LMFDB - Embedded newform 147.5.h.e.128.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,5,Mod(116,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("147.116");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	147.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.1953845733$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 82 x^{14} + 4707 x^{12} - 139354 x^{10} + 2999893 x^{8} - 26137356 x^{6} + 167995548 x^{4} + \cdots + 571536 $ x^16 - 82x^14 + 4707x^12 - 139354x^10 + 2999893x^8 - 26137356x^6 + 167995548x^4 - 9843120*x^2 + 571536
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{7}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			128.8
Root			$5.21989 + 3.01370i$ of defining polynomial
Character	$\chi$	$=$	147.128
Dual form			147.5.h.e.116.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.21989 + 3.01370i) q^{2} +(5.48314 + 7.13689i) q^{3} +(10.1648 + 17.6060i) q^{4} +(13.6433 + 7.87698i) q^{5} +(7.11292 + 53.7783i) q^{6} +26.0965i q^{8} +(-20.8703 + 78.2651i) q^{9} +O(q^{10})$	\(q+(5.21989 + 3.01370i) q^{2} +(5.48314 + 7.13689i) q^{3} +(10.1648 + 17.6060i) q^{4} +(13.6433 + 7.87698i) q^{5} +(7.11292 + 53.7783i) q^{6} +26.0965i q^{8} +(-20.8703 + 78.2651i) q^{9} +(47.4778 + 82.2339i) q^{10} +(-170.035 + 98.1700i) q^{11} +(-69.9167 + 169.081i) q^{12} +151.709 q^{13} +(18.5912 + 140.562i) q^{15} +(83.9901 - 145.475i) q^{16} +(364.888 - 210.668i) q^{17} +(-344.809 + 345.638i) q^{18} +(-98.2403 + 170.157i) q^{19} +320.272i q^{20} -1183.42 q^{22} +(124.236 + 71.7279i) q^{23} +(-186.247 + 143.091i) q^{24} +(-188.406 - 326.329i) q^{25} +(791.902 + 457.205i) q^{26} +(-673.004 + 280.190i) q^{27} -753.566i q^{29} +(-326.567 + 789.744i) q^{30} +(317.662 + 550.206i) q^{31} +(1238.44 - 715.014i) q^{32} +(-1632.96 - 675.243i) q^{33} +2539.57 q^{34} +(-1590.08 + 428.108i) q^{36} +(-668.261 + 1157.46i) q^{37} +(-1025.61 + 592.134i) q^{38} +(831.839 + 1082.73i) q^{39} +(-205.561 + 356.043i) q^{40} -2846.73i q^{41} +99.0370 q^{43} +(-3456.76 - 1995.76i) q^{44} +(-901.234 + 903.402i) q^{45} +(432.333 + 748.823i) q^{46} +(444.261 + 256.494i) q^{47} +(1498.77 - 198.233i) q^{48} -2271.20i q^{50} +(3504.25 + 1449.04i) q^{51} +(1542.09 + 2670.98i) q^{52} +(3682.48 - 2126.08i) q^{53} +(-4357.42 - 565.676i) q^{54} -3093.13 q^{55} +(-1753.06 + 231.866i) q^{57} +(2271.02 - 3933.53i) q^{58} +(2505.49 - 1446.55i) q^{59} +(-2285.75 + 1756.10i) q^{60} +(-1330.70 + 2304.84i) q^{61} +3829.35i q^{62} +5931.68 q^{64} +(2069.81 + 1195.01i) q^{65} +(-6488.86 - 8445.94i) q^{66} +(-1283.74 - 2223.50i) q^{67} +(7418.04 + 4282.81i) q^{68} +(169.292 + 1279.95i) q^{69} +1769.31i q^{71} +(-2042.44 - 544.641i) q^{72} +(1765.57 + 3058.06i) q^{73} +(-6976.49 + 4027.88i) q^{74} +(1295.92 - 3133.94i) q^{75} -3994.38 q^{76} +(1079.09 + 8158.63i) q^{78} +(-1125.98 + 1950.25i) q^{79} +(2291.81 - 1323.18i) q^{80} +(-5689.86 - 3266.83i) q^{81} +(8579.20 - 14859.6i) q^{82} -2063.23i q^{83} +6637.72 q^{85} +(516.962 + 298.468i) q^{86} +(5378.11 - 4131.91i) q^{87} +(-2561.89 - 4437.32i) q^{88} +(-2657.84 - 1534.51i) q^{89} +(-7426.92 + 1999.61i) q^{90} +2916.40i q^{92} +(-2184.98 + 5283.97i) q^{93} +(1546.00 + 2677.74i) q^{94} +(-2680.65 + 1547.67i) q^{95} +(11893.5 + 4918.09i) q^{96} +3416.07 q^{97} +(-4134.59 - 15356.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{3} + 36 q^{4} - 68 q^{6} - 64 q^{9}+O(q^{10}) $ 16 * q + 2 * q^3 + 36 * q^4 - 68 * q^6 - 64 * q^9	$ 16 q + 2 q^{3} + 36 q^{4} - 68 q^{6} - 64 q^{9} + 4 q^{10} - 98 q^{12} + 840 q^{13} + 152 q^{15} + 444 q^{16} + 712 q^{18} + 372 q^{19} - 32 q^{22} - 1146 q^{24} - 1056 q^{25} - 3724 q^{27} - 2348 q^{30} + 2776 q^{31} - 1396 q^{33} + 5856 q^{34} - 6536 q^{36} + 2560 q^{37} + 2540 q^{39} + 1980 q^{40} + 9440 q^{43} - 9700 q^{45} - 7536 q^{46} - 5924 q^{48} - 4764 q^{51} + 20252 q^{52} - 4886 q^{54} + 368 q^{55} - 28288 q^{57} + 7504 q^{58} + 13828 q^{60} - 972 q^{61} + 45544 q^{64} - 36020 q^{66} - 10200 q^{67} - 11520 q^{69} - 14304 q^{72} + 32008 q^{73} - 2114 q^{75} + 34664 q^{76} - 59336 q^{78} + 23168 q^{79} + 17216 q^{81} + 31976 q^{82} + 64032 q^{85} - 50764 q^{87} - 29208 q^{88} - 48704 q^{90} - 31848 q^{93} + 64992 q^{94} - 28630 q^{96} + 56224 q^{97} - 64864 q^{99}+O(q^{100}) $ 16 * q + 2 * q^3 + 36 * q^4 - 68 * q^6 - 64 * q^9 + 4 * q^10 - 98 * q^12 + 840 * q^13 + 152 * q^15 + 444 * q^16 + 712 * q^18 + 372 * q^19 - 32 * q^22 - 1146 * q^24 - 1056 * q^25 - 3724 * q^27 - 2348 * q^30 + 2776 * q^31 - 1396 * q^33 + 5856 * q^34 - 6536 * q^36 + 2560 * q^37 + 2540 * q^39 + 1980 * q^40 + 9440 * q^43 - 9700 * q^45 - 7536 * q^46 - 5924 * q^48 - 4764 * q^51 + 20252 * q^52 - 4886 * q^54 + 368 * q^55 - 28288 * q^57 + 7504 * q^58 + 13828 * q^60 - 972 * q^61 + 45544 * q^64 - 36020 * q^66 - 10200 * q^67 - 11520 * q^69 - 14304 * q^72 + 32008 * q^73 - 2114 * q^75 + 34664 * q^76 - 59336 * q^78 + 23168 * q^79 + 17216 * q^81 + 31976 * q^82 + 64032 * q^85 - 50764 * q^87 - 29208 * q^88 - 48704 * q^90 - 31848 * q^93 + 64992 * q^94 - 28630 * q^96 + 56224 * q^97 - 64864 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	5.21989	+	3.01370i	1.30497	+	0.753426i	0.981252	−	0.192727i	$-0.0617333\pi$
$2$	5.21989	+	3.01370i	1.30497	+	0.753426i	0.323719	+	0.946153i	$0.395067\pi$
$3$	5.48314	+	7.13689i	0.609238	+	0.792987i
$3$	5.48314	+	7.13689i	0.609238	+	0.792987i
$4$	10.1648	+	17.6060i	0.635301	+	1.10037i
$5$	13.6433	+	7.87698i	0.545733	+	0.315079i	0.747399	−	0.664375i	$-0.231302\pi$
$5$	13.6433	+	7.87698i	0.545733	+	0.315079i	−0.201666	+	0.979454i	$0.564636\pi$
$6$	7.11292	+	53.7783i	0.197581	+	1.49384i
$7$		0			0
$7$		0			0
$8$			26.0965i			0.407757i
$9$	−20.8703	+	78.2651i	−0.257658	+	0.966236i
$10$	47.4778	+	82.2339i	0.474778	+	0.822339i
$11$	−170.035	+	98.1700i	−1.40525	+	0.811322i	−0.994925	−	0.100617i	$-0.967918\pi$
$11$	−170.035	+	98.1700i	−1.40525	+	0.811322i	−0.410326	+	0.911939i	$0.634585\pi$
$12$	−69.9167	+	169.081i	−0.485533	+	1.17418i
$13$	151.709			0.897684			0.448842	−	0.893611i	$-0.351837\pi$
$13$	151.709			0.897684			0.448842	+	0.893611i	$0.351837\pi$
$14$		0			0
$15$	18.5912	+	140.562i	0.0826276	+	0.624718i
$16$	83.9901	−	145.475i	0.328086	−	0.568262i
$17$	364.888	−	210.668i	1.26259	−	0.728956i	0.289014	−	0.957325i	$-0.406673\pi$
$17$	364.888	−	210.668i	1.26259	−	0.728956i	0.973575	+	0.228369i	$0.0733392\pi$
$18$	−344.809	+	345.638i	−1.06422	+	1.06678i
$19$	−98.2403	+	170.157i	−0.272134	+	0.471350i	−0.969408	−	0.245455i	$-0.921063\pi$
$19$	−98.2403	+	170.157i	−0.272134	+	0.471350i	0.697274	+	0.716805i	$0.254396\pi$
$20$			320.272i			0.800681i
$21$		0			0
$22$	−1183.42			−2.44508
$23$	124.236	+	71.7279i	0.234851	+	0.135591i	0.612808	−	0.790232i	$-0.290040\pi$
$23$	124.236	+	71.7279i	0.234851	+	0.135591i	−0.377957	+	0.925823i	$0.623373\pi$
$24$	−186.247	+	143.091i	−0.323346	+	0.248421i
$25$	−188.406	−	326.329i	−0.301450	−	0.522127i
$26$	791.902	+	457.205i	1.17145	+	0.676338i
$27$	−673.004	+	280.190i	−0.923188	+	0.384348i
$28$		0			0
$29$		−	753.566i		−	0.896035i	−0.894025	−	0.448018i	$-0.852130\pi$
$29$		−	753.566i		−	0.896035i	0.894025	−	0.448018i	$-0.147870\pi$
$30$	−326.567	+	789.744i	−0.362852	+	0.877493i
$31$	317.662	+	550.206i	0.330553	+	0.572535i	0.982620	−	0.185626i	$-0.0594313\pi$
$31$	317.662	+	550.206i	0.330553	+	0.572535i	−0.652067	+	0.758161i	$0.726098\pi$
$32$	1238.44	−	715.014i	1.20941	−	0.698256i
$33$	−1632.96	−	675.243i	−1.49950	−	0.620058i
$34$	2539.57			2.19686
$35$		0			0
$36$	−1590.08	+	428.108i	−1.22691	+	0.330331i
$37$	−668.261	+	1157.46i	−0.488138	+	0.845480i	−0.999907	−	0.0136434i	$-0.995657\pi$
$37$	−668.261	+	1157.46i	−0.488138	+	0.845480i	0.511769	+	0.859123i	$0.328990\pi$
$38$	−1025.61	+	592.134i	−0.710254	+	0.410065i
$39$	831.839	+	1082.73i	0.546903	+	0.711852i
$40$	−205.561	+	356.043i	−0.128476	+	0.222527i
$41$		−	2846.73i		−	1.69347i	−0.532012	−	0.846737i	$-0.678564\pi$
$41$		−	2846.73i		−	1.69347i	0.532012	−	0.846737i	$-0.321436\pi$
$42$		0			0
$43$	99.0370			0.0535624			0.0267812	−	0.999641i	$-0.491474\pi$
$43$	99.0370			0.0535624			0.0267812	+	0.999641i	$0.491474\pi$
$44$	−3456.76	−	1995.76i	−1.78551	−	1.03087i
$45$	−901.234	+	903.402i	−0.445054	+	0.446125i
$46$	432.333	+	748.823i	0.204316	+	0.353886i
$47$	444.261	+	256.494i	0.201114	+	0.116113i	0.597175	−	0.802111i	$-0.296290\pi$
$47$	444.261	+	256.494i	0.201114	+	0.116113i	−0.396061	+	0.918224i	$0.629623\pi$
$48$	1498.77	−	198.233i	0.650507	−	0.0860386i
$49$		0			0
$50$		−	2271.20i		−	0.908481i
$51$	3504.25	+	1449.04i	1.34727	+	0.557109i
$52$	1542.09	+	2670.98i	0.570299	+	0.987787i
$53$	3682.48	−	2126.08i	1.31096	−	0.756881i	0.328702	−	0.944434i	$-0.393389\pi$
$53$	3682.48	−	2126.08i	1.31096	−	0.756881i	0.982255	+	0.187553i	$0.0600555\pi$
$54$	−4357.42	−	565.676i	−1.49431	−	0.193990i
$55$	−3093.13			−1.02252
$56$		0			0
$57$	−1753.06	+	231.866i	−0.539569	+	0.0713654i
$58$	2271.02	−	3933.53i	0.675096	−	1.16930i
$59$	2505.49	−	1446.55i	0.719763	−	0.415555i	−0.0949027	−	0.995487i	$-0.530254\pi$
$59$	2505.49	−	1446.55i	0.719763	−	0.415555i	0.814665	+	0.579931i	$0.196921\pi$
$60$	−2285.75	+	1756.10i	−0.634930	+	0.487805i
$61$	−1330.70	+	2304.84i	−0.357619	+	0.619414i	−0.987563	−	0.157227i	$-0.949745\pi$
$61$	−1330.70	+	2304.84i	−0.357619	+	0.619414i	0.629943	+	0.776641i	$0.283078\pi$
$62$			3829.35i			0.996190i
$63$		0			0
$64$	5931.68			1.44816
$65$	2069.81	+	1195.01i	0.489896	+	0.282842i
$66$	−6488.86	−	8445.94i	−1.48964	−	1.93892i
$67$	−1283.74	−	2223.50i	−0.285974	−	0.495321i	0.686871	−	0.726779i	$-0.258984\pi$
$67$	−1283.74	−	2223.50i	−0.285974	−	0.495321i	−0.972845	+	0.231458i	$0.925650\pi$
$68$	7418.04	+	4282.81i	1.60425	+	0.926213i
$69$	169.292	+	1279.95i	0.0355580	+	0.268842i
$70$		0			0
$71$			1769.31i			0.350983i	0.984481	+	0.175492i	$0.0561515\pi$
$71$			1769.31i			0.350983i	−0.984481	+	0.175492i	$0.943849\pi$
$72$	−2042.44	−	544.641i	−0.393990	−	0.105062i
$73$	1765.57	+	3058.06i	0.331314	+	0.573853i	0.982770	−	0.184834i	$-0.0591747\pi$
$73$	1765.57	+	3058.06i	0.331314	+	0.573853i	−0.651456	+	0.758687i	$0.725841\pi$
$74$	−6976.49	+	4027.88i	−1.27401	+	0.735551i
$75$	1295.92	−	3133.94i	0.230385	−	0.557146i
$76$	−3994.38			−0.691548
$77$		0			0
$78$	1079.09	+	8158.63i	0.177365	+	1.34100i
$79$	−1125.98	+	1950.25i	−0.180416	+	0.312489i	−0.942022	−	0.335551i	$-0.891078\pi$
$79$	−1125.98	+	1950.25i	−0.180416	+	0.312489i	0.761606	+	0.648040i	$0.224411\pi$
$80$	2291.81	−	1323.18i	0.358095	−	0.206746i
$81$	−5689.86	−	3266.83i	−0.867225	−	0.497917i
$82$	8579.20	−	14859.6i	1.27591	−	2.20994i
$83$		−	2063.23i		−	0.299496i	−0.988724	−	0.149748i	$-0.952154\pi$
$83$		−	2063.23i		−	0.299496i	0.988724	−	0.149748i	$-0.0478463\pi$
$84$		0			0
$85$	6637.72			0.918716
$86$	516.962	+	298.468i	0.0698975	+	0.0403553i
$87$	5378.11	−	4131.91i	0.710545	−	0.545899i
$88$	−2561.89	−	4437.32i	−0.330822	−	0.573001i
$89$	−2657.84	−	1534.51i	−0.335544	−	0.193726i	0.322756	−	0.946482i	$-0.395391\pi$
$89$	−2657.84	−	1534.51i	−0.335544	−	0.193726i	−0.658300	+	0.752756i	$0.728724\pi$
$90$	−7426.92	+	1999.61i	−0.916904	+	0.246865i
$91$		0			0
$92$			2916.40i			0.344566i
$93$	−2184.98	+	5283.97i	−0.252628	+	0.610935i
$94$	1546.00	+	2677.74i	0.174966	+	0.303049i
$95$	−2680.65	+	1547.67i	−0.297025	+	0.171487i
$96$	11893.5	+	4918.09i	1.29053	+	0.533647i
$97$	3416.07			0.363064			0.181532	−	0.983385i	$-0.441894\pi$
$97$	3416.07			0.363064			0.181532	+	0.983385i	$0.441894\pi$
$98$		0			0
$99$	−4134.59	−	15356.7i	−0.421854	−	1.56685i
$100$	3830.23	−	6634.15i	0.383023	−	0.663415i
$101$	751.816	−	434.061i	0.0737002	−	0.0425509i	−0.462697	−	0.886516i	$-0.653118\pi$
$101$	751.816	−	434.061i	0.0737002	−	0.0425509i	0.536397	+	0.843966i	$0.319785\pi$
$102$	13924.8	+	18124.6i	1.33841	+	1.74208i
$103$	−1210.46	+	2096.58i	−0.114098	+	0.197623i	−0.917419	−	0.397923i	$-0.869731\pi$
$103$	−1210.46	+	2096.58i	−0.114098	+	0.197623i	0.803321	+	0.595546i	$0.203064\pi$
$104$			3959.06i			0.366037i
$105$		0			0
$106$	25629.5			2.28102
$107$	4478.62	+	2585.73i	0.391180	+	0.225848i	0.682671	−	0.730726i	$-0.260818\pi$
$107$	4478.62	+	2585.73i	0.391180	+	0.225848i	−0.291491	+	0.956573i	$0.594151\pi$
$108$	−11774.0	−	9000.82i	−1.00943	−	0.771675i
$109$	−9092.03	−	15747.9i	−0.765258	−	1.32547i	−0.940110	−	0.340872i	$-0.889278\pi$
$109$	−9092.03	−	15747.9i	−0.765258	−	1.32547i	0.174852	−	0.984595i	$-0.444055\pi$
$110$	−16145.8	−	9321.78i	−1.33436	−	0.770395i
$111$	−11924.8	+	1577.22i	−0.967847	+	0.128011i
$112$		0			0
$113$			8272.19i			0.647834i	0.946086	+	0.323917i	$0.105000\pi$
$113$			8272.19i			0.647834i	−0.946086	+	0.323917i	$0.895000\pi$
$114$	−9849.54	−	4072.88i	−0.757890	−	0.313395i
$115$	1130.00	+	1957.21i	0.0854441	+	0.147994i
$116$	13267.3	−	7659.86i	0.985974	−	0.569252i
$117$	−3166.20	+	11873.5i	−0.231296	+	0.867374i
$118$	17437.9			1.25236
$119$		0			0
$120$	−3668.16	+	485.164i	−0.254733	+	0.0336920i
$121$	11954.2	−	20705.3i	0.816487	−	1.41420i
$122$	−13892.2	+	8020.67i	−0.933366	+	0.538879i
$123$	20316.8	−	15609.0i	1.34290	−	1.03173i
$124$	−6457.95	+	11185.5i	−0.420002	+	0.727464i
$125$		−	15782.5i		−	1.01008i
$126$		0			0
$127$	−23527.3			−1.45870			−0.729348	−	0.684143i	$-0.760176\pi$
$127$	−23527.3			−1.45870			−0.729348	+	0.684143i	$0.760176\pi$
$128$	11147.6	+	6436.09i	0.680398	+	0.392828i
$129$	543.034	+	706.816i	0.0326323	+	0.0424743i
$130$	7202.78	+	12475.6i	0.426200	+	0.738200i
$131$	−17091.9	−	9868.04i	−0.995976	−	0.575027i	−0.0889209	−	0.996039i	$-0.528342\pi$
$131$	−17091.9	−	9868.04i	−0.995976	−	0.575027i	−0.907055	+	0.421012i	$0.861675\pi$
$132$	−4710.38	−	35613.5i	−0.270339	−	2.04393i
$133$		0			0
$134$		−	15475.2i		−	0.861840i
$135$	−11389.1	−	1478.52i	−0.624915	−	0.0811259i
$136$	5497.70	+	9522.29i	0.297237	+	0.514830i
$137$	−11824.4	+	6826.82i	−0.629996	+	0.363728i	−0.780751	−	0.624843i	$-0.785163\pi$
$137$	−11824.4	+	6826.82i	−0.629996	+	0.363728i	0.150754	+	0.988571i	$0.451830\pi$
$138$	−2973.72	+	7191.42i	−0.156150	+	0.377621i
$139$	6654.45			0.344416			0.172208	−	0.985061i	$-0.444910\pi$
$139$	6654.45			0.344416			0.172208	+	0.985061i	$0.444910\pi$
$140$		0			0
$141$	605.376	+	4577.04i	0.0304500	+	0.230222i
$142$	−5332.17	+	9235.58i	−0.264440	+	0.458023i
$143$	−25795.8	+	14893.2i	−1.26147	+	0.728311i
$144$	9632.73	+	9609.60i	0.464541	+	0.463426i
$145$	5935.82	−	10281.1i	0.282322	−	0.488996i
$146$			21283.6i			0.998482i
$147$		0			0
$148$	−27171.0			−1.24046
$149$	−21996.0	−	12699.4i	−0.990768	−	0.572020i	−0.0852644	−	0.996358i	$-0.527174\pi$
$149$	−21996.0	−	12699.4i	−0.990768	−	0.572020i	−0.905504	+	0.424338i	$0.860507\pi$
$150$	16209.3	−	12453.3i	0.720414	−	0.553481i
$151$	1126.72	+	1951.54i	0.0494154	+	0.0855899i	0.889675	−	0.456594i	$-0.150931\pi$
$151$	1126.72	+	1951.54i	0.0494154	+	0.0855899i	−0.840260	+	0.542184i	$0.817598\pi$
$152$	−4440.50	−	2563.72i	−0.192196	−	0.110965i
$153$	8872.65	+	32954.7i	0.379027	+	1.40778i
$154$		0			0
$155$			10008.9i			0.416602i
$156$	−10607.0	+	25651.1i	−0.435855	+	1.05404i
$157$	20735.5	+	35915.0i	0.841232	+	1.45706i	0.888854	+	0.458191i	$0.151502\pi$
$157$	20735.5	+	35915.0i	0.841232	+	1.45706i	−0.0476216	+	0.998865i	$0.515164\pi$
$158$	−11754.9	+	6786.71i	−0.470875	+	0.271860i
$159$	35365.1	+	14623.8i	1.39888	+	0.578451i
$160$	22528.6			0.880024
$161$		0			0
$162$	−19855.2	−	34200.1i	−0.756560	−	1.30316i
$163$	−21511.2	+	37258.5i	−0.809635	+	1.40233i	0.103482	+	0.994631i	$0.467001\pi$
$163$	−21511.2	+	37258.5i	−0.809635	+	1.40233i	−0.913117	+	0.407697i	$0.866332\pi$
$164$	50119.4	−	28936.5i	1.86345	−	1.07587i
$165$	−16960.1	−	22075.3i	−0.622960	−	0.810848i
$166$	6217.96	−	10769.8i	0.225648	−	0.390834i
$167$			13076.2i			0.468867i	0.972132	+	0.234433i	$0.0753234\pi$
$167$			13076.2i			0.468867i	−0.972132	+	0.234433i	$0.924677\pi$
$168$		0			0
$169$	−5545.52			−0.194164
$170$	34648.2	+	20004.1i	1.19890	+	0.692184i
$171$	−11267.1	−	11240.0i	−0.385318	−	0.384393i
$172$	1006.69	+	1743.64i	0.0340283	+	0.0589387i
$173$	17399.7	+	10045.7i	0.581366	+	0.335652i	0.761676	−	0.647958i	$-0.224377\pi$
$173$	17399.7	+	10045.7i	0.581366	+	0.335652i	−0.180310	+	0.983610i	$0.557710\pi$
$174$	40525.5	−	5360.06i	1.33854	−	0.177040i
$175$		0			0
$176$			32981.2i			1.06473i
$177$	24061.8	+	9949.80i	0.768037	+	0.317591i
$178$	−9249.10	−	16019.9i	−0.291917	−	0.505615i
$179$	−34698.8	+	20033.4i	−1.08295	+	0.625242i	−0.931691	−	0.363253i	$-0.881666\pi$
$179$	−34698.8	+	20033.4i	−1.08295	+	0.625242i	−0.151259	+	0.988494i	$0.548333\pi$
$180$	−25066.2	−	6684.18i	−0.773647	−	0.206302i
$181$	−63926.2			−1.95129			−0.975645	−	0.219354i	$-0.929605\pi$
$181$	−63926.2			−1.95129			−0.975645	+	0.219354i	$0.929605\pi$
$182$		0			0
$183$	−23745.8	+	3140.71i	−0.709063	+	0.0937834i
$184$	−1871.84	+	3242.13i	−0.0552884	+	0.0957623i
$185$	−18234.6	+	10527.8i	−0.532786	+	0.307604i
$186$	−27329.7	+	20996.9i	−0.789966	+	0.606917i
$187$	−41362.6	+	71642.1i	−1.18284	+	2.04873i
$188$			10428.9i			0.295068i
$189$		0			0
$190$	−18656.9			−0.516812
$191$	−49976.8	−	28854.1i	−1.36994	−	0.790936i	−0.379021	−	0.925388i	$-0.623739\pi$
$191$	−49976.8	−	28854.1i	−1.36994	−	0.790936i	−0.990920	+	0.134452i	$0.957073\pi$
$192$	32524.2	+	42333.7i	0.882276	+	1.14838i
$193$	1197.81	+	2074.67i	0.0321568	+	0.0556973i	0.881656	−	0.471893i	$-0.156429\pi$
$193$	1197.81	+	2074.67i	0.0321568	+	0.0556973i	−0.849499	+	0.527590i	$0.823096\pi$
$194$	17831.5	+	10295.0i	0.473788	+	0.273542i
$195$	2820.44	+	21324.4i	0.0741734	+	0.560799i
$196$		0			0
$197$			2034.61i			0.0524263i	0.999656	+	0.0262132i	$0.00834487\pi$
$197$			2034.61i			0.0524263i	−0.999656	+	0.0262132i	$0.991655\pi$
$198$	24698.4	−	92620.6i	0.629996	−	2.36253i
$199$	−12989.4	−	22498.4i	−0.328008	−	0.568126i	0.654109	−	0.756401i	$-0.273044\pi$
$199$	−12989.4	−	22498.4i	−0.328008	−	0.568126i	−0.982116	+	0.188274i	$0.939711\pi$
$200$	8516.04	−	4916.74i	0.212901	−	0.122918i
$201$	8829.93	−	21353.6i	0.218557	−	0.528542i
$202$	5232.53			0.128236
$203$		0			0
$204$	10108.3	+	76425.0i	0.242894	+	1.83643i
$205$	22423.6	−	38838.9i	0.533578	−	0.924185i
$206$	−12636.9	+	7295.95i	−0.297788	+	0.171928i
$207$	−8206.64	+	8226.39i	−0.191525	+	0.191986i
$208$	12742.0	−	22069.8i	0.294518	−	0.510120i
$209$		−	38577.0i		−	0.883153i
$210$		0			0
$211$	60437.2			1.35750			0.678749	−	0.734370i	$-0.262522\pi$
$211$	60437.2			1.35750			0.678749	+	0.734370i	$0.262522\pi$
$212$	74863.4	+	43222.4i	1.66570	+	0.961695i
$213$	−12627.3	+	9701.36i	−0.278325	+	0.213832i
$214$	15585.2	+	26994.4i	0.340319	+	0.589450i
$215$	1351.19	+	780.112i	0.0292308	+	0.0168764i
$216$	−7311.96	−	17563.0i	−0.156721	−	0.376437i
$217$		0			0
$218$		−	109603.i		−	2.30626i
$219$	−12144.2	+	29368.5i	−0.253209	+	0.612341i
$220$	−31441.1	−	54457.6i	−0.649610	−	1.12516i
$221$	55356.7	−	31960.2i	1.13341	−	0.654372i
$222$	−66999.6	−	27705.0i	−1.35946	−	0.562150i
$223$	11036.5			0.221933			0.110966	−	0.993824i	$-0.464605\pi$
$223$	11036.5			0.221933			0.110966	+	0.993824i	$0.464605\pi$
$224$		0			0
$225$	29472.3	−	7935.05i	0.582169	−	0.156742i
$226$	−24929.9	+	43179.9i	−0.488095	+	0.845405i
$227$	63289.6	−	36540.3i	1.22823	−	0.709121i	0.261573	−	0.965184i	$-0.415759\pi$
$227$	63289.6	−	36540.3i	1.22823	−	0.709121i	0.966660	+	0.256063i	$0.0824253\pi$
$228$	−21901.7	−	28507.4i	−0.421317	−	0.548389i
$229$	−7853.28	+	13602.3i	−0.149755	+	0.259383i	−0.931137	−	0.364670i	$-0.881182\pi$
$229$	−7853.28	+	13602.3i	−0.149755	+	0.259383i	0.781382	+	0.624053i	$0.214515\pi$
$230$			13621.9i			0.257503i
$231$		0			0
$232$	19665.4			0.365365
$233$	−50654.1	−	29245.2i	−0.933046	−	0.538694i	−0.0452725	−	0.998975i	$-0.514416\pi$
$233$	−50654.1	−	29245.2i	−0.933046	−	0.538694i	−0.887774	+	0.460280i	$0.847749\pi$
$234$	−52310.4	+	52436.3i	−0.955336	+	0.957635i
$235$	4040.80	+	6998.88i	0.0731698	+	0.126734i
$236$	50935.8	+	29407.8i	0.914532	+	0.528005i
$237$	−20092.6	+	2657.52i	−0.357716	+	0.0473129i
$238$		0			0
$239$			13382.2i			0.234277i	0.993116	+	0.117139i	$0.0373722\pi$
$239$			13382.2i			0.234277i	−0.993116	+	0.117139i	$0.962628\pi$
$240$	22009.7	+	9101.22i	0.382112	+	0.158007i
$241$	155.422	+	269.198i	0.00267595	+	0.00463488i	0.867360	−	0.497681i	$-0.165815\pi$
$241$	155.422	+	269.198i	0.00267595	+	0.00463488i	−0.864684	+	0.502316i	$0.832482\pi$
$242$	124799.	−	72052.7i	2.13098	−	1.23032i
$243$	−7883.28	−	58520.4i	−0.133504	−	0.991048i
$244$	−54105.3			−0.908783
$245$		0			0
$246$	153092.	−	20248.6i	2.52978	−	0.334599i
$247$	−14903.9	+	25814.3i	−0.244290	+	0.423123i
$248$	−14358.4	+	8289.84i	−0.233455	+	0.134785i
$249$	14725.0	−	11313.0i	0.237497	−	0.182464i
$250$	47563.8	−	82383.0i	0.761021	−	1.31813i
$251$		−	82720.9i		−	1.31301i	−0.754322	−	0.656505i	$-0.772034\pi$
$251$		−	82720.9i		−	1.31301i	0.754322	−	0.656505i	$-0.227966\pi$
$252$		0			0
$253$	−28166.1			−0.440033
$254$	−122810.	−	70904.3i	−1.90356	−	1.09902i
$255$	36395.6	+	47372.7i	0.559717	+	0.728530i
$256$	−8660.47	−	15000.4i	−0.132148	−	0.228888i
$257$	−9395.97	−	5424.77i	−0.142258	−	0.0821324i	0.427182	−	0.904166i	$-0.359506\pi$
$257$	−9395.97	−	5424.77i	−0.142258	−	0.0821324i	−0.569439	+	0.822033i	$0.692840\pi$
$258$	704.442	+	5326.04i	0.0105829	+	0.0800138i
$259$		0			0
$260$			48588.0i			0.718758i
$261$	58977.9	+	15727.1i	0.865782	+	0.230871i
$262$	−59478.7	−	103020.i	−0.866481	−	1.50079i
$263$	−34712.3	+	20041.2i	−0.501848	+	0.289742i	−0.729476	−	0.684006i	$-0.760236\pi$
$263$	−34712.3	+	20041.2i	−0.501848	+	0.289742i	0.227628	+	0.973748i	$0.426903\pi$
$264$	17621.5	−	42614.4i	0.252833	−	0.611432i
$265$	66988.3			0.953910
$266$		0			0
$267$	−3621.73	−	27382.7i	−0.0508036	−	0.384108i
$268$	26097.9	−	45202.8i	0.363359	−	0.629356i
$269$	−65223.6	+	37656.9i	−0.901365	+	0.520403i	−0.877643	−	0.479316i	$-0.840885\pi$
$269$	−65223.6	+	37656.9i	−0.901365	+	0.520403i	−0.0237219	+	0.999719i	$0.507552\pi$
$270$	−54993.8	−	42041.0i	−0.754374	−	0.576694i
$271$	56535.9	−	97923.1i	0.769814	−	1.33336i	−0.167849	−	0.985813i	$-0.553682\pi$
$271$	56535.9	−	97923.1i	0.769814	−	1.33336i	0.937663	−	0.347545i	$-0.112985\pi$
$272$		−	70776.2i		−	0.956642i
$273$		0			0
$274$	−82296.0			−1.09617
$275$	64071.5	+	36991.7i	0.847226	+	0.489146i
$276$	−20814.0	+	15991.1i	−0.273236	+	0.209922i
$277$	26494.7	+	45890.3i	0.345303	+	0.598082i	0.985409	−	0.170205i	$-0.0544428\pi$
$277$	26494.7	+	45890.3i	0.345303	+	0.598082i	−0.640106	+	0.768287i	$0.721110\pi$
$278$	34735.5	+	20054.5i	0.449453	+	0.259492i
$279$	−49691.7	+	13378.9i	−0.638374	+	0.171874i
$280$		0			0
$281$		−	48221.1i		−	0.610695i	−0.952241	−	0.305347i	$-0.901227\pi$
$281$		−	48221.1i		−	0.610695i	0.952241	−	0.305347i	$-0.0987726\pi$
$282$	−10633.8	+	25716.0i	−0.133719	+	0.323375i
$283$	−31950.8	−	55340.4i	−0.398941	−	0.690986i	0.594654	−	0.803981i	$-0.297289\pi$
$283$	−31950.8	−	55340.4i	−0.398941	−	0.690986i	−0.993596	+	0.112995i	$0.963956\pi$
$284$	−31150.4	+	17984.7i	−0.386213	+	0.222980i
$285$	−25744.0	−	10645.4i	−0.316946	−	0.131060i
$286$	−179535.			−2.19491
$287$		0			0
$288$	30114.0	+	111849.i	0.363065	+	1.34849i
$289$	47001.8	−	81409.5i	0.562754	−	0.974718i
$290$	61968.7	−	35777.6i	0.736845	−	0.425418i
$291$	18730.8	+	24380.1i	0.221192	+	0.287905i
$292$	−35893.4	+	62169.3i	−0.420968	+	0.729138i
$293$			76356.1i			0.889423i	0.895674	+	0.444711i	$0.146694\pi$
$293$			76356.1i			0.889423i	−0.895674	+	0.444711i	$0.853306\pi$
$294$		0			0
$295$	45577.7			0.523731
$296$	−30205.6	−	17439.2i	−0.344750	−	0.199042i
$297$	86928.3	−	113711.i	0.985481	−	1.28911i
$298$	−76544.6	−	132579.i	−0.861950	−	1.49294i
$299$	18847.7	+	10881.7i	0.210822	+	0.121718i
$300$	68348.9	−	9040.09i	0.759432	−	0.100445i
$301$		0			0
$302$			13582.4i			0.148923i
$303$	7220.16	+	2985.61i	0.0786433	+	0.0325198i
$304$	16502.4	+	28583.0i	0.178567	+	0.309287i
$305$	−36310.4	+	20963.8i	−0.390329	+	0.225357i
$306$	−53001.5	+	198760.i	−0.566038	+	2.12268i
$307$	88506.5			0.939071			0.469535	−	0.882914i	$-0.344421\pi$
$307$	88506.5			0.939071			0.469535	+	0.882914i	$0.344421\pi$
$308$		0			0
$309$	−21600.2	+	2856.92i	−0.226225	+	0.0299214i
$310$	−30163.7	+	52245.1i	−0.313879	+	0.543654i
$311$	−20353.3	+	11751.0i	−0.210433	+	0.121494i	−0.601513	−	0.798863i	$-0.705435\pi$
$311$	−20353.3	+	11751.0i	−0.210433	+	0.121494i	0.391080	+	0.920357i	$0.372102\pi$
$312$	−28255.3	+	21708.1i	−0.290263	+	0.223004i
$313$	−79363.6	+	137462.i	−0.810089	+	1.40311i	0.102713	+	0.994711i	$0.467248\pi$
$313$	−79363.6	+	137462.i	−0.810089	+	1.40311i	−0.912801	+	0.408404i	$0.866086\pi$
$314$			249963.i			2.53522i
$315$		0			0
$316$	−45781.3			−0.458473
$317$	149982.	+	86592.3i	1.49252	+	0.861709i	0.999963	−	0.00856922i	$-0.00272770\pi$
$317$	149982.	+	86592.3i	1.49252	+	0.861709i	0.492560	+	0.870278i	$0.336061\pi$
$318$	140530.	+	182915.i	1.38968	+	1.80882i
$319$	73977.5	+	128133.i	0.726973	+	1.25915i
$320$	80927.9	+	46723.7i	0.790311	+	0.456286i
$321$	6102.82	+	46141.3i	0.0592271	+	0.447796i
$322$		0			0
$323$			82784.5i			0.793494i
$324$	−320.564	−	133382.i	−0.00305369	−	1.27060i
$325$	−28582.8	−	49506.9i	−0.270607	−	0.468705i
$326$	−224572.	+	129657.i	−2.11310	+	1.22000i
$327$	62537.8	−	151237.i	0.584854	−	1.41436i
$328$	74289.5			0.690526
$329$		0			0
$330$	−22001.2	−	166343.i	−0.202031	−	1.52749i
$331$	−42053.2	+	72838.4i	−0.383834	+	0.664820i	−0.991607	−	0.129291i	$-0.958730\pi$
$331$	−42053.2	+	72838.4i	−0.383834	+	0.664820i	0.607773	+	0.794111i	$0.292063\pi$
$332$	36325.2	−	20972.3i	0.329558	−	0.190270i
$333$	−76642.1	−	76458.1i	−0.691160	−	0.689501i
$334$	−39407.8	+	68256.4i	−0.353256	+	0.611858i
$335$		−	40447.9i		−	0.360418i
$336$		0			0
$337$	3077.59			0.0270989			0.0135494	−	0.999908i	$-0.495687\pi$
$337$	3077.59			0.0270989			0.0135494	+	0.999908i	$0.495687\pi$
$338$	−28947.0	−	16712.5i	−0.253379	−	0.146288i
$339$	−59037.7	+	45357.6i	−0.513724	+	0.394685i
$340$	67471.2	+	116864.i	0.583661	+	1.01093i
$341$	−108027.	−	62369.7i	−0.929021	−	0.536370i
$342$	−24938.7	−	92627.3i	−0.213217	−	0.791930i
$343$		0			0
$344$			2584.51i			0.0218405i
$345$	−7772.48	+	18796.4i	−0.0653012	+	0.157919i
$346$	60549.6	+	104875.i	0.505777	+	0.876032i
$347$	88750.5	−	51240.1i	0.737075	−	0.425551i	−0.0839296	−	0.996472i	$-0.526747\pi$
$347$	88750.5	−	51240.1i	0.737075	−	0.425551i	0.821005	+	0.570921i	$0.193414\pi$
$348$	127414.	+	52686.9i	1.05210	+	0.435055i
$349$	81452.0			0.668730			0.334365	−	0.942444i	$-0.391478\pi$
$349$	81452.0			0.668730			0.334365	+	0.942444i	$0.391478\pi$
$350$		0			0
$351$	−102100.	+	42507.2i	−0.828731	+	0.345023i
$352$	−140386.	+	243155.i	−1.13302	+	1.96245i
$353$	171821.	−	99201.1i	1.37888	−	0.796099i	0.386858	−	0.922139i	$-0.373560\pi$
$353$	171821.	−	99201.1i	1.37888	−	0.796099i	0.992025	+	0.126040i	$0.0402269\pi$
$354$	95614.3	+	124452.i	0.762985	+	0.993106i
$355$	−13936.8	+	24139.2i	−0.110588	+	0.191543i
$356$		−	62391.9i		−	0.492298i
$357$		0			0
$358$	−241498.			−1.88429
$359$	17572.2	+	10145.3i	0.136345	+	0.0787186i	0.566621	−	0.823979i	$-0.308250\pi$
$359$	17572.2	+	10145.3i	0.136345	+	0.0787186i	−0.430276	+	0.902697i	$0.641584\pi$
$360$	−23575.6	−	23519.0i	−0.181910	−	0.181474i
$361$	45858.2	+	79428.7i	0.351886	+	0.609485i
$362$	−333688.	−	192655.i	−2.54638	−	1.47015i
$363$	213318.	−	28214.2i	1.61888	−	0.214119i
$364$		0			0
$365$			55629.5i			0.417561i
$366$	−133416.	−	55168.7i	−0.995966	−	0.411842i
$367$	98374.8	+	170390.i	0.730385	+	1.26506i	0.956719	+	0.291014i	$0.0939925\pi$
$367$	98374.8	+	170390.i	0.730385	+	1.26506i	−0.226334	+	0.974050i	$0.572674\pi$
$368$	20869.2	−	12048.9i	0.154103	−	0.0889714i
$369$	222800.	+	59412.1i	1.63630	+	0.436337i
$370$	−126910.			−0.927028
$371$		0			0
$372$	−115239.	+	15242.0i	−0.832751	+	0.110143i
$373$	72036.1	−	124770.i	0.517765	−	0.896795i	−0.482022	−	0.876159i	$-0.660098\pi$
$373$	72036.1	−	124770.i	0.517765	−	0.896795i	0.999787	−	0.0206358i	$-0.00656904\pi$
$374$	−431816.	+	249309.i	−3.08714	+	1.78236i
$375$	112638.	−	86537.8i	0.800982	−	0.615380i
$376$	−6693.59	+	11593.6i	−0.0473460	+	0.0820057i
$377$		−	114322.i		−	0.804356i
$378$		0			0
$379$	134879.			0.939004			0.469502	−	0.882931i	$-0.344433\pi$
$379$	134879.			0.939004			0.469502	+	0.882931i	$0.344433\pi$
$380$	−54496.6	−	31463.7i	−0.377401	−	0.217892i
$381$	−129004.	−	167912.i	−0.888693	−	1.15673i
$382$	−173916.	−	301231.i	−1.19182	−	2.06430i
$383$	9001.03	+	5196.75i	0.0613613	+	0.0354270i	0.530367	−	0.847768i	$-0.322054\pi$
$383$	9001.03	+	5196.75i	0.0613613	+	0.0354270i	−0.469005	+	0.883195i	$0.655388\pi$
$384$	15190.4	+	114849.i	0.103017	+	0.778873i
$385$		0			0
$386$			14439.4i			0.0969112i
$387$	−2066.93	+	7751.14i	−0.0138008	+	0.0517540i
$388$	34723.7	+	60143.3i	0.230655	+	0.399506i
$389$	−19117.8	+	11037.7i	−0.126339	+	0.0729421i	−0.561838	−	0.827247i	$-0.689905\pi$
$389$	−19117.8	+	11037.7i	−0.126339	+	0.0729421i	0.435498	+	0.900190i	$0.356572\pi$
$390$	−49543.0	+	119811.i	−0.325726	+	0.787711i
$391$	60443.2			0.395361
$392$		0			0
$393$	−23290.5	−	176091.i	−0.150797	−	1.14012i
$394$	−6131.72	+	10620.5i	−0.0394994	+	0.0684149i
$395$	−30724.1	+	17738.6i	−0.196918	+	0.113691i
$396$	228342.	−	228891.i	1.45611	−	1.45962i
$397$	−19531.8	+	33830.1i	−0.123926	+	0.214646i	−0.921313	−	0.388823i	$-0.872882\pi$
$397$	−19531.8	+	33830.1i	−0.123926	+	0.214646i	0.797387	+	0.603469i	$0.206215\pi$
$398$		−	156585.i		−	0.988518i
$399$		0			0
$400$	−63297.0			−0.395607
$401$	36388.5	+	21008.9i	0.226295	+	0.130652i	0.608862	−	0.793276i	$-0.291626\pi$
$401$	36388.5	+	21008.9i	0.226295	+	0.130652i	−0.382567	+	0.923928i	$0.624960\pi$
$402$	110445.	−	84852.7i	0.683428	−	0.525066i
$403$	48192.0	+	83471.0i	0.296732	+	0.513955i
$404$	15284.1	+	8824.31i	0.0936437	+	0.0540652i
$405$	−51895.9	−	89389.4i	−0.316390	−	0.544975i
$406$		0			0
$407$		−	262413.i		−	1.58415i
$408$	−37814.8	+	91448.5i	−0.227165	+	0.549359i
$409$	−139780.	−	242105.i	−0.835598	−	1.44730i	−0.893543	−	0.448978i	$-0.851788\pi$
$409$	−139780.	−	242105.i	−0.835598	−	1.44730i	0.0579452	−	0.998320i	$-0.481545\pi$
$410$	234098.	−	135156.i	1.39261	−	0.804024i
$411$	−113557.	−	46957.0i	−0.672250	−	0.277982i
$412$	−49216.5			−0.289945
$413$		0			0
$414$	−67629.6	+	18208.4i	−0.394581	+	0.106236i
$415$	16252.0	−	28149.3i	0.0943650	−	0.163445i
$416$	187882.	−	108474.i	1.08567	−	0.626813i
$417$	36487.3	+	47492.1i	0.209831	+	0.273117i
$418$	116260.	−	201368.i	0.665390	−	1.15249i
$419$			230293.i			1.31175i	0.754868	+	0.655876i	$0.227701\pi$
$419$			230293.i			1.31175i	−0.754868	+	0.655876i	$0.772299\pi$
$420$		0			0
$421$	−50251.7			−0.283522			−0.141761	−	0.989901i	$-0.545276\pi$
$421$	−50251.7			−0.283522			−0.141761	+	0.989901i	$0.545276\pi$
$422$	315475.	+	182140.i	1.77150	+	1.02277i
$423$	−29346.4	+	29417.0i	−0.164012	+	0.164406i
$424$	55483.1	+	96099.6i	0.308624	+	0.534552i
$425$	−137494.	−	79382.5i	−0.761215	−	0.439488i
$426$	−95150.3	+	12584.9i	−0.524314	+	0.0693477i
$427$		0			0
$428$			105134.i			0.573925i
$429$	−247733.	−	102440.i	−1.34608	−	0.556616i
$430$	4702.05	+	8144.20i	0.0254303	+	0.0440465i
$431$	−77803.5	+	44919.9i	−0.418836	+	0.241815i	−0.694579	−	0.719416i	$-0.744409\pi$
$431$	−77803.5	+	44919.9i	−0.418836	+	0.241815i	0.275743	+	0.961231i	$0.411076\pi$
$432$	−15765.0	+	121439.i	−0.0844749	+	0.650712i
$433$	−204051.			−1.08833			−0.544167	−	0.838977i	$-0.683154\pi$
$433$	−204051.			−1.08833			−0.544167	+	0.838977i	$0.683154\pi$
$434$		0			0
$435$	105922.	−	14009.7i	0.559769	−	0.0740372i
$436$	184838.	−	320148.i	0.972339	−	1.68414i
$437$	−24410.0	+	14093.1i	−0.127822	+	0.0737981i
$438$	−151899.	+	116701.i	−0.791784	+	0.608313i
$439$	97554.8	−	168970.i	0.506197	−	0.876759i	−0.493777	−	0.869588i	$-0.664384\pi$
$439$	97554.8	−	168970.i	0.506197	−	0.876759i	0.999974	−	0.00717056i	$-0.00228248\pi$
$440$		−	80719.8i		−	0.416941i
$441$		0			0
$442$	385274.			1.97208
$443$	−262191.	−	151376.i	−1.33601	−	0.771346i	−0.349797	−	0.936825i	$-0.613750\pi$
$443$	−262191.	−	151376.i	−1.33601	−	0.771346i	−0.986213	+	0.165479i	$0.947083\pi$
$444$	−148982.	−	193916.i	−0.755734	−	0.983668i
$445$	−24174.6	−	41871.6i	−0.122078	−	0.211446i
$446$	57609.3	+	33260.7i	0.289616	+	0.167210i
$447$	−29973.1	−	226616.i	−0.150009	−	1.13416i
$448$		0			0
$449$			162997.i			0.808512i	0.914646	+	0.404256i	$0.132470\pi$
$449$			162997.i			0.808512i	−0.914646	+	0.404256i	$0.867530\pi$
$450$	177756.	+	47400.7i	0.877807	+	0.234078i
$451$	279463.	+	484045.i	1.37395	+	2.37976i
$452$	−145640.	+	84085.3i	−0.712859	+	0.411569i
$453$	−7749.93	+	18741.8i	−0.0377660	+	0.0913304i
$454$	440486.			2.13708
$455$		0			0
$456$	−6050.88	−	45748.6i	−0.0290997	−	0.220013i
$457$	78173.0	−	135400.i	0.374304	−	0.648313i	−0.615919	−	0.787810i	$-0.711215\pi$
$457$	78173.0	−	135400.i	0.374304	−	0.648313i	0.990223	+	0.139497i	$0.0445484\pi$
$458$	−81986.5	+	47334.9i	−0.390851	+	0.225658i
$459$	−186544.	+	244019.i	−0.885434	+	1.15824i
$460$	−22972.5	+	39789.5i	−0.108565	+	0.188041i
$461$			140167.i			0.659543i	0.944061	+	0.329772i	$0.106972\pi$
$461$			140167.i			0.659543i	−0.944061	+	0.329772i	$0.893028\pi$
$462$		0			0
$463$	46832.0			0.218464			0.109232	−	0.994016i	$-0.465161\pi$
$463$	46832.0			0.218464			0.109232	+	0.994016i	$0.465161\pi$
$464$	−109625.	−	63292.0i	−0.509183	−	0.293977i
$465$	−71432.1	+	54880.0i	−0.330360	+	0.253810i
$466$	−176273.	−	305313.i	−0.811733	−	1.40596i
$467$	315405.	+	182099.i	1.44622	+	0.834977i	0.998254	−	0.0590728i	$-0.0188144\pi$
$467$	315405.	+	182099.i	1.44622	+	0.834977i	0.447968	+	0.894049i	$0.352148\pi$
$468$	−241228.	+	64947.7i	−1.10138	+	0.296532i
$469$		0			0
$470$			48711.1i			0.220512i
$471$	−142625.	+	344914.i	−0.642917	+	1.55478i
$472$	37749.8	+	65384.5i	0.169446	+	0.293488i
$473$	−16839.8	+	9722.45i	−0.0752687	+	0.0434564i
$474$	−112890.	−	46681.1i	−0.502457	−	0.207771i
$475$	74036.4			0.328139
$476$		0			0
$477$	89543.4	+	332581.i	0.393547	+	1.46171i
$478$	−40329.8	+	69853.3i	−0.176511	+	0.305725i
$479$	120899.	−	69801.2i	0.526929	−	0.304223i	−0.212836	−	0.977088i	$-0.568270\pi$
$479$	120899.	−	69801.2i	0.526929	−	0.304223i	0.739765	+	0.672865i	$0.234937\pi$
$480$	123528.	+	160784.i	0.536144	+	0.697848i
$481$	−101381.	+	175597.i	−0.438193	+	0.758973i
$482$			1873.58i			0.00806451i
$483$		0			0
$484$	486048.			2.07486
$485$	46606.6	+	26908.3i	0.198136	+	0.114394i
$486$	135213.	−	329228.i	0.572462	−	1.39388i
$487$	61065.1	+	105768.i	0.257475	+	0.445960i	0.965565	−	0.260162i	$-0.0837761\pi$
$487$	61065.1	+	105768.i	0.257475	+	0.445960i	−0.708090	+	0.706123i	$0.750443\pi$
$488$	−60148.2	−	34726.6i	−0.252571	−	0.145822i
$489$	−383858.	+	50770.6i	−1.60529	+	0.212322i
$490$		0			0
$491$			239214.i			0.992257i	0.868249	+	0.496129i	$0.165246\pi$
$491$			239214.i			0.992257i	−0.868249	+	0.496129i	$0.834754\pi$
$492$	481328.	+	199034.i	1.98843	+	0.822237i
$493$	−158752.	−	274967.i	−0.653170	−	1.13132i
$494$	−155593.	+	89831.8i	−0.637583	+	0.368109i
$495$	64554.6	−	242084.i	0.263461	−	0.987999i
$496$	106722.			0.433800
$497$		0			0
$498$	110957.	−	14675.6i	0.447400	−	0.0591748i
$499$	−14289.4	+	24750.0i	−0.0573869	+	0.0993970i	−0.893292	−	0.449477i	$-0.851610\pi$
$499$	−14289.4	+	24750.0i	−0.0573869	+	0.0993970i	0.835905	+	0.548875i	$0.184944\pi$
$500$	277867.	−	160426.i	1.11147	−	0.641706i
$501$	−93323.5	+	71698.8i	−0.371805	+	0.285651i
$502$	249296.	−	431794.i	0.989255	−	1.71344i
$503$			394825.i			1.56052i	0.625457	+	0.780258i	$0.284912\pi$
$503$			394825.i			1.56052i	−0.625457	+	0.780258i	$0.715088\pi$
$504$		0			0
$505$	13676.4			0.0536276
$506$	−147024.	−	84884.3i	−0.574231	−	0.331532i
$507$	−30406.9	−	39577.7i	−0.118292	−	0.153970i
$508$	−239151.	−	414221.i	−0.926711	−	1.60511i
$509$	320606.	+	185102.i	1.23747	+	0.714455i	0.968577	−	0.248714i	$-0.0800080\pi$
$509$	320606.	+	185102.i	1.23747	+	0.714455i	0.268896	+	0.963169i	$0.413341\pi$
$510$	47213.6	+	356965.i	0.181521	+	1.37242i
$511$		0			0
$512$		−	310355.i		−	1.18391i
$513$	18439.8	−	142042.i	0.0700684	−	0.539739i
$514$	−32697.3	−	56633.3i	−0.123761	−	0.214361i
$515$	−33029.5	+	19069.6i	−0.124534	+	0.0718996i
$516$	−6924.34	+	16745.3i	−0.0260063	+	0.0628917i
$517$	−100720.			−0.376821
$518$		0			0
$519$	23709.8	+	179262.i	0.0880226	+	0.665508i
$520$	−31185.4	+	54014.7i	−0.115331	+	0.199759i
$521$	−277071.	+	159967.i	−1.02074	+	0.589325i	−0.914319	−	0.404996i	$-0.867273\pi$
$521$	−277071.	+	159967.i	−1.02074	+	0.589325i	−0.106423	+	0.994321i	$0.533940\pi$
$522$	260461.	+	259836.i	0.955877	+	0.953582i
$523$	−182847.	+	316700.i	−0.668474	+	1.15783i	0.309857	+	0.950783i	$0.399719\pi$
$523$	−182847.	+	316700.i	−0.668474	+	1.15783i	−0.978331	+	0.207048i	$0.933615\pi$
$524$		−	401227.i		−	1.46126i
$525$		0			0
$526$	−241592.			−0.873196
$527$	231822.	+	133843.i	0.834706	+	0.481918i
$528$	−235383.	+	180841.i	−0.844321	+	0.648677i
$529$	−129631.	−	224527.i	−0.463230	−	0.802338i
$530$	349672.	+	201883.i	1.24483	+	0.718701i
$531$	60923.8	+	226283.i	0.216072	+	0.802532i
$532$		0			0
$533$		−	431873.i		−	1.52020i
$534$	63618.2	−	153849.i	0.223100	−	0.539527i
$535$	40735.5	+	70556.0i	0.142320	+	0.246505i
$536$	58025.4	−	33501.0i	0.201971	−	0.116608i
$537$	−333234.	−	137796.i	−1.15558	−	0.477845i
$538$	−453947.			−1.56834
$539$		0			0
$540$	−89737.0	−	215545.i	−0.307740	−	0.739179i
$541$	199122.	−	344890.i	0.680339	−	1.17838i	−0.294539	−	0.955640i	$-0.595166\pi$
$541$	199122.	−	344890.i	0.680339	−	1.17838i	0.974878	−	0.222742i	$-0.0715006\pi$
$542$	590223.	−	340765.i	2.00917	−	1.16000i
$543$	−350517.	−	456234.i	−1.18880	−	1.54735i
$544$	301262.	−	521800.i	1.01800	−	1.76322i
$545$		−	286471.i		−	0.964468i
$546$		0			0
$547$	310182.			1.03667			0.518336	−	0.855177i	$-0.326552\pi$
$547$	310182.			1.03667			0.518336	+	0.855177i	$0.326552\pi$
$548$	−240386.	−	138787.i	−0.800474	−	0.462154i
$549$	−152617.	−	152250.i	−0.506357	−	0.505142i
$550$	222964.	+	386185.i	0.737071	+	1.27664i
$551$	128225.	+	74030.5i	0.422346	+	0.243842i
$552$	−33402.3	+	4417.91i	−0.109622	+	0.0144990i
$553$		0			0
$554$			319389.i			1.04064i
$555$	−175118.	−	72413.2i	−0.568520	−	0.235089i
$556$	67641.3	+	117158.i	0.218808	+	0.378986i
$557$	386356.	−	223063.i	1.24531	−	0.718980i	0.275140	−	0.961404i	$-0.411276\pi$
$557$	386356.	−	223063.i	1.24531	−	0.718980i	0.970170	+	0.242424i	$0.0779424\pi$
$558$	−299705.	−	79919.8i	−0.962554	−	0.256676i
$559$	15024.8			0.0480821
$560$		0			0
$561$	−738099.	+	97623.7i	−2.34525	+	0.310191i
$562$	145324.	−	251708.i	0.460113	−	0.796939i
$563$	−423974.	+	244782.i	−1.33759	+	0.772257i	−0.986449	−	0.164066i	$-0.947539\pi$
$563$	−423974.	+	244782.i	−1.33759	+	0.772257i	−0.351139	+	0.936323i	$0.614206\pi$
$564$	−74429.7	+	57183.0i	−0.233985	+	0.179766i
$565$	−65159.9	+	112860.i	−0.204119	+	0.353544i
$566$		−	385161.i		−	1.20229i
$567$		0			0
$568$	−46172.6			−0.143116
$569$	−385163.	−	222374.i	−1.18965	−	0.686846i	−0.231424	−	0.972853i	$-0.574339\pi$
$569$	−385163.	−	222374.i	−1.18965	−	0.686846i	−0.958227	+	0.286007i	$0.907672\pi$
$570$	−102299.	−	133152.i	−0.314862	−	0.409826i
$571$	−24447.1	−	42343.7i	−0.0749818	−	0.129872i	0.826097	−	0.563529i	$-0.190557\pi$
$571$	−24447.1	−	42343.7i	−0.0749818	−	0.129872i	−0.901078	+	0.433656i	$0.857223\pi$
$572$	−524419.	−	302774.i	−1.60283	−	0.925393i
$573$	−68101.4	−	514890.i	−0.207418	−	1.56821i
$574$		0			0
$575$		−	54055.9i		−	0.163496i
$576$	−123796.	+	464244.i	−0.373131	+	1.39927i
$577$	40237.4	+	69693.2i	0.120859	+	0.209333i	0.920107	−	0.391668i	$-0.128102\pi$
$577$	40237.4	+	69693.2i	0.120859	+	0.209333i	−0.799248	+	0.601002i	$0.794769\pi$
$578$	490688.	−	283299.i	1.46876	−	0.847987i
$579$	−8238.91	+	19924.3i	−0.0245761	+	0.0594329i
$580$	241346.			0.717438
$581$		0			0
$582$	24298.2	+	183710.i	0.0717347	+	0.542360i
$583$	−417434.	+	723017.i	−1.22815	+	2.12722i
$584$	−79804.6	+	46075.2i	−0.233993	+	0.135096i
$585$	−136725.	+	137054.i	−0.399517	+	0.400479i
$586$	−230115.	+	398570.i	−0.670114	+	1.16067i
$587$			54845.0i			0.159170i	0.996828	+	0.0795849i	$0.0253595\pi$
$587$			54845.0i			0.159170i	−0.996828	+	0.0795849i	$0.974641\pi$
$588$		0			0
$589$	−124829.			−0.359819
$590$	237911.	+	137358.i	0.683455	+	0.394593i
$591$	−14520.8	+	11156.1i	−0.0415734	+	0.0319401i
$592$	112255.	+	194431.i	0.320303	+	0.554781i
$593$	−166967.	−	96398.4i	−0.474811	−	0.274133i	0.243440	−	0.969916i	$-0.421724\pi$
$593$	−166967.	−	96398.4i	−0.474811	−	0.274133i	−0.718252	+	0.695783i	$0.755057\pi$
$594$	796447.	−	331582.i	2.25727	−	0.939763i
$595$		0			0
$596$		−	516349.i		−	1.45362i
$597$	89345.4	−	216066.i	0.250682	−	0.606230i
$598$	65588.6	+	113603.i	0.183411	+	0.317678i
$599$	404057.	−	233283.i	1.12613	−	0.650173i	0.183173	−	0.983081i	$-0.441363\pi$
$599$	404057.	−	233283.i	1.12613	−	0.650173i	0.942959	+	0.332908i	$0.108030\pi$
$600$	81784.8	+	33818.8i	0.227180	+	0.0939412i
$601$	125070.			0.346261			0.173130	−	0.984899i	$-0.444612\pi$
$601$	125070.			0.346261			0.173130	+	0.984899i	$0.444612\pi$
$602$		0			0
$603$	200814.	−	54066.7i	0.552280	−	0.148695i
$604$	−22905.8	+	39674.0i	−0.0627873	+	0.108751i
$605$	326190.	−	188326.i	0.891168	−	0.514516i
$606$	28690.7	+	37344.0i	0.0781260	+	0.101689i
$607$	192576.	−	333552.i	0.522667	−	0.905286i	−0.476985	−	0.878911i	$-0.658270\pi$
$607$	192576.	−	333552.i	0.522667	−	0.905286i	0.999652	−	0.0263746i	$-0.00839626\pi$
$608$			280973.i			0.760076i
$609$		0			0
$610$	−252715.			−0.679158
$611$	67398.2	+	38912.4i	0.180537	+	0.104233i
$612$	−490011.	+	491191.i	−1.30829	+	1.31144i
$613$	67625.9	+	117131.i	0.179967	+	0.311711i	0.941869	−	0.335981i	$-0.109068\pi$
$613$	67625.9	+	117131.i	0.179967	+	0.311711i	−0.761902	+	0.647692i	$0.775734\pi$
$614$	461994.	+	266732.i	1.22546	+	0.707520i
$615$	400141.	−	52924.1i	1.05794	−	0.139928i
$616$		0			0
$617$		−	378025.i		−	0.993003i	−0.868036	−	0.496502i	$-0.834618\pi$
$617$		−	378025.i		−	0.993003i	0.868036	−	0.496502i	$-0.165382\pi$
$618$	−121361.	−	50183.8i	−0.317761	−	0.131397i
$619$	143122.	+	247894.i	0.373529	+	0.646972i	0.990106	−	0.140323i	$-0.0448142\pi$
$619$	143122.	+	247894.i	0.373529	+	0.646972i	−0.616576	+	0.787295i	$0.711481\pi$
$620$	−176216.	+	101738.i	−0.458418	+	0.264668i
$621$	−103709.	−	13463.4i	−0.268926	−	0.0349118i
$622$	−141656.			−0.366146
$623$		0			0
$624$	227376.	−	30073.6i	0.583950	−	0.0772354i
$625$	6564.69	−	11370.4i	0.0168056	−	0.0291081i
$626$	−828538.	+	478357.i	−2.11429	+	1.22068i
$627$	275320.	−	211523.i	0.700329	−	0.538050i
$628$	−421546.	+	730139.i	−1.06887	+	1.85134i
$629$			563125.i			1.42332i
$630$		0			0
$631$	−104005.			−0.261214			−0.130607	−	0.991434i	$-0.541693\pi$
$631$	−104005.			−0.261214			−0.130607	+	0.991434i	$0.541693\pi$
$632$	−50894.5	−	29384.0i	−0.127420	−	0.0735658i
$633$	331386.	+	431333.i	0.827040	+	1.07648i
$634$	521927.	+	904004.i	1.29847	+	2.24901i
$635$	−320991.	−	185324.i	−0.796059	−	0.459605i
$636$	102013.	+	771286.i	0.252198	+	1.90678i
$637$		0			0
$638$			891785.i			2.19088i
$639$	−138475.	−	36926.0i	−0.339133	−	0.0904337i
$640$	101394.	+	175620.i	0.247544	+	0.428759i
$641$	−271750.	+	156895.i	−0.661383	+	0.381850i	−0.792804	−	0.609477i	$-0.791379\pi$
$641$	−271750.	+	156895.i	−0.661383	+	0.381850i	0.131421	+	0.991327i	$0.458046\pi$
$642$	−107200.	+	259245.i	−0.260091	+	0.628984i
$643$	−17439.4			−0.0421803			−0.0210902	−	0.999778i	$-0.506714\pi$
$643$	−17439.4			−0.0421803			−0.0210902	+	0.999778i	$0.506714\pi$
$644$		0			0
$645$	1841.22	+	13920.8i	0.00442573	+	0.0334614i
$646$	−249488.	+	432126.i	−0.597839	+	1.03549i
$647$	407179.	−	235085.i	0.972695	−	0.561586i	0.0726382	−	0.997358i	$-0.476858\pi$
$647$	407179.	−	235085.i	0.972695	−	0.561586i	0.900057	+	0.435773i	$0.143525\pi$
$648$	85252.8	−	148485.i	0.203029	−	0.353617i
$649$	−284015.	+	491928.i	−0.674298	+	1.16792i
$650$		−	344561.i		−	0.815529i
$651$		0			0
$652$	−874629.			−2.05745
$653$	369364.	+	213252.i	0.866220	+	0.500112i	0.866090	−	0.499888i	$-0.166625\pi$
$653$	369364.	+	213252.i	0.866220	+	0.500112i	0.000129792		1.00000i	$0.499959\pi$
$654$	782223.	−	600968.i	1.82884	−	1.40506i
$655$	−155461.	−	269266.i	−0.362358	−	0.627623i
$656$	−414128.	−	239097.i	−0.962337	−	0.555605i
$657$	−276188.	+	74360.1i	−0.639843	+	0.172270i
$658$		0			0
$659$		−	201868.i		−	0.464833i	−0.972616	−	0.232416i	$-0.925337\pi$
$659$		−	201868.i		−	0.464833i	0.972616	−	0.232416i	$-0.0746632\pi$
$660$	216262.	−	522991.i	0.496469	−	1.20062i
$661$	32389.0	+	56099.4i	0.0741301	+	0.128397i	0.900708	−	0.434426i	$-0.143049\pi$
$661$	32389.0	+	56099.4i	0.0741301	+	0.128397i	−0.826578	+	0.562823i	$0.809715\pi$
$662$	−439026.	+	253472.i	−1.00179	+	0.578381i
$663$	531625.	+	219832.i	1.20942	+	0.500108i
$664$	53843.0			0.122122
$665$		0			0
$666$	−169641.	−	630079.i	−0.382457	−	1.42052i
$667$	54051.7	−	93620.2i	0.121495	−	0.210435i
$668$	−230220.	+	132917.i	−0.515928	+	0.297871i
$669$	60514.7	+	78766.2i	0.135210	+	0.175990i
$670$	121898.	−	211133.i	0.271548	−	0.470335i
$671$		−	522539.i		−	1.16058i
$672$		0			0
$673$	−417567.			−0.921925			−0.460963	−	0.887420i	$-0.652496\pi$
$673$	−417567.			−0.921925			−0.460963	+	0.887420i	$0.652496\pi$
$674$	16064.7	+	9274.95i	0.0353633	+	0.0204170i
$675$	218232.	+	166831.i	0.478974	+	0.366160i
$676$	−56369.2	−	97634.3i	−0.123353	−	0.213653i
$677$	252703.	+	145898.i	0.551357	+	0.318326i	0.749669	−	0.661813i	$-0.230213\pi$
$677$	252703.	+	145898.i	0.551357	+	0.318326i	−0.198312	+	0.980139i	$0.563546\pi$
$678$	−444864.	+	58839.4i	−0.967761	+	0.128000i
$679$		0			0
$680$			173221.i			0.374613i
$681$	607810.	+	251335.i	1.31061	+	0.541950i
$682$	−375927.	−	651125.i	−0.808231	−	1.39990i
$683$	−427517.	+	246827.i	−0.916458	+	0.529117i	−0.882503	−	0.470306i	$-0.844143\pi$
$683$	−427517.	+	246827.i	−0.916458	+	0.529117i	−0.0339543	+	0.999423i	$0.510810\pi$
$684$	83363.9	−	312621.i	0.178183	−	0.668198i
$685$	−215099.			−0.458413
$686$		0			0
$687$	−140139.	+	18535.3i	−0.296923	+	0.0392722i
$688$	8318.12	−	14407.4i	0.0175731	−	0.0304375i
$689$	558663.	−	322544.i	1.17682	−	0.679440i
$690$	−97218.1	+	74690.9i	−0.204197	+	0.156881i
$691$	28343.7	−	49092.7i	0.0593609	−	0.102816i	−0.834818	−	0.550526i	$-0.814427\pi$
$691$	28343.7	−	49092.7i	0.0593609	−	0.102816i	0.894179	+	0.447710i	$0.147760\pi$
$692$			408452.i			0.852959i
$693$		0			0
$694$	617690.			1.28248
$695$	90788.9	+	52417.0i	0.187959	+	0.108518i
$696$	107828.	+	140350.i	0.222594	+	0.289730i
$697$	−599716.	−	1.03874e6i	−1.23447	−	2.13816i
$698$	425170.	+	245472.i	0.872674	+	0.503838i
$699$	−69024.3	−	521868.i	−0.141269	−	1.06809i
$700$		0			0
$701$			441765.i			0.898992i	0.893282	+	0.449496i	$0.148396\pi$
$701$			441765.i			0.898992i	−0.893282	+	0.449496i	$0.851604\pi$
$702$	−661057.	−	85817.9i	−1.34142	−	0.174142i
$703$	−131300.	−	227419.i	−0.265678	−	0.460167i
$704$	−1.00860e6	+	582313.i	−2.03503	+	1.17493i
$705$	−27793.9	+	67214.6i	−0.0559205	+	0.135234i
$706$	1.19585e6			2.39921
$707$		0			0
$708$	69408.0	+	524770.i	0.138466	+	1.04689i
$709$	295070.	−	511076.i	0.586992	−	1.01670i	−0.407632	−	0.913146i	$-0.633645\pi$
$709$	295070.	−	511076.i	0.586992	−	1.01670i	0.994624	−	0.103554i	$-0.0330213\pi$
$710$	−145497.	+	84002.7i	−0.288627	+	0.166639i
$711$	−129137.	−	128827.i	−0.255453	−	0.254840i
$712$	40045.2	−	69360.3i	0.0789933	−	0.136820i
$713$			91140.8i			0.179281i
$714$		0			0
$715$	−469255.			−0.917902
$716$	−705414.	−	407271.i	−1.37600	−	0.794433i
$717$	−95506.9	+	73376.2i	−0.185779	+	0.142731i
$718$	61150.0	+	105915.i	0.118617	+	0.205451i
$719$	−795186.	−	459101.i	−1.53819	−	0.888077i	−0.998945	−	0.0459308i	$-0.985375\pi$
$719$	−795186.	−	459101.i	−1.53819	−	0.888077i	−0.539250	−	0.842146i	$-0.681292\pi$
$720$	55727.8	+	206984.i	0.107500	+	0.399274i
$721$		0			0
$722$			552812.i			1.06048i
$723$	−1069.04	+	2585.28i	−0.00204511	+	0.00494573i
$724$	−649798.	−	1.12548e6i	−1.23966	−	2.14715i
$725$	−245911.	+	141977.i	−0.467844	+	0.270110i
$726$	1.19852e6	+	495601.i	2.27391	+	0.940284i
$727$	−242969.			−0.459708			−0.229854	−	0.973225i	$-0.573825\pi$
$727$	−242969.			−0.459708			−0.229854	+	0.973225i	$0.573825\pi$
$728$		0			0
$729$	374428.	−	377138.i	0.704553	−	0.709651i
$730$	−167651.	+	290380.i	−0.314601	+	0.544905i
$731$	36137.4	−	20863.9i	0.0676274	−	0.0390447i
$732$	−296667.	−	386143.i	−0.553665	−	0.720654i
$733$	72727.7	−	125968.i	0.135361	−	0.234451i	−0.790375	−	0.612624i	$-0.790114\pi$
$733$	72727.7	−	125968.i	0.135361	−	0.234451i	0.925735	+	0.378173i	$0.123447\pi$
$734$			1.18589e6i			2.20116i
$735$		0			0
$736$	205146.			0.378710
$737$	436561.	+	252049.i	0.803730	+	0.464033i
$738$	983938.	+	981576.i	1.80657	+	1.80224i
$739$	485924.	+	841644.i	0.889773	+	1.54113i	0.840144	+	0.542364i	$0.182471\pi$
$739$	485924.	+	841644.i	0.889773	+	1.54113i	0.0496288	+	0.998768i	$0.484196\pi$
$740$	−370703.	−	214025.i	−0.676959	−	0.390843i
$741$	−265954.	+	35176.1i	−0.484362	+	0.0640636i
$742$		0			0
$743$		−	26014.8i		−	0.0471241i	−0.999722	−	0.0235620i	$-0.992499\pi$
$743$		−	26014.8i		−	0.0471241i	0.999722	−	0.0235620i	$-0.00750072\pi$
$744$	−137893.	−	57020.1i	−0.249113	−	0.103011i
$745$	−200066.	−	346525.i	−0.360464	−	0.624341i
$746$	752040.	−	434191.i	1.35134	−	0.780195i
$747$	161479.	+	43060.2i	0.289384	+	0.0771676i
$748$	−1.68177e6			−3.00583
$749$		0			0
$750$	848757.	−	112260.i	1.50890	−	0.199573i
$751$	−212260.	+	367645.i	−0.376347	+	0.651852i	−0.990528	−	0.137314i	$-0.956153\pi$
$751$	−212260.	+	367645.i	−0.376347	+	0.651852i	0.614181	+	0.789165i	$0.289487\pi$
$752$	74627.1	−	43086.0i	0.131966	−	0.0761904i
$753$	590370.	−	453571.i	1.04120	−	0.799935i
$754$	344534.	−	596750.i	0.606023	−	1.04966i
$755$			35500.6i			0.0622790i
$756$		0			0
$757$	241891.			0.422112			0.211056	−	0.977474i	$-0.432310\pi$
$757$	241891.			0.422112			0.211056	+	0.977474i	$0.432310\pi$
$758$	704056.	+	406487.i	1.22537	+	0.707470i
$759$	−154439.	−	201018.i	−0.268085	−	0.348941i
$760$	−40388.8	−	69955.5i	−0.0699252	−	0.121114i
$761$	49678.5	+	28681.9i	0.0857825	+	0.0495266i	0.542278	−	0.840199i	$-0.317562\pi$
$761$	49678.5	+	28681.9i	0.0857825	+	0.0495266i	−0.456495	+	0.889726i	$0.650895\pi$
$762$	−167348.	−	1.26526e6i	−0.288211	−	2.17906i
$763$		0			0
$764$		−	1.17319e6i		−	2.00993i
$765$	−138531.	+	519502.i	−0.236715	+	0.887696i
$766$	31322.9	+	54252.9i	0.0533832	+	0.0924624i
$767$	380105.	−	219454.i	0.646119	−	0.373037i
$768$	59569.4	−	144058.i	0.100995	−	0.244239i
$769$	919966.			1.55568			0.777838	−	0.628465i	$-0.216316\pi$
$769$	919966.			1.55568			0.777838	+	0.628465i	$0.216316\pi$
$770$		0			0
$771$	−12803.5	−	96802.7i	−0.0215387	−	0.162847i
$772$	−24351.0	+	42177.3i	−0.0408586	+	0.0707691i
$773$	−537714.	+	310450.i	−0.899897	+	0.519556i	−0.877167	−	0.480186i	$-0.840569\pi$
$773$	−537714.	+	310450.i	−0.899897	+	0.519556i	−0.0227301	+	0.999742i	$0.507236\pi$
$774$	−34148.8	+	34231.0i	−0.0570024	+	0.0571396i
$775$	119699.	−	207325.i	0.199291	−	0.345182i
$776$			89147.3i			0.148042i
$777$		0			0
$778$	−133057.			−0.219826
$779$	484392.	+	279664.i	0.798218	+	0.460851i
$780$	−346767.	+	266415.i	−0.569966	+	0.437895i
$781$	−173693.	−	300845.i	−0.284760	−	0.493220i
$782$	315507.	+	182158.i	0.515935	+	0.297875i
$783$	211141.	+	507153.i	0.344389	+	0.827209i
$784$		0			0
$785$			653334.i			1.06022i
$786$	409113.	−	989367.i	0.662213	−	1.60145i
$787$	279667.	+	484398.i	0.451536	+	0.782083i	0.998482	−	0.0550853i	$-0.0175431\pi$
$787$	279667.	+	484398.i	0.451536	+	0.782083i	−0.546946	+	0.837168i	$0.684210\pi$
$788$	−35821.4	+	20681.5i	−0.0576886	+	0.0333065i
$789$	−333364.	−	137849.i	−0.535507	−	0.221437i
$790$	−213835.			−0.342630
$791$		0			0
$792$	400755.	−	107898.i	0.638893	−	0.172014i
$793$	−201879.	+	349664.i	−0.321029	+	0.556038i
$794$	−203908.	+	117726.i	−0.323439	+	0.186738i
$795$	367307.	+	478088.i	0.581158	+	0.756439i
$796$	264070.	−	457383.i	0.416767	−	0.721862i
$797$		−	280663.i		−	0.441843i	−0.975292	−	0.220922i	$-0.929093\pi$
$797$		−	280663.i		−	0.441843i	0.975292	−	0.220922i	$-0.0709065\pi$
$798$		0			0
$799$	216141.			0.338566
$800$	−466660.	−	269426.i	−0.729156	−	0.420979i
$801$	175568.	−	175991.i	0.273641	−	0.274300i
$802$	126629.	+	219328.i	0.196873	+	0.340993i
$803$	−600420.	−	346652.i	−0.931159	−	0.537605i
$804$	465706.	−	61596.0i	0.720443	−	0.0952885i
$805$		0			0
$806$			580946.i			0.894263i
$807$	−626383.	−	259016.i	−0.961819	−	0.397721i
$808$	11327.5	+	19619.7i	0.0173504	+	0.0300518i
$809$	495949.	−	286336.i	0.757774	−	0.437501i	−0.0707220	−	0.997496i	$-0.522530\pi$
$809$	495949.	−	286336.i	0.757774	−	0.437501i	0.828496	+	0.559995i	$0.189197\pi$
$810$	−1497.29	−	623002.i	−0.00228211	−	0.949553i
$811$	−980201.			−1.49030			−0.745149	−	0.666898i	$-0.767622\pi$
$811$	−980201.			−1.49030			−0.745149	+	0.666898i	$0.767622\pi$
$812$		0			0
$813$	1.00886e6	−	133436.i	1.52634	−	0.201879i
$814$	790834.	−	1.36976e6i	1.19354	−	2.06727i
$815$	−586969.	+	338886.i	−0.883689	+	0.510198i
$816$	505122.	−	388076.i	0.758605	−	0.582823i
$817$	−9729.42	+	16851.9i	−0.0145762	+	0.0252466i
$818$		−	1.68502e6i		−	2.51824i
$819$		0			0
$820$	911728.			1.35593
$821$	−228374.	−	131852.i	−0.338814	−	0.195614i	0.320934	−	0.947102i	$-0.396003\pi$
$821$	−228374.	−	131852.i	−0.338814	−	0.195614i	−0.659747	+	0.751488i	$0.729337\pi$
$822$	−451241.	−	587338.i	−0.667828	−	0.869249i
$823$	74323.6	+	128732.i	0.109730	+	0.190059i	0.915661	−	0.401951i	$-0.131668\pi$
$823$	74323.6	+	128732.i	0.109730	+	0.190059i	−0.805931	+	0.592010i	$0.798335\pi$
$824$	−54713.3	−	31588.8i	−0.0805821	−	0.0465241i
$825$	87307.5	+	660101.i	0.128276	+	0.969846i
$826$		0			0
$827$		−	30591.1i		−	0.0447285i	−0.999750	−	0.0223642i	$-0.992881\pi$
$827$		−	30591.1i		−	0.0447285i	0.999750	−	0.0223642i	$-0.00711935\pi$
$828$	−228253.	−	60866.2i	−0.332932	−	0.0887801i
$829$	−142731.	−	247217.i	−0.207687	−	0.359724i	0.743299	−	0.668960i	$-0.233260\pi$
$829$	−142731.	−	247217.i	−0.207687	−	0.359724i	−0.950985	+	0.309236i	$0.899927\pi$
$830$	169667.	−	97957.5i	0.246287	−	0.142194i
$831$	−182239.	+	440713.i	−0.263900	+	0.638195i
$832$	899886.			1.29999
$833$		0			0
$834$	47332.6	+	357865.i	0.0680500	+	0.514502i
$835$	−103001.	+	178403.i	−0.147730	+	0.255876i
$836$	679186.	−	392128.i	0.971798	−	0.561068i
$837$	−367950.	−	281286.i	−0.525216	−	0.401510i
$838$	−694033.	+	1.20210e6i	−0.988308	+	1.71180i
$839$		−	1.03015e6i		−	1.46345i	−0.681602	−	0.731723i	$-0.738716\pi$
$839$		−	1.03015e6i		−	1.46345i	0.681602	−	0.731723i	$-0.261284\pi$
$840$		0			0
$841$	139420.			0.197121
$842$	−262308.	−	151444.i	−0.369988	−	0.213613i
$843$	344148.	−	264403.i	0.484273	−	0.372058i
$844$	614333.	+	1.06406e6i	0.862420	+	1.49376i
$845$	−75659.3	−	43681.9i	−0.105962	−	0.0611770i
$846$	−241839.	+	65112.2i	−0.337898	+	0.0909750i
$847$		0			0
$848$		−	714278.i		−	0.993289i
$849$	219767.	−	531469.i	0.304893	−	0.737331i
$850$	−478470.	−	828735.i	−0.662243	−	1.14704i
$851$	−166045.	+	95865.9i	−0.229280	+	0.132375i
$852$	−299157.	−	123704.i	−0.412116	−	0.170414i
$853$	−1.02297e6			−1.40593			−0.702967	−	0.711223i	$-0.748142\pi$
$853$	−1.02297e6			−1.40593			−0.702967	+	0.711223i	$0.748142\pi$
$854$		0			0
$855$	−65182.9	−	242102.i	−0.0891665	−	0.331181i
$856$	−67478.4	+	116876.i	−0.0920910	+	0.159506i
$857$	−726106.	+	419217.i	−0.988640	+	0.570792i	−0.904868	−	0.425693i	$-0.860030\pi$
$857$	−726106.	+	419217.i	−0.988640	+	0.570792i	−0.0837728	+	0.996485i	$0.526697\pi$
$858$	−984416.	−	1.28132e6i	−1.33722	−	1.74054i
$859$	−136252.	+	235995.i	−0.184653	+	0.319828i	−0.943459	−	0.331488i	$-0.892449\pi$
$859$	−136252.	+	235995.i	−0.184653	+	0.319828i	0.758807	+	0.651316i	$0.225783\pi$
$860$			31718.8i			0.0428864i
$861$		0			0
$862$	−541501.			−0.728760
$863$	−520224.	−	300351.i	−0.698504	−	0.403281i	0.108286	−	0.994120i	$-0.465464\pi$
$863$	−520224.	−	300351.i	−0.698504	−	0.403281i	−0.806790	+	0.590838i	$0.798797\pi$
$864$	−633136.	+	828206.i	−0.848144	+	1.10946i
$865$	158260.	+	274114.i	0.211514	+	0.366353i
$866$	−1.06512e6	−	614948.i	−1.42024	−	0.819978i
$867$	838727.	−	110933.i	1.11579	−	0.147579i
$868$		0			0
$869$		−	442148.i		−	0.585501i
$870$	595124.	+	246090.i	0.786265	+	0.325128i
$871$	−194754.	−	337323.i	−0.256714	−	0.444642i
$872$	410963.	−	237270.i	0.540468	−	0.312040i
$873$	−71294.4	+	267359.i	−0.0935464	+	0.350806i
$874$	−169890.			−0.222405
$875$		0			0
$876$	−640504.	+	84715.5i	−0.834667	+	0.110396i
$877$	223410.	−	386958.i	0.290472	−	0.503111i	−0.683450	−	0.729998i	$-0.739521\pi$
$877$	223410.	−	386958.i	0.290472	−	0.503111i	0.973921	+	0.226886i	$0.0728545\pi$
$878$	1.01845e6	−	588002.i	1.32115	−	0.762764i
$879$	−544945.	+	418671.i	−0.705301	+	0.541870i
$880$	−259792.	+	449974.i	−0.335476	+	0.581061i
$881$		−	437687.i		−	0.563913i	−0.959427	−	0.281956i	$-0.909017\pi$
$881$		−	437687.i		−	0.563913i	0.959427	−	0.281956i	$-0.0909833\pi$
$882$		0			0
$883$	−80288.7			−0.102975			−0.0514876	−	0.998674i	$-0.516396\pi$
$883$	−80288.7			−0.102975			−0.0514876	+	0.998674i	$0.516396\pi$
$884$	1.12538e6	+	649739.i	1.44011	+	0.831446i
$885$	249909.	+	325283.i	0.319077	+	0.415312i
$886$	−912404.	−	1.58033e6i	−1.16230	−	2.01317i
$887$	1.25423e6	+	724128.i	1.59415	+	0.920381i	0.992585	+	0.121556i	$0.0387884\pi$
$887$	1.25423e6	+	724128.i	1.59415	+	0.920381i	0.601563	+	0.798825i	$0.294545\pi$
$888$	−41160.0	−	311196.i	−0.0521974	−	0.394646i
$889$		0			0
$890$		−	291420.i		−	0.367908i
$891$	1.28818e6	−	3095.95i	1.62264	−	0.00389977i
$892$	112184.	+	194308.i	0.140994	+	0.244209i
$893$	−87288.7	+	50396.2i	−0.109460	+	0.0631967i
$894$	526497.	−	1.27324e6i	0.658751	−	1.59307i
$895$	−631210.			−0.788003
$896$		0			0
$897$	25683.0	+	194180.i	0.0319198	+	0.241335i
$898$	−491224.	+	850825.i	−0.609154	+	1.05509i
$899$	414617.	−	239379.i	0.513012	−	0.296187i
$900$	439285.	+	438230.i	0.542327	+	0.541025i
$901$	895795.	−	1.55156e6i	1.10347	−	1.91126i
$902$			3.36888e6i			4.14069i
$903$		0			0
$904$	−215875.			−0.264159
$905$	−872167.	−	503546.i	−1.06488	−	0.614811i
$906$	−96936.0	+	74474.2i	−0.118094	+	0.0907297i
$907$	451688.	+	782347.i	0.549065	+	0.951009i	0.998339	+	0.0576149i	$0.0183495\pi$
$907$	451688.	+	782347.i	0.549065	+	0.951009i	−0.449273	+	0.893394i	$0.648317\pi$
$908$	1.28666e6	+	742851.i	1.56060	+	0.901010i
$909$	18281.2	+	67900.0i	0.0221247	+	0.0821754i
$910$		0			0
$911$			1.15959e6i			1.39723i	0.715499	+	0.698614i	$0.246200\pi$
$911$			1.15959e6i			1.39723i	−0.715499	+	0.698614i	$0.753800\pi$
$912$	−113509.	+	274501.i	−0.136471	+	0.330030i
$913$	202547.	+	350822.i	0.242988	+	0.420867i
$914$	816108.	−	471180.i	0.976912	−	0.564020i
$915$	−348711.	−	144196.i	−0.416508	−	0.172230i
$916$	−319309.			−0.380557
$917$		0			0
$918$	−1.70914e6	+	711561.i	−2.02811	+	0.844358i
$919$	−699040.	+	1.21077e6i	−0.827697	+	1.43361i	0.0721438	+	0.997394i	$0.477016\pi$
$919$	−699040.	+	1.21077e6i	−0.827697	+	1.43361i	−0.899841	+	0.436219i	$0.856317\pi$
$920$	−51076.4	+	29489.0i	−0.0603454	+	0.0348404i
$921$	485294.	+	631661.i	0.572118	+	0.744671i
$922$	−422421.	+	731655.i	−0.496917	+	0.860685i
$923$			268419.i			0.315072i
$924$		0			0
$925$	503618.			0.588597
$926$	244458.	+	141138.i	0.285090	+	0.164597i
$927$	−138827.	−	138493.i	−0.161552	−	0.161164i
$928$	−538810.	−	933246.i	−0.625662	−	1.08368i
$929$	1.07189e6	+	618857.i	1.24199	+	0.717066i	0.969500	−	0.245092i	$-0.0788181\pi$
$929$	1.07189e6	+	618857.i	1.24199	+	0.717066i	0.272494	+	0.962157i	$0.412151\pi$
$930$	−538260.	+	71192.3i	−0.622338	+	0.0823127i
$931$		0			0
$932$		−	1.18909e6i		−	1.36893i
$933$	−195465.	−	80826.9i	−0.224547	−	0.0928523i
$934$	1.09759e6	+	1.90107e6i	1.25819	+	2.17924i
$935$	−1.12865e6	+	651625.i	−1.29103	+	0.745374i
$936$	−309856.	−	82626.7i	−0.353678	−	0.0943124i
$937$	1.41105e6			1.60718			0.803589	−	0.595185i	$-0.202921\pi$
$937$	1.41105e6			1.60718			0.803589	+	0.595185i	$0.202921\pi$
$938$		0			0
$939$	−1.41621e6	+	187313.i	−1.60619	+	0.212441i
$940$	−82148.0	+	142285.i	−0.0929697	+	0.161028i
$941$	1.45975e6	−	842785.i	1.64854	−	0.951782i	0.670880	−	0.741566i	$-0.265916\pi$
$941$	1.45975e6	−	842785.i	1.64854	−	0.951782i	0.977655	−	0.210216i	$-0.0674169\pi$
$942$	−1.78396e6	+	1.37058e6i	−2.01040	+	1.54455i
$943$	204190.	−	353667.i	0.229621	−	0.397714i
$944$		−	485983.i		−	0.545352i
$945$		0			0
$946$	−117202.			−0.130965
$947$	−1.11402e6	−	643178.i	−1.24220	−	0.717185i	−0.272659	−	0.962111i	$-0.587903\pi$
$947$	−1.11402e6	−	643178.i	−1.24220	−	0.717185i	−0.969542	+	0.244926i	$0.921236\pi$
$948$	−251026.	−	326736.i	−0.279319	−	0.363564i
$949$	267852.	+	463934.i	0.297415	+	0.515138i
$950$	386462.	+	223124.i	0.428212	+	0.247228i
$951$	204375.	+	1.54520e6i	0.225978	+	1.70854i
$952$		0			0
$953$		−	261159.i		−	0.287553i	−0.989610	−	0.143777i	$-0.954075\pi$
$953$		−	261159.i		−	0.287553i	0.989610	−	0.143777i	$-0.0459247\pi$
$954$	−534895.	+	2.00589e6i	−0.587722	+	2.20400i
$955$	−454567.	−	787333.i	−0.498415	−	0.863280i
$956$	−235606.	+	136027.i	−0.257793	+	0.148837i
$957$	−508840.	+	1.23054e6i	−0.555594	+	1.34361i
$958$	841440.			0.916837
$959$		0			0
$960$	110277.	+	833766.i	0.119658	+	0.904694i
$961$	259943.	−	450234.i	0.281469	−	0.487519i
$962$	−1.05839e6	+	611064.i	−1.14366	+	0.660293i
$963$	−295843.	+	296554.i	−0.319013	+	0.319780i
$964$	−3159.67	+	5472.70i	−0.00340006	+	0.00588908i
$965$			37740.5i			0.0405278i
$966$		0			0
$967$	−522045.			−0.558284			−0.279142	−	0.960250i	$-0.590050\pi$
$967$	−522045.			−0.558284			−0.279142	+	0.960250i	$0.590050\pi$
$968$	540334.	+	311962.i	0.576649	+	0.332928i
$969$	−590824.	+	453919.i	−0.629231	+	0.483427i
$970$	162187.	+	280917.i	0.172375	+	0.298562i
$971$	457181.	+	263954.i	0.484897	+	0.279956i	0.722455	−	0.691418i	$-0.243014\pi$
$971$	457181.	+	263954.i	0.484897	+	0.279956i	−0.237558	+	0.971373i	$0.576347\pi$
$972$	950177.	−	733642.i	1.00571	−	0.776518i
$973$		0			0
$974$			736129.i			0.775954i
$975$	196602.	−	475446.i	0.206813	−	0.500141i
$976$	223531.	+	387168.i	0.234660	+	0.406443i
$977$	−632994.	+	365459.i	−0.663148	+	0.382869i	−0.793475	−	0.608602i	$-0.791730\pi$
$977$	−632994.	+	365459.i	−0.663148	+	0.382869i	0.130327	+	0.991471i	$0.458397\pi$
$978$	−2.15670e6	−	891819.i	−2.25483	−	0.932393i
$979$	602570.			0.628698
$980$		0			0
$981$	1.42226e6	−	382926.i	1.47789	−	0.397903i
$982$	−720921.	+	1.24867e6i	−0.747592	+	1.29487i
$983$	−141444.	+	81662.5i	−0.146378	+	0.0845115i	−0.571400	−	0.820671i	$-0.693600\pi$
$983$	−141444.	+	81662.5i	−0.146378	+	0.0845115i	0.425022	+	0.905183i	$0.360266\pi$
$984$	407340.	+	530196.i	0.420695	+	0.547578i
$985$	−16026.6	+	27758.9i	−0.0165185	+	0.0286108i
$986$		−	1.91373e6i		−	1.96846i
$987$		0			0
$988$	−605981.			−0.620791
$989$	12304.0	+	7103.71i	0.0125792	+	0.00726261i
$990$	1.06654e6	−	1.06910e6i	1.08819	−	1.09081i
$991$	−620178.	−	1.07418e6i	−0.631494	−	1.09378i	−0.987246	−	0.159200i	$-0.949109\pi$
$991$	−620178.	−	1.07418e6i	−0.631494	−	1.09378i	0.355752	−	0.934580i	$-0.384225\pi$
$992$	786810.	+	454265.i	0.799552	+	0.461622i
$993$	−750423.	+	99253.8i	−0.761040	+	0.100658i
$994$		0			0
$995$		−	409270.i		−	0.413394i
$996$	348853.	+	144254.i	0.351661	+	0.145415i
$997$	440866.	+	763602.i	0.443523	+	0.768205i	0.997948	−	0.0640291i	$-0.0203950\pi$
$997$	440866.	+	763602.i	0.443523	+	0.768205i	−0.554425	+	0.832234i	$0.687062\pi$
$998$	−149178.	+	86128.0i	−0.149777	+	0.0864735i
$999$	125433.	−	966216.i	0.125685	−	0.968152i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.5.h.e.128.8		16
3.2	odd	2	inner	147.5.h.e.128.1		16
7.2	even	3		21.5.b.a.8.1	✓	8
7.3	odd	6		147.5.h.c.116.1		16
7.4	even	3	inner	147.5.h.e.116.1		16
7.5	odd	6		147.5.b.e.50.1		8
7.6	odd	2		147.5.h.c.128.8		16
21.2	odd	6		21.5.b.a.8.8	yes	8
21.5	even	6		147.5.b.e.50.8		8
21.11	odd	6	inner	147.5.h.e.116.8		16
21.17	even	6		147.5.h.c.116.8		16
21.20	even	2		147.5.h.c.128.1		16
28.23	odd	6		336.5.d.b.113.7		8
84.23	even	6		336.5.d.b.113.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.5.b.a.8.1	✓	8	7.2	even	3
21.5.b.a.8.8	yes	8	21.2	odd	6
147.5.b.e.50.1		8	7.5	odd	6
147.5.b.e.50.8		8	21.5	even	6
147.5.h.c.116.1		16	7.3	odd	6
147.5.h.c.116.8		16	21.17	even	6
147.5.h.c.128.1		16	21.20	even	2
147.5.h.c.128.8		16	7.6	odd	2
147.5.h.e.116.1		16	7.4	even	3	inner
147.5.h.e.116.8		16	21.11	odd	6	inner
147.5.h.e.128.1		16	3.2	odd	2	inner
147.5.h.e.128.8		16	1.1	even	1	trivial
336.5.d.b.113.7		8	28.23	odd	6
336.5.d.b.113.8		8	84.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	147.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(5.21989 + 3.01370i) q^{2} +(5.48314 + 7.13689i) q^{3} +(10.1648 + 17.6060i) q^{4} +(13.6433 + 7.87698i) q^{5} +(7.11292 + 53.7783i) q^{6} +26.0965i q^{8} +(-20.8703 + 78.2651i) q^{9} +O(q^{10})\)	\(q+(5.21989 + 3.01370i) q^{2} +(5.48314 + 7.13689i) q^{3} +(10.1648 + 17.6060i) q^{4} +(13.6433 + 7.87698i) q^{5} +(7.11292 + 53.7783i) q^{6} +26.0965i q^{8} +(-20.8703 + 78.2651i) q^{9} +(47.4778 + 82.2339i) q^{10} +(-170.035 + 98.1700i) q^{11} +(-69.9167 + 169.081i) q^{12} +151.709 q^{13} +(18.5912 + 140.562i) q^{15} +(83.9901 - 145.475i) q^{16} +(364.888 - 210.668i) q^{17} +(-344.809 + 345.638i) q^{18} +(-98.2403 + 170.157i) q^{19} +320.272i q^{20} -1183.42 q^{22} +(124.236 + 71.7279i) q^{23} +(-186.247 + 143.091i) q^{24} +(-188.406 - 326.329i) q^{25} +(791.902 + 457.205i) q^{26} +(-673.004 + 280.190i) q^{27} -753.566i q^{29} +(-326.567 + 789.744i) q^{30} +(317.662 + 550.206i) q^{31} +(1238.44 - 715.014i) q^{32} +(-1632.96 - 675.243i) q^{33} +2539.57 q^{34} +(-1590.08 + 428.108i) q^{36} +(-668.261 + 1157.46i) q^{37} +(-1025.61 + 592.134i) q^{38} +(831.839 + 1082.73i) q^{39} +(-205.561 + 356.043i) q^{40} -2846.73i q^{41} +99.0370 q^{43} +(-3456.76 - 1995.76i) q^{44} +(-901.234 + 903.402i) q^{45} +(432.333 + 748.823i) q^{46} +(444.261 + 256.494i) q^{47} +(1498.77 - 198.233i) q^{48} -2271.20i q^{50} +(3504.25 + 1449.04i) q^{51} +(1542.09 + 2670.98i) q^{52} +(3682.48 - 2126.08i) q^{53} +(-4357.42 - 565.676i) q^{54} -3093.13 q^{55} +(-1753.06 + 231.866i) q^{57} +(2271.02 - 3933.53i) q^{58} +(2505.49 - 1446.55i) q^{59} +(-2285.75 + 1756.10i) q^{60} +(-1330.70 + 2304.84i) q^{61} +3829.35i q^{62} +5931.68 q^{64} +(2069.81 + 1195.01i) q^{65} +(-6488.86 - 8445.94i) q^{66} +(-1283.74 - 2223.50i) q^{67} +(7418.04 + 4282.81i) q^{68} +(169.292 + 1279.95i) q^{69} +1769.31i q^{71} +(-2042.44 - 544.641i) q^{72} +(1765.57 + 3058.06i) q^{73} +(-6976.49 + 4027.88i) q^{74} +(1295.92 - 3133.94i) q^{75} -3994.38 q^{76} +(1079.09 + 8158.63i) q^{78} +(-1125.98 + 1950.25i) q^{79} +(2291.81 - 1323.18i) q^{80} +(-5689.86 - 3266.83i) q^{81} +(8579.20 - 14859.6i) q^{82} -2063.23i q^{83} +6637.72 q^{85} +(516.962 + 298.468i) q^{86} +(5378.11 - 4131.91i) q^{87} +(-2561.89 - 4437.32i) q^{88} +(-2657.84 - 1534.51i) q^{89} +(-7426.92 + 1999.61i) q^{90} +2916.40i q^{92} +(-2184.98 + 5283.97i) q^{93} +(1546.00 + 2677.74i) q^{94} +(-2680.65 + 1547.67i) q^{95} +(11893.5 + 4918.09i) q^{96} +3416.07 q^{97} +(-4134.59 - 15356.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{3} + 36 q^{4} - 68 q^{6} - 64 q^{9}+O(q^{10}) \) 16 * q + 2 * q^3 + 36 * q^4 - 68 * q^6 - 64 * q^9	\( 16 q + 2 q^{3} + 36 q^{4} - 68 q^{6} - 64 q^{9} + 4 q^{10} - 98 q^{12} + 840 q^{13} + 152 q^{15} + 444 q^{16} + 712 q^{18} + 372 q^{19} - 32 q^{22} - 1146 q^{24} - 1056 q^{25} - 3724 q^{27} - 2348 q^{30} + 2776 q^{31} - 1396 q^{33} + 5856 q^{34} - 6536 q^{36} + 2560 q^{37} + 2540 q^{39} + 1980 q^{40} + 9440 q^{43} - 9700 q^{45} - 7536 q^{46} - 5924 q^{48} - 4764 q^{51} + 20252 q^{52} - 4886 q^{54} + 368 q^{55} - 28288 q^{57} + 7504 q^{58} + 13828 q^{60} - 972 q^{61} + 45544 q^{64} - 36020 q^{66} - 10200 q^{67} - 11520 q^{69} - 14304 q^{72} + 32008 q^{73} - 2114 q^{75} + 34664 q^{76} - 59336 q^{78} + 23168 q^{79} + 17216 q^{81} + 31976 q^{82} + 64032 q^{85} - 50764 q^{87} - 29208 q^{88} - 48704 q^{90} - 31848 q^{93} + 64992 q^{94} - 28630 q^{96} + 56224 q^{97} - 64864 q^{99}+O(q^{100}) \) 16 * q + 2 * q^3 + 36 * q^4 - 68 * q^6 - 64 * q^9 + 4 * q^10 - 98 * q^12 + 840 * q^13 + 152 * q^15 + 444 * q^16 + 712 * q^18 + 372 * q^19 - 32 * q^22 - 1146 * q^24 - 1056 * q^25 - 3724 * q^27 - 2348 * q^30 + 2776 * q^31 - 1396 * q^33 + 5856 * q^34 - 6536 * q^36 + 2560 * q^37 + 2540 * q^39 + 1980 * q^40 + 9440 * q^43 - 9700 * q^45 - 7536 * q^46 - 5924 * q^48 - 4764 * q^51 + 20252 * q^52 - 4886 * q^54 + 368 * q^55 - 28288 * q^57 + 7504 * q^58 + 13828 * q^60 - 972 * q^61 + 45544 * q^64 - 36020 * q^66 - 10200 * q^67 - 11520 * q^69 - 14304 * q^72 + 32008 * q^73 - 2114 * q^75 + 34664 * q^76 - 59336 * q^78 + 23168 * q^79 + 17216 * q^81 + 31976 * q^82 + 64032 * q^85 - 50764 * q^87 - 29208 * q^88 - 48704 * q^90 - 31848 * q^93 + 64992 * q^94 - 28630 * q^96 + 56224 * q^97 - 64864 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more