LMFDB - Embedded newform 49.10.c.e.18.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,10,Mod(18,49)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("49.18");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	49.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$25.2367559720$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 427x^{4} - 3606x^{3} + 183492x^{2} - 858816x + 4064256 $ x^6 - x^5 + 427x^4 - 3606x^3 + 183492x^2 - 858816x + 4064256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			18.1
Root			$2.48064 + 4.29659i$ of defining polynomial
Character	$\chi$	$=$	49.18
Dual form			49.10.c.e.30.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-20.9010 - 36.2015i) q^{2} +(0.116170 - 0.201212i) q^{3} +(-617.701 + 1069.89i) q^{4} +(-895.944 - 1551.82i) q^{5} -9.71222 q^{6} +30239.6 q^{8} +(9841.47 + 17045.9i) q^{9} +(-37452.2 + 64869.1i) q^{10} +(-8700.77 + 15070.2i) q^{11} +(143.516 + 248.577i) q^{12} +122541. q^{13} -416.326 q^{15} +(-315775. - 546938. i) q^{16} +(165966. - 287462. i) q^{17} +(411393. - 712553. i) q^{18} +(380853. + 659658. i) q^{19} +2.21370e6 q^{20} +727418. q^{22} +(-616243. - 1.06736e6i) q^{23} +(3512.93 - 6084.57i) q^{24} +(-628870. + 1.08923e6i) q^{25} +(-2.56123e6 - 4.43618e6i) q^{26} +9146.25 q^{27} +634604. q^{29} +(8701.61 + 15071.6i) q^{30} +(-2.69034e6 + 4.65981e6i) q^{31} +(-5.45866e6 + 9.45467e6i) q^{32} +(2021.53 + 3501.39i) q^{33} -1.38754e7 q^{34} -2.43164e7 q^{36} +(1.51806e6 + 2.62935e6i) q^{37} +(1.59204e7 - 2.75750e7i) q^{38} +(14235.5 - 24656.7i) q^{39} +(-2.70930e7 - 4.69265e7i) q^{40} +7.37009e6 q^{41} -2.06990e7 q^{43} +(-1.07490e7 - 1.86177e7i) q^{44} +(1.76348e7 - 3.05444e7i) q^{45} +(-2.57602e7 + 4.46179e7i) q^{46} +(1.01816e7 + 1.76350e7i) q^{47} -146734. q^{48} +5.25760e7 q^{50} +(-38560.5 - 66788.7i) q^{51} +(-7.56938e7 + 1.31106e8i) q^{52} +(2.98690e7 - 5.17346e7i) q^{53} +(-191165. - 331108. i) q^{54} +3.11816e7 q^{55} +176974. q^{57} +(-1.32638e7 - 2.29736e7i) q^{58} +(3.01730e7 - 5.22612e7i) q^{59} +(257165. - 445423. i) q^{60} +(-4.72179e6 - 8.17837e6i) q^{61} +2.24923e8 q^{62} +1.33012e8 q^{64} +(-1.09790e8 - 1.90162e8i) q^{65} +(84503.8 - 146365. i) q^{66} +(1.09593e8 - 1.89821e8i) q^{67} +(2.05035e8 + 3.55132e8i) q^{68} -286355. q^{69} -5.58741e7 q^{71} +(2.97603e8 + 5.15463e8i) q^{72} +(2.27166e8 - 3.93463e8i) q^{73} +(6.34577e7 - 1.09912e8i) q^{74} +(146111. + 253072. i) q^{75} -9.41015e8 q^{76} -1.19015e6 q^{78} +(-2.25528e7 - 3.90627e7i) q^{79} +(-5.65834e8 + 9.80053e8i) q^{80} +(-1.93709e8 + 3.35513e8i) q^{81} +(-1.54042e8 - 2.66809e8i) q^{82} +3.34665e8 q^{83} -5.94786e8 q^{85} +(4.32629e8 + 7.49336e8i) q^{86} +(73721.6 - 127690. i) q^{87} +(-2.63108e8 + 4.55717e8i) q^{88} +(3.25943e8 + 5.64550e8i) q^{89} -1.47434e9 q^{90} +1.52262e9 q^{92} +(625072. + 1.08266e6i) q^{93} +(4.25610e8 - 7.37178e8i) q^{94} +(6.82447e8 - 1.18203e9i) q^{95} +(1.26826e6 + 2.19669e6i) q^{96} +1.42804e9 q^{97} -3.42514e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 21 q^{2} + 84 q^{3} - 1557 q^{4} + 1554 q^{5} - 9828 q^{6} + 28110 q^{8} + 26001 q^{9} - 97860 q^{10} + 3444 q^{11} - 106386 q^{12} + 39564 q^{13} + 400608 q^{15} - 482961 q^{16} + 1016694 q^{17}+ \cdots - 3801958344 q^{99}+O(q^{100}) $ 6 * q - 21 * q^2 + 84 * q^3 - 1557 * q^4 + 1554 * q^5 - 9828 * q^6 + 28110 * q^8 + 26001 * q^9 - 97860 * q^10 + 3444 * q^11 - 106386 * q^12 + 39564 * q^13 + 400608 * q^15 - 482961 * q^16 + 1016694 * q^17 + 273267 * q^18 + 222852 * q^19 + 3844176 * q^20 - 5694096 * q^22 - 1885632 * q^23 - 1449630 * q^24 - 3073221 * q^25 - 8785056 * q^26 - 1103760 * q^27 + 8163636 * q^29 - 8053200 * q^30 + 2869440 * q^31 - 25221951 * q^32 - 20259792 * q^33 + 7963284 * q^34 - 70792758 * q^36 - 1395618 * q^37 + 43479870 * q^38 + 8990688 * q^39 - 82859280 * q^40 + 28841316 * q^41 - 123262344 * q^43 - 97011984 * q^44 + 29774682 * q^45 - 89747664 * q^46 - 10368960 * q^47 - 33597564 * q^48 + 146650110 * q^50 + 26146728 * q^51 - 80908044 * q^52 - 67502610 * q^53 - 117879300 * q^54 + 211646064 * q^55 + 16942224 * q^57 + 159163830 * q^58 - 42590100 * q^59 + 179551008 * q^60 + 191746842 * q^61 + 93966936 * q^62 + 15704322 * q^64 - 364283220 * q^65 - 8057952 * q^66 + 255175788 * q^67 + 743485806 * q^68 - 515807712 * q^69 + 593029008 * q^71 + 609314265 * q^72 + 344213310 * q^73 + 690696462 * q^74 + 279031116 * q^75 - 1457679972 * q^76 + 560265552 * q^78 + 960412656 * q^79 - 1333333344 * q^80 + 35827677 * q^81 + 562675302 * q^82 + 2201034360 * q^83 + 876358824 * q^85 + 880982256 * q^86 - 621821592 * q^87 - 1206124800 * q^88 + 506816478 * q^89 - 4606905240 * q^90 + 1382246976 * q^92 - 1693258512 * q^93 + 1388004828 * q^94 + 2203071072 * q^95 + 333385794 * q^96 + 1294996500 * q^97 - 3801958344 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

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

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 $

$2$	−20.9010	−	36.2015i	−0.923701	−	1.59990i	−0.793637	−	0.608392i	$-0.791815\pi$
$2$	−20.9010	−	36.2015i	−0.923701	−	1.59990i	−0.130065	−	0.991506i	$-0.541518\pi$
$3$	0.116170	−	0.201212i	0.000828031	−	0.00143419i	−0.865611	−	0.500717i	$-0.833070\pi$
$3$	0.116170	−	0.201212i	0.000828031	−	0.00143419i	0.866439	+	0.499283i	$0.166403\pi$
$4$	−617.701	+	1069.89i	−1.20645	+	2.08963i
$5$	−895.944	−	1551.82i	−0.641086	−	1.11039i	−0.985191	−	0.171462i	$-0.945151\pi$
$5$	−895.944	−	1551.82i	−0.641086	−	1.11039i	0.344105	−	0.938931i	$-0.388182\pi$
$6$	−9.71222			−0.00305941
$7$		0			0
$7$		0			0
$8$	30239.6			2.61019
$9$	9841.47	+	17045.9i	0.499999	+	0.866023i
$10$	−37452.2	+	64869.1i	−1.18434	+	2.05134i
$11$	−8700.77	+	15070.2i	−0.179180	+	0.310350i	−0.941600	−	0.336733i	$-0.890678\pi$
$11$	−8700.77	+	15070.2i	−0.179180	+	0.310350i	0.762420	+	0.647083i	$0.224011\pi$
$12$	143.516	+	248.577i	0.00199795	+	0.00346056i
$13$	122541.			1.18997			0.594986	−	0.803736i	$-0.297158\pi$
$13$	122541.			1.18997			0.594986	+	0.803736i	$0.297158\pi$
$14$		0			0
$15$	−416.326			−0.00212335
$16$	−315775.	−	546938.i	−1.20459	−	2.08640i
$17$	165966.	−	287462.i	0.481948	−	0.834758i	−0.517838	−	0.855479i	$-0.673263\pi$
$17$	165966.	−	287462.i	0.481948	−	0.834758i	0.999785	+	0.0207211i	$0.00659621\pi$
$18$	411393.	−	712553.i	0.923699	−	1.59989i
$19$	380853.	+	659658.i	0.670450	+	1.16125i	0.977777	+	0.209650i	$0.0672324\pi$
$19$	380853.	+	659658.i	0.670450	+	1.16125i	−0.307326	+	0.951604i	$0.599434\pi$
$20$	2.21370e6			3.09375
$21$		0			0
$22$	727418.			0.662037
$23$	−616243.	−	1.06736e6i	−0.459173	−	0.795312i	0.539744	−	0.841829i	$-0.318521\pi$
$23$	−616243.	−	1.06736e6i	−0.459173	−	0.795312i	−0.998917	+	0.0465175i	$0.985188\pi$
$24$	3512.93	−	6084.57i	0.00216132	−	0.00374351i
$25$	−628870.	+	1.08923e6i	−0.321981	+	0.557688i
$26$	−2.56123e6	−	4.43618e6i	−1.09918	−	1.90383i
$27$	9146.25			0.00331212
$28$		0			0
$29$	634604.			0.166614			0.0833071	−	0.996524i	$-0.473452\pi$
$29$	634604.			0.166614			0.0833071	+	0.996524i	$0.473452\pi$
$30$	8701.61	+	15071.6i	0.00196135	+	0.00339715i
$31$	−2.69034e6	+	4.65981e6i	−0.523215	+	0.906235i	0.476420	+	0.879218i	$0.341934\pi$
$31$	−2.69034e6	+	4.65981e6i	−0.523215	+	0.906235i	−0.999635	+	0.0270171i	$0.991399\pi$
$32$	−5.45866e6	+	9.45467e6i	−0.920261	+	1.59394i
$33$	2021.53	+	3501.39i	0.000296734	+	0.000513958i
$34$	−1.38754e7			−1.78070
$35$		0			0
$36$	−2.43164e7			−2.41289
$37$	1.51806e6	+	2.62935e6i	0.133162	+	0.230643i	0.924894	−	0.380226i	$-0.124154\pi$
$37$	1.51806e6	+	2.62935e6i	0.133162	+	0.230643i	−0.791732	+	0.610869i	$0.790820\pi$
$38$	1.59204e7	−	2.75750e7i	1.23859	−	2.14530i
$39$	14235.5	−	24656.7i	0.000985334	−	0.00170665i
$40$	−2.70930e7	−	4.69265e7i	−1.67335	−	2.89833i
$41$	7.37009e6			0.407329			0.203665	−	0.979041i	$-0.434715\pi$
$41$	7.37009e6			0.407329			0.203665	+	0.979041i	$0.434715\pi$
$42$		0			0
$43$	−2.06990e7			−0.923297			−0.461649	−	0.887063i	$-0.652742\pi$
$43$	−2.06990e7			−0.923297			−0.461649	+	0.887063i	$0.652742\pi$
$44$	−1.07490e7	−	1.86177e7i	−0.432344	−	0.748841i
$45$	1.76348e7	−	3.05444e7i	0.641084	−	1.11039i
$46$	−2.57602e7	+	4.46179e7i	−0.848278	+	1.46926i
$47$	1.01816e7	+	1.76350e7i	0.304351	+	0.527152i	0.977117	−	0.212704i	$-0.0682271\pi$
$47$	1.01816e7	+	1.76350e7i	0.304351	+	0.527152i	−0.672766	+	0.739856i	$0.734894\pi$
$48$	−146734.			−0.00398974
$49$		0			0
$50$	5.25760e7			1.18966
$51$	−38560.5	−	66788.7i	−0.000798135	−	0.00138241i
$52$	−7.56938e7	+	1.31106e8i	−1.43564	+	2.48660i
$53$	2.98690e7	−	5.17346e7i	0.519971	−	0.900616i	−0.479759	−	0.877400i	$-0.659276\pi$
$53$	2.98690e7	−	5.17346e7i	0.519971	−	0.900616i	0.999730	−	0.0232162i	$-0.00739062\pi$
$54$	−191165.	−	331108.i	−0.00305941	−	0.00529905i
$55$	3.11816e7			0.459480
$56$		0			0
$57$	176974.			0.00222061
$58$	−1.32638e7	−	2.29736e7i	−0.153902	−	0.266565i
$59$	3.01730e7	−	5.22612e7i	0.324179	−	0.561495i	−0.657167	−	0.753745i	$-0.728245\pi$
$59$	3.01730e7	−	5.22612e7i	0.324179	−	0.561495i	0.981346	+	0.192250i	$0.0615786\pi$
$60$	257165.	−	445423.i	0.00256172	−	0.00443702i
$61$	−4.72179e6	−	8.17837e6i	−0.0436639	−	0.0756280i	0.843368	−	0.537337i	$-0.180570\pi$
$61$	−4.72179e6	−	8.17837e6i	−0.0436639	−	0.0756280i	−0.887031	+	0.461709i	$0.847236\pi$
$62$	2.24923e8			1.93318
$63$		0			0
$64$	1.33012e8			0.991013
$65$	−1.09790e8	−	1.90162e8i	−0.762874	−	1.32134i
$66$	84503.8	−	146365.i	0.000548187	−	0.000949487i
$67$	1.09593e8	−	1.89821e8i	0.664427	−	1.15082i	−0.315013	−	0.949087i	$-0.602009\pi$
$67$	1.09593e8	−	1.89821e8i	0.664427	−	1.15082i	0.979440	−	0.201734i	$-0.0646577\pi$
$68$	2.05035e8	+	3.55132e8i	1.16289	+	2.01418i
$69$	−286355.			−0.00152084
$70$		0			0
$71$	−5.58741e7			−0.260944			−0.130472	−	0.991452i	$-0.541649\pi$
$71$	−5.58741e7			−0.260944			−0.130472	+	0.991452i	$0.541649\pi$
$72$	2.97603e8	+	5.15463e8i	1.30509	+	2.26048i
$73$	2.27166e8	−	3.93463e8i	0.936248	−	1.62163i	0.163855	−	0.986485i	$-0.447607\pi$
$73$	2.27166e8	−	3.93463e8i	0.936248	−	1.62163i	0.772393	−	0.635144i	$-0.219059\pi$
$74$	6.34577e7	−	1.09912e8i	0.246004	−	0.426091i
$75$	146111.	+	253072.i	0.000533221	+	0.000923566i
$76$	−9.41015e8			−3.23545
$77$		0			0
$78$	−1.19015e6			−0.00364062
$79$	−2.25528e7	−	3.90627e7i	−0.0651447	−	0.112834i	0.831613	−	0.555355i	$-0.187418\pi$
$79$	−2.25528e7	−	3.90627e7i	−0.0651447	−	0.112834i	−0.896758	+	0.442521i	$0.854084\pi$
$80$	−5.65834e8	+	9.80053e8i	−1.54449	+	2.67513i
$81$	−1.93709e8	+	3.35513e8i	−0.499996	+	0.866018i
$82$	−1.54042e8	−	2.66809e8i	−0.376250	−	0.651685i
$83$	3.34665e8			0.774031			0.387016	−	0.922073i	$-0.373506\pi$
$83$	3.34665e8			0.774031			0.387016	+	0.922073i	$0.373506\pi$
$84$		0			0
$85$	−5.94786e8			−1.23588
$86$	4.32629e8	+	7.49336e8i	0.852851	+	1.47718i
$87$	73721.6	−	127690.i	0.000137962	−	0.000238957i
$88$	−2.63108e8	+	4.55717e8i	−0.467695	+	0.810071i
$89$	3.25943e8	+	5.64550e8i	0.550664	+	0.953777i	0.998227	+	0.0595250i	$0.0189586\pi$
$89$	3.25943e8	+	5.64550e8i	0.550664	+	0.953777i	−0.447563	+	0.894252i	$0.647708\pi$
$90$	−1.47434e9			−2.36868
$91$		0			0
$92$	1.52262e9			2.21588
$93$	625072.	+	1.08266e6i	0.000866476	+	0.00150078i
$94$	4.25610e8	−	7.37178e8i	0.562259	−	0.973861i
$95$	6.82447e8	−	1.18203e9i	0.859632	−	1.48893i
$96$	1.26826e6	+	2.19669e6i	0.00152401	+	0.00263966i
$97$	1.42804e9			1.63783			0.818914	−	0.573916i	$-0.194576\pi$
$97$	1.42804e9			1.63783			0.818914	+	0.573916i	$0.194576\pi$
$98$		0			0
$99$	−3.42514e8			−0.358360
$100$	−7.76908e8	−	1.34564e9i	−0.776908	−	1.34564i
$101$	4.45766e8	−	7.72090e8i	0.426247	−	0.738281i	−0.570289	−	0.821444i	$-0.693169\pi$
$101$	4.45766e8	−	7.72090e8i	0.426247	−	0.738281i	0.996536	+	0.0831631i	$0.0265023\pi$
$102$	−1.61190e6	+	2.79190e6i	−0.00147448	+	0.00255387i
$103$	−3.56000e8	−	6.16610e8i	−0.311661	−	0.539813i	0.667061	−	0.745003i	$-0.267552\pi$
$103$	−3.56000e8	−	6.16610e8i	−0.311661	−	0.539813i	−0.978722	+	0.205190i	$0.934219\pi$
$104$	3.70560e9			3.10605
$105$		0			0
$106$	−2.49716e9			−1.92119
$107$	−1.24299e9	−	2.15292e9i	−0.916729	−	1.58782i	−0.804350	−	0.594156i	$-0.797486\pi$
$107$	−1.24299e9	−	2.15292e9i	−0.916729	−	1.58782i	−0.112379	−	0.993665i	$-0.535847\pi$
$108$	−5.64965e6	+	9.78548e6i	−0.00399590	+	0.00692110i
$109$	−1.91728e8	+	3.32082e8i	−0.130096	+	0.225334i	−0.923714	−	0.383084i	$-0.874862\pi$
$109$	−1.91728e8	+	3.32082e8i	−0.130096	+	0.225334i	0.793617	+	0.608418i	$0.208195\pi$
$110$	−6.51726e8	−	1.12882e9i	−0.424422	−	0.735121i
$111$	705407.			0.000441048
$112$		0			0
$113$	2.39582e9			1.38230			0.691148	−	0.722713i	$-0.257105\pi$
$113$	2.39582e9			1.38230			0.691148	+	0.722713i	$0.257105\pi$
$114$	−3.69893e6	−	6.40674e6i	−0.00205118	−	0.00355276i
$115$	−1.10424e9	+	1.91260e9i	−0.588739	+	1.01973i
$116$	−3.91996e8	+	6.78957e8i	−0.201011	+	0.348162i
$117$	1.20599e9	+	2.08883e9i	0.594985	+	1.03054i
$118$	−2.52258e9			−1.19778
$119$		0			0
$120$	−1.25895e7			−0.00554235
$121$	1.02757e9	+	1.77980e9i	0.435789	+	0.754808i
$122$	−1.97380e8	+	3.41872e8i	−0.0806647	+	0.139715i
$123$	856180.	−	1.48295e6i	0.000337281	−	0.000584188i
$124$	−3.32366e9	−	5.75675e9i	−1.26246	−	2.18665i
$125$	−1.24605e9			−0.456501
$126$		0			0
$127$	1.88261e9			0.642161			0.321080	−	0.947052i	$-0.395954\pi$
$127$	1.88261e9			0.642161			0.321080	+	0.947052i	$0.395954\pi$
$128$	1.47619e7	+	2.55683e7i	0.00486067	+	0.00841893i
$129$	−2.40459e6	+	4.16488e6i	−0.000764519	+	0.00132419i
$130$	−4.58944e9	+	7.94914e9i	−1.40934	+	2.44104i
$131$	−7.46207e8	−	1.29247e9i	−0.221380	−	0.383442i	0.733847	−	0.679315i	$-0.237723\pi$
$131$	−7.46207e8	−	1.29247e9i	−0.221380	−	0.383442i	−0.955227	+	0.295873i	$0.904389\pi$
$132$	−4.99480e6			−0.00143198
$133$		0			0
$134$	−9.16242e9			−2.45493
$135$	−8.19453e6	−	1.41933e7i	−0.00212335	−	0.00367775i
$136$	5.01876e9	−	8.69275e9i	1.25797	−	2.17887i
$137$	1.60559e9	−	2.78096e9i	0.389396	−	0.674454i	−0.602972	−	0.797762i	$-0.706017\pi$
$137$	1.60559e9	−	2.78096e9i	0.389396	−	0.674454i	0.992368	+	0.123308i	$0.0393504\pi$
$138$	5.98509e6	+	1.03665e7i	0.00140480	+	0.00243319i
$139$	3.03934e9			0.690577			0.345289	−	0.938497i	$-0.387781\pi$
$139$	3.03934e9			0.690577			0.345289	+	0.938497i	$0.387781\pi$
$140$		0			0
$141$	4.73116e6			0.00100805
$142$	1.16782e9	+	2.02273e9i	0.241035	+	0.417484i
$143$	−1.06620e9	+	1.84672e9i	−0.213220	+	0.369307i
$144$	6.21538e9	−	1.07654e10i	1.20458	−	2.08640i
$145$	−5.68570e8	−	9.84792e8i	−0.106814	−	0.185007i
$146$	−1.89920e10			−3.45925
$147$		0			0
$148$	−3.75082e9			−0.642611
$149$	1.82143e9	+	3.15481e9i	0.302743	+	0.524367i	0.976756	−	0.214353i	$-0.0687642\pi$
$149$	1.82143e9	+	3.15481e9i	0.302743	+	0.524367i	−0.674013	+	0.738719i	$0.735431\pi$
$150$	6.10773e6	−	1.05789e7i	0.000985074	−	0.00170620i
$151$	−2.52931e9	+	4.38089e9i	−0.395919	+	0.685751i	−0.993218	−	0.116267i	$-0.962907\pi$
$151$	−2.52931e9	+	4.38089e9i	−0.395919	+	0.685751i	0.597299	+	0.802018i	$0.296240\pi$
$152$	1.15169e10	+	1.99478e10i	1.75000	+	3.03109i
$153$	6.53341e9			0.963893
$154$		0			0
$155$	9.64159e9			1.34170
$156$	1.75866e7	+	3.04609e7i	0.00237751	+	0.00411797i
$157$	−5.98434e9	+	1.03652e10i	−0.786082	+	1.36153i	0.142269	+	0.989828i	$0.454560\pi$
$157$	−5.98434e9	+	1.03652e10i	−0.786082	+	1.36153i	−0.928351	+	0.371706i	$0.878773\pi$
$158$	−9.42753e8	+	1.63290e9i	−0.120349	+	0.208450i
$159$	−6.93973e6	−	1.20200e7i	−0.000861104	−	0.00149148i
$160$	1.95626e10			2.35986
$161$		0			0
$162$	1.61948e10			1.84739
$163$	−7.04800e9	−	1.22075e10i	−0.782027	−	1.35451i	−0.930759	−	0.365633i	$-0.880853\pi$
$163$	−7.04800e9	−	1.22075e10i	−0.782027	−	1.35451i	0.148733	−	0.988877i	$-0.452481\pi$
$164$	−4.55251e9	+	7.88519e9i	−0.491421	+	0.851167i
$165$	3.62235e6	−	6.27410e6i	0.000380464	−	0.000658982i
$166$	−6.99482e9	−	1.21154e10i	−0.714974	−	1.23837i
$167$	−3.56028e9			−0.354210			−0.177105	−	0.984192i	$-0.556673\pi$
$167$	−3.56028e9			−0.354210			−0.177105	+	0.984192i	$0.556673\pi$
$168$		0			0
$169$	4.41184e9			0.416034
$170$	1.24316e10	+	2.15322e10i	1.14158	+	1.97728i
$171$	−7.49632e9	+	1.29840e10i	−0.670449	+	1.16125i
$172$	1.27858e10	−	2.21457e10i	1.11391	−	1.92935i
$173$	1.32034e9	+	2.28689e9i	0.112067	+	0.194106i	0.916604	−	0.399797i	$-0.130920\pi$
$173$	1.32034e9	+	2.28689e9i	0.112067	+	0.194106i	−0.804537	+	0.593903i	$0.797586\pi$
$174$	−6.16342e6			−0.000509741
$175$		0			0
$176$	1.09899e10			0.863353
$177$	−7.01038e6	−	1.21423e7i	−0.000536861	−	0.000929870i
$178$	1.36250e10	−	2.35993e10i	1.01730	−	1.76201i
$179$	−6.34867e8	+	1.09962e9i	−0.0462215	+	0.0800580i	−0.888211	−	0.459437i	$-0.848051\pi$
$179$	−6.34867e8	+	1.09962e9i	−0.0462215	+	0.0800580i	0.841989	+	0.539495i	$0.181385\pi$
$180$	2.17861e10	+	3.77347e10i	1.54687	+	2.67926i
$181$	2.17242e10			1.50449			0.752247	−	0.658881i	$-0.228970\pi$
$181$	2.17242e10			1.50449			0.752247	+	0.658881i	$0.228970\pi$
$182$		0			0
$183$	−2.19411e6			−0.000144620
$184$	−1.86350e10	−	3.22767e10i	−1.19853	−	2.07591i
$185$	2.72019e9	−	4.71150e9i	0.170736	−	0.295724i
$186$	2.61292e7	−	4.52571e7i	0.00160073	−	0.00277255i
$187$	2.88807e9	+	5.00228e9i	0.172711	+	0.299144i
$188$	−2.51567e10			−1.46874
$189$		0			0
$190$	−5.70552e10			−3.17617
$191$	5.35175e9	+	9.26950e9i	0.290968	+	0.503972i	0.974039	−	0.226380i	$-0.0726893\pi$
$191$	5.35175e9	+	9.26950e9i	0.290968	+	0.503972i	−0.683071	+	0.730352i	$0.739356\pi$
$192$	1.54519e7	−	2.67635e7i	0.000820590	−	0.00142130i
$193$	−3.83031e9	+	6.63430e9i	−0.198713	+	0.344181i	−0.948111	−	0.317938i	$-0.897010\pi$
$193$	−3.83031e9	+	6.63430e9i	−0.198713	+	0.344181i	0.749398	+	0.662119i	$0.230343\pi$
$194$	−2.98475e10	−	5.16974e10i	−1.51286	−	2.62036i
$195$	−5.10170e7			−0.00252673
$196$		0			0
$197$	−4.26160e9			−0.201592			−0.100796	−	0.994907i	$-0.532139\pi$
$197$	−4.26160e9			−0.201592			−0.100796	+	0.994907i	$0.532139\pi$
$198$	7.15887e9	+	1.23995e10i	0.331017	+	0.573339i
$199$	1.58146e10	−	2.73916e10i	0.714856	−	1.23817i	−0.248159	−	0.968719i	$-0.579826\pi$
$199$	1.58146e10	−	2.73916e10i	0.714856	−	1.23817i	0.963015	−	0.269448i	$-0.0868411\pi$
$200$	−1.90168e10	+	3.29381e10i	−0.840432	+	1.45567i
$201$	−2.54628e7	−	4.41029e7i	−0.00110033	−	0.00190583i
$202$	−3.72678e10			−1.57490
$203$		0			0
$204$	9.52754e7			0.00385163
$205$	−6.60319e9	−	1.14371e10i	−0.261133	−	0.452295i
$206$	−1.48815e10	+	2.57755e10i	−0.575763	+	0.997251i
$207$	1.21295e10	−	2.10089e10i	0.459172	−	0.795310i
$208$	−3.86954e10	−	6.70225e10i	−1.43342	−	2.48276i
$209$	−1.32549e10			−0.480526
$210$		0			0
$211$	1.76561e10			0.613229			0.306615	−	0.951834i	$-0.400804\pi$
$211$	1.76561e10			0.613229			0.306615	+	0.951834i	$0.400804\pi$
$212$	3.69002e10	+	6.39131e10i	1.25464	+	2.17309i
$213$	−6.49087e6	+	1.12425e7i	−0.000216070	+	0.000374244i
$214$	−5.19594e10	+	8.99964e10i	−1.69357	+	2.93334i
$215$	1.85452e10	+	3.21212e10i	0.591913	+	1.02522i
$216$	2.76579e8			0.00864525
$217$		0			0
$218$	1.60292e10			0.480681
$219$	−5.27796e7	−	9.14169e7i	−0.00155048	−	0.00268552i
$220$	−1.92609e10	+	3.33609e10i	−0.554339	+	0.960143i
$221$	2.03377e10	−	3.52259e10i	0.573504	−	0.993339i
$222$	−1.47437e7	−	2.55368e7i	−0.000407397	−	0.000705632i
$223$	1.04686e10			0.283476			0.141738	−	0.989904i	$-0.454731\pi$
$223$	1.04686e10			0.283476			0.141738	+	0.989904i	$0.454731\pi$
$224$		0			0
$225$	−2.47560e10			−0.643961
$226$	−5.00749e10	−	8.67323e10i	−1.27683	−	2.21153i
$227$	9.75213e9	−	1.68912e10i	0.243772	−	0.422225i	−0.718014	−	0.696029i	$-0.754949\pi$
$227$	9.75213e9	−	1.68912e10i	0.243772	−	0.422225i	0.961786	+	0.273804i	$0.0882819\pi$
$228$	−1.09317e8	+	1.89343e8i	−0.00267906	+	0.00464026i
$229$	−2.98067e10	−	5.16268e10i	−0.716234	−	1.24055i	−0.962482	−	0.271347i	$-0.912531\pi$
$229$	−2.98067e10	−	5.16268e10i	−0.716234	−	1.24055i	0.246248	−	0.969207i	$-0.420802\pi$
$230$	9.23187e10			2.17528
$231$		0			0
$232$	1.91902e10			0.434894
$233$	−4.21309e10	−	7.29729e10i	−0.936482	−	1.62203i	−0.771970	−	0.635659i	$-0.780728\pi$
$233$	−4.21309e10	−	7.29729e10i	−0.936482	−	1.62203i	−0.164512	−	0.986375i	$-0.552605\pi$
$234$	5.04125e10	−	8.73171e10i	1.09918	−	1.90383i
$235$	1.82443e10	−	3.16000e10i	0.390230	−	0.675899i
$236$	3.72759e10	+	6.45637e10i	0.782211	+	1.35483i
$237$	−1.04798e7			−0.000215767
$238$		0			0
$239$	−7.28353e10			−1.44395			−0.721974	−	0.691920i	$-0.756765\pi$
$239$	−7.28353e10			−1.44395			−0.721974	+	0.691920i	$0.756765\pi$
$240$	1.31465e8	+	2.27704e8i	0.00255776	+	0.00443018i
$241$	2.22778e10	−	3.85862e10i	0.425397	−	0.736810i	−0.571060	−	0.820908i	$-0.693468\pi$
$241$	2.22778e10	−	3.85862e10i	0.425397	−	0.736810i	0.996457	+	0.0840985i	$0.0268010\pi$
$242$	4.29543e10	−	7.43990e10i	0.805077	−	1.39443i
$243$	1.35019e8	+	2.33860e8i	0.00248408	+	0.00430256i
$244$	1.16666e10			0.210713
$245$		0			0
$246$	−7.15800e7			−0.00124619
$247$	4.66702e10	+	8.08352e10i	0.797818	+	1.38186i
$248$	−8.13550e10	+	1.40911e11i	−1.36569	+	2.36544i
$249$	3.88778e7	−	6.73384e7i	0.000640922	−	0.00111011i
$250$	2.60437e10	+	4.51090e10i	0.421670	+	0.730354i
$251$	9.55068e10			1.51881			0.759404	−	0.650620i	$-0.225491\pi$
$251$	9.55068e10			1.51881			0.759404	+	0.650620i	$0.225491\pi$
$252$		0			0
$253$	2.14472e10			0.329100
$254$	−3.93484e10	−	6.81534e10i	−0.593165	−	1.02739i
$255$	−6.90960e7	+	1.19678e8i	−0.00102335	+	0.00177249i
$256$	3.46680e10	−	6.00468e10i	0.504486	−	0.873796i
$257$	4.56397e10	+	7.90503e10i	0.652595	+	1.13033i	0.982491	+	0.186310i	$0.0596530\pi$
$257$	4.56397e10	+	7.90503e10i	0.652595	+	1.13033i	−0.329896	+	0.944017i	$0.607014\pi$
$258$	2.01033e8			0.00282475
$259$		0			0
$260$	2.71270e11			3.68147
$261$	6.24544e9	+	1.08174e10i	0.0833068	+	0.144292i
$262$	−3.11929e10	+	5.40277e10i	−0.408978	+	0.708371i
$263$	−7.54881e10	+	1.30749e11i	−0.972921	+	1.68515i	−0.286289	+	0.958143i	$0.592422\pi$
$263$	−7.54881e10	+	1.30749e11i	−0.972921	+	1.68515i	−0.686632	+	0.727005i	$0.740912\pi$
$264$	6.11303e7	+	1.05881e8i	0.000774531	+	0.00134153i
$265$	−1.07044e11			−1.33338
$266$		0			0
$267$	1.51458e8			0.00182387
$268$	1.35392e11	+	2.34506e11i	1.60319	+	2.77681i
$269$	1.19811e10	−	2.07519e10i	0.139512	−	0.241642i	−0.787800	−	0.615931i	$-0.788780\pi$
$269$	1.19811e10	−	2.07519e10i	0.139512	−	0.241642i	0.927312	+	0.374289i	$0.122113\pi$
$270$	−3.42547e8	+	5.93309e8i	−0.00392269	+	0.00679429i
$271$	−2.75624e10	−	4.77395e10i	−0.310424	−	0.537670i	0.668030	−	0.744134i	$-0.267138\pi$
$271$	−2.75624e10	−	4.77395e10i	−0.310424	−	0.537670i	−0.978454	+	0.206464i	$0.933804\pi$
$272$	−2.09632e11			−2.32219
$273$		0			0
$274$	−1.34233e11			−1.43874
$275$	−1.09433e10	−	1.89544e10i	−0.115386	−	0.199854i
$276$	1.76882e8	−	3.06368e8i	0.00183481	−	0.00317799i
$277$	−1.09816e10	+	1.90207e10i	−0.112074	+	0.194118i	−0.916606	−	0.399791i	$-0.869083\pi$
$277$	−1.09816e10	+	1.90207e10i	−0.112074	+	0.194118i	0.804532	+	0.593909i	$0.202416\pi$
$278$	−6.35251e10	−	1.10029e11i	−0.637887	−	1.10485i
$279$	−1.05908e11			−1.04643
$280$		0			0
$281$	−1.62670e10			−0.155643			−0.0778213	−	0.996967i	$-0.524796\pi$
$281$	−1.62670e10			−0.155643			−0.0778213	+	0.996967i	$0.524796\pi$
$282$	−9.88858e7	−	1.71275e8i	−0.000931136	−	0.00161277i
$283$	6.77949e9	−	1.17424e10i	0.0628287	−	0.108823i	−0.832900	−	0.553423i	$-0.813321\pi$
$283$	6.77949e9	−	1.17424e10i	0.0628287	−	0.108823i	0.895729	+	0.444601i	$0.146654\pi$
$284$	3.45135e10	−	5.97792e10i	0.314816	−	0.545277i
$285$	−1.58559e8	−	2.74632e8i	−0.00142360	−	0.00246575i
$286$	8.91387e10			0.787805
$287$		0			0
$288$	−2.14885e11			−1.84052
$289$	4.20429e9	+	7.28205e9i	0.0354530	+	0.0614063i
$290$	−2.37673e10	+	4.11662e10i	−0.197328	+	0.341783i
$291$	1.65895e8	−	2.87339e8i	0.00135617	−	0.00234896i
$292$	2.80642e11	+	4.86086e11i	2.25907	+	3.91282i
$293$	−5.41900e10			−0.429551			−0.214776	−	0.976663i	$-0.568902\pi$
$293$	−5.41900e10			−0.429551			−0.214776	+	0.976663i	$0.568902\pi$
$294$		0			0
$295$	−1.08133e11			−0.831306
$296$	4.59055e10	+	7.95106e10i	0.347577	+	0.602022i
$297$	−7.95794e7	+	1.37836e8i	−0.000593467	+	0.00102791i
$298$	7.61394e10	−	1.31877e11i	0.559289	−	0.968716i
$299$	−7.55151e10	−	1.30796e11i	−0.546404	−	0.946399i
$300$	−3.61012e8			−0.00257321
$301$		0			0
$302$	2.11460e11			1.46284
$303$	−1.03569e8	−	1.79387e8i	−0.000705891	−	0.00122264i
$304$	2.40528e11	−	4.16607e11i	1.61523	−	2.79766i
$305$	−8.46092e9	+	1.46547e10i	−0.0559845	+	0.0969681i
$306$	−1.36555e11	−	2.36520e11i	−0.890349	−	1.54213i
$307$	−7.32498e10			−0.470634			−0.235317	−	0.971919i	$-0.575613\pi$
$307$	−7.32498e10			−0.470634			−0.235317	+	0.971919i	$0.575613\pi$
$308$		0			0
$309$	−1.65425e8			−0.00103226
$310$	−2.01519e11	−	3.49041e11i	−1.23933	−	2.14659i
$311$	−1.22251e11	+	2.11745e11i	−0.741021	+	1.28349i	0.211010	+	0.977484i	$0.432325\pi$
$311$	−1.22251e11	+	2.11745e11i	−0.741021	+	1.28349i	−0.952031	+	0.306002i	$0.901009\pi$
$312$	4.30478e8	−	7.45610e8i	0.00257191	−	0.00445467i
$313$	−2.19948e10	−	3.80960e10i	−0.129530	−	0.224352i	0.793965	−	0.607964i	$-0.208013\pi$
$313$	−2.19948e10	−	3.80960e10i	−0.129530	−	0.224352i	−0.923494	+	0.383612i	$0.874680\pi$
$314$	5.00314e11			2.90442
$315$		0			0
$316$	5.57237e10			0.314375
$317$	1.08827e11	+	1.88493e11i	0.605297	+	1.04841i	0.992004	+	0.126203i	$0.0402792\pi$
$317$	1.08827e11	+	1.88493e11i	0.605297	+	1.04841i	−0.386707	+	0.922203i	$0.626387\pi$
$318$	−2.90094e8	+	5.02458e8i	−0.00159081	+	0.00275536i
$319$	−5.52154e9	+	9.56359e9i	−0.0298540	+	0.0517086i
$320$	−1.19171e11	−	2.06410e11i	−0.635324	−	1.10041i
$321$	−5.77591e8			−0.00303632
$322$		0			0
$323$	2.52835e11			1.29249
$324$	−2.39308e11	−	4.14494e11i	−1.20644	−	2.08961i
$325$	−7.70625e10	+	1.33476e11i	−0.383149	+	0.663634i
$326$	−2.94620e11	+	5.10297e11i	−1.44472	+	2.50233i
$327$	4.45458e7	+	7.71556e7i	0.000215448	+	0.000373167i
$328$	2.22869e11			1.06321
$329$		0			0
$330$	−3.02843e8			−0.00140574
$331$	1.83473e11	+	3.17784e11i	0.840128	+	1.45514i	0.889786	+	0.456377i	$0.150853\pi$
$331$	1.83473e11	+	3.17784e11i	0.840128	+	1.45514i	−0.0496587	+	0.998766i	$0.515813\pi$
$332$	−2.06723e11	+	3.58055e11i	−0.933829	+	1.61744i
$333$	−2.98798e10	+	5.17533e10i	−0.133161	+	0.230642i
$334$	7.44134e10	+	1.28888e11i	0.327184	+	0.566699i
$335$	−3.92758e11			−1.70382
$336$		0			0
$337$	1.99451e11			0.842367			0.421183	−	0.906976i	$-0.361615\pi$
$337$	1.99451e11			0.842367			0.421183	+	0.906976i	$0.361615\pi$
$338$	−9.22117e10	−	1.59715e11i	−0.384291	−	0.665612i
$339$	2.78321e8	−	4.82066e8i	0.00114458	−	0.00198248i
$340$	3.67400e11	−	6.36356e11i	1.49102	−	2.58253i
$341$	−4.68161e10	−	8.10879e10i	−0.187500	−	0.324759i
$342$	6.26721e11			2.47718
$343$		0			0
$344$	−6.25931e11			−2.40998
$345$	2.56558e8	+	4.44371e8i	0.000974988	+	0.00168873i
$346$	5.51927e10	−	9.55966e10i	0.207033	−	0.358591i
$347$	−3.31590e10	+	5.74330e10i	−0.122777	+	0.212657i	−0.920862	−	0.389889i	$-0.872513\pi$
$347$	−3.31590e10	+	5.74330e10i	−0.122777	+	0.212657i	0.798085	+	0.602545i	$0.205847\pi$
$348$	9.10759e7	+	1.57748e8i	0.000332887	+	0.000576577i
$349$	1.20301e11			0.434065			0.217033	−	0.976164i	$-0.430362\pi$
$349$	1.20301e11			0.434065			0.217033	+	0.976164i	$0.430362\pi$
$350$		0			0
$351$	1.12079e9			0.00394133
$352$	−9.49890e10	−	1.64526e11i	−0.329786	−	0.571205i
$353$	1.21530e11	−	2.10497e11i	0.416580	−	0.721537i	−0.579013	−	0.815318i	$-0.696562\pi$
$353$	1.21530e11	−	2.10497e11i	0.416580	−	0.721537i	0.995593	+	0.0937810i	$0.0298953\pi$
$354$	−2.93047e8	+	5.07573e8i	−0.000991798	+	0.00171784i
$355$	5.00601e10	+	8.67066e10i	0.167288	+	0.289751i
$356$	−8.05341e11			−2.65739
$357$		0			0
$358$	5.30773e10			0.170779
$359$	−1.40827e11	−	2.43919e11i	−0.447466	−	0.775034i	0.550754	−	0.834668i	$-0.314340\pi$
$359$	−1.40827e11	−	2.43919e11i	−0.447466	−	0.775034i	−0.998220	+	0.0596332i	$0.981007\pi$
$360$	5.33271e11	−	9.23652e11i	1.67335	−	2.89833i
$361$	−1.28755e11	+	2.23010e11i	−0.399008	+	0.691101i
$362$	−4.54057e11	−	7.86450e11i	−1.38970	−	2.40704i
$363$	4.77488e8			0.00144339
$364$		0			0
$365$	−8.14113e11			−2.40086
$366$	4.58591e7	+	7.94302e7i	0.000133586	+	0.000231377i
$367$	−1.20500e11	+	2.08712e11i	−0.346729	+	0.600552i	−0.985666	−	0.168707i	$-0.946041\pi$
$367$	−1.20500e11	+	2.08712e11i	−0.346729	+	0.600552i	0.638937	+	0.769259i	$0.279374\pi$
$368$	−3.89188e11	+	6.74094e11i	−1.10623	+	1.91604i
$369$	7.25325e10	+	1.25630e11i	0.203664	+	0.352756i
$370$	−2.27418e11			−0.630837
$371$		0			0
$372$	−1.54443e9			−0.00418143
$373$	6.69605e10	+	1.15979e11i	0.179114	+	0.310234i	0.941577	−	0.336797i	$-0.109344\pi$
$373$	6.69605e10	+	1.15979e11i	0.179114	+	0.310234i	−0.762464	+	0.647031i	$0.776010\pi$
$374$	1.20727e11	−	2.09105e11i	0.319067	−	0.552640i
$375$	−1.44753e8	+	2.50720e8i	−0.000377997	+	0.000654709i
$376$	3.07887e11	+	5.33277e11i	0.794414	+	1.37596i
$377$	7.77651e10			0.198266
$378$		0			0
$379$	5.67201e11			1.41208			0.706042	−	0.708170i	$-0.250479\pi$
$379$	5.67201e11			1.41208			0.706042	+	0.708170i	$0.250479\pi$
$380$	8.43097e11	+	1.46029e12i	2.07420	+	3.59263i
$381$	2.18702e8	−	3.78803e8i	0.000531729	−	0.000920982i
$382$	2.23714e11	−	3.87483e11i	0.537536	−	0.931039i
$383$	−5.17543e10	−	8.96411e10i	−0.122900	−	0.212869i	0.798010	−	0.602644i	$-0.205886\pi$
$383$	−5.17543e10	−	8.96411e10i	−0.122900	−	0.212869i	−0.920910	+	0.389775i	$0.872553\pi$
$384$	6.85951e6			1.60991e−5
$385$		0			0
$386$	3.20229e11			0.734206
$387$	−2.03709e11	−	3.52834e11i	−0.461647	−	0.799597i
$388$	−8.82104e11	+	1.52785e12i	−1.97596	+	3.42245i
$389$	2.91800e11	−	5.05413e11i	0.646119	−	1.11911i	−0.337923	−	0.941174i	$-0.609724\pi$
$389$	2.91800e11	−	5.05413e11i	0.646119	−	1.11911i	0.984042	−	0.177937i	$-0.0569422\pi$
$390$	1.06631e9	+	1.84690e9i	0.00233395	+	0.00404251i
$391$	−4.09102e11			−0.885190
$392$		0			0
$393$	−3.46746e8			−0.000733238
$394$	8.90715e10	+	1.54276e11i	0.186211	+	0.322527i
$395$	−4.04122e10	+	6.99959e10i	−0.0835267	+	0.144672i
$396$	2.11571e11	−	3.66452e11i	0.432343	−	0.748839i
$397$	−3.27271e10	−	5.66850e10i	−0.0661226	−	0.114528i	0.831069	−	0.556170i	$-0.187730\pi$
$397$	−3.27271e10	−	5.66850e10i	−0.0661226	−	0.114528i	−0.897191	+	0.441642i	$0.854396\pi$
$398$	−1.32216e12			−2.64125
$399$		0			0
$400$	7.94326e11			1.55142
$401$	−2.03324e10	−	3.52167e10i	−0.0392679	−	0.0680141i	0.845723	−	0.533621i	$-0.179169\pi$
$401$	−2.03324e10	−	3.52167e10i	−0.0392679	−	0.0680141i	−0.884991	+	0.465607i	$0.845836\pi$
$402$	−1.06439e9	+	1.84359e9i	−0.00203276	+	0.00352084i
$403$	−3.29678e11	+	5.71019e11i	−0.622611	+	1.07839i
$404$	5.50701e11	+	9.53842e11i	1.02849	+	1.78139i
$405$	6.94209e11			1.28216
$406$		0			0
$407$	−5.28330e10			−0.0954400
$408$	−1.16605e9	−	2.01967e9i	−0.00208328	−	0.00360835i
$409$	5.30816e11	−	9.19400e11i	0.937970	−	1.62461i	0.168720	−	0.985664i	$-0.446037\pi$
$409$	5.30816e11	−	9.19400e11i	0.937970	−	1.62461i	0.769250	−	0.638948i	$-0.220630\pi$
$410$	−2.76026e11	+	4.78091e11i	−0.482417	+	0.835571i
$411$	−3.73041e8	−	6.46126e8i	−0.000644864	−	0.00111694i
$412$	8.79607e11			1.50401
$413$		0			0
$414$	−1.01407e12			−1.69655
$415$	−2.99841e11	−	5.19340e11i	−0.496220	−	0.859479i
$416$	−6.68910e11	+	1.15859e12i	−1.09509	+	1.89674i
$417$	3.53078e8	−	6.11550e8i	0.000571819	−	0.000990420i
$418$	2.77040e11	+	4.79847e11i	0.443863	+	0.768793i
$419$	1.19335e12			1.89149			0.945744	−	0.324912i	$-0.105335\pi$
$419$	1.19335e12			1.89149			0.945744	+	0.324912i	$0.105335\pi$
$420$		0			0
$421$	−5.88397e11			−0.912853			−0.456427	−	0.889761i	$-0.650871\pi$
$421$	−5.88397e11			−0.912853			−0.456427	+	0.889761i	$0.650871\pi$
$422$	−3.69029e11	−	6.39177e11i	−0.566441	−	0.981104i
$423$	−2.00404e11	+	3.47109e11i	−0.304350	+	0.527150i
$424$	9.03228e11	−	1.56444e12i	1.35722	−	2.35078i
$425$	2.08742e11	+	3.61553e11i	0.310356	+	0.537553i
$426$	5.42662e8			0.000798337
$427$		0			0
$428$	3.07119e12			4.42394
$429$	2.47720e8	+	4.29064e8i	0.000353105	+	0.000611596i
$430$	7.75224e11	−	1.34273e12i	1.09350	−	1.89400i
$431$	6.14658e11	−	1.06462e12i	0.857997	−	1.48609i	−0.0158402	−	0.999875i	$-0.505042\pi$
$431$	6.14658e11	−	1.06462e12i	0.857997	−	1.48609i	0.873837	−	0.486219i	$-0.161624\pi$
$432$	−2.88816e9	−	5.00243e9i	−0.00398973	−	0.00691042i
$433$	4.73819e10			0.0647764			0.0323882	−	0.999475i	$-0.489689\pi$
$433$	4.73819e10			0.0647764			0.0323882	+	0.999475i	$0.489689\pi$
$434$		0			0
$435$	−2.64202e8			−0.000353781
$436$	−2.36861e11	−	4.10255e11i	−0.313909	−	0.543707i
$437$	4.69397e11	−	8.13019e11i	0.615706	−	1.06643i
$438$	−2.20629e9	+	3.82141e9i	−0.00286437	+	0.00496123i
$439$	3.07118e11	+	5.31944e11i	0.394652	+	0.683558i	0.993057	−	0.117636i	$-0.0375317\pi$
$439$	3.07118e11	+	5.31944e11i	0.394652	+	0.683558i	−0.598404	+	0.801194i	$0.704198\pi$
$440$	9.42921e11			1.19933
$441$		0			0
$442$	−1.70031e12			−2.11899
$443$	4.09600e11	+	7.09447e11i	0.505292	+	0.875192i	0.999981	+	0.00612197i	$0.00194869\pi$
$443$	4.09600e11	+	7.09447e11i	0.505292	+	0.875192i	−0.494689	+	0.869070i	$0.664718\pi$
$444$	−4.35731e8	+	7.54708e8i	−0.000532102	+	0.000921628i
$445$	5.84053e11	−	1.01161e12i	0.706045	−	1.22291i
$446$	−2.18804e11	−	3.78979e11i	−0.261847	−	0.453532i
$447$	8.46379e8			0.00100272
$448$		0			0
$449$	4.81029e11			0.558551			0.279276	−	0.960211i	$-0.409906\pi$
$449$	4.81029e11			0.558551			0.279276	+	0.960211i	$0.409906\pi$
$450$	5.17425e11	+	8.96207e11i	0.594828	+	1.03027i
$451$	−6.41254e10	+	1.11069e11i	−0.0729854	+	0.126414i
$452$	−1.47990e12	+	2.56326e12i	−1.66767	+	2.88849i
$453$	5.87658e8	+	1.01785e9i	0.000655666	+	0.00113565i
$454$	−8.15316e11			−0.900689
$455$		0			0
$456$	5.35164e9			0.00579622
$457$	−5.76641e11	−	9.98771e11i	−0.618419	−	1.07113i	−0.989774	−	0.142642i	$-0.954440\pi$
$457$	−5.76641e11	−	9.98771e11i	−0.618419	−	1.07113i	0.371356	−	0.928491i	$-0.378893\pi$
$458$	−1.24598e12	+	2.15810e12i	−1.32317	+	2.29180i
$459$	1.51797e9	−	2.62920e9i	0.00159627	−	0.00276482i
$460$	−1.36418e12	−	2.36283e12i	−1.42057	−	2.46049i
$461$	6.06986e11			0.625928			0.312964	−	0.949765i	$-0.398678\pi$
$461$	6.06986e11			0.625928			0.312964	+	0.949765i	$0.398678\pi$
$462$		0			0
$463$	−8.87758e11			−0.897801			−0.448900	−	0.893582i	$-0.648184\pi$
$463$	−8.87758e11			−0.897801			−0.448900	+	0.893582i	$0.648184\pi$
$464$	−2.00392e11	−	3.47089e11i	−0.200701	−	0.347624i
$465$	1.12006e9	−	1.94000e9i	0.00111097	−	0.00192426i
$466$	−1.76115e12	+	3.05041e12i	−1.73006	+	2.99655i
$467$	−5.48897e11	−	9.50717e11i	−0.534029	−	0.924965i	−0.999210	−	0.0397495i	$-0.987344\pi$
$467$	−5.48897e11	−	9.50717e11i	−0.534029	−	0.924965i	0.465181	−	0.885216i	$-0.345989\pi$
$468$	−2.97976e12			−2.87127
$469$		0			0
$470$	−1.52529e12			−1.44182
$471$	1.39040e9	+	2.40824e9i	0.00130180	+	0.00225478i
$472$	9.12422e11	−	1.58036e12i	0.846169	−	1.46561i
$473$	1.80097e11	−	3.11938e11i	0.165437	−	0.286545i
$474$	2.19038e8	+	3.79385e8i	0.000199305	+	0.000345206i
$475$	−9.58029e11			−0.863490
$476$		0			0
$477$	1.17582e12			1.03994
$478$	1.52233e12	+	2.63675e12i	1.33378	+	2.31017i
$479$	−1.56114e11	+	2.70398e11i	−0.135498	+	0.234690i	−0.925788	−	0.378044i	$-0.876597\pi$
$479$	−1.56114e11	+	2.70398e11i	−0.135498	+	0.234690i	0.790290	+	0.612734i	$0.209930\pi$
$480$	2.27258e9	−	3.93622e9i	0.00195404	−	0.00338450i
$481$	1.86024e11	+	3.22203e11i	0.158459	+	0.274459i
$482$	−1.86251e12			−1.57176
$483$		0			0
$484$	−2.53892e12			−2.10303
$485$	−1.27945e12	−	2.21607e12i	−1.04999	−	1.81863i
$486$	5.64405e9	−	9.77578e9i	0.00458910	−	0.00794856i
$487$	−5.41887e11	+	9.38575e11i	−0.436544	+	0.756116i	−0.997420	−	0.0717832i	$-0.977131\pi$
$487$	−5.41887e11	+	9.38575e11i	−0.436544	+	0.756116i	0.560876	+	0.827900i	$0.310464\pi$
$488$	−1.42785e11	−	2.47311e11i	−0.113971	−	0.197403i
$489$	−3.27505e9			−0.00259017
$490$		0			0
$491$	2.14702e12			1.66713			0.833567	−	0.552419i	$-0.186295\pi$
$491$	2.14702e12			1.66713			0.833567	+	0.552419i	$0.186295\pi$
$492$	1.05773e9	+	1.83204e9i	0.000813824	+	0.00140958i
$493$	1.05323e11	−	1.82425e11i	0.0802993	−	0.139082i
$494$	1.95091e12	−	3.37907e12i	1.47389	−	2.55285i
$495$	3.06873e11	+	5.31520e11i	0.229739	+	0.397920i
$496$	3.39817e12			2.52103
$497$		0			0
$498$	−3.25034e9			−0.00236808
$499$	9.28525e11	+	1.60825e12i	0.670411	+	1.16119i	0.977788	+	0.209598i	$0.0672154\pi$
$499$	9.28525e11	+	1.60825e12i	0.670411	+	1.16119i	−0.307377	+	0.951588i	$0.599451\pi$
$500$	7.69688e11	−	1.33314e12i	0.550744	−	0.953917i
$501$	−4.13596e8	+	7.16370e8i	−0.000293297	+	0.000508005i
$502$	−1.99619e12	−	3.45750e12i	−1.40292	−	2.42994i
$503$	1.59040e12			1.10777			0.553885	−	0.832593i	$-0.313145\pi$
$503$	1.59040e12			1.10777			0.553885	+	0.832593i	$0.313145\pi$
$504$		0			0
$505$	−1.59753e12			−1.09304
$506$	−4.48266e11	−	7.76420e11i	−0.303990	−	0.526526i
$507$	5.12521e8	−	8.87712e8i	0.000344489	−	0.000596673i
$508$	−1.16289e12	+	2.01419e12i	−0.774734	+	1.34188i
$509$	1.16432e12	+	2.01667e12i	0.768853	+	1.33169i	0.938185	+	0.346133i	$0.112505\pi$
$509$	1.16432e12	+	2.01667e12i	0.768853	+	1.33169i	−0.169333	+	0.985559i	$0.554161\pi$
$510$	5.77670e9			0.00378106
$511$		0			0
$512$	−2.88327e12			−1.85426
$513$	3.48338e9	+	6.03339e9i	0.00222061	+	0.00384621i
$514$	1.90783e12	−	3.30446e12i	1.20561	−	2.08817i
$515$	−6.37912e11	+	1.10490e12i	−0.399603	+	0.692132i
$516$	−2.97064e9	−	5.14530e9i	−0.00184470	−	0.00319512i
$517$	−3.54350e11			−0.218135
$518$		0			0
$519$	6.13532e8			0.000371180
$520$	−3.32001e12	−	5.75043e12i	−1.99124	−	3.44894i
$521$	−7.41832e11	+	1.28489e12i	−0.441099	+	0.764005i	−0.997771	−	0.0667268i	$-0.978744\pi$
$521$	−7.41832e11	+	1.28489e12i	−0.441099	+	0.764005i	0.556673	+	0.830732i	$0.312078\pi$
$522$	2.61071e11	−	4.52189e11i	0.153901	−	0.266565i
$523$	−9.77922e11	−	1.69381e12i	−0.571540	−	0.989936i	−0.996408	−	0.0846808i	$-0.973013\pi$
$523$	−9.77922e11	−	1.69381e12i	−0.571540	−	0.989936i	0.424868	−	0.905255i	$-0.360320\pi$
$524$	1.84373e12			1.06833
$525$		0			0
$526$	6.31110e12			3.59475
$527$	8.93013e11	+	1.54674e12i	0.504324	+	0.873516i
$528$	1.27670e9	−	2.21130e9i	0.000714883	−	0.00123821i
$529$	1.41065e11	−	2.44332e11i	0.0783195	−	0.135653i
$530$	2.23732e12	+	3.87515e12i	1.23165	+	2.13328i
$531$	1.18779e12			0.648357
$532$		0			0
$533$	9.03139e11			0.484710
$534$	−3.16563e9	−	5.48303e9i	−0.00168471	−	0.00291800i
$535$	−2.22730e12	+	3.85780e12i	−1.17540	+	2.03586i
$536$	3.31406e12	−	5.74012e12i	1.73428	−	3.00386i
$537$	1.47504e8	+	2.55485e8i	7.65457e−5	+	0.000132581i
$538$	−1.00167e12			−0.515470
$539$		0			0
$540$	2.02471e10			0.0102469
$541$	6.74009e11	+	1.16742e12i	0.338281	+	0.585921i	0.984110	−	0.177562i	$-0.0568211\pi$
$541$	6.74009e11	+	1.16742e12i	0.338281	+	0.585921i	−0.645828	+	0.763483i	$0.723488\pi$
$542$	−1.15216e12	+	1.99560e12i	−0.573478	+	0.993294i
$543$	2.52369e9	−	4.37116e9i	0.00124577	−	0.00215773i
$544$	1.81191e12	+	3.13832e12i	0.887035	+	1.53639i
$545$	6.87109e11			0.333612
$546$		0			0
$547$	1.02503e12			0.489548			0.244774	−	0.969580i	$-0.421286\pi$
$547$	1.02503e12			0.489548			0.244774	+	0.969580i	$0.421286\pi$
$548$	1.98355e12	+	3.43561e12i	0.939572	+	1.62739i
$549$	9.29387e10	−	1.60975e11i	0.0436637	−	0.0756278i
$550$	−4.57451e11	+	7.92329e11i	−0.213164	+	0.369210i
$551$	2.41691e11	+	4.18621e11i	0.111706	+	0.193481i
$552$	−8.65926e9			−0.00396968
$553$		0			0
$554$	9.18103e11			0.414093
$555$	−6.32005e8	−	1.09467e9i	−0.000282750	−	0.000489737i
$556$	−1.87740e12	+	3.25176e12i	−0.833146	+	1.44305i
$557$	−8.76717e11	+	1.51852e12i	−0.385932	+	0.668454i	−0.991898	−	0.127037i	$-0.959453\pi$
$557$	−8.76717e11	+	1.51852e12i	−0.385932	+	0.668454i	0.605966	+	0.795491i	$0.292787\pi$
$558$	2.21358e12	+	3.83403e12i	0.966586	+	1.67418i
$559$	−2.53648e12			−1.09870
$560$		0			0
$561$	1.34202e9			0.000572041
$562$	3.39996e11	+	5.88890e11i	0.143767	+	0.249012i
$563$	−1.08728e12	+	1.88322e12i	−0.456092	+	0.789975i	−0.998750	−	0.0499786i	$-0.984085\pi$
$563$	−1.08728e12	+	1.88322e12i	−0.456092	+	0.789975i	0.542658	+	0.839954i	$0.317418\pi$
$564$	−2.92244e9	+	5.06182e9i	−0.00121616	+	0.00210645i
$565$	−2.14652e12	−	3.71788e12i	−0.886170	−	1.53489i
$566$	−5.66792e11			−0.232140
$567$		0			0
$568$	−1.68961e12			−0.681114
$569$	−1.56906e12	−	2.71770e12i	−0.627531	−	1.08692i	−0.988046	−	0.154162i	$-0.950732\pi$
$569$	−1.56906e12	−	2.71770e12i	−0.627531	−	1.08692i	0.360515	−	0.932753i	$-0.382601\pi$
$570$	−6.62808e9	+	1.14802e10i	−0.00262997	+	0.00455524i
$571$	−1.02990e12	+	1.78383e12i	−0.405444	+	0.702249i	−0.994373	−	0.105935i	$-0.966216\pi$
$571$	−1.02990e12	+	1.78383e12i	−0.405444	+	0.702249i	0.588929	+	0.808185i	$0.299550\pi$
$572$	−1.31719e12	−	2.28144e12i	−0.514477	−	0.891100i
$573$	2.48684e9			0.000963723
$574$		0			0
$575$	1.55015e12			0.591381
$576$	1.30903e12	+	2.26731e12i	0.495505	+	0.858240i
$577$	1.97190e12	−	3.41543e12i	0.740617	−	1.28279i	−0.211597	−	0.977357i	$-0.567866\pi$
$577$	1.97190e12	−	3.41543e12i	0.740617	−	1.28279i	0.952214	−	0.305430i	$-0.0988002\pi$
$578$	1.75748e11	−	3.04404e11i	0.0654959	−	0.113442i
$579$	8.89931e8	+	1.54141e9i	0.000329081	+	0.000569985i
$580$	1.40483e12			0.515462
$581$		0			0
$582$	−1.38695e10			−0.00501079
$583$	5.19766e11	+	9.00262e11i	0.186337	+	0.322746i
$584$	6.86943e12	−	1.18982e13i	2.44378	−	4.23276i
$585$	2.16099e12	−	3.74295e12i	0.762872	−	1.32133i
$586$	1.13262e12	+	1.96176e12i	0.396777	+	0.687238i
$587$	−3.68239e12			−1.28014			−0.640071	−	0.768315i	$-0.721095\pi$
$587$	−3.68239e12			−1.28014			−0.640071	+	0.768315i	$0.721095\pi$
$588$		0			0
$589$	−4.09851e12			−1.40316
$590$	2.26009e12	+	3.91460e12i	0.767879	+	1.33000i
$591$	−4.95068e8	+	8.57482e8i	−0.000166925	+	0.000289122i
$592$	9.58728e11	−	1.66057e12i	0.320810	−	0.555659i
$593$	−5.85568e11	−	1.01423e12i	−0.194460	−	0.336815i	0.752263	−	0.658863i	$-0.228962\pi$
$593$	−5.85568e11	−	1.01423e12i	−0.194460	−	0.336815i	−0.946724	+	0.322048i	$0.895629\pi$
$594$	6.65315e9			0.00219274
$595$		0			0
$596$	−4.50040e12			−1.46098
$597$	−3.67434e9	−	6.36415e9i	−0.00118385	−	0.00205048i
$598$	−3.15668e12	+	5.46753e12i	−1.00943	+	1.74838i
$599$	−1.41878e12	+	2.45740e12i	−0.450293	+	0.779931i	−0.998404	−	0.0564751i	$-0.982014\pi$
$599$	−1.41878e12	+	2.45740e12i	−0.450293	+	0.779931i	0.548111	+	0.836406i	$0.315347\pi$
$600$	4.41835e9	+	7.65280e9i	0.00139181	+	0.00241068i
$601$	−2.37066e12			−0.741198			−0.370599	−	0.928793i	$-0.620848\pi$
$601$	−2.37066e12			−0.741198			−0.370599	+	0.928793i	$0.620848\pi$
$602$		0			0
$603$	4.31424e12			1.32885
$604$	−3.12472e12	−	5.41217e12i	−0.955310	−	1.65465i
$605$	1.84129e12	−	3.18920e12i	0.558756	−	0.967793i
$606$	−4.32938e9	+	7.49871e9i	−0.00130406	+	0.00225871i
$607$	2.20040e12	+	3.81120e12i	0.657889	+	1.13950i	0.981161	+	0.193191i	$0.0618836\pi$
$607$	2.20040e12	+	3.81120e12i	0.657889	+	1.13950i	−0.323273	+	0.946306i	$0.604783\pi$
$608$	−8.31580e12			−2.46796
$609$		0			0
$610$	7.07366e11			0.206852
$611$	1.24766e12	+	2.16102e12i	0.362169	+	0.627296i
$612$	−4.03570e12	+	6.99003e12i	−1.16289	+	2.01418i
$613$	9.37851e11	−	1.62441e12i	0.268264	−	0.464646i	−0.700150	−	0.713996i	$-0.746883\pi$
$613$	9.37851e11	−	1.62441e12i	0.268264	−	0.464646i	0.968414	+	0.249350i	$0.0802168\pi$
$614$	1.53099e12	+	2.65176e12i	0.434726	+	0.752967i
$615$	−3.06836e9			−0.000864904
$616$		0			0
$617$	−3.18170e12			−0.883845			−0.441922	−	0.897053i	$-0.645703\pi$
$617$	−3.18170e12			−0.883845			−0.441922	+	0.897053i	$0.645703\pi$
$618$	3.45755e9	+	5.98865e9i	0.000953500	+	0.00165151i
$619$	−5.82378e10	+	1.00871e11i	−0.0159440	+	0.0276158i	−0.873887	−	0.486129i	$-0.838409\pi$
$619$	−5.82378e10	+	1.00871e11i	−0.0159440	+	0.0276158i	0.857943	+	0.513744i	$0.171742\pi$
$620$	−5.95563e12	+	1.03154e13i	−1.61869	+	2.80366i
$621$	−5.63631e9	−	9.76238e9i	−0.00152084	−	0.00263417i
$622$	1.02207e13			2.73793
$623$		0			0
$624$	−1.79809e10			−0.00474768
$625$	2.34466e12	+	4.06106e12i	0.614637	+	1.06458i
$626$	−9.19423e11	+	1.59249e12i	−0.239294	+	0.414469i
$627$	−1.53981e9	+	2.66703e9i	−0.000397891	+	0.000689167i
$628$	−7.39307e12	−	1.28052e13i	−1.89673	−	3.28524i
$629$	1.00778e12			0.256708
$630$		0			0
$631$	−3.71283e12			−0.932338			−0.466169	−	0.884696i	$-0.654366\pi$
$631$	−3.71283e12			−0.932338			−0.466169	+	0.884696i	$0.654366\pi$
$632$	−6.81990e11	−	1.18124e12i	−0.170040	−	0.294518i
$633$	2.05110e9	−	3.55260e9i	0.000507773	−	0.000879488i
$634$	4.54917e12	−	7.87939e12i	1.11823	−	1.93683i
$635$	−1.68671e12	−	2.92148e12i	−0.411680	−	0.713051i
$636$	1.71467e10			0.00415551
$637$		0			0
$638$	4.61622e11			0.110305
$639$	−5.49884e11	−	9.52426e11i	−0.130472	−	0.225984i
$640$	2.64516e10	−	4.58155e10i	0.00623221	−	0.0107945i
$641$	−1.46882e11	+	2.54407e11i	−0.0343642	+	0.0595206i	−0.882696	−	0.469944i	$-0.844274\pi$
$641$	−1.46882e11	+	2.54407e11i	−0.0343642	+	0.0595206i	0.848332	+	0.529465i	$0.177607\pi$
$642$	1.20722e10	+	2.09097e10i	0.00280465	+	0.00485780i
$643$	−5.27980e12			−1.21806			−0.609029	−	0.793148i	$-0.708441\pi$
$643$	−5.27980e12			−1.21806			−0.609029	+	0.793148i	$0.708441\pi$
$644$		0			0
$645$	8.61753e9			0.00196049
$646$	−5.28451e12	−	9.15303e12i	−1.19387	−	2.06785i
$647$	−1.31000e12	+	2.26899e12i	−0.293902	+	0.509053i	−0.974729	−	0.223391i	$-0.928287\pi$
$647$	−1.31000e12	+	2.26899e12i	−0.293902	+	0.509053i	0.680827	+	0.732444i	$0.261621\pi$
$648$	−5.85768e12	+	1.01458e13i	−1.30508	+	2.26047i
$649$	5.25057e11	+	9.09426e11i	0.116173	+	0.201218i
$650$	6.44272e12			1.41566
$651$		0			0
$652$	1.74142e13			3.77390
$653$	−1.57959e12	−	2.73593e12i	−0.339965	−	0.588837i	0.644460	−	0.764638i	$-0.277082\pi$
$653$	−1.57959e12	−	2.73593e12i	−0.339965	−	0.588837i	−0.984426	+	0.175800i	$0.943749\pi$
$654$	1.86210e9	−	3.22526e9i	0.000398019	−	0.000689389i
$655$	−1.33712e12	+	2.31596e12i	−0.283847	+	0.491638i
$656$	−2.32729e12	−	4.03098e12i	−0.490663	−	0.849853i
$657$	8.94260e12			1.87249
$658$		0			0
$659$	8.77292e11			0.181201			0.0906004	−	0.995887i	$-0.471121\pi$
$659$	8.77292e11			0.181201			0.0906004	+	0.995887i	$0.471121\pi$
$660$	4.47507e9	+	7.75104e9i	0.000918019	+	0.00159006i
$661$	4.11054e12	−	7.11966e12i	0.837514	−	1.45062i	−0.0544528	−	0.998516i	$-0.517341\pi$
$661$	4.11054e12	−	7.11966e12i	0.837514	−	1.45062i	0.891967	−	0.452101i	$-0.149325\pi$
$662$	7.66951e12	−	1.32840e13i	1.55205	−	2.68824i
$663$	−4.72524e9	−	8.18436e9i	−0.000949759	−	0.00164503i
$664$	1.01201e13			2.02037
$665$		0			0
$666$	2.49807e12			0.492006
$667$	−3.91070e11	−	6.77354e11i	−0.0765048	−	0.132510i
$668$	2.19919e12	−	3.80911e12i	0.427336	−	0.740167i
$669$	1.21613e9	−	2.10640e9i	0.000234727	−	0.000406559i
$670$	8.20902e12	+	1.42184e13i	1.57382	+	2.72593i
$671$	1.64333e11			0.0312948
$672$		0			0
$673$	−7.47304e12			−1.40420			−0.702101	−	0.712077i	$-0.747754\pi$
$673$	−7.47304e12			−1.40420			−0.702101	+	0.712077i	$0.747754\pi$
$674$	−4.16872e12	−	7.22043e12i	−0.778095	−	1.34770i
$675$	−5.75180e9	+	9.96241e9i	−0.00106644	+	0.00184713i
$676$	−2.72520e12	+	4.72018e12i	−0.501924	+	0.869358i
$677$	4.35654e12	+	7.54575e12i	0.797064	+	1.38055i	0.921521	+	0.388330i	$0.126948\pi$
$677$	4.35654e12	+	7.54575e12i	0.797064	+	1.38055i	−0.124457	+	0.992225i	$0.539719\pi$
$678$	−2.32687e10			−0.00422901
$679$		0			0
$680$	−1.79861e13			−3.22588
$681$	−2.26580e9	−	3.92448e9i	−0.000403701	−	0.000699231i
$682$	−1.95700e12	+	3.38963e12i	−0.346387	+	0.599961i
$683$	1.86952e12	−	3.23810e12i	0.328727	−	0.569373i	−0.653532	−	0.756899i	$-0.726714\pi$
$683$	1.86952e12	−	3.23810e12i	0.328727	−	0.569373i	0.982260	+	0.187526i	$0.0600469\pi$
$684$	−9.26097e12	−	1.60405e13i	−1.61772	−	2.80198i
$685$	−5.75407e12			−0.998545
$686$		0			0
$687$	−1.38505e10			−0.00237226
$688$	6.53623e12	+	1.13211e13i	1.11219	+	1.92637i
$689$	3.66018e12	−	6.33962e12i	0.618751	−	1.07171i
$690$	1.07246e10	−	1.85756e10i	0.00180120	−	0.00311976i
$691$	−3.13485e12	−	5.42973e12i	−0.523078	−	0.905997i	−0.999639	−	0.0268559i	$-0.991450\pi$
$691$	−3.13485e12	−	5.42973e12i	−0.523078	−	0.905997i	0.476562	−	0.879141i	$-0.341883\pi$
$692$	−3.26230e12			−0.540812
$693$		0			0
$694$	2.77222e12			0.453639
$695$	−2.72308e12	−	4.71651e12i	−0.442719	−	0.766812i
$696$	2.22932e9	−	3.86129e9i	0.000360106	−	0.000623721i
$697$	1.22319e12	−	2.11862e12i	0.196311	−	0.340021i
$698$	−2.51441e12	−	4.35508e12i	−0.400947	−	0.694460i
$699$	−1.95773e10			−0.00310174
$700$		0			0
$701$	−5.13904e12			−0.803805			−0.401903	−	0.915682i	$-0.631651\pi$
$701$	−5.13904e12			−0.803805			−0.401903	+	0.915682i	$0.631651\pi$
$702$	−2.34256e10	−	4.05744e10i	−0.00364061	−	0.00630572i
$703$	−1.15631e12	+	2.00279e12i	−0.178557	+	0.309270i
$704$	−1.15730e12	+	2.00451e12i	−0.177570	+	0.307561i
$705$	−4.23885e9	−	7.34191e9i	−0.000646245	−	0.00111933i
$706$	−1.01604e13			−1.53918
$707$		0			0
$708$	1.73213e10			0.00259078
$709$	1.47719e12	+	2.55857e12i	0.219547	+	0.380267i	0.954670	−	0.297667i	$-0.0962087\pi$
$709$	1.47719e12	+	2.55857e12i	0.219547	+	0.380267i	−0.735122	+	0.677934i	$0.762875\pi$
$710$	2.09261e12	−	3.62451e12i	0.309048	−	0.535287i
$711$	4.43906e11	−	7.68868e11i	0.0651445	−	0.112834i
$712$	9.85640e12	+	1.70718e13i	1.43734	+	2.48954i
$713$	6.63162e12			0.960986
$714$		0			0
$715$	3.82103e12			0.546768
$716$	−7.84316e11	−	1.35848e12i	−0.111528	−	0.193172i
$717$	−8.46125e9	+	1.46553e10i	−0.00119563	+	0.00207090i
$718$	−5.88684e12	+	1.01963e13i	−0.826650	+	1.43180i
$719$	−6.09094e12	−	1.05498e13i	−0.849971	−	1.47219i	−0.881233	−	0.472682i	$-0.843286\pi$
$719$	−6.09094e12	−	1.05498e13i	−0.849971	−	1.47219i	0.0312620	−	0.999511i	$-0.490047\pi$
$720$	−2.22745e13			−3.08896
$721$		0			0
$722$	1.07644e13			1.47426
$723$	−5.17599e9	−	8.96508e9i	−0.000704484	−	0.00122020i
$724$	−1.34191e13	+	2.32425e13i	−1.81509	+	3.14384i
$725$	−3.99083e11	+	6.91233e11i	−0.0536466	+	0.0929187i
$726$	−9.97996e9	−	1.72858e10i	−0.00133326	−	0.00230927i
$727$	−1.26291e13			−1.67675			−0.838376	−	0.545093i	$-0.816494\pi$
$727$	−1.26291e13			−1.67675			−0.838376	+	0.545093i	$0.816494\pi$
$728$		0			0
$729$	−7.62547e12			−0.999984
$730$	1.70158e13	+	2.94722e13i	2.21768	+	3.84113i
$731$	−3.43534e12	+	5.95018e12i	−0.444981	+	0.770730i
$732$	1.35531e9	−	2.34746e9i	0.000174477	−	0.000302202i
$733$	4.58297e12	+	7.93794e12i	0.586380	+	1.01564i	0.994702	+	0.102802i	$0.0327808\pi$
$733$	4.58297e12	+	7.93794e12i	0.586380	+	1.01564i	−0.408322	+	0.912838i	$0.633886\pi$
$734$	1.00743e13			1.28110
$735$		0			0
$736$	1.34554e13			1.69024
$737$	1.90709e12	+	3.30318e12i	0.238105	+	0.412409i
$738$	3.03200e12	−	5.25158e12i	0.376249	−	0.651683i
$739$	−5.53289e12	+	9.58324e12i	−0.682420	+	1.18199i	0.291820	+	0.956473i	$0.405739\pi$
$739$	−5.53289e12	+	9.58324e12i	−0.682420	+	1.18199i	−0.974240	+	0.225513i	$0.927594\pi$
$740$	3.36053e12	+	5.82060e12i	0.411969	+	0.713551i
$741$	2.16866e10			0.00264247
$742$		0			0
$743$	1.84642e12			0.222270			0.111135	−	0.993805i	$-0.464551\pi$
$743$	1.84642e12			0.222270			0.111135	+	0.993805i	$0.464551\pi$
$744$	1.89020e10	+	3.27391e10i	0.00226167	+	0.00391732i
$745$	3.26380e12	−	5.65307e12i	0.388169	−	0.672328i
$746$	2.79908e12	−	4.84815e12i	0.330895	−	0.573127i
$747$	3.29359e12	+	5.70467e12i	0.387015	+	0.670329i
$748$	−7.13586e12			−0.833468
$749$		0			0
$750$	1.21019e10			0.00139662
$751$	4.59836e12	+	7.96459e12i	0.527501	+	0.913658i	0.999486	+	0.0320518i	$0.0102041\pi$
$751$	4.59836e12	+	7.96459e12i	0.527501	+	0.913658i	−0.471985	+	0.881606i	$0.656463\pi$
$752$	6.43018e12	−	1.11374e13i	0.733234	−	1.27000i
$753$	1.10950e10	−	1.92171e10i	0.00125762	−	0.00217826i
$754$	−1.62537e12	−	2.81522e12i	−0.183139	−	0.317206i
$755$	9.06449e12			1.01527
$756$		0			0
$757$	8.81778e12			0.975950			0.487975	−	0.872858i	$-0.337736\pi$
$757$	8.81778e12			0.975950			0.487975	+	0.872858i	$0.337736\pi$
$758$	−1.18551e13	−	2.05336e13i	−1.30434	−	2.25919i
$759$	2.49151e9	−	4.31541e9i	0.000272505	−	0.000471992i
$760$	2.06370e13	−	3.57443e13i	2.24380	−	3.88638i
$761$	−1.21021e12	−	2.09615e12i	−0.130807	−	0.226564i	0.793181	−	0.608986i	$-0.208423\pi$
$761$	−1.21021e12	−	2.09615e12i	−0.130807	−	0.226564i	−0.923988	+	0.382422i	$0.875090\pi$
$762$	−1.82843e10			−0.00196464
$763$		0			0
$764$	−1.32231e13			−1.40415
$765$	−5.85357e12	−	1.01387e13i	−0.617938	−	1.07030i
$766$	−2.16343e12	+	3.74717e12i	−0.227046	+	0.393255i
$767$	3.69744e12	−	6.40415e12i	0.385764	−	0.668163i
$768$	−8.05474e9	−	1.39512e10i	−0.000835461	−	0.00144706i
$769$	−7.67945e12			−0.791885			−0.395942	−	0.918275i	$-0.629582\pi$
$769$	−7.67945e12			−0.791885			−0.395942	+	0.918275i	$0.629582\pi$
$770$		0			0
$771$	2.12078e10			0.00216148
$772$	−4.73198e12	−	8.19603e12i	−0.479474	−	0.830473i
$773$	5.23466e12	−	9.06670e12i	0.527328	−	0.913359i	−0.472165	−	0.881510i	$-0.656527\pi$
$773$	5.23466e12	−	9.06670e12i	0.527328	−	0.913359i	0.999493	−	0.0318488i	$-0.0101395\pi$
$774$	−8.51542e12	+	1.47491e13i	−0.852848	+	1.47718i
$775$	−3.38375e12	−	5.86083e12i	−0.336931	−	0.583582i
$776$	4.31835e13			4.27504
$777$		0			0
$778$	−2.43956e13			−2.38728
$779$	2.80692e12	+	4.86173e12i	0.273094	+	0.473013i
$780$	3.15133e10	−	5.45826e10i	0.00304837	−	0.00527994i
$781$	4.86148e11	−	8.42033e11i	0.0467561	−	0.0809840i
$782$	8.55064e12	+	1.48101e13i	0.817651	+	1.41621i
$783$	5.80424e9			0.000551846
$784$		0			0
$785$	2.14465e13			2.01578
$786$	7.24733e9	+	1.25527e10i	0.000677293	+	0.00117311i
$787$	−6.32449e12	+	1.09543e13i	−0.587677	+	1.01789i	0.406858	+	0.913491i	$0.366624\pi$
$787$	−6.32449e12	+	1.09543e13i	−0.587677	+	1.01789i	−0.994536	+	0.104396i	$0.966709\pi$
$788$	2.63239e12	−	4.55944e12i	0.243211	−	0.421254i
$789$	1.75388e10	+	3.03781e10i	0.00161122	+	0.00279071i
$790$	3.37862e12			0.308615
$791$		0			0
$792$	−1.03575e13			−0.935387
$793$	−5.78613e11	−	1.00219e12i	−0.0519588	−	0.0899953i
$794$	−1.36806e12	+	2.36954e12i	−0.122155	+	0.211579i
$795$	−1.24352e10	+	2.15384e10i	−0.00110408	+	0.00191233i
$796$	1.95374e13	+	3.38397e13i	1.72487	+	2.98757i
$797$	6.02337e11			0.0528782			0.0264391	−	0.999650i	$-0.491583\pi$
$797$	6.02337e11			0.0528782			0.0264391	+	0.999650i	$0.491583\pi$
$798$		0			0
$799$	6.75920e12			0.586725
$800$	−6.86557e12	−	1.18915e13i	−0.592614	−	1.02644i
$801$	−6.41551e12	+	1.11120e13i	−0.550662	+	0.953775i
$802$	−8.49932e11	+	1.47213e12i	−0.0725437	+	0.125649i
$803$	3.95304e12	+	6.84687e12i	0.335515	+	0.581128i
$804$	6.29136e10			0.00530997
$805$		0			0
$806$	2.75624e13			2.30043
$807$	−2.78368e9	−	4.82148e9i	−0.000231041	−	0.000400174i
$808$	1.34798e13	−	2.33477e13i	1.11258	−	1.92705i
$809$	3.86484e12	−	6.69409e12i	0.317222	−	0.549444i	−0.662686	−	0.748898i	$-0.730583\pi$
$809$	3.86484e12	−	6.69409e12i	0.317222	−	0.549444i	0.979907	+	0.199454i	$0.0639167\pi$
$810$	−1.45096e13	−	2.51314e13i	−1.18433	−	2.05133i
$811$	1.20157e13			0.975335			0.487668	−	0.873029i	$-0.337848\pi$
$811$	1.20157e13			0.975335			0.487668	+	0.873029i	$0.337848\pi$
$812$		0			0
$813$	−1.28077e10			−0.00102816
$814$	1.10426e12	+	1.91264e12i	0.0881580	+	0.152694i
$815$	−1.26292e13	+	2.18745e13i	−1.00269	+	1.73671i
$816$	−2.43529e10	+	4.21804e10i	−0.00192284	+	0.00333046i
$817$	−7.88329e12	−	1.36543e13i	−0.619025	−	1.07218i
$818$	−4.43783e13			−3.46562
$819$		0			0
$820$	1.63152e13			1.26017
$821$	−6.99760e12	−	1.21202e13i	−0.537533	−	0.931035i	−0.999036	−	0.0438959i	$-0.986023\pi$
$821$	−6.99760e12	−	1.21202e13i	−0.537533	−	0.931035i	0.461503	−	0.887139i	$-0.347310\pi$
$822$	−1.55938e10	+	2.70093e10i	−0.00119132	+	0.00206343i
$823$	−8.09909e12	+	1.40280e13i	−0.615371	+	1.06585i	0.374948	+	0.927046i	$0.377661\pi$
$823$	−8.09909e12	+	1.40280e13i	−0.615371	+	1.06585i	−0.990319	+	0.138808i	$0.955673\pi$
$824$	−1.07653e13	−	1.86461e13i	−0.813494	−	1.40901i
$825$	−5.08511e9			−0.000382171
$826$		0			0
$827$	−1.30127e13			−0.967374			−0.483687	−	0.875241i	$-0.660703\pi$
$827$	−1.30127e13			−0.967374			−0.483687	+	0.875241i	$0.660703\pi$
$828$	1.49848e13	+	2.59544e13i	1.10793	+	1.91900i
$829$	−6.56819e12	+	1.13764e13i	−0.483004	+	0.836587i	−0.999810	−	0.0195157i	$-0.993788\pi$
$829$	−6.56819e12	+	1.13764e13i	−0.483004	+	0.836587i	0.516806	+	0.856103i	$0.327121\pi$
$830$	−1.25339e13	+	2.17094e13i	−0.916719	+	1.58780i
$831$	2.55145e9	+	4.41924e9i	0.000185602	+	0.000321472i
$832$	1.62994e13			1.17928
$833$		0			0
$834$	−2.95187e10			−0.00211276
$835$	3.18982e12	+	5.52492e12i	0.227079	+	0.393312i
$836$	8.18755e12	−	1.41813e13i	0.579730	−	1.00412i
$837$	−2.46065e10	+	4.26198e10i	−0.00173295	+	0.00300156i
$838$	−2.49421e13	−	4.32010e13i	−1.74717	−	3.02619i
$839$	5.22420e12			0.363991			0.181996	−	0.983299i	$-0.441744\pi$
$839$	5.22420e12			0.363991			0.181996	+	0.983299i	$0.441744\pi$
$840$		0			0
$841$	−1.41044e13			−0.972240
$842$	1.22981e13	+	2.13009e13i	0.843204	+	1.46047i
$843$	−1.88973e9	+	3.27310e9i	−0.000128877	+	0.000223221i
$844$	−1.09062e13	+	1.88901e13i	−0.739829	+	1.28142i
$845$	−3.95276e12	−	6.84638e12i	−0.266714	−	0.461962i
$846$	1.67545e13			1.12452
$847$		0			0
$848$	−3.77275e13			−2.50540
$849$	−1.57514e9	−	2.72822e9i	−0.000104048	−	0.000180217i
$850$	8.72584e12	−	1.51136e13i	0.573353	−	0.993077i
$851$	1.87098e12	−	3.24064e12i	0.122289	−	0.211810i
$852$	−8.01884e9	−	1.38890e10i	−0.000521355	−	0.000903013i
$853$	5.65076e12			0.365457			0.182728	−	0.983163i	$-0.441507\pi$
$853$	5.65076e12			0.365457			0.182728	+	0.983163i	$0.441507\pi$
$854$		0			0
$855$	2.68651e13			1.71926
$856$	−3.75876e13	−	6.51036e13i	−2.39283	−	4.14451i
$857$	7.12578e11	−	1.23422e12i	0.0451251	−	0.0781590i	−0.842581	−	0.538570i	$-0.818965\pi$
$857$	7.12578e11	−	1.23422e12i	0.0451251	−	0.0781590i	0.887706	+	0.460411i	$0.152298\pi$
$858$	1.03552e10	−	1.79357e10i	0.000652327	−	0.00112986i
$859$	1.38980e13	+	2.40721e13i	0.870932	+	1.50850i	0.861034	+	0.508547i	$0.169817\pi$
$859$	1.38980e13	+	2.40721e13i	0.870932	+	1.50850i	0.00989732	+	0.999951i	$0.496850\pi$
$860$	−4.58215e13			−2.85645
$861$		0			0
$862$	−5.13878e13			−3.17013
$863$	5.70583e12	+	9.88279e12i	0.350163	+	0.606500i	0.986278	−	0.165094i	$-0.0527928\pi$
$863$	5.70583e12	+	9.88279e12i	0.350163	+	0.606500i	−0.636115	+	0.771595i	$0.719459\pi$
$864$	−4.99262e10	+	8.64748e10i	−0.00304801	+	0.00527932i
$865$	2.36590e12	−	4.09786e12i	0.143689	−	0.248877i
$866$	−9.90328e11	−	1.71530e12i	−0.0598341	−	0.103636i
$867$	1.95364e9			0.000117425
$868$		0			0
$869$	7.84908e11			0.0466906
$870$	5.52208e9	+	9.56452e9i	0.000326788	+	0.000566013i
$871$	1.34297e13	−	2.32609e13i	0.790650	−	1.36945i
$872$	−5.79778e12	+	1.00420e13i	−0.339576	+	0.588163i
$873$	1.40540e13	+	2.43423e13i	0.818912	+	1.41840i
$874$	−3.92434e13			−2.27491
$875$		0			0
$876$	1.30408e11			0.00748232
$877$	6.05939e12	+	1.04952e13i	0.345884	+	0.599089i	0.985514	−	0.169594i	$-0.0542456\pi$
$877$	6.05939e12	+	1.04952e13i	0.345884	+	0.599089i	−0.639630	+	0.768683i	$0.720912\pi$
$878$	1.28381e13	−	2.22363e13i	0.729082	−	1.26281i
$879$	−6.29523e9	+	1.09037e10i	−0.000355682	+	0.000616059i
$880$	−9.84637e12	−	1.70544e13i	−0.553483	−	0.958661i
$881$	4.60741e12			0.257671			0.128836	−	0.991666i	$-0.458876\pi$
$881$	4.60741e12			0.257671			0.128836	+	0.991666i	$0.458876\pi$
$882$		0			0
$883$	1.04709e13			0.579642			0.289821	−	0.957081i	$-0.406404\pi$
$883$	1.04709e13			0.579642			0.289821	+	0.957081i	$0.406404\pi$
$884$	2.51253e13	+	4.35182e13i	1.38381	+	2.39682i
$885$	−1.25618e10	+	2.17577e10i	−0.000688347	+	0.00119225i
$886$	1.71221e13	−	2.96563e13i	0.933478	−	1.61683i
$887$	−1.84355e12	−	3.19313e12i	−0.0999999	−	0.173205i	0.811684	−	0.584096i	$-0.198551\pi$
$887$	−1.84355e12	−	3.19313e12i	−0.0999999	−	0.173205i	−0.911684	+	0.410891i	$0.865218\pi$
$888$	2.13313e10			0.00115122
$889$		0			0
$890$	−4.88291e13			−2.60870
$891$	−3.37083e12	−	5.83845e12i	−0.179179	−	0.310347i
$892$	−6.46646e12	+	1.12002e13i	−0.341999	+	0.592360i
$893$	−7.75538e12	+	1.34327e13i	−0.408105	+	0.706858i
$894$	−1.76901e10	−	3.06402e10i	−0.000926217	−	0.00160425i
$895$	2.27522e12			0.118528
$896$		0			0
$897$	−3.50902e10			−0.00180976
$898$	−1.00540e13	−	1.74140e13i	−0.515935	−	0.893625i
$899$	−1.70730e12	+	2.95713e12i	−0.0871750	+	0.150992i
$900$	1.52918e13	−	2.64862e13i	0.776906	−	1.34564i
$901$	−9.91449e12	−	1.71724e13i	−0.501198	−	0.868100i
$902$	5.36114e12			0.269667
$903$		0			0
$904$	7.24487e13			3.60805
$905$	−1.94637e13	−	3.37121e13i	−0.964510	−	1.67058i
$906$	2.45652e10	−	4.25482e10i	0.00121128	−	0.00209800i
$907$	3.02605e11	−	5.24126e11i	0.0148471	−	0.0257160i	−0.858506	−	0.512803i	$-0.828607\pi$
$907$	3.02605e11	−	5.24126e11i	0.0148471	−	0.0257160i	0.873354	+	0.487087i	$0.161941\pi$
$908$	1.20478e13	+	2.08674e13i	0.588196	+	1.01878i
$909$	1.75480e13			0.852491
$910$		0			0
$911$	−3.27450e12			−0.157512			−0.0787559	−	0.996894i	$-0.525095\pi$
$911$	−3.27450e12			−0.157512			−0.0787559	+	0.996894i	$0.525095\pi$
$912$	−5.58840e10	−	9.67940e10i	−0.00267492	−	0.00463310i
$913$	−2.91184e12	+	5.04346e12i	−0.138691	+	0.240220i
$914$	−2.41047e13	+	4.17506e13i	−1.14247	+	1.97881i
$915$	1.96580e9	+	3.40487e9i	9.27139e−5	+	0.000160585i
$916$	7.36467e13			3.45640
$917$		0			0
$918$	−1.26908e11			−0.00589790
$919$	−1.10558e11	−	1.91493e11i	−0.00511295	−	0.00885589i	0.863458	−	0.504421i	$-0.168294\pi$
$919$	−1.10558e11	−	1.91493e11i	−0.00511295	−	0.00885589i	−0.868571	+	0.495566i	$0.834961\pi$
$920$	−3.33918e13	+	5.78363e13i	−1.53672	+	2.66168i
$921$	−8.50939e9	+	1.47387e10i	−0.000389700	+	0.000674980i
$922$	−1.26866e13	−	2.19738e13i	−0.578171	−	1.00142i
$923$	−6.84688e12			−0.310517
$924$		0			0
$925$	−3.81864e12			−0.171503
$926$	1.85550e13	+	3.21382e13i	0.829300	+	1.43639i
$927$	7.00713e12	−	1.21367e13i	0.311660	−	0.539811i
$928$	−3.46409e12	+	5.99997e12i	−0.153328	+	0.265573i
$929$	−2.00073e12	−	3.46537e12i	−0.0881290	−	0.152644i	0.818591	−	0.574376i	$-0.194755\pi$
$929$	−2.00073e12	−	3.46537e12i	−0.0881290	−	0.152644i	−0.906720	+	0.421733i	$0.861422\pi$
$930$	−9.36413e10			−0.00410482
$931$		0			0
$932$	1.04097e14			4.51927
$933$	2.84037e10	+	4.91966e10i	0.00122718	+	0.00212553i
$934$	−2.29450e13	+	3.97418e13i	−0.986566	+	1.70878i
$935$	5.17510e12	−	8.96353e12i	0.221445	−	0.383554i
$936$	3.64686e13	+	6.31654e13i	1.55302	+	2.68991i
$937$	3.76138e10			0.00159411			0.000797056	−	1.00000i	$-0.499746\pi$
$937$	3.76138e10			0.00159411			0.000797056		1.00000i	$0.499746\pi$
$938$		0			0
$939$	−1.02205e10			−0.000429019
$940$	2.25390e13	+	3.90387e13i	0.941585	+	1.63087i
$941$	−1.10747e12	+	1.91820e12i	−0.0460447	+	0.0797518i	−0.888129	−	0.459594i	$-0.847995\pi$
$941$	−1.10747e12	+	1.91820e12i	−0.0460447	+	0.0797518i	0.842085	+	0.539346i	$0.181328\pi$
$942$	5.81212e10	−	1.00669e11i	0.00240495	−	0.00416549i
$943$	−4.54177e12	−	7.86657e12i	−0.187035	−	0.323954i
$944$	−3.81116e13			−1.56201
$945$		0			0
$946$	−1.50568e13			−0.611257
$947$	−1.18133e13	−	2.04612e13i	−0.477305	−	0.826716i	0.522357	−	0.852727i	$-0.325053\pi$
$947$	−1.18133e13	−	2.04612e13i	−0.477305	−	0.826716i	−0.999662	+	0.0260107i	$0.991720\pi$
$948$	6.47339e9	−	1.12122e10i	0.000260312	−	0.000450874i
$949$	2.78372e13	−	4.82155e13i	1.11411	−	1.92969i
$950$	2.00237e13	+	3.46821e13i	0.797607	+	1.38150i
$951$	5.05694e10			0.00200482
$952$		0			0
$953$	−1.15037e13			−0.451771			−0.225885	−	0.974154i	$-0.572527\pi$
$953$	−1.15037e13			−0.451771			−0.225885	+	0.974154i	$0.572527\pi$
$954$	−2.45758e13	−	4.25665e13i	−0.960593	−	1.66380i
$955$	9.58974e12	−	1.66099e13i	0.373071	−	0.646178i
$956$	4.49905e13	−	7.79258e13i	1.74205	−	3.01732i
$957$	1.28287e9	+	2.22200e9i	4.94400e−5	+	8.56327e-5i
$958$	1.30518e13			0.500639
$959$		0			0
$960$	−5.53761e10			−0.00210427
$961$	−1.25609e12	−	2.17561e12i	−0.0475078	−	0.0822859i
$962$	7.77618e12	−	1.34687e13i	0.292737	−	0.507036i
$963$	2.44657e13	−	4.23759e13i	0.916726	−	1.58782i
$964$	2.75220e13	+	4.76695e13i	1.02644	+	1.77785i
$965$	1.37270e13			0.509568
$966$		0			0
$967$	−1.36863e13			−0.503346			−0.251673	−	0.967812i	$-0.580981\pi$
$967$	−1.36863e13			−0.503346			−0.251673	+	0.967812i	$0.580981\pi$
$968$	3.10733e13	+	5.38205e13i	1.13749	+	1.97019i
$969$	2.93718e10	−	5.08734e10i	0.00107022	−	0.00185368i
$970$	−5.34834e13	+	9.26359e13i	−1.93975	+	3.35975i
$971$	4.97630e12	+	8.61920e12i	0.179647	+	0.311158i	0.941760	−	0.336287i	$-0.109171\pi$
$971$	4.97630e12	+	8.61920e12i	0.179647	+	0.311158i	−0.762113	+	0.647444i	$0.775838\pi$
$972$	−3.33605e11			−0.0119877
$973$		0			0
$974$	4.53038e13			1.61295
$975$	1.79046e10	+	3.10117e10i	0.000634518	+	0.00109902i
$976$	−2.98204e12	+	5.16505e12i	−0.105194	+	0.182201i
$977$	−7.56937e12	+	1.31105e13i	−0.265787	+	0.460357i	−0.967770	−	0.251837i	$-0.918965\pi$
$977$	−7.56937e12	+	1.31105e13i	−0.265787	+	0.460357i	0.701982	+	0.712194i	$0.252299\pi$
$978$	6.84517e10	+	1.18562e11i	0.00239254	+	0.00414401i
$979$	−1.13438e13			−0.394673
$980$		0			0
$981$	−7.54753e12			−0.260192
$982$	−4.48749e13	−	7.77256e13i	−1.53993	−	2.66724i
$983$	2.73570e13	−	4.73838e13i	0.934497	−	1.61860i	0.158970	−	0.987283i	$-0.449183\pi$
$983$	2.73570e13	−	4.73838e13i	0.934497	−	1.61860i	0.775528	−	0.631314i	$-0.217484\pi$
$984$	2.58906e10	−	4.48438e10i	0.000880367	−	0.00152484i
$985$	3.81815e12	+	6.61324e12i	0.129238	+	0.223847i
$986$	−8.80540e12			−0.296690
$987$		0			0
$988$	−1.15313e14			−3.85010
$989$	1.27556e13	+	2.20934e13i	0.423954	+	0.734309i
$990$	1.28279e13	−	2.22186e13i	0.424421	−	0.735119i
$991$	−2.43192e13	+	4.21221e13i	−0.800974	+	1.38733i	0.118002	+	0.993013i	$0.462351\pi$
$991$	−2.43192e13	+	4.21221e13i	−0.800974	+	1.38733i	−0.918976	+	0.394314i	$0.870982\pi$
$992$	−2.93713e13	−	5.08726e13i	−0.962989	−	1.66795i
$993$	8.52557e10			0.00278261
$994$		0			0
$995$	−5.66759e13			−1.83314
$996$	4.80298e10	+	8.31901e10i	0.00154648	+	0.00267858i
$997$	1.38879e13	−	2.40545e13i	0.445152	−	0.771026i	−0.552911	−	0.833240i	$-0.686483\pi$
$997$	1.38879e13	−	2.40545e13i	0.445152	−	0.771026i	0.998063	+	0.0622146i	$0.0198163\pi$
$998$	3.88141e13	−	6.72281e13i	1.23852	−	2.14518i
$999$	1.38845e10	+	2.40487e10i	0.000441048	+	0.000763917i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.10.c.e.18.1		6
7.2	even	3	inner	49.10.c.e.30.1		6
7.3	odd	6		7.10.a.b.1.3	✓	3
7.4	even	3		49.10.a.c.1.3		3
7.5	odd	6		49.10.c.d.30.1		6
7.6	odd	2		49.10.c.d.18.1		6
21.17	even	6		63.10.a.e.1.1		3
28.3	even	6		112.10.a.h.1.2		3
35.3	even	12		175.10.b.d.99.1		6
35.17	even	12		175.10.b.d.99.6		6
35.24	odd	6		175.10.a.d.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.a.b.1.3	✓	3	7.3	odd	6
49.10.a.c.1.3		3	7.4	even	3
49.10.c.d.18.1		6	7.6	odd	2
49.10.c.d.30.1		6	7.5	odd	6
49.10.c.e.18.1		6	1.1	even	1	trivial
49.10.c.e.30.1		6	7.2	even	3	inner
63.10.a.e.1.1		3	21.17	even	6
112.10.a.h.1.2		3	28.3	even	6
175.10.a.d.1.1		3	35.24	odd	6
175.10.b.d.99.1		6	35.3	even	12
175.10.b.d.99.6		6	35.17	even	12

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	49.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-20.9010 - 36.2015i) q^{2} +(0.116170 - 0.201212i) q^{3} +(-617.701 + 1069.89i) q^{4} +(-895.944 - 1551.82i) q^{5} -9.71222 q^{6} +30239.6 q^{8} +(9841.47 + 17045.9i) q^{9} +(-37452.2 + 64869.1i) q^{10} +(-8700.77 + 15070.2i) q^{11} +(143.516 + 248.577i) q^{12} +122541. q^{13} -416.326 q^{15} +(-315775. - 546938. i) q^{16} +(165966. - 287462. i) q^{17} +(411393. - 712553. i) q^{18} +(380853. + 659658. i) q^{19} +2.21370e6 q^{20} +727418. q^{22} +(-616243. - 1.06736e6i) q^{23} +(3512.93 - 6084.57i) q^{24} +(-628870. + 1.08923e6i) q^{25} +(-2.56123e6 - 4.43618e6i) q^{26} +9146.25 q^{27} +634604. q^{29} +(8701.61 + 15071.6i) q^{30} +(-2.69034e6 + 4.65981e6i) q^{31} +(-5.45866e6 + 9.45467e6i) q^{32} +(2021.53 + 3501.39i) q^{33} -1.38754e7 q^{34} -2.43164e7 q^{36} +(1.51806e6 + 2.62935e6i) q^{37} +(1.59204e7 - 2.75750e7i) q^{38} +(14235.5 - 24656.7i) q^{39} +(-2.70930e7 - 4.69265e7i) q^{40} +7.37009e6 q^{41} -2.06990e7 q^{43} +(-1.07490e7 - 1.86177e7i) q^{44} +(1.76348e7 - 3.05444e7i) q^{45} +(-2.57602e7 + 4.46179e7i) q^{46} +(1.01816e7 + 1.76350e7i) q^{47} -146734. q^{48} +5.25760e7 q^{50} +(-38560.5 - 66788.7i) q^{51} +(-7.56938e7 + 1.31106e8i) q^{52} +(2.98690e7 - 5.17346e7i) q^{53} +(-191165. - 331108. i) q^{54} +3.11816e7 q^{55} +176974. q^{57} +(-1.32638e7 - 2.29736e7i) q^{58} +(3.01730e7 - 5.22612e7i) q^{59} +(257165. - 445423. i) q^{60} +(-4.72179e6 - 8.17837e6i) q^{61} +2.24923e8 q^{62} +1.33012e8 q^{64} +(-1.09790e8 - 1.90162e8i) q^{65} +(84503.8 - 146365. i) q^{66} +(1.09593e8 - 1.89821e8i) q^{67} +(2.05035e8 + 3.55132e8i) q^{68} -286355. q^{69} -5.58741e7 q^{71} +(2.97603e8 + 5.15463e8i) q^{72} +(2.27166e8 - 3.93463e8i) q^{73} +(6.34577e7 - 1.09912e8i) q^{74} +(146111. + 253072. i) q^{75} -9.41015e8 q^{76} -1.19015e6 q^{78} +(-2.25528e7 - 3.90627e7i) q^{79} +(-5.65834e8 + 9.80053e8i) q^{80} +(-1.93709e8 + 3.35513e8i) q^{81} +(-1.54042e8 - 2.66809e8i) q^{82} +3.34665e8 q^{83} -5.94786e8 q^{85} +(4.32629e8 + 7.49336e8i) q^{86} +(73721.6 - 127690. i) q^{87} +(-2.63108e8 + 4.55717e8i) q^{88} +(3.25943e8 + 5.64550e8i) q^{89} -1.47434e9 q^{90} +1.52262e9 q^{92} +(625072. + 1.08266e6i) q^{93} +(4.25610e8 - 7.37178e8i) q^{94} +(6.82447e8 - 1.18203e9i) q^{95} +(1.26826e6 + 2.19669e6i) q^{96} +1.42804e9 q^{97} -3.42514e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 21 q^{2} + 84 q^{3} - 1557 q^{4} + 1554 q^{5} - 9828 q^{6} + 28110 q^{8} + 26001 q^{9} - 97860 q^{10} + 3444 q^{11} - 106386 q^{12} + 39564 q^{13} + 400608 q^{15} - 482961 q^{16} + 1016694 q^{17}+ \cdots - 3801958344 q^{99}+O(q^{100}) \) 6 * q - 21 * q^2 + 84 * q^3 - 1557 * q^4 + 1554 * q^5 - 9828 * q^6 + 28110 * q^8 + 26001 * q^9 - 97860 * q^10 + 3444 * q^11 - 106386 * q^12 + 39564 * q^13 + 400608 * q^15 - 482961 * q^16 + 1016694 * q^17 + 273267 * q^18 + 222852 * q^19 + 3844176 * q^20 - 5694096 * q^22 - 1885632 * q^23 - 1449630 * q^24 - 3073221 * q^25 - 8785056 * q^26 - 1103760 * q^27 + 8163636 * q^29 - 8053200 * q^30 + 2869440 * q^31 - 25221951 * q^32 - 20259792 * q^33 + 7963284 * q^34 - 70792758 * q^36 - 1395618 * q^37 + 43479870 * q^38 + 8990688 * q^39 - 82859280 * q^40 + 28841316 * q^41 - 123262344 * q^43 - 97011984 * q^44 + 29774682 * q^45 - 89747664 * q^46 - 10368960 * q^47 - 33597564 * q^48 + 146650110 * q^50 + 26146728 * q^51 - 80908044 * q^52 - 67502610 * q^53 - 117879300 * q^54 + 211646064 * q^55 + 16942224 * q^57 + 159163830 * q^58 - 42590100 * q^59 + 179551008 * q^60 + 191746842 * q^61 + 93966936 * q^62 + 15704322 * q^64 - 364283220 * q^65 - 8057952 * q^66 + 255175788 * q^67 + 743485806 * q^68 - 515807712 * q^69 + 593029008 * q^71 + 609314265 * q^72 + 344213310 * q^73 + 690696462 * q^74 + 279031116 * q^75 - 1457679972 * q^76 + 560265552 * q^78 + 960412656 * q^79 - 1333333344 * q^80 + 35827677 * q^81 + 562675302 * q^82 + 2201034360 * q^83 + 876358824 * q^85 + 880982256 * q^86 - 621821592 * q^87 - 1206124800 * q^88 + 506816478 * q^89 - 4606905240 * q^90 + 1382246976 * q^92 - 1693258512 * q^93 + 1388004828 * q^94 + 2203071072 * q^95 + 333385794 * q^96 + 1294996500 * q^97 - 3801958344 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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