LMFDB - Embedded newform 570.2.u.j.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(61,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("570.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.u (of order $9$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			61.1
Root			$0.500000 + 1.96356i$ of defining polynomial
Character	$\chi$	$=$	570.61
Dual form			570.2.u.j.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(-0.897714 + 1.55489i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(-0.897714 + 1.55489i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-0.939693 + 0.342020i) q^{10} +(3.23307 + 5.59985i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.680785 - 3.86092i) q^{13} +(1.37538 - 1.15408i) q^{14} +(-0.766044 - 0.642788i) q^{15} +(0.173648 + 0.984808i) q^{16} +(4.33056 + 1.57619i) q^{17} +1.00000 q^{18} +(-1.99648 + 3.87480i) q^{19} +1.00000 q^{20} +(1.68715 + 0.614072i) q^{21} +(-1.12283 - 6.36791i) q^{22} +(2.62209 + 2.20020i) q^{23} +(-0.766044 + 0.642788i) q^{24} +(0.173648 - 0.984808i) q^{25} +(-1.96024 + 3.39524i) q^{26} +(0.500000 + 0.866025i) q^{27} +(-1.68715 + 0.614072i) q^{28} +(1.70179 - 0.619402i) q^{29} +(0.500000 + 0.866025i) q^{30} +(2.84116 - 4.92103i) q^{31} +(0.173648 - 0.984808i) q^{32} +(4.95336 - 4.15636i) q^{33} +(-3.53030 - 2.96227i) q^{34} +(0.311773 + 1.76815i) q^{35} +(-0.939693 - 0.342020i) q^{36} -6.08185 q^{37} +(3.20133 - 2.95829i) q^{38} -3.92048 q^{39} +(-0.939693 - 0.342020i) q^{40} +(0.0777275 + 0.440814i) q^{41} +(-1.37538 - 1.15408i) q^{42} +(6.73955 - 5.65516i) q^{43} +(-1.12283 + 6.36791i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-1.71145 - 2.96432i) q^{46} +(2.21210 - 0.805139i) q^{47} +(0.939693 - 0.342020i) q^{48} +(1.88822 + 3.27049i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.800254 - 4.53847i) q^{51} +(3.00326 - 2.52004i) q^{52} +(1.36844 + 1.14826i) q^{53} +(-0.173648 - 0.984808i) q^{54} +(6.07619 + 2.21155i) q^{55} +1.79543 q^{56} +(4.16262 + 1.29329i) q^{57} -1.81101 q^{58} +(7.80992 + 2.84258i) q^{59} +(-0.173648 - 0.984808i) q^{60} +(-2.49722 - 2.09542i) q^{61} +(-4.35290 + 3.65252i) q^{62} +(0.311773 - 1.76815i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.96024 - 3.39524i) q^{65} +(-6.07619 + 2.21155i) q^{66} +(11.5036 - 4.18698i) q^{67} +(2.30424 + 3.99106i) q^{68} +(1.71145 - 2.96432i) q^{69} +(0.311773 - 1.76815i) q^{70} +(-1.98897 + 1.66894i) q^{71} +(0.766044 + 0.642788i) q^{72} +(-0.341519 - 1.93685i) q^{73} +(5.71507 + 2.08011i) q^{74} -1.00000 q^{75} +(-4.02006 + 1.68496i) q^{76} -11.6095 q^{77} +(3.68405 + 1.34088i) q^{78} +(0.334911 + 1.89938i) q^{79} +(0.766044 + 0.642788i) q^{80} +(0.766044 - 0.642788i) q^{81} +(0.0777275 - 0.440814i) q^{82} +(2.26638 - 3.92548i) q^{83} +(0.897714 + 1.55489i) q^{84} +(4.33056 - 1.57619i) q^{85} +(-8.26729 + 3.00905i) q^{86} +(-0.905504 - 1.56838i) q^{87} +(3.23307 - 5.59985i) q^{88} +(-0.466024 + 2.64295i) q^{89} +(0.766044 - 0.642788i) q^{90} +(5.39214 + 4.52455i) q^{91} +(0.594380 + 3.37090i) q^{92} +(-5.33963 - 1.94347i) q^{93} -2.35407 q^{94} +(0.961285 + 4.25158i) q^{95} -1.00000 q^{96} +(-17.1731 - 6.25049i) q^{97} +(-0.655772 - 3.71907i) q^{98} +(-4.95336 - 4.15636i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q + 3 * q^7 - 6 * q^8	$ 12 q + 3 q^{7} - 6 q^{8} + 3 q^{11} + 6 q^{12} + 9 q^{13} + 9 q^{14} + 9 q^{17} + 12 q^{18} + 9 q^{19} + 12 q^{20} + 9 q^{21} - 6 q^{22} + 12 q^{23} + 9 q^{26} + 6 q^{27} - 9 q^{28} + 27 q^{29} + 6 q^{30} + 12 q^{31} - 3 q^{33} - 9 q^{34} - 42 q^{37} + 18 q^{38} + 18 q^{39} - 27 q^{41} - 9 q^{42} - 27 q^{43} - 6 q^{44} - 6 q^{45} + 9 q^{46} - 6 q^{47} + 3 q^{49} - 6 q^{50} + 9 q^{52} - 18 q^{53} + 3 q^{55} - 6 q^{56} + 6 q^{58} - 15 q^{59} - 9 q^{61} - 18 q^{62} - 6 q^{64} + 9 q^{65} - 3 q^{66} + 42 q^{67} + 6 q^{68} - 9 q^{69} + 24 q^{71} + 15 q^{73} + 18 q^{74} - 12 q^{75} + 3 q^{76} - 6 q^{77} + 18 q^{78} - 57 q^{79} - 27 q^{82} + 21 q^{83} - 3 q^{84} + 9 q^{85} + 9 q^{86} + 3 q^{87} + 3 q^{88} - 57 q^{89} + 21 q^{91} - 15 q^{92} - 9 q^{93} - 24 q^{94} - 18 q^{95} - 12 q^{96} - 6 q^{97} - 15 q^{98} + 3 q^{99}+O(q^{100}) $ 12 * q + 3 * q^7 - 6 * q^8 + 3 * q^11 + 6 * q^12 + 9 * q^13 + 9 * q^14 + 9 * q^17 + 12 * q^18 + 9 * q^19 + 12 * q^20 + 9 * q^21 - 6 * q^22 + 12 * q^23 + 9 * q^26 + 6 * q^27 - 9 * q^28 + 27 * q^29 + 6 * q^30 + 12 * q^31 - 3 * q^33 - 9 * q^34 - 42 * q^37 + 18 * q^38 + 18 * q^39 - 27 * q^41 - 9 * q^42 - 27 * q^43 - 6 * q^44 - 6 * q^45 + 9 * q^46 - 6 * q^47 + 3 * q^49 - 6 * q^50 + 9 * q^52 - 18 * q^53 + 3 * q^55 - 6 * q^56 + 6 * q^58 - 15 * q^59 - 9 * q^61 - 18 * q^62 - 6 * q^64 + 9 * q^65 - 3 * q^66 + 42 * q^67 + 6 * q^68 - 9 * q^69 + 24 * q^71 + 15 * q^73 + 18 * q^74 - 12 * q^75 + 3 * q^76 - 6 * q^77 + 18 * q^78 - 57 * q^79 - 27 * q^82 + 21 * q^83 - 3 * q^84 + 9 * q^85 + 9 * q^86 + 3 * q^87 + 3 * q^88 - 57 * q^89 + 21 * q^91 - 15 * q^92 - 9 * q^93 - 24 * q^94 - 18 * q^95 - 12 * q^96 - 6 * q^97 - 15 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$	$1$

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 $

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	0.766044	−	0.642788i	0.342585	−	0.287463i
$5$	0.766044	−	0.642788i	0.342585	−	0.287463i
$6$	−0.173648	+	0.984808i	−0.0708916	+	0.402046i
$7$	−0.897714	+	1.55489i	−0.339304	+	0.587692i	−0.984302	−	0.176493i	$-0.943525\pi$
$7$	−0.897714	+	1.55489i	−0.339304	+	0.587692i	0.644998	+	0.764184i	$0.276858\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$	−0.939693	+	0.342020i	−0.297157	+	0.108156i
$11$	3.23307	+	5.59985i	0.974809	+	1.68842i	0.680565	+	0.732687i	$0.261734\pi$
$11$	3.23307	+	5.59985i	0.974809	+	1.68842i	0.294243	+	0.955731i	$0.404932\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	0.680785	−	3.86092i	0.188816	−	1.07083i	−0.732138	−	0.681156i	$-0.761478\pi$
$13$	0.680785	−	3.86092i	0.188816	−	1.07083i	0.920954	−	0.389671i	$-0.127411\pi$
$14$	1.37538	−	1.15408i	0.367585	−	0.308440i
$15$	−0.766044	−	0.642788i	−0.197792	−	0.165967i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	4.33056	+	1.57619i	1.05031	+	0.382283i	0.808781	−	0.588110i	$-0.200128\pi$
$17$	4.33056	+	1.57619i	1.05031	+	0.382283i	0.241533	+	0.970393i	$0.422350\pi$
$18$	1.00000			0.235702
$19$	−1.99648	+	3.87480i	−0.458023	+	0.888940i
$19$	−1.99648	+	3.87480i	−0.458023	+	0.888940i
$20$	1.00000			0.223607
$21$	1.68715	+	0.614072i	0.368166	+	0.134002i
$22$	−1.12283	−	6.36791i	−0.239389	−	1.35764i
$23$	2.62209	+	2.20020i	0.546744	+	0.458773i	0.873837	−	0.486220i	$-0.161625\pi$
$23$	2.62209	+	2.20020i	0.546744	+	0.458773i	−0.327093	+	0.944992i	$0.606069\pi$
$24$	−0.766044	+	0.642788i	−0.156368	+	0.131208i
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$	−1.96024	+	3.39524i	−0.384435	+	0.665861i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	−1.68715	+	0.614072i	−0.318841	+	0.116049i
$29$	1.70179	−	0.619402i	0.316015	−	0.115020i	−0.179143	−	0.983823i	$-0.557332\pi$
$29$	1.70179	−	0.619402i	0.316015	−	0.115020i	0.495158	+	0.868803i	$0.335110\pi$
$30$	0.500000	+	0.866025i	0.0912871	+	0.158114i
$31$	2.84116	−	4.92103i	0.510287	−	0.883842i	−0.489642	−	0.871923i	$-0.662873\pi$
$31$	2.84116	−	4.92103i	0.510287	−	0.883842i	0.999929	−	0.0119190i	$-0.00379404\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	4.95336	−	4.15636i	0.862269	−	0.723529i
$34$	−3.53030	−	2.96227i	−0.605442	−	0.508026i
$35$	0.311773	+	1.76815i	0.0526992	+	0.298872i
$36$	−0.939693	−	0.342020i	−0.156615	−	0.0570034i
$37$	−6.08185			−0.999849			−0.499925	−	0.866069i	$-0.666639\pi$
$37$	−6.08185			−0.999849			−0.499925	+	0.866069i	$0.666639\pi$
$38$	3.20133	−	2.95829i	0.519325	−	0.479898i
$39$	−3.92048			−0.627780
$40$	−0.939693	−	0.342020i	−0.148578	−	0.0540781i
$41$	0.0777275	+	0.440814i	0.0121390	+	0.0688436i	0.990275	−	0.139120i	$-0.0444275\pi$
$41$	0.0777275	+	0.440814i	0.0121390	+	0.0688436i	−0.978137	+	0.207964i	$0.933316\pi$
$42$	−1.37538	−	1.15408i	−0.212225	−	0.178078i
$43$	6.73955	−	5.65516i	1.02777	−	0.862403i	0.0371882	−	0.999308i	$-0.488160\pi$
$43$	6.73955	−	5.65516i	1.02777	−	0.862403i	0.990584	+	0.136905i	$0.0437154\pi$
$44$	−1.12283	+	6.36791i	−0.169274	+	0.959999i
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	−1.71145	−	2.96432i	−0.252339	−	0.437064i
$47$	2.21210	−	0.805139i	0.322668	−	0.117442i	−0.175607	−	0.984460i	$-0.556189\pi$
$47$	2.21210	−	0.805139i	0.322668	−	0.117442i	0.498276	+	0.867019i	$0.333967\pi$
$48$	0.939693	−	0.342020i	0.135633	−	0.0493664i
$49$	1.88822	+	3.27049i	0.269746	+	0.467213i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	0.800254	−	4.53847i	0.112058	−	0.635513i
$52$	3.00326	−	2.52004i	0.416478	−	0.349466i
$53$	1.36844	+	1.14826i	0.187970	+	0.157726i	0.731916	−	0.681394i	$-0.238626\pi$
$53$	1.36844	+	1.14826i	0.187970	+	0.157726i	−0.543946	+	0.839120i	$0.683071\pi$
$54$	−0.173648	−	0.984808i	−0.0236305	−	0.134015i
$55$	6.07619	+	2.21155i	0.819314	+	0.298206i
$56$	1.79543			0.239924
$57$	4.16262	+	1.29329i	0.551352	+	0.171301i
$58$	−1.81101			−0.237797
$59$	7.80992	+	2.84258i	1.01677	+	0.370072i	0.796027	−	0.605261i	$-0.206931\pi$
$59$	7.80992	+	2.84258i	1.01677	+	0.370072i	0.220738	+	0.975333i	$0.429153\pi$
$60$	−0.173648	−	0.984808i	−0.0224179	−	0.127138i
$61$	−2.49722	−	2.09542i	−0.319736	−	0.268291i	0.468766	−	0.883322i	$-0.344699\pi$
$61$	−2.49722	−	2.09542i	−0.319736	−	0.268291i	−0.788502	+	0.615032i	$0.789143\pi$
$62$	−4.35290	+	3.65252i	−0.552819	+	0.463870i
$63$	0.311773	−	1.76815i	0.0392797	−	0.222766i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−1.96024	−	3.39524i	−0.243138	−	0.421127i
$66$	−6.07619	+	2.21155i	−0.747928	+	0.272223i
$67$	11.5036	−	4.18698i	1.40539	−	0.511521i	0.475619	−	0.879651i	$-0.342224\pi$
$67$	11.5036	−	4.18698i	1.40539	−	0.511521i	0.929774	+	0.368130i	$0.120002\pi$
$68$	2.30424	+	3.99106i	0.279430	+	0.483987i
$69$	1.71145	−	2.96432i	0.206034	−	0.356862i
$70$	0.311773	−	1.76815i	0.0372640	−	0.211334i
$71$	−1.98897	+	1.66894i	−0.236047	+	0.198067i	−0.753136	−	0.657864i	$-0.771460\pi$
$71$	−1.98897	+	1.66894i	−0.236047	+	0.198067i	0.517089	+	0.855932i	$0.327016\pi$
$72$	0.766044	+	0.642788i	0.0902792	+	0.0757532i
$73$	−0.341519	−	1.93685i	−0.0399717	−	0.226691i	0.958277	−	0.285840i	$-0.0922725\pi$
$73$	−0.341519	−	1.93685i	−0.0399717	−	0.226691i	−0.998249	+	0.0591488i	$0.981161\pi$
$74$	5.71507	+	2.08011i	0.664363	+	0.241808i
$75$	−1.00000			−0.115470
$76$	−4.02006	+	1.68496i	−0.461133	+	0.193278i
$77$	−11.6095			−1.32303
$78$	3.68405	+	1.34088i	0.417136	+	0.151825i
$79$	0.334911	+	1.89938i	0.0376805	+	0.213697i	0.997834	−	0.0657748i	$-0.0209519\pi$
$79$	0.334911	+	1.89938i	0.0376805	+	0.213697i	−0.960154	+	0.279471i	$0.909841\pi$
$80$	0.766044	+	0.642788i	0.0856464	+	0.0718658i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	0.0777275	−	0.440814i	0.00858356	−	0.0486798i
$83$	2.26638	−	3.92548i	0.248767	−	0.430878i	−0.714417	−	0.699720i	$-0.753308\pi$
$83$	2.26638	−	3.92548i	0.248767	−	0.430878i	0.963184	+	0.268843i	$0.0866412\pi$
$84$	0.897714	+	1.55489i	0.0979486	+	0.169652i
$85$	4.33056	−	1.57619i	0.469715	−	0.170962i
$86$	−8.26729	+	3.00905i	−0.891485	+	0.324474i
$87$	−0.905504	−	1.56838i	−0.0970803	−	0.168148i
$88$	3.23307	−	5.59985i	0.344647	−	0.596946i
$89$	−0.466024	+	2.64295i	−0.0493985	+	0.280153i	−0.999494	−	0.0318063i	$-0.989874\pi$
$89$	−0.466024	+	2.64295i	−0.0493985	+	0.280153i	0.950096	+	0.311959i	$0.100985\pi$
$90$	0.766044	−	0.642788i	0.0807482	−	0.0677558i
$91$	5.39214	+	4.52455i	0.565250	+	0.474301i
$92$	0.594380	+	3.37090i	0.0619684	+	0.351440i
$93$	−5.33963	−	1.94347i	−0.553693	−	0.201528i
$94$	−2.35407			−0.242804
$95$	0.961285	+	4.25158i	0.0986258	+	0.436203i
$96$	−1.00000			−0.102062
$97$	−17.1731	−	6.25049i	−1.74366	−	0.634641i	−0.744216	−	0.667939i	$-0.767177\pi$
$97$	−17.1731	−	6.25049i	−1.74366	−	0.634641i	−0.999445	+	0.0332981i	$0.989399\pi$
$98$	−0.655772	−	3.71907i	−0.0662430	−	0.375682i
$99$	−4.95336	−	4.15636i	−0.497831	−	0.417730i
$100$	0.766044	−	0.642788i	0.0766044	−	0.0642788i
$101$	0.266783	−	1.51300i	0.0265459	−	0.150549i	−0.968654	−	0.248415i	$-0.920090\pi$
$101$	0.266783	−	1.51300i	0.0265459	−	0.150549i	0.995200	+	0.0978655i	$0.0312015\pi$
$102$	−2.30424	+	3.99106i	−0.228154	+	0.395174i
$103$	−2.10567	−	3.64713i	−0.207478	−	0.359362i	0.743441	−	0.668801i	$-0.233192\pi$
$103$	−2.10567	−	3.64713i	−0.207478	−	0.359362i	−0.950919	+	0.309439i	$0.899859\pi$
$104$	−3.68405	+	1.34088i	−0.361251	+	0.131485i
$105$	1.68715	−	0.614072i	0.164649	−	0.0599273i
$106$	−0.893187	−	1.54705i	−0.0867540	−	0.150262i
$107$	−7.86116	+	13.6159i	−0.759967	+	1.31630i	0.182900	+	0.983131i	$0.441451\pi$
$107$	−7.86116	+	13.6159i	−0.759967	+	1.31630i	−0.942867	+	0.333169i	$0.891882\pi$
$108$	−0.173648	+	0.984808i	−0.0167093	+	0.0947632i
$109$	−6.54675	+	5.49337i	−0.627065	+	0.526170i	−0.900015	−	0.435858i	$-0.856445\pi$
$109$	−6.54675	+	5.49337i	−0.627065	+	0.526170i	0.272951	+	0.962028i	$0.412000\pi$
$110$	−4.95336	−	4.15636i	−0.472284	−	0.396293i
$111$	1.05610	+	5.98945i	0.100241	+	0.568493i
$112$	−1.68715	−	0.614072i	−0.159421	−	0.0580244i
$113$	−1.57641			−0.148296			−0.0741480	−	0.997247i	$-0.523624\pi$
$113$	−1.57641			−0.148296			−0.0741480	+	0.997247i	$0.523624\pi$
$114$	−3.46925	−	2.63900i	−0.324925	−	0.247165i
$115$	3.42290			0.319187
$116$	1.70179	+	0.619402i	0.158007	+	0.0575100i
$117$	0.680785	+	3.86092i	0.0629386	+	0.356942i
$118$	−6.36671	−	5.34230i	−0.586103	−	0.491799i
$119$	−6.33840	+	5.31855i	−0.581040	+	0.487551i
$120$	−0.173648	+	0.984808i	−0.0158518	+	0.0899002i
$121$	−15.4055	+	26.6832i	−1.40050	+	2.42574i
$122$	1.62994	+	2.82315i	0.147568	+	0.255596i
$123$	0.420620	−	0.153093i	0.0379260	−	0.0138040i
$124$	5.33963	−	1.94347i	0.479513	−	0.174528i
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$	−0.897714	+	1.55489i	−0.0799747	+	0.138520i
$127$	−2.23690	+	12.6861i	−0.198493	+	1.12571i	0.708862	+	0.705347i	$0.249209\pi$
$127$	−2.23690	+	12.6861i	−0.198493	+	1.12571i	−0.907356	+	0.420364i	$0.861902\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	−6.73955	−	5.65516i	−0.593385	−	0.497909i
$130$	0.680785	+	3.86092i	0.0597088	+	0.338625i
$131$	6.08475	+	2.21467i	0.531627	+	0.193497i	0.593865	−	0.804565i	$-0.297601\pi$
$131$	6.08475	+	2.21467i	0.531627	+	0.193497i	−0.0622374	+	0.998061i	$0.519824\pi$
$132$	6.46615			0.562806
$133$	−4.23261	−	6.58275i	−0.367014	−	0.570797i
$134$	−12.2419			−1.05754
$135$	0.939693	+	0.342020i	0.0808759	+	0.0294364i
$136$	−0.800254	−	4.53847i	−0.0686212	−	0.389170i
$137$	−1.70285	−	1.42886i	−0.145484	−	0.122076i	0.567141	−	0.823621i	$-0.308050\pi$
$137$	−1.70285	−	1.42886i	−0.145484	−	0.122076i	−0.712625	+	0.701545i	$0.752494\pi$
$138$	−2.62209	+	2.20020i	−0.223207	+	0.187293i
$139$	−2.02701	+	11.4957i	−0.171928	+	0.975054i	0.769701	+	0.638404i	$0.220405\pi$
$139$	−2.02701	+	11.4957i	−0.171928	+	0.975054i	−0.941630	+	0.336650i	$0.890706\pi$
$140$	−0.897714	+	1.55489i	−0.0758707	+	0.131412i
$141$	−1.17704	−	2.03868i	−0.0991242	−	0.171688i
$142$	2.43983	−	0.888027i	0.204746	−	0.0745216i
$143$	23.8216	−	8.67036i	1.99206	−	0.725052i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	0.905504	−	1.56838i	0.0751981	−	0.130247i
$146$	−0.341519	+	1.93685i	−0.0282643	+	0.160295i
$147$	2.89292	−	2.42745i	0.238604	−	0.200213i
$148$	−4.65896	−	3.90934i	−0.382965	−	0.321345i
$149$	−3.95399	−	22.4242i	−0.323923	−	1.83706i	−0.517135	−	0.855904i	$-0.673001\pi$
$149$	−3.95399	−	22.4242i	−0.323923	−	1.83706i	0.193211	−	0.981157i	$-0.438110\pi$
$150$	0.939693	+	0.342020i	0.0767256	+	0.0279258i
$151$	−22.1758			−1.80464			−0.902321	−	0.431065i	$-0.858138\pi$
$151$	−22.1758			−1.80464			−0.902321	+	0.431065i	$0.858138\pi$
$152$	4.35391	−	0.208402i	0.353149	−	0.0169036i
$153$	−4.60848			−0.372574
$154$	10.9094	+	3.97068i	0.879102	+	0.319967i
$155$	−0.986723	−	5.59598i	−0.0792555	−	0.449480i
$156$	−3.00326	−	2.52004i	−0.240454	−	0.201764i
$157$	−9.47879	+	7.95365i	−0.756490	+	0.634770i	−0.937210	−	0.348764i	$-0.886601\pi$
$157$	−9.47879	+	7.95365i	−0.756490	+	0.634770i	0.180721	+	0.983534i	$0.442157\pi$
$158$	0.334911	−	1.89938i	0.0266441	−	0.151106i
$159$	0.893187	−	1.54705i	0.0708344	−	0.122689i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−5.77494	+	2.10191i	−0.455129	+	0.165653i
$162$	−0.939693	+	0.342020i	−0.0738292	+	0.0268716i
$163$	−11.9976	−	20.7804i	−0.939724	−	1.62765i	−0.765986	−	0.642857i	$-0.777749\pi$
$163$	−11.9976	−	20.7804i	−0.939724	−	1.62765i	−0.173737	−	0.984792i	$-0.555584\pi$
$164$	−0.223807	+	0.387646i	−0.0174764	+	0.0302700i
$165$	1.12283	−	6.36791i	0.0874126	−	0.495741i
$166$	−3.47229	+	2.91360i	−0.269502	+	0.226139i
$167$	−7.08340	−	5.94368i	−0.548130	−	0.459936i	0.326177	−	0.945309i	$-0.394239\pi$
$167$	−7.08340	−	5.94368i	−0.548130	−	0.459936i	−0.874307	+	0.485373i	$0.838684\pi$
$168$	−0.311773	−	1.76815i	−0.0240538	−	0.136416i
$169$	−2.22725	−	0.810651i	−0.171327	−	0.0623578i
$170$	−4.60848			−0.353454
$171$	0.550813	−	4.32396i	0.0421217	−	0.330661i
$172$	8.79786			0.670831
$173$	12.2569	+	4.46113i	0.931872	+	0.339174i	0.762951	−	0.646456i	$-0.223750\pi$
$173$	12.2569	+	4.46113i	0.931872	+	0.339174i	0.168921	+	0.985630i	$0.445972\pi$
$174$	0.314478	+	1.78350i	0.0238405	+	0.135206i
$175$	1.37538	+	1.15408i	0.103969	+	0.0872401i
$176$	−4.95336	+	4.15636i	−0.373373	+	0.313297i
$177$	1.44321	−	8.18488i	0.108479	−	0.615213i
$178$	1.34186	−	2.32418i	0.100577	−	0.174204i
$179$	9.09217	+	15.7481i	0.679581	+	1.17707i	0.975107	+	0.221734i	$0.0711717\pi$
$179$	9.09217	+	15.7481i	0.679581	+	1.17707i	−0.295526	+	0.955335i	$0.595495\pi$
$180$	−0.939693	+	0.342020i	−0.0700406	+	0.0254927i
$181$	22.8903	−	8.33140i	1.70142	−	0.619268i	0.705438	−	0.708771i	$-0.250750\pi$
$181$	22.8903	−	8.33140i	1.70142	−	0.619268i	0.995987	+	0.0895032i	$0.0285279\pi$
$182$	−3.51947	−	6.09590i	−0.260881	−	0.451858i
$183$	−1.62994	+	2.82315i	−0.120489	+	0.208693i
$184$	0.594380	−	3.37090i	0.0438183	−	0.248506i
$185$	−4.65896	+	3.90934i	−0.342534	+	0.287420i
$186$	4.35290	+	3.65252i	0.319170	+	0.267816i
$187$	5.17456	+	29.3464i	0.378402	+	2.14602i
$188$	2.21210	+	0.805139i	0.161334	+	0.0587208i
$189$	−1.79543			−0.130598
$190$	0.550813	−	4.32396i	0.0399602	−	0.313693i
$191$	−12.7580			−0.923140			−0.461570	−	0.887104i	$-0.652714\pi$
$191$	−12.7580			−0.923140			−0.461570	+	0.887104i	$0.652714\pi$
$192$	0.939693	+	0.342020i	0.0678165	+	0.0246832i
$193$	1.56355	+	8.86735i	0.112547	+	0.638286i	0.987936	+	0.154866i	$0.0494945\pi$
$193$	1.56355	+	8.86735i	0.112547	+	0.638286i	−0.875389	+	0.483420i	$0.839394\pi$
$194$	13.9996	+	11.7471i	1.00511	+	0.843391i
$195$	−3.00326	+	2.52004i	−0.215068	+	0.180464i
$196$	−0.655772	+	3.71907i	−0.0468408	+	0.265648i
$197$	−5.21392	+	9.03077i	−0.371476	+	0.643415i	−0.989793	−	0.142514i	$-0.954482\pi$
$197$	−5.21392	+	9.03077i	−0.371476	+	0.643415i	0.618317	+	0.785929i	$0.287815\pi$
$198$	3.23307	+	5.59985i	0.229765	+	0.397964i
$199$	6.77522	−	2.46598i	0.480282	−	0.174808i	−0.0905222	−	0.995894i	$-0.528854\pi$
$199$	6.77522	−	2.46598i	0.480282	−	0.174808i	0.570805	+	0.821086i	$0.306631\pi$
$200$	−0.939693	+	0.342020i	−0.0664463	+	0.0241845i
$201$	−6.12096	−	10.6018i	−0.431739	−	0.747794i
$202$	−0.768171	+	1.33051i	−0.0540483	+	0.0936144i
$203$	−0.564623	+	3.20214i	−0.0396288	+	0.224746i
$204$	3.53030	−	2.96227i	0.247171	−	0.207401i
$205$	0.342893	+	0.287721i	0.0239487	+	0.0200953i
$206$	0.731292	+	4.14736i	0.0509515	+	0.288960i
$207$	−3.21647	−	1.17070i	−0.223560	−	0.0813693i
$208$	3.92048			0.271837
$209$	−28.1531	+	1.34756i	−1.94739	+	0.0932126i
$210$	−1.79543			−0.123896
$211$	−6.78077	−	2.46800i	−0.466807	−	0.169904i	0.0978983	−	0.995196i	$-0.468788\pi$
$211$	−6.78077	−	2.46800i	−0.466807	−	0.169904i	−0.564705	+	0.825293i	$0.691010\pi$
$212$	0.310201	+	1.75924i	0.0213047	+	0.120825i
$213$	1.98897	+	1.66894i	0.136282	+	0.114354i
$214$	12.0440	−	10.1061i	0.823310	−	0.690839i
$215$	1.52773	−	8.66420i	0.104191	−	0.590894i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	5.10109	+	8.83535i	0.346285	+	0.599782i
$218$	8.03077	−	2.92296i	0.543913	−	0.197968i
$219$	−1.84812	+	0.672660i	−0.124884	+	0.0454542i
$220$	3.23307	+	5.59985i	0.217974	+	0.377542i
$221$	9.03374	−	15.6469i	0.607675	−	1.05252i
$222$	1.05610	−	5.98945i	0.0708809	−	0.401986i
$223$	0.451653	−	0.378982i	0.0302449	−	0.0253785i	−0.627540	−	0.778584i	$-0.715938\pi$
$223$	0.451653	−	0.378982i	0.0302449	−	0.0253785i	0.657785	+	0.753206i	$0.271494\pi$
$224$	1.37538	+	1.15408i	0.0918963	+	0.0771101i
$225$	0.173648	+	0.984808i	0.0115765	+	0.0656539i
$226$	1.48134	+	0.539163i	0.0985371	+	0.0358646i
$227$	−24.7930			−1.64557			−0.822784	−	0.568354i	$-0.807580\pi$
$227$	−24.7930			−1.64557			−0.822784	+	0.568354i	$0.807580\pi$
$228$	2.35744	+	3.66640i	0.156125	+	0.242813i
$229$	24.0443			1.58889			0.794445	−	0.607336i	$-0.207762\pi$
$229$	24.0443			1.58889			0.794445	+	0.607336i	$0.207762\pi$
$230$	−3.21647	−	1.17070i	−0.212088	−	0.0771937i
$231$	2.01597	+	11.4331i	0.132641	+	0.752245i
$232$	−1.38731	−	1.16409i	−0.0910816	−	0.0764265i
$233$	11.7959	−	9.89792i	0.772774	−	0.648434i	−0.168644	−	0.985677i	$-0.553939\pi$
$233$	11.7959	−	9.89792i	0.772774	−	0.648434i	0.941418	+	0.337243i	$0.109494\pi$
$234$	0.680785	−	3.86092i	0.0445043	−	0.252396i
$235$	1.17704	−	2.03868i	0.0767813	−	0.132989i
$236$	4.15557	+	7.19766i	0.270505	+	0.468528i
$237$	1.81236	−	0.659647i	0.117726	−	0.0428487i
$238$	7.77520	−	2.82994i	0.503991	−	0.183438i
$239$	−12.1200	−	20.9924i	−0.783977	−	1.35789i	−0.929608	−	0.368549i	$-0.879855\pi$
$239$	−12.1200	−	20.9924i	−0.783977	−	1.35789i	0.145631	−	0.989339i	$-0.453479\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	2.88973	−	16.3885i	0.186144	−	1.05567i	−0.738333	−	0.674436i	$-0.764387\pi$
$241$	2.88973	−	16.3885i	0.186144	−	1.05567i	0.924477	−	0.381238i	$-0.124502\pi$
$242$	23.6027	−	19.8050i	1.51724	−	1.27311i
$243$	−0.766044	−	0.642788i	−0.0491418	−	0.0412348i
$244$	−0.566074	−	3.21036i	−0.0362392	−	0.205522i
$245$	3.54869	+	1.29162i	0.226718	+	0.0825185i
$246$	−0.447615			−0.0285389
$247$	13.6011	+	10.3461i	0.865419	+	0.658309i
$248$	−5.68231			−0.360827
$249$	−4.25940	−	1.55029i	−0.269928	−	0.0982459i
$250$	0.173648	+	0.984808i	0.0109825	+	0.0622847i
$251$	−3.90506	−	3.27674i	−0.246485	−	0.206826i	0.511172	−	0.859479i	$-0.329212\pi$
$251$	−3.90506	−	3.27674i	−0.246485	−	0.206826i	−0.757657	+	0.652653i	$0.773656\pi$
$252$	1.37538	−	1.15408i	0.0866406	−	0.0727001i
$253$	−3.84335	+	21.7967i	−0.241629	+	1.37035i
$254$	6.44091	−	11.1560i	0.404139	−	0.699989i
$255$	−2.30424	−	3.99106i	−0.144297	−	0.249930i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	18.5138	−	6.73847i	1.15486	−	0.420334i	0.307601	−	0.951515i	$-0.400474\pi$
$257$	18.5138	−	6.73847i	1.15486	−	0.420334i	0.847258	+	0.531181i	$0.178252\pi$
$258$	4.39893	+	7.61917i	0.273866	+	0.474349i
$259$	5.45976	−	9.45658i	0.339253	−	0.587603i
$260$	0.680785	−	3.86092i	0.0422205	−	0.239444i
$261$	−1.38731	+	1.16409i	−0.0858725	+	0.0720556i
$262$	−4.96034	−	4.16222i	−0.306451	−	0.257143i
$263$	2.80642	+	15.9160i	0.173051	+	0.981422i	0.940369	+	0.340155i	$0.110480\pi$
$263$	2.80642	+	15.9160i	0.173051	+	0.981422i	−0.767318	+	0.641267i	$0.778409\pi$
$264$	−6.07619	−	2.21155i	−0.373964	−	0.136112i
$265$	1.78637			0.109736
$266$	1.72592	+	7.63340i	0.105823	+	0.468034i
$267$	2.68373			0.164241
$268$	11.5036	+	4.18698i	0.702697	+	0.255761i
$269$	−0.898994	−	5.09845i	−0.0548127	−	0.310858i	0.945059	−	0.326901i	$-0.106004\pi$
$269$	−0.898994	−	5.09845i	−0.0548127	−	0.310858i	−0.999871	+	0.0160428i	$0.994893\pi$
$270$	−0.766044	−	0.642788i	−0.0466200	−	0.0391188i
$271$	20.6071	−	17.2914i	1.25179	−	1.05038i	0.255284	−	0.966866i	$-0.417831\pi$
$271$	20.6071	−	17.2914i	1.25179	−	1.05038i	0.996507	−	0.0835109i	$-0.0266134\pi$
$272$	−0.800254	+	4.53847i	−0.0485225	+	0.275185i
$273$	3.51947	−	6.09590i	0.213008	−	0.368941i
$274$	1.11146	+	1.92510i	0.0671456	+	0.116300i
$275$	6.07619	−	2.21155i	0.366408	−	0.133362i
$276$	3.21647	−	1.17070i	0.193609	−	0.0704678i
$277$	−10.4943	−	18.1767i	−0.630542	−	1.09213i	−0.987441	−	0.157988i	$-0.949499\pi$
$277$	−10.4943	−	18.1767i	−0.630542	−	1.09213i	0.356899	−	0.934143i	$-0.383834\pi$
$278$	5.83653	−	10.1092i	0.350052	−	0.606308i
$279$	−0.986723	+	5.59598i	−0.0590736	+	0.335023i
$280$	1.37538	−	1.15408i	0.0821945	−	0.0689694i
$281$	−12.2315	−	10.2635i	−0.729672	−	0.612268i	0.200370	−	0.979720i	$-0.435786\pi$
$281$	−12.2315	−	10.2635i	−0.729672	−	0.612268i	−0.930042	+	0.367453i	$0.880230\pi$
$282$	0.408780	+	2.31831i	0.0243425	+	0.138053i
$283$	−4.28101	−	1.55816i	−0.254479	−	0.0926229i	0.211631	−	0.977350i	$-0.432123\pi$
$283$	−4.28101	−	1.55816i	−0.254479	−	0.0926229i	−0.466110	+	0.884727i	$0.654345\pi$
$284$	−2.59642			−0.154069
$285$	4.02006	−	1.68496i	0.238128	−	0.0998084i
$286$	−25.3504			−1.49900
$287$	−0.755193	−	0.274868i	−0.0445776	−	0.0162249i
$288$	0.173648	+	0.984808i	0.0102323	+	0.0580304i
$289$	3.24657	+	2.72420i	0.190975	+	0.160247i
$290$	−1.38731	+	1.16409i	−0.0814658	+	0.0683580i
$291$	−3.17346	+	17.9976i	−0.186031	+	1.05504i
$292$	0.983363	−	1.70324i	0.0575470	−	0.0996743i
$293$	7.41986	+	12.8516i	0.433473	+	0.750797i	0.997170	−	0.0751845i	$-0.0239546\pi$
$293$	7.41986	+	12.8516i	0.433473	+	0.750797i	−0.563697	+	0.825982i	$0.690621\pi$
$294$	−3.54869	+	1.29162i	−0.206964	+	0.0753287i
$295$	7.80992	−	2.84258i	0.454711	−	0.165501i
$296$	3.04092	+	5.26703i	0.176750	+	0.306140i
$297$	−3.23307	+	5.59985i	−0.187602	+	0.324936i
$298$	−3.95399	+	22.4242i	−0.229048	+	1.29900i
$299$	10.2799	−	8.62583i	0.594500	−	0.498845i
$300$	−0.766044	−	0.642788i	−0.0442276	−	0.0371114i
$301$	2.74293	+	15.5560i	0.158100	+	0.896630i
$302$	20.8384	+	7.58457i	1.19912	+	0.436443i
$303$	−1.53634			−0.0882605
$304$	−4.16262	−	1.29329i	−0.238743	−	0.0741754i
$305$	−3.25989			−0.186661
$306$	4.33056	+	1.57619i	0.247561	+	0.0901050i
$307$	0.801489	+	4.54547i	0.0457434	+	0.259424i	0.999100	−	0.0424235i	$-0.0135079\pi$
$307$	0.801489	+	4.54547i	0.0457434	+	0.259424i	−0.953356	+	0.301847i	$0.902397\pi$
$308$	−8.89339	−	7.46244i	−0.506748	−	0.425212i
$309$	−3.22608	+	2.70700i	−0.183525	+	0.153996i
$310$	−0.986723	+	5.59598i	−0.0560421	+	0.317831i
$311$	10.5023	−	18.1906i	0.595532	−	1.03149i	−0.397939	−	0.917412i	$-0.630274\pi$
$311$	10.5023	−	18.1906i	0.595532	−	1.03149i	0.993472	−	0.114081i	$-0.0363922\pi$
$312$	1.96024	+	3.39524i	0.110977	+	0.192217i
$313$	−21.3513	+	7.77124i	−1.20685	+	0.439256i	−0.865609	−	0.500721i	$-0.833068\pi$
$313$	−21.3513	+	7.77124i	−1.20685	+	0.439256i	−0.341238	+	0.939977i	$0.610846\pi$
$314$	11.6275	−	4.23205i	0.656175	−	0.238828i
$315$	−0.897714	−	1.55489i	−0.0505804	−	0.0876079i
$316$	−0.964339	+	1.67028i	−0.0542483	+	0.0939608i
$317$	3.25305	−	18.4490i	0.182710	−	1.03620i	−0.746153	−	0.665774i	$-0.768101\pi$
$317$	3.25305	−	18.4490i	0.182710	−	1.03620i	0.928863	−	0.370424i	$-0.120787\pi$
$318$	−1.36844	+	1.14826i	−0.0767384	+	0.0643912i
$319$	8.97057	+	7.52721i	0.502256	+	0.421443i
$320$	0.173648	+	0.984808i	0.00970723	+	0.0550524i
$321$	14.7741	+	5.37735i	0.824612	+	0.300134i
$322$	6.14556			0.342479
$323$	−14.7533	+	13.6332i	−0.820895	+	0.758572i
$324$	1.00000			0.0555556
$325$	−3.68405	−	1.34088i	−0.204354	−	0.0743789i
$326$	4.16672	+	23.6306i	0.230773	+	1.30878i
$327$	6.54675	+	5.49337i	0.362036	+	0.303784i
$328$	0.342893	−	0.287721i	0.0189331	−	0.0158867i
$329$	−0.733935	+	4.16235i	−0.0404631	+	0.229478i
$330$	−3.23307	+	5.59985i	−0.177975	+	0.308262i
$331$	8.61831	+	14.9274i	0.473705	+	0.820482i	0.999547	−	0.0301008i	$-0.00958282\pi$
$331$	8.61831	+	14.9274i	0.473705	+	0.820482i	−0.525841	+	0.850583i	$0.676249\pi$
$332$	4.25940	−	1.55029i	0.233765	−	0.0850834i
$333$	5.71507	−	2.08011i	0.313184	−	0.113990i
$334$	4.62336	+	8.00789i	0.252979	+	0.438172i
$335$	6.12096	−	10.6018i	0.334424	−	0.579239i
$336$	−0.311773	+	1.76815i	−0.0170086	+	0.0964606i
$337$	21.6329	−	18.1522i	1.17842	−	0.988812i	0.178432	−	0.983952i	$-0.442898\pi$
$337$	21.6329	−	18.1522i	1.17842	−	0.988812i	0.999988	−	0.00485974i	$-0.00154691\pi$
$338$	1.81567	+	1.52353i	0.0987593	+	0.0828689i
$339$	0.273740	+	1.55246i	0.0148675	+	0.0843179i
$340$	4.33056	+	1.57619i	0.234857	+	0.0854811i
$341$	36.7427			1.98973
$342$	−1.99648	+	3.87480i	−0.107957	+	0.209525i
$343$	−19.3483			−1.04471
$344$	−8.26729	−	3.00905i	−0.445742	−	0.162237i
$345$	−0.594380	−	3.37090i	−0.0320003	−	0.181483i
$346$	−9.99189	−	8.38419i	−0.537167	−	0.450737i
$347$	−23.9933	+	20.1328i	−1.28803	+	1.08078i	−0.295945	+	0.955205i	$0.595634\pi$
$347$	−23.9933	+	20.1328i	−1.28803	+	1.08078i	−0.992084	+	0.125579i	$0.959921\pi$
$348$	0.314478	−	1.78350i	0.0168578	−	0.0956054i
$349$	−8.11701	+	14.0591i	−0.434494	+	0.752565i	−0.997254	−	0.0740550i	$-0.976406\pi$
$349$	−8.11701	+	14.0591i	−0.434494	+	0.752565i	0.562761	+	0.826620i	$0.309739\pi$
$350$	−0.897714	−	1.55489i	−0.0479848	−	0.0831122i
$351$	3.68405	−	1.34088i	0.196640	−	0.0715711i
$352$	6.07619	−	2.21155i	0.323862	−	0.117876i
$353$	−9.54534	−	16.5330i	−0.508047	−	0.879963i	−0.999957	−	0.00931693i	$-0.997034\pi$
$353$	−9.54534	−	16.5330i	−0.508047	−	0.879963i	0.491910	−	0.870646i	$-0.336299\pi$
$354$	−4.15557	+	7.19766i	−0.220866	+	0.382551i
$355$	−0.450863	+	2.55697i	−0.0239293	+	0.135710i
$356$	−2.05585	+	1.72507i	−0.108960	+	0.0914283i
$357$	6.33840	+	5.31855i	0.335464	+	0.281487i
$358$	−3.15768	−	17.9081i	−0.166888	−	0.946472i
$359$	34.3168	+	12.4903i	1.81117	+	0.659212i	0.996896	+	0.0787309i	$0.0250868\pi$
$359$	34.3168	+	12.4903i	1.81117	+	0.659212i	0.814274	+	0.580481i	$0.197135\pi$
$360$	1.00000			0.0527046
$361$	−11.0282	−	15.4719i	−0.580430	−	0.814310i
$362$	−24.3594			−1.28030
$363$	28.9529	+	10.5380i	1.51964	+	0.553102i
$364$	1.22230	+	6.93201i	0.0640659	+	0.363336i
$365$	−1.50660	−	1.26419i	−0.0788591	−	0.0661706i
$366$	2.49722	−	2.09542i	0.130532	−	0.109529i
$367$	1.09008	−	6.18213i	0.0569015	−	0.322704i	−0.943049	−	0.332654i	$-0.892056\pi$
$367$	1.09008	−	6.18213i	0.0569015	−	0.322704i	0.999951	+	0.00994937i	$0.00316703\pi$
$368$	−1.71145	+	2.96432i	−0.0892154	+	0.154526i
$369$	−0.223807	−	0.387646i	−0.0116509	−	0.0201800i
$370$	5.71507	−	2.08011i	0.297112	−	0.108140i
$371$	−3.01388	+	1.09696i	−0.156473	+	0.0569515i
$372$	−2.84116	−	4.92103i	−0.147307	−	0.255143i
$373$	2.29133	−	3.96871i	0.118641	−	0.205492i	−0.800588	−	0.599215i	$-0.795480\pi$
$373$	2.29133	−	3.96871i	0.118641	−	0.205492i	0.919229	+	0.393723i	$0.128813\pi$
$374$	5.17456	−	29.3464i	0.267570	−	1.51747i
$375$	−0.766044	+	0.642788i	−0.0395584	+	0.0331934i
$376$	−1.80332	−	1.51317i	−0.0929993	−	0.0780356i
$377$	−1.23291	−	6.99216i	−0.0634979	−	0.360115i
$378$	1.68715	+	0.614072i	0.0867776	+	0.0315845i
$379$	11.9080			0.611675			0.305837	−	0.952084i	$-0.401064\pi$
$379$	11.9080			0.611675			0.305837	+	0.952084i	$0.401064\pi$
$380$	−1.99648	+	3.87480i	−0.102417	+	0.198773i
$381$	12.8818			0.659956
$382$	11.9886	+	4.36351i	0.613392	+	0.223257i
$383$	−4.02635	−	22.8346i	−0.205737	−	1.16679i	−0.896276	−	0.443497i	$-0.853738\pi$
$383$	−4.02635	−	22.8346i	−0.205737	−	1.16679i	0.690539	−	0.723295i	$-0.257373\pi$
$384$	−0.766044	−	0.642788i	−0.0390920	−	0.0328021i
$385$	−8.89339	+	7.46244i	−0.453249	+	0.380321i
$386$	1.56355	−	8.86735i	0.0795827	−	0.451336i
$387$	−4.39893	+	7.61917i	−0.223610	+	0.387304i
$388$	−9.13760	−	15.8268i	−0.463891	−	0.803484i
$389$	−31.1426	+	11.3350i	−1.57899	+	0.574707i	−0.974985	−	0.222270i	$-0.928653\pi$
$389$	−31.1426	+	11.3350i	−1.57899	+	0.574707i	−0.604010	+	0.796977i	$0.706431\pi$
$390$	3.68405	−	1.34088i	0.186549	−	0.0678983i
$391$	7.88718	+	13.6610i	0.398872	+	0.690866i
$392$	1.88822	−	3.27049i	0.0953695	−	0.165185i
$393$	1.12442	−	6.37689i	0.0567193	−	0.321671i
$394$	7.98818	−	6.70288i	0.402439	−	0.337686i
$395$	1.47745	+	1.23973i	0.0743387	+	0.0623776i
$396$	−1.12283	−	6.36791i	−0.0564246	−	0.320000i
$397$	−12.4573	−	4.53407i	−0.625212	−	0.227558i	0.00993416	−	0.999951i	$-0.496838\pi$
$397$	−12.4573	−	4.53407i	−0.625212	−	0.227558i	−0.635146	+	0.772392i	$0.719060\pi$
$398$	−7.21003			−0.361406
$399$	−5.74776	+	5.31139i	−0.287748	+	0.265902i
$400$	1.00000			0.0500000
$401$	−28.5267	−	10.3829i	−1.42455	−	0.518495i	−0.489189	−	0.872178i	$-0.662707\pi$
$401$	−28.5267	−	10.3829i	−1.42455	−	0.518495i	−0.935366	+	0.353682i	$0.884929\pi$
$402$	2.12579	+	12.0559i	0.106025	+	0.601296i
$403$	−17.0655	−	14.3196i	−0.850092	−	0.713312i
$404$	1.17691	−	0.987542i	0.0585533	−	0.0491320i
$405$	0.173648	−	0.984808i	0.00862865	−	0.0489355i
$406$	1.62577	−	2.81591i	0.0806855	−	0.139751i
$407$	−19.6631	−	34.0574i	−0.974662	−	1.68816i
$408$	−4.33056	+	1.57619i	−0.214394	+	0.0780332i
$409$	−14.8225	+	5.39496i	−0.732926	+	0.266763i	−0.681403	−	0.731908i	$-0.738630\pi$
$409$	−14.8225	+	5.39496i	−0.732926	+	0.266763i	−0.0515234	+	0.998672i	$0.516408\pi$
$410$	−0.223807	−	0.387646i	−0.0110531	−	0.0191445i
$411$	−1.11146	+	1.92510i	−0.0548242	+	0.0949582i
$412$	0.731292	−	4.14736i	0.0360282	−	0.204326i
$413$	−11.4310	+	9.59171i	−0.562481	+	0.471977i
$414$	2.62209	+	2.20020i	0.128869	+	0.108134i
$415$	−0.787105	−	4.46389i	−0.0386375	−	0.219124i
$416$	−3.68405	−	1.34088i	−0.180625	−	0.0657423i
$417$	11.6731			0.571632
$418$	26.9161	+	8.36262i	1.31651	+	0.409029i
$419$	21.7360			1.06187			0.530937	−	0.847411i	$-0.321840\pi$
$419$	21.7360			1.06187			0.530937	+	0.847411i	$0.321840\pi$
$420$	1.68715	+	0.614072i	0.0823245	+	0.0299637i
$421$	−2.68505	−	15.2277i	−0.130861	−	0.742151i	−0.977653	−	0.210226i	$-0.932580\pi$
$421$	−2.68505	−	15.2277i	−0.130861	−	0.742151i	0.846791	−	0.531925i	$-0.178531\pi$
$422$	5.52773	+	4.63832i	0.269086	+	0.225790i
$423$	−1.80332	+	1.51317i	−0.0876805	+	0.0735727i
$424$	0.310201	−	1.75924i	0.0150647	−	0.0854360i
$425$	2.30424	−	3.99106i	0.111772	−	0.193595i
$426$	−1.29821	−	2.24856i	−0.0628984	−	0.108943i
$427$	5.49992	−	2.00181i	0.266160	−	0.0968743i
$428$	−14.7741	+	5.37735i	−0.714135	+	0.259924i
$429$	−12.6752	−	21.9541i	−0.611965	−	1.05995i
$430$	−4.39893	+	7.61917i	−0.212135	+	0.367429i
$431$	−4.32724	+	24.5410i	−0.208436	+	1.18210i	0.683505	+	0.729946i	$0.260455\pi$
$431$	−4.32724	+	24.5410i	−0.208436	+	1.18210i	−0.891941	+	0.452153i	$0.850656\pi$
$432$	−0.766044	+	0.642788i	−0.0368563	+	0.0309261i
$433$	−23.3824	−	19.6202i	−1.12369	−	0.942885i	−0.124901	−	0.992169i	$-0.539861\pi$
$433$	−23.3824	−	19.6202i	−1.12369	−	0.942885i	−0.998785	+	0.0492845i	$0.984306\pi$
$434$	−1.77159	−	10.0472i	−0.0850390	−	0.482280i
$435$	−1.70179	−	0.619402i	−0.0815947	−	0.0296980i
$436$	−8.54617			−0.409287
$437$	−13.7603	+	5.76745i	−0.658243	+	0.275894i
$438$	1.96673			0.0939738
$439$	21.8400	+	7.94912i	1.04237	+	0.379391i	0.805777	−	0.592218i	$-0.201748\pi$
$439$	21.8400	+	7.94912i	1.04237	+	0.379391i	0.236591	+	0.971609i	$0.423970\pi$
$440$	−1.12283	−	6.36791i	−0.0535291	−	0.303578i
$441$	−2.89292	−	2.42745i	−0.137758	−	0.115593i
$442$	−13.8405	+	11.6135i	−0.658325	+	0.552400i
$443$	−6.85964	+	38.9030i	−0.325912	+	1.84834i	0.177279	+	0.984161i	$0.443271\pi$
$443$	−6.85964	+	38.9030i	−0.325912	+	1.84834i	−0.503190	+	0.864176i	$0.667841\pi$
$444$	−3.04092	+	5.26703i	−0.144316	+	0.249962i
$445$	1.34186	+	2.32418i	0.0636104	+	0.110176i
$446$	−0.554034	+	0.201652i	−0.0262343	+	0.00954849i
$447$	−21.3969	+	7.78784i	−1.01204	+	0.368352i
$448$	−0.897714	−	1.55489i	−0.0424130	−	0.0734615i
$449$	18.9008	−	32.7372i	0.891984	−	1.54496i	0.0544910	−	0.998514i	$-0.482646\pi$
$449$	18.9008	−	32.7372i	0.891984	−	1.54496i	0.837493	−	0.546448i	$-0.184020\pi$
$450$	0.173648	−	0.984808i	0.00818585	−	0.0464243i
$451$	−2.21720	+	1.86045i	−0.104404	+	0.0876051i
$452$	−1.20760	−	1.01329i	−0.0568006	−	0.0476614i
$453$	3.85079	+	21.8389i	0.180926	+	1.02608i
$454$	23.2978	+	8.47970i	1.09342	+	0.397972i
$455$	7.03894			0.329991
$456$	−0.961285	−	4.25158i	−0.0450163	−	0.199098i
$457$	−22.2025			−1.03859			−0.519296	−	0.854595i	$-0.673806\pi$
$457$	−22.2025			−1.03859			−0.519296	+	0.854595i	$0.673806\pi$
$458$	−22.5942	−	8.22362i	−1.05576	−	0.384265i
$459$	0.800254	+	4.53847i	0.0373527	+	0.211838i
$460$	2.62209	+	2.20020i	0.122256	+	0.102585i
$461$	21.7565	−	18.2559i	1.01330	−	0.850262i	0.0245320	−	0.999699i	$-0.492190\pi$
$461$	21.7565	−	18.2559i	1.01330	−	0.850262i	0.988771	+	0.149437i	$0.0477460\pi$
$462$	2.01597	−	11.4331i	0.0937914	−	0.531917i
$463$	−8.13843	+	14.0962i	−0.378225	+	0.655105i	−0.990804	−	0.135305i	$-0.956799\pi$
$463$	−8.13843	+	14.0962i	−0.378225	+	0.655105i	0.612579	+	0.790409i	$0.290132\pi$
$464$	0.905504	+	1.56838i	0.0420370	+	0.0728102i
$465$	−5.33963	+	1.94347i	−0.247619	+	0.0901260i
$466$	−14.4698	+	5.26657i	−0.670300	+	0.243969i
$467$	−7.42229	−	12.8558i	−0.343463	−	0.594895i	0.641611	−	0.767030i	$-0.278267\pi$
$467$	−7.42229	−	12.8558i	−0.343463	−	0.594895i	−0.985073	+	0.172136i	$0.944933\pi$
$468$	−1.96024	+	3.39524i	−0.0906122	+	0.156945i
$469$	−3.81670	+	21.6456i	−0.176239	+	0.999499i
$470$	−1.80332	+	1.51317i	−0.0831811	+	0.0697972i
$471$	9.47879	+	7.95365i	0.436759	+	0.366485i
$472$	−1.44321	−	8.18488i	−0.0664294	−	0.376740i
$473$	53.4575	+	19.4569i	2.45798	+	0.894631i
$474$	−1.92868			−0.0885871
$475$	3.46925	+	2.63900i	0.159180	+	0.121085i
$476$	−8.27419			−0.379247
$477$	−1.67864	−	0.610976i	−0.0768598	−	0.0279747i
$478$	4.20923	+	23.8717i	0.192526	+	1.09187i
$479$	−24.3790	−	20.4564i	−1.11391	−	0.934677i	−0.115624	−	0.993293i	$-0.536887\pi$
$479$	−24.3790	−	20.4564i	−1.11391	−	0.934677i	−0.998281	+	0.0586156i	$0.981331\pi$
$480$	−0.766044	+	0.642788i	−0.0349650	+	0.0293391i
$481$	−4.14043	+	23.4815i	−0.188787	+	1.07067i
$482$	−8.32064	+	14.4118i	−0.378995	+	0.656439i
$483$	3.07278	+	5.32221i	0.139816	+	0.242169i
$484$	−28.9529	+	10.5380i	−1.31604	+	0.479000i
$485$	−17.1731	+	6.25049i	−0.779789	+	0.283820i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	18.9155	−	32.7627i	0.857145	−	1.48462i	−0.0174958	−	0.999847i	$-0.505569\pi$
$487$	18.9155	−	32.7627i	0.857145	−	1.48462i	0.874641	−	0.484772i	$-0.161097\pi$
$488$	−0.566074	+	3.21036i	−0.0256250	+	0.145326i
$489$	−18.3814	+	15.4238i	−0.831234	+	0.697488i
$490$	−2.89292	−	2.42745i	−0.130689	−	0.109661i
$491$	−0.162249	−	0.920160i	−0.00732220	−	0.0415262i	0.980928	−	0.194373i	$-0.0622671\pi$
$491$	−0.162249	−	0.920160i	−0.00732220	−	0.0415262i	−0.988250	+	0.152846i	$0.951156\pi$
$492$	0.420620	+	0.153093i	0.0189630	+	0.00690198i
$493$	8.34600			0.375885
$494$	−9.24230	−	14.3741i	−0.415831	−	0.646719i
$495$	−6.46615			−0.290632
$496$	5.33963	+	1.94347i	0.239756	+	0.0872642i
$497$	−0.809492	−	4.59086i	−0.0363107	−	0.205928i
$498$	3.47229	+	2.91360i	0.155597	+	0.130561i
$499$	20.9853	−	17.6088i	0.939432	−	0.788277i	−0.0380543	−	0.999276i	$-0.512116\pi$
$499$	20.9853	−	17.6088i	0.939432	−	0.788277i	0.977486	+	0.210999i	$0.0676715\pi$
$500$	0.173648	−	0.984808i	0.00776578	−	0.0440419i
$501$	−4.62336	+	8.00789i	−0.206556	+	0.357766i
$502$	2.54885	+	4.41474i	0.113761	+	0.197039i
$503$	−17.1582	+	6.24507i	−0.765045	+	0.278454i	−0.694923	−	0.719085i	$-0.744561\pi$
$503$	−17.1582	+	6.24507i	−0.765045	+	0.278454i	−0.0701228	+	0.997538i	$0.522339\pi$
$504$	−1.68715	+	0.614072i	−0.0751516	+	0.0273530i
$505$	−0.768171	−	1.33051i	−0.0341832	−	0.0592070i
$506$	11.0665	−	19.1677i	0.491965	−	0.852108i
$507$	−0.411578	+	2.33418i	−0.0182788	+	0.103664i
$508$	−9.86805	+	8.28028i	−0.437824	+	0.367378i
$509$	−7.56769	−	6.35005i	−0.335432	−	0.281461i	0.459477	−	0.888190i	$-0.348037\pi$
$509$	−7.56769	−	6.35005i	−0.335432	−	0.281461i	−0.794909	+	0.606729i	$0.792481\pi$
$510$	0.800254	+	4.53847i	0.0354359	+	0.200967i
$511$	3.31816	+	1.20771i	0.146787	+	0.0534261i
$512$	1.00000			0.0441942
$513$	−4.35391	+	0.208402i	−0.192230	+	0.00920118i
$514$	−19.7020			−0.869017
$515$	−3.95737	−	1.44036i	−0.174382	−	0.0634700i
$516$	−1.52773	−	8.66420i	−0.0672547	−	0.381420i
$517$	11.6606	+	9.78436i	0.512830	+	0.430316i
$518$	−8.36483	+	7.01893i	−0.367530	+	0.308394i
$519$	2.26498	−	12.8453i	0.0994214	−	0.563847i
$520$	−1.96024	+	3.39524i	−0.0859623	+	0.148891i
$521$	1.48451	+	2.57124i	0.0650374	+	0.112648i	0.896711	−	0.442617i	$-0.145950\pi$
$521$	1.48451	+	2.57124i	0.0650374	+	0.112648i	−0.831673	+	0.555265i	$0.812617\pi$
$522$	1.70179	−	0.619402i	0.0744854	−	0.0271105i
$523$	−18.0067	+	6.55390i	−0.787378	+	0.286582i	−0.704246	−	0.709956i	$-0.748715\pi$
$523$	−18.0067	+	6.55390i	−0.787378	+	0.286582i	−0.0831323	+	0.996539i	$0.526492\pi$
$524$	3.23763	+	5.60774i	0.141437	+	0.244975i
$525$	0.897714	−	1.55489i	0.0391794	−	0.0678608i
$526$	2.80642	−	15.9160i	0.122366	−	0.693970i
$527$	20.0603	−	16.8326i	0.873839	−	0.733238i
$528$	4.95336	+	4.15636i	0.215567	+	0.180882i
$529$	−1.95941	−	11.1124i	−0.0851916	−	0.483146i
$530$	−1.67864	−	0.610976i	−0.0729156	−	0.0265391i
$531$	−8.31114			−0.360673
$532$	0.988945	−	7.76335i	0.0428762	−	0.336584i
$533$	1.75487			0.0760117
$534$	−2.52188	−	0.917889i	−0.109132	−	0.0397209i
$535$	2.73015	+	15.4835i	0.118035	+	0.669408i
$536$	−9.37786	−	7.86896i	−0.405062	−	0.339887i
$537$	13.9300	−	11.6887i	0.601125	−	0.504403i
$538$	−0.898994	+	5.09845i	−0.0387584	+	0.219810i
$539$	−12.2095	+	21.1475i	−0.525901	+	0.910887i
$540$	0.500000	+	0.866025i	0.0215166	+	0.0372678i
$541$	33.7814	−	12.2954i	1.45238	−	0.528622i	0.509123	−	0.860694i	$-0.329970\pi$
$541$	33.7814	−	12.2954i	1.45238	−	0.528622i	0.943254	+	0.332072i	$0.107748\pi$
$542$	−25.2783	+	9.20056i	−1.08580	+	0.395198i
$543$	−12.1797	−	21.0958i	−0.522681	−	0.905309i
$544$	2.30424	−	3.99106i	0.0987935	−	0.171115i
$545$	−1.48403	+	8.41634i	−0.0635687	+	0.360516i
$546$	−5.39214	+	4.52455i	−0.230762	+	0.193633i
$547$	−16.6414	−	13.9638i	−0.711533	−	0.597047i	0.213496	−	0.976944i	$-0.431515\pi$
$547$	−16.6414	−	13.9638i	−0.711533	−	0.597047i	−0.925029	+	0.379897i	$0.875960\pi$
$548$	−0.386005	−	2.18914i	−0.0164893	−	0.0935156i
$549$	3.06329	+	1.11495i	0.130738	+	0.0475848i
$550$	−6.46615			−0.275718
$551$	−0.997528	+	7.83072i	−0.0424961	+	0.333600i
$552$	−3.42290			−0.145688
$553$	−3.25397	−	1.18435i	−0.138373	−	0.0503636i
$554$	3.64464	+	20.6698i	0.154846	+	0.878174i
$555$	4.65896	+	3.90934i	0.197762	+	0.165942i
$556$	−8.94208	+	7.50330i	−0.379229	+	0.318211i
$557$	−2.13771	+	12.1236i	−0.0905777	+	0.513692i	0.905435	+	0.424484i	$0.139545\pi$
$557$	−2.13771	+	12.1236i	−0.0905777	+	0.513692i	−0.996013	+	0.0892076i	$0.971567\pi$
$558$	2.84116	−	4.92103i	0.120276	−	0.208324i
$559$	−17.2459	−	29.8708i	−0.729425	−	1.26340i
$560$	−1.68715	+	0.614072i	−0.0712951	+	0.0259493i
$561$	28.0020	−	10.1919i	1.18225	−	0.430302i
$562$	7.98357	+	13.8279i	0.336767	+	0.583297i
$563$	−16.8942	+	29.2617i	−0.712007	+	1.23323i	0.252095	+	0.967702i	$0.418880\pi$
$563$	−16.8942	+	29.2617i	−0.712007	+	1.23323i	−0.964103	+	0.265530i	$0.914453\pi$
$564$	0.408780	−	2.31831i	0.0172127	−	0.0976183i
$565$	−1.20760	+	1.01329i	−0.0508040	+	0.0426296i
$566$	3.48991	+	2.92838i	0.146692	+	0.123089i
$567$	0.311773	+	1.76815i	0.0130932	+	0.0742554i
$568$	2.43983	+	0.888027i	0.102373	+	0.0372608i
$569$	−4.86194			−0.203823			−0.101911	−	0.994793i	$-0.532496\pi$
$569$	−4.86194			−0.203823			−0.101911	+	0.994793i	$0.532496\pi$
$570$	−4.35391	+	0.208402i	−0.182365	+	0.00872900i
$571$	−17.9849			−0.752643			−0.376322	−	0.926489i	$-0.622811\pi$
$571$	−17.9849			−0.752643			−0.376322	+	0.926489i	$0.622811\pi$
$572$	23.8216	+	8.67036i	0.996031	+	0.362526i
$573$	2.21541	+	12.5642i	0.0925501	+	0.524878i
$574$	0.615639	+	0.516583i	0.0256963	+	0.0215617i
$575$	2.62209	−	2.20020i	0.109349	−	0.0917545i
$576$	0.173648	−	0.984808i	0.00723534	−	0.0410337i
$577$	−10.4086	+	18.0282i	−0.433316	+	0.750525i	−0.997156	−	0.0753588i	$-0.975990\pi$
$577$	−10.4086	+	18.0282i	−0.433316	+	0.750525i	0.563841	+	0.825883i	$0.309323\pi$
$578$	−2.11905	−	3.67030i	−0.0881408	−	0.152664i
$579$	8.46113	−	3.07960i	0.351632	−	0.127984i
$580$	1.70179	−	0.619402i	0.0706631	−	0.0257192i
$581$	4.06912	+	7.04792i	0.168815	+	0.292397i
$582$	9.13760	−	15.8268i	0.378766	−	0.656042i
$583$	−2.00580	+	11.3755i	−0.0830719	+	0.471124i
$584$	−1.50660	+	1.26419i	−0.0623436	+	0.0523125i
$585$	3.00326	+	2.52004i	0.124170	+	0.104191i
$586$	−2.57689	−	14.6143i	−0.106450	−	0.603710i
$587$	40.5117	+	14.7450i	1.67210	+	0.608593i	0.992193	−	0.124710i	$-0.0398001\pi$
$587$	40.5117	+	14.7450i	1.67210	+	0.608593i	0.679902	+	0.733303i	$0.262022\pi$
$588$	3.77644			0.155738
$589$	13.3957	+	20.8336i	0.551960	+	0.858435i
$590$	−8.31114			−0.342164
$591$	9.79896	+	3.56653i	0.403075	+	0.146707i
$592$	−1.05610	−	5.98945i	−0.0434055	−	0.246165i
$593$	18.2791	+	15.3380i	0.750632	+	0.629855i	0.935670	−	0.352877i	$-0.114796\pi$
$593$	18.2791	+	15.3380i	0.750632	+	0.629855i	−0.185038	+	0.982731i	$0.559241\pi$
$594$	4.95336	−	4.15636i	0.203239	−	0.170538i
$595$	−1.43680	+	8.14849i	−0.0589030	+	0.334056i
$596$	11.3851	−	19.7195i	0.466350	−	0.807742i
$597$	−3.60502	−	6.24407i	−0.147544	−	0.255553i
$598$	−12.6101	+	4.58971i	−0.515666	+	0.187687i
$599$	−22.1191	+	8.05068i	−0.903761	+	0.328942i	−0.751759	−	0.659438i	$-0.770794\pi$
$599$	−22.1191	+	8.05068i	−0.903761	+	0.328942i	−0.152002	+	0.988380i	$0.548572\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	6.00462	−	10.4003i	0.244933	−	0.424237i	−0.717179	−	0.696889i	$-0.754567\pi$
$601$	6.00462	−	10.4003i	0.244933	−	0.424237i	0.962113	+	0.272651i	$0.0879005\pi$
$602$	2.74293	−	15.5560i	0.111794	−	0.634013i
$603$	−9.37786	+	7.86896i	−0.381896	+	0.320449i
$604$	−16.9877	−	14.2543i	−0.691218	−	0.580001i
$605$	5.35029	+	30.3430i	0.217520	+	1.23362i
$606$	1.44369	+	0.525460i	0.0586459	+	0.0213454i
$607$	−33.9793			−1.37918			−0.689590	−	0.724200i	$-0.742209\pi$
$607$	−33.9793			−1.37918			−0.689590	+	0.724200i	$0.742209\pi$
$608$	3.46925	+	2.63900i	0.140697	+	0.107025i
$609$	3.25154			0.131759
$610$	3.06329	+	1.11495i	0.124029	+	0.0451429i
$611$	−1.60262	−	9.08888i	−0.0648349	−	0.367697i
$612$	−3.53030	−	2.96227i	−0.142704	−	0.119743i
$613$	1.74919	−	1.46775i	0.0706492	−	0.0592817i	−0.606779	−	0.794870i	$-0.707539\pi$
$613$	1.74919	−	1.46775i	0.0706492	−	0.0592817i	0.677428	+	0.735589i	$0.263094\pi$
$614$	0.801489	−	4.54547i	0.0323455	−	0.183440i
$615$	0.223807	−	0.387646i	0.00902478	−	0.0156314i
$616$	5.80475	+	10.0541i	0.233880	+	0.405092i
$617$	3.05613	−	1.11234i	0.123035	−	0.0447812i	−0.279769	−	0.960067i	$-0.590258\pi$
$617$	3.05613	−	1.11234i	0.123035	−	0.0447812i	0.402804	+	0.915286i	$0.368036\pi$
$618$	3.95737	−	1.44036i	0.159189	−	0.0579399i
$619$	6.20744	+	10.7516i	0.249498	+	0.432143i	0.963387	−	0.268116i	$-0.0864011\pi$
$619$	6.20744	+	10.7516i	0.249498	+	0.432143i	−0.713889	+	0.700259i	$0.753068\pi$
$620$	2.84116	−	4.92103i	0.114104	−	0.197633i
$621$	−0.594380	+	3.37090i	−0.0238516	+	0.135269i
$622$	−16.0905	+	13.5015i	−0.645170	+	0.541362i
$623$	−3.69114	−	3.09723i	−0.147882	−	0.124088i
$624$	−0.680785	−	3.86092i	−0.0272532	−	0.154561i
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$	22.7216			0.908137
$627$	6.21581	+	27.4913i	0.248236	+	1.09790i
$628$	−12.3737			−0.493763
$629$	−26.3378	−	9.58617i	−1.05016	−	0.382225i
$630$	0.311773	+	1.76815i	0.0124213	+	0.0704448i
$631$	−29.2711	−	24.5614i	−1.16526	−	0.977773i	−0.165301	−	0.986243i	$-0.552859\pi$
$631$	−29.2711	−	24.5614i	−1.16526	−	0.977773i	−0.999964	+	0.00846990i	$0.997304\pi$
$632$	1.47745	−	1.23973i	0.0587699	−	0.0493138i
$633$	−1.25303	+	7.10631i	−0.0498037	+	0.282451i
$634$	−9.36679	+	16.2238i	−0.372003	+	0.644328i
$635$	6.44091	+	11.1560i	0.255600	+	0.442712i
$636$	1.67864	−	0.610976i	0.0665625	−	0.0242268i
$637$	13.9126	−	5.06377i	0.551237	−	0.200634i
$638$	−5.85513	−	10.1414i	−0.231807	−	0.401501i
$639$	1.29821	−	2.24856i	0.0513563	−	0.0889518i
$640$	0.173648	−	0.984808i	0.00686405	−	0.0389279i
$641$	25.0432	−	21.0137i	0.989146	−	0.829992i	0.00370195	−	0.999993i	$-0.498822\pi$
$641$	25.0432	−	21.0137i	0.989146	−	0.829992i	0.985444	+	0.170001i	$0.0543772\pi$
$642$	−12.0440	−	10.1061i	−0.475338	−	0.398856i
$643$	−6.96922	−	39.5244i	−0.274839	−	1.55869i	−0.739472	−	0.673187i	$-0.764925\pi$
$643$	−6.96922	−	39.5244i	−0.274839	−	1.55869i	0.464633	−	0.885503i	$-0.346186\pi$
$644$	−5.77494	−	2.10191i	−0.227565	−	0.0828267i
$645$	−8.79786			−0.346416
$646$	18.5264	−	7.76511i	0.728911	−	0.305514i
$647$	0.664339			0.0261179			0.0130589	−	0.999915i	$-0.495843\pi$
$647$	0.664339			0.0261179			0.0130589	+	0.999915i	$0.495843\pi$
$648$	−0.939693	−	0.342020i	−0.0369146	−	0.0134358i
$649$	9.33204	+	52.9246i	0.366315	+	2.07747i
$650$	3.00326	+	2.52004i	0.117798	+	0.0988440i
$651$	7.81532	−	6.55784i	0.306307	−	0.257022i
$652$	4.16672	−	23.6306i	0.163181	−	0.925447i
$653$	5.21875	−	9.03914i	0.204226	−	0.353729i	−0.745660	−	0.666326i	$-0.767866\pi$
$653$	5.21875	−	9.03914i	0.204226	−	0.353729i	0.949886	+	0.312597i	$0.101199\pi$
$654$	−4.27309	−	7.40120i	−0.167091	−	0.289410i
$655$	6.08475	−	2.21467i	0.237751	−	0.0865343i
$656$	−0.420620	+	0.153093i	−0.0164225	+	0.00597729i
$657$	0.983363	+	1.70324i	0.0383647	+	0.0664495i
$658$	2.11328	−	3.66031i	0.0823843	−	0.142694i
$659$	−7.63394	+	43.2943i	−0.297376	+	1.68650i	0.360008	+	0.932949i	$0.382774\pi$
$659$	−7.63394	+	43.2943i	−0.297376	+	1.68650i	−0.657384	+	0.753555i	$0.728337\pi$
$660$	4.95336	−	4.15636i	0.192809	−	0.161786i
$661$	−9.06118	−	7.60324i	−0.352439	−	0.295732i	0.449329	−	0.893366i	$-0.351663\pi$
$661$	−9.06118	−	7.60324i	−0.352439	−	0.295732i	−0.801769	+	0.597635i	$0.796107\pi$
$662$	−2.99311	−	16.9748i	−0.116330	−	0.659743i
$663$	−16.9779	−	6.17944i	−0.659366	−	0.239990i
$664$	−4.53276			−0.175905
$665$	−7.47368	−	2.32201i	−0.289817	−	0.0900438i
$666$	−6.08185			−0.235667
$667$	5.82506	+	2.12015i	0.225547	+	0.0820924i
$668$	−1.60568	−	9.10624i	−0.0621255	−	0.352331i
$669$	−0.451653	−	0.378982i	−0.0174619	−	0.0146523i
$670$	−9.37786	+	7.86896i	−0.362298	+	0.304004i
$671$	3.66032	−	20.7587i	0.141305	−	0.801380i
$672$	0.897714	−	1.55489i	0.0346301	−	0.0599810i
$673$	2.11055	+	3.65558i	0.0813557	+	0.140912i	0.903833	−	0.427886i	$-0.140742\pi$
$673$	2.11055	+	3.65558i	0.0813557	+	0.140912i	−0.822477	+	0.568799i	$0.807408\pi$
$674$	−26.5367	+	9.65857i	−1.02216	+	0.372034i
$675$	0.939693	−	0.342020i	0.0361688	−	0.0131644i
$676$	−1.18509	−	2.05264i	−0.0455805	−	0.0789477i
$677$	8.94498	−	15.4932i	0.343783	−	0.595450i	−0.641349	−	0.767250i	$-0.721625\pi$
$677$	8.94498	−	15.4932i	0.343783	−	0.595450i	0.985132	+	0.171799i	$0.0549581\pi$
$678$	0.273740	−	1.55246i	0.0105129	−	0.0596218i
$679$	25.1353	−	21.0910i	0.964604	−	0.809399i
$680$	−3.53030	−	2.96227i	−0.135381	−	0.113598i
$681$	4.30526	+	24.4163i	0.164978	+	0.935636i
$682$	−34.5268	−	12.5667i	−1.32210	−	0.481205i
$683$	14.8779			0.569285			0.284643	−	0.958634i	$-0.408125\pi$
$683$	14.8779			0.569285			0.284643	+	0.958634i	$0.408125\pi$
$684$	3.20133	−	2.95829i	0.122406	−	0.113113i
$685$	−2.22291			−0.0849332
$686$	18.1815	+	6.61751i	0.694172	+	0.252658i
$687$	−4.17524	−	23.6790i	−0.159295	−	0.903410i
$688$	6.73955	+	5.65516i	0.256943	+	0.215601i
$689$	5.36495	−	4.50173i	0.204388	−	0.171502i
$690$	−0.594380	+	3.37090i	−0.0226277	+	0.128328i
$691$	−1.99614	+	3.45742i	−0.0759369	+	0.131527i	−0.901493	−	0.432793i	$-0.857528\pi$
$691$	−1.99614	+	3.45742i	−0.0759369	+	0.131527i	0.825556	+	0.564320i	$0.190861\pi$
$692$	6.52174	+	11.2960i	0.247919	+	0.429409i
$693$	10.9094	−	3.97068i	0.414412	−	0.150834i
$694$	29.4322	−	10.7124i	1.11723	−	0.406638i
$695$	5.83653	+	10.1092i	0.221392	+	0.383463i
$696$	−0.905504	+	1.56838i	−0.0343231	+	0.0594493i
$697$	−0.358206	+	2.03148i	−0.0135680	+	0.0769480i
$698$	12.4360	−	10.4350i	0.470709	−	0.394972i
$699$	−11.7959	−	9.89792i	−0.446161	−	0.374374i
$700$	0.311773	+	1.76815i	0.0117839	+	0.0668298i
$701$	−19.8871	−	7.23830i	−0.751124	−	0.273387i	−0.0620451	−	0.998073i	$-0.519762\pi$
$701$	−19.8871	−	7.23830i	−0.751124	−	0.273387i	−0.689079	+	0.724687i	$0.741984\pi$
$702$	−3.92048			−0.147969
$703$	12.1423	−	23.5659i	0.457954	−	0.888807i
$704$	−6.46615			−0.243702
$705$	−2.21210	−	0.805139i	−0.0833126	−	0.0303233i
$706$	3.31506	+	18.8006i	0.124764	+	0.707572i
$707$	2.11305	+	1.77306i	0.0794694	+	0.0666828i
$708$	6.36671	−	5.34230i	0.239275	−	0.200776i
$709$	6.41923	−	36.4052i	0.241079	−	1.36723i	−0.588346	−	0.808609i	$-0.700221\pi$
$709$	6.41923	−	36.4052i	0.241079	−	1.36723i	0.829425	−	0.558618i	$-0.188668\pi$
$710$	1.29821	−	2.24856i	0.0487209	−	0.0843871i
$711$	−0.964339	−	1.67028i	−0.0361655	−	0.0626405i
$712$	2.52188	−	0.917889i	0.0945114	−	0.0343993i
$713$	18.2770	−	6.65228i	0.684479	−	0.249130i
$714$	−4.13710	−	7.16566i	−0.154827	−	0.268168i
$715$	12.6752	−	21.9541i	0.474026	−	0.821037i
$716$	−3.15768	+	17.9081i	−0.118008	+	0.669257i
$717$	−18.5689	+	15.5812i	−0.693468	+	0.581889i
$718$	−27.9753	−	23.4741i	−1.04403	−	0.876044i
$719$	2.89168	+	16.3995i	0.107842	+	0.611600i	0.990047	+	0.140735i	$0.0449467\pi$
$719$	2.89168	+	16.3995i	0.107842	+	0.611600i	−0.882206	+	0.470864i	$0.843942\pi$
$720$	−0.939693	−	0.342020i	−0.0350203	−	0.0127463i
$721$	7.56116			0.281592
$722$	5.07139	+	18.3107i	0.188738	+	0.681453i
$723$	−16.6413			−0.618896
$724$	22.8903	+	8.33140i	0.850712	+	0.309634i
$725$	−0.314478	−	1.78350i	−0.0116794	−	0.0662374i
$726$	−23.6027	−	19.8050i	−0.875977	−	0.735032i
$727$	38.9244	−	32.6615i	1.44363	−	1.21135i	0.506555	−	0.862207i	$-0.330919\pi$
$727$	38.9244	−	32.6615i	1.44363	−	1.21135i	0.937071	−	0.349139i	$-0.113526\pi$
$728$	1.22230	−	6.93201i	0.0453014	−	0.256917i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	0.983363	+	1.70324i	0.0363959	+	0.0630396i
$731$	38.0996	−	13.8671i	1.40917	−	0.512894i
$732$	−3.06329	+	1.11495i	−0.113223	+	0.0412096i
$733$	14.6797	+	25.4260i	0.542206	+	0.939129i	0.998777	+	0.0494419i	$0.0157443\pi$
$733$	14.6797	+	25.4260i	0.542206	+	0.939129i	−0.456571	+	0.889687i	$0.650922\pi$
$734$	−3.13875	+	5.43647i	−0.115853	+	0.200664i
$735$	0.655772	−	3.71907i	0.0241885	−	0.137180i
$736$	2.62209	−	2.20020i	0.0966516	−	0.0811003i
$737$	60.6386	+	50.8818i	2.23365	+	1.87426i
$738$	0.0777275	+	0.440814i	0.00286119	+	0.0162266i
$739$	35.6609	+	12.9795i	1.31181	+	0.477459i	0.900824	−	0.434184i	$-0.142963\pi$
$739$	35.6609	+	12.9795i	1.31181	+	0.477459i	0.410983	+	0.911643i	$0.365185\pi$
$740$	−6.08185			−0.223573
$741$	7.82715	−	15.1911i	0.287537	−	0.558059i
$742$	3.20731			0.117744
$743$	−44.9002	−	16.3423i	−1.64723	−	0.599542i	−0.658946	−	0.752190i	$-0.728998\pi$
$743$	−44.9002	−	16.3423i	−1.64723	−	0.599542i	−0.988281	+	0.152648i	$0.951220\pi$
$744$	0.986723	+	5.59598i	0.0361750	+	0.205159i
$745$	−17.4429	−	14.6364i	−0.639059	−	0.536234i
$746$	−3.51053	+	2.94568i	−0.128530	+	0.107849i
$747$	−0.787105	+	4.46389i	−0.0287987	+	0.163325i
$748$	−14.8996	+	25.8068i	−0.544782	+	0.943590i
$749$	−14.1141	−	24.4464i	−0.515719	−	0.893252i
$750$	0.939693	−	0.342020i	0.0343127	−	0.0124888i
$751$	43.8009	−	15.9422i	1.59832	−	0.581740i	0.619236	−	0.785205i	$-0.287443\pi$
$751$	43.8009	−	15.9422i	1.59832	−	0.581740i	0.979082	+	0.203465i	$0.0652204\pi$
$752$	1.17704	+	2.03868i	0.0429221	+	0.0743432i
$753$	−2.54885	+	4.41474i	−0.0928852	+	0.160882i
$754$	−1.23291	+	6.99216i	−0.0448998	+	0.254640i
$755$	−16.9877	+	14.2543i	−0.618244	+	0.518768i
$756$	−1.37538	−	1.15408i	−0.0500220	−	0.0419734i
$757$	−0.341977	−	1.93945i	−0.0124294	−	0.0704905i	0.977962	−	0.208782i	$-0.0669500\pi$
$757$	−0.341977	−	1.93945i	−0.0124294	−	0.0704905i	−0.990392	+	0.138292i	$0.955839\pi$
$758$	−11.1899	−	4.07279i	−0.406435	−	0.147930i
$759$	22.1330			0.803376
$760$	3.20133	−	2.95829i	0.116125	−	0.107308i
$761$	7.61690			0.276112			0.138056	−	0.990424i	$-0.455915\pi$
$761$	7.61690			0.276112			0.138056	+	0.990424i	$0.455915\pi$
$762$	−12.1050	−	4.40584i	−0.438516	−	0.159607i
$763$	−2.66446	−	15.1109i	−0.0964600	−	0.547052i
$764$	−9.77323	−	8.20071i	−0.353583	−	0.296691i
$765$	−3.53030	+	2.96227i	−0.127638	+	0.107101i
$766$	−4.02635	+	22.8346i	−0.145478	+	0.825047i
$767$	16.2918	−	28.2183i	0.588265	−	1.01890i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	1.20283	−	0.437794i	0.0433751	−	0.0157872i	−0.320242	−	0.947336i	$-0.603764\pi$
$769$	1.20283	−	0.437794i	0.0433751	−	0.0157872i	0.363617	+	0.931549i	$0.381542\pi$
$770$	10.9094	−	3.97068i	0.393146	−	0.143094i
$771$	−9.85099	−	17.0624i	−0.354775	−	0.614488i
$772$	−4.50207	+	7.79782i	−0.162033	+	0.280650i
$773$	−0.975294	+	5.53116i	−0.0350789	+	0.198942i	−0.997311	−	0.0732890i	$-0.976650\pi$
$773$	−0.975294	+	5.53116i	−0.0350789	+	0.198942i	0.962232	+	0.272231i	$0.0877616\pi$
$774$	6.73955	−	5.65516i	0.242248	−	0.203270i
$775$	−4.35290	−	3.65252i	−0.156361	−	0.131202i
$776$	3.17346	+	17.9976i	0.113920	+	0.646075i
$777$	−10.2610	−	3.73469i	−0.368111	−	0.133981i
$778$	33.1413			1.18817
$779$	−1.86325	−	0.578897i	−0.0667578	−	0.0207411i
$780$	−3.92048			−0.140376
$781$	−15.7763	−	5.74211i	−0.564521	−	0.205469i
$782$	−2.73919	−	15.5347i	−0.0979532	−	0.555520i
$783$	1.38731	+	1.16409i	0.0495785	+	0.0416013i
$784$	−2.89292	+	2.42745i	−0.103319	+	0.0866946i
$785$	−2.14867	+	12.1857i	−0.0766892	+	0.434926i
$786$	−3.23763	+	5.60774i	−0.115482	+	0.200021i
$787$	19.4402	+	33.6714i	0.692967	+	1.20025i	0.970861	+	0.239643i	$0.0770304\pi$
$787$	19.4402	+	33.6714i	0.692967	+	1.20025i	−0.277894	+	0.960612i	$0.589636\pi$
$788$	−9.79896	+	3.56653i	−0.349073	+	0.127052i
$789$	15.1869	−	5.52756i	0.540666	−	0.196786i
$790$	−0.964339	−	1.67028i	−0.0343096	−	0.0594260i
$791$	1.41516	−	2.45113i	0.0503174	−	0.0871523i
$792$	−1.12283	+	6.36791i	−0.0398982	+	0.226274i
$793$	−9.79031	+	8.21504i	−0.347664	+	0.291725i
$794$	10.1552	+	8.52126i	0.360396	+	0.302408i
$795$	−0.310201	−	1.75924i	−0.0110017	−	0.0623937i
$796$	6.77522	+	2.46598i	0.240141	+	0.0874042i
$797$	−21.4482			−0.759734			−0.379867	−	0.925041i	$-0.624030\pi$
$797$	−21.4482			−0.759734			−0.379867	+	0.925041i	$0.624030\pi$
$798$	7.21773	−	3.02522i	0.255505	−	0.107092i
$799$	10.8487			0.383799
$800$	−0.939693	−	0.342020i	−0.0332232	−	0.0120922i
$801$	−0.466024	−	2.64295i	−0.0164662	−	0.0933842i
$802$	23.2552	+	19.5134i	0.821168	+	0.689042i
$803$	9.74190	−	8.17443i	0.343784	−	0.288469i
$804$	2.12579	−	12.0559i	0.0749707	−	0.425180i
$805$	−3.07278	+	5.32221i	−0.108301	+	0.187583i
$806$	11.1387	+	19.2928i	0.392344	+	0.679560i
$807$	−4.86488	+	1.77067i	−0.171252	+	0.0623306i
$808$	−1.44369	+	0.525460i	−0.0507888	+	0.0184856i
$809$	−3.97207	−	6.87982i	−0.139650	−	0.241882i	0.787714	−	0.616041i	$-0.211265\pi$
$809$	−3.97207	−	6.87982i	−0.139650	−	0.241882i	−0.927364	+	0.374160i	$0.877931\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	0.856126	−	4.85533i	0.0300626	−	0.170494i	−0.966080	−	0.258243i	$-0.916856\pi$
$811$	0.856126	−	4.85533i	0.0300626	−	0.170494i	0.996143	+	0.0877495i	$0.0279675\pi$
$812$	−2.49082	+	2.09005i	−0.0874107	+	0.0733463i
$813$	−20.6071	−	17.2914i	−0.722722	−	0.606436i
$814$	6.82891	+	38.7287i	0.239353	+	1.35744i
$815$	−22.5481	−	8.20683i	−0.789825	−	0.287473i
$816$	4.60848			0.161329
$817$	8.45726	+	37.4048i	0.295882	+	1.30863i
$818$	15.7738			0.551518
$819$	−6.61444	−	2.40746i	−0.231127	−	0.0841235i
$820$	0.0777275	+	0.440814i	0.00271436	+	0.0153939i
$821$	−9.07214	−	7.61243i	−0.316620	−	0.265675i	0.470602	−	0.882346i	$-0.344037\pi$
$821$	−9.07214	−	7.61243i	−0.316620	−	0.265675i	−0.787222	+	0.616670i	$0.788481\pi$
$822$	1.70285	−	1.42886i	0.0593938	−	0.0498373i
$823$	2.30337	−	13.0631i	0.0802904	−	0.455350i	−0.917983	−	0.396619i	$-0.870183\pi$
$823$	2.30337	−	13.0631i	0.0802904	−	0.455350i	0.998274	−	0.0587309i	$-0.0187054\pi$
$824$	−2.10567	+	3.64713i	−0.0733545	+	0.127054i
$825$	−3.23307	−	5.59985i	−0.112561	−	0.194962i
$826$	14.0221	−	5.10364i	0.487893	−	0.177578i
$827$	4.53531	−	1.65072i	0.157708	−	0.0574011i	−0.261960	−	0.965079i	$-0.584369\pi$
$827$	4.53531	−	1.65072i	0.157708	−	0.0574011i	0.419668	+	0.907678i	$0.362147\pi$
$828$	−1.71145	−	2.96432i	−0.0594769	−	0.103017i
$829$	−16.5626	+	28.6873i	−0.575243	+	0.996351i	0.420772	+	0.907166i	$0.361759\pi$
$829$	−16.5626	+	28.6873i	−0.575243	+	0.996351i	−0.996015	+	0.0891841i	$0.971574\pi$
$830$	−0.787105	+	4.46389i	−0.0273208	+	0.154944i
$831$	−16.0782	+	13.4912i	−0.557747	+	0.468006i
$832$	3.00326	+	2.52004i	0.104119	+	0.0873666i
$833$	3.02211	+	17.1392i	0.104710	+	0.593840i
$834$	−10.9691	−	3.99242i	−0.379829	−	0.138246i
$835$	−9.24672			−0.319996
$836$	−22.4327	−	17.0641i	−0.775851	−	0.590176i
$837$	5.68231			0.196409
$838$	−20.4252	−	7.43415i	−0.705576	−	0.256809i
$839$	3.72618	+	21.1322i	0.128642	+	0.729566i	0.979078	+	0.203486i	$0.0652273\pi$
$839$	3.72618	+	21.1322i	0.128642	+	0.729566i	−0.850436	+	0.526079i	$0.823662\pi$
$840$	−1.37538	−	1.15408i	−0.0474550	−	0.0398195i
$841$	−19.7029	+	16.5327i	−0.679409	+	0.570092i
$842$	−2.68505	+	15.2277i	−0.0925329	+	0.524780i
$843$	−7.98357	+	13.8279i	−0.274969	+	0.476260i
$844$	−3.60797	−	6.24919i	−0.124191	−	0.215106i
$845$	−2.22725	+	0.810651i	−0.0766196	+	0.0278872i
$846$	2.21210	−	0.805139i	0.0760537	−	0.0276813i
$847$	−27.6595	−	47.9077i	−0.950393	−	1.64613i
$848$	−0.893187	+	1.54705i	−0.0306722	+	0.0531258i
$849$	−0.791098	+	4.48654i	−0.0271504	+	0.153978i
$850$	−3.53030	+	2.96227i	−0.121088	+	0.101605i
$851$	−15.9472	−	13.3813i	−0.546661	−	0.458703i
$852$	0.450863	+	2.55697i	0.0154463	+	0.0876004i
$853$	−6.79118	−	2.47179i	−0.232526	−	0.0846324i	0.223129	−	0.974789i	$-0.428373\pi$
$853$	−6.79118	−	2.47179i	−0.232526	−	0.0846324i	−0.455655	+	0.890156i	$0.650595\pi$
$854$	−5.85289			−0.200282
$855$	−2.35744	−	3.66640i	−0.0806227	−	0.125388i
$856$	15.7223			0.537378
$857$	32.6850	+	11.8964i	1.11650	+	0.406372i	0.833373	−	0.552712i	$-0.186407\pi$
$857$	32.6850	+	11.8964i	1.11650	+	0.406372i	0.283124	+	0.959083i	$0.408629\pi$
$858$	4.40205	+	24.9653i	0.150284	+	0.852301i
$859$	−2.25587	−	1.89290i	−0.0769693	−	0.0645849i	0.603491	−	0.797370i	$-0.293776\pi$
$859$	−2.25587	−	1.89290i	−0.0769693	−	0.0645849i	−0.680461	+	0.732785i	$0.738220\pi$
$860$	6.73955	−	5.65516i	0.229817	−	0.192839i
$861$	−0.139554	+	0.791450i	−0.00475599	+	0.0269726i
$862$	12.4598	−	21.5810i	0.424382	−	0.735052i
$863$	16.5593	+	28.6816i	0.563686	+	0.976332i	0.997171	+	0.0751716i	$0.0239504\pi$
$863$	16.5593	+	28.6816i	0.563686	+	0.976332i	−0.433485	+	0.901161i	$0.642716\pi$
$864$	0.939693	−	0.342020i	0.0319690	−	0.0116358i
$865$	12.2569	−	4.46113i	0.416746	−	0.151683i
$866$	15.2618	+	26.4342i	0.518616	+	0.898270i
$867$	2.11905	−	3.67030i	0.0719667	−	0.124650i
$868$	−1.77159	+	10.0472i	−0.0601317	+	0.341024i
$869$	−9.55343	+	8.01628i	−0.324078	+	0.271934i
$870$	1.38731	+	1.16409i	0.0470343	+	0.0394665i
$871$	−8.33411	−	47.2651i	−0.282391	−	1.60152i
$872$	8.03077	+	2.92296i	0.271956	+	0.0989840i
$873$	18.2752			0.618522
$874$	14.9030	−	0.713339i	0.504101	−	0.0241290i
$875$	1.79543			0.0606965
$876$	−1.84812	−	0.672660i	−0.0624421	−	0.0227271i
$877$	5.42424	+	30.7624i	0.183164	+	1.03877i	0.928292	+	0.371852i	$0.121277\pi$
$877$	5.42424	+	30.7624i	0.183164	+	1.03877i	−0.745128	+	0.666921i	$0.767612\pi$
$878$	−17.8042	−	14.9395i	−0.600861	−	0.504183i
$879$	11.3679	−	9.53879i	0.383429	−	0.321736i
$880$	−1.12283	+	6.36791i	−0.0378508	+	0.214662i
$881$	−6.98851	+	12.1045i	−0.235449	+	0.407809i	−0.959403	−	0.282039i	$-0.908989\pi$
$881$	−6.98851	+	12.1045i	−0.235449	+	0.407809i	0.723954	+	0.689848i	$0.242323\pi$
$882$	1.88822	+	3.27049i	0.0635797	+	0.110123i
$883$	−0.315010	+	0.114654i	−0.0106009	+	0.00385843i	−0.347315	−	0.937748i	$-0.612907\pi$
$883$	−0.315010	+	0.114654i	−0.0106009	+	0.00385843i	0.336714	+	0.941607i	$0.390684\pi$
$884$	16.9779	−	6.17944i	0.571028	−	0.207837i
$885$	−4.15557	−	7.19766i	−0.139688	−	0.241947i
$886$	19.7516	−	34.2107i	0.663567	−	1.14933i
$887$	−6.19300	+	35.1223i	−0.207941	+	1.17929i	0.684804	+	0.728727i	$0.259888\pi$
$887$	−6.19300	+	35.1223i	−0.207941	+	1.17929i	−0.892745	+	0.450563i	$0.851223\pi$
$888$	4.65896	−	3.90934i	0.156345	−	0.131189i
$889$	−17.7174	−	14.8666i	−0.594221	−	0.498611i
$890$	−0.466024	−	2.64295i	−0.0156212	−	0.0885921i
$891$	6.07619	+	2.21155i	0.203560	+	0.0740898i
$892$	0.589591			0.0197410
$893$	−1.29665	+	10.1789i	−0.0433908	+	0.340624i
$894$	22.7701			0.761547
$895$	17.0877	+	6.21941i	0.571179	+	0.207892i
$896$	0.311773	+	1.76815i	0.0104156	+	0.0590698i
$897$	−10.2799	−	8.62583i	−0.343235	−	0.288008i
$898$	−28.9577	+	24.2984i	−0.966331	+	0.810848i
$899$	1.78696	−	10.1344i	0.0595986	−	0.338000i
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	4.11624	+	7.12953i	0.137132	+	0.237519i
$902$	2.71979	−	0.989924i	0.0905592	−	0.0329609i
$903$	14.8433	−	5.40253i	0.493955	−	0.179785i
$904$	0.788204	+	1.36521i	0.0262153	+	0.0454062i
$905$	12.1797	−	21.0958i	0.404867	−	0.701250i
$906$	3.85079	−	21.8389i	0.127934	−	0.725549i
$907$	16.5706	−	13.9044i	0.550218	−	0.461688i	−0.324797	−	0.945784i	$-0.605296\pi$
$907$	16.5706	−	13.9044i	0.550218	−	0.461688i	0.875015	+	0.484096i	$0.160851\pi$
$908$	−18.9925	−	15.9366i	−0.630289	−	0.528875i
$909$	0.266783	+	1.51300i	0.00884863	+	0.0501831i
$910$	−6.61444	−	2.40746i	−0.219267	−	0.0798065i
$911$	18.6006			0.616265			0.308133	−	0.951343i	$-0.400296\pi$
$911$	18.6006			0.616265			0.308133	+	0.951343i	$0.400296\pi$
$912$	−0.550813	+	4.32396i	−0.0182392	+	0.143181i
$913$	29.3095			0.970002
$914$	20.8636	+	7.59372i	0.690106	+	0.251178i
$915$	0.566074	+	3.21036i	0.0187138	+	0.106131i
$916$	18.4190	+	15.4554i	0.608580	+	0.510659i
$917$	−8.90593	+	7.47296i	−0.294100	+	0.246779i
$918$	0.800254	−	4.53847i	0.0264123	−	0.149792i
$919$	13.3342	−	23.0954i	0.439853	−	0.761848i	−0.557825	−	0.829959i	$-0.688364\pi$
$919$	13.3342	−	23.0954i	0.439853	−	0.761848i	0.997678	+	0.0681108i	$0.0216971\pi$
$920$	−1.71145	−	2.96432i	−0.0564248	−	0.0977306i
$921$	4.33724	−	1.57863i	0.142917	−	0.0520175i
$922$	−26.6884	+	9.71377i	−0.878934	+	0.319906i
$923$	5.08960	+	8.81545i	0.167526	+	0.290164i
$924$	−5.80475	+	10.0541i	−0.190962	+	0.330756i
$925$	−1.05610	+	5.98945i	−0.0347244	+	0.196932i
$926$	12.4688	−	10.4626i	0.409750	−	0.343821i
$927$	3.22608	+	2.70700i	0.105958	+	0.0889095i
$928$	−0.314478	−	1.78350i	−0.0103233	−	0.0585461i
$929$	19.7404	+	7.18492i	0.647662	+	0.235730i	0.644900	−	0.764267i	$-0.276899\pi$
$929$	19.7404	+	7.18492i	0.647662	+	0.235730i	0.00276136	+	0.999996i	$0.499121\pi$
$930$	5.68231			0.186330
$931$	−16.4423	+	0.787018i	−0.538874	+	0.0257935i
$932$	15.3984			0.504392
$933$	−19.7379	−	7.18402i	−0.646190	−	0.235194i
$934$	2.57773	+	14.6191i	0.0843460	+	0.478350i
$935$	22.8275	+	19.1545i	0.746538	+	0.626419i
$936$	3.00326	−	2.52004i	0.0981648	−	0.0823700i
$937$	5.16194	−	29.2748i	0.168633	−	0.956367i	−0.776605	−	0.629987i	$-0.783060\pi$
$937$	5.16194	−	29.2748i	0.168633	−	0.956367i	0.945239	−	0.326380i	$-0.105829\pi$
$938$	10.9897	−	19.0348i	0.358828	−	0.621508i
$939$	11.3608	+	19.6775i	0.370745	+	0.642150i
$940$	2.21210	−	0.805139i	0.0721508	−	0.0262608i
$941$	−29.8770	+	10.8743i	−0.973961	+	0.354493i	−0.779490	−	0.626415i	$-0.784521\pi$
$941$	−29.8770	+	10.8743i	−0.973961	+	0.354493i	−0.194472	+	0.980908i	$0.562299\pi$
$942$	−6.18684	−	10.7159i	−0.201578	−	0.349144i
$943$	−0.766069	+	1.32687i	−0.0249467	+	0.0432089i
$944$	−1.44321	+	8.18488i	−0.0469726	+	0.266395i
$945$	−1.37538	+	1.15408i	−0.0447410	+	0.0375422i
$946$	−43.5790	−	36.5671i	−1.41687	−	1.18890i
$947$	3.61275	+	20.4889i	0.117399	+	0.665801i	0.985535	+	0.169474i	$0.0542069\pi$
$947$	3.61275	+	20.4889i	0.117399	+	0.665801i	−0.868136	+	0.496326i	$0.834682\pi$
$948$	1.81236	+	0.659647i	0.0588629	+	0.0214243i
$949$	−7.71052			−0.250294
$950$	−2.35744	−	3.66640i	−0.0764854	−	0.118954i
$951$	−18.7336			−0.607478
$952$	7.77520	+	2.82994i	0.251996	+	0.0917189i
$953$	−1.02390	−	5.80683i	−0.0331674	−	0.188102i	0.963723	−	0.266905i	$-0.0860011\pi$
$953$	−1.02390	−	5.80683i	−0.0331674	−	0.188102i	−0.996890	+	0.0788036i	$0.974890\pi$
$954$	1.36844	+	1.14826i	0.0443050	+	0.0371763i
$955$	−9.77323	+	8.20071i	−0.316254	+	0.265369i
$956$	4.20923	−	23.8717i	0.136136	−	0.772067i
$957$	5.85513	−	10.1414i	0.189269	−	0.327824i
$958$	15.9123	+	27.5609i	0.514102	+	0.890451i
$959$	3.75039	−	1.36503i	0.121106	−	0.0440791i
$960$	0.939693	−	0.342020i	0.0303284	−	0.0110387i
$961$	−0.644335	−	1.11602i	−0.0207850	−	0.0360007i
$962$	11.9219	−	20.6493i	0.384377	−	0.665761i
$963$	2.73015	−	15.4835i	0.0879779	−	0.498947i
$964$	12.7480	−	10.6968i	0.410584	−	0.344521i
$965$	6.89757	+	5.78775i	0.222041	+	0.186314i
$966$	−1.06717	−	6.05220i	−0.0343355	−	0.194726i
$967$	−53.2875	−	19.3951i	−1.71361	−	0.623704i	−0.716356	−	0.697735i	$-0.754191\pi$
$967$	−53.2875	−	19.3951i	−1.71361	−	0.623704i	−0.997256	+	0.0740317i	$0.976413\pi$
$968$	30.8111			0.990306
$969$	15.9880	+	12.1618i	0.513608	+	0.390692i
$970$	18.2752			0.586781
$971$	−58.3046	−	21.2211i	−1.87108	−	0.681019i	−0.967653	−	0.252286i	$-0.918817\pi$
$971$	−58.3046	−	21.2211i	−1.87108	−	0.681019i	−0.903432	−	0.428732i	$-0.858960\pi$
$972$	−0.173648	−	0.984808i	−0.00556977	−	0.0315877i
$973$	−16.0549	−	13.4716i	−0.514695	−	0.431881i
$974$	−28.9803	+	24.3174i	−0.928588	+	0.779178i
$975$	−0.680785	+	3.86092i	−0.0218026	+	0.123648i
$976$	1.62994	−	2.82315i	0.0521732	−	0.0903667i
$977$	17.0758	+	29.5762i	0.546304	+	0.946226i	0.998524	+	0.0543197i	$0.0172990\pi$
$977$	17.0758	+	29.5762i	0.546304	+	0.946226i	−0.452220	+	0.891907i	$0.649368\pi$
$978$	22.5481	−	8.20683i	0.721008	−	0.262426i
$979$	−16.3068	+	5.93520i	−0.521169	+	0.189690i
$980$	1.88822	+	3.27049i	0.0603170	+	0.104472i
$981$	4.27309	−	7.40120i	0.136429	−	0.236302i
$982$	−0.162249	+	0.920160i	−0.00517757	+	0.0293635i
$983$	−1.13750	+	0.954479i	−0.0362807	+	0.0304431i	−0.660748	−	0.750608i	$-0.729761\pi$
$983$	−1.13750	+	0.954479i	−0.0362807	+	0.0304431i	0.624467	+	0.781051i	$0.285316\pi$
$984$	−0.342893	−	0.287721i	−0.0109310	−	0.00917222i
$985$	1.81077	+	10.2694i	0.0576961	+	0.327211i
$986$	−7.84267	−	2.85450i	−0.249762	−	0.0909058i
$987$	4.22656			0.134533
$988$	3.76870	+	16.6682i	0.119898	+	0.530288i
$989$	30.1142			0.957575
$990$	6.07619	+	2.21155i	0.193114	+	0.0702878i
$991$	1.69412	+	9.60784i	0.0538155	+	0.305203i	0.999820	−	0.0189492i	$-0.00603209\pi$
$991$	1.69412	+	9.60784i	0.0538155	+	0.305203i	−0.946005	+	0.324152i	$0.894921\pi$
$992$	−4.35290	−	3.65252i	−0.138205	−	0.115968i
$993$	13.2040	−	11.0795i	0.419017	−	0.351597i
$994$	−0.809492	+	4.59086i	−0.0256755	+	0.145613i
$995$	3.60502	−	6.24407i	0.114287	−	0.197950i
$996$	−2.26638	−	3.92548i	−0.0718129	−	0.124384i
$997$	10.5505	−	3.84005i	0.334136	−	0.121616i	−0.169503	−	0.985530i	$-0.554216\pi$
$997$	10.5505	−	3.84005i	0.334136	−	0.121616i	0.503639	+	0.863914i	$0.331994\pi$
$998$	−25.7423	+	9.36943i	−0.814859	+	0.296584i
$999$	−3.04092	−	5.26703i	−0.0962106	−	0.166642i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.u.j.61.1	✓	12
19.5	even	9	inner	570.2.u.j.271.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.u.j.61.1	✓	12	1.1	even	1	trivial
570.2.u.j.271.1	yes	12	19.5	even	9	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(-0.897714 + 1.55489i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(-0.897714 + 1.55489i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-0.939693 + 0.342020i) q^{10} +(3.23307 + 5.59985i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.680785 - 3.86092i) q^{13} +(1.37538 - 1.15408i) q^{14} +(-0.766044 - 0.642788i) q^{15} +(0.173648 + 0.984808i) q^{16} +(4.33056 + 1.57619i) q^{17} +1.00000 q^{18} +(-1.99648 + 3.87480i) q^{19} +1.00000 q^{20} +(1.68715 + 0.614072i) q^{21} +(-1.12283 - 6.36791i) q^{22} +(2.62209 + 2.20020i) q^{23} +(-0.766044 + 0.642788i) q^{24} +(0.173648 - 0.984808i) q^{25} +(-1.96024 + 3.39524i) q^{26} +(0.500000 + 0.866025i) q^{27} +(-1.68715 + 0.614072i) q^{28} +(1.70179 - 0.619402i) q^{29} +(0.500000 + 0.866025i) q^{30} +(2.84116 - 4.92103i) q^{31} +(0.173648 - 0.984808i) q^{32} +(4.95336 - 4.15636i) q^{33} +(-3.53030 - 2.96227i) q^{34} +(0.311773 + 1.76815i) q^{35} +(-0.939693 - 0.342020i) q^{36} -6.08185 q^{37} +(3.20133 - 2.95829i) q^{38} -3.92048 q^{39} +(-0.939693 - 0.342020i) q^{40} +(0.0777275 + 0.440814i) q^{41} +(-1.37538 - 1.15408i) q^{42} +(6.73955 - 5.65516i) q^{43} +(-1.12283 + 6.36791i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-1.71145 - 2.96432i) q^{46} +(2.21210 - 0.805139i) q^{47} +(0.939693 - 0.342020i) q^{48} +(1.88822 + 3.27049i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.800254 - 4.53847i) q^{51} +(3.00326 - 2.52004i) q^{52} +(1.36844 + 1.14826i) q^{53} +(-0.173648 - 0.984808i) q^{54} +(6.07619 + 2.21155i) q^{55} +1.79543 q^{56} +(4.16262 + 1.29329i) q^{57} -1.81101 q^{58} +(7.80992 + 2.84258i) q^{59} +(-0.173648 - 0.984808i) q^{60} +(-2.49722 - 2.09542i) q^{61} +(-4.35290 + 3.65252i) q^{62} +(0.311773 - 1.76815i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.96024 - 3.39524i) q^{65} +(-6.07619 + 2.21155i) q^{66} +(11.5036 - 4.18698i) q^{67} +(2.30424 + 3.99106i) q^{68} +(1.71145 - 2.96432i) q^{69} +(0.311773 - 1.76815i) q^{70} +(-1.98897 + 1.66894i) q^{71} +(0.766044 + 0.642788i) q^{72} +(-0.341519 - 1.93685i) q^{73} +(5.71507 + 2.08011i) q^{74} -1.00000 q^{75} +(-4.02006 + 1.68496i) q^{76} -11.6095 q^{77} +(3.68405 + 1.34088i) q^{78} +(0.334911 + 1.89938i) q^{79} +(0.766044 + 0.642788i) q^{80} +(0.766044 - 0.642788i) q^{81} +(0.0777275 - 0.440814i) q^{82} +(2.26638 - 3.92548i) q^{83} +(0.897714 + 1.55489i) q^{84} +(4.33056 - 1.57619i) q^{85} +(-8.26729 + 3.00905i) q^{86} +(-0.905504 - 1.56838i) q^{87} +(3.23307 - 5.59985i) q^{88} +(-0.466024 + 2.64295i) q^{89} +(0.766044 - 0.642788i) q^{90} +(5.39214 + 4.52455i) q^{91} +(0.594380 + 3.37090i) q^{92} +(-5.33963 - 1.94347i) q^{93} -2.35407 q^{94} +(0.961285 + 4.25158i) q^{95} -1.00000 q^{96} +(-17.1731 - 6.25049i) q^{97} +(-0.655772 - 3.71907i) q^{98} +(-4.95336 - 4.15636i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q + 3 * q^7 - 6 * q^8	\( 12 q + 3 q^{7} - 6 q^{8} + 3 q^{11} + 6 q^{12} + 9 q^{13} + 9 q^{14} + 9 q^{17} + 12 q^{18} + 9 q^{19} + 12 q^{20} + 9 q^{21} - 6 q^{22} + 12 q^{23} + 9 q^{26} + 6 q^{27} - 9 q^{28} + 27 q^{29} + 6 q^{30} + 12 q^{31} - 3 q^{33} - 9 q^{34} - 42 q^{37} + 18 q^{38} + 18 q^{39} - 27 q^{41} - 9 q^{42} - 27 q^{43} - 6 q^{44} - 6 q^{45} + 9 q^{46} - 6 q^{47} + 3 q^{49} - 6 q^{50} + 9 q^{52} - 18 q^{53} + 3 q^{55} - 6 q^{56} + 6 q^{58} - 15 q^{59} - 9 q^{61} - 18 q^{62} - 6 q^{64} + 9 q^{65} - 3 q^{66} + 42 q^{67} + 6 q^{68} - 9 q^{69} + 24 q^{71} + 15 q^{73} + 18 q^{74} - 12 q^{75} + 3 q^{76} - 6 q^{77} + 18 q^{78} - 57 q^{79} - 27 q^{82} + 21 q^{83} - 3 q^{84} + 9 q^{85} + 9 q^{86} + 3 q^{87} + 3 q^{88} - 57 q^{89} + 21 q^{91} - 15 q^{92} - 9 q^{93} - 24 q^{94} - 18 q^{95} - 12 q^{96} - 6 q^{97} - 15 q^{98} + 3 q^{99}+O(q^{100}) \) 12 * q + 3 * q^7 - 6 * q^8 + 3 * q^11 + 6 * q^12 + 9 * q^13 + 9 * q^14 + 9 * q^17 + 12 * q^18 + 9 * q^19 + 12 * q^20 + 9 * q^21 - 6 * q^22 + 12 * q^23 + 9 * q^26 + 6 * q^27 - 9 * q^28 + 27 * q^29 + 6 * q^30 + 12 * q^31 - 3 * q^33 - 9 * q^34 - 42 * q^37 + 18 * q^38 + 18 * q^39 - 27 * q^41 - 9 * q^42 - 27 * q^43 - 6 * q^44 - 6 * q^45 + 9 * q^46 - 6 * q^47 + 3 * q^49 - 6 * q^50 + 9 * q^52 - 18 * q^53 + 3 * q^55 - 6 * q^56 + 6 * q^58 - 15 * q^59 - 9 * q^61 - 18 * q^62 - 6 * q^64 + 9 * q^65 - 3 * q^66 + 42 * q^67 + 6 * q^68 - 9 * q^69 + 24 * q^71 + 15 * q^73 + 18 * q^74 - 12 * q^75 + 3 * q^76 - 6 * q^77 + 18 * q^78 - 57 * q^79 - 27 * q^82 + 21 * q^83 - 3 * q^84 + 9 * q^85 + 9 * q^86 + 3 * q^87 + 3 * q^88 - 57 * q^89 + 21 * q^91 - 15 * q^92 - 9 * q^93 - 24 * q^94 - 18 * q^95 - 12 * q^96 - 6 * q^97 - 15 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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