LMFDB - Embedded newform 156.2.w.c.115.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,2,Mod(7,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 11]))

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

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

chi := DirichletCharacter("156.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	156.w (of order $12$, degree $4$, 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:	$1.24566627153$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.2
Character	$\chi$	$=$	156.115
Dual form			156.2.w.c.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15700 + 0.813242i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.677275 - 1.88183i) q^{4} +(1.41026 + 1.41026i) q^{5} +(0.595366 - 1.28279i) q^{6} +(0.844432 - 0.226265i) q^{7} +(0.746782 + 2.72806i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.15700 + 0.813242i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.677275 - 1.88183i) q^{4} +(1.41026 + 1.41026i) q^{5} +(0.595366 - 1.28279i) q^{6} +(0.844432 - 0.226265i) q^{7} +(0.746782 + 2.72806i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.77854 - 0.484781i) q^{10} +(-1.07958 + 4.02904i) q^{11} +(0.354379 + 1.96835i) q^{12} +(-0.495087 + 3.57140i) q^{13} +(-0.792995 + 0.948514i) q^{14} +(-1.92645 - 0.516191i) q^{15} +(-3.08260 - 2.54904i) q^{16} +(1.03232 + 0.596013i) q^{17} +(0.125791 + 1.40861i) q^{18} +(0.113660 + 0.424187i) q^{19} +(3.60901 - 1.69874i) q^{20} +(-0.618167 + 0.618167i) q^{21} +(-2.02752 - 5.53954i) q^{22} +(2.80928 + 4.86581i) q^{23} +(-2.01076 - 1.98918i) q^{24} -1.02234i q^{25} +(-2.33160 - 4.53472i) q^{26} +1.00000i q^{27} +(0.146120 - 1.74232i) q^{28} +(-3.58411 - 6.20785i) q^{29} +(2.64868 - 0.969439i) q^{30} +(3.11370 - 3.11370i) q^{31} +(5.63953 + 0.442328i) q^{32} +(-1.07958 - 4.02904i) q^{33} +(-1.67910 + 0.149946i) q^{34} +(1.50996 + 0.871775i) q^{35} +(-1.29108 - 1.52745i) q^{36} +(9.94255 + 2.66410i) q^{37} +(-0.476471 - 0.398348i) q^{38} +(-1.35694 - 3.34047i) q^{39} +(-2.79412 + 4.90043i) q^{40} +(1.53322 - 5.72207i) q^{41} +(0.212497 - 1.21794i) q^{42} +(2.62888 - 4.55336i) q^{43} +(6.85081 + 4.76035i) q^{44} +(1.92645 - 0.516191i) q^{45} +(-7.20740 - 3.34509i) q^{46} +(-6.03968 - 6.03968i) q^{47} +(3.94413 + 0.666233i) q^{48} +(-5.40031 + 3.11787i) q^{49} +(0.831410 + 1.18284i) q^{50} -1.19203 q^{51} +(6.38547 + 3.35049i) q^{52} -7.41414 q^{53} +(-0.813242 - 1.15700i) q^{54} +(-7.20447 + 4.15950i) q^{55} +(1.24787 + 2.13469i) q^{56} +(-0.310526 - 0.310526i) q^{57} +(9.19528 + 4.26771i) q^{58} +(1.37049 - 0.367222i) q^{59} +(-2.27612 + 3.27565i) q^{60} +(0.725851 - 1.25721i) q^{61} +(-1.07034 + 6.13472i) q^{62} +(0.226265 - 0.844432i) q^{63} +(-6.88463 + 4.07453i) q^{64} +(-5.73480 + 4.33840i) q^{65} +(4.52565 + 3.78362i) q^{66} +(11.7190 + 3.14010i) q^{67} +(1.82076 - 1.53900i) q^{68} +(-4.86581 - 2.80928i) q^{69} +(-2.45598 + 0.219322i) q^{70} +(-3.85314 - 14.3801i) q^{71} +(2.73596 + 0.717298i) q^{72} +(-8.51251 + 8.51251i) q^{73} +(-13.6700 + 5.00335i) q^{74} +(0.511170 + 0.885373i) q^{75} +(0.875228 + 0.0734009i) q^{76} +3.64652i q^{77} +(4.28658 + 2.76138i) q^{78} -9.00208i q^{79} +(-0.752456 - 7.94206i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.87950 + 7.86729i) q^{82} +(-2.23286 + 2.23286i) q^{83} +(0.744618 + 1.58196i) q^{84} +(0.615312 + 2.29638i) q^{85} +(0.661378 + 7.40613i) q^{86} +(6.20785 + 3.58411i) q^{87} +(-11.7977 + 0.0636610i) q^{88} +(14.6401 + 3.92279i) q^{89} +(-1.80910 + 2.16390i) q^{90} +(0.390015 + 3.12782i) q^{91} +(11.0593 - 1.99110i) q^{92} +(-1.13969 + 4.25339i) q^{93} +(11.8996 + 2.07616i) q^{94} +(-0.437922 + 0.758504i) q^{95} +(-5.10514 + 2.43670i) q^{96} +(5.99911 - 1.60746i) q^{97} +(3.71255 - 7.99912i) q^{98} +(2.94946 + 2.94946i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9} + 12 q^{10} + 4 q^{11} - 4 q^{12} - 22 q^{14} - 4 q^{15} + 12 q^{16} - 2 q^{18} - 22 q^{19} - 4 q^{20} + 10 q^{21} - 34 q^{22} + 2 q^{24} - 4 q^{26} - 14 q^{28} + 8 q^{29} - 16 q^{30} - 2 q^{31} - 34 q^{32} + 4 q^{33} + 20 q^{34} + 24 q^{35} - 4 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} + 28 q^{40} - 36 q^{41} + 6 q^{42} + 10 q^{43} + 20 q^{44} + 4 q^{45} - 2 q^{46} + 20 q^{47} + 32 q^{48} - 54 q^{49} - 24 q^{50} + 36 q^{51} + 4 q^{52} - 36 q^{53} - 4 q^{54} - 24 q^{55} + 70 q^{56} - 32 q^{57} + 48 q^{58} - 36 q^{59} - 28 q^{60} - 2 q^{61} + 64 q^{62} + 8 q^{63} - 8 q^{64} + 16 q^{65} + 20 q^{66} - 16 q^{67} - 10 q^{68} + 12 q^{69} + 36 q^{71} - 2 q^{72} - 40 q^{73} - 30 q^{74} - 8 q^{75} + 58 q^{76} + 24 q^{78} - 48 q^{80} - 12 q^{81} - 30 q^{82} - 24 q^{83} - 26 q^{84} + 18 q^{85} + 30 q^{86} + 6 q^{87} - 78 q^{88} + 66 q^{89} + 12 q^{90} + 42 q^{91} + 36 q^{92} - 10 q^{93} + 6 q^{94} - 28 q^{95} + 8 q^{96} + 4 q^{97} + 44 q^{98} - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9 + 12 * q^10 + 4 * q^11 - 4 * q^12 - 22 * q^14 - 4 * q^15 + 12 * q^16 - 2 * q^18 - 22 * q^19 - 4 * q^20 + 10 * q^21 - 34 * q^22 + 2 * q^24 - 4 * q^26 - 14 * q^28 + 8 * q^29 - 16 * q^30 - 2 * q^31 - 34 * q^32 + 4 * q^33 + 20 * q^34 + 24 * q^35 - 4 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 + 28 * q^40 - 36 * q^41 + 6 * q^42 + 10 * q^43 + 20 * q^44 + 4 * q^45 - 2 * q^46 + 20 * q^47 + 32 * q^48 - 54 * q^49 - 24 * q^50 + 36 * q^51 + 4 * q^52 - 36 * q^53 - 4 * q^54 - 24 * q^55 + 70 * q^56 - 32 * q^57 + 48 * q^58 - 36 * q^59 - 28 * q^60 - 2 * q^61 + 64 * q^62 + 8 * q^63 - 8 * q^64 + 16 * q^65 + 20 * q^66 - 16 * q^67 - 10 * q^68 + 12 * q^69 + 36 * q^71 - 2 * q^72 - 40 * q^73 - 30 * q^74 - 8 * q^75 + 58 * q^76 + 24 * q^78 - 48 * q^80 - 12 * q^81 - 30 * q^82 - 24 * q^83 - 26 * q^84 + 18 * q^85 + 30 * q^86 + 6 * q^87 - 78 * q^88 + 66 * q^89 + 12 * q^90 + 42 * q^91 + 36 * q^92 - 10 * q^93 + 6 * q^94 - 28 * q^95 + 8 * q^96 + 4 * q^97 + 44 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−1.15700	+	0.813242i	−0.818119	+	0.575049i
$2$	−1.15700	+	0.813242i	−0.818119	+	0.575049i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.677275	−	1.88183i	0.338638	−	0.940917i
$5$	1.41026	+	1.41026i	0.630687	+	0.630687i	0.948240	−	0.317553i	$-0.102861\pi$
$5$	1.41026	+	1.41026i	0.630687	+	0.630687i	−0.317553	+	0.948240i	$0.602861\pi$
$6$	0.595366	−	1.28279i	0.243057	−	0.523695i
$7$	0.844432	−	0.226265i	0.319165	−	0.0855200i	−0.0956798	−	0.995412i	$-0.530502\pi$
$7$	0.844432	−	0.226265i	0.319165	−	0.0855200i	0.414845	+	0.909892i	$0.363836\pi$
$8$	0.746782	+	2.72806i	0.264027	+	0.964515i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−2.77854	−	0.484781i	−0.878653	−	0.153301i
$11$	−1.07958	+	4.02904i	−0.325505	+	1.21480i	0.588298	+	0.808644i	$0.299798\pi$
$11$	−1.07958	+	4.02904i	−0.325505	+	1.21480i	−0.913803	+	0.406157i	$0.866869\pi$
$12$	0.354379	+	1.96835i	0.102301	+	0.568215i
$13$	−0.495087	+	3.57140i	−0.137312	+	0.990528i
$13$	−0.495087	+	3.57140i	−0.137312	+	0.990528i
$14$	−0.792995	+	0.948514i	−0.211937	+	0.253501i
$15$	−1.92645	−	0.516191i	−0.497407	−	0.133280i
$16$	−3.08260	−	2.54904i	−0.770649	−	0.637260i
$17$	1.03232	+	0.596013i	0.250375	+	0.144554i	0.619936	−	0.784652i	$-0.287158\pi$
$17$	1.03232	+	0.596013i	0.250375	+	0.144554i	−0.369561	+	0.929207i	$0.620492\pi$
$18$	0.125791	+	1.40861i	0.0296491	+	0.332012i
$19$	0.113660	+	0.424187i	0.0260755	+	0.0973151i	0.977737	−	0.209833i	$-0.0672920\pi$
$19$	0.113660	+	0.424187i	0.0260755	+	0.0973151i	−0.951662	+	0.307148i	$0.900625\pi$
$20$	3.60901	−	1.69874i	0.806998	−	0.379850i
$21$	−0.618167	+	0.618167i	−0.134895	+	0.134895i
$22$	−2.02752	−	5.53954i	−0.432268	−	1.18103i
$23$	2.80928	+	4.86581i	0.585774	+	1.01459i	0.994778	+	0.102058i	$0.0325429\pi$
$23$	2.80928	+	4.86581i	0.585774	+	1.01459i	−0.409004	+	0.912533i	$0.634124\pi$
$24$	−2.01076	−	1.98918i	−0.410445	−	0.406039i
$25$		−	1.02234i		−	0.204468i
$26$	−2.33160	−	4.53472i	−0.457264	−	0.889331i
$27$			1.00000i			0.192450i
$28$	0.146120	−	1.74232i	0.0276140	−	0.329268i
$29$	−3.58411	−	6.20785i	−0.665552	−	1.15277i	−0.979135	−	0.203209i	$-0.934863\pi$
$29$	−3.58411	−	6.20785i	−0.665552	−	1.15277i	0.313584	−	0.949561i	$-0.398470\pi$
$30$	2.64868	−	0.969439i	0.483581	−	0.176995i
$31$	3.11370	−	3.11370i	0.559237	−	0.559237i	−0.369853	−	0.929090i	$-0.620592\pi$
$31$	3.11370	−	3.11370i	0.559237	−	0.559237i	0.929090	+	0.369853i	$0.120592\pi$
$32$	5.63953	+	0.442328i	0.996938	+	0.0781932i
$33$	−1.07958	−	4.02904i	−0.187930	−	0.701366i
$34$	−1.67910	+	0.149946i	−0.287963	+	0.0257155i
$35$	1.50996	+	0.871775i	0.255230	+	0.147357i
$36$	−1.29108	−	1.52745i	−0.215180	−	0.254576i
$37$	9.94255	+	2.66410i	1.63455	+	0.437975i	0.955228	−	0.295870i	$-0.0956095\pi$
$37$	9.94255	+	2.66410i	1.63455	+	0.437975i	0.679317	+	0.733845i	$0.262276\pi$
$38$	−0.476471	−	0.398348i	−0.0772938	−	0.0646206i
$39$	−1.35694	−	3.34047i	−0.217285	−	0.534903i
$40$	−2.79412	+	4.90043i	−0.441788	+	0.774826i
$41$	1.53322	−	5.72207i	0.239449	−	0.893638i	−0.736643	−	0.676282i	$-0.763590\pi$
$41$	1.53322	−	5.72207i	0.239449	−	0.893638i	0.976092	−	0.217356i	$-0.0697432\pi$
$42$	0.212497	−	1.21794i	0.0327890	−	0.187931i
$43$	2.62888	−	4.55336i	0.400901	−	0.694381i	−0.592934	−	0.805251i	$-0.702030\pi$
$43$	2.62888	−	4.55336i	0.400901	−	0.694381i	0.993835	+	0.110870i	$0.0353638\pi$
$44$	6.85081	+	4.76035i	1.03280	+	0.717650i
$45$	1.92645	−	0.516191i	0.287178	−	0.0769491i
$46$	−7.20740	−	3.34509i	−1.06267	−	0.493207i
$47$	−6.03968	−	6.03968i	−0.880979	−	0.880979i	0.112656	−	0.993634i	$-0.464064\pi$
$47$	−6.03968	−	6.03968i	−0.880979	−	0.880979i	−0.993634	+	0.112656i	$0.964064\pi$
$48$	3.94413	+	0.666233i	0.569286	+	0.0961625i
$49$	−5.40031	+	3.11787i	−0.771473	+	0.445410i
$50$	0.831410	+	1.18284i	0.117579	+	0.167279i
$51$	−1.19203			−0.166917
$52$	6.38547	+	3.35049i	0.885505	+	0.464629i
$53$	−7.41414			−1.01841			−0.509205	−	0.860645i	$-0.670061\pi$
$53$	−7.41414			−1.01841			−0.509205	+	0.860645i	$0.670061\pi$
$54$	−0.813242	−	1.15700i	−0.110668	−	0.157447i
$55$	−7.20447	+	4.15950i	−0.971451	+	0.560867i
$56$	1.24787	+	2.13469i	0.166754	+	0.285260i
$57$	−0.310526	−	0.310526i	−0.0411302	−	0.0411302i
$58$	9.19528	+	4.26771i	1.20740	+	0.560378i
$59$	1.37049	−	0.367222i	0.178423	−	0.0478082i	−0.168501	−	0.985701i	$-0.553893\pi$
$59$	1.37049	−	0.367222i	0.178423	−	0.0478082i	0.346924	+	0.937893i	$0.387226\pi$
$60$	−2.27612	+	3.27565i	−0.293846	+	0.422885i
$61$	0.725851	−	1.25721i	0.0929357	−	0.160969i	−0.815810	−	0.578321i	$-0.803708\pi$
$61$	0.725851	−	1.25721i	0.0929357	−	0.160969i	0.908745	+	0.417351i	$0.137042\pi$
$62$	−1.07034	+	6.13472i	−0.135934	+	0.779111i
$63$	0.226265	−	0.844432i	0.0285067	−	0.106388i
$64$	−6.88463	+	4.07453i	−0.860579	+	0.509317i
$65$	−5.73480	+	4.33840i	−0.711314	+	0.538112i
$66$	4.52565	+	3.78362i	0.557069	+	0.465731i
$67$	11.7190	+	3.14010i	1.43171	+	0.383624i	0.889621	−	0.456699i	$-0.150968\pi$
$67$	11.7190	+	3.14010i	1.43171	+	0.383624i	0.542085	+	0.840324i	$0.317635\pi$
$68$	1.82076	−	1.53900i	0.220800	−	0.186631i
$69$	−4.86581	−	2.80928i	−0.585774	−	0.338197i
$70$	−2.45598	+	0.219322i	−0.293546	+	0.0262140i
$71$	−3.85314	−	14.3801i	−0.457283	−	1.70660i	−0.681287	−	0.732016i	$-0.738580\pi$
$71$	−3.85314	−	14.3801i	−0.457283	−	1.70660i	0.224004	−	0.974588i	$-0.428087\pi$
$72$	2.73596	+	0.717298i	0.322436	+	0.0845344i
$73$	−8.51251	+	8.51251i	−0.996314	+	0.996314i	−0.999993	−	0.00367902i	$-0.998829\pi$
$73$	−8.51251	+	8.51251i	−0.996314	+	0.996314i	0.00367902	+	0.999993i	$0.498829\pi$
$74$	−13.6700	+	5.00335i	−1.58911	+	0.581628i
$75$	0.511170	+	0.885373i	0.0590249	+	0.102234i
$76$	0.875228	+	0.0734009i	0.100396	+	0.00841966i
$77$			3.64652i			0.415559i
$78$	4.28658	+	2.76138i	0.485360	+	0.312665i
$79$		−	9.00208i		−	1.01281i	−0.862295	−	0.506407i	$-0.830973\pi$
$79$		−	9.00208i		−	1.01281i	0.862295	−	0.506407i	$-0.169027\pi$
$80$	−0.752456	−	7.94206i	−0.0841271	−	0.887950i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.87950	+	7.86729i	0.317987	+	0.868797i
$83$	−2.23286	+	2.23286i	−0.245089	+	0.245089i	−0.818951	−	0.573863i	$-0.805444\pi$
$83$	−2.23286	+	2.23286i	−0.245089	+	0.245089i	0.573863	+	0.818951i	$0.305444\pi$
$84$	0.744618	+	1.58196i	0.0812445	+	0.172606i
$85$	0.615312	+	2.29638i	0.0667400	+	0.249077i
$86$	0.661378	+	7.40613i	0.0713182	+	0.798624i
$87$	6.20785	+	3.58411i	0.665552	+	0.384256i
$88$	−11.7977	+	0.0636610i	−1.25764	+	0.00678629i
$89$	14.6401	+	3.92279i	1.55184	+	0.415815i	0.930070	−	0.367383i	$-0.119746\pi$
$89$	14.6401	+	3.92279i	1.55184	+	0.415815i	0.621773	+	0.783198i	$0.286413\pi$
$90$	−1.80910	+	2.16390i	−0.190696	+	0.228095i
$91$	0.390015	+	3.12782i	0.0408846	+	0.327885i
$92$	11.0593	−	1.99110i	1.15301	−	0.207586i
$93$	−1.13969	+	4.25339i	−0.118181	+	0.441056i
$94$	11.8996	+	2.07616i	1.22735	+	0.214140i
$95$	−0.437922	+	0.758504i	−0.0449299	+	0.0778208i
$96$	−5.10514	+	2.43670i	−0.521042	+	0.248695i
$97$	5.99911	−	1.60746i	0.609118	−	0.163213i	0.0589418	−	0.998261i	$-0.481227\pi$
$97$	5.99911	−	1.60746i	0.609118	−	0.163213i	0.550176	+	0.835049i	$0.314561\pi$
$98$	3.71255	−	7.99912i	0.375024	−	0.808033i
$99$	2.94946	+	2.94946i	0.296432	+	0.296432i
$100$	−1.92388	−	0.692406i	−0.192388	−	0.0692406i
$101$	−8.03498	+	4.63900i	−0.799510	+	0.461597i	−0.843300	−	0.537443i	$-0.819390\pi$
$101$	−8.03498	+	4.63900i	−0.799510	+	0.461597i	0.0437898	+	0.999041i	$0.486057\pi$
$102$	1.37917	−	0.969405i	0.136558	−	0.0959854i
$103$	−0.0634589			−0.00625279			−0.00312640	−	0.999995i	$-0.500995\pi$
$103$	−0.0634589			−0.00625279			−0.00312640	+	0.999995i	$0.500995\pi$
$104$	−10.1127	+	1.31643i	−0.991633	+	0.129087i
$105$	−1.74355			−0.170153
$106$	8.57813	−	6.02949i	0.833181	−	0.585636i
$107$	2.65606	−	1.53348i	0.256771	−	0.148247i	−0.366090	−	0.930580i	$-0.619304\pi$
$107$	2.65606	−	1.53348i	0.256771	−	0.148247i	0.622861	+	0.782333i	$0.285970\pi$
$108$	1.88183	+	0.677275i	0.181080	+	0.0651708i
$109$	−6.40259	−	6.40259i	−0.613257	−	0.613257i	0.330536	−	0.943793i	$-0.392770\pi$
$109$	−6.40259	−	6.40259i	−0.613257	−	0.613257i	−0.943793	+	0.330536i	$0.892770\pi$
$110$	4.95286	−	10.6715i	0.472236	−	1.01749i
$111$	−9.94255	+	2.66410i	−0.943705	+	0.252865i
$112$	−3.17980	−	1.45501i	−0.300463	−	0.137485i
$113$	6.39715	−	11.0802i	0.601793	−	1.04234i	−0.390756	−	0.920494i	$-0.627786\pi$
$113$	6.39715	−	11.0802i	0.601793	−	1.04234i	0.992549	−	0.121842i	$-0.0388802\pi$
$114$	0.611810	+	0.106744i	0.0573013	+	0.00999752i
$115$	−2.90024	+	10.8239i	−0.270449	+	1.00933i
$116$	−14.1096	+	2.54027i	−1.31004	+	0.235858i
$117$	2.84538	+	2.21446i	0.263055	+	0.204727i
$118$	−1.28701	+	1.53941i	−0.118479	+	0.141715i
$119$	1.00658	+	0.269713i	0.0922734	+	0.0247246i
$120$	−0.0304390	−	5.64095i	−0.00277868	−	0.514946i
$121$	−5.54139	−	3.19932i	−0.503763	−	0.290847i
$122$	0.182610	+	2.04488i	0.0165328	+	0.185135i
$123$	1.53322	+	5.72207i	0.138246	+	0.515942i
$124$	−3.75063	−	7.96829i	−0.336817	−	0.715574i
$125$	8.49306	−	8.49306i	0.759642	−	0.759642i
$126$	0.424940	+	1.16101i	0.0378567	+	0.103431i
$127$	−9.33641	−	16.1711i	−0.828472	−	1.43496i	−0.899236	−	0.437463i	$-0.855877\pi$
$127$	−9.33641	−	16.1711i	−0.828472	−	1.43496i	0.0707642	−	0.997493i	$-0.477456\pi$
$128$	4.65190	−	10.3131i	0.411174	−	0.911557i
$129$			5.25777i			0.462921i
$130$	3.10697	−	9.68328i	0.272499	−	0.849280i
$131$		−	1.99640i		−	0.174426i	−0.996190	−	0.0872132i	$-0.972204\pi$
$131$		−	1.99640i		−	0.174426i	0.996190	−	0.0872132i	$-0.0277961\pi$
$132$	−8.31315	−	0.697182i	−0.723567	−	0.0606819i
$133$	0.191957	+	0.332479i	0.0166448	+	0.0288296i
$134$	−16.1125	+	5.89731i	−1.39191	+	0.509450i
$135$	−1.41026	+	1.41026i	−0.121376	+	0.121376i
$136$	−0.855038	+	3.26134i	−0.0733189	+	0.279657i
$137$	1.23880	+	4.62328i	0.105838	+	0.394993i	0.998439	−	0.0558547i	$-0.0177884\pi$
$137$	1.23880	+	4.62328i	0.105838	+	0.394993i	−0.892601	+	0.450848i	$0.851122\pi$
$138$	7.91434	−	0.706761i	0.673713	−	0.0601635i
$139$	17.6034	+	10.1634i	1.49310	+	0.862044i	0.999969	−	0.00790774i	$-0.00251714\pi$
$139$	17.6034	+	10.1634i	1.49310	+	0.862044i	0.493136	+	0.869952i	$0.335850\pi$
$140$	2.66319	−	2.25106i	0.225081	−	0.190249i
$141$	8.25036	+	2.21068i	0.694806	+	0.186173i
$142$	16.1526	+	13.5042i	1.35549	+	1.13325i
$143$	−13.8548	−	5.85033i	−1.15860	−	0.489229i
$144$	−3.74883	+	1.39509i	−0.312403	+	0.116257i
$145$	3.70016	−	13.8092i	0.307282	−	1.14679i
$146$	2.92620	−	16.7717i	0.242174	−	1.38803i
$147$	3.11787	−	5.40031i	0.257158	−	0.445410i
$148$	11.7472	−	16.9059i	0.965617	−	1.38966i
$149$	−3.92425	+	1.05150i	−0.321487	+	0.0861423i	−0.415954	−	0.909386i	$-0.636552\pi$
$149$	−3.92425	+	1.05150i	−0.321487	+	0.0861423i	0.0944664	+	0.995528i	$0.469885\pi$
$150$	−1.31144	−	0.608667i	−0.107079	−	0.0496975i
$151$	5.52004	+	5.52004i	0.449215	+	0.449215i	0.895093	−	0.445879i	$-0.147109\pi$
$151$	5.52004	+	5.52004i	0.449215	+	0.449215i	−0.445879	+	0.895093i	$0.647109\pi$
$152$	−1.07233	+	0.626848i	−0.0869772	+	0.0508441i
$153$	1.03232	−	0.596013i	0.0834585	−	0.0481848i
$154$	−2.96550	−	4.21900i	−0.238967	−	0.339977i
$155$	8.78224			0.705407
$156$	−7.20522	+	0.291124i	−0.576880	+	0.0233086i
$157$	13.8194			1.10291			0.551454	−	0.834206i	$-0.314073\pi$
$157$	13.8194			1.10291			0.551454	+	0.834206i	$0.314073\pi$
$158$	7.32087	+	10.4154i	0.582417	+	0.828602i
$159$	6.42084	−	3.70707i	0.509205	−	0.293990i
$160$	7.32941	+	8.57700i	0.579440	+	0.678071i
$161$	3.47320	+	3.47320i	0.273727	+	0.273727i
$162$	1.28279	+	0.595366i	0.100785	+	0.0467764i
$163$	−21.8117	+	5.84443i	−1.70842	+	0.457771i	−0.975037	−	0.222041i	$-0.928728\pi$
$163$	−21.8117	+	5.84443i	−1.70842	+	0.457771i	−0.733387	+	0.679812i	$0.762062\pi$
$164$	−9.72958	−	6.76069i	−0.759752	−	0.527921i
$165$	4.15950	−	7.20447i	0.323817	−	0.560867i
$166$	0.767554	−	4.39927i	0.0595738	−	0.341450i
$167$	−4.68444	+	17.4826i	−0.362493	+	1.35284i	0.508295	+	0.861183i	$0.330276\pi$
$167$	−4.68444	+	17.4826i	−0.362493	+	1.35284i	−0.870788	+	0.491659i	$0.836391\pi$
$168$	−2.14803	−	1.22476i	−0.165724	−	0.0944923i
$169$	−12.5098	−	3.53631i	−0.962291	−	0.272024i
$170$	−2.57942	−	2.15650i	−0.197833	−	0.165396i
$171$	0.424187	+	0.113660i	0.0324384	+	0.00869183i
$172$	−6.78819	−	8.03100i	−0.517595	−	0.612358i
$173$	−10.4553	−	6.03640i	−0.794906	−	0.458939i	0.0467811	−	0.998905i	$-0.485104\pi$
$173$	−10.4553	−	6.03640i	−0.794906	−	0.458939i	−0.841687	+	0.539966i	$0.818437\pi$
$174$	−10.0972	+	0.901694i	−0.765467	+	0.0683572i
$175$	−0.231320	−	0.863297i	−0.0174861	−	0.0652591i
$176$	13.5981	−	9.66802i	1.02499	−	0.728754i
$177$	−1.00327	+	1.00327i	−0.0754103	+	0.0754103i
$178$	−20.1286	+	7.36726i	−1.50871	+	0.552199i
$179$	10.1517	+	17.5832i	0.758773	+	1.31423i	0.943477	+	0.331439i	$0.107534\pi$
$179$	10.1517	+	17.5832i	0.758773	+	1.31423i	−0.184704	+	0.982794i	$0.559133\pi$
$180$	0.333351	−	3.97486i	0.0248465	−	0.296269i
$181$		−	8.22467i		−	0.611335i	−0.952138	−	0.305667i	$-0.901120\pi$
$181$		−	8.22467i		−	0.611335i	0.952138	−	0.305667i	$-0.0988796\pi$
$182$	−2.99492	−	3.30170i	−0.221998	−	0.244738i
$183$			1.45170i			0.107313i
$184$	−11.1763	+	11.2976i	−0.823928	+	0.832868i
$185$	10.2645	+	17.7786i	0.754661	+	1.30711i
$186$	−2.14042	−	5.84800i	−0.156943	−	0.428796i
$187$	−3.51583	+	3.51583i	−0.257103	+	0.257103i
$188$	−15.4562	+	7.27516i	−1.12726	+	0.530595i
$189$	0.226265	+	0.844432i	0.0164583	+	0.0614234i
$190$	−0.110173	−	1.23372i	−0.00799279	−	0.0895036i
$191$	3.99876	+	2.30868i	0.289340	+	0.167050i	0.637644	−	0.770331i	$-0.279909\pi$
$191$	3.99876	+	2.30868i	0.289340	+	0.167050i	−0.348304	+	0.937382i	$0.613242\pi$
$192$	3.92500	−	6.97097i	0.283262	−	0.503086i
$193$	5.34321	+	1.43171i	0.384613	+	0.103057i	0.445944	−	0.895061i	$-0.352868\pi$
$193$	5.34321	+	1.43171i	0.384613	+	0.103057i	−0.0613315	+	0.998117i	$0.519535\pi$
$194$	−5.63369	+	6.73855i	−0.404475	+	0.483800i
$195$	2.79728	−	6.62456i	0.200318	−	0.474395i
$196$	2.20982	+	12.2741i	0.157844	+	0.876724i
$197$	−0.548417	+	2.04672i	−0.0390731	+	0.145823i	−0.982707	−	0.185169i	$-0.940717\pi$
$197$	−0.548417	+	2.04672i	−0.0390731	+	0.145823i	0.943634	+	0.330992i	$0.107383\pi$
$198$	−5.81114	−	1.01389i	−0.412980	−	0.0720538i
$199$	−3.51919	+	6.09542i	−0.249469	+	0.432093i	−0.963379	−	0.268145i	$-0.913589\pi$
$199$	−3.51919	+	6.09542i	−0.249469	+	0.432093i	0.713910	+	0.700238i	$0.246923\pi$
$200$	2.78901	−	0.763466i	0.197213	−	0.0539852i
$201$	−11.7190	+	3.14010i	−0.826596	+	0.221486i
$202$	5.52380	−	11.9017i	0.388653	−	0.837399i
$203$	−4.43115	−	4.43115i	−0.311006	−	0.311006i
$204$	−0.807329	+	2.24319i	−0.0565244	+	0.157055i
$205$	10.2318	−	5.90736i	0.714623	−	0.412588i
$206$	0.0734216	−	0.0516074i	0.00511553	−	0.00359566i
$207$	5.61855			0.390516
$208$	10.6298	−	9.74719i	0.737043	−	0.675846i
$209$	−1.83177			−0.126706
$210$	2.01728	−	1.41793i	0.139205	−	0.0978463i
$211$	−16.0677	+	9.27668i	−1.10614	+	0.638633i	−0.937828	−	0.347100i	$-0.887166\pi$
$211$	−16.0677	+	9.27668i	−1.10614	+	0.638633i	−0.168316	+	0.985733i	$0.553833\pi$
$212$	−5.02141	+	13.9522i	−0.344872	+	0.958240i
$213$	10.5270	+	10.5270i	0.721296	+	0.721296i
$214$	−1.82596	+	3.93425i	−0.124820	+	0.268940i
$215$	10.1288	−	2.71401i	0.690780	−	0.185094i
$216$	−2.72806	+	0.746782i	−0.185621	+	0.0508121i
$217$	1.92479	−	3.33383i	0.130663	−	0.226315i
$218$	12.6146	+	2.20091i	0.854370	+	0.149064i
$219$	3.11580	−	11.6283i	0.210546	−	0.785768i
$220$	2.94809	+	16.3747i	0.198760	+	1.10399i
$221$	−2.63969	+	3.39176i	−0.177565	+	0.228155i
$222$	9.33693	−	11.1680i	0.626653	−	0.749550i
$223$	−15.1392	−	4.05654i	−1.01380	−	0.271646i	−0.286582	−	0.958056i	$-0.592519\pi$
$223$	−15.1392	−	4.05654i	−1.01380	−	0.271646i	−0.727215	+	0.686410i	$0.759186\pi$
$224$	4.86228	−	0.902512i	0.324875	−	0.0603017i
$225$	−0.885373	−	0.511170i	−0.0590249	−	0.0340780i
$226$	1.60940	+	18.0222i	0.107056	+	1.19882i
$227$	3.44372	+	12.8521i	0.228568	+	0.853027i	0.980944	+	0.194293i	$0.0622412\pi$
$227$	3.44372	+	12.8521i	0.228568	+	0.853027i	−0.752376	+	0.658734i	$0.771092\pi$
$228$	−0.794670	+	0.374047i	−0.0526283	+	0.0247719i
$229$	−2.10197	+	2.10197i	−0.138902	+	0.138902i	−0.773139	−	0.634237i	$-0.781315\pi$
$229$	−2.10197	+	2.10197i	−0.138902	+	0.138902i	0.634237	+	0.773139i	$0.281315\pi$
$230$	−5.44684	−	14.8817i	−0.359154	−	0.981273i
$231$	−1.82326	−	3.15798i	−0.119962	−	0.207780i
$232$	14.2589	−	14.4136i	0.936140	−	0.946297i
$233$			17.3311i			1.13540i	0.823236	+	0.567699i	$0.192166\pi$
$233$			17.3311i			1.13540i	−0.823236	+	0.567699i	$0.807834\pi$
$234$	−5.09298	−	0.248135i	−0.332938	−	0.0162211i
$235$		−	17.0350i		−	1.11124i
$236$	0.237149	−	2.82775i	0.0154371	−	0.184071i
$237$	4.50104	+	7.79603i	0.292374	+	0.506407i
$238$	−1.38396	+	0.506539i	−0.0897085	+	0.0328341i
$239$	14.3197	−	14.3197i	0.926263	−	0.926263i	−0.0711994	−	0.997462i	$-0.522683\pi$
$239$	14.3197	−	14.3197i	0.926263	−	0.926263i	0.997462	+	0.0711994i	$0.0226827\pi$
$240$	4.62268	+	6.50180i	0.298393	+	0.419689i
$241$	5.75279	+	21.4697i	0.370570	+	1.38299i	0.859711	+	0.510781i	$0.170644\pi$
$241$	5.75279	+	21.4697i	0.370570	+	1.38299i	−0.489141	+	0.872205i	$0.662690\pi$
$242$	9.01318	−	0.804890i	0.579389	−	0.0517403i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−1.87426	−	2.21741i	−0.119987	−	0.141955i
$245$	−12.0128	−	3.21883i	−0.767472	−	0.205643i
$246$	−6.42736	−	5.37353i	−0.409794	−	0.342604i
$247$	−1.57121	+	0.195918i	−0.0999738	+	0.0124659i
$248$	10.8196	+	6.16911i	0.687046	+	0.391739i
$249$	0.817285	−	3.05015i	0.0517933	−	0.193295i
$250$	−2.91952	+	16.7333i	−0.184646	+	1.05831i
$251$	9.99140	−	17.3056i	0.630652	−	1.09232i	−0.356767	−	0.934193i	$-0.616121\pi$
$251$	9.99140	−	17.3056i	0.630652	−	1.09232i	0.987419	−	0.158128i	$-0.0505457\pi$
$252$	−1.43584	−	0.997705i	−0.0904492	−	0.0628495i
$253$	−22.6374	+	6.06566i	−1.42320	+	0.381345i
$254$	23.9532	+	11.1172i	1.50296	+	0.697553i
$255$	−1.68106	−	1.68106i	−0.105272	−	0.105272i
$256$	3.00481	+	15.7153i	0.187800	+	0.982207i
$257$	8.97472	−	5.18155i	0.559827	−	0.323217i	−0.193249	−	0.981150i	$-0.561902\pi$
$257$	8.97472	−	5.18155i	0.559827	−	0.323217i	0.753076	+	0.657933i	$0.228569\pi$
$258$	−4.27584	−	6.08321i	−0.266202	−	0.378724i
$259$	8.99859			0.559145
$260$	4.28010	+	13.7302i	0.265441	+	0.851512i
$261$	−7.16821			−0.443701
$262$	1.62356	+	2.30983i	0.100304	+	0.142702i
$263$	0.156182	−	0.0901719i	0.00963061	−	0.00556024i	−0.495177	−	0.868792i	$-0.664897\pi$
$263$	0.156182	−	0.0901719i	0.00963061	−	0.00556024i	0.504808	+	0.863232i	$0.331563\pi$
$264$	10.1853	−	5.95397i	0.626859	−	0.366441i
$265$	−10.4559	−	10.4559i	−0.642298	−	0.642298i
$266$	−0.492479	−	0.228569i	−0.0301958	−	0.0140145i
$267$	−14.6401	+	3.92279i	−0.895957	+	0.240071i
$268$	13.8461	−	19.9265i	0.845788	−	1.21721i
$269$	7.06284	−	12.2332i	0.430629	−	0.745871i	−0.566299	−	0.824200i	$-0.691625\pi$
$269$	7.06284	−	12.2332i	0.430629	−	0.745871i	0.996928	+	0.0783291i	$0.0249585\pi$
$270$	0.484781	−	2.77854i	0.0295028	−	0.169097i
$271$	−2.56276	+	9.56434i	−0.155676	+	0.580992i	0.843370	+	0.537333i	$0.180568\pi$
$271$	−2.56276	+	9.56434i	−0.155676	+	0.580992i	−0.999046	+	0.0436590i	$0.986098\pi$
$272$	−1.66298	−	4.46870i	−0.100833	−	0.270955i
$273$	−1.90167	−	2.51377i	−0.115095	−	0.152140i
$274$	−5.19313	−	4.34166i	−0.313729	−	0.262289i
$275$	4.11905	+	1.10370i	0.248388	+	0.0665554i
$276$	−8.58208	+	7.25399i	−0.516580	+	0.436639i
$277$	−1.72886	−	0.998158i	−0.103877	−	0.0599735i	0.447161	−	0.894453i	$-0.352435\pi$
$277$	−1.72886	−	0.998158i	−0.103877	−	0.0599735i	−0.551039	+	0.834480i	$0.685768\pi$
$278$	−28.6324	+	2.55691i	−1.71726	+	0.153353i
$279$	−1.13969	−	4.25339i	−0.0682316	−	0.254644i
$280$	−1.25065	+	4.77029i	−0.0747403	+	0.285079i
$281$	−3.96986	+	3.96986i	−0.236822	+	0.236822i	−0.815533	−	0.578711i	$-0.803556\pi$
$281$	−3.96986	+	3.96986i	−0.236822	+	0.236822i	0.578711	+	0.815533i	$0.303556\pi$
$282$	−11.3434	+	4.15180i	−0.675492	+	0.247236i
$283$	−14.1808	−	24.5618i	−0.842959	−	1.46005i	−0.887382	−	0.461034i	$-0.847479\pi$
$283$	−14.1808	−	24.5618i	−0.842959	−	1.46005i	0.0444238	−	0.999013i	$-0.485855\pi$
$284$	−29.6706	−	2.48832i	−1.76063	−	0.147655i
$285$		−	0.875844i		−	0.0518805i
$286$	20.7877	−	4.49852i	1.22920	−	0.266003i
$287$		−	5.17881i		−	0.305696i
$288$	3.20283	−	4.66282i	0.188729	−	0.274759i
$289$	−7.78954	−	13.4919i	−0.458208	−	0.793640i
$290$	6.94915	+	18.9863i	0.408068	+	1.11491i
$291$	−4.39166	+	4.39166i	−0.257443	+	0.257443i
$292$	10.2538	+	21.7844i	0.600059	+	1.27484i
$293$	−0.0383827	−	0.143246i	−0.00224234	−	0.00836854i	0.964796	−	0.263001i	$-0.0847122\pi$
$293$	−0.0383827	−	0.143246i	−0.00224234	−	0.00836854i	−0.967038	+	0.254632i	$0.918046\pi$
$294$	0.784398	+	8.78371i	0.0457470	+	0.512277i
$295$	2.45062	+	1.41487i	0.142681	+	0.0823768i
$296$	0.157098	+	29.1134i	0.00913112	+	1.69218i
$297$	−4.02904	−	1.07958i	−0.233789	−	0.0626435i
$298$	3.68522	−	4.40795i	0.213479	−	0.255346i
$299$	−18.7686	+	7.62404i	−1.08541	+	0.440910i
$300$	2.01233	−	0.362297i	0.116182	−	0.0209172i
$301$	1.18965	−	4.43983i	0.0685702	−	0.255907i
$302$	−10.8758	−	1.89753i	−0.625831	−	0.109191i
$303$	4.63900	−	8.03498i	0.266503	−	0.461597i
$304$	0.730899	−	1.59732i	0.0419199	−	0.0916127i
$305$	2.79663	−	0.749354i	0.160134	−	0.0429079i
$306$	−0.709692	+	1.52911i	−0.0405704	+	0.0874136i
$307$	8.00463	+	8.00463i	0.456848	+	0.456848i	0.897619	−	0.440771i	$-0.145295\pi$
$307$	8.00463	+	8.00463i	0.456848	+	0.456848i	−0.440771	+	0.897619i	$0.645295\pi$
$308$	6.86214	+	2.46970i	0.391007	+	0.140724i
$309$	0.0549570	−	0.0317294i	0.00312640	−	0.00180503i
$310$	−10.1610	+	7.14209i	−0.577107	+	0.405643i
$311$	8.45104			0.479214			0.239607	−	0.970870i	$-0.422981\pi$
$311$	8.45104			0.479214			0.239607	+	0.970870i	$0.422981\pi$
$312$	8.09965	−	6.19642i	0.458553	−	0.350803i
$313$	−6.93005			−0.391709			−0.195855	−	0.980633i	$-0.562748\pi$
$313$	−6.93005			−0.391709			−0.195855	+	0.980633i	$0.562748\pi$
$314$	−15.9890	+	11.2385i	−0.902309	+	0.634225i
$315$	1.50996	−	0.871775i	0.0850765	−	0.0491190i
$316$	−16.9404	−	6.09689i	−0.952973	−	0.342977i
$317$	−11.6668	−	11.6668i	−0.655275	−	0.655275i	0.298984	−	0.954258i	$-0.403352\pi$
$317$	−11.6668	−	11.6668i	−0.655275	−	0.655275i	−0.954258	+	0.298984i	$0.903352\pi$
$318$	−4.41413	+	9.51076i	−0.247532	+	0.533337i
$319$	28.8810	−	7.73864i	1.61703	−	0.433281i
$320$	−15.4553	−	3.96296i	−0.863975	−	0.221536i
$321$	−1.53348	+	2.65606i	−0.0855904	+	0.148247i
$322$	−6.84303	−	1.19392i	−0.381347	−	0.0665348i
$323$	−0.135486	+	0.505641i	−0.00753865	+	0.0281346i
$324$	−1.96835	+	0.354379i	−0.109353	+	0.0196877i
$325$	3.65119	+	0.506148i	0.202531	+	0.0280760i
$326$	20.4831	−	24.5002i	1.13445	−	1.35694i
$327$	8.74610	+	2.34351i	0.483660	+	0.129596i
$328$	16.7551	−	0.0904119i	0.925148	−	0.00499216i
$329$	−6.46667	−	3.73353i	−0.356519	−	0.205836i
$330$	1.04645	+	11.7182i	0.0576054	+	0.645067i
$331$	−2.96926	−	11.0814i	−0.163206	−	0.609091i	−0.998262	−	0.0589276i	$-0.981232\pi$
$331$	−2.96926	−	11.0814i	−0.163206	−	0.609091i	0.835057	−	0.550164i	$-0.185435\pi$
$332$	2.68962	+	5.71414i	0.147612	+	0.313604i
$333$	7.27845	−	7.27845i	0.398857	−	0.398857i
$334$	−8.79768	−	24.0368i	−0.481388	−	1.31524i
$335$	12.0985	+	20.9552i	0.661011	+	1.14490i
$336$	3.48129	−	0.329828i	0.189920	−	0.0179936i
$337$		−	27.7472i		−	1.51149i	−0.654867	−	0.755744i	$-0.727276\pi$
$337$		−	27.7472i		−	1.51149i	0.654867	−	0.755744i	$-0.272724\pi$
$338$	17.3496	−	6.08199i	0.943695	−	0.330817i
$339$			12.7943i			0.694891i
$340$	4.73814	+	0.397363i	0.256961	+	0.0215501i
$341$	9.18373	+	15.9067i	0.497327	+	0.861396i
$342$	−0.583215	+	0.213462i	−0.0315367	+	0.0115427i
$343$	−8.18189	+	8.18189i	−0.441781	+	0.441781i
$344$	14.3851	+	3.77139i	0.775590	+	0.203340i
$345$	−2.90024	−	10.8239i	−0.156144	−	0.582737i
$346$	17.0058	−	1.51865i	0.914240	−	0.0816429i
$347$	−21.8676	−	12.6253i	−1.17391	−	0.677759i	−0.219315	−	0.975654i	$-0.570382\pi$
$347$	−21.8676	−	12.6253i	−1.17391	−	0.677759i	−0.954599	+	0.297895i	$0.903716\pi$
$348$	10.9491	−	9.25472i	0.586934	−	0.496105i
$349$	−5.09218	−	1.36445i	−0.272578	−	0.0730371i	0.119941	−	0.992781i	$-0.461730\pi$
$349$	−5.09218	−	1.36445i	−0.272578	−	0.0730371i	−0.392519	+	0.919744i	$0.628396\pi$
$350$	0.969705	+	0.810711i	0.0518329	+	0.0433343i
$351$	−3.57140	−	0.495087i	−0.190627	−	0.0264258i
$352$	−7.87047	+	22.2444i	−0.419498	+	1.18563i
$353$	−4.06618	+	15.1752i	−0.216421	+	0.807694i	0.769241	+	0.638959i	$0.220635\pi$
$353$	−4.06618	+	15.1752i	−0.216421	+	0.807694i	−0.985662	+	0.168735i	$0.946032\pi$
$354$	0.344877	−	1.97668i	0.0183300	−	0.105059i
$355$	14.8457	−	25.7136i	0.787930	−	1.36474i
$356$	17.2974	−	24.8933i	0.916759	−	1.31934i
$357$	−1.00658	+	0.269713i	−0.0532741	+	0.0142747i
$358$	−26.0449	−	12.0879i	−1.37651	−	0.638868i
$359$	−10.6521	−	10.6521i	−0.562196	−	0.562196i	0.367734	−	0.929931i	$-0.380134\pi$
$359$	−10.6521	−	10.6521i	−0.562196	−	0.562196i	−0.929931	+	0.367734i	$0.880134\pi$
$360$	2.84684	+	4.86999i	0.150041	+	0.256671i
$361$	16.2875	−	9.40357i	0.857235	−	0.494925i
$362$	6.68865	+	9.51590i	0.351547	+	0.500145i
$363$	6.39864			0.335842
$364$	6.15019	+	1.38445i	0.322358	+	0.0725651i
$365$	−24.0097			−1.25672
$366$	−1.18058	−	1.67961i	−0.0617101	−	0.0877947i
$367$	5.35029	−	3.08899i	0.279283	−	0.161244i	−0.353816	−	0.935315i	$-0.615116\pi$
$367$	5.35029	−	3.08899i	0.279283	−	0.161244i	0.633099	+	0.774071i	$0.281783\pi$
$368$	3.74327	−	22.1603i	0.195131	−	1.15518i
$369$	−4.18885	−	4.18885i	−0.218063	−	0.218063i
$370$	−26.3343	−	12.2223i	−1.36906	−	0.635406i
$371$	−6.26074	+	1.67756i	−0.325041	+	0.0870945i
$372$	7.23229	+	5.02543i	0.374977	+	0.260556i
$373$	−9.26753	+	16.0518i	−0.479854	+	0.831132i	−0.999733	−	0.0231080i	$-0.992644\pi$
$373$	−9.26753	+	16.0518i	−0.479854	+	0.831132i	0.519879	+	0.854240i	$0.325977\pi$
$374$	1.20858	−	6.92703i	0.0624941	−	0.358188i
$375$	−3.10868	+	11.6017i	−0.160531	+	0.599111i
$376$	11.9663	−	20.9870i	0.617115	−	1.08232i
$377$	23.9452	−	9.72684i	1.23324	−	0.500958i
$378$	−0.948514	−	0.792995i	−0.0487863	−	0.0407873i
$379$	−6.99426	−	1.87411i	−0.359271	−	0.0962664i	0.0746684	−	0.997208i	$-0.476210\pi$
$379$	−6.99426	−	1.87411i	−0.359271	−	0.0962664i	−0.433939	+	0.900942i	$0.642877\pi$
$380$	1.13078	+	1.33781i	0.0580080	+	0.0686283i
$381$	16.1711	+	9.33641i	0.828472	+	0.478319i
$382$	−6.50406	+	0.580822i	−0.332777	+	0.0297174i
$383$	−6.33304	−	23.6352i	−0.323603	−	1.20770i	−0.915709	−	0.401843i	$-0.868370\pi$
$383$	−6.33304	−	23.6352i	−0.323603	−	1.20770i	0.592105	−	0.805861i	$-0.298297\pi$
$384$	1.12788	+	11.2573i	0.0575568	+	0.574474i
$385$	−5.14253	+	5.14253i	−0.262088	+	0.262088i
$386$	−7.34639	+	2.68884i	−0.373921	+	0.136858i
$387$	−2.62888	−	4.55336i	−0.133634	−	0.231460i
$388$	1.03808	−	12.3780i	0.0527006	−	0.628399i
$389$		−	30.2731i		−	1.53491i	−0.641104	−	0.767454i	$-0.721523\pi$
$389$		−	30.2731i		−	1.53491i	0.641104	−	0.767454i	$-0.278477\pi$
$390$	2.15093	+	9.93945i	0.108916	+	0.503304i
$391$			6.69746i			0.338705i
$392$	−12.5386	−	12.4040i	−0.633295	−	0.626497i
$393$	0.998200	+	1.72893i	0.0503526	+	0.0872132i
$394$	−1.02996	−	2.81404i	−0.0518888	−	0.141769i
$395$	12.6953	−	12.6953i	0.638768	−	0.638768i
$396$	7.54799	−	3.55280i	0.379301	−	0.178535i
$397$	8.68943	+	32.4294i	0.436110	+	1.62759i	0.738396	+	0.674368i	$0.235584\pi$
$397$	8.68943	+	32.4294i	0.436110	+	1.62759i	−0.302285	+	0.953217i	$0.597750\pi$
$398$	−0.885363	−	9.91433i	−0.0443792	−	0.496960i
$399$	−0.332479	−	0.191957i	−0.0166448	−	0.00960987i
$400$	−2.60599	+	3.15146i	−0.130299	+	0.157573i
$401$	2.45452	+	0.657686i	0.122573	+	0.0328433i	0.319584	−	0.947558i	$-0.396457\pi$
$401$	2.45452	+	0.657686i	0.122573	+	0.0328433i	−0.197011	+	0.980401i	$0.563124\pi$
$402$	11.0052	−	13.1635i	0.548889	−	0.656535i
$403$	9.57871	+	12.6618i	0.477149	+	0.630730i
$404$	3.28793	+	18.2624i	0.163581	+	0.908587i
$405$	0.516191	−	1.92645i	0.0256497	−	0.0957260i
$406$	8.73042	+	1.52322i	0.433283	+	0.0755962i
$407$	−21.4675	+	37.1828i	−1.06411	+	1.84308i
$408$	−0.890184	−	3.25192i	−0.0440707	−	0.160994i
$409$	11.3051	−	3.02919i	0.559001	−	0.149784i	0.0317536	−	0.999496i	$-0.489891\pi$
$409$	11.3051	−	3.02919i	0.559001	−	0.149784i	0.527247	+	0.849712i	$0.323224\pi$
$410$	−7.03408	+	15.1558i	−0.347389	+	0.748489i
$411$	−3.38447	−	3.38447i	−0.166944	−	0.166944i
$412$	−0.0429791	+	0.119419i	−0.00211743	+	0.00588336i
$413$	1.07420	−	0.620188i	0.0528577	−	0.0305174i
$414$	−6.50063	+	4.56924i	−0.319489	+	0.224566i
$415$	−6.29783			−0.309148
$416$	−4.37179	+	19.9220i	−0.214345	+	0.976758i
$417$	−20.3267			−0.995403
$418$	2.11935	−	1.48967i	0.103661	−	0.0728622i
$419$	7.14605	−	4.12577i	0.349107	−	0.201557i	−0.315185	−	0.949030i	$-0.602066\pi$
$419$	7.14605	−	4.12577i	0.349107	−	0.201557i	0.664292	+	0.747473i	$0.268733\pi$
$420$	−1.18086	+	3.28107i	−0.0576202	+	0.160100i
$421$	0.904777	+	0.904777i	0.0440961	+	0.0440961i	0.728811	−	0.684715i	$-0.240073\pi$
$421$	0.904777	+	0.904777i	0.0440961	+	0.0440961i	−0.684715	+	0.728811i	$0.740073\pi$
$422$	11.0460	−	23.8000i	0.537713	−	1.15856i
$423$	−8.25036	+	2.21068i	−0.401146	+	0.107487i
$424$	−5.53675	−	20.2262i	−0.268888	−	0.982273i
$425$	0.609328	−	1.05539i	0.0295568	−	0.0511938i
$426$	−20.7406	−	3.61868i	−1.00489	−	0.175325i
$427$	0.328469	−	1.22586i	0.0158957	−	0.0593236i
$428$	−1.08687	−	6.03685i	−0.0525356	−	0.291802i
$429$	14.9238	−	1.86088i	0.720527	−	0.0898440i
$430$	−9.51185	+	11.3773i	−0.458702	+	0.548661i
$431$	0.754647	+	0.202207i	0.0363501	+	0.00973997i	0.276948	−	0.960885i	$-0.410677\pi$
$431$	0.754647	+	0.202207i	0.0363501	+	0.00973997i	−0.240598	+	0.970625i	$0.577344\pi$
$432$	2.54904	−	3.08260i	0.122641	−	0.148312i
$433$	25.1791	+	14.5371i	1.21003	+	0.698610i	0.962765	−	0.270338i	$-0.0871355\pi$
$433$	25.1791	+	14.5371i	1.21003	+	0.698610i	0.247263	+	0.968948i	$0.420469\pi$
$434$	0.484240	+	5.42254i	0.0232443	+	0.260290i
$435$	3.70016	+	13.8092i	0.177409	+	0.662100i
$436$	−16.3849	+	7.71229i	−0.784695	+	0.369352i
$437$	−1.74471	+	1.74471i	−0.0834606	+	0.0834606i
$438$	5.85167	+	15.9878i	0.279603	+	0.763926i
$439$	18.7202	+	32.4243i	0.893466	+	1.54753i	0.835692	+	0.549199i	$0.185067\pi$
$439$	18.7202	+	32.4243i	0.893466	+	1.54753i	0.0577741	+	0.998330i	$0.481600\pi$
$440$	−16.7276	−	16.5480i	−0.797455	−	0.788895i
$441$			6.23574i			0.296940i
$442$	0.295783	−	6.07096i	0.0140690	−	0.288766i
$443$			13.1681i			0.625634i	0.949813	+	0.312817i	$0.101273\pi$
$443$			13.1681i			0.625634i	−0.949813	+	0.312817i	$0.898727\pi$
$444$	−1.72045	+	20.5146i	−0.0816490	+	0.973578i
$445$	15.1141	+	26.1784i	0.716478	+	1.24098i
$446$	20.8149	−	7.61845i	0.985616	−	0.360744i
$447$	2.87275	−	2.87275i	0.135877	−	0.135877i
$448$	−4.89168	+	4.99842i	−0.231110	+	0.236153i
$449$	−4.47798	−	16.7121i	−0.211329	−	0.788691i	−0.987427	−	0.158078i	$-0.949470\pi$
$449$	−4.47798	−	16.7121i	−0.211329	−	0.788691i	0.776098	−	0.630613i	$-0.217196\pi$
$450$	1.44008	−	0.128601i	0.0678859	−	0.00606231i
$451$	21.3992	+	12.3548i	1.00765	+	0.581767i
$452$	−16.5184	−	19.5427i	−0.776962	−	0.919212i
$453$	−7.54052	−	2.02048i	−0.354284	−	0.0949302i
$454$	−14.4363	−	12.0693i	−0.677528	−	0.566440i
$455$	−3.86102	+	4.96106i	−0.181007	+	0.232578i
$456$	0.615239	−	1.07903i	0.0288112	−	0.0505302i
$457$	−5.01155	+	18.7034i	−0.234431	+	0.874907i	0.743974	+	0.668208i	$0.232939\pi$
$457$	−5.01155	+	18.7034i	−0.234431	+	0.874907i	−0.978405	+	0.206698i	$0.933728\pi$
$458$	0.722560	−	4.14139i	0.0337630	−	0.193514i
$459$	−0.596013	+	1.03232i	−0.0278195	+	0.0481848i
$460$	18.4044	+	12.7885i	0.858111	+	0.596267i
$461$	−10.5317	+	2.82196i	−0.490510	+	0.131432i	−0.495592	−	0.868555i	$-0.665049\pi$
$461$	−10.5317	+	2.82196i	−0.490510	+	0.131432i	0.00508232	+	0.999987i	$0.498382\pi$
$462$	4.67770	+	2.17101i	0.217626	+	0.101005i
$463$	8.32815	+	8.32815i	0.387042	+	0.387042i	0.873631	−	0.486589i	$-0.161759\pi$
$463$	8.32815	+	8.32815i	0.387042	+	0.387042i	−0.486589	+	0.873631i	$0.661759\pi$
$464$	−4.77570	+	28.2723i	−0.221706	+	1.31251i
$465$	−7.60564	+	4.39112i	−0.352703	+	0.203633i
$466$	−14.0944	−	20.0520i	−0.652909	−	0.928891i
$467$	−22.3466			−1.03408			−0.517040	−	0.855961i	$-0.672966\pi$
$467$	−22.3466			−1.03408			−0.517040	+	0.855961i	$0.672966\pi$
$468$	6.09434	−	3.85473i	0.281711	−	0.178185i
$469$	10.6064			0.489758
$470$	13.8536	+	19.7095i	0.639019	+	0.909129i
$471$	−11.9679	+	6.90969i	−0.551454	+	0.318382i
$472$	2.02526	+	3.46455i	0.0932202	+	0.159469i
$473$	15.5076	+	15.5076i	0.713039	+	0.713039i
$474$	−11.5477	−	5.35954i	−0.530405	−	0.246172i
$475$	0.433663	−	0.116200i	0.0198978	−	0.00533161i
$476$	1.18929	−	1.71155i	0.0545110	−	0.0784489i
$477$	−3.70707	+	6.42084i	−0.169735	+	0.293990i
$478$	−4.92243	+	28.2132i	−0.225147	+	1.29044i
$479$	−1.89699	+	7.07967i	−0.0866757	+	0.323478i	−0.995626	−	0.0934258i	$-0.970218\pi$
$479$	−1.89699	+	7.07967i	−0.0866757	+	0.323478i	0.908951	+	0.416904i	$0.136885\pi$
$480$	−10.6360	−	3.76320i	−0.485463	−	0.171766i
$481$	−14.4370	+	34.1899i	−0.658270	+	1.55892i
$482$	−24.1160	−	20.1619i	−1.09845	−	0.918351i
$483$	−4.74448	−	1.27128i	−0.215881	−	0.0578452i
$484$	−9.77364	+	8.26115i	−0.444256	+	0.375507i
$485$	10.7272	+	6.19337i	0.487098	+	0.281226i
$486$	−1.40861	+	0.125791i	−0.0638958	+	0.00570598i
$487$	−1.59138	−	5.93910i	−0.0721122	−	0.269126i	0.920451	−	0.390858i	$-0.127822\pi$
$487$	−1.59138	−	5.93910i	−0.0721122	−	0.269126i	−0.992563	+	0.121732i	$0.961155\pi$
$488$	3.97180	+	1.04130i	0.179795	+	0.0471375i
$489$	15.9673	−	15.9673i	0.722065	−	0.722065i
$490$	16.5165	−	6.04517i	0.746138	−	0.273093i
$491$	−12.3285	−	21.3536i	−0.556377	−	0.963673i	−0.997795	−	0.0663711i	$-0.978858\pi$
$491$	−12.3285	−	21.3536i	−0.556377	−	0.963673i	0.441418	−	0.897301i	$-0.354475\pi$
$492$	11.8064	+	0.990143i	0.532274	+	0.0446391i
$493$		−	8.54469i		−	0.384834i
$494$	1.65856	−	1.50445i	0.0746219	−	0.0676884i
$495$			8.31901i			0.373912i
$496$	−17.5352	+	1.66134i	−0.787354	+	0.0745964i
$497$	−6.50742	−	11.2712i	−0.291898	−	0.505582i
$498$	1.53491	+	4.19366i	0.0687812	+	0.187922i
$499$	−15.6797	+	15.6797i	−0.701920	+	0.701920i	−0.964822	−	0.262903i	$-0.915320\pi$
$499$	−15.6797	+	15.6797i	−0.701920	+	0.701920i	0.262903	+	0.964822i	$0.415320\pi$
$500$	−10.2304	−	21.7347i	−0.457517	−	0.972004i
$501$	−4.68444	−	17.4826i	−0.209285	−	0.781064i
$502$	2.51365	+	28.1479i	0.112190	+	1.25630i
$503$	4.08836	+	2.36042i	0.182291	+	0.105246i	0.588369	−	0.808593i	$-0.299770\pi$
$503$	4.08836	+	2.36042i	0.182291	+	0.105246i	−0.406078	+	0.913839i	$0.633104\pi$
$504$	2.47263	−	0.0133425i	0.110140	−	0.000594322i
$505$	−17.8736	−	4.78921i	−0.795364	−	0.213117i
$506$	21.2585	−	25.4276i	0.945054	−	1.13039i
$507$	12.6019	−	3.19236i	0.559672	−	0.141778i
$508$	−36.7547	+	6.61726i	−1.63073	+	0.293594i
$509$	−1.74055	+	6.49582i	−0.0771485	+	0.287922i	−0.993712	−	0.111967i	$-0.964285\pi$
$509$	−1.74055	+	6.49582i	−0.0771485	+	0.287922i	0.916563	+	0.399889i	$0.130951\pi$
$510$	3.31210	+	0.577871i	0.146662	+	0.0255886i
$511$	−5.26215	+	9.11432i	−0.232784	+	0.403194i
$512$	−16.2569	−	15.7389i	−0.718460	−	0.695568i
$513$	−0.424187	+	0.113660i	−0.0187283	+	0.00501823i
$514$	−6.16984	+	13.2936i	−0.272140	+	0.586358i
$515$	−0.0894935	−	0.0894935i	−0.00394355	−	0.00394355i
$516$	9.89425	+	3.56096i	0.435570	+	0.156762i
$517$	30.8544	−	17.8138i	1.35698	−	0.783451i
$518$	−10.4113	+	7.31803i	−0.457448	+	0.321536i
$519$	12.0728			0.529937
$520$	−16.1181	−	12.4050i	−0.706823	−	0.543997i
$521$	38.2326			1.67500			0.837500	−	0.546437i	$-0.184016\pi$
$521$	38.2326			1.67500			0.837500	+	0.546437i	$0.184016\pi$
$522$	8.29359	−	5.82949i	0.363000	−	0.255150i
$523$	0.620722	−	0.358374i	0.0271423	−	0.0156706i	−0.486367	−	0.873754i	$-0.661678\pi$
$523$	0.620722	−	0.358374i	0.0271423	−	0.0156706i	0.513510	+	0.858084i	$0.328345\pi$
$524$	−3.75689	−	1.35211i	−0.164121	−	0.0590673i
$525$	0.631977	+	0.631977i	0.0275817	+	0.0275817i
$526$	−0.107371	+	0.231342i	−0.00468158	+	0.0100870i
$527$	5.07015	−	1.35854i	0.220859	−	0.0591791i
$528$	−6.94227	+	15.1718i	−0.302124	+	0.660267i
$529$	−4.28405	+	7.42020i	−0.186263	+	0.322617i
$530$	20.6005	+	3.59423i	0.894829	+	0.156124i
$531$	0.367222	−	1.37049i	0.0159361	−	0.0594742i
$532$	0.755678	−	0.136051i	0.0327628	−	0.00589857i
$533$	19.6767	+	8.30868i	0.852294	+	0.359889i
$534$	13.7483	−	16.4446i	0.594947	−	0.711625i
$535$	5.90833	+	1.58313i	0.255440	+	0.0684448i
$536$	0.185167	+	34.3152i	0.00799799	+	1.48219i
$537$	−17.5832	−	10.1517i	−0.758773	−	0.438078i
$538$	1.77688	+	19.8975i	0.0766066	+	0.857844i
$539$	−6.73197	−	25.1240i	−0.289966	−	1.08217i
$540$	1.69874	+	3.60901i	0.0731021	+	0.155307i
$541$	−7.47724	+	7.47724i	−0.321472	+	0.321472i	−0.849332	−	0.527860i	$-0.822995\pi$
$541$	−7.47724	+	7.47724i	−0.321472	+	0.321472i	0.527860	+	0.849332i	$0.322995\pi$
$542$	−4.81302	−	13.1500i	−0.206737	−	0.564842i
$543$	4.11234	+	7.12277i	0.176477	+	0.305667i
$544$	5.55820	+	3.81786i	0.238306	+	0.163689i
$545$		−	18.0586i		−	0.773546i
$546$	4.24453	+	1.36189i	0.181649	+	0.0582837i
$547$		−	39.2431i		−	1.67791i	−0.544197	−	0.838957i	$-0.683166\pi$
$547$		−	39.2431i		−	1.67791i	0.544197	−	0.838957i	$-0.316834\pi$
$548$	9.53925	+	0.800008i	0.407496	+	0.0341747i
$549$	−0.725851	−	1.25721i	−0.0309786	−	0.0536564i
$550$	−5.66329	+	2.07281i	−0.241484	+	0.0883851i
$551$	2.22592	−	2.22592i	0.0948273	−	0.0948273i
$552$	4.03018	−	15.3721i	0.171536	−	0.654282i
$553$	−2.03685	−	7.60164i	−0.0866159	−	0.323255i
$554$	2.81203	−	0.251118i	0.119472	−	0.0106690i
$555$	−17.7786	−	10.2645i	−0.754661	−	0.435704i
$556$	31.0481	−	26.2434i	1.31673	−	1.11297i
$557$	−33.3696	−	8.94137i	−1.41392	−	0.378858i	−0.530595	−	0.847625i	$-0.678032\pi$
$557$	−33.3696	−	8.94137i	−1.41392	−	0.378858i	−0.883322	+	0.468767i	$0.844698\pi$
$558$	4.77766	+	3.99431i	0.202254	+	0.169093i
$559$	14.9603	+	11.6431i	0.632755	+	0.492451i
$560$	−2.43241	−	6.53627i	−0.102788	−	0.276208i
$561$	1.28688	−	4.80272i	0.0543323	−	0.202771i
$562$	1.36465	−	7.82157i	0.0575644	−	0.329933i
$563$	−14.7468	+	25.5421i	−0.621502	+	1.07647i	0.367704	+	0.929943i	$0.380144\pi$
$563$	−14.7468	+	25.5421i	−0.621502	+	1.07647i	−0.989206	+	0.146530i	$0.953189\pi$
$564$	9.74789	−	14.0286i	0.410460	−	0.590710i
$565$	24.6476	−	6.60430i	1.03693	−	0.277845i
$566$	36.3817	+	16.8855i	1.52924	+	0.709750i
$567$	−0.618167	−	0.618167i	−0.0259606	−	0.0259606i
$568$	36.3523	−	21.2504i	1.52531	−	0.891647i
$569$	−19.5291	+	11.2752i	−0.818704	+	0.472679i	−0.849970	−	0.526832i	$-0.823380\pi$
$569$	−19.5291	+	11.2752i	−0.818704	+	0.472679i	0.0312650	+	0.999511i	$0.490046\pi$
$570$	0.712273	+	1.01335i	0.0298339	+	0.0424445i
$571$	−37.3848			−1.56450			−0.782252	−	0.622963i	$-0.785929\pi$
$571$	−37.3848			−1.56450			−0.782252	+	0.622963i	$0.785929\pi$
$572$	−20.3929	+	22.1102i	−0.852669	+	0.924473i
$573$	−4.61737			−0.192893
$574$	4.21163	+	5.99186i	0.175790	+	0.250095i
$575$	4.97451	−	2.87204i	0.207452	−	0.119772i
$576$	0.0863346	+	7.99953i	0.00359727	+	0.333314i
$577$	4.04431	+	4.04431i	0.168367	+	0.168367i	0.786261	−	0.617894i	$-0.212014\pi$
$577$	4.04431	+	4.04431i	0.168367	+	0.168367i	−0.617894	+	0.786261i	$0.712014\pi$
$578$	19.9846	+	9.27525i	0.831250	+	0.385800i
$579$	−5.34321	+	1.43171i	−0.222056	+	0.0594998i
$580$	−23.4806	−	16.3157i	−0.974978	−	0.677473i
$581$	−1.38028	+	2.39072i	−0.0572638	+	0.0991838i
$582$	1.50965	−	8.65260i	0.0625768	−	0.358662i
$583$	8.00414	−	29.8719i	0.331498	−	1.23717i
$584$	−29.5796	−	16.8657i	−1.22401	−	0.697906i
$585$	0.889762	+	7.13568i	0.0367871	+	0.295024i
$586$	0.160902	+	0.134521i	0.00664682	+	0.00555700i
$587$	11.3399	+	3.03851i	0.468047	+	0.125413i	0.485131	−	0.874441i	$-0.338772\pi$
$587$	11.3399	+	3.03851i	0.468047	+	0.125413i	−0.0170846	+	0.999854i	$0.505438\pi$
$588$	−8.05083	−	9.52481i	−0.332011	−	0.392796i
$589$	1.67469	+	0.966885i	0.0690046	+	0.0398398i
$590$	−3.98599	+	0.355955i	−0.164101	+	0.0146544i
$591$	−0.548417	−	2.04672i	−0.0225589	−	0.0841908i
$592$	−23.8580	−	33.5563i	−0.980557	−	1.37915i
$593$	6.76464	−	6.76464i	0.277790	−	0.277790i	−0.554436	−	0.832226i	$-0.687066\pi$
$593$	6.76464	−	6.76464i	0.277790	−	0.277790i	0.832226	+	0.554436i	$0.187066\pi$
$594$	5.53954	−	2.02752i	0.227290	−	0.0831900i
$595$	1.03918	+	1.79991i	0.0426022	+	0.0737891i
$596$	−0.679050	+	8.09695i	−0.0278150	+	0.331664i
$597$		−	7.03839i		−	0.288062i
$598$	15.5150	−	24.0844i	0.634454	−	0.984883i
$599$			10.7441i			0.438992i	0.975613	+	0.219496i	$0.0704413\pi$
$599$			10.7441i			0.438992i	−0.975613	+	0.219496i	$0.929559\pi$
$600$	−2.03362	+	2.05568i	−0.0830221	+	0.0839230i
$601$	−19.9926	−	34.6282i	−0.815514	−	1.41251i	−0.908958	−	0.416888i	$-0.863121\pi$
$601$	−19.9926	−	34.6282i	−0.815514	−	1.41251i	0.0934435	−	0.995625i	$-0.470213\pi$
$602$	2.23424	+	6.10433i	0.0910607	+	0.248794i
$603$	8.57892	−	8.57892i	0.349360	−	0.349360i
$604$	14.1264	−	6.64921i	0.574794	−	0.270553i
$605$	−3.30292	−	12.3267i	−0.134283	−	0.501150i
$606$	1.16708	+	13.0691i	0.0474096	+	0.530894i
$607$	−20.5709	−	11.8766i	−0.834946	−	0.482056i	0.0205970	−	0.999788i	$-0.493443\pi$
$607$	−20.5709	−	11.8766i	−0.834946	−	0.482056i	−0.855543	+	0.517731i	$0.826777\pi$
$608$	0.453363	+	2.44249i	0.0183863	+	0.0990561i
$609$	6.05306	+	1.62191i	0.245283	+	0.0657233i
$610$	−2.62628	+	3.14134i	−0.106335	+	0.127189i
$611$	24.5603	−	18.5800i	0.993603	−	0.751664i
$612$	−0.422429	−	2.34633i	−0.0170757	−	0.0948447i
$613$	−3.92862	+	14.6618i	−0.158675	+	0.592185i	0.840087	+	0.542451i	$0.182504\pi$
$613$	−3.92862	+	14.6618i	−0.158675	+	0.592185i	−0.998763	+	0.0497331i	$0.984163\pi$
$614$	−15.7710	−	2.75162i	−0.636466	−	0.111046i
$615$	−5.90736	+	10.2318i	−0.238208	+	0.412588i
$616$	−9.94792	+	2.72316i	−0.400813	+	0.109719i
$617$	−7.65869	+	2.05214i	−0.308327	+	0.0826161i	−0.409665	−	0.912236i	$-0.634354\pi$
$617$	−7.65869	+	2.05214i	−0.308327	+	0.0826161i	0.101338	+	0.994852i	$0.467688\pi$
$618$	−0.0377813	+	0.0814042i	−0.00151979	+	0.00327456i
$619$	12.3353	+	12.3353i	0.495799	+	0.495799i	0.910127	−	0.414328i	$-0.135983\pi$
$619$	12.3353	+	12.3353i	0.495799	+	0.495799i	−0.414328	+	0.910127i	$0.635983\pi$
$620$	5.94799	−	16.5267i	0.238877	−	0.663729i
$621$	−4.86581	+	2.80928i	−0.195258	+	0.112732i
$622$	−9.77781	+	6.87274i	−0.392054	+	0.275572i
$623$	13.2501			0.530855
$624$	−4.33207	+	13.7562i	−0.173422	+	0.550689i
$625$	18.8431			0.753725
$626$	8.01803	−	5.63580i	0.320465	−	0.225252i
$627$	1.58636	−	0.915885i	0.0633531	−	0.0365769i
$628$	9.35953	−	26.0058i	0.373486	−	1.03774i
$629$	8.67610	+	8.67610i	0.345939	+	0.345939i
$630$	−1.03805	+	2.23660i	−0.0413569	+	0.0891083i
$631$	32.2201	−	8.63335i	1.28266	−	0.343688i	0.447793	−	0.894137i	$-0.352210\pi$
$631$	32.2201	−	8.63335i	1.28266	−	0.343688i	0.834869	+	0.550449i	$0.185543\pi$
$632$	24.5582	−	6.72260i	0.976874	−	0.267411i
$633$	9.27668	−	16.0677i	0.368715	−	0.638633i
$634$	22.9864	+	4.01051i	0.912908	+	0.159278i
$635$	9.63873	−	35.9722i	0.382501	−	1.42751i
$636$	−2.62742	−	14.5937i	−0.104184	−	0.578676i
$637$	−8.46153	−	20.8303i	−0.335258	−	0.825325i
$638$	−27.1218	+	32.4408i	−1.07376	+	1.28434i
$639$	−14.3801	−	3.85314i	−0.568868	−	0.152428i
$640$	21.1045	−	7.98374i	0.834229	−	0.315585i
$641$	−12.7096	−	7.33787i	−0.501998	−	0.289828i	0.227541	−	0.973769i	$-0.426932\pi$
$641$	−12.7096	−	7.33787i	−0.501998	−	0.289828i	−0.729538	+	0.683940i	$0.760265\pi$
$642$	−0.385794	−	4.32014i	−0.0152261	−	0.170502i
$643$	8.92896	+	33.3233i	0.352124	+	1.31414i	0.884065	+	0.467363i	$0.154796\pi$
$643$	8.92896	+	33.3233i	0.352124	+	1.31414i	−0.531941	+	0.846781i	$0.678537\pi$
$644$	8.88830	−	4.18367i	0.350248	−	0.164860i
$645$	−7.41481	+	7.41481i	−0.291958	+	0.291958i
$646$	−0.254452	−	0.695208i	−0.0100113	−	0.0273526i
$647$	12.2842	+	21.2769i	0.482943	+	0.836482i	0.999808	−	0.0195848i	$-0.00623442\pi$
$647$	12.2842	+	21.2769i	0.482943	+	0.836482i	−0.516865	+	0.856067i	$0.672901\pi$
$648$	1.98918	−	2.01076i	0.0781423	−	0.0789902i
$649$			5.91821i			0.232310i
$650$	−4.63603	+	2.38369i	−0.181840	+	0.0934959i
$651$			3.84957i			0.150877i
$652$	−3.77428	+	45.0043i	−0.147812	+	1.76250i
$653$	−5.33550	−	9.24136i	−0.208794	−	0.361642i	0.742541	−	0.669801i	$-0.233621\pi$
$653$	−5.33550	−	9.24136i	−0.208794	−	0.361642i	−0.951335	+	0.308159i	$0.900287\pi$
$654$	−12.0250	+	4.40126i	−0.470216	+	0.172103i
$655$	2.81544	−	2.81544i	0.110008	−	0.110008i
$656$	−19.3121	+	13.7306i	−0.754011	+	0.536090i
$657$	3.11580	+	11.6283i	0.121559	+	0.453664i
$658$	10.5182	−	0.939287i	0.410041	−	0.0366172i
$659$	0.434582	+	0.250906i	0.0169289	+	0.00977391i	0.508441	−	0.861097i	$-0.330222\pi$
$659$	0.434582	+	0.250906i	0.0169289	+	0.00977391i	−0.491512	+	0.870871i	$0.663555\pi$
$660$	−10.7405	−	12.7069i	−0.418073	−	0.494616i
$661$	−40.3603	−	10.8145i	−1.56984	−	0.420636i	−0.634075	−	0.773272i	$-0.718619\pi$
$661$	−40.3603	−	10.8145i	−1.56984	−	0.420636i	−0.935761	+	0.352636i	$0.885286\pi$
$662$	12.4473	+	10.4064i	0.483779	+	0.404458i
$663$	0.590156	−	4.25720i	0.0229198	−	0.165336i
$664$	−7.75885	−	4.42393i	−0.301102	−	0.171682i
$665$	−0.198173	+	0.739591i	−0.00768481	+	0.0286801i
$666$	−2.50199	+	14.3403i	−0.0969502	+	0.555674i
$667$	20.1375	−	34.8791i	0.779726	−	1.35053i
$668$	29.7266	+	20.6558i	1.15016	+	0.799199i
$669$	15.1392	−	4.05654i	0.585316	−	0.156835i
$670$	−31.0395	−	14.4061i	−1.19916	−	0.556555i
$671$	4.28174	+	4.28174i	0.165295	+	0.165295i
$672$	−3.75961	+	3.21274i	−0.145030	+	0.123934i
$673$	−25.1407	+	14.5150i	−0.969101	+	0.559511i	−0.898962	−	0.438026i	$-0.855678\pi$
$673$	−25.1407	+	14.5150i	−0.969101	+	0.559511i	−0.0701392	+	0.997537i	$0.522344\pi$
$674$	22.5652	+	32.1034i	0.869179	+	1.23658i
$675$	1.02234			0.0393499
$676$	−15.1273	+	21.1463i	−0.581819	+	0.813318i
$677$	−42.0062			−1.61443			−0.807214	−	0.590259i	$-0.799026\pi$
$677$	−42.0062			−1.61443			−0.807214	+	0.590259i	$0.799026\pi$
$678$	−10.4049	−	14.8029i	−0.399596	−	0.568504i
$679$	4.70213	−	2.71478i	0.180451	−	0.104184i
$680$	−5.80515	+	3.39350i	−0.222617	+	0.130135i
$681$	−9.40842	−	9.40842i	−0.360532	−	0.360532i
$682$	−23.5615	−	10.9354i	−0.902218	−	0.418737i
$683$	−38.6088	+	10.3452i	−1.47732	+	0.395848i	−0.905435	−	0.424484i	$-0.860455\pi$
$683$	−38.6088	+	10.3452i	−1.47732	+	0.395848i	−0.571888	+	0.820332i	$0.693789\pi$
$684$	0.501181	−	0.721269i	0.0191631	−	0.0275784i
$685$	−4.77298	+	8.26705i	−0.182366	+	0.315868i
$686$	2.81255	−	16.1203i	0.107384	−	0.615475i
$687$	0.769376	−	2.87135i	0.0293535	−	0.109549i
$688$	−19.7105	+	7.33505i	−0.751455	+	0.279646i
$689$	3.67065	−	26.4789i	0.139840	−	1.00876i
$690$	12.1580	+	10.1645i	0.462846	+	0.386958i
$691$	−24.0222	−	6.43672i	−0.913846	−	0.244864i	−0.228893	−	0.973452i	$-0.573511\pi$
$691$	−24.0222	−	6.43672i	−0.913846	−	0.244864i	−0.684953	+	0.728587i	$0.740177\pi$
$692$	−18.4406	+	15.5869i	−0.701008	+	0.592526i
$693$	3.15798	+	1.82326i	0.119962	+	0.0692599i
$694$	35.5681	−	3.17628i	1.35015	−	0.120570i
$695$	10.4925	+	39.1584i	0.398001	+	1.48536i
$696$	−5.14174	+	19.6119i	−0.194897	+	0.743389i
$697$	4.99321	−	4.99321i	0.189132	−	0.189132i
$698$	7.00125	−	2.56252i	0.265001	−	0.0969927i
$699$	−8.66555	−	15.0092i	−0.327761	−	0.567699i
$700$	−1.78125	−	0.149384i	−0.0673249	−	0.00564619i
$701$			11.8045i			0.445850i	0.974836	+	0.222925i	$0.0715605\pi$
$701$			11.8045i			0.445850i	−0.974836	+	0.222925i	$0.928440\pi$
$702$	4.53472	−	2.33160i	0.171152	−	0.0880005i
$703$			4.52030i			0.170486i
$704$	−8.98396	−	32.1372i	−0.338596	−	1.21122i
$705$	8.51752	+	14.7528i	0.320788	+	0.555622i
$706$	−7.63655	−	20.8644i	−0.287405	−	0.785242i
$707$	−5.73535	+	5.73535i	−0.215700	+	0.215700i
$708$	1.20850	+	2.56747i	0.0454181	+	0.0964916i
$709$	4.84468	+	18.0806i	0.181946	+	0.679031i	0.995264	+	0.0972115i	$0.0309923\pi$
$709$	4.84468	+	18.0806i	0.181946	+	0.679031i	−0.813318	+	0.581820i	$0.802341\pi$
$710$	3.73491	+	41.8237i	0.140169	+	1.56961i
$711$	−7.79603	−	4.50104i	−0.292374	−	0.168802i
$712$	0.231321	+	42.8684i	0.00866912	+	1.60656i
$713$	23.8979	+	6.40342i	0.894983	+	0.239810i
$714$	0.945271	−	1.13065i	0.0353759	−	0.0423136i
$715$	−11.2884	−	27.7894i	−0.422162	−	1.03926i
$716$	39.9642	−	7.19510i	1.49353	−	0.268894i
$717$	−5.24136	+	19.5610i	−0.195742	+	0.730520i
$718$	20.9872	+	3.66169i	0.783234	+	0.136653i
$719$	0.912550	−	1.58058i	0.0340324	−	0.0589458i	−0.848508	−	0.529183i	$-0.822498\pi$
$719$	0.912550	−	1.58058i	0.0340324	−	0.0589458i	0.882540	+	0.470237i	$0.155832\pi$
$720$	−7.25426	−	3.31939i	−0.270350	−	0.123706i
$721$	−0.0535867	+	0.0143585i	−0.00199567	+	0.000534739i
$722$	−11.1971	+	24.1255i	−0.416714	+	0.897860i
$723$	−15.7169	−	15.7169i	−0.584518	−	0.584518i
$724$	−15.4775	−	5.57036i	−0.575215	−	0.207021i
$725$	−6.34654	+	3.66418i	−0.235705	+	0.136084i
$726$	−7.40320	+	5.20365i	−0.274759	+	0.193125i
$727$	−22.1054			−0.819845			−0.409922	−	0.912120i	$-0.634444\pi$
$727$	−22.1054			−0.819845			−0.409922	+	0.912120i	$0.634444\pi$
$728$	−8.24163	+	3.39979i	−0.305455	+	0.126004i
$729$	−1.00000			−0.0370370
$730$	27.7791	−	19.5257i	1.02815	−	0.722678i
$731$	5.42772	−	3.13370i	0.200752	−	0.115904i
$732$	2.73186	+	0.983201i	0.100972	+	0.0363402i
$733$	−8.94364	−	8.94364i	−0.330341	−	0.330341i	0.522375	−	0.852716i	$-0.325046\pi$
$733$	−8.94364	−	8.94364i	−0.330341	−	0.330341i	−0.852716	+	0.522375i	$0.825046\pi$
$734$	−3.67816	+	7.92502i	−0.135763	+	0.292518i
$735$	12.0128	−	3.21883i	0.443100	−	0.118728i
$736$	13.6907	+	28.6835i	0.504647	+	1.05729i
$737$	−25.3032	+	43.8264i	−0.932055	+	1.61437i
$738$	8.25302	+	1.43993i	0.303798	+	0.0530045i
$739$	10.4262	−	38.9112i	0.383535	−	1.43137i	−0.456928	−	0.889504i	$-0.651050\pi$
$739$	10.4262	−	38.9112i	0.383535	−	1.43137i	0.840463	−	0.541869i	$-0.182283\pi$
$740$	40.4083	−	7.27506i	1.48544	−	0.267436i
$741$	1.26275	−	0.955275i	0.0463883	−	0.0350929i
$742$	5.87938	−	7.03242i	0.215839	−	0.258168i
$743$	24.8455	+	6.65734i	0.911495	+	0.244234i	0.683946	−	0.729532i	$-0.260262\pi$
$743$	24.8455	+	6.65734i	0.911495	+	0.244234i	0.227549	+	0.973767i	$0.426929\pi$
$744$	−12.4546	+	0.0672059i	−0.456608	+	0.00246389i
$745$	−7.01710	−	4.05132i	−0.257087	−	0.148429i
$746$	−2.33154	−	26.1086i	−0.0853636	−	0.955905i
$747$	0.817285	+	3.05015i	0.0299029	+	0.111599i
$748$	4.23503	+	8.99740i	0.154848	+	0.328978i
$749$	1.89589	−	1.89589i	0.0692743	−	0.0692743i
$750$	−5.83829	−	15.9513i	−0.213184	−	0.582457i
$751$	−6.52654	−	11.3043i	−0.238157	−	0.412500i	0.722029	−	0.691863i	$-0.243210\pi$
$751$	−6.52654	−	11.3043i	−0.238157	−	0.412500i	−0.960185	+	0.279364i	$0.909877\pi$
$752$	3.22253	+	34.0133i	0.117513	+	1.24034i
$753$			19.9828i			0.728214i
$754$	−19.7942	+	30.7271i	−0.720861	+	1.11902i
$755$			15.5694i			0.566627i
$756$	1.74232	+	0.146120i	0.0633677	+	0.00531433i
$757$	−25.1197	−	43.5085i	−0.912990	−	1.58134i	−0.809818	−	0.586681i	$-0.800434\pi$
$757$	−25.1197	−	43.5085i	−0.912990	−	1.58134i	−0.103171	−	0.994664i	$-0.532899\pi$
$758$	9.61643	−	3.51969i	0.349284	−	0.127841i
$759$	16.5717	−	16.5717i	0.601514	−	0.601514i
$760$	−2.39628	−	0.628242i	−0.0869221	−	0.0227887i
$761$	1.56202	+	5.82953i	0.0566231	+	0.211320i	0.988441	−	0.151606i	$-0.0484444\pi$
$761$	1.56202	+	5.82953i	0.0566231	+	0.211320i	−0.931818	+	0.362926i	$0.881778\pi$
$762$	−26.3027	+	2.34887i	−0.952846	+	0.0850904i
$763$	−6.85523	−	3.95787i	−0.248176	−	0.143284i
$764$	7.05282	−	5.96138i	0.255162	−	0.215675i
$765$	2.29638	+	0.615312i	0.0830257	+	0.0222467i
$766$	26.5485	+	22.1955i	0.959235	+	0.801958i
$767$	0.632984	+	5.07638i	0.0228557	+	0.183297i
$768$	−10.4599	−	12.1075i	−0.377439	−	0.436890i
$769$	0.866941	−	3.23547i	0.0312627	−	0.116674i	−0.948531	−	0.316684i	$-0.897431\pi$
$769$	0.866941	−	3.23547i	0.0312627	−	0.116674i	0.979794	+	0.200010i	$0.0640973\pi$
$770$	1.76776	−	10.1320i	0.0637057	−	0.365132i
$771$	−5.18155	+	8.97472i	−0.186609	+	0.323217i
$772$	6.31306	−	9.08537i	0.227212	−	0.326990i
$773$	10.9292	−	2.92846i	0.393095	−	0.105329i	−0.0568568	−	0.998382i	$-0.518108\pi$
$773$	10.9292	−	2.92846i	0.393095	−	0.105329i	0.449952	+	0.893053i	$0.351441\pi$
$774$	6.74459	+	3.13030i	0.242429	+	0.112516i
$775$	−3.18326	−	3.18326i	−0.114346	−	0.114346i
$776$	8.86527	+	15.1655i	0.318245	+	0.544411i
$777$	−7.79301	+	4.49930i	−0.279573	+	0.161411i
$778$	24.6194	+	35.0259i	0.882647	+	1.25574i
$779$	2.60149			0.0932082
$780$	−10.5718	−	9.75067i	−0.378531	−	0.349130i
$781$	62.0978			2.22203
$782$	−5.44665	−	7.74892i	−0.194772	−	0.277101i
$783$	6.20785	−	3.58411i	0.221851	−	0.128085i
$784$	24.5945	+	4.15446i	0.878377	+	0.148374i
$785$	19.4889	+	19.4889i	0.695589	+	0.695589i
$786$	−2.56095	−	1.18859i	−0.0913462	−	0.0423956i
$787$	9.17182	−	2.45758i	0.326940	−	0.0876034i	−0.0916156	−	0.995794i	$-0.529203\pi$
$787$	9.17182	−	2.45758i	0.326940	−	0.0876034i	0.418556	+	0.908191i	$0.362536\pi$
$788$	3.48016	+	2.41822i	0.123975	+	0.0861456i
$789$	−0.0901719	+	0.156182i	−0.00321020	+	0.00556024i
$790$	−4.36404	+	25.0127i	−0.155265	+	0.889911i
$791$	2.89490	−	10.8039i	0.102931	−	0.384143i
$792$	−5.84370	+	10.2489i	−0.207647	+	0.364179i
$793$	4.13064	+	3.21473i	0.146683	+	0.114158i
$794$	−36.4266	−	30.4541i	−1.29273	−	1.08077i
$795$	14.2830	+	3.82711i	0.506565	+	0.135734i
$796$	9.08711	+	10.7508i	0.322084	+	0.381052i
$797$	13.4998	+	7.79411i	0.478187	+	0.276082i	0.719661	−	0.694326i	$-0.244297\pi$
$797$	13.4998	+	7.79411i	0.478187	+	0.276082i	−0.241473	+	0.970407i	$0.577631\pi$
$798$	0.540784	−	0.0482928i	0.0191436	−	0.00170955i
$799$	−2.63519	−	9.83465i	−0.0932262	−	0.347925i
$800$	0.452210	−	5.76553i	0.0159880	−	0.203842i
$801$	10.7173	−	10.7173i	0.378676	−	0.378676i
$802$	−3.37472	+	1.23518i	−0.119166	+	0.0436157i
$803$	−25.1073	−	43.4872i	−0.886018	−	1.53463i
$804$	−2.02785	+	24.1800i	−0.0715167	+	0.852761i
$805$			9.79622i			0.345272i
$806$	−21.3796	−	6.85985i	−0.753066	−	0.241628i
$807$			14.1257i			0.497247i
$808$	−18.6558	−	18.4556i	−0.656310	−	0.649265i
$809$	1.84032	+	3.18753i	0.0647023	+	0.112068i	0.896562	−	0.442918i	$-0.146057\pi$
$809$	1.84032	+	3.18753i	0.0647023	+	0.112068i	−0.831860	+	0.554986i	$0.812724\pi$
$810$	0.969439	+	2.64868i	0.0340626	+	0.0930651i
$811$	−31.0704	+	31.0704i	−1.09103	+	1.09103i	−0.0956110	+	0.995419i	$0.530480\pi$
$811$	−31.0704	+	31.0704i	−1.09103	+	1.09103i	−0.995419	+	0.0956110i	$0.969520\pi$
$812$	−11.3398	+	5.33758i	−0.397949	+	0.187312i
$813$	−2.56276	−	9.56434i	−0.0898798	−	0.335436i
$814$	−5.40083	−	60.4786i	−0.189299	−	2.11977i
$815$	−39.0023	−	22.5180i	−1.36619	−	0.788771i
$816$	3.67453	+	3.03852i	0.128634	+	0.106369i
$817$	2.23028	+	0.597600i	0.0780274	+	0.0209074i
$818$	−10.6165	+	12.6985i	−0.371196	+	0.443994i
$819$	2.90378	+	1.22615i	0.101466	+	0.0428451i
$820$	−4.18689	−	23.2555i	−0.146213	−	0.812119i
$821$	4.17894	−	15.5960i	0.145846	−	0.544304i	−0.853870	−	0.520486i	$-0.825751\pi$
$821$	4.17894	−	15.5960i	0.145846	−	0.544304i	0.999716	−	0.0238187i	$-0.00758245\pi$
$822$	6.66821	+	1.16342i	0.232581	+	0.0405790i
$823$	−8.54450	+	14.7995i	−0.297842	+	0.515878i	−0.975642	−	0.219368i	$-0.929600\pi$
$823$	−8.54450	+	14.7995i	−0.297842	+	0.515878i	0.677800	+	0.735247i	$0.262934\pi$
$824$	−0.0473900	−	0.173120i	−0.00165091	−	0.00603091i
$825$	−4.11905	+	1.10370i	−0.143407	+	0.0384258i
$826$	−0.738477	+	1.59114i	−0.0256949	+	0.0553627i
$827$	26.8175	+	26.8175i	0.932536	+	0.932536i	0.997864	−	0.0653277i	$-0.0208093\pi$
$827$	26.8175	+	26.8175i	0.932536	+	0.932536i	−0.0653277	+	0.997864i	$0.520809\pi$
$828$	3.80530	−	10.5732i	0.132243	−	0.367443i
$829$	4.67078	−	2.69668i	0.162223	−	0.0936594i	−0.416691	−	0.909048i	$-0.636810\pi$
$829$	4.67078	−	2.69668i	0.162223	−	0.0936594i	0.578914	+	0.815389i	$0.303477\pi$
$830$	7.28656	−	5.12166i	0.252920	−	0.177775i
$831$	1.99632			0.0692514
$832$	−11.1433	−	26.6050i	−0.386324	−	0.922363i
$833$	−7.43316			−0.257544
$834$	23.5179	−	16.5305i	0.814358	−	0.572406i
$835$	−31.2612	+	18.0487i	−1.08184	+	0.624600i
$836$	−1.24061	+	3.44709i	−0.0429075	+	0.119220i
$837$	3.11370	+	3.11370i	0.107625	+	0.107625i
$838$	−4.91269	+	10.5850i	−0.169706	+	0.365651i
$839$	32.4670	−	8.69950i	1.12088	−	0.300340i	0.349643	−	0.936883i	$-0.386303\pi$
$839$	32.4670	−	8.69950i	1.12088	−	0.300340i	0.771241	+	0.636543i	$0.219636\pi$
$840$	−1.30205	−	4.75651i	−0.0449251	−	0.164115i
$841$	−11.1916	+	19.3845i	−0.385918	+	0.668430i
$842$	−1.78263	−	0.311020i	−0.0614333	−	0.0107185i
$843$	1.45307	−	5.42293i	0.0500464	−	0.186776i
$844$	6.57493	+	36.5196i	0.226318	+	1.25706i
$845$	−12.6549	−	22.6291i	−0.435342	−	0.778466i
$846$	7.74781	−	9.26728i	0.266375	−	0.318616i
$847$	−5.40322	−	1.44779i	−0.185657	−	0.0497466i
$848$	22.8548	+	18.8989i	0.784838	+	0.648992i
$849$	24.5618	+	14.1808i	0.842959	+	0.486682i
$850$	0.153296	+	1.71661i	0.00525800	+	0.0588792i
$851$	14.9684	+	55.8627i	0.513109	+	1.91495i
$852$	26.9397	−	12.6803i	0.922937	−	0.434422i
$853$	13.9088	−	13.9088i	0.476227	−	0.476227i	−0.427696	−	0.903923i	$-0.640674\pi$
$853$	13.9088	−	13.9088i	0.476227	−	0.476227i	0.903923	+	0.427696i	$0.140674\pi$
$854$	0.616886	+	1.68544i	0.0211094	+	0.0576746i
$855$	0.437922	+	0.758504i	0.0149766	+	0.0259403i
$856$	6.16692	+	6.10072i	0.210781	+	0.208518i
$857$			40.9336i			1.39826i	0.714993	+	0.699132i	$0.246430\pi$
$857$			40.9336i			1.39826i	−0.714993	+	0.699132i	$0.753570\pi$
$858$	−15.7534	+	14.2897i	−0.537812	+	0.487842i
$859$			36.8747i			1.25815i	0.777345	+	0.629075i	$0.216566\pi$
$859$			36.8747i			1.25815i	−0.777345	+	0.629075i	$0.783434\pi$
$860$	1.75268	−	20.8989i	0.0597660	−	0.712646i
$861$	2.58941	+	4.48498i	0.0882468	+	0.152848i
$862$	−1.03757	+	0.379758i	−0.0353397	+	0.0129346i
$863$	6.91353	−	6.91353i	0.235339	−	0.235339i	−0.579578	−	0.814917i	$-0.696783\pi$
$863$	6.91353	−	6.91353i	0.235339	−	0.235339i	0.814917	+	0.579578i	$0.196783\pi$
$864$	−0.442328	+	5.63953i	−0.0150483	+	0.191861i
$865$	−6.23186	−	23.2576i	−0.211890	−	0.790783i
$866$	−40.9543	+	3.65727i	−1.39168	+	0.124279i
$867$	13.4919	+	7.78954i	0.458208	+	0.264547i
$868$	−4.97010	−	5.88004i	−0.168696	−	0.199582i
$869$	36.2697	+	9.71845i	1.23037	+	0.329676i
$870$	−15.5113	−	12.9680i	−0.525882	−	0.439658i
$871$	−17.0165	+	40.2987i	−0.576582	+	1.36547i
$872$	12.6853	−	22.2480i	0.429579	−	0.753412i
$873$	1.60746	−	5.99911i	0.0544042	−	0.203039i
$874$	0.599748	−	3.43749i	0.0202868	−	0.116275i
$875$	5.25013	−	9.09349i	0.177487	−	0.307416i
$876$	−19.7723	−	13.7390i	−0.668044	−	0.464197i
$877$	0.709563	−	0.190127i	0.0239602	−	0.00642013i	−0.246819	−	0.969062i	$-0.579385\pi$
$877$	0.709563	−	0.190127i	0.0239602	−	0.00642013i	0.270779	+	0.962641i	$0.412719\pi$
$878$	−48.0280	−	22.2907i	−1.62087	−	0.752276i
$879$	0.104864	+	0.104864i	0.00353696	+	0.00353696i
$880$	32.8112	+	5.54240i	1.10607	+	0.186834i
$881$	−6.37564	+	3.68098i	−0.214801	+	0.124015i	−0.603541	−	0.797332i	$-0.706244\pi$
$881$	−6.37564	+	3.68098i	−0.214801	+	0.124015i	0.388740	+	0.921348i	$0.372911\pi$
$882$	−5.07117	−	7.21472i	−0.170755	−	0.242932i
$883$	7.20794			0.242567			0.121283	−	0.992618i	$-0.461299\pi$
$883$	7.20794			0.242567			0.121283	+	0.992618i	$0.461299\pi$
$884$	4.59494	+	7.26462i	0.154545	+	0.244335i
$885$	−2.82974			−0.0951206
$886$	−10.7088	−	15.2354i	−0.359770	−	0.511843i
$887$	−3.89737	+	2.25015i	−0.130861	+	0.0755525i	−0.564001	−	0.825774i	$-0.690739\pi$
$887$	−3.89737	+	2.25015i	−0.130861	+	0.0755525i	0.433141	+	0.901326i	$0.357405\pi$
$888$	−14.6927	−	25.1344i	−0.493056	−	0.843455i
$889$	−11.5429	−	11.5429i	−0.387137	−	0.387137i
$890$	−38.7763	−	17.9969i	−1.29979	−	0.603256i
$891$	4.02904	−	1.07958i	0.134978	−	0.0361672i
$892$	−17.8871	+	25.7421i	−0.598906	+	0.861909i
$893$	1.87548	−	3.24843i	0.0627606	−	0.108704i
$894$	−0.987517	+	5.66000i	−0.0330275	+	0.189299i
$895$	−10.4804	+	39.1134i	−0.350322	+	1.30742i
$896$	1.59473	−	9.76126i	0.0532760	−	0.326101i
$897$	12.4420	−	15.9869i	0.415428	−	0.533787i
$898$	18.7719	+	15.6941i	0.626428	+	0.523718i
$899$	−30.4892	−	8.16956i	−1.01687	−	0.272470i
$900$	−1.56158	+	1.31992i	−0.0520526	+	0.0439974i
$901$	−7.65380	−	4.41892i	−0.254985	−	0.147216i
$902$	−34.8063	+	3.10825i	−1.15892	+	0.103493i
$903$	1.18965	+	4.43983i	0.0395890	+	0.147748i
$904$	35.0047	+	9.17733i	1.16424	+	0.305233i
$905$	11.5989	−	11.5989i	0.385561	−	0.385561i
$906$	10.3675	−	3.79458i	0.344436	−	0.126067i
$907$	−1.51506	−	2.62416i	−0.0503067	−	0.0871337i	0.839776	−	0.542934i	$-0.182687\pi$
$907$	−1.51506	−	2.62416i	−0.0503067	−	0.0871337i	−0.890082	+	0.455800i	$0.849353\pi$
$908$	26.5180	+	2.22393i	0.880029	+	0.0738036i
$909$			9.27799i			0.307732i
$910$	0.432636	−	8.87986i	0.0143417	−	0.294365i
$911$		−	20.7153i		−	0.686330i	−0.939275	−	0.343165i	$-0.888501\pi$
$911$		−	20.7153i		−	0.686330i	0.939275	−	0.343165i	$-0.111499\pi$
$912$	0.165684	+	1.74877i	0.00548634	+	0.0579076i
$913$	−6.58575	−	11.4069i	−0.217956	−	0.377512i
$914$	−9.41202	−	25.7153i	−0.311322	−	0.850587i
$915$	−2.04727	+	2.04727i	−0.0676808	+	0.0676808i
$916$	2.53195	+	5.37918i	0.0836580	+	0.177733i
$917$	−0.451715	−	1.68582i	−0.0149169	−	0.0556708i
$918$	−0.149946	−	1.67910i	−0.00494895	−	0.0554185i
$919$	8.67994	+	5.01136i	0.286325	+	0.165310i	0.636283	−	0.771456i	$-0.280471\pi$
$919$	8.67994	+	5.01136i	0.286325	+	0.165310i	−0.349958	+	0.936765i	$0.613804\pi$
$920$	−31.6940	+	0.171023i	−1.04492	+	0.00563846i
$921$	−10.9345	−	2.92990i	−0.360305	−	0.0965434i
$922$	9.89018	−	11.8298i	0.325716	−	0.389594i
$923$	53.2647	−	6.64169i	1.75323	−	0.218614i
$924$	−7.17764	+	1.29225i	−0.236127	+	0.0425119i
$925$	2.72362	−	10.1647i	0.0895520	−	0.334212i
$926$	−16.4084	−	2.86283i	−0.539214	−	0.0940784i
$927$	−0.0317294	+	0.0549570i	−0.00104213	+	0.00180503i
$928$	−17.4668	−	36.5947i	−0.573375	−	1.20128i
$929$	14.7317	−	3.94734i	0.483331	−	0.129508i	−0.00892220	−	0.999960i	$-0.502840\pi$
$929$	14.7317	−	3.94734i	0.483331	−	0.129508i	0.492253	+	0.870452i	$0.336173\pi$
$930$	5.22865	−	11.2657i	0.171454	−	0.369418i
$931$	−1.93636	−	1.93636i	−0.0634616	−	0.0634616i
$932$	32.6143	+	11.7379i	1.06832	+	0.384488i
$933$	−7.31881	+	4.22552i	−0.239607	+	0.138337i
$934$	25.8550	−	18.1732i	0.846000	−	0.594646i
$935$	−9.91647			−0.324303
$936$	−3.91630	+	9.41608i	−0.128008	+	0.307774i
$937$	21.1203			0.689969			0.344984	−	0.938608i	$-0.387884\pi$
$937$	21.1203			0.689969			0.344984	+	0.938608i	$0.387884\pi$
$938$	−12.2716	+	8.62557i	−0.400680	+	0.281635i
$939$	6.00160	−	3.46502i	0.195855	−	0.113077i
$940$	−32.0571	−	11.5374i	−1.04559	−	0.376309i
$941$	−9.41817	−	9.41817i	−0.307024	−	0.307024i	0.536730	−	0.843754i	$-0.319659\pi$
$941$	−9.41817	−	9.41817i	−0.307024	−	0.307024i	−0.843754	+	0.536730i	$0.819659\pi$
$942$	8.22759	−	17.7273i	0.268070	−	0.577587i
$943$	32.1498	−	8.61450i	1.04694	−	0.280527i
$944$	−5.16073	−	2.36144i	−0.167968	−	0.0768582i
$945$	−0.871775	+	1.50996i	−0.0283588	+	0.0491190i
$946$	−30.5536	−	5.33078i	−0.993384	−	0.173319i
$947$	6.07900	−	22.6871i	0.197541	−	0.737233i	−0.794054	−	0.607848i	$-0.792033\pi$
$947$	6.07900	−	22.6871i	0.197541	−	0.737233i	0.991594	−	0.129385i	$-0.0413003\pi$
$948$	17.7193	−	3.19015i	0.575496	−	0.103611i
$949$	−26.1871	−	34.6160i	−0.850071	−	1.12368i
$950$	−0.407248	+	0.487116i	−0.0132129	+	0.0158041i
$951$	15.9372	+	4.27036i	0.516799	+	0.138476i
$952$	0.0159046	+	2.94744i	0.000515471	+	0.0955271i
$953$	−1.31568	−	0.759610i	−0.0426192	−	0.0246062i	0.478539	−	0.878066i	$-0.341167\pi$
$953$	−1.31568	−	0.759610i	−0.0426192	−	0.0246062i	−0.521158	+	0.853460i	$0.674500\pi$
$954$	−0.932630	−	10.4436i	−0.0301950	−	0.338125i
$955$	2.38344	+	8.89512i	0.0771263	+	0.287839i
$956$	−17.2489	−	36.6456i	−0.557869	−	1.18520i
$957$	−21.1424	+	21.1424i	−0.683436	+	0.683436i
$958$	−3.56267	−	9.73385i	−0.115105	−	0.314486i
$959$	2.09217	+	3.62374i	0.0675597	+	0.117017i
$960$	15.3661	−	4.29560i	0.495940	−	0.138640i
$961$			11.6098i			0.374508i
$962$	−11.1011	−	51.2983i	−0.357914	−	1.65392i
$963$		−	3.06695i		−	0.0988312i
$964$	44.2986	+	3.71510i	1.42676	+	0.119655i
$965$	5.51623	+	9.55439i	0.177574	+	0.307567i
$966$	6.52320	−	2.38755i	0.209880	−	0.0768180i
$967$	−26.2677	+	26.2677i	−0.844711	+	0.844711i	−0.989467	−	0.144757i	$-0.953760\pi$
$967$	−26.2677	+	26.2677i	−0.844711	+	0.844711i	0.144757	+	0.989467i	$0.453760\pi$
$968$	4.58974	−	17.5064i	0.147520	−	0.562678i
$969$	−0.135486	−	0.505641i	−0.00435244	−	0.0162435i
$970$	−17.4481	+	1.55814i	−0.560223	+	0.0500287i
$971$	14.6842	+	8.47794i	0.471239	+	0.272070i	0.716758	−	0.697322i	$-0.245625\pi$
$971$	14.6842	+	8.47794i	0.471239	+	0.272070i	−0.245519	+	0.969392i	$0.578958\pi$
$972$	1.52745	−	1.29108i	0.0489931	−	0.0414114i
$973$	17.1645	+	4.59922i	0.550269	+	0.147444i
$974$	6.67114	+	5.57733i	0.213757	+	0.178709i
$975$	−3.41509	+	1.38726i	−0.109371	+	0.0444278i
$976$	−5.44218	+	2.02525i	−0.174200	+	0.0648267i
$977$	1.44364	−	5.38773i	0.0461861	−	0.172369i	−0.938980	−	0.343971i	$-0.888228\pi$
$977$	1.44364	−	5.38773i	0.0461861	−	0.172369i	0.985166	+	0.171602i	$0.0548944\pi$
$978$	−5.48880	+	31.4593i	−0.175512	+	1.00596i
$979$	−31.6102	+	54.7504i	−1.01026	+	1.74983i
$980$	−14.1933	+	20.4261i	−0.453388	+	0.652489i
$981$	−8.74610	+	2.34351i	−0.279241	+	0.0748225i
$982$	31.6296	+	14.6799i	1.00934	+	0.468455i
$983$	−37.9677	−	37.9677i	−1.21098	−	1.21098i	−0.970705	−	0.240276i	$-0.922762\pi$
$983$	−37.9677	−	37.9677i	−1.21098	−	1.21098i	−0.240276	−	0.970705i	$-0.577238\pi$
$984$	−14.4652	+	8.45587i	−0.461133	+	0.269563i
$985$	−3.65981	+	2.11299i	−0.116611	+	0.0673256i
$986$	6.94890	+	9.88617i	0.221298	+	0.314840i
$987$	7.46707			0.237679
$988$	−0.695458	+	3.08945i	−0.0221255	+	0.0982885i
$989$	29.5410			0.939350
$990$	−6.76537	−	9.62505i	−0.215017	−	0.305904i
$991$	34.4714	−	19.9021i	1.09502	−	0.632210i	0.160112	−	0.987099i	$-0.448814\pi$
$991$	34.4714	−	19.9021i	1.09502	−	0.632210i	0.934909	+	0.354888i	$0.115481\pi$
$992$	18.9371	−	16.1825i	0.601253	−	0.513796i
$993$	8.11218	+	8.11218i	0.257432	+	0.257432i
$994$	16.6953	+	7.74860i	0.529541	+	0.245771i
$995$	−13.5591	+	3.63315i	−0.429852	+	0.115179i
$996$	−5.18635	−	3.60379i	−0.164336	−	0.114190i
$997$	1.52818	−	2.64689i	0.0483980	−	0.0838278i	−0.840812	−	0.541328i	$-0.817922\pi$
$997$	1.52818	−	2.64689i	0.0483980	−	0.0838278i	0.889210	+	0.457500i	$0.151255\pi$
$998$	5.38995	−	30.8927i	0.170616	−	0.977892i
$999$	−2.66410	+	9.94255i	−0.0842883	+	0.314568i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.2.w.c.115.2	yes	24
3.2	odd	2		468.2.cb.h.271.5		24
4.3	odd	2		156.2.w.d.115.4	yes	24
12.11	even	2		468.2.cb.g.271.3		24
13.6	odd	12		156.2.w.d.19.4	yes	24
39.32	even	12		468.2.cb.g.19.3		24
52.19	even	12	inner	156.2.w.c.19.2	✓	24
156.71	odd	12		468.2.cb.h.19.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.w.c.19.2	✓	24	52.19	even	12	inner
156.2.w.c.115.2	yes	24	1.1	even	1	trivial
156.2.w.d.19.4	yes	24	13.6	odd	12
156.2.w.d.115.4	yes	24	4.3	odd	2
468.2.cb.g.19.3		24	39.32	even	12
468.2.cb.g.271.3		24	12.11	even	2
468.2.cb.h.19.5		24	156.71	odd	12
468.2.cb.h.271.5		24	3.2	odd	2

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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	156.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15700 + 0.813242i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.677275 - 1.88183i) q^{4} +(1.41026 + 1.41026i) q^{5} +(0.595366 - 1.28279i) q^{6} +(0.844432 - 0.226265i) q^{7} +(0.746782 + 2.72806i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.15700 + 0.813242i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.677275 - 1.88183i) q^{4} +(1.41026 + 1.41026i) q^{5} +(0.595366 - 1.28279i) q^{6} +(0.844432 - 0.226265i) q^{7} +(0.746782 + 2.72806i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.77854 - 0.484781i) q^{10} +(-1.07958 + 4.02904i) q^{11} +(0.354379 + 1.96835i) q^{12} +(-0.495087 + 3.57140i) q^{13} +(-0.792995 + 0.948514i) q^{14} +(-1.92645 - 0.516191i) q^{15} +(-3.08260 - 2.54904i) q^{16} +(1.03232 + 0.596013i) q^{17} +(0.125791 + 1.40861i) q^{18} +(0.113660 + 0.424187i) q^{19} +(3.60901 - 1.69874i) q^{20} +(-0.618167 + 0.618167i) q^{21} +(-2.02752 - 5.53954i) q^{22} +(2.80928 + 4.86581i) q^{23} +(-2.01076 - 1.98918i) q^{24} -1.02234i q^{25} +(-2.33160 - 4.53472i) q^{26} +1.00000i q^{27} +(0.146120 - 1.74232i) q^{28} +(-3.58411 - 6.20785i) q^{29} +(2.64868 - 0.969439i) q^{30} +(3.11370 - 3.11370i) q^{31} +(5.63953 + 0.442328i) q^{32} +(-1.07958 - 4.02904i) q^{33} +(-1.67910 + 0.149946i) q^{34} +(1.50996 + 0.871775i) q^{35} +(-1.29108 - 1.52745i) q^{36} +(9.94255 + 2.66410i) q^{37} +(-0.476471 - 0.398348i) q^{38} +(-1.35694 - 3.34047i) q^{39} +(-2.79412 + 4.90043i) q^{40} +(1.53322 - 5.72207i) q^{41} +(0.212497 - 1.21794i) q^{42} +(2.62888 - 4.55336i) q^{43} +(6.85081 + 4.76035i) q^{44} +(1.92645 - 0.516191i) q^{45} +(-7.20740 - 3.34509i) q^{46} +(-6.03968 - 6.03968i) q^{47} +(3.94413 + 0.666233i) q^{48} +(-5.40031 + 3.11787i) q^{49} +(0.831410 + 1.18284i) q^{50} -1.19203 q^{51} +(6.38547 + 3.35049i) q^{52} -7.41414 q^{53} +(-0.813242 - 1.15700i) q^{54} +(-7.20447 + 4.15950i) q^{55} +(1.24787 + 2.13469i) q^{56} +(-0.310526 - 0.310526i) q^{57} +(9.19528 + 4.26771i) q^{58} +(1.37049 - 0.367222i) q^{59} +(-2.27612 + 3.27565i) q^{60} +(0.725851 - 1.25721i) q^{61} +(-1.07034 + 6.13472i) q^{62} +(0.226265 - 0.844432i) q^{63} +(-6.88463 + 4.07453i) q^{64} +(-5.73480 + 4.33840i) q^{65} +(4.52565 + 3.78362i) q^{66} +(11.7190 + 3.14010i) q^{67} +(1.82076 - 1.53900i) q^{68} +(-4.86581 - 2.80928i) q^{69} +(-2.45598 + 0.219322i) q^{70} +(-3.85314 - 14.3801i) q^{71} +(2.73596 + 0.717298i) q^{72} +(-8.51251 + 8.51251i) q^{73} +(-13.6700 + 5.00335i) q^{74} +(0.511170 + 0.885373i) q^{75} +(0.875228 + 0.0734009i) q^{76} +3.64652i q^{77} +(4.28658 + 2.76138i) q^{78} -9.00208i q^{79} +(-0.752456 - 7.94206i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.87950 + 7.86729i) q^{82} +(-2.23286 + 2.23286i) q^{83} +(0.744618 + 1.58196i) q^{84} +(0.615312 + 2.29638i) q^{85} +(0.661378 + 7.40613i) q^{86} +(6.20785 + 3.58411i) q^{87} +(-11.7977 + 0.0636610i) q^{88} +(14.6401 + 3.92279i) q^{89} +(-1.80910 + 2.16390i) q^{90} +(0.390015 + 3.12782i) q^{91} +(11.0593 - 1.99110i) q^{92} +(-1.13969 + 4.25339i) q^{93} +(11.8996 + 2.07616i) q^{94} +(-0.437922 + 0.758504i) q^{95} +(-5.10514 + 2.43670i) q^{96} +(5.99911 - 1.60746i) q^{97} +(3.71255 - 7.99912i) q^{98} +(2.94946 + 2.94946i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9} + 12 q^{10} + 4 q^{11} - 4 q^{12} - 22 q^{14} - 4 q^{15} + 12 q^{16} - 2 q^{18} - 22 q^{19} - 4 q^{20} + 10 q^{21} - 34 q^{22} + 2 q^{24} - 4 q^{26} - 14 q^{28} + 8 q^{29} - 16 q^{30} - 2 q^{31} - 34 q^{32} + 4 q^{33} + 20 q^{34} + 24 q^{35} - 4 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} + 28 q^{40} - 36 q^{41} + 6 q^{42} + 10 q^{43} + 20 q^{44} + 4 q^{45} - 2 q^{46} + 20 q^{47} + 32 q^{48} - 54 q^{49} - 24 q^{50} + 36 q^{51} + 4 q^{52} - 36 q^{53} - 4 q^{54} - 24 q^{55} + 70 q^{56} - 32 q^{57} + 48 q^{58} - 36 q^{59} - 28 q^{60} - 2 q^{61} + 64 q^{62} + 8 q^{63} - 8 q^{64} + 16 q^{65} + 20 q^{66} - 16 q^{67} - 10 q^{68} + 12 q^{69} + 36 q^{71} - 2 q^{72} - 40 q^{73} - 30 q^{74} - 8 q^{75} + 58 q^{76} + 24 q^{78} - 48 q^{80} - 12 q^{81} - 30 q^{82} - 24 q^{83} - 26 q^{84} + 18 q^{85} + 30 q^{86} + 6 q^{87} - 78 q^{88} + 66 q^{89} + 12 q^{90} + 42 q^{91} + 36 q^{92} - 10 q^{93} + 6 q^{94} - 28 q^{95} + 8 q^{96} + 4 q^{97} + 44 q^{98} - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9 + 12 * q^10 + 4 * q^11 - 4 * q^12 - 22 * q^14 - 4 * q^15 + 12 * q^16 - 2 * q^18 - 22 * q^19 - 4 * q^20 + 10 * q^21 - 34 * q^22 + 2 * q^24 - 4 * q^26 - 14 * q^28 + 8 * q^29 - 16 * q^30 - 2 * q^31 - 34 * q^32 + 4 * q^33 + 20 * q^34 + 24 * q^35 - 4 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 + 28 * q^40 - 36 * q^41 + 6 * q^42 + 10 * q^43 + 20 * q^44 + 4 * q^45 - 2 * q^46 + 20 * q^47 + 32 * q^48 - 54 * q^49 - 24 * q^50 + 36 * q^51 + 4 * q^52 - 36 * q^53 - 4 * q^54 - 24 * q^55 + 70 * q^56 - 32 * q^57 + 48 * q^58 - 36 * q^59 - 28 * q^60 - 2 * q^61 + 64 * q^62 + 8 * q^63 - 8 * q^64 + 16 * q^65 + 20 * q^66 - 16 * q^67 - 10 * q^68 + 12 * q^69 + 36 * q^71 - 2 * q^72 - 40 * q^73 - 30 * q^74 - 8 * q^75 + 58 * q^76 + 24 * q^78 - 48 * q^80 - 12 * q^81 - 30 * q^82 - 24 * q^83 - 26 * q^84 + 18 * q^85 + 30 * q^86 + 6 * q^87 - 78 * q^88 + 66 * q^89 + 12 * q^90 + 42 * q^91 + 36 * q^92 - 10 * q^93 + 6 * q^94 - 28 * q^95 + 8 * q^96 + 4 * q^97 + 44 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

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