LMFDB - Embedded newform 429.2.be.a.89.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(89,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 7]))

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

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

chi := DirichletCharacter("429.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.be (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$46$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			89.14
Character	$\chi$	$=$	429.89
Dual form			429.2.be.a.188.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32901 - 0.356107i) q^{2} +(1.71883 - 0.213571i) q^{3} +(-0.0925961 - 0.0534604i) q^{4} +(-2.48553 + 2.48553i) q^{5} +(-2.36040 - 0.328250i) q^{6} +(-0.825366 - 3.08031i) q^{7} +(2.04983 + 2.04983i) q^{8} +(2.90877 - 0.734187i) q^{9} +O(q^{10})$	\(q+(-1.32901 - 0.356107i) q^{2} +(1.71883 - 0.213571i) q^{3} +(-0.0925961 - 0.0534604i) q^{4} +(-2.48553 + 2.48553i) q^{5} +(-2.36040 - 0.328250i) q^{6} +(-0.825366 - 3.08031i) q^{7} +(2.04983 + 2.04983i) q^{8} +(2.90877 - 0.734187i) q^{9} +(4.18841 - 2.41818i) q^{10} +(-0.258819 + 0.965926i) q^{11} +(-0.170575 - 0.0721136i) q^{12} +(-1.73432 - 3.16103i) q^{13} +4.38768i q^{14} +(-3.74137 + 4.80305i) q^{15} +(-1.88736 - 3.26901i) q^{16} +(3.78908 - 6.56288i) q^{17} +(-4.12724 - 0.0600930i) q^{18} +(3.55905 - 0.953644i) q^{19} +(0.363028 - 0.0972730i) q^{20} +(-2.07653 - 5.11826i) q^{21} +(0.687946 - 1.19156i) q^{22} +(-4.10059 - 7.10243i) q^{23} +(3.96110 + 3.08553i) q^{24} -7.35570i q^{25} +(1.17926 + 4.81865i) q^{26} +(4.84290 - 1.88318i) q^{27} +(-0.0882488 + 0.329349i) q^{28} +(-4.91592 + 2.83821i) q^{29} +(6.68272 - 5.05097i) q^{30} +(0.707199 + 0.707199i) q^{31} +(-0.156372 - 0.583589i) q^{32} +(-0.238573 + 1.71554i) q^{33} +(-7.37282 + 7.37282i) q^{34} +(9.70766 + 5.60472i) q^{35} +(-0.308591 - 0.0875213i) q^{36} +(0.865853 + 0.232005i) q^{37} -5.06961 q^{38} +(-3.65611 - 5.06289i) q^{39} -10.1898 q^{40} +(5.57239 + 1.49312i) q^{41} +(0.937083 + 7.54169i) q^{42} +(0.679178 + 0.392123i) q^{43} +(0.0756044 - 0.0756044i) q^{44} +(-5.40500 + 9.05468i) q^{45} +(2.92050 + 10.8995i) q^{46} +(-5.12140 - 5.12140i) q^{47} +(-3.94223 - 5.21579i) q^{48} +(-2.74489 + 1.58477i) q^{49} +(-2.61942 + 9.77580i) q^{50} +(5.11116 - 12.0897i) q^{51} +(-0.00839870 + 0.385417i) q^{52} +3.67297i q^{53} +(-7.10687 + 0.778171i) q^{54} +(-1.75753 - 3.04414i) q^{55} +(4.62225 - 8.00597i) q^{56} +(5.91374 - 2.39927i) q^{57} +(7.54401 - 2.02141i) q^{58} +(-7.12296 + 1.90859i) q^{59} +(0.603209 - 0.244728i) q^{60} +(4.53903 - 7.86184i) q^{61} +(-0.688036 - 1.19171i) q^{62} +(-4.66233 - 8.35395i) q^{63} +8.38073i q^{64} +(12.1675 + 3.54613i) q^{65} +(0.927982 - 2.19501i) q^{66} +(-0.0660630 + 0.246550i) q^{67} +(-0.701709 + 0.405132i) q^{68} +(-8.56511 - 11.3321i) q^{69} +(-10.9057 - 10.9057i) q^{70} +(-1.58612 - 5.91947i) q^{71} +(7.46745 + 4.45753i) q^{72} +(2.21677 - 2.21677i) q^{73} +(-1.06811 - 0.616673i) q^{74} +(-1.57097 - 12.6432i) q^{75} +(-0.380536 - 0.101964i) q^{76} +3.18897 q^{77} +(3.05608 + 8.03059i) q^{78} +0.760405 q^{79} +(12.8163 + 3.43412i) q^{80} +(7.92194 - 4.27117i) q^{81} +(-6.87405 - 3.96874i) q^{82} +(-0.415987 + 0.415987i) q^{83} +(-0.0813454 + 0.584944i) q^{84} +(6.89436 + 25.7301i) q^{85} +(-0.762996 - 0.762996i) q^{86} +(-7.84348 + 5.92830i) q^{87} +(-2.51052 + 1.44945i) q^{88} +(-0.729514 + 2.72258i) q^{89} +(10.4077 - 10.1090i) q^{90} +(-8.30551 + 7.95125i) q^{91} +0.876877i q^{92} +(1.36660 + 1.06452i) q^{93} +(4.98262 + 8.63015i) q^{94} +(-6.47580 + 11.2164i) q^{95} +(-0.393415 - 0.969695i) q^{96} +(-6.06921 + 1.62624i) q^{97} +(4.21234 - 1.12869i) q^{98} +(-0.0436756 + 2.99968i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 12 q^{6} + 12 q^{7}+O(q^{10}) $ 184 * q - 12 * q^6 + 12 * q^7	$ 184 q - 12 q^{6} + 12 q^{7} - 48 q^{10} - 16 q^{13} + 16 q^{15} + 80 q^{16} - 8 q^{18} - 4 q^{19} - 24 q^{24} - 48 q^{27} - 40 q^{28} + 48 q^{30} - 20 q^{31} + 16 q^{34} - 36 q^{36} + 44 q^{37} + 48 q^{39} - 80 q^{40} + 20 q^{42} - 84 q^{43} - 4 q^{45} - 64 q^{46} + 44 q^{48} - 60 q^{49} - 200 q^{52} - 4 q^{54} - 64 q^{57} - 48 q^{58} - 148 q^{60} - 48 q^{61} + 40 q^{66} + 48 q^{67} - 12 q^{69} + 24 q^{70} - 128 q^{72} + 108 q^{73} - 60 q^{75} - 24 q^{76} + 148 q^{78} + 32 q^{79} + 16 q^{81} - 48 q^{82} + 116 q^{84} + 104 q^{85} - 24 q^{87} + 72 q^{88} + 60 q^{91} + 36 q^{93} + 16 q^{94} - 72 q^{96} + 4 q^{97}+O(q^{100}) $ 184 * q - 12 * q^6 + 12 * q^7 - 48 * q^10 - 16 * q^13 + 16 * q^15 + 80 * q^16 - 8 * q^18 - 4 * q^19 - 24 * q^24 - 48 * q^27 - 40 * q^28 + 48 * q^30 - 20 * q^31 + 16 * q^34 - 36 * q^36 + 44 * q^37 + 48 * q^39 - 80 * q^40 + 20 * q^42 - 84 * q^43 - 4 * q^45 - 64 * q^46 + 44 * q^48 - 60 * q^49 - 200 * q^52 - 4 * q^54 - 64 * q^57 - 48 * q^58 - 148 * q^60 - 48 * q^61 + 40 * q^66 + 48 * q^67 - 12 * q^69 + 24 * q^70 - 128 * q^72 + 108 * q^73 - 60 * q^75 - 24 * q^76 + 148 * q^78 + 32 * q^79 + 16 * q^81 - 48 * q^82 + 116 * q^84 + 104 * q^85 - 24 * q^87 + 72 * q^88 + 60 * q^91 + 36 * q^93 + 16 * q^94 - 72 * q^96 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$-1$

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 $

$2$	−1.32901	−	0.356107i	−0.939752	−	0.251806i	−0.243744	−	0.969840i	$-0.578376\pi$
$2$	−1.32901	−	0.356107i	−0.939752	−	0.251806i	−0.696008	+	0.718034i	$0.745042\pi$
$3$	1.71883	−	0.213571i	0.992369	−	0.123306i
$3$	1.71883	−	0.213571i	0.992369	−	0.123306i
$4$	−0.0925961	−	0.0534604i	−0.0462981	−	0.0267302i
$5$	−2.48553	+	2.48553i	−1.11156	+	1.11156i	−0.118623	+	0.992939i	$0.537848\pi$
$5$	−2.48553	+	2.48553i	−1.11156	+	1.11156i	−0.992939	+	0.118623i	$0.962152\pi$
$6$	−2.36040	−	0.328250i	−0.963629	−	0.134008i
$7$	−0.825366	−	3.08031i	−0.311959	−	1.16425i	−0.926787	−	0.375586i	$-0.877441\pi$
$7$	−0.825366	−	3.08031i	−0.311959	−	1.16425i	0.614828	−	0.788661i	$-0.289225\pi$
$8$	2.04983	+	2.04983i	0.724724	+	0.724724i
$9$	2.90877	−	0.734187i	0.969591	−	0.244729i
$10$	4.18841	−	2.41818i	1.32449	−	0.764695i
$11$	−0.258819	+	0.965926i	−0.0780369	+	0.291238i
$11$	−0.258819	+	0.965926i	−0.0780369	+	0.291238i
$12$	−0.170575	−	0.0721136i	−0.0492407	−	0.0208174i
$13$	−1.73432	−	3.16103i	−0.481014	−	0.876713i
$13$	−1.73432	−	3.16103i	−0.481014	−	0.876713i
$14$			4.38768i			1.17266i
$15$	−3.74137	+	4.80305i	−0.966018	+	1.24014i
$16$	−1.88736	−	3.26901i	−0.471841	−	0.817252i
$17$	3.78908	−	6.56288i	0.918988	−	1.59173i	0.118032	−	0.993010i	$-0.462342\pi$
$17$	3.78908	−	6.56288i	0.918988	−	1.59173i	0.800956	−	0.598723i	$-0.204325\pi$
$18$	−4.12724	−	0.0600930i	−0.972800	−	0.0141640i
$19$	3.55905	−	0.953644i	0.816501	−	0.218781i	0.173685	−	0.984801i	$-0.444433\pi$
$19$	3.55905	−	0.953644i	0.816501	−	0.218781i	0.642816	+	0.766020i	$0.277766\pi$
$20$	0.363028	−	0.0972730i	0.0811754	−	0.0217509i
$21$	−2.07653	−	5.11826i	−0.453137	−	1.11690i
$22$	0.687946	−	1.19156i	0.146671	−	0.254041i
$23$	−4.10059	−	7.10243i	−0.855033	−	1.48096i	−0.876615	−	0.481193i	$-0.840204\pi$
$23$	−4.10059	−	7.10243i	−0.855033	−	1.48096i	0.0215823	−	0.999767i	$-0.493130\pi$
$24$	3.96110	+	3.08553i	0.808556	+	0.629831i
$25$		−	7.35570i		−	1.47114i
$26$	1.17926	+	4.81865i	0.231273	+	0.945015i
$27$	4.84290	−	1.88318i	0.932016	−	0.362418i
$28$	−0.0882488	+	0.329349i	−0.0166775	+	0.0622411i
$29$	−4.91592	+	2.83821i	−0.912863	+	0.527042i	−0.881351	−	0.472462i	$-0.843366\pi$
$29$	−4.91592	+	2.83821i	−0.912863	+	0.527042i	−0.0315120	+	0.999503i	$0.510032\pi$
$30$	6.68272	−	5.05097i	1.22009	−	0.922176i
$31$	0.707199	+	0.707199i	0.127017	+	0.127017i	0.767757	−	0.640741i	$-0.221373\pi$
$31$	0.707199	+	0.707199i	0.127017	+	0.127017i	−0.640741	+	0.767757i	$0.721373\pi$
$32$	−0.156372	−	0.583589i	−0.0276429	−	0.103165i
$33$	−0.238573	+	1.71554i	−0.0415301	+	0.298637i
$34$	−7.37282	+	7.37282i	−1.26443	+	1.26443i
$35$	9.70766	+	5.60472i	1.64089	+	0.947371i
$36$	−0.308591	−	0.0875213i	−0.0514319	−	0.0145869i
$37$	0.865853	+	0.232005i	0.142345	+	0.0381413i	0.329288	−	0.944229i	$-0.393191\pi$
$37$	0.865853	+	0.232005i	0.142345	+	0.0381413i	−0.186943	+	0.982371i	$0.559858\pi$
$38$	−5.06961			−0.822399
$39$	−3.65611	−	5.06289i	−0.585447	−	0.810711i
$40$	−10.1898			−1.61115
$41$	5.57239	+	1.49312i	0.870262	+	0.233186i	0.666201	−	0.745772i	$-0.267919\pi$
$41$	5.57239	+	1.49312i	0.870262	+	0.233186i	0.204061	+	0.978958i	$0.434586\pi$
$42$	0.937083	+	7.54169i	0.144595	+	1.16371i
$43$	0.679178	+	0.392123i	0.103574	+	0.0597983i	0.550892	−	0.834577i	$-0.314288\pi$
$43$	0.679178	+	0.392123i	0.103574	+	0.0597983i	−0.447318	+	0.894375i	$0.647621\pi$
$44$	0.0756044	−	0.0756044i	0.0113978	−	0.0113978i
$45$	−5.40500	+	9.05468i	−0.805729	+	1.34979i
$46$	2.92050	+	10.8995i	0.430604	+	1.60704i
$47$	−5.12140	−	5.12140i	−0.747033	−	0.747033i	0.226888	−	0.973921i	$-0.427145\pi$
$47$	−5.12140	−	5.12140i	−0.747033	−	0.747033i	−0.973921	+	0.226888i	$0.927145\pi$
$48$	−3.94223	−	5.21579i	−0.569012	−	0.752835i
$49$	−2.74489	+	1.58477i	−0.392128	+	0.226395i
$50$	−2.61942	+	9.77580i	−0.370441	+	1.38251i
$51$	5.11116	−	12.0897i	0.715705	−	1.69290i
$52$	−0.00839870	+	0.385417i	−0.00116469	+	0.0534477i
$53$			3.67297i			0.504522i	0.967659	+	0.252261i	$0.0811741\pi$
$53$			3.67297i			0.504522i	−0.967659	+	0.252261i	$0.918826\pi$
$54$	−7.10687	+	0.778171i	−0.967122	+	0.105896i
$55$	−1.75753	−	3.04414i	−0.236986	−	0.410471i
$56$	4.62225	−	8.00597i	0.617674	−	1.06984i
$57$	5.91374	−	2.39927i	0.783294	−	0.317790i
$58$	7.54401	−	2.02141i	0.990577	−	0.265424i
$59$	−7.12296	+	1.90859i	−0.927331	+	0.248478i	−0.690716	−	0.723126i	$-0.742705\pi$
$59$	−7.12296	+	1.90859i	−0.927331	+	0.248478i	−0.236615	+	0.971604i	$0.576038\pi$
$60$	0.603209	−	0.244728i	0.0778740	−	0.0315943i
$61$	4.53903	−	7.86184i	0.581164	−	1.00661i	−0.414178	−	0.910196i	$-0.635931\pi$
$61$	4.53903	−	7.86184i	0.581164	−	1.00661i	0.995342	−	0.0964093i	$-0.0307358\pi$
$62$	−0.688036	−	1.19171i	−0.0873807	−	0.151348i
$63$	−4.66233	−	8.35395i	−0.587398	−	1.05250i
$64$			8.38073i			1.04759i
$65$	12.1675	+	3.54613i	1.50920	+	0.439844i
$66$	0.927982	−	2.19501i	0.114227	−	0.270188i
$67$	−0.0660630	+	0.246550i	−0.00807088	+	0.0301209i	−0.969844	−	0.243727i	$-0.921630\pi$
$67$	−0.0660630	+	0.246550i	−0.00807088	+	0.0301209i	0.961773	+	0.273848i	$0.0882965\pi$
$68$	−0.701709	+	0.405132i	−0.0850947	+	0.0491294i
$69$	−8.56511	−	11.3321i	−1.03112	−	1.36423i
$70$	−10.9057	−	10.9057i	−1.30348	−	1.30348i
$71$	−1.58612	−	5.91947i	−0.188237	−	0.702512i	−0.993914	−	0.110156i	$-0.964865\pi$
$71$	−1.58612	−	5.91947i	−0.188237	−	0.702512i	0.805677	−	0.592355i	$-0.201802\pi$
$72$	7.46745	+	4.45753i	0.880047	+	0.525325i
$73$	2.21677	−	2.21677i	0.259453	−	0.259453i	−0.565379	−	0.824832i	$-0.691270\pi$
$73$	2.21677	−	2.21677i	0.259453	−	0.259453i	0.824832	+	0.565379i	$0.191270\pi$
$74$	−1.06811	−	0.616673i	−0.124165	−	0.0716868i
$75$	−1.57097	−	12.6432i	−0.181400	−	1.45991i
$76$	−0.380536	−	0.101964i	−0.0436505	−	0.0116961i
$77$	3.18897			0.363417
$78$	3.05608	+	8.03059i	0.346033	+	0.909286i
$79$	0.760405			0.0855523			0.0427761	−	0.999085i	$-0.486380\pi$
$79$	0.760405			0.0855523			0.0427761	+	0.999085i	$0.486380\pi$
$80$	12.8163	+	3.43412i	1.43291	+	0.383946i
$81$	7.92194	−	4.27117i	0.880215	−	0.474575i
$82$	−6.87405	−	3.96874i	−0.759112	−	0.438274i
$83$	−0.415987	+	0.415987i	−0.0456605	+	0.0456605i	−0.729568	−	0.683908i	$-0.760279\pi$
$83$	−0.415987	+	0.415987i	−0.0456605	+	0.0456605i	0.683908	+	0.729568i	$0.260279\pi$
$84$	−0.0813454	+	0.584944i	−0.00887551	+	0.0638226i
$85$	6.89436	+	25.7301i	0.747798	+	2.79082i
$86$	−0.762996	−	0.762996i	−0.0822759	−	0.0822759i
$87$	−7.84348	+	5.92830i	−0.840910	+	0.635581i
$88$	−2.51052	+	1.44945i	−0.267622	+	0.154512i
$89$	−0.729514	+	2.72258i	−0.0773284	+	0.288593i	−0.993751	−	0.111618i	$-0.964397\pi$
$89$	−0.729514	+	2.72258i	−0.0773284	+	0.288593i	0.916423	+	0.400211i	$0.131063\pi$
$90$	10.4077	−	10.1090i	1.09707	−	1.06558i
$91$	−8.30551	+	7.95125i	−0.870654	+	0.833518i
$92$			0.876877i			0.0914208i
$93$	1.36660	+	1.06452i	0.141709	+	0.110386i
$94$	4.98262	+	8.63015i	0.513918	+	0.890132i
$95$	−6.47580	+	11.2164i	−0.664403	+	1.15078i
$96$	−0.393415	−	0.969695i	−0.0401528	−	0.0989690i
$97$	−6.06921	+	1.62624i	−0.616235	+	0.165120i	−0.553416	−	0.832905i	$-0.686676\pi$
$97$	−6.06921	+	1.62624i	−0.616235	+	0.165120i	−0.0628195	+	0.998025i	$0.520009\pi$
$98$	4.21234	−	1.12869i	0.425510	−	0.114015i
$99$	−0.0436756	+	2.99968i	−0.00438957	+	0.301479i
$100$	−0.393239	+	0.681109i	−0.0393239	+	0.0681109i
$101$	8.25018	+	14.2897i	0.820923	+	1.42188i	0.904995	+	0.425421i	$0.139874\pi$
$101$	8.25018	+	14.2897i	0.820923	+	1.42188i	−0.0840722	+	0.996460i	$0.526793\pi$
$102$	−11.0980	+	14.2473i	−1.09887	+	1.41069i
$103$			1.00233i			0.0987629i	0.998780	+	0.0493814i	$0.0157250\pi$
$103$			1.00233i			0.0987629i	−0.998780	+	0.0493814i	$0.984275\pi$
$104$	2.92452	−	10.0346i	0.286772	−	0.983977i
$105$	17.8829	+	7.56030i	1.74519	+	0.737810i
$106$	1.30797	−	4.88142i	0.127041	−	0.474125i
$107$	−5.36978	+	3.10025i	−0.519116	+	0.299712i	−0.736573	−	0.676358i	$-0.763557\pi$
$107$	−5.36978	+	3.10025i	−0.519116	+	0.299712i	0.217457	+	0.976070i	$0.430224\pi$
$108$	−0.549109	−	0.0845283i	−0.0528380	−	0.00813374i
$109$	6.28193	+	6.28193i	0.601700	+	0.601700i	0.940763	−	0.339064i	$-0.110110\pi$
$109$	6.28193	+	6.28193i	0.601700	+	0.601700i	−0.339064	+	0.940763i	$0.610110\pi$
$110$	1.25174	+	4.67156i	0.119349	+	0.445416i
$111$	1.53781	+	0.213856i	0.145962	+	0.0202983i
$112$	−8.51179	+	8.51179i	−0.804289	+	0.804289i
$113$	15.5461	+	8.97555i	1.46246	+	0.844349i	0.999124	−	0.0418362i	$-0.0133208\pi$
$113$	15.5461	+	8.97555i	1.46246	+	0.844349i	0.463331	+	0.886185i	$0.346654\pi$
$114$	−8.71381	+	1.08272i	−0.816123	+	0.101406i
$115$	27.8454	+	7.46116i	2.59660	+	0.695757i
$116$	0.606927			0.0563517
$117$	−7.36554	−	7.92142i	−0.680944	−	0.732335i
$118$	10.1462			0.934029
$119$	−23.3431	−	6.25476i	−2.13986	−	0.573373i
$120$	−17.5146	+	2.17625i	−1.59886	+	0.198664i
$121$	−0.866025	−	0.500000i	−0.0787296	−	0.0454545i
$122$	−8.83208	+	8.83208i	−0.799619	+	0.799619i
$123$	9.89690	+	1.37632i	0.892373	+	0.124098i
$124$	−0.0276768	−	0.103291i	−0.00248545	−	0.00927582i
$125$	5.85516	+	5.85516i	0.523701	+	0.523701i
$126$	3.22138	+	12.7628i	0.286983	+	1.13700i
$127$	4.88996	−	2.82322i	0.433914	−	0.250520i	−0.267099	−	0.963669i	$-0.586065\pi$
$127$	4.88996	−	2.82322i	0.433914	−	0.250520i	0.701013	+	0.713149i	$0.252732\pi$
$128$	2.67169	−	9.97090i	0.236147	−	0.881311i
$129$	1.25114	+	0.528942i	0.110157	+	0.0465707i
$130$	−14.9080	−	9.04579i	−1.30752	−	0.793369i
$131$		−	5.91793i		−	0.517052i	−0.966004	−	0.258526i	$-0.916763\pi$
$131$		−	5.91793i		−	0.517052i	0.966004	−	0.258526i	$-0.0832367\pi$
$132$	0.113804	−	0.146098i	0.00990541	−	0.0127162i
$133$	−5.87503	−	10.1759i	−0.509430	−	0.882359i
$134$	0.175597	−	0.304142i	0.0151692	−	0.0262739i
$135$	−7.35647	+	16.7178i	−0.633144	+	1.43884i
$136$	21.2198	−	5.68582i	1.81958	−	0.487555i
$137$	−20.7454	+	5.55872i	−1.77240	+	0.474914i	−0.989165	−	0.146808i	$-0.953100\pi$
$137$	−20.7454	+	5.55872i	−1.77240	+	0.474914i	−0.783238	+	0.621722i	$0.786433\pi$
$138$	7.34766	+	18.1106i	0.625475	+	1.54168i
$139$	−8.44696	+	14.6306i	−0.716462	+	1.24095i	0.245931	+	0.969287i	$0.420906\pi$
$139$	−8.44696	+	14.6306i	−0.716462	+	1.24095i	−0.962393	+	0.271661i	$0.912427\pi$
$140$	−0.599262	−	1.03795i	−0.0506468	−	0.0877229i
$141$	−9.89661	−	7.70904i	−0.833445	−	0.649219i
$142$			8.43186i			0.707586i
$143$	3.50220	−	0.857090i	0.292869	−	0.0716734i
$144$	−7.88998	−	8.12313i	−0.657498	−	0.676928i
$145$	5.16421	−	19.2731i	0.428864	−	1.60054i
$146$	−3.73551	+	2.15670i	−0.309153	+	0.178490i
$147$	−4.37955	+	3.31018i	−0.361220	+	0.273019i
$148$	−0.0677716	−	0.0677716i	−0.00557079	−	0.00557079i
$149$	−2.73844	−	10.2200i	−0.224342	−	0.837254i	−0.982667	−	0.185378i	$-0.940649\pi$
$149$	−2.73844	−	10.2200i	−0.224342	−	0.837254i	0.758326	−	0.651876i	$-0.226018\pi$
$150$	−2.41451	+	17.3624i	−0.197144	+	1.41763i
$151$	7.53037	−	7.53037i	0.612813	−	0.612813i	−0.330865	−	0.943678i	$-0.607341\pi$
$151$	7.53037	−	7.53037i	0.612813	−	0.612813i	0.943678	+	0.330865i	$0.107341\pi$
$152$	9.25024	+	5.34063i	0.750294	+	0.433182i
$153$	6.20320	−	21.8718i	0.501499	−	1.76823i
$154$	−4.23817	−	1.13561i	−0.341522	−	0.0915105i
$155$	−3.51553			−0.282374
$156$	0.0678781	+	0.664261i	0.00543460	+	0.0531835i
$157$	8.80486			0.702704			0.351352	−	0.936243i	$-0.385722\pi$
$157$	8.80486			0.702704			0.351352	+	0.936243i	$0.385722\pi$
$158$	−1.01059	−	0.270786i	−0.0803979	−	0.0215426i
$159$	0.784442	+	6.31323i	0.0622103	+	0.500672i
$160$	1.83919	+	1.06186i	0.145401	+	0.0839473i
$161$	−18.4932	+	18.4932i	−1.45747	+	1.45747i
$162$	−12.0493	+	2.85537i	−0.946685	+	0.224339i
$163$	0.170284	+	0.635509i	0.0133377	+	0.0497769i	0.972274	−	0.233845i	$-0.0751307\pi$
$163$	0.170284	+	0.635509i	0.0133377	+	0.0497769i	−0.958936	+	0.283622i	$0.908464\pi$
$164$	−0.436159	−	0.436159i	−0.0340583	−	0.0340583i
$165$	−3.67105	−	4.85701i	−0.285791	−	0.378117i
$166$	0.700986	−	0.404714i	0.0544071	−	0.0314119i
$167$	4.85204	−	18.1080i	0.375462	−	1.40124i	−0.477207	−	0.878791i	$-0.658351\pi$
$167$	4.85204	−	18.1080i	0.375462	−	1.40124i	0.852669	−	0.522452i	$-0.174983\pi$
$168$	6.23502	−	14.7481i	0.481043	−	1.13784i
$169$	−6.98426	+	10.9645i	−0.537251	+	0.843422i
$170$		−	36.6507i		−	2.81098i
$171$	9.65231	−	5.38694i	0.738131	−	0.411950i
$172$	−0.0419261	−	0.0726182i	−0.00319684	−	0.00553709i
$173$	2.22204	−	3.84869i	0.168939	−	0.292610i	−0.769108	−	0.639118i	$-0.779299\pi$
$173$	2.22204	−	3.84869i	0.168939	−	0.292610i	0.938047	+	0.346508i	$0.112633\pi$
$174$	12.5352	−	5.08565i	0.950289	−	0.385542i
$175$	−22.6578	+	6.07115i	−1.71277	+	0.458936i
$176$	3.64611	−	0.976971i	0.274836	−	0.0736420i
$177$	−11.8356	+	4.80181i	−0.889615	+	0.360926i
$178$	1.93906	−	3.35856i	0.145339	−	0.251734i
$179$	0.0957311	+	0.165811i	0.00715527	+	0.0123933i	0.869581	−	0.493791i	$-0.164389\pi$
$179$	0.0957311	+	0.165811i	0.00715527	+	0.0123933i	−0.862426	+	0.506184i	$0.831056\pi$
$180$	0.984549	−	0.549475i	0.0733839	−	0.0409555i
$181$			7.33902i			0.545505i	0.962084	+	0.272753i	$0.0879341\pi$
$181$			7.33902i			0.545505i	−0.962084	+	0.272753i	$0.912066\pi$
$182$	13.8696	−	7.60964i	1.02808	−	0.564064i
$183$	6.12278	−	14.4826i	0.452609	−	1.07058i
$184$	6.15326	−	22.9643i	0.453624	−	1.69295i
$185$	−2.72876	+	1.57545i	−0.200622	+	0.115829i
$186$	−1.43714	−	1.90141i	−0.105376	−	0.139418i
$187$	5.35857	+	5.35857i	0.391858	+	0.391858i
$188$	0.200430	+	0.748014i	0.0146178	+	0.0545545i
$189$	−9.79793	−	13.3633i	−0.712694	−	0.972037i
$190$	12.6007	−	12.6007i	0.914147	−	0.914147i
$191$	17.2210	+	9.94253i	1.24607	+	0.719416i	0.970322	−	0.241815i	$-0.0777427\pi$
$191$	17.2210	+	9.94253i	1.24607	+	0.719416i	0.275743	+	0.961231i	$0.411076\pi$
$192$	1.78989	+	14.4051i	0.129174	+	1.03960i
$193$	−0.906665	−	0.242940i	−0.0652632	−	0.0174872i	0.226040	−	0.974118i	$-0.427422\pi$
$193$	−0.906665	−	0.242940i	−0.0652632	−	0.0174872i	−0.291303	+	0.956631i	$0.594089\pi$
$194$	8.64516			0.620686
$195$	21.6713	+	3.49657i	1.55192	+	0.250395i
$196$	0.338889			0.0242063
$197$	17.9747	+	4.81631i	1.28065	+	0.343148i	0.834100	−	0.551613i	$-0.185987\pi$
$197$	17.9747	+	4.81631i	1.28065	+	0.343148i	0.446546	+	0.894761i	$0.352654\pi$
$198$	1.12625	−	3.97105i	0.0800393	−	0.282210i
$199$	0.547477	+	0.316086i	0.0388096	+	0.0224067i	0.519279	−	0.854605i	$-0.326200\pi$
$199$	0.547477	+	0.316086i	0.0388096	+	0.0224067i	−0.480470	+	0.877011i	$0.659534\pi$
$200$	15.0779	−	15.0779i	1.06617	−	1.06617i
$201$	−0.0608951	+	0.437888i	−0.00429521	+	0.0308863i
$202$	−5.87589	−	21.9291i	−0.413426	−	1.54293i
$203$	12.8000	+	12.8000i	0.898383	+	0.898383i
$204$	−1.11960	+	0.846219i	−0.0783874	+	0.0592472i
$205$	−17.5615	+	10.1392i	−1.22655	+	0.708149i
$206$	0.356938	−	1.33211i	0.0248691	−	0.0928126i
$207$	−17.1422	−	17.6488i	−1.19147	−	1.22667i
$208$	−7.06015	+	11.6355i	−0.489533	+	0.806779i
$209$			3.68460i			0.254869i
$210$	−21.0742	−	16.4159i	−1.45426	−	1.13281i
$211$	−9.85833	−	17.0751i	−0.678675	−	1.17550i	−0.975380	−	0.220531i	$-0.929221\pi$
$211$	−9.85833	−	17.0751i	−0.678675	−	1.17550i	0.296705	−	0.954969i	$-0.404112\pi$
$212$	0.196359	−	0.340103i	0.0134860	−	0.0233584i
$213$	−3.99050	−	9.83583i	−0.273425	−	0.673940i
$214$	8.24051	−	2.20804i	0.563310	−	0.150938i
$215$	−2.66275	+	0.713481i	−0.181598	+	0.0486590i
$216$	13.7873	+	6.06692i	0.938107	+	0.412802i
$217$	1.59469	−	2.76209i	0.108255	−	0.187503i
$218$	−6.11171	−	10.5858i	−0.413937	−	0.716960i
$219$	3.33681	−	4.28369i	0.225481	−	0.289465i
$220$			0.375834i			0.0253387i
$221$	−27.3170	−	0.595270i	−1.83754	−	0.0400422i
$222$	−1.96760	−	0.831840i	−0.132057	−	0.0558295i
$223$	−6.43106	+	24.0010i	−0.430656	+	1.60723i	0.320598	+	0.947215i	$0.396116\pi$
$223$	−6.43106	+	24.0010i	−0.430656	+	1.60723i	−0.751254	+	0.660014i	$0.770550\pi$
$224$	−1.66857	+	0.963349i	−0.111486	+	0.0643664i
$225$	−5.40046	−	21.3961i	−0.360031	−	1.42640i
$226$	−17.4647	−	17.4647i	−1.16173	−	1.16173i
$227$	−3.23754	−	12.0827i	−0.214883	−	0.801955i	−0.986208	−	0.165513i	$-0.947072\pi$
$227$	−3.23754	−	12.0827i	−0.214883	−	0.801955i	0.771324	−	0.636442i	$-0.219595\pi$
$228$	−0.675855	−	0.0939881i	−0.0447596	−	0.00622451i
$229$	−7.53181	+	7.53181i	−0.497716	+	0.497716i	−0.910726	−	0.413010i	$-0.864477\pi$
$229$	−7.53181	+	7.53181i	−0.497716	+	0.497716i	0.413010	+	0.910726i	$0.364477\pi$
$230$	−34.3499	−	19.8319i	−2.26496	−	1.30768i
$231$	5.48131	−	0.681073i	0.360644	−	0.0448113i
$232$	−15.8946	−	4.25895i	−1.04353	−	0.279614i
$233$	−22.0923			−1.44732			−0.723658	−	0.690159i	$-0.757541\pi$
$233$	−22.0923			−1.44732			−0.723658	+	0.690159i	$0.757541\pi$
$234$	6.96800	+	13.1506i	0.455512	+	0.859679i
$235$	25.4588			1.66075
$236$	0.761593	+	0.204068i	0.0495755	+	0.0132837i
$237$	1.30701	−	0.162401i	0.0848994	−	0.0105491i
$238$	28.7958	+	16.6253i	1.86656	+	1.07766i
$239$	−2.92273	+	2.92273i	−0.189056	+	0.189056i	−0.795288	−	0.606232i	$-0.792680\pi$
$239$	−2.92273	+	2.92273i	−0.189056	+	0.189056i	0.606232	+	0.795288i	$0.292680\pi$
$240$	22.7625	+	3.16548i	1.46931	+	0.204331i
$241$	0.603980	+	2.25408i	0.0389058	+	0.145198i	0.982647	−	0.185488i	$-0.0593865\pi$
$241$	0.603980	+	2.25408i	0.0389058	+	0.145198i	−0.943741	+	0.330686i	$0.892720\pi$
$242$	0.972903	+	0.972903i	0.0625406	+	0.0625406i
$243$	12.7043	−	9.03333i	0.814980	−	0.579488i
$244$	−0.840594	+	0.485317i	−0.0538135	+	0.0310693i
$245$	2.88353	−	10.7615i	0.184222	−	0.687526i
$246$	−12.6630	−	5.35349i	−0.807361	−	0.341326i
$247$	−9.18703	−	9.59634i	−0.584557	−	0.610601i
$248$			2.89928i			0.184104i
$249$	−0.626169	+	0.803854i	−0.0396818	+	0.0509422i
$250$	−5.69650	−	9.86662i	−0.360278	−	0.624020i
$251$	4.36121	−	7.55383i	0.275277	−	0.476793i	−0.694928	−	0.719079i	$-0.744564\pi$
$251$	4.36121	−	7.55383i	0.275277	−	0.476793i	0.970205	+	0.242286i	$0.0778972\pi$
$252$	−0.0148920	+	1.02279i	−0.000938106	+	0.0644299i
$253$	7.92174	−	2.12262i	0.498035	−	0.133448i
$254$	−7.50417	+	2.01074i	−0.470854	+	0.126165i
$255$	17.3455	+	42.7533i	1.08622	+	2.67732i
$256$	1.27932	−	2.21584i	0.0799573	−	0.138490i
$257$	−10.3648	−	17.9523i	−0.646538	−	1.11984i	−0.983944	−	0.178477i	$-0.942883\pi$
$257$	−10.3648	−	17.9523i	−0.646538	−	1.11984i	0.337406	−	0.941359i	$-0.390450\pi$
$258$	−1.47442	−	1.14851i	−0.0917932	−	0.0715030i
$259$		−	2.85858i		−	0.177624i
$260$	−0.937089	−	0.978840i	−0.0581158	−	0.0607051i
$261$	−12.2155	+	11.8649i	−0.756122	+	0.734420i
$262$	−2.10742	+	7.86498i	−0.130197	+	0.485900i
$263$	8.86954	−	5.12083i	0.546919	−	0.315764i	−0.200959	−	0.979600i	$-0.564406\pi$
$263$	8.86954	−	5.12083i	0.546919	−	0.315764i	0.747879	+	0.663836i	$0.231073\pi$
$264$	−4.00560	+	3.02753i	−0.246528	+	0.186332i
$265$	−9.12928	−	9.12928i	−0.560807	−	0.560807i
$266$	4.18428	+	15.6160i	0.256555	+	0.957476i
$267$	−0.672447	+	4.83547i	−0.0411531	+	0.295926i
$268$	0.0192979	−	0.0192979i	0.00117880	−	0.00117880i
$269$	−7.62021	−	4.39953i	−0.464612	−	0.268244i	0.249369	−	0.968408i	$-0.419777\pi$
$269$	−7.62021	−	4.39953i	−0.464612	−	0.268244i	−0.713982	+	0.700164i	$0.753110\pi$
$270$	15.7302	−	19.5985i	0.957307	−	1.19273i
$271$	−10.5987	−	2.83992i	−0.643826	−	0.172513i	−0.0778901	−	0.996962i	$-0.524818\pi$
$271$	−10.5987	−	2.83992i	−0.643826	−	0.172513i	−0.565936	+	0.824449i	$0.691485\pi$
$272$	−28.6055			−1.73446
$273$	−12.5776	+	15.4407i	−0.761232	+	0.934514i
$274$	29.5504			1.78520
$275$	7.10506	+	1.90380i	0.428451	+	0.114803i
$276$	0.187276	+	1.50721i	0.0112727	+	0.0907231i
$277$	18.5614	+	10.7164i	1.11525	+	0.643888i	0.940183	−	0.340669i	$-0.110653\pi$
$277$	18.5614	+	10.7164i	1.11525	+	0.643888i	0.175064	+	0.984557i	$0.443987\pi$
$278$	16.4361	−	16.4361i	0.985774	−	0.985774i
$279$	2.57630	+	1.53787i	0.154239	+	0.0920697i
$280$	8.41033	+	31.3878i	0.502613	+	1.87578i
$281$	−7.86272	−	7.86272i	−0.469051	−	0.469051i	0.432556	−	0.901607i	$-0.357612\pi$
$281$	−7.86272	−	7.86272i	−0.469051	−	0.469051i	−0.901607	+	0.432556i	$0.857612\pi$
$282$	10.4074	+	13.7696i	0.619755	+	0.819971i
$283$	−18.5496	+	10.7096i	−1.10266	+	0.636621i	−0.936918	−	0.349549i	$-0.886335\pi$
$283$	−18.5496	+	10.7096i	−1.10266	+	0.636621i	−0.165741	+	0.986169i	$0.553002\pi$
$284$	−0.169589	+	0.632914i	−0.0100633	+	0.0375566i
$285$	−8.73532	+	20.6622i	−0.517436	+	1.22392i
$286$	−4.95967	−	0.108077i	−0.293272	−	0.00639074i
$287$		−	18.3971i		−	1.08594i
$288$	−0.883314	−	1.58272i	−0.0520498	−	0.0932627i
$289$	−20.2143	−	35.0122i	−1.18908	−	2.05954i
$290$	−13.7266	+	23.7751i	−0.806052	+	1.39612i
$291$	−10.0846	+	4.09145i	−0.591172	+	0.239845i
$292$	−0.323773	+	0.0867548i	−0.0189474	+	0.00507694i
$293$	17.0649	−	4.57252i	0.996942	−	0.267130i	0.276778	−	0.960934i	$-0.410733\pi$
$293$	17.0649	−	4.57252i	0.996942	−	0.267130i	0.720164	+	0.693804i	$0.244067\pi$
$294$	6.99925	−	2.83967i	0.408205	−	0.165613i
$295$	12.9605	−	22.4482i	0.754587	−	1.30698i
$296$	1.29928	+	2.25042i	0.0755192	+	0.130803i
$297$	0.565575	+	5.16528i	0.0328180	+	0.299720i
$298$			14.5576i			0.843302i
$299$	−15.3393	+	25.2800i	−0.887094	+	1.46198i
$300$	−0.530446	+	1.25470i	−0.0306253	+	0.0724400i
$301$	0.647291	−	2.41572i	0.0373092	−	0.139240i
$302$	−12.6896	+	7.32632i	−0.730202	+	0.421582i
$303$	17.2326	+	22.7997i	0.989984	+	1.30981i
$304$	−9.83468	−	9.83468i	−0.564058	−	0.564058i
$305$	8.25892	+	30.8227i	0.472904	+	1.76490i
$306$	−16.0328	+	26.8589i	−0.916536	+	1.53542i
$307$	10.5285	−	10.5285i	0.600895	−	0.600895i	−0.339655	−	0.940550i	$-0.610310\pi$
$307$	10.5285	−	10.5285i	0.600895	−	0.600895i	0.940550	+	0.339655i	$0.110310\pi$
$308$	−0.295286	−	0.170484i	−0.0168255	−	0.00971421i
$309$	0.214070	+	1.72284i	0.0121780	+	0.0980092i
$310$	4.67217	+	1.25190i	0.265362	+	0.0711034i
$311$	26.7482			1.51675			0.758376	−	0.651817i	$-0.225993\pi$
$311$	26.7482			1.51675			0.758376	+	0.651817i	$0.225993\pi$
$312$	2.88364	−	17.8725i	0.163254	−	1.01183i
$313$	11.5772			0.654380			0.327190	−	0.944959i	$-0.393898\pi$
$313$	11.5772			0.654380			0.327190	+	0.944959i	$0.393898\pi$
$314$	−11.7017	−	3.13547i	−0.660368	−	0.176945i
$315$	32.3523	+	9.17563i	1.82285	+	0.516988i
$316$	−0.0704106	−	0.0406516i	−0.00396091	−	0.00228683i
$317$	2.27038	−	2.27038i	0.127517	−	0.127517i	−0.640468	−	0.767985i	$-0.721259\pi$
$317$	2.27038	−	2.27038i	0.127517	−	0.127517i	0.767985	+	0.640468i	$0.221259\pi$
$318$	1.20565	−	8.66969i	0.0676097	−	0.486172i
$319$	−1.46916	−	5.48300i	−0.0822574	−	0.306989i
$320$	−20.8305	−	20.8305i	−1.16446	−	1.16446i
$321$	−8.56764	+	6.47564i	−0.478199	+	0.361435i
$322$	31.1632	−	17.9921i	1.73666	−	1.00266i
$323$	7.22687	−	26.9710i	0.402114	−	1.50071i
$324$	−0.961879	−	0.0280160i	−0.0534377	−	0.00155645i
$325$	−23.2516	+	12.7571i	−1.28977	+	0.707639i
$326$		−	0.905237i		−	0.0501364i
$327$	12.1392	+	9.45595i	0.671301	+	0.522915i
$328$	8.36181	+	14.4831i	0.461704	+	0.799695i
$329$	−11.5485	+	20.0025i	−0.636687	+	1.10277i
$330$	3.14924	+	7.76229i	0.173360	+	0.427300i
$331$	5.97665	−	1.60144i	0.328506	−	0.0880230i	−0.0907965	−	0.995869i	$-0.528941\pi$
$331$	5.97665	−	1.60144i	0.328506	−	0.0880230i	0.419303	+	0.907847i	$0.362275\pi$
$332$	0.0607576	−	0.0162799i	0.00333450	−	0.000893478i
$333$	2.68891	+	0.0391507i	0.147351	+	0.00214545i
$334$	−12.8968	+	22.3379i	−0.705682	+	1.22228i
$335$	−0.448607	−	0.777010i	−0.0245100	−	0.0424526i
$336$	−12.8125	+	16.4482i	−0.698978	+	0.897324i
$337$		−	28.7102i		−	1.56394i	−0.623315	−	0.781971i	$-0.714214\pi$
$337$		−	28.7102i		−	1.56394i	0.623315	−	0.781971i	$-0.285786\pi$
$338$	13.1867	−	12.0848i	0.717261	−	0.657325i
$339$	28.6381	+	12.1073i	1.55541	+	0.657577i
$340$	0.737151	−	2.75108i	0.0399776	−	0.149198i
$341$	−0.866139	+	0.500066i	−0.0469041	+	0.0270801i
$342$	−14.7463	+	3.72204i	−0.797391	+	0.201265i
$343$	−8.63749	−	8.63749i	−0.466380	−	0.466380i
$344$	0.588412	+	2.19598i	0.0317251	+	0.118400i
$345$	49.4551	+	6.87750i	2.66258	+	0.370272i
$346$	−4.32366	+	4.32366i	−0.232441	+	0.232441i
$347$	28.2122	+	16.2883i	1.51451	+	0.874401i	0.999855	+	0.0170023i	$0.00541225\pi$
$347$	28.2122	+	16.2883i	1.51451	+	0.874401i	0.514652	+	0.857399i	$0.327921\pi$
$348$	1.04321	−	0.129622i	0.0559217	−	0.00694848i
$349$	−16.1994	−	4.34060i	−0.867132	−	0.232347i	−0.202285	−	0.979327i	$-0.564837\pi$
$349$	−16.1994	−	4.34060i	−0.867132	−	0.232347i	−0.664847	+	0.746980i	$0.731503\pi$
$350$	32.2744			1.72514
$351$	−14.3519	−	12.0425i	−0.766049	−	0.642782i
$352$	0.604175			0.0322027
$353$	28.5573	+	7.65191i	1.51995	+	0.407270i	0.919726	−	0.392560i	$-0.128410\pi$
$353$	28.5573	+	7.65191i	1.51995	+	0.407270i	0.600226	+	0.799830i	$0.295077\pi$
$354$	17.4395	−	2.16693i	0.926901	−	0.115171i
$355$	18.6553	+	10.7707i	0.990123	+	0.571648i
$356$	0.213101	−	0.213101i	0.0112943	−	0.0112943i
$357$	−41.4587	−	5.76547i	−2.19423	−	0.305141i
$358$	−0.0681810	−	0.254455i	−0.00360348	−	0.0134484i
$359$	1.93073	+	1.93073i	0.101900	+	0.101900i	0.756219	−	0.654319i	$-0.227045\pi$
$359$	1.93073	+	1.93073i	0.101900	+	0.101900i	−0.654319	+	0.756219i	$0.727045\pi$
$360$	−29.6399	+	7.48123i	−1.56216	+	0.394296i
$361$	−4.69710	+	2.71187i	−0.247216	+	0.142730i
$362$	2.61348	−	9.75363i	0.137361	−	0.512640i
$363$	−1.59534	−	0.674458i	−0.0837336	−	0.0353999i
$364$	1.19414	−	0.292240i	0.0625897	−	0.0153175i
$365$			11.0197i			0.576796i
$366$	−13.2946	+	17.0671i	−0.694919	+	0.892114i
$367$	15.9424	+	27.6131i	0.832188	+	1.44139i	0.896300	+	0.443449i	$0.146245\pi$
$367$	15.9424	+	27.6131i	0.832188	+	1.44139i	−0.0641120	+	0.997943i	$0.520421\pi$
$368$	−15.4786	+	26.8097i	−0.806878	+	1.39755i
$369$	17.3051	+	0.251963i	0.900866	+	0.0131167i
$370$	4.18757	−	1.12206i	0.217702	−	0.0583329i
$371$	11.3139	−	3.03155i	0.587388	−	0.157390i
$372$	−0.0696318	−	0.171629i	−0.00361024	−	0.00889856i
$373$	−5.77918	+	10.0098i	−0.299235	+	0.518289i	−0.975961	−	0.217945i	$-0.930065\pi$
$373$	−5.77918	+	10.0098i	−0.299235	+	0.518289i	0.676726	+	0.736235i	$0.263398\pi$
$374$	−5.21337	−	9.02982i	−0.269577	−	0.466921i
$375$	11.3145	+	8.81354i	0.584280	+	0.455129i
$376$		−	20.9960i		−	1.08278i
$377$	17.4974	+	10.6170i	0.901164	+	0.546804i
$378$	8.26278	+	21.2491i	0.424991	+	1.09293i
$379$	1.02454	−	3.82364i	0.0526271	−	0.196407i	−0.934607	−	0.355682i	$-0.884249\pi$
$379$	1.02454	−	3.82364i	0.0526271	−	0.196407i	0.987234	+	0.159274i	$0.0509154\pi$
$380$	1.19927	−	0.692398i	0.0615212	−	0.0355193i
$381$	7.80206	−	5.89700i	0.399712	−	0.302112i
$382$	−19.3462	−	19.3462i	−0.989839	−	0.989839i
$383$	−7.92522	−	29.5773i	−0.404960	−	1.51133i	−0.804130	−	0.594454i	$-0.797368\pi$
$383$	−7.92522	−	29.5773i	−0.404960	−	1.51133i	0.399170	−	0.916877i	$-0.369298\pi$
$384$	2.46270	−	17.7089i	0.125674	−	0.903704i
$385$	−7.92628	+	7.92628i	−0.403960	+	0.403960i
$386$	1.11845	+	0.645740i	0.0569278	+	0.0328673i
$387$	2.26347	+	0.641955i	0.115058	+	0.0326324i
$388$	0.648925	+	0.173879i	0.0329442	+	0.00882737i
$389$	−36.0696			−1.82880			−0.914401	−	0.404810i	$-0.867338\pi$
$389$	−36.0696			−1.82880			−0.914401	+	0.404810i	$0.867338\pi$
$390$	−27.5562	−	12.3643i	−1.39536	−	0.626090i
$391$	−62.1499			−3.14306
$392$	−8.87506	−	2.37807i	−0.448258	−	0.120110i
$393$	−1.26390	−	10.1719i	−0.0637553	−	0.513106i
$394$	−22.1735	−	12.8019i	−1.11708	−	0.644948i
$395$	−1.89001	+	1.89001i	−0.0950967	+	0.0950967i
$396$	0.164408	−	0.275424i	0.00826183	−	0.0138406i
$397$	9.78684	+	36.5250i	0.491187	+	1.83314i	0.550415	+	0.834891i	$0.314469\pi$
$397$	9.78684	+	36.5250i	0.491187	+	1.83314i	−0.0592280	+	0.998244i	$0.518864\pi$
$398$	−0.615041	−	0.615041i	−0.0308292	−	0.0308292i
$399$	−12.2715	−	16.2359i	−0.614342	−	0.812810i
$400$	−24.0458	+	13.8829i	−1.20229	+	0.694144i
$401$	−1.85876	+	6.93698i	−0.0928219	+	0.346416i	−0.996680	−	0.0814158i	$-0.974056\pi$
$401$	−1.85876	+	6.93698i	−0.0928219	+	0.346416i	0.903858	+	0.427832i	$0.140722\pi$
$402$	0.236865	−	0.560273i	0.0118138	−	0.0279439i
$403$	1.00897	−	3.46199i	0.0502604	−	0.172454i
$404$		−	1.76423i		−	0.0877738i
$405$	−9.07408	+	30.3063i	−0.450895	+	1.50593i
$406$	−12.4531	−	21.5695i	−0.618039	−	1.07048i
$407$	−0.448199	+	0.776303i	−0.0222164	+	0.0384799i
$408$	35.2589	−	14.3049i	1.74558	−	0.708198i
$409$	8.23058	−	2.20538i	0.406976	−	0.109049i	−0.0495225	−	0.998773i	$-0.515770\pi$
$409$	8.23058	−	2.20538i	0.406976	−	0.109049i	0.456499	+	0.889724i	$0.349103\pi$
$410$	26.9501	−	7.22125i	1.33097	−	0.356632i
$411$	−34.4708	+	13.9852i	−1.70032	+	0.689837i
$412$	0.0535852	−	0.0928122i	0.00263995	−	0.00457253i
$413$	11.7581	+	20.3656i	0.578579	+	1.00213i
$414$	16.4973	+	29.5599i	0.810799	+	1.45279i
$415$		−	2.06789i		−	0.101509i
$416$	−1.57354	+	1.50643i	−0.0771493	+	0.0738587i
$417$	−11.3942	+	26.9515i	−0.557979	+	1.31982i
$418$	1.31211	−	4.89686i	0.0641774	−	0.239513i
$419$	−13.0406	+	7.52901i	−0.637076	+	0.367816i	−0.783487	−	0.621408i	$-0.786561\pi$
$419$	−13.0406	+	7.52901i	−0.637076	+	0.367816i	0.146411	+	0.989224i	$0.453228\pi$
$420$	−1.25171	−	1.65608i	−0.0610771	−	0.0808084i
$421$	19.6312	+	19.6312i	0.956766	+	0.956766i	0.999103	−	0.0423370i	$-0.0134803\pi$
$421$	19.6312	+	19.6312i	0.956766	+	0.956766i	−0.0423370	+	0.999103i	$0.513480\pi$
$422$	7.02124	+	26.2036i	0.341789	+	1.27557i
$423$	−18.6571	−	11.1369i	−0.907137	−	0.541496i
$424$	−7.52897	+	7.52897i	−0.365639	+	0.365639i
$425$	−48.2746	−	27.8714i	−2.34166	−	1.35196i
$426$	1.80080	+	14.4930i	0.0872493	+	0.702186i
$427$	−27.9633	−	7.49273i	−1.35324	−	0.362599i
$428$	0.662962			0.0320455
$429$	5.83665	−	2.22116i	0.281796	−	0.107239i
$430$	3.79289			0.182910
$431$	11.2303	+	3.00916i	0.540946	+	0.144946i	0.518938	−	0.854812i	$-0.326328\pi$
$431$	11.2303	+	3.00916i	0.540946	+	0.144946i	0.0220076	+	0.999758i	$0.492994\pi$
$432$	−15.2964	−	12.2772i	−0.735950	−	0.590689i
$433$	23.2344	+	13.4144i	1.11657	+	0.644653i	0.940524	−	0.339728i	$-0.110335\pi$
$433$	23.2344	+	13.4144i	1.11657	+	0.644653i	0.176049	+	0.984381i	$0.443668\pi$
$434$	−3.10296	+	3.10296i	−0.148947	+	0.148947i
$435$	4.76023	−	34.2302i	0.228236	−	1.64121i
$436$	−0.245848	−	0.917517i	−0.0117740	−	0.0439411i
$437$	−21.3674	−	21.3674i	−1.02214	−	1.02214i
$438$	−5.96011	+	4.50480i	−0.284785	+	0.215248i
$439$	32.9015	−	18.9957i	1.57030	−	0.906615i	0.574172	−	0.818735i	$-0.305324\pi$
$439$	32.9015	−	18.9957i	1.57030	−	0.906615i	0.996131	−	0.0878803i	$-0.0280093\pi$
$440$	2.63732	−	9.84260i	0.125729	−	0.469228i
$441$	−6.82076	+	6.62499i	−0.324798	+	0.315476i
$442$	36.0926	+	10.5189i	1.71675	+	0.500333i
$443$		−	7.58765i		−	0.360500i	−0.983621	−	0.180250i	$-0.942309\pi$
$443$		−	7.58765i		−	0.360500i	0.983621	−	0.180250i	$-0.0576907\pi$
$444$	−0.130962	−	0.102014i	−0.00621519	−	0.00484137i
$445$	−4.95383	−	8.58029i	−0.234834	−	0.406745i
$446$	17.0939	−	29.6075i	0.809419	−	1.40195i
$447$	−6.88962	−	16.9816i	−0.325868	−	0.803202i
$448$	25.8152	−	6.91717i	1.21966	−	0.326806i
$449$	24.8897	−	6.66918i	1.17462	−	0.314738i	0.381829	−	0.924233i	$-0.375294\pi$
$449$	24.8897	−	6.66918i	1.17462	−	0.314738i	0.792790	+	0.609495i	$0.208628\pi$
$450$	−0.442026	+	30.3587i	−0.0208373	+	1.43112i
$451$	−2.88448	+	4.99607i	−0.135825	+	0.235256i
$452$	−0.959673	−	1.66220i	−0.0451392	−	0.0781835i
$453$	11.3352	−	14.5517i	0.532573	−	0.683700i
$454$			17.2109i			0.807748i
$455$	0.880510	−	40.4066i	0.0412789	−	1.89429i
$456$	17.0402	+	7.20406i	0.797982	+	0.337361i
$457$	0.392585	−	1.46515i	0.0183643	−	0.0685366i	−0.956136	−	0.292924i	$-0.905372\pi$
$457$	0.392585	−	1.46515i	0.0183643	−	0.0685366i	0.974500	+	0.224388i	$0.0720382\pi$
$458$	12.6920	−	7.32772i	0.593057	−	0.342402i
$459$	5.99106	−	38.9189i	0.279639	−	1.81658i
$460$	−2.17950	−	2.17950i	−0.101620	−	0.101620i
$461$	4.64675	+	17.3419i	0.216421	+	0.807692i	0.985662	+	0.168734i	$0.0539678\pi$
$461$	4.64675	+	17.3419i	0.216421	+	0.807692i	−0.769241	+	0.638959i	$0.779366\pi$
$462$	−7.52725	−	1.04678i	−0.350199	−	0.0487006i
$463$	17.3905	−	17.3905i	0.808205	−	0.808205i	−0.176157	−	0.984362i	$-0.556367\pi$
$463$	17.3905	−	17.3905i	0.808205	−	0.808205i	0.984362	+	0.176157i	$0.0563667\pi$
$464$	18.5562	+	10.7135i	0.861452	+	0.497360i
$465$	−6.04261	+	0.750817i	−0.280219	+	0.0348183i
$466$	29.3609	+	7.86723i	1.36012	+	0.364442i
$467$	20.9801			0.970841			0.485421	−	0.874281i	$-0.338666\pi$
$467$	20.9801			0.970841			0.485421	+	0.874281i	$0.338666\pi$
$468$	0.258538	+	1.12726i	0.0119509	+	0.0521075i
$469$	0.813978			0.0375860
$470$	−33.8349	−	9.06604i	−1.56069	−	0.418185i
$471$	15.1341	−	1.88047i	0.697342	−	0.0866474i
$472$	−18.5131	−	10.6886i	−0.852136	−	0.491981i
$473$	−0.554546	+	0.554546i	−0.0254981	+	0.0254981i
$474$	−1.79486	−	0.249603i	−0.0824407	−	0.0114647i
$475$	−7.01472	−	26.1793i	−0.321857	−	1.20119i
$476$	1.82710	+	1.82710i	0.0837449	+	0.0837449i
$477$	2.69665	+	10.6839i	0.123471	+	0.489180i
$478$	4.92514	−	2.84353i	0.225271	−	0.130060i
$479$	−4.58805	+	17.1228i	−0.209633	+	0.782362i	0.778354	+	0.627826i	$0.216055\pi$
$479$	−4.58805	+	17.1228i	−0.209633	+	0.782362i	−0.987987	+	0.154536i	$0.950612\pi$
$480$	3.38805	+	1.43236i	0.154643	+	0.0653779i
$481$	−0.768293	−	3.13936i	−0.0350311	−	0.143143i
$482$		−	3.21078i		−	0.146247i
$483$	−27.8371	+	35.7363i	−1.26663	+	1.62606i
$484$	0.0534604	+	0.0925961i	0.00243002	+	0.00420892i
$485$	11.0431	−	19.1273i	0.501443	−	0.868525i
$486$	−20.1010	+	7.48130i	−0.911798	+	0.339359i
$487$	11.6761	−	3.12860i	0.529095	−	0.141771i	0.0156245	−	0.999878i	$-0.495026\pi$
$487$	11.6761	−	3.12860i	0.529095	−	0.141771i	0.513470	+	0.858107i	$0.328360\pi$
$488$	25.4197	−	6.81118i	1.15069	−	0.308328i
$489$	0.428416	+	1.05597i	0.0193737	+	0.0477524i
$490$	−7.66449	+	13.2753i	−0.346246	+	0.599716i
$491$	6.85676	+	11.8763i	0.309441	+	0.535968i	0.978240	−	0.207475i	$-0.0665247\pi$
$491$	6.85676	+	11.8763i	0.309441	+	0.535968i	−0.668799	+	0.743443i	$0.733191\pi$
$492$	−0.842836	−	0.656534i	−0.0379980	−	0.0295988i
$493$			43.0168i			1.93738i
$494$	8.79233	+	16.0252i	0.395585	+	0.721008i
$495$	−7.34724	−	7.56435i	−0.330234	−	0.339992i
$496$	0.977099	−	3.64658i	0.0438730	−	0.163736i
$497$	−16.9247	+	9.77146i	−0.759175	+	0.438310i
$498$	1.11844	−	0.845347i	0.0501186	−	0.0378809i
$499$	13.6061	+	13.6061i	0.609094	+	0.609094i	0.942709	−	0.333615i	$-0.108269\pi$
$499$	13.6061	+	13.6061i	0.609094	+	0.609094i	−0.333615	+	0.942709i	$0.608269\pi$
$500$	−0.229146	−	0.855184i	−0.0102477	−	0.0382450i
$501$	4.47248	−	32.1610i	0.199816	−	1.43685i
$502$	−8.48606	+	8.48606i	−0.378751	+	0.378751i
$503$	7.36994	+	4.25504i	0.328609	+	0.189723i	0.655223	−	0.755435i	$-0.272574\pi$
$503$	7.36994	+	4.25504i	0.328609	+	0.189723i	−0.326614	+	0.945158i	$0.605908\pi$
$504$	7.56719	−	26.6811i	0.337070	−	1.18847i
$505$	−56.0236	−	15.0115i	−2.49302	−	0.668002i
$506$	−11.2839			−0.501633
$507$	−9.66308	+	20.3378i	−0.429152	+	0.903232i
$508$	−0.603722			−0.0267858
$509$	−7.52067	−	2.01516i	−0.333348	−	0.0893202i	0.0882630	−	0.996097i	$-0.471868\pi$
$509$	−7.52067	−	2.01516i	−0.333348	−	0.0893202i	−0.421611	+	0.906777i	$0.638535\pi$
$510$	−7.82754	−	62.9964i	−0.346609	−	2.78953i
$511$	−8.65797	−	4.99868i	−0.383006	−	0.221129i
$512$	−17.0877	+	17.0877i	−0.755177	+	0.755177i
$513$	15.4402	−	11.3207i	0.681702	−	0.499822i
$514$	7.38195	+	27.5498i	0.325604	+	1.21517i
$515$	−2.49133	−	2.49133i	−0.109781	−	0.109781i
$516$	−0.0875732	−	0.115864i	−0.00385520	−	0.00510064i
$517$	6.27241	−	3.62138i	0.275860	−	0.159268i
$518$	−1.01796	+	3.79909i	−0.0447267	+	0.166922i
$519$	2.99735	−	7.08982i	0.131569	−	0.311208i
$520$	17.6724	+	32.2103i	0.774986	+	1.41252i
$521$			5.15721i			0.225941i	0.993598	+	0.112971i	$0.0360366\pi$
$521$			5.15721i			0.225941i	−0.993598	+	0.112971i	$0.963963\pi$
$522$	20.4597	−	11.4185i	0.895498	−	0.499776i
$523$	−0.666036	−	1.15361i	−0.0291237	−	0.0504437i	0.851096	−	0.525010i	$-0.175938\pi$
$523$	−0.666036	−	1.15361i	−0.0291237	−	0.0504437i	−0.880220	+	0.474566i	$0.842605\pi$
$524$	−0.316375	+	0.547977i	−0.0138209	+	0.0239385i
$525$	−37.6484	+	15.2744i	−1.64311	+	0.666627i
$526$	−13.6113	+	3.64713i	−0.593480	+	0.159022i
$527$	7.32091	−	1.96163i	0.318904	−	0.0854500i
$528$	6.05839	−	2.45795i	0.263658	−	0.106969i
$529$	−22.1297	+	38.3298i	−0.962161	+	1.66651i
$530$	8.88190	+	15.3839i	0.385805	+	0.668234i
$531$	−19.3178	+	10.7813i	−0.838322	+	0.467867i
$532$			1.25633i			0.0544687i
$533$	−4.94452	−	20.2041i	−0.214171	−	0.875135i
$534$	2.61563	−	6.18693i	0.113190	−	0.267734i
$535$	5.64100	−	21.0525i	0.243882	−	0.910179i
$536$	−0.640804	+	0.369968i	−0.0276785	+	0.0159802i
$537$	0.199958	+	0.264556i	0.00862883	+	0.0114164i
$538$	8.56063	+	8.56063i	0.369075	+	0.369075i
$539$	−0.820335	−	3.06153i	−0.0353343	−	0.131870i
$540$	1.57492	−	1.15473i	0.0677739	−	0.0496916i
$541$	−19.3065	+	19.3065i	−0.830051	+	0.830051i	−0.987523	−	0.157472i	$-0.949666\pi$
$541$	−19.3065	+	19.3065i	−0.830051	+	0.830051i	0.157472	+	0.987523i	$0.449666\pi$
$542$	13.0745	+	7.54855i	0.561597	+	0.324238i
$543$	1.56741	+	12.6146i	0.0672638	+	0.541342i
$544$	−4.42253	−	1.18501i	−0.189614	−	0.0508070i
$545$	−31.2278			−1.33765
$546$	22.2143	−	16.0419i	0.950685	−	0.686528i
$547$	24.3722			1.04208			0.521040	−	0.853532i	$-0.325544\pi$
$547$	24.3722			1.04208			0.521040	+	0.853532i	$0.325544\pi$
$548$	2.21812	+	0.594343i	0.0947534	+	0.0253891i
$549$	7.43096	−	26.2008i	0.317146	−	1.11822i
$550$	−8.76474	−	5.06032i	−0.373730	−	0.215773i
$551$	−14.7893	+	14.7893i	−0.630047	+	0.630047i
$552$	5.67191	−	40.7859i	0.241413	−	1.73596i
$553$	−0.627613	−	2.34228i	−0.0266888	−	0.0996040i
$554$	−20.8521	−	20.8521i	−0.885921	−	0.885921i
$555$	−4.35381	+	3.29072i	−0.184809	+	0.139683i
$556$	1.56431	−	0.903156i	0.0663416	−	0.0383023i
$557$	−0.0652746	+	0.243608i	−0.00276577	+	0.0103220i	−0.967295	−	0.253654i	$-0.918367\pi$
$557$	−0.0652746	+	0.243608i	−0.00276577	+	0.0103220i	0.964529	+	0.263976i	$0.0850341\pi$
$558$	−2.87628	−	2.96128i	−0.121763	−	0.125361i
$559$	0.0616031	−	2.82697i	0.00260553	−	0.119568i
$560$		−	42.3126i		−	1.78803i
$561$	10.3549	+	8.06605i	0.437185	+	0.340549i
$562$	7.64966	+	13.2496i	0.322682	+	0.558901i
$563$	4.58501	−	7.94147i	0.193235	−	0.334693i	−0.753085	−	0.657923i	$-0.771435\pi$
$563$	4.58501	−	7.94147i	0.193235	−	0.334693i	0.946321	+	0.323230i	$0.104769\pi$
$564$	0.504260	+	1.24290i	0.0212332	+	0.0523357i
$565$	−60.9493	+	16.3313i	−2.56416	+	0.687064i
$566$	28.4664	−	7.62754i	1.19653	−	0.320609i
$567$	−19.6950	−	20.8767i	−0.827113	−	0.876740i
$568$	8.88263	−	15.3852i	0.372707	−	0.645547i
$569$	9.51653	+	16.4831i	0.398954	+	0.691008i	0.993597	−	0.112981i	$-0.0360401\pi$
$569$	9.51653	+	16.4831i	0.398954	+	0.691008i	−0.594643	+	0.803990i	$0.702707\pi$
$570$	18.9673	−	24.3496i	0.794452	−	1.01989i
$571$		−	15.1355i		−	0.633402i	−0.948525	−	0.316701i	$-0.897425\pi$
$571$		−	15.1355i		−	0.633402i	0.948525	−	0.316701i	$-0.102575\pi$
$572$	−0.370110	−	0.107866i	−0.0154751	−	0.00451009i
$573$	31.7234	+	13.4116i	1.32526	+	0.560280i
$574$	−6.55132	+	24.4499i	−0.273447	+	1.02052i
$575$	−52.2434	+	30.1627i	−2.17870	+	1.25787i
$576$	6.15303	+	24.3777i	0.256376	+	1.01574i
$577$	0.0504223	+	0.0504223i	0.00209911	+	0.00209911i	0.708156	−	0.706056i	$-0.249528\pi$
$577$	0.0504223	+	0.0504223i	0.00209911	+	0.00209911i	−0.706056	+	0.708156i	$0.749528\pi$
$578$	14.3969	+	53.7300i	0.598832	+	2.23487i
$579$	−1.61029	−	0.223936i	−0.0669214	−	0.00930646i
$580$	−1.50853	+	1.50853i	−0.0626385	+	0.0626385i
$581$	1.62471	+	0.938026i	0.0674043	+	0.0389159i
$582$	14.8596	−	1.84636i	0.615950	−	0.0765341i
$583$	−3.54782	−	0.950636i	−0.146936	−	0.0393713i
$584$	9.08798			0.376063
$585$	37.9962	+	1.38165i	1.57095	+	0.0571241i
$586$	−24.3077			−1.00414
$587$	−3.97593	−	1.06535i	−0.164104	−	0.0439715i	0.175832	−	0.984420i	$-0.443739\pi$
$587$	−3.97593	−	1.06535i	−0.164104	−	0.0439715i	−0.339936	+	0.940449i	$0.610405\pi$
$588$	0.582493	−	0.0723770i	0.0240216	−	0.00298478i
$589$	3.19137	+	1.84254i	0.131498	+	0.0759205i
$590$	−25.2185	+	25.2185i	−1.03823	+	1.03823i
$591$	31.9242	+	4.43955i	1.31319	+	0.182619i
$592$	−0.875754	−	3.26836i	−0.0359933	−	0.134329i
$593$	−6.83319	−	6.83319i	−0.280605	−	0.280605i	0.552745	−	0.833350i	$-0.313580\pi$
$593$	−6.83319	−	6.83319i	−0.280605	−	0.280605i	−0.833350	+	0.552745i	$0.813580\pi$
$594$	1.08774	−	7.06611i	0.0446304	−	0.289926i
$595$	73.5663	−	42.4735i	3.01592	−	1.74124i
$596$	−0.292796	+	1.09273i	−0.0119934	+	0.0447599i
$597$	1.00853	+	0.426373i	0.0412763	+	0.0174503i
$598$	29.3885	−	28.1349i	1.20178	−	1.15052i
$599$			20.1735i			0.824268i	0.911123	+	0.412134i	$0.135216\pi$
$599$			20.1735i			0.824268i	−0.911123	+	0.412134i	$0.864784\pi$
$600$	22.6962	−	29.1367i	0.926569	−	1.18950i
$601$	12.5942	+	21.8138i	0.513727	+	0.889802i	0.999873	+	0.0159240i	$0.00506899\pi$
$601$	12.5942	+	21.8138i	0.513727	+	0.889802i	−0.486146	+	0.873878i	$0.661598\pi$
$602$	−1.72051	+	2.98001i	−0.0701228	+	0.121456i
$603$	−0.0111481	+	0.765662i	−0.000453986	+	0.0311802i
$604$	−1.09986	+	0.294707i	−0.0447527	+	0.0119914i
$605$	3.39529	−	0.909766i	0.138038	−	0.0369873i
$606$	−14.7831	−	36.4376i	−0.600523	−	1.48018i
$607$	−12.6822	+	21.9662i	−0.514755	+	0.891582i	0.485099	+	0.874459i	$0.338784\pi$
$607$	−12.6822	+	21.9662i	−0.514755	+	0.891582i	−0.999853	+	0.0171221i	$0.994550\pi$
$608$	−1.11307	−	1.92790i	−0.0451410	−	0.0781865i
$609$	24.7348	+	19.2673i	1.00230	+	0.780752i
$610$		−	43.9047i		−	1.77765i
$611$	−7.30676	+	25.0711i	−0.295600	+	1.01427i
$612$	−1.74367	+	1.69362i	−0.0704837	+	0.0684606i
$613$	7.06006	−	26.3485i	0.285153	−	1.06421i	−0.663574	−	0.748110i	$-0.730961\pi$
$613$	7.06006	−	26.3485i	0.285153	−	1.06421i	0.948727	−	0.316096i	$-0.102372\pi$
$614$	−17.7418	+	10.2432i	−0.716000	+	0.413383i
$615$	−28.0199	+	21.1782i	−1.12987	+	0.853985i
$616$	6.53684	+	6.53684i	0.263377	+	0.263377i
$617$	3.77807	+	14.1000i	0.152100	+	0.567643i	0.999336	+	0.0364278i	$0.0115979\pi$
$617$	3.77807	+	14.1000i	0.152100	+	0.567643i	−0.847237	+	0.531216i	$0.821735\pi$
$618$	0.329016	−	2.36591i	0.0132350	−	0.0951708i
$619$	14.5322	−	14.5322i	0.584100	−	0.584100i	−0.351927	−	0.936027i	$-0.614474\pi$
$619$	14.5322	−	14.5322i	0.584100	−	0.584100i	0.936027	+	0.351927i	$0.114474\pi$
$620$	0.325524	+	0.187942i	0.0130734	+	0.00754792i
$621$	−33.2339	−	26.6742i	−1.33363	−	1.07040i
$622$	−35.5486	−	9.52523i	−1.42537	−	0.381927i
$623$	8.98852			0.360117
$624$	−9.65021	+	21.5074i	−0.386317	+	0.860984i
$625$	7.67218			0.306887
$626$	−15.3862	−	4.12271i	−0.614955	−	0.164777i
$627$	0.786925	+	6.33321i	0.0314267	+	0.252924i
$628$	−0.815296	−	0.470711i	−0.0325339	−	0.0187834i
$629$	4.80341	−	4.80341i	0.191524	−	0.191524i
$630$	−39.7290	−	23.7154i	−1.58284	−	0.944844i
$631$	−6.04515	−	22.5608i	−0.240654	−	0.898132i	−0.975518	−	0.219918i	$-0.929421\pi$
$631$	−6.04515	−	22.5608i	−0.240654	−	0.898132i	0.734864	−	0.678214i	$-0.237246\pi$
$632$	1.55870	+	1.55870i	0.0620018	+	0.0620018i
$633$	−20.5916	−	27.2438i	−0.818442	−	1.08285i
$634$	−3.82586	+	2.20886i	−0.151944	+	0.0877251i
$635$	−5.13694	+	19.1713i	−0.203853	+	0.760791i
$636$	0.264871	−	0.626517i	0.0105028	−	0.0248430i
$637$	9.77002	+	5.92821i	0.387102	+	0.234884i
$638$			7.81013i			0.309206i
$639$	−8.95966	−	16.0539i	−0.354439	−	0.635082i
$640$	18.1424	+	31.4235i	0.717140	+	1.24212i
$641$	−4.14982	+	7.18770i	−0.163908	+	0.283897i	−0.936267	−	0.351289i	$-0.885743\pi$
$641$	−4.14982	+	7.18770i	−0.163908	+	0.283897i	0.772359	+	0.635186i	$0.219077\pi$
$642$	13.6925	−	5.55519i	0.540400	−	0.219246i
$643$	3.84865	−	1.03124i	0.151776	−	0.0406683i	−0.182131	−	0.983274i	$-0.558299\pi$
$643$	3.84865	−	1.03124i	0.151776	−	0.0406683i	0.333907	+	0.942606i	$0.391633\pi$
$644$	2.70105	−	0.723745i	0.106436	−	0.0285195i
$645$	−4.42444	+	1.79504i	−0.174212	+	0.0706797i
$646$	−19.2092	+	33.2712i	−0.755774	+	1.30904i
$647$	21.6189	+	37.4450i	0.849927	+	1.47212i	0.881273	+	0.472607i	$0.156687\pi$
$647$	21.6189	+	37.4450i	0.849927	+	1.47212i	−0.0313464	+	0.999509i	$0.509980\pi$
$648$	24.9938	+	7.48345i	0.981849	+	0.293978i
$649$		−	7.37423i		−	0.289464i
$650$	35.4445	−	8.67430i	1.39025	−	0.340234i
$651$	2.15111	−	5.08816i	0.0843086	−	0.199421i
$652$	0.0182069	−	0.0679491i	0.000713038	−	0.00266109i
$653$	−15.3255	+	8.84817i	−0.599732	+	0.346256i	−0.768936	−	0.639325i	$-0.779214\pi$
$653$	−15.3255	+	8.84817i	−0.599732	+	0.346256i	0.169204	+	0.985581i	$0.445880\pi$
$654$	−12.7658	−	16.8899i	−0.499183	−	0.660448i
$655$	14.7092	+	14.7092i	0.574735	+	0.574735i
$656$	−5.63611	−	21.0343i	−0.220053	−	0.821250i
$657$	4.82055	−	8.07560i	0.188068	−	0.315059i
$658$	22.4711	−	22.4711i	0.876013	−	0.876013i
$659$	−35.7771	−	20.6559i	−1.39368	−	0.804641i	−0.399959	−	0.916533i	$-0.630976\pi$
$659$	−35.7771	−	20.6559i	−1.39368	−	0.804641i	−0.993720	+	0.111892i	$0.964309\pi$
$660$	0.0802674	+	0.645996i	0.00312440	+	0.0251453i
$661$	35.1671	+	9.42300i	1.36784	+	0.366512i	0.866690	−	0.498847i	$-0.166243\pi$
$661$	35.1671	+	9.42300i	1.36784	+	0.366512i	0.501152	+	0.865359i	$0.332910\pi$
$662$	−8.51330			−0.330879
$663$	−47.0805	+	4.81096i	−1.82845	+	0.186842i
$664$	−1.70540			−0.0661825
$665$	39.8949	+	10.6898i	1.54706	+	0.414533i
$666$	−3.55964	−	1.00957i	−0.137933	−	0.0391201i
$667$	40.3164	+	23.2767i	1.56106	+	0.901276i
$668$	−1.41734	+	1.41734i	−0.0548387	+	0.0548387i
$669$	−5.92798	+	42.6273i	−0.229189	+	1.64807i
$670$	0.319504	+	1.19241i	0.0123435	+	0.0460666i
$671$	6.41916	+	6.41916i	0.247809	+	0.247809i
$672$	−2.66225	+	2.01219i	−0.102698	+	0.0776221i
$673$	−15.4521	+	8.92130i	−0.595636	+	0.343891i	−0.767323	−	0.641261i	$-0.778412\pi$
$673$	−15.4521	+	8.92130i	−0.595636	+	0.343891i	0.171687	+	0.985152i	$0.445078\pi$
$674$	−10.2239	+	38.1561i	−0.393810	+	1.46972i
$675$	−13.8521	−	35.6229i	−0.533167	−	1.37113i
$676$	1.23288	−	0.641888i	0.0474185	−	0.0246880i
$677$		−	3.28424i		−	0.126223i	−0.998006	−	0.0631117i	$-0.979898\pi$
$677$		−	3.28424i		−	0.126223i	0.998006	−	0.0631117i	$-0.0201024\pi$
$678$	−33.7488	−	26.2889i	−1.29612	−	1.00962i
$679$	10.0186	+	17.3528i	0.384480	+	0.665940i
$680$	−38.6101	+	66.8746i	−1.48063	+	2.56452i
$681$	−8.14531	−	20.0767i	−0.312129	−	0.769339i
$682$	1.32918	−	0.356154i	0.0508971	−	0.0136378i
$683$	7.26092	−	1.94556i	0.277831	−	0.0744447i	−0.117213	−	0.993107i	$-0.537396\pi$
$683$	7.26092	−	1.94556i	0.277831	−	0.0744447i	0.395044	+	0.918662i	$0.370729\pi$
$684$	−1.18175	−	0.0172065i	−0.0451855	−	0.000657905i
$685$	37.7470	−	65.3797i	1.44224	−	2.49803i
$686$	8.40343	+	14.5552i	0.320845	+	0.555719i
$687$	−11.3373	+	14.5545i	−0.432547	+	0.555289i
$688$		−	2.96032i		−	0.112861i
$689$	11.6104	−	6.37011i	0.442321	−	0.242682i
$690$	−63.2772	−	26.7516i	−2.40892	−	1.01842i
$691$	0.174149	−	0.649934i	0.00662495	−	0.0247246i	−0.962534	−	0.271160i	$-0.912593\pi$
$691$	0.174149	−	0.649934i	0.00662495	−	0.0247246i	0.969159	+	0.246436i	$0.0792594\pi$
$692$	−0.411505	+	0.237582i	−0.0156431	+	0.00903153i
$693$	9.27600	−	2.34130i	0.352366	−	0.0889387i
$694$	−31.6938	−	31.6938i	−1.20308	−	1.20308i
$695$	−15.3695	−	57.3598i	−0.582999	−	2.17578i
$696$	−28.2298	−	3.92579i	−1.07005	−	0.148807i
$697$	30.9134	−	30.9134i	1.17093	−	1.17093i
$698$	19.9834	+	11.5374i	0.756382	+	0.436697i
$699$	−37.9730	+	4.71829i	−1.43627	+	0.178462i
$700$	2.42259	+	0.649132i	0.0915654	+	0.0245349i
$701$	28.6555			1.08230			0.541152	−	0.840925i	$-0.317988\pi$
$701$	28.6555			1.08230			0.541152	+	0.840925i	$0.317988\pi$
$702$	14.7854	+	21.1155i	0.558040	+	0.796951i
$703$	3.30286			0.124570
$704$	−8.09517	−	2.16909i	−0.305098	−	0.0817508i
$705$	43.7594	−	5.43726i	1.64807	−	0.204779i
$706$	−35.2281	−	20.3389i	−1.32583	−	0.765466i
$707$	37.2073	−	37.2073i	1.39933	−	1.39933i
$708$	1.35263	+	0.188105i	0.0508351	+	0.00706941i
$709$	−5.92665	−	22.1186i	−0.222580	−	0.830680i	−0.983360	−	0.181670i	$-0.941850\pi$
$709$	−5.92665	−	22.1186i	−0.222580	−	0.830680i	0.760780	−	0.649010i	$-0.224817\pi$
$710$	−20.9576	−	20.9576i	−0.786526	−	0.786526i
$711$	2.21185	−	0.558280i	0.0829508	−	0.0209371i
$712$	−7.07621	+	4.08545i	−0.265192	+	0.153109i
$713$	2.12290	−	7.92277i	0.0795033	−	0.296710i
$714$	53.0459	+	22.4261i	1.98519	+	0.839276i
$715$	−6.57449	+	10.8351i	−0.245872	+	0.405211i
$716$		−	0.0204713i		−	0.000765048i
$717$	−4.39947	+	5.64789i	−0.164301	+	0.210924i
$718$	−1.87841	−	3.25351i	−0.0701018	−	0.121420i
$719$	17.9834	−	31.1482i	0.670669	−	1.16163i	−0.307046	−	0.951695i	$-0.599341\pi$
$719$	17.9834	−	31.1482i	0.670669	−	1.16163i	0.977715	−	0.209938i	$-0.0673261\pi$
$720$	39.8010	+	0.579507i	1.48330	+	0.0215969i
$721$	3.08750	−	0.827292i	0.114984	−	0.0308100i
$722$	7.20821	−	1.93143i	0.268262	−	0.0718806i
$723$	1.51955	+	3.74540i	0.0565126	+	0.139293i
$724$	0.392347	−	0.679565i	0.0145815	−	0.0252558i
$725$	20.8770	+	36.1600i	0.775352	+	1.34295i
$726$	1.88004	+	1.46447i	0.0697749	+	0.0543517i
$727$			41.1433i			1.52592i	0.646446	+	0.762959i	$0.276254\pi$
$727$			41.1433i			1.52592i	−0.646446	+	0.762959i	$0.723746\pi$
$728$	−33.3236	−	0.726161i	−1.23505	−	0.0269133i
$729$	19.9073	−	18.2401i	0.737307	−	0.675558i
$730$	3.92418	−	14.6452i	0.145241	−	0.542045i
$731$	5.14692	−	2.97158i	0.190366	−	0.109908i
$732$	−1.34119	+	1.01371i	−0.0495718	+	0.0374677i
$733$	−27.7067	−	27.7067i	−1.02337	−	1.02337i	−0.999720	−	0.0236499i	$-0.992471\pi$
$733$	−27.7067	−	27.7067i	−1.02337	−	1.02337i	−0.0236499	−	0.999720i	$-0.507529\pi$
$734$	−11.3544	−	42.3753i	−0.419099	−	1.56410i
$735$	2.65796	−	19.1130i	0.0980405	−	0.704995i
$736$	−3.50368	+	3.50368i	−0.129147	+	0.129147i
$737$	−0.221051	−	0.127624i	−0.00814252	−	0.00470109i
$738$	−22.9089	−	6.49732i	−0.843287	−	0.239170i
$739$	−25.3228	−	6.78522i	−0.931514	−	0.249598i	−0.239014	−	0.971016i	$-0.576824\pi$
$739$	−25.3228	−	6.78522i	−0.931514	−	0.249598i	−0.692500	+	0.721418i	$0.743491\pi$
$740$	0.336896			0.0123846
$741$	−17.8405	−	14.5324i	−0.655386	−	0.533862i
$742$	−16.1158			−0.591631
$743$	19.7141	+	5.28238i	0.723241	+	0.193792i	0.601617	−	0.798784i	$-0.294523\pi$
$743$	19.7141	+	5.28238i	0.723241	+	0.193792i	0.121624	+	0.992576i	$0.461190\pi$
$744$	0.619203	+	4.98337i	0.0227011	+	0.182699i
$745$	32.2085	+	18.5956i	1.18003	+	0.681290i
$746$	11.2452	−	11.2452i	0.411714	−	0.411714i
$747$	−0.904599	+	1.51542i	−0.0330975	+	0.0554464i
$748$	−0.209712	−	0.782655i	−0.00766782	−	0.0286167i
$749$	13.9818	+	13.9818i	0.510882	+	0.510882i
$750$	−11.8986	−	15.7425i	−0.434474	−	0.574834i
$751$	−18.5960	+	10.7364i	−0.678576	+	0.391776i	−0.799318	−	0.600908i	$-0.794806\pi$
$751$	−18.5960	+	10.7364i	−0.678576	+	0.391776i	0.120742	+	0.992684i	$0.461473\pi$
$752$	−7.07596	+	26.4078i	−0.258034	+	0.962995i
$753$	5.88290	−	13.9152i	0.214385	−	0.507098i
$754$	−19.4735	−	20.3411i	−0.709182	−	0.740779i
$755$			37.4339i			1.36236i
$756$	0.192843	+	1.76119i	0.00701362	+	0.0640539i
$757$	−20.0687	−	34.7601i	−0.729411	−	1.26338i	−0.957132	−	0.289651i	$-0.906461\pi$
$757$	−20.0687	−	34.7601i	−0.729411	−	1.26338i	0.227721	−	0.973726i	$-0.426872\pi$
$758$	−2.72325	+	4.71681i	−0.0989129	+	0.171322i
$759$	13.1628	−	5.34029i	0.477780	−	0.193840i
$760$	−36.2660	+	9.71745i	−1.31551	+	0.352489i
$761$	−8.66950	+	2.32299i	−0.314269	+	0.0842082i	−0.412506	−	0.910955i	$-0.635346\pi$
$761$	−8.66950	+	2.32299i	−0.314269	+	0.0842082i	0.0982368	+	0.995163i	$0.468680\pi$
$762$	−12.4690	+	5.05880i	−0.451704	+	0.183261i
$763$	14.1654	−	24.5352i	0.512821	−	0.888233i
$764$	−1.06306	−	1.84128i	−0.0384603	−	0.0666152i
$765$	38.9449	+	69.7813i	1.40805	+	2.52295i
$766$			42.1308i			1.52225i
$767$	18.3866	+	19.2058i	0.663903	+	0.693482i
$768$	1.72569	−	4.08189i	0.0622706	−	0.147293i
$769$	−0.277171	+	1.03442i	−0.00999504	+	0.0373020i	−0.970743	−	0.240120i	$-0.922813\pi$
$769$	−0.277171	+	1.03442i	−0.00999504	+	0.0373020i	0.960748	+	0.277422i	$0.0894799\pi$
$770$	13.3567	−	7.71149i	0.481342	−	0.277903i
$771$	−21.6495	−	28.6435i	−0.779686	−	1.03157i
$772$	0.0709660	+	0.0709660i	0.00255412	+	0.00255412i
$773$	−9.49415	−	35.4327i	−0.341481	−	1.27442i	−0.896670	−	0.442700i	$-0.854021\pi$
$773$	−9.49415	−	35.4327i	−0.341481	−	1.27442i	0.555189	−	0.831724i	$-0.312646\pi$
$774$	−2.77956	−	1.65920i	−0.0999094	−	0.0596387i
$775$	5.20195	−	5.20195i	0.186859	−	0.186859i
$776$	−15.7744	−	9.10733i	−0.566267	−	0.326934i
$777$	−0.610512	−	4.91343i	−0.0219020	−	0.176268i
$778$	47.9369	+	12.8446i	1.71862	+	0.460503i
$779$	21.2563			0.761586
$780$	−1.81975	−	1.48233i	−0.0651576	−	0.0530758i
$781$	6.12829			0.219287
$782$	82.5979	+	22.1320i	2.95369	+	0.791440i
$783$	−18.4624	+	23.0027i	−0.659794	+	0.822049i
$784$	10.3612	+	5.98206i	0.370044	+	0.213645i
$785$	−21.8847	+	21.8847i	−0.781100	+	0.781100i
$786$	−1.94256	+	13.9687i	−0.0692888	+	0.498246i
$787$	3.31399	+	12.3680i	0.118131	+	0.440871i	0.999502	−	0.0315540i	$-0.0100456\pi$
$787$	3.31399	+	12.3680i	0.118131	+	0.440871i	−0.881371	+	0.472424i	$0.843379\pi$
$788$	−1.40691	−	1.40691i	−0.0501190	−	0.0501190i
$789$	14.1516	−	10.6961i	0.503810	−	0.380793i
$790$	3.18489	−	1.83879i	0.113313	−	0.0654214i
$791$	14.8162	−	55.2950i	0.526805	−	1.96606i
$792$	−6.23836	+	6.05931i	−0.221671	+	0.215308i
$793$	−32.7237	−	0.713088i	−1.16205	−	0.0253225i
$794$		−	52.0272i		−	1.84638i
$795$	−17.6415	−	13.7420i	−0.625678	−	0.487377i
$796$	−0.0337961	−	0.0585366i	−0.00119787	−	0.00207478i
$797$	−18.0658	+	31.2908i	−0.639922	+	1.10838i	0.345527	+	0.938409i	$0.387700\pi$
$797$	−18.0658	+	31.2908i	−0.639922	+	1.10838i	−0.985449	+	0.169969i	$0.945633\pi$
$798$	10.5272	+	25.9476i	0.372659	+	0.918534i
$799$	−53.0165	+	14.2057i	−1.87559	+	0.502563i
$800$	−4.29270	+	1.15023i	−0.151770	+	0.0406666i
$801$	−0.123105	+	8.45498i	−0.00434971	+	0.298742i
$802$	4.94061	−	8.55739i	0.174459	−	0.302172i
$803$	1.56749	+	2.71497i	0.0553155	+	0.0958093i
$804$	0.0290483	−	0.0372913i	0.00102446	−	0.00131516i
$805$		−	91.9307i		−	3.24013i
$806$	−2.57377	+	4.24172i	−0.0906572	+	0.149408i
$807$	−14.0375	−	5.93460i	−0.494143	−	0.208908i
$808$	−12.3800	+	46.2029i	−0.435528	+	1.62541i
$809$	25.8642	−	14.9327i	0.909338	−	0.525007i	0.0291202	−	0.999576i	$-0.490729\pi$
$809$	25.8642	−	14.9327i	0.909338	−	0.525007i	0.880218	+	0.474569i	$0.157396\pi$
$810$	22.8518	−	37.0460i	0.802932	−	1.30167i
$811$	−1.68061	−	1.68061i	−0.0590143	−	0.0590143i	0.676984	−	0.735998i	$-0.263287\pi$
$811$	−1.68061	−	1.68061i	−0.0590143	−	0.0590143i	−0.735998	+	0.676984i	$0.763287\pi$
$812$	−0.500937	−	1.86952i	−0.0175794	−	0.0656074i
$813$	−18.8239	−	2.61776i	−0.660184	−	0.0918088i
$814$	0.872107	−	0.872107i	0.0305673	−	0.0305673i
$815$	−2.00282	−	1.15633i	−0.0701558	−	0.0405044i
$816$	−49.1681	+	6.10932i	−1.72123	+	0.213869i
$817$	2.79117	+	0.747892i	0.0976507	+	0.0261654i
$818$	−11.7239			−0.409916
$819$	−18.3211	+	29.2262i	−0.640192	+	1.02125i
$820$	2.16817			0.0757159
$821$	−39.3086	−	10.5327i	−1.37188	−	0.367594i	−0.503715	−	0.863870i	$-0.668034\pi$
$821$	−39.3086	−	10.5327i	−1.37188	−	0.367594i	−0.868165	+	0.496276i	$0.834700\pi$
$822$	50.7922	−	6.31112i	1.77158	−	0.220126i
$823$	−2.06115	−	1.19001i	−0.0718472	−	0.0414810i	0.463646	−	0.886021i	$-0.346541\pi$
$823$	−2.06115	−	1.19001i	−0.0718472	−	0.0414810i	−0.535493	+	0.844540i	$0.679874\pi$
$824$	−2.05461	+	2.05461i	−0.0715758	+	0.0715758i
$825$	12.6190	+	1.75487i	0.439337	+	0.0610967i
$826$	−8.37429	−	31.2533i	−0.291379	−	1.08744i
$827$	−7.38294	−	7.38294i	−0.256730	−	0.256730i	0.566993	−	0.823723i	$-0.308107\pi$
$827$	−7.38294	−	7.38294i	−0.256730	−	0.256730i	−0.823723	+	0.566993i	$0.808107\pi$
$828$	0.643792	+	2.55064i	0.0223733	+	0.0886408i
$829$	−33.6712	+	19.4401i	−1.16945	+	0.675181i	−0.953550	−	0.301235i	$-0.902601\pi$
$829$	−33.6712	+	19.4401i	−1.16945	+	0.675181i	−0.215898	+	0.976416i	$0.569268\pi$
$830$	−0.736391	+	2.74825i	−0.0255605	+	0.0953931i
$831$	34.1927	+	14.4556i	1.18613	+	0.501459i
$832$	26.4918	−	14.5349i	0.918437	−	0.503906i
$833$			24.0192i			0.832217i
$834$	24.7407	−	31.7613i	0.856700	−	1.09980i
$835$	32.9482	+	57.0679i	1.14022	+	1.97492i
$836$	0.196980	−	0.341179i	0.00681270	−	0.0117999i
$837$	4.75668	+	2.09311i	0.164415	+	0.0723485i
$838$	20.0122	−	5.36226i	0.691312	−	0.185236i
$839$	−32.0238	+	8.58076i	−1.10559	+	0.296241i	−0.765037	−	0.643986i	$-0.777279\pi$
$839$	−32.0238	+	8.58076i	−1.10559	+	0.296241i	−0.340549	+	0.940227i	$0.610613\pi$
$840$	21.1595	+	52.1541i	0.730072	+	1.79949i
$841$	1.61084	−	2.79006i	0.0555462	−	0.0962089i
$842$	−19.0993	−	33.0809i	−0.658204	−	1.14004i
$843$	−15.1940	−	11.8355i	−0.523308	−	0.407635i
$844$			2.10812i			0.0725645i
$845$	−9.89297	−	44.6121i	−0.340329	−	1.53470i
$846$	20.8295	+	21.4450i	0.716132	+	0.737294i
$847$	−0.825366	+	3.08031i	−0.0283599	+	0.105841i
$848$	12.0070	−	6.93224i	0.412322	−	0.238054i
$849$	−29.5964	+	22.3697i	−1.01575	+	0.767726i
$850$	54.2322	+	54.2322i	1.86015	+	1.86015i
$851$	−1.90271	−	7.10102i	−0.0652242	−	0.243420i
$852$	−0.156323	+	1.12409i	−0.00535552	+	0.0385108i
$853$	−8.37909	+	8.37909i	−0.286895	+	0.286895i	−0.835851	−	0.548956i	$-0.815025\pi$
$853$	−8.37909	+	8.37909i	−0.286895	+	0.286895i	0.548956	+	0.835851i	$0.315025\pi$
$854$	34.4952	+	19.9158i	1.18040	+	0.681506i
$855$	−10.6017	+	37.3805i	−0.362570	+	1.27839i
$856$	−17.3621	−	4.65216i	−0.593425	−	0.159008i
$857$	14.4596			0.493931			0.246966	−	0.969024i	$-0.420566\pi$
$857$	14.4596			0.493931			0.246966	+	0.969024i	$0.420566\pi$
$858$	−8.54793	+	0.873478i	−0.291822	+	0.0298200i
$859$	35.9361			1.22612			0.613062	−	0.790035i	$-0.289938\pi$
$859$	35.9361			1.22612			0.613062	+	0.790035i	$0.289938\pi$
$860$	0.284703	+	0.0762860i	0.00970830	+	0.00260133i
$861$	−3.92909	−	31.6215i	−0.133903	−	1.07766i
$862$	−13.8536	−	7.99840i	−0.471856	−	0.272426i
$863$	18.7896	−	18.7896i	0.639607	−	0.639607i	−0.310852	−	0.950458i	$-0.600614\pi$
$863$	18.7896	−	18.7896i	0.639607	−	0.639607i	0.950458	+	0.310852i	$0.100614\pi$
$864$	−1.85629	−	2.53178i	−0.0631524	−	0.0861330i
$865$	4.04308	+	15.0890i	0.137469	+	0.513040i
$866$	−26.1018	−	26.1018i	−0.886974	−	0.886974i
$867$	−42.2226	−	55.8629i	−1.43395	−	1.89720i
$868$	−0.295325	+	0.170506i	−0.0100240	+	0.00578735i
$869$	−0.196807	+	0.734495i	−0.00667623	+	0.0249160i
$870$	−18.5160	+	43.7971i	−0.627751	+	1.48486i
$871$	0.893929	−	0.218770i	0.0302896	−	0.00741275i
$872$			25.7538i			0.872132i
$873$	−16.4600	+	9.18631i	−0.557087	+	0.310909i
$874$	20.7884	+	36.0066i	0.703178	+	1.21794i
$875$	13.2030	−	22.8683i	0.446344	−	0.773091i
$876$	−0.537984	+	0.218266i	−0.0181768	+	0.00737452i
$877$	35.5217	−	9.51801i	1.19948	−	0.321400i	0.396855	−	0.917881i	$-0.370101\pi$
$877$	35.5217	−	9.51801i	1.19948	−	0.321400i	0.802627	+	0.596481i	$0.203435\pi$
$878$	−50.4909	+	13.5290i	−1.70399	+	0.456582i
$879$	28.3551	−	11.5040i	0.956395	−	0.388020i
$880$	−6.63421	+	11.4908i	−0.223639	+	0.387354i
$881$	20.1000	+	34.8142i	0.677185	+	1.17292i	0.975825	+	0.218554i	$0.0701339\pi$
$881$	20.1000	+	34.8142i	0.677185	+	1.17292i	−0.298639	+	0.954366i	$0.596533\pi$
$882$	11.4241	−	6.37576i	0.384668	−	0.214683i
$883$			13.7893i			0.464046i	0.972710	+	0.232023i	$0.0745344\pi$
$883$			13.7893i			0.464046i	−0.972710	+	0.232023i	$0.925466\pi$
$884$	2.49762	+	1.51550i	0.0840042	+	0.0509717i
$885$	17.4826	−	41.3527i	0.587671	−	1.39005i
$886$	−2.70202	+	10.0841i	−0.0907761	+	0.338781i
$887$	−25.2915	+	14.6021i	−0.849206	+	0.490289i	−0.860383	−	0.509648i	$-0.829776\pi$
$887$	−25.2915	+	14.6021i	−0.849206	+	0.490289i	0.0111768	+	0.999938i	$0.496442\pi$
$888$	2.71387	+	3.59061i	0.0910716	+	0.120493i
$889$	−12.7324	−	12.7324i	−0.427031	−	0.427031i
$890$	3.52819	+	13.1674i	0.118265	+	0.441372i
$891$	2.07529	+	8.75746i	0.0695247	+	0.293386i
$892$	1.87860	−	1.87860i	0.0629001	−	0.0629001i
$893$	−23.1113	−	13.3433i	−0.773390	−	0.446517i
$894$	3.10910	+	25.0222i	0.103984	+	0.836866i
$895$	−0.650070	−	0.174186i	−0.0217295	−	0.00582239i
$896$	−32.9186			−1.09973
$897$	−20.9666	+	46.7281i	−0.700054	+	1.56021i
$898$	−35.4536			−1.18310
$899$	−5.48371	−	1.46936i	−0.182892	−	0.0490058i
$900$	−0.643781	+	2.26990i	−0.0214594	+	0.0756635i
$901$	24.1053	+	13.9172i	0.803064	+	0.463649i
$902$	5.61264	−	5.61264i	0.186881	−	0.186881i
$903$	0.596655	−	4.29047i	0.0198555	−	0.142778i
$904$	13.4685	+	50.2652i	0.447957	+	1.67180i
$905$	−18.2413	−	18.2413i	−0.606363	−	0.606363i
$906$	−20.2465	+	15.3028i	−0.672646	+	0.508403i
$907$	19.6981	−	11.3727i	0.654065	−	0.377624i	−0.135947	−	0.990716i	$-0.543408\pi$
$907$	19.6981	−	11.3727i	0.654065	−	0.377624i	0.790012	+	0.613092i	$0.210074\pi$
$908$	−0.346161	+	1.29189i	−0.0114877	+	0.0428728i
$909$	34.4892	+	35.5084i	1.14394	+	1.17774i
$910$	−15.5593	+	53.3873i	−0.515786	+	1.76977i
$911$		−	47.0911i		−	1.56020i	−0.625655	−	0.780100i	$-0.715168\pi$
$911$		−	47.0911i		−	1.56020i	0.625655	−	0.780100i	$-0.284832\pi$
$912$	−19.0046	−	14.8038i	−0.629305	−	0.490202i
$913$	−0.294147	−	0.509477i	−0.00973484	−	0.0168612i
$914$	−1.04350	+	1.80739i	−0.0345158	+	0.0597832i
$915$	20.7786	+	51.2152i	0.686918	+	1.69312i
$916$	1.10007	−	0.294763i	0.0363473	−	0.00973924i
$917$	−18.2290	+	4.88446i	−0.601976	+	0.161299i
$918$	−21.8215	+	49.5901i	−0.720216	+	1.63672i
$919$	16.7044	−	28.9328i	0.551026	−	0.954405i	−0.447175	−	0.894447i	$-0.647570\pi$
$919$	16.7044	−	28.9328i	0.551026	−	0.954405i	0.998201	−	0.0599586i	$-0.0190969\pi$
$920$	41.7843	+	72.3725i	1.37759	+	2.38605i
$921$	15.8482	−	20.3454i	0.522215	−	0.670403i
$922$		−	24.7023i		−	0.813526i
$923$	−15.9608	+	15.2800i	−0.525356	+	0.502948i
$924$	−0.543958	−	0.229968i	−0.0178949	−	0.00756540i
$925$	1.70656	−	6.36896i	0.0561112	−	0.209410i
$926$	−29.3050	+	16.9193i	−0.963022	+	0.556001i
$927$	0.735901	+	2.91556i	0.0241702	+	0.0957596i
$928$	2.42506	+	2.42506i	0.0796064	+	0.0796064i
$929$	14.7562	+	55.0710i	0.484136	+	1.80682i	0.583919	+	0.811812i	$0.301519\pi$
$929$	14.7562	+	55.0710i	0.484136	+	1.80682i	−0.0997827	+	0.995009i	$0.531815\pi$
$930$	8.29805	+	1.15397i	0.272104	+	0.0378402i
$931$	−8.25791	+	8.25791i	−0.270642	+	0.270642i
$932$	2.04566	+	1.18106i	0.0670079	+	0.0386870i
$933$	45.9757	−	5.71266i	1.50518	−	0.187024i
$934$	−27.8827	−	7.47115i	−0.912350	−	0.244463i
$935$	−26.6378			−0.871148
$936$	1.13945	−	31.3356i	0.0372442	−	1.02424i
$937$	−41.6698			−1.36129			−0.680646	−	0.732612i	$-0.738301\pi$
$937$	−41.6698			−1.36129			−0.680646	+	0.732612i	$0.738301\pi$
$938$	−1.08178	−	0.289863i	−0.0353215	−	0.00946437i
$939$	19.8992	−	2.47255i	0.649387	−	0.0806887i
$940$	−2.35738	−	1.36104i	−0.0768893	−	0.0443921i
$941$	31.6970	−	31.6970i	1.03329	−	1.03329i	0.0338665	−	0.999426i	$-0.489218\pi$
$941$	31.6970	−	31.6970i	1.03329	−	1.03329i	0.999426	−	0.0338665i	$-0.0107821\pi$
$942$	−20.7830	−	2.89020i	−0.677147	−	0.0941677i
$943$	−12.2453	−	45.7002i	−0.398763	−	1.48820i
$944$	19.6828	+	19.6828i	0.640621	+	0.640621i
$945$	57.5679	+	8.86184i	1.87268	+	0.288276i
$946$	0.934475	−	0.539519i	0.0303824	−	0.0175413i
$947$	−8.38352	+	31.2877i	−0.272428	+	1.01671i	0.685118	+	0.728432i	$0.259751\pi$
$947$	−8.38352	+	31.2877i	−0.272428	+	1.01671i	−0.957546	+	0.288282i	$0.906916\pi$
$948$	−0.129706	−	0.0548356i	−0.00421266	−	0.00178098i
$949$	−10.8519	−	3.16269i	−0.352266	−	0.102665i
$950$			37.2905i			1.20986i
$951$	3.41752	−	4.38730i	0.110821	−	0.142268i
$952$	−35.0281	−	60.6705i	−1.13527	−	1.96634i
$953$	8.63735	−	14.9603i	0.279791	−	0.484613i	−0.691542	−	0.722337i	$-0.743068\pi$
$953$	8.63735	−	14.9603i	0.279791	−	0.484613i	0.971333	+	0.237724i	$0.0764014\pi$
$954$	0.220720	−	15.1592i	0.00714607	−	0.490799i
$955$	−67.5157	+	18.0908i	−2.18476	+	0.585403i
$956$	0.426884	−	0.114383i	0.0138064	−	0.00369941i
$957$	−3.69626	−	9.11058i	−0.119483	−	0.294503i
$958$	12.1951	−	21.1226i	0.394007	−	0.682439i
$959$	34.2452	+	59.3144i	1.10583	+	1.91536i
$960$	−40.2530	−	31.3554i	−1.29916	−	1.01199i
$961$		−	29.9997i		−	0.967733i
$962$	−0.0968802	+	4.44584i	−0.00312354	+	0.143340i
$963$	−13.3433	+	12.9603i	−0.429983	+	0.417641i
$964$	0.0645780	−	0.241008i	0.00207992	−	0.00776236i
$965$	2.85738	−	1.64971i	0.0919822	−	0.0531060i
$966$	49.7217	−	37.5810i	1.59977	−	1.20915i
$967$	15.2504	+	15.2504i	0.490420	+	0.490420i	0.908438	−	0.418019i	$-0.137275\pi$
$967$	15.2504	+	15.2504i	0.490420	+	0.490420i	−0.418019	+	0.908438i	$0.637275\pi$
$968$	−0.750289	−	2.80012i	−0.0241152	−	0.0899992i
$969$	6.66154	−	47.9022i	0.213999	−	1.53884i
$970$	−21.4878	+	21.4878i	−0.689931	+	0.689931i
$971$	−26.5137	−	15.3077i	−0.850864	−	0.491247i	0.0100780	−	0.999949i	$-0.496792\pi$
$971$	−26.5137	−	15.3077i	−0.850864	−	0.491247i	−0.860942	+	0.508702i	$0.830125\pi$
$972$	−1.65929	+	0.157275i	−0.0532219	+	0.00504460i
$973$	52.0385	+	13.9437i	1.66828	+	0.447014i
$974$	−16.6318			−0.532916
$975$	−37.2411	+	26.8933i	−1.19267	+	0.861274i
$976$	−34.2672			−1.09687
$977$	−10.3194	−	2.76507i	−0.330147	−	0.0884625i	0.0899383	−	0.995947i	$-0.471333\pi$
$977$	−10.3194	−	2.76507i	−0.330147	−	0.0884625i	−0.420085	+	0.907485i	$0.638000\pi$
$978$	−0.193333	−	1.55595i	−0.00618210	−	0.0497538i
$979$	−2.44100	−	1.40931i	−0.0780148	−	0.0450418i
$980$	−0.842318	+	0.842318i	−0.0269069	+	0.0269069i
$981$	22.8848	+	13.6606i	0.730656	+	0.436149i
$982$	−4.88348	−	18.2254i	−0.155838	−	0.581596i
$983$	4.16297	+	4.16297i	0.132778	+	0.132778i	0.770372	−	0.637594i	$-0.220070\pi$
$983$	4.16297	+	4.16297i	0.132778	+	0.132778i	−0.637594	+	0.770372i	$0.720070\pi$
$984$	17.4657	+	23.1082i	0.556787	+	0.736661i
$985$	−56.6478	+	32.7056i	−1.80495	+	1.04209i
$986$	15.3186	−	57.1698i	0.487843	−	1.82066i
$987$	−15.5779	+	36.8474i	−0.495850	+	1.17287i
$988$	0.337659	+	1.37973i	0.0107424	+	0.0438949i
$989$		−	6.43175i		−	0.204518i
$990$	7.07083	+	12.6695i	0.224726	+	0.402663i
$991$	−4.03327	−	6.98583i	−0.128121	−	0.221912i	0.794828	−	0.606835i	$-0.207561\pi$
$991$	−4.03327	−	6.98583i	−0.128121	−	0.221912i	−0.922949	+	0.384923i	$0.874228\pi$
$992$	0.302127	−	0.523300i	0.00959255	−	0.0166148i
$993$	9.93084	−	4.02904i	0.315146	−	0.127858i
$994$	25.9727	−	6.95937i	0.823805	−	0.220738i
$995$	−2.14641	+	0.575128i	−0.0680457	+	0.0182328i
$996$	0.100955	−	0.0409586i	0.00319889	−	0.00129782i
$997$	6.11693	−	10.5948i	0.193725	−	0.335542i	−0.752757	−	0.658299i	$-0.771276\pi$
$997$	6.11693	−	10.5948i	0.193725	−	0.335542i	0.946482	+	0.322757i	$0.104610\pi$
$998$	−13.2374	−	22.9279i	−0.419024	−	0.725771i
$999$	4.63014	−	0.506980i	0.146491	−	0.0160401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.be.a.89.14	✓	184
3.2	odd	2	inner	429.2.be.a.89.33	yes	184
13.6	odd	12	inner	429.2.be.a.188.33	yes	184
39.32	even	12	inner	429.2.be.a.188.14	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.be.a.89.14	✓	184	1.1	even	1	trivial
429.2.be.a.89.33	yes	184	3.2	odd	2	inner
429.2.be.a.188.14	yes	184	39.32	even	12	inner
429.2.be.a.188.33	yes	184	13.6	odd	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32901 - 0.356107i) q^{2} +(1.71883 - 0.213571i) q^{3} +(-0.0925961 - 0.0534604i) q^{4} +(-2.48553 + 2.48553i) q^{5} +(-2.36040 - 0.328250i) q^{6} +(-0.825366 - 3.08031i) q^{7} +(2.04983 + 2.04983i) q^{8} +(2.90877 - 0.734187i) q^{9} +O(q^{10})\)	\(q+(-1.32901 - 0.356107i) q^{2} +(1.71883 - 0.213571i) q^{3} +(-0.0925961 - 0.0534604i) q^{4} +(-2.48553 + 2.48553i) q^{5} +(-2.36040 - 0.328250i) q^{6} +(-0.825366 - 3.08031i) q^{7} +(2.04983 + 2.04983i) q^{8} +(2.90877 - 0.734187i) q^{9} +(4.18841 - 2.41818i) q^{10} +(-0.258819 + 0.965926i) q^{11} +(-0.170575 - 0.0721136i) q^{12} +(-1.73432 - 3.16103i) q^{13} +4.38768i q^{14} +(-3.74137 + 4.80305i) q^{15} +(-1.88736 - 3.26901i) q^{16} +(3.78908 - 6.56288i) q^{17} +(-4.12724 - 0.0600930i) q^{18} +(3.55905 - 0.953644i) q^{19} +(0.363028 - 0.0972730i) q^{20} +(-2.07653 - 5.11826i) q^{21} +(0.687946 - 1.19156i) q^{22} +(-4.10059 - 7.10243i) q^{23} +(3.96110 + 3.08553i) q^{24} -7.35570i q^{25} +(1.17926 + 4.81865i) q^{26} +(4.84290 - 1.88318i) q^{27} +(-0.0882488 + 0.329349i) q^{28} +(-4.91592 + 2.83821i) q^{29} +(6.68272 - 5.05097i) q^{30} +(0.707199 + 0.707199i) q^{31} +(-0.156372 - 0.583589i) q^{32} +(-0.238573 + 1.71554i) q^{33} +(-7.37282 + 7.37282i) q^{34} +(9.70766 + 5.60472i) q^{35} +(-0.308591 - 0.0875213i) q^{36} +(0.865853 + 0.232005i) q^{37} -5.06961 q^{38} +(-3.65611 - 5.06289i) q^{39} -10.1898 q^{40} +(5.57239 + 1.49312i) q^{41} +(0.937083 + 7.54169i) q^{42} +(0.679178 + 0.392123i) q^{43} +(0.0756044 - 0.0756044i) q^{44} +(-5.40500 + 9.05468i) q^{45} +(2.92050 + 10.8995i) q^{46} +(-5.12140 - 5.12140i) q^{47} +(-3.94223 - 5.21579i) q^{48} +(-2.74489 + 1.58477i) q^{49} +(-2.61942 + 9.77580i) q^{50} +(5.11116 - 12.0897i) q^{51} +(-0.00839870 + 0.385417i) q^{52} +3.67297i q^{53} +(-7.10687 + 0.778171i) q^{54} +(-1.75753 - 3.04414i) q^{55} +(4.62225 - 8.00597i) q^{56} +(5.91374 - 2.39927i) q^{57} +(7.54401 - 2.02141i) q^{58} +(-7.12296 + 1.90859i) q^{59} +(0.603209 - 0.244728i) q^{60} +(4.53903 - 7.86184i) q^{61} +(-0.688036 - 1.19171i) q^{62} +(-4.66233 - 8.35395i) q^{63} +8.38073i q^{64} +(12.1675 + 3.54613i) q^{65} +(0.927982 - 2.19501i) q^{66} +(-0.0660630 + 0.246550i) q^{67} +(-0.701709 + 0.405132i) q^{68} +(-8.56511 - 11.3321i) q^{69} +(-10.9057 - 10.9057i) q^{70} +(-1.58612 - 5.91947i) q^{71} +(7.46745 + 4.45753i) q^{72} +(2.21677 - 2.21677i) q^{73} +(-1.06811 - 0.616673i) q^{74} +(-1.57097 - 12.6432i) q^{75} +(-0.380536 - 0.101964i) q^{76} +3.18897 q^{77} +(3.05608 + 8.03059i) q^{78} +0.760405 q^{79} +(12.8163 + 3.43412i) q^{80} +(7.92194 - 4.27117i) q^{81} +(-6.87405 - 3.96874i) q^{82} +(-0.415987 + 0.415987i) q^{83} +(-0.0813454 + 0.584944i) q^{84} +(6.89436 + 25.7301i) q^{85} +(-0.762996 - 0.762996i) q^{86} +(-7.84348 + 5.92830i) q^{87} +(-2.51052 + 1.44945i) q^{88} +(-0.729514 + 2.72258i) q^{89} +(10.4077 - 10.1090i) q^{90} +(-8.30551 + 7.95125i) q^{91} +0.876877i q^{92} +(1.36660 + 1.06452i) q^{93} +(4.98262 + 8.63015i) q^{94} +(-6.47580 + 11.2164i) q^{95} +(-0.393415 - 0.969695i) q^{96} +(-6.06921 + 1.62624i) q^{97} +(4.21234 - 1.12869i) q^{98} +(-0.0436756 + 2.99968i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 12 q^{6} + 12 q^{7}+O(q^{10}) \) 184 * q - 12 * q^6 + 12 * q^7	\( 184 q - 12 q^{6} + 12 q^{7} - 48 q^{10} - 16 q^{13} + 16 q^{15} + 80 q^{16} - 8 q^{18} - 4 q^{19} - 24 q^{24} - 48 q^{27} - 40 q^{28} + 48 q^{30} - 20 q^{31} + 16 q^{34} - 36 q^{36} + 44 q^{37} + 48 q^{39} - 80 q^{40} + 20 q^{42} - 84 q^{43} - 4 q^{45} - 64 q^{46} + 44 q^{48} - 60 q^{49} - 200 q^{52} - 4 q^{54} - 64 q^{57} - 48 q^{58} - 148 q^{60} - 48 q^{61} + 40 q^{66} + 48 q^{67} - 12 q^{69} + 24 q^{70} - 128 q^{72} + 108 q^{73} - 60 q^{75} - 24 q^{76} + 148 q^{78} + 32 q^{79} + 16 q^{81} - 48 q^{82} + 116 q^{84} + 104 q^{85} - 24 q^{87} + 72 q^{88} + 60 q^{91} + 36 q^{93} + 16 q^{94} - 72 q^{96} + 4 q^{97}+O(q^{100}) \) 184 * q - 12 * q^6 + 12 * q^7 - 48 * q^10 - 16 * q^13 + 16 * q^15 + 80 * q^16 - 8 * q^18 - 4 * q^19 - 24 * q^24 - 48 * q^27 - 40 * q^28 + 48 * q^30 - 20 * q^31 + 16 * q^34 - 36 * q^36 + 44 * q^37 + 48 * q^39 - 80 * q^40 + 20 * q^42 - 84 * q^43 - 4 * q^45 - 64 * q^46 + 44 * q^48 - 60 * q^49 - 200 * q^52 - 4 * q^54 - 64 * q^57 - 48 * q^58 - 148 * q^60 - 48 * q^61 + 40 * q^66 + 48 * q^67 - 12 * q^69 + 24 * q^70 - 128 * q^72 + 108 * q^73 - 60 * q^75 - 24 * q^76 + 148 * q^78 + 32 * q^79 + 16 * q^81 - 48 * q^82 + 116 * q^84 + 104 * q^85 - 24 * q^87 + 72 * q^88 + 60 * q^91 + 36 * q^93 + 16 * q^94 - 72 * q^96 + 4 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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