LMFDB - Embedded newform 462.2.y.c.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(25,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 24]))

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

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

chi := DirichletCharacter("462.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.y (of order $15$, degree $8$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			37.4
Character	$\chi$	$=$	462.37
Dual form			462.2.y.c.25.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.913545 + 0.406737i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.171980 + 1.63628i) q^{5} +(0.809017 - 0.587785i) q^{6} +(2.59574 - 0.512007i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.913545 - 0.406737i) q^{9} +O(q^{10})$	\(q+(-0.913545 + 0.406737i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.171980 + 1.63628i) q^{5} +(0.809017 - 0.587785i) q^{6} +(2.59574 - 0.512007i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.913545 - 0.406737i) q^{9} +(-0.822649 - 1.42487i) q^{10} +(3.21007 + 0.833949i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-5.56988 - 4.04675i) q^{13} +(-2.16307 + 1.52352i) q^{14} +(-0.508425 - 1.56477i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(3.87324 + 1.72448i) q^{17} +(-0.669131 + 0.743145i) q^{18} +(1.08214 + 1.20183i) q^{19} +(1.33107 + 0.967082i) q^{20} +(-2.43256 + 1.04050i) q^{21} +(-3.27174 + 0.543801i) q^{22} +(0.325395 - 0.563601i) q^{23} +(0.104528 - 0.994522i) q^{24} +(2.24289 - 0.476741i) q^{25} +(6.73430 + 1.43142i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(1.35639 - 2.27161i) q^{28} +(2.81930 + 8.67692i) q^{29} +(1.10092 + 1.22269i) q^{30} +(-0.745242 + 7.09051i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.31331 - 0.148315i) q^{33} -4.23979 q^{34} +(1.28420 + 4.15931i) q^{35} +(0.309017 - 0.951057i) q^{36} +(11.2099 + 2.38274i) q^{37} +(-1.47741 - 0.657786i) q^{38} +(6.28953 + 2.80028i) q^{39} +(-1.60934 - 0.342077i) q^{40} +(1.12248 - 3.45465i) q^{41} +(1.79905 - 1.93996i) q^{42} -7.34892 q^{43} +(2.76770 - 1.82752i) q^{44} +(0.822649 + 1.42487i) q^{45} +(-0.0680261 + 0.647225i) q^{46} +(-0.820780 - 0.911569i) q^{47} +(0.309017 + 0.951057i) q^{48} +(6.47570 - 2.65807i) q^{49} +(-1.85507 + 1.34779i) q^{50} +(-4.14714 - 0.881501i) q^{51} +(-6.73430 + 1.43142i) q^{52} +(-0.588312 + 5.59742i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.812510 + 5.39601i) q^{55} +(-0.315180 + 2.62691i) q^{56} +(-1.30836 - 0.950583i) q^{57} +(-6.10478 - 6.78005i) q^{58} +(-3.53098 + 3.92155i) q^{59} +(-1.50305 - 0.669203i) q^{60} +(-0.173825 - 1.65383i) q^{61} +(-2.20316 - 6.78062i) q^{62} +(2.16307 - 1.52352i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(5.66373 - 9.80987i) q^{65} +(3.08718 - 1.21215i) q^{66} +(1.35847 + 2.35294i) q^{67} +(3.87324 - 1.72448i) q^{68} +(-0.201105 + 0.618939i) q^{69} +(-2.86492 - 3.27738i) q^{70} +(-7.98970 + 5.80486i) q^{71} +(0.104528 + 0.994522i) q^{72} +(8.68442 - 9.64502i) q^{73} +(-11.2099 + 2.38274i) q^{74} +(-2.09476 + 0.932645i) q^{75} +1.61723 q^{76} +(8.75948 + 0.521137i) q^{77} -6.88475 q^{78} +(0.977823 - 0.435355i) q^{79} +(1.60934 - 0.342077i) q^{80} +(0.669131 - 0.743145i) q^{81} +(0.379692 + 3.61253i) q^{82} +(5.91038 - 4.29414i) q^{83} +(-0.854458 + 2.50398i) q^{84} +(-2.15561 + 6.63430i) q^{85} +(6.71358 - 2.98908i) q^{86} +(-4.56173 - 7.90114i) q^{87} +(-1.78510 + 2.79525i) q^{88} +(-1.61350 + 2.79466i) q^{89} +(-1.33107 - 0.967082i) q^{90} +(-16.5299 - 7.65249i) q^{91} +(-0.201105 - 0.618939i) q^{92} +(-0.745242 - 7.09051i) q^{93} +(1.12059 + 0.498918i) q^{94} +(-1.78044 + 1.97738i) q^{95} +(-0.669131 - 0.743145i) q^{96} +(-6.15550 - 4.47224i) q^{97} +(-4.83471 + 5.06217i) q^{98} +(3.27174 - 0.543801i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9}+O(q^{10}) $ 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9	\( 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9} + 4 q^{10} + 2 q^{11} - 20 q^{12} - 2 q^{13} - 3 q^{14} - 2 q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} - q^{19} - 2 q^{20} - 2 q^{21} + 4 q^{22} - 20 q^{23} - 5 q^{24} + 16 q^{25} + 4 q^{26} - 10 q^{27} + 13 q^{28} + 16 q^{29} - q^{30} + 30 q^{31} + 20 q^{32} + 2 q^{33} + 32 q^{34} + 3 q^{35} - 10 q^{36} + 19 q^{37} + 6 q^{38} + q^{39} - q^{40} - 12 q^{41} + 11 q^{42} - 36 q^{43} - 3 q^{44} - 4 q^{45} + 10 q^{46} + 25 q^{47} - 10 q^{48} + 29 q^{49} + 12 q^{50} - 14 q^{51} - 4 q^{52} - 18 q^{53} + 20 q^{54} + 12 q^{55} - 4 q^{56} + 12 q^{57} + 8 q^{58} - 14 q^{59} + q^{60} + 35 q^{61} - 40 q^{62} + 3 q^{63} - 10 q^{64} - 2 q^{65} + 3 q^{66} - 24 q^{67} + 6 q^{68} - 40 q^{69} - 32 q^{70} - 34 q^{71} - 5 q^{72} - 39 q^{73} - 19 q^{74} + 6 q^{75} - 28 q^{76} - 31 q^{77} + 12 q^{78} - 17 q^{79} + q^{80} + 5 q^{81} + 4 q^{82} - 24 q^{83} + 3 q^{84} - 112 q^{85} + 7 q^{86} + 2 q^{87} - 2 q^{88} - 38 q^{89} + 2 q^{90} - 36 q^{91} - 40 q^{92} + 30 q^{93} - 10 q^{94} - 42 q^{95} - 5 q^{96} + 4 q^{97} - 50 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9 + 4 * q^10 + 2 * q^11 - 20 * q^12 - 2 * q^13 - 3 * q^14 - 2 * q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 - q^19 - 2 * q^20 - 2 * q^21 + 4 * q^22 - 20 * q^23 - 5 * q^24 + 16 * q^25 + 4 * q^26 - 10 * q^27 + 13 * q^28 + 16 * q^29 - q^30 + 30 * q^31 + 20 * q^32 + 2 * q^33 + 32 * q^34 + 3 * q^35 - 10 * q^36 + 19 * q^37 + 6 * q^38 + q^39 - q^40 - 12 * q^41 + 11 * q^42 - 36 * q^43 - 3 * q^44 - 4 * q^45 + 10 * q^46 + 25 * q^47 - 10 * q^48 + 29 * q^49 + 12 * q^50 - 14 * q^51 - 4 * q^52 - 18 * q^53 + 20 * q^54 + 12 * q^55 - 4 * q^56 + 12 * q^57 + 8 * q^58 - 14 * q^59 + q^60 + 35 * q^61 - 40 * q^62 + 3 * q^63 - 10 * q^64 - 2 * q^65 + 3 * q^66 - 24 * q^67 + 6 * q^68 - 40 * q^69 - 32 * q^70 - 34 * q^71 - 5 * q^72 - 39 * q^73 - 19 * q^74 + 6 * q^75 - 28 * q^76 - 31 * q^77 + 12 * q^78 - 17 * q^79 + q^80 + 5 * q^81 + 4 * q^82 - 24 * q^83 + 3 * q^84 - 112 * q^85 + 7 * q^86 + 2 * q^87 - 2 * q^88 - 38 * q^89 + 2 * q^90 - 36 * q^91 - 40 * q^92 + 30 * q^93 - 10 * q^94 - 42 * q^95 - 5 * q^96 + 4 * q^97 - 50 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.913545	+	0.406737i	−0.645974	+	0.287606i
$2$	−0.913545	+	0.406737i	−0.645974	+	0.287606i
$3$	−0.978148	+	0.207912i	−0.564734	+	0.120038i
$3$	−0.978148	+	0.207912i	−0.564734	+	0.120038i
$4$	0.669131	−	0.743145i	0.334565	−	0.371572i
$5$	0.171980	+	1.63628i	0.0769120	+	0.731769i	0.963228	+	0.268687i	$0.0865897\pi$
$5$	0.171980	+	1.63628i	0.0769120	+	0.731769i	−0.886316	+	0.463082i	$0.846744\pi$
$6$	0.809017	−	0.587785i	0.330280	−	0.239962i
$7$	2.59574	−	0.512007i	0.981096	−	0.193520i
$7$	2.59574	−	0.512007i	0.981096	−	0.193520i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	0.913545	−	0.406737i	0.304515	−	0.135579i
$10$	−0.822649	−	1.42487i	−0.260144	−	0.450583i
$11$	3.21007	+	0.833949i	0.967872	+	0.251445i
$11$	3.21007	+	0.833949i	0.967872	+	0.251445i
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−5.56988	−	4.04675i	−1.54481	−	1.12237i	−0.947230	−	0.320556i	$-0.896130\pi$
$13$	−5.56988	−	4.04675i	−1.54481	−	1.12237i	−0.597577	−	0.801812i	$-0.703870\pi$
$14$	−2.16307	+	1.52352i	−0.578105	+	0.407179i
$15$	−0.508425	−	1.56477i	−0.131275	−	0.404022i
$16$	−0.104528	−	0.994522i	−0.0261321	−	0.248630i
$17$	3.87324	+	1.72448i	0.939398	+	0.418247i	0.818557	−	0.574425i	$-0.194774\pi$
$17$	3.87324	+	1.72448i	0.939398	+	0.418247i	0.120841	+	0.992672i	$0.461441\pi$
$18$	−0.669131	+	0.743145i	−0.157716	+	0.175161i
$19$	1.08214	+	1.20183i	0.248259	+	0.275720i	0.854375	−	0.519656i	$-0.173940\pi$
$19$	1.08214	+	1.20183i	0.248259	+	0.275720i	−0.606116	+	0.795376i	$0.707273\pi$
$20$	1.33107	+	0.967082i	0.297637	+	0.216246i
$21$	−2.43256	+	1.04050i	−0.530828	+	0.227056i
$22$	−3.27174	+	0.543801i	−0.697537	+	0.115939i
$23$	0.325395	−	0.563601i	0.0678496	−	0.117519i	−0.830105	−	0.557607i	$-0.811720\pi$
$23$	0.325395	−	0.563601i	0.0678496	−	0.117519i	0.897954	+	0.440088i	$0.145053\pi$
$24$	0.104528	−	0.994522i	0.0213368	−	0.203006i
$25$	2.24289	−	0.476741i	0.448578	−	0.0953481i
$26$	6.73430	+	1.43142i	1.32070	+	0.280724i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	1.35639	−	2.27161i	0.256334	−	0.429293i
$29$	2.81930	+	8.67692i	0.523531	+	1.61126i	0.767202	+	0.641405i	$0.221648\pi$
$29$	2.81930	+	8.67692i	0.523531	+	1.61126i	−0.243671	+	0.969858i	$0.578352\pi$
$30$	1.10092	+	1.22269i	0.200999	+	0.223232i
$31$	−0.745242	+	7.09051i	−0.133849	+	1.27349i	0.697031	+	0.717041i	$0.254504\pi$
$31$	−0.745242	+	7.09051i	−0.133849	+	1.27349i	−0.830880	+	0.556451i	$0.812163\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−3.31331	−	0.148315i	−0.576773	−	0.0258183i
$34$	−4.23979			−0.727117
$35$	1.28420	+	4.15931i	0.217070	+	0.703052i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	11.2099	+	2.38274i	1.84290	+	0.391720i	0.991206	−	0.132327i	$-0.0422449\pi$
$37$	11.2099	+	2.38274i	1.84290	+	0.391720i	0.851690	+	0.524046i	$0.175578\pi$
$38$	−1.47741	−	0.657786i	−0.239668	−	0.106707i
$39$	6.28953	+	2.80028i	1.00713	+	0.448404i
$40$	−1.60934	−	0.342077i	−0.254460	−	0.0540871i
$41$	1.12248	−	3.45465i	0.175302	−	0.539525i	−0.824345	−	0.566088i	$-0.808456\pi$
$41$	1.12248	−	3.45465i	0.175302	−	0.539525i	0.999647	+	0.0265630i	$0.00845626\pi$
$42$	1.79905	−	1.93996i	0.277599	−	0.299342i
$43$	−7.34892			−1.12070			−0.560350	−	0.828256i	$-0.689333\pi$
$43$	−7.34892			−1.12070			−0.560350	+	0.828256i	$0.689333\pi$
$44$	2.76770	−	1.82752i	0.417246	−	0.275510i
$45$	0.822649	+	1.42487i	0.122633	+	0.212407i
$46$	−0.0680261	+	0.647225i	−0.0100299	+	0.0954282i
$47$	−0.820780	−	0.911569i	−0.119723	−	0.132966i	0.680303	−	0.732931i	$-0.261848\pi$
$47$	−0.820780	−	0.911569i	−0.119723	−	0.132966i	−0.800027	+	0.599965i	$0.795181\pi$
$48$	0.309017	+	0.951057i	0.0446028	+	0.137273i
$49$	6.47570	−	2.65807i	0.925100	−	0.379724i
$50$	−1.85507	+	1.34779i	−0.262347	+	0.190606i
$51$	−4.14714	−	0.881501i	−0.580715	−	0.123435i
$52$	−6.73430	+	1.43142i	−0.933879	+	0.198502i
$53$	−0.588312	+	5.59742i	−0.0808109	+	0.768864i	0.876811	+	0.480835i	$0.159667\pi$
$53$	−0.588312	+	5.59742i	−0.0808109	+	0.768864i	−0.957622	+	0.288029i	$0.907000\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−0.812510	+	5.39601i	−0.109559	+	0.727597i
$56$	−0.315180	+	2.62691i	−0.0421176	+	0.351036i
$57$	−1.30836	−	0.950583i	−0.173297	−	0.125908i
$58$	−6.10478	−	6.78005i	−0.801597	−	0.890264i
$59$	−3.53098	+	3.92155i	−0.459694	+	0.510542i	−0.927773	−	0.373144i	$-0.878280\pi$
$59$	−3.53098	+	3.92155i	−0.459694	+	0.510542i	0.468079	+	0.883687i	$0.344946\pi$
$60$	−1.50305	−	0.669203i	−0.194043	−	0.0863937i
$61$	−0.173825	−	1.65383i	−0.0222560	−	0.211752i	−0.999998	−	0.00194133i	$-0.999382\pi$
$61$	−0.173825	−	1.65383i	−0.0222560	−	0.211752i	0.977742	−	0.209810i	$-0.0672846\pi$
$62$	−2.20316	−	6.78062i	−0.279801	−	0.861139i
$63$	2.16307	−	1.52352i	0.272521	−	0.191946i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	5.66373	−	9.80987i	0.702499	−	1.21676i
$66$	3.08718	−	1.21215i	0.380006	−	0.149205i
$67$	1.35847	+	2.35294i	0.165963	+	0.287457i	0.936997	−	0.349337i	$-0.113593\pi$
$67$	1.35847	+	2.35294i	0.165963	+	0.287457i	−0.771034	+	0.636794i	$0.780260\pi$
$68$	3.87324	−	1.72448i	0.469699	−	0.209124i
$69$	−0.201105	+	0.618939i	−0.0242102	+	0.0745114i
$70$	−2.86492	−	3.27738i	−0.342424	−	0.391722i
$71$	−7.98970	+	5.80486i	−0.948203	+	0.688910i	−0.950381	−	0.311087i	$-0.899307\pi$
$71$	−7.98970	+	5.80486i	−0.948203	+	0.688910i	0.00217781	+	0.999998i	$0.499307\pi$
$72$	0.104528	+	0.994522i	0.0123188	+	0.117206i
$73$	8.68442	−	9.64502i	1.01643	−	1.12886i	0.0248120	−	0.999692i	$-0.492101\pi$
$73$	8.68442	−	9.64502i	1.01643	−	1.12886i	0.991622	−	0.129172i	$-0.0412321\pi$
$74$	−11.2099	+	2.38274i	−1.30312	+	0.276988i
$75$	−2.09476	+	0.932645i	−0.241882	+	0.107693i
$76$	1.61723			0.185509
$77$	8.75948	+	0.521137i	0.998235	+	0.0593891i
$78$	−6.88475			−0.779544
$79$	0.977823	−	0.435355i	0.110014	−	0.0489813i	−0.350992	−	0.936379i	$-0.614156\pi$
$79$	0.977823	−	0.435355i	0.110014	−	0.0489813i	0.461006	+	0.887397i	$0.347489\pi$
$80$	1.60934	−	0.342077i	0.179930	−	0.0382453i
$81$	0.669131	−	0.743145i	0.0743478	−	0.0825716i
$82$	0.379692	+	3.61253i	0.0419300	+	0.398937i
$83$	5.91038	−	4.29414i	0.648748	−	0.471343i	−0.214096	−	0.976813i	$-0.568681\pi$
$83$	5.91038	−	4.29414i	0.648748	−	0.471343i	0.862845	+	0.505469i	$0.168681\pi$
$84$	−0.854458	+	2.50398i	−0.0932290	+	0.273206i
$85$	−2.15561	+	6.63430i	−0.233809	+	0.719590i
$86$	6.71358	−	2.98908i	0.723944	−	0.322320i
$87$	−4.56173	−	7.90114i	−0.489068	−	0.847091i
$88$	−1.78510	+	2.79525i	−0.190292	+	0.297975i
$89$	−1.61350	+	2.79466i	−0.171031	+	0.296234i	−0.938780	−	0.344516i	$-0.888043\pi$
$89$	−1.61350	+	2.79466i	−0.171031	+	0.296234i	0.767750	+	0.640750i	$0.221376\pi$
$90$	−1.33107	−	0.967082i	−0.140307	−	0.101939i
$91$	−16.5299	−	7.65249i	−1.73280	−	0.802199i
$92$	−0.201105	−	0.618939i	−0.0209667	−	0.0645288i
$93$	−0.745242	−	7.09051i	−0.0772780	−	0.735251i
$94$	1.12059	+	0.498918i	0.115580	+	0.0514595i
$95$	−1.78044	+	1.97738i	−0.182669	+	0.202874i
$96$	−0.669131	−	0.743145i	−0.0682929	−	0.0758469i
$97$	−6.15550	−	4.47224i	−0.624997	−	0.454087i	0.229667	−	0.973269i	$-0.426236\pi$
$97$	−6.15550	−	4.47224i	−0.624997	−	0.454087i	−0.854663	+	0.519183i	$0.826236\pi$
$98$	−4.83471	+	5.06217i	−0.488380	+	0.511356i
$99$	3.27174	−	0.543801i	0.328822	−	0.0546541i
$100$	1.14650	−	1.98579i	0.114650	−	0.198579i
$101$	0.253390	−	2.41084i	0.0252132	−	0.239888i	−0.974656	−	0.223709i	$-0.928183\pi$
$101$	0.253390	−	2.41084i	0.0252132	−	0.239888i	0.999869	−	0.0161785i	$-0.00515000\pi$
$102$	4.14714	−	0.881501i	0.410628	−	0.0872816i
$103$	−12.5504	−	2.66767i	−1.23663	−	0.262853i	−0.457209	−	0.889359i	$-0.651151\pi$
$103$	−12.5504	−	2.66767i	−1.23663	−	0.262853i	−0.779416	+	0.626506i	$0.784484\pi$
$104$	5.56988	−	4.04675i	0.546172	−	0.396817i
$105$	−2.12091	−	3.80142i	−0.206980	−	0.370980i
$106$	−1.73922	−	5.35278i	−0.168928	−	0.519908i
$107$	−7.24279	−	8.04394i	−0.700187	−	0.777637i	0.283219	−	0.959055i	$-0.408598\pi$
$107$	−7.24279	−	8.04394i	−0.700187	−	0.777637i	−0.983406	+	0.181419i	$0.941931\pi$
$108$	−0.104528	+	0.994522i	−0.0100583	+	0.0956979i
$109$	−4.71406	−	8.16498i	−0.451525	−	0.782064i	0.546956	−	0.837161i	$-0.315786\pi$
$109$	−4.71406	−	8.16498i	−0.451525	−	0.782064i	−0.998481	+	0.0550975i	$0.982453\pi$
$110$	−1.45249	−	5.25997i	−0.138489	−	0.501519i
$111$	−11.4603			−1.08777
$112$	−0.780530	−	2.52800i	−0.0737532	−	0.238873i
$113$	5.48348	−	16.8764i	0.515842	−	1.58760i	−0.265903	−	0.964000i	$-0.585670\pi$
$113$	5.48348	−	16.8764i	0.515842	−	1.58760i	0.781745	−	0.623599i	$-0.214330\pi$
$114$	1.58189	+	0.336241i	0.148157	+	0.0314918i
$115$	0.978173	+	0.435511i	0.0912151	+	0.0406116i
$116$	8.33469	+	3.71084i	0.773856	+	0.344543i
$117$	−6.73430	−	1.43142i	−0.622586	−	0.132335i
$118$	1.63067	−	5.01869i	0.150116	−	0.462008i
$119$	10.9368	+	2.49316i	1.00258	+	0.228548i
$120$	1.64530			0.150194
$121$	9.60906	+	5.35407i	0.873551	+	0.486733i
$122$	0.831471	+	1.44015i	0.0752779	+	0.130385i
$123$	−0.379692	+	3.61253i	−0.0342357	+	0.325731i
$124$	4.77061	+	5.29830i	0.428413	+	0.475801i
$125$	3.70794	+	11.4119i	0.331648	+	1.02071i
$126$	−1.35639	+	2.27161i	−0.120837	+	0.202371i
$127$	13.8293	−	10.0476i	1.22715	−	0.891577i	0.230477	−	0.973078i	$-0.425971\pi$
$127$	13.8293	−	10.0476i	1.22715	−	0.891577i	0.996673	+	0.0815006i	$0.0259712\pi$
$128$	0.978148	+	0.207912i	0.0864569	+	0.0183770i
$129$	7.18833	−	1.52793i	0.632897	−	0.134527i
$130$	−1.18404	+	11.2654i	−0.103847	+	0.988042i
$131$	−8.95642	+	15.5130i	−0.782526	+	1.35537i	0.147940	+	0.988996i	$0.452736\pi$
$131$	−8.95642	+	15.5130i	−0.782526	+	1.35537i	−0.930466	+	0.366378i	$0.880598\pi$
$132$	−2.32725	+	2.36302i	−0.202562	+	0.205675i
$133$	3.42429	+	2.56559i	0.296924	+	0.222464i
$134$	−2.19805	−	1.59698i	−0.189882	−	0.137958i
$135$	−1.10092	−	1.22269i	−0.0947520	−	0.105233i
$136$	−2.83697	+	3.15078i	−0.243268	+	0.270177i
$137$	1.67906	+	0.747564i	0.143451	+	0.0638687i	0.477207	−	0.878791i	$-0.341649\pi$
$137$	1.67906	+	0.747564i	0.143451	+	0.0638687i	−0.333755	+	0.942660i	$0.608316\pi$
$138$	−0.0680261	−	0.647225i	−0.00579077	−	0.0550955i
$139$	−3.62806	−	11.1660i	−0.307728	−	0.947089i	−0.978645	−	0.205557i	$-0.934099\pi$
$139$	−3.62806	−	11.1660i	−0.307728	−	0.947089i	0.670917	−	0.741532i	$-0.265901\pi$
$140$	3.95027	+	1.82877i	0.333859	+	0.154559i
$141$	0.992370	+	0.720999i	0.0835726	+	0.0607191i
$142$	4.93791	−	8.55271i	0.414380	−	0.717727i
$143$	−14.5049	−	17.6353i	−1.21296	−	1.47474i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−13.7130	+	6.10544i	−1.13881	+	0.507029i
$146$	−4.01063	+	12.3434i	−0.331922	+	1.02155i
$147$	−5.78155	+	3.94636i	−0.476854	+	0.325490i
$148$	9.27160	−	6.73621i	0.762121	−	0.553713i
$149$	−1.20533	−	11.4679i	−0.0987445	−	0.939491i	−0.925964	−	0.377612i	$-0.876745\pi$
$149$	−1.20533	−	11.4679i	−0.0987445	−	0.939491i	0.827219	−	0.561879i	$-0.189921\pi$
$150$	1.53431	−	1.70403i	0.125276	−	0.139133i
$151$	22.7807	−	4.84219i	1.85387	−	0.394052i	0.860540	−	0.509382i	$-0.170126\pi$
$151$	22.7807	−	4.84219i	1.85387	−	0.394052i	0.993327	+	0.115331i	$0.0367928\pi$
$152$	−1.47741	+	0.657786i	−0.119834	+	0.0533535i
$153$	4.23979			0.342766
$154$	−8.21414	+	3.08672i	−0.661915	+	0.248735i
$155$	−11.7303			−0.942197
$156$	6.28953	−	2.80028i	0.503565	−	0.224202i
$157$	−5.87203	+	1.24814i	−0.468639	+	0.0996124i	−0.436178	−	0.899861i	$-0.643668\pi$
$157$	−5.87203	+	1.24814i	−0.468639	+	0.0996124i	−0.0324617	+	0.999473i	$0.510335\pi$
$158$	−0.716211	+	0.795433i	−0.0569787	+	0.0632813i
$159$	−0.588312	−	5.59742i	−0.0466562	−	0.443904i
$160$	−1.33107	+	0.967082i	−0.105231	+	0.0764545i
$161$	0.556073	−	1.62956i	0.0438247	−	0.128428i
$162$	−0.309017	+	0.951057i	−0.0242787	+	0.0747221i
$163$	4.92224	−	2.19152i	0.385540	−	0.171653i	−0.204808	−	0.978802i	$-0.565657\pi$
$163$	4.92224	−	2.19152i	0.385540	−	0.171653i	0.590348	+	0.807149i	$0.298990\pi$
$164$	−1.81621	−	3.14578i	−0.141823	−	0.245644i
$165$	−0.327138	−	5.44702i	−0.0254677	−	0.424050i
$166$	−3.65282	+	6.32686i	−0.283513	+	0.491060i
$167$	−16.8765	−	12.2615i	−1.30594	−	0.948821i	−0.305945	−	0.952049i	$-0.598972\pi$
$167$	−16.8765	−	12.2615i	−1.30594	−	0.948821i	−0.999995	+	0.00322872i	$0.998972\pi$
$168$	−0.237873	−	2.63504i	−0.0183523	−	0.203297i
$169$	10.6301	+	32.7161i	0.817701	+	2.51662i
$170$	−0.729160	−	6.93750i	−0.0559240	−	0.532082i
$171$	1.47741	+	0.657786i	0.112980	+	0.0503021i
$172$	−4.91739	+	5.46132i	−0.374948	+	0.416421i
$173$	4.04062	+	4.48756i	0.307202	+	0.341183i	0.876901	−	0.480671i	$-0.159607\pi$
$173$	4.04062	+	4.48756i	0.307202	+	0.341183i	−0.569699	+	0.821854i	$0.692940\pi$
$174$	7.38103	+	5.36263i	0.559554	+	0.406540i
$175$	5.57785	−	2.38587i	0.421646	−	0.180355i
$176$	0.493837	−	3.27965i	0.0372244	−	0.247213i
$177$	2.63848	−	4.56999i	0.198321	−	0.343501i
$178$	0.337313	−	3.20932i	0.0252827	−	0.240549i
$179$	−9.58250	+	2.03682i	−0.716230	+	0.152239i	−0.551591	−	0.834115i	$-0.685979\pi$
$179$	−9.58250	+	2.03682i	−0.716230	+	0.152239i	−0.164639	+	0.986354i	$0.552646\pi$
$180$	1.60934	+	0.342077i	0.119953	+	0.0254969i
$181$	−5.60056	+	4.06904i	−0.416286	+	0.302449i	−0.776142	−	0.630558i	$-0.782826\pi$
$181$	−5.60056	+	4.06904i	−0.416286	+	0.302449i	0.359856	+	0.933008i	$0.382826\pi$
$182$	18.2134	+	0.267583i	1.35006	+	0.0198346i
$183$	0.513877	+	1.58155i	0.0379869	+	0.116912i
$184$	0.435464	+	0.483632i	0.0321028	+	0.0356538i
$185$	−1.97095	+	18.7524i	−0.144907	+	1.37870i
$186$	3.56478	+	6.17438i	0.261382	+	0.452728i
$187$	10.9952	+	8.76577i	0.804051	+	0.641016i
$188$	−1.22664			−0.0894617
$189$	−1.79905	+	1.93996i	−0.130861	+	0.141111i
$190$	0.822239	−	2.53059i	0.0596515	−	0.183588i
$191$	−3.82470	−	0.812964i	−0.276745	−	0.0588240i	0.0674482	−	0.997723i	$-0.478514\pi$
$191$	−3.82470	−	0.812964i	−0.276745	−	0.0588240i	−0.344193	+	0.938899i	$0.611848\pi$
$192$	0.913545	+	0.406737i	0.0659295	+	0.0293537i
$193$	−6.09376	−	2.71312i	−0.438638	−	0.195294i	0.175522	−	0.984475i	$-0.443839\pi$
$193$	−6.09376	−	2.71312i	−0.438638	−	0.195294i	−0.614161	+	0.789181i	$0.710505\pi$
$194$	7.44236	+	1.58192i	0.534330	+	0.113575i
$195$	−3.50038	+	10.7731i	−0.250667	+	0.771475i
$196$	2.35776	−	6.59098i	0.168411	−	0.470784i
$197$	−24.2690			−1.72909			−0.864547	−	0.502551i	$-0.832395\pi$
$197$	−24.2690			−1.72909			−0.864547	+	0.502551i	$0.832395\pi$
$198$	−2.76770	+	1.82752i	−0.196692	+	0.129876i
$199$	7.01827	+	12.1560i	0.497512	+	0.861716i	0.999996	−	0.00287028i	$-0.000913638\pi$
$199$	7.01827	+	12.1560i	0.497512	+	0.861716i	−0.502484	+	0.864587i	$0.667580\pi$
$200$	−0.239683	+	2.28043i	−0.0169482	+	0.161251i
$201$	−1.81799	−	2.01908i	−0.128231	−	0.142415i
$202$	0.749095	+	2.30548i	0.0527062	+	0.162213i
$203$	11.7608	+	21.0795i	0.825446	+	1.47949i
$204$	−3.43006	+	2.49208i	−0.240152	+	0.174481i
$205$	5.84583	+	1.24257i	0.408290	+	0.0867848i
$206$	12.5504	−	2.66767i	0.874426	−	0.185865i
$207$	0.0680261	−	0.647225i	0.00472814	−	0.0449853i
$208$	−3.44237	+	5.96237i	−0.238686	+	0.413416i
$209$	2.47146	+	4.76042i	0.170955	+	0.329285i
$210$	3.48372	+	2.61012i	0.240400	+	0.180115i
$211$	−1.96942	−	1.43086i	−0.135580	−	0.0985048i	0.517928	−	0.855424i	$-0.326704\pi$
$211$	−1.96942	−	1.43086i	−0.135580	−	0.0985048i	−0.653508	+	0.756919i	$0.726704\pi$
$212$	3.76603	+	4.18260i	0.258652	+	0.287262i
$213$	6.60821	−	7.33916i	0.452787	−	0.502871i
$214$	9.88838	+	4.40259i	0.675956	+	0.300955i
$215$	−1.26387	−	12.0249i	−0.0861953	−	0.820094i
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	1.69593	+	18.7867i	0.115127	+	1.27532i
$218$	7.62750	+	5.54171i	0.516600	+	0.375332i
$219$	−6.48933	+	11.2398i	−0.438508	+	0.759519i
$220$	3.46634	+	4.21444i	0.233701	+	0.284138i
$221$	−14.5949	−	25.2792i	−0.981761	−	1.70046i
$222$	10.4695	−	4.66134i	0.702669	−	0.312848i
$223$	−7.44449	+	22.9118i	−0.498520	+	1.53429i	0.312878	+	0.949793i	$0.398707\pi$
$223$	−7.44449	+	22.9118i	−0.498520	+	1.53429i	−0.811398	+	0.584494i	$0.801293\pi$
$224$	1.74128	+	1.99197i	0.116344	+	0.133094i
$225$	1.85507	−	1.34779i	0.123671	−	0.0898526i
$226$	1.85485	+	17.6477i	0.123383	+	1.17391i
$227$	2.28953	−	2.54279i	0.151962	−	0.168771i	−0.662357	−	0.749188i	$-0.730444\pi$
$227$	2.28953	−	2.54279i	0.151962	−	0.168771i	0.814319	+	0.580417i	$0.197111\pi$
$228$	−1.58189	+	0.336241i	−0.104763	+	0.0222681i
$229$	19.3527	−	8.61636i	1.27886	−	0.569385i	0.348939	−	0.937145i	$-0.386542\pi$
$229$	19.3527	−	8.61636i	1.27886	−	0.569385i	0.929920	+	0.367761i	$0.119875\pi$
$230$	−1.07074			−0.0706028
$231$	−8.67641	+	1.31145i	−0.570866	+	0.0862870i
$232$	−9.12345			−0.598984
$233$	5.08221	−	2.26275i	0.332947	−	0.148237i	−0.233453	−	0.972368i	$-0.575003\pi$
$233$	5.08221	−	2.26275i	0.332947	−	0.148237i	0.566400	+	0.824131i	$0.308336\pi$
$234$	6.73430	−	1.43142i	0.440235	−	0.0935748i
$235$	1.35043	−	1.49980i	0.0880922	−	0.0978363i
$236$	0.551593	+	5.24806i	0.0359057	+	0.341619i
$237$	−0.865940	+	0.629142i	−0.0562488	+	0.0408672i
$238$	−11.0054	+	2.17080i	−0.713372	+	0.140712i
$239$	2.45291	−	7.54927i	0.158665	−	0.488322i	−0.839849	−	0.542821i	$-0.817356\pi$
$239$	2.45291	−	7.54927i	0.158665	−	0.488322i	0.998514	+	0.0544993i	$0.0173563\pi$
$240$	−1.50305	+	0.669203i	−0.0970217	+	0.0431969i
$241$	−6.62184	−	11.4694i	−0.426550	−	0.738807i	0.570013	−	0.821635i	$-0.306938\pi$
$241$	−6.62184	−	11.4694i	−0.426550	−	0.738807i	−0.996564	+	0.0828283i	$0.973605\pi$
$242$	−10.9560	−	0.982826i	−0.704279	−	0.0631785i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−1.34535	−	0.977453i	−0.0861271	−	0.0625750i
$245$	5.46305	+	10.1390i	0.349021	+	0.647754i
$246$	−1.12248	−	3.45465i	−0.0715669	−	0.220260i
$247$	−1.16384	−	11.0732i	−0.0740535	−	0.704572i
$248$	−6.51318	−	2.89985i	−0.413587	−	0.184141i
$249$	−4.88842	+	5.42914i	−0.309791	+	0.344058i
$250$	−8.02900	−	8.91711i	−0.507798	−	0.563967i
$251$	−13.0619	−	9.49002i	−0.824460	−	0.599005i	0.0935269	−	0.995617i	$-0.470186\pi$
$251$	−13.0619	−	9.49002i	−0.824460	−	0.599005i	−0.917986	+	0.396612i	$0.870186\pi$
$252$	0.315180	−	2.62691i	0.0198544	−	0.165480i
$253$	1.51456	−	1.53783i	0.0952193	−	0.0966828i
$254$	−8.54697	+	14.8038i	−0.536284	+	0.928872i
$255$	0.729160	−	6.93750i	0.0456618	−	0.434443i
$256$	−0.978148	+	0.207912i	−0.0611342	+	0.0129945i
$257$	11.0930	+	2.35789i	0.691963	+	0.147081i	0.540453	−	0.841374i	$-0.318253\pi$
$257$	11.0930	+	2.35789i	0.691963	+	0.147081i	0.151510	+	0.988456i	$0.451586\pi$
$258$	−5.94540	+	4.31959i	−0.370145	+	0.268926i
$259$	30.3179	+	0.445418i	1.88386	+	0.0276769i
$260$	−3.50038	−	10.7731i	−0.217084	−	0.668117i
$261$	6.10478	+	6.78005i	0.377876	+	0.419674i
$262$	1.87240	−	17.8147i	0.115677	−	1.10060i
$263$	8.43427	+	14.6086i	0.520079	+	0.900803i	0.999728	+	0.0233426i	$0.00743087\pi$
$263$	8.43427	+	14.6086i	0.520079	+	0.900803i	−0.479648	+	0.877461i	$0.659236\pi$
$264$	1.16492	−	3.10531i	0.0716961	−	0.191119i
$265$	−9.26015			−0.568846
$266$	−4.17176	−	0.950995i	−0.255787	−	0.0583092i
$267$	0.997197	−	3.06906i	0.0610275	−	0.187823i
$268$	2.65757	+	0.564883i	0.162337	+	0.0345057i
$269$	6.11767	+	2.72376i	0.373001	+	0.166071i	0.584671	−	0.811270i	$-0.301224\pi$
$269$	6.11767	+	2.72376i	0.373001	+	0.166071i	−0.211670	+	0.977341i	$0.567890\pi$
$270$	1.50305	+	0.669203i	0.0914730	+	0.0407264i
$271$	−5.92459	−	1.25931i	−0.359893	−	0.0764977i	0.0244164	−	0.999702i	$-0.492227\pi$
$271$	−5.92459	−	1.25931i	−0.359893	−	0.0764977i	−0.384310	+	0.923204i	$0.625561\pi$
$272$	1.31017	−	4.03228i	0.0794405	−	0.244493i
$273$	17.7597	+	4.04851i	1.07487	+	0.245027i
$274$	−1.83796			−0.111035
$275$	7.59740	+	0.340086i	0.458140	+	0.0205079i
$276$	0.325395	+	0.563601i	0.0195865	+	0.0339248i
$277$	0.747003	−	7.10726i	0.0448830	−	0.427034i	−0.948890	−	0.315608i	$-0.897792\pi$
$277$	0.747003	−	7.10726i	0.0448830	−	0.427034i	0.993773	−	0.111426i	$-0.0355417\pi$
$278$	7.85603	+	8.72500i	0.471173	+	0.523291i
$279$	2.20316	+	6.78062i	0.131900	+	0.405945i
$280$	−4.35258	−	0.0639462i	−0.260116	−	0.00382152i
$281$	16.7011	−	12.1341i	0.996307	−	0.723859i	0.0350135	−	0.999387i	$-0.488853\pi$
$281$	16.7011	−	12.1341i	0.996307	−	0.723859i	0.961293	+	0.275528i	$0.0888526\pi$
$282$	−1.19983	−	0.255032i	−0.0714489	−	0.0151869i
$283$	−15.7079	+	3.33882i	−0.933738	+	0.198472i	−0.649570	−	0.760302i	$-0.725051\pi$
$283$	−15.7079	+	3.33882i	−0.933738	+	0.198472i	−0.284169	+	0.958774i	$0.591718\pi$
$284$	−1.03230	+	9.82172i	−0.0612560	+	0.582812i
$285$	1.33041	−	2.30434i	0.0788067	−	0.136497i
$286$	20.4238	+	10.2110i	1.20769	+	0.603790i
$287$	1.14487	−	9.54207i	0.0675794	−	0.563250i
$288$	0.809017	+	0.587785i	0.0476718	+	0.0346356i
$289$	0.652931	+	0.725154i	0.0384077	+	0.0426561i
$290$	10.0442	−	11.1552i	0.589815	−	0.655055i
$291$	6.95082	+	3.09471i	0.407464	+	0.181415i
$292$	−1.35664	−	12.9076i	−0.0793913	−	0.755358i
$293$	−7.90938	−	24.3426i	−0.462071	−	1.42211i	−0.862629	−	0.505837i	$-0.831184\pi$
$293$	−7.90938	−	24.3426i	−0.462071	−	1.42211i	0.400558	−	0.916271i	$-0.368816\pi$
$294$	3.67658	−	5.95674i	0.214422	−	0.347404i
$295$	−7.02403	−	5.10326i	−0.408955	−	0.297123i
$296$	−5.73017	+	9.92494i	−0.333059	+	0.576875i
$297$	−3.08718	+	1.21215i	−0.179136	+	0.0703361i
$298$	5.76556	+	9.98624i	0.333990	+	0.578487i
$299$	−4.09317	+	1.82240i	−0.236714	+	0.105392i
$300$	−0.708575	+	2.18077i	−0.0409096	+	0.125907i
$301$	−19.0759	+	3.76270i	−1.09952	+	0.216878i
$302$	−18.8417	+	13.6893i	−1.08422	+	0.787731i
$303$	0.253390	+	2.41084i	0.0145569	+	0.138499i
$304$	1.08214	−	1.20183i	0.0620648	−	0.0689299i
$305$	2.67625	−	0.568854i	0.153241	−	0.0325725i
$306$	−3.87324	+	1.72448i	−0.221418	+	0.0985818i
$307$	0.759787			0.0433634			0.0216817	−	0.999765i	$-0.493098\pi$
$307$	0.759787			0.0433634			0.0216817	+	0.999765i	$0.493098\pi$
$308$	6.24851	−	6.16085i	0.356042	−	0.351047i
$309$	12.8308			0.729917
$310$	10.7161	−	4.77112i	0.608635	−	0.270982i
$311$	15.9534	−	3.39101i	0.904636	−	0.192286i	0.267971	−	0.963427i	$-0.413647\pi$
$311$	15.9534	−	3.39101i	0.904636	−	0.192286i	0.636665	+	0.771141i	$0.280313\pi$
$312$	−4.60680	+	5.11637i	−0.260808	+	0.289657i
$313$	0.571759	+	5.43992i	0.0323177	+	0.307482i	0.998726	+	0.0504693i	$0.0160717\pi$
$313$	0.571759	+	5.43992i	0.0323177	+	0.307482i	−0.966408	+	0.257013i	$0.917262\pi$
$314$	4.85671	−	3.52860i	0.274080	−	0.199131i
$315$	2.86492	+	3.27738i	0.161420	+	0.184660i
$316$	0.330760	−	1.01797i	0.0186067	−	0.0572655i
$317$	−14.4842	+	6.44879i	−0.813514	+	0.362200i	−0.770951	−	0.636894i	$-0.780219\pi$
$317$	−14.4842	+	6.44879i	−0.813514	+	0.362200i	−0.0425628	+	0.999094i	$0.513552\pi$
$318$	2.81412	+	4.87421i	0.157808	+	0.273332i
$319$	1.81404	+	30.2046i	0.101567	+	1.69114i
$320$	0.822649	−	1.42487i	0.0459875	−	0.0796526i
$321$	8.75695	+	6.36230i	0.488765	+	0.355109i
$322$	0.154806	+	1.71486i	0.00862698	+	0.0955652i
$323$	2.11884	+	6.52111i	0.117895	+	0.362844i
$324$	−0.104528	−	0.994522i	−0.00580714	−	0.0552512i
$325$	−14.4219	−	6.42103i	−0.799981	−	0.356175i
$326$	−3.60532	+	4.00411i	−0.199680	+	0.221767i
$327$	6.30864	+	7.00645i	0.348868	+	0.387458i
$328$	2.93870	+	2.13509i	0.162262	+	0.117891i
$329$	−2.59726	−	1.94595i	−0.143191	−	0.107284i
$330$	2.51436	+	4.84304i	0.138411	+	0.266601i
$331$	4.19239	−	7.26143i	0.230434	−	0.399124i	−0.727502	−	0.686106i	$-0.759319\pi$
$331$	4.19239	−	7.26143i	0.230434	−	0.399124i	0.957936	+	0.286982i	$0.0926519\pi$
$332$	0.763646	−	7.26561i	0.0419105	−	0.398752i
$333$	11.2099	−	2.38274i	0.614299	−	0.130573i
$334$	20.4046	+	4.33713i	1.11649	+	0.237317i
$335$	−3.61644	+	2.62750i	−0.197587	+	0.143556i
$336$	1.28907	+	2.31047i	0.0703247	+	0.126047i
$337$	−4.59574	−	14.1442i	−0.250346	−	0.770485i	−0.994711	−	0.102713i	$-0.967248\pi$
$337$	−4.59574	−	14.1442i	−0.250346	−	0.770485i	0.744365	−	0.667773i	$-0.232752\pi$
$338$	−23.0179	−	25.5640i	−1.25201	−	1.39050i
$339$	−1.85485	+	17.6477i	−0.100741	+	0.958491i
$340$	3.48786	+	6.04114i	0.189156	+	0.327627i
$341$	−8.30540	+	22.1395i	−0.449763	+	1.19892i
$342$	−1.61723			−0.0874497
$343$	15.4483	−	10.2152i	0.834128	−	0.551571i
$344$	2.27094	−	6.98924i	0.122441	−	0.376835i
$345$	−1.04735	−	0.222620i	−0.0563872	−	0.0119855i
$346$	−5.51654	−	2.45612i	−0.296571	−	0.132042i
$347$	−15.6090	−	6.94958i	−0.837936	−	0.373073i	−0.0575278	−	0.998344i	$-0.518322\pi$
$347$	−15.6090	−	6.94958i	−0.837936	−	0.373073i	−0.780408	+	0.625271i	$0.784988\pi$
$348$	−8.92408	−	1.89687i	−0.478381	−	0.101683i
$349$	−4.09636	+	12.6073i	−0.219273	+	0.674854i	0.779549	+	0.626341i	$0.215448\pi$
$349$	−4.09636	+	12.6073i	−0.219273	+	0.674854i	−0.998823	+	0.0485129i	$0.984552\pi$
$350$	−4.12520	+	4.44831i	−0.220501	+	0.237772i
$351$	6.88475			0.367481
$352$	0.882812	+	3.19697i	0.0470540	+	0.170399i
$353$	−11.5415	−	19.9905i	−0.614292	−	1.06399i	−0.990508	−	0.137453i	$-0.956108\pi$
$353$	−11.5415	−	19.9905i	−0.614292	−	1.06399i	0.376216	−	0.926532i	$-0.377225\pi$
$354$	−0.551593	+	5.24806i	−0.0293168	+	0.278931i
$355$	−10.8725	−	12.0751i	−0.577051	−	0.640880i
$356$	0.997197	+	3.06906i	0.0528513	+	0.162660i
$357$	−11.2162	−	0.164784i	−0.593625	−	0.00872128i
$358$	7.92560	−	5.75828i	0.418881	−	0.304335i
$359$	−23.3796	−	4.96948i	−1.23393	−	0.262279i	−0.455626	−	0.890171i	$-0.650585\pi$
$359$	−23.3796	−	4.96948i	−1.23393	−	0.262279i	−0.778301	+	0.627892i	$0.783918\pi$
$360$	−1.60934	+	0.342077i	−0.0848199	+	0.0180290i
$361$	1.71265	−	16.2948i	0.0901397	−	0.857622i
$362$	3.46133	−	5.99521i	0.181924	−	0.315101i
$363$	−10.5122	−	3.23923i	−0.551750	−	0.170016i
$364$	−16.7476	+	7.16359i	−0.877811	+	0.375474i
$365$	17.2756	+	12.5514i	0.904244	+	0.656972i
$366$	−1.11273	−	1.23581i	−0.0581631	−	0.0645967i
$367$	−8.20989	+	9.11801i	−0.428553	+	0.475956i	−0.918287	−	0.395916i	$-0.870427\pi$
$367$	−8.20989	+	9.11801i	−0.428553	+	0.475956i	0.489734	+	0.871872i	$0.337094\pi$
$368$	−0.594527	−	0.264700i	−0.0309918	−	0.0137985i
$369$	−0.379692	−	3.61253i	−0.0197660	−	0.188061i
$370$	−5.82672	−	17.9328i	−0.302917	−	0.932282i
$371$	1.33881	+	14.8306i	0.0695076	+	0.769968i
$372$	−5.76794	−	4.19065i	−0.299054	−	0.217275i
$373$	−12.2348	+	21.1912i	−0.633493	+	1.09724i	0.353340	+	0.935495i	$0.385046\pi$
$373$	−12.2348	+	21.1912i	−0.633493	+	1.09724i	−0.986832	+	0.161746i	$0.948287\pi$
$374$	−13.6100	−	3.53577i	−0.703756	−	0.182830i
$375$	−5.99957	−	10.3916i	−0.309817	−	0.536618i
$376$	1.12059	−	0.498918i	0.0577899	−	0.0257297i
$377$	19.4102	−	59.7384i	0.999675	−	3.07668i
$378$	0.854458	−	2.50398i	0.0439486	−	0.128791i
$379$	−3.83757	+	2.78816i	−0.197123	+	0.143218i	−0.681968	−	0.731382i	$-0.738876\pi$
$379$	−3.83757	+	2.78816i	−0.197123	+	0.143218i	0.484846	+	0.874600i	$0.338876\pi$
$380$	0.278132	+	2.64625i	0.0142678	+	0.135750i
$381$	−11.4381	+	12.7033i	−0.585990	+	0.650808i
$382$	3.82470	−	0.812964i	0.195688	−	0.0415949i
$383$	−29.8144	+	13.2742i	−1.52344	+	0.678281i	−0.986262	−	0.165186i	$-0.947178\pi$
$383$	−29.8144	+	13.2742i	−1.52344	+	0.678281i	−0.537181	+	0.843467i	$0.680511\pi$
$384$	−1.00000			−0.0510310
$385$	0.653729	+	14.4226i	0.0333171	+	0.735045i
$386$	6.67045			0.339517
$387$	−6.71358	+	2.98908i	−0.341270	+	0.151943i
$388$	−7.44236	+	1.58192i	−0.377828	+	0.0803099i
$389$	−8.73509	+	9.70130i	−0.442887	+	0.491876i	−0.922713	−	0.385488i	$-0.874033\pi$
$389$	−8.73509	+	9.70130i	−0.442887	+	0.491876i	0.479826	+	0.877364i	$0.340700\pi$
$390$	−1.18404	−	11.2654i	−0.0599563	−	0.570446i
$391$	2.23225	−	1.62182i	0.112890	−	0.0820192i
$392$	0.526872	+	6.98014i	0.0266111	+	0.352550i
$393$	5.53537	−	17.0361i	0.279223	−	0.859359i
$394$	22.1708	−	9.87109i	1.11695	−	0.497298i
$395$	0.880531	+	1.52512i	0.0443043	+	0.0767373i
$396$	1.78510	−	2.79525i	0.0897045	−	0.140467i
$397$	9.04291	−	15.6628i	0.453851	−	0.786092i	−0.544771	−	0.838585i	$-0.683383\pi$
$397$	9.04291	−	15.6628i	0.453851	−	0.786092i	0.998621	+	0.0524927i	$0.0167166\pi$
$398$	−11.3558	−	8.25048i	−0.569215	−	0.413559i
$399$	−3.88288	−	1.79757i	−0.194387	−	0.0899911i
$400$	−0.708575	−	2.18077i	−0.0354287	−	0.109038i
$401$	−1.25805	−	11.9695i	−0.0628240	−	0.597731i	−0.979965	−	0.199168i	$-0.936176\pi$
$401$	−1.25805	−	11.9695i	−0.0628240	−	0.597731i	0.917141	−	0.398562i	$-0.130491\pi$
$402$	2.48205	+	1.10508i	0.123793	+	0.0551163i
$403$	32.8444	−	36.4774i	1.63610	−	1.81707i
$404$	−1.62206	−	1.80147i	−0.0807003	−	0.0896267i
$405$	1.33107	+	0.967082i	0.0661416	+	0.0480547i
$406$	−19.3178	−	14.4735i	−0.958728	−	0.718309i
$407$	33.9974	+	16.9972i	1.68519	+	0.842521i
$408$	2.11989	−	3.67176i	0.104950	−	0.181779i
$409$	−1.36285	+	12.9666i	−0.0673884	+	0.641158i	0.907742	+	0.419528i	$0.137804\pi$
$409$	−1.36285	+	12.9666i	−0.0673884	+	0.641158i	−0.975131	+	0.221630i	$0.928862\pi$
$410$	−5.84583	+	1.24257i	−0.288705	+	0.0613661i
$411$	−1.79779	−	0.382133i	−0.0886786	−	0.0188492i
$412$	−10.3803	+	7.54173i	−0.511401	+	0.371555i
$413$	−7.15763	+	11.9872i	−0.352204	+	0.589851i
$414$	0.201105	+	0.618939i	0.00988379	+	0.0304192i
$415$	8.04291	+	8.93256i	0.394811	+	0.438482i
$416$	0.719652	−	6.84703i	0.0352839	−	0.335703i
$417$	5.87032	+	10.1677i	0.287471	+	0.497914i
$418$	−4.19403	−	3.34362i	−0.205137	−	0.163542i
$419$	15.7575			0.769805			0.384903	−	0.922957i	$-0.374235\pi$
$419$	15.7575			0.769805			0.384903	+	0.922957i	$0.374235\pi$
$420$	−4.24417	−	0.967501i	−0.207094	−	0.0472092i
$421$	0.572412	−	1.76170i	0.0278976	−	0.0858601i	−0.936138	−	0.351632i	$-0.885627\pi$
$421$	0.572412	−	1.76170i	0.0278976	−	0.0858601i	0.964036	+	0.265772i	$0.0856268\pi$
$422$	2.38114	+	0.506126i	0.115912	+	0.0246378i
$423$	−1.12059	−	0.498918i	−0.0544849	−	0.0242582i
$424$	−5.14166	−	2.28922i	−0.249701	−	0.111174i
$425$	9.50937	+	2.02128i	0.461272	+	0.0980464i
$426$	−3.05180	+	9.39246i	−0.147860	+	0.455066i
$427$	−1.29798	−	4.20391i	−0.0628135	−	0.203442i
$428$	−10.8242			−0.523207
$429$	17.8545	+	14.2342i	0.862024	+	0.687235i
$430$	6.04558	+	10.4713i	0.291544	+	0.504969i
$431$	0.768047	−	7.30748i	0.0369955	−	0.351989i	−0.960328	−	0.278873i	$-0.910039\pi$
$431$	0.768047	−	7.30748i	0.0369955	−	0.351989i	0.997323	−	0.0731157i	$-0.0232942\pi$
$432$	0.669131	+	0.743145i	0.0321936	+	0.0357546i
$433$	−8.71178	−	26.8121i	−0.418662	−	1.28851i	−0.908935	−	0.416939i	$-0.863103\pi$
$433$	−8.71178	−	26.8121i	−0.418662	−	1.28851i	0.490273	−	0.871569i	$-0.336897\pi$
$434$	−9.19053	−	16.4727i	−0.441160	−	0.790713i
$435$	12.1440	−	8.82312i	0.582260	−	0.423036i
$436$	−9.22209	−	1.96021i	−0.441658	−	0.0938773i
$437$	1.02948	−	0.218822i	0.0492466	−	0.0104677i
$438$	1.35664	−	12.9076i	0.0648227	−	0.616747i
$439$	14.6574	−	25.3874i	0.699561	−	1.21168i	−0.269057	−	0.963124i	$-0.586712\pi$
$439$	14.6574	−	25.3874i	0.699561	−	1.21168i	0.968619	−	0.248552i	$-0.0799545\pi$
$440$	−4.88083	−	2.44020i	−0.232684	−	0.116332i
$441$	4.83471	−	5.06217i	0.230224	−	0.241056i
$442$	23.6151	+	17.1574i	1.12326	+	0.816093i
$443$	−7.04927	−	7.82900i	−0.334921	−	0.371967i	0.552036	−	0.833821i	$-0.313851\pi$
$443$	−7.04927	−	7.82900i	−0.334921	−	0.371967i	−0.886956	+	0.461853i	$0.847185\pi$
$444$	−7.66846	+	8.51669i	−0.363929	+	0.404184i
$445$	−4.85035	−	2.15952i	−0.229929	−	0.102371i
$446$	−2.51818	−	23.9589i	−0.119239	−	1.13449i
$447$	3.56331	+	10.9667i	0.168539	+	0.518709i
$448$	−2.40095	−	1.11151i	−0.113434	−	0.0525141i
$449$	−17.2834	−	12.5571i	−0.815655	−	0.592608i	0.0998094	−	0.995007i	$-0.468177\pi$
$449$	−17.2834	−	12.5571i	−0.815655	−	0.592608i	−0.915465	+	0.402398i	$0.868177\pi$
$450$	−1.14650	+	1.98579i	−0.0540464	+	0.0936111i
$451$	6.48424	−	10.1535i	0.305331	−	0.478112i
$452$	−8.87245	−	15.3675i	−0.417325	−	0.722828i
$453$	−21.2761	+	9.47275i	−0.999640	+	0.445069i
$454$	−1.05735	+	3.25419i	−0.0496239	+	0.152727i
$455$	9.67884	−	28.3637i	0.453751	−	1.32971i
$456$	1.30836	−	0.950583i	0.0612698	−	0.0445151i
$457$	0.938455	+	8.92880i	0.0438991	+	0.417672i	0.994298	+	0.106638i	$0.0340086\pi$
$457$	0.938455	+	8.92880i	0.0438991	+	0.417672i	−0.950399	+	0.311034i	$0.899325\pi$
$458$	−14.1749	+	15.7429i	−0.662351	+	0.735616i
$459$	−4.14714	+	0.881501i	−0.193572	+	0.0411450i
$460$	0.978173	−	0.435511i	0.0456076	−	0.0203058i
$461$	22.2225			1.03501			0.517503	−	0.855681i	$-0.326862\pi$
$461$	22.2225			1.03501			0.517503	+	0.855681i	$0.326862\pi$
$462$	7.39288	−	4.72708i	0.343948	−	0.219924i
$463$	−11.3715			−0.528479			−0.264240	−	0.964457i	$-0.585121\pi$
$463$	−11.3715			−0.528479			−0.264240	+	0.964457i	$0.585121\pi$
$464$	8.33469	−	3.71084i	0.386928	−	0.172271i
$465$	11.4739	−	2.43886i	0.532090	−	0.113099i
$466$	−3.72249	+	4.13424i	−0.172441	+	0.191515i
$467$	0.253863	+	2.41535i	0.0117474	+	0.111769i	0.998824	−	0.0484788i	$-0.0154373\pi$
$467$	0.253863	+	2.41535i	0.0117474	+	0.111769i	−0.987077	+	0.160248i	$0.948771\pi$
$468$	−5.56988	+	4.04675i	−0.257468	+	0.187061i
$469$	4.73095	+	5.41206i	0.218455	+	0.249906i
$470$	−0.623653	+	1.91941i	−0.0287670	+	0.0885356i
$471$	5.48421	−	2.44173i	0.252699	−	0.112509i
$472$	−2.63848	−	4.56999i	−0.121446	−	0.210351i
$473$	−23.5905	−	6.12863i	−1.08469	−	0.281795i
$474$	0.535180	−	0.926960i	0.0245816	−	0.0425767i
$475$	3.00007	+	2.17968i	0.137653	+	0.100011i
$476$	9.17096	−	6.45941i	0.420350	−	0.296067i
$477$	1.73922	+	5.35278i	0.0796336	+	0.245087i
$478$	0.829723	+	7.89429i	0.0379506	+	0.361076i
$479$	−10.5247	−	4.68590i	−0.480886	−	0.214104i	0.151953	−	0.988388i	$-0.451444\pi$
$479$	−10.5247	−	4.68590i	−0.480886	−	0.214104i	−0.632839	+	0.774283i	$0.718111\pi$
$480$	1.10092	−	1.22269i	0.0502499	−	0.0558081i
$481$	−52.7954	−	58.6352i	−2.40726	−	2.67354i
$482$	10.7144	+	7.78444i	0.488026	+	0.354572i
$483$	−0.205116	+	1.70957i	−0.00933310	+	0.0777881i
$484$	10.4086	−	3.55835i	0.473116	−	0.161743i
$485$	6.25922	−	10.8413i	0.284217	−	0.492278i
$486$	0.104528	−	0.994522i	0.00474151	−	0.0451124i
$487$	−12.9447	+	2.75147i	−0.586579	+	0.124681i	−0.491635	−	0.870801i	$-0.663601\pi$
$487$	−12.9447	+	2.75147i	−0.586579	+	0.124681i	−0.0949439	+	0.995483i	$0.530267\pi$
$488$	1.62660	+	0.345745i	0.0736329	+	0.0156511i
$489$	−4.35904	+	3.16703i	−0.197122	+	0.143218i
$490$	−9.11463	−	7.04037i	−0.411757	−	0.318051i
$491$	12.0229	+	37.0027i	0.542586	+	1.66991i	0.726662	+	0.686996i	$0.241071\pi$
$491$	12.0229	+	37.0027i	0.542586	+	1.66991i	−0.184076	+	0.982912i	$0.558929\pi$
$492$	2.43057	+	2.69942i	0.109579	+	0.121699i
$493$	−4.04332	+	38.4696i	−0.182102	+	1.73258i
$494$	5.56710	+	9.64251i	0.250476	+	0.433837i
$495$	1.45249	+	5.25997i	0.0652845	+	0.236418i
$496$	7.12956			0.320127
$497$	−17.7670	+	19.1587i	−0.796961	+	0.859384i
$498$	2.25756	−	6.94807i	0.101164	−	0.311350i
$499$	−23.1145	−	4.91314i	−1.03475	−	0.219942i	−0.340926	−	0.940090i	$-0.610741\pi$
$499$	−23.1145	−	4.91314i	−1.03475	−	0.219942i	−0.693821	+	0.720148i	$0.744074\pi$
$500$	10.9618	+	4.88049i	0.490225	+	0.218262i
$501$	19.0570	+	8.48471i	0.851403	+	0.379069i
$502$	15.7926	+	3.35682i	0.704857	+	0.149822i
$503$	−5.61971	+	17.2957i	−0.250571	+	0.771177i	0.744100	+	0.668069i	$0.232879\pi$
$503$	−5.61971	+	17.2957i	−0.250571	+	0.771177i	−0.994670	+	0.103108i	$0.967121\pi$
$504$	0.780530	+	2.52800i	0.0347676	+	0.112606i
$505$	3.98840			0.177482
$506$	−0.758122	+	2.02091i	−0.0337026	+	0.0898402i
$507$	−17.1999	−	29.7911i	−0.763873	−	1.32307i
$508$	1.78680	−	17.0003i	0.0792766	−	0.754266i
$509$	25.3640	+	28.1696i	1.12424	+	1.24860i	0.965253	+	0.261316i	$0.0841564\pi$
$509$	25.3640	+	28.1696i	1.12424	+	1.24860i	0.158988	+	0.987281i	$0.449177\pi$
$510$	2.15561	+	6.63430i	0.0954522	+	0.293772i
$511$	17.6041	−	29.4824i	0.778762	−	1.30423i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−1.58189	−	0.336241i	−0.0698420	−	0.0148454i
$514$	−11.0930	+	2.35789i	−0.489292	+	0.104002i
$515$	2.20664	−	20.9948i	0.0972362	−	0.925140i
$516$	3.67446	−	6.36436i	0.161759	−	0.280175i
$517$	−1.87456	−	3.61069i	−0.0824429	−	0.158798i
$518$	−27.8780	+	11.9245i	−1.22489	+	0.523932i
$519$	−4.88533	−	3.54940i	−0.214442	−	0.155802i
$520$	7.57955	+	8.41794i	0.332385	+	0.369151i
$521$	−8.59406	+	9.54467i	−0.376512	+	0.418159i	−0.901383	−	0.433023i	$-0.857447\pi$
$521$	−8.59406	+	9.54467i	−0.376512	+	0.418159i	0.524871	+	0.851182i	$0.324114\pi$
$522$	−8.33469	−	3.71084i	−0.364799	−	0.162419i
$523$	−1.13404	−	10.7897i	−0.0495883	−	0.471801i	−0.990933	−	0.134355i	$-0.957104\pi$
$523$	−1.13404	−	10.7897i	−0.0495883	−	0.471801i	0.941345	−	0.337446i	$-0.109563\pi$
$524$	5.53537	+	17.0361i	0.241814	+	0.744226i
$525$	−4.95991	+	3.49343i	−0.216468	+	0.152466i
$526$	−13.6469	−	9.91507i	−0.595034	−	0.432318i
$527$	−15.1139	+	26.1781i	−0.658372	+	1.14033i
$528$	0.198832	+	3.31066i	0.00865307	+	0.144078i
$529$	11.2882	+	19.5518i	0.490793	+	0.850078i
$530$	8.45956	−	3.76644i	0.367460	−	0.163604i
$531$	−1.63067	+	5.01869i	−0.0707651	+	0.217793i
$532$	4.19790	−	0.828031i	0.182002	−	0.0358997i
$533$	−20.2322	+	14.6995i	−0.876353	+	0.636708i
$534$	0.337313	+	3.20932i	0.0145970	+	0.138881i
$535$	11.9165	−	13.2347i	0.515197	−	0.572185i
$536$	−2.65757	+	0.564883i	−0.114789	+	0.0243992i
$537$	8.94962	−	3.98463i	0.386205	−	0.171949i
$538$	−6.69663			−0.288712
$539$	23.0041	−	3.13217i	0.990858	−	0.134912i
$540$	−1.64530			−0.0708023
$541$	−28.0655	+	12.4956i	−1.20663	+	0.537227i	−0.908736	−	0.417371i	$-0.862951\pi$
$541$	−28.0655	+	12.4956i	−1.20663	+	0.537227i	−0.297896	+	0.954598i	$0.596285\pi$
$542$	5.92459	−	1.25931i	0.254483	−	0.0540920i
$543$	4.63217	−	5.14454i	0.198785	−	0.220774i
$544$	0.443178	+	4.21656i	0.0190011	+	0.180784i
$545$	12.5495	−	9.11775i	0.537562	−	0.390562i
$546$	−17.8710	+	3.52504i	−0.764808	+	0.150858i
$547$	−10.1177	+	31.1390i	−0.432601	+	1.33141i	0.462924	+	0.886398i	$0.346800\pi$
$547$	−10.1177	+	31.1390i	−0.432601	+	1.33141i	−0.895525	+	0.445011i	$0.853200\pi$
$548$	1.67906	−	0.747564i	0.0717257	−	0.0319344i
$549$	−0.831471	−	1.44015i	−0.0354863	−	0.0614641i
$550$	−7.07889	+	2.77946i	−0.301845	+	0.118516i
$551$	−7.37735	+	12.7779i	−0.314286	+	0.544359i
$552$	−0.526501	−	0.382525i	−0.0224094	−	0.0162813i
$553$	2.31527	−	1.63072i	0.0984552	−	0.0693452i
$554$	2.20836	+	6.79664i	0.0938243	+	0.288761i
$555$	−1.97095	−	18.7524i	−0.0836623	−	0.795994i
$556$	−10.7256	−	4.77535i	−0.454867	−	0.202520i
$557$	4.85305	−	5.38986i	0.205630	−	0.228376i	−0.631504	−	0.775372i	$-0.717562\pi$
$557$	4.85305	−	5.38986i	0.205630	−	0.228376i	0.837135	+	0.546997i	$0.184229\pi$
$558$	−4.77061	−	5.29830i	−0.201956	−	0.224295i
$559$	40.9326	+	29.7393i	1.73127	+	1.25784i
$560$	4.00229	−	1.71194i	0.169128	−	0.0723425i
$561$	−12.5775	−	6.28818i	−0.531021	−	0.265487i
$562$	−10.3219	+	17.8780i	−0.435402	+	0.754138i
$563$	−0.681632	+	6.48529i	−0.0287274	+	0.273323i	0.970724	+	0.240198i	$0.0772124\pi$
$563$	−0.681632	+	6.48529i	−0.0287274	+	0.273323i	−0.999451	+	0.0331244i	$0.989454\pi$
$564$	1.19983	−	0.255032i	0.0505220	−	0.0107388i
$565$	28.5577	+	6.07012i	1.20143	+	0.255372i
$566$	12.9919	−	9.43914i	0.546089	−	0.396757i
$567$	1.35639	−	2.27161i	0.0569631	−	0.0953986i
$568$	−3.05180	−	9.39246i	−0.128050	−	0.394099i
$569$	22.9530	+	25.4919i	0.962238	+	1.06867i	0.997596	+	0.0692993i	$0.0220763\pi$
$569$	22.9530	+	25.4919i	0.962238	+	1.06867i	−0.0353575	+	0.999375i	$0.511257\pi$
$570$	−0.278132	+	2.64625i	−0.0116497	+	0.110839i
$571$	−0.216173	−	0.374423i	−0.00904656	−	0.0156691i	0.861467	−	0.507814i	$-0.169546\pi$
$571$	−0.216173	−	0.374423i	−0.00904656	−	0.0156691i	−0.870513	+	0.492145i	$0.836213\pi$
$572$	−22.8113	−	1.02111i	−0.953788	−	0.0426948i
$573$	3.91014			0.163349
$574$	2.83522	+	9.18277i	0.118340	+	0.383281i
$575$	0.461134	−	1.41922i	0.0192306	−	0.0591857i
$576$	−0.978148	−	0.207912i	−0.0407562	−	0.00866299i
$577$	26.5960	+	11.8413i	1.10721	+	0.492960i	0.877150	−	0.480217i	$-0.159442\pi$
$577$	26.5960	+	11.8413i	1.10721	+	0.492960i	0.230057	+	0.973177i	$0.426109\pi$
$578$	−0.891429	−	0.396890i	−0.0370786	−	0.0165084i
$579$	6.52468	+	1.38686i	0.271157	+	0.0576361i
$580$	−4.63859	+	14.2761i	−0.192607	+	0.592783i
$581$	13.1432	−	14.1726i	0.545270	−	0.587979i
$582$	−7.60862			−0.315388
$583$	−6.55648	+	17.4775i	−0.271542	+	0.723842i
$584$	6.48933	+	11.2398i	0.268530	+	0.465108i
$585$	1.18404	−	11.2654i	0.0489541	−	0.465767i
$586$	17.1266	+	19.0210i	0.707493	+	0.785751i
$587$	−5.90476	−	18.1730i	−0.243716	−	0.750079i	−0.995845	−	0.0910640i	$-0.970973\pi$
$587$	−5.90476	−	18.1730i	−0.243716	−	0.750079i	0.752129	−	0.659015i	$-0.229027\pi$
$588$	−0.935895	+	6.93715i	−0.0385956	+	0.286083i
$589$	−9.32807	+	6.77724i	−0.384356	+	0.279251i
$590$	8.49245	+	1.80513i	0.349629	+	0.0743159i
$591$	23.7387	−	5.04581i	0.976478	−	0.207557i
$592$	1.19793	−	11.3976i	0.0492347	−	0.468437i
$593$	11.2855	−	19.5471i	0.463440	−	0.802702i	−0.535690	−	0.844415i	$-0.679948\pi$
$593$	11.2855	−	19.5471i	0.463440	−	0.802702i	0.999130	+	0.0417134i	$0.0132816\pi$
$594$	2.32725	−	2.36302i	0.0954884	−	0.0969561i
$595$	−2.19860	+	18.3246i	−0.0901339	+	0.751234i
$596$	−9.32887	−	6.77782i	−0.382125	−	0.277630i
$597$	−9.39228	−	10.4312i	−0.384401	−	0.426920i
$598$	2.99806	−	3.32968i	0.122600	−	0.136161i
$599$	−7.68797	−	3.42291i	−0.314122	−	0.139856i	0.243619	−	0.969871i	$-0.421665\pi$
$599$	−7.68797	−	3.42291i	−0.314122	−	0.139856i	−0.557741	+	0.830015i	$0.688332\pi$
$600$	−0.239683	−	2.28043i	−0.00978503	−	0.0930983i
$601$	−2.55321	−	7.85798i	−0.104148	−	0.320534i	0.885382	−	0.464865i	$-0.153897\pi$
$601$	−2.55321	−	7.85798i	−0.104148	−	0.320534i	−0.989529	+	0.144331i	$0.953897\pi$
$602$	15.8963	−	11.1963i	0.647883	−	0.456325i
$603$	2.19805	+	1.59698i	0.0895115	+	0.0650339i
$604$	11.6448	−	20.1694i	0.473821	−	0.820682i
$605$	−7.10820	+	16.6439i	−0.288990	+	0.676673i
$606$	−1.21206	−	2.09935i	−0.0492366	−	0.0852804i
$607$	−30.9631	+	13.7857i	−1.25675	+	0.559543i	−0.923610	−	0.383333i	$-0.874776\pi$
$607$	−30.9631	+	13.7857i	−1.25675	+	0.559543i	−0.333144	+	0.942876i	$0.608110\pi$
$608$	−0.499751	+	1.53808i	−0.0202676	+	0.0623772i
$609$	−15.8865	−	18.1736i	−0.643752	−	0.736433i
$610$	−2.21350	+	1.60820i	−0.0896219	+	0.0651142i
$611$	0.882752	+	8.39882i	0.0357123	+	0.339780i
$612$	2.83697	−	3.15078i	0.114678	−	0.127363i
$613$	1.09600	−	0.232962i	0.0442670	−	0.00940924i	−0.185725	−	0.982602i	$-0.559463\pi$
$613$	1.09600	−	0.232962i	0.0442670	−	0.00940924i	0.229992	+	0.973193i	$0.426130\pi$
$614$	−0.694100	+	0.309033i	−0.0280116	+	0.0124716i
$615$	−5.97643			−0.240993
$616$	−3.20246	+	8.16972i	−0.129031	+	0.329167i
$617$	39.7611			1.60072			0.800362	−	0.599517i	$-0.204641\pi$
$617$	39.7611			1.60072			0.800362	+	0.599517i	$0.204641\pi$
$618$	−11.7215	+	5.21874i	−0.471507	+	0.209929i
$619$	11.4640	−	2.43676i	0.460779	−	0.0979416i	0.0283273	−	0.999599i	$-0.490982\pi$
$619$	11.4640	−	2.43676i	0.460779	−	0.0979416i	0.432452	+	0.901657i	$0.357649\pi$
$620$	−7.84907	+	8.71728i	−0.315226	+	0.350094i
$621$	0.0680261	+	0.647225i	0.00272979	+	0.0259723i
$622$	−13.1949	+	9.58668i	−0.529069	+	0.384391i
$623$	−2.75733	+	8.08033i	−0.110470	+	0.323732i
$624$	2.12750	−	6.54778i	0.0851683	−	0.262121i
$625$	−7.56159	+	3.36664i	−0.302464	+	0.134666i
$626$	−2.73494	−	4.73706i	−0.109310	−	0.189331i
$627$	−3.40720	−	4.14254i	−0.136071	−	0.165437i
$628$	−3.00161	+	5.19894i	−0.119777	+	0.207460i
$629$	39.3096	+	28.5601i	1.56738	+	1.13877i
$630$	−3.95027	−	1.82877i	−0.157382	−	0.0728600i
$631$	0.180548	+	0.555669i	0.00718749	+	0.0221208i	0.954586	−	0.297936i	$-0.0962981\pi$
$631$	0.180548	+	0.555669i	0.00718749	+	0.0221208i	−0.947398	+	0.320057i	$0.896298\pi$
$632$	0.111883	+	1.06450i	0.00445047	+	0.0423434i
$633$	2.22387	+	0.990132i	0.0883910	+	0.0393542i
$634$	10.6090	−	11.7825i	0.421338	−	0.467944i
$635$	18.8190	+	20.9007i	0.746811	+	0.829417i
$636$	−4.55335	−	3.30820i	−0.180552	−	0.131179i
$637$	−46.8254	−	11.4004i	−1.85529	−	0.451702i
$638$	−13.9425	−	26.8555i	−0.551990	−	1.06322i
$639$	−4.93791	+	8.55271i	−0.195341	+	0.338340i
$640$	−0.171980	+	1.63628i	−0.00679812	+	0.0646798i
$641$	−19.0969	+	4.05916i	−0.754281	+	0.160327i	−0.568976	−	0.822354i	$-0.692660\pi$
$641$	−19.0969	+	4.05916i	−0.754281	+	0.160327i	−0.185304	+	0.982681i	$0.559327\pi$
$642$	−10.5876	−	2.25047i	−0.417861	−	0.0888191i
$643$	23.6677	−	17.1956i	0.933363	−	0.678128i	−0.0134506	−	0.999910i	$-0.504282\pi$
$643$	23.6677	−	17.1956i	0.933363	−	0.678128i	0.946814	+	0.321781i	$0.104282\pi$
$644$	−0.838917	−	1.50363i	−0.0330580	−	0.0592515i
$645$	3.73638	+	11.4994i	0.147120	+	0.452788i
$646$	−4.58803	−	5.09552i	−0.180514	−	0.200481i
$647$	−2.53080	+	24.0790i	−0.0994961	+	0.946642i	0.824918	+	0.565252i	$0.191221\pi$
$647$	−2.53080	+	24.0790i	−0.0994961	+	0.946642i	−0.924414	+	0.381390i	$0.875446\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−14.6051	+	9.64378i	−0.573298	+	0.378551i
$650$	15.7867			0.619205
$651$	−5.56484	−	18.0235i	−0.218103	−	0.706397i
$652$	1.66500	−	5.12436i	0.0652066	−	0.200685i
$653$	24.4976	+	5.20714i	0.958667	+	0.203771i	0.660570	−	0.750765i	$-0.270315\pi$
$653$	24.4976	+	5.20714i	0.958667	+	0.203771i	0.298097	+	0.954536i	$0.403648\pi$
$654$	−8.61301	−	3.83476i	−0.336795	−	0.149951i
$655$	−26.9240	−	11.9873i	−1.05201	−	0.468383i
$656$	−3.55305	−	0.755224i	−0.138723	−	0.0294866i
$657$	4.01063	−	12.3434i	0.156469	−	0.481563i
$658$	3.16420	+	0.721311i	0.123353	+	0.0281196i
$659$	13.6516			0.531789			0.265894	−	0.964002i	$-0.414333\pi$
$659$	13.6516			0.531789			0.265894	+	0.964002i	$0.414333\pi$
$660$	−4.26682	−	3.40166i	−0.166086	−	0.132409i
$661$	12.9415	+	22.4153i	0.503365	+	0.871854i	0.999992	+	0.00389023i	$0.00123830\pi$
$661$	12.9415	+	22.4153i	0.503365	+	0.871854i	−0.496627	+	0.867964i	$0.665428\pi$
$662$	−0.876448	+	8.33884i	−0.0340641	+	0.324098i
$663$	19.5318	+	21.6923i	0.758553	+	0.842459i
$664$	2.25756	+	6.94807i	0.0876105	+	0.269637i
$665$	−3.60912	+	6.04434i	−0.139956	+	0.234390i
$666$	−9.27160	+	6.73621i	−0.359267	+	0.261023i
$667$	5.80771	+	1.23447i	0.224875	+	0.0477987i
$668$	−20.4046	+	4.33713i	−0.789478	+	0.167809i
$669$	2.51818	−	23.9589i	0.0973586	−	0.926305i
$670$	2.23509	−	3.87128i	0.0863489	−	0.149561i
$671$	0.821223	−	5.45387i	0.0317030	−	0.210544i
$672$	−2.11738	−	1.58641i	−0.0816798	−	0.0611971i
$673$	3.20608	+	2.32935i	0.123585	+	0.0897900i	0.647861	−	0.761759i	$-0.275664\pi$
$673$	3.20608	+	2.32935i	0.123585	+	0.0897900i	−0.524276	+	0.851549i	$0.675664\pi$
$674$	9.95139	+	11.0521i	0.383313	+	0.425713i
$675$	−1.53431	+	1.70403i	−0.0590558	+	0.0655881i
$676$	31.4257	+	13.9916i	1.20868	+	0.538140i
$677$	−0.661914	−	6.29770i	−0.0254394	−	0.242040i	−0.999851	−	0.0172684i	$-0.994503\pi$
$677$	−0.661914	−	6.29770i	−0.0254394	−	0.242040i	0.974411	−	0.224772i	$-0.0721636\pi$
$678$	−5.48348	−	16.8764i	−0.210592	−	0.648134i
$679$	−18.2679	−	8.45709i	−0.701057	−	0.324553i
$680$	−5.64347	−	4.10022i	−0.216417	−	0.157236i
$681$	−1.71083	+	2.96324i	−0.0655591	+	0.113552i
$682$	−1.41759	−	23.6036i	−0.0542822	−	0.903827i
$683$	−3.05700	−	5.29488i	−0.116973	−	0.202603i	0.801594	−	0.597869i	$-0.203986\pi$
$683$	−3.05700	−	5.29488i	−0.116973	−	0.202603i	−0.918567	+	0.395266i	$0.870652\pi$
$684$	1.47741	−	0.657786i	0.0564902	−	0.0251511i
$685$	−0.934463	+	2.87598i	−0.0357040	+	0.109886i
$686$	−9.95777	+	15.6155i	−0.380190	+	0.596201i
$687$	−17.1383	+	12.4517i	−0.653867	+	0.475062i
$688$	0.768172	+	7.30867i	0.0292863	+	0.278640i
$689$	25.9282	−	28.7962i	0.987786	−	1.09705i
$690$	1.04735	−	0.222620i	0.0398718	−	0.00847501i
$691$	5.85452	−	2.60660i	0.222716	−	0.0991597i	−0.292345	−	0.956313i	$-0.594436\pi$
$691$	5.85452	−	2.60660i	0.222716	−	0.0991597i	0.515062	+	0.857153i	$0.327769\pi$
$692$	6.03861			0.229553
$693$	8.21414	−	3.08672i	0.312030	−	0.117255i
$694$	17.0862			0.648583
$695$	17.6468	−	7.85688i	0.669382	−	0.298028i
$696$	8.92408	−	1.89687i	0.338266	−	0.0719007i
$697$	10.3051	−	11.4450i	0.390333	−	0.433509i
$698$	−1.38564	−	13.1835i	−0.0524473	−	0.499003i
$699$	−4.50070	+	3.26995i	−0.170232	+	0.123681i
$700$	1.95927	−	5.74161i	0.0740534	−	0.217012i
$701$	8.26847	−	25.4477i	0.312296	−	0.961147i	−0.664558	−	0.747237i	$-0.731380\pi$
$701$	8.26847	−	25.4477i	0.312296	−	0.961147i	0.976853	−	0.213910i	$-0.0686200\pi$
$702$	−6.28953	+	2.80028i	−0.237383	+	0.105690i
$703$	9.26699	+	16.0509i	0.349511	+	0.605371i
$704$	−2.10682	−	2.56151i	−0.0794036	−	0.0965405i
$705$	−1.00909	+	1.74780i	−0.0380046	+	0.0658259i
$706$	18.6745	+	13.5678i	0.702826	+	0.510633i
$707$	−0.576634	−	6.38765i	−0.0216866	−	0.240232i
$708$	−1.63067	−	5.01869i	−0.0612844	−	0.188614i
$709$	3.80302	+	36.1833i	0.142825	+	1.35889i	0.797654	+	0.603115i	$0.206074\pi$
$709$	3.80302	+	36.1833i	0.142825	+	1.35889i	−0.654829	+	0.755777i	$0.727259\pi$
$710$	14.8439	+	6.60893i	0.557081	+	0.248029i
$711$	0.716211	−	0.795433i	0.0268600	−	0.0298311i
$712$	−2.15928	−	2.39813i	−0.0809225	−	0.0898736i
$713$	3.75372	+	2.72724i	0.140578	+	0.102136i
$714$	10.3135	−	4.41151i	0.385975	−	0.165096i
$715$	26.3619	−	26.7671i	0.985879	−	1.00103i
$716$	−4.89829	+	8.48409i	−0.183058	+	0.317065i
$717$	−0.829723	+	7.89429i	−0.0309866	+	0.294818i
$718$	23.3796	−	4.96948i	0.872518	−	0.185459i
$719$	23.8088	+	5.06072i	0.887919	+	0.188733i	0.629222	−	0.777225i	$-0.283374\pi$
$719$	23.8088	+	5.06072i	0.887919	+	0.188733i	0.258697	+	0.965958i	$0.416707\pi$
$720$	1.33107	−	0.967082i	0.0496062	−	0.0360410i
$721$	−33.9433	−	0.498681i	−1.26412	−	0.0185719i
$722$	5.06311	+	15.5827i	0.188430	+	0.579926i
$723$	8.86176	+	9.84198i	0.329572	+	0.366027i
$724$	−0.723616	+	6.88474i	−0.0268930	+	0.255870i
$725$	10.4600	+	18.1173i	0.388475	+	0.672859i
$726$	10.9209	−	1.31653i	0.405314	−	0.0488611i
$727$	−3.70800			−0.137522			−0.0687611	−	0.997633i	$-0.521905\pi$
$727$	−3.70800			−0.137522			−0.0687611	+	0.997633i	$0.521905\pi$
$728$	12.3860	−	13.3561i	0.459055	−	0.495011i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−20.8871	−	4.43970i	−0.773067	−	0.164321i
$731$	−28.4641	−	12.6730i	−1.05278	−	0.468730i
$732$	1.51917	+	0.676379i	0.0561503	+	0.0249997i
$733$	20.5891	+	4.37635i	0.760476	+	0.161644i	0.571797	−	0.820395i	$-0.306246\pi$
$733$	20.5891	+	4.37635i	0.760476	+	0.161644i	0.188678	+	0.982039i	$0.439580\pi$
$734$	3.79148	−	11.6690i	0.139946	−	0.430710i
$735$	−7.45168	−	8.78156i	−0.274859	−	0.323913i
$736$	0.650790			0.0239885
$737$	2.39855	+	8.68598i	0.0883516	+	0.319952i
$738$	1.81621	+	3.14578i	0.0668558	+	0.115798i
$739$	0.0337616	−	0.321220i	0.00124194	−	0.0118163i	−0.993883	−	0.110435i	$-0.964776\pi$
$739$	0.0337616	−	0.321220i	0.00124194	−	0.0118163i	0.995125	+	0.0986185i	$0.0314423\pi$
$740$	12.6169	+	14.0125i	0.463806	+	0.515109i
$741$	3.44066	+	10.5893i	0.126396	+	0.389006i
$742$	−7.25523	−	13.0039i	−0.266348	−	0.477389i
$743$	−30.9143	+	22.4605i	−1.13413	+	0.823997i	−0.986291	−	0.165014i	$-0.947233\pi$
$743$	−30.9143	+	22.4605i	−1.13413	+	0.823997i	−0.147843	+	0.989011i	$0.547233\pi$
$744$	6.97376	+	1.48232i	0.255671	+	0.0543445i
$745$	18.5575	−	3.94453i	0.679895	−	0.144516i
$746$	2.55776	−	24.3355i	0.0936464	−	0.890986i
$747$	3.65282	−	6.32686i	0.133650	−	0.231488i
$748$	13.8715	−	2.30560i	0.507191	−	0.0843011i
$749$	−22.9189	−	17.1716i	−0.837439	−	0.627436i
$750$	9.70752	+	7.05292i	0.354468	+	0.257536i
$751$	−18.0847	−	20.0851i	−0.659920	−	0.732915i	0.316548	−	0.948576i	$-0.397476\pi$
$751$	−18.0847	−	20.0851i	−0.659920	−	0.732915i	−0.976468	+	0.215661i	$0.930809\pi$
$752$	−0.820780	+	0.911569i	−0.0299308	+	0.0332415i
$753$	14.7495	+	6.56692i	0.537503	+	0.239312i
$754$	6.56571	+	62.4686i	0.239109	+	2.27497i
$755$	11.8410	+	36.4430i	0.430939	+	1.32629i
$756$	0.237873	+	2.63504i	0.00865137	+	0.0958353i
$757$	−36.1367	−	26.2549i	−1.31341	−	0.954250i	−0.999989	−	0.00463612i	$-0.998524\pi$
$757$	−36.1367	−	26.2549i	−1.31341	−	0.954250i	−0.313423	−	0.949614i	$-0.601476\pi$
$758$	2.37175	−	4.10799i	0.0861458	−	0.149209i
$759$	−1.16172	+	1.81912i	−0.0421679	+	0.0660300i
$760$	−1.33041	−	2.30434i	−0.0482591	−	0.0835872i
$761$	−29.1934	+	12.9977i	−1.05826	+	0.471167i	−0.860694	−	0.509123i	$-0.829970\pi$
$761$	−29.1934	+	12.9977i	−1.05826	+	0.471167i	−0.197564	+	0.980290i	$0.563303\pi$
$762$	5.28232	−	16.2573i	0.191358	−	0.588940i
$763$	−16.4170	−	18.7805i	−0.594334	−	0.679901i
$764$	−3.16337	+	2.29832i	−0.114447	+	0.0831504i
$765$	0.729160	+	6.93750i	0.0263628	+	0.250826i
$766$	21.8377	−	24.2532i	0.789027	−	0.876304i
$767$	35.5367	−	7.55355i	1.28315	−	0.272743i
$768$	0.913545	−	0.406737i	0.0329647	−	0.0146768i
$769$	−2.77670			−0.100130			−0.0500652	−	0.998746i	$-0.515943\pi$
$769$	−2.77670			−0.100130			−0.0500652	+	0.998746i	$0.515943\pi$
$770$	−6.46342	−	12.9098i	−0.232925	−	0.465238i
$771$	−11.3408			−0.408430
$772$	−6.09376	+	2.71312i	−0.219319	+	0.0976472i
$773$	−7.12440	+	1.51434i	−0.256247	+	0.0544670i	−0.334244	−	0.942487i	$-0.608481\pi$
$773$	−7.12440	+	1.51434i	−0.256247	+	0.0544670i	0.0779969	+	0.996954i	$0.475148\pi$
$774$	4.91739	−	5.46132i	0.176752	−	0.196303i
$775$	1.70884	+	16.2585i	0.0613832	+	0.584023i
$776$	6.15550	−	4.47224i	0.220970	−	0.160544i
$777$	−29.7480	+	5.86777i	−1.06720	+	0.210505i
$778$	4.03403	−	12.4155i	0.144627	−	0.445116i
$779$	5.36659	−	2.38936i	0.192278	−	0.0856077i
$780$	5.66373	+	9.80987i	0.202794	+	0.351250i
$781$	−30.4884	+	11.9710i	−1.09096	+	0.428355i
$782$	−1.37961	+	2.38955i	−0.0493346	+	0.0854501i
$783$	−7.38103	−	5.36263i	−0.263776	−	0.191645i
$784$	−3.32040	−	6.16238i	−0.118586	−	0.220085i
$785$	−3.05219	−	9.39366i	−0.108937	−	0.335274i
$786$	1.87240	+	17.8147i	0.0667863	+	0.635430i
$787$	0.852803	+	0.379692i	0.0303991	+	0.0135346i	0.421880	−	0.906652i	$-0.361370\pi$
$787$	0.852803	+	0.379692i	0.0303991	+	0.0135346i	−0.391481	+	0.920186i	$0.628037\pi$
$788$	−16.2391	+	18.0354i	−0.578495	+	0.642484i
$789$	−11.2873	−	12.5358i	−0.401837	−	0.446285i
$790$	−1.42473	−	1.03513i	−0.0506896	−	0.0368281i
$791$	5.59283	−	46.6143i	0.198858	−	1.65741i
$792$	−0.493837	+	3.27965i	−0.0175477	+	0.116537i
$793$	−5.72447	+	9.91507i	−0.203282	+	0.352094i
$794$	−1.89048	+	17.9867i	−0.0670907	+	0.638326i
$795$	9.05779	−	1.92529i	0.321247	−	0.0682831i
$796$	13.7298	+	2.91836i	0.486640	+	0.103439i
$797$	−4.04248	+	2.93703i	−0.143192	+	0.104035i	−0.657075	−	0.753825i	$-0.728207\pi$
$797$	−4.04248	+	2.93703i	−0.143192	+	0.104035i	0.513883	+	0.857860i	$0.328207\pi$
$798$	4.27832	+	0.0628553i	0.151451	+	0.00222505i
$799$	−1.60710	−	4.94614i	−0.0568550	−	0.174982i
$800$	1.53431	+	1.70403i	0.0542462	+	0.0602465i
$801$	−0.337313	+	3.20932i	−0.0119184	+	0.113396i
$802$	6.01774	+	10.4230i	0.212494	+	0.368050i
$803$	35.9210	−	23.7188i	1.26763	−	0.837018i
$804$	−2.71694			−0.0958190
$805$	2.76207	+	0.629640i	0.0973500	+	0.0221919i
$806$	−15.1682	+	46.6828i	−0.534276	+	1.64433i
$807$	−6.55029	−	1.39231i	−0.230581	−	0.0490115i
$808$	2.21455	+	0.985980i	0.0779075	+	0.0346867i
$809$	−47.8977	−	21.3255i	−1.68400	−	0.749763i	−0.999790	−	0.0204730i	$-0.993483\pi$
$809$	−47.8977	−	21.3255i	−1.68400	−	0.749763i	−0.684205	−	0.729290i	$-0.739851\pi$
$810$	−1.60934	−	0.342077i	−0.0565466	−	0.0120193i
$811$	−4.25946	+	13.1093i	−0.149570	+	0.460329i	−0.997570	−	0.0696667i	$-0.977806\pi$
$811$	−4.25946	+	13.1093i	−0.149570	+	0.460329i	0.848000	+	0.529996i	$0.177806\pi$
$812$	23.5346	+	5.36495i	0.825904	+	0.188273i
$813$	6.05695			0.212427
$814$	−37.9716	−	1.69974i	−1.33090	−	0.0595758i
$815$	4.43249	+	7.67729i	0.155263	+	0.268924i
$816$	−0.443178	+	4.21656i	−0.0155143	+	0.147609i
$817$	−7.95254	−	8.83219i	−0.278224	−	0.308999i
$818$	−4.02898	−	12.3999i	−0.140870	−	0.433553i
$819$	−18.2134	−	0.267583i	−0.636427	−	0.00935011i
$820$	4.83503	−	3.51286i	0.168847	−	0.122674i
$821$	−52.7365	−	11.2095i	−1.84052	−	0.391214i	−0.849794	−	0.527114i	$-0.823274\pi$
$821$	−52.7365	−	11.2095i	−1.84052	−	0.391214i	−0.990722	+	0.135901i	$0.956607\pi$
$822$	1.79779	−	0.382133i	0.0627052	−	0.0133284i
$823$	3.70923	−	35.2910i	0.129296	−	1.23017i	−0.716855	−	0.697223i	$-0.754419\pi$
$823$	3.70923	−	35.2910i	0.129296	−	1.23017i	0.846150	−	0.532944i	$-0.178914\pi$
$824$	6.41538	−	11.1118i	0.223490	−	0.387097i
$825$	−7.50208	+	1.24693i	−0.261189	+	0.0434127i
$826$	1.66319	−	13.8621i	0.0578699	−	0.482325i
$827$	10.7112	+	7.78215i	0.372465	+	0.270612i	0.758233	−	0.651984i	$-0.226063\pi$
$827$	10.7112	+	7.78215i	0.372465	+	0.270612i	−0.385767	+	0.922596i	$0.626063\pi$
$828$	−0.435464	−	0.483632i	−0.0151334	−	0.0168074i
$829$	−4.21117	+	4.67698i	−0.146260	+	0.162438i	−0.811823	−	0.583903i	$-0.801525\pi$
$829$	−4.21117	+	4.67698i	−0.146260	+	0.162438i	0.665563	+	0.746342i	$0.268191\pi$
$830$	−10.9808	−	4.88895i	−0.381148	−	0.169698i
$831$	0.747003	+	7.10726i	0.0259132	+	0.246548i
$832$	2.12750	+	6.54778i	0.0737579	+	0.227004i
$833$	29.6657	+	0.871860i	1.02786	+	0.0302081i
$834$	−9.49838	−	6.90098i	−0.328902	−	0.238961i
$835$	17.1608	−	29.7234i	0.593875	−	1.02862i
$836$	5.19141	+	1.34869i	0.179549	+	0.0466453i
$837$	−3.56478	−	6.17438i	−0.123217	−	0.213418i
$838$	−14.3952	+	6.40916i	−0.497274	+	0.221401i
$839$	−0.432617	+	1.33146i	−0.0149356	+	0.0459670i	−0.958247	−	0.285943i	$-0.907693\pi$
$839$	−0.432617	+	1.33146i	−0.0149356	+	0.0459670i	0.943311	+	0.331910i	$0.107693\pi$
$840$	4.27076	−	0.842403i	0.147355	−	0.0290657i
$841$	−43.8789	+	31.8799i	−1.51307	+	1.09931i
$842$	0.193625	+	1.84222i	0.00667275	+	0.0634870i
$843$	−13.8134	+	15.3413i	−0.475757	+	0.528382i
$844$	−2.38114	+	0.506126i	−0.0819621	+	0.0174216i
$845$	−51.7047	+	23.0204i	−1.77870	+	0.791926i
$846$	1.22664			0.0421726
$847$	27.6839	+	8.97784i	0.951230	+	0.308482i
$848$	5.62825			0.193275
$849$	14.6705	−	6.53171i	0.503489	−	0.224168i
$850$	−9.50937	+	2.02128i	−0.326169	+	0.0693293i
$851$	4.99056	−	5.54258i	0.171074	−	0.189997i
$852$	−1.03230	−	9.82172i	−0.0353662	−	0.336486i
$853$	−25.3971	+	18.4521i	−0.869580	+	0.631787i	−0.930474	−	0.366357i	$-0.880605\pi$
$853$	−25.3971	+	18.4521i	−0.869580	+	0.631787i	0.0608940	+	0.998144i	$0.480605\pi$
$854$	2.89565	+	3.31253i	0.0990870	+	0.113353i
$855$	−0.822239	+	2.53059i	−0.0281200	+	0.0865444i
$856$	9.88838	−	4.40259i	0.337978	−	0.150477i
$857$	21.4393	+	37.1339i	0.732351	+	1.26847i	0.955876	+	0.293771i	$0.0949103\pi$
$857$	21.4393	+	37.1339i	0.732351	+	1.26847i	−0.223525	+	0.974698i	$0.571756\pi$
$858$	−22.1005	−	5.74153i	−0.754499	−	0.196013i
$859$	22.3264	−	38.6705i	0.761768	−	1.31942i	−0.180171	−	0.983635i	$-0.557665\pi$
$859$	22.3264	−	38.6705i	0.761768	−	1.31942i	0.941938	−	0.335785i	$-0.109002\pi$
$860$	−9.78196	−	7.10701i	−0.333562	−	0.242347i
$861$	0.864058	+	9.57158i	0.0294470	+	0.326199i
$862$	2.27057	+	6.98811i	0.0773361	+	0.238016i
$863$	−2.88193	−	27.4197i	−0.0981019	−	0.933378i	−0.927274	−	0.374384i	$-0.877854\pi$
$863$	−2.88193	−	27.4197i	−0.0981019	−	0.933378i	0.829172	−	0.558994i	$-0.188812\pi$
$864$	−0.913545	−	0.406737i	−0.0310794	−	0.0138375i
$865$	−6.64802	+	7.38337i	−0.226039	+	0.251042i
$866$	18.8641	+	20.9507i	0.641027	+	0.711933i
$867$	−0.789431	−	0.573555i	−0.0268105	−	0.0194790i
$868$	15.0960	+	11.3104i	0.512392	+	0.383900i
$869$	3.50194	−	0.582064i	0.118795	−	0.0197452i
$870$	−7.50540	+	12.9997i	−0.254457	+	0.440732i
$871$	1.95525	−	18.6030i	0.0662511	−	0.630337i
$872$	9.22209	−	1.96021i	0.312299	−	0.0663812i
$873$	−7.44236	−	1.58192i	−0.251886	−	0.0535399i
$874$	−0.851471	+	0.618630i	−0.0288015	+	0.0209255i
$875$	15.4678	+	27.7237i	0.522907	+	0.937233i
$876$	4.01063	+	12.3434i	0.135506	+	0.417046i
$877$	15.2984	+	16.9906i	0.516591	+	0.573733i	0.943841	−	0.330401i	$-0.107184\pi$
$877$	15.2984	+	16.9906i	0.516591	+	0.573733i	−0.427249	+	0.904134i	$0.640517\pi$
$878$	−3.06424	+	29.1543i	−0.103413	+	0.983909i
$879$	12.7977	+	22.1662i	0.431654	+	0.747647i
$880$	5.45138	+	0.244022i	0.183766	+	0.00822599i
$881$	−5.43120			−0.182982			−0.0914909	−	0.995806i	$-0.529163\pi$
$881$	−5.43120			−0.182982			−0.0914909	+	0.995806i	$0.529163\pi$
$882$	−2.35776	+	6.59098i	−0.0793899	+	0.221930i
$883$	5.87532	−	18.0824i	0.197720	−	0.608520i	−0.802214	−	0.597037i	$-0.796345\pi$
$883$	5.87532	−	18.0824i	0.197720	−	0.608520i	0.999934	−	0.0114833i	$-0.00365531\pi$
$884$	−28.5520	−	6.06891i	−0.960308	−	0.204120i
$885$	7.93157	+	3.53136i	0.266617	+	0.118705i
$886$	9.62417	+	4.28496i	0.323330	+	0.143956i
$887$	45.8461	+	9.74489i	1.53936	+	0.327201i	0.897985	−	0.440025i	$-0.145031\pi$
$887$	45.8461	+	9.74489i	1.53936	+	0.327201i	0.641376	+	0.767227i	$0.278364\pi$
$888$	3.54144	−	10.8994i	0.118843	−	0.365761i
$889$	30.7528	−	33.1615i	1.03141	−	1.11220i
$890$	5.30937			0.177971
$891$	2.76770	−	1.82752i	0.0927214	−	0.0612243i
$892$	12.0454	+	20.8633i	0.403311	+	0.698556i
$893$	0.207358	−	1.97288i	0.00693899	−	0.0660200i
$894$	−7.71582	−	8.56929i	−0.258056	−	0.286600i
$895$	−4.98082	−	15.3294i	−0.166491	−	0.512405i
$896$	2.64547	+	0.0388660i	0.0883788	+	0.00129842i
$897$	3.62482	−	2.63359i	0.121029	−	0.0879330i
$898$	20.8966	+	4.44172i	0.697330	+	0.148222i
$899$	−63.6248	+	13.5239i	−2.12201	+	0.451046i
$900$	0.239683	−	2.28043i	0.00798944	−	0.0760145i
$901$	−11.9313	+	20.6656i	−0.397489	+	0.688471i
$902$	−1.79383	+	11.9131i	−0.0597280	+	0.396663i
$903$	17.8767	−	7.64657i	0.594900	−	0.254462i
$904$	14.3559	+	10.4302i	0.477471	+	0.346903i
$905$	−7.62130	−	8.46431i	−0.253340	−	0.281363i
$906$	15.5838	−	17.3076i	0.517737	−	0.575006i
$907$	5.38509	+	2.39760i	0.178809	+	0.0796109i	0.494189	−	0.869355i	$-0.335465\pi$
$907$	5.38509	+	2.39760i	0.178809	+	0.0796109i	−0.315380	+	0.948966i	$0.602132\pi$
$908$	−0.357660	−	3.40291i	−0.0118694	−	0.112930i
$909$	−0.749095	−	2.30548i	−0.0248459	−	0.0764679i
$910$	2.69450	+	29.8483i	0.0893218	+	0.989461i
$911$	−4.76784	−	3.46404i	−0.157966	−	0.114769i	0.505995	−	0.862537i	$-0.331126\pi$
$911$	−4.76784	−	3.46404i	−0.157966	−	0.114769i	−0.663960	+	0.747768i	$0.731126\pi$
$912$	−0.808614	+	1.40056i	−0.0267759	+	0.0463772i
$913$	22.5538	−	8.85553i	0.746422	−	0.293075i
$914$	−4.48899	−	7.77516i	−0.148483	−	0.257179i
$915$	−2.49949	+	1.11285i	−0.0826307	+	0.0367895i
$916$	6.54625	−	20.1473i	0.216294	−	0.665685i
$917$	−15.3058	+	44.8533i	−0.505441	+	1.48119i
$918$	3.43006	−	2.49208i	0.113209	−	0.0822510i
$919$	−1.24205	−	11.8173i	−0.0409714	−	0.389817i	−0.995721	−	0.0924069i	$-0.970544\pi$
$919$	−1.24205	−	11.8173i	−0.0409714	−	0.389817i	0.954750	−	0.297410i	$-0.0961227\pi$
$920$	−0.716468	+	0.795718i	−0.0236212	+	0.0262340i
$921$	−0.743184	+	0.157969i	−0.0244888	+	0.00520525i
$922$	−20.3013	+	9.03872i	−0.668588	+	0.297674i
$923$	67.9925			2.23800
$924$	−4.83106	+	7.32536i	−0.158930	+	0.240987i
$925$	26.2785			0.864032
$926$	10.3884	−	4.62521i	0.341384	−	0.151994i
$927$	−12.5504	+	2.66767i	−0.412209	+	0.0876176i
$928$	−6.10478	+	6.78005i	−0.200399	+	0.222566i
$929$	−5.44260	−	51.7829i	−0.178566	−	1.69894i	−0.606462	−	0.795112i	$-0.707412\pi$
$929$	−5.44260	−	51.7829i	−0.178566	−	1.69894i	0.427896	−	0.903828i	$-0.359255\pi$
$930$	−9.48997	+	6.89487i	−0.311189	+	0.226092i
$931$	10.2021	+	4.90633i	0.334362	+	0.160798i
$932$	1.71912	−	5.29089i	0.0563115	−	0.173309i
$933$	−14.8998	+	6.63381i	−0.487797	+	0.217181i
$934$	−1.21433	−	2.10327i	−0.0397340	−	0.0688212i
$935$	−12.4523	+	19.4989i	−0.407235	+	0.637681i
$936$	3.44237	−	5.96237i	0.112518	−	0.194886i
$937$	4.07491	+	2.96060i	0.133122	+	0.0967184i	0.652353	−	0.757915i	$-0.273782\pi$
$937$	4.07491	+	2.96060i	0.133122	+	0.0967184i	−0.519232	+	0.854633i	$0.673782\pi$
$938$	−6.52322	−	3.01991i	−0.212991	−	0.0986037i
$939$	−1.69029	−	5.20217i	−0.0551604	−	0.169766i
$940$	−0.210958	−	2.00713i	−0.00688068	−	0.0654653i
$941$	11.8830	+	5.29064i	0.387374	+	0.172470i	0.591177	−	0.806542i	$-0.298664\pi$
$941$	11.8830	+	5.29064i	0.387374	+	0.172470i	−0.203803	+	0.979012i	$0.565330\pi$
$942$	−4.01694	+	4.46126i	−0.130879	+	0.145356i
$943$	−1.58179	−	1.75676i	−0.0515102	−	0.0572079i
$944$	4.26916	+	3.10172i	0.138949	+	0.100952i
$945$	−3.48372	−	2.61012i	−0.113326	−	0.0849071i
$946$	24.0438	−	3.99635i	0.781730	−	0.129933i
$947$	−0.0827760	+	0.143372i	−0.00268986	+	0.00465897i	−0.867367	−	0.497669i	$-0.834190\pi$
$947$	−0.0827760	+	0.143372i	−0.00268986	+	0.00465897i	0.864677	+	0.502328i	$0.167523\pi$
$948$	−0.111883	+	1.06450i	−0.00363380	+	0.0345733i
$949$	−87.4022	+	18.5779i	−2.83719	+	0.603064i
$950$	−3.62726	−	0.770998i	−0.117684	−	0.0250145i
$951$	12.8269	−	9.31930i	0.415941	−	0.302199i
$952$	−5.75081	+	9.63113i	−0.186385	+	0.312147i
$953$	8.77589	+	27.0094i	0.284279	+	0.874921i	0.986614	+	0.163074i	$0.0521410\pi$
$953$	8.77589	+	27.0094i	0.284279	+	0.874921i	−0.702335	+	0.711847i	$0.747859\pi$
$954$	−3.76603	−	4.18260i	−0.121930	−	0.135417i
$955$	0.672468	−	6.39811i	0.0217606	−	0.207038i
$956$	−3.96889	−	6.87431i	−0.128363	−	0.222331i
$957$	−8.05429	−	29.1674i	−0.260358	−	0.942849i
$958$	11.5207			0.372218
$959$	4.74115	+	1.08079i	0.153100	+	0.0349006i
$960$	−0.508425	+	1.56477i	−0.0164093	+	0.0505028i
$961$	−19.3973	−	4.12303i	−0.625720	−	0.133001i
$962$	72.0801	+	32.0921i	2.32396	+	1.03469i
$963$	−9.88838	−	4.40259i	−0.318649	−	0.141872i
$964$	−12.9543	−	2.75352i	−0.417229	−	0.0886848i
$965$	3.39142	−	10.4377i	0.109174	−	0.336002i
$966$	−0.507962	−	1.64520i	−0.0163434	−	0.0529333i
$967$	−45.3629			−1.45877			−0.729387	−	0.684101i	$-0.760195\pi$
$967$	−45.3629			−1.45877			−0.729387	+	0.684101i	$0.760195\pi$
$968$	−8.06138	+	7.48426i	−0.259103	+	0.240553i
$969$	−3.42835	−	5.93808i	−0.110134	−	0.190759i
$970$	−1.30853	+	12.4499i	−0.0420145	+	0.399741i
$971$	1.99710	+	2.21801i	0.0640901	+	0.0711792i	0.774337	−	0.632773i	$-0.218083\pi$
$971$	1.99710	+	2.21801i	0.0640901	+	0.0711792i	−0.710247	+	0.703952i	$0.751417\pi$
$972$	0.309017	+	0.951057i	0.00991172	+	0.0305052i
$973$	−15.1346	−	27.1265i	−0.485192	−	0.869634i
$974$	10.7064	−	7.77867i	0.343056	−	0.249245i
$975$	15.4417	+	3.28224i	0.494531	+	0.105116i
$976$	−1.62660	+	0.345745i	−0.0520663	+	0.0110670i
$977$	−4.56542	+	43.4370i	−0.146061	+	1.38967i	0.638500	+	0.769622i	$0.279555\pi$
$977$	−4.56542	+	43.4370i	−0.146061	+	1.38967i	−0.784561	+	0.620052i	$0.787112\pi$
$978$	2.69403	−	4.66620i	0.0861457	−	0.149209i
$979$	−7.51004	+	7.62548i	−0.240022	+	0.243711i
$980$	11.1902	+	2.72444i	0.357458	+	0.0870292i
$981$	−7.62750	−	5.54171i	−0.243527	−	0.176933i
$982$	−26.0338	−	28.9135i	−0.830772	−	0.922666i
$983$	39.3584	−	43.7119i	1.25534	−	1.39419i	0.370142	−	0.928975i	$-0.379309\pi$
$983$	39.3584	−	43.7119i	1.25534	−	1.39419i	0.885196	−	0.465219i	$-0.154024\pi$
$984$	−3.31839	−	1.47744i	−0.105786	−	0.0470991i
$985$	−4.17379	−	39.7110i	−0.132988	−	1.26530i
$986$	−11.9532	−	36.7883i	−0.380669	−	1.17158i
$987$	2.94509	+	1.36342i	0.0937432	+	0.0433983i
$988$	−9.00776	−	6.54452i	−0.286575	−	0.208209i
$989$	−2.39131	+	4.14186i	−0.0760391	+	0.131704i
$990$	−3.46634	−	4.21444i	−0.110167	−	0.133944i
$991$	8.81442	+	15.2670i	0.279999	+	0.484973i	0.971384	−	0.237513i	$-0.0763324\pi$
$991$	8.81442	+	15.2670i	0.279999	+	0.484973i	−0.691385	+	0.722487i	$0.742999\pi$
$992$	−6.51318	+	2.89985i	−0.206794	+	0.0920705i
$993$	−2.59104	+	7.97440i	−0.0822241	+	0.253060i
$994$	8.43847	−	24.7288i	0.267652	−	0.784351i
$995$	−18.6837	+	13.5745i	−0.592312	+	0.430340i
$996$	0.763646	+	7.26561i	0.0241971	+	0.230220i
$997$	22.4726	−	24.9583i	0.711713	−	0.790438i	−0.273481	−	0.961877i	$-0.588175\pi$
$997$	22.4726	−	24.9583i	0.711713	−	0.790438i	0.985195	+	0.171440i	$0.0548418\pi$
$998$	23.1145	−	4.91314i	0.731677	−	0.155523i
$999$	−10.4695	+	4.66134i	−0.331241	+	0.147478i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.c.37.4	yes	40
7.4	even	3	inner	462.2.y.c.235.2	yes	40
11.3	even	5	inner	462.2.y.c.289.2	yes	40
77.25	even	15	inner	462.2.y.c.25.4	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.c.25.4	✓	40	77.25	even	15	inner
462.2.y.c.37.4	yes	40	1.1	even	1	trivial
462.2.y.c.235.2	yes	40	7.4	even	3	inner
462.2.y.c.289.2	yes	40	11.3	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.913545 + 0.406737i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.171980 + 1.63628i) q^{5} +(0.809017 - 0.587785i) q^{6} +(2.59574 - 0.512007i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.913545 - 0.406737i) q^{9} +O(q^{10})\)	\(q+(-0.913545 + 0.406737i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.171980 + 1.63628i) q^{5} +(0.809017 - 0.587785i) q^{6} +(2.59574 - 0.512007i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.913545 - 0.406737i) q^{9} +(-0.822649 - 1.42487i) q^{10} +(3.21007 + 0.833949i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-5.56988 - 4.04675i) q^{13} +(-2.16307 + 1.52352i) q^{14} +(-0.508425 - 1.56477i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(3.87324 + 1.72448i) q^{17} +(-0.669131 + 0.743145i) q^{18} +(1.08214 + 1.20183i) q^{19} +(1.33107 + 0.967082i) q^{20} +(-2.43256 + 1.04050i) q^{21} +(-3.27174 + 0.543801i) q^{22} +(0.325395 - 0.563601i) q^{23} +(0.104528 - 0.994522i) q^{24} +(2.24289 - 0.476741i) q^{25} +(6.73430 + 1.43142i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(1.35639 - 2.27161i) q^{28} +(2.81930 + 8.67692i) q^{29} +(1.10092 + 1.22269i) q^{30} +(-0.745242 + 7.09051i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.31331 - 0.148315i) q^{33} -4.23979 q^{34} +(1.28420 + 4.15931i) q^{35} +(0.309017 - 0.951057i) q^{36} +(11.2099 + 2.38274i) q^{37} +(-1.47741 - 0.657786i) q^{38} +(6.28953 + 2.80028i) q^{39} +(-1.60934 - 0.342077i) q^{40} +(1.12248 - 3.45465i) q^{41} +(1.79905 - 1.93996i) q^{42} -7.34892 q^{43} +(2.76770 - 1.82752i) q^{44} +(0.822649 + 1.42487i) q^{45} +(-0.0680261 + 0.647225i) q^{46} +(-0.820780 - 0.911569i) q^{47} +(0.309017 + 0.951057i) q^{48} +(6.47570 - 2.65807i) q^{49} +(-1.85507 + 1.34779i) q^{50} +(-4.14714 - 0.881501i) q^{51} +(-6.73430 + 1.43142i) q^{52} +(-0.588312 + 5.59742i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.812510 + 5.39601i) q^{55} +(-0.315180 + 2.62691i) q^{56} +(-1.30836 - 0.950583i) q^{57} +(-6.10478 - 6.78005i) q^{58} +(-3.53098 + 3.92155i) q^{59} +(-1.50305 - 0.669203i) q^{60} +(-0.173825 - 1.65383i) q^{61} +(-2.20316 - 6.78062i) q^{62} +(2.16307 - 1.52352i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(5.66373 - 9.80987i) q^{65} +(3.08718 - 1.21215i) q^{66} +(1.35847 + 2.35294i) q^{67} +(3.87324 - 1.72448i) q^{68} +(-0.201105 + 0.618939i) q^{69} +(-2.86492 - 3.27738i) q^{70} +(-7.98970 + 5.80486i) q^{71} +(0.104528 + 0.994522i) q^{72} +(8.68442 - 9.64502i) q^{73} +(-11.2099 + 2.38274i) q^{74} +(-2.09476 + 0.932645i) q^{75} +1.61723 q^{76} +(8.75948 + 0.521137i) q^{77} -6.88475 q^{78} +(0.977823 - 0.435355i) q^{79} +(1.60934 - 0.342077i) q^{80} +(0.669131 - 0.743145i) q^{81} +(0.379692 + 3.61253i) q^{82} +(5.91038 - 4.29414i) q^{83} +(-0.854458 + 2.50398i) q^{84} +(-2.15561 + 6.63430i) q^{85} +(6.71358 - 2.98908i) q^{86} +(-4.56173 - 7.90114i) q^{87} +(-1.78510 + 2.79525i) q^{88} +(-1.61350 + 2.79466i) q^{89} +(-1.33107 - 0.967082i) q^{90} +(-16.5299 - 7.65249i) q^{91} +(-0.201105 - 0.618939i) q^{92} +(-0.745242 - 7.09051i) q^{93} +(1.12059 + 0.498918i) q^{94} +(-1.78044 + 1.97738i) q^{95} +(-0.669131 - 0.743145i) q^{96} +(-6.15550 - 4.47224i) q^{97} +(-4.83471 + 5.06217i) q^{98} +(3.27174 - 0.543801i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9}+O(q^{10}) \) 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9	\( 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9} + 4 q^{10} + 2 q^{11} - 20 q^{12} - 2 q^{13} - 3 q^{14} - 2 q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} - q^{19} - 2 q^{20} - 2 q^{21} + 4 q^{22} - 20 q^{23} - 5 q^{24} + 16 q^{25} + 4 q^{26} - 10 q^{27} + 13 q^{28} + 16 q^{29} - q^{30} + 30 q^{31} + 20 q^{32} + 2 q^{33} + 32 q^{34} + 3 q^{35} - 10 q^{36} + 19 q^{37} + 6 q^{38} + q^{39} - q^{40} - 12 q^{41} + 11 q^{42} - 36 q^{43} - 3 q^{44} - 4 q^{45} + 10 q^{46} + 25 q^{47} - 10 q^{48} + 29 q^{49} + 12 q^{50} - 14 q^{51} - 4 q^{52} - 18 q^{53} + 20 q^{54} + 12 q^{55} - 4 q^{56} + 12 q^{57} + 8 q^{58} - 14 q^{59} + q^{60} + 35 q^{61} - 40 q^{62} + 3 q^{63} - 10 q^{64} - 2 q^{65} + 3 q^{66} - 24 q^{67} + 6 q^{68} - 40 q^{69} - 32 q^{70} - 34 q^{71} - 5 q^{72} - 39 q^{73} - 19 q^{74} + 6 q^{75} - 28 q^{76} - 31 q^{77} + 12 q^{78} - 17 q^{79} + q^{80} + 5 q^{81} + 4 q^{82} - 24 q^{83} + 3 q^{84} - 112 q^{85} + 7 q^{86} + 2 q^{87} - 2 q^{88} - 38 q^{89} + 2 q^{90} - 36 q^{91} - 40 q^{92} + 30 q^{93} - 10 q^{94} - 42 q^{95} - 5 q^{96} + 4 q^{97} - 50 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9 + 4 * q^10 + 2 * q^11 - 20 * q^12 - 2 * q^13 - 3 * q^14 - 2 * q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 - q^19 - 2 * q^20 - 2 * q^21 + 4 * q^22 - 20 * q^23 - 5 * q^24 + 16 * q^25 + 4 * q^26 - 10 * q^27 + 13 * q^28 + 16 * q^29 - q^30 + 30 * q^31 + 20 * q^32 + 2 * q^33 + 32 * q^34 + 3 * q^35 - 10 * q^36 + 19 * q^37 + 6 * q^38 + q^39 - q^40 - 12 * q^41 + 11 * q^42 - 36 * q^43 - 3 * q^44 - 4 * q^45 + 10 * q^46 + 25 * q^47 - 10 * q^48 + 29 * q^49 + 12 * q^50 - 14 * q^51 - 4 * q^52 - 18 * q^53 + 20 * q^54 + 12 * q^55 - 4 * q^56 + 12 * q^57 + 8 * q^58 - 14 * q^59 + q^60 + 35 * q^61 - 40 * q^62 + 3 * q^63 - 10 * q^64 - 2 * q^65 + 3 * q^66 - 24 * q^67 + 6 * q^68 - 40 * q^69 - 32 * q^70 - 34 * q^71 - 5 * q^72 - 39 * q^73 - 19 * q^74 + 6 * q^75 - 28 * q^76 - 31 * q^77 + 12 * q^78 - 17 * q^79 + q^80 + 5 * q^81 + 4 * q^82 - 24 * q^83 + 3 * q^84 - 112 * q^85 + 7 * q^86 + 2 * q^87 - 2 * q^88 - 38 * q^89 + 2 * q^90 - 36 * q^91 - 40 * q^92 + 30 * q^93 - 10 * q^94 - 42 * q^95 - 5 * q^96 + 4 * q^97 - 50 * q^98 - 4 * q^99

Introduction

L-functions

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