LMFDB - Embedded newform 336.2.bs.a.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(19,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 0, 10]))

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

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

chi := DirichletCharacter("336.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bs (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	336.19
Dual form			336.2.bs.a.283.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35023 - 0.420569i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(1.64624 + 1.13573i) q^{4} +(2.34159 - 0.627426i) q^{5} +(0.755704 - 1.19537i) q^{6} +(2.44702 - 1.00602i) q^{7} +(-1.74516 - 2.22586i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-1.35023 - 0.420569i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(1.64624 + 1.13573i) q^{4} +(2.34159 - 0.627426i) q^{5} +(0.755704 - 1.19537i) q^{6} +(2.44702 - 1.00602i) q^{7} +(-1.74516 - 2.22586i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-3.42556 - 0.137628i) q^{10} +(1.14477 - 4.27235i) q^{11} +(-1.52311 + 1.29620i) q^{12} +(-2.40484 + 2.40484i) q^{13} +(-3.72715 + 0.329214i) q^{14} +2.42419i q^{15} +(1.42024 + 3.73938i) q^{16} +(-2.17215 + 1.25409i) q^{17} +(0.959049 + 1.03934i) q^{18} +(5.20109 - 1.39363i) q^{19} +(4.56741 + 1.62651i) q^{20} +(0.338402 + 2.62402i) q^{21} +(-3.34253 + 5.28720i) q^{22} +(2.78900 - 4.83069i) q^{23} +(2.60169 - 1.10960i) q^{24} +(0.759236 - 0.438345i) q^{25} +(4.25849 - 2.23569i) q^{26} +(0.707107 - 0.707107i) q^{27} +(5.17096 + 1.12301i) q^{28} +(0.962214 + 0.962214i) q^{29} +(1.01954 - 3.27321i) q^{30} +(-0.220090 - 0.381207i) q^{31} +(-0.344983 - 5.64633i) q^{32} +(3.83049 + 2.21153i) q^{33} +(3.46033 - 0.779773i) q^{34} +(5.09872 - 3.89100i) q^{35} +(-0.857824 - 1.80669i) q^{36} +(0.596202 + 2.22506i) q^{37} +(-7.60878 - 0.305697i) q^{38} +(-1.70048 - 2.94532i) q^{39} +(-5.48299 - 4.11708i) q^{40} -1.45203 q^{41} +(0.646661 - 3.68535i) q^{42} +(8.53016 + 8.53016i) q^{43} +(6.73681 - 5.73318i) q^{44} +(-2.34159 - 0.627426i) q^{45} +(-5.79743 + 5.34957i) q^{46} +(-3.59301 + 6.22327i) q^{47} +(-3.97954 + 0.404023i) q^{48} +(4.97586 - 4.92350i) q^{49} +(-1.20950 + 0.272556i) q^{50} +(-0.649165 - 2.42272i) q^{51} +(-6.69021 + 1.22771i) q^{52} +(1.48322 + 0.397428i) q^{53} +(-1.25214 + 0.657370i) q^{54} -10.7223i q^{55} +(-6.50969 - 3.69106i) q^{56} +5.38456i q^{57} +(-0.894533 - 1.70389i) q^{58} +(2.86721 + 0.768265i) q^{59} +(-2.75322 + 3.99081i) q^{60} +(0.575220 + 2.14675i) q^{61} +(0.136848 + 0.607280i) q^{62} +(-2.62219 - 0.352275i) q^{63} +(-1.90886 + 7.76893i) q^{64} +(-4.12228 + 7.14001i) q^{65} +(-4.24194 - 4.59706i) q^{66} +(-12.7211 - 3.40860i) q^{67} +(-5.00019 - 0.402434i) q^{68} +(3.94424 + 3.94424i) q^{69} +(-8.52088 + 3.10939i) q^{70} -9.28298 q^{71} +(0.398422 + 2.80022i) q^{72} +(-1.40733 - 2.43756i) q^{73} +(0.130779 - 3.25508i) q^{74} +(0.226904 + 0.846818i) q^{75} +(10.1450 + 3.61278i) q^{76} +(-1.49677 - 11.6062i) q^{77} +(1.05733 + 4.69203i) q^{78} +(-5.93453 - 3.42630i) q^{79} +(5.67179 + 7.86498i) q^{80} +(0.500000 + 0.866025i) q^{81} +(1.96057 + 0.610678i) q^{82} +(10.7397 + 10.7397i) q^{83} +(-2.42309 + 4.70411i) q^{84} +(-4.29942 + 4.29942i) q^{85} +(-7.93016 - 15.1052i) q^{86} +(-1.17847 + 0.680388i) q^{87} +(-11.5074 + 4.90782i) q^{88} +(-8.48740 + 14.7006i) q^{89} +(2.89781 + 1.83197i) q^{90} +(-3.46539 + 8.30402i) q^{91} +(10.0777 - 4.78494i) q^{92} +(0.425181 - 0.113927i) q^{93} +(7.46870 - 6.89174i) q^{94} +(11.3044 - 6.52659i) q^{95} +(5.54322 + 1.12815i) q^{96} +8.13728i q^{97} +(-8.78922 + 4.55517i) q^{98} +(-3.12758 + 3.12758i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{4} - 24 q^{8}+O(q^{10}) $ 128 * q + 4 * q^4 - 24 * q^8	$ 128 q + 4 q^{4} - 24 q^{8} + 36 q^{10} - 8 q^{11} - 32 q^{14} - 4 q^{16} + 4 q^{18} + 16 q^{22} + 16 q^{23} - 32 q^{28} + 32 q^{29} - 24 q^{35} - 16 q^{37} + 60 q^{40} - 20 q^{42} - 16 q^{43} - 12 q^{44} - 20 q^{46} - 32 q^{50} - 144 q^{52} - 16 q^{53} - 56 q^{56} - 40 q^{58} - 96 q^{59} - 24 q^{60} - 32 q^{64} - 72 q^{66} + 16 q^{67} - 60 q^{68} + 28 q^{70} + 128 q^{71} - 4 q^{72} - 72 q^{74} + 72 q^{78} - 36 q^{80} + 64 q^{81} - 60 q^{82} + 24 q^{84} - 44 q^{86} - 48 q^{88} - 8 q^{91} + 56 q^{92} + 36 q^{94} + 60 q^{96} + 148 q^{98} - 16 q^{99}+O(q^{100}) $ 128 * q + 4 * q^4 - 24 * q^8 + 36 * q^10 - 8 * q^11 - 32 * q^14 - 4 * q^16 + 4 * q^18 + 16 * q^22 + 16 * q^23 - 32 * q^28 + 32 * q^29 - 24 * q^35 - 16 * q^37 + 60 * q^40 - 20 * q^42 - 16 * q^43 - 12 * q^44 - 20 * q^46 - 32 * q^50 - 144 * q^52 - 16 * q^53 - 56 * q^56 - 40 * q^58 - 96 * q^59 - 24 * q^60 - 32 * q^64 - 72 * q^66 + 16 * q^67 - 60 * q^68 + 28 * q^70 + 128 * q^71 - 4 * q^72 - 72 * q^74 + 72 * q^78 - 36 * q^80 + 64 * q^81 - 60 * q^82 + 24 * q^84 - 44 * q^86 - 48 * q^88 - 8 * q^91 + 56 * q^92 + 36 * q^94 + 60 * q^96 + 148 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.35023	−	0.420569i	−0.954757	−	0.297387i
$2$	−1.35023	−	0.420569i	−0.954757	−	0.297387i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$	1.64624	+	1.13573i	0.823122	+	0.567865i
$5$	2.34159	−	0.627426i	1.04719	−	0.280594i	0.306100	−	0.952000i	$-0.400976\pi$
$5$	2.34159	−	0.627426i	1.04719	−	0.280594i	0.741090	+	0.671406i	$0.234309\pi$
$6$	0.755704	−	1.19537i	0.308515	−	0.488008i
$7$	2.44702	−	1.00602i	0.924888	−	0.380239i
$7$	2.44702	−	1.00602i	0.924888	−	0.380239i
$8$	−1.74516	−	2.22586i	−0.617006	−	0.786959i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−3.42556	−	0.137628i	−1.08326	−	0.0435219i
$11$	1.14477	−	4.27235i	0.345162	−	1.28816i	−0.547261	−	0.836962i	$-0.684329\pi$
$11$	1.14477	−	4.27235i	0.345162	−	1.28816i	0.892423	−	0.451200i	$-0.149004\pi$
$12$	−1.52311	+	1.29620i	−0.439684	+	0.374181i
$13$	−2.40484	+	2.40484i	−0.666983	+	0.666983i	−0.957017	−	0.290033i	$-0.906334\pi$
$13$	−2.40484	+	2.40484i	−0.666983	+	0.666983i	0.290033	+	0.957017i	$0.406334\pi$
$14$	−3.72715	+	0.329214i	−0.996122	+	0.0879860i
$15$			2.42419i			0.625923i
$16$	1.42024	+	3.73938i	0.355059	+	0.934844i
$17$	−2.17215	+	1.25409i	−0.526823	+	0.304162i	−0.739722	−	0.672913i	$-0.765043\pi$
$17$	−2.17215	+	1.25409i	−0.526823	+	0.304162i	0.212899	+	0.977074i	$0.431710\pi$
$18$	0.959049	+	1.03934i	0.226050	+	0.244974i
$19$	5.20109	−	1.39363i	1.19321	−	0.319720i	0.393057	−	0.919514i	$-0.371418\pi$
$19$	5.20109	−	1.39363i	1.19321	−	0.319720i	0.800154	+	0.599794i	$0.204751\pi$
$20$	4.56741	+	1.62651i	1.02130	+	0.363699i
$21$	0.338402	+	2.62402i	0.0738454	+	0.572608i
$22$	−3.34253	+	5.28720i	−0.712629	+	1.12724i
$23$	2.78900	−	4.83069i	0.581546	−	1.00727i	−0.413750	−	0.910391i	$-0.635781\pi$
$23$	2.78900	−	4.83069i	0.581546	−	1.00727i	0.995296	−	0.0968774i	$-0.0308855\pi$
$24$	2.60169	−	1.10960i	0.531068	−	0.226496i
$25$	0.759236	−	0.438345i	0.151847	−	0.0876690i
$26$	4.25849	−	2.23569i	0.835159	−	0.438455i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	5.17096	+	1.12301i	0.977220	+	0.212228i
$29$	0.962214	+	0.962214i	0.178679	+	0.178679i	0.790780	−	0.612101i	$-0.209675\pi$
$29$	0.962214	+	0.962214i	0.178679	+	0.178679i	−0.612101	+	0.790780i	$0.709675\pi$
$30$	1.01954	−	3.27321i	0.186141	−	0.597604i
$31$	−0.220090	−	0.381207i	−0.0395293	−	0.0684668i	0.845584	−	0.533843i	$-0.179253\pi$
$31$	−0.220090	−	0.381207i	−0.0395293	−	0.0684668i	−0.885113	+	0.465376i	$0.845919\pi$
$32$	−0.344983	−	5.64633i	−0.0609850	−	0.998139i
$33$	3.83049	+	2.21153i	0.666802	+	0.384978i
$34$	3.46033	−	0.779773i	0.593442	−	0.133730i
$35$	5.09872	−	3.89100i	0.861840	−	0.657700i
$36$	−0.857824	−	1.80669i	−0.142971	−	0.301115i
$37$	0.596202	+	2.22506i	0.0980150	+	0.365797i	0.997459	−	0.0712385i	$-0.0226951\pi$
$37$	0.596202	+	2.22506i	0.0980150	+	0.365797i	−0.899444	+	0.437035i	$0.856028\pi$
$38$	−7.60878	−	0.305697i	−1.23431	−	0.0495906i
$39$	−1.70048	−	2.94532i	−0.272295	−	0.471628i
$40$	−5.48299	−	4.11708i	−0.866937	−	0.650967i
$41$	−1.45203			−0.226769			−0.113384	−	0.993551i	$-0.536169\pi$
$41$	−1.45203			−0.226769			−0.113384	+	0.993551i	$0.536169\pi$
$42$	0.646661	−	3.68535i	0.0997819	−	0.568662i
$43$	8.53016	+	8.53016i	1.30084	+	1.30084i	0.927828	+	0.373009i	$0.121674\pi$
$43$	8.53016	+	8.53016i	1.30084	+	1.30084i	0.373009	+	0.927828i	$0.378326\pi$
$44$	6.73681	−	5.73318i	1.01561	−	0.864309i
$45$	−2.34159	−	0.627426i	−0.349063	−	0.0935312i
$46$	−5.79743	+	5.34957i	−0.854784	+	0.788752i
$47$	−3.59301	+	6.22327i	−0.524094	+	0.907757i	0.475513	+	0.879709i	$0.342263\pi$
$47$	−3.59301	+	6.22327i	−0.524094	+	0.907757i	−0.999607	+	0.0280482i	$0.991071\pi$
$48$	−3.97954	+	0.404023i	−0.574398	+	0.0583156i
$49$	4.97586	−	4.92350i	0.710837	−	0.703357i
$50$	−1.20950	+	0.272556i	−0.171049	+	0.0385452i
$51$	−0.649165	−	2.42272i	−0.0909013	−	0.339248i
$52$	−6.69021	+	1.22771i	−0.927765	+	0.170252i
$53$	1.48322	+	0.397428i	0.203736	+	0.0545910i	0.359244	−	0.933244i	$-0.383035\pi$
$53$	1.48322	+	0.397428i	0.203736	+	0.0545910i	−0.155508	+	0.987835i	$0.549701\pi$
$54$	−1.25214	+	0.657370i	−0.170395	+	0.0894567i
$55$		−	10.7223i		−	1.44580i
$56$	−6.50969	−	3.69106i	−0.869894	−	0.493239i
$57$			5.38456i			0.713202i
$58$	−0.894533	−	1.70389i	−0.117458	−	0.223731i
$59$	2.86721	+	0.768265i	0.373278	+	0.100020i	0.440581	−	0.897713i	$-0.354773\pi$
$59$	2.86721	+	0.768265i	0.373278	+	0.100020i	−0.0673024	+	0.997733i	$0.521439\pi$
$60$	−2.75322	+	3.99081i	−0.355439	+	0.515211i
$61$	0.575220	+	2.14675i	0.0736494	+	0.274863i	0.992924	−	0.118754i	$-0.0378901\pi$
$61$	0.575220	+	2.14675i	0.0736494	+	0.274863i	−0.919274	+	0.393618i	$0.871223\pi$
$62$	0.136848	+	0.607280i	0.0173798	+	0.0771247i
$63$	−2.62219	−	0.352275i	−0.330365	−	0.0443825i
$64$	−1.90886	+	7.76893i	−0.238608	+	0.971116i
$65$	−4.12228	+	7.14001i	−0.511306	+	0.885609i
$66$	−4.24194	−	4.59706i	−0.522146	−	0.565859i
$67$	−12.7211	−	3.40860i	−1.55412	−	0.416426i	−0.623327	−	0.781962i	$-0.714219\pi$
$67$	−12.7211	−	3.40860i	−1.55412	−	0.416426i	−0.930797	+	0.365535i	$0.880886\pi$
$68$	−5.00019	−	0.402434i	−0.606362	−	0.0488023i
$69$	3.94424	+	3.94424i	0.474831	+	0.474831i
$70$	−8.52088	+	3.10939i	−1.01844	+	0.371643i
$71$	−9.28298			−1.10169			−0.550844	−	0.834608i	$-0.685694\pi$
$71$	−9.28298			−1.10169			−0.550844	+	0.834608i	$0.685694\pi$
$72$	0.398422	+	2.80022i	0.0469545	+	0.330010i
$73$	−1.40733	−	2.43756i	−0.164715	−	0.285295i	0.771839	−	0.635818i	$-0.219337\pi$
$73$	−1.40733	−	2.43756i	−0.164715	−	0.285295i	−0.936554	+	0.350523i	$0.886004\pi$
$74$	0.130779	−	3.25508i	0.0152028	−	0.378396i
$75$	0.226904	+	0.846818i	0.0262006	+	0.0977821i
$76$	10.1450	+	3.61278i	1.16372	+	0.414414i
$77$	−1.49677	−	11.6062i	−0.170573	−	1.32265i
$78$	1.05733	+	4.69203i	0.119719	+	0.531267i
$79$	−5.93453	−	3.42630i	−0.667687	−	0.385489i	0.127513	−	0.991837i	$-0.459301\pi$
$79$	−5.93453	−	3.42630i	−0.667687	−	0.385489i	−0.795200	+	0.606348i	$0.792634\pi$
$80$	5.67179	+	7.86498i	0.634125	+	0.879331i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	1.96057	+	0.610678i	0.216509	+	0.0674381i
$83$	10.7397	+	10.7397i	1.17883	+	1.17883i	0.980042	+	0.198792i	$0.0637019\pi$
$83$	10.7397	+	10.7397i	1.17883	+	1.17883i	0.198792	+	0.980042i	$0.436298\pi$
$84$	−2.42309	+	4.70411i	−0.264380	+	0.513261i
$85$	−4.29942	+	4.29942i	−0.466338	+	0.466338i
$86$	−7.93016	−	15.1052i	−0.855131	−	1.62884i
$87$	−1.17847	+	0.680388i	−0.126345	+	0.0729453i
$88$	−11.5074	+	4.90782i	−1.22670	+	0.523176i
$89$	−8.48740	+	14.7006i	−0.899662	+	1.55826i	−0.0717366	+	0.997424i	$0.522854\pi$
$89$	−8.48740	+	14.7006i	−0.899662	+	1.55826i	−0.827926	+	0.560838i	$0.810479\pi$
$90$	2.89781	+	1.83197i	0.305455	+	0.193106i
$91$	−3.46539	+	8.30402i	−0.363272	+	0.870498i
$92$	10.0777	−	4.78494i	1.05068	−	0.498865i
$93$	0.425181	−	0.113927i	0.0440892	−	0.0118137i
$94$	7.46870	−	6.89174i	0.770337	−	0.710829i
$95$	11.3044	−	6.52659i	1.15981	−	0.669615i
$96$	5.54322	+	1.12815i	0.565752	+	0.115141i
$97$			8.13728i			0.826216i	0.910682	+	0.413108i	$0.135557\pi$
$97$			8.13728i			0.826216i	−0.910682	+	0.413108i	$0.864443\pi$
$98$	−8.78922	+	4.55517i	−0.887846	+	0.460142i
$99$	−3.12758	+	3.12758i	−0.314333	+	0.314333i
$100$	1.74773	+	0.140664i	0.174773	+	0.0140664i
$101$	3.27581	−	12.2255i	0.325955	−	1.21648i	−0.587394	−	0.809301i	$-0.699846\pi$
$101$	3.27581	−	12.2255i	0.325955	−	1.21648i	0.913348	−	0.407179i	$-0.133487\pi$
$102$	−0.142397	+	3.54424i	−0.0140994	+	0.350932i
$103$	−9.03340	−	5.21544i	−0.890087	−	0.513892i	−0.0161163	−	0.999870i	$-0.505130\pi$
$103$	−9.03340	−	5.21544i	−0.890087	−	0.513892i	−0.873971	+	0.485978i	$0.838464\pi$
$104$	9.54965	+	1.15601i	0.936421	+	0.113356i
$105$	2.43878	+	5.93205i	0.238000	+	0.578909i
$106$	−1.83555	−	1.16042i	−0.178284	−	0.112710i
$107$	−18.6315	+	4.99229i	−1.80117	+	0.482623i	−0.994160	−	0.107912i	$-0.965583\pi$
$107$	−18.6315	+	4.99229i	−1.80117	+	0.482623i	−0.807012	+	0.590535i	$0.798917\pi$
$108$	1.96715	−	0.360988i	0.189289	−	0.0347361i
$109$	3.78255	−	14.1167i	0.362303	−	1.35213i	−0.508737	−	0.860922i	$-0.669888\pi$
$109$	3.78255	−	14.1167i	0.362303	−	1.35213i	0.871040	−	0.491211i	$-0.163446\pi$
$110$	−4.50948	+	14.4776i	−0.429962	+	1.38039i
$111$	−2.30355			−0.218643
$112$	7.23723	+	7.72156i	0.683854	+	0.729619i
$113$	−10.2795			−0.967017			−0.483508	−	0.875340i	$-0.660638\pi$
$113$	−10.2795			−0.967017			−0.483508	+	0.875340i	$0.660638\pi$
$114$	2.26458	−	7.27040i	0.212097	−	0.680935i
$115$	3.49978	−	13.0614i	0.326356	−	1.21798i
$116$	0.491224	+	2.67685i	0.0456090	+	0.248540i
$117$	3.28508	−	0.880233i	0.303705	−	0.0813776i
$118$	−3.54828	−	2.24319i	−0.326646	−	0.206503i
$119$	−4.05366	+	5.25401i	−0.371599	+	0.481634i
$120$	5.39589	−	4.23059i	0.492575	−	0.386198i
$121$	−7.41621	−	4.28175i	−0.674201	−	0.389250i
$122$	0.126177	−	3.14053i	0.0114235	−	0.284330i
$123$	0.375813	−	1.40255i	0.0338859	−	0.126464i
$124$	0.0706263	−	0.877522i	0.00634242	−	0.0788038i
$125$	−7.06801	+	7.06801i	−0.632182	+	0.632182i
$126$	3.39241	+	1.57847i	0.302220	+	0.140621i
$127$		−	13.5296i		−	1.20056i	−0.799789	−	0.600281i	$-0.795055\pi$
$127$		−	13.5296i		−	1.20056i	0.799789	−	0.600281i	$-0.204945\pi$
$128$	5.84477	−	9.68704i	0.516610	−	0.856221i
$129$	−10.4473	+	6.03173i	−0.919831	+	0.531064i
$130$	8.56890	−	7.90695i	0.751542	−	0.693485i
$131$	11.8234	−	3.16808i	1.03302	−	0.276796i	0.297800	−	0.954628i	$-0.403747\pi$
$131$	11.8234	−	3.16808i	1.03302	−	0.276796i	0.735217	+	0.677832i	$0.237080\pi$
$132$	3.79421	+	7.99112i	0.330244	+	0.695537i
$133$	11.3252	−	8.64262i	0.982017	−	0.749410i
$134$	15.7428	+	9.95247i	1.35997	+	0.859762i
$135$	1.21209	−	2.09941i	0.104320	−	0.180688i
$136$	6.58216	+	2.64630i	0.564416	+	0.226919i
$137$	−11.5639	+	6.67643i	−0.987972	+	0.570406i	−0.904667	−	0.426118i	$-0.859881\pi$
$137$	−11.5639	+	6.67643i	−0.987972	+	0.570406i	−0.0833044	+	0.996524i	$0.526547\pi$
$138$	−3.66681	−	6.98446i	−0.312139	−	0.594556i
$139$	12.2683	−	12.2683i	1.04058	−	1.04058i	0.0414400	−	0.999141i	$-0.486805\pi$
$139$	12.2683	−	12.2683i	1.04058	−	1.04058i	0.999141	−	0.0414400i	$-0.0131946\pi$
$140$	12.8129	−	0.614779i	1.08288	−	0.0519583i
$141$	−5.08128	−	5.08128i	−0.427921	−	0.427921i
$142$	12.5342	+	3.90413i	1.05184	+	0.327628i
$143$	7.52133	+	13.0273i	0.628966	+	1.08940i
$144$	0.639726	−	3.94851i	0.0533105	−	0.329043i
$145$	2.85683	+	1.64939i	0.237246	+	0.136974i
$146$	0.875053	+	3.88315i	0.0724199	+	0.321371i
$147$	3.46789	+	6.08060i	0.286027	+	0.501520i
$148$	−1.54557	+	4.34011i	−0.127045	+	0.356755i
$149$	0.848717	+	3.16745i	0.0695296	+	0.259488i	0.991937	−	0.126730i	$-0.0404481\pi$
$149$	0.848717	+	3.16745i	0.0695296	+	0.259488i	−0.922408	+	0.386218i	$0.873781\pi$
$150$	0.0497723	−	1.23883i	0.00406389	−	0.101150i
$151$	−12.0326	−	20.8411i	−0.979198	−	1.69602i	−0.665322	−	0.746557i	$-0.731706\pi$
$151$	−12.0326	−	20.8411i	−0.979198	−	1.69602i	−0.313876	−	0.949464i	$-0.601628\pi$
$152$	−12.1787	−	9.14477i	−0.987824	−	0.741739i
$153$	2.50818			0.202774
$154$	−2.86022	+	16.3006i	−0.230483	+	1.31354i
$155$	−0.754539	−	0.754539i	−0.0606060	−	0.0606060i
$156$	0.545679	−	6.78000i	0.0436893	−	0.542834i
$157$	3.20431	+	0.858593i	0.255732	+	0.0685232i	0.384407	−	0.923164i	$-0.374406\pi$
$157$	3.20431	+	0.858593i	0.255732	+	0.0685232i	−0.128675	+	0.991687i	$0.541073\pi$
$158$	6.57199	+	7.12217i	0.522839	+	0.566610i
$159$	−0.767773	+	1.32982i	−0.0608883	+	0.105462i
$160$	−4.35046	−	13.0049i	−0.343934	−	1.02813i
$161$	1.96499	−	14.6266i	0.154863	−	1.15274i
$162$	−0.310892	−	1.37962i	−0.0244260	−	0.108393i
$163$	2.69070	+	10.0418i	0.210752	+	0.786538i	0.987619	+	0.156873i	$0.0501413\pi$
$163$	2.69070	+	10.0418i	0.210752	+	0.786538i	−0.776867	+	0.629665i	$0.783192\pi$
$164$	−2.39039	−	1.64911i	−0.186658	−	0.128774i
$165$	10.3570	+	2.77515i	0.806290	+	0.216045i
$166$	−9.98428	−	19.0178i	−0.774930	−	1.47607i
$167$		−	0.0908142i		−	0.00702741i	−0.999994	−	0.00351371i	$-0.998882\pi$
$167$		−	0.0908142i		−	0.00702741i	0.999994	−	0.00351371i	$-0.00111845\pi$
$168$	5.25013	−	5.33256i	0.405056	−	0.411416i
$169$			1.43347i			0.110267i
$170$	7.61341	−	3.99701i	0.583922	−	0.306557i
$171$	−5.20109	−	1.39363i	−0.397737	−	0.106573i
$172$	4.35477	+	23.7307i	0.332048	+	1.80945i
$173$	−2.46655	−	9.20529i	−0.187528	−	0.699865i	−0.994075	−	0.108695i	$-0.965333\pi$
$173$	−2.46655	−	9.20529i	−0.187528	−	0.699865i	0.806547	−	0.591170i	$-0.201334\pi$
$174$	1.87735	−	0.423054i	0.142322	−	0.0320717i
$175$	1.41689	−	1.83645i	0.107107	−	0.138822i
$176$	17.6018	−	1.78702i	1.32678	−	0.134702i
$177$	−1.48417	+	2.57067i	−0.111557	+	0.193223i
$178$	17.6426	−	16.2797i	1.32237	−	1.22021i
$179$	−2.76843	−	0.741799i	−0.206922	−	0.0554447i	0.153869	−	0.988091i	$-0.450827\pi$
$179$	−2.76843	−	0.741799i	−0.206922	−	0.0554447i	−0.360791	+	0.932647i	$0.617493\pi$
$180$	−3.14224	−	3.69230i	−0.234208	−	0.275208i
$181$	12.5911	+	12.5911i	0.935890	+	0.935890i	0.998065	−	0.0621753i	$-0.0198038\pi$
$181$	12.5911	+	12.5911i	0.935890	+	0.935890i	−0.0621753	+	0.998065i	$0.519804\pi$
$182$	8.17149	−	9.75490i	0.605711	−	0.723082i
$183$	−2.22248			−0.164290
$184$	−15.6196	+	2.22240i	−1.15150	+	0.163837i
$185$	2.79212	+	4.83609i	0.205280	+	0.355556i
$186$	−0.622007	−	0.0249903i	−0.0456077	−	0.00183238i
$187$	2.87130	+	10.7158i	0.209970	+	0.783619i
$188$	−12.9829	+	6.16434i	−0.946876	+	0.449580i
$189$	1.01895	−	2.44167i	0.0741174	−	0.177605i
$190$	−18.0084	+	4.05813i	−1.30647	+	0.294408i
$191$	4.18475	+	2.41607i	0.302798	+	0.174820i	0.643699	−	0.765279i	$-0.277399\pi$
$191$	4.18475	+	2.41607i	0.302798	+	0.174820i	−0.340901	+	0.940099i	$0.610732\pi$
$192$	−7.01016	−	3.85456i	−0.505915	−	0.278179i
$193$	10.1698	+	17.6147i	0.732040	+	1.26793i	0.956010	+	0.293335i	$0.0947650\pi$
$193$	10.1698	+	17.6147i	0.732040	+	1.26793i	−0.223970	+	0.974596i	$0.571902\pi$
$194$	3.42229	−	10.9872i	0.245706	−	0.788835i
$195$	−5.82979	−	5.82979i	−0.417480	−	0.417480i
$196$	13.7832	−	2.45405i	0.984517	−	0.175290i
$197$	−14.1651	+	14.1651i	−1.00922	+	1.00922i	−0.00926226	+	0.999957i	$0.502948\pi$
$197$	−14.1651	+	14.1651i	−1.00922	+	1.00922i	−0.999957	+	0.00926226i	$0.997052\pi$
$198$	5.53831	−	2.90759i	0.393591	−	0.206633i
$199$	−20.9977	+	12.1230i	−1.48849	+	0.859378i	−0.999914	−	0.0131450i	$-0.995816\pi$
$199$	−20.9977	+	12.1230i	−1.48849	+	0.859378i	−0.488573	+	0.872523i	$0.662482\pi$
$200$	−2.30068	−	0.924969i	−0.162683	−	0.0654052i
$201$	6.58490	−	11.4054i	0.464463	−	0.804474i
$202$	−9.56475	+	15.1295i	−0.672973	+	1.06451i
$203$	3.32257	+	1.38656i	0.233198	+	0.0973172i
$204$	1.68287	−	4.72566i	0.117824	−	0.330862i
$205$	−3.40005	+	0.911041i	−0.237470	+	0.0636299i
$206$	10.0037	+	10.8412i	0.696992	+	0.755343i
$207$	−4.83069	+	2.78900i	−0.335756	+	0.193849i
$208$	−12.4081	−	5.57716i	−0.860344	−	0.386706i
$209$		−	23.8163i		−	1.64740i
$210$	−0.798076	−	9.03531i	−0.0550725	−	0.623495i
$211$	12.7220	−	12.7220i	0.875821	−	0.875821i	−0.117278	−	0.993099i	$-0.537417\pi$
$211$	12.7220	−	12.7220i	0.875821	−	0.875821i	0.993099	+	0.117278i	$0.0374170\pi$
$212$	1.99038	+	2.33880i	0.136700	+	0.160630i
$213$	2.40261	−	8.96667i	0.164624	−	0.614386i
$214$	27.2564	+	1.09508i	1.86321	+	0.0748579i
$215$	25.3261	+	14.6221i	1.72723	+	0.997216i
$216$	−2.80793	−	0.339906i	−0.191055	−	0.0231276i
$217$	−0.922066	−	0.711408i	−0.0625939	−	0.0482935i
$218$	−11.0444	+	17.4700i	−0.748018	+	1.18321i
$219$	2.71875	−	0.728486i	0.183716	−	0.0492265i
$220$	12.1777	−	17.6516i	0.821019	−	1.19007i
$221$	2.20778	−	8.23956i	0.148512	−	0.554253i
$222$	3.11032	+	0.968800i	0.208751	+	0.0650216i
$223$	−1.89320			−0.126778			−0.0633891	−	0.997989i	$-0.520191\pi$
$223$	−1.89320			−0.126778			−0.0633891	+	0.997989i	$0.520191\pi$
$224$	−6.52449	−	13.4696i	−0.435936	−	0.899978i
$225$	−0.876690			−0.0584460
$226$	13.8797	+	4.32325i	0.923266	+	0.287578i
$227$	−4.56253	+	17.0276i	−0.302825	+	1.13016i	0.631976	+	0.774988i	$0.282244\pi$
$227$	−4.56253	+	17.0276i	−0.302825	+	1.13016i	−0.934801	+	0.355172i	$0.884422\pi$
$228$	−6.11540	+	8.86430i	−0.405003	+	0.587053i
$229$	−21.0784	+	5.64795i	−1.39290	+	0.373227i	−0.875791	−	0.482691i	$-0.839660\pi$
$229$	−21.0784	+	5.64795i	−1.39290	+	0.373227i	−0.517112	+	0.855918i	$0.672993\pi$
$230$	−10.2187	+	16.1639i	−0.673802	+	1.06582i
$231$	11.5981	+	1.55814i	0.763101	+	0.102518i
$232$	0.462535	−	3.82096i	0.0303669	−	0.250858i
$233$	−9.33083	−	5.38716i	−0.611283	−	0.352924i	0.162184	−	0.986760i	$-0.448146\pi$
$233$	−9.33083	−	5.38716i	−0.611283	−	0.352924i	−0.773467	+	0.633836i	$0.781479\pi$
$234$	−4.80581	−	0.193082i	−0.314165	−	0.0126222i
$235$	−4.50869	+	16.8267i	−0.294115	+	1.09765i
$236$	3.84758	+	4.52112i	0.250456	+	0.294300i
$237$	4.84552	−	4.84552i	0.314751	−	0.314751i
$238$	7.68305	−	5.38928i	0.498018	−	0.349335i
$239$		−	1.65026i		−	0.106746i	−0.998575	−	0.0533732i	$-0.983003\pi$
$239$		−	1.65026i		−	0.106746i	0.998575	−	0.0533732i	$-0.0169973\pi$
$240$	−9.06495	+	3.44292i	−0.585140	+	0.222240i
$241$	15.3990	−	8.89064i	0.991940	−	0.572697i	0.0860861	−	0.996288i	$-0.472564\pi$
$241$	15.3990	−	8.89064i	0.991940	−	0.572697i	0.905854	+	0.423591i	$0.139231\pi$
$242$	8.21282	+	8.90037i	0.527940	+	0.572138i
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	−1.49118	+	4.18737i	−0.0954627	+	0.268069i
$245$	8.56227	−	14.6508i	0.547023	−	0.936004i
$246$	−1.09730	+	1.73571i	−0.0699615	+	0.110665i
$247$	−9.15634	+	15.8592i	−0.582604	+	1.00910i
$248$	−0.464420	+	1.15515i	−0.0294907	+	0.0733523i
$249$	−13.1534	+	7.59411i	−0.833562	+	0.481257i
$250$	12.5160	−	6.57086i	0.791583	−	0.415578i
$251$	4.32903	−	4.32903i	0.273246	−	0.273246i	−0.557159	−	0.830406i	$-0.688109\pi$
$251$	4.32903	−	4.32903i	0.273246	−	0.273246i	0.830406	+	0.557159i	$0.188109\pi$
$252$	−3.91668	−	3.55803i	−0.246728	−	0.224135i
$253$	−17.4456	−	17.4456i	−1.09680	−	1.09680i
$254$	−5.69015	+	18.2681i	−0.357032	+	1.14624i
$255$	−3.04015	−	5.26570i	−0.190382	−	0.329751i
$256$	−11.9659	+	10.6216i	−0.747866	+	0.663850i
$257$	4.80107	+	2.77190i	0.299483	+	0.172906i	0.642210	−	0.766528i	$-0.278018\pi$
$257$	4.80107	+	2.77190i	0.299483	+	0.172906i	−0.342728	+	0.939435i	$0.611351\pi$
$258$	16.6430	−	3.75043i	1.03615	−	0.233492i
$259$	3.69737	+	4.84498i	0.229743	+	0.301052i
$260$	−14.8954	+	7.07239i	−0.923774	+	0.438611i
$261$	−0.352195	−	1.31441i	−0.0218003	−	0.0813599i
$262$	−17.2967	−	0.694929i	−1.06860	−	0.0429329i
$263$	6.03539	+	10.4536i	0.372158	+	0.644596i	0.989897	−	0.141787i	$-0.0452847\pi$
$263$	6.03539	+	10.4536i	0.372158	+	0.644596i	−0.617739	+	0.786383i	$0.711951\pi$
$264$	−1.76225	−	12.3856i	−0.108459	−	0.762279i
$265$	3.72245			0.228668
$266$	−18.9264	+	6.90652i	−1.16045	+	0.423466i
$267$	−12.0030	−	12.0030i	−0.734571	−	0.734571i
$268$	−17.0707	−	20.0591i	−1.04276	−	1.22530i
$269$	31.3763	+	8.40725i	1.91305	+	0.512599i	0.992549	+	0.121849i	$0.0388825\pi$
$269$	31.3763	+	8.40725i	1.91305	+	0.512599i	0.920497	+	0.390750i	$0.127784\pi$
$270$	−2.51955	+	2.32492i	−0.153335	+	0.141490i
$271$	−7.75611	+	13.4340i	−0.471150	+	0.816056i	−0.999455	−	0.0329982i	$-0.989494\pi$
$271$	−7.75611	+	13.4340i	−0.471150	+	0.816056i	0.528305	+	0.849055i	$0.322828\pi$
$272$	−7.77448	−	6.34137i	−0.471397	−	0.384502i
$273$	−7.12416	−	5.49655i	−0.431174	−	0.332666i
$274$	18.4218	−	4.15130i	1.11290	−	0.250789i
$275$	−1.00361	−	3.74553i	−0.0605201	−	0.225864i
$276$	2.01359	+	10.9728i	0.121204	+	0.660483i
$277$	−23.6957	−	6.34925i	−1.42374	−	0.381490i	−0.536930	−	0.843627i	$-0.680416\pi$
$277$	−23.6957	−	6.34925i	−1.42374	−	0.381490i	−0.886808	+	0.462137i	$0.847083\pi$
$278$	−21.7246	+	11.4053i	−1.30296	+	0.684047i
$279$			0.440180i			0.0263529i
$280$	−17.5589	−	4.55860i	−1.04934	−	0.272428i
$281$		−	4.94605i		−	0.295056i	−0.989058	−	0.147528i	$-0.952868\pi$
$281$		−	4.94605i		−	0.295056i	0.989058	−	0.147528i	$-0.0471317\pi$
$282$	4.72387	+	8.99792i	0.281302	+	0.535818i
$283$	−12.9245	−	3.46312i	−0.768285	−	0.205861i	−0.146671	−	0.989185i	$-0.546856\pi$
$283$	−12.9245	−	3.46312i	−0.768285	−	0.205861i	−0.621614	+	0.783324i	$0.713523\pi$
$284$	−15.2821	−	10.5430i	−0.906823	−	0.625609i
$285$	3.37841	+	12.6084i	0.200120	+	0.746858i
$286$	−4.67664	−	20.7531i	−0.276536	−	1.22716i
$287$	−3.55315	+	1.46077i	−0.209736	+	0.0862263i
$288$	−2.52440	+	5.06235i	−0.148752	+	0.298302i
$289$	−5.35452	+	9.27429i	−0.314972	+	0.545547i
$290$	−3.16369	−	3.42855i	−0.185778	−	0.201331i
$291$	−7.86001	−	2.10608i	−0.460762	−	0.123461i
$292$	0.451607	−	5.61116i	0.0264283	−	0.328368i
$293$	−12.6321	−	12.6321i	−0.737977	−	0.737977i	0.234209	−	0.972186i	$-0.424750\pi$
$293$	−12.6321	−	12.6321i	−0.737977	−	0.737977i	−0.972186	+	0.234209i	$0.924750\pi$
$294$	−2.12514	−	9.66870i	−0.123940	−	0.563890i
$295$	7.19584			0.418958
$296$	3.91219	−	5.21013i	0.227391	−	0.302833i
$297$	−2.21153	−	3.83049i	−0.128326	−	0.222267i
$298$	0.186169	−	4.63374i	0.0107845	−	0.268425i
$299$	4.90994	+	18.3241i	0.283949	+	1.05971i
$300$	−0.588216	+	1.65177i	−0.0339607	+	0.0953650i
$301$	29.4550	+	12.2920i	1.69776	+	0.708500i
$302$	7.48167	+	33.2007i	0.430522	+	1.91049i
$303$	10.9611	+	6.32837i	0.629696	+	0.363555i
$304$	12.5981	+	17.4695i	0.722549	+	1.00195i
$305$	2.69386	+	4.66589i	0.154250	+	0.267168i
$306$	−3.38662	−	1.05486i	−0.193600	−	0.0603025i
$307$	14.9745	+	14.9745i	0.854642	+	0.854642i	0.990701	−	0.136059i	$-0.0434435\pi$
$307$	14.9745	+	14.9745i	0.854642	+	0.854642i	−0.136059	+	0.990701i	$0.543444\pi$
$308$	10.7175	−	20.8066i	0.610684	−	1.18557i
$309$	7.37574	−	7.37574i	0.419591	−	0.419591i
$310$	0.701466	+	1.33614i	0.0398406	+	0.0758875i
$311$	−14.3950	+	8.31098i	−0.816267	+	0.471272i	−0.849128	−	0.528188i	$-0.822872\pi$
$311$	−14.3950	+	8.31098i	−0.816267	+	0.471272i	0.0328602	+	0.999460i	$0.489538\pi$
$312$	−3.58825	+	8.92506i	−0.203145	+	0.505282i
$313$	15.8923	−	27.5263i	0.898288	−	1.55588i	0.0686069	−	0.997644i	$-0.478145\pi$
$313$	15.8923	−	27.5263i	0.898288	−	1.55588i	0.829681	−	0.558237i	$-0.188522\pi$
$314$	−3.96546	−	2.50693i	−0.223784	−	0.141474i
$315$	−6.36112	+	0.820350i	−0.358409	+	0.0462215i
$316$	−5.87833	−	12.3805i	−0.330682	−	0.696460i
$317$	−8.91556	+	2.38892i	−0.500748	+	0.134175i	−0.500347	−	0.865825i	$-0.666794\pi$
$317$	−8.91556	+	2.38892i	−0.500748	+	0.134175i	−0.000400866		1.00000i	$0.500128\pi$
$318$	1.59595	−	1.47266i	0.0894965	−	0.0825829i
$319$	5.21243	−	3.00940i	0.291840	−	0.168494i
$320$	0.404666	+	19.3893i	0.0226215	+	1.08389i
$321$		−	19.2887i		−	1.07659i
$322$	−8.80468	+	18.9229i	−0.490666	+	1.05453i
$323$	−9.54979	+	9.54979i	−0.531365	+	0.531365i
$324$	−0.160449	+	1.99355i	−0.00891381	+	0.110753i
$325$	−0.771692	+	2.87999i	−0.0428058	+	0.159753i
$326$	0.590216	−	14.6904i	0.0326890	−	0.813628i
$327$	12.6567	+	7.30733i	0.699916	+	0.404096i
$328$	2.53402	+	3.23201i	0.139918	+	0.178458i
$329$	−2.53145	+	18.8431i	−0.139564	+	1.03885i
$330$	−12.8172	−	8.10291i	−0.705562	−	0.446051i
$331$	−14.5596	+	3.90124i	−0.800270	+	0.214432i	−0.635703	−	0.771934i	$-0.719290\pi$
$331$	−14.5596	+	3.90124i	−0.800270	+	0.214432i	−0.164568	+	0.986366i	$0.552623\pi$
$332$	5.48277	+	29.8775i	0.300906	+	1.63974i
$333$	0.596202	−	2.22506i	0.0326717	−	0.121932i
$334$	−0.0381936	+	0.122620i	−0.00208986	+	0.00670947i
$335$	−31.9261			−1.74431
$336$	−9.33159	+	4.99214i	−0.509080	+	0.272344i
$337$	11.2973			0.615405			0.307703	−	0.951483i	$-0.400440\pi$
$337$	11.2973			0.615405			0.307703	+	0.951483i	$0.400440\pi$
$338$	0.602872	−	1.93551i	0.0327919	−	0.105278i
$339$	2.66054	−	9.92926i	0.144501	−	0.539284i
$340$	−11.9609	+	2.19492i	−0.648670	+	0.119036i
$341$	−1.88060	+	0.503906i	−0.101840	+	0.0272880i
$342$	6.43655	+	4.06913i	0.348049	+	0.220033i
$343$	7.22292	−	17.0537i	0.390001	−	0.920815i
$344$	4.10044	−	33.8733i	0.221081	−	1.82633i
$345$	11.7105	+	6.76106i	0.630472	+	0.364003i
$346$	−0.541047	+	13.4666i	−0.0290868	+	0.723969i
$347$	6.50895	−	24.2917i	0.349419	−	1.30405i	−0.537945	−	0.842980i	$-0.680799\pi$
$347$	6.50895	−	24.2917i	0.349419	−	1.30405i	0.887364	−	0.461069i	$-0.152534\pi$
$348$	−2.71278	−	0.218335i	−0.145420	−	0.0117040i
$349$	5.41974	−	5.41974i	0.290112	−	0.290112i	−0.547012	−	0.837124i	$-0.684235\pi$
$349$	5.41974	−	5.41974i	0.290112	−	0.290112i	0.837124	+	0.547012i	$0.184235\pi$
$350$	−2.68547	+	1.88373i	−0.143545	+	0.100689i
$351$			3.40096i			0.181530i
$352$	−24.5180	−	4.98987i	−1.30681	−	0.265961i
$353$	14.8839	−	8.59323i	0.792191	−	0.457372i	−0.0485424	−	0.998821i	$-0.515458\pi$
$353$	14.8839	−	8.59323i	0.792191	−	0.457372i	0.840733	+	0.541450i	$0.182124\pi$
$354$	3.08512	−	2.84679i	0.163972	−	0.151305i
$355$	−21.7369	+	5.82439i	−1.15368	+	0.309126i
$356$	−30.6682	+	14.5614i	−1.62541	+	0.771752i
$357$	−4.02582	−	5.27537i	−0.213069	−	0.279202i
$358$	3.42604	+	2.16592i	0.181072	+	0.114472i
$359$	12.2506	−	21.2187i	0.646562	−	1.11988i	−0.337376	−	0.941370i	$-0.609539\pi$
$359$	12.2506	−	21.2187i	0.646562	−	1.11988i	0.983938	−	0.178509i	$-0.0571274\pi$
$360$	2.68987	+	6.30699i	0.141769	+	0.332407i
$361$	8.65462	−	4.99675i	0.455506	−	0.262987i
$362$	−11.7055	−	22.2963i	−0.615226	−	1.17187i
$363$	6.05531	−	6.05531i	0.317821	−	0.317821i
$364$	−15.1360	+	9.73469i	−0.793342	+	0.510237i
$365$	−4.82477	−	4.82477i	−0.252540	−	0.252540i
$366$	3.00086	+	0.934706i	0.156857	+	0.0488578i
$367$	2.72200	+	4.71465i	0.142087	+	0.246103i	0.928283	−	0.371876i	$-0.121285\pi$
$367$	2.72200	+	4.71465i	0.142087	+	0.246103i	−0.786195	+	0.617978i	$0.787952\pi$
$368$	22.0248	+	3.56839i	1.14812	+	0.186015i
$369$	1.25749	+	0.726014i	0.0654625	+	0.0377948i
$370$	−1.73609	−	7.70411i	−0.0902552	−	0.400518i
$371$	4.02930	−	0.519632i	0.209191	−	0.0269779i
$372$	0.829342	+	0.295339i	0.0429994	+	0.0153126i
$373$	0.760760	+	2.83919i	0.0393907	+	0.147008i	0.982820	−	0.184565i	$-0.0590875\pi$
$373$	0.760760	+	2.83919i	0.0393907	+	0.147008i	−0.943430	+	0.331573i	$0.892421\pi$
$374$	0.629830	−	15.6764i	0.0325677	−	0.810608i
$375$	−4.99784	−	8.65651i	−0.258087	−	0.447020i
$376$	20.1224	−	2.86306i	1.03774	−	0.147651i
$377$	−4.62795			−0.238351
$378$	−2.40270	+	2.86828i	−0.123582	+	0.147528i
$379$	20.0922	+	20.0922i	1.03207	+	1.03207i	0.999469	+	0.0325965i	$0.0103776\pi$
$379$	20.0922	+	20.0922i	1.03207	+	1.03207i	0.0325965	+	0.999469i	$0.489622\pi$
$380$	26.0222	+	2.09437i	1.33491	+	0.107439i
$381$	13.0686	+	3.50173i	0.669526	+	0.179399i
$382$	−4.63425	−	5.02222i	−0.237109	−	0.256959i
$383$	15.8961	−	27.5329i	0.812253	−	1.40686i	−0.0990301	−	0.995084i	$-0.531574\pi$
$383$	15.8961	−	27.5329i	0.812253	−	1.40686i	0.911283	−	0.411780i	$-0.135093\pi$
$384$	7.84422	+	8.15280i	0.400299	+	0.416046i
$385$	−10.7869	−	26.2378i	−0.549750	−	1.33720i
$386$	−6.32343	−	28.0610i	−0.321854	−	1.42827i
$387$	−3.12225	−	11.6524i	−0.158713	−	0.592325i
$388$	−9.24175	+	13.3959i	−0.469179	+	0.680076i
$389$	−1.69103	−	0.453109i	−0.0857385	−	0.0229736i	0.215695	−	0.976461i	$-0.430798\pi$
$389$	−1.69103	−	0.453109i	−0.0857385	−	0.0229736i	−0.301433	+	0.953487i	$0.597465\pi$
$390$	5.41973	+	10.3234i	0.274439	+	0.522745i
$391$			13.9906i			0.707536i
$392$	−19.6426	−	2.48326i	−0.992103	−	0.125424i
$393$			12.2405i			0.617452i
$394$	25.0835	−	13.1687i	1.26369	−	0.663431i
$395$	−16.0460	−	4.29950i	−0.807360	−	0.216331i
$396$	−8.70084	+	1.59667i	−0.437234	+	0.0802359i
$397$	1.12236	+	4.18870i	0.0563295	+	0.210225i	0.988354	−	0.152170i	$-0.0486260\pi$
$397$	1.12236	+	4.18870i	0.0563295	+	0.210225i	−0.932025	+	0.362394i	$0.881959\pi$
$398$	33.4503	−	7.53790i	1.67671	−	0.377841i
$399$	5.41696	+	13.1762i	0.271187	+	0.659633i
$400$	2.71743	+	2.21651i	0.135872	+	0.110826i
$401$	−5.46346	+	9.46299i	−0.272832	+	0.472559i	−0.969586	−	0.244751i	$-0.921294\pi$
$401$	−5.46346	+	9.46299i	−0.272832	+	0.472559i	0.696754	+	0.717310i	$0.254627\pi$
$402$	−13.6879	+	12.6305i	−0.682690	+	0.629952i
$403$	1.44602	+	0.387461i	0.0720316	+	0.0193008i
$404$	19.2776	−	16.4057i	0.959097	−	0.816213i
$405$	1.71416	+	1.71416i	0.0851773	+	0.0851773i
$406$	−3.90309	−	3.26954i	−0.193707	−	0.162264i
$407$	10.1887			0.505037
$408$	−4.25972	+	5.67296i	−0.210888	+	0.280854i
$409$	3.73199	+	6.46400i	0.184535	+	0.319624i	0.943420	−	0.331601i	$-0.107589\pi$
$409$	3.73199	+	6.46400i	0.184535	+	0.319624i	−0.758885	+	0.651225i	$0.774255\pi$
$410$	4.97401	+	0.199840i	0.245649	+	0.00986940i
$411$	−3.45597	−	12.8979i	−0.170471	−	0.636205i
$412$	−8.94786	−	18.8454i	−0.440829	−	0.928445i
$413$	7.78901	−	1.00450i	0.383272	−	0.0494280i
$414$	7.69551	−	1.73415i	0.378213	−	0.0852290i
$415$	31.8863	+	18.4095i	1.56524	+	0.903689i
$416$	14.4082	+	12.7489i	0.706418	+	0.625066i
$417$	8.67498	+	15.0255i	0.424815	+	0.735802i
$418$	−10.0164	+	32.1574i	−0.489917	+	1.57287i
$419$	−5.53586	−	5.53586i	−0.270444	−	0.270444i	0.558835	−	0.829279i	$-0.311249\pi$
$419$	−5.53586	−	5.53586i	−0.270444	−	0.270444i	−0.829279	+	0.558835i	$0.811249\pi$
$420$	−2.72238	+	12.5354i	−0.132839	+	0.611664i
$421$	−8.26266	+	8.26266i	−0.402697	+	0.402697i	−0.879183	−	0.476485i	$-0.841911\pi$
$421$	−8.26266	+	8.26266i	−0.402697	+	0.402697i	0.476485	+	0.879183i	$0.341911\pi$
$422$	−22.5282	+	11.8272i	−1.09665	+	0.575738i
$423$	6.22327	−	3.59301i	0.302586	−	0.174698i
$424$	−1.70384	−	3.99501i	−0.0827457	−	0.194015i
$425$	−1.09945	+	1.90430i	−0.0533311	+	0.0923722i
$426$	−7.01518	+	11.0966i	−0.339887	+	0.537632i
$427$	3.56725	+	4.67447i	0.172631	+	0.226213i
$428$	−36.3418	−	12.9418i	−1.75665	−	0.625565i
$429$	−14.5301	+	3.89333i	−0.701520	+	0.187972i
$430$	−28.0465	−	30.3945i	−1.35252	−	1.46575i
$431$	6.10326	−	3.52372i	0.293983	−	0.169731i	−0.345753	−	0.938325i	$-0.612377\pi$
$431$	6.10326	−	3.52372i	0.293983	−	0.169731i	0.639737	+	0.768594i	$0.279043\pi$
$432$	3.64840	+	1.63988i	0.175534	+	0.0788987i
$433$			3.39440i			0.163124i	0.996668	+	0.0815622i	$0.0259909\pi$
$433$			3.39440i			0.163124i	−0.996668	+	0.0815622i	$0.974009\pi$
$434$	0.945806	+	1.34836i	0.0454001	+	0.0647232i
$435$	−2.33259	+	2.33259i	−0.111839	+	0.111839i
$436$	22.2597	−	18.9435i	1.06605	−	0.907231i
$437$	7.77365	−	29.0116i	0.371864	−	1.38782i
$438$	−3.97731	−	0.159796i	−0.190043	−	0.00763535i
$439$	2.34179	+	1.35203i	0.111768	+	0.0645291i	0.554842	−	0.831956i	$-0.312779\pi$
$439$	2.34179	+	1.35203i	0.111768	+	0.0645291i	−0.443074	+	0.896485i	$0.646112\pi$
$440$	−23.8664	+	18.7122i	−1.13778	+	0.892067i
$441$	−6.77097	+	1.77595i	−0.322427	+	0.0845689i
$442$	−6.44632	+	10.1968i	−0.306620	+	0.485011i
$443$	5.41580	−	1.45116i	0.257312	−	0.0689467i	−0.127857	−	0.991793i	$-0.540810\pi$
$443$	5.41580	−	1.45116i	0.257312	−	0.0689467i	0.385169	+	0.922846i	$0.374143\pi$
$444$	−3.79220	−	2.61621i	−0.179970	−	0.124160i
$445$	−10.6504	+	39.7480i	−0.504879	+	1.88423i
$446$	2.55626	+	0.796222i	0.121042	+	0.0377022i
$447$	−3.27919			−0.155100
$448$	3.14465	+	20.9311i	0.148571	+	0.988902i
$449$	16.0880			0.759239			0.379620	−	0.925143i	$-0.376055\pi$
$449$	16.0880			0.759239			0.379620	+	0.925143i	$0.376055\pi$
$450$	1.18373	+	0.368709i	0.0558017	+	0.0173811i
$451$	−1.66224	+	6.20358i	−0.0782720	+	0.292115i
$452$	−16.9226	−	11.6748i	−0.795973	−	0.549135i
$453$	23.2452	−	6.22852i	1.09215	−	0.292642i
$454$	13.3217	−	21.0723i	0.625220	−	0.988972i
$455$	−2.90436	+	21.6189i	−0.136158	+	1.01351i
$456$	11.9853	−	9.39690i	0.561261	−	0.440050i
$457$	17.6712	+	10.2025i	0.826624	+	0.477251i	0.852695	−	0.522409i	$-0.174966\pi$
$457$	17.6712	+	10.2025i	0.826624	+	0.477251i	−0.0260715	+	0.999660i	$0.508300\pi$
$458$	30.8361	+	1.23890i	1.44088	+	0.0578900i
$459$	−0.649165	+	2.42272i	−0.0303004	+	0.113083i
$460$	20.5957	−	17.5274i	0.960278	−	0.817218i
$461$	−24.2472	+	24.2472i	−1.12931	+	1.12931i	−0.139015	+	0.990290i	$0.544394\pi$
$461$	−24.2472	+	24.2472i	−1.12931	+	1.12931i	−0.990290	+	0.139015i	$0.955606\pi$
$462$	−15.0048	−	6.98166i	−0.698089	−	0.324816i
$463$		−	30.8810i		−	1.43516i	−0.696475	−	0.717581i	$-0.745249\pi$
$463$		−	30.8810i		−	1.43516i	0.696475	−	0.717581i	$-0.254751\pi$
$464$	−2.23151	+	4.96465i	−0.103595	+	0.230478i
$465$	0.924118	−	0.533540i	0.0428549	−	0.0247423i
$466$	10.3331	+	11.1982i	0.478671	+	0.518745i
$467$	23.7308	−	6.35865i	1.09813	−	0.294243i	0.336128	−	0.941816i	$-0.390883\pi$
$467$	23.7308	−	6.35865i	1.09813	−	0.294243i	0.762004	+	0.647573i	$0.224216\pi$
$468$	6.40774	+	2.28188i	0.296198	+	0.105480i
$469$	−34.5578	+	4.45669i	−1.59573	+	0.205791i
$470$	13.1645	−	20.8237i	0.607235	−	0.960524i
$471$	−1.65867	+	2.87291i	−0.0764277	+	0.132377i
$472$	−3.29367	−	7.72273i	−0.151604	−	0.355467i
$473$	46.2089	−	26.6787i	2.12469	−	1.22669i
$474$	−8.58045	+	4.50470i	−0.394113	+	0.206908i
$475$	3.33796	−	3.33796i	0.153156	−	0.153156i
$476$	−12.6404	+	4.04552i	−0.579374	+	0.185426i
$477$	−1.08579	−	1.08579i	−0.0497151	−	0.0497151i
$478$	−0.694048	+	2.22823i	−0.0317450	+	0.101917i
$479$	−8.23156	−	14.2575i	−0.376110	−	0.651441i	0.614383	−	0.789008i	$-0.289405\pi$
$479$	−8.23156	−	14.2575i	−0.376110	−	0.651441i	−0.990492	+	0.137567i	$0.956072\pi$
$480$	13.6878	−	0.836304i	0.624758	−	0.0381719i
$481$	−6.78468	−	3.91714i	−0.309355	−	0.178606i
$482$	−24.5314	+	5.52806i	−1.11737	+	0.251796i
$483$	13.6196	+	5.68368i	0.619714	+	0.258616i
$484$	−7.34598	−	15.4716i	−0.333908	−	0.703255i
$485$	5.10554	+	19.0541i	0.231831	+	0.865204i
$486$	1.41307	+	0.0567729i	0.0640983	+	0.00257527i
$487$	5.37839	+	9.31565i	0.243718	+	0.422132i	0.961770	−	0.273857i	$-0.0882995\pi$
$487$	5.37839	+	9.31565i	0.243718	+	0.422132i	−0.718052	+	0.695989i	$0.754966\pi$
$488$	3.77451	−	5.02677i	0.170864	−	0.227551i
$489$	−10.3961			−0.470127
$490$	−17.7227	+	16.1809i	−0.800630	+	0.730979i
$491$	15.7656	+	15.7656i	0.711492	+	0.711492i	0.966847	−	0.255355i	$-0.0821925\pi$
$491$	15.7656	+	15.7656i	0.711492	+	0.711492i	−0.255355	+	0.966847i	$0.582192\pi$
$492$	2.21160	−	1.88212i	0.0997066	−	0.0848526i
$493$	−3.29677	−	0.883368i	−0.148479	−	0.0397849i
$494$	19.0331	−	17.5628i	0.856338	−	0.790186i
$495$	−5.36117	+	9.28582i	−0.240967	+	0.417367i
$496$	1.11290	−	1.36440i	0.0499705	−	0.0612635i
$497$	−22.7157	+	9.33884i	−1.01894	+	0.418904i
$498$	20.9539	−	4.72189i	0.938968	−	0.211593i
$499$	−4.08733	−	15.2541i	−0.182974	−	0.682868i	−0.995055	−	0.0993235i	$-0.968332\pi$
$499$	−4.08733	−	15.2541i	−0.182974	−	0.682868i	0.812081	−	0.583544i	$-0.198335\pi$
$500$	−19.6630	+	3.60832i	−0.879357	+	0.161369i
$501$	0.0877198	+	0.0235044i	0.00391903	+	0.00105010i
$502$	−7.66585	+	4.02454i	−0.342144	+	0.179624i
$503$			10.6906i			0.476669i	0.971183	+	0.238334i	$0.0766014\pi$
$503$			10.6906i			0.476669i	−0.971183	+	0.238334i	$0.923399\pi$
$504$	3.79202	+	6.45140i	0.168910	+	0.287368i
$505$		−	30.6823i		−	1.36535i
$506$	16.2185	+	30.8927i	0.721001	+	1.37335i
$507$	−1.38462	−	0.371009i	−0.0614933	−	0.0164771i
$508$	15.3660	−	22.2731i	0.681757	−	0.988209i
$509$	1.39401	+	5.20253i	0.0617886	+	0.230598i	0.989914	−	0.141669i	$-0.0452470\pi$
$509$	1.39401	+	5.20253i	0.0617886	+	0.230598i	−0.928125	+	0.372268i	$0.878580\pi$
$510$	1.89032	+	8.38849i	0.0837046	+	0.371449i
$511$	−5.89599	−	4.54898i	−0.260823	−	0.201235i
$512$	20.6238	−	9.30914i	0.911450	−	0.411410i
$513$	2.69228	−	4.66317i	0.118867	−	0.205884i
$514$	−5.31678	−	5.76188i	−0.234513	−	0.254146i
$515$	−24.4248	−	6.54460i	−1.07628	−	0.288390i
$516$	−24.0492	−	1.93557i	−1.05871	−	0.0852085i
$517$	22.4748	+	22.4748i	0.988441	+	0.988441i
$518$	−2.95465	−	8.09683i	−0.129820	−	0.355754i
$519$	9.53001			0.418321
$520$	23.0866	−	3.28482i	1.01242	−	0.144049i
$521$	−2.18217	−	3.77963i	−0.0956027	−	0.165589i	0.814257	−	0.580504i	$-0.197144\pi$
$521$	−2.18217	−	3.77963i	−0.0956027	−	0.165589i	−0.909860	+	0.414915i	$0.863811\pi$
$522$	−0.0772552	+	1.92288i	−0.00338137	+	0.0841620i
$523$	2.36865	+	8.83993i	0.103574	+	0.386543i	0.998179	−	0.0603136i	$-0.0192101\pi$
$523$	2.36865	+	8.83993i	0.103574	+	0.386543i	−0.894606	+	0.446857i	$0.852543\pi$
$524$	23.0623	+	8.21278i	1.00748	+	0.358777i
$525$	1.40715	+	1.84391i	0.0614132	+	0.0804750i
$526$	−3.75271	−	16.6531i	−0.163626	−	0.726108i
$527$	0.956136	+	0.552025i	0.0416499	+	0.0240466i
$528$	−2.82955	+	17.4645i	−0.123140	+	0.760046i
$529$	−4.05703	−	7.02698i	−0.176392	−	0.305521i
$530$	−5.02617	−	1.56555i	−0.218323	−	0.0680030i
$531$	−2.09894	−	2.09894i	−0.0910862	−	0.0910862i
$532$	28.4597	−	1.36554i	1.23388	−	0.0592035i
$533$	3.49190	−	3.49190i	0.151251	−	0.151251i
$534$	11.1587	+	21.2549i	0.482885	+	0.919789i
$535$	−40.4949	+	23.3797i	−1.75075	+	1.01079i
$536$	14.6132	+	34.2638i	0.631193	+	1.47997i
$537$	1.43305	−	2.48211i	0.0618405	−	0.107111i
$538$	−38.8294	−	24.5476i	−1.67405	−	1.05832i
$539$	−15.3387	−	26.8949i	−0.660684	−	1.15845i
$540$	4.37976	−	2.07953i	0.188475	−	0.0894886i
$541$	5.47321	−	1.46654i	0.235311	−	0.0630515i	−0.139236	−	0.990259i	$-0.544465\pi$
$541$	5.47321	−	1.46654i	0.235311	−	0.0630515i	0.374548	+	0.927208i	$0.377798\pi$
$542$	16.1225	−	14.8770i	0.692519	−	0.639022i
$543$	−15.4209	+	8.90326i	−0.661774	+	0.382075i
$544$	7.83036	+	11.8320i	0.335724	+	0.507293i
$545$		−	35.4287i		−	1.51760i
$546$	7.30758	+	10.4178i	0.312735	+	0.445841i
$547$	−0.185636	+	0.185636i	−0.00793721	+	0.00793721i	−0.711064	−	0.703127i	$-0.751787\pi$
$547$	−0.185636	+	0.185636i	−0.00793721	+	0.00793721i	0.703127	+	0.711064i	$0.251787\pi$
$548$	−26.6196	−	2.14245i	−1.13713	−	0.0915208i
$549$	0.575220	−	2.14675i	0.0245498	−	0.0916211i
$550$	−0.220146	+	5.47942i	−0.00938705	+	0.233643i
$551$	6.34553	+	3.66359i	0.270328	+	0.156074i
$552$	1.89599	−	15.6626i	0.0806988	−	0.666645i
$553$	−17.9689	−	2.41400i	−0.764114	−	0.102654i
$554$	29.3244	+	18.5386i	1.24587	+	0.787631i
$555$	−5.39395	+	1.44531i	−0.228961	+	0.0613498i
$556$	34.1300	−	6.26313i	1.44743	−	0.265616i
$557$	0.319513	−	1.19244i	0.0135382	−	0.0505252i	−0.958826	−	0.283993i	$-0.908341\pi$
$557$	0.319513	−	1.19244i	0.0135382	−	0.0505252i	0.972365	+	0.233468i	$0.0750074\pi$
$558$	0.185126	−	0.594344i	0.00783700	−	0.0251606i
$559$	−41.0274			−1.73527
$560$	21.7913	+	13.5399i	0.920851	+	0.572164i
$561$	−11.0938			−0.468382
$562$	−2.08015	+	6.67830i	−0.0877459	+	0.281707i
$563$	−7.08508	+	26.4419i	−0.298601	+	1.11439i	0.639715	+	0.768612i	$0.279052\pi$
$563$	−7.08508	+	26.4419i	−0.298601	+	1.11439i	−0.938315	+	0.345780i	$0.887614\pi$
$564$	−2.59407	−	14.1360i	−0.109230	−	0.595232i
$565$	−24.0704	+	6.44965i	−1.01265	+	0.271339i
$566$	15.9946	+	10.1117i	0.672305	+	0.425025i
$567$	2.09475	+	1.61618i	0.0879712	+	0.0678730i
$568$	16.2003	+	20.6626i	0.679747	+	0.866982i
$569$	−3.97832	−	2.29689i	−0.166780	−	0.0962905i	0.414287	−	0.910146i	$-0.364031\pi$
$569$	−3.97832	−	2.29689i	−0.166780	−	0.0962905i	−0.581067	+	0.813856i	$0.697364\pi$
$570$	0.741068	−	18.4451i	0.0310399	−	0.772581i
$571$	7.32966	−	27.3547i	0.306737	−	1.14476i	−0.624703	−	0.780862i	$-0.714780\pi$
$571$	7.32966	−	27.3547i	0.306737	−	1.14476i	0.931440	−	0.363895i	$-0.118553\pi$
$572$	−2.41358	+	29.9884i	−0.100917	+	1.25388i
$573$	−3.41683	+	3.41683i	−0.142740	+	0.142740i
$574$	5.41192	−	0.478028i	0.225889	−	0.0199525i
$575$		−	4.89018i		−	0.203934i
$576$	5.53759	−	5.77366i	0.230733	−	0.240569i
$577$	−21.8849	+	12.6352i	−0.911079	+	0.526012i	−0.880778	−	0.473529i	$-0.842980\pi$
$577$	−21.8849	+	12.6352i	−0.911079	+	0.526012i	−0.0303008	+	0.999541i	$0.509647\pi$
$578$	11.1303	−	10.2705i	0.462960	−	0.427196i
$579$	−19.6466	+	5.26429i	−0.816485	+	0.218776i
$580$	2.82977	+	5.95988i	0.117500	+	0.247470i
$581$	37.0846	+	15.4760i	1.53853	+	0.642051i
$582$	9.72707	+	6.14937i	0.403200	+	0.254900i
$583$	3.39591	−	5.88189i	0.140644	−	0.243603i
$584$	−2.96965	+	7.38643i	−0.122885	+	0.305653i
$585$	7.14001	−	4.12228i	0.295203	−	0.170435i
$586$	11.7436	+	22.3690i	0.485124	+	0.924054i
$587$	7.69114	−	7.69114i	0.317447	−	0.317447i	−0.530339	−	0.847786i	$-0.677935\pi$
$587$	7.69114	−	7.69114i	0.317447	−	0.317447i	0.847786	+	0.530339i	$0.177935\pi$
$588$	−1.19693	+	13.9487i	−0.0493606	+	0.575236i
$589$	−1.67597	−	1.67597i	−0.0690570	−	0.0690570i
$590$	−9.71604	−	3.02634i	−0.400003	−	0.124593i
$591$	−10.0162	−	17.3486i	−0.412012	−	0.713626i
$592$	−7.47357	+	5.38953i	−0.307162	+	0.221508i
$593$	−21.9302	−	12.6614i	−0.900564	−	0.519941i	−0.0231811	−	0.999731i	$-0.507379\pi$
$593$	−21.9302	−	12.6614i	−0.900564	−	0.519941i	−0.877383	+	0.479790i	$0.840713\pi$
$594$	1.37509	+	6.10214i	0.0564208	+	0.250374i
$595$	−6.19550	+	14.8461i	−0.253991	+	0.608630i
$596$	−2.20018	+	6.17831i	−0.0901227	+	0.253074i
$597$	−6.27534	−	23.4199i	−0.256832	−	0.958512i
$598$	1.07701	−	26.8068i	0.0440424	−	1.09621i
$599$	−19.1368	−	33.1459i	−0.781907	−	1.35430i	−0.930829	−	0.365455i	$-0.880914\pi$
$599$	−19.1368	−	33.1459i	−0.781907	−	1.35430i	0.148922	−	0.988849i	$-0.452420\pi$
$600$	1.48891	−	1.98288i	0.0607845	−	0.0809509i
$601$	12.9002			0.526211			0.263105	−	0.964767i	$-0.415253\pi$
$601$	12.9002			0.526211			0.263105	+	0.964767i	$0.415253\pi$
$602$	−34.6014	−	28.9849i	−1.41025	−	1.18134i
$603$	9.31246	+	9.31246i	0.379233	+	0.379233i
$604$	3.86122	−	47.9752i	0.157111	−	1.95208i
$605$	−20.0522	−	5.37296i	−0.815237	−	0.218442i
$606$	−12.1384	−	13.1546i	−0.493090	−	0.534371i
$607$	14.1850	−	24.5692i	0.575753	−	0.997233i	−0.420207	−	0.907428i	$-0.638043\pi$
$607$	14.1850	−	24.5692i	0.575753	−	0.997233i	0.995959	−	0.0898043i	$-0.0286242\pi$
$608$	−9.66316	−	28.8862i	−0.391893	−	1.17149i
$609$	−2.19925	+	2.85048i	−0.0891183	+	0.115507i
$610$	−1.67500	−	7.43298i	−0.0678186	−	0.300953i
$611$	−6.32537	−	23.6066i	−0.255897	−	0.955020i
$612$	4.12908	+	2.84861i	0.166908	+	0.115148i
$613$	18.9478	+	5.07704i	0.765294	+	0.205060i	0.620291	−	0.784371i	$-0.287014\pi$
$613$	18.9478	+	5.07704i	0.765294	+	0.205060i	0.145002	+	0.989431i	$0.453681\pi$
$614$	−13.9213	−	26.5169i	−0.561816	−	1.07014i
$615$		−	3.51999i		−	0.141940i
$616$	−23.2216	+	23.5863i	−0.935627	+	0.950317i
$617$		−	8.08504i		−	0.325491i	−0.986668	−	0.162746i	$-0.947965\pi$
$617$		−	8.08504i		−	0.325491i	0.986668	−	0.162746i	$-0.0520350\pi$
$618$	−13.0610	+	6.85694i	−0.525389	+	0.275827i
$619$	4.83693	+	1.29605i	0.194413	+	0.0520927i	0.354712	−	0.934976i	$-0.384579\pi$
$619$	4.83693	+	1.29605i	0.194413	+	0.0520927i	−0.160299	+	0.987069i	$0.551246\pi$
$620$	−0.385203	−	2.09911i	−0.0154701	−	0.0843022i
$621$	−1.44369	−	5.38793i	−0.0579334	−	0.216210i
$622$	22.9319	−	5.16763i	0.919487	−	0.207203i
$623$	−5.97980	+	44.5112i	−0.239576	+	1.78330i
$624$	8.59856	−	10.5418i	0.344218	−	0.422009i
$625$	−14.3074	+	24.7812i	−0.572297	+	0.991248i
$626$	−33.0350	+	30.4831i	−1.32035	+	1.21835i
$627$	23.0047	+	6.16410i	0.918721	+	0.246170i
$628$	4.29995	+	5.05269i	0.171587	+	0.201624i
$629$	−4.08546	−	4.08546i	−0.162898	−	0.162898i
$630$	8.93399	+	1.56763i	0.355939	+	0.0624558i
$631$	10.1186			0.402814			0.201407	−	0.979508i	$-0.435449\pi$
$631$	10.1186			0.402814			0.201407	+	0.979508i	$0.435449\pi$
$632$	2.73023	+	19.1888i	0.108603	+	0.763291i
$633$	8.99583	+	15.5812i	0.357552	+	0.619299i
$634$	13.0428	+	0.524018i	0.517995	+	0.0208114i
$635$	−8.48885	−	31.6808i	−0.336870	−	1.25722i
$636$	−2.77426	+	1.31723i	−0.110007	+	0.0522315i
$637$	−0.125911	+	23.8064i	−0.00498877	+	0.943244i
$638$	−8.30365	+	1.87120i	−0.328745	+	0.0740814i
$639$	8.03930	+	4.64149i	0.318030	+	0.183615i
$640$	7.60814	−	26.3502i	0.300738	−	1.04158i
$641$	16.8383	+	29.1648i	0.665073	+	1.15194i	0.979265	+	0.202581i	$0.0649331\pi$
$641$	16.8383	+	29.1648i	0.665073	+	1.15194i	−0.314192	+	0.949359i	$0.601734\pi$
$642$	−8.11223	+	26.0442i	−0.320164	+	1.02788i
$643$	0.913474	+	0.913474i	0.0360239	+	0.0360239i	0.724889	−	0.688865i	$-0.241891\pi$
$643$	0.913474	+	0.913474i	0.0360239	+	0.0360239i	−0.688865	+	0.724889i	$0.741891\pi$
$644$	19.8467	−	21.8472i	0.782070	−	0.860902i
$645$	−20.6787	+	20.6787i	−0.814223	+	0.814223i
$646$	16.9108	−	8.87808i	0.665345	−	0.349303i
$647$	14.2145	−	8.20676i	0.558831	−	0.322641i	−0.193845	−	0.981032i	$-0.562096\pi$
$647$	14.2145	−	8.20676i	0.558831	−	0.322641i	0.752676	+	0.658391i	$0.228763\pi$
$648$	1.05507	−	2.62428i	0.0414470	−	0.103091i
$649$	6.56460	−	11.3702i	0.257683	−	0.446320i
$650$	2.25320	−	3.56411i	0.0883777	−	0.139796i
$651$	0.925816	−	0.706522i	0.0362856	−	0.0276908i
$652$	−6.97526	+	19.5872i	−0.273172	+	0.767096i
$653$	16.2739	−	4.36057i	0.636846	−	0.170642i	0.0740717	−	0.997253i	$-0.476401\pi$
$653$	16.2739	−	4.36057i	0.636846	−	0.170642i	0.562774	+	0.826611i	$0.309734\pi$
$654$	−14.0162	−	15.1896i	−0.548076	−	0.593960i
$655$	25.6978	−	14.8366i	1.00410	−	0.579716i
$656$	−2.06223	−	5.42968i	−0.0805164	−	0.211993i
$657$			2.81465i			0.109810i
$658$	11.3429	−	24.3779i	0.442191	−	0.950349i
$659$	−10.3214	+	10.3214i	−0.402065	+	0.402065i	−0.878960	−	0.476895i	$-0.841762\pi$
$659$	−10.3214	+	10.3214i	−0.402065	+	0.402065i	0.476895	+	0.878960i	$0.341762\pi$
$660$	13.8983	+	16.3313i	0.540991	+	0.635695i
$661$	−6.21082	+	23.1791i	−0.241573	+	0.901562i	0.733502	+	0.679687i	$0.237884\pi$
$661$	−6.21082	+	23.1791i	−0.241573	+	0.901562i	−0.975075	+	0.221875i	$0.928782\pi$
$662$	21.2996	+	0.855752i	0.827833	+	0.0332598i
$663$	7.38739	+	4.26511i	0.286902	+	0.165643i
$664$	5.16256	−	42.6474i	0.200346	−	1.65504i
$665$	21.0963	−	27.3432i	0.818078	−	1.06032i
$666$	−1.74080	+	2.75359i	−0.0674546	+	0.106700i
$667$	7.33177	−	1.96454i	0.283887	−	0.0760674i
$668$	0.103140	−	0.149502i	0.00399062	−	0.00578442i
$669$	0.489997	−	1.82869i	0.0189444	−	0.0707014i
$670$	43.1076	+	13.4271i	1.66539	+	0.518735i
$671$	9.83017			0.379490
$672$	14.6993	−	2.81597i	0.567039	−	0.108628i
$673$	19.5621			0.754063			0.377031	−	0.926201i	$-0.376945\pi$
$673$	19.5621			0.754063			0.377031	+	0.926201i	$0.376945\pi$
$674$	−15.2540	−	4.75131i	−0.587562	−	0.183013i
$675$	0.226904	−	0.846818i	0.00873354	−	0.0325940i
$676$	−1.62803	+	2.35984i	−0.0626166	+	0.0907630i
$677$	−20.8557	+	5.58828i	−0.801551	+	0.214775i	−0.636265	−	0.771471i	$-0.719521\pi$
$677$	−20.8557	+	5.58828i	−0.801551	+	0.214775i	−0.165286	+	0.986246i	$0.552855\pi$
$678$	−7.76828	+	12.2879i	−0.298339	+	0.471912i
$679$	8.18625	+	19.9121i	0.314159	+	0.764157i
$680$	17.0731	+	2.06673i	0.654722	+	0.0792554i
$681$	−15.2665	−	8.81412i	−0.585014	−	0.337758i
$682$	2.75118	+	0.110534i	0.105348	+	0.00423255i
$683$	4.18594	−	15.6221i	0.160170	−	0.597764i	−0.838437	−	0.544999i	$-0.816530\pi$
$683$	4.18594	−	15.6221i	0.160170	−	0.597764i	0.998607	−	0.0527649i	$-0.0168034\pi$
$684$	−6.97947	−	8.20128i	−0.266867	−	0.313584i
$685$	−22.8889	+	22.8889i	−0.874541	+	0.874541i
$686$	−16.9249	+	19.9887i	−0.646194	+	0.763173i
$687$		−	21.8220i		−	0.832562i
$688$	−19.7826	+	44.0123i	−0.754205	+	1.67795i
$689$	−4.52267	+	2.61117i	−0.172300	+	0.0994775i
$690$	−12.9684	−	14.0541i	−0.493698	−	0.535029i
$691$	−24.9840	+	6.69444i	−0.950435	+	0.254668i	−0.700547	−	0.713606i	$-0.747061\pi$
$691$	−24.9840	+	6.69444i	−0.950435	+	0.254668i	−0.249888	+	0.968275i	$0.580394\pi$
$692$	6.39417	−	17.9555i	0.243070	−	0.682565i
$693$	−4.50686	+	10.7997i	−0.171202	+	0.410245i
$694$	−19.0049	+	30.0620i	−0.721417	+	1.14114i
$695$	21.0298	−	36.4246i	0.797705	−	1.38167i
$696$	3.57105	+	1.43571i	0.135360	+	0.0544206i
$697$	3.15402	−	1.82097i	0.119467	−	0.0689743i
$698$	−9.59727	+	5.03852i	−0.363262	+	0.190711i
$699$	7.61859	−	7.61859i	0.288162	−	0.288162i
$700$	4.41825	−	1.41404i	0.166994	−	0.0534456i
$701$	−10.5374	−	10.5374i	−0.397991	−	0.397991i	0.479533	−	0.877524i	$-0.340806\pi$
$701$	−10.5374	−	10.5374i	−0.397991	−	0.397991i	−0.877524	+	0.479533i	$0.840806\pi$
$702$	1.43034	−	4.59208i	0.0539846	−	0.173317i
$703$	6.20179	+	10.7418i	0.233905	+	0.405136i
$704$	31.0064	+	17.0490i	1.16860	+	0.642558i
$705$	−15.0864	−	8.71012i	−0.568186	−	0.328042i
$706$	−23.7108	+	5.34313i	−0.892366	+	0.201091i
$707$	−4.28307	−	33.2116i	−0.161081	−	1.24905i
$708$	−5.36289	+	2.54632i	−0.201550	+	0.0956966i
$709$	−9.55579	−	35.6627i	−0.358875	−	1.33934i	−0.875537	−	0.483151i	$-0.839492\pi$
$709$	−9.55579	−	35.6627i	−0.358875	−	1.33934i	0.516661	−	0.856190i	$-0.327175\pi$
$710$	31.7994	+	1.27760i	1.19341	+	0.0479475i
$711$	3.42630	+	5.93453i	0.128496	+	0.222562i
$712$	47.5333	−	6.76313i	1.78138	−	0.253459i
$713$	−2.45532			−0.0919525
$714$	3.21712	+	8.81610i	0.120398	+	0.329934i
$715$	25.7855	+	25.7855i	0.964325	+	0.964325i
$716$	−3.71503	−	4.36537i	−0.138837	−	0.163142i
$717$	1.59403	+	0.427119i	0.0595301	+	0.0159510i
$718$	−25.4651	+	23.4979i	−0.950348	+	0.876933i
$719$	−14.9264	+	25.8532i	−0.556659	+	0.964162i	0.441113	+	0.897451i	$0.354584\pi$
$719$	−14.9264	+	25.8532i	−0.556659	+	0.964162i	−0.997772	+	0.0667105i	$0.978750\pi$
$720$	−0.979427	−	9.64716i	−0.0365011	−	0.359529i
$721$	−27.3518	−	3.67454i	−1.01863	−	0.136847i
$722$	−13.7872	+	3.10690i	−0.513107	+	0.115627i
$723$	4.60214	+	17.1754i	0.171155	+	0.638760i
$724$	6.42794	+	35.0281i	0.238893	+	1.30181i
$725$	1.15233	+	0.308766i	0.0427964	+	0.0114673i
$726$	−10.7227	+	5.62939i	−0.397958	+	0.208926i
$727$		−	10.1945i		−	0.378092i	−0.981968	−	0.189046i	$-0.939460\pi$
$727$		−	10.1945i		−	0.378092i	0.981968	−	0.189046i	$-0.0605395\pi$
$728$	24.5312	−	6.77835i	0.909187	−	0.251222i
$729$		−	1.00000i		−	0.0370370i
$730$	4.48540	+	8.54369i	0.166012	+	0.316216i
$731$	−29.2263	−	7.83118i	−1.08098	−	0.289647i
$732$	−3.65874	−	2.52414i	−0.135231	−	0.0932947i
$733$	−5.43706	−	20.2914i	−0.200823	−	0.749480i	−0.990682	−	0.136192i	$-0.956513\pi$
$733$	−5.43706	−	20.2914i	−0.200823	−	0.749480i	0.789860	−	0.613287i	$-0.210153\pi$
$734$	−1.69250	−	7.51065i	−0.0624712	−	0.277223i
$735$	11.9355	+	12.0624i	0.440247	+	0.444929i
$736$	−28.2378	−	14.0811i	−1.04086	−	0.519036i
$737$	−29.1254	+	50.4467i	−1.07285	+	1.85823i
$738$	−1.39257	−	1.50915i	−0.0512611	−	0.0555526i
$739$	−46.3419	−	12.4173i	−1.70471	−	0.456777i	−0.730595	−	0.682811i	$-0.760757\pi$
$739$	−46.3419	−	12.4173i	−1.70471	−	0.456777i	−0.974119	+	0.226034i	$0.927424\pi$
$740$	−0.895982	+	11.1325i	−0.0329370	+	0.409238i
$741$	−12.9490	−	12.9490i	−0.475694	−	0.475694i
$742$	−5.65903	−	0.992977i	−0.207749	−	0.0364533i
$743$	47.1641			1.73028			0.865141	−	0.501528i	$-0.167229\pi$
$743$	47.1641			1.73028			0.865141	+	0.501528i	$0.167229\pi$
$744$	−0.995592	−	0.747571i	−0.0365002	−	0.0274073i
$745$	3.97469	+	6.88436i	0.145621	+	0.252223i
$746$	0.166876	−	4.15352i	0.00610975	−	0.152071i
$747$	−3.93100	−	14.6707i	−0.143828	−	0.536772i
$748$	−7.44343	+	20.9019i	−0.272159	+	0.764249i
$749$	−40.5693	+	30.9598i	−1.48237	+	1.13125i
$750$	3.10758	+	13.7902i	0.113473	+	0.503548i
$751$	28.9955	+	16.7406i	1.05806	+	0.610872i	0.924896	−	0.380221i	$-0.124152\pi$
$751$	28.9955	+	16.7406i	1.05806	+	0.610872i	0.133166	+	0.991094i	$0.457486\pi$
$752$	−28.3741	−	4.59708i	−1.03470	−	0.167638i
$753$	3.06109	+	5.30196i	0.111552	+	0.193214i
$754$	6.24879	+	1.94637i	0.227568	+	0.0708826i
$755$	−41.2516	−	41.2516i	−1.50130	−	1.50130i
$756$	4.45051	−	2.86234i	0.161863	−	0.104102i
$757$	−24.0059	+	24.0059i	−0.872508	+	0.872508i	−0.992745	−	0.120237i	$-0.961635\pi$
$757$	−24.0059	+	24.0059i	−0.872508	+	0.872508i	0.120237	+	0.992745i	$0.461635\pi$
$758$	−18.6789	−	35.5792i	−0.678449	−	1.29229i
$759$	21.3664	−	12.3359i	0.775553	−	0.447766i
$760$	−34.2552	−	13.7720i	−1.24257	−	0.499564i
$761$	−17.2157	+	29.8186i	−0.624070	+	1.08092i	0.364649	+	0.931145i	$0.381189\pi$
$761$	−17.2157	+	29.8186i	−0.624070	+	1.08092i	−0.988720	+	0.149777i	$0.952144\pi$
$762$	−16.1729	−	10.2244i	−0.585884	−	0.370391i
$763$	−4.94563	−	38.3492i	−0.179044	−	1.38833i
$764$	4.14512	+	8.73017i	0.149965	+	0.315847i
$765$	5.87312	−	1.57370i	0.212343	−	0.0568972i
$766$	−33.0429	+	30.4903i	−1.19389	+	1.10166i
$767$	−8.74273	+	5.04762i	−0.315682	+	0.182259i
$768$	−7.16269	−	14.3072i	−0.258461	−	0.516267i
$769$			24.5562i			0.885518i	0.896641	+	0.442759i	$0.146000\pi$
$769$			24.5562i			0.885518i	−0.896641	+	0.442759i	$0.854000\pi$
$770$	3.52994	+	39.9637i	0.127210	+	1.44019i
$771$	−3.92006	+	3.92006i	−0.141177	+	0.141177i
$772$	−3.26347	+	40.5482i	−0.117455	+	1.45936i
$773$	0.684896	−	2.55607i	0.0246340	−	0.0919354i	−0.952514	−	0.304493i	$-0.901513\pi$
$773$	0.684896	−	2.55607i	0.0246340	−	0.0919354i	0.977148	+	0.212558i	$0.0681795\pi$
$774$	−0.684878	+	17.0466i	−0.0246174	+	0.612726i
$775$	−0.334200	−	0.192951i	−0.0120048	−	0.00693099i
$776$	18.1124	−	14.2008i	0.650198	−	0.509780i
$777$	−5.63684	+	2.31741i	−0.202220	+	0.0831366i
$778$	2.09271	+	1.32299i	0.0750274	+	0.0474317i
$779$	−7.55213	+	2.02359i	−0.270583	+	0.0725025i
$780$	−2.97619	−	16.2183i	−0.106565	−	0.580709i
$781$	−10.6269	+	39.6602i	−0.380261	+	1.41915i
$782$	5.88402	−	18.8906i	0.210412	−	0.675525i
$783$	1.36078			0.0486302
$784$	25.4777	+	11.6141i	0.909918	+	0.414788i
$785$	8.04188			0.287027
$786$	5.14797	−	16.5275i	0.183622	−	0.589516i
$787$	−1.02164	+	3.81281i	−0.0364175	+	0.135912i	−0.981741	−	0.190222i	$-0.939079\pi$
$787$	−1.02164	+	3.81281i	−0.0364175	+	0.135912i	0.945324	+	0.326134i	$0.105746\pi$
$788$	−39.4068	+	7.23147i	−1.40381	+	0.257611i
$789$	−11.6595	+	3.12415i	−0.415088	+	0.111223i
$790$	19.8575	+	12.5537i	0.706498	+	0.446642i
$791$	−25.1543	+	10.3414i	−0.894382	+	0.367697i
$792$	12.4196	+	1.50342i	0.441313	+	0.0534218i
$793$	−6.54591	−	3.77928i	−0.232452	−	0.134206i
$794$	0.246193	−	6.12773i	0.00873707	−	0.217465i
$795$	−0.963442	+	3.59561i	−0.0341698	+	0.127523i
$796$	−48.3358	−	3.89024i	−1.71322	−	0.137886i
$797$	21.2467	−	21.2467i	0.752597	−	0.752597i	−0.222366	−	0.974963i	$-0.571378\pi$
$797$	21.2467	−	21.2467i	0.752597	−	0.752597i	0.974963	+	0.222366i	$0.0713780\pi$
$798$	−1.77267	−	20.0690i	−0.0627518	−	0.710436i
$799$		−	18.0238i		−	0.637637i
$800$	−2.73696	−	4.13567i	−0.0967663	−	0.146218i
$801$	14.7006	−	8.48740i	0.519420	−	0.299887i
$802$	11.3568	−	10.4795i	0.401022	−	0.370043i
$803$	−12.0252	+	3.22214i	−0.424360	+	0.113707i
$804$	23.7938	−	11.2974i	0.839142	−	0.398428i
$805$	−4.57591	−	35.4823i	−0.161280	−	1.25059i
$806$	−1.78951	−	1.13131i	−0.0630329	−	0.0398488i
$807$	−16.2416	+	28.1312i	−0.571730	+	0.990265i
$808$	−32.9289	+	14.0439i	−1.15844	+	0.494062i
$809$	−2.97214	+	1.71596i	−0.104495	+	0.0603300i	−0.551337	−	0.834283i	$-0.685882\pi$
$809$	−2.97214	+	1.71596i	−0.104495	+	0.0603300i	0.446842	+	0.894613i	$0.352549\pi$
$810$	−1.59359	−	3.03543i	−0.0559930	−	0.106654i
$811$	−3.81271	+	3.81271i	−0.133882	+	0.133882i	−0.770872	−	0.636990i	$-0.780179\pi$
$811$	−3.81271	+	3.81271i	−0.133882	+	0.133882i	0.636990	+	0.770872i	$0.280179\pi$
$812$	3.89500	+	6.05615i	0.136688	+	0.212529i
$813$	−10.9688	−	10.9688i	−0.384693	−	0.384693i
$814$	−13.7571	−	4.28506i	−0.482188	−	0.150191i
$815$	12.6010	+	21.8256i	0.441395	+	0.764519i
$816$	8.13748	−	5.86830i	0.284869	−	0.205432i
$817$	56.2539	+	32.4782i	1.96808	+	1.13627i
$818$	−2.32049	−	10.2975i	−0.0811342	−	0.360042i
$819$	7.15313	−	5.45880i	0.249951	−	0.190746i
$820$	−6.63201	−	2.36174i	−0.231600	−	0.0824756i
$821$	9.30415	+	34.7236i	0.324717	+	1.21186i	0.914596	+	0.404369i	$0.132509\pi$
$821$	9.30415	+	34.7236i	0.324717	+	1.21186i	−0.589879	+	0.807492i	$0.700824\pi$
$822$	−0.758081	+	18.8686i	−0.0264411	+	0.658117i
$823$	−4.80101	−	8.31559i	−0.167353	−	0.289863i	0.770136	−	0.637880i	$-0.220189\pi$
$823$	−4.80101	−	8.31559i	−0.167353	−	0.289863i	−0.937488	+	0.348017i	$0.886855\pi$
$824$	4.15589	+	29.2088i	0.144777	+	1.01754i
$825$	3.87766			0.135003
$826$	−10.9394	−	1.91951i	−0.380631	−	0.0667884i
$827$	−0.959658	−	0.959658i	−0.0333706	−	0.0333706i	0.690225	−	0.723595i	$-0.257512\pi$
$827$	−0.959658	−	0.959658i	−0.0333706	−	0.0333706i	−0.723595	+	0.690225i	$0.757512\pi$
$828$	−11.1200	−	0.894982i	−0.386448	−	0.0311028i
$829$	−21.7609	−	5.83081i	−0.755786	−	0.202512i	−0.139703	−	0.990193i	$-0.544615\pi$
$829$	−21.7609	−	5.83081i	−0.755786	−	0.202512i	−0.616083	+	0.787681i	$0.711281\pi$
$830$	−35.3113	−	38.2675i	−1.22567	−	1.32828i
$831$	12.2658	−	21.2450i	0.425496	−	0.736981i
$832$	−14.0925	−	23.2736i	−0.488571	−	0.806865i
$833$	−4.63378	+	16.9347i	−0.160551	+	0.586754i
$834$	−5.39396	−	23.9363i	−0.186778	−	0.828847i
$835$	−0.0569792	−	0.212649i	−0.00197185	−	0.00735903i
$836$	27.0488	−	39.2074i	0.935503	−	1.35602i
$837$	−0.425181	−	0.113927i	−0.0146964	−	0.00393789i
$838$	5.14648	+	9.80290i	0.177782	+	0.338635i
$839$			23.1481i			0.799162i	0.916698	+	0.399581i	$0.130844\pi$
$839$			23.1481i			0.799162i	−0.916698	+	0.399581i	$0.869156\pi$
$840$	8.94783	−	15.7807i	0.308730	−	0.544486i
$841$		−	27.1483i		−	0.936148i
$842$	14.6315	−	7.68148i	0.504235	−	0.264721i
$843$	4.77751	+	1.28013i	0.164546	+	0.0440900i
$844$	35.3923	−	6.49478i	1.21825	−	0.223560i
$845$	0.899395	+	3.35659i	0.0309401	+	0.115470i
$846$	−9.91395	+	2.23407i	−0.340849	+	0.0768090i
$847$	−22.4552	−	3.01671i	−0.771568	−	0.103655i
$848$	0.620395	+	6.11077i	0.0213045	+	0.209845i
$849$	6.69024	−	11.5878i	0.229608	−	0.397693i
$850$	2.28540	−	2.10885i	0.0783885	−	0.0723330i
$851$	12.4114	+	3.32561i	0.425456	+	0.114001i
$852$	14.1390	−	12.0326i	0.484394	−	0.412230i
$853$	3.49507	+	3.49507i	0.119669	+	0.119669i	0.764405	−	0.644736i	$-0.223033\pi$
$853$	3.49507	+	3.49507i	0.119669	+	0.119669i	−0.644736	+	0.764405i	$0.723033\pi$
$854$	−2.85067	−	7.81188i	−0.0975479	−	0.267317i
$855$	−13.0532			−0.446410
$856$	43.6269	+	32.7586i	1.49114	+	1.11967i
$857$	−1.00286	−	1.73701i	−0.0342571	−	0.0593351i	0.848389	−	0.529374i	$-0.177573\pi$
$857$	−1.00286	−	1.73701i	−0.0342571	−	0.0593351i	−0.882646	+	0.470039i	$0.844240\pi$
$858$	21.2564	+	0.854016i	0.725681	+	0.0291556i
$859$	−8.30968	−	31.0122i	−0.283523	−	1.05812i	−0.949912	−	0.312517i	$-0.898828\pi$
$859$	−8.30968	−	31.0122i	−0.283523	−	1.05812i	0.666389	−	0.745604i	$-0.267839\pi$
$860$	25.0863	+	52.8351i	0.855436	+	1.80166i
$861$	−0.491369	−	3.81015i	−0.0167458	−	0.129850i
$862$	−9.72277	+	2.19099i	−0.331159	+	0.0746254i
$863$	5.25318	+	3.03293i	0.178820	+	0.103242i	0.586738	−	0.809777i	$-0.300412\pi$
$863$	5.25318	+	3.03293i	0.178820	+	0.103242i	−0.407918	+	0.913019i	$0.633745\pi$
$864$	−4.23649	−	3.74861i	−0.144128	−	0.127530i
$865$	−11.5513	−	20.0074i	−0.392755	−	0.680272i
$866$	1.42758	−	4.58322i	0.0485111	−	0.155744i
$867$	−7.57243	−	7.57243i	−0.257173	−	0.257173i
$868$	−0.709979	−	2.21837i	−0.0240982	−	0.0752964i
$869$	−21.4321	+	21.4321i	−0.727033	+	0.727033i
$870$	4.13055	−	2.16852i	0.140039	−	0.0735196i
$871$	38.7893	−	22.3950i	1.31432	−	0.758825i
$872$	−38.0228	+	16.2164i	−1.28762	+	0.549157i
$873$	4.06864	−	7.04709i	0.137703	−	0.238508i
$874$	−22.6976	+	35.9030i	−0.767758	+	1.21444i
$875$	−10.1851	+	24.4061i	−0.344318	+	0.825078i
$876$	5.30308	+	1.88849i	0.179174	+	0.0638063i
$877$	38.9504	−	10.4367i	1.31526	−	0.352423i	0.468060	−	0.883697i	$-0.344953\pi$
$877$	38.9504	−	10.4367i	1.31526	−	0.352423i	0.847200	+	0.531274i	$0.178286\pi$
$878$	−2.59334	−	2.81044i	−0.0875209	−	0.0948479i
$879$	15.4711	−	8.93227i	0.521829	−	0.301278i
$880$	40.0949	−	15.2283i	1.35160	−	0.513345i
$881$			26.1054i			0.879514i	0.898117	+	0.439757i	$0.144935\pi$
$881$			26.1054i			0.879514i	−0.898117	+	0.439757i	$0.855065\pi$
$882$	9.88927	+	0.449720i	0.332989	+	0.0151429i
$883$	14.7022	−	14.7022i	0.494768	−	0.494768i	−0.415037	−	0.909805i	$-0.636231\pi$
$883$	14.7022	−	14.7022i	0.494768	−	0.494768i	0.909805	+	0.415037i	$0.136231\pi$
$884$	12.9925	−	11.0569i	0.436984	−	0.371883i
$885$	−1.86242	+	6.95065i	−0.0626046	+	0.233643i
$886$	−7.92289	−	0.318317i	−0.266175	−	0.0106941i
$887$	−30.3666	−	17.5322i	−1.01961	−	0.588673i	−0.105620	−	0.994407i	$-0.533683\pi$
$887$	−30.3666	−	17.5322i	−1.01961	−	0.588673i	−0.913991	+	0.405733i	$0.867016\pi$
$888$	4.02005	+	5.12736i	0.134904	+	0.172063i
$889$	−13.6111	−	33.1074i	−0.456500	−	1.11039i
$890$	31.0973	−	49.1897i	1.04238	−	1.64884i
$891$	4.27235	−	1.14477i	0.143129	−	0.0383513i
$892$	−3.11667	−	2.15017i	−0.104354	−	0.0719929i
$893$	−10.0146	+	37.3751i	−0.335126	+	1.25071i
$894$	4.42766	+	1.37912i	0.148083	+	0.0461248i
$895$	−6.94795			−0.232244
$896$	4.55697	−	29.5844i	0.152238	−	0.988344i
$897$	−18.9705			−0.633408
$898$	−21.7225	−	6.76611i	−0.724889	−	0.225788i
$899$	0.155029	−	0.578576i	0.00517051	−	0.0192966i
$900$	−1.44325	−	0.995683i	−0.0481082	−	0.0331894i
$901$	−3.72019	+	0.996822i	−0.123938	+	0.0332090i
$902$	4.85344	−	7.67717i	0.161602	−	0.255622i
$903$	−19.4967	+	25.2699i	−0.648809	+	0.840931i
$904$	17.9394	+	22.8807i	0.596655	+	0.761002i
$905$	37.3832	+	21.5832i	1.24266	+	0.717449i
$906$	−34.0059	−	1.36625i	−1.12977	−	0.0453906i
$907$	−9.47407	+	35.3577i	−0.314581	+	1.17403i	0.609797	+	0.792557i	$0.291251\pi$
$907$	−9.47407	+	35.3577i	−0.314581	+	1.17403i	−0.924379	+	0.381476i	$0.875416\pi$
$908$	−26.8497	+	22.8497i	−0.891040	+	0.758295i
$909$	−8.94967	+	8.94967i	−0.296842	+	0.296842i
$910$	13.0138	−	27.9690i	0.431402	−	0.927162i
$911$		−	28.8004i		−	0.954201i	−0.878849	−	0.477100i	$-0.841688\pi$
$911$		−	28.8004i		−	0.954201i	0.878849	−	0.477100i	$-0.158312\pi$
$912$	−20.1349	+	7.64735i	−0.666733	+	0.253229i
$913$	58.1782	−	33.5892i	1.92542	−	1.11164i
$914$	−19.5693	−	21.2076i	−0.647296	−	0.701486i
$915$	−5.20413	+	1.39444i	−0.172043	+	0.0460988i
$916$	−41.1148	−	14.6415i	−1.35847	−	0.483769i
$917$	25.7451	−	19.6469i	0.850177	−	0.648799i
$918$	1.89544	−	2.99821i	0.0625589	−	0.0989556i
$919$	7.39818	−	12.8140i	0.244043	−	0.422695i	−0.717819	−	0.696230i	$-0.754859\pi$
$919$	7.39818	−	12.8140i	0.244043	−	0.422695i	0.961862	+	0.273534i	$0.0881928\pi$
$920$	−35.1804	+	15.0041i	−1.15986	+	0.494671i
$921$	−18.3400	+	10.5886i	−0.604323	+	0.348906i
$922$	42.9369	−	22.5417i	1.41405	−	0.742371i
$923$	22.3241	−	22.3241i	0.734807	−	0.734807i
$924$	17.3237	+	15.7374i	0.569909	+	0.517723i
$925$	1.42800	+	1.42800i	0.0469524	+	0.0469524i
$926$	−12.9876	+	41.6965i	−0.426799	+	1.37023i
$927$	5.21544	+	9.03340i	0.171297	+	0.296696i
$928$	5.10103	−	5.76492i	0.167449	−	0.189243i
$929$	15.3531	+	8.86413i	0.503720	+	0.290823i	0.730248	−	0.683182i	$-0.239404\pi$
$929$	15.3531	+	8.86413i	0.503720	+	0.290823i	−0.226529	+	0.974005i	$0.572738\pi$
$930$	−1.47216	+	0.331746i	−0.0482741	+	0.0108784i
$931$	19.0183	−	32.5420i	0.623301	−	1.06652i
$932$	−9.24247	−	19.4659i	−0.302747	−	0.637626i
$933$	−4.30208	−	16.0556i	−0.140844	−	0.525636i
$934$	−34.7163	−	1.39479i	−1.13595	−	0.0456391i
$935$	13.4468	+	23.2905i	0.439757	+	0.761681i
$936$	−7.69224	−	5.77596i	−0.251429	−	0.188793i
$937$	−12.3329			−0.402899			−0.201449	−	0.979499i	$-0.564565\pi$
$937$	−12.3329			−0.402899			−0.201449	+	0.979499i	$0.564565\pi$
$938$	48.5354	+	8.51639i	1.58474	+	0.278070i
$939$	22.4752	+	22.4752i	0.733449	+	0.733449i
$940$	−26.5329	+	22.5801i	−0.865409	+	0.736483i
$941$	56.1715	+	15.0511i	1.83114	+	0.490652i	0.998046	−	0.0624819i	$-0.0199016\pi$
$941$	56.1715	+	15.0511i	1.83114	+	0.490652i	0.833092	+	0.553134i	$0.186568\pi$
$942$	3.44785	−	3.18150i	0.112337	−	0.103659i
$943$	−4.04971	+	7.01430i	−0.131877	+	0.228417i
$944$	1.19928	+	11.8127i	0.0390332	+	0.384470i
$945$	0.853982	−	6.35669i	0.0277800	−	0.206783i
$946$	−73.6129	+	16.5884i	−2.39336	+	0.539336i
$947$	−11.0665	−	41.3008i	−0.359613	−	1.34210i	−0.874579	−	0.484884i	$-0.838862\pi$
$947$	−11.0665	−	41.3008i	−0.359613	−	1.34210i	0.514965	−	0.857211i	$-0.327805\pi$
$948$	13.4801	−	2.47371i	0.437814	−	0.0803423i
$949$	9.24635	+	2.47755i	0.300149	+	0.0804247i
$950$	−5.91086	+	3.10318i	−0.191774	+	0.100680i
$951$		−	9.23007i		−	0.299306i
$952$	18.7689	−	0.146200i	0.608305	−	0.00473838i
$953$		−	17.8131i		−	0.577024i	−0.957476	−	0.288512i	$-0.906839\pi$
$953$		−	17.8131i		−	0.577024i	0.957476	−	0.288512i	$-0.0931605\pi$
$954$	1.00942	+	1.92272i	0.0326812	+	0.0622505i
$955$	11.3149	+	3.03181i	0.366140	+	0.0981069i
$956$	1.87425	−	2.71673i	0.0606175	−	0.0878654i
$957$	1.55778	+	5.81371i	0.0503559	+	0.187931i
$958$	5.11825	+	22.7128i	0.165363	+	0.733818i
$959$	−21.5806	+	27.9709i	−0.696873	+	0.903227i
$960$	−18.8333	−	4.62744i	−0.607844	−	0.149350i
$961$	15.4031	−	26.6790i	0.496875	−	0.860613i
$962$	7.51345	+	8.14246i	0.242243	+	0.262523i
$963$	18.6315	+	4.99229i	0.600391	+	0.160874i
$964$	35.4479	+	2.85298i	1.14170	+	0.0918884i
$965$	34.8654	+	34.8654i	1.12236	+	1.12236i
$966$	−15.9993	−	13.4023i	−0.514768	−	0.431211i
$967$	26.3868			0.848542			0.424271	−	0.905535i	$-0.360530\pi$
$967$	26.3868			0.848542			0.424271	+	0.905535i	$0.360530\pi$
$968$	3.41189	+	23.9797i	0.109662	+	0.770737i
$969$	−6.75272	−	11.6961i	−0.216929	−	0.375732i
$970$	1.11992	−	27.8747i	0.0359585	−	0.895003i
$971$	10.4268	+	38.9135i	0.334613	+	1.24879i	0.904288	+	0.426923i	$0.140402\pi$
$971$	10.4268	+	38.9135i	0.334613	+	1.24879i	−0.569675	+	0.821870i	$0.692931\pi$
$972$	−1.88410	−	0.670951i	−0.0604325	−	0.0215208i
$973$	17.6787	−	42.3629i	0.566752	−	1.35809i
$974$	−3.34420	−	14.8403i	−0.107155	−	0.475512i
$975$	−2.58213	−	1.49079i	−0.0826944	−	0.0477436i
$976$	−7.21056	+	5.19986i	−0.230804	+	0.166443i
$977$	−0.647020	−	1.12067i	−0.0207000	−	0.0358535i	0.855490	−	0.517820i	$-0.173256\pi$
$977$	−0.647020	−	1.12067i	−0.0207000	−	0.0358535i	−0.876190	+	0.481966i	$0.839923\pi$
$978$	14.0371	+	4.37227i	0.448857	+	0.139810i
$979$	53.0900	+	53.0900i	1.69676	+	1.69676i
$980$	30.7349	−	14.3943i	0.981790	−	0.459810i
$981$	−10.3341	+	10.3341i	−0.329943	+	0.329943i
$982$	−14.6567	−	27.9177i	−0.467713	−	0.890890i
$983$	14.3660	−	8.29419i	0.458203	−	0.264544i	−0.253085	−	0.967444i	$-0.581445\pi$
$983$	14.3660	−	8.29419i	0.458203	−	0.264544i	0.711288	+	0.702900i	$0.248112\pi$
$984$	−3.77773	+	1.61117i	−0.120430	+	0.0513621i
$985$	−24.2812	+	42.0563i	−0.773663	+	1.34002i
$986$	4.07989	+	2.57927i	0.129930	+	0.0821407i
$987$	−17.5459	−	7.32216i	−0.558491	−	0.233067i
$988$	−33.0854	+	15.7091i	−1.05259	+	0.499772i
$989$	64.9971	−	17.4159i	2.06679	−	0.553794i
$990$	11.1441	−	10.2833i	0.354184	−	0.326823i
$991$	29.4044	−	16.9766i	0.934062	−	0.539281i	0.0459679	−	0.998943i	$-0.485363\pi$
$991$	29.4044	−	16.9766i	0.934062	−	0.539281i	0.888094	+	0.459662i	$0.152029\pi$
$992$	−2.07649	+	1.37421i	−0.0659287	+	0.0436312i
$993$		−	15.0733i		−	0.478335i
$994$	34.5990	−	3.05608i	1.09741	−	0.0969331i
$995$	−41.5616	+	41.5616i	−1.31759	+	1.31759i
$996$	−30.2785	−	2.43693i	−0.959412	−	0.0772170i
$997$	6.85685	−	25.5901i	0.217159	−	0.810447i	−0.768237	−	0.640166i	$-0.778866\pi$
$997$	6.85685	−	25.5901i	0.217159	−	0.810447i	0.985395	−	0.170282i	$-0.0544677\pi$
$998$	−0.896570	+	22.3156i	−0.0283804	+	0.706387i
$999$	1.99493	+	1.15177i	0.0631168	+	0.0364405i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bs.a.19.3	✓	128
7.3	odd	6	inner	336.2.bs.a.115.24	yes	128
16.11	odd	4	inner	336.2.bs.a.187.24	yes	128
112.59	even	12	inner	336.2.bs.a.283.3	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bs.a.19.3	✓	128	1.1	even	1	trivial
336.2.bs.a.115.24	yes	128	7.3	odd	6	inner
336.2.bs.a.187.24	yes	128	16.11	odd	4	inner
336.2.bs.a.283.3	yes	128	112.59	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bs (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35023 - 0.420569i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(1.64624 + 1.13573i) q^{4} +(2.34159 - 0.627426i) q^{5} +(0.755704 - 1.19537i) q^{6} +(2.44702 - 1.00602i) q^{7} +(-1.74516 - 2.22586i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-1.35023 - 0.420569i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(1.64624 + 1.13573i) q^{4} +(2.34159 - 0.627426i) q^{5} +(0.755704 - 1.19537i) q^{6} +(2.44702 - 1.00602i) q^{7} +(-1.74516 - 2.22586i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-3.42556 - 0.137628i) q^{10} +(1.14477 - 4.27235i) q^{11} +(-1.52311 + 1.29620i) q^{12} +(-2.40484 + 2.40484i) q^{13} +(-3.72715 + 0.329214i) q^{14} +2.42419i q^{15} +(1.42024 + 3.73938i) q^{16} +(-2.17215 + 1.25409i) q^{17} +(0.959049 + 1.03934i) q^{18} +(5.20109 - 1.39363i) q^{19} +(4.56741 + 1.62651i) q^{20} +(0.338402 + 2.62402i) q^{21} +(-3.34253 + 5.28720i) q^{22} +(2.78900 - 4.83069i) q^{23} +(2.60169 - 1.10960i) q^{24} +(0.759236 - 0.438345i) q^{25} +(4.25849 - 2.23569i) q^{26} +(0.707107 - 0.707107i) q^{27} +(5.17096 + 1.12301i) q^{28} +(0.962214 + 0.962214i) q^{29} +(1.01954 - 3.27321i) q^{30} +(-0.220090 - 0.381207i) q^{31} +(-0.344983 - 5.64633i) q^{32} +(3.83049 + 2.21153i) q^{33} +(3.46033 - 0.779773i) q^{34} +(5.09872 - 3.89100i) q^{35} +(-0.857824 - 1.80669i) q^{36} +(0.596202 + 2.22506i) q^{37} +(-7.60878 - 0.305697i) q^{38} +(-1.70048 - 2.94532i) q^{39} +(-5.48299 - 4.11708i) q^{40} -1.45203 q^{41} +(0.646661 - 3.68535i) q^{42} +(8.53016 + 8.53016i) q^{43} +(6.73681 - 5.73318i) q^{44} +(-2.34159 - 0.627426i) q^{45} +(-5.79743 + 5.34957i) q^{46} +(-3.59301 + 6.22327i) q^{47} +(-3.97954 + 0.404023i) q^{48} +(4.97586 - 4.92350i) q^{49} +(-1.20950 + 0.272556i) q^{50} +(-0.649165 - 2.42272i) q^{51} +(-6.69021 + 1.22771i) q^{52} +(1.48322 + 0.397428i) q^{53} +(-1.25214 + 0.657370i) q^{54} -10.7223i q^{55} +(-6.50969 - 3.69106i) q^{56} +5.38456i q^{57} +(-0.894533 - 1.70389i) q^{58} +(2.86721 + 0.768265i) q^{59} +(-2.75322 + 3.99081i) q^{60} +(0.575220 + 2.14675i) q^{61} +(0.136848 + 0.607280i) q^{62} +(-2.62219 - 0.352275i) q^{63} +(-1.90886 + 7.76893i) q^{64} +(-4.12228 + 7.14001i) q^{65} +(-4.24194 - 4.59706i) q^{66} +(-12.7211 - 3.40860i) q^{67} +(-5.00019 - 0.402434i) q^{68} +(3.94424 + 3.94424i) q^{69} +(-8.52088 + 3.10939i) q^{70} -9.28298 q^{71} +(0.398422 + 2.80022i) q^{72} +(-1.40733 - 2.43756i) q^{73} +(0.130779 - 3.25508i) q^{74} +(0.226904 + 0.846818i) q^{75} +(10.1450 + 3.61278i) q^{76} +(-1.49677 - 11.6062i) q^{77} +(1.05733 + 4.69203i) q^{78} +(-5.93453 - 3.42630i) q^{79} +(5.67179 + 7.86498i) q^{80} +(0.500000 + 0.866025i) q^{81} +(1.96057 + 0.610678i) q^{82} +(10.7397 + 10.7397i) q^{83} +(-2.42309 + 4.70411i) q^{84} +(-4.29942 + 4.29942i) q^{85} +(-7.93016 - 15.1052i) q^{86} +(-1.17847 + 0.680388i) q^{87} +(-11.5074 + 4.90782i) q^{88} +(-8.48740 + 14.7006i) q^{89} +(2.89781 + 1.83197i) q^{90} +(-3.46539 + 8.30402i) q^{91} +(10.0777 - 4.78494i) q^{92} +(0.425181 - 0.113927i) q^{93} +(7.46870 - 6.89174i) q^{94} +(11.3044 - 6.52659i) q^{95} +(5.54322 + 1.12815i) q^{96} +8.13728i q^{97} +(-8.78922 + 4.55517i) q^{98} +(-3.12758 + 3.12758i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{4} - 24 q^{8}+O(q^{10}) \) 128 * q + 4 * q^4 - 24 * q^8	\( 128 q + 4 q^{4} - 24 q^{8} + 36 q^{10} - 8 q^{11} - 32 q^{14} - 4 q^{16} + 4 q^{18} + 16 q^{22} + 16 q^{23} - 32 q^{28} + 32 q^{29} - 24 q^{35} - 16 q^{37} + 60 q^{40} - 20 q^{42} - 16 q^{43} - 12 q^{44} - 20 q^{46} - 32 q^{50} - 144 q^{52} - 16 q^{53} - 56 q^{56} - 40 q^{58} - 96 q^{59} - 24 q^{60} - 32 q^{64} - 72 q^{66} + 16 q^{67} - 60 q^{68} + 28 q^{70} + 128 q^{71} - 4 q^{72} - 72 q^{74} + 72 q^{78} - 36 q^{80} + 64 q^{81} - 60 q^{82} + 24 q^{84} - 44 q^{86} - 48 q^{88} - 8 q^{91} + 56 q^{92} + 36 q^{94} + 60 q^{96} + 148 q^{98} - 16 q^{99}+O(q^{100}) \) 128 * q + 4 * q^4 - 24 * q^8 + 36 * q^10 - 8 * q^11 - 32 * q^14 - 4 * q^16 + 4 * q^18 + 16 * q^22 + 16 * q^23 - 32 * q^28 + 32 * q^29 - 24 * q^35 - 16 * q^37 + 60 * q^40 - 20 * q^42 - 16 * q^43 - 12 * q^44 - 20 * q^46 - 32 * q^50 - 144 * q^52 - 16 * q^53 - 56 * q^56 - 40 * q^58 - 96 * q^59 - 24 * q^60 - 32 * q^64 - 72 * q^66 + 16 * q^67 - 60 * q^68 + 28 * q^70 + 128 * q^71 - 4 * q^72 - 72 * q^74 + 72 * q^78 - 36 * q^80 + 64 * q^81 - 60 * q^82 + 24 * q^84 - 44 * q^86 - 48 * q^88 - 8 * q^91 + 56 * q^92 + 36 * q^94 + 60 * q^96 + 148 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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