LMFDB - Embedded newform 669.2.i.b.4.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [669,2,Mod(4,669)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(669, base_ring=CyclotomicField(74)) chi = DirichletCharacter(H, H._module([0, 46])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("669.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 669 = 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	669.i (of order $37$, degree $36$, minimal)

Newform invariants

comment:select newform

sage:traces = [720] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.34199189522$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$20$ over $\Q(\zeta_{37})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{37}]$

Embedding invariants

Embedding label			4.6
Character	$\chi$	$=$	669.4
Dual form			669.2.i.b.502.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.27818 + 0.451610i) q^{2} +(0.372856 - 0.927889i) q^{3} +(-0.126276 + 0.101961i) q^{4} +(-2.03001 - 3.29695i) q^{5} +(-0.0575340 + 1.35440i) q^{6} +(0.0912925 - 0.712916i) q^{7} +(1.53688 - 2.49605i) q^{8} +(-0.721956 - 0.691939i) q^{9} +(4.08366 + 3.29733i) q^{10} +(0.0732452 - 1.72425i) q^{11} +(0.0475255 + 0.155187i) q^{12} +(-0.0228080 - 0.0567600i) q^{13} +(0.205272 + 0.952464i) q^{14} +(-3.81611 + 0.654338i) q^{15} +(-0.768780 + 3.56715i) q^{16} +(0.0857237 - 2.01800i) q^{17} +(1.23528 + 0.558381i) q^{18} +(0.532378 - 0.138620i) q^{19} +(0.592502 + 0.209344i) q^{20} +(-0.627468 - 0.350525i) q^{21} +(0.685068 + 2.23698i) q^{22} +(0.737605 + 1.19795i) q^{23} +(-1.74302 - 2.35672i) q^{24} +(-4.49792 + 8.92109i) q^{25} +(0.0547862 + 0.0622492i) q^{26} +(-0.911228 + 0.411901i) q^{27} +(0.0611615 + 0.0993325i) q^{28} +(0.209048 - 0.969985i) q^{29} +(4.58217 - 2.55976i) q^{30} +(-9.11271 + 0.775606i) q^{31} +(0.116321 + 0.908365i) q^{32} +(-1.57260 - 0.710861i) q^{33} +(0.801780 + 2.61809i) q^{34} +(-2.53577 + 1.14624i) q^{35} +(0.161717 + 0.0137641i) q^{36} +(-0.135454 - 3.18870i) q^{37} +(-0.617873 + 0.417609i) q^{38} -0.0611711 q^{39} -11.3492 q^{40} +(-6.71389 + 4.53780i) q^{41} +(0.960318 + 0.164663i) q^{42} +(0.224685 + 0.445635i) q^{43} +(0.166557 + 0.225200i) q^{44} +(-0.815708 + 3.78490i) q^{45} +(-1.48380 - 1.19808i) q^{46} +(0.0791304 + 0.0206040i) q^{47} +(3.02328 + 2.04338i) q^{48} +(6.27422 + 1.63368i) q^{49} +(1.72030 - 13.4341i) q^{50} +(-1.84052 - 0.831968i) q^{51} +(0.00866741 + 0.00484190i) q^{52} +(-2.02494 + 2.30078i) q^{53} +(0.978696 - 0.938004i) q^{54} +(-5.83345 + 3.25876i) q^{55} +(-1.63917 - 1.32353i) q^{56} +(0.0698762 - 0.545673i) q^{57} +(0.170854 + 1.33422i) q^{58} +(1.80760 - 5.90243i) q^{59} +(0.415167 - 0.471721i) q^{60} +(0.123148 + 0.306465i) q^{61} +(11.2974 - 5.10676i) q^{62} +(-0.559203 + 0.451525i) q^{63} +(-3.84454 - 7.62520i) q^{64} +(-0.140834 + 0.190421i) q^{65} +(2.33110 + 0.198406i) q^{66} +(-8.59660 + 6.94127i) q^{67} +(0.194932 + 0.263566i) q^{68} +(1.38658 - 0.237754i) q^{69} +(2.72352 - 2.61029i) q^{70} +(1.58454 - 5.17406i) q^{71} +(-2.83667 + 0.738612i) q^{72} +(2.75665 + 1.53996i) q^{73} +(1.61318 + 4.01456i) q^{74} +(6.60070 + 7.49985i) q^{75} +(-0.0530927 + 0.0717861i) q^{76} +(-1.22256 - 0.209629i) q^{77} +(0.0781877 - 0.0276255i) q^{78} +(-7.15005 + 4.83259i) q^{79} +(13.3214 - 4.70674i) q^{80} +(0.0424412 + 0.999099i) q^{81} +(6.53225 - 8.83219i) q^{82} +(2.53843 - 5.03467i) q^{83} +(0.114974 - 0.0197143i) q^{84} +(-6.82728 + 3.81395i) q^{85} +(-0.488441 - 0.468133i) q^{86} +(-0.822093 - 0.555638i) q^{87} +(-4.19124 - 2.83278i) q^{88} +(-3.55048 + 5.76634i) q^{89} +(-0.666676 - 5.20617i) q^{90} +(-0.0425473 + 0.0110785i) q^{91} +(-0.215286 - 0.0760653i) q^{92} +(-2.67806 + 8.74477i) q^{93} +(-0.110448 + 0.00940051i) q^{94} +(-1.53776 - 1.47382i) q^{95} +(0.886233 + 0.230757i) q^{96} +(3.87286 - 6.28992i) q^{97} +(-8.75737 + 0.745362i) q^{98} +(-1.24595 + 1.19415i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q - q^{2} - 20 q^{3} - 23 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} - 9 q^{8} - 20 q^{9} - 16 q^{10} - 14 q^{11} - 23 q^{12} - 14 q^{13} - 28 q^{14} - 4 q^{15} - 37 q^{16} - 20 q^{17} - q^{18} + 42 q^{19}+ \cdots - 14 q^{99}+O(q^{100}) $ 720 * q - q^2 - 20 * q^3 - 23 * q^4 - 4 * q^5 - q^6 - 12 * q^7 - 9 * q^8 - 20 * q^9 - 16 * q^10 - 14 * q^11 - 23 * q^12 - 14 * q^13 - 28 * q^14 - 4 * q^15 - 37 * q^16 - 20 * q^17 - q^18 + 42 * q^19 - 34 * q^20 - 12 * q^21 - 32 * q^22 - 18 * q^23 - 9 * q^24 - 48 * q^25 - 48 * q^26 - 20 * q^27 - 80 * q^28 + 7 * q^29 - 16 * q^30 - 40 * q^31 - 59 * q^32 - 14 * q^33 + 22 * q^34 - 32 * q^35 - 23 * q^36 - 44 * q^37 - 36 * q^38 + 60 * q^39 + 124 * q^40 + 176 * q^41 + 46 * q^42 - 42 * q^43 + 76 * q^44 - 4 * q^45 - 88 * q^46 - 26 * q^47 - 37 * q^48 - 94 * q^49 - 87 * q^50 + 54 * q^51 + 206 * q^52 - 54 * q^53 - q^54 - 74 * q^55 - 107 * q^56 - 32 * q^57 + 13 * q^58 - 50 * q^59 - 34 * q^60 - 86 * q^61 - 83 * q^62 - 12 * q^63 + 99 * q^64 + 52 * q^65 + 42 * q^66 - 68 * q^67 + 63 * q^68 - 18 * q^69 - 62 * q^70 - 68 * q^71 - 9 * q^72 - 58 * q^73 - 82 * q^74 - 48 * q^75 - 145 * q^76 + 40 * q^77 + 26 * q^78 - 90 * q^79 + 325 * q^80 - 20 * q^81 + 62 * q^82 + 58 * q^83 - 80 * q^84 - 14 * q^85 - 153 * q^86 - 30 * q^87 - 152 * q^88 - 110 * q^89 - 16 * q^90 - 114 * q^91 - 110 * q^92 - 40 * q^93 + 102 * q^94 - 118 * q^95 - 59 * q^96 - 110 * q^97 - 154 * q^98 - 14 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/669\mathbb{Z}\right)^\times$.

$n$	$224$	$226$
$\chi(n)$	$1$	$e\left(\frac{23}{37}\right)$

Coefficient data

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

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

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

$2$	−1.27818	+	0.451610i	−0.903811	+	0.319337i	−0.744289	−	0.667858i	$-0.767211\pi$
$2$	−1.27818	+	0.451610i	−0.903811	+	0.319337i	−0.159522	+	0.987194i	$0.550995\pi$
$3$	0.372856	−	0.927889i	0.215269	−	0.535717i
$3$	0.372856	−	0.927889i	0.215269	−	0.535717i
$4$	−0.126276	+	0.101961i	−0.0631381	+	0.0509804i
$5$	−2.03001	−	3.29695i	−0.907850	−	1.47444i	−0.880079	−	0.474828i	$-0.842510\pi$
$5$	−2.03001	−	3.29695i	−0.907850	−	1.47444i	−0.0277709	−	0.999614i	$-0.508841\pi$
$6$	−0.0575340	+	1.35440i	−0.0234882	+	0.552930i
$7$	0.0912925	−	0.712916i	0.0345053	−	0.269457i	−0.965455	−	0.260569i	$-0.916090\pi$
$7$	0.0912925	−	0.712916i	0.0345053	−	0.269457i	0.999961	−	0.00888778i	$-0.00282911\pi$
$8$	1.53688	−	2.49605i	0.543368	−	0.882486i
$9$	−0.721956	−	0.691939i	−0.240652	−	0.230646i
$10$	4.08366	+	3.29733i	1.29137	+	1.04271i
$11$	0.0732452	−	1.72425i	0.0220843	−	0.519881i	−0.953649	−	0.300920i	$-0.902706\pi$
$11$	0.0732452	−	1.72425i	0.0220843	−	0.519881i	0.975734	−	0.218961i	$-0.0702666\pi$
$12$	0.0475255	+	0.155187i	0.0137194	+	0.0447986i
$13$	−0.0228080	−	0.0567600i	−0.00632581	−	0.0157424i	0.924693	−	0.380714i	$-0.124322\pi$
$13$	−0.0228080	−	0.0567600i	−0.00632581	−	0.0157424i	−0.931019	+	0.364972i	$0.881079\pi$
$14$	0.205272	+	0.952464i	0.0548612	+	0.254557i
$15$	−3.81611	+	0.654338i	−0.985315	+	0.168949i
$16$	−0.768780	+	3.56715i	−0.192195	+	0.891788i
$17$	0.0857237	−	2.01800i	0.0207911	−	0.489438i	−0.958269	−	0.285867i	$-0.907718\pi$
$17$	0.0857237	−	2.01800i	0.0207911	−	0.489438i	0.979060	−	0.203570i	$-0.0652546\pi$
$18$	1.23528	+	0.558381i	0.291158	+	0.131612i
$19$	0.532378	−	0.138620i	0.122136	−	0.0318017i	−0.190408	−	0.981705i	$-0.560981\pi$
$19$	0.532378	−	0.138620i	0.122136	−	0.0318017i	0.312544	+	0.949903i	$0.398819\pi$
$20$	0.592502	+	0.209344i	0.132488	+	0.0468108i
$21$	−0.627468	−	0.350525i	−0.136925	−	0.0764907i
$22$	0.685068	+	2.23698i	0.146057	+	0.476926i
$23$	0.737605	+	1.19795i	0.153801	+	0.249789i	0.919221	−	0.393742i	$-0.128820\pi$
$23$	0.737605	+	1.19795i	0.153801	+	0.249789i	−0.765419	+	0.643532i	$0.777468\pi$
$24$	−1.74302	−	2.35672i	−0.355793	−	0.481063i
$25$	−4.49792	+	8.92109i	−0.899584	+	1.78422i
$26$	0.0547862	+	0.0622492i	0.0107445	+	0.0122081i
$27$	−0.911228	+	0.411901i	−0.175366	+	0.0792704i
$28$	0.0611615	+	0.0993325i	0.0115584	+	0.0187721i
$29$	0.209048	−	0.969985i	0.0388192	−	0.180122i	−0.953988	−	0.299844i	$-0.903065\pi$
$29$	0.209048	−	0.969985i	0.0388192	−	0.180122i	0.992807	+	0.119722i	$0.0382005\pi$
$30$	4.58217	−	2.55976i	0.836587	−	0.467345i
$31$	−9.11271	+	0.775606i	−1.63669	+	0.139303i	−0.866727	−	0.498784i	$-0.833780\pi$
$31$	−9.11271	+	0.775606i	−1.63669	+	0.139303i	−0.769965	+	0.638087i	$0.779726\pi$
$32$	0.116321	+	0.908365i	0.0205628	+	0.160578i
$33$	−1.57260	−	0.710861i	−0.273755	−	0.123745i
$34$	0.801780	+	2.61809i	0.137504	+	0.448998i
$35$	−2.53577	+	1.14624i	−0.428624	+	0.193750i
$36$	0.161717	+	0.0137641i	0.0269528	+	0.00229402i
$37$	−0.135454	−	3.18870i	−0.0222685	−	0.524219i	−0.975239	−	0.221155i	$-0.929017\pi$
$37$	−0.135454	−	3.18870i	−0.0222685	−	0.524219i	0.952970	−	0.303064i	$-0.0980096\pi$
$38$	−0.617873	+	0.417609i	−0.100232	+	0.0677451i
$39$	−0.0611711			−0.00979521
$40$	−11.3492			−1.79447
$41$	−6.71389	+	4.53780i	−1.04853	+	0.708685i	−0.957872	−	0.287197i	$-0.907277\pi$
$41$	−6.71389	+	4.53780i	−1.04853	+	0.708685i	−0.0906622	+	0.995882i	$0.528898\pi$
$42$	0.960318	+	0.164663i	0.148180	+	0.0254081i
$43$	0.224685	+	0.445635i	0.0342641	+	0.0679587i	0.909411	−	0.415898i	$-0.136533\pi$
$43$	0.224685	+	0.445635i	0.0342641	+	0.0679587i	−0.875147	+	0.483857i	$0.839235\pi$
$44$	0.166557	+	0.225200i	0.0251094	+	0.0339501i
$45$	−0.815708	+	3.78490i	−0.121599	+	0.564220i
$46$	−1.48380	−	1.19808i	−0.218774	−	0.176648i
$47$	0.0791304	+	0.0206040i	0.0115424	+	0.00300540i	0.257745	−	0.966213i	$-0.417021\pi$
$47$	0.0791304	+	0.0206040i	0.0115424	+	0.00300540i	−0.246202	+	0.969218i	$0.579183\pi$
$48$	3.02328	+	2.04338i	0.436373	+	0.294936i
$49$	6.27422	+	1.63368i	0.896317	+	0.233383i
$50$	1.72030	−	13.4341i	0.243287	−	1.89986i
$51$	−1.84052	−	0.831968i	−0.257724	−	0.116499i
$52$	0.00866741	+	0.00484190i	0.00120195	+	0.000671451i
$53$	−2.02494	+	2.30078i	−0.278147	+	0.316036i	−0.872926	−	0.487853i	$-0.837780\pi$
$53$	−2.02494	+	2.30078i	−0.278147	+	0.316036i	0.594779	+	0.803889i	$0.297240\pi$
$54$	0.978696	−	0.938004i	0.133184	−	0.127646i
$55$	−5.83345	+	3.25876i	−0.786583	+	0.439412i
$56$	−1.63917	−	1.32353i	−0.219043	−	0.176865i
$57$	0.0698762	−	0.545673i	0.00925532	−	0.0722761i
$58$	0.170854	+	1.33422i	0.0224342	+	0.175192i
$59$	1.80760	−	5.90243i	0.235329	−	0.768431i	−0.757911	−	0.652358i	$-0.773780\pi$
$59$	1.80760	−	5.90243i	0.235329	−	0.768431i	0.993241	−	0.116073i	$-0.0370308\pi$
$60$	0.415167	−	0.471721i	0.0535978	−	0.0608989i
$61$	0.123148	+	0.306465i	0.0157674	+	0.0392388i	0.935565	−	0.353154i	$-0.114891\pi$
$61$	0.123148	+	0.306465i	0.0157674	+	0.0392388i	−0.919798	+	0.392393i	$0.871647\pi$
$62$	11.2974	−	5.10676i	1.43477	−	0.648559i
$63$	−0.559203	+	0.451525i	−0.0704530	+	0.0568868i
$64$	−3.84454	−	7.62520i	−0.480568	−	0.953150i
$65$	−0.140834	+	0.190421i	−0.0174683	+	0.0236188i
$66$	2.33110	+	0.198406i	0.286939	+	0.0244221i
$67$	−8.59660	+	6.94127i	−1.05024	+	0.848011i	−0.988672	−	0.150092i	$-0.952043\pi$
$67$	−8.59660	+	6.94127i	−1.05024	+	0.848011i	−0.0615693	+	0.998103i	$0.519611\pi$
$68$	0.194932	+	0.263566i	0.0236390	+	0.0319621i
$69$	1.38658	−	0.237754i	0.166925	−	0.0286222i
$70$	2.72352	−	2.61029i	0.325523	−	0.311989i
$71$	1.58454	−	5.17406i	0.188050	−	0.614048i	−0.811509	−	0.584340i	$-0.801353\pi$
$71$	1.58454	−	5.17406i	0.188050	−	0.614048i	0.999559	−	0.0297073i	$-0.00945753\pi$
$72$	−2.83667	+	0.738612i	−0.334305	+	0.0870462i
$73$	2.75665	+	1.53996i	0.322641	+	0.180238i	0.640617	−	0.767861i	$-0.278679\pi$
$73$	2.75665	+	1.53996i	0.322641	+	0.180238i	−0.317976	+	0.948099i	$0.603003\pi$
$74$	1.61318	+	4.01456i	0.187529	+	0.466683i
$75$	6.60070	+	7.49985i	0.762183	+	0.866009i
$76$	−0.0530927	+	0.0717861i	−0.00609016	+	0.00823443i
$77$	−1.22256	−	0.209629i	−0.139323	−	0.0238894i
$78$	0.0781877	−	0.0276255i	0.00885302	−	0.00312797i
$79$	−7.15005	+	4.83259i	−0.804443	+	0.543709i	−0.891780	−	0.452470i	$-0.850543\pi$
$79$	−7.15005	+	4.83259i	−0.804443	+	0.543709i	0.0873362	+	0.996179i	$0.472165\pi$
$80$	13.3214	−	4.70674i	1.48937	−	0.526229i
$81$	0.0424412	+	0.999099i	0.00471569	+	0.111011i
$82$	6.53225	−	8.83219i	0.721367	−	0.975352i
$83$	2.53843	−	5.03467i	0.278628	−	0.552627i	−0.709784	−	0.704420i	$-0.751207\pi$
$83$	2.53843	−	5.03467i	0.278628	−	0.552627i	0.988412	+	0.151793i	$0.0485047\pi$
$84$	0.114974	−	0.0197143i	0.0125447	−	0.00215100i
$85$	−6.82728	+	3.81395i	−0.740523	+	0.413681i
$86$	−0.488441	−	0.468133i	−0.0526699	−	0.0504800i
$87$	−0.822093	−	0.555638i	−0.0881376	−	0.0595707i
$88$	−4.19124	−	2.83278i	−0.446787	−	0.301976i
$89$	−3.55048	+	5.76634i	−0.376350	+	0.611231i	−0.982971	−	0.183760i	$-0.941173\pi$
$89$	−3.55048	+	5.76634i	−0.376350	+	0.611231i	0.606621	+	0.794991i	$0.292524\pi$
$90$	−0.666676	−	5.20617i	−0.0702738	−	0.548779i
$91$	−0.0425473	+	0.0110785i	−0.00446017	+	0.00116134i
$92$	−0.215286	−	0.0760653i	−0.0224451	−	0.00793035i
$93$	−2.67806	+	8.74477i	−0.277702	+	0.906791i
$94$	−0.110448	+	0.00940051i	−0.0113918	+	0.000969589i
$95$	−1.53776	−	1.47382i	−0.157771	−	0.151211i
$96$	0.886233	+	0.230757i	0.0904508	+	0.0235516i
$97$	3.87286	−	6.28992i	0.393229	−	0.638645i	−0.592774	−	0.805369i	$-0.701967\pi$
$97$	3.87286	−	6.28992i	0.393229	−	0.638645i	0.986004	+	0.166724i	$0.0533187\pi$
$98$	−8.75737	+	0.745362i	−0.884628	+	0.0752929i
$99$	−1.24595	+	1.19415i	−0.125223	+	0.120017i
$100$	−0.341622	−	1.58513i	−0.0341622	−	0.158513i
$101$	−5.26047	−	5.97705i	−0.523436	−	0.594739i	0.427543	−	0.903995i	$-0.359379\pi$
$101$	−5.26047	−	5.97705i	−0.523436	−	0.594739i	−0.950979	+	0.309256i	$0.899920\pi$
$102$	2.72824	+	0.232208i	0.270136	+	0.0229920i
$103$	−5.97984	+	14.8814i	−0.589211	+	1.46631i	0.274133	+	0.961692i	$0.411609\pi$
$103$	−5.97984	+	14.8814i	−0.589211	+	1.46631i	−0.863344	+	0.504616i	$0.831634\pi$
$104$	−0.176729	−	0.0303032i	−0.0173297	−	0.00297147i
$105$	0.118106	+	2.78030i	0.0115259	+	0.271330i
$106$	1.54919	−	3.85530i	0.150470	−	0.374460i
$107$	−6.44903	−	12.7909i	−0.623451	−	1.23654i	−0.955975	−	0.293447i	$-0.905197\pi$
$107$	−6.44903	−	12.7909i	−0.623451	−	1.23654i	0.332524	−	0.943095i	$-0.392100\pi$
$108$	0.0730686	−	0.144923i	0.00703103	−	0.0139452i
$109$	−2.21772	−	10.2902i	−0.212419	−	0.985626i	−0.950454	−	0.310864i	$-0.899381\pi$
$109$	−2.21772	−	10.2902i	−0.212419	−	0.985626i	0.738036	−	0.674762i	$-0.235754\pi$
$110$	5.98452	−	6.79974i	0.570602	−	0.648329i
$111$	−3.00926	−	1.06324i	−0.285627	−	0.100918i
$112$	2.47290	+	0.873730i	0.233667	+	0.0825597i
$113$	−5.06094	+	5.75034i	−0.476093	+	0.540947i	−0.938299	−	0.345826i	$-0.887599\pi$
$113$	−5.06094	+	5.75034i	−0.476093	+	0.540947i	0.462206	+	0.886773i	$0.347058\pi$
$114$	0.157117	+	0.729026i	0.0147154	+	0.0682795i
$115$	2.45223	−	4.86370i	0.228671	−	0.453542i
$116$	0.0725027	+	0.143801i	0.00673171	+	0.0133515i
$117$	−0.0228080	+	0.0567600i	−0.00210860	+	0.00524746i
$118$	0.355158	+	8.36071i	0.0326950	+	0.769665i
$119$	−1.43084	−	0.245342i	−0.131165	−	0.0224905i
$120$	−4.23163	+	10.5308i	−0.386294	+	0.961329i
$121$	7.99270	+	0.680279i	0.726609	+	0.0618436i
$122$	−0.295808	−	0.336103i	−0.0267812	−	0.0304293i
$123$	1.70726	+	7.92170i	0.153938	+	0.714275i
$124$	1.07164	−	1.02708i	0.0962358	−	0.0922345i
$125$	19.2540	−	1.63875i	1.72213	−	0.146575i
$126$	0.510850	−	0.829673i	0.0455101	−	0.0739131i
$127$	17.3137	+	4.50814i	1.53634	+	0.400033i	0.921425	−	0.388557i	$-0.127026\pi$
$127$	17.3137	+	4.50814i	1.53634	+	0.400033i	0.614919	+	0.788590i	$0.289189\pi$
$128$	7.03533	+	6.74282i	0.621841	+	0.595986i
$129$	0.497275	−	0.0423243i	0.0437826	−	0.00372645i
$130$	0.0940159	−	0.306994i	0.00824574	−	0.0269252i
$131$	−15.1521	−	5.35356i	−1.32384	−	0.467743i	−0.424673	−	0.905347i	$-0.639611\pi$
$131$	−15.1521	−	5.35356i	−1.32384	−	0.467743i	−0.899168	+	0.437604i	$0.855827\pi$
$132$	0.271062	−	0.0705791i	0.0235929	−	0.00614312i
$133$	−0.0502226	−	0.392196i	−0.00435485	−	0.0340077i
$134$	7.85326	−	12.7545i	0.678418	−	1.10182i
$135$	3.20783	+	2.16811i	0.276086	+	0.186601i
$136$	−4.90529	−	3.31539i	−0.420625	−	0.284293i
$137$	9.43649	+	9.04414i	0.806213	+	0.772693i	0.977141	−	0.212591i	$-0.0681901\pi$
$137$	9.43649	+	9.04414i	0.806213	+	0.772693i	−0.170928	+	0.985284i	$0.554677\pi$
$138$	−1.66493	+	0.930087i	−0.141728	+	0.0791743i
$139$	18.1813	−	3.11750i	1.54212	−	0.264423i	0.665791	−	0.746138i	$-0.268094\pi$
$139$	18.1813	−	3.11750i	1.54212	−	0.264423i	0.876328	+	0.481715i	$0.159986\pi$
$140$	0.203336	−	0.403293i	0.0171850	−	0.0340845i
$141$	0.0486225	−	0.0657419i	0.00409475	−	0.00553647i
$142$	0.311331	+	7.32898i	0.0261263	+	0.615034i
$143$	−0.0995389	+	0.0351693i	−0.00832386	+	0.00294101i
$144$	3.02328	−	2.04338i	0.251940	−	0.170282i
$145$	−3.62236	+	1.27986i	−0.300821	+	0.106287i
$146$	−4.21896	−	0.723413i	−0.349163	−	0.0598701i
$147$	3.85525	−	5.21265i	0.317976	−	0.429932i
$148$	0.342227	+	0.388845i	0.0281309	+	0.0319629i
$149$	−1.36342	−	3.39301i	−0.111696	−	0.277966i	0.861573	−	0.507633i	$-0.169480\pi$
$149$	−1.36342	−	3.39301i	−0.111696	−	0.277966i	−0.973269	+	0.229667i	$0.926236\pi$
$150$	−11.8239	−	6.60523i	−0.965418	−	0.539315i
$151$	−9.37790	+	2.44181i	−0.763162	+	0.198712i	−0.613144	−	0.789971i	$-0.710095\pi$
$151$	−9.37790	+	2.44181i	−0.763162	+	0.198712i	−0.150018	+	0.988683i	$0.547933\pi$
$152$	0.472196	−	1.54188i	0.0383002	−	0.125063i
$153$	−1.45822	+	1.39759i	−0.117890	+	0.112989i
$154$	1.65732	−	0.284176i	0.133551	−	0.0228996i
$155$	21.0561	+	28.4697i	1.69126	+	2.28674i
$156$	0.00772445	−	0.00623706i	0.000618451	−	0.000499364i
$157$	6.66217	+	0.567034i	0.531699	+	0.0452542i	0.347581	−	0.937650i	$-0.387003\pi$
$157$	6.66217	+	0.567034i	0.531699	+	0.0452542i	0.184118	+	0.982904i	$0.441057\pi$
$158$	6.95661	−	9.40596i	0.553438	−	0.748298i
$159$	1.37986	+	2.73678i	0.109430	+	0.217041i
$160$	2.75870	−	2.22750i	0.218095	−	0.176099i
$161$	0.921373	−	0.416487i	0.0726144	−	0.0328238i
$162$	−0.505451	−	1.25786i	−0.0397120	−	0.0988270i
$163$	8.10966	−	9.21437i	0.635198	−	0.721725i	−0.340647	−	0.940191i	$-0.610646\pi$
$163$	8.10966	−	9.21437i	0.635198	−	0.721725i	0.975844	+	0.218466i	$0.0701054\pi$
$164$	0.385126	−	1.25757i	0.0300733	−	0.0981997i
$165$	0.848729	+	6.62785i	0.0660735	+	0.515977i
$166$	−0.970861	+	7.58160i	−0.0753535	+	0.588446i
$167$	−3.33380	−	2.69185i	−0.257977	−	0.208302i	0.490538	−	0.871420i	$-0.336800\pi$
$167$	−3.33380	−	2.69185i	−0.257977	−	0.208302i	−0.748515	+	0.663118i	$0.769233\pi$
$168$	−1.83927	+	1.02748i	−0.141903	+	0.0792715i
$169$	9.38273	−	8.99262i	0.721748	−	0.691740i
$170$	7.00408	−	7.95819i	0.537189	−	0.610365i
$171$	−0.480270	−	0.268295i	−0.0367272	−	0.0205170i
$172$	−0.0738096	−	0.0333641i	−0.00562793	−	0.00254399i
$173$	−0.272844	+	2.13068i	−0.0207439	+	0.161992i	−0.998960	−	0.0455974i	$-0.985481\pi$
$173$	−0.272844	+	2.13068i	−0.0207439	+	0.161992i	0.978216	+	0.207590i	$0.0665619\pi$
$174$	1.30172	+	0.338940i	0.0986828	+	0.0256950i
$175$	5.94936	+	4.02107i	0.449729	+	0.303964i
$176$	6.09435	+	1.58685i	0.459379	+	0.119613i
$177$	−4.80283	−	3.87801i	−0.361002	−	0.291489i
$178$	1.93401	−	8.97386i	0.144960	−	0.672619i
$179$	4.58148	+	6.19457i	0.342436	+	0.463004i	0.941165	−	0.337948i	$-0.109733\pi$
$179$	4.58148	+	6.19457i	0.342436	+	0.463004i	−0.598729	+	0.800952i	$0.704327\pi$
$180$	−0.282907	−	0.561113i	−0.0210867	−	0.0418229i
$181$	14.4128	+	2.47132i	1.07129	+	0.183692i	0.677512	−	0.735512i	$-0.263058\pi$
$181$	14.4128	+	2.47132i	1.07129	+	0.183692i	0.393782	+	0.919204i	$0.371166\pi$
$182$	0.0493800	−	0.0333751i	0.00366029	−	0.00247392i
$183$	0.330282			0.0244151
$184$	4.12374			0.304006
$185$	−10.2380	+	6.91969i	−0.752713	+	0.508745i
$186$	−0.526187	−	12.3868i	−0.0385819	−	0.908247i
$187$	−3.47326	−	0.295618i	−0.253990	−	0.0216177i
$188$	−0.0120931	+	0.00546642i	−0.000881979	+	0.000398680i
$189$	0.210463	+	0.687233i	0.0153089	+	0.0499888i
$190$	2.63113	+	1.18934i	0.190882	+	0.0862841i
$191$	−0.255278	−	1.99350i	−0.0184713	−	0.144245i	0.980039	−	0.198804i	$-0.0637057\pi$
$191$	−0.255278	−	1.99350i	−0.0184713	−	0.144245i	−0.998511	+	0.0545592i	$0.982625\pi$
$192$	−8.50880	+	0.724206i	−0.614070	+	0.0522650i
$193$	−5.48493	+	3.06406i	−0.394814	+	0.220556i	−0.672470	−	0.740124i	$-0.734767\pi$
$193$	−5.48493	+	3.06406i	−0.394814	+	0.220556i	0.277656	+	0.960680i	$0.410442\pi$
$194$	−2.10962	+	9.78869i	−0.151462	+	0.702787i
$195$	0.124178	+	0.201678i	0.00889258	+	0.0144425i
$196$	−0.958855	+	0.433430i	−0.0684896	+	0.0309593i
$197$	−9.50601	−	10.8009i	−0.677275	−	0.769534i	0.305927	−	0.952055i	$-0.401034\pi$
$197$	−9.50601	−	10.8009i	−0.677275	−	0.769534i	−0.983202	+	0.182521i	$0.941574\pi$
$198$	1.05327	−	2.08903i	0.0748523	−	0.148461i
$199$	−8.16240	−	11.0363i	−0.578618	−	0.782343i	0.413113	−	0.910680i	$-0.364441\pi$
$199$	−8.16240	−	11.0363i	−0.578618	−	0.782343i	−0.991731	+	0.128337i	$0.959036\pi$
$200$	15.3547	+	24.9376i	1.08574	+	1.76336i
$201$	3.23543	+	10.5648i	0.228210	+	0.745182i
$202$	9.42312	+	5.26407i	0.663009	+	0.370379i
$203$	−0.672433	−	0.237586i	−0.0471955	−	0.0166752i
$204$	0.317242	−	0.0826034i	0.0222114	−	0.00578339i
$205$	28.5902	+	12.9236i	1.99683	+	0.902622i
$206$	0.922726	−	21.7217i	0.0642894	−	1.51342i
$207$	0.296388	−	1.37524i	0.0206004	−	0.0955860i
$208$	0.220006	−	0.0377238i	0.0152547	−	0.00261568i
$209$	−0.200022	−	0.928105i	−0.0138358	−	0.0641984i
$210$	−1.40657	−	3.50039i	−0.0970627	−	0.241550i
$211$	3.68782	+	12.0420i	0.253880	+	0.829005i	0.988591	+	0.150625i	$0.0481286\pi$
$211$	3.68782	+	12.0420i	0.253880	+	0.829005i	−0.734711	+	0.678380i	$0.762682\pi$
$212$	0.0211122	−	0.496998i	0.00144999	−	0.0341340i
$213$	−4.21015	−	3.39946i	−0.288475	−	0.232927i
$214$	14.0195	+	13.4366i	0.958355	+	0.918509i
$215$	1.01313	−	1.64542i	0.0690946	−	0.112217i
$216$	−0.372321	+	2.90751i	−0.0253333	+	0.197831i
$217$	−0.278980	+	6.56740i	−0.0189384	+	0.445824i
$218$	7.48182	+	12.1512i	0.506733	+	0.822986i
$219$	2.45674	−	1.98368i	0.166011	−	0.134045i
$220$	0.404360	−	1.00629i	0.0272619	−	0.0678439i
$221$	−0.116497	+	0.0411610i	−0.00783644	+	0.00276879i
$222$	4.32655			0.290379
$223$	−7.29166	−	13.0319i	−0.488286	−	0.872684i
$223$	−7.29166	−	13.0319i	−0.488286	−	0.872684i
$224$	0.658207			0.0439783
$225$	9.42015	−	3.32835i	0.628010	−	0.221890i
$226$	3.87188	−	9.63555i	0.257554	−	0.640947i
$227$	−2.71188	+	2.18969i	−0.179994	+	0.145335i	−0.714000	−	0.700146i	$-0.753118\pi$
$227$	−2.71188	+	2.18969i	−0.179994	+	0.145335i	0.534006	+	0.845480i	$0.320686\pi$
$228$	0.0468136	+	0.0760301i	0.00310031	+	0.00503522i
$229$	1.19659	−	28.1686i	0.0790729	−	1.86144i	−0.323729	−	0.946150i	$-0.604937\pi$
$229$	1.19659	−	28.1686i	0.0790729	−	1.86144i	0.402802	−	0.915287i	$-0.368036\pi$
$230$	−0.937893	+	7.32414i	−0.0618428	+	0.482939i
$231$	−0.650351	+	1.05624i	−0.0427899	+	0.0694953i
$232$	−2.09985	−	2.01254i	−0.137862	−	0.132130i
$233$	2.73897	+	2.21157i	0.179436	+	0.144884i	0.713747	−	0.700403i	$-0.246997\pi$
$233$	2.73897	+	2.21157i	0.179436	+	0.144884i	−0.534311	+	0.845288i	$0.679429\pi$
$234$	0.00351942	−	0.0828499i	0.000230072	−	0.00541607i
$235$	−0.0927056	−	0.302716i	−0.00604745	−	0.0197470i
$236$	0.373560	+	0.929640i	0.0243167	+	0.0605144i
$237$	1.81816	+	8.43631i	0.118102	+	0.547998i
$238$	1.93967	−	0.332590i	0.125730	−	0.0215586i
$239$	2.90365	−	13.4730i	0.187822	−	0.871495i	−0.781154	−	0.624338i	$-0.785369\pi$
$239$	2.90365	−	13.4730i	0.187822	−	0.871495i	0.968976	−	0.247157i	$-0.0794962\pi$
$240$	0.599627	−	14.1157i	0.0387058	−	0.911164i
$241$	−26.9213	−	12.1692i	−1.73416	−	0.783888i	−0.993737	−	0.111743i	$-0.964357\pi$
$241$	−26.9213	−	12.1692i	−1.73416	−	0.783888i	−0.740419	−	0.672145i	$-0.765373\pi$
$242$	−10.5233	+	2.74007i	−0.676466	+	0.176138i
$243$	0.942877	+	0.333140i	0.0604856	+	0.0213709i
$244$	−0.0467980	−	0.0261429i	−0.00299594	−	0.00167363i
$245$	−7.35058	−	24.0022i	−0.469612	−	1.53344i
$246$	−5.75970	−	9.35435i	−0.367225	−	0.596411i
$247$	−0.0200106	−	0.0270561i	−0.00127324	−	0.00172154i
$248$	−12.0692	+	23.9378i	−0.766393	+	1.52005i
$249$	−3.72514	−	4.23259i	−0.236071	−	0.268229i
$250$	−23.8700	+	10.7899i	−1.50967	+	0.682414i
$251$	10.2184	+	16.5957i	0.644980	+	1.04751i	0.993892	+	0.110358i	$0.0351999\pi$
$251$	10.2184	+	16.5957i	0.644980	+	1.04751i	−0.348912	+	0.937155i	$0.613449\pi$
$252$	0.0245761	−	0.114034i	0.00154815	−	0.00718345i
$253$	2.11958	−	1.18407i	0.133257	−	0.0744419i
$254$	−24.1660	+	2.05683i	−1.51631	+	0.129057i
$255$	0.993324	+	7.75701i	0.0622044	+	0.485763i
$256$	3.52544	+	1.59360i	0.220340	+	0.0995999i
$257$	−7.37447	−	24.0802i	−0.460007	−	1.50208i	−0.821775	−	0.569812i	$-0.807016\pi$
$257$	−7.37447	−	24.0802i	−0.460007	−	1.50208i	0.361768	−	0.932268i	$-0.382173\pi$
$258$	−0.616494	+	0.278673i	−0.0383812	+	0.0173494i
$259$	−2.28564	−	0.194537i	−0.142023	−	0.0120879i
$260$	−0.00163143	−	0.0384052i	−0.000101177	−	0.00238179i
$261$	−0.822093	+	0.555638i	−0.0508863	+	0.0343931i
$262$	21.7848			1.34587
$263$	−5.60750			−0.345773			−0.172887	−	0.984942i	$-0.555309\pi$
$263$	−5.60750			−0.345773			−0.172887	+	0.984942i	$0.555309\pi$
$264$	−4.19124	+	2.83278i	−0.257953	+	0.174346i
$265$	11.6962	+	2.00552i	0.718493	+	0.123198i
$266$	0.241313	+	0.478616i	0.0147959	+	0.0293458i
$267$	4.02670	+	5.44446i	0.246430	+	0.333196i
$268$	0.377807	−	1.75303i	0.0230783	−	0.107084i
$269$	−18.6883	−	15.0897i	−1.13945	−	0.920038i	−0.141887	−	0.989883i	$-0.545317\pi$
$269$	−18.6883	−	15.0897i	−1.13945	−	0.920038i	−0.997558	+	0.0698451i	$0.977750\pi$
$270$	−5.07932	−	1.32255i	−0.309118	−	0.0804880i
$271$	−7.89499	−	5.33608i	−0.479587	−	0.324144i	0.296214	−	0.955121i	$-0.404276\pi$
$271$	−7.89499	−	5.33608i	−0.479587	−	0.324144i	−0.775801	+	0.630977i	$0.782654\pi$
$272$	7.13262	+	1.85719i	0.432479	+	0.112609i
$273$	−0.00558446	+	0.0436098i	−0.000337987	+	0.00263939i
$274$	−16.1460	−	7.29844i	−0.975413	−	0.440915i
$275$	15.0527	+	8.40896i	0.907713	+	0.507079i
$276$	−0.150851	+	0.171400i	−0.00908015	+	0.0103171i
$277$	−7.03519	+	6.74268i	−0.422703	+	0.405128i	−0.872976	−	0.487763i	$-0.837813\pi$
$277$	−7.03519	+	6.74268i	−0.422703	+	0.405128i	0.450273	+	0.892891i	$0.351327\pi$
$278$	−21.8311	+	12.1956i	−1.30934	+	0.731443i
$279$	7.11565	+	5.74549i	0.426003	+	0.343973i
$280$	−1.03610	+	8.09105i	−0.0619188	+	0.483533i
$281$	−0.789806	−	6.16771i	−0.0471159	−	0.367935i	−0.998249	−	0.0591532i	$-0.981160\pi$
$281$	−0.789806	−	6.16771i	−0.0471159	−	0.367935i	0.951133	−	0.308781i	$-0.0999211\pi$
$282$	−0.0324586	+	0.105989i	−0.00193288	+	0.00631153i
$283$	−11.9529	+	13.5811i	−0.710526	+	0.807315i	−0.988169	−	0.153370i	$-0.950987\pi$
$283$	−11.9529	+	13.5811i	−0.710526	+	0.807315i	0.277643	+	0.960684i	$0.410447\pi$
$284$	0.327462	+	0.814921i	0.0194313	+	0.0483567i
$285$	−1.94091	+	0.877345i	−0.114969	+	0.0519695i
$286$	0.111346	−	0.0899055i	0.00658402	−	0.00531623i
$287$	2.62214	+	5.20071i	0.154780	+	0.306988i
$288$	0.544555	−	0.736287i	0.0320882	−	0.0433861i
$289$	12.8738	+	1.09572i	0.757281	+	0.0644541i
$290$	4.05204	−	3.27179i	0.237944	−	0.192126i
$291$	−4.39233	−	5.93882i	−0.257483	−	0.348140i
$292$	−0.505114	+	0.0866105i	−0.0295596	+	0.00506850i
$293$	−7.78221	+	7.45864i	−0.454641	+	0.435738i	−0.884064	−	0.467365i	$-0.845203\pi$
$293$	−7.78221	+	7.45864i	−0.454641	+	0.435738i	0.429423	+	0.903103i	$0.358717\pi$
$294$	−2.57363	+	8.40378i	−0.150097	+	0.490118i
$295$	−23.1295	+	6.02245i	−1.34665	+	0.350641i
$296$	−8.16732	−	4.56254i	−0.474716	−	0.265192i
$297$	0.643477	+	1.60135i	0.0373383	+	0.0929200i
$298$	3.27502	+	3.72115i	0.189717	+	0.215560i
$299$	0.0511721	−	0.0691893i	0.00295936	−	0.00400132i
$300$	−1.59820	−	0.274039i	−0.0922723	−	0.0158217i
$301$	0.338212	−	0.119498i	0.0194942	−	0.00688775i
$302$	10.8839	−	7.35623i	0.626298	−	0.423304i
$303$	−7.50744	+	2.65255i	−0.431291	+	0.152385i
$304$	0.0851986	+	2.00564i	0.00488648	+	0.115031i
$305$	0.760408	−	1.02814i	0.0435408	−	0.0588711i
$306$	1.23271	−	2.44493i	0.0704691	−	0.139767i
$307$	10.6615	−	1.82809i	0.608481	−	0.104335i	0.143493	−	0.989651i	$-0.454167\pi$
$307$	10.6615	−	1.82809i	0.608481	−	0.104335i	0.464988	+	0.885317i	$0.346058\pi$
$308$	0.175754	−	0.0981819i	0.0100145	−	0.00559444i
$309$	11.5787	+	11.0973i	0.658687	+	0.631301i
$310$	−39.7707	−	26.8803i	−2.25882	−	1.52670i
$311$	−21.4670	−	14.5092i	−1.21728	−	0.822740i	−0.228712	−	0.973494i	$-0.573451\pi$
$311$	−21.4670	−	14.5092i	−1.21728	−	0.822740i	−0.988571	+	0.150754i	$0.951830\pi$
$312$	−0.0940125	+	0.152686i	−0.00532241	+	0.00864414i
$313$	−0.102242	−	0.798419i	−0.00577904	−	0.0451293i	0.988754	−	0.149550i	$-0.0477824\pi$
$313$	−0.102242	−	0.798419i	−0.00577904	−	0.0451293i	−0.994533	+	0.104420i	$0.966701\pi$
$314$	−8.77153	+	2.28393i	−0.495006	+	0.128890i
$315$	2.62385	+	0.927064i	0.147837	+	0.0522342i
$316$	0.410146	−	1.33927i	0.0230725	−	0.0753396i
$317$	−21.0511	+	1.79171i	−1.18235	+	0.100633i	−0.659441	−	0.751756i	$-0.729207\pi$
$317$	−21.0511	+	1.79171i	−1.18235	+	0.100633i	−0.522908	+	0.852389i	$0.675153\pi$
$318$	−2.99966	−	2.87495i	−0.168213	−	0.161219i
$319$	−1.65718	−	0.431497i	−0.0927844	−	0.0241592i
$320$	−17.3354	+	28.1545i	−0.969080	+	1.57389i
$321$	−14.2731	+	1.21482i	−0.796646	+	0.0678046i
$322$	−0.989592	+	0.948447i	−0.0551478	+	0.0528549i
$323$	−0.234099	−	1.08622i	−0.0130256	−	0.0604391i
$324$	−0.107228	−	0.121835i	−0.00595713	−	0.00676861i
$325$	0.608949	+	0.0518292i	0.0337784	+	0.00287497i
$326$	−6.20432	+	15.4400i	−0.343625	+	0.855145i
$327$	−10.3751	−	1.77899i	−0.573744	−	0.0983783i
$328$	1.00813	+	23.7322i	0.0556648	+	1.31039i
$329$	0.0219129	−	0.0545324i	0.00120810	−	0.00300647i
$330$	−4.07803	−	8.08830i	−0.224488	−	0.445246i
$331$	−3.85404	+	7.64404i	−0.211837	+	0.420154i	−0.973781	−	0.227489i	$-0.926948\pi$
$331$	−3.85404	+	7.64404i	−0.211837	+	0.420154i	0.761943	+	0.647644i	$0.224246\pi$
$332$	0.192796	+	0.894578i	0.0105811	+	0.0490964i
$333$	−2.10859	+	2.39583i	−0.115550	+	0.131290i
$334$	5.47686	+	1.93510i	0.299681	+	0.105884i
$335$	40.3362	+	14.2517i	2.20380	+	0.778653i
$336$	1.73276	−	1.96880i	0.0945298	−	0.107407i
$337$	−5.28979	−	24.5447i	−0.288153	−	1.33704i	−0.857307	−	0.514805i	$-0.827864\pi$
$337$	−5.28979	−	24.5447i	−0.288153	−	1.33704i	0.569154	−	0.822231i	$-0.307271\pi$
$338$	−7.93167	+	15.7315i	−0.431426	+	0.855682i
$339$	3.44868	+	6.84004i	0.187306	+	0.371500i
$340$	0.473249	−	1.17773i	0.0256655	−	0.0638712i
$341$	0.669875	+	15.7694i	0.0362758	+	0.853960i
$342$	0.735037	+	0.126035i	0.0397463	+	0.00681518i
$343$	3.61337	−	8.99221i	0.195103	−	0.485533i
$344$	1.45764	+	0.124063i	0.0785906	+	0.00668905i
$345$	−3.59864	−	4.08885i	−0.193745	−	0.220137i
$346$	−0.613492	−	2.84661i	−0.0329815	−	0.153035i
$347$	−18.0960	+	17.3437i	−0.971447	+	0.931056i	−0.997644	−	0.0686005i	$-0.978147\pi$
$347$	−18.0960	+	17.3437i	−0.971447	+	0.931056i	0.0261974	+	0.999657i	$0.491660\pi$
$348$	0.160464	−	0.0136575i	0.00860178	−	0.000732119i
$349$	12.0238	−	19.5279i	0.643618	−	1.04530i	−0.350454	−	0.936580i	$-0.613973\pi$
$349$	12.0238	−	19.5279i	0.643618	−	1.04530i	0.994072	−	0.108723i	$-0.0346760\pi$
$350$	−9.42031	−	2.45286i	−0.503537	−	0.131111i
$351$	0.0441628	+	0.0423266i	0.00235724	+	0.00225923i
$352$	1.57477	−	0.134032i	0.0839354	−	0.00714395i
$353$	1.96006	−	6.40026i	0.104323	−	0.340651i	−0.888712	−	0.458465i	$-0.848399\pi$
$353$	1.96006	−	6.40026i	0.104323	−	0.340651i	0.993036	+	0.117814i	$0.0375886\pi$
$354$	7.89023	+	2.78780i	0.419361	+	0.148170i
$355$	−20.2753	+	5.27927i	−1.07610	+	0.280194i
$356$	−0.139601	−	1.09016i	−0.00739881	−	0.0577784i
$357$	−0.761149	+	1.23618i	−0.0402843	+	0.0654258i
$358$	−8.65349	−	5.84874i	−0.457351	−	0.309115i
$359$	−5.93480	−	4.01122i	−0.313227	−	0.211704i	0.393266	−	0.919425i	$-0.371345\pi$
$359$	−5.93480	−	4.01122i	−0.313227	−	0.211704i	−0.706492	+	0.707721i	$0.749724\pi$
$360$	8.19365	+	7.85297i	0.431843	+	0.413888i
$361$	−16.3231	+	9.11861i	−0.859108	+	0.479927i
$362$	−19.5382	+	3.35017i	−1.02691	+	0.176081i
$363$	3.61136	−	7.16270i	0.189547	−	0.375944i
$364$	0.00424314	−	0.00573710i	0.000222401	−	0.000300706i
$365$	−0.518873	−	12.2147i	−0.0271590	−	0.639345i
$366$	−0.422160	+	0.149159i	−0.0220666	+	0.00779664i
$367$	8.22625	−	5.55998i	0.429407	−	0.290228i	−0.326142	−	0.945321i	$-0.605749\pi$
$367$	8.22625	−	5.55998i	0.429407	−	0.290228i	0.755549	+	0.655092i	$0.227370\pi$
$368$	−4.84032	+	1.71019i	−0.252319	+	0.0891500i
$369$	7.98702	+	1.36951i	0.415787	+	0.0712939i
$370$	9.96103	−	13.4682i	0.517849	−	0.700178i
$371$	1.45540	+	1.65366i	0.0755607	+	0.0858536i
$372$	−0.553450	−	1.37731i	−0.0286950	−	0.0714104i
$373$	−26.2671	−	14.6737i	−1.36006	−	0.759774i	−0.374199	−	0.927348i	$-0.622082\pi$
$373$	−26.2671	−	14.6737i	−1.36006	−	0.759774i	−0.985860	+	0.167574i	$0.946407\pi$
$374$	4.57296	−	1.19071i	0.236462	−	0.0615700i
$375$	5.65838	−	18.4766i	0.292198	−	0.954126i
$376$	0.173042	−	0.165848i	0.00892397	−	0.00855294i
$377$	−0.0598243	+	0.0102579i	−0.00308111	+	0.000528309i
$378$	−0.579371	−	0.783361i	−0.0297996	−	0.0402917i
$379$	12.4130	−	10.0228i	0.637614	−	0.514837i	−0.254252	−	0.967138i	$-0.581829\pi$
$379$	12.4130	−	10.0228i	0.637614	−	0.514837i	0.891865	+	0.452301i	$0.149397\pi$
$380$	0.344454	+	0.0293174i	0.0176701	+	0.00150395i
$381$	10.6386	−	14.3843i	0.545031	−	0.736931i
$382$	1.22658	+	2.43277i	0.0627572	+	0.124471i
$383$	−12.1326	+	9.79641i	−0.619948	+	0.500573i	−0.886183	−	0.463335i	$-0.846653\pi$
$383$	−12.1326	+	9.79641i	−0.619948	+	0.500573i	0.266235	+	0.963908i	$0.414220\pi$
$384$	8.87975	−	4.01390i	0.453143	−	0.204834i
$385$	1.79067	+	4.45626i	0.0912612	+	0.227112i
$386$	5.62697	−	6.39348i	0.286405	−	0.325419i
$387$	0.146140	−	0.477197i	0.00742871	−	0.0242573i
$388$	0.152276	+	1.18915i	0.00773066	+	0.0603698i
$389$	0.105873	−	0.826775i	0.00536796	−	0.0419192i	−0.988995	−	0.147949i	$-0.952733\pi$
$389$	0.105873	−	0.826775i	0.00536796	−	0.0419192i	0.994363	+	0.106030i	$0.0338139\pi$
$390$	−0.249802	−	0.201701i	−0.0126492	−	0.0102135i
$391$	2.48069	−	1.38580i	0.125454	−	0.0700828i
$392$	13.7204	−	13.1500i	0.692987	−	0.664174i
$393$	−10.6171	+	12.0633i	−0.535559	+	0.608514i
$394$	17.0282	+	9.51253i	0.857869	+	0.479234i
$395$	30.4475	+	13.7631i	1.53198	+	0.692499i
$396$	0.0355777	−	0.277831i	0.00178785	−	0.0139615i
$397$	−19.8869	−	5.17816i	−0.998097	−	0.259884i	−0.283160	−	0.959073i	$-0.591383\pi$
$397$	−19.8869	−	5.17816i	−0.998097	−	0.259884i	−0.714937	+	0.699188i	$0.753545\pi$
$398$	15.4171	+	10.4202i	0.772791	+	0.522316i
$399$	−0.382640	−	0.0996316i	−0.0191559	−	0.00498782i
$400$	−28.3650	−	22.9031i	−1.41825	−	1.14516i
$401$	3.31777	−	15.3945i	0.165681	−	0.768764i	−0.815972	−	0.578091i	$-0.803798\pi$
$401$	3.31777	−	15.3945i	0.165681	−	0.768764i	0.981654	−	0.190673i	$-0.0610671\pi$
$402$	−8.90663	−	12.0426i	−0.444222	−	0.600628i
$403$	0.251866	+	0.499547i	0.0125464	+	0.0248842i
$404$	1.27370	+	0.218397i	0.0633688	+	0.0108657i
$405$	3.20783	−	2.16811i	0.159398	−	0.107734i
$406$	0.966787			0.0479808
$407$	−5.50803			−0.273023
$408$	−4.90529	+	3.31539i	−0.242848	+	0.164136i
$409$	−1.22851	−	28.9201i	−0.0607460	−	1.43001i	−0.728204	−	0.685360i	$-0.759645\pi$
$409$	−1.22851	−	28.9201i	−0.0607460	−	1.43001i	0.667458	−	0.744647i	$-0.267382\pi$
$410$	−42.3799	−	3.60706i	−2.09299	−	0.178140i
$411$	11.9104	−	5.38385i	0.587497	−	0.265566i
$412$	−0.762210	−	2.48888i	−0.0375514	−	0.122618i
$413$	−4.04292	−	1.82751i	−0.198939	−	0.0899261i
$414$	0.242237	+	1.89166i	0.0119053	+	0.0929701i
$415$	−21.7521	+	1.85138i	−1.06777	+	0.0908805i
$416$	0.0489057	−	0.0273204i	0.00239780	−	0.00133949i
$417$	3.88633	−	18.0326i	0.190314	−	0.883061i
$418$	0.674806	+	1.09595i	0.0330058	+	0.0536049i
$419$	−15.9005	+	7.18748i	−0.776790	+	0.351131i	−0.761007	−	0.648744i	$-0.775295\pi$
$419$	−15.9005	+	7.18748i	−0.776790	+	0.351131i	−0.0157836	+	0.999875i	$0.505024\pi$
$420$	−0.298396	−	0.339044i	−0.0145602	−	0.0165436i
$421$	16.0674	−	31.8678i	0.783077	−	1.55314i	−0.0492044	−	0.998789i	$-0.515669\pi$
$421$	16.0674	−	31.8678i	0.783077	−	1.55314i	0.832282	−	0.554353i	$-0.187034\pi$
$422$	−10.1520	−	13.7264i	−0.494191	−	0.668191i
$423$	−0.0428720	−	0.0696286i	−0.00208451	−	0.00338546i
$424$	2.63077	+	8.59037i	0.127762	+	0.417185i
$425$	17.6172	+	9.84156i	0.854560	+	0.477386i
$426$	6.91656	+	2.44378i	0.335108	+	0.118401i
$427$	0.229726	−	0.0598160i	0.0111172	−	0.00289470i
$428$	2.11853	+	0.957635i	0.102403	+	0.0462891i
$429$	−0.00448049	+	0.105474i	−0.000216320	+	0.00509234i
$430$	−0.551869	+	2.56068i	−0.0266135	+	0.123487i
$431$	18.9749	−	3.25357i	0.913989	−	0.156719i	0.307258	−	0.951626i	$-0.400589\pi$
$431$	18.9749	−	3.25357i	0.913989	−	0.156719i	0.606731	+	0.794907i	$0.292481\pi$
$432$	−0.768780	−	3.56715i	−0.0369880	−	0.171625i
$433$	−6.02573	−	14.9956i	−0.289578	−	0.720643i	−0.999860	−	0.0167254i	$-0.994676\pi$
$433$	−6.02573	−	14.9956i	−0.289578	−	0.720643i	0.710282	−	0.703917i	$-0.248567\pi$
$434$	−2.60932	−	8.52032i	−0.125251	−	0.408989i
$435$	−0.163051	+	3.83836i	−0.00781771	+	0.184035i
$436$	1.32925	+	1.07329i	0.0636594	+	0.0514013i
$437$	0.558745	+	0.535513i	0.0267284	+	0.0256171i
$438$	−2.24431	+	3.64499i	−0.107237	+	0.174165i
$439$	1.74273	−	13.6093i	0.0831761	−	0.649534i	−0.895638	−	0.444784i	$-0.853281\pi$
$439$	1.74273	−	13.6093i	0.0831761	−	0.649534i	0.978814	−	0.204751i	$-0.0656383\pi$
$440$	−0.831277	+	19.5689i	−0.0396296	+	0.932911i
$441$	−3.39930	−	5.52082i	−0.161872	−	0.262896i
$442$	0.130316	−	0.105222i	0.00619848	−	0.00500492i
$443$	−2.55375	+	6.35525i	−0.121332	+	0.301947i	−0.976191	−	0.216914i	$-0.930401\pi$
$443$	−2.55375	+	6.35525i	−0.121332	+	0.301947i	0.854858	+	0.518862i	$0.173644\pi$
$444$	0.488407	−	0.172565i	0.0231788	−	0.00818958i
$445$	26.2189			1.24289
$446$	15.2054	+	13.3642i	0.719998	+	0.632813i
$447$	−3.65670			−0.172956
$448$	−5.78710	+	2.04471i	−0.273415	+	0.0966036i
$449$	3.94572	−	9.81929i	0.186210	−	0.463401i	−0.805390	−	0.592745i	$-0.798044\pi$
$449$	3.94572	−	9.81929i	0.186210	−	0.463401i	0.991600	+	0.129344i	$0.0412873\pi$
$450$	−10.5375	+	8.50847i	−0.496744	+	0.401093i
$451$	7.33253	+	11.9088i	0.345276	+	0.560763i
$452$	0.0527658	−	1.24215i	0.00248190	−	0.0584258i
$453$	−1.23088	+	9.61209i	−0.0578316	+	0.451616i
$454$	2.47738	−	4.02353i	0.116269	−	0.188833i
$455$	0.122897	+	0.117787i	0.00576149	+	0.00552194i
$456$	−1.25463	−	1.01305i	−0.0587536	−	0.0474403i
$457$	−1.35611	+	31.9240i	−0.0634363	+	1.49334i	0.632122	+	0.774869i	$0.282184\pi$
$457$	−1.35611	+	31.9240i	−0.0634363	+	1.49334i	−0.695558	+	0.718470i	$0.744843\pi$
$458$	11.1918	+	36.5450i	0.522958	+	1.70764i
$459$	0.753104	+	1.87417i	0.0351519	+	0.0874788i
$460$	0.186249	+	0.864200i	0.00868392	+	0.0402935i
$461$	34.1310	−	5.85235i	1.58964	−	0.272571i	0.694882	−	0.719124i	$-0.255457\pi$
$461$	34.1310	−	5.85235i	1.58964	−	0.272571i	0.894757	+	0.446553i	$0.147349\pi$
$462$	0.354259	−	1.64377i	0.0164816	−	0.0764749i
$463$	−0.206454	+	4.86008i	−0.00959472	+	0.225867i	0.987898	+	0.155103i	$0.0495709\pi$
$463$	−0.206454	+	4.86008i	−0.00959472	+	0.225867i	−0.997493	+	0.0707644i	$0.977456\pi$
$464$	3.29937	+	1.49141i	0.153170	+	0.0692370i
$465$	34.2676	−	8.92259i	1.58912	−	0.413775i
$466$	−4.49967	−	1.58983i	−0.208443	−	0.0736476i
$467$	28.0107	+	15.6477i	1.29618	+	0.724091i	0.974847	−	0.222875i	$-0.0715441\pi$
$467$	28.0107	+	15.6477i	1.29618	+	0.724091i	0.321335	+	0.946966i	$0.395868\pi$
$468$	−0.00290719	−	0.00949296i	−0.000134385	−	0.000438812i
$469$	4.16373	+	6.76233i	0.192263	+	0.312256i
$470$	0.255204	+	0.345059i	0.0117717	+	0.0159164i
$471$	3.01018	−	5.97033i	0.138702	−	0.275098i
$472$	−11.9547	−	13.5832i	−0.550259	−	0.625216i
$473$	0.784843	−	0.354771i	0.0360871	−	0.0163124i
$474$	−6.13387	−	9.96204i	−0.281738	−	0.457571i
$475$	−1.15795	+	5.37289i	−0.0531302	+	0.246525i
$476$	0.205696	−	0.114909i	0.00942808	−	0.00526684i
$477$	3.05392	−	0.259927i	0.139829	−	0.0119012i
$478$	2.37315	+	18.5322i	0.108545	+	0.847645i
$479$	2.04417	+	0.924021i	0.0934003	+	0.0422196i	0.458060	−	0.888921i	$-0.348544\pi$
$479$	2.04417	+	0.924021i	0.0934003	+	0.0422196i	−0.364660	+	0.931141i	$0.618815\pi$
$480$	−1.03827	−	3.39031i	−0.0473903	−	0.154746i
$481$	−0.177901	+	0.0804163i	−0.00811158	+	0.00366667i
$482$	39.9061	+	3.39651i	1.81767	+	0.154707i
$483$	−0.0429137	−	1.01022i	−0.00195264	−	0.0459667i
$484$	−1.07865	+	0.729040i	−0.0490295	+	0.0331382i
$485$	−28.5995			−1.29864
$486$	−1.35562			−0.0614921
$487$	−23.2953	+	15.7449i	−1.05561	+	0.713470i	−0.959445	−	0.281895i	$-0.909037\pi$
$487$	−23.2953	+	15.7449i	−1.05561	+	0.713470i	−0.0961678	+	0.995365i	$0.530659\pi$
$488$	0.954213	+	0.163616i	0.0431952	+	0.00740656i
$489$	−5.52617	−	10.9605i	−0.249902	−	0.495651i
$490$	20.2350	+	27.3595i	0.914124	+	1.23598i
$491$	−6.96963	+	32.3392i	−0.314535	+	1.45945i	0.493207	+	0.869912i	$0.335824\pi$
$491$	−6.96963	+	32.3392i	−0.314535	+	1.45945i	−0.807742	+	0.589536i	$0.799311\pi$
$492$	−1.02329	−	0.826248i	−0.0461334	−	0.0372501i
$493$	−1.93951	−	0.505010i	−0.0873512	−	0.0227445i
$494$	0.0377959	+	0.0255456i	0.00170052	+	0.00114935i
$495$	6.46636	+	1.68371i	0.290641	+	0.0756771i
$496$	4.23897	−	33.1027i	0.190335	−	1.48636i
$497$	−3.54401	−	1.60199i	−0.158971	−	0.0718593i
$498$	6.67289	+	3.72770i	0.299019	+	0.167042i
$499$	−25.6365	+	29.1288i	−1.14765	+	1.30398i	−0.201781	+	0.979431i	$0.564673\pi$
$499$	−25.6365	+	29.1288i	−1.14765	+	1.30398i	−0.945868	+	0.324552i	$0.894786\pi$
$500$	−2.26423	+	2.17009i	−0.101259	+	0.0970492i
$501$	−3.74077	+	2.08972i	−0.167125	+	0.0933617i
$502$	−20.5558	−	16.5976i	−0.917449	−	0.740788i
$503$	−5.15814	+	40.2807i	−0.229990	+	1.79603i	0.306241	+	0.951954i	$0.400929\pi$
$503$	−5.15814	+	40.2807i	−0.229990	+	1.79603i	−0.536231	+	0.844071i	$0.680152\pi$
$504$	0.267601	+	2.08974i	0.0119199	+	0.0930843i
$505$	−9.02723	+	29.4770i	−0.401706	+	1.31171i
$506$	−2.17447	+	2.47068i	−0.0966672	+	0.109835i
$507$	−4.84574	−	12.0591i	−0.215207	−	0.535563i
$508$	−2.64596	+	1.19605i	−0.117396	+	0.0530662i
$509$	8.57799	−	6.92624i	0.380213	−	0.307000i	−0.419072	−	0.907953i	$-0.637644\pi$
$509$	8.57799	−	6.92624i	0.380213	−	0.307000i	0.799285	+	0.600953i	$0.205212\pi$
$510$	−4.77279	−	9.46627i	−0.211343	−	0.419174i
$511$	1.34952	−	1.82467i	0.0596993	−	0.0807188i
$512$	−24.6453	−	2.09762i	−1.08918	−	0.0927026i
$513$	−0.428020	+	0.345602i	−0.0188975	+	0.0152587i
$514$	20.3008	+	27.4484i	0.895428	+	1.21070i
$515$	61.2024	−	10.4942i	2.69690	−	0.462430i
$516$	−0.0584785	+	0.0560471i	−0.00257437	+	0.00246734i
$517$	0.0413223	−	0.134931i	0.00181735	−	0.00593428i
$518$	3.00932	−	0.783565i	0.132222	−	0.0344279i
$519$	1.87530	+	1.04761i	0.0823166	+	0.0459848i
$520$	0.258854	+	0.644182i	0.0113515	+	0.0282493i
$521$	−25.9813	−	29.5204i	−1.13826	−	1.29331i	−0.950369	−	0.311124i	$-0.899295\pi$
$521$	−25.9813	−	29.5204i	−1.13826	−	1.29331i	−0.187890	−	0.982190i	$-0.560165\pi$
$522$	0.799852	−	1.08147i	0.0350086	−	0.0473347i
$523$	13.9997	+	2.40050i	0.612166	+	0.104966i	0.466728	−	0.884401i	$-0.345433\pi$
$523$	13.9997	+	2.40050i	0.612166	+	0.104966i	0.145438	+	0.989367i	$0.453541\pi$
$524$	2.45920	−	0.868889i	0.107431	−	0.0379576i
$525$	5.94936	−	4.02107i	0.259651	−	0.175494i
$526$	7.16740	−	2.53240i	0.312513	−	0.110418i
$527$	0.784000	+	18.4560i	0.0341516	+	0.803955i
$528$	3.74473	−	5.06322i	0.162969	−	0.220348i
$529$	9.46367	−	18.7701i	0.411464	−	0.816090i
$530$	−15.8556	+	2.71872i	−0.688723	+	0.118093i
$531$	−5.38913	+	3.01055i	−0.233868	+	0.130647i
$532$	0.0463305	+	0.0444042i	0.00200868	+	0.00192517i
$533$	0.410696	+	0.277582i	0.0177892	+	0.0120234i
$534$	−7.60563	−	5.14051i	−0.329128	−	0.222452i
$535$	−29.0793	+	47.2278i	−1.25721	+	2.04184i
$536$	4.11382	+	32.1254i	0.177690	+	1.38761i
$537$	7.45611	−	1.94142i	0.321755	−	0.0837784i
$538$	30.7017	+	10.8476i	1.32364	+	0.467673i
$539$	3.27642	−	10.6986i	0.141126	−	0.460823i
$540$	−0.626134	+	0.0532919i	−0.0269445	+	0.00229332i
$541$	17.3949	+	16.6717i	0.747866	+	0.716772i	0.965828	−	0.259186i	$-0.0834541\pi$
$541$	17.3949	+	16.6717i	0.747866	+	0.716772i	−0.217961	+	0.975957i	$0.569941\pi$
$542$	12.5011	+	3.25502i	0.536967	+	0.139815i
$543$	7.66701	−	12.4520i	0.329023	−	0.534367i
$544$	1.84306	−	0.156867i	0.0790203	−	0.00672562i
$545$	−29.4244	+	28.2010i	−1.26040	+	1.20800i
$546$	−0.0125567	−	0.0582633i	−0.000537377	−	0.00249344i
$547$	22.3551	+	25.4004i	0.955836	+	1.08604i	0.996221	+	0.0868565i	$0.0276822\pi$
$547$	22.3551	+	25.4004i	0.955836	+	1.08604i	−0.0403848	+	0.999184i	$0.512858\pi$
$548$	−2.11375	−	0.179907i	−0.0902950	−	0.00768524i
$549$	0.123148	−	0.306465i	0.00525581	−	0.0130796i
$550$	−23.0377	−	3.95021i	−0.982330	−	0.168437i
$551$	−0.0231673	−	0.545376i	−0.000986960	−	0.0232338i
$552$	1.53756	−	3.82637i	0.0654431	−	0.162861i
$553$	2.79248	+	5.53856i	0.118749	+	0.235524i
$554$	5.94718	−	11.7955i	0.252671	−	0.501144i
$555$	2.60339	+	12.0798i	0.110508	+	0.512758i
$556$	−1.97800	+	2.24745i	−0.0838860	+	0.0953130i
$557$	19.8495	+	7.01329i	0.841052	+	0.297163i	0.718697	−	0.695324i	$-0.244739\pi$
$557$	19.8495	+	7.01329i	0.841052	+	0.297163i	0.122355	+	0.992486i	$0.460955\pi$
$558$	−11.6898	−	4.13027i	−0.494869	−	0.174848i
$559$	0.0201696	−	0.0229172i	0.000853084	−	0.000969292i
$560$	−2.13937	−	9.92671i	−0.0904048	−	0.419480i
$561$	−1.56933	+	3.11258i	−0.0662571	+	0.131413i
$562$	3.79491	+	7.52676i	0.160079	+	0.317497i
$563$	11.1186	−	27.6698i	0.468595	−	1.16614i	−0.487510	−	0.873118i	$-0.662095\pi$
$563$	11.1186	−	27.6698i	0.468595	−	1.16614i	0.956105	−	0.293026i	$-0.0946621\pi$
$564$	0.000563245		0.0132592i	2.37169e−5		0.000558314i
$565$	29.2324	+	5.01239i	1.22982	+	0.210873i
$566$	9.14460	−	22.7572i	0.384376	−	0.956557i
$567$	0.716148	+	0.0609532i	0.0300754	+	0.00255979i
$568$	−10.4795	−	11.9070i	−0.439708	−	0.499606i
$569$	−5.15115	−	23.9014i	−0.215948	−	1.00200i	−0.947386	−	0.320093i	$-0.896286\pi$
$569$	−5.15115	−	23.9014i	−0.215948	−	1.00200i	0.731439	−	0.681907i	$-0.238849\pi$
$570$	2.08461	−	1.99794i	0.0873148	−	0.0836845i
$571$	41.7259	−	3.55140i	1.74618	−	0.148621i	0.832223	−	0.554441i	$-0.187068\pi$
$571$	41.7259	−	3.55140i	1.74618	−	0.148621i	0.913953	+	0.405820i	$0.133014\pi$
$572$	0.00898349	−	0.0145901i	0.000375619	−	0.000610043i
$573$	−1.94493	−	0.506421i	−0.0812507	−	0.0211560i
$574$	−5.70026	−	5.46326i	−0.237924	−	0.228032i
$575$	−14.0047	+	1.19197i	−0.584036	+	0.0497087i
$576$	−2.50058	+	8.16525i	−0.104191	+	0.340219i
$577$	42.2747	+	14.9366i	1.75992	+	0.621819i	0.999615	−	0.0277499i	$-0.00883420\pi$
$577$	42.2747	+	14.9366i	1.75992	+	0.621819i	0.760303	+	0.649568i	$0.225050\pi$
$578$	−16.9498	+	4.41340i	−0.705021	+	0.183573i
$579$	0.798021	+	6.23186i	0.0331646	+	0.258987i
$580$	0.326922	−	0.530955i	0.0135747	−	0.0220467i
$581$	−3.35756	−	2.26931i	−0.139295	−	0.0941469i
$582$	8.29623	+	5.60727i	0.343890	+	0.232429i
$583$	3.81880	+	3.66002i	0.158159	+	0.151583i
$584$	8.08044	−	4.51400i	0.334371	−	0.186791i
$585$	0.233436	−	0.0400265i	0.00965137	−	0.00165489i
$586$	6.57867	−	13.0480i	0.271762	−	0.539009i
$587$	15.3194	−	20.7132i	0.632300	−	0.854926i	−0.364795	−	0.931088i	$-0.618861\pi$
$587$	15.3194	−	20.7132i	0.632300	−	0.854926i	0.997095	+	0.0761615i	$0.0242665\pi$
$588$	0.0446594	+	1.05132i	0.00184172	+	0.0433556i
$589$	−4.74389	+	1.67612i	−0.195469	+	0.0690634i
$590$	26.8439	−	18.1433i	1.10514	−	0.746947i
$591$	−13.5664	+	4.79333i	−0.558049	+	0.197171i
$592$	11.4787	+	1.96822i	0.471772	+	0.0808934i
$593$	−4.79978	+	6.48974i	−0.197103	+	0.266502i	−0.891430	−	0.453159i	$-0.850297\pi$
$593$	−4.79978	+	6.48974i	−0.197103	+	0.266502i	0.694326	+	0.719660i	$0.255702\pi$
$594$	−1.54567	−	1.75622i	−0.0634195	−	0.0720586i
$595$	2.09574	+	5.21546i	0.0859172	+	0.213813i
$596$	0.518122	+	0.289441i	0.0212231	+	0.0118559i
$597$	−13.2839	+	3.45885i	−0.543672	+	0.141561i
$598$	−0.0341607	+	0.111546i	−0.00139693	+	0.00456147i
$599$	15.3794	−	14.7400i	0.628387	−	0.602260i	−0.308783	−	0.951132i	$-0.599922\pi$
$599$	15.3794	−	14.7400i	0.628387	−	0.602260i	0.937170	+	0.348872i	$0.113435\pi$
$600$	28.8645	−	4.94931i	1.17839	−	0.202055i
$601$	−2.84898	−	3.85207i	−0.116212	−	0.157129i	0.742043	−	0.670352i	$-0.233857\pi$
$601$	−2.84898	−	3.85207i	−0.116212	−	0.157129i	−0.858255	+	0.513223i	$0.828451\pi$
$602$	−0.378330	+	0.305480i	−0.0154196	+	0.0124504i
$603$	11.0093	+	0.937029i	0.448333	+	0.0381588i
$604$	0.935235	−	1.26452i	0.0380542	−	0.0514526i
$605$	−13.9825	−	27.7325i	−0.568467	−	1.12749i
$606$	8.39795	−	6.78087i	0.341143	−	0.275454i
$607$	−6.51096	+	2.94314i	−0.264272	+	0.119458i	−0.539684	−	0.841868i	$-0.681456\pi$
$607$	−6.51096	+	2.94314i	−0.264272	+	0.119458i	0.275412	+	0.961326i	$0.411186\pi$
$608$	0.187844	+	0.467469i	0.00761810	+	0.0189584i
$609$	−0.471174	+	0.535358i	−0.0190929	+	0.0216938i
$610$	−0.507621	+	1.65756i	−0.0205530	+	0.0671125i
$611$	−0.000635329	−	0.00496138i	−2.57027e−5	−	0.000200716i
$612$	0.0416389	−	0.325165i	0.00168315	−	0.0131440i
$613$	−10.1934	−	8.23061i	−0.411708	−	0.332431i	0.399978	−	0.916525i	$-0.369018\pi$
$613$	−10.1934	−	8.23061i	−0.411708	−	0.332431i	−0.811686	+	0.584093i	$0.801450\pi$
$614$	−12.8017	+	7.15145i	−0.516634	+	0.288609i
$615$	22.6517	−	21.7099i	0.913405	−	0.875427i
$616$	−2.40216	+	2.72939i	−0.0967859	+	0.109970i
$617$	−31.8302	−	17.7814i	−1.28144	−	0.715853i	−0.309455	−	0.950914i	$-0.600147\pi$
$617$	−31.8302	−	17.7814i	−1.28144	−	0.715853i	−0.971981	+	0.235061i	$0.924471\pi$
$618$	−19.8113	−	8.95526i	−0.796926	−	0.360233i
$619$	−2.54214	+	19.8520i	−0.102177	+	0.797918i	0.857040	+	0.515249i	$0.172301\pi$
$619$	−2.54214	+	19.8520i	−0.102177	+	0.797918i	−0.959218	+	0.282668i	$0.908780\pi$
$620$	−5.56167	−	1.44815i	−0.223362	−	0.0581590i
$621$	−1.16556	−	0.787783i	−0.0467724	−	0.0316126i
$622$	33.9912	+	8.85063i	1.36292	+	0.354878i
$623$	3.78678	+	3.05761i	0.151714	+	0.122501i
$624$	0.0470271	−	0.218207i	0.00188259	−	0.00873526i
$625$	−14.7843	−	19.9896i	−0.591371	−	0.799586i
$626$	0.491257	+	0.974351i	0.0196346	+	0.0389429i
$627$	−0.935758	−	0.160452i	−0.0373706	−	0.00640783i
$628$	−0.899088	+	0.607677i	−0.0358775	+	0.0242490i
$629$	−6.44641			−0.257035
$630$	−3.77242			−0.150297
$631$	18.6491	−	12.6046i	0.742409	−	0.501781i	−0.129421	−	0.991590i	$-0.541312\pi$
$631$	18.6491	−	12.6046i	0.742409	−	0.501781i	0.871830	+	0.489809i	$0.162933\pi$
$632$	1.07362	+	25.2740i	0.0427065	+	1.00534i
$633$	12.5487	+	1.06805i	0.498765	+	0.0424511i
$634$	26.0980	−	11.7970i	1.03648	−	0.468520i
$635$	−20.2840	−	66.2341i	−0.804944	−	2.62842i
$636$	−0.453288	−	0.204899i	−0.0179740	−	0.00812477i
$637$	−0.0503750	−	0.393385i	−0.00199593	−	0.0155865i
$638$	2.31305	−	0.196869i	0.0915745	−	0.00779414i
$639$	−4.72410	+	2.63904i	−0.186882	+	0.104399i
$640$	7.94893	−	36.8832i	0.314209	−	1.45793i
$641$	−16.1765	−	26.2723i	−0.638934	−	1.03769i	−0.994670	−	0.103108i	$-0.967121\pi$
$641$	−16.1765	−	26.2723i	−0.638934	−	1.03769i	0.355736	−	0.934586i	$-0.384230\pi$
$642$	17.6950	−	7.99863i	0.698365	−	0.315681i
$643$	−7.88301	−	8.95684i	−0.310876	−	0.353223i	0.574163	−	0.818741i	$-0.305328\pi$
$643$	−7.88301	−	8.95684i	−0.310876	−	0.353223i	−0.885039	+	0.465518i	$0.845868\pi$
$644$	−0.0738821	+	0.146536i	−0.00291136	+	0.00577434i
$645$	−1.14902	−	1.55357i	−0.0452425	−	0.0611719i
$646$	0.789770	+	1.28267i	0.0310731	+	0.0504659i
$647$	−5.18405	−	16.9277i	−0.203806	−	0.665496i	−0.998303	−	0.0582287i	$-0.981455\pi$
$647$	−5.18405	−	16.9277i	−0.203806	−	0.665496i	0.794497	−	0.607268i	$-0.207734\pi$
$648$	2.55903	+	1.42956i	0.100528	+	0.0561583i
$649$	−10.0449	−	3.54907i	−0.394295	−	0.139313i
$650$	−0.801754	+	0.208761i	−0.0314474	+	0.00818826i
$651$	5.98980	+	2.70756i	0.234759	+	0.106118i
$652$	−0.0845521	+	1.99042i	−0.00331132	+	0.0779510i
$653$	−4.88691	+	22.6753i	−0.191240	+	0.887354i	0.775451	+	0.631407i	$0.217522\pi$
$653$	−4.88691	+	22.6753i	−0.191240	+	0.887354i	−0.966691	+	0.255947i	$0.917613\pi$
$654$	14.0647	−	2.41163i	0.549971	−	0.0943021i
$655$	13.1084	+	60.8234i	0.512189	+	2.37657i
$656$	−11.0255	−	27.4381i	−0.430474	−	1.07128i
$657$	−0.924624	−	3.01921i	−0.0360730	−	0.117791i
$658$	−0.00338130	+	0.0795983i	−0.000131817	+	0.00310307i
$659$	8.64801	+	6.98278i	0.336879	+	0.272011i	0.781761	−	0.623579i	$-0.214322\pi$
$659$	8.64801	+	6.98278i	0.336879	+	0.272011i	−0.444882	+	0.895589i	$0.646754\pi$
$660$	−0.782955	−	0.750402i	−0.0304765	−	0.0292094i
$661$	0.702695	−	1.14125i	0.0273317	−	0.0443895i	−0.837574	−	0.546324i	$-0.816027\pi$
$661$	0.702695	−	1.14125i	0.0273317	−	0.0443895i	0.864906	+	0.501934i	$0.167378\pi$
$662$	1.47404	−	11.5110i	0.0572902	−	0.447388i
$663$	−0.00524381	+	0.123443i	−0.000203653	+	0.00479415i
$664$	−8.66552	−	14.0737i	−0.336287	−	0.546165i
$665$	−1.19110	+	0.961744i	−0.0461888	+	0.0372948i
$666$	1.61318	−	4.01456i	0.0625096	−	0.155561i
$667$	1.31618	−	0.465038i	0.0509629	−	0.0180063i
$668$	0.695442			0.0269075
$669$	−14.8109	+	1.90681i	−0.572624	+	0.0737214i
$670$	−57.9932			−2.24047
$671$	0.537441	−	0.189890i	0.0207477	−	0.00733063i
$672$	0.245417	−	0.610743i	0.00946716	−	0.0235599i
$673$	−10.7738	+	8.69921i	−0.415298	+	0.335330i	−0.813082	−	0.582149i	$-0.802212\pi$
$673$	−10.7738	+	8.69921i	−0.415298	+	0.335330i	0.397784	+	0.917479i	$0.369779\pi$
$674$	17.8460	+	28.9837i	0.687401	+	1.11641i
$675$	0.424024	−	9.98185i	0.0163207	−	0.384202i
$676$	−0.267920	+	2.09222i	−0.0103046	+	0.0804701i
$677$	23.7202	−	38.5240i	0.911640	−	1.48060i	0.0350350	−	0.999386i	$-0.488846\pi$
$677$	23.7202	−	38.5240i	0.911640	−	1.48060i	0.876605	−	0.481211i	$-0.159803\pi$
$678$	−7.49707	−	7.18536i	−0.287923	−	0.275952i
$679$	−4.13062	−	3.33525i	−0.158519	−	0.127995i
$680$	−0.972898	+	22.9028i	−0.0373090	+	0.878282i
$681$	1.02065	+	3.33276i	0.0391112	+	0.127712i
$682$	−7.97784	−	19.8536i	−0.305487	−	0.760234i
$683$	10.4732	+	48.5956i	0.400744	+	1.85946i	0.502391	+	0.864640i	$0.332454\pi$
$683$	10.4732	+	48.5956i	0.400744	+	1.85946i	−0.101647	+	0.994821i	$0.532411\pi$
$684$	0.0880023	−	0.0150895i	0.00336485	−	0.000576962i
$685$	10.6619	−	49.4714i	0.407370	−	1.89020i
$686$	−0.557564	+	13.1255i	−0.0212879	+	0.501134i
$687$	−25.6912	−	11.6132i	−0.980181	−	0.443070i
$688$	−1.76238	+	0.458889i	−0.0671902	+	0.0174950i
$689$	0.176777	+	0.0624593i	0.00673467	+	0.00237951i
$690$	6.44629	+	3.60111i	0.245406	+	0.137092i
$691$	−13.5731	−	44.3207i	−0.516344	−	1.68604i	−0.709362	−	0.704845i	$-0.751017\pi$
$691$	−13.5731	−	44.3207i	−0.516344	−	1.68604i	0.193018	−	0.981195i	$-0.438172\pi$
$692$	−0.182792	−	0.296873i	−0.00694871	−	0.0112854i
$693$	0.737583	+	0.997278i	0.0280185	+	0.0378834i
$694$	15.2975	−	30.3407i	0.580684	−	1.15172i
$695$	−47.1866	−	53.6143i	−1.78989	−	2.03371i
$696$	−2.65036	+	1.19804i	−0.100461	+	0.0454114i
$697$	8.58175	+	13.9377i	0.325057	+	0.527926i
$698$	−6.54959	+	30.3902i	−0.247906	+	1.15029i
$699$	3.07333	−	1.71687i	0.116244	−	0.0649378i
$700$	−1.16125	+	0.0988372i	−0.0438913	+	0.00373570i
$701$	6.64464	+	51.8889i	0.250964	+	1.95982i	0.279253	+	0.960218i	$0.409913\pi$
$701$	6.64464	+	51.8889i	0.250964	+	1.95982i	−0.0282881	+	0.999600i	$0.509006\pi$
$702$	−0.0755632	−	0.0341567i	−0.00285195	−	0.00128916i
$703$	−0.514131	−	1.67881i	−0.0193908	−	0.0633177i
$704$	−13.4293	+	6.07044i	−0.506137	+	0.228788i
$705$	−0.315452	−	0.0268490i	−0.0118806	−	0.00101119i
$706$	0.385113	+	9.06587i	0.0144939	+	0.341198i
$707$	−4.74137	+	3.20461i	−0.178318	+	0.120522i
$708$	1.00189			0.0376532
$709$	−28.7011			−1.07789			−0.538946	−	0.842341i	$-0.681177\pi$
$709$	−28.7011			−1.07789			−0.538946	+	0.842341i	$0.681177\pi$
$710$	23.5313	−	15.9044i	0.883113	−	0.596880i
$711$	8.50588	+	1.45848i	0.318995	+	0.0546972i
$712$	8.93641	+	17.7243i	0.334906	+	0.664247i
$713$	−7.65072	−	10.3445i	−0.286522	−	0.387403i
$714$	0.414613	−	1.92381i	0.0155165	−	0.0719968i
$715$	0.318017	+	0.256781i	0.0118932	+	0.00960305i
$716$	−1.21013	−	0.315095i	−0.0452249	−	0.0117756i
$717$	−11.4188	−	7.71776i	−0.426443	−	0.288225i
$718$	9.39725	+	2.44685i	0.350702	+	0.0913158i
$719$	6.61452	−	51.6538i	0.246680	−	1.92636i	−0.113621	−	0.993524i	$-0.536245\pi$
$719$	6.61452	−	51.6538i	0.246680	−	1.92636i	0.360302	−	0.932836i	$-0.382674\pi$
$720$	−12.8742	−	5.81951i	−0.479794	−	0.216881i
$721$	10.0633	+	5.62168i	0.374776	+	0.209362i
$722$	16.7458	−	19.0269i	0.623213	−	0.708108i
$723$	−21.3295	+	20.4427i	−0.793252	+	0.760270i
$724$	−2.07197	+	1.15747i	−0.0770041	+	0.0430171i
$725$	7.71304	+	6.22784i	0.286455	+	0.231296i
$726$	−1.38122	+	10.7861i	−0.0512619	+	0.400311i
$727$	2.17567	+	16.9901i	0.0806910	+	0.630128i	0.980878	+	0.194624i	$0.0623486\pi$
$727$	2.17567	+	16.9901i	0.0806910	+	0.630128i	−0.900187	+	0.435504i	$0.856570\pi$
$728$	−0.0377376	+	0.123226i	−0.00139865	+	0.00456707i
$729$	0.660675	−	0.750672i	0.0244694	−	0.0278027i
$730$	6.17948	+	15.3782i	0.228713	+	0.569174i
$731$	0.918554	−	0.415213i	0.0339739	−	0.0153572i
$732$	−0.0417067	+	0.0336758i	−0.00154152	+	0.00124469i
$733$	−4.08955	−	8.11113i	−0.151051	−	0.299592i	0.804746	−	0.593619i	$-0.202301\pi$
$733$	−4.08955	−	8.11113i	−0.151051	−	0.299592i	−0.955797	+	0.294028i	$0.905004\pi$
$734$	−8.00370	+	10.8217i	−0.295422	+	0.399437i
$735$	−25.0121	−	2.12884i	−0.922584	−	0.0785235i
$736$	−1.00237	+	0.809361i	−0.0369480	+	0.0298334i
$737$	11.3388	+	15.3311i	0.417670	+	0.564728i
$738$	−10.8273	+	1.85653i	−0.398560	+	0.0683399i
$739$	21.7917	−	20.8857i	0.801622	−	0.768292i	−0.174699	−	0.984622i	$-0.555895\pi$
$739$	21.7917	−	20.8857i	0.801622	−	0.768292i	0.976320	+	0.216330i	$0.0694086\pi$
$740$	0.587279	−	1.91767i	0.0215888	−	0.0704949i
$741$	−0.0325661	+	0.00847956i	−0.00119635	+	0.000311504i
$742$	−2.60707	−	1.45640i	−0.0957087	−	0.0534661i
$743$	6.34463	+	15.7892i	0.232762	+	0.579250i	0.997911	−	0.0646030i	$-0.0205781\pi$
$743$	6.34463	+	15.7892i	0.232762	+	0.579250i	−0.765149	+	0.643853i	$0.777335\pi$
$744$	17.7115	+	20.1242i	0.649336	+	0.737789i
$745$	−8.41883	+	11.3830i	−0.308442	+	0.417041i
$746$	40.2009	+	6.89313i	1.47186	+	0.252376i
$747$	−5.31631	+	1.87837i	−0.194514	+	0.0687261i
$748$	0.468731	−	0.316807i	0.0171385	−	0.0115836i
$749$	−9.70758	+	3.42991i	−0.354707	+	0.125326i
$750$	1.11176	+	26.1718i	0.0405959	+	0.955658i
$751$	−16.1198	+	21.7954i	−0.588220	+	0.795326i	−0.992877	−	0.119143i	$-0.961985\pi$
$751$	−16.1198	+	21.7954i	−0.588220	+	0.795326i	0.404657	+	0.914468i	$0.367391\pi$
$752$	−0.134331	+	0.266431i	−0.00489856	+	0.00971572i
$753$	19.2090	−	3.29371i	0.700015	−	0.120030i
$754$	0.0718337	−	0.0401287i	0.00261603	−	0.00146140i
$755$	27.0878	+	25.9616i	0.985826	+	0.944838i
$756$	−0.0966473	−	0.0653221i	−0.00351503	−	0.00237574i
$757$	−4.59329	−	3.10453i	−0.166946	−	0.112836i	0.473652	−	0.880712i	$-0.342935\pi$
$757$	−4.59329	−	3.10453i	−0.166946	−	0.112836i	−0.640599	+	0.767876i	$0.721314\pi$
$758$	−11.3397	+	18.4168i	−0.411876	+	0.668929i
$759$	−0.308386	−	2.40823i	−0.0111937	−	0.0874131i
$760$	−6.04208	+	1.57323i	−0.219169	+	0.0570672i
$761$	33.5574	+	11.8566i	1.21645	+	0.429800i	0.862785	−	0.505571i	$-0.168718\pi$
$761$	33.5574	+	11.8566i	1.21645	+	0.429800i	0.353668	+	0.935371i	$0.384934\pi$
$762$	−7.10194	+	23.1903i	−0.257276	+	0.840094i
$763$	−7.53854	+	0.641624i	−0.272913	+	0.0232283i
$764$	0.235495	+	0.225703i	0.00851990	+	0.00816566i
$765$	7.56802	+	1.97056i	0.273622	+	0.0712457i
$766$	11.0835	−	18.0008i	0.400464	−	0.650395i
$767$	−0.376250	+	0.0320236i	−0.0135856	+	0.00115630i
$768$	2.79316	−	2.67703i	0.100790	−	0.0965990i
$769$	8.23804	+	38.2246i	0.297071	+	1.37842i	0.841794	+	0.539799i	$0.181500\pi$
$769$	8.23804	+	38.2246i	0.297071	+	1.37842i	−0.544723	+	0.838616i	$0.683365\pi$
$770$	−4.30130	−	4.88722i	−0.155008	−	0.176123i
$771$	−25.0933	−	2.13576i	−0.903715	−	0.0769175i
$772$	0.380201	−	0.946166i	0.0136837	−	0.0340533i
$773$	−3.26398	−	0.559665i	−0.117397	−	0.0201298i	0.110002	−	0.993931i	$-0.464914\pi$
$773$	−3.26398	−	0.559665i	−0.117397	−	0.0201298i	−0.227399	+	0.973802i	$0.573022\pi$
$774$	0.0287137	+	0.675942i	0.00103209	+	0.0242963i
$775$	34.0690	−	84.7839i	1.22379	−	3.04553i
$776$	−9.74784	−	19.3337i	−0.349927	−	0.694039i
$777$	−1.03272	+	2.04829i	−0.0370488	+	0.0734818i
$778$	0.238055	+	1.10458i	0.00853470	+	0.0396012i
$779$	−2.94530	+	3.34651i	−0.105526	+	0.119901i
$780$	−0.0362440	−	0.0128058i	−0.00129774	−	0.000458522i
$781$	−8.80530	−	3.11111i	−0.315079	−	0.111324i
$782$	−2.54493	+	2.89161i	−0.0910066	+	0.103404i
$783$	0.209048	+	0.969985i	0.00747075	+	0.0346644i
$784$	−10.6511	+	21.1252i	−0.380396	+	0.754470i
$785$	−11.6548	−	23.1159i	−0.415978	−	0.825043i
$786$	8.12260	−	20.2139i	0.289724	−	0.721005i
$787$	0.155592	+	3.66276i	0.00554627	+	0.130563i	0.999737	+	0.0229312i	$0.00729987\pi$
$787$	0.155592	+	3.66276i	0.00554627	+	0.130563i	−0.994191	+	0.107632i	$0.965673\pi$
$788$	2.30165	+	0.394658i	0.0819930	+	0.0140591i
$789$	−2.09079	+	5.20314i	−0.0744342	+	0.185237i
$790$	−45.1330	−	3.84139i	−1.60576	−	0.136670i
$791$	3.63749	+	4.13299i	0.129334	+	0.146952i
$792$	1.06578	+	4.94522i	0.0378708	+	0.175721i
$793$	0.0145862	−	0.0139797i	0.000517970	−	0.000496434i
$794$	27.7576	−	2.36252i	0.985081	−	0.0838428i
$795$	6.22191	−	10.1050i	0.220668	−	0.358388i
$796$	2.15599	+	0.561375i	0.0764170	+	0.0198974i
$797$	−14.9868	−	14.3637i	−0.530860	−	0.508788i	0.378048	−	0.925786i	$-0.376596\pi$
$797$	−14.9868	−	14.3637i	−0.530860	−	0.508788i	−0.908907	+	0.416998i	$0.863082\pi$
$798$	0.534078	−	0.0454567i	0.0189061	−	0.00160915i
$799$	0.0483622	−	0.157919i	0.00171093	−	0.00558678i
$800$	−8.62681	−	3.04804i	−0.305004	−	0.107765i
$801$	6.55324	−	1.70633i	0.231547	−	0.0602903i
$802$	2.71160	+	21.1753i	0.0957500	+	0.747726i
$803$	2.85718	−	4.64035i	0.100828	−	0.163755i
$804$	−1.48575	−	1.00419i	−0.0523984	−	0.0354152i
$805$	−3.24354	−	2.19225i	−0.114320	−	0.0772666i
$806$	−0.547531	−	0.524766i	−0.0192860	−	0.0184841i
$807$	−20.9697	+	11.7144i	−0.738167	+	0.412365i
$808$	−23.0037	+	3.94438i	−0.809267	+	0.138763i
$809$	−9.68627	+	19.2116i	−0.340551	+	0.675443i	−0.996871	−	0.0790396i	$-0.974815\pi$
$809$	−9.68627	+	19.2116i	−0.340551	+	0.675443i	0.656320	+	0.754482i	$0.272112\pi$
$810$	−3.12104	+	4.21993i	−0.109662	+	0.148273i
$811$	−0.294072	−	6.92267i	−0.0103262	−	0.243088i	−0.996841	−	0.0794180i	$-0.974694\pi$
$811$	−0.294072	−	6.92267i	−0.0103262	−	0.243088i	0.986515	−	0.163670i	$-0.0523332\pi$
$812$	0.109137	−	0.0385604i	0.00382995	−	0.00135321i
$813$	−7.89499	+	5.33608i	−0.276890	+	0.187145i
$814$	7.04026	−	2.48748i	0.246761	−	0.0871862i
$815$	−46.8421	−	8.03188i	−1.64081	−	0.281344i
$816$	4.38271	−	5.92582i	0.153426	−	0.207445i
$817$	0.181391	+	0.206100i	0.00634607	+	0.00721054i
$818$	14.6309	+	36.4103i	0.511556	+	1.27306i
$819$	0.0383829	+	0.0214420i	0.00134121	+	0.000749243i
$820$	−4.92796	+	1.28314i	−0.172092	+	0.0448092i
$821$	4.20099	−	13.7177i	0.146616	−	0.478750i	−0.852410	−	0.522873i	$-0.824860\pi$
$821$	4.20099	−	13.7177i	0.146616	−	0.478750i	0.999026	+	0.0441229i	$0.0140493\pi$
$822$	−12.7923	+	12.2604i	−0.446181	+	0.427630i
$823$	−20.8216	+	3.57022i	−0.725796	+	0.124450i	−0.520026	−	0.854150i	$-0.674078\pi$
$823$	−20.8216	+	3.57022i	−0.725796	+	0.124450i	−0.205770	+	0.978600i	$0.565970\pi$
$824$	27.9544	+	37.7969i	0.973838	+	1.31672i
$825$	13.4151	−	10.8319i	0.467053	−	0.377119i
$826$	5.99290	+	0.510071i	0.208520	+	0.0177476i
$827$	−1.28273	+	1.73437i	−0.0446049	+	0.0603098i	−0.825734	−	0.564060i	$-0.809239\pi$
$827$	−1.28273	+	1.73437i	−0.0446049	+	0.0603098i	0.781129	+	0.624370i	$0.214644\pi$
$828$	0.102794	+	0.203880i	0.00357235	+	0.00708533i
$829$	27.7523	−	22.4084i	0.963878	−	0.778277i	−0.0112464	−	0.999937i	$-0.503580\pi$
$829$	27.7523	−	22.4084i	0.963878	−	0.778277i	0.975124	+	0.221660i	$0.0711475\pi$
$830$	26.9670	−	12.1899i	0.936039	−	0.423116i
$831$	3.63334	+	9.04192i	0.126039	+	0.313661i
$832$	−0.345119	+	0.392132i	−0.0119649	+	0.0135947i
$833$	3.83462	−	12.5213i	0.132862	−	0.433839i
$834$	3.17628	+	24.8041i	0.109986	+	0.858894i
$835$	−2.10726	+	16.4559i	−0.0729246	+	0.569479i
$836$	0.119888	+	0.0968031i	0.00414643	+	0.00334800i
$837$	7.98429	−	4.46029i	0.275977	−	0.154170i
$838$	17.0778	−	16.3677i	0.589942	−	0.565414i
$839$	−21.6493	+	24.5984i	−0.747418	+	0.849232i	−0.992749	−	0.120208i	$-0.961644\pi$
$839$	−21.6493	+	24.5984i	−0.747418	+	0.849232i	0.245331	+	0.969439i	$0.421103\pi$
$840$	7.12128	+	3.97818i	0.245707	+	0.137260i
$841$	25.5285	+	11.5396i	0.880292	+	0.397917i
$842$	−6.14523	+	47.9890i	−0.211779	+	1.65381i
$843$	−6.01743	−	1.56682i	−0.207251	−	0.0539641i
$844$	−1.69350	−	1.14460i	−0.0582925	−	0.0393989i
$845$	−48.6953	−	12.6793i	−1.67517	−	0.436180i
$846$	0.0862432	+	0.0696365i	0.00296510	+	0.00239415i
$847$	1.21466	−	5.63602i	0.0417361	−	0.193656i
$848$	−6.65050	−	8.99207i	−0.228379	−	0.308789i
$849$	8.14507	+	16.1548i	0.279538	+	0.554431i
$850$	−26.9625	−	4.62319i	−0.924807	−	0.158574i
$851$	3.71998	−	2.51427i	0.127519	−	0.0861880i
$852$	0.878253			0.0300884
$853$	−4.85989			−0.166399			−0.0831997	−	0.996533i	$-0.526514\pi$
$853$	−4.85989			−0.166399			−0.0831997	+	0.996533i	$0.526514\pi$
$854$	−0.266618	+	0.180202i	−0.00912348	+	0.00616639i
$855$	0.0903993	+	2.12807i	0.00309159	+	0.0727785i
$856$	−41.8380	−	3.56094i	−1.42999	−	0.121711i
$857$	31.9285	−	14.4326i	1.09066	−	0.493008i	0.215331	−	0.976541i	$-0.430917\pi$
$857$	31.9285	−	14.4326i	1.09066	−	0.493008i	0.875326	+	0.483533i	$0.160647\pi$
$858$	−0.0419063	−	0.136839i	−0.00143066	−	0.00467159i
$859$	−26.1976	−	11.8420i	−0.893849	−	0.404045i	−0.0879685	−	0.996123i	$-0.528037\pi$
$859$	−26.1976	−	11.8420i	−0.893849	−	0.404045i	−0.805881	+	0.592078i	$0.798308\pi$
$860$	0.0398349	+	0.311076i	0.00135836	+	0.0106076i
$861$	5.80336	−	0.493939i	0.197778	−	0.0168334i
$862$	−22.7840	+	12.7279i	−0.776026	+	0.433514i
$863$	−4.04075	+	18.7491i	−0.137549	+	0.638228i	0.855228	+	0.518252i	$0.173417\pi$
$863$	−4.04075	+	18.7491i	−0.137549	+	0.638228i	−0.992777	+	0.119976i	$0.961718\pi$
$864$	−0.480151	−	0.779816i	−0.0163351	−	0.0265299i
$865$	7.57862	−	3.42575i	0.257681	−	0.116479i
$866$	14.4741	+	16.4458i	0.491851	+	0.558852i
$867$	5.81677	−	11.5369i	0.197548	−	0.391813i
$868$	−0.634390	−	0.857751i	−0.0215326	−	0.0291140i
$869$	7.80888	+	12.6824i	0.264898	+	0.430222i
$870$	−1.52503	−	4.97975i	−0.0517034	−	0.168829i
$871$	0.590058	+	0.329626i	0.0199933	+	0.0111689i
$872$	−29.0933	−	10.2793i	−0.985223	−	0.348101i
$873$	−7.14828	+	1.86127i	−0.241933	+	0.0629943i
$874$	−0.956020	−	0.432148i	−0.0323379	−	0.0146176i
$875$	0.589448	−	13.8761i	0.0199270	−	0.469097i
$876$	−0.107970	+	0.500983i	−0.00364797	+	0.0169267i
$877$	48.5174	−	8.31914i	1.63831	−	0.280917i	0.725175	−	0.688564i	$-0.241759\pi$
$877$	48.5174	−	8.31914i	1.63831	−	0.280917i	0.913140	+	0.407647i	$0.133651\pi$
$878$	3.91855	+	18.1821i	0.132245	+	0.613617i
$879$	4.01914	+	10.0020i	0.135562	+	0.337360i
$880$	−7.13986	−	23.3141i	−0.240685	−	0.785918i
$881$	−1.43885	+	33.8718i	−0.0484763	+	1.14117i	0.795903	+	0.605424i	$0.206996\pi$
$881$	−1.43885	+	33.8718i	−0.0484763	+	1.14117i	−0.844380	+	0.535745i	$0.820031\pi$
$882$	6.83818	+	5.52145i	0.230254	+	0.185917i
$883$	23.9611	+	22.9648i	0.806354	+	0.772827i	0.977166	−	0.212476i	$-0.0681528\pi$
$883$	23.9611	+	22.9648i	0.806354	+	0.772827i	−0.170813	+	0.985304i	$0.554639\pi$
$884$	0.0105140	−	0.0170758i	0.000353623	−	0.000574321i
$885$	−3.03581	+	23.7071i	−0.102048	+	0.796906i
$886$	0.394059	−	9.27647i	0.0132387	−	0.311649i
$887$	−3.09302	−	5.02339i	−0.103853	−	0.168669i	0.795416	−	0.606064i	$-0.207252\pi$
$887$	−3.09302	−	5.02339i	−0.103853	−	0.168669i	−0.899269	+	0.437395i	$0.855901\pi$
$888$	−7.27876	+	5.87719i	−0.244259	+	0.197226i
$889$	4.79454	−	11.9317i	0.160804	−	0.400175i
$890$	−33.5125	+	11.8407i	−1.12334	+	0.396901i
$891$	1.72580			0.0578166
$892$	2.24951	+	0.902160i	0.0753192	+	0.0302066i
$893$	0.0449834			0.00150531
$894$	4.67393	−	1.65140i	0.156319	−	0.0552312i
$895$	11.1227	−	27.6800i	0.371792	−	0.925239i
$896$	5.44933	−	4.40003i	0.182049	−	0.146995i
$897$	−0.0451201	−	0.0732797i	−0.00150652	−	0.00244674i
$898$	−0.608848	+	14.3328i	−0.0203175	+	0.478290i
$899$	−1.15267	+	9.00133i	−0.0384435	+	0.300211i
$900$	−0.850178	+	1.38078i	−0.0283393	+	0.0460259i
$901$	4.46940	+	4.28357i	0.148897	+	0.142706i
$902$	−14.7504	−	11.9101i	−0.491136	−	0.396565i
$903$	0.0152238	−	0.358379i	0.000506615	−	0.0119261i
$904$	6.57509	+	21.4699i	0.218684	+	0.714079i
$905$	−21.1103	−	52.5351i	−0.701731	−	1.74633i
$906$	−2.76764	−	12.8419i	−0.0919485	−	0.426643i
$907$	−16.5069	+	2.83040i	−0.548104	+	0.0939819i	−0.436389	−	0.899758i	$-0.643743\pi$
$907$	−16.5069	+	2.83040i	−0.548104	+	0.0939819i	−0.111716	+	0.993740i	$0.535635\pi$
$908$	0.119183	−	0.553010i	0.00395522	−	0.0183523i
$909$	−0.337928	+	7.95509i	−0.0112084	+	0.263854i
$910$	−0.210278	−	0.0950517i	−0.00697065	−	0.00315093i
$911$	−14.2343	+	3.70634i	−0.471605	+	0.122796i	−0.480186	−	0.877167i	$-0.659431\pi$
$911$	−14.2343	+	3.70634i	−0.471605	+	0.122796i	0.00858084	+	0.999963i	$0.497269\pi$
$912$	1.89278	+	0.668762i	0.0626762	+	0.0221449i
$913$	−8.49509	−	4.74564i	−0.281146	−	0.157058i
$914$	−12.6838	−	41.4170i	−0.419544	−	1.36995i
$915$	−0.670476	−	1.08892i	−0.0221653	−	0.0359987i
$916$	2.72100	+	3.67903i	0.0899043	+	0.121559i
$917$	−5.19991	+	10.3134i	−0.171716	+	0.340579i
$918$	−1.80900	−	2.05542i	−0.0597058	−	0.0678390i
$919$	−33.5968	+	15.1867i	−1.10825	+	0.500963i	−0.881116	−	0.472900i	$-0.843207\pi$
$919$	−33.5968	+	15.1867i	−1.10825	+	0.500963i	−0.227138	+	0.973862i	$0.572937\pi$
$920$	−8.37125	−	13.5958i	−0.275992	−	0.448240i
$921$	2.27893	−	10.5743i	0.0750932	−	0.348434i
$922$	−40.9826	+	22.8943i	−1.34969	+	0.753982i
$923$	−0.329820	+	0.0280718i	−0.0108561	+	0.000923994i
$924$	−0.0255710	−	0.199688i	−0.000841225	−	0.00656924i
$925$	29.0559	+	13.1341i	0.955352	+	0.431847i
$926$	−1.93098	−	6.30530i	−0.0634559	−	0.207205i
$927$	14.6142	−	6.60604i	0.479993	−	0.216971i
$928$	0.905417	+	0.0770623i	0.0297218	+	0.00252969i
$929$	0.540423	+	12.7220i	0.0177307	+	0.417395i	0.985924	+	0.167192i	$0.0534701\pi$
$929$	0.540423	+	12.7220i	0.0177307	+	0.417395i	−0.968194	+	0.250202i	$0.919503\pi$
$930$	−39.7707	+	26.8803i	−1.30413	+	0.881439i
$931$	3.56671			0.116894
$932$	−0.571360			−0.0187155
$933$	−21.4670	+	14.5092i	−0.702799	+	0.475009i
$934$	−42.8695	−	7.35071i	−1.40273	−	0.240523i
$935$	6.07613	+	12.0513i	0.198711	+	0.394119i
$936$	0.106622	+	0.144163i	0.00348506	+	0.00471212i
$937$	3.22715	−	14.9740i	0.105426	−	0.489180i	−0.893749	−	0.448568i	$-0.851934\pi$
$937$	3.22715	−	14.9740i	0.105426	−	0.489180i	0.999175	−	0.0406116i	$-0.0129306\pi$
$938$	−8.37595	−	6.76310i	−0.273484	−	0.220823i
$939$	−0.778966	−	0.202827i	−0.0254206	−	0.00661901i
$940$	0.0425717	+	0.0287734i	0.00138853	+	0.000938485i
$941$	25.2958	+	6.58652i	0.824621	+	0.214714i	0.640274	−	0.768147i	$-0.278821\pi$
$941$	25.2958	+	6.58652i	0.824621	+	0.214714i	0.184347	+	0.982861i	$0.440983\pi$
$942$	−1.15129	+	8.99059i	−0.0375110	+	0.292929i
$943$	−10.3882	−	4.69578i	−0.338288	−	0.152916i
$944$	19.6652	+	10.9857i	0.640049	+	0.357553i
$945$	1.83853	−	2.08898i	0.0598074	−	0.0679544i
$946$	−0.842953	+	0.807905i	−0.0274068	+	0.0262673i
$947$	23.8280	−	13.3111i	0.774306	−	0.432553i	−0.0499634	−	0.998751i	$-0.515910\pi$
$947$	23.8280	−	13.3111i	0.774306	−	0.432553i	0.824269	+	0.566198i	$0.191586\pi$
$948$	−1.08976	−	0.879924i	−0.0353939	−	0.0285786i
$949$	0.0245341	−	0.191591i	0.000796412	−	0.00621930i
$950$	−0.946387	−	7.39047i	−0.0307048	−	0.239778i
$951$	−6.18653	+	20.2012i	−0.200612	+	0.655067i
$952$	−2.81141	+	3.19439i	−0.0911184	+	0.103531i
$953$	−13.3664	−	33.2636i	−0.432981	−	1.07751i	−0.971950	−	0.235188i	$-0.924429\pi$
$953$	−13.3664	−	33.2636i	−0.432981	−	1.07751i	0.538969	−	0.842326i	$-0.318814\pi$
$954$	−3.78607	+	1.71141i	−0.122579	+	0.0554091i
$955$	−6.05426	+	4.88848i	−0.195911	+	0.158187i
$956$	1.00706	+	1.99738i	0.0325705	+	0.0645997i
$957$	−1.01827	+	1.37680i	−0.0329161	+	0.0445055i
$958$	−3.03011	−	0.257901i	−0.0978985	−	0.00833239i
$959$	7.30919	−	5.90176i	0.236026	−	0.190578i
$960$	19.6607	+	26.5830i	0.634545	+	0.857961i
$961$	51.8858	−	8.89672i	1.67374	−	0.286991i
$962$	0.191073	−	0.183128i	0.00616043	−	0.00590430i
$963$	−4.19460	+	13.6968i	−0.135169	+	0.441373i
$964$	4.64031	−	1.20824i	0.149454	−	0.0389149i
$965$	21.2365	+	11.8634i	0.683629	+	0.381898i
$966$	0.511078	+	1.27187i	0.0164437	+	0.0409216i
$967$	5.38934	+	6.12348i	0.173309	+	0.196918i	0.830842	−	0.556508i	$-0.187859\pi$
$967$	5.38934	+	6.12348i	0.173309	+	0.196918i	−0.657533	+	0.753426i	$0.728400\pi$
$968$	13.9818	−	18.9047i	0.449393	−	0.607619i
$969$	−1.09518	−	0.187787i	−0.0351822	−	0.00603260i
$970$	36.5554	−	12.9158i	1.17372	−	0.414703i
$971$	−2.77210	+	1.87362i	−0.0889611	+	0.0601272i	−0.603648	−	0.797251i	$-0.706287\pi$
$971$	−2.77210	+	1.87362i	−0.0889611	+	0.0601272i	0.514687	+	0.857378i	$0.327908\pi$
$972$	−0.153030	+	0.0540690i	−0.00490844	+	0.00173426i
$973$	−0.562698	−	13.2464i	−0.0180393	−	0.424659i
$974$	22.6651	−	30.6453i	0.726237	−	0.981937i
$975$	0.275143	−	0.545713i	0.00881161	−	0.0174768i
$976$	−1.18788	+	0.203682i	−0.0380231	+	0.00651972i
$977$	24.8488	−	13.8814i	0.794984	−	0.444105i	−0.0367189	−	0.999326i	$-0.511691\pi$
$977$	24.8488	−	13.8814i	0.794984	−	0.444105i	0.831703	+	0.555221i	$0.187366\pi$
$978$	12.0133	+	11.5138i	0.384144	+	0.368172i
$979$	9.68255	+	6.54426i	0.309456	+	0.209155i
$980$	3.37549	+	2.28143i	0.107826	+	0.0728776i
$981$	−5.51912	+	8.96363i	−0.176212	+	0.286187i
$982$	−5.69626	−	44.4829i	−0.181775	−	1.41951i
$983$	−38.6155	+	10.0547i	−1.23164	+	0.320695i	−0.810197	−	0.586158i	$-0.800640\pi$
$983$	−38.6155	+	10.0547i	−1.23164	+	0.320695i	−0.421447	+	0.906853i	$0.638478\pi$
$984$	22.3968	+	7.91328i	0.713983	+	0.252266i
$985$	−16.3128	+	53.2669i	−0.519769	+	1.69722i
$986$	2.70711	−	0.230409i	0.0862121	−	0.00733773i
$987$	−0.0424296	−	0.0406655i	−0.00135055	−	0.00129440i
$988$	0.00528552	+	0.00137624i	0.000168155	+	4.37841e-5i
$989$	−0.368119	+	0.597863i	−0.0117055	+	0.0190109i
$990$	−9.02556	+	0.768189i	−0.286851	+	0.0244146i
$991$	−10.5906	+	10.1503i	−0.336422	+	0.322435i	−0.841107	−	0.540869i	$-0.818095\pi$
$991$	−10.5906	+	10.1503i	−0.336422	+	0.322435i	0.504684	+	0.863304i	$0.331609\pi$
$992$	−1.76453	−	8.18745i	−0.0560239	−	0.259952i
$993$	5.65582	+	6.42626i	0.179482	+	0.203931i
$994$	5.25337	+	0.447127i	0.166627	+	0.0141820i
$995$	−19.8164	+	49.3149i	−0.628221	+	1.56339i
$996$	0.901955	+	0.154656i	0.0285795	+	0.00490045i
$997$	1.18380	+	27.8677i	0.0374914	+	0.882578i	0.915107	+	0.403212i	$0.132106\pi$
$997$	1.18380	+	27.8677i	0.0374914	+	0.882578i	−0.877615	+	0.479366i	$0.840867\pi$
$998$	19.6133	−	48.8096i	0.620848	−	1.54504i
$999$	1.43686	+	2.84984i	0.0454602	+	0.0901649i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	669.2.i.b.4.6	✓	720
223.56	even	37	inner	669.2.i.b.502.6	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
669.2.i.b.4.6	✓	720	1.1	even	1	trivial
669.2.i.b.502.6	yes	720	223.56	even	37	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 669 = 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	669.i (of order \(37\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27818 + 0.451610i) q^{2} +(0.372856 - 0.927889i) q^{3} +(-0.126276 + 0.101961i) q^{4} +(-2.03001 - 3.29695i) q^{5} +(-0.0575340 + 1.35440i) q^{6} +(0.0912925 - 0.712916i) q^{7} +(1.53688 - 2.49605i) q^{8} +(-0.721956 - 0.691939i) q^{9} +(4.08366 + 3.29733i) q^{10} +(0.0732452 - 1.72425i) q^{11} +(0.0475255 + 0.155187i) q^{12} +(-0.0228080 - 0.0567600i) q^{13} +(0.205272 + 0.952464i) q^{14} +(-3.81611 + 0.654338i) q^{15} +(-0.768780 + 3.56715i) q^{16} +(0.0857237 - 2.01800i) q^{17} +(1.23528 + 0.558381i) q^{18} +(0.532378 - 0.138620i) q^{19} +(0.592502 + 0.209344i) q^{20} +(-0.627468 - 0.350525i) q^{21} +(0.685068 + 2.23698i) q^{22} +(0.737605 + 1.19795i) q^{23} +(-1.74302 - 2.35672i) q^{24} +(-4.49792 + 8.92109i) q^{25} +(0.0547862 + 0.0622492i) q^{26} +(-0.911228 + 0.411901i) q^{27} +(0.0611615 + 0.0993325i) q^{28} +(0.209048 - 0.969985i) q^{29} +(4.58217 - 2.55976i) q^{30} +(-9.11271 + 0.775606i) q^{31} +(0.116321 + 0.908365i) q^{32} +(-1.57260 - 0.710861i) q^{33} +(0.801780 + 2.61809i) q^{34} +(-2.53577 + 1.14624i) q^{35} +(0.161717 + 0.0137641i) q^{36} +(-0.135454 - 3.18870i) q^{37} +(-0.617873 + 0.417609i) q^{38} -0.0611711 q^{39} -11.3492 q^{40} +(-6.71389 + 4.53780i) q^{41} +(0.960318 + 0.164663i) q^{42} +(0.224685 + 0.445635i) q^{43} +(0.166557 + 0.225200i) q^{44} +(-0.815708 + 3.78490i) q^{45} +(-1.48380 - 1.19808i) q^{46} +(0.0791304 + 0.0206040i) q^{47} +(3.02328 + 2.04338i) q^{48} +(6.27422 + 1.63368i) q^{49} +(1.72030 - 13.4341i) q^{50} +(-1.84052 - 0.831968i) q^{51} +(0.00866741 + 0.00484190i) q^{52} +(-2.02494 + 2.30078i) q^{53} +(0.978696 - 0.938004i) q^{54} +(-5.83345 + 3.25876i) q^{55} +(-1.63917 - 1.32353i) q^{56} +(0.0698762 - 0.545673i) q^{57} +(0.170854 + 1.33422i) q^{58} +(1.80760 - 5.90243i) q^{59} +(0.415167 - 0.471721i) q^{60} +(0.123148 + 0.306465i) q^{61} +(11.2974 - 5.10676i) q^{62} +(-0.559203 + 0.451525i) q^{63} +(-3.84454 - 7.62520i) q^{64} +(-0.140834 + 0.190421i) q^{65} +(2.33110 + 0.198406i) q^{66} +(-8.59660 + 6.94127i) q^{67} +(0.194932 + 0.263566i) q^{68} +(1.38658 - 0.237754i) q^{69} +(2.72352 - 2.61029i) q^{70} +(1.58454 - 5.17406i) q^{71} +(-2.83667 + 0.738612i) q^{72} +(2.75665 + 1.53996i) q^{73} +(1.61318 + 4.01456i) q^{74} +(6.60070 + 7.49985i) q^{75} +(-0.0530927 + 0.0717861i) q^{76} +(-1.22256 - 0.209629i) q^{77} +(0.0781877 - 0.0276255i) q^{78} +(-7.15005 + 4.83259i) q^{79} +(13.3214 - 4.70674i) q^{80} +(0.0424412 + 0.999099i) q^{81} +(6.53225 - 8.83219i) q^{82} +(2.53843 - 5.03467i) q^{83} +(0.114974 - 0.0197143i) q^{84} +(-6.82728 + 3.81395i) q^{85} +(-0.488441 - 0.468133i) q^{86} +(-0.822093 - 0.555638i) q^{87} +(-4.19124 - 2.83278i) q^{88} +(-3.55048 + 5.76634i) q^{89} +(-0.666676 - 5.20617i) q^{90} +(-0.0425473 + 0.0110785i) q^{91} +(-0.215286 - 0.0760653i) q^{92} +(-2.67806 + 8.74477i) q^{93} +(-0.110448 + 0.00940051i) q^{94} +(-1.53776 - 1.47382i) q^{95} +(0.886233 + 0.230757i) q^{96} +(3.87286 - 6.28992i) q^{97} +(-8.75737 + 0.745362i) q^{98} +(-1.24595 + 1.19415i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - q^{2} - 20 q^{3} - 23 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} - 9 q^{8} - 20 q^{9} - 16 q^{10} - 14 q^{11} - 23 q^{12} - 14 q^{13} - 28 q^{14} - 4 q^{15} - 37 q^{16} - 20 q^{17} - q^{18} + 42 q^{19}+ \cdots - 14 q^{99}+O(q^{100}) \) 720 * q - q^2 - 20 * q^3 - 23 * q^4 - 4 * q^5 - q^6 - 12 * q^7 - 9 * q^8 - 20 * q^9 - 16 * q^10 - 14 * q^11 - 23 * q^12 - 14 * q^13 - 28 * q^14 - 4 * q^15 - 37 * q^16 - 20 * q^17 - q^18 + 42 * q^19 - 34 * q^20 - 12 * q^21 - 32 * q^22 - 18 * q^23 - 9 * q^24 - 48 * q^25 - 48 * q^26 - 20 * q^27 - 80 * q^28 + 7 * q^29 - 16 * q^30 - 40 * q^31 - 59 * q^32 - 14 * q^33 + 22 * q^34 - 32 * q^35 - 23 * q^36 - 44 * q^37 - 36 * q^38 + 60 * q^39 + 124 * q^40 + 176 * q^41 + 46 * q^42 - 42 * q^43 + 76 * q^44 - 4 * q^45 - 88 * q^46 - 26 * q^47 - 37 * q^48 - 94 * q^49 - 87 * q^50 + 54 * q^51 + 206 * q^52 - 54 * q^53 - q^54 - 74 * q^55 - 107 * q^56 - 32 * q^57 + 13 * q^58 - 50 * q^59 - 34 * q^60 - 86 * q^61 - 83 * q^62 - 12 * q^63 + 99 * q^64 + 52 * q^65 + 42 * q^66 - 68 * q^67 + 63 * q^68 - 18 * q^69 - 62 * q^70 - 68 * q^71 - 9 * q^72 - 58 * q^73 - 82 * q^74 - 48 * q^75 - 145 * q^76 + 40 * q^77 + 26 * q^78 - 90 * q^79 + 325 * q^80 - 20 * q^81 + 62 * q^82 + 58 * q^83 - 80 * q^84 - 14 * q^85 - 153 * q^86 - 30 * q^87 - 152 * q^88 - 110 * q^89 - 16 * q^90 - 114 * q^91 - 110 * q^92 - 40 * q^93 + 102 * q^94 - 118 * q^95 - 59 * q^96 - 110 * q^97 - 154 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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