LMFDB - Embedded newform 570.2.u.e.301.1

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:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			301.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	570.301
Dual form			570.2.u.e.481.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(0.939693 - 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.173648 + 0.984808i) q^{5} +(0.939693 + 0.342020i) q^{6} +(1.26604 + 2.19285i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(0.939693 - 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.173648 + 0.984808i) q^{5} +(0.939693 + 0.342020i) q^{6} +(1.26604 + 2.19285i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +(-0.766044 + 0.642788i) q^{10} +(0.326352 - 0.565258i) q^{11} +(0.500000 + 0.866025i) q^{12} +(0.213011 + 0.0775297i) q^{13} +(-0.439693 + 2.49362i) q^{14} +(0.173648 + 0.984808i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(0.624485 + 0.524005i) q^{17} +1.00000 q^{18} +(0.0320889 + 4.35878i) q^{19} -1.00000 q^{20} +(1.93969 + 1.62760i) q^{21} +(0.613341 - 0.223238i) q^{22} +(-0.680922 - 3.86170i) q^{23} +(-0.173648 + 0.984808i) q^{24} +(-0.939693 - 0.342020i) q^{25} +(0.113341 + 0.196312i) q^{26} +(0.500000 - 0.866025i) q^{27} +(-1.93969 + 1.62760i) q^{28} +(-1.14156 + 0.957882i) q^{29} +(-0.500000 + 0.866025i) q^{30} +(0.479055 + 0.829748i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.113341 - 0.642788i) q^{33} +(0.141559 + 0.802823i) q^{34} +(-2.37939 + 0.866025i) q^{35} +(0.766044 + 0.642788i) q^{36} +1.34730 q^{37} +(-2.77719 + 3.35965i) q^{38} +0.226682 q^{39} +(-0.766044 - 0.642788i) q^{40} +(4.35844 - 1.58634i) q^{41} +(0.439693 + 2.49362i) q^{42} +(-0.273318 + 1.55007i) q^{43} +(0.613341 + 0.223238i) q^{44} +(0.500000 + 0.866025i) q^{45} +(1.96064 - 3.39592i) q^{46} +(6.06805 - 5.09170i) q^{47} +(-0.766044 + 0.642788i) q^{48} +(0.294263 - 0.509678i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(0.766044 + 0.278817i) q^{51} +(-0.0393628 + 0.223238i) q^{52} +(-1.06031 - 6.01330i) q^{53} +(0.939693 - 0.342020i) q^{54} +(0.500000 + 0.419550i) q^{55} -2.53209 q^{56} +(1.52094 + 4.08494i) q^{57} -1.49020 q^{58} +(-2.37939 - 1.99654i) q^{59} +(-0.939693 + 0.342020i) q^{60} +(-0.553033 - 3.13641i) q^{61} +(-0.166374 + 0.943555i) q^{62} +(2.37939 + 0.866025i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.113341 + 0.196312i) q^{65} +(0.500000 - 0.419550i) q^{66} +(-0.690722 + 0.579585i) q^{67} +(-0.407604 + 0.705990i) q^{68} +(-1.96064 - 3.39592i) q^{69} +(-2.37939 - 0.866025i) q^{70} +(1.60354 - 9.09413i) q^{71} +(0.173648 + 0.984808i) q^{72} +(-10.1912 + 3.70929i) q^{73} +(1.03209 + 0.866025i) q^{74} -1.00000 q^{75} +(-4.28699 + 0.788496i) q^{76} +1.65270 q^{77} +(0.173648 + 0.145708i) q^{78} +(2.69207 - 0.979832i) q^{79} +(-0.173648 - 0.984808i) q^{80} +(0.173648 - 0.984808i) q^{81} +(4.35844 + 1.58634i) q^{82} +(-4.46198 - 7.72838i) q^{83} +(-1.26604 + 2.19285i) q^{84} +(-0.624485 + 0.524005i) q^{85} +(-1.20574 + 1.01173i) q^{86} +(-0.745100 + 1.29055i) q^{87} +(0.326352 + 0.565258i) q^{88} +(-14.2023 - 5.16923i) q^{89} +(-0.173648 + 0.984808i) q^{90} +(0.0996702 + 0.565258i) q^{91} +(3.68479 - 1.34115i) q^{92} +(0.733956 + 0.615862i) q^{93} +7.92127 q^{94} +(-4.29813 - 0.725293i) q^{95} -1.00000 q^{96} +(-0.603541 - 0.506431i) q^{97} +(0.553033 - 0.201288i) q^{98} +(-0.113341 - 0.642788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{7} - 3 q^{8}+O(q^{10}) $ 6 * q + 3 * q^7 - 3 * q^8	$ 6 q + 3 q^{7} - 3 q^{8} + 3 q^{11} + 3 q^{12} + 9 q^{13} + 3 q^{14} - 9 q^{17} + 6 q^{18} - 9 q^{19} - 6 q^{20} + 6 q^{21} - 3 q^{22} - 21 q^{23} - 6 q^{26} + 3 q^{27} - 6 q^{28} - 15 q^{29} - 3 q^{30} + 6 q^{31} - 6 q^{33} + 9 q^{34} - 3 q^{35} + 6 q^{37} - 6 q^{38} - 12 q^{39} + 18 q^{41} - 3 q^{42} - 15 q^{43} - 3 q^{44} + 3 q^{45} + 3 q^{46} - 6 q^{47} + 12 q^{49} - 3 q^{50} - 9 q^{52} - 12 q^{53} + 3 q^{55} - 6 q^{56} + 6 q^{57} - 6 q^{58} - 3 q^{59} + 9 q^{61} + 18 q^{62} + 3 q^{63} - 3 q^{64} + 6 q^{65} + 3 q^{66} - 24 q^{67} - 6 q^{68} - 3 q^{69} - 3 q^{70} - 15 q^{73} - 3 q^{74} - 6 q^{75} - 18 q^{76} + 12 q^{77} + 27 q^{79} + 18 q^{82} - 9 q^{83} - 3 q^{84} + 9 q^{85} + 3 q^{86} - 3 q^{87} + 3 q^{88} - 33 q^{89} + 15 q^{91} + 15 q^{92} + 9 q^{93} + 30 q^{94} - 12 q^{95} - 6 q^{96} + 6 q^{97} - 9 q^{98} + 6 q^{99}+O(q^{100}) $ 6 * q + 3 * q^7 - 3 * q^8 + 3 * q^11 + 3 * q^12 + 9 * q^13 + 3 * q^14 - 9 * q^17 + 6 * q^18 - 9 * q^19 - 6 * q^20 + 6 * q^21 - 3 * q^22 - 21 * q^23 - 6 * q^26 + 3 * q^27 - 6 * q^28 - 15 * q^29 - 3 * q^30 + 6 * q^31 - 6 * q^33 + 9 * q^34 - 3 * q^35 + 6 * q^37 - 6 * q^38 - 12 * q^39 + 18 * q^41 - 3 * q^42 - 15 * q^43 - 3 * q^44 + 3 * q^45 + 3 * q^46 - 6 * q^47 + 12 * q^49 - 3 * q^50 - 9 * q^52 - 12 * q^53 + 3 * q^55 - 6 * q^56 + 6 * q^57 - 6 * q^58 - 3 * q^59 + 9 * q^61 + 18 * q^62 + 3 * q^63 - 3 * q^64 + 6 * q^65 + 3 * q^66 - 24 * q^67 - 6 * q^68 - 3 * q^69 - 3 * q^70 - 15 * q^73 - 3 * q^74 - 6 * q^75 - 18 * q^76 + 12 * q^77 + 27 * q^79 + 18 * q^82 - 9 * q^83 - 3 * q^84 + 9 * q^85 + 3 * q^86 - 3 * q^87 + 3 * q^88 - 33 * q^89 + 15 * q^91 + 15 * q^92 + 9 * q^93 + 30 * q^94 - 12 * q^95 - 6 * q^96 + 6 * q^97 - 9 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$	$1$

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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	0.939693	−	0.342020i	0.542532	−	0.197465i
$3$	0.939693	−	0.342020i	0.542532	−	0.197465i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−0.173648	+	0.984808i	−0.0776578	+	0.440419i
$5$	−0.173648	+	0.984808i	−0.0776578	+	0.440419i
$6$	0.939693	+	0.342020i	0.383628	+	0.139629i
$7$	1.26604	+	2.19285i	0.478520	+	0.828821i	0.999697	−	0.0246281i	$-0.00784015\pi$
$7$	1.26604	+	2.19285i	0.478520	+	0.828821i	−0.521177	+	0.853449i	$0.674507\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	0.766044	−	0.642788i	0.255348	−	0.214263i
$10$	−0.766044	+	0.642788i	−0.242245	+	0.203267i
$11$	0.326352	−	0.565258i	0.0983988	−	0.170432i	−0.812623	−	0.582789i	$-0.801961\pi$
$11$	0.326352	−	0.565258i	0.0983988	−	0.170432i	0.911022	+	0.412358i	$0.135295\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	0.213011	+	0.0775297i	0.0590786	+	0.0215029i	0.371390	−	0.928477i	$-0.378881\pi$
$13$	0.213011	+	0.0775297i	0.0590786	+	0.0215029i	−0.312312	+	0.949980i	$0.601103\pi$
$14$	−0.439693	+	2.49362i	−0.117513	+	0.666448i
$15$	0.173648	+	0.984808i	0.0448358	+	0.254276i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	0.624485	+	0.524005i	0.151460	+	0.127090i	0.715369	−	0.698747i	$-0.246259\pi$
$17$	0.624485	+	0.524005i	0.151460	+	0.127090i	−0.563909	+	0.825837i	$0.690703\pi$
$18$	1.00000			0.235702
$19$	0.0320889	+	4.35878i	0.00736170	+	0.999973i
$19$	0.0320889	+	4.35878i	0.00736170	+	0.999973i
$20$	−1.00000			−0.223607
$21$	1.93969	+	1.62760i	0.423276	+	0.355170i
$22$	0.613341	−	0.223238i	0.130765	−	0.0475945i
$23$	−0.680922	−	3.86170i	−0.141982	−	0.805220i	−0.969741	−	0.244136i	$-0.921496\pi$
$23$	−0.680922	−	3.86170i	−0.141982	−	0.805220i	0.827759	−	0.561084i	$-0.189616\pi$
$24$	−0.173648	+	0.984808i	−0.0354458	+	0.201023i
$25$	−0.939693	−	0.342020i	−0.187939	−	0.0684040i
$26$	0.113341	+	0.196312i	0.0222280	+	0.0385000i
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$	−1.93969	+	1.62760i	−0.366567	+	0.307587i
$29$	−1.14156	+	0.957882i	−0.211982	+	0.177874i	−0.742596	−	0.669739i	$-0.766406\pi$
$29$	−1.14156	+	0.957882i	−0.211982	+	0.177874i	0.530614	+	0.847614i	$0.321961\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	0.479055	+	0.829748i	0.0860409	+	0.149027i	0.905834	−	0.423632i	$-0.139245\pi$
$31$	0.479055	+	0.829748i	0.0860409	+	0.149027i	−0.819793	+	0.572659i	$0.805912\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	0.113341	−	0.642788i	0.0197301	−	0.111895i
$34$	0.141559	+	0.802823i	0.0242772	+	0.137683i
$35$	−2.37939	+	0.866025i	−0.402190	+	0.146385i
$36$	0.766044	+	0.642788i	0.127674	+	0.107131i
$37$	1.34730			0.221494			0.110747	−	0.993849i	$-0.464676\pi$
$37$	1.34730			0.221494			0.110747	+	0.993849i	$0.464676\pi$
$38$	−2.77719	+	3.35965i	−0.450520	+	0.545007i
$39$	0.226682			0.0362981
$40$	−0.766044	−	0.642788i	−0.121122	−	0.101634i
$41$	4.35844	−	1.58634i	0.680674	−	0.247745i	0.0215372	−	0.999768i	$-0.493144\pi$
$41$	4.35844	−	1.58634i	0.680674	−	0.247745i	0.659137	+	0.752023i	$0.270922\pi$
$42$	0.439693	+	2.49362i	0.0678460	+	0.384774i
$43$	−0.273318	+	1.55007i	−0.0416807	+	0.236383i	−0.998530	−	0.0542017i	$-0.982739\pi$
$43$	−0.273318	+	1.55007i	−0.0416807	+	0.236383i	0.956849	+	0.290584i	$0.0938497\pi$
$44$	0.613341	+	0.223238i	0.0924646	+	0.0336544i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	1.96064	−	3.39592i	0.289080	−	0.500702i
$47$	6.06805	−	5.09170i	0.885116	−	0.742700i	−0.0821086	−	0.996623i	$-0.526165\pi$
$47$	6.06805	−	5.09170i	0.885116	−	0.742700i	0.967224	+	0.253923i	$0.0817210\pi$
$48$	−0.766044	+	0.642788i	−0.110569	+	0.0927784i
$49$	0.294263	−	0.509678i	0.0420376	−	0.0728112i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	0.766044	+	0.278817i	0.107268	+	0.0390422i
$52$	−0.0393628	+	0.223238i	−0.00545864	+	0.0309575i
$53$	−1.06031	−	6.01330i	−0.145644	−	0.825991i	−0.966847	−	0.255354i	$-0.917808\pi$
$53$	−1.06031	−	6.01330i	−0.145644	−	0.825991i	0.821203	−	0.570636i	$-0.193303\pi$
$54$	0.939693	−	0.342020i	0.127876	−	0.0465430i
$55$	0.500000	+	0.419550i	0.0674200	+	0.0565721i
$56$	−2.53209			−0.338365
$57$	1.52094	+	4.08494i	0.201454	+	0.541063i
$58$	−1.49020			−0.195673
$59$	−2.37939	−	1.99654i	−0.309770	−	0.259928i	0.474627	−	0.880187i	$-0.342583\pi$
$59$	−2.37939	−	1.99654i	−0.309770	−	0.259928i	−0.784397	+	0.620259i	$0.787027\pi$
$60$	−0.939693	+	0.342020i	−0.121314	+	0.0441546i
$61$	−0.553033	−	3.13641i	−0.0708087	−	0.401576i	−0.999526	−	0.0307873i	$-0.990199\pi$
$61$	−0.553033	−	3.13641i	−0.0708087	−	0.401576i	0.928717	−	0.370789i	$-0.120913\pi$
$62$	−0.166374	+	0.943555i	−0.0211295	+	0.119832i
$63$	2.37939	+	0.866025i	0.299774	+	0.109109i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.113341	+	0.196312i	−0.0140582	+	0.0243495i
$66$	0.500000	−	0.419550i	0.0615457	−	0.0516430i
$67$	−0.690722	+	0.579585i	−0.0843852	+	0.0708076i	−0.684004	−	0.729478i	$-0.739763\pi$
$67$	−0.690722	+	0.579585i	−0.0843852	+	0.0708076i	0.599619	+	0.800285i	$0.295319\pi$
$68$	−0.407604	+	0.705990i	−0.0494292	+	0.0856139i
$69$	−1.96064	−	3.39592i	−0.236033	−	0.408821i
$70$	−2.37939	−	0.866025i	−0.284391	−	0.103510i
$71$	1.60354	−	9.09413i	0.190305	−	1.07927i	−0.728642	−	0.684895i	$-0.759848\pi$
$71$	1.60354	−	9.09413i	0.190305	−	1.07927i	0.918947	−	0.394380i	$-0.129041\pi$
$72$	0.173648	+	0.984808i	0.0204646	+	0.116061i
$73$	−10.1912	+	3.70929i	−1.19279	+	0.434139i	−0.860702	−	0.509109i	$-0.829975\pi$
$73$	−10.1912	+	3.70929i	−1.19279	+	0.434139i	−0.332087	+	0.943249i	$0.607753\pi$
$74$	1.03209	+	0.866025i	0.119978	+	0.100673i
$75$	−1.00000			−0.115470
$76$	−4.28699	+	0.788496i	−0.491751	+	0.0904467i
$77$	1.65270			0.188343
$78$	0.173648	+	0.145708i	0.0196618	+	0.0164982i
$79$	2.69207	−	0.979832i	0.302881	−	0.110240i	−0.186109	−	0.982529i	$-0.559588\pi$
$79$	2.69207	−	0.979832i	0.302881	−	0.110240i	0.488990	+	0.872289i	$0.337365\pi$
$80$	−0.173648	−	0.984808i	−0.0194145	−	0.110105i
$81$	0.173648	−	0.984808i	0.0192942	−	0.109423i
$82$	4.35844	+	1.58634i	0.481309	+	0.175182i
$83$	−4.46198	−	7.72838i	−0.489766	−	0.848300i	0.510165	−	0.860077i	$-0.329584\pi$
$83$	−4.46198	−	7.72838i	−0.489766	−	0.848300i	−0.999931	+	0.0117771i	$0.996251\pi$
$84$	−1.26604	+	2.19285i	−0.138137	+	0.239260i
$85$	−0.624485	+	0.524005i	−0.0677349	+	0.0568364i
$86$	−1.20574	+	1.01173i	−0.130018	+	0.109098i
$87$	−0.745100	+	1.29055i	−0.0798831	+	0.138362i
$88$	0.326352	+	0.565258i	0.0347892	+	0.0602567i
$89$	−14.2023	−	5.16923i	−1.50544	−	0.547937i	−0.547981	−	0.836491i	$-0.684603\pi$
$89$	−14.2023	−	5.16923i	−1.50544	−	0.547937i	−0.957464	+	0.288554i	$0.906826\pi$
$90$	−0.173648	+	0.984808i	−0.0183041	+	0.103808i
$91$	0.0996702	+	0.565258i	0.0104483	+	0.0592551i
$92$	3.68479	−	1.34115i	0.384166	−	0.139825i
$93$	0.733956	+	0.615862i	0.0761076	+	0.0638619i
$94$	7.92127			0.817017
$95$	−4.29813	−	0.725293i	−0.440979	−	0.0744135i
$96$	−1.00000			−0.102062
$97$	−0.603541	−	0.506431i	−0.0612803	−	0.0514202i	0.611633	−	0.791142i	$-0.290513\pi$
$97$	−0.603541	−	0.506431i	−0.0612803	−	0.0514202i	−0.672913	+	0.739721i	$0.734957\pi$
$98$	0.553033	−	0.201288i	0.0558648	−	0.0203331i
$99$	−0.113341	−	0.642788i	−0.0113912	−	0.0646026i
$100$	0.173648	−	0.984808i	0.0173648	−	0.0984808i
$101$	8.39053	+	3.05390i	0.834889	+	0.303875i	0.723864	−	0.689943i	$-0.242364\pi$
$101$	8.39053	+	3.05390i	0.834889	+	0.303875i	0.111025	+	0.993818i	$0.464587\pi$
$102$	0.407604	+	0.705990i	0.0403588	+	0.0699035i
$103$	0.730552	−	1.26535i	0.0719834	−	0.124679i	−0.827787	−	0.561042i	$-0.810400\pi$
$103$	0.730552	−	1.26535i	0.0719834	−	0.124679i	0.899770	+	0.436363i	$0.143734\pi$
$104$	−0.173648	+	0.145708i	−0.0170276	+	0.0142879i
$105$	−1.93969	+	1.62760i	−0.189295	+	0.158837i
$106$	3.05303	−	5.28801i	0.296537	−	0.513617i
$107$	−3.66637	−	6.35035i	−0.354442	−	0.613911i	0.632580	−	0.774495i	$-0.281996\pi$
$107$	−3.66637	−	6.35035i	−0.354442	−	0.613911i	−0.987022	+	0.160583i	$0.948662\pi$
$108$	0.939693	+	0.342020i	0.0904220	+	0.0329109i
$109$	1.23143	−	6.98378i	0.117950	−	0.668925i	−0.867298	−	0.497789i	$-0.834145\pi$
$109$	1.23143	−	6.98378i	0.117950	−	0.668925i	0.985247	−	0.171136i	$-0.0547436\pi$
$110$	0.113341	+	0.642788i	0.0108066	+	0.0612874i
$111$	1.26604	−	0.460802i	0.120168	−	0.0437374i
$112$	−1.93969	−	1.62760i	−0.183284	−	0.153793i
$113$	−14.7101			−1.38381			−0.691904	−	0.721990i	$-0.743228\pi$
$113$	−14.7101			−1.38381			−0.691904	+	0.721990i	$0.743228\pi$
$114$	−1.46064	+	4.10689i	−0.136801	+	0.384645i
$115$	3.92127			0.365661
$116$	−1.14156	−	0.957882i	−0.105991	−	0.0889371i
$117$	0.213011	−	0.0775297i	0.0196929	−	0.00716762i
$118$	−0.539363	−	3.05888i	−0.0496524	−	0.281593i
$119$	−0.358441	+	2.03282i	−0.0328582	+	0.186348i
$120$	−0.939693	−	0.342020i	−0.0857818	−	0.0312220i
$121$	5.28699	+	9.15733i	0.480635	+	0.832485i
$122$	1.59240	−	2.75811i	0.144169	−	0.249708i
$123$	3.55303	−	2.98135i	0.320366	−	0.268819i
$124$	−0.733956	+	0.615862i	−0.0659112	+	0.0553060i
$125$	0.500000	−	0.866025i	0.0447214	−	0.0774597i
$126$	1.26604	+	2.19285i	0.112788	+	0.195355i
$127$	0.113341	+	0.0412527i	0.0100574	+	0.00366058i	0.347044	−	0.937849i	$-0.387185\pi$
$127$	0.113341	+	0.0412527i	0.0100574	+	0.00366058i	−0.336987	+	0.941509i	$0.609408\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	0.273318	+	1.55007i	0.0240643	+	0.136476i
$130$	−0.213011	+	0.0775297i	−0.0186823	+	0.00679980i
$131$	7.53983	+	6.32667i	0.658758	+	0.552764i	0.909714	−	0.415235i	$-0.136301\pi$
$131$	7.53983	+	6.32667i	0.658758	+	0.552764i	−0.250956	+	0.967998i	$0.580745\pi$
$132$	0.652704			0.0568106
$133$	−9.51754	+	5.58878i	−0.825275	+	0.484608i
$134$	−0.901674			−0.0778928
$135$	0.766044	+	0.642788i	0.0659306	+	0.0553223i
$136$	−0.766044	+	0.278817i	−0.0656878	+	0.0239084i
$137$	−2.38326	−	13.5161i	−0.203615	−	1.15476i	−0.899604	−	0.436707i	$-0.856145\pi$
$137$	−2.38326	−	13.5161i	−0.203615	−	1.15476i	0.695989	−	0.718053i	$-0.254966\pi$
$138$	0.680922	−	3.86170i	0.0579639	−	0.328730i
$139$	16.6766	+	6.06980i	1.41449	+	0.514834i	0.932446	−	0.361311i	$-0.117671\pi$
$139$	16.6766	+	6.06980i	1.41449	+	0.514834i	0.482049	+	0.876144i	$0.339893\pi$
$140$	−1.26604	−	2.19285i	−0.107000	−	0.185330i
$141$	3.96064	−	6.86002i	0.333546	−	0.577718i
$142$	7.07398	−	5.93577i	0.593635	−	0.498119i
$143$	0.113341	−	0.0951042i	0.00947803	−	0.00795301i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−0.745100	−	1.29055i	−0.0618772	−	0.107174i
$146$	−10.1912	−	3.70929i	−0.843429	−	0.306983i
$147$	0.102196	−	0.579585i	0.00842902	−	0.0478034i
$148$	0.233956	+	1.32683i	0.0192310	+	0.109065i
$149$	−6.00640	+	2.18615i	−0.492063	+	0.179096i	−0.576121	−	0.817365i	$-0.695434\pi$
$149$	−6.00640	+	2.18615i	−0.492063	+	0.179096i	0.0840576	+	0.996461i	$0.473212\pi$
$150$	−0.766044	−	0.642788i	−0.0625473	−	0.0524834i
$151$	10.6527			0.866905			0.433452	−	0.901176i	$-0.357295\pi$
$151$	10.6527			0.866905			0.433452	+	0.901176i	$0.357295\pi$
$152$	−3.79086	−	2.15160i	−0.307479	−	0.174518i
$153$	0.815207			0.0659056
$154$	1.26604	+	1.06234i	0.102021	+	0.0856056i
$155$	−0.900330	+	0.327693i	−0.0723162	+	0.0263210i
$156$	0.0393628	+	0.223238i	0.00315155	+	0.0178733i
$157$	−1.98158	+	11.2381i	−0.158147	+	0.896899i	0.797704	+	0.603049i	$0.206048\pi$
$157$	−1.98158	+	11.2381i	−0.158147	+	0.896899i	−0.955852	+	0.293850i	$0.905063\pi$
$158$	2.69207	+	0.979832i	0.214169	+	0.0779513i
$159$	−3.05303	−	5.28801i	−0.242121	−	0.419366i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	7.60607	−	6.38225i	0.599442	−	0.502992i
$162$	0.766044	−	0.642788i	0.0601861	−	0.0505022i
$163$	−5.47178	+	9.47740i	−0.428583	+	0.742328i	−0.996748	−	0.0805874i	$-0.974320\pi$
$163$	−5.47178	+	9.47740i	−0.428583	+	0.742328i	0.568165	+	0.822915i	$0.307654\pi$
$164$	2.31908	+	4.01676i	0.181090	+	0.313656i
$165$	0.613341	+	0.223238i	0.0477485	+	0.0173790i
$166$	1.54963	−	8.78839i	0.120275	−	0.682111i
$167$	−2.12923	−	12.0755i	−0.164765	−	0.934429i	−0.949306	−	0.314352i	$-0.898213\pi$
$167$	−2.12923	−	12.0755i	−0.164765	−	0.934429i	0.784541	−	0.620076i	$-0.212898\pi$
$168$	−2.37939	+	0.866025i	−0.183574	+	0.0668153i
$169$	−9.91921	−	8.32321i	−0.763017	−	0.640247i
$170$	−0.815207			−0.0625236
$171$	2.82635	+	3.31839i	0.216137	+	0.253764i
$172$	−1.57398			−0.120015
$173$	−0.260115	−	0.218262i	−0.0197762	−	0.0165942i	0.632846	−	0.774278i	$-0.281887\pi$
$173$	−0.260115	−	0.218262i	−0.0197762	−	0.0165942i	−0.652622	+	0.757684i	$0.726331\pi$
$174$	−1.40033	+	0.509678i	−0.106159	+	0.0386386i
$175$	−0.439693	−	2.49362i	−0.0332376	−	0.188500i
$176$	−0.113341	+	0.642788i	−0.00854338	+	0.0484519i
$177$	−2.91875	−	1.06234i	−0.219387	−	0.0798502i
$178$	−7.55690	−	13.0889i	−0.566414	−	0.981058i
$179$	−7.30541	+	12.6533i	−0.546032	+	0.945755i	0.452509	+	0.891760i	$0.350529\pi$
$179$	−7.30541	+	12.6533i	−0.546032	+	0.945755i	−0.998541	+	0.0539952i	$0.982804\pi$
$180$	−0.766044	+	0.642788i	−0.0570976	+	0.0479106i
$181$	4.07532	−	3.41960i	0.302916	−	0.254177i	−0.478641	−	0.878011i	$-0.658870\pi$
$181$	4.07532	−	3.41960i	0.302916	−	0.254177i	0.781557	+	0.623834i	$0.214426\pi$
$182$	−0.286989	+	0.497079i	−0.0212730	+	0.0368460i
$183$	−1.59240	−	2.75811i	−0.117713	−	0.203885i
$184$	3.68479	+	1.34115i	0.271647	+	0.0988712i
$185$	−0.233956	+	1.32683i	−0.0172008	+	0.0975503i
$186$	0.166374	+	0.943555i	0.0121991	+	0.0691848i
$187$	0.500000	−	0.181985i	0.0365636	−	0.0133081i
$188$	6.06805	+	5.09170i	0.442558	+	0.371350i
$189$	2.53209			0.184182
$190$	−2.82635	−	3.31839i	−0.205045	−	0.240742i
$191$	19.2959			1.39620			0.698102	−	0.715999i	$-0.254028\pi$
$191$	19.2959			1.39620			0.698102	+	0.715999i	$0.254028\pi$
$192$	−0.766044	−	0.642788i	−0.0552845	−	0.0463892i
$193$	−15.9153	+	5.79271i	−1.14561	+	0.416969i	−0.843937	−	0.536442i	$-0.819768\pi$
$193$	−15.9153	+	5.79271i	−1.14561	+	0.416969i	−0.301675	+	0.953411i	$0.597546\pi$
$194$	−0.136812	−	0.775897i	−0.00982250	−	0.0557061i
$195$	−0.0393628	+	0.223238i	−0.00281883	+	0.0159864i
$196$	0.553033	+	0.201288i	0.0395024	+	0.0143777i
$197$	−8.16637	−	14.1446i	−0.581830	−	1.00776i	−0.995262	−	0.0972244i	$-0.969004\pi$
$197$	−8.16637	−	14.1446i	−0.581830	−	1.00776i	0.413432	−	0.910535i	$-0.364330\pi$
$198$	0.326352	−	0.565258i	0.0231928	−	0.0401711i
$199$	13.7554	−	11.5421i	0.975092	−	0.818199i	−0.00824961	−	0.999966i	$-0.502626\pi$
$199$	13.7554	−	11.5421i	0.975092	−	0.818199i	0.983342	+	0.181767i	$0.0581815\pi$
$200$	0.766044	−	0.642788i	0.0541675	−	0.0454519i
$201$	−0.450837	+	0.780873i	−0.0317996	+	0.0550785i
$202$	4.46451	+	7.73275i	0.314122	+	0.544075i
$203$	−3.54576	−	1.29055i	−0.248864	−	0.0905789i
$204$	−0.141559	+	0.802823i	−0.00991113	+	0.0562088i
$205$	0.805407	+	4.56769i	0.0562521	+	0.319021i
$206$	1.37299	−	0.499727i	0.0956607	−	0.0348176i
$207$	−3.00387	−	2.52055i	−0.208783	−	0.175190i
$208$	−0.226682			−0.0157175
$209$	2.47431	+	1.40436i	0.171151	+	0.0971414i
$210$	−2.53209			−0.174731
$211$	18.1400	+	15.2212i	1.24881	+	1.04787i	0.996783	+	0.0801524i	$0.0255407\pi$
$211$	18.1400	+	15.2212i	1.24881	+	1.04787i	0.252024	+	0.967721i	$0.418904\pi$
$212$	5.73783	−	2.08840i	0.394076	−	0.143432i
$213$	−1.60354	−	9.09413i	−0.109873	−	0.623120i
$214$	1.27332	−	7.22135i	0.0870423	−	0.493641i
$215$	−1.47906	−	0.538332i	−0.100871	−	0.0367139i
$216$	0.500000	+	0.866025i	0.0340207	+	0.0589256i
$217$	−1.21301	+	2.10100i	−0.0823446	+	0.142625i
$218$	5.43242	−	4.55834i	0.367930	−	0.308730i
$219$	−8.30793	+	6.97118i	−0.561398	+	0.471069i
$220$	−0.326352	+	0.565258i	−0.0220026	+	0.0381097i
$221$	0.0923963	+	0.160035i	0.00621525	+	0.0107651i
$222$	1.26604	+	0.460802i	0.0849713	+	0.0309270i
$223$	−0.0132037	+	0.0748822i	−0.000884188	+	0.00501448i	−0.985247	−	0.171140i	$-0.945255\pi$
$223$	−0.0132037	+	0.0748822i	−0.000884188	+	0.00501448i	0.984362	+	0.176155i	$0.0563659\pi$
$224$	−0.439693	−	2.49362i	−0.0293782	−	0.166612i
$225$	−0.939693	+	0.342020i	−0.0626462	+	0.0228013i
$226$	−11.2686	−	9.45545i	−0.749574	−	0.628967i
$227$	11.9385			0.792387			0.396193	−	0.918167i	$-0.370331\pi$
$227$	11.9385			0.792387			0.396193	+	0.918167i	$0.370331\pi$
$228$	−3.75877	+	2.20718i	−0.248931	+	0.146174i
$229$	17.5303			1.15844			0.579219	−	0.815172i	$-0.303358\pi$
$229$	17.5303			1.15844			0.579219	+	0.815172i	$0.303358\pi$
$230$	3.00387	+	2.52055i	0.198069	+	0.166200i
$231$	1.55303	−	0.565258i	0.102182	−	0.0371912i
$232$	−0.258770	−	1.46756i	−0.0169891	−	0.0963501i
$233$	−4.79561	+	27.1972i	−0.314171	+	1.78175i	0.262662	+	0.964888i	$0.415400\pi$
$233$	−4.79561	+	27.1972i	−0.314171	+	1.78175i	−0.576833	+	0.816862i	$0.695711\pi$
$234$	0.213011	+	0.0775297i	0.0139250	+	0.00506827i
$235$	3.96064	+	6.86002i	0.258363	+	0.447499i
$236$	1.55303	−	2.68993i	0.101094	−	0.175100i
$237$	2.19459	−	1.84148i	0.142554	−	0.119617i
$238$	−1.58125	+	1.32683i	−0.102497	+	0.0860055i
$239$	−10.3525	+	17.9311i	−0.669648	+	1.15986i	0.308354	+	0.951272i	$0.400222\pi$
$239$	−10.3525	+	17.9311i	−0.669648	+	1.15986i	−0.978002	+	0.208593i	$0.933112\pi$
$240$	−0.500000	−	0.866025i	−0.0322749	−	0.0559017i
$241$	−12.1766	−	4.43193i	−0.784366	−	0.285486i	−0.0813742	−	0.996684i	$-0.525931\pi$
$241$	−12.1766	−	4.43193i	−0.784366	−	0.285486i	−0.702992	+	0.711198i	$0.748153\pi$
$242$	−1.83615	+	10.4133i	−0.118032	+	0.669395i
$243$	−0.173648	−	0.984808i	−0.0111395	−	0.0631754i
$244$	2.99273	−	1.08926i	0.191590	−	0.0697329i
$245$	0.450837	+	0.378297i	0.0288029	+	0.0241685i
$246$	4.63816			0.295718
$247$	−0.331100	+	0.930956i	−0.0210674	+	0.0592353i
$248$	−0.958111			−0.0608401
$249$	−6.83615	−	5.73621i	−0.433224	−	0.363518i
$250$	0.939693	−	0.342020i	0.0594314	−	0.0216313i
$251$	1.28359	+	7.27957i	0.0810192	+	0.459483i	0.998145	+	0.0608844i	$0.0193921\pi$
$251$	1.28359	+	7.27957i	0.0810192	+	0.459483i	−0.917126	+	0.398598i	$0.869497\pi$
$252$	−0.439693	+	2.49362i	−0.0276980	+	0.157083i
$253$	−2.40508	−	0.875377i	−0.151206	−	0.0550345i
$254$	0.0603074	+	0.104455i	0.00378402	+	0.00655412i
$255$	−0.407604	+	0.705990i	−0.0255251	+	0.0442108i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	0.476996	−	0.400247i	0.0297542	−	0.0249667i	−0.627789	−	0.778383i	$-0.716040\pi$
$257$	0.476996	−	0.400247i	0.0297542	−	0.0249667i	0.657543	+	0.753417i	$0.271596\pi$
$258$	−0.786989	+	1.36310i	−0.0489958	+	0.0848632i
$259$	1.70574	+	2.95442i	0.105989	+	0.183579i
$260$	−0.213011	−	0.0775297i	−0.0132104	−	0.00480819i
$261$	−0.258770	+	1.46756i	−0.0160175	+	0.0908397i
$262$	1.70914	+	9.69302i	0.105591	+	0.598837i
$263$	−3.61974	+	1.31748i	−0.223203	+	0.0812391i	−0.451201	−	0.892422i	$-0.649004\pi$
$263$	−3.61974	+	1.31748i	−0.223203	+	0.0812391i	0.227998	+	0.973662i	$0.426782\pi$
$264$	0.500000	+	0.419550i	0.0307729	+	0.0258215i
$265$	6.10607			0.375093
$266$	−10.8833	−	1.83651i	−0.667295	−	0.112603i
$267$	−15.1138			−0.924950
$268$	−0.690722	−	0.579585i	−0.0421926	−	0.0354038i
$269$	−10.6630	+	3.88100i	−0.650133	+	0.236629i	−0.645971	−	0.763362i	$-0.723547\pi$
$269$	−10.6630	+	3.88100i	−0.650133	+	0.236629i	−0.00416227	+	0.999991i	$0.501325\pi$
$270$	0.173648	+	0.984808i	0.0105679	+	0.0599335i
$271$	−1.76470	+	10.0081i	−0.107198	+	0.607950i	0.883122	+	0.469144i	$0.155437\pi$
$271$	−1.76470	+	10.0081i	−0.107198	+	0.607950i	−0.990320	+	0.138806i	$0.955674\pi$
$272$	−0.766044	−	0.278817i	−0.0464483	−	0.0169058i
$273$	0.286989	+	0.497079i	0.0173694	+	0.0300846i
$274$	6.86231	−	11.8859i	0.414567	−	0.718052i
$275$	−0.500000	+	0.419550i	−0.0301511	+	0.0252998i
$276$	3.00387	−	2.52055i	0.180812	−	0.151719i
$277$	−14.6138	+	25.3119i	−0.878059	+	1.52084i	−0.0245901	+	0.999698i	$0.507828\pi$
$277$	−14.6138	+	25.3119i	−0.878059	+	1.52084i	−0.853468	+	0.521144i	$0.825505\pi$
$278$	8.87346	+	15.3693i	0.532194	+	0.921788i
$279$	0.900330	+	0.327693i	0.0539013	+	0.0196185i
$280$	0.439693	−	2.49362i	0.0262767	−	0.149022i
$281$	2.86690	+	16.2590i	0.171025	+	0.969929i	0.942633	+	0.333831i	$0.108342\pi$
$281$	2.86690	+	16.2590i	0.171025	+	0.969929i	−0.771608	+	0.636098i	$0.780547\pi$
$282$	7.44356	−	2.70924i	0.443258	−	0.161333i
$283$	−1.46270	−	1.22735i	−0.0869483	−	0.0729583i	0.598278	−	0.801289i	$-0.295852\pi$
$283$	−1.46270	−	1.22735i	−0.0869483	−	0.0729583i	−0.685226	+	0.728331i	$0.740296\pi$
$284$	9.23442			0.547962
$285$	−4.28699	+	0.788496i	−0.253939	+	0.0467065i
$286$	0.147956			0.00874882
$287$	8.99660	+	7.54904i	0.531052	+	0.445606i
$288$	−0.939693	+	0.342020i	−0.0553719	+	0.0201537i
$289$	−2.83662	−	16.0873i	−0.166860	−	0.946310i
$290$	0.258770	−	1.46756i	0.0151955	−	0.0861781i
$291$	−0.740352	−	0.269466i	−0.0434002	−	0.0157964i
$292$	−5.42262	−	9.39225i	−0.317335	−	0.549640i
$293$	−1.42262	+	2.46405i	−0.0831103	+	0.143951i	−0.904584	−	0.426295i	$-0.859819\pi$
$293$	−1.42262	+	2.46405i	−0.0831103	+	0.143951i	0.821474	+	0.570246i	$0.193152\pi$
$294$	0.450837	−	0.378297i	0.0262933	−	0.0220627i
$295$	2.37939	−	1.99654i	0.138533	−	0.116243i
$296$	−0.673648	+	1.16679i	−0.0391550	+	0.0678185i
$297$	−0.326352	−	0.565258i	−0.0189369	−	0.0327996i
$298$	−6.00640	−	2.18615i	−0.347941	−	0.126640i
$299$	0.154353	−	0.875377i	0.00892644	−	0.0506243i
$300$	−0.173648	−	0.984808i	−0.0100256	−	0.0568579i
$301$	−3.74510	+	1.36310i	−0.215864	+	0.0785681i
$302$	8.16044	+	6.84743i	0.469581	+	0.394025i
$303$	8.92902			0.512959
$304$	−1.52094	−	4.08494i	−0.0872322	−	0.234287i
$305$	3.18479			0.182361
$306$	0.624485	+	0.524005i	0.0356994	+	0.0299554i
$307$	−5.19372	+	1.89036i	−0.296421	+	0.107888i	−0.485950	−	0.873987i	$-0.661526\pi$
$307$	−5.19372	+	1.89036i	−0.296421	+	0.107888i	0.189529	+	0.981875i	$0.439304\pi$
$308$	0.286989	+	1.62760i	0.0163527	+	0.0927409i
$309$	0.253718	−	1.43891i	0.0144335	−	0.0818565i
$310$	−0.900330	−	0.327693i	−0.0511353	−	0.0186117i
$311$	6.83662	+	11.8414i	0.387669	+	0.671463i	0.992136	−	0.125168i	$-0.0399470\pi$
$311$	6.83662	+	11.8414i	0.387669	+	0.671463i	−0.604466	+	0.796631i	$0.706614\pi$
$312$	−0.113341	+	0.196312i	−0.00641666	+	0.0111140i
$313$	−22.1348	+	18.5733i	−1.25113	+	1.04982i	−0.254561	+	0.967057i	$0.581931\pi$
$313$	−22.1348	+	18.5733i	−1.25113	+	1.04982i	−0.996569	+	0.0827662i	$0.973625\pi$
$314$	−8.74170	+	7.33515i	−0.493322	+	0.413947i
$315$	−1.26604	+	2.19285i	−0.0713335	+	0.123553i
$316$	1.43242	+	2.48102i	0.0805798	+	0.139568i
$317$	−0.500000	−	0.181985i	−0.0280828	−	0.0102213i	0.327941	−	0.944698i	$-0.393645\pi$
$317$	−0.500000	−	0.181985i	−0.0280828	−	0.0102213i	−0.356023	+	0.934477i	$0.615868\pi$
$318$	1.06031	−	6.01330i	0.0594591	−	0.337209i
$319$	0.168900	+	0.957882i	0.00945661	+	0.0536311i
$320$	0.939693	−	0.342020i	0.0525304	−	0.0191195i
$321$	−5.61721	−	4.71340i	−0.313522	−	0.263076i
$322$	9.92902			0.553322
$323$	−2.26399	+	2.73881i	−0.125971	+	0.152391i
$324$	1.00000			0.0555556
$325$	−0.173648	−	0.145708i	−0.00963227	−	0.00808243i
$326$	−10.2836	+	3.74292i	−0.569555	+	0.207301i
$327$	−1.23143	−	6.98378i	−0.0680982	−	0.386204i
$328$	−0.805407	+	4.56769i	−0.0444712	+	0.252209i
$329$	18.8478	+	6.86002i	1.03911	+	0.378205i
$330$	0.326352	+	0.565258i	0.0179651	+	0.0311164i
$331$	−7.35117	+	12.7326i	−0.404057	+	0.699847i	−0.994211	−	0.107444i	$-0.965733\pi$
$331$	−7.35117	+	12.7326i	−0.404057	+	0.699847i	0.590155	+	0.807290i	$0.299067\pi$
$332$	6.83615	−	5.73621i	0.375183	−	0.314816i
$333$	1.03209	−	0.866025i	0.0565581	−	0.0474579i
$334$	6.13088	−	10.6190i	0.335467	−	0.581046i
$335$	−0.450837	−	0.780873i	−0.0246319	−	0.0426636i
$336$	−2.37939	−	0.866025i	−0.129806	−	0.0472456i
$337$	−0.101014	+	0.572881i	−0.00550260	+	0.0312068i	−0.987435	−	0.158023i	$-0.949488\pi$
$337$	−0.101014	+	0.572881i	−0.00550260	+	0.0312068i	0.981933	+	0.189230i	$0.0605991\pi$
$338$	−2.24850	−	12.7519i	−0.122302	−	0.693612i
$339$	−13.8229	+	5.03114i	−0.750759	+	0.273254i
$340$	−0.624485	−	0.524005i	−0.0338675	−	0.0284182i
$341$	0.625362			0.0338653
$342$	0.0320889	+	4.35878i	0.00173517	+	0.235696i
$343$	19.2148			1.03750
$344$	−1.20574	−	1.01173i	−0.0650090	−	0.0545490i
$345$	3.68479	−	1.34115i	0.198383	−	0.0722053i
$346$	−0.0589632	−	0.334397i	−0.00316988	−	0.0179773i
$347$	−5.55391	+	31.4978i	−0.298150	+	1.69089i	0.355969	+	0.934498i	$0.384151\pi$
$347$	−5.55391	+	31.4978i	−0.298150	+	1.69089i	−0.654118	+	0.756392i	$0.726960\pi$
$348$	−1.40033	−	0.509678i	−0.0750656	−	0.0273216i
$349$	−8.94491	−	15.4930i	−0.478810	−	0.829323i	0.520895	−	0.853621i	$-0.325598\pi$
$349$	−8.94491	−	15.4930i	−0.478810	−	0.829323i	−0.999705	+	0.0242978i	$0.992265\pi$
$350$	1.26604	−	2.19285i	0.0676729	−	0.117213i
$351$	0.173648	−	0.145708i	0.00926865	−	0.00777732i
$352$	−0.500000	+	0.419550i	−0.0266501	+	0.0223621i
$353$	−0.00774079	+	0.0134074i	−0.000412000	+	0.000713606i	−0.866231	−	0.499643i	$-0.833464\pi$
$353$	−0.00774079	+	0.0134074i	−0.000412000	+	0.000713606i	0.865819	+	0.500357i	$0.166798\pi$
$354$	−1.55303	−	2.68993i	−0.0825428	−	0.142968i
$355$	8.67752	+	3.15836i	0.460555	+	0.167628i
$356$	2.62449	−	14.8842i	0.139097	−	0.788861i
$357$	0.358441	+	2.03282i	0.0189707	+	0.107588i
$358$	−13.7297	+	4.99719i	−0.725636	+	0.264110i
$359$	13.9945	+	11.7428i	0.738603	+	0.619762i	0.932462	−	0.361268i	$-0.117656\pi$
$359$	13.9945	+	11.7428i	0.738603	+	0.619762i	−0.193859	+	0.981029i	$0.562100\pi$
$360$	−1.00000			−0.0527046
$361$	−18.9979	+	0.279737i	−0.999892	+	0.0147230i
$362$	5.31996			0.279611
$363$	8.10014	+	6.79682i	0.425147	+	0.356741i
$364$	−0.539363	+	0.196312i	−0.0282703	+	0.0102895i
$365$	−1.88326	−	10.6805i	−0.0985741	−	0.559042i
$366$	0.553033	−	3.13641i	0.0289075	−	0.163943i
$367$	−8.55690	−	3.11446i	−0.446667	−	0.162573i	0.108887	−	0.994054i	$-0.465271\pi$
$367$	−8.55690	−	3.11446i	−0.446667	−	0.162573i	−0.555554	+	0.831481i	$0.687494\pi$
$368$	1.96064	+	3.39592i	0.102205	+	0.177025i
$369$	2.31908	−	4.01676i	0.120726	−	0.209104i
$370$	−1.03209	+	0.866025i	−0.0536557	+	0.0450225i
$371$	11.8439	−	9.93821i	0.614904	−	0.515966i
$372$	−0.479055	+	0.829748i	−0.0248379	+	0.0430205i
$373$	−0.0243481	−	0.0421721i	−0.00126070	−	0.00218359i	0.865394	−	0.501091i	$-0.167068\pi$
$373$	−0.0243481	−	0.0421721i	−0.00126070	−	0.00218359i	−0.866655	+	0.498908i	$0.833735\pi$
$374$	0.500000	+	0.181985i	0.0258544	+	0.00941023i
$375$	0.173648	−	0.984808i	0.00896715	−	0.0508553i
$376$	1.37551	+	7.80093i	0.0709368	+	0.402302i
$377$	−0.317429	+	0.115535i	−0.0163484	+	0.00595034i
$378$	1.93969	+	1.62760i	0.0997670	+	0.0837145i
$379$	21.5885			1.10893			0.554464	−	0.832208i	$-0.312923\pi$
$379$	21.5885			1.10893			0.554464	+	0.832208i	$0.312923\pi$
$380$	−0.0320889	−	4.35878i	−0.00164613	−	0.223601i
$381$	0.120615			0.00617928
$382$	14.7815	+	12.4032i	0.756289	+	0.634602i
$383$	4.53462	−	1.65046i	0.231708	−	0.0843348i	−0.223557	−	0.974691i	$-0.571767\pi$
$383$	4.53462	−	1.65046i	0.231708	−	0.0843348i	0.455265	+	0.890356i	$0.349545\pi$
$384$	−0.173648	−	0.984808i	−0.00886145	−	0.0502558i
$385$	−0.286989	+	1.62760i	−0.0146263	+	0.0829499i
$386$	−15.9153	−	5.79271i	−0.810070	−	0.294841i
$387$	0.786989	+	1.36310i	0.0400049	+	0.0692905i
$388$	0.393933	−	0.682312i	0.0199989	−	0.0346392i
$389$	13.6964	−	11.4926i	0.694435	−	0.582700i	−0.225749	−	0.974185i	$-0.572483\pi$
$389$	13.6964	−	11.4926i	0.694435	−	0.582700i	0.920184	+	0.391485i	$0.128039\pi$
$390$	−0.173648	+	0.145708i	−0.00879302	+	0.00737822i
$391$	1.59833	−	2.76838i	0.0808308	−	0.140003i
$392$	0.294263	+	0.509678i	0.0148625	+	0.0257426i
$393$	9.24897	+	3.36635i	0.466549	+	0.169810i
$394$	2.83615	−	16.0846i	0.142883	−	0.810331i
$395$	0.497474	+	2.82131i	0.0250306	+	0.141956i
$396$	0.613341	−	0.223238i	0.0308215	−	0.0112181i
$397$	−25.5692	−	21.4551i	−1.28328	−	1.07680i	−0.992783	−	0.119927i	$-0.961734\pi$
$397$	−25.5692	−	21.4551i	−1.28328	−	1.07680i	−0.290500	−	0.956875i	$-0.593822\pi$
$398$	17.9564			0.900071
$399$	−7.03209	+	8.50692i	−0.352045	+	0.425879i
$400$	1.00000			0.0500000
$401$	22.1275	+	18.5672i	1.10499	+	0.927200i	0.997751	−	0.0670332i	$-0.0213533\pi$
$401$	22.1275	+	18.5672i	1.10499	+	0.927200i	0.107243	+	0.994233i	$0.465798\pi$
$402$	−0.847296	+	0.308391i	−0.0422593	+	0.0153811i
$403$	0.0377140	+	0.213887i	0.00187867	+	0.0106544i
$404$	−1.55051	+	8.79336i	−0.0771406	+	0.437486i
$405$	0.939693	+	0.342020i	0.0466937	+	0.0169951i
$406$	−1.88666	−	3.26779i	−0.0936333	−	0.162178i
$407$	0.439693	−	0.761570i	0.0217948	−	0.0377496i
$408$	−0.624485	+	0.524005i	−0.0309166	+	0.0259421i
$409$	19.3025	−	16.1967i	0.954446	−	0.800875i	−0.0255949	−	0.999672i	$-0.508148\pi$
$409$	19.3025	−	16.1967i	0.954446	−	0.800875i	0.980041	+	0.198797i	$0.0637035\pi$
$410$	−2.31908	+	4.01676i	−0.114531	+	0.198374i
$411$	−6.86231	−	11.8859i	−0.338493	−	0.586287i
$412$	1.37299	+	0.499727i	0.0676423	+	0.0246198i
$413$	1.36571	−	7.74535i	0.0672024	−	0.381124i
$414$	−0.680922	−	3.86170i	−0.0334655	−	0.189792i
$415$	8.38578	−	3.05217i	0.411642	−	0.149825i
$416$	−0.173648	−	0.145708i	−0.00851380	−	0.00714393i
$417$	17.7469			0.869070
$418$	0.992726	+	2.66625i	0.0485558	+	0.130411i
$419$	5.66456			0.276732			0.138366	−	0.990381i	$-0.455815\pi$
$419$	5.66456			0.276732			0.138366	+	0.990381i	$0.455815\pi$
$420$	−1.93969	−	1.62760i	−0.0946473	−	0.0794185i
$421$	−22.8542	+	8.31823i	−1.11384	+	0.405406i	−0.832402	−	0.554172i	$-0.813035\pi$
$421$	−22.8542	+	8.31823i	−1.11384	+	0.405406i	−0.281442	+	0.959578i	$0.590813\pi$
$422$	4.11200	+	23.3203i	0.200169	+	1.13521i
$423$	1.37551	−	7.80093i	0.0668798	−	0.379294i
$424$	5.73783	+	2.08840i	0.278653	+	0.101422i
$425$	−0.407604	−	0.705990i	−0.0197717	−	0.0342456i
$426$	4.61721	−	7.99724i	0.223705	−	0.387468i
$427$	6.17752	−	5.18355i	0.298951	−	0.250850i
$428$	5.61721	−	4.71340i	0.271518	−	0.227831i
$429$	0.0739780	−	0.128134i	0.00357169	−	0.00618635i
$430$	−0.786989	−	1.36310i	−0.0379520	−	0.0657348i
$431$	−27.2327	−	9.91188i	−1.31175	−	0.477438i	−0.410945	−	0.911660i	$-0.634801\pi$
$431$	−27.2327	−	9.91188i	−1.31175	−	0.477438i	−0.900806	+	0.434222i	$0.857024\pi$
$432$	−0.173648	+	0.984808i	−0.00835465	+	0.0473816i
$433$	1.55556	+	8.82202i	0.0747554	+	0.423959i	0.999101	+	0.0424018i	$0.0135010\pi$
$433$	1.55556	+	8.82202i	0.0747554	+	0.423959i	−0.924345	+	0.381557i	$0.875388\pi$
$434$	−2.27972	+	0.829748i	−0.109430	+	0.0398292i
$435$	−1.14156	−	0.957882i	−0.0547336	−	0.0459269i
$436$	7.09152			0.339622
$437$	16.8105	−	3.09191i	0.804153	−	0.147906i
$438$	−10.8452			−0.518205
$439$	−17.9270	−	15.0425i	−0.855607	−	0.717939i	0.105410	−	0.994429i	$-0.466384\pi$
$439$	−17.9270	−	15.0425i	−0.855607	−	0.717939i	−0.961017	+	0.276489i	$0.910829\pi$
$440$	−0.613341	+	0.223238i	−0.0292399	+	0.0106424i
$441$	−0.102196	−	0.579585i	−0.00486650	−	0.0275993i
$442$	−0.0320889	+	0.181985i	−0.00152631	+	0.00865615i
$443$	29.5710	+	10.7630i	1.40496	+	0.511365i	0.929647	−	0.368451i	$-0.120112\pi$
$443$	29.5710	+	10.7630i	1.40496	+	0.511365i	0.475315	+	0.879815i	$0.342334\pi$
$444$	0.673648	+	1.16679i	0.0319699	+	0.0553735i
$445$	7.55690	−	13.0889i	0.358232	−	0.620475i
$446$	−0.0582480	+	0.0488759i	−0.00275812	+	0.00231434i
$447$	−4.89646	+	4.10862i	−0.231595	+	0.194331i
$448$	1.26604	−	2.19285i	0.0598150	−	0.103603i
$449$	−6.77110	−	11.7279i	−0.319548	−	0.553473i	0.660846	−	0.750522i	$-0.270198\pi$
$449$	−6.77110	−	11.7279i	−0.319548	−	0.553473i	−0.980394	+	0.197049i	$0.936864\pi$
$450$	−0.939693	−	0.342020i	−0.0442975	−	0.0161230i
$451$	0.525692	−	2.98135i	0.0247539	−	0.140386i
$452$	−2.55438	−	14.4866i	−0.120148	−	0.681392i
$453$	10.0103	−	3.64344i	0.470323	−	0.171184i
$454$	9.14543	+	7.67393i	0.429216	+	0.360155i
$455$	−0.573978			−0.0269085
$456$	−4.29813	−	0.725293i	−0.201279	−	0.0339650i
$457$	−17.9195			−0.838240			−0.419120	−	0.907931i	$-0.637661\pi$
$457$	−17.9195			−0.838240			−0.419120	+	0.907931i	$0.637661\pi$
$458$	13.4290	+	11.2683i	0.627497	+	0.526532i
$459$	0.766044	−	0.278817i	0.0357559	−	0.0130141i
$460$	0.680922	+	3.86170i	0.0317482	+	0.180053i
$461$	−4.26873	+	24.2092i	−0.198815	+	1.12753i	0.708066	+	0.706146i	$0.249568\pi$
$461$	−4.26873	+	24.2092i	−0.198815	+	1.12753i	−0.906881	+	0.421388i	$0.861543\pi$
$462$	1.55303	+	0.565258i	0.0722537	+	0.0262982i
$463$	−10.9636	−	18.9896i	−0.509523	−	0.882520i	−0.999939	−	0.0110315i	$-0.996489\pi$
$463$	−10.9636	−	18.9896i	−0.509523	−	0.882520i	0.490416	−	0.871488i	$-0.336845\pi$
$464$	0.745100	−	1.29055i	0.0345904	−	0.0599123i
$465$	−0.733956	+	0.615862i	−0.0340364	+	0.0285599i
$466$	−21.1557	+	17.7517i	−0.980019	+	0.822333i
$467$	−9.57650	+	16.5870i	−0.443148	+	0.767554i	−0.997921	−	0.0644471i	$-0.979472\pi$
$467$	−9.57650	+	16.5870i	−0.443148	+	0.767554i	0.554773	+	0.832002i	$0.312805\pi$
$468$	0.113341	+	0.196312i	0.00523918	+	0.00907453i
$469$	−2.14543	−	0.780873i	−0.0990667	−	0.0360573i
$470$	−1.37551	+	7.80093i	−0.0634478	+	0.359830i
$471$	1.98158	+	11.2381i	0.0913065	+	0.517825i
$472$	2.91875	−	1.06234i	0.134346	−	0.0488980i
$473$	0.786989	+	0.660362i	0.0361858	+	0.0303635i
$474$	2.86484			0.131586
$475$	1.46064	−	4.10689i	0.0670186	−	0.188437i
$476$	−2.06418			−0.0946114
$477$	−4.67752	−	3.92490i	−0.214169	−	0.179709i
$478$	−19.4564	+	7.08153i	−0.889913	+	0.323902i
$479$	−1.93464	−	10.9719i	−0.0883960	−	0.501318i	−0.996572	−	0.0827300i	$-0.973636\pi$
$479$	−1.93464	−	10.9719i	−0.0883960	−	0.501318i	0.908176	−	0.418588i	$-0.137475\pi$
$480$	0.173648	−	0.984808i	0.00792592	−	0.0449501i
$481$	0.286989	+	0.104455i	0.0130856	+	0.00476276i
$482$	−6.47906	−	11.2221i	−0.295113	−	0.511151i
$483$	4.96451	−	8.59878i	0.225893	−	0.391258i
$484$	−8.10014	+	6.79682i	−0.368188	+	0.308946i
$485$	0.603541	−	0.506431i	0.0274054	−	0.0229958i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−12.1566	−	21.0558i	−0.550867	−	0.954130i	−0.998212	−	0.0597682i	$-0.980964\pi$
$487$	−12.1566	−	21.0558i	−0.550867	−	0.954130i	0.447345	−	0.894361i	$-0.352369\pi$
$488$	2.99273	+	1.08926i	0.135474	+	0.0493086i
$489$	−1.90033	+	10.7773i	−0.0859359	+	0.487367i
$490$	0.102196	+	0.579585i	0.00461676	+	0.0261830i
$491$	−21.9008	+	7.97124i	−0.988369	+	0.359737i	−0.785089	−	0.619384i	$-0.787383\pi$
$491$	−21.9008	+	7.97124i	−0.988369	+	0.359737i	−0.203281	+	0.979121i	$0.565160\pi$
$492$	3.55303	+	2.98135i	0.160183	+	0.134410i
$493$	−1.21482			−0.0547128
$494$	−0.852044	+	0.500327i	−0.0383353	+	0.0225108i
$495$	0.652704			0.0293368
$496$	−0.733956	−	0.615862i	−0.0329556	−	0.0276530i
$497$	21.9722	−	7.99724i	0.985590	−	0.358725i
$498$	−1.54963	−	8.78839i	−0.0694406	−	0.393817i
$499$	0.187319	−	1.06234i	0.00838554	−	0.0475568i	−0.980328	−	0.197376i	$-0.936758\pi$
$499$	0.187319	−	1.06234i	0.00838554	−	0.0475568i	0.988713	+	0.149819i	$0.0478692\pi$
$500$	0.939693	+	0.342020i	0.0420243	+	0.0152956i
$501$	−6.13088	−	10.6190i	−0.273908	−	0.474422i
$502$	−3.69594	+	6.40155i	−0.164958	+	0.285715i
$503$	26.2631	−	22.0374i	1.17101	−	0.982597i	0.171018	−	0.985268i	$-0.445294\pi$
$503$	26.2631	−	22.0374i	1.17101	−	0.982597i	0.999996	+	0.00267047i	$0.000850038\pi$
$504$	−1.93969	+	1.62760i	−0.0864008	+	0.0724989i
$505$	−4.46451	+	7.73275i	−0.198668	+	0.344103i
$506$	−1.27972	−	2.21653i	−0.0568903	−	0.0985368i
$507$	−12.1677	−	4.42869i	−0.540387	−	0.196685i
$508$	−0.0209445	+	0.118782i	−0.000929263	+	0.00527011i
$509$	1.16519	+	6.60813i	0.0516462	+	0.292900i	0.999681	−	0.0252672i	$-0.00804365\pi$
$509$	1.16519	+	6.60813i	0.0516462	+	0.292900i	−0.948034	+	0.318168i	$0.896933\pi$
$510$	−0.766044	+	0.278817i	−0.0339210	+	0.0123462i
$511$	−21.0364	−	17.6517i	−0.930597	−	0.780863i
$512$	1.00000			0.0441942
$513$	3.79086	+	2.15160i	0.167371	+	0.0949955i
$514$	0.622674			0.0274650
$515$	1.11927	+	0.939180i	0.0493210	+	0.0413852i
$516$	−1.47906	+	0.538332i	−0.0651118	+	0.0236988i
$517$	−0.897804	−	5.09170i	−0.0394854	−	0.223933i
$518$	−0.592396	+	3.35965i	−0.0260284	+	0.147614i
$519$	−0.319078	−	0.116135i	−0.0140060	−	0.00509775i
$520$	−0.113341	−	0.196312i	−0.00497032	−	0.00860885i
$521$	17.6215	−	30.5214i	0.772014	−	1.33717i	−0.164443	−	0.986387i	$-0.552583\pi$
$521$	17.6215	−	30.5214i	0.772014	−	1.33717i	0.936458	−	0.350781i	$-0.114084\pi$
$522$	−1.14156	+	0.957882i	−0.0499647	+	0.0419254i
$523$	30.0592	−	25.2226i	1.31440	−	1.10291i	0.326935	−	0.945047i	$-0.393984\pi$
$523$	30.0592	−	25.2226i	1.31440	−	1.10291i	0.987461	−	0.157863i	$-0.0504603\pi$
$524$	−4.92127	+	8.52390i	−0.214987	+	0.372368i
$525$	−1.26604	−	2.19285i	−0.0552547	−	0.0957040i
$526$	−3.61974	−	1.31748i	−0.157828	−	0.0574447i
$527$	−0.135630	+	0.769193i	−0.00590811	+	0.0335066i
$528$	0.113341	+	0.642788i	0.00493253	+	0.0279737i
$529$	7.16385	−	2.60743i	0.311472	−	0.113366i
$530$	4.67752	+	3.92490i	0.203178	+	0.170487i
$531$	−3.10607			−0.134792
$532$	−7.15657	−	8.40247i	−0.310277	−	0.364293i
$533$	1.05138			0.0455405
$534$	−11.5778	−	9.71497i	−0.501022	−	0.420408i
$535$	6.89053	−	2.50795i	0.297904	−	0.108428i
$536$	−0.156574	−	0.887975i	−0.00676297	−	0.0383547i
$537$	−2.53714	+	14.3888i	−0.109486	+	0.620924i
$538$	−10.6630	−	3.88100i	−0.459713	−	0.167322i
$539$	−0.192066	−	0.332669i	−0.00827289	−	0.0143291i
$540$	−0.500000	+	0.866025i	−0.0215166	+	0.0372678i
$541$	−24.5737	+	20.6198i	−1.05651	+	0.886515i	−0.993763	−	0.111515i	$-0.964430\pi$
$541$	−24.5737	+	20.6198i	−1.05651	+	0.886515i	−0.0627444	+	0.998030i	$0.519985\pi$
$542$	−7.78493	+	6.53233i	−0.334391	+	0.280588i
$543$	2.65998	−	4.60722i	0.114151	−	0.197715i
$544$	−0.407604	−	0.705990i	−0.0174759	−	0.0302691i
$545$	6.66385	+	2.42544i	0.285448	+	0.103895i
$546$	−0.0996702	+	0.565258i	−0.00426549	+	0.0241908i
$547$	−7.45770	−	42.2947i	−0.318868	−	1.80839i	−0.549660	−	0.835388i	$-0.685243\pi$
$547$	−7.45770	−	42.2947i	−0.318868	−	1.80839i	0.230792	−	0.973003i	$-0.425868\pi$
$548$	12.8969	−	4.69410i	0.550929	−	0.200522i
$549$	−2.43969	−	2.04715i	−0.104124	−	0.0873700i
$550$	−0.652704			−0.0278314
$551$	−4.21183	−	4.94507i	−0.179430	−	0.210667i
$552$	3.92127			0.166901
$553$	5.55690	+	4.66280i	0.236304	+	0.198282i
$554$	−27.4650	+	9.99643i	−1.16687	+	0.424708i
$555$	0.233956	+	1.32683i	0.00993086	+	0.0563207i
$556$	−3.08172	+	17.4773i	−0.130694	+	0.741202i
$557$	−27.7935	−	10.1160i	−1.17765	−	0.428630i	−0.322279	−	0.946645i	$-0.604449\pi$
$557$	−27.7935	−	10.1160i	−1.17765	−	0.428630i	−0.855371	+	0.518015i	$0.826671\pi$
$558$	0.479055	+	0.829748i	0.0202800	+	0.0351261i
$559$	−0.178396	+	0.308991i	−0.00754534	+	0.0130689i
$560$	1.93969	−	1.62760i	0.0819670	−	0.0687785i
$561$	0.407604	−	0.342020i	0.0172090	−	0.0144401i
$562$	−8.25490	+	14.2979i	−0.348212	+	0.603121i
$563$	−10.3241	−	17.8819i	−0.435110	−	0.753633i	0.562194	−	0.827005i	$-0.309957\pi$
$563$	−10.3241	−	17.8819i	−0.435110	−	0.753633i	−0.997305	+	0.0733721i	$0.976624\pi$
$564$	7.44356	+	2.70924i	0.313431	+	0.114079i
$565$	2.55438	−	14.4866i	0.107463	−	0.609456i
$566$	−0.331566	−	1.88041i	−0.0139368	−	0.0790394i
$567$	2.37939	−	0.866025i	0.0999248	−	0.0363696i
$568$	7.07398	+	5.93577i	0.296818	+	0.249059i
$569$	−8.50030			−0.356351			−0.178176	−	0.983999i	$-0.557020\pi$
$569$	−8.50030			−0.356351			−0.178176	+	0.983999i	$0.557020\pi$
$570$	−3.79086	−	2.15160i	−0.158782	−	0.0901206i
$571$	4.27900			0.179071			0.0895353	−	0.995984i	$-0.471462\pi$
$571$	4.27900			0.179071			0.0895353	+	0.995984i	$0.471462\pi$
$572$	0.113341	+	0.0951042i	0.00473902	+	0.00397651i
$573$	18.1322	−	6.59959i	0.757485	−	0.275702i
$574$	2.03936	+	11.5658i	0.0851214	+	0.482747i
$575$	−0.680922	+	3.86170i	−0.0283964	+	0.161044i
$576$	−0.939693	−	0.342020i	−0.0391539	−	0.0142508i
$577$	−7.31449	−	12.6691i	−0.304506	−	0.527420i	0.672645	−	0.739965i	$-0.265158\pi$
$577$	−7.31449	−	12.6691i	−0.304506	−	0.527420i	−0.977151	+	0.212545i	$0.931825\pi$
$578$	8.16772	−	14.1469i	0.339732	−	0.588434i
$579$	−12.9743	+	10.8867i	−0.539194	+	0.452437i
$580$	1.14156	−	0.957882i	0.0474007	−	0.0397739i
$581$	11.2981	−	19.5689i	0.468726	−	0.811856i
$582$	−0.393933	−	0.682312i	−0.0163291	−	0.0282828i
$583$	−3.74510	−	1.36310i	−0.155106	−	0.0564540i
$584$	1.88326	−	10.6805i	0.0779297	−	0.441961i
$585$	0.0393628	+	0.223238i	0.00162745	+	0.00922975i
$586$	−2.67365	+	0.973128i	−0.110447	+	0.0401996i
$587$	9.35432	+	7.84921i	0.386094	+	0.323971i	0.815089	−	0.579335i	$-0.196688\pi$
$587$	9.35432	+	7.84921i	0.386094	+	0.323971i	−0.428995	+	0.903307i	$0.641132\pi$
$588$	0.588526			0.0242704
$589$	−3.60132	+	2.11472i	−0.148390	+	0.0871357i
$590$	3.10607			0.127875
$591$	−12.5116	−	10.4985i	−0.514659	−	0.431850i
$592$	−1.26604	+	0.460802i	−0.0520341	+	0.0189389i
$593$	2.61169	+	14.8116i	0.107249	+	0.608241i	0.990298	+	0.138960i	$0.0443759\pi$
$593$	2.61169	+	14.8116i	0.107249	+	0.608241i	−0.883049	+	0.469281i	$0.844513\pi$
$594$	0.113341	−	0.642788i	0.00465043	−	0.0263739i
$595$	−1.93969	−	0.705990i	−0.0795196	−	0.0289428i
$596$	−3.19594	−	5.53553i	−0.130911	−	0.226744i
$597$	8.97818	−	15.5507i	0.367452	−	0.636446i
$598$	0.680922	−	0.571362i	0.0278450	−	0.0233647i
$599$	7.06805	−	5.93080i	0.288793	−	0.242326i	−0.486869	−	0.873475i	$-0.661861\pi$
$599$	7.06805	−	5.93080i	0.288793	−	0.242326i	0.775661	+	0.631149i	$0.217417\pi$
$600$	0.500000	−	0.866025i	0.0204124	−	0.0353553i
$601$	−11.4829	−	19.8890i	−0.468398	−	0.811290i	0.530949	−	0.847404i	$-0.321835\pi$
$601$	−11.4829	−	19.8890i	−0.468398	−	0.811290i	−0.999348	+	0.0361139i	$0.988502\pi$
$602$	−3.74510	−	1.36310i	−0.152639	−	0.0555560i
$603$	−0.156574	+	0.887975i	−0.00637619	+	0.0361612i
$604$	1.84982	+	10.4909i	0.0752682	+	0.426867i
$605$	−9.93629	+	3.61651i	−0.403968	+	0.147032i
$606$	6.84002	+	5.73946i	0.277857	+	0.233150i
$607$	42.2559			1.71511			0.857557	−	0.514389i	$-0.171981\pi$
$607$	42.2559			1.71511			0.857557	+	0.514389i	$0.171981\pi$
$608$	1.46064	−	4.10689i	0.0592367	−	0.166556i
$609$	−3.77332			−0.152903
$610$	2.43969	+	2.04715i	0.0987803	+	0.0828865i
$611$	1.68732	−	0.614134i	0.0682616	−	0.0248452i
$612$	0.141559	+	0.802823i	0.00572220	+	0.0324522i
$613$	−3.94010	+	22.3454i	−0.159139	+	0.902524i	0.795764	+	0.605607i	$0.207070\pi$
$613$	−3.94010	+	22.3454i	−0.159139	+	0.902524i	−0.954903	+	0.296917i	$0.904042\pi$
$614$	−5.19372	−	1.89036i	−0.209601	−	0.0762886i
$615$	2.31908	+	4.01676i	0.0935142	+	0.161971i
$616$	−0.826352	+	1.43128i	−0.0332947	+	0.0576680i
$617$	−4.67680	+	3.92430i	−0.188281	+	0.157987i	−0.732056	−	0.681245i	$-0.761439\pi$
$617$	−4.67680	+	3.92430i	−0.188281	+	0.157987i	0.543775	+	0.839231i	$0.316995\pi$
$618$	1.11927	−	0.939180i	0.0450237	−	0.0377793i
$619$	−22.1536	+	38.3712i	−0.890430	+	1.54227i	−0.0510690	+	0.998695i	$0.516263\pi$
$619$	−22.1536	+	38.3712i	−0.890430	+	1.54227i	−0.839361	+	0.543575i	$0.817070\pi$
$620$	−0.479055	−	0.829748i	−0.0192393	−	0.0333235i
$621$	−3.68479	−	1.34115i	−0.147866	−	0.0538187i
$622$	−2.37433	+	13.4655i	−0.0952021	+	0.539918i
$623$	−6.64543	−	37.6881i	−0.266244	−	1.50994i
$624$	−0.213011	+	0.0775297i	−0.00852727	+	0.00310367i
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$	−28.8949			−1.15487
$627$	2.80541	+	0.473401i	0.112037	+	0.0189058i
$628$	−11.4115			−0.455367
$629$	0.841367	+	0.705990i	0.0335475	+	0.0281497i
$630$	−2.37939	+	0.866025i	−0.0947970	+	0.0345033i
$631$	−8.49232	−	48.1623i	−0.338074	−	1.91731i	−0.394482	−	0.918904i	$-0.629076\pi$
$631$	−8.49232	−	48.1623i	−0.338074	−	1.91731i	0.0564082	−	0.998408i	$-0.482035\pi$
$632$	−0.497474	+	2.82131i	−0.0197884	+	0.112226i
$633$	22.2520	+	8.09905i	0.884436	+	0.321908i
$634$	−0.266044	−	0.460802i	−0.0105660	−	0.0183008i
$635$	−0.0603074	+	0.104455i	−0.00239323	+	0.00414519i
$636$	4.67752	−	3.92490i	0.185476	−	0.155633i
$637$	0.102196	−	0.0857530i	0.00404917	−	0.00339766i
$638$	−0.486329	+	0.842347i	−0.0192540	+	0.0333488i
$639$	−4.61721	−	7.99724i	−0.182654	−	0.316366i
$640$	0.939693	+	0.342020i	0.0371446	+	0.0135195i
$641$	−3.38326	+	19.1874i	−0.133631	+	0.757857i	0.842173	+	0.539207i	$0.181276\pi$
$641$	−3.38326	+	19.1874i	−0.133631	+	0.757857i	−0.975804	+	0.218649i	$0.929835\pi$
$642$	−1.27332	−	7.22135i	−0.0502539	−	0.285004i
$643$	37.1190	−	13.5102i	1.46383	−	0.532791i	0.517413	−	0.855736i	$-0.326895\pi$
$643$	37.1190	−	13.5102i	1.46383	−	0.532791i	0.946418	+	0.322945i	$0.104673\pi$
$644$	7.60607	+	6.38225i	0.299721	+	0.251496i
$645$	−1.57398			−0.0619753
$646$	−3.49479	+	0.642788i	−0.137500	+	0.0252901i
$647$	−8.23947			−0.323927			−0.161964	−	0.986797i	$-0.551783\pi$
$647$	−8.23947			−0.323927			−0.161964	+	0.986797i	$0.551783\pi$
$648$	0.766044	+	0.642788i	0.0300931	+	0.0252511i
$649$	−1.90508	+	0.693392i	−0.0747808	+	0.0272180i
$650$	−0.0393628	−	0.223238i	−0.00154394	−	0.00875611i
$651$	−0.421274	+	2.38917i	−0.0165110	+	0.0936388i
$652$	−10.2836	−	3.74292i	−0.402736	−	0.146584i
$653$	0.0368366	+	0.0638029i	0.00144153	+	0.00249680i	0.866745	−	0.498751i	$-0.166208\pi$
$653$	0.0368366	+	0.0638029i	0.00144153	+	0.00249680i	−0.865304	+	0.501248i	$0.832874\pi$
$654$	3.54576	−	6.14144i	0.138650	−	0.240149i
$655$	−7.53983	+	6.32667i	−0.294606	+	0.247203i
$656$	−3.55303	+	2.98135i	−0.138723	+	0.116402i
$657$	−5.42262	+	9.39225i	−0.211556	+	0.366427i
$658$	10.0287	+	17.3702i	0.390959	+	0.677161i
$659$	−30.6634	−	11.1606i	−1.19448	−	0.434754i	−0.333184	−	0.942862i	$-0.608123\pi$
$659$	−30.6634	−	11.1606i	−1.19448	−	0.434754i	−0.861294	+	0.508107i	$0.830345\pi$
$660$	−0.113341	+	0.642788i	−0.00441178	+	0.0250205i
$661$	3.53508	+	20.0484i	0.137499	+	0.779794i	0.973087	+	0.230438i	$0.0740159\pi$
$661$	3.53508	+	20.0484i	0.137499	+	0.779794i	−0.835588	+	0.549356i	$0.814873\pi$
$662$	−13.8157	+	5.02849i	−0.536961	+	0.195438i
$663$	0.141559	+	0.118782i	0.00549771	+	0.00461312i
$664$	8.92396			0.346317
$665$	−3.85117	−	10.3434i	−0.149342	−	0.401101i
$666$	1.34730			0.0522067
$667$	4.47637	+	3.75612i	0.173326	+	0.145437i
$668$	11.5223	−	4.19377i	0.445811	−	0.162262i
$669$	0.0132037	+	0.0748822i	0.000510486	+	0.00289511i
$670$	0.156574	−	0.887975i	0.00604898	−	0.0343055i
$671$	−1.95336	−	0.710966i	−0.0754087	−	0.0274465i
$672$	−1.26604	−	2.19285i	−0.0488387	−	0.0845912i
$673$	13.1471	−	22.7714i	0.506783	−	0.877773i	−0.493187	−	0.869924i	$-0.664168\pi$
$673$	13.1471	−	22.7714i	0.506783	−	0.877773i	0.999969	−	0.00784970i	$-0.00249866\pi$
$674$	−0.445622	+	0.373922i	−0.0171647	+	0.0144029i
$675$	−0.766044	+	0.642788i	−0.0294851	+	0.0247409i
$676$	6.47431	−	11.2138i	0.249012	−	0.431301i
$677$	−14.0025	−	24.2531i	−0.538161	−	0.932122i	−0.999003	−	0.0446398i	$-0.985786\pi$
$677$	−14.0025	−	24.2531i	−0.538161	−	0.932122i	0.460842	−	0.887482i	$-0.347547\pi$
$678$	−13.8229	−	5.03114i	−0.530867	−	0.193220i
$679$	0.346419	−	1.96464i	0.0132943	−	0.0753960i
$680$	−0.141559	−	0.802823i	−0.00542855	−	0.0307868i
$681$	11.2185	−	4.08321i	0.429895	−	0.156469i
$682$	0.479055	+	0.401975i	0.0183440	+	0.0153924i
$683$	−26.3651			−1.00883			−0.504417	−	0.863460i	$-0.668293\pi$
$683$	−26.3651			−1.00883			−0.504417	+	0.863460i	$0.668293\pi$
$684$	−2.77719	+	3.35965i	−0.106188	+	0.128459i
$685$	13.7246			0.524391
$686$	14.7194	+	12.3510i	0.561990	+	0.471565i
$687$	16.4731	−	5.99573i	0.628489	−	0.228751i
$688$	−0.273318	−	1.55007i	−0.0104202	−	0.0590957i
$689$	0.240352	−	1.36310i	0.00915669	−	0.0519302i
$690$	3.68479	+	1.34115i	0.140278	+	0.0510569i
$691$	0.752374	+	1.30315i	0.0286217	+	0.0495742i	0.879981	−	0.475008i	$-0.157555\pi$
$691$	0.752374	+	1.30315i	0.0286217	+	0.0495742i	−0.851360	+	0.524582i	$0.824222\pi$
$692$	0.169778	−	0.294064i	0.00645398	−	0.0111786i
$693$	1.26604	−	1.06234i	0.0480931	−	0.0403549i
$694$	−24.5009	+	20.5587i	−0.930043	+	0.780399i
$695$	−8.87346	+	15.3693i	−0.336589	+	0.582990i
$696$	−0.745100	−	1.29055i	−0.0282429	−	0.0489182i
$697$	3.55303	+	1.29320i	0.134581	+	0.0489834i
$698$	3.10653	−	17.6180i	0.117584	−	0.666852i
$699$	4.79561	+	27.1972i	0.181387	+	1.02869i
$700$	2.37939	−	0.866025i	0.0899323	−	0.0327327i
$701$	−2.54988	−	2.13960i	−0.0963076	−	0.0808116i	0.593363	−	0.804935i	$-0.297800\pi$
$701$	−2.54988	−	2.13960i	−0.0963076	−	0.0808116i	−0.689670	+	0.724124i	$0.742244\pi$
$702$	0.226682			0.00855555
$703$	0.0432332	+	5.87257i	0.00163057	+	0.221488i
$704$	−0.652704			−0.0245997
$705$	6.06805	+	5.09170i	0.228536	+	0.191764i
$706$	−0.0145479	+	0.00529501i	−0.000547518	+	0.000199280i
$707$	3.92602	+	22.2656i	0.147653	+	0.837383i
$708$	0.539363	−	3.05888i	0.0202705	−	0.114960i
$709$	42.1117	+	15.3274i	1.58154	+	0.575633i	0.975538	−	0.219830i	$-0.0705502\pi$
$709$	42.1117	+	15.3274i	1.58154	+	0.575633i	0.606002	+	0.795463i	$0.292772\pi$
$710$	4.61721	+	7.99724i	0.173281	+	0.300131i
$711$	1.43242	−	2.48102i	0.0537199	−	0.0930456i
$712$	11.5778	−	9.71497i	0.433898	−	0.364084i
$713$	2.87804	−	2.41496i	0.107783	−	0.0904411i
$714$	−1.03209	+	1.78763i	−0.0386250	+	0.0669004i
$715$	0.0739780	+	0.128134i	0.00276662	+	0.00479192i
$716$	−13.7297	−	4.99719i	−0.513102	−	0.186754i
$717$	−3.59539	+	20.3905i	−0.134272	+	0.761496i
$718$	3.17230	+	17.9910i	0.118389	+	0.671419i
$719$	−41.7533	+	15.1970i	−1.55714	+	0.566751i	−0.970078	−	0.242794i	$-0.921936\pi$
$719$	−41.7533	+	15.1970i	−1.55714	+	0.566751i	−0.587058	+	0.809545i	$0.699714\pi$
$720$	−0.766044	−	0.642788i	−0.0285488	−	0.0239553i
$721$	3.69965			0.137782
$722$	−14.7331	−	11.9973i	−0.548308	−	0.446495i
$723$	−12.9581			−0.481917
$724$	4.07532	+	3.41960i	0.151458	+	0.127088i
$725$	1.40033	−	0.509678i	0.0520069	−	0.0189290i
$726$	1.83615	+	10.4133i	0.0681460	+	0.386475i
$727$	1.49676	−	8.48854i	0.0555117	−	0.314823i	−0.944390	−	0.328827i	$-0.893347\pi$
$727$	1.49676	−	8.48854i	0.0555117	−	0.314823i	0.999902	+	0.0140043i	$0.00445786\pi$
$728$	−0.539363	−	0.196312i	−0.0199901	−	0.00727581i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	5.42262	−	9.39225i	0.200700	−	0.347623i
$731$	−0.982926	+	0.824773i	−0.0363548	+	0.0305053i
$732$	2.43969	−	2.04715i	0.0901736	−	0.0756647i
$733$	2.12495	−	3.68052i	0.0784869	−	0.135943i	−0.824110	−	0.566429i	$-0.808324\pi$
$733$	2.12495	−	3.68052i	0.0784869	−	0.135943i	0.902597	+	0.430486i	$0.141658\pi$
$734$	−4.55303	−	7.88609i	−0.168056	−	0.291081i
$735$	0.553033	+	0.201288i	0.0203989	+	0.00742461i
$736$	−0.680922	+	3.86170i	−0.0250991	+	0.142344i
$737$	0.102196	+	0.579585i	0.00376445	+	0.0213493i
$738$	4.35844	−	1.58634i	0.160436	−	0.0583941i
$739$	−5.48474	−	4.60224i	−0.201759	−	0.169296i	0.536310	−	0.844021i	$-0.319818\pi$
$739$	−5.48474	−	4.60224i	−0.201759	−	0.169296i	−0.738069	+	0.674725i	$0.764262\pi$
$740$	−1.34730			−0.0495276
$741$	0.00727396	+	0.988055i	0.000267216	+	0.0362971i
$742$	15.4611			0.567595
$743$	−12.8136	−	10.7519i	−0.470086	−	0.394449i	0.376740	−	0.926319i	$-0.377045\pi$
$743$	−12.8136	−	10.7519i	−0.470086	−	0.394449i	−0.846826	+	0.531870i	$0.821489\pi$
$744$	−0.900330	+	0.327693i	−0.0330077	+	0.0120138i
$745$	−1.10994	−	6.29477i	−0.0406650	−	0.230622i
$746$	0.00845601	−	0.0479564i	0.000309596	−	0.00175581i
$747$	−8.38578	−	3.05217i	−0.306820	−	0.111673i
$748$	0.266044	+	0.460802i	0.00972755	+	0.0168486i
$749$	9.28359	−	16.0796i	0.339215	−	0.587537i
$750$	0.766044	−	0.642788i	0.0279720	−	0.0234713i
$751$	0.611281	−	0.512926i	0.0223060	−	0.0187169i	−0.631566	−	0.775322i	$-0.717588\pi$
$751$	0.611281	−	0.512926i	0.0223060	−	0.0187169i	0.653872	+	0.756605i	$0.273143\pi$
$752$	−3.96064	+	6.86002i	−0.144430	+	0.250159i
$753$	3.69594	+	6.40155i	0.134687	+	0.233285i
$754$	−0.317429	−	0.115535i	−0.0115601	−	0.00420753i
$755$	−1.84982	+	10.4909i	−0.0673219	+	0.381802i
$756$	0.439693	+	2.49362i	0.0159915	+	0.0906921i
$757$	19.3109	−	7.02860i	0.701868	−	0.255459i	0.0336595	−	0.999433i	$-0.489284\pi$
$757$	19.3109	−	7.02860i	0.701868	−	0.255459i	0.668208	+	0.743974i	$0.267062\pi$
$758$	16.5378	+	13.8768i	0.600679	+	0.504029i
$759$	−2.55943			−0.0929014
$760$	2.77719	−	3.35965i	0.100739	−	0.121867i
$761$	17.7110			0.642024			0.321012	−	0.947075i	$-0.395977\pi$
$761$	17.7110			0.642024			0.321012	+	0.947075i	$0.395977\pi$
$762$	0.0923963	+	0.0775297i	0.00334716	+	0.00280860i
$763$	16.8735	−	6.14144i	0.610860	−	0.222335i
$764$	3.35070	+	19.0028i	0.121224	+	0.687496i
$765$	−0.141559	+	0.802823i	−0.00511809	+	0.0290261i
$766$	4.53462	+	1.65046i	0.163842	+	0.0596337i
$767$	−0.352044	−	0.609758i	−0.0127116	−	0.0220171i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	6.04891	−	5.07564i	0.218129	−	0.183032i	−0.527175	−	0.849757i	$-0.676749\pi$
$769$	6.04891	−	5.07564i	0.218129	−	0.183032i	0.745304	+	0.666725i	$0.232304\pi$
$770$	−1.26604	+	1.06234i	−0.0456251	+	0.0382840i
$771$	0.311337	−	0.539252i	0.0112125	−	0.0194207i
$772$	−8.46838	−	14.6677i	−0.304784	−	0.527901i
$773$	2.37299	+	0.863697i	0.0853505	+	0.0310650i	0.384342	−	0.923191i	$-0.374428\pi$
$773$	2.37299	+	0.863697i	0.0853505	+	0.0310650i	−0.298992	+	0.954256i	$0.596650\pi$
$774$	−0.273318	+	1.55007i	−0.00982423	+	0.0557160i
$775$	−0.166374	−	0.943555i	−0.00597634	−	0.0338935i
$776$	0.740352	−	0.269466i	0.0265771	−	0.00967327i
$777$	2.61334	+	2.19285i	0.0937531	+	0.0786682i
$778$	17.8794			0.641007
$779$	7.05438	+	18.9466i	0.252749	+	0.678832i
$780$	−0.226682			−0.00811650
$781$	−4.61721	−	3.87430i	−0.165217	−	0.138633i
$782$	3.00387	−	1.09332i	0.107418	−	0.0390970i
$783$	0.258770	+	1.46756i	0.00924770	+	0.0524463i
$784$	−0.102196	+	0.579585i	−0.00364987	+	0.0206995i
$785$	−10.7233	−	3.90295i	−0.382730	−	0.139302i
$786$	4.92127	+	8.52390i	0.175536	+	0.304037i
$787$	1.14883	−	1.98984i	0.0409515	−	0.0709300i	−0.844823	−	0.535046i	$-0.820294\pi$
$787$	1.14883	−	1.98984i	0.0409515	−	0.0709300i	0.885775	+	0.464116i	$0.153628\pi$
$788$	12.5116	−	10.4985i	0.445708	−	0.373993i
$789$	−2.95084	+	2.47605i	−0.105053	+	0.0881496i
$790$	−1.43242	+	2.48102i	−0.0509632	+	0.0882708i
$791$	−18.6236	−	32.2570i	−0.662179	−	1.14693i
$792$	0.613341	+	0.223238i	0.0217941	+	0.00793241i
$793$	0.125362	−	0.710966i	0.00445175	−	0.0252471i
$794$	−5.79607	−	32.8712i	−0.205695	−	1.16655i
$795$	5.73783	−	2.08840i	0.203500	−	0.0740678i
$796$	13.7554	+	11.5421i	0.487546	+	0.409100i
$797$	−6.78013			−0.240164			−0.120082	−	0.992764i	$-0.538316\pi$
$797$	−6.78013			−0.240164			−0.120082	+	0.992764i	$0.538316\pi$
$798$	−10.8550	+	1.99654i	−0.384264	+	0.0706768i
$799$	6.45748			0.228449
$800$	0.766044	+	0.642788i	0.0270838	+	0.0227260i
$801$	−14.2023	+	5.16923i	−0.501815	+	0.182646i
$802$	5.01589	+	28.4465i	0.177117	+	1.00448i
$803$	−1.22921	+	6.97118i	−0.0433778	+	0.246008i
$804$	−0.847296	−	0.308391i	−0.0298818	−	0.0108761i
$805$	4.96451	+	8.59878i	0.174976	+	0.303067i
$806$	−0.108593	+	0.188089i	−0.00382503	+	0.00662514i
$807$	−8.69253	+	7.29390i	−0.305992	+	0.256757i
$808$	−6.84002	+	5.73946i	−0.240631	+	0.201914i
$809$	8.21823	−	14.2344i	0.288937	−	0.500454i	−0.684619	−	0.728901i	$-0.740031\pi$
$809$	8.21823	−	14.2344i	0.288937	−	0.500454i	0.973556	+	0.228447i	$0.0733647\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$	29.1758	+	10.6191i	1.02450	+	0.372887i	0.798984	−	0.601352i	$-0.205371\pi$
$811$	29.1758	+	10.6191i	1.02450	+	0.372887i	0.225516	+	0.974240i	$0.427593\pi$
$812$	0.655230	−	3.71599i	0.0229941	−	0.130406i
$813$	1.76470	+	10.0081i	0.0618907	+	0.351000i
$814$	0.826352	−	0.300767i	0.0289636	−	0.0105419i
$815$	−8.38326	−	7.03439i	−0.293653	−	0.246404i
$816$	−0.815207			−0.0285380
$817$	−6.76517	−	1.14160i	−0.236683	−	0.0399394i
$818$	25.1976			0.881013
$819$	0.439693	+	0.368946i	0.0153641	+	0.0128920i
$820$	−4.35844	+	1.58634i	−0.152203	+	0.0553975i
$821$	5.28317	+	29.9624i	0.184384	+	1.04569i	0.926744	+	0.375693i	$0.122595\pi$
$821$	5.28317	+	29.9624i	0.184384	+	1.04569i	−0.742360	+	0.670001i	$0.766294\pi$
$822$	2.38326	−	13.5161i	0.0831256	−	0.471429i
$823$	28.8273	+	10.4923i	1.00486	+	0.365738i	0.791455	−	0.611227i	$-0.209324\pi$
$823$	28.8273	+	10.4923i	1.00486	+	0.365738i	0.213401	+	0.976965i	$0.431546\pi$
$824$	0.730552	+	1.26535i	0.0254500	+	0.0440807i
$825$	−0.326352	+	0.565258i	−0.0113621	+	0.0196798i
$826$	6.02481	−	5.05542i	0.209630	−	0.175901i
$827$	−23.2683	+	19.5244i	−0.809119	+	0.678931i	−0.950397	−	0.311039i	$-0.899323\pi$
$827$	−23.2683	+	19.5244i	−0.809119	+	0.678931i	0.141278	+	0.989970i	$0.454879\pi$
$828$	1.96064	−	3.39592i	0.0681369	−	0.118016i
$829$	0.687786	+	1.19128i	0.0238878	+	0.0413748i	0.877722	−	0.479170i	$-0.159062\pi$
$829$	0.687786	+	1.19128i	0.0238878	+	0.0413748i	−0.853834	+	0.520545i	$0.825729\pi$
$830$	8.38578	+	3.05217i	0.291075	+	0.105943i
$831$	−5.07532	+	28.7836i	−0.176061	+	0.998491i
$832$	−0.0393628	−	0.223238i	−0.00136466	−	0.00773938i
$833$	0.450837	−	0.164091i	0.0156206	−	0.00568542i
$834$	13.5949	+	11.4075i	0.470754	+	0.395009i
$835$	12.2618			0.424336
$836$	−0.953363	+	2.68058i	−0.0329728	+	0.0927099i
$837$	0.958111			0.0331172
$838$	4.33931	+	3.64111i	0.149899	+	0.125780i
$839$	−19.9577	+	7.26401i	−0.689016	+	0.250781i	−0.662714	−	0.748873i	$-0.730595\pi$
$839$	−19.9577	+	7.26401i	−0.689016	+	0.250781i	−0.0263023	+	0.999654i	$0.508373\pi$
$840$	−0.439693	−	2.49362i	−0.0151708	−	0.0860381i
$841$	−4.65018	+	26.3725i	−0.160351	+	0.909395i
$842$	−22.8542	−	8.31823i	−0.787606	−	0.286665i
$843$	8.25490	+	14.2979i	0.284314	+	0.492446i
$844$	−11.8400	+	20.5075i	−0.407550	+	0.705898i
$845$	9.91921	−	8.32321i	0.341231	−	0.286327i
$846$	6.06805	−	5.09170i	0.208624	−	0.175056i
$847$	−13.3871	+	23.1872i	−0.459987	+	0.796721i
$848$	3.05303	+	5.28801i	0.104842	+	0.181591i
$849$	−1.79426	−	0.653058i	−0.0615789	−	0.0224129i
$850$	0.141559	−	0.802823i	0.00485544	−	0.0275366i
$851$	−0.917404	−	5.20286i	−0.0314482	−	0.178352i
$852$	8.67752	−	3.15836i	0.297287	−	0.108204i
$853$	24.1728	+	20.2834i	0.827660	+	0.694489i	0.954752	−	0.297402i	$-0.0961201\pi$
$853$	24.1728	+	20.2834i	0.827660	+	0.694489i	−0.127093	+	0.991891i	$0.540565\pi$
$854$	8.06418			0.275950
$855$	−3.75877	+	2.20718i	−0.128547	+	0.0754840i
$856$	7.33275			0.250628
$857$	32.1937	+	27.0137i	1.09972	+	0.922772i	0.997406	−	0.0719809i	$-0.0229321\pi$
$857$	32.1937	+	27.0137i	1.09972	+	0.922772i	0.102310	+	0.994753i	$0.467377\pi$
$858$	0.139033	−	0.0506039i	0.00474651	−	0.00172759i
$859$	3.95084	+	22.4063i	0.134801	+	0.764493i	0.974998	+	0.222213i	$0.0713279\pi$
$859$	3.95084	+	22.4063i	0.134801	+	0.764493i	−0.840197	+	0.542281i	$0.817561\pi$
$860$	0.273318	−	1.55007i	0.00932008	−	0.0528568i
$861$	11.0360	+	4.01676i	0.376104	+	0.136891i
$862$	−14.4902	−	25.0978i	−0.493538	−	0.854833i
$863$	6.04189	−	10.4649i	0.205668	−	0.356228i	−0.744677	−	0.667425i	$-0.767397\pi$
$863$	6.04189	−	10.4649i	0.205668	−	0.356228i	0.950345	+	0.311197i	$0.100730\pi$
$864$	−0.766044	+	0.642788i	−0.0260614	+	0.0218681i
$865$	0.260115	−	0.218262i	0.00884416	−	0.00742113i
$866$	−4.47906	+	7.75795i	−0.152205	+	0.263626i
$867$	−8.16772	−	14.1469i	−0.277390	−	0.480454i
$868$	−2.27972	−	0.829748i	−0.0773786	−	0.0281635i
$869$	0.324703	−	1.84148i	0.0110148	−	0.0624680i
$870$	−0.258770	−	1.46756i	−0.00877314	−	0.0497550i
$871$	−0.192066	+	0.0699065i	−0.00650792	+	0.00236869i
$872$	5.43242	+	4.55834i	0.183965	+	0.154365i
$873$	−0.787866			−0.0266652
$874$	14.8650	+	8.43702i	0.502816	+	0.285386i
$875$	2.53209			0.0856002
$876$	−8.30793	−	6.97118i	−0.280699	−	0.235534i
$877$	35.4487	−	12.9023i	1.19702	−	0.435678i	0.334835	−	0.942277i	$-0.391320\pi$
$877$	35.4487	−	12.9023i	1.19702	−	0.435678i	0.862182	+	0.506599i	$0.169097\pi$
$878$	−4.06371	−	23.0465i	−0.137144	−	0.777780i
$879$	−0.494070	+	2.80201i	−0.0166646	+	0.0945095i
$880$	−0.613341	−	0.223238i	−0.0206757	−	0.00752534i
$881$	−2.39899	−	4.15516i	−0.0808239	−	0.139991i	0.822780	−	0.568360i	$-0.192422\pi$
$881$	−2.39899	−	4.15516i	−0.0808239	−	0.139991i	−0.903604	+	0.428369i	$0.859088\pi$
$882$	0.294263	−	0.509678i	0.00990835	−	0.0171618i
$883$	−40.8489	+	34.2763i	−1.37468	+	1.15349i	−0.403541	+	0.914962i	$0.632221\pi$
$883$	−40.8489	+	34.2763i	−1.37468	+	1.15349i	−0.971135	+	0.238529i	$0.923335\pi$
$884$	−0.141559	+	0.118782i	−0.00476115	+	0.00399508i
$885$	1.55303	−	2.68993i	0.0522046	−	0.0904211i
$886$	15.7344	+	27.2528i	0.528608	+	0.915576i
$887$	18.6582	+	6.79104i	0.626482	+	0.228021i	0.635699	−	0.771937i	$-0.280712\pi$
$887$	18.6582	+	6.79104i	0.626482	+	0.228021i	−0.00921749	+	0.999958i	$0.502934\pi$
$888$	−0.233956	+	1.32683i	−0.00785103	+	0.0445254i
$889$	0.0530334	+	0.300767i	0.00177868	+	0.0100874i
$890$	14.2023	−	5.16923i	0.476063	−	0.173273i
$891$	−0.500000	−	0.419550i	−0.0167506	−	0.0140554i
$892$	−0.0760373			−0.00254592
$893$	22.3883	+	26.2859i	0.749196	+	0.879624i
$894$	−6.39187			−0.213776
$895$	−11.1925	−	9.39165i	−0.374125	−	0.313928i
$896$	2.37939	−	0.866025i	0.0794897	−	0.0289319i
$897$	−0.154353	−	0.875377i	−0.00515368	−	0.0292280i
$898$	2.35158	−	13.3365i	0.0784731	−	0.445043i
$899$	−1.34167	−	0.488328i	−0.0447472	−	0.0162867i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	2.48886	−	4.31082i	0.0829158	−	0.143614i
$902$	2.31908	−	1.94594i	0.0772168	−	0.0647926i
$903$	−3.05303	+	2.56180i	−0.101599	+	0.0852513i
$904$	7.35504	−	12.7393i	0.244625	−	0.423703i
$905$	2.65998	+	4.60722i	0.0884206	+	0.153149i
$906$	10.0103	+	3.64344i	0.332569	+	0.121045i
$907$	−7.89693	+	44.7857i	−0.262213	+	1.48708i	0.514642	+	0.857405i	$0.327925\pi$
$907$	−7.89693	+	44.7857i	−0.262213	+	1.48708i	−0.776855	+	0.629679i	$0.783186\pi$
$908$	2.07310	+	11.7571i	0.0687983	+	0.390174i
$909$	8.39053	−	3.05390i	0.278296	−	0.101292i
$910$	−0.439693	−	0.368946i	−0.0145757	−	0.0122304i
$911$	−33.7033			−1.11664			−0.558320	−	0.829626i	$-0.688554\pi$
$911$	−33.7033			−1.11664			−0.558320	+	0.829626i	$0.688554\pi$
$912$	−2.82635	−	3.31839i	−0.0935899	−	0.109883i
$913$	−5.82470			−0.192770
$914$	−13.7271	−	11.5184i	−0.454054	−	0.380996i
$915$	2.99273	−	1.08926i	0.0989365	−	0.0360099i
$916$	3.04411	+	17.2640i	0.100580	+	0.570419i
$917$	−4.32770	+	24.5436i	−0.142913	+	0.810501i
$918$	0.766044	+	0.278817i	0.0252832	+	0.00920234i
$919$	7.00253	+	12.1287i	0.230992	+	0.400090i	0.958100	−	0.286433i	$-0.0924695\pi$
$919$	7.00253	+	12.1287i	0.230992	+	0.400090i	−0.727108	+	0.686523i	$0.759136\pi$
$920$	−1.96064	+	3.39592i	−0.0646403	+	0.111960i
$921$	−4.23396	+	3.55271i	−0.139514	+	0.117066i
$922$	−18.8314	+	15.8014i	−0.620179	+	0.520392i
$923$	1.04664	−	1.81283i	0.0344505	−	0.0596700i
$924$	0.826352	+	1.43128i	0.0271850	+	0.0470858i
$925$	−1.26604	−	0.460802i	−0.0416273	−	0.0151511i
$926$	3.80763	−	21.5941i	0.125126	−	0.709627i
$927$	−0.253718	−	1.43891i	−0.00833319	−	0.0472599i
$928$	1.40033	−	0.509678i	0.0459681	−	0.0167310i
$929$	28.5815	+	23.9827i	0.937728	+	0.786847i	0.977188	−	0.212374i	$-0.0681196\pi$
$929$	28.5815	+	23.9827i	0.937728	+	0.786847i	−0.0394608	+	0.999221i	$0.512564\pi$
$930$	−0.958111			−0.0314177
$931$	2.23102	+	1.26627i	0.0731187	+	0.0415004i
$932$	−27.6168			−0.904618
$933$	10.4743	+	8.78899i	0.342913	+	0.287739i
$934$	−17.9979	+	6.55071i	−0.588911	+	0.214346i
$935$	0.0923963	+	0.524005i	0.00302168	+	0.0171368i
$936$	−0.0393628	+	0.223238i	−0.00128661	+	0.00729676i
$937$	14.2258	+	5.17777i	0.464737	+	0.169150i	0.563767	−	0.825934i	$-0.309352\pi$
$937$	14.2258	+	5.17777i	0.464737	+	0.169150i	−0.0990299	+	0.995084i	$0.531574\pi$
$938$	−1.14156	−	1.97724i	−0.0372732	−	0.0645591i
$939$	−14.4474	+	25.0237i	−0.471474	+	0.816617i
$940$	−6.06805	+	5.09170i	−0.197918	+	0.166073i
$941$	16.6009	−	13.9298i	0.541172	−	0.454097i	−0.330766	−	0.943713i	$-0.607307\pi$
$941$	16.6009	−	13.9298i	0.541172	−	0.454097i	0.871939	+	0.489615i	$0.162863\pi$
$942$	−5.70574	+	9.88263i	−0.185903	+	0.321993i
$943$	−9.09374	−	15.7508i	−0.296133	−	0.512917i
$944$	2.91875	+	1.06234i	0.0949972	+	0.0345761i
$945$	−0.439693	+	2.49362i	−0.0143032	+	0.0811175i
$946$	0.178396	+	1.01173i	0.00580015	+	0.0328943i
$947$	−22.9748	+	8.36213i	−0.746580	+	0.271733i	−0.687166	−	0.726501i	$-0.741145\pi$
$947$	−22.9748	+	8.36213i	−0.746580	+	0.271733i	−0.0594140	+	0.998233i	$0.518923\pi$
$948$	2.19459	+	1.84148i	0.0712771	+	0.0598086i
$949$	−2.45842			−0.0798035
$950$	3.75877	−	2.20718i	0.121951	−	0.0716104i
$951$	−0.532089			−0.0172542
$952$	−1.58125	−	1.32683i	−0.0512487	−	0.0430027i
$953$	−40.9013	+	14.8868i	−1.32492	+	0.482232i	−0.905032	−	0.425343i	$-0.860153\pi$
$953$	−40.9013	+	14.8868i	−1.32492	+	0.482232i	−0.419890	+	0.907575i	$0.637931\pi$
$954$	−1.06031	−	6.01330i	−0.0343287	−	0.194688i
$955$	−3.35070	+	19.0028i	−0.108426	+	0.614915i
$956$	−19.4564	−	7.08153i	−0.629264	−	0.229033i
$957$	0.486329	+	0.842347i	0.0157208	+	0.0272292i
$958$	5.57057	−	9.64852i	0.179977	−	0.311729i
$959$	26.6215	−	22.3381i	0.859655	−	0.721336i
$960$	0.766044	−	0.642788i	0.0247240	−	0.0207459i
$961$	15.0410	−	26.0518i	0.485194	−	0.840381i
$962$	0.152704	+	0.264490i	0.00492336	+	0.00852752i
$963$	−6.89053	−	2.50795i	−0.222044	−	0.0808175i
$964$	2.25015	−	12.7612i	0.0724725	−	0.411012i
$965$	−2.94104	−	16.6794i	−0.0946753	−	0.536930i
$966$	9.33022	−	3.39592i	0.300195	−	0.109262i
$967$	−7.13223	−	5.98465i	−0.229357	−	0.192453i	0.520866	−	0.853639i	$-0.325609\pi$
$967$	−7.13223	−	5.98465i	−0.229357	−	0.192453i	−0.750223	+	0.661185i	$0.770054\pi$
$968$	−10.5740			−0.339861
$969$	−1.19072	+	3.34797i	−0.0382515	+	0.107552i
$970$	0.787866			0.0252969
$971$	7.09555	+	5.95387i	0.227707	+	0.191069i	0.749502	−	0.662002i	$-0.230293\pi$
$971$	7.09555	+	5.95387i	0.227707	+	0.191069i	−0.521795	+	0.853071i	$0.674737\pi$
$972$	0.939693	−	0.342020i	0.0301407	−	0.0109703i
$973$	7.80319	+	44.2541i	0.250159	+	1.41872i
$974$	4.22193	−	23.9438i	0.135279	−	0.767208i
$975$	−0.213011	−	0.0775297i	−0.00682181	−	0.00248294i
$976$	1.59240	+	2.75811i	0.0509714	+	0.0882850i
$977$	8.73009	−	15.1210i	0.279300	−	0.483762i	−0.691911	−	0.721983i	$-0.743231\pi$
$977$	8.73009	−	15.1210i	0.279300	−	0.483762i	0.971211	+	0.238221i	$0.0765642\pi$
$978$	−8.38326	+	7.03439i	−0.268067	+	0.224935i
$979$	−7.55690	+	6.34100i	−0.241520	+	0.202659i
$980$	−0.294263	+	0.509678i	−0.00939988	+	0.0162811i
$981$	−3.54576	−	6.14144i	−0.113207	−	0.196081i
$982$	−21.9008	−	7.97124i	−0.698883	−	0.254372i
$983$	5.22297	−	29.6210i	0.166587	−	0.944762i	−0.780826	−	0.624748i	$-0.785202\pi$
$983$	5.22297	−	29.6210i	0.166587	−	0.944762i	0.947413	−	0.320013i	$-0.103687\pi$
$984$	0.805407	+	4.56769i	0.0256754	+	0.145613i
$985$	15.3478	−	5.58613i	0.489020	−	0.177989i
$986$	−0.930608	−	0.780873i	−0.0296366	−	0.0248680i
$987$	20.0574			0.638433
$988$	−0.974308	−	0.164411i	−0.0309969	−	0.00523060i
$989$	6.17200			0.196258
$990$	0.500000	+	0.419550i	0.0158910	+	0.0133342i
$991$	−42.7798	+	15.5706i	−1.35894	+	0.494615i	−0.915728	−	0.401799i	$-0.868385\pi$
$991$	−42.7798	+	15.5706i	−1.35894	+	0.494615i	−0.443216	+	0.896415i	$0.646163\pi$
$992$	−0.166374	−	0.943555i	−0.00528239	−	0.0299579i
$993$	−2.55303	+	14.4790i	−0.0810181	+	0.459476i
$994$	21.9722	+	7.99724i	0.696917	+	0.253657i
$995$	8.97818	+	15.5507i	0.284627	+	0.492989i
$996$	4.46198	−	7.72838i	0.141383	−	0.244883i
$997$	−34.8057	+	29.2055i	−1.10231	+	0.924946i	−0.997578	−	0.0695545i	$-0.977842\pi$
$997$	−34.8057	+	29.2055i	−1.10231	+	0.924946i	−0.104730	+	0.994501i	$0.533398\pi$
$998$	0.826352	−	0.693392i	0.0261577	−	0.0219489i
$999$	0.673648	−	1.16679i	0.0213133	−	0.0369157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.u.e.301.1	✓	6
19.6	even	9	inner	570.2.u.e.481.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.u.e.301.1	✓	6	1.1	even	1	trivial
570.2.u.e.481.1	yes	6	19.6	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)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.939693 - 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.173648 + 0.984808i) q^{5} +(0.939693 + 0.342020i) q^{6} +(1.26604 + 2.19285i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.939693 - 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.173648 + 0.984808i) q^{5} +(0.939693 + 0.342020i) q^{6} +(1.26604 + 2.19285i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +(-0.766044 + 0.642788i) q^{10} +(0.326352 - 0.565258i) q^{11} +(0.500000 + 0.866025i) q^{12} +(0.213011 + 0.0775297i) q^{13} +(-0.439693 + 2.49362i) q^{14} +(0.173648 + 0.984808i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(0.624485 + 0.524005i) q^{17} +1.00000 q^{18} +(0.0320889 + 4.35878i) q^{19} -1.00000 q^{20} +(1.93969 + 1.62760i) q^{21} +(0.613341 - 0.223238i) q^{22} +(-0.680922 - 3.86170i) q^{23} +(-0.173648 + 0.984808i) q^{24} +(-0.939693 - 0.342020i) q^{25} +(0.113341 + 0.196312i) q^{26} +(0.500000 - 0.866025i) q^{27} +(-1.93969 + 1.62760i) q^{28} +(-1.14156 + 0.957882i) q^{29} +(-0.500000 + 0.866025i) q^{30} +(0.479055 + 0.829748i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.113341 - 0.642788i) q^{33} +(0.141559 + 0.802823i) q^{34} +(-2.37939 + 0.866025i) q^{35} +(0.766044 + 0.642788i) q^{36} +1.34730 q^{37} +(-2.77719 + 3.35965i) q^{38} +0.226682 q^{39} +(-0.766044 - 0.642788i) q^{40} +(4.35844 - 1.58634i) q^{41} +(0.439693 + 2.49362i) q^{42} +(-0.273318 + 1.55007i) q^{43} +(0.613341 + 0.223238i) q^{44} +(0.500000 + 0.866025i) q^{45} +(1.96064 - 3.39592i) q^{46} +(6.06805 - 5.09170i) q^{47} +(-0.766044 + 0.642788i) q^{48} +(0.294263 - 0.509678i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(0.766044 + 0.278817i) q^{51} +(-0.0393628 + 0.223238i) q^{52} +(-1.06031 - 6.01330i) q^{53} +(0.939693 - 0.342020i) q^{54} +(0.500000 + 0.419550i) q^{55} -2.53209 q^{56} +(1.52094 + 4.08494i) q^{57} -1.49020 q^{58} +(-2.37939 - 1.99654i) q^{59} +(-0.939693 + 0.342020i) q^{60} +(-0.553033 - 3.13641i) q^{61} +(-0.166374 + 0.943555i) q^{62} +(2.37939 + 0.866025i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.113341 + 0.196312i) q^{65} +(0.500000 - 0.419550i) q^{66} +(-0.690722 + 0.579585i) q^{67} +(-0.407604 + 0.705990i) q^{68} +(-1.96064 - 3.39592i) q^{69} +(-2.37939 - 0.866025i) q^{70} +(1.60354 - 9.09413i) q^{71} +(0.173648 + 0.984808i) q^{72} +(-10.1912 + 3.70929i) q^{73} +(1.03209 + 0.866025i) q^{74} -1.00000 q^{75} +(-4.28699 + 0.788496i) q^{76} +1.65270 q^{77} +(0.173648 + 0.145708i) q^{78} +(2.69207 - 0.979832i) q^{79} +(-0.173648 - 0.984808i) q^{80} +(0.173648 - 0.984808i) q^{81} +(4.35844 + 1.58634i) q^{82} +(-4.46198 - 7.72838i) q^{83} +(-1.26604 + 2.19285i) q^{84} +(-0.624485 + 0.524005i) q^{85} +(-1.20574 + 1.01173i) q^{86} +(-0.745100 + 1.29055i) q^{87} +(0.326352 + 0.565258i) q^{88} +(-14.2023 - 5.16923i) q^{89} +(-0.173648 + 0.984808i) q^{90} +(0.0996702 + 0.565258i) q^{91} +(3.68479 - 1.34115i) q^{92} +(0.733956 + 0.615862i) q^{93} +7.92127 q^{94} +(-4.29813 - 0.725293i) q^{95} -1.00000 q^{96} +(-0.603541 - 0.506431i) q^{97} +(0.553033 - 0.201288i) q^{98} +(-0.113341 - 0.642788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{7} - 3 q^{8}+O(q^{10}) \) 6 * q + 3 * q^7 - 3 * q^8	\( 6 q + 3 q^{7} - 3 q^{8} + 3 q^{11} + 3 q^{12} + 9 q^{13} + 3 q^{14} - 9 q^{17} + 6 q^{18} - 9 q^{19} - 6 q^{20} + 6 q^{21} - 3 q^{22} - 21 q^{23} - 6 q^{26} + 3 q^{27} - 6 q^{28} - 15 q^{29} - 3 q^{30} + 6 q^{31} - 6 q^{33} + 9 q^{34} - 3 q^{35} + 6 q^{37} - 6 q^{38} - 12 q^{39} + 18 q^{41} - 3 q^{42} - 15 q^{43} - 3 q^{44} + 3 q^{45} + 3 q^{46} - 6 q^{47} + 12 q^{49} - 3 q^{50} - 9 q^{52} - 12 q^{53} + 3 q^{55} - 6 q^{56} + 6 q^{57} - 6 q^{58} - 3 q^{59} + 9 q^{61} + 18 q^{62} + 3 q^{63} - 3 q^{64} + 6 q^{65} + 3 q^{66} - 24 q^{67} - 6 q^{68} - 3 q^{69} - 3 q^{70} - 15 q^{73} - 3 q^{74} - 6 q^{75} - 18 q^{76} + 12 q^{77} + 27 q^{79} + 18 q^{82} - 9 q^{83} - 3 q^{84} + 9 q^{85} + 3 q^{86} - 3 q^{87} + 3 q^{88} - 33 q^{89} + 15 q^{91} + 15 q^{92} + 9 q^{93} + 30 q^{94} - 12 q^{95} - 6 q^{96} + 6 q^{97} - 9 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q + 3 * q^7 - 3 * q^8 + 3 * q^11 + 3 * q^12 + 9 * q^13 + 3 * q^14 - 9 * q^17 + 6 * q^18 - 9 * q^19 - 6 * q^20 + 6 * q^21 - 3 * q^22 - 21 * q^23 - 6 * q^26 + 3 * q^27 - 6 * q^28 - 15 * q^29 - 3 * q^30 + 6 * q^31 - 6 * q^33 + 9 * q^34 - 3 * q^35 + 6 * q^37 - 6 * q^38 - 12 * q^39 + 18 * q^41 - 3 * q^42 - 15 * q^43 - 3 * q^44 + 3 * q^45 + 3 * q^46 - 6 * q^47 + 12 * q^49 - 3 * q^50 - 9 * q^52 - 12 * q^53 + 3 * q^55 - 6 * q^56 + 6 * q^57 - 6 * q^58 - 3 * q^59 + 9 * q^61 + 18 * q^62 + 3 * q^63 - 3 * q^64 + 6 * q^65 + 3 * q^66 - 24 * q^67 - 6 * q^68 - 3 * q^69 - 3 * q^70 - 15 * q^73 - 3 * q^74 - 6 * q^75 - 18 * q^76 + 12 * q^77 + 27 * q^79 + 18 * q^82 - 9 * q^83 - 3 * q^84 + 9 * q^85 + 3 * q^86 - 3 * q^87 + 3 * q^88 - 33 * q^89 + 15 * q^91 + 15 * q^92 + 9 * q^93 + 30 * q^94 - 12 * q^95 - 6 * q^96 + 6 * q^97 - 9 * q^98 + 6 * q^99

Introduction

L-functions

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