LMFDB - Embedded newform 690.2.m.b.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.1
Root			$0.959493 - 0.281733i$ of defining polynomial
Character	$\chi$	$=$	690.121
Dual form			690.2.m.b.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.0867074 + 0.603063i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.0867074 + 0.603063i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(0.142315 + 0.989821i) q^{10} +(-0.0982369 - 0.215109i) q^{11} +(0.415415 + 0.909632i) q^{12} +(-0.227916 - 1.58519i) q^{13} +(-0.512546 - 0.329393i) q^{14} +(-0.959493 + 0.281733i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(0.744123 - 0.858763i) q^{17} +(-0.841254 + 0.540641i) q^{18} +(0.557730 + 0.643655i) q^{19} +(-0.959493 - 0.281733i) q^{20} +(0.253098 - 0.554206i) q^{21} +0.236479 q^{22} +(-1.17376 - 4.64998i) q^{23} -1.00000 q^{24} +(0.415415 - 0.909632i) q^{25} +(1.53662 + 0.451193i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(0.512546 - 0.329393i) q^{28} +(2.69973 - 3.11565i) q^{29} +(0.142315 - 0.989821i) q^{30} +(8.03302 - 2.35871i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(0.0336545 + 0.234072i) q^{33} +(0.472039 + 1.03362i) q^{34} +(0.253098 + 0.554206i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(3.81143 + 2.44946i) q^{37} +(-0.817178 + 0.239945i) q^{38} +(-0.227916 + 1.58519i) q^{39} +(0.654861 - 0.755750i) q^{40} +(6.93886 - 4.45934i) q^{41} +(0.398983 + 0.460451i) q^{42} +(-0.394911 - 0.115956i) q^{43} +(-0.0982369 + 0.215109i) q^{44} +1.00000 q^{45} +(4.71737 + 0.863983i) q^{46} -5.06547 q^{47} +(0.415415 - 0.909632i) q^{48} +(6.36028 + 1.86755i) q^{49} +(0.654861 + 0.755750i) q^{50} +(-0.955922 + 0.614334i) q^{51} +(-1.04875 + 1.21033i) q^{52} +(1.01292 - 7.04505i) q^{53} +(0.959493 - 0.281733i) q^{54} +(-0.198939 - 0.127850i) q^{55} +(0.0867074 + 0.603063i) q^{56} +(-0.353799 - 0.774713i) q^{57} +(1.71259 + 3.75005i) q^{58} +(-0.0718473 - 0.499709i) q^{59} +(0.841254 + 0.540641i) q^{60} +(11.5663 - 3.39616i) q^{61} +(-1.19148 + 8.28694i) q^{62} +(-0.398983 + 0.460451i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-1.04875 - 1.21033i) q^{65} +(-0.226900 - 0.0666238i) q^{66} +(-1.41111 + 3.08990i) q^{67} -1.13631 q^{68} +(-0.183838 + 4.79231i) q^{69} -0.609264 q^{70} +(0.611970 - 1.34003i) q^{71} +(0.959493 + 0.281733i) q^{72} +(3.10434 + 3.58260i) q^{73} +(-3.81143 + 2.44946i) q^{74} +(-0.654861 + 0.755750i) q^{75} +(0.121206 - 0.843008i) q^{76} +(0.138242 - 0.0405915i) q^{77} +(-1.34726 - 0.865832i) q^{78} +(0.829194 + 5.76717i) q^{79} +(0.415415 + 0.909632i) q^{80} +(0.415415 + 0.909632i) q^{81} +(1.17385 + 8.16428i) q^{82} +(-3.06369 - 1.96891i) q^{83} +(-0.584585 + 0.171650i) q^{84} +(0.161713 - 1.12474i) q^{85} +(0.269529 - 0.311053i) q^{86} +(-3.46815 + 2.22885i) q^{87} +(-0.154861 - 0.178719i) q^{88} +(-3.23278 - 0.949230i) q^{89} +(-0.415415 + 0.909632i) q^{90} +0.975733 q^{91} +(-2.74557 + 3.93215i) q^{92} -8.37216 q^{93} +(2.10427 - 4.60771i) q^{94} +(0.817178 + 0.239945i) q^{95} +(0.654861 + 0.755750i) q^{96} +(-0.0626320 + 0.0402511i) q^{97} +(-4.34094 + 5.00971i) q^{98} +(0.0336545 - 0.234072i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + q^{8} - q^{9}+O(q^{10}) $ 10 * q + q^2 - q^3 - q^4 - q^5 + q^6 + q^8 - q^9	$ 10 q + q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + q^{8} - q^{9} + q^{10} - 4 q^{11} - q^{12} + 2 q^{13} - q^{15} - q^{16} - 2 q^{17} + q^{18} - q^{20} + 4 q^{22} - q^{23} - 10 q^{24} - q^{25} + 9 q^{26} - q^{27} - 6 q^{29} + q^{30} + 22 q^{31} + q^{32} - 4 q^{33} - 9 q^{34} - q^{36} + 20 q^{37} + 2 q^{39} + q^{40} + 9 q^{41} - 11 q^{42} + 12 q^{43} - 4 q^{44} + 10 q^{45} + q^{46} - 8 q^{47} - q^{48} + 7 q^{49} + q^{50} - 13 q^{51} + 2 q^{52} - 20 q^{53} + q^{54} + 7 q^{55} + 11 q^{57} + 6 q^{58} - 22 q^{59} - q^{60} + 49 q^{61} + 11 q^{63} - q^{64} + 2 q^{65} - 7 q^{66} + 10 q^{67} - 2 q^{68} - q^{69} - q^{71} + q^{72} + 17 q^{73} - 20 q^{74} - q^{75} - 13 q^{78} + 18 q^{79} - q^{80} - q^{81} + 13 q^{82} + 15 q^{83} - 11 q^{84} + 9 q^{85} + 10 q^{86} - 6 q^{87} + 4 q^{88} - 5 q^{89} + q^{90} + 22 q^{91} - 12 q^{92} - 22 q^{93} - 3 q^{94} + q^{96} - q^{97} - 7 q^{98} - 4 q^{99}+O(q^{100}) $ 10 * q + q^2 - q^3 - q^4 - q^5 + q^6 + q^8 - q^9 + q^10 - 4 * q^11 - q^12 + 2 * q^13 - q^15 - q^16 - 2 * q^17 + q^18 - q^20 + 4 * q^22 - q^23 - 10 * q^24 - q^25 + 9 * q^26 - q^27 - 6 * q^29 + q^30 + 22 * q^31 + q^32 - 4 * q^33 - 9 * q^34 - q^36 + 20 * q^37 + 2 * q^39 + q^40 + 9 * q^41 - 11 * q^42 + 12 * q^43 - 4 * q^44 + 10 * q^45 + q^46 - 8 * q^47 - q^48 + 7 * q^49 + q^50 - 13 * q^51 + 2 * q^52 - 20 * q^53 + q^54 + 7 * q^55 + 11 * q^57 + 6 * q^58 - 22 * q^59 - q^60 + 49 * q^61 + 11 * q^63 - q^64 + 2 * q^65 - 7 * q^66 + 10 * q^67 - 2 * q^68 - q^69 - q^71 + q^72 + 17 * q^73 - 20 * q^74 - q^75 - 13 * q^78 + 18 * q^79 - q^80 - q^81 + 13 * q^82 + 15 * q^83 - 11 * q^84 + 9 * q^85 + 10 * q^86 - 6 * q^87 + 4 * q^88 - 5 * q^89 + q^90 + 22 * q^91 - 12 * q^92 - 22 * q^93 - 3 * q^94 + q^96 - q^97 - 7 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{11}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	0.841254	−	0.540641i	0.376220	−	0.241782i
$5$	0.841254	−	0.540641i	0.376220	−	0.241782i
$6$	0.654861	−	0.755750i	0.267346	−	0.308533i
$7$	−0.0867074	+	0.603063i	−0.0327723	+	0.227936i	−0.999625	−	0.0274001i	$-0.991277\pi$
$7$	−0.0867074	+	0.603063i	−0.0327723	+	0.227936i	0.966852	+	0.255337i	$0.0821863\pi$
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	0.142315	+	0.989821i	0.0450039	+	0.313009i
$11$	−0.0982369	−	0.215109i	−0.0296195	−	0.0648577i	0.894244	−	0.447580i	$-0.147714\pi$
$11$	−0.0982369	−	0.215109i	−0.0296195	−	0.0648577i	−0.923864	+	0.382722i	$0.874987\pi$
$12$	0.415415	+	0.909632i	0.119920	+	0.262588i
$13$	−0.227916	−	1.58519i	−0.0632126	−	0.439653i	−0.996709	−	0.0810658i	$-0.974168\pi$
$13$	−0.227916	−	1.58519i	−0.0632126	−	0.439653i	0.933496	−	0.358587i	$-0.116741\pi$
$14$	−0.512546	−	0.329393i	−0.136984	−	0.0880340i
$15$	−0.959493	+	0.281733i	−0.247740	+	0.0727430i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	0.744123	−	0.858763i	0.180476	−	0.208281i	−0.658302	−	0.752754i	$-0.728725\pi$
$17$	0.744123	−	0.858763i	0.180476	−	0.208281i	0.838778	+	0.544473i	$0.183270\pi$
$18$	−0.841254	+	0.540641i	−0.198285	+	0.127430i
$19$	0.557730	+	0.643655i	0.127952	+	0.147664i	0.816110	−	0.577896i	$-0.196126\pi$
$19$	0.557730	+	0.643655i	0.127952	+	0.147664i	−0.688158	+	0.725560i	$0.741581\pi$
$20$	−0.959493	−	0.281733i	−0.214549	−	0.0629973i
$21$	0.253098	−	0.554206i	0.0552304	−	0.120938i
$22$	0.236479			0.0504175
$23$	−1.17376	−	4.64998i	−0.244745	−	0.969587i
$23$	−1.17376	−	4.64998i	−0.244745	−	0.969587i
$24$	−1.00000			−0.204124
$25$	0.415415	−	0.909632i	0.0830830	−	0.181926i
$26$	1.53662	+	0.451193i	0.301356	+	0.0884862i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	0.512546	−	0.329393i	0.0968621	−	0.0622495i
$29$	2.69973	−	3.11565i	0.501327	−	0.578562i	−0.447530	−	0.894269i	$-0.647696\pi$
$29$	2.69973	−	3.11565i	0.501327	−	0.578562i	0.948857	+	0.315707i	$0.102242\pi$
$30$	0.142315	−	0.989821i	0.0259830	−	0.180716i
$31$	8.03302	−	2.35871i	1.44277	−	0.423637i	0.535628	−	0.844454i	$-0.320075\pi$
$31$	8.03302	−	2.35871i	1.44277	−	0.423637i	0.907145	+	0.420817i	$0.138257\pi$
$32$	−0.841254	−	0.540641i	−0.148714	−	0.0955727i
$33$	0.0336545	+	0.234072i	0.00585849	+	0.0407467i
$34$	0.472039	+	1.03362i	0.0809540	+	0.177265i
$35$	0.253098	+	0.554206i	0.0427813	+	0.0936780i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	3.81143	+	2.44946i	0.626595	+	0.402688i	0.815048	−	0.579394i	$-0.196711\pi$
$37$	3.81143	+	2.44946i	0.626595	+	0.402688i	−0.188452	+	0.982082i	$0.560347\pi$
$38$	−0.817178	+	0.239945i	−0.132564	+	0.0389242i
$39$	−0.227916	+	1.58519i	−0.0364958	+	0.253834i
$40$	0.654861	−	0.755750i	0.103543	−	0.119494i
$41$	6.93886	−	4.45934i	1.08367	−	0.696431i	0.128266	−	0.991740i	$-0.459059\pi$
$41$	6.93886	−	4.45934i	1.08367	−	0.696431i	0.955402	+	0.295309i	$0.0954225\pi$
$42$	0.398983	+	0.460451i	0.0615645	+	0.0710492i
$43$	−0.394911	−	0.115956i	−0.0602233	−	0.0176832i	0.251482	−	0.967862i	$-0.419082\pi$
$43$	−0.394911	−	0.115956i	−0.0602233	−	0.0176832i	−0.311705	+	0.950179i	$0.600900\pi$
$44$	−0.0982369	+	0.215109i	−0.0148098	+	0.0324289i
$45$	1.00000			0.149071
$46$	4.71737	+	0.863983i	0.695538	+	0.127387i
$47$	−5.06547			−0.738875			−0.369437	−	0.929256i	$-0.620450\pi$
$47$	−5.06547			−0.738875			−0.369437	+	0.929256i	$0.620450\pi$
$48$	0.415415	−	0.909632i	0.0599600	−	0.131294i
$49$	6.36028	+	1.86755i	0.908612	+	0.266793i
$50$	0.654861	+	0.755750i	0.0926113	+	0.106879i
$51$	−0.955922	+	0.614334i	−0.133856	+	0.0860239i
$52$	−1.04875	+	1.21033i	−0.145436	+	0.167842i
$53$	1.01292	−	7.04505i	0.139136	−	0.967712i	−0.793931	−	0.608008i	$-0.791969\pi$
$53$	1.01292	−	7.04505i	0.139136	−	0.967712i	0.933067	−	0.359703i	$-0.117122\pi$
$54$	0.959493	−	0.281733i	0.130570	−	0.0383389i
$55$	−0.198939	−	0.127850i	−0.0268249	−	0.0172393i
$56$	0.0867074	+	0.603063i	0.0115868	+	0.0805877i
$57$	−0.353799	−	0.774713i	−0.0468619	−	0.102613i
$58$	1.71259	+	3.75005i	0.224874	+	0.492406i
$59$	−0.0718473	−	0.499709i	−0.00935372	−	0.0650566i	0.984610	−	0.174766i	$-0.0559170\pi$
$59$	−0.0718473	−	0.499709i	−0.00935372	−	0.0650566i	−0.993964	+	0.109710i	$0.965008\pi$
$60$	0.841254	+	0.540641i	0.108605	+	0.0697964i
$61$	11.5663	−	3.39616i	1.48091	−	0.434834i	0.561281	−	0.827626i	$-0.310309\pi$
$61$	11.5663	−	3.39616i	1.48091	−	0.434834i	0.919627	+	0.392792i	$0.128491\pi$
$62$	−1.19148	+	8.28694i	−0.151318	+	1.05244i
$63$	−0.398983	+	0.460451i	−0.0502672	+	0.0580114i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−1.04875	−	1.21033i	−0.130082	−	0.150123i
$66$	−0.226900	−	0.0666238i	−0.0279294	−	0.00820082i
$67$	−1.41111	+	3.08990i	−0.172395	+	0.377492i	−0.976032	−	0.217628i	$-0.930168\pi$
$67$	−1.41111	+	3.08990i	−0.172395	+	0.377492i	0.803637	+	0.595120i	$0.202895\pi$
$68$	−1.13631			−0.137797
$69$	−0.183838	+	4.79231i	−0.0221315	+	0.576926i
$70$	−0.609264			−0.0728210
$71$	0.611970	−	1.34003i	0.0726275	−	0.159032i	−0.869836	−	0.493341i	$-0.835776\pi$
$71$	0.611970	−	1.34003i	0.0726275	−	0.159032i	0.942464	+	0.334309i	$0.108503\pi$
$72$	0.959493	+	0.281733i	0.113077	+	0.0332025i
$73$	3.10434	+	3.58260i	0.363336	+	0.419312i	0.907755	−	0.419502i	$-0.137795\pi$
$73$	3.10434	+	3.58260i	0.363336	+	0.419312i	−0.544419	+	0.838814i	$0.683250\pi$
$74$	−3.81143	+	2.44946i	−0.443070	+	0.284744i
$75$	−0.654861	+	0.755750i	−0.0756168	+	0.0872664i
$76$	0.121206	−	0.843008i	0.0139033	−	0.0966997i
$77$	0.138242	−	0.0405915i	0.0157541	−	0.00462583i
$78$	−1.34726	−	0.865832i	−0.152547	−	0.0980362i
$79$	0.829194	+	5.76717i	0.0932917	+	0.648858i	0.981789	+	0.189976i	$0.0608409\pi$
$79$	0.829194	+	5.76717i	0.0932917	+	0.648858i	−0.888497	+	0.458882i	$0.848250\pi$
$80$	0.415415	+	0.909632i	0.0464448	+	0.101700i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	1.17385	+	8.16428i	0.129630	+	0.901594i
$83$	−3.06369	−	1.96891i	−0.336284	−	0.216116i	0.361590	−	0.932337i	$-0.382234\pi$
$83$	−3.06369	−	1.96891i	−0.336284	−	0.216116i	−0.697874	+	0.716221i	$0.745870\pi$
$84$	−0.584585	+	0.171650i	−0.0637835	+	0.0187285i
$85$	0.161713	−	1.12474i	0.0175403	−	0.121995i
$86$	0.269529	−	0.311053i	0.0290641	−	0.0335417i
$87$	−3.46815	+	2.22885i	−0.371825	+	0.238957i
$88$	−0.154861	−	0.178719i	−0.0165082	−	0.0190515i
$89$	−3.23278	−	0.949230i	−0.342674	−	0.100618i	0.105867	−	0.994380i	$-0.466238\pi$
$89$	−3.23278	−	0.949230i	−0.342674	−	0.100618i	−0.448541	+	0.893762i	$0.648056\pi$
$90$	−0.415415	+	0.909632i	−0.0437886	+	0.0958836i
$91$	0.975733			0.102285
$92$	−2.74557	+	3.93215i	−0.286246	+	0.409955i
$93$	−8.37216			−0.868152
$94$	2.10427	−	4.60771i	0.217039	−	0.475249i
$95$	0.817178	+	0.239945i	0.0838407	+	0.0246179i
$96$	0.654861	+	0.755750i	0.0668364	+	0.0771334i
$97$	−0.0626320	+	0.0402511i	−0.00635931	+	0.00408688i	−0.543817	−	0.839204i	$-0.683021\pi$
$97$	−0.0626320	+	0.0402511i	−0.00635931	+	0.00408688i	0.537457	+	0.843291i	$0.319385\pi$
$98$	−4.34094	+	5.00971i	−0.438501	+	0.506057i
$99$	0.0336545	−	0.234072i	0.00338240	−	0.0235251i
$100$	−0.959493	+	0.281733i	−0.0959493	+	0.0281733i
$101$	−10.6532	−	6.84637i	−1.06003	−	0.681239i	−0.110169	−	0.993913i	$-0.535139\pi$
$101$	−10.6532	−	6.84637i	−1.06003	−	0.681239i	−0.949861	+	0.312674i	$0.898775\pi$
$102$	−0.161713	−	1.12474i	−0.0160120	−	0.111366i
$103$	1.48276	+	3.24679i	0.146101	+	0.319916i	0.968508	−	0.248984i	$-0.0800965\pi$
$103$	1.48276	+	3.24679i	0.146101	+	0.319916i	−0.822407	+	0.568900i	$0.807369\pi$
$104$	−0.665284	−	1.45677i	−0.0652365	−	0.142848i
$105$	−0.0867074	−	0.603063i	−0.00846177	−	0.0588529i
$106$	5.98762	+	3.84801i	0.581569	+	0.373751i
$107$	−5.60513	+	1.64582i	−0.541869	+	0.159107i	−0.541202	−	0.840893i	$-0.682030\pi$
$107$	−5.60513	+	1.64582i	−0.541869	+	0.159107i	−0.000666953		1.00000i	$0.500212\pi$
$108$	−0.142315	+	0.989821i	−0.0136943	+	0.0952456i
$109$	−2.88637	+	3.33105i	−0.276464	+	0.319056i	−0.876953	−	0.480577i	$-0.840427\pi$
$109$	−2.88637	+	3.33105i	−0.276464	+	0.319056i	0.600489	+	0.799633i	$0.294973\pi$
$110$	0.198939	−	0.127850i	0.0189681	−	0.0121900i
$111$	−2.96695	−	3.42404i	−0.281610	−	0.324996i
$112$	−0.584585	−	0.171650i	−0.0552381	−	0.0162194i
$113$	4.08574	−	8.94651i	0.384354	−	0.841617i	−0.614266	−	0.789099i	$-0.710548\pi$
$113$	4.08574	−	8.94651i	0.384354	−	0.841617i	0.998620	−	0.0525183i	$-0.0167248\pi$
$114$	0.851677			0.0797669
$115$	−3.50140	−	3.27723i	−0.326507	−	0.305603i
$116$	−4.12260			−0.382774
$117$	0.665284	−	1.45677i	0.0615055	−	0.134678i
$118$	0.484398	+	0.142232i	0.0445924	+	0.0130935i
$119$	0.453367	+	0.523214i	0.0415601	+	0.0479629i
$120$	−0.841254	+	0.540641i	−0.0767956	+	0.0493535i
$121$	7.16685	−	8.27098i	0.651532	−	0.751907i
$122$	−1.71554	+	11.9319i	−0.155318	+	1.08026i
$123$	−7.91413	+	2.32380i	−0.713593	+	0.209530i
$124$	−7.04311	−	4.52633i	−0.632490	−	0.406476i
$125$	−0.142315	−	0.989821i	−0.0127290	−	0.0885323i
$126$	−0.253098	−	0.554206i	−0.0225477	−	0.0493726i
$127$	−1.34025	−	2.93475i	−0.118928	−	0.260417i	0.840800	−	0.541345i	$-0.182085\pi$
$127$	−1.34025	−	2.93475i	−0.118928	−	0.260417i	−0.959729	+	0.280929i	$0.909358\pi$
$128$	0.142315	+	0.989821i	0.0125790	+	0.0874887i
$129$	0.346245	+	0.222518i	0.0304852	+	0.0195916i
$130$	1.53662	−	0.451193i	0.134771	−	0.0395722i
$131$	−1.18707	+	8.25626i	−0.103715	+	0.721353i	0.869912	+	0.493207i	$0.164175\pi$
$131$	−1.18707	+	8.25626i	−0.103715	+	0.721353i	−0.973627	+	0.228146i	$0.926734\pi$
$132$	0.154861	−	0.178719i	0.0134789	−	0.0155555i
$133$	−0.436524	+	0.280537i	−0.0378514	+	0.0243256i
$134$	−2.22448	−	2.56719i	−0.192166	−	0.221771i
$135$	−0.959493	−	0.281733i	−0.0825800	−	0.0242477i
$136$	0.472039	−	1.03362i	0.0404770	−	0.0886323i
$137$	−18.2322			−1.55769			−0.778843	−	0.627219i	$-0.784193\pi$
$137$	−18.2322			−1.55769			−0.778843	+	0.627219i	$0.784193\pi$
$138$	−4.28287	−	2.15802i	−0.364582	−	0.183703i
$139$	−17.4626			−1.48116			−0.740580	−	0.671969i	$-0.765449\pi$
$139$	−17.4626			−1.48116			−0.740580	+	0.671969i	$0.765449\pi$
$140$	0.253098	−	0.554206i	0.0213907	−	0.0468390i
$141$	4.86028	+	1.42711i	0.409310	+	0.120184i
$142$	0.964710	+	1.11333i	0.0809567	+	0.0934290i
$143$	−0.318599	+	0.204751i	−0.0266426	+	0.0171221i
$144$	−0.654861	+	0.755750i	−0.0545717	+	0.0629791i
$145$	0.586707	−	4.08064i	0.0487234	−	0.338879i
$146$	−4.54844	+	1.33554i	−0.376432	+	0.110530i
$147$	−5.57650	−	3.58380i	−0.459942	−	0.295587i
$148$	−0.644780	−	4.48454i	−0.0530006	−	0.368627i
$149$	4.29742	+	9.41004i	0.352058	+	0.770900i	0.999958	+	0.00917457i	$0.00292040\pi$
$149$	4.29742	+	9.41004i	0.352058	+	0.770900i	−0.647899	+	0.761726i	$0.724352\pi$
$150$	−0.415415	−	0.909632i	−0.0339185	−	0.0742711i
$151$	−0.815730	−	5.67352i	−0.0663831	−	0.461705i	−0.995716	−	0.0924623i	$-0.970526\pi$
$151$	−0.815730	−	5.67352i	−0.0663831	−	0.461705i	0.929333	−	0.369243i	$-0.120383\pi$
$152$	0.716476	+	0.460451i	0.0581139	+	0.0373475i
$153$	1.09028	−	0.320135i	0.0881438	−	0.0258813i
$154$	−0.0205045	+	0.142612i	−0.00165230	+	0.0114920i
$155$	5.48260	−	6.32725i	0.440373	−	0.508217i
$156$	1.34726	−	0.865832i	0.107867	−	0.0693221i
$157$	−2.06627	−	2.38461i	−0.164907	−	0.190312i	0.667282	−	0.744805i	$-0.267458\pi$
$157$	−2.06627	−	2.38461i	−0.164907	−	0.190312i	−0.832188	+	0.554493i	$0.812912\pi$
$158$	−5.59047	−	1.64151i	−0.444754	−	0.130591i
$159$	−2.95671	+	6.47430i	−0.234483	+	0.513445i
$160$	−1.00000			−0.0790569
$161$	2.90600	−	0.304662i	0.229025	−	0.0240108i
$162$	−1.00000			−0.0785674
$163$	−6.16105	+	13.4908i	−0.482570	+	1.05668i	0.499178	+	0.866499i	$0.333635\pi$
$163$	−6.16105	+	13.4908i	−0.482570	+	1.05668i	−0.981749	+	0.190183i	$0.939092\pi$
$164$	−7.91413	−	2.32380i	−0.617990	−	0.181458i
$165$	0.154861	+	0.178719i	0.0120559	+	0.0139132i
$166$	3.06369	−	1.96891i	0.237789	−	0.152817i
$167$	0.0122509	−	0.0141383i	0.000948007	−	0.00109406i	−0.755275	−	0.655408i	$-0.772497\pi$
$167$	0.0122509	−	0.0141383i	0.000948007	−	0.00109406i	0.756223	+	0.654314i	$0.227042\pi$
$168$	0.0867074	−	0.603063i	0.00668962	−	0.0465273i
$169$	10.0125	−	2.93994i	0.770194	−	0.226149i
$170$	0.955922	+	0.614334i	0.0733159	+	0.0471173i
$171$	0.121206	+	0.843008i	0.00926888	+	0.0644664i
$172$	0.170978	+	0.374389i	0.0130369	+	0.0285469i
$173$	1.31200	+	2.87288i	0.0997496	+	0.218421i	0.952927	−	0.303200i	$-0.0980549\pi$
$173$	1.31200	+	2.87288i	0.0997496	+	0.218421i	−0.853177	+	0.521621i	$0.825328\pi$
$174$	−0.586707	−	4.08064i	−0.0444782	−	0.309352i
$175$	0.512546	+	0.329393i	0.0387448	+	0.0248998i
$176$	0.226900	−	0.0666238i	0.0171032	−	0.00502196i
$177$	−0.0718473	+	0.499709i	−0.00540037	+	0.0375604i
$178$	2.20640	−	2.54632i	0.165376	−	0.190854i
$179$	−0.898290	+	0.577296i	−0.0671413	+	0.0431491i	−0.573781	−	0.819009i	$-0.694524\pi$
$179$	−0.898290	+	0.577296i	−0.0671413	+	0.0431491i	0.506640	+	0.862158i	$0.330888\pi$
$180$	−0.654861	−	0.755750i	−0.0488104	−	0.0563302i
$181$	1.38231	+	0.405882i	0.102746	+	0.0301690i	0.332701	−	0.943032i	$-0.392040\pi$
$181$	1.38231	+	0.405882i	0.102746	+	0.0301690i	−0.229955	+	0.973201i	$0.573858\pi$
$182$	−0.405334	+	0.887558i	−0.0300454	+	0.0657902i
$183$	−12.0546			−0.891098
$184$	−2.43626	−	4.13094i	−0.179604	−	0.304537i
$185$	4.53066			0.333101
$186$	3.47792	−	7.61558i	0.255013	−	0.558401i
$187$	−0.257828	−	0.0757051i	−0.0188542	−	0.00553610i
$188$	3.31718	+	3.82823i	0.241930	+	0.279202i
$189$	0.512546	−	0.329393i	0.0372822	−	0.0239598i
$190$	−0.557730	+	0.643655i	−0.0404620	+	0.0466956i
$191$	1.54429	−	10.7408i	0.111741	−	0.777176i	−0.854484	−	0.519477i	$-0.826127\pi$
$191$	1.54429	−	10.7408i	0.111741	−	0.777176i	0.966225	−	0.257699i	$-0.0829643\pi$
$192$	−0.959493	+	0.281733i	−0.0692454	+	0.0203323i
$193$	−13.3182	−	8.55906i	−0.958662	−	0.616095i	−0.0350349	−	0.999386i	$-0.511154\pi$
$193$	−13.3182	−	8.55906i	−0.958662	−	0.616095i	−0.923628	+	0.383291i	$0.874791\pi$
$194$	−0.0105955	−	0.0736930i	−0.000760709	−	0.00529085i
$195$	0.665284	+	1.45677i	0.0476420	+	0.104321i
$196$	−2.75370	−	6.02977i	−0.196693	−	0.430698i
$197$	0.928657	+	6.45895i	0.0661641	+	0.460181i	0.995789	+	0.0916742i	$0.0292218\pi$
$197$	0.928657	+	6.45895i	0.0661641	+	0.460181i	−0.929625	+	0.368507i	$0.879869\pi$
$198$	0.198939	+	0.127850i	0.0141380	+	0.00908591i
$199$	−6.16585	+	1.81046i	−0.437086	+	0.128340i	−0.492870	−	0.870103i	$-0.664052\pi$
$199$	−6.16585	+	1.81046i	−0.437086	+	0.128340i	0.0557845	+	0.998443i	$0.482234\pi$
$200$	0.142315	−	0.989821i	0.0100632	−	0.0699909i
$201$	2.22448	−	2.56719i	0.156903	−	0.181075i
$202$	10.6532	−	6.84637i	0.749554	−	0.481709i
$203$	1.64485	+	1.89826i	0.115446	+	0.133232i
$204$	1.09028	+	0.320135i	0.0763348	+	0.0224139i
$205$	3.42644	−	7.50286i	0.239313	−	0.524023i
$206$	−3.56935			−0.248688
$207$	1.52654	−	4.54639i	0.106102	−	0.315996i
$208$	1.60149			0.111044
$209$	0.0836661	−	0.183203i	0.00578730	−	0.0126724i
$210$	0.584585	+	0.171650i	0.0403402	+	0.0118450i
$211$	1.73383	+	2.00095i	0.119362	+	0.137751i	0.812285	−	0.583260i	$-0.198223\pi$
$211$	1.73383	+	2.00095i	0.119362	+	0.137751i	−0.692924	+	0.721011i	$0.743678\pi$
$212$	−5.98762	+	3.84801i	−0.411231	+	0.264282i
$213$	−0.964710	+	1.11333i	−0.0661008	+	0.0762844i
$214$	0.831370	−	5.78231i	0.0568313	−	0.395270i
$215$	−0.394911	+	0.115956i	−0.0269327	+	0.00790815i
$216$	−0.841254	−	0.540641i	−0.0572401	−	0.0367859i
$217$	0.725928	+	5.04894i	0.0492792	+	0.342744i
$218$	−1.83099	−	4.00930i	−0.124010	−	0.271544i
$219$	−1.96926	−	4.31208i	−0.133070	−	0.291383i
$220$	0.0336545	+	0.234072i	0.00226898	+	0.0157811i
$221$	−1.53090	−	0.983851i	−0.102980	−	0.0661810i
$222$	4.34713	−	1.27643i	0.291761	−	0.0856686i
$223$	−3.35275	+	23.3189i	−0.224517	+	1.56155i	0.496132	+	0.868247i	$0.334753\pi$
$223$	−3.35275	+	23.3189i	−0.224517	+	1.56155i	−0.720649	+	0.693300i	$0.756156\pi$
$224$	0.398983	−	0.460451i	0.0266582	−	0.0307652i
$225$	0.841254	−	0.540641i	0.0560836	−	0.0360427i
$226$	6.44076	+	7.43303i	0.428433	+	0.494438i
$227$	−3.83932	−	1.12733i	−0.254825	−	0.0748232i	0.151825	−	0.988407i	$-0.451485\pi$
$227$	−3.83932	−	1.12733i	−0.254825	−	0.0748232i	−0.406650	+	0.913584i	$0.633303\pi$
$228$	−0.353799	+	0.774713i	−0.0234309	+	0.0513066i
$229$	−16.7025			−1.10373			−0.551865	−	0.833933i	$-0.686084\pi$
$229$	−16.7025			−1.10373			−0.551865	+	0.833933i	$0.686084\pi$
$230$	4.43560	−	1.82357i	0.292475	−	0.120243i
$231$	−0.144078			−0.00947965
$232$	1.71259	−	3.75005i	0.112437	−	0.246203i
$233$	25.0096	+	7.34347i	1.63843	+	0.481087i	0.965886	−	0.258968i	$-0.0833825\pi$
$233$	25.0096	+	7.34347i	1.63843	+	0.481087i	0.672546	+	0.740055i	$0.265201\pi$
$234$	1.04875	+	1.21033i	0.0685593	+	0.0791216i
$235$	−4.26135	+	2.73860i	−0.277980	+	0.178647i
$236$	−0.330605	+	0.381538i	−0.0215205	+	0.0248360i
$237$	0.829194	−	5.76717i	0.0538620	−	0.374618i
$238$	−0.664268	+	0.195047i	−0.0430581	+	0.0126430i
$239$	5.09987	+	3.27749i	0.329883	+	0.212003i	0.695089	−	0.718924i	$-0.255365\pi$
$239$	5.09987	+	3.27749i	0.329883	+	0.212003i	−0.365206	+	0.930927i	$0.619001\pi$
$240$	−0.142315	−	0.989821i	−0.00918638	−	0.0638927i
$241$	7.05766	+	15.4541i	0.454624	+	0.995487i	0.988680	+	0.150038i	$0.0479398\pi$
$241$	7.05766	+	15.4541i	0.454624	+	0.995487i	−0.534056	+	0.845449i	$0.679333\pi$
$242$	4.54633	+	9.95508i	0.292249	+	0.639937i
$243$	−0.142315	−	0.989821i	−0.00912950	−	0.0634971i
$244$	−10.1409	−	6.51719i	−0.649207	−	0.417220i
$245$	6.36028	−	1.86755i	0.406344	−	0.119313i
$246$	1.17385	−	8.16428i	0.0748417	−	0.520536i
$247$	0.893200	−	1.03081i	0.0568330	−	0.0655888i
$248$	7.04311	−	4.52633i	0.447238	−	0.287422i
$249$	2.38488	+	2.75230i	0.151136	+	0.174420i
$250$	0.959493	+	0.281733i	0.0606837	+	0.0178183i
$251$	1.40735	−	3.08166i	0.0888309	−	0.194513i	−0.860002	−	0.510290i	$-0.829538\pi$
$251$	1.40735	−	3.08166i	0.0888309	−	0.194513i	0.948833	+	0.315777i	$0.102265\pi$
$252$	0.609264			0.0383801
$253$	−0.884945	+	0.709285i	−0.0556360	+	0.0445924i
$254$	3.22630			0.202436
$255$	−0.472039	+	1.03362i	−0.0295602	+	0.0647279i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	−9.92439	−	11.4534i	−0.619066	−	0.714441i	0.356463	−	0.934309i	$-0.383983\pi$
$257$	−9.92439	−	11.4534i	−0.619066	−	0.714441i	−0.975529	+	0.219869i	$0.929437\pi$
$258$	−0.346245	+	0.222518i	−0.0215563	+	0.0138534i
$259$	−1.80766	+	2.08615i	−0.112322	+	0.129627i
$260$	−0.227916	+	1.58519i	−0.0141348	+	0.0983094i
$261$	3.95561	−	1.16147i	0.244846	−	0.0718933i
$262$	−7.01703	−	4.50957i	−0.433514	−	0.278602i
$263$	0.876015	+	6.09282i	0.0540174	+	0.375699i	0.998842	+	0.0481212i	$0.0153234\pi$
$263$	0.876015	+	6.09282i	0.0540174	+	0.375699i	−0.944824	+	0.327578i	$0.893768\pi$
$264$	0.0982369	+	0.215109i	0.00604606	+	0.0132390i
$265$	−2.95671	−	6.47430i	−0.181629	−	0.397713i
$266$	−0.0738467	−	0.513615i	−0.00452783	−	0.0314918i
$267$	2.83440	+	1.82156i	0.173463	+	0.111478i
$268$	3.25928	−	0.957010i	0.199092	−	0.0584587i
$269$	−4.43811	+	30.8677i	−0.270596	+	1.88204i	0.171671	+	0.985154i	$0.445084\pi$
$269$	−4.43811	+	30.8677i	−0.270596	+	1.88204i	−0.442267	+	0.896884i	$0.645826\pi$
$270$	0.654861	−	0.755750i	0.0398536	−	0.0459935i
$271$	7.49171	−	4.81463i	0.455089	−	0.292468i	−0.292944	−	0.956130i	$-0.594635\pi$
$271$	7.49171	−	4.81463i	0.455089	−	0.292468i	0.748033	+	0.663662i	$0.230999\pi$
$272$	0.744123	+	0.858763i	0.0451191	+	0.0520702i
$273$	−0.936209	−	0.274896i	−0.0566619	−	0.0166374i
$274$	7.57395	−	16.5846i	0.457559	−	1.00191i
$275$	−0.236479			−0.0142602
$276$	3.74217	−	2.99936i	0.225252	−	0.180540i
$277$	−18.3796			−1.10432			−0.552162	−	0.833737i	$-0.686197\pi$
$277$	−18.3796			−1.10432			−0.552162	+	0.833737i	$0.686197\pi$
$278$	7.25423	−	15.8846i	0.435080	−	0.952692i
$279$	8.03302	+	2.35871i	0.480925	+	0.141212i
$280$	0.398983	+	0.460451i	0.0238438	+	0.0275172i
$281$	−11.0550	+	7.10461i	−0.659485	+	0.423825i	−0.827121	−	0.562023i	$-0.810023\pi$
$281$	−11.0550	+	7.10461i	−0.659485	+	0.423825i	0.167636	+	0.985849i	$0.446387\pi$
$282$	−3.31718	+	3.82823i	−0.197535	+	0.227968i
$283$	−1.27559	+	8.87195i	−0.0758262	+	0.527383i	0.916138	+	0.400863i	$0.131290\pi$
$283$	−1.27559	+	8.87195i	−0.0758262	+	0.527383i	−0.991964	+	0.126520i	$0.959619\pi$
$284$	−1.41348	+	0.415035i	−0.0838746	+	0.0246278i
$285$	−0.716476	−	0.460451i	−0.0424404	−	0.0272748i
$286$	−0.0538974	−	0.374864i	−0.00318702	−	0.0221662i
$287$	2.08761	+	4.57123i	0.123228	+	0.269831i
$288$	−0.415415	−	0.909632i	−0.0244786	−	0.0536006i
$289$	2.23560	+	15.5489i	0.131506	+	0.914642i
$290$	3.46815	+	2.22885i	0.203657	+	0.130882i
$291$	0.0714350	−	0.0209752i	0.00418759	−	0.00122959i
$292$	0.674638	−	4.69221i	0.0394802	−	0.274591i
$293$	5.25829	−	6.06839i	0.307192	−	0.354519i	−0.581071	−	0.813853i	$-0.697366\pi$
$293$	5.25829	−	6.06839i	0.307192	−	0.354519i	0.888264	+	0.459334i	$0.151912\pi$
$294$	5.57650	−	3.58380i	0.325228	−	0.209011i
$295$	−0.330605	−	0.381538i	−0.0192486	−	0.0222140i
$296$	4.34713	+	1.27643i	0.252672	+	0.0741912i
$297$	−0.0982369	+	0.215109i	−0.00570028	+	0.0124819i
$298$	−10.3449			−0.599263
$299$	−7.10359	+	2.92044i	−0.410811	+	0.168893i
$300$	1.00000			0.0577350
$301$	0.104171	−	0.228102i	0.00600429	−	0.0131476i
$302$	5.49969	+	1.61485i	0.316471	+	0.0929244i
$303$	8.29279	+	9.57039i	0.476408	+	0.549804i
$304$	−0.716476	+	0.460451i	−0.0410927	+	0.0264087i
$305$	7.89406	−	9.11023i	0.452012	−	0.521650i
$306$	−0.161713	+	1.12474i	−0.00924453	+	0.0642971i
$307$	2.43092	−	0.713784i	0.138740	−	0.0407378i	−0.211625	−	0.977351i	$-0.567876\pi$
$307$	2.43092	−	0.713784i	0.138740	−	0.0407378i	0.350365	+	0.936613i	$0.386057\pi$
$308$	−0.121206	−	0.0778945i	−0.00690637	−	0.00443845i
$309$	−0.507971	−	3.53302i	−0.0288975	−	0.200986i
$310$	3.47792	+	7.61558i	0.197533	+	0.432536i
$311$	6.50536	+	14.2448i	0.368885	+	0.807746i	0.999499	+	0.0316494i	$0.0100760\pi$
$311$	6.50536	+	14.2448i	0.368885	+	0.807746i	−0.630614	+	0.776097i	$0.717197\pi$
$312$	0.227916	+	1.58519i	0.0129032	+	0.0897438i
$313$	23.4128	+	15.0465i	1.32337	+	0.850479i	0.995548	−	0.0942606i	$-0.0300487\pi$
$313$	23.4128	+	15.0465i	1.32337	+	0.850479i	0.327823	+	0.944739i	$0.393685\pi$
$314$	3.02747	−	0.888947i	0.170850	−	0.0501662i
$315$	−0.0867074	+	0.603063i	−0.00488541	+	0.0339788i
$316$	3.81553	−	4.40336i	0.214640	−	0.247708i
$317$	4.46146	−	2.86721i	0.250581	−	0.161039i	−0.409321	−	0.912391i	$-0.634234\pi$
$317$	4.46146	−	2.86721i	0.250581	−	0.161039i	0.659902	+	0.751352i	$0.270598\pi$
$318$	−4.66097	−	5.37904i	−0.261374	−	0.301642i
$319$	−0.935418	−	0.274663i	−0.0523733	−	0.0153782i
$320$	0.415415	−	0.909632i	0.0232224	−	0.0508500i
$321$	5.84177			0.326056
$322$	−0.930067	+	2.76995i	−0.0518306	+	0.154364i
$323$	0.967766			0.0538480
$324$	0.415415	−	0.909632i	0.0230786	−	0.0505351i
$325$	−1.53662	−	0.451193i	−0.0852364	−	0.0250277i
$326$	−9.71228	−	11.2086i	−0.537914	−	0.620785i
$327$	3.70791	−	2.38293i	0.205048	−	0.131776i
$328$	5.40145	−	6.23360i	0.298245	−	0.344193i
$329$	0.439214	−	3.05480i	0.0242146	−	0.168416i
$330$	−0.226900	+	0.0666238i	−0.0124904	+	0.00366752i
$331$	−16.2923	−	10.4704i	−0.895505	−	0.575506i	0.00994926	−	0.999951i	$-0.496833\pi$
$331$	−16.2923	−	10.4704i	−0.895505	−	0.575506i	−0.905454	+	0.424445i	$0.860469\pi$
$332$	0.518285	+	3.60475i	0.0284446	+	0.197836i
$333$	1.88210	+	4.12123i	0.103139	+	0.225842i
$334$	0.00777147	+	0.0170171i	0.000425236	+	0.000931136i
$335$	0.483426	+	3.36230i	0.0264124	+	0.183702i
$336$	0.512546	+	0.329393i	0.0279617	+	0.0179699i
$337$	9.65570	−	2.83517i	0.525979	−	0.154442i	−0.00795341	−	0.999968i	$-0.502532\pi$
$337$	9.65570	−	2.83517i	0.525979	−	0.154442i	0.533933	+	0.845527i	$0.320713\pi$
$338$	−1.48509	+	10.3290i	−0.0807781	+	0.561824i
$339$	−6.44076	+	7.43303i	−0.349814	+	0.403707i
$340$	−0.955922	+	0.614334i	−0.0518422	+	0.0333169i
$341$	−1.29652	−	1.49626i	−0.0702104	−	0.0810271i
$342$	−0.817178	−	0.239945i	−0.0441879	−	0.0129747i
$343$	−3.44942	+	7.55317i	−0.186251	+	0.407833i
$344$	−0.411583			−0.0221910
$345$	2.43626	+	4.13094i	0.131164	+	0.222402i
$346$	−3.15829			−0.169791
$347$	7.96447	−	17.4398i	0.427555	−	0.936215i	−0.566162	−	0.824294i	$-0.691572\pi$
$347$	7.96447	−	17.4398i	0.427555	−	0.936215i	0.993717	−	0.111921i	$-0.0357004\pi$
$348$	3.95561	+	1.16147i	0.212043	+	0.0622614i
$349$	3.77598	+	4.35772i	0.202124	+	0.233263i	0.847758	−	0.530384i	$-0.177952\pi$
$349$	3.77598	+	4.35772i	0.202124	+	0.233263i	−0.645634	+	0.763647i	$0.723407\pi$
$350$	−0.512546	+	0.329393i	−0.0273967	+	0.0176068i
$351$	−1.04875	+	1.21033i	−0.0559784	+	0.0646025i
$352$	−0.0336545	+	0.234072i	−0.00179379	+	0.0124761i
$353$	2.09795	−	0.616014i	0.111663	−	0.0327871i	−0.225424	−	0.974261i	$-0.572377\pi$
$353$	2.09795	−	0.616014i	0.111663	−	0.0327871i	0.337087	+	0.941474i	$0.390559\pi$
$354$	−0.424705	−	0.272941i	−0.0225728	−	0.0145067i
$355$	−0.209651	−	1.45816i	−0.0111271	−	0.0773910i
$356$	1.39964	+	3.06479i	0.0741808	+	0.162433i
$357$	−0.287597	−	0.629749i	−0.0152212	−	0.0333298i
$358$	−0.151964	−	1.05693i	−0.00803153	−	0.0558605i
$359$	23.2905	+	14.9679i	1.22923	+	0.789976i	0.983770	−	0.179432i	$-0.0574260\pi$
$359$	23.2905	+	14.9679i	1.22923	+	0.789976i	0.245456	+	0.969408i	$0.421062\pi$
$360$	0.959493	−	0.281733i	0.0505697	−	0.0148486i
$361$	2.60075	−	18.0886i	0.136882	−	0.952034i
$362$	−0.943434	+	1.08878i	−0.0495858	+	0.0572251i
$363$	−9.20674	+	5.91682i	−0.483229	+	0.310552i
$364$	−0.638969	−	0.737410i	−0.0334911	−	0.0386508i
$365$	4.54844	+	1.33554i	0.238076	+	0.0699055i
$366$	5.00764	−	10.9652i	0.261754	−	0.573161i
$367$	−17.3193			−0.904062			−0.452031	−	0.892002i	$-0.649300\pi$
$367$	−17.3193			−0.904062			−0.452031	+	0.892002i	$0.649300\pi$
$368$	4.76969	−	0.500049i	0.248637	−	0.0260669i
$369$	8.24824			0.429386
$370$	−1.88210	+	4.12123i	−0.0978459	+	0.214253i
$371$	4.16078	+	1.22172i	0.216017	+	0.0634283i
$372$	5.48260	+	6.32725i	0.284259	+	0.328053i
$373$	11.4135	−	7.33503i	0.590971	−	0.379794i	−0.210708	−	0.977549i	$-0.567577\pi$
$373$	11.4135	−	7.33503i	0.590971	−	0.379794i	0.801679	+	0.597755i	$0.203941\pi$
$374$	0.175969	−	0.203079i	0.00909916	−	0.0105010i
$375$	−0.142315	+	0.989821i	−0.00734911	+	0.0511142i
$376$	−4.86028	+	1.42711i	−0.250650	+	0.0735975i
$377$	−5.55422	−	3.56948i	−0.286057	−	0.183838i
$378$	0.0867074	+	0.603063i	0.00445975	+	0.0310182i
$379$	5.73747	+	12.5633i	0.294714	+	0.645334i	0.997837	−	0.0657342i	$-0.0209389\pi$
$379$	5.73747	+	12.5633i	0.294714	+	0.645334i	−0.703123	+	0.711068i	$0.748212\pi$
$380$	−0.353799	−	0.774713i	−0.0181495	−	0.0397419i
$381$	0.459150	+	3.19346i	0.0235230	+	0.163606i
$382$	9.12865	+	5.86662i	0.467062	+	0.300163i
$383$	22.1766	−	6.51164i	1.13317	−	0.332729i	0.339219	−	0.940708i	$-0.389837\pi$
$383$	22.1766	−	6.51164i	1.13317	−	0.332729i	0.793954	+	0.607978i	$0.208019\pi$
$384$	0.142315	−	0.989821i	0.00726247	−	0.0505116i
$385$	0.0943511	−	0.108887i	0.00480858	−	0.00554940i
$386$	13.3182	−	8.55906i	0.677877	−	0.435645i
$387$	−0.269529	−	0.311053i	−0.0137009	−	0.0158117i
$388$	0.0714350	+	0.0209752i	0.00362656	+	0.00106485i
$389$	10.8486	−	23.7551i	0.550045	−	1.20443i	−0.406715	−	0.913555i	$-0.633326\pi$
$389$	10.8486	−	23.7551i	0.550045	−	1.20443i	0.956761	−	0.290876i	$-0.0939468\pi$
$390$	−1.60149			−0.0810948
$391$	−4.86665	−	2.45217i	−0.246117	−	0.124012i
$392$	6.62880			0.334805
$393$	3.46504	−	7.58739i	0.174788	−	0.382733i
$394$	−6.26105	−	1.83841i	−0.315427	−	0.0926177i
$395$	3.81553	+	4.40336i	0.191980	+	0.221557i
$396$	−0.198939	+	0.127850i	−0.00999705	+	0.00642471i
$397$	−8.03750	+	9.27577i	−0.403390	+	0.465537i	−0.920706	−	0.390257i	$-0.872386\pi$
$397$	−8.03750	+	9.27577i	−0.403390	+	0.465537i	0.517315	+	0.855795i	$0.326931\pi$
$398$	0.914537	−	6.36075i	0.0458416	−	0.318835i
$399$	0.497878	−	0.146190i	0.0249251	−	0.00731866i
$400$	0.841254	+	0.540641i	0.0420627	+	0.0270320i
$401$	3.77099	+	26.2278i	0.188314	+	1.30975i	0.836372	+	0.548162i	$0.184672\pi$
$401$	3.77099	+	26.2278i	0.188314	+	1.30975i	−0.648058	+	0.761591i	$0.724419\pi$
$402$	1.41111	+	3.08990i	0.0703799	+	0.154110i
$403$	−5.56986	−	12.1963i	−0.277455	−	0.607541i
$404$	1.80220	+	12.5345i	0.0896626	+	0.623617i
$405$	0.841254	+	0.540641i	0.0418022	+	0.0268647i
$406$	−2.41001	+	0.707643i	−0.119607	+	0.0351197i
$407$	0.152477	−	1.06050i	0.00755799	−	0.0525670i
$408$	−0.744123	+	0.858763i	−0.0368396	+	0.0425151i
$409$	−7.53400	+	4.84181i	−0.372532	+	0.239412i	−0.713488	−	0.700667i	$-0.752886\pi$
$409$	−7.53400	+	4.84181i	−0.372532	+	0.239412i	0.340956	+	0.940079i	$0.389249\pi$
$410$	5.40145	+	6.23360i	0.266759	+	0.307856i
$411$	17.4937	+	5.13662i	0.862901	+	0.253371i
$412$	1.48276	−	3.24679i	0.0730504	−	0.159958i
$413$	0.307586			0.0151353
$414$	3.50140	+	3.27723i	0.172084	+	0.161067i
$415$	−3.64182			−0.178770
$416$	−0.665284	+	1.45677i	−0.0326182	+	0.0714240i
$417$	16.7553	+	4.91979i	0.820508	+	0.240923i
$418$	0.131891	+	0.152211i	0.00645102	+	0.00744487i
$419$	−6.29172	+	4.04344i	−0.307371	+	0.197535i	−0.685228	−	0.728329i	$-0.740297\pi$
$419$	−6.29172	+	4.04344i	−0.307371	+	0.197535i	0.377857	+	0.925864i	$0.376661\pi$
$420$	−0.398983	+	0.460451i	−0.0194684	+	0.0224677i
$421$	2.74951	−	19.1233i	0.134003	−	0.932012i	−0.806260	−	0.591562i	$-0.798512\pi$
$421$	2.74951	−	19.1233i	0.134003	−	0.932012i	0.940263	−	0.340450i	$-0.110579\pi$
$422$	−2.54038	+	0.745924i	−0.123664	+	0.0363110i
$423$	−4.26135	−	2.73860i	−0.207194	−	0.133155i
$424$	−1.01292	−	7.04505i	−0.0491920	−	0.342138i
$425$	−0.472039	−	1.03362i	−0.0228972	−	0.0501380i
$426$	−0.611970	−	1.34003i	−0.0296500	−	0.0649245i
$427$	1.04522	+	7.26966i	0.0505817	+	0.351803i
$428$	4.91441	+	3.15830i	0.237547	+	0.152662i
$429$	0.363378	−	0.106698i	0.0175441	−	0.00515141i
$430$	0.0585743	−	0.407393i	0.00282470	−	0.0196462i
$431$	−7.34611	+	8.47787i	−0.353850	+	0.408365i	−0.904570	−	0.426326i	$-0.859808\pi$
$431$	−7.34611	+	8.47787i	−0.353850	+	0.408365i	0.550720	+	0.834690i	$0.314353\pi$
$432$	0.841254	−	0.540641i	0.0404748	−	0.0260116i
$433$	2.57378	+	2.97030i	0.123688	+	0.142743i	0.814216	−	0.580562i	$-0.197167\pi$
$433$	2.57378	+	2.97030i	0.123688	+	0.142743i	−0.690528	+	0.723306i	$0.742622\pi$
$434$	−4.89424	−	1.43708i	−0.234931	−	0.0689819i
$435$	−1.71259	+	3.75005i	−0.0821124	+	0.179801i
$436$	4.40761			0.211086
$437$	2.33834	−	3.34893i	0.111858	−	0.160201i
$438$	4.74046			0.226508
$439$	5.24584	−	11.4868i	0.250370	−	0.548235i	−0.742161	−	0.670221i	$-0.766199\pi$
$439$	5.24584	−	11.4868i	0.250370	−	0.548235i	0.992532	+	0.121987i	$0.0389265\pi$
$440$	−0.226900	−	0.0666238i	−0.0108170	−	0.00317617i
$441$	4.34094	+	5.00971i	0.206711	+	0.238558i
$442$	1.53090	−	0.983851i	0.0728176	−	0.0467970i
$443$	24.5352	−	28.3152i	1.16570	−	1.34530i	0.238320	−	0.971187i	$-0.423403\pi$
$443$	24.5352	−	28.3152i	1.16570	−	1.34530i	0.927385	−	0.374108i	$-0.122051\pi$
$444$	−0.644780	+	4.48454i	−0.0305999	+	0.212827i
$445$	−3.23278	+	0.949230i	−0.153248	+	0.0449978i
$446$	−19.8188	−	12.7368i	−0.938448	−	0.603104i
$447$	−1.47223	−	10.2396i	−0.0696341	−	0.484316i
$448$	0.253098	+	0.554206i	0.0119577	+	0.0261838i
$449$	−4.87669	−	10.6785i	−0.230145	−	0.503948i	0.758964	−	0.651133i	$-0.225706\pi$
$449$	−4.87669	−	10.6785i	−0.230145	−	0.503948i	−0.989109	+	0.147185i	$0.952979\pi$
$450$	0.142315	+	0.989821i	0.00670879	+	0.0466606i
$451$	−1.64089	−	1.05454i	−0.0772667	−	0.0496563i
$452$	−9.43691	+	2.77093i	−0.443875	+	0.130333i
$453$	−0.815730	+	5.67352i	−0.0383263	+	0.266565i
$454$	2.62036	−	3.02406i	0.122980	−	0.141926i
$455$	0.820839	−	0.527521i	0.0384815	−	0.0247306i
$456$	−0.557730	−	0.643655i	−0.0261181	−	0.0301419i
$457$	28.3417	+	8.32187i	1.32577	+	0.389281i	0.866571	−	0.499053i	$-0.166319\pi$
$457$	28.3417	+	8.32187i	1.32577	+	0.389281i	0.459197	+	0.888334i	$0.348137\pi$
$458$	6.93846	−	15.1931i	0.324213	−	0.709927i
$459$	−1.13631			−0.0530383
$460$	−0.183838	+	4.79231i	−0.00857150	+	0.223442i
$461$	−32.8558			−1.53025			−0.765123	−	0.643885i	$-0.777322\pi$
$461$	−32.8558			−1.53025			−0.765123	+	0.643885i	$0.777322\pi$
$462$	0.0598522	−	0.131058i	0.00278458	−	0.00609738i
$463$	−2.94729	−	0.865401i	−0.136972	−	0.0402186i	0.212528	−	0.977155i	$-0.431830\pi$
$463$	−2.94729	−	0.865401i	−0.136972	−	0.0402186i	−0.349500	+	0.936936i	$0.613649\pi$
$464$	2.69973	+	3.11565i	0.125332	+	0.144641i
$465$	−7.04311	+	4.52633i	−0.326616	+	0.209903i
$466$	−17.0692	+	19.6989i	−0.790716	+	0.912535i
$467$	2.99302	−	20.8169i	0.138500	−	0.963292i	−0.795483	−	0.605976i	$-0.792783\pi$
$467$	2.99302	−	20.8169i	0.138500	−	0.963292i	0.933983	−	0.357316i	$-0.116308\pi$
$468$	−1.53662	+	0.451193i	−0.0710303	+	0.0208564i
$469$	−1.74105	−	1.11891i	−0.0803944	−	0.0516663i
$470$	−0.720892	−	5.01391i	−0.0332523	−	0.231275i
$471$	1.31075	+	2.87015i	0.0603963	+	0.132249i
$472$	−0.209721	−	0.459225i	−0.00965320	−	0.0211376i
$473$	0.0138516	+	0.0963399i	0.000636897	+	0.00442971i
$474$	4.90155	+	3.15003i	0.225135	+	0.144686i
$475$	0.817178	−	0.239945i	0.0374947	−	0.0110094i
$476$	0.0985262	−	0.685265i	0.00451594	−	0.0314091i
$477$	4.66097	−	5.37904i	0.213411	−	0.246289i
$478$	−5.09987	+	3.27749i	−0.233263	+	0.149909i
$479$	−10.5234	−	12.1446i	−0.480825	−	0.554901i	0.462566	−	0.886585i	$-0.346929\pi$
$479$	−10.5234	−	12.1446i	−0.480825	−	0.554901i	−0.943391	+	0.331684i	$0.892383\pi$
$480$	0.959493	+	0.281733i	0.0437947	+	0.0128593i
$481$	3.01417	−	6.60012i	0.137435	−	0.300940i
$482$	−16.9894			−0.773847
$483$	−2.87412	−	0.526394i	−0.130777	−	0.0239518i
$484$	−10.9441			−0.497458
$485$	−0.0309280	+	0.0677228i	−0.00140437	+	0.00307513i
$486$	0.959493	+	0.281733i	0.0435235	+	0.0127796i
$487$	−15.5446	−	17.9394i	−0.704391	−	0.812911i	0.284948	−	0.958543i	$-0.408024\pi$
$487$	−15.5446	−	17.9394i	−0.704391	−	0.812911i	−0.989339	+	0.145632i	$0.953478\pi$
$488$	10.1409	−	6.51719i	0.459059	−	0.295019i
$489$	9.71228	−	11.2086i	0.439205	−	0.506869i
$490$	−0.943376	+	6.56133i	−0.0426174	+	0.296410i
$491$	−23.5710	+	6.92107i	−1.06374	+	0.312343i	−0.766358	−	0.642414i	$-0.777933\pi$
$491$	−23.5710	+	6.92107i	−1.06374	+	0.312343i	−0.297386	+	0.954757i	$0.596115\pi$
$492$	6.93886	+	4.45934i	0.312828	+	0.201042i
$493$	−0.666680	−	4.63686i	−0.0300257	−	0.208834i
$494$	0.566607	+	1.24070i	0.0254929	+	0.0558216i
$495$	−0.0982369	−	0.215109i	−0.00441542	−	0.00966842i
$496$	1.19148	+	8.28694i	0.0534991	+	0.372095i
$497$	0.755058	+	0.485247i	0.0338690	+	0.0217663i
$498$	−3.49430	+	1.02602i	−0.156583	+	0.0459770i
$499$	4.10311	−	28.5377i	0.183680	−	1.27752i	−0.664288	−	0.747477i	$-0.731265\pi$
$499$	4.10311	−	28.5377i	0.183680	−	1.27752i	0.847968	−	0.530047i	$-0.177826\pi$
$500$	−0.654861	+	0.755750i	−0.0292863	+	0.0337981i
$501$	−0.0157379	+	0.0101142i	−0.000703119	+	0.000451867i
$502$	2.21854	+	2.56033i	0.0990184	+	0.114273i
$503$	24.0952	+	7.07497i	1.07435	+	0.315458i	0.770616	−	0.637300i	$-0.219949\pi$
$503$	24.0952	+	7.07497i	1.07435	+	0.315458i	0.303733	+	0.952757i	$0.401767\pi$
$504$	−0.253098	+	0.554206i	−0.0112739	+	0.0246863i
$505$	−12.6634			−0.563516
$506$	−0.277569	−	1.09962i	−0.0123394	−	0.0488841i
$507$	−10.4352			−0.463444
$508$	−1.34025	+	2.93475i	−0.0594641	+	0.130208i
$509$	10.7548	+	3.15790i	0.476699	+	0.139972i	0.511251	−	0.859431i	$-0.329182\pi$
$509$	10.7548	+	3.15790i	0.476699	+	0.139972i	−0.0345517	+	0.999403i	$0.511000\pi$
$510$	−0.744123	−	0.858763i	−0.0329503	−	0.0380267i
$511$	−2.42970	+	1.56148i	−0.107484	+	0.0690756i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$	0.121206	−	0.843008i	0.00535139	−	0.0372197i
$514$	14.5411	−	4.26965i	0.641380	−	0.188326i
$515$	3.00273	+	1.92974i	0.132316	+	0.0850343i
$516$	−0.0585743	−	0.407393i	−0.00257859	−	0.0179345i
$517$	0.497616	+	1.08963i	0.0218851	+	0.0479217i
$518$	−1.14670	−	2.51092i	−0.0503830	−	0.110323i
$519$	−0.449471	−	3.12614i	−0.0197296	−	0.137222i
$520$	−1.34726	−	0.865832i	−0.0590813	−	0.0379693i
$521$	−26.1642	+	7.68251i	−1.14628	+	0.336577i	−0.799085	−	0.601218i	$-0.794682\pi$
$521$	−26.1642	+	7.68251i	−1.14628	+	0.336577i	−0.347191	+	0.937795i	$0.612864\pi$
$522$	−0.586707	+	4.08064i	−0.0256795	+	0.178605i
$523$	−25.8457	+	29.8275i	−1.13015	+	1.30427i	−0.183136	+	0.983088i	$0.558625\pi$
$523$	−25.8457	+	29.8275i	−1.13015	+	1.30427i	−0.947018	+	0.321179i	$0.895921\pi$
$524$	7.01703	−	4.50957i	0.306541	−	0.197002i
$525$	−0.398983	−	0.460451i	−0.0174131	−	0.0200957i
$526$	−5.90613	−	1.73420i	−0.257520	−	0.0756146i
$527$	3.95198	−	8.65364i	0.172151	−	0.376958i
$528$	−0.236479			−0.0102914
$529$	−20.2446	+	10.9159i	−0.880199	+	0.474604i
$530$	7.11749			0.309164
$531$	0.209721	−	0.459225i	0.00910113	−	0.0199287i
$532$	0.497878	+	0.146190i	0.0215857	+	0.00633814i
$533$	−8.65038	−	9.98307i	−0.374690	−	0.432415i
$534$	−2.83440	+	1.82156i	−0.122657	+	0.0788266i
$535$	−3.82554	+	4.41491i	−0.165393	+	0.190873i
$536$	−0.483426	+	3.36230i	−0.0208808	+	0.145229i
$537$	1.02455	−	0.300834i	0.0442124	−	0.0129819i
$538$	−26.2346	−	16.8600i	−1.13105	−	0.726884i
$539$	−0.223089	−	1.55161i	−0.00960910	−	0.0668328i
$540$	0.415415	+	0.909632i	0.0178766	+	0.0391443i
$541$	−5.81319	−	12.7291i	−0.249928	−	0.547267i	0.742535	−	0.669807i	$-0.233623\pi$
$541$	−5.81319	−	12.7291i	−0.249928	−	0.547267i	−0.992464	+	0.122540i	$0.960896\pi$
$542$	1.26737	+	8.81476i	0.0544383	+	0.378627i
$543$	−1.21196	−	0.778882i	−0.0520103	−	0.0334250i
$544$	−1.09028	+	0.320135i	−0.0467453	+	0.0137257i
$545$	−0.627268	+	4.36274i	−0.0268692	+	0.186879i
$546$	0.638969	−	0.737410i	0.0273454	−	0.0315582i
$547$	9.79119	−	6.29241i	0.418641	−	0.269044i	−0.314317	−	0.949318i	$-0.601776\pi$
$547$	9.79119	−	6.29241i	0.418641	−	0.269044i	0.732958	+	0.680274i	$0.238139\pi$
$548$	11.9396	+	13.7790i	0.510034	+	0.588610i
$549$	11.5663	+	3.39616i	0.493636	+	0.144945i
$550$	0.0982369	−	0.215109i	0.00418883	−	0.00917227i
$551$	3.51113			0.149579
$552$	1.17376	+	4.64998i	0.0499584	+	0.197916i
$553$	−3.54987			−0.150956
$554$	7.63516	−	16.7187i	0.324387	−	0.710308i
$555$	−4.34713	−	1.27643i	−0.184526	−	0.0541816i
$556$	11.4356	+	13.1974i	0.484977	+	0.559693i
$557$	−10.9544	+	7.03996i	−0.464153	+	0.298293i	−0.751738	−	0.659462i	$-0.770784\pi$
$557$	−10.9544	+	7.03996i	−0.464153	+	0.298293i	0.287585	+	0.957755i	$0.407148\pi$
$558$	−5.48260	+	6.32725i	−0.232097	+	0.267854i
$559$	−0.0938063	+	0.652437i	−0.00396759	+	0.0275952i
$560$	−0.584585	+	0.171650i	−0.0247032	+	0.00725352i
$561$	0.226055	+	0.145277i	0.00954407	+	0.00613360i
$562$	−1.87017	−	13.0073i	−0.0788885	−	0.548681i
$563$	5.80357	+	12.7080i	0.244591	+	0.535580i	0.991617	−	0.129216i	$-0.0412459\pi$
$563$	5.80357	+	12.7080i	0.244591	+	0.535580i	−0.747025	+	0.664796i	$0.768519\pi$
$564$	−2.10427	−	4.60771i	−0.0886059	−	0.194020i
$565$	−1.39971	−	9.73520i	−0.0588863	−	0.409563i
$566$	−7.54031	−	4.84586i	−0.316943	−	0.203687i
$567$	−0.584585	+	0.171650i	−0.0245503	+	0.00720861i
$568$	0.209651	−	1.45816i	0.00879678	−	0.0611830i
$569$	−13.2282	+	15.2662i	−0.554557	+	0.639993i	−0.961939	−	0.273265i	$-0.911896\pi$
$569$	−13.2282	+	15.2662i	−0.554557	+	0.639993i	0.407382	+	0.913258i	$0.366442\pi$
$570$	0.716476	−	0.460451i	0.0300099	−	0.0192862i
$571$	−13.1055	−	15.1246i	−0.548448	−	0.632943i	0.412073	−	0.911151i	$-0.364805\pi$
$571$	−13.1055	−	15.1246i	−0.548448	−	0.632943i	−0.960521	+	0.278208i	$0.910260\pi$
$572$	0.363378	+	0.106698i	0.0151936	+	0.00446125i
$573$	−4.50777	+	9.87064i	−0.188315	+	0.412352i
$574$	−5.02536			−0.209754
$575$	−4.71737	−	0.863983i	−0.196728	−	0.0360306i
$576$	1.00000			0.0416667
$577$	−7.49912	+	16.4208i	−0.312192	+	0.683606i	−0.999068	−	0.0431691i	$-0.986255\pi$
$577$	−7.49912	+	16.4208i	−0.312192	+	0.683606i	0.686875	+	0.726775i	$0.258982\pi$
$578$	−15.0725	−	4.42568i	−0.626933	−	0.184084i
$579$	10.3673	+	11.9645i	0.430851	+	0.497229i
$580$	−3.46815	+	2.22885i	−0.144007	+	0.0925478i
$581$	1.45302	−	1.67688i	0.0602816	−	0.0695687i
$582$	−0.0105955	+	0.0736930i	−0.000439196	+	0.00305467i
$583$	−1.61496	+	0.474194i	−0.0668847	+	0.0196391i
$584$	3.98793	+	2.56289i	0.165022	+	0.106053i
$585$	−0.227916	−	1.58519i	−0.00942318	−	0.0655396i
$586$	3.33563	+	7.30401i	0.137794	+	0.301726i
$587$	−17.7479	−	38.8624i	−0.732532	−	1.60402i	−0.795462	−	0.606004i	$-0.792772\pi$
$587$	−17.7479	−	38.8624i	−0.732532	−	1.60402i	0.0629295	−	0.998018i	$-0.479956\pi$
$588$	0.943376	+	6.56133i	0.0389042	+	0.270584i
$589$	5.99845	+	3.85497i	0.247162	+	0.158841i
$590$	0.484398	−	0.142232i	0.0199423	−	0.00585560i
$591$	0.928657	−	6.45895i	0.0381998	−	0.265686i
$592$	−2.96695	+	3.42404i	−0.121941	+	0.140727i
$593$	9.23810	−	5.93697i	0.379363	−	0.243802i	−0.337037	−	0.941491i	$-0.609425\pi$
$593$	9.23810	−	5.93697i	0.379363	−	0.243802i	0.716400	+	0.697689i	$0.245788\pi$
$594$	−0.154861	−	0.178719i	−0.00635401	−	0.00733292i
$595$	0.664268	+	0.195047i	0.0272323	+	0.00799613i
$596$	4.29742	−	9.41004i	0.176029	−	0.385450i
$597$	6.42615			0.263005
$598$	0.294416	−	7.67485i	0.0120396	−	0.313848i
$599$	9.42965			0.385285			0.192643	−	0.981269i	$-0.438294\pi$
$599$	9.42965			0.385285			0.192643	+	0.981269i	$0.438294\pi$
$600$	−0.415415	+	0.909632i	−0.0169592	+	0.0371356i
$601$	2.56894	+	0.754309i	0.104789	+	0.0307689i	0.333707	−	0.942677i	$-0.391700\pi$
$601$	2.56894	+	0.754309i	0.104789	+	0.0307689i	−0.228918	+	0.973446i	$0.573519\pi$
$602$	0.164215	+	0.189514i	0.00669289	+	0.00772400i
$603$	−2.85763	+	1.83649i	−0.116372	+	0.0747876i
$604$	−3.75357	+	4.33186i	−0.152731	+	0.176261i
$605$	1.55750	−	10.8327i	0.0633216	−	0.440411i
$606$	−12.1505	+	3.56770i	−0.493579	+	0.144928i
$607$	−10.2079	−	6.56023i	−0.414327	−	0.266272i	0.316828	−	0.948483i	$-0.397382\pi$
$607$	−10.2079	−	6.56023i	−0.414327	−	0.266272i	−0.731155	+	0.682211i	$0.761018\pi$
$608$	−0.121206	−	0.843008i	−0.00491556	−	0.0341885i
$609$	−1.04342	−	2.28477i	−0.0422815	−	0.0925837i
$610$	5.00764	+	10.9652i	0.202754	+	0.443968i
$611$	1.15450	+	8.02974i	0.0467062	+	0.324849i
$612$	−0.955922	−	0.614334i	−0.0386409	−	0.0248330i
$613$	19.7352	−	5.79477i	0.797097	−	0.234049i	0.142270	−	0.989828i	$-0.454560\pi$
$613$	19.7352	−	5.79477i	0.797097	−	0.234049i	0.654827	+	0.755779i	$0.272742\pi$
$614$	−0.360562	+	2.50776i	−0.0145511	+	0.101205i
$615$	−5.40145	+	6.23360i	−0.217807	+	0.251363i
$616$	0.121206	−	0.0778945i	0.00488354	−	0.00313846i
$617$	−2.20632	−	2.54623i	−0.0888231	−	0.102507i	0.709598	−	0.704607i	$-0.248877\pi$
$617$	−2.20632	−	2.54623i	−0.0888231	−	0.102507i	−0.798421	+	0.602099i	$0.794331\pi$
$618$	3.42476	+	1.00560i	0.137764	+	0.0404512i
$619$	11.6203	−	25.4450i	0.467060	−	1.02272i	−0.518761	−	0.854919i	$-0.673606\pi$
$619$	11.6203	−	25.4450i	0.467060	−	1.02272i	0.985821	−	0.167800i	$-0.0536662\pi$
$620$	−8.37216			−0.336234
$621$	−2.74557	+	3.93215i	−0.110176	+	0.157792i
$622$	−15.6599			−0.627905
$623$	0.852751	−	1.86727i	0.0341648	−	0.0748104i
$624$	−1.53662	−	0.451193i	−0.0615141	−	0.0180622i
$625$	−0.654861	−	0.755750i	−0.0261944	−	0.0302300i
$626$	−23.4128	+	15.0465i	−0.935764	+	0.601379i
$627$	−0.131891	+	0.152211i	−0.00526723	+	0.00607871i
$628$	−0.449044	+	3.12317i	−0.0179188	+	0.124628i
$629$	4.93968	−	1.45042i	0.196958	−	0.0578320i
$630$	−0.512546	−	0.329393i	−0.0204203	−	0.0131233i
$631$	5.44279	+	37.8554i	0.216674	+	1.50700i	0.750197	+	0.661215i	$0.229959\pi$
$631$	5.44279	+	37.8554i	0.216674	+	1.50700i	−0.533523	+	0.845786i	$0.679132\pi$
$632$	2.42041	+	5.29995i	0.0962786	+	0.210821i
$633$	−1.09987	−	2.40837i	−0.0437157	−	0.0957241i
$634$	0.754746	+	5.24937i	0.0299748	+	0.208479i
$635$	−2.71414	−	1.74427i	−0.107707	−	0.0692192i
$636$	6.82918	−	2.00523i	0.270795	−	0.0795125i
$637$	1.51081	−	10.5079i	0.0598605	−	0.416339i
$638$	0.638429	−	0.736786i	0.0252757	−	0.0291697i
$639$	1.23929	−	0.796447i	0.0490258	−	0.0315069i
$640$	0.654861	+	0.755750i	0.0258856	+	0.0298736i
$641$	−42.1498	−	12.3763i	−1.66482	−	0.488835i	−0.692290	−	0.721619i	$-0.743398\pi$
$641$	−42.1498	−	12.3763i	−1.66482	−	0.488835i	−0.972528	+	0.232785i	$0.925216\pi$
$642$	−2.42676	+	5.31386i	−0.0957765	+	0.209721i
$643$	−44.9495			−1.77264			−0.886318	−	0.463077i	$-0.846745\pi$
$643$	−44.9495			−1.77264			−0.886318	+	0.463077i	$0.846745\pi$
$644$	−2.13328	−	1.99670i	−0.0840628	−	0.0786810i
$645$	0.411583			0.0162060
$646$	−0.402025	+	0.880311i	−0.0158174	+	0.0346354i
$647$	35.1426	+	10.3188i	1.38160	+	0.405674i	0.886325	−	0.463064i	$-0.153250\pi$
$647$	35.1426	+	10.3188i	1.38160	+	0.405674i	0.495273	+	0.868737i	$0.335068\pi$
$648$	0.654861	+	0.755750i	0.0257254	+	0.0296886i
$649$	−0.100434	+	0.0645448i	−0.00394237	+	0.00253361i
$650$	1.04875	−	1.21033i	0.0411356	−	0.0474730i
$651$	0.725928	−	5.04894i	0.0284513	−	0.197883i
$652$	14.2303	−	4.17839i	0.557302	−	0.163639i
$653$	9.57243	+	6.15182i	0.374598	+	0.240740i	0.714370	−	0.699768i	$-0.246713\pi$
$653$	9.57243	+	6.15182i	0.374598	+	0.240740i	−0.339772	+	0.940508i	$0.610350\pi$
$654$	0.627268	+	4.36274i	0.0245281	+	0.170597i
$655$	3.46504	+	7.58739i	0.135390	+	0.296464i
$656$	3.42644	+	7.50286i	0.133780	+	0.292938i
$657$	0.674638	+	4.69221i	0.0263201	+	0.183061i
$658$	2.59629	+	1.66853i	0.101214	+	0.0650461i
$659$	−34.3975	+	10.1000i	−1.33994	+	0.393441i	−0.871647	−	0.490134i	$-0.836948\pi$
$659$	−34.3975	+	10.1000i	−1.33994	+	0.393441i	−0.468290	+	0.883575i	$0.655130\pi$
$660$	0.0336545	−	0.234072i	0.00131000	−	0.00911124i
$661$	−21.8958	+	25.2691i	−0.851650	+	0.982856i	−0.999982	−	0.00608164i	$-0.998064\pi$
$661$	−21.8958	+	25.2691i	−0.851650	+	0.982856i	0.148332	+	0.988938i	$0.452610\pi$
$662$	16.2923	−	10.4704i	0.633217	−	0.406944i
$663$	1.19171	+	1.37530i	0.0462821	+	0.0534124i
$664$	−3.49430	−	1.02602i	−0.135605	−	0.0398172i
$665$	−0.215557	+	0.472005i	−0.00835896	+	0.0183036i
$666$	−4.53066			−0.175559
$667$	−17.6566	−	8.89666i	−0.683664	−	0.344480i
$668$	−0.0187077			−0.000723823
$669$	9.78662	−	21.4297i	0.378373	−	0.828521i
$670$	−3.25928	−	0.957010i	−0.125917	−	0.0369725i
$671$	−1.86678	−	2.15438i	−0.0720661	−	0.0831688i
$672$	−0.512546	+	0.329393i	−0.0197719	+	0.0127066i
$673$	20.9626	−	24.1921i	0.808048	−	0.932537i	−0.190746	−	0.981639i	$-0.561091\pi$
$673$	20.9626	−	24.1921i	0.808048	−	0.932537i	0.998794	+	0.0491027i	$0.0156362\pi$
$674$	−1.43216	+	9.96091i	−0.0551648	+	0.383680i
$675$	−0.959493	+	0.281733i	−0.0369309	+	0.0108439i
$676$	−8.77867	−	5.64171i	−0.337641	−	0.216989i
$677$	3.92011	+	27.2649i	0.150662	+	1.04788i	0.915114	+	0.403196i	$0.132101\pi$
$677$	3.92011	+	27.2649i	0.150662	+	1.04788i	−0.764452	+	0.644681i	$0.776990\pi$
$678$	−4.08574	−	8.94651i	−0.156912	−	0.343589i
$679$	−0.0188433	−	0.0412611i	−0.000723140	−	0.00158346i
$680$	−0.161713	−	1.12474i	−0.00620142	−	0.0431318i
$681$	3.36619	+	2.16332i	0.128993	+	0.0828987i
$682$	1.89964	−	0.557785i	0.0727410	−	0.0213587i
$683$	−4.65452	+	32.3729i	−0.178100	+	1.23872i	0.683052	+	0.730369i	$0.260652\pi$
$683$	−4.65452	+	32.3729i	−0.178100	+	1.23872i	−0.861153	+	0.508346i	$0.830257\pi$
$684$	0.557730	−	0.643655i	0.0213253	−	0.0246107i
$685$	−15.3379	+	9.85710i	−0.586033	+	0.376620i
$686$	−5.43766	−	6.27540i	−0.207611	−	0.239596i
$687$	16.0259	+	4.70563i	0.611426	+	0.179531i
$688$	0.170978	−	0.374389i	0.00651846	−	0.0142734i
$689$	−11.3986			−0.434253
$690$	−4.76969	+	0.500049i	−0.181579	+	0.0190366i
$691$	−32.3436			−1.23041			−0.615204	−	0.788368i	$-0.710927\pi$
$691$	−32.3436			−1.23041			−0.615204	+	0.788368i	$0.710927\pi$
$692$	1.31200	−	2.87288i	0.0498748	−	0.109211i
$693$	0.138242	+	0.0405915i	0.00525138	+	0.00154194i
$694$	12.5552	+	14.4895i	0.476589	+	0.550013i
$695$	−14.6905	+	9.44100i	−0.557242	+	0.358118i
$696$	−2.69973	+	3.11565i	−0.102333	+	0.118099i
$697$	1.33385	−	9.27713i	0.0505232	−	0.351396i
$698$	−5.53252	+	1.62449i	−0.209409	+	0.0614880i
$699$	−21.9276	−	14.0920i	−0.829379	−	0.533009i
$700$	−0.0867074	−	0.603063i	−0.00327723	−	0.0227936i
$701$	20.5290	+	44.9522i	0.775368	+	1.69782i	0.714460	+	0.699676i	$0.246672\pi$
$701$	20.5290	+	44.9522i	0.775368	+	1.69782i	0.0609080	+	0.998143i	$0.480600\pi$
$702$	−0.665284	−	1.45677i	−0.0251095	−	0.0549822i
$703$	0.549144	+	3.81938i	0.0207114	+	0.144051i
$704$	−0.198939	−	0.127850i	−0.00749778	−	0.00481853i
$705$	4.86028	−	1.42711i	0.183049	−	0.0537480i
$706$	−0.311174	+	2.16426i	−0.0117112	+	0.0814532i
$707$	5.05250	−	5.83090i	0.190019	−	0.219293i
$708$	0.424705	−	0.272941i	0.0159614	−	0.0102578i
$709$	−12.2056	−	14.0860i	−0.458391	−	0.529011i	0.478755	−	0.877948i	$-0.341088\pi$
$709$	−12.2056	−	14.0860i	−0.458391	−	0.529011i	−0.937146	+	0.348937i	$0.886543\pi$
$710$	1.41348	+	0.415035i	0.0530469	+	0.0155760i
$711$	−2.42041	+	5.29995i	−0.0907723	+	0.198764i
$712$	−3.36926			−0.126268
$713$	−20.3968	−	34.5848i	−0.763865	−	1.29521i
$714$	0.692311			0.0259091
$715$	−0.157326	+	0.344495i	−0.00588365	+	0.0128834i
$716$	1.02455	+	0.300834i	0.0382891	+	0.0112427i
$717$	−3.96992	−	4.58153i	−0.148259	−	0.171100i
$718$	−23.2905	+	14.9679i	−0.869194	+	0.558597i
$719$	25.2064	−	29.0897i	0.940040	−	1.08486i	−0.0562168	−	0.998419i	$-0.517904\pi$
$719$	25.2064	−	29.0897i	0.940040	−	1.08486i	0.996257	−	0.0864452i	$-0.0275507\pi$
$720$	−0.142315	+	0.989821i	−0.00530376	+	0.0368885i
$721$	−2.08659	+	0.612677i	−0.0777086	+	0.0228173i
$722$	15.3736	+	9.88002i	0.572147	+	0.367696i
$723$	−2.41785	−	16.8165i	−0.0899207	−	0.625412i
$724$	−0.598473	−	1.31047i	−0.0222421	−	0.0487034i
$725$	−1.71259	−	3.75005i	−0.0636040	−	0.139273i
$726$	−1.55750	−	10.8327i	−0.0578044	−	0.402039i
$727$	42.2803	+	27.1719i	1.56809	+	1.00775i	0.980010	+	0.198949i	$0.0637527\pi$
$727$	42.2803	+	27.1719i	1.56809	+	1.00775i	0.588081	+	0.808802i	$0.299884\pi$
$728$	0.936209	−	0.274896i	0.0346982	−	0.0101883i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−3.10434	+	3.58260i	−0.114897	+	0.132598i
$731$	−0.393441	+	0.252849i	−0.0145519	+	0.00935196i
$732$	7.89406	+	9.11023i	0.291773	+	0.336724i
$733$	2.16304	+	0.635127i	0.0798939	+	0.0234590i	0.321435	−	0.946932i	$-0.395835\pi$
$733$	2.16304	+	0.635127i	0.0798939	+	0.0234590i	−0.241541	+	0.970391i	$0.577653\pi$
$734$	7.19472	−	15.7542i	0.265562	−	0.581499i
$735$	−6.62880			−0.244507
$736$	−1.52654	+	4.54639i	−0.0562690	+	0.167582i
$737$	0.803289			0.0295895
$738$	−3.42644	+	7.50286i	−0.126129	+	0.276184i
$739$	5.22460	+	1.53408i	0.192190	+	0.0564321i	0.376411	−	0.926453i	$-0.377158\pi$
$739$	5.22460	+	1.53408i	0.192190	+	0.0564321i	−0.184221	+	0.982885i	$0.558976\pi$
$740$	−2.96695	−	3.42404i	−0.109067	−	0.125870i
$741$	−1.14743	+	0.737410i	−0.0421520	+	0.0270894i
$742$	−2.83976	+	3.27726i	−0.104251	+	0.120312i
$743$	0.566162	−	3.93774i	0.0207705	−	0.144462i	−0.976797	−	0.214166i	$-0.931297\pi$
$743$	0.566162	−	3.93774i	0.0207705	−	0.144462i	0.997568	+	0.0697046i	$0.0222057\pi$
$744$	−8.03302	+	2.35871i	−0.294505	+	0.0864745i
$745$	8.70267	+	5.59287i	0.318841	+	0.204907i
$746$	1.93083	+	13.4292i	0.0706926	+	0.491678i
$747$	−1.51287	−	3.31271i	−0.0553528	−	0.121206i
$748$	0.111627	+	0.244430i	0.00408150	+	0.00893723i
$749$	−0.506524	−	3.52295i	−0.0185080	−	0.128726i
$750$	−0.841254	−	0.540641i	−0.0307182	−	0.0197414i
$751$	24.3112	−	7.13840i	0.887127	−	0.260484i	0.193743	−	0.981052i	$-0.437937\pi$
$751$	24.3112	−	7.13840i	0.887127	−	0.260484i	0.693384	+	0.720568i	$0.256119\pi$
$752$	0.720892	−	5.01391i	0.0262882	−	0.182839i
$753$	−2.21854	+	2.56033i	−0.0808482	+	0.0933038i
$754$	5.55422	−	3.56948i	0.202273	−	0.129993i
$755$	−3.75357	−	4.33186i	−0.136607	−	0.157652i
$756$	−0.584585	−	0.171650i	−0.0212612	−	0.00624284i
$757$	6.32408	−	13.8478i	0.229852	−	0.503307i	−0.759202	−	0.650855i	$-0.774411\pi$
$757$	6.32408	−	13.8478i	0.229852	−	0.503307i	0.989055	+	0.147548i	$0.0471380\pi$
$758$	−13.8114			−0.501654
$759$	1.04893	−	0.431236i	0.0380736	−	0.0156529i
$760$	0.851677			0.0308936
$761$	−5.60433	+	12.2718i	−0.203157	+	0.444851i	−0.983597	−	0.180379i	$-0.942268\pi$
$761$	−5.60433	+	12.2718i	−0.203157	+	0.444851i	0.780441	+	0.625230i	$0.214995\pi$
$762$	−3.09561	−	0.908954i	−0.112142	−	0.0329279i
$763$	−1.75856	−	2.02949i	−0.0636642	−	0.0734724i
$764$	−9.12865	+	5.86662i	−0.330263	+	0.212247i
$765$	0.744123	−	0.858763i	0.0269038	−	0.0310487i
$766$	−3.28930	+	22.8776i	−0.118847	+	0.826601i
$767$	−0.775759	+	0.227784i	−0.0280111	+	0.00822479i
$768$	0.841254	+	0.540641i	0.0303561	+	0.0195087i
$769$	2.61978	+	18.2210i	0.0944717	+	0.657065i	0.980945	+	0.194285i	$0.0622388\pi$
$769$	2.61978	+	18.2210i	0.0944717	+	0.657065i	−0.886473	+	0.462780i	$0.846852\pi$
$770$	0.0598522	+	0.131058i	0.00215693	+	0.00472301i
$771$	6.29560	+	13.7854i	0.226730	+	0.496470i
$772$	2.25303	+	15.6702i	0.0810885	+	0.563983i
$773$	−7.48739	−	4.81185i	−0.269303	−	0.173070i	0.399019	−	0.916943i	$-0.369351\pi$
$773$	−7.48739	−	4.81185i	−0.269303	−	0.173070i	−0.668322	+	0.743872i	$0.732987\pi$
$774$	0.394911	−	0.115956i	0.0141948	−	0.00416796i
$775$	1.19148	−	8.28694i	0.0427993	−	0.297676i
$776$	−0.0487549	+	0.0562661i	−0.00175020	+	0.00201984i
$777$	2.32217	−	1.49237i	0.0833074	−	0.0535384i
$778$	17.1017	+	19.7364i	0.613127	+	0.707586i
$779$	6.74028	+	1.97913i	0.241496	+	0.0709095i
$780$	0.665284	−	1.45677i	0.0238210	−	0.0521607i
$781$	−0.348370			−0.0124656
$782$	4.25226	−	3.40819i	0.152060	−	0.121877i
$783$	−4.12260			−0.147330
$784$	−2.75370	+	6.02977i	−0.0983465	+	0.215349i
$785$	−3.02747	−	0.888947i	−0.108055	−	0.0317279i
$786$	5.46230	+	6.30383i	0.194834	+	0.224850i
$787$	3.95730	−	2.54320i	0.141062	−	0.0906553i	−0.468206	−	0.883619i	$-0.655100\pi$
$787$	3.95730	−	2.54320i	0.141062	−	0.0906553i	0.609269	+	0.792964i	$0.291463\pi$
$788$	4.27321	−	4.93154i	0.152227	−	0.175679i
$789$	0.876015	−	6.09282i	0.0311870	−	0.216910i
$790$	−5.59047	+	1.64151i	−0.198900	+	0.0584023i
$791$	5.04105	+	3.23968i	0.179239	+	0.115190i
$792$	−0.0336545	−	0.234072i	−0.00119586	−	0.00831738i
$793$	−8.01971	−	17.5607i	−0.284788	−	0.623599i
$794$	−5.09864	−	11.1645i	−0.180944	−	0.396212i
$795$	1.01292	+	7.04505i	0.0359247	+	0.249862i
$796$	5.40603	+	3.47424i	0.191611	+	0.123141i
$797$	−46.1147	+	13.5405i	−1.63347	+	0.479629i	−0.964592	−	0.263746i	$-0.915042\pi$
$797$	−46.1147	+	13.5405i	−1.63347	+	0.479629i	−0.668875	+	0.743375i	$0.733224\pi$
$798$	−0.0738467	+	0.513615i	−0.00261414	+	0.0181818i
$799$	−3.76933	+	4.35004i	−0.133349	+	0.153893i
$800$	−0.841254	+	0.540641i	−0.0297428	+	0.0191145i
$801$	−2.20640	−	2.54632i	−0.0779591	−	0.0899697i
$802$	−25.4242	−	7.46521i	−0.897758	−	0.263606i
$803$	0.465688	−	1.01971i	0.0164338	−	0.0359850i
$804$	−3.39687			−0.119798
$805$	2.27997	−	1.82740i	0.0803585	−	0.0644075i
$806$	13.4079			0.472275
$807$	12.9548	−	28.3670i	0.456030	−	0.998566i
$808$	−12.1505	−	3.56770i	−0.427452	−	0.125511i
$809$	−19.7185	−	22.7564i	−0.693267	−	0.800072i	0.294560	−	0.955633i	$-0.404827\pi$
$809$	−19.7185	−	22.7564i	−0.693267	−	0.800072i	−0.987826	+	0.155561i	$0.950282\pi$
$810$	−0.841254	+	0.540641i	−0.0295586	+	0.0189962i
$811$	20.8503	−	24.0626i	0.732154	−	0.844951i	−0.260559	−	0.965458i	$-0.583907\pi$
$811$	20.8503	−	24.0626i	0.732154	−	0.844951i	0.992712	+	0.120508i	$0.0384522\pi$
$812$	0.357460	−	2.48619i	0.0125444	−	0.0872481i
$813$	−8.54468	+	2.50894i	−0.299675	+	0.0879925i
$814$	0.901323	+	0.579245i	0.0315914	+	0.0203025i
$815$	2.11068	+	14.6801i	0.0739339	+	0.514222i
$816$	−0.472039	−	1.03362i	−0.0165247	−	0.0361840i
$817$	−0.145618	−	0.318858i	−0.00509452	−	0.0111554i
$818$	−1.27453	−	8.86453i	−0.0445628	−	0.309941i
$819$	0.820839	+	0.527521i	0.0286824	+	0.0184331i
$820$	−7.91413	+	2.32380i	−0.276373	+	0.0811505i
$821$	−1.23588	+	8.59573i	−0.0431325	+	0.299993i	0.956824	+	0.290668i	$0.0938774\pi$
$821$	−1.23588	+	8.59573i	−0.0431325	+	0.299993i	−0.999957	+	0.00932520i	$0.997032\pi$
$822$	−11.9396	+	13.7790i	−0.416441	+	0.480598i
$823$	−26.9003	+	17.2878i	−0.937687	+	0.602615i	−0.917738	−	0.397186i	$-0.869987\pi$
$823$	−26.9003	+	17.2878i	−0.937687	+	0.602615i	−0.0199491	+	0.999801i	$0.506350\pi$
$824$	2.33743	+	2.69753i	0.0814281	+	0.0939730i
$825$	0.226900	+	0.0666238i	0.00789964	+	0.00231954i
$826$	−0.127776	+	0.279790i	−0.00444589	+	0.00973513i
$827$	25.2690			0.878688			0.439344	−	0.898319i	$-0.355211\pi$
$827$	25.2690			0.878688			0.439344	+	0.898319i	$0.355211\pi$
$828$	−4.43560	+	1.82357i	−0.154148	+	0.0633735i
$829$	33.9850			1.18035			0.590173	−	0.807277i	$-0.299059\pi$
$829$	33.9850			1.18035			0.590173	+	0.807277i	$0.299059\pi$
$830$	1.51287	−	3.31271i	0.0525123	−	0.114986i
$831$	17.6351	+	5.17813i	0.611755	+	0.179627i
$832$	−1.04875	−	1.21033i	−0.0363590	−	0.0419606i
$833$	6.33661	−	4.07229i	0.219551	−	0.141097i
$834$	−11.4356	+	13.1974i	−0.395982	+	0.456987i
$835$	0.00266239	−	0.0185173i	9.21357e−5	−	0.000640818i
$836$	−0.193245	+	0.0567420i	−0.00668353	+	0.00196246i
$837$	−7.04311	−	4.52633i	−0.243445	−	0.156453i
$838$	−1.06437	−	7.40285i	−0.0367680	−	0.255727i
$839$	14.6291	+	32.0332i	0.505051	+	1.10591i	0.974794	+	0.223105i	$0.0716192\pi$
$839$	14.6291	+	32.0332i	0.505051	+	1.10591i	−0.469743	+	0.882803i	$0.655654\pi$
$840$	−0.253098	−	0.554206i	−0.00873270	−	0.0191219i
$841$	1.70837	+	11.8820i	0.0589093	+	0.409723i
$842$	16.2530	+	10.4451i	0.560114	+	0.359963i
$843$	12.6088	−	3.70227i	0.434270	−	0.127513i
$844$	0.376797	−	2.62068i	0.0129699	−	0.0902076i
$845$	6.83362	−	7.88641i	0.235084	−	0.271301i
$846$	4.26135	−	2.73860i	0.146508	−	0.0941550i
$847$	4.36651	+	5.03922i	0.150035	+	0.173149i
$848$	6.82918	+	2.00523i	0.234515	+	0.0688599i
$849$	3.72344	−	8.15320i	0.127788	−	0.279817i
$850$	1.13631			0.0389750
$851$	6.91623	−	20.5981i	0.237085	−	0.706095i
$852$	1.47315			0.0504694
$853$	3.90295	−	8.54626i	0.133634	−	0.292618i	−0.830971	−	0.556315i	$-0.812215\pi$
$853$	3.90295	−	8.54626i	0.133634	−	0.292618i	0.964606	+	0.263697i	$0.0849419\pi$
$854$	−7.04691	−	2.06916i	−0.241140	−	0.0708052i
$855$	0.557730	+	0.643655i	0.0190740	+	0.0220125i
$856$	−4.91441	+	3.15830i	−0.167971	+	0.107948i
$857$	11.0702	−	12.7757i	0.378151	−	0.436409i	−0.534488	−	0.845176i	$-0.679496\pi$
$857$	11.0702	−	12.7757i	0.378151	−	0.436409i	0.912639	+	0.408767i	$0.134041\pi$
$858$	−0.0538974	+	0.374864i	−0.00184003	+	0.0127977i
$859$	−0.670232	+	0.196798i	−0.0228680	+	0.00671466i	−0.293147	−	0.956068i	$-0.594702\pi$
$859$	−0.670232	+	0.196798i	−0.0228680	+	0.00671466i	0.270279	+	0.962782i	$0.412884\pi$
$860$	0.346245	+	0.222518i	0.0118069	+	0.00758781i
$861$	−0.715183	−	4.97421i	−0.0243734	−	0.169521i
$862$	−4.66005	−	10.2041i	−0.158722	−	0.347553i
$863$	14.8071	+	32.4230i	0.504040	+	1.10369i	0.975135	+	0.221611i	$0.0711315\pi$
$863$	14.8071	+	32.4230i	0.504040	+	1.10369i	−0.471095	+	0.882082i	$0.656141\pi$
$864$	0.142315	+	0.989821i	0.00484165	+	0.0336744i
$865$	2.65692	+	1.70750i	0.0903381	+	0.0580567i
$866$	−3.77106	+	1.10728i	−0.128146	+	0.0376270i
$867$	2.23560	−	15.5489i	0.0759248	−	0.528069i
$868$	3.34035	−	3.85497i	0.113379	−	0.130846i
$869$	1.15911	−	0.744916i	0.0393202	−	0.0252695i
$870$	−2.69973	−	3.11565i	−0.0915294	−	0.105631i
$871$	5.21971	+	1.53264i	0.176863	+	0.0519317i
$872$	−1.83099	+	4.00930i	−0.0620050	+	0.135772i
$873$	−0.0744508			−0.00251978
$874$	2.07491	+	3.51822i	0.0701848	+	0.119006i
$875$	0.609264			0.0205969
$876$	−1.96926	+	4.31208i	−0.0665351	+	0.145692i
$877$	27.0453	+	7.94123i	0.913256	+	0.268156i	0.704411	−	0.709793i	$-0.251211\pi$
$877$	27.0453	+	7.94123i	0.913256	+	0.268156i	0.208845	+	0.977949i	$0.433030\pi$
$878$	8.26955	+	9.54357i	0.279084	+	0.322080i
$879$	−6.75495	+	4.34114i	−0.227839	+	0.146423i
$880$	0.154861	−	0.178719i	0.00522035	−	0.00602461i
$881$	−4.19596	+	29.1835i	−0.141365	+	0.983218i	0.788426	+	0.615130i	$0.210896\pi$
$881$	−4.19596	+	29.1835i	−0.141365	+	0.983218i	−0.929791	+	0.368088i	$0.880013\pi$
$882$	−6.36028	+	1.86755i	−0.214162	+	0.0628836i
$883$	−7.51271	−	4.82813i	−0.252823	−	0.162479i	0.408091	−	0.912941i	$-0.366195\pi$
$883$	−7.51271	−	4.82813i	−0.252823	−	0.162479i	−0.660914	+	0.750462i	$0.729831\pi$
$884$	0.258983	+	1.80126i	0.00871053	+	0.0605831i
$885$	0.209721	+	0.459225i	0.00704970	+	0.0154367i
$886$	15.5641	+	34.0806i	0.522886	+	1.14496i
$887$	−0.102113	−	0.710214i	−0.00342863	−	0.0238467i	0.988035	−	0.154228i	$-0.0492890\pi$
$887$	−0.102113	−	0.710214i	−0.00342863	−	0.0238467i	−0.991464	+	0.130381i	$0.958380\pi$
$888$	−3.81143	−	2.44946i	−0.127903	−	0.0821984i
$889$	1.88605	−	0.553793i	0.0632560	−	0.0185736i
$890$	0.479496	−	3.33496i	0.0160727	−	0.111788i
$891$	0.154861	−	0.178719i	0.00518803	−	0.00598731i
$892$	19.8188	−	12.7368i	0.663583	−	0.426459i
$893$	−2.82516	−	3.26041i	−0.0945405	−	0.109106i
$894$	9.92584	+	2.91449i	0.331970	+	0.0974752i
$895$	−0.443580	+	0.971304i	−0.0148272	+	0.0324671i
$896$	−0.609264			−0.0203541
$897$	7.63863	−	0.800825i	0.255046	−	0.0267388i
$898$	11.7393			0.391746
$899$	14.3381	−	31.3960i	0.478202	−	1.04712i
$900$	−0.959493	−	0.281733i	−0.0319831	−	0.00939109i
$901$	−5.29629	−	6.11224i	−0.176445	−	0.203628i
$902$	1.64089	−	1.05454i	0.0546358	−	0.0351123i
$903$	−0.164215	+	0.189514i	−0.00546472	+	0.00630662i
$904$	1.39971	−	9.73520i	0.0465537	−	0.323788i
$905$	1.38231	−	0.405882i	0.0459494	−	0.0134920i
$906$	−4.82195	−	3.09888i	−0.160199	−	0.102953i
$907$	0.348463	+	2.42361i	0.0115705	+	0.0804747i	0.994789	−	0.101960i	$-0.0325113\pi$
$907$	0.348463	+	2.42361i	0.0115705	+	0.0804747i	−0.983218	+	0.182435i	$0.941602\pi$
$908$	1.66224	+	3.63980i	0.0551635	+	0.120791i
$909$	−5.26058	−	11.5191i	−0.174482	−	0.382063i
$910$	0.138861	+	0.965801i	0.00460321	+	0.0320160i
$911$	−0.514100	−	0.330392i	−0.0170329	−	0.0109464i	0.532097	−	0.846684i	$-0.321404\pi$
$911$	−0.514100	−	0.330392i	−0.0170329	−	0.0109464i	−0.549130	+	0.835737i	$0.685041\pi$
$912$	0.817178	−	0.239945i	0.0270595	−	0.00794538i
$913$	−0.122563	+	0.852447i	−0.00405626	+	0.0282119i
$914$	−19.3434	+	22.3235i	−0.639823	+	0.738395i
$915$	−10.1409	+	6.51719i	−0.335249	+	0.215452i
$916$	10.9378	+	12.6229i	0.361395	+	0.417072i
$917$	−4.87612	−	1.43176i	−0.161024	−	0.0472808i
$918$	0.472039	−	1.03362i	0.0155796	−	0.0341146i
$919$	60.1092			1.98282			0.991410	−	0.130793i	$-0.0417524\pi$
$919$	60.1092			1.98282			0.991410	+	0.130793i	$0.0417524\pi$
$920$	−4.28287	−	2.15802i	−0.141202	−	0.0711479i
$921$	−2.53355			−0.0834833
$922$	13.6488	−	29.8866i	0.449498	−	0.984264i
$923$	−2.26368	−	0.664676i	−0.0745099	−	0.0218781i
$924$	0.0943511	+	0.108887i	0.00310392	+	0.00358212i
$925$	3.81143	−	2.44946i	0.125319	−	0.0805377i
$926$	2.01154	−	2.32145i	0.0661034	−	0.0762874i
$927$	−0.507971	+	3.53302i	−0.0166840	+	0.116040i
$928$	−3.95561	+	1.16147i	−0.129849	+	0.0381272i
$929$	3.05004	+	1.96014i	0.100069	+	0.0643102i	0.589718	−	0.807609i	$-0.299239\pi$
$929$	3.05004	+	1.96014i	0.100069	+	0.0643102i	−0.489649	+	0.871919i	$0.662875\pi$
$930$	−1.19148	−	8.28694i	−0.0390702	−	0.271739i
$931$	2.34526	+	5.13541i	0.0768629	+	0.168306i
$932$	−10.8280	−	23.7099i	−0.354682	−	0.776645i
$933$	−2.22864	−	15.5005i	−0.0729624	−	0.507464i
$934$	17.6924	+	11.3702i	0.578913	+	0.372045i
$935$	−0.257828	+	0.0757051i	−0.00843187	+	0.00247582i
$936$	0.227916	−	1.58519i	0.00744967	−	0.0518136i
$937$	−11.6689	+	13.4666i	−0.381206	+	0.439935i	−0.913632	−	0.406541i	$-0.866735\pi$
$937$	−11.6689	+	13.4666i	−0.381206	+	0.439935i	0.532427	+	0.846476i	$0.321280\pi$
$938$	1.74105	−	1.11891i	0.0568474	−	0.0365336i
$939$	−18.2253	−	21.0332i	−0.594762	−	0.686391i
$940$	4.86028	+	1.42711i	0.158525	+	0.0465471i
$941$	−24.0231	+	52.6032i	−0.783130	+	1.71482i	−0.0877861	+	0.996139i	$0.527979\pi$
$941$	−24.0231	+	52.6032i	−0.783130	+	1.71482i	−0.695344	+	0.718677i	$0.744748\pi$
$942$	−3.15529			−0.102805
$943$	−28.8803	−	27.0314i	−0.940474	−	0.880263i
$944$	0.504848			0.0164314
$945$	0.253098	−	0.554206i	0.00823327	−	0.0180283i
$946$	−0.0933880	−	0.0274212i	−0.00303631	−	0.000891540i
$947$	−2.63525	−	3.04124i	−0.0856342	−	0.0988272i	0.711315	−	0.702873i	$-0.248100\pi$
$947$	−2.63525	−	3.04124i	−0.0856342	−	0.0988272i	−0.796950	+	0.604046i	$0.793554\pi$
$948$	−4.90155	+	3.15003i	−0.159195	+	0.102308i
$949$	4.97158	−	5.73751i	0.161384	−	0.186248i
$950$	−0.121206	+	0.843008i	−0.00393245	+	0.0273508i
$951$	−5.08853	+	1.49413i	−0.165007	+	0.0484504i
$952$	0.582409	+	0.374292i	0.0188760	+	0.0121309i
$953$	−0.285874	−	1.98830i	−0.00926038	−	0.0644073i	0.984667	−	0.174443i	$-0.0558125\pi$
$953$	−0.285874	−	1.98830i	−0.00926038	−	0.0644073i	−0.993928	+	0.110036i	$0.964903\pi$
$954$	2.95671	+	6.47430i	0.0957271	+	0.209613i
$955$	−4.50777	−	9.87064i	−0.145868	−	0.319406i
$956$	−0.862745	−	6.00053i	−0.0279032	−	0.194071i
$957$	0.820145	+	0.527075i	0.0265115	+	0.0170379i
$958$	15.4187	−	4.52733i	0.498155	−	0.146272i
$959$	1.58087	−	10.9952i	0.0510490	−	0.355053i
$960$	−0.654861	+	0.755750i	−0.0211355	+	0.0243917i
$961$	32.8871	−	21.1353i	1.06087	−	0.681783i
$962$	4.75155	+	5.48358i	0.153196	+	0.176798i
$963$	−5.60513	−	1.64582i	−0.180623	−	0.0530357i
$964$	7.05766	−	15.4541i	0.227312	−	0.497744i
$965$	−15.8313			−0.509629
$966$	1.67278	−	2.39572i	0.0538208	−	0.0770811i
$967$	39.9728			1.28544			0.642719	−	0.766102i	$-0.277806\pi$
$967$	39.9728			1.28544			0.642719	+	0.766102i	$0.277806\pi$
$968$	4.54633	−	9.95508i	0.146125	−	0.319968i
$969$	−0.928565	−	0.272651i	−0.0298298	−	0.00875882i
$970$	−0.0487549	−	0.0562661i	−0.00156543	−	0.00180660i
$971$	−14.6664	+	9.42549i	−0.470666	+	0.302478i	−0.754389	−	0.656428i	$-0.772067\pi$
$971$	−14.6664	+	9.42549i	−0.470666	+	0.302478i	0.283723	+	0.958906i	$0.408430\pi$
$972$	−0.654861	+	0.755750i	−0.0210047	+	0.0242407i
$973$	1.51414	−	10.5311i	0.0485410	−	0.337610i
$974$	22.7757	−	6.68754i	0.729780	−	0.214283i
$975$	1.34726	+	0.865832i	0.0431469	+	0.0277288i
$976$	1.71554	+	11.9319i	0.0549132	+	0.381929i
$977$	−3.12880	−	6.85112i	−0.100099	−	0.219187i	0.852956	−	0.521982i	$-0.174807\pi$
$977$	−3.12880	−	6.85112i	−0.100099	−	0.219187i	−0.953056	+	0.302796i	$0.902080\pi$
$978$	6.16105	+	13.4908i	0.197009	+	0.431389i
$979$	0.113391	+	0.788649i	0.00362398	+	0.0252053i
$980$	−5.57650	−	3.58380i	−0.178135	−	0.114480i
$981$	−4.22907	+	1.24177i	−0.135024	+	0.0396465i
$982$	3.49612	−	24.3160i	0.111566	−	0.775956i
$983$	2.17290	−	2.50765i	0.0693046	−	0.0799818i	−0.720038	−	0.693934i	$-0.755876\pi$
$983$	2.17290	−	2.50765i	0.0693046	−	0.0799818i	0.789343	+	0.613952i	$0.210421\pi$
$984$	−6.93886	+	4.45934i	−0.221203	+	0.142158i
$985$	4.27321	+	4.93154i	0.136156	+	0.157132i
$986$	4.49478	+	1.31979i	0.143143	+	0.0420306i
$987$	−1.28206	+	2.80732i	−0.0408084	+	0.0893579i
$988$	−1.36395			−0.0433932
$989$	−0.0756646	+	1.97243i	−0.00240599	+	0.0627196i
$990$	0.236479			0.00751579
$991$	24.5287	−	53.7104i	0.779180	−	1.70617i	0.0738690	−	0.997268i	$-0.476465\pi$
$991$	24.5287	−	53.7104i	0.779180	−	1.70617i	0.705311	−	0.708898i	$-0.250807\pi$
$992$	−8.03302	−	2.35871i	−0.255049	−	0.0748891i
$993$	12.6825	+	14.6364i	0.402466	+	0.464471i
$994$	−0.755058	+	0.485247i	−0.0239490	+	0.0153911i
$995$	−4.20824	+	4.85656i	−0.133410	+	0.153963i
$996$	0.518285	−	3.60475i	0.0164225	−	0.114221i
$997$	24.3515	−	7.15023i	0.771218	−	0.226450i	0.127630	−	0.991822i	$-0.459263\pi$
$997$	24.3515	−	7.15023i	0.771218	−	0.226450i	0.643589	+	0.765372i	$0.277445\pi$
$998$	24.2543	+	15.5873i	0.767758	+	0.493408i
$999$	−0.644780	−	4.48454i	−0.0203999	−	0.141885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.b.121.1	✓	10
23.4	even	11	inner	690.2.m.b.211.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.b.121.1	✓	10	1.1	even	1	trivial
690.2.m.b.211.1	yes	10	23.4	even	11	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.0867074 + 0.603063i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.0867074 + 0.603063i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(0.142315 + 0.989821i) q^{10} +(-0.0982369 - 0.215109i) q^{11} +(0.415415 + 0.909632i) q^{12} +(-0.227916 - 1.58519i) q^{13} +(-0.512546 - 0.329393i) q^{14} +(-0.959493 + 0.281733i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(0.744123 - 0.858763i) q^{17} +(-0.841254 + 0.540641i) q^{18} +(0.557730 + 0.643655i) q^{19} +(-0.959493 - 0.281733i) q^{20} +(0.253098 - 0.554206i) q^{21} +0.236479 q^{22} +(-1.17376 - 4.64998i) q^{23} -1.00000 q^{24} +(0.415415 - 0.909632i) q^{25} +(1.53662 + 0.451193i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(0.512546 - 0.329393i) q^{28} +(2.69973 - 3.11565i) q^{29} +(0.142315 - 0.989821i) q^{30} +(8.03302 - 2.35871i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(0.0336545 + 0.234072i) q^{33} +(0.472039 + 1.03362i) q^{34} +(0.253098 + 0.554206i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(3.81143 + 2.44946i) q^{37} +(-0.817178 + 0.239945i) q^{38} +(-0.227916 + 1.58519i) q^{39} +(0.654861 - 0.755750i) q^{40} +(6.93886 - 4.45934i) q^{41} +(0.398983 + 0.460451i) q^{42} +(-0.394911 - 0.115956i) q^{43} +(-0.0982369 + 0.215109i) q^{44} +1.00000 q^{45} +(4.71737 + 0.863983i) q^{46} -5.06547 q^{47} +(0.415415 - 0.909632i) q^{48} +(6.36028 + 1.86755i) q^{49} +(0.654861 + 0.755750i) q^{50} +(-0.955922 + 0.614334i) q^{51} +(-1.04875 + 1.21033i) q^{52} +(1.01292 - 7.04505i) q^{53} +(0.959493 - 0.281733i) q^{54} +(-0.198939 - 0.127850i) q^{55} +(0.0867074 + 0.603063i) q^{56} +(-0.353799 - 0.774713i) q^{57} +(1.71259 + 3.75005i) q^{58} +(-0.0718473 - 0.499709i) q^{59} +(0.841254 + 0.540641i) q^{60} +(11.5663 - 3.39616i) q^{61} +(-1.19148 + 8.28694i) q^{62} +(-0.398983 + 0.460451i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-1.04875 - 1.21033i) q^{65} +(-0.226900 - 0.0666238i) q^{66} +(-1.41111 + 3.08990i) q^{67} -1.13631 q^{68} +(-0.183838 + 4.79231i) q^{69} -0.609264 q^{70} +(0.611970 - 1.34003i) q^{71} +(0.959493 + 0.281733i) q^{72} +(3.10434 + 3.58260i) q^{73} +(-3.81143 + 2.44946i) q^{74} +(-0.654861 + 0.755750i) q^{75} +(0.121206 - 0.843008i) q^{76} +(0.138242 - 0.0405915i) q^{77} +(-1.34726 - 0.865832i) q^{78} +(0.829194 + 5.76717i) q^{79} +(0.415415 + 0.909632i) q^{80} +(0.415415 + 0.909632i) q^{81} +(1.17385 + 8.16428i) q^{82} +(-3.06369 - 1.96891i) q^{83} +(-0.584585 + 0.171650i) q^{84} +(0.161713 - 1.12474i) q^{85} +(0.269529 - 0.311053i) q^{86} +(-3.46815 + 2.22885i) q^{87} +(-0.154861 - 0.178719i) q^{88} +(-3.23278 - 0.949230i) q^{89} +(-0.415415 + 0.909632i) q^{90} +0.975733 q^{91} +(-2.74557 + 3.93215i) q^{92} -8.37216 q^{93} +(2.10427 - 4.60771i) q^{94} +(0.817178 + 0.239945i) q^{95} +(0.654861 + 0.755750i) q^{96} +(-0.0626320 + 0.0402511i) q^{97} +(-4.34094 + 5.00971i) q^{98} +(0.0336545 - 0.234072i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + q^{8} - q^{9}+O(q^{10}) \) 10 * q + q^2 - q^3 - q^4 - q^5 + q^6 + q^8 - q^9	\( 10 q + q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + q^{8} - q^{9} + q^{10} - 4 q^{11} - q^{12} + 2 q^{13} - q^{15} - q^{16} - 2 q^{17} + q^{18} - q^{20} + 4 q^{22} - q^{23} - 10 q^{24} - q^{25} + 9 q^{26} - q^{27} - 6 q^{29} + q^{30} + 22 q^{31} + q^{32} - 4 q^{33} - 9 q^{34} - q^{36} + 20 q^{37} + 2 q^{39} + q^{40} + 9 q^{41} - 11 q^{42} + 12 q^{43} - 4 q^{44} + 10 q^{45} + q^{46} - 8 q^{47} - q^{48} + 7 q^{49} + q^{50} - 13 q^{51} + 2 q^{52} - 20 q^{53} + q^{54} + 7 q^{55} + 11 q^{57} + 6 q^{58} - 22 q^{59} - q^{60} + 49 q^{61} + 11 q^{63} - q^{64} + 2 q^{65} - 7 q^{66} + 10 q^{67} - 2 q^{68} - q^{69} - q^{71} + q^{72} + 17 q^{73} - 20 q^{74} - q^{75} - 13 q^{78} + 18 q^{79} - q^{80} - q^{81} + 13 q^{82} + 15 q^{83} - 11 q^{84} + 9 q^{85} + 10 q^{86} - 6 q^{87} + 4 q^{88} - 5 q^{89} + q^{90} + 22 q^{91} - 12 q^{92} - 22 q^{93} - 3 q^{94} + q^{96} - q^{97} - 7 q^{98} - 4 q^{99}+O(q^{100}) \) 10 * q + q^2 - q^3 - q^4 - q^5 + q^6 + q^8 - q^9 + q^10 - 4 * q^11 - q^12 + 2 * q^13 - q^15 - q^16 - 2 * q^17 + q^18 - q^20 + 4 * q^22 - q^23 - 10 * q^24 - q^25 + 9 * q^26 - q^27 - 6 * q^29 + q^30 + 22 * q^31 + q^32 - 4 * q^33 - 9 * q^34 - q^36 + 20 * q^37 + 2 * q^39 + q^40 + 9 * q^41 - 11 * q^42 + 12 * q^43 - 4 * q^44 + 10 * q^45 + q^46 - 8 * q^47 - q^48 + 7 * q^49 + q^50 - 13 * q^51 + 2 * q^52 - 20 * q^53 + q^54 + 7 * q^55 + 11 * q^57 + 6 * q^58 - 22 * q^59 - q^60 + 49 * q^61 + 11 * q^63 - q^64 + 2 * q^65 - 7 * q^66 + 10 * q^67 - 2 * q^68 - q^69 - q^71 + q^72 + 17 * q^73 - 20 * q^74 - q^75 - 13 * q^78 + 18 * q^79 - q^80 - q^81 + 13 * q^82 + 15 * q^83 - 11 * q^84 + 9 * q^85 + 10 * q^86 - 6 * q^87 + 4 * q^88 - 5 * q^89 + q^90 + 22 * q^91 - 12 * q^92 - 22 * q^93 - 3 * q^94 + q^96 - q^97 - 7 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

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