LMFDB - Embedded newform 80.11.p.b.17.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [80,11,Mod(17,80)] 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("80.17"); S:= CuspForms(chi, 11); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(80, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 11, names="a")

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	80.p (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,366] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$50.8285802139$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	80.17
Dual form			80.11.p.b.33.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(183.000 - 183.000i) q^{3} +(-1875.00 - 2500.00i) q^{5} +(8407.00 + 8407.00i) q^{7} -7929.00i q^{9} +173398. q^{11} +(-232623. + 232623. i) q^{13} +(-800625. - 114375. i) q^{15} +(1.88003e6 + 1.88003e6i) q^{17} +1.10156e6i q^{19} +3.07696e6 q^{21} +(5.22826e6 - 5.22826e6i) q^{23} +(-2.73438e6 + 9.37500e6i) q^{25} +(9.35496e6 + 9.35496e6i) q^{27} -2.47908e7i q^{29} +1.00660e7 q^{31} +(3.17318e7 - 3.17318e7i) q^{33} +(5.25438e6 - 3.67806e7i) q^{35} +(5.63879e7 + 5.63879e7i) q^{37} +8.51400e7i q^{39} -1.53004e8 q^{41} +(-5.93725e7 + 5.93725e7i) q^{43} +(-1.98225e7 + 1.48669e7i) q^{45} +(-1.72339e8 - 1.72339e8i) q^{47} -1.41120e8i q^{49} +6.88092e8 q^{51} +(1.96386e8 - 1.96386e8i) q^{53} +(-3.25121e8 - 4.33495e8i) q^{55} +(2.01585e8 + 2.01585e8i) q^{57} -6.94069e8i q^{59} +9.06186e8 q^{61} +(6.66591e7 - 6.66591e7i) q^{63} +(1.01773e9 + 1.45389e8i) q^{65} +(9.62074e8 + 9.62074e8i) q^{67} -1.91354e9i q^{69} +3.12088e9 q^{71} +(-6.36339e8 + 6.36339e8i) q^{73} +(1.21523e9 + 2.21602e9i) q^{75} +(1.45776e9 + 1.45776e9i) q^{77} +1.96800e9i q^{79} +3.89211e9 q^{81} +(5.18382e9 - 5.18382e9i) q^{83} +(1.17502e9 - 8.22514e9i) q^{85} +(-4.53672e9 - 4.53672e9i) q^{87} +7.77138e9i q^{89} -3.91132e9 q^{91} +(1.84208e9 - 1.84208e9i) q^{93} +(2.75390e9 - 2.06542e9i) q^{95} +(-6.40361e8 - 6.40361e8i) q^{97} -1.37487e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 366 q^{3} - 3750 q^{5} + 16814 q^{7} + 346796 q^{11} - 465246 q^{13} - 1601250 q^{15} + 3760066 q^{17} + 6153924 q^{21} + 10456526 q^{23} - 5468750 q^{25} + 18709920 q^{27} + 20131996 q^{31} + 63463668 q^{33}+ \cdots - 1280722494 q^{97}+O(q^{100}) $ 2 * q + 366 * q^3 - 3750 * q^5 + 16814 * q^7 + 346796 * q^11 - 465246 * q^13 - 1601250 * q^15 + 3760066 * q^17 + 6153924 * q^21 + 10456526 * q^23 - 5468750 * q^25 + 18709920 * q^27 + 20131996 * q^31 + 63463668 * q^33 + 10508750 * q^35 + 112775826 * q^37 - 306007196 * q^41 - 118744914 * q^43 - 39645000 * q^45 - 344678706 * q^47 + 1376184156 * q^51 + 392771234 * q^53 - 650242500 * q^55 + 403170960 * q^57 + 1812371604 * q^61 + 133318206 * q^63 + 2035451250 * q^65 + 1924147934 * q^67 + 6241755196 * q^71 - 1272678526 * q^73 + 2430468750 * q^75 + 2915513972 * q^77 + 7784229762 * q^81 + 10367644206 * q^83 + 2350041250 * q^85 - 9073447440 * q^87 - 7822646244 * q^91 + 3684155268 * q^93 + 5507800000 * q^95 - 1280722494 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	183.000	−	183.000i	0.753086	−	0.753086i	−0.221968	−	0.975054i	$-0.571248\pi$
$3$	183.000	−	183.000i	0.753086	−	0.753086i	0.975054	+	0.221968i	$0.0712479\pi$
$4$		0			0
$5$	−1875.00	−	2500.00i	−0.600000	−	0.800000i
$5$	−1875.00	−	2500.00i	−0.600000	−	0.800000i
$6$		0			0
$7$	8407.00	+	8407.00i	0.500208	+	0.500208i	0.911503	−	0.411294i	$-0.134923\pi$
$7$	8407.00	+	8407.00i	0.500208	+	0.500208i	−0.411294	+	0.911503i	$0.634923\pi$
$8$		0			0
$9$		−	7929.00i		−	0.134278i
$10$		0			0
$11$	173398.			1.07667			0.538333	−	0.842732i	$-0.319054\pi$
$11$	173398.			1.07667			0.538333	+	0.842732i	$0.319054\pi$
$12$		0			0
$13$	−232623.	+	232623.i	−0.626521	+	0.626521i	−0.947191	−	0.320670i	$-0.896092\pi$
$13$	−232623.	+	232623.i	−0.626521	+	0.626521i	0.320670	+	0.947191i	$0.396092\pi$
$14$		0			0
$15$	−800625.	−	114375.i	−1.05432	−	0.150617i
$16$		0			0
$17$	1.88003e6	+	1.88003e6i	1.32410	+	1.32410i	0.910424	+	0.413676i	$0.135755\pi$
$17$	1.88003e6	+	1.88003e6i	1.32410	+	1.32410i	0.413676	+	0.910424i	$0.364245\pi$
$18$		0			0
$19$			1.10156e6i			0.444877i	0.974947	+	0.222439i	$0.0714017\pi$
$19$			1.10156e6i			0.444877i	−0.974947	+	0.222439i	$0.928598\pi$
$20$		0			0
$21$	3.07696e6			0.753400
$22$		0			0
$23$	5.22826e6	−	5.22826e6i	0.812303	−	0.812303i	−0.172675	−	0.984979i	$-0.555241\pi$
$23$	5.22826e6	−	5.22826e6i	0.812303	−	0.812303i	0.984979	+	0.172675i	$0.0552412\pi$
$24$		0			0
$25$	−2.73438e6	+	9.37500e6i	−0.280000	+	0.960000i
$26$		0			0
$27$	9.35496e6	+	9.35496e6i	0.651963	+	0.651963i
$28$		0			0
$29$		−	2.47908e7i		−	1.20865i	−0.796737	−	0.604326i	$-0.793442\pi$
$29$		−	2.47908e7i		−	1.20865i	0.796737	−	0.604326i	$-0.206558\pi$
$30$		0			0
$31$	1.00660e7			0.351600			0.175800	−	0.984426i	$-0.443749\pi$
$31$	1.00660e7			0.351600			0.175800	+	0.984426i	$0.443749\pi$
$32$		0			0
$33$	3.17318e7	−	3.17318e7i	0.810822	−	0.810822i
$34$		0			0
$35$	5.25438e6	−	3.67806e7i	0.100042	−	0.700292i
$36$		0			0
$37$	5.63879e7	+	5.63879e7i	0.813163	+	0.813163i	0.985107	−	0.171944i	$-0.0550048\pi$
$37$	5.63879e7	+	5.63879e7i	0.813163	+	0.813163i	−0.171944	+	0.985107i	$0.555005\pi$
$38$		0			0
$39$			8.51400e7i			0.943649i
$40$		0			0
$41$	−1.53004e8			−1.32063			−0.660317	−	0.750987i	$-0.729578\pi$
$41$	−1.53004e8			−1.32063			−0.660317	+	0.750987i	$0.729578\pi$
$42$		0			0
$43$	−5.93725e7	+	5.93725e7i	−0.403871	+	0.403871i	−0.879595	−	0.475724i	$-0.842186\pi$
$43$	−5.93725e7	+	5.93725e7i	−0.403871	+	0.403871i	0.475724	+	0.879595i	$0.342186\pi$
$44$		0			0
$45$	−1.98225e7	+	1.48669e7i	−0.107423	+	0.0805670i
$46$		0			0
$47$	−1.72339e8	−	1.72339e8i	−0.751441	−	0.751441i	0.223307	−	0.974748i	$-0.428315\pi$
$47$	−1.72339e8	−	1.72339e8i	−0.751441	−	0.751441i	−0.974748	+	0.223307i	$0.928315\pi$
$48$		0			0
$49$		−	1.41120e8i		−	0.499583i
$50$		0			0
$51$	6.88092e8			1.99432
$52$		0			0
$53$	1.96386e8	−	1.96386e8i	0.469602	−	0.469602i	−0.432183	−	0.901786i	$-0.642257\pi$
$53$	1.96386e8	−	1.96386e8i	0.469602	−	0.469602i	0.901786	+	0.432183i	$0.142257\pi$
$54$		0			0
$55$	−3.25121e8	−	4.33495e8i	−0.645999	−	0.861332i
$56$		0			0
$57$	2.01585e8	+	2.01585e8i	0.335031	+	0.335031i
$58$		0			0
$59$		−	6.94069e8i		−	0.970829i	−0.874284	−	0.485414i	$-0.838669\pi$
$59$		−	6.94069e8i		−	0.970829i	0.874284	−	0.485414i	$-0.161331\pi$
$60$		0			0
$61$	9.06186e8			1.07292			0.536461	−	0.843925i	$-0.319761\pi$
$61$	9.06186e8			1.07292			0.536461	+	0.843925i	$0.319761\pi$
$62$		0			0
$63$	6.66591e7	−	6.66591e7i	0.0671671	−	0.0671671i
$64$		0			0
$65$	1.01773e9	+	1.45389e8i	0.877130	+	0.125304i
$66$		0			0
$67$	9.62074e8	+	9.62074e8i	0.712581	+	0.712581i	0.967075	−	0.254493i	$-0.0819087\pi$
$67$	9.62074e8	+	9.62074e8i	0.712581	+	0.712581i	−0.254493	+	0.967075i	$0.581909\pi$
$68$		0			0
$69$		−	1.91354e9i		−	1.22347i
$70$		0			0
$71$	3.12088e9			1.72976			0.864878	−	0.501982i	$-0.167395\pi$
$71$	3.12088e9			1.72976			0.864878	+	0.501982i	$0.167395\pi$
$72$		0			0
$73$	−6.36339e8	+	6.36339e8i	−0.306955	+	0.306955i	−0.843727	−	0.536772i	$-0.819643\pi$
$73$	−6.36339e8	+	6.36339e8i	−0.306955	+	0.306955i	0.536772	+	0.843727i	$0.319643\pi$
$74$		0			0
$75$	1.21523e9	+	2.21602e9i	0.512099	+	0.933827i
$76$		0			0
$77$	1.45776e9	+	1.45776e9i	0.538557	+	0.538557i
$78$		0			0
$79$			1.96800e9i			0.639571i	0.947490	+	0.319786i	$0.103611\pi$
$79$			1.96800e9i			0.639571i	−0.947490	+	0.319786i	$0.896389\pi$
$80$		0			0
$81$	3.89211e9			1.11625
$82$		0			0
$83$	5.18382e9	−	5.18382e9i	1.31601	−	1.31601i	0.399107	−	0.916904i	$-0.369320\pi$
$83$	5.18382e9	−	5.18382e9i	1.31601	−	1.31601i	0.916904	−	0.399107i	$-0.130680\pi$
$84$		0			0
$85$	1.17502e9	−	8.22514e9i	0.264820	−	1.85374i
$86$		0			0
$87$	−4.53672e9	−	4.53672e9i	−0.910219	−	0.910219i
$88$		0			0
$89$			7.77138e9i			1.39171i	0.718183	+	0.695854i	$0.244974\pi$
$89$			7.77138e9i			1.39171i	−0.718183	+	0.695854i	$0.755026\pi$
$90$		0			0
$91$	−3.91132e9			−0.626782
$92$		0			0
$93$	1.84208e9	−	1.84208e9i	0.264785	−	0.264785i
$94$		0			0
$95$	2.75390e9	−	2.06542e9i	0.355902	−	0.266926i
$96$		0			0
$97$	−6.40361e8	−	6.40361e8i	−0.0745704	−	0.0745704i	0.668838	−	0.743408i	$-0.266792\pi$
$97$	−6.40361e8	−	6.40361e8i	−0.0745704	−	0.0745704i	−0.743408	+	0.668838i	$0.766792\pi$
$98$		0			0
$99$		−	1.37487e9i		−	0.144573i
$100$		0			0
$101$	2.02434e9			0.192609			0.0963047	−	0.995352i	$-0.469298\pi$
$101$	2.02434e9			0.192609			0.0963047	+	0.995352i	$0.469298\pi$
$102$		0			0
$103$	1.50252e9	−	1.50252e9i	0.129609	−	0.129609i	−0.639326	−	0.768935i	$-0.720787\pi$
$103$	1.50252e9	−	1.50252e9i	0.129609	−	0.129609i	0.768935	+	0.639326i	$0.220787\pi$
$104$		0			0
$105$	−5.76930e9	−	7.69240e9i	−0.452040	−	0.602720i
$106$		0			0
$107$	−1.41812e9	−	1.41812e9i	−0.101110	−	0.101110i	0.654742	−	0.755852i	$-0.272777\pi$
$107$	−1.41812e9	−	1.41812e9i	−0.101110	−	0.101110i	−0.755852	+	0.654742i	$0.772777\pi$
$108$		0			0
$109$		−	6.21296e9i		−	0.403800i	−0.979406	−	0.201900i	$-0.935288\pi$
$109$		−	6.21296e9i		−	0.403800i	0.979406	−	0.201900i	$-0.0647116\pi$
$110$		0			0
$111$	2.06380e10			1.22476
$112$		0			0
$113$	−1.79511e10	+	1.79511e10i	−0.974313	+	0.974313i	−0.999678	−	0.0253650i	$-0.991925\pi$
$113$	−1.79511e10	+	1.79511e10i	−0.974313	+	0.974313i	0.0253650	+	0.999678i	$0.491925\pi$
$114$		0			0
$115$	−2.28737e10	−	3.26766e9i	−1.13722	−	0.162461i
$116$		0			0
$117$	1.84447e9	+	1.84447e9i	0.0841282	+	0.0841282i
$118$		0			0
$119$			3.16109e10i			1.32465i
$120$		0			0
$121$	4.12944e9			0.159208
$122$		0			0
$123$	−2.79997e10	+	2.79997e10i	−0.994551	+	0.994551i
$124$		0			0
$125$	2.85645e10	−	1.07422e10i	0.936000	−	0.352000i
$126$		0			0
$127$	−1.30621e10	−	1.30621e10i	−0.395362	−	0.395362i	0.481232	−	0.876593i	$-0.340190\pi$
$127$	−1.30621e10	−	1.30621e10i	−0.395362	−	0.395362i	−0.876593	+	0.481232i	$0.840190\pi$
$128$		0			0
$129$			2.17303e10i			0.608300i
$130$		0			0
$131$	5.20222e10			1.34844			0.674221	−	0.738530i	$-0.264480\pi$
$131$	5.20222e10			1.34844			0.674221	+	0.738530i	$0.264480\pi$
$132$		0			0
$133$	−9.26081e9	+	9.26081e9i	−0.222531	+	0.222531i
$134$		0			0
$135$	5.84685e9	−	4.09280e10i	0.130393	−	0.912749i
$136$		0			0
$137$	−1.63815e10	−	1.63815e10i	−0.339429	−	0.339429i	0.516723	−	0.856153i	$-0.327152\pi$
$137$	−1.63815e10	−	1.63815e10i	−0.339429	−	0.339429i	−0.856153	+	0.516723i	$0.827152\pi$
$138$		0			0
$139$			2.61490e10i			0.503942i	0.967735	+	0.251971i	$0.0810787\pi$
$139$			2.61490e10i			0.503942i	−0.967735	+	0.251971i	$0.918921\pi$
$140$		0			0
$141$	−6.30762e10			−1.13180
$142$		0			0
$143$	−4.03364e10	+	4.03364e10i	−0.674554	+	0.674554i
$144$		0			0
$145$	−6.19771e10	+	4.64828e10i	−0.966922	+	0.725191i
$146$		0			0
$147$	−2.58250e10	−	2.58250e10i	−0.376229	−	0.376229i
$148$		0			0
$149$			4.31363e9i			0.0587369i	0.999569	+	0.0293685i	$0.00934962\pi$
$149$			4.31363e9i			0.0587369i	−0.999569	+	0.0293685i	$0.990650\pi$
$150$		0			0
$151$	−1.13868e11			−1.45050			−0.725251	−	0.688484i	$-0.758276\pi$
$151$	−1.13868e11			−1.45050			−0.725251	+	0.688484i	$0.758276\pi$
$152$		0			0
$153$	1.49068e10	−	1.49068e10i	0.177798	−	0.177798i
$154$		0			0
$155$	−1.88737e10	−	2.51650e10i	−0.210960	−	0.281280i
$156$		0			0
$157$	1.04428e10	+	1.04428e10i	0.109476	+	0.109476i	0.759723	−	0.650247i	$-0.225335\pi$
$157$	1.04428e10	+	1.04428e10i	0.109476	+	0.109476i	−0.650247	+	0.759723i	$0.725335\pi$
$158$		0			0
$159$		−	7.18771e10i		−	0.707302i
$160$		0			0
$161$	8.79080e10			0.812642
$162$		0			0
$163$	−4.78305e10	+	4.78305e10i	−0.415688	+	0.415688i	−0.883714	−	0.468027i	$-0.844965\pi$
$163$	−4.78305e10	+	4.78305e10i	−0.415688	+	0.415688i	0.468027	+	0.883714i	$0.344965\pi$
$164$		0			0
$165$	−1.38827e11	−	1.98324e10i	−1.13515	−	0.162164i
$166$		0			0
$167$	1.18281e10	+	1.18281e10i	0.0910613	+	0.0910613i	0.751170	−	0.660109i	$-0.229490\pi$
$167$	1.18281e10	+	1.18281e10i	0.0910613	+	0.0910613i	−0.660109	+	0.751170i	$0.729490\pi$
$168$		0			0
$169$			2.96316e10i			0.214942i
$170$		0			0
$171$	8.73427e9			0.0597374
$172$		0			0
$173$	−1.16377e11	+	1.16377e11i	−0.750997	+	0.750997i	−0.974665	−	0.223669i	$-0.928197\pi$
$173$	−1.16377e11	+	1.16377e11i	−0.750997	+	0.750997i	0.223669	+	0.974665i	$0.428197\pi$
$174$		0			0
$175$	−1.01804e11	+	5.58277e10i	−0.620258	+	0.340142i
$176$		0			0
$177$	−1.27015e11	−	1.27015e11i	−0.731118	−	0.731118i
$178$		0			0
$179$			1.81011e11i			0.985008i	0.870310	+	0.492504i	$0.163918\pi$
$179$			1.81011e11i			0.985008i	−0.870310	+	0.492504i	$0.836082\pi$
$180$		0			0
$181$	1.33000e11			0.684636			0.342318	−	0.939584i	$-0.388788\pi$
$181$	1.33000e11			0.684636			0.342318	+	0.939584i	$0.388788\pi$
$182$		0			0
$183$	1.65832e11	−	1.65832e11i	0.808003	−	0.808003i
$184$		0			0
$185$	3.52424e10	−	2.46697e11i	0.162633	−	1.13843i
$186$		0			0
$187$	3.25994e11	+	3.25994e11i	1.42561	+	1.42561i
$188$		0			0
$189$			1.57294e11i			0.652235i
$190$		0			0
$191$	−1.31044e11			−0.515525			−0.257762	−	0.966208i	$-0.582985\pi$
$191$	−1.31044e11			−0.515525			−0.257762	+	0.966208i	$0.582985\pi$
$192$		0			0
$193$	2.12792e11	−	2.12792e11i	0.794639	−	0.794639i	−0.187606	−	0.982244i	$-0.560073\pi$
$193$	2.12792e11	−	2.12792e11i	0.794639	−	0.794639i	0.982244	+	0.187606i	$0.0600727\pi$
$194$		0			0
$195$	2.12850e11	−	1.59638e11i	0.754920	−	0.566190i
$196$		0			0
$197$	7.90246e10	+	7.90246e10i	0.266337	+	0.266337i	0.827622	−	0.561285i	$-0.189693\pi$
$197$	7.90246e10	+	7.90246e10i	0.266337	+	0.266337i	−0.561285	+	0.827622i	$0.689693\pi$
$198$		0			0
$199$		−	4.52657e11i		−	1.45045i	−0.688510	−	0.725227i	$-0.741735\pi$
$199$		−	4.52657e11i		−	1.45045i	0.688510	−	0.725227i	$-0.258265\pi$
$200$		0			0
$201$	3.52119e11			1.07327
$202$		0			0
$203$	2.08417e11	−	2.08417e11i	0.604578	−	0.604578i
$204$		0			0
$205$	2.86882e11	+	3.82509e11i	0.792380	+	1.05651i
$206$		0			0
$207$	−4.14549e10	−	4.14549e10i	−0.109075	−	0.109075i
$208$		0			0
$209$			1.91008e11i			0.478984i
$210$		0			0
$211$	−1.37995e11			−0.329951			−0.164976	−	0.986298i	$-0.552755\pi$
$211$	−1.37995e11			−0.329951			−0.164976	+	0.986298i	$0.552755\pi$
$212$		0			0
$213$	5.71121e11	−	5.71121e11i	1.30266	−	1.30266i
$214$		0			0
$215$	2.59754e11	+	3.71078e10i	0.565419	+	0.0807742i
$216$		0			0
$217$	8.46248e10	+	8.46248e10i	0.175873	+	0.175873i
$218$		0			0
$219$			2.32900e11i			0.462327i
$220$		0			0
$221$	−8.74678e11			−1.65915
$222$		0			0
$223$	1.26054e11	−	1.26054e11i	0.228576	−	0.228576i	−0.583521	−	0.812098i	$-0.698326\pi$
$223$	1.26054e11	−	1.26054e11i	0.228576	−	0.228576i	0.812098	+	0.583521i	$0.198326\pi$
$224$		0			0
$225$	7.43344e10	+	2.16809e10i	0.128907	+	0.0375979i
$226$		0			0
$227$	−1.15268e11	−	1.15268e11i	−0.191241	−	0.191241i	0.604991	−	0.796232i	$-0.293177\pi$
$227$	−1.15268e11	−	1.15268e11i	−0.191241	−	0.191241i	−0.796232	+	0.604991i	$0.793177\pi$
$228$		0			0
$229$		−	3.29124e11i		−	0.522615i	−0.965256	−	0.261308i	$-0.915846\pi$
$229$		−	3.29124e11i		−	0.522615i	0.965256	−	0.261308i	$-0.0841537\pi$
$230$		0			0
$231$	5.33539e11			0.811160
$232$		0			0
$233$	−9.97948e10	+	9.97948e10i	−0.145321	+	0.145321i	−0.776024	−	0.630703i	$-0.782767\pi$
$233$	−9.97948e10	+	9.97948e10i	−0.145321	+	0.145321i	0.630703	+	0.776024i	$0.282767\pi$
$234$		0			0
$235$	−1.07712e11	+	7.53985e11i	−0.150288	+	1.05202i
$236$		0			0
$237$	3.60143e11	+	3.60143e11i	0.481652	+	0.481652i
$238$		0			0
$239$			3.95622e10i			0.0507331i	0.999678	+	0.0253665i	$0.00807529\pi$
$239$			3.95622e10i			0.0507331i	−0.999678	+	0.0253665i	$0.991925\pi$
$240$		0			0
$241$	−8.14271e11			−1.00158			−0.500788	−	0.865570i	$-0.666956\pi$
$241$	−8.14271e11			−1.00158			−0.500788	+	0.865570i	$0.666956\pi$
$242$		0			0
$243$	1.59856e11	−	1.59856e11i	0.188668	−	0.188668i
$244$		0			0
$245$	−3.52800e11	+	2.64600e11i	−0.399667	+	0.299750i
$246$		0			0
$247$	−2.56248e11	−	2.56248e11i	−0.278725	−	0.278725i
$248$		0			0
$249$		−	1.89728e12i		−	1.98214i
$250$		0			0
$251$	−4.53171e11			−0.454877			−0.227438	−	0.973793i	$-0.573035\pi$
$251$	−4.53171e11			−0.454877			−0.227438	+	0.973793i	$0.573035\pi$
$252$		0			0
$253$	9.06570e11	−	9.06570e11i	0.874579	−	0.874579i
$254$		0			0
$255$	−1.29017e12	−	1.72023e12i	−1.19659	−	1.59546i
$256$		0			0
$257$	1.33579e12	+	1.33579e12i	1.19144	+	1.19144i	0.976663	+	0.214777i	$0.0689025\pi$
$257$	1.33579e12	+	1.33579e12i	1.19144	+	1.19144i	0.214777	+	0.976663i	$0.431098\pi$
$258$		0			0
$259$			9.48106e11i			0.813501i
$260$		0			0
$261$	−1.96567e11			−0.162296
$262$		0			0
$263$	9.12065e11	−	9.12065e11i	0.724848	−	0.724848i	−0.244740	−	0.969589i	$-0.578703\pi$
$263$	9.12065e11	−	9.12065e11i	0.724848	−	0.724848i	0.969589	+	0.244740i	$0.0787027\pi$
$264$		0			0
$265$	−8.59187e11	−	1.22741e11i	−0.657443	−	0.0939205i
$266$		0			0
$267$	1.42216e12	+	1.42216e12i	1.04808	+	1.04808i
$268$		0			0
$269$			1.04348e12i			0.740835i	0.928865	+	0.370417i	$0.120785\pi$
$269$			1.04348e12i			0.740835i	−0.928865	+	0.370417i	$0.879215\pi$
$270$		0			0
$271$	−7.19445e11			−0.492211			−0.246105	−	0.969243i	$-0.579151\pi$
$271$	−7.19445e11			−0.492211			−0.246105	+	0.969243i	$0.579151\pi$
$272$		0			0
$273$	−7.15772e11	+	7.15772e11i	−0.472021	+	0.472021i
$274$		0			0
$275$	−4.74135e11	+	1.62561e12i	−0.301466	+	1.03360i
$276$		0			0
$277$	−8.62576e11	−	8.62576e11i	−0.528931	−	0.528931i	0.391323	−	0.920253i	$-0.372018\pi$
$277$	−8.62576e11	−	8.62576e11i	−0.528931	−	0.528931i	−0.920253	+	0.391323i	$0.872018\pi$
$278$		0			0
$279$		−	7.98133e10i		−	0.0472122i
$280$		0			0
$281$	−7.89300e11			−0.450516			−0.225258	−	0.974299i	$-0.572323\pi$
$281$	−7.89300e11			−0.450516			−0.225258	+	0.974299i	$0.572323\pi$
$282$		0			0
$283$	6.60245e11	−	6.60245e11i	0.363725	−	0.363725i	−0.501457	−	0.865182i	$-0.667203\pi$
$283$	6.60245e11	−	6.60245e11i	0.363725	−	0.363725i	0.865182	+	0.501457i	$0.167203\pi$
$284$		0			0
$285$	1.25991e11	−	8.81936e11i	0.0670062	−	0.469043i
$286$		0			0
$287$	−1.28630e12	−	1.28630e12i	−0.660592	−	0.660592i
$288$		0			0
$289$			5.05305e12i			2.50648i
$290$		0			0
$291$	−2.34372e11			−0.112316
$292$		0			0
$293$	1.79236e11	−	1.79236e11i	0.0830019	−	0.0830019i	−0.664387	−	0.747389i	$-0.731307\pi$
$293$	1.79236e11	−	1.79236e11i	0.0830019	−	0.0830019i	0.747389	+	0.664387i	$0.231307\pi$
$294$		0			0
$295$	−1.73517e12	+	1.30138e12i	−0.776663	+	0.582497i
$296$		0			0
$297$	1.62213e12	+	1.62213e12i	0.701946	+	0.701946i
$298$		0			0
$299$			2.43243e12i			1.01785i
$300$		0			0
$301$	−9.98288e11			−0.404039
$302$		0			0
$303$	3.70455e11	−	3.70455e11i	0.145051	−	0.145051i
$304$		0			0
$305$	−1.69910e12	−	2.26546e12i	−0.643753	−	0.858337i
$306$		0			0
$307$	1.10155e12	+	1.10155e12i	0.403937	+	0.403937i	0.879618	−	0.475681i	$-0.157798\pi$
$307$	1.10155e12	+	1.10155e12i	0.403937	+	0.403937i	−0.475681	+	0.879618i	$0.657798\pi$
$308$		0			0
$309$		−	5.49924e11i		−	0.195214i
$310$		0			0
$311$	−5.31138e12			−1.82560			−0.912800	−	0.408406i	$-0.866085\pi$
$311$	−5.31138e12			−1.82560			−0.912800	+	0.408406i	$0.866085\pi$
$312$		0			0
$313$	−8.40078e11	+	8.40078e11i	−0.279639	+	0.279639i	−0.832965	−	0.553326i	$-0.813358\pi$
$313$	−8.40078e11	+	8.40078e11i	−0.279639	+	0.279639i	0.553326	+	0.832965i	$0.313358\pi$
$314$		0			0
$315$	−2.91634e11	−	4.16619e10i	−0.0940340	−	0.0134334i
$316$		0			0
$317$	−1.16635e12	−	1.16635e12i	−0.364361	−	0.364361i	0.501055	−	0.865416i	$-0.332946\pi$
$317$	−1.16635e12	−	1.16635e12i	−0.364361	−	0.364361i	−0.865416	+	0.501055i	$0.832946\pi$
$318$		0			0
$319$		−	4.29868e12i		−	1.30131i
$320$		0			0
$321$	−5.19031e11			−0.152289
$322$		0			0
$323$	−2.07097e12	+	2.07097e12i	−0.589062	+	0.589062i
$324$		0			0
$325$	−1.54476e12	−	2.81692e12i	−0.426035	−	0.776887i
$326$		0			0
$327$	−1.13697e12	−	1.13697e12i	−0.304096	−	0.304096i
$328$		0			0
$329$		−	2.89771e12i		−	0.751754i
$330$		0			0
$331$	4.82042e12			1.21324			0.606618	−	0.794994i	$-0.292526\pi$
$331$	4.82042e12			1.21324			0.606618	+	0.794994i	$0.292526\pi$
$332$		0			0
$333$	4.47100e11	−	4.47100e11i	0.109190	−	0.109190i
$334$		0			0
$335$	6.01296e11	−	4.20907e12i	0.142516	−	0.997614i
$336$		0			0
$337$	−3.68550e12	−	3.68550e12i	−0.847904	−	0.847904i	0.141967	−	0.989871i	$-0.454657\pi$
$337$	−3.68550e12	−	3.68550e12i	−0.847904	−	0.847904i	−0.989871	+	0.141967i	$0.954657\pi$
$338$		0			0
$339$			6.57010e12i			1.46748i
$340$		0			0
$341$	1.74542e12			0.378555
$342$		0			0
$343$	3.56116e12	−	3.56116e12i	0.750104	−	0.750104i
$344$		0			0
$345$	−4.78386e12	+	3.58790e12i	−0.978775	+	0.734082i
$346$		0			0
$347$	5.38450e12	+	5.38450e12i	1.07028	+	1.07028i	0.997336	+	0.0729452i	$0.0232398\pi$
$347$	5.38450e12	+	5.38450e12i	1.07028	+	1.07028i	0.0729452	+	0.997336i	$0.476760\pi$
$348$		0			0
$349$			8.12658e12i			1.56957i	0.619768	+	0.784785i	$0.287227\pi$
$349$			8.12658e12i			1.56957i	−0.619768	+	0.784785i	$0.712773\pi$
$350$		0			0
$351$	−4.35236e12			−0.816938
$352$		0			0
$353$	5.49274e12	−	5.49274e12i	1.00211	−	1.00211i	0.00211203	−	0.999998i	$-0.499328\pi$
$353$	5.49274e12	−	5.49274e12i	1.00211	−	1.00211i	0.999998	−	0.00211203i	$-0.000672280\pi$
$354$		0			0
$355$	−5.85165e12	−	7.80219e12i	−1.03785	−	1.38381i
$356$		0			0
$357$	5.78479e12	+	5.78479e12i	0.997577	+	0.997577i
$358$		0			0
$359$			5.91305e12i			0.991606i	0.868435	+	0.495803i	$0.165126\pi$
$359$			5.91305e12i			0.991606i	−0.868435	+	0.495803i	$0.834874\pi$
$360$		0			0
$361$	4.91763e12			0.802084
$362$		0			0
$363$	7.55688e11	−	7.55688e11i	0.119897	−	0.119897i
$364$		0			0
$365$	2.78398e12	+	3.97712e11i	0.429737	+	0.0613910i
$366$		0			0
$367$	−1.75360e12	−	1.75360e12i	−0.263390	−	0.263390i	0.563040	−	0.826430i	$-0.309632\pi$
$367$	−1.75360e12	−	1.75360e12i	−0.263390	−	0.263390i	−0.826430	+	0.563040i	$0.809632\pi$
$368$		0			0
$369$			1.21317e12i			0.177332i
$370$		0			0
$371$	3.30203e12			0.469798
$372$		0			0
$373$	4.25717e12	−	4.25717e12i	0.589627	−	0.589627i	−0.347904	−	0.937530i	$-0.613106\pi$
$373$	4.25717e12	−	4.25717e12i	0.589627	−	0.589627i	0.937530	+	0.347904i	$0.113106\pi$
$374$		0			0
$375$	3.26147e12	−	7.19312e12i	0.439802	−	0.969975i
$376$		0			0
$377$	5.76692e12	+	5.76692e12i	0.757246	+	0.757246i
$378$		0			0
$379$			7.20999e12i			0.922016i	0.887396	+	0.461008i	$0.152512\pi$
$379$			7.20999e12i			0.922016i	−0.887396	+	0.461008i	$0.847488\pi$
$380$		0			0
$381$	−4.78073e12			−0.595483
$382$		0			0
$383$	6.93832e12	−	6.93832e12i	0.841900	−	0.841900i	−0.147206	−	0.989106i	$-0.547028\pi$
$383$	6.93832e12	−	6.93832e12i	0.841900	−	0.841900i	0.989106	+	0.147206i	$0.0470281\pi$
$384$		0			0
$385$	9.11098e11	−	6.37769e12i	0.107711	−	0.753980i
$386$		0			0
$387$	4.70764e11	+	4.70764e11i	0.0542311	+	0.0542311i
$388$		0			0
$389$			1.12518e13i			1.26320i	0.775293	+	0.631601i	$0.217602\pi$
$389$			1.12518e13i			1.26320i	−0.775293	+	0.631601i	$0.782398\pi$
$390$		0			0
$391$	1.96586e13			2.15114
$392$		0			0
$393$	9.52006e12	−	9.52006e12i	1.01549	−	1.01549i
$394$		0			0
$395$	4.91999e12	−	3.68999e12i	0.511657	−	0.383743i
$396$		0			0
$397$	−7.94628e12	−	7.94628e12i	−0.805770	−	0.805770i	0.178221	−	0.983991i	$-0.442966\pi$
$397$	−7.94628e12	−	7.94628e12i	−0.805770	−	0.805770i	−0.983991	+	0.178221i	$0.942966\pi$
$398$		0			0
$399$			3.38946e12i			0.335171i
$400$		0			0
$401$	8.81072e12			0.849747			0.424874	−	0.905253i	$-0.360319\pi$
$401$	8.81072e12			0.849747			0.424874	+	0.905253i	$0.360319\pi$
$402$		0			0
$403$	−2.34158e12	+	2.34158e12i	−0.220285	+	0.220285i
$404$		0			0
$405$	−7.29772e12	−	9.73029e12i	−0.669749	−	0.892998i
$406$		0			0
$407$	9.77755e12	+	9.77755e12i	0.875504	+	0.875504i
$408$		0			0
$409$		−	1.00160e13i		−	0.875141i	−0.899184	−	0.437571i	$-0.855839\pi$
$409$		−	1.00160e13i		−	0.875141i	0.899184	−	0.437571i	$-0.144161\pi$
$410$		0			0
$411$	−5.99561e12			−0.511239
$412$		0			0
$413$	5.83504e12	−	5.83504e12i	0.485616	−	0.485616i
$414$		0			0
$415$	−2.26792e13	−	3.23989e12i	−1.84242	−	0.263202i
$416$		0			0
$417$	4.78526e12	+	4.78526e12i	0.379512	+	0.379512i
$418$		0			0
$419$		−	1.48244e13i		−	1.14791i	−0.818888	−	0.573954i	$-0.805409\pi$
$419$		−	1.48244e13i		−	1.14791i	0.818888	−	0.573954i	$-0.194591\pi$
$420$		0			0
$421$	−4.68500e12			−0.354241			−0.177121	−	0.984189i	$-0.556678\pi$
$421$	−4.68500e12			−0.354241			−0.177121	+	0.984189i	$0.556678\pi$
$422$		0			0
$423$	−1.36648e12	+	1.36648e12i	−0.100902	+	0.100902i
$424$		0			0
$425$	−2.27660e13	+	1.24846e13i	−1.64188	+	0.900388i
$426$		0			0
$427$	7.61830e12	+	7.61830e12i	0.536684	+	0.536684i
$428$		0			0
$429$			1.47631e13i			1.01599i
$430$		0			0
$431$	−2.39126e13			−1.60783			−0.803917	−	0.594741i	$-0.797254\pi$
$431$	−2.39126e13			−1.60783			−0.803917	+	0.594741i	$0.797254\pi$
$432$		0			0
$433$	−7.41823e11	+	7.41823e11i	−0.0487372	+	0.0487372i	−0.731055	−	0.682318i	$-0.760972\pi$
$433$	−7.41823e11	+	7.41823e11i	−0.0487372	+	0.0487372i	0.682318	+	0.731055i	$0.260972\pi$
$434$		0			0
$435$	−2.83545e12	+	1.98482e13i	−0.182044	+	1.27431i
$436$		0			0
$437$	5.75925e12	+	5.75925e12i	0.361375	+	0.361375i
$438$		0			0
$439$		−	2.09704e13i		−	1.28613i	−0.765811	−	0.643065i	$-0.777662\pi$
$439$		−	2.09704e13i		−	1.28613i	0.765811	−	0.643065i	$-0.222338\pi$
$440$		0			0
$441$	−1.11894e12			−0.0670832
$442$		0			0
$443$	2.38909e13	−	2.38909e13i	1.40028	−	1.40028i	0.601118	−	0.799160i	$-0.294722\pi$
$443$	2.38909e13	−	2.38909e13i	1.40028	−	1.40028i	0.799160	−	0.601118i	$-0.205278\pi$
$444$		0			0
$445$	1.94285e13	−	1.45713e13i	1.11337	−	0.835025i
$446$		0			0
$447$	7.89394e11	+	7.89394e11i	0.0442340	+	0.0442340i
$448$		0			0
$449$		−	2.04535e13i		−	1.12082i	−0.828215	−	0.560411i	$-0.810643\pi$
$449$		−	2.04535e13i		−	1.12082i	0.828215	−	0.560411i	$-0.189357\pi$
$450$		0			0
$451$	−2.65305e13			−1.42188
$452$		0			0
$453$	−2.08379e13	+	2.08379e13i	−1.09235	+	1.09235i
$454$		0			0
$455$	7.33373e12	+	9.77831e12i	0.376069	+	0.501426i
$456$		0			0
$457$	6.88521e12	+	6.88521e12i	0.345411	+	0.345411i	0.858397	−	0.512986i	$-0.171461\pi$
$457$	6.88521e12	+	6.88521e12i	0.345411	+	0.345411i	−0.512986	+	0.858397i	$0.671461\pi$
$458$		0			0
$459$			3.51753e13i			1.72653i
$460$		0			0
$461$	−1.72039e13			−0.826268			−0.413134	−	0.910670i	$-0.635566\pi$
$461$	−1.72039e13			−0.826268			−0.413134	+	0.910670i	$0.635566\pi$
$462$		0			0
$463$	4.67192e11	−	4.67192e11i	0.0219579	−	0.0219579i	−0.696043	−	0.718000i	$-0.745058\pi$
$463$	4.67192e11	−	4.67192e11i	0.0219579	−	0.0219579i	0.718000	+	0.696043i	$0.245058\pi$
$464$		0			0
$465$	−8.05909e12	−	1.15130e12i	−0.370699	−	0.0529570i
$466$		0			0
$467$	−1.62768e13	−	1.62768e13i	−0.732799	−	0.732799i	0.238374	−	0.971173i	$-0.423385\pi$
$467$	−1.62768e13	−	1.62768e13i	−0.732799	−	0.732799i	−0.971173	+	0.238374i	$0.923385\pi$
$468$		0			0
$469$			1.61763e13i			0.712878i
$470$		0			0
$471$	3.82206e12			0.164889
$472$		0			0
$473$	−1.02951e13	+	1.02951e13i	−0.434834	+	0.434834i
$474$		0			0
$475$	−1.03271e13	−	3.01208e12i	−0.427082	−	0.124566i
$476$		0			0
$477$	−1.55714e12	−	1.55714e12i	−0.0630574	−	0.0630574i
$478$		0			0
$479$			3.26759e13i			1.29584i	0.761710	+	0.647918i	$0.224360\pi$
$479$			3.26759e13i			1.29584i	−0.761710	+	0.647918i	$0.775640\pi$
$480$		0			0
$481$	−2.62343e13			−1.01893
$482$		0			0
$483$	1.60872e13	−	1.60872e13i	0.611989	−	0.611989i
$484$		0			0
$485$	−4.00226e11	+	2.80158e12i	−0.0149141	+	0.104399i
$486$		0			0
$487$	−3.91617e12	−	3.91617e12i	−0.142961	−	0.142961i	0.632004	−	0.774965i	$-0.282232\pi$
$487$	−3.91617e12	−	3.91617e12i	−0.142961	−	0.142961i	−0.774965	+	0.632004i	$0.782232\pi$
$488$		0			0
$489$			1.75060e13i			0.626098i
$490$		0			0
$491$	1.66945e12			0.0585015			0.0292508	−	0.999572i	$-0.490688\pi$
$491$	1.66945e12			0.0585015			0.0292508	+	0.999572i	$0.490688\pi$
$492$		0			0
$493$	4.66076e13	−	4.66076e13i	1.60038	−	1.60038i
$494$		0			0
$495$	−3.43718e12	+	2.57789e12i	−0.115658	+	0.0867437i
$496$		0			0
$497$	2.62372e13	+	2.62372e13i	0.865239	+	0.865239i
$498$		0			0
$499$		−	2.69113e13i		−	0.869824i	−0.900473	−	0.434912i	$-0.856779\pi$
$499$		−	2.69113e13i		−	0.869824i	0.900473	−	0.434912i	$-0.143221\pi$
$500$		0			0
$501$	4.32910e12			0.137154
$502$		0			0
$503$	−2.35501e13	+	2.35501e13i	−0.731397	+	0.731397i	−0.970897	−	0.239499i	$-0.923017\pi$
$503$	−2.35501e13	+	2.35501e13i	−0.731397	+	0.731397i	0.239499	+	0.970897i	$0.423017\pi$
$504$		0			0
$505$	−3.79564e12	−	5.06086e12i	−0.115566	−	0.154087i
$506$		0			0
$507$	5.42258e12	+	5.42258e12i	0.161870	+	0.161870i
$508$		0			0
$509$		−	8.63621e12i		−	0.252775i	−0.991981	−	0.126388i	$-0.959662\pi$
$509$		−	8.63621e12i		−	0.252775i	0.991981	−	0.126388i	$-0.0403383\pi$
$510$		0			0
$511$	−1.06994e13			−0.307083
$512$		0			0
$513$	−1.03050e13	+	1.03050e13i	−0.290044	+	0.290044i
$514$		0			0
$515$	−6.57355e12	−	9.39078e11i	−0.181453	−	0.0259218i
$516$		0			0
$517$	−2.98833e13	−	2.98833e13i	−0.809051	−	0.809051i
$518$		0			0
$519$			4.25941e13i			1.13113i
$520$		0			0
$521$	−6.27326e13			−1.63420			−0.817099	−	0.576497i	$-0.804419\pi$
$521$	−6.27326e13			−1.63420			−0.817099	+	0.576497i	$0.804419\pi$
$522$		0			0
$523$	−1.48951e12	+	1.48951e12i	−0.0380659	+	0.0380659i	−0.725884	−	0.687818i	$-0.758569\pi$
$523$	−1.48951e12	+	1.48951e12i	−0.0380659	+	0.0380659i	0.687818	+	0.725884i	$0.258569\pi$
$524$		0			0
$525$	−8.41357e12	+	2.88465e13i	−0.210952	+	0.723264i
$526$		0			0
$527$	1.89244e13	+	1.89244e13i	0.465553	+	0.465553i
$528$		0			0
$529$		−	1.32430e13i		−	0.319673i
$530$		0			0
$531$	−5.50327e12			−0.130361
$532$		0			0
$533$	3.55922e13	−	3.55922e13i	0.827405	−	0.827405i
$534$		0			0
$535$	−8.86323e11	+	6.20426e12i	−0.0202219	+	0.141554i
$536$		0			0
$537$	3.31250e13	+	3.31250e13i	0.741796	+	0.741796i
$538$		0			0
$539$		−	2.44699e13i		−	0.537884i
$540$		0			0
$541$	−8.97115e13			−1.93581			−0.967903	−	0.251324i	$-0.919134\pi$
$541$	−8.97115e13			−1.93581			−0.967903	+	0.251324i	$0.919134\pi$
$542$		0			0
$543$	2.43391e13	−	2.43391e13i	0.515590	−	0.515590i
$544$		0			0
$545$	−1.55324e13	+	1.16493e13i	−0.323040	+	0.242280i
$546$		0			0
$547$	−3.39955e13	−	3.39955e13i	−0.694200	−	0.694200i	0.268953	−	0.963153i	$-0.413322\pi$
$547$	−3.39955e13	−	3.39955e13i	−0.694200	−	0.694200i	−0.963153	+	0.268953i	$0.913322\pi$
$548$		0			0
$549$		−	7.18515e12i		−	0.144070i
$550$		0			0
$551$	2.73086e13			0.537702
$552$		0			0
$553$	−1.65449e13	+	1.65449e13i	−0.319919	+	0.319919i
$554$		0			0
$555$	−3.86962e13	−	5.15949e13i	−0.734858	−	0.979811i
$556$		0			0
$557$	9.51915e12	+	9.51915e12i	0.177551	+	0.177551i	0.790287	−	0.612737i	$-0.209931\pi$
$557$	9.51915e12	+	9.51915e12i	0.177551	+	0.177551i	−0.612737	+	0.790287i	$0.709931\pi$
$558$		0			0
$559$		−	2.76228e13i		−	0.506068i
$560$		0			0
$561$	1.19314e14			2.14722
$562$		0			0
$563$	−3.63651e13	+	3.63651e13i	−0.642900	+	0.642900i	−0.951267	−	0.308367i	$-0.900217\pi$
$563$	−3.63651e13	+	3.63651e13i	−0.642900	+	0.642900i	0.308367	+	0.951267i	$0.400217\pi$
$564$		0			0
$565$	7.85360e13	+	1.12194e13i	1.36404	+	0.194863i
$566$		0			0
$567$	3.27210e13	+	3.27210e13i	0.558356	+	0.558356i
$568$		0			0
$569$		−	2.82859e13i		−	0.474252i	−0.971479	−	0.237126i	$-0.923795\pi$
$569$		−	2.82859e13i		−	0.474252i	0.971479	−	0.237126i	$-0.0762054\pi$
$570$		0			0
$571$	−2.19201e12			−0.0361129			−0.0180564	−	0.999837i	$-0.505748\pi$
$571$	−2.19201e12			−0.0361129			−0.0180564	+	0.999837i	$0.505748\pi$
$572$		0			0
$573$	−2.39810e13	+	2.39810e13i	−0.388235	+	0.388235i
$574$		0			0
$575$	3.47189e13	+	6.33110e13i	0.552366	+	1.00726i
$576$		0			0
$577$	−2.97579e13	−	2.97579e13i	−0.465289	−	0.465289i	0.435095	−	0.900384i	$-0.356715\pi$
$577$	−2.97579e13	−	2.97579e13i	−0.465289	−	0.465289i	−0.900384	+	0.435095i	$0.856715\pi$
$578$		0			0
$579$		−	7.78821e13i		−	1.19686i
$580$		0			0
$581$	8.71608e13			1.31656
$582$		0			0
$583$	3.40529e13	−	3.40529e13i	0.505605	−	0.505605i
$584$		0			0
$585$	1.15279e12	−	8.06955e12i	0.0168256	−	0.117780i
$586$		0			0
$587$	−4.60333e13	−	4.60333e13i	−0.660513	−	0.660513i	0.294988	−	0.955501i	$-0.404684\pi$
$587$	−4.60333e13	−	4.60333e13i	−0.660513	−	0.660513i	−0.955501	+	0.294988i	$0.904684\pi$
$588$		0			0
$589$			1.10883e13i			0.156419i
$590$		0			0
$591$	2.89230e13			0.401149
$592$		0			0
$593$	−6.17714e12	+	6.17714e12i	−0.0842391	+	0.0842391i	−0.747971	−	0.663732i	$-0.768972\pi$
$593$	−6.17714e12	+	6.17714e12i	−0.0842391	+	0.0842391i	0.663732	+	0.747971i	$0.268972\pi$
$594$		0			0
$595$	7.90272e13	−	5.92704e13i	1.05972	−	0.794791i
$596$		0			0
$597$	−8.28363e13	−	8.28363e13i	−1.09232	−	1.09232i
$598$		0			0
$599$			5.80310e13i			0.752534i	0.926511	+	0.376267i	$0.122792\pi$
$599$			5.80310e13i			0.752534i	−0.926511	+	0.376267i	$0.877208\pi$
$600$		0			0
$601$	1.24750e14			1.59100			0.795499	−	0.605955i	$-0.207209\pi$
$601$	1.24750e14			1.59100			0.795499	+	0.605955i	$0.207209\pi$
$602$		0			0
$603$	7.62828e12	−	7.62828e12i	0.0956842	−	0.0956842i
$604$		0			0
$605$	−7.74270e12	−	1.03236e13i	−0.0955247	−	0.127366i
$606$		0			0
$607$	9.34184e13	+	9.34184e13i	1.13368	+	1.13368i	0.989561	+	0.144115i	$0.0460335\pi$
$607$	9.34184e13	+	9.34184e13i	1.13368	+	1.13368i	0.144115	+	0.989561i	$0.453967\pi$
$608$		0			0
$609$		−	7.62805e13i		−	0.910598i
$610$		0			0
$611$	8.01802e13			0.941588
$612$		0			0
$613$	1.42802e13	−	1.42802e13i	0.164980	−	0.164980i	−0.619789	−	0.784769i	$-0.712782\pi$
$613$	1.42802e13	−	1.42802e13i	0.164980	−	0.164980i	0.784769	+	0.619789i	$0.212782\pi$
$614$		0			0
$615$	1.22499e14	+	1.74998e13i	1.39237	+	0.198910i
$616$		0			0
$617$	−4.17740e12	−	4.17740e12i	−0.0467176	−	0.0467176i	0.683362	−	0.730080i	$-0.260517\pi$
$617$	−4.17740e12	−	4.17740e12i	−0.0467176	−	0.0467176i	−0.730080	+	0.683362i	$0.760517\pi$
$618$		0			0
$619$		−	4.07977e13i		−	0.448934i	−0.974482	−	0.224467i	$-0.927936\pi$
$619$		−	4.07977e13i		−	0.448934i	0.974482	−	0.224467i	$-0.0720642\pi$
$620$		0			0
$621$	9.78204e13			1.05918
$622$		0			0
$623$	−6.53340e13	+	6.53340e13i	−0.696144	+	0.696144i
$624$		0			0
$625$	−8.04138e13	−	5.12695e13i	−0.843200	−	0.537600i
$626$		0			0
$627$	3.49545e13	+	3.49545e13i	0.360716	+	0.360716i
$628$		0			0
$629$			2.12022e14i			2.15342i
$630$		0			0
$631$	−8.03556e13			−0.803284			−0.401642	−	0.915797i	$-0.631560\pi$
$631$	−8.03556e13			−0.803284			−0.401642	+	0.915797i	$0.631560\pi$
$632$		0			0
$633$	−2.52530e13	+	2.52530e13i	−0.248482	+	0.248482i
$634$		0			0
$635$	−8.16382e12	+	5.71467e13i	−0.0790723	+	0.553506i
$636$		0			0
$637$	3.28277e13	+	3.28277e13i	0.313000	+	0.313000i
$638$		0			0
$639$		−	2.47454e13i		−	0.232269i
$640$		0			0
$641$	9.43477e13			0.871849			0.435924	−	0.899983i	$-0.356421\pi$
$641$	9.43477e13			0.871849			0.435924	+	0.899983i	$0.356421\pi$
$642$		0			0
$643$	−1.98925e13	+	1.98925e13i	−0.180981	+	0.180981i	−0.791783	−	0.610802i	$-0.790847\pi$
$643$	−1.98925e13	+	1.98925e13i	−0.180981	+	0.180981i	0.610802	+	0.791783i	$0.290847\pi$
$644$		0			0
$645$	5.43258e13	−	4.07443e13i	0.486640	−	0.364980i
$646$		0			0
$647$	−5.97289e13	−	5.97289e13i	−0.526821	−	0.526821i	0.392802	−	0.919623i	$-0.371506\pi$
$647$	−5.97289e13	−	5.97289e13i	−0.526821	−	0.526821i	−0.919623	+	0.392802i	$0.871506\pi$
$648$		0			0
$649$		−	1.20350e14i		−	1.04526i
$650$		0			0
$651$	3.09727e13			0.264895
$652$		0			0
$653$	−9.87072e13	+	9.87072e13i	−0.831349	+	0.831349i	−0.987701	−	0.156353i	$-0.950026\pi$
$653$	−9.87072e13	+	9.87072e13i	−0.831349	+	0.831349i	0.156353	+	0.987701i	$0.450026\pi$
$654$		0			0
$655$	−9.75416e13	−	1.30055e14i	−0.809065	−	1.07875i
$656$		0			0
$657$	5.04553e12	+	5.04553e12i	0.0412174	+	0.0412174i
$658$		0			0
$659$		−	5.80689e13i		−	0.467215i	−0.972331	−	0.233607i	$-0.924947\pi$
$659$		−	5.80689e13i		−	0.467215i	0.972331	−	0.233607i	$-0.0750530\pi$
$660$		0			0
$661$	−1.53137e14			−1.21360			−0.606798	−	0.794856i	$-0.707546\pi$
$661$	−1.53137e14			−1.21360			−0.606798	+	0.794856i	$0.707546\pi$
$662$		0			0
$663$	−1.60066e14	+	1.60066e14i	−1.24949	+	1.24949i
$664$		0			0
$665$	4.05161e13	+	5.78801e12i	0.311544	+	0.0445062i
$666$		0			0
$667$	−1.29613e14	−	1.29613e14i	−0.981792	−	0.981792i
$668$		0			0
$669$		−	4.61357e13i		−	0.344275i
$670$		0			0
$671$	1.57131e14			1.15518
$672$		0			0
$673$	−8.75360e13	+	8.75360e13i	−0.634032	+	0.634032i	−0.949077	−	0.315045i	$-0.897980\pi$
$673$	−8.75360e13	+	8.75360e13i	−0.634032	+	0.634032i	0.315045	+	0.949077i	$0.397980\pi$
$674$		0			0
$675$	−1.13283e14	+	6.21228e13i	−0.808434	+	0.443335i
$676$		0			0
$677$	1.59452e12	+	1.59452e12i	0.0112121	+	0.0112121i	0.712691	−	0.701478i	$-0.247476\pi$
$677$	1.59452e12	+	1.59452e12i	0.0112121	+	0.0112121i	−0.701478	+	0.712691i	$0.747476\pi$
$678$		0			0
$679$		−	1.07670e13i		−	0.0746014i
$680$		0			0
$681$	−4.21882e13			−0.288042
$682$		0			0
$683$	5.65796e13	−	5.65796e13i	0.380677	−	0.380677i	−0.490669	−	0.871346i	$-0.663248\pi$
$683$	5.65796e13	−	5.65796e13i	0.380677	−	0.380677i	0.871346	+	0.490669i	$0.163248\pi$
$684$		0			0
$685$	−1.02384e13	+	7.16689e13i	−0.0678859	+	0.475201i
$686$		0			0
$687$	−6.02297e13	−	6.02297e13i	−0.393575	−	0.393575i
$688$		0			0
$689$			9.13676e13i			0.588432i
$690$		0			0
$691$	−4.98558e12			−0.0316465			−0.0158232	−	0.999875i	$-0.505037\pi$
$691$	−4.98558e12			−0.0316465			−0.0158232	+	0.999875i	$0.505037\pi$
$692$		0			0
$693$	1.15586e13	−	1.15586e13i	0.0723165	−	0.0723165i
$694$		0			0
$695$	6.53724e13	−	4.90293e13i	0.403153	−	0.302365i
$696$		0			0
$697$	−2.87652e14	−	2.87652e14i	−1.74865	−	1.74865i
$698$		0			0
$699$			3.65249e13i			0.218879i
$700$		0			0
$701$	−1.80303e14			−1.06516			−0.532578	−	0.846381i	$-0.678777\pi$
$701$	−1.80303e14			−1.06516			−0.532578	+	0.846381i	$0.678777\pi$
$702$		0			0
$703$	−6.21147e13	+	6.21147e13i	−0.361758	+	0.361758i
$704$		0			0
$705$	1.18268e14	+	1.57691e14i	0.679080	+	0.905441i
$706$		0			0
$707$	1.70187e13	+	1.70187e13i	0.0963448	+	0.0963448i
$708$		0			0
$709$		−	3.11543e14i		−	1.73895i	−0.493979	−	0.869474i	$-0.664458\pi$
$709$		−	3.11543e14i		−	1.73895i	0.493979	−	0.869474i	$-0.335542\pi$
$710$		0			0
$711$	1.56042e13			0.0858805
$712$		0			0
$713$	5.26277e13	−	5.26277e13i	0.285606	−	0.285606i
$714$		0			0
$715$	1.76472e14	+	2.52102e13i	0.944375	+	0.134911i
$716$		0			0
$717$	7.23989e12	+	7.23989e12i	0.0382064	+	0.0382064i
$718$		0			0
$719$			1.65068e14i			0.859051i	0.903055	+	0.429525i	$0.141319\pi$
$719$			1.65068e14i			0.859051i	−0.903055	+	0.429525i	$0.858681\pi$
$720$		0			0
$721$	2.52634e13			0.129663
$722$		0			0
$723$	−1.49012e14	+	1.49012e14i	−0.754273	+	0.754273i
$724$		0			0
$725$	2.32414e14	+	6.77875e13i	1.16031	+	0.338423i
$726$		0			0
$727$	−2.15314e14	−	2.15314e14i	−1.06023	−	1.06023i	−0.998066	−	0.0621642i	$-0.980200\pi$
$727$	−2.15314e14	−	2.15314e14i	−1.06023	−	1.06023i	−0.0621642	−	0.998066i	$-0.519800\pi$
$728$		0			0
$729$			1.71318e14i			0.832081i
$730$		0			0
$731$	−2.23244e14			−1.06953
$732$		0			0
$733$	−2.78787e14	+	2.78787e14i	−1.31750	+	1.31750i	−0.401759	+	0.915746i	$0.631601\pi$
$733$	−2.78787e14	+	2.78787e14i	−1.31750	+	1.31750i	−0.915746	+	0.401759i	$0.868399\pi$
$734$		0			0
$735$	−1.61406e13	+	1.12984e14i	−0.0752459	+	0.526721i
$736$		0			0
$737$	1.66822e14	+	1.66822e14i	0.767212	+	0.767212i
$738$		0			0
$739$			2.05171e14i			0.930879i	0.885080	+	0.465440i	$0.154104\pi$
$739$			2.05171e14i			0.930879i	−0.885080	+	0.465440i	$0.845896\pi$
$740$		0			0
$741$	−9.37868e13			−0.419808
$742$		0			0
$743$	−1.59047e14	+	1.59047e14i	−0.702396	+	0.702396i	−0.964924	−	0.262528i	$-0.915444\pi$
$743$	−1.59047e14	+	1.59047e14i	−0.702396	+	0.702396i	0.262528	+	0.964924i	$0.415444\pi$
$744$		0			0
$745$	1.07841e13	−	8.08805e12i	0.0469895	−	0.0352422i
$746$		0			0
$747$	−4.11025e13	−	4.11025e13i	−0.176712	−	0.176712i
$748$		0			0
$749$		−	2.38442e13i		−	0.101152i
$750$		0			0
$751$	1.40008e14			0.586074			0.293037	−	0.956101i	$-0.405334\pi$
$751$	1.40008e14			0.586074			0.293037	+	0.956101i	$0.405334\pi$
$752$		0			0
$753$	−8.29303e13	+	8.29303e13i	−0.342561	+	0.342561i
$754$		0			0
$755$	2.13503e14	+	2.84671e14i	0.870302	+	1.16040i
$756$		0			0
$757$	7.07881e13	+	7.07881e13i	0.284761	+	0.284761i	0.835004	−	0.550243i	$-0.185465\pi$
$757$	7.07881e13	+	7.07881e13i	0.284761	+	0.284761i	−0.550243	+	0.835004i	$0.685465\pi$
$758$		0			0
$759$		−	3.31805e14i		−	1.31727i
$760$		0			0
$761$	−2.84953e14			−1.11648			−0.558238	−	0.829681i	$-0.688523\pi$
$761$	−2.84953e14			−1.11648			−0.558238	+	0.829681i	$0.688523\pi$
$762$		0			0
$763$	5.22324e13	−	5.22324e13i	0.201984	−	0.201984i
$764$		0			0
$765$	−6.52172e13	−	9.31674e12i	−0.248917	−	0.0355596i
$766$		0			0
$767$	1.61456e14	+	1.61456e14i	0.608245	+	0.608245i
$768$		0			0
$769$		−	3.59991e14i		−	1.33863i	−0.742980	−	0.669314i	$-0.766588\pi$
$769$		−	3.59991e14i		−	1.33863i	0.742980	−	0.669314i	$-0.233412\pi$
$770$		0			0
$771$	4.88899e14			1.79451
$772$		0			0
$773$	1.40032e14	−	1.40032e14i	0.507375	−	0.507375i	−0.406345	−	0.913720i	$-0.633197\pi$
$773$	1.40032e14	−	1.40032e14i	0.507375	−	0.507375i	0.913720	+	0.406345i	$0.133197\pi$
$774$		0			0
$775$	−2.75242e13	+	9.43687e13i	−0.0984479	+	0.337536i
$776$		0			0
$777$	1.73503e14	+	1.73503e14i	0.612637	+	0.612637i
$778$		0			0
$779$		−	1.68543e14i		−	0.587520i
$780$		0			0
$781$	5.41154e14			1.86237
$782$		0			0
$783$	2.31917e14	−	2.31917e14i	0.787997	−	0.787997i
$784$		0			0
$785$	6.52674e12	−	4.56872e13i	0.0218951	−	0.153266i
$786$		0			0
$787$	−2.99888e14	−	2.99888e14i	−0.993312	−	0.993312i	0.00666595	−	0.999978i	$-0.497878\pi$
$787$	−2.99888e14	−	2.99888e14i	−0.993312	−	0.993312i	−0.999978	+	0.00666595i	$0.997878\pi$
$788$		0			0
$789$		−	3.33816e14i		−	1.09175i
$790$		0			0
$791$	−3.01830e14			−0.974719
$792$		0			0
$793$	−2.10800e14	+	2.10800e14i	−0.672208	+	0.672208i
$794$		0			0
$795$	−1.79693e14	+	1.34770e14i	−0.565842	+	0.424381i
$796$		0			0
$797$	−2.14433e14	−	2.14433e14i	−0.666807	−	0.666807i	0.290169	−	0.956976i	$-0.406289\pi$
$797$	−2.14433e14	−	2.14433e14i	−0.666807	−	0.666807i	−0.956976	+	0.290169i	$0.906289\pi$
$798$		0			0
$799$		−	6.48007e14i		−	1.98997i
$800$		0			0
$801$	6.16193e13			0.186876
$802$		0			0
$803$	−1.10340e14	+	1.10340e14i	−0.330488	+	0.330488i
$804$		0			0
$805$	−1.64828e14	−	2.19770e14i	−0.487585	−	0.650113i
$806$		0			0
$807$	1.90956e14	+	1.90956e14i	0.557913	+	0.557913i
$808$		0			0
$809$			3.71569e14i			1.07225i	0.844138	+	0.536126i	$0.180113\pi$
$809$			3.71569e14i			1.07225i	−0.844138	+	0.536126i	$0.819887\pi$
$810$		0			0
$811$	−4.25889e14			−1.21393			−0.606963	−	0.794730i	$-0.707612\pi$
$811$	−4.25889e14			−1.21393			−0.606963	+	0.794730i	$0.707612\pi$
$812$		0			0
$813$	−1.31658e14	+	1.31658e14i	−0.370677	+	0.370677i
$814$		0			0
$815$	2.09259e14	+	2.98941e13i	0.581963	+	0.0831376i
$816$		0			0
$817$	−6.54023e13	−	6.54023e13i	−0.179673	−	0.179673i
$818$		0			0
$819$			3.10129e13i			0.0841633i
$820$		0			0
$821$	4.73944e14			1.27061			0.635304	−	0.772262i	$-0.280875\pi$
$821$	4.73944e14			1.27061			0.635304	+	0.772262i	$0.280875\pi$
$822$		0			0
$823$	3.93378e14	−	3.93378e14i	1.04186	−	1.04186i	0.0427794	−	0.999085i	$-0.486379\pi$
$823$	3.93378e14	−	3.93378e14i	1.04186	−	1.04186i	0.999085	−	0.0427794i	$-0.0136212\pi$
$824$		0			0
$825$	2.10719e14	+	3.84253e14i	0.551359	+	1.00542i
$826$		0			0
$827$	2.32822e14	+	2.32822e14i	0.601861	+	0.601861i	0.940806	−	0.338945i	$-0.110070\pi$
$827$	2.32822e14	+	2.32822e14i	0.601861	+	0.601861i	−0.338945	+	0.940806i	$0.610070\pi$
$828$		0			0
$829$		−	9.73337e13i		−	0.248594i	−0.992245	−	0.124297i	$-0.960332\pi$
$829$		−	9.73337e13i		−	0.248594i	0.992245	−	0.124297i	$-0.0396675\pi$
$830$		0			0
$831$	−3.15703e14			−0.796661
$832$		0			0
$833$	2.65310e14	−	2.65310e14i	0.661499	−	0.661499i
$834$		0			0
$835$	7.39258e12	−	5.17481e13i	0.0182123	−	0.127486i
$836$		0			0
$837$	9.41670e13	+	9.41670e13i	0.229230	+	0.229230i
$838$		0			0
$839$		−	3.82848e14i		−	0.920910i	−0.887683	−	0.460455i	$-0.847686\pi$
$839$		−	3.82848e14i		−	0.920910i	0.887683	−	0.460455i	$-0.152314\pi$
$840$		0			0
$841$	−1.93879e14			−0.460840
$842$		0			0
$843$	−1.44442e14	+	1.44442e14i	−0.339278	+	0.339278i
$844$		0			0
$845$	7.40789e13	−	5.55592e13i	0.171954	−	0.128965i
$846$		0			0
$847$	3.47162e13	+	3.47162e13i	0.0796371	+	0.0796371i
$848$		0			0
$849$		−	2.41650e14i		−	0.547833i
$850$		0			0
$851$	5.89622e14			1.32107
$852$		0			0
$853$	4.25918e14	−	4.25918e14i	0.943149	−	0.943149i	−0.0553196	−	0.998469i	$-0.517618\pi$
$853$	4.25918e14	−	4.25918e14i	0.943149	−	0.943149i	0.998469	+	0.0553196i	$0.0176178\pi$
$854$		0			0
$855$	−1.63768e13	−	2.18357e13i	−0.0358424	−	0.0477899i
$856$		0			0
$857$	−3.58497e14	−	3.58497e14i	−0.775498	−	0.775498i	0.203563	−	0.979062i	$-0.434748\pi$
$857$	−3.58497e14	−	3.58497e14i	−0.775498	−	0.775498i	−0.979062	+	0.203563i	$0.934748\pi$
$858$		0			0
$859$			7.30888e14i			1.56273i	0.624071	+	0.781367i	$0.285477\pi$
$859$			7.30888e14i			1.56273i	−0.624071	+	0.781367i	$0.714523\pi$
$860$		0			0
$861$	−4.70786e14			−0.994965
$862$		0			0
$863$	−1.48513e14	+	1.48513e14i	−0.310249	+	0.310249i	−0.845006	−	0.534757i	$-0.820403\pi$
$863$	−1.48513e14	+	1.48513e14i	−0.310249	+	0.310249i	0.534757	+	0.845006i	$0.320403\pi$
$864$		0			0
$865$	5.09151e14	+	7.27359e13i	1.05140	+	0.150199i
$866$		0			0
$867$	9.24709e14	+	9.24709e14i	1.88760	+	1.88760i
$868$		0			0
$869$			3.41247e14i			0.688604i
$870$		0			0
$871$	−4.47601e14			−0.892895
$872$		0			0
$873$	−5.07742e12	+	5.07742e12i	−0.0100132	+	0.0100132i
$874$		0			0
$875$	3.30451e14	+	1.49832e14i	0.644268	+	0.292122i
$876$		0			0
$877$	−3.85609e13	−	3.85609e13i	−0.0743274	−	0.0743274i	0.668966	−	0.743293i	$-0.266737\pi$
$877$	−3.85609e13	−	3.85609e13i	−0.0743274	−	0.0743274i	−0.743293	+	0.668966i	$0.766737\pi$
$878$		0			0
$879$		−	6.56005e13i		−	0.125015i
$880$		0			0
$881$	−4.11264e14			−0.774892			−0.387446	−	0.921892i	$-0.626643\pi$
$881$	−4.11264e14			−0.774892			−0.387446	+	0.921892i	$0.626643\pi$
$882$		0			0
$883$	6.34116e14	−	6.34116e14i	1.18131	−	1.18131i	0.201908	−	0.979404i	$-0.435286\pi$
$883$	6.34116e14	−	6.34116e14i	1.18131	−	1.18131i	0.979404	−	0.201908i	$-0.0647143\pi$
$884$		0			0
$885$	−7.93841e13	+	5.55689e14i	−0.146224	+	1.02356i
$886$		0			0
$887$	−7.15241e14	−	7.15241e14i	−1.30267	−	1.30267i	−0.926586	−	0.376083i	$-0.877271\pi$
$887$	−7.15241e14	−	7.15241e14i	−1.30267	−	1.30267i	−0.376083	−	0.926586i	$-0.622729\pi$
$888$		0			0
$889$		−	2.19626e14i		−	0.395526i
$890$		0			0
$891$	6.74885e14			1.20182
$892$		0			0
$893$	1.89842e14	−	1.89842e14i	0.334299	−	0.334299i
$894$		0			0
$895$	4.52527e14	−	3.39395e14i	0.788006	−	0.591005i
$896$		0			0
$897$	4.45134e14	+	4.45134e14i	0.766530	+	0.766530i
$898$		0			0
$899$		−	2.49545e14i		−	0.424962i
$900$		0			0
$901$	7.38423e14			1.24360
$902$		0			0
$903$	−1.82687e14	+	1.82687e14i	−0.304276	+	0.304276i
$904$		0			0
$905$	−2.49376e14	−	3.32501e14i	−0.410782	−	0.547709i
$906$		0			0
$907$	−4.62743e14	−	4.62743e14i	−0.753882	−	0.753882i	0.221320	−	0.975201i	$-0.428964\pi$
$907$	−4.62743e14	−	4.62743e14i	−0.753882	−	0.753882i	−0.975201	+	0.221320i	$0.928964\pi$
$908$		0			0
$909$		−	1.60510e13i		−	0.0258633i
$910$		0			0
$911$	2.41312e14			0.384580			0.192290	−	0.981338i	$-0.438409\pi$
$911$	2.41312e14			0.384580			0.192290	+	0.981338i	$0.438409\pi$
$912$		0			0
$913$	8.98864e14	−	8.98864e14i	1.41690	−	1.41690i
$914$		0			0
$915$	−7.25515e14	−	1.03645e14i	−1.13120	−	0.161601i
$916$		0			0
$917$	4.37351e14	+	4.37351e14i	0.674502	+	0.674502i
$918$		0			0
$919$			3.74682e14i			0.571591i	0.958291	+	0.285795i	$0.0922577\pi$
$919$			3.74682e14i			0.571591i	−0.958291	+	0.285795i	$0.907742\pi$
$920$		0			0
$921$	4.03169e14			0.608399
$922$		0			0
$923$	−7.25988e14	+	7.25988e14i	−1.08373	+	1.08373i
$924$		0			0
$925$	−6.82822e14	+	3.74451e14i	−1.00832	+	0.552951i
$926$		0			0
$927$	−1.19135e13	−	1.19135e13i	−0.0174037	−	0.0174037i
$928$		0			0
$929$			4.47351e14i			0.646501i	0.946313	+	0.323251i	$0.104776\pi$
$929$			4.47351e14i			0.646501i	−0.946313	+	0.323251i	$0.895224\pi$
$930$		0			0
$931$	1.55452e14			0.222253
$932$		0			0
$933$	−9.71983e14	+	9.71983e14i	−1.37484	+	1.37484i
$934$		0			0
$935$	2.03746e14	−	1.42622e15i	0.285123	−	1.99586i
$936$		0			0
$937$	−2.34215e14	−	2.34215e14i	−0.324278	−	0.324278i	0.526128	−	0.850405i	$-0.323643\pi$
$937$	−2.34215e14	−	2.34215e14i	−0.324278	−	0.324278i	−0.850405	+	0.526128i	$0.823643\pi$
$938$		0			0
$939$			3.07469e14i			0.421185i
$940$		0			0
$941$	−3.80526e13			−0.0515746			−0.0257873	−	0.999667i	$-0.508209\pi$
$941$	−3.80526e13			−0.0515746			−0.0257873	+	0.999667i	$0.508209\pi$
$942$		0			0
$943$	−7.99943e14	+	7.99943e14i	−1.07276	+	1.07276i
$944$		0			0
$945$	3.93236e14	−	2.94927e14i	0.521788	−	0.391341i
$946$		0			0
$947$	−1.26567e13	−	1.26567e13i	−0.0166176	−	0.0166176i	0.698749	−	0.715367i	$-0.253740\pi$
$947$	−1.26567e13	−	1.26567e13i	−0.0166176	−	0.0166176i	−0.715367	+	0.698749i	$0.753740\pi$
$948$		0			0
$949$		−	2.96054e14i		−	0.384627i
$950$		0			0
$951$	−4.26883e14			−0.548790
$952$		0			0
$953$	−7.73544e14	+	7.73544e14i	−0.984057	+	0.984057i	−0.999875	−	0.0158178i	$-0.994965\pi$
$953$	−7.73544e14	+	7.73544e14i	−0.984057	+	0.984057i	0.0158178	+	0.999875i	$0.494965\pi$
$954$		0			0
$955$	2.45707e14	+	3.27610e14i	0.309315	+	0.412420i
$956$		0			0
$957$	−7.86659e14	−	7.86659e14i	−0.980001	−	0.980001i
$958$		0			0
$959$		−	2.75438e14i		−	0.339571i
$960$		0			0
$961$	−7.18304e14			−0.876378
$962$		0			0
$963$	−1.12442e13	+	1.12442e13i	−0.0135768	+	0.0135768i
$964$		0			0
$965$	−9.30967e14	−	1.32995e14i	−1.11249	−	0.158928i
$966$		0			0
$967$	5.57904e14	+	5.57904e14i	0.659822	+	0.659822i	0.955338	−	0.295516i	$-0.0954915\pi$
$967$	5.57904e14	+	5.57904e14i	0.659822	+	0.659822i	−0.295516	+	0.955338i	$0.595492\pi$
$968$		0			0
$969$			7.57975e14i			0.887229i
$970$		0			0
$971$	−1.01087e14			−0.117112			−0.0585559	−	0.998284i	$-0.518650\pi$
$971$	−1.01087e14			−0.117112			−0.0585559	+	0.998284i	$0.518650\pi$
$972$		0			0
$973$	−2.19834e14	+	2.19834e14i	−0.252076	+	0.252076i
$974$		0			0
$975$	−7.98188e14	−	2.32805e14i	−0.905903	−	0.264222i
$976$		0			0
$977$	−7.13366e14	−	7.13366e14i	−0.801382	−	0.801382i	0.181929	−	0.983312i	$-0.441766\pi$
$977$	−7.13366e14	−	7.13366e14i	−0.801382	−	0.801382i	−0.983312	+	0.181929i	$0.941766\pi$
$978$		0			0
$979$			1.34754e15i			1.49840i
$980$		0			0
$981$	−4.92626e13			−0.0542215
$982$		0			0
$983$	5.14731e14	−	5.14731e14i	0.560806	−	0.560806i	−0.368731	−	0.929536i	$-0.620208\pi$
$983$	5.14731e14	−	5.14731e14i	0.560806	−	0.560806i	0.929536	+	0.368731i	$0.120208\pi$
$984$		0			0
$985$	4.93904e13	−	3.45733e14i	0.0532674	−	0.372872i
$986$		0			0
$987$	−5.30282e14	−	5.30282e14i	−0.566136	−	0.566136i
$988$		0			0
$989$			6.20830e14i			0.656132i
$990$		0			0
$991$	−1.13356e15			−1.18598			−0.592990	−	0.805210i	$-0.702053\pi$
$991$	−1.13356e15			−1.18598			−0.592990	+	0.805210i	$0.702053\pi$
$992$		0			0
$993$	8.82137e14	−	8.82137e14i	0.913671	−	0.913671i
$994$		0			0
$995$	−1.13164e15	+	8.48732e14i	−1.16036	+	0.870273i
$996$		0			0
$997$	6.55685e14	+	6.55685e14i	0.665609	+	0.665609i	0.956696	−	0.291087i	$-0.0940171\pi$
$997$	6.55685e14	+	6.55685e14i	0.665609	+	0.665609i	−0.291087	+	0.956696i	$0.594017\pi$
$998$		0			0
$999$			1.05501e15i			1.06030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.11.p.b.17.1		2
4.3	odd	2		10.11.c.a.7.1	yes	2
5.3	odd	4	inner	80.11.p.b.33.1		2
12.11	even	2		90.11.g.b.37.1		2
20.3	even	4		10.11.c.a.3.1	✓	2
20.7	even	4		50.11.c.c.43.1		2
20.19	odd	2		50.11.c.c.7.1		2
60.23	odd	4		90.11.g.b.73.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.11.c.a.3.1	✓	2	20.3	even	4
10.11.c.a.7.1	yes	2	4.3	odd	2
50.11.c.c.7.1		2	20.19	odd	2
50.11.c.c.43.1		2	20.7	even	4
80.11.p.b.17.1		2	1.1	even	1	trivial
80.11.p.b.33.1		2	5.3	odd	4	inner
90.11.g.b.37.1		2	12.11	even	2
90.11.g.b.73.1		2	60.23	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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	80.p (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(183.000 - 183.000i) q^{3} +(-1875.00 - 2500.00i) q^{5} +(8407.00 + 8407.00i) q^{7} -7929.00i q^{9} +173398. q^{11} +(-232623. + 232623. i) q^{13} +(-800625. - 114375. i) q^{15} +(1.88003e6 + 1.88003e6i) q^{17} +1.10156e6i q^{19} +3.07696e6 q^{21} +(5.22826e6 - 5.22826e6i) q^{23} +(-2.73438e6 + 9.37500e6i) q^{25} +(9.35496e6 + 9.35496e6i) q^{27} -2.47908e7i q^{29} +1.00660e7 q^{31} +(3.17318e7 - 3.17318e7i) q^{33} +(5.25438e6 - 3.67806e7i) q^{35} +(5.63879e7 + 5.63879e7i) q^{37} +8.51400e7i q^{39} -1.53004e8 q^{41} +(-5.93725e7 + 5.93725e7i) q^{43} +(-1.98225e7 + 1.48669e7i) q^{45} +(-1.72339e8 - 1.72339e8i) q^{47} -1.41120e8i q^{49} +6.88092e8 q^{51} +(1.96386e8 - 1.96386e8i) q^{53} +(-3.25121e8 - 4.33495e8i) q^{55} +(2.01585e8 + 2.01585e8i) q^{57} -6.94069e8i q^{59} +9.06186e8 q^{61} +(6.66591e7 - 6.66591e7i) q^{63} +(1.01773e9 + 1.45389e8i) q^{65} +(9.62074e8 + 9.62074e8i) q^{67} -1.91354e9i q^{69} +3.12088e9 q^{71} +(-6.36339e8 + 6.36339e8i) q^{73} +(1.21523e9 + 2.21602e9i) q^{75} +(1.45776e9 + 1.45776e9i) q^{77} +1.96800e9i q^{79} +3.89211e9 q^{81} +(5.18382e9 - 5.18382e9i) q^{83} +(1.17502e9 - 8.22514e9i) q^{85} +(-4.53672e9 - 4.53672e9i) q^{87} +7.77138e9i q^{89} -3.91132e9 q^{91} +(1.84208e9 - 1.84208e9i) q^{93} +(2.75390e9 - 2.06542e9i) q^{95} +(-6.40361e8 - 6.40361e8i) q^{97} -1.37487e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 366 q^{3} - 3750 q^{5} + 16814 q^{7} + 346796 q^{11} - 465246 q^{13} - 1601250 q^{15} + 3760066 q^{17} + 6153924 q^{21} + 10456526 q^{23} - 5468750 q^{25} + 18709920 q^{27} + 20131996 q^{31} + 63463668 q^{33}+ \cdots - 1280722494 q^{97}+O(q^{100}) \) 2 * q + 366 * q^3 - 3750 * q^5 + 16814 * q^7 + 346796 * q^11 - 465246 * q^13 - 1601250 * q^15 + 3760066 * q^17 + 6153924 * q^21 + 10456526 * q^23 - 5468750 * q^25 + 18709920 * q^27 + 20131996 * q^31 + 63463668 * q^33 + 10508750 * q^35 + 112775826 * q^37 - 306007196 * q^41 - 118744914 * q^43 - 39645000 * q^45 - 344678706 * q^47 + 1376184156 * q^51 + 392771234 * q^53 - 650242500 * q^55 + 403170960 * q^57 + 1812371604 * q^61 + 133318206 * q^63 + 2035451250 * q^65 + 1924147934 * q^67 + 6241755196 * q^71 - 1272678526 * q^73 + 2430468750 * q^75 + 2915513972 * q^77 + 7784229762 * q^81 + 10367644206 * q^83 + 2350041250 * q^85 - 9073447440 * q^87 - 7822646244 * q^91 + 3684155268 * q^93 + 5507800000 * q^95 - 1280722494 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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