LMFDB - Embedded newform 280.2.s.c.13.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(13,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 3, 2]))

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

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

chi := DirichletCharacter("280.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.s (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.14
Character	$\chi$	$=$	280.13
Dual form			280.2.s.c.237.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.482209 - 1.32946i) q^{2} +(0.851048 + 0.851048i) q^{3} +(-1.53495 + 1.28216i) q^{4} +(-2.18999 - 0.451591i) q^{5} +(0.721055 - 1.54182i) q^{6} +(-0.844017 - 2.50752i) q^{7} +(2.44475 + 1.42239i) q^{8} -1.55144i q^{9} +O(q^{10})$	\(q+(-0.482209 - 1.32946i) q^{2} +(0.851048 + 0.851048i) q^{3} +(-1.53495 + 1.28216i) q^{4} +(-2.18999 - 0.451591i) q^{5} +(0.721055 - 1.54182i) q^{6} +(-0.844017 - 2.50752i) q^{7} +(2.44475 + 1.42239i) q^{8} -1.55144i q^{9} +(0.455660 + 3.12928i) q^{10} -2.51177i q^{11} +(-2.39749 - 0.215137i) q^{12} +(-2.05614 - 2.05614i) q^{13} +(-2.92666 + 2.33124i) q^{14} +(-1.47946 - 2.24811i) q^{15} +(0.712139 - 3.93610i) q^{16} +(-0.323302 - 0.323302i) q^{17} +(-2.06258 + 0.748116i) q^{18} +0.414250i q^{19} +(3.94054 - 2.11475i) q^{20} +(1.41572 - 2.85231i) q^{21} +(-3.33930 + 1.21120i) q^{22} +(-5.60285 - 5.60285i) q^{23} +(0.870076 + 3.29112i) q^{24} +(4.59213 + 1.97796i) q^{25} +(-1.74207 + 3.72505i) q^{26} +(3.87349 - 3.87349i) q^{27} +(4.51056 + 2.76675i) q^{28} +2.48079 q^{29} +(-2.27538 + 3.05095i) q^{30} +7.18461i q^{31} +(-5.57630 + 0.951258i) q^{32} +(2.13763 - 2.13763i) q^{33} +(-0.273919 + 0.585718i) q^{34} +(0.716018 + 5.87259i) q^{35} +(1.98919 + 2.38137i) q^{36} +(4.54475 + 4.54475i) q^{37} +(0.550730 - 0.199755i) q^{38} -3.49974i q^{39} +(-4.71164 - 4.21905i) q^{40} +1.40978i q^{41} +(-4.47472 - 0.506734i) q^{42} +(-4.10811 + 4.10811i) q^{43} +(3.22048 + 3.85543i) q^{44} +(-0.700614 + 3.39763i) q^{45} +(-4.74704 + 10.1505i) q^{46} +(-5.84872 - 5.84872i) q^{47} +(3.95587 - 2.74374i) q^{48} +(-5.57527 + 4.23277i) q^{49} +(0.415262 - 7.05886i) q^{50} -0.550291i q^{51} +(5.79236 + 0.519772i) q^{52} +(7.59714 - 7.59714i) q^{53} +(-7.01749 - 3.28183i) q^{54} +(-1.13429 + 5.50075i) q^{55} +(1.50326 - 7.33077i) q^{56} +(-0.352547 + 0.352547i) q^{57} +(-1.19626 - 3.29812i) q^{58} +1.24364i q^{59} +(5.15334 + 1.55383i) q^{60} +11.7206 q^{61} +(9.55169 - 3.46448i) q^{62} +(-3.89025 + 1.30944i) q^{63} +(3.95360 + 6.95478i) q^{64} +(3.57439 + 5.43146i) q^{65} +(-3.87269 - 1.81112i) q^{66} +(2.90850 + 2.90850i) q^{67} +(0.910777 + 0.0817277i) q^{68} -9.53658i q^{69} +(7.46213 - 3.78374i) q^{70} -0.972317 q^{71} +(2.20675 - 3.79287i) q^{72} +(10.4999 - 10.4999i) q^{73} +(3.85056 - 8.23359i) q^{74} +(2.22478 + 5.59146i) q^{75} +(-0.531134 - 0.635853i) q^{76} +(-6.29829 + 2.11997i) q^{77} +(-4.65278 + 1.68761i) q^{78} +5.80828i q^{79} +(-3.33708 + 8.29843i) q^{80} +1.93874 q^{81} +(1.87425 - 0.679808i) q^{82} +(-9.17675 - 9.17675i) q^{83} +(1.48406 + 6.19333i) q^{84} +(0.562029 + 0.854029i) q^{85} +(7.44255 + 3.48062i) q^{86} +(2.11127 + 2.11127i) q^{87} +(3.57272 - 6.14064i) q^{88} +10.0566 q^{89} +(4.85487 - 0.706927i) q^{90} +(-3.42038 + 6.89121i) q^{91} +(15.7838 + 1.41635i) q^{92} +(-6.11445 + 6.11445i) q^{93} +(-4.95536 + 10.5960i) q^{94} +(0.187072 - 0.907204i) q^{95} +(-5.55526 - 3.93613i) q^{96} +(-1.18210 - 1.18210i) q^{97} +(8.31576 + 5.37104i) q^{98} -3.89684 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8}+O(q^{10}) $ 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8	$ 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8} - 8 q^{15} + 40 q^{16} - 40 q^{18} + 4 q^{22} + 40 q^{23} - 8 q^{25} - 4 q^{28} - 44 q^{30} - 24 q^{32} - 72 q^{36} + 40 q^{42} + 16 q^{46} - 60 q^{50} + 32 q^{56} + 32 q^{57} - 68 q^{58} + 64 q^{60} - 100 q^{63} - 56 q^{65} + 16 q^{70} - 80 q^{71} + 16 q^{72} - 4 q^{78} + 72 q^{81} - 72 q^{86} + 48 q^{88} + 72 q^{92} + 80 q^{95} + 40 q^{98}+O(q^{100}) $ 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8 - 8 * q^15 + 40 * q^16 - 40 * q^18 + 4 * q^22 + 40 * q^23 - 8 * q^25 - 4 * q^28 - 44 * q^30 - 24 * q^32 - 72 * q^36 + 40 * q^42 + 16 * q^46 - 60 * q^50 + 32 * q^56 + 32 * q^57 - 68 * q^58 + 64 * q^60 - 100 * q^63 - 56 * q^65 + 16 * q^70 - 80 * q^71 + 16 * q^72 - 4 * q^78 + 72 * q^81 - 72 * q^86 + 48 * q^88 + 72 * q^92 + 80 * q^95 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$	$-1$

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 $

$2$	−0.482209	−	1.32946i	−0.340973	−	0.940073i
$2$	−0.482209	−	1.32946i	−0.340973	−	0.940073i
$3$	0.851048	+	0.851048i	0.491353	+	0.491353i	0.908732	−	0.417380i	$-0.137051\pi$
$3$	0.851048	+	0.851048i	0.491353	+	0.491353i	−0.417380	+	0.908732i	$0.637051\pi$
$4$	−1.53495	+	1.28216i	−0.767475	+	0.641079i
$5$	−2.18999	−	0.451591i	−0.979394	−	0.201958i
$5$	−2.18999	−	0.451591i	−0.979394	−	0.201958i
$6$	0.721055	−	1.54182i	0.294369	−	0.629445i
$7$	−0.844017	−	2.50752i	−0.319008	−	0.947752i
$7$	−0.844017	−	2.50752i	−0.319008	−	0.947752i
$8$	2.44475	+	1.42239i	0.864350	+	0.502891i
$9$		−	1.55144i		−	0.517145i
$10$	0.455660	+	3.12928i	0.144092	+	0.989564i
$11$		−	2.51177i		−	0.757326i	−0.925535	−	0.378663i	$-0.876384\pi$
$11$		−	2.51177i		−	0.757326i	0.925535	−	0.378663i	$-0.123616\pi$
$12$	−2.39749	−	0.215137i	−0.692097	−	0.0621047i
$13$	−2.05614	−	2.05614i	−0.570270	−	0.570270i	0.361934	−	0.932204i	$-0.382117\pi$
$13$	−2.05614	−	2.05614i	−0.570270	−	0.570270i	−0.932204	+	0.361934i	$0.882117\pi$
$14$	−2.92666	+	2.33124i	−0.782183	+	0.623049i
$15$	−1.47946	−	2.24811i	−0.381996	−	0.580460i
$16$	0.712139	−	3.93610i	0.178035	−	0.984024i
$17$	−0.323302	−	0.323302i	−0.0784123	−	0.0784123i	0.666813	−	0.745225i	$-0.267658\pi$
$17$	−0.323302	−	0.323302i	−0.0784123	−	0.0784123i	−0.745225	+	0.666813i	$0.767658\pi$
$18$	−2.06258	+	0.748116i	−0.486154	+	0.176333i
$19$			0.414250i			0.0950355i	0.998870	+	0.0475177i	$0.0151311\pi$
$19$			0.414250i			0.0950355i	−0.998870	+	0.0475177i	$0.984869\pi$
$20$	3.94054	−	2.11475i	0.881131	−	0.472872i
$21$	1.41572	−	2.85231i	0.308935	−	0.622426i
$22$	−3.33930	+	1.21120i	−0.711942	+	0.258228i
$23$	−5.60285	−	5.60285i	−1.16827	−	1.16827i	−0.982614	−	0.185660i	$-0.940558\pi$
$23$	−5.60285	−	5.60285i	−1.16827	−	1.16827i	−0.185660	−	0.982614i	$-0.559442\pi$
$24$	0.870076	+	3.29112i	0.177603	+	0.671797i
$25$	4.59213	+	1.97796i	0.918426	+	0.395592i
$26$	−1.74207	+	3.72505i	−0.341649	+	0.730542i
$27$	3.87349	−	3.87349i	0.745453	−	0.745453i
$28$	4.51056	+	2.76675i	0.852415	+	0.522866i
$29$	2.48079			0.460670			0.230335	−	0.973111i	$-0.426018\pi$
$29$	2.48079			0.460670			0.230335	+	0.973111i	$0.426018\pi$
$30$	−2.27538	+	3.05095i	−0.415425	+	0.557025i
$31$			7.18461i			1.29039i	0.764016	+	0.645197i	$0.223225\pi$
$31$			7.18461i			1.29039i	−0.764016	+	0.645197i	$0.776775\pi$
$32$	−5.57630	+	0.951258i	−0.985760	+	0.168160i
$33$	2.13763	−	2.13763i	0.372114	−	0.372114i
$34$	−0.273919	+	0.585718i	−0.0469768	+	0.100450i
$35$	0.716018	+	5.87259i	0.121029	+	0.992649i
$36$	1.98919	+	2.38137i	0.331531	+	0.396896i
$37$	4.54475	+	4.54475i	0.747152	+	0.747152i	0.973943	−	0.226792i	$-0.0728237\pi$
$37$	4.54475	+	4.54475i	0.747152	+	0.747152i	−0.226792	+	0.973943i	$0.572824\pi$
$38$	0.550730	−	0.199755i	0.0893403	−	0.0324045i
$39$		−	3.49974i		−	0.560407i
$40$	−4.71164	−	4.21905i	−0.744976	−	0.667091i
$41$			1.40978i			0.220171i	0.993922	+	0.110085i	$0.0351124\pi$
$41$			1.40978i			0.220171i	−0.993922	+	0.110085i	$0.964888\pi$
$42$	−4.47472	−	0.506734i	−0.690464	−	0.0781908i
$43$	−4.10811	+	4.10811i	−0.626481	+	0.626481i	−0.947181	−	0.320700i	$-0.896082\pi$
$43$	−4.10811	+	4.10811i	−0.626481	+	0.626481i	0.320700	+	0.947181i	$0.396082\pi$
$44$	3.22048	+	3.85543i	0.485506	+	0.581229i
$45$	−0.700614	+	3.39763i	−0.104441	+	0.506489i
$46$	−4.74704	+	10.1505i	−0.699913	+	1.49661i
$47$	−5.84872	−	5.84872i	−0.853124	−	0.853124i	0.137393	−	0.990517i	$-0.456128\pi$
$47$	−5.84872	−	5.84872i	−0.853124	−	0.853124i	−0.990517	+	0.137393i	$0.956128\pi$
$48$	3.95587	−	2.74374i	0.570981	−	0.396025i
$49$	−5.57527	+	4.23277i	−0.796467	+	0.604681i
$50$	0.415262	−	7.05886i	0.0587269	−	0.998274i
$51$		−	0.550291i		−	0.0770562i
$52$	5.79236	+	0.519772i	0.803256	+	0.0720795i
$53$	7.59714	−	7.59714i	1.04355	−	1.04355i	0.0445393	−	0.999008i	$-0.485818\pi$
$53$	7.59714	−	7.59714i	1.04355	−	1.04355i	0.999008	−	0.0445393i	$-0.0141820\pi$
$54$	−7.01749	−	3.28183i	−0.954960	−	0.446601i
$55$	−1.13429	+	5.50075i	−0.152948	+	0.741721i
$56$	1.50326	−	7.33077i	0.200882	−	0.979616i
$57$	−0.352547	+	0.352547i	−0.0466959	+	0.0466959i
$58$	−1.19626	−	3.29812i	−0.157076	−	0.433064i
$59$			1.24364i			0.161909i	0.996718	+	0.0809543i	$0.0257968\pi$
$59$			1.24364i			0.161909i	−0.996718	+	0.0809543i	$0.974203\pi$
$60$	5.15334	+	1.55383i	0.665293	+	0.200599i
$61$	11.7206			1.50067			0.750335	−	0.661058i	$-0.229892\pi$
$61$	11.7206			1.50067			0.750335	+	0.661058i	$0.229892\pi$
$62$	9.55169	−	3.46448i	1.21307	−	0.439990i
$63$	−3.89025	+	1.30944i	−0.490125	+	0.164974i
$64$	3.95360	+	6.95478i	0.494201	+	0.869348i
$65$	3.57439	+	5.43146i	0.443349	+	0.673690i
$66$	−3.87269	−	1.81112i	−0.476695	−	0.222934i
$67$	2.90850	+	2.90850i	0.355329	+	0.355329i	0.862088	−	0.506759i	$-0.169156\pi$
$67$	2.90850	+	2.90850i	0.355329	+	0.355329i	−0.506759	+	0.862088i	$0.669156\pi$
$68$	0.910777	+	0.0817277i	0.110448	+	0.00991094i
$69$		−	9.53658i		−	1.14807i
$70$	7.46213	−	3.78374i	0.891895	−	0.452243i
$71$	−0.972317			−0.115393			−0.0576964	−	0.998334i	$-0.518376\pi$
$71$	−0.972317			−0.115393			−0.0576964	+	0.998334i	$0.518376\pi$
$72$	2.20675	−	3.79287i	0.260068	−	0.446994i
$73$	10.4999	−	10.4999i	1.22892	−	1.22892i	0.264550	−	0.964372i	$-0.414777\pi$
$73$	10.4999	−	10.4999i	1.22892	−	1.22892i	0.964372	−	0.264550i	$-0.0852235\pi$
$74$	3.85056	−	8.23359i	0.447618	−	0.957136i
$75$	2.22478	+	5.59146i	0.256896	+	0.645646i
$76$	−0.531134	−	0.635853i	−0.0609253	−	0.0729373i
$77$	−6.29829	+	2.11997i	−0.717757	+	0.241593i
$78$	−4.65278	+	1.68761i	−0.526824	+	0.191084i
$79$			5.80828i			0.653483i	0.945114	+	0.326741i	$0.105951\pi$
$79$			5.80828i			0.653483i	−0.945114	+	0.326741i	$0.894049\pi$
$80$	−3.33708	+	8.29843i	−0.373097	+	0.927792i
$81$	1.93874			0.215416
$82$	1.87425	−	0.679808i	0.206976	−	0.0750722i
$83$	−9.17675	−	9.17675i	−1.00728	−	1.00728i	−0.999973	−	0.00730635i	$-0.997674\pi$
$83$	−9.17675	−	9.17675i	−1.00728	−	1.00728i	−0.00730635	−	0.999973i	$-0.502326\pi$
$84$	1.48406	+	6.19333i	0.161925	+	0.675748i
$85$	0.562029	+	0.854029i	0.0609606	+	0.0926325i
$86$	7.44255	+	3.48062i	0.802551	+	0.375325i
$87$	2.11127	+	2.11127i	0.226352	+	0.226352i
$88$	3.57272	−	6.14064i	0.380853	−	0.654595i
$89$	10.0566			1.06600			0.533000	−	0.846115i	$-0.321065\pi$
$89$	10.0566			1.06600			0.533000	+	0.846115i	$0.321065\pi$
$90$	4.85487	−	0.706927i	0.511748	−	0.0745166i
$91$	−3.42038	+	6.89121i	−0.358554	+	0.722395i
$92$	15.7838	+	1.41635i	1.64558	+	0.147664i
$93$	−6.11445	+	6.11445i	−0.634039	+	0.634039i
$94$	−4.95536	+	10.5960i	−0.511106	+	1.09289i
$95$	0.187072	−	0.907204i	0.0191931	−	0.0930772i
$96$	−5.55526	−	3.93613i	−0.566982	−	0.401730i
$97$	−1.18210	−	1.18210i	−0.120025	−	0.120025i	0.644543	−	0.764568i	$-0.277048\pi$
$97$	−1.18210	−	1.18210i	−0.120025	−	0.120025i	−0.764568	+	0.644543i	$0.777048\pi$
$98$	8.31576	+	5.37104i	0.840019	+	0.542557i
$99$	−3.89684			−0.391648
$100$	−9.58475	+	2.85177i	−0.958475	+	0.285177i
$101$	0.133613			0.0132949			0.00664747	−	0.999978i	$-0.497884\pi$
$101$	0.133613			0.0132949			0.00664747	+	0.999978i	$0.497884\pi$
$102$	−0.731592	+	0.265355i	−0.0724384	+	0.0262741i
$103$	13.2794	−	13.2794i	1.30846	−	1.30846i	0.385932	−	0.922527i	$-0.373880\pi$
$103$	13.2794	−	13.2794i	1.30846	−	1.30846i	0.922527	−	0.385932i	$-0.126120\pi$
$104$	−2.10211	−	7.95138i	−0.206129	−	0.779697i
$105$	−4.38849	+	5.60722i	−0.428273	+	0.547209i
$106$	−13.7635	−	6.43671i	−1.33683	−	0.625189i
$107$	−8.93593	−	8.93593i	−0.863869	−	0.863869i	0.127916	−	0.991785i	$-0.459171\pi$
$107$	−8.93593	−	8.93593i	−0.863869	−	0.863869i	−0.991785	+	0.127916i	$0.959171\pi$
$108$	−0.979182	+	10.9120i	−0.0942218	+	1.05001i
$109$	−17.1604			−1.64367			−0.821836	−	0.569724i	$-0.807050\pi$
$109$	−17.1604			−1.64367			−0.821836	+	0.569724i	$0.807050\pi$
$110$	7.86001	−	1.14451i	0.749423	−	0.109125i
$111$			7.73559i			0.734230i
$112$	−10.4709	+	1.53643i	−0.989405	+	0.145179i
$113$	3.28379	+	3.28379i	0.308913	+	0.308913i	0.844488	−	0.535575i	$-0.179905\pi$
$113$	3.28379	+	3.28379i	0.308913	+	0.308913i	−0.535575	+	0.844488i	$0.679905\pi$
$114$	0.638699	+	0.298697i	0.0598196	+	0.0279755i
$115$	9.73999	+	14.8004i	0.908259	+	1.38014i
$116$	−3.80788	+	3.18076i	−0.353553	+	0.295326i
$117$	−3.18997	+	3.18997i	−0.294912	+	0.294912i
$118$	1.65338	−	0.599696i	0.152206	−	0.0552065i
$119$	−0.537813	+	1.08356i	−0.0493012	+	0.0993295i
$120$	−0.419218	−	7.60045i	−0.0382692	−	0.693823i
$121$	4.69103			0.426457
$122$	−5.65178	−	15.5821i	−0.511688	−	1.41074i
$123$	−1.19979	+	1.19979i	−0.108181	+	0.108181i
$124$	−9.21181	−	11.0280i	−0.827245	−	0.990345i
$125$	−9.16350	−	6.40548i	−0.819609	−	0.572924i
$126$	3.61676	+	4.54052i	0.322207	+	0.404502i
$127$	−2.75474	+	2.75474i	−0.244444	+	0.244444i	−0.818686	−	0.574242i	$-0.805297\pi$
$127$	−2.75474	+	2.75474i	−0.244444	+	0.244444i	0.574242	+	0.818686i	$0.305297\pi$
$128$	7.33967	−	8.60983i	0.648741	−	0.761009i
$129$	−6.99239			−0.615646
$130$	5.49733	−	7.37112i	0.482147	−	0.646490i
$131$	4.14619			0.362254			0.181127	−	0.983460i	$-0.442025\pi$
$131$	4.14619			0.362254			0.181127	+	0.983460i	$0.442025\pi$
$132$	−0.540374	+	6.02194i	−0.0470335	+	0.524143i
$133$	1.03874	−	0.349634i	0.0900700	−	0.0303171i
$134$	2.46424	−	5.26924i	0.212878	−	0.455193i
$135$	−10.2321	+	6.73368i	−0.880643	+	0.579543i
$136$	−0.330531	−	1.25025i	−0.0283428	−	0.107208i
$137$	−8.52736	+	8.52736i	−0.728542	+	0.728542i	−0.970329	−	0.241787i	$-0.922266\pi$
$137$	−8.52736	+	8.52736i	−0.728542	+	0.728542i	0.241787	+	0.970329i	$0.422266\pi$
$138$	−12.6785	+	4.59862i	−1.07927	+	0.391461i
$139$		−	5.99846i		−	0.508783i	−0.967101	−	0.254391i	$-0.918125\pi$
$139$		−	5.99846i		−	0.508783i	0.967101	−	0.254391i	$-0.0818751\pi$
$140$	−8.62864	−	8.09608i	−0.729254	−	0.684244i
$141$		−	9.95508i		−	0.838369i
$142$	0.468860	+	1.29266i	0.0393458	+	0.108478i
$143$	−5.16454	+	5.16454i	−0.431880	+	0.431880i
$144$	−6.10660	−	1.10484i	−0.508883	−	0.0920698i
$145$	−5.43290	−	1.12030i	−0.451178	−	0.0930359i
$146$	−19.0224	−	8.89611i	−1.57431	−	0.736247i
$147$	−8.34711	−	1.14253i	−0.688458	−	0.0942345i
$148$	−12.8030	−	1.14887i	−1.05240	−	0.0944365i
$149$	5.59017			0.457965			0.228982	−	0.973431i	$-0.426460\pi$
$149$	5.59017			0.457965			0.228982	+	0.973431i	$0.426460\pi$
$150$	6.36084	−	5.65402i	0.519360	−	0.461649i
$151$	7.05684			0.574278			0.287139	−	0.957889i	$-0.407296\pi$
$151$	7.05684			0.574278			0.287139	+	0.957889i	$0.407296\pi$
$152$	−0.589226	+	1.01274i	−0.0477925	+	0.0821439i
$153$	−0.501582	+	0.501582i	−0.0405505	+	0.0405505i
$154$	5.85552	+	7.35109i	0.471851	+	0.592367i
$155$	3.24451	−	15.7342i	0.260605	−	1.26381i
$156$	4.48723	+	5.37193i	0.359266	+	0.430098i
$157$	−12.7347	+	12.7347i	−1.01634	+	1.01634i	−0.0164774	+	0.999864i	$0.505245\pi$
$157$	−12.7347	+	12.7347i	−1.01634	+	1.01634i	−0.999864	+	0.0164774i	$0.994755\pi$
$158$	7.72190	−	2.80081i	0.614322	−	0.222820i
$159$	12.9311			1.02550
$160$	12.6416	+	0.434958i	0.999409	+	0.0343864i
$161$	−9.32033	+	18.7781i	−0.734545	+	1.47992i
$162$	−0.934878	−	2.57749i	−0.0734510	−	0.202506i
$163$	−3.78159	+	3.78159i	−0.296197	+	0.296197i	−0.839522	−	0.543325i	$-0.817165\pi$
$163$	−3.78159	+	3.78159i	−0.296197	+	0.296197i	0.543325	+	0.839522i	$0.317165\pi$
$164$	−1.80756	−	2.16394i	−0.141147	−	0.168975i
$165$	−5.64674	+	3.71606i	−0.439598	+	0.289295i
$166$	−7.77505	+	16.6253i	−0.603461	+	1.29037i
$167$	−5.05575	−	5.05575i	−0.391225	−	0.391225i	0.483899	−	0.875124i	$-0.339220\pi$
$167$	−5.05575	−	5.05575i	−0.391225	−	0.391225i	−0.875124	+	0.483899i	$0.839220\pi$
$168$	7.51818	−	4.95949i	0.580040	−	0.382633i
$169$		−	4.54459i		−	0.349584i
$170$	0.864386	−	1.15902i	0.0662954	−	0.0888926i
$171$	0.642682			0.0491471
$172$	1.03849	−	11.5730i	0.0791842	−	0.882432i
$173$	15.9087	+	15.9087i	1.20951	+	1.20951i	0.971184	+	0.238329i	$0.0765998\pi$
$173$	15.9087	+	15.9087i	1.20951	+	1.20951i	0.238329	+	0.971184i	$0.423400\pi$
$174$	1.78878	−	3.82493i	0.135607	−	0.289967i
$175$	1.08393	−	13.1843i	0.0819377	−	0.996637i
$176$	−9.88656	−	1.78873i	−0.745227	−	0.134830i
$177$	−1.05840	+	1.05840i	−0.0795542	+	0.0795542i
$178$	−4.84939	−	13.3699i	−0.363477	−	1.00212i
$179$	−1.92015			−0.143519			−0.0717593	−	0.997422i	$-0.522861\pi$
$179$	−1.92015			−0.143519			−0.0717593	+	0.997422i	$0.522861\pi$
$180$	−3.28090	−	6.11349i	−0.244544	−	0.455673i
$181$	8.92242			0.663199			0.331599	−	0.943420i	$-0.392412\pi$
$181$	8.92242			0.663199			0.331599	+	0.943420i	$0.392412\pi$
$182$	10.8110	+	1.22427i	0.801362	+	0.0907492i
$183$	9.97479	+	9.97479i	0.737358	+	0.737358i
$184$	−5.72812	−	21.6670i	−0.422282	−	1.59731i
$185$	−7.90059	−	12.0053i	−0.580863	−	0.882649i
$186$	11.0774	+	5.18050i	0.812233	+	0.379853i
$187$	−0.812059	+	0.812059i	−0.0593837	+	0.0593837i
$188$	16.4765	+	1.47850i	1.20167	+	0.107831i
$189$	−12.9821	−	6.44355i	−0.944311	−	0.468699i
$190$	−1.29630	+	0.188757i	−0.0940437	+	0.0136939i
$191$	25.8617			1.87129			0.935643	−	0.352947i	$-0.114820\pi$
$191$	25.8617			1.87129			0.935643	+	0.352947i	$0.114820\pi$
$192$	−2.55415	+	9.28356i	−0.184330	+	0.669983i
$193$	−3.91271	−	3.91271i	−0.281643	−	0.281643i	0.552121	−	0.833764i	$-0.313819\pi$
$193$	−3.91271	−	3.91271i	−0.281643	−	0.281643i	−0.833764	+	0.552121i	$0.813819\pi$
$194$	−1.00154	+	2.14159i	−0.0719067	+	0.153757i
$195$	−1.58045	+	7.66441i	−0.113179	+	0.548860i
$196$	3.13068	−	13.6455i	0.223620	−	0.974676i
$197$	11.3964	+	11.3964i	0.811963	+	0.811963i	0.984928	−	0.172965i	$-0.0553348\pi$
$197$	11.3964	+	11.3964i	0.811963	+	0.811963i	−0.172965	+	0.984928i	$0.555335\pi$
$198$	1.87909	+	5.18071i	0.133541	+	0.368177i
$199$	2.32255			0.164641			0.0823205	−	0.996606i	$-0.473767\pi$
$199$	2.32255			0.164641			0.0823205	+	0.996606i	$0.473767\pi$
$200$	8.41318	+	11.3674i	0.594901	+	0.803799i
$201$			4.95054i			0.349184i
$202$	−0.0644292	−	0.177633i	−0.00453322	−	0.0124982i
$203$	−2.09382	−	6.22061i	−0.146958	−	0.436601i
$204$	0.705560	+	0.844669i	0.0493991	+	0.0591386i
$205$	0.636644	−	3.08741i	0.0444651	−	0.215634i
$206$	−24.0579	−	11.2510i	−1.67620	−	0.783898i
$207$	−8.69245	+	8.69245i	−0.604167	+	0.604167i
$208$	−9.55741	+	6.62890i	−0.662687	+	0.459632i
$209$	1.04050			0.0719728
$210$	9.57077	+	3.13049i	0.660446	+	0.216024i
$211$		−	6.55987i		−	0.451600i	−0.974174	−	0.225800i	$-0.927500\pi$
$211$		−	6.55987i		−	0.451600i	0.974174	−	0.225800i	$-0.0724996\pi$
$212$	−1.92049	+	21.4020i	−0.131899	+	1.46989i
$213$	−0.827488	−	0.827488i	−0.0566985	−	0.0566985i
$214$	−7.57101	+	16.1890i	−0.517544	+	1.10666i
$215$	10.8519	−	7.14154i	0.740094	−	0.487049i
$216$	14.9793	−	3.96009i	1.01921	−	0.269450i
$217$	18.0155	−	6.06393i	1.22297	−	0.411647i
$218$	8.27492	+	22.8142i	0.560448	+	1.54517i
$219$	17.8719			1.20767
$220$	−5.31175	−	9.89771i	−0.358118	−	0.667304i
$221$			1.32951i			0.0894323i
$222$	10.2842	−	3.73017i	0.690230	−	0.250353i
$223$	−12.6328	+	12.6328i	−0.845955	+	0.845955i	−0.989626	−	0.143670i	$-0.954110\pi$
$223$	−12.6328	+	12.6328i	−0.845955	+	0.845955i	0.143670	+	0.989626i	$0.454110\pi$
$224$	7.09178	+	13.1798i	0.473840	+	0.880611i
$225$	3.06868	−	7.12440i	0.204579	−	0.474960i
$226$	2.78221	−	5.94915i	0.185070	−	0.395732i
$227$	14.9681	−	14.9681i	0.993467	−	0.993467i	−0.00651216	−	0.999979i	$-0.502073\pi$
$227$	14.9681	−	14.9681i	0.993467	−	0.993467i	0.999979	+	0.00651216i	$0.00207290\pi$
$228$	0.0891205	−	0.993162i	0.00590215	−	0.0657737i
$229$		−	6.01142i		−	0.397246i	−0.980076	−	0.198623i	$-0.936353\pi$
$229$		−	6.01142i		−	0.397246i	0.980076	−	0.198623i	$-0.0636469\pi$
$230$	14.9799	−	20.0858i	0.987743	−	1.32442i
$231$	−7.16435	−	3.55595i	−0.471379	−	0.233964i
$232$	6.06490	+	3.52865i	0.398180	+	0.231667i
$233$	−12.6385	−	12.6385i	−0.827974	−	0.827974i	0.159262	−	0.987236i	$-0.449089\pi$
$233$	−12.6385	−	12.6385i	−0.827974	−	0.827974i	−0.987236	+	0.159262i	$0.949089\pi$
$234$	5.77917	+	2.70271i	0.377796	+	0.176682i
$235$	10.1674	+	15.4499i	0.663250	+	1.00784i
$236$	−1.59455	−	1.90893i	−0.103796	−	0.124261i
$237$	−4.94313	+	4.94313i	−0.321091	+	0.321091i
$238$	1.69989	+	0.192502i	0.110187	+	0.0124780i
$239$			1.33783i			0.0865372i	0.999063	+	0.0432686i	$0.0137771\pi$
$239$			1.33783i			0.0865372i	−0.999063	+	0.0432686i	$0.986223\pi$
$240$	−9.90237	+	4.22234i	−0.639195	+	0.272551i
$241$		−	27.6357i		−	1.78017i	−0.455795	−	0.890085i	$-0.650645\pi$
$241$		−	27.6357i		−	1.78017i	0.455795	−	0.890085i	$-0.349355\pi$
$242$	−2.26206	−	6.23655i	−0.145410	−	0.400901i
$243$	−9.97051	−	9.97051i	−0.639608	−	0.639608i
$244$	−17.9905	+	15.0277i	−1.15173	+	0.962048i
$245$	14.1213	−	6.75199i	0.902176	−	0.431369i
$246$	2.17363	+	1.01653i	0.138585	+	0.0648115i
$247$	0.851755	−	0.851755i	0.0541959	−	0.0541959i
$248$	−10.2193	+	17.5646i	−0.648928	+	1.11535i
$249$		−	15.6197i		−	0.989859i
$250$	−4.09714	+	15.2713i	−0.259126	+	0.965844i
$251$	−5.69321			−0.359352			−0.179676	−	0.983726i	$-0.557505\pi$
$251$	−5.69321			−0.359352			−0.179676	+	0.983726i	$0.557505\pi$
$252$	4.29243	−	6.99784i	0.270398	−	0.440822i
$253$	−14.0730	+	14.0730i	−0.884764	+	0.884764i
$254$	4.99069	+	2.33397i	0.313144	+	0.146446i
$255$	−0.248506	+	1.20513i	−0.0155621	+	0.0754684i
$256$	−14.9857	−	5.60609i	−0.936607	−	0.350381i
$257$	21.1061	+	21.1061i	1.31656	+	1.31656i	0.916478	+	0.400085i	$0.131020\pi$
$257$	21.1061	+	21.1061i	1.31656	+	1.31656i	0.400085	+	0.916478i	$0.368980\pi$
$258$	3.37179	+	9.29614i	0.209919	+	0.578752i
$259$	7.56018	−	15.2319i	0.469767	−	0.946462i
$260$	−12.4505	−	3.75408i	−0.772147	−	0.232818i
$261$		−	3.84878i		−	0.238233i
$262$	−1.99933	−	5.51221i	−0.123519	−	0.340545i
$263$	5.43843	+	5.43843i	0.335348	+	0.335348i	0.854613	−	0.519265i	$-0.173794\pi$
$263$	5.43843	+	5.43843i	0.335348	+	0.335348i	−0.519265	+	0.854613i	$0.673794\pi$
$264$	8.26653	−	2.18543i	0.508770	−	0.134504i
$265$	−20.0685	+	13.2069i	−1.23280	+	0.811292i
$266$	−0.965715	−	1.21237i	−0.0592118	−	0.0743351i
$267$	8.55867	+	8.55867i	0.523782	+	0.523782i
$268$	−8.19355	−	0.735241i	−0.500501	−	0.0449120i
$269$		−	7.06975i		−	0.431050i	−0.976498	−	0.215525i	$-0.930854\pi$
$269$		−	7.06975i		−	0.431050i	0.976498	−	0.215525i	$-0.0691463\pi$
$270$	13.8862	+	10.3562i	0.845088	+	0.630260i
$271$		−	19.4793i		−	1.18328i	−0.806201	−	0.591642i	$-0.798480\pi$
$271$		−	19.4793i		−	1.18328i	0.806201	−	0.591642i	$-0.201520\pi$
$272$	−1.50278	+	1.04231i	−0.0911197	+	0.0631995i
$273$	−8.77566	+	2.95384i	−0.531127	+	0.178775i
$274$	15.4488	+	7.22485i	0.933296	+	0.436469i
$275$	4.96818	−	11.5344i	0.299592	−	0.695548i
$276$	12.2274	+	14.6382i	0.736003	+	0.881114i
$277$	15.4758	+	15.4758i	0.929850	+	0.929850i	0.997696	−	0.0678454i	$-0.0216125\pi$
$277$	15.4758	+	15.4758i	0.929850	+	0.929850i	−0.0678454	+	0.997696i	$0.521612\pi$
$278$	−7.97474	+	2.89251i	−0.478293	+	0.173481i
$279$	11.1465			0.667321
$280$	−6.60264	+	15.3755i	−0.394583	+	0.918860i
$281$	−20.4129			−1.21773			−0.608865	−	0.793274i	$-0.708375\pi$
$281$	−20.4129			−1.21773			−0.608865	+	0.793274i	$0.708375\pi$
$282$	−13.2349	+	4.80043i	−0.788128	+	0.285861i
$283$	−4.96318	−	4.96318i	−0.295031	−	0.295031i	0.544033	−	0.839064i	$-0.316897\pi$
$283$	−4.96318	−	4.96318i	−0.295031	−	0.295031i	−0.839064	+	0.544033i	$0.816897\pi$
$284$	1.49246	−	1.24666i	0.0885610	−	0.0739759i
$285$	0.931281	−	0.612867i	0.0551643	−	0.0363031i
$286$	9.35645	+	4.37568i	0.553259	+	0.258739i
$287$	3.53504	−	1.18988i	0.208667	−	0.0702362i
$288$	1.47582	+	8.65127i	0.0869633	+	0.509781i
$289$		−	16.7910i		−	0.987703i
$290$	1.13039	+	7.76307i	0.0663790	+	0.455863i
$291$		−	2.01205i		−	0.117949i
$292$	−2.65428	+	29.5794i	−0.155330	+	1.73100i
$293$	−8.15190	−	8.15190i	−0.476239	−	0.476239i	0.427688	−	0.903927i	$-0.359328\pi$
$293$	−8.15190	−	8.15190i	−0.476239	−	0.476239i	−0.903927	+	0.427688i	$0.859328\pi$
$294$	2.50609	+	11.6481i	0.146158	+	0.679332i
$295$	0.561618	−	2.72357i	0.0326987	−	0.158572i
$296$	4.64636	+	17.5752i	0.270064	+	1.02154i
$297$	−9.72930	−	9.72930i	−0.564551	−	0.564551i
$298$	−2.69563	−	7.43193i	−0.156154	−	0.430520i
$299$			23.0404i			1.33246i
$300$	−10.5841	−	5.73009i	−0.611072	−	0.330827i
$301$	13.7685	+	6.83384i	0.793601	+	0.393896i
$302$	−3.40287	−	9.38182i	−0.195813	−	0.539863i
$303$	0.113711	+	0.113711i	0.00653251	+	0.00653251i
$304$	1.63053	+	0.295003i	0.0935172	+	0.0169196i
$305$	−25.6680	−	5.29292i	−1.46975	−	0.303072i
$306$	0.908703	+	0.424968i	0.0519471	+	0.0242938i
$307$	10.8162	−	10.8162i	0.617313	−	0.617313i	−0.327529	−	0.944841i	$-0.606216\pi$
$307$	10.8162	−	10.8162i	0.617313	−	0.617313i	0.944841	+	0.327529i	$0.106216\pi$
$308$	6.94942	−	11.3295i	0.395980	−	0.645556i
$309$	22.6028			1.28583
$310$	−22.4826	+	3.27374i	−1.27693	+	0.185936i
$311$			24.5558i			1.39243i	0.717833	+	0.696215i	$0.245134\pi$
$311$			24.5558i			1.39243i	−0.717833	+	0.696215i	$0.754866\pi$
$312$	4.97800	−	8.55600i	0.281824	−	0.484388i
$313$	−15.0111	+	15.0111i	−0.848478	+	0.848478i	−0.989943	−	0.141465i	$-0.954819\pi$
$313$	−15.0111	+	15.0111i	−0.848478	+	0.848478i	0.141465	+	0.989943i	$0.454819\pi$
$314$	23.0712	+	10.7896i	1.30198	+	0.608890i
$315$	9.11095	−	1.11086i	0.513344	−	0.0625897i
$316$	−7.44714	−	8.91542i	−0.418934	−	0.501531i
$317$	−18.2459	−	18.2459i	−1.02479	−	1.02479i	−0.999685	−	0.0251044i	$-0.992008\pi$
$317$	−18.2459	−	18.2459i	−1.02479	−	1.02479i	−0.0251044	−	0.999685i	$-0.507992\pi$
$318$	−6.23547	−	17.1914i	−0.349668	−	0.964044i
$319$		−	6.23115i		−	0.348878i
$320$	−5.51764	−	17.0163i	−0.308446	−	0.951242i
$321$		−	15.2098i		−	0.848929i
$322$	29.4592	+	3.33607i	1.64170	+	0.185912i
$323$	0.133928	−	0.133928i	0.00745195	−	0.00745195i
$324$	−2.97587	+	2.48577i	−0.165326	+	0.138099i
$325$	−5.37509	−	13.5090i	−0.298157	−	0.749345i
$326$	6.85101	+	3.20397i	0.379442	+	0.177452i
$327$	−14.6044	−	14.6044i	−0.807623	−	0.807623i
$328$	−2.00526	+	3.44656i	−0.110722	+	0.190304i
$329$	−9.72934	+	19.6022i	−0.536396	+	1.08070i
$330$	7.66328	+	5.71521i	0.421850	+	0.314612i
$331$			25.0233i			1.37541i	0.725991	+	0.687704i	$0.241381\pi$
$331$			25.0233i			1.37541i	−0.725991	+	0.687704i	$0.758619\pi$
$332$	25.8519	+	2.31980i	1.41881	+	0.127315i
$333$	7.05088	−	7.05088i	0.386386	−	0.386386i
$334$	−4.28351	+	9.15936i	−0.234383	+	0.501178i
$335$	−5.05613	−	7.68303i	−0.276246	−	0.419769i
$336$	−10.2188	−	7.60364i	−0.557481	−	0.414813i
$337$	12.7250	−	12.7250i	0.693173	−	0.693173i	−0.269756	−	0.962929i	$-0.586943\pi$
$337$	12.7250	−	12.7250i	0.693173	−	0.693173i	0.962929	+	0.269756i	$0.0869430\pi$
$338$	−6.04188	+	2.19144i	−0.328635	+	0.119199i
$339$			5.58932i			0.303570i
$340$	−1.95769	−	0.590282i	−0.106170	−	0.0320125i
$341$	18.0461			0.977250
$342$	−0.309907	−	0.854423i	−0.0167579	−	0.0462019i
$343$	15.3194	+	10.4076i	0.827168	+	0.561955i
$344$	−15.8866	+	4.19996i	−0.856550	+	0.226447i
$345$	−4.30663	+	20.8850i	−0.231861	+	1.12441i
$346$	13.4787	−	28.8213i	0.724620	−	1.54944i
$347$	−8.40787	−	8.40787i	−0.451358	−	0.451358i	0.444447	−	0.895805i	$-0.353400\pi$
$347$	−8.40787	−	8.40787i	−0.451358	−	0.451358i	−0.895805	+	0.444447i	$0.853400\pi$
$348$	−5.94767	−	0.533709i	−0.318828	−	0.0286098i
$349$			26.6448i			1.42626i	0.701030	+	0.713132i	$0.252724\pi$
$349$			26.6448i			1.42626i	−0.701030	+	0.713132i	$0.747276\pi$
$350$	−18.0507	+	4.91652i	−0.964851	+	0.262799i
$351$	−15.9289			−0.850219
$352$	2.38934	+	14.0064i	0.127352	+	0.746542i
$353$	2.82560	−	2.82560i	0.150391	−	0.150391i	−0.627902	−	0.778293i	$-0.716086\pi$
$353$	2.82560	−	2.82560i	0.150391	−	0.150391i	0.778293	+	0.627902i	$0.216086\pi$
$354$	1.91747	+	0.896735i	0.101913	+	0.0476609i
$355$	2.12937	+	0.439089i	0.113015	+	0.0233044i
$356$	−15.4364	+	12.8942i	−0.818128	+	0.683391i
$357$	−1.37986	+	0.464455i	−0.0730301	+	0.0245816i
$358$	0.925913	+	2.55277i	0.0489360	+	0.134918i
$359$		−	24.9399i		−	1.31628i	−0.752896	−	0.658140i	$-0.771344\pi$
$359$		−	24.9399i		−	1.31628i	0.752896	−	0.658140i	$-0.228656\pi$
$360$	−6.54559	+	7.30981i	−0.344983	+	0.385261i
$361$	18.8284			0.990968
$362$	−4.30247	−	11.8620i	−0.226133	−	0.623455i
$363$	3.99229	+	3.99229i	0.209541	+	0.209541i
$364$	−3.58551	−	14.9631i	−0.187932	−	0.784281i
$365$	−27.7364	+	18.2531i	−1.45179	+	0.955409i
$366$	8.45119	−	18.0711i	0.441751	−	0.944589i
$367$	17.0197	+	17.0197i	0.888422	+	0.888422i	0.994371	−	0.105950i	$-0.0337883\pi$
$367$	17.0197	+	17.0197i	0.888422	+	0.888422i	−0.105950	+	0.994371i	$0.533788\pi$
$368$	−26.0433	+	18.0633i	−1.35760	+	0.941617i
$369$	2.18718			0.113860
$370$	−12.1509	+	16.2926i	−0.631696	+	0.847013i
$371$	−25.4621	−	12.6378i	−1.32192	−	0.656123i
$372$	1.54568	−	17.2251i	0.0801395	−	0.893078i
$373$	14.7233	−	14.7233i	0.762342	−	0.762342i	−0.214403	−	0.976745i	$-0.568781\pi$
$373$	14.7233	−	14.7233i	0.762342	−	0.762342i	0.976745	+	0.214403i	$0.0687805\pi$
$374$	1.47119	+	0.688021i	0.0760732	+	0.0355767i
$375$	−2.34721	−	13.2500i	−0.121209	−	0.684225i
$376$	−5.97949	−	22.6178i	−0.308369	−	1.16643i
$377$	−5.10084	−	5.10084i	−0.262706	−	0.262706i
$378$	−2.30637	+	20.3664i	−0.118627	+	1.04753i
$379$	−11.4933			−0.590371			−0.295185	−	0.955440i	$-0.595381\pi$
$379$	−11.4933			−0.590371			−0.295185	+	0.955440i	$0.595381\pi$
$380$	0.876034	+	1.63237i	0.0449396	+	0.0837387i
$381$	−4.68883			−0.240216
$382$	−12.4707	−	34.3822i	−0.638058	−	1.75915i
$383$	6.48827	−	6.48827i	0.331535	−	0.331535i	−0.521634	−	0.853169i	$-0.674677\pi$
$383$	6.48827	−	6.48827i	0.331535	−	0.331535i	0.853169	+	0.521634i	$0.174677\pi$
$384$	13.5738	−	1.08097i	0.692685	−	0.0551629i
$385$	14.7506	−	1.79847i	0.751759	−	0.0916586i
$386$	−3.31507	+	7.08855i	−0.168732	+	0.360798i
$387$	6.37347	+	6.37347i	0.323981	+	0.323981i
$388$	3.33012	+	0.298825i	0.169061	+	0.0151705i
$389$	6.70580			0.339998			0.169999	−	0.985444i	$-0.445624\pi$
$389$	6.70580			0.339998			0.169999	+	0.985444i	$0.445624\pi$
$390$	10.9517	−	1.59469i	0.554559	−	0.0807504i
$391$			3.62282i			0.183214i
$392$	−19.6508	+	2.41784i	−0.992515	+	0.122120i
$393$	3.52860	+	3.52860i	0.177994	+	0.177994i
$394$	9.65569	−	20.6466i	0.486447	−	1.04016i
$395$	2.62297	−	12.7201i	0.131976	−	0.640017i
$396$	5.98146	−	4.99637i	0.300580	−	0.251077i
$397$	−5.39493	+	5.39493i	−0.270764	+	0.270764i	−0.829408	−	0.558644i	$-0.811322\pi$
$397$	−5.39493	+	5.39493i	−0.270764	+	0.270764i	0.558644	+	0.829408i	$0.311322\pi$
$398$	−1.11995	−	3.08774i	−0.0561381	−	0.154774i
$399$	1.18157	+	0.586461i	0.0591525	+	0.0293598i
$400$	11.0557	−	16.6665i	0.552784	−	0.833325i
$401$	−5.72101			−0.285693			−0.142847	−	0.989745i	$-0.545626\pi$
$401$	−5.72101			−0.285693			−0.142847	+	0.989745i	$0.545626\pi$
$402$	6.58156	−	2.38719i	0.328259	−	0.119062i
$403$	14.7726	−	14.7726i	0.735873	−	0.735873i
$404$	−0.205089	+	0.171312i	−0.0102035	+	0.00852312i
$405$	−4.24583	−	0.875518i	−0.210977	−	0.0435048i
$406$	−7.26042	+	5.78330i	−0.360328	+	0.287020i
$407$	11.4153	−	11.4153i	0.565837	−	0.565837i
$408$	0.782729	−	1.34532i	0.0387509	−	0.0666035i
$409$	21.0532			1.04102			0.520508	−	0.853857i	$-0.325743\pi$
$409$	21.0532			1.04102			0.520508	+	0.853857i	$0.325743\pi$
$410$	−4.41159	+	0.642380i	−0.217873	+	0.0317249i
$411$	−14.5144			−0.715942
$412$	−3.35691	+	37.4095i	−0.165383	+	1.84304i
$413$	3.11846	−	1.04966i	0.153449	−	0.0516502i
$414$	15.7479	+	7.36473i	0.773966	+	0.361957i
$415$	15.9529	+	24.2412i	0.783096	+	1.18995i
$416$	13.4216	+	9.50972i	0.658046	+	0.466252i
$417$	5.10498	−	5.10498i	0.249992	−	0.249992i
$418$	−0.501738	−	1.38331i	−0.0245408	−	0.0676597i
$419$			35.9170i			1.75466i	0.479887	+	0.877330i	$0.340678\pi$
$419$			35.9170i			1.75466i	−0.479887	+	0.877330i	$0.659322\pi$
$420$	−0.453238	−	14.2335i	−0.0221158	−	0.694526i
$421$		−	18.7985i		−	0.916182i	−0.888905	−	0.458091i	$-0.848533\pi$
$421$		−	18.7985i		−	0.916182i	0.888905	−	0.458091i	$-0.151467\pi$
$422$	−8.72111	+	3.16323i	−0.424537	+	0.153984i
$423$	−9.07391	+	9.07391i	−0.441189	+	0.441189i
$424$	29.3792	−	7.76700i	1.42678	−	0.377199i
$425$	−0.845167	−	2.12412i	−0.0409966	−	0.103035i
$426$	−0.701093	+	1.49914i	−0.0339681	+	0.0726334i
$427$	−9.89238	−	29.3896i	−0.478726	−	1.42226i
$428$	25.1735	+	2.25892i	1.21681	+	0.109189i
$429$	−8.79054			−0.424411
$430$	−14.7273	−	10.9835i	−0.710214	−	0.529672i
$431$	6.87702			0.331255			0.165627	−	0.986188i	$-0.447035\pi$
$431$	6.87702			0.331255			0.165627	+	0.986188i	$0.447035\pi$
$432$	−12.4880	−	18.0049i	−0.600828	−	0.866261i
$433$	2.77952	−	2.77952i	0.133575	−	0.133575i	−0.637158	−	0.770733i	$-0.719890\pi$
$433$	2.77952	−	2.77952i	0.133575	−	0.133575i	0.770733	+	0.637158i	$0.219890\pi$
$434$	−16.7490	−	21.0269i	−0.803979	−	1.00932i
$435$	−3.67023	−	5.57709i	−0.175974	−	0.267401i
$436$	26.3404	−	22.0024i	1.26148	−	1.05372i
$437$	2.32098	−	2.32098i	0.111027	−	0.111027i
$438$	−8.61797	−	23.7600i	−0.411782	−	1.13530i
$439$	−24.3654			−1.16290			−0.581448	−	0.813583i	$-0.697514\pi$
$439$	−24.3654			−1.16290			−0.581448	+	0.813583i	$0.697514\pi$
$440$	−10.5973	+	11.8345i	−0.505205	+	0.564190i
$441$	6.56687	+	8.64967i	0.312708	+	0.411889i
$442$	1.76753	−	0.641100i	0.0840729	−	0.0304940i
$443$	−8.80104	+	8.80104i	−0.418150	+	0.418150i	−0.884566	−	0.466416i	$-0.845545\pi$
$443$	−8.80104	+	8.80104i	−0.418150	+	0.418150i	0.466416	+	0.884566i	$0.345545\pi$
$444$	−9.91825	−	11.8737i	−0.470699	−	0.563503i
$445$	−22.0239	−	4.54148i	−1.04403	−	0.215287i
$446$	22.8865	+	10.7032i	1.08371	+	0.506812i
$447$	4.75750	+	4.75750i	0.225022	+	0.225022i
$448$	14.1023	−	15.7837i	0.666272	−	0.745709i
$449$			20.2530i			0.955799i	0.878415	+	0.477900i	$0.158602\pi$
$449$			20.2530i			0.955799i	−0.878415	+	0.477900i	$0.841398\pi$
$450$	−10.9514	−	0.644252i	−0.516253	−	0.0303703i
$451$	3.54104			0.166741
$452$	−9.25079	−	0.830111i	−0.435120	−	0.0390451i
$453$	6.00571	+	6.00571i	0.282173	+	0.282173i
$454$	−27.1173	−	12.6818i	−1.27268	−	0.595186i
$455$	10.6026	−	13.5471i	0.497059	−	0.635097i
$456$	−1.36335	+	0.360429i	−0.0638446	+	0.0168786i
$457$	2.82521	−	2.82521i	0.132158	−	0.132158i	−0.637934	−	0.770091i	$-0.720211\pi$
$457$	2.82521	−	2.82521i	0.132158	−	0.132158i	0.770091	+	0.637934i	$0.220211\pi$
$458$	−7.99196	+	2.89876i	−0.373440	+	0.135450i
$459$	−2.50461			−0.116905
$460$	−33.9268	−	10.2296i	−1.58185	−	0.476958i
$461$	−4.24667			−0.197787			−0.0988936	−	0.995098i	$-0.531530\pi$
$461$	−4.24667			−0.197787			−0.0988936	+	0.995098i	$0.531530\pi$
$462$	−1.27280	+	11.2395i	−0.0592159	+	0.522907i
$463$	−7.90420	−	7.90420i	−0.367339	−	0.367339i	0.499167	−	0.866506i	$-0.333639\pi$
$463$	−7.90420	−	7.90420i	−0.367339	−	0.367339i	−0.866506	+	0.499167i	$0.833639\pi$
$464$	1.76666	−	9.76461i	0.0820153	−	0.453311i
$465$	16.1518	−	10.6294i	0.749023	−	0.492925i
$466$	−10.7080	+	22.8968i	−0.496039	+	1.06067i
$467$	5.43216	−	5.43216i	0.251370	−	0.251370i	−0.570162	−	0.821532i	$-0.693120\pi$
$467$	5.43216	−	5.43216i	0.251370	−	0.251370i	0.821532	+	0.570162i	$0.193120\pi$
$468$	0.806393	−	8.98648i	0.0372755	−	0.415400i
$469$	4.83828	−	9.74792i	0.223411	−	0.450117i
$470$	15.6372	−	20.9673i	0.721292	−	0.967149i
$471$	−21.6757			−0.998764
$472$	−1.76895	+	3.04040i	−0.0814224	+	0.139946i
$473$	10.3186	+	10.3186i	0.474450	+	0.474450i
$474$	8.95533	+	4.18809i	0.411332	+	0.192365i
$475$	−0.819370	+	1.90229i	−0.0375953	+	0.0872831i
$476$	−0.563777	−	2.35277i	−0.0258407	−	0.107839i
$477$	−11.7865	−	11.7865i	−0.539665	−	0.539665i
$478$	1.77860	−	0.645115i	0.0813513	−	0.0295069i
$479$	−9.52909			−0.435395			−0.217698	−	0.976016i	$-0.569855\pi$
$479$	−9.52909			−0.435395			−0.217698	+	0.976016i	$0.569855\pi$
$480$	10.3885	+	11.1288i	0.474166	+	0.507958i
$481$		−	18.6892i		−	0.852156i
$482$	−36.7406	+	13.3262i	−1.67349	+	0.606990i
$483$	−23.9131	+	8.04903i	−1.08808	+	0.366244i
$484$	−7.20049	+	6.01464i	−0.327295	+	0.273393i
$485$	2.05497	+	3.12263i	0.0933115	+	0.141791i
$486$	−8.44756	+	18.0633i	−0.383189	+	0.819368i
$487$	−20.9631	+	20.9631i	−0.949928	+	0.949928i	−0.998805	−	0.0488768i	$-0.984436\pi$
$487$	−20.9631	+	20.9631i	−0.949928	+	0.949928i	0.0488768	+	0.998805i	$0.484436\pi$
$488$	28.6539	+	16.6713i	1.29710	+	0.754674i
$489$	−6.43663			−0.291074
$490$	−15.7859	−	15.5179i	−0.713136	−	0.701026i
$491$			14.3399i			0.647149i	0.946203	+	0.323575i	$0.104885\pi$
$491$			14.3399i			0.647149i	−0.946203	+	0.323575i	$0.895115\pi$
$492$	0.303296	−	3.37994i	0.0136736	−	0.152379i
$493$	−0.802043	−	0.802043i	−0.0361222	−	0.0361222i
$494$	−1.54310	−	0.721654i	−0.0694274	−	0.0324687i
$495$	8.53406	+	1.75978i	0.383577	+	0.0790962i
$496$	28.2793	+	5.11644i	1.26978	+	0.229735i
$497$	0.820651	+	2.43810i	0.0368112	+	0.109364i
$498$	−20.7658	+	7.53196i	−0.930540	+	0.337515i
$499$	−18.4667			−0.826681			−0.413340	−	0.910577i	$-0.635638\pi$
$499$	−18.4667			−0.826681			−0.413340	+	0.910577i	$0.635638\pi$
$500$	22.2784	−	1.91697i	0.996318	−	0.0857295i
$501$		−	8.60536i		−	0.384459i
$502$	2.74532	+	7.56892i	0.122529	+	0.337817i
$503$	−18.4374	+	18.4374i	−0.822085	+	0.822085i	−0.986407	−	0.164322i	$-0.947456\pi$
$503$	−18.4374	+	18.4374i	−0.822085	+	0.822085i	0.164322	+	0.986407i	$0.447456\pi$
$504$	−11.3732	−	2.33221i	−0.506603	−	0.103885i
$505$	−0.292610	−	0.0603382i	−0.0130210	−	0.00268502i
$506$	25.4957	+	11.9235i	1.13342	+	0.530062i
$507$	3.86767	−	3.86767i	0.171769	−	0.171769i
$508$	0.696373	−	7.76040i	0.0308965	−	0.344312i
$509$			2.89831i			0.128465i	0.997935	+	0.0642326i	$0.0204600\pi$
$509$			2.89831i			0.128465i	−0.997935	+	0.0642326i	$0.979540\pi$
$510$	1.72201	−	0.250745i	0.0762520	−	0.0111032i
$511$	−35.1908	−	17.4666i	−1.55675	−	0.772677i
$512$	−0.226853	+	22.6263i	−0.0100256	+	0.999950i
$513$	1.60459	+	1.60459i	0.0708445	+	0.0708445i
$514$	17.8823	−	38.2374i	0.788753	−	1.68658i
$515$	−35.0787	+	23.0849i	−1.54575	+	1.01724i
$516$	10.7330	−	8.96536i	0.472493	−	0.394678i
$517$	−14.6906	+	14.6906i	−0.646093	+	0.646093i
$518$	−23.8958	−	2.70605i	−1.04992	−	0.118897i
$519$			27.0781i			1.18860i
$520$	1.01283	+	18.3627i	0.0444157	+	0.805260i
$521$		−	9.89476i		−	0.433497i	−0.976227	−	0.216749i	$-0.930455\pi$
$521$		−	9.89476i		−	0.433497i	0.976227	−	0.216749i	$-0.0695452\pi$
$522$	−5.11681	+	1.85592i	−0.223957	+	0.0812312i
$523$	3.93390	+	3.93390i	0.172018	+	0.172018i	0.787865	−	0.615848i	$-0.211186\pi$
$523$	3.93390	+	3.93390i	0.172018	+	0.172018i	−0.615848	+	0.787865i	$0.711186\pi$
$524$	−6.36419	+	5.31607i	−0.278021	+	0.232234i
$525$	12.1429	−	10.2980i	0.529961	−	0.449440i
$526$	4.60774	−	9.85266i	0.200907	−	0.429596i
$527$	2.32280	−	2.32280i	0.101183	−	0.101183i
$528$	−6.89164	−	9.93622i	−0.299920	−	0.432419i
$529$			39.7838i			1.72973i
$530$	27.2353	+	20.3118i	1.18302	+	0.882290i
$531$	1.92943			0.0837303
$532$	−1.14612	+	1.86850i	−0.0496908	+	0.0810097i
$533$	2.89870	−	2.89870i	0.125557	−	0.125557i
$534$	7.25138	−	15.5055i	0.313798	−	0.670989i
$535$	15.5342	+	23.6050i	0.671603	+	1.02053i
$536$	2.97353	+	11.2476i	0.128437	+	0.485821i
$537$	−1.63414	−	1.63414i	−0.0705183	−	0.0705183i
$538$	−9.39898	+	3.40910i	−0.405219	+	0.146977i
$539$	10.6317	+	14.0038i	0.457941	+	0.603186i
$540$	7.07218	−	23.4551i	0.304338	−	1.00935i
$541$			14.7951i			0.636092i	0.948075	+	0.318046i	$0.103027\pi$
$541$			14.7951i			0.636092i	−0.948075	+	0.318046i	$0.896973\pi$
$542$	−25.8971	+	9.39310i	−1.11237	+	0.403468i
$543$	7.59341	+	7.59341i	0.325864	+	0.325864i
$544$	2.11037	+	1.49529i	0.0904815	+	0.0641098i
$545$	37.5812	+	7.74950i	1.60980	+	0.331952i
$546$	8.15873	+	10.2426i	0.349161	+	0.438341i
$547$	22.6498	+	22.6498i	0.968434	+	0.968434i	0.999517	−	0.0310824i	$-0.00989542\pi$
$547$	22.6498	+	22.6498i	0.968434	+	0.968434i	−0.0310824	+	0.999517i	$0.509895\pi$
$548$	2.15564	−	24.0225i	0.0920843	−	1.02619i
$549$		−	18.1838i		−	0.776064i
$550$	−17.7302	−	1.04304i	−0.756019	−	0.0444754i
$551$			1.02767i			0.0437800i
$552$	13.5647	−	23.3145i	0.577354	−	0.992333i
$553$	14.5644	−	4.90229i	0.619340	−	0.208466i
$554$	13.1119	−	28.0371i	0.557073	−	1.19118i
$555$	3.49332	−	16.9409i	0.148283	−	0.719100i
$556$	7.69098	+	9.20733i	0.326170	+	0.390478i
$557$	12.9631	+	12.9631i	0.549263	+	0.549263i	0.926228	−	0.376965i	$-0.123032\pi$
$557$	12.9631	+	12.9631i	0.549263	+	0.549263i	−0.376965	+	0.926228i	$0.623032\pi$
$558$	−5.37492	−	14.8188i	−0.227539	−	0.627331i
$559$	16.8937			0.714526
$560$	23.6250	+	1.36378i	0.998338	+	0.0576302i
$561$	−1.38220			−0.0583566
$562$	9.84327	+	27.1382i	0.415213	+	1.14476i
$563$	16.6820	+	16.6820i	0.703064	+	0.703064i	0.965067	−	0.262003i	$-0.0843830\pi$
$563$	16.6820	+	16.6820i	0.703064	+	0.703064i	−0.262003	+	0.965067i	$0.584383\pi$
$564$	12.7640	+	15.2805i	0.537461	+	0.643427i
$565$	−5.70854	−	8.67440i	−0.240160	−	0.364935i
$566$	−4.20508	+	8.99166i	−0.176753	+	0.377948i
$567$	−1.63633	−	4.86142i	−0.0687194	−	0.204161i
$568$	−2.37707	−	1.38302i	−0.0997397	−	0.0580300i
$569$			21.6112i			0.905989i	0.891513	+	0.452994i	$0.149644\pi$
$569$			21.6112i			0.905989i	−0.891513	+	0.452994i	$0.850356\pi$
$570$	−1.26386	−	0.942574i	−0.0529371	−	0.0394801i
$571$		−	22.2231i		−	0.930008i	−0.885309	−	0.465004i	$-0.846053\pi$
$571$		−	22.2231i		−	0.930008i	0.885309	−	0.465004i	$-0.153947\pi$
$572$	1.30555	−	14.5491i	0.0545877	−	0.608327i
$573$	22.0095	+	22.0095i	0.919462	+	0.919462i
$574$	−3.28653	−	4.12594i	−0.137177	−	0.172214i
$575$	−14.6468	−	36.8112i	−0.610813	−	1.53513i
$576$	10.7899	−	6.13376i	0.449579	−	0.255573i
$577$	14.1964	+	14.1964i	0.591003	+	0.591003i	0.937902	−	0.346900i	$-0.112766\pi$
$577$	14.1964	+	14.1964i	0.591003	+	0.591003i	−0.346900	+	0.937902i	$0.612766\pi$
$578$	−22.3230	+	8.09675i	−0.928513	+	0.336780i
$579$		−	6.65981i		−	0.276772i
$580$	9.77563	−	5.24624i	0.405911	−	0.217838i
$581$	−15.2655	+	30.7562i	−0.633321	+	1.27598i
$582$	−2.67495	+	0.970231i	−0.110880	+	0.0402174i
$583$	−19.0822	−	19.0822i	−0.790305	−	0.790305i
$584$	40.6047	−	10.7347i	1.68023	−	0.444204i
$585$	8.42656	−	5.54544i	0.348395	−	0.229276i
$586$	−6.90674	+	14.7686i	−0.285315	+	0.610084i
$587$	−4.98042	+	4.98042i	−0.205564	+	0.205564i	−0.802379	−	0.596815i	$-0.796433\pi$
$587$	−4.98042	+	4.98042i	−0.205564	+	0.205564i	0.596815	+	0.802379i	$0.296433\pi$
$588$	14.2773	−	8.94859i	0.588786	−	0.369034i
$589$	−2.97623			−0.122633
$590$	−3.89171	+	0.566678i	−0.160219	+	0.0233298i
$591$			19.3978i			0.797920i
$592$	21.1250	−	14.6521i	0.868234	−	0.602196i
$593$	−21.3875	+	21.3875i	−0.878280	+	0.878280i	−0.993357	−	0.115077i	$-0.963289\pi$
$593$	−21.3875	+	21.3875i	−0.878280	+	0.878280i	0.115077	+	0.993357i	$0.463289\pi$
$594$	−8.24320	+	17.6263i	−0.338223	+	0.723216i
$595$	1.66713	−	2.13011i	0.0683457	−	0.0873260i
$596$	−8.58063	+	7.16748i	−0.351476	+	0.293592i
$597$	1.97660	+	1.97660i	0.0808967	+	0.0808967i
$598$	30.6314	−	11.1103i	1.25261	−	0.454334i
$599$		−	16.9265i		−	0.691599i	−0.938308	−	0.345799i	$-0.887608\pi$
$599$		−	16.9265i		−	0.691599i	0.938308	−	0.345799i	$-0.112392\pi$
$600$	−2.51421	+	16.8342i	−0.102642	+	0.687255i
$601$			2.76188i			0.112659i	0.998412	+	0.0563297i	$0.0179398\pi$
$601$			2.76188i			0.112659i	−0.998412	+	0.0563297i	$0.982060\pi$
$602$	2.44607	−	21.6000i	0.0996942	−	0.880351i
$603$	4.51234	−	4.51234i	0.183757	−	0.183757i
$604$	−10.8319	+	9.04799i	−0.440743	+	0.368157i
$605$	−10.2733	−	2.11843i	−0.417670	−	0.0861263i
$606$	0.0963420	−	0.206007i	0.00391362	−	0.00836844i
$607$	−5.52065	−	5.52065i	−0.224076	−	0.224076i	0.586136	−	0.810213i	$-0.300648\pi$
$607$	−5.52065	−	5.52065i	−0.224076	−	0.224076i	−0.810213	+	0.586136i	$0.800648\pi$
$608$	−0.394059	−	2.30998i	−0.0159812	−	0.0936821i
$609$	3.51209	−	7.07598i	0.142317	−	0.286733i
$610$	5.34061	+	36.6770i	0.216235	+	1.48501i
$611$			24.0516i			0.973022i
$612$	0.126795	−	1.41301i	0.00512540	−	0.0571176i
$613$	16.4031	−	16.4031i	0.662513	−	0.662513i	−0.293459	−	0.955972i	$-0.594806\pi$
$613$	16.4031	−	16.4031i	0.662513	−	0.662513i	0.955972	+	0.293459i	$0.0948063\pi$
$614$	−19.5954	−	9.16407i	−0.790806	−	0.369832i
$615$	3.16934	−	2.08572i	0.127800	−	0.0841042i
$616$	−18.4132	−	3.77584i	−0.741888	−	0.152133i
$617$	−24.2013	+	24.2013i	−0.974306	+	0.974306i	−0.999678	−	0.0253716i	$-0.991923\pi$
$617$	−24.2013	+	24.2013i	−0.974306	+	0.974306i	0.0253716	+	0.999678i	$0.491923\pi$
$618$	−10.8993	−	30.0496i	−0.438433	−	1.20877i
$619$		−	18.2586i		−	0.733873i	−0.930246	−	0.366937i	$-0.880407\pi$
$619$		−	18.2586i		−	0.733873i	0.930246	−	0.366937i	$-0.119593\pi$
$620$	15.1936	+	28.3112i	0.610192	+	1.13701i
$621$	−43.4051			−1.74179
$622$	32.6460	−	11.8410i	1.30899	−	0.474781i
$623$	−8.48796	−	25.2171i	−0.340063	−	1.01030i
$624$	−13.7753	−	2.49230i	−0.551454	−	0.0997719i
$625$	17.1753	+	18.1661i	0.687014	+	0.726645i
$626$	27.1952	+	12.7182i	1.08694	+	0.508323i
$627$	0.885515	+	0.885515i	0.0353640	+	0.0353640i
$628$	3.21922	−	35.8751i	0.128461	−	1.43157i
$629$		−	2.93865i		−	0.117172i
$630$	−5.87022	−	11.5770i	−0.233875	−	0.461239i
$631$	17.6351			0.702041			0.351021	−	0.936368i	$-0.385835\pi$
$631$	17.6351			0.702041			0.351021	+	0.936368i	$0.385835\pi$
$632$	−8.26165	+	14.1998i	−0.328631	+	0.564838i
$633$	5.58276	−	5.58276i	0.221895	−	0.221895i
$634$	−15.4589	+	33.0555i	−0.613951	+	1.31280i
$635$	7.27688	−	4.78884i	0.288774	−	0.190039i
$636$	−19.8485	+	16.5797i	−0.787045	+	0.657426i
$637$	20.1667	+	2.76037i	0.799033	+	0.109370i
$638$	−8.28410	+	3.00472i	−0.327970	+	0.118958i
$639$			1.50849i			0.0596748i
$640$	−19.9619	+	15.5409i	−0.789065	+	0.614309i
$641$	21.4669			0.847892			0.423946	−	0.905688i	$-0.360645\pi$
$641$	21.4669			0.847892			0.423946	+	0.905688i	$0.360645\pi$
$642$	−20.2209	+	7.33430i	−0.798055	+	0.289462i
$643$	25.8525	+	25.8525i	1.01952	+	1.01952i	0.999806	+	0.0197188i	$0.00627711\pi$
$643$	25.8525	+	25.8525i	1.01952	+	1.01952i	0.0197188	+	0.999806i	$0.493723\pi$
$644$	−9.77029	−	40.7736i	−0.385004	−	1.60670i
$645$	15.3133	+	3.15770i	0.602960	+	0.124334i
$646$	−0.242634	−	0.113471i	−0.00954629	−	0.00446446i
$647$	−4.65011	−	4.65011i	−0.182815	−	0.182815i	0.609766	−	0.792581i	$-0.291263\pi$
$647$	−4.65011	−	4.65011i	−0.182815	−	0.182815i	−0.792581	+	0.609766i	$0.791263\pi$
$648$	4.73974	+	2.75765i	0.186194	+	0.108331i
$649$	3.12374			0.122618
$650$	−15.3678	+	13.6602i	−0.602776	+	0.535796i
$651$	20.4928	+	10.1714i	0.803175	+	0.398648i
$652$	0.955951	−	10.6532i	0.0374379	−	0.417210i
$653$	−15.5113	+	15.5113i	−0.607003	+	0.607003i	−0.942162	−	0.335159i	$-0.891210\pi$
$653$	−15.5113	+	15.5113i	−0.607003	+	0.607003i	0.335159	+	0.942162i	$0.391210\pi$
$654$	−12.3736	+	26.4583i	−0.483847	+	1.03460i
$655$	−9.08012	−	1.87238i	−0.354789	−	0.0731599i
$656$	5.54903	+	1.00396i	0.216653	+	0.0391980i
$657$	−16.2899	−	16.2899i	−0.635531	−	0.635531i
$658$	30.7520	+	3.48247i	1.19884	+	0.135761i
$659$	−16.0797			−0.626376			−0.313188	−	0.949691i	$-0.601397\pi$
$659$	−16.0797			−0.626376			−0.313188	+	0.949691i	$0.601397\pi$
$660$	3.90287	−	12.9440i	0.151919	−	0.503844i
$661$	−31.7560			−1.23517			−0.617583	−	0.786505i	$-0.711888\pi$
$661$	−31.7560			−1.23517			−0.617583	+	0.786505i	$0.711888\pi$
$662$	33.2676	−	12.0665i	1.29298	−	0.468977i
$663$	−1.13147	+	1.13147i	−0.0439428	+	0.0439428i
$664$	−9.38193	−	35.4878i	−0.364090	−	1.37719i
$665$	−2.43272	+	0.296611i	−0.0943369	+	0.0115021i
$666$	−12.7739	−	5.97389i	−0.494978	−	0.231484i
$667$	−13.8995	−	13.8995i	−0.538189	−	0.538189i
$668$	14.2426	+	1.27805i	0.551062	+	0.0494491i
$669$	−21.5022			−0.831325
$670$	−7.77621	+	10.4268i	−0.300421	+	0.402821i
$671$		−	29.4394i		−	1.13650i
$672$	−5.18118	+	17.2521i	−0.199868	+	0.665513i
$673$	25.3785	+	25.3785i	0.978269	+	0.978269i	0.999769	−	0.0215000i	$-0.00684418\pi$
$673$	25.3785	+	25.3785i	0.978269	+	0.978269i	−0.0215000	+	0.999769i	$0.506844\pi$
$674$	−23.0535	−	10.7813i	−0.887986	−	0.415280i
$675$	25.4492	−	10.1260i	0.979539	−	0.389748i
$676$	5.82689	+	6.97572i	0.224111	+	0.268297i
$677$	33.3281	−	33.3281i	1.28090	−	1.28090i	0.340751	−	0.940154i	$-0.389319\pi$
$677$	33.3281	−	33.3281i	1.28090	−	1.28090i	0.940154	−	0.340751i	$-0.110681\pi$
$678$	7.43080	−	2.69522i	0.285378	−	0.103509i
$679$	−1.96643	+	3.96186i	−0.0754647	+	0.152042i
$680$	0.159256	+	2.88731i	0.00610717	+	0.110723i
$681$	25.4771			0.976285
$682$	−8.70197	−	23.9916i	−0.333216	−	0.918686i
$683$	−3.99641	+	3.99641i	−0.152918	+	0.152918i	−0.779420	−	0.626502i	$-0.784486\pi$
$683$	−3.99641	+	3.99641i	−0.152918	+	0.152918i	0.626502	+	0.779420i	$0.284486\pi$
$684$	−0.986485	+	0.824020i	−0.0377192	+	0.0315072i
$685$	22.5257	−	14.8240i	0.860664	−	0.566395i
$686$	6.44934	−	25.3852i	0.246237	−	0.969210i
$687$	5.11600	−	5.11600i	0.195188	−	0.195188i
$688$	13.2444	+	19.0955i	0.504937	+	0.728008i
$689$	−31.2415			−1.19021
$690$	29.8426	−	4.34543i	1.13609	−	0.165428i
$691$	−37.9666			−1.44432			−0.722158	−	0.691728i	$-0.756850\pi$
$691$	−37.9666			−1.44432			−0.722158	+	0.691728i	$0.756850\pi$
$692$	−44.8164	−	4.02156i	−1.70367	−	0.152877i
$693$	3.28900	+	9.77140i	0.124939	+	0.371185i
$694$	−7.12361	+	15.2323i	−0.270408	+	0.578210i
$695$	−2.70885	+	13.1366i	−0.102753	+	0.498299i
$696$	2.15847	+	8.16457i	0.0818166	+	0.309477i
$697$	0.455785	−	0.455785i	0.0172641	−	0.0172641i
$698$	35.4233	−	12.8484i	1.34079	−	0.486318i
$699$		−	21.5119i		−	0.813655i
$700$	15.2405	+	21.6270i	0.576039	+	0.817423i
$701$		−	35.0204i		−	1.32270i	−0.750077	−	0.661350i	$-0.769984\pi$
$701$		−	35.0204i		−	1.32270i	0.750077	−	0.661350i	$-0.230016\pi$
$702$	7.68103	+	21.1768i	0.289902	+	0.799268i
$703$	−1.88266	+	1.88266i	−0.0710059	+	0.0710059i
$704$	17.4688	−	9.93053i	0.658380	−	0.374271i
$705$	−4.49562	+	21.8015i	−0.169315	+	0.821094i
$706$	−5.11906	−	2.39400i	−0.192658	−	0.0900994i
$707$	−0.112771	−	0.335036i	−0.00424120	−	0.0126003i
$708$	0.267554	−	2.98163i	0.0100553	−	0.112056i
$709$	36.6280			1.37559			0.687797	−	0.725903i	$-0.258578\pi$
$709$	36.6280			1.37559			0.687797	+	0.725903i	$0.258578\pi$
$710$	−0.443046	−	3.04265i	−0.0166272	−	0.114189i
$711$	9.01118			0.337945
$712$	24.5859	+	14.3045i	0.921397	+	0.536082i
$713$	40.2543	−	40.2543i	1.50753	−	1.50753i
$714$	1.28286	+	1.61051i	0.0480098	+	0.0602720i
$715$	13.6426	−	8.97804i	0.510203	−	0.335760i
$716$	2.94733	−	2.46194i	0.110147	−	0.0920068i
$717$	−1.13856	+	1.13856i	−0.0425203	+	0.0425203i
$718$	−33.1568	+	12.0263i	−1.23740	+	0.448816i
$719$	−35.7912			−1.33478			−0.667392	−	0.744706i	$-0.732590\pi$
$719$	−35.7912			−1.33478			−0.667392	+	0.744706i	$0.732590\pi$
$720$	12.8745	+	5.17727i	0.479803	+	0.192945i
$721$	−44.5064	−	22.0903i	−1.65750	−	0.822685i
$722$	−9.07922	−	25.0317i	−0.337894	−	0.931583i
$723$	23.5193	−	23.5193i	0.874691	−	0.874691i
$724$	−13.6955	+	11.4400i	−0.508988	+	0.425163i
$725$	11.3921	+	4.90690i	0.423092	+	0.182238i
$726$	3.38249	−	7.23272i	0.125536	−	0.268432i
$727$	17.9668	+	17.9668i	0.666353	+	0.666353i	0.956870	−	0.290517i	$-0.0938272\pi$
$727$	17.9668	+	17.9668i	0.666353	+	0.666353i	−0.290517	+	0.956870i	$0.593827\pi$
$728$	−18.1640	+	11.9822i	−0.673202	+	0.444089i
$729$		−	22.7870i		−	0.843962i
$730$	37.6415	+	28.0728i	1.39318	+	1.03902i
$731$	2.65632			0.0982476
$732$	−28.1001	−	2.52153i	−1.03861	−	0.0931986i
$733$	−14.2478	−	14.2478i	−0.526254	−	0.526254i	0.393199	−	0.919453i	$-0.371368\pi$
$733$	−14.2478	−	14.2478i	−0.526254	−	0.526254i	−0.919453	+	0.393199i	$0.871368\pi$
$734$	14.4200	−	30.8341i	0.532253	−	1.13811i
$735$	17.7642	+	6.27162i	0.655241	+	0.231332i
$736$	36.5729	+	25.9134i	1.34809	+	0.955180i
$737$	7.30546	−	7.30546i	0.269100	−	0.269100i
$738$	−1.05468	−	2.90778i	−0.0388232	−	0.107037i
$739$	27.1860			1.00005			0.500027	−	0.866010i	$-0.333323\pi$
$739$	27.1860			1.00005			0.500027	+	0.866010i	$0.333323\pi$
$740$	27.5197	+	8.29775i	1.01165	+	0.305031i
$741$	1.44977			0.0532586
$742$	−4.52352	+	39.9450i	−0.166064	+	1.46643i
$743$	4.15036	+	4.15036i	0.152262	+	0.152262i	0.779127	−	0.626866i	$-0.215662\pi$
$743$	4.15036	+	4.15036i	0.152262	+	0.152262i	−0.626866	+	0.779127i	$0.715662\pi$
$744$	−23.6454	+	6.25116i	−0.866884	+	0.229179i
$745$	−12.2424	−	2.52447i	−0.448528	−	0.0924894i
$746$	−26.6738	−	12.4744i	−0.976596	−	0.456719i
$747$	−14.2371	+	14.2371i	−0.520910	+	0.520910i
$748$	0.205281	−	2.28766i	0.00750582	−	0.0836451i
$749$	−14.8649	+	29.9491i	−0.543152	+	1.09431i
$750$	−16.4835	+	9.50977i	−0.601892	+	0.347248i
$751$	−5.39262			−0.196779			−0.0983897	−	0.995148i	$-0.531369\pi$
$751$	−5.39262			−0.196779			−0.0983897	+	0.995148i	$0.531369\pi$
$752$	−27.1862	+	18.8560i	−0.991380	+	0.687609i
$753$	−4.84519	−	4.84519i	−0.176569	−	0.176569i
$754$	−4.32171	+	9.24105i	−0.157387	+	0.336539i
$755$	−15.4544	−	3.18681i	−0.562444	−	0.115980i
$756$	28.1885	−	6.75463i	1.02521	−	0.245663i
$757$	−34.4647	−	34.4647i	−1.25264	−	1.25264i	−0.954532	−	0.298108i	$-0.903644\pi$
$757$	−34.4647	−	34.4647i	−1.25264	−	1.25264i	−0.298108	−	0.954532i	$-0.596356\pi$
$758$	5.54216	+	15.2799i	0.201300	+	0.554991i
$759$	−23.9537			−0.869463
$760$	1.74774	−	1.95180i	0.0633973	−	0.0707992i
$761$			46.5220i			1.68642i	0.537583	+	0.843211i	$0.319337\pi$
$761$			46.5220i			1.68642i	−0.537583	+	0.843211i	$0.680663\pi$
$762$	2.26100	+	6.23363i	0.0819072	+	0.225821i
$763$	14.4837	+	43.0301i	0.524345	+	1.55779i
$764$	−39.6964	+	33.1588i	−1.43616	+	1.19964i
$765$	1.32497	−	0.871951i	0.0479044	−	0.0315255i
$766$	−11.7546	−	5.49722i	−0.424712	−	0.198623i
$767$	2.55710	−	2.55710i	0.0923316	−	0.0923316i
$768$	−7.98251	−	17.5246i	−0.288044	−	0.632365i
$769$	−21.4981			−0.775240			−0.387620	−	0.921819i	$-0.626703\pi$
$769$	−21.4981			−0.775240			−0.387620	+	0.921819i	$0.626703\pi$
$770$	−9.50386	−	18.7431i	−0.342495	−	0.675455i
$771$			35.9246i			1.29379i
$772$	11.0225	+	0.989097i	0.396710	+	0.0355984i
$773$	12.2376	+	12.2376i	0.440157	+	0.440157i	0.892065	−	0.451907i	$-0.149256\pi$
$773$	12.2376	+	12.2376i	0.440157	+	0.440157i	−0.451907	+	0.892065i	$0.649256\pi$
$774$	5.39995	−	11.5466i	0.194097	−	0.415035i
$775$	−14.2109	+	32.9927i	−0.510470	+	1.18513i
$776$	−1.20853	−	4.57137i	−0.0433839	−	0.164102i
$777$	19.3971	−	6.52897i	0.695868	−	0.234225i
$778$	−3.23360	−	8.91512i	−0.115930	−	0.319622i
$779$	−0.584001			−0.0209240
$780$	−7.40107	−	13.7909i	−0.265001	−	0.493792i
$781$			2.44223i			0.0873899i
$782$	4.81641	−	1.74696i	0.172235	−	0.0624711i
$783$	9.60930	−	9.60930i	0.343408	−	0.343408i
$784$	12.6902	+	24.9591i	0.453222	+	0.891397i
$785$	33.6398	−	22.1381i	1.20066	−	0.790141i
$786$	2.98963	−	6.39267i	0.106636	−	0.228019i
$787$	−31.2056	+	31.2056i	−1.11236	+	1.11236i	−0.119529	+	0.992831i	$0.538138\pi$
$787$	−31.2056	+	31.2056i	−1.11236	+	1.11236i	−0.992831	+	0.119529i	$0.961862\pi$
$788$	−32.1050	−	2.88091i	−1.14369	−	0.102628i
$789$			9.25673i			0.329548i
$790$	−18.1757	+	2.64660i	−0.646663	+	0.0941618i
$791$	5.46258	−	11.0057i	0.194227	−	0.391318i
$792$	−9.52681	−	5.54284i	−0.338520	−	0.196956i
$793$	−24.0992	−	24.0992i	−0.855787	−	0.855787i
$794$	9.77385	+	4.57088i	0.346861	+	0.162215i
$795$	−28.3189	−	5.83955i	−1.00437	−	0.207107i
$796$	−3.56499	+	2.97787i	−0.126358	+	0.105548i
$797$	14.3254	−	14.3254i	0.507431	−	0.507431i	−0.406306	−	0.913737i	$-0.633183\pi$
$797$	14.3254	−	14.3254i	0.507431	−	0.507431i	0.913737	+	0.406306i	$0.133183\pi$
$798$	0.209915	−	1.85365i	0.00743090	−	0.0656186i
$799$			3.78181i			0.133791i
$800$	−27.4886	−	6.66140i	−0.971870	−	0.235516i
$801$		−	15.6022i		−	0.551277i
$802$	2.75872	+	7.60587i	0.0974138	+	0.268573i
$803$	−26.3733	−	26.3733i	−0.930695	−	0.930695i
$804$	−6.34738	−	7.59883i	−0.223855	−	0.267990i
$805$	28.8915	−	36.9150i	1.01829	−	1.30108i
$806$	−26.7630	−	12.5161i	−0.942688	−	0.440862i
$807$	6.01670	−	6.01670i	0.211798	−	0.211798i
$808$	0.326649	+	0.190049i	0.0114915	+	0.00668591i
$809$		−	26.5709i		−	0.934183i	−0.884209	−	0.467091i	$-0.845302\pi$
$809$		−	26.5709i		−	0.934183i	0.884209	−	0.467091i	$-0.154698\pi$
$810$	0.883406	+	6.06686i	0.0310397	+	0.213168i
$811$	−5.10317			−0.179197			−0.0895983	−	0.995978i	$-0.528558\pi$
$811$	−5.10317			−0.179197			−0.0895983	+	0.995978i	$0.528558\pi$
$812$	11.1897	+	6.86371i	0.392682	+	0.240869i
$813$	16.5778	−	16.5778i	0.581410	−	0.581410i
$814$	−20.6809	−	9.67170i	−0.724864	−	0.338993i
$815$	9.98939	−	6.57392i	0.349913	−	0.230275i
$816$	−2.16600	−	0.391883i	−0.0758251	−	0.0137187i
$817$	−1.70178	−	1.70178i	−0.0595379	−	0.0595379i
$818$	−10.1521	−	27.9895i	−0.354959	−	0.978631i
$819$	10.6913	+	5.30650i	0.373583	+	0.185424i
$820$	2.98133	+	5.55529i	0.104113	+	0.193999i
$821$			24.8927i			0.868760i	0.900730	+	0.434380i	$0.143033\pi$
$821$			24.8927i			0.868760i	−0.900730	+	0.434380i	$0.856967\pi$
$822$	6.99897	+	19.2964i	0.244117	+	0.673038i
$823$	−8.95105	−	8.95105i	−0.312014	−	0.312014i	0.533675	−	0.845689i	$-0.320810\pi$
$823$	−8.95105	−	8.95105i	−0.312014	−	0.312014i	−0.845689	+	0.533675i	$0.820810\pi$
$824$	51.3534	−	13.5763i	1.78898	−	0.472953i
$825$	14.0444	−	5.58814i	0.488965	−	0.194554i
$826$	−2.89923	−	3.63972i	−0.100877	−	0.126642i
$827$	5.03438	+	5.03438i	0.175063	+	0.175063i	0.789200	−	0.614137i	$-0.210496\pi$
$827$	5.03438	+	5.03438i	0.175063	+	0.175063i	−0.614137	+	0.789200i	$0.710496\pi$
$828$	2.19737	−	24.4876i	0.0763639	−	0.851002i
$829$			15.1494i			0.526161i	0.964774	+	0.263081i	$0.0847385\pi$
$829$			15.1494i			0.526161i	−0.964774	+	0.263081i	$0.915261\pi$
$830$	24.5351	−	32.8981i	0.851627	−	1.14191i
$831$			26.3413i			0.913769i
$832$	6.17084	−	22.4291i	0.213935	−	0.777591i
$833$	3.17096	+	0.434034i	0.109867	+	0.0150384i
$834$	−9.24855	−	4.32522i	−0.320251	−	0.149770i
$835$	8.78892	+	13.3552i	0.304153	+	0.462175i
$836$	−1.59711	+	1.33409i	−0.0552373	+	0.0461403i
$837$	27.8295	+	27.8295i	0.961929	+	0.961929i
$838$	47.7504	−	17.3195i	1.64951	−	0.598292i
$839$	−20.9224			−0.722320			−0.361160	−	0.932504i	$-0.617619\pi$
$839$	−20.9224			−0.722320			−0.361160	+	0.932504i	$0.617619\pi$
$840$	−18.7044	+	7.46610i	−0.645364	+	0.257605i
$841$	−22.8457			−0.787783
$842$	−24.9919	+	9.06479i	−0.861278	+	0.312393i
$843$	−17.3723	−	17.3723i	−0.598335	−	0.598335i
$844$	8.41080	+	10.0691i	0.289512	+	0.346592i
$845$	−2.05230	+	9.95263i	−0.0706012	+	0.342381i
$846$	16.4390	+	7.68792i	0.565183	+	0.264316i
$847$	−3.95931	−	11.7628i	−0.136043	−	0.404176i
$848$	−24.4929	−	35.3133i	−0.841088	−	1.21266i
$849$		−	8.44781i		−	0.289928i
$850$	−2.41640	+	2.14789i	−0.0828818	+	0.0736720i
$851$		−	50.9270i		−	1.74576i
$852$	2.33112	+	0.209181i	0.0798629	+	0.00716643i
$853$	−9.15082	−	9.15082i	−0.313318	−	0.313318i	0.532876	−	0.846194i	$-0.321111\pi$
$853$	−9.15082	−	9.15082i	−0.313318	−	0.313318i	−0.846194	+	0.532876i	$0.821111\pi$
$854$	−34.3022	+	27.3235i	−1.17380	+	0.934991i
$855$	−1.40747	−	0.290229i	−0.0481344	−	0.00992564i
$856$	−9.13572	−	34.5565i	−0.312253	−	1.18112i
$857$	−14.9046	−	14.9046i	−0.509131	−	0.509131i	0.405128	−	0.914260i	$-0.367227\pi$
$857$	−14.9046	−	14.9046i	−0.509131	−	0.509131i	−0.914260	+	0.405128i	$0.867227\pi$
$858$	4.23887	+	11.6867i	0.144713	+	0.398977i
$859$		−	27.4269i		−	0.935793i	−0.883783	−	0.467897i	$-0.845012\pi$
$859$		−	27.4269i		−	0.935793i	0.883783	−	0.467897i	$-0.154988\pi$
$860$	−7.50054	+	24.8758i	−0.255766	+	0.848257i
$861$	4.02113	+	1.99585i	0.137040	+	0.0680184i
$862$	−3.31616	−	9.14275i	−0.112949	−	0.311403i
$863$	−7.01745	−	7.01745i	−0.238877	−	0.238877i	0.577508	−	0.816385i	$-0.304025\pi$
$863$	−7.01745	−	7.01745i	−0.238877	−	0.238877i	−0.816385	+	0.577508i	$0.804025\pi$
$864$	−17.9150	+	25.2844i	−0.609482	+	0.860193i
$865$	−27.6557	−	42.0241i	−0.940320	−	1.42886i
$866$	−5.03558	−	2.35496i	−0.171116	−	0.0800248i
$867$	14.2899	−	14.2899i	0.485310	−	0.485310i
$868$	−19.8780	+	32.4066i	−0.674703	+	1.09995i
$869$	14.5890			0.494900
$870$	−5.64472	+	7.56876i	−0.191374	+	0.256605i
$871$		−	11.9605i		−	0.405267i
$872$	−41.9530	−	24.4089i	−1.42071	−	0.826589i
$873$	−1.83396	+	1.83396i	−0.0620701	+	0.0620701i
$874$	−4.20485	−	1.96646i	−0.142231	−	0.0665165i
$875$	−8.32770	+	28.3840i	−0.281528	+	0.959553i
$876$	−27.4324	+	22.9146i	−0.926855	+	0.774211i
$877$	−26.0087	−	26.0087i	−0.878250	−	0.878250i	0.115104	−	0.993353i	$-0.463280\pi$
$877$	−26.0087	−	26.0087i	−0.878250	−	0.878250i	−0.993353	+	0.115104i	$0.963280\pi$
$878$	11.7492	+	32.3929i	0.396517	+	1.09321i
$879$		−	13.8753i		−	0.468003i
$880$	20.8437	+	8.38197i	0.702641	+	0.282556i
$881$			0.348598i			0.0117446i	0.999983	+	0.00587228i	$0.00186922\pi$
$881$			0.348598i			0.0117446i	−0.999983	+	0.00587228i	$0.998131\pi$
$882$	8.33283	−	12.9014i	0.280581	−	0.434412i
$883$	38.4627	−	38.4627i	1.29437	−	1.29437i	0.362319	−	0.932054i	$-0.381985\pi$
$883$	38.4627	−	38.4627i	1.29437	−	1.29437i	0.932054	−	0.362319i	$-0.118015\pi$
$884$	−1.70464	−	2.04073i	−0.0573332	−	0.0686370i
$885$	2.79585	−	1.83992i	0.0939815	−	0.0618484i
$886$	15.9446	+	7.45673i	0.535670	+	0.250514i
$887$	12.0426	+	12.0426i	0.404351	+	0.404351i	0.879763	−	0.475412i	$-0.157701\pi$
$887$	12.0426	+	12.0426i	0.404351	+	0.404351i	−0.475412	+	0.879763i	$0.657701\pi$
$888$	−11.0030	+	18.9116i	−0.369238	+	0.634631i
$889$	9.23260	+	4.58251i	0.309652	+	0.153692i
$890$	4.58240	+	31.4700i	0.153602	+	1.05488i
$891$		−	4.86967i		−	0.163140i
$892$	3.19346	−	35.5880i	0.106925	−	1.19157i
$893$	2.42283	−	2.42283i	0.0810770	−	0.0810770i
$894$	4.03082	−	8.61904i	0.134811	−	0.288264i
$895$	4.20511	+	0.867122i	0.140561	+	0.0289847i
$896$	−27.7841	−	11.1375i	−0.928202	−	0.372078i
$897$	−19.6085	+	19.6085i	−0.654709	+	0.654709i
$898$	26.9257	−	9.76618i	0.898521	−	0.325902i
$899$			17.8235i			0.594447i
$900$	4.42434	+	14.8701i	0.147478	+	0.495671i
$901$	−4.91234			−0.163654
$902$	−1.70752	−	4.70768i	−0.0568542	−	0.156749i
$903$	5.90170	+	17.5335i	0.196396	+	0.583480i
$904$	3.35721	+	12.6989i	0.111659	+	0.422358i
$905$	−19.5400	−	4.02929i	−0.649533	−	0.133938i
$906$	5.08837	−	10.8804i	0.169050	−	0.361476i
$907$	15.6043	+	15.6043i	0.518132	+	0.518132i	0.917006	−	0.398874i	$-0.130599\pi$
$907$	15.6043	+	15.6043i	0.518132	+	0.518132i	−0.398874	+	0.917006i	$0.630599\pi$
$908$	−3.78379	+	42.1667i	−0.125570	+	1.39935i
$909$		−	0.207291i		−	0.00687542i
$910$	−23.1230	−	7.56328i	−0.766521	−	0.250720i
$911$	27.1278			0.898784			0.449392	−	0.893335i	$-0.351641\pi$
$911$	27.1278			0.898784			0.449392	+	0.893335i	$0.351641\pi$
$912$	1.13660	+	1.63872i	0.0376364	+	0.0542634i
$913$	−23.0499	+	23.0499i	−0.762839	+	0.762839i
$914$	−5.11836	−	2.39367i	−0.169300	−	0.0791757i
$915$	−17.3402	−	26.3492i	−0.573249	−	0.871079i
$916$	7.70759	+	9.22722i	0.254666	+	0.304876i
$917$	−3.49945	−	10.3966i	−0.115562	−	0.343327i
$918$	1.20775	+	3.32979i	0.0398616	+	0.109900i
$919$			16.0238i			0.528576i	0.964444	+	0.264288i	$0.0851370\pi$
$919$			16.0238i			0.528576i	−0.964444	+	0.264288i	$0.914863\pi$
$920$	2.75991	+	50.0373i	0.0909915	+	1.64968i
$921$	18.4102			0.606636
$922$	2.04778	+	5.64580i	0.0674401	+	0.185934i
$923$	1.99922	+	1.99922i	0.0658050	+	0.0658050i
$924$	15.5562	−	3.72762i	0.511761	−	0.122630i
$925$	11.8807	+	29.8594i	0.390636	+	0.981771i
$926$	−6.69687	+	14.3198i	−0.220073	+	0.470578i
$927$	−20.6021	−	20.6021i	−0.676663	−	0.676663i
$928$	−13.8336	+	2.35987i	−0.454110	+	0.0774664i
$929$	−25.8081			−0.846735			−0.423367	−	0.905958i	$-0.639152\pi$
$929$	−25.8081			−0.846735			−0.423367	+	0.905958i	$0.639152\pi$
$930$	−21.9199	−	16.3477i	−0.718782	−	0.536062i
$931$	−1.75343	−	2.30956i	−0.0574662	−	0.0756927i
$932$	35.6040	+	3.19489i	1.16625	+	0.104652i
$933$	−20.8981	+	20.8981i	−0.684174	+	0.684174i
$934$	−9.84130	−	4.60243i	−0.322017	−	0.150596i
$935$	2.14512	−	1.41168i	0.0701530	−	0.0461670i
$936$	−12.3360	+	3.26129i	−0.403216	+	0.106599i
$937$	0.712338	+	0.712338i	0.0232711	+	0.0232711i	0.718647	−	0.695376i	$-0.244762\pi$
$937$	0.712338	+	0.712338i	0.0232711	+	0.0232711i	−0.695376	+	0.718647i	$0.744762\pi$
$938$	−15.2926	−	1.73179i	−0.499320	−	0.0565449i
$939$	−25.5503			−0.833804
$940$	−35.4157	−	10.6785i	−1.15513	−	0.348295i
$941$	19.4618			0.634436			0.317218	−	0.948353i	$-0.397251\pi$
$941$	19.4618			0.634436			0.317218	+	0.948353i	$0.397251\pi$
$942$	10.4522	+	28.8171i	0.340552	+	0.938911i
$943$	7.89878	−	7.89878i	0.257220	−	0.257220i
$944$	4.89510	+	0.885647i	0.159322	+	0.0288253i
$945$	25.5209	+	19.9739i	0.830195	+	0.649752i
$946$	8.74250	−	18.6939i	0.284243	−	0.607793i
$947$	−16.5040	−	16.5040i	−0.536309	−	0.536309i	0.386134	−	0.922443i	$-0.373810\pi$
$947$	−16.5040	−	16.5040i	−0.536309	−	0.536309i	−0.922443	+	0.386134i	$0.873810\pi$
$948$	1.24958	−	13.9253i	0.0405843	−	0.452273i
$949$	−43.1785			−1.40163
$950$	2.92413	+	0.172022i	0.0948714	+	0.00558114i
$951$		−	31.0562i		−	1.00707i
$952$	−2.85606	+	1.88405i	−0.0925655	+	0.0610623i
$953$	−15.0426	−	15.0426i	−0.487279	−	0.487279i	0.420168	−	0.907446i	$-0.361971\pi$
$953$	−15.0426	−	15.0426i	−0.487279	−	0.487279i	−0.907446	+	0.420168i	$0.861971\pi$
$954$	−9.98615	+	21.3532i	−0.323313	+	0.691336i
$955$	−56.6369	−	11.6789i	−1.83273	−	0.377921i
$956$	−1.71531	−	2.05351i	−0.0554772	−	0.0664151i
$957$	5.30301	−	5.30301i	0.171422	−	0.171422i
$958$	4.59501	+	12.6686i	0.148458	+	0.409303i
$959$	28.5797	+	14.1853i	0.922888	+	0.458066i
$960$	9.78593	−	19.1775i	0.315840	−	0.618951i
$961$	−20.6187			−0.665118
$962$	−24.8467	+	9.01212i	−0.801089	+	0.290562i
$963$	−13.8635	+	13.8635i	−0.446746	+	0.446746i
$964$	35.4333	+	42.4193i	1.14123	+	1.36624i
$965$	6.80186	+	10.3358i	0.218960	+	0.332720i
$966$	22.2320	+	27.9103i	0.715303	+	0.898000i
$967$	13.5634	−	13.5634i	0.436171	−	0.436171i	−0.454550	−	0.890721i	$-0.650200\pi$
$967$	13.5634	−	13.5634i	0.436171	−	0.436171i	0.890721	+	0.454550i	$0.150200\pi$
$968$	11.4684	+	6.67248i	0.368608	+	0.214462i
$969$	0.227958			0.00732307
$970$	3.16049	−	4.23777i	0.101477	−	0.136067i
$971$	56.7239			1.82036			0.910178	−	0.414217i	$-0.135945\pi$
$971$	56.7239			1.82036			0.910178	+	0.414217i	$0.135945\pi$
$972$	28.0880	+	2.52045i	0.900923	+	0.0808435i
$973$	−15.0412	+	5.06280i	−0.482200	+	0.162306i
$974$	37.9782	+	17.7611i	1.21690	+	0.569102i
$975$	6.92236	−	16.0713i	0.221693	−	0.514693i
$976$	8.34669	−	46.1334i	0.267171	−	1.47669i
$977$	−18.9559	+	18.9559i	−0.606455	+	0.606455i	−0.942018	−	0.335563i	$-0.891073\pi$
$977$	−18.9559	+	18.9559i	−0.606455	+	0.606455i	0.335563	+	0.942018i	$0.391073\pi$
$978$	3.10380	+	8.55727i	0.0992486	+	0.273631i
$979$		−	25.2599i		−	0.807310i
$980$	−13.0183	+	28.4697i	−0.415855	+	0.909431i
$981$			26.6233i			0.850017i
$982$	19.0643	−	6.91481i	0.608368	−	0.220661i
$983$	14.6499	−	14.6499i	0.467260	−	0.467260i	−0.433765	−	0.901026i	$-0.642815\pi$
$983$	14.6499	−	14.6499i	0.467260	−	0.467260i	0.901026	+	0.433765i	$0.142815\pi$
$984$	−4.63976	+	1.22661i	−0.147910	+	0.0391030i
$985$	−19.8116	−	30.1046i	−0.631250	−	0.959214i
$986$	−0.679535	+	1.45304i	−0.0216408	+	0.0462742i
$987$	−24.9625	+	8.40225i	−0.794566	+	0.267447i
$988$	−0.215316	+	2.39949i	−0.00685011	+	0.0763378i
$989$	46.0342			1.46380
$990$	−1.77563	−	12.1943i	−0.0564334	−	0.387560i
$991$	4.37107			0.138852			0.0694258	−	0.997587i	$-0.477883\pi$
$991$	4.37107			0.138852			0.0694258	+	0.997587i	$0.477883\pi$
$992$	−6.83442	−	40.0636i	−0.216993	−	1.27202i
$993$	−21.2961	+	21.2961i	−0.675810	+	0.675810i
$994$	2.84564	−	2.26670i	0.0902582	−	0.0718954i
$995$	−5.08636	−	1.04884i	−0.161248	−	0.0332505i
$996$	20.0269	+	23.9755i	0.634578	+	0.759692i
$997$	−3.54219	+	3.54219i	−0.112182	+	0.112182i	−0.760970	−	0.648787i	$-0.775276\pi$
$997$	−3.54219	+	3.54219i	−0.112182	+	0.112182i	0.648787	+	0.760970i	$0.275276\pi$
$998$	8.90478	+	24.5508i	0.281876	+	0.777140i
$999$	35.2080			1.11393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.s.c.13.14	yes	72
4.3	odd	2		1120.2.w.c.433.12		72
5.2	odd	4	inner	280.2.s.c.237.34	yes	72
7.6	odd	2	inner	280.2.s.c.13.13	✓	72
8.3	odd	2		1120.2.w.c.433.25		72
8.5	even	2	inner	280.2.s.c.13.33	yes	72
20.7	even	4		1120.2.w.c.657.11		72
28.27	even	2		1120.2.w.c.433.26		72
35.27	even	4	inner	280.2.s.c.237.33	yes	72
40.27	even	4		1120.2.w.c.657.26		72
40.37	odd	4	inner	280.2.s.c.237.13	yes	72
56.13	odd	2	inner	280.2.s.c.13.34	yes	72
56.27	even	2		1120.2.w.c.433.11		72
140.27	odd	4		1120.2.w.c.657.25		72
280.27	odd	4		1120.2.w.c.657.12		72
280.237	even	4	inner	280.2.s.c.237.14	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.s.c.13.13	✓	72	7.6	odd	2	inner
280.2.s.c.13.14	yes	72	1.1	even	1	trivial
280.2.s.c.13.33	yes	72	8.5	even	2	inner
280.2.s.c.13.34	yes	72	56.13	odd	2	inner
280.2.s.c.237.13	yes	72	40.37	odd	4	inner
280.2.s.c.237.14	yes	72	280.237	even	4	inner
280.2.s.c.237.33	yes	72	35.27	even	4	inner
280.2.s.c.237.34	yes	72	5.2	odd	4	inner
1120.2.w.c.433.11		72	56.27	even	2
1120.2.w.c.433.12		72	4.3	odd	2
1120.2.w.c.433.25		72	8.3	odd	2
1120.2.w.c.433.26		72	28.27	even	2
1120.2.w.c.657.11		72	20.7	even	4
1120.2.w.c.657.12		72	280.27	odd	4
1120.2.w.c.657.25		72	140.27	odd	4
1120.2.w.c.657.26		72	40.27	even	4

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.482209 - 1.32946i) q^{2} +(0.851048 + 0.851048i) q^{3} +(-1.53495 + 1.28216i) q^{4} +(-2.18999 - 0.451591i) q^{5} +(0.721055 - 1.54182i) q^{6} +(-0.844017 - 2.50752i) q^{7} +(2.44475 + 1.42239i) q^{8} -1.55144i q^{9} +O(q^{10})\)	\(q+(-0.482209 - 1.32946i) q^{2} +(0.851048 + 0.851048i) q^{3} +(-1.53495 + 1.28216i) q^{4} +(-2.18999 - 0.451591i) q^{5} +(0.721055 - 1.54182i) q^{6} +(-0.844017 - 2.50752i) q^{7} +(2.44475 + 1.42239i) q^{8} -1.55144i q^{9} +(0.455660 + 3.12928i) q^{10} -2.51177i q^{11} +(-2.39749 - 0.215137i) q^{12} +(-2.05614 - 2.05614i) q^{13} +(-2.92666 + 2.33124i) q^{14} +(-1.47946 - 2.24811i) q^{15} +(0.712139 - 3.93610i) q^{16} +(-0.323302 - 0.323302i) q^{17} +(-2.06258 + 0.748116i) q^{18} +0.414250i q^{19} +(3.94054 - 2.11475i) q^{20} +(1.41572 - 2.85231i) q^{21} +(-3.33930 + 1.21120i) q^{22} +(-5.60285 - 5.60285i) q^{23} +(0.870076 + 3.29112i) q^{24} +(4.59213 + 1.97796i) q^{25} +(-1.74207 + 3.72505i) q^{26} +(3.87349 - 3.87349i) q^{27} +(4.51056 + 2.76675i) q^{28} +2.48079 q^{29} +(-2.27538 + 3.05095i) q^{30} +7.18461i q^{31} +(-5.57630 + 0.951258i) q^{32} +(2.13763 - 2.13763i) q^{33} +(-0.273919 + 0.585718i) q^{34} +(0.716018 + 5.87259i) q^{35} +(1.98919 + 2.38137i) q^{36} +(4.54475 + 4.54475i) q^{37} +(0.550730 - 0.199755i) q^{38} -3.49974i q^{39} +(-4.71164 - 4.21905i) q^{40} +1.40978i q^{41} +(-4.47472 - 0.506734i) q^{42} +(-4.10811 + 4.10811i) q^{43} +(3.22048 + 3.85543i) q^{44} +(-0.700614 + 3.39763i) q^{45} +(-4.74704 + 10.1505i) q^{46} +(-5.84872 - 5.84872i) q^{47} +(3.95587 - 2.74374i) q^{48} +(-5.57527 + 4.23277i) q^{49} +(0.415262 - 7.05886i) q^{50} -0.550291i q^{51} +(5.79236 + 0.519772i) q^{52} +(7.59714 - 7.59714i) q^{53} +(-7.01749 - 3.28183i) q^{54} +(-1.13429 + 5.50075i) q^{55} +(1.50326 - 7.33077i) q^{56} +(-0.352547 + 0.352547i) q^{57} +(-1.19626 - 3.29812i) q^{58} +1.24364i q^{59} +(5.15334 + 1.55383i) q^{60} +11.7206 q^{61} +(9.55169 - 3.46448i) q^{62} +(-3.89025 + 1.30944i) q^{63} +(3.95360 + 6.95478i) q^{64} +(3.57439 + 5.43146i) q^{65} +(-3.87269 - 1.81112i) q^{66} +(2.90850 + 2.90850i) q^{67} +(0.910777 + 0.0817277i) q^{68} -9.53658i q^{69} +(7.46213 - 3.78374i) q^{70} -0.972317 q^{71} +(2.20675 - 3.79287i) q^{72} +(10.4999 - 10.4999i) q^{73} +(3.85056 - 8.23359i) q^{74} +(2.22478 + 5.59146i) q^{75} +(-0.531134 - 0.635853i) q^{76} +(-6.29829 + 2.11997i) q^{77} +(-4.65278 + 1.68761i) q^{78} +5.80828i q^{79} +(-3.33708 + 8.29843i) q^{80} +1.93874 q^{81} +(1.87425 - 0.679808i) q^{82} +(-9.17675 - 9.17675i) q^{83} +(1.48406 + 6.19333i) q^{84} +(0.562029 + 0.854029i) q^{85} +(7.44255 + 3.48062i) q^{86} +(2.11127 + 2.11127i) q^{87} +(3.57272 - 6.14064i) q^{88} +10.0566 q^{89} +(4.85487 - 0.706927i) q^{90} +(-3.42038 + 6.89121i) q^{91} +(15.7838 + 1.41635i) q^{92} +(-6.11445 + 6.11445i) q^{93} +(-4.95536 + 10.5960i) q^{94} +(0.187072 - 0.907204i) q^{95} +(-5.55526 - 3.93613i) q^{96} +(-1.18210 - 1.18210i) q^{97} +(8.31576 + 5.37104i) q^{98} -3.89684 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8}+O(q^{10}) \) 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8	\( 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8} - 8 q^{15} + 40 q^{16} - 40 q^{18} + 4 q^{22} + 40 q^{23} - 8 q^{25} - 4 q^{28} - 44 q^{30} - 24 q^{32} - 72 q^{36} + 40 q^{42} + 16 q^{46} - 60 q^{50} + 32 q^{56} + 32 q^{57} - 68 q^{58} + 64 q^{60} - 100 q^{63} - 56 q^{65} + 16 q^{70} - 80 q^{71} + 16 q^{72} - 4 q^{78} + 72 q^{81} - 72 q^{86} + 48 q^{88} + 72 q^{92} + 80 q^{95} + 40 q^{98}+O(q^{100}) \) 72 * q - 4 * q^2 - 4 * q^7 - 16 * q^8 - 8 * q^15 + 40 * q^16 - 40 * q^18 + 4 * q^22 + 40 * q^23 - 8 * q^25 - 4 * q^28 - 44 * q^30 - 24 * q^32 - 72 * q^36 + 40 * q^42 + 16 * q^46 - 60 * q^50 + 32 * q^56 + 32 * q^57 - 68 * q^58 + 64 * q^60 - 100 * q^63 - 56 * q^65 + 16 * q^70 - 80 * q^71 + 16 * q^72 - 4 * q^78 + 72 * q^81 - 72 * q^86 + 48 * q^88 + 72 * q^92 + 80 * q^95 + 40 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more