LMFDB - Embedded newform 570.2.u.j.481.1

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			481.1
Root			$0.500000 - 0.168222i$ of defining polynomial
Character	$\chi$	$=$	570.481
Dual form			570.2.u.j.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(0.939693 + 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.173648 + 0.984808i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-0.965167 + 1.67172i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +O(q^{10})$	\(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} +(-0.965167 + 1.67172i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +(0.766044 + 0.642788i) q^{10} +(0.732941 + 1.26949i) q^{11} +(0.500000 - 0.866025i) q^{12} +(4.09397 - 1.49008i) q^{13} +(0.335199 + 1.90101i) q^{14} +(-0.173648 + 0.984808i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(5.27163 - 4.42343i) q^{17} +1.00000 q^{18} +(3.99418 + 1.74542i) q^{19} +1.00000 q^{20} +(-1.47872 + 1.24079i) q^{21} +(1.37748 + 0.501361i) q^{22} +(-1.26672 + 7.18395i) q^{23} +(-0.173648 - 0.984808i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(2.17836 - 3.77302i) q^{26} +(0.500000 + 0.866025i) q^{27} +(1.47872 + 1.24079i) q^{28} +(-3.03527 - 2.54689i) q^{29} +(0.500000 + 0.866025i) q^{30} +(1.44277 - 2.49894i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.254548 + 1.44361i) q^{33} +(1.19498 - 6.77708i) q^{34} +(-1.81392 - 0.660213i) q^{35} +(0.766044 - 0.642788i) q^{36} -10.0326 q^{37} +(4.18166 - 1.23034i) q^{38} +4.35671 q^{39} +(0.766044 - 0.642788i) q^{40} +(-7.54722 - 2.74696i) q^{41} +(-0.335199 + 1.90101i) q^{42} +(-0.0773486 - 0.438666i) q^{43} +(1.37748 - 0.501361i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(3.64739 + 6.31746i) q^{46} +(-6.66509 - 5.59267i) q^{47} +(-0.766044 - 0.642788i) q^{48} +(1.63691 + 2.83521i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(6.46662 - 2.35366i) q^{51} +(-0.756535 - 4.29052i) q^{52} +(-1.32227 + 7.49898i) q^{53} +(0.939693 + 0.342020i) q^{54} +(-1.12293 + 0.942250i) q^{55} +1.93033 q^{56} +(3.15633 + 3.00625i) q^{57} -3.96226 q^{58} +(-5.40769 + 4.53759i) q^{59} +(0.939693 + 0.342020i) q^{60} +(2.10494 - 11.9377i) q^{61} +(-0.501067 - 2.84169i) q^{62} +(-1.81392 + 0.660213i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.17836 + 3.77302i) q^{65} +(1.12293 + 0.942250i) q^{66} +(0.817439 + 0.685913i) q^{67} +(-3.44081 - 5.95967i) q^{68} +(-3.64739 + 6.31746i) q^{69} +(-1.81392 + 0.660213i) q^{70} +(-2.09603 - 11.8872i) q^{71} +(0.173648 - 0.984808i) q^{72} +(5.10361 + 1.85756i) q^{73} +(-7.68541 + 6.44882i) q^{74} -1.00000 q^{75} +(2.41249 - 3.63041i) q^{76} -2.82964 q^{77} +(3.33743 - 2.80044i) q^{78} +(1.20036 + 0.436896i) q^{79} +(0.173648 - 0.984808i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-7.54722 + 2.74696i) q^{82} +(5.57704 - 9.65972i) q^{83} +(0.965167 + 1.67172i) q^{84} +(5.27163 + 4.42343i) q^{85} +(-0.341221 - 0.286319i) q^{86} +(-1.98113 - 3.43142i) q^{87} +(0.732941 - 1.26949i) q^{88} +(-11.4657 + 4.17316i) q^{89} +(0.173648 + 0.984808i) q^{90} +(-1.46036 + 8.28214i) q^{91} +(6.85485 + 2.49496i) q^{92} +(2.21044 - 1.85478i) q^{93} -8.70065 q^{94} +(-1.02532 + 4.23659i) q^{95} -1.00000 q^{96} +(9.63869 - 8.08783i) q^{97} +(3.07638 + 1.11971i) q^{98} +(-0.254548 + 1.44361i) 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$	$1$

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
$7$	−0.965167	+	1.67172i	−0.364799	+	0.631850i	−0.988744	−	0.149618i	$-0.952196\pi$
$7$	−0.965167	+	1.67172i	−0.364799	+	0.631850i	0.623945	+	0.781468i	$0.285529\pi$
$8$	−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
$11$	0.732941	+	1.26949i	0.220990	+	0.382766i	0.955109	−	0.296255i	$-0.0957379\pi$
$11$	0.732941	+	1.26949i	0.220990	+	0.382766i	−0.734119	+	0.679021i	$0.762405\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	4.09397	−	1.49008i	1.13546	−	0.413275i	0.295190	−	0.955439i	$-0.404617\pi$
$13$	4.09397	−	1.49008i	1.13546	−	0.413275i	0.840273	+	0.542164i	$0.182395\pi$
$14$	0.335199	+	1.90101i	0.0895857	+	0.508065i
$15$	−0.173648	+	0.984808i	−0.0448358	+	0.254276i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	5.27163	−	4.42343i	1.27856	−	1.07284i	0.285118	−	0.958492i	$-0.407967\pi$
$17$	5.27163	−	4.42343i	1.27856	−	1.07284i	0.993441	−	0.114346i	$-0.0364773\pi$
$18$	1.00000			0.235702
$19$	3.99418	+	1.74542i	0.916328	+	0.400428i
$19$	3.99418	+	1.74542i	0.916328	+	0.400428i
$20$	1.00000			0.223607
$21$	−1.47872	+	1.24079i	−0.322683	+	0.270763i
$22$	1.37748	+	0.501361i	0.293679	+	0.106890i
$23$	−1.26672	+	7.18395i	−0.264130	+	1.49796i	0.507370	+	0.861729i	$0.330618\pi$
$23$	−1.26672	+	7.18395i	−0.264130	+	1.49796i	−0.771500	+	0.636229i	$0.780493\pi$
$24$	−0.173648	−	0.984808i	−0.0354458	−	0.201023i
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$	2.17836	−	3.77302i	0.427211	−	0.739951i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	1.47872	+	1.24079i	0.279452	+	0.234488i
$29$	−3.03527	−	2.54689i	−0.563635	−	0.472946i	0.315892	−	0.948795i	$-0.397696\pi$
$29$	−3.03527	−	2.54689i	−0.563635	−	0.472946i	−0.879527	+	0.475849i	$0.842141\pi$
$30$	0.500000	+	0.866025i	0.0912871	+	0.158114i
$31$	1.44277	−	2.49894i	0.259128	−	0.448823i	−0.706880	−	0.707333i	$-0.749898\pi$
$31$	1.44277	−	2.49894i	0.259128	−	0.448823i	0.966009	+	0.258510i	$0.0832314\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	0.254548	+	1.44361i	0.0443110	+	0.251300i
$34$	1.19498	−	6.77708i	0.204938	−	1.16226i
$35$	−1.81392	−	0.660213i	−0.306608	−	0.111596i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$	−10.0326			−1.64935			−0.824673	−	0.565609i	$-0.808641\pi$
$37$	−10.0326			−1.64935			−0.824673	+	0.565609i	$0.808641\pi$
$38$	4.18166	−	1.23034i	0.678355	−	0.199587i
$39$	4.35671			0.697632
$40$	0.766044	−	0.642788i	0.121122	−	0.101634i
$41$	−7.54722	−	2.74696i	−1.17868	−	0.429003i	−0.322943	−	0.946419i	$-0.604672\pi$
$41$	−7.54722	−	2.74696i	−1.17868	−	0.429003i	−0.855735	+	0.517415i	$0.826894\pi$
$42$	−0.335199	+	1.90101i	−0.0517223	+	0.293332i
$43$	−0.0773486	−	0.438666i	−0.0117956	−	0.0668959i	0.978342	−	0.206996i	$-0.0663687\pi$
$43$	−0.0773486	−	0.438666i	−0.0117956	−	0.0668959i	−0.990137	+	0.140100i	$0.955258\pi$
$44$	1.37748	−	0.501361i	0.207663	−	0.0755830i
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	3.64739	+	6.31746i	0.537778	+	0.931459i
$47$	−6.66509	−	5.59267i	−0.972203	−	0.815775i	0.0106920	−	0.999943i	$-0.496597\pi$
$47$	−6.66509	−	5.59267i	−0.972203	−	0.815775i	−0.982895	+	0.184168i	$0.941041\pi$
$48$	−0.766044	−	0.642788i	−0.110569	−	0.0927784i
$49$	1.63691	+	2.83521i	0.233844	+	0.405029i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	6.46662	−	2.35366i	0.905507	−	0.329578i
$52$	−0.756535	−	4.29052i	−0.104913	−	0.594988i
$53$	−1.32227	+	7.49898i	−0.181628	+	1.03006i	0.748583	+	0.663041i	$0.230734\pi$
$53$	−1.32227	+	7.49898i	−0.181628	+	1.03006i	−0.930212	+	0.367024i	$0.880377\pi$
$54$	0.939693	+	0.342020i	0.127876	+	0.0465430i
$55$	−1.12293	+	0.942250i	−0.151416	+	0.127053i
$56$	1.93033			0.257952
$57$	3.15633	+	3.00625i	0.418067	+	0.398188i
$58$	−3.96226			−0.520270
$59$	−5.40769	+	4.53759i	−0.704021	+	0.590744i	−0.922914	−	0.385005i	$-0.874200\pi$
$59$	−5.40769	+	4.53759i	−0.704021	+	0.590744i	0.218894	+	0.975749i	$0.429755\pi$
$60$	0.939693	+	0.342020i	0.121314	+	0.0441546i
$61$	2.10494	−	11.9377i	0.269509	−	1.52846i	−0.486370	−	0.873753i	$-0.661679\pi$
$61$	2.10494	−	11.9377i	0.269509	−	1.52846i	0.755879	−	0.654711i	$-0.227210\pi$
$62$	−0.501067	−	2.84169i	−0.0636356	−	0.360895i
$63$	−1.81392	+	0.660213i	−0.228532	+	0.0831790i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	2.17836	+	3.77302i	0.270192	+	0.467986i
$66$	1.12293	+	0.942250i	0.138223	+	0.115983i
$67$	0.817439	+	0.685913i	0.0998661	+	0.0837976i	0.691354	−	0.722517i	$-0.257015\pi$
$67$	0.817439	+	0.685913i	0.0998661	+	0.0837976i	−0.591488	+	0.806314i	$0.701459\pi$
$68$	−3.44081	−	5.95967i	−0.417260	−	0.722716i
$69$	−3.64739	+	6.31746i	−0.439094	+	0.760533i
$70$	−1.81392	+	0.660213i	−0.216805	+	0.0789105i
$71$	−2.09603	−	11.8872i	−0.248753	−	1.41075i	−0.811614	−	0.584195i	$-0.801410\pi$
$71$	−2.09603	−	11.8872i	−0.248753	−	1.41075i	0.562861	−	0.826552i	$-0.309701\pi$
$72$	0.173648	−	0.984808i	0.0204646	−	0.116061i
$73$	5.10361	+	1.85756i	0.597332	+	0.217411i	0.622951	−	0.782261i	$-0.285933\pi$
$73$	5.10361	+	1.85756i	0.597332	+	0.217411i	−0.0256189	+	0.999672i	$0.508156\pi$
$74$	−7.68541	+	6.44882i	−0.893410	+	0.749660i
$75$	−1.00000			−0.115470
$76$	2.41249	−	3.63041i	0.276731	−	0.416437i
$77$	−2.82964			−0.322467
$78$	3.33743	−	2.80044i	0.377890	−	0.317087i
$79$	1.20036	+	0.436896i	0.135051	+	0.0491546i	0.408662	−	0.912686i	$-0.365996\pi$
$79$	1.20036	+	0.436896i	0.135051	+	0.0491546i	−0.273610	+	0.961841i	$0.588218\pi$
$80$	0.173648	−	0.984808i	0.0194145	−	0.110105i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	−7.54722	+	2.74696i	−0.833451	+	0.303351i
$83$	5.57704	−	9.65972i	0.612160	−	1.06029i	−0.378716	−	0.925513i	$-0.623634\pi$
$83$	5.57704	−	9.65972i	0.612160	−	1.06029i	0.990876	−	0.134779i	$-0.0430324\pi$
$84$	0.965167	+	1.67172i	0.105308	+	0.182399i
$85$	5.27163	+	4.42343i	0.571789	+	0.479788i
$86$	−0.341221	−	0.286319i	−0.0367949	−	0.0308745i
$87$	−1.98113	−	3.43142i	−0.212400	−	0.367887i
$88$	0.732941	−	1.26949i	0.0781317	−	0.135328i
$89$	−11.4657	+	4.17316i	−1.21536	+	0.442354i	−0.868559	−	0.495585i	$-0.834954\pi$
$89$	−11.4657	+	4.17316i	−1.21536	+	0.442354i	−0.346799	+	0.937940i	$0.612731\pi$
$90$	0.173648	+	0.984808i	0.0183041	+	0.103808i
$91$	−1.46036	+	8.28214i	−0.153088	+	0.868204i
$92$	6.85485	+	2.49496i	0.714667	+	0.260118i
$93$	2.21044	−	1.85478i	0.229212	−	0.192332i
$94$	−8.70065			−0.897404
$95$	−1.02532	+	4.23659i	−0.105196	+	0.434665i
$96$	−1.00000			−0.102062
$97$	9.63869	−	8.08783i	0.978661	−	0.821194i	−0.00522568	−	0.999986i	$-0.501663\pi$
$97$	9.63869	−	8.08783i	0.978661	−	0.821194i	0.983887	+	0.178792i	$0.0572189\pi$
$98$	3.07638	+	1.11971i	0.310761	+	0.113108i
$99$	−0.254548	+	1.44361i	−0.0255830	+	0.145088i
$100$	0.173648	+	0.984808i	0.0173648	+	0.0984808i
$101$	−15.5919	+	5.67499i	−1.55145	+	0.564683i	−0.968758	−	0.248008i	$-0.920224\pi$
$101$	−15.5919	+	5.67499i	−1.55145	+	0.564683i	−0.582695	+	0.812691i	$0.698002\pi$
$102$	3.44081	−	5.95967i	0.340691	−	0.590095i
$103$	6.03680	+	10.4560i	0.594823	+	1.03026i	0.993572	+	0.113204i	$0.0361113\pi$
$103$	6.03680	+	10.4560i	0.594823	+	1.03026i	−0.398749	+	0.917060i	$0.630555\pi$
$104$	−3.33743	−	2.80044i	−0.327262	−	0.274606i
$105$	−1.47872	−	1.24079i	−0.144308	−	0.121089i
$106$	3.80733	+	6.59449i	0.369801	+	0.640514i
$107$	−4.84044	+	8.38388i	−0.467943	+	0.810500i	−0.999329	−	0.0366292i	$-0.988338\pi$
$107$	−4.84044	+	8.38388i	−0.467943	+	0.810500i	0.531386	+	0.847130i	$0.321671\pi$
$108$	0.939693	−	0.342020i	0.0904220	−	0.0329109i
$109$	−3.43055	−	19.4556i	−0.328587	−	1.86351i	−0.483168	−	0.875527i	$-0.660514\pi$
$109$	−3.43055	−	19.4556i	−0.328587	−	1.86351i	0.154582	−	0.987980i	$-0.450597\pi$
$110$	−0.254548	+	1.44361i	−0.0242702	+	0.137643i
$111$	−9.42755	−	3.43135i	−0.894823	−	0.325689i
$112$	1.47872	−	1.24079i	0.139726	−	0.117244i
$113$	−7.70275			−0.724614			−0.362307	−	0.932059i	$-0.618011\pi$
$113$	−7.70275			−0.724614			−0.362307	+	0.932059i	$0.618011\pi$
$114$	4.35027	+	0.274071i	0.407441	+	0.0256691i
$115$	−7.29478			−0.680242
$116$	−3.03527	+	2.54689i	−0.281818	+	0.236473i
$117$	4.09397	+	1.49008i	0.378488	+	0.137758i
$118$	−1.22582	+	6.95199i	−0.112846	+	0.639982i
$119$	2.30671	+	13.0820i	0.211456	+	1.19923i
$120$	0.939693	−	0.342020i	0.0857818	−	0.0312220i
$121$	4.42560	−	7.66536i	0.402327	−	0.696851i
$122$	−6.06092	−	10.4978i	−0.548730	−	0.950428i
$123$	−6.15255	−	5.16260i	−0.554756	−	0.465496i
$124$	−2.21044	−	1.85478i	−0.198504	−	0.166564i
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$	−0.965167	+	1.67172i	−0.0859839	+	0.148928i
$127$	0.0865880	−	0.0315155i	0.00768345	−	0.00279655i	−0.338176	−	0.941083i	$-0.609810\pi$
$127$	0.0865880	−	0.0315155i	0.00768345	−	0.00279655i	0.345859	+	0.938286i	$0.387588\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	0.0773486	−	0.438666i	0.00681017	−	0.0386224i
$130$	4.09397	+	1.49008i	0.359065	+	0.130689i
$131$	3.74493	−	3.14237i	0.327196	−	0.274550i	−0.464360	−	0.885646i	$-0.653716\pi$
$131$	3.74493	−	3.14237i	0.327196	−	0.274550i	0.791556	+	0.611096i	$0.209271\pi$
$132$	1.46588			0.127589
$133$	−6.77291	+	4.99252i	−0.587285	+	0.432906i
$134$	1.06709			0.0921827
$135$	−0.766044	+	0.642788i	−0.0659306	+	0.0553223i
$136$	−6.46662	−	2.35366i	−0.554508	−	0.201824i
$137$	1.24244	−	7.04623i	0.106149	−	0.602000i	−0.884606	−	0.466338i	$-0.845573\pi$
$137$	1.24244	−	7.04623i	0.106149	−	0.602000i	0.990755	−	0.135662i	$-0.0433160\pi$
$138$	1.26672	+	7.18395i	0.107831	+	0.611539i
$139$	3.35033	−	1.21942i	0.284171	−	0.103430i	−0.196002	−	0.980603i	$-0.562796\pi$
$139$	3.35033	−	1.21942i	0.284171	−	0.103430i	0.480173	+	0.877174i	$0.340574\pi$
$140$	−0.965167	+	1.67172i	−0.0815715	+	0.141286i
$141$	−4.35033	−	7.53499i	−0.366364	−	0.634560i
$142$	−9.24657	−	7.75879i	−0.775955	−	0.651103i
$143$	4.89228	+	4.10511i	0.409113	+	0.343287i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	1.98113	−	3.43142i	0.164524	−	0.284964i
$146$	5.10361	−	1.85756i	0.422378	−	0.153733i
$147$	0.568492	+	3.22408i	0.0468884	+	0.265917i
$148$	−1.74214	+	9.88017i	−0.143203	+	0.812145i
$149$	13.3033	+	4.84200i	1.08985	+	0.396672i	0.823565	−	0.567222i	$-0.191982\pi$
$149$	13.3033	+	4.84200i	1.08985	+	0.396672i	0.266284	+	0.963895i	$0.414204\pi$
$150$	−0.766044	+	0.642788i	−0.0625473	+	0.0524834i
$151$	3.40847			0.277378			0.138689	−	0.990336i	$-0.455711\pi$
$151$	3.40847			0.277378			0.138689	+	0.990336i	$0.455711\pi$
$152$	−0.485510	−	4.33178i	−0.0393801	−	0.351353i
$153$	6.88163			0.556347
$154$	−2.16763	+	1.81886i	−0.174673	+	0.146568i
$155$	2.71151	+	0.986909i	0.217794	+	0.0792705i
$156$	0.756535	−	4.29052i	0.0605713	−	0.343517i
$157$	2.71579	+	15.4020i	0.216744	+	1.22922i	0.877855	+	0.478927i	$0.158974\pi$
$157$	2.71579	+	15.4020i	0.216744	+	1.22922i	−0.661111	+	0.750288i	$0.729915\pi$
$158$	1.20036	−	0.436896i	0.0954956	−	0.0347575i
$159$	−3.80733	+	6.59449i	−0.301941	+	0.522977i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−10.7869	−	9.05132i	−0.850130	−	0.713344i
$162$	0.766044	+	0.642788i	0.0601861	+	0.0505022i
$163$	9.60827	+	16.6420i	0.752578	+	1.30350i	0.946570	+	0.322500i	$0.104523\pi$
$163$	9.60827	+	16.6420i	0.752578	+	1.30350i	−0.193992	+	0.981003i	$0.562144\pi$
$164$	−4.01579	+	6.95555i	−0.313581	+	0.543137i
$165$	−1.37748	+	0.501361i	−0.107236	+	0.0390309i
$166$	−1.93689	−	10.9846i	−0.150332	−	0.852572i
$167$	0.994738	−	5.64144i	0.0769751	−	0.436548i	−0.921826	−	0.387603i	$-0.873303\pi$
$167$	0.994738	−	5.64144i	0.0769751	−	0.436548i	0.998801	−	0.0489445i	$-0.0155858\pi$
$168$	1.81392	+	0.660213i	0.139947	+	0.0509365i
$169$	4.58166	−	3.84447i	0.352435	−	0.295728i
$170$	6.88163			0.527797
$171$	1.93779	+	3.90448i	0.148186	+	0.298583i
$172$	−0.445433			−0.0339639
$173$	−17.8377	+	14.9676i	−1.35618	+	1.13797i	−0.379032	+	0.925384i	$0.623743\pi$
$173$	−17.8377	+	14.9676i	−1.35618	+	1.13797i	−0.977143	+	0.212582i	$0.931813\pi$
$174$	−3.72331	−	1.35517i	−0.282263	−	0.102735i
$175$	0.335199	−	1.90101i	0.0253386	−	0.143703i
$176$	−0.254548	−	1.44361i	−0.0191872	−	0.108816i
$177$	−6.63351	+	2.41440i	−0.498605	+	0.181477i
$178$	−6.10075	+	10.5668i	−0.457271	+	0.792016i
$179$	−8.68246	−	15.0385i	−0.648957	−	1.12403i	−0.983372	−	0.181601i	$-0.941872\pi$
$179$	−8.68246	−	15.0385i	−0.648957	−	1.12403i	0.334415	−	0.942426i	$-0.391461\pi$
$180$	0.766044	+	0.642788i	0.0570976	+	0.0479106i
$181$	−6.56051	−	5.50492i	−0.487639	−	0.409178i	0.365540	−	0.930796i	$-0.380884\pi$
$181$	−6.56051	−	5.50492i	−0.487639	−	0.409178i	−0.853179	+	0.521618i	$0.825329\pi$
$182$	4.20495	+	7.28319i	0.311692	+	0.539866i
$183$	6.06092	−	10.4978i	0.448036	−	0.776021i
$184$	6.85485	−	2.49496i	0.505346	−	0.183931i
$185$	−1.74214	−	9.88017i	−0.128085	−	0.726404i
$186$	0.501067	−	2.84169i	0.0367400	−	0.208363i
$187$	9.47929	+	3.45018i	0.693194	+	0.252302i
$188$	−6.66509	+	5.59267i	−0.486101	+	0.407887i
$189$	−1.93033			−0.140411
$190$	1.93779	+	3.90448i	0.140582	+	0.283261i
$191$	−14.0286			−1.01507			−0.507536	−	0.861631i	$-0.669444\pi$
$191$	−14.0286			−1.01507			−0.507536	+	0.861631i	$0.669444\pi$
$192$	−0.766044	+	0.642788i	−0.0552845	+	0.0463892i
$193$	−5.23748	−	1.90629i	−0.377002	−	0.137218i	0.146567	−	0.989201i	$-0.453178\pi$
$193$	−5.23748	−	1.90629i	−0.377002	−	0.137218i	−0.523569	+	0.851983i	$0.675400\pi$
$194$	2.18491	−	12.3913i	0.156868	−	0.889641i
$195$	0.756535	+	4.29052i	0.0541766	+	0.307251i
$196$	3.07638	−	1.11971i	0.219741	−	0.0799793i
$197$	2.76735	−	4.79319i	0.197166	−	0.341501i	−0.750443	−	0.660936i	$-0.770160\pi$
$197$	2.76735	−	4.79319i	0.197166	−	0.341501i	0.947608	+	0.319435i	$0.103493\pi$
$198$	0.732941	+	1.26949i	0.0520878	+	0.0902187i
$199$	1.56135	+	1.31013i	0.110681	+	0.0928725i	0.696449	−	0.717607i	$-0.254762\pi$
$199$	1.56135	+	1.31013i	0.110681	+	0.0928725i	−0.585768	+	0.810479i	$0.699207\pi$
$200$	0.766044	+	0.642788i	0.0541675	+	0.0454519i
$201$	0.533546	+	0.924128i	0.0376334	+	0.0651830i
$202$	−8.29628	+	14.3696i	−0.583724	+	1.01104i
$203$	7.18723	−	2.61594i	0.504444	−	0.183603i
$204$	−1.19498	−	6.77708i	−0.0836655	−	0.474491i
$205$	1.39467	−	7.90956i	0.0974079	−	0.552428i
$206$	11.3455	+	4.12941i	0.790476	+	0.287710i
$207$	−5.58812	+	4.68899i	−0.388401	+	0.325908i
$208$	−4.35671			−0.302084
$209$	0.711701	+	6.34987i	0.0492294	+	0.439230i
$210$	−1.93033			−0.133206
$211$	−14.1523	+	11.8752i	−0.974285	+	0.817522i	−0.983217	−	0.182438i	$-0.941601\pi$
$211$	−14.1523	+	11.8752i	−0.974285	+	0.817522i	0.00893222	+	0.999960i	$0.497157\pi$
$212$	7.15545	+	2.60437i	0.491438	+	0.178869i
$213$	2.09603	−	11.8872i	0.143617	−	0.814495i
$214$	1.68107	+	9.53380i	0.114915	+	0.651717i
$215$	0.418570	−	0.152347i	0.0285462	−	0.0103900i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	2.78502	+	4.82379i	0.189059	+	0.327460i
$218$	−15.1338	−	12.6987i	−1.02499	−	0.860067i
$219$	4.16050	+	3.49108i	0.281141	+	0.235905i
$220$	0.732941	+	1.26949i	0.0494148	+	0.0855890i
$221$	14.9906	−	25.9645i	1.00838	−	1.74656i
$222$	−9.42755	+	3.43135i	−0.632735	+	0.230297i
$223$	4.51075	+	25.5817i	0.302062	+	1.71308i	0.637022	+	0.770846i	$0.280166\pi$
$223$	4.51075	+	25.5817i	0.302062	+	1.71308i	−0.334960	+	0.942232i	$0.608723\pi$
$224$	0.335199	−	1.90101i	0.0223964	−	0.127016i
$225$	−0.939693	−	0.342020i	−0.0626462	−	0.0228013i
$226$	−5.90065	+	4.95123i	−0.392505	+	0.329351i
$227$	22.3729			1.48494			0.742470	−	0.669879i	$-0.233654\pi$
$227$	22.3729			1.48494			0.742470	+	0.669879i	$0.233654\pi$
$228$	3.50867	−	2.58635i	0.232368	−	0.171285i
$229$	7.74863			0.512044			0.256022	−	0.966671i	$-0.417588\pi$
$229$	7.74863			0.512044			0.256022	+	0.966671i	$0.417588\pi$
$230$	−5.58812	+	4.68899i	−0.368470	+	0.309183i
$231$	−2.65899	−	0.967793i	−0.174949	−	0.0636761i
$232$	−0.688040	+	3.90207i	−0.0451720	+	0.256183i
$233$	0.429253	+	2.43442i	0.0281213	+	0.159484i	0.995635	−	0.0933360i	$-0.0297531\pi$
$233$	0.429253	+	2.43442i	0.0281213	+	0.159484i	−0.967513	+	0.252820i	$0.918642\pi$
$234$	4.09397	−	1.49008i	0.267631	−	0.0974098i
$235$	4.35033	−	7.53499i	0.283784	−	0.491528i
$236$	3.52962	+	6.11348i	0.229758	+	0.397953i
$237$	0.978543	+	0.821095i	0.0635632	+	0.0533359i
$238$	10.1760	+	8.53869i	0.659613	+	0.553481i
$239$	2.53390	+	4.38885i	0.163904	+	0.283891i	0.936266	−	0.351293i	$-0.114258\pi$
$239$	2.53390	+	4.38885i	0.163904	+	0.283891i	−0.772361	+	0.635184i	$0.780924\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	−1.52230	+	0.554071i	−0.0980598	+	0.0356909i	−0.390584	−	0.920567i	$-0.627727\pi$
$241$	−1.52230	+	0.554071i	−0.0980598	+	0.0356909i	0.292524	+	0.956258i	$0.405505\pi$
$242$	−1.53699	−	8.71672i	−0.0988017	−	0.560332i
$243$	−0.173648	+	0.984808i	−0.0111395	+	0.0631754i
$244$	−11.3908	−	4.14591i	−0.729222	−	0.265415i
$245$	−2.50789	+	2.10437i	−0.160223	+	0.134443i
$246$	−8.03158			−0.512075
$247$	18.9529	+	1.19405i	1.20594	+	0.0759753i
$248$	−2.88553			−0.183231
$249$	8.54452	−	7.16971i	0.541487	−	0.454362i
$250$	−0.939693	−	0.342020i	−0.0594314	−	0.0216313i
$251$	1.77997	−	10.0947i	0.112351	−	0.637174i	−0.875677	−	0.482898i	$-0.839584\pi$
$251$	1.77997	−	10.0947i	0.112351	−	0.637174i	0.988028	−	0.154276i	$-0.0493045\pi$
$252$	0.335199	+	1.90101i	0.0211155	+	0.119752i
$253$	−10.0484	+	3.65732i	−0.631737	+	0.229933i
$254$	0.0460725	−	0.0798000i	0.00289085	−	0.00500710i
$255$	3.44081	+	5.95967i	0.215472	+	0.373209i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−1.51635	−	1.27237i	−0.0945876	−	0.0793684i	0.594268	−	0.804267i	$-0.297442\pi$
$257$	−1.51635	−	1.27237i	−0.0945876	−	0.0793684i	−0.688855	+	0.724899i	$0.741886\pi$
$258$	−0.222716	−	0.385756i	−0.0138657	−	0.0240161i
$259$	9.68312	−	16.7716i	0.601679	−	1.04214i
$260$	4.09397	−	1.49008i	0.253897	−	0.0924110i
$261$	−0.688040	−	3.90207i	−0.0425886	−	0.241532i
$262$	0.848907	−	4.81439i	0.0524456	−	0.297434i
$263$	6.27219	+	2.28289i	0.386760	+	0.140769i	0.528080	−	0.849195i	$-0.322912\pi$
$263$	6.27219	+	2.28289i	0.386760	+	0.140769i	−0.141320	+	0.989964i	$0.545135\pi$
$264$	1.12293	−	0.942250i	0.0691116	−	0.0579915i
$265$	−7.61467			−0.467765
$266$	−1.97922	+	8.17803i	−0.121354	+	0.501427i
$267$	−12.2015			−0.746720
$268$	0.817439	−	0.685913i	0.0499331	−	0.0418988i
$269$	8.53288	+	3.10571i	0.520259	+	0.189359i	0.588784	−	0.808291i	$-0.299607\pi$
$269$	8.53288	+	3.10571i	0.520259	+	0.189359i	−0.0685249	+	0.997649i	$0.521829\pi$
$270$	−0.173648	+	0.984808i	−0.0105679	+	0.0599335i
$271$	−1.79179	−	10.1617i	−0.108843	−	0.617282i	−0.989615	−	0.143741i	$-0.954087\pi$
$271$	−1.79179	−	10.1617i	−0.108843	−	0.617282i	0.880772	−	0.473541i	$-0.157024\pi$
$272$	−6.46662	+	2.35366i	−0.392096	+	0.142711i
$273$	−4.20495	+	7.28319i	−0.254495	+	0.440799i
$274$	−3.57746	−	6.19635i	−0.216123	−	0.374335i
$275$	−1.12293	−	0.942250i	−0.0677152	−	0.0568198i
$276$	5.58812	+	4.68899i	0.336366	+	0.282244i
$277$	−10.9104	−	18.8975i	−0.655545	−	1.13544i	−0.981757	−	0.190141i	$-0.939105\pi$
$277$	−10.9104	−	18.8975i	−0.655545	−	1.13544i	0.326211	−	0.945297i	$-0.394228\pi$
$278$	1.78267	−	3.08768i	0.106918	−	0.185187i
$279$	2.71151	−	0.986909i	0.162334	−	0.0590847i
$280$	0.335199	+	1.90101i	0.0200320	+	0.113607i
$281$	2.20442	−	12.5019i	0.131505	−	0.745801i	−0.845725	−	0.533618i	$-0.820832\pi$
$281$	2.20442	−	12.5019i	0.131505	−	0.745801i	0.977230	−	0.212182i	$-0.0680570\pi$
$282$	−8.17594	−	2.97580i	−0.486870	−	0.177206i
$283$	16.4185	−	13.7767i	0.975976	−	0.818941i	−0.00750116	−	0.999972i	$-0.502388\pi$
$283$	16.4185	−	13.7767i	0.975976	−	0.818941i	0.983477	+	0.181030i	$0.0579433\pi$
$284$	−12.0705			−0.716255
$285$	−2.41249	+	3.63041i	−0.142904	+	0.215047i
$286$	6.38642			0.377637
$287$	11.8765	−	9.96554i	0.701046	−	0.588247i
$288$	−0.939693	−	0.342020i	−0.0553719	−	0.0201537i
$289$	5.27141	−	29.8956i	0.310083	−	1.75857i
$290$	−0.688040	−	3.90207i	−0.0404031	−	0.229137i
$291$	11.8236	−	4.30344i	0.693112	−	0.252272i
$292$	2.71557	−	4.70351i	0.158917	−	0.275252i
$293$	5.35874	+	9.28161i	0.313061	+	0.542238i	0.979023	−	0.203748i	$-0.0653122\pi$
$293$	5.35874	+	9.28161i	0.313061	+	0.542238i	−0.665962	+	0.745985i	$0.731979\pi$
$294$	2.50789	+	2.10437i	0.146263	+	0.122729i
$295$	−5.40769	−	4.53759i	−0.314848	−	0.264189i
$296$	5.01629	+	8.68847i	0.291566	+	0.505007i
$297$	−0.732941	+	1.26949i	−0.0425295	+	0.0736633i
$298$	13.3033	−	4.84200i	0.770639	−	0.280490i
$299$	5.51875	+	31.2984i	0.319158	+	1.81003i
$300$	−0.173648	+	0.984808i	−0.0100256	+	0.0568579i
$301$	0.807980	+	0.294081i	0.0465712	+	0.0169505i
$302$	2.61104	−	2.19093i	0.150249	−	0.126074i
$303$	−16.5926			−0.953218
$304$	−3.15633	−	3.00625i	−0.181028	−	0.172420i
$305$	12.1218			0.694095
$306$	5.27163	−	4.42343i	0.301359	−	0.252870i
$307$	12.5330	+	4.56164i	0.715296	+	0.260347i	0.673928	−	0.738797i	$-0.264606\pi$
$307$	12.5330	+	4.56164i	0.715296	+	0.260347i	0.0413687	+	0.999144i	$0.486828\pi$
$308$	−0.491362	+	2.78665i	−0.0279979	+	0.158784i
$309$	2.09656	+	11.8902i	0.119269	+	0.676408i
$310$	2.71151	−	0.986909i	0.154004	−	0.0560527i
$311$	−8.52970	+	14.7739i	−0.483675	+	0.837749i	−0.999824	−	0.0187491i	$-0.994032\pi$
$311$	−8.52970	+	14.7739i	−0.483675	+	0.837749i	0.516149	+	0.856499i	$0.327365\pi$
$312$	−2.17836	−	3.77302i	−0.123325	−	0.213605i
$313$	−4.58971	−	3.85123i	−0.259426	−	0.217684i	0.503793	−	0.863825i	$-0.331938\pi$
$313$	−4.58971	−	3.85123i	−0.259426	−	0.217684i	−0.763219	+	0.646140i	$0.776382\pi$
$314$	11.9806	+	10.0530i	0.676107	+	0.567321i
$315$	−0.965167	−	1.67172i	−0.0543810	−	0.0941906i
$316$	0.638699	−	1.10626i	0.0359296	−	0.0622319i
$317$	29.3006	−	10.6646i	1.64569	−	0.598981i	0.657667	−	0.753309i	$-0.271544\pi$
$317$	29.3006	−	10.6646i	1.64569	−	0.598981i	0.988020	+	0.154328i	$0.0493213\pi$
$318$	1.32227	+	7.49898i	0.0741494	+	0.420522i
$319$	1.00858	−	5.71997i	0.0564699	−	0.320257i
$320$	−0.939693	−	0.342020i	−0.0525304	−	0.0191195i
$321$	−7.41598	+	6.22274i	−0.413920	+	0.347320i
$322$	−14.0814			−0.784723
$323$	28.7766	−	8.46674i	1.60117	−	0.471102i
$324$	1.00000			0.0555556
$325$	−3.33743	+	2.80044i	−0.185128	+	0.155340i
$326$	18.0576	+	6.57244i	1.00012	+	0.364014i
$327$	3.43055	−	19.4556i	0.189710	−	1.07590i
$328$	1.39467	+	7.90956i	0.0770077	+	0.436733i
$329$	15.7823	−	5.74428i	0.870106	−	0.316693i
$330$	−0.732941	+	1.26949i	−0.0403470	+	0.0698831i
$331$	−5.22747	−	9.05425i	−0.287328	−	0.497667i	0.685843	−	0.727749i	$-0.259434\pi$
$331$	−5.22747	−	9.05425i	−0.287328	−	0.497667i	−0.973171	+	0.230083i	$0.926100\pi$
$332$	−8.54452	−	7.16971i	−0.468942	−	0.393489i
$333$	−7.68541	−	6.44882i	−0.421158	−	0.353393i
$334$	−2.86423	−	4.96100i	−0.156724	−	0.271454i
$335$	−0.533546	+	0.924128i	−0.0291507	+	0.0504905i
$336$	1.81392	−	0.660213i	0.0989574	−	0.0360176i
$337$	0.313103	+	1.77569i	0.0170558	+	0.0967282i	0.992147	−	0.125075i	$-0.0399170\pi$
$337$	0.313103	+	1.77569i	0.0170558	+	0.0967282i	−0.975092	+	0.221803i	$0.928806\pi$
$338$	1.03858	−	5.89007i	0.0564912	−	0.320377i
$339$	−7.23822	−	2.63450i	−0.393126	−	0.143086i
$340$	5.27163	−	4.42343i	0.285895	−	0.239894i
$341$	4.22984			0.229059
$342$	3.99418	+	1.74542i	0.215981	+	0.0943817i
$343$	−19.8319			−1.07082
$344$	−0.341221	+	0.286319i	−0.0183974	+	0.0154373i
$345$	−6.85485	−	2.49496i	−0.369053	−	0.134324i
$346$	−4.04348	+	22.9317i	−0.217379	+	1.23282i
$347$	6.04084	+	34.2593i	0.324289	+	1.83914i	0.514622	+	0.857417i	$0.327932\pi$
$347$	6.04084	+	34.2593i	0.324289	+	1.83914i	−0.190333	+	0.981720i	$0.560957\pi$
$348$	−3.72331	+	1.35517i	−0.199590	+	0.0726449i
$349$	17.6312	−	30.5382i	0.943778	−	1.63467i	0.185597	−	0.982626i	$-0.440578\pi$
$349$	17.6312	−	30.5382i	0.943778	−	1.63467i	0.758180	−	0.652045i	$-0.226089\pi$
$350$	−0.965167	−	1.67172i	−0.0515903	−	0.0893571i
$351$	3.33743	+	2.80044i	0.178139	+	0.149476i
$352$	−1.12293	−	0.942250i	−0.0598524	−	0.0502221i
$353$	10.0199	+	17.3551i	0.533308	+	0.923716i	0.999243	+	0.0388976i	$0.0123846\pi$
$353$	10.0199	+	17.3551i	0.533308	+	0.923716i	−0.465935	+	0.884819i	$0.654282\pi$
$354$	−3.52962	+	6.11348i	−0.187597	+	0.324928i
$355$	11.3426	−	4.12837i	0.602002	−	0.219111i
$356$	2.11877	+	12.0161i	0.112295	+	0.636854i
$357$	−2.30671	+	13.0820i	−0.122084	+	0.692374i
$358$	−16.3177	−	5.93915i	−0.862416	−	0.313894i
$359$	−1.46849	+	1.23221i	−0.0775037	+	0.0650334i	−0.680716	−	0.732547i	$-0.738331\pi$
$359$	−1.46849	+	1.23221i	−0.0775037	+	0.0650334i	0.603213	+	0.797580i	$0.293887\pi$
$360$	1.00000			0.0527046
$361$	12.9070	+	13.9431i	0.679315	+	0.733846i
$362$	−8.56414			−0.450121
$363$	6.78041	−	5.68944i	0.355879	−	0.298618i
$364$	7.90272	+	2.87636i	0.414215	+	0.150762i
$365$	−0.943109	+	5.34864i	−0.0493646	+	0.279960i
$366$	−2.10494	−	11.9377i	−0.110027	−	0.623993i
$367$	−25.9586	+	9.44817i	−1.35503	+	0.493190i	−0.914514	−	0.404554i	$-0.867427\pi$
$367$	−25.9586	+	9.44817i	−1.35503	+	0.493190i	−0.440516	+	0.897745i	$0.645204\pi$
$368$	3.64739	−	6.31746i	0.190133	−	0.329321i
$369$	−4.01579	−	6.95555i	−0.209054	−	0.362092i
$370$	−7.68541	−	6.44882i	−0.399545	−	0.335258i
$371$	−11.2600	−	9.44823i	−0.584588	−	0.490528i
$372$	−1.44277	−	2.49894i	−0.0748039	−	0.129564i
$373$	−5.41455	+	9.37827i	−0.280355	+	0.485589i	−0.971472	−	0.237154i	$-0.923785\pi$
$373$	−5.41455	+	9.37827i	−0.280355	+	0.485589i	0.691117	+	0.722743i	$0.257119\pi$
$374$	9.47929	−	3.45018i	0.490162	−	0.178405i
$375$	−0.173648	−	0.984808i	−0.00896715	−	0.0508553i
$376$	−1.51085	+	8.56847i	−0.0779163	+	0.441885i
$377$	−16.2214	−	5.90410i	−0.835444	−	0.304077i
$378$	−1.47872	+	1.24079i	−0.0760572	+	0.0638196i
$379$	−5.71692			−0.293658			−0.146829	−	0.989162i	$-0.546907\pi$
$379$	−5.71692			−0.293658			−0.146829	+	0.989162i	$0.546907\pi$
$380$	3.99418	+	1.74542i	0.204897	+	0.0895383i
$381$	0.0921451			0.00472074
$382$	−10.7465	+	9.01739i	−0.549839	+	0.461370i
$383$	7.43101	+	2.70467i	0.379707	+	0.138202i	0.524820	−	0.851213i	$-0.324132\pi$
$383$	7.43101	+	2.70467i	0.379707	+	0.138202i	−0.145113	+	0.989415i	$0.546355\pi$
$384$	−0.173648	+	0.984808i	−0.00886145	+	0.0502558i
$385$	−0.491362	−	2.78665i	−0.0250421	−	0.142021i
$386$	−5.23748	+	1.90629i	−0.266581	+	0.0970274i
$387$	0.222716	−	0.385756i	0.0113213	−	0.0196091i
$388$	−6.29121	−	10.8967i	−0.319388	−	0.553196i
$389$	−18.5011	−	15.5243i	−0.938042	−	0.787111i	0.0392013	−	0.999231i	$-0.487519\pi$
$389$	−18.5011	−	15.5243i	−0.938042	−	0.787111i	−0.977244	+	0.212120i	$0.931963\pi$
$390$	3.33743	+	2.80044i	0.168998	+	0.141806i
$391$	25.1000	+	43.4744i	1.26936	+	2.19860i
$392$	1.63691	−	2.83521i	0.0826763	−	0.143200i
$393$	4.59384	−	1.67202i	0.231728	−	0.0843422i
$394$	−0.961091	−	5.45062i	−0.0484191	−	0.274598i
$395$	−0.221818	+	1.25799i	−0.0111609	+	0.0632964i
$396$	1.37748	+	0.501361i	0.0692209	+	0.0251943i
$397$	−6.14574	+	5.15689i	−0.308446	+	0.258817i	−0.783849	−	0.620951i	$-0.786747\pi$
$397$	−6.14574	+	5.15689i	−0.308446	+	0.258817i	0.475403	+	0.879768i	$0.342302\pi$
$398$	2.03820			0.102166
$399$	−8.07199	+	2.37496i	−0.404105	+	0.118897i
$400$	1.00000			0.0500000
$401$	7.08440	−	5.94451i	0.353778	−	0.296855i	−0.448527	−	0.893769i	$-0.648051\pi$
$401$	7.08440	−	5.94451i	0.353778	−	0.296855i	0.802305	+	0.596914i	$0.203607\pi$
$402$	1.00274	+	0.364967i	0.0500120	+	0.0182029i
$403$	2.18300	−	12.3804i	0.108743	−	0.616713i
$404$	2.88127	+	16.3405i	0.143348	+	0.812969i
$405$	−0.939693	+	0.342020i	−0.0466937	+	0.0169951i
$406$	3.82424	−	6.62378i	0.189794	−	0.328733i
$407$	−7.35329	−	12.7363i	−0.364489	−	0.631313i
$408$	−5.27163	−	4.42343i	−0.260985	−	0.218992i
$409$	−11.8992	−	9.98462i	−0.588378	−	0.493708i	0.299308	−	0.954156i	$-0.403244\pi$
$409$	−11.8992	−	9.98462i	−0.588378	−	0.493708i	−0.887686	+	0.460449i	$0.847688\pi$
$410$	−4.01579	−	6.95555i	−0.198326	−	0.343510i
$411$	3.57746	−	6.19635i	0.176463	−	0.305643i
$412$	11.3455	−	4.12941i	0.558951	−	0.203442i
$413$	−2.36625	−	13.4197i	−0.116435	−	0.660338i
$414$	−1.26672	+	7.18395i	−0.0622561	+	0.353072i
$415$	10.4814	+	3.81492i	0.514512	+	0.187267i
$416$	−3.33743	+	2.80044i	−0.163631	+	0.137303i
$417$	3.56534			0.174596
$418$	4.62681	+	4.40681i	0.226305	+	0.215544i
$419$	−4.71743			−0.230461			−0.115231	−	0.993339i	$-0.536761\pi$
$419$	−4.71743			−0.230461			−0.115231	+	0.993339i	$0.536761\pi$
$420$	−1.47872	+	1.24079i	−0.0721542	+	0.0605446i
$421$	−19.6130	−	7.13856i	−0.955881	−	0.347912i	−0.183463	−	0.983027i	$-0.558731\pi$
$421$	−19.6130	−	7.13856i	−0.955881	−	0.347912i	−0.772418	+	0.635114i	$0.780953\pi$
$422$	−3.20807	+	18.1939i	−0.156166	+	0.885663i
$423$	−1.51085	−	8.56847i	−0.0734602	−	0.416613i
$424$	7.15545	−	2.60437i	0.347499	−	0.126479i
$425$	−3.44081	+	5.95967i	−0.166904	+	0.289086i
$426$	−6.03527	−	10.4534i	−0.292410	−	0.506468i
$427$	17.9248	+	15.0407i	0.867443	+	0.727871i
$428$	7.41598	+	6.22274i	0.358465	+	0.300788i
$429$	3.19321	+	5.53080i	0.154170	+	0.267030i
$430$	0.222716	−	0.385756i	0.0107403	−	0.0186028i
$431$	0.130699	−	0.0475704i	0.00629553	−	0.00229139i	−0.338870	−	0.940833i	$-0.610045\pi$
$431$	0.130699	−	0.0475704i	0.00629553	−	0.00229139i	0.345166	+	0.938542i	$0.387823\pi$
$432$	−0.173648	−	0.984808i	−0.00835465	−	0.0473816i
$433$	−0.758157	+	4.29972i	−0.0364347	+	0.206631i	−0.997591	−	0.0693742i	$-0.977900\pi$
$433$	−0.758157	+	4.29972i	−0.0364347	+	0.206631i	0.961156	+	0.276006i	$0.0890109\pi$
$434$	5.23412	+	1.90506i	0.251246	+	0.0914460i
$435$	3.03527	−	2.54689i	0.145530	−	0.122114i
$436$	−19.7557			−0.946128
$437$	−17.5986	+	26.4831i	−0.841854	+	1.26686i
$438$	5.43115			0.259510
$439$	−23.3854	+	19.6227i	−1.11612	+	0.936539i	−0.998402	−	0.0565072i	$-0.982004\pi$
$439$	−23.3854	+	19.6227i	−1.11612	+	0.936539i	−0.117722	+	0.993047i	$0.537559\pi$
$440$	1.37748	+	0.501361i	0.0656687	+	0.0239014i
$441$	−0.568492	+	3.22408i	−0.0270710	+	0.153528i
$442$	−5.20619	−	29.5258i	−0.247633	−	1.40440i
$443$	14.7908	−	5.38341i	0.702732	−	0.255774i	0.0341553	−	0.999417i	$-0.489126\pi$
$443$	14.7908	−	5.38341i	0.702732	−	0.255774i	0.668577	+	0.743643i	$0.266904\pi$
$444$	−5.01629	+	8.68847i	−0.238063	+	0.412337i
$445$	−6.10075	−	10.5668i	−0.289203	−	0.500915i
$446$	19.8990	+	16.6973i	0.942247	+	0.790639i
$447$	10.8449	+	9.09999i	0.512948	+	0.430415i
$448$	−0.965167	−	1.67172i	−0.0455998	−	0.0789812i
$449$	3.98540	−	6.90291i	0.188082	−	0.325768i	−0.756528	−	0.653961i	$-0.773106\pi$
$449$	3.98540	−	6.90291i	0.188082	−	0.325768i	0.944611	+	0.328192i	$0.106439\pi$
$450$	−0.939693	+	0.342020i	−0.0442975	+	0.0161230i
$451$	−2.04442	−	11.5945i	−0.0962679	−	0.545963i
$452$	−1.33757	+	7.58573i	−0.0629139	+	0.356803i
$453$	3.20292	+	1.16577i	0.150486	+	0.0547725i
$454$	17.1386	−	14.3810i	0.804355	−	0.674934i
$455$	−8.40990			−0.394262
$456$	1.02532	−	4.23659i	0.0480152	−	0.198397i
$457$	2.30855			0.107989			0.0539947	−	0.998541i	$-0.482805\pi$
$457$	2.30855			0.107989			0.0539947	+	0.998541i	$0.482805\pi$
$458$	5.93580	−	4.98072i	0.277362	−	0.232734i
$459$	6.46662	+	2.35366i	0.301836	+	0.109859i
$460$	−1.26672	+	7.18395i	−0.0590614	+	0.334954i
$461$	5.06558	+	28.7283i	0.235928	+	1.33801i	0.840652	+	0.541576i	$0.182172\pi$
$461$	5.06558	+	28.7283i	0.235928	+	1.33801i	−0.604724	+	0.796435i	$0.706717\pi$
$462$	−2.65899	+	0.967793i	−0.123707	+	0.0450258i
$463$	6.31458	−	10.9372i	0.293463	−	0.508293i	−0.681163	−	0.732132i	$-0.738525\pi$
$463$	6.31458	−	10.9372i	0.293463	−	0.508293i	0.974626	+	0.223839i	$0.0718588\pi$
$464$	1.98113	+	3.43142i	0.0919717	+	0.159300i
$465$	2.21044	+	1.85478i	0.102507	+	0.0860135i
$466$	1.89364	+	1.58895i	0.0877212	+	0.0736068i
$467$	9.79246	+	16.9610i	0.453141	+	0.784863i	0.998579	−	0.0532876i	$-0.0169700\pi$
$467$	9.79246	+	16.9610i	0.453141	+	0.784863i	−0.545438	+	0.838151i	$0.683637\pi$
$468$	2.17836	−	3.77302i	0.100695	−	0.174408i
$469$	−1.93562	+	0.704507i	−0.0893785	+	0.0325311i
$470$	−1.51085	−	8.56847i	−0.0696904	−	0.395234i
$471$	−2.71579	+	15.4020i	−0.125137	+	0.709688i
$472$	6.63351	+	2.41440i	0.305332	+	0.111132i
$473$	0.500190	−	0.419709i	0.0229988	−	0.0192983i
$474$	1.27740			0.0586728
$475$	−4.35027	−	0.274071i	−0.199604	−	0.0125752i
$476$	13.2838			0.608864
$477$	−5.83317	+	4.89461i	−0.267083	+	0.224109i
$478$	4.76218	+	1.73329i	0.217817	+	0.0792789i
$479$	−3.60378	+	20.4380i	−0.164661	+	0.933838i	0.784753	+	0.619809i	$0.212790\pi$
$479$	−3.60378	+	20.4380i	−0.164661	+	0.933838i	−0.949413	+	0.314029i	$0.898321\pi$
$480$	−0.173648	−	0.984808i	−0.00792592	−	0.0449501i
$481$	−41.0731	+	14.9494i	−1.87277	+	0.681633i
$482$	−0.809998	+	1.40296i	−0.0368944	+	0.0639029i
$483$	−7.04068	−	12.1948i	−0.320362	−	0.554883i
$484$	−6.78041	−	5.68944i	−0.308200	−	0.258611i
$485$	9.63869	+	8.08783i	0.437671	+	0.367249i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−3.53486	+	6.12255i	−0.160180	+	0.277439i	−0.934933	−	0.354824i	$-0.884541\pi$
$487$	−3.53486	+	6.12255i	−0.160180	+	0.277439i	0.774753	+	0.632264i	$0.217874\pi$
$488$	−11.3908	+	4.14591i	−0.515638	+	0.187677i
$489$	3.33692	+	18.9246i	0.150901	+	0.855800i
$490$	−0.568492	+	3.22408i	−0.0256818	+	0.145649i
$491$	28.5744	+	10.4002i	1.28955	+	0.469356i	0.893578	−	0.448908i	$-0.148187\pi$
$491$	28.5744	+	10.4002i	1.28955	+	0.469356i	0.395968	+	0.918264i	$0.370409\pi$
$492$	−6.15255	+	5.16260i	−0.277378	+	0.232748i
$493$	−27.2668			−1.22804
$494$	15.2863	−	11.2680i	0.687762	−	0.506971i
$495$	−1.46588			−0.0658865
$496$	−2.21044	+	1.85478i	−0.0992519	+	0.0832822i
$497$	21.8950	+	7.96912i	0.982124	+	0.357464i
$498$	1.93689	−	10.9846i	0.0867939	−	0.492233i
$499$	4.53584	+	25.7240i	0.203052	+	1.15157i	0.900475	+	0.434907i	$0.143219\pi$
$499$	4.53584	+	25.7240i	0.203052	+	1.15157i	−0.697423	+	0.716660i	$0.745670\pi$
$500$	−0.939693	+	0.342020i	−0.0420243	+	0.0152956i
$501$	2.86423	−	4.96100i	0.127964	−	0.221641i
$502$	−5.12523	−	8.87715i	−0.228750	−	0.396207i
$503$	−21.5960	−	18.1212i	−0.962918	−	0.807984i	0.0185071	−	0.999829i	$-0.494109\pi$
$503$	−21.5960	−	18.1212i	−0.962918	−	0.807984i	−0.981425	+	0.191844i	$0.938553\pi$
$504$	1.47872	+	1.24079i	0.0658675	+	0.0552694i
$505$	−8.29628	−	14.3696i	−0.369180	−	0.639438i
$506$	−5.34664	+	9.26065i	−0.237687	+	0.411686i
$507$	5.62024	−	2.04560i	0.249604	−	0.0908482i
$508$	−0.0160008	−	0.0907452i	−0.000709922	−	0.00402617i
$509$	1.40798	−	7.98505i	0.0624076	−	0.353931i	−0.937574	−	0.347787i	$-0.886933\pi$
$509$	1.40798	−	7.98505i	0.0624076	−	0.353931i	0.999981	−	0.00614389i	$-0.00195567\pi$
$510$	6.46662	+	2.35366i	0.286347	+	0.104222i
$511$	−8.03115	+	6.73894i	−0.355277	+	0.298113i
$512$	1.00000			0.0441942
$513$	0.485510	+	4.33178i	0.0214358	+	0.191253i
$514$	−1.97946			−0.0873103
$515$	−9.24891	+	7.76076i	−0.407556	+	0.341980i
$516$	−0.418570	−	0.152347i	−0.0184265	−	0.00670670i
$517$	2.21473	−	12.5604i	0.0974037	−	0.552404i
$518$	−3.36291	−	19.0720i	−0.147758	−	0.837976i
$519$	−21.8812	+	7.96410i	−0.960477	+	0.349585i
$520$	2.17836	−	3.77302i	0.0955272	−	0.165458i
$521$	−7.98663	−	13.8333i	−0.349901	−	0.606046i	0.636331	−	0.771416i	$-0.280451\pi$
$521$	−7.98663	−	13.8333i	−0.349901	−	0.606046i	−0.986232	+	0.165370i	$0.947118\pi$
$522$	−3.03527	−	2.54689i	−0.132850	−	0.111474i
$523$	−21.0691	−	17.6790i	−0.921286	−	0.773051i	0.0529463	−	0.998597i	$-0.483139\pi$
$523$	−21.0691	−	17.6790i	−0.921286	−	0.773051i	−0.974232	+	0.225547i	$0.927583\pi$
$524$	−2.44433	−	4.23370i	−0.106781	−	0.184950i
$525$	0.965167	−	1.67172i	0.0421233	−	0.0729597i
$526$	6.27219	−	2.28289i	0.273481	−	0.0995388i
$527$	−3.44816	−	19.5555i	−0.150204	−	0.851850i
$528$	0.254548	−	1.44361i	0.0110778	−	0.0628251i
$529$	−28.3917	−	10.3337i	−1.23442	−	0.449292i
$530$	−5.83317	+	4.89461i	−0.253377	+	0.212608i
$531$	−7.05923			−0.306345
$532$	3.74057	+	7.53695i	0.162174	+	0.326768i
$533$	−34.9913			−1.51564
$534$	−9.34689	+	7.84298i	−0.404480	+	0.339399i
$535$	−9.09704	−	3.31105i	−0.393300	−	0.143149i
$536$	0.185298	−	1.05088i	0.00800368	−	0.0453911i
$537$	−3.01539	−	17.1011i	−0.130123	−	0.737967i
$538$	8.53288	−	3.10571i	0.367878	−	0.133897i
$539$	−2.39951	+	4.15608i	−0.103354	+	0.179015i
$540$	0.500000	+	0.866025i	0.0215166	+	0.0372678i
$541$	18.5584	+	15.5723i	0.797888	+	0.669507i	0.947684	−	0.319210i	$-0.103417\pi$
$541$	18.5584	+	15.5723i	0.797888	+	0.669507i	−0.149797	+	0.988717i	$0.547862\pi$
$542$	−7.90443	−	6.63261i	−0.339524	−	0.284895i
$543$	−4.28207	−	7.41676i	−0.183761	−	0.318284i
$544$	−3.44081	+	5.95967i	−0.147524	+	0.255519i
$545$	18.5643	−	6.75686i	0.795208	−	0.289432i
$546$	1.46036	+	8.28214i	0.0624978	+	0.354443i
$547$	−2.14342	+	12.1559i	−0.0916459	+	0.519750i	0.904078	+	0.427368i	$0.140559\pi$
$547$	−2.14342	+	12.1559i	−0.0916459	+	0.519750i	−0.995724	+	0.0923818i	$0.970552\pi$
$548$	−6.72343	−	2.44713i	−0.287211	−	0.104536i
$549$	9.28587	−	7.79177i	0.396311	−	0.332545i
$550$	−1.46588			−0.0625054
$551$	−7.67801	−	15.4706i	−0.327094	−	0.659069i
$552$	7.29478			0.310486
$553$	−1.88891	+	1.58499i	−0.0803248	+	0.0674005i
$554$	−20.5049	−	7.46319i	−0.871171	−	0.317080i
$555$	1.74214	−	9.88017i	0.0739497	−	0.419390i
$556$	−0.619115	−	3.51118i	−0.0262563	−	0.148907i
$557$	−12.9807	+	4.72458i	−0.550009	+	0.200187i	−0.602051	−	0.798458i	$-0.705649\pi$
$557$	−12.9807	+	4.72458i	−0.550009	+	0.200187i	0.0520414	+	0.998645i	$0.483427\pi$
$558$	1.44277	−	2.49894i	0.0610771	−	0.105789i
$559$	−0.970311	−	1.68063i	−0.0410398	−	0.0710830i
$560$	1.47872	+	1.24079i	0.0624874	+	0.0524331i
$561$	7.72759	+	6.48422i	0.326259	+	0.273764i
$562$	−6.34738	−	10.9940i	−0.267748	−	0.463753i
$563$	10.9729	−	19.0056i	0.462453	−	0.800992i	−0.536630	−	0.843818i	$-0.680303\pi$
$563$	10.9729	−	19.0056i	0.462453	−	0.800992i	0.999083	+	0.0428259i	$0.0136361\pi$
$564$	−8.17594	+	2.97580i	−0.344269	+	0.125304i
$565$	−1.33757	−	7.58573i	−0.0562719	−	0.319134i
$566$	3.72176	−	21.1072i	0.156437	−	0.887200i
$567$	−1.81392	−	0.660213i	−0.0761775	−	0.0277263i
$568$	−9.24657	+	7.75879i	−0.387977	+	0.325552i
$569$	33.6549			1.41089			0.705443	−	0.708767i	$-0.250748\pi$
$569$	33.6549			1.41089			0.705443	+	0.708767i	$0.250748\pi$
$570$	0.485510	+	4.33178i	0.0203358	+	0.181438i
$571$	4.11932			0.172388			0.0861941	−	0.996278i	$-0.472529\pi$
$571$	4.11932			0.172388			0.0861941	+	0.996278i	$0.472529\pi$
$572$	4.89228	−	4.10511i	0.204557	−	0.171643i
$573$	−13.1825	−	4.79805i	−0.550709	−	0.200442i
$574$	2.69218	−	15.2681i	0.112369	−	0.637278i
$575$	−1.26672	−	7.18395i	−0.0528261	−	0.299592i
$576$	−0.939693	+	0.342020i	−0.0391539	+	0.0142508i
$577$	6.71756	−	11.6352i	0.279656	−	0.484378i	−0.691644	−	0.722239i	$-0.743113\pi$
$577$	6.71756	−	11.6352i	0.279656	−	0.484378i	0.971299	+	0.237861i	$0.0764464\pi$
$578$	−15.1784	−	26.2898i	−0.631339	−	1.09351i
$579$	−4.26963	−	3.58265i	−0.177440	−	0.148890i
$580$	−3.03527	−	2.54689i	−0.126033	−	0.105754i
$581$	10.7655	+	18.6465i	0.446630	+	0.773586i
$582$	6.29121	−	10.8967i	0.260779	−	0.451683i
$583$	−10.4890	+	3.81770i	−0.434411	+	0.158113i
$584$	−0.943109	−	5.34864i	−0.0390261	−	0.221328i
$585$	−0.756535	+	4.29052i	−0.0312789	+	0.177391i
$586$	10.0711	+	3.66559i	0.416035	+	0.151424i
$587$	−12.5974	+	10.5705i	−0.519950	+	0.436290i	−0.864614	−	0.502436i	$-0.832437\pi$
$587$	−12.5974	+	10.5705i	−0.519950	+	0.436290i	0.344664	+	0.938726i	$0.387993\pi$
$588$	3.27381			0.135010
$589$	10.1244	−	7.46300i	0.417168	−	0.307507i
$590$	−7.05923			−0.290624
$591$	4.23983	−	3.55764i	0.174403	−	0.146342i
$592$	9.42755	+	3.43135i	0.387470	+	0.141027i
$593$	1.43204	−	8.12148i	0.0588067	−	0.333509i	−0.941184	−	0.337895i	$-0.890285\pi$
$593$	1.43204	−	8.12148i	0.0588067	−	0.333509i	0.999990	+	0.00438605i	$0.00139613\pi$
$594$	0.254548	+	1.44361i	0.0104442	+	0.0592321i
$595$	−12.4827	+	4.54334i	−0.511742	+	0.186259i
$596$	7.07853	−	12.2604i	0.289948	−	0.502205i
$597$	1.01910	+	1.76513i	0.0417089	+	0.0722420i
$598$	24.3458	+	20.4286i	0.995576	+	0.835387i
$599$	−16.9758	−	14.2444i	−0.693613	−	0.582010i	0.226336	−	0.974049i	$-0.427325\pi$
$599$	−16.9758	−	14.2444i	−0.693613	−	0.582010i	−0.919949	+	0.392039i	$0.871770\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	−17.9653	+	31.1168i	−0.732819	+	1.26928i	0.222855	+	0.974852i	$0.428462\pi$
$601$	−17.9653	+	31.1168i	−0.732819	+	1.26928i	−0.955674	+	0.294428i	$0.904871\pi$
$602$	0.807980	−	0.294081i	0.0329308	−	0.0119858i
$603$	0.185298	+	1.05088i	0.00754594	+	0.0427951i
$604$	0.591875	−	3.35669i	0.0240831	−	0.136582i
$605$	8.31740	+	3.02729i	0.338150	+	0.123077i
$606$	−12.7106	+	10.6655i	−0.516334	+	0.433256i
$607$	−27.6766			−1.12336			−0.561679	−	0.827355i	$-0.689844\pi$
$607$	−27.6766			−1.12336			−0.561679	+	0.827355i	$0.689844\pi$
$608$	−4.35027	−	0.274071i	−0.176427	−	0.0111150i
$609$	7.64849			0.309932
$610$	9.28587	−	7.79177i	0.375974	−	0.315480i
$611$	−35.6202	−	12.9647i	−1.44104	−	0.524495i
$612$	1.19498	−	6.77708i	0.0483043	−	0.273947i
$613$	6.35542	+	36.0434i	0.256693	+	1.45578i	0.791689	+	0.610924i	$0.209202\pi$
$613$	6.35542	+	36.0434i	0.256693	+	1.45578i	−0.534996	+	0.844855i	$0.679687\pi$
$614$	12.5330	−	4.56164i	0.505791	−	0.184093i
$615$	4.01579	−	6.95555i	0.161932	−	0.280475i
$616$	1.41482	+	2.45054i	0.0570047	+	0.0987350i
$617$	−6.23717	−	5.23361i	−0.251099	−	0.210697i	0.508546	−	0.861035i	$-0.330183\pi$
$617$	−6.23717	−	5.23361i	−0.251099	−	0.210697i	−0.759645	+	0.650338i	$0.774627\pi$
$618$	9.24891	+	7.76076i	0.372046	+	0.312183i
$619$	−1.88729	−	3.26889i	−0.0758567	−	0.131388i	0.825602	−	0.564253i	$-0.190836\pi$
$619$	−1.88729	−	3.26889i	−0.0758567	−	0.131388i	−0.901459	+	0.432866i	$0.857502\pi$
$620$	1.44277	−	2.49894i	0.0579428	−	0.100360i
$621$	−6.85485	+	2.49496i	−0.275076	+	0.100119i
$622$	2.96233	+	16.8002i	0.118779	+	0.673628i
$623$	4.08993	−	23.1951i	0.163860	−	0.929294i
$624$	−4.09397	−	1.49008i	−0.163890	−	0.0596511i
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$	−5.99144			−0.239466
$627$	−1.50300	+	6.21034i	−0.0600242	+	0.248017i
$628$	15.6396			0.624089
$629$	−52.8881	+	44.3784i	−2.10879	+	1.76948i
$630$	−1.81392	−	0.660213i	−0.0722683	−	0.0263035i
$631$	−3.02440	+	17.1522i	−0.120400	+	0.682820i	0.863535	+	0.504289i	$0.168245\pi$
$631$	−3.02440	+	17.1522i	−0.120400	+	0.682820i	−0.983934	+	0.178531i	$0.942866\pi$
$632$	−0.221818	−	1.25799i	−0.00882343	−	0.0500402i
$633$	−17.3604	+	6.31866i	−0.690013	+	0.251144i
$634$	15.5905	−	27.0036i	0.619179	−	1.07245i
$635$	0.0460725	+	0.0798000i	0.00182833	+	0.00316677i
$636$	5.83317	+	4.89461i	0.231300	+	0.194084i
$637$	10.9261	+	9.16812i	0.432909	+	0.363254i
$638$	−2.90410	−	5.03005i	−0.114975	−	0.199142i
$639$	6.03527	−	10.4534i	0.238752	−	0.413530i
$640$	−0.939693	+	0.342020i	−0.0371446	+	0.0135195i
$641$	5.94708	+	33.7276i	0.234895	+	1.33216i	0.842834	+	0.538174i	$0.180886\pi$
$641$	5.94708	+	33.7276i	0.234895	+	1.33216i	−0.607938	+	0.793984i	$0.708003\pi$
$642$	−1.68107	+	9.53380i	−0.0663464	+	0.376269i
$643$	−11.8345	−	4.30741i	−0.466707	−	0.169868i	0.0979529	−	0.995191i	$-0.468771\pi$
$643$	−11.8345	−	4.30741i	−0.466707	−	0.169868i	−0.564660	+	0.825323i	$0.690993\pi$
$644$	−10.7869	+	9.05132i	−0.425065	+	0.356672i
$645$	0.445433			0.0175389
$646$	16.6019	−	24.9832i	0.653191	−	0.982949i
$647$	−40.6017			−1.59622			−0.798109	−	0.602513i	$-0.794166\pi$
$647$	−40.6017			−1.59622			−0.798109	+	0.602513i	$0.794166\pi$
$648$	0.766044	−	0.642788i	0.0300931	−	0.0252511i
$649$	−9.72394	−	3.53922i	−0.381698	−	0.138927i
$650$	−0.756535	+	4.29052i	−0.0296737	+	0.168288i
$651$	0.967226	+	5.48541i	0.0379086	+	0.214990i
$652$	18.0576	−	6.57244i	0.707192	−	0.257397i
$653$	−9.11379	+	15.7855i	−0.356650	+	0.617736i	−0.987399	−	0.158251i	$-0.949415\pi$
$653$	−9.11379	+	15.7855i	−0.356650	+	0.617736i	0.630749	+	0.775987i	$0.282748\pi$
$654$	−9.87786	−	17.1090i	−0.386255	−	0.669013i
$655$	3.74493	+	3.14237i	0.146327	+	0.122783i
$656$	6.15255	+	5.16260i	0.240217	+	0.201566i
$657$	2.71557	+	4.70351i	0.105945	+	0.183502i
$658$	8.39758	−	14.5450i	0.327372	−	0.567024i
$659$	17.8107	−	6.48258i	0.693808	−	0.252525i	0.0290432	−	0.999578i	$-0.490754\pi$
$659$	17.8107	−	6.48258i	0.693808	−	0.252525i	0.664765	+	0.747053i	$0.268532\pi$
$660$	0.254548	+	1.44361i	0.00990825	+	0.0561925i
$661$	6.12883	−	34.7583i	0.238384	−	1.35194i	−0.596985	−	0.802252i	$-0.703635\pi$
$661$	6.12883	−	34.7583i	0.238384	−	1.35194i	0.835369	−	0.549690i	$-0.185254\pi$
$662$	−9.82444	−	3.57580i	−0.381838	−	0.138977i
$663$	22.9670	−	19.2716i	0.891964	−	0.748447i
$664$	−11.1541			−0.432862
$665$	−6.09278	−	5.80307i	−0.236268	−	0.225033i
$666$	−10.0326			−0.388755
$667$	22.1416	−	18.5790i	0.857327	−	0.719382i
$668$	−5.38300	−	1.95925i	−0.208274	−	0.0758057i
$669$	−4.51075	+	25.5817i	−0.174396	+	0.989046i
$670$	0.185298	+	1.05088i	0.00715871	+	0.0405990i
$671$	16.6976	−	6.07742i	0.644602	−	0.234616i
$672$	0.965167	−	1.67172i	0.0372321	−	0.0644879i
$673$	−20.2514	−	35.0764i	−0.780632	−	1.35209i	−0.931574	−	0.363552i	$-0.881564\pi$
$673$	−20.2514	−	35.0764i	−0.780632	−	1.35209i	0.150942	−	0.988543i	$-0.451769\pi$
$674$	1.38124	+	1.15900i	0.0532035	+	0.0446431i
$675$	−0.766044	−	0.642788i	−0.0294851	−	0.0247409i
$676$	−2.99047	−	5.17964i	−0.115018	−	0.199217i
$677$	21.3867	−	37.0429i	0.821958	−	1.42367i	−0.0822645	−	0.996611i	$-0.526215\pi$
$677$	21.3867	−	37.0429i	0.821958	−	1.42367i	0.904222	−	0.427062i	$-0.140451\pi$
$678$	−7.23822	+	2.63450i	−0.277982	+	0.101177i
$679$	4.21761	+	23.9193i	0.161857	+	0.917937i
$680$	1.19498	−	6.77708i	0.0458255	−	0.259889i
$681$	21.0236	+	7.65198i	0.805627	+	0.293224i
$682$	3.24025	−	2.71889i	0.124076	−	0.104112i
$683$	−4.70302			−0.179956			−0.0899781	−	0.995944i	$-0.528680\pi$
$683$	−4.70302			−0.179956			−0.0899781	+	0.995944i	$0.528680\pi$
$684$	4.18166	−	1.23034i	0.159890	−	0.0470432i
$685$	7.15493			0.273376
$686$	−15.1921	+	12.7477i	−0.580037	+	0.486709i
$687$	7.28133	+	2.65019i	0.277800	+	0.101111i
$688$	−0.0773486	+	0.438666i	−0.00294889	+	0.0167240i
$689$	5.76076	+	32.6709i	0.219468	+	1.24466i
$690$	−6.85485	+	2.49496i	−0.260960	+	0.0949815i
$691$	−6.80800	+	11.7918i	−0.258988	+	0.448581i	−0.965971	−	0.258650i	$-0.916722\pi$
$691$	−6.80800	+	11.7918i	−0.258988	+	0.448581i	0.706983	+	0.707231i	$0.250056\pi$
$692$	11.6427	+	20.1658i	0.442590	+	0.766589i
$693$	−2.16763	−	1.81886i	−0.0823414	−	0.0690927i
$694$	26.6490	+	22.3612i	1.01158	+	0.848819i
$695$	1.78267	+	3.08768i	0.0676206	+	0.117122i
$696$	−1.98113	+	3.43142i	−0.0750946	+	0.130068i
$697$	−51.9371	+	18.9036i	−1.96726	+	0.716024i
$698$	−6.12326	−	34.7267i	−0.231769	−	1.31443i
$699$	−0.429253	+	2.43442i	−0.0162359	+	0.0920781i
$700$	−1.81392	−	0.660213i	−0.0685597	−	0.0249537i
$701$	−27.5373	+	23.1066i	−1.04007	+	0.872723i	−0.992015	−	0.126122i	$-0.959747\pi$
$701$	−27.5373	+	23.1066i	−1.04007	+	0.872723i	−0.0480560	+	0.998845i	$0.515303\pi$
$702$	4.35671			0.164433
$703$	−40.0720	−	17.5111i	−1.51134	−	0.660444i
$704$	−1.46588			−0.0552475
$705$	6.66509	−	5.59267i	0.251022	−	0.210632i
$706$	18.8313	+	6.85405i	0.708727	+	0.257955i
$707$	5.56181	−	31.5426i	0.209173	−	1.18628i
$708$	1.22582	+	6.95199i	0.0460693	+	0.261272i
$709$	24.3081	−	8.84743i	0.912910	−	0.332272i	0.157496	−	0.987520i	$-0.449658\pi$
$709$	24.3081	−	8.84743i	0.912910	−	0.332272i	0.755414	+	0.655247i	$0.227436\pi$
$710$	6.03527	−	10.4534i	0.226500	−	0.392309i
$711$	0.638699	+	1.10626i	0.0239531	+	0.0414879i
$712$	9.34689	+	7.84298i	0.350290	+	0.293928i
$713$	16.1247	+	13.5302i	0.603875	+	0.506711i
$714$	6.64192	+	11.5041i	0.248568	+	0.430532i
$715$	−3.19321	+	5.53080i	−0.119419	+	0.206840i
$716$	−16.3177	+	5.93915i	−0.609820	+	0.221956i
$717$	0.880015	+	4.99081i	0.0328648	+	0.186385i
$718$	−0.332879	+	1.88785i	−0.0124229	+	0.0704539i
$719$	−10.8627	−	3.95370i	−0.405110	−	0.147448i	0.131425	−	0.991326i	$-0.458045\pi$
$719$	−10.8627	−	3.95370i	−0.405110	−	0.147448i	−0.536535	+	0.843878i	$0.680267\pi$
$720$	0.766044	−	0.642788i	0.0285488	−	0.0239553i
$721$	−23.3061			−0.867963
$722$	18.8498	+	2.38456i	0.701516	+	0.0887443i
$723$	−1.62000			−0.0602483
$724$	−6.56051	+	5.50492i	−0.243819	+	0.204589i
$725$	3.72331	+	1.35517i	0.138280	+	0.0503299i
$726$	1.53699	−	8.71672i	0.0570432	−	0.323508i
$727$	4.86305	+	27.5797i	0.180361	+	1.02288i	0.931773	+	0.363042i	$0.118262\pi$
$727$	4.86305	+	27.5797i	0.180361	+	1.02288i	−0.751412	+	0.659833i	$0.770627\pi$
$728$	7.90272	−	2.87636i	0.292894	−	0.106605i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	2.71557	+	4.70351i	0.100508	+	0.174085i
$731$	−2.34816	−	1.97034i	−0.0868498	−	0.0728757i
$732$	−9.28587	−	7.79177i	−0.343216	−	0.287992i
$733$	26.2914	+	45.5381i	0.971096	+	1.68199i	0.692259	+	0.721649i	$0.256616\pi$
$733$	26.2914	+	45.5381i	0.971096	+	1.68199i	0.278837	+	0.960338i	$0.410051\pi$
$734$	−13.8123	+	23.9236i	−0.509821	+	0.883036i
$735$	−3.07638	+	1.11971i	−0.113474	+	0.0413011i
$736$	−1.26672	−	7.18395i	−0.0466921	−	0.264804i
$737$	−0.271626	+	1.54047i	−0.0100055	+	0.0567438i
$738$	−7.54722	−	2.74696i	−0.277817	−	0.101117i
$739$	23.1804	−	19.4507i	0.852706	−	0.715505i	−0.107678	−	0.994186i	$-0.534342\pi$
$739$	23.1804	−	19.4507i	0.852706	−	0.715505i	0.960384	+	0.278681i	$0.0898971\pi$
$740$	−10.0326			−0.368805
$741$	17.4015	+	7.60431i	0.639260	+	0.279351i
$742$	−14.6988			−0.539611
$743$	9.48239	−	7.95667i	0.347875	−	0.291902i	−0.452061	−	0.891987i	$-0.649311\pi$
$743$	9.48239	−	7.95667i	0.347875	−	0.291902i	0.799936	+	0.600085i	$0.204867\pi$
$744$	−2.71151	−	0.986909i	−0.0994088	−	0.0361819i
$745$	−2.45835	+	13.9420i	−0.0900670	+	0.510795i
$746$	1.88045	+	10.6646i	0.0688483	+	0.390458i
$747$	10.4814	−	3.81492i	0.383495	−	0.139581i
$748$	5.04383	−	8.73616i	0.184421	−	0.319426i
$749$	−9.34365	−	16.1837i	−0.341410	−	0.591339i
$750$	−0.766044	−	0.642788i	−0.0279720	−	0.0234713i
$751$	32.9462	+	27.6451i	1.20222	+	1.00878i	0.999564	+	0.0295355i	$0.00940281\pi$
$751$	32.9462	+	27.6451i	1.20222	+	1.00878i	0.202659	+	0.979249i	$0.435042\pi$
$752$	4.35033	+	7.53499i	0.158640	+	0.274773i
$753$	5.12523	−	8.87715i	0.186774	−	0.323502i
$754$	−16.2214	+	5.90410i	−0.590748	+	0.215015i
$755$	0.591875	+	3.35669i	0.0215406	+	0.122163i
$756$	−0.335199	+	1.90101i	−0.0121911	+	0.0691390i
$757$	35.6973	+	12.9928i	1.29744	+	0.472230i	0.896162	−	0.443727i	$-0.146344\pi$
$757$	35.6973	+	12.9928i	1.29744	+	0.472230i	0.401278	+	0.915956i	$0.368566\pi$
$758$	−4.37941	+	3.67476i	−0.159067	+	0.133473i
$759$	−10.6933			−0.388141
$760$	4.18166	−	1.23034i	0.151685	−	0.0446291i
$761$	16.3329			0.592069			0.296034	−	0.955177i	$-0.404336\pi$
$761$	16.3329			0.592069			0.296034	+	0.955177i	$0.404336\pi$
$762$	0.0705872	−	0.0592297i	0.00255711	−	0.00214567i
$763$	35.8353	+	13.0430i	1.29732	+	0.472188i
$764$	−2.43604	+	13.8154i	−0.0881327	+	0.499825i
$765$	1.19498	+	6.77708i	0.0432047	+	0.245026i
$766$	7.43101	−	2.70467i	0.268493	−	0.0977236i
$767$	−15.3775	+	26.6346i	−0.555250	+	0.961721i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	36.4961	+	30.6238i	1.31608	+	1.10432i	0.987120	+	0.159980i	$0.0511429\pi$
$769$	36.4961	+	30.6238i	1.31608	+	1.10432i	0.328961	+	0.944344i	$0.393302\pi$
$770$	−2.16763	−	1.81886i	−0.0781159	−	0.0655470i
$771$	−0.989730	−	1.71426i	−0.0356443	−	0.0617377i
$772$	−2.78680	+	4.82689i	−0.100299	+	0.173723i
$773$	44.3565	−	16.1444i	1.59539	−	0.580675i	0.616915	−	0.787030i	$-0.288382\pi$
$773$	44.3565	−	16.1444i	1.59539	−	0.580675i	0.978477	+	0.206354i	$0.0661599\pi$
$774$	−0.0773486	−	0.438666i	−0.00278024	−	0.0157675i
$775$	−0.501067	+	2.84169i	−0.0179989	+	0.102077i
$776$	−11.8236	−	4.30344i	−0.424443	−	0.154485i
$777$	14.8354	−	12.4484i	0.532217	−	0.446583i
$778$	−24.1515			−0.865872
$779$	−25.3504	−	24.1450i	−0.908271	−	0.865083i
$780$	4.35671			0.155995
$781$	13.5544	−	11.3735i	0.485013	−	0.406975i
$782$	47.1725	+	17.1694i	1.68689	+	0.613976i
$783$	0.688040	−	3.90207i	0.0245885	−	0.139448i
$784$	−0.568492	−	3.22408i	−0.0203033	−	0.115146i
$785$	−14.6964	+	5.34907i	−0.524539	+	0.190916i
$786$	2.44433	−	4.23370i	0.0871863	−	0.151011i
$787$	−1.74199	−	3.01721i	−0.0620952	−	0.107552i	0.833307	−	0.552811i	$-0.186445\pi$
$787$	−1.74199	−	3.01721i	−0.0620952	−	0.107552i	−0.895402	+	0.445259i	$0.853112\pi$
$788$	−4.23983	−	3.55764i	−0.151038	−	0.126736i
$789$	5.11314	+	4.29043i	0.182033	+	0.152743i
$790$	0.638699	+	1.10626i	0.0227239	+	0.0393589i
$791$	7.43444	−	12.8768i	0.264338	−	0.457847i
$792$	1.37748	−	0.501361i	0.0489465	−	0.0178151i
$793$	−9.17060	−	52.0090i	−0.325657	−	1.84690i
$794$	−1.39313	+	7.90082i	−0.0494402	+	0.280389i
$795$	−7.15545	−	2.60437i	−0.253777	−	0.0923675i
$796$	1.56135	−	1.31013i	0.0553406	−	0.0464363i
$797$	27.4738			0.973170			0.486585	−	0.873633i	$-0.338242\pi$
$797$	27.4738			0.973170			0.486585	+	0.873633i	$0.338242\pi$
$798$	−4.65691	+	7.00791i	−0.164853	+	0.248077i
$799$	−59.8747			−2.11821
$800$	0.766044	−	0.642788i	0.0270838	−	0.0227260i
$801$	−11.4657	−	4.17316i	−0.405119	−	0.147451i
$802$	1.60590	−	9.10753i	0.0567064	−	0.321598i
$803$	1.38249	+	7.84047i	0.0487869	+	0.276684i
$804$	1.00274	−	0.364967i	0.0353638	−	0.0128714i
$805$	7.04068	−	12.1948i	0.248151	−	0.429810i
$806$	−6.28571	−	10.8872i	−0.221405	−	0.383484i
$807$	6.95606	+	5.83683i	0.244865	+	0.205466i
$808$	12.7106	+	10.6655i	0.447159	+	0.375211i
$809$	6.96000	+	12.0551i	0.244701	+	0.423834i	0.962047	−	0.272882i	$-0.0879770\pi$
$809$	6.96000	+	12.0551i	0.244701	+	0.423834i	−0.717347	+	0.696716i	$0.754644\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	28.7972	−	10.4813i	1.01121	−	0.368050i	0.217311	−	0.976102i	$-0.430271\pi$
$811$	28.7972	−	10.4813i	1.01121	−	0.368050i	0.793897	+	0.608053i	$0.208049\pi$
$812$	−1.32815	−	7.53229i	−0.0466088	−	0.264331i
$813$	1.79179	−	10.1617i	0.0628408	−	0.356388i
$814$	−13.8197	−	5.02995i	−0.484379	−	0.176299i
$815$	−14.7207	+	12.3522i	−0.515644	+	0.432677i
$816$	−6.88163			−0.240905
$817$	0.456713	−	1.88712i	0.0159784	−	0.0660219i
$818$	−15.5333			−0.543109
$819$	−6.44236	+	5.40578i	−0.225114	+	0.188893i
$820$	−7.54722	−	2.74696i	−0.263560	−	0.0959281i
$821$	−4.63929	+	26.3107i	−0.161912	+	0.918251i	0.790279	+	0.612748i	$0.209936\pi$
$821$	−4.63929	+	26.3107i	−0.161912	+	0.918251i	−0.952191	+	0.305503i	$0.901175\pi$
$822$	−1.24244	−	7.04623i	−0.0433351	−	0.245765i
$823$	28.8366	−	10.4957i	1.00518	−	0.365856i	0.213600	−	0.976921i	$-0.431481\pi$
$823$	28.8366	−	10.4957i	1.00518	−	0.365856i	0.791580	+	0.611065i	$0.209259\pi$
$824$	6.03680	−	10.4560i	0.210302	−	0.364253i
$825$	−0.732941	−	1.26949i	−0.0255177	−	0.0441980i
$826$	−10.4386	−	8.75906i	−0.363207	−	0.304767i
$827$	−38.1056	−	31.9744i	−1.32506	−	1.11186i	−0.985205	−	0.171383i	$-0.945176\pi$
$827$	−38.1056	−	31.9744i	−1.32506	−	1.11186i	−0.339858	−	0.940477i	$-0.610379\pi$
$828$	3.64739	+	6.31746i	0.126756	+	0.219547i
$829$	13.8393	−	23.9704i	0.480660	−	0.832528i	−0.519094	−	0.854717i	$-0.673730\pi$
$829$	13.8393	−	23.9704i	0.480660	−	0.832528i	0.999754	+	0.0221897i	$0.00706379\pi$
$830$	10.4814	−	3.81492i	0.363815	−	0.132418i
$831$	−3.78916	−	21.4894i	−0.131444	−	0.745459i
$832$	−0.756535	+	4.29052i	−0.0262281	+	0.148747i
$833$	21.1705	+	7.70543i	0.733514	+	0.266977i
$834$	2.73121	−	2.29176i	0.0945741	−	0.0793571i
$835$	5.72847			0.198242
$836$	6.37698	+	0.401755i	0.220553	+	0.0138950i
$837$	2.88553			0.0997385
$838$	−3.61376	+	3.03230i	−0.124835	+	0.104749i
$839$	28.8986	+	10.5182i	0.997690	+	0.363130i	0.788693	−	0.614787i	$-0.210758\pi$
$839$	28.8986	+	10.5182i	0.997690	+	0.363130i	0.208997	+	0.977916i	$0.432980\pi$
$840$	−0.335199	+	1.90101i	−0.0115655	+	0.0655910i
$841$	−2.30960	−	13.0984i	−0.0796415	−	0.451670i
$842$	−19.6130	+	7.13856i	−0.675910	+	0.246011i
$843$	6.34738	−	10.9940i	0.218615	−	0.378653i
$844$	9.23726	+	15.9994i	0.317960	+	0.550722i
$845$	4.58166	+	3.84447i	0.157614	+	0.132254i
$846$	−6.66509	−	5.59267i	−0.229150	−	0.192280i
$847$	8.54287	+	14.7967i	0.293537	+	0.508420i
$848$	3.80733	−	6.59449i	0.130744	−	0.226456i
$849$	20.1402	−	7.33044i	0.691211	−	0.251580i
$850$	1.19498	+	6.77708i	0.0409876	+	0.232452i
$851$	12.7085	−	72.0736i	0.435643	−	2.47065i
$852$	−11.3426	−	4.12837i	−0.388591	−	0.141436i
$853$	15.8924	−	13.3353i	0.544146	−	0.456593i	−0.328807	−	0.944397i	$-0.606646\pi$
$853$	15.8924	−	13.3353i	0.544146	−	0.456593i	0.872953	+	0.487804i	$0.162202\pi$
$854$	23.3992			0.800704
$855$	−3.50867	+	2.58635i	−0.119994	+	0.0884514i
$856$	9.68087			0.330885
$857$	−24.0298	+	20.1634i	−0.820841	+	0.688767i	−0.953169	−	0.302439i	$-0.902199\pi$
$857$	−24.0298	+	20.1634i	−0.820841	+	0.688767i	0.132328	+	0.991206i	$0.457755\pi$
$858$	6.00127	+	2.18428i	0.204880	+	0.0745702i
$859$	−8.32167	+	47.1945i	−0.283932	+	1.61026i	0.425145	+	0.905125i	$0.360223\pi$
$859$	−8.32167	+	47.1945i	−0.283932	+	1.61026i	−0.709077	+	0.705131i	$0.750888\pi$
$860$	−0.0773486	−	0.438666i	−0.00263757	−	0.0149584i
$861$	14.5686	−	5.30255i	0.496498	−	0.180710i
$862$	0.0695433	−	0.120453i	0.00236865	−	0.00410263i
$863$	4.24643	+	7.35503i	0.144550	+	0.250368i	0.929205	−	0.369565i	$-0.120493\pi$
$863$	4.24643	+	7.35503i	0.144550	+	0.250368i	−0.784655	+	0.619933i	$0.787160\pi$
$864$	−0.766044	−	0.642788i	−0.0260614	−	0.0218681i
$865$	−17.8377	−	14.9676i	−0.606500	−	0.508914i
$866$	2.18303	+	3.78111i	0.0741822	+	0.128487i
$867$	15.1784	−	26.2898i	0.515486	−	0.892848i
$868$	5.23412	−	1.90506i	0.177658	−	0.0646621i
$869$	0.325158	+	1.84406i	0.0110302	+	0.0625556i
$870$	0.688040	−	3.90207i	0.0233267	−	0.132292i
$871$	4.36864	+	1.59005i	0.148026	+	0.0538770i
$872$	−15.1338	+	12.6987i	−0.512494	+	0.430033i
$873$	12.5824			0.425850
$874$	3.54169	+	31.5993i	0.119799	+	1.06886i
$875$	1.93033			0.0652572
$876$	4.16050	−	3.49108i	0.140570	−	0.117953i
$877$	43.1865	+	15.7186i	1.45831	+	0.530780i	0.944898	−	0.327365i	$-0.106161\pi$
$877$	43.1865	+	15.7186i	1.45831	+	0.530780i	0.513408	+	0.858145i	$0.328383\pi$
$878$	−5.30104	+	30.0637i	−0.178901	+	1.01460i
$879$	1.86107	+	10.5547i	0.0627724	+	0.356000i
$880$	1.37748	−	0.501361i	0.0464348	−	0.0169009i
$881$	16.7737	−	29.0529i	0.565121	−	0.978818i	−0.431918	−	0.901913i	$-0.642163\pi$
$881$	16.7737	−	29.0529i	0.565121	−	0.978818i	0.997038	−	0.0769049i	$-0.0245038\pi$
$882$	1.63691	+	2.83521i	0.0551175	+	0.0954664i
$883$	4.17309	+	3.50164i	0.140436	+	0.117839i	0.710299	−	0.703900i	$-0.248560\pi$
$883$	4.17309	+	3.50164i	0.140436	+	0.117839i	−0.569864	+	0.821739i	$0.693004\pi$
$884$	−22.9670	−	19.2716i	−0.772463	−	0.648174i
$885$	−3.52962	−	6.11348i	−0.118647	−	0.205502i
$886$	7.87002	−	13.6313i	0.264399	−	0.457952i
$887$	−5.96361	+	2.17058i	−0.200238	+	0.0728808i	−0.440192	−	0.897903i	$-0.645090\pi$
$887$	−5.96361	+	2.17058i	−0.200238	+	0.0728808i	0.239954	+	0.970784i	$0.422868\pi$
$888$	1.74214	+	9.88017i	0.0584624	+	0.331557i
$889$	−0.0308869	+	0.175168i	−0.00103591	+	0.00587496i
$890$	−11.4657	−	4.17316i	−0.384330	−	0.139885i
$891$	−1.12293	+	0.942250i	−0.0376196	+	0.0315666i
$892$	25.9763			0.869753
$893$	−16.8600	−	33.9716i	−0.564198	−	1.13681i
$894$	14.1571			0.473483
$895$	13.3023	−	11.1619i	0.444647	−	0.373103i
$896$	−1.81392	−	0.660213i	−0.0605988	−	0.0220562i
$897$	−5.51875	+	31.2984i	−0.184266	+	1.04502i
$898$	−1.38411	−	7.84970i	−0.0461885	−	0.261948i
$899$	−10.7437	+	3.91039i	−0.358323	+	0.130419i
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	26.2007	+	45.3809i	0.872870	+	1.51186i
$902$	−9.01890	−	7.56776i	−0.300297	−	0.251979i
$903$	0.658671	+	0.552691i	0.0219192	+	0.0183924i
$904$	3.85137	+	6.67078i	0.128095	+	0.221867i
$905$	4.28207	−	7.41676i	0.142341	−	0.246542i
$906$	3.20292	−	1.16577i	0.106410	−	0.0387300i
$907$	−9.70336	−	55.0305i	−0.322195	−	1.82726i	−0.528696	−	0.848811i	$-0.677319\pi$
$907$	−9.70336	−	55.0305i	−0.322195	−	1.82726i	0.206501	−	0.978446i	$-0.433792\pi$
$908$	3.88501	−	22.0330i	0.128929	−	0.731190i
$909$	−15.5919	−	5.67499i	−0.517151	−	0.188228i
$910$	−6.44236	+	5.40578i	−0.213562	+	0.179200i
$911$	−37.3065			−1.23602			−0.618010	−	0.786171i	$-0.712061\pi$
$911$	−37.3065			−1.23602			−0.618010	+	0.786171i	$0.712061\pi$
$912$	−1.93779	−	3.90448i	−0.0641665	−	0.129290i
$913$	16.3506			0.541125
$914$	1.76845	−	1.48391i	0.0584951	−	0.0490833i
$915$	11.3908	+	4.14591i	0.376568	+	0.137060i
$916$	1.34554	−	7.63091i	0.0444577	−	0.252132i
$917$	1.63867	+	9.29337i	0.0541137	+	0.306894i
$918$	6.46662	−	2.35366i	0.213430	−	0.0776822i
$919$	−20.0403	+	34.7108i	−0.661067	+	1.14500i	0.319268	+	0.947664i	$0.396563\pi$
$919$	−20.0403	+	34.7108i	−0.661067	+	1.14500i	−0.980336	+	0.197338i	$0.936770\pi$
$920$	3.64739	+	6.31746i	0.120251	+	0.208281i
$921$	10.2170	+	8.57308i	0.336662	+	0.282493i
$922$	22.3467	+	18.7511i	0.735948	+	0.617534i
$923$	−26.2939	−	45.5424i	−0.865475	−	1.49905i
$924$	−1.41482	+	2.45054i	−0.0465441	+	0.0806168i
$925$	9.42755	−	3.43135i	0.309976	−	0.112822i
$926$	−2.19303	−	12.4373i	−0.0720674	−	0.408715i
$927$	−2.09656	+	11.8902i	−0.0688600	+	0.390524i
$928$	3.72331	+	1.35517i	0.122224	+	0.0444857i
$929$	28.2590	−	23.7121i	0.927147	−	0.777969i	−0.0481558	−	0.998840i	$-0.515334\pi$
$929$	28.2590	−	23.7121i	0.927147	−	0.777969i	0.975303	+	0.220871i	$0.0708899\pi$
$930$	2.88553			0.0946203
$931$	1.58947	+	14.1814i	0.0520928	+	0.464778i
$932$	2.47197			0.0809721
$933$	−13.0683	+	10.9656i	−0.427836	+	0.358997i
$934$	18.4038	+	6.69844i	0.602191	+	0.219180i
$935$	−1.75170	+	9.93440i	−0.0572868	+	0.324890i
$936$	−0.756535	−	4.29052i	−0.0247281	−	0.140240i
$937$	−51.4526	+	18.7272i	−1.68088	+	0.611791i	−0.993430	−	0.114438i	$-0.963493\pi$
$937$	−51.4526	+	18.7272i	−1.68088	+	0.611791i	−0.687453	+	0.726229i	$0.741271\pi$
$938$	−1.02992	+	1.78388i	−0.0336281	+	0.0582456i
$939$	−2.99572	−	5.18874i	−0.0977617	−	0.169328i
$940$	−6.66509	−	5.59267i	−0.217391	−	0.182413i
$941$	−10.5980	−	8.89278i	−0.345485	−	0.289896i	0.453489	−	0.891262i	$-0.350179\pi$
$941$	−10.5980	−	8.89278i	−0.345485	−	0.289896i	−0.798974	+	0.601365i	$0.794624\pi$
$942$	7.81981	+	13.5443i	0.254783	+	0.441298i
$943$	29.2943	−	50.7392i	0.953954	−	1.65230i
$944$	6.63351	−	2.41440i	0.215902	−	0.0785820i
$945$	−0.335199	−	1.90101i	−0.0109040	−	0.0618398i
$946$	0.113384	−	0.643032i	0.00368643	−	0.0209068i
$947$	32.7047	+	11.9035i	1.06276	+	0.386813i	0.813464	−	0.581615i	$-0.197579\pi$
$947$	32.7047	+	11.9035i	1.06276	+	0.386813i	0.249295	+	0.968428i	$0.419801\pi$
$948$	0.978543	−	0.821095i	0.0317816	−	0.0266679i
$949$	23.6619			0.768099
$950$	−3.50867	+	2.58635i	−0.113836	+	0.0839123i
$951$	31.1811			1.01112
$952$	10.1760	−	8.53869i	0.329806	−	0.276740i
$953$	−23.7844	−	8.65683i	−0.770453	−	0.280422i	−0.0732674	−	0.997312i	$-0.523343\pi$
$953$	−23.7844	−	8.65683i	−0.770453	−	0.280422i	−0.697186	+	0.716890i	$0.745565\pi$
$954$	−1.32227	+	7.49898i	−0.0428102	+	0.242788i
$955$	−2.43604	−	13.8154i	−0.0788283	−	0.447057i
$956$	4.76218	−	1.73329i	0.154020	−	0.0560586i
$957$	2.90410	−	5.03005i	0.0938763	−	0.162599i
$958$	10.3767	+	17.9729i	0.335255	+	0.580679i
$959$	10.5801	+	8.87780i	0.341651	+	0.286679i
$960$	−0.766044	−	0.642788i	−0.0247240	−	0.0207459i
$961$	11.3369	+	19.6360i	0.365705	+	0.633420i
$962$	−21.8545	+	37.8532i	−0.704619	+	1.22044i
$963$	−9.09704	+	3.31105i	−0.293148	+	0.106697i
$964$	0.281309	+	1.59538i	0.00906036	+	0.0513839i
$965$	0.967847	−	5.48893i	0.0311561	−	0.176695i
$966$	−13.2321	−	4.81611i	−0.425737	−	0.154956i
$967$	12.9840	−	10.8948i	0.417536	−	0.350355i	−0.409689	−	0.912225i	$-0.634363\pi$
$967$	12.9840	−	10.8948i	0.417536	−	0.350355i	0.827225	+	0.561871i	$0.189918\pi$
$968$	−8.85119			−0.284488
$969$	29.9370	+	1.88605i	0.961714	+	0.0605887i
$970$	12.5824			0.403997
$971$	28.0815	−	23.5632i	0.901179	−	0.756179i	−0.0692415	−	0.997600i	$-0.522058\pi$
$971$	28.0815	−	23.5632i	0.901179	−	0.756179i	0.970420	+	0.241421i	$0.0776134\pi$
$972$	0.939693	+	0.342020i	0.0301407	+	0.0109703i
$973$	−1.19510	+	6.77774i	−0.0383131	+	0.217284i
$974$	1.22764	+	6.96231i	0.0393362	+	0.223087i
$975$	−4.09397	+	1.49008i	−0.131112	+	0.0477208i
$976$	−6.06092	+	10.4978i	−0.194005	+	0.336027i
$977$	13.6796	+	23.6938i	0.437650	+	0.758032i	0.997508	−	0.0705567i	$-0.0224776\pi$
$977$	13.6796	+	23.6938i	0.437650	+	0.758032i	−0.559858	+	0.828589i	$0.689144\pi$
$978$	14.7207	+	12.3522i	0.470717	+	0.394978i
$979$	−13.7014	−	11.4969i	−0.437900	−	0.367442i
$980$	1.63691	+	2.83521i	0.0522891	+	0.0905673i
$981$	9.87786	−	17.1090i	0.315376	−	0.546247i
$982$	28.5744	−	10.4002i	0.911847	−	0.331885i
$983$	3.64572	+	20.6759i	0.116280	+	0.659458i	0.986108	+	0.166103i	$0.0531185\pi$
$983$	3.64572	+	20.6759i	0.116280	+	0.659458i	−0.869828	+	0.493355i	$0.835770\pi$
$984$	−1.39467	+	7.90956i	−0.0444604	+	0.252148i
$985$	5.20092	+	1.89298i	0.165715	+	0.0603154i
$986$	−20.8876	+	17.5268i	−0.665197	+	0.558166i
$987$	16.7952			0.534596
$988$	4.46704	−	18.4576i	0.142115	−	0.587215i
$989$	3.24933			0.103323
$990$	−1.12293	+	0.942250i	−0.0356891	+	0.0299467i
$991$	10.1310	+	3.68737i	0.321821	+	0.117133i	0.497879	−	0.867247i	$-0.334112\pi$
$991$	10.1310	+	3.68737i	0.321821	+	0.117133i	−0.176058	+	0.984380i	$0.556335\pi$
$992$	−0.501067	+	2.84169i	−0.0159089	+	0.0902238i
$993$	−1.81548	−	10.2961i	−0.0576126	−	0.326737i
$994$	21.8950	−	7.96912i	0.694467	−	0.252765i
$995$	−1.01910	+	1.76513i	−0.0323076	+	0.0559584i
$996$	−5.57704	−	9.65972i	−0.176715	−	0.306080i
$997$	−6.11294	−	5.12937i	−0.193599	−	0.162449i	0.540836	−	0.841128i	$-0.318108\pi$
$997$	−6.11294	−	5.12937i	−0.193599	−	0.162449i	−0.734435	+	0.678680i	$0.762553\pi$
$998$	20.0098	+	16.7902i	0.633398	+	0.531484i
$999$	−5.01629	−	8.68847i	−0.158708	−	0.274891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.u.j.481.1	yes	12
19.16	even	9	inner	570.2.u.j.301.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.u.j.301.1	✓	12	19.16	even	9	inner
570.2.u.j.481.1	yes	12	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(0.939693 + 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.173648 + 0.984808i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-0.965167 + 1.67172i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +O(q^{10})\)	\(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} +(-0.965167 + 1.67172i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +(0.766044 + 0.642788i) q^{10} +(0.732941 + 1.26949i) q^{11} +(0.500000 - 0.866025i) q^{12} +(4.09397 - 1.49008i) q^{13} +(0.335199 + 1.90101i) q^{14} +(-0.173648 + 0.984808i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(5.27163 - 4.42343i) q^{17} +1.00000 q^{18} +(3.99418 + 1.74542i) q^{19} +1.00000 q^{20} +(-1.47872 + 1.24079i) q^{21} +(1.37748 + 0.501361i) q^{22} +(-1.26672 + 7.18395i) q^{23} +(-0.173648 - 0.984808i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(2.17836 - 3.77302i) q^{26} +(0.500000 + 0.866025i) q^{27} +(1.47872 + 1.24079i) q^{28} +(-3.03527 - 2.54689i) q^{29} +(0.500000 + 0.866025i) q^{30} +(1.44277 - 2.49894i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.254548 + 1.44361i) q^{33} +(1.19498 - 6.77708i) q^{34} +(-1.81392 - 0.660213i) q^{35} +(0.766044 - 0.642788i) q^{36} -10.0326 q^{37} +(4.18166 - 1.23034i) q^{38} +4.35671 q^{39} +(0.766044 - 0.642788i) q^{40} +(-7.54722 - 2.74696i) q^{41} +(-0.335199 + 1.90101i) q^{42} +(-0.0773486 - 0.438666i) q^{43} +(1.37748 - 0.501361i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(3.64739 + 6.31746i) q^{46} +(-6.66509 - 5.59267i) q^{47} +(-0.766044 - 0.642788i) q^{48} +(1.63691 + 2.83521i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(6.46662 - 2.35366i) q^{51} +(-0.756535 - 4.29052i) q^{52} +(-1.32227 + 7.49898i) q^{53} +(0.939693 + 0.342020i) q^{54} +(-1.12293 + 0.942250i) q^{55} +1.93033 q^{56} +(3.15633 + 3.00625i) q^{57} -3.96226 q^{58} +(-5.40769 + 4.53759i) q^{59} +(0.939693 + 0.342020i) q^{60} +(2.10494 - 11.9377i) q^{61} +(-0.501067 - 2.84169i) q^{62} +(-1.81392 + 0.660213i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.17836 + 3.77302i) q^{65} +(1.12293 + 0.942250i) q^{66} +(0.817439 + 0.685913i) q^{67} +(-3.44081 - 5.95967i) q^{68} +(-3.64739 + 6.31746i) q^{69} +(-1.81392 + 0.660213i) q^{70} +(-2.09603 - 11.8872i) q^{71} +(0.173648 - 0.984808i) q^{72} +(5.10361 + 1.85756i) q^{73} +(-7.68541 + 6.44882i) q^{74} -1.00000 q^{75} +(2.41249 - 3.63041i) q^{76} -2.82964 q^{77} +(3.33743 - 2.80044i) q^{78} +(1.20036 + 0.436896i) q^{79} +(0.173648 - 0.984808i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-7.54722 + 2.74696i) q^{82} +(5.57704 - 9.65972i) q^{83} +(0.965167 + 1.67172i) q^{84} +(5.27163 + 4.42343i) q^{85} +(-0.341221 - 0.286319i) q^{86} +(-1.98113 - 3.43142i) q^{87} +(0.732941 - 1.26949i) q^{88} +(-11.4657 + 4.17316i) q^{89} +(0.173648 + 0.984808i) q^{90} +(-1.46036 + 8.28214i) q^{91} +(6.85485 + 2.49496i) q^{92} +(2.21044 - 1.85478i) q^{93} -8.70065 q^{94} +(-1.02532 + 4.23659i) q^{95} -1.00000 q^{96} +(9.63869 - 8.08783i) q^{97} +(3.07638 + 1.11971i) q^{98} +(-0.254548 + 1.44361i) 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

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