LMFDB - Embedded newform 260.2.o.a.27.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(27,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("260.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.o (of order $4$, degree $2$, 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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.14
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.505980 + 1.32060i) q^{2} +(0.658144 + 0.658144i) q^{3} +(-1.48797 - 1.33639i) q^{4} +(0.820865 - 2.07995i) q^{5} +(-1.20215 + 0.536137i) q^{6} +(1.89124 - 1.89124i) q^{7} +(2.51772 - 1.28882i) q^{8} -2.13369i q^{9} +O(q^{10})$	\(q+(-0.505980 + 1.32060i) q^{2} +(0.658144 + 0.658144i) q^{3} +(-1.48797 - 1.33639i) q^{4} +(0.820865 - 2.07995i) q^{5} +(-1.20215 + 0.536137i) q^{6} +(1.89124 - 1.89124i) q^{7} +(2.51772 - 1.28882i) q^{8} -2.13369i q^{9} +(2.33144 + 2.13645i) q^{10} -1.63773i q^{11} +(-0.0997585 - 1.85884i) q^{12} +(-0.707107 + 0.707107i) q^{13} +(1.54064 + 3.45450i) q^{14} +(1.90915 - 0.828657i) q^{15} +(0.428104 + 3.97702i) q^{16} +(2.78023 + 2.78023i) q^{17} +(2.81776 + 1.07961i) q^{18} -3.52807 q^{19} +(-4.00105 + 1.99790i) q^{20} +2.48941 q^{21} +(2.16278 + 0.828656i) q^{22} +(-0.868383 - 0.868383i) q^{23} +(2.50526 + 0.808792i) q^{24} +(-3.65236 - 3.41471i) q^{25} +(-0.576024 - 1.29159i) q^{26} +(3.37871 - 3.37871i) q^{27} +(-5.34155 + 0.286666i) q^{28} +7.97596i q^{29} +(0.128332 + 2.94051i) q^{30} +7.80040i q^{31} +(-5.46867 - 1.44694i) q^{32} +(1.07786 - 1.07786i) q^{33} +(-5.07832 + 2.26484i) q^{34} +(-2.38122 - 5.48613i) q^{35} +(-2.85145 + 3.17487i) q^{36} +(4.02786 + 4.02786i) q^{37} +(1.78513 - 4.65917i) q^{38} -0.930756 q^{39} +(-0.613974 - 6.29468i) q^{40} +5.49168 q^{41} +(-1.25959 + 3.28752i) q^{42} +(-5.16654 - 5.16654i) q^{43} +(-2.18865 + 2.43688i) q^{44} +(-4.43797 - 1.75148i) q^{45} +(1.58617 - 0.707403i) q^{46} +(8.12719 - 8.12719i) q^{47} +(-2.33570 + 2.89921i) q^{48} -0.153571i q^{49} +(6.35749 - 3.09553i) q^{50} +3.65959i q^{51} +(1.99713 - 0.107180i) q^{52} +(-0.551967 + 0.551967i) q^{53} +(2.75236 + 6.17148i) q^{54} +(-3.40638 - 1.34435i) q^{55} +(2.32414 - 7.19909i) q^{56} +(-2.32198 - 2.32198i) q^{57} +(-10.5331 - 4.03567i) q^{58} +8.09322 q^{59} +(-3.94817 - 1.31836i) q^{60} -8.43976 q^{61} +(-10.3012 - 3.94684i) q^{62} +(-4.03533 - 4.03533i) q^{63} +(4.67786 - 6.48981i) q^{64} +(0.890305 + 2.05118i) q^{65} +(0.878045 + 1.96879i) q^{66} +(-1.32687 + 1.32687i) q^{67} +(-0.421416 - 7.85239i) q^{68} -1.14304i q^{69} +(8.44984 - 0.368776i) q^{70} +6.50923i q^{71} +(-2.74996 - 5.37205i) q^{72} +(-4.95717 + 4.95717i) q^{73} +(-7.35721 + 3.28118i) q^{74} +(-0.156406 - 4.65115i) q^{75} +(5.24966 + 4.71489i) q^{76} +(-3.09733 - 3.09733i) q^{77} +(0.470943 - 1.22916i) q^{78} -14.6164 q^{79} +(8.62342 + 2.37417i) q^{80} -1.95373 q^{81} +(-2.77868 + 7.25231i) q^{82} +(6.57539 + 6.57539i) q^{83} +(-3.70417 - 3.32684i) q^{84} +(8.06494 - 3.50054i) q^{85} +(9.43710 - 4.20877i) q^{86} +(-5.24933 + 5.24933i) q^{87} +(-2.11074 - 4.12334i) q^{88} -13.8436i q^{89} +(4.55852 - 4.97457i) q^{90} +2.67462i q^{91} +(0.131626 + 2.45263i) q^{92} +(-5.13378 + 5.13378i) q^{93} +(6.62058 + 14.8450i) q^{94} +(-2.89607 + 7.33819i) q^{95} +(-2.64688 - 4.55146i) q^{96} +(-0.0106669 - 0.0106669i) q^{97} +(0.202807 + 0.0777041i) q^{98} -3.49440 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) $ 72 * q - 8 * q^6 - 12 * q^8	$ 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) $ 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.505980	+	1.32060i	−0.357782	+	0.933805i
$2$	−0.505980	+	1.32060i	−0.357782	+	0.933805i
$3$	0.658144	+	0.658144i	0.379979	+	0.379979i	0.871095	−	0.491115i	$-0.163411\pi$
$3$	0.658144	+	0.658144i	0.379979	+	0.379979i	−0.491115	+	0.871095i	$0.663411\pi$
$4$	−1.48797	−	1.33639i	−0.743985	−	0.668197i
$5$	0.820865	−	2.07995i	0.367102	−	0.930181i
$5$	0.820865	−	2.07995i	0.367102	−	0.930181i
$6$	−1.20215	+	0.536137i	−0.490776	+	0.218877i
$7$	1.89124	−	1.89124i	0.714821	−	0.714821i	−0.252719	−	0.967540i	$-0.581325\pi$
$7$	1.89124	−	1.89124i	0.714821	−	0.714821i	0.967540	+	0.252719i	$0.0813247\pi$
$8$	2.51772	−	1.28882i	0.890150	−	0.455668i
$9$		−	2.13369i		−	0.711231i
$10$	2.33144	+	2.13645i	0.737265	+	0.675603i
$11$		−	1.63773i		−	0.493793i	−0.969042	−	0.246896i	$-0.920589\pi$
$11$		−	1.63773i		−	0.493793i	0.969042	−	0.246896i	$-0.0794107\pi$
$12$	−0.0997585	−	1.85884i	−0.0287978	−	0.536600i
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i
$14$	1.54064	+	3.45450i	0.411754	+	0.923254i
$15$	1.90915	−	0.828657i	0.492941	−	0.213958i
$16$	0.428104	+	3.97702i	0.107026	+	0.994256i
$17$	2.78023	+	2.78023i	0.674306	+	0.674306i	0.958706	−	0.284400i	$-0.0917943\pi$
$17$	2.78023	+	2.78023i	0.674306	+	0.674306i	−0.284400	+	0.958706i	$0.591794\pi$
$18$	2.81776	+	1.07961i	0.664152	+	0.254466i
$19$	−3.52807			−0.809394			−0.404697	−	0.914451i	$-0.632623\pi$
$19$	−3.52807			−0.809394			−0.404697	+	0.914451i	$0.632623\pi$
$20$	−4.00105	+	1.99790i	−0.894662	+	0.446744i
$21$	2.48941			0.543235
$22$	2.16278	+	0.828656i	0.461106	+	0.176670i
$23$	−0.868383	−	0.868383i	−0.181070	−	0.181070i	0.610752	−	0.791822i	$-0.290867\pi$
$23$	−0.868383	−	0.868383i	−0.181070	−	0.181070i	−0.791822	+	0.610752i	$0.790867\pi$
$24$	2.50526	+	0.808792i	0.511383	+	0.165094i
$25$	−3.65236	−	3.41471i	−0.730472	−	0.682943i
$26$	−0.576024	−	1.29159i	−0.112968	−	0.253301i
$27$	3.37871	−	3.37871i	0.650233	−	0.650233i
$28$	−5.34155	+	0.286666i	−1.00946	+	0.0541747i
$29$			7.97596i			1.48110i	0.672002	+	0.740549i	$0.265435\pi$
$29$			7.97596i			1.48110i	−0.672002	+	0.740549i	$0.734565\pi$
$30$	0.128332	+	2.94051i	0.0234302	+	0.536861i
$31$			7.80040i			1.40099i	0.713656	+	0.700496i	$0.247038\pi$
$31$			7.80040i			1.40099i	−0.713656	+	0.700496i	$0.752962\pi$
$32$	−5.46867	−	1.44694i	−0.966734	−	0.255785i
$33$	1.07786	−	1.07786i	0.187631	−	0.187631i
$34$	−5.07832	+	2.26484i	−0.870925	+	0.388416i
$35$	−2.38122	−	5.48613i	−0.402500	−	0.927325i
$36$	−2.85145	+	3.17487i	−0.475242	+	0.529145i
$37$	4.02786	+	4.02786i	0.662176	+	0.662176i	0.955893	−	0.293716i	$-0.0948921\pi$
$37$	4.02786	+	4.02786i	0.662176	+	0.662176i	−0.293716	+	0.955893i	$0.594892\pi$
$38$	1.78513	−	4.65917i	0.289586	−	0.755817i
$39$	−0.930756			−0.149040
$40$	−0.613974	−	6.29468i	−0.0970779	−	0.995277i
$41$	5.49168			0.857656			0.428828	−	0.903386i	$-0.358927\pi$
$41$	5.49168			0.857656			0.428828	+	0.903386i	$0.358927\pi$
$42$	−1.25959	+	3.28752i	−0.194359	+	0.507275i
$43$	−5.16654	−	5.16654i	−0.787890	−	0.787890i	0.193258	−	0.981148i	$-0.438095\pi$
$43$	−5.16654	−	5.16654i	−0.787890	−	0.787890i	−0.981148	+	0.193258i	$0.938095\pi$
$44$	−2.18865	+	2.43688i	−0.329951	+	0.367374i
$45$	−4.43797	−	1.75148i	−0.661574	−	0.261095i
$46$	1.58617	−	0.707403i	0.233868	−	0.104301i
$47$	8.12719	−	8.12719i	1.18547	−	1.18547i	0.207167	−	0.978306i	$-0.433576\pi$
$47$	8.12719	−	8.12719i	1.18547	−	1.18547i	0.978306	−	0.207167i	$-0.0664244\pi$
$48$	−2.33570	+	2.89921i	−0.337129	+	0.418465i
$49$		−	0.153571i		−	0.0219388i
$50$	6.35749	−	3.09553i	0.899085	−	0.437774i
$51$			3.65959i			0.512445i
$52$	1.99713	−	0.107180i	0.276952	−	0.0148632i
$53$	−0.551967	+	0.551967i	−0.0758185	+	0.0758185i	−0.743999	−	0.668181i	$-0.767073\pi$
$53$	−0.551967	+	0.551967i	−0.0758185	+	0.0758185i	0.668181	+	0.743999i	$0.267073\pi$
$54$	2.75236	+	6.17148i	0.374549	+	0.839832i
$55$	−3.40638	−	1.34435i	−0.459316	−	0.181272i
$56$	2.32414	−	7.19909i	0.310577	−	0.962019i
$57$	−2.32198	−	2.32198i	−0.307553	−	0.307553i
$58$	−10.5331	−	4.03567i	−1.38306	−	0.529910i
$59$	8.09322			1.05365			0.526824	−	0.849975i	$-0.323383\pi$
$59$	8.09322			1.05365			0.526824	+	0.849975i	$0.323383\pi$
$60$	−3.94817	−	1.31836i	−0.509706	−	0.170200i
$61$	−8.43976			−1.08060			−0.540300	−	0.841472i	$-0.681689\pi$
$61$	−8.43976			−1.08060			−0.540300	+	0.841472i	$0.681689\pi$
$62$	−10.3012	−	3.94684i	−1.30825	−	0.501249i
$63$	−4.03533	−	4.03533i	−0.508403	−	0.508403i
$64$	4.67786	−	6.48981i	0.584733	−	0.811226i
$65$	0.890305	+	2.05118i	0.110429	+	0.254418i
$66$	0.878045	+	1.96879i	0.108080	+	0.242342i
$67$	−1.32687	+	1.32687i	−0.162103	+	0.162103i	−0.783498	−	0.621395i	$-0.786566\pi$
$67$	−1.32687	+	1.32687i	−0.162103	+	0.162103i	0.621395	+	0.783498i	$0.286566\pi$
$68$	−0.421416	−	7.85239i	−0.0511041	−	0.952242i
$69$		−	1.14304i		−	0.137606i
$70$	8.44984	−	0.368776i	1.00995	−	0.0440771i
$71$			6.50923i			0.772504i	0.922393	+	0.386252i	$0.126230\pi$
$71$			6.50923i			0.772504i	−0.922393	+	0.386252i	$0.873770\pi$
$72$	−2.74996	−	5.37205i	−0.324085	−	0.633102i
$73$	−4.95717	+	4.95717i	−0.580193	+	0.580193i	−0.934956	−	0.354763i	$-0.884561\pi$
$73$	−4.95717	+	4.95717i	−0.580193	+	0.580193i	0.354763	+	0.934956i	$0.384561\pi$
$74$	−7.35721	+	3.28118i	−0.855258	+	0.381429i
$75$	−0.156406	−	4.65115i	−0.0180602	−	0.537068i
$76$	5.24966	+	4.71489i	0.602177	+	0.540835i
$77$	−3.09733	−	3.09733i	−0.352974	−	0.352974i
$78$	0.470943	−	1.22916i	0.0533238	−	0.139175i
$79$	−14.6164			−1.64448			−0.822238	−	0.569143i	$-0.807275\pi$
$79$	−14.6164			−1.64448			−0.822238	+	0.569143i	$0.807275\pi$
$80$	8.62342	+	2.37417i	0.964127	+	0.265440i
$81$	−1.95373			−0.217081
$82$	−2.77868	+	7.25231i	−0.306854	+	0.800884i
$83$	6.57539	+	6.57539i	0.721743	+	0.721743i	0.968960	−	0.247217i	$-0.0795161\pi$
$83$	6.57539	+	6.57539i	0.721743	+	0.721743i	−0.247217	+	0.968960i	$0.579516\pi$
$84$	−3.70417	−	3.32684i	−0.404158	−	0.362988i
$85$	8.06494	−	3.50054i	0.874765	−	0.379687i
$86$	9.43710	−	4.20877i	1.01763	−	0.453843i
$87$	−5.24933	+	5.24933i	−0.562787	+	0.562787i
$88$	−2.11074	−	4.12334i	−0.225006	−	0.439549i
$89$		−	13.8436i		−	1.46742i	−0.679462	−	0.733710i	$-0.737787\pi$
$89$		−	13.8436i		−	1.46742i	0.679462	−	0.733710i	$-0.262213\pi$
$90$	4.55852	−	4.97457i	0.480510	−	0.524366i
$91$			2.67462i			0.280376i
$92$	0.131626	+	2.45263i	0.0137229	+	0.255704i
$93$	−5.13378	+	5.13378i	−0.532348	+	0.532348i
$94$	6.62058	+	14.8450i	0.682860	+	1.53114i
$95$	−2.89607	+	7.33819i	−0.297130	+	0.752883i
$96$	−2.64688	−	4.55146i	−0.270146	−	0.464532i
$97$	−0.0106669	−	0.0106669i	−0.00108306	−	0.00108306i	0.706565	−	0.707648i	$-0.250244\pi$
$97$	−0.0106669	−	0.0106669i	−0.00108306	−	0.00108306i	−0.707648	+	0.706565i	$0.750244\pi$
$98$	0.202807	+	0.0777041i	0.0204866	+	0.00784929i
$99$	−3.49440			−0.351201
$100$	0.871199	+	9.96198i	0.0871199	+	0.996198i
$101$	−8.35420			−0.831274			−0.415637	−	0.909531i	$-0.636441\pi$
$101$	−8.35420			−0.831274			−0.415637	+	0.909531i	$0.636441\pi$
$102$	−4.83285	−	1.85168i	−0.478524	−	0.183343i
$103$	12.8239	+	12.8239i	1.26358	+	1.26358i	0.949347	+	0.314230i	$0.101746\pi$
$103$	12.8239	+	12.8239i	1.26358	+	1.26358i	0.314230	+	0.949347i	$0.398254\pi$
$104$	−0.868963	+	2.69164i	−0.0852088	+	0.263937i
$105$	2.04347	−	5.17785i	0.199423	−	0.505306i
$106$	−0.449644	−	1.00821i	−0.0436733	−	0.0979262i
$107$	−2.23737	+	2.23737i	−0.216295	+	0.216295i	−0.806935	−	0.590640i	$-0.798875\pi$
$107$	−2.23737	+	2.23737i	−0.216295	+	0.216295i	0.590640	+	0.806935i	$0.298875\pi$
$108$	−9.54270	+	0.512130i	−0.918246	+	0.0492797i
$109$			4.09811i			0.392528i	0.980551	+	0.196264i	$0.0628809\pi$
$109$			4.09811i			0.392528i	−0.980551	+	0.196264i	$0.937119\pi$
$110$	3.49891	−	3.81825i	0.333608	−	0.364056i
$111$			5.30182i			0.503227i
$112$	8.33115	+	6.71186i	0.787220	+	0.634211i
$113$	3.86201	−	3.86201i	0.363308	−	0.363308i	−0.501722	−	0.865029i	$-0.667300\pi$
$113$	3.86201	−	3.86201i	0.363308	−	0.363308i	0.865029	+	0.501722i	$0.167300\pi$
$114$	4.24127	−	1.89153i	0.397232	−	0.177158i
$115$	−2.51902	+	1.09337i	−0.234900	+	0.101957i
$116$	10.6590	−	11.8680i	0.989665	−	1.10191i
$117$	1.50875	+	1.50875i	0.139484	+	0.139484i
$118$	−4.09501	+	10.6879i	−0.376976	+	0.983902i
$119$	10.5162			0.964016
$120$	3.73872	−	4.54689i	0.341297	−	0.415072i
$121$	8.31786			0.756169
$122$	4.27035	−	11.1455i	0.386619	−	1.00907i
$123$	3.61431	+	3.61431i	0.325892	+	0.325892i
$124$	10.4244	−	11.6067i	0.936139	−	1.04232i
$125$	−10.1005	+	4.79370i	−0.903418	+	0.428761i
$126$	7.37084	−	3.28726i	0.656647	−	0.292852i
$127$	2.46133	−	2.46133i	0.218408	−	0.218408i	−0.589419	−	0.807827i	$-0.700643\pi$
$127$	2.46133	−	2.46133i	0.218408	−	0.218408i	0.807827	+	0.589419i	$0.200643\pi$
$128$	6.20353	+	9.46130i	0.548320	+	0.836269i
$129$		−	6.80065i		−	0.598764i
$130$	−3.15927	+	0.137880i	−0.277086	+	0.0120929i
$131$			1.40309i			0.122589i	0.998120	+	0.0612943i	$0.0195228\pi$
$131$			1.40309i			0.122589i	−0.998120	+	0.0612943i	$0.980477\pi$
$132$	−3.04426	+	0.163377i	−0.264969	+	0.0142201i
$133$	−6.67242	+	6.67242i	−0.578572	+	0.578572i
$134$	−1.08089	−	2.42363i	−0.0933750	−	0.209370i
$135$	−4.25407	−	9.80100i	−0.366132	−	0.843536i
$136$	10.5831	+	3.41663i	0.907493	+	0.292973i
$137$	−0.493480	−	0.493480i	−0.0421609	−	0.0421609i	0.685712	−	0.727873i	$-0.259491\pi$
$137$	−0.493480	−	0.493480i	−0.0421609	−	0.0421609i	−0.727873	+	0.685712i	$0.759491\pi$
$138$	1.50950	+	0.578356i	0.128497	+	0.0492329i
$139$	−10.7648			−0.913056			−0.456528	−	0.889709i	$-0.650907\pi$
$139$	−10.7648			−0.913056			−0.456528	+	0.889709i	$0.650907\pi$
$140$	−3.78844	+	11.3454i	−0.320182	+	0.958865i
$141$	10.6977			0.900910
$142$	−8.59609	−	3.29354i	−0.721368	−	0.276388i
$143$	1.15805	+	1.15805i	0.0968407	+	0.0968407i
$144$	8.48575	−	0.913444i	0.707146	−	0.0761203i
$145$	16.5896	+	6.54719i	1.37769	+	0.543714i
$146$	−4.03821	−	9.05467i	−0.334205	−	0.749370i
$147$	0.101072	−	0.101072i	0.00833629	−	0.00833629i
$148$	−0.610525	−	11.3761i	−0.0501849	−	0.935113i
$149$			13.1342i			1.07599i	0.842947	+	0.537996i	$0.180818\pi$
$149$			13.1342i			1.07599i	−0.842947	+	0.537996i	$0.819182\pi$
$150$	6.22145	+	2.14684i	0.507979	+	0.175288i
$151$			20.5019i			1.66842i	0.551443	+	0.834212i	$0.314077\pi$
$151$			20.5019i			1.66842i	−0.551443	+	0.834212i	$0.685923\pi$
$152$	−8.88270	+	4.54706i	−0.720482	+	0.368815i
$153$	5.93217	−	5.93217i	0.479588	−	0.479588i
$154$	5.65752	−	2.52315i	0.455896	−	0.203321i
$155$	16.2244	+	6.40307i	1.30318	+	0.514307i
$156$	1.38494	+	1.24386i	0.110884	+	0.0995882i
$157$	−3.84213	−	3.84213i	−0.306635	−	0.306635i	0.536968	−	0.843603i	$-0.319570\pi$
$157$	−3.84213	−	3.84213i	−0.306635	−	0.306635i	−0.843603	+	0.536968i	$0.819570\pi$
$158$	7.39562	−	19.3025i	0.588364	−	1.53562i
$159$	−0.726547			−0.0576189
$160$	−7.49860	+	10.1868i	−0.592816	+	0.805338i
$161$	−3.28464			−0.258866
$162$	0.988549	−	2.58010i	0.0776677	−	0.202712i
$163$	8.79662	+	8.79662i	0.689005	+	0.689005i	0.962012	−	0.273007i	$-0.0880183\pi$
$163$	8.79662	+	8.79662i	0.689005	+	0.689005i	−0.273007	+	0.962012i	$0.588018\pi$
$164$	−8.17145	−	7.33904i	−0.638083	−	0.573083i
$165$	−1.35711	−	3.12666i	−0.105651	−	0.243411i
$166$	−12.0105	+	5.35645i	−0.932194	+	0.415741i
$167$	15.1016	−	15.1016i	1.16859	−	1.16859i	0.186054	−	0.982539i	$-0.440430\pi$
$167$	15.1016	−	15.1016i	1.16859	−	1.16859i	0.982539	−	0.186054i	$-0.0595700\pi$
$168$	6.26766	−	3.20842i	0.483560	−	0.247535i
$169$		−	1.00000i		−	0.0769231i
$170$	0.542122	+	12.4218i	0.0415789	+	0.952706i
$171$			7.52782i			0.575667i
$172$	0.783121	+	14.5922i	0.0597124	+	1.11264i
$173$	−13.3665	+	13.3665i	−1.01624	+	1.01624i	−0.0163696	+	0.999866i	$0.505211\pi$
$173$	−13.3665	+	13.3665i	−1.01624	+	1.01624i	−0.999866	+	0.0163696i	$0.994789\pi$
$174$	−4.27621	−	9.58831i	−0.324179	−	0.726888i
$175$	−13.3655	+	0.449448i	−1.01034	+	0.0339751i
$176$	6.51327	−	0.701117i	0.490956	−	0.0528487i
$177$	5.32650	+	5.32650i	0.400364	+	0.400364i
$178$	18.2819	+	7.00459i	1.37029	+	0.525016i
$179$	−12.2037			−0.912148			−0.456074	−	0.889942i	$-0.650745\pi$
$179$	−12.2037			−0.912148			−0.456074	+	0.889942i	$0.650745\pi$
$180$	4.26290	+	8.53702i	0.317738	+	0.636312i
$181$	−12.8690			−0.956543			−0.478271	−	0.878212i	$-0.658736\pi$
$181$	−12.8690			−0.956543			−0.478271	+	0.878212i	$0.658736\pi$
$182$	−3.53210	−	1.35330i	−0.261817	−	0.100313i
$183$	−5.55457	−	5.55457i	−0.410606	−	0.410606i
$184$	−3.30554	−	1.06716i	−0.243688	−	0.0786718i
$185$	11.6841	−	5.07141i	0.859030	−	0.372857i
$186$	−4.18208	−	9.37726i	−0.306645	−	0.687574i
$187$	4.55326	−	4.55326i	0.332967	−	0.332967i
$188$	−22.9541	+	1.23188i	−1.67410	+	0.0898443i
$189$		−	12.7799i		−	0.929600i
$190$	−8.22547	−	7.53753i	−0.596738	−	0.546830i
$191$		−	16.8603i		−	1.21997i	−0.792414	−	0.609984i	$-0.791176\pi$
$191$		−	16.8603i		−	1.21997i	0.792414	−	0.609984i	$-0.208824\pi$
$192$	7.34993	−	1.19252i	0.530436	−	0.0860626i
$193$	5.67678	−	5.67678i	0.408624	−	0.408624i	−0.472635	−	0.881258i	$-0.656697\pi$
$193$	5.67678	−	5.67678i	0.408624	−	0.408624i	0.881258	+	0.472635i	$0.156697\pi$
$194$	0.0194840	−	0.00868950i	0.00139887	−	0.000623870i
$195$	−0.764025	+	1.93592i	−0.0547130	+	0.138634i
$196$	−0.205232	+	0.228510i	−0.0146594	+	0.0163221i
$197$	−11.9805	−	11.9805i	−0.853578	−	0.853578i	0.136994	−	0.990572i	$-0.456256\pi$
$197$	−11.9805	−	11.9805i	−0.853578	−	0.853578i	−0.990572	+	0.136994i	$0.956256\pi$
$198$	1.76810	−	4.61471i	0.125653	−	0.327953i
$199$	−13.4943			−0.956583			−0.478291	−	0.878201i	$-0.658744\pi$
$199$	−13.4943			−0.956583			−0.478291	+	0.878201i	$0.658744\pi$
$200$	−13.5966	−	3.89005i	−0.961425	−	0.275068i
$201$	−1.74654			−0.123191
$202$	4.22705	−	11.0326i	0.297415	−	0.776248i
$203$	15.0844	+	15.0844i	1.05872	+	1.05872i
$204$	4.89065	−	5.44535i	0.342414	−	0.381251i
$205$	4.50793	−	11.4224i	0.314847	−	0.797775i
$206$	−23.4239	+	10.4466i	−1.63202	+	0.727850i
$207$	−1.85286	+	1.85286i	−0.128783	+	0.128783i
$208$	−3.11490	−	2.50947i	−0.215979	−	0.174000i
$209$			5.77800i			0.399673i
$210$	5.80391	+	5.31850i	0.400508	+	0.367011i
$211$		−	22.3207i		−	1.53662i	−0.640077	−	0.768311i	$-0.721097\pi$
$211$		−	22.3207i		−	1.53662i	0.640077	−	0.768311i	$-0.278903\pi$
$212$	1.55896	−	0.0836647i	0.107070	−	0.00574612i
$213$	−4.28401	+	4.28401i	−0.293535	+	0.293535i
$214$	−1.82261	−	4.08673i	−0.124591	−	0.279363i
$215$	−14.9872	+	6.50510i	−1.02212	+	0.443644i
$216$	4.15209	−	12.8612i	0.282514	−	0.875095i
$217$	14.7524	+	14.7524i	1.00146	+	1.00146i
$218$	−5.41196	−	2.07356i	−0.366544	−	0.140439i
$219$	−6.52506			−0.440923
$220$	3.27201	+	6.55262i	0.220599	+	0.441778i
$221$	−3.93185			−0.264485
$222$	−7.00159	−	2.68261i	−0.469916	−	0.180045i
$223$	−15.1774	−	15.1774i	−1.01635	−	1.01635i	−0.999864	−	0.0164909i	$-0.994751\pi$
$223$	−15.1774	−	15.1774i	−1.01635	−	1.01635i	−0.0164909	−	0.999864i	$-0.505249\pi$
$224$	−13.0791	+	7.60606i	−0.873882	+	0.508201i
$225$	−7.28595	+	7.79302i	−0.485730	+	0.519535i
$226$	3.14607	+	7.05427i	0.209274	+	0.469243i
$227$	−1.67416	+	1.67416i	−0.111118	+	0.111118i	−0.760480	−	0.649362i	$-0.775036\pi$
$227$	−1.67416	+	1.67416i	−0.111118	+	0.111118i	0.649362	+	0.760480i	$0.275036\pi$
$228$	0.351955	+	6.55810i	0.0233088	+	0.434321i
$229$		−	9.37677i		−	0.619634i	−0.950796	−	0.309817i	$-0.899732\pi$
$229$		−	9.37677i		−	0.619634i	0.950796	−	0.309817i	$-0.100268\pi$
$230$	−0.169327	−	3.87983i	−0.0111651	−	0.255829i
$231$		−	4.07698i		−	0.268245i
$232$	10.2796	+	20.0813i	0.674889	+	1.31840i
$233$	16.0668	−	16.0668i	1.05257	−	1.05257i	0.0540344	−	0.998539i	$-0.482792\pi$
$233$	16.0668	−	16.0668i	1.05257	−	1.05257i	0.998539	−	0.0540344i	$-0.0172081\pi$
$234$	−2.75585	+	1.22906i	−0.180156	+	0.0803460i
$235$	−10.2328	−	23.5755i	−0.667514	−	1.53789i
$236$	−12.0425	−	10.8157i	−0.783898	−	0.704044i
$237$	−9.61971	−	9.61971i	−0.624867	−	0.624867i
$238$	−5.32097	+	13.8877i	−0.344907	+	0.900204i
$239$	19.5885			1.26707			0.633537	−	0.773712i	$-0.281602\pi$
$239$	19.5885			1.26707			0.633537	+	0.773712i	$0.281602\pi$
$240$	4.11290	+	7.23799i	0.265487	+	0.467210i
$241$	−0.764560			−0.0492496			−0.0246248	−	0.999697i	$-0.507839\pi$
$241$	−0.764560			−0.0492496			−0.0246248	+	0.999697i	$0.507839\pi$
$242$	−4.20867	+	10.9846i	−0.270543	+	0.706114i
$243$	−11.4220	−	11.4220i	−0.732719	−	0.732719i
$244$	12.5581	+	11.2788i	0.803950	+	0.722054i
$245$	−0.319421	−	0.126062i	−0.0204070	−	0.00805377i
$246$	−6.60183	+	2.94429i	−0.420917	+	0.187721i
$247$	2.49472	−	2.49472i	0.158735	−	0.158735i
$248$	10.0533	+	19.6392i	0.638388	+	1.24709i
$249$			8.65511i			0.548495i
$250$	−1.21990	−	15.7643i	−0.0771533	−	0.997019i
$251$		−	4.66905i		−	0.294708i	−0.989084	−	0.147354i	$-0.952924\pi$
$251$		−	4.66905i		−	0.294708i	0.989084	−	0.147354i	$-0.0470756\pi$
$252$	0.611657	+	11.3972i	0.0385308	+	0.717958i
$253$	−1.42217	+	1.42217i	−0.0894113	+	0.0894113i
$254$	2.00505	+	4.49582i	0.125808	+	0.282093i
$255$	7.61175	+	3.00403i	0.476666	+	0.188120i
$256$	−15.6335	+	3.40516i	−0.977091	+	0.212823i
$257$	8.66539	+	8.66539i	0.540532	+	0.540532i	0.923685	−	0.383153i	$-0.125162\pi$
$257$	8.66539	+	8.66539i	0.540532	+	0.540532i	−0.383153	+	0.923685i	$0.625162\pi$
$258$	8.98094	+	3.44099i	0.559129	+	0.214227i
$259$	15.2353			0.946675
$260$	1.41644	−	4.24190i	0.0878440	−	0.263071i
$261$	17.0183			1.05340
$262$	−1.85292	−	0.709935i	−0.114474	−	0.0438599i
$263$	7.99625	+	7.99625i	0.493070	+	0.493070i	0.909272	−	0.416202i	$-0.136639\pi$
$263$	7.99625	+	7.99625i	0.493070	+	0.493070i	−0.416202	+	0.909272i	$0.636639\pi$
$264$	1.32458	−	4.10292i	0.0815222	−	0.252517i
$265$	0.694972	+	1.60115i	0.0426918	+	0.0983581i
$266$	−5.43549	−	12.1877i	−0.333271	−	0.747276i
$267$	9.11109	−	9.11109i	0.557590	−	0.557590i
$268$	3.74756	−	0.201121i	0.228918	−	0.0122854i
$269$			20.9021i			1.27442i	0.770689	+	0.637211i	$0.219912\pi$
$269$			20.9021i			1.27442i	−0.770689	+	0.637211i	$0.780088\pi$
$270$	15.0957	−	0.658819i	0.918693	−	0.0400945i
$271$		−	21.2210i		−	1.28908i	−0.764570	−	0.644541i	$-0.777049\pi$
$271$		−	21.2210i		−	1.28908i	0.764570	−	0.644541i	$-0.222951\pi$
$272$	−9.86683	+	12.2473i	−0.598265	+	0.742601i
$273$	−1.76028	+	1.76028i	−0.106537	+	0.106537i
$274$	0.901381	−	0.401999i	0.0544544	−	0.0242856i
$275$	−5.59236	+	5.98156i	−0.337232	+	0.360702i
$276$	−1.52755	+	1.70081i	−0.0919479	+	0.102377i
$277$	10.6769	+	10.6769i	0.641511	+	0.641511i	0.950927	−	0.309415i	$-0.100133\pi$
$277$	10.6769	+	10.6769i	0.641511	+	0.641511i	−0.309415	+	0.950927i	$0.600133\pi$
$278$	5.44676	−	14.2160i	0.326675	−	0.852617i
$279$	16.6437			0.996430
$280$	−13.0659	−	10.7436i	−0.780838	−	0.642052i
$281$	−26.8589			−1.60227			−0.801135	−	0.598484i	$-0.795770\pi$
$281$	−26.8589			−1.60227			−0.801135	+	0.598484i	$0.795770\pi$
$282$	−5.41283	+	14.1274i	−0.322329	+	0.841275i
$283$	−5.29625	−	5.29625i	−0.314829	−	0.314829i	0.531948	−	0.846777i	$-0.321460\pi$
$283$	−5.29625	−	5.29625i	−0.314829	−	0.314829i	−0.846777	+	0.531948i	$0.821460\pi$
$284$	8.69890	−	9.68554i	0.516185	−	0.574731i
$285$	−6.73561	+	2.92356i	−0.398983	+	0.173177i
$286$	−2.11526	+	0.943368i	−0.125078	+	0.0557825i
$287$	10.3861	−	10.3861i	0.613071	−	0.613071i
$288$	−3.08733	+	11.6685i	−0.181922	+	0.687571i
$289$		−	1.54059i		−	0.0906230i
$290$	−17.0402	+	18.5954i	−1.00064	+	1.09196i
$291$		−	0.0140407i		−	0.000823083i
$292$	14.0008	−	0.751386i	0.819338	−	0.0439715i
$293$	−12.1353	+	12.1353i	−0.708953	+	0.708953i	−0.966315	−	0.257362i	$-0.917147\pi$
$293$	−12.1353	+	12.1353i	−0.708953	+	0.708953i	0.257362	+	0.966315i	$0.417147\pi$
$294$	0.0823354	+	0.184616i	0.00480190	+	0.0107670i
$295$	6.64344	−	16.8335i	0.386796	−	0.980083i
$296$	15.3322	+	4.94984i	0.891169	+	0.287703i
$297$	−5.53339	−	5.53339i	−0.321080	−	0.321080i
$298$	−17.3450	−	6.64562i	−1.00477	−	0.384970i
$299$	1.22808			0.0710217
$300$	−5.98304	+	7.12979i	−0.345431	+	0.411638i
$301$	−19.5423			−1.12640
$302$	−27.0749	−	10.3736i	−1.55798	−	0.596932i
$303$	−5.49826	−	5.49826i	−0.315867	−	0.315867i
$304$	−1.51038	−	14.0312i	−0.0866263	−	0.804745i
$305$	−6.92790	+	17.5542i	−0.396691	+	1.00515i
$306$	4.83247	+	10.8356i	0.276254	+	0.619429i
$307$	−16.9432	+	16.9432i	−0.966997	+	0.966997i	−0.999473	−	0.0324756i	$-0.989661\pi$
$307$	−16.9432	+	16.9432i	−0.966997	+	0.966997i	0.0324756	+	0.999473i	$0.489661\pi$
$308$	0.469480	+	8.74798i	0.0267511	+	0.498463i
$309$			16.8799i			0.960266i
$310$	−16.6651	+	18.1861i	−0.946515	+	1.03290i
$311$		−	2.12910i		−	0.120730i	−0.998176	−	0.0603652i	$-0.980773\pi$
$311$		−	2.12910i		−	0.120730i	0.998176	−	0.0603652i	$-0.0192265\pi$
$312$	−2.34339	+	1.19958i	−0.132668	+	0.0679129i
$313$	19.7564	−	19.7564i	1.11670	−	1.11670i	0.124474	−	0.992223i	$-0.460276\pi$
$313$	19.7564	−	19.7564i	1.11670	−	1.11670i	0.992223	−	0.124474i	$-0.0397242\pi$
$314$	7.01795	−	3.12988i	0.396046	−	0.176629i
$315$	−11.7057	+	5.08081i	−0.659543	+	0.286271i
$316$	21.7488	+	19.5333i	1.22347	+	1.09883i
$317$	5.16186	+	5.16186i	0.289919	+	0.289919i	0.837048	−	0.547129i	$-0.184279\pi$
$317$	5.16186	+	5.16186i	0.289919	+	0.289919i	−0.547129	+	0.837048i	$0.684279\pi$
$318$	0.367618	−	0.959478i	0.0206150	−	0.0538049i
$319$	13.0624			0.731356
$320$	−9.65856	−	15.0570i	−0.539930	−	0.841710i
$321$	−2.94502			−0.164375
$322$	1.66196	−	4.33770i	0.0926175	−	0.241730i
$323$	−9.80886	−	9.80886i	−0.545779	−	0.545779i
$324$	2.90709	+	2.61096i	0.161505	+	0.145053i
$325$	4.99718	−	0.168042i	0.277193	−	0.00932130i
$326$	−16.0677	+	7.16591i	−0.889909	+	0.396883i
$327$	−2.69714	+	2.69714i	−0.149152	+	0.149152i
$328$	13.8265	−	7.07781i	0.763442	−	0.390806i
$329$		−	30.7409i		−	1.69480i
$330$	4.81574	−	0.210173i	0.265098	−	0.0115697i
$331$		−	7.47804i		−	0.411030i	−0.978654	−	0.205515i	$-0.934113\pi$
$331$		−	7.47804i		−	0.411030i	0.978654	−	0.205515i	$-0.0658869\pi$
$332$	−0.996669	−	18.5713i	−0.0546993	−	1.01923i
$333$	8.59422	−	8.59422i	0.470961	−	0.470961i
$334$	12.3020	+	27.5842i	0.673138	+	1.50934i
$335$	1.67064	+	3.84899i	0.0912765	+	0.210293i
$336$	1.06573	+	9.90046i	0.0581403	+	0.540114i
$337$	16.1356	+	16.1356i	0.878963	+	0.878963i	0.993427	−	0.114464i	$-0.0365152\pi$
$337$	16.1356	+	16.1356i	0.878963	+	0.878963i	−0.114464	+	0.993427i	$0.536515\pi$
$338$	1.32060	+	0.505980i	0.0718312	+	0.0275217i
$339$	5.08352			0.276099
$340$	−16.6785	−	5.56923i	−0.904518	−	0.302034i
$341$	12.7749			0.691800
$342$	−9.94124	−	3.80892i	−0.537560	−	0.205963i
$343$	12.9482	+	12.9482i	0.699139	+	0.699139i
$344$	−19.6667	−	6.34916i	−1.06036	−	0.342324i
$345$	−2.37747	−	0.938283i	−0.127998	−	0.0505155i
$346$	−10.8886	−	24.4150i	−0.585376	−	1.31256i
$347$	−1.13829	+	1.13829i	−0.0611068	+	0.0611068i	−0.737000	−	0.675893i	$-0.763758\pi$
$347$	−1.13829	+	1.13829i	−0.0611068	+	0.0611068i	0.675893	+	0.737000i	$0.263758\pi$
$348$	14.8260	−	0.795670i	0.794757	−	0.0426524i
$349$		−	28.5647i		−	1.52903i	−0.644604	−	0.764517i	$-0.722978\pi$
$349$		−	28.5647i		−	1.52903i	0.644604	−	0.764517i	$-0.277022\pi$
$350$	6.16914	−	17.8779i	0.329755	−	0.955615i
$351$			4.77821i			0.255042i
$352$	−2.36969	+	8.95618i	−0.126305	+	0.477366i
$353$	18.0473	−	18.0473i	0.960558	−	0.960558i	−0.0386928	−	0.999251i	$-0.512319\pi$
$353$	18.0473	−	18.0473i	0.960558	−	0.960558i	0.999251	+	0.0386928i	$0.0123194\pi$
$354$	−9.72928	+	4.33908i	−0.517105	+	0.230619i
$355$	13.5389	+	5.34320i	0.718568	+	0.283588i
$356$	−18.5005	+	20.5989i	−0.980526	+	1.09174i
$357$	6.92115	+	6.92115i	0.366306	+	0.366306i
$358$	6.17483	−	16.1162i	0.326350	−	0.851769i
$359$	−6.18564			−0.326466			−0.163233	−	0.986588i	$-0.552192\pi$
$359$	−6.18564			−0.326466			−0.163233	+	0.986588i	$0.552192\pi$
$360$	−13.4309	+	1.31003i	−0.707872	+	0.0690448i
$361$	−6.55274			−0.344881
$362$	6.51143	−	16.9948i	0.342233	−	0.893225i
$363$	5.47434	+	5.47434i	0.287329	+	0.287329i
$364$	3.57434	−	3.97975i	0.187346	−	0.208595i
$365$	6.24148	+	14.3798i	0.326694	+	0.752674i
$366$	10.1459	−	4.52487i	0.530333	−	0.236519i
$367$	−19.2253	+	19.2253i	−1.00355	+	1.00355i	−0.00355779	+	0.999994i	$0.501132\pi$
$367$	−19.2253	+	19.2253i	−1.00355	+	1.00355i	−0.999994	+	0.00355779i	$0.998868\pi$
$368$	3.08182	−	3.82534i	0.160651	−	0.199410i
$369$		−	11.7176i		−	0.609992i
$370$	0.785399	+	17.9960i	0.0408309	+	0.935568i
$371$			2.08780i			0.108393i
$372$	14.4997	−	0.778156i	0.751772	−	0.0403455i
$373$	13.1719	−	13.1719i	0.682016	−	0.682016i	−0.278438	−	0.960454i	$-0.589817\pi$
$373$	13.1719	−	13.1719i	0.682016	−	0.682016i	0.960454	+	0.278438i	$0.0898166\pi$
$374$	3.70918	+	8.31689i	0.191797	+	0.430056i
$375$	−9.80253	−	3.49265i	−0.506201	−	0.180360i
$376$	9.98750	−	30.9365i	0.515066	−	1.59543i
$377$	−5.63986	−	5.63986i	−0.290467	−	0.290467i
$378$	16.8771	+	6.46636i	0.868066	+	0.332594i
$379$	6.67592			0.342919			0.171460	−	0.985191i	$-0.445152\pi$
$379$	6.67592			0.342919			0.171460	+	0.985191i	$0.445152\pi$
$380$	14.1160	−	7.04872i	0.724134	−	0.361592i
$381$	3.23982			0.165981
$382$	22.2657	+	8.53096i	1.13921	+	0.436482i
$383$	18.1276	+	18.1276i	0.926279	+	0.926279i	0.997463	−	0.0711841i	$-0.0226778\pi$
$383$	18.1276	+	18.1276i	0.926279	+	0.926279i	−0.0711841	+	0.997463i	$0.522678\pi$
$384$	−2.14408	+	10.3097i	−0.109414	+	0.526115i
$385$	−8.98477	+	3.89979i	−0.457906	+	0.198752i
$386$	4.62442	+	10.3691i	0.235377	+	0.527773i
$387$	−11.0238	+	11.0238i	−0.560372	+	0.560372i
$388$	0.00161685	+	0.0301273i	8.20829e−5	+	0.00152948i
$389$			35.4186i			1.79579i	0.440205	+	0.897897i	$0.354906\pi$
$389$			35.4186i			1.79579i	−0.440205	+	0.897897i	$0.645094\pi$
$390$	−2.17000	−	1.98851i	−0.109882	−	0.100692i
$391$		−	4.82862i		−	0.244194i
$392$	−0.197927	−	0.386651i	−0.00999681	−	0.0195288i
$393$	−0.923435	+	0.923435i	−0.0465811	+	0.0465811i
$394$	21.8834	−	9.75959i	1.10247	−	0.491681i
$395$	−11.9981	+	30.4014i	−0.603691	+	1.52966i
$396$	5.19957	+	4.66990i	0.261288	+	0.234671i
$397$	−9.88325	−	9.88325i	−0.496026	−	0.496026i	0.414172	−	0.910199i	$-0.364071\pi$
$397$	−9.88325	−	9.88325i	−0.496026	−	0.496026i	−0.910199	+	0.414172i	$0.864071\pi$
$398$	6.82782	−	17.8205i	0.342248	−	0.893262i
$399$	−8.78282			−0.439691
$400$	12.0168	−	15.9874i	0.600840	−	0.799369i
$401$	10.1583			0.507281			0.253641	−	0.967299i	$-0.418372\pi$
$401$	10.1583			0.507281			0.253641	+	0.967299i	$0.418372\pi$
$402$	0.883713	−	2.30648i	0.0440756	−	0.115037i
$403$	−5.51571	−	5.51571i	−0.274757	−	0.274757i
$404$	12.4308	+	11.1645i	0.618455	+	0.555454i
$405$	−1.60375	+	4.06366i	−0.0796910	+	0.201925i
$406$	−27.5529	+	12.2881i	−1.36743	+	0.609848i
$407$	6.59653	−	6.59653i	0.326978	−	0.326978i
$408$	4.71656	+	9.21383i	0.233505	+	0.456153i
$409$		−	5.50011i		−	0.271963i	−0.990711	−	0.135982i	$-0.956581\pi$
$409$		−	5.50011i		−	0.271963i	0.990711	−	0.135982i	$-0.0434188\pi$
$410$	12.8035	+	11.7327i	0.632320	+	0.579435i
$411$		−	0.649562i		−	0.0320405i
$412$	−1.94379	−	36.2194i	−0.0957637	−	1.78440i
$413$	15.3062	−	15.3062i	0.753170	−	0.753170i
$414$	−1.50938	−	3.38440i	−0.0741820	−	0.166334i
$415$	19.0740	−	8.27896i	0.936305	−	0.406398i
$416$	4.89008	−	2.84379i	0.239756	−	0.139428i
$417$	−7.08477	−	7.08477i	−0.346943	−	0.346943i
$418$	−7.63043	−	2.92355i	−0.373217	−	0.142996i
$419$	18.5620			0.906815			0.453407	−	0.891303i	$-0.350208\pi$
$419$	18.5620			0.906815			0.453407	+	0.891303i	$0.350208\pi$
$420$	−9.96027	+	4.97360i	−0.486011	+	0.242687i
$421$	10.2994			0.501962			0.250981	−	0.967992i	$-0.419247\pi$
$421$	10.2994			0.501962			0.250981	+	0.967992i	$0.419247\pi$
$422$	29.4768	+	11.2938i	1.43491	+	0.549775i
$423$	−17.3409	−	17.3409i	−0.843145	−	0.843145i
$424$	−0.678312	+	2.10109i	−0.0329417	+	0.102038i
$425$	−0.660716	−	19.6481i	−0.0320494	−	0.953074i
$426$	−3.48984	−	7.82509i	−0.169083	−	0.379127i
$427$	−15.9616	+	15.9616i	−0.772436	+	0.772436i
$428$	6.31914	−	0.339130i	0.305447	−	0.0163925i
$429$			1.52432i			0.0735950i
$430$	−1.00743	−	23.0835i	−0.0485826	−	1.11318i
$431$			13.4505i			0.647889i	0.946076	+	0.323944i	$0.105009\pi$
$431$			13.4505i			0.647889i	−0.946076	+	0.323944i	$0.894991\pi$
$432$	14.8836	+	11.9908i	0.716090	+	0.576906i
$433$	−5.29244	+	5.29244i	−0.254338	+	0.254338i	−0.822747	−	0.568408i	$-0.807559\pi$
$433$	−5.29244	+	5.29244i	−0.254338	+	0.254338i	0.568408	+	0.822747i	$0.307559\pi$
$434$	−26.9465	+	12.0176i	−1.29347	+	0.576864i
$435$	6.60933	+	15.2273i	0.316893	+	0.730094i
$436$	5.47669	−	6.09786i	0.262286	−	0.292035i
$437$	3.06371	+	3.06371i	0.146557	+	0.146557i
$438$	3.30155	−	8.61700i	0.157754	−	0.411736i
$439$	5.70933			0.272491			0.136246	−	0.990675i	$-0.456496\pi$
$439$	5.70933			0.272491			0.136246	+	0.990675i	$0.456496\pi$
$440$	−10.3090	+	1.00552i	−0.491460	+	0.0479363i
$441$	−0.327675			−0.0156036
$442$	1.98943	−	5.19240i	0.0946277	−	0.246977i
$443$	−21.3935	−	21.3935i	−1.01644	−	1.01644i	−0.999863	−	0.0165752i	$-0.994724\pi$
$443$	−21.3935	−	21.3935i	−1.01644	−	1.01644i	−0.0165752	−	0.999863i	$-0.505276\pi$
$444$	7.08532	−	7.88895i	0.336255	−	0.374393i
$445$	−28.7940	−	11.3637i	−1.36497	−	0.538693i
$446$	27.7228	−	12.3638i	1.31271	−	0.585444i
$447$	−8.64416	+	8.64416i	−0.408855	+	0.408855i
$448$	−3.42682	−	21.1207i	−0.161902	−	0.997861i
$449$			2.92123i			0.137861i	0.997621	+	0.0689307i	$0.0219587\pi$
$449$			2.92123i			0.137861i	−0.997621	+	0.0689307i	$0.978041\pi$
$450$	−6.60492	−	13.5649i	−0.311359	−	0.639457i
$451$		−	8.99386i		−	0.423504i
$452$	−10.9077	+	0.585387i	−0.513056	+	0.0275343i
$453$	−13.4932	+	13.4932i	−0.633967	+	0.633967i
$454$	−1.36380	−	3.05798i	−0.0640064	−	0.143518i
$455$	5.56306	+	2.19550i	0.260800	+	0.102927i
$456$	−8.83871	−	2.85347i	−0.413910	−	0.133626i
$457$	−23.3601	−	23.3601i	−1.09274	−	1.09274i	−0.995235	−	0.0975018i	$-0.968915\pi$
$457$	−23.3601	−	23.3601i	−1.09274	−	1.09274i	−0.0975018	−	0.995235i	$-0.531085\pi$
$458$	12.3830	+	4.74445i	0.578618	+	0.221694i
$459$	18.7872			0.876911
$460$	5.20939	+	1.73950i	0.242889	+	0.0811048i
$461$	11.0916			0.516586			0.258293	−	0.966067i	$-0.416840\pi$
$461$	11.0916			0.516586			0.258293	+	0.966067i	$0.416840\pi$
$462$	5.38405	+	2.06287i	0.250489	+	0.0959732i
$463$	13.4705	+	13.4705i	0.626026	+	0.626026i	0.947066	−	0.321040i	$-0.104032\pi$
$463$	13.4705	+	13.4705i	0.626026	+	0.626026i	−0.321040	+	0.947066i	$0.604032\pi$
$464$	−31.7206	+	3.41454i	−1.47259	+	0.158516i
$465$	6.46385	+	14.8921i	0.299754	+	0.690606i
$466$	13.0884	+	29.3474i	0.606307	+	1.35949i
$467$	−7.11784	+	7.11784i	−0.329374	+	0.329374i	−0.852348	−	0.522974i	$-0.824822\pi$
$467$	−7.11784	+	7.11784i	−0.329374	+	0.329374i	0.522974	+	0.852348i	$0.324822\pi$
$468$	−0.228690	−	4.26126i	−0.0105712	−	0.196977i
$469$			5.01885i			0.231749i
$470$	36.3113	−	1.58473i	1.67492	−	0.0730983i
$471$		−	5.05735i		−	0.233030i
$472$	20.3765	−	10.4307i	0.937904	−	0.480114i
$473$	−8.46137	+	8.46137i	−0.389054	+	0.389054i
$474$	17.5712	−	7.83641i	0.807070	−	0.359938i
$475$	12.8858	+	12.0473i	0.591240	+	0.552770i
$476$	−15.6477	−	14.0538i	−0.717213	−	0.644153i
$477$	1.17773	+	1.17773i	0.0539245	+	0.0539245i
$478$	−9.91138	+	25.8686i	−0.453336	+	1.18320i
$479$	−36.7990			−1.68139			−0.840695	−	0.541508i	$-0.817853\pi$
$479$	−36.7990			−1.68139			−0.840695	+	0.541508i	$0.817853\pi$
$480$	−11.6395	+	1.76923i	−0.531270	+	0.0807537i
$481$	−5.69626			−0.259727
$482$	0.386852	−	1.00968i	0.0176206	−	0.0459896i
$483$	−2.16177	−	2.16177i	−0.0983637	−	0.0983637i
$484$	−12.3767	−	11.1159i	−0.562578	−	0.505270i
$485$	−0.0309428	+	0.0134305i	−0.00140504	+	0.000609850i
$486$	20.8631	−	9.30456i	0.946370	−	0.422063i
$487$	−0.572155	+	0.572155i	−0.0259268	+	0.0259268i	−0.719951	−	0.694025i	$-0.755836\pi$
$487$	−0.572155	+	0.572155i	−0.0259268	+	0.0259268i	0.694025	+	0.719951i	$0.255836\pi$
$488$	−21.2490	+	10.8774i	−0.961896	+	0.492395i
$489$			11.5789i			0.523615i
$490$	0.328097	−	0.358042i	0.0148219	−	0.0161747i
$491$			7.77959i			0.351088i	0.984472	+	0.175544i	$0.0561684\pi$
$491$			7.77959i			0.351088i	−0.984472	+	0.175544i	$0.943832\pi$
$492$	−0.547841	−	10.2081i	−0.0246986	−	0.460218i
$493$	−22.1750	+	22.1750i	−0.998714	+	0.998714i
$494$	2.03225	+	4.55681i	0.0914353	+	0.205020i
$495$	−2.86844	+	7.26818i	−0.128927	+	0.326680i
$496$	−31.0224	+	3.33938i	−1.39295	+	0.149943i
$497$	12.3105	+	12.3105i	0.552202	+	0.552202i
$498$	−11.4299	−	4.37931i	−0.512188	−	0.196241i
$499$	−2.74891			−0.123058			−0.0615291	−	0.998105i	$-0.519598\pi$
$499$	−2.74891			−0.123058			−0.0615291	+	0.998105i	$0.519598\pi$
$500$	21.4355	+	6.36539i	0.958626	+	0.284669i
$501$	19.8780			0.888083
$502$	6.16595	+	2.36244i	0.275200	+	0.105441i
$503$	12.1149	+	12.1149i	0.540178	+	0.540178i	0.923581	−	0.383403i	$-0.125248\pi$
$503$	12.1149	+	12.1149i	0.540178	+	0.540178i	−0.383403	+	0.923581i	$0.625248\pi$
$504$	−15.3607	−	4.95901i	−0.684218	−	0.220892i
$505$	−6.85767	+	17.3763i	−0.305162	+	0.773235i
$506$	−1.15853	−	2.59771i	−0.0515030	−	0.115482i
$507$	0.658144	−	0.658144i	0.0292292	−	0.0292292i
$508$	−6.95170	+	0.373078i	−0.308432	+	0.0165527i
$509$		−	19.3655i		−	0.858361i	−0.903219	−	0.429180i	$-0.858802\pi$
$509$		−	19.3655i		−	0.858361i	0.903219	−	0.429180i	$-0.141198\pi$
$510$	−7.81851	+	8.53210i	−0.346209	+	0.377808i
$511$			18.7504i			0.829469i
$512$	3.41335	−	22.3685i	0.150850	−	0.988557i
$513$	−11.9203	+	11.9203i	−0.526295	+	0.526295i
$514$	−15.8280	+	7.05900i	−0.698144	+	0.311359i
$515$	37.1997	−	16.1463i	1.63922	−	0.711493i
$516$	−9.08834	+	10.1192i	−0.400092	+	0.445471i
$517$	−13.3101	−	13.3101i	−0.585378	−	0.585378i
$518$	−7.70875	+	20.1197i	−0.338703	+	0.884011i
$519$	−17.5941			−0.772297
$520$	4.88516	+	4.01687i	0.214228	+	0.176151i
$521$	−35.2285			−1.54339			−0.771695	−	0.635993i	$-0.780591\pi$
$521$	−35.2285			−1.54339			−0.771695	+	0.635993i	$0.780591\pi$
$522$	−8.61089	+	22.4743i	−0.376889	+	0.983674i
$523$	17.8598	+	17.8598i	0.780954	+	0.780954i	0.979992	−	0.199038i	$-0.0637818\pi$
$523$	17.8598	+	17.8598i	0.780954	+	0.780954i	−0.199038	+	0.979992i	$0.563782\pi$
$524$	1.87508	−	2.08775i	0.0819133	−	0.0912040i
$525$	−9.09224	−	8.50063i	−0.396818	−	0.370998i
$526$	−14.6058	+	6.51390i	−0.636842	+	0.284020i
$527$	−21.6869	+	21.6869i	−0.944698	+	0.944698i
$528$	4.74811	+	3.82523i	0.206635	+	0.166472i
$529$		−	21.4918i		−	0.934427i
$530$	−2.46612	+	0.107629i	−0.107122	+	0.00467510i
$531$		−	17.2685i		−	0.749387i
$532$	18.8453	−	1.01138i	0.817049	−	0.0438487i
$533$	−3.88320	+	3.88320i	−0.168200	+	0.168200i
$534$	7.42208	+	16.6421i	0.321185	+	0.720175i
$535$	2.81703	+	6.49018i	0.121791	+	0.280595i
$536$	−1.63059	+	5.05079i	−0.0704306	+	0.218161i
$537$	−8.03179	−	8.03179i	−0.346597	−	0.346597i
$538$	−27.6033	−	10.5760i	−1.19006	−	0.455965i
$539$	−0.251508			−0.0108332
$540$	−6.76807	+	20.2687i	−0.291251	+	0.872226i
$541$	33.8314			1.45452			0.727262	−	0.686359i	$-0.240792\pi$
$541$	33.8314			1.45452			0.727262	+	0.686359i	$0.240792\pi$
$542$	28.0244	+	10.7374i	1.20375	+	0.461210i
$543$	−8.46963	−	8.46963i	−0.363466	−	0.363466i
$544$	−11.1814	−	19.2270i	−0.479397	−	0.824352i
$545$	8.52385	+	3.36400i	0.365122	+	0.144098i
$546$	−1.43396	−	3.21529i	−0.0613679	−	0.137602i
$547$	2.95286	−	2.95286i	0.126255	−	0.126255i	−0.641156	−	0.767411i	$-0.721545\pi$
$547$	2.95286	−	2.95286i	0.126255	−	0.126255i	0.767411	+	0.641156i	$0.221545\pi$
$548$	0.0747995	+	1.39377i	0.00319528	+	0.0595388i
$549$			18.0079i			0.768557i
$550$	−5.06963	−	10.4118i	−0.216170	−	0.443962i
$551$		−	28.1397i		−	1.19879i
$552$	−1.47318	−	2.87786i	−0.0627027	−	0.122490i
$553$	−27.6432	+	27.6432i	−1.17551	+	1.17551i
$554$	−19.5022	+	8.69760i	−0.828568	+	0.369526i
$555$	11.0275	+	4.35208i	0.468092	+	0.184736i
$556$	16.0177	+	14.3860i	0.679300	+	0.610101i
$557$	3.80718	+	3.80718i	0.161315	+	0.161315i	0.783149	−	0.621834i	$-0.213612\pi$
$557$	3.80718	+	3.80718i	0.161315	+	0.161315i	−0.621834	+	0.783149i	$0.713612\pi$
$558$	−8.42135	+	21.9796i	−0.356504	+	0.930471i
$559$	7.30659			0.309036
$560$	20.7991	−	11.8188i	0.878921	−	0.499437i
$561$	5.99340			0.253041
$562$	13.5901	−	35.4699i	0.573263	−	1.49621i
$563$	−31.6788	−	31.6788i	−1.33510	−	1.33510i	−0.900736	−	0.434368i	$-0.856972\pi$
$563$	−31.6788	−	31.6788i	−1.33510	−	1.33510i	−0.434368	−	0.900736i	$-0.643028\pi$
$564$	−15.9179	−	14.2964i	−0.670263	−	0.601985i
$565$	−4.86259	−	11.2030i	−0.204571	−	0.471313i
$566$	9.67402	−	4.31443i	0.406629	−	0.181349i
$567$	−3.69497	+	3.69497i	−0.155174	+	0.155174i
$568$	8.38926	+	16.3884i	0.352005	+	0.687644i
$569$			25.1606i			1.05479i	0.849621	+	0.527393i	$0.176830\pi$
$569$			25.1606i			1.05479i	−0.849621	+	0.527393i	$0.823170\pi$
$570$	−0.452765	−	10.3743i	−0.0189643	−	0.434532i
$571$			42.4686i			1.77726i	0.458627	+	0.888629i	$0.348341\pi$
$571$			42.4686i			1.77726i	−0.458627	+	0.888629i	$0.651659\pi$
$572$	−0.175532	−	3.27074i	−0.00733934	−	0.136757i
$573$	11.0965	−	11.0965i	0.463562	−	0.463562i
$574$	8.46071	+	18.9710i	0.353143	+	0.791834i
$575$	0.206369	+	6.13693i	0.00860618	+	0.255928i
$576$	−13.8473	−	9.98113i	−0.576969	−	0.415880i
$577$	−16.1672	−	16.1672i	−0.673048	−	0.673048i	0.285370	−	0.958418i	$-0.407884\pi$
$577$	−16.1672	−	16.1672i	−0.673048	−	0.673048i	−0.958418	+	0.285370i	$0.907884\pi$
$578$	2.03451	+	0.779508i	0.0846243	+	0.0324233i
$579$	7.47227			0.310537
$580$	−15.9352	−	31.9122i	−0.661671	−	1.32508i
$581$	24.8713			1.03183
$582$	0.0185422	+	0.00710433i	0.000768599	+	0.000294484i
$583$	0.903970	+	0.903970i	0.0374386	+	0.0374386i
$584$	−6.09186	+	18.8697i	−0.252083	+	0.780834i
$585$	4.37660	−	1.89964i	0.180950	−	0.0785404i
$586$	−9.88568	−	22.1661i	−0.408374	−	0.915674i
$587$	12.3005	−	12.3005i	0.507697	−	0.507697i	−0.406122	−	0.913819i	$-0.633119\pi$
$587$	12.3005	−	12.3005i	0.507697	−	0.507697i	0.913819	+	0.406122i	$0.133119\pi$
$588$	−0.285464	+	0.0153201i	−0.0117723	+	0.000631789i
$589$		−	27.5203i		−	1.13396i
$590$	18.8688	+	17.2907i	0.776818	+	0.711848i
$591$		−	15.7698i		−	0.648684i
$592$	−14.2946	+	17.7433i	−0.587503	+	0.729243i
$593$	10.0432	−	10.0432i	0.412424	−	0.412424i	−0.470158	−	0.882582i	$-0.655803\pi$
$593$	10.0432	−	10.0432i	0.412424	−	0.412424i	0.882582	+	0.470158i	$0.155803\pi$
$594$	10.1072	−	4.50762i	0.414703	−	0.184950i
$595$	8.63236	−	21.8731i	0.353892	−	0.896709i
$596$	17.5524	−	19.5432i	0.718974	−	0.800522i
$597$	−8.88116	−	8.88116i	−0.363482	−	0.363482i
$598$	−0.621383	+	1.62180i	−0.0254102	+	0.0663204i
$599$	−11.5903			−0.473568			−0.236784	−	0.971562i	$-0.576093\pi$
$599$	−11.5903			−0.473568			−0.236784	+	0.971562i	$0.576093\pi$
$600$	−6.38830	−	11.5087i	−0.260801	−	0.469842i
$601$	−3.91441			−0.159672			−0.0798360	−	0.996808i	$-0.525440\pi$
$601$	−3.91441			−0.159672			−0.0798360	+	0.996808i	$0.525440\pi$
$602$	9.88802	−	25.8076i	0.403006	−	1.05184i
$603$	2.83113	+	2.83113i	0.115293	+	0.115293i
$604$	27.3987	−	30.5063i	1.11484	−	1.24128i
$605$	6.82784	−	17.3007i	0.277591	−	0.703374i
$606$	10.0430	−	4.47900i	0.407970	−	0.181947i
$607$	−8.20464	+	8.20464i	−0.333016	+	0.333016i	−0.853731	−	0.520715i	$-0.825666\pi$
$607$	−8.20464	+	8.20464i	−0.333016	+	0.333016i	0.520715	+	0.853731i	$0.325666\pi$
$608$	19.2938	+	5.10490i	0.782469	+	0.207031i
$609$			19.8555i			0.804584i
$610$	−19.6768	−	18.0311i	−0.796689	−	0.730057i
$611$			11.4936i			0.464981i
$612$	−16.7546	+	0.899172i	−0.677265	+	0.0363469i
$613$	−23.7346	+	23.7346i	−0.958631	+	0.958631i	−0.999178	−	0.0405471i	$-0.987090\pi$
$613$	−23.7346	+	23.7346i	−0.958631	+	0.958631i	0.0405471	+	0.999178i	$0.487090\pi$
$614$	−13.8022	−	30.9480i	−0.557013	−	1.24896i
$615$	10.4844	−	4.55071i	0.422773	−	0.183503i
$616$	−11.7901	−	3.80631i	−0.475038	−	0.153360i
$617$	−22.7013	−	22.7013i	−0.913921	−	0.913921i	0.0826571	−	0.996578i	$-0.473659\pi$
$617$	−22.7013	−	22.7013i	−0.913921	−	0.913921i	−0.996578	+	0.0826571i	$0.973659\pi$
$618$	−22.2916	−	8.54091i	−0.896702	−	0.343566i
$619$	−33.7105			−1.35494			−0.677471	−	0.735550i	$-0.736924\pi$
$619$	−33.7105			−1.35494			−0.677471	+	0.735550i	$0.736924\pi$
$620$	−15.5844	−	31.2098i	−0.625884	−	1.25341i
$621$	−5.86803			−0.235476
$622$	2.81169	+	1.07728i	0.112739	+	0.0431951i
$623$	−26.1816	−	26.1816i	−1.04894	−	1.04894i
$624$	−0.398461	−	3.70164i	−0.0159512	−	0.148184i
$625$	1.67947	+	24.9435i	0.0671789	+	0.997741i
$626$	16.0939	+	36.0866i	0.643244	+	1.44231i
$627$	−3.80276	+	3.80276i	−0.151867	+	0.151867i
$628$	0.582373	+	10.8516i	0.0232392	+	0.433025i
$629$			22.3968i			0.893019i
$630$	−0.786854	−	18.0294i	−0.0313490	−	0.718307i
$631$		−	17.6344i		−	0.702013i	−0.936373	−	0.351006i	$-0.885840\pi$
$631$		−	17.6344i		−	0.702013i	0.936373	−	0.351006i	$-0.114160\pi$
$632$	−36.8001	+	18.8380i	−1.46383	+	0.749336i
$633$	14.6902	−	14.6902i	0.583885	−	0.583885i
$634$	−9.42855	+	4.20496i	−0.374456	+	0.167000i
$635$	−3.09902	−	7.13987i	−0.122981	−	0.283337i
$636$	1.08108	+	0.970953i	0.0428676	+	0.0385008i
$637$	0.108591	+	0.108591i	0.00430255	+	0.00430255i
$638$	−6.60932	+	17.2502i	−0.261666	+	0.682944i
$639$	13.8887			0.549429
$640$	24.7713	−	5.13657i	0.979170	−	0.203041i
$641$	−1.15882			−0.0457705			−0.0228853	−	0.999738i	$-0.507285\pi$
$641$	−1.15882			−0.0457705			−0.0228853	+	0.999738i	$0.507285\pi$
$642$	1.49012	−	3.88919i	0.0588103	−	0.153494i
$643$	0.553083	+	0.553083i	0.0218115	+	0.0218115i	0.717928	−	0.696117i	$-0.245090\pi$
$643$	0.553083	+	0.553083i	0.0218115	+	0.0218115i	−0.696117	+	0.717928i	$0.745090\pi$
$644$	4.88744	+	4.38957i	0.192592	+	0.172973i
$645$	−14.1450	−	5.58242i	−0.556958	−	0.219807i
$646$	17.9167	−	7.99049i	0.704921	−	0.314382i
$647$	7.94092	−	7.94092i	0.312190	−	0.312190i	−0.533568	−	0.845757i	$-0.679149\pi$
$647$	7.94092	−	7.94092i	0.312190	−	0.312190i	0.845757	+	0.533568i	$0.179149\pi$
$648$	−4.91896	+	2.51802i	−0.193235	+	0.0989171i
$649$		−	13.2545i		−	0.520283i
$650$	−2.30655	+	6.68430i	−0.0904704	+	0.262180i
$651$			19.4184i			0.761068i
$652$	−1.33335	−	24.8449i	−0.0522181	−	0.973000i
$653$	22.2142	−	22.2142i	0.869311	−	0.869311i	−0.123085	−	0.992396i	$-0.539279\pi$
$653$	22.2142	−	22.2142i	0.869311	−	0.869311i	0.992396	+	0.123085i	$0.0392789\pi$
$654$	−2.19715	−	4.92655i	−0.0859153	−	0.192643i
$655$	2.91835	+	1.15175i	0.114029	+	0.0450025i
$656$	2.35101	+	21.8405i	0.0917916	+	0.852730i
$657$	10.5771	+	10.5771i	0.412651	+	0.412651i
$658$	40.5965	+	15.5543i	1.58262	+	0.606369i
$659$	−3.57200			−0.139145			−0.0695727	−	0.997577i	$-0.522164\pi$
$659$	−3.57200			−0.139145			−0.0695727	+	0.997577i	$0.522164\pi$
$660$	−2.15911	+	6.46602i	−0.0840434	+	0.251689i
$661$	26.8543			1.04451			0.522256	−	0.852789i	$-0.325091\pi$
$661$	26.8543			1.04451			0.522256	+	0.852789i	$0.325091\pi$
$662$	9.87549	+	3.78373i	0.383822	+	0.147059i
$663$	−2.58772	−	2.58772i	−0.100499	−	0.100499i
$664$	25.0295	+	8.08050i	0.971335	+	0.313584i
$665$	8.40112	+	19.3554i	0.325782	+	0.750572i
$666$	7.00103	+	15.6980i	0.271284	+	0.608287i
$667$	6.92619	−	6.92619i	0.268183	−	0.268183i
$668$	−42.6523	+	2.28903i	−1.65027	+	0.0885651i
$669$		−	19.9778i		−	0.772388i
$670$	−5.92829	+	0.258728i	−0.229030	+	0.00999553i
$671$			13.8220i			0.533592i
$672$	−13.6138	−	3.60203i	−0.525163	−	0.138951i
$673$	−15.5979	+	15.5979i	−0.601256	+	0.601256i	−0.940646	−	0.339390i	$-0.889779\pi$
$673$	−15.5979	+	15.5979i	−0.601256	+	0.601256i	0.339390	+	0.940646i	$0.389779\pi$
$674$	−29.4730	+	13.1444i	−1.13526	+	0.506303i
$675$	−23.8776	+	0.802941i	−0.919048	+	0.0309052i
$676$	−1.33639	+	1.48797i	−0.0513998	+	0.0572296i
$677$	−9.60445	−	9.60445i	−0.369129	−	0.369129i	0.498031	−	0.867159i	$-0.334057\pi$
$677$	−9.60445	−	9.60445i	−0.369129	−	0.369129i	−0.867159	+	0.498031i	$0.834057\pi$
$678$	−2.57216	+	6.71329i	−0.0987831	+	0.257822i
$679$	−0.0403474			−0.00154839
$680$	15.7937	−	19.2077i	0.605661	−	0.736581i
$681$	−2.20367			−0.0844449
$682$	−6.46384	+	16.8705i	−0.247513	+	0.646006i
$683$	−26.8209	−	26.8209i	−1.02627	−	1.02627i	−0.999645	−	0.0266268i	$-0.991523\pi$
$683$	−26.8209	−	26.8209i	−1.02627	−	1.02627i	−0.0266268	−	0.999645i	$-0.508477\pi$
$684$	10.0601	−	11.2012i	0.384659	−	0.428287i
$685$	−1.43149	+	0.621332i	−0.0546946	+	0.0237399i
$686$	−23.6510	+	10.5479i	−0.902999	+	0.402721i
$687$	6.17126	−	6.17126i	0.235448	−	0.235448i
$688$	18.3356	−	22.7593i	0.699040	−	0.867689i
$689$		−	0.780599i		−	0.0297385i
$690$	2.44205	−	2.66493i	0.0929671	−	0.101452i
$691$		−	17.8773i		−	0.680085i	−0.940410	−	0.340043i	$-0.889558\pi$
$691$		−	17.8773i		−	0.680085i	0.940410	−	0.340043i	$-0.110442\pi$
$692$	37.7518	−	2.02603i	1.43511	−	0.0770182i
$693$	−6.60875	+	6.60875i	−0.251046	+	0.251046i
$694$	−0.927276	−	2.07918i	−0.0351989	−	0.0789247i
$695$	−8.83643	+	22.3902i	−0.335185	+	0.849307i
$696$	−6.45089	+	19.9818i	−0.244521	+	0.757409i
$697$	15.2682	+	15.2682i	0.578322	+	0.578322i
$698$	37.7225	+	14.4532i	1.42782	+	0.547060i
$699$	21.1486			0.799912
$700$	20.4881	+	17.1928i	0.774379	+	0.649828i
$701$	−5.70121			−0.215332			−0.107666	−	0.994187i	$-0.534338\pi$
$701$	−5.70121			−0.215332			−0.107666	+	0.994187i	$0.534338\pi$
$702$	−6.31011	−	2.41768i	−0.238160	−	0.0912494i
$703$	−14.2106	−	14.2106i	−0.535962	−	0.535962i
$704$	−10.6285	−	7.66106i	−0.400577	−	0.288737i
$705$	8.78138	−	22.2507i	0.330726	−	0.838009i
$706$	14.7017	+	32.9647i	0.553304	+	1.24064i
$707$	−15.7998	+	15.7998i	−0.594212	+	0.594212i
$708$	−0.807367	−	15.0440i	−0.0303427	−	0.565387i
$709$			16.2277i			0.609445i	0.952441	+	0.304723i	$0.0985638\pi$
$709$			16.2277i			0.609445i	−0.952441	+	0.304723i	$0.901436\pi$
$710$	−13.9066	+	15.1759i	−0.521906	+	0.569540i
$711$			31.1870i			1.16960i
$712$	−17.8420	−	34.8544i	−0.668657	−	1.30622i
$713$	6.77373	−	6.77373i	0.253678	−	0.253678i
$714$	−12.6420	+	5.63811i	−0.473116	+	0.211001i
$715$	3.35928	−	1.45808i	0.125630	−	0.0545289i
$716$	18.1587	+	16.3090i	0.678624	+	0.609494i
$717$	12.8920	+	12.8920i	0.481462	+	0.481462i
$718$	3.12981	−	8.16876i	0.116803	−	0.304855i
$719$	14.0007			0.522137			0.261068	−	0.965320i	$-0.415925\pi$
$719$	14.0007			0.522137			0.261068	+	0.965320i	$0.415925\pi$
$720$	5.06575	−	18.3997i	0.188789	−	0.685718i
$721$	48.5061			1.80646
$722$	3.31555	−	8.65355i	0.123392	−	0.322052i
$723$	−0.503190	−	0.503190i	−0.0187138	−	0.0187138i
$724$	19.1486	+	17.1980i	0.711653	+	0.639159i
$725$	27.2356	−	29.1311i	1.01151	−	1.08190i
$726$	−9.99933	+	4.45951i	−0.371110	+	0.165508i
$727$	−10.0262	+	10.0262i	−0.371852	+	0.371852i	−0.868151	−	0.496299i	$-0.834692\pi$
$727$	−10.0262	+	10.0262i	−0.371852	+	0.371852i	0.496299	+	0.868151i	$0.334692\pi$
$728$	3.44711	+	6.73394i	0.127758	+	0.249577i
$729$		−	9.17338i		−	0.339755i
$730$	−22.1481	+	0.966606i	−0.819737	+	0.0357757i
$731$		−	28.7284i		−	1.06256i
$732$	0.841937	+	15.6881i	0.0311189	+	0.579850i
$733$	−4.28988	+	4.28988i	−0.158450	+	0.158450i	−0.781880	−	0.623429i	$-0.785739\pi$
$733$	−4.28988	+	4.28988i	−0.158450	+	0.158450i	0.623429	+	0.781880i	$0.285739\pi$
$734$	−15.6613	−	35.1165i	−0.578069	−	1.29617i
$735$	−0.127258	−	0.293191i	−0.00469398	−	0.0108145i
$736$	3.49240	+	6.00540i	0.128732	+	0.221362i
$737$	2.17304	+	2.17304i	0.0800451	+	0.0800451i
$738$	15.4742	+	5.92885i	0.569613	+	0.218244i
$739$	41.3148			1.51979			0.759895	−	0.650045i	$-0.225250\pi$
$739$	41.3148			1.51979			0.759895	+	0.650045i	$0.225250\pi$
$740$	−24.1629	−	8.06842i	−0.888247	−	0.296601i
$741$	3.28377			0.120632
$742$	−2.75715	−	1.05639i	−0.101218	−	0.0387812i
$743$	0.849593	+	0.849593i	0.0311686	+	0.0311686i	0.722519	−	0.691351i	$-0.242984\pi$
$743$	0.849593	+	0.849593i	0.0311686	+	0.0311686i	−0.691351	+	0.722519i	$0.742984\pi$
$744$	−6.30890	+	19.5420i	−0.231296	+	0.716444i
$745$	27.3184	+	10.7814i	1.00087	+	0.394999i
$746$	10.7301	+	24.0596i	0.392858	+	0.880883i
$747$	14.0299	−	14.0299i	0.513326	−	0.513326i
$748$	−12.8601	+	0.690163i	−0.470210	+	0.0252349i
$749$			8.46280i			0.309224i
$750$	9.57228	−	11.1780i	0.349530	−	0.408163i
$751$		−	29.7557i		−	1.08580i	−0.839797	−	0.542900i	$-0.817326\pi$
$751$		−	29.7557i		−	1.08580i	0.839797	−	0.542900i	$-0.182674\pi$
$752$	35.8013	+	28.8428i	1.30554	+	1.05179i
$753$	3.07291	−	3.07291i	0.111983	−	0.111983i
$754$	10.3016	−	4.59434i	0.375164	−	0.167316i
$755$	42.6430	+	16.8293i	1.55194	+	0.612482i
$756$	−17.0790	+	19.0161i	−0.621156	+	0.691608i
$757$	−3.39816	−	3.39816i	−0.123508	−	0.123508i	0.642651	−	0.766159i	$-0.277835\pi$
$757$	−3.39816	−	3.39816i	−0.123508	−	0.123508i	−0.766159	+	0.642651i	$0.777835\pi$
$758$	−3.37788	+	8.81622i	−0.122690	+	0.320220i
$759$	−1.87199			−0.0679489
$760$	2.16614	+	22.2081i	0.0785743	+	0.805571i
$761$	−30.3122			−1.09882			−0.549409	−	0.835554i	$-0.685147\pi$
$761$	−30.3122			−1.09882			−0.549409	+	0.835554i	$0.685147\pi$
$762$	−1.63928	+	4.27851i	−0.0593850	+	0.154994i
$763$	7.75051	+	7.75051i	0.280587	+	0.280587i
$764$	−22.5320	+	25.0876i	−0.815178	+	0.907637i
$765$	−7.46909	−	17.2081i	−0.270045	−	0.622161i
$766$	−33.1116	+	14.7671i	−1.19637	+	0.533559i
$767$	−5.72277	+	5.72277i	−0.206637	+	0.206637i
$768$	−12.5301	−	8.04797i	−0.452143	−	0.290406i
$769$			33.2340i			1.19845i	0.800581	+	0.599225i	$0.204525\pi$
$769$			33.2340i			1.19845i	−0.800581	+	0.599225i	$0.795475\pi$
$770$	−0.603953	−	13.8385i	−0.0217650	−	0.498705i
$771$			11.4061i			0.410782i
$772$	−16.0333	+	0.860461i	−0.577051	+	0.0309687i

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.505980 + 1.32060i) q^{2} +(0.658144 + 0.658144i) q^{3} +(-1.48797 - 1.33639i) q^{4} +(0.820865 - 2.07995i) q^{5} +(-1.20215 + 0.536137i) q^{6} +(1.89124 - 1.89124i) q^{7} +(2.51772 - 1.28882i) q^{8} -2.13369i q^{9} +O(q^{10})\)	\(q+(-0.505980 + 1.32060i) q^{2} +(0.658144 + 0.658144i) q^{3} +(-1.48797 - 1.33639i) q^{4} +(0.820865 - 2.07995i) q^{5} +(-1.20215 + 0.536137i) q^{6} +(1.89124 - 1.89124i) q^{7} +(2.51772 - 1.28882i) q^{8} -2.13369i q^{9} +(2.33144 + 2.13645i) q^{10} -1.63773i q^{11} +(-0.0997585 - 1.85884i) q^{12} +(-0.707107 + 0.707107i) q^{13} +(1.54064 + 3.45450i) q^{14} +(1.90915 - 0.828657i) q^{15} +(0.428104 + 3.97702i) q^{16} +(2.78023 + 2.78023i) q^{17} +(2.81776 + 1.07961i) q^{18} -3.52807 q^{19} +(-4.00105 + 1.99790i) q^{20} +2.48941 q^{21} +(2.16278 + 0.828656i) q^{22} +(-0.868383 - 0.868383i) q^{23} +(2.50526 + 0.808792i) q^{24} +(-3.65236 - 3.41471i) q^{25} +(-0.576024 - 1.29159i) q^{26} +(3.37871 - 3.37871i) q^{27} +(-5.34155 + 0.286666i) q^{28} +7.97596i q^{29} +(0.128332 + 2.94051i) q^{30} +7.80040i q^{31} +(-5.46867 - 1.44694i) q^{32} +(1.07786 - 1.07786i) q^{33} +(-5.07832 + 2.26484i) q^{34} +(-2.38122 - 5.48613i) q^{35} +(-2.85145 + 3.17487i) q^{36} +(4.02786 + 4.02786i) q^{37} +(1.78513 - 4.65917i) q^{38} -0.930756 q^{39} +(-0.613974 - 6.29468i) q^{40} +5.49168 q^{41} +(-1.25959 + 3.28752i) q^{42} +(-5.16654 - 5.16654i) q^{43} +(-2.18865 + 2.43688i) q^{44} +(-4.43797 - 1.75148i) q^{45} +(1.58617 - 0.707403i) q^{46} +(8.12719 - 8.12719i) q^{47} +(-2.33570 + 2.89921i) q^{48} -0.153571i q^{49} +(6.35749 - 3.09553i) q^{50} +3.65959i q^{51} +(1.99713 - 0.107180i) q^{52} +(-0.551967 + 0.551967i) q^{53} +(2.75236 + 6.17148i) q^{54} +(-3.40638 - 1.34435i) q^{55} +(2.32414 - 7.19909i) q^{56} +(-2.32198 - 2.32198i) q^{57} +(-10.5331 - 4.03567i) q^{58} +8.09322 q^{59} +(-3.94817 - 1.31836i) q^{60} -8.43976 q^{61} +(-10.3012 - 3.94684i) q^{62} +(-4.03533 - 4.03533i) q^{63} +(4.67786 - 6.48981i) q^{64} +(0.890305 + 2.05118i) q^{65} +(0.878045 + 1.96879i) q^{66} +(-1.32687 + 1.32687i) q^{67} +(-0.421416 - 7.85239i) q^{68} -1.14304i q^{69} +(8.44984 - 0.368776i) q^{70} +6.50923i q^{71} +(-2.74996 - 5.37205i) q^{72} +(-4.95717 + 4.95717i) q^{73} +(-7.35721 + 3.28118i) q^{74} +(-0.156406 - 4.65115i) q^{75} +(5.24966 + 4.71489i) q^{76} +(-3.09733 - 3.09733i) q^{77} +(0.470943 - 1.22916i) q^{78} -14.6164 q^{79} +(8.62342 + 2.37417i) q^{80} -1.95373 q^{81} +(-2.77868 + 7.25231i) q^{82} +(6.57539 + 6.57539i) q^{83} +(-3.70417 - 3.32684i) q^{84} +(8.06494 - 3.50054i) q^{85} +(9.43710 - 4.20877i) q^{86} +(-5.24933 + 5.24933i) q^{87} +(-2.11074 - 4.12334i) q^{88} -13.8436i q^{89} +(4.55852 - 4.97457i) q^{90} +2.67462i q^{91} +(0.131626 + 2.45263i) q^{92} +(-5.13378 + 5.13378i) q^{93} +(6.62058 + 14.8450i) q^{94} +(-2.89607 + 7.33819i) q^{95} +(-2.64688 - 4.55146i) q^{96} +(-0.0106669 - 0.0106669i) q^{97} +(0.202807 + 0.0777041i) q^{98} -3.49440 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) \) 72 * q - 8 * q^6 - 12 * q^8	\( 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) \) 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more