LMFDB - Embedded newform 49.10.c.d.30.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,10,Mod(18,49)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [6,-21,-84] 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:	$25.2367559720$
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			30.2
Root			$-11.1179 + 19.2567i$ of defining polynomial
Character	$\chi$	$=$	49.30
Dual form			49.10.c.d.18.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.68036 + 11.5707i) q^{2} +(-81.7073 - 141.521i) q^{3} +(166.746 + 288.812i) q^{4} +(-961.094 + 1664.66i) q^{5} +2183.34 q^{6} -11296.4 q^{8} +(-3510.66 + 6080.64i) q^{9} +(-12840.9 - 22241.1i) q^{10} +(45099.9 + 78115.4i) q^{11} +(27248.6 - 47196.0i) q^{12} -3199.89 q^{13} +314114. q^{15} +(-9909.84 + 17164.3i) q^{16} +(-58247.1 - 100887. i) q^{17} +(-46904.9 - 81241.8i) q^{18} +(71224.7 - 123365. i) q^{19} -641033. q^{20} -1.20514e6 q^{22} +(-636955. + 1.10324e6i) q^{23} +(922996. + 1.59868e6i) q^{24} +(-870842. - 1.50834e6i) q^{25} +(21376.4 - 37025.0i) q^{26} -2.06910e6 q^{27} -1.42931e6 q^{29} +(-2.09839e6 + 3.63452e6i) q^{30} +(-4.83747e6 - 8.37875e6i) q^{31} +(-3.02427e6 - 5.23820e6i) q^{32} +(7.36999e6 - 1.27652e7i) q^{33} +1.55645e6 q^{34} -2.34155e6 q^{36} +(4.33872e6 - 7.51488e6i) q^{37} +(951614. + 1.64824e6i) q^{38} +(261454. + 452851. i) q^{39} +(1.08569e7 - 1.88047e7i) q^{40} +1.32544e7 q^{41} -2.97554e7 q^{43} +(-1.50404e7 + 2.60508e7i) q^{44} +(-6.74815e6 - 1.16881e7i) q^{45} +(-8.51018e6 - 1.47401e7i) q^{46} +(5.39846e6 - 9.35041e6i) q^{47} +3.23882e6 q^{48} +2.32702e7 q^{50} +(-9.51843e6 + 1.64864e7i) q^{51} +(-533567. - 924164. i) q^{52} +(-3.53700e7 - 6.12626e7i) q^{53} +(1.38224e7 - 2.39410e7i) q^{54} -1.73381e8 q^{55} -2.32783e7 q^{57} +(9.54828e6 - 1.65381e7i) q^{58} +(-3.20200e6 - 5.54603e6i) q^{59} +(5.23770e7 + 9.07197e7i) q^{60} +(-8.45948e7 + 1.46523e8i) q^{61} +1.29264e8 q^{62} +7.06653e7 q^{64} +(3.07539e6 - 5.32673e6i) q^{65} +(9.84684e7 + 1.70552e8i) q^{66} +(5.81380e7 + 1.00698e8i) q^{67} +(1.94249e7 - 3.36449e7i) q^{68} +2.08176e8 q^{69} +1.44496e8 q^{71} +(3.96577e7 - 6.86892e7i) q^{72} +(-8.00775e7 - 1.38698e8i) q^{73} +(5.79684e7 + 1.00404e8i) q^{74} +(-1.42308e8 + 2.46485e8i) q^{75} +4.75056e7 q^{76} -6.98643e6 q^{78} +(2.44661e8 - 4.23766e8i) q^{79} +(-1.90486e7 - 3.29931e7i) q^{80} +(2.38161e8 + 4.12507e8i) q^{81} +(-8.85441e7 + 1.53363e8i) q^{82} -8.31590e7 q^{83} +2.23924e8 q^{85} +(1.98777e8 - 3.44291e8i) q^{86} +(1.16785e8 + 2.02277e8i) q^{87} +(-5.09466e8 - 8.82421e8i) q^{88} +(-1.04042e6 + 1.80205e6i) q^{89} +1.80320e8 q^{90} -4.24838e8 q^{92} +(-7.90513e8 + 1.36921e9i) q^{93} +(7.21274e7 + 1.24928e8i) q^{94} +(1.36907e8 + 2.37131e8i) q^{95} +(-4.94210e8 + 8.55998e8i) q^{96} -3.15885e8 q^{97} -6.33322e8 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 $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−6.68036	+	11.5707i	−0.295233	+	0.511359i	−0.975039	−	0.222033i	$-0.928731\pi$
$2$	−6.68036	+	11.5707i	−0.295233	+	0.511359i	0.679806	+	0.733392i	$0.262064\pi$
$3$	−81.7073	−	141.521i	−0.582392	−	1.00873i	−0.995195	−	0.0979117i	$-0.968784\pi$
$3$	−81.7073	−	141.521i	−0.582392	−	1.00873i	0.412804	−	0.910820i	$-0.364550\pi$
$4$	166.746	+	288.812i	0.325675	+	0.564085i
$5$	−961.094	+	1664.66i	−0.687703	+	1.19114i	0.284876	+	0.958564i	$0.408048\pi$
$5$	−961.094	+	1664.66i	−0.687703	+	1.19114i	−0.972579	+	0.232572i	$0.925286\pi$
$6$	2183.34			0.687765
$7$		0			0
$7$		0			0
$8$	−11296.4			−0.975066
$9$	−3510.66	+	6080.64i	−0.178360	+	0.308928i
$10$	−12840.9	−	22241.1i	−0.406065	−	0.703326i
$11$	45099.9	+	78115.4i	0.928772	+	1.60868i	0.785380	+	0.619014i	$0.212467\pi$
$11$	45099.9	+	78115.4i	0.928772	+	1.60868i	0.143391	+	0.989666i	$0.454199\pi$
$12$	27248.6	−	47196.0i	0.379341	−	0.657037i
$13$	−3199.89			−0.0310734			−0.0155367	−	0.999879i	$-0.504946\pi$
$13$	−3199.89			−0.0310734			−0.0155367	+	0.999879i	$0.504946\pi$
$14$		0			0
$15$	314114.			1.60205
$16$	−9909.84	+	17164.3i	−0.0378030	+	0.0654768i
$17$	−58247.1	−	100887.i	−0.169143	−	0.292965i	0.768976	−	0.639278i	$-0.220767\pi$
$17$	−58247.1	−	100887.i	−0.169143	−	0.292965i	−0.938119	+	0.346313i	$0.887433\pi$
$18$	−46904.9	−	81241.8i	−0.105316	−	0.182412i
$19$	71224.7	−	123365.i	0.125383	−	0.217170i	−0.796499	−	0.604639i	$-0.793317\pi$
$19$	71224.7	−	123365.i	0.125383	−	0.217170i	0.921883	+	0.387469i	$0.126651\pi$
$20$	−641033.			−0.895870
$21$		0			0
$22$	−1.20514e6			−1.09682
$23$	−636955.	+	1.10324e6i	−0.474606	+	0.822043i	−0.999577	−	0.0290778i	$-0.990743\pi$
$23$	−636955.	+	1.10324e6i	−0.474606	+	0.822043i	0.524971	+	0.851120i	$0.324076\pi$
$24$	922996.	+	1.59868e6i	0.567870	+	0.983580i
$25$	−870842.	−	1.50834e6i	−0.445871	−	0.772272i
$26$	21376.4	−	37025.0i	0.00917391	−	0.0158897i
$27$	−2.06910e6			−0.749282
$28$		0			0
$29$	−1.42931e6			−0.375262			−0.187631	−	0.982240i	$-0.560081\pi$
$29$	−1.42931e6			−0.375262			−0.187631	+	0.982240i	$0.560081\pi$
$30$	−2.09839e6	+	3.63452e6i	−0.472978	+	0.819222i
$31$	−4.83747e6	−	8.37875e6i	−0.940786	−	1.62949i	−0.763977	−	0.645244i	$-0.776756\pi$
$31$	−4.83747e6	−	8.37875e6i	−0.940786	−	1.62949i	−0.176809	−	0.984245i	$-0.556578\pi$
$32$	−3.02427e6	−	5.23820e6i	−0.509854	−	0.883094i
$33$	7.36999e6	−	1.27652e7i	1.08182	−	1.87376i
$34$	1.55645e6			0.199747
$35$		0			0
$36$	−2.34155e6			−0.232349
$37$	4.33872e6	−	7.51488e6i	0.380587	−	0.659196i	−0.610559	−	0.791971i	$-0.709055\pi$
$37$	4.33872e6	−	7.51488e6i	0.380587	−	0.659196i	0.991146	+	0.132775i	$0.0423886\pi$
$38$	951614.	+	1.64824e6i	0.0740346	+	0.128232i
$39$	261454.	+	452851.i	0.0180969	+	0.0313448i
$40$	1.08569e7	−	1.88047e7i	0.670556	−	1.16144i
$41$	1.32544e7			0.732541			0.366271	−	0.930508i	$-0.380634\pi$
$41$	1.32544e7			0.732541			0.366271	+	0.930508i	$0.380634\pi$
$42$		0			0
$43$	−2.97554e7			−1.32726			−0.663632	−	0.748060i	$-0.730986\pi$
$43$	−2.97554e7			−1.32726			−0.663632	+	0.748060i	$0.730986\pi$
$44$	−1.50404e7	+	2.60508e7i	−0.604955	+	1.04781i
$45$	−6.74815e6	−	1.16881e7i	−0.245317	−	0.424902i
$46$	−8.51018e6	−	1.47401e7i	−0.280239	−	0.485388i
$47$	5.39846e6	−	9.35041e6i	0.161373	−	0.279506i	−0.773989	−	0.633200i	$-0.781741\pi$
$47$	5.39846e6	−	9.35041e6i	0.161373	−	0.279506i	0.935361	+	0.353694i	$0.115075\pi$
$48$	3.23882e6			0.0880647
$49$		0			0
$50$	2.32702e7			0.526544
$51$	−9.51843e6	+	1.64864e7i	−0.197015	+	0.341240i
$52$	−533567.	−	924164.i	−0.0101198	−	0.0175281i
$53$	−3.53700e7	−	6.12626e7i	−0.615734	−	1.06648i	−0.990255	−	0.139264i	$-0.955526\pi$
$53$	−3.53700e7	−	6.12626e7i	−0.615734	−	1.06648i	0.374521	−	0.927218i	$-0.377807\pi$
$54$	1.38224e7	−	2.39410e7i	0.221213	−	0.383152i
$55$	−1.73381e8			−2.55488
$56$		0			0
$57$	−2.32783e7			−0.292089
$58$	9.54828e6	−	1.65381e7i	0.110790	−	0.191893i
$59$	−3.20200e6	−	5.54603e6i	−0.0344023	−	0.0595865i	0.848312	−	0.529497i	$-0.177619\pi$
$59$	−3.20200e6	−	5.54603e6i	−0.0344023	−	0.0595865i	−0.882714	+	0.469911i	$0.844286\pi$
$60$	5.23770e7	+	9.07197e7i	0.521747	+	0.903693i
$61$	−8.45948e7	+	1.46523e8i	−0.782275	+	1.35494i	0.148338	+	0.988937i	$0.452608\pi$
$61$	−8.45948e7	+	1.46523e8i	−0.782275	+	1.35494i	−0.930613	+	0.366004i	$0.880726\pi$
$62$	1.29264e8			1.11100
$63$		0			0
$64$	7.06653e7			0.526498
$65$	3.07539e6	−	5.32673e6i	0.0213693	−	0.0370127i
$66$	9.84684e7	+	1.70552e8i	0.638777	+	1.10639i
$67$	5.81380e7	+	1.00698e8i	0.352471	+	0.610498i	0.986682	−	0.162662i	$-0.0520081\pi$
$67$	5.81380e7	+	1.00698e8i	0.352471	+	0.610498i	−0.634210	+	0.773160i	$0.718675\pi$
$68$	1.94249e7	−	3.36449e7i	0.110171	−	0.190822i
$69$	2.08176e8			1.10563
$70$		0			0
$71$	1.44496e8			0.674826			0.337413	−	0.941357i	$-0.390448\pi$
$71$	1.44496e8			0.674826			0.337413	+	0.941357i	$0.390448\pi$
$72$	3.96577e7	−	6.86892e7i	0.173913	−	0.301226i
$73$	−8.00775e7	−	1.38698e8i	−0.330033	−	0.571634i	0.652485	−	0.757802i	$-0.273727\pi$
$73$	−8.00775e7	−	1.38698e8i	−0.330033	−	0.571634i	−0.982518	+	0.186168i	$0.940393\pi$
$74$	5.79684e7	+	1.00404e8i	0.224724	+	0.389233i
$75$	−1.42308e8	+	2.46485e8i	−0.519343	+	0.899529i
$76$	4.75056e7			0.163337
$77$		0			0
$78$	−6.98643e6			−0.0213712
$79$	2.44661e8	−	4.23766e8i	0.706713	−	1.22406i	−0.259357	−	0.965782i	$-0.583511\pi$
$79$	2.44661e8	−	4.23766e8i	0.706713	−	1.22406i	0.966070	−	0.258281i	$-0.0831561\pi$
$80$	−1.90486e7	−	3.29931e7i	−0.0519945	−	0.0900572i
$81$	2.38161e8	+	4.12507e8i	0.614735	+	1.06475i
$82$	−8.85441e7	+	1.53363e8i	−0.216270	+	0.374591i
$83$	−8.31590e7			−0.192335			−0.0961674	−	0.995365i	$-0.530658\pi$
$83$	−8.31590e7			−0.192335			−0.0961674	+	0.995365i	$0.530658\pi$
$84$		0			0
$85$	2.23924e8			0.465281
$86$	1.98777e8	−	3.44291e8i	0.391852	−	0.678708i
$87$	1.16785e8	+	2.02277e8i	0.218549	+	0.378538i
$88$	−5.09466e8	−	8.82421e8i	−0.905614	−	1.56857i
$89$	−1.04042e6	+	1.80205e6i	−0.00175773	+	0.00304448i	−0.866903	−	0.498477i	$-0.833893\pi$
$89$	−1.04042e6	+	1.80205e6i	−0.00175773	+	0.00304448i	0.865145	+	0.501521i	$0.167226\pi$
$90$	1.80320e8			0.289703
$91$		0			0
$92$	−4.24838e8			−0.618270
$93$	−7.90513e8	+	1.36921e9i	−1.09581	+	1.89800i
$94$	7.21274e7	+	1.24928e8i	0.0952851	+	0.165039i
$95$	1.36907e8	+	2.37131e8i	0.172453	+	0.298697i
$96$	−4.94210e8	+	8.55998e8i	−0.593870	+	1.02861i
$97$	−3.15885e8			−0.362290			−0.181145	−	0.983456i	$-0.557980\pi$
$97$	−3.15885e8			−0.362290			−0.181145	+	0.983456i	$0.557980\pi$
$98$		0			0
$99$	−6.33322e8			−0.662623
$100$	2.90418e8	−	5.03019e8i	0.290418	−	0.503019i
$101$	2.87420e8	+	4.97827e8i	0.274835	+	0.476028i	0.970093	−	0.242732i	$-0.0780436\pi$
$101$	2.87420e8	+	4.97827e8i	0.274835	+	0.476028i	−0.695259	+	0.718760i	$0.744710\pi$
$102$	−1.27173e8	−	2.20270e8i	−0.116331	−	0.201491i
$103$	7.59350e8	−	1.31523e9i	0.664775	−	1.15142i	−0.314571	−	0.949234i	$-0.601861\pi$
$103$	7.59350e8	−	1.31523e9i	0.664775	−	1.15142i	0.979346	−	0.202190i	$-0.0648059\pi$
$104$	3.61471e7			0.0302987
$105$		0			0
$106$	9.45137e8			0.727140
$107$	1.00932e8	−	1.74819e8i	0.0744390	−	0.128932i	−0.826403	−	0.563079i	$-0.809617\pi$
$107$	1.00932e8	−	1.74819e8i	0.0744390	−	0.128932i	0.900842	+	0.434147i	$0.142950\pi$
$108$	−3.45014e8	−	5.97581e8i	−0.244022	−	0.422659i
$109$	4.36976e8	+	7.56865e8i	0.296509	+	0.513569i	0.975335	−	0.220730i	$-0.0708441\pi$
$109$	4.36976e8	+	7.56865e8i	0.296509	+	0.513569i	−0.678826	+	0.734300i	$0.737511\pi$
$110$	1.15825e9	−	2.00615e9i	0.754284	−	1.30646i
$111$	−1.41802e9			−0.886603
$112$		0			0
$113$	1.52955e9			0.882491			0.441245	−	0.897386i	$-0.354537\pi$
$113$	1.52955e9			0.882491			0.441245	+	0.897386i	$0.354537\pi$
$114$	1.55508e8	−	2.69347e8i	0.0862343	−	0.149362i
$115$	−1.22435e9	−	2.12063e9i	−0.652777	−	1.13064i
$116$	−2.38330e8	−	4.12800e8i	−0.122213	−	0.211680i
$117$	1.12337e7	−	1.94573e7i	0.00554226	−	0.00959947i
$118$	8.55621e7			0.0406268
$119$		0			0
$120$	−3.54834e9			−1.56210
$121$	−2.88904e9	+	5.00396e9i	−1.22523	+	2.12217i
$122$	−1.13025e9	−	1.95765e9i	−0.461907	−	0.800046i
$123$	−1.08298e9	−	1.87578e9i	−0.426626	−	0.738938i
$124$	1.61325e9	−	2.79424e9i	0.612781	−	1.06137i
$125$	−4.06429e8			−0.148898
$126$		0			0
$127$	−8.71958e8			−0.297426			−0.148713	−	0.988880i	$-0.547513\pi$
$127$	−8.71958e8			−0.297426			−0.148713	+	0.988880i	$0.547513\pi$
$128$	1.07636e9	−	1.86431e9i	0.354415	−	0.613865i
$129$	2.43123e9	+	4.21101e9i	0.772987	+	1.33885i
$130$	4.10895e7	+	7.11690e7i	0.0126179	+	0.0218548i
$131$	−1.12202e9	+	1.94339e9i	−0.332874	+	0.576554i	−0.983074	−	0.183209i	$-0.941352\pi$
$131$	−1.12202e9	+	1.94339e9i	−0.332874	+	0.576554i	0.650200	+	0.759763i	$0.274685\pi$
$132$	4.91565e9			1.40928
$133$		0			0
$134$	−1.55353e9			−0.416245
$135$	1.98860e9	−	3.44436e9i	0.515283	−	0.892497i
$136$	6.57981e8	+	1.13966e9i	0.164926	+	0.285660i
$137$	−2.08071e9	−	3.60389e9i	−0.504624	−	0.874035i	−0.999986	−	0.00534799i	$-0.998298\pi$
$137$	−2.08071e9	−	3.60389e9i	−0.504624	−	0.874035i	0.495361	−	0.868687i	$-0.335036\pi$
$138$	−1.39069e9	+	2.40874e9i	−0.326418	+	0.565372i
$139$	−6.03383e9			−1.37097			−0.685483	−	0.728089i	$-0.740409\pi$
$139$	−6.03383e9			−1.37097			−0.685483	+	0.728089i	$0.740409\pi$
$140$		0			0
$141$	−1.76438e9			−0.375928
$142$	−9.65283e8	+	1.67192e9i	−0.199231	+	0.345078i
$143$	−1.44315e8	−	2.49960e8i	−0.0288601	−	0.0499872i
$144$	−6.95801e7	−	1.20516e8i	−0.0134851	−	0.0233569i
$145$	1.37370e9	−	2.37931e9i	0.258069	−	0.446988i
$146$	2.13979e9			0.389747
$147$		0			0
$148$	2.89385e9			0.495790
$149$	2.18916e9	−	3.79173e9i	0.363864	−	0.630231i	−0.624729	−	0.780841i	$-0.714791\pi$
$149$	2.18916e9	−	3.79173e9i	0.363864	−	0.630231i	0.988593	+	0.150611i	$0.0481240\pi$
$150$	−1.90134e9	−	3.29322e9i	−0.306655	−	0.531141i
$151$	1.34682e9	+	2.33277e9i	0.210821	+	0.365153i	0.951972	−	0.306186i	$-0.0990529\pi$
$151$	1.34682e9	+	2.33277e9i	0.210821	+	0.365153i	−0.741151	+	0.671339i	$0.765720\pi$
$152$	−8.04581e8	+	1.39358e9i	−0.122257	+	0.211755i
$153$	8.17943e8			0.120673
$154$		0			0
$155$	1.85971e10			2.58793
$156$	−8.71925e7	+	1.51022e8i	−0.0117874	+	0.0204164i
$157$	6.65221e8	+	1.15220e9i	0.0873810	+	0.151348i	0.906403	−	0.422413i	$-0.138817\pi$
$157$	6.65221e8	+	1.15220e9i	0.0873810	+	0.151348i	−0.819022	+	0.573762i	$0.805484\pi$
$158$	3.26885e9	+	5.66181e9i	0.417290	+	0.722768i
$159$	−5.77997e9	+	1.00112e10i	−0.717197	+	1.24222i
$160$	1.16265e10			1.40251
$161$		0			0
$162$	−6.36401e9			−0.725961
$163$	1.78047e9	−	3.08387e9i	0.197556	−	0.342177i	−0.750179	−	0.661234i	$-0.770033\pi$
$163$	1.78047e9	−	3.08387e9i	0.197556	−	0.342177i	0.947736	+	0.319057i	$0.103366\pi$
$164$	2.21011e9	+	3.82802e9i	0.238570	+	0.413216i
$165$	1.41665e10	+	2.45371e10i	1.48794	+	2.57719i
$166$	5.55532e8	−	9.62210e8i	0.0567836	−	0.0983521i
$167$	−1.04285e10			−1.03752			−0.518762	−	0.854919i	$-0.673607\pi$
$167$	−1.04285e10			−1.03752			−0.518762	+	0.854919i	$0.673607\pi$
$168$		0			0
$169$	−1.05943e10			−0.999034
$170$	−1.49589e9	+	2.59096e9i	−0.137366	+	0.237926i
$171$	5.00092e8	+	8.66184e8i	0.0447267	+	0.0774690i
$172$	−4.96157e9	−	8.59369e9i	−0.432256	−	0.748690i
$173$	−1.02358e10	+	1.77290e10i	−0.868793	+	1.50479i	−0.00556121	+	0.999985i	$0.501770\pi$
$173$	−1.02358e10	+	1.77290e10i	−0.868793	+	1.50479i	−0.863231	+	0.504808i	$0.831563\pi$
$174$	−3.12066e9			−0.258092
$175$		0			0
$176$	−1.78773e9			−0.140442
$177$	−5.23254e8	+	9.06302e8i	−0.0400712	+	0.0694054i
$178$	−1.39007e7	−	2.40768e7i	−0.00103788	−	0.00179766i
$179$	−2.73353e9	−	4.73461e9i	−0.199014	−	0.344703i	0.749195	−	0.662350i	$-0.230441\pi$
$179$	−2.73353e9	−	4.73461e9i	−0.199014	−	0.344703i	−0.948209	+	0.317647i	$0.897107\pi$
$180$	2.25045e9	−	3.89789e9i	0.159787	−	0.276760i
$181$	−2.11628e9			−0.146561			−0.0732807	−	0.997311i	$-0.523347\pi$
$181$	−2.11628e9			−0.146561			−0.0732807	+	0.997311i	$0.523347\pi$
$182$		0			0
$183$	2.76481e10			1.82236
$184$	7.19528e9	−	1.24626e10i	0.462773	−	0.801546i
$185$	8.33984e9	+	1.44450e10i	0.523462	+	0.906662i
$186$	−1.05618e10	−	1.82936e10i	−0.647040	−	1.12071i
$187$	5.25389e9	−	9.10000e9i	0.314191	−	0.544194i
$188$	3.60068e9			0.210220
$189$		0			0
$190$	−3.65836e9			−0.203655
$191$	−8.62104e9	+	1.49321e10i	−0.468715	+	0.811839i	−0.999361	−	0.0357551i	$-0.988616\pi$
$191$	−8.62104e9	+	1.49321e10i	−0.468715	+	0.811839i	0.530645	+	0.847594i	$0.321950\pi$
$192$	−5.77387e9	−	1.00006e10i	−0.306628	−	0.531095i
$193$	−1.01015e10	−	1.74963e10i	−0.524055	−	0.907691i	−0.999608	−	0.0280032i	$-0.991085\pi$
$193$	−1.01015e10	−	1.74963e10i	−0.524055	−	0.907691i	0.475552	−	0.879687i	$-0.342248\pi$
$194$	2.11023e9	−	3.65502e9i	0.106960	−	0.185260i
$195$	−1.00513e9			−0.0497812
$196$		0			0
$197$	−2.22592e10			−1.05296			−0.526481	−	0.850187i	$-0.676489\pi$
$197$	−2.22592e10			−1.05296			−0.526481	+	0.850187i	$0.676489\pi$
$198$	4.23082e9	−	7.32800e9i	0.195628	−	0.338838i
$199$	−8.52940e9	−	1.47733e10i	−0.385549	−	0.667790i	0.606296	−	0.795239i	$-0.292655\pi$
$199$	−8.52940e9	−	1.47733e10i	−0.385549	−	0.667790i	−0.991845	+	0.127449i	$0.959321\pi$
$200$	9.83736e9	+	1.70388e10i	0.434754	+	0.753016i
$201$	9.50060e9	−	1.64555e10i	0.410553	−	0.711098i
$202$	−7.68029e9			−0.324561
$203$		0			0
$204$	−6.34862e9			−0.256651
$205$	−1.27387e10	+	2.20641e10i	−0.503771	+	0.872557i
$206$	1.01455e10	+	1.75725e10i	0.392527	+	0.679877i
$207$	−4.47227e9	−	7.74619e9i	−0.169302	−	0.293239i
$208$	3.17104e7	−	5.49239e7i	0.00117467	−	0.00203459i
$209$	1.28489e10			0.465810
$210$		0			0
$211$	−3.19873e10			−1.11098			−0.555490	−	0.831523i	$-0.687469\pi$
$211$	−3.19873e10			−1.11098			−0.555490	+	0.831523i	$0.687469\pi$
$212$	1.17956e10	−	2.04305e10i	0.401058	−	0.694653i
$213$	−1.18063e10	−	2.04492e10i	−0.393013	−	0.680719i
$214$	1.34852e9	+	2.33571e9i	0.0439537	+	0.0761300i
$215$	2.85977e10	−	4.95327e10i	0.912763	−	1.58095i
$216$	2.33734e10			0.730599
$217$		0			0
$218$	−1.16766e10			−0.350157
$219$	−1.30858e10	+	2.26653e10i	−0.384417	+	0.665830i
$220$	−2.89105e10	−	5.00745e10i	−0.832059	−	1.44117i
$221$	1.86384e8	+	3.22827e8i	0.00525586	+	0.00910342i
$222$	9.47289e9	−	1.64075e10i	0.261754	−	0.453372i
$223$	−2.30967e10			−0.625428			−0.312714	−	0.949847i	$-0.601238\pi$
$223$	−2.30967e10			−0.625428			−0.312714	+	0.949847i	$0.601238\pi$
$224$		0			0
$225$	1.22289e10			0.318102
$226$	−1.02179e10	+	1.76980e10i	−0.260540	+	0.451269i
$227$	1.15447e10	+	1.99960e10i	0.288580	+	0.499836i	0.973471	−	0.228810i	$-0.0734835\pi$
$227$	1.15447e10	+	1.99960e10i	0.288580	+	0.499836i	−0.684891	+	0.728646i	$0.740150\pi$
$228$	−3.88156e9	−	6.72305e9i	−0.0951260	−	0.164763i
$229$	−2.12748e10	+	3.68490e10i	−0.511218	+	0.885455i	0.488698	+	0.872453i	$0.337472\pi$
$229$	−2.12748e10	+	3.68490e10i	−0.511218	+	0.885455i	−0.999915	+	0.0130017i	$0.995861\pi$
$230$	3.27164e10			0.770885
$231$		0			0
$232$	1.61460e10			0.365905
$233$	6.33397e9	−	1.09708e10i	0.140791	−	0.243857i	−0.787004	−	0.616948i	$-0.788369\pi$
$233$	6.33397e9	−	1.09708e10i	0.140791	−	0.243857i	0.927795	+	0.373091i	$0.121702\pi$
$234$	1.50090e8	+	2.59964e8i	0.00327252	+	0.00566816i
$235$	1.03769e10	+	1.79733e10i	0.221953	+	0.384434i
$236$	1.06784e9	−	1.84955e9i	0.0224079	−	0.0388117i
$237$	−7.99624e10			−1.64633
$238$		0			0
$239$	6.37875e10			1.26458			0.632289	−	0.774733i	$-0.282116\pi$
$239$	6.37875e10			1.26458			0.632289	+	0.774733i	$0.282116\pi$
$240$	−3.11282e9	+	5.39156e9i	−0.0605624	+	0.104897i
$241$	1.45802e10	+	2.52537e10i	0.278412	+	0.482223i	0.970990	−	0.239119i	$-0.0768587\pi$
$241$	1.45802e10	+	2.52537e10i	0.278412	+	0.482223i	−0.692579	+	0.721342i	$0.743525\pi$
$242$	−3.85996e10	−	6.68565e10i	−0.723459	−	1.25307i
$243$	1.85559e10	−	3.21398e10i	0.341393	−	0.591309i
$244$	−5.64232e10			−1.01907
$245$		0			0
$246$	2.89388e10			0.503816
$247$	−2.27911e8	+	3.94753e8i	−0.00389609	+	0.00674823i
$248$	5.46459e10	+	9.46494e10i	0.917328	+	1.58886i
$249$	6.79470e9	+	1.17688e10i	0.112014	+	0.194014i
$250$	2.71509e9	−	4.70268e9i	0.0439597	−	0.0761404i
$251$	6.28939e10			1.00018			0.500088	−	0.865974i	$-0.333301\pi$
$251$	6.28939e10			1.00018			0.500088	+	0.865974i	$0.333301\pi$
$252$		0			0
$253$	−1.14907e11			−1.76320
$254$	5.82500e9	−	1.00892e10i	0.0878100	−	0.152091i
$255$	−1.82962e10	−	3.16900e10i	−0.270976	−	0.469344i
$256$	3.24712e10	+	5.62419e10i	0.472519	+	0.818427i
$257$	−5.72402e10	+	9.91429e10i	−0.818469	+	1.41763i	0.0883418	+	0.996090i	$0.471843\pi$
$257$	−5.72402e10	+	9.91429e10i	−0.818469	+	1.41763i	−0.906810	+	0.421539i	$0.861490\pi$
$258$	−6.49660e10			−0.912845
$259$		0			0
$260$	2.05123e9			0.0278378
$261$	5.01780e9	−	8.69109e9i	0.0669316	−	0.115929i
$262$	−1.49910e10	−	2.59651e10i	−0.196551	−	0.340436i
$263$	−7.03523e9	−	1.21854e10i	−0.0906728	−	0.157050i	0.817122	−	0.576465i	$-0.195568\pi$
$263$	−7.03523e9	−	1.21854e10i	−0.0906728	−	0.157050i	−0.907794	+	0.419415i	$0.862235\pi$
$264$	−8.32541e10	+	1.44200e11i	−1.05484	+	1.82704i
$265$	1.35975e11			1.69377
$266$		0			0
$267$	3.40038e8			0.00409475
$268$	−1.93885e10	+	3.35819e10i	−0.229582	+	0.397648i
$269$	−4.19572e10	−	7.26719e10i	−0.488563	−	0.846216i	0.511350	−	0.859372i	$-0.329146\pi$
$269$	−4.19572e10	−	7.26719e10i	−0.488563	−	0.846216i	−0.999913	+	0.0131560i	$0.995812\pi$
$270$	2.65692e10	+	4.60192e10i	0.304257	+	0.526989i
$271$	−9.92007e9	+	1.71821e10i	−0.111726	+	0.193514i	−0.916466	−	0.400112i	$-0.868971\pi$
$271$	−9.92007e9	+	1.71821e10i	−0.111726	+	0.193514i	0.804740	+	0.593627i	$0.202304\pi$
$272$	2.30888e9			0.0255765
$273$		0			0
$274$	5.55995e10			0.595927
$275$	7.85499e10	−	1.36052e11i	0.828225	−	1.43453i
$276$	3.47123e10	+	6.01235e10i	0.360075	+	0.623668i
$277$	3.58956e10	+	6.21729e10i	0.366338	+	0.634516i	0.988990	−	0.147983i	$-0.0472781\pi$
$277$	3.58956e10	+	6.21729e10i	0.366338	+	0.634516i	−0.622652	+	0.782499i	$0.713945\pi$
$278$	4.03082e10	−	6.98158e10i	0.404754	−	0.701055i
$279$	6.79308e10			0.671194
$280$		0			0
$281$	1.02853e11			0.984101			0.492050	−	0.870567i	$-0.336248\pi$
$281$	1.02853e11			0.984101			0.492050	+	0.870567i	$0.336248\pi$
$282$	1.17867e10	−	2.04151e10i	0.110986	−	0.192234i
$283$	2.76441e10	+	4.78810e10i	0.256191	+	0.443736i	0.965218	−	0.261445i	$-0.0841990\pi$
$283$	2.76441e10	+	4.78810e10i	0.256191	+	0.443736i	−0.709027	+	0.705181i	$0.750866\pi$
$284$	2.40940e10	+	4.17320e10i	0.219774	+	0.380660i
$285$	2.23727e10	−	3.87506e10i	0.200870	−	0.347918i
$286$	3.85630e9			0.0340819
$287$		0			0
$288$	4.24688e10			0.363750
$289$	5.25085e10	−	9.09474e10i	0.442781	−	0.766920i
$290$	1.83536e10	+	3.17894e10i	0.152381	+	0.263931i
$291$	2.58101e10	+	4.47044e10i	0.210995	+	0.365453i
$292$	2.67051e10	−	4.62546e10i	0.214967	−	0.372334i
$293$	1.05721e11			0.838028			0.419014	−	0.907980i	$-0.362376\pi$
$293$	1.05721e11			0.838028			0.419014	+	0.907980i	$0.362376\pi$
$294$		0			0
$295$	1.23097e10			0.0946343
$296$	−4.90118e10	+	8.48909e10i	−0.371097	+	0.642760i
$297$	−9.33164e10	−	1.61629e11i	−0.695912	−	1.20535i
$298$	2.92487e10	+	5.06603e10i	0.214849	+	0.372130i
$299$	2.03818e9	−	3.53024e9i	0.0147477	−	0.0255437i
$300$	−9.49171e10			−0.676548
$301$		0			0
$302$	−3.59891e10			−0.248966
$303$	4.69687e10	−	8.13521e10i	0.320123	−	0.554469i
$304$	1.41165e9	+	2.44505e9i	0.00947974	+	0.0164194i
$305$	−1.62607e11	−	2.81644e11i	−1.07595	−	1.86359i
$306$	−5.46416e9	+	9.46420e9i	−0.0356268	+	0.0617074i
$307$	−8.10064e10			−0.520471			−0.260236	−	0.965545i	$-0.583800\pi$
$307$	−8.10064e10			−0.520471			−0.260236	+	0.965545i	$0.583800\pi$
$308$		0			0
$309$	−2.48178e11			−1.54864
$310$	−1.24235e11	+	2.15182e11i	−0.764041	+	1.32336i
$311$	1.59217e11	+	2.75772e11i	0.965091	+	1.67159i	0.709369	+	0.704837i	$0.248980\pi$
$311$	1.59217e11	+	2.75772e11i	0.965091	+	1.67159i	0.255722	+	0.966750i	$0.417687\pi$
$312$	−2.95348e9	−	5.11558e9i	−0.0176457	−	0.0305632i
$313$	−6.44379e10	+	1.11610e11i	−0.379483	+	0.657283i	−0.990987	−	0.133958i	$-0.957231\pi$
$313$	−6.44379e10	+	1.11610e11i	−0.379483	+	0.657283i	0.611504	+	0.791241i	$0.290565\pi$
$314$	−1.77757e10			−0.103191
$315$		0			0
$316$	1.63185e11			0.920635
$317$	3.72361e10	−	6.44948e10i	0.207108	−	0.358722i	−0.743694	−	0.668520i	$-0.766928\pi$
$317$	3.72361e10	−	6.44948e10i	0.207108	−	0.358722i	0.950802	+	0.309798i	$0.100261\pi$
$318$	−7.72245e10	−	1.33757e11i	−0.423480	−	0.733490i
$319$	−6.44616e10	−	1.11651e11i	−0.348532	−	0.603676i
$320$	−6.79160e10	+	1.17634e11i	−0.362074	+	0.627131i
$321$	−3.29874e10			−0.173411
$322$		0			0
$323$	−1.65945e10			−0.0848309
$324$	−7.94246e10	+	1.37567e11i	−0.400408	+	0.693526i
$325$	2.78660e9	+	4.82652e9i	0.0138548	+	0.0239971i
$326$	2.37884e10	+	4.12027e10i	0.116650	+	0.202044i
$327$	7.14082e10	−	1.23683e11i	0.345369	−	0.598197i
$328$	−1.49726e11			−0.714276
$329$		0			0
$330$	−3.78550e11			−1.75715
$331$	−1.41920e11	+	2.45813e11i	−0.649857	+	1.12559i	0.333300	+	0.942821i	$0.391838\pi$
$331$	−1.41920e11	+	2.45813e11i	−0.649857	+	1.12559i	−0.983157	+	0.182764i	$0.941495\pi$
$332$	−1.38664e10	−	2.40173e10i	−0.0626386	−	0.108493i
$333$	3.04635e10	+	5.27644e10i	0.135763	+	0.235148i
$334$	6.96662e10	−	1.20665e11i	0.306311	−	0.530547i
$335$	−2.23505e11			−0.969583
$336$		0			0
$337$	−5.61414e9			−0.0237109			−0.0118555	−	0.999930i	$-0.503774\pi$
$337$	−5.61414e9			−0.0237109			−0.0118555	+	0.999930i	$0.503774\pi$
$338$	7.07735e10	−	1.22583e11i	0.294948	−	0.510865i
$339$	−1.24975e11	−	2.16463e11i	−0.513955	−	0.890197i
$340$	3.73383e10	+	6.46719e10i	0.151530	+	0.262458i
$341$	4.36339e11	−	7.55762e11i	1.74755	−	3.02685i
$342$	−1.33632e10			−0.0528192
$343$		0			0
$344$	3.36128e11			1.29417
$345$	−2.00076e11	+	3.46542e11i	−0.760343	+	1.31695i
$346$	−1.36758e11	−	2.36872e11i	−0.512993	−	0.888529i
$347$	−1.69923e11	−	2.94315e11i	−0.629171	−	1.08976i	−0.987718	−	0.156245i	$-0.950061\pi$
$347$	−1.69923e11	−	2.94315e11i	−0.629171	−	1.08976i	0.358547	−	0.933512i	$-0.383272\pi$
$348$	−3.89466e10	+	6.74576e10i	−0.142352	+	0.246561i
$349$	3.46718e10			0.125101			0.0625506	−	0.998042i	$-0.480077\pi$
$349$	3.46718e10			0.125101			0.0625506	+	0.998042i	$0.480077\pi$
$350$		0			0
$351$	6.62089e9			0.0232828
$352$	2.72789e11	−	4.72485e11i	0.947077	−	1.64039i
$353$	1.73450e11	+	3.00424e11i	0.594550	+	1.02979i	0.993610	+	0.112866i	$0.0360031\pi$
$353$	1.73450e11	+	3.00424e11i	0.594550	+	1.02979i	−0.399060	+	0.916925i	$0.630664\pi$
$354$	−6.99105e9	−	1.21088e10i	−0.0236607	−	0.0409815i
$355$	−1.38874e11	+	2.40537e11i	−0.464080	+	0.803811i
$356$	−6.93939e8			−0.00228979
$357$		0			0
$358$	7.30438e10			0.235023
$359$	1.25506e11	−	2.17382e11i	0.398785	−	0.690715i	−0.594792	−	0.803880i	$-0.702765\pi$
$359$	1.25506e11	−	2.17382e11i	0.398785	−	0.690715i	0.993576	+	0.113165i	$0.0360988\pi$
$360$	7.62296e10	+	1.32034e11i	0.239201	+	0.414308i
$361$	1.51198e11	+	2.61882e11i	0.468558	+	0.811566i
$362$	1.41375e10	−	2.44869e10i	0.0432698	−	0.0749455i
$363$	9.44221e11			2.85426
$364$		0			0
$365$	3.07848e11			0.907859
$366$	−1.84699e11	+	3.19908e11i	−0.538022	+	0.931881i
$367$	−2.39936e11	−	4.15581e11i	−0.690394	−	1.19580i	−0.971709	−	0.236183i	$-0.924104\pi$
$367$	−2.39936e11	−	4.15581e11i	−0.690394	−	1.19580i	0.281314	−	0.959616i	$-0.409230\pi$
$368$	−1.26243e10	−	2.18658e10i	−0.0358831	−	0.0621514i
$369$	−4.65316e10	+	8.05951e10i	−0.130656	+	0.226303i
$370$	−2.22853e11			−0.618173
$371$		0			0
$372$	−5.27258e11			−1.42751
$373$	9.23970e10	−	1.60036e11i	0.247154	−	0.428084i	−0.715581	−	0.698530i	$-0.753838\pi$
$373$	9.23970e10	−	1.60036e11i	0.247154	−	0.428084i	0.962735	+	0.270446i	$0.0871713\pi$
$374$	7.01957e10	+	1.21583e11i	0.185519	+	0.321328i
$375$	3.32082e10	+	5.75183e10i	0.0867171	+	0.150198i
$376$	−6.09831e10	+	1.05626e11i	−0.157349	+	0.272536i
$377$	4.57361e9			0.0116607
$378$		0			0
$379$	−7.08908e11			−1.76487			−0.882437	−	0.470431i	$-0.844098\pi$
$379$	−7.08908e11			−1.76487			−0.882437	+	0.470431i	$0.844098\pi$
$380$	−4.56574e10	+	7.90809e10i	−0.112327	+	0.194556i
$381$	7.12453e10	+	1.23401e11i	0.173218	+	0.300023i
$382$	−1.15183e11	−	1.99503e11i	−0.276761	−	0.479364i
$383$	−6.18945e10	+	1.07204e11i	−0.146980	+	0.254576i	−0.930110	−	0.367282i	$-0.880289\pi$
$383$	−6.18945e10	+	1.07204e11i	−0.146980	+	0.254576i	0.783130	+	0.621858i	$0.213622\pi$
$384$	−3.51785e11			−0.825633
$385$		0			0
$386$	2.69926e11			0.618874
$387$	1.04461e11	−	1.80932e11i	0.236731	−	0.410029i
$388$	−5.26724e10	−	9.12313e10i	−0.117989	−	0.204362i
$389$	1.48985e11	+	2.58050e11i	0.329891	+	0.571388i	0.982490	−	0.186315i	$-0.0596547\pi$
$389$	1.48985e11	+	2.58050e11i	0.329891	+	0.571388i	−0.652599	+	0.757704i	$0.726321\pi$
$390$	6.71462e9	−	1.16301e10i	0.0146971	−	0.0254561i
$391$	1.48403e11			0.321106
$392$		0			0
$393$	3.66708e11			0.775451
$394$	1.48700e11	−	2.57556e11i	0.310869	−	0.538441i
$395$	4.70285e11	+	8.14557e11i	0.972018	+	1.68358i
$396$	−1.05604e11	−	1.82911e11i	−0.215800	−	0.373776i
$397$	−2.66713e11	+	4.61960e11i	−0.538873	+	0.933356i	0.460092	+	0.887871i	$0.347817\pi$
$397$	−2.66713e11	+	4.61960e11i	−0.538873	+	0.933356i	−0.998965	+	0.0454846i	$0.985517\pi$
$398$	2.27918e11			0.455307
$399$		0			0
$400$	3.45196e10			0.0674212
$401$	−2.07820e11	+	3.59954e11i	−0.401363	+	0.695181i	−0.993891	−	0.110369i	$-0.964797\pi$
$401$	−2.07820e11	+	3.59954e11i	−0.401363	+	0.695181i	0.592528	+	0.805550i	$0.298130\pi$
$402$	1.26935e11	+	2.19858e11i	0.242418	+	0.419879i
$403$	1.54794e10	+	2.68110e10i	0.0292335	+	0.0506338i
$404$	−9.58521e10	+	1.66021e11i	−0.179013	+	0.310060i
$405$	−9.15581e11			−1.69102
$406$		0			0
$407$	7.82704e11			1.41391
$408$	1.07524e11	−	1.86237e11i	0.192103	−	0.332732i
$409$	−5.39891e11	−	9.35118e11i	−0.954006	−	1.65239i	−0.736627	−	0.676299i	$-0.763583\pi$
$409$	−5.39891e11	−	9.35118e11i	−0.954006	−	1.65239i	−0.217379	−	0.976087i	$-0.569751\pi$
$410$	−1.70198e11	−	2.94792e11i	−0.297460	−	0.515215i
$411$	−3.40018e11	+	5.88928e11i	−0.587778	+	1.01806i
$412$	5.06473e11			0.866002
$413$		0			0
$414$	1.19505e11			0.199934
$415$	7.99237e10	−	1.38432e11i	0.132269	−	0.229097i
$416$	9.67733e9	+	1.67616e10i	0.0158429	+	0.0274408i
$417$	4.93008e11	+	8.53914e11i	0.798439	+	1.38294i
$418$	−8.58355e10	+	1.48671e11i	−0.137522	+	0.238196i
$419$	−2.20998e11			−0.350289			−0.175144	−	0.984543i	$-0.556039\pi$
$419$	−2.20998e11			−0.350289			−0.175144	+	0.984543i	$0.556039\pi$
$420$		0			0
$421$	3.47478e11			0.539086			0.269543	−	0.962988i	$-0.413127\pi$
$421$	3.47478e11			0.539086			0.269543	+	0.962988i	$0.413127\pi$
$422$	2.13687e11	−	3.70116e11i	0.327998	−	0.568109i
$423$	3.79043e10	+	6.56522e10i	0.0575648	+	0.0997052i
$424$	3.99552e11	+	6.92045e11i	0.600381	+	1.03989i
$425$	−1.01448e11	+	1.75713e11i	−0.150832	+	0.261249i
$426$	3.15483e11			0.464122
$427$		0			0
$428$	6.73196e10			0.0969716
$429$	−2.35831e10	+	4.08472e10i	−0.0336158	+	0.0582243i
$430$	3.82086e11	+	6.61792e11i	0.538956	+	0.933499i
$431$	−6.17869e10	−	1.07018e11i	−0.0862479	−	0.149386i	0.819674	−	0.572830i	$-0.194154\pi$
$431$	−6.17869e10	−	1.07018e11i	−0.0862479	−	0.149386i	−0.905922	+	0.423444i	$0.860821\pi$
$432$	2.05045e10	−	3.55148e10i	0.0283251	−	0.0490606i
$433$	−7.27679e11			−0.994820			−0.497410	−	0.867516i	$-0.665716\pi$
$433$	−7.27679e11			−0.994820			−0.497410	+	0.867516i	$0.665716\pi$
$434$		0			0
$435$	−4.48964e11			−0.601188
$436$	−1.45728e11	+	2.52408e11i	−0.193131	+	0.334513i
$437$	9.07340e10	+	1.57156e11i	0.119015	+	0.206141i
$438$	−1.74836e11	−	3.02825e11i	−0.226985	−	0.393150i
$439$	2.92983e11	−	5.07461e11i	0.376489	−	0.652097i	−0.614060	−	0.789259i	$-0.710465\pi$
$439$	2.92983e11	−	5.07461e11i	0.376489	−	0.652097i	0.990549	+	0.137162i	$0.0437981\pi$
$440$	1.95858e12			2.49117
$441$		0			0
$442$	−4.98045e9			−0.00620681
$443$	1.05773e11	−	1.83204e11i	0.130484	−	0.226006i	−0.793379	−	0.608728i	$-0.791680\pi$
$443$	1.05773e11	−	1.83204e11i	0.130484	−	0.226006i	0.923863	+	0.382722i	$0.125013\pi$
$444$	−2.36448e11	−	4.09541e11i	−0.288744	−	0.500120i
$445$	−1.99988e9	−	3.46389e9i	−0.00241759	−	0.00418739i
$446$	1.54294e11	−	2.67245e11i	0.184647	−	0.319818i
$447$	−7.15480e11			−0.847645
$448$		0			0
$449$	−9.21048e11			−1.06948			−0.534741	−	0.845016i	$-0.679591\pi$
$449$	−9.21048e11			−1.06948			−0.534741	+	0.845016i	$0.679591\pi$
$450$	−8.16936e10	+	1.41497e11i	−0.0939143	+	0.162664i
$451$	5.97772e11	+	1.03537e12i	0.680363	+	1.17842i
$452$	2.55045e11	+	4.41751e11i	0.287405	+	0.497800i
$453$	2.20090e11	−	3.81208e11i	0.245561	−	0.425324i
$454$	−3.08491e11			−0.340794
$455$		0			0
$456$	2.62961e11			0.284806
$457$	−4.05592e11	+	7.02506e11i	−0.434977	+	0.753403i	−0.997294	−	0.0735191i	$-0.976577\pi$
$457$	−4.05592e11	+	7.02506e11i	−0.434977	+	0.753403i	0.562316	+	0.826922i	$0.309910\pi$
$458$	−2.84247e11	−	4.92330e11i	−0.301857	−	0.522831i
$459$	1.20519e11	+	2.08746e11i	0.126736	+	0.219513i
$460$	4.08309e11	−	7.07212e11i	0.425186	−	0.736444i
$461$	−1.90069e11			−0.196001			−0.0980004	−	0.995186i	$-0.531245\pi$
$461$	−1.90069e11			−0.196001			−0.0980004	+	0.995186i	$0.531245\pi$
$462$		0			0
$463$	4.76945e11			0.482341			0.241170	−	0.970483i	$-0.422469\pi$
$463$	4.76945e11			0.482341			0.241170	+	0.970483i	$0.422469\pi$
$464$	1.41642e10	−	2.45331e10i	0.0141860	−	0.0245709i
$465$	−1.51952e12	−	2.63188e12i	−1.50719	−	2.61052i
$466$	8.46264e10	+	1.46577e11i	0.0831322	+	0.143989i
$467$	−5.31958e11	+	9.21379e11i	−0.517549	+	0.896422i	0.482243	+	0.876038i	$0.339822\pi$
$467$	−5.31958e11	+	9.21379e11i	−0.517549	+	0.896422i	−0.999792	+	0.0203841i	$0.993511\pi$
$468$	7.49268e9			0.00721990
$469$		0			0
$470$	−2.77285e11			−0.262111
$471$	1.08707e11	−	1.88286e11i	0.101780	−	0.176288i
$472$	3.61710e10	+	6.26500e10i	0.0335445	+	0.0581008i
$473$	−1.34196e12	−	2.32435e12i	−1.23272	−	2.13514i
$474$	5.34178e11	−	9.25223e11i	0.486053	−	0.841868i
$475$	−2.48102e11			−0.223619
$476$		0			0
$477$	4.96687e11			0.439289
$478$	−4.26124e11	+	7.38068e11i	−0.373345	+	0.646653i
$479$	4.21707e11	+	7.30419e11i	0.366017	+	0.633960i	0.988939	−	0.148324i	$-0.0473878\pi$
$479$	4.21707e11	+	7.30419e11i	0.366017	+	0.633960i	−0.622922	+	0.782284i	$0.714054\pi$
$480$	−9.49966e11	−	1.64539e12i	−0.816812	−	1.41476i
$481$	−1.38834e10	+	2.40468e10i	−0.0118261	+	0.0204835i
$482$	−3.89605e11			−0.328785
$483$		0			0
$484$	−1.92694e12			−1.59611
$485$	3.03595e11	−	5.25842e11i	0.249148	−	0.431537i
$486$	2.47920e11	+	4.29411e11i	0.201581	+	0.349148i
$487$	−5.76008e11	−	9.97675e11i	−0.464032	−	0.803728i	0.535125	−	0.844773i	$-0.320265\pi$
$487$	−5.76008e11	−	9.97675e11i	−0.464032	−	0.803728i	−0.999157	+	0.0410453i	$0.986931\pi$
$488$	9.55615e11	−	1.65517e12i	0.762770	−	1.32116i
$489$	−5.81910e11			−0.460220
$490$		0			0
$491$	−9.68703e11			−0.752184			−0.376092	−	0.926582i	$-0.622732\pi$
$491$	−9.68703e11			−0.752184			−0.376092	+	0.926582i	$0.622732\pi$
$492$	3.61164e11	−	6.25554e11i	0.277883	−	0.481307i
$493$	8.32530e10	+	1.44198e11i	0.0634729	+	0.109938i
$494$	−3.04506e9	−	5.27419e9i	−0.00230051	−	0.00398460i
$495$	6.08682e11	−	1.05427e12i	0.455688	−	0.789274i
$496$	1.91754e11			0.142258
$497$		0			0
$498$	−1.81564e11			−0.132281
$499$	−1.31410e12	+	2.27609e12i	−0.948805	+	1.64338i	−0.200857	+	0.979621i	$0.564373\pi$
$499$	−1.31410e12	+	2.27609e12i	−0.948805	+	1.64338i	−0.747948	+	0.663758i	$0.768961\pi$
$500$	−6.77702e10	−	1.17381e11i	−0.0484924	−	0.0839913i
$501$	8.52085e11	+	1.47585e12i	0.604245	+	1.04658i
$502$	−4.20154e11	+	7.27728e11i	−0.295285	+	0.511449i
$503$	3.95070e11			0.275181			0.137590	−	0.990489i	$-0.456064\pi$
$503$	3.95070e11			0.275181			0.137590	+	0.990489i	$0.456064\pi$
$504$		0			0
$505$	−1.10495e12			−0.756019
$506$	7.67618e11	−	1.32955e12i	0.520556	−	0.901630i
$507$	8.65628e11	+	1.49931e12i	0.581829	+	1.00776i
$508$	−1.45395e11	−	2.51832e11i	−0.0968641	−	0.167774i
$509$	−3.32078e11	+	5.75177e11i	−0.219286	+	0.379814i	−0.954590	−	0.297923i	$-0.903706\pi$
$509$	−3.32078e11	+	5.75177e11i	−0.219286	+	0.379814i	0.735304	+	0.677737i	$0.237039\pi$
$510$	4.88901e11			0.320004
$511$		0			0
$512$	2.34512e11			0.150817
$513$	−1.47371e11	+	2.55255e11i	−0.0939474	+	0.162722i
$514$	−7.64770e11	−	1.32462e12i	−0.483278	−	0.837062i
$515$	1.45961e12	+	2.52813e12i	0.914336	+	1.58368i
$516$	−8.10793e11	+	1.40433e12i	−0.503485	+	0.872061i
$517$	9.73882e11			0.599513
$518$		0			0
$519$	3.34537e12			2.02391
$520$	−3.47408e10	+	6.01728e10i	−0.0208365	+	0.0360898i
$521$	−2.61383e11	−	4.52729e11i	−0.155420	−	0.269196i	0.777792	−	0.628522i	$-0.216340\pi$
$521$	−2.61383e11	−	4.52729e11i	−0.155420	−	0.269196i	−0.933212	+	0.359326i	$0.883007\pi$
$522$	6.70415e10	+	1.16119e11i	0.0395209	+	0.0684522i
$523$	1.54568e12	−	2.67719e12i	0.903360	−	1.56467i	0.0802570	−	0.996774i	$-0.474426\pi$
$523$	1.54568e12	−	2.67719e12i	0.903360	−	1.56467i	0.823103	−	0.567892i	$-0.192241\pi$
$524$	−7.48366e11			−0.433634
$525$		0			0
$526$	1.87991e11			0.107078
$527$	−5.63538e11	+	9.76076e11i	−0.318255	+	0.551234i
$528$	1.46071e11	+	2.53002e11i	0.0817920	+	0.141668i
$529$	8.91523e10	+	1.54416e11i	0.0494974	+	0.0857319i
$530$	−9.08365e11	+	1.57334e12i	−0.500057	+	0.866124i
$531$	4.49645e10			0.0245440
$532$		0			0
$533$	−4.24125e10			−0.0227626
$534$	−2.27158e9	+	3.93449e9i	−0.00120891	+	0.00209389i
$535$	1.94010e11	+	3.36035e11i	0.102384	+	0.177334i
$536$	−6.56749e11	−	1.13752e12i	−0.343683	−	0.595276i
$537$	−4.46698e11	+	7.73704e11i	−0.231809	+	0.401504i
$538$	1.12116e12			0.576960
$539$		0			0
$540$	1.32636e12			0.671259
$541$	7.37449e11	−	1.27730e12i	0.370121	−	0.641069i	−0.619462	−	0.785026i	$-0.712649\pi$
$541$	7.37449e11	−	1.27730e12i	0.370121	−	0.641069i	0.989584	+	0.143957i	$0.0459827\pi$
$542$	−1.32539e11	−	2.29565e11i	−0.0659702	−	0.114264i
$543$	1.72916e11	+	2.99499e11i	0.0853561	+	0.147841i
$544$	−3.52311e11	+	6.10220e11i	−0.172477	+	0.298739i
$545$	−1.67990e12			−0.815642
$546$		0			0
$547$	2.12294e12			1.01390			0.506949	−	0.861976i	$-0.330773\pi$
$547$	2.12294e12			1.01390			0.506949	+	0.861976i	$0.330773\pi$
$548$	6.93897e11	−	1.20186e12i	0.328687	−	0.569302i
$549$	−5.93967e11	−	1.02878e12i	−0.279053	−	0.483334i
$550$	1.04948e12	+	1.81776e12i	0.489039	+	0.847040i
$551$	−1.01802e11	+	1.76326e11i	−0.0470515	+	0.0814957i
$552$	−2.35163e12			−1.07806
$553$		0			0
$554$	−9.59181e11			−0.432620
$555$	1.36285e12	−	2.36053e12i	0.609719	−	1.05606i
$556$	−1.00611e12	−	1.74264e12i	−0.446489	−	0.773341i
$557$	1.76428e12	+	3.05583e12i	0.776641	+	1.34518i	0.933868	+	0.357619i	$0.116411\pi$
$557$	1.76428e12	+	3.05583e12i	0.776641	+	1.34518i	−0.157227	+	0.987563i	$0.550255\pi$
$558$	−4.53803e11	+	7.86009e11i	−0.198159	+	0.343221i
$559$	9.52137e10			0.0412426
$560$		0			0
$561$	−1.71712e12			−0.731928
$562$	−6.87097e11	+	1.19009e12i	−0.290539	+	0.503228i
$563$	1.67640e12	+	2.90361e12i	0.703218	+	1.21801i	0.967331	+	0.253517i	$0.0815875\pi$
$563$	1.67640e12	+	2.90361e12i	0.703218	+	1.21801i	−0.264113	+	0.964492i	$0.585079\pi$
$564$	−2.94202e11	−	5.09572e11i	−0.122430	−	0.212056i
$565$	−1.47004e12	+	2.54618e12i	−0.606892	+	1.05117i
$566$	−7.38691e11			−0.302544
$567$		0			0
$568$	−1.63228e12			−0.658000
$569$	−1.49682e12	+	2.59257e12i	−0.598637	+	1.03687i	0.394385	+	0.918945i	$0.370958\pi$
$569$	−1.49682e12	+	2.59257e12i	−0.598637	+	1.03687i	−0.993022	+	0.117925i	$0.962376\pi$
$570$	2.98915e11	+	5.17736e11i	0.118607	+	0.205434i
$571$	−2.33634e12	−	4.04665e12i	−0.919756	−	1.59306i	−0.799785	−	0.600287i	$-0.795053\pi$
$571$	−2.33634e12	−	4.04665e12i	−0.919756	−	1.59306i	−0.119971	−	0.992777i	$-0.538280\pi$
$572$	4.81276e10	−	8.33595e10i	0.0187980	−	0.0325592i
$573$	2.81761e12			1.09190
$574$		0			0
$575$	2.21875e12			0.846453
$576$	−2.48082e11	+	4.29690e11i	−0.0939061	+	0.162650i
$577$	1.81399e12	+	3.14193e12i	0.681310	+	1.18006i	0.974581	+	0.224034i	$0.0719228\pi$
$577$	1.81399e12	+	3.14193e12i	0.681310	+	1.18006i	−0.293271	+	0.956029i	$0.594744\pi$
$578$	7.01551e11	+	1.21512e12i	0.261447	+	0.452840i
$579$	−1.65073e12	+	2.85915e12i	−0.610411	+	1.05726i
$580$	9.16232e11			0.336186
$581$		0			0
$582$	−6.89683e11			−0.249170
$583$	3.19037e12	−	5.52588e12i	1.14375	−	1.98104i
$584$	9.04585e11	+	1.56679e12i	0.321804	+	0.557381i
$585$	2.15933e10	+	3.74007e10i	0.00762286	+	0.0132032i
$586$	−7.06258e11	+	1.22327e12i	−0.247414	+	0.428533i
$587$	3.97200e12			1.38082			0.690411	−	0.723417i	$-0.257430\pi$
$587$	3.97200e12			1.38082			0.690411	+	0.723417i	$0.257430\pi$
$588$		0			0
$589$	−1.37819e12			−0.471835
$590$	−8.22332e10	+	1.42432e11i	−0.0279392	+	0.0483921i
$591$	1.81874e12	+	3.15015e12i	0.613236	+	1.06216i
$592$	8.59921e10	+	1.48943e11i	0.0287747	+	0.0498392i
$593$	−1.33718e12	+	2.31606e12i	−0.444061	+	0.769137i	−0.997986	−	0.0634297i	$-0.979796\pi$
$593$	−1.33718e12	+	2.31606e12i	−0.444061	+	0.769137i	0.553925	+	0.832567i	$0.313129\pi$
$594$	2.49355e12			0.821825
$595$		0			0
$596$	1.46013e12			0.474005
$597$	−1.39383e12	+	2.41418e12i	−0.449081	+	0.777831i
$598$	2.72316e10	+	4.71665e10i	0.00870799	+	0.0150827i
$599$	−2.42261e12	−	4.19608e12i	−0.768887	−	1.33175i	−0.938167	−	0.346184i	$-0.887477\pi$
$599$	−2.42261e12	−	4.19608e12i	−0.768887	−	1.33175i	0.169279	−	0.985568i	$-0.445856\pi$
$600$	1.60757e12	−	2.78439e12i	0.506394	−	0.877100i
$601$	−4.64764e12			−1.45311			−0.726553	−	0.687110i	$-0.758879\pi$
$601$	−4.64764e12			−1.45311			−0.726553	+	0.687110i	$0.758879\pi$
$602$		0			0
$603$	−8.16411e11			−0.251467
$604$	−4.49153e11	+	7.77956e11i	−0.137318	+	0.237842i
$605$	−5.55327e12	−	9.61855e12i	−1.68519	−	2.91884i
$606$	6.27536e11	+	1.08692e12i	0.189022	+	0.327395i
$607$	3.26224e12	−	5.65036e12i	0.975363	−	1.68938i	0.296633	−	0.954992i	$-0.404136\pi$
$607$	3.26224e12	−	5.65036e12i	0.975363	−	1.68938i	0.678731	−	0.734387i	$-0.262530\pi$
$608$	−8.61613e11			−0.255709
$609$		0			0
$610$	4.34510e12			1.27062
$611$	−1.72745e10	+	2.99203e10i	−0.00501440	+	0.00868520i
$612$	1.36388e11	+	2.36232e11i	0.0393003	+	0.0680701i
$613$	4.77268e11	+	8.26652e11i	0.136518	+	0.236456i	0.926176	−	0.377091i	$-0.123075\pi$
$613$	4.77268e11	+	8.26652e11i	0.136518	+	0.236456i	−0.789658	+	0.613547i	$0.789742\pi$
$614$	5.41152e11	−	9.37303e11i	0.153660	−	0.266148i
$615$	4.16338e12			1.17357
$616$		0			0
$617$	−4.50764e12			−1.25218			−0.626088	−	0.779752i	$-0.715345\pi$
$617$	−4.50764e12			−1.25218			−0.626088	+	0.779752i	$0.715345\pi$
$618$	1.65792e12	−	2.87160e12i	0.457209	−	0.791909i
$619$	−1.82173e12	−	3.15533e12i	−0.498742	−	0.863847i	0.501257	−	0.865298i	$-0.332871\pi$
$619$	−1.82173e12	−	3.15533e12i	−0.498742	−	0.863847i	−0.999999	+	0.00145199i	$0.999538\pi$
$620$	3.10098e12	+	5.37105e12i	0.842822	+	1.45981i
$621$	1.31793e12	−	2.28272e12i	0.355614	−	0.615942i
$622$	−4.25452e12			−1.13971
$623$		0			0
$624$	−1.03639e10			−0.00273647
$625$	2.09148e12	−	3.62255e12i	0.548269	−	0.949630i
$626$	−8.60937e11	−	1.49119e12i	−0.224072	−	0.388104i
$627$	−1.04985e12	−	1.81840e12i	−0.271284	−	0.469877i
$628$	−2.21845e11	+	3.84247e11i	−0.0569156	+	0.0985807i
$629$	−1.01087e12			−0.257495
$630$		0			0
$631$	3.61498e12			0.907766			0.453883	−	0.891061i	$-0.350038\pi$
$631$	3.61498e12			0.907766			0.453883	+	0.891061i	$0.350038\pi$
$632$	−2.76378e12	+	4.78701e12i	−0.689092	+	1.19354i
$633$	2.61359e12	+	4.52687e12i	0.647025	+	1.12068i
$634$	4.97501e11	+	8.61698e11i	0.122290	+	0.211813i
$635$	8.38034e11	−	1.45152e12i	0.204541	−	0.354275i
$636$	−3.85513e12			−0.934292
$637$		0			0
$638$	1.72251e12			0.411593
$639$	−5.07275e11	+	8.78626e11i	−0.120362	+	0.208473i
$640$	2.06896e12	+	3.58355e12i	0.487465	+	0.844313i
$641$	1.33152e12	+	2.30626e12i	0.311521	+	0.539570i	0.978692	−	0.205335i	$-0.0658283\pi$
$641$	1.33152e12	+	2.30626e12i	0.311521	+	0.539570i	−0.667171	+	0.744905i	$0.732495\pi$
$642$	2.20368e11	−	3.81688e11i	0.0511965	−	0.0886750i
$643$	4.09899e12			0.945644			0.472822	−	0.881158i	$-0.343235\pi$
$643$	4.09899e12			0.945644			0.472822	+	0.881158i	$0.343235\pi$
$644$		0			0
$645$	−9.34656e12			−2.12634
$646$	1.10858e11	−	1.92011e11i	0.0250449	−	0.0433790i
$647$	−3.05663e12	−	5.29423e12i	−0.685761	−	1.18777i	−0.973197	−	0.229973i	$-0.926136\pi$
$647$	−3.05663e12	−	5.29423e12i	−0.685761	−	1.18777i	0.287436	−	0.957800i	$-0.407197\pi$
$648$	−2.69036e12	−	4.65983e12i	−0.599408	−	1.03820i
$649$	2.88820e11	−	5.00251e11i	0.0639037	−	0.110685i
$650$	−7.44619e10			−0.0163615
$651$		0			0
$652$	1.18754e12			0.257356
$653$	−3.83135e12	+	6.63609e12i	−0.824598	+	1.42825i	0.0776274	+	0.996982i	$0.475266\pi$
$653$	−3.83135e12	+	6.63609e12i	−0.824598	+	1.42825i	−0.902226	+	0.431264i	$0.858068\pi$
$654$	9.54066e11	+	1.65249e12i	0.203929	+	0.353215i
$655$	−2.15673e12	−	3.73557e12i	−0.457836	−	0.792996i
$656$	−1.31349e11	+	2.27503e11i	−0.0276923	+	0.0479644i
$657$	1.12450e12			0.235459
$658$		0			0
$659$	−8.20110e9			−0.00169390			−0.000846950	−	1.00000i	$-0.500270\pi$
$659$	−8.20110e9			−0.00169390			−0.000846950		1.00000i	$0.500270\pi$
$660$	−4.72440e12	+	8.18291e12i	−0.969168	+	1.67865i
$661$	−1.60461e12	−	2.77927e12i	−0.326936	−	0.566270i	0.654966	−	0.755658i	$-0.272683\pi$
$661$	−1.60461e12	−	2.77927e12i	−0.326936	−	0.566270i	−0.981902	+	0.189388i	$0.939350\pi$
$662$	−1.89615e12	−	3.28424e12i	−0.383719	−	0.664620i
$663$	3.04579e10	−	5.27546e10i	0.00612194	−	0.0106035i
$664$	9.39395e11			0.187539
$665$		0			0
$666$	−8.14030e11			−0.160327
$667$	9.10404e11	−	1.57687e12i	0.178102	−	0.308481i
$668$	−1.73891e12	−	3.01188e12i	−0.337895	−	0.585252i
$669$	1.88717e12	+	3.26867e12i	0.364244	+	0.630889i
$670$	1.49309e12	−	2.58611e12i	0.286253	−	0.495805i
$671$	−1.52609e13			−2.90622
$672$		0			0
$673$	−4.91229e12			−0.923031			−0.461515	−	0.887132i	$-0.652694\pi$
$673$	−4.91229e12			−0.923031			−0.461515	+	0.887132i	$0.652694\pi$
$674$	3.75045e10	−	6.49596e10i	0.00700025	−	0.0121248i
$675$	1.80186e12	+	3.12092e12i	0.334083	+	0.578649i
$676$	−1.76655e12	−	3.05975e12i	−0.325360	−	0.563541i
$677$	1.55955e12	−	2.70122e12i	0.285332	−	0.494209i	−0.687358	−	0.726319i	$-0.741230\pi$
$677$	1.55955e12	−	2.70122e12i	0.285332	−	0.494209i	0.972690	+	0.232110i	$0.0745628\pi$
$678$	3.33952e12			0.606946
$679$		0			0
$680$	−2.52953e12			−0.453680
$681$	1.88657e12	−	3.26764e12i	0.336133	−	0.582200i
$682$	5.82981e12	+	1.00975e13i	1.03187	+	1.78725i
$683$	−1.45903e12	−	2.52712e12i	−0.256550	−	0.444357i	0.708766	−	0.705444i	$-0.249252\pi$
$683$	−1.45903e12	−	2.52712e12i	−0.256550	−	0.444357i	−0.965315	+	0.261087i	$0.915919\pi$
$684$	−1.66776e11	+	2.88865e11i	−0.0291327	+	0.0504594i
$685$	7.99902e12			1.38813
$686$		0			0
$687$	6.95322e12			1.19092
$688$	2.94871e11	−	5.10731e11i	0.0501746	−	0.0869049i
$689$	1.13180e11	+	1.96033e11i	0.0191330	+	0.0331393i
$690$	−2.67316e12	−	4.63006e12i	−0.448957	−	0.777616i
$691$	−2.37348e12	+	4.11100e12i	−0.396037	+	0.685955i	−0.993233	−	0.116140i	$-0.962948\pi$
$691$	−2.37348e12	+	4.11100e12i	−0.396037	+	0.685955i	0.597196	+	0.802095i	$0.296281\pi$
$692$	−6.82712e12			−1.13178
$693$		0			0
$694$	4.54058e12			0.743009
$695$	5.79908e12	−	1.00443e13i	0.942817	−	1.63301i
$696$	−1.31924e12	−	2.28500e12i	−0.213100	−	0.369100i
$697$	−7.72030e11	−	1.33719e12i	−0.123904	−	0.214609i
$698$	−2.31620e11	+	4.01177e11i	−0.0369340	+	0.0639716i
$699$	−2.07013e12			−0.327981
$700$		0			0
$701$	−2.24423e11			−0.0351023			−0.0175512	−	0.999846i	$-0.505587\pi$
$701$	−2.24423e11			−0.0351023			−0.0175512	+	0.999846i	$0.505587\pi$
$702$	−4.42300e10	+	7.66085e10i	−0.00687384	+	0.0119058i
$703$	−6.18048e11	−	1.07049e12i	−0.0954385	−	0.165304i
$704$	3.18700e12	+	5.52005e12i	0.488996	+	0.846966i
$705$	1.69573e12	−	2.93709e12i	0.258527	−	0.447782i
$706$	−4.63484e12			−0.702123
$707$		0			0
$708$	−3.49001e11			−0.0522007
$709$	−2.12731e12	+	3.68462e12i	−0.316172	+	0.547626i	−0.979686	−	0.200538i	$-0.935731\pi$
$709$	−2.12731e12	+	3.68462e12i	−0.316172	+	0.547626i	0.663514	+	0.748164i	$0.269064\pi$
$710$	−1.85546e12	−	3.21374e12i	−0.274024	−	0.474623i
$711$	1.71784e12	+	2.97539e12i	0.252099	+	0.436648i
$712$	1.17529e10	−	2.03567e10i	0.00171390	−	0.00296857i
$713$	1.23250e13			1.78601
$714$		0			0
$715$	5.54800e11			0.0793888
$716$	9.11606e11	−	1.57895e12i	0.129628	−	0.224522i
$717$	−5.21191e12	−	9.02729e12i	−0.736479	−	1.27562i
$718$	1.67685e12	+	2.90438e12i	0.235469	+	0.407844i
$719$	2.14465e12	−	3.71465e12i	0.299280	−	0.518368i	−0.676692	−	0.736267i	$-0.736587\pi$
$719$	2.14465e12	−	3.71465e12i	0.299280	−	0.518368i	0.975971	+	0.217899i	$0.0699203\pi$
$720$	2.67492e11			0.0370950
$721$		0			0
$722$	−4.04023e12			−0.553335
$723$	2.38262e12	−	4.12682e12i	0.324289	−	0.561685i
$724$	−3.52880e11	−	6.11207e11i	−0.0477314	−	0.0826732i
$725$	1.24470e12	+	2.15588e12i	0.167318	+	0.289804i
$726$	−6.30774e12	+	1.09253e13i	−0.842673	+	1.45955i
$727$	1.28935e13			1.71185			0.855926	−	0.517098i	$-0.172988\pi$
$727$	1.28935e13			1.71185			0.855926	+	0.517098i	$0.172988\pi$
$728$		0			0
$729$	3.31084e12			0.434174
$730$	−2.05654e12	+	3.56203e12i	−0.268030	+	0.464242i
$731$	1.73316e12	+	3.00193e12i	0.224497	+	0.388841i
$732$	4.61019e12	+	7.98508e12i	0.593497	+	1.02797i
$733$	−1.35724e12	+	2.35080e12i	−0.173655	+	0.300780i	−0.939695	−	0.342013i	$-0.888891\pi$
$733$	−1.35724e12	+	2.35080e12i	−0.173655	+	0.300780i	0.766040	+	0.642793i	$0.222225\pi$
$734$	6.41143e12			0.815309
$735$		0			0
$736$	7.70531e12			0.967921
$737$	−5.24405e12	+	9.08295e12i	−0.654731	+	1.13403i
$738$	−6.21696e11	−	1.07681e12i	−0.0771480	−	0.133624i
$739$	4.81290e12	+	8.33618e12i	0.593617	+	1.02818i	0.993740	+	0.111714i	$0.0356340\pi$
$739$	4.81290e12	+	8.33618e12i	0.593617	+	1.02818i	−0.400123	+	0.916461i	$0.631033\pi$
$740$	−2.78126e12	+	4.81729e12i	−0.340957	+	0.590554i
$741$	7.44880e10			0.00907620
$742$		0			0
$743$	−1.24362e13			−1.49706			−0.748529	−	0.663103i	$-0.769239\pi$
$743$	−1.24362e13			−1.49706			−0.748529	+	0.663103i	$0.769239\pi$
$744$	8.92993e12	−	1.54671e13i	1.06849	−	1.85068i
$745$	4.20797e12	+	7.28842e12i	0.500460	+	0.866823i
$746$	1.23449e12	+	2.13820e12i	0.145936	+	0.252769i
$747$	2.91943e11	−	5.05660e11i	0.0343048	−	0.0594177i
$748$	3.50425e12			0.409296
$749$		0			0
$750$	−8.87371e11			−0.102407
$751$	−2.13480e12	+	3.69758e12i	−0.244893	+	0.424168i	−0.962102	−	0.272691i	$-0.912086\pi$
$751$	−2.13480e12	+	3.69758e12i	−0.244893	+	0.424168i	0.717208	+	0.696859i	$0.245420\pi$
$752$	1.06996e11	+	1.85322e11i	0.0122008	+	0.0211323i
$753$	−5.13889e12	−	8.90081e12i	−0.582494	−	1.00891i
$754$	−3.05534e10	+	5.29200e10i	−0.00344262	+	0.00596278i
$755$	−5.17770e12			−0.579930
$756$		0			0
$757$	9.76840e12			1.08116			0.540582	−	0.841291i	$-0.318204\pi$
$757$	9.76840e12			1.08116			0.540582	+	0.841291i	$0.318204\pi$
$758$	4.73576e12	−	8.20258e12i	0.521049	−	0.902484i
$759$	9.38871e12	+	1.62617e13i	1.02688	+	1.77860i
$760$	−1.54656e12	−	2.67872e12i	−0.168153	−	0.291250i
$761$	−6.16679e12	+	1.06812e13i	−0.666543	+	1.15449i	0.312321	+	0.949977i	$0.398893\pi$
$761$	−6.16679e12	+	1.06812e13i	−0.666543	+	1.15449i	−0.978864	+	0.204510i	$0.934440\pi$
$762$	−1.90378e12			−0.204559
$763$		0			0
$764$	−5.75008e12			−0.610595
$765$	−7.86121e11	+	1.36160e12i	−0.0829875	+	0.143739i
$766$	−8.26955e11	−	1.43233e12i	−0.0867865	−	0.150319i
$767$	1.02460e10	+	1.77467e10i	0.00106900	+	0.00185156i
$768$	5.30627e12	−	9.19074e12i	0.550382	−	0.953290i
$769$	−1.68919e13			−1.74185			−0.870926	−	0.491415i	$-0.836480\pi$
$769$	−1.68919e13			−1.74185			−0.870926	+	0.491415i	$0.836480\pi$
$770$		0			0
$771$	1.87078e13			1.90668
$772$	3.36875e12	−	5.83485e12i	0.341343	−	0.591224i
$773$	−7.35930e12	−	1.27467e13i	−0.741359	−	1.28407i	−0.951877	−	0.306481i	$-0.900848\pi$
$773$	−7.35930e12	−	1.27467e13i	−0.741359	−	1.28407i	0.210518	−	0.977590i	$-0.432485\pi$
$774$	1.39567e12	+	2.41738e12i	0.139781	+	0.242108i
$775$	−8.42535e12	+	1.45931e13i	−0.838939	+	1.45308i
$776$	3.56835e12			0.353257
$777$		0			0
$778$	−3.98111e12			−0.389579
$779$	9.44040e11	−	1.63512e12i	0.0918484	−	0.159086i
$780$	−1.67601e11	−	2.90293e11i	−0.0162125	−	0.0280809i
$781$	6.51674e12	+	1.12873e13i	0.626760	+	1.08558i
$782$	−9.91388e11	+	1.71713e12i	−0.0948010	+	0.164200i
$783$	2.95738e12			0.281177
$784$		0			0
$785$	−2.55736e12			−0.240369
$786$	−2.44974e12	+	4.24308e12i	−0.228939	+	0.396534i
$787$	9.12328e12	+	1.58020e13i	0.847744	+	1.46834i	0.883217	+	0.468965i	$0.155373\pi$
$787$	9.12328e12	+	1.58020e13i	0.847744	+	1.46834i	−0.0354729	+	0.999371i	$0.511294\pi$
$788$	−3.71163e12	−	6.42873e12i	−0.342923	−	0.593960i
$789$	−1.14966e12	+	1.99127e12i	−0.105614	+	0.182929i
$790$	−1.25667e13			−1.14789
$791$		0			0
$792$	7.15424e12			0.646101
$793$	2.70694e11	−	4.68855e11i	0.0243080	−	0.0421027i
$794$	−3.56348e12	−	6.17212e12i	−0.318186	−	0.551115i
$795$	−1.11102e13	−	1.92434e13i	−0.986437	−	1.70856i
$796$	2.84448e12	−	4.92678e12i	0.251127	−	0.434965i
$797$	−1.21558e13			−1.06714			−0.533568	−	0.845757i	$-0.679149\pi$
$797$	−1.21558e13			−1.06714			−0.533568	+	0.845757i	$0.679149\pi$
$798$		0			0
$799$	−1.25778e12			−0.109180
$800$	−5.26733e12	+	9.12328e12i	−0.454659	+	0.787492i
$801$	−7.30510e9	−	1.26528e10i	−0.000627017	−	0.00108603i
$802$	−2.77662e12	−	4.80925e12i	−0.236991	−	0.410481i
$803$	7.22298e12	−	1.25106e13i	0.613051	−	1.06184i
$804$	6.33673e12			0.534827
$805$		0			0
$806$	−4.13631e11			−0.0345227
$807$	−6.85641e12	+	1.18757e13i	−0.569070	+	0.985659i
$808$	−3.24681e12	−	5.62364e12i	−0.267982	−	0.464158i
$809$	1.30946e12	+	2.26806e12i	0.107479	+	0.186160i	0.914749	−	0.404024i	$-0.132389\pi$
$809$	1.30946e12	+	2.26806e12i	0.107479	+	0.186160i	−0.807269	+	0.590184i	$0.799055\pi$
$810$	6.11641e12	−	1.05939e13i	0.499246	−	0.864719i
$811$	1.16994e13			0.949662			0.474831	−	0.880077i	$-0.342509\pi$
$811$	1.16994e13			0.949662			0.474831	+	0.880077i	$0.342509\pi$
$812$		0			0
$813$	3.24217e12			0.260272
$814$	−5.22875e12	+	9.05646e12i	−0.417434	+	0.723017i
$815$	3.42240e12	+	5.92777e12i	0.271720	+	0.470633i
$816$	−1.88652e11	−	3.26755e11i	−0.0148955	−	0.0257998i
$817$	−2.11932e12	+	3.67077e12i	−0.166417	+	0.288242i
$818$	1.44267e13			1.12662
$819$		0			0
$820$	−8.49649e12			−0.656262
$821$	−2.58836e12	+	4.48318e12i	−0.198830	+	0.344383i	−0.948149	−	0.317826i	$-0.897047\pi$
$821$	−2.58836e12	+	4.48318e12i	−0.198830	+	0.344383i	0.749320	+	0.662209i	$0.230381\pi$
$822$	−4.54288e12	−	7.86850e12i	−0.347063	−	0.601131i
$823$	3.92009e12	+	6.78979e12i	0.297849	+	0.515890i	0.975644	−	0.219362i	$-0.0703974\pi$
$823$	3.92009e12	+	6.78979e12i	0.297849	+	0.515890i	−0.677795	+	0.735251i	$0.737064\pi$
$824$	−8.57790e12	+	1.48574e13i	−0.648200	+	1.12271i
$825$	−2.56724e13			−1.92941
$826$		0			0
$827$	−1.43263e13			−1.06502			−0.532512	−	0.846422i	$-0.678752\pi$
$827$	−1.43263e13			−1.06502			−0.532512	+	0.846422i	$0.678752\pi$
$828$	1.49146e12	−	2.58329e12i	0.110275	−	0.191001i
$829$	−2.47773e12	−	4.29155e12i	−0.182204	−	0.315587i	0.760427	−	0.649424i	$-0.224990\pi$
$829$	−2.47773e12	−	4.29155e12i	−0.182204	−	0.315587i	−0.942631	+	0.333837i	$0.891657\pi$
$830$	1.06784e12	+	1.84955e12i	0.0781005	+	0.135274i
$831$	5.86586e12	−	1.01600e13i	0.426704	−	0.739073i
$832$	−2.26121e11			−0.0163601
$833$		0			0
$834$	−1.31739e13			−0.942902
$835$	1.00228e13	−	1.73600e13i	0.713508	−	1.23583i
$836$	2.14250e12	+	3.71092e12i	0.151703	+	0.262757i
$837$	1.00092e13	+	1.73365e13i	0.704914	+	1.22095i
$838$	1.47635e12	−	2.55711e12i	0.103417	−	0.179123i
$839$	7.38235e12			0.514358			0.257179	−	0.966364i	$-0.417207\pi$
$839$	7.38235e12			0.514358			0.257179	+	0.966364i	$0.417207\pi$
$840$		0			0
$841$	−1.24642e13			−0.859179
$842$	−2.32128e12	+	4.02058e12i	−0.159156	+	0.275666i
$843$	−8.40386e12	−	1.45559e13i	−0.573132	−	0.992694i
$844$	−5.33373e12	−	9.23830e12i	−0.361818	−	0.626687i
$845$	1.01821e13	−	1.76359e13i	0.687039	−	1.18999i
$846$	−1.01286e12			−0.0679802
$847$		0			0
$848$	1.40204e12			0.0931065
$849$	4.51745e12	−	7.82446e12i	0.298407	−	0.516856i
$850$	−1.35542e12	−	2.34766e12i	−0.0890613	−	0.154259i
$851$	5.52714e12	+	9.57329e12i	0.361258	+	0.625717i
$852$	3.93731e12	−	6.81962e12i	0.255989	−	0.443386i
$853$	2.13356e13			1.37985			0.689927	−	0.723879i	$-0.257643\pi$
$853$	2.13356e13			1.37985			0.689927	+	0.723879i	$0.257643\pi$
$854$		0			0
$855$	−1.92254e12			−0.123035
$856$	−1.14016e12	+	1.97482e12i	−0.0725829	+	0.125717i
$857$	−8.25038e12	−	1.42901e13i	−0.522468	−	0.904942i	−0.999658	−	0.0261416i	$-0.991678\pi$
$857$	−8.25038e12	−	1.42901e13i	−0.522468	−	0.904942i	0.477190	−	0.878800i	$-0.341655\pi$
$858$	−3.15088e11	−	5.45748e11i	−0.0198490	−	0.0343795i
$859$	9.74083e12	−	1.68716e13i	0.610417	−	1.05727i	−0.380753	−	0.924677i	$-0.624335\pi$
$859$	9.74083e12	−	1.68716e13i	0.610417	−	1.05727i	0.991170	−	0.132597i	$-0.0423315\pi$
$860$	1.90742e13			1.18906
$861$		0			0
$862$	1.65103e12			0.101853
$863$	−8.05297e12	+	1.39482e13i	−0.494205	+	0.855989i	−0.999978	−	0.00667822i	$-0.997874\pi$
$863$	−8.05297e12	+	1.39482e13i	−0.494205	+	0.855989i	0.505772	+	0.862667i	$0.331208\pi$
$864$	6.25754e12	+	1.08384e13i	0.382025	+	0.661686i
$865$	−1.96752e13	−	3.40785e13i	−1.19494	−	2.06970i
$866$	4.86116e12	−	8.41978e12i	0.293704	−	0.508710i
$867$	−1.71613e13			−1.03149
$868$		0			0
$869$	4.41368e13			2.62550
$870$	2.99924e12	−	5.19484e12i	0.177491	−	0.307423i
$871$	−1.86035e11	−	3.22222e11i	−0.0109525	−	0.0189703i
$872$	−4.93624e12	−	8.54983e12i	−0.289116	−	0.500764i
$873$	1.10896e12	−	1.92078e12i	0.0646180	−	0.111922i
$874$	−2.42454e12			−0.140549
$875$		0			0
$876$	−8.72801e12			−0.500780
$877$	9.24594e12	−	1.60144e13i	0.527780	−	0.914142i	−0.471696	−	0.881761i	$-0.656358\pi$
$877$	9.24594e12	−	1.60144e13i	0.527780	−	0.914142i	0.999476	−	0.0323804i	$-0.0103088\pi$
$878$	3.91446e12	+	6.78005e12i	0.222304	+	0.385041i
$879$	−8.63821e12	−	1.49618e13i	−0.488061	−	0.845346i
$880$	1.71818e12	−	2.97598e12i	0.0965821	−	0.167285i
$881$	−2.83078e13			−1.58312			−0.791562	−	0.611089i	$-0.790732\pi$
$881$	−2.83078e13			−1.58312			−0.791562	+	0.611089i	$0.790732\pi$
$882$		0			0
$883$	−7.32328e12			−0.405399			−0.202700	−	0.979241i	$-0.564971\pi$
$883$	−7.32328e12			−0.405399			−0.202700	+	0.979241i	$0.564971\pi$
$884$	−6.21574e10	+	1.07660e11i	−0.00342340	+	0.00592951i
$885$	−1.00579e12	−	1.74208e12i	−0.0551142	−	0.0954606i
$886$	1.41321e12	+	2.44774e12i	0.0770466	+	0.133449i
$887$	−7.56860e12	+	1.31092e13i	−0.410544	+	0.711083i	−0.994949	−	0.100379i	$-0.967994\pi$
$887$	−7.56860e12	+	1.31092e13i	−0.410544	+	0.711083i	0.584406	+	0.811462i	$0.301328\pi$
$888$	1.60185e13			0.864496
$889$		0			0
$890$	5.34396e10			0.00285501
$891$	−2.14821e13	+	3.72081e13i	−1.14190	+	1.97782i
$892$	−3.85126e12	−	6.67059e12i	−0.203686	−	0.352795i
$893$	−7.69008e11	−	1.33196e12i	−0.0404669	−	0.0700907i
$894$	4.77967e12	−	8.27863e12i	0.250253	−	0.433451i
$895$	1.05087e13			0.547451
$896$		0			0
$897$	−6.66138e11			−0.0343556
$898$	6.15293e12	−	1.06572e13i	0.315747	−	0.546889i
$899$	6.91423e12	+	1.19758e13i	0.353041	+	0.611485i
$900$	2.03912e12	+	3.53186e12i	0.103598	+	0.179437i
$901$	−4.12040e12	+	7.13674e12i	−0.208294	+	0.360776i
$902$	−1.59733e13			−0.803463
$903$		0			0
$904$	−1.72783e13			−0.860487
$905$	2.03395e12	−	3.52290e12i	0.100791	−	0.174575i
$906$	2.94057e12	+	5.09321e12i	0.144995	+	0.251139i
$907$	1.12169e13	+	1.94282e13i	0.550349	+	0.953233i	0.998249	+	0.0591491i	$0.0188387\pi$
$907$	1.12169e13	+	1.94282e13i	0.550349	+	0.953233i	−0.447900	+	0.894084i	$0.647828\pi$
$908$	−3.85006e12	+	6.66849e12i	−0.187967	+	0.325568i
$909$	−4.03614e12			−0.196078
$910$		0			0
$911$	−6.34178e12			−0.305055			−0.152528	−	0.988299i	$-0.548741\pi$
$911$	−6.34178e12			−0.305055			−0.152528	+	0.988299i	$0.548741\pi$
$912$	2.30684e11	−	3.99557e11i	0.0110418	−	0.0191250i
$913$	−3.75047e12	−	6.49600e12i	−0.178635	−	0.309405i
$914$	−5.41901e12	−	9.38600e12i	−0.256839	−	0.444859i
$915$	−2.65724e13	+	4.60247e13i	−1.25324	+	2.17068i
$916$	−1.41899e13			−0.665963
$917$		0			0
$918$	−3.22045e12			−0.149667
$919$	−4.52236e12	+	7.83295e12i	−0.209144	+	0.362248i	−0.951445	−	0.307819i	$-0.900401\pi$
$919$	−4.52236e12	+	7.83295e12i	−0.209144	+	0.362248i	0.742301	+	0.670066i	$0.233734\pi$
$920$	1.38307e13	+	2.39555e13i	0.636500	+	1.10245i
$921$	6.61882e12	+	1.14641e13i	0.303118	+	0.525016i
$922$	1.26973e12	−	2.19924e12i	0.0578659	−	0.100227i
$923$	−4.62369e11			−0.0209692
$924$		0			0
$925$	−1.51134e13			−0.678771
$926$	−3.18617e12	+	5.51860e12i	−0.142403	+	0.246649i
$927$	5.33164e12	+	9.23467e12i	0.237138	+	0.410736i
$928$	4.32261e12	+	7.48698e12i	0.191329	+	0.331391i
$929$	−4.25320e12	+	7.36677e12i	−0.187346	+	0.324494i	−0.944365	−	0.328900i	$-0.893322\pi$
$929$	−4.25320e12	+	7.36677e12i	−0.187346	+	0.324494i	0.757018	+	0.653394i	$0.226655\pi$
$930$	4.06037e13			1.77988
$931$		0			0
$932$	4.22464e12			0.183408
$933$	2.60184e13	−	4.50652e13i	1.12412	−	1.94704i
$934$	−7.10735e12	−	1.23103e13i	−0.305595	−	0.529307i
$935$	1.00990e13	+	1.74919e13i	0.432140	+	0.748488i
$936$	−1.26900e11	+	2.19797e11i	−0.00540407	+	0.00936012i
$937$	−3.00276e13			−1.27260			−0.636300	−	0.771442i	$-0.719536\pi$
$937$	−3.00276e13			−1.27260			−0.636300	+	0.771442i	$0.719536\pi$
$938$		0			0
$939$	2.10602e13			0.884030
$940$	−3.46059e12	+	5.99392e12i	−0.144569	+	0.250401i
$941$	1.57991e13	+	2.73649e13i	0.656870	+	1.13773i	0.981422	+	0.191864i	$0.0614532\pi$
$941$	1.57991e13	+	2.73649e13i	0.656870	+	1.13773i	−0.324552	+	0.945868i	$0.605213\pi$
$942$	1.45240e12	+	2.51563e12i	0.0600976	+	0.104092i
$943$	−8.44245e12	+	1.46227e13i	−0.347669	+	0.602180i
$944$	1.26925e11			0.00520205
$945$		0			0
$946$	3.58592e13			1.45576
$947$	4.42442e12	−	7.66332e12i	0.178765	−	0.309630i	−0.762693	−	0.646761i	$-0.776123\pi$
$947$	4.42442e12	−	7.66332e12i	0.178765	−	0.309630i	0.941458	+	0.337131i	$0.109457\pi$
$948$	−1.33334e13	−	2.30941e13i	−0.536170	−	0.928673i
$949$	2.56239e11	+	4.43819e11i	0.0102553	+	0.0177626i
$950$	1.65741e12	−	2.87072e12i	0.0660198	−	0.114350i
$951$	−1.21698e13			−0.482473
$952$		0			0
$953$	−4.90260e12			−0.192534			−0.0962672	−	0.995356i	$-0.530690\pi$
$953$	−4.90260e12			−0.192534			−0.0962672	+	0.995356i	$0.530690\pi$
$954$	−3.31805e12	+	5.74704e12i	−0.129693	+	0.224634i
$955$	−1.65713e13	−	2.87023e13i	−0.644674	−	1.11661i
$956$	1.06363e13	+	1.84226e13i	0.411841	+	0.713329i
$957$	−1.05340e13	+	1.82454e13i	−0.405965	+	0.703151i
$958$	−1.12686e13			−0.432241
$959$		0			0
$960$	2.21969e13			0.843476
$961$	−3.35824e13	+	5.81665e13i	−1.27016	+	2.19998i
$962$	−1.85492e11	−	3.21282e11i	−0.00698294	−	0.0120948i
$963$	7.08673e11	+	1.22746e12i	0.0265539	+	0.0459926i
$964$	−4.86237e12	+	8.42188e12i	−0.181343	+	0.314096i
$965$	3.88339e13			1.44158
$966$		0			0
$967$	1.55633e13			0.572378			0.286189	−	0.958173i	$-0.407612\pi$
$967$	1.55633e13			0.572378			0.286189	+	0.958173i	$0.407612\pi$
$968$	3.26356e13	−	5.65266e13i	1.19468	−	2.06925i
$969$	1.35590e12	+	2.34848e12i	0.0494048	+	0.0855716i
$970$	4.05625e12	+	7.02564e12i	0.147113	+	0.254808i
$971$	1.24598e13	−	2.15811e13i	0.449806	−	0.779087i	−0.548567	−	0.836107i	$-0.684826\pi$
$971$	1.24598e13	−	2.15811e13i	0.449806	−	0.779087i	0.998373	+	0.0570194i	$0.0181597\pi$
$972$	1.23765e13			0.444732
$973$		0			0
$974$	1.53918e13			0.547991
$975$	4.55370e11	−	7.88724e11i	0.0161378	−	0.0279515i
$976$	−1.67664e12	−	2.90403e12i	−0.0591448	−	0.102442i
$977$	−2.23949e12	−	3.87891e12i	−0.0786364	−	0.136202i	0.824025	−	0.566553i	$-0.191723\pi$
$977$	−2.23949e12	−	3.87891e12i	−0.0786364	−	0.136202i	−0.902662	+	0.430351i	$0.858390\pi$
$978$	3.88737e12	−	6.73312e12i	0.135872	−	0.235338i
$979$	−1.87691e11			−0.00653012
$980$		0			0
$981$	−6.13629e12			−0.211542
$982$	6.47129e12	−	1.12086e13i	0.222070	−	0.384636i
$983$	7.16166e12	+	1.24044e13i	0.244637	+	0.423724i	0.962030	−	0.272945i	$-0.0879978\pi$
$983$	7.16166e12	+	1.24044e13i	0.244637	+	0.423724i	−0.717392	+	0.696669i	$0.754664\pi$
$984$	1.22337e13	+	2.11895e13i	0.415988	+	0.720513i
$985$	2.13932e13	−	3.70542e13i	0.724125	−	1.25422i
$986$	−2.22464e12			−0.0749572
$987$		0			0
$988$	−1.52013e11			−0.00507543
$989$	1.89528e13	−	3.28273e13i	0.629928	−	1.09107i
$990$	8.13244e12	+	1.40858e13i	0.269068	+	0.466040i
$991$	1.14287e13	+	1.97951e13i	0.376415	+	0.651969i	0.990538	−	0.137241i	$-0.0438235\pi$
$991$	1.14287e13	+	1.97951e13i	0.376415	+	0.651969i	−0.614123	+	0.789210i	$0.710490\pi$
$992$	−2.92597e13	+	5.06793e13i	−0.959328	+	1.66160i
$993$	4.63836e13			1.51388
$994$		0			0
$995$	3.27902e13			1.06057
$996$	−2.26597e12	+	3.92478e12i	−0.0729604	+	0.126371i
$997$	1.33566e13	+	2.31343e13i	0.428121	+	0.741528i	0.996706	−	0.0810966i	$-0.0258422\pi$
$997$	1.33566e13	+	2.31343e13i	0.428121	+	0.741528i	−0.568585	+	0.822625i	$0.692509\pi$
$998$	−1.75574e13	−	3.04103e13i	−0.560237	−	0.970359i
$999$	−8.97726e12	+	1.55491e13i	−0.285167	+	0.493924i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.10.c.d.30.2		6
7.2	even	3		7.10.a.b.1.2	✓	3
7.3	odd	6		49.10.c.e.18.2		6
7.4	even	3	inner	49.10.c.d.18.2		6
7.5	odd	6		49.10.a.c.1.2		3
7.6	odd	2		49.10.c.e.30.2		6
21.2	odd	6		63.10.a.e.1.2		3
28.23	odd	6		112.10.a.h.1.1		3
35.2	odd	12		175.10.b.d.99.4		6
35.9	even	6		175.10.a.d.1.2		3
35.23	odd	12		175.10.b.d.99.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.a.b.1.2	✓	3	7.2	even	3
49.10.a.c.1.2		3	7.5	odd	6
49.10.c.d.18.2		6	7.4	even	3	inner
49.10.c.d.30.2		6	1.1	even	1	trivial
49.10.c.e.18.2		6	7.3	odd	6
49.10.c.e.30.2		6	7.6	odd	2
63.10.a.e.1.2		3	21.2	odd	6
112.10.a.h.1.1		3	28.23	odd	6
175.10.a.d.1.2		3	35.9	even	6
175.10.b.d.99.3		6	35.23	odd	12
175.10.b.d.99.4		6	35.2	odd	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-6.68036 + 11.5707i) q^{2} +(-81.7073 - 141.521i) q^{3} +(166.746 + 288.812i) q^{4} +(-961.094 + 1664.66i) q^{5} +2183.34 q^{6} -11296.4 q^{8} +(-3510.66 + 6080.64i) q^{9} +(-12840.9 - 22241.1i) q^{10} +(45099.9 + 78115.4i) q^{11} +(27248.6 - 47196.0i) q^{12} -3199.89 q^{13} +314114. q^{15} +(-9909.84 + 17164.3i) q^{16} +(-58247.1 - 100887. i) q^{17} +(-46904.9 - 81241.8i) q^{18} +(71224.7 - 123365. i) q^{19} -641033. q^{20} -1.20514e6 q^{22} +(-636955. + 1.10324e6i) q^{23} +(922996. + 1.59868e6i) q^{24} +(-870842. - 1.50834e6i) q^{25} +(21376.4 - 37025.0i) q^{26} -2.06910e6 q^{27} -1.42931e6 q^{29} +(-2.09839e6 + 3.63452e6i) q^{30} +(-4.83747e6 - 8.37875e6i) q^{31} +(-3.02427e6 - 5.23820e6i) q^{32} +(7.36999e6 - 1.27652e7i) q^{33} +1.55645e6 q^{34} -2.34155e6 q^{36} +(4.33872e6 - 7.51488e6i) q^{37} +(951614. + 1.64824e6i) q^{38} +(261454. + 452851. i) q^{39} +(1.08569e7 - 1.88047e7i) q^{40} +1.32544e7 q^{41} -2.97554e7 q^{43} +(-1.50404e7 + 2.60508e7i) q^{44} +(-6.74815e6 - 1.16881e7i) q^{45} +(-8.51018e6 - 1.47401e7i) q^{46} +(5.39846e6 - 9.35041e6i) q^{47} +3.23882e6 q^{48} +2.32702e7 q^{50} +(-9.51843e6 + 1.64864e7i) q^{51} +(-533567. - 924164. i) q^{52} +(-3.53700e7 - 6.12626e7i) q^{53} +(1.38224e7 - 2.39410e7i) q^{54} -1.73381e8 q^{55} -2.32783e7 q^{57} +(9.54828e6 - 1.65381e7i) q^{58} +(-3.20200e6 - 5.54603e6i) q^{59} +(5.23770e7 + 9.07197e7i) q^{60} +(-8.45948e7 + 1.46523e8i) q^{61} +1.29264e8 q^{62} +7.06653e7 q^{64} +(3.07539e6 - 5.32673e6i) q^{65} +(9.84684e7 + 1.70552e8i) q^{66} +(5.81380e7 + 1.00698e8i) q^{67} +(1.94249e7 - 3.36449e7i) q^{68} +2.08176e8 q^{69} +1.44496e8 q^{71} +(3.96577e7 - 6.86892e7i) q^{72} +(-8.00775e7 - 1.38698e8i) q^{73} +(5.79684e7 + 1.00404e8i) q^{74} +(-1.42308e8 + 2.46485e8i) q^{75} +4.75056e7 q^{76} -6.98643e6 q^{78} +(2.44661e8 - 4.23766e8i) q^{79} +(-1.90486e7 - 3.29931e7i) q^{80} +(2.38161e8 + 4.12507e8i) q^{81} +(-8.85441e7 + 1.53363e8i) q^{82} -8.31590e7 q^{83} +2.23924e8 q^{85} +(1.98777e8 - 3.44291e8i) q^{86} +(1.16785e8 + 2.02277e8i) q^{87} +(-5.09466e8 - 8.82421e8i) q^{88} +(-1.04042e6 + 1.80205e6i) q^{89} +1.80320e8 q^{90} -4.24838e8 q^{92} +(-7.90513e8 + 1.36921e9i) q^{93} +(7.21274e7 + 1.24928e8i) q^{94} +(1.36907e8 + 2.37131e8i) q^{95} +(-4.94210e8 + 8.55998e8i) q^{96} -3.15885e8 q^{97} -6.33322e8 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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