LMFDB - Embedded newform 98.10.c.i.67.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,10,Mod(67,98)] 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("98.67"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(98, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	98.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,32,0] 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:	$50.4735119441$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{43})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 43x^{2} + 1849 $ x^4 + 43*x^2 + 1849
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$-3.27872 + 5.67891i$ of defining polynomial
Character	$\chi$	$=$	98.67
Dual form			98.10.c.i.79.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(8.00000 + 13.8564i) q^{2} +(-26.2298 + 45.4313i) q^{3} +(-128.000 + 221.703i) q^{4} +(-918.041 - 1590.09i) q^{5} -839.352 q^{6} -4096.00 q^{8} +(8465.50 + 14662.7i) q^{9} +(14688.7 - 25441.5i) q^{10} +(-4690.00 + 8123.32i) q^{11} +(-6714.82 - 11630.4i) q^{12} +179044. q^{13} +96320.0 q^{15} +(-32768.0 - 56755.8i) q^{16} +(-48944.7 + 84774.7i) q^{17} +(-135448. + 234603. i) q^{18} +(-281367. - 487341. i) q^{19} +470037. q^{20} -150080. q^{22} +(489468. + 847783. i) q^{23} +(107437. - 186086. i) q^{24} +(-709038. + 1.22809e6i) q^{25} +(1.43235e6 + 2.48091e6i) q^{26} -1.92075e6 q^{27} -4.31721e6 q^{29} +(770560. + 1.33465e6i) q^{30} +(-3.98729e6 + 6.90619e6i) q^{31} +(524288. - 908093. i) q^{32} +(-246035. - 426145. i) q^{33} -1.56623e6 q^{34} -4.33434e6 q^{36} +(-1.35720e6 - 2.35073e6i) q^{37} +(4.50187e6 - 7.79746e6i) q^{38} +(-4.69629e6 + 8.13421e6i) q^{39} +(3.76030e6 + 6.51303e6i) q^{40} +9.00237e6 q^{41} -3.47557e7 q^{43} +(-1.20064e6 - 2.07957e6i) q^{44} +(1.55434e7 - 2.69219e7i) q^{45} +(-7.83149e6 + 1.35645e7i) q^{46} +(-2.10888e7 - 3.65268e7i) q^{47} +3.43799e6 q^{48} -2.26892e7 q^{50} +(-2.56762e6 - 4.44724e6i) q^{51} +(-2.29177e7 + 3.96946e7i) q^{52} +(-3.40340e7 + 5.89486e7i) q^{53} +(-1.53660e7 - 2.66147e7i) q^{54} +1.72225e7 q^{55} +2.95207e7 q^{57} +(-3.45377e7 - 5.98211e7i) q^{58} +(1.71159e7 - 2.96456e7i) q^{59} +(-1.23290e7 + 2.13544e7i) q^{60} +(8.29163e7 + 1.43615e8i) q^{61} -1.27593e8 q^{62} +1.67772e7 q^{64} +(-1.64370e8 - 2.84697e8i) q^{65} +(3.93656e6 - 6.81832e6i) q^{66} +(-1.21472e8 + 2.10396e8i) q^{67} +(-1.25298e7 - 2.17023e7i) q^{68} -5.13545e7 q^{69} -9.42925e7 q^{71} +(-3.46747e7 - 6.00583e7i) q^{72} +(-6.66672e7 + 1.15471e8i) q^{73} +(2.17152e7 - 3.76117e7i) q^{74} +(-3.71958e7 - 6.44249e7i) q^{75} +1.44060e8 q^{76} -1.50281e8 q^{78} +(-3.38813e8 - 5.86841e8i) q^{79} +(-6.01648e7 + 1.04208e8i) q^{80} +(-1.16246e8 + 2.01343e8i) q^{81} +(7.20189e7 + 1.24740e8i) q^{82} +4.41313e8 q^{83} +1.79733e8 q^{85} +(-2.78046e8 - 4.81589e8i) q^{86} +(1.13239e8 - 1.96137e8i) q^{87} +(1.92102e7 - 3.32731e7i) q^{88} +(-2.77639e8 - 4.80885e8i) q^{89} +4.97387e8 q^{90} -2.50608e8 q^{92} +(-2.09171e8 - 3.62295e8i) q^{93} +(3.37420e8 - 5.84429e8i) q^{94} +(-5.16612e8 + 8.94799e8i) q^{95} +(2.75039e7 + 4.76381e7i) q^{96} -1.26895e9 q^{97} -1.58813e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 32 q^{2} - 512 q^{4} - 16384 q^{8} + 33862 q^{9} - 18760 q^{11} + 385280 q^{15} - 131072 q^{16} - 541792 q^{18} - 600320 q^{22} + 1957872 q^{23} - 2836150 q^{25} - 17268856 q^{29} + 3082240 q^{30}+ \cdots - 635251120 q^{99}+O(q^{100}) $ 4 * q + 32 * q^2 - 512 * q^4 - 16384 * q^8 + 33862 * q^9 - 18760 * q^11 + 385280 * q^15 - 131072 * q^16 - 541792 * q^18 - 600320 * q^22 + 1957872 * q^23 - 2836150 * q^25 - 17268856 * q^29 + 3082240 * q^30 + 2097152 * q^32 - 17337344 * q^36 - 5428788 * q^37 - 18785152 * q^39 - 139022768 * q^43 - 4802560 * q^44 - 31325952 * q^46 - 90756800 * q^50 - 10270464 * q^51 - 136135852 * q^53 + 118082816 * q^57 - 138150848 * q^58 - 49315840 * q^60 + 67108864 * q^64 - 657480320 * q^65 - 485888840 * q^67 - 377169856 * q^71 - 138698752 * q^72 + 86860608 * q^74 - 601124864 * q^78 - 1355250320 * q^79 - 464982290 * q^81 + 718932480 * q^85 - 1112182144 * q^86 + 76840960 * q^88 - 1002430464 * q^92 - 836685056 * q^93 - 2066449280 * q^95 - 635251120 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	8.00000	+	13.8564i	0.353553	+	0.612372i
$2$	8.00000	+	13.8564i	0.353553	+	0.612372i
$3$	−26.2298	+	45.4313i	−0.186960	+	0.323824i	−0.944235	−	0.329272i	$-0.893197\pi$
$3$	−26.2298	+	45.4313i	−0.186960	+	0.323824i	0.757275	+	0.653096i	$0.226530\pi$
$4$	−128.000	+	221.703i	−0.250000	+	0.433013i
$5$	−918.041	−	1590.09i	−0.656897	−	1.13778i	−0.981415	−	0.191899i	$-0.938535\pi$
$5$	−918.041	−	1590.09i	−0.656897	−	1.13778i	0.324518	−	0.945880i	$-0.394798\pi$
$6$	−839.352			−0.264401
$7$		0			0
$7$		0			0
$8$	−4096.00			−0.353553
$9$	8465.50	+	14662.7i	0.430092	+	0.744941i
$10$	14688.7	−	25441.5i	0.464496	−	0.804531i
$11$	−4690.00	+	8123.32i	−0.0965841	+	0.167289i	−0.910269	−	0.414018i	$-0.864125\pi$
$11$	−4690.00	+	8123.32i	−0.0965841	+	0.167289i	0.813685	+	0.581307i	$0.197458\pi$
$12$	−6714.82	−	11630.4i	−0.0934800	−	0.161912i
$13$	179044.			1.73866			0.869332	−	0.494229i	$-0.164550\pi$
$13$	179044.			1.73866			0.869332	+	0.494229i	$0.164550\pi$
$14$		0			0
$15$	96320.0			0.491254
$16$	−32768.0	−	56755.8i	−0.125000	−	0.216506i
$17$	−48944.7	+	84774.7i	−0.142130	+	0.246176i	−0.928299	−	0.371836i	$-0.878728\pi$
$17$	−48944.7	+	84774.7i	−0.142130	+	0.246176i	0.786169	+	0.618012i	$0.212062\pi$
$18$	−135448.	+	234603.i	−0.304121	+	0.526753i
$19$	−281367.	−	487341.i	−0.495315	−	0.857910i	0.504671	−	0.863312i	$-0.331614\pi$
$19$	−281367.	−	487341.i	−0.495315	−	0.857910i	−0.999985	+	0.00540159i	$0.998281\pi$
$20$	470037.			0.656897
$21$		0			0
$22$	−150080.			−0.136591
$23$	489468.	+	847783.i	0.364711	+	0.631698i	0.988730	−	0.149711i	$-0.0478344\pi$
$23$	489468.	+	847783.i	0.364711	+	0.631698i	−0.624019	+	0.781409i	$0.714501\pi$
$24$	107437.	−	186086.i	0.0661003	−	0.114489i
$25$	−709038.	+	1.22809e6i	−0.363027	+	0.628782i
$26$	1.43235e6	+	2.48091e6i	0.614710	+	1.06471i
$27$	−1.92075e6			−0.695560
$28$		0			0
$29$	−4.31721e6			−1.13348			−0.566738	−	0.823898i	$-0.691795\pi$
$29$	−4.31721e6			−1.13348			−0.566738	+	0.823898i	$0.691795\pi$
$30$	770560.	+	1.33465e6i	0.173684	+	0.300830i
$31$	−3.98729e6	+	6.90619e6i	−0.775444	+	1.34311i	0.159101	+	0.987262i	$0.449140\pi$
$31$	−3.98729e6	+	6.90619e6i	−0.775444	+	1.34311i	−0.934545	+	0.355845i	$0.884193\pi$
$32$	524288.	−	908093.i	0.0883883	−	0.153093i
$33$	−246035.	−	426145.i	−0.0361147	−	0.0625525i
$34$	−1.56623e6			−0.201002
$35$		0			0
$36$	−4.33434e6			−0.430092
$37$	−1.35720e6	−	2.35073e6i	−0.119052	−	0.206203i	0.800341	−	0.599546i	$-0.204652\pi$
$37$	−1.35720e6	−	2.35073e6i	−0.119052	−	0.206203i	−0.919392	+	0.393342i	$0.871319\pi$
$38$	4.50187e6	−	7.79746e6i	0.350240	−	0.606634i
$39$	−4.69629e6	+	8.13421e6i	−0.325060	+	0.563021i
$40$	3.76030e6	+	6.51303e6i	0.232248	+	0.402266i
$41$	9.00237e6			0.497542			0.248771	−	0.968562i	$-0.419973\pi$
$41$	9.00237e6			0.497542			0.248771	+	0.968562i	$0.419973\pi$
$42$		0			0
$43$	−3.47557e7			−1.55031			−0.775154	−	0.631773i	$-0.782328\pi$
$43$	−3.47557e7			−1.55031			−0.775154	+	0.631773i	$0.782328\pi$
$44$	−1.20064e6	−	2.07957e6i	−0.0482921	−	0.0836443i
$45$	1.55434e7	−	2.69219e7i	0.565052	−	0.978699i
$46$	−7.83149e6	+	1.35645e7i	−0.257890	+	0.446678i
$47$	−2.10888e7	−	3.65268e7i	−0.630392	−	1.09187i	−0.987471	−	0.157798i	$-0.949561\pi$
$47$	−2.10888e7	−	3.65268e7i	−0.630392	−	1.09187i	0.357079	−	0.934074i	$-0.383773\pi$
$48$	3.43799e6			0.0934800
$49$		0			0
$50$	−2.26892e7			−0.513398
$51$	−2.56762e6	−	4.44724e6i	−0.0531452	−	0.0920502i
$52$	−2.29177e7	+	3.96946e7i	−0.434666	+	0.752863i
$53$	−3.40340e7	+	5.89486e7i	−0.592476	+	1.02620i	0.401421	+	0.915894i	$0.368516\pi$
$53$	−3.40340e7	+	5.89486e7i	−0.592476	+	1.02620i	−0.993898	+	0.110306i	$0.964817\pi$
$54$	−1.53660e7	−	2.66147e7i	−0.245918	−	0.425942i
$55$	1.72225e7			0.253783
$56$		0			0
$57$	2.95207e7			0.370416
$58$	−3.45377e7	−	5.98211e7i	−0.400745	−	0.694110i
$59$	1.71159e7	−	2.96456e7i	0.183893	−	0.318512i	−0.759310	−	0.650729i	$-0.774463\pi$
$59$	1.71159e7	−	2.96456e7i	0.183893	−	0.318512i	0.943203	+	0.332217i	$0.107797\pi$
$60$	−1.23290e7	+	2.13544e7i	−0.122813	+	0.212719i
$61$	8.29163e7	+	1.43615e8i	0.766753	+	1.32806i	0.939315	+	0.343056i	$0.111462\pi$
$61$	8.29163e7	+	1.43615e8i	0.766753	+	1.32806i	−0.172562	+	0.984999i	$0.555204\pi$
$62$	−1.27593e8			−1.09664
$63$		0			0
$64$	1.67772e7			0.125000
$65$	−1.64370e8	−	2.84697e8i	−1.14212	−	1.97821i
$66$	3.93656e6	−	6.81832e6i	0.0255370	−	0.0442313i
$67$	−1.21472e8	+	2.10396e8i	−0.736445	+	1.27556i	0.217641	+	0.976029i	$0.430164\pi$
$67$	−1.21472e8	+	2.10396e8i	−0.736445	+	1.27556i	−0.954086	+	0.299531i	$0.903170\pi$
$68$	−1.25298e7	−	2.17023e7i	−0.0710650	−	0.123088i
$69$	−5.13545e7			−0.272746
$70$		0			0
$71$	−9.42925e7			−0.440367			−0.220183	−	0.975459i	$-0.570666\pi$
$71$	−9.42925e7			−0.440367			−0.220183	+	0.975459i	$0.570666\pi$
$72$	−3.46747e7	−	6.00583e7i	−0.152060	−	0.263376i
$73$	−6.66672e7	+	1.15471e8i	−0.274764	+	0.475905i	−0.970076	−	0.242803i	$-0.921933\pi$
$73$	−6.66672e7	+	1.15471e8i	−0.274764	+	0.475905i	0.695312	+	0.718708i	$0.255266\pi$
$74$	2.17152e7	−	3.76117e7i	0.0841822	−	0.145808i
$75$	−3.71958e7	−	6.44249e7i	−0.135743	−	0.235114i
$76$	1.44060e8			0.495315
$77$		0			0
$78$	−1.50281e8			−0.459705
$79$	−3.38813e8	−	5.86841e8i	−0.978673	−	1.69511i	−0.667239	−	0.744844i	$-0.732524\pi$
$79$	−3.38813e8	−	5.86841e8i	−0.978673	−	1.69511i	−0.311434	−	0.950268i	$-0.600809\pi$
$80$	−6.01648e7	+	1.04208e8i	−0.164224	+	0.284445i
$81$	−1.16246e8	+	2.01343e8i	−0.300050	+	0.519702i
$82$	7.20189e7	+	1.24740e8i	0.175907	+	0.304681i
$83$	4.41313e8			1.02069			0.510347	−	0.859968i	$-0.329517\pi$
$83$	4.41313e8			1.02069			0.510347	+	0.859968i	$0.329517\pi$
$84$		0			0
$85$	1.79733e8			0.373459
$86$	−2.78046e8	−	4.81589e8i	−0.548117	−	0.949366i
$87$	1.13239e8	−	1.96137e8i	0.211915	−	0.367047i
$88$	1.92102e7	−	3.32731e7i	0.0341476	−	0.0591455i
$89$	−2.77639e8	−	4.80885e8i	−0.469056	−	0.812430i	0.530318	−	0.847799i	$-0.322073\pi$
$89$	−2.77639e8	−	4.80885e8i	−0.469056	−	0.812430i	−0.999374	+	0.0353693i	$0.988739\pi$
$90$	4.97387e8			0.799104
$91$		0			0
$92$	−2.50608e8			−0.364711
$93$	−2.09171e8	−	3.62295e8i	−0.289954	−	0.502215i
$94$	3.37420e8	−	5.84429e8i	0.445755	−	0.772070i
$95$	−5.16612e8	+	8.94799e8i	−0.650742	+	1.12712i
$96$	2.75039e7	+	4.76381e7i	0.0330502	+	0.0572446i
$97$	−1.26895e9			−1.45536			−0.727680	−	0.685917i	$-0.759401\pi$
$97$	−1.26895e9			−1.45536			−0.727680	+	0.685917i	$0.759401\pi$
$98$		0			0
$99$	−1.58813e8			−0.166160
$100$	−1.81514e8	−	3.14391e8i	−0.181514	−	0.314391i
$101$	−6.84150e8	+	1.18498e9i	−0.654191	+	1.13309i	0.327904	+	0.944711i	$0.393658\pi$
$101$	−6.84150e8	+	1.18498e9i	−0.654191	+	1.13309i	−0.982096	+	0.188382i	$0.939676\pi$
$102$	4.10819e7	−	7.11559e7i	0.0375794	−	0.0650893i
$103$	9.60758e7	+	1.66408e8i	0.0841097	+	0.145682i	0.905012	−	0.425387i	$-0.139862\pi$
$103$	9.60758e7	+	1.66408e8i	0.0841097	+	0.145682i	−0.820902	+	0.571069i	$0.806529\pi$
$104$	−7.33365e8			−0.614710
$105$		0			0
$106$	−1.08909e9			−0.837888
$107$	5.24275e8	+	9.08071e8i	0.386663	+	0.669719i	0.991998	−	0.126251i	$-0.0402945\pi$
$107$	5.24275e8	+	9.08071e8i	0.386663	+	0.669719i	−0.605336	+	0.795970i	$0.706961\pi$
$108$	2.45856e8	−	4.25836e8i	0.173890	−	0.301186i
$109$	−1.01879e9	+	1.76459e9i	−0.691297	+	1.19736i	0.280116	+	0.959966i	$0.409627\pi$
$109$	−1.01879e9	+	1.76459e9i	−0.691297	+	1.19736i	−0.971413	+	0.237395i	$0.923706\pi$
$110$	1.37780e8	+	2.38641e8i	0.0897259	+	0.155410i
$111$	1.42396e8			0.0890315
$112$		0			0
$113$	−4.70999e8			−0.271748			−0.135874	−	0.990726i	$-0.543384\pi$
$113$	−4.70999e8			−0.271748			−0.135874	+	0.990726i	$0.543384\pi$
$114$	2.36166e8	+	4.09051e8i	0.130962	+	0.226833i
$115$	8.98704e8	−	1.55660e9i	0.479155	−	0.829921i
$116$	5.52603e8	−	9.57137e8i	0.283369	−	0.490810i
$117$	1.51570e9	+	2.62527e9i	0.747785	+	1.29520i
$118$	5.47708e8			0.260064
$119$		0			0
$120$	−3.94527e8			−0.173684
$121$	1.13498e9	+	1.96585e9i	0.481343	+	0.833711i
$122$	−1.32666e9	+	2.29784e9i	−0.542176	+	0.939077i
$123$	−2.36130e8	+	4.08989e8i	−0.0930203	+	0.161116i
$124$	−1.02075e9	−	1.76798e9i	−0.387722	−	0.671554i
$125$	−9.82396e8			−0.359908
$126$		0			0
$127$	2.87598e9			0.981001			0.490500	−	0.871441i	$-0.336814\pi$
$127$	2.87598e9			0.981001			0.490500	+	0.871441i	$0.336814\pi$
$128$	1.34218e8	+	2.32472e8i	0.0441942	+	0.0765466i
$129$	9.11633e8	−	1.57900e9i	0.289845	−	0.502027i
$130$	2.62992e9	−	4.55516e9i	0.807603	−	1.39881i
$131$	−2.98553e9	−	5.17109e9i	−0.885729	−	1.53413i	−0.844875	−	0.534963i	$-0.820325\pi$
$131$	−2.98553e9	−	5.17109e9i	−0.885729	−	1.53413i	−0.0408540	−	0.999165i	$-0.513008\pi$
$132$	1.25970e8			0.0361147
$133$		0			0
$134$	−3.88711e9			−1.04149
$135$	1.76333e9	+	3.05418e9i	0.456911	+	0.791393i
$136$	2.00478e8	−	3.47237e8i	0.0502505	−	0.0870365i
$137$	6.98550e8	−	1.20992e9i	0.169416	−	0.293437i	−0.768799	−	0.639491i	$-0.779145\pi$
$137$	6.98550e8	−	1.20992e9i	0.169416	−	0.293437i	0.938215	+	0.346054i	$0.112478\pi$
$138$	−4.10836e8	−	7.11589e8i	−0.0964301	−	0.167022i
$139$	7.96582e9			1.80994			0.904969	−	0.425477i	$-0.139894\pi$
$139$	7.96582e9			1.80994			0.904969	+	0.425477i	$0.139894\pi$
$140$		0			0
$141$	2.21261e9			0.471433
$142$	−7.54340e8	−	1.30655e9i	−0.155693	−	0.269668i
$143$	−8.39718e8	+	1.45443e9i	−0.167927	+	0.290859i
$144$	5.54795e8	−	9.60933e8i	0.107523	−	0.186235i
$145$	3.96338e9	+	6.86478e9i	0.744577	+	1.28965i
$146$	−2.13335e9			−0.388575
$147$		0			0
$148$	6.94885e8			0.119052
$149$	5.51302e9	+	9.54884e9i	0.916329	+	1.58713i	0.804943	+	0.593352i	$0.202196\pi$
$149$	5.51302e9	+	9.54884e9i	0.916329	+	1.58713i	0.111386	+	0.993777i	$0.464471\pi$
$150$	5.95132e8	−	1.03080e9i	0.0959849	−	0.166251i
$151$	1.97237e9	−	3.41624e9i	0.308739	−	0.534752i	−0.669348	−	0.742949i	$-0.733426\pi$
$151$	1.97237e9	−	3.41624e9i	0.308739	−	0.534752i	0.978087	+	0.208197i	$0.0667596\pi$
$152$	1.15248e9	+	1.99615e9i	0.175120	+	0.303317i
$153$	−1.65737e9			−0.244516
$154$		0			0
$155$	1.46420e10			2.03755
$156$	−1.20225e9	−	2.08236e9i	−0.162530	−	0.281511i
$157$	−3.38171e9	+	5.85729e9i	−0.444209	+	0.769393i	−0.997997	−	0.0632648i	$-0.979849\pi$
$157$	−3.38171e9	+	5.85729e9i	−0.444209	+	0.769393i	0.553787	+	0.832658i	$0.313182\pi$
$158$	5.42100e9	−	9.38945e9i	0.692026	−	1.19862i
$159$	−1.78540e9	−	3.09241e9i	−0.221539	−	0.383716i
$160$	−1.92527e9			−0.232248
$161$		0			0
$162$	−3.71986e9			−0.424335
$163$	1.47237e9	+	2.55021e9i	0.163370	+	0.282965i	0.936075	−	0.351800i	$-0.114430\pi$
$163$	1.47237e9	+	2.55021e9i	0.163370	+	0.282965i	−0.772705	+	0.634765i	$0.781097\pi$
$164$	−1.15230e9	+	1.99585e9i	−0.124385	+	0.215442i
$165$	−4.51741e8	+	7.82438e8i	−0.0474473	+	0.0821811i
$166$	3.53051e9	+	6.11502e9i	0.360870	+	0.625045i
$167$	−1.59064e10			−1.58251			−0.791256	−	0.611485i	$-0.790573\pi$
$167$	−1.59064e10			−1.58251			−0.791256	+	0.611485i	$0.790573\pi$
$168$		0			0
$169$	2.14524e10			2.02295
$170$	1.43786e9	+	2.49046e9i	0.132038	+	0.228696i
$171$	4.76382e9	−	8.25117e9i	0.426062	−	0.737961i
$172$	4.44873e9	−	7.70542e9i	0.387577	−	0.671303i
$173$	−5.16493e9	−	8.94592e9i	−0.438386	−	0.759307i	0.559179	−	0.829047i	$-0.311116\pi$
$173$	−5.16493e9	−	8.94592e9i	−0.438386	−	0.759307i	−0.997565	+	0.0697397i	$0.977783\pi$
$174$	3.62366e9			0.299693
$175$		0			0
$176$	6.14728e8			0.0482921
$177$	8.97891e8	+	1.55519e9i	0.0687613	+	0.119098i
$178$	4.44222e9	−	7.69415e9i	0.331673	−	0.574475i
$179$	−5.40127e9	+	9.35527e9i	−0.393239	+	0.681110i	−0.992875	−	0.119163i	$-0.961979\pi$
$179$	−5.40127e9	+	9.35527e9i	−0.393239	+	0.681110i	0.599635	+	0.800273i	$0.295312\pi$
$180$	3.97910e9	+	6.89200e9i	0.282526	+	0.489350i
$181$	6.13942e9			0.425181			0.212591	−	0.977141i	$-0.431810\pi$
$181$	6.13942e9			0.425181			0.212591	+	0.977141i	$0.431810\pi$
$182$		0			0
$183$	−8.69949e9			−0.573408
$184$	−2.00486e9	−	3.47252e9i	−0.128945	−	0.223339i
$185$	−2.49193e9	+	4.31614e9i	−0.156409	+	0.270909i
$186$	3.34674e9	−	5.79672e9i	0.205028	−	0.355119i
$187$	−4.59101e8	−	7.95187e8i	−0.0274550	−	0.0475535i
$188$	1.07975e10			0.630392
$189$		0			0
$190$	−1.65316e10			−0.920288
$191$	4.69356e9	+	8.12948e9i	0.255183	+	0.441990i	0.964945	−	0.262451i	$-0.0845309\pi$
$191$	4.69356e9	+	8.12948e9i	0.255183	+	0.441990i	−0.709762	+	0.704441i	$0.751198\pi$
$192$	−4.40062e8	+	7.62210e8i	−0.0233700	+	0.0404780i
$193$	−4.53204e9	+	7.84973e9i	−0.235118	+	0.407237i	−0.959307	−	0.282365i	$-0.908881\pi$
$193$	−4.53204e9	+	7.84973e9i	−0.235118	+	0.407237i	0.724189	+	0.689602i	$0.242214\pi$
$194$	−1.01516e10	−	1.75830e10i	−0.514547	−	0.891222i
$195$	1.72455e10			0.854125
$196$		0			0
$197$	−7.31102e9			−0.345844			−0.172922	−	0.984936i	$-0.555321\pi$
$197$	−7.31102e9			−0.345844			−0.172922	+	0.984936i	$0.555321\pi$
$198$	−1.27050e9	−	2.20057e9i	−0.0587465	−	0.101752i
$199$	7.55250e8	−	1.30813e9i	0.0341391	−	0.0591306i	−0.848451	−	0.529274i	$-0.822464\pi$
$199$	7.55250e8	−	1.30813e9i	0.0341391	−	0.0591306i	0.882590	+	0.470143i	$0.155798\pi$
$200$	2.90422e9	−	5.03025e9i	0.128349	−	0.222308i
$201$	−6.37237e9	−	1.10373e10i	−0.275371	−	0.476957i
$202$	−2.18928e10			−0.925166
$203$		0			0
$204$	1.31462e9			0.0531452
$205$	−8.26454e9	−	1.43146e10i	−0.326834	−	0.566092i
$206$	−1.53721e9	+	2.66253e9i	−0.0594746	+	0.103013i
$207$	−8.28718e9	+	1.43538e10i	−0.313719	+	0.543377i
$208$	−5.86692e9	−	1.01618e10i	−0.217333	−	0.376432i
$209$	5.27844e9			0.191358
$210$		0			0
$211$	−1.89147e10			−0.656945			−0.328472	−	0.944514i	$-0.606534\pi$
$211$	−1.89147e10			−0.656945			−0.328472	+	0.944514i	$0.606534\pi$
$212$	−8.71269e9	−	1.50908e10i	−0.296238	−	0.513100i
$213$	2.47327e9	−	4.28383e9i	0.0823309	−	0.142601i
$214$	−8.38840e9	+	1.45291e10i	−0.273412	+	0.473563i
$215$	3.19072e10	+	5.52648e10i	1.01839	+	1.76391i
$216$	7.86740e9			0.245918
$217$		0			0
$218$	−3.26012e10			−0.977641
$219$	−3.49733e9	−	6.05755e9i	−0.102740	−	0.177950i
$220$	−2.20447e9	+	3.81826e9i	−0.0634458	+	0.109891i
$221$	−8.76327e9	+	1.51784e10i	−0.247116	+	0.428018i
$222$	1.13917e9	+	1.97309e9i	0.0314774	+	0.0545204i
$223$	−5.37387e10			−1.45518			−0.727588	−	0.686015i	$-0.759359\pi$
$223$	−5.37387e10			−1.45518			−0.727588	+	0.686015i	$0.759359\pi$
$224$		0			0
$225$	−2.40094e10			−0.624540
$226$	−3.76799e9	−	6.52635e9i	−0.0960775	−	0.166411i
$227$	3.25667e9	−	5.64073e9i	0.0814063	−	0.141000i	−0.822448	−	0.568840i	$-0.807392\pi$
$227$	3.25667e9	−	5.64073e9i	0.0814063	−	0.141000i	0.903854	+	0.427841i	$0.140726\pi$
$228$	−3.77865e9	+	6.54481e9i	−0.0926040	+	0.160395i
$229$	1.04276e10	+	1.80611e10i	0.250567	+	0.433995i	0.963682	−	0.267052i	$-0.0860496\pi$
$229$	1.04276e10	+	1.80611e10i	0.250567	+	0.433995i	−0.713115	+	0.701047i	$0.752716\pi$
$230$	2.87585e10			0.677628
$231$		0			0
$232$	1.76833e10			0.400745
$233$	−9.57793e9	−	1.65895e10i	−0.212897	−	0.368749i	0.739723	−	0.672912i	$-0.234957\pi$
$233$	−9.57793e9	−	1.65895e10i	−0.212897	−	0.368749i	−0.952620	+	0.304163i	$0.901623\pi$
$234$	−2.42512e10	+	4.20043e10i	−0.528764	+	0.915846i
$235$	−3.87207e10	+	6.70663e10i	−0.828206	+	1.43449i
$236$	4.38167e9	+	7.58927e9i	0.0919465	+	0.159256i
$237$	3.55479e10			0.731891
$238$		0			0
$239$	−2.58648e10			−0.512764			−0.256382	−	0.966575i	$-0.582531\pi$
$239$	−2.58648e10			−0.512764			−0.256382	+	0.966575i	$0.582531\pi$
$240$	−3.15621e9	−	5.46672e9i	−0.0614067	−	0.106360i
$241$	−1.60903e10	+	2.78692e10i	−0.307246	+	0.532167i	−0.977759	−	0.209732i	$-0.932741\pi$
$241$	−1.60903e10	+	2.78692e10i	−0.307246	+	0.532167i	0.670512	+	0.741898i	$0.266074\pi$
$242$	−1.81597e10	+	3.14535e10i	−0.340361	+	0.589522i
$243$	−2.50013e10	−	4.33035e10i	−0.459975	−	0.796699i
$244$	−4.24531e10			−0.766753
$245$		0			0
$246$	−7.55616e9			−0.131551
$247$	−5.03771e10	−	8.72557e10i	−0.861186	−	1.49162i
$248$	1.63319e10	−	2.82877e10i	0.274161	−	0.474860i
$249$	−1.15755e10	+	2.00494e10i	−0.190829	+	0.330525i
$250$	−7.85917e9	−	1.36125e10i	−0.127247	−	0.220398i
$251$	−2.42280e10			−0.385288			−0.192644	−	0.981269i	$-0.561706\pi$
$251$	−2.42280e10			−0.385288			−0.192644	+	0.981269i	$0.561706\pi$
$252$		0			0
$253$	−9.18242e9			−0.140901
$254$	2.30079e10	+	3.98508e10i	0.346836	+	0.600738i
$255$	−4.71436e9	+	8.16550e9i	−0.0698219	+	0.120935i
$256$	−2.14748e9	+	3.71955e9i	−0.0312500	+	0.0541266i
$257$	−1.78270e10	−	3.08773e10i	−0.254906	−	0.441510i	0.709964	−	0.704238i	$-0.248711\pi$
$257$	−1.78270e10	−	3.08773e10i	−0.254906	−	0.441510i	−0.964870	+	0.262728i	$0.915378\pi$
$258$	2.91723e10			0.409903
$259$		0			0
$260$	8.41575e10			1.14212
$261$	−3.65474e10	−	6.33019e10i	−0.487499	−	0.844373i
$262$	4.77685e10	−	8.27375e10i	0.626305	−	1.08479i
$263$	5.96845e10	−	1.03377e11i	0.769238	−	1.33236i	−0.168739	−	0.985661i	$-0.553970\pi$
$263$	5.96845e10	−	1.03377e11i	0.769238	−	1.33236i	0.937977	−	0.346698i	$-0.112697\pi$
$264$	1.00776e9	+	1.74549e9i	0.0127685	+	0.0221157i
$265$	1.24978e11			1.55678
$266$		0			0
$267$	2.91296e10			0.350779
$268$	−3.10969e10	−	5.38614e10i	−0.368223	−	0.637780i
$269$	5.27901e10	−	9.14352e10i	0.614706	−	1.06470i	−0.375730	−	0.926729i	$-0.622608\pi$
$269$	5.27901e10	−	9.14352e10i	0.614706	−	1.06470i	0.990436	−	0.137973i	$-0.0440586\pi$
$270$	−2.82133e10	+	4.88668e10i	−0.323085	+	0.559600i
$271$	−3.15264e10	−	5.46053e10i	−0.355069	−	0.614997i	0.632061	−	0.774919i	$-0.282209\pi$
$271$	−3.15264e10	−	5.46053e10i	−0.355069	−	0.614997i	−0.987130	+	0.159921i	$0.948876\pi$
$272$	6.41528e9			0.0710650
$273$		0			0
$274$	2.23536e10			0.239591
$275$	−6.65077e9	−	1.15195e10i	−0.0701253	−	0.121461i
$276$	6.57338e9	−	1.13854e10i	0.0681864	−	0.118102i
$277$	4.41476e10	−	7.64659e10i	0.450556	−	0.780385i	−0.547865	−	0.836567i	$-0.684559\pi$
$277$	4.41476e10	−	7.64659e10i	0.450556	−	0.780385i	0.998421	+	0.0561815i	$0.0178925\pi$
$278$	6.37265e10	+	1.10378e11i	0.639910	+	1.10836i
$279$	−1.35018e11			−1.33405
$280$		0			0
$281$	−1.42216e10			−0.136072			−0.0680361	−	0.997683i	$-0.521673\pi$
$281$	−1.42216e10			−0.136072			−0.0680361	+	0.997683i	$0.521673\pi$
$282$	1.77009e10	+	3.06589e10i	0.166677	+	0.288692i
$283$	−7.20956e10	+	1.24873e11i	−0.668144	+	1.15726i	0.310279	+	0.950646i	$0.399578\pi$
$283$	−7.20956e10	+	1.24873e11i	−0.668144	+	1.15726i	−0.978423	+	0.206613i	$0.933756\pi$
$284$	1.20694e10	−	2.09049e10i	0.110092	−	0.190684i
$285$	−2.71012e10	−	4.69407e10i	−0.243325	−	0.421452i
$286$	−2.68710e10			−0.237485
$287$		0			0
$288$	1.77534e10			0.152060
$289$	5.45028e10	+	9.44016e10i	0.459598	+	0.796047i
$290$	−6.34141e10	+	1.09836e11i	−0.526496	+	0.911917i
$291$	3.32841e10	−	5.76498e10i	0.272094	−	0.471280i
$292$	−1.70668e10	−	2.95606e10i	−0.137382	−	0.237952i
$293$	−7.39164e10			−0.585918			−0.292959	−	0.956125i	$-0.594640\pi$
$293$	−7.39164e10			−0.585918			−0.292959	+	0.956125i	$0.594640\pi$
$294$		0			0
$295$	−6.28524e10			−0.483195
$296$	5.55908e9	+	9.62861e9i	0.0420911	+	0.0729039i
$297$	9.00833e9	−	1.56029e10i	0.0671800	−	0.116359i
$298$	−8.82084e10	+	1.52781e11i	−0.647943	+	1.12227i
$299$	8.76365e10	+	1.51791e11i	0.634110	+	1.09831i
$300$	1.90442e10			0.135743
$301$		0			0
$302$	6.31158e10			0.436623
$303$	−3.58902e10	−	6.21636e10i	−0.244615	−	0.423686i
$304$	−1.84396e10	+	3.19384e10i	−0.123829	+	0.214478i
$305$	1.52241e11	−	2.63689e11i	1.00736	−	1.74479i
$306$	−1.32589e10	−	2.29651e10i	−0.0864494	−	0.149735i
$307$	1.11736e11			0.717908			0.358954	−	0.933355i	$-0.383134\pi$
$307$	1.11736e11			0.717908			0.358954	+	0.933355i	$0.383134\pi$
$308$		0			0
$309$	−1.00802e10			−0.0629006
$310$	1.17136e11	+	2.02885e11i	0.720381	+	1.24774i
$311$	1.10520e11	−	1.91426e11i	0.669912	−	1.16032i	−0.308017	−	0.951381i	$-0.599665\pi$
$311$	1.10520e11	−	1.91426e11i	0.669912	−	1.16032i	0.977928	−	0.208940i	$-0.0670015\pi$
$312$	1.92360e10	−	3.33177e10i	0.114926	−	0.199058i
$313$	5.38133e10	+	9.32074e10i	0.316913	+	0.548909i	0.979842	−	0.199773i	$-0.0640203\pi$
$313$	5.38133e10	+	9.32074e10i	0.316913	+	0.548909i	−0.662929	+	0.748682i	$0.730687\pi$
$314$	−1.08215e11			−0.628207
$315$		0			0
$316$	1.73472e11			0.978673
$317$	1.62817e11	+	2.82008e11i	0.905594	+	1.56853i	0.820118	+	0.572195i	$0.193908\pi$
$317$	1.62817e11	+	2.82008e11i	0.905594	+	1.56853i	0.0854764	+	0.996340i	$0.472759\pi$
$318$	2.85665e10	−	4.94786e10i	0.156652	−	0.271328i
$319$	2.02477e10	−	3.50701e10i	0.109476	−	0.189618i
$320$	−1.54022e10	−	2.66774e10i	−0.0821121	−	0.142222i
$321$	−5.50064e10			−0.289162
$322$		0			0
$323$	5.50856e10			0.281596
$324$	−2.97589e10	−	5.15439e10i	−0.150025	−	0.259851i
$325$	−1.26949e11	+	2.19882e11i	−0.631182	+	1.09324i
$326$	−2.35579e10	+	4.08034e10i	−0.115520	+	0.200086i
$327$	−5.34451e10	−	9.25697e10i	−0.258490	−	0.447717i
$328$	−3.68737e10			−0.175907
$329$		0			0
$330$	−1.44557e10			−0.0671006
$331$	8.47723e10	+	1.46830e11i	0.388175	+	0.672339i	0.992204	−	0.124623i	$-0.0397722\pi$
$331$	8.47723e10	+	1.46830e11i	0.388175	+	0.672339i	−0.604029	+	0.796962i	$0.706439\pi$
$332$	−5.64881e10	+	9.78403e10i	−0.255174	+	0.441974i
$333$	2.29787e10	−	3.98003e10i	0.102406	−	0.177373i
$334$	−1.27251e11	−	2.20405e11i	−0.559503	−	0.969087i
$335$	4.46066e11			1.93507
$336$		0			0
$337$	−1.26756e11			−0.535347			−0.267673	−	0.963510i	$-0.586255\pi$
$337$	−1.26756e11			−0.535347			−0.267673	+	0.963510i	$0.586255\pi$
$338$	1.71619e11	+	2.97253e11i	0.715221	+	1.23880i
$339$	1.23542e10	−	2.13981e10i	0.0508060	−	0.0879986i
$340$	−2.30058e10	+	3.98473e10i	−0.0933648	+	0.161712i
$341$	−3.74008e10	−	6.47800e10i	−0.149791	−	0.259446i
$342$	1.52442e11			0.602542
$343$		0			0
$344$	1.42359e11			0.548117
$345$	4.71456e10	+	8.16585e10i	0.179166	+	0.310324i
$346$	8.26389e10	−	1.43135e11i	0.309986	−	0.536911i
$347$	8.95539e10	−	1.55112e11i	0.331590	−	0.574331i	−0.651234	−	0.758877i	$-0.725748\pi$
$347$	8.95539e10	−	1.55112e11i	0.331590	−	0.574331i	0.982824	+	0.184546i	$0.0590815\pi$
$348$	2.89893e10	+	5.02109e10i	0.105957	+	0.183524i
$349$	−1.73876e11			−0.627372			−0.313686	−	0.949527i	$-0.601564\pi$
$349$	−1.73876e11			−0.627372			−0.313686	+	0.949527i	$0.601564\pi$
$350$		0			0
$351$	−3.43900e11			−1.20934
$352$	4.91782e9	+	8.51792e9i	0.0170738	+	0.0295727i
$353$	4.51749e10	−	7.82452e10i	0.154850	−	0.268208i	−0.778154	−	0.628073i	$-0.783844\pi$
$353$	4.51749e10	−	7.82452e10i	0.154850	−	0.268208i	0.933004	+	0.359865i	$0.117177\pi$
$354$	−1.43663e10	+	2.48831e10i	−0.0486216	+	0.0842150i
$355$	8.65644e10	+	1.49934e11i	0.289276	+	0.501040i
$356$	1.42151e11			0.469056
$357$		0			0
$358$	−1.72841e11			−0.556124
$359$	9.19748e10	+	1.59305e11i	0.292243	+	0.506180i	0.974340	−	0.225082i	$-0.0722651\pi$
$359$	9.19748e10	+	1.59305e11i	0.292243	+	0.506180i	−0.682097	+	0.731262i	$0.738932\pi$
$360$	−6.36656e10	+	1.10272e11i	−0.199776	+	0.346022i
$361$	3.00955e9	−	5.21270e9i	0.00932652	−	0.0161540i
$362$	4.91154e10	+	8.50703e10i	0.150324	+	0.260369i
$363$	−1.19081e11			−0.359967
$364$		0			0
$365$	2.44813e11			0.721966
$366$	−6.95959e10	−	1.20544e11i	−0.202730	−	0.351139i
$367$	1.80656e11	−	3.12906e11i	0.519823	−	0.900360i	−0.479911	−	0.877317i	$-0.659331\pi$
$367$	1.80656e11	−	3.12906e11i	0.519823	−	0.900360i	0.999734	−	0.0230430i	$-0.00733546\pi$
$368$	3.20778e10	−	5.55603e10i	0.0911778	−	0.157925i
$369$	7.62095e10	+	1.31999e11i	0.213989	+	0.370639i
$370$	−7.97416e10			−0.221196
$371$		0			0
$372$	1.07096e11			0.289954
$373$	−8.12103e10	−	1.40660e11i	−0.217231	−	0.376255i	0.736730	−	0.676187i	$-0.236369\pi$
$373$	−8.12103e10	−	1.40660e11i	−0.217231	−	0.376255i	−0.953960	+	0.299933i	$0.903036\pi$
$374$	7.34562e9	−	1.27230e10i	0.0194136	−	0.0336254i
$375$	2.57680e10	−	4.46315e10i	0.0672884	−	0.116547i
$376$	8.63796e10	+	1.49614e11i	0.222877	+	0.386035i
$377$	−7.72973e11			−1.97073
$378$		0			0
$379$	−1.07832e10			−0.0268455			−0.0134227	−	0.999910i	$-0.504273\pi$
$379$	−1.07832e10			−0.0268455			−0.0134227	+	0.999910i	$0.504273\pi$
$380$	−1.32253e11	−	2.29068e11i	−0.325371	−	0.563559i
$381$	−7.54363e10	+	1.30660e11i	−0.183408	+	0.317672i
$382$	−7.50969e10	+	1.30072e11i	−0.180442	+	0.312534i
$383$	−3.48928e11	−	6.04362e11i	−0.828594	−	1.43517i	−0.899141	−	0.437659i	$-0.855808\pi$
$383$	−3.48928e11	−	6.04362e11i	−0.828594	−	1.43517i	0.0705472	−	0.997508i	$-0.477525\pi$
$384$	−1.40820e10			−0.0330502
$385$		0			0
$386$	−1.45025e11			−0.332507
$387$	−2.94224e11	−	5.09611e11i	−0.666775	−	1.15489i
$388$	1.62425e11	−	2.81328e11i	0.363840	−	0.630189i
$389$	2.99480e11	−	5.18714e11i	0.663123	−	1.14856i	−0.316667	−	0.948537i	$-0.602564\pi$
$389$	2.99480e11	−	5.18714e11i	0.663123	−	1.14856i	0.979791	−	0.200026i	$-0.0641028\pi$
$390$	1.37964e11	+	2.38961e11i	0.301979	+	0.523042i
$391$	−9.58275e10			−0.207346
$392$		0			0
$393$	3.13239e11			0.662384
$394$	−5.84882e10	−	1.01305e11i	−0.122274	−	0.211785i
$395$	−6.22088e11	+	1.07749e12i	−1.28577	+	2.22703i
$396$	2.03280e10	−	3.52092e10i	0.0415401	−	0.0719495i
$397$	1.84080e11	+	3.18835e11i	0.371919	+	0.644183i	0.989861	−	0.142041i	$-0.0453665\pi$
$397$	1.84080e11	+	3.18835e11i	0.371919	+	0.644183i	−0.617942	+	0.786224i	$0.712033\pi$
$398$	2.41680e10			0.0482800
$399$		0			0
$400$	9.29350e10			0.181514
$401$	−5.56095e10	−	9.63185e10i	−0.107399	−	0.186020i	0.807317	−	0.590118i	$-0.200919\pi$
$401$	−5.56095e10	−	9.63185e10i	−0.107399	−	0.186020i	−0.914716	+	0.404098i	$0.867586\pi$
$402$	1.01958e11	−	1.76596e11i	0.194717	−	0.337260i
$403$	−7.13902e11	+	1.23651e12i	−1.34824	+	2.33521i
$404$	−1.75142e11	−	3.03355e11i	−0.327096	−	0.566546i
$405$	4.26873e11			0.788408
$406$		0			0
$407$	2.54610e10			0.0459940
$408$	1.05170e10	+	1.82159e10i	0.0187897	+	0.0325447i
$409$	2.21216e11	−	3.83157e11i	0.390896	−	0.677051i	−0.601672	−	0.798743i	$-0.705499\pi$
$409$	2.21216e11	−	3.83157e11i	0.390896	−	0.677051i	0.992568	+	0.121692i	$0.0388320\pi$
$410$	1.32233e11	−	2.29034e11i	0.231106	−	0.400288i
$411$	3.66456e10	+	6.34720e10i	0.0633481	+	0.109722i
$412$	−4.91908e10			−0.0841097
$413$		0			0
$414$	−2.65190e11			−0.443665
$415$	−4.05144e11	−	7.01730e11i	−0.670491	−	1.16132i
$416$	9.38708e10	−	1.62589e11i	0.153678	−	0.266177i
$417$	−2.08941e11	+	3.61897e11i	−0.338386	+	0.586102i
$418$	4.22275e10	+	7.31402e10i	0.0676553	+	0.117182i
$419$	7.54997e11			1.19669			0.598346	−	0.801238i	$-0.295825\pi$
$419$	7.54997e11			1.19669			0.598346	+	0.801238i	$0.295825\pi$
$420$		0			0
$421$	4.31285e11			0.669106			0.334553	−	0.942377i	$-0.391415\pi$
$421$	4.31285e11			0.669106			0.334553	+	0.942377i	$0.391415\pi$
$422$	−1.51318e11	−	2.62090e11i	−0.232265	−	0.402295i
$423$	3.57054e11	−	6.18436e11i	0.542253	−	0.939210i
$424$	1.39403e11	−	2.41453e11i	0.209472	−	0.362816i
$425$	−6.94073e10	−	1.20217e11i	−0.103194	−	0.178737i
$426$	7.91446e10			0.116434
$427$		0			0
$428$	−2.68429e11			−0.386663
$429$	−4.40512e10	−	7.62989e10i	−0.0627913	−	0.108758i
$430$	−5.10515e11	+	8.84237e11i	−0.720112	+	1.24727i
$431$	−5.06876e11	+	8.77935e11i	−0.707545	+	1.22550i	0.258221	+	0.966086i	$0.416864\pi$
$431$	−5.06876e11	+	8.77935e11i	−0.707545	+	1.22550i	−0.965765	+	0.259417i	$0.916470\pi$
$432$	6.29392e10	+	1.09014e11i	0.0869450	+	0.150593i
$433$	6.02971e11			0.824329			0.412165	−	0.911109i	$-0.364773\pi$
$433$	6.02971e11			0.824329			0.412165	+	0.911109i	$0.364773\pi$
$434$		0			0
$435$	−4.15834e11			−0.556825
$436$	−2.60810e11	−	4.51736e11i	−0.345648	−	0.598681i
$437$	2.75440e11	−	4.77076e11i	0.361294	−	0.625779i
$438$	5.59573e10	−	9.69208e10i	0.0726479	−	0.125830i
$439$	−2.27143e11	−	3.93423e11i	−0.291883	−	0.505556i	0.682372	−	0.731005i	$-0.260948\pi$
$439$	−2.27143e11	−	3.93423e11i	−0.291883	−	0.505556i	−0.974255	+	0.225449i	$0.927615\pi$
$440$	−7.05432e10			−0.0897259
$441$		0			0
$442$	−2.80425e11			−0.349475
$443$	−5.04444e11	−	8.73722e11i	−0.622294	−	1.07785i	−0.989057	−	0.147531i	$-0.952867\pi$
$443$	−5.04444e11	−	8.73722e11i	−0.622294	−	1.07785i	0.366763	−	0.930314i	$-0.380466\pi$
$444$	−1.82267e10	+	3.15695e10i	−0.0222579	+	0.0385518i
$445$	−5.09768e11	+	8.82944e11i	−0.616244	+	1.06737i
$446$	−4.29910e11	−	7.44625e11i	−0.514482	−	0.891109i
$447$	−5.78421e11			−0.685268
$448$		0			0
$449$	1.51070e10			0.0175416			0.00877082	−	0.999962i	$-0.497208\pi$
$449$	1.51070e10			0.0175416			0.00877082	+	0.999962i	$0.497208\pi$
$450$	−1.92075e11	−	3.32684e11i	−0.220808	−	0.382451i
$451$	−4.22211e10	+	7.31291e10i	−0.0480546	+	0.0832330i
$452$	6.02878e10	−	1.04422e11i	0.0679371	−	0.117670i
$453$	1.03469e11	+	1.79214e11i	0.115444	+	0.199954i
$454$	1.04214e11			0.115126
$455$		0			0
$456$	−1.20917e11			−0.130962
$457$	5.16899e11	+	8.95295e11i	0.554348	+	0.960159i	0.997954	+	0.0639369i	$0.0203657\pi$
$457$	5.16899e11	+	8.95295e11i	0.554348	+	0.960159i	−0.443606	+	0.896222i	$0.646301\pi$
$458$	−1.66841e11	+	2.88978e11i	−0.177178	+	0.306881i
$459$	9.40107e10	−	1.62831e11i	0.0988599	−	0.171230i
$460$	2.30068e11	+	3.98490e11i	0.239578	+	0.414961i
$461$	−6.16178e11			−0.635407			−0.317704	−	0.948190i	$-0.602912\pi$
$461$	−6.16178e11			−0.635407			−0.317704	+	0.948190i	$0.602912\pi$
$462$		0			0
$463$	8.87425e11			0.897464			0.448732	−	0.893666i	$-0.351876\pi$
$463$	8.87425e11			0.897464			0.448732	+	0.893666i	$0.351876\pi$
$464$	1.41466e11	+	2.45027e11i	0.141685	+	0.245405i
$465$	−3.84056e11	+	6.65204e11i	−0.380939	+	0.659807i
$466$	1.53247e11	−	2.65431e11i	0.150541	−	0.260745i
$467$	8.81241e11	+	1.52635e12i	0.857371	+	1.48501i	0.874428	+	0.485156i	$0.161237\pi$
$467$	8.81241e11	+	1.52635e12i	0.857371	+	1.48501i	−0.0170568	+	0.999855i	$0.505430\pi$
$468$	−7.76038e11			−0.747785
$469$		0			0
$470$	−1.23906e12			−1.17126
$471$	−1.77403e11	−	3.07271e11i	−0.166099	−	0.287691i
$472$	−7.01067e10	+	1.21428e11i	−0.0650160	+	0.112611i
$473$	1.63004e11	−	2.82332e11i	0.149735	−	0.259349i
$474$	2.84383e11	+	4.92566e11i	0.258762	+	0.448190i
$475$	7.97998e11			0.719251
$476$		0			0
$477$	−1.15246e12			−1.01928
$478$	−2.06918e11	−	3.58393e11i	−0.181290	−	0.314003i
$479$	6.26066e10	−	1.08438e11i	0.0543388	−	0.0941176i	−0.837576	−	0.546320i	$-0.816028\pi$
$479$	6.26066e10	−	1.08438e11i	0.0543388	−	0.0941176i	0.891915	+	0.452202i	$0.149362\pi$
$480$	5.04994e10	−	8.74676e10i	0.0434211	−	0.0752076i
$481$	−2.42998e11	−	4.20886e11i	−0.206991	−	0.358518i
$482$	−5.14889e11			−0.434512
$483$		0			0
$484$	−5.81111e11			−0.481343
$485$	1.16494e12	+	2.01774e12i	0.956021	+	1.65588i
$486$	4.00020e11	−	6.92856e11i	0.325251	−	0.563352i
$487$	−9.59535e11	+	1.66196e12i	−0.773001	+	1.33888i	0.162909	+	0.986641i	$0.447912\pi$
$487$	−9.59535e11	+	1.66196e12i	−0.773001	+	1.33888i	−0.935911	+	0.352237i	$0.885421\pi$
$488$	−3.39625e11	−	5.88248e11i	−0.271088	−	0.469538i
$489$	−1.54479e11			−0.122174
$490$		0			0
$491$	−1.29801e12			−1.00789			−0.503944	−	0.863736i	$-0.668118\pi$
$491$	−1.29801e12			−1.00789			−0.503944	+	0.863736i	$0.668118\pi$
$492$	−6.04492e10	−	1.04701e11i	−0.0465102	−	0.0805580i
$493$	2.11305e11	−	3.65991e11i	0.161101	−	0.279035i
$494$	8.06033e11	−	1.39609e12i	0.608950	−	1.05473i
$495$	1.45797e11	+	2.52527e11i	0.109150	+	0.189054i
$496$	5.22622e11			0.387722
$497$		0			0
$498$	−3.70417e11			−0.269873
$499$	2.13038e11	+	3.68992e11i	0.153817	+	0.266419i	0.932628	−	0.360840i	$-0.117510\pi$
$499$	2.13038e11	+	3.68992e11i	0.153817	+	0.266419i	−0.778811	+	0.627259i	$0.784177\pi$
$500$	1.25747e11	−	2.17800e11i	0.0899770	−	0.155845i
$501$	4.17220e11	−	7.22647e11i	0.295866	−	0.512456i
$502$	−1.93824e11	−	3.35713e11i	−0.136220	−	0.235940i
$503$	−1.75682e12			−1.22369			−0.611844	−	0.790978i	$-0.709572\pi$
$503$	−1.75682e12			−1.22369			−0.611844	+	0.790978i	$0.709572\pi$
$504$		0			0
$505$	2.51231e12			1.71895
$506$	−7.34594e10	−	1.27235e11i	−0.0498161	−	0.0862840i
$507$	−5.62690e11	+	9.74608e11i	−0.378210	+	0.655080i
$508$	−3.68126e11	+	6.37612e11i	−0.245250	+	0.424786i
$509$	−1.29517e12	−	2.24330e12i	−0.855258	−	1.48135i	−0.876406	−	0.481574i	$-0.840065\pi$
$509$	−1.29517e12	−	2.24330e12i	−0.855258	−	1.48135i	0.0211477	−	0.999776i	$-0.493268\pi$
$510$	−1.50859e11			−0.0987430
$511$		0			0
$512$	−6.87195e10			−0.0441942
$513$	5.40436e11	+	9.36062e11i	0.344521	+	0.596728i
$514$	2.85233e11	−	4.94037e11i	0.180246	−	0.312195i
$515$	1.76403e11	−	3.05539e11i	0.110503	−	0.191397i
$516$	2.33378e11	+	4.04223e11i	0.144923	+	0.251014i
$517$	3.95625e11			0.243544
$518$		0			0
$519$	5.41899e11			0.327843
$520$	6.73260e11	+	1.16612e12i	0.403801	+	0.699404i
$521$	4.81815e11	−	8.34527e11i	0.286490	−	0.496216i	−0.686479	−	0.727150i	$-0.740845\pi$
$521$	4.81815e11	−	8.34527e11i	0.286490	−	0.496216i	0.972970	+	0.230933i	$0.0741780\pi$
$522$	5.84758e11	−	1.01283e12i	0.344714	−	0.597062i
$523$	−3.13995e11	−	5.43855e11i	−0.183512	−	0.317852i	0.759562	−	0.650435i	$-0.225413\pi$
$523$	−3.13995e11	−	5.43855e11i	−0.183512	−	0.317852i	−0.943074	+	0.332582i	$0.892080\pi$
$524$	1.52859e12			0.885729
$525$		0			0
$526$	1.90990e12			1.08787
$527$	−3.90314e11	−	6.76043e11i	−0.220428	−	0.381792i
$528$	−1.61242e10	+	2.79279e10i	−0.00902868	+	0.0156381i
$529$	4.21418e11	−	7.29918e11i	0.233972	−	0.405251i
$530$	9.99827e11	+	1.73175e12i	0.550406	+	0.953332i
$531$	5.79578e11			0.316364
$532$		0			0
$533$	1.61182e12			0.865057
$534$	2.33037e11	+	4.03631e11i	0.124019	+	0.214807i
$535$	9.62612e11	−	1.66729e12i	0.507995	−	0.879873i
$536$	4.97550e11	−	8.61782e11i	0.260373	−	0.450979i
$537$	−2.83348e11	−	4.90773e11i	−0.147040	−	0.254681i
$538$	1.68928e12			0.869325
$539$		0			0
$540$	−9.02825e11			−0.456911
$541$	1.55786e12	+	2.69830e12i	0.781884	+	1.35426i	0.930843	+	0.365419i	$0.119074\pi$
$541$	1.55786e12	+	2.69830e12i	0.781884	+	1.35426i	−0.148960	+	0.988843i	$0.547592\pi$
$542$	5.04422e11	−	8.73685e11i	0.251072	−	0.434869i
$543$	−1.61036e11	+	2.78922e11i	−0.0794918	+	0.137684i
$544$	5.13223e10	+	8.88928e10i	0.0251253	+	0.0435182i
$545$	3.74116e12			1.81644
$546$		0			0
$547$	1.73766e12			0.829890			0.414945	−	0.909846i	$-0.363801\pi$
$547$	1.73766e12			0.829890			0.414945	+	0.909846i	$0.363801\pi$
$548$	1.78829e11	+	3.09740e11i	0.0847081	+	0.146719i
$549$	−1.40386e12	+	2.43155e12i	−0.659549	+	1.14237i
$550$	1.06412e11	−	1.84312e11i	0.0495861	−	0.0858856i
$551$	1.21472e12	+	2.10396e12i	0.561428	+	0.972421i
$552$	2.10348e11			0.0964301
$553$		0			0
$554$	1.41272e12			0.637182
$555$	−1.30725e11	−	2.26423e11i	−0.0584845	−	0.101298i
$556$	−1.01962e12	+	1.76604e12i	−0.452485	+	0.783726i
$557$	2.19213e12	−	3.79688e12i	0.964980	−	1.67139i	0.255312	−	0.966859i	$-0.417822\pi$
$557$	2.19213e12	−	3.79688e12i	0.964980	−	1.67139i	0.709668	−	0.704536i	$-0.248845\pi$
$558$	−1.08014e12	−	1.87086e12i	−0.471657	−	0.816934i
$559$	−6.22281e12			−2.69546
$560$		0			0
$561$	4.81685e10			0.0205319
$562$	−1.13773e11	−	1.97060e11i	−0.0481088	−	0.0833269i
$563$	−1.30264e12	+	2.25625e12i	−0.546434	+	0.946452i	0.452081	+	0.891977i	$0.350682\pi$
$563$	−1.30264e12	+	2.25625e12i	−0.546434	+	0.946452i	−0.998515	+	0.0544751i	$0.982651\pi$
$564$	−2.83215e11	+	4.90542e11i	−0.117858	+	0.204136i
$565$	4.32396e11	+	7.48932e11i	0.178511	+	0.309189i
$566$	−2.30706e12			−0.944898
$567$		0			0
$568$	3.86222e11			0.155693
$569$	5.10258e11	+	8.83793e11i	0.204073	+	0.353464i	0.949837	−	0.312746i	$-0.101249\pi$
$569$	5.10258e11	+	8.83793e11i	0.204073	+	0.353464i	−0.745764	+	0.666210i	$0.767915\pi$
$570$	4.33620e11	−	7.51051e11i	0.172057	−	0.298011i
$571$	−1.51016e11	+	2.61567e11i	−0.0594512	+	0.102972i	−0.894219	−	0.447629i	$-0.852268\pi$
$571$	−1.51016e11	+	2.61567e11i	−0.0594512	+	0.102972i	0.834768	+	0.550602i	$0.185602\pi$
$572$	−2.14968e11	−	3.72335e11i	−0.0839636	−	0.145429i
$573$	−4.92443e11			−0.190836
$574$		0			0
$575$	−1.38820e12			−0.529600
$576$	1.42028e11	+	2.45999e11i	0.0537615	+	0.0931176i
$577$	3.61791e11	−	6.26641e11i	0.135884	−	0.235357i	−0.790051	−	0.613041i	$-0.789946\pi$
$577$	3.61791e11	−	6.26641e11i	0.135884	−	0.235357i	0.925935	+	0.377684i	$0.123279\pi$
$578$	−8.72044e11	+	1.51042e12i	−0.324985	+	0.562890i
$579$	−2.37749e11	−	4.11793e11i	−0.0879154	−	0.152274i
$580$	−2.02925e12			−0.744577
$581$		0			0
$582$	1.06509e12			0.384799
$583$	−3.19239e11	−	5.52937e11i	−0.114448	−	0.198229i
$584$	2.73069e11	−	4.72969e11i	0.0971437	−	0.168258i
$585$	2.78295e12	−	4.82021e12i	0.982435	−	1.70163i
$586$	−5.91332e11	−	1.02422e12i	−0.207153	−	0.358800i
$587$	4.21402e12			1.46496			0.732479	−	0.680789i	$-0.238363\pi$
$587$	4.21402e12			1.46496			0.732479	+	0.680789i	$0.238363\pi$
$588$		0			0
$589$	4.48756e12			1.53635
$590$	−5.02819e11	−	8.70908e11i	−0.170835	−	0.295895i
$591$	1.91766e11	−	3.32149e11i	0.0646590	−	0.111993i
$592$	−8.89453e10	+	1.54058e11i	−0.0297629	+	0.0515508i
$593$	2.81140e12	+	4.86948e12i	0.933633	+	1.61710i	0.777054	+	0.629434i	$0.216713\pi$
$593$	2.81140e12	+	4.86948e12i	0.933633	+	1.61710i	0.156578	+	0.987666i	$0.449954\pi$
$594$	2.88267e11			0.0950069
$595$		0			0
$596$	−2.82267e12			−0.916329
$597$	3.96201e10	+	6.86239e10i	0.0127653	+	0.0221101i
$598$	−1.40218e12	+	2.42865e12i	−0.448383	+	0.776623i
$599$	−3.82867e11	+	6.63145e11i	−0.121514	+	0.210469i	−0.920365	−	0.391060i	$-0.872108\pi$
$599$	−3.82867e11	+	6.63145e11i	−0.121514	+	0.210469i	0.798851	+	0.601529i	$0.205442\pi$
$600$	1.52354e11	+	2.63885e11i	0.0479924	+	0.0831253i
$601$	−9.63630e11			−0.301283			−0.150642	−	0.988588i	$-0.548134\pi$
$601$	−9.63630e11			−0.301283			−0.150642	+	0.988588i	$0.548134\pi$
$602$		0			0
$603$	−4.11329e12			−1.26696
$604$	5.04926e11	+	8.74558e11i	0.154370	+	0.267376i
$605$	2.08392e12	−	3.60946e12i	0.632386	−	1.09532i
$606$	5.74242e11	−	9.94617e11i	0.172969	−	0.299591i
$607$	−1.14247e12	−	1.97882e12i	−0.341583	−	0.591640i	0.643144	−	0.765746i	$-0.277630\pi$
$607$	−1.14247e12	−	1.97882e12i	−0.341583	−	0.591640i	−0.984727	+	0.174106i	$0.944297\pi$
$608$	−5.90068e11			−0.175120
$609$		0			0
$610$	4.87172e12			1.42462
$611$	−3.77582e12	−	6.53992e12i	−1.09604	−	1.89840i
$612$	2.12143e11	−	3.67442e11i	0.0611290	−	0.105878i
$613$	−5.97297e11	+	1.03455e12i	−0.170851	+	0.295923i	−0.938718	−	0.344687i	$-0.887985\pi$
$613$	−5.97297e11	+	1.03455e12i	−0.170851	+	0.295923i	0.767866	+	0.640610i	$0.221318\pi$
$614$	8.93884e11	+	1.54825e12i	0.253819	+	0.439627i
$615$	8.67108e11			0.244419
$616$		0			0
$617$	−3.40574e12			−0.946082			−0.473041	−	0.881040i	$-0.656844\pi$
$617$	−3.40574e12			−0.946082			−0.473041	+	0.881040i	$0.656844\pi$
$618$	−8.06414e10	−	1.39675e11i	−0.0222387	−	0.0385186i
$619$	8.08150e9	−	1.39976e10i	0.00221250	−	0.00383217i	−0.864917	−	0.501915i	$-0.832629\pi$
$619$	8.08150e9	−	1.39976e10i	0.00221250	−	0.00383217i	0.867130	+	0.498083i	$0.165962\pi$
$620$	−1.87417e12	+	3.24617e12i	−0.509386	+	0.882283i
$621$	−9.40147e11	−	1.62838e12i	−0.253678	−	0.439384i
$622$	3.53663e12			0.947398
$623$		0			0
$624$	6.15552e11			0.162530
$625$	2.28672e12	+	3.96071e12i	0.599450	+	1.03828i
$626$	−8.61013e11	+	1.49132e12i	−0.224091	+	0.388138i
$627$	−1.38452e11	+	2.39806e11i	−0.0357763	+	0.0619664i
$628$	−8.65718e11	−	1.49947e12i	−0.222105	−	0.384697i
$629$	2.65711e11			0.0676832
$630$		0			0
$631$	−4.72735e12			−1.18710			−0.593548	−	0.804799i	$-0.702273\pi$
$631$	−4.72735e12			−1.18710			−0.593548	+	0.804799i	$0.702273\pi$
$632$	1.38778e12	+	2.40370e12i	0.346013	+	0.599312i
$633$	4.96128e11	−	8.59320e11i	0.122822	−	0.212735i
$634$	−2.60508e12	+	4.51212e12i	−0.640352	+	1.10912i
$635$	−2.64027e12	−	4.57308e12i	−0.644416	−	1.11616i
$636$	9.14127e11			0.221539
$637$		0			0
$638$	6.47927e11			0.154822
$639$	−7.98233e11	−	1.38258e12i	−0.189398	−	0.328047i
$640$	2.46435e11	−	4.26838e11i	0.0580620	−	0.100566i
$641$	9.17348e11	−	1.58889e12i	0.214621	−	0.371735i	−0.738534	−	0.674216i	$-0.764482\pi$
$641$	9.17348e11	−	1.58889e12i	0.214621	−	0.371735i	0.953155	+	0.302481i	$0.0978149\pi$
$642$	−4.40051e11	−	7.62191e11i	−0.102234	−	0.177075i
$643$	3.00823e12			0.694003			0.347001	−	0.937865i	$-0.387200\pi$
$643$	3.00823e12			0.694003			0.347001	+	0.937865i	$0.387200\pi$
$644$		0			0
$645$	−3.34767e12			−0.761594
$646$	4.40685e11	+	7.63289e11i	0.0995593	+	0.172442i
$647$	2.55178e12	−	4.41982e12i	0.572499	−	0.991596i	−0.423810	−	0.905751i	$-0.639308\pi$
$647$	2.55178e12	−	4.41982e12i	0.572499	−	0.991596i	0.996308	−	0.0858454i	$-0.0273591\pi$
$648$	4.76142e11	−	8.24702e11i	0.106084	−	0.183742i
$649$	1.60547e11	+	2.78076e11i	0.0355223	+	0.0615264i
$650$	−4.06237e12			−0.892626
$651$		0			0
$652$	−7.53852e11			−0.163370
$653$	−2.06171e12	−	3.57098e12i	−0.443729	−	0.768561i	0.554234	−	0.832361i	$-0.313011\pi$
$653$	−2.06171e12	−	3.57098e12i	−0.443729	−	0.768561i	−0.997963	+	0.0637999i	$0.979678\pi$
$654$	8.55122e11	−	1.48111e12i	0.182780	−	0.316584i
$655$	−5.48169e12	+	9.49456e12i	−1.16367	+	2.01553i
$656$	−2.94990e11	−	5.10937e11i	−0.0621927	−	0.107721i
$657$	−2.25749e12			−0.472695
$658$		0			0
$659$	−7.14612e12			−1.47600			−0.737999	−	0.674802i	$-0.764229\pi$
$659$	−7.14612e12			−1.47600			−0.737999	+	0.674802i	$0.764229\pi$
$660$	−1.15646e11	−	2.00304e11i	−0.0237237	−	0.0410906i
$661$	−3.76809e12	+	6.52652e12i	−0.767740	+	1.32976i	0.171046	+	0.985263i	$0.445285\pi$
$661$	−3.76809e12	+	6.52652e12i	−0.767740	+	1.32976i	−0.938786	+	0.344502i	$0.888048\pi$
$662$	−1.35636e12	+	2.34928e12i	−0.274481	+	0.475416i
$663$	−4.59717e11	−	7.96253e11i	−0.0924016	−	0.160044i
$664$	−1.80762e12			−0.360870
$665$		0			0
$666$	7.35318e11			0.144824
$667$	−2.11314e12	−	3.66006e12i	−0.413392	−	0.716015i
$668$	2.03602e12	−	3.52648e12i	0.395628	−	0.685248i
$669$	1.40955e12	−	2.44142e12i	0.272060	−	0.471221i
$670$	3.56853e12	+	6.18087e12i	0.684152	+	1.18499i
$671$	−1.55551e12			−0.296225
$672$		0			0
$673$	2.71281e12			0.509743			0.254872	−	0.966975i	$-0.417967\pi$
$673$	2.71281e12			0.509743			0.254872	+	0.966975i	$0.417967\pi$
$674$	−1.01405e12	−	1.75639e12i	−0.189274	−	0.327831i
$675$	1.36189e12	−	2.35885e12i	0.252507	−	0.437355i
$676$	−2.74590e12	+	4.75604e12i	−0.505737	+	0.875963i
$677$	8.40789e11	+	1.45629e12i	0.153829	+	0.266439i	0.932632	−	0.360829i	$-0.117506\pi$
$677$	8.40789e11	+	1.45629e12i	0.153829	+	0.266439i	−0.778803	+	0.627268i	$0.784173\pi$
$678$	3.95334e11			0.0718506
$679$		0			0
$680$	−7.36187e11			−0.132038
$681$	1.70844e11	+	2.95910e11i	0.0304394	+	0.0527226i
$682$	5.98412e11	−	1.03648e12i	0.105918	−	0.183456i
$683$	−1.78968e12	+	3.09982e12i	−0.314690	+	0.545059i	−0.979372	−	0.202067i	$-0.935234\pi$
$683$	−1.78968e12	+	3.09982e12i	−0.314690	+	0.545059i	0.664681	+	0.747127i	$0.268567\pi$
$684$	1.21954e12	+	2.11230e12i	0.213031	+	0.368980i
$685$	−2.56519e12			−0.445156
$686$		0			0
$687$	−1.09405e12			−0.187384
$688$	1.13887e12	+	1.97259e12i	0.193788	+	0.335651i
$689$	−6.09359e12	+	1.05544e13i	−1.03012	+	1.78421i
$690$	−7.54329e11	+	1.30654e12i	−0.126689	+	0.219432i
$691$	2.10678e12	+	3.64905e12i	0.351535	+	0.608876i	0.986519	−	0.163649i	$-0.0523266\pi$
$691$	2.10678e12	+	3.64905e12i	0.351535	+	0.608876i	−0.634984	+	0.772525i	$0.718993\pi$
$692$	2.64444e12			0.438386
$693$		0			0
$694$	2.86572e12			0.468939
$695$	−7.31295e12	−	1.26664e13i	−1.18894	−	2.05931i
$696$	−4.63829e11	+	8.03375e11i	−0.0749232	+	0.129771i
$697$	−4.40618e11	+	7.63173e11i	−0.0707156	+	0.122483i
$698$	−1.39101e12	−	2.40930e12i	−0.221810	−	0.384185i
$699$	1.00491e12			0.159213
$700$		0			0
$701$	−6.32382e12			−0.989119			−0.494560	−	0.869144i	$-0.664671\pi$
$701$	−6.32382e12			−0.989119			−0.494560	+	0.869144i	$0.664671\pi$
$702$	−2.75120e12	−	4.76522e12i	−0.427568	−	0.740569i
$703$	−7.63740e11	+	1.32284e12i	−0.117936	+	0.204271i
$704$	−7.86851e10	+	1.36287e11i	−0.0120730	+	0.0209111i
$705$	−2.03127e12	−	3.51826e12i	−0.309683	−	0.536386i
$706$	1.44560e12			0.218991
$707$		0			0
$708$	−4.59720e11			−0.0687613
$709$	4.00660e12	+	6.93964e12i	0.595481	+	1.03140i	0.993479	+	0.114017i	$0.0363720\pi$
$709$	4.00660e12	+	6.93964e12i	0.595481	+	1.03140i	−0.397997	+	0.917387i	$0.630295\pi$
$710$	−1.38503e12	+	2.39894e12i	−0.204549	+	0.354289i
$711$	5.73644e12	−	9.93580e12i	0.841839	−	1.45811i
$712$	1.13721e12	+	1.96970e12i	0.165837	+	0.287237i
$713$	−7.80660e12			−1.13125
$714$		0			0
$715$	3.08358e12			0.441244
$716$	−1.38272e12	−	2.39495e12i	−0.196620	−	0.340555i
$717$	6.78426e11	−	1.17507e12i	0.0958664	−	0.166045i
$718$	−1.47160e12	+	2.54888e12i	−0.206647	+	0.357923i
$719$	−9.23989e11	−	1.60040e12i	−0.128940	−	0.223330i	0.794326	−	0.607491i	$-0.207824\pi$
$719$	−9.23989e11	−	1.60040e12i	−0.128940	−	0.223330i	−0.923266	+	0.384161i	$0.874491\pi$
$720$	−2.03730e12			−0.282526
$721$		0			0
$722$	9.63057e10			0.0131897
$723$	−8.44088e11	−	1.46200e12i	−0.114886	−	0.198988i
$724$	−7.85846e11	+	1.36113e12i	−0.106295	+	0.184109i
$725$	3.06107e12	−	5.30192e12i	0.411483	−	0.712709i
$726$	−9.52649e11	−	1.65004e12i	−0.127268	−	0.220434i
$727$	9.54988e12			1.26792			0.633962	−	0.773365i	$-0.281428\pi$
$727$	9.54988e12			1.26792			0.633962	+	0.773365i	$0.281428\pi$
$728$		0			0
$729$	−1.95301e12			−0.256113
$730$	1.95850e12	+	3.39223e12i	0.255254	+	0.442112i
$731$	1.70111e12	−	2.94640e12i	0.220345	−	0.381649i
$732$	1.11354e12	−	1.92870e12i	0.143352	−	0.248293i
$733$	1.22639e12	+	2.12417e12i	0.156914	+	0.271783i	0.933754	−	0.357915i	$-0.116512\pi$
$733$	1.22639e12	+	2.12417e12i	0.156914	+	0.271783i	−0.776840	+	0.629698i	$0.783179\pi$
$734$	5.78100e12			0.735141
$735$		0			0
$736$	1.02649e12			0.128945
$737$	−1.13941e12	−	1.97351e12i	−0.142258	−	0.246398i
$738$	−1.21935e12	+	2.11198e12i	−0.151313	+	0.262081i
$739$	−5.16570e12	+	8.94725e12i	−0.637131	+	1.10354i	0.348928	+	0.937149i	$0.386546\pi$
$739$	−5.16570e12	+	8.94725e12i	−0.637131	+	1.10354i	−0.986059	+	0.166394i	$0.946788\pi$
$740$	−6.37933e11	−	1.10493e12i	−0.0782046	−	0.135454i
$741$	5.28551e12			0.644029
$742$		0			0
$743$	2.90098e12			0.349216			0.174608	−	0.984638i	$-0.444134\pi$
$743$	2.90098e12			0.349216			0.174608	+	0.984638i	$0.444134\pi$
$744$	8.56765e11	+	1.48396e12i	0.102514	+	0.177560i
$745$	1.01224e13	−	1.75325e13i	1.20387	−	2.08516i
$746$	1.29936e12	−	2.25057e12i	0.153605	−	0.266052i
$747$	3.73594e12	+	6.47084e12i	0.438992	+	0.760357i
$748$	2.35060e11			0.0274550
$749$		0			0
$750$	8.24576e11			0.0951602
$751$	−8.77661e11	−	1.52015e12i	−0.100681	−	0.174384i	0.811284	−	0.584652i	$-0.198769\pi$
$751$	−8.77661e11	−	1.52015e12i	−0.100681	−	0.174384i	−0.911965	+	0.410267i	$0.865435\pi$
$752$	−1.38207e12	+	2.39382e12i	−0.157598	+	0.272968i
$753$	6.35494e11	−	1.10071e12i	0.0720334	−	0.124765i
$754$	−6.18378e12	−	1.07106e13i	−0.696760	−	1.20682i
$755$	−7.24286e12			−0.811240
$756$		0			0
$757$	1.28835e13			1.42594			0.712972	−	0.701193i	$-0.247349\pi$
$757$	1.28835e13			1.42594			0.712972	+	0.701193i	$0.247349\pi$
$758$	−8.62655e10	−	1.49416e11i	−0.00949130	−	0.0164394i
$759$	2.40853e11	−	4.17169e11i	0.0263429	−	0.0456272i
$760$	2.11604e12	−	3.66510e12i	0.230072	−	0.398496i
$761$	9.85743e11	+	1.70736e12i	0.106545	+	0.184541i	0.914368	−	0.404883i	$-0.132688\pi$
$761$	9.85743e11	+	1.70736e12i	0.106545	+	0.184541i	−0.807823	+	0.589425i	$0.799355\pi$
$762$	−2.41396e12			−0.259378
$763$		0			0
$764$	−2.40310e12			−0.255183
$765$	1.52153e12	+	2.63537e12i	0.160622	+	0.278205i
$766$	5.58285e12	−	9.66979e12i	0.585904	−	1.01482i
$767$	3.06450e12	−	5.30787e12i	0.319728	−	0.553785i
$768$	−1.12656e11	−	1.95126e11i	−0.0116850	−	0.0202390i
$769$	8.44373e12			0.870694			0.435347	−	0.900263i	$-0.356626\pi$
$769$	8.44373e12			0.870694			0.435347	+	0.900263i	$0.356626\pi$
$770$		0			0
$771$	1.87039e12			0.190629
$772$	−1.16020e12	−	2.00953e12i	−0.117559	−	0.203618i
$773$	−6.39625e12	+	1.10786e13i	−0.644344	+	1.11604i	0.340109	+	0.940386i	$0.389536\pi$
$773$	−6.39625e12	+	1.10786e13i	−0.644344	+	1.11604i	−0.984453	+	0.175650i	$0.943797\pi$
$774$	4.70759e12	−	8.15378e12i	0.471481	−	0.816629i
$775$	−5.65428e12	−	9.79349e12i	−0.563014	−	0.975169i
$776$	5.19760e12			0.514547
$777$		0			0
$778$	9.58335e12			0.937798
$779$	−2.53296e12	−	4.38722e12i	−0.246440	−	0.426846i
$780$	−2.20743e12	+	3.82338e12i	−0.213531	+	0.369847i
$781$	4.42232e11	−	7.65968e11i	0.0425324	−	0.0736683i
$782$	−7.66620e11	−	1.32782e12i	−0.0733077	−	0.126973i
$783$	8.29230e12			0.788401
$784$		0			0
$785$	1.24182e13			1.16720
$786$	2.50591e12	+	4.34037e12i	0.234188	+	0.405625i
$787$	−7.34166e12	+	1.27161e13i	−0.682194	+	1.18159i	0.292116	+	0.956383i	$0.405641\pi$
$787$	−7.34166e12	+	1.27161e13i	−0.682194	+	1.18159i	−0.974310	+	0.225212i	$0.927693\pi$
$788$	9.35811e11	−	1.62087e12i	0.0864610	−	0.149755i
$789$	3.13102e12	+	5.42308e12i	0.287633	+	0.498195i
$790$	−1.99068e13			−1.81836
$791$		0			0
$792$	6.50497e11			0.0587465
$793$	1.48457e13	+	2.57135e13i	1.33313	+	2.30904i
$794$	−2.94527e12	+	5.10136e12i	−0.262987	+	0.455506i
$795$	−3.27815e12	+	5.67792e12i	−0.291056	+	0.504124i
$796$	1.93344e11	+	3.34882e11i	0.0170695	+	0.0295653i
$797$	−1.35485e13			−1.18940			−0.594699	−	0.803948i	$-0.702729\pi$
$797$	−1.35485e13			−1.18940			−0.594699	+	0.803948i	$0.702729\pi$
$798$		0			0
$799$	4.12874e12			0.358391
$800$	7.43480e11	+	1.28774e12i	0.0641747	+	0.111154i
$801$	4.70070e12	−	8.14186e12i	0.403475	−	0.698839i
$802$	8.89753e11	−	1.54110e12i	0.0759424	−	0.131536i
$803$	−6.25339e11	−	1.08312e12i	−0.0530756	−	0.0919297i
$804$	3.26265e12			0.275371
$805$		0			0
$806$	−2.28448e13			−1.90669
$807$	2.76934e12	+	4.79664e12i	0.229851	+	0.398113i
$808$	2.80228e12	−	4.85369e12i	0.231292	−	0.400609i
$809$	7.16152e12	−	1.24041e13i	0.587810	−	1.01812i	−0.406708	−	0.913558i	$-0.633324\pi$
$809$	7.16152e12	−	1.24041e13i	0.587810	−	1.01812i	0.994519	−	0.104559i	$-0.0333431\pi$
$810$	3.41498e12	+	5.91493e12i	0.278744	+	0.482799i
$811$	−2.09686e13			−1.70206			−0.851030	−	0.525117i	$-0.824021\pi$
$811$	−2.09686e13			−1.70206			−0.851030	+	0.525117i	$0.824021\pi$
$812$		0			0
$813$	3.30772e12			0.265535
$814$	2.03688e11	+	3.52798e11i	0.0162613	+	0.0281654i
$815$	2.70339e12	−	4.68241e12i	0.214634	−	0.371758i
$816$	−1.68271e11	+	2.91454e11i	−0.0132863	+	0.0230126i
$817$	9.77909e12	+	1.69379e13i	0.767890	+	1.33003i
$818$	7.07890e12			0.552810
$819$		0			0
$820$	4.23145e12			0.326834
$821$	7.26689e12	+	1.25866e13i	0.558219	+	0.966863i	0.997645	+	0.0685847i	$0.0218483\pi$
$821$	7.26689e12	+	1.25866e13i	0.558219	+	0.966863i	−0.439427	+	0.898279i	$0.644818\pi$
$822$	−5.86329e11	+	1.01555e12i	−0.0447938	+	0.0775852i
$823$	−9.17660e12	+	1.58943e13i	−0.697240	+	1.20766i	0.272179	+	0.962247i	$0.412256\pi$
$823$	−9.17660e12	+	1.58943e13i	−0.697240	+	1.20766i	−0.969420	+	0.245409i	$0.921078\pi$
$824$	−3.93526e11	−	6.81608e11i	−0.0297373	−	0.0515065i
$825$	6.97792e11			0.0524425
$826$		0			0
$827$	−7.78350e11			−0.0578629			−0.0289315	−	0.999581i	$-0.509210\pi$
$827$	−7.78350e11			−0.0578629			−0.0289315	+	0.999581i	$0.509210\pi$
$828$	−2.12152e12	−	3.67458e12i	−0.156859	−	0.271688i
$829$	4.89759e12	−	8.48288e12i	0.360153	−	0.623803i	−0.627833	−	0.778348i	$-0.716058\pi$
$829$	4.89759e12	−	8.48288e12i	0.360153	−	0.623803i	0.987986	+	0.154545i	$0.0493911\pi$
$830$	6.48230e12	−	1.12277e13i	0.474109	−	0.821181i
$831$	2.31596e12	+	4.01137e12i	0.168472	+	0.291802i
$832$	3.00386e12			0.217333
$833$		0			0
$834$	−6.68613e12			−0.478550
$835$	1.46027e13	+	2.52926e13i	1.03955	+	1.80055i
$836$	−6.75640e11	+	1.17024e12i	−0.0478395	+	0.0828605i
$837$	7.65860e12	−	1.32651e13i	0.539367	−	0.934212i
$838$	6.03998e12	+	1.04615e13i	0.423094	+	0.732821i
$839$	2.38998e12			0.166520			0.0832598	−	0.996528i	$-0.473467\pi$
$839$	2.38998e12			0.166520			0.0832598	+	0.996528i	$0.473467\pi$
$840$		0			0
$841$	4.13119e12			0.284769
$842$	3.45028e12	+	5.97606e12i	0.236565	+	0.409742i
$843$	3.73029e11	−	6.46105e11i	0.0254401	−	0.0440635i
$844$	2.42108e12	−	4.19344e12i	0.164236	−	0.284465i
$845$	−1.96942e13	−	3.41113e13i	−1.32887	−	2.30167i
$846$	1.14257e13			0.766862
$847$		0			0
$848$	4.46090e12			0.296238
$849$	−3.78210e12	−	6.55079e12i	−0.249832	−	0.432722i
$850$	1.11052e12	−	1.92347e12i	0.0729692	−	0.126386i
$851$	1.32861e12	−	2.30122e12i	0.0868389	−	0.150409i
$852$	6.33157e11	+	1.09666e12i	0.0411655	+	0.0713007i
$853$	1.36355e13			0.881860			0.440930	−	0.897541i	$-0.354649\pi$
$853$	1.36355e13			0.881860			0.440930	+	0.897541i	$0.354649\pi$
$854$		0			0
$855$	−1.74935e13			−1.11951
$856$	−2.14743e12	−	3.71946e12i	−0.136706	−	0.236781i
$857$	−1.63491e12	+	2.83175e12i	−0.103533	+	0.179325i	−0.913138	−	0.407650i	$-0.866348\pi$
$857$	−1.63491e12	+	2.83175e12i	−0.103533	+	0.179325i	0.809605	+	0.586976i	$0.199682\pi$
$858$	7.04819e11	−	1.22078e12i	0.0444002	−	0.0769034i
$859$	−9.81679e10	−	1.70032e11i	−0.00615177	−	0.0106552i	0.862933	−	0.505318i	$-0.168625\pi$
$859$	−9.81679e10	−	1.70032e11i	−0.00615177	−	0.0106552i	−0.869085	+	0.494663i	$0.835292\pi$
$860$	−1.63365e13			−1.01839
$861$		0			0
$862$	−1.62200e13			−1.00062
$863$	4.51676e12	+	7.82325e12i	0.277190	+	0.480108i	0.970685	−	0.240354i	$-0.0772634\pi$
$863$	4.51676e12	+	7.82325e12i	0.277190	+	0.480108i	−0.693495	+	0.720461i	$0.743930\pi$
$864$	−1.00703e12	+	1.74422e12i	−0.0614794	+	0.106485i
$865$	−9.48324e12	+	1.64255e13i	−0.575949	+	0.997573i
$866$	4.82376e12	+	8.35501e12i	0.291444	+	0.504796i
$867$	−5.71838e12			−0.343706
$868$		0			0
$869$	6.35612e12			0.378097
$870$	−3.32667e12	−	5.76197e12i	−0.196867	−	0.340984i
$871$	−2.17489e13	+	3.76702e13i	−1.28043	+	2.21777i
$872$	4.17296e12	−	7.22777e12i	0.244410	−	0.423331i
$873$	−1.07423e13	−	1.86061e13i	−0.625938	−	1.08416i
$874$	8.81408e12			0.510946
$875$		0			0
$876$	1.79063e12			0.102740
$877$	−3.52657e12	−	6.10819e12i	−0.201305	−	0.348670i	0.747644	−	0.664099i	$-0.231185\pi$
$877$	−3.52657e12	−	6.10819e12i	−0.201305	−	0.348670i	−0.948949	+	0.315429i	$0.897851\pi$
$878$	3.63428e12	−	6.29476e12i	0.206392	−	0.357482i
$879$	1.93881e12	−	3.35812e12i	0.109543	−	0.189734i
$880$	−5.64345e11	−	9.77475e11i	−0.0317229	−	0.0549457i
$881$	3.36898e13			1.88411			0.942056	−	0.335456i	$-0.108890\pi$
$881$	3.36898e13			1.88411			0.942056	+	0.335456i	$0.108890\pi$
$882$		0			0
$883$	2.36891e13			1.31137			0.655686	−	0.755034i	$-0.272379\pi$
$883$	2.36891e13			1.31137			0.655686	+	0.755034i	$0.272379\pi$
$884$	−2.24340e12	−	3.88568e12i	−0.123558	−	0.214009i
$885$	1.64860e12	−	2.85546e12i	0.0903381	−	0.156470i
$886$	8.07110e12	−	1.39796e13i	0.440029	−	0.762152i
$887$	1.09498e13	+	1.89656e13i	0.593948	+	1.02875i	0.993694	+	0.112123i	$0.0357649\pi$
$887$	1.09498e13	+	1.89656e13i	0.593948	+	1.02875i	−0.399746	+	0.916626i	$0.630902\pi$
$888$	−5.83253e11			−0.0314774
$889$		0			0
$890$	−1.63126e13			−0.871500
$891$	−1.09038e12	−	1.88860e12i	−0.0579602	−	0.100390i
$892$	6.87856e12	−	1.19140e13i	0.363794	−	0.630109i
$893$	−1.18674e13	+	2.05549e13i	−0.624485	+	1.08164i
$894$	−4.62737e12	−	8.01484e12i	−0.242279	−	0.419639i
$895$	1.98343e13			1.03327
$896$		0			0
$897$	−9.19473e12			−0.474213
$898$	1.20856e11	+	2.09329e11i	0.00620190	+	0.0107420i
$899$	1.72140e13	−	2.98155e13i	0.878947	−	1.52238i
$900$	3.07321e12	−	5.32295e12i	0.156135	−	0.270434i
$901$	−3.33157e12	−	5.77044e12i	−0.168417	−	0.291707i
$902$	−1.35108e12			−0.0679595
$903$		0			0
$904$	1.92921e12			0.0960775
$905$	−5.63624e12	−	9.76226e12i	−0.279300	−	0.483762i
$906$	−1.65551e12	+	2.86743e12i	−0.0816311	+	0.141389i
$907$	−7.08986e12	+	1.22800e13i	−0.347860	+	0.602511i	−0.985869	−	0.167518i	$-0.946425\pi$
$907$	−7.08986e12	+	1.22800e13i	−0.347860	+	0.602511i	0.638009	+	0.770029i	$0.279758\pi$
$908$	8.33709e11	+	1.44403e12i	0.0407031	+	0.0704999i
$909$	−2.31667e13			−1.12545
$910$		0			0
$911$	−5.44567e12			−0.261950			−0.130975	−	0.991386i	$-0.541811\pi$
$911$	−5.44567e12			−0.261950			−0.130975	+	0.991386i	$0.541811\pi$
$912$	−9.67334e11	−	1.67547e12i	−0.0463020	−	0.0801974i
$913$	−2.06976e12	+	3.58493e12i	−0.0985829	+	0.170751i
$914$	−8.27038e12	+	1.43247e13i	−0.391983	+	0.678935i
$915$	7.98649e12	+	1.38330e13i	0.376670	+	0.652412i
$916$	−5.33893e12			−0.250567
$917$		0			0
$918$	3.00834e12			0.139809
$919$	−1.37792e13	−	2.38662e13i	−0.637240	−	1.10373i	−0.986036	−	0.166534i	$-0.946743\pi$
$919$	−1.37792e13	−	2.38662e13i	−0.637240	−	1.10373i	0.348795	−	0.937199i	$-0.386591\pi$
$920$	−3.68109e12	+	6.37584e12i	−0.169407	+	0.293421i
$921$	−2.93080e12	+	5.07629e12i	−0.134220	+	0.232476i
$922$	−4.92943e12	−	8.53802e12i	−0.224650	−	0.389106i
$923$	−1.68825e13			−0.765649
$924$		0			0
$925$	3.84921e12			0.172876
$926$	7.09940e12	+	1.22965e13i	0.317302	+	0.549582i
$927$	−1.62666e12	+	2.81746e12i	−0.0723498	+	0.125314i
$928$	−2.26346e12	+	3.92043e12i	−0.100186	+	0.173527i
$929$	5.08846e12	+	8.81346e12i	0.224138	+	0.388218i	0.956060	−	0.293170i	$-0.0947101\pi$
$929$	5.08846e12	+	8.81346e12i	0.224138	+	0.388218i	−0.731923	+	0.681388i	$0.761377\pi$
$930$	−1.22898e13			−0.538730
$931$		0			0
$932$	4.90390e12			0.212897
$933$	5.79781e12	+	1.00421e13i	0.250493	+	0.433867i
$934$	−1.40999e13	+	2.44217e13i	−0.606253	+	1.05006i
$935$	−8.42948e11	+	1.46003e12i	−0.0360702	+	0.0624754i
$936$	−6.20831e12	−	1.07531e13i	−0.264382	−	0.457923i
$937$	−1.96831e13			−0.834192			−0.417096	−	0.908863i	$-0.636952\pi$
$937$	−1.96831e13			−0.834192			−0.417096	+	0.908863i	$0.636952\pi$
$938$		0			0
$939$	−5.64604e12			−0.237000
$940$	−9.91251e12	−	1.71690e13i	−0.414103	−	0.717247i
$941$	3.78017e12	−	6.54744e12i	0.157166	−	0.272219i	−0.776680	−	0.629896i	$-0.783098\pi$
$941$	3.78017e12	−	6.54744e12i	0.157166	−	0.272219i	0.933845	+	0.357677i	$0.116431\pi$
$942$	2.83844e12	−	4.91633e12i	0.117450	−	0.203429i
$943$	4.40637e12	+	7.63206e12i	0.181459	+	0.314296i
$944$	−2.24341e12			−0.0919465
$945$		0			0
$946$	5.21613e12			0.211757
$947$	−1.21185e13	−	2.09899e13i	−0.489637	−	0.848076i	0.510292	−	0.860001i	$-0.329537\pi$
$947$	−1.21185e13	−	2.09899e13i	−0.489637	−	0.848076i	−0.999929	+	0.0119251i	$0.996204\pi$
$948$	−4.55013e12	+	7.88105e12i	−0.182973	+	0.316918i
$949$	−1.19364e13	+	2.06744e13i	−0.477722	+	0.827438i
$950$	6.38398e12	+	1.10574e13i	0.254294	+	0.440449i
$951$	−1.70826e13			−0.677239
$952$		0			0
$953$	2.69411e13			1.05803			0.529015	−	0.848613i	$-0.322562\pi$
$953$	2.69411e13			1.05803			0.529015	+	0.848613i	$0.322562\pi$
$954$	−9.21966e12	−	1.59689e13i	−0.360369	−	0.624177i
$955$	8.61776e12	−	1.49264e13i	0.335258	−	0.580684i
$956$	3.31069e12	−	5.73428e12i	0.128191	−	0.222034i
$957$	1.06219e12	+	1.83976e12i	0.0409352	+	0.0709018i
$958$	2.00341e12			0.0768467
$959$		0			0
$960$	1.61598e12			0.0614067
$961$	−1.85771e13	−	3.21766e13i	−0.702625	−	1.21698i
$962$	3.88797e12	−	6.73417e12i	0.146364	−	0.253511i
$963$	−8.87650e12	+	1.53745e13i	−0.332601	+	0.576082i
$964$	−4.11911e12	−	7.13451e12i	−0.153623	−	0.266083i
$965$	1.66424e13			0.617794
$966$		0			0
$967$	2.13513e13			0.785245			0.392623	−	0.919700i	$-0.371568\pi$
$967$	2.13513e13			0.785245			0.392623	+	0.919700i	$0.371568\pi$
$968$	−4.64888e12	−	8.05210e12i	−0.170180	−	0.294761i
$969$	−1.44488e12	+	2.50261e12i	−0.0526472	+	0.0911877i
$970$	−1.86391e13	+	3.22839e13i	−0.676009	+	1.17088i
$971$	−3.10576e11	−	5.37933e11i	−0.0112119	−	0.0194197i	0.860365	−	0.509678i	$-0.170236\pi$
$971$	−3.10576e11	−	5.37933e11i	−0.0112119	−	0.0194197i	−0.871577	+	0.490259i	$0.836902\pi$
$972$	1.28007e13			0.459975
$973$		0			0
$974$	−3.07051e13			−1.09319
$975$	−6.65969e12	−	1.15349e13i	−0.236011	−	0.408784i
$976$	5.43400e12	−	9.41196e12i	0.191688	−	0.332014i
$977$	1.06440e13	−	1.84359e13i	0.373748	−	0.647350i	−0.616391	−	0.787440i	$-0.711406\pi$
$977$	1.06440e13	−	1.84359e13i	0.373748	−	0.647350i	0.990139	+	0.140090i	$0.0447392\pi$
$978$	−1.23583e12	−	2.14053e12i	−0.0431952	−	0.0748163i
$979$	5.20850e12			0.181214
$980$		0			0
$981$	−3.44982e13			−1.18928
$982$	−1.03841e13	−	1.79858e13i	−0.356342	−	0.617203i
$983$	−2.82842e12	+	4.89897e12i	−0.0966169	+	0.167345i	−0.910282	−	0.413988i	$-0.864135\pi$
$983$	−2.82842e12	+	4.89897e12i	−0.0966169	+	0.167345i	0.813665	+	0.581334i	$0.197469\pi$
$984$	9.67188e11	−	1.67522e12i	0.0328877	−	0.0569631i
$985$	6.71182e12	+	1.16252e13i	0.227184	+	0.393494i
$986$	6.76175e12			0.227831
$987$		0			0
$988$	2.57931e13			0.861186
$989$	−1.70118e13	−	2.94653e13i	−0.565414	−	0.979327i
$990$	−2.33275e12	+	4.04044e12i	−0.0771808	+	0.133681i
$991$	9.12288e12	−	1.58013e13i	0.300469	−	0.520428i	−0.675773	−	0.737110i	$-0.736190\pi$
$991$	9.12288e12	−	1.58013e13i	0.300469	−	0.520428i	0.976242	+	0.216682i	$0.0695233\pi$
$992$	4.18098e12	+	7.24166e12i	0.137080	+	0.237430i
$993$	−8.89422e12			−0.290293
$994$		0			0
$995$	−2.77340e12			−0.0897035
$996$	−2.96334e12	−	5.13265e12i	−0.0954145	−	0.165263i
$997$	4.83657e12	−	8.37719e12i	0.155028	−	0.268516i	−0.778041	−	0.628213i	$-0.783787\pi$
$997$	4.83657e12	−	8.37719e12i	0.155028	−	0.268516i	0.933069	+	0.359697i	$0.117120\pi$
$998$	−3.40861e12	+	5.90388e12i	−0.108765	+	0.188387i
$999$	2.60684e12	+	4.51518e12i	0.0828075	+	0.143427i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.c.i.67.1		4
7.2	even	3	inner	98.10.c.i.79.1		4
7.3	odd	6		98.10.a.d.1.1	✓	2
7.4	even	3		98.10.a.d.1.2	yes	2
7.5	odd	6	inner	98.10.c.i.79.2		4
7.6	odd	2	inner	98.10.c.i.67.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.10.a.d.1.1	✓	2	7.3	odd	6
98.10.a.d.1.2	yes	2	7.4	even	3
98.10.c.i.67.1		4	1.1	even	1	trivial
98.10.c.i.67.2		4	7.6	odd	2	inner
98.10.c.i.79.1		4	7.2	even	3	inner
98.10.c.i.79.2		4	7.5	odd	6	inner

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(8.00000 + 13.8564i) q^{2} +(-26.2298 + 45.4313i) q^{3} +(-128.000 + 221.703i) q^{4} +(-918.041 - 1590.09i) q^{5} -839.352 q^{6} -4096.00 q^{8} +(8465.50 + 14662.7i) q^{9} +(14688.7 - 25441.5i) q^{10} +(-4690.00 + 8123.32i) q^{11} +(-6714.82 - 11630.4i) q^{12} +179044. q^{13} +96320.0 q^{15} +(-32768.0 - 56755.8i) q^{16} +(-48944.7 + 84774.7i) q^{17} +(-135448. + 234603. i) q^{18} +(-281367. - 487341. i) q^{19} +470037. q^{20} -150080. q^{22} +(489468. + 847783. i) q^{23} +(107437. - 186086. i) q^{24} +(-709038. + 1.22809e6i) q^{25} +(1.43235e6 + 2.48091e6i) q^{26} -1.92075e6 q^{27} -4.31721e6 q^{29} +(770560. + 1.33465e6i) q^{30} +(-3.98729e6 + 6.90619e6i) q^{31} +(524288. - 908093. i) q^{32} +(-246035. - 426145. i) q^{33} -1.56623e6 q^{34} -4.33434e6 q^{36} +(-1.35720e6 - 2.35073e6i) q^{37} +(4.50187e6 - 7.79746e6i) q^{38} +(-4.69629e6 + 8.13421e6i) q^{39} +(3.76030e6 + 6.51303e6i) q^{40} +9.00237e6 q^{41} -3.47557e7 q^{43} +(-1.20064e6 - 2.07957e6i) q^{44} +(1.55434e7 - 2.69219e7i) q^{45} +(-7.83149e6 + 1.35645e7i) q^{46} +(-2.10888e7 - 3.65268e7i) q^{47} +3.43799e6 q^{48} -2.26892e7 q^{50} +(-2.56762e6 - 4.44724e6i) q^{51} +(-2.29177e7 + 3.96946e7i) q^{52} +(-3.40340e7 + 5.89486e7i) q^{53} +(-1.53660e7 - 2.66147e7i) q^{54} +1.72225e7 q^{55} +2.95207e7 q^{57} +(-3.45377e7 - 5.98211e7i) q^{58} +(1.71159e7 - 2.96456e7i) q^{59} +(-1.23290e7 + 2.13544e7i) q^{60} +(8.29163e7 + 1.43615e8i) q^{61} -1.27593e8 q^{62} +1.67772e7 q^{64} +(-1.64370e8 - 2.84697e8i) q^{65} +(3.93656e6 - 6.81832e6i) q^{66} +(-1.21472e8 + 2.10396e8i) q^{67} +(-1.25298e7 - 2.17023e7i) q^{68} -5.13545e7 q^{69} -9.42925e7 q^{71} +(-3.46747e7 - 6.00583e7i) q^{72} +(-6.66672e7 + 1.15471e8i) q^{73} +(2.17152e7 - 3.76117e7i) q^{74} +(-3.71958e7 - 6.44249e7i) q^{75} +1.44060e8 q^{76} -1.50281e8 q^{78} +(-3.38813e8 - 5.86841e8i) q^{79} +(-6.01648e7 + 1.04208e8i) q^{80} +(-1.16246e8 + 2.01343e8i) q^{81} +(7.20189e7 + 1.24740e8i) q^{82} +4.41313e8 q^{83} +1.79733e8 q^{85} +(-2.78046e8 - 4.81589e8i) q^{86} +(1.13239e8 - 1.96137e8i) q^{87} +(1.92102e7 - 3.32731e7i) q^{88} +(-2.77639e8 - 4.80885e8i) q^{89} +4.97387e8 q^{90} -2.50608e8 q^{92} +(-2.09171e8 - 3.62295e8i) q^{93} +(3.37420e8 - 5.84429e8i) q^{94} +(-5.16612e8 + 8.94799e8i) q^{95} +(2.75039e7 + 4.76381e7i) q^{96} -1.26895e9 q^{97} -1.58813e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{2} - 512 q^{4} - 16384 q^{8} + 33862 q^{9} - 18760 q^{11} + 385280 q^{15} - 131072 q^{16} - 541792 q^{18} - 600320 q^{22} + 1957872 q^{23} - 2836150 q^{25} - 17268856 q^{29} + 3082240 q^{30}+ \cdots - 635251120 q^{99}+O(q^{100}) \) 4 * q + 32 * q^2 - 512 * q^4 - 16384 * q^8 + 33862 * q^9 - 18760 * q^11 + 385280 * q^15 - 131072 * q^16 - 541792 * q^18 - 600320 * q^22 + 1957872 * q^23 - 2836150 * q^25 - 17268856 * q^29 + 3082240 * q^30 + 2097152 * q^32 - 17337344 * q^36 - 5428788 * q^37 - 18785152 * q^39 - 139022768 * q^43 - 4802560 * q^44 - 31325952 * q^46 - 90756800 * q^50 - 10270464 * q^51 - 136135852 * q^53 + 118082816 * q^57 - 138150848 * q^58 - 49315840 * q^60 + 67108864 * q^64 - 657480320 * q^65 - 485888840 * q^67 - 377169856 * q^71 - 138698752 * q^72 + 86860608 * q^74 - 601124864 * q^78 - 1355250320 * q^79 - 464982290 * q^81 + 718932480 * q^85 - 1112182144 * q^86 + 76840960 * q^88 - 1002430464 * q^92 - 836685056 * q^93 - 2066449280 * q^95 - 635251120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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