LMFDB - Embedded newform 117.2.x.a.2.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(2,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

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

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

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

chi := DirichletCharacter("117.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.x (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:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			2.4
Character	$\chi$	$=$	117.2
Dual form			117.2.x.a.59.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.13966 - 1.13966i) q^{2} +(-0.338004 - 1.69875i) q^{3} +0.597661i q^{4} +(-0.184916 + 0.690114i) q^{5} +(-1.55079 + 2.32121i) q^{6} +(1.13668 - 4.24215i) q^{7} +(-1.59819 + 1.59819i) q^{8} +(-2.77151 + 1.14837i) q^{9} +(0.997239 - 0.575756i) q^{10} +(-1.23914 + 1.23914i) q^{11} +(1.01528 - 0.202012i) q^{12} +(-1.52321 + 3.26800i) q^{13} +(-6.13006 + 3.53919i) q^{14} +(1.23483 + 0.0808637i) q^{15} +4.83812 q^{16} +(2.96481 - 5.13520i) q^{17} +(4.46734 + 1.84983i) q^{18} +(-0.836286 - 3.12106i) q^{19} +(-0.412454 - 0.110517i) q^{20} +(-7.59056 - 0.497071i) q^{21} +2.82440 q^{22} +(3.99653 - 6.92220i) q^{23} +(3.25513 + 2.17474i) q^{24} +(3.88806 + 2.24477i) q^{25} +(5.46036 - 1.98848i) q^{26} +(2.88758 + 4.31994i) q^{27} +(2.53537 + 0.679350i) q^{28} -0.668637i q^{29} +(-1.31514 - 1.49945i) q^{30} +(1.11973 + 0.300031i) q^{31} +(-2.31744 - 2.31744i) q^{32} +(2.52382 + 1.68615i) q^{33} +(-9.23127 + 2.47351i) q^{34} +(2.71738 + 1.56888i) q^{35} +(-0.686336 - 1.65642i) q^{36} +(-0.0149826 + 0.0559159i) q^{37} +(-2.60387 + 4.51004i) q^{38} +(6.06637 + 1.48295i) q^{39} +(-0.807405 - 1.39847i) q^{40} +(-1.92301 + 0.515270i) q^{41} +(8.08419 + 9.21717i) q^{42} +(3.58669 - 2.07078i) q^{43} +(-0.740585 - 0.740585i) q^{44} +(-0.280012 - 2.12501i) q^{45} +(-12.4437 + 3.33427i) q^{46} +(1.49759 + 5.58909i) q^{47} +(-1.63531 - 8.21876i) q^{48} +(-10.6416 - 6.14395i) q^{49} +(-1.87279 - 6.98936i) q^{50} +(-9.72554 - 3.30075i) q^{51} +(-1.95316 - 0.910361i) q^{52} -4.09535i q^{53} +(1.63241 - 8.21414i) q^{54} +(-0.626011 - 1.08428i) q^{55} +(4.96314 + 8.59642i) q^{56} +(-5.01924 + 2.47557i) q^{57} +(-0.762020 + 0.762020i) q^{58} +(-0.983077 + 0.983077i) q^{59} +(-0.0483290 + 0.738012i) q^{60} +(4.09503 + 7.09280i) q^{61} +(-0.934180 - 1.61805i) q^{62} +(1.72124 + 13.0625i) q^{63} -4.39405i q^{64} +(-1.97363 - 1.65549i) q^{65} +(-0.954660 - 4.79795i) q^{66} +(3.13514 + 11.7005i) q^{67} +(3.06910 + 1.77195i) q^{68} +(-13.1099 - 4.44938i) q^{69} +(-1.30890 - 4.88489i) q^{70} +(-3.11758 + 0.835353i) q^{71} +(2.59408 - 6.26472i) q^{72} +(-3.59223 - 3.59223i) q^{73} +(0.0808003 - 0.0466501i) q^{74} +(2.49913 - 7.36359i) q^{75} +(1.86534 - 0.499815i) q^{76} +(3.84811 + 6.66512i) q^{77} +(-5.22355 - 8.60368i) q^{78} +(-4.63097 + 8.02108i) q^{79} +(-0.894644 + 3.33886i) q^{80} +(6.36249 - 6.36543i) q^{81} +(2.77882 + 1.60435i) q^{82} +(8.32953 - 2.23189i) q^{83} +(0.297080 - 4.53658i) q^{84} +(2.99563 + 2.99563i) q^{85} +(-6.44760 - 1.72763i) q^{86} +(-1.13585 + 0.226002i) q^{87} -3.96077i q^{88} +(4.89110 + 1.31057i) q^{89} +(-2.10267 + 2.74091i) q^{90} +(12.1320 + 10.1764i) q^{91} +(4.13712 + 2.38857i) q^{92} +(0.131204 - 2.00355i) q^{93} +(4.66292 - 8.07642i) q^{94} +2.30853 q^{95} +(-3.15345 + 4.72006i) q^{96} +(-12.6583 - 3.39178i) q^{97} +(5.12584 + 19.1299i) q^{98} +(2.01129 - 4.85727i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9} - 12 q^{10} - 6 q^{11} + 18 q^{12} - 2 q^{13} - 12 q^{14} - 26 q^{15} - 28 q^{16} - 14 q^{18} - 4 q^{19} - 18 q^{20} - 8 q^{21}+ \cdots - 8 q^{99}+O(q^{100}) $ 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9 - 12 * q^10 - 6 * q^11 + 18 * q^12 - 2 * q^13 - 12 * q^14 - 26 * q^15 - 28 * q^16 - 14 * q^18 - 4 * q^19 - 18 * q^20 - 8 * q^21 - 4 * q^22 - 6 * q^23 + 6 * q^24 - 48 * q^26 - 32 * q^27 + 42 * q^30 - 18 * q^31 + 54 * q^32 + 28 * q^33 + 6 * q^34 + 6 * q^35 + 24 * q^36 - 6 * q^37 + 36 * q^38 + 10 * q^39 - 12 * q^40 + 18 * q^41 - 70 * q^42 - 30 * q^43 + 12 * q^44 + 40 * q^45 - 12 * q^46 - 36 * q^47 - 14 * q^48 - 6 * q^49 - 60 * q^50 + 56 * q^52 + 34 * q^54 - 4 * q^55 - 6 * q^56 - 56 * q^57 + 50 * q^58 - 6 * q^59 + 44 * q^60 + 2 * q^61 + 18 * q^62 + 22 * q^63 + 72 * q^65 + 32 * q^66 + 26 * q^67 + 42 * q^68 + 30 * q^69 - 16 * q^70 - 48 * q^71 + 30 * q^72 - 22 * q^73 + 30 * q^74 - 24 * q^75 + 6 * q^76 + 72 * q^77 - 20 * q^78 + 8 * q^79 - 54 * q^80 + 82 * q^81 - 12 * q^82 + 54 * q^83 - 38 * q^84 - 24 * q^85 - 54 * q^86 + 2 * q^87 - 114 * q^90 - 16 * q^91 + 120 * q^92 + 52 * q^93 + 26 * q^94 - 12 * q^95 + 94 * q^96 - 24 * q^97 + 36 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.13966	−	1.13966i	−0.805863	−	0.805863i	0.178142	−	0.984005i	$-0.442991\pi$
$2$	−1.13966	−	1.13966i	−0.805863	−	0.805863i	−0.984005	+	0.178142i	$0.942991\pi$
$3$	−0.338004	−	1.69875i	−0.195147	−	0.980774i
$3$	−0.338004	−	1.69875i	−0.195147	−	0.980774i
$4$			0.597661i			0.298830i
$5$	−0.184916	+	0.690114i	−0.0826968	+	0.308629i	−0.994868	−	0.101181i	$-0.967738\pi$
$5$	−0.184916	+	0.690114i	−0.0826968	+	0.308629i	0.912171	+	0.409809i	$0.134405\pi$
$6$	−1.55079	+	2.32121i	−0.633108	+	0.947631i
$7$	1.13668	−	4.24215i	0.429625	−	1.60338i	−0.323985	−	0.946062i	$-0.605023\pi$
$7$	1.13668	−	4.24215i	0.429625	−	1.60338i	0.753611	−	0.657321i	$-0.228310\pi$
$8$	−1.59819	+	1.59819i	−0.565047	+	0.565047i
$9$	−2.77151	+	1.14837i	−0.923835	+	0.382790i
$10$	0.997239	−	0.575756i	0.315355	−	0.182070i
$11$	−1.23914	+	1.23914i	−0.373614	+	0.373614i	−0.868792	−	0.495177i	$-0.835103\pi$
$11$	−1.23914	+	1.23914i	−0.373614	+	0.373614i	0.495177	+	0.868792i	$0.335103\pi$
$12$	1.01528	−	0.202012i	0.293085	−	0.0583158i
$13$	−1.52321	+	3.26800i	−0.422462	+	0.906381i
$13$	−1.52321	+	3.26800i	−0.422462	+	0.906381i
$14$	−6.13006	+	3.53919i	−1.63833	+	0.945888i
$15$	1.23483	+	0.0808637i	0.318833	+	0.0208789i
$16$	4.83812			1.20953
$17$	2.96481	−	5.13520i	0.719071	−	1.24547i	−0.242297	−	0.970202i	$-0.577901\pi$
$17$	2.96481	−	5.13520i	0.719071	−	1.24547i	0.961368	−	0.275266i	$-0.0887659\pi$
$18$	4.46734	+	1.84983i	1.05296	+	0.436008i
$19$	−0.836286	−	3.12106i	−0.191857	−	0.716021i	−0.993058	−	0.117625i	$-0.962472\pi$
$19$	−0.836286	−	3.12106i	−0.191857	−	0.716021i	0.801201	−	0.598395i	$-0.204195\pi$
$20$	−0.412454	−	0.110517i	−0.0922275	−	0.0247123i
$21$	−7.59056	−	0.497071i	−1.65640	−	0.108470i
$22$	2.82440			0.602164
$23$	3.99653	−	6.92220i	0.833335	−	1.44338i	−0.0620443	−	0.998073i	$-0.519762\pi$
$23$	3.99653	−	6.92220i	0.833335	−	1.44338i	0.895379	−	0.445305i	$-0.146905\pi$
$24$	3.25513	+	2.17474i	0.664450	+	0.443916i
$25$	3.88806	+	2.24477i	0.777613	+	0.448955i
$26$	5.46036	−	1.98848i	1.07087	−	0.389972i
$27$	2.88758	+	4.31994i	0.555714	+	0.831373i
$28$	2.53537	+	0.679350i	0.479139	+	0.128385i
$29$		−	0.668637i		−	0.124163i	−0.998071	−	0.0620814i	$-0.980226\pi$
$29$		−	0.668637i		−	0.124163i	0.998071	−	0.0620814i	$-0.0197738\pi$
$30$	−1.31514	−	1.49945i	−0.240110	−	0.273761i
$31$	1.11973	+	0.300031i	0.201109	+	0.0538871i	0.357967	−	0.933734i	$-0.383470\pi$
$31$	1.11973	+	0.300031i	0.201109	+	0.0538871i	−0.156858	+	0.987621i	$0.550137\pi$
$32$	−2.31744	−	2.31744i	−0.409669	−	0.409669i
$33$	2.52382	+	1.68615i	0.439341	+	0.293522i
$34$	−9.23127	+	2.47351i	−1.58315	+	0.424204i
$35$	2.71738	+	1.56888i	0.459321	+	0.265189i
$36$	−0.686336	−	1.65642i	−0.114389	−	0.276070i
$37$	−0.0149826	+	0.0559159i	−0.00246313	+	0.00919251i	−0.967146	−	0.254220i	$-0.918181\pi$
$37$	−0.0149826	+	0.0559159i	−0.00246313	+	0.00919251i	0.964683	+	0.263412i	$0.0848480\pi$
$38$	−2.60387	+	4.51004i	−0.422404	+	0.731625i
$39$	6.06637	+	1.48295i	0.971397	+	0.237462i
$40$	−0.807405	−	1.39847i	−0.127662	−	0.221117i
$41$	−1.92301	+	0.515270i	−0.300324	+	0.0804717i	−0.405835	−	0.913947i	$-0.633019\pi$
$41$	−1.92301	+	0.515270i	−0.300324	+	0.0804717i	0.105510	+	0.994418i	$0.466352\pi$
$42$	8.08419	+	9.21717i	1.24742	+	1.42224i
$43$	3.58669	−	2.07078i	0.546965	−	0.315790i	−0.200932	−	0.979605i	$-0.564397\pi$
$43$	3.58669	−	2.07078i	0.546965	−	0.315790i	0.747897	+	0.663815i	$0.231064\pi$
$44$	−0.740585	−	0.740585i	−0.111647	−	0.111647i
$45$	−0.280012	−	2.12501i	−0.0417418	−	0.316777i
$46$	−12.4437	+	3.33427i	−1.83472	+	0.491611i
$47$	1.49759	+	5.58909i	0.218446	+	0.815252i	0.984925	+	0.172983i	$0.0553404\pi$
$47$	1.49759	+	5.58909i	0.218446	+	0.815252i	−0.766479	+	0.642270i	$0.777993\pi$
$48$	−1.63531	−	8.21876i	−0.236036	−	1.18628i
$49$	−10.6416	−	6.14395i	−1.52023	−	0.877708i
$50$	−1.87279	−	6.98936i	−0.264853	−	0.988445i
$51$	−9.72554	−	3.30075i	−1.36185	−	0.462197i
$52$	−1.95316	−	0.910361i	−0.270854	−	0.126244i
$53$		−	4.09535i		−	0.562540i	−0.959629	−	0.281270i	$-0.909244\pi$
$53$		−	4.09535i		−	0.562540i	0.959629	−	0.281270i	$-0.0907556\pi$
$54$	1.63241	−	8.21414i	0.222143	−	1.11780i
$55$	−0.626011	−	1.08428i	−0.0844114	−	0.146205i
$56$	4.96314	+	8.59642i	0.663228	+	1.14874i
$57$	−5.01924	+	2.47557i	−0.664814	+	0.327898i
$58$	−0.762020	+	0.762020i	−0.100058	+	0.100058i
$59$	−0.983077	+	0.983077i	−0.127986	+	0.127986i	−0.768198	−	0.640212i	$-0.778846\pi$
$59$	−0.983077	+	0.983077i	−0.127986	+	0.127986i	0.640212	+	0.768198i	$0.278846\pi$
$60$	−0.0483290	+	0.738012i	−0.00623925	+	0.0952769i
$61$	4.09503	+	7.09280i	0.524315	+	0.908139i	0.999599	+	0.0283074i	$0.00901172\pi$
$61$	4.09503	+	7.09280i	0.524315	+	0.908139i	−0.475285	+	0.879832i	$0.657655\pi$
$62$	−0.934180	−	1.61805i	−0.118641	−	0.205492i
$63$	1.72124	+	13.0625i	0.216856	+	1.64572i
$64$		−	4.39405i		−	0.549256i
$65$	−1.97363	−	1.65549i	−0.244799	−	0.205339i
$66$	−0.954660	−	4.79795i	−0.117511	−	0.590587i
$67$	3.13514	+	11.7005i	0.383019	+	1.42945i	0.841266	+	0.540621i	$0.181811\pi$
$67$	3.13514	+	11.7005i	0.383019	+	1.42945i	−0.458248	+	0.888825i	$0.651523\pi$
$68$	3.06910	+	1.77195i	0.372184	+	0.214880i
$69$	−13.1099	−	4.44938i	−1.57825	−	0.535642i
$70$	−1.30890	−	4.88489i	−0.156444	−	0.583856i
$71$	−3.11758	+	0.835353i	−0.369988	+	0.0991381i	−0.439022	−	0.898476i	$-0.644675\pi$
$71$	−3.11758	+	0.835353i	−0.369988	+	0.0991381i	0.0690337	+	0.997614i	$0.478008\pi$
$72$	2.59408	−	6.26472i	0.305716	−	0.738304i
$73$	−3.59223	−	3.59223i	−0.420439	−	0.420439i	0.464916	−	0.885355i	$-0.346085\pi$
$73$	−3.59223	−	3.59223i	−0.420439	−	0.420439i	−0.885355	+	0.464916i	$0.846085\pi$
$74$	0.0808003	−	0.0466501i	0.00939285	−	0.00542296i
$75$	2.49913	−	7.36359i	0.288574	−	0.850274i
$76$	1.86534	−	0.499815i	0.213969	−	0.0573327i
$77$	3.84811	+	6.66512i	0.438533	+	0.759561i
$78$	−5.22355	−	8.60368i	−0.591451	−	0.974175i
$79$	−4.63097	+	8.02108i	−0.521025	+	0.902441i	0.478676	+	0.877992i	$0.341117\pi$
$79$	−4.63097	+	8.02108i	−0.521025	+	0.902441i	−0.999701	+	0.0244500i	$0.992217\pi$
$80$	−0.894644	+	3.33886i	−0.100024	+	0.373296i
$81$	6.36249	−	6.36543i	0.706943	−	0.707270i
$82$	2.77882	+	1.60435i	0.306869	+	0.177171i
$83$	8.32953	−	2.23189i	0.914285	−	0.244982i	0.229144	−	0.973393i	$-0.426407\pi$
$83$	8.32953	−	2.23189i	0.914285	−	0.244982i	0.685141	+	0.728411i	$0.259741\pi$
$84$	0.297080	−	4.53658i	0.0324141	−	0.494981i
$85$	2.99563	+	2.99563i	0.324922	+	0.324922i
$86$	−6.44760	−	1.72763i	−0.695262	−	0.186295i
$87$	−1.13585	+	0.226002i	−0.121776	+	0.0242300i
$88$		−	3.96077i		−	0.422219i
$89$	4.89110	+	1.31057i	0.518455	+	0.138920i	0.508552	−	0.861031i	$-0.330181\pi$
$89$	4.89110	+	1.31057i	0.518455	+	0.138920i	0.00990324	+	0.999951i	$0.496848\pi$
$90$	−2.10267	+	2.74091i	−0.221641	+	0.288917i
$91$	12.1320	+	10.1764i	1.27178	+	1.06677i
$92$	4.13712	+	2.38857i	0.431325	+	0.249026i
$93$	0.131204	−	2.00355i	0.0136052	−	0.207759i
$94$	4.66292	−	8.07642i	0.480944	−	0.833019i
$95$	2.30853			0.236850
$96$	−3.15345	+	4.72006i	−0.321847	+	0.481739i
$97$	−12.6583	−	3.39178i	−1.28526	−	0.344383i	−0.449399	−	0.893331i	$-0.648362\pi$
$97$	−12.6583	−	3.39178i	−1.28526	−	0.344383i	−0.835857	+	0.548948i	$0.815029\pi$
$98$	5.12584	+	19.1299i	0.517788	+	1.93241i
$99$	2.01129	−	4.85727i	0.202142	−	0.488174i
$100$	−1.34161	+	2.32374i	−0.134161	+	0.232374i
$101$	12.2336			1.21729			0.608644	−	0.793444i	$-0.291714\pi$
$101$	12.2336			1.21729			0.608644	+	0.793444i	$0.291714\pi$
$102$	7.32209	+	14.8456i	0.724995	+	1.46993i
$103$	9.33513	−	5.38964i	0.919818	−	0.531057i	0.0362409	−	0.999343i	$-0.488462\pi$
$103$	9.33513	−	5.38964i	0.919818	−	0.531057i	0.883577	+	0.468286i	$0.155128\pi$
$104$	−2.78852	−	7.65728i	−0.273437	−	0.750858i
$105$	1.74665	−	5.14644i	0.170456	−	0.502241i
$106$	−4.66732	+	4.66732i	−0.453330	+	0.453330i
$107$	−2.85766	+	1.64987i	−0.276261	+	0.159499i	−0.631729	−	0.775189i	$-0.717655\pi$
$107$	−2.85766	+	1.64987i	−0.276261	+	0.159499i	0.355469	+	0.934688i	$0.384321\pi$
$108$	−2.58186	+	1.72579i	−0.248440	+	0.166064i
$109$	0.650028	−	0.650028i	0.0622613	−	0.0622613i	−0.675291	−	0.737552i	$-0.735982\pi$
$109$	0.650028	−	0.650028i	0.0622613	−	0.0622613i	0.737552	+	0.675291i	$0.235982\pi$
$110$	−0.522276	+	1.94916i	−0.0497970	+	0.185845i
$111$	0.100051	+	0.00655190i	0.00949645	+	0.000621879i
$112$	5.49941	−	20.5241i	0.519645	−	1.93934i
$113$			18.0509i			1.69808i	0.528327	+	0.849041i	$0.322820\pi$
$113$			18.0509i			1.69808i	−0.528327	+	0.849041i	$0.677180\pi$
$114$	8.54155	+	2.89892i	0.799990	+	0.271508i
$115$	4.03809	+	4.03809i	0.376554	+	0.376554i
$116$	0.399618			0.0371036
$117$	0.468703	−	10.8065i	0.0433316	−	0.999061i
$118$	2.24075			0.206278
$119$	−18.4143	−	18.4143i	−1.68803	−	1.68803i
$120$	−2.10274	+	1.84427i	−0.191953	+	0.168358i
$121$			7.92907i			0.720824i
$122$	3.41644	−	12.7503i	0.309310	−	1.15436i
$123$	1.52530	+	3.09256i	0.137532	+	0.278846i
$124$	−0.179316	+	0.669218i	−0.0161031	+	0.0600976i
$125$	−4.79411	+	4.79411i	−0.428798	+	0.428798i
$126$	12.9252	−	16.8485i	1.15147	−	1.50098i
$127$	0.642814	−	0.371129i	0.0570405	−	0.0329323i	−0.471209	−	0.882022i	$-0.656182\pi$
$127$	0.642814	−	0.371129i	0.0570405	−	0.0329323i	0.528249	+	0.849089i	$0.322849\pi$
$128$	−9.64261	+	9.64261i	−0.852294	+	0.852294i
$129$	−4.73005	−	5.39296i	−0.416457	−	0.474823i
$130$	0.362570	+	4.13597i	0.0317995	+	0.362749i
$131$	−3.97273	+	2.29366i	−0.347099	+	0.200398i	−0.663407	−	0.748259i	$-0.730890\pi$
$131$	−3.97273	+	2.29366i	−0.347099	+	0.200398i	0.316308	+	0.948657i	$0.397557\pi$
$132$	−1.00775	+	1.50839i	−0.0877131	+	0.131288i
$133$	−14.1906			−1.23048
$134$	9.76163	−	16.9076i	0.843277	−	1.46060i
$135$	−3.51521	+	1.19393i	−0.302541	+	0.102757i
$136$	3.46870	+	12.9454i	0.297439	+	1.11006i
$137$	4.28899	+	1.14923i	0.366434	+	0.0981856i	0.437337	−	0.899298i	$-0.355922\pi$
$137$	4.28899	+	1.14923i	0.366434	+	0.0981856i	−0.0709037	+	0.997483i	$0.522588\pi$
$138$	9.87011	+	20.0117i	0.840199	+	1.70351i
$139$	−22.4431			−1.90360			−0.951799	−	0.306724i	$-0.900767\pi$
$139$	−22.4431			−1.90360			−0.951799	+	0.306724i	$0.900767\pi$
$140$	−0.937658	+	1.62407i	−0.0792466	+	0.137259i
$141$	8.98827	−	4.43317i	0.756949	−	0.373340i
$142$	4.50501	+	2.60097i	0.378052	+	0.218268i
$143$	−2.16204	−	5.93698i	−0.180799	−	0.496475i
$144$	−13.4089	+	5.55596i	−1.11741	+	0.462996i
$145$	0.461436	+	0.123641i	0.0383202	+	0.0102679i
$146$			8.18786i			0.677632i
$147$	−6.84012	+	20.1542i	−0.564164	+	1.66229i
$148$	−0.0334187	−	0.00895451i	−0.00274700	−	0.000736057i
$149$	4.05750	+	4.05750i	0.332403	+	0.332403i	0.853499	−	0.521095i	$-0.174476\pi$
$149$	4.05750	+	4.05750i	0.332403	+	0.332403i	−0.521095	+	0.853499i	$0.674476\pi$
$150$	−11.2402	+	5.54385i	−0.917756	+	0.452653i
$151$	21.7048	−	5.81580i	1.76632	−	0.473283i	0.778333	−	0.627851i	$-0.216065\pi$
$151$	21.7048	−	5.81580i	1.76632	−	0.473283i	0.987982	+	0.154568i	$0.0493987\pi$
$152$	6.32461	+	3.65151i	0.512993	+	0.296177i
$153$	−2.31987	+	17.6369i	−0.187551	+	1.42586i
$154$	3.21044	−	11.9815i	0.258705	−	0.965500i
$155$	−0.414111	+	0.717261i	−0.0332622	+	0.0576118i
$156$	−0.886301	+	3.62563i	−0.0709609	+	0.290283i
$157$	3.80152	+	6.58443i	0.303394	+	0.525494i	0.976903	−	0.213685i	$-0.0685467\pi$
$157$	3.80152	+	6.58443i	0.303394	+	0.525494i	−0.673508	+	0.739180i	$0.735213\pi$
$158$	14.4191	−	3.86358i	1.14712	−	0.307370i
$159$	−6.95698	+	1.38425i	−0.551724	+	0.109778i
$160$	2.02783	−	1.17077i	0.160314	−	0.0925573i
$161$	−24.8222	−	24.8222i	−1.95627	−	1.95627i
$162$	−14.5055	+	0.00335139i	−1.13966	+	0.000263310i
$163$	−3.50378	+	0.938834i	−0.274437	+	0.0735352i	−0.393413	−	0.919362i	$-0.628706\pi$
$163$	−3.50378	+	0.938834i	−0.274437	+	0.0735352i	0.118976	+	0.992897i	$0.462039\pi$
$164$	−0.307957	−	1.14931i	−0.0240474	−	0.0897460i
$165$	−1.63033	+	1.42993i	−0.126921	+	0.111320i
$166$	−12.0365	−	6.94925i	−0.934210	−	0.539366i
$167$	−5.44449	−	20.3191i	−0.421308	−	1.57234i	−0.771856	−	0.635797i	$-0.780672\pi$
$167$	−5.44449	−	20.3191i	−0.421308	−	1.57234i	0.350549	−	0.936545i	$-0.385995\pi$
$168$	12.9256	−	11.3368i	0.997232	−	0.874651i
$169$	−8.35967	−	9.95569i	−0.643052	−	0.765823i
$170$		−	6.82802i		−	0.523685i
$171$	5.90191	+	7.68968i	0.451330	+	0.588044i
$172$	1.23762	+	2.14362i	0.0943677	+	0.163450i
$173$	−9.16488	−	15.8740i	−0.696793	−	1.20688i	−0.969573	−	0.244804i	$-0.921276\pi$
$173$	−9.16488	−	15.8740i	−0.696793	−	1.20688i	0.272780	−	0.962077i	$-0.412057\pi$
$174$	1.55205	+	1.03692i	0.117660	+	0.0786084i
$175$	13.9422	−	13.9422i	1.05393	−	1.05393i
$176$	−5.99511	+	5.99511i	−0.451898	+	0.451898i
$177$	2.00229	+	1.33772i	0.150501	+	0.100549i
$178$	−4.08060	−	7.06780i	−0.305854	−	0.529754i
$179$	8.60225	+	14.8995i	0.642962	+	1.11364i	0.984768	+	0.173872i	$0.0556281\pi$
$179$	8.60225	+	14.8995i	0.642962	+	1.11364i	−0.341806	+	0.939771i	$0.611039\pi$
$180$	1.27003	−	0.167352i	0.0946627	−	0.0124737i
$181$		−	1.08994i		−	0.0810148i	−0.999179	−	0.0405074i	$-0.987103\pi$
$181$		−	1.08994i		−	0.0810148i	0.999179	−	0.0405074i	$-0.0128974\pi$
$182$	−2.22873	−	25.4240i	−0.165204	−	1.88455i
$183$	10.6648	−	9.35383i	0.788361	−	0.691455i
$184$	4.67578	+	17.4502i	0.344703	+	1.28645i
$185$	−0.0358178	−	0.0206794i	−0.00263338	−	0.00152038i
$186$	−2.43290	+	2.13385i	−0.178389	+	0.156461i
$187$	2.68941	+	10.0370i	0.196669	+	0.733980i
$188$	−3.34038	+	0.895051i	−0.243622	+	0.0652783i
$189$	21.6081	−	7.33914i	1.57176	−	0.533844i
$190$	−2.63095	−	2.63095i	−0.190869	−	0.190869i
$191$	−2.42622	+	1.40078i	−0.175555	+	0.101357i	−0.585203	−	0.810887i	$-0.698985\pi$
$191$	−2.42622	+	1.40078i	−0.175555	+	0.101357i	0.409647	+	0.912244i	$0.365652\pi$
$192$	−7.46439	+	1.48521i	−0.538696	+	0.107186i
$193$	−2.46717	+	0.661077i	−0.177591	+	0.0475854i	−0.346519	−	0.938043i	$-0.612636\pi$
$193$	−2.46717	+	0.661077i	−0.177591	+	0.0475854i	0.168928	+	0.985628i	$0.445970\pi$
$194$	10.5607	+	18.2917i	0.758214	+	1.31327i
$195$	−2.14517	+	3.91227i	−0.153619	+	0.280163i
$196$	3.67200	−	6.36009i	0.262286	−	0.454292i
$197$	−1.48877	+	5.55616i	−0.106070	+	0.395860i	−0.998464	−	0.0553970i	$-0.982358\pi$
$197$	−1.48877	+	5.55616i	−0.106070	+	0.395860i	0.892394	+	0.451257i	$0.149024\pi$
$198$	−7.82784	+	3.24346i	−0.556301	+	0.230503i
$199$	−2.16918	−	1.25238i	−0.153769	−	0.0887788i	0.421141	−	0.906995i	$-0.361630\pi$
$199$	−2.16918	−	1.25238i	−0.153769	−	0.0887788i	−0.574910	+	0.818216i	$0.694963\pi$
$200$	−9.80146	+	2.62629i	−0.693068	+	0.185707i
$201$	18.8166	−	9.28065i	1.32722	−	0.654607i
$202$	−13.9422	−	13.9422i	−0.980967	−	0.980967i
$203$	−2.83646	−	0.760027i	−0.199080	−	0.0533434i
$204$	1.97273	−	5.81257i	0.138119	−	0.406961i
$205$		−	1.42238i		−	0.0993434i
$206$	−16.7813	−	4.49653i	−1.16921	−	0.313288i
$207$	−3.12717	+	23.7744i	−0.217353	+	1.65244i
$208$	−7.36947	+	15.8110i	−0.510981	+	1.09630i
$209$	4.90370	+	2.83115i	0.339196	+	0.195835i
$210$	−7.85579	+	3.87461i	−0.542101	+	0.267374i
$211$	0.947470	−	1.64107i	0.0652265	−	0.112976i	−0.831568	−	0.555423i	$-0.812556\pi$
$211$	0.947470	−	1.64107i	0.0652265	−	0.112976i	0.896794	+	0.442447i	$0.145890\pi$
$212$	2.44763			0.168104
$213$	2.47281	+	5.01363i	0.169434	+	0.343529i
$214$	5.13707	+	1.37647i	0.351163	+	0.0940938i
$215$	0.765837	+	2.85814i	0.0522297	+	0.194924i
$216$	−11.5190	−	2.28920i	−0.783769	−	0.155760i
$217$	2.54555	−	4.40902i	0.172803	−	0.299304i
$218$	−1.48162			−0.100348
$219$	−4.88811	+	7.31649i	−0.330308	+	0.494403i
$220$	0.648034	−	0.374142i	0.0436904	−	0.0252247i
$221$	12.2658	+	17.5110i	0.825088	+	1.17792i
$222$	−0.106558	−	0.121492i	−0.00715169	−	0.00815398i
$223$	10.7566	−	10.7566i	0.720318	−	0.720318i	−0.248352	−	0.968670i	$-0.579889\pi$
$223$	10.7566	−	10.7566i	0.720318	−	0.720318i	0.968670	+	0.248352i	$0.0798890\pi$
$224$	−12.4651	+	7.19674i	−0.832861	+	0.480853i
$225$	−13.3536	−	1.75647i	−0.890241	−	0.117098i
$226$	20.5719	−	20.5719i	1.36842	−	1.36842i
$227$	5.15691	−	19.2458i	0.342276	−	1.27739i	−0.553487	−	0.832858i	$-0.686703\pi$
$227$	5.15691	−	19.2458i	0.342276	−	1.27739i	0.895762	−	0.444533i	$-0.146630\pi$
$228$	−1.47955	−	2.99980i	−0.0979858	−	0.198667i
$229$	−2.15370	+	8.03772i	−0.142321	+	0.531148i	0.857539	+	0.514418i	$0.171992\pi$
$229$	−2.15370	+	8.03772i	−0.142321	+	0.531148i	−0.999860	+	0.0167295i	$0.994675\pi$
$230$		−	9.20411i		−	0.606901i
$231$	10.0217	−	8.78982i	0.659380	−	0.578328i
$232$	1.06861	+	1.06861i	0.0701578	+	0.0701578i
$233$	−12.2606			−0.803216			−0.401608	−	0.915812i	$-0.631548\pi$
$233$	−12.2606			−0.803216			−0.401608	+	0.915812i	$0.631548\pi$
$234$	−12.8499	+	11.7816i	−0.840025	+	0.770187i
$235$	−4.13404			−0.269675
$236$	−0.587546	−	0.587546i	−0.0382460	−	0.0382460i
$237$	15.1911	+	5.15570i	0.986768	+	0.334899i
$238$			41.9721i			2.72064i
$239$	−2.44430	+	9.12224i	−0.158108	+	0.590069i	0.840711	+	0.541485i	$0.182138\pi$
$239$	−2.44430	+	9.12224i	−0.158108	+	0.590069i	−0.998819	+	0.0485841i	$0.984529\pi$
$240$	5.97428	+	0.391228i	0.385638	+	0.0252537i
$241$	−1.40622	+	5.24807i	−0.0905823	+	0.338058i	−0.996313	−	0.0857965i	$-0.972657\pi$
$241$	−1.40622	+	5.24807i	−0.0905823	+	0.338058i	0.905730	+	0.423854i	$0.139323\pi$
$242$	9.03646	−	9.03646i	0.580886	−	0.580886i
$243$	−12.9638	−	8.65674i	−0.831630	−	0.555330i
$244$	−4.23908	+	2.44744i	−0.271380	+	0.156681i
$245$	6.20784	−	6.20784i	0.396604	−	0.396604i
$246$	1.78614	−	5.26280i	0.113880	−	0.335544i
$247$	11.4735	+	2.02104i	0.730040	+	0.128596i
$248$	−2.26905	+	1.31004i	−0.144085	+	0.0831875i
$249$	−6.60684	−	13.3954i	−0.418692	−	0.848899i
$250$	10.9273			0.691105
$251$	−8.35500	+	14.4713i	−0.527363	+	0.913420i	0.472128	+	0.881530i	$0.343486\pi$
$251$	−8.35500	+	14.4713i	−0.527363	+	0.913420i	−0.999491	+	0.0318898i	$0.989847\pi$
$252$	−7.80693	+	1.02872i	−0.491790	+	0.0648032i
$253$	3.62531	+	13.5298i	0.227921	+	0.850613i
$254$	−1.15555	−	0.309629i	−0.0725058	−	0.0194279i
$255$	4.07630	−	6.10137i	0.255268	−	0.382083i
$256$	13.1905			0.824409
$257$	−9.11059	+	15.7800i	−0.568303	+	0.984329i	0.428431	+	0.903574i	$0.359066\pi$
$257$	−9.11059	+	15.7800i	−0.568303	+	0.984329i	−0.996734	+	0.0807549i	$0.974267\pi$
$258$	−0.755493	+	11.5368i	−0.0470349	+	0.718250i
$259$	0.220173	+	0.127117i	0.0136809	+	0.00789867i
$260$	0.989422	−	1.17956i	0.0613614	−	0.0731533i
$261$	0.767843	+	1.85313i	0.0475283	+	0.114706i
$262$	7.14157	+	1.91358i	0.441208	+	0.118221i
$263$		−	3.30117i		−	0.203559i	−0.994807	−	0.101779i	$-0.967546\pi$
$263$		−	3.30117i		−	0.203559i	0.994807	−	0.101779i	$-0.0324536\pi$
$264$	−6.72836	+	1.33876i	−0.414102	+	0.0823948i
$265$	2.82626	+	0.757294i	0.173616	+	0.0465202i
$266$	16.1725	+	16.1725i	0.991600	+	0.991600i
$267$	0.573111	−	8.75173i	0.0350738	−	0.535597i
$268$	−6.99294	+	1.87375i	−0.427162	+	0.114458i
$269$	12.9794	+	7.49365i	0.791367	+	0.456896i	0.840444	−	0.541899i	$-0.182294\pi$
$269$	12.9794	+	7.49365i	0.791367	+	0.456896i	−0.0490765	+	0.998795i	$0.515628\pi$
$270$	5.36684	+	2.64547i	0.326615	+	0.160998i
$271$	6.77811	−	25.2963i	0.411741	−	1.53664i	−0.379534	−	0.925178i	$-0.623916\pi$
$271$	6.77811	−	25.2963i	0.411741	−	1.53664i	0.791275	−	0.611460i	$-0.209418\pi$
$272$	14.3441	−	24.8447i	0.869739	−	1.50643i
$273$	13.1864	−	24.0488i	0.798080	−	1.45550i
$274$	−3.57827	−	6.19774i	−0.216171	−	0.374419i
$275$	−7.59944	+	2.03626i	−0.458263	+	0.122791i
$276$	2.65922	−	7.83529i	0.160066	−	0.471629i
$277$	15.9646	−	9.21717i	0.959221	−	0.553806i	0.0632875	−	0.997995i	$-0.479841\pi$
$277$	15.9646	−	9.21717i	0.959221	−	0.553806i	0.895933	+	0.444189i	$0.146508\pi$
$278$	25.5775	+	25.5775i	1.53404	+	1.53404i
$279$	−3.44788	+	0.454328i	−0.206419	+	0.0271999i
$280$	−6.85027	+	1.83553i	−0.409382	+	0.109694i
$281$	7.20538	+	26.8908i	0.429837	+	1.60417i	0.753128	+	0.657873i	$0.228544\pi$
$281$	7.20538	+	26.8908i	0.429837	+	1.60417i	−0.323292	+	0.946299i	$0.604789\pi$
$282$	−15.2959	−	5.19128i	−0.910858	−	0.309136i
$283$	−6.91192	−	3.99060i	−0.410871	−	0.237216i	0.280293	−	0.959914i	$-0.409568\pi$
$283$	−6.91192	−	3.99060i	−0.410871	−	0.237216i	−0.691164	+	0.722698i	$0.742902\pi$
$284$	−0.499257	−	1.86325i	−0.0296255	−	0.110564i
$285$	−0.780294	−	3.92162i	−0.0462206	−	0.232297i
$286$	−4.30215	+	9.23015i	−0.254391	+	0.545790i
$287$			8.74342i			0.516108i
$288$	9.08408	+	3.76152i	0.535284	+	0.221650i
$289$	−9.08016	−	15.7273i	−0.534127	−	0.925136i
$290$	−0.384972	−	0.666790i	−0.0226063	−	0.0391553i
$291$	−1.48323	+	22.6497i	−0.0869484	+	1.32775i
$292$	2.14693	−	2.14693i	0.125640	−	0.125640i
$293$	21.2995	−	21.2995i	1.24433	−	1.24433i	0.286144	−	0.958187i	$-0.407626\pi$
$293$	21.2995	−	21.2995i	1.24433	−	1.24433i	0.958187	−	0.286144i	$-0.0923735\pi$
$294$	30.7644	−	15.1735i	1.79422	−	0.884938i
$295$	−0.496649	−	0.860222i	−0.0289160	−	0.0500840i
$296$	−0.0654193	−	0.113309i	−0.00380242	−	0.00658598i
$297$	−8.93112	−	1.77490i	−0.518236	−	0.102990i
$298$		−	9.24836i		−	0.535743i
$299$	16.5342	+	23.6046i	0.956198	+	1.36509i
$300$	4.40093	+	1.49363i	0.254088	+	0.0862348i
$301$	−4.70762	−	17.5691i	−0.271343	−	1.01267i
$302$	−31.3642	−	18.1082i	−1.80481	−	1.04201i
$303$	−4.13501	−	20.7818i	−0.237550	−	1.19388i
$304$	−4.04605	−	15.1001i	−0.232057	−	0.866049i
$305$	−5.65207	+	1.51447i	−0.323637	+	0.0867182i
$306$	22.7440	−	17.4563i	1.30019	−	0.997908i
$307$	−9.91862	−	9.91862i	−0.566086	−	0.566086i	0.364944	−	0.931029i	$-0.381088\pi$
$307$	−9.91862	−	9.91862i	−0.566086	−	0.566086i	−0.931029	+	0.364944i	$0.881088\pi$
$308$	−3.98348	+	2.29986i	−0.226980	+	0.131047i
$309$	−12.3110	−	14.0363i	−0.700347	−	0.798499i
$310$	1.28938	−	0.345489i	0.0732320	−	0.0196224i
$311$	−4.71379	−	8.16452i	−0.267294	−	0.462967i	0.700868	−	0.713291i	$-0.252796\pi$
$311$	−4.71379	−	8.16452i	−0.267294	−	0.462967i	−0.968162	+	0.250324i	$0.919463\pi$
$312$	−12.0653	+	7.32519i	−0.683062	+	0.414707i
$313$	−4.20593	+	7.28489i	−0.237733	+	0.411766i	−0.960064	−	0.279782i	$-0.909738\pi$
$313$	−4.20593	+	7.28489i	−0.237733	+	0.411766i	0.722330	+	0.691548i	$0.243071\pi$
$314$	3.17157	−	11.8365i	0.178982	−	0.667971i
$315$	−9.33289	−	1.22760i	−0.525849	−	0.0691675i
$316$	−4.79388	−	2.76775i	−0.269677	−	0.155698i
$317$	−9.27710	+	2.48579i	−0.521054	+	0.139616i	−0.509754	−	0.860320i	$-0.670264\pi$
$317$	−9.27710	+	2.48579i	−0.521054	+	0.139616i	−0.0112997	+	0.999936i	$0.503597\pi$
$318$	9.50618	+	6.35103i	0.533080	+	0.356148i
$319$	0.828534	+	0.828534i	0.0463890	+	0.0463890i
$320$	3.03240	+	0.812528i	0.169516	+	0.0454217i
$321$	3.76863	+	4.29679i	0.210344	+	0.239824i
$322$			56.5779i			3.15297i
$323$	−18.5067	−	4.95885i	−1.02974	−	0.275918i
$324$	3.80437	+	3.80261i	0.211354	+	0.211256i
$325$	−13.2583	+	9.28694i	−0.735436	+	0.515147i
$326$	5.06308	+	2.92317i	0.280418	+	0.161899i
$327$	−1.32395	−	0.884522i	−0.0732144	−	0.0489142i
$328$	2.24985	−	3.89685i	0.124227	−	0.215167i
$329$	25.4121			1.40101
$330$	3.48767	+	0.228391i	0.191990	+	0.0125725i
$331$	−4.47131	−	1.19809i	−0.245766	−	0.0658527i	0.133833	−	0.991004i	$-0.457271\pi$
$331$	−4.47131	−	1.19809i	−0.245766	−	0.0658527i	−0.379599	+	0.925151i	$0.623938\pi$
$332$	1.33391	+	4.97823i	0.0732080	+	0.273216i
$333$	−0.0226877	−	0.172177i	−0.00124328	−	0.00943523i
$334$	−16.9521	+	29.3618i	−0.927576	+	1.60661i
$335$	−8.65443			−0.472842
$336$	−36.7241	−	2.40489i	−2.00346	−	0.131198i
$337$	−19.8285	+	11.4480i	−1.08013	+	0.623612i	−0.930931	−	0.365196i	$-0.881002\pi$
$337$	−19.8285	+	11.4480i	−1.08013	+	0.623612i	−0.149197	+	0.988808i	$0.547669\pi$
$338$	−1.81892	+	20.8733i	−0.0989364	+	1.13536i
$339$	30.6639	−	6.10127i	1.66544	−	0.331376i
$340$	−1.79037	+	1.79037i	−0.0970966	+	0.0970966i
$341$	−1.75928	+	1.01572i	−0.0952704	+	0.0550044i
$342$	2.03745	−	15.4898i	0.110173	−	0.837593i
$343$	−16.4215	+	16.4215i	−0.886675	+	0.886675i
$344$	−2.42272	+	9.04172i	−0.130624	+	0.487497i
$345$	5.49481	−	8.22459i	0.295831	−	0.442797i
$346$	−7.64617	+	28.5359i	−0.411061	+	1.53410i
$347$		−	24.1630i		−	1.29714i	−0.761155	−	0.648570i	$-0.775367\pi$
$347$		−	24.1630i		−	1.29714i	0.761155	−	0.648570i	$-0.224633\pi$
$348$	−0.135073	−	0.678851i	−0.00724065	−	0.0363902i
$349$	−9.03762	−	9.03762i	−0.483773	−	0.483773i	0.422562	−	0.906334i	$-0.361131\pi$
$349$	−9.03762	−	9.03762i	−0.483773	−	0.483773i	−0.906334	+	0.422562i	$0.861131\pi$
$350$	−31.7787			−1.69864
$351$	−18.5160	+	2.85643i	−0.988309	+	0.152465i
$352$	5.74326			0.306117
$353$	14.5109	+	14.5109i	0.772338	+	0.772338i	0.978515	−	0.206177i	$-0.0661023\pi$
$353$	14.5109	+	14.5109i	0.772338	+	0.772338i	−0.206177	+	0.978515i	$0.566102\pi$
$354$	−0.757384	−	3.80648i	−0.0402545	−	0.202312i
$355$		−	2.30596i		−	0.122387i
$356$	−0.783273	+	2.92322i	−0.0415134	+	0.154930i
$357$	−25.0571	+	37.5053i	−1.32616	+	1.98499i
$358$	7.17677	−	26.7841i	0.379304	−	1.41558i
$359$	9.59235	−	9.59235i	0.506265	−	0.506265i	−0.407113	−	0.913378i	$-0.633464\pi$
$359$	9.59235	−	9.59235i	0.506265	−	0.506265i	0.913378	+	0.407113i	$0.133464\pi$
$360$	3.84369	+	2.94866i	0.202580	+	0.155408i
$361$	7.41283	−	4.27980i	0.390149	−	0.225253i
$362$	−1.24217	+	1.24217i	−0.0652868	+	0.0652868i
$363$	13.4695	−	2.68006i	0.706966	−	0.140667i
$364$	−6.08201	+	7.25080i	−0.318784	+	0.380045i
$365$	3.14331	−	1.81479i	0.164528	−	0.0949905i
$366$	−22.8144	−	1.49401i	−1.19253	−	0.0780933i
$367$	−12.8169			−0.669034			−0.334517	−	0.942390i	$-0.608573\pi$
$367$	−12.8169			−0.669034			−0.334517	+	0.942390i	$0.608573\pi$
$368$	19.3357	−	33.4904i	1.00794	−	1.74581i
$369$	4.73792	−	3.63641i	0.246646	−	0.189304i
$370$	0.0172527	+	0.0643878i	0.000896923	+	0.00334736i
$371$	−17.3731	−	4.65511i	−0.901967	−	0.241681i
$372$	1.19744	+	0.0784152i	0.0620846	+	0.00406564i
$373$	5.00205			0.258996			0.129498	−	0.991580i	$-0.458663\pi$
$373$	5.00205			0.258996			0.129498	+	0.991580i	$0.458663\pi$
$374$	8.37380	−	14.5039i	0.432999	−	0.749976i
$375$	9.76442	+	6.52356i	0.504233	+	0.336875i
$376$	−11.3259	−	6.53900i	−0.584088	−	0.337223i
$377$	2.18511	+	1.01847i	0.112539	+	0.0524540i
$378$	−32.9901	−	16.2618i	−1.69683	−	0.836417i
$379$	−14.1436	−	3.78976i	−0.726507	−	0.194667i	−0.123434	−	0.992353i	$-0.539391\pi$
$379$	−14.1436	−	3.78976i	−0.726507	−	0.194667i	−0.603073	+	0.797686i	$0.706057\pi$
$380$			1.37972i			0.0707781i
$381$	−0.847729	−	0.966537i	−0.0434305	−	0.0495172i
$382$	4.36149	+	1.16866i	0.223153	+	0.0597938i
$383$	−10.7793	−	10.7793i	−0.550794	−	0.550794i	0.375876	−	0.926670i	$-0.377342\pi$
$383$	−10.7793	−	10.7793i	−0.550794	−	0.550794i	−0.926670	+	0.375876i	$0.877342\pi$
$384$	19.6396	+	13.1211i	1.00223	+	0.669586i
$385$	−5.31127	+	1.42315i	−0.270688	+	0.0725305i
$386$	3.56515	+	2.05834i	0.181461	+	0.104767i
$387$	−7.56251	+	9.85801i	−0.384424	+	0.501111i
$388$	2.02713	−	7.56537i	0.102912	−	0.384073i
$389$	6.32765	−	10.9598i	0.320824	−	0.555684i	−0.659834	−	0.751411i	$-0.729373\pi$
$389$	6.32765	−	10.9598i	0.320824	−	0.555684i	0.980658	+	0.195727i	$0.0627067\pi$
$390$	6.90344	−	2.01389i	0.349569	−	0.101977i
$391$	−23.6979	−	41.0460i	−1.19845	−	2.07578i
$392$	26.8266	−	7.18817i	1.35495	−	0.363058i
$393$	5.23916	+	5.97342i	0.264280	+	0.301319i
$394$	8.02884	−	4.63545i	0.404487	−	0.233531i
$395$	−4.67912	−	4.67912i	−0.235432	−	0.235432i
$396$	2.90300	+	1.20207i	0.145881	+	0.0604062i
$397$	−25.0026	+	6.69943i	−1.25485	+	0.336235i	−0.824207	−	0.566289i	$-0.808378\pi$
$397$	−25.0026	+	6.69943i	−1.25485	+	0.336235i	−0.430639	+	0.902524i	$0.641712\pi$
$398$	1.04485	+	3.89942i	0.0523735	+	0.195461i
$399$	4.79649	+	24.1063i	0.240125	+	1.20683i
$400$	18.8109	+	10.8605i	0.940546	+	0.543025i
$401$	4.96481	+	18.5289i	0.247931	+	0.925291i	0.971888	+	0.235445i	$0.0756549\pi$
$401$	4.96481	+	18.5289i	0.247931	+	0.925291i	−0.723957	+	0.689845i	$0.757678\pi$
$402$	−32.0213	−	10.8677i	−1.59708	−	0.542032i
$403$	−2.68608	+	3.20227i	−0.133803	+	0.159516i
$404$			7.31153i			0.363762i
$405$	3.21635	+	5.56791i	0.159822	+	0.276672i
$406$	2.36643	+	4.09878i	0.117444	+	0.203419i
$407$	−0.0507220	−	0.0878531i	−0.00251420	−	0.00435471i
$408$	20.8185	−	10.2681i	1.03067	−	0.508344i
$409$	11.9022	−	11.9022i	0.588524	−	0.588524i	−0.348708	−	0.937232i	$-0.613379\pi$
$409$	11.9022	−	11.9022i	0.588524	−	0.588524i	0.937232	+	0.348708i	$0.113379\pi$
$410$	−1.62103	+	1.62103i	−0.0800572	+	0.0800572i
$411$	0.502560	−	7.67438i	0.0247895	−	0.378549i
$412$	3.22118	+	5.57924i	0.158696	+	0.274869i
$413$	3.05292	+	5.28781i	0.150224	+	0.260196i
$414$	30.6587	−	23.5309i	1.50679	−	1.15648i
$415$			6.16104i			0.302433i
$416$	11.1033	−	4.04345i	0.544386	−	0.198247i
$417$	7.58586	+	38.1252i	0.371481	+	1.86700i
$418$	−2.36201	−	8.81513i	−0.115530	−	0.431162i
$419$	16.9681	+	9.79652i	0.828944	+	0.478591i	0.853491	−	0.521107i	$-0.174481\pi$
$419$	16.9681	+	9.79652i	0.828944	+	0.478591i	−0.0245467	+	0.999699i	$0.507814\pi$
$420$	3.07582	+	1.04390i	0.150085	+	0.0509373i
$421$	10.3718	+	38.7080i	0.505489	+	1.88651i	0.460787	+	0.887511i	$0.347567\pi$
$421$	10.3718	+	38.7080i	0.505489	+	1.88651i	0.0447018	+	0.999000i	$0.485766\pi$
$422$	−2.95006	+	0.790465i	−0.143606	+	0.0384792i
$423$	−10.5689	−	13.7704i	−0.513879	−	0.669540i
$424$	6.54516	+	6.54516i	0.317861	+	0.317861i
$425$	23.0547	−	13.3106i	1.11832	−	0.645661i
$426$	2.89568	−	8.53202i	0.140296	−	0.413378i
$427$	34.7435	−	9.30948i	1.68135	−	0.450518i
$428$	−0.986064	−	1.70791i	−0.0476632	−	0.0825551i
$429$	−9.35466	+	5.67949i	−0.451647	+	0.274209i
$430$	2.38452	−	4.13011i	0.114992	−	0.199172i
$431$	−0.489822	+	1.82804i	−0.0235939	+	0.0880536i	−0.976719	−	0.214523i	$-0.931180\pi$
$431$	−0.489822	+	1.82804i	−0.0235939	+	0.0880536i	0.953125	+	0.302577i	$0.0978469\pi$
$432$	13.9704	+	20.9004i	0.672154	+	1.00557i
$433$	8.22301	+	4.74756i	0.395173	+	0.228153i	0.684399	−	0.729108i	$-0.260065\pi$
$433$	8.22301	+	4.74756i	0.395173	+	0.228153i	−0.289226	+	0.957261i	$0.593398\pi$
$434$	−7.92587	+	2.12373i	−0.380454	+	0.101942i
$435$	0.0540684	−	0.825656i	0.00259238	−	0.0395872i
$436$	0.388496	+	0.388496i	0.0186056	+	0.0186056i
$437$	−24.9469	−	6.68449i	−1.19337	−	0.319763i
$438$	13.9091	−	2.76753i	0.664604	−	0.132238i
$439$		−	6.29908i		−	0.300639i	−0.988637	−	0.150319i	$-0.951970\pi$
$439$		−	6.29908i		−	0.300639i	0.988637	−	0.150319i	$-0.0480302\pi$
$440$	2.73338	+	0.732408i	0.130309	+	0.0349162i
$441$	36.5489	+	4.80746i	1.74042	+	0.228927i
$442$	5.97771	−	33.9355i	0.284330	−	1.61415i
$443$	−5.45146	−	3.14740i	−0.259007	−	0.149538i	0.364875	−	0.931057i	$-0.381112\pi$
$443$	−5.45146	−	3.14740i	−0.259007	−	0.149538i	−0.623881	+	0.781519i	$0.714445\pi$
$444$	−0.00391581	+	0.0597967i	−0.000185836	+	0.00283783i
$445$	−1.80888	+	3.13307i	−0.0857491	+	0.148522i
$446$	−24.5179			−1.16095
$447$	5.52123	−	8.26414i	0.261145	−	0.390880i
$448$	−18.6402	−	4.99463i	−0.880668	−	0.235974i
$449$	9.61952	+	35.9005i	0.453973	+	1.69425i	0.691089	+	0.722770i	$0.257131\pi$
$449$	9.61952	+	35.9005i	0.453973	+	1.69425i	−0.237115	+	0.971481i	$0.576202\pi$
$450$	13.2168	+	17.2204i	0.623048	+	0.811778i
$451$	1.74439	−	3.02137i	0.0821401	−	0.142271i
$452$	−10.7883			−0.507438
$453$	−17.2159	−	34.9054i	−0.808875	−	1.64000i
$454$	−27.8109	+	16.0566i	−1.30523	+	0.753575i
$455$	−9.26624	+	6.49067i	−0.434408	+	0.304287i
$456$	4.06527	−	11.9782i	0.190373	−	0.560929i
$457$	4.91219	−	4.91219i	0.229782	−	0.229782i	−0.582819	−	0.812602i	$-0.698050\pi$
$457$	4.91219	−	4.91219i	0.229782	−	0.229782i	0.812602	+	0.582819i	$0.198050\pi$
$458$	11.6148	−	6.70580i	0.542723	−	0.313341i
$459$	30.7449	−	2.02048i	1.43505	−	0.0943077i
$460$	−2.41341	+	2.41341i	−0.112526	+	0.112526i
$461$	3.23594	−	12.0767i	0.150713	−	0.562468i	−0.848721	−	0.528840i	$-0.822627\pi$
$461$	3.23594	−	12.0767i	0.150713	−	0.562468i	0.999434	−	0.0336282i	$-0.0107062\pi$
$462$	−21.4388	−	1.40393i	−0.997423	−	0.0653167i
$463$	5.13957	−	19.1811i	0.238856	−	0.891423i	−0.737517	−	0.675329i	$-0.764002\pi$
$463$	5.13957	−	19.1811i	0.238856	−	0.891423i	0.976373	−	0.216094i	$-0.0693317\pi$
$464$		−	3.23495i		−	0.150179i
$465$	1.35842	+	0.461033i	0.0629952	+	0.0213799i
$466$	13.9729	+	13.9729i	0.647282	+	0.647282i
$467$	−17.4746			−0.808628			−0.404314	−	0.914620i	$-0.632490\pi$
$467$	−17.4746			−0.808628			−0.404314	+	0.914620i	$0.632490\pi$
$468$	6.45862	+	0.280125i	0.298550	+	0.0129488i
$469$	53.1990			2.45650
$470$	4.71141	+	4.71141i	0.217321	+	0.217321i
$471$	9.90037	−	8.68340i	0.456185	−	0.400110i
$472$		−	3.14229i		−	0.144636i
$473$	−1.87843	+	7.01038i	−0.0863702	+	0.322338i
$474$	−11.4370	−	23.1885i	−0.525317	−	1.06508i
$475$	3.75455	−	14.0122i	0.172270	−	0.642922i
$476$	11.0055	−	11.0055i	0.504435	−	0.504435i
$477$	4.70298	+	11.3503i	0.215335	+	0.519694i
$478$	13.1819	−	7.61060i	0.602928	−	0.348101i
$479$	−19.6654	+	19.6654i	−0.898533	+	0.898533i	−0.995306	−	0.0967735i	$-0.969148\pi$
$479$	−19.6654	+	19.6654i	−0.898533	+	0.898533i	0.0967735	+	0.995306i	$0.469148\pi$
$480$	−2.67426	−	3.04905i	−0.122063	−	0.139169i
$481$	−0.159912	−	0.134135i	−0.00729134	−	0.00611602i
$482$	7.58364	−	4.37842i	0.345425	−	0.199431i
$483$	−33.7768	+	50.5568i	−1.53690	+	2.30042i
$484$	−4.73889			−0.215404
$485$	4.68143	−	8.10848i	0.212573	−	0.368187i
$486$	4.90863	+	24.6401i	0.222660	+	1.11770i
$487$	3.96000	+	14.7789i	0.179445	+	0.669696i	0.995752	+	0.0920783i	$0.0293510\pi$
$487$	3.96000	+	14.7789i	0.179445	+	0.669696i	−0.816307	+	0.577618i	$0.803982\pi$
$488$	−17.8803	−	4.79101i	−0.809403	−	0.216879i
$489$	2.77914	+	5.63471i	0.125677	+	0.254810i
$490$	−14.1497			−0.639217
$491$	−17.1774	+	29.7522i	−0.775207	+	1.34270i	0.159471	+	0.987203i	$0.449021\pi$
$491$	−17.1774	+	29.7522i	−0.775207	+	1.34270i	−0.934678	+	0.355495i	$0.884312\pi$
$492$	−1.84830	+	0.911613i	−0.0833278	+	0.0410987i
$493$	−3.43358	−	1.98238i	−0.154641	−	0.0892819i
$494$	−10.7726	−	15.3792i	−0.484681	−	0.691943i
$495$	2.98015	+	2.28621i	0.133948	+	0.102757i
$496$	5.41739	+	1.45158i	0.243248	+	0.0651781i
$497$			14.1748i			0.635826i
$498$	−7.73667	+	22.7958i	−0.346688	+	1.02150i
$499$	33.0590	+	8.85813i	1.47992	+	0.396545i	0.906321	−	0.422589i	$-0.138879\pi$
$499$	33.0590	+	8.85813i	1.47992	+	0.396545i	0.573603	+	0.819133i	$0.305545\pi$
$500$	−2.86525	−	2.86525i	−0.128138	−	0.128138i
$501$	−32.6769	+	16.1168i	−1.45989	+	0.720045i
$502$	26.0143	−	6.97050i	1.16107	−	0.311109i
$503$	24.2079	+	13.9764i	1.07938	+	0.623179i	0.930728	−	0.365711i	$-0.119174\pi$
$503$	24.2079	+	13.9764i	1.07938	+	0.623179i	0.148649	+	0.988890i	$0.452508\pi$
$504$	−23.6273	−	18.1255i	−1.05244	−	0.807374i
$505$	−2.26218	+	8.44257i	−0.100666	+	0.375690i
$506$	11.2878	−	19.5511i	0.501804	−	0.869151i
$507$	−14.0866	+	17.5661i	−0.625609	+	0.780137i
$508$	0.221809	+	0.384184i	0.00984118	+	0.0170454i
$509$	−15.3674	+	4.11767i	−0.681146	+	0.182513i	−0.582771	−	0.812637i	$-0.698031\pi$
$509$	−15.3674	+	4.11767i	−0.681146	+	0.182513i	−0.0983757	+	0.995149i	$0.531365\pi$
$510$	−11.5991	+	2.30790i	−0.513617	+	0.102196i
$511$	−19.3220	+	11.1556i	−0.854755	+	0.493493i
$512$	4.25246	+	4.25246i	0.187934	+	0.187934i
$513$	11.0680	−	12.6250i	0.488663	−	0.557408i
$514$	28.3669	−	7.60088i	1.25121	−	0.335260i
$515$	1.99326	+	7.43894i	0.0878334	+	0.327799i
$516$	3.22316	−	2.82696i	0.141892	−	0.124450i
$517$	−8.78138	−	5.06993i	−0.386205	−	0.222975i
$518$	−0.106053	−	0.395794i	−0.00465968	−	0.0173902i
$519$	−23.8683	+	20.9343i	−1.04770	+	0.918915i
$520$	5.80004	−	0.508446i	0.254349	−	0.0222968i
$521$		−	42.9931i		−	1.88356i	−0.336227	−	0.941781i	$-0.609151\pi$
$521$		−	42.9931i		−	1.88356i	0.336227	−	0.941781i	$-0.390849\pi$
$522$	1.23686	−	2.98703i	0.0541360	−	0.130739i
$523$	12.4275	+	21.5251i	0.543417	+	0.941226i	0.998705	+	0.0508813i	$0.0162030\pi$
$523$	12.4275	+	21.5251i	0.543417	+	0.941226i	−0.455288	+	0.890344i	$0.650464\pi$
$524$	−1.37083	−	2.37435i	−0.0598850	−	0.103724i
$525$	−28.3968	−	18.9717i	−1.23934	−	0.827995i
$526$	−3.76222	+	3.76222i	−0.164041	+	0.164041i
$527$	4.86050	−	4.86050i	0.211727	−	0.211727i
$528$	12.2106	+	8.15782i	0.531397	+	0.355023i
$529$	−20.4446	−	35.4110i	−0.888894	−	1.53961i
$530$	−2.35792	−	4.08404i	−0.102422	−	0.177399i
$531$	1.59567	−	3.85354i	0.0692461	−	0.167229i
$532$		−	8.48117i		−	0.367705i
$533$	1.24525	−	7.06928i	0.0539376	−	0.306204i
$534$	−10.6272	+	9.32086i	−0.459883	+	0.403353i
$535$	−0.610174	−	2.27720i	−0.0263801	−	0.0984520i
$536$	−23.7103	−	13.6891i	−1.02413	−	0.591280i
$537$	22.4030	−	19.6492i	0.966760	−	0.847925i
$538$	−6.25188	−	23.3324i	−0.269538	−	1.00593i
$539$	20.7997	−	5.57326i	0.895906	−	0.240057i
$540$	−0.713567	−	2.10090i	−0.0307070	−	0.0904085i
$541$	27.8867	+	27.8867i	1.19894	+	1.19894i	0.974484	+	0.224459i	$0.0720615\pi$
$541$	27.8867	+	27.8867i	1.19894	+	1.19894i	0.224459	+	0.974484i	$0.427938\pi$
$542$	−36.5539	+	21.1044i	−1.57013	+	0.906513i
$543$	−1.85154	+	0.368405i	−0.0794572	+	0.0158098i
$544$	−18.7713	+	5.02975i	−0.804812	+	0.215649i
$545$	0.328393	+	0.568794i	0.0140668	+	0.0243644i
$546$	−42.4356	+	12.3795i	−1.81608	+	0.529792i
$547$	−8.19854	+	14.2003i	−0.350544	+	0.607161i	−0.986345	−	0.164693i	$-0.947337\pi$
$547$	−8.19854	+	14.2003i	−0.350544	+	0.607161i	0.635801	+	0.771853i	$0.280670\pi$
$548$	−0.686851	+	2.56336i	−0.0293408	+	0.109501i
$549$	−19.4945	−	14.9551i	−0.832007	−	0.638269i
$550$	10.9814	+	6.34014i	0.468250	+	0.270345i
$551$	−2.08686	+	0.559172i	−0.0889031	+	0.0238215i
$552$	28.0632	−	13.8412i	1.19445	−	0.589122i
$553$	28.7627	+	28.7627i	1.22311	+	1.22311i
$554$	−28.6987	−	7.68980i	−1.21929	−	0.326708i
$555$	−0.0230226	+	0.0678353i	−0.000977255	+	0.00287945i
$556$		−	13.4133i		−	0.568852i
$557$	−3.78199	−	1.01338i	−0.160248	−	0.0429384i	0.177803	−	0.984066i	$-0.443101\pi$
$557$	−3.78199	−	1.01338i	−0.160248	−	0.0429384i	−0.338051	+	0.941128i	$0.609768\pi$
$558$	4.44720	+	3.41164i	0.188265	+	0.144426i
$559$	1.30403	+	14.8755i	0.0551544	+	0.629168i
$560$	13.1470	+	7.59044i	0.555563	+	0.320754i
$561$	16.1414	−	7.96121i	0.681489	−	0.336122i
$562$	22.4348	−	38.8582i	0.946354	−	1.63913i
$563$	−33.6179			−1.41682			−0.708412	−	0.705799i	$-0.750588\pi$
$563$	−33.6179			−1.41682			−0.708412	+	0.705799i	$0.750588\pi$
$564$	2.64953	+	5.37194i	0.111565	+	0.226199i
$565$	−12.4572	−	3.33789i	−0.524077	−	0.140426i
$566$	3.32932	+	12.4252i	0.139942	+	0.522269i
$567$	−19.7710	−	34.2261i	−0.830304	−	1.43736i
$568$	3.64744	−	6.31755i	0.153043	−	0.265078i
$569$	−36.4572			−1.52837			−0.764183	−	0.645000i	$-0.776858\pi$
$569$	−36.4572			−1.52837			−0.764183	+	0.645000i	$0.776858\pi$
$570$	−3.58005	+	5.35859i	−0.149952	+	0.224447i
$571$	−11.6292	+	6.71410i	−0.486665	+	0.280976i	−0.723190	−	0.690649i	$-0.757325\pi$
$571$	−11.6292	+	6.71410i	−0.486665	+	0.280976i	0.236525	+	0.971625i	$0.423992\pi$
$572$	3.54830	−	1.29217i	0.148362	−	0.0540282i
$573$	3.19965	+	3.64808i	0.133667	+	0.152401i
$574$	9.96454	−	9.96454i	0.415912	−	0.415912i
$575$	31.0775	−	17.9426i	1.29602	−	0.748259i
$576$	5.04600	+	12.1781i	0.210250	+	0.507422i
$577$	16.9279	−	16.9279i	0.704716	−	0.704716i	−0.260703	−	0.965419i	$-0.583954\pi$
$577$	16.9279	−	16.9279i	0.704716	−	0.704716i	0.965419	+	0.260703i	$0.0839544\pi$
$578$	−7.57550	+	28.2721i	−0.315099	+	1.17597i
$579$	1.95692	+	3.96766i	0.0813268	+	0.164890i
$580$	−0.0738956	+	0.275782i	−0.00306835	+	0.0114512i
$581$		−	37.8721i		−	1.57120i
$582$	27.5034	−	24.1227i	1.14005	−	0.999917i
$583$	5.07471	+	5.07471i	0.210173	+	0.210173i
$584$	11.4822			0.475135
$585$	7.37105	+	2.32175i	0.304755	+	0.0959925i
$586$	−48.5485			−2.00552
$587$	12.1670	+	12.1670i	0.502186	+	0.502186i	0.912117	−	0.409930i	$-0.134447\pi$
$587$	12.1670	+	12.1670i	0.502186	+	0.502186i	−0.409930	+	0.912117i	$0.634447\pi$
$588$	−12.0454	−	4.08807i	−0.496742	−	0.168589i
$589$		−	3.74566i		−	0.154337i
$590$	−0.414350	+	1.54637i	−0.0170585	+	0.0636632i
$591$	9.94174	+	0.651039i	0.408949	+	0.0267802i
$592$	−0.0724877	+	0.270528i	−0.00297923	+	0.0111186i
$593$	6.78670	−	6.78670i	0.278696	−	0.278696i	−0.553892	−	0.832589i	$-0.686858\pi$
$593$	6.78670	−	6.78670i	0.278696	−	0.278696i	0.832589	+	0.553892i	$0.186858\pi$
$594$	8.15567	+	12.2012i	0.334631	+	0.500623i
$595$	16.1130	−	9.30286i	0.660569	−	0.381380i
$596$	−2.42501	+	2.42501i	−0.0993322	+	0.0993322i
$597$	−1.39428	+	4.10821i	−0.0570643	+	0.168138i
$598$	8.05789	−	45.7447i	0.329512	−	1.87064i
$599$	5.90268	−	3.40791i	0.241177	−	0.139244i	−0.374541	−	0.927210i	$-0.622200\pi$
$599$	5.90268	−	3.40791i	0.241177	−	0.139244i	0.615718	+	0.787967i	$0.288866\pi$
$600$	7.77435	+	15.7625i	0.317387	+	0.643503i
$601$	−4.01629			−0.163828			−0.0819139	−	0.996639i	$-0.526103\pi$
$601$	−4.01629			−0.163828			−0.0819139	+	0.996639i	$0.526103\pi$
$602$	−14.6577	+	25.3879i	−0.597405	+	1.03474i
$603$	−22.1256	−	28.8277i	−0.901024	−	1.17396i
$604$	3.47587	+	12.9721i	0.141431	+	0.527829i
$605$	−5.47196	−	1.46621i	−0.222467	−	0.0596098i
$606$	−18.9717	+	28.3968i	−0.770674	+	1.15354i
$607$	−21.6306			−0.877957			−0.438979	−	0.898498i	$-0.644660\pi$
$607$	−21.6306			−0.877957			−0.438979	+	0.898498i	$0.644660\pi$
$608$	−5.29483	+	9.17091i	−0.214734	+	0.371930i
$609$	−0.332360	+	5.07533i	−0.0134679	+	0.205663i
$610$	8.16744	+	4.71547i	0.330690	+	0.190924i
$611$	−20.5463	−	3.61921i	−0.831214	−	0.146418i
$612$	−10.5409	−	1.38650i	−0.426090	−	0.0560458i
$613$	−43.4028	−	11.6297i	−1.75302	−	0.469721i	−0.767754	−	0.640745i	$-0.778626\pi$
$613$	−43.4028	−	11.6297i	−1.75302	−	0.469721i	−0.985267	+	0.171024i	$0.945292\pi$
$614$			22.6078i			0.912375i
$615$	−2.41627	+	0.480771i	−0.0974334	+	0.0193866i
$616$	−16.8022	−	4.50213i	−0.676979	−	0.181396i
$617$	−0.921413	−	0.921413i	−0.0370947	−	0.0370947i	0.688316	−	0.725411i	$-0.258350\pi$
$617$	−0.921413	−	0.921413i	−0.0370947	−	0.0370947i	−0.725411	+	0.688316i	$0.758350\pi$
$618$	−1.96633	+	30.0270i	−0.0790976	+	1.20786i
$619$	−21.8232	+	5.84752i	−0.877150	+	0.235032i	−0.669177	−	0.743103i	$-0.733353\pi$
$619$	−21.8232	+	5.84752i	−0.877150	+	0.235032i	−0.207973	+	0.978135i	$0.566687\pi$
$620$	−0.428679	−	0.247498i	−0.0172161	−	0.00993975i
$621$	41.4438	−	2.72358i	1.66308	−	0.109294i
$622$	−3.93267	+	14.6769i	−0.157686	+	0.588491i
$623$	11.1192	−	19.2591i	0.445483	−	0.771599i
$624$	29.3498	+	7.17470i	1.17493	+	0.287218i
$625$	8.80189	+	15.2453i	0.352076	+	0.609813i
$626$	13.0957	−	3.50897i	0.523408	−	0.140247i
$627$	3.15195	−	9.28711i	0.125877	−	0.370892i
$628$	−3.93525	+	2.27202i	−0.157034	+	0.0906634i
$629$	0.242718	+	0.242718i	0.00967782	+	0.00967782i
$630$	9.23729	+	12.0354i	0.368023	+	0.479502i
$631$	−5.14920	+	1.37972i	−0.204986	+	0.0549259i	−0.359851	−	0.933010i	$-0.617173\pi$
$631$	−5.14920	+	1.37972i	−0.204986	+	0.0549259i	0.154865	+	0.987936i	$0.450506\pi$
$632$	−5.41804	−	20.2204i	−0.215518	−	0.804325i
$633$	−3.10801	−	1.05483i	−0.123532	−	0.0419256i
$634$	13.4057	+	7.73980i	0.532409	+	0.307387i
$635$	0.137255	+	0.512242i	0.00544680	+	0.0203277i
$636$	−0.827310	−	4.15791i	−0.0328050	−	0.164872i
$637$	36.2879	−	25.4184i	1.43778	−	1.00711i
$638$		−	1.88850i		−	0.0747664i
$639$	7.68109	−	5.89532i	0.303859	−	0.233215i
$640$	−4.87143	−	8.43757i	−0.192560	−	0.333524i
$641$	7.92073	+	13.7191i	0.312850	+	0.541872i	0.978978	−	0.203965i	$-0.0653830\pi$
$641$	7.92073	+	13.7191i	0.312850	+	0.541872i	−0.666128	+	0.745837i	$0.732050\pi$
$642$	0.601933	−	9.19185i	0.0237564	−	0.362773i
$643$	−9.36379	+	9.36379i	−0.369272	+	0.369272i	−0.867212	−	0.497940i	$-0.834090\pi$
$643$	−9.36379	+	9.36379i	−0.369272	+	0.369272i	0.497940	+	0.867212i	$0.334090\pi$
$644$	14.8353	−	14.8353i	0.584592	−	0.584592i
$645$	4.59642	−	2.26703i	0.180984	−	0.0892643i
$646$	15.4400	+	26.7428i	0.607477	+	1.05218i
$647$	−8.92652	−	15.4612i	−0.350938	−	0.607842i	0.635476	−	0.772120i	$-0.280804\pi$
$647$	−8.92652	−	15.4612i	−0.350938	−	0.607842i	−0.986414	+	0.164278i	$0.947470\pi$
$648$	0.00469979	+	20.3417i	0.000184625	+	0.799097i
$649$		−	2.43634i		−	0.0956346i
$650$	25.6939	+	4.52596i	1.00780	+	0.177523i
$651$	−8.35024	−	2.83399i	−0.327272	−	0.111073i
$652$	−0.561104	−	2.09407i	−0.0219745	−	0.0820101i
$653$	20.9913	+	12.1194i	0.821455	+	0.474267i	0.850918	−	0.525299i	$-0.176046\pi$
$653$	20.9913	+	12.1194i	0.821455	+	0.474267i	−0.0294630	+	0.999566i	$0.509380\pi$
$654$	0.500795	+	2.51691i	0.0195827	+	0.0984189i
$655$	−0.848267	−	3.16577i	−0.0331445	−	0.123697i
$656$	−9.30378	+	2.49294i	−0.363251	+	0.0973329i
$657$	14.0811	+	5.83068i	0.549356	+	0.227476i
$658$	−28.9612	−	28.9612i	−1.12902	−	1.12902i
$659$	−25.0065	+	14.4375i	−0.974114	+	0.562405i	−0.900488	−	0.434881i	$-0.856790\pi$
$659$	−25.0065	+	14.4375i	−0.974114	+	0.562405i	−0.0736257	+	0.997286i	$0.523457\pi$
$660$	−0.854613	−	0.974386i	−0.0332658	−	0.0379279i
$661$	−9.56817	+	2.56378i	−0.372159	+	0.0997196i	−0.440050	−	0.897973i	$-0.645039\pi$
$661$	−9.56817	+	2.56378i	−0.372159	+	0.0997196i	0.0678918	+	0.997693i	$0.478373\pi$
$662$	3.73038	+	6.46120i	0.144985	+	0.251122i
$663$	25.6009	−	26.7553i	0.994255	−	1.03909i
$664$	−9.74521	+	16.8792i	−0.378187	+	0.655040i
$665$	2.62407	−	9.79315i	0.101757	−	0.379762i
$666$	−0.170367	+	0.222080i	−0.00660159	+	0.00860541i
$667$	−4.62844	−	2.67223i	−0.179214	−	0.103469i
$668$	12.1439	−	3.25396i	0.469863	−	0.125899i
$669$	−21.9086	−	14.6370i	−0.847037	−	0.565901i
$670$	9.86313	+	9.86313i	0.381046	+	0.381046i
$671$	−13.8633	−	3.71465i	−0.535186	−	0.143403i
$672$	16.4387	+	18.7426i	0.634138	+	0.723012i
$673$		−	4.35718i		−	0.167957i	−0.996468	−	0.0839785i	$-0.973237\pi$
$673$		−	4.35718i		−	0.167957i	0.996468	−	0.0839785i	$-0.0267627\pi$
$674$	35.6446	+	9.55095i	1.37298	+	0.367889i
$675$	1.52978	+	23.2782i	0.0588814	+	0.895977i
$676$	5.95013	−	4.99625i	0.228851	−	0.192163i
$677$	0.418860	+	0.241829i	0.0160981	+	0.00929424i	0.508027	−	0.861341i	$-0.330375\pi$
$677$	0.418860	+	0.241829i	0.0160981	+	0.00929424i	−0.491929	+	0.870635i	$0.663708\pi$
$678$	−41.8999	−	27.9931i	−1.60916	−	1.07507i
$679$	−28.7769	+	49.8431i	−1.10436	+	1.91280i
$680$	−9.57520			−0.367192
$681$	−34.4369	−	2.25512i	−1.31963	−	0.0864163i
$682$	3.16256	+	0.847406i	0.121101	+	0.0324489i
$683$	−9.36965	−	34.9680i	−0.358520	−	1.33801i	−0.875997	−	0.482317i	$-0.839795\pi$
$683$	−9.36965	−	34.9680i	−0.358520	−	1.33801i	0.517477	−	0.855697i	$-0.326871\pi$
$684$	−4.59582	+	3.52734i	−0.175725	+	0.134871i
$685$	−1.58620	+	2.74739i	−0.0606057	+	0.104972i
$686$	37.4298			1.42908
$687$	14.3820	+	0.941815i	0.548709	+	0.0359325i
$688$	17.3528	−	10.0187i	0.661571	−	0.381958i
$689$	13.3836	+	6.23807i	0.509875	+	0.237652i
$690$	−15.6355	+	3.11103i	−0.595233	+	0.118435i
$691$	14.1316	−	14.1316i	0.537593	−	0.537593i	−0.385229	−	0.922821i	$-0.625877\pi$
$691$	14.1316	−	14.1316i	0.537593	−	0.537593i	0.922821	+	0.385229i	$0.125877\pi$
$692$	9.48728	−	5.47749i	0.360652	−	0.208223i
$693$	−18.3191	−	14.0534i	−0.695885	−	0.533844i
$694$	−27.5377	+	27.5377i	−1.04532	+	1.04532i
$695$	4.15008	−	15.4883i	0.157421	−	0.587504i
$696$	1.45411	−	2.17650i	0.0551178	−	0.0825000i
$697$	−3.05535	+	11.4027i	−0.115730	+	0.431909i
$698$			20.5997i			0.779709i
$699$	4.14412	+	20.8276i	0.156745	+	0.787773i
$700$	8.33268	+	8.33268i	0.314946	+	0.314946i
$701$	35.3690			1.33587			0.667933	−	0.744221i	$-0.267179\pi$
$701$	35.3690			1.33587			0.667933	+	0.744221i	$0.267179\pi$
$702$	24.3573	+	17.8466i	0.919308	+	0.673576i
$703$	0.187047			0.00705460
$704$	5.44484	+	5.44484i	0.205210	+	0.205210i
$705$	1.39732	+	7.02270i	0.0526262	+	0.264490i
$706$		−	33.0751i		−	1.24480i
$707$	13.9057	−	51.8968i	0.522977	−	1.95178i
$708$	−0.799501	+	1.19669i	−0.0300471	+	0.0449743i
$709$	−12.3025	+	45.9137i	−0.462032	+	1.72433i	0.204515	+	0.978863i	$0.434438\pi$
$709$	−12.3025	+	45.9137i	−0.462032	+	1.72433i	−0.666547	+	0.745463i	$0.732228\pi$
$710$	−2.62801	+	2.62801i	−0.0986275	+	0.0986275i
$711$	3.62359	−	27.5485i	0.135895	−	1.03315i
$712$	−9.91146	+	5.72238i	−0.371447	+	0.214455i
$713$	6.55191	−	6.55191i	0.245371	−	0.245371i
$714$	71.3000	−	14.1867i	2.66834	−	0.530925i
$715$	4.49699	−	0.394217i	0.168178	−	0.0147429i
$716$	−8.90486	+	5.14122i	−0.332790	+	0.192137i
$717$	16.3226	+	1.06889i	0.609578	+	0.0399185i
$718$	−21.8641			−0.815961
$719$	−17.0324	+	29.5010i	−0.635201	+	1.10020i	0.351271	+	0.936274i	$0.385749\pi$
$719$	−17.0324	+	29.5010i	−0.635201	+	1.10020i	−0.986472	+	0.163927i	$0.947584\pi$
$720$	−1.35473	−	10.2810i	−0.0504880	−	0.383152i
$721$	−12.2526	−	45.7274i	−0.456311	−	1.70298i
$722$	−13.3256	−	3.57060i	−0.495929	−	0.132884i
$723$	9.39047	+	0.614939i	0.349235	+	0.0228698i
$724$	0.651416			0.0242097
$725$	1.50094	−	2.59970i	0.0557435	−	0.0965505i
$726$	−18.4051	−	12.2963i	−0.683076	−	0.456360i
$727$	32.3631	+	18.6848i	1.20028	+	0.692983i	0.960618	−	0.277873i	$-0.0896296\pi$
$727$	32.3631	+	18.6848i	1.20028	+	0.692983i	0.239663	+	0.970856i	$0.422963\pi$
$728$	−35.6530	+	3.12543i	−1.32139	+	0.115836i
$729$	−10.3238	+	24.9483i	−0.382363	+	0.924012i
$730$	−5.65056	−	1.51406i	−0.209137	−	0.0560380i
$731$		−	24.5578i		−	0.908303i
$732$	5.59041	+	6.37390i	0.206628	+	0.235586i
$733$	−11.2118	−	3.00419i	−0.414116	−	0.110962i	0.0457444	−	0.998953i	$-0.485434\pi$
$733$	−11.2118	−	3.00419i	−0.414116	−	0.110962i	−0.459861	+	0.887991i	$0.652101\pi$
$734$	14.6069	+	14.6069i	0.539150	+	0.539150i
$735$	−12.6438	−	8.44729i	−0.466375	−	0.311583i
$736$	−25.3035	+	6.78005i	−0.932699	+	0.249916i
$737$	−18.3834	−	10.6137i	−0.677163	−	0.390960i
$738$	−9.54391	−	1.25536i	−0.351316	−	0.0462104i
$739$	0.0173171	−	0.0646284i	0.000637021	−	0.00237739i	−0.965607	−	0.260008i	$-0.916275\pi$
$739$	0.0173171	−	0.0646284i	0.000637021	−	0.00237739i	0.966244	+	0.257630i	$0.0829416\pi$
$740$	0.0123593	−	0.0214069i	0.000454336	−	0.000786933i
$741$	−0.444839	−	20.1737i	−0.0163416	−	0.741099i
$742$	14.4942	+	25.1047i	0.532100	+	0.921624i
$743$	39.7695	−	10.6562i	1.45900	−	0.390938i	0.559856	−	0.828590i	$-0.310857\pi$
$743$	39.7695	−	10.6562i	1.45900	−	0.390938i	0.899144	+	0.437652i	$0.144190\pi$
$744$	2.99238	+	3.41175i	0.109706	+	0.125081i
$745$	−3.55044	+	2.04984i	−0.130078	+	0.0751005i
$746$	−5.70065	−	5.70065i	−0.208716	−	0.208716i
$747$	−20.5223	+	15.7511i	−0.750872	+	0.576302i
$748$	−5.99874	+	1.60736i	−0.219336	+	0.0587708i
$749$	3.75076	+	13.9980i	0.137050	+	0.511477i
$750$	−3.69349	−	18.5628i	−0.134867	−	0.677818i
$751$	3.04244	+	1.75655i	0.111020	+	0.0640975i	0.554482	−	0.832196i	$-0.312916\pi$
$751$	3.04244	+	1.75655i	0.111020	+	0.0640975i	−0.443462	+	0.896293i	$0.646250\pi$
$752$	7.24553	+	27.0407i	0.264217	+	0.986073i
$753$	27.4071	+	9.30170i	0.998772	+	0.338973i
$754$	−1.32957	−	3.65100i	−0.0484200	−	0.132962i
$755$			16.0543i			0.584274i
$756$	4.38632	+	12.9143i	0.159529	+	0.469689i
$757$	10.0417	+	17.3928i	0.364973	+	0.632152i	0.988772	−	0.149433i	$-0.0477448\pi$
$757$	10.0417	+	17.3928i	0.364973	+	0.632152i	−0.623799	+	0.781585i	$0.714411\pi$
$758$	11.7999	+	20.4380i	0.428590	+	0.742340i
$759$	21.7584	−	10.7316i	0.789781	−	0.389534i
$760$	−3.68948	+	3.68948i	−0.133832	+	0.133832i
$761$	13.8092	−	13.8092i	0.500584	−	0.500584i	−0.411035	−	0.911619i	$-0.634833\pi$
$761$	13.8092	−	13.8092i	0.500584	−	0.500584i	0.911619	+	0.411035i	$0.134833\pi$
$762$	−0.135401	+	2.06765i	−0.00490506	+	0.0749031i
$763$	−2.01864	−	3.49639i	−0.0730798	−	0.126578i
$764$	−0.837191	−	1.45006i	−0.0302885	−	0.0524613i
$765$	−11.7425	−	4.86232i	−0.424551	−	0.175798i
$766$			24.5694i			0.887729i
$767$	−1.71527	−	4.71013i	−0.0619347	−	0.170073i
$768$	−4.45846	−	22.4074i	−0.160881	−	0.808559i
$769$	−5.47730	−	20.4415i	−0.197516	−	0.737141i	−0.991601	−	0.129334i	$-0.958716\pi$
$769$	−5.47730	−	20.4415i	−0.197516	−	0.737141i	0.794085	−	0.607807i	$-0.207951\pi$
$770$	7.67497	+	4.43115i	0.276587	+	0.159687i
$771$	29.8857	+	10.1429i	1.07631	+	0.365288i
$772$	−0.395100	−	1.47453i	−0.0142199	−	0.0530696i
$773$	−25.5328	+	6.84148i	−0.918349	+	0.246071i	−0.686880	−	0.726771i	$-0.741020\pi$
$773$	−25.5328	+	6.84148i	−0.918349	+	0.246071i	−0.231470	+	0.972842i	$0.574353\pi$
$774$	19.8535	−	2.61610i	0.713620	−	0.0940337i
$775$	3.68008	+	3.68008i	0.132192	+	0.132192i
$776$	25.6511	−	14.8097i	0.920822	−	0.531637i
$777$	0.141521	−	0.416985i	0.00507702	−	0.0149593i
$778$	−19.7019	+	5.27910i	−0.706346	+	0.189265i
$779$	3.21638	+	5.57093i	0.115239	+	0.199599i
$780$	−2.33821	−	1.28208i	−0.0837213	−	0.0459060i
$781$	2.82800	−	4.89823i	0.101194	−	0.175272i
$782$	−19.7709	+	73.7862i	−0.707007	+	2.63859i
$783$	2.88847	−	1.93074i	0.103226	−	0.0689990i
$784$	−51.4856	−	29.7252i	−1.83877	−	1.06161i
$785$	−5.24697	+	1.40592i	−0.187272	+	0.0501795i
$786$	0.836809	−	12.7785i	0.0298480	−	0.455796i
$787$	7.52822	+	7.52822i	0.268352	+	0.268352i	0.828436	−	0.560084i	$-0.189231\pi$
$787$	7.52822	+	7.52822i	0.268352	+	0.268352i	−0.560084	+	0.828436i	$0.689231\pi$
$788$	−3.32070	−	0.889778i	−0.118295	−	0.0316970i
$789$	−5.60786	+	1.11581i	−0.199645	+	0.0397239i
$790$			10.6652i			0.379452i
$791$	76.5745	+	20.5181i	2.72268	+	0.729539i
$792$	4.54843	+	10.9773i	0.161621	+	0.390061i
$793$	−29.4168	+	2.57875i	−1.04462	+	0.0915742i
$794$	36.1296	+	20.8595i	1.28219	+	0.740274i
$795$	0.331165	−	5.05708i	0.0117452	−	0.179356i
$796$	0.748497	−	1.29644i	0.0265298	−	0.0459509i
$797$	−16.5088			−0.584773			−0.292387	−	0.956300i	$-0.594449\pi$
$797$	−16.5088			−0.584773			−0.292387	+	0.956300i	$0.594449\pi$
$798$	22.0067	−	32.9394i	0.779028	−	1.16604i
$799$	33.1411	+	8.88014i	1.17245	+	0.314157i
$800$	−3.80822	−	14.2125i	−0.134641	−	0.502487i
$801$	−15.0607	+	1.98455i	−0.532144	+	0.0701207i
$802$	15.4585	−	26.7749i	0.545859	−	0.945456i
$803$	8.90254			0.314164
$804$	5.54668	+	11.2459i	0.195616	+	0.396613i
$805$	21.7202	−	12.5402i	0.765537	−	0.441983i
$806$	6.71073	−	0.588279i	0.236375	−	0.0207213i
$807$	8.34275	−	24.5816i	0.293679	−	0.865314i
$808$	−19.5516	+	19.5516i	−0.687824	+	0.687824i
$809$	−23.6058	+	13.6288i	−0.829937	+	0.479164i	−0.853831	−	0.520550i	$-0.825727\pi$
$809$	−23.6058	+	13.6288i	−0.829937	+	0.479164i	0.0238940	+	0.999714i	$0.492394\pi$
$810$	2.67999	−	10.0111i	0.0941651	−	0.351754i
$811$	8.22029	−	8.22029i	0.288654	−	0.288654i	−0.547894	−	0.836548i	$-0.684570\pi$
$811$	8.22029	−	8.22029i	0.288654	−	0.288654i	0.836548	+	0.547894i	$0.184570\pi$
$812$	0.454238	−	1.69524i	0.0159406	−	0.0594913i
$813$	−45.2630	−	2.96407i	−1.58744	−	0.103955i
$814$	−0.0423169	+	0.157929i	−0.00148321	+	0.00553540i
$815$		−	2.59161i		−	0.0907802i
$816$	−47.0533	−	15.9694i	−1.64720	−	0.559042i
$817$	−9.46251	−	9.46251i	−0.331051	−	0.331051i
$818$	−27.1289			−0.948539
$819$	−45.3100	−	14.2719i	−1.58326	−	0.498699i
$820$	0.850101			0.0296868
$821$	−18.8769	−	18.8769i	−0.658808	−	0.658808i	0.296290	−	0.955098i	$-0.404251\pi$
$821$	−18.8769	−	18.8769i	−0.658808	−	0.658808i	−0.955098	+	0.296290i	$0.904251\pi$
$822$	−9.31895	+	8.17345i	−0.325036	+	0.285082i
$823$			26.1132i			0.910248i	0.890428	+	0.455124i	$0.150405\pi$
$823$			26.1132i			0.910248i	−0.890428	+	0.455124i	$0.849595\pi$
$824$	−6.30566	+	23.5330i	−0.219668	+	0.819812i
$825$	6.02775	+	12.2213i	0.209859	+	0.425490i
$826$	2.54702	−	9.50561i	0.0886222	−	0.330743i
$827$	15.0891	−	15.0891i	0.524701	−	0.524701i	−0.394287	−	0.918988i	$-0.629008\pi$
$827$	15.0891	−	15.0891i	0.524701	−	0.524701i	0.918988	+	0.394287i	$0.129008\pi$
$828$	−14.2090	−	1.86898i	−0.493798	−	0.0649517i
$829$	12.8441	−	7.41555i	0.446095	−	0.257553i	−0.260085	−	0.965586i	$-0.583751\pi$
$829$	12.8441	−	7.41555i	0.446095	−	0.257553i	0.706179	+	0.708033i	$0.250417\pi$
$830$	7.02150	−	7.02150i	0.243720	−	0.243720i
$831$	−21.0538	−	24.0044i	−0.730348	−	0.832705i
$832$	14.3598	+	6.69305i	0.497835	+	0.232040i
$833$	−63.1008	+	36.4313i	−2.18631	+	1.26227i
$834$	34.8045	−	52.0952i	1.20518	−	1.80391i
$835$	15.0293			0.520110
$836$	−1.69207	+	2.93075i	−0.0585215	+	0.101362i
$837$	1.93719	+	5.70353i	0.0669591	+	0.197143i
$838$	−8.17315	−	30.5026i	−0.282337	−	1.05369i
$839$	−24.2278	−	6.49183i	−0.836438	−	0.224123i	−0.184917	−	0.982754i	$-0.559202\pi$
$839$	−24.2278	−	6.49183i	−0.836438	−	0.224123i	−0.651520	+	0.758631i	$0.725868\pi$
$840$	5.43352	+	11.0165i	0.187474	+	0.380105i
$841$	28.5529			0.984584
$842$	32.2937	−	55.9343i	1.11291	−	1.92762i
$843$	43.2454	−	21.3294i	1.48945	−	0.734622i
$844$	0.980800	+	0.566265i	0.0337605	+	0.0194917i
$845$	8.41640	−	3.92817i	0.289533	−	0.135133i
$846$	−3.64860	+	27.7386i	−0.125441	+	0.953673i
$847$	33.6363	+	9.01283i	1.15576	+	0.309684i
$848$		−	19.8138i		−	0.680409i
$849$	−4.44277	+	13.0905i	−0.152475	+	0.449263i
$850$	−41.4442	−	11.1049i	−1.42153	−	0.380897i
$851$	0.327182	+	0.327182i	0.0112157	+	0.0112157i
$852$	−2.99645	+	1.47790i	−0.102657	+	0.0506321i
$853$	18.1733	−	4.86952i	0.622242	−	0.166729i	0.0660950	−	0.997813i	$-0.478946\pi$
$853$	18.1733	−	4.86952i	0.622242	−	0.166729i	0.556147	+	0.831084i	$0.312279\pi$
$854$	−50.2055	−	28.9862i	−1.71800	−	0.991886i
$855$	−6.39811	+	2.65105i	−0.218811	+	0.0906640i
$856$	1.93028	−	7.20392i	0.0659757	−	0.246225i
$857$	−15.0231	+	26.0207i	−0.513178	+	0.888850i	0.486705	+	0.873566i	$0.338199\pi$
$857$	−15.0231	+	26.0207i	−0.513178	+	0.888850i	−0.999883	+	0.0152842i	$0.995135\pi$
$858$	17.1339	+	4.18845i	0.584940	+	0.142991i
$859$	−4.29719	−	7.44295i	−0.146618	−	0.253950i	0.783357	−	0.621572i	$-0.213506\pi$
$859$	−4.29719	−	7.44295i	−0.146618	−	0.253950i	−0.929975	+	0.367622i	$0.880172\pi$
$860$	−1.70820	+	0.457711i	−0.0582491	+	0.0156078i
$861$	14.8529	−	2.95531i	0.506185	−	0.100717i
$862$	2.64158	−	1.52512i	0.0899725	−	0.0519457i
$863$	22.4798	+	22.4798i	0.765221	+	0.765221i	0.977261	−	0.212040i	$-0.0680108\pi$
$863$	22.4798	+	22.4798i	0.765221	+	0.765221i	−0.212040	+	0.977261i	$0.568011\pi$
$864$	3.31942	−	16.7030i	0.112929	−	0.568247i
$865$	12.6496	−	3.38946i	0.430100	−	0.115245i
$866$	−3.96084	−	14.7821i	−0.134595	−	0.502315i
$867$	−23.6476	+	20.7408i	−0.803116	+	0.704396i
$868$	2.63510	+	1.52138i	0.0894411	+	0.0516389i
$869$	−4.20081	−	15.6776i	−0.142503	−	0.531828i
$870$	−1.00259	+	0.879349i	−0.0339909	+	0.0298127i
$871$	−43.0128	−	7.57666i	−1.45743	−	0.256725i
$872$			2.07774i			0.0703611i
$873$	38.9776	−	5.13608i	1.31919	−	0.173830i
$874$	20.8129	+	36.0491i	0.704008	+	1.21938i
$875$	14.8880	+	25.7867i	0.503305	+	0.871750i
$876$	−4.37278	−	2.92143i	−0.147742	−	0.0987060i
$877$	−15.6746	+	15.6746i	−0.529292	+	0.529292i	−0.920361	−	0.391069i	$-0.872105\pi$
$877$	−15.6746	+	15.6746i	−0.529292	+	0.529292i	0.391069	+	0.920361i	$0.372105\pi$
$878$	−7.17883	+	7.17883i	−0.242274	+	0.242274i
$879$	−43.3819	−	28.9832i	−1.46323	−	0.977580i
$880$	−3.02872	−	5.24590i	−0.102098	−	0.176839i
$881$	−4.67983	−	8.10570i	−0.157667	−	0.273088i	0.776360	−	0.630290i	$-0.217064\pi$
$881$	−4.67983	−	8.10570i	−0.157667	−	0.273088i	−0.934027	+	0.357202i	$0.883731\pi$
$882$	−36.1745	−	47.1323i	−1.21806	−	1.58703i
$883$			20.6234i			0.694033i	0.937859	+	0.347016i	$0.112805\pi$
$883$			20.6234i			0.694033i	−0.937859	+	0.347016i	$0.887195\pi$
$884$	−10.4656	+	7.33079i	−0.351997	+	0.246561i
$885$	−1.29343	+	1.13444i	−0.0434783	+	0.0381338i
$886$	2.62585	+	9.79980i	0.0882171	+	0.329231i
$887$	37.5859	+	21.7002i	1.26201	+	0.728622i	0.973463	−	0.228844i	$-0.0734944\pi$
$887$	37.5859	+	21.7002i	1.26201	+	0.728622i	0.288547	+	0.957466i	$0.406828\pi$
$888$	−0.170373	+	0.149430i	−0.00571733	+	0.00501455i
$889$	−0.843710	−	3.14877i	−0.0282971	−	0.105606i
$890$	5.63216	−	1.50913i	0.188790	−	0.0505862i
$891$	0.00364392	+	15.7717i	0.000122076	+	0.528371i
$892$	6.42882	+	6.42882i	0.215253	+	0.215253i
$893$	16.1915	−	9.34815i	0.541827	−	0.312824i
$894$	−15.7107	+	3.12599i	−0.525443	+	0.104549i
$895$	−11.8731	+	3.18138i	−0.396873	+	0.106342i
$896$	29.9449	+	51.8660i	1.00039	+	1.73272i
$897$	34.5097	−	36.0660i	1.15225	−	1.20421i
$898$	29.9515	−	51.8775i	0.999494	−	1.73117i
$899$	0.200612	−	0.748692i	0.00669077	−	0.0249703i
$900$	1.04977	−	7.98093i	0.0349924	−	0.266031i
$901$	−21.0304	−	12.1419i	−0.700625	−	0.404506i
$902$	−5.43136	+	1.45533i	−0.180845	+	0.0484571i
$903$	−28.2543	+	13.9355i	−0.940244	+	0.463745i
$904$	−28.8488	−	28.8488i	−0.959496	−	0.959496i
$905$	0.752185	+	0.201547i	0.0250035	+	0.00669966i
$906$	−20.1600	+	59.4007i	−0.669770	+	1.97345i
$907$		−	33.9799i		−	1.12828i	−0.825678	−	0.564142i	$-0.809207\pi$
$907$		−	33.9799i		−	1.12828i	0.825678	−	0.564142i	$-0.190793\pi$
$908$	11.5025	+	3.08208i	0.381723	+	0.102282i
$909$	−33.9055	+	14.0487i	−1.12457	+	0.465966i
$910$	17.9576	+	3.16321i	0.595287	+	0.104859i
$911$	−1.44338	−	0.833335i	−0.0478213	−	0.0276096i	0.475899	−	0.879500i	$-0.342123\pi$
$911$	−1.44338	−	0.833335i	−0.0478213	−	0.0276096i	−0.523720	+	0.851890i	$0.675456\pi$
$912$	−24.2837	+	11.9771i	−0.804113	+	0.396602i
$913$	−7.55582	+	13.0871i	−0.250061	+	0.433119i
$914$	−11.1965			−0.370346
$915$	4.48313	+	9.08957i	0.148208	+	0.300492i
$916$	−4.80383	−	1.28718i	−0.158723	−	0.0425297i
$917$	5.21432	+	19.4601i	0.172192	+	0.642629i
$918$	−37.3414	−	32.7361i	−1.23245	−	1.08045i
$919$	20.6189	−	35.7129i	0.680153	−	1.17806i	−0.294781	−	0.955565i	$-0.595247\pi$
$919$	20.6189	−	35.7129i	0.680153	−	1.17806i	0.974934	−	0.222495i	$-0.0714201\pi$
$920$	−12.9073			−0.425541
$921$	−13.4967	+	20.2018i	−0.444732	+	0.665672i
$922$	−17.4513	+	10.0755i	−0.574726	+	0.331818i
$923$	2.01879	−	11.4607i	0.0664492	−	0.377232i
$924$	5.25333	+	5.98958i	0.172822	+	0.197043i
$925$	−0.183772	+	0.183772i	−0.00604238	+	0.00604238i
$926$	−27.7174	+	16.0026i	−0.910850	+	0.525879i
$927$	−19.6831	+	25.6576i	−0.646477	+	0.842707i
$928$	−1.54953	+	1.54953i	−0.0508657	+	0.0508657i
$929$	5.81197	−	21.6906i	0.190685	−	0.711645i	−0.802657	−	0.596441i	$-0.796581\pi$
$929$	5.81197	−	21.6906i	0.190685	−	0.711645i	0.993342	−	0.115204i	$-0.0367522\pi$
$930$	−1.02272	−	2.07356i	−0.0335362	−	0.0679947i
$931$	−10.2762	+	38.3513i	−0.336789	+	1.25691i
$932$		−	7.32765i		−	0.240025i
$933$	−12.2762	+	10.7672i	−0.401905	+	0.352502i
$934$	19.9151	+	19.9151i	0.651643	+	0.651643i
$935$	−7.42401			−0.242791
$936$	16.5218	+	18.0199i	0.540032	+	0.589000i
$937$	−25.0543			−0.818490			−0.409245	−	0.912425i	$-0.634208\pi$
$937$	−25.0543			−0.818490			−0.409245	+	0.912425i	$0.634208\pi$
$938$	−60.6289	−	60.6289i	−1.97961	−	1.97961i
$939$	13.7968	+	4.68250i	0.450243	+	0.152808i
$940$		−	2.47075i		−	0.0805870i
$941$	0.550735	−	2.05537i	0.0179535	−	0.0670032i	−0.956368	−	0.292165i	$-0.905624\pi$
$941$	0.550735	−	2.05537i	0.0179535	−	0.0670032i	0.974321	+	0.225162i	$0.0722910\pi$
$942$	−21.1792	−	1.38693i	−0.690056	−	0.0451886i
$943$	−4.11859	+	15.3708i	−0.134120	+	0.500541i
$944$	−4.75625	+	4.75625i	−0.154803	+	0.154803i
$945$	1.06917	+	16.2692i	0.0347801	+	0.529237i
$946$	10.1302	−	5.84870i	0.329363	−	0.190158i
$947$	−33.2596	+	33.2596i	−1.08079	+	1.08079i	−0.0843553	+	0.996436i	$0.526883\pi$
$947$	−33.2596	+	33.2596i	−1.08079	+	1.08079i	−0.996436	+	0.0843553i	$0.973117\pi$
$948$	−3.08136	+	9.07912i	−0.100078	+	0.294876i
$949$	17.2111	−	6.26770i	0.558697	−	0.203458i
$950$	−20.2480	+	11.6902i	−0.656933	+	0.379281i
$951$	7.35844	+	14.9193i	0.238614	+	0.483790i
$952$	58.8591			1.90763
$953$	5.00845	−	8.67489i	0.162240	−	0.281007i	−0.773432	−	0.633879i	$-0.781462\pi$
$953$	5.00845	−	8.67489i	0.162240	−	0.281007i	0.935672	+	0.352872i	$0.114795\pi$
$954$	7.57569	−	18.2953i	0.245272	−	0.592332i
$955$	−0.518052	−	1.93340i	−0.0167638	−	0.0625633i
$956$	−5.45200	−	1.46086i	−0.176330	−	0.0472476i
$957$	1.12742	−	1.68752i	0.0364445	−	0.0545498i
$958$	44.8237			1.44819
$959$	9.75044	−	16.8883i	0.314858	−	0.545350i
$960$	0.355319	−	5.42592i	0.0114679	−	0.175121i
$961$	−25.6830	−	14.8281i	−0.828484	−	0.478326i
$962$	0.0293769	+	0.335113i	0.000947148	+	0.0108045i
$963$	6.02537	−	7.85429i	0.194165	−	0.253101i
$964$	−3.13656	−	0.840440i	−0.101022	−	0.0270687i
$965$		−	1.82487i		−	0.0587448i
$966$	96.1118	−	19.1236i	3.09235	−	0.615292i
$967$	−11.5896	−	3.10543i	−0.372697	−	0.0998638i	0.0676085	−	0.997712i	$-0.478463\pi$
$967$	−11.5896	−	3.10543i	−0.372697	−	0.0998638i	−0.440305	+	0.897848i	$0.645130\pi$
$968$	−12.6722	−	12.6722i	−0.407299	−	0.407299i
$969$	−2.16851	+	33.1144i	−0.0696626	+	1.06379i
$970$	−14.5762	+	3.90568i	−0.468013	+	0.125404i
$971$	19.6884	+	11.3671i	0.631831	+	0.364788i	0.781461	−	0.623954i	$-0.214475\pi$
$971$	19.6884	+	11.3671i	0.631831	+	0.364788i	−0.149630	+	0.988742i	$0.547808\pi$
$972$	5.17379	−	7.74797i	0.165949	−	0.248516i
$973$	−25.5106	+	95.2070i	−0.817833	+	3.05220i
$974$	12.3299	−	21.3560i	0.395076	−	0.684291i
$975$	20.2575	+	19.3834i	0.648761	+	0.620767i
$976$	19.8122	+	34.3158i	0.634175	+	1.09842i
$977$	−47.2286	+	12.6549i	−1.51098	+	0.404865i	−0.916760	−	0.399439i	$-0.869205\pi$
$977$	−47.2286	+	12.6549i	−1.51098	+	0.404865i	−0.594218	+	0.804304i	$0.702538\pi$
$978$	3.25439	−	9.58895i	0.104064	−	0.306621i
$979$	−7.68472	+	4.43678i	−0.245605	+	0.141800i
$980$	3.71018	+	3.71018i	0.118517	+	0.118517i
$981$	−1.05508	+	2.54803i	−0.0336862	+	0.0813523i
$982$	53.4839	−	14.3310i	1.70674	−	0.457320i
$983$	9.77062	+	36.4645i	0.311634	+	1.16304i	0.927082	+	0.374858i	$0.122308\pi$
$983$	9.77062	+	36.4645i	0.311634	+	1.16304i	−0.615448	+	0.788178i	$0.711025\pi$
$984$	−7.38023	−	2.50478i	−0.235273	−	0.0798493i
$985$	−3.55909	−	2.05484i	−0.113402	−	0.0654727i
$986$	1.65388	+	6.17237i	0.0526703	+	0.196568i
$987$	−8.58939	−	43.1687i	−0.273403	−	1.37408i
$988$	−1.20790	+	6.85724i	−0.0384283	+	0.218158i
$989$		−	33.1037i		−	1.05264i
$990$	−0.790867	−	6.00187i	−0.0251354	−	0.190752i
$991$	−20.1358	−	34.8762i	−0.639635	−	1.10788i	−0.985513	−	0.169600i	$-0.945752\pi$
$991$	−20.1358	−	34.8762i	−0.639635	−	1.10788i	0.345878	−	0.938279i	$-0.387581\pi$
$992$	−1.89960	−	3.29021i	−0.0603124	−	0.104464i
$993$	−0.523923	+	8.00061i	−0.0166262	+	0.253892i
$994$	16.1545	−	16.1545i	0.512388	−	0.512388i
$995$	1.26540	−	1.26540i	0.0401159	−	0.0401159i
$996$	8.00590	−	3.94865i	0.253677	−	0.125118i
$997$	24.3542	+	42.1827i	0.771306	+	1.33594i	0.936848	+	0.349738i	$0.113729\pi$
$997$	24.3542	+	42.1827i	0.771306	+	1.33594i	−0.165542	+	0.986203i	$0.552937\pi$
$998$	−27.5808	−	47.7714i	−0.873056	−	1.51218i
$999$	−0.284817	+	0.0967373i	−0.00901120	+	0.00306063i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.x.a.2.4	✓	48
3.2	odd	2		351.2.ba.a.197.9		48
9.4	even	3		351.2.bf.a.314.9		48
9.5	odd	6		117.2.bc.a.41.4	yes	48
13.7	odd	12		117.2.bc.a.20.4	yes	48
39.20	even	12		351.2.bf.a.332.9		48
117.59	even	12	inner	117.2.x.a.59.4	yes	48
117.85	odd	12		351.2.ba.a.98.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.2.4	✓	48	1.1	even	1	trivial
117.2.x.a.59.4	yes	48	117.59	even	12	inner
117.2.bc.a.20.4	yes	48	13.7	odd	12
117.2.bc.a.41.4	yes	48	9.5	odd	6
351.2.ba.a.98.9		48	117.85	odd	12
351.2.ba.a.197.9		48	3.2	odd	2
351.2.bf.a.314.9		48	9.4	even	3
351.2.bf.a.332.9		48	39.20	even	12

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13966 - 1.13966i) q^{2} +(-0.338004 - 1.69875i) q^{3} +0.597661i q^{4} +(-0.184916 + 0.690114i) q^{5} +(-1.55079 + 2.32121i) q^{6} +(1.13668 - 4.24215i) q^{7} +(-1.59819 + 1.59819i) q^{8} +(-2.77151 + 1.14837i) q^{9} +(0.997239 - 0.575756i) q^{10} +(-1.23914 + 1.23914i) q^{11} +(1.01528 - 0.202012i) q^{12} +(-1.52321 + 3.26800i) q^{13} +(-6.13006 + 3.53919i) q^{14} +(1.23483 + 0.0808637i) q^{15} +4.83812 q^{16} +(2.96481 - 5.13520i) q^{17} +(4.46734 + 1.84983i) q^{18} +(-0.836286 - 3.12106i) q^{19} +(-0.412454 - 0.110517i) q^{20} +(-7.59056 - 0.497071i) q^{21} +2.82440 q^{22} +(3.99653 - 6.92220i) q^{23} +(3.25513 + 2.17474i) q^{24} +(3.88806 + 2.24477i) q^{25} +(5.46036 - 1.98848i) q^{26} +(2.88758 + 4.31994i) q^{27} +(2.53537 + 0.679350i) q^{28} -0.668637i q^{29} +(-1.31514 - 1.49945i) q^{30} +(1.11973 + 0.300031i) q^{31} +(-2.31744 - 2.31744i) q^{32} +(2.52382 + 1.68615i) q^{33} +(-9.23127 + 2.47351i) q^{34} +(2.71738 + 1.56888i) q^{35} +(-0.686336 - 1.65642i) q^{36} +(-0.0149826 + 0.0559159i) q^{37} +(-2.60387 + 4.51004i) q^{38} +(6.06637 + 1.48295i) q^{39} +(-0.807405 - 1.39847i) q^{40} +(-1.92301 + 0.515270i) q^{41} +(8.08419 + 9.21717i) q^{42} +(3.58669 - 2.07078i) q^{43} +(-0.740585 - 0.740585i) q^{44} +(-0.280012 - 2.12501i) q^{45} +(-12.4437 + 3.33427i) q^{46} +(1.49759 + 5.58909i) q^{47} +(-1.63531 - 8.21876i) q^{48} +(-10.6416 - 6.14395i) q^{49} +(-1.87279 - 6.98936i) q^{50} +(-9.72554 - 3.30075i) q^{51} +(-1.95316 - 0.910361i) q^{52} -4.09535i q^{53} +(1.63241 - 8.21414i) q^{54} +(-0.626011 - 1.08428i) q^{55} +(4.96314 + 8.59642i) q^{56} +(-5.01924 + 2.47557i) q^{57} +(-0.762020 + 0.762020i) q^{58} +(-0.983077 + 0.983077i) q^{59} +(-0.0483290 + 0.738012i) q^{60} +(4.09503 + 7.09280i) q^{61} +(-0.934180 - 1.61805i) q^{62} +(1.72124 + 13.0625i) q^{63} -4.39405i q^{64} +(-1.97363 - 1.65549i) q^{65} +(-0.954660 - 4.79795i) q^{66} +(3.13514 + 11.7005i) q^{67} +(3.06910 + 1.77195i) q^{68} +(-13.1099 - 4.44938i) q^{69} +(-1.30890 - 4.88489i) q^{70} +(-3.11758 + 0.835353i) q^{71} +(2.59408 - 6.26472i) q^{72} +(-3.59223 - 3.59223i) q^{73} +(0.0808003 - 0.0466501i) q^{74} +(2.49913 - 7.36359i) q^{75} +(1.86534 - 0.499815i) q^{76} +(3.84811 + 6.66512i) q^{77} +(-5.22355 - 8.60368i) q^{78} +(-4.63097 + 8.02108i) q^{79} +(-0.894644 + 3.33886i) q^{80} +(6.36249 - 6.36543i) q^{81} +(2.77882 + 1.60435i) q^{82} +(8.32953 - 2.23189i) q^{83} +(0.297080 - 4.53658i) q^{84} +(2.99563 + 2.99563i) q^{85} +(-6.44760 - 1.72763i) q^{86} +(-1.13585 + 0.226002i) q^{87} -3.96077i q^{88} +(4.89110 + 1.31057i) q^{89} +(-2.10267 + 2.74091i) q^{90} +(12.1320 + 10.1764i) q^{91} +(4.13712 + 2.38857i) q^{92} +(0.131204 - 2.00355i) q^{93} +(4.66292 - 8.07642i) q^{94} +2.30853 q^{95} +(-3.15345 + 4.72006i) q^{96} +(-12.6583 - 3.39178i) q^{97} +(5.12584 + 19.1299i) q^{98} +(2.01129 - 4.85727i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9} - 12 q^{10} - 6 q^{11} + 18 q^{12} - 2 q^{13} - 12 q^{14} - 26 q^{15} - 28 q^{16} - 14 q^{18} - 4 q^{19} - 18 q^{20} - 8 q^{21}+ \cdots - 8 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9 - 12 * q^10 - 6 * q^11 + 18 * q^12 - 2 * q^13 - 12 * q^14 - 26 * q^15 - 28 * q^16 - 14 * q^18 - 4 * q^19 - 18 * q^20 - 8 * q^21 - 4 * q^22 - 6 * q^23 + 6 * q^24 - 48 * q^26 - 32 * q^27 + 42 * q^30 - 18 * q^31 + 54 * q^32 + 28 * q^33 + 6 * q^34 + 6 * q^35 + 24 * q^36 - 6 * q^37 + 36 * q^38 + 10 * q^39 - 12 * q^40 + 18 * q^41 - 70 * q^42 - 30 * q^43 + 12 * q^44 + 40 * q^45 - 12 * q^46 - 36 * q^47 - 14 * q^48 - 6 * q^49 - 60 * q^50 + 56 * q^52 + 34 * q^54 - 4 * q^55 - 6 * q^56 - 56 * q^57 + 50 * q^58 - 6 * q^59 + 44 * q^60 + 2 * q^61 + 18 * q^62 + 22 * q^63 + 72 * q^65 + 32 * q^66 + 26 * q^67 + 42 * q^68 + 30 * q^69 - 16 * q^70 - 48 * q^71 + 30 * q^72 - 22 * q^73 + 30 * q^74 - 24 * q^75 + 6 * q^76 + 72 * q^77 - 20 * q^78 + 8 * q^79 - 54 * q^80 + 82 * q^81 - 12 * q^82 + 54 * q^83 - 38 * q^84 - 24 * q^85 - 54 * q^86 + 2 * q^87 - 114 * q^90 - 16 * q^91 + 120 * q^92 + 52 * q^93 + 26 * q^94 - 12 * q^95 + 94 * q^96 - 24 * q^97 + 36 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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