LMFDB - Embedded newform 147.2.i.b.127.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,2,Mod(22,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("147.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	147.i (of order $7$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.17380090971$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			127.2
Character	$\chi$	$=$	147.127
Dual form			147.2.i.b.22.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.60360 - 0.772253i) q^{2} +(-0.222521 - 0.974928i) q^{3} +(0.728177 + 0.913105i) q^{4} +(0.987738 + 4.32756i) q^{5} +(-0.396056 + 1.73524i) q^{6} +(-2.63181 + 0.271221i) q^{7} +(0.329556 + 1.44388i) q^{8} +(-0.900969 + 0.433884i) q^{9} +O(q^{10})$	\(q+(-1.60360 - 0.772253i) q^{2} +(-0.222521 - 0.974928i) q^{3} +(0.728177 + 0.913105i) q^{4} +(0.987738 + 4.32756i) q^{5} +(-0.396056 + 1.73524i) q^{6} +(-2.63181 + 0.271221i) q^{7} +(0.329556 + 1.44388i) q^{8} +(-0.900969 + 0.433884i) q^{9} +(1.75804 - 7.70246i) q^{10} +(0.951225 + 0.458086i) q^{11} +(0.728177 - 0.913105i) q^{12} +(4.24896 + 2.04619i) q^{13} +(4.42982 + 1.59749i) q^{14} +(3.99927 - 1.92595i) q^{15} +(1.10633 - 4.84715i) q^{16} +(-2.95622 + 3.70698i) q^{17} +1.77986 q^{18} +2.09671 q^{19} +(-3.23227 + 4.05314i) q^{20} +(0.850055 + 2.50548i) q^{21} +(-1.17163 - 1.46917i) q^{22} +(-0.565574 - 0.709207i) q^{23} +(1.33435 - 0.642587i) q^{24} +(-13.2473 + 6.37957i) q^{25} +(-5.23345 - 6.56254i) q^{26} +(0.623490 + 0.781831i) q^{27} +(-2.16408 - 2.20562i) q^{28} +(1.79593 - 2.25202i) q^{29} -7.90054 q^{30} +1.97581 q^{31} +(-3.67055 + 4.60272i) q^{32} +(0.234933 - 1.02931i) q^{33} +(7.60332 - 3.66156i) q^{34} +(-3.77327 - 11.1214i) q^{35} +(-1.05225 - 0.506735i) q^{36} +(0.285021 - 0.357405i) q^{37} +(-3.36228 - 1.61919i) q^{38} +(1.04941 - 4.59775i) q^{39} +(-5.92297 + 2.85235i) q^{40} +(0.917612 + 4.02032i) q^{41} +(0.571713 - 4.67424i) q^{42} +(-1.67837 + 7.35342i) q^{43} +(0.274380 + 1.20214i) q^{44} +(-2.76758 - 3.47043i) q^{45} +(0.359267 + 1.57405i) q^{46} +(-7.33253 - 3.53116i) q^{47} -4.97181 q^{48} +(6.85288 - 1.42761i) q^{49} +26.1700 q^{50} +(4.27186 + 2.05722i) q^{51} +(1.22561 + 5.36974i) q^{52} +(-0.774992 - 0.971809i) q^{53} +(-0.396056 - 1.73524i) q^{54} +(-1.04283 + 4.56895i) q^{55} +(-1.25894 - 3.71064i) q^{56} +(-0.466561 - 2.04414i) q^{57} +(-4.61908 + 2.22443i) q^{58} +(0.293639 - 1.28652i) q^{59} +(4.67077 + 2.24932i) q^{60} +(7.12459 - 8.93395i) q^{61} +(-3.16841 - 1.52583i) q^{62} +(2.25350 - 1.38626i) q^{63} +(0.481665 - 0.231958i) q^{64} +(-4.65816 + 20.4087i) q^{65} +(-1.17163 + 1.46917i) q^{66} +2.75438 q^{67} -5.53752 q^{68} +(-0.565574 + 0.709207i) q^{69} +(-2.53775 + 20.7482i) q^{70} +(-2.88977 - 3.62366i) q^{71} +(-0.923396 - 1.15790i) q^{72} +(4.97674 - 2.39667i) q^{73} +(-0.733067 + 0.353027i) q^{74} +(9.16743 + 11.4956i) q^{75} +(1.52677 + 1.91452i) q^{76} +(-2.62769 - 0.947604i) q^{77} +(-5.23345 + 6.56254i) q^{78} +8.21672 q^{79} +22.0691 q^{80} +(0.623490 - 0.781831i) q^{81} +(1.63322 - 7.15562i) q^{82} +(13.7077 - 6.60126i) q^{83} +(-1.66877 + 2.60062i) q^{84} +(-18.9622 - 9.13169i) q^{85} +(8.37014 - 10.4958i) q^{86} +(-2.59519 - 1.24978i) q^{87} +(-0.347939 + 1.52442i) q^{88} +(10.0755 - 4.85213i) q^{89} +(1.75804 + 7.70246i) q^{90} +(-11.7374 - 4.23278i) q^{91} +(0.235743 - 1.03286i) q^{92} +(-0.439659 - 1.92627i) q^{93} +(9.03149 + 11.3251i) q^{94} +(2.07100 + 9.07363i) q^{95} +(5.30410 + 2.55432i) q^{96} +5.72620 q^{97} +(-12.0917 - 3.00284i) q^{98} -1.05578 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{2} - 6 q^{3} - 9 q^{4} - 4 q^{5} - q^{6} - 6 q^{7} - 15 q^{8} - 6 q^{9}+O(q^{10}) $ 36 * q - q^2 - 6 * q^3 - 9 * q^4 - 4 * q^5 - q^6 - 6 * q^7 - 15 * q^8 - 6 * q^9	\( 36 q - q^{2} - 6 q^{3} - 9 q^{4} - 4 q^{5} - q^{6} - 6 q^{7} - 15 q^{8} - 6 q^{9} + 10 q^{10} - 7 q^{11} - 9 q^{12} - 12 q^{13} - q^{14} + 3 q^{15} - 3 q^{16} - 3 q^{17} + 6 q^{18} + 6 q^{19} + 25 q^{20} + q^{21} - 21 q^{22} - 20 q^{23} + 6 q^{24} - 2 q^{25} + 6 q^{26} - 6 q^{27} - q^{28} - 22 q^{29} - 4 q^{30} + 16 q^{31} + 26 q^{32} + 6 q^{34} - 9 q^{35} - 9 q^{36} + 32 q^{37} + 17 q^{38} + 23 q^{39} - 21 q^{40} - 5 q^{41} - 8 q^{42} - 34 q^{43} + 2 q^{44} + 3 q^{45} - 32 q^{46} - 7 q^{47} + 74 q^{48} + 20 q^{49} + 236 q^{50} + 18 q^{51} + 20 q^{52} - 32 q^{53} - q^{54} - 17 q^{55} - 39 q^{56} - 8 q^{57} - 53 q^{58} - q^{59} - 17 q^{60} + 14 q^{61} - 60 q^{62} + 22 q^{63} - 21 q^{64} - 39 q^{65} - 21 q^{66} - 22 q^{67} - 110 q^{68} - 20 q^{69} - 40 q^{70} + 36 q^{71} + 6 q^{72} - 11 q^{73} - 46 q^{74} - 9 q^{75} - 101 q^{76} - 17 q^{77} + 6 q^{78} - 14 q^{79} - 112 q^{80} - 6 q^{81} + 2 q^{82} + 12 q^{83} - 22 q^{84} - 44 q^{85} + 184 q^{86} - q^{87} + 204 q^{88} + 12 q^{89} + 10 q^{90} - 16 q^{91} - 105 q^{92} - 19 q^{93} - 5 q^{94} + 18 q^{95} - 9 q^{96} + 172 q^{97} + q^{98}+O(q^{100}) \) 36 * q - q^2 - 6 * q^3 - 9 * q^4 - 4 * q^5 - q^6 - 6 * q^7 - 15 * q^8 - 6 * q^9 + 10 * q^10 - 7 * q^11 - 9 * q^12 - 12 * q^13 - q^14 + 3 * q^15 - 3 * q^16 - 3 * q^17 + 6 * q^18 + 6 * q^19 + 25 * q^20 + q^21 - 21 * q^22 - 20 * q^23 + 6 * q^24 - 2 * q^25 + 6 * q^26 - 6 * q^27 - q^28 - 22 * q^29 - 4 * q^30 + 16 * q^31 + 26 * q^32 + 6 * q^34 - 9 * q^35 - 9 * q^36 + 32 * q^37 + 17 * q^38 + 23 * q^39 - 21 * q^40 - 5 * q^41 - 8 * q^42 - 34 * q^43 + 2 * q^44 + 3 * q^45 - 32 * q^46 - 7 * q^47 + 74 * q^48 + 20 * q^49 + 236 * q^50 + 18 * q^51 + 20 * q^52 - 32 * q^53 - q^54 - 17 * q^55 - 39 * q^56 - 8 * q^57 - 53 * q^58 - q^59 - 17 * q^60 + 14 * q^61 - 60 * q^62 + 22 * q^63 - 21 * q^64 - 39 * q^65 - 21 * q^66 - 22 * q^67 - 110 * q^68 - 20 * q^69 - 40 * q^70 + 36 * q^71 + 6 * q^72 - 11 * q^73 - 46 * q^74 - 9 * q^75 - 101 * q^76 - 17 * q^77 + 6 * q^78 - 14 * q^79 - 112 * q^80 - 6 * q^81 + 2 * q^82 + 12 * q^83 - 22 * q^84 - 44 * q^85 + 184 * q^86 - q^87 + 204 * q^88 + 12 * q^89 + 10 * q^90 - 16 * q^91 - 105 * q^92 - 19 * q^93 - 5 * q^94 + 18 * q^95 - 9 * q^96 + 172 * q^97 + q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{3}{7}\right)$

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 $

$2$	−1.60360	−	0.772253i	−1.13392	−	0.546065i	−0.229751	−	0.973249i	$-0.573791\pi$
$2$	−1.60360	−	0.772253i	−1.13392	−	0.546065i	−0.904165	+	0.427184i	$0.859506\pi$
$3$	−0.222521	−	0.974928i	−0.128473	−	0.562875i
$3$	−0.222521	−	0.974928i	−0.128473	−	0.562875i
$4$	0.728177	+	0.913105i	0.364089	+	0.456553i
$5$	0.987738	+	4.32756i	0.441730	+	1.93534i	0.339588	+	0.940574i	$0.389712\pi$
$5$	0.987738	+	4.32756i	0.441730	+	1.93534i	0.102141	+	0.994770i	$0.467431\pi$
$6$	−0.396056	+	1.73524i	−0.161689	+	0.708407i
$7$	−2.63181	+	0.271221i	−0.994732	+	0.102512i
$7$	−2.63181	+	0.271221i	−0.994732	+	0.102512i
$8$	0.329556	+	1.44388i	0.116516	+	0.510489i
$9$	−0.900969	+	0.433884i	−0.300323	+	0.144628i
$10$	1.75804	−	7.70246i	0.555940	−	2.43573i
$11$	0.951225	+	0.458086i	0.286805	+	0.138118i	0.571755	−	0.820424i	$-0.306263\pi$
$11$	0.951225	+	0.458086i	0.286805	+	0.138118i	−0.284950	+	0.958542i	$0.591977\pi$
$12$	0.728177	−	0.913105i	0.210207	−	0.263591i
$13$	4.24896	+	2.04619i	1.17845	+	0.567511i	0.917459	−	0.397830i	$-0.130237\pi$
$13$	4.24896	+	2.04619i	1.17845	+	0.567511i	0.260990	+	0.965341i	$0.415951\pi$
$14$	4.42982	+	1.59749i	1.18392	+	0.426948i
$15$	3.99927	−	1.92595i	1.03261	−	0.497277i
$16$	1.10633	−	4.84715i	0.276583	−	1.21179i
$17$	−2.95622	+	3.70698i	−0.716988	+	0.899075i	−0.998163	−	0.0605815i	$-0.980704\pi$
$17$	−2.95622	+	3.70698i	−0.716988	+	0.899075i	0.281175	+	0.959657i	$0.409276\pi$
$18$	1.77986			0.419517
$19$	2.09671			0.481018			0.240509	−	0.970647i	$-0.422686\pi$
$19$	2.09671			0.481018			0.240509	+	0.970647i	$0.422686\pi$
$20$	−3.23227	+	4.05314i	−0.722758	+	0.906309i
$21$	0.850055	+	2.50548i	0.185497	+	0.546740i
$22$	−1.17163	−	1.46917i	−0.249792	−	0.313229i
$23$	−0.565574	−	0.709207i	−0.117930	−	0.147880i	0.719362	−	0.694635i	$-0.244434\pi$
$23$	−0.565574	−	0.709207i	−0.117930	−	0.147880i	−0.837292	+	0.546755i	$0.815863\pi$
$24$	1.33435	−	0.642587i	0.272372	−	0.131168i
$25$	−13.2473	+	6.37957i	−2.64946	+	1.27591i
$26$	−5.23345	−	6.56254i	−1.02636	−	1.28702i
$27$	0.623490	+	0.781831i	0.119991	+	0.150464i
$28$	−2.16408	−	2.20562i	−0.408973	−	0.416824i
$29$	1.79593	−	2.25202i	0.333495	−	0.418190i	−0.586605	−	0.809873i	$-0.699536\pi$
$29$	1.79593	−	2.25202i	0.333495	−	0.418190i	0.920100	+	0.391684i	$0.128107\pi$
$30$	−7.90054			−1.44243
$31$	1.97581			0.354866			0.177433	−	0.984133i	$-0.443221\pi$
$31$	1.97581			0.354866			0.177433	+	0.984133i	$0.443221\pi$
$32$	−3.67055	+	4.60272i	−0.648867	+	0.813654i
$33$	0.234933	−	1.02931i	0.0408966	−	0.179180i
$34$	7.60332	−	3.66156i	1.30396	−	0.627953i
$35$	−3.77327	−	11.1214i	−0.637799	−	1.87987i
$36$	−1.05225	−	0.506735i	−0.175374	−	0.0844559i
$37$	0.285021	−	0.357405i	0.0468572	−	0.0587571i	−0.757851	−	0.652428i	$-0.773750\pi$
$37$	0.285021	−	0.357405i	0.0468572	−	0.0587571i	0.804708	+	0.593671i	$0.202322\pi$
$38$	−3.36228	−	1.61919i	−0.545434	−	0.262667i
$39$	1.04941	−	4.59775i	0.168039	−	0.736229i
$40$	−5.92297	+	2.85235i	−0.936503	+	0.450996i
$41$	0.917612	+	4.02032i	0.143307	+	0.627869i	0.994654	+	0.103266i	$0.0329292\pi$
$41$	0.917612	+	4.02032i	0.143307	+	0.627869i	−0.851347	+	0.524603i	$0.824214\pi$
$42$	0.571713	−	4.67424i	0.0882173	−	0.721250i
$43$	−1.67837	+	7.35342i	−0.255949	+	1.12139i	0.669589	+	0.742732i	$0.266470\pi$
$43$	−1.67837	+	7.35342i	−0.255949	+	1.12139i	−0.925538	+	0.378655i	$0.876387\pi$
$44$	0.274380	+	1.20214i	0.0413643	+	0.181229i
$45$	−2.76758	−	3.47043i	−0.412566	−	0.517342i
$46$	0.359267	+	1.57405i	0.0529710	+	0.232081i
$47$	−7.33253	−	3.53116i	−1.06956	−	0.515073i	−0.185595	−	0.982626i	$-0.559421\pi$
$47$	−7.33253	−	3.53116i	−1.06956	−	0.515073i	−0.883965	+	0.467554i	$0.845136\pi$
$48$	−4.97181			−0.717619
$49$	6.85288	−	1.42761i	0.978983	−	0.203944i
$50$	26.1700			3.70100
$51$	4.27186	+	2.05722i	0.598180	+	0.288068i
$52$	1.22561	+	5.36974i	0.169961	+	0.744648i
$53$	−0.774992	−	0.971809i	−0.106453	−	0.133488i	0.725751	−	0.687958i	$-0.241493\pi$
$53$	−0.774992	−	0.971809i	−0.106453	−	0.133488i	−0.832204	+	0.554470i	$0.812921\pi$
$54$	−0.396056	−	1.73524i	−0.0538964	−	0.236136i
$55$	−1.04283	+	4.56895i	−0.140616	+	0.616078i
$56$	−1.25894	−	3.71064i	−0.168233	−	0.495855i
$57$	−0.466561	−	2.04414i	−0.0617976	−	0.270753i
$58$	−4.61908	+	2.22443i	−0.606514	+	0.292082i
$59$	0.293639	−	1.28652i	0.0382286	−	0.167490i	−0.952210	−	0.305444i	$-0.901195\pi$
$59$	0.293639	−	1.28652i	0.0382286	−	0.167490i	0.990439	+	0.137953i	$0.0440524\pi$
$60$	4.67077	+	2.24932i	0.602993	+	0.290386i
$61$	7.12459	−	8.93395i	0.912210	−	1.14388i	−0.0769500	−	0.997035i	$-0.524518\pi$
$61$	7.12459	−	8.93395i	0.912210	−	1.14388i	0.989160	−	0.146840i	$-0.0469104\pi$
$62$	−3.16841	−	1.52583i	−0.402388	−	0.193780i
$63$	2.25350	−	1.38626i	0.283915	−	0.174653i
$64$	0.481665	−	0.231958i	0.0602081	−	0.0289947i
$65$	−4.65816	+	20.4087i	−0.577774	+	2.53139i
$66$	−1.17163	+	1.46917i	−0.144217	+	0.180843i
$67$	2.75438			0.336502			0.168251	−	0.985744i	$-0.446188\pi$
$67$	2.75438			0.336502			0.168251	+	0.985744i	$0.446188\pi$
$68$	−5.53752			−0.671522
$69$	−0.565574	+	0.709207i	−0.0680871	+	0.0853785i
$70$	−2.53775	+	20.7482i	−0.303319	+	2.47989i
$71$	−2.88977	−	3.62366i	−0.342953	−	0.430049i	0.580205	−	0.814470i	$-0.302972\pi$
$71$	−2.88977	−	3.62366i	−0.342953	−	0.430049i	−0.923158	+	0.384421i	$0.874401\pi$
$72$	−0.923396	−	1.15790i	−0.108823	−	0.136460i
$73$	4.97674	−	2.39667i	0.582483	−	0.280509i	−0.119348	−	0.992852i	$-0.538080\pi$
$73$	4.97674	−	2.39667i	0.582483	−	0.280509i	0.701831	+	0.712343i	$0.252366\pi$
$74$	−0.733067	+	0.353027i	−0.0852173	+	0.0410385i
$75$	9.16743	+	11.4956i	1.05856	+	1.32740i
$76$	1.52677	+	1.91452i	0.175133	+	0.219610i
$77$	−2.62769	−	0.947604i	−0.299453	−	0.107990i
$78$	−5.23345	+	6.56254i	−0.592572	+	0.743061i
$79$	8.21672			0.924453			0.462226	−	0.886762i	$-0.347051\pi$
$79$	8.21672			0.924453			0.462226	+	0.886762i	$0.347051\pi$
$80$	22.0691			2.46740
$81$	0.623490	−	0.781831i	0.0692766	−	0.0868702i
$82$	1.63322	−	7.15562i	0.180359	−	0.790206i
$83$	13.7077	−	6.60126i	1.50461	−	0.724583i	0.513559	−	0.858054i	$-0.328327\pi$
$83$	13.7077	−	6.60126i	1.50461	−	0.724583i	0.991053	+	0.133471i	$0.0426124\pi$
$84$	−1.66877	+	2.60062i	−0.182078	+	0.283751i
$85$	−18.9622	−	9.13169i	−2.05673	−	0.990471i
$86$	8.37014	−	10.4958i	0.902575	−	1.13179i
$87$	−2.59519	−	1.24978i	−0.278233	−	0.133990i
$88$	−0.347939	+	1.52442i	−0.0370904	+	0.162504i
$89$	10.0755	−	4.85213i	1.06801	−	0.514324i	0.184542	−	0.982825i	$-0.440920\pi$
$89$	10.0755	−	4.85213i	1.06801	−	0.514324i	0.883463	+	0.468500i	$0.155206\pi$
$90$	1.75804	+	7.70246i	0.185313	+	0.811910i
$91$	−11.7374	−	4.23278i	−1.23042	−	0.443716i
$92$	0.235743	−	1.03286i	0.0245779	−	0.107683i
$93$	−0.439659	−	1.92627i	−0.0455905	−	0.199745i
$94$	9.03149	+	11.3251i	0.931528	+	1.16810i
$95$	2.07100	+	9.07363i	0.212480	+	0.930935i
$96$	5.30410	+	2.55432i	0.541347	+	0.260699i
$97$	5.72620			0.581408			0.290704	−	0.956813i	$-0.406111\pi$
$97$	5.72620			0.581408			0.290704	+	0.956813i	$0.406111\pi$
$98$	−12.0917	−	3.00284i	−1.22145	−	0.303333i
$99$	−1.05578			−0.106110
$100$	−15.4716	−	7.45073i	−1.54716	−	0.745073i
$101$	−0.638061	−	2.79553i	−0.0634894	−	0.278165i	0.933211	−	0.359328i	$-0.116994\pi$
$101$	−0.638061	−	2.79553i	−0.0634894	−	0.278165i	−0.996701	+	0.0811623i	$0.974137\pi$
$102$	−5.26166	−	6.59791i	−0.520982	−	0.653291i
$103$	−3.11171	−	13.6333i	−0.306606	−	1.34333i	−0.859951	−	0.510377i	$-0.829506\pi$
$103$	−3.11171	−	13.6333i	−0.306606	−	1.34333i	0.553345	−	0.832952i	$-0.313351\pi$
$104$	−1.55418	+	6.80932i	−0.152400	+	0.667709i
$105$	−10.0030	+	6.15342i	−0.976190	+	0.600512i
$106$	0.492294	+	2.15688i	0.0478158	+	0.209495i
$107$	−2.49968	+	1.20378i	−0.241654	+	0.116374i	−0.550791	−	0.834643i	$-0.685674\pi$
$107$	−2.49968	+	1.20378i	−0.241654	+	0.116374i	0.309138	+	0.951017i	$0.399960\pi$
$108$	−0.259883	+	1.13862i	−0.0250073	+	0.109564i
$109$	0.0742165	+	0.0357408i	0.00710865	+	0.00342335i	0.437435	−	0.899250i	$-0.355887\pi$
$109$	0.0742165	+	0.0357408i	0.00710865	+	0.00342335i	−0.430326	+	0.902674i	$0.641601\pi$
$110$	5.20068	−	6.52144i	0.495865	−	0.621795i
$111$	−0.411868	−	0.198345i	−0.0390927	−	0.0188261i
$112$	−1.59701	+	13.0569i	−0.150903	+	1.23376i
$113$	−12.7135	+	6.12248i	−1.19598	+	0.575954i	−0.922528	−	0.385931i	$-0.873880\pi$
$113$	−12.7135	+	6.12248i	−1.19598	+	0.575954i	−0.273454	+	0.961885i	$0.588166\pi$
$114$	−0.830415	+	3.63828i	−0.0777754	+	0.340756i
$115$	2.51050	−	3.14807i	0.234105	−	0.293559i
$116$	3.36408			0.312347
$117$	−4.71599			−0.435993
$118$	−1.46440	+	1.83629i	−0.134809	+	0.169045i
$119$	6.77480	−	10.5579i	0.621045	−	0.967838i
$120$	4.09882	+	5.13976i	0.374169	+	0.469194i
$121$	−6.16340	−	7.72866i	−0.560309	−	0.702605i
$122$	−18.3243	+	8.82450i	−1.65900	+	0.798932i
$123$	3.71534	−	1.78921i	0.335001	−	0.161328i
$124$	1.43874	+	1.80412i	0.129203	+	0.162015i
$125$	−26.8550	−	33.6750i	−2.40198	−	3.01199i
$126$	−4.68426	+	0.482736i	−0.417307	+	0.0430056i
$127$	−0.699528	+	0.877180i	−0.0620731	+	0.0778372i	−0.811899	−	0.583798i	$-0.801566\pi$
$127$	−0.699528	+	0.877180i	−0.0620731	+	0.0778372i	0.749826	+	0.661635i	$0.230137\pi$
$128$	10.8227			0.956598
$129$	7.54253			0.664083
$130$	23.2305	−	29.1301i	2.03745	−	2.55488i
$131$	−3.68194	+	16.1316i	−0.321692	+	1.40943i	0.512848	+	0.858480i	$0.328591\pi$
$131$	−3.68194	+	16.1316i	−0.321692	+	1.40943i	−0.834540	+	0.550947i	$0.814267\pi$
$132$	1.11094	−	0.535001i	0.0966950	−	0.0465659i
$133$	−5.51814	+	0.568672i	−0.478484	+	0.0493101i
$134$	−4.41693	−	2.12708i	−0.381564	−	0.183752i
$135$	−2.76758	+	3.47043i	−0.238195	+	0.298687i
$136$	−6.32668	−	3.04677i	−0.542508	−	0.261258i
$137$	−0.272365	+	1.19331i	−0.0232697	+	0.101951i	−0.985229	−	0.171241i	$-0.945222\pi$
$137$	−0.272365	+	1.19331i	−0.0232697	+	0.101951i	0.961959	+	0.273192i	$0.0880795\pi$
$138$	1.45464	−	0.700518i	0.123827	−	0.0596321i
$139$	2.53972	+	11.1272i	0.215416	+	0.943801i	0.960817	+	0.277184i	$0.0894011\pi$
$139$	2.53972	+	11.1272i	0.215416	+	0.943801i	−0.745401	+	0.666617i	$0.767742\pi$
$140$	7.40743	−	11.5438i	0.626042	−	0.975626i
$141$	−1.81099	+	7.93445i	−0.152513	+	0.668201i
$142$	1.83565	+	8.04253i	0.154045	+	0.674914i
$143$	3.10439	+	3.89278i	0.259602	+	0.325530i
$144$	1.10633	+	4.84715i	0.0921943	+	0.403930i
$145$	11.5197	+	5.54758i	0.956656	+	0.460701i
$146$	−9.83153			−0.813663
$147$	−2.91672	−	6.36339i	−0.240567	−	0.524844i
$148$	0.533895			0.0438859
$149$	2.67461	+	1.28802i	0.219112	+	0.105519i	0.540220	−	0.841524i	$-0.318341\pi$
$149$	2.67461	+	1.28802i	0.219112	+	0.105519i	−0.321108	+	0.947043i	$0.604055\pi$
$150$	−5.82338	−	25.5139i	−0.475477	−	2.08320i
$151$	10.4934	+	13.1583i	0.853937	+	1.07080i	0.996710	+	0.0810482i	$0.0258268\pi$
$151$	10.4934	+	13.1583i	0.853937	+	1.07080i	−0.142773	+	0.989755i	$0.545602\pi$
$152$	0.690983	+	3.02740i	0.0560462	+	0.245554i
$153$	1.05506	−	4.62253i	0.0852967	−	0.373709i
$154$	3.48197	+	3.54882i	0.280585	+	0.285972i
$155$	1.95158	+	8.55044i	0.156755	+	0.686788i
$156$	4.96238	−	2.38976i	0.397309	−	0.191334i
$157$	0.502985	−	2.20372i	0.0401426	−	0.175876i	−0.950883	−	0.309552i	$-0.899821\pi$
$157$	0.502985	−	2.20372i	0.0401426	−	0.175876i	0.991025	+	0.133676i	$0.0426781\pi$
$158$	−13.1763	−	6.34538i	−1.04825	−	0.504811i
$159$	−0.774992	+	0.971809i	−0.0614609	+	0.0770695i
$160$	−23.5441	−	11.3382i	−1.86132	−	0.896366i
$161$	1.68084	+	1.71311i	0.132469	+	0.135012i
$162$	−1.60360	+	0.772253i	−0.125991	+	0.0606739i
$163$	1.94093	−	8.50376i	0.152025	−	0.666066i	−0.840270	−	0.542168i	$-0.817604\pi$
$163$	1.94093	−	8.50376i	0.152025	−	0.666066i	0.992295	−	0.123897i	$-0.0395393\pi$
$164$	−3.00279	+	3.76538i	−0.234479	+	0.294027i
$165$	4.68645			0.364840
$166$	−27.0794			−2.10177
$167$	9.43677	−	11.8333i	0.730239	−	0.915691i	−0.268629	−	0.963244i	$-0.586571\pi$
$167$	9.43677	−	11.8333i	0.730239	−	0.915691i	0.998869	+	0.0475523i	$0.0151421\pi$
$168$	−3.33747	+	2.05307i	−0.257491	+	0.158398i
$169$	5.76139	+	7.22455i	0.443184	+	0.555735i
$170$	23.3557	+	29.2872i	1.79130	+	2.24622i
$171$	−1.88907	+	0.909728i	−0.144461	+	0.0695686i
$172$	−7.93660	+	3.82207i	−0.605160	+	0.291430i
$173$	13.2846	+	16.6583i	1.01001	+	1.26651i	0.963533	+	0.267588i	$0.0862265\pi$
$173$	13.2846	+	16.6583i	1.01001	+	1.26651i	0.0464724	+	0.998920i	$0.485202\pi$
$174$	3.19650	+	4.00828i	0.242326	+	0.303867i
$175$	33.1342	−	20.3828i	2.50471	−	1.54079i
$176$	3.27278	−	4.10394i	0.246695	−	0.309346i
$177$	−1.31960			−0.0991874
$178$	−19.9042			−1.49188
$179$	3.17234	−	3.97799i	0.237112	−	0.297329i	−0.649011	−	0.760779i	$-0.724817\pi$
$179$	3.17234	−	3.97799i	0.237112	−	0.297329i	0.886123	+	0.463450i	$0.153389\pi$
$180$	1.15358	−	5.05418i	0.0859831	−	0.376716i
$181$	1.65415	−	0.796597i	0.122952	−	0.0592106i	−0.371397	−	0.928474i	$-0.621121\pi$
$181$	1.65415	−	0.796597i	0.122952	−	0.0592106i	0.494349	+	0.869264i	$0.335407\pi$
$182$	15.5534	+	15.8520i	1.15289	+	1.17503i
$183$	−10.2953	−	4.95797i	−0.761053	−	0.366504i
$184$	0.837622	−	1.05035i	0.0617503	−	0.0774325i
$185$	1.82822	+	0.880424i	0.134413	+	0.0647301i
$186$	−0.782532	+	3.42850i	−0.0573781	+	0.251390i
$187$	−4.51015	+	2.17197i	−0.329815	+	0.158830i
$188$	−2.11506	−	9.26668i	−0.154257	−	0.675842i
$189$	−1.85296	−	1.88853i	−0.134783	−	0.137370i
$190$	3.68609	−	16.1498i	0.267417	−	1.17163i
$191$	−2.95936	−	12.9658i	−0.214131	−	0.938171i	−0.961725	−	0.274015i	$-0.911648\pi$
$191$	−2.95936	−	12.9658i	−0.214131	−	0.938171i	0.747594	−	0.664156i	$-0.231209\pi$
$192$	−0.333322	−	0.417973i	−0.0240555	−	0.0301646i
$193$	3.35030	+	14.6786i	0.241160	+	1.05659i	0.939963	+	0.341277i	$0.110859\pi$
$193$	3.35030	+	14.6786i	0.241160	+	1.05659i	−0.698802	+	0.715315i	$0.746283\pi$
$194$	−9.18254	−	4.42208i	−0.659268	−	0.317487i
$195$	20.9336			1.49908
$196$	6.29366	+	5.21785i	0.449547	+	0.372703i
$197$	11.2917			0.804498			0.402249	−	0.915530i	$-0.368229\pi$
$197$	11.2917			0.804498			0.402249	+	0.915530i	$0.368229\pi$
$198$	1.69305	+	0.815329i	0.120320	+	0.0579429i
$199$	5.34073	+	23.3992i	0.378594	+	1.65873i	0.701780	+	0.712393i	$0.252389\pi$
$199$	5.34073	+	23.3992i	0.378594	+	1.65873i	−0.323186	+	0.946335i	$0.604754\pi$
$200$	−13.5771	−	17.0251i	−0.960044	−	1.20386i
$201$	−0.612908	−	2.68533i	−0.0432312	−	0.189408i
$202$	−1.13566	+	4.97565i	−0.0799047	+	0.350085i
$203$	−4.11575	+	6.41399i	−0.288869	+	0.450174i
$204$	1.23221	+	5.39868i	0.0862722	+	0.377983i
$205$	−16.4918	+	7.94205i	−1.15184	+	0.554697i
$206$	−5.53841	+	24.2654i	−0.385880	+	1.69065i
$207$	0.817278	+	0.393580i	0.0568048	+	0.0273557i
$208$	14.6190	−	18.3316i	1.01364	−	1.27107i
$209$	1.99444	+	0.960473i	0.137958	+	0.0664373i
$210$	20.7927	−	2.14279i	1.43484	−	0.147867i
$211$	−13.1458	+	6.33066i	−0.904991	+	0.435821i	−0.827689	−	0.561187i	$-0.810345\pi$
$211$	−13.1458	+	6.33066i	−0.904991	+	0.435821i	−0.0773021	+	0.997008i	$0.524631\pi$
$212$	0.323033	−	1.41530i	0.0221860	−	0.0972031i
$213$	−2.88977	+	3.62366i	−0.198004	+	0.248289i
$214$	4.93812			0.337563
$215$	−33.4802			−2.28333
$216$	−0.923396	+	1.15790i	−0.0628292	+	0.0787853i
$217$	−5.19996	+	0.535882i	−0.352997	+	0.0363780i
$218$	−0.0914126	−	0.114628i	−0.00619124	−	0.00776358i
$219$	−3.44401	−	4.31865i	−0.232725	−	0.291827i
$220$	−4.93130	+	2.37479i	−0.332468	+	0.160108i
$221$	−20.1460	+	9.70182i	−1.35517	+	0.652615i
$222$	0.507298	+	0.636132i	0.0340476	+	0.0426944i
$223$	0.163765	+	0.205355i	0.0109665	+	0.0137516i	0.787284	−	0.616590i	$-0.211486\pi$
$223$	0.163765	+	0.205355i	0.0109665	+	0.0137516i	−0.776318	+	0.630341i	$0.782915\pi$
$224$	8.41184	−	13.1090i	0.562040	−	0.875884i
$225$	9.16743	−	11.4956i	0.611162	−	0.766373i
$226$	25.1154			1.67065
$227$	−6.43940			−0.427398			−0.213699	−	0.976900i	$-0.568551\pi$
$227$	−6.43940			−0.427398			−0.213699	+	0.976900i	$0.568551\pi$
$228$	1.52677	−	1.91452i	0.101113	−	0.126792i
$229$	−2.37820	+	10.4196i	−0.157156	+	0.688545i	0.833541	+	0.552458i	$0.186310\pi$
$229$	−2.37820	+	10.4196i	−0.157156	+	0.688545i	−0.990697	+	0.136087i	$0.956547\pi$
$230$	−6.45694	+	3.10950i	−0.425758	+	0.205034i
$231$	−0.339130	+	2.77267i	−0.0223131	+	0.182428i
$232$	3.84351	+	1.85094i	0.252339	+	0.121520i
$233$	7.86250	−	9.85926i	0.515089	−	0.645902i	−0.454469	−	0.890763i	$-0.650171\pi$
$233$	7.86250	−	9.85926i	0.515089	−	0.645902i	0.969558	+	0.244861i	$0.0787424\pi$
$234$	7.56256	+	3.64194i	0.494380	+	0.238081i
$235$	8.03870	−	35.2198i	0.524387	−	2.29749i
$236$	1.38855	−	0.668689i	0.0903867	−	0.0435279i
$237$	−1.82839	−	8.01071i	−0.118767	−	0.520351i
$238$	−19.0174	+	11.6987i	−1.23272	+	0.758316i
$239$	5.59499	−	24.5133i	0.361910	−	1.58563i	−0.386432	−	0.922318i	$-0.626292\pi$
$239$	5.59499	−	24.5133i	0.361910	−	1.58563i	0.748342	−	0.663313i	$-0.230850\pi$
$240$	−4.91084	−	21.5158i	−0.316993	−	1.38884i
$241$	−10.0426	−	12.5930i	−0.646900	−	0.811187i	0.344947	−	0.938622i	$-0.387897\pi$
$241$	−10.0426	−	12.5930i	−0.646900	−	0.811187i	−0.991847	+	0.127435i	$0.959326\pi$
$242$	3.91515	+	17.1534i	0.251675	+	1.10266i
$243$	−0.900969	−	0.433884i	−0.0577972	−	0.0278337i
$244$	13.3456			0.854365
$245$	12.9469	+	28.2461i	0.827147	+	1.80458i
$246$	−7.33964			−0.467958
$247$	8.90883	+	4.29026i	0.566855	+	0.272983i
$248$	0.651141	+	2.85284i	0.0413475	+	0.181155i
$249$	−9.48600	−	11.8951i	−0.601151	−	0.753819i
$250$	17.0589	+	74.7401i	1.07890	+	4.72698i
$251$	−2.71050	+	11.8755i	−0.171085	+	0.749574i	0.814468	+	0.580209i	$0.197029\pi$
$251$	−2.71050	+	11.8755i	−0.171085	+	0.749574i	−0.985553	+	0.169366i	$0.945828\pi$
$252$	2.90675	+	1.04824i	0.183108	+	0.0660329i
$253$	−0.213110	−	0.933698i	−0.0133981	−	0.0587011i
$254$	1.79917	−	0.866433i	0.112890	−	0.0543649i
$255$	−4.68327	+	20.5187i	−0.293277	+	1.28493i
$256$	−18.3186	−	8.82176i	−1.14491	−	0.551360i
$257$	−10.2907	+	12.9042i	−0.641919	+	0.804940i	−0.991241	−	0.132062i	$-0.957840\pi$
$257$	−10.2907	+	12.9042i	−0.641919	+	0.804940i	0.349323	+	0.937002i	$0.386412\pi$
$258$	−12.0952	−	5.82474i	−0.753014	−	0.362632i
$259$	−0.653187	+	1.01793i	−0.0405870	+	0.0632510i
$260$	−22.0273	+	10.6078i	−1.36607	+	0.657867i
$261$	−0.640959	+	2.80822i	−0.0396743	+	0.173825i
$262$	18.3620	−	23.0253i	1.13441	−	1.42251i
$263$	−5.58393			−0.344320			−0.172160	−	0.985069i	$-0.555075\pi$
$263$	−5.58393			−0.344320			−0.172160	+	0.985069i	$0.555075\pi$
$264$	1.56362			0.0962344
$265$	3.44007	−	4.31372i	0.211322	−	0.264990i
$266$	9.28805	+	3.34948i	0.569487	+	0.205370i
$267$	−6.97249	−	8.74323i	−0.426710	−	0.535077i
$268$	2.00568	+	2.51504i	0.122516	+	0.153631i
$269$	10.3472	−	4.98296i	0.630882	−	0.303817i	−0.0909812	−	0.995853i	$-0.529000\pi$
$269$	10.3472	−	4.98296i	0.630882	−	0.303817i	0.721863	+	0.692036i	$0.243286\pi$
$270$	7.11814	−	3.42792i	0.433196	−	0.208616i
$271$	2.07215	+	2.59840i	0.125874	+	0.157841i	0.840775	−	0.541384i	$-0.182100\pi$
$271$	2.07215	+	2.59840i	0.125874	+	0.157841i	−0.714901	+	0.699226i	$0.753528\pi$
$272$	14.6978	+	18.4304i	0.891182	+	1.11751i
$273$	−1.51483	+	12.3850i	−0.0916819	+	0.749576i
$274$	1.35830	−	1.70326i	0.0820580	−	0.102897i
$275$	−15.5236			−0.936107
$276$	−1.05942			−0.0637695
$277$	−1.61162	+	2.02091i	−0.0968328	+	0.121424i	−0.827887	−	0.560895i	$-0.810457\pi$
$277$	−1.61162	+	2.02091i	−0.0968328	+	0.121424i	0.731054	+	0.682319i	$0.239029\pi$
$278$	4.52035	−	19.8050i	0.271113	−	1.18782i
$279$	−1.78014	+	0.857272i	−0.106574	+	0.0513235i
$280$	14.8145	−	9.11329i	0.885337	−	0.544623i
$281$	11.8811	+	5.72163i	0.708766	+	0.341324i	0.753293	−	0.657685i	$-0.228464\pi$
$281$	11.8811	+	5.72163i	0.708766	+	0.341324i	−0.0445277	+	0.999008i	$0.514178\pi$
$282$	9.03149	−	11.3251i	0.537818	−	0.674402i
$283$	−5.13752	−	2.47410i	−0.305394	−	0.147070i	0.274910	−	0.961470i	$-0.411352\pi$
$283$	−5.13752	−	2.47410i	−0.305394	−	0.147070i	−0.580304	+	0.814400i	$0.697066\pi$
$284$	1.20452	−	5.27733i	0.0714749	−	0.313152i
$285$	8.38530	−	4.03815i	0.496702	−	0.239199i
$286$	−1.97198	−	8.63983i	−0.116606	−	0.510884i
$287$	−3.50538	−	10.3319i	−0.206916	−	0.609870i
$288$	1.31000	−	5.73950i	0.0771927	−	0.338203i
$289$	−1.21962	−	5.34352i	−0.0717426	−	0.314325i
$290$	−14.1888	−	17.7922i	−0.833194	−	1.04479i
$291$	−1.27420	−	5.58264i	−0.0746949	−	0.327260i
$292$	5.81236	+	2.79908i	0.340143	+	0.163804i
$293$	1.16842			0.0682596			0.0341298	−	0.999417i	$-0.489134\pi$
$293$	1.16842			0.0682596			0.0341298	+	0.999417i	$0.489134\pi$
$294$	−0.236890	+	12.4568i	−0.0138157	+	0.726494i
$295$	5.85752			0.341038
$296$	0.609981	+	0.293751i	0.0354544	+	0.0170740i
$297$	0.234933	+	1.02931i	0.0136322	+	0.0597266i
$298$	−3.29432	−	4.13095i	−0.190835	−	0.239299i
$299$	−0.951927	−	4.17067i	−0.0550514	−	0.241196i
$300$	−3.82117	+	16.7416i	−0.220615	+	0.966580i
$301$	2.42275	−	19.8080i	0.139645	−	1.14172i
$302$	−6.66564	−	29.2041i	−0.383565	−	1.68051i
$303$	−2.58345	+	1.24413i	−0.148416	+	0.0714732i
$304$	2.31965	−	10.1631i	0.133041	−	0.582892i
$305$	45.6994	+	22.0077i	2.61674	+	1.26016i
$306$	−5.26166	+	6.59791i	−0.300789	+	0.377178i
$307$	−13.6585	−	6.57757i	−0.779530	−	0.375402i	0.00141723	−	0.999999i	$-0.499549\pi$
$307$	−13.6585	−	6.57757i	−0.779530	−	0.375402i	−0.780947	+	0.624597i	$0.785263\pi$
$308$	−1.04816	−	3.08938i	−0.0597245	−	0.176034i
$309$	−12.5991	+	6.06739i	−0.716736	+	0.345162i
$310$	3.47355	−	15.2186i	0.197284	−	0.864358i
$311$	0.334482	−	0.419427i	0.0189667	−	0.0237835i	−0.772258	−	0.635309i	$-0.780873\pi$
$311$	0.334482	−	0.419427i	0.0189667	−	0.0237835i	0.791224	+	0.611526i	$0.209444\pi$
$312$	6.98444			0.395416
$313$	29.7171			1.67971			0.839854	−	0.542813i	$-0.182641\pi$
$313$	29.7171			1.67971			0.839854	+	0.542813i	$0.182641\pi$
$314$	−2.50842	+	3.14546i	−0.141558	+	0.177508i
$315$	8.22501	+	8.38291i	0.463427	+	0.472323i
$316$	5.98322	+	7.50273i	0.336583	+	0.422061i
$317$	−17.5060	−	21.9518i	−0.983235	−	1.23294i	−0.972478	−	0.232996i	$-0.925147\pi$
$317$	−17.5060	−	21.9518i	−0.983235	−	1.23294i	−0.0107577	−	0.999942i	$-0.503424\pi$
$318$	1.99326	−	0.959903i	0.111776	−	0.0538287i
$319$	2.73995	−	1.31949i	0.153408	−	0.0738773i
$320$	1.47957	+	1.85532i	0.0827104	+	0.103716i
$321$	1.72983	+	2.16914i	0.0965499	+	0.121070i
$322$	−1.37244	−	4.04517i	−0.0764830	−	0.225428i
$323$	−6.19833	+	7.77246i	−0.344884	+	0.432471i
$324$	1.16791			0.0648836
$325$	−69.3411			−3.84635
$326$	−9.67952	+	12.1377i	−0.536099	+	0.672247i
$327$	0.0183300	−	0.0803088i	0.00101365	−	0.00444109i
$328$	−5.50246	+	2.64985i	−0.303823	+	0.146313i
$329$	20.2556	+	7.30462i	1.11673	+	0.402717i
$330$	−7.51519	−	3.61913i	−0.413698	−	0.199226i
$331$	−3.87933	+	4.86453i	−0.213227	+	0.267379i	−0.876930	−	0.480618i	$-0.840412\pi$
$331$	−3.87933	+	4.86453i	−0.213227	+	0.267379i	0.663703	+	0.747996i	$0.268984\pi$
$332$	16.0093	+	7.70965i	0.878622	+	0.423122i
$333$	−0.101723	+	0.445677i	−0.00557438	+	0.0244230i
$334$	−24.2711	+	11.6884i	−1.32806	+	0.639559i
$335$	2.72061	+	11.9198i	0.148643	+	0.651246i
$336$	13.0849	−	1.34846i	0.713838	−	0.0735645i
$337$	2.98668	−	13.0855i	0.162695	−	0.712812i	−0.826099	−	0.563525i	$-0.809445\pi$
$337$	2.98668	−	13.0855i	0.162695	−	0.712812i	0.988794	−	0.149287i	$-0.0476980\pi$
$338$	−3.65978	−	16.0345i	−0.199066	−	0.872164i
$339$	8.79799	+	11.0323i	0.477841	+	0.599194i
$340$	−5.46961	−	23.9639i	−0.296631	−	1.29963i
$341$	1.87944	+	0.905091i	0.101777	+	0.0490134i
$342$	3.73185			0.201795
$343$	−17.6483	+	5.61584i	−0.952918	+	0.303227i
$344$	−11.1706			−0.602277
$345$	−3.62778	−	1.74705i	−0.195313	−	0.0940577i
$346$	−8.43868	−	36.9723i	−0.453666	−	1.98764i
$347$	−9.30336	−	11.6660i	−0.499430	−	0.626266i	0.466670	−	0.884431i	$-0.345453\pi$
$347$	−9.30336	−	11.6660i	−0.499430	−	0.626266i	−0.966101	+	0.258165i	$0.916882\pi$
$348$	−0.748579	−	3.27974i	−0.0401281	−	0.175812i
$349$	−5.49929	+	24.0939i	−0.294370	+	1.28972i	0.584006	+	0.811749i	$0.301484\pi$
$349$	−5.49929	+	24.0939i	−0.294370	+	1.28972i	−0.878376	+	0.477970i	$0.841373\pi$
$350$	−68.8746	+	7.09787i	−3.68150	+	0.379397i
$351$	1.04941	+	4.59775i	0.0560132	+	0.245410i
$352$	−5.59996	+	2.69680i	−0.298479	+	0.143740i
$353$	0.741409	−	3.24833i	0.0394612	−	0.172891i	−0.951357	−	0.308090i	$-0.900310\pi$
$353$	0.741409	−	3.24833i	0.0394612	−	0.172891i	0.990818	+	0.135199i	$0.0431674\pi$
$354$	2.11611	+	1.01907i	0.112470	+	0.0541628i
$355$	12.8273	−	16.0849i	0.680800	−	0.853697i
$356$	11.7673	+	5.66682i	0.623665	+	0.300341i
$357$	−11.8007	−	4.25560i	−0.624559	−	0.225230i
$358$	−8.15918	+	3.92925i	−0.431226	+	0.207667i
$359$	−2.08440	+	9.13234i	−0.110010	+	0.481987i	0.889668	+	0.456609i	$0.150936\pi$
$359$	−2.08440	+	9.13234i	−0.110010	+	0.481987i	−0.999678	+	0.0253779i	$0.991921\pi$
$360$	4.09882	−	5.13976i	0.216027	−	0.270889i
$361$	−14.6038			−0.768622
$362$	−3.26777			−0.171750
$363$	−6.16340	+	7.72866i	−0.323495	+	0.405649i
$364$	−4.68196	−	13.7997i	−0.245401	−	0.723302i
$365$	15.2874	+	19.1699i	0.800182	+	1.00340i
$366$	12.6808	+	15.9012i	0.662835	+	0.831169i
$367$	27.8010	−	13.3883i	1.45120	−	0.698862i	0.468399	−	0.883517i	$-0.344831\pi$
$367$	27.8010	−	13.3883i	1.45120	−	0.698862i	0.982803	+	0.184655i	$0.0591166\pi$
$368$	−4.06335	+	1.95681i	−0.211817	+	0.102006i
$369$	−2.57109	−	3.22405i	−0.133846	−	0.167837i
$370$	−2.25182	−	2.82370i	−0.117067	−	0.146797i
$371$	2.30321	+	2.34743i	0.119577	+	0.121872i
$372$	1.43874	−	1.80412i	0.0745952	−	0.0935394i
$373$	14.0696			0.728496			0.364248	−	0.931302i	$-0.381326\pi$
$373$	14.0696			0.728496			0.364248	+	0.931302i	$0.381326\pi$
$374$	8.90978			0.460714
$375$	−26.8550	+	33.6750i	−1.38678	+	1.73897i
$376$	2.68209	−	11.7510i	0.138318	−	0.606012i
$377$	12.2389	−	5.89393i	0.630334	−	0.303553i
$378$	1.51298	+	4.45940i	0.0778193	+	0.229367i
$379$	−28.4035	−	13.6784i	−1.45899	−	0.702611i	−0.474858	−	0.880062i	$-0.657501\pi$
$379$	−28.4035	−	13.6784i	−1.45899	−	0.702611i	−0.984130	+	0.177451i	$0.943215\pi$
$380$	−6.77713	+	8.49825i	−0.347659	+	0.435951i
$381$	1.01085	+	0.486798i	0.0517873	+	0.0249394i
$382$	−5.26724	+	23.0773i	−0.269496	+	1.18074i
$383$	−0.793314	+	0.382040i	−0.0405365	+	0.0195213i	−0.454042	−	0.890980i	$-0.650018\pi$
$383$	−0.793314	+	0.382040i	−0.0405365	+	0.0195213i	0.413506	+	0.910502i	$0.364304\pi$
$384$	−2.40827	−	10.5513i	−0.122897	−	0.538445i
$385$	1.50535	−	12.3075i	0.0767196	−	0.627247i
$386$	5.96308	−	26.1259i	0.303513	−	1.32978i
$387$	−1.67837	−	7.35342i	−0.0853164	−	0.373796i
$388$	4.16969	+	5.22863i	0.211684	+	0.265443i
$389$	−6.50001	−	28.4784i	−0.329563	−	1.44391i	−0.819964	−	0.572415i	$-0.806007\pi$
$389$	−6.50001	−	28.4784i	−0.329563	−	1.44391i	0.490401	−	0.871497i	$-0.336850\pi$
$390$	−33.5691	−	16.1660i	−1.69984	−	0.818598i
$391$	4.30098			0.217510
$392$	4.31970	+	9.42426i	0.218178	+	0.475997i
$393$	16.5465			0.834659
$394$	−18.1073	−	8.72002i	−0.912233	−	0.439308i
$395$	8.11596	+	35.5583i	0.408358	+	1.78913i
$396$	−0.768795	−	0.964039i	−0.0386334	−	0.0484448i
$397$	2.48669	+	10.8949i	0.124804	+	0.546800i	0.998210	+	0.0598080i	$0.0190488\pi$
$397$	2.48669	+	10.8949i	0.124804	+	0.546800i	−0.873406	+	0.486992i	$0.838094\pi$
$398$	9.50575	−	41.6474i	0.476480	−	2.08760i
$399$	1.78232	+	5.25325i	0.0892274	+	0.262991i
$400$	16.2668	+	71.2697i	0.813342	+	3.56348i
$401$	28.7143	−	13.8281i	1.43392	−	0.690542i	0.454201	−	0.890899i	$-0.349925\pi$
$401$	28.7143	−	13.8281i	1.43392	−	0.690542i	0.979723	+	0.200358i	$0.0642104\pi$
$402$	−1.09089	+	4.77951i	−0.0544087	+	0.238380i
$403$	8.39514	+	4.04289i	0.418192	+	0.201390i
$404$	2.08799	−	2.61825i	0.103881	−	0.130263i
$405$	3.99927	+	1.92595i	0.198725	+	0.0957010i
$406$	11.5532	−	7.10707i	0.573377	−	0.352718i
$407$	0.434842	−	0.209409i	0.0215543	−	0.0103800i
$408$	−1.56256	+	6.84603i	−0.0773583	+	0.338929i
$409$	−20.2302	+	25.3679i	−1.00032	+	1.25436i	−0.0333591	+	0.999443i	$0.510621\pi$
$409$	−20.2302	+	25.3679i	−1.00032	+	1.25436i	−0.966962	+	0.254920i	$0.917951\pi$
$410$	32.5796			1.60899
$411$	1.22400			0.0603754
$412$	10.1828	−	12.7688i	0.501669	−	0.629073i
$413$	−0.423872	+	3.46551i	−0.0208574	+	0.170527i
$414$	−1.00664	−	1.26229i	−0.0494738	−	0.0620382i
$415$	42.1069	+	52.8004i	2.06695	+	2.59187i
$416$	−25.0141	+	12.0461i	−1.22641	+	0.590610i
$417$	10.2831	−	4.95209i	0.503567	−	0.242505i
$418$	−2.45656	−	3.08043i	−0.120154	−	0.150669i
$419$	6.05176	+	7.58867i	0.295648	+	0.370731i	0.907363	−	0.420347i	$-0.138092\pi$
$419$	6.05176	+	7.58867i	0.295648	+	0.370731i	−0.611716	+	0.791078i	$0.709520\pi$
$420$	−12.9026	−	4.65298i	−0.629585	−	0.227042i
$421$	12.5823	−	15.7777i	0.613224	−	0.768958i	−0.374149	−	0.927368i	$-0.622065\pi$
$421$	12.5823	−	15.7777i	0.613224	−	0.768958i	0.987373	+	0.158410i	$0.0506367\pi$
$422$	25.9694			1.26417
$423$	8.13850			0.395707
$424$	1.14777	−	1.43926i	0.0557408	−	0.0698967i
$425$	15.5130	−	67.9670i	0.752492	−	3.29688i
$426$	7.43241	−	3.57926i	0.360102	−	0.173416i
$427$	−16.3275	+	25.4448i	−0.790143	+	1.23136i
$428$	−2.91939	−	1.40591i	−0.141114	−	0.0679570i
$429$	3.10439	−	3.89278i	0.149881	−	0.187945i
$430$	53.6888	+	25.8552i	2.58910	+	1.24685i
$431$	−2.20568	+	9.66374i	−0.106244	+	0.465486i	0.893617	+	0.448830i	$0.148159\pi$
$431$	−2.20568	+	9.66374i	−0.106244	+	0.465486i	−0.999861	+	0.0166558i	$0.994698\pi$
$432$	4.47944	−	2.15719i	0.215517	−	0.103788i
$433$	−4.44868	−	19.4909i	−0.213790	−	0.936674i	−0.961965	−	0.273173i	$-0.911927\pi$
$433$	−4.44868	−	19.4909i	−0.213790	−	0.936674i	0.748175	−	0.663501i	$-0.230930\pi$
$434$	8.75250	+	3.15635i	0.420133	+	0.151510i
$435$	2.84512	−	12.4653i	0.136413	−	0.597665i
$436$	0.0214077	+	0.0937931i	0.00102524	+	0.00449188i
$437$	−1.18584	−	1.48700i	−0.0567266	−	0.0711329i
$438$	2.18772	+	9.58503i	0.104533	+	0.457991i
$439$	−30.0813	−	14.4864i	−1.43570	−	0.691399i	−0.455656	−	0.890156i	$-0.650595\pi$
$439$	−30.0813	−	14.4864i	−1.43570	−	0.691399i	−0.980049	+	0.198757i	$0.936309\pi$
$440$	−6.94070			−0.330885
$441$	−5.55481	+	4.25958i	−0.264515	+	0.202837i
$442$	39.7984			1.89302
$443$	−19.8332	−	9.55118i	−0.942306	−	0.453790i	−0.101324	−	0.994854i	$-0.532308\pi$
$443$	−19.8332	−	9.55118i	−0.942306	−	0.453790i	−0.840982	+	0.541063i	$0.818022\pi$
$444$	−0.118803	−	0.520509i	−0.00563813	−	0.0247023i
$445$	30.9499	+	38.8099i	1.46716	+	1.83977i
$446$	−0.104028	−	0.455774i	−0.00492585	−	0.0215815i
$447$	0.660574	−	2.89416i	0.0312441	−	0.136889i
$448$	−1.20474	+	0.741107i	−0.0569186	+	0.0350140i
$449$	−1.68875	−	7.39891i	−0.0796972	−	0.349176i	0.919319	−	0.393512i	$-0.128740\pi$
$449$	−1.68875	−	7.39891i	−0.0796972	−	0.349176i	−0.999017	+	0.0443357i	$0.985883\pi$
$450$	−23.5784	+	11.3547i	−1.11150	+	0.535268i
$451$	−0.968797	+	4.24458i	−0.0456189	+	0.199869i
$452$	−14.8481	−	7.15048i	−0.698397	−	0.336330i
$453$	10.4934	−	13.1583i	0.493021	−	0.618229i
$454$	10.3262	+	4.97284i	0.484633	+	0.233387i
$455$	6.72412	−	54.9753i	0.315232	−	2.57728i
$456$	2.79773	−	1.34732i	0.131016	−	0.0630939i
$457$	−6.05373	+	26.5231i	−0.283182	+	1.24070i	0.610506	+	0.792011i	$0.290966\pi$
$457$	−6.05373	+	26.5231i	−0.283182	+	1.24070i	−0.893688	+	0.448689i	$0.851891\pi$
$458$	11.8602	−	14.8722i	0.554192	−	0.694935i
$459$	−4.74141			−0.221310
$460$	4.70260			0.219260
$461$	1.31974	−	1.65490i	0.0614664	−	0.0770764i	−0.750148	−	0.661270i	$-0.770018\pi$
$461$	1.31974	−	1.65490i	0.0614664	−	0.0770764i	0.811614	+	0.584194i	$0.198589\pi$
$462$	2.68503	−	4.18436i	0.124919	−	0.194674i
$463$	16.9110	+	21.2058i	0.785923	+	0.985516i	0.999962	+	0.00869098i	$0.00276646\pi$
$463$	16.9110	+	21.2058i	0.785923	+	0.985516i	−0.214039	+	0.976825i	$0.568662\pi$
$464$	−8.92900	−	11.1966i	−0.414518	−	0.519790i
$465$	7.90180	−	3.80530i	0.366437	−	0.176467i
$466$	−20.2221	+	9.73847i	−0.936772	+	0.451126i
$467$	21.7853	+	27.3179i	1.00810	+	1.26412i	0.964225	+	0.265084i	$0.0853998\pi$
$467$	21.7853	+	27.3179i	1.00810	+	1.26412i	0.0438778	+	0.999037i	$0.486029\pi$
$468$	−3.43408	−	4.30619i	−0.158740	−	0.199054i
$469$	−7.24902	+	0.747047i	−0.334729	+	0.0344954i
$470$	−40.0895	+	50.2706i	−1.84919	+	2.31881i
$471$	−2.26040			−0.104154
$472$	1.95435			0.0899561
$473$	−4.96501	+	6.22592i	−0.228291	+	0.286268i
$474$	−3.25428	+	14.2579i	−0.149474	+	0.654889i
$475$	−27.7757	+	13.3761i	−1.27444	+	0.613737i
$476$	14.5737	−	1.50189i	0.667985	−	0.0688391i
$477$	1.11990	+	0.539313i	0.0512765	+	0.0246935i
$478$	−27.9026	+	34.9887i	−1.27623	+	1.60035i
$479$	−16.0365	−	7.72275i	−0.732725	−	0.352862i	0.0300304	−	0.999549i	$-0.490440\pi$
$479$	−16.0365	−	7.72275i	−0.732725	−	0.352862i	−0.762755	+	0.646687i	$0.776154\pi$
$480$	−5.81491	+	25.4768i	−0.265413	+	1.16285i
$481$	1.94236	−	0.935393i	0.0885641	−	0.0426502i
$482$	6.37930	+	27.9496i	0.290569	+	1.27307i
$483$	1.29613	−	2.01990i	0.0589761	−	0.0919085i
$484$	2.56903	−	11.2557i	0.116774	−	0.511621i
$485$	5.65599	+	24.7805i	0.256825	+	1.12522i
$486$	1.10973	+	1.39155i	0.0503382	+	0.0631221i
$487$	0.502855	+	2.20315i	0.0227865	+	0.0998343i	0.985042	−	0.172312i	$-0.0551237\pi$
$487$	0.502855	+	2.20315i	0.0227865	+	0.0998343i	−0.962256	+	0.272146i	$0.912267\pi$
$488$	15.2475	+	7.34282i	0.690223	+	0.332394i
$489$	−8.72245			−0.394443
$490$	1.05152	−	55.2938i	0.0475028	−	2.49792i
$491$	−1.77691			−0.0801910			−0.0400955	−	0.999196i	$-0.512766\pi$
$491$	−1.77691			−0.0801910			−0.0400955	+	0.999196i	$0.512766\pi$
$492$	4.33916	+	2.08963i	0.195625	+	0.0942078i
$493$	3.03905	+	13.3149i	0.136872	+	0.599674i
$494$	−10.9730	−	13.7597i	−0.493700	−	0.619080i
$495$	−1.04283	−	4.56895i	−0.0468719	−	0.205359i
$496$	2.18590	−	9.57706i	0.0981499	−	0.430023i
$497$	8.58815	+	8.75302i	0.385231	+	0.392627i
$498$	6.02574	+	26.4005i	0.270020	+	1.18304i
$499$	−22.9011	+	11.0286i	−1.02519	+	0.493708i	−0.869414	−	0.494084i	$-0.835504\pi$
$499$	−22.9011	+	11.0286i	−1.02519	+	0.493708i	−0.155780	+	0.987792i	$0.549789\pi$
$500$	11.1937	−	49.0428i	0.500597	−	2.19326i
$501$	−13.6365	−	6.56701i	−0.609235	−	0.293392i
$502$	13.5174	−	16.9503i	0.603313	−	0.756531i
$503$	−28.2066	−	13.5836i	−1.25767	−	0.605661i	−0.318111	−	0.948053i	$-0.603048\pi$
$503$	−28.2066	−	13.5836i	−1.25767	−	0.605661i	−0.939557	+	0.342392i	$0.888763\pi$
$504$	2.74425	+	2.79694i	0.122239	+	0.124586i
$505$	11.4676	−	5.52249i	0.510300	−	0.245748i
$506$	−0.379307	+	1.66185i	−0.0168622	+	0.0738783i
$507$	5.76139	−	7.22455i	0.255872	−	0.320854i
$508$	−1.31034			−0.0581369
$509$	−11.6124			−0.514712			−0.257356	−	0.966317i	$-0.582851\pi$
$509$	−11.6124			−0.514712			−0.257356	+	0.966317i	$0.582851\pi$
$510$	23.3557	−	29.2872i	1.03421	−	1.29686i
$511$	−12.4478	+	7.65739i	−0.550659	+	0.338743i
$512$	9.06736	+	11.3701i	0.400724	+	0.502493i
$513$	1.30728	+	1.63927i	0.0577176	+	0.0723756i
$514$	26.4675	−	12.7461i	1.16743	−	0.562205i
$515$	55.9254	−	26.9322i	2.46437	−	1.18678i
$516$	5.49230	+	6.88712i	0.241785	+	0.303189i
$517$	−5.35732	−	6.71786i	−0.235614	−	0.295451i
$518$	1.83355	−	1.12792i	0.0805614	−	0.0495581i
$519$	13.2846	−	16.6583i	0.583127	−	0.731218i
$520$	−31.0029			−1.35957
$521$	36.5984			1.60340			0.801702	−	0.597724i	$-0.203928\pi$
$521$	36.5984			1.60340			0.801702	+	0.597724i	$0.203928\pi$
$522$	3.19650	−	4.00828i	0.139907	−	0.175438i
$523$	−3.55728	+	15.5855i	−0.155549	+	0.681505i	0.835665	+	0.549239i	$0.185082\pi$
$523$	−3.55728	+	15.5855i	−0.155549	+	0.681505i	−0.991214	+	0.132266i	$0.957775\pi$
$524$	−17.4110	+	8.38468i	−0.760602	+	0.366287i
$525$	−27.2448	−	27.7678i	−1.18906	−	1.21189i
$526$	8.95438	+	4.31220i	0.390430	+	0.188021i
$527$	−5.84093	+	7.32429i	−0.254435	+	0.319051i
$528$	−4.72931	−	2.27752i	−0.205817	−	0.0991161i
$529$	4.93488	−	21.6211i	0.214560	−	0.940049i
$530$	−8.84778	+	4.26087i	−0.384323	+	0.185080i
$531$	0.293639	+	1.28652i	0.0127429	+	0.0558301i
$532$	−4.53744	−	4.62455i	−0.196723	−	0.200500i
$533$	−4.32745	+	18.9598i	−0.187443	+	0.821240i
$534$	4.42910	+	19.4052i	0.191666	+	0.839743i
$535$	−7.67848	−	9.62851i	−0.331970	−	0.416277i
$536$	0.907725	+	3.97700i	0.0392077	+	0.171780i
$537$	−4.58417	−	2.20762i	−0.197821	−	0.0952657i
$538$	−20.4409			−0.881271
$539$	7.17260	+	1.78123i	0.308946	+	0.0767231i
$540$	−5.18416			−0.223091
$541$	−33.8972	−	16.3240i	−1.45735	−	0.701824i	−0.473499	−	0.880795i	$-0.657009\pi$
$541$	−33.8972	−	16.3240i	−1.45735	−	0.701824i	−0.983854	+	0.178970i	$0.942723\pi$
$542$	−1.31628	−	5.76701i	−0.0565392	−	0.247714i
$543$	−1.14471	−	1.43542i	−0.0491241	−	0.0615997i
$544$	−6.21126	−	27.2133i	−0.266306	−	1.16676i
$545$	−0.0813640	+	0.356479i	−0.00348525	+	0.0152699i
$546$	11.9936	−	18.6908i	0.513277	−	0.799892i
$547$	−8.76534	−	38.4034i	−0.374779	−	1.64201i	−0.713158	−	0.701003i	$-0.752736\pi$
$547$	−8.76534	−	38.4034i	−0.374779	−	1.64201i	0.338379	−	0.941010i	$-0.390121\pi$
$548$	−1.28795	+	0.620243i	−0.0550184	+	0.0264955i
$549$	−2.54274	+	11.1405i	−0.108521	+	0.475463i
$550$	24.8936	+	11.9881i	1.06147	+	0.511175i
$551$	3.76553	−	4.72183i	0.160417	−	0.201157i
$552$	−1.21040	−	0.582898i	−0.0515180	−	0.0248098i
$553$	−21.6249	+	2.22855i	−0.919583	+	0.0947675i
$554$	4.14504	−	1.99615i	0.176106	−	0.0848081i
$555$	0.451533	−	1.97830i	0.0191665	−	0.0839740i
$556$	−8.31098	+	10.4216i	−0.352464	+	0.441976i
$557$	−2.56930			−0.108865			−0.0544323	−	0.998517i	$-0.517335\pi$
$557$	−2.56930			−0.108865			−0.0544323	+	0.998517i	$0.517335\pi$
$558$	3.51667			0.148872
$559$	−22.1778	+	27.8101i	−0.938022	+	1.17624i
$560$	−58.0818	+	5.98561i	−2.45440	+	0.252938i
$561$	3.12112	+	3.91376i	0.131774	+	0.165239i
$562$	−14.6339	−	18.3504i	−0.617296	−	0.774065i
$563$	10.2219	−	4.92262i	0.430802	−	0.207464i	−0.205900	−	0.978573i	$-0.566012\pi$
$563$	10.2219	−	4.92262i	0.430802	−	0.207464i	0.636703	+	0.771109i	$0.280298\pi$
$564$	−8.56370	+	4.12406i	−0.360597	+	0.173654i
$565$	−39.0530	−	48.9709i	−1.64297	−	2.06022i
$566$	6.32789	+	7.93493i	0.265981	+	0.333530i
$567$	−1.42886	+	2.22674i	−0.0600064	+	0.0935142i
$568$	4.27979	−	5.36668i	0.179576	−	0.225181i
$569$	−42.9685			−1.80133			−0.900666	−	0.434512i	$-0.856921\pi$
$569$	−42.9685			−1.80133			−0.900666	+	0.434512i	$0.856921\pi$
$570$	−16.5651			−0.693837
$571$	5.03117	−	6.30888i	0.210548	−	0.264019i	−0.665332	−	0.746547i	$-0.731710\pi$
$571$	5.03117	−	6.30888i	0.210548	−	0.264019i	0.875880	+	0.482529i	$0.160282\pi$
$572$	−1.29397	+	5.66926i	−0.0541037	+	0.237044i
$573$	−11.9822	+	5.77032i	−0.500563	+	0.241058i
$574$	−2.35758	+	19.2752i	−0.0984035	+	0.804532i
$575$	12.0168	+	5.78697i	0.501134	+	0.241333i
$576$	−0.333322	+	0.417973i	−0.0138884	+	0.0174155i
$577$	−9.01622	−	4.34198i	−0.375350	−	0.180759i	0.236691	−	0.971585i	$-0.423937\pi$
$577$	−9.01622	−	4.34198i	−0.375350	−	0.180759i	−0.612041	+	0.790826i	$0.709651\pi$
$578$	−2.17076	+	9.51073i	−0.0902918	+	0.395594i
$579$	13.5651	−	6.53261i	0.563747	−	0.271486i
$580$	3.32283	+	14.5583i	0.137973	+	0.604500i
$581$	−34.2856	+	21.0911i	−1.42241	+	0.875006i
$582$	−2.26790	+	9.93632i	−0.0940074	+	0.411874i
$583$	−0.292020	−	1.27942i	−0.0120942	−	0.0529883i
$584$	5.10062	+	6.39598i	0.211065	+	0.264667i
$585$	−4.65816	−	20.4087i	−0.192591	−	0.843797i
$586$	−1.87367	−	0.902312i	−0.0774006	−	0.0372742i
$587$	13.7235			0.566428			0.283214	−	0.959057i	$-0.408599\pi$
$587$	13.7235			0.566428			0.283214	+	0.959057i	$0.408599\pi$
$588$	3.68655	−	7.29695i	0.152031	−	0.300921i
$589$	4.14270			0.170697
$590$	−9.39311	−	4.52349i	−0.386708	−	0.186229i
$591$	−2.51263	−	11.0086i	−0.103356	−	0.452832i
$592$	−1.41707	−	1.77695i	−0.0582413	−	0.0730322i
$593$	0.0918112	+	0.402251i	0.00377023	+	0.0165185i	0.976778	−	0.214254i	$-0.0687319\pi$
$593$	0.0918112	+	0.402251i	0.00377023	+	0.0165185i	−0.973008	+	0.230772i	$0.925875\pi$
$594$	0.418149	−	1.83203i	0.0171568	−	0.0751690i
$595$	52.3816	+	18.8900i	2.14743	+	0.774413i
$596$	0.771487	+	3.38011i	0.0316014	+	0.138455i
$597$	21.6242	−	10.4136i	0.885018	−	0.426202i
$598$	−1.69430	+	7.42320i	−0.0692850	+	0.303557i
$599$	−30.2099	−	14.5483i	−1.23435	−	0.594429i	−0.301074	−	0.953601i	$-0.597345\pi$
$599$	−30.2099	−	14.5483i	−1.23435	−	0.594429i	−0.933272	+	0.359172i	$0.883059\pi$
$600$	−13.5771	+	17.0251i	−0.554282	+	0.695047i
$601$	36.7318	+	17.6891i	1.49832	+	0.721553i	0.990190	−	0.139726i	$-0.0446223\pi$
$601$	36.7318	+	17.6891i	1.49832	+	0.721553i	0.508131	+	0.861280i	$0.330337\pi$
$602$	−19.1819	+	29.8932i	−0.781798	+	1.21836i
$603$	−2.48161	+	1.19508i	−0.101059	+	0.0486675i
$604$	−4.37385	+	19.1631i	−0.177969	+	0.779735i
$605$	27.3584	−	34.3064i	1.11228	−	1.39475i
$606$	5.10361			0.207320
$607$	−10.2488			−0.415986			−0.207993	−	0.978130i	$-0.566693\pi$
$607$	−10.2488			−0.415986			−0.207993	+	0.978130i	$0.566693\pi$
$608$	−7.69607	+	9.65056i	−0.312117	+	0.391382i
$609$	7.16902	+	2.58531i	0.290503	+	0.104762i
$610$	−56.2881	−	70.5831i	−2.27904	−	2.85782i
$611$	−23.9302	−	30.0075i	−0.968112	−	1.21397i
$612$	4.98913	−	2.40264i	0.201674	−	0.0971209i
$613$	38.6038	−	18.5906i	1.55919	−	0.750867i	0.562099	−	0.827070i	$-0.309994\pi$
$613$	38.6038	−	18.5906i	1.55919	−	0.750867i	0.997092	+	0.0762034i	$0.0242798\pi$
$614$	16.8232	+	21.0956i	0.678928	+	0.851348i
$615$	11.4127	+	14.3111i	0.460205	+	0.577078i
$616$	0.502255	−	4.10636i	0.0202364	−	0.165450i
$617$	−22.1784	+	27.8109i	−0.892870	+	1.11962i	0.0993410	+	0.995053i	$0.468327\pi$
$617$	−22.1784	+	27.8109i	−0.892870	+	1.11962i	−0.992211	+	0.124570i	$0.960245\pi$
$618$	24.8894			1.00120
$619$	43.8561			1.76272			0.881362	−	0.472442i	$-0.156627\pi$
$619$	43.8561			1.76272			0.881362	+	0.472442i	$0.156627\pi$
$620$	−6.38636	+	8.00824i	−0.256482	+	0.321619i
$621$	0.201851	−	0.884367i	0.00810000	−	0.0354884i
$622$	−0.860279	+	0.414289i	−0.0344941	+	0.0166115i
$623$	−25.2009	+	15.5026i	−1.00965	+	0.621098i
$624$	−21.1250	−	10.1733i	−0.845677	−	0.407257i
$625$	73.3680	−	92.0006i	2.93472	−	3.68002i
$626$	−47.6543	−	22.9491i	−1.90465	−	0.917230i
$627$	0.492586	−	2.15816i	0.0196720	−	0.0861887i
$628$	2.37849	−	1.14542i	0.0949122	−	0.0457073i
$629$	0.482310	+	2.11314i	0.0192309	+	0.0842563i
$630$	−6.71589	−	19.7946i	−0.267568	−	0.788636i
$631$	1.01075	−	4.42840i	0.0402375	−	0.176292i	−0.950816	−	0.309756i	$-0.899753\pi$
$631$	1.01075	−	4.42840i	0.0402375	−	0.176292i	0.991054	+	0.133464i	$0.0426099\pi$
$632$	2.70787	+	11.8640i	0.107713	+	0.471923i
$633$	9.09715	+	11.4075i	0.361579	+	0.453406i
$634$	11.1203	+	48.7210i	0.441642	+	1.93496i
$635$	−4.48700	−	2.16083i	−0.178061	−	0.0857498i
$636$	−1.45170			−0.0575635
$637$	32.0388	+	7.95645i	1.26942	+	0.315246i
$638$	−5.41276			−0.214293
$639$	4.17584	+	2.01098i	0.165194	+	0.0795531i
$640$	10.6900	+	46.8358i	0.422558	+	1.85135i
$641$	23.7547	+	29.7874i	0.938253	+	1.17653i	0.984106	+	0.177584i	$0.0568281\pi$
$641$	23.7547	+	29.7874i	0.938253	+	1.17653i	−0.0458528	+	0.998948i	$0.514601\pi$
$642$	−1.09883	−	4.81431i	−0.0433675	−	0.190006i
$643$	4.49401	−	19.6896i	0.177227	−	0.776480i	−0.805676	−	0.592356i	$-0.798198\pi$
$643$	4.49401	−	19.6896i	0.177227	−	0.776480i	0.982903	−	0.184124i	$-0.0589449\pi$
$644$	−0.340298	+	2.78223i	−0.0134096	+	0.109635i
$645$	7.45004	+	32.6408i	0.293345	+	1.28523i
$646$	15.9419	−	7.67723i	0.627227	−	0.302057i
$647$	5.86678	−	25.7041i	0.230647	−	1.01053i	−0.718458	−	0.695571i	$-0.755152\pi$
$647$	5.86678	−	25.7041i	0.230647	−	1.01053i	0.949105	−	0.314960i	$-0.101991\pi$
$648$	1.33435	+	0.642587i	0.0524181	+	0.0252432i
$649$	0.868652	−	1.08926i	0.0340976	−	0.0427570i
$650$	111.195	+	53.5489i	4.36144	+	2.10036i
$651$	1.67955	+	4.95035i	0.0658266	+	0.194019i
$652$	9.17816	−	4.41997i	0.359445	−	0.173099i
$653$	−1.23294	+	5.40187i	−0.0482487	+	0.211391i	−0.993306	−	0.115514i	$-0.963149\pi$
$653$	−1.23294	+	5.40187i	−0.0482487	+	0.211391i	0.945057	+	0.326905i	$0.106006\pi$
$654$	−0.0914126	+	0.114628i	−0.00357452	+	0.00448230i
$655$	−73.4474			−2.86983
$656$	20.5023			0.800481
$657$	−3.44401	+	4.31865i	−0.134364	+	0.168487i
$658$	−26.8408	−	27.3561i	−1.04636	−	1.06645i
$659$	−23.3548	−	29.2860i	−0.909773	−	1.14082i	−0.989576	−	0.144009i	$-0.954001\pi$
$659$	−23.3548	−	29.2860i	−0.909773	−	1.14082i	0.0798035	−	0.996811i	$-0.474571\pi$
$660$	3.41257	+	4.27923i	0.132834	+	0.166569i
$661$	−9.44590	+	4.54891i	−0.367403	+	0.176932i	−0.608471	−	0.793576i	$-0.708217\pi$
$661$	−9.44590	+	4.54891i	−0.367403	+	0.176932i	0.241068	+	0.970508i	$0.422502\pi$
$662$	9.97753	−	4.80493i	0.387788	−	0.186749i
$663$	13.9415	+	17.4821i	0.541443	+	0.678948i
$664$	14.0489	+	17.6167i	0.545202	+	0.683662i
$665$	−7.91144	−	23.3184i	−0.306792	−	0.904249i
$666$	0.507298	−	0.636132i	0.0196574	−	0.0246496i
$667$	−2.61288			−0.101171
$668$	17.6767			0.683933
$669$	0.163765	−	0.205355i	0.00633151	−	0.00793947i
$670$	4.84230	−	21.2155i	0.187075	−	0.819627i
$671$	10.8696	−	5.23453i	0.419617	−	0.202077i
$672$	−14.6522	−	5.28390i	−0.565220	−	0.203831i
$673$	21.4344	+	10.3222i	0.826234	+	0.397893i	0.798701	−	0.601728i	$-0.205521\pi$
$673$	21.4344	+	10.3222i	0.826234	+	0.397893i	0.0275325	+	0.999621i	$0.491235\pi$
$674$	−14.8947	+	18.6774i	−0.573724	+	0.719427i
$675$	−13.2473	−	6.37957i	−0.509889	−	0.245550i
$676$	−2.40147	+	10.5215i	−0.0923640	+	0.404673i
$677$	15.6971	−	7.55932i	0.603289	−	0.290528i	−0.107200	−	0.994238i	$-0.534188\pi$
$677$	15.6971	−	7.55932i	0.603289	−	0.290528i	0.710488	+	0.703709i	$0.248474\pi$
$678$	−5.58870	−	24.4857i	−0.214633	−	0.940368i
$679$	−15.0703	+	1.55307i	−0.578345	+	0.0596013i
$680$	6.93598	−	30.3885i	0.265983	−	1.16535i
$681$	1.43290	+	6.27795i	0.0549089	+	0.240572i
$682$	−2.31491	−	2.90281i	−0.0886426	−	0.111154i
$683$	6.07595	+	26.6205i	0.232490	+	1.01860i	0.947567	+	0.319559i	$0.103535\pi$
$683$	6.07595	+	26.6205i	0.232490	+	1.01860i	−0.715077	+	0.699046i	$0.753608\pi$
$684$	−2.20625	−	1.06248i	−0.0843582	−	0.0406248i
$685$	−5.43315			−0.207590
$686$	32.6376	+	4.62338i	1.24611	+	0.176522i
$687$	10.6875			0.407755
$688$	33.7863	+	16.2706i	1.28809	+	0.620312i
$689$	−1.30440	−	5.71496i	−0.0496938	−	0.217723i
$690$	4.46834	+	5.60312i	0.170107	+	0.213307i
$691$	−0.113414	−	0.496899i	−0.00431447	−	0.0189029i	0.972725	−	0.231962i	$-0.0745145\pi$
$691$	−0.113414	−	0.496899i	−0.00431447	−	0.0189029i	−0.977039	+	0.213059i	$0.931657\pi$
$692$	−5.53728	+	24.2604i	−0.210496	+	0.922242i
$693$	2.77862	−	0.286350i	0.105551	−	0.0108775i
$694$	5.90973	+	25.8922i	0.224330	+	0.982854i
$695$	−45.6453	+	21.9816i	−1.73142	+	0.833810i
$696$	0.949268	−	4.15901i	0.0359819	−	0.157647i
$697$	−17.6159	−	8.48338i	−0.667251	−	0.321331i
$698$	27.4253	−	34.3902i	1.03806	−	1.30169i
$699$	−11.3616	−	5.47148i	−0.429737	−	0.206950i
$700$	42.7392	+	15.4127i	1.61539	+	0.582546i
$701$	18.7213	−	9.01569i	0.707093	−	0.340518i	−0.0455362	−	0.998963i	$-0.514500\pi$
$701$	18.7213	−	9.01569i	0.707093	−	0.340518i	0.752629	+	0.658445i	$0.228785\pi$
$702$	1.86780	−	8.18335i	0.0704955	−	0.308861i
$703$	0.597606	−	0.749375i	0.0225392	−	0.0282632i
$704$	0.564428			0.0212727
$705$	−36.1256			−1.36057
$706$	−3.69745	+	4.63646i	−0.139155	+	0.174495i
$707$	2.43746	+	7.18425i	0.0916702	+	0.270191i
$708$	−0.960904	−	1.20494i	−0.0361130	−	0.0452843i
$709$	−16.4628	−	20.6437i	−0.618274	−	0.775291i	0.369826	−	0.929101i	$-0.379417\pi$
$709$	−16.4628	−	20.6437i	−0.618274	−	0.775291i	−0.988100	+	0.153810i	$0.950846\pi$
$710$	−32.9914	+	15.8878i	−1.23814	+	0.596259i
$711$	−7.40301	+	3.56510i	−0.277634	+	0.133702i
$712$	10.3263	+	12.9488i	0.386996	+	0.485278i
$713$	−1.11747	−	1.40126i	−0.0418495	−	0.0524776i
$714$	15.6372	+	15.9374i	0.585207	+	0.596442i
$715$	−13.7799	+	17.2795i	−0.515339	+	0.646215i
$716$	5.94235			0.222076
$717$	−25.1437			−0.939008
$718$	10.3950	−	13.0349i	0.387939	−	0.486460i
$719$	−8.87998	+	38.9057i	−0.331167	+	1.45094i	0.485706	+	0.874122i	$0.338562\pi$
$719$	−8.87998	+	38.9057i	−0.331167	+	1.45094i	−0.816874	+	0.576817i	$0.804295\pi$
$720$	−19.8836	+	9.57543i	−0.741018	+	0.356855i
$721$	11.8871	+	35.0363i	0.442698	+	1.30482i
$722$	23.4187	+	11.2778i	0.871553	+	0.419718i
$723$	−10.0426	+	12.5930i	−0.373488	+	0.468339i
$724$	1.93189	+	0.930350i	0.0717982	+	0.0345762i
$725$	−9.42428	+	41.2905i	−0.350009	+	1.53349i
$726$	15.8521	−	7.63397i	0.588327	−	0.283323i
$727$	−7.61269	−	33.3534i	−0.282339	−	1.23701i	−0.894786	−	0.446496i	$-0.852672\pi$
$727$	−7.61269	−	33.3534i	−0.282339	−	1.23701i	0.612447	−	0.790512i	$-0.290185\pi$
$728$	2.24349	−	18.3424i	0.0831492	−	0.679814i
$729$	−0.222521	+	0.974928i	−0.00824152	+	0.0361084i
$730$	−9.71097	−	42.5465i	−0.359419	−	1.57472i
$731$	−22.2974	−	27.9600i	−0.824698	−	1.03414i
$732$	−2.96968	−	13.0110i	−0.109762	−	0.480900i
$733$	6.93137	+	3.33797i	0.256016	+	0.123291i	0.557490	−	0.830183i	$-0.311764\pi$
$733$	6.93137	+	3.33797i	0.256016	+	0.123291i	−0.301474	+	0.953474i	$0.597479\pi$
$734$	−54.9209			−2.02717
$735$	24.6570	−	18.9077i	0.909487	−	0.697419i
$736$	5.34025			0.196844
$737$	2.62004	+	1.26174i	0.0965104	+	0.0464770i
$738$	1.63322	+	7.15562i	0.0601198	+	0.263402i
$739$	−12.8130	−	16.0670i	−0.471334	−	0.591034i	0.488163	−	0.872752i	$-0.337667\pi$
$739$	−12.8130	−	16.0670i	−0.471334	−	0.591034i	−0.959497	+	0.281718i	$0.909096\pi$
$740$	0.527348	+	2.31046i	0.0193857	+	0.0849343i
$741$	2.20030	−	9.64014i	0.0808300	−	0.354139i
$742$	−1.88062	−	5.54299i	−0.0690397	−	0.203490i
$743$	0.406060	+	1.77907i	0.0148969	+	0.0652676i	0.981830	−	0.189762i	$-0.0607718\pi$
$743$	0.406060	+	1.77907i	0.0148969	+	0.0652676i	−0.966933	+	0.255030i	$0.917915\pi$
$744$	2.63642	−	1.26963i	0.0966557	−	0.0465469i
$745$	−2.93219	+	12.8468i	−0.107427	+	0.470669i
$746$	−22.5620	−	10.8653i	−0.826053	−	0.397806i
$747$	−9.48600	+	11.8951i	−0.347075	+	0.435218i
$748$	−5.26743	−	2.53666i	−0.192596	−	0.0927494i
$749$	6.25221	−	3.84610i	0.228451	−	0.140533i
$750$	69.0702	−	33.2625i	2.52209	−	1.21457i
$751$	−5.31651	+	23.2932i	−0.194002	+	0.849980i	0.780420	+	0.625256i	$0.215005\pi$
$751$	−5.31651	+	23.2932i	−0.194002	+	0.849980i	−0.974422	+	0.224724i	$0.927852\pi$
$752$	−25.2283	+	31.6353i	−0.919981	+	1.15362i
$753$	12.1809			0.443896
$754$	−24.1779			−0.880506
$755$	−46.5785	+	58.4076i	−1.69516	+	2.12567i
$756$	0.375146	−	3.06713i	0.0136439	−	0.111550i
$757$	−8.52170	−	10.6859i	−0.309727	−	0.388385i	0.602467	−	0.798143i	$-0.294184\pi$
$757$	−8.52170	−	10.6859i	−0.309727	−	0.388385i	−0.912194	+	0.409759i	$0.865613\pi$
$758$	34.9846	+	43.8693i	1.27070	+	1.59340i
$759$	−0.862866	+	0.415535i	−0.0313201	+	0.0150829i
$760$	−12.4187	+	5.98055i	−0.450475	+	0.216937i
$761$	19.7430	+	24.7569i	0.715682	+	0.897437i	0.998085	−	0.0618589i	$-0.0197029\pi$
$761$	19.7430	+	24.7569i	0.715682	+	0.897437i	−0.282403	+	0.959296i	$0.591131\pi$
$762$	−1.24506	−	1.56126i	−0.0451039	−	0.0565584i
$763$	−0.205018	−	0.0739340i	−0.00742214	−	0.00267659i
$764$	9.68419	−	12.1436i	0.350362	−	0.439340i
$765$	21.0464			0.760934
$766$	1.56719			0.0566249
$767$	3.88012	−	4.86552i	0.140103	−	0.175684i
$768$	−4.52431	+	19.8223i	−0.163257	+	0.715276i
$769$	25.4821	−	12.2715i	0.918908	−	0.442523i	0.0862270	−	0.996276i	$-0.472519\pi$
$769$	25.4821	−	12.2715i	0.918908	−	0.442523i	0.832681	+	0.553753i	$0.186805\pi$
$770$	−11.9185	+	18.5737i	−0.429511	+	0.669351i
$771$	14.8705	+	7.16128i	0.535550	+	0.257907i
$772$	−10.9635	+	13.7478i	−0.394586	+	0.494795i
$773$	−35.5234	−	17.1071i	−1.27769	−	0.615301i	−0.332892	−	0.942965i	$-0.608024\pi$
$773$	−35.5234	−	17.1071i	−1.27769	−	0.615301i	−0.944794	+	0.327664i	$0.893739\pi$
$774$	−2.98727	+	13.0881i	−0.107375	+	0.470441i
$775$	−26.1742	+	12.6048i	−0.940204	+	0.452779i
$776$	1.88711	+	8.26795i	0.0677432	+	0.296802i
$777$	1.13775	+	0.410300i	0.0408167	+	0.0147194i
$778$	−11.5691	+	50.6876i	−0.414773	+	1.81724i
$779$	1.92397	+	8.42944i	0.0689332	+	0.302016i
$780$	15.2434	+	19.1146i	0.545800	+	0.684411i
$781$	−1.08888	−	4.77068i	−0.0389631	−	0.170708i
$782$	−6.89705	−	3.32144i	−0.246638	−	0.118775i
$783$	2.88044			0.102939
$784$	0.661721	−	34.7964i	0.0236329	−	1.24273i
$785$	10.0336			0.358113
$786$	−26.5339	−	12.7781i	−0.946434	−	0.455778i
$787$	−10.3457	−	45.3276i	−0.368785	−	1.61575i	−0.730121	−	0.683317i	$-0.760537\pi$
$787$	−10.3457	−	45.3276i	−0.368785	−	1.61575i	0.361336	−	0.932436i	$-0.382321\pi$
$788$	8.22233	+	10.3105i	0.292908	+	0.367296i
$789$	1.24254	+	5.44393i	0.0442356	+	0.193809i
$790$	14.4453	−	63.2889i	0.513940	−	2.25172i
$791$	31.7989	−	19.5614i	1.13064	−	0.695523i
$792$	−0.347939	−	1.52442i	−0.0123635	−	0.0541679i
$793$	48.5527	−	23.3817i	1.72416	−	0.830310i
$794$	4.42597	−	19.3914i	0.157072	−	0.688176i
$795$	−4.97105	−	2.39393i	−0.176305	−	0.0849040i
$796$	−17.4770	+	21.9154i	−0.619455	+	0.776772i
$797$	−14.1608	−	6.81948i	−0.501601	−	0.241558i	0.165934	−	0.986137i	$-0.446936\pi$
$797$	−14.1608	−	6.81948i	−0.501601	−	0.241558i	−0.667535	+	0.744578i	$0.732651\pi$
$798$	1.19872	−	9.80051i	0.0424341	−	0.346934i
$799$	34.7665	−	16.7427i	1.22995	−	0.592313i
$800$	19.2615	−	84.3902i	0.680997	−	2.98364i
$801$	−6.97249	+	8.74323i	−0.246361	+	0.308927i
$802$	−56.7250			−2.00303
$803$	5.83188			0.205803
$804$	2.00568	−	2.51504i	0.0707348	−	0.0886987i
$805$	−5.75334	+	8.96602i	−0.202779	+	0.316011i
$806$	−10.3403	−	12.9663i	−0.364222	−	0.456720i
$807$	−7.16051	−	8.97899i	−0.252062	−	0.316075i
$808$	3.82613	−	1.84257i	0.134603	−	0.0648213i
$809$	24.0544	−	11.5840i	0.845709	−	0.407272i	0.0397260	−	0.999211i	$-0.487351\pi$
$809$	24.0544	−	11.5840i	0.845709	−	0.407272i	0.805983	+	0.591939i	$0.201637\pi$
$810$	−4.92591	−	6.17689i	−0.173079	−	0.217034i
$811$	23.4997	+	29.4676i	0.825184	+	1.03475i	0.998753	+	0.0499268i	$0.0158988\pi$
$811$	23.4997	+	29.4676i	0.825184	+	1.03475i	−0.173568	+	0.984822i	$0.555530\pi$
$812$	−8.85364	+	0.912411i	−0.310702	+	0.0320194i
$813$	2.07215	−	2.59840i	0.0726735	−	0.0911297i
$814$	−0.859029			−0.0301089
$815$	38.7176			1.35622
$816$	14.6978	−	18.4304i	0.514524	−	0.645193i
$817$	−3.51905	+	15.4180i	−0.123116	+	0.539407i
$818$	52.0317	−	25.0571i	1.81924	−	0.876102i
$819$	12.4116	−	1.27908i	0.433696	−	0.0446945i
$820$	−19.2609	−	9.27556i	−0.672620	−	0.323917i
$821$	15.1994	−	19.0595i	0.530463	−	0.665180i	−0.442331	−	0.896852i	$-0.645848\pi$
$821$	15.1994	−	19.0595i	0.530463	−	0.665180i	0.972794	+	0.231672i	$0.0744197\pi$
$822$	−1.96280	−	0.945236i	−0.0684606	−	0.0329689i
$823$	−1.45249	+	6.36376i	−0.0506305	+	0.221827i	−0.993914	−	0.110163i	$-0.964863\pi$
$823$	−1.45249	+	6.36376i	−0.0506305	+	0.221827i	0.943283	+	0.331990i	$0.107720\pi$
$824$	18.6594	−	8.98588i	0.650030	−	0.313038i
$825$	3.45432	+	15.1344i	0.120264	+	0.526911i
$826$	3.35597	−	5.22996i	0.116769	−	0.181974i
$827$	−8.30420	+	36.3831i	−0.288765	+	1.26516i	0.597456	+	0.801901i	$0.296178\pi$
$827$	−8.30420	+	36.3831i	−0.288765	+	1.26516i	−0.886222	+	0.463262i	$0.846679\pi$
$828$	0.235743	+	1.03286i	0.00819263	+	0.0358943i
$829$	9.20208	+	11.5390i	0.319602	+	0.400768i	0.915517	−	0.402280i	$-0.131782\pi$
$829$	9.20208	+	11.5390i	0.319602	+	0.400768i	−0.595915	+	0.803047i	$0.703211\pi$
$830$	−26.7474	−	117.188i	−0.928415	−	4.06765i
$831$	2.32886	+	1.12152i	0.0807871	+	0.0389050i
$832$	2.52120			0.0874070
$833$	−14.9665	+	29.6238i	−0.518558	+	1.02640i
$834$	−20.3143			−0.703426
$835$	60.5306	+	29.1500i	2.09475	+	1.00878i
$836$	0.575294	+	2.52053i	0.0198970	+	0.0871743i
$837$	1.23190	+	1.54475i	0.0425806	+	0.0533944i
$838$	−3.84423	−	16.8427i	−0.132797	−	0.581820i
$839$	9.18022	−	40.2212i	0.316936	−	1.38859i	−0.525958	−	0.850510i	$-0.676293\pi$
$839$	9.18022	−	40.2212i	0.316936	−	1.38859i	0.842895	−	0.538079i	$-0.180850\pi$
$840$	−12.1813	−	12.4152i	−0.420296	−	0.428365i
$841$	4.60686	+	20.1840i	0.158857	+	0.695999i
$842$	−32.3614	+	15.5844i	−1.11525	+	0.537074i
$843$	2.93438	−	12.8564i	0.101066	−	0.442797i
$844$	−15.3530	−	7.39362i	−0.528472	−	0.254499i
$845$	−25.5739	+	32.0687i	−0.879771	+	1.10320i
$846$	−13.0509	−	6.28498i	−0.448699	−	0.216082i
$847$	18.3171	+	18.6687i	0.629383	+	0.641466i
$848$	−5.56791	+	2.68136i	−0.191203	+	0.0920784i
$849$	−1.26886	+	5.55925i	−0.0435472	+	0.190793i
$850$	−77.3643	+	97.0118i	−2.65357	+	3.32748i
$851$	−0.414675			−0.0142149
$852$	−5.41304			−0.185448
$853$	24.9444	−	31.2793i	0.854082	−	1.07098i	−0.142616	−	0.989778i	$-0.545551\pi$
$853$	24.9444	−	31.2793i	0.854082	−	1.07098i	0.996697	−	0.0812063i	$-0.0258773\pi$
$854$	45.8326	−	28.1944i	1.56836	−	0.964791i
$855$	−5.80281	−	7.27649i	−0.198452	−	0.248851i
$856$	−2.56191	−	3.21253i	−0.0875642	−	0.109802i
$857$	−45.1751	+	21.7552i	−1.54315	+	0.743143i	−0.995607	−	0.0936335i	$-0.970152\pi$
$857$	−45.1751	+	21.7552i	−1.54315	+	0.743143i	−0.547545	+	0.836776i	$0.684438\pi$
$858$	−7.98440	+	3.84508i	−0.272583	+	0.131269i
$859$	−22.6519	−	28.4046i	−0.772874	−	0.969154i	0.227115	−	0.973868i	$-0.427071\pi$
$859$	−22.6519	−	28.4046i	−0.772874	−	0.969154i	−0.999989	+	0.00471448i	$0.998499\pi$
$860$	−24.3795	−	30.5709i	−0.831334	−	1.04246i
$861$	−9.29280	+	5.71655i	−0.316698	+	0.194819i
$862$	10.9999	−	13.7934i	0.374657	−	0.469806i
$863$	31.1095			1.05898			0.529489	−	0.848317i	$-0.322384\pi$
$863$	31.1095			1.05898			0.529489	+	0.848317i	$0.322384\pi$
$864$	−5.88710			−0.200283
$865$	−58.9682	+	73.9437i	−2.00498	+	2.51416i
$866$	−7.91803	+	34.6911i	−0.269065	+	1.17885i
$867$	−4.93816	+	2.37809i	−0.167709	+	0.0807642i
$868$	−4.27581	−	4.35790i	−0.145131	−	0.147917i
$869$	7.81595	+	3.76396i	0.265138	+	0.127684i
$870$	−14.1888	+	17.7922i	−0.481045	+	0.603211i
$871$	11.7033	+	5.63599i	0.396550	+	0.190968i
$872$	−0.0271469	+	0.118938i	−0.000919310	+	0.00402776i
$873$	−5.15913	+	2.48451i	−0.174610	+	0.0840878i
$874$	0.753278	+	3.30032i	0.0254800	+	0.111635i
$875$	79.8106	+	81.3428i	2.69809	+	2.74989i
$876$	1.43553	−	6.28949i	0.0485022	−	0.212502i
$877$	−3.38184	−	14.8168i	−0.114197	−	0.500329i	−0.999384	−	0.0350938i	$-0.988827\pi$
$877$	−3.38184	−	14.8168i	−0.114197	−	0.500329i	0.885187	−	0.465235i	$-0.154030\pi$
$878$	37.0513	+	46.4608i	1.25042	+	1.56798i
$879$	−0.259997	−	1.13912i	−0.00876948	−	0.0384216i
$880$	20.9927	+	10.1096i	0.707664	+	0.340793i
$881$	−31.5540			−1.06308			−0.531540	−	0.847033i	$-0.678387\pi$
$881$	−31.5540			−1.06308			−0.531540	+	0.847033i	$0.678387\pi$
$882$	12.1972	−	2.54094i	0.410700	−	0.0855580i
$883$	−39.3376			−1.32382			−0.661908	−	0.749585i	$-0.730253\pi$
$883$	−39.3376			−1.32382			−0.661908	+	0.749585i	$0.730253\pi$
$884$	−23.5287	−	11.3308i	−0.791355	−	0.381096i
$885$	−1.30342	−	5.71066i	−0.0438140	−	0.191962i
$886$	24.4286	+	30.6325i	0.820696	+	1.02912i
$887$	0.242856	+	1.06402i	0.00815429	+	0.0357263i	0.978841	−	0.204620i	$-0.0655960\pi$
$887$	0.242856	+	1.06402i	0.00815429	+	0.0357263i	−0.970687	+	0.240347i	$0.922739\pi$
$888$	0.150653	−	0.660054i	0.00505558	−	0.0221499i
$889$	1.60312	−	2.49830i	0.0537668	−	0.0837903i
$890$	−19.6601	−	86.1366i	−0.659009	−	2.88731i
$891$	0.951225	−	0.458086i	0.0318673	−	0.0153465i
$892$	−0.0682606	+	0.299069i	−0.00228553	+	0.0100136i
$893$	−15.3742	−	7.40381i	−0.514477	−	0.247759i
$894$	−3.29432	+	4.13095i	−0.110179	+	0.138160i
$895$	20.3484	+	9.79929i	0.680173	+	0.327554i
$896$	−28.4833	+	2.93534i	−0.951559	+	0.0980628i
$897$	−3.85427	+	1.85612i	−0.128690	+	0.0619741i
$898$	−3.00575	+	13.1690i	−0.100303	+	0.439457i
$899$	3.54841	−	4.44957i	0.118346	−	0.148401i
$900$	17.1722			0.572406
$901$	5.89352			0.196342
$902$	4.83145	−	6.05845i	0.160870	−	0.201724i
$903$	−19.8505	+	2.04569i	−0.660584	+	0.0680765i
$904$	−13.0299	−	16.3390i	−0.433369	−	0.543427i
$905$	5.08119	+	6.37161i	0.168904	+	0.211799i
$906$	−26.9886	+	12.9970i	−0.896638	+	0.431798i
$907$	−4.83211	+	2.32702i	−0.160448	+	0.0772675i	−0.512384	−	0.858756i	$-0.671238\pi$
$907$	−4.83211	+	2.32702i	−0.160448	+	0.0772675i	0.351937	+	0.936024i	$0.385523\pi$
$908$	−4.68902	−	5.87985i	−0.155611	−	0.195130i
$909$	1.78781	+	2.24184i	0.0592978	+	0.0743571i
$910$	−53.2377	+	82.9657i	−1.76481	+	2.75029i
$911$	−2.87417	+	3.60410i	−0.0952256	+	0.119409i	−0.827161	−	0.561965i	$-0.810046\pi$
$911$	−2.87417	+	3.60410i	−0.0952256	+	0.119409i	0.731936	+	0.681374i	$0.238617\pi$
$912$	−10.4244			−0.345187
$913$	16.0630			0.531609
$914$	30.1903	−	37.8575i	0.998607	−	1.25221i
$915$	11.2868	−	49.4508i	0.373131	−	1.63479i
$916$	−11.2459	+	5.41575i	−0.371576	+	0.178941i
$917$	5.31493	−	43.4540i	0.175515	−	1.43498i
$918$	7.60332	+	3.66156i	0.250947	+	0.120850i
$919$	−10.8458	+	13.6002i	−0.357769	+	0.448629i	−0.927846	−	0.372963i	$-0.878342\pi$
$919$	−10.8458	+	13.6002i	−0.357769	+	0.448629i	0.570077	+	0.821591i	$0.306913\pi$
$920$	5.37278	+	2.58740i	0.177135	+	0.0853039i
$921$	−3.37336	+	14.7797i	−0.111156	+	0.487007i
$922$	−3.39433	+	1.63463i	−0.111786	+	0.0538335i
$923$	−4.86382	−	21.3098i	−0.160095	−	0.701420i
$924$	−2.77869	+	1.70933i	−0.0914121	+	0.0562330i
$925$	−1.49567	+	6.55297i	−0.0491774	+	0.215460i
$926$	−10.7423	−	47.0652i	−0.353014	−	1.54666i
$927$	8.71882	+	10.9331i	0.286364	+	0.359089i
$928$	3.77339	+	16.5323i	0.123868	+	0.542699i
$929$	−2.83484	−	1.36518i	−0.0930079	−	0.0447903i	0.386801	−	0.922163i	$-0.373580\pi$
$929$	−2.83484	−	1.36518i	−0.0930079	−	0.0447903i	−0.479809	+	0.877373i	$0.659294\pi$
$930$	−15.6100			−0.511871
$931$	14.3685	−	2.99328i	0.470908	−	0.0981007i
$932$	14.7278			0.482426
$933$	−0.483341	−	0.232765i	−0.0158239	−	0.00762037i
$934$	−13.8386	−	60.6307i	−0.452812	−	1.98390i
$935$	−13.8542	−	17.3726i	−0.453080	−	0.568145i
$936$	−1.55418	−	6.80932i	−0.0508001	−	0.222570i
$937$	−4.31828	+	18.9196i	−0.141072	+	0.618076i	0.854115	+	0.520084i	$0.174099\pi$
$937$	−4.31828	+	18.9196i	−0.141072	+	0.618076i	−0.995187	+	0.0979926i	$0.968758\pi$
$938$	12.2014	+	4.40011i	0.398391	+	0.143669i
$939$	−6.61267	−	28.9720i	−0.215796	−	0.945465i
$940$	38.0130	−	18.3061i	1.23985	−	0.597079i
$941$	7.00672	−	30.6985i	0.228413	−	1.00074i	−0.722522	−	0.691348i	$-0.757017\pi$
$941$	7.00672	−	30.6985i	0.228413	−	1.00074i	0.950934	−	0.309393i	$-0.100126\pi$
$942$	3.62477	+	1.74560i	0.118101	+	0.0568746i
$943$	2.33226	−	2.92457i	0.0759490	−	0.0952370i
$944$	−5.91108	−	2.84663i	−0.192389	−	0.0926499i
$945$	6.34249	−	9.88416i	0.206321	−	0.321532i
$946$	12.7699	−	6.14965i	0.415184	−	0.199942i
$947$	4.38498	−	19.2119i	0.142493	−	0.624301i	−0.852359	−	0.522957i	$-0.824829\pi$
$947$	4.38498	−	19.2119i	0.142493	−	0.624301i	0.994851	−	0.101344i	$-0.0323142\pi$
$948$	5.98322	−	7.50273i	0.194326	−	0.243677i
$949$	26.0500			0.845619
$950$	54.8709			1.78025
$951$	−17.5060	+	21.9518i	−0.567671	+	0.711837i
$952$	17.4770	+	6.30259i	0.566432	+	0.204268i
$953$	−19.4009	−	24.3279i	−0.628456	−	0.788058i	0.361051	−	0.932546i	$-0.382418\pi$
$953$	−19.4009	−	24.3279i	−0.628456	−	0.788058i	−0.989507	+	0.144488i	$0.953847\pi$
$954$	−1.37938	−	1.72969i	−0.0446590	−	0.0560006i
$955$	53.1872	−	25.6136i	1.72110	−	0.828836i
$956$	26.4573	−	12.7412i	0.855691	−	0.412079i
$957$	−1.89610	−	2.37764i	−0.0612923	−	0.0768582i
$958$	19.7521	+	24.7684i	0.638163	+	0.800231i
$959$	0.393163	−	3.21444i	0.0126959	−	0.103800i
$960$	1.47957	−	1.85532i	0.0477529	−	0.0598802i
$961$	−27.0962			−0.874070
$962$	−3.83713			−0.123714
$963$	1.72983	−	2.16914i	0.0557431	−	0.0698997i
$964$	4.18596	−	18.3399i	0.134821	−	0.590688i
$965$	−60.2135	+	28.9973i	−1.93834	+	0.933456i
$966$	−3.63835	+	2.23816i	−0.117062	+	0.0720117i
$967$	−26.4059	−	12.7164i	−0.849157	−	0.408932i	−0.0418923	−	0.999122i	$-0.513339\pi$
$967$	−26.4059	−	12.7164i	−0.849157	−	0.408932i	−0.807265	+	0.590190i	$0.799053\pi$
$968$	9.12807	−	11.4462i	0.293387	−	0.367896i
$969$	8.95684	+	4.31339i	0.287735	+	0.138566i
$970$	10.0669	−	44.1058i	0.323228	−	1.41615i
$971$	−30.2071	+	14.5470i	−0.969391	+	0.466834i	−0.850443	−	0.526067i	$-0.823666\pi$
$971$	−30.2071	+	14.5470i	−0.969391	+	0.466834i	−0.118947	+	0.992901i	$0.537952\pi$
$972$	−0.259883	−	1.13862i	−0.00833576	−	0.0365214i
$973$	−9.70202	−	28.5960i	−0.311032	−	0.916746i
$974$	0.895011	−	3.92130i	0.0286780	−	0.125647i
$975$	15.4298	+	67.6026i	0.494151	+	2.16502i
$976$	−35.4221	−	44.4179i	−1.13383	−	1.42178i
$977$	−6.25671	−	27.4124i	−0.200170	−	0.877002i	−0.970833	−	0.239758i	$-0.922932\pi$
$977$	−6.25671	−	27.4124i	−0.200170	−	0.877002i	0.770663	−	0.637243i	$-0.219925\pi$
$978$	13.9873	+	6.73593i	0.447265	+	0.215391i
$979$	11.8068			0.377347
$980$	−16.3641	+	32.3901i	−0.522731	+	1.03466i
$981$	−0.0823741			−0.00263000
$982$	2.84946	+	1.37223i	0.0909299	+	0.0437895i
$983$	8.13210	+	35.6290i	0.259374	+	1.13639i	0.921923	+	0.387372i	$0.126617\pi$
$983$	8.13210	+	35.6290i	0.259374	+	1.13639i	−0.662550	+	0.749018i	$0.730526\pi$
$984$	3.80782	+	4.77486i	0.121389	+	0.152217i
$985$	11.1532	+	48.8654i	0.355371	+	1.55698i
$986$	5.40908	−	23.6987i	0.172260	−	0.754721i
$987$	2.61418	−	21.3732i	0.0832104	−	0.680315i
$988$	2.56974	+	11.2588i	0.0817543	+	0.358189i
$989$	6.16434	−	2.96859i	0.196015	−	0.0943957i
$990$	−1.85610	+	8.13210i	−0.0589907	+	0.258455i
$991$	21.7661	+	10.4820i	0.691422	+	0.332971i	0.746383	−	0.665517i	$-0.231789\pi$
$991$	21.7661	+	10.4820i	0.691422	+	0.332971i	−0.0549604	+	0.998489i	$0.517503\pi$
$992$	−7.25231	+	9.09411i	−0.230261	+	0.288738i
$993$	5.60579	+	2.69961i	0.177894	+	0.0856695i
$994$	−7.01240	−	20.6686i	−0.222420	−	0.655567i
$995$	−95.9864	+	46.2246i	−3.04297	+	1.46542i
$996$	3.95396	−	17.3234i	0.125286	−	0.548914i
$997$	13.2055	−	16.5592i	0.418222	−	0.524434i	−0.527437	−	0.849594i	$-0.676847\pi$
$997$	13.2055	−	16.5592i	0.418222	−	0.524434i	0.945659	+	0.325160i	$0.105418\pi$
$998$	45.2411			1.43208
$999$	0.457139			0.0144632

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.2.i.b.127.2	yes	36
3.2	odd	2		441.2.u.d.127.5		36
49.13	odd	14		7203.2.a.g.1.13		18
49.22	even	7	inner	147.2.i.b.22.2	✓	36
49.36	even	7		7203.2.a.h.1.13		18
147.71	odd	14		441.2.u.d.316.5		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.i.b.22.2	✓	36	49.22	even	7	inner
147.2.i.b.127.2	yes	36	1.1	even	1	trivial
441.2.u.d.127.5		36	3.2	odd	2
441.2.u.d.316.5		36	147.71	odd	14
7203.2.a.g.1.13		18	49.13	odd	14
7203.2.a.h.1.13		18	49.36	even	7

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	147.i (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.60360 - 0.772253i) q^{2} +(-0.222521 - 0.974928i) q^{3} +(0.728177 + 0.913105i) q^{4} +(0.987738 + 4.32756i) q^{5} +(-0.396056 + 1.73524i) q^{6} +(-2.63181 + 0.271221i) q^{7} +(0.329556 + 1.44388i) q^{8} +(-0.900969 + 0.433884i) q^{9} +O(q^{10})\)	\(q+(-1.60360 - 0.772253i) q^{2} +(-0.222521 - 0.974928i) q^{3} +(0.728177 + 0.913105i) q^{4} +(0.987738 + 4.32756i) q^{5} +(-0.396056 + 1.73524i) q^{6} +(-2.63181 + 0.271221i) q^{7} +(0.329556 + 1.44388i) q^{8} +(-0.900969 + 0.433884i) q^{9} +(1.75804 - 7.70246i) q^{10} +(0.951225 + 0.458086i) q^{11} +(0.728177 - 0.913105i) q^{12} +(4.24896 + 2.04619i) q^{13} +(4.42982 + 1.59749i) q^{14} +(3.99927 - 1.92595i) q^{15} +(1.10633 - 4.84715i) q^{16} +(-2.95622 + 3.70698i) q^{17} +1.77986 q^{18} +2.09671 q^{19} +(-3.23227 + 4.05314i) q^{20} +(0.850055 + 2.50548i) q^{21} +(-1.17163 - 1.46917i) q^{22} +(-0.565574 - 0.709207i) q^{23} +(1.33435 - 0.642587i) q^{24} +(-13.2473 + 6.37957i) q^{25} +(-5.23345 - 6.56254i) q^{26} +(0.623490 + 0.781831i) q^{27} +(-2.16408 - 2.20562i) q^{28} +(1.79593 - 2.25202i) q^{29} -7.90054 q^{30} +1.97581 q^{31} +(-3.67055 + 4.60272i) q^{32} +(0.234933 - 1.02931i) q^{33} +(7.60332 - 3.66156i) q^{34} +(-3.77327 - 11.1214i) q^{35} +(-1.05225 - 0.506735i) q^{36} +(0.285021 - 0.357405i) q^{37} +(-3.36228 - 1.61919i) q^{38} +(1.04941 - 4.59775i) q^{39} +(-5.92297 + 2.85235i) q^{40} +(0.917612 + 4.02032i) q^{41} +(0.571713 - 4.67424i) q^{42} +(-1.67837 + 7.35342i) q^{43} +(0.274380 + 1.20214i) q^{44} +(-2.76758 - 3.47043i) q^{45} +(0.359267 + 1.57405i) q^{46} +(-7.33253 - 3.53116i) q^{47} -4.97181 q^{48} +(6.85288 - 1.42761i) q^{49} +26.1700 q^{50} +(4.27186 + 2.05722i) q^{51} +(1.22561 + 5.36974i) q^{52} +(-0.774992 - 0.971809i) q^{53} +(-0.396056 - 1.73524i) q^{54} +(-1.04283 + 4.56895i) q^{55} +(-1.25894 - 3.71064i) q^{56} +(-0.466561 - 2.04414i) q^{57} +(-4.61908 + 2.22443i) q^{58} +(0.293639 - 1.28652i) q^{59} +(4.67077 + 2.24932i) q^{60} +(7.12459 - 8.93395i) q^{61} +(-3.16841 - 1.52583i) q^{62} +(2.25350 - 1.38626i) q^{63} +(0.481665 - 0.231958i) q^{64} +(-4.65816 + 20.4087i) q^{65} +(-1.17163 + 1.46917i) q^{66} +2.75438 q^{67} -5.53752 q^{68} +(-0.565574 + 0.709207i) q^{69} +(-2.53775 + 20.7482i) q^{70} +(-2.88977 - 3.62366i) q^{71} +(-0.923396 - 1.15790i) q^{72} +(4.97674 - 2.39667i) q^{73} +(-0.733067 + 0.353027i) q^{74} +(9.16743 + 11.4956i) q^{75} +(1.52677 + 1.91452i) q^{76} +(-2.62769 - 0.947604i) q^{77} +(-5.23345 + 6.56254i) q^{78} +8.21672 q^{79} +22.0691 q^{80} +(0.623490 - 0.781831i) q^{81} +(1.63322 - 7.15562i) q^{82} +(13.7077 - 6.60126i) q^{83} +(-1.66877 + 2.60062i) q^{84} +(-18.9622 - 9.13169i) q^{85} +(8.37014 - 10.4958i) q^{86} +(-2.59519 - 1.24978i) q^{87} +(-0.347939 + 1.52442i) q^{88} +(10.0755 - 4.85213i) q^{89} +(1.75804 + 7.70246i) q^{90} +(-11.7374 - 4.23278i) q^{91} +(0.235743 - 1.03286i) q^{92} +(-0.439659 - 1.92627i) q^{93} +(9.03149 + 11.3251i) q^{94} +(2.07100 + 9.07363i) q^{95} +(5.30410 + 2.55432i) q^{96} +5.72620 q^{97} +(-12.0917 - 3.00284i) q^{98} -1.05578 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{2} - 6 q^{3} - 9 q^{4} - 4 q^{5} - q^{6} - 6 q^{7} - 15 q^{8} - 6 q^{9}+O(q^{10}) \) 36 * q - q^2 - 6 * q^3 - 9 * q^4 - 4 * q^5 - q^6 - 6 * q^7 - 15 * q^8 - 6 * q^9	\( 36 q - q^{2} - 6 q^{3} - 9 q^{4} - 4 q^{5} - q^{6} - 6 q^{7} - 15 q^{8} - 6 q^{9} + 10 q^{10} - 7 q^{11} - 9 q^{12} - 12 q^{13} - q^{14} + 3 q^{15} - 3 q^{16} - 3 q^{17} + 6 q^{18} + 6 q^{19} + 25 q^{20} + q^{21} - 21 q^{22} - 20 q^{23} + 6 q^{24} - 2 q^{25} + 6 q^{26} - 6 q^{27} - q^{28} - 22 q^{29} - 4 q^{30} + 16 q^{31} + 26 q^{32} + 6 q^{34} - 9 q^{35} - 9 q^{36} + 32 q^{37} + 17 q^{38} + 23 q^{39} - 21 q^{40} - 5 q^{41} - 8 q^{42} - 34 q^{43} + 2 q^{44} + 3 q^{45} - 32 q^{46} - 7 q^{47} + 74 q^{48} + 20 q^{49} + 236 q^{50} + 18 q^{51} + 20 q^{52} - 32 q^{53} - q^{54} - 17 q^{55} - 39 q^{56} - 8 q^{57} - 53 q^{58} - q^{59} - 17 q^{60} + 14 q^{61} - 60 q^{62} + 22 q^{63} - 21 q^{64} - 39 q^{65} - 21 q^{66} - 22 q^{67} - 110 q^{68} - 20 q^{69} - 40 q^{70} + 36 q^{71} + 6 q^{72} - 11 q^{73} - 46 q^{74} - 9 q^{75} - 101 q^{76} - 17 q^{77} + 6 q^{78} - 14 q^{79} - 112 q^{80} - 6 q^{81} + 2 q^{82} + 12 q^{83} - 22 q^{84} - 44 q^{85} + 184 q^{86} - q^{87} + 204 q^{88} + 12 q^{89} + 10 q^{90} - 16 q^{91} - 105 q^{92} - 19 q^{93} - 5 q^{94} + 18 q^{95} - 9 q^{96} + 172 q^{97} + q^{98}+O(q^{100}) \) 36 * q - q^2 - 6 * q^3 - 9 * q^4 - 4 * q^5 - q^6 - 6 * q^7 - 15 * q^8 - 6 * q^9 + 10 * q^10 - 7 * q^11 - 9 * q^12 - 12 * q^13 - q^14 + 3 * q^15 - 3 * q^16 - 3 * q^17 + 6 * q^18 + 6 * q^19 + 25 * q^20 + q^21 - 21 * q^22 - 20 * q^23 + 6 * q^24 - 2 * q^25 + 6 * q^26 - 6 * q^27 - q^28 - 22 * q^29 - 4 * q^30 + 16 * q^31 + 26 * q^32 + 6 * q^34 - 9 * q^35 - 9 * q^36 + 32 * q^37 + 17 * q^38 + 23 * q^39 - 21 * q^40 - 5 * q^41 - 8 * q^42 - 34 * q^43 + 2 * q^44 + 3 * q^45 - 32 * q^46 - 7 * q^47 + 74 * q^48 + 20 * q^49 + 236 * q^50 + 18 * q^51 + 20 * q^52 - 32 * q^53 - q^54 - 17 * q^55 - 39 * q^56 - 8 * q^57 - 53 * q^58 - q^59 - 17 * q^60 + 14 * q^61 - 60 * q^62 + 22 * q^63 - 21 * q^64 - 39 * q^65 - 21 * q^66 - 22 * q^67 - 110 * q^68 - 20 * q^69 - 40 * q^70 + 36 * q^71 + 6 * q^72 - 11 * q^73 - 46 * q^74 - 9 * q^75 - 101 * q^76 - 17 * q^77 + 6 * q^78 - 14 * q^79 - 112 * q^80 - 6 * q^81 + 2 * q^82 + 12 * q^83 - 22 * q^84 - 44 * q^85 + 184 * q^86 - q^87 + 204 * q^88 + 12 * q^89 + 10 * q^90 - 16 * q^91 - 105 * q^92 - 19 * q^93 - 5 * q^94 + 18 * q^95 - 9 * q^96 + 172 * q^97 + q^98

Introduction

L-functions

Modular forms

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