LMFDB - Embedded newform 196.14.e.a.177.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [196,14,Mod(165,196)] 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("196.165"); S:= CuspForms(chi, 14); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(196, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 14, names="a")

Level:	$N$	$=$	$196 = 2^{2} \cdot 7^{2}$
Weight:	$k$	$=$	$14$
Character orbit:	$[\chi]$	$=$	196.e (of order $3$ , degree $2$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,-468] 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:	$210.172620746$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{2} - x + 1$ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 4)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	196.177
Dual form			196.14.e.a.165.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-234.000 - 405.300i) q^{3} +(-28107.0 + 48682.8i) q^{5} +(687650. - 1.19104e6i) q^{9} +(3.19869e6 + 5.54029e6i) q^{11} +1.51997e7 q^{13} +2.63082e7 q^{15} +(-2.15571e7 - 3.73380e7i) q^{17} +(1.82558e8 - 3.16199e8i) q^{19} +(2.86134e7 - 4.95599e7i) q^{23} +(-9.69655e8 - 1.67949e9i) q^{25} -1.38978e9 q^{27} -4.64190e7 q^{29} +(2.84109e9 + 4.92092e9i) q^{31} +(1.49699e9 - 2.59286e9i) q^{33} +(9.43593e8 - 1.63435e9i) q^{37} +(-3.55674e9 - 6.16045e9i) q^{39} -7.33680e9 q^{41} -2.68867e10 q^{43} +(3.86555e10 + 6.69533e10i) q^{45} +(-5.09199e10 + 8.81959e10i) q^{47} +(-1.00887e10 + 1.74742e10i) q^{51} +(-1.39366e11 - 2.41389e11i) q^{53} -3.59622e11 q^{55} -1.70874e11 q^{57} +(-2.97870e10 - 5.15926e10i) q^{59} +(1.37422e10 - 2.38022e10i) q^{61} +(-4.27219e11 + 7.39965e11i) q^{65} +(-3.92205e11 - 6.79319e11i) q^{67} -2.67822e10 q^{69} -3.60365e11 q^{71} +(7.96318e11 + 1.37926e12i) q^{73} +(-4.53799e11 + 7.86002e11i) q^{75} +(1.15806e10 - 2.00582e10i) q^{79} +(-7.71126e11 - 1.33563e12i) q^{81} +2.05016e12 q^{83} +2.42362e12 q^{85} +(1.08620e10 + 1.88136e10i) q^{87} +(1.74270e12 - 3.01844e12i) q^{89} +(1.32963e12 - 2.30299e12i) q^{93} +(1.02623e13 + 1.77748e13i) q^{95} +6.70667e12 q^{97} +8.79831e12 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q - 468 q^{3} - 56214 q^{5} + 1375299 q^{9} + 6397380 q^{11} + 30399484 q^{13} + 52616304 q^{15} - 43114194 q^{17} + 365115484 q^{19} + 57226824 q^{23} - 1939310671 q^{25} - 2779566192 q^{27} - 92837988 q^{29}+ \cdots + 17596620633240 q^{99}+O(q^{100})$ 2 * q - 468 * q^3 - 56214 * q^5 + 1375299 * q^9 + 6397380 * q^11 + 30399484 * q^13 + 52616304 * q^15 - 43114194 * q^17 + 365115484 * q^19 + 57226824 * q^23 - 1939310671 * q^25 - 2779566192 * q^27 - 92837988 * q^29 + 5682185824 * q^31 + 2993973840 * q^33 + 1887185098 * q^37 - 7113479256 * q^39 - 14673605868 * q^41 - 53773349960 * q^43 + 77311057986 * q^45 - 101839834224 * q^47 - 20177442792 * q^51 - 278731884294 * q^53 - 719244638640 * q^55 - 341748093024 * q^57 - 59573945772 * q^59 + 27484470418 * q^61 - 854438296788 * q^65 - 784410054932 * q^67 - 53564307264 * q^69 - 720730455984 * q^71 + 1592635413718 * q^73 - 907597394028 * q^75 + 23161184752 * q^79 - 1542252338649 * q^81 + 4100316220872 * q^83 + 4847242603032 * q^85 + 21724089192 * q^87 + 3485391237126 * q^89 + 2659262965632 * q^93 + 20524601817576 * q^95 + 13413334833604 * q^97 + 17596620633240 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$ .

$n$	$99$	$101$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−234.000	−	405.300i	−0.185322	−	0.320988i	0.758363	−	0.651833i	$-0.226000\pi$
$3$	−234.000	−	405.300i	−0.185322	−	0.320988i	−0.943685	+	0.330845i	$0.892666\pi$
$4$		0			0
$5$	−28107.0	+	48682.8i	−0.804469	+	1.39338i	0.112179	+	0.993688i	$0.464217\pi$
$5$	−28107.0	+	48682.8i	−0.804469	+	1.39338i	−0.916649	+	0.399694i	$0.869116\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	687650.	−	1.19104e6i	0.431311	−	0.747053i
$10$		0			0
$11$	3.19869e6	+	5.54029e6i	0.544402	+	0.942932i	0.998644	+	0.0520537i	$0.0165767\pi$
$11$	3.19869e6	+	5.54029e6i	0.544402	+	0.942932i	−0.454242	+	0.890878i	$0.650090\pi$
$12$		0			0
$13$	1.51997e7			0.873382			0.436691	−	0.899611i	$-0.356150\pi$
$13$	1.51997e7			0.873382			0.436691	+	0.899611i	$0.356150\pi$
$14$		0			0
$15$	2.63082e7			0.596344
$16$		0			0
$17$	−2.15571e7	−	3.73380e7i	−0.216607	−	0.375174i	0.737162	−	0.675717i	$-0.236166\pi$
$17$	−2.15571e7	−	3.73380e7i	−0.216607	−	0.375174i	−0.953768	+	0.300542i	$0.902832\pi$
$18$		0			0
$19$	1.82558e8	−	3.16199e8i	0.890229	−	1.54192i	0.0506289	−	0.998718i	$-0.483877\pi$
$19$	1.82558e8	−	3.16199e8i	0.890229	−	1.54192i	0.839600	−	0.543205i	$-0.182789\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.86134e7	−	4.95599e7i	0.0403031	−	0.0698071i	−0.845170	−	0.534497i	$-0.820501\pi$
$23$	2.86134e7	−	4.95599e7i	0.0403031	−	0.0698071i	0.885473	+	0.464690i	$0.153834\pi$
$24$		0			0
$25$	−9.69655e8	−	1.67949e9i	−0.794342	−	1.37584i
$26$		0			0
$27$	−1.38978e9			−0.690371
$28$		0			0
$29$	−4.64190e7			−0.0144913			−0.00724567	−	0.999974i	$-0.502306\pi$
$29$	−4.64190e7			−0.0144913			−0.00724567	+	0.999974i	$0.502306\pi$
$30$		0			0
$31$	2.84109e9	+	4.92092e9i	0.574956	+	0.995853i	0.996046	+	0.0888340i	$0.0283141\pi$
$31$	2.84109e9	+	4.92092e9i	0.574956	+	0.995853i	−0.421091	+	0.907019i	$0.638353\pi$
$32$		0			0
$33$	1.49699e9	−	2.59286e9i	0.201780	−	0.349493i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	9.43593e8	−	1.63435e9i	0.0604607	−	0.104721i	−0.834211	−	0.551446i	$-0.814076\pi$
$37$	9.43593e8	−	1.63435e9i	0.0604607	−	0.104721i	0.894671	+	0.446725i	$0.147410\pi$
$38$		0			0
$39$	−3.55674e9	−	6.16045e9i	−0.161857	−	0.280345i
$40$		0			0
$41$	−7.33680e9			−0.241219			−0.120610	−	0.992700i	$-0.538485\pi$
$41$	−7.33680e9			−0.241219			−0.120610	+	0.992700i	$0.538485\pi$
$42$		0			0
$43$	−2.68867e10			−0.648623			−0.324311	−	0.945950i	$-0.605133\pi$
$43$	−2.68867e10			−0.648623			−0.324311	+	0.945950i	$0.605133\pi$
$44$		0			0
$45$	3.86555e10	+	6.69533e10i	0.693953	+	1.20196i
$46$		0			0
$47$	−5.09199e10	+	8.81959e10i	−0.689051	+	1.19347i	0.283094	+	0.959092i	$0.408639\pi$
$47$	−5.09199e10	+	8.81959e10i	−0.689051	+	1.19347i	−0.972145	+	0.234380i	$0.924694\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−1.00887e10	+	1.74742e10i	−0.0802842	+	0.139056i
$52$		0			0
$53$	−1.39366e11	−	2.41389e11i	−0.863701	−	1.49597i	−0.868331	−	0.495985i	$-0.834807\pi$
$53$	−1.39366e11	−	2.41389e11i	−0.863701	−	1.49597i	0.00462992	−	0.999989i	$-0.498526\pi$
$54$		0			0
$55$	−3.59622e11			−1.75182
$56$		0			0
$57$	−1.70874e11			−0.659917
$58$		0			0
$59$	−2.97870e10	−	5.15926e10i	−0.0919366	−	0.159239i	0.816389	−	0.577502i	$-0.195972\pi$
$59$	−2.97870e10	−	5.15926e10i	−0.0919366	−	0.159239i	−0.908326	+	0.418263i	$0.862639\pi$
$60$		0			0
$61$	1.37422e10	−	2.38022e10i	0.0341518	−	0.0591526i	−0.848444	−	0.529285i	$-0.822460\pi$
$61$	1.37422e10	−	2.38022e10i	0.0341518	−	0.0591526i	0.882596	+	0.470132i	$0.155794\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.27219e11	+	7.39965e11i	−0.702609	+	1.21695i
$66$		0			0
$67$	−3.92205e11	−	6.79319e11i	−0.529696	−	0.917461i	−0.999400	−	0.0346368i	$-0.988973\pi$
$67$	−3.92205e11	−	6.79319e11i	−0.529696	−	0.917461i	0.469704	−	0.882824i	$-0.344361\pi$
$68$		0			0
$69$	−2.67822e10			−0.0298763
$70$		0			0
$71$	−3.60365e11			−0.333859			−0.166930	−	0.985969i	$-0.553385\pi$
$71$	−3.60365e11			−0.333859			−0.166930	+	0.985969i	$0.553385\pi$
$72$		0			0
$73$	7.96318e11	+	1.37926e12i	0.615868	+	1.06672i	0.990232	+	0.139433i	$0.0445280\pi$
$73$	7.96318e11	+	1.37926e12i	0.615868	+	1.06672i	−0.374363	+	0.927282i	$0.622139\pi$
$74$		0			0
$75$	−4.53799e11	+	7.86002e11i	−0.294418	+	0.509948i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	1.15806e10	−	2.00582e10i	0.00535988	−	0.00928358i	−0.863333	−	0.504635i	$-0.831627\pi$
$79$	1.15806e10	−	2.00582e10i	0.00535988	−	0.00928358i	0.868693	+	0.495351i	$0.164961\pi$
$80$		0			0
$81$	−7.71126e11	−	1.33563e12i	−0.303370	−	0.525452i
$82$		0			0
$83$	2.05016e12			0.688303			0.344152	−	0.938914i	$-0.388167\pi$
$83$	2.05016e12			0.688303			0.344152	+	0.938914i	$0.388167\pi$
$84$		0			0
$85$	2.42362e12			0.697014
$86$		0			0
$87$	1.08620e10	+	1.88136e10i	0.00268557	+	0.00465154i
$88$		0			0
$89$	1.74270e12	−	3.01844e12i	0.371695	−	0.643794i	−0.618132	−	0.786075i	$-0.712110\pi$
$89$	1.74270e12	−	3.01844e12i	0.371695	−	0.643794i	0.989826	+	0.142280i	$0.0454435\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.32963e12	−	2.30299e12i	0.213104	−	0.369107i
$94$		0			0
$95$	1.02623e13	+	1.77748e13i	1.43232	+	2.48086i
$96$		0			0
$97$	6.70667e12			0.817505			0.408753	−	0.912645i	$-0.365964\pi$
$97$	6.70667e12			0.817505			0.408753	+	0.912645i	$0.365964\pi$
$98$		0			0
$99$	8.79831e12			0.939227
$100$		0			0
$101$	−5.32687e12	−	9.22641e12i	−0.499325	−	0.864856i	0.500675	−	0.865635i	$-0.333085\pi$
$101$	−5.32687e12	−	9.22641e12i	−0.499325	−	0.864856i	−1.00000		0.000779647i	$0.999752\pi$
$102$		0			0
$103$	5.46223e12	−	9.46086e12i	0.450742	−	0.780708i	−0.547690	−	0.836681i	$-0.684493\pi$
$103$	5.46223e12	−	9.46086e12i	0.450742	−	0.780708i	0.998432	+	0.0559729i	$0.0178260\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.29378e12	+	1.09012e13i	−0.405431	+	0.702227i	−0.994372	−	0.105949i	$-0.966212\pi$
$107$	−6.29378e12	+	1.09012e13i	−0.405431	+	0.702227i	0.588940	+	0.808177i	$0.299545\pi$
$108$		0			0
$109$	2.18321e11	+	3.78143e11i	0.0124688	+	0.0215965i	0.872192	−	0.489163i	$-0.162698\pi$
$109$	2.18321e11	+	3.78143e11i	0.0124688	+	0.0215965i	−0.859724	+	0.510759i	$0.829364\pi$
$110$		0			0
$111$	−8.83203e11			−0.0448189
$112$		0			0
$113$	−3.18312e13			−1.43828			−0.719139	−	0.694866i	$-0.755464\pi$
$113$	−3.18312e13			−1.43828			−0.719139	+	0.694866i	$0.755464\pi$
$114$		0			0
$115$	1.60847e12	+	2.78596e12i	0.0648453	+	0.112315i
$116$		0			0
$117$	1.04521e13	−	1.81036e13i	0.376700	−	0.652463i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−3.20188e12	+	5.54582e12i	−0.0927470	+	0.160643i
$122$		0			0
$123$	1.71681e12	+	2.97361e12i	0.0447033	+	0.0774284i
$124$		0			0
$125$	4.03958e13			0.947155
$126$		0			0
$127$	3.94077e13			0.833406			0.416703	−	0.909043i	$-0.363185\pi$
$127$	3.94077e13			0.833406			0.416703	+	0.909043i	$0.363185\pi$
$128$		0			0
$129$	6.29148e12	+	1.08972e13i	0.120204	+	0.208200i
$130$		0			0
$131$	−3.68720e13	+	6.38642e13i	−0.637431	+	1.10406i	0.348563	+	0.937285i	$0.386670\pi$
$131$	−3.68720e13	+	6.38642e13i	−0.637431	+	1.10406i	−0.985994	+	0.166778i	$0.946664\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	3.90626e13	−	6.76585e13i	0.555382	−	0.961950i
$136$		0			0
$137$	−4.27050e13	−	7.39673e13i	−0.551817	−	0.955775i	−0.998144	−	0.0609051i	$-0.980601\pi$
$137$	−4.27050e13	−	7.39673e13i	−0.551817	−	0.955775i	0.446326	−	0.894870i	$-0.352732\pi$
$138$		0			0
$139$	−7.97827e13			−0.938237			−0.469119	−	0.883135i	$-0.655428\pi$
$139$	−7.97827e13			−0.938237			−0.469119	+	0.883135i	$0.655428\pi$
$140$		0			0
$141$	4.76610e13			0.510786
$142$		0			0
$143$	4.86193e13	+	8.42110e13i	0.475471	+	0.823540i
$144$		0			0
$145$	1.30470e12	−	2.25980e12i	0.0116578	−	0.0201920i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.46703e13	+	1.63974e14i	−0.708766	+	1.22762i	0.256549	+	0.966531i	$0.417415\pi$
$149$	−9.46703e13	+	1.63974e14i	−0.708766	+	1.22762i	−0.965315	+	0.261088i	$0.915919\pi$
$150$		0			0
$151$	−1.41966e14	−	2.45892e14i	−0.974617	−	1.68809i	−0.681194	−	0.732103i	$-0.738539\pi$
$151$	−1.41966e14	−	2.45892e14i	−0.974617	−	1.68809i	−0.293423	−	0.955983i	$-0.594794\pi$
$152$		0			0
$153$	−5.92949e13			−0.373700
$154$		0			0
$155$	−3.19418e14			−1.85014
$156$		0			0
$157$	−1.37466e13	−	2.38098e13i	−0.0732567	−	0.126884i	0.827070	−	0.562099i	$-0.190006\pi$
$157$	−1.37466e13	−	2.38098e13i	−0.0732567	−	0.126884i	−0.900327	+	0.435214i	$0.856673\pi$
$158$		0			0
$159$	−6.52233e13	+	1.12970e14i	−0.320126	+	0.554475i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	1.87326e14	−	3.24458e14i	0.782309	−	1.35500i	−0.148284	−	0.988945i	$-0.547375\pi$
$163$	1.87326e14	−	3.24458e14i	0.782309	−	1.35500i	0.930593	−	0.366055i	$-0.119292\pi$
$164$		0			0
$165$	8.41516e13	+	1.45755e14i	0.324651	+	0.562312i
$166$		0			0
$167$	1.26477e14			0.451183			0.225592	−	0.974222i	$-0.427569\pi$
$167$	1.26477e14			0.451183			0.225592	+	0.974222i	$0.427569\pi$
$168$		0			0
$169$	−7.18429e13			−0.237203
$170$		0			0
$171$	−2.51071e14	−	4.34869e14i	−0.767932	−	1.33010i
$172$		0			0
$173$	1.81366e14	−	3.14135e14i	0.514347	−	0.890875i	−0.485514	−	0.874229i	$-0.661368\pi$
$173$	1.81366e14	−	3.14135e14i	0.514347	−	0.890875i	0.999861	−	0.0166467i	$-0.00529905\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.39403e13	+	2.41453e13i	−0.0340758	+	0.0590210i
$178$		0			0
$179$	1.58607e14	+	2.74716e14i	0.360394	+	0.624221i	0.988026	−	0.154289i	$-0.0493088\pi$
$179$	1.58607e14	+	2.74716e14i	0.360394	+	0.624221i	−0.627631	+	0.778511i	$0.715975\pi$
$180$		0			0
$181$	4.55669e14			0.963249			0.481625	−	0.876378i	$-0.340047\pi$
$181$	4.55669e14			0.963249			0.481625	+	0.876378i	$0.340047\pi$
$182$		0			0
$183$	−1.28627e13			−0.0253164
$184$		0			0
$185$	5.30431e13	+	9.18734e13i	0.0972776	+	0.168490i
$186$		0			0
$187$	1.37909e14	−	2.38865e14i	0.235842	−	0.408491i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.83015e14	−	8.36606e14i	0.719853	−	1.24682i	−0.241205	−	0.970474i	$-0.577543\pi$
$191$	4.83015e14	−	8.36606e14i	0.719853	−	1.24682i	0.961058	−	0.276347i	$-0.0891239\pi$
$192$		0			0
$193$	9.10315e13	+	1.57671e14i	0.126785	+	0.219599i	0.922429	−	0.386166i	$-0.126201\pi$
$193$	9.10315e13	+	1.57671e14i	0.126785	+	0.219599i	−0.795644	+	0.605764i	$0.792867\pi$
$194$		0			0
$195$	3.99877e14			0.520837
$196$		0			0
$197$	8.62598e14			1.05142			0.525712	−	0.850663i	$-0.323799\pi$
$197$	8.62598e14			1.05142			0.525712	+	0.850663i	$0.323799\pi$
$198$		0			0
$199$	−1.62410e14	−	2.81302e14i	−0.185382	−	0.321091i	0.758323	−	0.651879i	$-0.226019\pi$
$199$	−1.62410e14	−	2.81302e14i	−0.185382	−	0.321091i	−0.943705	+	0.330788i	$0.892686\pi$
$200$		0			0
$201$	−1.83552e14	+	3.17921e14i	−0.196329	+	0.340052i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	2.06216e14	−	3.57176e14i	0.194053	−	0.336110i
$206$		0			0
$207$	−3.93520e13	−	6.81597e13i	−0.0347664	−	0.0602171i
$208$		0			0
$209$	2.33578e15			1.93857
$210$		0			0
$211$	−7.03123e14			−0.548523			−0.274262	−	0.961655i	$-0.588433\pi$
$211$	−7.03123e14			−0.548523			−0.274262	+	0.961655i	$0.588433\pi$
$212$		0			0
$213$	8.43255e13	+	1.46056e14i	0.0618716	+	0.107165i
$214$		0			0
$215$	7.55704e14	−	1.30892e15i	0.521797	−	0.903779i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	3.72677e14	−	6.45495e14i	0.228268	−	0.395372i
$220$		0			0
$221$	−3.27662e14	−	5.67528e14i	−0.189181	−	0.327670i
$222$		0			0
$223$	1.50865e15			0.821499			0.410749	−	0.911748i	$-0.365267\pi$
$223$	1.50865e15			0.821499			0.410749	+	0.911748i	$0.365267\pi$
$224$		0			0
$225$	−2.66713e15			−1.37043
$226$		0			0
$227$	−1.25153e15	−	2.16771e15i	−0.607118	−	1.05156i	−0.991713	−	0.128474i	$-0.958992\pi$
$227$	−1.25153e15	−	2.16771e15i	−0.607118	−	1.05156i	0.384595	−	0.923086i	$-0.374341\pi$
$228$		0			0
$229$	6.10558e14	−	1.05752e15i	0.279767	−	0.484571i	−0.691560	−	0.722319i	$-0.743076\pi$
$229$	6.10558e14	−	1.05752e15i	0.279767	−	0.484571i	0.971327	+	0.237749i	$0.0764094\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.76895e15	+	3.06392e15i	−0.724274	+	1.25448i	0.234998	+	0.971996i	$0.424492\pi$
$233$	−1.76895e15	+	3.06392e15i	−0.724274	+	1.25448i	−0.959272	+	0.282484i	$0.908842\pi$
$234$		0			0
$235$	−2.86241e15	−	4.95784e15i	−1.10864	−	1.92022i
$236$		0			0
$237$	−1.08394e13			−0.00397322
$238$		0			0
$239$	−3.11280e15			−1.08035			−0.540175	−	0.841553i	$-0.681642\pi$
$239$	−3.11280e15			−1.08035			−0.540175	+	0.841553i	$0.681642\pi$
$240$		0			0
$241$	2.28546e15	+	3.95853e15i	0.751385	+	1.30144i	0.947152	+	0.320786i	$0.103947\pi$
$241$	2.28546e15	+	3.95853e15i	0.751385	+	1.30144i	−0.195767	+	0.980650i	$0.562720\pi$
$242$		0			0
$243$	−1.46877e15	+	2.54398e15i	−0.457628	+	0.792635i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.77483e15	−	4.80615e15i	0.777511	−	1.34669i
$248$		0			0
$249$	−4.79737e14	−	8.30929e14i	−0.127558	−	0.220937i
$250$		0			0
$251$	−1.66332e15			−0.419852			−0.209926	−	0.977717i	$-0.567322\pi$
$251$	−1.66332e15			−0.419852			−0.209926	+	0.977717i	$0.567322\pi$
$252$		0			0
$253$	3.66102e14			0.0877644
$254$		0			0
$255$	−5.67127e14	−	9.82293e14i	−0.129172	−	0.223733i
$256$		0			0
$257$	1.87026e15	−	3.23939e15i	0.404890	−	0.701290i	−0.589419	−	0.807828i	$-0.700643\pi$
$257$	1.87026e15	−	3.23939e15i	0.404890	−	0.701290i	0.994309	+	0.106538i	$0.0339765\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−3.19200e13	+	5.52871e13i	−0.00625028	+	0.0108258i
$262$		0			0
$263$	−1.25308e15	−	2.17040e15i	−0.233489	−	0.404414i	0.725344	−	0.688387i	$-0.241681\pi$
$263$	−1.25308e15	−	2.17040e15i	−0.233489	−	0.404414i	−0.958832	+	0.283973i	$0.908348\pi$
$264$		0			0
$265$	1.56686e16			2.77928
$266$		0			0
$267$	−1.63116e15			−0.275533
$268$		0			0
$269$	4.05650e13	+	7.02606e13i	0.00652772	+	0.0113063i	0.869271	−	0.494336i	$-0.164589\pi$
$269$	4.05650e13	+	7.02606e13i	0.00652772	+	0.0113063i	−0.862743	+	0.505643i	$0.831255\pi$
$270$		0			0
$271$	1.14570e15	−	1.98442e15i	0.175700	−	0.304322i	−0.764703	−	0.644383i	$-0.777114\pi$
$271$	1.14570e15	−	1.98442e15i	0.175700	−	0.304322i	0.940403	+	0.340061i	$0.110448\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.20325e15	−	1.07444e16i	0.864882	−	1.49802i
$276$		0			0
$277$	−4.99480e14	−	8.65125e14i	−0.0664354	−	0.115070i	0.830894	−	0.556430i	$-0.187829\pi$
$277$	−4.99480e14	−	8.65125e14i	−0.0664354	−	0.115070i	−0.897330	+	0.441361i	$0.854496\pi$
$278$		0			0
$279$	7.81470e15			0.991940
$280$		0			0
$281$	−1.17580e16			−1.42476			−0.712381	−	0.701793i	$-0.752383\pi$
$281$	−1.17580e16			−1.42476			−0.712381	+	0.701793i	$0.752383\pi$
$282$		0			0
$283$	−1.90619e15	−	3.30161e15i	−0.220574	−	0.382045i	0.734409	−	0.678708i	$-0.237460\pi$
$283$	−1.90619e15	−	3.30161e15i	−0.220574	−	0.382045i	−0.954982	+	0.296663i	$0.904126\pi$
$284$		0			0
$285$	4.80276e15	−	8.31862e15i	0.530883	−	0.919517i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	4.02287e15	−	6.96782e15i	0.406163	−	0.703495i
$290$		0			0
$291$	−1.56936e15	−	2.71821e15i	−0.151502	−	0.262409i
$292$		0			0
$293$	1.89831e16			1.75278			0.876389	−	0.481603i	$-0.159945\pi$
$293$	1.89831e16			1.75278			0.876389	+	0.481603i	$0.159945\pi$
$294$		0			0
$295$	3.34889e15			0.295841
$296$		0			0
$297$	−4.44549e15	−	7.69981e15i	−0.375839	−	0.650973i
$298$		0			0
$299$	4.34916e14	−	7.53297e14i	0.0352000	−	0.0609683i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−2.49297e15	+	4.31796e15i	−0.185072	+	0.320554i
$304$		0			0
$305$	7.72506e14	+	1.33802e15i	0.0549481	+	0.0951730i
$306$		0			0
$307$	1.52021e16			1.03634			0.518172	−	0.855276i	$-0.326613\pi$
$307$	1.52021e16			1.03634			0.518172	+	0.855276i	$0.326613\pi$
$308$		0			0
$309$	−5.11265e15			−0.334130
$310$		0			0
$311$	−9.82431e15	−	1.70162e16i	−0.615687	−	1.06640i	−0.990264	−	0.139205i	$-0.955545\pi$
$311$	−9.82431e15	−	1.70162e16i	−0.615687	−	1.06640i	0.374577	−	0.927196i	$-0.377788\pi$
$312$		0			0
$313$	9.99713e15	−	1.73155e16i	0.600948	−	1.04087i	−0.391730	−	0.920080i	$-0.628123\pi$
$313$	9.99713e15	−	1.73155e16i	0.600948	−	1.04087i	0.992678	−	0.120792i	$-0.0385435\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.22282e16	−	2.11799e16i	0.676828	−	1.17230i	−0.299103	−	0.954221i	$-0.596687\pi$
$317$	1.22282e16	−	2.11799e16i	0.676828	−	1.17230i	0.975931	−	0.218080i	$-0.0699793\pi$
$318$		0			0
$319$	−1.48480e14	−	2.57175e14i	−0.00788912	−	0.0136644i
$320$		0			0
$321$	5.89098e15			0.300542
$322$		0			0
$323$	−1.57417e16			−0.771319
$324$		0			0
$325$	−1.47385e16	−	2.55278e16i	−0.693764	−	1.20163i
$326$		0			0
$327$	1.02174e14	−	1.76971e14i	0.00462148	−	0.00800463i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.69962e16	−	2.94383e16i	0.710347	−	1.23036i	−0.254380	−	0.967104i	$-0.581871\pi$
$331$	1.69962e16	−	2.94383e16i	0.710347	−	1.23036i	0.964727	−	0.263252i	$-0.0847952\pi$
$332$		0			0
$333$	−1.29772e15	−	2.24772e15i	−0.0521548	−	0.0903347i
$334$		0			0
$335$	4.40948e16			1.70450
$336$		0			0
$337$	−2.88718e15			−0.107369			−0.0536846	−	0.998558i	$-0.517097\pi$
$337$	−2.88718e15			−0.107369			−0.0536846	+	0.998558i	$0.517097\pi$
$338$		0			0
$339$	7.44850e15	+	1.29012e16i	0.266545	+	0.461670i
$340$		0			0
$341$	−1.81756e16	+	3.14810e16i	−0.626014	+	1.08429i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	7.52766e14	−	1.30383e15i	0.0240345	−	0.0416290i
$346$		0			0
$347$	−1.68006e16	−	2.90994e16i	−0.516633	−	0.894835i	−0.999813	−	0.0193139i	$-0.993852\pi$
$347$	−1.68006e16	−	2.90994e16i	−0.516633	−	0.894835i	0.483180	−	0.875521i	$-0.339482\pi$
$348$		0			0
$349$	−1.90527e16			−0.564405			−0.282203	−	0.959355i	$-0.591065\pi$
$349$	−1.90527e16			−0.564405			−0.282203	+	0.959355i	$0.591065\pi$
$350$		0			0
$351$	−2.11243e16			−0.602958
$352$		0			0
$353$	3.42737e16	+	5.93638e16i	0.942812	+	1.63300i	0.760073	+	0.649837i	$0.225163\pi$
$353$	3.42737e16	+	5.93638e16i	0.942812	+	1.63300i	0.182739	+	0.983161i	$0.441504\pi$
$354$		0			0
$355$	1.01288e16	−	1.75436e16i	0.268580	−	0.465194i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	5.75771e15	−	9.97264e15i	0.141950	−	0.245865i	−0.786281	−	0.617869i	$-0.787996\pi$
$359$	5.75771e15	−	9.97264e15i	0.141950	−	0.245865i	0.928231	+	0.372005i	$0.121329\pi$
$360$		0			0
$361$	−4.56282e16	−	7.90303e16i	−1.08502	−	1.87930i
$362$		0			0
$363$	2.99696e15			0.0687524
$364$		0			0
$365$	−8.95284e16			−1.98179
$366$		0			0
$367$	4.71539e14	+	8.16730e14i	0.0100737	+	0.0174481i	0.871018	−	0.491251i	$-0.163460\pi$
$367$	4.71539e14	+	8.16730e14i	0.0100737	+	0.0174481i	−0.860945	+	0.508699i	$0.830127\pi$
$368$		0			0
$369$	−5.04515e15	+	8.73845e15i	−0.104041	+	0.180204i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−1.37172e16	+	2.37589e16i	−0.263730	+	0.456793i	−0.967230	−	0.253902i	$-0.918286\pi$
$373$	−1.37172e16	+	2.37589e16i	−0.263730	+	0.456793i	0.703500	+	0.710695i	$0.251619\pi$
$374$		0			0
$375$	−9.45262e15	−	1.63724e16i	−0.175529	−	0.304025i
$376$		0			0
$377$	−7.05557e14			−0.0126565
$378$		0			0
$379$	6.51327e16			1.12887			0.564435	−	0.825478i	$-0.309094\pi$
$379$	6.51327e16			1.12887			0.564435	+	0.825478i	$0.309094\pi$
$380$		0			0
$381$	−9.22140e15	−	1.59719e16i	−0.154449	−	0.267513i
$382$		0			0
$383$	4.39172e16	−	7.60669e16i	0.710956	−	1.23141i	−0.253542	−	0.967324i	$-0.581596\pi$
$383$	4.39172e16	−	7.60669e16i	0.710956	−	1.23141i	0.964499	−	0.264088i	$-0.0850709\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.84886e16	+	3.20232e16i	−0.279758	+	0.484556i
$388$		0			0
$389$	2.04641e16	+	3.54449e16i	0.299448	+	0.518658i	0.976010	−	0.217727i	$-0.0698643\pi$
$389$	2.04641e16	+	3.54449e16i	0.299448	+	0.518658i	−0.676562	+	0.736386i	$0.736531\pi$
$390$		0			0
$391$	−2.46729e15			−0.0349197
$392$		0			0
$393$	3.45122e16			0.472521
$394$		0			0
$395$	6.50991e14	+	1.12755e15i	0.00862371	+	0.0149367i
$396$		0			0
$397$	−1.26888e16	+	2.19777e16i	−0.162661	+	0.281736i	−0.935822	−	0.352473i	$-0.885341\pi$
$397$	−1.26888e16	+	2.19777e16i	−0.162661	+	0.281736i	0.773161	+	0.634209i	$0.218674\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	4.05992e16	−	7.03199e16i	0.487618	−	0.844578i	−0.512281	−	0.858818i	$-0.671199\pi$
$401$	4.05992e16	−	7.03199e16i	0.487618	−	0.844578i	0.999899	+	0.0142394i	$0.00453270\pi$
$402$		0			0
$403$	4.31839e16	+	7.47967e16i	0.502156	+	0.869760i
$404$		0			0
$405$	8.66962e16			0.976208
$406$		0			0
$407$	1.20730e16			0.131660
$408$		0			0
$409$	−7.84515e16	−	1.35882e17i	−0.828705	−	1.43536i	−0.899055	−	0.437837i	$-0.855745\pi$
$409$	−7.84515e16	−	1.35882e17i	−0.828705	−	1.43536i	0.0703496	−	0.997522i	$-0.477589\pi$
$410$		0			0
$411$	−1.99859e16	+	3.46167e16i	−0.204528	+	0.354253i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−5.76238e16	+	9.98073e16i	−0.553719	+	0.959069i
$416$		0			0
$417$	1.86692e16	+	3.23359e16i	0.173876	+	0.301163i
$418$		0			0
$419$	−1.91659e16			−0.173036			−0.0865182	−	0.996250i	$-0.527574\pi$
$419$	−1.91659e16			−0.173036			−0.0865182	+	0.996250i	$0.527574\pi$
$420$		0			0
$421$	2.20629e16			0.193120			0.0965602	−	0.995327i	$-0.469216\pi$
$421$	2.20629e16			0.193120			0.0965602	+	0.995327i	$0.469216\pi$
$422$		0			0
$423$	7.00301e16	+	1.21296e17i	0.594391	+	1.02952i
$424$		0			0
$425$	−4.18059e16	+	7.24100e16i	−0.344120	+	0.596033i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	2.27538e16	−	3.94108e16i	0.176231	−	0.305241i
$430$		0			0
$431$	6.81734e16	+	1.18080e17i	0.512286	+	0.887306i	0.999899	+	0.0142457i	$0.00453469\pi$
$431$	6.81734e16	+	1.18080e17i	0.512286	+	0.887306i	−0.487612	+	0.873060i	$0.662132\pi$
$432$		0			0
$433$	−4.34949e16			−0.317152			−0.158576	−	0.987347i	$-0.550690\pi$
$433$	−4.34949e16			−0.317152			−0.158576	+	0.987347i	$0.550690\pi$
$434$		0			0
$435$	−1.22120e15			−0.00864183
$436$		0			0
$437$	−1.04472e16	−	1.80951e16i	−0.0717580	−	0.124289i
$438$		0			0
$439$	1.04249e17	−	1.80564e17i	0.695107	−	1.20396i	−0.275038	−	0.961433i	$-0.588690\pi$
$439$	1.04249e17	−	1.80564e17i	0.695107	−	1.20396i	0.970145	−	0.242527i	$-0.0779763\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.24641e17	+	2.15885e17i	−0.783498	+	1.35706i	0.146395	+	0.989226i	$0.453233\pi$
$443$	−1.24641e17	+	2.15885e17i	−0.783498	+	1.35706i	−0.929892	+	0.367832i	$0.880100\pi$
$444$		0			0
$445$	9.79639e16	+	1.69678e17i	0.598034	+	1.03583i
$446$		0			0
$447$	8.86114e16			0.525401
$448$		0			0
$449$	1.45110e17			0.835787			0.417894	−	0.908496i	$-0.362768\pi$
$449$	1.45110e17			0.835787			0.417894	+	0.908496i	$0.362768\pi$
$450$		0			0
$451$	−2.34682e16	−	4.06480e16i	−0.131320	−	0.227453i
$452$		0			0
$453$	−6.64400e16	+	1.15078e17i	−0.361236	+	0.625680i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	9.90636e16	−	1.71583e17i	0.508696	−	0.881088i	−0.491253	−	0.871017i	$-0.663461\pi$
$457$	9.90636e16	−	1.71583e17i	0.508696	−	0.881088i	0.999949	−	0.0100711i	$-0.00320579\pi$
$458$		0			0
$459$	2.99597e16	+	5.18917e16i	0.149539	+	0.259009i
$460$		0			0
$461$	−2.30382e17			−1.11787			−0.558937	−	0.829210i	$-0.688790\pi$
$461$	−2.30382e17			−1.11787			−0.558937	+	0.829210i	$0.688790\pi$
$462$		0			0
$463$	3.64296e17			1.71861			0.859307	−	0.511460i	$-0.170895\pi$
$463$	3.64296e17			1.71861			0.859307	+	0.511460i	$0.170895\pi$
$464$		0			0
$465$	7.47439e16	+	1.29460e17i	0.342872	+	0.593871i
$466$		0			0
$467$	1.08587e16	−	1.88079e16i	0.0484417	−	0.0839036i	−0.840788	−	0.541365i	$-0.817908\pi$
$467$	1.08587e16	−	1.88079e16i	0.0484417	−	0.0839036i	0.889230	+	0.457461i	$0.151241\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−6.43340e15	+	1.11430e16i	−0.0271522	+	0.0470290i
$472$		0			0
$473$	−8.60021e16	−	1.48960e17i	−0.353111	−	0.611607i
$474$		0			0
$475$	−7.08072e17			−2.82858
$476$		0			0
$477$	−3.83340e17			−1.49010
$478$		0			0
$479$	9.93595e16	+	1.72096e17i	0.375862	+	0.651012i	0.990456	−	0.137832i	$-0.0440133\pi$
$479$	9.93595e16	+	1.72096e17i	0.375862	+	0.651012i	−0.614594	+	0.788844i	$0.710680\pi$
$480$		0			0
$481$	1.43424e16	−	2.48417e16i	0.0528053	−	0.0914615i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.88504e17	+	3.26499e17i	−0.657658	+	1.13910i
$486$		0			0
$487$	−2.35799e17	−	4.08416e17i	−0.800947	−	1.38728i	−0.918994	−	0.394272i	$-0.870997\pi$
$487$	−2.35799e17	−	4.08416e17i	−0.800947	−	1.38728i	0.118047	−	0.993008i	$-0.462337\pi$
$488$		0			0
$489$	−1.75337e17			−0.579917
$490$		0			0
$491$	−1.14636e17			−0.369226			−0.184613	−	0.982811i	$-0.559103\pi$
$491$	−1.14636e17			−0.369226			−0.184613	+	0.982811i	$0.559103\pi$
$492$		0			0
$493$	1.00066e15	+	1.73319e15i	0.00313893	+	0.00543678i
$494$		0			0
$495$	−2.47294e17	+	4.28326e17i	−0.755579	+	1.30870i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−6.43968e15	+	1.11539e16i	−0.0186729	+	0.0323423i	−0.875211	−	0.483742i	$-0.839277\pi$
$499$	−6.43968e15	+	1.11539e16i	−0.0186729	+	0.0323423i	0.856538	+	0.516084i	$0.172611\pi$
$500$		0			0
$501$	−2.95955e16	−	5.12609e16i	−0.0836143	−	0.144824i
$502$		0			0
$503$	−2.72812e17			−0.751055			−0.375528	−	0.926811i	$-0.622538\pi$
$503$	−2.72812e17			−0.751055			−0.375528	+	0.926811i	$0.622538\pi$
$504$		0			0
$505$	5.98889e17			1.60677
$506$		0			0
$507$	1.68113e16	+	2.91179e16i	0.0439590	+	0.0761393i
$508$		0			0
$509$	−2.04412e17	+	3.54052e17i	−0.521004	+	0.902405i	0.478698	+	0.877980i	$0.341109\pi$
$509$	−2.04412e17	+	3.54052e17i	−0.521004	+	0.902405i	−0.999702	+	0.0244256i	$0.992224\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−2.53716e17	+	4.39448e17i	−0.614588	+	1.06450i
$514$		0			0
$515$	3.07054e17	+	5.31833e17i	0.725217	+	1.25611i
$516$		0			0
$517$	−6.51508e17			−1.50048
$518$		0			0
$519$	−1.69759e17			−0.381280
$520$		0			0
$521$	2.34488e17	+	4.06145e17i	0.513659	+	0.889684i	0.999874	+	0.0158446i	$0.00504371\pi$
$521$	2.34488e17	+	4.06145e17i	0.513659	+	0.889684i	−0.486215	+	0.873839i	$0.661623\pi$
$522$		0			0
$523$	−3.06179e17	+	5.30318e17i	−0.654207	+	1.13312i	0.327885	+	0.944717i	$0.393664\pi$
$523$	−3.06179e17	+	5.30318e17i	−0.654207	+	1.13312i	−0.982092	+	0.188402i	$0.939669\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.22491e17	−	2.12161e17i	0.249079	−	0.431417i
$528$		0			0
$529$	2.50381e17	+	4.33672e17i	0.496751	+	0.860399i
$530$		0			0
$531$	−8.19320e16			−0.158613
$532$		0			0
$533$	−1.11518e17			−0.210677
$534$		0			0
$535$	−3.53799e17	−	6.12797e17i	−0.652314	−	1.12984i
$536$		0			0
$537$	7.42281e16	−	1.28567e17i	0.133578	−	0.231364i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−2.34135e17	+	4.05534e17i	−0.401499	+	0.695417i	−0.993907	−	0.110221i	$-0.964844\pi$
$541$	−2.34135e17	+	4.05534e17i	−0.401499	+	0.695417i	0.592408	+	0.805638i	$0.298177\pi$
$542$		0			0
$543$	−1.06627e17	−	1.84683e17i	−0.178512	−	0.309191i
$544$		0			0
$545$	−2.45454e16			−0.0401229
$546$		0			0
$547$	1.11611e18			1.78151			0.890756	−	0.454482i	$-0.150176\pi$
$547$	1.11611e18			1.78151			0.890756	+	0.454482i	$0.150176\pi$
$548$		0			0
$549$	−1.88997e16	−	3.27352e16i	−0.0294601	−	0.0510264i
$550$		0			0
$551$	−8.47415e15	+	1.46777e16i	−0.0129006	+	0.0223445i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	2.48242e16	−	4.29967e16i	0.0360554	−	0.0624498i
$556$		0			0
$557$	1.39486e17	+	2.41598e17i	0.197913	+	0.342795i	0.947851	−	0.318713i	$-0.103250\pi$
$557$	1.39486e17	+	2.41598e17i	0.197913	+	0.342795i	−0.749939	+	0.661507i	$0.769917\pi$
$558$		0			0
$559$	−4.08671e17			−0.566496
$560$		0			0
$561$	−1.29083e17			−0.174827
$562$		0			0
$563$	2.48723e17	+	4.30801e17i	0.329163	+	0.570128i	0.982346	−	0.187073i	$-0.0599000\pi$
$563$	2.48723e17	+	4.30801e17i	0.329163	+	0.570128i	−0.653183	+	0.757200i	$0.726567\pi$
$564$		0			0
$565$	8.94680e17	−	1.54963e18i	1.15705	−	2.00407i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.78268e17	+	1.00159e18i	−0.714330	+	1.23726i	0.248887	+	0.968533i	$0.419935\pi$
$569$	−5.78268e17	+	1.00159e18i	−0.714330	+	1.23726i	−0.963217	+	0.268724i	$0.913398\pi$
$570$		0			0
$571$	−4.40075e16	−	7.62232e16i	−0.0531364	−	0.0920349i	0.838234	−	0.545311i	$-0.183588\pi$
$571$	−4.40075e16	−	7.62232e16i	−0.0531364	−	0.0920349i	−0.891370	+	0.453276i	$0.850255\pi$
$572$		0			0
$573$	−4.52102e17			−0.533619
$574$		0			0
$575$	−1.10981e17			−0.128058
$576$		0			0
$577$	7.70241e16	+	1.33410e17i	0.0868928	+	0.150503i	0.906196	−	0.422857i	$-0.138973\pi$
$577$	7.70241e16	+	1.33410e17i	0.0868928	+	0.150503i	−0.819303	+	0.573360i	$0.805640\pi$
$578$		0			0
$579$	4.26028e16	−	7.37901e16i	0.0469923	−	0.0813931i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	8.91577e17	−	1.54426e18i	0.940401	−	1.62882i
$584$		0			0
$585$	5.87554e17	+	1.01767e18i	0.606087	+	1.04977i
$586$		0			0
$587$	1.46111e18			1.47413			0.737066	−	0.675821i	$-0.236211\pi$
$587$	1.46111e18			1.47413			0.737066	+	0.675821i	$0.236211\pi$
$588$		0			0
$589$	2.07465e18			2.04737
$590$		0			0
$591$	−2.01848e17	−	3.49611e17i	−0.194852	−	0.337494i
$592$		0			0
$593$	−6.61859e17	+	1.14637e18i	−0.625043	+	1.08261i	0.363490	+	0.931598i	$0.381585\pi$
$593$	−6.61859e17	+	1.14637e18i	−0.625043	+	1.08261i	−0.988533	+	0.151008i	$0.951748\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−7.60078e16	+	1.31649e17i	−0.0687108	+	0.119011i
$598$		0			0
$599$	7.71625e17	+	1.33649e18i	0.682546	+	1.18220i	0.974201	+	0.225681i	$0.0724608\pi$
$599$	7.71625e17	+	1.33649e18i	0.682546	+	1.18220i	−0.291655	+	0.956524i	$0.594206\pi$
$600$		0			0
$601$	2.66564e17			0.230737			0.115369	−	0.993323i	$-0.463195\pi$
$601$	2.66564e17			0.230737			0.115369	+	0.993323i	$0.463195\pi$
$602$		0			0
$603$	−1.07880e18			−0.913856
$604$		0			0
$605$	−1.79990e17	−	3.11753e17i	−0.149224	−	0.258464i
$606$		0			0
$607$	5.16407e17	−	8.94443e17i	0.419049	−	0.725815i	−0.576795	−	0.816889i	$-0.695697\pi$
$607$	5.16407e17	−	8.94443e17i	0.419049	−	0.725815i	0.995844	+	0.0910742i	$0.0290300\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−7.73970e17	+	1.34055e18i	−0.601805	+	1.04236i
$612$		0			0
$613$	2.25771e17	+	3.91046e17i	0.171860	+	0.297670i	0.939070	−	0.343726i	$-0.111689\pi$
$613$	2.25771e17	+	3.91046e17i	0.171860	+	0.297670i	−0.767210	+	0.641396i	$0.778356\pi$
$614$		0			0
$615$	−1.93018e17			−0.143850
$616$		0			0
$617$	−1.86870e18			−1.36360			−0.681798	−	0.731541i	$-0.738802\pi$
$617$	−1.86870e18			−1.36360			−0.681798	+	0.731541i	$0.738802\pi$
$618$		0			0
$619$	6.18619e17	+	1.07148e18i	0.442012	+	0.765587i	0.997839	−	0.0657111i	$-0.0209316\pi$
$619$	6.18619e17	+	1.07148e18i	0.442012	+	0.765587i	−0.555827	+	0.831298i	$0.687598\pi$
$620$		0			0
$621$	−3.97664e16	+	6.88775e16i	−0.0278241	+	0.0481928i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	4.82564e16	−	8.35826e16i	0.0323843	−	0.0560913i
$626$		0			0
$627$	−5.46573e17	−	9.46692e17i	−0.359260	−	0.622257i
$628$		0			0
$629$	−8.13645e16			−0.0523848
$630$		0			0
$631$	6.02949e17			0.380268			0.190134	−	0.981758i	$-0.439108\pi$
$631$	6.02949e17			0.380268			0.190134	+	0.981758i	$0.439108\pi$
$632$		0			0
$633$	1.64531e17	+	2.84976e17i	0.101654	+	0.176069i
$634$		0			0
$635$	−1.10763e18	+	1.91847e18i	−0.670450	+	1.16125i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−2.47805e17	+	4.29211e17i	−0.143997	+	0.249411i
$640$		0			0
$641$	−1.34392e18	−	2.32773e18i	−0.765236	−	1.32543i	−0.940122	−	0.340838i	$-0.889289\pi$
$641$	−1.34392e18	−	2.32773e18i	−0.765236	−	1.32543i	0.174886	−	0.984589i	$-0.444044\pi$
$642$		0			0
$643$	−1.92261e18			−1.07280			−0.536400	−	0.843964i	$-0.680216\pi$
$643$	−1.92261e18			−1.07280			−0.536400	+	0.843964i	$0.680216\pi$
$644$		0			0
$645$	−7.07339e17			−0.386803
$646$		0			0
$647$	−7.74147e17	−	1.34086e18i	−0.414902	−	0.718632i	0.580516	−	0.814249i	$-0.302851\pi$
$647$	−7.74147e17	−	1.34086e18i	−0.414902	−	0.718632i	−0.995418	+	0.0956170i	$0.969518\pi$
$648$		0			0
$649$	1.90559e17	−	3.30057e17i	0.100101	−	0.173380i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.05934e18	−	1.83483e18i	0.534687	−	0.926105i	−0.464492	−	0.885577i	$-0.653763\pi$
$653$	1.05934e18	−	1.83483e18i	0.534687	−	0.926105i	0.999178	−	0.0405271i	$-0.0129037\pi$
$654$		0			0
$655$	−2.07272e18	−	3.59006e18i	−1.02559	−	1.77637i
$656$		0			0
$657$	2.19035e18			1.06252
$658$		0			0
$659$	−1.71376e18			−0.815069			−0.407534	−	0.913190i	$-0.633611\pi$
$659$	−1.71376e18			−0.815069			−0.407534	+	0.913190i	$0.633611\pi$
$660$		0			0
$661$	1.69613e17	+	2.93778e17i	0.0790951	+	0.136997i	0.902860	−	0.429935i	$-0.141464\pi$
$661$	1.69613e17	+	2.93778e17i	0.0790951	+	0.136997i	−0.823765	+	0.566932i	$0.808130\pi$
$662$		0			0
$663$	−1.53346e17	+	2.65603e17i	−0.0701188	+	0.121449i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−1.32821e15	+	2.30052e15i	−0.000584047	+	0.00101160i
$668$		0			0
$669$	−3.53024e17	−	6.11456e17i	−0.152242	−	0.263691i
$670$		0			0
$671$	1.75829e17			0.0743692
$672$		0			0
$673$	1.99607e16			0.00828089			0.00414045	−	0.999991i	$-0.498682\pi$
$673$	1.99607e16			0.00828089			0.00414045	+	0.999991i	$0.498682\pi$
$674$		0			0
$675$	1.34761e18	+	2.33413e18i	0.548390	+	0.949840i
$676$		0			0
$677$	1.63372e18	−	2.82969e18i	0.652157	−	1.12957i	−0.330442	−	0.943826i	$-0.607198\pi$
$677$	1.63372e18	−	2.82969e18i	0.652157	−	1.12957i	0.982599	−	0.185742i	$-0.0594689\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−5.85716e17	+	1.01449e18i	−0.225025	+	0.389755i
$682$		0			0
$683$	−4.90065e17	−	8.48817e17i	−0.184722	−	0.319948i	0.758761	−	0.651370i	$-0.225805\pi$
$683$	−4.90065e17	−	8.48817e17i	−0.184722	−	0.319948i	−0.943483	+	0.331421i	$0.892472\pi$
$684$		0			0
$685$	4.80124e18			1.77568
$686$		0			0
$687$	−5.71483e17			−0.207388
$688$		0			0
$689$	−2.11833e18	−	3.66905e18i	−0.754341	−	1.30656i
$690$		0			0
$691$	1.36073e18	−	2.35685e18i	0.475514	−	0.823615i	−0.524093	−	0.851661i	$-0.675595\pi$
$691$	1.36073e18	−	2.35685e18i	0.475514	−	0.823615i	0.999607	+	0.0280468i	$0.00892874\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.24245e18	−	3.88404e18i	0.754783	−	1.30732i
$696$		0			0
$697$	1.58160e17	+	2.73941e17i	0.0522497	+	0.0904992i
$698$		0			0
$699$	1.65574e18			0.536897
$700$		0			0
$701$	5.87143e17			0.186886			0.0934430	−	0.995625i	$-0.470213\pi$
$701$	5.87143e17			0.186886			0.0934430	+	0.995625i	$0.470213\pi$
$702$		0			0
$703$	−3.44520e17	−	5.96727e17i	−0.107648	−	0.186451i
$704$		0			0
$705$	−1.33961e18	+	2.32027e18i	−0.410912	+	0.711720i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	1.83902e18	−	3.18527e18i	0.543733	−	0.941773i	−0.454952	−	0.890516i	$-0.650344\pi$
$709$	1.83902e18	−	3.18527e18i	0.543733	−	0.941773i	0.998685	−	0.0512575i	$-0.0163229\pi$
$710$		0			0
$711$	−1.59268e16	−	2.75860e16i	−0.00462355	−	0.00800822i
$712$		0			0
$713$	3.25173e17			0.0926901
$714$		0			0
$715$	−5.46617e18			−1.53001
$716$		0			0
$717$	7.28395e17	+	1.26162e18i	0.200213	+	0.346779i
$718$		0			0
$719$	1.12304e18	−	1.94517e18i	0.303151	−	0.525073i	−0.673697	−	0.739008i	$-0.735295\pi$
$719$	1.12304e18	−	1.94517e18i	0.303151	−	0.525073i	0.976848	+	0.213935i	$0.0686279\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	1.06959e18	−	1.85259e18i	0.278497	−	0.482370i
$724$		0			0
$725$	4.50104e16	+	7.79603e16i	0.0115111	+	0.0199378i
$726$		0			0
$727$	6.28082e18			1.57777			0.788883	−	0.614543i	$-0.210660\pi$
$727$	6.28082e18			1.57777			0.788883	+	0.614543i	$0.210660\pi$
$728$		0			0
$729$	−1.08408e18			−0.267506
$730$		0			0
$731$	5.79599e17	+	1.00389e18i	0.140496	+	0.243346i
$732$		0			0
$733$	−2.92034e18	+	5.05818e18i	−0.695436	+	1.20453i	0.274597	+	0.961559i	$0.411456\pi$
$733$	−2.92034e18	+	5.05818e18i	−0.695436	+	1.20453i	−0.970033	+	0.242972i	$0.921878\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.50908e18	−	4.34586e18i	0.576735	−	0.998935i
$738$		0			0
$739$	3.20125e18	+	5.54472e18i	0.722986	+	1.25225i	0.959797	+	0.280693i	$0.0905644\pi$
$739$	3.20125e18	+	5.54472e18i	0.722986	+	1.25225i	−0.236811	+	0.971556i	$0.576102\pi$
$740$		0			0
$741$	−2.59724e18			−0.576360
$742$		0			0
$743$	6.61717e18			1.44293			0.721465	−	0.692451i	$-0.243469\pi$
$743$	6.61717e18			1.44293			0.721465	+	0.692451i	$0.243469\pi$
$744$		0			0
$745$	−5.32180e18	−	9.21762e18i	−1.14036	−	1.97516i
$746$		0			0
$747$	1.40979e18	−	2.44183e18i	0.296873	−	0.514199i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−5.48800e17	+	9.50549e17i	−0.111623	+	0.193337i	−0.916425	−	0.400207i	$-0.868938\pi$
$751$	−5.48800e17	+	9.50549e17i	−0.111623	+	0.193337i	0.804802	+	0.593544i	$0.202272\pi$
$752$		0			0
$753$	3.89216e17	+	6.74142e17i	0.0778079	+	0.134767i
$754$		0			0
$755$	1.59609e19			3.13620
$756$		0			0
$757$	−8.91699e18			−1.72225			−0.861123	−	0.508397i	$-0.830238\pi$
$757$	−8.91699e18			−1.72225			−0.861123	+	0.508397i	$0.830238\pi$
$758$		0			0
$759$	−8.56678e16	−	1.48381e17i	−0.0162647	−	0.0281713i
$760$		0			0
$761$	4.27583e18	−	7.40596e18i	0.798032	−	1.38223i	−0.122863	−	0.992424i	$-0.539208\pi$
$761$	4.27583e18	−	7.40596e18i	0.798032	−	1.38223i	0.920896	−	0.389809i	$-0.127459\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	1.66660e18	−	2.88664e18i	0.300630	−	0.520707i
$766$		0			0
$767$	−4.52754e17	−	7.84193e17i	−0.0802958	−	0.139076i
$768$		0			0
$769$	−3.40420e18			−0.593600			−0.296800	−	0.954940i	$-0.595920\pi$
$769$	−3.40420e18			−0.593600			−0.296800	+	0.954940i	$0.595920\pi$
$770$		0			0
$771$	−1.75056e18			−0.300141
$772$		0			0
$773$	−2.13593e18	−	3.69955e18i	−0.360098	−	0.623709i	0.627878	−	0.778311i	$-0.283924\pi$
$773$	−2.13593e18	−	3.69955e18i	−0.360098	−	0.623709i	−0.987977	+	0.154603i	$0.950590\pi$
$774$		0			0
$775$	5.50976e18	−	9.54319e18i	0.913423	−	1.58209i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.33939e18	+	2.31989e18i	−0.214740	+	0.371941i
$780$		0			0
$781$	−1.15270e18	−	1.99653e18i	−0.181754	−	0.314807i
$782$		0			0
$783$	6.45123e16			0.0100044
$784$		0			0
$785$	1.54550e18			0.235731
$786$		0			0
$787$	1.00510e18	+	1.74089e18i	0.150790	+	0.261177i	0.931518	−	0.363695i	$-0.118485\pi$
$787$	1.00510e18	+	1.74089e18i	0.150790	+	0.261177i	−0.780728	+	0.624871i	$0.785151\pi$
$788$		0			0
$789$	−5.86441e17	+	1.01575e18i	−0.0865414	+	0.149894i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	2.08878e17	−	3.61788e17i	0.0298276	−	0.0516629i
$794$		0			0
$795$	−3.66646e18	−	6.35050e18i	−0.515063	−	0.892116i
$796$		0			0
$797$	−1.68131e18			−0.232364			−0.116182	−	0.993228i	$-0.537066\pi$
$797$	−1.68131e18			−0.232364			−0.116182	+	0.993228i	$0.537066\pi$
$798$		0			0
$799$	4.39074e18			0.597013
$800$		0			0
$801$	−2.39673e18	−	4.15125e18i	−0.320632	−	0.555351i
$802$		0			0
$803$	−5.09435e18	+	8.82367e18i	−0.670560	+	1.16144i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.89844e16	−	3.28820e16i	0.00241946	−	0.00419064i
$808$		0			0
$809$	−4.44871e18	−	7.70539e18i	−0.557916	−	0.966338i	−0.997670	−	0.0682204i	$-0.978268\pi$
$809$	−4.44871e18	−	7.70539e18i	−0.557916	−	0.966338i	0.439755	−	0.898118i	$-0.355065\pi$
$810$		0			0
$811$	7.39152e18			0.912217			0.456108	−	0.889924i	$-0.349243\pi$
$811$	7.39152e18			0.912217			0.456108	+	0.889924i	$0.349243\pi$
$812$		0			0
$813$	−1.07238e18			−0.130245
$814$		0			0
$815$	1.05303e19	+	1.82391e19i	1.25869	+	2.18011i
$816$		0			0
$817$	−4.90837e18	+	8.50155e18i	−0.577423	+	1.00013i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−2.36288e18	+	4.09262e18i	−0.269284	+	0.466414i	−0.968677	−	0.248324i	$-0.920120\pi$
$821$	−2.36288e18	+	4.09262e18i	−0.269284	+	0.466414i	0.699393	+	0.714737i	$0.253454\pi$
$822$		0			0
$823$	−1.24045e18	−	2.14852e18i	−0.139149	−	0.241013i	0.788026	−	0.615642i	$-0.211103\pi$
$823$	−1.24045e18	−	2.14852e18i	−0.139149	−	0.241013i	−0.927175	+	0.374629i	$0.877770\pi$
$824$		0			0
$825$	−5.80625e18			−0.641128
$826$		0			0
$827$	−1.02026e19			−1.10898			−0.554492	−	0.832189i	$-0.687087\pi$
$827$	−1.02026e19			−1.10898			−0.554492	+	0.832189i	$0.687087\pi$
$828$		0			0
$829$	3.95802e18	+	6.85548e18i	0.423519	+	0.733557i	0.996281	−	0.0861652i	$-0.0274613\pi$
$829$	3.95802e18	+	6.85548e18i	0.423519	+	0.733557i	−0.572762	+	0.819722i	$0.694128\pi$
$830$		0			0
$831$	−2.33757e17	+	4.04879e17i	−0.0246239	+	0.0426499i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−3.55488e18	+	6.15723e18i	−0.362963	+	0.628670i
$836$		0			0
$837$	−3.94850e18	−	6.83901e18i	−0.396933	−	0.687508i
$838$		0			0
$839$	−1.37076e19			−1.35678			−0.678389	−	0.734703i	$-0.737322\pi$
$839$	−1.37076e19			−1.35678			−0.678389	+	0.734703i	$0.737322\pi$
$840$		0			0
$841$	−1.02585e19			−0.999790
$842$		0			0
$843$	2.75137e18	+	4.76552e18i	0.264040	+	0.457331i
$844$		0			0
$845$	2.01929e18	−	3.49751e18i	0.190823	−	0.330515i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−8.92095e17	+	1.54515e18i	−0.0817544	+	0.141603i
$850$		0			0
$851$	−5.39988e16	−	9.35287e16i	−0.00487351	−	0.00844117i
$852$		0			0
$853$	9.04601e18			0.804060			0.402030	−	0.915627i	$-0.368305\pi$
$853$	9.04601e18			0.804060			0.402030	+	0.915627i	$0.368305\pi$
$854$		0			0
$855$	2.82275e19			2.47111
$856$		0			0
$857$	−2.98471e18	−	5.16966e18i	−0.257351	−	0.445746i	0.708180	−	0.706032i	$-0.249516\pi$
$857$	−2.98471e18	−	5.16966e18i	−0.257351	−	0.445746i	−0.965532	+	0.260286i	$0.916183\pi$
$858$		0			0
$859$	−5.17751e18	+	8.96770e18i	−0.439709	+	0.761598i	−0.997667	−	0.0682714i	$-0.978252\pi$
$859$	−5.17751e18	+	8.96770e18i	−0.439709	+	0.761598i	0.557958	+	0.829869i	$0.311585\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.97961e18	−	3.42879e18i	0.163121	−	0.282534i	−0.772865	−	0.634570i	$-0.781177\pi$
$863$	1.97961e18	−	3.42879e18i	0.163121	−	0.282534i	0.935986	+	0.352036i	$0.114511\pi$
$864$		0			0
$865$	1.01953e19	+	1.76588e19i	0.827553	+	1.43336i
$866$		0			0
$867$	−3.76541e18			−0.301084
$868$		0			0
$869$	1.48171e17			0.0116717
$870$		0			0
$871$	−5.96142e18	−	1.03255e19i	−0.462627	−	0.801294i
$872$		0			0
$873$	4.61184e18	−	7.98794e18i	0.352599	−	0.610720i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−2.19202e18	+	3.79668e18i	−0.162685	+	0.281778i	−0.935831	−	0.352450i	$-0.885349\pi$
$877$	−2.19202e18	+	3.79668e18i	−0.162685	+	0.281778i	0.773146	+	0.634228i	$0.218682\pi$
$878$		0			0
$879$	−4.44204e18	−	7.69384e18i	−0.324829	−	0.562620i
$880$		0			0
$881$	−4.00058e18			−0.288257			−0.144129	−	0.989559i	$-0.546038\pi$
$881$	−4.00058e18			−0.288257			−0.144129	+	0.989559i	$0.546038\pi$
$882$		0			0
$883$	−9.47450e18			−0.672685			−0.336343	−	0.941740i	$-0.609190\pi$
$883$	−9.47450e18			−0.672685			−0.336343	+	0.941740i	$0.609190\pi$
$884$		0			0
$885$	−7.83640e17	−	1.35730e18i	−0.0548259	−	0.0949612i
$886$		0			0
$887$	6.10507e18	−	1.05743e19i	0.420908	−	0.729034i	−0.575120	−	0.818069i	$-0.695045\pi$
$887$	6.10507e18	−	1.05743e19i	0.420908	−	0.729034i	0.996029	+	0.0890346i	$0.0283782\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	4.93319e18	−	8.54453e18i	0.330311	−	0.572115i
$892$		0			0
$893$	1.85917e19	+	3.22017e19i	1.22683	+	2.12493i
$894$		0			0
$895$	−1.78319e19			−1.15970
$896$		0			0
$897$	−4.07082e17			−0.0260934
$898$		0			0
$899$	−1.31881e17	−	2.28424e17i	−0.00833188	−	0.0144312i
$900$		0			0
$901$	−6.00865e18	+	1.04073e19i	−0.374167	+	0.648077i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.28075e19	+	2.21832e19i	−0.774904	+	1.34217i
$906$		0			0
$907$	−1.63653e18	−	2.83455e18i	−0.0976057	−	0.169058i	0.813087	−	0.582142i	$-0.197785\pi$
$907$	−1.63653e18	−	2.83455e18i	−0.0976057	−	0.169058i	−0.910693	+	0.413084i	$0.864452\pi$
$908$		0			0
$909$	−1.46521e19			−0.861457
$910$		0			0
$911$	2.50694e19			1.45303			0.726514	−	0.687151i	$-0.241139\pi$
$911$	2.50694e19			1.45303			0.726514	+	0.687151i	$0.241139\pi$
$912$		0			0
$913$	6.55782e18	+	1.13585e19i	0.374714	+	0.649023i
$914$		0			0
$915$	3.61533e17	−	6.26193e17i	0.0203662	−	0.0352753i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−2.63274e18	+	4.56003e18i	−0.144164	+	0.249699i	−0.929061	−	0.369927i	$-0.879383\pi$
$919$	−2.63274e18	+	4.56003e18i	−0.144164	+	0.249699i	0.784897	+	0.619626i	$0.212716\pi$
$920$		0			0
$921$	−3.55729e18	−	6.16141e18i	−0.192058	−	0.332654i
$922$		0			0
$923$	−5.47746e18			−0.291587
$924$		0			0
$925$	−3.65984e18			−0.192106
$926$		0			0
$927$	−7.51220e18	−	1.30115e19i	−0.388820	−	0.673457i
$928$		0			0
$929$	−9.13597e17	+	1.58240e18i	−0.0466286	+	0.0807631i	−0.888398	−	0.459075i	$-0.848181\pi$
$929$	−9.13597e17	+	1.58240e18i	−0.0466286	+	0.0807631i	0.841769	+	0.539838i	$0.181514\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−4.59778e18	+	7.96359e18i	−0.228201	+	0.395256i
$934$		0			0
$935$	7.75241e18	+	1.34276e19i	0.379456	+	0.657237i
$936$		0			0
$937$	3.72615e16			0.00179867			0.000899337	−	1.00000i	$-0.499714\pi$
$937$	3.72615e16			0.00179867			0.000899337		1.00000i	$0.499714\pi$
$938$		0			0
$939$	−9.35731e18			−0.445476
$940$		0			0
$941$	−2.04378e19	−	3.53992e19i	−0.959623	−	1.66212i	−0.723415	−	0.690413i	$-0.757429\pi$
$941$	−2.04378e19	−	3.53992e19i	−0.959623	−	1.66212i	−0.236208	−	0.971703i	$-0.575905\pi$
$942$		0			0
$943$	−2.09931e17	+	3.63611e17i	−0.00972189	+	0.0168388i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.25245e19	−	2.16930e19i	0.564267	−	0.977339i	−0.432851	−	0.901466i	$-0.642492\pi$
$947$	1.25245e19	−	2.16930e19i	0.564267	−	0.977339i	0.997117	−	0.0758731i	$-0.0241744\pi$
$948$		0			0
$949$	1.21038e19	+	2.09644e19i	0.537888	+	0.931650i
$950$		0			0
$951$	−1.14456e19			−0.501725
$952$		0			0
$953$	2.88981e19			1.24958			0.624791	−	0.780792i	$-0.285184\pi$
$953$	2.88981e19			1.24958			0.624791	+	0.780792i	$0.285184\pi$
$954$		0			0
$955$	2.71522e19	+	4.70290e19i	1.15820	+	2.00606i
$956$		0			0
$957$	−6.94886e16	+	1.20358e17i	−0.00292406	+	0.00506462i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−3.93484e18	+	6.81535e18i	−0.161148	+	0.279117i
$962$		0			0
$963$	8.65583e18	+	1.49923e19i	0.349734	+	0.605757i
$964$		0			0
$965$	−1.02345e19			−0.407980
$966$		0			0
$967$	3.95693e19			1.55627			0.778137	−	0.628094i	$-0.216165\pi$
$967$	3.95693e19			1.55627			0.778137	+	0.628094i	$0.216165\pi$
$968$		0			0
$969$	3.68355e18	+	6.38009e18i	0.142943	+	0.247584i
$970$		0			0
$971$	−7.69274e18	+	1.33242e19i	−0.294548	+	0.510172i	−0.974880	−	0.222732i	$-0.928502\pi$
$971$	−7.69274e18	+	1.33242e19i	−0.294548	+	0.510172i	0.680332	+	0.732904i	$0.261836\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−6.89762e18	+	1.19470e19i	−0.257140	+	0.445379i
$976$		0			0
$977$	1.00232e19	+	1.73608e19i	0.368717	+	0.638637i	0.989365	−	0.145452i	$-0.0464637\pi$
$977$	1.00232e19	+	1.73608e19i	0.368717	+	0.638637i	−0.620648	+	0.784089i	$0.713130\pi$
$978$		0			0
$979$	2.22974e19			0.809406
$980$		0			0
$981$	6.00513e17			0.0215117
$982$		0			0
$983$	2.92003e18	+	5.05765e18i	0.103226	+	0.178793i	0.913012	−	0.407932i	$-0.133750\pi$
$983$	2.92003e18	+	5.05765e18i	0.103226	+	0.178793i	−0.809786	+	0.586725i	$0.800417\pi$
$984$		0			0
$985$	−2.42450e19	+	4.19937e19i	−0.845839	+	1.46504i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−7.69320e17	+	1.33250e18i	−0.0261415	+	0.0452784i
$990$		0			0
$991$	−1.60844e19	−	2.78589e19i	−0.539417	−	0.934298i	−0.998935	−	0.0461297i	$-0.985311\pi$
$991$	−1.60844e19	−	2.78589e19i	−0.539417	−	0.934298i	0.459518	−	0.888168i	$-0.348022\pi$
$992$		0			0
$993$	−1.59085e19			−0.526572
$994$		0			0
$995$	1.82594e19			0.596536
$996$		0			0
$997$	−1.47087e18	−	2.54762e18i	−0.0474302	−	0.0821515i	0.841336	−	0.540513i	$-0.181770\pi$
$997$	−1.47087e18	−	2.54762e18i	−0.0474302	−	0.0821515i	−0.888766	+	0.458362i	$0.848437\pi$
$998$		0			0
$999$	−1.31139e18	+	2.27139e18i	−0.0417403	+	0.0722964i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.14.e.a.177.1		2
7.2	even	3		4.14.a.a.1.1	✓	1
7.3	odd	6		196.14.e.b.165.1		2
7.4	even	3	inner	196.14.e.a.165.1		2
7.5	odd	6		196.14.a.a.1.1		1
7.6	odd	2		196.14.e.b.177.1		2
21.2	odd	6		36.14.a.a.1.1		1
28.23	odd	6		16.14.a.b.1.1		1
35.2	odd	12		100.14.c.a.49.1		2
35.9	even	6		100.14.a.a.1.1		1
35.23	odd	12		100.14.c.a.49.2		2
56.37	even	6		64.14.a.c.1.1		1
56.51	odd	6		64.14.a.g.1.1		1
84.23	even	6		144.14.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.14.a.a.1.1	✓	1	7.2	even	3
16.14.a.b.1.1		1	28.23	odd	6
36.14.a.a.1.1		1	21.2	odd	6
64.14.a.c.1.1		1	56.37	even	6
64.14.a.g.1.1		1	56.51	odd	6
100.14.a.a.1.1		1	35.9	even	6
100.14.c.a.49.1		2	35.2	odd	12
100.14.c.a.49.2		2	35.23	odd	12
144.14.a.a.1.1		1	84.23	even	6
196.14.a.a.1.1		1	7.5	odd	6
196.14.e.a.165.1		2	7.4	even	3	inner
196.14.e.a.177.1		2	1.1	even	1	trivial
196.14.e.b.165.1		2	7.3	odd	6
196.14.e.b.177.1		2	7.6	odd	2

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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	196.14.e.a.177.1

Level	$196$
Weight	$14$
Character	196.177
Analytic conductor	$210.173$
Analytic rank	$0$
Dimension	$2$
Inner twists	$2$