LMFDB - Embedded newform 1785.2.g.g.1429.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1785,2,Mod(1429,1785)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1785, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1785.1429");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1785 = 3 \cdot 5 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1785.g (of order $2$, degree $1$, 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:	$14.2532967608$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1429.1
Character	$\chi$	$=$	1785.1429
Dual form			1785.2.g.g.1429.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.80343i q^{2} +1.00000i q^{3} -5.85923 q^{4} +(1.01291 - 1.99350i) q^{5} +2.80343 q^{6} -1.00000i q^{7} +10.8191i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.80343i q^{2} +1.00000i q^{3} -5.85923 q^{4} +(1.01291 - 1.99350i) q^{5} +2.80343 q^{6} -1.00000i q^{7} +10.8191i q^{8} -1.00000 q^{9} +(-5.58863 - 2.83961i) q^{10} +3.37847 q^{11} -5.85923i q^{12} -2.98612i q^{13} -2.80343 q^{14} +(1.99350 + 1.01291i) q^{15} +18.6122 q^{16} +1.00000i q^{17} +2.80343i q^{18} +8.20136 q^{19} +(-5.93485 + 11.6804i) q^{20} +1.00000 q^{21} -9.47132i q^{22} -5.84024i q^{23} -10.8191 q^{24} +(-2.94805 - 4.03844i) q^{25} -8.37138 q^{26} -1.00000i q^{27} +5.85923i q^{28} -6.80762 q^{29} +(2.83961 - 5.58863i) q^{30} -0.491153 q^{31} -30.5397i q^{32} +3.37847i q^{33} +2.80343 q^{34} +(-1.99350 - 1.01291i) q^{35} +5.85923 q^{36} -2.87265i q^{37} -22.9920i q^{38} +2.98612 q^{39} +(21.5678 + 10.9587i) q^{40} +8.72402 q^{41} -2.80343i q^{42} +7.93970i q^{43} -19.7953 q^{44} +(-1.01291 + 1.99350i) q^{45} -16.3727 q^{46} -5.43126i q^{47} +18.6122i q^{48} -1.00000 q^{49} +(-11.3215 + 8.26465i) q^{50} -1.00000 q^{51} +17.4964i q^{52} -0.419890i q^{53} -2.80343 q^{54} +(3.42207 - 6.73497i) q^{55} +10.8191 q^{56} +8.20136i q^{57} +19.0847i q^{58} +4.91201 q^{59} +(-11.6804 - 5.93485i) q^{60} -2.97619 q^{61} +1.37692i q^{62} +1.00000i q^{63} -48.3918 q^{64} +(-5.95281 - 3.02465i) q^{65} +9.47132 q^{66} -16.0362i q^{67} -5.85923i q^{68} +5.84024 q^{69} +(-2.83961 + 5.58863i) q^{70} -9.40560 q^{71} -10.8191i q^{72} +8.53815i q^{73} -8.05329 q^{74} +(4.03844 - 2.94805i) q^{75} -48.0537 q^{76} -3.37847i q^{77} -8.37138i q^{78} -7.24024 q^{79} +(18.8524 - 37.1033i) q^{80} +1.00000 q^{81} -24.4572i q^{82} +0.00138848i q^{83} -5.85923 q^{84} +(1.99350 + 1.01291i) q^{85} +22.2584 q^{86} -6.80762i q^{87} +36.5521i q^{88} -7.58835 q^{89} +(5.58863 + 2.83961i) q^{90} -2.98612 q^{91} +34.2194i q^{92} -0.491153i q^{93} -15.2262 q^{94} +(8.30720 - 16.3494i) q^{95} +30.5397 q^{96} +10.1653i q^{97} +2.80343i q^{98} -3.37847 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 34 q^{4} + 6 q^{6} - 28 q^{9}+O(q^{10}) $ 28 * q - 34 * q^4 + 6 * q^6 - 28 * q^9	$ 28 q - 34 q^{4} + 6 q^{6} - 28 q^{9} + 4 q^{10} + 8 q^{11} - 6 q^{14} + 38 q^{16} + 12 q^{19} - 4 q^{20} + 28 q^{21} - 30 q^{24} - 4 q^{26} - 40 q^{29} + 10 q^{30} - 14 q^{31} + 6 q^{34} + 34 q^{36} + 2 q^{39} + 30 q^{40} + 50 q^{41} - 48 q^{44} - 20 q^{46} - 28 q^{49} - 22 q^{50} - 28 q^{51} - 6 q^{54} + 2 q^{55} + 30 q^{56} - 28 q^{59} - 6 q^{60} - 18 q^{61} - 54 q^{64} - 24 q^{65} + 24 q^{66} - 14 q^{69} - 10 q^{70} + 4 q^{71} - 128 q^{74} - 8 q^{75} - 84 q^{76} + 8 q^{79} + 48 q^{80} + 28 q^{81} - 34 q^{84} + 88 q^{86} - 76 q^{89} - 4 q^{90} - 2 q^{91} - 16 q^{94} + 16 q^{95} + 66 q^{96} - 8 q^{99}+O(q^{100}) $ 28 * q - 34 * q^4 + 6 * q^6 - 28 * q^9 + 4 * q^10 + 8 * q^11 - 6 * q^14 + 38 * q^16 + 12 * q^19 - 4 * q^20 + 28 * q^21 - 30 * q^24 - 4 * q^26 - 40 * q^29 + 10 * q^30 - 14 * q^31 + 6 * q^34 + 34 * q^36 + 2 * q^39 + 30 * q^40 + 50 * q^41 - 48 * q^44 - 20 * q^46 - 28 * q^49 - 22 * q^50 - 28 * q^51 - 6 * q^54 + 2 * q^55 + 30 * q^56 - 28 * q^59 - 6 * q^60 - 18 * q^61 - 54 * q^64 - 24 * q^65 + 24 * q^66 - 14 * q^69 - 10 * q^70 + 4 * q^71 - 128 * q^74 - 8 * q^75 - 84 * q^76 + 8 * q^79 + 48 * q^80 + 28 * q^81 - 34 * q^84 + 88 * q^86 - 76 * q^89 - 4 * q^90 - 2 * q^91 - 16 * q^94 + 16 * q^95 + 66 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1785\mathbb{Z}\right)^\times$.

$n$	$596$	$766$	$1072$	$1261$
$\chi(n)$	$1$	$1$	$-1$	$1$

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 $

$2$		−	2.80343i		−	1.98233i	−0.132649	−	0.991163i	$-0.542348\pi$
$2$		−	2.80343i		−	1.98233i	0.132649	−	0.991163i	$-0.457652\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−5.85923			−2.92962
$5$	1.01291	−	1.99350i	0.452985	−	0.891518i
$5$	1.01291	−	1.99350i	0.452985	−	0.891518i
$6$	2.80343			1.14450
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$			10.8191i			3.82513i
$9$	−1.00000			−0.333333
$10$	−5.58863	−	2.83961i	−1.76728	−	0.897964i
$11$	3.37847			1.01865			0.509324	−	0.860575i	$-0.329895\pi$
$11$	3.37847			1.01865			0.509324	+	0.860575i	$0.329895\pi$
$12$		−	5.85923i		−	1.69142i
$13$		−	2.98612i		−	0.828200i	−0.910231	−	0.414100i	$-0.864096\pi$
$13$		−	2.98612i		−	0.828200i	0.910231	−	0.414100i	$-0.135904\pi$
$14$	−2.80343			−0.749249
$15$	1.99350	+	1.01291i	0.514718	+	0.261531i
$16$	18.6122			4.65304
$17$			1.00000i			0.242536i
$17$			1.00000i			0.242536i
$18$			2.80343i			0.660775i
$19$	8.20136			1.88152			0.940761	−	0.339072i	$-0.110113\pi$
$19$	8.20136			1.88152			0.940761	+	0.339072i	$0.110113\pi$
$20$	−5.93485	+	11.6804i	−1.32707	+	2.61181i
$21$	1.00000			0.218218
$22$		−	9.47132i		−	2.01929i
$23$		−	5.84024i		−	1.21778i	−0.793257	−	0.608888i	$-0.791616\pi$
$23$		−	5.84024i		−	1.21778i	0.793257	−	0.608888i	$-0.208384\pi$
$24$	−10.8191			−2.20844
$25$	−2.94805	−	4.03844i	−0.589609	−	0.807689i
$26$	−8.37138			−1.64176
$27$		−	1.00000i		−	0.192450i
$28$			5.85923i			1.10729i
$29$	−6.80762			−1.26414			−0.632072	−	0.774910i	$-0.717795\pi$
$29$	−6.80762			−1.26414			−0.632072	+	0.774910i	$0.717795\pi$
$30$	2.83961	−	5.58863i	0.518440	−	1.02034i
$31$	−0.491153			−0.0882137			−0.0441069	−	0.999027i	$-0.514044\pi$
$31$	−0.491153			−0.0882137			−0.0441069	+	0.999027i	$0.514044\pi$
$32$		−	30.5397i		−	5.39871i
$33$			3.37847i			0.588117i
$34$	2.80343			0.480785
$35$	−1.99350	−	1.01291i	−0.336962	−	0.171212i
$36$	5.85923			0.976539
$37$		−	2.87265i		−	0.472261i	−0.971721	−	0.236131i	$-0.924121\pi$
$37$		−	2.87265i		−	0.472261i	0.971721	−	0.236131i	$-0.0758793\pi$
$38$		−	22.9920i		−	3.72979i
$39$	2.98612			0.478161
$40$	21.5678	+	10.9587i	3.41017	+	1.73273i
$41$	8.72402			1.36246			0.681232	−	0.732068i	$-0.261445\pi$
$41$	8.72402			1.36246			0.681232	+	0.732068i	$0.261445\pi$
$42$		−	2.80343i		−	0.432579i
$43$			7.93970i			1.21079i	0.795924	+	0.605396i	$0.206985\pi$
$43$			7.93970i			1.21079i	−0.795924	+	0.605396i	$0.793015\pi$
$44$	−19.7953			−2.98425
$45$	−1.01291	+	1.99350i	−0.150995	+	0.297173i
$46$	−16.3727			−2.41403
$47$		−	5.43126i		−	0.792231i	−0.918201	−	0.396115i	$-0.870358\pi$
$47$		−	5.43126i		−	0.792231i	0.918201	−	0.396115i	$-0.129642\pi$
$48$			18.6122i			2.68643i
$49$	−1.00000			−0.142857
$50$	−11.3215	+	8.26465i	−1.60110	+	1.16880i
$51$	−1.00000			−0.140028
$52$			17.4964i			2.42631i
$53$		−	0.419890i		−	0.0576763i	−0.999584	−	0.0288381i	$-0.990819\pi$
$53$		−	0.419890i		−	0.0576763i	0.999584	−	0.0288381i	$-0.00918074\pi$
$54$	−2.80343			−0.381499
$55$	3.42207	−	6.73497i	0.461432	−	0.908143i
$56$	10.8191			1.44576
$57$			8.20136i			1.08630i
$58$			19.0847i			2.50595i
$59$	4.91201			0.639490			0.319745	−	0.947504i	$-0.396403\pi$
$59$	4.91201			0.639490			0.319745	+	0.947504i	$0.396403\pi$
$60$	−11.6804	−	5.93485i	−1.50793	−	0.766186i
$61$	−2.97619			−0.381062			−0.190531	−	0.981681i	$-0.561021\pi$
$61$	−2.97619			−0.381062			−0.190531	+	0.981681i	$0.561021\pi$
$62$			1.37692i			0.174868i
$63$			1.00000i			0.125988i
$64$	−48.3918			−6.04897
$65$	−5.95281	−	3.02465i	−0.738355	−	0.375162i
$66$	9.47132			1.16584
$67$		−	16.0362i		−	1.95913i	−0.201124	−	0.979566i	$-0.564459\pi$
$67$		−	16.0362i		−	1.95913i	0.201124	−	0.979566i	$-0.435541\pi$
$68$		−	5.85923i		−	0.710537i
$69$	5.84024			0.703083
$70$	−2.83961	+	5.58863i	−0.339399	+	0.667969i
$71$	−9.40560			−1.11624			−0.558120	−	0.829761i	$-0.688477\pi$
$71$	−9.40560			−1.11624			−0.558120	+	0.829761i	$0.688477\pi$
$72$		−	10.8191i		−	1.27504i
$73$			8.53815i			0.999315i	0.866223	+	0.499657i	$0.166541\pi$
$73$			8.53815i			0.999315i	−0.866223	+	0.499657i	$0.833459\pi$
$74$	−8.05329			−0.936176
$75$	4.03844	−	2.94805i	0.466319	−	0.340411i
$76$	−48.0537			−5.51214
$77$		−	3.37847i		−	0.385013i
$78$		−	8.37138i		−	0.947872i
$79$	−7.24024			−0.814590			−0.407295	−	0.913297i	$-0.633528\pi$
$79$	−7.24024			−0.814590			−0.407295	+	0.913297i	$0.633528\pi$
$80$	18.8524	−	37.1033i	2.10776	−	4.14827i
$81$	1.00000			0.111111
$82$		−	24.4572i		−	2.70085i
$83$			0.00138848i			0.000152405i	1.00000		7.62027e-5i	$2.42561e-5\pi$
$83$			0.00138848i			0.000152405i	−1.00000		7.62027e-5i	$0.999976\pi$
$84$	−5.85923			−0.639295
$85$	1.99350	+	1.01291i	0.216225	+	0.109865i
$86$	22.2584			2.40019
$87$		−	6.80762i		−	0.729854i
$88$			36.5521i			3.89646i
$89$	−7.58835			−0.804364			−0.402182	−	0.915560i	$-0.631748\pi$
$89$	−7.58835			−0.804364			−0.402182	+	0.915560i	$0.631748\pi$
$90$	5.58863	+	2.83961i	0.589093	+	0.299321i
$91$	−2.98612			−0.313030
$92$			34.2194i			3.56761i
$93$		−	0.491153i		−	0.0509302i
$94$	−15.2262			−1.57046
$95$	8.30720	−	16.3494i	0.852301	−	1.67741i
$96$	30.5397			3.11695
$97$			10.1653i			1.03213i	0.856550	+	0.516064i	$0.172603\pi$
$97$			10.1653i			1.03213i	−0.856550	+	0.516064i	$0.827397\pi$
$98$			2.80343i			0.283189i
$99$	−3.37847			−0.339549
$100$	17.2733	+	23.6622i	1.72733	+	2.36622i
$101$	−13.7816			−1.37132			−0.685659	−	0.727923i	$-0.740486\pi$
$101$	−13.7816			−1.37132			−0.685659	+	0.727923i	$0.740486\pi$
$102$			2.80343i			0.277581i
$103$		−	3.83305i		−	0.377681i	−0.982008	−	0.188841i	$-0.939527\pi$
$103$		−	3.83305i		−	0.377681i	0.982008	−	0.188841i	$-0.0604730\pi$
$104$	32.3071			3.16797
$105$	1.01291	−	1.99350i	0.0988494	−	0.194545i
$106$	−1.17713			−0.114333
$107$			3.76661i			0.364132i	0.983286	+	0.182066i	$0.0582785\pi$
$107$			3.76661i			0.364132i	−0.983286	+	0.182066i	$0.941722\pi$
$108$			5.85923i			0.563805i
$109$	13.1888			1.26326			0.631628	−	0.775272i	$-0.282387\pi$
$109$	13.1888			1.26326			0.631628	+	0.775272i	$0.282387\pi$
$110$	−18.8810	−	9.59355i	−1.80024	−	0.914709i
$111$	2.87265			0.272660
$112$		−	18.6122i		−	1.75868i
$113$		−	15.3505i		−	1.44405i	−0.691867	−	0.722025i	$-0.743212\pi$
$113$		−	15.3505i		−	1.44405i	0.691867	−	0.722025i	$-0.256788\pi$
$114$	22.9920			2.15339
$115$	−11.6425	−	5.91561i	−1.08567	−	0.551634i
$116$	39.8875			3.70346
$117$			2.98612i			0.276067i
$118$		−	13.7705i		−	1.26768i
$119$	1.00000			0.0916698
$120$	−10.9587	+	21.5678i	−1.00039	+	1.96886i
$121$	0.414084			0.0376440
$122$			8.34354i			0.755389i
$123$			8.72402i			0.786618i
$124$	2.87778			0.258432
$125$	−11.0367	+	1.78635i	−0.987153	+	0.159776i
$126$	2.80343			0.249750
$127$			11.2110i			0.994815i	0.867517	+	0.497407i	$0.165715\pi$
$127$			11.2110i			0.994815i	−0.867517	+	0.497407i	$0.834285\pi$
$128$			74.5836i			6.59232i
$129$	−7.93970			−0.699052
$130$	−8.47941	+	16.6883i	−0.743694	+	1.46366i
$131$	−9.55141			−0.834510			−0.417255	−	0.908789i	$-0.637008\pi$
$131$	−9.55141			−0.834510			−0.417255	+	0.908789i	$0.637008\pi$
$132$		−	19.7953i		−	1.72296i
$133$		−	8.20136i		−	0.711148i
$134$	−44.9564			−3.88364
$135$	−1.99350	−	1.01291i	−0.171573	−	0.0871770i
$136$	−10.8191			−0.927731
$137$			12.6457i			1.08040i	0.841537	+	0.540199i	$0.181651\pi$
$137$			12.6457i			1.08040i	−0.841537	+	0.540199i	$0.818349\pi$
$138$		−	16.3727i		−	1.39374i
$139$	8.08133			0.685449			0.342725	−	0.939436i	$-0.388650\pi$
$139$	8.08133			0.685449			0.342725	+	0.939436i	$0.388650\pi$
$140$	11.6804	+	5.93485i	0.987170	+	0.501586i
$141$	5.43126			0.457395
$142$			26.3680i			2.21275i
$143$		−	10.0885i		−	0.843644i
$144$	−18.6122			−1.55101
$145$	−6.89548	+	13.5710i	−0.572638	+	1.12701i
$146$	23.9361			1.98097
$147$		−	1.00000i		−	0.0824786i
$148$			16.8315i			1.38354i
$149$	14.1370			1.15815			0.579074	−	0.815275i	$-0.303414\pi$
$149$	14.1370			1.15815			0.579074	+	0.815275i	$0.303414\pi$
$150$	−8.26465	−	11.3215i	−0.674806	−	0.924397i
$151$	−13.7500			−1.11896			−0.559479	−	0.828845i	$-0.688999\pi$
$151$	−13.7500			−1.11896			−0.559479	+	0.828845i	$0.688999\pi$
$152$			88.7314i			7.19706i
$153$		−	1.00000i		−	0.0808452i
$154$	−9.47132			−0.763221
$155$	−0.497492	+	0.979112i	−0.0399595	+	0.0786441i
$156$	−17.4964			−1.40083
$157$		−	9.26551i		−	0.739468i	−0.929138	−	0.369734i	$-0.879449\pi$
$157$		−	9.26551i		−	0.739468i	0.929138	−	0.369734i	$-0.120551\pi$
$158$			20.2975i			1.61478i
$159$	0.419890			0.0332994
$160$	−60.8808	−	30.9339i	−4.81305	−	2.44554i
$161$	−5.84024			−0.460276
$162$		−	2.80343i		−	0.220258i
$163$		−	6.61304i		−	0.517973i	−0.965881	−	0.258987i	$-0.916611\pi$
$163$		−	6.61304i		−	0.517973i	0.965881	−	0.258987i	$-0.0833886\pi$
$164$	−51.1161			−3.99150
$165$	6.73497	+	3.42207i	0.524317	+	0.266408i
$166$	0.00389251			0.000302117
$167$		−	5.97930i		−	0.462692i	−0.972872	−	0.231346i	$-0.925687\pi$
$167$		−	5.97930i		−	0.462692i	0.972872	−	0.231346i	$-0.0743129\pi$
$168$			10.8191i			0.834712i
$169$	4.08310			0.314085
$170$	2.83961	−	5.58863i	0.217788	−	0.428628i
$171$	−8.20136			−0.627174
$172$		−	46.5206i		−	3.54716i
$173$		−	9.67349i		−	0.735462i	−0.929932	−	0.367731i	$-0.880135\pi$
$173$		−	9.67349i		−	0.735462i	0.929932	−	0.367731i	$-0.119865\pi$
$174$	−19.0847			−1.44681
$175$	−4.03844	+	2.94805i	−0.305278	+	0.222851i
$176$	62.8807			4.73981
$177$			4.91201i			0.369210i
$178$			21.2734i			1.59451i
$179$	16.1835			1.20961			0.604807	−	0.796372i	$-0.293250\pi$
$179$	16.1835			1.20961			0.604807	+	0.796372i	$0.293250\pi$
$180$	5.93485	−	11.6804i	0.442358	−	0.870602i
$181$	1.01069			0.0751243			0.0375621	−	0.999294i	$-0.488041\pi$
$181$	1.01069			0.0751243			0.0375621	+	0.999294i	$0.488041\pi$
$182$			8.37138i			0.620528i
$183$		−	2.97619i		−	0.220006i
$184$	63.1862			4.65815
$185$	−5.72662	−	2.90972i	−0.421029	−	0.213927i
$186$	−1.37692			−0.100960
$187$			3.37847i			0.247058i
$188$			31.8230i			2.32093i
$189$	−1.00000			−0.0727393
$190$	−45.8344	−	23.2887i	−3.32517	−	1.68954i
$191$	11.2168			0.811616			0.405808	−	0.913958i	$-0.366990\pi$
$191$	11.2168			0.811616			0.405808	+	0.913958i	$0.366990\pi$
$192$		−	48.3918i		−	3.49237i
$193$			13.0305i			0.937955i	0.883210	+	0.468978i	$0.155378\pi$
$193$			13.0305i			0.937955i	−0.883210	+	0.468978i	$0.844622\pi$
$194$	28.4977			2.04601
$195$	3.02465	−	5.95281i	0.216600	−	0.426290i
$196$	5.85923			0.418517
$197$		−	3.36117i		−	0.239473i	−0.992806	−	0.119737i	$-0.961795\pi$
$197$		−	3.36117i		−	0.239473i	0.992806	−	0.119737i	$-0.0382050\pi$
$198$			9.47132i			0.673098i
$199$	−3.11797			−0.221027			−0.110513	−	0.993875i	$-0.535249\pi$
$199$	−3.11797			−0.221027			−0.110513	+	0.993875i	$0.535249\pi$
$200$	43.6923	−	31.8952i	3.08952	−	2.25533i
$201$	16.0362			1.13111
$202$			38.6357i			2.71840i
$203$			6.80762i			0.477802i
$204$	5.85923			0.410228
$205$	8.83661	−	17.3913i	0.617175	−	1.21466i
$206$	−10.7457			−0.748688
$207$			5.84024i			0.405925i
$208$		−	55.5781i		−	3.85365i
$209$	27.7081			1.91661
$210$	−5.58863	−	2.83961i	−0.385652	−	0.195952i
$211$	1.18361			0.0814831			0.0407416	−	0.999170i	$-0.487028\pi$
$211$	1.18361			0.0814831			0.0407416	+	0.999170i	$0.487028\pi$
$212$			2.46023i			0.168969i
$213$		−	9.40560i		−	0.644461i
$214$	10.5594			0.721829
$215$	15.8278	+	8.04216i	1.07944	+	0.548471i
$216$	10.8191			0.736147
$217$			0.491153i			0.0333417i
$218$		−	36.9739i		−	2.50419i
$219$	−8.53815			−0.576955
$220$	−20.0507	+	39.4618i	−1.35182	+	2.66051i
$221$	2.98612			0.200868
$222$		−	8.05329i		−	0.540501i
$223$			0.645242i			0.0432086i	0.999767	+	0.0216043i	$0.00687740\pi$
$223$			0.645242i			0.0432086i	−0.999767	+	0.0216043i	$0.993123\pi$
$224$	−30.5397			−2.04052
$225$	2.94805	+	4.03844i	0.196536	+	0.269230i
$226$	−43.0340			−2.86258
$227$		−	20.6531i		−	1.37079i	−0.728170	−	0.685397i	$-0.759629\pi$
$227$		−	20.6531i		−	1.37079i	0.728170	−	0.685397i	$-0.240371\pi$
$228$		−	48.0537i		−	3.18243i
$229$	−8.46699			−0.559515			−0.279757	−	0.960071i	$-0.590254\pi$
$229$	−8.46699			−0.559515			−0.279757	+	0.960071i	$0.590254\pi$
$230$	−16.5840	+	32.6390i	−1.09352	+	2.15215i
$231$	3.37847			0.222287
$232$		−	73.6524i		−	4.83552i
$233$		−	24.4882i		−	1.60427i	−0.597141	−	0.802136i	$-0.703697\pi$
$233$		−	24.4882i		−	1.60427i	0.597141	−	0.802136i	$-0.296303\pi$
$234$	8.37138			0.547254
$235$	−10.8272	−	5.50135i	−0.706288	−	0.358869i
$236$	−28.7806			−1.87346
$237$		−	7.24024i		−	0.470304i
$238$		−	2.80343i		−	0.181720i
$239$	21.1704			1.36940			0.684700	−	0.728825i	$-0.259933\pi$
$239$	21.1704			1.36940			0.684700	+	0.728825i	$0.259933\pi$
$240$	37.1033	+	18.8524i	2.39500	+	1.21691i
$241$	9.48083			0.610714			0.305357	−	0.952238i	$-0.401224\pi$
$241$	9.48083			0.610714			0.305357	+	0.952238i	$0.401224\pi$
$242$		−	1.16086i		−	0.0746226i
$243$			1.00000i			0.0641500i
$244$	17.4382			1.11637
$245$	−1.01291	+	1.99350i	−0.0647121	+	0.127360i
$246$	24.4572			1.55933
$247$		−	24.4902i		−	1.55828i
$248$		−	5.31384i		−	0.337429i
$249$	−0.00138848			−8.79912e−5
$250$	5.00792	+	30.9407i	0.316729	+	1.95686i
$251$	−2.33881			−0.147624			−0.0738121	−	0.997272i	$-0.523517\pi$
$251$	−2.33881			−0.147624			−0.0738121	+	0.997272i	$0.523517\pi$
$252$		−	5.85923i		−	0.369097i
$253$		−	19.7311i		−	1.24048i
$254$	31.4293			1.97205
$255$	−1.01291	+	1.99350i	−0.0634306	+	0.124838i
$256$	112.306			7.01916
$257$		−	22.9292i		−	1.43028i	−0.698979	−	0.715142i	$-0.746362\pi$
$257$		−	22.9292i		−	1.43028i	0.698979	−	0.715142i	$-0.253638\pi$
$258$			22.2584i			1.38575i
$259$	−2.87265			−0.178498
$260$	34.8789	+	17.7222i	2.16310	+	1.09908i
$261$	6.80762			0.421381
$262$			26.7767i			1.65427i
$263$		−	6.17182i		−	0.380571i	−0.981729	−	0.190285i	$-0.939059\pi$
$263$		−	6.17182i		−	0.380571i	0.981729	−	0.190285i	$-0.0609414\pi$
$264$	−36.5521			−2.24962
$265$	−0.837048	−	0.425308i	−0.0514194	−	0.0261265i
$266$	−22.9920			−1.40973
$267$		−	7.58835i		−	0.464400i
$268$			93.9598i			5.73951i
$269$	21.9597			1.33891			0.669453	−	0.742855i	$-0.266529\pi$
$269$	21.9597			1.33891			0.669453	+	0.742855i	$0.266529\pi$
$270$	−2.83961	+	5.58863i	−0.172813	+	0.340113i
$271$	−29.7006			−1.80418			−0.902091	−	0.431546i	$-0.857968\pi$
$271$	−29.7006			−1.80418			−0.902091	+	0.431546i	$0.857968\pi$
$272$			18.6122i			1.12853i
$273$		−	2.98612i		−	0.180728i
$274$	35.4515			2.14170
$275$	−9.95989	−	13.6438i	−0.600604	−	0.822751i
$276$	−34.2194			−2.05976
$277$			0.330767i			0.0198739i	0.999951	+	0.00993694i	$0.00316308\pi$
$277$			0.330767i			0.0198739i	−0.999951	+	0.00993694i	$0.996837\pi$
$278$		−	22.6555i		−	1.35878i
$279$	0.491153			0.0294046
$280$	10.9587	−	21.5678i	0.654909	−	1.28892i
$281$	−8.44777			−0.503952			−0.251976	−	0.967733i	$-0.581080\pi$
$281$	−8.44777			−0.503952			−0.251976	+	0.967733i	$0.581080\pi$
$282$		−	15.2262i		−	0.906706i
$283$			20.5216i			1.21989i	0.792446	+	0.609943i	$0.208807\pi$
$283$			20.5216i			1.21989i	−0.792446	+	0.609943i	$0.791193\pi$
$284$	55.1096			3.27015
$285$	16.3494	+	8.30720i	0.968453	+	0.492076i
$286$	−28.2825			−1.67238
$287$		−	8.72402i		−	0.514963i
$288$			30.5397i			1.79957i
$289$	−1.00000			−0.0588235
$290$	38.0453	+	19.3310i	2.23410	+	1.13516i
$291$	−10.1653			−0.595899
$292$		−	50.0270i		−	2.92761i
$293$		−	17.9089i		−	1.04625i	−0.852257	−	0.523124i	$-0.824766\pi$
$293$		−	17.9089i		−	1.04625i	0.852257	−	0.523124i	$-0.175234\pi$
$294$	−2.80343			−0.163500
$295$	4.97541	−	9.79208i	0.289679	−	0.570117i
$296$	31.0795			1.80646
$297$		−	3.37847i		−	0.196039i
$298$		−	39.6321i		−	2.29583i
$299$	−17.4397			−1.00856
$300$	−23.6622	+	17.2733i	−1.36614	+	0.997274i
$301$	7.93970			0.457637
$302$			38.5471i			2.21814i
$303$		−	13.7816i		−	0.791731i
$304$	152.645			8.75479
$305$	−3.01460	+	5.93302i	−0.172615	+	0.339724i
$306$	−2.80343			−0.160262
$307$			19.8061i			1.13039i	0.824957	+	0.565196i	$0.191199\pi$
$307$			19.8061i			1.13039i	−0.824957	+	0.565196i	$0.808801\pi$
$308$			19.7953i			1.12794i
$309$	3.83305			0.218054
$310$	2.74487	+	1.39468i	0.155898	+	0.0792128i
$311$	−4.30912			−0.244348			−0.122174	−	0.992509i	$-0.538987\pi$
$311$	−4.30912			−0.244348			−0.122174	+	0.992509i	$0.538987\pi$
$312$			32.3071i			1.82903i
$313$		−	27.4270i		−	1.55026i	−0.631800	−	0.775131i	$-0.717684\pi$
$313$		−	27.4270i		−	1.55026i	0.631800	−	0.775131i	$-0.282316\pi$
$314$	−25.9752			−1.46587
$315$	1.99350	+	1.01291i	0.112321	+	0.0570707i
$316$	42.4223			2.38644
$317$			22.6461i			1.27193i	0.771716	+	0.635967i	$0.219399\pi$
$317$			22.6461i			1.27193i	−0.771716	+	0.635967i	$0.780601\pi$
$318$		−	1.17713i		−	0.0660103i
$319$	−22.9994			−1.28772
$320$	−49.0163	+	96.4687i	−2.74009	+	5.39277i
$321$	−3.76661			−0.210232
$322$			16.3727i			0.912417i
$323$			8.20136i			0.456336i
$324$	−5.85923			−0.325513
$325$	−12.0593	+	8.80321i	−0.668928	+	0.488314i
$326$	−18.5392			−1.02679
$327$			13.1888i			0.729341i
$328$			94.3861i			5.21160i
$329$	−5.43126			−0.299435
$330$	9.59355	−	18.8810i	0.528108	−	1.03937i
$331$	18.3691			1.00966			0.504829	−	0.863219i	$-0.331555\pi$
$331$	18.3691			1.00966			0.504829	+	0.863219i	$0.331555\pi$
$332$		−	0.00813542i		−	0.000446489i
$333$			2.87265i			0.157420i
$334$	−16.7626			−0.917206
$335$	−31.9681	−	16.2431i	−1.74660	−	0.887457i
$336$	18.6122			1.01538
$337$			22.7393i			1.23869i	0.785119	+	0.619345i	$0.212602\pi$
$337$			22.7393i			1.23869i	−0.785119	+	0.619345i	$0.787398\pi$
$338$		−	11.4467i		−	0.622618i
$339$	15.3505			0.833722
$340$	−11.6804	−	5.93485i	−0.633456	−	0.321862i
$341$	−1.65935			−0.0898588
$342$			22.9920i			1.24326i
$343$			1.00000i			0.0539949i
$344$	−85.9004			−4.63144
$345$	5.91561	−	11.6425i	0.318486	−	0.626811i
$346$	−27.1190			−1.45793
$347$			5.38634i			0.289154i	0.989494	+	0.144577i	$0.0461821\pi$
$347$			5.38634i			0.289154i	−0.989494	+	0.144577i	$0.953818\pi$
$348$			39.8875i			2.13819i
$349$	4.94714			0.264814			0.132407	−	0.991195i	$-0.457729\pi$
$349$	4.94714			0.264814			0.132407	+	0.991195i	$0.457729\pi$
$350$	8.26465	+	11.3215i	0.441764	+	0.605160i
$351$	−2.98612			−0.159387
$352$		−	103.178i		−	5.49939i
$353$			24.9950i			1.33035i	0.746687	+	0.665175i	$0.231643\pi$
$353$			24.9950i			1.33035i	−0.746687	+	0.665175i	$0.768357\pi$
$354$	13.7705			0.731894
$355$	−9.52698	+	18.7500i	−0.505640	+	0.995147i
$356$	44.4619			2.35648
$357$			1.00000i			0.0529256i
$358$		−	45.3694i		−	2.39785i
$359$	−30.5447			−1.61209			−0.806045	−	0.591855i	$-0.798396\pi$
$359$	−30.5447			−1.61209			−0.806045	+	0.591855i	$0.798396\pi$
$360$	−21.5678	−	10.9587i	−1.13672	−	0.577576i
$361$	48.2623			2.54012
$362$		−	2.83341i		−	0.148921i
$363$			0.414084i			0.0217338i
$364$	17.4964			0.917059
$365$	17.0208	+	8.64833i	0.890907	+	0.452675i
$366$	−8.34354			−0.436124
$367$		−	1.26006i		−	0.0657744i	−0.999459	−	0.0328872i	$-0.989530\pi$
$367$		−	1.26006i		−	0.0657744i	0.999459	−	0.0328872i	$-0.0104702\pi$
$368$		−	108.700i		−	5.66636i
$369$	−8.72402			−0.454154
$370$	−8.15722	+	16.0542i	−0.424074	+	0.834617i
$371$	−0.419890			−0.0217996
$372$			2.87778i			0.149206i
$373$			20.5582i			1.06447i	0.846598	+	0.532233i	$0.178647\pi$
$373$			20.5582i			1.06447i	−0.846598	+	0.532233i	$0.821353\pi$
$374$	9.47132			0.489750
$375$	−1.78635	−	11.0367i	−0.0922469	−	0.569933i
$376$	58.7614			3.03039
$377$			20.3284i			1.04696i
$378$			2.80343i			0.144193i
$379$	3.33561			0.171339			0.0856693	−	0.996324i	$-0.472697\pi$
$379$	3.33561			0.171339			0.0856693	+	0.996324i	$0.472697\pi$
$380$	−48.6738	+	95.7948i	−2.49692	+	4.91417i
$381$	−11.2110			−0.574357
$382$		−	31.4454i		−	1.60889i
$383$		−	1.72119i		−	0.0879485i	−0.999033	−	0.0439742i	$-0.985998\pi$
$383$		−	1.72119i		−	0.0879485i	0.999033	−	0.0439742i	$-0.0140020\pi$
$384$	−74.5836			−3.80608
$385$	−6.73497	−	3.42207i	−0.343246	−	0.174405i
$386$	36.5301			1.85933
$387$		−	7.93970i		−	0.403598i
$388$		−	59.5608i		−	3.02374i
$389$	20.4186			1.03526			0.517632	−	0.855603i	$-0.326814\pi$
$389$	20.4186			1.03526			0.517632	+	0.855603i	$0.326814\pi$
$390$	−16.6883	−	8.47941i	−0.845045	−	0.429372i
$391$	5.84024			0.295354
$392$		−	10.8191i		−	0.546447i
$393$		−	9.55141i		−	0.481805i
$394$	−9.42281			−0.474714
$395$	−7.33368	+	14.4334i	−0.368997	+	0.726222i
$396$	19.7953			0.994750
$397$		−	7.58930i		−	0.380896i	−0.981697	−	0.190448i	$-0.939006\pi$
$397$		−	7.58930i		−	0.380896i	0.981697	−	0.190448i	$-0.0609941\pi$
$398$			8.74101i			0.438147i
$399$	8.20136			0.410582
$400$	−54.8695	−	75.1642i	−2.74347	−	3.75821i
$401$	−1.65683			−0.0827380			−0.0413690	−	0.999144i	$-0.513172\pi$
$401$	−1.65683			−0.0827380			−0.0413690	+	0.999144i	$0.513172\pi$
$402$		−	44.9564i		−	2.24222i
$403$			1.46664i			0.0730586i
$404$	80.7495			4.01744
$405$	1.01291	−	1.99350i	0.0503317	−	0.0990576i
$406$	19.0847			0.947159
$407$		−	9.70518i		−	0.481068i
$408$		−	10.8191i		−	0.535625i
$409$	6.04520			0.298916			0.149458	−	0.988768i	$-0.452247\pi$
$409$	6.04520			0.298916			0.149458	+	0.988768i	$0.452247\pi$
$410$	−48.7553	−	24.7728i	−2.40785	−	1.22344i
$411$	−12.6457			−0.623769
$412$			22.4587i			1.10646i
$413$		−	4.91201i		−	0.241704i
$414$	16.3727			0.804676
$415$	0.00276792	+	0.00140640i	0.000135872	+	6.90373e-5i
$416$	−91.1952			−4.47121
$417$			8.08133i			0.395744i
$418$		−	77.6777i		−	3.79934i
$419$	2.06017			0.100646			0.0503230	−	0.998733i	$-0.483975\pi$
$419$	2.06017			0.100646			0.0503230	+	0.998733i	$0.483975\pi$
$420$	−5.93485	+	11.6804i	−0.289591	+	0.569943i
$421$	9.05757			0.441439			0.220719	−	0.975337i	$-0.429159\pi$
$421$	9.05757			0.441439			0.220719	+	0.975337i	$0.429159\pi$
$422$		−	3.31817i		−	0.161526i
$423$			5.43126i			0.264077i
$424$	4.54283			0.220619
$425$	4.03844	−	2.94805i	0.195893	−	0.143001i
$426$	−26.3680			−1.27753
$427$			2.97619i			0.144028i
$428$		−	22.0695i		−	1.06677i
$429$	10.0885			0.487078
$430$	22.5457	−	44.3720i	1.08725	−	2.13981i
$431$	13.5639			0.653348			0.326674	−	0.945137i	$-0.394072\pi$
$431$	13.5639			0.653348			0.326674	+	0.945137i	$0.394072\pi$
$432$		−	18.6122i		−	0.895478i
$433$		−	5.31344i		−	0.255348i	−0.991816	−	0.127674i	$-0.959249\pi$
$433$		−	5.31344i		−	0.255348i	0.991816	−	0.127674i	$-0.0407511\pi$
$434$	1.37692			0.0660940
$435$	−13.5710	−	6.89548i	−0.650678	−	0.330613i
$436$	−77.2762			−3.70086
$437$		−	47.8979i		−	2.29127i
$438$			23.9361i			1.14371i
$439$	−22.5460			−1.07606			−0.538030	−	0.842926i	$-0.680831\pi$
$439$	−22.5460			−1.07606			−0.538030	+	0.842926i	$0.680831\pi$
$440$	72.8663	+	37.0238i	3.47377	+	1.76504i
$441$	1.00000			0.0476190
$442$		−	8.37138i		−	0.398186i
$443$			14.2922i			0.679041i	0.940599	+	0.339521i	$0.110265\pi$
$443$			14.2922i			0.679041i	−0.940599	+	0.339521i	$0.889735\pi$
$444$	−16.8315			−0.798790
$445$	−7.68628	+	15.1273i	−0.364365	+	0.717105i
$446$	1.80889			0.0856536
$447$			14.1370i			0.668657i
$448$			48.3918i			2.28630i
$449$	−2.03457			−0.0960175			−0.0480087	−	0.998847i	$-0.515288\pi$
$449$	−2.03457			−0.0960175			−0.0480087	+	0.998847i	$0.515288\pi$
$450$	11.3215	−	8.26465i	0.533701	−	0.389599i
$451$	29.4739			1.38787
$452$			89.9419i			4.23051i
$453$		−	13.7500i		−	0.646030i
$454$	−57.8995			−2.71736
$455$	−3.02465	+	5.95281i	−0.141798	+	0.279072i
$456$	−88.7314			−4.15523
$457$		−	6.67114i		−	0.312063i	−0.987752	−	0.156031i	$-0.950130\pi$
$457$		−	6.67114i		−	0.312063i	0.987752	−	0.156031i	$-0.0498701\pi$
$458$			23.7366i			1.10914i
$459$	1.00000			0.0466760
$460$	68.2161	+	34.6610i	3.18059	+	1.61608i
$461$	33.1967			1.54612			0.773062	−	0.634330i	$-0.218724\pi$
$461$	33.1967			1.54612			0.773062	+	0.634330i	$0.218724\pi$
$462$		−	9.47132i		−	0.440646i
$463$			1.31144i			0.0609477i	0.999536	+	0.0304739i	$0.00970163\pi$
$463$			1.31144i			0.0609477i	−0.999536	+	0.0304739i	$0.990298\pi$
$464$	−126.705			−5.88211
$465$	−0.979112	−	0.497492i	−0.0454052	−	0.0230706i
$466$	−68.6509			−3.18019
$467$		−	35.3652i		−	1.63650i	−0.574859	−	0.818252i	$-0.694943\pi$
$467$		−	35.3652i		−	1.63650i	0.574859	−	0.818252i	$-0.305057\pi$
$468$		−	17.4964i		−	0.808770i
$469$	−16.0362			−0.740482
$470$	−15.4227	+	30.3533i	−0.711395	+	1.40009i
$471$	9.26551			0.426932
$472$			53.1436i			2.44613i
$473$			26.8241i			1.23337i
$474$	−20.2975			−0.932296
$475$	−24.1780	−	33.1207i	−1.10936	−	1.51968i
$476$	−5.85923			−0.268558
$477$			0.419890i			0.0192254i
$478$		−	59.3498i		−	2.71460i
$479$	−26.9709			−1.23233			−0.616166	−	0.787616i	$-0.711315\pi$
$479$	−26.9709			−1.23233			−0.616166	+	0.787616i	$0.711315\pi$
$480$	30.9339	−	60.8808i	1.41193	−	2.77882i
$481$	−8.57808			−0.391127
$482$		−	26.5789i		−	1.21063i
$483$		−	5.84024i		−	0.265740i
$484$	−2.42621			−0.110282
$485$	20.2644	+	10.2965i	0.920161	+	0.467539i
$486$	2.80343			0.127166
$487$			33.3994i			1.51347i	0.653720	+	0.756737i	$0.273208\pi$
$487$			33.3994i			1.51347i	−0.653720	+	0.756737i	$0.726792\pi$
$488$		−	32.1997i		−	1.45761i
$489$	6.61304			0.299052
$490$	5.58863	+	2.83961i	0.252469	+	0.128281i
$491$	31.6594			1.42877			0.714385	−	0.699753i	$-0.246707\pi$
$491$	31.6594			1.42877			0.714385	+	0.699753i	$0.246707\pi$
$492$		−	51.1161i		−	2.30449i
$493$		−	6.80762i		−	0.306600i
$494$	−68.6567			−3.08901
$495$	−3.42207	+	6.73497i	−0.153811	+	0.302714i
$496$	−9.14142			−0.410462
$497$			9.40560i			0.421899i
$498$			0.00389251i			0.000174427i
$499$	7.88306			0.352894			0.176447	−	0.984310i	$-0.443540\pi$
$499$	7.88306			0.352894			0.176447	+	0.984310i	$0.443540\pi$
$500$	64.6667	−	10.4667i	2.89198	−	0.468083i
$501$	5.97930			0.267135
$502$			6.55669i			0.292639i
$503$			14.1621i			0.631455i	0.948850	+	0.315727i	$0.102249\pi$
$503$			14.1621i			0.631455i	−0.948850	+	0.315727i	$0.897751\pi$
$504$	−10.8191			−0.481921
$505$	−13.9594	+	27.4735i	−0.621186	+	1.22255i
$506$	−55.3148			−2.45904
$507$			4.08310i			0.181337i
$508$		−	65.6878i		−	2.91443i
$509$	9.81696			0.435129			0.217565	−	0.976046i	$-0.430189\pi$
$509$	9.81696			0.435129			0.217565	+	0.976046i	$0.430189\pi$
$510$	5.58863	+	2.83961i	0.247469	+	0.125740i
$511$	8.53815			0.377705
$512$		−	165.677i		−	7.32194i
$513$		−	8.20136i		−	0.362099i
$514$	−64.2805			−2.83529
$515$	−7.64116	−	3.88251i	−0.336710	−	0.171084i
$516$	46.5206			2.04795
$517$		−	18.3494i		−	0.807005i
$518$			8.05329i			0.353841i
$519$	9.67349			0.424619
$520$	32.7240	−	64.4041i	1.43504	−	2.82431i
$521$	26.3114			1.15272			0.576362	−	0.817195i	$-0.304472\pi$
$521$	26.3114			1.15272			0.576362	+	0.817195i	$0.304472\pi$
$522$		−	19.0847i		−	0.835315i
$523$			34.5725i			1.51175i	0.654716	+	0.755875i	$0.272788\pi$
$523$			34.5725i			1.51175i	−0.654716	+	0.755875i	$0.727212\pi$
$524$	55.9639			2.44480
$525$	−2.94805	−	4.03844i	−0.128663	−	0.176252i
$526$	−17.3023			−0.754416
$527$		−	0.491153i		−	0.0213950i
$528$			62.8807i			2.73653i
$529$	−11.1085			−0.482976
$530$	−1.19232	+	2.34661i	−0.0517912	+	0.101930i
$531$	−4.91201			−0.213163
$532$			48.0537i			2.08339i
$533$		−	26.0510i		−	1.12839i
$534$	−21.2734			−0.920592
$535$	7.50872	+	3.81522i	0.324630	+	0.164946i
$536$	173.497			7.49393
$537$			16.1835i			0.698371i
$538$		−	61.5625i		−	2.65415i
$539$	−3.37847			−0.145521
$540$	11.6804	+	5.93485i	0.502642	+	0.255395i
$541$	2.91743			0.125430			0.0627151	−	0.998031i	$-0.480024\pi$
$541$	2.91743			0.125430			0.0627151	+	0.998031i	$0.480024\pi$
$542$			83.2636i			3.57648i
$543$			1.01069i			0.0433730i
$544$	30.5397			1.30938
$545$	13.3590	−	26.2918i	0.572236	−	1.12622i
$546$	−8.37138			−0.358262
$547$			17.4499i			0.746105i	0.927810	+	0.373053i	$0.121689\pi$
$547$			17.4499i			0.746105i	−0.927810	+	0.373053i	$0.878311\pi$
$548$		−	74.0944i		−	3.16516i
$549$	2.97619			0.127021
$550$	−38.2494	+	27.9219i	−1.63096	+	1.19059i
$551$	−55.8318			−2.37851
$552$			63.1862i			2.68938i
$553$			7.24024i			0.307886i
$554$	0.927283			0.0393965
$555$	2.90972	−	5.72662i	0.123511	−	0.243081i
$556$	−47.3504			−2.00810
$557$		−	1.58407i		−	0.0671191i	−0.999437	−	0.0335596i	$-0.989316\pi$
$557$		−	1.58407i		−	0.0671191i	0.999437	−	0.0335596i	$-0.0106843\pi$
$558$		−	1.37692i		−	0.0582895i
$559$	23.7089			1.00278
$560$	−37.1033	−	18.8524i	−1.56790	−	0.796657i
$561$	−3.37847			−0.142639
$562$			23.6828i			0.998997i
$563$			21.9428i			0.924780i	0.886677	+	0.462390i	$0.153008\pi$
$563$			21.9428i			0.924780i	−0.886677	+	0.462390i	$0.846992\pi$
$564$	−31.8230			−1.33999
$565$	−30.6011	−	15.5486i	−1.28740	−	0.654133i
$566$	57.5310			2.41821
$567$		−	1.00000i		−	0.0419961i
$568$		−	101.760i		−	4.26976i
$569$	25.0638			1.05073			0.525365	−	0.850877i	$-0.323929\pi$
$569$	25.0638			1.05073			0.525365	+	0.850877i	$0.323929\pi$
$570$	23.2887	−	45.8344i	0.975455	−	1.91979i
$571$	4.84213			0.202637			0.101318	−	0.994854i	$-0.467694\pi$
$571$	4.84213			0.202637			0.101318	+	0.994854i	$0.467694\pi$
$572$			59.1110i			2.47156i
$573$			11.2168i			0.468587i
$574$	−24.4572			−1.02082
$575$	−23.5855	+	17.2173i	−0.983583	+	0.718011i
$576$	48.3918			2.01632
$577$		−	21.1366i		−	0.879927i	−0.898016	−	0.439964i	$-0.854991\pi$
$577$		−	21.1366i		−	0.879927i	0.898016	−	0.439964i	$-0.145009\pi$
$578$			2.80343i			0.116607i
$579$	−13.0305			−0.541529
$580$	40.4022	−	79.5155i	1.67761	−	3.30170i
$581$	0.00138848			5.76038e−5
$582$			28.4977i			1.18127i
$583$		−	1.41859i		−	0.0587518i
$584$	−92.3751			−3.82251
$585$	5.95281	+	3.02465i	0.246118	+	0.125054i
$586$	−50.2063			−2.07400
$587$		−	9.36669i		−	0.386605i	−0.981139	−	0.193302i	$-0.938080\pi$
$587$		−	9.36669i		−	0.386605i	0.981139	−	0.193302i	$-0.0619198\pi$
$588$			5.85923i			0.241631i
$589$	−4.02813			−0.165976
$590$	−27.4514	−	13.9482i	−1.13016	−	0.574239i
$591$	3.36117			0.138260
$592$		−	53.4663i		−	2.19745i
$593$			12.1261i			0.497961i	0.968509	+	0.248980i	$0.0800955\pi$
$593$			12.1261i			0.497961i	−0.968509	+	0.248980i	$0.919905\pi$
$594$	−9.47132			−0.388613
$595$	1.01291	−	1.99350i	0.0415251	−	0.0817253i
$596$	−82.8319			−3.39293
$597$		−	3.11797i		−	0.127610i
$598$			48.8909i			1.99930i
$599$	−19.9848			−0.816558			−0.408279	−	0.912857i	$-0.633871\pi$
$599$	−19.9848			−0.816558			−0.408279	+	0.912857i	$0.633871\pi$
$600$	31.8952	+	43.6923i	1.30212	+	1.78373i
$601$	−29.9290			−1.22083			−0.610415	−	0.792081i	$-0.708998\pi$
$601$	−29.9290			−1.22083			−0.610415	+	0.792081i	$0.708998\pi$
$602$		−	22.2584i		−	0.907185i
$603$			16.0362i			0.653044i
$604$	80.5643			3.27812
$605$	0.419428	−	0.825474i	0.0170522	−	0.0335603i
$606$	−38.6357			−1.56947
$607$			22.5262i			0.914309i	0.889387	+	0.457154i	$0.151131\pi$
$607$			22.5262i			0.914309i	−0.889387	+	0.457154i	$0.848869\pi$
$608$		−	250.467i		−	10.1578i
$609$	−6.80762			−0.275859
$610$	16.6328	+	8.45122i	0.673443	+	0.342180i
$611$	−16.2184			−0.656126
$612$			5.85923i			0.236846i
$613$			28.3171i			1.14372i	0.820352	+	0.571858i	$0.193777\pi$
$613$			28.3171i			1.14372i	−0.820352	+	0.571858i	$0.806223\pi$
$614$	55.5249			2.24080
$615$	17.3913	+	8.83661i	0.701285	+	0.356326i
$616$	36.5521			1.47272
$617$			25.0388i			1.00802i	0.863697	+	0.504012i	$0.168143\pi$
$617$			25.0388i			1.00802i	−0.863697	+	0.504012i	$0.831857\pi$
$618$		−	10.7457i		−	0.432255i
$619$	20.2234			0.812847			0.406424	−	0.913685i	$-0.366776\pi$
$619$	20.2234			0.812847			0.406424	+	0.913685i	$0.366776\pi$
$620$	2.91492	−	5.73684i	0.117066	−	0.230397i
$621$	−5.84024			−0.234361
$622$			12.0803i			0.484377i
$623$			7.58835i			0.304021i
$624$	55.5781			2.22490
$625$	−7.61805	+	23.8110i	−0.304722	+	0.952441i
$626$	−76.8896			−3.07313
$627$			27.7081i			1.10655i
$628$			54.2888i			2.16636i
$629$	2.87265			0.114540
$630$	2.83961	−	5.58863i	0.113133	−	0.222656i
$631$	19.9504			0.794212			0.397106	−	0.917773i	$-0.370015\pi$
$631$	19.9504			0.794212			0.397106	+	0.917773i	$0.370015\pi$
$632$		−	78.3329i		−	3.11591i
$633$			1.18361i			0.0470443i
$634$	63.4869			2.52139
$635$	22.3491	+	11.3557i	0.886895	+	0.450636i
$636$	−2.46023			−0.0975545
$637$			2.98612i			0.118314i
$638$			64.4772i			2.55268i
$639$	9.40560			0.372080
$640$	148.682	+	75.5461i	5.87717	+	2.98622i
$641$	24.0841			0.951264			0.475632	−	0.879644i	$-0.342219\pi$
$641$	24.0841			0.951264			0.475632	+	0.879644i	$0.342219\pi$
$642$			10.5594i			0.416748i
$643$		−	28.7066i		−	1.13208i	−0.824379	−	0.566039i	$-0.808475\pi$
$643$		−	28.7066i		−	1.13208i	0.824379	−	0.566039i	$-0.191525\pi$
$644$	34.2194			1.34843
$645$	−8.04216	+	15.8278i	−0.316660	+	0.623217i
$646$	22.9920			0.904607
$647$			0.387706i			0.0152423i	0.999971	+	0.00762116i	$0.00242591\pi$
$647$			0.387706i			0.0152423i	−0.999971	+	0.00762116i	$0.997574\pi$
$648$			10.8191i			0.425015i
$649$	16.5951			0.651415
$650$	24.6792	+	33.8073i	0.967998	+	1.32603i
$651$	−0.491153			−0.0192498
$652$			38.7473i			1.51746i
$653$		−	18.8767i		−	0.738704i	−0.929290	−	0.369352i	$-0.879580\pi$
$653$		−	18.8767i		−	0.738704i	0.929290	−	0.369352i	$-0.120420\pi$
$654$	36.9739			1.44579
$655$	−9.67467	+	19.0407i	−0.378021	+	0.743981i
$656$	162.373			6.33960
$657$		−	8.53815i		−	0.333105i
$658$			15.2262i			0.593578i
$659$	1.85135			0.0721185			0.0360592	−	0.999350i	$-0.488520\pi$
$659$	1.85135			0.0721185			0.0360592	+	0.999350i	$0.488520\pi$
$660$	−39.4618	−	20.0507i	−1.53605	−	0.780474i
$661$	−40.4450			−1.57313			−0.786564	−	0.617509i	$-0.788142\pi$
$661$	−40.4450			−1.57313			−0.786564	+	0.617509i	$0.788142\pi$
$662$		−	51.4966i		−	2.00147i
$663$			2.98612i			0.115971i
$664$	−0.0150221			−0.000582970
$665$	−16.3494	−	8.30720i	−0.634001	−	0.322139i
$666$	8.05329			0.312059
$667$			39.7582i			1.53944i
$668$			35.0341i			1.35551i
$669$	−0.645242			−0.0249465
$670$	−45.5365	+	89.6203i	−1.75923	+	3.46233i
$671$	−10.0550			−0.388168
$672$		−	30.5397i		−	1.17810i
$673$			27.7127i			1.06825i	0.845407	+	0.534123i	$0.179358\pi$
$673$			27.7127i			1.06825i	−0.845407	+	0.534123i	$0.820642\pi$
$674$	63.7482			2.45549
$675$	−4.03844	+	2.94805i	−0.155440	+	0.113470i
$676$	−23.9239			−0.920148
$677$			22.7354i			0.873792i	0.899512	+	0.436896i	$0.143922\pi$
$677$			22.7354i			0.873792i	−0.899512	+	0.436896i	$0.856078\pi$
$678$		−	43.0340i		−	1.65271i
$679$	10.1653			0.390108
$680$	−10.9587	+	21.5678i	−0.420248	+	0.827089i
$681$	20.6531			0.791428
$682$			4.65187i			0.178129i
$683$		−	21.6837i		−	0.829704i	−0.909889	−	0.414852i	$-0.863833\pi$
$683$		−	21.6837i		−	0.829704i	0.909889	−	0.414852i	$-0.136167\pi$
$684$	48.0537			1.83738
$685$	25.2092	+	12.8089i	0.963195	+	0.489405i
$686$	2.80343			0.107036
$687$		−	8.46699i		−	0.323036i
$688$			147.775i			5.63387i
$689$	−1.25384			−0.0477675
$690$	−32.6390	−	16.5840i	−1.24254	−	0.631343i
$691$	7.63112			0.290301			0.145151	−	0.989410i	$-0.453633\pi$
$691$	7.63112			0.290301			0.145151	+	0.989410i	$0.453633\pi$
$692$			56.6792i			2.15462i
$693$			3.37847i			0.128338i
$694$	15.1002			0.573197
$695$	8.18562	−	16.1101i	0.310498	−	0.611091i
$696$	73.6524			2.79179
$697$			8.72402i			0.330446i
$698$		−	13.8690i		−	0.524948i
$699$	24.4882			0.926227
$700$	23.6622	−	17.2733i	0.894347	−	0.652869i
$701$	17.9592			0.678308			0.339154	−	0.940731i	$-0.389859\pi$
$701$	17.9592			0.678308			0.339154	+	0.940731i	$0.389859\pi$
$702$			8.37138i			0.315957i
$703$		−	23.5597i		−	0.888569i
$704$	−163.490			−6.16177
$705$	5.50135	−	10.8272i	0.207193	−	0.407776i
$706$	70.0718			2.63719
$707$			13.7816i			0.518309i
$708$		−	28.7806i		−	1.08164i
$709$	48.8046			1.83290			0.916448	−	0.400155i	$-0.131044\pi$
$709$	48.8046			1.83290			0.916448	+	0.400155i	$0.131044\pi$
$710$	52.5644	+	26.7082i	1.97271	+	1.00234i
$711$	7.24024			0.271530
$712$		−	82.0992i		−	3.07680i
$713$			2.86846i			0.107424i
$714$	2.80343			0.104916
$715$	−20.1114	−	10.2187i	−0.752124	−	0.382158i
$716$	−94.8231			−3.54370
$717$			21.1704i			0.790624i
$718$			85.6301i			3.19569i
$719$	−21.4308			−0.799234			−0.399617	−	0.916682i	$-0.630857\pi$
$719$	−21.4308			−0.799234			−0.399617	+	0.916682i	$0.630857\pi$
$720$	−18.8524	+	37.1033i	−0.702586	+	1.38276i
$721$	−3.83305			−0.142750
$722$		−	135.300i		−	5.03535i
$723$			9.48083i			0.352596i
$724$	−5.92189			−0.220085
$725$	20.0692	+	27.4922i	0.745351	+	1.02103i
$726$	1.16086			0.0430834
$727$		−	10.3818i		−	0.385038i	−0.981293	−	0.192519i	$-0.938334\pi$
$727$		−	10.3818i		−	0.385038i	0.981293	−	0.192519i	$-0.0616657\pi$
$728$		−	32.3071i		−	1.19738i
$729$	−1.00000			−0.0370370
$730$	24.2450	−	47.7165i	0.897349	−	1.76607i
$731$	−7.93970			−0.293660
$732$			17.4382i			0.644534i
$733$			44.0321i			1.62636i	0.582011	+	0.813181i	$0.302266\pi$
$733$			44.0321i			1.62636i	−0.582011	+	0.813181i	$0.697734\pi$
$734$	−3.53249			−0.130386
$735$	−1.99350	−	1.01291i	−0.0735312	−	0.0373616i
$736$	−178.359			−6.57442
$737$		−	54.1778i		−	1.99567i
$738$			24.4572i			0.900282i
$739$	18.5124			0.680989			0.340494	−	0.940247i	$-0.389406\pi$
$739$	18.5124			0.680989			0.340494	+	0.940247i	$0.389406\pi$
$740$	33.5536	+	17.0488i	1.23345	+	0.626725i
$741$	24.4902			0.899671
$742$			1.17713i			0.0432139i
$743$			16.9028i			0.620103i	0.950720	+	0.310051i	$0.100346\pi$
$743$			16.9028i			0.620103i	−0.950720	+	0.310051i	$0.899654\pi$
$744$	5.31384			0.194815
$745$	14.3194	−	28.1820i	0.524623	−	1.03251i
$746$	57.6336			2.11012
$747$		−	0.00138848i		−	5.08018e-5i
$748$		−	19.7953i		−	0.723787i
$749$	3.76661			0.137629
$750$	−30.9407	+	5.00792i	−1.12979	+	0.182863i
$751$	−2.02812			−0.0740073			−0.0370037	−	0.999315i	$-0.511781\pi$
$751$	−2.02812			−0.0740073			−0.0370037	+	0.999315i	$0.511781\pi$
$752$		−	101.088i		−	3.68628i
$753$		−	2.33881i		−	0.0852309i
$754$	56.9892			2.07542
$755$	−13.9274	+	27.4105i	−0.506871	+	0.997571i
$756$	5.85923			0.213098
$757$			13.1802i			0.479042i	0.970891	+	0.239521i	$0.0769905\pi$
$757$			13.1802i			0.479042i	−0.970891	+	0.239521i	$0.923010\pi$
$758$		−	9.35115i		−	0.339649i
$759$	19.7311			0.716194
$760$	176.886	+	89.8765i	6.41631	+	3.26016i
$761$	7.26906			0.263503			0.131752	−	0.991283i	$-0.457940\pi$
$761$	7.26906			0.263503			0.131752	+	0.991283i	$0.457940\pi$
$762$			31.4293i			1.13856i
$763$		−	13.1888i		−	0.477466i
$764$	−65.7216			−2.37773
$765$	−1.99350	−	1.01291i	−0.0720750	−	0.0366217i
$766$	−4.82523			−0.174343
$767$		−	14.6679i		−	0.529625i
$768$			112.306i			4.05251i
$769$	−20.8807			−0.752977			−0.376488	−	0.926421i	$-0.622868\pi$
$769$	−20.8807			−0.752977			−0.376488	+	0.926421i	$0.622868\pi$
$770$	−9.59355	+	18.8810i	−0.345728	+	0.680425i
$771$	22.9292			0.825775
$772$		−	76.3487i		−	2.74785i
$773$			41.1634i			1.48054i	0.672307	+	0.740272i	$0.265303\pi$
$773$			41.1634i			1.48054i	−0.672307	+	0.740272i	$0.734697\pi$
$774$	−22.2584			−0.800062
$775$	1.44794	+	1.98349i	0.0520116	+	0.0712492i
$776$	−109.979			−3.94802
$777$		−	2.87265i		−	0.103056i
$778$		−	57.2422i		−	2.05223i
$779$	71.5488			2.56350
$780$	−17.7222	+	34.8789i	−0.634555	+	1.24887i
$781$	−31.7766			−1.13705
$782$		−	16.3727i		−	0.585488i
$783$			6.80762i			0.243285i
$784$	−18.6122			−0.664720
$785$	−18.4707	−	9.38508i	−0.659249	−	0.334968i
$786$	−26.7767			−0.955094
$787$			37.7603i			1.34601i	0.739639	+	0.673004i	$0.234996\pi$
$787$			37.7603i			1.34601i	−0.739639	+	0.673004i	$0.765004\pi$
$788$			19.6939i			0.701565i
$789$	6.17182			0.219723
$790$	40.4630	+	20.5595i	1.43961	+	0.731473i
$791$	−15.3505			−0.545799
$792$		−	36.5521i		−	1.29882i
$793$			8.88725i			0.315595i
$794$	−21.2761			−0.755061
$795$	0.425308	−	0.837048i	0.0150841	−	0.0296870i
$796$	18.2689			0.647524
$797$		−	45.9127i		−	1.62631i	−0.582047	−	0.813155i	$-0.697748\pi$
$797$		−	45.9127i		−	1.62631i	0.582047	−	0.813155i	$-0.302252\pi$
$798$		−	22.9920i		−	0.813907i
$799$	5.43126			0.192144
$800$	−123.333	+	90.0325i	−4.36048	+	3.18313i
$801$	7.58835			0.268121
$802$			4.64480i			0.164014i
$803$			28.8459i			1.01795i
$804$	−93.9598			−3.31371
$805$	−5.91561	+	11.6425i	−0.208498	+	0.410344i
$806$	4.11163			0.144826
$807$			21.9597i			0.773018i
$808$		−	149.104i		−	5.24547i
$809$	−28.9703			−1.01854			−0.509270	−	0.860607i	$-0.670085\pi$
$809$	−28.9703			−1.01854			−0.509270	+	0.860607i	$0.670085\pi$
$810$	−5.58863	−	2.83961i	−0.196364	−	0.0997738i
$811$	−28.6073			−1.00454			−0.502270	−	0.864711i	$-0.667502\pi$
$811$	−28.6073			−1.00454			−0.502270	+	0.864711i	$0.667502\pi$
$812$		−	39.8875i		−	1.39978i
$813$		−	29.7006i		−	1.04164i
$814$	−27.2078			−0.953633
$815$	−13.1831	−	6.69838i	−0.461783	−	0.234634i
$816$	−18.6122			−0.651556
$817$			65.1163i			2.27813i
$818$		−	16.9473i		−	0.592549i
$819$	2.98612			0.104343
$820$	−51.7758	+	101.900i	−1.80809	+	3.55849i
$821$	−21.6958			−0.757188			−0.378594	−	0.925563i	$-0.623592\pi$
$821$	−21.6958			−0.757188			−0.378594	+	0.925563i	$0.623592\pi$
$822$			35.4515i			1.23651i
$823$			33.1277i			1.15476i	0.816476	+	0.577379i	$0.195925\pi$
$823$			33.1277i			1.15476i	−0.816476	+	0.577379i	$0.804075\pi$
$824$	41.4701			1.44468
$825$	13.6438	−	9.95989i	0.475015	−	0.346759i
$826$	−13.7705			−0.479137
$827$		−	31.8796i		−	1.10856i	−0.832330	−	0.554280i	$-0.812994\pi$
$827$		−	31.8796i		−	1.10856i	0.832330	−	0.554280i	$-0.187006\pi$
$828$		−	34.2194i		−	1.18920i
$829$	−12.0622			−0.418937			−0.209469	−	0.977815i	$-0.567173\pi$
$829$	−12.0622			−0.418937			−0.209469	+	0.977815i	$0.567173\pi$
$830$	0.00394274	−	0.00775969i	0.000136854	−	0.000269343i
$831$	−0.330767			−0.0114742
$832$			144.503i			5.00976i
$833$		−	1.00000i		−	0.0346479i
$834$	22.6555			0.784495
$835$	−11.9197	−	6.05646i	−0.412498	−	0.209593i
$836$	−162.348			−5.61493
$837$			0.491153i			0.0169767i
$838$		−	5.77555i		−	0.199513i
$839$	31.0708			1.07268			0.536342	−	0.844001i	$-0.319806\pi$
$839$	31.0708			1.07268			0.536342	+	0.844001i	$0.319806\pi$
$840$	21.5678	+	10.9587i	0.744161	+	0.378112i
$841$	17.3438			0.598060
$842$		−	25.3923i		−	0.875076i
$843$		−	8.44777i		−	0.290957i
$844$	−6.93505			−0.238714
$845$	4.13580	−	8.13964i	0.142276	−	0.280012i
$846$	15.2262			0.523487
$847$		−	0.414084i		−	0.0142281i
$848$		−	7.81505i		−	0.268370i
$849$	−20.5216			−0.704301
$850$	−8.26465	−	11.3215i	−0.283475	−	0.388324i
$851$	−16.7770			−0.575108
$852$			55.1096i			1.88802i
$853$			0.590902i			0.0202321i	0.999949	+	0.0101161i	$0.00322010\pi$
$853$			0.590902i			0.0202321i	−0.999949	+	0.0101161i	$0.996780\pi$
$854$	8.34354			0.285510
$855$	−8.30720	+	16.3494i	−0.284100	+	0.559137i
$856$	−40.7514			−1.39285
$857$			27.9253i			0.953909i	0.878928	+	0.476955i	$0.158259\pi$
$857$			27.9253i			0.953909i	−0.878928	+	0.476955i	$0.841741\pi$
$858$		−	28.2825i		−	0.965548i
$859$	−10.1726			−0.347084			−0.173542	−	0.984826i	$-0.555521\pi$
$859$	−10.1726			−0.347084			−0.173542	+	0.984826i	$0.555521\pi$
$860$	−92.7385	−	47.1209i	−3.16236	−	1.60681i
$861$	8.72402			0.297314
$862$		−	38.0254i		−	1.29515i
$863$		−	29.5369i		−	1.00545i	−0.864447	−	0.502723i	$-0.832331\pi$
$863$		−	29.5369i		−	1.00545i	0.864447	−	0.502723i	$-0.167669\pi$
$864$	−30.5397			−1.03898
$865$	−19.2841	−	9.79833i	−0.655678	−	0.333153i
$866$	−14.8959			−0.506182
$867$		−	1.00000i		−	0.0339618i
$868$		−	2.87778i		−	0.0976783i
$869$	−24.4610			−0.829781
$870$	−19.3310	+	38.0453i	−0.655383	+	1.28986i
$871$	−47.8859			−1.62255
$872$			142.691i			4.83212i
$873$		−	10.1653i		−	0.344043i
$874$	−134.279			−4.54204
$875$	1.78635	+	11.0367i	0.0603898	+	0.373109i
$876$	50.0270			1.69026
$877$		−	23.9038i		−	0.807173i	−0.914941	−	0.403587i	$-0.867763\pi$
$877$		−	23.9038i		−	0.807173i	0.914941	−	0.403587i	$-0.132237\pi$
$878$			63.2061i			2.13310i
$879$	17.9089			0.604052
$880$	63.6922	−	125.352i	2.14706	−	4.22563i
$881$	38.0782			1.28289			0.641443	−	0.767170i	$-0.278336\pi$
$881$	38.0782			1.28289			0.641443	+	0.767170i	$0.278336\pi$
$882$		−	2.80343i		−	0.0943965i
$883$			17.5620i			0.591007i	0.955342	+	0.295503i	$0.0954874\pi$
$883$			17.5620i			0.591007i	−0.955342	+	0.295503i	$0.904513\pi$
$884$	−17.4964			−0.588466
$885$	9.79208	+	4.97541i	0.329157	+	0.167246i
$886$	40.0671			1.34608
$887$		−	35.3014i		−	1.18530i	−0.805459	−	0.592652i	$-0.798081\pi$
$887$		−	35.3014i		−	1.18530i	0.805459	−	0.592652i	$-0.201919\pi$
$888$			31.0795i			1.04296i
$889$	11.2110			0.376005
$890$	42.4085	+	21.5480i	1.42154	+	0.722290i
$891$	3.37847			0.113183
$892$		−	3.78062i		−	0.126585i
$893$		−	44.5437i		−	1.49060i
$894$	39.6321			1.32550
$895$	16.3924	−	32.2618i	0.547937	−	1.07839i
$896$	74.5836			2.49166
$897$		−	17.4397i		−	0.582293i
$898$			5.70379i			0.190338i
$899$	3.34359			0.111515
$900$	−17.2733	−	23.6622i	−0.575776	−	0.788740i
$901$	0.419890			0.0139886
$902$		−	82.6280i		−	2.75121i
$903$			7.93970i			0.264217i
$904$	166.078			5.52368
$905$	1.02374	−	2.01481i	0.0340302	−	0.0669747i
$906$	−38.5471			−1.28064
$907$			33.4468i			1.11058i	0.831656	+	0.555292i	$0.187393\pi$
$907$			33.4468i			1.11058i	−0.831656	+	0.555292i	$0.812607\pi$
$908$			121.011i			4.01590i
$909$	13.7816			0.457106
$910$	16.6883	+	8.47941i	0.553212	+	0.281090i
$911$	−16.4216			−0.544071			−0.272036	−	0.962287i	$-0.587697\pi$
$911$	−16.4216			−0.544071			−0.272036	+	0.962287i	$0.587697\pi$
$912$			152.645i			5.05458i
$913$			0.00469094i			0.000155247i
$914$	−18.7021			−0.618610
$915$	−5.93302	−	3.01460i	−0.196140	−	0.0996595i
$916$	49.6101			1.63916
$917$			9.55141i			0.315415i
$918$		−	2.80343i		−	0.0925271i
$919$	44.7007			1.47454			0.737271	−	0.675598i	$-0.236114\pi$
$919$	44.7007			1.47454			0.737271	+	0.675598i	$0.236114\pi$
$920$	64.0016	−	125.961i	2.11007	−	4.15282i
$921$	−19.8061			−0.652632
$922$		−	93.0647i		−	3.06492i
$923$			28.0862i			0.924469i
$924$	−19.7953			−0.651217
$925$	−11.6010	+	8.46871i	−0.381440	+	0.278449i
$926$	3.67653			0.120818
$927$			3.83305i			0.125894i
$928$			207.903i			6.82475i
$929$	45.7602			1.50134			0.750672	−	0.660676i	$-0.229730\pi$
$929$	45.7602			1.50134			0.750672	+	0.660676i	$0.229730\pi$
$930$	−1.39468	+	2.74487i	−0.0457335	+	0.0900080i
$931$	−8.20136			−0.268789
$932$			143.482i			4.69991i
$933$		−	4.30912i		−	0.141074i
$934$	−99.1438			−3.24409
$935$	6.73497	+	3.42207i	0.220257	+	0.111914i
$936$	−32.3071			−1.05599
$937$		−	21.8797i		−	0.714779i	−0.933955	−	0.357390i	$-0.883667\pi$
$937$		−	21.8797i		−	0.714779i	0.933955	−	0.357390i	$-0.116333\pi$
$938$			44.9564i			1.46788i
$939$	27.4270			0.895045
$940$	63.4391	+	32.2337i	2.06915	+	1.05135i
$941$	21.9504			0.715563			0.357782	−	0.933805i	$-0.383533\pi$
$941$	21.9504			0.715563			0.357782	+	0.933805i	$0.383533\pi$
$942$		−	25.9752i		−	0.846318i
$943$		−	50.9504i		−	1.65917i
$944$	91.4232			2.97557
$945$	−1.01291	+	1.99350i	−0.0329498	+	0.0648484i
$946$	75.1995			2.44495
$947$			6.14205i			0.199590i	0.995008	+	0.0997949i	$0.0318187\pi$
$947$			6.14205i			0.199590i	−0.995008	+	0.0997949i	$0.968181\pi$
$948$			42.4223i			1.37781i
$949$	25.4959			0.827632
$950$	−92.8517	+	67.7814i	−3.01251	+	2.19912i
$951$	−22.6461			−0.734352
$952$			10.8191i			0.350649i
$953$			51.4151i			1.66550i	0.553650	+	0.832750i	$0.313235\pi$
$953$			51.4151i			1.66550i	−0.553650	+	0.832750i	$0.686765\pi$
$954$	1.17713			0.0381111
$955$	11.3615	−	22.3606i	0.367650	−	0.723571i
$956$	−124.042			−4.01182
$957$		−	22.9994i		−	0.743464i
$958$			75.6112i			2.44289i
$959$	12.6457			0.408352
$960$	−96.4687	−	49.0163i	−3.11351	−	1.58199i
$961$	−30.7588			−0.992218
$962$			24.0481i			0.775341i
$963$		−	3.76661i		−	0.121377i
$964$	−55.5504			−1.78916
$965$	25.9762	+	13.1987i	0.836204	+	0.424880i
$966$	−16.3727			−0.526784
$967$		−	19.1624i		−	0.616221i	−0.951351	−	0.308110i	$-0.900303\pi$
$967$		−	19.1624i		−	0.616221i	0.951351	−	0.308110i	$-0.0996966\pi$
$968$			4.48001i			0.143993i
$969$	−8.20136			−0.263466
$970$	28.8655	−	56.8100i	0.926814	−	1.82406i
$971$	30.0374			0.963946			0.481973	−	0.876186i	$-0.339920\pi$
$971$	30.0374			0.963946			0.481973	+	0.876186i	$0.339920\pi$
$972$		−	5.85923i		−	0.187935i
$973$		−	8.08133i		−	0.259076i
$974$	93.6331			3.00020
$975$	−8.80321	−	12.0593i	−0.281928	−	0.386206i
$976$	−55.3933			−1.77310
$977$		−	55.6869i		−	1.78158i	−0.454412	−	0.890792i	$-0.650151\pi$
$977$		−	55.6869i		−	1.78158i	0.454412	−	0.890792i	$-0.349849\pi$
$978$		−	18.5392i		−	0.592819i
$979$	−25.6371			−0.819364
$980$	5.93485	−	11.6804i	0.189582	−	0.373115i
$981$	−13.1888			−0.421085
$982$		−	88.7550i		−	2.83229i
$983$		−	33.8445i		−	1.07947i	−0.841835	−	0.539736i	$-0.818524\pi$
$983$		−	33.8445i		−	1.07947i	0.841835	−	0.539736i	$-0.181476\pi$
$984$	−94.3861			−3.00892
$985$	−6.70047	−	3.40454i	−0.213495	−	0.108478i
$986$	−19.0847			−0.607781
$987$		−	5.43126i		−	0.172879i
$988$			143.494i			4.56515i
$989$	46.3698			1.47447
$990$	18.8810	+	9.59355i	0.600079	+	0.304903i
$991$	−32.8709			−1.04418			−0.522089	−	0.852891i	$-0.674847\pi$
$991$	−32.8709			−1.04418			−0.522089	+	0.852891i	$0.674847\pi$
$992$			14.9997i			0.476241i
$993$			18.3691i			0.582927i
$994$	26.3680			0.836341
$995$	−3.15820	+	6.21565i	−0.100122	+	0.197049i
$996$	0.00813542			0.000257781
$997$			17.3006i			0.547915i	0.961742	+	0.273958i	$0.0883328\pi$
$997$			17.3006i			0.547915i	−0.961742	+	0.273958i	$0.911667\pi$
$998$		−	22.0996i		−	0.699551i
$999$	−2.87265			−0.0908867

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1785.2.g.g.1429.1	✓	28
5.2	odd	4		8925.2.a.cx.1.14		14
5.3	odd	4		8925.2.a.cu.1.1		14
5.4	even	2	inner	1785.2.g.g.1429.28	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1785.2.g.g.1429.1	✓	28	1.1	even	1	trivial
1785.2.g.g.1429.28	yes	28	5.4	even	2	inner
8925.2.a.cu.1.1		14	5.3	odd	4
8925.2.a.cx.1.14		14	5.2	odd	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:	\( N \)	\(=\)	\( 1785 = 3 \cdot 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1785.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.80343i q^{2} +1.00000i q^{3} -5.85923 q^{4} +(1.01291 - 1.99350i) q^{5} +2.80343 q^{6} -1.00000i q^{7} +10.8191i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.80343i q^{2} +1.00000i q^{3} -5.85923 q^{4} +(1.01291 - 1.99350i) q^{5} +2.80343 q^{6} -1.00000i q^{7} +10.8191i q^{8} -1.00000 q^{9} +(-5.58863 - 2.83961i) q^{10} +3.37847 q^{11} -5.85923i q^{12} -2.98612i q^{13} -2.80343 q^{14} +(1.99350 + 1.01291i) q^{15} +18.6122 q^{16} +1.00000i q^{17} +2.80343i q^{18} +8.20136 q^{19} +(-5.93485 + 11.6804i) q^{20} +1.00000 q^{21} -9.47132i q^{22} -5.84024i q^{23} -10.8191 q^{24} +(-2.94805 - 4.03844i) q^{25} -8.37138 q^{26} -1.00000i q^{27} +5.85923i q^{28} -6.80762 q^{29} +(2.83961 - 5.58863i) q^{30} -0.491153 q^{31} -30.5397i q^{32} +3.37847i q^{33} +2.80343 q^{34} +(-1.99350 - 1.01291i) q^{35} +5.85923 q^{36} -2.87265i q^{37} -22.9920i q^{38} +2.98612 q^{39} +(21.5678 + 10.9587i) q^{40} +8.72402 q^{41} -2.80343i q^{42} +7.93970i q^{43} -19.7953 q^{44} +(-1.01291 + 1.99350i) q^{45} -16.3727 q^{46} -5.43126i q^{47} +18.6122i q^{48} -1.00000 q^{49} +(-11.3215 + 8.26465i) q^{50} -1.00000 q^{51} +17.4964i q^{52} -0.419890i q^{53} -2.80343 q^{54} +(3.42207 - 6.73497i) q^{55} +10.8191 q^{56} +8.20136i q^{57} +19.0847i q^{58} +4.91201 q^{59} +(-11.6804 - 5.93485i) q^{60} -2.97619 q^{61} +1.37692i q^{62} +1.00000i q^{63} -48.3918 q^{64} +(-5.95281 - 3.02465i) q^{65} +9.47132 q^{66} -16.0362i q^{67} -5.85923i q^{68} +5.84024 q^{69} +(-2.83961 + 5.58863i) q^{70} -9.40560 q^{71} -10.8191i q^{72} +8.53815i q^{73} -8.05329 q^{74} +(4.03844 - 2.94805i) q^{75} -48.0537 q^{76} -3.37847i q^{77} -8.37138i q^{78} -7.24024 q^{79} +(18.8524 - 37.1033i) q^{80} +1.00000 q^{81} -24.4572i q^{82} +0.00138848i q^{83} -5.85923 q^{84} +(1.99350 + 1.01291i) q^{85} +22.2584 q^{86} -6.80762i q^{87} +36.5521i q^{88} -7.58835 q^{89} +(5.58863 + 2.83961i) q^{90} -2.98612 q^{91} +34.2194i q^{92} -0.491153i q^{93} -15.2262 q^{94} +(8.30720 - 16.3494i) q^{95} +30.5397 q^{96} +10.1653i q^{97} +2.80343i q^{98} -3.37847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 34 q^{4} + 6 q^{6} - 28 q^{9}+O(q^{10}) \) 28 * q - 34 * q^4 + 6 * q^6 - 28 * q^9	\( 28 q - 34 q^{4} + 6 q^{6} - 28 q^{9} + 4 q^{10} + 8 q^{11} - 6 q^{14} + 38 q^{16} + 12 q^{19} - 4 q^{20} + 28 q^{21} - 30 q^{24} - 4 q^{26} - 40 q^{29} + 10 q^{30} - 14 q^{31} + 6 q^{34} + 34 q^{36} + 2 q^{39} + 30 q^{40} + 50 q^{41} - 48 q^{44} - 20 q^{46} - 28 q^{49} - 22 q^{50} - 28 q^{51} - 6 q^{54} + 2 q^{55} + 30 q^{56} - 28 q^{59} - 6 q^{60} - 18 q^{61} - 54 q^{64} - 24 q^{65} + 24 q^{66} - 14 q^{69} - 10 q^{70} + 4 q^{71} - 128 q^{74} - 8 q^{75} - 84 q^{76} + 8 q^{79} + 48 q^{80} + 28 q^{81} - 34 q^{84} + 88 q^{86} - 76 q^{89} - 4 q^{90} - 2 q^{91} - 16 q^{94} + 16 q^{95} + 66 q^{96} - 8 q^{99}+O(q^{100}) \) 28 * q - 34 * q^4 + 6 * q^6 - 28 * q^9 + 4 * q^10 + 8 * q^11 - 6 * q^14 + 38 * q^16 + 12 * q^19 - 4 * q^20 + 28 * q^21 - 30 * q^24 - 4 * q^26 - 40 * q^29 + 10 * q^30 - 14 * q^31 + 6 * q^34 + 34 * q^36 + 2 * q^39 + 30 * q^40 + 50 * q^41 - 48 * q^44 - 20 * q^46 - 28 * q^49 - 22 * q^50 - 28 * q^51 - 6 * q^54 + 2 * q^55 + 30 * q^56 - 28 * q^59 - 6 * q^60 - 18 * q^61 - 54 * q^64 - 24 * q^65 + 24 * q^66 - 14 * q^69 - 10 * q^70 + 4 * q^71 - 128 * q^74 - 8 * q^75 - 84 * q^76 + 8 * q^79 + 48 * q^80 + 28 * q^81 - 34 * q^84 + 88 * q^86 - 76 * q^89 - 4 * q^90 - 2 * q^91 - 16 * q^94 + 16 * q^95 + 66 * q^96 - 8 * q^99

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