LMFDB - Embedded newform 840.2.e.d.491.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(491,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.491"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [44,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			491.10
Character	$\chi$	$=$	840.491
Dual form			840.2.e.d.491.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.17505 + 0.786923i) q^{2} +(1.39892 - 1.02128i) q^{3} +(0.761505 - 1.84935i) q^{4} -1.00000 q^{5} +(-0.840138 + 2.30091i) q^{6} +1.00000i q^{7} +(0.560490 + 2.77234i) q^{8} +(0.913962 - 2.85739i) q^{9} +(1.17505 - 0.786923i) q^{10} +2.60621i q^{11} +(-0.823428 - 3.36481i) q^{12} +3.64377i q^{13} +(-0.786923 - 1.17505i) q^{14} +(-1.39892 + 1.02128i) q^{15} +(-2.84022 - 2.81658i) q^{16} +4.39342i q^{17} +(1.17459 + 4.07681i) q^{18} +6.32881 q^{19} +(-0.761505 + 1.84935i) q^{20} +(1.02128 + 1.39892i) q^{21} +(-2.05089 - 3.06244i) q^{22} -0.872985 q^{23} +(3.61542 + 3.30586i) q^{24} +1.00000 q^{25} +(-2.86737 - 4.28163i) q^{26} +(-1.63964 - 4.93068i) q^{27} +(1.84935 + 0.761505i) q^{28} +2.82610 q^{29} +(0.840138 - 2.30091i) q^{30} +4.51893i q^{31} +(5.55385 + 1.07460i) q^{32} +(2.66168 + 3.64589i) q^{33} +(-3.45729 - 5.16251i) q^{34} -1.00000i q^{35} +(-4.58834 - 3.86616i) q^{36} -0.410585i q^{37} +(-7.43670 + 4.98029i) q^{38} +(3.72132 + 5.09735i) q^{39} +(-0.560490 - 2.77234i) q^{40} +1.31574i q^{41} +(-2.30091 - 0.840138i) q^{42} -2.37889 q^{43} +(4.81981 + 1.98464i) q^{44} +(-0.913962 + 2.85739i) q^{45} +(1.02581 - 0.686972i) q^{46} +12.8953 q^{47} +(-6.84978 - 1.03951i) q^{48} -1.00000 q^{49} +(-1.17505 + 0.786923i) q^{50} +(4.48693 + 6.14606i) q^{51} +(6.73862 + 2.77475i) q^{52} +6.44201 q^{53} +(5.80673 + 4.50354i) q^{54} -2.60621i q^{55} +(-2.77234 + 0.560490i) q^{56} +(8.85351 - 6.46351i) q^{57} +(-3.32082 + 2.22392i) q^{58} -10.3119i q^{59} +(0.823428 + 3.36481i) q^{60} -11.4151i q^{61} +(-3.55605 - 5.30998i) q^{62} +(2.85739 + 0.913962i) q^{63} +(-7.37170 + 3.10773i) q^{64} -3.64377i q^{65} +(-5.99665 - 2.18958i) q^{66} -9.90769 q^{67} +(8.12500 + 3.34561i) q^{68} +(-1.22124 + 0.891565i) q^{69} +(0.786923 + 1.17505i) q^{70} +2.67806 q^{71} +(8.43391 + 0.932274i) q^{72} +14.6519 q^{73} +(0.323099 + 0.482460i) q^{74} +(1.39892 - 1.02128i) q^{75} +(4.81942 - 11.7042i) q^{76} -2.60621 q^{77} +(-8.38398 - 3.06127i) q^{78} +11.3895i q^{79} +(2.84022 + 2.81658i) q^{80} +(-7.32935 - 5.22309i) q^{81} +(-1.03538 - 1.54606i) q^{82} +15.8054i q^{83} +(3.36481 - 0.823428i) q^{84} -4.39342i q^{85} +(2.79533 - 1.87201i) q^{86} +(3.95349 - 2.88625i) q^{87} +(-7.22530 + 1.46076i) q^{88} +1.07306i q^{89} +(-1.17459 - 4.07681i) q^{90} -3.64377 q^{91} +(-0.664782 + 1.61446i) q^{92} +(4.61510 + 6.32162i) q^{93} +(-15.1526 + 10.1476i) q^{94} -6.32881 q^{95} +(8.86687 - 4.16876i) q^{96} -11.4590 q^{97} +(1.17505 - 0.786923i) q^{98} +(7.44697 + 2.38198i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{2} + 4 q^{3} - 2 q^{4} - 44 q^{5} - 6 q^{6} - 22 q^{8} + 4 q^{9} - 2 q^{10} + 6 q^{12} + 4 q^{14} - 4 q^{15} + 22 q^{16} + 2 q^{18} + 16 q^{19} + 2 q^{20} + 16 q^{23} + 10 q^{24} + 44 q^{25}+ \cdots - 64 q^{99}+O(q^{100}) $ 44 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 - 44 * q^5 - 6 * q^6 - 22 * q^8 + 4 * q^9 - 2 * q^10 + 6 * q^12 + 4 * q^14 - 4 * q^15 + 22 * q^16 + 2 * q^18 + 16 * q^19 + 2 * q^20 + 16 * q^23 + 10 * q^24 + 44 * q^25 - 16 * q^26 + 4 * q^27 + 16 * q^29 + 6 * q^30 - 18 * q^32 + 24 * q^33 + 20 * q^34 - 46 * q^36 + 8 * q^38 - 16 * q^39 + 22 * q^40 - 4 * q^42 + 24 * q^43 + 32 * q^44 - 4 * q^45 - 24 * q^47 + 18 * q^48 - 44 * q^49 + 2 * q^50 - 20 * q^52 - 32 * q^53 + 2 * q^54 + 8 * q^56 - 4 * q^58 - 6 * q^60 + 32 * q^62 - 50 * q^64 - 8 * q^66 + 24 * q^67 - 28 * q^68 - 8 * q^69 - 4 * q^70 + 8 * q^71 + 2 * q^72 + 8 * q^73 - 48 * q^74 + 4 * q^75 + 12 * q^76 + 8 * q^77 - 84 * q^78 - 22 * q^80 + 20 * q^81 - 8 * q^82 + 4 * q^84 - 4 * q^86 - 16 * q^87 - 28 * q^88 - 2 * q^90 - 16 * q^91 + 76 * q^92 + 16 * q^93 - 16 * q^95 + 38 * q^96 + 24 * q^97 - 2 * q^98 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$1$	$-1$	$1$	$-1$	$-1$

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 $

$2$	−1.17505	+	0.786923i	−0.830889	+	0.556439i
$2$	−1.17505	+	0.786923i	−0.830889	+	0.556439i
$3$	1.39892	−	1.02128i	0.807668	−	0.589638i
$3$	1.39892	−	1.02128i	0.807668	−	0.589638i
$4$	0.761505	−	1.84935i	0.380752	−	0.924677i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.840138	+	2.30091i	−0.342985	+	0.939341i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	0.560490	+	2.77234i	0.198163	+	0.980169i
$9$	0.913962	−	2.85739i	0.304654	−	0.952463i
$10$	1.17505	−	0.786923i	0.371585	−	0.248847i
$11$			2.60621i			0.785803i	0.919581	+	0.392901i	$0.128529\pi$
$11$			2.60621i			0.785803i	−0.919581	+	0.392901i	$0.871471\pi$
$12$	−0.823428	−	3.36481i	−0.237703	−	0.971338i
$13$			3.64377i			1.01060i	0.862944	+	0.505300i	$0.168618\pi$
$13$			3.64377i			1.01060i	−0.862944	+	0.505300i	$0.831382\pi$
$14$	−0.786923	−	1.17505i	−0.210314	−	0.314046i
$15$	−1.39892	+	1.02128i	−0.361200	+	0.263694i
$16$	−2.84022	−	2.81658i	−0.710055	−	0.704146i
$17$			4.39342i			1.06556i	0.846253	+	0.532781i	$0.178853\pi$
$17$			4.39342i			1.06556i	−0.846253	+	0.532781i	$0.821147\pi$
$18$	1.17459	+	4.07681i	0.276853	+	0.960912i
$19$	6.32881			1.45193			0.725965	−	0.687732i	$-0.241394\pi$
$19$	6.32881			1.45193			0.725965	+	0.687732i	$0.241394\pi$
$20$	−0.761505	+	1.84935i	−0.170278	+	0.413528i
$21$	1.02128	+	1.39892i	0.222862	+	0.305270i
$22$	−2.05089	−	3.06244i	−0.437251	−	0.652915i
$23$	−0.872985			−0.182030			−0.0910150	−	0.995850i	$-0.529011\pi$
$23$	−0.872985			−0.182030			−0.0910150	+	0.995850i	$0.529011\pi$
$24$	3.61542	+	3.30586i	0.737995	+	0.674806i
$25$	1.00000			0.200000
$26$	−2.86737	−	4.28163i	−0.562337	−	0.839696i
$27$	−1.63964	−	4.93068i	−0.315549	−	0.948909i
$28$	1.84935	+	0.761505i	0.349495	+	0.143911i
$29$	2.82610			0.524793			0.262397	−	0.964960i	$-0.415487\pi$
$29$	2.82610			0.524793			0.262397	+	0.964960i	$0.415487\pi$
$30$	0.840138	−	2.30091i	0.153387	−	0.420086i
$31$			4.51893i			0.811623i	0.913957	+	0.405812i	$0.133011\pi$
$31$			4.51893i			0.811623i	−0.913957	+	0.405812i	$0.866989\pi$
$32$	5.55385	+	1.07460i	0.981791	+	0.189965i
$33$	2.66168	+	3.64589i	0.463339	+	0.634668i
$34$	−3.45729	−	5.16251i	−0.592920	−	0.885364i
$35$		−	1.00000i		−	0.169031i
$36$	−4.58834	−	3.86616i	−0.764723	−	0.644359i
$37$		−	0.410585i		−	0.0674998i	−0.999430	−	0.0337499i	$-0.989255\pi$
$37$		−	0.410585i		−	0.0674998i	0.999430	−	0.0337499i	$-0.0107450\pi$
$38$	−7.43670	+	4.98029i	−1.20639	+	0.807909i
$39$	3.72132	+	5.09735i	0.595888	+	0.816229i
$40$	−0.560490	−	2.77234i	−0.0886212	−	0.438345i
$41$			1.31574i			0.205484i	0.994708	+	0.102742i	$0.0327616\pi$
$41$			1.31574i			0.205484i	−0.994708	+	0.102742i	$0.967238\pi$
$42$	−2.30091	−	0.840138i	−0.355038	−	0.129636i
$43$	−2.37889			−0.362778			−0.181389	−	0.983411i	$-0.558059\pi$
$43$	−2.37889			−0.362778			−0.181389	+	0.983411i	$0.558059\pi$
$44$	4.81981	+	1.98464i	0.726614	+	0.299196i
$45$	−0.913962	+	2.85739i	−0.136245	+	0.425954i
$46$	1.02581	−	0.686972i	0.151247	−	0.101289i
$47$	12.8953			1.88097			0.940483	−	0.339840i	$-0.110373\pi$
$47$	12.8953			1.88097			0.940483	+	0.339840i	$0.110373\pi$
$48$	−6.84978	−	1.03951i	−0.988680	−	0.150040i
$49$	−1.00000			−0.142857
$50$	−1.17505	+	0.786923i	−0.166178	+	0.111288i
$51$	4.48693	+	6.14606i	0.628296	+	0.860620i
$52$	6.73862	+	2.77475i	0.934479	+	0.384788i
$53$	6.44201			0.884879			0.442439	−	0.896798i	$-0.354113\pi$
$53$	6.44201			0.884879			0.442439	+	0.896798i	$0.354113\pi$
$54$	5.80673	+	4.50354i	0.790196	+	0.612854i
$55$		−	2.60621i		−	0.351422i
$56$	−2.77234	+	0.560490i	−0.370469	+	0.0748986i
$57$	8.85351	−	6.46351i	1.17268	−	0.856113i
$58$	−3.32082	+	2.22392i	−0.436045	+	0.292015i
$59$		−	10.3119i		−	1.34250i	−0.741232	−	0.671249i	$-0.765758\pi$
$59$		−	10.3119i		−	1.34250i	0.741232	−	0.671249i	$-0.234242\pi$
$60$	0.823428	+	3.36481i	0.106304	+	0.434395i
$61$		−	11.4151i		−	1.46156i	−0.682614	−	0.730779i	$-0.739157\pi$
$61$		−	11.4151i		−	1.46156i	0.682614	−	0.730779i	$-0.260843\pi$
$62$	−3.55605	−	5.30998i	−0.451618	−	0.674369i
$63$	2.85739	+	0.913962i	0.359997	+	0.115148i
$64$	−7.37170	+	3.10773i	−0.921463	+	0.388467i
$65$		−	3.64377i		−	0.451954i
$66$	−5.99665	−	2.18958i	−0.738137	−	0.269518i
$67$	−9.90769			−1.21042			−0.605208	−	0.796067i	$-0.706910\pi$
$67$	−9.90769			−1.21042			−0.605208	+	0.796067i	$0.706910\pi$
$68$	8.12500	+	3.34561i	0.985301	+	0.405715i
$69$	−1.22124	+	0.891565i	−0.147020	+	0.107332i
$70$	0.786923	+	1.17505i	0.0940553	+	0.140446i
$71$	2.67806			0.317828			0.158914	−	0.987292i	$-0.449201\pi$
$71$	2.67806			0.317828			0.158914	+	0.987292i	$0.449201\pi$
$72$	8.43391	+	0.932274i	0.993946	+	0.109870i
$73$	14.6519			1.71487			0.857435	−	0.514592i	$-0.172056\pi$
$73$	14.6519			1.71487			0.857435	+	0.514592i	$0.172056\pi$
$74$	0.323099	+	0.482460i	0.0375595	+	0.0560848i
$75$	1.39892	−	1.02128i	0.161534	−	0.117928i
$76$	4.81942	−	11.7042i	0.552825	−	1.34257i
$77$	−2.60621			−0.297006
$78$	−8.38398	−	3.06127i	−0.949298	−	0.346621i
$79$			11.3895i			1.28142i	0.767784	+	0.640709i	$0.221359\pi$
$79$			11.3895i			1.28142i	−0.767784	+	0.640709i	$0.778641\pi$
$80$	2.84022	+	2.81658i	0.317546	+	0.314904i
$81$	−7.32935	−	5.22309i	−0.814372	−	0.580344i
$82$	−1.03538	−	1.54606i	−0.114339	−	0.170734i
$83$			15.8054i			1.73487i	0.497551	+	0.867435i	$0.334233\pi$
$83$			15.8054i			1.73487i	−0.497551	+	0.867435i	$0.665767\pi$
$84$	3.36481	−	0.823428i	0.367131	−	0.0898434i
$85$		−	4.39342i		−	0.476534i
$86$	2.79533	−	1.87201i	0.301428	−	0.201864i
$87$	3.95349	−	2.88625i	0.423858	−	0.309438i
$88$	−7.22530	+	1.46076i	−0.770220	+	0.155717i
$89$			1.07306i			0.113744i	0.998381	+	0.0568720i	$0.0181127\pi$
$89$			1.07306i			0.113744i	−0.998381	+	0.0568720i	$0.981887\pi$
$90$	−1.17459	−	4.07681i	−0.123813	−	0.429733i
$91$	−3.64377			−0.381971
$92$	−0.664782	+	1.61446i	−0.0693084	+	0.168319i
$93$	4.61510	+	6.32162i	0.478564	+	0.655522i
$94$	−15.1526	+	10.1476i	−1.56287	+	1.04664i
$95$	−6.32881			−0.649322
$96$	8.86687	−	4.16876i	0.904971	−	0.425473i
$97$	−11.4590			−1.16349			−0.581743	−	0.813373i	$-0.697629\pi$
$97$	−11.4590			−1.16349			−0.581743	+	0.813373i	$0.697629\pi$
$98$	1.17505	−	0.786923i	0.118698	−	0.0794912i
$99$	7.44697	+	2.38198i	0.748448	+	0.239398i
$100$	0.761505	−	1.84935i	0.0761505	−	0.184935i
$101$	−8.86572			−0.882173			−0.441086	−	0.897465i	$-0.645407\pi$
$101$	−8.86572			−0.882173			−0.441086	+	0.897465i	$0.645407\pi$
$102$	−10.1089	−	3.69108i	−1.00093	−	0.365472i
$103$			4.62254i			0.455472i	0.973723	+	0.227736i	$0.0731323\pi$
$103$			4.62254i			0.455472i	−0.973723	+	0.227736i	$0.926868\pi$
$104$	−10.1018	+	2.04230i	−0.990559	+	0.200264i
$105$	−1.02128	−	1.39892i	−0.0996670	−	0.136521i
$106$	−7.56971	+	5.06937i	−0.735236	+	0.492381i
$107$			2.82698i			0.273295i	0.990620	+	0.136647i	$0.0436327\pi$
$107$			2.82698i			0.273295i	−0.990620	+	0.136647i	$0.956367\pi$
$108$	−10.3672	−	0.722457i	−0.997581	−	0.0695185i
$109$		−	1.54341i		−	0.147832i	−0.997264	−	0.0739158i	$-0.976450\pi$
$109$		−	1.54341i		−	0.147832i	0.997264	−	0.0739158i	$-0.0235496\pi$
$110$	2.05089	+	3.06244i	0.195545	+	0.291992i
$111$	−0.419324	−	0.574377i	−0.0398005	−	0.0545174i
$112$	2.81658	−	2.84022i	0.266142	−	0.268376i
$113$			6.52668i			0.613978i	0.951713	+	0.306989i	$0.0993215\pi$
$113$			6.52668i			0.613978i	−0.951713	+	0.306989i	$0.900678\pi$
$114$	−5.31707	+	14.5620i	−0.497990	+	1.36386i
$115$	0.872985			0.0814063
$116$	2.15209	−	5.22646i	0.199816	−	0.485264i
$117$	10.4117	+	3.33027i	0.962559	+	0.307884i
$118$	8.11469	+	12.1171i	0.747017	+	1.11547i
$119$	−4.39342			−0.402745
$120$	−3.61542	−	3.30586i	−0.330041	−	0.301783i
$121$	4.20765			0.382514
$122$	8.98283	+	13.4134i	0.813267	+	1.21439i
$123$	1.34374	+	1.84062i	0.121161	+	0.165963i
$124$	8.35710	+	3.44118i	0.750489	+	0.309027i
$125$	−1.00000			−0.0894427
$126$	−4.07681	+	1.17459i	−0.363191	+	0.104641i
$127$			16.4148i			1.45658i	0.685270	+	0.728289i	$0.259684\pi$
$127$			16.4148i			1.45658i	−0.685270	+	0.728289i	$0.740316\pi$
$128$	6.21660	−	9.45272i	0.549475	−	0.835510i
$129$	−3.32789	+	2.42952i	−0.293004	+	0.213908i
$130$	2.86737	+	4.28163i	0.251485	+	0.375524i
$131$		−	13.1259i		−	1.14681i	−0.819271	−	0.573406i	$-0.805622\pi$
$131$		−	13.1259i		−	1.14681i	0.819271	−	0.573406i	$-0.194378\pi$
$132$	8.76942	−	2.14603i	0.763280	−	0.186788i
$133$			6.32881i			0.548778i
$134$	11.6421	−	7.79659i	1.00572	−	0.673523i
$135$	1.63964	+	4.93068i	0.141118	+	0.424365i
$136$	−12.1801	+	2.46247i	−1.04443	+	0.211155i
$137$			5.14434i			0.439510i	0.975555	+	0.219755i	$0.0705258\pi$
$137$			5.14434i			0.439510i	−0.975555	+	0.219755i	$0.929474\pi$
$138$	0.733428	−	2.00866i	0.0624335	−	0.170988i
$139$	−23.0112			−1.95179			−0.975893	−	0.218251i	$-0.929965\pi$
$139$	−23.0112			−1.95179			−0.975893	+	0.218251i	$0.929965\pi$
$140$	−1.84935	−	0.761505i	−0.156299	−	0.0643589i
$141$	18.0395	−	13.1697i	1.51920	−	1.10909i
$142$	−3.14687	+	2.10743i	−0.264080	+	0.176852i
$143$	−9.49645			−0.794133
$144$	−10.6439	+	5.54137i	−0.886994	+	0.461780i
$145$	−2.82610			−0.234695
$146$	−17.2167	+	11.5299i	−1.42487	+	0.954220i
$147$	−1.39892	+	1.02128i	−0.115381	+	0.0842340i
$148$	−0.759318	−	0.312663i	−0.0624155	−	0.0257007i
$149$	12.1682			0.996860			0.498430	−	0.866930i	$-0.333910\pi$
$149$	12.1682			0.996860			0.498430	+	0.866930i	$0.333910\pi$
$150$	−0.840138	+	2.30091i	−0.0685969	+	0.187868i
$151$		−	0.557777i		−	0.0453912i	−0.999742	−	0.0226956i	$-0.992775\pi$
$151$		−	0.557777i		−	0.0453912i	0.999742	−	0.0226956i	$-0.00722486\pi$
$152$	3.54723	+	17.5456i	0.287719	+	1.42314i
$153$	12.5537	+	4.01543i	1.01491	+	0.324628i
$154$	3.06244	−	2.05089i	0.246779	−	0.165265i
$155$		−	4.51893i		−	0.362969i
$156$	12.2606	−	3.00038i	0.981634	−	0.240223i
$157$		−	15.7226i		−	1.25480i	−0.778698	−	0.627399i	$-0.784120\pi$
$157$		−	15.7226i		−	1.25480i	0.778698	−	0.627399i	$-0.215880\pi$
$158$	−8.96265	−	13.3833i	−0.713030	−	1.06472i
$159$	9.01187	−	6.57912i	0.714688	−	0.521758i
$160$	−5.55385	−	1.07460i	−0.439070	−	0.0849549i
$161$		−	0.872985i		−	0.0688009i
$162$	12.7225	+	0.369787i	0.999578	+	0.0290532i
$163$	−15.7464			−1.23335			−0.616677	−	0.787217i	$-0.711521\pi$
$163$	−15.7464			−1.23335			−0.616677	+	0.787217i	$0.711521\pi$
$164$	2.43327	+	1.00194i	0.190006	+	0.0782385i
$165$	−2.66168	−	3.64589i	−0.207212	−	0.283832i
$166$	−12.4376	−	18.5722i	−0.965348	−	1.44148i
$167$	−24.0522			−1.86122			−0.930608	−	0.366016i	$-0.880721\pi$
$167$	−24.0522			−1.86122			−0.930608	+	0.366016i	$0.880721\pi$
$168$	−3.30586	+	3.61542i	−0.255053	+	0.278936i
$169$	−0.277070			−0.0213131
$170$	3.45729	+	5.16251i	0.265162	+	0.395947i
$171$	5.78430	−	18.0839i	0.442336	−	1.38291i
$172$	−1.81154	+	4.39942i	−0.138129	+	0.335452i
$173$	10.8040			0.821412			0.410706	−	0.911768i	$-0.365282\pi$
$173$	10.8040			0.821412			0.410706	+	0.911768i	$0.365282\pi$
$174$	−2.37431	+	6.50259i	−0.179996	+	0.492960i
$175$			1.00000i			0.0755929i
$176$	7.34062	−	7.40222i	0.553320	−	0.557963i
$177$	−10.5314	−	14.4256i	−0.791588	−	1.08429i
$178$	−0.844414	−	1.26090i	−0.0632915	−	0.0945085i
$179$		−	5.38759i		−	0.402687i	−0.979521	−	0.201344i	$-0.935469\pi$
$179$		−	5.38759i		−	0.402687i	0.979521	−	0.201344i	$-0.0645308\pi$
$180$	4.58834	+	3.86616i	0.341994	+	0.288166i
$181$		−	10.3954i		−	0.772684i	−0.922356	−	0.386342i	$-0.873738\pi$
$181$		−	10.3954i		−	0.772684i	0.922356	−	0.386342i	$-0.126262\pi$
$182$	4.28163	−	2.86737i	0.317375	−	0.212543i
$183$	−11.6581	−	15.9689i	−0.861790	−	1.18045i
$184$	−0.489299	−	2.42021i	−0.0360716	−	0.178420i
$185$			0.410585i			0.0301868i
$186$	−10.3976	−	3.79652i	−0.762391	−	0.278374i
$187$	−11.4502			−0.837322
$188$	9.81980	−	23.8479i	0.716183	−	1.73929i
$189$	4.93068	−	1.63964i	0.358654	−	0.119266i
$190$	7.43670	−	4.98029i	0.539515	−	0.361308i
$191$	−22.6073			−1.63580			−0.817902	−	0.575358i	$-0.804863\pi$
$191$	−22.6073			−1.63580			−0.817902	+	0.575358i	$0.804863\pi$
$192$	−7.13856	+	11.8761i	−0.515181	+	0.857081i
$193$	17.1364			1.23351			0.616753	−	0.787157i	$-0.288448\pi$
$193$	17.1364			1.23351			0.616753	+	0.787157i	$0.288448\pi$
$194$	13.4649	−	9.01735i	0.966727	−	0.647408i
$195$	−3.72132	−	5.09735i	−0.266489	−	0.365029i
$196$	−0.761505	+	1.84935i	−0.0543932	+	0.132097i
$197$	9.63654			0.686575			0.343287	−	0.939230i	$-0.388460\pi$
$197$	9.63654			0.686575			0.343287	+	0.939230i	$0.388460\pi$
$198$	−10.6250	+	3.06123i	−0.755088	+	0.217552i
$199$		−	6.03091i		−	0.427520i	−0.976886	−	0.213760i	$-0.931429\pi$
$199$		−	6.03091i		−	0.427520i	0.976886	−	0.213760i	$-0.0685711\pi$
$200$	0.560490	+	2.77234i	0.0396326	+	0.196034i
$201$	−13.8601	+	10.1186i	−0.977614	+	0.713708i
$202$	10.4177	−	6.97664i	0.732987	−	0.490875i
$203$			2.82610i			0.198353i
$204$	14.7831	−	3.61767i	1.03502	−	0.253288i
$205$		−	1.31574i		−	0.0918952i
$206$	−3.63758	−	5.43173i	−0.253442	−	0.378447i
$207$	−0.797876	+	2.49446i	−0.0554562	+	0.173377i
$208$	10.2630	−	10.3491i	0.711610	−	0.717582i
$209$			16.4942i			1.14093i
$210$	2.30091	+	0.840138i	0.158778	+	0.0579750i
$211$	9.41330			0.648039			0.324019	−	0.946050i	$-0.394966\pi$
$211$	9.41330			0.648039			0.324019	+	0.946050i	$0.394966\pi$
$212$	4.90562	−	11.9136i	0.336920	−	0.818227i
$213$	3.74640	−	2.73506i	0.256699	−	0.187403i
$214$	−2.22462	−	3.32186i	−0.152072	−	0.227077i
$215$	2.37889			0.162239
$216$	12.7505	−	7.30923i	0.867561	−	0.497330i
$217$	−4.51893			−0.306765
$218$	1.21454	+	1.81359i	0.0822592	+	0.122832i
$219$	20.4968	−	14.9637i	1.38505	−	1.01115i
$220$	−4.81981	−	1.98464i	−0.324952	−	0.133805i
$221$	−16.0086			−1.07686
$222$	0.944718	+	0.344948i	0.0634054	+	0.0231514i
$223$		−	2.79614i		−	0.187243i	−0.995608	−	0.0936217i	$-0.970156\pi$
$223$		−	2.79614i		−	0.187243i	0.995608	−	0.0936217i	$-0.0298444\pi$
$224$	−1.07460	+	5.55385i	−0.0718000	+	0.371082i
$225$	0.913962	−	2.85739i	0.0609308	−	0.190493i
$226$	−5.13599	−	7.66920i	−0.341641	−	0.510148i
$227$		−	23.8776i		−	1.58481i	−0.609996	−	0.792405i	$-0.708829\pi$
$227$		−	23.8776i		−	1.58481i	0.609996	−	0.792405i	$-0.291171\pi$
$228$	−5.21132	−	21.2953i	−0.345128	−	1.41031i
$229$		−	19.4866i		−	1.28771i	−0.765147	−	0.643856i	$-0.777334\pi$
$229$		−	19.4866i		−	1.28771i	0.765147	−	0.643856i	$-0.222666\pi$
$230$	−1.02581	+	0.686972i	−0.0676396	+	0.0452976i
$231$	−3.64589	+	2.66168i	−0.239882	+	0.175126i
$232$	1.58400	+	7.83490i	0.103995	+	0.514386i
$233$		−	16.8441i		−	1.10349i	−0.834012	−	0.551746i	$-0.813962\pi$
$233$		−	16.8441i		−	1.10349i	0.834012	−	0.551746i	$-0.186038\pi$
$234$	−14.8549	+	4.27994i	−0.971098	+	0.279788i
$235$	−12.8953			−0.841194
$236$	−19.0704	−	7.85258i	−1.24138	−	0.511159i
$237$	11.6319	+	15.9330i	0.755573	+	1.03496i
$238$	5.16251	−	3.45729i	0.334636	−	0.224103i
$239$	−7.03283			−0.454916			−0.227458	−	0.973788i	$-0.573041\pi$
$239$	−7.03283			−0.454916			−0.227458	+	0.973788i	$0.573041\pi$
$240$	6.84978	+	1.03951i	0.442151	+	0.0671001i
$241$	4.94865			0.318771			0.159385	−	0.987216i	$-0.449049\pi$
$241$	4.94865			0.318771			0.159385	+	0.987216i	$0.449049\pi$
$242$	−4.94422	+	3.31110i	−0.317826	+	0.212845i
$243$	−15.5874	+	0.178639i	−0.999934	+	0.0114597i
$244$	−21.1106	−	8.69268i	−1.35147	−	0.556492i
$245$	1.00000			0.0638877
$246$	−3.02739	−	1.10540i	−0.193019	−	0.0704778i
$247$			23.0607i			1.46732i
$248$	−12.5280	+	2.53281i	−0.795528	+	0.160834i
$249$	16.1418	+	22.1105i	1.02294	+	1.40120i
$250$	1.17505	−	0.786923i	0.0743170	−	0.0497694i
$251$			2.99335i			0.188939i	0.995528	+	0.0944693i	$0.0301154\pi$
$251$			2.99335i			0.188939i	−0.995528	+	0.0944693i	$0.969885\pi$
$252$	3.86616	−	4.58834i	0.243545	−	0.289038i
$253$		−	2.27519i		−	0.143040i
$254$	−12.9172	−	19.2883i	−0.810496	−	1.21025i
$255$	−4.48693	−	6.14606i	−0.280982	−	0.384881i
$256$	0.133712	+	15.9994i	0.00835699	+	0.999965i
$257$		−	10.2629i		−	0.640184i	−0.947386	−	0.320092i	$-0.896286\pi$
$257$		−	10.2629i		−	0.640184i	0.947386	−	0.320092i	$-0.103714\pi$
$258$	1.99860	−	5.47361i	0.124427	−	0.340772i
$259$	0.410585			0.0255125
$260$	−6.73862	−	2.77475i	−0.417912	−	0.172083i
$261$	2.58295	−	8.07526i	0.159880	−	0.499846i
$262$	10.3290	+	15.4236i	0.638131	+	0.952874i
$263$	18.3429			1.13107			0.565536	−	0.824723i	$-0.308669\pi$
$263$	18.3429			1.13107			0.565536	+	0.824723i	$0.308669\pi$
$264$	−8.61578	+	9.42256i	−0.530265	+	0.579918i
$265$	−6.44201			−0.395730
$266$	−4.98029	−	7.43670i	−0.305361	−	0.455973i
$267$	1.09590	+	1.50112i	0.0670677	+	0.0918673i
$268$	−7.54475	+	18.3228i	−0.460869	+	1.11924i
$269$	−24.8952			−1.51789			−0.758944	−	0.651156i	$-0.774284\pi$
$269$	−24.8952			−1.51789			−0.758944	+	0.651156i	$0.774284\pi$
$270$	−5.80673	−	4.50354i	−0.353386	−	0.274077i
$271$		−	5.68426i		−	0.345294i	−0.984984	−	0.172647i	$-0.944768\pi$
$271$		−	5.68426i		−	0.345294i	0.984984	−	0.172647i	$-0.0552320\pi$
$272$	12.3744	−	12.4783i	0.750311	−	0.756608i
$273$	−5.09735	+	3.72132i	−0.308506	+	0.225225i
$274$	−4.04820	−	6.04487i	−0.244560	−	0.365184i
$275$			2.60621i			0.157161i
$276$	0.718841	+	2.93743i	0.0432691	+	0.176813i
$277$			20.4907i			1.23117i	0.788072	+	0.615583i	$0.211079\pi$
$277$			20.4907i			1.23117i	−0.788072	+	0.615583i	$0.788921\pi$
$278$	27.0394	−	18.1080i	1.62172	−	1.08605i
$279$	12.9123	+	4.13013i	0.773041	+	0.247264i
$280$	2.77234	−	0.560490i	0.165679	−	0.0334957i
$281$		−	1.78658i		−	0.106579i	−0.998579	−	0.0532893i	$-0.983029\pi$
$281$		−	1.78658i		−	0.106579i	0.998579	−	0.0532893i	$-0.0169706\pi$
$282$	−10.8338	+	29.6708i	−0.645143	+	1.76687i
$283$	−3.73574			−0.222067			−0.111033	−	0.993817i	$-0.535416\pi$
$283$	−3.73574			−0.222067			−0.111033	+	0.993817i	$0.535416\pi$
$284$	2.03936	−	4.95269i	0.121014	−	0.293888i
$285$	−8.85351	+	6.46351i	−0.524437	+	0.382865i
$286$	11.1588	−	7.47297i	0.659836	−	0.441886i
$287$	−1.31574			−0.0776656
$288$	8.14657	−	14.8874i	0.480041	−	0.877246i
$289$	−2.30218			−0.135422
$290$	3.32082	−	2.22392i	0.195005	−	0.130593i
$291$	−16.0302	+	11.7029i	−0.939709	+	0.686035i
$292$	11.1575	−	27.0965i	0.652941	−	1.58570i
$293$	5.42748			0.317077			0.158538	−	0.987353i	$-0.449322\pi$
$293$	5.42748			0.317077			0.158538	+	0.987353i	$0.449322\pi$
$294$	0.840138	−	2.30091i	0.0489978	−	0.134192i
$295$			10.3119i			0.600383i
$296$	1.13828	−	0.230129i	0.0661612	−	0.0133760i
$297$	12.8504	−	4.27325i	0.745656	−	0.247959i
$298$	−14.2983	+	9.57545i	−0.828280	+	0.554691i
$299$		−	3.18096i		−	0.183960i
$300$	−0.823428	−	3.36481i	−0.0475407	−	0.194268i
$301$		−	2.37889i		−	0.137117i
$302$	0.438927	+	0.655418i	0.0252574	+	0.0377151i
$303$	−12.4025	+	9.05441i	−0.712502	+	0.520162i
$304$	−17.9752	−	17.8256i	−1.03095	−	1.02237i
$305$			11.4151i			0.653628i
$306$	−17.9111	+	5.16047i	−1.02391	+	0.295004i
$307$	−3.30494			−0.188623			−0.0943114	−	0.995543i	$-0.530065\pi$
$307$	−3.30494			−0.188623			−0.0943114	+	0.995543i	$0.530065\pi$
$308$	−1.98464	+	4.81981i	−0.113086	+	0.274634i
$309$	4.72092	+	6.46657i	0.268564	+	0.367870i
$310$	3.55605	+	5.30998i	0.201970	+	0.301587i
$311$	−18.9308			−1.07347			−0.536734	−	0.843751i	$-0.680342\pi$
$311$	−18.9308			−1.07347			−0.536734	+	0.843751i	$0.680342\pi$
$312$	−12.0458	+	13.1738i	−0.681960	+	0.745818i
$313$	19.4397			1.09879			0.549397	−	0.835561i	$-0.314857\pi$
$313$	19.4397			1.09879			0.549397	+	0.835561i	$0.314857\pi$
$314$	12.3724	+	18.4749i	0.698218	+	1.04260i
$315$	−2.85739	−	0.913962i	−0.160996	−	0.0514960i
$316$	21.0632	+	8.67315i	1.18490	+	0.487903i
$317$	−13.4464			−0.755224			−0.377612	−	0.925964i	$-0.623255\pi$
$317$	−13.4464			−0.755224			−0.377612	+	0.925964i	$0.623255\pi$
$318$	−5.41218	+	14.8225i	−0.303500	+	0.831203i
$319$			7.36541i			0.412384i
$320$	7.37170	−	3.10773i	0.412091	−	0.173728i
$321$	2.88715	+	3.95472i	0.161145	+	0.220731i
$322$	0.686972	+	1.02581i	0.0382835	+	0.0571659i
$323$			27.8052i			1.54712i
$324$	−15.2407	+	9.57714i	−0.846704	+	0.532064i
$325$			3.64377i			0.202120i
$326$	18.5029	−	12.3912i	1.02478	−	0.686285i
$327$	−1.57626	−	2.15911i	−0.0871671	−	0.119399i
$328$	−3.64767	+	0.737458i	−0.201409	+	0.0407193i
$329$			12.8953i			0.710939i
$330$	5.99665	+	2.18958i	0.330105	+	0.120532i
$331$	22.3577			1.22889			0.614445	−	0.788960i	$-0.289380\pi$
$331$	22.3577			1.22889			0.614445	+	0.788960i	$0.289380\pi$
$332$	29.2298	+	12.0359i	1.60419	+	0.660556i
$333$	−1.17320	−	0.375260i	−0.0642911	−	0.0205641i
$334$	28.2627	−	18.9272i	1.54646	−	1.03565i
$335$	9.90769			0.541315
$336$	1.03951	−	6.84978i	0.0567099	−	0.373686i
$337$	−25.2446			−1.37516			−0.687581	−	0.726108i	$-0.741327\pi$
$337$	−25.2446			−1.37516			−0.687581	+	0.726108i	$0.741327\pi$
$338$	0.325572	−	0.218033i	0.0177088	−	0.0118594i
$339$	6.66559	+	9.13031i	0.362025	+	0.495890i
$340$	−8.12500	−	3.34561i	−0.440640	−	0.181441i
$341$	−11.7773			−0.637776
$342$	7.43376	+	25.8013i	0.401972	+	1.39518i
$343$		−	1.00000i		−	0.0539949i
$344$	−1.33335	−	6.59510i	−0.0718892	−	0.355584i
$345$	1.22124	−	0.891565i	0.0657492	−	0.0480002i
$346$	−12.6953	+	8.50190i	−0.682502	+	0.457065i
$347$		−	10.8735i		−	0.583721i	−0.956461	−	0.291860i	$-0.905726\pi$
$347$		−	10.8735i		−	0.583721i	0.956461	−	0.291860i	$-0.0942742\pi$
$348$	−2.32709	−	9.50929i	−0.124745	−	0.509751i
$349$		−	32.5032i		−	1.73986i	−0.493180	−	0.869928i	$-0.664165\pi$
$349$		−	32.5032i		−	1.73986i	0.493180	−	0.869928i	$-0.335835\pi$
$350$	−0.786923	−	1.17505i	−0.0420628	−	0.0628093i
$351$	17.9663	−	5.97448i	0.958968	−	0.318894i
$352$	−2.80065	+	14.4745i	−0.149275	+	0.771494i
$353$		−	9.36201i		−	0.498290i	−0.968466	−	0.249145i	$-0.919850\pi$
$353$		−	9.36201i		−	0.498290i	0.968466	−	0.249145i	$-0.0801495\pi$
$354$	23.7268	+	8.66343i	1.26106	+	0.460456i
$355$	−2.67806			−0.142137
$356$	1.98446	+	0.817139i	0.105176	+	0.0433083i
$357$	−6.14606	+	4.48693i	−0.325284	+	0.237474i
$358$	4.23962	+	6.33071i	0.224071	+	0.334589i
$359$	−5.27997			−0.278666			−0.139333	−	0.990246i	$-0.544496\pi$
$359$	−5.27997			−0.278666			−0.139333	+	0.990246i	$0.544496\pi$
$360$	−8.43391	−	0.932274i	−0.444506	−	0.0491352i
$361$	21.0539			1.10810
$362$	8.18038	+	12.2152i	0.429951	+	0.642014i
$363$	5.88617	−	4.29720i	0.308944	−	0.225545i
$364$	−2.77475	+	6.73862i	−0.145436	+	0.353200i
$365$	−14.6519			−0.766913
$366$	26.2651	+	9.59028i	1.37290	+	0.501292i
$367$			27.9027i			1.45651i	0.685306	+	0.728255i	$0.259668\pi$
$367$			27.9027i			1.45651i	−0.685306	+	0.728255i	$0.740332\pi$
$368$	2.47947	+	2.45884i	0.129251	+	0.128176i
$369$	3.75958	+	1.20254i	0.195716	+	0.0626015i
$370$	−0.323099	−	0.482460i	−0.0167971	−	0.0250819i
$371$			6.44201i			0.334453i
$372$	15.2053	−	3.72101i	0.788360	−	0.192926i
$373$		−	28.1209i		−	1.45604i	−0.685554	−	0.728021i	$-0.740440\pi$
$373$		−	28.1209i		−	1.45604i	0.685554	−	0.728021i	$-0.259560\pi$
$374$	13.4546	−	9.01043i	0.695721	−	0.465918i
$375$	−1.39892	+	1.02128i	−0.0722400	+	0.0527388i
$376$	7.22766	+	35.7500i	0.372738	+	1.84367i
$377$			10.2977i			0.530356i
$378$	−4.50354	+	5.80673i	−0.231637	+	0.298666i
$379$	26.7110			1.37205			0.686027	−	0.727576i	$-0.259353\pi$
$379$	26.7110			1.37205			0.686027	+	0.727576i	$0.259353\pi$
$380$	−4.81942	+	11.7042i	−0.247231	+	0.600414i
$381$	16.7642	+	22.9630i	0.858854	+	1.17643i
$382$	26.5648	−	17.7902i	1.35917	−	0.910224i
$383$	−29.7598			−1.52065			−0.760327	−	0.649541i	$-0.774961\pi$
$383$	−29.7598			−1.52065			−0.760327	+	0.649541i	$0.774961\pi$
$384$	−0.957356	−	19.5725i	−0.0488549	−	0.998806i
$385$	2.60621			0.132825
$386$	−20.1362	+	13.4850i	−1.02491	+	0.686370i
$387$	−2.17422	+	6.79743i	−0.110522	+	0.345533i
$388$	−8.72608	+	21.1917i	−0.443000	+	1.07585i
$389$	−7.44233			−0.377341			−0.188670	−	0.982040i	$-0.560418\pi$
$389$	−7.44233			−0.377341			−0.188670	+	0.982040i	$0.560418\pi$
$390$	8.38398	+	3.06127i	0.424539	+	0.155013i
$391$		−	3.83540i		−	0.193964i
$392$	−0.560490	−	2.77234i	−0.0283090	−	0.140024i
$393$	−13.4052	−	18.3621i	−0.676204	−	0.926244i
$394$	−11.3235	+	7.58321i	−0.570467	+	0.382037i
$395$		−	11.3895i		−	0.573067i
$396$	10.0760	−	11.9582i	0.506339	−	0.600921i
$397$		−	16.3521i		−	0.820687i	−0.911931	−	0.410343i	$-0.865409\pi$
$397$		−	16.3521i		−	0.820687i	0.911931	−	0.410343i	$-0.134591\pi$
$398$	4.74586	+	7.08665i	0.237889	+	0.355222i
$399$	6.46351	+	8.85351i	0.323580	+	0.443230i
$400$	−2.84022	−	2.81658i	−0.142011	−	0.140829i
$401$			7.07083i			0.353100i	0.984292	+	0.176550i	$0.0564938\pi$
$401$			7.07083i			0.353100i	−0.984292	+	0.176550i	$0.943506\pi$
$402$	8.32382	−	22.7967i	0.415154	−	1.13699i
$403$	−16.4659			−0.820227
$404$	−6.75129	+	16.3959i	−0.335889	+	0.815725i
$405$	7.32935	+	5.22309i	0.364198	+	0.259538i
$406$	−2.22392	−	3.32082i	−0.110371	−	0.164809i
$407$	1.07007			0.0530416
$408$	−14.5241	+	15.8841i	−0.719048	+	0.786379i
$409$	4.95747			0.245131			0.122566	−	0.992460i	$-0.460888\pi$
$409$	4.95747			0.245131			0.122566	+	0.992460i	$0.460888\pi$
$410$	1.03538	+	1.54606i	0.0511340	+	0.0763547i
$411$	5.25382	+	7.19652i	0.259152	+	0.354978i
$412$	8.54871	+	3.52008i	0.421165	+	0.173422i
$413$	10.3119			0.507416
$414$	−1.02540	−	3.55899i	−0.0503956	−	0.174915i
$415$		−	15.8054i		−	0.775857i
$416$	−3.91561	+	20.2370i	−0.191979	+	0.992198i
$417$	−32.1909	+	23.5010i	−1.57639	+	1.15085i
$418$	−12.9797	−	19.3816i	−0.634857	−	0.947986i
$419$			21.0449i			1.02811i	0.857758	+	0.514054i	$0.171857\pi$
$419$			21.0449i			1.02811i	−0.857758	+	0.514054i	$0.828143\pi$
$420$	−3.36481	+	0.823428i	−0.164186	+	0.0401792i
$421$		−	5.58224i		−	0.272062i	−0.990705	−	0.136031i	$-0.956565\pi$
$421$		−	5.58224i		−	0.272062i	0.990705	−	0.136031i	$-0.0434346\pi$
$422$	−11.0611	+	7.40754i	−0.538448	+	0.360594i
$423$	11.7858	−	36.8468i	0.573044	−	1.79155i
$424$	3.61068	+	17.8594i	0.175350	+	0.867331i
$425$			4.39342i			0.213112i
$426$	−2.24994	+	6.16197i	−0.109010	+	0.298549i
$427$	11.4151			0.552417
$428$	5.22809	+	2.15276i	0.252709	+	0.104058i
$429$	−13.2848	+	9.69856i	−0.641395	+	0.468251i
$430$	−2.79533	+	1.87201i	−0.134803	+	0.0902761i
$431$	−22.2746			−1.07293			−0.536465	−	0.843923i	$-0.680241\pi$
$431$	−22.2746			−1.07293			−0.536465	+	0.843923i	$0.680241\pi$
$432$	−9.23072	+	18.6224i	−0.444113	+	0.895971i
$433$	27.3240			1.31311			0.656553	−	0.754280i	$-0.272014\pi$
$433$	27.3240			1.31311			0.656553	+	0.754280i	$0.272014\pi$
$434$	5.30998	−	3.55605i	0.254887	−	0.170696i
$435$	−3.95349	+	2.88625i	−0.189555	+	0.138385i
$436$	−2.85431	−	1.17531i	−0.136697	−	0.0562872i
$437$	−5.52496			−0.264295
$438$	−12.3096	+	33.7126i	−0.588174	+	1.61085i
$439$		−	2.62754i		−	0.125406i	−0.998032	−	0.0627029i	$-0.980028\pi$
$439$		−	2.62754i		−	0.125406i	0.998032	−	0.0627029i	$-0.0199721\pi$
$440$	7.22530	−	1.46076i	0.344453	−	0.0696388i
$441$	−0.913962	+	2.85739i	−0.0435220	+	0.136066i
$442$	18.8110	−	12.5976i	0.894749	−	0.599205i
$443$			27.5339i			1.30818i	0.756418	+	0.654088i	$0.226948\pi$
$443$			27.5339i			1.30818i	−0.756418	+	0.654088i	$0.773052\pi$
$444$	−1.38154	+	0.338088i	−0.0655651	+	0.0160449i
$445$		−	1.07306i		−	0.0508678i
$446$	2.20035	+	3.28562i	0.104189	+	0.155578i
$447$	17.0224	−	12.4272i	0.805131	−	0.587786i
$448$	−3.10773	−	7.37170i	−0.146827	−	0.348280i
$449$			30.5641i			1.44241i	0.692722	+	0.721205i	$0.256411\pi$
$449$			30.5641i			1.44241i	−0.692722	+	0.721205i	$0.743589\pi$
$450$	1.17459	+	4.07681i	0.0553707	+	0.192182i
$451$	−3.42910			−0.161470
$452$	12.0701	+	4.97010i	0.567732	+	0.233774i
$453$	−0.569648	−	0.780286i	−0.0267644	−	0.0366610i
$454$	18.7898	+	28.0574i	0.881849	+	1.31680i
$455$	3.64377			0.170823
$456$	22.8813	+	20.9222i	1.07152	+	0.979771i
$457$	−30.6201			−1.43235			−0.716174	−	0.697922i	$-0.754108\pi$
$457$	−30.6201			−1.43235			−0.716174	+	0.697922i	$0.754108\pi$
$458$	15.3345	+	22.8978i	0.716533	+	1.06995i
$459$	21.6626	−	7.20364i	1.01112	−	0.336237i
$460$	0.664782	−	1.61446i	0.0309956	−	0.0752745i
$461$	3.21566			0.149768			0.0748841	−	0.997192i	$-0.476141\pi$
$461$	3.21566			0.149768			0.0748841	+	0.997192i	$0.476141\pi$
$462$	2.18958	−	5.99665i	0.101868	−	0.278990i
$463$		−	26.6753i		−	1.23971i	−0.784717	−	0.619854i	$-0.787192\pi$
$463$		−	26.6753i		−	1.23971i	0.784717	−	0.619854i	$-0.212808\pi$
$464$	−8.02674	−	7.95994i	−0.372632	−	0.369531i
$465$	−4.61510	−	6.32162i	−0.214020	−	0.293158i
$466$	13.2550	+	19.7927i	0.614026	+	0.916880i
$467$			22.6319i			1.04728i	0.851941	+	0.523639i	$0.175426\pi$
$467$			22.6319i			1.04728i	−0.851941	+	0.523639i	$0.824574\pi$
$468$	14.0874	−	16.7189i	0.651190	−	0.772829i
$469$		−	9.90769i		−	0.457495i
$470$	15.1526	−	10.1476i	0.698939	−	0.468073i
$471$	−16.0572	−	21.9946i	−0.739876	−	1.01346i
$472$	28.5881	−	5.77973i	1.31587	−	0.266033i
$473$		−	6.19991i		−	0.285072i
$474$	−26.2061	−	9.56874i	−1.20369	−	0.439507i
$475$	6.32881			0.290386
$476$	−3.34561	+	8.12500i	−0.153346	+	0.372409i
$477$	5.88776	−	18.4073i	0.269582	−	0.842814i
$478$	8.26396	−	5.53430i	0.377985	−	0.253133i
$479$	12.8958			0.589226			0.294613	−	0.955617i	$-0.404809\pi$
$479$	12.8958			0.589226			0.294613	+	0.955617i	$0.404809\pi$
$480$	−8.86687	+	4.16876i	−0.404715	+	0.190277i
$481$	1.49608			0.0682153
$482$	−5.81493	+	3.89421i	−0.264863	+	0.177376i
$483$	−0.891565	−	1.22124i	−0.0405676	−	0.0555682i
$484$	3.20415	−	7.78144i	0.145643	−	0.353702i
$485$	11.4590			0.520326
$486$	18.1755	−	12.4760i	0.824458	−	0.565924i
$487$		−	0.438571i		−	0.0198736i	−0.999951	−	0.00993678i	$-0.996837\pi$
$487$		−	0.438571i		−	0.0198736i	0.999951	−	0.00993678i	$-0.00316303\pi$
$488$	31.6466	−	6.39806i	1.43257	−	0.289627i
$489$	−22.0280	+	16.0815i	−0.996139	+	0.727232i
$490$	−1.17505	+	0.786923i	−0.0530835	+	0.0355496i
$491$			22.4073i			1.01123i	0.862760	+	0.505614i	$0.168734\pi$
$491$			22.4073i			1.01123i	−0.862760	+	0.505614i	$0.831266\pi$
$492$	4.42721	−	1.08342i	0.199594	−	0.0488442i
$493$			12.4162i			0.559200i
$494$	−18.1470	−	27.0976i	−0.816473	−	1.21918i
$495$	−7.44697	−	2.38198i	−0.334716	−	0.107062i
$496$	12.7279	−	12.8348i	0.571501	−	0.576297i
$497$			2.67806i			0.120128i
$498$	−36.3668	−	13.2787i	−1.62963	−	0.595034i
$499$	20.1466			0.901884			0.450942	−	0.892553i	$-0.351088\pi$
$499$	20.1466			0.901884			0.450942	+	0.892553i	$0.351088\pi$
$500$	−0.761505	+	1.84935i	−0.0340555	+	0.0827056i
$501$	−33.6472	+	24.5641i	−1.50324	+	1.09744i
$502$	−2.35554	−	3.51735i	−0.105133	−	0.156987i
$503$	16.2587			0.724942			0.362471	−	0.931995i	$-0.381933\pi$
$503$	16.2587			0.724942			0.362471	+	0.931995i	$0.381933\pi$
$504$	−0.932274	+	8.43391i	−0.0415268	+	0.375676i
$505$	8.86572			0.394520
$506$	1.79040	+	2.67347i	0.0795928	+	0.118850i
$507$	−0.387599	+	0.282967i	−0.0172139	+	0.0125670i
$508$	30.3568	+	12.5000i	1.34686	+	0.554596i
$509$	5.87104			0.260229			0.130115	−	0.991499i	$-0.458465\pi$
$509$	5.87104			0.260229			0.130115	+	0.991499i	$0.458465\pi$
$510$	10.1089	+	3.69108i	0.447628	+	0.163444i
$511$			14.6519i			0.648160i
$512$	−12.7474	−	18.6950i	−0.563363	−	0.826210i
$513$	−10.3770	−	31.2053i	−0.458155	−	1.37775i
$514$	8.07614	+	12.0595i	0.356223	+	0.531922i
$515$		−	4.62254i		−	0.203693i
$516$	1.95885	+	8.00453i	0.0862335	+	0.352380i
$517$			33.6078i			1.47807i
$518$	−0.482460	+	0.323099i	−0.0211981	+	0.0141962i
$519$	15.1139	−	11.0339i	0.663428	−	0.484335i
$520$	10.1018	−	2.04230i	0.442992	−	0.0895606i
$521$		−	26.7975i		−	1.17402i	−0.809579	−	0.587010i	$-0.800305\pi$
$521$		−	26.7975i		−	1.17402i	0.809579	−	0.587010i	$-0.199695\pi$
$522$	3.31950	+	11.5214i	0.145291	+	0.504280i
$523$	20.0527			0.876844			0.438422	−	0.898769i	$-0.355538\pi$
$523$	20.0527			0.876844			0.438422	+	0.898769i	$0.355538\pi$
$524$	−24.2744	−	9.99541i	−1.06043	−	0.436652i
$525$	1.02128	+	1.39892i	0.0445724	+	0.0610539i
$526$	−21.5539	+	14.4345i	−0.939796	+	0.629372i
$527$	−19.8536			−0.864835
$528$	2.70919	−	17.8520i	0.117902	−	0.776908i
$529$	−22.2379			−0.966865
$530$	7.56971	−	5.06937i	0.328807	−	0.220199i
$531$	−29.4652	−	9.42471i	−1.27868	−	0.408997i
$532$	11.7042	+	4.81942i	0.507442	+	0.208948i
$533$	−4.79425			−0.207662
$534$	−2.46901	−	0.901516i	−0.106844	−	0.0390124i
$535$		−	2.82698i		−	0.122221i
$536$	−5.55316	−	27.4674i	−0.239860	−	1.18641i
$537$	−5.50225	−	7.53682i	−0.237440	−	0.325238i
$538$	29.2532	−	19.5906i	1.26120	−	0.844611i
$539$		−	2.60621i		−	0.112258i
$540$	10.3672	+	0.722457i	0.446132	+	0.0310896i
$541$			3.77748i			0.162406i	0.996698	+	0.0812032i	$0.0258763\pi$
$541$			3.77748i			0.162406i	−0.996698	+	0.0812032i	$0.974124\pi$
$542$	4.47308	+	6.67932i	0.192135	+	0.286901i
$543$	−10.6166	−	14.5423i	−0.455604	−	0.624072i
$544$	−4.72119	+	24.4004i	−0.202419	+	1.04616i
$545$			1.54341i			0.0661123i
$546$	3.06127	−	8.38398i	0.131010	−	0.358801i
$547$	−33.2021			−1.41962			−0.709811	−	0.704393i	$-0.751219\pi$
$547$	−33.2021			−1.41962			−0.709811	+	0.704393i	$0.751219\pi$
$548$	9.51370	+	3.91744i	0.406405	+	0.167345i
$549$	−32.6175	−	10.4330i	−1.39208	−	0.445270i
$550$	−2.05089	−	3.06244i	−0.0874502	−	0.130583i
$551$	17.8858			0.761963
$552$	−3.15621	−	2.88597i	−0.134337	−	0.122835i
$553$	−11.3895			−0.484330
$554$	−16.1246	−	24.0777i	−0.685068	−	1.02296i
$555$	0.419324	+	0.574377i	0.0177993	+	0.0243809i
$556$	−17.5231	+	42.5559i	−0.743147	+	1.80477i
$557$	−19.9269			−0.844329			−0.422165	−	0.906519i	$-0.638730\pi$
$557$	−19.9269			−0.844329			−0.422165	+	0.906519i	$0.638730\pi$
$558$	−18.4228	+	5.30788i	−0.779899	+	0.224701i
$559$		−	8.66815i		−	0.366623i
$560$	−2.81658	+	2.84022i	−0.119022	+	0.120021i
$561$	−16.0179	+	11.6939i	−0.676278	+	0.493717i
$562$	1.40590	+	2.09933i	0.0593045	+	0.0885550i
$563$		−	22.0502i		−	0.929304i	−0.885493	−	0.464652i	$-0.846180\pi$
$563$		−	22.0502i		−	0.929304i	0.885493	−	0.464652i	$-0.153820\pi$
$564$	−10.6183	−	43.3901i	−0.447112	−	1.82705i
$565$		−	6.52668i		−	0.274579i
$566$	4.38970	−	2.93974i	0.184513	−	0.123566i
$567$	5.22309	−	7.32935i	0.219349	−	0.307804i
$568$	1.50103	+	7.42450i	0.0629817	+	0.311525i
$569$		−	20.5477i		−	0.861406i	−0.902494	−	0.430703i	$-0.858266\pi$
$569$		−	20.5477i		−	0.861406i	0.902494	−	0.430703i	$-0.141734\pi$
$570$	5.31707	−	14.5620i	0.222708	−	0.609935i
$571$	−5.11523			−0.214066			−0.107033	−	0.994255i	$-0.534135\pi$
$571$	−5.11523			−0.214066			−0.107033	+	0.994255i	$0.534135\pi$
$572$	−7.23159	+	17.5623i	−0.302368	+	0.734316i
$573$	−31.6258	+	23.0884i	−1.32119	+	0.964532i
$574$	1.54606	−	1.03538i	0.0645315	−	0.0432161i
$575$	−0.872985			−0.0364060
$576$	2.14254	+	23.9042i	0.0892726	+	0.996007i
$577$	42.2812			1.76019			0.880094	−	0.474800i	$-0.157480\pi$
$577$	42.2812			1.76019			0.880094	+	0.474800i	$0.157480\pi$
$578$	2.70519	−	1.81164i	0.112521	−	0.0753543i
$579$	23.9725	−	17.5011i	0.996262	−	0.727321i
$580$	−2.15209	+	5.22646i	−0.0893605	+	0.217017i
$581$	−15.8054			−0.655719
$582$	9.62714	−	26.3661i	0.399058	−	1.09291i
$583$			16.7893i			0.695340i
$584$	8.21222	+	40.6199i	0.339824	+	1.68086i
$585$	−10.4117	−	3.33027i	−0.430470	−	0.137690i
$586$	−6.37758	+	4.27101i	−0.263455	+	0.176434i
$587$		−	38.6250i		−	1.59422i	−0.603833	−	0.797111i	$-0.706360\pi$
$587$		−	38.6250i		−	1.59422i	0.603833	−	0.797111i	$-0.293640\pi$
$588$	0.823428	+	3.36481i	0.0339576	+	0.138763i
$589$			28.5994i			1.17842i
$590$	−8.11469	−	12.1171i	−0.334076	−	0.498852i
$591$	13.4808	−	9.84163i	0.554524	−	0.404831i
$592$	−1.15645	+	1.16615i	−0.0475297	+	0.0479286i
$593$		−	15.3379i		−	0.629854i	−0.949116	−	0.314927i	$-0.898020\pi$
$593$		−	15.3379i		−	0.629854i	0.949116	−	0.314927i	$-0.101980\pi$
$594$	−11.7372	+	15.1336i	−0.481583	+	0.620938i
$595$	4.39342			0.180113
$596$	9.26616	−	22.5034i	0.379557	−	0.921773i
$597$	−6.15927	−	8.43677i	−0.252082	−	0.345294i
$598$	2.50317	+	3.73780i	0.102362	+	0.152850i
$599$	29.8200			1.21841			0.609207	−	0.793011i	$-0.291488\pi$
$599$	29.8200			1.21841			0.609207	+	0.793011i	$0.291488\pi$
$600$	3.61542	+	3.30586i	0.147599	+	0.134961i
$601$	45.2523			1.84588			0.922939	−	0.384946i	$-0.125780\pi$
$601$	45.2523			1.84588			0.922939	+	0.384946i	$0.125780\pi$
$602$	1.87201	+	2.79533i	0.0762973	+	0.113929i
$603$	−9.05525	+	28.3101i	−0.368758	+	1.15288i
$604$	−1.03153	−	0.424750i	−0.0419722	−	0.0172828i
$605$	−4.20765			−0.171065
$606$	7.44843	−	20.3992i	0.302572	−	0.828661i
$607$		−	35.2729i		−	1.43168i	−0.698264	−	0.715841i	$-0.746044\pi$
$607$		−	35.2729i		−	1.43168i	0.698264	−	0.715841i	$-0.253956\pi$
$608$	35.1493	+	6.80096i	1.42549	+	0.275816i
$609$	2.88625	+	3.95349i	0.116957	+	0.160203i
$610$	−8.98283	−	13.4134i	−0.363704	−	0.543093i
$611$			46.9874i			1.90091i
$612$	16.9857	−	20.1585i	0.686605	−	0.814860i
$613$			15.4175i			0.622709i	0.950294	+	0.311354i	$0.100783\pi$
$613$			15.4175i			0.622709i	−0.950294	+	0.311354i	$0.899217\pi$
$614$	3.88348	−	2.60073i	0.156725	−	0.104957i
$615$	−1.34374	−	1.84062i	−0.0541849	−	0.0742208i
$616$	−1.46076	−	7.22530i	−0.0588555	−	0.291116i
$617$		−	15.6194i		−	0.628812i	−0.949289	−	0.314406i	$-0.898195\pi$
$617$		−	15.6194i		−	0.628812i	0.949289	−	0.314406i	$-0.101805\pi$
$618$	−10.6360	−	3.88357i	−0.427844	−	0.156220i
$619$	31.7001			1.27413			0.637067	−	0.770808i	$-0.280147\pi$
$619$	31.7001			1.27413			0.637067	+	0.770808i	$0.280147\pi$
$620$	−8.35710	−	3.44118i	−0.335629	−	0.138201i
$621$	1.43138	+	4.30441i	0.0574394	+	0.172730i
$622$	22.2448	−	14.8971i	0.891933	−	0.597319i
$623$	−1.07306			−0.0429912
$624$	3.78774	−	24.9590i	0.151631	−	0.999160i
$625$	1.00000			0.0400000
$626$	−22.8427	+	15.2975i	−0.912976	+	0.611412i
$627$	16.8453	+	23.0741i	0.672736	+	0.921492i
$628$	−29.0766	−	11.9728i	−1.16028	−	0.477767i
$629$	1.80388			0.0719253
$630$	4.07681	−	1.17459i	0.162424	−	0.0467968i
$631$			36.6634i			1.45955i	0.683688	+	0.729774i	$0.260375\pi$
$631$			36.6634i			1.45955i	−0.683688	+	0.729774i	$0.739625\pi$
$632$	−31.5755	+	6.38369i	−1.25601	+	0.253930i
$633$	13.1685	−	9.61365i	0.523400	−	0.382108i
$634$	15.8002	−	10.5813i	0.627507	−	0.420236i
$635$		−	16.4148i		−	0.651402i
$636$	−5.30454	−	21.6762i	−0.210339	−	0.859516i
$637$		−	3.64377i		−	0.144371i
$638$	−5.79601	−	8.65476i	−0.229466	−	0.342645i
$639$	2.44765	−	7.65227i	0.0968275	−	0.302719i
$640$	−6.21660	+	9.45272i	−0.245733	+	0.373651i
$641$			3.14434i			0.124194i	0.998070	+	0.0620969i	$0.0197788\pi$
$641$			3.14434i			0.124194i	−0.998070	+	0.0620969i	$0.980221\pi$
$642$	−6.50462	−	2.37505i	−0.256717	−	0.0937358i
$643$	−32.3300			−1.27497			−0.637486	−	0.770462i	$-0.720025\pi$
$643$	−32.3300			−1.27497			−0.637486	+	0.770462i	$0.720025\pi$
$644$	−1.61446	−	0.664782i	−0.0636186	−	0.0261961i
$645$	3.32789	−	2.42952i	0.131035	−	0.0956624i
$646$	−21.8805	−	32.6726i	−0.860877	−	1.28549i
$647$	−11.3287			−0.445379			−0.222689	−	0.974889i	$-0.571484\pi$
$647$	−11.3287			−0.445379			−0.222689	+	0.974889i	$0.571484\pi$
$648$	10.3721	−	23.2469i	0.407457	−	0.913225i
$649$	26.8751			1.05494
$650$	−2.86737	−	4.28163i	−0.112467	−	0.167939i
$651$	−6.32162	+	4.61510i	−0.247764	+	0.180880i
$652$	−11.9910	+	29.1207i	−0.469602	+	1.14045i
$653$	29.7903			1.16579			0.582893	−	0.812549i	$-0.301921\pi$
$653$	29.7903			1.16579			0.582893	+	0.812549i	$0.301921\pi$
$654$	3.55124	+	1.29667i	0.138864	+	0.0507040i
$655$			13.1259i			0.512870i
$656$	3.70589	−	3.73699i	0.144691	−	0.145905i
$657$	13.3913	−	41.8661i	0.522442	−	1.63335i
$658$	−10.1476	−	15.1526i	−0.395594	−	0.590711i
$659$			37.0098i			1.44170i	0.693092	+	0.720849i	$0.256248\pi$
$659$			37.0098i			1.44170i	−0.693092	+	0.720849i	$0.743752\pi$
$660$	−8.76942	+	2.14603i	−0.341349	+	0.0835341i
$661$			6.31954i			0.245802i	0.992419	+	0.122901i	$0.0392197\pi$
$661$			6.31954i			0.245802i	−0.992419	+	0.122901i	$0.960780\pi$
$662$	−26.2715	+	17.5938i	−1.02107	+	0.683801i
$663$	−22.3948	+	16.3493i	−0.869743	+	0.634956i
$664$	−43.8179	+	8.85877i	−1.70047	+	0.343787i
$665$		−	6.32881i		−	0.245421i
$666$	1.67388	−	0.482269i	0.0648614	−	0.0186876i
$667$	−2.46714			−0.0955281
$668$	−18.3159	+	44.4811i	−0.708663	+	1.72102i
$669$	−2.85565	−	3.91158i	−0.110406	−	0.151230i
$670$	−11.6421	+	7.79659i	−0.449772	+	0.301208i
$671$	29.7503			1.14850
$672$	4.16876	+	8.86687i	0.160814	+	0.342047i
$673$	−37.4069			−1.44193			−0.720964	−	0.692972i	$-0.756301\pi$
$673$	−37.4069			−1.44193			−0.720964	+	0.692972i	$0.756301\pi$
$674$	29.6638	−	19.8656i	1.14261	−	0.765193i
$675$	−1.63964	−	4.93068i	−0.0631098	−	0.189782i
$676$	−0.210990	+	0.512400i	−0.00811500	+	0.0197077i
$677$	−24.4385			−0.939248			−0.469624	−	0.882866i	$-0.655611\pi$
$677$	−24.4385			−0.939248			−0.469624	+	0.882866i	$0.655611\pi$
$678$	−15.0173	−	5.48331i	−0.576735	−	0.210585i
$679$		−	11.4590i		−	0.439756i
$680$	12.1801	−	2.46247i	0.467084	−	0.0944314i
$681$	−24.3857	−	33.4028i	−0.934464	−	1.28000i
$682$	13.8390	−	9.26782i	0.529921	−	0.354883i
$683$		−	35.3525i		−	1.35273i	−0.736568	−	0.676363i	$-0.763555\pi$
$683$		−	35.3525i		−	1.35273i	0.736568	−	0.676363i	$-0.236445\pi$
$684$	−29.0387	−	24.4682i	−1.11032	−	0.935564i
$685$		−	5.14434i		−	0.196555i
$686$	0.786923	+	1.17505i	0.0300449	+	0.0448638i
$687$	−19.9014	−	27.2603i	−0.759284	−	1.04004i
$688$	6.75658	+	6.70035i	0.257592	+	0.255449i
$689$			23.4732i			0.894259i
$690$	−0.733428	+	2.00866i	−0.0279211	+	0.0764683i
$691$	10.8725			0.413610			0.206805	−	0.978382i	$-0.433694\pi$
$691$	10.8725			0.413610			0.206805	+	0.978382i	$0.433694\pi$
$692$	8.22728	−	19.9804i	0.312754	−	0.759540i
$693$	−2.38198	+	7.44697i	−0.0904840	+	0.282887i
$694$	8.55661	+	12.7770i	0.324805	+	0.485007i
$695$	23.0112			0.872865
$696$	10.2175	+	9.34269i	0.387295	+	0.354134i
$697$	−5.78060			−0.218956
$698$	25.5775	+	38.1930i	0.968122	+	1.44563i
$699$	−17.2026	−	23.5636i	−0.650661	−	0.891255i
$700$	1.84935	+	0.761505i	0.0698990	+	0.0287822i
$701$	24.9216			0.941276			0.470638	−	0.882326i	$-0.344024\pi$
$701$	24.9216			0.941276			0.470638	+	0.882326i	$0.344024\pi$
$702$	−16.4099	+	21.1584i	−0.619351	+	0.798572i
$703$		−	2.59852i		−	0.0980050i
$704$	−8.09941	−	19.2122i	−0.305258	−	0.724088i
$705$	−18.0395	+	13.1697i	−0.679405	+	0.496000i
$706$	7.36718	+	11.0009i	0.277268	+	0.414023i
$707$		−	8.86572i		−	0.333430i
$708$	−34.6977	+	8.49113i	−1.30402	+	0.319116i
$709$		−	42.2314i		−	1.58603i	−0.609200	−	0.793016i	$-0.708510\pi$
$709$		−	42.2314i		−	1.58603i	0.609200	−	0.793016i	$-0.291490\pi$
$710$	3.14687	−	2.10743i	0.118100	−	0.0790904i
$711$	32.5442	+	10.4096i	1.22050	+	0.390389i
$712$	−2.97488	+	0.601438i	−0.111488	+	0.0225398i
$713$		−	3.94496i		−	0.147740i
$714$	3.69108	−	10.1089i	0.138135	−	0.378315i
$715$	9.49645			0.355147
$716$	−9.96356	−	4.10268i	−0.372356	−	0.153324i
$717$	−9.83838	+	7.18251i	−0.367421	+	0.268236i
$718$	6.20425	−	4.15493i	0.231540	−	0.155060i
$719$	27.6757			1.03213			0.516064	−	0.856550i	$-0.327397\pi$
$719$	27.6757			1.03213			0.516064	+	0.856550i	$0.327397\pi$
$720$	10.6439	−	5.54137i	0.396676	−	0.206514i
$721$	−4.62254			−0.172152
$722$	−24.7394	+	16.5678i	−0.920706	+	0.616588i
$723$	6.92277	−	5.05397i	0.257461	−	0.187959i
$724$	−19.2248	−	7.91614i	−0.714483	−	0.294201i
$725$	2.82610			0.104959
$726$	−3.53501	+	9.68141i	−0.131196	+	0.359311i
$727$		−	38.7201i		−	1.43605i	−0.696018	−	0.718024i	$-0.745047\pi$
$727$		−	38.7201i		−	1.43605i	0.696018	−	0.718024i	$-0.254953\pi$
$728$	−2.04230	−	10.1018i	−0.0756925	−	0.374396i
$729$	−21.6232	+	16.1691i	−0.800858	+	0.598855i
$730$	17.2167	−	11.5299i	0.637220	−	0.426740i
$731$		−	10.4515i		−	0.386562i
$732$	−38.4098	+	9.39954i	−1.41967	+	0.347417i
$733$			30.8836i			1.14071i	0.821397	+	0.570356i	$0.193195\pi$
$733$			30.8836i			1.14071i	−0.821397	+	0.570356i	$0.806805\pi$
$734$	−21.9573	−	32.7872i	−0.810458	−	1.21020i
$735$	1.39892	−	1.02128i	0.0516000	−	0.0376706i
$736$	−4.84843	−	0.938113i	−0.178715	−	0.0345793i
$737$		−	25.8215i		−	0.951149i
$738$	−5.36401	+	1.54545i	−0.197452	+	0.0568889i
$739$	−11.8412			−0.435586			−0.217793	−	0.975995i	$-0.569886\pi$
$739$	−11.8412			−0.435586			−0.217793	+	0.975995i	$0.569886\pi$
$740$	0.759318	+	0.312663i	0.0279131	+	0.0114937i
$741$	23.5515	+	32.2602i	0.865188	+	1.18511i
$742$	−5.06937	−	7.56971i	−0.186102	−	0.277893i
$743$	18.3374			0.672734			0.336367	−	0.941731i	$-0.390802\pi$
$743$	18.3374			0.672734			0.336367	+	0.941731i	$0.390802\pi$
$744$	−14.9390	+	16.3378i	−0.547689	+	0.598974i
$745$	−12.1682			−0.445809
$746$	22.1289	+	33.0435i	0.810198	+	1.20981i
$747$	45.1622	+	14.4456i	1.65240	+	0.528535i
$748$	−8.71938	+	21.1755i	−0.318812	+	0.774252i
$749$	−2.82698			−0.103296
$750$	0.840138	−	2.30091i	0.0306775	−	0.0840172i
$751$		−	31.9649i		−	1.16642i	−0.812323	−	0.583208i	$-0.801797\pi$
$751$		−	31.9649i		−	1.16642i	0.812323	−	0.583208i	$-0.198203\pi$
$752$	−36.6254	−	36.3206i	−1.33559	−	1.32448i
$753$	3.05706	+	4.18746i	0.111405	+	0.152600i
$754$	−8.10346	−	12.1003i	−0.295111	−	0.440667i
$755$			0.557777i			0.0202996i
$756$	0.722457	−	10.3672i	0.0262755	−	0.377050i
$757$			9.13341i			0.331960i	0.986129	+	0.165980i	$0.0530787\pi$
$757$			9.13341i			0.331960i	−0.986129	+	0.165980i	$0.946921\pi$
$758$	−31.3869	+	21.0195i	−1.14002	+	0.763463i
$759$	−2.32361	−	3.18281i	−0.0843416	−	0.115529i
$760$	−3.54723	−	17.5456i	−0.128672	−	0.636446i
$761$		−	51.4586i		−	1.86537i	−0.360687	−	0.932687i	$-0.617458\pi$
$761$		−	51.4586i		−	1.86537i	0.360687	−	0.932687i	$-0.382542\pi$
$762$	−37.7689	−	13.7907i	−1.36822	−	0.499584i
$763$	1.54341			0.0558751
$764$	−17.2155	+	41.8088i	−0.622836	+	1.51259i
$765$	−12.5537	−	4.01543i	−0.453881	−	0.145178i
$766$	34.9694	−	23.4187i	1.26349	−	0.846150i
$767$	37.5743			1.35673
$768$	16.5270	+	22.2454i	0.596367	+	0.802712i
$769$	−4.72688			−0.170456			−0.0852279	−	0.996361i	$-0.527162\pi$
$769$	−4.72688			−0.170456			−0.0852279	+	0.996361i	$0.527162\pi$
$770$	−3.06244	+	2.05089i	−0.110363	+	0.0739089i
$771$	−10.4814	−	14.3570i	−0.377477	−	0.517056i
$772$	13.0495	−	31.6913i	0.469660	−	1.14059i
$773$	7.49571			0.269602			0.134801	−	0.990873i	$-0.456960\pi$
$773$	7.49571			0.269602			0.134801	+	0.990873i	$0.456960\pi$
$774$	−2.79422	−	9.69829i	−0.100436	−	0.348598i
$775$			4.51893i			0.162325i
$776$	−6.42265	−	31.7682i	−0.230560	−	1.14041i
$777$	0.574377	−	0.419324i	0.0206057	−	0.0150432i
$778$	8.74514	−	5.85654i	0.313528	−	0.209967i
$779$			8.32706i			0.298348i
$780$	−12.2606	+	3.00038i	−0.439000	+	0.107431i
$781$			6.97961i			0.249750i
$782$	3.01816	+	4.50680i	0.107929	+	0.161163i
$783$	−4.63379	−	13.9346i	−0.165598	−	0.497981i
$784$	2.84022	+	2.81658i	0.101436	+	0.100592i
$785$			15.7226i			0.561163i
$786$	30.2014	+	11.0275i	1.07725	+	0.393339i
$787$	−15.6092			−0.556408			−0.278204	−	0.960522i	$-0.589739\pi$
$787$	−15.6092			−0.556408			−0.278204	+	0.960522i	$0.589739\pi$
$788$	7.33827	−	17.8214i	0.261415	−	0.634860i
$789$	25.6603	−	18.7333i	0.913531	−	0.666923i
$790$	8.96265	+	13.3833i	0.318877	+	0.476155i
$791$	−6.52668			−0.232062
$792$	−2.42971	+	21.9806i	−0.0863358	+	0.781046i
$793$	41.5941			1.47705
$794$	12.8678	+	19.2146i	0.456662	+	0.681899i
$795$	−9.01187	+	6.57912i	−0.319618	+	0.233337i
$796$	−11.1533	−	4.59257i	−0.395318	−	0.162779i
$797$	−31.1859			−1.10466			−0.552331	−	0.833625i	$-0.686262\pi$
$797$	−31.1859			−1.10466			−0.552331	+	0.833625i	$0.686262\pi$
$798$	−14.5620	−	5.31707i	−0.515489	−	0.188222i
$799$			56.6543i			2.00429i
$800$	5.55385	+	1.07460i	0.196358	+	0.0379930i
$801$	3.06614	+	0.980735i	0.108337	+	0.0346526i
$802$	−5.56420	−	8.30861i	−0.196479	−	0.293387i
$803$			38.1859i			1.34755i
$804$	8.15827	+	33.3375i	0.287720	+	1.17572i
$805$			0.872985i			0.0307687i
$806$	19.3484	−	12.9574i	0.681517	−	0.456406i
$807$	−34.8264	+	25.4251i	−1.22595	+	0.895004i
$808$	−4.96915	−	24.5788i	−0.174814	−	0.864678i
$809$		−	7.84808i		−	0.275924i	−0.990438	−	0.137962i	$-0.955945\pi$
$809$		−	7.84808i		−	0.275924i	0.990438	−	0.137962i	$-0.0440551\pi$
$810$	−12.7225	−	0.369787i	−0.447025	−	0.0129930i
$811$	33.3680			1.17171			0.585855	−	0.810416i	$-0.300759\pi$
$811$	33.3680			1.17171			0.585855	+	0.810416i	$0.300759\pi$
$812$	5.22646	+	2.15209i	0.183413	+	0.0755234i
$813$	−5.80524	−	7.95184i	−0.203599	−	0.278883i
$814$	−1.25739	+	0.842065i	−0.0440716	+	0.0295144i
$815$	15.7464			0.551572
$816$	4.56701	−	30.0940i	0.159877	−	1.05350i
$817$	−15.0556			−0.526728
$818$	−5.82530	+	3.90115i	−0.203677	+	0.136400i
$819$	−3.33027	+	10.4117i	−0.116369	+	0.363813i
$820$	−2.43327	−	1.00194i	−0.0849734	−	0.0349893i
$821$	37.6886			1.31534			0.657670	−	0.753306i	$-0.271542\pi$
$821$	37.6886			1.31534			0.657670	+	0.753306i	$0.271542\pi$
$822$	−11.8366	−	4.32195i	−0.412850	−	0.150745i
$823$		−	16.6410i		−	0.580068i	−0.957016	−	0.290034i	$-0.906333\pi$
$823$		−	16.6410i		−	0.580068i	0.957016	−	0.290034i	$-0.0936667\pi$
$824$	−12.8152	+	2.59088i	−0.446440	+	0.0902577i
$825$	2.66168	+	3.64589i	0.0926678	+	0.126934i
$826$	−12.1171	+	8.11469i	−0.421607	+	0.282346i
$827$		−	12.5710i		−	0.437136i	−0.975822	−	0.218568i	$-0.929861\pi$
$827$		−	12.5710i		−	0.437136i	0.975822	−	0.218568i	$-0.0701386\pi$
$828$	4.00555	+	3.37510i	0.139203	+	0.117293i
$829$			20.9681i			0.728251i	0.931350	+	0.364125i	$0.118632\pi$
$829$			20.9681i			0.728251i	−0.931350	+	0.364125i	$0.881368\pi$
$830$	12.4376	+	18.5722i	0.431717	+	0.644651i
$831$	20.9268	+	28.6649i	0.725942	+	0.994373i
$832$	−11.3239	−	26.8608i	−0.392584	−	0.931231i
$833$		−	4.39342i		−	0.152223i
$834$	19.3326	−	52.9466i	0.669433	−	1.83339i
$835$	24.0522			0.832362
$836$	30.5037	+	12.5604i	1.05499	+	0.434412i
$837$	22.2814	−	7.40942i	0.770157	−	0.256107i
$838$	−16.5607	−	24.7289i	−0.572079	−	0.854244i
$839$	31.7318			1.09550			0.547752	−	0.836641i	$-0.315484\pi$
$839$	31.7318			1.09550			0.547752	+	0.836641i	$0.315484\pi$
$840$	3.30586	−	3.61542i	0.114063	−	0.124744i
$841$	−21.0132			−0.724592
$842$	4.39279	+	6.55943i	0.151386	+	0.226053i
$843$	−1.82461	−	2.49929i	−0.0628428	−	0.0860801i
$844$	7.16828	−	17.4085i	0.246742	−	0.599226i
$845$	0.277070			0.00953149
$846$	15.1466	+	52.5715i	0.520752	+	1.80744i
$847$			4.20765i			0.144577i
$848$	−18.2967	−	18.1445i	−0.628313	−	0.623084i
$849$	−5.22601	+	3.81525i	−0.179356	+	0.130939i
$850$	−3.45729	−	5.16251i	−0.118584	−	0.177073i
$851$			0.358435i			0.0122870i
$852$	−2.20519	−	9.01118i	−0.0755487	−	0.308718i
$853$			38.4646i			1.31700i	0.752580	+	0.658501i	$0.228809\pi$
$853$			38.4646i			1.31700i	−0.752580	+	0.658501i	$0.771191\pi$
$854$	−13.4134	+	8.98283i	−0.458997	+	0.307386i
$855$	−5.78430	+	18.0839i	−0.197819	+	0.618456i
$856$	−7.83734	+	1.58449i	−0.267875	+	0.0541569i
$857$		−	43.6229i		−	1.49013i	−0.666991	−	0.745066i	$-0.732418\pi$
$857$		−	43.6229i		−	1.49013i	0.666991	−	0.745066i	$-0.267582\pi$
$858$	7.97832	−	21.8504i	0.272375	−	0.745961i
$859$	−2.10572			−0.0718463			−0.0359232	−	0.999355i	$-0.511437\pi$
$859$	−2.10572			−0.0718463			−0.0359232	+	0.999355i	$0.511437\pi$
$860$	1.81154	−	4.39942i	0.0617730	−	0.150019i
$861$	−1.84062	+	1.34374i	−0.0627280	+	0.0457946i
$862$	26.1739	−	17.5284i	0.891485	−	0.597019i
$863$	14.1968			0.483263			0.241632	−	0.970368i	$-0.422317\pi$
$863$	14.1968			0.483263			0.241632	+	0.970368i	$0.422317\pi$
$864$	−3.80779	−	29.1462i	−0.129544	−	0.991574i
$865$	−10.8040			−0.367346
$866$	−32.1071	+	21.5018i	−1.09104	+	0.730662i
$867$	−3.22057	+	2.35118i	−0.109376	+	0.0798502i
$868$	−3.44118	+	8.35710i	−0.116801	+	0.283658i
$869$	−29.6834			−1.00694
$870$	2.37431	−	6.50259i	0.0804967	−	0.220458i
$871$		−	36.1014i		−	1.22325i
$872$	4.27885	−	0.865064i	0.144900	−	0.0292948i
$873$	−10.4731	+	32.7428i	−0.354461	+	1.10818i
$874$	6.49213	−	4.34772i	0.219599	−	0.147064i
$875$		−	1.00000i		−	0.0338062i
$876$	−12.0648	−	49.3008i	−0.407630	−	1.66572i
$877$			38.8947i			1.31338i	0.754161	+	0.656690i	$0.228044\pi$
$877$			38.8947i			1.31338i	−0.754161	+	0.656690i	$0.771956\pi$
$878$	2.06767	+	3.08751i	0.0697806	+	0.104198i
$879$	7.59261	−	5.54299i	0.256093	−	0.186960i
$880$	−7.34062	+	7.40222i	−0.247452	+	0.249529i
$881$			37.6748i			1.26930i	0.772801	+	0.634649i	$0.218855\pi$
$881$			37.6748i			1.26930i	−0.772801	+	0.634649i	$0.781145\pi$
$882$	−1.17459	−	4.07681i	−0.0395505	−	0.137273i
$883$	−7.31822			−0.246278			−0.123139	−	0.992389i	$-0.539296\pi$
$883$	−7.31822			−0.246278			−0.123139	+	0.992389i	$0.539296\pi$
$884$	−12.1907	+	29.6056i	−0.410016	+	0.995745i
$885$	10.5314	+	14.4256i	0.354009	+	0.484910i
$886$	−21.6671	−	32.3539i	−0.727920	−	1.08695i
$887$	−8.75464			−0.293952			−0.146976	−	0.989140i	$-0.546954\pi$
$887$	−8.75464			−0.293952			−0.146976	+	0.989140i	$0.546954\pi$
$888$	1.35734	−	1.48444i	0.0455493	−	0.0498145i
$889$	−16.4148			−0.550535
$890$	0.844414	+	1.26090i	0.0283048	+	0.0422655i
$891$	13.6125	−	19.1018i	0.456036	−	0.639936i
$892$	−5.17105	−	2.12927i	−0.173140	−	0.0712933i
$893$	81.6117			2.73103
$894$	−10.2230	+	27.9979i	−0.341908	+	0.936391i
$895$			5.38759i			0.180087i
$896$	9.45272	+	6.21660i	0.315793	+	0.207682i
$897$	−3.24866	−	4.44991i	−0.108470	−	0.148578i
$898$	−24.0516	−	35.9145i	−0.802612	−	1.19848i
$899$			12.7709i			0.425934i
$900$	−4.58834	−	3.86616i	−0.152945	−	0.128872i
$901$			28.3025i			0.942893i
$902$	4.02937	−	2.69843i	0.134163	−	0.0898480i
$903$	−2.42952	−	3.32789i	−0.0808495	−	0.110745i
$904$	−18.0942	+	3.65814i	−0.601803	+	0.121668i
$905$			10.3954i			0.345555i
$906$	1.28339	+	0.468609i	0.0426378	+	0.0155685i
$907$	−50.4547			−1.67532			−0.837660	−	0.546191i	$-0.816077\pi$
$907$	−50.4547			−1.67532			−0.837660	+	0.546191i	$0.816077\pi$
$908$	−44.1581	−	18.1829i	−1.46544	−	0.603420i
$909$	−8.10294	+	25.3328i	−0.268758	+	0.840237i
$910$	−4.28163	+	2.86737i	−0.141935	+	0.0950523i
$911$	26.7091			0.884913			0.442456	−	0.896790i	$-0.354107\pi$
$911$	26.7091			0.884913			0.442456	+	0.896790i	$0.354107\pi$
$912$	−43.3509	−	6.57886i	−1.43549	−	0.217848i
$913$	−41.1923			−1.36327
$914$	35.9803	−	24.0957i	1.19012	−	0.797014i
$915$	11.6581	+	15.9689i	0.385404	+	0.527915i
$916$	−36.0377	−	14.8392i	−1.19072	−	0.490299i
$917$	13.1259			0.433454
$918$	−19.7860	+	25.5114i	−0.653034	+	0.842003i
$919$			18.4650i			0.609104i	0.952496	+	0.304552i	$0.0985067\pi$
$919$			18.4650i			0.609104i	−0.952496	+	0.304552i	$0.901493\pi$
$920$	0.489299	+	2.42021i	0.0161317	+	0.0797919i
$921$	−4.62335	+	3.37528i	−0.152344	+	0.111219i
$922$	−3.77857	+	2.53047i	−0.124441	+	0.0833367i
$923$			9.75825i			0.321197i
$924$	2.14603	+	8.76942i	0.0705992	+	0.288493i
$925$		−	0.410585i		−	0.0135000i
$926$	20.9914	+	31.3450i	0.689821	+	1.03006i
$927$	13.2084	+	4.22483i	0.433820	+	0.138761i
$928$	15.6957	+	3.03693i	0.515237	+	0.0996923i
$929$		−	30.4117i		−	0.997777i	−0.866666	−	0.498889i	$-0.833742\pi$
$929$		−	30.4117i		−	0.997777i	0.866666	−	0.498889i	$-0.166258\pi$
$930$	10.3976	+	3.79652i	0.340952	+	0.124493i
$931$	−6.32881			−0.207418
$932$	−31.1507	−	12.8269i	−1.02037	−	0.420158i
$933$	−26.4827	+	19.3337i	−0.867006	+	0.632958i
$934$	−17.8095	−	26.5937i	−0.582745	−	0.870171i
$935$	11.4502			0.374462
$936$	−3.39699	+	30.7312i	−0.111034	+	1.00448i
$937$	27.8966			0.911343			0.455671	−	0.890148i	$-0.349399\pi$
$937$	27.8966			0.911343			0.455671	+	0.890148i	$0.349399\pi$
$938$	7.79659	+	11.6421i	0.254568	+	0.380127i
$939$	27.1946	−	19.8534i	0.887461	−	0.647891i
$940$	−9.81980	+	23.8479i	−0.320287	+	0.777833i
$941$	−25.9404			−0.845633			−0.422816	−	0.906215i	$-0.638959\pi$
$941$	−25.9404			−0.845633			−0.422816	+	0.906215i	$0.638959\pi$
$942$	36.1762	+	13.2091i	1.17868	+	0.430376i
$943$		−	1.14862i		−	0.0374042i
$944$	−29.0444	+	29.2881i	−0.945314	+	0.953248i
$945$	−4.93068	+	1.63964i	−0.160395	+	0.0533375i
$946$	4.87885	+	7.28522i	0.158625	+	0.236863i
$947$		−	22.9262i		−	0.745001i	−0.928032	−	0.372501i	$-0.878500\pi$
$947$		−	22.9262i		−	0.745001i	0.928032	−	0.372501i	$-0.121500\pi$
$948$	38.3235	−	9.37843i	1.24469	−	0.304597i
$949$			53.3880i			1.73305i
$950$	−7.43670	+	4.98029i	−0.241278	+	0.161582i
$951$	−18.8104	+	13.7326i	−0.609970	+	0.445309i
$952$	−2.46247	−	12.1801i	−0.0798091	−	0.394758i
$953$		−	9.26963i		−	0.300273i	−0.988665	−	0.150136i	$-0.952029\pi$
$953$		−	9.26963i		−	0.300273i	0.988665	−	0.150136i	$-0.0479713\pi$
$954$	7.56672	+	26.2628i	0.244982	+	0.850291i
$955$	22.6073			0.731554
$956$	−5.35554	+	13.0062i	−0.173210	+	0.420651i
$957$	7.52217	+	10.3036i	0.243157	+	0.333069i
$958$	−15.1533	+	10.1480i	−0.489581	+	0.327868i
$959$	−5.14434			−0.166119
$960$	7.13856	−	11.8761i	0.230396	−	0.383298i
$961$	10.5793			0.341268
$962$	−1.75797	+	1.17730i	−0.0566794	+	0.0379576i
$963$	8.07778	+	2.58375i	0.260303	+	0.0832603i
$964$	3.76842	−	9.15181i	0.121373	−	0.294760i
$965$	−17.1364			−0.551640
$966$	2.00866	+	0.733428i	0.0646275	+	0.0235977i
$967$			37.2682i			1.19846i	0.800575	+	0.599232i	$0.204527\pi$
$967$			37.2682i			1.19846i	−0.800575	+	0.599232i	$0.795473\pi$
$968$	2.35835	+	11.6650i	0.0758001	+	0.374928i
$969$	28.3969	+	38.8972i	0.912241	+	1.24956i
$970$	−13.4649	+	9.01735i	−0.432333	+	0.289530i
$971$		−	43.3878i		−	1.39238i	−0.717857	−	0.696191i	$-0.754877\pi$
$971$		−	43.3878i		−	1.39238i	0.717857	−	0.696191i	$-0.245123\pi$
$972$	−11.5395	+	28.9627i	−0.370131	+	0.928980i
$973$		−	23.0112i		−	0.737706i
$974$	0.345122	+	0.515345i	0.0110584	+	0.0165127i
$975$	3.72132	+	5.09735i	0.119178	+	0.163246i
$976$	−32.1517	+	32.4215i	−1.02915	+	1.03779i
$977$			48.3279i			1.54615i	0.634318	+	0.773073i	$0.281281\pi$
$977$			48.3279i			1.54615i	−0.634318	+	0.773073i	$0.718719\pi$
$978$	13.2291	−	36.2310i	0.423021	−	1.15854i
$979$	−2.79662			−0.0893803
$980$	0.761505	−	1.84935i	0.0243254	−	0.0590754i
$981$	−4.41012	−	1.41062i	−0.140804	−	0.0450375i
$982$	−17.6328	−	26.3298i	−0.562686	−	0.840217i
$983$	6.14477			0.195988			0.0979938	−	0.995187i	$-0.468757\pi$
$983$	6.14477			0.195988			0.0979938	+	0.995187i	$0.468757\pi$
$984$	−4.34965	+	4.75695i	−0.138662	+	0.151646i
$985$	−9.63654			−0.307046
$986$	−9.77063	−	14.5898i	−0.311160	−	0.464633i
$987$	13.1697	+	18.0395i	0.419196	+	0.574202i
$988$	42.6475	+	17.5609i	1.35680	+	0.558686i
$989$	2.07674			0.0660365
$990$	10.6250	−	3.06123i	0.337685	−	0.0972923i
$991$			10.6251i			0.337518i	0.985657	+	0.168759i	$0.0539759\pi$
$991$			10.6251i			0.337518i	−0.985657	+	0.168759i	$0.946024\pi$
$992$	−4.85605	+	25.0974i	−0.154180	+	0.796844i
$993$	31.2766	−	22.8335i	0.992534	−	0.724600i
$994$	−2.10743	−	3.14687i	−0.0668436	−	0.0998127i
$995$			6.03091i			0.191193i
$996$	53.1823	−	13.0146i	1.68514	−	0.412384i
$997$		−	56.9151i		−	1.80252i	−0.433280	−	0.901259i	$-0.642644\pi$
$997$		−	56.9151i		−	1.80252i	0.433280	−	0.901259i	$-0.357356\pi$
$998$	−23.6733	+	15.8538i	−0.749365	+	0.501843i
$999$	−2.02446	+	0.673213i	−0.0640512	+	0.0212995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.e.d.491.10	yes	44
3.2	odd	2		840.2.e.c.491.35	✓	44
4.3	odd	2		3360.2.e.c.911.12		44
8.3	odd	2		840.2.e.c.491.36	yes	44
8.5	even	2		3360.2.e.d.911.12		44
12.11	even	2		3360.2.e.d.911.11		44
24.5	odd	2		3360.2.e.c.911.11		44
24.11	even	2	inner	840.2.e.d.491.9	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.e.c.491.35	✓	44	3.2	odd	2
840.2.e.c.491.36	yes	44	8.3	odd	2
840.2.e.d.491.9	yes	44	24.11	even	2	inner
840.2.e.d.491.10	yes	44	1.1	even	1	trivial
3360.2.e.c.911.11		44	24.5	odd	2
3360.2.e.c.911.12		44	4.3	odd	2
3360.2.e.d.911.11		44	12.11	even	2
3360.2.e.d.911.12		44	8.5	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17505 + 0.786923i) q^{2} +(1.39892 - 1.02128i) q^{3} +(0.761505 - 1.84935i) q^{4} -1.00000 q^{5} +(-0.840138 + 2.30091i) q^{6} +1.00000i q^{7} +(0.560490 + 2.77234i) q^{8} +(0.913962 - 2.85739i) q^{9} +(1.17505 - 0.786923i) q^{10} +2.60621i q^{11} +(-0.823428 - 3.36481i) q^{12} +3.64377i q^{13} +(-0.786923 - 1.17505i) q^{14} +(-1.39892 + 1.02128i) q^{15} +(-2.84022 - 2.81658i) q^{16} +4.39342i q^{17} +(1.17459 + 4.07681i) q^{18} +6.32881 q^{19} +(-0.761505 + 1.84935i) q^{20} +(1.02128 + 1.39892i) q^{21} +(-2.05089 - 3.06244i) q^{22} -0.872985 q^{23} +(3.61542 + 3.30586i) q^{24} +1.00000 q^{25} +(-2.86737 - 4.28163i) q^{26} +(-1.63964 - 4.93068i) q^{27} +(1.84935 + 0.761505i) q^{28} +2.82610 q^{29} +(0.840138 - 2.30091i) q^{30} +4.51893i q^{31} +(5.55385 + 1.07460i) q^{32} +(2.66168 + 3.64589i) q^{33} +(-3.45729 - 5.16251i) q^{34} -1.00000i q^{35} +(-4.58834 - 3.86616i) q^{36} -0.410585i q^{37} +(-7.43670 + 4.98029i) q^{38} +(3.72132 + 5.09735i) q^{39} +(-0.560490 - 2.77234i) q^{40} +1.31574i q^{41} +(-2.30091 - 0.840138i) q^{42} -2.37889 q^{43} +(4.81981 + 1.98464i) q^{44} +(-0.913962 + 2.85739i) q^{45} +(1.02581 - 0.686972i) q^{46} +12.8953 q^{47} +(-6.84978 - 1.03951i) q^{48} -1.00000 q^{49} +(-1.17505 + 0.786923i) q^{50} +(4.48693 + 6.14606i) q^{51} +(6.73862 + 2.77475i) q^{52} +6.44201 q^{53} +(5.80673 + 4.50354i) q^{54} -2.60621i q^{55} +(-2.77234 + 0.560490i) q^{56} +(8.85351 - 6.46351i) q^{57} +(-3.32082 + 2.22392i) q^{58} -10.3119i q^{59} +(0.823428 + 3.36481i) q^{60} -11.4151i q^{61} +(-3.55605 - 5.30998i) q^{62} +(2.85739 + 0.913962i) q^{63} +(-7.37170 + 3.10773i) q^{64} -3.64377i q^{65} +(-5.99665 - 2.18958i) q^{66} -9.90769 q^{67} +(8.12500 + 3.34561i) q^{68} +(-1.22124 + 0.891565i) q^{69} +(0.786923 + 1.17505i) q^{70} +2.67806 q^{71} +(8.43391 + 0.932274i) q^{72} +14.6519 q^{73} +(0.323099 + 0.482460i) q^{74} +(1.39892 - 1.02128i) q^{75} +(4.81942 - 11.7042i) q^{76} -2.60621 q^{77} +(-8.38398 - 3.06127i) q^{78} +11.3895i q^{79} +(2.84022 + 2.81658i) q^{80} +(-7.32935 - 5.22309i) q^{81} +(-1.03538 - 1.54606i) q^{82} +15.8054i q^{83} +(3.36481 - 0.823428i) q^{84} -4.39342i q^{85} +(2.79533 - 1.87201i) q^{86} +(3.95349 - 2.88625i) q^{87} +(-7.22530 + 1.46076i) q^{88} +1.07306i q^{89} +(-1.17459 - 4.07681i) q^{90} -3.64377 q^{91} +(-0.664782 + 1.61446i) q^{92} +(4.61510 + 6.32162i) q^{93} +(-15.1526 + 10.1476i) q^{94} -6.32881 q^{95} +(8.86687 - 4.16876i) q^{96} -11.4590 q^{97} +(1.17505 - 0.786923i) q^{98} +(7.44697 + 2.38198i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} + 4 q^{3} - 2 q^{4} - 44 q^{5} - 6 q^{6} - 22 q^{8} + 4 q^{9} - 2 q^{10} + 6 q^{12} + 4 q^{14} - 4 q^{15} + 22 q^{16} + 2 q^{18} + 16 q^{19} + 2 q^{20} + 16 q^{23} + 10 q^{24} + 44 q^{25}+ \cdots - 64 q^{99}+O(q^{100}) \) 44 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 - 44 * q^5 - 6 * q^6 - 22 * q^8 + 4 * q^9 - 2 * q^10 + 6 * q^12 + 4 * q^14 - 4 * q^15 + 22 * q^16 + 2 * q^18 + 16 * q^19 + 2 * q^20 + 16 * q^23 + 10 * q^24 + 44 * q^25 - 16 * q^26 + 4 * q^27 + 16 * q^29 + 6 * q^30 - 18 * q^32 + 24 * q^33 + 20 * q^34 - 46 * q^36 + 8 * q^38 - 16 * q^39 + 22 * q^40 - 4 * q^42 + 24 * q^43 + 32 * q^44 - 4 * q^45 - 24 * q^47 + 18 * q^48 - 44 * q^49 + 2 * q^50 - 20 * q^52 - 32 * q^53 + 2 * q^54 + 8 * q^56 - 4 * q^58 - 6 * q^60 + 32 * q^62 - 50 * q^64 - 8 * q^66 + 24 * q^67 - 28 * q^68 - 8 * q^69 - 4 * q^70 + 8 * q^71 + 2 * q^72 + 8 * q^73 - 48 * q^74 + 4 * q^75 + 12 * q^76 + 8 * q^77 - 84 * q^78 - 22 * q^80 + 20 * q^81 - 8 * q^82 + 4 * q^84 - 4 * q^86 - 16 * q^87 - 28 * q^88 - 2 * q^90 - 16 * q^91 + 76 * q^92 + 16 * q^93 - 16 * q^95 + 38 * q^96 + 24 * q^97 - 2 * q^98 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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