LMFDB - Embedded newform 49.10.c.g.18.4

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)

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);

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")

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 = [10,-18,-161] 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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 430 x^{8} + 61 x^{7} + 146753 x^{6} + 23608 x^{5} + 16136944 x^{4} + 30575648 x^{3} + \cdots + 761760000 $ x^10 - x^9 + 430x^8 + 61x^7 + 146753x^6 + 23608x^5 + 16136944x^4 + 30575648x^3 + 1399072384x^2 + 1034227200x + 761760000
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{3}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			18.4
Root			$5.89912 - 10.2176i$ of defining polynomial
Character	$\chi$	$=$	49.18
Dual form			49.10.c.g.30.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(9.79824 + 16.9710i) q^{2} +(-104.977 + 181.826i) q^{3} +(63.9892 - 110.832i) q^{4} +(-983.791 - 1703.98i) q^{5} -4114.37 q^{6} +12541.3 q^{8} +(-12198.9 - 21129.2i) q^{9} +(19278.8 - 33391.9i) q^{10} +(-15898.9 + 27537.7i) q^{11} +(13434.8 + 23269.8i) q^{12} +100188. q^{13} +413103. q^{15} +(90120.3 + 156093. i) q^{16} +(169129. - 292940. i) q^{17} +(239056. - 414058. i) q^{18} +(130759. + 226480. i) q^{19} -251808. q^{20} -623124. q^{22} +(272337. + 471702. i) q^{23} +(-1.31655e6 + 2.28034e6i) q^{24} +(-959125. + 1.66125e6i) q^{25} +(981664. + 1.70029e6i) q^{26} +989914. q^{27} +2.32128e6 q^{29} +(4.04768e6 + 7.01078e6i) q^{30} +(-2.53535e6 + 4.39136e6i) q^{31} +(1.44454e6 - 2.50201e6i) q^{32} +(-3.33804e6 - 5.78166e6i) q^{33} +6.62867e6 q^{34} -3.12240e6 q^{36} +(-2.93235e6 - 5.07897e6i) q^{37} +(-2.56241e6 + 4.43822e6i) q^{38} +(-1.05174e7 + 1.82167e7i) q^{39} +(-1.23380e7 - 2.13701e7i) q^{40} +2.81312e7 q^{41} +3.88522e7 q^{43} +(2.03471e6 + 3.52423e6i) q^{44} +(-2.40024e7 + 4.15734e7i) q^{45} +(-5.33685e6 + 9.24370e6i) q^{46} +(1.26741e7 + 2.19521e7i) q^{47} -3.78423e7 q^{48} -3.75909e7 q^{50} +(3.55094e7 + 6.15041e7i) q^{51} +(6.41094e6 - 1.11041e7i) q^{52} +(2.26489e7 - 3.92291e7i) q^{53} +(9.69941e6 + 1.67999e7i) q^{54} +6.25647e7 q^{55} -5.49067e7 q^{57} +(2.27445e7 + 3.93946e7i) q^{58} +(9.44557e6 - 1.63602e7i) q^{59} +(2.64341e7 - 4.57852e7i) q^{60} +(5.08255e7 + 8.80323e7i) q^{61} -9.93680e7 q^{62} +1.48899e8 q^{64} +(-9.85638e7 - 1.70718e8i) q^{65} +(6.54138e7 - 1.13300e8i) q^{66} +(-6.55496e7 + 1.13535e8i) q^{67} +(-2.16449e7 - 3.74900e7i) q^{68} -1.14357e8 q^{69} +9.51959e7 q^{71} +(-1.52991e8 - 2.64988e8i) q^{72} +(1.19056e8 - 2.06211e8i) q^{73} +(5.74636e7 - 9.95299e7i) q^{74} +(-2.01373e8 - 3.48788e8i) q^{75} +3.34685e7 q^{76} -4.12210e8 q^{78} +(-9.42601e7 - 1.63263e8i) q^{79} +(1.77319e8 - 3.07126e8i) q^{80} +(1.36193e8 - 2.35894e8i) q^{81} +(2.75636e8 + 4.77416e8i) q^{82} +1.76014e8 q^{83} -6.65551e8 q^{85} +(3.80683e8 + 6.59362e8i) q^{86} +(-2.43682e8 + 4.22070e8i) q^{87} +(-1.99393e8 + 3.45359e8i) q^{88} +(-2.41517e8 - 4.18319e8i) q^{89} -9.40725e8 q^{90} +6.97066e7 q^{92} +(-5.32309e8 - 9.21986e8i) q^{93} +(-2.48367e8 + 4.30184e8i) q^{94} +(2.57278e8 - 4.45619e8i) q^{95} +(3.03287e8 + 5.25309e8i) q^{96} +2.28821e7 q^{97} +7.75799e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 18 q^{2} - 161 q^{3} - 940 q^{4} - 1533 q^{5} + 8708 q^{6} + 34272 q^{8} - 35734 q^{9} - 4298 q^{10} + 42213 q^{11} - 135604 q^{12} + 319676 q^{13} + 151394 q^{15} + 322064 q^{16} - 324681 q^{17}+ \cdots - 1900777180 q^{99}+O(q^{100}) $ 10 * q - 18 * q^2 - 161 * q^3 - 940 * q^4 - 1533 * q^5 + 8708 * q^6 + 34272 * q^8 - 35734 * q^9 - 4298 * q^10 + 42213 * q^11 - 135604 * q^12 + 319676 * q^13 + 151394 * q^15 + 322064 * q^16 - 324681 * q^17 - 1012868 * q^18 + 16121 * q^19 + 350616 * q^20 - 62692 * q^22 + 2638863 * q^23 - 8449728 * q^24 - 1304092 * q^25 - 4179252 * q^26 + 18331558 * q^27 + 15292500 * q^29 + 20557942 * q^30 - 19179237 * q^31 - 6263520 * q^32 - 1689359 * q^33 + 62909700 * q^34 + 71476528 * q^36 + 39566985 * q^37 - 67365270 * q^38 - 44299486 * q^39 - 5721744 * q^40 + 53436852 * q^41 + 101835992 * q^43 + 99704916 * q^44 - 85098230 * q^45 - 14489202 * q^46 - 32509659 * q^47 + 185141600 * q^48 + 3328464 * q^50 + 44168403 * q^51 - 103893272 * q^52 - 25714707 * q^53 - 51200926 * q^54 + 144695222 * q^55 - 121710346 * q^57 - 46645516 * q^58 - 46776513 * q^59 + 132391756 * q^60 + 113075039 * q^61 - 467465628 * q^62 - 192008960 * q^64 - 338113566 * q^65 + 836682602 * q^66 - 126707879 * q^67 - 32262636 * q^68 - 1323616182 * q^69 - 1188736032 * q^71 - 950557728 * q^72 + 859257651 * q^73 + 591757530 * q^74 + 169061732 * q^75 - 1101475592 * q^76 + 519432424 * q^78 - 527065417 * q^79 + 1257352656 * q^80 + 551662715 * q^81 + 1341703076 * q^82 + 144863208 * q^83 - 1197360222 * q^85 - 678648216 * q^86 + 340781350 * q^87 + 903700608 * q^88 - 1661554797 * q^89 - 1967758744 * q^90 - 1301840952 * q^92 - 423057489 * q^93 + 272580882 * q^94 - 1197123495 * q^95 + 1441922272 * q^96 - 869770188 * q^97 - 1900777180 * 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 $

$2$	9.79824	+	16.9710i	0.433025	+	0.750021i	0.997132	−	0.0756804i	$-0.0241129\pi$
$2$	9.79824	+	16.9710i	0.433025	+	0.750021i	−0.564107	+	0.825702i	$0.690780\pi$
$3$	−104.977	+	181.826i	−0.748255	+	1.29602i	0.200404	+	0.979713i	$0.435775\pi$
$3$	−104.977	+	181.826i	−0.748255	+	1.29602i	−0.948659	+	0.316302i	$0.897559\pi$
$4$	63.9892	−	110.832i	0.124979	−	0.216470i
$5$	−983.791	−	1703.98i	−0.703943	−	1.21927i	−0.967072	−	0.254505i	$-0.918088\pi$
$5$	−983.791	−	1703.98i	−0.703943	−	1.21927i	0.263128	−	0.964761i	$-0.415246\pi$
$6$	−4114.37			−1.29605
$7$		0			0
$7$		0			0
$8$	12541.3			1.08253
$9$	−12198.9	−	21129.2i	−0.619771	−	1.07347i
$10$	19278.8	−	33391.9i	0.609650	−	1.05594i
$11$	−15898.9	+	27537.7i	−0.327416	+	0.567101i	−0.981998	−	0.188890i	$-0.939511\pi$
$11$	−15898.9	+	27537.7i	−0.327416	+	0.567101i	0.654583	+	0.755991i	$0.272844\pi$
$12$	13434.8	+	23269.8i	0.187032	+	0.323949i
$13$	100188.			0.972904			0.486452	−	0.873707i	$-0.338291\pi$
$13$	100188.			0.972904			0.486452	+	0.873707i	$0.338291\pi$
$14$		0			0
$15$	413103.			2.10692
$16$	90120.3	+	156093.i	0.343782	+	0.595447i
$17$	169129.	−	292940.i	0.491132	−	0.850666i	−0.508816	−	0.860875i	$-0.669917\pi$
$17$	169129.	−	292940.i	0.491132	−	0.850666i	0.999948	+	0.0102097i	$0.00324991\pi$
$18$	239056.	−	414058.i	0.536752	−	0.929682i
$19$	130759.	+	226480.i	0.230186	+	0.398694i	0.957863	−	0.287226i	$-0.0927332\pi$
$19$	130759.	+	226480.i	0.230186	+	0.398694i	−0.727677	+	0.685920i	$0.759400\pi$
$20$	−251808.			−0.351912
$21$		0			0
$22$	−623124.			−0.567117
$23$	272337.	+	471702.i	0.202923	+	0.351474i	0.949469	−	0.313860i	$-0.101622\pi$
$23$	272337.	+	471702.i	0.202923	+	0.351474i	−0.746546	+	0.665334i	$0.768289\pi$
$24$	−1.31655e6	+	2.28034e6i	−0.810005	+	1.40297i
$25$	−959125.	+	1.66125e6i	−0.491072	+	0.850562i
$26$	981664.	+	1.70029e6i	0.421292	+	0.729698i
$27$	989914.			0.358476
$28$		0			0
$29$	2.32128e6			0.609449			0.304724	−	0.952441i	$-0.401436\pi$
$29$	2.32128e6			0.609449			0.304724	+	0.952441i	$0.401436\pi$
$30$	4.04768e6	+	7.01078e6i	0.912347	+	1.58023i
$31$	−2.53535e6	+	4.39136e6i	−0.493073	+	0.854027i	−0.999968	−	0.00798051i	$-0.997460\pi$
$31$	−2.53535e6	+	4.39136e6i	−0.493073	+	0.854027i	0.506895	+	0.862008i	$0.330793\pi$
$32$	1.44454e6	−	2.50201e6i	0.243531	−	0.421808i
$33$	−3.33804e6	−	5.78166e6i	−0.489981	−	0.848672i
$34$	6.62867e6			0.850690
$35$		0			0
$36$	−3.12240e6			−0.309833
$37$	−2.93235e6	−	5.07897e6i	−0.257222	−	0.445521i	0.708275	−	0.705937i	$-0.249474\pi$
$37$	−2.93235e6	−	5.07897e6i	−0.257222	−	0.445521i	−0.965497	+	0.260416i	$0.916140\pi$
$38$	−2.56241e6	+	4.43822e6i	−0.199353	+	0.345289i
$39$	−1.05174e7	+	1.82167e7i	−0.727980	+	1.26090i
$40$	−1.23380e7	−	2.13701e7i	−0.762037	−	1.31989i
$41$	2.81312e7			1.55475			0.777376	−	0.629036i	$-0.216550\pi$
$41$	2.81312e7			1.55475			0.777376	+	0.629036i	$0.216550\pi$
$42$		0			0
$43$	3.88522e7			1.73304			0.866518	−	0.499147i	$-0.166353\pi$
$43$	3.88522e7			1.73304			0.866518	+	0.499147i	$0.166353\pi$
$44$	2.03471e6	+	3.52423e6i	0.0818401	+	0.141751i
$45$	−2.40024e7	+	4.15734e7i	−0.872567	+	1.51133i
$46$	−5.33685e6	+	9.24370e6i	−0.175742	+	0.304394i
$47$	1.26741e7	+	2.19521e7i	0.378857	+	0.656199i	0.990896	−	0.134628i	$-0.0429839\pi$
$47$	1.26741e7	+	2.19521e7i	0.378857	+	0.656199i	−0.612039	+	0.790827i	$0.709651\pi$
$48$	−3.78423e7			−1.02895
$49$		0			0
$50$	−3.75909e7			−0.850586
$51$	3.55094e7	+	6.15041e7i	0.734984	+	1.27303i
$52$	6.41094e6	−	1.11041e7i	0.121592	−	0.210604i
$53$	2.26489e7	−	3.92291e7i	0.394281	−	0.682915i	−0.598728	−	0.800953i	$-0.704327\pi$
$53$	2.26489e7	−	3.92291e7i	0.394281	−	0.682915i	0.993009	+	0.118037i	$0.0376602\pi$
$54$	9.69941e6	+	1.67999e7i	0.155229	+	0.268865i
$55$	6.25647e7			0.921928
$56$		0			0
$57$	−5.49067e7			−0.688951
$58$	2.27445e7	+	3.93946e7i	0.263907	+	0.457099i
$59$	9.44557e6	−	1.63602e7i	0.101483	−	0.175774i	−0.810813	−	0.585306i	$-0.800975\pi$
$59$	9.44557e6	−	1.63602e7i	0.101483	−	0.175774i	0.912296	+	0.409532i	$0.134308\pi$
$60$	2.64341e7	−	4.57852e7i	0.263320	−	0.456083i
$61$	5.08255e7	+	8.80323e7i	0.469999	+	0.814062i	0.999412	−	0.0343023i	$-0.0109209\pi$
$61$	5.08255e7	+	8.80323e7i	0.469999	+	0.814062i	−0.529412	+	0.848365i	$0.677588\pi$
$62$	−9.93680e7			−0.854051
$63$		0			0
$64$	1.48899e8			1.10938
$65$	−9.85638e7	−	1.70718e8i	−0.684869	−	1.18623i
$66$	6.54138e7	−	1.13300e8i	0.424348	−	0.734992i
$67$	−6.55496e7	+	1.13535e8i	−0.397405	+	0.688326i	−0.993405	−	0.114659i	$-0.963423\pi$
$67$	−6.55496e7	+	1.13535e8i	−0.397405	+	0.688326i	0.596000	+	0.802985i	$0.296756\pi$
$68$	−2.16449e7	−	3.74900e7i	−0.122762	−	0.212630i
$69$	−1.14357e8			−0.607354
$70$		0			0
$71$	9.51959e7			0.444586			0.222293	−	0.974980i	$-0.428646\pi$
$71$	9.51959e7			0.444586			0.222293	+	0.974980i	$0.428646\pi$
$72$	−1.52991e8	−	2.64988e8i	−0.670918	−	1.16206i
$73$	1.19056e8	−	2.06211e8i	0.490679	−	0.849881i	−0.509264	−	0.860611i	$-0.670082\pi$
$73$	1.19056e8	−	2.06211e8i	0.490679	−	0.849881i	0.999942	+	0.0107300i	$0.00341552\pi$
$74$	5.74636e7	−	9.95299e7i	0.222767	−	0.385843i
$75$	−2.01373e8	−	3.48788e8i	−0.734894	−	1.27287i
$76$	3.34685e7			0.115074
$77$		0			0
$78$	−4.12210e8			−1.26093
$79$	−9.42601e7	−	1.63263e8i	−0.272274	−	0.471592i	0.697170	−	0.716906i	$-0.254442\pi$
$79$	−9.42601e7	−	1.63263e8i	−0.272274	−	0.471592i	−0.969444	+	0.245314i	$0.921109\pi$
$80$	1.77319e8	−	3.07126e8i	0.484006	−	0.838322i
$81$	1.36193e8	−	2.35894e8i	0.351539	−	0.608884i
$82$	2.75636e8	+	4.77416e8i	0.673247	+	1.16610i
$83$	1.76014e8			0.407095			0.203547	−	0.979065i	$-0.434753\pi$
$83$	1.76014e8			0.407095			0.203547	+	0.979065i	$0.434753\pi$
$84$		0			0
$85$	−6.65551e8			−1.38292
$86$	3.80683e8	+	6.59362e8i	0.750447	+	1.29981i
$87$	−2.43682e8	+	4.22070e8i	−0.456023	+	0.789855i
$88$	−1.99393e8	+	3.45359e8i	−0.354436	+	0.613901i
$89$	−2.41517e8	−	4.18319e8i	−0.408030	−	0.706729i	0.586639	−	0.809849i	$-0.300451\pi$
$89$	−2.41517e8	−	4.18319e8i	−0.408030	−	0.706729i	−0.994669	+	0.103120i	$0.967118\pi$
$90$	−9.40725e8			−1.51137
$91$		0			0
$92$	6.97066e7			0.101445
$93$	−5.32309e8	−	9.21986e8i	−0.737888	−	1.27806i
$94$	−2.48367e8	+	4.30184e8i	−0.328109	+	0.568301i
$95$	2.57278e8	−	4.45619e8i	0.324076	−	0.561316i
$96$	3.03287e8	+	5.25309e8i	0.364446	+	0.631239i
$97$	2.28821e7			0.0262436			0.0131218	−	0.999914i	$-0.495823\pi$
$97$	2.28821e7			0.0262436			0.0131218	+	0.999914i	$0.495823\pi$
$98$		0			0
$99$	7.75799e8			0.811691
$100$	1.22747e8	+	2.12604e8i	0.122747	+	0.212604i
$101$	1.03216e8	−	1.78776e8i	0.0986966	−	0.170948i	−0.812449	−	0.583033i	$-0.801866\pi$
$101$	1.03216e8	−	1.78776e8i	0.0986966	−	0.170948i	0.911145	+	0.412085i	$0.135199\pi$
$102$	−6.95859e8	+	1.20526e9i	−0.636533	+	1.10251i
$103$	−1.47590e8	−	2.55634e8i	−0.129208	−	0.223795i	0.794162	−	0.607706i	$-0.207910\pi$
$103$	−1.47590e8	−	2.55634e8i	−0.129208	−	0.223795i	−0.923370	+	0.383911i	$0.874577\pi$
$104$	1.25649e9			1.05319
$105$		0			0
$106$	8.87678e8			0.682935
$107$	1.22501e9	+	2.12179e9i	0.903471	+	1.56486i	0.822956	+	0.568105i	$0.192323\pi$
$107$	1.22501e9	+	2.12179e9i	0.903471	+	1.56486i	0.0805150	+	0.996753i	$0.474344\pi$
$108$	6.33438e7	−	1.09715e8i	0.0448020	−	0.0775993i
$109$	1.02280e9	−	1.77153e9i	0.694016	−	1.20207i	−0.276495	−	0.961015i	$-0.589173\pi$
$109$	1.02280e9	−	1.77153e9i	0.694016	−	1.20207i	0.970511	−	0.241056i	$-0.0774937\pi$
$110$	6.13023e8	+	1.06179e9i	0.399218	+	0.691466i
$111$	1.23132e9			0.769869
$112$		0			0
$113$	1.59772e8			0.0921822			0.0460911	−	0.998937i	$-0.485324\pi$
$113$	1.59772e8			0.0921822			0.0460911	+	0.998937i	$0.485324\pi$
$114$	−5.37989e8	−	9.31824e8i	−0.298333	−	0.516728i
$115$	5.35846e8	−	9.28113e8i	0.285693	−	0.494835i
$116$	1.48537e8	−	2.57274e8i	0.0761682	−	0.131927i
$117$	−1.22219e9	−	2.11689e9i	−0.602977	−	1.04439i
$118$	3.70200e8			0.175779
$119$		0			0
$120$	5.18085e9			2.28079
$121$	6.73425e8	+	1.16641e9i	0.285598	+	0.494670i
$122$	−9.96000e8	+	1.72512e9i	−0.407043	+	0.705019i
$123$	−2.95314e9	+	5.11499e9i	−1.16335	+	2.01498i
$124$	3.24470e8	+	5.61999e8i	0.123247	+	0.213471i
$125$	−6.86192e7			−0.0251392
$126$		0			0
$127$	−5.15074e9			−1.75692			−0.878462	−	0.477813i	$-0.841430\pi$
$127$	−5.15074e9			−1.75692			−0.878462	+	0.477813i	$0.841430\pi$
$128$	7.19343e8	+	1.24594e9i	0.236860	+	0.410253i
$129$	−4.07860e9	+	7.06433e9i	−1.29675	+	2.24604i
$130$	1.93150e9	−	3.34546e9i	0.593131	−	1.02733i
$131$	5.08431e8	+	8.80628e8i	0.150838	+	0.261259i	0.931536	−	0.363650i	$-0.118469\pi$
$131$	5.08431e8	+	8.80628e8i	0.150838	+	0.261259i	−0.780698	+	0.624909i	$0.785136\pi$
$132$	−8.54394e8			−0.244949
$133$		0			0
$134$	−2.56908e9			−0.688345
$135$	−9.73868e8	−	1.68679e9i	−0.252347	−	0.437078i
$136$	2.12110e9	−	3.67386e9i	0.531663	−	0.920867i
$137$	−1.60440e9	+	2.77891e9i	−0.389108	+	0.673956i	−0.992330	−	0.123618i	$-0.960550\pi$
$137$	−1.60440e9	+	2.77891e9i	−0.389108	+	0.673956i	0.603221	+	0.797574i	$0.293884\pi$
$138$	−1.12050e9	−	1.94076e9i	−0.262999	−	0.455528i
$139$	−6.36396e8			−0.144598			−0.0722988	−	0.997383i	$-0.523034\pi$
$139$	−6.36396e8			−0.144598			−0.0722988	+	0.997383i	$0.523034\pi$
$140$		0			0
$141$	−5.32195e9			−1.13393
$142$	9.32752e8	+	1.61557e9i	0.192517	+	0.333449i
$143$	−1.59287e9	+	2.75894e9i	−0.318544	+	0.551734i
$144$	2.19875e9	−	3.80834e9i	0.426132	−	0.738082i
$145$	−2.28366e9	−	3.95541e9i	−0.429017	−	0.743080i
$146$	4.66614e9			0.849905
$147$		0			0
$148$	−7.50554e8			−0.128589
$149$	−2.50376e9	−	4.33664e9i	−0.416154	−	0.720800i	0.579395	−	0.815047i	$-0.303289\pi$
$149$	−2.50376e9	−	4.33664e9i	−0.416154	−	0.720800i	−0.995549	+	0.0942469i	$0.969956\pi$
$150$	3.94619e9	−	6.83501e9i	0.636455	−	1.10237i
$151$	1.27205e9	−	2.20326e9i	0.199118	−	0.344882i	−0.749125	−	0.662429i	$-0.769526\pi$
$151$	1.27205e9	−	2.20326e9i	0.199118	−	0.344882i	0.948243	+	0.317547i	$0.102859\pi$
$152$	1.63988e9	+	2.84036e9i	0.249182	+	0.431596i
$153$	−8.25279e9			−1.21756
$154$		0			0
$155$	9.97703e9			1.38838
$156$	1.34600e9	+	2.33135e9i	0.181964	+	0.315171i
$157$	5.71100e9	−	9.89174e9i	0.750177	−	1.29934i	−0.197560	−	0.980291i	$-0.563302\pi$
$157$	5.71100e9	−	9.89174e9i	0.750177	−	1.29934i	0.947737	−	0.319053i	$-0.103365\pi$
$158$	1.84716e9	−	3.19938e9i	0.235803	−	0.408422i
$159$	4.75524e9	+	8.23632e9i	0.590046	+	1.02199i
$160$	−5.68449e9			−0.685727
$161$		0			0
$162$	5.33782e9			0.608901
$163$	−5.67212e9	−	9.82441e9i	−0.629364	−	1.09009i	−0.987680	−	0.156489i	$-0.949982\pi$
$163$	−5.67212e9	−	9.82441e9i	−0.629364	−	1.09009i	0.358316	−	0.933600i	$-0.383351\pi$
$164$	1.80009e9	−	3.11785e9i	0.194311	−	0.336557i
$165$	−6.56787e9	+	1.13759e10i	−0.689837	+	1.19483i
$166$	1.72462e9	+	2.98714e9i	0.176282	+	0.305330i
$167$	1.04555e10			1.04021			0.520103	−	0.854104i	$-0.325894\pi$
$167$	1.04555e10			1.04021			0.520103	+	0.854104i	$0.325894\pi$
$168$		0			0
$169$	−5.66897e8			−0.0534582
$170$	−6.52122e9	−	1.12951e10i	−0.598837	−	1.03722i
$171$	3.19023e9	−	5.52565e9i	0.285325	−	0.494198i
$172$	2.48612e9	−	4.30608e9i	0.216593	−	0.375150i
$173$	−5.63685e9	−	9.76331e9i	−0.478442	−	0.828685i	0.521253	−	0.853402i	$-0.325465\pi$
$173$	−5.63685e9	−	9.76331e9i	−0.478442	−	0.828685i	−0.999694	+	0.0247172i	$0.992131\pi$
$174$	−9.55061e9			−0.789877
$175$		0			0
$176$	−5.73125e9			−0.450238
$177$	1.98314e9	+	3.43490e9i	0.151871	+	0.263048i
$178$	4.73288e9	−	8.19759e9i	0.353375	−	0.612063i
$179$	6.78310e9	−	1.17487e10i	0.493844	−	0.855363i	−0.506131	−	0.862457i	$-0.668925\pi$
$179$	6.78310e9	−	1.17487e10i	0.493844	−	0.855363i	0.999975	+	0.00709392i	$0.00225808\pi$
$180$	3.07179e9	+	5.32050e9i	0.218105	+	0.377769i
$181$	−2.03119e10			−1.40668			−0.703342	−	0.710851i	$-0.748310\pi$
$181$	−2.03119e10			−1.40668			−0.703342	+	0.710851i	$0.748310\pi$
$182$		0			0
$183$	−2.13421e10			−1.40672
$184$	3.41547e9	+	5.91577e9i	0.219670	+	0.380479i
$185$	−5.76963e9	+	9.99329e9i	−0.362139	+	0.627243i
$186$	1.04314e10	−	1.80677e10i	0.639048	−	1.10686i
$187$	5.37793e9	+	9.31485e9i	0.321609	+	0.557043i
$188$	3.24401e9			0.189396
$189$		0			0
$190$	1.00835e10			0.561331
$191$	1.71927e10	+	2.97787e10i	0.934748	+	1.61903i	0.775083	+	0.631859i	$0.217708\pi$
$191$	1.71927e10	+	2.97787e10i	0.934748	+	1.61903i	0.159664	+	0.987171i	$0.448959\pi$
$192$	−1.56310e10	+	2.70737e10i	−0.830101	+	1.43778i
$193$	−1.36102e10	+	2.35735e10i	−0.706084	+	1.22297i	0.260215	+	0.965551i	$0.416207\pi$
$193$	−1.36102e10	+	2.35735e10i	−0.706084	+	1.22297i	−0.966299	+	0.257422i	$0.917127\pi$
$194$	2.24204e8	+	3.88333e8i	0.0113641	+	0.0196833i
$195$	4.13878e10			2.04983
$196$		0			0
$197$	−1.52311e9			−0.0720499			−0.0360249	−	0.999351i	$-0.511470\pi$
$197$	−1.52311e9			−0.0720499			−0.0360249	+	0.999351i	$0.511470\pi$
$198$	7.60146e9	+	1.31661e10i	0.351482	+	0.608785i
$199$	−6.15674e9	+	1.06638e10i	−0.278299	+	0.482028i	−0.970962	−	0.239233i	$-0.923104\pi$
$199$	−6.15674e9	+	1.06638e10i	−0.278299	+	0.482028i	0.692663	+	0.721261i	$0.256437\pi$
$200$	−1.20287e10	+	2.08343e10i	−0.531598	+	0.920755i
$201$	−1.37624e10	−	2.38372e10i	−0.594721	−	1.03009i
$202$	4.04535e9			0.170952
$203$		0			0
$204$	9.08887e9			0.367430
$205$	−2.76752e10	−	4.79349e10i	−1.09446	−	1.89566i
$206$	2.89225e9	−	5.00952e9i	0.111901	−	0.193818i
$207$	6.64446e9	−	1.15085e10i	0.251532	−	0.435666i
$208$	9.02896e9	+	1.56386e10i	0.334467	+	0.579313i
$209$	−8.31566e9			−0.301466
$210$		0			0
$211$	−2.60114e10			−0.903426			−0.451713	−	0.892163i	$-0.649187\pi$
$211$	−2.60114e10			−0.903426			−0.451713	+	0.892163i	$0.649187\pi$
$212$	−2.89857e9	−	5.02047e9i	−0.0985536	−	0.170700i
$213$	−9.99341e9	+	1.73091e10i	−0.332664	+	0.576190i
$214$	−2.40060e10	+	4.15796e10i	−0.782451	+	1.35525i
$215$	−3.82224e10	−	6.62031e10i	−1.21996	−	2.11303i
$216$	1.24148e10			0.388060
$217$		0			0
$218$	4.00864e10			1.20210
$219$	2.49963e10	+	4.32948e10i	0.734306	+	1.27185i
$220$	4.00346e9	−	6.93420e9i	0.115222	−	0.199570i
$221$	1.69447e10	−	2.93491e10i	0.477824	−	0.827616i
$222$	1.20648e10	+	2.08968e10i	0.333373	+	0.577418i
$223$	−1.83087e10			−0.495777			−0.247889	−	0.968789i	$-0.579737\pi$
$223$	−1.83087e10			−0.495777			−0.247889	+	0.968789i	$0.579737\pi$
$224$		0			0
$225$	4.68013e10			1.21741
$226$	1.56548e9	+	2.71149e9i	0.0399172	+	0.0691386i
$227$	−1.19844e10	+	2.07575e10i	−0.299570	+	0.518871i	−0.976038	−	0.217602i	$-0.930177\pi$
$227$	−1.19844e10	+	2.07575e10i	−0.299570	+	0.518871i	0.676467	+	0.736473i	$0.263510\pi$
$228$	−3.51343e9	+	6.08545e9i	−0.0861043	+	0.149137i
$229$	1.50424e10	+	2.60541e10i	0.361457	+	0.626061i	0.988201	−	0.153164i	$-0.0489462\pi$
$229$	1.50424e10	+	2.60541e10i	0.361457	+	0.626061i	−0.626744	+	0.779225i	$0.715613\pi$
$230$	2.10014e10			0.494849
$231$		0			0
$232$	2.91120e10			0.659744
$233$	−6.75130e9	−	1.16936e10i	−0.150067	−	0.259924i	0.781185	−	0.624300i	$-0.214616\pi$
$233$	−6.75130e9	−	1.16936e10i	−0.150067	−	0.259924i	−0.931252	+	0.364376i	$0.881282\pi$
$234$	2.39505e10	−	4.14835e10i	0.522208	−	0.904492i
$235$	2.49372e10	−	4.31926e10i	0.533388	−	0.923854i
$236$	−1.20883e9	−	2.09375e9i	−0.0253665	−	0.0439361i
$237$	3.95806e10			0.814921
$238$		0			0
$239$	−3.75005e9			−0.0743440			−0.0371720	−	0.999309i	$-0.511835\pi$
$239$	−3.75005e9			−0.0743440			−0.0371720	+	0.999309i	$0.511835\pi$
$240$	3.72289e10	+	6.44824e10i	0.724319	+	1.25456i
$241$	−1.34568e10	+	2.33078e10i	−0.256960	+	0.445067i	−0.965426	−	0.260678i	$-0.916054\pi$
$241$	−1.34568e10	+	2.33078e10i	−0.256960	+	0.445067i	0.708466	+	0.705745i	$0.249387\pi$
$242$	−1.31968e10	+	2.28574e10i	−0.247342	+	0.428409i
$243$	3.83367e10	+	6.64011e10i	0.705320	+	1.22165i
$244$	1.30091e10			0.234960
$245$		0			0
$246$	−1.15742e11			−2.01504
$247$	1.31004e10	+	2.26906e10i	0.223949	+	0.387891i
$248$	−3.17967e10	+	5.50735e10i	−0.533764	+	0.924506i
$249$	−1.84774e10	+	3.20039e10i	−0.304610	+	0.527601i
$250$	−6.72347e8	−	1.16454e9i	−0.0108859	−	0.0188549i
$251$	−1.56458e10			−0.248810			−0.124405	−	0.992232i	$-0.539702\pi$
$251$	−1.56458e10			−0.248810			−0.124405	+	0.992232i	$0.539702\pi$
$252$		0			0
$253$	−1.73194e10			−0.265761
$254$	−5.04681e10	−	8.74134e10i	−0.760791	−	1.31773i
$255$	6.98677e10	−	1.21014e11i	1.03477	−	1.79228i
$256$	2.40215e10	−	4.16065e10i	0.349559	−	0.605454i
$257$	3.63435e10	+	6.29487e10i	0.519670	+	0.900094i	0.999739	+	0.0228635i	$0.00727831\pi$
$257$	3.63435e10	+	6.29487e10i	0.519670	+	0.900094i	−0.480069	+	0.877231i	$0.659388\pi$
$258$	−1.59852e11			−2.24610
$259$		0			0
$260$	−2.52281e10			−0.342377
$261$	−2.83172e10	−	4.90469e10i	−0.377719	−	0.654228i
$262$	−9.96345e9	+	1.72572e10i	−0.130633	+	0.226264i
$263$	4.11041e10	−	7.11943e10i	0.529766	−	0.917581i	−0.469631	−	0.882863i	$-0.655613\pi$
$263$	4.11041e10	−	7.11943e10i	0.529766	−	0.917581i	0.999397	−	0.0347186i	$-0.0110535\pi$
$264$	−4.18634e10	−	7.25096e10i	−0.530417	−	0.918709i
$265$	−8.91272e10			−1.11021
$266$		0			0
$267$	1.01415e11			1.22124
$268$	8.38893e9	+	1.45301e10i	0.0993345	+	0.172052i
$269$	1.64537e10	−	2.84986e10i	0.191592	−	0.331847i	−0.754186	−	0.656661i	$-0.771968\pi$
$269$	1.64537e10	−	2.84986e10i	0.191592	−	0.331847i	0.945778	+	0.324814i	$0.105302\pi$
$270$	1.90844e10	−	3.30551e10i	0.218545	−	0.378531i
$271$	−6.71241e10	−	1.16262e11i	−0.755991	−	1.30941i	−0.944880	−	0.327416i	$-0.893822\pi$
$271$	−6.71241e10	−	1.16262e11i	−0.755991	−	1.30941i	0.188889	−	0.981998i	$-0.439511\pi$
$272$	6.09679e10			0.675369
$273$		0			0
$274$	−6.28812e10			−0.673975
$275$	−3.04980e10	−	5.28241e10i	−0.321569	−	0.556975i
$276$	−7.31761e9	+	1.26745e10i	−0.0759064	+	0.131474i
$277$	−9.65495e10	+	1.67229e11i	−0.985351	+	1.70668i	−0.344986	+	0.938608i	$0.612116\pi$
$277$	−9.65495e10	+	1.67229e11i	−0.985351	+	1.70668i	−0.640365	+	0.768071i	$0.721217\pi$
$278$	−6.23556e9	−	1.08003e10i	−0.0626143	−	0.108451i
$279$	1.23715e11			1.22237
$280$		0			0
$281$	1.81503e10			0.173663			0.0868313	−	0.996223i	$-0.472326\pi$
$281$	1.81503e10			0.173663			0.0868313	+	0.996223i	$0.472326\pi$
$282$	−5.21457e10	−	9.03190e10i	−0.491018	−	0.850469i
$283$	6.52307e10	−	1.12983e11i	0.604523	−	1.04707i	−0.387603	−	0.921826i	$-0.626697\pi$
$283$	6.52307e10	−	1.12983e11i	0.604523	−	1.04707i	0.992127	−	0.125239i	$-0.0399697\pi$
$284$	6.09151e9	−	1.05508e10i	0.0555638	−	0.0962394i
$285$	5.40167e10	+	9.35596e10i	0.484982	+	0.840014i
$286$	−6.24294e10			−0.551750
$287$		0			0
$288$	−7.04873e10			−0.603733
$289$	2.08461e9	+	3.61064e9i	0.0175786	+	0.0304470i
$290$	4.47516e10	−	7.75121e10i	0.371550	−	0.643544i
$291$	−2.40210e9	+	4.16056e9i	−0.0196369	+	0.0340121i
$292$	−1.52365e10	−	2.63905e10i	−0.122649	−	0.212434i
$293$	1.61941e11			1.28367			0.641834	−	0.766843i	$-0.278174\pi$
$293$	1.61941e11			1.28367			0.641834	+	0.766843i	$0.278174\pi$
$294$		0			0
$295$	−3.71699e10			−0.285754
$296$	−3.67755e10	−	6.36970e10i	−0.278449	−	0.482288i
$297$	−1.57385e10	+	2.72599e10i	−0.117371	+	0.203292i
$298$	4.90648e10	−	8.49828e10i	0.360410	−	0.624249i
$299$	2.72849e10	+	4.72588e10i	0.197425	+	0.341950i
$300$	−5.15427e10			−0.367385
$301$		0			0
$302$	4.98556e10			0.344891
$303$	2.16707e10	+	3.75348e10i	0.147700	+	0.255825i
$304$	−2.35680e10	+	4.08210e10i	−0.158267	+	0.274127i
$305$	1.00003e11	−	1.73211e11i	0.661705	−	1.14611i
$306$	−8.08628e10	−	1.40058e11i	−0.527233	−	0.913194i
$307$	−2.13521e11			−1.37188			−0.685942	−	0.727656i	$-0.740610\pi$
$307$	−2.13521e11			−1.37188			−0.685942	+	0.727656i	$0.740610\pi$
$308$		0			0
$309$	6.19745e10			0.386723
$310$	9.77573e10	+	1.69321e11i	0.601203	+	1.04132i
$311$	−6.44473e10	+	1.11626e11i	−0.390646	+	0.676618i	−0.992535	−	0.121961i	$-0.961082\pi$
$311$	−6.44473e10	+	1.11626e11i	−0.390646	+	0.676618i	0.601889	+	0.798580i	$0.294415\pi$
$312$	−1.31903e11	+	2.28462e11i	−0.788057	+	1.36495i
$313$	8.90227e10	+	1.54192e11i	0.524265	+	0.908054i	0.999601	+	0.0282496i	$0.00899332\pi$
$313$	8.90227e10	+	1.54192e11i	0.524265	+	0.908054i	−0.475336	+	0.879805i	$0.657673\pi$
$314$	2.23831e11			1.29938
$315$		0			0
$316$	−2.41265e10			−0.136114
$317$	7.34098e10	+	1.27149e11i	0.408307	+	0.707209i	0.994700	−	0.102818i	$-0.0327858\pi$
$317$	7.34098e10	+	1.27149e11i	0.408307	+	0.707209i	−0.586393	+	0.810027i	$0.699452\pi$
$318$	−9.31860e10	+	1.61403e11i	−0.511009	+	0.885094i
$319$	−3.69058e10	+	6.39227e10i	−0.199543	+	0.345619i
$320$	−1.46485e11	−	2.53720e11i	−0.780943	−	1.35263i
$321$	−5.14395e11			−2.70411
$322$		0			0
$323$	8.84603e10			0.452207
$324$	−1.74298e10	−	3.01893e10i	−0.0878699	−	0.152195i
$325$	−9.60927e10	+	1.66437e11i	−0.477766	+	0.827515i
$326$	1.11154e11	−	1.92524e11i	0.545060	−	0.944072i
$327$	2.14740e11	+	3.71941e11i	1.03860	+	1.79891i
$328$	3.52803e11			1.68306
$329$		0			0
$330$	−2.57414e11			−1.19487
$331$	8.55668e10	+	1.48206e11i	0.391813	+	0.678641i	0.992689	−	0.120702i	$-0.0385145\pi$
$331$	8.55668e10	+	1.48206e11i	0.391813	+	0.678641i	−0.600875	+	0.799343i	$0.705181\pi$
$332$	1.12630e10	−	1.95080e10i	0.0508782	−	0.0881236i
$333$	−7.15431e10	+	1.23916e11i	−0.318837	+	0.552242i
$334$	1.02445e11	+	1.77440e11i	0.450435	+	0.780176i
$335$	2.57948e11			1.11900
$336$		0			0
$337$	1.14022e11			0.481564			0.240782	−	0.970579i	$-0.422596\pi$
$337$	1.14022e11			0.481564			0.240782	+	0.970579i	$0.422596\pi$
$338$	−5.55459e9	−	9.62084e9i	−0.0231487	−	0.0400948i
$339$	−1.67724e10	+	2.90506e10i	−0.0689758	+	0.119470i
$340$	−4.25880e10	+	7.37646e10i	−0.172835	+	0.299359i
$341$	−8.06186e10	−	1.39635e11i	−0.322880	−	0.559244i
$342$	1.25035e11			0.494212
$343$		0			0
$344$	4.87257e11			1.87605
$345$	1.12503e11	+	1.94861e11i	0.427543	+	0.740525i
$346$	1.10462e11	−	1.91326e11i	0.414354	−	0.717683i
$347$	−1.43423e10	+	2.48416e10i	−0.0531051	+	0.0919808i	−0.891356	−	0.453304i	$-0.850245\pi$
$347$	−1.43423e10	+	2.48416e10i	−0.0531051	+	0.0919808i	0.838251	+	0.545285i	$0.183579\pi$
$348$	3.11860e10	+	5.40158e10i	0.113986	+	0.197430i
$349$	3.10537e11			1.12047			0.560234	−	0.828334i	$-0.310711\pi$
$349$	3.10537e11			1.12047			0.560234	+	0.828334i	$0.310711\pi$
$350$		0			0
$351$	9.91774e10			0.348763
$352$	4.59330e10	+	7.95584e10i	0.159472	+	0.276213i
$353$	2.42567e11	−	4.20138e11i	0.831467	−	1.44014i	−0.0654074	−	0.997859i	$-0.520835\pi$
$353$	2.42567e11	−	4.20138e11i	0.831467	−	1.44014i	0.896875	−	0.442285i	$-0.145832\pi$
$354$	−3.88626e10	+	6.73119e10i	−0.131528	+	0.227812i
$355$	−9.36528e10	−	1.62211e11i	−0.312963	−	0.542068i
$356$	−6.18178e10			−0.203981
$357$		0			0
$358$	2.65850e11			0.855387
$359$	−1.53427e11	−	2.65743e11i	−0.487501	−	0.844377i	0.512395	−	0.858750i	$-0.328758\pi$
$359$	−1.53427e11	−	2.65743e11i	−0.487501	−	0.844377i	−0.999897	+	0.0143725i	$0.995425\pi$
$360$	−3.01022e11	+	5.21385e11i	−0.944576	+	1.63605i
$361$	1.27148e11	−	2.20227e11i	0.394029	−	0.682478i
$362$	−1.99021e11	−	3.44714e11i	−0.609129	−	1.05504i
$363$	−2.82777e11			−0.854800
$364$		0			0
$365$	−4.68503e11			−1.38164
$366$	−2.09115e11	−	3.62197e11i	−0.609143	−	1.05507i
$367$	−2.54740e11	+	4.41223e11i	−0.732993	+	1.26958i	0.222605	+	0.974909i	$0.428544\pi$
$367$	−2.54740e11	+	4.41223e11i	−0.732993	+	1.26958i	−0.955598	+	0.294673i	$0.904789\pi$
$368$	−4.90863e10	+	8.50199e10i	−0.139523	+	0.241660i
$369$	−3.43171e11	−	5.94390e11i	−0.963590	−	1.66899i
$370$	−2.26129e11			−0.627261
$371$		0			0
$372$	−1.36248e11			−0.368882
$373$	2.13628e11	+	3.70015e11i	0.571438	+	0.989759i	0.996419	+	0.0845567i	$0.0269474\pi$
$373$	2.13628e11	+	3.70015e11i	0.571438	+	0.989759i	−0.424981	+	0.905202i	$0.639719\pi$
$374$	−1.05388e11	+	1.82538e11i	−0.278529	+	0.482427i
$375$	7.20346e9	−	1.24768e10i	0.0188105	−	0.0325807i
$376$	1.58949e11	+	2.75308e11i	0.410122	+	0.710353i
$377$	2.32564e11			0.592935
$378$		0			0
$379$	4.28378e7			0.000106647			5.33237e−5	−	1.00000i	$-0.499983\pi$
$379$	4.28378e7			0.000106647			5.33237e−5		1.00000i	$0.499983\pi$
$380$	−3.29260e10	−	5.70295e10i	−0.0810052	−	0.140305i
$381$	5.40710e11	−	9.36538e11i	1.31463	−	2.27700i
$382$	−3.36917e11	+	5.83557e11i	−0.809538	+	1.40216i
$383$	8.72269e9	+	1.51081e10i	0.0207136	+	0.0358770i	0.876196	−	0.481954i	$-0.160073\pi$
$383$	8.72269e9	+	1.51081e10i	0.0207136	+	0.0358770i	−0.855483	+	0.517831i	$0.826740\pi$
$384$	−3.02059e11			−0.708926
$385$		0			0
$386$	−5.33423e11			−1.22301
$387$	−4.73956e11	−	8.20915e11i	−1.07408	−	1.86037i
$388$	1.46421e9	−	2.53608e9i	0.00327989	−	0.00568094i
$389$	3.04707e11	−	5.27768e11i	0.674698	−	1.16861i	−0.301859	−	0.953353i	$-0.597607\pi$
$389$	3.04707e11	−	5.27768e11i	0.674698	−	1.16861i	0.976557	−	0.215259i	$-0.0690594\pi$
$390$	4.05528e11	+	7.02395e11i	0.887626	+	1.53741i
$391$	1.84241e11			0.398649
$392$		0			0
$393$	−2.13495e11			−0.451462
$394$	−1.49238e10	−	2.58488e10i	−0.0311994	−	0.0540389i
$395$	−1.85464e11	+	3.21234e11i	−0.383330	+	0.663948i
$396$	4.96427e10	−	8.59837e10i	0.101444	−	0.175706i
$397$	2.73104e11	+	4.73030e11i	0.551786	+	0.955721i	0.998146	+	0.0608675i	$0.0193867\pi$
$397$	2.73104e11	+	4.73030e11i	0.551786	+	0.955721i	−0.446360	+	0.894853i	$0.647280\pi$
$398$	−2.41301e11			−0.482042
$399$		0			0
$400$	−3.45747e11			−0.675286
$401$	2.93880e11	+	5.09014e11i	0.567570	+	0.983061i	0.996805	+	0.0798679i	$0.0254498\pi$
$401$	2.93880e11	+	5.09014e11i	0.567570	+	0.983061i	−0.429235	+	0.903193i	$0.641217\pi$
$402$	2.69695e11	−	4.67126e11i	0.515058	−	0.892106i
$403$	−2.54012e11	+	4.39961e11i	−0.479712	+	0.830886i
$404$	−1.32095e10	−	2.28794e10i	−0.0246700	−	0.0427296i
$405$	−5.35943e11			−0.989854
$406$		0			0
$407$	1.86484e11			0.336874
$408$	4.45335e11	+	7.71343e11i	0.795639	+	1.37809i
$409$	−2.06201e11	+	3.57151e11i	−0.364365	+	0.631099i	−0.988674	−	0.150079i	$-0.952047\pi$
$409$	−2.06201e11	+	3.57151e11i	−0.364365	+	0.631099i	0.624309	+	0.781178i	$0.285381\pi$
$410$	5.42337e11	−	9.39355e11i	0.947855	−	1.64173i
$411$	−3.36851e11	−	5.83444e11i	−0.582305	−	1.00858i
$412$	−3.77767e10			−0.0645932
$413$		0			0
$414$	2.60416e11			0.435679
$415$	−1.73161e11	−	2.99923e11i	−0.286571	−	0.496356i
$416$	1.44725e11	−	2.50671e11i	0.236932	−	0.410378i
$417$	6.68071e10	−	1.15713e11i	0.108196	−	0.187401i
$418$	−8.14788e10	−	1.41125e11i	−0.130542	−	0.226106i
$419$	4.82213e11			0.764322			0.382161	−	0.924096i	$-0.375180\pi$
$419$	4.82213e11			0.764322			0.382161	+	0.924096i	$0.375180\pi$
$420$		0			0
$421$	−2.29026e11			−0.355317			−0.177658	−	0.984092i	$-0.556852\pi$
$421$	−2.29026e11			−0.355317			−0.177658	+	0.984092i	$0.556852\pi$
$422$	−2.54866e11	−	4.41440e11i	−0.391206	−	0.677589i
$423$	3.09220e11	−	5.35585e11i	0.469609	−	0.813387i
$424$	2.84047e11	−	4.91984e11i	0.426820	−	0.739273i
$425$	3.24432e11	+	5.61933e11i	0.482362	+	0.835476i
$426$	−3.91671e11			−0.576207
$427$		0			0
$428$	3.13551e11			0.451659
$429$	−3.34431e11	−	5.79252e11i	−0.476704	−	0.825676i
$430$	7.49024e11	−	1.29735e12i	1.05654	−	1.82999i
$431$	4.94384e10	−	8.56299e10i	0.0690108	−	0.119530i	−0.829455	−	0.558573i	$-0.811349\pi$
$431$	4.94384e10	−	8.56299e10i	0.0690108	−	0.119530i	0.898466	+	0.439043i	$0.144682\pi$
$432$	8.92114e10	+	1.54519e11i	0.123238	+	0.213454i
$433$	−1.10144e12			−1.50580			−0.752899	−	0.658136i	$-0.771345\pi$
$433$	−1.10144e12			−1.50580			−0.752899	+	0.658136i	$0.771345\pi$
$434$		0			0
$435$	9.58928e11			1.28406
$436$	−1.30896e11	−	2.26718e11i	−0.173475	−	0.300467i
$437$	−7.12209e10	+	1.23358e11i	−0.0934202	+	0.161809i
$438$	−4.89839e11	+	8.48426e11i	−0.635945	+	1.10149i
$439$	−8.29491e10	−	1.43672e11i	−0.106591	−	0.184621i	0.807796	−	0.589462i	$-0.200660\pi$
$439$	−8.29491e10	−	1.43672e11i	−0.106591	−	0.184621i	−0.914387	+	0.404841i	$0.867327\pi$
$440$	7.84643e11			0.998011
$441$		0			0
$442$	6.64112e11			0.827639
$443$	−7.64532e11	−	1.32421e12i	−0.943146	−	1.63358i	−0.759422	−	0.650599i	$-0.774518\pi$
$443$	−7.64532e11	−	1.32421e12i	−0.943146	−	1.63358i	−0.183724	−	0.982978i	$-0.558815\pi$
$444$	7.87910e10	−	1.36470e11i	0.0962174	−	0.166653i
$445$	−4.75204e11	+	8.23077e11i	−0.574460	+	0.994994i
$446$	−1.79393e11	−	3.10718e11i	−0.214684	−	0.371843i
$447$	1.05135e12			1.24556
$448$		0			0
$449$	1.61276e11			0.187268			0.0936338	−	0.995607i	$-0.470152\pi$
$449$	1.61276e11			0.187268			0.0936338	+	0.995607i	$0.470152\pi$
$450$	4.58570e11	+	7.94266e11i	0.527168	+	0.913082i
$451$	−4.47255e11	+	7.74668e11i	−0.509050	+	0.881701i
$452$	1.02237e10	−	1.77079e10i	0.0115208	−	0.0199546i
$453$	2.67074e11	+	4.62585e11i	0.297981	+	0.516119i
$454$	−4.69702e11			−0.518885
$455$		0			0
$456$	−6.88602e11			−0.745807
$457$	4.91038e11	+	8.50503e11i	0.526614	+	0.912122i	0.999519	+	0.0310087i	$0.00987197\pi$
$457$	4.91038e11	+	8.50503e11i	0.526614	+	0.912122i	−0.472905	+	0.881113i	$0.656795\pi$
$458$	−2.94777e11	+	5.10569e11i	−0.313040	+	0.542200i
$459$	1.67423e11	−	2.89986e11i	0.176059	−	0.304944i
$460$	−6.85767e10	−	1.18778e11i	−0.0714112	−	0.123688i
$461$	1.27083e12			1.31049			0.655245	−	0.755417i	$-0.272565\pi$
$461$	1.27083e12			1.31049			0.655245	+	0.755417i	$0.272565\pi$
$462$		0			0
$463$	−1.18923e12			−1.20268			−0.601342	−	0.798992i	$-0.705367\pi$
$463$	−1.18923e12			−1.20268			−0.601342	+	0.798992i	$0.705367\pi$
$464$	2.09195e11	+	3.62336e11i	0.209517	+	0.362895i
$465$	−1.04736e12	+	1.81408e12i	−1.03886	+	1.79936i
$466$	1.32302e11	−	2.29153e11i	0.129966	−	0.225107i
$467$	−8.47027e11	−	1.46709e12i	−0.824083	−	1.42735i	−0.902618	−	0.430443i	$-0.858357\pi$
$467$	−8.47027e11	−	1.46709e12i	−0.824083	−	1.42735i	0.0785347	−	0.996911i	$-0.474976\pi$
$468$	−3.12827e11			−0.301438
$469$		0			0
$470$	9.77363e11			0.923880
$471$	1.19905e12	+	2.07681e12i	1.12265	+	1.94448i
$472$	1.18460e11	−	2.05179e11i	0.109858	−	0.190280i
$473$	−6.17706e11	+	1.06990e12i	−0.567423	+	0.982805i
$474$	3.87820e11	+	6.71725e11i	0.352881	+	0.611208i
$475$	−5.01655e11			−0.452152
$476$		0			0
$477$	−1.10517e12			−0.977456
$478$	−3.67438e10	−	6.36422e10i	−0.0321928	−	0.0557596i
$479$	−3.77462e11	+	6.53783e11i	−0.327614	+	0.567445i	−0.982038	−	0.188683i	$-0.939578\pi$
$479$	−3.77462e11	+	6.53783e11i	−0.327614	+	0.567445i	0.654423	+	0.756128i	$0.272911\pi$
$480$	5.96742e11	−	1.03359e12i	0.513099	−	0.888713i
$481$	−2.93785e11	−	5.08851e11i	−0.250252	−	0.433449i
$482$	−5.27411e11			−0.445080
$483$		0			0
$484$	1.72368e11			0.142775
$485$	−2.25112e10	−	3.89906e10i	−0.0184740	−	0.0319979i
$486$	−7.51263e11	+	1.30123e12i	−0.610842	+	1.05801i
$487$	5.45763e11	−	9.45290e11i	0.439667	−	0.761526i	−0.557997	−	0.829843i	$-0.688430\pi$
$487$	5.45763e11	−	9.45290e11i	0.439667	−	0.761526i	0.997664	+	0.0683175i	$0.0217631\pi$
$488$	6.37418e11	+	1.10404e12i	0.508786	+	0.881243i
$489$	2.38178e12			1.88370
$490$		0			0
$491$	−6.37184e11			−0.494764			−0.247382	−	0.968918i	$-0.579570\pi$
$491$	−6.37184e11			−0.494764			−0.247382	+	0.968918i	$0.579570\pi$
$492$	3.77938e11	+	6.54607e11i	0.290789	+	0.503661i
$493$	3.92597e11	−	6.79997e11i	0.299320	−	0.518437i
$494$	−2.56722e11	+	4.44655e11i	−0.193951	+	0.335933i
$495$	−7.63223e11	−	1.32194e12i	−0.571384	−	0.989666i
$496$	−9.13948e11			−0.678038
$497$		0			0
$498$	−7.24185e11			−0.527616
$499$	−7.17606e11	−	1.24293e12i	−0.518124	−	0.897417i	−0.999778	−	0.0210554i	$-0.993297\pi$
$499$	−7.17606e11	−	1.24293e12i	−0.518124	−	0.897417i	0.481655	−	0.876361i	$-0.340036\pi$
$500$	−4.39089e9	+	7.60524e9i	−0.00314186	+	0.00544187i
$501$	−1.09759e12	+	1.90107e12i	−0.778339	+	1.34812i
$502$	−1.53302e11	−	2.65526e11i	−0.107741	−	0.186612i
$503$	−1.29165e12			−0.899683			−0.449842	−	0.893108i	$-0.648520\pi$
$503$	−1.29165e12			−0.899683			−0.449842	+	0.893108i	$0.648520\pi$
$504$		0			0
$505$	−4.06173e11			−0.277907
$506$	−1.69700e11	−	2.93929e11i	−0.115081	−	0.199327i
$507$	5.95113e10	−	1.03077e11i	0.0400003	−	0.0692826i
$508$	−3.29591e11	+	5.70869e11i	−0.219578	+	0.380321i
$509$	1.06901e11	+	1.85158e11i	0.0705914	+	0.122268i	0.899161	−	0.437619i	$-0.144178\pi$
$509$	1.06901e11	+	1.85158e11i	0.0705914	+	0.122268i	−0.828569	+	0.559887i	$0.810845\pi$
$510$	2.73832e12			1.79233
$511$		0			0
$512$	1.67808e12			1.07919
$513$	1.29440e11	+	2.24196e11i	0.0825163	+	0.142922i
$514$	−7.12204e11	+	1.23357e12i	−0.450060	+	0.779526i
$515$	−2.90396e11	+	5.02981e11i	−0.181911	+	0.315078i
$516$	5.21972e11	+	9.04082e11i	0.324133	+	0.561415i
$517$	−8.06013e11			−0.496175
$518$		0			0
$519$	2.36696e12			1.43198
$520$	−1.23612e12	−	2.14102e12i	−0.741388	−	1.28412i
$521$	−2.67755e11	+	4.63764e11i	−0.159209	+	0.275758i	−0.934584	−	0.355744i	$-0.884228\pi$
$521$	−2.67755e11	+	4.63764e11i	−0.159209	+	0.275758i	0.775375	+	0.631501i	$0.217561\pi$
$522$	5.54918e11	−	9.61145e11i	0.327123	−	0.566594i
$523$	1.84565e11	+	3.19677e11i	0.107868	+	0.186833i	0.914906	−	0.403666i	$-0.132264\pi$
$523$	1.84565e11	+	3.19677e11i	0.107868	+	0.186833i	−0.807038	+	0.590499i	$0.798931\pi$
$524$	1.30136e11			0.0754063
$525$		0			0
$526$	1.61099e12			0.917607
$527$	8.57605e11	+	1.48541e12i	0.484328	+	0.838880i
$528$	6.01651e11	−	1.04209e12i	0.336893	−	0.583516i
$529$	7.52241e11	−	1.30292e12i	0.417644	−	0.723381i
$530$	−8.73289e11	−	1.51258e12i	−0.480747	−	0.832678i
$531$	−4.60904e11			−0.251585
$532$		0			0
$533$	2.81841e12			1.51262
$534$	9.93689e11	+	1.72112e12i	0.528829	+	0.915958i
$535$	2.41032e12	−	4.17479e12i	1.27198	−	2.20314i
$536$	−8.22078e11	+	1.42388e12i	−0.430201	+	0.745131i
$537$	1.42414e12	+	2.46669e12i	0.739042	+	1.28006i
$538$	6.44868e11			0.331857
$539$		0			0
$540$	−2.49268e11			−0.126152
$541$	−1.01264e12	−	1.75394e12i	−0.508237	−	0.880293i	−0.999955	−	0.00953769i	$-0.996964\pi$
$541$	−1.01264e12	−	1.75394e12i	−0.508237	−	0.880293i	0.491717	−	0.870755i	$-0.336369\pi$
$542$	1.31540e12	−	2.27833e12i	0.654726	−	1.13402i
$543$	2.13229e12	−	3.69323e12i	1.05256	−	1.82308i
$544$	−4.88627e11	−	8.46326e11i	−0.239211	−	0.414326i
$545$	−4.02487e12			−1.95419
$546$		0			0
$547$	−3.52443e12			−1.68324			−0.841621	−	0.540069i	$-0.818398\pi$
$547$	−3.52443e12			−1.68324			−0.841621	+	0.540069i	$0.818398\pi$
$548$	2.05329e11	+	3.55640e11i	0.0972606	+	0.168460i
$549$	1.24003e12	−	2.14780e12i	0.582583	−	1.00906i
$550$	5.97654e11	−	1.03517e12i	0.278495	−	0.482368i
$551$	3.03528e11	+	5.25725e11i	0.140287	+	0.242983i
$552$	−1.43419e12			−0.657476
$553$		0			0
$554$	−3.78406e12			−1.70673
$555$	−1.21136e12	−	2.09814e12i	−0.541944	−	0.938675i
$556$	−4.07225e10	+	7.05334e10i	−0.0180716	+	0.0313010i
$557$	−3.55817e11	+	6.16292e11i	−0.156631	+	0.271293i	−0.933652	−	0.358182i	$-0.883397\pi$
$557$	−3.55817e11	+	6.16292e11i	−0.156631	+	0.271293i	0.777021	+	0.629475i	$0.216730\pi$
$558$	1.21219e12	+	2.09957e12i	0.529316	+	0.916802i
$559$	3.89252e12			1.68608
$560$		0			0
$561$	−2.25824e12			−0.962581
$562$	1.77841e11	+	3.08030e11i	0.0752003	+	0.130251i
$563$	−1.82812e12	+	3.16640e12i	−0.766863	+	1.32825i	0.172393	+	0.985028i	$0.444850\pi$
$563$	−1.82812e12	+	3.16640e12i	−0.766863	+	1.32825i	−0.939256	+	0.343218i	$0.888483\pi$
$564$	−3.40547e11	+	5.89845e11i	−0.141717	+	0.245461i
$565$	−1.57182e11	−	2.72247e11i	−0.0648910	−	0.112395i
$566$	2.55658e12			1.04709
$567$		0			0
$568$	1.19388e12			0.481276
$569$	5.35022e11	+	9.26686e11i	0.213977	+	0.370619i	0.952956	−	0.303110i	$-0.0980250\pi$
$569$	5.35022e11	+	9.26686e11i	0.213977	+	0.370619i	−0.738979	+	0.673729i	$0.764692\pi$
$570$	−1.05854e12	+	1.83344e12i	−0.420019	+	0.727494i
$571$	−4.09702e11	+	7.09624e11i	−0.161289	+	0.279361i	−0.935331	−	0.353773i	$-0.884899\pi$
$571$	−4.09702e11	+	7.09624e11i	−0.161289	+	0.279361i	0.774042	+	0.633134i	$0.218232\pi$
$572$	2.03853e11	+	3.53084e11i	0.0796225	+	0.137910i
$573$	−7.21938e12			−2.79772
$574$		0			0
$575$	−1.04482e12			−0.398600
$576$	−1.81641e12	−	3.14611e12i	−0.687563	−	1.19089i
$577$	−1.30100e12	+	2.25340e12i	−0.488637	+	0.846343i	−0.999915	−	0.0130720i	$-0.995839\pi$
$577$	−1.30100e12	+	2.25340e12i	−0.488637	+	0.846343i	0.511278	+	0.859415i	$0.329172\pi$
$578$	−4.08509e10	+	7.07558e10i	−0.0152239	+	0.0263686i
$579$	−2.85752e12	−	4.94937e12i	−1.05666	−	1.83019i
$580$	−5.84517e11			−0.214472
$581$		0			0
$582$	−9.41455e10			−0.0340131
$583$	7.20185e11	+	1.24740e12i	0.258188	+	0.447194i
$584$	1.49312e12	−	2.58615e12i	0.531172	−	0.920018i
$585$	−2.40475e12	+	4.16515e12i	−0.848924	+	1.47038i
$586$	1.58674e12	+	2.74831e12i	0.555860	+	0.962779i
$587$	5.66219e11			0.196840			0.0984199	−	0.995145i	$-0.468621\pi$
$587$	5.66219e11			0.196840			0.0984199	+	0.995145i	$0.468621\pi$
$588$		0			0
$589$	−1.32608e12			−0.453994
$590$	−3.64199e11	−	6.30811e11i	−0.123738	−	0.214321i
$591$	1.59892e11	−	2.76941e11i	0.0539117	−	0.0933777i
$592$	5.28528e11	−	9.15437e11i	0.176856	−	0.306324i
$593$	1.44623e12	+	2.50495e12i	0.480278	+	0.831865i	0.999744	−	0.0226255i	$-0.00720255\pi$
$593$	1.44623e12	+	2.50495e12i	0.480278	+	0.831865i	−0.519466	+	0.854491i	$0.673869\pi$
$594$	−6.16839e11			−0.203298
$595$		0			0
$596$	−6.40854e11			−0.208042
$597$	−1.29263e12	−	2.23891e12i	−0.416477	−	0.721360i
$598$	−5.34688e11	+	9.26106e11i	−0.170980	+	0.296146i
$599$	2.96101e12	−	5.12862e12i	0.939764	−	1.62772i	0.173855	−	0.984771i	$-0.444378\pi$
$599$	2.96101e12	−	5.12862e12i	0.939764	−	1.62772i	0.765910	−	0.642948i	$-0.222289\pi$
$600$	−2.52548e12	−	4.37426e12i	−0.795542	−	1.37792i
$601$	−2.24993e12			−0.703450			−0.351725	−	0.936103i	$-0.614405\pi$
$601$	−2.24993e12			−0.703450			−0.351725	+	0.936103i	$0.614405\pi$
$602$		0			0
$603$	3.19855e12			0.985201
$604$	−1.62795e11	−	2.81970e11i	−0.0497710	−	0.0862058i
$605$	1.32502e12	−	2.29500e12i	0.402089	−	0.696439i
$606$	−4.24670e11	+	7.35550e11i	−0.127916	+	0.221557i
$607$	4.72003e11	+	8.17534e11i	0.141122	+	0.244431i	0.927920	−	0.372780i	$-0.121596\pi$
$607$	4.72003e11	+	8.17534e11i	0.141122	+	0.244431i	−0.786797	+	0.617212i	$0.788262\pi$
$608$	7.55542e11			0.224229
$609$		0			0
$610$	3.91942e12			1.14614
$611$	1.26979e12	+	2.19933e12i	0.368591	+	0.638419i
$612$	−5.28089e11	+	9.14677e11i	−0.152169	+	0.263564i
$613$	−9.56847e11	+	1.65731e12i	−0.273697	+	0.474058i	−0.969806	−	0.243879i	$-0.921580\pi$
$613$	−9.56847e11	+	1.65731e12i	−0.273697	+	0.474058i	0.696108	+	0.717937i	$0.254913\pi$
$614$	−2.09213e12	−	3.62367e12i	−0.594060	−	1.02894i
$615$	1.16211e13			3.27573
$616$		0			0
$617$	−5.85573e12			−1.62666			−0.813332	−	0.581800i	$-0.802349\pi$
$617$	−5.85573e12			−1.62666			−0.813332	+	0.581800i	$0.802349\pi$
$618$	6.07241e11	+	1.05177e12i	0.167461	+	0.290050i
$619$	3.15408e11	−	5.46303e11i	0.0863505	−	0.149563i	−0.819615	−	0.572914i	$-0.805813\pi$
$619$	3.15408e11	−	5.46303e11i	0.0863505	−	0.149563i	0.905966	+	0.423351i	$0.139146\pi$
$620$	6.38422e11	−	1.10578e12i	0.173518	−	0.300542i
$621$	2.69591e11	+	4.66945e11i	0.0727433	+	0.125995i
$622$	−2.52588e12			−0.676638
$623$		0			0
$624$	−3.79134e12			−1.00107
$625$	1.94080e12	+	3.36156e12i	0.508769	+	0.881213i
$626$	−1.74453e12	+	3.02162e12i	−0.454040	+	0.786420i
$627$	8.72955e11	−	1.51200e12i	0.225573	−	0.390705i
$628$	−7.30884e11	−	1.26593e12i	−0.187512	−	0.324781i
$629$	−1.98378e12			−0.505319
$630$		0			0
$631$	5.39720e12			1.35530			0.677652	−	0.735383i	$-0.262998\pi$
$631$	5.39720e12			1.35530			0.677652	+	0.735383i	$0.262998\pi$
$632$	−1.18215e12	−	2.04754e12i	−0.294743	−	0.510510i
$633$	2.73060e12	−	4.72955e12i	0.675993	−	1.17085i
$634$	−1.43857e12	+	2.49168e12i	−0.353615	+	0.612478i
$635$	5.06725e12	+	8.77673e12i	1.23677	+	2.14216i
$636$	1.21714e12			0.294973
$637$		0			0
$638$	−1.44645e12			−0.345629
$639$	−1.16129e12	−	2.01141e12i	−0.275541	−	0.477252i
$640$	1.41537e12	−	2.45149e12i	0.333472	−	0.577590i
$641$	−4.05089e12	+	7.01635e12i	−0.947741	+	1.64154i	−0.197572	+	0.980288i	$0.563306\pi$
$641$	−4.05089e12	+	7.01635e12i	−0.947741	+	1.64154i	−0.750169	+	0.661247i	$0.770028\pi$
$642$	−5.04016e12	−	8.72982e12i	−1.17095	−	2.02814i
$643$	7.06646e12			1.63024			0.815122	−	0.579290i	$-0.196670\pi$
$643$	7.06646e12			1.63024			0.815122	+	0.579290i	$0.196670\pi$
$644$		0			0
$645$	1.60499e13			3.65136
$646$	8.66755e11	+	1.50126e12i	0.195817	+	0.339165i
$647$	−1.87113e12	+	3.24089e12i	−0.419792	+	0.727100i	−0.995918	−	0.0902600i	$-0.971230\pi$
$647$	−1.87113e12	+	3.24089e12i	−0.419792	+	0.727100i	0.576127	+	0.817360i	$0.304564\pi$
$648$	1.70805e12	−	2.95842e12i	0.380550	−	0.659132i
$649$	3.00348e11	+	5.20218e11i	0.0664544	+	0.115102i
$650$	−3.76615e12			−0.827538
$651$		0			0
$652$	−1.45182e12			−0.314628
$653$	2.90962e12	+	5.03961e12i	0.626220	+	1.08465i	0.988304	+	0.152500i	$0.0487323\pi$
$653$	2.90962e12	+	5.03961e12i	0.626220	+	1.08465i	−0.362083	+	0.932146i	$0.617934\pi$
$654$	−4.20816e12	+	7.28874e12i	−0.899481	+	1.55795i
$655$	1.00038e12	−	1.73271e12i	0.212363	−	0.367824i
$656$	2.53520e12	+	4.39109e12i	0.534496	+	0.925773i
$657$	−5.80942e12			−1.21643
$658$		0			0
$659$	5.67402e12			1.17194			0.585971	−	0.810332i	$-0.300713\pi$
$659$	5.67402e12			1.17194			0.585971	+	0.810332i	$0.300713\pi$
$660$	8.40545e11	+	1.45587e12i	0.172430	+	0.298658i
$661$	−3.81176e12	+	6.60217e12i	−0.776640	+	1.34518i	0.157229	+	0.987562i	$0.449744\pi$
$661$	−3.81176e12	+	6.60217e12i	−0.776640	+	1.34518i	−0.933868	+	0.357617i	$0.883589\pi$
$662$	−1.67681e12	+	2.90432e12i	−0.339330	+	0.587737i
$663$	3.55761e12	+	6.16197e12i	0.715069	+	1.23854i
$664$	2.20744e12			0.440690
$665$		0			0
$666$	−2.80398e12			−0.552257
$667$	6.32173e11	+	1.09495e12i	0.123671	+	0.214205i
$668$	6.69036e11	−	1.15880e12i	0.130004	−	0.225173i
$669$	1.92200e12	−	3.32900e12i	0.370968	−	0.642535i
$670$	2.52744e12	+	4.37765e12i	0.484556	+	0.839276i
$671$	−3.23227e12			−0.615540
$672$		0			0
$673$	−6.37901e12			−1.19863			−0.599315	−	0.800513i	$-0.704560\pi$
$673$	−6.37901e12			−1.19863			−0.599315	+	0.800513i	$0.704560\pi$
$674$	1.11721e12	+	1.93507e12i	0.208529	+	0.361183i
$675$	−9.49451e11	+	1.64450e12i	−0.176038	+	0.304906i
$676$	−3.62753e10	+	6.28306e10i	−0.00668114	+	0.0115721i
$677$	−4.97630e12	−	8.61921e12i	−0.910454	−	1.57695i	−0.813425	−	0.581670i	$-0.802399\pi$
$677$	−4.97630e12	−	8.61921e12i	−0.910454	−	1.57695i	−0.0970291	−	0.995282i	$-0.530934\pi$
$678$	−6.57360e11			−0.119473
$679$		0			0
$680$	−8.34688e12			−1.49704
$681$	−2.51617e12	−	4.35814e12i	−0.448310	−	0.776495i
$682$	1.57984e12	−	2.73636e12i	0.279630	−	0.484333i
$683$	1.37743e12	−	2.38579e12i	0.242202	−	0.419506i	−0.719139	−	0.694866i	$-0.755464\pi$
$683$	1.37743e12	−	2.38579e12i	0.242202	−	0.419506i	0.961341	+	0.275360i	$0.0887970\pi$
$684$	−4.08281e11	−	7.07163e11i	−0.0713192	−	0.123528i
$685$	6.31358e12			1.09564
$686$		0			0
$687$	−6.31642e12			−1.08185
$688$	3.50137e12	+	6.06455e12i	0.595786	+	1.03193i
$689$	2.26915e12	−	3.93028e12i	0.383598	−	0.664411i
$690$	−2.20467e12	+	3.81860e12i	−0.370273	+	0.641332i
$691$	−4.92067e12	−	8.52285e12i	−0.821057	−	1.42211i	−0.904896	−	0.425633i	$-0.860051\pi$
$691$	−4.92067e12	−	8.52285e12i	−0.821057	−	1.42211i	0.0838390	−	0.996479i	$-0.473282\pi$
$692$	−1.44279e12			−0.239180
$693$		0			0
$694$	−5.62117e11			−0.0919834
$695$	6.26081e11	+	1.08440e12i	0.101788	+	0.176303i
$696$	−3.05609e12	+	5.29331e12i	−0.493657	+	0.855038i
$697$	4.75781e12	−	8.24077e12i	0.763589	−	1.32257i
$698$	3.04272e12	+	5.27014e12i	0.485191	+	0.840375i
$699$	2.83493e12			0.449154
$700$		0			0
$701$	4.83994e12			0.757022			0.378511	−	0.925597i	$-0.376436\pi$
$701$	4.83994e12			0.757022			0.378511	+	0.925597i	$0.376436\pi$
$702$	9.71763e11	+	1.68314e12i	0.151023	+	0.261580i
$703$	7.66859e11	−	1.32824e12i	0.118418	−	0.205105i
$704$	−2.36733e12	+	4.10033e12i	−0.363229	+	0.629132i
$705$	5.23568e12	+	9.06847e12i	0.798220	+	1.38256i
$706$	9.50691e12			1.44018
$707$		0			0
$708$	5.07598e11			0.0759225
$709$	−2.36329e12	−	4.09334e12i	−0.351244	−	0.608372i	0.635224	−	0.772328i	$-0.280908\pi$
$709$	−2.36329e12	−	4.09334e12i	−0.351244	−	0.608372i	−0.986468	+	0.163956i	$0.947575\pi$
$710$	1.83527e12	−	3.17877e12i	0.271042	−	0.469458i
$711$	−2.29975e12	+	3.98328e12i	−0.337495	+	0.584558i
$712$	−3.02894e12	−	5.24628e12i	−0.441703	−	0.765053i
$713$	−2.76189e12			−0.400224
$714$		0			0
$715$	6.26822e12			0.896947
$716$	−8.68090e11	−	1.50358e12i	−0.123440	−	0.213804i
$717$	3.93669e11	−	6.81855e11i	0.0556283	−	0.0963510i
$718$	3.00662e12	−	5.20762e12i	0.422201	−	0.731273i
$719$	−3.31967e11	−	5.74984e11i	−0.0463250	−	0.0802372i	0.841933	−	0.539582i	$-0.181418\pi$
$719$	−3.31967e11	−	5.74984e11i	−0.0463250	−	0.0802372i	−0.888258	+	0.459345i	$0.848084\pi$
$720$	−8.65242e12			−1.19989
$721$		0			0
$722$	4.98331e12			0.682497
$723$	−2.82531e12	−	4.89359e12i	−0.384543	−	0.666047i
$724$	−1.29974e12	+	2.25122e12i	−0.175806	+	0.304505i
$725$	−2.22640e12	+	3.85624e12i	−0.299283	+	0.518374i
$726$	−2.77072e12	−	4.79902e12i	−0.370150	−	0.641118i
$727$	−5.45701e11			−0.0724520			−0.0362260	−	0.999344i	$-0.511534\pi$
$727$	−5.45701e11			−0.0724520			−0.0362260	+	0.999344i	$0.511534\pi$
$728$		0			0
$729$	−1.07365e13			−1.40796
$730$	−4.59051e12	−	7.95099e12i	−0.598285	−	1.03626i
$731$	6.57104e12	−	1.13814e13i	0.851149	−	1.47423i
$732$	−1.36566e12	+	2.36539e12i	−0.175810	+	0.304511i
$733$	−3.78254e12	−	6.55155e12i	−0.483967	−	0.838255i	0.515864	−	0.856671i	$-0.327471\pi$
$733$	−3.78254e12	−	6.55155e12i	−0.483967	−	0.838255i	−0.999830	+	0.0184156i	$0.994138\pi$
$734$	−9.98401e12			−1.26962
$735$		0			0
$736$	1.57361e12			0.197672
$737$	−2.08433e12	−	3.61017e12i	−0.260233	−	0.450737i
$738$	6.72495e12	−	1.16480e13i	0.834517	−	1.44543i
$739$	−1.29852e11	+	2.24911e11i	−0.0160158	+	0.0277402i	−0.873922	−	0.486066i	$-0.838432\pi$
$739$	−1.29852e11	+	2.24911e11i	−0.0160158	+	0.0277402i	0.857906	+	0.513806i	$0.171765\pi$
$740$	7.38387e11	+	1.27892e12i	0.0905194	+	0.156784i
$741$	−5.50098e12			−0.670283
$742$		0			0
$743$	2.96088e12			0.356427			0.178214	−	0.983992i	$-0.442968\pi$
$743$	2.96088e12			0.356427			0.178214	+	0.983992i	$0.442968\pi$
$744$	−6.67586e12	−	1.15629e13i	−0.798783	−	1.38353i
$745$	−4.92635e12	+	8.53269e12i	−0.585898	+	1.01480i
$746$	−4.18636e12	+	7.25099e12i	−0.494893	+	0.857181i
$747$	−2.14718e12	−	3.71903e12i	−0.252305	−	0.437006i
$748$	1.37652e12			0.160777
$749$		0			0
$750$	2.82325e11			0.0325817
$751$	−3.27838e12	−	5.67833e12i	−0.376080	−	0.651390i	0.614408	−	0.788988i	$-0.289395\pi$
$751$	−3.27838e12	−	5.67833e12i	−0.376080	−	0.651390i	−0.990488	+	0.137599i	$0.956062\pi$
$752$	−2.28438e12	+	3.95666e12i	−0.260488	+	0.451179i
$753$	1.64246e12	−	2.84482e12i	0.186173	−	0.322461i
$754$	2.27872e12	+	3.94686e12i	0.256756	+	0.444714i
$755$	−5.00574e12			−0.560670
$756$		0			0
$757$	−7.49463e12			−0.829504			−0.414752	−	0.909934i	$-0.636132\pi$
$757$	−7.49463e12			−0.829504			−0.414752	+	0.909934i	$0.636132\pi$
$758$	4.19735e8	+	7.27002e8i	4.61810e−5	+	7.99878e-5i
$759$	1.81815e12	−	3.14912e12i	0.198857	−	0.344431i
$760$	3.22661e12	−	5.58864e12i	0.350820	−	0.607639i
$761$	3.14710e12	+	5.45093e12i	0.340157	+	0.589169i	0.984462	−	0.175600i	$-0.0561864\pi$
$761$	3.14710e12	+	5.45093e12i	0.340157	+	0.589169i	−0.644305	+	0.764769i	$0.722853\pi$
$762$	2.11920e13			2.27706
$763$		0			0
$764$	4.40059e12			0.467295
$765$	8.11902e12	+	1.40626e13i	0.857091	+	1.48453i
$766$	−1.70934e11	+	2.96066e11i	−0.0179390	+	0.0310713i
$767$	9.46331e11	−	1.63909e12i	0.0987334	−	0.171011i
$768$	5.04343e12	+	8.73547e12i	0.523119	+	0.906068i
$769$	−1.16579e13			−1.20214			−0.601068	−	0.799198i	$-0.705258\pi$
$769$	−1.16579e13			−1.20214			−0.601068	+	0.799198i	$0.705258\pi$
$770$		0			0
$771$	−1.52610e13			−1.55538
$772$	1.74181e12	+	3.01690e12i	0.176491	+	0.305691i
$773$	8.64199e12	−	1.49684e13i	0.870574	−	1.50788i	0.00917093	−	0.999958i	$-0.497081\pi$
$773$	8.64199e12	−	1.49684e13i	0.870574	−	1.50788i	0.861404	−	0.507921i	$-0.169586\pi$
$774$	9.28786e12	−	1.60870e13i	0.930211	−	1.61117i
$775$	−4.86344e12	−	8.42373e12i	−0.484268	−	0.838778i
$776$	2.86972e11			0.0284094
$777$		0			0
$778$	1.19424e13			1.16864
$779$	3.67840e12	+	6.37117e12i	0.357882	+	0.619870i
$780$	2.64837e12	−	4.58712e12i	0.256185	−	0.443725i
$781$	−1.51351e12	+	2.62147e12i	−0.145564	+	0.252125i
$782$	1.80523e12	+	3.12676e12i	0.172625	+	0.298995i
$783$	2.29787e12			0.218473
$784$		0			0
$785$	−2.24737e13			−2.11233
$786$	−2.09187e12	−	3.62323e12i	−0.195494	−	0.338606i
$787$	−1.92920e12	+	3.34147e12i	−0.179263	+	0.310492i	−0.941628	−	0.336654i	$-0.890705\pi$
$787$	−1.92920e12	+	3.34147e12i	−0.179263	+	0.310492i	0.762365	+	0.647147i	$0.224038\pi$
$788$	−9.74625e10	+	1.68810e11i	−0.00900471	+	0.0155966i
$789$	8.62998e12	+	1.49476e13i	0.792800	+	1.37317i
$790$	−7.26889e12			−0.663967
$791$		0			0
$792$	9.72954e12			0.878676
$793$	5.09209e12	+	8.81976e12i	0.457264	+	0.792004i
$794$	−5.35187e12	+	9.26971e12i	−0.477874	+	0.827702i
$795$	9.35633e12	−	1.62056e13i	0.830717	−	1.43884i
$796$	7.87929e11	+	1.36473e12i	0.0695630	+	0.120487i
$797$	−1.07296e12			−0.0941935			−0.0470967	−	0.998890i	$-0.514997\pi$
$797$	−1.07296e12			−0.0941935			−0.0470967	+	0.998890i	$0.514997\pi$
$798$		0			0
$799$	8.57421e12			0.744275
$800$	2.77098e12	+	4.79948e12i	0.239182	+	0.414276i
$801$	−5.89250e12	+	1.02061e13i	−0.505771	+	0.876020i
$802$	−5.75900e12	+	9.97488e12i	−0.491544	+	0.851380i
$803$	3.78570e12	+	6.55703e12i	0.321312	+	0.556528i
$804$	−3.52259e12			−0.297310
$805$		0			0
$806$	−9.95546e12			−0.830910
$807$	3.45452e12	+	5.98341e12i	0.286719	+	0.496613i
$808$	1.29447e12	−	2.24209e12i	0.106842	−	0.185055i
$809$	−4.81093e12	+	8.33277e12i	−0.394876	+	0.683945i	−0.993085	−	0.117395i	$-0.962546\pi$
$809$	−4.81093e12	+	8.33277e12i	−0.394876	+	0.683945i	0.598210	+	0.801340i	$0.295879\pi$
$810$	−5.25130e12	−	9.09552e12i	−0.428632	−	0.742412i
$811$	1.42997e12			0.116074			0.0580369	−	0.998314i	$-0.481516\pi$
$811$	1.42997e12			0.116074			0.0580369	+	0.998314i	$0.481516\pi$
$812$		0			0
$813$	2.81860e13			2.26270
$814$	1.82722e12	+	3.16483e12i	0.145875	+	0.252662i
$815$	−1.11604e13	+	1.93303e13i	−0.886072	+	1.53472i
$816$	−6.40024e12	+	1.10855e13i	−0.505348	+	0.875289i
$817$	5.08025e12	+	8.79926e12i	0.398920	+	0.690950i
$818$	−8.08164e12			−0.631117
$819$		0			0
$820$	−7.08366e12			−0.547136
$821$	−8.91175e12	−	1.54356e13i	−0.684571	−	1.18571i	−0.973571	−	0.228383i	$-0.926656\pi$
$821$	−8.91175e12	−	1.54356e13i	−0.684571	−	1.18571i	0.289000	−	0.957329i	$-0.406677\pi$
$822$	6.60110e12	−	1.14334e13i	0.504305	−	0.873482i
$823$	−6.67366e12	+	1.15591e13i	−0.507066	+	0.878264i	0.492900	+	0.870086i	$0.335937\pi$
$823$	−6.67366e12	+	1.15591e13i	−0.507066	+	0.878264i	−0.999967	+	0.00817863i	$0.997397\pi$
$824$	−1.85098e12	−	3.20599e12i	−0.139871	−	0.242264i
$825$	1.28064e13			0.962463
$826$		0			0
$827$	1.34978e13			1.00344			0.501718	−	0.865031i	$-0.332702\pi$
$827$	1.34978e13			1.00344			0.501718	+	0.865031i	$0.332702\pi$
$828$	−8.50347e11	−	1.47284e12i	−0.0628724	−	0.108898i
$829$	4.99503e12	−	8.65164e12i	0.367318	−	0.636214i	−0.621827	−	0.783155i	$-0.713609\pi$
$829$	4.99503e12	−	8.65164e12i	0.367318	−	0.636214i	0.989145	+	0.146941i	$0.0469427\pi$
$830$	3.39334e12	−	5.87743e12i	0.248185	−	0.429869i
$831$	−2.02710e13	−	3.51104e13i	−1.47459	−	2.55406i
$832$	1.49179e13			1.07932
$833$		0			0
$834$	2.61837e12			0.187406
$835$	−1.02860e13	−	1.78158e13i	−0.732245	−	1.26829i
$836$	−5.32112e11	+	9.21645e11i	−0.0376769	+	0.0652583i
$837$	−2.50978e12	+	4.34707e12i	−0.176755	+	0.306149i
$838$	4.72484e12	+	8.18366e12i	0.330970	+	0.573257i
$839$	4.86136e12			0.338711			0.169355	−	0.985555i	$-0.445831\pi$
$839$	4.86136e12			0.338711			0.169355	+	0.985555i	$0.445831\pi$
$840$		0			0
$841$	−9.11879e12			−0.628572
$842$	−2.24405e12	−	3.88681e12i	−0.153861	−	0.266495i
$843$	−1.90537e12	+	3.30020e12i	−0.129944	+	0.225069i
$844$	−1.66445e12	+	2.88291e12i	−0.112909	+	0.195564i
$845$	5.57708e11	+	9.65979e11i	0.0376315	+	0.0651797i
$846$	1.21193e13			0.813410
$847$		0			0
$848$	8.16451e12			0.542187
$849$	1.36955e13	+	2.37213e13i	0.904675	+	1.56694i
$850$	−6.35772e12	+	1.10119e13i	−0.417750	+	0.723564i
$851$	1.59718e12	−	2.76639e12i	0.104393	−	0.180813i
$852$	1.27894e12	+	2.21519e12i	0.0831518	+	0.144023i
$853$	2.85346e12			0.184544			0.0922722	−	0.995734i	$-0.470587\pi$
$853$	2.85346e12			0.184544			0.0922722	+	0.995734i	$0.470587\pi$
$854$		0			0
$855$	−1.25541e13			−0.803411
$856$	1.53633e13	+	2.66100e13i	0.978031	+	1.69400i
$857$	−6.98986e12	+	1.21068e13i	−0.442644	+	0.766682i	−0.997885	−	0.0650077i	$-0.979293\pi$
$857$	−6.98986e12	+	1.21068e13i	−0.442644	+	0.766682i	0.555241	+	0.831690i	$0.312626\pi$
$858$	6.55367e12	−	1.13513e13i	0.412850	−	0.715076i
$859$	−5.05054e12	−	8.74780e12i	−0.316496	−	0.548188i	0.663258	−	0.748391i	$-0.269173\pi$
$859$	−5.05054e12	−	8.74780e12i	−0.316496	−	0.548188i	−0.979754	+	0.200203i	$0.935840\pi$
$860$	−9.78328e12			−0.609876
$861$		0			0
$862$	1.93764e12			0.119534
$863$	−1.00407e13	−	1.73910e13i	−0.616190	−	1.06727i	−0.990174	−	0.139838i	$-0.955342\pi$
$863$	−1.00407e13	−	1.73910e13i	−0.616190	−	1.06727i	0.373984	−	0.927435i	$-0.377991\pi$
$864$	1.42997e12	−	2.47678e12i	0.0873000	−	0.151208i
$865$	−1.10910e13	+	1.92101e13i	−0.673591	+	1.16669i
$866$	−1.07922e13	−	1.86926e13i	−0.652048	−	1.12938i
$867$	−8.75345e11			−0.0526130
$868$		0			0
$869$	5.99452e12			0.356587
$870$	9.39580e12	+	1.62740e13i	0.556029	+	0.963070i
$871$	−6.56727e12	+	1.13749e13i	−0.386637	+	0.669675i
$872$	1.28272e13	−	2.22174e13i	0.751290	−	1.30127i
$873$	−2.79138e11	−	4.83481e11i	−0.0162650	−	0.0281718i
$874$	−2.79136e12			−0.161813
$875$		0			0
$876$	6.39796e12			0.367091
$877$	−1.07426e13	−	1.86068e13i	−0.613215	−	1.06212i	−0.990695	−	0.136102i	$-0.956542\pi$
$877$	−1.07426e13	−	1.86068e13i	−0.613215	−	1.06212i	0.377480	−	0.926018i	$-0.376791\pi$
$878$	1.62551e12	−	2.81547e12i	0.0923133	−	0.159891i
$879$	−1.70001e13	+	2.94451e13i	−0.960511	+	1.66365i
$880$	5.63835e12	+	9.76591e12i	0.316942	+	0.548960i
$881$	2.78108e13			1.55533			0.777664	−	0.628680i	$-0.216404\pi$
$881$	2.78108e13			1.55533			0.777664	+	0.628680i	$0.216404\pi$
$882$		0			0
$883$	3.49281e12			0.193353			0.0966767	−	0.995316i	$-0.469179\pi$
$883$	3.49281e12			0.193353			0.0966767	+	0.995316i	$0.469179\pi$
$884$	−2.16855e12	−	3.75604e12i	−0.119436	−	0.206869i
$885$	3.90199e12	−	6.75844e12i	0.213817	−	0.370341i
$886$	1.49821e13	−	2.59498e13i	0.816811	−	1.41476i
$887$	−1.49021e12	−	2.58112e12i	−0.0808336	−	0.140008i	0.822775	−	0.568368i	$-0.192425\pi$
$887$	−1.49021e12	−	2.58112e12i	−0.0808336	−	0.140008i	−0.903608	+	0.428360i	$0.859092\pi$
$888$	1.54424e13			0.833403
$889$		0			0
$890$	−1.86246e13			−0.995023
$891$	4.33065e12	+	7.50090e12i	0.230199	+	0.398716i
$892$	−1.17156e12	+	2.02920e12i	−0.0619616	+	0.107321i
$893$	−3.31448e12	+	5.74085e12i	−0.174415	+	0.302096i
$894$	1.03014e13	+	1.78425e13i	0.539358	+	0.934195i
$895$	−2.66926e13			−1.39055
$896$		0			0
$897$	−1.14572e13			−0.590897
$898$	1.58023e12	+	2.73703e12i	0.0810915	+	0.140455i
$899$	−5.88528e12	+	1.01936e13i	−0.300503	+	0.520486i
$900$	2.99477e12	−	5.18710e12i	0.152150	−	0.263532i
$901$	−7.66119e12	−	1.32696e13i	−0.387288	−	0.670803i
$902$	−1.75292e13			−0.881726
$903$		0			0
$904$	2.00375e12			0.0997896
$905$	1.99826e13	+	3.46110e13i	0.990226	+	1.71512i
$906$	−5.23370e12	+	9.06504e12i	−0.258067	+	0.446985i
$907$	−1.17327e13	+	2.03217e13i	−0.575661	+	0.997075i	0.420308	+	0.907381i	$0.361922\pi$
$907$	−1.17327e13	+	2.03217e13i	−0.575661	+	0.997075i	−0.995969	+	0.0896931i	$0.971411\pi$
$908$	1.53374e12	+	2.65651e12i	0.0748799	+	0.129696i
$909$	−5.03652e12			−0.244677
$910$		0			0
$911$	−1.39221e13			−0.669688			−0.334844	−	0.942274i	$-0.608684\pi$
$911$	−1.39221e13			−0.669688			−0.334844	+	0.942274i	$0.608684\pi$
$912$	−4.94821e12	−	8.57055e12i	−0.236849	−	0.410234i
$913$	−2.79842e12	+	4.84701e12i	−0.133289	+	0.230864i
$914$	−9.62261e12	+	1.66669e13i	−0.456074	+	0.789943i
$915$	2.09961e13	+	3.63664e13i	0.990248	+	1.71516i
$916$	3.85019e12			0.180698
$917$		0			0
$918$	6.56181e12			0.304952
$919$	−8.05476e12	−	1.39513e13i	−0.372506	−	0.645199i	0.617445	−	0.786614i	$-0.288168\pi$
$919$	−8.05476e12	−	1.39513e13i	−0.372506	−	0.645199i	−0.989950	+	0.141416i	$0.954835\pi$
$920$	6.72021e12	−	1.16398e13i	0.309270	−	0.535672i
$921$	2.24148e13	−	3.88236e13i	1.02652	−	1.77798i
$922$	1.24519e13	+	2.15673e13i	0.567475	+	0.982895i
$923$	9.53747e12			0.432539
$924$		0			0
$925$	1.12499e13			0.505257
$926$	−1.16524e13	−	2.01825e13i	−0.520792	−	0.902038i
$927$	−3.60089e12	+	6.23693e12i	−0.160159	+	0.277404i
$928$	3.35318e12	−	5.80788e12i	0.148419	−	0.257070i
$929$	−3.96121e12	−	6.86101e12i	−0.174485	−	0.302216i	0.765498	−	0.643438i	$-0.222493\pi$
$929$	−3.96121e12	−	6.86101e12i	−0.174485	−	0.302216i	−0.939983	+	0.341222i	$0.889159\pi$
$930$	−4.10492e13			−1.79941
$931$		0			0
$932$	−1.72804e12			−0.0750209
$933$	−1.35310e13	−	2.34364e13i	−0.584605	−	1.01257i
$934$	1.65987e13	−	2.87498e13i	0.713697	−	1.23616i
$935$	1.05815e13	−	1.83277e13i	0.452789	−	0.784253i
$936$	−1.53278e13	−	2.65486e13i	−0.652738	−	1.13058i
$937$	−8.84621e12			−0.374912			−0.187456	−	0.982273i	$-0.560024\pi$
$937$	−8.84621e12			−0.374912			−0.187456	+	0.982273i	$0.560024\pi$
$938$		0			0
$939$	−3.73814e13			−1.56914
$940$	−3.19143e12	−	5.52771e12i	−0.133324	−	0.230924i
$941$	1.75672e13	−	3.04272e13i	0.730379	−	1.26505i	−0.226342	−	0.974048i	$-0.572677\pi$
$941$	1.75672e13	−	3.04272e13i	0.730379	−	1.26505i	0.956721	−	0.291006i	$-0.0939900\pi$
$942$	−2.34971e13	+	4.06982e13i	−0.972268	+	1.68402i
$943$	7.66119e12	+	1.32696e13i	0.315496	+	0.546455i
$944$	3.40495e12			0.139552
$945$		0			0
$946$	−2.42097e13			−0.982833
$947$	1.08238e13	+	1.87474e13i	0.437325	+	0.757470i	0.997482	−	0.0709167i	$-0.0225924\pi$
$947$	1.08238e13	+	1.87474e13i	0.437325	+	0.757470i	−0.560157	+	0.828387i	$0.689259\pi$
$948$	2.53273e12	−	4.38682e12i	0.101848	−	0.176406i
$949$	1.19279e13	−	2.06598e13i	0.477383	−	0.826852i
$950$	−4.91534e12	−	8.51361e12i	−0.195793	−	0.339123i
$951$	−3.08254e13			−1.22207
$952$		0			0
$953$	4.63945e13			1.82200			0.911001	−	0.412404i	$-0.135311\pi$
$953$	4.63945e13			1.82200			0.911001	+	0.412404i	$0.135311\pi$
$954$	−1.08287e13	−	1.87559e13i	−0.423263	−	0.733113i
$955$	3.38281e13	−	5.85919e13i	1.31602	−	2.27941i
$956$	−2.39962e11	+	4.15627e11i	−0.00929143	+	0.0160932i
$957$	−7.74854e12	−	1.34209e13i	−0.298618	−	0.517222i
$958$	−1.47938e13			−0.567461
$959$		0			0
$960$	6.15105e13			2.33738
$961$	3.63770e11	+	6.30068e11i	0.0137585	+	0.0238305i
$962$	5.75716e12	−	9.97169e12i	0.216731	−	0.375388i
$963$	2.98878e13	−	5.17672e13i	1.11989	−	1.93971i
$964$	1.72218e12	+	2.98290e12i	0.0642290	+	0.111248i
$965$	5.35583e13			1.98817
$966$		0			0
$967$	2.17411e12			0.0799581			0.0399791	−	0.999201i	$-0.487271\pi$
$967$	2.17411e12			0.0799581			0.0399791	+	0.999201i	$0.487271\pi$
$968$	8.44564e12	+	1.46283e13i	0.309167	+	0.535493i
$969$	−9.28632e12	+	1.60844e13i	−0.338366	+	0.586067i
$970$	4.41140e11	−	7.64077e11i	0.0159994	−	0.0277118i
$971$	−8.88797e12	−	1.53944e13i	−0.320860	−	0.555746i	0.659805	−	0.751436i	$-0.270639\pi$
$971$	−8.88797e12	−	1.53944e13i	−0.320860	−	0.555746i	−0.980666	+	0.195690i	$0.937305\pi$
$972$	9.81253e12			0.352600
$973$		0			0
$974$	2.13901e13			0.761547
$975$	−2.01751e13	−	3.49443e13i	−0.714981	−	1.23838i
$976$	−9.16081e12	+	1.58670e13i	−0.323154	+	0.559720i
$977$	−6.14244e12	+	1.06390e13i	−0.215683	+	0.373574i	−0.953484	−	0.301445i	$-0.902531\pi$
$977$	−6.14244e12	+	1.06390e13i	−0.215683	+	0.373574i	0.737801	+	0.675019i	$0.235864\pi$
$978$	2.33372e13	+	4.04212e13i	0.815688	+	1.41281i
$979$	1.53594e13			0.534382
$980$		0			0
$981$	−4.99081e13			−1.72052
$982$	−6.24328e12	−	1.08137e13i	−0.214245	−	0.371083i
$983$	−1.38063e13	+	2.39131e13i	−0.471612	+	0.816856i	−0.999473	−	0.0324748i	$-0.989661\pi$
$983$	−1.38063e13	+	2.39131e13i	−0.471612	+	0.816856i	0.527860	+	0.849331i	$0.322994\pi$
$984$	−3.70362e13	+	6.41487e13i	−1.25936	+	2.18127i
$985$	1.49842e12	+	2.59534e12i	0.0507190	+	0.0878479i
$986$	1.53870e13			0.518452
$987$		0			0
$988$	3.35314e12			0.111955
$989$	1.05809e13	+	1.83267e13i	0.351673	+	0.609116i
$990$	1.49565e13	−	2.59054e13i	0.494847	−	0.857100i
$991$	1.44913e13	−	2.50997e13i	0.477284	−	0.826680i	−0.522377	−	0.852714i	$-0.674955\pi$
$991$	1.44913e13	−	2.50997e13i	0.477284	−	0.826680i	0.999661	+	0.0260347i	$0.00828804\pi$
$992$	7.32482e12	+	1.26870e13i	0.240157	+	0.415964i
$993$	−3.59303e13			−1.17271
$994$		0			0
$995$	2.42278e13			0.783627
$996$	2.36471e12	+	4.09580e12i	0.0761397	+	0.131878i
$997$	7.66674e12	−	1.32792e13i	0.245744	−	0.425641i	−0.716597	−	0.697488i	$-0.754301\pi$
$997$	7.66674e12	−	1.32792e13i	0.245744	−	0.425641i	0.962340	+	0.271847i	$0.0876345\pi$
$998$	1.40625e13	−	2.43570e13i	0.448721	−	0.777207i
$999$	−2.90277e12	−	5.02775e12i	−0.0922079	−	0.159709i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.10.c.g.18.4		10
7.2	even	3	inner	49.10.c.g.30.4		10
7.3	odd	6		49.10.a.e.1.2		5
7.4	even	3		49.10.a.f.1.2		5
7.5	odd	6		7.10.c.a.2.4	✓	10
7.6	odd	2		7.10.c.a.4.4	yes	10
21.5	even	6		63.10.e.b.37.2		10
21.20	even	2		63.10.e.b.46.2		10
28.19	even	6		112.10.i.c.65.2		10
28.27	even	2		112.10.i.c.81.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.c.a.2.4	✓	10	7.5	odd	6
7.10.c.a.4.4	yes	10	7.6	odd	2
49.10.a.e.1.2		5	7.3	odd	6
49.10.a.f.1.2		5	7.4	even	3
49.10.c.g.18.4		10	1.1	even	1	trivial
49.10.c.g.30.4		10	7.2	even	3	inner
63.10.e.b.37.2		10	21.5	even	6
63.10.e.b.46.2		10	21.20	even	2
112.10.i.c.65.2		10	28.19	even	6
112.10.i.c.81.2		10	28.27	even	2

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+(9.79824 + 16.9710i) q^{2} +(-104.977 + 181.826i) q^{3} +(63.9892 - 110.832i) q^{4} +(-983.791 - 1703.98i) q^{5} -4114.37 q^{6} +12541.3 q^{8} +(-12198.9 - 21129.2i) q^{9} +(19278.8 - 33391.9i) q^{10} +(-15898.9 + 27537.7i) q^{11} +(13434.8 + 23269.8i) q^{12} +100188. q^{13} +413103. q^{15} +(90120.3 + 156093. i) q^{16} +(169129. - 292940. i) q^{17} +(239056. - 414058. i) q^{18} +(130759. + 226480. i) q^{19} -251808. q^{20} -623124. q^{22} +(272337. + 471702. i) q^{23} +(-1.31655e6 + 2.28034e6i) q^{24} +(-959125. + 1.66125e6i) q^{25} +(981664. + 1.70029e6i) q^{26} +989914. q^{27} +2.32128e6 q^{29} +(4.04768e6 + 7.01078e6i) q^{30} +(-2.53535e6 + 4.39136e6i) q^{31} +(1.44454e6 - 2.50201e6i) q^{32} +(-3.33804e6 - 5.78166e6i) q^{33} +6.62867e6 q^{34} -3.12240e6 q^{36} +(-2.93235e6 - 5.07897e6i) q^{37} +(-2.56241e6 + 4.43822e6i) q^{38} +(-1.05174e7 + 1.82167e7i) q^{39} +(-1.23380e7 - 2.13701e7i) q^{40} +2.81312e7 q^{41} +3.88522e7 q^{43} +(2.03471e6 + 3.52423e6i) q^{44} +(-2.40024e7 + 4.15734e7i) q^{45} +(-5.33685e6 + 9.24370e6i) q^{46} +(1.26741e7 + 2.19521e7i) q^{47} -3.78423e7 q^{48} -3.75909e7 q^{50} +(3.55094e7 + 6.15041e7i) q^{51} +(6.41094e6 - 1.11041e7i) q^{52} +(2.26489e7 - 3.92291e7i) q^{53} +(9.69941e6 + 1.67999e7i) q^{54} +6.25647e7 q^{55} -5.49067e7 q^{57} +(2.27445e7 + 3.93946e7i) q^{58} +(9.44557e6 - 1.63602e7i) q^{59} +(2.64341e7 - 4.57852e7i) q^{60} +(5.08255e7 + 8.80323e7i) q^{61} -9.93680e7 q^{62} +1.48899e8 q^{64} +(-9.85638e7 - 1.70718e8i) q^{65} +(6.54138e7 - 1.13300e8i) q^{66} +(-6.55496e7 + 1.13535e8i) q^{67} +(-2.16449e7 - 3.74900e7i) q^{68} -1.14357e8 q^{69} +9.51959e7 q^{71} +(-1.52991e8 - 2.64988e8i) q^{72} +(1.19056e8 - 2.06211e8i) q^{73} +(5.74636e7 - 9.95299e7i) q^{74} +(-2.01373e8 - 3.48788e8i) q^{75} +3.34685e7 q^{76} -4.12210e8 q^{78} +(-9.42601e7 - 1.63263e8i) q^{79} +(1.77319e8 - 3.07126e8i) q^{80} +(1.36193e8 - 2.35894e8i) q^{81} +(2.75636e8 + 4.77416e8i) q^{82} +1.76014e8 q^{83} -6.65551e8 q^{85} +(3.80683e8 + 6.59362e8i) q^{86} +(-2.43682e8 + 4.22070e8i) q^{87} +(-1.99393e8 + 3.45359e8i) q^{88} +(-2.41517e8 - 4.18319e8i) q^{89} -9.40725e8 q^{90} +6.97066e7 q^{92} +(-5.32309e8 - 9.21986e8i) q^{93} +(-2.48367e8 + 4.30184e8i) q^{94} +(2.57278e8 - 4.45619e8i) q^{95} +(3.03287e8 + 5.25309e8i) q^{96} +2.28821e7 q^{97} +7.75799e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 18 q^{2} - 161 q^{3} - 940 q^{4} - 1533 q^{5} + 8708 q^{6} + 34272 q^{8} - 35734 q^{9} - 4298 q^{10} + 42213 q^{11} - 135604 q^{12} + 319676 q^{13} + 151394 q^{15} + 322064 q^{16} - 324681 q^{17}+ \cdots - 1900777180 q^{99}+O(q^{100}) \) 10 * q - 18 * q^2 - 161 * q^3 - 940 * q^4 - 1533 * q^5 + 8708 * q^6 + 34272 * q^8 - 35734 * q^9 - 4298 * q^10 + 42213 * q^11 - 135604 * q^12 + 319676 * q^13 + 151394 * q^15 + 322064 * q^16 - 324681 * q^17 - 1012868 * q^18 + 16121 * q^19 + 350616 * q^20 - 62692 * q^22 + 2638863 * q^23 - 8449728 * q^24 - 1304092 * q^25 - 4179252 * q^26 + 18331558 * q^27 + 15292500 * q^29 + 20557942 * q^30 - 19179237 * q^31 - 6263520 * q^32 - 1689359 * q^33 + 62909700 * q^34 + 71476528 * q^36 + 39566985 * q^37 - 67365270 * q^38 - 44299486 * q^39 - 5721744 * q^40 + 53436852 * q^41 + 101835992 * q^43 + 99704916 * q^44 - 85098230 * q^45 - 14489202 * q^46 - 32509659 * q^47 + 185141600 * q^48 + 3328464 * q^50 + 44168403 * q^51 - 103893272 * q^52 - 25714707 * q^53 - 51200926 * q^54 + 144695222 * q^55 - 121710346 * q^57 - 46645516 * q^58 - 46776513 * q^59 + 132391756 * q^60 + 113075039 * q^61 - 467465628 * q^62 - 192008960 * q^64 - 338113566 * q^65 + 836682602 * q^66 - 126707879 * q^67 - 32262636 * q^68 - 1323616182 * q^69 - 1188736032 * q^71 - 950557728 * q^72 + 859257651 * q^73 + 591757530 * q^74 + 169061732 * q^75 - 1101475592 * q^76 + 519432424 * q^78 - 527065417 * q^79 + 1257352656 * q^80 + 551662715 * q^81 + 1341703076 * q^82 + 144863208 * q^83 - 1197360222 * q^85 - 678648216 * q^86 + 340781350 * q^87 + 903700608 * q^88 - 1661554797 * q^89 - 1967758744 * q^90 - 1301840952 * q^92 - 423057489 * q^93 + 272580882 * q^94 - 1197123495 * q^95 + 1441922272 * q^96 - 869770188 * q^97 - 1900777180 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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