LMFDB - Embedded newform 867.2.e.j.829.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(616,867)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("867.616");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.e (of order $4$, degree $2$, not 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:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.722204136308736.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{8} + 69x^{4} + 1 $ x^12 + 18x^8 + 69x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			829.3
Root			$-1.08335 - 1.08335i$ of defining polynomial
Character	$\chi$	$=$	867.829
Dual form			867.2.e.j.616.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.34730i q^{2} +(-0.707107 - 0.707107i) q^{3} +0.184793 q^{4} +(-1.79046 - 1.79046i) q^{5} +(0.952682 - 0.952682i) q^{6} +(0.130668 - 0.130668i) q^{7} +2.94356i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+1.34730i q^{2} +(-0.707107 - 0.707107i) q^{3} +0.184793 q^{4} +(-1.79046 - 1.79046i) q^{5} +(0.952682 - 0.952682i) q^{6} +(0.130668 - 0.130668i) q^{7} +2.94356i q^{8} +1.00000i q^{9} +(2.41228 - 2.41228i) q^{10} +(-2.52718 + 2.52718i) q^{11} +(-0.130668 - 0.130668i) q^{12} +6.53209 q^{13} +(0.176049 + 0.176049i) q^{14} +2.53209i q^{15} -3.59627 q^{16} -1.34730 q^{18} -4.63816i q^{19} +(-0.330863 - 0.330863i) q^{20} -0.184793 q^{21} +(-3.40487 - 3.40487i) q^{22} +(2.19632 - 2.19632i) q^{23} +(2.08141 - 2.08141i) q^{24} +1.41147i q^{25} +8.80066i q^{26} +(0.707107 - 0.707107i) q^{27} +(0.0241465 - 0.0241465i) q^{28} +(4.49369 + 4.49369i) q^{29} -3.41147 q^{30} +(5.24070 + 5.24070i) q^{31} +1.04189i q^{32} +3.57398 q^{33} -0.467911 q^{35} +0.184793i q^{36} +(5.93752 + 5.93752i) q^{37} +6.24897 q^{38} +(-4.61888 - 4.61888i) q^{39} +(5.27032 - 5.27032i) q^{40} +(5.08042 - 5.08042i) q^{41} -0.248970i q^{42} -4.93582i q^{43} +(-0.467005 + 0.467005i) q^{44} +(1.79046 - 1.79046i) q^{45} +(2.95910 + 2.95910i) q^{46} +9.04963 q^{47} +(2.54294 + 2.54294i) q^{48} +6.96585i q^{49} -1.90167 q^{50} +1.20708 q^{52} +7.65270i q^{53} +(0.952682 + 0.952682i) q^{54} +9.04963 q^{55} +(0.384630 + 0.384630i) q^{56} +(-3.27967 + 3.27967i) q^{57} +(-6.05433 + 6.05433i) q^{58} -6.55438i q^{59} +0.467911i q^{60} +(2.11103 - 2.11103i) q^{61} +(-7.06078 + 7.06078i) q^{62} +(0.130668 + 0.130668i) q^{63} -8.59627 q^{64} +(-11.6954 - 11.6954i) q^{65} +4.81521i q^{66} -13.5175 q^{67} -3.10607 q^{69} -0.630415i q^{70} +(2.55323 + 2.55323i) q^{71} -2.94356 q^{72} +(5.94781 + 5.94781i) q^{73} +(-7.99960 + 7.99960i) q^{74} +(0.998063 - 0.998063i) q^{75} -0.857097i q^{76} +0.660444i q^{77} +(6.22301 - 6.22301i) q^{78} +(5.53166 - 5.53166i) q^{79} +(6.43896 + 6.43896i) q^{80} -1.00000 q^{81} +(6.84483 + 6.84483i) q^{82} -2.51249i q^{83} -0.0341483 q^{84} +6.65002 q^{86} -6.35504i q^{87} +(-7.43893 - 7.43893i) q^{88} -1.32770 q^{89} +(2.41228 + 2.41228i) q^{90} +(0.853535 - 0.853535i) q^{91} +(0.405864 - 0.405864i) q^{92} -7.41147i q^{93} +12.1925i q^{94} +(-8.30442 + 8.30442i) q^{95} +(0.736727 - 0.736727i) q^{96} +(-6.19339 - 6.19339i) q^{97} -9.38507 q^{98} +(-2.52718 - 2.52718i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4}+O(q^{10}) $ 12 * q - 12 * q^4	$ 12 q - 12 q^{4} + 60 q^{13} + 12 q^{16} - 12 q^{18} + 12 q^{21} + 12 q^{33} - 24 q^{35} + 24 q^{38} + 24 q^{50} - 24 q^{52} - 48 q^{64} - 72 q^{67} + 12 q^{69} + 24 q^{72} - 12 q^{81} - 84 q^{84} + 120 q^{86} + 108 q^{98}+O(q^{100}) $ 12 * q - 12 * q^4 + 60 * q^13 + 12 * q^16 - 12 * q^18 + 12 * q^21 + 12 * q^33 - 24 * q^35 + 24 * q^38 + 24 * q^50 - 24 * q^52 - 48 * q^64 - 72 * q^67 + 12 * q^69 + 24 * q^72 - 12 * q^81 - 84 * q^84 + 120 * q^86 + 108 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$			1.34730i			0.952682i	0.879261	+	0.476341i	$0.158037\pi$
$2$			1.34730i			0.952682i	−0.879261	+	0.476341i	$0.841963\pi$
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	0.184793			0.0923963
$5$	−1.79046	−	1.79046i	−0.800717	−	0.800717i	0.182491	−	0.983208i	$-0.441584\pi$
$5$	−1.79046	−	1.79046i	−0.800717	−	0.800717i	−0.983208	+	0.182491i	$0.941584\pi$
$6$	0.952682	−	0.952682i	0.388931	−	0.388931i
$7$	0.130668	−	0.130668i	0.0493879	−	0.0493879i	−0.681982	−	0.731369i	$-0.738882\pi$
$7$	0.130668	−	0.130668i	0.0493879	−	0.0493879i	0.731369	+	0.681982i	$0.238882\pi$
$8$			2.94356i			1.04071i
$9$			1.00000i			0.333333i
$10$	2.41228	−	2.41228i	0.762829	−	0.762829i
$11$	−2.52718	+	2.52718i	−0.761975	+	0.761975i	−0.976679	−	0.214704i	$-0.931121\pi$
$11$	−2.52718	+	2.52718i	−0.761975	+	0.761975i	0.214704	+	0.976679i	$0.431121\pi$
$12$	−0.130668	−	0.130668i	−0.0377206	−	0.0377206i
$13$	6.53209			1.81168			0.905838	−	0.423625i	$-0.139242\pi$
$13$	6.53209			1.81168			0.905838	+	0.423625i	$0.139242\pi$
$14$	0.176049	+	0.176049i	0.0470510	+	0.0470510i
$15$			2.53209i			0.653783i
$16$	−3.59627			−0.899067
$17$		0			0
$17$		0			0
$18$	−1.34730			−0.317561
$19$		−	4.63816i		−	1.06407i	−0.846724	−	0.532033i	$-0.821428\pi$
$19$		−	4.63816i		−	1.06407i	0.846724	−	0.532033i	$-0.178572\pi$
$20$	−0.330863	−	0.330863i	−0.0739832	−	0.0739832i
$21$	−0.184793			−0.0403250
$22$	−3.40487	−	3.40487i	−0.725920	−	0.725920i
$23$	2.19632	−	2.19632i	0.457965	−	0.457965i	−0.440022	−	0.897987i	$-0.645029\pi$
$23$	2.19632	−	2.19632i	0.457965	−	0.457965i	0.897987	+	0.440022i	$0.145029\pi$
$24$	2.08141	−	2.08141i	0.424867	−	0.424867i
$25$			1.41147i			0.282295i
$26$			8.80066i			1.72595i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	0.0241465	−	0.0241465i	0.00456326	−	0.00456326i
$29$	4.49369	+	4.49369i	0.834457	+	0.834457i	0.988123	−	0.153666i	$-0.0491079\pi$
$29$	4.49369	+	4.49369i	0.834457	+	0.834457i	−0.153666	+	0.988123i	$0.549108\pi$
$30$	−3.41147			−0.622847
$31$	5.24070	+	5.24070i	0.941258	+	0.941258i	0.998368	−	0.0571098i	$-0.0181885\pi$
$31$	5.24070	+	5.24070i	0.941258	+	0.941258i	−0.0571098	+	0.998368i	$0.518188\pi$
$32$			1.04189i			0.184182i
$33$	3.57398			0.622150
$34$		0			0
$35$	−0.467911			−0.0790914
$36$			0.184793i			0.0307988i
$37$	5.93752	+	5.93752i	0.976123	+	0.976123i	0.999722	−	0.0235987i	$-0.00751239\pi$
$37$	5.93752	+	5.93752i	0.976123	+	0.976123i	−0.0235987	+	0.999722i	$0.507512\pi$
$38$	6.24897			1.01372
$39$	−4.61888	−	4.61888i	−0.739613	−	0.739613i
$40$	5.27032	−	5.27032i	0.833311	−	0.833311i
$41$	5.08042	−	5.08042i	0.793428	−	0.793428i	−0.188622	−	0.982050i	$-0.560402\pi$
$41$	5.08042	−	5.08042i	0.793428	−	0.793428i	0.982050	+	0.188622i	$0.0604021\pi$
$42$		−	0.248970i		−	0.0384170i
$43$		−	4.93582i		−	0.752706i	−0.926476	−	0.376353i	$-0.877178\pi$
$43$		−	4.93582i		−	0.752706i	0.926476	−	0.376353i	$-0.122822\pi$
$44$	−0.467005	+	0.467005i	−0.0704036	+	0.0704036i
$45$	1.79046	−	1.79046i	0.266906	−	0.266906i
$46$	2.95910	+	2.95910i	0.436295	+	0.436295i
$47$	9.04963			1.32002			0.660012	−	0.751255i	$-0.270551\pi$
$47$	9.04963			1.32002			0.660012	+	0.751255i	$0.270551\pi$
$48$	2.54294	+	2.54294i	0.367042	+	0.367042i
$49$			6.96585i			0.995122i
$50$	−1.90167			−0.268937
$51$		0			0
$52$	1.20708			0.167392
$53$			7.65270i			1.05118i	0.850738	+	0.525590i	$0.176155\pi$
$53$			7.65270i			1.05118i	−0.850738	+	0.525590i	$0.823845\pi$
$54$	0.952682	+	0.952682i	0.129644	+	0.129644i
$55$	9.04963			1.22025
$56$	0.384630	+	0.384630i	0.0513983	+	0.0513983i
$57$	−3.27967	+	3.27967i	−0.434403	+	0.434403i
$58$	−6.05433	+	6.05433i	−0.794973	+	0.794973i
$59$		−	6.55438i		−	0.853307i	−0.904415	−	0.426654i	$-0.859692\pi$
$59$		−	6.55438i		−	0.853307i	0.904415	−	0.426654i	$-0.140308\pi$
$60$			0.467911i			0.0604071i
$61$	2.11103	−	2.11103i	0.270290	−	0.270290i	−0.558927	−	0.829217i	$-0.688787\pi$
$61$	2.11103	−	2.11103i	0.270290	−	0.270290i	0.829217	+	0.558927i	$0.188787\pi$
$62$	−7.06078	+	7.06078i	−0.896720	+	0.896720i
$63$	0.130668	+	0.130668i	0.0164626	+	0.0164626i
$64$	−8.59627			−1.07453
$65$	−11.6954	−	11.6954i	−1.45064	−	1.45064i
$66$			4.81521i			0.592711i
$67$	−13.5175			−1.65143			−0.825715	−	0.564087i	$-0.809228\pi$
$67$	−13.5175			−1.65143			−0.825715	+	0.564087i	$0.809228\pi$
$68$		0			0
$69$	−3.10607			−0.373927
$70$		−	0.630415i		−	0.0753490i
$71$	2.55323	+	2.55323i	0.303013	+	0.303013i	0.842191	−	0.539179i	$-0.181265\pi$
$71$	2.55323	+	2.55323i	0.303013	+	0.303013i	−0.539179	+	0.842191i	$0.681265\pi$
$72$	−2.94356			−0.346902
$73$	5.94781	+	5.94781i	0.696139	+	0.696139i	0.963575	−	0.267437i	$-0.0861767\pi$
$73$	5.94781	+	5.94781i	0.696139	+	0.696139i	−0.267437	+	0.963575i	$0.586177\pi$
$74$	−7.99960	+	7.99960i	−0.929935	+	0.929935i
$75$	0.998063	−	0.998063i	0.115246	−	0.115246i
$76$		−	0.857097i		−	0.0983157i
$77$			0.660444i			0.0752646i
$78$	6.22301	−	6.22301i	0.704617	−	0.704617i
$79$	5.53166	−	5.53166i	0.622360	−	0.622360i	−0.323774	−	0.946134i	$-0.604952\pi$
$79$	5.53166	−	5.53166i	0.622360	−	0.622360i	0.946134	+	0.323774i	$0.104952\pi$
$80$	6.43896	+	6.43896i	0.719898	+	0.719898i
$81$	−1.00000			−0.111111
$82$	6.84483	+	6.84483i	0.755885	+	0.755885i
$83$		−	2.51249i		−	0.275781i	−0.990447	−	0.137891i	$-0.955968\pi$
$83$		−	2.51249i		−	0.275781i	0.990447	−	0.137891i	$-0.0440323\pi$
$84$	−0.0341483			−0.00372588
$85$		0			0
$86$	6.65002			0.717090
$87$		−	6.35504i		−	0.681331i
$88$	−7.43893	−	7.43893i	−0.792992	−	0.792992i
$89$	−1.32770			−0.140735			−0.0703677	−	0.997521i	$-0.522417\pi$
$89$	−1.32770			−0.140735			−0.0703677	+	0.997521i	$0.522417\pi$
$90$	2.41228	+	2.41228i	0.254276	+	0.254276i
$91$	0.853535	−	0.853535i	0.0894748	−	0.0894748i
$92$	0.405864	−	0.405864i	0.0423142	−	0.0423142i
$93$		−	7.41147i		−	0.768534i
$94$			12.1925i			1.25756i
$95$	−8.30442	+	8.30442i	−0.852015	+	0.852015i
$96$	0.736727	−	0.736727i	0.0751919	−	0.0751919i
$97$	−6.19339	−	6.19339i	−0.628843	−	0.628843i	0.318934	−	0.947777i	$-0.396675\pi$
$97$	−6.19339	−	6.19339i	−0.628843	−	0.628843i	−0.947777	+	0.318934i	$0.896675\pi$
$98$	−9.38507			−0.948035
$99$	−2.52718	−	2.52718i	−0.253992	−	0.253992i
$100$			0.260830i			0.0260830i
$101$	−11.0273			−1.09726			−0.548631	−	0.836065i	$-0.684851\pi$
$101$	−11.0273			−1.09726			−0.548631	+	0.836065i	$0.684851\pi$
$102$		0			0
$103$	6.27126			0.617926			0.308963	−	0.951074i	$-0.400018\pi$
$103$	6.27126			0.617926			0.308963	+	0.951074i	$0.400018\pi$
$104$			19.2276i			1.88542i
$105$	0.330863	+	0.330863i	0.0322889	+	0.0322889i
$106$	−10.3105			−1.00144
$107$	2.51332	+	2.51332i	0.242972	+	0.242972i	0.818079	−	0.575106i	$-0.195039\pi$
$107$	2.51332	+	2.51332i	0.242972	+	0.242972i	−0.575106	+	0.818079i	$0.695039\pi$
$108$	0.130668	−	0.130668i	0.0125735	−	0.0125735i
$109$	2.54294	−	2.54294i	0.243570	−	0.243570i	−0.574755	−	0.818325i	$-0.694903\pi$
$109$	2.54294	−	2.54294i	0.243570	−	0.243570i	0.818325	+	0.574755i	$0.194903\pi$
$110$			12.1925i			1.16251i
$111$		−	8.39693i		−	0.797001i
$112$	−0.469917	+	0.469917i	−0.0444030	+	0.0444030i
$113$	−3.32987	+	3.32987i	−0.313247	+	0.313247i	−0.846166	−	0.532919i	$-0.821095\pi$
$113$	−3.32987	+	3.32987i	−0.313247	+	0.313247i	0.532919	+	0.846166i	$0.321095\pi$
$114$	−4.41869	−	4.41869i	−0.413848	−	0.413848i
$115$	−7.86484			−0.733400
$116$	0.830400	+	0.830400i	0.0771007	+	0.0771007i
$117$			6.53209i			0.603892i
$118$	8.83069			0.812931
$119$		0			0
$120$	−7.45336			−0.680396
$121$		−	1.77332i		−	0.161211i
$122$	2.84419	+	2.84419i	0.257501	+	0.257501i
$123$	−7.18479			−0.647831
$124$	0.968443	+	0.968443i	0.0869687	+	0.0869687i
$125$	−6.42510	+	6.42510i	−0.574679	+	0.574679i
$126$	−0.176049	+	0.176049i	−0.0156837	+	0.0156837i
$127$		−	7.76651i		−	0.689166i	−0.938756	−	0.344583i	$-0.888020\pi$
$127$		−	7.76651i		−	0.689166i	0.938756	−	0.344583i	$-0.111980\pi$
$128$		−	9.49794i		−	0.839507i
$129$	−3.49015	+	3.49015i	−0.307291	+	0.307291i
$130$	15.7572	−	15.7572i	1.38200	−	1.38200i
$131$	−3.50110	−	3.50110i	−0.305893	−	0.305893i	0.537421	−	0.843314i	$-0.319399\pi$
$131$	−3.50110	−	3.50110i	−0.305893	−	0.305893i	−0.843314	+	0.537421i	$0.819399\pi$
$132$	0.660444			0.0574843
$133$	−0.606059	−	0.606059i	−0.0525520	−	0.0525520i
$134$		−	18.2121i		−	1.57329i
$135$	−2.53209			−0.217928
$136$		0			0
$137$	−11.5885			−0.990075			−0.495037	−	0.868872i	$-0.664846\pi$
$137$	−11.5885			−0.990075			−0.495037	+	0.868872i	$0.664846\pi$
$138$		−	4.18479i		−	0.356233i
$139$	1.90179	+	1.90179i	0.161308	+	0.161308i	0.783146	−	0.621838i	$-0.213614\pi$
$139$	1.90179	+	1.90179i	0.161308	+	0.161308i	−0.621838	+	0.783146i	$0.713614\pi$
$140$	−0.0864665			−0.00730775
$141$	−6.39905	−	6.39905i	−0.538898	−	0.538898i
$142$	−3.43996	+	3.43996i	−0.288675	+	0.288675i
$143$	−16.5078	+	16.5078i	−1.38045	+	1.38045i
$144$		−	3.59627i		−	0.299689i
$145$		−	16.0915i		−	1.33633i
$146$	−8.01346	+	8.01346i	−0.663199	+	0.663199i
$147$	4.92560	−	4.92560i	0.406257	−	0.406257i
$148$	1.09721	+	1.09721i	0.0901901	+	0.0901901i
$149$	15.9290			1.30496			0.652478	−	0.757808i	$-0.273730\pi$
$149$	15.9290			1.30496			0.652478	+	0.757808i	$0.273730\pi$
$150$	1.34469	+	1.34469i	0.109793	+	0.109793i
$151$		−	1.38919i		−	0.113050i	−0.998401	−	0.0565252i	$-0.981998\pi$
$151$		−	1.38919i		−	0.113050i	0.998401	−	0.0565252i	$-0.0180021\pi$
$152$	13.6527			1.10738
$153$		0			0
$154$	−0.889814			−0.0717033
$155$		−	18.7665i		−	1.50736i
$156$	−0.853535	−	0.853535i	−0.0683375	−	0.0683375i
$157$	−1.78106			−0.142144			−0.0710720	−	0.997471i	$-0.522642\pi$
$157$	−1.78106			−0.142144			−0.0710720	+	0.997471i	$0.522642\pi$
$158$	7.45279	+	7.45279i	0.592912	+	0.592912i
$159$	5.41128	−	5.41128i	0.429142	−	0.429142i
$160$	1.86546	−	1.86546i	0.147477	−	0.147477i
$161$		−	0.573978i		−	0.0452358i
$162$		−	1.34730i		−	0.105854i
$163$	−2.22784	+	2.22784i	−0.174498	+	0.174498i	−0.788952	−	0.614454i	$-0.789376\pi$
$163$	−2.22784	+	2.22784i	−0.174498	+	0.174498i	0.614454	+	0.788952i	$0.289376\pi$
$164$	0.938823	−	0.938823i	0.0733097	−	0.0733097i
$165$	−6.39905	−	6.39905i	−0.498166	−	0.498166i
$166$	3.38507			0.262732
$167$	−17.2168	−	17.2168i	−1.33228	−	1.33228i	−0.903330	−	0.428946i	$-0.858885\pi$
$167$	−17.2168	−	17.2168i	−1.33228	−	1.33228i	−0.428946	−	0.903330i	$-0.641115\pi$
$168$		−	0.543948i		−	0.0419665i
$169$	29.6682			2.28217
$170$		0			0
$171$	4.63816			0.354689
$172$		−	0.912103i		−	0.0695472i
$173$	−10.6556	−	10.6556i	−0.810127	−	0.810127i	0.174526	−	0.984653i	$-0.444161\pi$
$173$	−10.6556	−	10.6556i	−0.810127	−	0.810127i	−0.984653	+	0.174526i	$0.944161\pi$
$174$	8.56212			0.649093
$175$	0.184435	+	0.184435i	0.0139419	+	0.0139419i
$176$	9.08843	−	9.08843i	0.685066	−	0.685066i
$177$	−4.63464	+	4.63464i	−0.348361	+	0.348361i
$178$		−	1.78880i		−	0.134076i
$179$			16.9017i			1.26329i	0.775258	+	0.631645i	$0.217620\pi$
$179$			16.9017i			1.26329i	−0.775258	+	0.631645i	$0.782380\pi$
$180$	0.330863	−	0.330863i	0.0246611	−	0.0246611i
$181$	−7.54355	+	7.54355i	−0.560707	+	0.560707i	−0.929508	−	0.368801i	$-0.879768\pi$
$181$	−7.54355	+	7.54355i	−0.560707	+	0.560707i	0.368801	+	0.929508i	$0.379768\pi$
$182$	1.14997	+	1.14997i	0.0852411	+	0.0852411i
$183$	−2.98545			−0.220691
$184$	6.46501	+	6.46501i	0.476607	+	0.476607i
$185$		−	21.2618i		−	1.56320i
$186$	9.98545			0.732169
$187$		0			0
$188$	1.67230			0.121965
$189$		−	0.184793i		−	0.0134417i
$190$	−11.1885	−	11.1885i	−0.811700	−	0.811700i
$191$	−1.77837			−0.128678			−0.0643392	−	0.997928i	$-0.520494\pi$
$191$	−1.77837			−0.128678			−0.0643392	+	0.997928i	$0.520494\pi$
$192$	6.07848	+	6.07848i	0.438676	+	0.438676i
$193$	−3.58449	+	3.58449i	−0.258017	+	0.258017i	−0.824247	−	0.566230i	$-0.808401\pi$
$193$	−3.58449	+	3.58449i	−0.258017	+	0.258017i	0.566230	+	0.824247i	$0.308401\pi$
$194$	8.34433	−	8.34433i	0.599088	−	0.599088i
$195$			16.5398i			1.18444i
$196$			1.28724i			0.0919455i
$197$	5.68838	−	5.68838i	0.405280	−	0.405280i	−0.474809	−	0.880089i	$-0.657483\pi$
$197$	5.68838	−	5.68838i	0.405280	−	0.405280i	0.880089	+	0.474809i	$0.157483\pi$
$198$	3.40487	−	3.40487i	0.241973	−	0.241973i
$199$	−8.44347	−	8.44347i	−0.598542	−	0.598542i	0.341382	−	0.939924i	$-0.389105\pi$
$199$	−8.44347	−	8.44347i	−0.598542	−	0.598542i	−0.939924	+	0.341382i	$0.889105\pi$
$200$	−4.15476			−0.293786
$201$	9.55834	+	9.55834i	0.674194	+	0.674194i
$202$		−	14.8571i		−	1.04534i
$203$	1.17436			0.0824242
$204$		0			0
$205$	−18.1925			−1.27062
$206$			8.44924i			0.588687i
$207$	2.19632	+	2.19632i	0.152655	+	0.152655i
$208$	−23.4911			−1.62882
$209$	11.7215	+	11.7215i	0.810791	+	0.810791i
$210$	−0.445771	+	0.445771i	−0.0307611	+	0.0307611i
$211$	−1.80074	+	1.80074i	−0.123968	+	0.123968i	−0.766369	−	0.642401i	$-0.777939\pi$
$211$	−1.80074	+	1.80074i	−0.123968	+	0.123968i	0.642401	+	0.766369i	$0.277939\pi$
$212$			1.41416i			0.0971251i
$213$		−	3.61081i		−	0.247409i
$214$	−3.38619	+	3.38619i	−0.231475	+	0.231475i
$215$	−8.83738	+	8.83738i	−0.602704	+	0.602704i
$216$	2.08141	+	2.08141i	0.141622	+	0.141622i
$217$	1.36959			0.0929735
$218$	3.42610	+	3.42610i	0.232045	+	0.232045i
$219$		−	8.41147i		−	0.568395i
$220$	1.67230			0.112747
$221$		0			0
$222$	11.3131			0.759289
$223$		−	4.44562i		−	0.297701i	−0.988860	−	0.148850i	$-0.952443\pi$
$223$		−	4.44562i		−	0.297701i	0.988860	−	0.148850i	$-0.0475573\pi$
$224$	0.136142	+	0.136142i	0.00909634	+	0.00909634i
$225$	−1.41147			−0.0940983
$226$	−4.48632	−	4.48632i	−0.298425	−	0.298425i
$227$	5.31761	−	5.31761i	0.352942	−	0.352942i	−0.508261	−	0.861203i	$-0.669712\pi$
$227$	5.31761	−	5.31761i	0.352942	−	0.352942i	0.861203	+	0.508261i	$0.169712\pi$
$228$	−0.606059	+	0.606059i	−0.0401372	+	0.0401372i
$229$			13.7374i			0.907794i	0.891054	+	0.453897i	$0.149967\pi$
$229$			13.7374i			0.907794i	−0.891054	+	0.453897i	$0.850033\pi$
$230$		−	10.5963i		−	0.698697i
$231$	0.467005	−	0.467005i	0.0307267	−	0.0307267i
$232$	−13.2275	+	13.2275i	−0.868425	+	0.868425i
$233$	−14.5136	−	14.5136i	−0.950815	−	0.950815i	0.0480306	−	0.998846i	$-0.484706\pi$
$233$	−14.5136	−	14.5136i	−0.950815	−	0.950815i	−0.998846	+	0.0480306i	$0.984706\pi$
$234$	−8.80066			−0.575317
$235$	−16.2030	−	16.2030i	−1.05697	−	1.05697i
$236$		−	1.21120i		−	0.0788424i
$237$	−7.82295			−0.508155
$238$		0			0
$239$	25.9145			1.67627			0.838134	−	0.545465i	$-0.183647\pi$
$239$	25.9145			1.67627			0.838134	+	0.545465i	$0.183647\pi$
$240$		−	9.10607i		−	0.587794i
$241$	8.04498	+	8.04498i	0.518223	+	0.518223i	0.917033	−	0.398810i	$-0.130577\pi$
$241$	8.04498	+	8.04498i	0.518223	+	0.518223i	−0.398810	+	0.917033i	$0.630577\pi$
$242$	2.38919			0.153583
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	0.390103	−	0.390103i	0.0249738	−	0.0249738i
$245$	12.4721	−	12.4721i	0.796811	−	0.796811i
$246$		−	9.68004i		−	0.617177i
$247$		−	30.2968i		−	1.92774i
$248$	−15.4263	+	15.4263i	−0.979574	+	0.979574i
$249$	−1.77660	+	1.77660i	−0.112587	+	0.112587i
$250$	−8.65652	−	8.65652i	−0.547486	−	0.547486i
$251$	0.859785			0.0542691			0.0271346	−	0.999632i	$-0.491362\pi$
$251$	0.859785			0.0542691			0.0271346	+	0.999632i	$0.491362\pi$
$252$	0.0241465	+	0.0241465i	0.00152109	+	0.00152109i
$253$			11.1010i			0.697915i
$254$	10.4638			0.656557
$255$		0			0
$256$	−4.39599			−0.274750
$257$		−	0.0300295i		−	0.00187319i	−1.00000		0.000936594i	$-0.999702\pi$
$257$		−	0.0300295i		−	0.00187319i	1.00000		0.000936594i	$-0.000298127\pi$
$258$	−4.70227	−	4.70227i	−0.292751	−	0.292751i
$259$	1.55169			0.0964173
$260$	−2.16123	−	2.16123i	−0.134034	−	0.134034i
$261$	−4.49369	+	4.49369i	−0.278152	+	0.278152i
$262$	4.71702	−	4.71702i	0.291418	−	0.291418i
$263$			12.2422i			0.754884i	0.926033	+	0.377442i	$0.123196\pi$
$263$			12.2422i			0.754884i	−0.926033	+	0.377442i	$0.876804\pi$
$264$			10.5202i			0.647475i
$265$	13.7018	−	13.7018i	0.841697	−	0.841697i
$266$	0.816541	−	0.816541i	0.0500653	−	0.0500653i
$267$	0.938823	+	0.938823i	0.0574550	+	0.0574550i
$268$	−2.49794			−0.152586
$269$	15.2503	+	15.2503i	0.929827	+	0.929827i	0.997694	−	0.0678676i	$-0.0216195\pi$
$269$	15.2503	+	15.2503i	0.929827	+	0.929827i	−0.0678676	+	0.997694i	$0.521620\pi$
$270$		−	3.41147i		−	0.207616i
$271$	3.39693			0.206349			0.103174	−	0.994663i	$-0.467100\pi$
$271$	3.39693			0.206349			0.103174	+	0.994663i	$0.467100\pi$
$272$		0			0
$273$	−1.20708			−0.0730559
$274$		−	15.6132i		−	0.943227i
$275$	−3.56705	−	3.56705i	−0.215102	−	0.215102i
$276$	−0.573978			−0.0345494
$277$	−11.2551	−	11.2551i	−0.676255	−	0.676255i	0.282896	−	0.959151i	$-0.408705\pi$
$277$	−11.2551	−	11.2551i	−0.676255	−	0.676255i	−0.959151	+	0.282896i	$0.908705\pi$
$278$	−2.56228	+	2.56228i	−0.153675	+	0.153675i
$279$	−5.24070	+	5.24070i	−0.313753	+	0.313753i
$280$		−	1.37733i		−	0.0823110i
$281$		−	16.0155i		−	0.955404i	−0.878522	−	0.477702i	$-0.841470\pi$
$281$		−	16.0155i		−	0.955404i	0.878522	−	0.477702i	$-0.158530\pi$
$282$	8.62142	−	8.62142i	0.513398	−	0.513398i
$283$	−18.9757	+	18.9757i	−1.12799	+	1.12799i	−0.137487	+	0.990504i	$0.543902\pi$
$283$	−18.9757	+	18.9757i	−1.12799	+	1.12799i	−0.990504	+	0.137487i	$0.956098\pi$
$284$	0.471818	+	0.471818i	0.0279973	+	0.0279973i
$285$	11.7442			0.695668
$286$	−22.2409	−	22.2409i	−1.31513	−	1.31513i
$287$		−	1.32770i		−	0.0783714i
$288$	−1.04189			−0.0613939
$289$		0			0
$290$	21.6800			1.27310
$291$			8.75877i			0.513448i
$292$	1.09911	+	1.09911i	0.0643206	+	0.0643206i
$293$	−2.40879			−0.140723			−0.0703614	−	0.997522i	$-0.522415\pi$
$293$	−2.40879			−0.140723			−0.0703614	+	0.997522i	$0.522415\pi$
$294$	6.63624	+	6.63624i	0.387034	+	0.387034i
$295$	−11.7353	+	11.7353i	−0.683257	+	0.683257i
$296$	−17.4775	+	17.4775i	−1.01586	+	1.01586i
$297$			3.57398i			0.207383i
$298$			21.4611i			1.24321i
$299$	14.3466	−	14.3466i	0.829683	−	0.829683i
$300$	0.184435	−	0.184435i	0.0106483	−	0.0106483i
$301$	−0.644954	−	0.644954i	−0.0371745	−	0.0371745i
$302$	1.87164			0.107701
$303$	7.79751	+	7.79751i	0.447955	+	0.447955i
$304$			16.6800i			0.956666i
$305$	−7.55943			−0.432852
$306$		0			0
$307$	−6.41921			−0.366364			−0.183182	−	0.983079i	$-0.558640\pi$
$307$	−6.41921			−0.366364			−0.183182	+	0.983079i	$0.558640\pi$
$308$			0.122045i			0.00695417i
$309$	−4.43445	−	4.43445i	−0.252267	−	0.252267i
$310$	25.2841			1.43604
$311$	0.384630	+	0.384630i	0.0218103	+	0.0218103i	0.717928	−	0.696118i	$-0.245091\pi$
$311$	0.384630	+	0.384630i	0.0218103	+	0.0218103i	−0.696118	+	0.717928i	$0.745091\pi$
$312$	13.5960	−	13.5960i	0.769721	−	0.769721i
$313$	11.7511	−	11.7511i	0.664211	−	0.664211i	−0.292159	−	0.956370i	$-0.594374\pi$
$313$	11.7511	−	11.7511i	0.664211	−	0.664211i	0.956370	+	0.292159i	$0.0943736\pi$
$314$		−	2.39961i		−	0.135418i
$315$		−	0.467911i		−	0.0263638i
$316$	1.02221	−	1.02221i	0.0575038	−	0.0575038i
$317$	18.4253	−	18.4253i	1.03487	−	1.03487i	0.0355007	−	0.999370i	$-0.488697\pi$
$317$	18.4253	−	18.4253i	1.03487	−	1.03487i	0.999370	−	0.0355007i	$-0.0113026\pi$
$318$	7.29060	+	7.29060i	0.408836	+	0.408836i
$319$	−22.7128			−1.27167
$320$	15.3912	+	15.3912i	0.860397	+	0.860397i
$321$		−	3.55438i		−	0.198386i
$322$	0.773318			0.0430953
$323$		0			0
$324$	−0.184793			−0.0102663
$325$			9.21987i			0.511427i
$326$	−3.00156	−	3.00156i	−0.166241	−	0.166241i
$327$	−3.59627			−0.198874
$328$	14.9545	+	14.9545i	0.825725	+	0.825725i
$329$	1.18250	−	1.18250i	0.0651932	−	0.0651932i
$330$	8.62142	−	8.62142i	0.474594	−	0.474594i
$331$		−	22.5107i		−	1.23730i	−0.785666	−	0.618651i	$-0.787680\pi$
$331$		−	22.5107i		−	1.23730i	0.785666	−	0.618651i	$-0.212320\pi$
$332$		−	0.464289i		−	0.0254812i
$333$	−5.93752	+	5.93752i	−0.325374	+	0.325374i
$334$	23.1961	−	23.1961i	1.26924	−	1.26924i
$335$	24.2026	+	24.2026i	1.32233	+	1.32233i
$336$	0.664563			0.0362549
$337$	−0.351437	−	0.351437i	−0.0191440	−	0.0191440i	0.697470	−	0.716614i	$-0.254309\pi$
$337$	−0.351437	−	0.351437i	−0.0191440	−	0.0191440i	−0.716614	+	0.697470i	$0.754309\pi$
$338$			39.9718i			2.17418i
$339$	4.70914			0.255765
$340$		0			0
$341$	−26.4884			−1.43443
$342$			6.24897i			0.337906i
$343$	1.82489	+	1.82489i	0.0985348	+	0.0985348i
$344$	14.5289			0.783346
$345$	5.56128	+	5.56128i	0.299409	+	0.299409i
$346$	14.3562	−	14.3562i	0.771794	−	0.771794i
$347$	−9.80392	+	9.80392i	−0.526302	+	0.526302i	−0.919468	−	0.393166i	$-0.871380\pi$
$347$	−9.80392	+	9.80392i	−0.526302	+	0.526302i	0.393166	+	0.919468i	$0.371380\pi$
$348$		−	1.17436i		−	0.0629525i
$349$			27.0479i			1.44784i	0.689884	+	0.723920i	$0.257661\pi$
$349$			27.0479i			1.44784i	−0.689884	+	0.723920i	$0.742339\pi$
$350$	−0.248488	+	0.248488i	−0.0132822	+	0.0132822i
$351$	4.61888	−	4.61888i	0.246538	−	0.246538i
$352$	−2.63305	−	2.63305i	−0.140342	−	0.140342i
$353$	−8.96997			−0.477423			−0.238712	−	0.971090i	$-0.576725\pi$
$353$	−8.96997			−0.477423			−0.238712	+	0.971090i	$0.576725\pi$
$354$	−6.24424	−	6.24424i	−0.331878	−	0.331878i
$355$		−	9.14290i		−	0.485255i
$356$	−0.245348			−0.0130034
$357$		0			0
$358$	−22.7716			−1.20351
$359$		−	6.12567i		−	0.323300i	−0.986848	−	0.161650i	$-0.948318\pi$
$359$		−	6.12567i		−	0.323300i	0.986848	−	0.161650i	$-0.0516816\pi$
$360$	5.27032	+	5.27032i	0.277770	+	0.277770i
$361$	−2.51249			−0.132236
$362$	−10.1634	−	10.1634i	−0.534176	−	0.534176i
$363$	−1.25393	+	1.25393i	−0.0658140	+	0.0658140i
$364$	0.157727	−	0.157727i	0.00826714	−	0.00826714i
$365$		−	21.2986i		−	1.11482i
$366$		−	4.02229i		−	0.210248i
$367$	−12.6723	+	12.6723i	−0.661486	+	0.661486i	−0.955730	−	0.294244i	$-0.904932\pi$
$367$	−12.6723	+	12.6723i	−0.661486	+	0.661486i	0.294244	+	0.955730i	$0.404932\pi$
$368$	−7.89856	+	7.89856i	−0.411741	+	0.411741i
$369$	5.08042	+	5.08042i	0.264476	+	0.264476i
$370$	28.6459			1.48923
$371$	0.999964	+	0.999964i	0.0519155	+	0.0519155i
$372$		−	1.36959i		−	0.0710097i
$373$	−15.5389			−0.804574			−0.402287	−	0.915514i	$-0.631785\pi$
$373$	−15.5389			−0.804574			−0.402287	+	0.915514i	$0.631785\pi$
$374$		0			0
$375$	9.08647			0.469223
$376$			26.6382i			1.37376i
$377$	29.3532	+	29.3532i	1.51177	+	1.51177i
$378$	0.248970			0.0128057
$379$	−26.8762	−	26.8762i	−1.38054	−	1.38054i	−0.843661	−	0.536876i	$-0.819604\pi$
$379$	−26.8762	−	26.8762i	−1.38054	−	1.38054i	−0.536876	−	0.843661i	$-0.680396\pi$
$380$	−1.53459	+	1.53459i	−0.0787230	+	0.0787230i
$381$	−5.49175	+	5.49175i	−0.281351	+	0.281351i
$382$		−	2.39599i		−	0.122590i
$383$			21.2686i			1.08677i	0.839483	+	0.543387i	$0.182858\pi$
$383$			21.2686i			1.08677i	−0.839483	+	0.543387i	$0.817142\pi$
$384$	−6.71606	+	6.71606i	−0.342727	+	0.342727i
$385$	1.18250	−	1.18250i	0.0602657	−	0.0602657i
$386$	−4.82937	−	4.82937i	−0.245808	−	0.245808i
$387$	4.93582			0.250902
$388$	−1.14449	−	1.14449i	−0.0581028	−	0.0581028i
$389$		−	13.8016i		−	0.699769i	−0.936793	−	0.349884i	$-0.886221\pi$
$389$		−	13.8016i		−	0.699769i	0.936793	−	0.349884i	$-0.113779\pi$
$390$	−22.2841			−1.12840
$391$		0			0
$392$	−20.5044			−1.03563
$393$			4.95130i			0.249760i
$394$	7.66393	+	7.66393i	0.386103	+	0.386103i
$395$	−19.8084			−0.996669
$396$	−0.467005	−	0.467005i	−0.0234679	−	0.0234679i
$397$	−20.1965	+	20.1965i	−1.01363	+	1.01363i	−0.0137259	+	0.999906i	$0.504369\pi$
$397$	−20.1965	+	20.1965i	−1.01363	+	1.01363i	−0.999906	+	0.0137259i	$0.995631\pi$
$398$	11.3759	−	11.3759i	0.570220	−	0.570220i
$399$			0.857097i			0.0429085i
$400$		−	5.07604i		−	0.253802i
$401$	18.9339	−	18.9339i	0.945515	−	0.945515i	−0.0530753	−	0.998591i	$-0.516902\pi$
$401$	18.9339	−	18.9339i	0.945515	−	0.945515i	0.998591	+	0.0530753i	$0.0169023\pi$
$402$	−12.8779	+	12.8779i	−0.642292	+	0.642292i
$403$	34.2327	+	34.2327i	1.70525	+	1.70525i
$404$	−2.03777			−0.101383
$405$	1.79046	+	1.79046i	0.0889685	+	0.0889685i
$406$			1.58222i			0.0785240i
$407$	−30.0104			−1.48756
$408$		0			0
$409$	38.8357			1.92030			0.960152	−	0.279479i	$-0.0901616\pi$
$409$	38.8357			1.92030			0.960152	+	0.279479i	$0.0901616\pi$
$410$		−	24.5107i		−	1.21050i
$411$	8.19433	+	8.19433i	0.404196	+	0.404196i
$412$	1.15888			0.0570940
$413$	−0.856448	−	0.856448i	−0.0421430	−	0.0421430i
$414$	−2.95910	+	2.95910i	−0.145432	+	0.145432i
$415$	−4.49850	+	4.49850i	−0.220823	+	0.220823i
$416$			6.80571i			0.333677i
$417$		−	2.68954i		−	0.131707i
$418$	−15.7923	+	15.7923i	−0.772427	+	0.772427i
$419$	13.4598	−	13.4598i	0.657556	−	0.657556i	−0.297245	−	0.954801i	$-0.596068\pi$
$419$	13.4598	−	13.4598i	0.657556	−	0.657556i	0.954801	+	0.297245i	$0.0960679\pi$
$420$	0.0611410	+	0.0611410i	0.00298338	+	0.00298338i
$421$	−6.41653			−0.312722			−0.156361	−	0.987700i	$-0.549976\pi$
$421$	−6.41653			−0.312722			−0.156361	+	0.987700i	$0.549976\pi$
$422$	−2.42614	−	2.42614i	−0.118102	−	0.118102i
$423$			9.04963i			0.440008i
$424$	−22.5262			−1.09397
$425$		0			0
$426$	4.86484			0.235702
$427$		−	0.551689i		−	0.0266981i
$428$	0.464444	+	0.464444i	0.0224497	+	0.0224497i
$429$	23.3455			1.12713
$430$	−11.9066	−	11.9066i	−0.574186	−	0.574186i
$431$	6.11714	−	6.11714i	0.294652	−	0.294652i	−0.544262	−	0.838915i	$-0.683190\pi$
$431$	6.11714	−	6.11714i	0.294652	−	0.294652i	0.838915	+	0.544262i	$0.183190\pi$
$432$	−2.54294	+	2.54294i	−0.122347	+	0.122347i
$433$			23.3182i			1.12060i	0.828289	+	0.560301i	$0.189314\pi$
$433$			23.3182i			1.12060i	−0.828289	+	0.560301i	$0.810686\pi$
$434$			1.84524i			0.0885742i
$435$	−11.3784	+	11.3784i	−0.545554	+	0.545554i
$436$	0.469917	−	0.469917i	0.0225050	−	0.0225050i
$437$	−10.1869	−	10.1869i	−0.487304	−	0.487304i
$438$	11.3327			0.541500
$439$	9.33334	+	9.33334i	0.445456	+	0.445456i	0.893841	−	0.448385i	$-0.148000\pi$
$439$	9.33334	+	9.33334i	0.445456	+	0.445456i	−0.448385	+	0.893841i	$0.648000\pi$
$440$			26.6382i			1.26992i
$441$	−6.96585			−0.331707
$442$		0			0
$443$	−30.5235			−1.45022			−0.725108	−	0.688635i	$-0.758210\pi$
$443$	−30.5235			−1.45022			−0.725108	+	0.688635i	$0.758210\pi$
$444$		−	1.55169i		−	0.0736399i
$445$	2.37718	+	2.37718i	0.112689	+	0.112689i
$446$	5.98957			0.283614
$447$	−11.2635	−	11.2635i	−0.532746	−	0.532746i
$448$	−1.12326	+	1.12326i	−0.0530689	+	0.0530689i
$449$	−1.91755	+	1.91755i	−0.0904949	+	0.0904949i	−0.750905	−	0.660410i	$-0.770382\pi$
$449$	−1.91755	+	1.91755i	−0.0904949	+	0.0904949i	0.660410	+	0.750905i	$0.270382\pi$
$450$		−	1.90167i		−	0.0896458i
$451$			25.6783i			1.20914i
$452$	−0.615334	+	0.615334i	−0.0289429	+	0.0289429i
$453$	−0.982302	+	0.982302i	−0.0461526	+	0.0461526i
$454$	7.16439	+	7.16439i	0.336241	+	0.336241i
$455$	−3.05644			−0.143288
$456$	−9.65392	−	9.65392i	−0.452086	−	0.452086i
$457$			26.2668i			1.22871i	0.789030	+	0.614355i	$0.210584\pi$
$457$			26.2668i			1.22871i	−0.789030	+	0.614355i	$0.789416\pi$
$458$	−18.5084			−0.864839
$459$		0			0
$460$	−1.45336			−0.0677634
$461$			25.5202i			1.18860i	0.804245	+	0.594298i	$0.202570\pi$
$461$			25.5202i			1.18860i	−0.804245	+	0.594298i	$0.797430\pi$
$462$	0.629194	+	0.629194i	0.0292727	+	0.0292727i
$463$	2.82564			0.131318			0.0656592	−	0.997842i	$-0.479085\pi$
$463$	2.82564			0.131318			0.0656592	+	0.997842i	$0.479085\pi$
$464$	−16.1605	−	16.1605i	−0.750233	−	0.750233i
$465$	−13.2699	+	13.2699i	−0.615378	+	0.615378i
$466$	19.5541	−	19.5541i	0.905825	−	0.905825i
$467$		−	32.9992i		−	1.52702i	−0.645796	−	0.763510i	$-0.723474\pi$
$467$		−	32.9992i		−	1.52702i	0.645796	−	0.763510i	$-0.276526\pi$
$468$			1.20708i			0.0557973i
$469$	−1.76631	+	1.76631i	−0.0815607	+	0.0815607i
$470$	21.8302	−	21.8302i	1.00695	−	1.00695i
$471$	1.25940	+	1.25940i	0.0580300	+	0.0580300i
$472$	19.2932			0.888043
$473$	12.4737	+	12.4737i	0.573543	+	0.573543i
$474$		−	10.5398i		−	0.484110i
$475$	6.54664			0.300380
$476$		0			0
$477$	−7.65270			−0.350393
$478$			34.9145i			1.59695i
$479$	−24.6206	−	24.6206i	−1.12495	−	1.12495i	−0.990987	−	0.133958i	$-0.957231\pi$
$479$	−24.6206	−	24.6206i	−1.12495	−	1.12495i	−0.133958	−	0.990987i	$-0.542769\pi$
$480$	−2.63816			−0.120415
$481$	38.7844	+	38.7844i	1.76842	+	1.76842i
$482$	−10.8390	+	10.8390i	−0.493702	+	0.493702i
$483$	−0.405864	+	0.405864i	−0.0184674	+	0.0184674i
$484$		−	0.327696i		−	0.0148953i
$485$			22.1780i			1.00705i
$486$	−0.952682	+	0.952682i	−0.0432146	+	0.0432146i
$487$	−15.2612	+	15.2612i	−0.691553	+	0.691553i	−0.962574	−	0.271021i	$-0.912639\pi$
$487$	−15.2612	+	15.2612i	−0.691553	+	0.691553i	0.271021	+	0.962574i	$0.412639\pi$
$488$	6.21396	+	6.21396i	0.281293	+	0.281293i
$489$	3.15064			0.142477
$490$	16.8036	+	16.8036i	0.759107	+	0.759107i
$491$			34.3209i			1.54888i	0.632647	+	0.774440i	$0.281968\pi$
$491$			34.3209i			1.54888i	−0.632647	+	0.774440i	$0.718032\pi$
$492$	−1.32770			−0.0598572
$493$		0			0
$494$	40.8188			1.83653
$495$			9.04963i			0.406751i
$496$	−18.8470	−	18.8470i	−0.846254	−	0.846254i
$497$	0.667252			0.0299303
$498$	−2.39360	−	2.39360i	−0.107260	−	0.107260i
$499$	12.8313	−	12.8313i	0.574408	−	0.574408i	−0.358949	−	0.933357i	$-0.616865\pi$
$499$	12.8313	−	12.8313i	0.574408	−	0.574408i	0.933357	+	0.358949i	$0.116865\pi$
$500$	−1.18731	+	1.18731i	−0.0530982	+	0.0530982i
$501$			24.3482i			1.08780i
$502$			1.15839i			0.0517013i
$503$	17.8296	−	17.8296i	0.794981	−	0.794981i	−0.187318	−	0.982299i	$-0.559979\pi$
$503$	17.8296	−	17.8296i	0.794981	−	0.794981i	0.982299	+	0.187318i	$0.0599795\pi$
$504$	−0.384630	+	0.384630i	−0.0171328	+	0.0171328i
$505$	19.7440	+	19.7440i	0.878596	+	0.878596i
$506$	−14.9564			−0.664891
$507$	−20.9786	−	20.9786i	−0.931691	−	0.931691i
$508$		−	1.43519i		−	0.0636764i
$509$	−2.82026			−0.125006			−0.0625029	−	0.998045i	$-0.519908\pi$
$509$	−2.82026			−0.125006			−0.0625029	+	0.998045i	$0.519908\pi$
$510$		0			0
$511$	1.55438			0.0687616
$512$		−	24.9186i		−	1.10126i
$513$	−3.27967	−	3.27967i	−0.144801	−	0.144801i
$514$	0.0404586			0.00178455
$515$	−11.2284	−	11.2284i	−0.494783	−	0.494783i
$516$	−0.644954	+	0.644954i	−0.0283925	+	0.0283925i
$517$	−22.8701	+	22.8701i	−1.00582	+	1.00582i
$518$			2.09059i			0.0918550i
$519$			15.0692i			0.661466i
$520$	34.4262	−	34.4262i	1.50969	−	1.50969i
$521$	−0.744101	+	0.744101i	−0.0325997	+	0.0325997i	−0.723219	−	0.690619i	$-0.757338\pi$
$521$	−0.744101	+	0.744101i	−0.0325997	+	0.0325997i	0.690619	+	0.723219i	$0.257338\pi$
$522$	−6.05433	−	6.05433i	−0.264991	−	0.264991i
$523$	−15.0915			−0.659906			−0.329953	−	0.943997i	$-0.607033\pi$
$523$	−15.0915			−0.659906			−0.329953	+	0.943997i	$0.607033\pi$
$524$	−0.646977	−	0.646977i	−0.0282633	−	0.0282633i
$525$		−	0.260830i		−	0.0113835i
$526$	−16.4938			−0.719165
$527$		0			0
$528$	−12.8530			−0.559354
$529$			13.3523i			0.580537i
$530$	18.4604	+	18.4604i	0.801870	+	0.801870i
$531$	6.55438			0.284436
$532$	−0.111995	−	0.111995i	−0.00485560	−	0.00485560i
$533$	33.1857	−	33.1857i	1.43743	−	1.43743i
$534$	−1.26487	+	1.26487i	−0.0547364	+	0.0547364i
$535$		−	9.00000i		−	0.389104i
$536$		−	39.7897i		−	1.71865i
$537$	11.9513	−	11.9513i	0.515736	−	0.515736i
$538$	−20.5467	+	20.5467i	−0.885830	+	0.885830i
$539$	−17.6040	−	17.6040i	−0.758257	−	0.758257i
$540$	−0.467911			−0.0201357
$541$	13.6600	+	13.6600i	0.587291	+	0.587291i	0.936897	−	0.349606i	$-0.113685\pi$
$541$	13.6600	+	13.6600i	0.587291	+	0.587291i	−0.349606	+	0.936897i	$0.613685\pi$
$542$			4.57667i			0.196585i
$543$	10.6682			0.457816
$544$		0			0
$545$	−9.10607			−0.390061
$546$		−	1.62630i		−	0.0695991i
$547$	−11.8383	−	11.8383i	−0.506168	−	0.506168i	0.407180	−	0.913348i	$-0.366512\pi$
$547$	−11.8383	−	11.8383i	−0.506168	−	0.506168i	−0.913348	+	0.407180i	$0.866512\pi$
$548$	−2.14147			−0.0914792
$549$	2.11103	+	2.11103i	0.0900967	+	0.0900967i
$550$	4.80588	−	4.80588i	0.204923	−	0.204923i
$551$	20.8424	−	20.8424i	0.887918	−	0.887918i
$552$		−	9.14290i		−	0.389148i
$553$		−	1.44562i		−	0.0614741i
$554$	15.1640	−	15.1640i	0.644256	−	0.644256i
$555$	−15.0343	+	15.0343i	−0.638172	+	0.638172i
$556$	0.351437	+	0.351437i	0.0149042	+	0.0149042i
$557$	19.8084			0.839309			0.419654	−	0.907684i	$-0.362151\pi$
$557$	19.8084			0.839309			0.419654	+	0.907684i	$0.362151\pi$
$558$	−7.06078	−	7.06078i	−0.298907	−	0.298907i
$559$		−	32.2412i		−	1.36366i
$560$	1.68273			0.0711085
$561$		0			0
$562$	21.5776			0.910196
$563$		−	35.4020i		−	1.49202i	−0.665937	−	0.746008i	$-0.731968\pi$
$563$		−	35.4020i		−	1.49202i	0.665937	−	0.746008i	$-0.268032\pi$
$564$	−1.18250	−	1.18250i	−0.0497921	−	0.0497921i
$565$	11.9240			0.501645
$566$	−25.5659	−	25.5659i	−1.07462	−	1.07462i
$567$	−0.130668	+	0.130668i	−0.00548754	+	0.00548754i
$568$	−7.51560	+	7.51560i	−0.315347	+	0.315347i
$569$			18.0060i			0.754850i	0.926040	+	0.377425i	$0.123190\pi$
$569$			18.0060i			0.754850i	−0.926040	+	0.377425i	$0.876810\pi$
$570$			15.8229i			0.662750i
$571$	−9.82325	+	9.82325i	−0.411090	+	0.411090i	−0.882118	−	0.471028i	$-0.843883\pi$
$571$	−9.82325	+	9.82325i	−0.411090	+	0.411090i	0.471028	+	0.882118i	$0.343883\pi$
$572$	−3.05052	+	3.05052i	−0.127549	+	0.127549i
$573$	1.25750	+	1.25750i	0.0525327	+	0.0525327i
$574$	1.78880			0.0746631
$575$	3.10005	+	3.10005i	0.129281	+	0.129281i
$576$		−	8.59627i		−	0.358178i
$577$	−4.15570			−0.173004			−0.0865020	−	0.996252i	$-0.527569\pi$
$577$	−4.15570			−0.173004			−0.0865020	+	0.996252i	$0.527569\pi$
$578$		0			0
$579$	5.06923			0.210670
$580$		−	2.97359i		−	0.123472i
$581$	−0.328302	−	0.328302i	−0.0136203	−	0.0136203i
$582$	−11.8007			−0.489153
$583$	−19.3398	−	19.3398i	−0.800972	−	0.800972i
$584$	−17.5078	+	17.5078i	−0.724476	+	0.724476i
$585$	11.6954	−	11.6954i	0.483546	−	0.483546i
$586$		−	3.24535i		−	0.134064i
$587$		−	25.9341i		−	1.07041i	−0.844721	−	0.535207i	$-0.820234\pi$
$587$		−	25.9341i		−	1.07041i	0.844721	−	0.535207i	$-0.179766\pi$
$588$	0.910214	−	0.910214i	0.0375366	−	0.0375366i
$589$	24.3072	−	24.3072i	1.00156	−	1.00156i
$590$	−15.8110	−	15.8110i	−0.650927	−	0.650927i
$591$	−8.04458			−0.330910
$592$	−21.3529	−	21.3529i	−0.877600	−	0.877600i
$593$			37.6459i			1.54593i	0.634448	+	0.772966i	$0.281228\pi$
$593$			37.6459i			1.54593i	−0.634448	+	0.772966i	$0.718772\pi$
$594$	−4.81521			−0.197570
$595$		0			0
$596$	2.94356			0.120573
$597$			11.9409i			0.488707i
$598$	19.3291	+	19.3291i	0.790425	+	0.790425i
$599$	9.59720			0.392131			0.196065	−	0.980591i	$-0.437183\pi$
$599$	9.59720			0.392131			0.196065	+	0.980591i	$0.437183\pi$
$600$	2.93786	+	2.93786i	0.119938	+	0.119938i
$601$	19.9139	−	19.9139i	0.812305	−	0.812305i	−0.172674	−	0.984979i	$-0.555241\pi$
$601$	19.9139	−	19.9139i	0.812305	−	0.812305i	0.984979	+	0.172674i	$0.0552408\pi$
$602$	0.868945	−	0.868945i	0.0354155	−	0.0354155i
$603$		−	13.5175i		−	0.550477i
$604$		−	0.256711i		−	0.0104454i
$605$	−3.17505	+	3.17505i	−0.129084	+	0.129084i
$606$	−10.5056	+	10.5056i	−0.426759	+	0.426759i
$607$	−11.5036	−	11.5036i	−0.466917	−	0.466917i	0.433997	−	0.900914i	$-0.357103\pi$
$607$	−11.5036	−	11.5036i	−0.466917	−	0.466917i	−0.900914	+	0.433997i	$0.857103\pi$
$608$	4.83244			0.195981
$609$	−0.830400	−	0.830400i	−0.0336495	−	0.0336495i
$610$		−	10.1848i		−	0.412370i
$611$	59.1130			2.39146
$612$		0			0
$613$	−4.12330			−0.166539			−0.0832693	−	0.996527i	$-0.526536\pi$
$613$	−4.12330			−0.166539			−0.0832693	+	0.996527i	$0.526536\pi$
$614$		−	8.64858i		−	0.349028i
$615$	12.8641	+	12.8641i	0.518729	+	0.518729i
$616$	−1.94406			−0.0783284
$617$	8.97519	+	8.97519i	0.361328	+	0.361328i	0.864302	−	0.502974i	$-0.167761\pi$
$617$	8.97519	+	8.97519i	0.361328	+	0.361328i	−0.502974	+	0.864302i	$0.667761\pi$
$618$	5.97452	−	5.97452i	0.240330	−	0.240330i
$619$	18.3310	−	18.3310i	0.736785	−	0.736785i	−0.235169	−	0.971954i	$-0.575564\pi$
$619$	18.3310	−	18.3310i	0.736785	−	0.736785i	0.971954	+	0.235169i	$0.0755644\pi$
$620$		−	3.46791i		−	0.139275i
$621$		−	3.10607i		−	0.124642i
$622$	−0.518210	+	0.518210i	−0.0207783	+	0.0207783i
$623$	−0.173487	+	0.173487i	−0.00695063	+	0.00695063i
$624$	16.6107	+	16.6107i	0.664962	+	0.664962i
$625$	30.0651			1.20260
$626$	15.8322	+	15.8322i	0.632782	+	0.632782i
$627$		−	16.5767i		−	0.662008i
$628$	−0.329126			−0.0131336
$629$		0			0
$630$	0.630415			0.0251163
$631$		−	30.1411i		−	1.19990i	−0.800037	−	0.599950i	$-0.795187\pi$
$631$		−	30.1411i		−	1.19990i	0.800037	−	0.599950i	$-0.204813\pi$
$632$	16.2828	+	16.2828i	0.647695	+	0.647695i
$633$	2.54664			0.101220
$634$	24.8244	+	24.8244i	0.985903	+	0.985903i
$635$	−13.9056	+	13.9056i	−0.551827	+	0.551827i
$636$	0.999964	−	0.999964i	0.0396511	−	0.0396511i
$637$			45.5016i			1.80284i
$638$		−	30.6008i		−	1.21150i
$639$	−2.55323	+	2.55323i	−0.101004	+	0.101004i
$640$	−17.0057	+	17.0057i	−0.672208	+	0.672208i
$641$	−0.422865	−	0.422865i	−0.0167022	−	0.0167022i	0.698706	−	0.715409i	$-0.253759\pi$
$641$	−0.422865	−	0.422865i	−0.0167022	−	0.0167022i	−0.715409	+	0.698706i	$0.753759\pi$
$642$	4.78880			0.188999
$643$	23.0394	+	23.0394i	0.908586	+	0.908586i	0.996158	−	0.0875723i	$-0.0279109\pi$
$643$	23.0394	+	23.0394i	0.908586	+	0.908586i	−0.0875723	+	0.996158i	$0.527911\pi$
$644$		−	0.106067i		−	0.00417962i
$645$	12.4979			0.492106
$646$		0			0
$647$	−13.8648			−0.545083			−0.272542	−	0.962144i	$-0.587864\pi$
$647$	−13.8648			−0.545083			−0.272542	+	0.962144i	$0.587864\pi$
$648$		−	2.94356i		−	0.115634i
$649$	16.5641	+	16.5641i	0.650199	+	0.650199i
$650$	−12.4219			−0.487227
$651$	−0.968443	−	0.968443i	−0.0379563	−	0.0379563i
$652$	−0.411689	+	0.411689i	−0.0161230	+	0.0161230i
$653$	1.05796	−	1.05796i	0.0414013	−	0.0414013i	−0.686103	−	0.727504i	$-0.740680\pi$
$653$	1.05796	−	1.05796i	0.0414013	−	0.0414013i	0.727504	+	0.686103i	$0.240680\pi$
$654$		−	4.84524i		−	0.189464i
$655$			12.5371i			0.489867i
$656$	−18.2705	+	18.2705i	−0.713344	+	0.713344i
$657$	−5.94781	+	5.94781i	−0.232046	+	0.232046i
$658$	1.59317	+	1.59317i	0.0621084	+	0.0621084i
$659$	−49.3441			−1.92217			−0.961087	−	0.276246i	$-0.910909\pi$
$659$	−49.3441			−1.92217			−0.961087	+	0.276246i	$0.910909\pi$
$660$	−1.18250	−	1.18250i	−0.0460287	−	0.0460287i
$661$		−	45.9077i		−	1.78560i	−0.450452	−	0.892801i	$-0.648737\pi$
$661$		−	45.9077i		−	1.78560i	0.450452	−	0.892801i	$-0.351263\pi$
$662$	30.3286			1.17876
$663$		0			0
$664$	7.39567			0.287008
$665$			2.17024i			0.0841585i
$666$	−7.99960	−	7.99960i	−0.309978	−	0.309978i
$667$	19.7392			0.764304
$668$	−3.18154	−	3.18154i	−0.123097	−	0.123097i
$669$	−3.14353	+	3.14353i	−0.121536	+	0.121536i
$670$	−32.6080	+	32.6080i	−1.25976	+	1.25976i
$671$			10.6699i			0.411908i
$672$		−	0.192533i		−	0.00742713i
$673$	−24.6049	+	24.6049i	−0.948448	+	0.948448i	−0.998735	−	0.0502868i	$-0.983986\pi$
$673$	−24.6049	+	24.6049i	−0.948448	+	0.948448i	0.0502868	+	0.998735i	$0.483986\pi$
$674$	0.473490	−	0.473490i	0.0182381	−	0.0182381i
$675$	0.998063	+	0.998063i	0.0384155	+	0.0384155i
$676$	5.48246			0.210864
$677$	10.0321	+	10.0321i	0.385564	+	0.385564i	0.873102	−	0.487538i	$-0.162105\pi$
$677$	10.0321	+	10.0321i	0.385564	+	0.385564i	−0.487538	+	0.873102i	$0.662105\pi$
$678$			6.34461i			0.243663i
$679$	−1.61856			−0.0621145
$680$		0			0
$681$	−7.52023			−0.288176
$682$		−	35.6878i		−	1.36656i
$683$	−31.4867	−	31.4867i	−1.20480	−	1.20480i	−0.972688	−	0.232117i	$-0.925435\pi$
$683$	−31.4867	−	31.4867i	−1.20480	−	1.20480i	−0.232117	−	0.972688i	$-0.574565\pi$
$684$	0.857097			0.0327719
$685$	20.7488	+	20.7488i	0.792769	+	0.792769i
$686$	−2.45867	+	2.45867i	−0.0938724	+	0.0938724i
$687$	9.71382	−	9.71382i	0.370605	−	0.370605i
$688$			17.7505i			0.676733i
$689$			49.9881i			1.90440i
$690$	−7.49269	+	7.49269i	−0.285242	+	0.285242i
$691$	−4.23403	+	4.23403i	−0.161070	+	0.161070i	−0.783041	−	0.621971i	$-0.786332\pi$
$691$	−4.23403	+	4.23403i	−0.161070	+	0.161070i	0.621971	+	0.783041i	$0.286332\pi$
$692$	−1.96907	−	1.96907i	−0.0748527	−	0.0748527i
$693$	−0.660444			−0.0250882
$694$	−13.2088	−	13.2088i	−0.501399	−	0.501399i
$695$		−	6.81016i		−	0.258324i
$696$	18.7065			0.709066
$697$		0			0
$698$	−36.4415			−1.37933
$699$			20.5253i			0.776337i
$700$	0.0340821	+	0.0340821i	0.00128818	+	0.00128818i
$701$	−15.4739			−0.584441			−0.292221	−	0.956351i	$-0.594394\pi$
$701$	−15.4739			−0.584441			−0.292221	+	0.956351i	$0.594394\pi$
$702$	6.22301	+	6.22301i	0.234872	+	0.234872i
$703$	27.5392	−	27.5392i	1.03866	−	1.03866i
$704$	21.7243	−	21.7243i	0.818767	−	0.818767i
$705$			22.9145i			0.863009i
$706$		−	12.0852i		−	0.454833i
$707$	−1.44092	+	1.44092i	−0.0541914	+	0.0541914i
$708$	−0.856448	+	0.856448i	−0.0321873	+	0.0321873i
$709$	−22.6262	−	22.6262i	−0.849744	−	0.849744i	0.140357	−	0.990101i	$-0.455175\pi$
$709$	−22.6262	−	22.6262i	−0.849744	−	0.849744i	−0.990101	+	0.140357i	$0.955175\pi$
$710$	12.3182			0.462294
$711$	5.53166	+	5.53166i	0.207453	+	0.207453i
$712$		−	3.90816i		−	0.146464i
$713$	23.0205			0.862126
$714$		0			0
$715$	59.1130			2.21070
$716$			3.12330i			0.116723i
$717$	−18.3243	−	18.3243i	−0.684333	−	0.684333i
$718$	8.25309			0.308003
$719$	16.5013	+	16.5013i	0.615395	+	0.615395i	0.944347	−	0.328952i	$-0.106695\pi$
$719$	16.5013	+	16.5013i	0.615395	+	0.615395i	−0.328952	+	0.944347i	$0.606695\pi$
$720$	−6.43896	+	6.43896i	−0.239966	+	0.239966i
$721$	0.819453	−	0.819453i	0.0305180	−	0.0305180i
$722$		−	3.38507i		−	0.125979i
$723$		−	11.3773i		−	0.423127i
$724$	−1.39399	+	1.39399i	−0.0518073	+	0.0518073i
$725$	−6.34273	+	6.34273i	−0.235563	+	0.235563i
$726$	−1.68941	−	1.68941i	−0.0626999	−	0.0626999i
$727$	4.75372			0.176306			0.0881528	−	0.996107i	$-0.471904\pi$
$727$	4.75372			0.176306			0.0881528	+	0.996107i	$0.471904\pi$
$728$	2.51244	+	2.51244i	0.0931170	+	0.0931170i
$729$		−	1.00000i		−	0.0370370i
$730$	28.6955			1.06207
$731$		0			0
$732$	−0.551689			−0.0203910
$733$			0.982764i			0.0362992i	0.999835	+	0.0181496i	$0.00577752\pi$
$733$			0.982764i			0.0362992i	−0.999835	+	0.0181496i	$0.994222\pi$
$734$	−17.0733	−	17.0733i	−0.630186	−	0.630186i
$735$	−17.6382			−0.650593
$736$	2.28832	+	2.28832i	0.0843487	+	0.0843487i
$737$	34.1613	−	34.1613i	1.25835	−	1.25835i
$738$	−6.84483	+	6.84483i	−0.251962	+	0.251962i
$739$		−	9.95636i		−	0.366250i	−0.983090	−	0.183125i	$-0.941379\pi$
$739$		−	9.95636i		−	0.366250i	0.983090	−	0.183125i	$-0.0586214\pi$
$740$		−	3.92902i		−	0.144433i
$741$	−21.4231	+	21.4231i	−0.786997	+	0.786997i
$742$	−1.34725	+	1.34725i	−0.0494590	+	0.0494590i
$743$	32.8990	+	32.8990i	1.20695	+	1.20695i	0.972011	+	0.234937i	$0.0754883\pi$
$743$	32.8990	+	32.8990i	1.20695	+	1.20695i	0.234937	+	0.972011i	$0.424512\pi$
$744$	21.8161			0.799819
$745$	−28.5202	−	28.5202i	−1.04490	−	1.04490i
$746$		−	20.9355i		−	0.766503i
$747$	2.51249			0.0919271
$748$		0			0
$749$	0.656822			0.0239998
$750$			12.2422i			0.447021i
$751$	−9.41549	−	9.41549i	−0.343576	−	0.343576i	0.514134	−	0.857710i	$-0.328113\pi$
$751$	−9.41549	−	9.41549i	−0.343576	−	0.343576i	−0.857710	+	0.514134i	$0.828113\pi$
$752$	−32.5449			−1.18679
$753$	−0.607960	−	0.607960i	−0.0221553	−	0.0221553i
$754$	−39.5474	+	39.5474i	−1.44023	+	1.44023i
$755$	−2.48728	+	2.48728i	−0.0905213	+	0.0905213i
$756$		−	0.0341483i		−	0.00124196i
$757$		−	45.0874i		−	1.63873i	−0.573273	−	0.819365i	$-0.694326\pi$
$757$		−	45.0874i		−	1.63873i	0.573273	−	0.819365i	$-0.305674\pi$
$758$	36.2102	−	36.2102i	1.31521	−	1.31521i
$759$	7.84960	−	7.84960i	0.284923	−	0.284923i
$760$	−24.4446	−	24.4446i	−0.886698	−	0.886698i
$761$	−24.0036			−0.870131			−0.435065	−	0.900399i	$-0.643275\pi$
$761$	−24.0036			−0.870131			−0.435065	+	0.900399i	$0.643275\pi$
$762$	−7.39902	−	7.39902i	−0.268038	−	0.268038i
$763$		−	0.664563i		−	0.0240588i
$764$	−0.328630			−0.0118894
$765$		0			0
$766$	−28.6551			−1.03535
$767$		−	42.8138i		−	1.54592i
$768$	3.10844	+	3.10844i	0.112166	+	0.112166i
$769$	30.5773			1.10264			0.551322	−	0.834292i	$-0.314123\pi$
$769$	30.5773			1.10264			0.551322	+	0.834292i	$0.314123\pi$
$770$	1.59317	+	1.59317i	0.0574140	+	0.0574140i
$771$	−0.0212341	+	0.0212341i	−0.000764726	+	0.000764726i
$772$	−0.662386	+	0.662386i	−0.0238398	+	0.0238398i
$773$		−	45.3346i		−	1.63057i	−0.579058	−	0.815286i	$-0.696579\pi$
$773$		−	45.3346i		−	1.63057i	0.579058	−	0.815286i	$-0.303421\pi$
$774$			6.65002i			0.239030i
$775$	−7.39712	+	7.39712i	−0.265712	+	0.265712i
$776$	18.2306	−	18.2306i	0.654441	−	0.654441i
$777$	−1.09721	−	1.09721i	−0.0393622	−	0.0393622i
$778$	18.5948			0.666657
$779$	−23.5638	−	23.5638i	−0.844259	−	0.844259i
$780$			3.05644i			0.109438i
$781$	−12.9050			−0.461776
$782$		0			0
$783$	6.35504			0.227110
$784$		−	25.0511i		−	0.894681i
$785$	3.18891	+	3.18891i	0.113817	+	0.113817i
$786$	−6.67087			−0.237942
$787$	−13.2542	−	13.2542i	−0.472460	−	0.472460i	0.430250	−	0.902710i	$-0.358425\pi$
$787$	−13.2542	−	13.2542i	−0.472460	−	0.472460i	−0.902710	+	0.430250i	$0.858425\pi$
$788$	1.05117	−	1.05117i	0.0374464	−	0.0374464i
$789$	8.65652	−	8.65652i	0.308180	−	0.308180i
$790$		−	26.6878i		−	0.949509i
$791$			0.870214i			0.0309412i
$792$	7.43893	−	7.43893i	0.264331	−	0.264331i
$793$	13.7895	−	13.7895i	0.489678	−	0.489678i
$794$	−27.2106	−	27.2106i	−0.965669	−	0.965669i
$795$	−19.3773			−0.687243
$796$	−1.56029	−	1.56029i	−0.0553030	−	0.0553030i
$797$		−	44.5681i		−	1.57868i	−0.613954	−	0.789342i	$-0.710422\pi$
$797$		−	44.5681i		−	1.57868i	0.613954	−	0.789342i	$-0.289578\pi$
$798$	−1.15476			−0.0408782
$799$		0			0
$800$	−1.47060			−0.0519935
$801$		−	1.32770i		−	0.0469118i
$802$	25.5096	+	25.5096i	0.900776	+	0.900776i
$803$	−30.0624			−1.06088
$804$	1.76631	+	1.76631i	0.0622930	+	0.0622930i
$805$	−1.02768	+	1.02768i	−0.0362211	+	0.0362211i
$806$	−46.1216	+	46.1216i	−1.62457	+	1.62457i
$807$		−	21.5672i		−	0.759200i
$808$		−	32.4597i		−	1.14193i
$809$	5.98582	−	5.98582i	0.210450	−	0.210450i	−0.594009	−	0.804459i	$-0.702455\pi$
$809$	5.98582	−	5.98582i	0.210450	−	0.210450i	0.804459	+	0.594009i	$0.202455\pi$
$810$	−2.41228	+	2.41228i	−0.0847588	+	0.0847588i
$811$	−7.72965	−	7.72965i	−0.271425	−	0.271425i	0.558249	−	0.829674i	$-0.311473\pi$
$811$	−7.72965	−	7.72965i	−0.271425	−	0.271425i	−0.829674	+	0.558249i	$0.811473\pi$
$812$	0.217014			0.00761568
$813$	−2.40199	−	2.40199i	−0.0842415	−	0.0842415i
$814$		−	40.4329i		−	1.41717i
$815$	7.97771			0.279447
$816$		0			0
$817$	−22.8931			−0.800929
$818$			52.3233i			1.82944i
$819$	0.853535	+	0.853535i	0.0298249	+	0.0298249i
$820$	−3.36184			−0.117401
$821$	8.88691	+	8.88691i	0.310155	+	0.310155i	0.844970	−	0.534814i	$-0.179618\pi$
$821$	8.88691	+	8.88691i	0.310155	+	0.310155i	−0.534814	+	0.844970i	$0.679618\pi$
$822$	−11.0402	+	11.0402i	−0.385071	+	0.385071i
$823$	−36.2530	+	36.2530i	−1.26370	+	1.26370i	−0.314415	+	0.949286i	$0.601808\pi$
$823$	−36.2530	+	36.2530i	−1.26370	+	1.26370i	−0.949286	+	0.314415i	$0.898192\pi$
$824$			18.4598i			0.643079i
$825$			5.04458i			0.175630i
$826$	1.15389	−	1.15389i	0.0401489	−	0.0401489i
$827$	20.1849	−	20.1849i	0.701899	−	0.701899i	−0.262919	−	0.964818i	$-0.584685\pi$
$827$	20.1849	−	20.1849i	0.701899	−	0.701899i	0.964818	+	0.262919i	$0.0846851\pi$
$828$	0.405864	+	0.405864i	0.0141047	+	0.0141047i
$829$	−4.09865			−0.142352			−0.0711760	−	0.997464i	$-0.522675\pi$
$829$	−4.09865			−0.142352			−0.0711760	+	0.997464i	$0.522675\pi$
$830$	−6.06082	−	6.06082i	−0.210374	−	0.210374i
$831$			15.9172i			0.552160i
$832$	−56.1516			−1.94671
$833$		0			0
$834$	3.62361			0.125475
$835$			61.6519i			2.13355i
$836$	2.16604	+	2.16604i	0.0749141	+	0.0749141i
$837$	7.41147			0.256178
$838$	18.1344	+	18.1344i	0.626442	+	0.626442i
$839$	−26.4436	+	26.4436i	−0.912935	+	0.912935i	−0.996502	−	0.0835670i	$-0.973369\pi$
$839$	−26.4436	+	26.4436i	−0.912935	+	0.912935i	0.0835670	+	0.996502i	$0.473369\pi$
$840$	−0.973916	+	0.973916i	−0.0336033	+	0.0336033i
$841$			11.3865i			0.392638i
$842$		−	8.64496i		−	0.297925i
$843$	−11.3247	+	11.3247i	−0.390042	+	0.390042i
$844$	−0.332764	+	0.332764i	−0.0114542	+	0.0114542i
$845$	−53.1196	−	53.1196i	−1.82737	−	1.82737i
$846$	−12.1925			−0.419188
$847$	−0.231716	−	0.231716i	−0.00796186	−	0.00796186i
$848$		−	27.5212i		−	0.945081i
$849$	26.8357			0.921000
$850$		0			0
$851$	26.0814			0.894059
$852$		−	0.667252i		−	0.0228597i
$853$	−39.7808	−	39.7808i	−1.36207	−	1.36207i	−0.871276	−	0.490793i	$-0.836707\pi$
$853$	−39.7808	−	39.7808i	−1.36207	−	1.36207i	−0.490793	−	0.871276i	$-0.663293\pi$
$854$	0.743289			0.0254348
$855$	−8.30442	−	8.30442i	−0.284005	−	0.284005i
$856$	−7.39813	+	7.39813i	−0.252863	+	0.252863i
$857$	12.6008	−	12.6008i	0.430436	−	0.430436i	−0.458341	−	0.888777i	$-0.651556\pi$
$857$	12.6008	−	12.6008i	0.430436	−	0.430436i	0.888777	+	0.458341i	$0.151556\pi$
$858$			31.4534i			1.07380i
$859$		−	5.45935i		−	0.186271i	−0.995653	−	0.0931353i	$-0.970311\pi$
$859$		−	5.45935i		−	0.186271i	0.995653	−	0.0931353i	$-0.0296889\pi$
$860$	−1.63308	+	1.63308i	−0.0556876	+	0.0556876i
$861$	−0.938823	+	0.938823i	−0.0319950	+	0.0319950i
$862$	8.24161	+	8.24161i	0.280710	+	0.280710i
$863$	−8.23947			−0.280475			−0.140237	−	0.990118i	$-0.544787\pi$
$863$	−8.23947			−0.280475			−0.140237	+	0.990118i	$0.544787\pi$
$864$	0.736727	+	0.736727i	0.0250640	+	0.0250640i
$865$			38.1566i			1.29736i
$866$	−31.4165			−1.06758
$867$		0			0
$868$	0.253089			0.00859040
$869$			27.9590i			0.948446i
$870$	−15.3301	−	15.3301i	−0.519739	−	0.519739i
$871$	−88.2978			−2.99186
$872$	7.48532	+	7.48532i	0.253485	+	0.253485i
$873$	6.19339	−	6.19339i	0.209614	−	0.209614i
$874$	13.7247	−	13.7247i	0.464246	−	0.464246i
$875$			1.67911i			0.0567643i
$876$		−	1.55438i		−	0.0525176i
$877$	−5.76315	+	5.76315i	−0.194608	+	0.194608i	−0.797684	−	0.603076i	$-0.793942\pi$
$877$	−5.76315	+	5.76315i	−0.194608	+	0.194608i	0.603076	+	0.797684i	$0.293942\pi$
$878$	−12.5748	+	12.5748i	−0.424378	+	0.424378i
$879$	1.70327	+	1.70327i	0.0574498	+	0.0574498i
$880$	−32.5449			−1.09709
$881$	13.3327	+	13.3327i	0.449191	+	0.449191i	0.895086	−	0.445894i	$-0.147114\pi$
$881$	13.3327	+	13.3327i	0.449191	+	0.449191i	−0.445894	+	0.895086i	$0.647114\pi$
$882$		−	9.38507i		−	0.316012i
$883$	17.2189			0.579463			0.289732	−	0.957108i	$-0.406434\pi$
$883$	17.2189			0.579463			0.289732	+	0.957108i	$0.406434\pi$
$884$		0			0
$885$	16.5963			0.557877
$886$		−	41.1242i		−	1.38160i
$887$	−7.91242	−	7.91242i	−0.265673	−	0.265673i	0.561681	−	0.827354i	$-0.310155\pi$
$887$	−7.91242	−	7.91242i	−0.265673	−	0.265673i	−0.827354	+	0.561681i	$0.810155\pi$
$888$	24.7169			0.829444
$889$	−1.01483	−	1.01483i	−0.0340365	−	0.0340365i
$890$	−3.20277	+	3.20277i	−0.107357	+	0.107357i
$891$	2.52718	−	2.52718i	0.0846639	−	0.0846639i
$892$		−	0.821518i		−	0.0275065i
$893$		−	41.9736i		−	1.40459i
$894$	15.1753	−	15.1753i	0.507538	−	0.507538i
$895$	30.2617	−	30.2617i	1.01154	−	1.01154i
$896$	−1.24108	−	1.24108i	−0.0414615	−	0.0414615i
$897$	−20.2891			−0.677433
$898$	−2.58351	−	2.58351i	−0.0862129	−	0.0862129i
$899$			47.1002i			1.57088i
$900$	−0.260830			−0.00869433
$901$		0			0
$902$	−34.5963			−1.15193
$903$			0.912103i			0.0303529i
$904$	−9.80167	−	9.80167i	−0.325999	−	0.325999i
$905$	27.0128			0.897936
$906$	−1.32345	−	1.32345i	−0.0439688	−	0.0439688i
$907$	−29.0477	+	29.0477i	−0.964513	+	0.964513i	−0.999392	−	0.0348783i	$-0.988896\pi$
$907$	−29.0477	+	29.0477i	−0.964513	+	0.964513i	0.0348783	+	0.999392i	$0.488896\pi$
$908$	0.982654	−	0.982654i	0.0326105	−	0.0326105i
$909$		−	11.0273i		−	0.365754i
$910$		−	4.11793i		−	0.136508i
$911$	−27.1308	+	27.1308i	−0.898884	+	0.898884i	−0.995337	−	0.0964535i	$-0.969250\pi$
$911$	−27.1308	+	27.1308i	−0.898884	+	0.898884i	0.0964535	+	0.995337i	$0.469250\pi$
$912$	11.7946	−	11.7946i	0.390557	−	0.390557i
$913$	6.34952	+	6.34952i	0.210138	+	0.210138i
$914$	−35.3892			−1.17057
$915$	5.34532	+	5.34532i	0.176711	+	0.176711i
$916$			2.53857i			0.0838768i
$917$	−0.914964			−0.0302148
$918$		0			0
$919$	22.7110			0.749167			0.374584	−	0.927193i	$-0.377786\pi$
$919$	22.7110			0.749167			0.374584	+	0.927193i	$0.377786\pi$
$920$		−	23.1506i		−	0.763254i
$921$	4.53907	+	4.53907i	0.149567	+	0.149567i
$922$	−34.3833			−1.13235
$923$	16.6779	+	16.6779i	0.548961	+	0.548961i
$924$	0.0862990	−	0.0862990i	0.00283903	−	0.00283903i
$925$	−8.38066	+	8.38066i	−0.275554	+	0.275554i
$926$			3.80697i			0.125105i
$927$			6.27126i			0.205975i
$928$	−4.68193	+	4.68193i	−0.153692	+	0.153692i
$929$	15.2339	−	15.2339i	0.499807	−	0.499807i	−0.411571	−	0.911378i	$-0.635020\pi$
$929$	15.2339	−	15.2339i	0.499807	−	0.499807i	0.911378	+	0.411571i	$0.135020\pi$
$930$	−17.8785	−	17.8785i	−0.586260	−	0.586260i
$931$	32.3087			1.05888
$932$	−2.68200	−	2.68200i	−0.0878518	−	0.0878518i
$933$		−	0.543948i		−	0.0178081i
$934$	44.4597			1.45476
$935$		0			0
$936$	−19.2276			−0.628474
$937$			37.5476i			1.22663i	0.789840	+	0.613313i	$0.210163\pi$
$937$			37.5476i			1.22663i	−0.789840	+	0.613313i	$0.789837\pi$
$938$	−2.37974	−	2.37974i	−0.0777014	−	0.0777014i
$939$	−16.6186			−0.542326
$940$	−2.99419	−	2.99419i	−0.0976597	−	0.0976597i
$941$	−27.4877	+	27.4877i	−0.896074	+	0.896074i	−0.995086	−	0.0990120i	$-0.968432\pi$
$941$	−27.4877	+	27.4877i	−0.896074	+	0.896074i	0.0990120	+	0.995086i	$0.468432\pi$
$942$	−1.69678	+	1.69678i	−0.0552842	+	0.0552842i
$943$		−	22.3164i		−	0.726723i
$944$			23.5713i			0.767180i
$945$	−0.330863	+	0.330863i	−0.0107630	+	0.0107630i
$946$	−16.8058	+	16.8058i	−0.546404	+	0.546404i
$947$	33.6097	+	33.6097i	1.09217	+	1.09217i	0.995297	+	0.0968710i	$0.0308834\pi$
$947$	33.6097	+	33.6097i	1.09217	+	1.09217i	0.0968710	+	0.995297i	$0.469117\pi$
$948$	−1.44562			−0.0469516
$949$	38.8516	+	38.8516i	1.26118	+	1.26118i
$950$			8.82026i			0.286167i
$951$	−26.0574			−0.844968
$952$		0			0
$953$	48.6332			1.57538			0.787692	−	0.616069i	$-0.211276\pi$
$953$	48.6332			1.57538			0.787692	+	0.616069i	$0.211276\pi$
$954$		−	10.3105i		−	0.333813i
$955$	3.18410	+	3.18410i	0.103035	+	0.103035i
$956$	4.78880			0.154881
$957$	16.0603	+	16.0603i	0.519157	+	0.519157i
$958$	33.1713	−	33.1713i	1.07172	−	1.07172i
$959$	−1.51425	+	1.51425i	−0.0488977	+	0.0488977i
$960$		−	21.7665i		−	0.702511i
$961$			23.9299i			0.771934i
$962$	−52.2541	+	52.2541i	−1.68474	+	1.68474i
$963$	−2.51332	+	2.51332i	−0.0809908	+	0.0809908i
$964$	1.48665	+	1.48665i	0.0478819	+	0.0478819i
$965$	12.8357			0.413197
$966$	−0.546819	−	0.546819i	−0.0175936	−	0.0175936i
$967$		−	1.39281i		−	0.0447897i	−0.999749	−	0.0223948i	$-0.992871\pi$
$967$		−	1.39281i		−	0.0447897i	0.999749	−	0.0223948i	$-0.00712909\pi$
$968$	5.21987			0.167773
$969$		0			0
$970$	−29.8803			−0.959399
$971$		−	13.0892i		−	0.420051i	−0.977696	−	0.210025i	$-0.932645\pi$
$971$		−	13.0892i		−	0.420051i	0.977696	−	0.210025i	$-0.0673547\pi$
$972$	0.130668	+	0.130668i	0.00419118	+	0.00419118i
$973$	0.497007			0.0159333
$974$	−20.5614	−	20.5614i	−0.658830	−	0.658830i
$975$	6.51944	−	6.51944i	0.208789	−	0.208789i
$976$	−7.59184	+	7.59184i	−0.243009	+	0.243009i
$977$			3.40230i			0.108849i	0.998518	+	0.0544247i	$0.0173325\pi$
$977$			3.40230i			0.108849i	−0.998518	+	0.0544247i	$0.982668\pi$
$978$			4.24485i			0.135735i
$979$	3.35533	−	3.35533i	0.107237	−	0.107237i
$980$	2.30474	−	2.30474i	0.0736223	−	0.0736223i
$981$	2.54294	+	2.54294i	0.0811900	+	0.0811900i
$982$	−46.2404			−1.47559
$983$	−10.3677	−	10.3677i	−0.330680	−	0.330680i	0.522165	−	0.852845i	$-0.325125\pi$
$983$	−10.3677	−	10.3677i	−0.330680	−	0.330680i	−0.852845	+	0.522165i	$0.825125\pi$
$984$		−	21.1489i		−	0.674202i
$985$	−20.3696			−0.649029
$986$		0			0
$987$	−1.67230			−0.0532300
$988$		−	5.59863i		−	0.178116i
$989$	−10.8406	−	10.8406i	−0.344713	−	0.344713i
$990$	−12.1925			−0.387504
$991$	32.9988	+	32.9988i	1.04824	+	1.04824i	0.998776	+	0.0494659i	$0.0157519\pi$
$991$	32.9988	+	32.9988i	1.04824	+	1.04824i	0.0494659	+	0.998776i	$0.484248\pi$
$992$	−5.46023	+	5.46023i	−0.173363	+	0.173363i
$993$	−15.9175	+	15.9175i	−0.505126	+	0.505126i
$994$			0.898986i			0.0285141i
$995$			30.2354i			0.958525i
$996$	−0.328302	+	0.328302i	−0.0104026	+	0.0104026i
$997$	1.09597	−	1.09597i	0.0347097	−	0.0347097i	−0.689539	−	0.724249i	$-0.742187\pi$
$997$	1.09597	−	1.09597i	0.0347097	−	0.0347097i	0.724249	+	0.689539i	$0.242187\pi$
$998$	17.2876	+	17.2876i	0.547228	+	0.547228i
$999$	8.39693			0.265667

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.e.j.829.3		12
17.2	even	8		867.2.a.i.1.2	✓	3
17.3	odd	16		867.2.h.l.712.3		24
17.4	even	4	inner	867.2.e.j.616.3		12
17.5	odd	16		867.2.h.l.733.4		24
17.6	odd	16		867.2.h.l.757.3		24
17.7	odd	16		867.2.h.l.688.3		24
17.8	even	8		867.2.d.d.577.4		6
17.9	even	8		867.2.d.d.577.3		6
17.10	odd	16		867.2.h.l.688.4		24
17.11	odd	16		867.2.h.l.757.4		24
17.12	odd	16		867.2.h.l.733.3		24
17.13	even	4	inner	867.2.e.j.616.4		12
17.14	odd	16		867.2.h.l.712.4		24
17.15	even	8		867.2.a.j.1.2	yes	3
17.16	even	2	inner	867.2.e.j.829.4		12
51.2	odd	8		2601.2.a.y.1.2		3
51.32	odd	8		2601.2.a.z.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
867.2.a.i.1.2	✓	3	17.2	even	8
867.2.a.j.1.2	yes	3	17.15	even	8
867.2.d.d.577.3		6	17.9	even	8
867.2.d.d.577.4		6	17.8	even	8
867.2.e.j.616.3		12	17.4	even	4	inner
867.2.e.j.616.4		12	17.13	even	4	inner
867.2.e.j.829.3		12	1.1	even	1	trivial
867.2.e.j.829.4		12	17.16	even	2	inner
867.2.h.l.688.3		24	17.7	odd	16
867.2.h.l.688.4		24	17.10	odd	16
867.2.h.l.712.3		24	17.3	odd	16
867.2.h.l.712.4		24	17.14	odd	16
867.2.h.l.733.3		24	17.12	odd	16
867.2.h.l.733.4		24	17.5	odd	16
867.2.h.l.757.3		24	17.6	odd	16
867.2.h.l.757.4		24	17.11	odd	16
2601.2.a.y.1.2		3	51.2	odd	8
2601.2.a.z.1.2		3	51.32	odd	8

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.34730i q^{2} +(-0.707107 - 0.707107i) q^{3} +0.184793 q^{4} +(-1.79046 - 1.79046i) q^{5} +(0.952682 - 0.952682i) q^{6} +(0.130668 - 0.130668i) q^{7} +2.94356i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+1.34730i q^{2} +(-0.707107 - 0.707107i) q^{3} +0.184793 q^{4} +(-1.79046 - 1.79046i) q^{5} +(0.952682 - 0.952682i) q^{6} +(0.130668 - 0.130668i) q^{7} +2.94356i q^{8} +1.00000i q^{9} +(2.41228 - 2.41228i) q^{10} +(-2.52718 + 2.52718i) q^{11} +(-0.130668 - 0.130668i) q^{12} +6.53209 q^{13} +(0.176049 + 0.176049i) q^{14} +2.53209i q^{15} -3.59627 q^{16} -1.34730 q^{18} -4.63816i q^{19} +(-0.330863 - 0.330863i) q^{20} -0.184793 q^{21} +(-3.40487 - 3.40487i) q^{22} +(2.19632 - 2.19632i) q^{23} +(2.08141 - 2.08141i) q^{24} +1.41147i q^{25} +8.80066i q^{26} +(0.707107 - 0.707107i) q^{27} +(0.0241465 - 0.0241465i) q^{28} +(4.49369 + 4.49369i) q^{29} -3.41147 q^{30} +(5.24070 + 5.24070i) q^{31} +1.04189i q^{32} +3.57398 q^{33} -0.467911 q^{35} +0.184793i q^{36} +(5.93752 + 5.93752i) q^{37} +6.24897 q^{38} +(-4.61888 - 4.61888i) q^{39} +(5.27032 - 5.27032i) q^{40} +(5.08042 - 5.08042i) q^{41} -0.248970i q^{42} -4.93582i q^{43} +(-0.467005 + 0.467005i) q^{44} +(1.79046 - 1.79046i) q^{45} +(2.95910 + 2.95910i) q^{46} +9.04963 q^{47} +(2.54294 + 2.54294i) q^{48} +6.96585i q^{49} -1.90167 q^{50} +1.20708 q^{52} +7.65270i q^{53} +(0.952682 + 0.952682i) q^{54} +9.04963 q^{55} +(0.384630 + 0.384630i) q^{56} +(-3.27967 + 3.27967i) q^{57} +(-6.05433 + 6.05433i) q^{58} -6.55438i q^{59} +0.467911i q^{60} +(2.11103 - 2.11103i) q^{61} +(-7.06078 + 7.06078i) q^{62} +(0.130668 + 0.130668i) q^{63} -8.59627 q^{64} +(-11.6954 - 11.6954i) q^{65} +4.81521i q^{66} -13.5175 q^{67} -3.10607 q^{69} -0.630415i q^{70} +(2.55323 + 2.55323i) q^{71} -2.94356 q^{72} +(5.94781 + 5.94781i) q^{73} +(-7.99960 + 7.99960i) q^{74} +(0.998063 - 0.998063i) q^{75} -0.857097i q^{76} +0.660444i q^{77} +(6.22301 - 6.22301i) q^{78} +(5.53166 - 5.53166i) q^{79} +(6.43896 + 6.43896i) q^{80} -1.00000 q^{81} +(6.84483 + 6.84483i) q^{82} -2.51249i q^{83} -0.0341483 q^{84} +6.65002 q^{86} -6.35504i q^{87} +(-7.43893 - 7.43893i) q^{88} -1.32770 q^{89} +(2.41228 + 2.41228i) q^{90} +(0.853535 - 0.853535i) q^{91} +(0.405864 - 0.405864i) q^{92} -7.41147i q^{93} +12.1925i q^{94} +(-8.30442 + 8.30442i) q^{95} +(0.736727 - 0.736727i) q^{96} +(-6.19339 - 6.19339i) q^{97} -9.38507 q^{98} +(-2.52718 - 2.52718i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4}+O(q^{10}) \) 12 * q - 12 * q^4	\( 12 q - 12 q^{4} + 60 q^{13} + 12 q^{16} - 12 q^{18} + 12 q^{21} + 12 q^{33} - 24 q^{35} + 24 q^{38} + 24 q^{50} - 24 q^{52} - 48 q^{64} - 72 q^{67} + 12 q^{69} + 24 q^{72} - 12 q^{81} - 84 q^{84} + 120 q^{86} + 108 q^{98}+O(q^{100}) \) 12 * q - 12 * q^4 + 60 * q^13 + 12 * q^16 - 12 * q^18 + 12 * q^21 + 12 * q^33 - 24 * q^35 + 24 * q^38 + 24 * q^50 - 24 * q^52 - 48 * q^64 - 72 * q^67 + 12 * q^69 + 24 * q^72 - 12 * q^81 - 84 * q^84 + 120 * q^86 + 108 * q^98

Introduction

L-functions

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