LMFDB - Embedded newform 494.2.d.c.77.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [494,2,Mod(77,494)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("494.77"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(494, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 494 = 2 \cdot 13 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	494.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.94460985985$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 36x^{12} + 492x^{10} + 3171x^{8} + 9678x^{6} + 11765x^{4} + 1893x^{2} + 4 $ x^14 + 36x^12 + 492x^10 + 3171x^8 + 9678x^6 + 11765x^4 + 1893x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			77.1
Root			$3.29705i$ of defining polynomial
Character	$\chi$	$=$	494.77
Dual form			494.2.d.c.77.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} -3.29705 q^{3} -1.00000 q^{4} +3.53833i q^{5} +3.29705i q^{6} -0.150781i q^{7} +1.00000i q^{8} +7.87054 q^{9} +3.53833 q^{10} -2.38888i q^{11} +3.29705 q^{12} +(-3.19751 + 1.66611i) q^{13} -0.150781 q^{14} -11.6661i q^{15} +1.00000 q^{16} -4.64914 q^{17} -7.87054i q^{18} -1.00000i q^{19} -3.53833i q^{20} +0.497134i q^{21} -2.38888 q^{22} +5.53743 q^{23} -3.29705i q^{24} -7.51979 q^{25} +(1.66611 + 3.19751i) q^{26} -16.0584 q^{27} +0.150781i q^{28} -4.48871 q^{29} -11.6661 q^{30} -5.48738i q^{31} -1.00000i q^{32} +7.87626i q^{33} +4.64914i q^{34} +0.533514 q^{35} -7.87054 q^{36} -10.9060i q^{37} -1.00000 q^{38} +(10.5424 - 5.49323i) q^{39} -3.53833 q^{40} +1.62883i q^{41} +0.497134 q^{42} -10.5431 q^{43} +2.38888i q^{44} +27.8486i q^{45} -5.53743i q^{46} -7.02837i q^{47} -3.29705 q^{48} +6.97726 q^{49} +7.51979i q^{50} +15.3284 q^{51} +(3.19751 - 1.66611i) q^{52} +2.39084 q^{53} +16.0584i q^{54} +8.45265 q^{55} +0.150781 q^{56} +3.29705i q^{57} +4.48871i q^{58} -2.86108i q^{59} +11.6661i q^{60} -4.18186 q^{61} -5.48738 q^{62} -1.18673i q^{63} -1.00000 q^{64} +(-5.89523 - 11.3139i) q^{65} +7.87626 q^{66} -9.26189i q^{67} +4.64914 q^{68} -18.2572 q^{69} -0.533514i q^{70} -3.13752i q^{71} +7.87054i q^{72} -2.07937i q^{73} -10.9060 q^{74} +24.7931 q^{75} +1.00000i q^{76} -0.360199 q^{77} +(-5.49323 - 10.5424i) q^{78} -5.29827 q^{79} +3.53833i q^{80} +29.3338 q^{81} +1.62883 q^{82} +12.0013i q^{83} -0.497134i q^{84} -16.4502i q^{85} +10.5431i q^{86} +14.7995 q^{87} +2.38888 q^{88} -18.8413i q^{89} +27.8486 q^{90} +(0.251218 + 0.482125i) q^{91} -5.53743 q^{92} +18.0922i q^{93} -7.02837 q^{94} +3.53833 q^{95} +3.29705i q^{96} +12.5681i q^{97} -6.97726i q^{98} -18.8018i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 4 q^{3} - 14 q^{4} + 30 q^{9} - 4 q^{10} - 4 q^{12} - 2 q^{13} + 2 q^{14} + 14 q^{16} - 32 q^{17} + 10 q^{22} - 6 q^{23} - 14 q^{25} + 10 q^{26} + 10 q^{27} - 14 q^{29} - 26 q^{30} + 2 q^{35} - 30 q^{36}+ \cdots - 4 q^{95}+O(q^{100}) $ 14 * q + 4 * q^3 - 14 * q^4 + 30 * q^9 - 4 * q^10 - 4 * q^12 - 2 * q^13 + 2 * q^14 + 14 * q^16 - 32 * q^17 + 10 * q^22 - 6 * q^23 - 14 * q^25 + 10 * q^26 + 10 * q^27 - 14 * q^29 - 26 * q^30 + 2 * q^35 - 30 * q^36 - 14 * q^38 + 36 * q^39 + 4 * q^40 - 6 * q^42 - 46 * q^43 + 4 * q^48 - 28 * q^49 + 32 * q^51 + 2 * q^52 + 42 * q^53 + 16 * q^55 - 2 * q^56 - 12 * q^61 - 22 * q^62 - 14 * q^64 + 2 * q^65 + 12 * q^66 + 32 * q^68 - 96 * q^69 - 6 * q^74 - 10 * q^75 + 52 * q^77 + 22 * q^78 - 8 * q^79 + 102 * q^81 - 30 * q^82 - 32 * q^87 - 10 * q^88 + 76 * q^90 + 22 * q^91 + 6 * q^92 - 2 * q^94 - 4 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/494\mathbb{Z}\right)^\times$.

$n$	$287$	$457$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−3.29705			−1.90355			−0.951776	−	0.306792i	$-0.900744\pi$
$3$	−3.29705			−1.90355			−0.951776	+	0.306792i	$0.900744\pi$
$4$	−1.00000			−0.500000
$5$			3.53833i			1.58239i	0.611564	+	0.791195i	$0.290541\pi$
$5$			3.53833i			1.58239i	−0.611564	+	0.791195i	$0.709459\pi$
$6$			3.29705i			1.34602i
$7$		−	0.150781i		−	0.0569900i	−0.999594	−	0.0284950i	$-0.990929\pi$
$7$		−	0.150781i		−	0.0569900i	0.999594	−	0.0284950i	$-0.00907147\pi$
$8$			1.00000i			0.353553i
$9$	7.87054			2.62351
$10$	3.53833			1.11892
$11$		−	2.38888i		−	0.720274i	−0.932899	−	0.360137i	$-0.882730\pi$
$11$		−	2.38888i		−	0.720274i	0.932899	−	0.360137i	$-0.117270\pi$
$12$	3.29705			0.951776
$13$	−3.19751	+	1.66611i	−0.886831	+	0.462095i
$13$	−3.19751	+	1.66611i	−0.886831	+	0.462095i
$14$	−0.150781			−0.0402980
$15$		−	11.6661i		−	3.01216i
$16$	1.00000			0.250000
$17$	−4.64914			−1.12758			−0.563790	−	0.825918i	$-0.690657\pi$
$17$	−4.64914			−1.12758			−0.563790	+	0.825918i	$0.690657\pi$
$18$		−	7.87054i		−	1.85510i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$		−	3.53833i		−	0.791195i
$21$			0.497134i			0.108483i
$22$	−2.38888			−0.509311
$23$	5.53743			1.15463			0.577317	−	0.816520i	$-0.304100\pi$
$23$	5.53743			1.15463			0.577317	+	0.816520i	$0.304100\pi$
$24$		−	3.29705i		−	0.673008i
$25$	−7.51979			−1.50396
$26$	1.66611	+	3.19751i	0.326750	+	0.627084i
$27$	−16.0584			−3.09044
$28$			0.150781i			0.0284950i
$29$	−4.48871			−0.833532			−0.416766	−	0.909014i	$-0.636837\pi$
$29$	−4.48871			−0.833532			−0.416766	+	0.909014i	$0.636837\pi$
$30$	−11.6661			−2.12992
$31$		−	5.48738i		−	0.985562i	−0.870153	−	0.492781i	$-0.835980\pi$
$31$		−	5.48738i		−	0.985562i	0.870153	−	0.492781i	$-0.164020\pi$
$32$		−	1.00000i		−	0.176777i
$33$			7.87626i			1.37108i
$34$			4.64914i			0.797320i
$35$	0.533514			0.0901804
$36$	−7.87054			−1.31176
$37$		−	10.9060i		−	1.79294i	−0.443108	−	0.896468i	$-0.646124\pi$
$37$		−	10.9060i		−	1.79294i	0.443108	−	0.896468i	$-0.353876\pi$
$38$	−1.00000			−0.162221
$39$	10.5424	−	5.49323i	1.68813	−	0.879621i
$40$	−3.53833			−0.559459
$41$			1.62883i			0.254381i	0.991878	+	0.127190i	$0.0405959\pi$
$41$			1.62883i			0.254381i	−0.991878	+	0.127190i	$0.959404\pi$
$42$	0.497134			0.0767094
$43$	−10.5431			−1.60781			−0.803907	−	0.594754i	$-0.797249\pi$
$43$	−10.5431			−1.60781			−0.803907	+	0.594754i	$0.797249\pi$
$44$			2.38888i			0.360137i
$45$			27.8486i			4.15142i
$46$		−	5.53743i		−	0.816450i
$47$		−	7.02837i		−	1.02519i	−0.858630	−	0.512597i	$-0.828684\pi$
$47$		−	7.02837i		−	1.02519i	0.858630	−	0.512597i	$-0.171316\pi$
$48$	−3.29705			−0.475888
$49$	6.97726			0.996752
$50$			7.51979i			1.06346i
$51$	15.3284			2.14641
$52$	3.19751	−	1.66611i	0.443415	−	0.231047i
$53$	2.39084			0.328407			0.164204	−	0.986426i	$-0.447495\pi$
$53$	2.39084			0.328407			0.164204	+	0.986426i	$0.447495\pi$
$54$			16.0584i			2.18527i
$55$	8.45265			1.13975
$56$	0.150781			0.0201490
$57$			3.29705i			0.436705i
$58$			4.48871i			0.589396i
$59$		−	2.86108i		−	0.372481i	−0.982504	−	0.186241i	$-0.940370\pi$
$59$		−	2.86108i		−	0.372481i	0.982504	−	0.186241i	$-0.0596304\pi$
$60$			11.6661i			1.50608i
$61$	−4.18186			−0.535432			−0.267716	−	0.963498i	$-0.586269\pi$
$61$	−4.18186			−0.535432			−0.267716	+	0.963498i	$0.586269\pi$
$62$	−5.48738			−0.696898
$63$		−	1.18673i		−	0.149514i
$64$	−1.00000			−0.125000
$65$	−5.89523	−	11.3139i	−0.731214	−	1.40331i
$66$	7.87626			0.969500
$67$		−	9.26189i		−	1.13152i	−0.824570	−	0.565760i	$-0.808583\pi$
$67$		−	9.26189i		−	1.13152i	0.824570	−	0.565760i	$-0.191417\pi$
$68$	4.64914			0.563790
$69$	−18.2572			−2.19791
$70$		−	0.533514i		−	0.0637672i
$71$		−	3.13752i		−	0.372355i	−0.982516	−	0.186178i	$-0.940390\pi$
$71$		−	3.13752i		−	0.372355i	0.982516	−	0.186178i	$-0.0596100\pi$
$72$			7.87054i			0.927552i
$73$		−	2.07937i		−	0.243372i	−0.992569	−	0.121686i	$-0.961170\pi$
$73$		−	2.07937i		−	0.243372i	0.992569	−	0.121686i	$-0.0388301\pi$
$74$	−10.9060			−1.26780
$75$	24.7931			2.86286
$76$			1.00000i			0.114708i
$77$	−0.360199			−0.0410484
$78$	−5.49323	−	10.5424i	−0.621986	−	1.19369i
$79$	−5.29827			−0.596102			−0.298051	−	0.954550i	$-0.596337\pi$
$79$	−5.29827			−0.596102			−0.298051	+	0.954550i	$0.596337\pi$
$80$			3.53833i			0.395597i
$81$	29.3338			3.25931
$82$	1.62883			0.179874
$83$			12.0013i			1.31732i	0.752442	+	0.658658i	$0.228876\pi$
$83$			12.0013i			1.31732i	−0.752442	+	0.658658i	$0.771124\pi$
$84$		−	0.497134i		−	0.0542417i
$85$		−	16.4502i		−	1.78427i
$86$			10.5431i			1.13690i
$87$	14.7995			1.58667
$88$	2.38888			0.254655
$89$		−	18.8413i		−	1.99718i	−0.0531164	−	0.998588i	$-0.516915\pi$
$89$		−	18.8413i		−	1.99718i	0.0531164	−	0.998588i	$-0.483085\pi$
$90$	27.8486			2.93550
$91$	0.251218	+	0.482125i	0.0263348	+	0.0505405i
$92$	−5.53743			−0.577317
$93$			18.0922i			1.87607i
$94$	−7.02837			−0.724921
$95$	3.53833			0.363025
$96$			3.29705i			0.336504i
$97$			12.5681i			1.27610i	0.769997	+	0.638048i	$0.220258\pi$
$97$			12.5681i			1.27610i	−0.769997	+	0.638048i	$0.779742\pi$
$98$		−	6.97726i		−	0.704810i
$99$		−	18.8018i		−	1.88965i
$100$	7.51979			0.751979
$101$	8.78739			0.874378			0.437189	−	0.899370i	$-0.355974\pi$
$101$	8.78739			0.874378			0.437189	+	0.899370i	$0.355974\pi$
$102$		−	15.3284i		−	1.51774i
$103$	−12.1560			−1.19776			−0.598882	−	0.800837i	$-0.704388\pi$
$103$	−12.1560			−1.19776			−0.598882	+	0.800837i	$0.704388\pi$
$104$	−1.66611	−	3.19751i	−0.163375	−	0.313542i
$105$	−1.75902			−0.171663
$106$		−	2.39084i		−	0.232219i
$107$	3.42816			0.331413			0.165706	−	0.986175i	$-0.447010\pi$
$107$	3.42816			0.331413			0.165706	+	0.986175i	$0.447010\pi$
$108$	16.0584			1.54522
$109$			4.98056i			0.477051i	0.971136	+	0.238525i	$0.0766640\pi$
$109$			4.98056i			0.477051i	−0.971136	+	0.238525i	$0.923336\pi$
$110$		−	8.45265i		−	0.805928i
$111$			35.9577i			3.41295i
$112$		−	0.150781i		−	0.0142475i
$113$	4.29254			0.403808			0.201904	−	0.979405i	$-0.435287\pi$
$113$	4.29254			0.403808			0.201904	+	0.979405i	$0.435287\pi$
$114$	3.29705			0.308797
$115$			19.5933i			1.82708i
$116$	4.48871			0.416766
$117$	−25.1662	+	13.1132i	−2.32661	+	1.21231i
$118$	−2.86108			−0.263384
$119$			0.701003i			0.0642608i
$120$	11.6661			1.06496
$121$	5.29325			0.481205
$122$			4.18186i			0.378608i
$123$		−	5.37034i		−	0.484227i
$124$			5.48738i			0.492781i
$125$		−	8.91584i		−	0.797457i
$126$	−1.18673			−0.105722
$127$	−18.5562			−1.64659			−0.823296	−	0.567612i	$-0.807867\pi$
$127$	−18.5562			−1.64659			−0.823296	+	0.567612i	$0.807867\pi$
$128$			1.00000i			0.0883883i
$129$	34.7613			3.06056
$130$	−11.3139	+	5.89523i	−0.992291	+	0.517046i
$131$	6.91047			0.603770			0.301885	−	0.953344i	$-0.402384\pi$
$131$	6.91047			0.603770			0.301885	+	0.953344i	$0.402384\pi$
$132$		−	7.87626i		−	0.685540i
$133$	−0.150781			−0.0130744
$134$	−9.26189			−0.800105
$135$		−	56.8200i		−	4.89029i
$136$		−	4.64914i		−	0.398660i
$137$			6.09803i			0.520990i	0.965475	+	0.260495i	$0.0838857\pi$
$137$			6.09803i			0.520990i	−0.965475	+	0.260495i	$0.916114\pi$
$138$			18.2572i			1.55416i
$139$	−11.5019			−0.975579			−0.487789	−	0.872961i	$-0.662197\pi$
$139$	−11.5019			−0.975579			−0.487789	+	0.872961i	$0.662197\pi$
$140$	−0.533514			−0.0450902
$141$			23.1729i			1.95151i
$142$	−3.13752			−0.263295
$143$	3.98013	+	7.63848i	0.332835	+	0.638761i
$144$	7.87054			0.655879
$145$		−	15.8825i		−	1.31897i
$146$	−2.07937			−0.172090
$147$	−23.0044			−1.89737
$148$			10.9060i			0.896468i
$149$		−	2.14754i		−	0.175934i	−0.996123	−	0.0879668i	$-0.971963\pi$
$149$		−	2.14754i		−	0.175934i	0.996123	−	0.0879668i	$-0.0280369\pi$
$150$		−	24.7931i		−	2.02435i
$151$			11.1518i			0.907524i	0.891123	+	0.453762i	$0.149918\pi$
$151$			11.1518i			0.907524i	−0.891123	+	0.453762i	$0.850082\pi$
$152$	1.00000			0.0811107
$153$	−36.5912			−2.95822
$154$			0.360199i			0.0290256i
$155$	19.4162			1.55954
$156$	−10.5424	+	5.49323i	−0.844065	+	0.439811i
$157$	−13.4492			−1.07336			−0.536680	−	0.843786i	$-0.680322\pi$
$157$	−13.4492			−1.07336			−0.536680	+	0.843786i	$0.680322\pi$
$158$			5.29827i			0.421508i
$159$	−7.88273			−0.625141
$160$	3.53833			0.279730
$161$		−	0.834942i		−	0.0658026i
$162$		−	29.3338i		−	2.30468i
$163$		−	0.853731i		−	0.0668694i	−0.999441	−	0.0334347i	$-0.989355\pi$
$163$		−	0.853731i		−	0.0668694i	0.999441	−	0.0334347i	$-0.0106446\pi$
$164$		−	1.62883i		−	0.127190i
$165$	−27.8688			−2.16958
$166$	12.0013			0.931483
$167$			6.29325i			0.486986i	0.969903	+	0.243493i	$0.0782934\pi$
$167$			6.29325i			0.486986i	−0.969903	+	0.243493i	$0.921707\pi$
$168$	−0.497134			−0.0383547
$169$	7.44819	−	10.6548i	0.572937	−	0.819599i
$170$	−16.4502			−1.26167
$171$		−	7.87054i		−	0.601875i
$172$	10.5431			0.803907
$173$	8.41116			0.639488			0.319744	−	0.947504i	$-0.396403\pi$
$173$	8.41116			0.639488			0.319744	+	0.947504i	$0.396403\pi$
$174$		−	14.7995i		−	1.12195i
$175$			1.13384i			0.0857105i
$176$		−	2.38888i		−	0.180069i
$177$			9.43313i			0.709038i
$178$	−18.8413			−1.41222
$179$	−10.2337			−0.764902			−0.382451	−	0.923976i	$-0.624920\pi$
$179$	−10.2337			−0.764902			−0.382451	+	0.923976i	$0.624920\pi$
$180$		−	27.8486i		−	2.07571i
$181$	−14.0040			−1.04091			−0.520454	−	0.853890i	$-0.674237\pi$
$181$	−14.0040			−1.04091			−0.520454	+	0.853890i	$0.674237\pi$
$182$	0.482125	−	0.251218i	0.0357375	−	0.0186215i
$183$	13.7878			1.01922
$184$			5.53743i			0.408225i
$185$	38.5891			2.83712
$186$	18.0922			1.32658
$187$			11.1062i			0.812168i
$188$			7.02837i			0.512597i
$189$			2.42131i			0.176124i
$190$		−	3.53833i		−	0.256698i
$191$	5.05349			0.365658			0.182829	−	0.983145i	$-0.441475\pi$
$191$	5.05349			0.365658			0.182829	+	0.983145i	$0.441475\pi$
$192$	3.29705			0.237944
$193$			12.1526i			0.874764i	0.899276	+	0.437382i	$0.144094\pi$
$193$			12.1526i			0.874764i	−0.899276	+	0.437382i	$0.855906\pi$
$194$	12.5681			0.902336
$195$	19.4369	+	37.3024i	1.39190	+	2.67128i
$196$	−6.97726			−0.498376
$197$		−	8.00854i		−	0.570585i	−0.958440	−	0.285293i	$-0.907909\pi$
$197$		−	8.00854i		−	0.570585i	0.958440	−	0.285293i	$-0.0920908\pi$
$198$	−18.8018			−1.33618
$199$	−17.3501			−1.22991			−0.614957	−	0.788561i	$-0.710827\pi$
$199$	−17.3501			−1.22991			−0.614957	+	0.788561i	$0.710827\pi$
$200$		−	7.51979i		−	0.531729i
$201$			30.5369i			2.15391i
$202$		−	8.78739i		−	0.618279i
$203$			0.676814i			0.0475030i
$204$	−15.3284			−1.07321
$205$	−5.76334			−0.402529
$206$			12.1560i			0.846948i
$207$	43.5826			3.02920
$208$	−3.19751	+	1.66611i	−0.221708	+	0.115524i
$209$	−2.38888			−0.165242
$210$			1.75902i			0.121384i
$211$	−7.54866			−0.519671			−0.259836	−	0.965653i	$-0.583668\pi$
$211$	−7.54866			−0.519671			−0.259836	+	0.965653i	$0.583668\pi$
$212$	−2.39084			−0.164204
$213$			10.3446i			0.708798i
$214$		−	3.42816i		−	0.234344i
$215$		−	37.3051i		−	2.54419i
$216$		−	16.0584i		−	1.09264i
$217$	−0.827394			−0.0561672
$218$	4.98056			0.337326
$219$			6.85579i			0.463272i
$220$	−8.45265			−0.569877
$221$	14.8657	−	7.74595i	0.999973	−	0.521049i
$222$	35.9577			2.41332
$223$		−	28.7643i		−	1.92620i	−0.269146	−	0.963099i	$-0.586741\pi$
$223$		−	28.7643i		−	1.92620i	0.269146	−	0.963099i	$-0.413259\pi$
$224$	−0.150781			−0.0100745
$225$	−59.1848			−3.94565
$226$		−	4.29254i		−	0.285535i
$227$			1.92833i			0.127988i	0.997950	+	0.0639939i	$0.0203838\pi$
$227$			1.92833i			0.127988i	−0.997950	+	0.0639939i	$0.979616\pi$
$228$		−	3.29705i		−	0.218353i
$229$			17.3072i			1.14369i	0.820361	+	0.571845i	$0.193772\pi$
$229$			17.3072i			1.14369i	−0.820361	+	0.571845i	$0.806228\pi$
$230$	19.5933			1.29194
$231$	1.18759			0.0781379
$232$		−	4.48871i		−	0.294698i
$233$	−23.2739			−1.52472			−0.762362	−	0.647150i	$-0.775961\pi$
$233$	−23.2739			−1.52472			−0.762362	+	0.647150i	$0.775961\pi$
$234$	13.1132	+	25.1662i	0.857234	+	1.64516i
$235$	24.8687			1.62226
$236$			2.86108i			0.186241i
$237$	17.4687			1.13471
$238$	0.701003			0.0454393
$239$		−	14.6296i		−	0.946313i	−0.880978	−	0.473156i	$-0.843115\pi$
$239$		−	14.6296i		−	0.946313i	0.880978	−	0.473156i	$-0.156885\pi$
$240$		−	11.6661i		−	0.753041i
$241$			14.5700i			0.938534i	0.883056	+	0.469267i	$0.155482\pi$
$241$			14.5700i			0.938534i	−0.883056	+	0.469267i	$0.844518\pi$
$242$		−	5.29325i		−	0.340263i
$243$	−48.5398			−3.11383
$244$	4.18186			0.267716
$245$			24.6879i			1.57725i
$246$	−5.37034			−0.342400
$247$	1.66611	+	3.19751i	0.106012	+	0.203453i
$248$	5.48738			0.348449
$249$		−	39.5690i		−	2.50758i
$250$	−8.91584			−0.563887
$251$	22.4809			1.41898			0.709491	−	0.704715i	$-0.248925\pi$
$251$	22.4809			1.41898			0.709491	+	0.704715i	$0.248925\pi$
$252$			1.18673i			0.0747570i
$253$		−	13.2283i		−	0.831654i
$254$			18.5562i			1.16432i
$255$			54.2371i			3.39646i
$256$	1.00000			0.0625000
$257$	−6.16163			−0.384352			−0.192176	−	0.981360i	$-0.561554\pi$
$257$	−6.16163			−0.384352			−0.192176	+	0.981360i	$0.561554\pi$
$258$		−	34.7613i		−	2.16414i
$259$	−1.64442			−0.102179
$260$	5.89523	+	11.3139i	0.365607	+	0.701656i
$261$	−35.3286			−2.18678
$262$		−	6.91047i		−	0.426930i
$263$	−11.3849			−0.702021			−0.351011	−	0.936372i	$-0.614162\pi$
$263$	−11.3849			−0.702021			−0.351011	+	0.936372i	$0.614162\pi$
$264$	−7.87626			−0.484750
$265$			8.45959i			0.519668i
$266$			0.150781i			0.00924500i
$267$			62.1208i			3.80173i
$268$			9.26189i			0.565760i
$269$	1.99978			0.121929			0.0609644	−	0.998140i	$-0.480582\pi$
$269$	1.99978			0.121929			0.0609644	+	0.998140i	$0.480582\pi$
$270$	−56.8200			−3.45796
$271$		−	23.7845i		−	1.44480i	−0.691474	−	0.722401i	$-0.743038\pi$
$271$		−	23.7845i		−	1.44480i	0.691474	−	0.722401i	$-0.256962\pi$
$272$	−4.64914			−0.281895
$273$	−0.828277	−	1.58959i	−0.0501296	−	0.0962065i
$274$	6.09803			0.368395
$275$			17.9639i			1.08326i
$276$	18.2572			1.09895
$277$	−1.25069			−0.0751465			−0.0375733	−	0.999294i	$-0.511963\pi$
$277$	−1.25069			−0.0751465			−0.0375733	+	0.999294i	$0.511963\pi$
$278$			11.5019i			0.689839i
$279$		−	43.1886i		−	2.58564i
$280$			0.533514i			0.0318836i
$281$		−	27.4423i		−	1.63707i	−0.574455	−	0.818536i	$-0.694786\pi$
$281$		−	27.4423i		−	1.63707i	0.574455	−	0.818536i	$-0.305214\pi$
$282$	23.1729			1.37993
$283$	−20.5950			−1.22424			−0.612122	−	0.790764i	$-0.709684\pi$
$283$	−20.5950			−1.22424			−0.612122	+	0.790764i	$0.709684\pi$
$284$			3.13752i			0.186178i
$285$	−11.6661			−0.691038
$286$	7.63848	−	3.98013i	0.451673	−	0.235350i
$287$	0.245597			0.0144971
$288$		−	7.87054i		−	0.463776i
$289$	4.61446			0.271439
$290$	−15.8825			−0.932655
$291$		−	41.4376i		−	2.42911i
$292$			2.07937i			0.121686i
$293$		−	9.00761i		−	0.526230i	−0.964764	−	0.263115i	$-0.915250\pi$
$293$		−	9.00761i		−	0.526230i	0.964764	−	0.263115i	$-0.0847499\pi$
$294$			23.0044i			1.34164i
$295$	10.1235			0.589410
$296$	10.9060			0.633899
$297$			38.3616i			2.22597i
$298$	−2.14754			−0.124404
$299$	−17.7060	+	9.22595i	−1.02397	+	0.533550i
$300$	−24.7931			−1.43143
$301$			1.58971i			0.0916294i
$302$	11.1518			0.641716
$303$	−28.9725			−1.66443
$304$		−	1.00000i		−	0.0573539i
$305$		−	14.7968i		−	0.847263i
$306$			36.5912i			2.09178i
$307$			5.40794i			0.308647i	0.988020	+	0.154324i	$0.0493198\pi$
$307$			5.40794i			0.308647i	−0.988020	+	0.154324i	$0.950680\pi$
$308$	0.360199			0.0205242
$309$	40.0789			2.28001
$310$		−	19.4162i		−	1.10276i
$311$	−9.55248			−0.541672			−0.270836	−	0.962626i	$-0.587300\pi$
$311$	−9.55248			−0.541672			−0.270836	+	0.962626i	$0.587300\pi$
$312$	5.49323	+	10.5424i	0.310993	+	0.596844i
$313$	15.7527			0.890397			0.445198	−	0.895432i	$-0.353133\pi$
$313$	15.7527			0.890397			0.445198	+	0.895432i	$0.353133\pi$
$314$			13.4492i			0.758980i
$315$	4.19905			0.236590
$316$	5.29827			0.298051
$317$			3.14485i			0.176632i	0.996092	+	0.0883161i	$0.0281486\pi$
$317$			3.14485i			0.176632i	−0.996092	+	0.0883161i	$0.971851\pi$
$318$			7.88273i			0.442041i
$319$			10.7230i			0.600372i
$320$		−	3.53833i		−	0.197799i
$321$	−11.3028			−0.630862
$322$	−0.834942			−0.0465295
$323$			4.64914i			0.258685i
$324$	−29.3338			−1.62966
$325$	24.0446	−	12.5288i	1.33376	−	0.694970i
$326$	−0.853731			−0.0472838
$327$		−	16.4211i		−	0.908092i
$328$	−1.62883			−0.0899371
$329$	−1.05975			−0.0584258
$330$			27.8688i			1.53413i
$331$			0.269421i			0.0148087i	0.999973	+	0.00740436i	$0.00235690\pi$
$331$			0.269421i			0.0148087i	−0.999973	+	0.00740436i	$0.997643\pi$
$332$		−	12.0013i		−	0.658658i
$333$		−	85.8362i		−	4.70379i
$334$	6.29325			0.344351
$335$	32.7716			1.79051
$336$			0.497134i			0.0271209i
$337$	−2.80206			−0.152638			−0.0763191	−	0.997083i	$-0.524317\pi$
$337$	−2.80206			−0.152638			−0.0763191	+	0.997083i	$0.524317\pi$
$338$	−10.6548	−	7.44819i	−0.579544	−	0.405128i
$339$	−14.1527			−0.768670
$340$			16.4502i			0.892136i
$341$	−13.1087			−0.709875
$342$	−7.87054			−0.425590
$343$		−	2.10751i		−	0.113795i
$344$		−	10.5431i		−	0.568448i
$345$		−	64.6000i		−	3.47795i
$346$		−	8.41116i		−	0.452187i
$347$	26.5610			1.42587			0.712935	−	0.701231i	$-0.247366\pi$
$347$	26.5610			1.42587			0.712935	+	0.701231i	$0.247366\pi$
$348$	−14.7995			−0.793336
$349$		−	12.9895i		−	0.695311i	−0.937622	−	0.347656i	$-0.886978\pi$
$349$		−	12.9895i		−	0.695311i	0.937622	−	0.347656i	$-0.113022\pi$
$350$	1.13384			0.0606065
$351$	51.3470	−	26.7550i	2.74070	−	1.42808i
$352$	−2.38888			−0.127328
$353$			12.7132i			0.676656i	0.941028	+	0.338328i	$0.109861\pi$
$353$			12.7132i			0.676656i	−0.941028	+	0.338328i	$0.890139\pi$
$354$	9.43313			0.501365
$355$	11.1016			0.589211
$356$			18.8413i			0.998588i
$357$		−	2.31124i		−	0.122324i
$358$			10.2337i			0.540868i
$359$		−	1.98013i		−	0.104507i	−0.998634	−	0.0522535i	$-0.983360\pi$
$359$		−	1.98013i		−	0.104507i	0.998634	−	0.0522535i	$-0.0166404\pi$
$360$	−27.8486			−1.46775
$361$	−1.00000			−0.0526316
$362$			14.0040i			0.736033i
$363$	−17.4521			−0.915999
$364$	−0.251218	−	0.482125i	−0.0131674	−	0.0252702i
$365$	7.35751			0.385109
$366$		−	13.7878i		−	0.720700i
$367$	−30.9704			−1.61664			−0.808321	−	0.588742i	$-0.799623\pi$
$367$	−30.9704			−1.61664			−0.808321	+	0.588742i	$0.799623\pi$
$368$	5.53743			0.288659
$369$			12.8198i			0.667371i
$370$		−	38.5891i		−	2.00615i
$371$		−	0.360494i		−	0.0187159i
$372$		−	18.0922i		−	0.938035i
$373$	18.5731			0.961681			0.480840	−	0.876808i	$-0.340332\pi$
$373$	18.5731			0.961681			0.480840	+	0.876808i	$0.340332\pi$
$374$	11.1062			0.574289
$375$			29.3960i			1.51800i
$376$	7.02837			0.362460
$377$	14.3527	−	7.47866i	0.739202	−	0.385171i
$378$	2.42131			0.124539
$379$		−	19.3298i		−	0.992903i	−0.868064	−	0.496451i	$-0.834636\pi$
$379$		−	19.3298i		−	0.992903i	0.868064	−	0.496451i	$-0.165364\pi$
$380$	−3.53833			−0.181513
$381$	61.1806			3.13438
$382$		−	5.05349i		−	0.258559i
$383$			18.9244i			0.966991i	0.875347	+	0.483496i	$0.160633\pi$
$383$			18.9244i			0.966991i	−0.875347	+	0.483496i	$0.839367\pi$
$384$		−	3.29705i		−	0.168252i
$385$		−	1.27450i		−	0.0649546i
$386$	12.1526			0.618552
$387$	−82.9803			−4.21813
$388$		−	12.5681i		−	0.638048i
$389$	−30.1046			−1.52636			−0.763181	−	0.646185i	$-0.776363\pi$
$389$	−30.1046			−1.52636			−0.763181	+	0.646185i	$0.776363\pi$
$390$	37.3024	−	19.4369i	1.88888	−	0.984225i
$391$	−25.7443			−1.30194
$392$			6.97726i			0.352405i
$393$	−22.7842			−1.14931
$394$	−8.00854			−0.403465
$395$		−	18.7470i		−	0.943266i
$396$			18.8018i			0.944825i
$397$		−	19.7312i		−	0.990279i	−0.868813	−	0.495140i	$-0.835117\pi$
$397$		−	19.7312i		−	0.990279i	0.868813	−	0.495140i	$-0.164883\pi$
$398$			17.3501i			0.869680i
$399$	0.497134			0.0248878
$400$	−7.51979			−0.375989
$401$			38.5836i			1.92677i	0.268119	+	0.963386i	$0.413598\pi$
$401$			38.5836i			1.92677i	−0.268119	+	0.963386i	$0.586402\pi$
$402$	30.5369			1.52304
$403$	9.14255	+	17.5460i	0.455423	+	0.874027i
$404$	−8.78739			−0.437189
$405$			103.793i			5.15750i
$406$	0.676814			0.0335897
$407$	−26.0531			−1.29141
$408$			15.3284i			0.758871i
$409$		−	2.63015i		−	0.130052i	−0.997884	−	0.0650262i	$-0.979287\pi$
$409$		−	2.63015i		−	0.130052i	0.997884	−	0.0650262i	$-0.0207131\pi$
$410$			5.76334i			0.284631i
$411$		−	20.1055i		−	0.991732i
$412$	12.1560			0.598882
$413$	−0.431398			−0.0212277
$414$		−	43.5826i		−	2.14197i
$415$	−42.4647			−2.08451
$416$	1.66611	+	3.19751i	0.0816875	+	0.156771i
$417$	37.9224			1.85707
$418$			2.38888i			0.116844i
$419$	−21.0823			−1.02994			−0.514970	−	0.857208i	$-0.672197\pi$
$419$	−21.0823			−1.02994			−0.514970	+	0.857208i	$0.672197\pi$
$420$	1.75902			0.0858316
$421$			29.9487i			1.45961i	0.683654	+	0.729806i	$0.260390\pi$
$421$			29.9487i			1.45961i	−0.683654	+	0.729806i	$0.739610\pi$
$422$			7.54866i			0.367463i
$423$		−	55.3171i		−	2.68961i
$424$			2.39084i			0.116110i
$425$	34.9605			1.69583
$426$	10.3446			0.501196
$427$			0.630547i			0.0305143i
$428$	−3.42816			−0.165706
$429$	−13.1227	−	25.1844i	−0.633569	−	1.21592i
$430$	−37.3051			−1.79901
$431$			28.3577i			1.36594i	0.730446	+	0.682971i	$0.239312\pi$
$431$			28.3577i			1.36594i	−0.730446	+	0.682971i	$0.760688\pi$
$432$	−16.0584			−0.772611
$433$	26.4624			1.27170			0.635851	−	0.771812i	$-0.280649\pi$
$433$	26.4624			1.27170			0.635851	+	0.771812i	$0.280649\pi$
$434$			0.827394i			0.0397162i
$435$			52.3655i			2.51073i
$436$		−	4.98056i		−	0.238525i
$437$		−	5.53743i		−	0.264891i
$438$	6.85579			0.327582
$439$	−2.22341			−0.106117			−0.0530587	−	0.998591i	$-0.516897\pi$
$439$	−2.22341			−0.106117			−0.0530587	+	0.998591i	$0.516897\pi$
$440$			8.45265i			0.402964i
$441$	54.9149			2.61499
$442$	−7.74595	−	14.8657i	−0.368437	−	0.707088i
$443$	17.6039			0.836387			0.418194	−	0.908358i	$-0.362663\pi$
$443$	17.6039			0.836387			0.418194	+	0.908358i	$0.362663\pi$
$444$		−	35.9577i		−	1.70647i
$445$	66.6669			3.16031
$446$	−28.7643			−1.36203
$447$			7.08056i			0.334899i
$448$			0.150781i			0.00712375i
$449$			27.8127i			1.31256i	0.754516	+	0.656282i	$0.227872\pi$
$449$			27.8127i			1.31256i	−0.754516	+	0.656282i	$0.772128\pi$
$450$			59.1848i			2.79000i
$451$	3.89108			0.183224
$452$	−4.29254			−0.201904
$453$		−	36.7682i		−	1.72752i
$454$	1.92833			0.0905010
$455$	−1.70592	+	0.888891i	−0.0799747	+	0.0416719i
$456$	−3.29705			−0.154399
$457$		−	33.2600i		−	1.55584i	−0.628366	−	0.777918i	$-0.716276\pi$
$457$		−	33.2600i		−	1.55584i	0.628366	−	0.777918i	$-0.283724\pi$
$458$	17.3072			0.808711
$459$	74.6578			3.48473
$460$		−	19.5933i		−	0.913541i
$461$		−	19.6577i		−	0.915553i	−0.889067	−	0.457776i	$-0.848646\pi$
$461$		−	19.6577i		−	0.915553i	0.889067	−	0.457776i	$-0.151354\pi$
$462$		−	1.18759i		−	0.0552518i
$463$		−	9.51924i		−	0.442396i	−0.975229	−	0.221198i	$-0.929003\pi$
$463$		−	9.51924i		−	0.442396i	0.975229	−	0.221198i	$-0.0709968\pi$
$464$	−4.48871			−0.208383
$465$	−64.0161			−2.96867
$466$			23.2739i			1.07814i
$467$	3.59653			0.166428			0.0832138	−	0.996532i	$-0.473482\pi$
$467$	3.59653			0.166428			0.0832138	+	0.996532i	$0.473482\pi$
$468$	25.1662	−	13.1132i	1.16331	−	0.606156i
$469$	−1.39652			−0.0644853
$470$		−	24.8687i		−	1.14711i
$471$	44.3425			2.04320
$472$	2.86108			0.131692
$473$			25.1863i			1.15807i
$474$		−	17.4687i		−	0.802362i
$475$			7.51979i			0.345032i
$476$		−	0.701003i		−	0.0321304i
$477$	18.8172			0.861581
$478$	−14.6296			−0.669144
$479$			28.3976i			1.29752i	0.760994	+	0.648759i	$0.224712\pi$
$479$			28.3976i			1.29752i	−0.760994	+	0.648759i	$0.775288\pi$
$480$	−11.6661			−0.532480
$481$	18.1706	+	34.8721i	0.828506	+	1.59003i
$482$	14.5700			0.663644
$483$			2.75284i			0.125259i
$484$	−5.29325			−0.240602
$485$	−44.4700			−2.01928
$486$			48.5398i			2.20181i
$487$			32.9147i			1.49151i	0.666222	+	0.745754i	$0.267910\pi$
$487$			32.9147i			1.49151i	−0.666222	+	0.745754i	$0.732090\pi$
$488$		−	4.18186i		−	0.189304i
$489$			2.81479i			0.127289i
$490$	24.6879			1.11528
$491$	−0.282195			−0.0127353			−0.00636764	−	0.999980i	$-0.502027\pi$
$491$	−0.282195			−0.0127353			−0.00636764	+	0.999980i	$0.502027\pi$
$492$			5.37034i			0.242113i
$493$	20.8686			0.939875
$494$	3.19751	−	1.66611i	0.143863	−	0.0749616i
$495$	66.5269			2.99016
$496$		−	5.48738i		−	0.246391i
$497$	−0.473080			−0.0212205
$498$	−39.5690			−1.77313
$499$			29.4739i			1.31944i	0.751514	+	0.659718i	$0.229324\pi$
$499$			29.4739i			1.31944i	−0.751514	+	0.659718i	$0.770676\pi$
$500$			8.91584i			0.398729i
$501$		−	20.7492i		−	0.927005i
$502$		−	22.4809i		−	1.00337i
$503$	−0.929384			−0.0414392			−0.0207196	−	0.999785i	$-0.506596\pi$
$503$	−0.929384			−0.0414392			−0.0207196	+	0.999785i	$0.506596\pi$
$504$	1.18673			0.0528612
$505$			31.0927i			1.38361i
$506$	−13.2283			−0.588068
$507$	−24.5570	+	35.1294i	−1.09062	+	1.56015i
$508$	18.5562			0.823296
$509$			10.8326i			0.480145i	0.970755	+	0.240072i	$0.0771712\pi$
$509$			10.8326i			0.480145i	−0.970755	+	0.240072i	$0.922829\pi$
$510$	54.2371			2.40166
$511$	−0.313531			−0.0138698
$512$		−	1.00000i		−	0.0441942i
$513$			16.0584i			0.708997i
$514$			6.16163i			0.271778i
$515$		−	43.0119i		−	1.89533i
$516$	−34.7613			−1.53028
$517$	−16.7899			−0.738420
$518$			1.64442i			0.0722518i
$519$	−27.7320			−1.21730
$520$	11.3139	−	5.89523i	0.496146	−	0.258523i
$521$	−14.6684			−0.642634			−0.321317	−	0.946972i	$-0.604126\pi$
$521$	−14.6684			−0.642634			−0.321317	+	0.946972i	$0.604126\pi$
$522$			35.3286i			1.54629i
$523$	44.7432			1.95648			0.978241	−	0.207471i	$-0.0665234\pi$
$523$	44.7432			1.95648			0.978241	+	0.207471i	$0.0665234\pi$
$524$	−6.91047			−0.301885
$525$		−	3.73834i		−	0.163155i
$526$			11.3849i			0.496404i
$527$			25.5116i			1.11130i
$528$			7.87626i			0.342770i
$529$	7.66315			0.333181
$530$	8.45959			0.367461
$531$		−	22.5183i		−	0.977209i
$532$	0.150781			0.00653720
$533$	−2.71380	−	5.20821i	−0.117548	−	0.225593i
$534$	62.1208			2.68823
$535$			12.1300i			0.524424i
$536$	9.26189			0.400053
$537$	33.7410			1.45603
$538$		−	1.99978i		−	0.0862166i
$539$		−	16.6678i		−	0.717935i
$540$			56.8200i			2.44514i
$541$			3.61109i			0.155253i	0.996983	+	0.0776265i	$0.0247342\pi$
$541$			3.61109i			0.155253i	−0.996983	+	0.0776265i	$0.975266\pi$
$542$	−23.7845			−1.02163
$543$	46.1718			1.98142
$544$			4.64914i			0.199330i
$545$	−17.6229			−0.754880
$546$	−1.58959	+	0.828277i	−0.0680283	+	0.0354470i
$547$	24.1186			1.03124			0.515618	−	0.856819i	$-0.327563\pi$
$547$	24.1186			1.03124			0.515618	+	0.856819i	$0.327563\pi$
$548$		−	6.09803i		−	0.260495i
$549$	−32.9135			−1.40471
$550$	17.9639			0.765982
$551$			4.48871i			0.191225i
$552$		−	18.2572i		−	0.777078i
$553$			0.798880i			0.0339719i
$554$			1.25069i			0.0531366i
$555$	−127.230			−5.40062
$556$	11.5019			0.487789
$557$			0.381806i			0.0161777i	0.999967	+	0.00808883i	$0.00257478\pi$
$557$			0.381806i			0.0161777i	−0.999967	+	0.00808883i	$0.997425\pi$
$558$	−43.1886			−1.82832
$559$	33.7119	−	17.5660i	1.42586	−	0.742962i
$560$	0.533514			0.0225451
$561$		−	36.6178i		−	1.54600i
$562$	−27.4423			−1.15758
$563$	−13.4387			−0.566372			−0.283186	−	0.959065i	$-0.591391\pi$
$563$	−13.4387			−0.566372			−0.283186	+	0.959065i	$0.591391\pi$
$564$		−	23.1729i		−	0.975755i
$565$			15.1884i			0.638982i
$566$			20.5950i			0.865671i
$567$		−	4.42299i		−	0.185748i
$568$	3.13752			0.131648
$569$	−26.7295			−1.12056			−0.560278	−	0.828304i	$-0.689306\pi$
$569$	−26.7295			−1.12056			−0.560278	+	0.828304i	$0.689306\pi$
$570$			11.6661i			0.488637i
$571$	−23.7707			−0.994774			−0.497387	−	0.867529i	$-0.665707\pi$
$571$	−23.7707			−0.994774			−0.497387	+	0.867529i	$0.665707\pi$
$572$	−3.98013	−	7.63848i	−0.166417	−	0.319381i
$573$	−16.6616			−0.696049
$574$		−	0.245597i		−	0.0102510i
$575$	−41.6403			−1.73652
$576$	−7.87054			−0.327939
$577$		−	43.6306i		−	1.81636i	−0.418575	−	0.908182i	$-0.637470\pi$
$577$		−	43.6306i		−	1.81636i	0.418575	−	0.908182i	$-0.362530\pi$
$578$		−	4.61446i		−	0.191936i
$579$		−	40.0678i		−	1.66516i
$580$			15.8825i			0.659486i
$581$	1.80958			0.0750739
$582$	−41.4376			−1.71764
$583$		−	5.71143i		−	0.236543i
$584$	2.07937			0.0860450
$585$	−46.3987	−	89.0462i	−1.91835	−	3.68161i
$586$	−9.00761			−0.372101
$587$		−	4.46031i		−	0.184097i	−0.995755	−	0.0920483i	$-0.970659\pi$
$587$		−	4.46031i		−	0.184097i	0.995755	−	0.0920483i	$-0.0293414\pi$
$588$	23.0044			0.948685
$589$	−5.48738			−0.226103
$590$		−	10.1235i		−	0.416776i
$591$			26.4046i			1.08614i
$592$		−	10.9060i		−	0.448234i
$593$		−	13.3387i		−	0.547753i	−0.961765	−	0.273877i	$-0.911694\pi$
$593$		−	13.3387i		−	0.547753i	0.961765	−	0.273877i	$-0.0883060\pi$
$594$	38.3616			1.57400
$595$	−2.48038			−0.101686
$596$			2.14754i			0.0879668i
$597$	57.2041			2.34121
$598$	9.22595	+	17.7060i	0.377277	+	0.724053i
$599$	37.0831			1.51517			0.757587	−	0.652734i	$-0.226378\pi$
$599$	37.0831			1.51517			0.757587	+	0.652734i	$0.226378\pi$
$600$			24.7931i			1.01217i
$601$	−10.1680			−0.414761			−0.207381	−	0.978260i	$-0.566494\pi$
$601$	−10.1680			−0.414761			−0.207381	+	0.978260i	$0.566494\pi$
$602$	1.58971			0.0647918
$603$		−	72.8961i		−	2.96856i
$604$		−	11.1518i		−	0.453762i
$605$			18.7293i			0.761453i
$606$			28.9725i			1.17693i
$607$	22.2624			0.903601			0.451800	−	0.892119i	$-0.350782\pi$
$607$	22.2624			0.903601			0.451800	+	0.892119i	$0.350782\pi$
$608$	−1.00000			−0.0405554
$609$		−	2.23149i		−	0.0904245i
$610$	−14.7968			−0.599105
$611$	11.7100	+	22.4733i	0.473736	+	0.909173i
$612$	36.5912			1.47911
$613$			27.2117i			1.09907i	0.835471	+	0.549535i	$0.185195\pi$
$613$			27.2117i			1.09907i	−0.835471	+	0.549535i	$0.814805\pi$
$614$	5.40794			0.218247
$615$	19.0020			0.766236
$616$		−	0.360199i		−	0.0145128i
$617$		−	40.4879i		−	1.62998i	−0.579473	−	0.814992i	$-0.696741\pi$
$617$		−	40.4879i		−	1.62998i	0.579473	−	0.814992i	$-0.303259\pi$
$618$		−	40.0789i		−	1.61221i
$619$		−	1.63008i		−	0.0655183i	−0.999463	−	0.0327591i	$-0.989571\pi$
$619$		−	1.63008i		−	0.0655183i	0.999463	−	0.0327591i	$-0.0104294\pi$
$620$	−19.4162			−0.779772
$621$	−88.9224			−3.56833
$622$			9.55248i			0.383020i
$623$	−2.84092			−0.113819
$624$	10.5424	−	5.49323i	0.422032	−	0.219905i
$625$	−6.05173			−0.242069
$626$		−	15.7527i		−	0.629605i
$627$	7.87626			0.314547
$628$	13.4492			0.536680
$629$			50.7035i			2.02168i
$630$		−	4.19905i		−	0.167294i
$631$			1.05111i			0.0418439i	0.999781	+	0.0209220i	$0.00666015\pi$
$631$			1.05111i			0.0418439i	−0.999781	+	0.0209220i	$0.993340\pi$
$632$		−	5.29827i		−	0.210754i
$633$	24.8883			0.989222
$634$	3.14485			0.124898
$635$		−	65.6578i		−	2.60555i
$636$	7.88273			0.312570
$637$	−22.3099	+	11.6249i	−0.883950	+	0.460594i
$638$	10.7230			0.424527
$639$		−	24.6940i		−	0.976880i
$640$	−3.53833			−0.139865
$641$	18.0793			0.714091			0.357045	−	0.934087i	$-0.383784\pi$
$641$	18.0793			0.714091			0.357045	+	0.934087i	$0.383784\pi$
$642$			11.3028i			0.446087i
$643$		−	10.2623i		−	0.404705i	−0.979313	−	0.202352i	$-0.935141\pi$
$643$		−	10.2623i		−	0.404705i	0.979313	−	0.202352i	$-0.0648586\pi$
$644$			0.834942i			0.0329013i
$645$			122.997i			4.84300i
$646$	4.64914			0.182918
$647$	3.53071			0.138807			0.0694033	−	0.997589i	$-0.477890\pi$
$647$	3.53071			0.138807			0.0694033	+	0.997589i	$0.477890\pi$
$648$			29.3338i			1.15234i
$649$	−6.83478			−0.268289
$650$	−12.5288	−	24.0446i	−0.491418	−	0.943108i
$651$	2.72796			0.106917
$652$			0.853731i			0.0334347i
$653$	−10.1156			−0.395855			−0.197928	−	0.980217i	$-0.563421\pi$
$653$	−10.1156			−0.395855			−0.197928	+	0.980217i	$0.563421\pi$
$654$	−16.4211			−0.642118
$655$			24.4515i			0.955400i
$656$			1.62883i			0.0635951i
$657$		−	16.3658i		−	0.638490i
$658$			1.05975i			0.0413132i
$659$	−17.5458			−0.683486			−0.341743	−	0.939794i	$-0.611017\pi$
$659$	−17.5458			−0.683486			−0.341743	+	0.939794i	$0.611017\pi$
$660$	27.8688			1.08479
$661$		−	14.0163i		−	0.545171i	−0.962132	−	0.272586i	$-0.912121\pi$
$661$		−	14.0163i		−	0.545171i	0.962132	−	0.272586i	$-0.0878788\pi$
$662$	0.269421			0.0104714
$663$	−49.0129	+	25.5388i	−1.90350	+	0.991844i
$664$	−12.0013			−0.465742
$665$		−	0.533514i		−	0.0206888i
$666$	−85.8362			−3.32608
$667$	−24.8559			−0.962425
$668$		−	6.29325i		−	0.243493i
$669$			94.8373i			3.66662i
$670$		−	32.7716i		−	1.26608i
$671$			9.98996i			0.385658i
$672$	0.497134			0.0191774
$673$	−31.1907			−1.20231			−0.601157	−	0.799131i	$-0.705293\pi$
$673$	−31.1907			−1.20231			−0.601157	+	0.799131i	$0.705293\pi$
$674$			2.80206i			0.107931i
$675$	120.756			4.64790
$676$	−7.44819	+	10.6548i	−0.286469	+	0.409800i
$677$	13.2383			0.508789			0.254394	−	0.967101i	$-0.418124\pi$
$677$	13.2383			0.508789			0.254394	+	0.967101i	$0.418124\pi$
$678$			14.1527i			0.543532i
$679$	1.89503			0.0727247
$680$	16.4502			0.630836
$681$		−	6.35780i		−	0.243632i
$682$			13.1087i			0.501958i
$683$		−	11.3659i		−	0.434905i	−0.976071	−	0.217453i	$-0.930225\pi$
$683$		−	11.3659i		−	0.434905i	0.976071	−	0.217453i	$-0.0697748\pi$
$684$			7.87054i			0.300938i
$685$	−21.5768			−0.824409
$686$	−2.10751			−0.0804651
$687$		−	57.0626i		−	2.17708i
$688$	−10.5431			−0.401954
$689$	−7.64475	+	3.98339i	−0.291242	+	0.151755i
$690$	−64.6000			−2.45928
$691$		−	37.7882i		−	1.43753i	−0.695253	−	0.718765i	$-0.744708\pi$
$691$		−	37.7882i		−	1.43753i	0.695253	−	0.718765i	$-0.255292\pi$
$692$	−8.41116			−0.319744
$693$	−2.83496			−0.107691
$694$		−	26.5610i		−	1.00824i
$695$		−	40.6976i		−	1.54375i
$696$			14.7995i			0.560974i
$697$		−	7.57265i		−	0.286835i
$698$	−12.9895			−0.491659
$699$	76.7353			2.90239
$700$		−	1.13384i		−	0.0428553i
$701$	29.1278			1.10014			0.550070	−	0.835118i	$-0.314601\pi$
$701$	29.1278			1.10014			0.550070	+	0.835118i	$0.314601\pi$
$702$	−26.7550	−	51.3470i	−1.00980	−	1.93797i
$703$	−10.9060			−0.411328
$704$			2.38888i			0.0900343i
$705$	−81.9934			−3.08805
$706$	12.7132			0.478468
$707$		−	1.32498i		−	0.0498308i
$708$		−	9.43313i		−	0.354519i
$709$		−	45.5773i		−	1.71169i	−0.517230	−	0.855846i	$-0.673037\pi$
$709$		−	45.5773i		−	1.71169i	0.517230	−	0.855846i	$-0.326963\pi$
$710$		−	11.1016i		−	0.416635i
$711$	−41.7003			−1.56388
$712$	18.8413			0.706109
$713$		−	30.3860i		−	1.13796i
$714$	−2.31124			−0.0864961
$715$	−27.0275	+	14.0830i	−1.01077	+	0.526674i
$716$	10.2337			0.382451
$717$			48.2347i			1.80136i
$718$	−1.98013			−0.0738976
$719$	−1.91188			−0.0713012			−0.0356506	−	0.999364i	$-0.511350\pi$
$719$	−1.91188			−0.0713012			−0.0356506	+	0.999364i	$0.511350\pi$
$720$			27.8486i			1.03786i
$721$			1.83290i			0.0682606i
$722$			1.00000i			0.0372161i
$723$		−	48.0379i		−	1.78655i
$724$	14.0040			0.520454
$725$	33.7541			1.25360
$726$			17.4521i			0.647709i
$727$	−27.5738			−1.02265			−0.511327	−	0.859386i	$-0.670846\pi$
$727$	−27.5738			−1.02265			−0.511327	+	0.859386i	$0.670846\pi$
$728$	−0.482125	+	0.251218i	−0.0178688	+	0.00931075i
$729$	72.0367			2.66802
$730$		−	7.35751i		−	0.272314i
$731$	49.0165			1.81294
$732$	−13.7878			−0.509612
$733$		−	47.5901i		−	1.75778i	−0.477025	−	0.878890i	$-0.658285\pi$
$733$		−	47.5901i		−	1.75778i	0.477025	−	0.878890i	$-0.341715\pi$
$734$			30.9704i			1.14314i
$735$		−	81.3972i		−	3.00238i
$736$		−	5.53743i		−	0.204112i
$737$	−22.1255			−0.815005
$738$	12.8198			0.471903
$739$		−	12.4006i		−	0.456162i	−0.973642	−	0.228081i	$-0.926755\pi$
$739$		−	12.4006i		−	0.456162i	0.973642	−	0.228081i	$-0.0732450\pi$
$740$	−38.5891			−1.41856
$741$	−5.49323	−	10.5424i	−0.201799	−	0.387283i
$742$	−0.360494			−0.0132342
$743$		−	1.90025i		−	0.0697135i	−0.999392	−	0.0348568i	$-0.988902\pi$
$743$		−	1.90025i		−	0.0697135i	0.999392	−	0.0348568i	$-0.0110975\pi$
$744$	−18.0922			−0.663291
$745$	7.59872			0.278395
$746$		−	18.5731i		−	0.680011i
$747$			94.4569i			3.45600i
$748$		−	11.1062i		−	0.406084i
$749$		−	0.516903i		−	0.0188872i
$750$	29.3960			1.07339
$751$	−44.9955			−1.64191			−0.820955	−	0.570993i	$-0.806558\pi$
$751$	−44.9955			−1.64191			−0.820955	+	0.570993i	$0.806558\pi$
$752$		−	7.02837i		−	0.256298i
$753$	−74.1206			−2.70111
$754$	−7.47866	−	14.3527i	−0.272357	−	0.522695i
$755$	−39.4589			−1.43606
$756$		−	2.42131i		−	0.0880622i
$757$	9.53993			0.346735			0.173367	−	0.984857i	$-0.444535\pi$
$757$	9.53993			0.346735			0.173367	+	0.984857i	$0.444535\pi$
$758$	−19.3298			−0.702088
$759$			43.6142i			1.58310i
$760$			3.53833i			0.128349i
$761$			23.0991i			0.837343i	0.908138	+	0.418671i	$0.137504\pi$
$761$			23.0991i			0.837343i	−0.908138	+	0.418671i	$0.862496\pi$
$762$		−	61.1806i		−	2.21634i
$763$	0.750975			0.0271871
$764$	−5.05349			−0.182829
$765$		−	129.472i		−	4.68106i
$766$	18.9244			0.683766
$767$	4.76686	+	9.14835i	0.172121	+	0.330328i
$768$	−3.29705			−0.118972
$769$			33.4512i			1.20628i	0.797634	+	0.603141i	$0.206084\pi$
$769$			33.4512i			1.20628i	−0.797634	+	0.603141i	$0.793916\pi$
$770$	−1.27450			−0.0459299
$771$	20.3152			0.731634
$772$		−	12.1526i		−	0.437382i
$773$		−	14.1395i		−	0.508564i	−0.967130	−	0.254282i	$-0.918161\pi$
$773$		−	14.1395i		−	0.508564i	0.967130	−	0.254282i	$-0.0818391\pi$
$774$			82.9803i			2.98266i
$775$			41.2639i			1.48224i
$776$	−12.5681			−0.451168
$777$	5.42174			0.194504
$778$			30.1046i			1.07930i
$779$	1.62883			0.0583589
$780$	−19.4369	−	37.3024i	−0.695952	−	1.33564i
$781$	−7.49517			−0.268198
$782$			25.7443i			0.920613i
$783$	72.0816			2.57599
$784$	6.97726			0.249188
$785$		−	47.5876i		−	1.69847i
$786$			22.7842i			0.812684i
$787$			44.7650i			1.59570i	0.602855	+	0.797851i	$0.294030\pi$
$787$			44.7650i			1.59570i	−0.602855	+	0.797851i	$0.705970\pi$
$788$			8.00854i			0.285293i
$789$	37.5365			1.33633
$790$	−18.7470			−0.666990
$791$		−	0.647235i		−	0.0230130i
$792$	18.8018			0.668092
$793$	13.3716	−	6.96742i	0.474838	−	0.247420i
$794$	−19.7312			−0.700233
$795$		−	27.8917i		−	0.989216i
$796$	17.3501			0.614957
$797$	−8.86399			−0.313979			−0.156989	−	0.987600i	$-0.550179\pi$
$797$	−8.86399			−0.313979			−0.156989	+	0.987600i	$0.550179\pi$
$798$		−	0.497134i		−	0.0175983i
$799$			32.6758i			1.15599i
$800$			7.51979i			0.265865i
$801$		−	148.291i		−	5.23962i
$802$	38.5836			1.36243
$803$	−4.96737			−0.175295
$804$		−	30.5369i		−	1.07695i
$805$	2.95430			0.104125
$806$	17.5460	−	9.14255i	0.618030	−	0.322033i
$807$	−6.59338			−0.232098
$808$			8.78739i			0.309139i
$809$	−11.5701			−0.406783			−0.203392	−	0.979097i	$-0.565196\pi$
$809$	−11.5701			−0.406783			−0.203392	+	0.979097i	$0.565196\pi$
$810$	103.793			3.64690
$811$			42.2403i			1.48326i	0.670811	+	0.741629i	$0.265946\pi$
$811$			42.2403i			1.48326i	−0.670811	+	0.741629i	$0.734054\pi$
$812$		−	0.676814i		−	0.0237515i
$813$			78.4186i			2.75026i
$814$			26.0531i			0.913162i
$815$	3.02078			0.105813
$816$	15.3284			0.536603
$817$			10.5431i			0.368858i
$818$	−2.63015			−0.0919609
$819$	1.97722	+	3.79459i	0.0690896	+	0.132594i
$820$	5.76334			0.201265
$821$			54.5203i			1.90277i	0.308001	+	0.951386i	$0.400340\pi$
$821$			54.5203i			1.90277i	−0.308001	+	0.951386i	$0.599660\pi$
$822$	−20.1055			−0.701260
$823$	−10.0705			−0.351034			−0.175517	−	0.984476i	$-0.556160\pi$
$823$	−10.0705			−0.351034			−0.175517	+	0.984476i	$0.556160\pi$
$824$		−	12.1560i		−	0.423474i
$825$		−	59.2278i		−	2.06205i
$826$			0.431398i			0.0150102i
$827$			10.9110i			0.379411i	0.981841	+	0.189706i	$0.0607533\pi$
$827$			10.9110i			0.379411i	−0.981841	+	0.189706i	$0.939247\pi$
$828$	−43.5826			−1.51460
$829$	−53.0765			−1.84342			−0.921711	−	0.387877i	$-0.873209\pi$
$829$	−53.0765			−1.84342			−0.921711	+	0.387877i	$0.873209\pi$
$830$			42.4647i			1.47397i
$831$	4.12358			0.143045
$832$	3.19751	−	1.66611i	0.110854	−	0.0577618i
$833$	−32.4382			−1.12392
$834$		−	37.9224i		−	1.31314i
$835$	−22.2676			−0.770602
$836$	2.38888			0.0826211
$837$			88.1186i			3.04583i
$838$			21.0823i			0.728277i
$839$			16.1528i			0.557658i	0.960341	+	0.278829i	$0.0899462\pi$
$839$			16.1528i			0.557658i	−0.960341	+	0.278829i	$0.910054\pi$
$840$		−	1.75902i		−	0.0606921i
$841$	−8.85150			−0.305224
$842$	29.9487			1.03210
$843$			90.4787i			3.11625i
$844$	7.54866			0.259836
$845$	37.7002	+	26.3541i	1.29693	+	0.906610i
$846$	−55.3171			−1.90184
$847$		−	0.798124i		−	0.0274239i
$848$	2.39084			0.0821018
$849$	67.9026			2.33041
$850$		−	34.9605i		−	1.19914i
$851$		−	60.3913i		−	2.07019i
$852$		−	10.3446i		−	0.354399i
$853$		−	32.2364i		−	1.10375i	−0.833926	−	0.551877i	$-0.813912\pi$
$853$		−	32.2364i		−	1.10375i	0.833926	−	0.551877i	$-0.186088\pi$
$854$	0.630547			0.0215769
$855$	27.8486			0.952401
$856$			3.42816i			0.117172i
$857$	14.4059			0.492095			0.246048	−	0.969258i	$-0.420868\pi$
$857$	14.4059			0.492095			0.246048	+	0.969258i	$0.420868\pi$
$858$	−25.1844	+	13.1227i	−0.859783	+	0.448001i
$859$	14.0342			0.478842			0.239421	−	0.970916i	$-0.423042\pi$
$859$	14.0342			0.478842			0.239421	+	0.970916i	$0.423042\pi$
$860$			37.3051i			1.27210i
$861$	−0.809747			−0.0275961
$862$	28.3577			0.965866
$863$		−	2.54991i		−	0.0868000i	−0.999058	−	0.0434000i	$-0.986181\pi$
$863$		−	2.54991i		−	0.0868000i	0.999058	−	0.0434000i	$-0.0138190\pi$
$864$			16.0584i			0.546319i
$865$			29.7615i			1.01192i
$866$		−	26.4624i		−	0.899229i
$867$	−15.2141			−0.516698
$868$	0.827394			0.0280836
$869$			12.6569i			0.429357i
$870$	52.3655			1.77536
$871$	15.4313	+	29.6150i	0.522869	+	1.00347i
$872$	−4.98056			−0.168663
$873$			98.9176i			3.34785i
$874$	−5.53743			−0.187306
$875$	−1.34434			−0.0454471
$876$		−	6.85579i		−	0.231636i
$877$		−	47.0463i		−	1.58864i	−0.607499	−	0.794320i	$-0.707827\pi$
$877$		−	47.0463i		−	1.58864i	0.607499	−	0.794320i	$-0.292173\pi$
$878$			2.22341i			0.0750364i
$879$			29.6985i			1.00171i
$880$	8.45265			0.284939
$881$	45.2418			1.52423			0.762117	−	0.647440i	$-0.224160\pi$
$881$	45.2418			1.52423			0.762117	+	0.647440i	$0.224160\pi$
$882$		−	54.9149i		−	1.84908i
$883$	6.45909			0.217366			0.108683	−	0.994076i	$-0.465337\pi$
$883$	6.45909			0.217366			0.108683	+	0.994076i	$0.465337\pi$
$884$	−14.8657	+	7.74595i	−0.499987	+	0.260524i
$885$	−33.3775			−1.12197
$886$		−	17.6039i		−	0.591415i
$887$	−27.7245			−0.930899			−0.465449	−	0.885074i	$-0.654107\pi$
$887$	−27.7245			−0.930899			−0.465449	+	0.885074i	$0.654107\pi$
$888$	−35.9577			−1.20666
$889$			2.79792i			0.0938393i
$890$		−	66.6669i		−	2.23468i
$891$		−	70.0749i		−	2.34760i
$892$			28.7643i			0.963099i
$893$	−7.02837			−0.235195
$894$	7.08056			0.236809
$895$		−	36.2102i		−	1.21037i
$896$	0.150781			0.00503725
$897$	58.3776	−	30.4184i	1.94917	−	1.01564i
$898$	27.8127			0.928123
$899$			24.6312i			0.821498i
$900$	59.1848			1.97283
$901$	−11.1153			−0.370306
$902$		−	3.89108i		−	0.129559i
$903$		−	5.24135i		−	0.174421i
$904$			4.29254i			0.142768i
$905$		−	49.5507i		−	1.64712i
$906$	−36.7682			−1.22154
$907$	20.0680			0.666348			0.333174	−	0.942865i	$-0.391880\pi$
$907$	20.0680			0.666348			0.333174	+	0.942865i	$0.391880\pi$
$908$		−	1.92833i		−	0.0639939i
$909$	69.1616			2.29394
$910$	0.888891	+	1.70592i	0.0294665	+	0.0565507i
$911$	−57.8610			−1.91702			−0.958510	−	0.285059i	$-0.907987\pi$
$911$	−57.8610			−1.91702			−0.958510	+	0.285059i	$0.907987\pi$
$912$			3.29705i			0.109176i
$913$	28.6697			0.948829
$914$	−33.2600			−1.10014
$915$			48.7858i			1.61281i
$916$		−	17.3072i		−	0.571845i
$917$		−	1.04197i		−	0.0344089i
$918$		−	74.6578i		−	2.46407i
$919$	33.5024			1.10514			0.552572	−	0.833465i	$-0.313646\pi$
$919$	33.5024			1.10514			0.552572	+	0.833465i	$0.313646\pi$
$920$	−19.5933			−0.645971
$921$		−	17.8302i		−	0.587526i
$922$	−19.6577			−0.647393
$923$	5.22744	+	10.0323i	0.172063	+	0.330216i
$924$	−1.18759			−0.0390689
$925$			82.0109i			2.69650i
$926$	−9.51924			−0.312822
$927$	−95.6742			−3.14235
$928$			4.48871i			0.147349i
$929$		−	44.0193i		−	1.44423i	−0.691775	−	0.722113i	$-0.743171\pi$
$929$		−	44.0193i		−	1.44423i	0.691775	−	0.722113i	$-0.256829\pi$
$930$			64.0161i			2.09917i
$931$		−	6.97726i		−	0.228671i
$932$	23.2739			0.762362
$933$	31.4950			1.03110
$934$		−	3.59653i		−	0.117682i
$935$	−39.2975			−1.28517
$936$	−13.1132	−	25.1662i	−0.428617	−	0.822582i
$937$	23.9226			0.781519			0.390759	−	0.920493i	$-0.372212\pi$
$937$	23.9226			0.781519			0.390759	+	0.920493i	$0.372212\pi$
$938$			1.39652i			0.0455980i
$939$	−51.9375			−1.69492
$940$	−24.8687			−0.811128
$941$			11.9315i			0.388955i	0.980907	+	0.194478i	$0.0623012\pi$
$941$			11.9315i			0.388955i	−0.980907	+	0.194478i	$0.937699\pi$
$942$		−	44.3425i		−	1.44476i
$943$			9.01954i			0.293717i
$944$		−	2.86108i		−	0.0931203i
$945$	−8.56740			−0.278698
$946$	25.1863			0.818878
$947$			44.4175i			1.44338i	0.692219	+	0.721688i	$0.256633\pi$
$947$			44.4175i			1.44338i	−0.692219	+	0.721688i	$0.743367\pi$
$948$	−17.4687			−0.567356
$949$	3.46445	+	6.64882i	0.112461	+	0.215830i
$950$	7.51979			0.243974
$951$		−	10.3687i		−	0.336229i
$952$	−0.701003			−0.0227196
$953$	−19.1284			−0.619631			−0.309816	−	0.950797i	$-0.600267\pi$
$953$	−19.1284			−0.619631			−0.309816	+	0.950797i	$0.600267\pi$
$954$		−	18.8172i		−	0.609230i
$955$			17.8809i			0.578613i
$956$			14.6296i			0.473156i
$957$		−	35.3542i		−	1.14284i
$958$	28.3976			0.917484
$959$	0.919469			0.0296912
$960$			11.6661i			0.376520i
$961$	0.888682			0.0286672
$962$	34.8721	−	18.1706i	1.12432	−	0.585842i
$963$	26.9815			0.869466
$964$		−	14.5700i		−	0.469267i
$965$	−43.0000			−1.38422
$966$	2.75284			0.0885713
$967$			25.1740i			0.809543i	0.914418	+	0.404771i	$0.132649\pi$
$967$			25.1740i			0.809543i	−0.914418	+	0.404771i	$0.867351\pi$
$968$			5.29325i			0.170132i
$969$		−	15.3284i		−	0.492420i
$970$			44.4700i			1.42785i
$971$	−36.4759			−1.17057			−0.585284	−	0.810828i	$-0.699017\pi$
$971$	−36.4759			−1.17057			−0.585284	+	0.810828i	$0.699017\pi$
$972$	48.5398			1.55691
$973$			1.73427i			0.0555982i
$974$	32.9147			1.05465
$975$	−79.2763	+	41.3080i	−2.53887	+	1.32291i
$976$	−4.18186			−0.133858
$977$		−	3.72604i		−	0.119206i	−0.998222	−	0.0596032i	$-0.981016\pi$
$977$		−	3.72604i		−	0.119206i	0.998222	−	0.0596032i	$-0.0189836\pi$
$978$	2.81479			0.0900072
$979$	−45.0097			−1.43852
$980$		−	24.6879i		−	0.788625i
$981$			39.1997i			1.25155i
$982$			0.282195i			0.00900521i
$983$		−	2.94137i		−	0.0938151i	−0.998899	−	0.0469075i	$-0.985063\pi$
$983$		−	2.94137i		−	0.0938151i	0.998899	−	0.0469075i	$-0.0149366\pi$
$984$	5.37034			0.171200
$985$	28.3369			0.902888
$986$		−	20.8686i		−	0.664592i
$987$	3.49404			0.111217
$988$	−1.66611	−	3.19751i	−0.0530059	−	0.101726i
$989$	−58.3820			−1.85644
$990$		−	66.5269i		−	2.11436i
$991$	−0.474014			−0.0150575			−0.00752877	−	0.999972i	$-0.502397\pi$
$991$	−0.474014			−0.0150575			−0.00752877	+	0.999972i	$0.502397\pi$
$992$	−5.48738			−0.174224
$993$		−	0.888295i		−	0.0281892i
$994$			0.473080i			0.0150052i
$995$		−	61.3903i		−	1.94620i
$996$			39.5690i			1.25379i
$997$	−27.5785			−0.873421			−0.436711	−	0.899602i	$-0.643857\pi$
$997$	−27.5785			−0.873421			−0.436711	+	0.899602i	$0.643857\pi$
$998$	29.4739			0.932981
$999$			175.133i			5.54097i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	494.2.d.c.77.1	✓	14
13.5	odd	4		6422.2.a.be.1.1		7
13.8	odd	4		6422.2.a.bf.1.1		7
13.12	even	2	inner	494.2.d.c.77.8	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.d.c.77.1	✓	14	1.1	even	1	trivial
494.2.d.c.77.8	yes	14	13.12	even	2	inner
6422.2.a.be.1.1		7	13.5	odd	4
6422.2.a.bf.1.1		7	13.8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 494 = 2 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	494.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -3.29705 q^{3} -1.00000 q^{4} +3.53833i q^{5} +3.29705i q^{6} -0.150781i q^{7} +1.00000i q^{8} +7.87054 q^{9} +3.53833 q^{10} -2.38888i q^{11} +3.29705 q^{12} +(-3.19751 + 1.66611i) q^{13} -0.150781 q^{14} -11.6661i q^{15} +1.00000 q^{16} -4.64914 q^{17} -7.87054i q^{18} -1.00000i q^{19} -3.53833i q^{20} +0.497134i q^{21} -2.38888 q^{22} +5.53743 q^{23} -3.29705i q^{24} -7.51979 q^{25} +(1.66611 + 3.19751i) q^{26} -16.0584 q^{27} +0.150781i q^{28} -4.48871 q^{29} -11.6661 q^{30} -5.48738i q^{31} -1.00000i q^{32} +7.87626i q^{33} +4.64914i q^{34} +0.533514 q^{35} -7.87054 q^{36} -10.9060i q^{37} -1.00000 q^{38} +(10.5424 - 5.49323i) q^{39} -3.53833 q^{40} +1.62883i q^{41} +0.497134 q^{42} -10.5431 q^{43} +2.38888i q^{44} +27.8486i q^{45} -5.53743i q^{46} -7.02837i q^{47} -3.29705 q^{48} +6.97726 q^{49} +7.51979i q^{50} +15.3284 q^{51} +(3.19751 - 1.66611i) q^{52} +2.39084 q^{53} +16.0584i q^{54} +8.45265 q^{55} +0.150781 q^{56} +3.29705i q^{57} +4.48871i q^{58} -2.86108i q^{59} +11.6661i q^{60} -4.18186 q^{61} -5.48738 q^{62} -1.18673i q^{63} -1.00000 q^{64} +(-5.89523 - 11.3139i) q^{65} +7.87626 q^{66} -9.26189i q^{67} +4.64914 q^{68} -18.2572 q^{69} -0.533514i q^{70} -3.13752i q^{71} +7.87054i q^{72} -2.07937i q^{73} -10.9060 q^{74} +24.7931 q^{75} +1.00000i q^{76} -0.360199 q^{77} +(-5.49323 - 10.5424i) q^{78} -5.29827 q^{79} +3.53833i q^{80} +29.3338 q^{81} +1.62883 q^{82} +12.0013i q^{83} -0.497134i q^{84} -16.4502i q^{85} +10.5431i q^{86} +14.7995 q^{87} +2.38888 q^{88} -18.8413i q^{89} +27.8486 q^{90} +(0.251218 + 0.482125i) q^{91} -5.53743 q^{92} +18.0922i q^{93} -7.02837 q^{94} +3.53833 q^{95} +3.29705i q^{96} +12.5681i q^{97} -6.97726i q^{98} -18.8018i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 4 q^{3} - 14 q^{4} + 30 q^{9} - 4 q^{10} - 4 q^{12} - 2 q^{13} + 2 q^{14} + 14 q^{16} - 32 q^{17} + 10 q^{22} - 6 q^{23} - 14 q^{25} + 10 q^{26} + 10 q^{27} - 14 q^{29} - 26 q^{30} + 2 q^{35} - 30 q^{36}+ \cdots - 4 q^{95}+O(q^{100}) \) 14 * q + 4 * q^3 - 14 * q^4 + 30 * q^9 - 4 * q^10 - 4 * q^12 - 2 * q^13 + 2 * q^14 + 14 * q^16 - 32 * q^17 + 10 * q^22 - 6 * q^23 - 14 * q^25 + 10 * q^26 + 10 * q^27 - 14 * q^29 - 26 * q^30 + 2 * q^35 - 30 * q^36 - 14 * q^38 + 36 * q^39 + 4 * q^40 - 6 * q^42 - 46 * q^43 + 4 * q^48 - 28 * q^49 + 32 * q^51 + 2 * q^52 + 42 * q^53 + 16 * q^55 - 2 * q^56 - 12 * q^61 - 22 * q^62 - 14 * q^64 + 2 * q^65 + 12 * q^66 + 32 * q^68 - 96 * q^69 - 6 * q^74 - 10 * q^75 + 52 * q^77 + 22 * q^78 - 8 * q^79 + 102 * q^81 - 30 * q^82 - 32 * q^87 - 10 * q^88 + 76 * q^90 + 22 * q^91 + 6 * q^92 - 2 * q^94 - 4 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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