.967316i
$906$	4.40028	+	1.35731i	0.146190	+	0.0450935i
$907$	−49.2777	−	15.2001i	−1.63624	−	0.504713i	−0.665813	−	0.746118i	$-0.731915\pi$
$907$	−49.2777	−	15.2001i	−1.63624	−	0.504713i	−0.970424	+	0.241406i	$0.922392\pi$
$908$	0.808321	+	10.7863i	0.0268251	+	0.357956i
$909$	−7.75680	−	3.73548i	−0.257277	−	0.123898i
$910$	4.75433	+	1.89276i	0.157604	+	0.0627443i
$911$	−42.8513	+	20.6361i	−1.41973	+	0.683704i	−0.977056	−	0.212981i	$-0.931683\pi$
$911$	−42.8513	+	20.6361i	−1.41973	+	0.683704i	−0.442670	+	0.896685i	$0.645969\pi$
$912$	0.160926	+	0.278731i	0.00532878	+	0.00922971i
$913$	0.774969	−	1.34228i	0.0256477	−	0.0444231i
$914$	0.181572	−	2.42291i	0.00600586	−	0.0801426i
$915$	−0.772255	+	1.96767i	−0.0255300	+	0.0650493i
$916$	5.53923	+	24.2690i	0.183021	+	0.801869i
$917$	−22.9096	−	18.4534i	−0.756543	−	0.609384i
$918$	0.829378	−	3.63374i	0.0273736	−	0.119931i
$919$	34.2498	+	23.3511i	1.12980	+	0.770283i	0.975989	−	0.217818i	$-0.0698940\pi$
$919$	34.2498	+	23.3511i	1.12980	+	0.770283i	0.153808	+	0.988101i	$0.450846\pi$
$920$	0.792081	+	0.734944i	0.0261142	+	0.0242304i
$921$	3.10531	−	0.468050i	0.102323	−	0.0154228i
$922$	21.1988	−	19.6696i	0.698144	−	0.647783i
$923$	−10.0510	+	12.6035i	−0.330832	+	0.414850i
$924$	−0.527655	−	0.0421320i	−0.0173586	−	0.00138604i
$925$	22.1513	+	27.7768i	0.728329	+	0.913295i
$926$	−17.6040	−	2.65338i	−0.578504	−	0.0871954i
$927$	−7.29479	+	4.97350i	−0.239592	+	0.163351i
$928$	−0.444117	−	1.13159i	−0.0145789	−	0.0371463i
$929$	32.7515	−	10.1025i	1.07454	−	0.331452i	0.293518	−	0.955954i	$-0.405174\pi$
$929$	32.7515	−	10.1025i	1.07454	−	0.331452i	0.781024	+	0.624501i	$0.214698\pi$
$930$	−1.10639			−0.0362799
$931$	0.190277	−	2.24491i	0.00623608	−	0.0735739i
$932$	−11.6096			−0.380286
$933$	−6.21963	+	1.91850i	−0.203622	+	0.0628090i
$934$	14.6357	+	37.2911i	0.478893	+	1.22020i
$935$	0.761791	−	0.519380i	0.0249132	−	0.0169855i
$936$	−1.54683	−	0.233147i	−0.0505596	−	0.00762064i
$937$	23.5685	+	29.5540i	0.769950	+	0.965487i	0.999970	−	0.00769872i	$-0.00245060\pi$
$937$	23.5685	+	29.5540i	0.769950	+	0.965487i	−0.230020	+	0.973186i	$0.573879\pi$
$938$	−3.98662	−	2.32768i	−0.130168	−	0.0760015i
$939$	6.89738	−	8.64904i	0.225088	−	0.282251i
$940$	10.8090	−	10.0293i	0.352551	−	0.327119i
$941$	26.5678	−	4.00445i	0.866086	−	0.130541i	0.299053	−	0.954237i	$-0.403329\pi$
$941$	26.5678	−	4.00445i	0.866086	−	0.130541i	0.567033	+	0.823695i	$0.308091\pi$
$942$	10.8005	+	10.0214i	0.351899	+	0.326515i
$943$	−4.13221	−	2.81729i	−0.134563	−	0.0917437i
$944$	−1.43591	+	6.29115i	−0.0467350	+	0.204760i
$945$	−2.56750	+	2.02710i	−0.0835208	+	0.0659416i
$946$	0.218070	+	0.955427i	0.00709007	+	0.0310636i
$947$	1.26444	−	3.22173i	0.0410886	−	0.104692i	−0.908856	−	0.417109i	$-0.863043\pi$
$947$	1.26444	−	3.22173i	0.0410886	−	0.104692i	0.949945	+	0.312417i	$0.101139\pi$
$948$	1.02888	−	13.7294i	0.0334163	−	0.445910i
$949$	−2.68230	+	4.64587i	−0.0870710	+	0.150811i
$950$	−0.558614	−	0.967548i	−0.0181238	−	0.0313914i
$951$	−23.2796	+	11.2109i	−0.754893	+	0.363537i
$952$	8.56402	−	4.88889i	0.277562	−	0.158450i
$953$	31.7689	+	15.2991i	1.02910	+	0.495586i	0.870713	−	0.491791i	$-0.163658\pi$
$953$	31.7689	+	15.2991i	1.02910	+	0.495586i	0.158383	+	0.987378i	$0.449372\pi$
$954$	−0.905239	−	12.0796i	−0.0293082	−	0.391090i
$955$	27.1891	+	8.38672i	0.879818	+	0.271388i
$956$	−23.7987	−	7.34094i	−0.769707	−	0.237423i
$957$	−0.0181751	−	0.242529i	−0.000587516	−	0.00783986i
$958$	−6.74270	−	3.24712i	−0.217847	−	0.104910i
$959$	1.40790	−	9.04127i	0.0454634	−	0.291958i
$960$	1.11398	−	0.536464i	0.0359535	−	0.0173143i
$961$	15.0996	+	26.1533i	0.487085	+	0.843656i
$962$	8.00519	−	13.8654i	0.258098	−	0.447039i
$963$	−0.0881556	+	1.17636i	−0.00284078	+	0.0379075i
$964$	8.55824	−	21.8060i	0.275642	−	0.702325i
$965$	6.41622	+	28.1113i	0.206545	+	0.904935i
$966$	0.993031	+	2.08805i	0.0319503	+	0.0671819i
$967$	1.73298	−	7.59266i	0.0557287	−	0.244164i	−0.939390	−	0.342851i	$-0.888607\pi$
$967$	1.73298	−	7.59266i	0.0557287	−	0.244164i	0.995118	+	0.0986877i	$0.0314645\pi$
$968$	−9.05555	−	6.17397i	−0.291057	−	0.198439i
$969$	−0.879370	−	0.815936i	−0.0282494	−	0.0262116i
$970$	−8.74101	+	1.31749i	−0.280657	+	0.0423022i
$971$	−40.7627	+	37.8223i	−1.30814	+	1.21377i	−0.346948	+	0.937885i	$0.612782\pi$
$971$	−40.7627	+	37.8223i	−1.30814	+	1.21377i	−0.961189	+	0.275889i	$0.911028\pi$
$972$	0.623490	−	0.781831i	0.0199984	−	0.0250773i
$973$	2.89233	+	4.28706i	0.0927238	+	0.137437i
$974$	19.1187	+	23.9741i	0.612602	+	0.768179i
$975$	5.36944	+	0.809312i	0.171960	+	0.0259187i
$976$	1.41254	−	0.963053i	0.0452143	−	0.0308266i
$977$	7.70058	+	19.6208i	0.246363	+	0.627723i	0.999547	−	0.0300864i	$-0.00957825\pi$
$977$	7.70058	+	19.6208i	0.246363	+	0.627723i	−0.753184	+	0.657810i	$0.771483\pi$
$978$	18.0612	−	5.57115i	0.577534	−	0.178146i
$979$	−1.63604			−0.0522881
$980$	−8.54530	−	1.37340i	−0.272970	−	0.0438716i
$981$	−11.5794			−0.369702
$982$	−25.1360	+	7.75342i	−0.802121	+	0.247422i
$983$	−8.84040	−	22.5250i	−0.281965	−	0.718435i	−0.999754	−	0.0221747i	$-0.992941\pi$
$983$	−8.84040	−	22.5250i	−0.281965	−	0.718435i	0.717789	−	0.696261i	$-0.245154\pi$
$984$	−4.72840	+	3.22377i	−0.150736	+	0.102770i
$985$	6.72487	+	1.01361i	0.214272	+	0.0322963i
$986$	2.82495	+	3.54237i	0.0899647	+	0.112812i
$987$	29.4272	−	11.3840i	0.936679	−	0.362356i
$988$	−0.313909	+	0.393630i	−0.00998679	+	0.0125230i
$989$	3.13796	−	2.91160i	0.0997812	−	0.0925834i
$990$	0.244608	−	0.0368687i	0.00777414	−	0.00117176i
$991$	−35.5316	−	32.9685i	−1.12870	−	1.04728i	−0.998442	−	0.0557984i	$-0.982230\pi$
$991$	−35.5316	−	32.9685i	−1.12870	−	1.04728i	−0.130256	−	0.991480i	$-0.541580\pi$
$992$	0.739344	+	0.504076i	0.0234742	+	0.0160044i
$993$	−4.48640	+	19.6562i	−0.142372	+	0.623771i
$994$	11.9496	−	24.5070i	0.379018	−	0.777316i
$995$	5.55149	+	24.3227i	0.175994	+	0.771080i
$996$	−2.83029	+	7.21147i	−0.0896813	+	0.228504i
$997$	0.592327	−	7.90405i	0.0187592	−	0.250324i	−0.979938	−	0.199301i	$-0.936133\pi$
$997$	0.592327	−	7.90405i	0.0187592	−	0.250324i	0.998697	−	0.0510227i	$-0.0162481\pi$
$998$	3.07643	−	5.32854i	0.0973828	−	0.168672i
$999$	5.11743	+	8.86365i	0.161908	+	0.280434i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.m.b.25.2	✓	24
3.2	odd	2		882.2.z.a.613.1		24
49.2	even	21	inner	294.2.m.b.247.2	yes	24
147.2	odd	42		882.2.z.a.541.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.m.b.25.2	✓	24	1.1	even	1	trivial
294.2.m.b.247.2	yes	24	49.2	even	21	inner
882.2.z.a.541.1		24	147.2	odd	42
882.2.z.a.613.1		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)

\(f(q)\)	\(=\)	\(q+(0.955573 - 0.294755i) q^{2} +(0.365341 + 0.930874i) q^{3} +(0.826239 - 0.563320i) q^{4} +(1.22261 + 0.184279i) q^{5} +(0.623490 + 0.781831i) q^{6} +(0.792174 - 2.52437i) q^{7} +(0.623490 - 0.781831i) q^{8} +(-0.733052 + 0.680173i) q^{9} +O(q^{10})\)	\(q+(0.955573 - 0.294755i) q^{2} +(0.365341 + 0.930874i) q^{3} +(0.826239 - 0.563320i) q^{4} +(1.22261 + 0.184279i) q^{5} +(0.623490 + 0.781831i) q^{6} +(0.792174 - 2.52437i) q^{7} +(0.623490 - 0.781831i) q^{8} +(-0.733052 + 0.680173i) q^{9} +(1.22261 - 0.184279i) q^{10} +(-0.146661 - 0.136082i) q^{11} +(0.826239 + 0.563320i) q^{12} +(-0.348089 + 1.52508i) q^{13} +(0.0129079 - 2.64572i) q^{14} +(0.275130 + 1.20542i) q^{15} +(0.365341 - 0.930874i) q^{16} +(-0.278533 + 3.71677i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(0.160926 + 0.278731i) q^{19} +(1.11398 - 0.536464i) q^{20} +(2.63929 - 0.184843i) q^{21} +(-0.180256 - 0.0868069i) q^{22} +(0.0653076 + 0.871469i) q^{23} +(0.955573 + 0.294755i) q^{24} +(-3.31704 - 1.02317i) q^{25} +(0.116900 + 1.55993i) q^{26} +(-0.900969 - 0.433884i) q^{27} +(-0.767505 - 2.53198i) q^{28} +(1.09524 - 0.527439i) q^{29} +(0.618212 + 1.07077i) q^{30} +(-0.447415 + 0.774946i) q^{31} +(0.0747301 - 0.997204i) q^{32} +(0.0730936 - 0.186239i) q^{33} +(0.829378 + 3.63374i) q^{34} +(1.43371 - 2.94035i) q^{35} +(-0.222521 + 0.974928i) q^{36} +(-8.45644 - 5.76550i) q^{37} +(0.235934 + 0.218914i) q^{38} +(-1.54683 + 0.233147i) q^{39} +(0.906362 - 0.840981i) q^{40} +(-3.56811 + 4.47427i) q^{41} +(2.46755 - 0.954574i) q^{42} +(-3.05403 - 3.82963i) q^{43} +(-0.197835 - 0.0298188i) q^{44} +(-1.02158 + 0.696502i) q^{45} +(0.319276 + 0.813502i) q^{46} +(11.3959 - 3.51516i) q^{47} +1.00000 q^{48} +(-5.74492 - 3.99949i) q^{49} -3.47126 q^{50} +(-3.56160 + 1.09861i) q^{51} +(0.571503 + 1.45617i) q^{52} +(-10.0086 + 6.82374i) q^{53} +(-0.988831 - 0.149042i) q^{54} +(-0.154233 - 0.193402i) q^{55} +(-1.47972 - 2.19327i) q^{56} +(-0.200671 + 0.251633i) q^{57} +(0.891115 - 0.826834i) q^{58} +(-6.38087 + 0.961761i) q^{59} +(0.906362 + 0.840981i) q^{60} +(1.41254 + 0.963053i) q^{61} +(-0.199119 + 0.872395i) q^{62} +(1.13631 + 2.38931i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-0.706619 + 1.80044i) q^{65} +(0.0149512 - 0.199510i) q^{66} +(0.872419 - 1.51107i) q^{67} +(1.86360 + 3.22784i) q^{68} +(-0.787368 + 0.379176i) q^{69} +(0.503333 - 3.23231i) q^{70} +(9.28471 + 4.47128i) q^{71} +(0.0747301 + 0.997204i) q^{72} +(3.27703 + 1.01083i) q^{73} +(-9.78016 - 3.01678i) q^{74} +(-0.259407 - 3.46155i) q^{75} +(0.289978 + 0.139646i) q^{76} +(-0.459703 + 0.262428i) q^{77} +(-1.40938 + 0.678724i) q^{78} +(-6.88394 - 11.9233i) q^{79} +(0.618212 - 1.07077i) q^{80} +(0.0747301 - 0.997204i) q^{81} +(-2.09078 + 5.32721i) q^{82} +(1.72387 + 7.55276i) q^{83} +(2.07655 - 1.63949i) q^{84} +(-1.02546 + 4.49285i) q^{85} +(-4.04715 - 2.75930i) q^{86} +(0.891115 + 0.826834i) q^{87} +(-0.197835 + 0.0298188i) q^{88} +(5.99443 - 5.56202i) q^{89} +(-0.770897 + 0.966675i) q^{90} +(3.57412 + 2.08684i) q^{91} +(0.544876 + 0.683252i) q^{92} +(-0.884836 - 0.133368i) q^{93} +(9.85348 - 6.71799i) q^{94} +(0.145385 + 0.370436i) q^{95} +(0.955573 - 0.294755i) q^{96} -7.14944 q^{97} +(-6.66856 - 2.12845i) q^{98} +0.200070 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

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