LMFDB - Embedded newform 15.5.f.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,5,Mod(7,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("15.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	15.f (of order $4$, degree $2$, 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:	$1.55054944626$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 60x^{5} + 1973x^{4} - 3300x^{3} + 1800x^{2} + 31560x + 276676 $ x^8 - 60x^5 + 1973x^4 - 3300x^3 + 1800x^2 + 31560*x + 276676
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.1
Root			$-5.02811 + 5.02811i$ of defining polynomial
Character	$\chi$	$=$	15.13
Dual form			15.5.f.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.02811 + 5.02811i) q^{2} +(-3.67423 - 3.67423i) q^{3} -34.5637i q^{4} +(-23.8949 + 7.35070i) q^{5} +36.9489 q^{6} +(-38.5593 + 38.5593i) q^{7} +(93.3405 + 93.3405i) q^{8} +27.0000i q^{9} +O(q^{10})$	\(q+(-5.02811 + 5.02811i) q^{2} +(-3.67423 - 3.67423i) q^{3} -34.5637i q^{4} +(-23.8949 + 7.35070i) q^{5} +36.9489 q^{6} +(-38.5593 + 38.5593i) q^{7} +(93.3405 + 93.3405i) q^{8} +27.0000i q^{9} +(83.1861 - 157.106i) q^{10} -40.4333 q^{11} +(-126.995 + 126.995i) q^{12} +(20.8688 + 20.8688i) q^{13} -387.760i q^{14} +(114.804 + 60.7873i) q^{15} -385.633 q^{16} +(15.8713 - 15.8713i) q^{17} +(-135.759 - 135.759i) q^{18} +314.926i q^{19} +(254.068 + 825.898i) q^{20} +283.352 q^{21} +(203.303 - 203.303i) q^{22} +(-572.869 - 572.869i) q^{23} -685.910i q^{24} +(516.934 - 351.289i) q^{25} -209.862 q^{26} +(99.2043 - 99.2043i) q^{27} +(1332.75 + 1332.75i) q^{28} +824.433i q^{29} +(-882.891 + 271.600i) q^{30} -1347.19 q^{31} +(445.555 - 445.555i) q^{32} +(148.561 + 148.561i) q^{33} +159.606i q^{34} +(637.933 - 1204.81i) q^{35} +933.221 q^{36} +(-589.843 + 589.843i) q^{37} +(-1583.48 - 1583.48i) q^{38} -153.354i q^{39} +(-2916.48 - 1544.25i) q^{40} +1856.55 q^{41} +(-1424.72 + 1424.72i) q^{42} +(-671.078 - 671.078i) q^{43} +1397.53i q^{44} +(-198.469 - 645.163i) q^{45} +5760.90 q^{46} +(504.865 - 504.865i) q^{47} +(1416.91 + 1416.91i) q^{48} -572.636i q^{49} +(-832.883 + 4365.52i) q^{50} -116.630 q^{51} +(721.305 - 721.305i) q^{52} +(2251.32 + 2251.32i) q^{53} +997.620i q^{54} +(966.151 - 297.213i) q^{55} -7198.29 q^{56} +(1157.11 - 1157.11i) q^{57} +(-4145.34 - 4145.34i) q^{58} +2585.03i q^{59} +(2101.04 - 3968.05i) q^{60} -3276.74 q^{61} +(6773.81 - 6773.81i) q^{62} +(-1041.10 - 1041.10i) q^{63} -1689.53i q^{64} +(-652.060 - 345.259i) q^{65} -1493.97 q^{66} +(-3428.94 + 3428.94i) q^{67} +(-548.573 - 548.573i) q^{68} +4209.71i q^{69} +(2850.31 + 9265.50i) q^{70} -5679.51 q^{71} +(-2520.19 + 2520.19i) q^{72} +(4450.06 + 4450.06i) q^{73} -5931.59i q^{74} +(-3190.06 - 608.620i) q^{75} +10885.0 q^{76} +(1559.08 - 1559.08i) q^{77} +(771.081 + 771.081i) q^{78} -6465.77i q^{79} +(9214.66 - 2834.67i) q^{80} -729.000 q^{81} +(-9334.92 + 9334.92i) q^{82} +(-621.380 - 621.380i) q^{83} -9793.70i q^{84} +(-262.579 + 495.910i) q^{85} +6748.50 q^{86} +(3029.16 - 3029.16i) q^{87} +(-3774.07 - 3774.07i) q^{88} +1856.76i q^{89} +(4241.87 + 2246.02i) q^{90} -1609.37 q^{91} +(-19800.5 + 19800.5i) q^{92} +(4949.89 + 4949.89i) q^{93} +5077.03i q^{94} +(-2314.93 - 7525.13i) q^{95} -3274.14 q^{96} +(12383.5 - 12383.5i) q^{97} +(2879.27 + 2879.27i) q^{98} -1091.70i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 84 q^{5} + 36 q^{6} + 20 q^{7} + 180 q^{8}+O(q^{10}) $ 8 * q - 84 * q^5 + 36 * q^6 + 20 * q^7 + 180 * q^8	\( 8 q - 84 q^{5} + 36 q^{6} + 20 q^{7} + 180 q^{8} + 104 q^{10} - 288 q^{11} - 360 q^{12} - 340 q^{13} + 144 q^{15} + 620 q^{16} + 900 q^{17} + 564 q^{20} + 792 q^{21} - 1100 q^{22} - 1560 q^{23} - 1204 q^{25} - 3024 q^{26} + 3580 q^{28} - 2664 q^{30} - 512 q^{31} + 4980 q^{32} + 2700 q^{33} + 6600 q^{35} + 2484 q^{36} - 3820 q^{37} - 7680 q^{38} - 2952 q^{40} - 2712 q^{41} - 7380 q^{42} - 1240 q^{43} - 1944 q^{45} + 13528 q^{46} + 4800 q^{47} + 3600 q^{48} + 3744 q^{50} + 6264 q^{51} - 1240 q^{52} + 1020 q^{53} - 3644 q^{55} - 30720 q^{56} - 5400 q^{57} + 2340 q^{58} - 1044 q^{60} - 4760 q^{61} + 28680 q^{62} + 540 q^{63} - 1212 q^{65} + 10008 q^{66} - 8920 q^{67} - 1920 q^{68} + 7380 q^{70} + 7536 q^{71} - 4860 q^{72} + 11600 q^{73} - 5976 q^{75} + 4344 q^{76} - 360 q^{77} - 4680 q^{78} + 10644 q^{80} - 5832 q^{81} - 27200 q^{82} - 32400 q^{83} - 15628 q^{85} + 14592 q^{86} + 10620 q^{87} - 14340 q^{88} + 8964 q^{90} + 16528 q^{91} - 31800 q^{92} + 14040 q^{93} + 18864 q^{95} - 4068 q^{96} + 58640 q^{97} + 46440 q^{98}+O(q^{100}) \) 8 * q - 84 * q^5 + 36 * q^6 + 20 * q^7 + 180 * q^8 + 104 * q^10 - 288 * q^11 - 360 * q^12 - 340 * q^13 + 144 * q^15 + 620 * q^16 + 900 * q^17 + 564 * q^20 + 792 * q^21 - 1100 * q^22 - 1560 * q^23 - 1204 * q^25 - 3024 * q^26 + 3580 * q^28 - 2664 * q^30 - 512 * q^31 + 4980 * q^32 + 2700 * q^33 + 6600 * q^35 + 2484 * q^36 - 3820 * q^37 - 7680 * q^38 - 2952 * q^40 - 2712 * q^41 - 7380 * q^42 - 1240 * q^43 - 1944 * q^45 + 13528 * q^46 + 4800 * q^47 + 3600 * q^48 + 3744 * q^50 + 6264 * q^51 - 1240 * q^52 + 1020 * q^53 - 3644 * q^55 - 30720 * q^56 - 5400 * q^57 + 2340 * q^58 - 1044 * q^60 - 4760 * q^61 + 28680 * q^62 + 540 * q^63 - 1212 * q^65 + 10008 * q^66 - 8920 * q^67 - 1920 * q^68 + 7380 * q^70 + 7536 * q^71 - 4860 * q^72 + 11600 * q^73 - 5976 * q^75 + 4344 * q^76 - 360 * q^77 - 4680 * q^78 + 10644 * q^80 - 5832 * q^81 - 27200 * q^82 - 32400 * q^83 - 15628 * q^85 + 14592 * q^86 + 10620 * q^87 - 14340 * q^88 + 8964 * q^90 + 16528 * q^91 - 31800 * q^92 + 14040 * q^93 + 18864 * q^95 - 4068 * q^96 + 58640 * q^97 + 46440 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−5.02811	+	5.02811i	−1.25703	+	1.25703i	−0.304522	+	0.952505i	$0.598497\pi$
$2$	−5.02811	+	5.02811i	−1.25703	+	1.25703i	−0.952505	+	0.304522i	$0.901503\pi$
$3$	−3.67423	−	3.67423i	−0.408248	−	0.408248i
$3$	−3.67423	−	3.67423i	−0.408248	−	0.408248i
$4$		−	34.5637i		−	2.16023i
$5$	−23.8949	+	7.35070i	−0.955797	+	0.294028i
$5$	−23.8949	+	7.35070i	−0.955797	+	0.294028i
$6$	36.9489			1.02636
$7$	−38.5593	+	38.5593i	−0.786924	+	0.786924i	−0.980989	−	0.194065i	$-0.937833\pi$
$7$	−38.5593	+	38.5593i	−0.786924	+	0.786924i	0.194065	+	0.980989i	$0.437833\pi$
$8$	93.3405	+	93.3405i	1.45845	+	1.45845i
$9$			27.0000i			0.333333i
$10$	83.1861	−	157.106i	0.831861	−	1.57106i
$11$	−40.4333			−0.334160			−0.167080	−	0.985943i	$-0.553434\pi$
$11$	−40.4333			−0.334160			−0.167080	+	0.985943i	$0.553434\pi$
$12$	−126.995	+	126.995i	−0.881912	+	0.881912i
$13$	20.8688	+	20.8688i	0.123484	+	0.123484i	0.766148	−	0.642664i	$-0.222171\pi$
$13$	20.8688	+	20.8688i	0.123484	+	0.123484i	−0.642664	+	0.766148i	$0.722171\pi$
$14$		−	387.760i		−	1.97837i
$15$	114.804	+	60.7873i	0.510239	+	0.270166i
$16$	−385.633			−1.50638
$17$	15.8713	−	15.8713i	0.0549181	−	0.0549181i	−0.679114	−	0.734032i	$-0.737636\pi$
$17$	15.8713	−	15.8713i	0.0549181	−	0.0549181i	0.734032	+	0.679114i	$0.237636\pi$
$18$	−135.759	−	135.759i	−0.419009	−	0.419009i
$19$			314.926i			0.872371i	0.899857	+	0.436185i	$0.143671\pi$
$19$			314.926i			0.872371i	−0.899857	+	0.436185i	$0.856329\pi$
$20$	254.068	+	825.898i	0.635170	+	2.06474i
$21$	283.352			0.642521
$22$	203.303	−	203.303i	0.420048	−	0.420048i
$23$	−572.869	−	572.869i	−1.08293	−	1.08293i	−0.996235	−	0.0866935i	$-0.972370\pi$
$23$	−572.869	−	572.869i	−1.08293	−	1.08293i	−0.0866935	−	0.996235i	$-0.527630\pi$
$24$		−	685.910i		−	1.19082i
$25$	516.934	−	351.289i	0.827095	−	0.562062i
$26$	−209.862			−0.310446
$27$	99.2043	−	99.2043i	0.136083	−	0.136083i
$28$	1332.75	+	1332.75i	1.69994	+	1.69994i
$29$			824.433i			0.980301i	0.871638	+	0.490151i	$0.163058\pi$
$29$			824.433i			0.980301i	−0.871638	+	0.490151i	$0.836942\pi$
$30$	−882.891	+	271.600i	−0.980990	+	0.301778i
$31$	−1347.19			−1.40186			−0.700931	−	0.713229i	$-0.747232\pi$
$31$	−1347.19			−1.40186			−0.700931	+	0.713229i	$0.747232\pi$
$32$	445.555	−	445.555i	0.435112	−	0.435112i
$33$	148.561	+	148.561i	0.136420	+	0.136420i
$34$			159.606i			0.138067i
$35$	637.933	−	1204.81i	0.520762	−	0.983517i
$36$	933.221			0.720078
$37$	−589.843	+	589.843i	−0.430857	+	0.430857i	−0.888920	−	0.458063i	$-0.848543\pi$
$37$	−589.843	+	589.843i	−0.430857	+	0.430857i	0.458063	+	0.888920i	$0.348543\pi$
$38$	−1583.48	−	1583.48i	−1.09659	−	1.09659i
$39$		−	153.354i		−	0.100824i
$40$	−2916.48	−	1544.25i	−1.82280	−	0.965154i
$41$	1856.55			1.10443			0.552215	−	0.833702i	$-0.313783\pi$
$41$	1856.55			1.10443			0.552215	+	0.833702i	$0.313783\pi$
$42$	−1424.72	+	1424.72i	−0.807666	+	0.807666i
$43$	−671.078	−	671.078i	−0.362941	−	0.362941i	0.501954	−	0.864894i	$-0.332615\pi$
$43$	−671.078	−	671.078i	−0.362941	−	0.362941i	−0.864894	+	0.501954i	$0.832615\pi$
$44$			1397.53i			0.721863i
$45$	−198.469	−	645.163i	−0.0980094	−	0.318599i
$46$	5760.90			2.72254
$47$	504.865	−	504.865i	0.228549	−	0.228549i	−0.583537	−	0.812086i	$-0.698332\pi$
$47$	504.865	−	504.865i	0.228549	−	0.228549i	0.812086	+	0.583537i	$0.198332\pi$
$48$	1416.91	+	1416.91i	0.614976	+	0.614976i
$49$		−	572.636i		−	0.238499i
$50$	−832.883	+	4365.52i	−0.333153	+	1.74621i
$51$	−116.630			−0.0448405
$52$	721.305	−	721.305i	0.266755	−	0.266755i
$53$	2251.32	+	2251.32i	0.801468	+	0.801468i	0.983325	−	0.181857i	$-0.0582107\pi$
$53$	2251.32	+	2251.32i	0.801468	+	0.801468i	−0.181857	+	0.983325i	$0.558211\pi$
$54$			997.620i			0.342119i
$55$	966.151	−	297.213i	0.319389	−	0.0982523i
$56$	−7198.29			−2.29537
$57$	1157.11	−	1157.11i	0.356144	−	0.356144i
$58$	−4145.34	−	4145.34i	−1.23227	−	1.23227i
$59$			2585.03i			0.742610i	0.928511	+	0.371305i	$0.121090\pi$
$59$			2585.03i			0.742610i	−0.928511	+	0.371305i	$0.878910\pi$
$60$	2101.04	−	3968.05i	0.583622	−	1.10224i
$61$	−3276.74			−0.880607			−0.440304	−	0.897849i	$-0.645129\pi$
$61$	−3276.74			−0.880607			−0.440304	+	0.897849i	$0.645129\pi$
$62$	6773.81	−	6773.81i	1.76218	−	1.76218i
$63$	−1041.10	−	1041.10i	−0.262308	−	0.262308i
$64$		−	1689.53i		−	0.412483i
$65$	−652.060	−	345.259i	−0.154334	−	0.0817180i
$66$	−1493.97			−0.342967
$67$	−3428.94	+	3428.94i	−0.763854	+	0.763854i	−0.977017	−	0.213163i	$-0.931624\pi$
$67$	−3428.94	+	3428.94i	−0.763854	+	0.763854i	0.213163	+	0.977017i	$0.431624\pi$
$68$	−548.573	−	548.573i	−0.118636	−	0.118636i
$69$			4209.71i			0.884207i
$70$	2850.31	+	9265.50i	0.581696	+	1.89092i
$71$	−5679.51			−1.12666			−0.563331	−	0.826231i	$-0.690481\pi$
$71$	−5679.51			−1.12666			−0.563331	+	0.826231i	$0.690481\pi$
$72$	−2520.19	+	2520.19i	−0.486149	+	0.486149i
$73$	4450.06	+	4450.06i	0.835065	+	0.835065i	0.988205	−	0.153140i	$-0.0489385\pi$
$73$	4450.06	+	4450.06i	0.835065	+	0.835065i	−0.153140	+	0.988205i	$0.548939\pi$
$74$		−	5931.59i		−	1.08320i
$75$	−3190.06	−	608.620i	−0.567121	−	0.108199i
$76$	10885.0			1.88453
$77$	1559.08	−	1559.08i	0.262958	−	0.262958i
$78$	771.081	+	771.081i	0.126739	+	0.126739i
$79$		−	6465.77i		−	1.03602i	−0.855376	−	0.518008i	$-0.826674\pi$
$79$		−	6465.77i		−	1.03602i	0.855376	−	0.518008i	$-0.173326\pi$
$80$	9214.66	−	2834.67i	1.43979	−	0.442918i
$81$	−729.000			−0.111111
$82$	−9334.92	+	9334.92i	−1.38830	+	1.38830i
$83$	−621.380	−	621.380i	−0.0901988	−	0.0901988i	0.660568	−	0.750766i	$-0.270316\pi$
$83$	−621.380	−	621.380i	−0.0901988	−	0.0901988i	−0.750766	+	0.660568i	$0.770316\pi$
$84$		−	9793.70i		−	1.38800i
$85$	−262.579	+	495.910i	−0.0363431	+	0.0686380i
$86$	6748.50			0.912453
$87$	3029.16	−	3029.16i	0.400206	−	0.400206i
$88$	−3774.07	−	3774.07i	−0.487354	−	0.487354i
$89$			1856.76i			0.234410i	0.993108	+	0.117205i	$0.0373935\pi$
$89$			1856.76i			0.234410i	−0.993108	+	0.117205i	$0.962606\pi$
$90$	4241.87	+	2246.02i	0.523688	+	0.277287i
$91$	−1609.37			−0.194345
$92$	−19800.5	+	19800.5i	−2.33938	+	2.33938i
$93$	4949.89	+	4949.89i	0.572308	+	0.572308i
$94$			5077.03i			0.574585i
$95$	−2314.93	−	7525.13i	−0.256502	−	0.833809i
$96$	−3274.14			−0.355267
$97$	12383.5	−	12383.5i	1.31614	−	1.31614i	0.399332	−	0.916806i	$-0.369242\pi$
$97$	12383.5	−	12383.5i	1.31614	−	1.31614i	0.916806	−	0.399332i	$-0.130758\pi$
$98$	2879.27	+	2879.27i	0.299800	+	0.299800i
$99$		−	1091.70i		−	0.111387i
$100$	−12141.9	−	17867.2i	−1.21419	−	1.78672i
$101$	−189.344			−0.0185613			−0.00928067	−	0.999957i	$-0.502954\pi$
$101$	−189.344			−0.0185613			−0.00928067	+	0.999957i	$0.502954\pi$
$102$	586.428	−	586.428i	0.0563657	−	0.0563657i
$103$	14330.9	+	14330.9i	1.35083	+	1.35083i	0.884736	+	0.466092i	$0.154338\pi$
$103$	14330.9	+	14330.9i	1.35083	+	1.35083i	0.466092	+	0.884736i	$0.345662\pi$
$104$			3895.82i			0.360190i
$105$	−6770.67	+	2082.83i	−0.614119	+	0.188919i
$106$	−22639.8			−2.01493
$107$	−384.065	+	384.065i	−0.0335457	+	0.0335457i	−0.723681	−	0.690135i	$-0.757551\pi$
$107$	−384.065	+	384.065i	−0.0335457	+	0.0335457i	0.690135	+	0.723681i	$0.257551\pi$
$108$	−3428.87	−	3428.87i	−0.293971	−	0.293971i
$109$		−	14104.7i		−	1.18717i	−0.804773	−	0.593583i	$-0.797713\pi$
$109$		−	14104.7i		−	1.18717i	0.804773	−	0.593583i	$-0.202287\pi$
$110$	−3363.49	+	6352.33i	−0.277974	+	0.524986i
$111$	4334.44			0.351793
$112$	14869.7	−	14869.7i	1.18540	−	1.18540i
$113$	−12599.1	−	12599.1i	−0.986693	−	0.986693i	0.0132199	−	0.999913i	$-0.495792\pi$
$113$	−12599.1	−	12599.1i	−0.986693	−	0.986693i	−0.999913	+	0.0132199i	$0.995792\pi$
$114$			11636.2i			0.895365i
$115$	17899.7	+	9477.67i	1.35347	+	0.716648i
$116$	28495.5			2.11768
$117$	−563.459	+	563.459i	−0.0411614	+	0.0411614i
$118$	−12997.8	−	12997.8i	−0.933481	−	0.933481i
$119$			1223.97i			0.0864328i
$120$	5041.92	+	16389.8i	0.350134	+	1.13818i
$121$	−13006.1			−0.888337
$122$	16475.8	−	16475.8i	1.10695	−	1.10695i
$123$	−6821.39	−	6821.39i	−0.450882	−	0.450882i
$124$			46563.9i			3.02835i
$125$	−9769.88	+	12193.9i	−0.625272	+	0.780407i
$126$	10469.5			0.659457
$127$	−10957.5	+	10957.5i	−0.679367	+	0.679367i	−0.959857	−	0.280490i	$-0.909503\pi$
$127$	−10957.5	+	10957.5i	−0.679367	+	0.679367i	0.280490	+	0.959857i	$0.409503\pi$
$128$	15624.0	+	15624.0i	0.953614	+	0.953614i
$129$			4931.39i			0.296340i
$130$	5014.63	−	1542.63i	0.296723	−	0.0912799i
$131$	10872.8			0.633579			0.316789	−	0.948496i	$-0.397395\pi$
$131$	10872.8			0.633579			0.316789	+	0.948496i	$0.397395\pi$
$132$	5134.84	−	5134.84i	0.294699	−	0.294699i
$133$	−12143.3	−	12143.3i	−0.686489	−	0.686489i
$134$		−	34482.2i		−	1.92037i
$135$	−1641.26	+	3099.70i	−0.0900553	+	0.170080i
$136$	2962.88			0.160190
$137$	−3387.27	+	3387.27i	−0.180471	+	0.180471i	−0.791561	−	0.611090i	$-0.790731\pi$
$137$	−3387.27	+	3387.27i	−0.180471	+	0.180471i	0.611090	+	0.791561i	$0.290731\pi$
$138$	−21166.9	−	21166.9i	−1.11147	−	1.11147i
$139$			6096.09i			0.315516i	0.987478	+	0.157758i	$0.0504266\pi$
$139$			6096.09i			0.315516i	−0.987478	+	0.157758i	$0.949573\pi$
$140$	−41642.7	−	22049.4i	−2.12463	−	1.12497i
$141$	−3709.98			−0.186610
$142$	28557.2	−	28557.2i	1.41625	−	1.41625i
$143$	−843.796	−	843.796i	−0.0412634	−	0.0412634i
$144$		−	10412.1i		−	0.502126i
$145$	−6060.17	−	19699.8i	−0.288236	−	0.936969i
$146$	−44750.8			−2.09940
$147$	−2104.00	+	2104.00i	−0.0973668	+	0.0973668i
$148$	20387.2	+	20387.2i	0.930752	+	0.930752i
$149$			41060.3i			1.84948i	0.380600	+	0.924740i	$0.375718\pi$
$149$			41060.3i			1.84948i	−0.380600	+	0.924740i	$0.624282\pi$
$150$	19100.2	−	12979.7i	0.848896	−	0.576877i
$151$	12096.5			0.530523			0.265262	−	0.964176i	$-0.414542\pi$
$151$	12096.5			0.530523			0.265262	+	0.964176i	$0.414542\pi$
$152$	−29395.3	+	29395.3i	−1.27231	+	1.27231i
$153$	428.526	+	428.526i	0.0183060	+	0.0183060i
$154$			15678.4i			0.661091i
$155$	32191.0	−	9902.79i	1.33989	−	0.412187i
$156$	−5300.49			−0.217804
$157$	−21184.3	+	21184.3i	−0.859440	+	0.859440i	−0.991272	−	0.131832i	$-0.957914\pi$
$157$	−21184.3	+	21184.3i	−0.859440	+	0.859440i	0.131832	+	0.991272i	$0.457914\pi$
$158$	32510.6	+	32510.6i	1.30230	+	1.30230i
$159$		−	16543.8i		−	0.654396i
$160$	−7371.35	+	13921.6i	−0.287943	+	0.543814i
$161$	44178.8			1.70436
$162$	3665.49	−	3665.49i	0.139670	−	0.139670i
$163$	3953.29	+	3953.29i	0.148793	+	0.148793i	0.777579	−	0.628786i	$-0.216448\pi$
$163$	3953.29	+	3953.29i	0.148793	+	0.148793i	−0.628786	+	0.777579i	$0.716448\pi$
$164$		−	64169.2i		−	2.38583i
$165$	−4641.90	−	2457.83i	−0.170501	−	0.0902785i
$166$	6248.73			0.226765
$167$	−7863.94	+	7863.94i	−0.281973	+	0.281973i	−0.833895	−	0.551922i	$-0.813894\pi$
$167$	−7863.94	+	7863.94i	−0.281973	+	0.281973i	0.551922	+	0.833895i	$0.313894\pi$
$168$	26448.2	+	26448.2i	0.937082	+	0.937082i
$169$		−	27690.0i		−	0.969503i
$170$	−1173.21	−	3813.76i	−0.0405956	−	0.131964i
$171$	−8503.00			−0.290790
$172$	−23195.0	+	23195.0i	−0.784037	+	0.784037i
$173$	−20563.0	−	20563.0i	−0.687059	−	0.687059i	0.274522	−	0.961581i	$-0.411480\pi$
$173$	−20563.0	−	20563.0i	−0.687059	−	0.687059i	−0.961581	+	0.274522i	$0.911480\pi$
$174$			30461.9i			1.00614i
$175$	−6387.16	+	33478.1i	−0.208560	+	1.09316i
$176$	15592.4			0.503371
$177$	9498.00	−	9498.00i	0.303169	−	0.303169i
$178$	−9336.01	−	9336.01i	−0.294660	−	0.294660i
$179$		−	11578.3i		−	0.361360i	−0.983542	−	0.180680i	$-0.942170\pi$
$179$		−	11578.3i		−	0.361360i	0.983542	−	0.180680i	$-0.0578298\pi$
$180$	−22299.2	+	6859.83i	−0.688248	+	0.211723i
$181$	15410.3			0.470385			0.235193	−	0.971949i	$-0.424428\pi$
$181$	15410.3			0.470385			0.235193	+	0.971949i	$0.424428\pi$
$182$	8092.11	−	8092.11i	0.244298	−	0.244298i
$183$	12039.5	+	12039.5i	0.359506	+	0.359506i
$184$		−	106944.i		−	3.15879i
$185$	9758.49	−	18430.0i	0.285128	−	0.538496i
$186$	−49777.1			−1.43881
$187$	−641.731	+	641.731i	−0.0183514	+	0.0183514i
$188$	−17450.0	−	17450.0i	−0.493720	−	0.493720i
$189$			7650.49i			0.214174i
$190$	49476.9	+	26197.5i	1.37055	+	0.725691i
$191$	−8129.00			−0.222828			−0.111414	−	0.993774i	$-0.535538\pi$
$191$	−8129.00			−0.222828			−0.111414	+	0.993774i	$0.535538\pi$
$192$	−6207.73	+	6207.73i	−0.168395	+	0.168395i
$193$	−28495.5	−	28495.5i	−0.765001	−	0.765001i	0.212220	−	0.977222i	$-0.431931\pi$
$193$	−28495.5	−	28495.5i	−0.765001	−	0.765001i	−0.977222	+	0.212220i	$0.931931\pi$
$194$			124532.i			3.30884i
$195$	1127.26	+	3664.38i	0.0296452	+	0.0963677i
$196$	−19792.4			−0.515213
$197$	−14908.5	+	14908.5i	−0.384150	+	0.384150i	−0.872595	−	0.488445i	$-0.837564\pi$
$197$	−14908.5	+	14908.5i	−0.384150	+	0.384150i	0.488445	+	0.872595i	$0.337564\pi$
$198$	5489.18	+	5489.18i	0.140016	+	0.140016i
$199$			3870.42i			0.0977353i	0.998805	+	0.0488677i	$0.0155613\pi$
$199$			3870.42i			0.0977353i	−0.998805	+	0.0488677i	$0.984439\pi$
$200$	81040.4	+	15461.4i	2.02601	+	0.386536i
$201$	25197.5			0.623684
$202$	952.043	−	952.043i	0.0233321	−	0.0233321i
$203$	−31789.6	−	31789.6i	−0.771423	−	0.771423i
$204$			4031.17i			0.0968659i
$205$	−44362.1	+	13646.9i	−1.05561	+	0.324734i
$206$	−144115.			−3.39606
$207$	15467.5	−	15467.5i	0.360976	−	0.360976i
$208$	−8047.71	−	8047.71i	−0.186014	−	0.186014i
$209$		−	12733.5i		−	0.291511i
$210$	23570.9	−	44516.4i	0.534488	−	1.00944i
$211$	−17666.9			−0.396822			−0.198411	−	0.980119i	$-0.563578\pi$
$211$	−17666.9			−0.396822			−0.198411	+	0.980119i	$0.563578\pi$
$212$	77814.2	−	77814.2i	1.73136	−	1.73136i
$213$	20867.8	+	20867.8i	0.459958	+	0.459958i
$214$		−	3862.24i		−	0.0843358i
$215$	20968.2	+	11102.4i	0.453612	+	0.240183i
$216$	18519.6			0.396939
$217$	51946.6	−	51946.6i	1.10316	−	1.10316i
$218$	70920.0	+	70920.0i	1.49230	+	1.49230i
$219$		−	32701.1i		−	0.681827i
$220$	−10272.8	−	33393.8i	−0.212248	−	0.689954i
$221$	662.433			0.0135630
$222$	−21794.1	+	21794.1i	−0.442214	+	0.442214i
$223$	10730.0	+	10730.0i	0.215768	+	0.215768i	0.806713	−	0.590944i	$-0.201245\pi$
$223$	10730.0	+	10730.0i	0.215768	+	0.215768i	−0.590944	+	0.806713i	$0.701245\pi$
$224$			34360.5i			0.684800i
$225$	9484.80	+	13957.2i	0.187354	+	0.275698i
$226$	126699.			2.48060
$227$	−34199.9	+	34199.9i	−0.663703	+	0.663703i	−0.956251	−	0.292548i	$-0.905497\pi$
$227$	−34199.9	+	34199.9i	−0.663703	+	0.663703i	0.292548	+	0.956251i	$0.405497\pi$
$228$	−39994.1	−	39994.1i	−0.769354	−	0.769354i
$229$			73430.0i			1.40024i	0.714026	+	0.700120i	$0.246870\pi$
$229$			73430.0i			1.40024i	−0.714026	+	0.700120i	$0.753130\pi$
$230$	−137656.	+	42346.7i	−2.60220	+	0.800504i
$231$	−11456.8			−0.214704
$232$	−76953.1	+	76953.1i	−1.42972	+	1.42972i
$233$	18203.1	+	18203.1i	0.335300	+	0.335300i	0.854595	−	0.519295i	$-0.173805\pi$
$233$	18203.1	+	18203.1i	0.335300	+	0.335300i	−0.519295	+	0.854595i	$0.673805\pi$
$234$		−	5666.26i		−	0.103482i
$235$	−8352.59	+	15774.8i	−0.151247	+	0.285646i
$236$	89348.2			1.60421
$237$	−23756.8	+	23756.8i	−0.422952	+	0.422952i
$238$	−6154.28	−	6154.28i	−0.108648	−	0.108648i
$239$		−	102775.i		−	1.79925i	−0.436661	−	0.899626i	$-0.643839\pi$
$239$		−	102775.i		−	1.79925i	0.436661	−	0.899626i	$-0.356161\pi$
$240$	−44272.1	−	23441.6i	−0.768613	−	0.406972i
$241$	69403.6			1.19495			0.597473	−	0.801889i	$-0.296172\pi$
$241$	69403.6			1.19495			0.597473	+	0.801889i	$0.296172\pi$
$242$	65396.3	−	65396.3i	1.11666	−	1.11666i
$243$	2678.52	+	2678.52i	0.0453609	+	0.0453609i
$244$			113256.i			1.90232i
$245$	4209.28	+	13683.1i	0.0701254	+	0.227956i
$246$	68597.4			1.13354
$247$	−6572.14	+	6572.14i	−0.107724	+	0.107724i
$248$	−125747.	−	125747.i	−2.04454	−	2.04454i
$249$			4566.19i			0.0736470i
$250$	−12188.0	−	110436.i	−0.195008	−	1.76698i
$251$	−40858.0			−0.648530			−0.324265	−	0.945966i	$-0.605117\pi$
$251$	−40858.0			−0.648530			−0.324265	+	0.945966i	$0.605117\pi$
$252$	−35984.3	+	35984.3i	−0.566647	+	0.566647i
$253$	23163.0	+	23163.0i	0.361871	+	0.361871i
$254$		−	110191.i		−	1.70796i
$255$	2786.87	−	857.313i	0.0428584	−	0.0131844i
$256$	−130086.			−1.98495
$257$	53271.7	−	53271.7i	0.806548	−	0.806548i	−0.177562	−	0.984110i	$-0.556821\pi$
$257$	53271.7	−	53271.7i	0.806548	−	0.806548i	0.984110	+	0.177562i	$0.0568211\pi$
$258$	−24795.6	−	24795.6i	−0.372507	−	0.372507i
$259$		−	45487.9i		−	0.678103i
$260$	−11933.4	+	22537.6i	−0.176530	+	0.333397i
$261$	−22259.7			−0.326767
$262$	−54669.8	+	54669.8i	−0.796425	+	0.796425i
$263$	47788.6	+	47788.6i	0.690896	+	0.690896i	0.962429	−	0.271533i	$-0.0875306\pi$
$263$	47788.6	+	47788.6i	0.690896	+	0.690896i	−0.271533	+	0.962429i	$0.587531\pi$
$264$			27733.6i			0.397923i
$265$	−70344.0	−	37246.4i	−1.00170	−	0.530387i
$266$	122116.			1.72587
$267$	6822.19	−	6822.19i	0.0956976	−	0.0956976i
$268$	118517.	+	118517.i	1.65010	+	1.65010i
$269$			130832.i			1.80805i	0.427483	+	0.904023i	$0.359400\pi$
$269$			130832.i			1.80805i	−0.427483	+	0.904023i	$0.640600\pi$
$270$	−7333.21	−	23838.1i	−0.100593	−	0.326997i
$271$	−116029.			−1.57989			−0.789945	−	0.613178i	$-0.789891\pi$
$271$	−116029.			−1.57989			−0.789945	+	0.613178i	$0.789891\pi$
$272$	−6120.51	+	6120.51i	−0.0827274	+	0.0827274i
$273$	5913.22	+	5913.22i	0.0793412	+	0.0793412i
$274$		−	34063.1i		−	0.453715i
$275$	−20901.4	+	14203.8i	−0.276382	+	0.187819i
$276$	145503.			1.91010
$277$	41111.1	−	41111.1i	0.535796	−	0.535796i	−0.386495	−	0.922291i	$-0.626314\pi$
$277$	41111.1	−	41111.1i	0.535796	−	0.535796i	0.922291	+	0.386495i	$0.126314\pi$
$278$	−30651.8	−	30651.8i	−0.396613	−	0.396613i
$279$		−	36374.1i		−	0.467287i
$280$	172003.	−	52912.5i	2.19391	−	0.674904i
$281$	−61086.4			−0.773627			−0.386814	−	0.922158i	$-0.626424\pi$
$281$	−61086.4			−0.773627			−0.386814	+	0.922158i	$0.626424\pi$
$282$	18654.2	−	18654.2i	0.234573	−	0.234573i
$283$	54739.9	+	54739.9i	0.683489	+	0.683489i	0.960785	−	0.277296i	$-0.0894382\pi$
$283$	54739.9	+	54739.9i	0.683489	+	0.683489i	−0.277296	+	0.960785i	$0.589438\pi$
$284$			196305.i			2.43386i
$285$	−19143.5	+	36154.7i	−0.235685	+	0.445117i
$286$	8485.40			0.103739
$287$	−71587.1	+	71587.1i	−0.869103	+	0.869103i
$288$	12030.0	+	12030.0i	0.145037	+	0.145037i
$289$			83017.2i			0.993968i
$290$	129524.	+	68581.4i	1.54012	+	0.815474i
$291$	−91000.1			−1.07462
$292$	153811.	−	153811.i	1.80394	−	1.80394i
$293$	−33601.9	−	33601.9i	−0.391406	−	0.391406i	0.483782	−	0.875189i	$-0.339263\pi$
$293$	−33601.9	−	33601.9i	−0.391406	−	0.391406i	−0.875189	+	0.483782i	$0.839263\pi$
$294$		−	21158.3i		−	0.244785i
$295$	−19001.8	−	61769.0i	−0.218348	−	0.709785i
$296$	−110113.			−1.25676
$297$	−4011.16	+	4011.16i	−0.0454734	+	0.0454734i
$298$	−206456.	−	206456.i	−2.32485	−	2.32485i
$299$		−	23910.2i		−	0.267449i
$300$	−21036.2	+	110260.i	−0.233735	+	1.22511i
$301$	51752.5			0.571214
$302$	−60822.3	+	60822.3i	−0.666882	+	0.666882i
$303$	695.695	+	695.695i	0.00757763	+	0.00757763i
$304$		−	121446.i		−	1.31412i
$305$	78297.4	−	24086.3i	0.841681	−	0.258923i
$306$	−4309.35			−0.0460224
$307$	84437.4	−	84437.4i	0.895897	−	0.895897i	−0.0991732	−	0.995070i	$-0.531620\pi$
$307$	84437.4	−	84437.4i	0.895897	−	0.895897i	0.995070	+	0.0991732i	$0.0316198\pi$
$308$	−53887.6	−	53887.6i	−0.568051	−	0.568051i
$309$		−	105310.i		−	1.10295i
$310$	−112067.	+	211652.i	−1.16615	+	2.20241i
$311$	93477.0			0.966460			0.483230	−	0.875493i	$-0.339463\pi$
$311$	93477.0			0.966460			0.483230	+	0.875493i	$0.339463\pi$
$312$	14314.1	−	14314.1i	0.147047	−	0.147047i
$313$	−6979.59	−	6979.59i	−0.0712429	−	0.0712429i	0.670588	−	0.741830i	$-0.266042\pi$
$313$	−6979.59	−	6979.59i	−0.0712429	−	0.0712429i	−0.741830	+	0.670588i	$0.766042\pi$
$314$		−	213034.i		−	2.16068i
$315$	32529.8	+	17224.2i	0.327839	+	0.173587i
$316$	−223481.			−2.23804
$317$	41396.6	−	41396.6i	0.411951	−	0.411951i	−0.470467	−	0.882418i	$-0.655914\pi$
$317$	41396.6	−	41396.6i	0.411951	−	0.411951i	0.882418	+	0.470467i	$0.155914\pi$
$318$	83184.0	+	83184.0i	0.822594	+	0.822594i
$319$		−	33334.6i		−	0.327577i
$320$	12419.2	+	40371.2i	0.121282	+	0.394250i
$321$	2822.29			0.0273900
$322$	−222136.	+	222136.i	−2.14243	+	2.14243i
$323$	4998.29	+	4998.29i	0.0479090	+	0.0479090i
$324$			25197.0i			0.240026i
$325$	18118.8	+	3456.82i	0.171539	+	0.0327273i
$326$	−39755.1			−0.374074
$327$	−51824.0	+	51824.0i	−0.484658	+	0.484658i
$328$	173291.	+	173291.i	1.61075	+	1.61075i
$329$			38934.5i			0.359702i
$330$	35698.2	−	10981.7i	0.327807	−	0.100842i
$331$	65879.3			0.601303			0.300651	−	0.953734i	$-0.402796\pi$
$331$	65879.3			0.601303			0.300651	+	0.953734i	$0.402796\pi$
$332$	−21477.2	+	21477.2i	−0.194851	+	0.194851i
$333$	−15925.8	−	15925.8i	−0.143619	−	0.143619i
$334$		−	79081.5i		−	0.708895i
$335$	56729.1	−	107139.i	0.505495	−	0.954684i
$336$	−109270.			−0.967879
$337$	18022.9	−	18022.9i	0.158696	−	0.158696i	−0.623293	−	0.781989i	$-0.714205\pi$
$337$	18022.9	−	18022.9i	0.158696	−	0.158696i	0.781989	+	0.623293i	$0.214205\pi$
$338$	139228.	+	139228.i	1.21869	+	1.21869i
$339$			92583.9i			0.805631i
$340$	17140.5	+	9075.71i	0.148274	+	0.0785096i
$341$	54471.3			0.468445
$342$	42754.0	−	42754.0i	0.365531	−	0.365531i
$343$	−70500.4	−	70500.4i	−0.599244	−	0.599244i
$344$		−	125277.i		−	1.05866i
$345$	−30944.3	−	100591.i	−0.259982	−	0.845123i
$346$	206786.			1.72730
$347$	−32583.8	+	32583.8i	−0.270610	+	0.270610i	−0.829346	−	0.558736i	$-0.811287\pi$
$347$	−32583.8	+	32583.8i	−0.270610	+	0.270610i	0.558736	+	0.829346i	$0.311287\pi$
$348$	−104699.	−	104699.i	−0.864539	−	0.864539i
$349$			54340.9i			0.446145i	0.974802	+	0.223072i	$0.0716086\pi$
$349$			54340.9i			0.446145i	−0.974802	+	0.223072i	$0.928391\pi$
$350$	−136216.	−	200447.i	−1.11197	−	1.63630i
$351$	4140.56			0.0336082
$352$	−18015.2	+	18015.2i	−0.145397	+	0.145397i
$353$	−11345.9	−	11345.9i	−0.0910524	−	0.0910524i	0.660114	−	0.751166i	$-0.270508\pi$
$353$	−11345.9	−	11345.9i	−0.0910524	−	0.0910524i	−0.751166	+	0.660114i	$0.770508\pi$
$354$			95513.9i			0.762184i
$355$	135711.	−	41748.4i	1.07686	−	0.331271i
$356$	64176.7			0.506381
$357$	4497.17	−	4497.17i	0.0352860	−	0.0352860i
$358$	58217.1	+	58217.1i	0.454239	+	0.454239i
$359$			26830.8i			0.208183i	0.994568	+	0.104091i	$0.0331934\pi$
$359$			26830.8i			0.208183i	−0.994568	+	0.104091i	$0.966807\pi$
$360$	41694.6	−	78745.1i	0.321718	−	0.607601i
$361$	31142.7			0.238969
$362$	−77484.6	+	77484.6i	−0.591287	+	0.591287i
$363$	47787.6	+	47787.6i	0.362662	+	0.362662i
$364$			55626.0i			0.419832i
$365$	−139045.	−	73622.7i	−1.04368	−	0.552620i
$366$	−121072.			−0.903818
$367$	−112367.	+	112367.i	−0.834267	+	0.834267i	−0.988097	−	0.153830i	$-0.950839\pi$
$367$	−112367.	+	112367.i	−0.834267	+	0.834267i	0.153830	+	0.988097i	$0.450839\pi$
$368$	220917.	+	220917.i	1.63130	+	1.63130i
$369$			50126.8i			0.368143i
$370$	43601.4	+	141735.i	0.318491	+	1.03532i
$371$	−173619.			−1.26139
$372$	171087.	−	171087.i	1.23632	−	1.23632i
$373$	−16877.0	−	16877.0i	−0.121305	−	0.121305i	0.643848	−	0.765153i	$-0.277337\pi$
$373$	−16877.0	−	16877.0i	−0.121305	−	0.121305i	−0.765153	+	0.643848i	$0.777337\pi$
$374$		−	6453.38i		−	0.0461364i
$375$	80699.9	−	8906.24i	0.573866	−	0.0633333i
$376$	94248.7			0.666653
$377$	−17205.0	+	17205.0i	−0.121052	+	0.121052i
$378$	−38467.5	−	38467.5i	−0.269222	−	0.269222i
$379$			50523.2i			0.351733i	0.984414	+	0.175866i	$0.0562726\pi$
$379$			50523.2i			0.351733i	−0.984414	+	0.175866i	$0.943727\pi$
$380$	−260097.	+	80012.5i	−1.80122	+	0.554104i
$381$	80520.9			0.554700
$382$	40873.5	−	40873.5i	0.280101	−	0.280101i
$383$	17592.0	+	17592.0i	0.119927	+	0.119927i	0.764523	−	0.644596i	$-0.222974\pi$
$383$	17592.0	+	17592.0i	0.119927	+	0.119927i	−0.644596	+	0.764523i	$0.722974\pi$
$384$		−	114813.i		−	0.778623i
$385$	−25793.7	+	48714.4i	−0.174017	+	0.328652i
$386$	286557.			1.92325
$387$	18119.1	−	18119.1i	0.120980	−	0.120980i
$388$	−428022.	−	428022.i	−2.84317	−	2.84317i
$389$			6343.53i			0.0419210i	0.999780	+	0.0209605i	$0.00667242\pi$
$389$			6343.53i			0.0419210i	−0.999780	+	0.0209605i	$0.993328\pi$
$390$	−24092.9	−	12756.9i	−0.158402	−	0.0838719i
$391$	−18184.4			−0.118945
$392$	53450.1	−	53450.1i	0.347838	−	0.347838i
$393$	−39949.4	−	39949.4i	−0.258657	−	0.258657i
$394$		−	149923.i		−	0.965773i
$395$	47528.0	+	154499.i	0.304618	+	0.990221i
$396$	−37733.2			−0.240621
$397$	−145003.	+	145003.i	−0.920018	+	0.920018i	−0.997030	−	0.0770121i	$-0.975462\pi$
$397$	−145003.	+	145003.i	−0.920018	+	0.920018i	0.0770121	+	0.997030i	$0.475462\pi$
$398$	−19460.9	−	19460.9i	−0.122856	−	0.122856i
$399$			89234.8i			0.560516i
$400$	−199347.	+	135469.i	−1.24592	+	0.846678i
$401$	−299021.			−1.85957			−0.929786	−	0.368100i	$-0.880008\pi$
$401$	−299021.			−1.85957			−0.929786	+	0.368100i	$0.880008\pi$
$402$	−126696.	+	126696.i	−0.783988	+	0.783988i
$403$	−28114.3	−	28114.3i	−0.173108	−	0.173108i
$404$			6544.44i			0.0400968i
$405$	17419.4	−	5358.66i	0.106200	−	0.0326698i
$406$	319683.			1.93940
$407$	23849.3	−	23849.3i	0.143975	−	0.143975i
$408$	−10886.3	−	10886.3i	−0.0653974	−	0.0653974i
$409$			17363.2i			0.103796i	0.998652	+	0.0518982i	$0.0165271\pi$
$409$			17363.2i			0.103796i	−0.998652	+	0.0518982i	$0.983473\pi$
$410$	154439.	−	291675.i	0.918733	−	1.73513i
$411$	24891.2			0.147354
$412$	495331.	−	495331.i	2.91811	−	2.91811i
$413$	−99676.8	−	99676.8i	−0.584378	−	0.584378i
$414$			155544.i			0.907514i
$415$	19415.4	+	10280.2i	0.112733	+	0.0596907i
$416$	18596.4			0.107459
$417$	22398.5	−	22398.5i	0.128809	−	0.128809i
$418$	64025.4	+	64025.4i	0.366437	+	0.366437i
$419$		−	36236.3i		−	0.206403i	−0.994660	−	0.103201i	$-0.967091\pi$
$419$		−	36236.3i		−	0.206403i	0.994660	−	0.103201i	$-0.0329086\pi$
$420$	71990.6	+	234020.i	0.408110	+	1.32664i
$421$	−121899.			−0.687761			−0.343881	−	0.939013i	$-0.611742\pi$
$421$	−121899.			−0.687761			−0.343881	+	0.939013i	$0.611742\pi$
$422$	88831.2	−	88831.2i	0.498817	−	0.498817i
$423$	13631.4	+	13631.4i	0.0761830	+	0.0761830i
$424$			420280.i			2.33780i
$425$	2629.01	−	13779.9i	0.0145551	−	0.0762899i
$426$	−209852.			−1.15636
$427$	126349.	−	126349.i	0.692971	−	0.692971i
$428$	13274.7	+	13274.7i	0.0724666	+	0.0724666i
$429$			6200.61i			0.0336915i
$430$	−161255.	+	49606.2i	−0.872119	+	0.268287i
$431$	330169.			1.77739			0.888693	−	0.458504i	$-0.151614\pi$
$431$	330169.			1.77739			0.888693	+	0.458504i	$0.151614\pi$
$432$	−38256.4	+	38256.4i	−0.204992	+	0.204992i
$433$	140458.	+	140458.i	0.749151	+	0.749151i	0.974320	−	0.225169i	$-0.0722934\pi$
$433$	140458.	+	140458.i	0.749151	+	0.749151i	−0.225169	+	0.974320i	$0.572293\pi$
$434$			522387.i			2.77340i
$435$	−50115.1	+	94648.0i	−0.264844	+	0.500188i
$436$	−487512.			−2.56455
$437$	180411.	−	180411.i	0.944715	−	0.944715i
$438$	164425.	+	164425.i	0.857076	+	0.857076i
$439$		−	25797.9i		−	0.133861i	−0.997758	−	0.0669306i	$-0.978679\pi$
$439$		−	25797.9i		−	0.133861i	0.997758	−	0.0669306i	$-0.0213206\pi$
$440$	117923.	+	62439.0i	0.609107	+	0.322515i
$441$	15461.2			0.0794996
$442$	−3330.78	+	3330.78i	−0.0170491	+	0.0170491i
$443$	131776.	+	131776.i	0.671473	+	0.671473i	0.958056	−	0.286583i	$-0.0925193\pi$
$443$	131776.	+	131776.i	0.671473	+	0.671473i	−0.286583	+	0.958056i	$0.592519\pi$
$444$		−	149815.i		−	0.759956i
$445$	−13648.5	−	44367.2i	−0.0689232	−	0.224049i
$446$	−107903.			−0.542454
$447$	150865.	−	150865.i	0.755047	−	0.755047i
$448$	65147.1	+	65147.1i	0.324593	+	0.324593i
$449$		−	133600.i		−	0.662697i	−0.943508	−	0.331349i	$-0.892496\pi$
$449$		−	133600.i		−	0.662697i	0.943508	−	0.331349i	$-0.107504\pi$
$450$	−117869.	−	22487.8i	−0.582069	−	0.111051i
$451$	−75066.4			−0.369056
$452$	−435471.	+	435471.i	−2.13149	+	2.13149i
$453$	−44445.3	−	44445.3i	−0.216585	−	0.216585i
$454$		−	343922.i		−	1.66858i
$455$	38455.9	−	11830.0i	0.185755	−	0.0571430i
$456$	216011.			1.03883
$457$	−147483.	+	147483.i	−0.706170	+	0.706170i	−0.965728	−	0.259558i	$-0.916423\pi$
$457$	−147483.	+	147483.i	−0.706170	+	0.706170i	0.259558	+	0.965728i	$0.416423\pi$
$458$	−369214.	−	369214.i	−1.76014	−	1.76014i
$459$		−	3149.01i		−	0.0149468i
$460$	327584.	−	618679.i	1.54813	−	2.92381i
$461$	206578.			0.972034			0.486017	−	0.873949i	$-0.338449\pi$
$461$	206578.			0.972034			0.486017	+	0.873949i	$0.338449\pi$
$462$	57606.3	−	57606.3i	0.269889	−	0.269889i
$463$	−156702.	−	156702.i	−0.730990	−	0.730990i	0.239826	−	0.970816i	$-0.422910\pi$
$463$	−156702.	−	156702.i	−0.730990	−	0.730990i	−0.970816	+	0.239826i	$0.922910\pi$
$464$		−	317928.i		−	1.47670i
$465$	−154662.	−	81892.0i	−0.715284	−	0.378735i
$466$	−183055.			−0.842963
$467$	−100008.	+	100008.i	−0.458566	+	0.458566i	−0.898184	−	0.439619i	$-0.855114\pi$
$467$	−100008.	+	100008.i	−0.458566	+	0.458566i	0.439619	+	0.898184i	$0.355114\pi$
$468$	19475.2	+	19475.2i	0.0889183	+	0.0889183i
$469$		−	264435.i		−	1.20219i
$470$	−37319.8	−	121315.i	−0.168944	−	0.549186i
$471$	155672.			0.701730
$472$	−241288.	+	241288.i	−1.08306	+	1.08306i
$473$	27133.9	+	27133.9i	0.121280	+	0.121280i
$474$		−	238903.i		−	1.06332i
$475$	110630.	+	162796.i	0.490327	+	0.721533i
$476$	42305.1			0.186715
$477$	−60785.8	+	60785.8i	−0.267156	+	0.267156i
$478$	516764.	+	516764.i	2.26171	+	2.26171i
$479$			124818.i			0.544010i	0.962296	+	0.272005i	$0.0876867\pi$
$479$			124818.i			0.544010i	−0.962296	+	0.272005i	$0.912313\pi$
$480$	78235.4	−	24067.3i	0.339563	−	0.104459i
$481$	−24618.7			−0.106408
$482$	−348969.	+	348969.i	−1.50208	+	1.50208i
$483$	−162323.	−	162323.i	−0.695804	−	0.695804i
$484$			449541.i			1.91902i
$485$	−204876.	+	386932.i	−0.870979	+	1.64494i
$486$	−26935.7			−0.114040
$487$	−106165.	+	106165.i	−0.447635	+	0.447635i	−0.894568	−	0.446932i	$-0.852516\pi$
$487$	−106165.	+	106165.i	−0.447635	+	0.447635i	0.446932	+	0.894568i	$0.352516\pi$
$488$	−305853.	−	305853.i	−1.28432	−	1.28432i
$489$		−	29050.6i		−	0.121489i
$490$	−89964.7	−	47635.3i	−0.374697	−	0.198398i
$491$	185092.			0.767758			0.383879	−	0.923383i	$-0.374588\pi$
$491$	185092.			0.767758			0.383879	+	0.923383i	$0.374588\pi$
$492$	−235773.	+	235773.i	−0.974010	+	0.974010i
$493$	13084.9	+	13084.9i	0.0538363	+	0.0538363i
$494$		−	66090.8i		−	0.270824i
$495$	8024.76	+	26086.1i	0.0327508	+	0.106463i
$496$	519520.			2.11173
$497$	218998.	−	218998.i	0.886598	−	0.886598i
$498$	−22959.3	−	22959.3i	−0.0925763	−	0.0925763i
$499$		−	482480.i		−	1.93766i	−0.247723	−	0.968831i	$-0.579682\pi$
$499$		−	482480.i		−	1.93766i	0.247723	−	0.968831i	$-0.420318\pi$
$500$	421465.	+	337684.i	1.68586	+	1.35073i
$501$	57787.9			0.230230
$502$	205439.	−	205439.i	0.815220	−	0.815220i
$503$	224311.	+	224311.i	0.886572	+	0.886572i	0.994192	−	0.107620i	$-0.0343230\pi$
$503$	224311.	+	224311.i	0.886572	+	0.886572i	−0.107620	+	0.994192i	$0.534323\pi$
$504$		−	194354.i		−	0.765124i
$505$	4524.36	−	1391.81i	0.0177409	−	0.00545756i
$506$	−232932.			−0.909763
$507$	−101739.	+	101739.i	−0.395798	+	0.395798i
$508$	378732.	+	378732.i	1.46759	+	1.46759i
$509$		−	390482.i		−	1.50718i	−0.657344	−	0.753591i	$-0.728320\pi$
$509$		−	390482.i		−	1.50718i	0.657344	−	0.753591i	$-0.271680\pi$
$510$	−9702.00	+	18323.3i	−0.0373010	+	0.0704472i
$511$	−343182.			−1.31426
$512$	404102.	−	404102.i	1.54153	−	1.54153i
$513$	31242.0	+	31242.0i	0.118715	+	0.118715i
$514$			535711.i			2.02770i
$515$	−447779.	−	237094.i	−1.68830	−	0.893936i
$516$	170447.			0.640164
$517$	−20413.4	+	20413.4i	−0.0763719	+	0.0763719i
$518$	228718.	+	228718.i	0.852394	+	0.852394i
$519$			151107.i			0.560981i
$520$	−28637.0	−	93090.2i	−0.105906	−	0.344269i
$521$	−71234.7			−0.262432			−0.131216	−	0.991354i	$-0.541888\pi$
$521$	−71234.7			−0.262432			−0.131216	+	0.991354i	$0.541888\pi$
$522$	111924.	−	111924.i	0.410755	−	0.410755i
$523$	−26895.3	−	26895.3i	−0.0983272	−	0.0983272i	0.656232	−	0.754559i	$-0.272149\pi$
$523$	−26895.3	−	26895.3i	−0.0983272	−	0.0983272i	−0.754559	+	0.656232i	$0.772149\pi$
$524$		−	375806.i		−	1.36868i
$525$	146474.	−	99538.3i	0.531426	−	0.361137i
$526$	−480573.			−1.73695
$527$	−21381.7	+	21381.7i	−0.0769876	+	0.0769876i
$528$	−57290.2	−	57290.2i	−0.205500	−	0.205500i
$529$			376517.i			1.34547i
$530$	540976.	−	166419.i	1.92587	−	0.592448i
$531$	−69795.7			−0.247537
$532$	−419718.	+	419718.i	−1.48298	+	1.48298i
$533$	38744.0	+	38744.0i	0.136380	+	0.136380i
$534$			68605.4i			0.240589i
$535$	6354.05	−	12000.3i	0.0221995	−	0.0419263i
$536$	−640119.			−2.22808
$537$	−42541.5	+	42541.5i	−0.147525	+	0.147525i
$538$	−657838.	−	657838.i	−2.27276	−	2.27276i
$539$			23153.6i			0.0796967i
$540$	107137.	+	56728.0i	0.367412	+	0.194541i
$541$	293490.			1.00276			0.501382	−	0.865226i	$-0.332825\pi$
$541$	293490.			1.00276			0.501382	+	0.865226i	$0.332825\pi$
$542$	583405.	−	583405.i	1.98596	−	1.98596i
$543$	−56621.0	−	56621.0i	−0.192034	−	0.192034i
$544$		−	14143.1i		−	0.0477911i
$545$	103680.	+	337031.i	0.349060	+	1.13469i
$546$	−59464.6			−0.199468
$547$	178128.	−	178128.i	0.595330	−	0.595330i	−0.343736	−	0.939066i	$-0.611693\pi$
$547$	178128.	−	178128.i	0.595330	−	0.595330i	0.939066	+	0.343736i	$0.111693\pi$
$548$	117077.	+	117077.i	0.389860	+	0.389860i
$549$		−	88471.9i		−	0.293536i
$550$	33676.2	−	176512.i	0.111326	−	0.583512i
$551$	−259635.			−0.855186
$552$	−392937.	+	392937.i	−1.28957	+	1.28957i
$553$	249316.	+	249316.i	0.815266	+	0.815266i
$554$			413422.i			1.34702i
$555$	−103571.	+	31861.2i	−0.336243	+	0.103437i
$556$	210704.			0.681589
$557$	122805.	−	122805.i	0.395827	−	0.395827i	−0.480931	−	0.876758i	$-0.659701\pi$
$557$	122805.	−	122805.i	0.395827	−	0.395827i	0.876758	+	0.480931i	$0.159701\pi$
$558$	182893.	+	182893.i	0.587393	+	0.587393i
$559$		−	28009.2i		−	0.0896349i
$560$	−246008.	+	464614.i	−0.784464	+	1.48155i
$561$	4715.74			0.0149839
$562$	307149.	−	307149.i	0.972470	−	0.972470i
$563$	−86662.0	−	86662.0i	−0.273408	−	0.273408i	0.557062	−	0.830471i	$-0.311928\pi$
$563$	−86662.0	−	86662.0i	−0.273408	−	0.273408i	−0.830471	+	0.557062i	$0.811928\pi$
$564$			128231.i			0.403120i
$565$	393666.	+	208442.i	1.23319	+	0.652962i
$566$	−550477.			−1.71833
$567$	28109.7	−	28109.7i	0.0874360	−	0.0874360i
$568$	−530128.	−	530128.i	−1.64318	−	1.64318i
$569$			358179.i			1.10631i	0.833080	+	0.553153i	$0.186575\pi$
$569$			358179.i			1.10631i	−0.833080	+	0.553153i	$0.813425\pi$
$570$	−85534.0	−	278045.i	−0.263263	−	0.855787i
$571$	420094.			1.28847			0.644234	−	0.764828i	$-0.277176\pi$
$571$	420094.			1.28847			0.644234	+	0.764828i	$0.277176\pi$
$572$	−29164.8	+	29164.8i	−0.0891387	+	0.0891387i
$573$	29867.9	+	29867.9i	0.0909693	+	0.0909693i
$574$		−	719896.i		−	2.18497i
$575$	−497378.	−	94893.1i	−1.50436	−	0.287011i
$576$	45617.3			0.137494
$577$	−167153.	+	167153.i	−0.502068	+	0.502068i	−0.912080	−	0.410012i	$-0.865524\pi$
$577$	−167153.	+	167153.i	−0.502068	+	0.502068i	0.410012	+	0.912080i	$0.365524\pi$
$578$	−417419.	−	417419.i	−1.24944	−	1.24944i
$579$			209399.i			0.624621i
$580$	−680898.	+	209462.i	−2.02407	+	0.622658i
$581$	47919.9			0.141959
$582$	457558.	−	457558.i	1.35083	−	1.35083i
$583$	−91028.5	−	91028.5i	−0.267818	−	0.267818i
$584$			830742.i			2.43579i
$585$	9321.98	−	17605.6i	0.0272393	−	0.0514446i
$586$	337908.			0.984017
$587$	−43094.6	+	43094.6i	−0.125068	+	0.125068i	−0.766870	−	0.641802i	$-0.778187\pi$
$587$	−43094.6	+	43094.6i	−0.125068	+	0.125068i	0.641802	+	0.766870i	$0.278187\pi$
$588$	72722.1	+	72722.1i	0.210335	+	0.210335i
$589$		−	424265.i		−	1.22294i
$590$	406124.	+	215038.i	1.16669	+	0.617749i
$591$	109554.			0.313657
$592$	227463.	−	227463.i	0.649033	−	0.649033i
$593$	−114499.	−	114499.i	−0.325605	−	0.325605i	0.525307	−	0.850912i	$-0.323950\pi$
$593$	−114499.	−	114499.i	−0.325605	−	0.325605i	−0.850912	+	0.525307i	$0.823950\pi$
$594$		−	40337.1i		−	0.114322i
$595$	−8997.08	−	29246.8i	−0.0254137	−	0.0826122i
$596$	1.41920e6			3.99531
$597$	14220.8	−	14220.8i	0.0399003	−	0.0399003i
$598$	120223.	+	120223.i	0.336191	+	0.336191i
$599$		−	282109.i		−	0.786254i	−0.919484	−	0.393127i	$-0.871393\pi$
$599$		−	282109.i		−	0.786254i	0.919484	−	0.393127i	$-0.128607\pi$
$600$	−240953.	−	354570.i	−0.669313	−	0.984918i
$601$	−155225.			−0.429747			−0.214874	−	0.976642i	$-0.568934\pi$
$601$	−155225.			−0.429747			−0.214874	+	0.976642i	$0.568934\pi$
$602$	−260217.	+	260217.i	−0.718031	+	0.718031i
$603$	−92581.4	−	92581.4i	−0.254618	−	0.254618i
$604$		−	418099.i		−	1.14605i
$605$	310781.	−	95604.4i	0.849070	−	0.261196i
$606$	−6996.06			−0.0190506
$607$	−262539.	+	262539.i	−0.712553	+	0.712553i	−0.967069	−	0.254516i	$-0.918084\pi$
$607$	−262539.	+	262539.i	−0.712553	+	0.712553i	0.254516	+	0.967069i	$0.418084\pi$
$608$	140317.	+	140317.i	0.379579	+	0.379579i
$609$			233605.i			0.629864i
$610$	−272579.	+	514797.i	−0.732543	+	1.38349i
$611$	21071.9			0.0564444
$612$	14811.5	−	14811.5i	0.0395453	−	0.0395453i
$613$	−98919.2	−	98919.2i	−0.263245	−	0.263245i	0.563126	−	0.826371i	$-0.309598\pi$
$613$	−98919.2	−	98919.2i	−0.263245	−	0.263245i	−0.826371	+	0.563126i	$0.809598\pi$
$614$			849121.i			2.25233i
$615$	213139.	+	112855.i	0.563523	+	0.298379i
$616$	291051.			0.767021
$617$	−440524.	+	440524.i	−1.15717	+	1.15717i	−0.172095	+	0.985080i	$0.555053\pi$
$617$	−440524.	+	440524.i	−1.15717	+	1.15717i	−0.985080	+	0.172095i	$0.944947\pi$
$618$	529512.	+	529512.i	1.38643	+	1.38643i
$619$			468975.i			1.22396i	0.790871	+	0.611982i	$0.209628\pi$
$619$			468975.i			1.22396i	−0.790871	+	0.611982i	$0.790372\pi$
$620$	−342277.	−	1.11264e6i	−0.890420	−	2.89449i
$621$	−113662.			−0.294736
$622$	−470012.	+	470012.i	−1.21487	+	1.21487i
$623$	−71595.5	−	71595.5i	−0.184463	−	0.184463i
$624$			59138.3i			0.151880i
$625$	143817.	−	363187.i	0.368172	−	0.929758i
$626$	70188.3			0.179108
$627$	−46785.8	+	46785.8i	−0.119009	+	0.119009i
$628$	732210.	+	732210.i	1.85659	+	1.85659i
$629$			18723.2i			0.0473237i
$630$	−250169.	+	76958.4i	−0.630306	+	0.193899i
$631$	327190.			0.821752			0.410876	−	0.911691i	$-0.365223\pi$
$631$	327190.			0.821752			0.410876	+	0.911691i	$0.365223\pi$
$632$	603519.	−	603519.i	1.51097	−	1.51097i
$633$	64912.4	+	64912.4i	0.162002	+	0.162002i
$634$			416293.i			1.03567i
$635$	181283.	−	342374.i	0.449583	−	0.849089i
$636$	−571815.			−1.41365
$637$	11950.2	−	11950.2i	0.0294509	−	0.0294509i
$638$	167610.	+	167610.i	0.411773	+	0.411773i
$639$		−	153347.i		−	0.375554i
$640$	−488182.	−	258487.i	−1.19185	−	0.631072i
$641$	−584738.			−1.42313			−0.711567	−	0.702619i	$-0.752014\pi$
$641$	−584738.			−1.42313			−0.711567	+	0.702619i	$0.752014\pi$
$642$	−14190.8	+	14190.8i	−0.0344299	+	0.0344299i
$643$	−202062.	−	202062.i	−0.488723	−	0.488723i	0.419180	−	0.907903i	$-0.362318\pi$
$643$	−202062.	−	202062.i	−0.488723	−	0.488723i	−0.907903	+	0.419180i	$0.862318\pi$
$644$		−	1.52699e6i		−	3.68183i
$645$	−36249.2	−	117835.i	−0.0871323	−	0.283241i
$646$	−50263.9			−0.120446
$647$	119543.	−	119543.i	0.285573	−	0.285573i	−0.549754	−	0.835327i	$-0.685278\pi$
$647$	119543.	−	119543.i	0.285573	−	0.285573i	0.835327	+	0.549754i	$0.185278\pi$
$648$	−68045.3	−	68045.3i	−0.162050	−	0.162050i
$649$		−	104521.i		−	0.248150i
$650$	−108485.	+	73722.1i	−0.256768	+	0.174490i
$651$	−381728.			−0.900725
$652$	136640.	−	136640.i	0.321428	−	0.321428i
$653$	−279985.	−	279985.i	−0.656611	−	0.656611i	0.297965	−	0.954577i	$-0.403692\pi$
$653$	−279985.	−	279985.i	−0.656611	−	0.656611i	−0.954577	+	0.297965i	$0.903692\pi$
$654$		−	521153.i		−	1.21846i
$655$	−259806.	+	79923.0i	−0.605572	+	0.186290i
$656$	−715946.			−1.66369
$657$	−120152.	+	120152.i	−0.278355	+	0.278355i
$658$	−195767.	−	195767.i	−0.452155	−	0.452155i
$659$			171782.i			0.395555i	0.980247	+	0.197778i	$0.0633724\pi$
$659$			171782.i			0.395555i	−0.980247	+	0.197778i	$0.936628\pi$
$660$	−84951.9	+	160441.i	−0.195023	+	0.368323i
$661$	566188.			1.29586			0.647929	−	0.761701i	$-0.275635\pi$
$661$	566188.			1.29586			0.647929	+	0.761701i	$0.275635\pi$
$662$	−331248.	+	331248.i	−0.755854	+	0.755854i
$663$	−2433.93	−	2433.93i	−0.00553709	−	0.00553709i
$664$		−	116000.i		−	0.263100i
$665$	379425.	+	200902.i	0.857992	+	0.454297i
$666$	160153.			0.361066
$667$	472292.	−	472292.i	1.06160	−	1.06160i
$668$	271807.	+	271807.i	0.609128	+	0.609128i
$669$		−	78848.7i		−	0.176174i
$670$	253468.	+	823949.i	0.564643	+	1.83548i
$671$	132489.			0.294263
$672$	126249.	−	126249.i	0.279568	−	0.279568i
$673$	−115466.	−	115466.i	−0.254932	−	0.254932i	0.568057	−	0.822989i	$-0.307695\pi$
$673$	−115466.	−	115466.i	−0.254932	−	0.254932i	−0.822989	+	0.568057i	$0.807695\pi$
$674$			181243.i			0.398970i
$675$	16432.7	−	86131.5i	0.0360664	−	0.189040i
$676$	−957070.			−2.09435
$677$	255557.	−	255557.i	0.557584	−	0.557584i	−0.371035	−	0.928619i	$-0.620997\pi$
$677$	255557.	−	255557.i	0.557584	−	0.557584i	0.928619	+	0.371035i	$0.120997\pi$
$678$	−465522.	−	465522.i	−1.01270	−	1.01270i
$679$			955001.i			2.07140i
$680$	−70797.7	+	21779.2i	−0.153109	+	0.0471004i
$681$	251317.			0.541911
$682$	−273888.	+	273888.i	−0.588849	+	0.588849i
$683$	97131.8	+	97131.8i	0.208219	+	0.208219i	0.803510	−	0.595291i	$-0.202963\pi$
$683$	97131.8	+	97131.8i	0.208219	+	0.208219i	−0.595291	+	0.803510i	$0.702963\pi$
$684$			293895.i			0.628175i
$685$	56039.6	−	105837.i	0.119430	−	0.225558i
$686$	708967.			1.50653
$687$	269799.	−	269799.i	0.571645	−	0.571645i
$688$	258789.	+	258789.i	0.546726	+	0.546726i
$689$			93965.1i			0.197937i
$690$	661373.	+	350189.i	1.38915	+	0.735538i
$691$	−40145.6			−0.0840778			−0.0420389	−	0.999116i	$-0.513385\pi$
$691$	−40145.6			−0.0840778			−0.0420389	+	0.999116i	$0.513385\pi$
$692$	−710734.	+	710734.i	−1.48421	+	1.48421i
$693$	42095.1	+	42095.1i	0.0876527	+	0.0876527i
$694$		−	327670.i		−	0.680327i
$695$	−44810.6	−	145666.i	−0.0927707	−	0.301569i
$696$	565487.			1.16736
$697$	29465.9	−	29465.9i	0.0606532	−	0.0606532i
$698$	−273232.	−	273232.i	−0.560816	−	0.560816i
$699$		−	133765.i		−	0.273772i
$700$	1.15713e6	+	220764.i	2.36148	+	0.450539i
$701$	225909.			0.459724			0.229862	−	0.973223i	$-0.426172\pi$
$701$	225909.			0.459724			0.229862	+	0.973223i	$0.426172\pi$
$702$	−20819.2	+	20819.2i	−0.0422464	+	0.0422464i
$703$	−185757.	−	185757.i	−0.375867	−	0.375867i
$704$			68313.3i			0.137835i
$705$	88649.8	−	27271.0i	0.178361	−	0.0548685i
$706$	114097.			0.228911
$707$	7300.97	−	7300.97i	0.0146064	−	0.0146064i
$708$	−328286.	−	328286.i	−0.654917	−	0.654917i
$709$		−	459779.i		−	0.914654i	−0.889299	−	0.457327i	$-0.848807\pi$
$709$		−	459779.i		−	0.914654i	0.889299	−	0.457327i	$-0.151193\pi$
$710$	−472456.	+	892287.i	−0.937227	+	1.77006i
$711$	174576.			0.345339
$712$	−173311.	+	173311.i	−0.341875	+	0.341875i
$713$	771763.	+	771763.i	1.51812	+	1.51812i
$714$			45224.5i			0.0887110i
$715$	26364.9	+	13959.9i	0.0515721	+	0.0273068i
$716$	−400191.			−0.780622
$717$	−377620.	+	377620.i	−0.734542	+	0.734542i
$718$	−134908.	−	134908.i	−0.261691	−	0.261691i
$719$		−	633365.i		−	1.22517i	−0.790405	−	0.612585i	$-0.790130\pi$
$719$		−	633365.i		−	1.22517i	0.790405	−	0.612585i	$-0.209870\pi$
$720$	76536.2	+	248796.i	0.147639	+	0.479930i
$721$	−1.10518e6			−2.12600
$722$	−156589.	+	156589.i	−0.300391	+	0.300391i
$723$	−255005.	−	255005.i	−0.487835	−	0.487835i
$724$		−	532637.i		−	1.01614i
$725$	289614.	+	426178.i	0.550990	+	0.810802i
$726$	−480563.			−0.911752
$727$	483916.	−	483916.i	0.915590	−	0.915590i	−0.0811152	−	0.996705i	$-0.525848\pi$
$727$	483916.	−	483916.i	0.915590	−	0.915590i	0.996705	+	0.0811152i	$0.0258482\pi$
$728$	−150220.	−	150220.i	−0.283442	−	0.283442i
$729$		−	19683.0i		−	0.0370370i
$730$	1.06932e6	−	328950.i	2.00660	−	0.617282i
$731$	−21301.8			−0.0398641
$732$	416130.	−	416130.i	0.776618	−	0.776618i
$733$	−79446.4	−	79446.4i	−0.147865	−	0.147865i	0.629298	−	0.777164i	$-0.283342\pi$
$733$	−79446.4	−	79446.4i	−0.147865	−	0.147865i	−0.777164	+	0.629298i	$0.783342\pi$
$734$		−	1.12998e6i		−	2.09739i
$735$	34809.0	−	65740.7i	0.0644343	−	0.121691i
$736$	−510489.			−0.942390
$737$	138643.	−	138643.i	0.255249	−	0.255249i
$738$	−252043.	−	252043.i	−0.462766	−	0.462766i
$739$			885328.i			1.62112i	0.585655	+	0.810561i	$0.300837\pi$
$739$			885328.i			1.62112i	−0.585655	+	0.810561i	$0.699163\pi$
$740$	−637010.	−	337290.i	−1.16328	−	0.615942i
$741$	48295.1			0.0879563
$742$	872975.	−	872975.i	1.58560	−	1.58560i
$743$	693877.	+	693877.i	1.25691	+	1.25691i	0.952560	+	0.304352i	$0.0984400\pi$
$743$	693877.	+	693877.i	1.25691	+	1.25691i	0.304352	+	0.952560i	$0.401560\pi$
$744$			924050.i			1.66936i
$745$	−301822.	−	981133.i	−0.543799	−	1.76773i
$746$	169719.			0.304967
$747$	16777.2	−	16777.2i	0.0300663	−	0.0300663i
$748$	22180.6	+	22180.6i	0.0396434	+	0.0396434i
$749$		−	29618.5i		−	0.0527959i
$750$	−360986.	+	450549.i	−0.641754	+	0.800977i
$751$	−1.03267e6			−1.83097			−0.915487	−	0.402347i	$-0.868194\pi$
$751$	−1.03267e6			−1.83097			−0.915487	+	0.402347i	$0.868194\pi$
$752$	−194692.	+	194692.i	−0.344281	+	0.344281i
$753$	150122.	+	150122.i	0.264761	+	0.264761i
$754$		−	173017.i		−	0.304331i
$755$	−289044.	+	88917.5i	−0.507073	+	0.155989i
$756$	264430.			0.462665
$757$	−366937.	+	366937.i	−0.640323	+	0.640323i	−0.950635	−	0.310312i	$-0.899567\pi$
$757$	−366937.	+	366937.i	−0.640323	+	0.640323i	0.310312	+	0.950635i	$0.399567\pi$
$758$	−254036.	−	254036.i	−0.442137	−	0.442137i
$759$		−	170213.i		−	0.295466i
$760$	486323.	−	918476.i	0.841972	−	1.59016i
$761$	−721432.			−1.24574			−0.622868	−	0.782327i	$-0.714033\pi$
$761$	−721432.			−1.24574			−0.622868	+	0.782327i	$0.714033\pi$
$762$	−404868.	+	404868.i	−0.697274	+	0.697274i
$763$	543867.	+	543867.i	0.934209	+	0.934209i
$764$			280969.i			0.481361i
$765$	−13389.6	−	7089.63i	−0.0228793	−	0.0121144i
$766$	−176909.			−0.301504
$767$	−53946.5	+	53946.5i	−0.0917007	+	0.0917007i
$768$	477966.	+	477966.i	0.810354	+	0.810354i
$769$			543034.i			0.918279i	0.888364	+	0.459139i	$0.151842\pi$
$769$			543034.i			0.918279i	−0.888364	+	0.459139i	$0.848158\pi$
$770$	−115248.	−	374635.i	−0.194379	−	0.631869i
$771$	−391465.			−0.658543
$772$	−984913.	+	984913.i	−1.65258	+	1.65258i
$773$	−501793.	−	501793.i	−0.839780	−	0.839780i	0.149050	−	0.988830i	$-0.452378\pi$
$773$	−501793.	−	501793.i	−0.839780	−	0.839780i	−0.988830	+	0.149050i	$0.952378\pi$
$774$			182210.i			0.304151i
$775$	−696408.	+	473253.i	−1.15947	+	0.787934i
$776$	2.31177e6			3.83903
$777$	−167133.	+	167133.i	−0.276835	+	0.276835i
$778$	−31895.9	−	31895.9i	−0.0526958	−	0.0526958i
$779$			584675.i			0.963473i
$780$	126655.	−	38962.3i	0.208177	−	0.0640407i
$781$	229641.			0.376485
$782$	91433.1	−	91433.1i	0.149517	−	0.149517i
$783$	81787.4	+	81787.4i	0.133402	+	0.133402i
$784$			220827.i			0.359269i
$785$	350478.	−	661918.i	0.568750	−	1.07415i
$786$	401740.			0.650279
$787$	−219605.	+	219605.i	−0.354562	+	0.354562i	−0.861804	−	0.507242i	$-0.830665\pi$
$787$	−219605.	+	219605.i	−0.354562	+	0.354562i	0.507242	+	0.861804i	$0.330665\pi$
$788$	515293.	+	515293.i	0.829854	+	0.829854i
$789$		−	351173.i		−	0.564115i
$790$	−1.01581e6	−	537863.i	−1.62765	−	0.861821i
$791$	971623.			1.55290
$792$	101900.	−	101900.i	0.162451	−	0.162451i
$793$	−68381.7	−	68381.7i	−0.108741	−	0.108741i
$794$		−	1.45818e6i		−	2.31298i
$795$	121609.	+	395312.i	0.192411	+	0.625470i
$796$	133776.			0.211131
$797$	−311150.	+	311150.i	−0.489839	+	0.489839i	−0.908255	−	0.418416i	$-0.862585\pi$
$797$	−311150.	+	311150.i	−0.489839	+	0.489839i	0.418416	+	0.908255i	$0.362585\pi$
$798$	−448682.	−	448682.i	−0.704584	−	0.704584i
$799$		−	16025.8i		−	0.0251030i
$800$	73804.0	−	386841.i	0.115319	−	0.604439i
$801$	−50132.6			−0.0781368
$802$	1.50351e6	−	1.50351e6i	2.33753	−	2.33753i
$803$	−179931.	−	179931.i	−0.279045	−	0.279045i
$804$		−	870919.i		−	1.34730i
$805$	−1.05565e6	+	324746.i	−1.62903	+	0.501131i
$806$	282723.			0.435202
$807$	480708.	−	480708.i	0.738132	−	0.738132i
$808$	−17673.5	−	17673.5i	−0.0270707	−	0.0270707i
$809$		−	827176.i		−	1.26387i	−0.775023	−	0.631933i	$-0.782262\pi$
$809$		−	827176.i		−	1.26387i	0.775023	−	0.631933i	$-0.217738\pi$
$810$	−60642.7	+	114531.i	−0.0924290	+	0.174563i
$811$	1.22035e6			1.85542			0.927711	−	0.373300i	$-0.121774\pi$
$811$	1.22035e6			1.85542			0.927711	+	0.373300i	$0.121774\pi$
$812$	−1.09877e6	+	1.09877e6i	−1.66645	+	1.66645i
$813$	426317.	+	426317.i	0.644987	+	0.644987i
$814$			239834.i			0.361961i
$815$	−123523.	−	65404.0i	−0.185966	−	0.0984667i
$816$	44976.4			0.0675467
$817$	211340.	−	211340.i	0.316619	−	0.316619i
$818$	−87303.8	−	87303.8i	−0.130475	−	0.130475i
$819$		−	43453.1i		−	0.0647818i
$820$	471689.	+	1.53332e6i	0.701501	+	2.28037i
$821$	−1.13223e6			−1.67977			−0.839884	−	0.542766i	$-0.817377\pi$
$821$	−1.13223e6			−1.67977			−0.839884	+	0.542766i	$0.817377\pi$
$822$	−125156.	+	125156.i	−0.185228	+	0.185228i
$823$	504583.	+	504583.i	0.744961	+	0.744961i	0.973528	−	0.228567i	$-0.0734041\pi$
$823$	504583.	+	504583.i	0.744961	+	0.744961i	−0.228567	+	0.973528i	$0.573404\pi$
$824$			2.67531e6i			3.94022i
$825$	128985.	+	24608.5i	0.189509	+	0.0361557i
$826$	1.00237e6			1.46916
$827$	−707633.	+	707633.i	−1.03466	+	1.03466i	−0.0352807	+	0.999377i	$0.511233\pi$
$827$	−707633.	+	707633.i	−1.03466	+	1.03466i	−0.999377	+	0.0352807i	$0.988767\pi$
$828$	−534614.	−	534614.i	−0.779793	−	0.779793i
$829$		−	846141.i		−	1.23121i	−0.788053	−	0.615607i	$-0.788911\pi$
$829$		−	846141.i		−	1.23121i	0.788053	−	0.615607i	$-0.211089\pi$
$830$	−149313.	+	45932.6i	−0.216741	+	0.0666752i
$831$	−302104.			−0.437476
$832$	35258.5	−	35258.5i	0.0509352	−	0.0509352i
$833$	−9088.50	−	9088.50i	−0.0130979	−	0.0130979i
$834$			225244.i			0.323833i
$835$	130103.	−	245714.i	0.186601	−	0.352417i
$836$	−440117.			−0.629732
$837$	−133647.	+	133647.i	−0.190769	+	0.190769i
$838$	182200.	+	182200.i	0.259454	+	0.259454i
$839$			499671.i			0.709839i	0.934897	+	0.354920i	$0.115492\pi$
$839$			499671.i			0.709839i	−0.934897	+	0.354920i	$0.884508\pi$
$840$	−826390.	−	437565.i	−1.17119	−	0.620131i
$841$	27590.7			0.0390096
$842$	612924.	−	612924.i	0.864534	−	0.864534i
$843$	224446.	+	224446.i	0.315832	+	0.315832i
$844$			610635.i			0.857229i
$845$	203541.	+	661650.i	0.285061	+	0.926648i
$846$	−137080.			−0.191528
$847$	501508.	−	501508.i	0.699054	−	0.699054i
$848$	−868184.	−	868184.i	−1.20731	−	1.20731i
$849$		−	402255.i		−	0.558066i
$850$	56067.7	+	82505.6i	0.0776023	+	0.114195i
$851$	675806.			0.933175
$852$	721271.	−	721271.i	0.993617	−	0.993617i
$853$	−175495.	−	175495.i	−0.241194	−	0.241194i	0.576150	−	0.817344i	$-0.304554\pi$
$853$	−175495.	−	175495.i	−0.241194	−	0.241194i	−0.817344	+	0.576150i	$0.804554\pi$
$854$			1.27059e6i			1.74217i
$855$	203178.	−	62503.0i	0.277936	−	0.0855005i
$856$	−71697.7			−0.0978492
$857$	932907.	−	932907.i	1.27021	−	1.27021i	0.324237	−	0.945976i	$-0.394892\pi$
$857$	932907.	−	932907.i	1.27021	−	1.27021i	0.945976	−	0.324237i	$-0.105108\pi$
$858$	−31177.3	−	31177.3i	−0.0423511	−	0.0423511i
$859$		−	318689.i		−	0.431897i	−0.976405	−	0.215948i	$-0.930716\pi$
$859$		−	318689.i		−	0.431897i	0.976405	−	0.215948i	$-0.0692843\pi$
$860$	383742.	−	724741.i	0.518851	−	0.979909i
$861$	526056.			0.709619
$862$	−1.66012e6	+	1.66012e6i	−2.23422	+	2.23422i
$863$	−834366.	−	834366.i	−1.12030	−	1.12030i	−0.991696	−	0.128606i	$-0.958950\pi$
$863$	−834366.	−	834366.i	−1.12030	−	1.12030i	−0.128606	−	0.991696i	$-0.541050\pi$
$864$		−	88401.9i		−	0.118422i
$865$	642504.	+	340199.i	0.858704	+	0.454674i
$866$	−1.41247e6			−1.88341
$867$	305025.	−	305025.i	0.405786	−	0.405786i
$868$	−1.79547e6	−	1.79547e6i	−2.38308	−	2.38308i
$869$			261433.i			0.346195i
$870$	−223916.	−	727885.i	−0.295834	−	0.961666i
$871$	−143116.			−0.188648
$872$	1.31654e6	−	1.31654e6i	1.73142	−	1.73142i
$873$	334356.	+	334356.i	0.438713	+	0.438713i
$874$			1.81426e6i			2.37507i
$875$	−93466.6	−	846906.i	−0.122079	−	1.10616i
$876$	−1.13027e6			−1.47291
$877$	−218162.	+	218162.i	−0.283648	+	0.283648i	−0.834562	−	0.550914i	$-0.814279\pi$
$877$	−218162.	+	218162.i	−0.283648	+	0.283648i	0.550914	+	0.834562i	$0.314279\pi$
$878$	129714.	+	129714.i	0.168267	+	0.168267i
$879$			246922.i			0.319582i
$880$	−372579.	+	114615.i	−0.481120	+	0.148005i
$881$	−279844.			−0.360549			−0.180274	−	0.983616i	$-0.557699\pi$
$881$	−279844.			−0.360549			−0.180274	+	0.983616i	$0.557699\pi$
$882$	−77740.4	+	77740.4i	−0.0999332	+	0.0999332i
$883$	269641.	+	269641.i	0.345831	+	0.345831i	0.858554	−	0.512723i	$-0.171363\pi$
$883$	269641.	+	269641.i	0.345831	+	0.345831i	−0.512723	+	0.858554i	$0.671363\pi$
$884$		−	22896.2i		−	0.0292994i
$885$	−157137.	+	296771.i	−0.200628	+	0.378909i
$886$	−1.32517e6			−1.68812
$887$	566987.	−	566987.i	0.720653	−	0.720653i	−0.248085	−	0.968738i	$-0.579801\pi$
$887$	566987.	−	566987.i	0.720653	−	0.720653i	0.968738	+	0.248085i	$0.0798013\pi$
$888$	404579.	+	404579.i	0.513071	+	0.513071i
$889$		−	845027.i		−	1.06922i
$890$	291710.	+	154457.i	0.368274	+	0.194997i
$891$	29475.9			0.0371288
$892$	370867.	−	370867.i	0.466110	−	0.466110i
$893$	158995.	+	158995.i	0.199380	+	0.199380i
$894$			1.51713e6i			1.89823i
$895$	85108.9	+	276663.i	0.106250	+	0.345387i
$896$	−1.20490e6			−1.50084
$897$	−87851.8	+	87851.8i	−0.109186	+	0.109186i
$898$	671758.	+	671758.i	0.833029	+	0.833029i
$899$		−	1.11067e6i		−	1.37425i
$900$	482414.	−	327830.i	0.595573	−	0.404729i
$901$	71463.1			0.0880303
$902$	377442.	−	377442.i	0.463913	−	0.463913i
$903$	−190151.	−	190151.i	−0.233197	−	0.233197i
$904$		−	2.35201e6i		−	2.87808i
$905$	−368228.	+	113276.i	−0.449593	+	0.138306i
$906$	446951.			0.544507
$907$	256644.	−	256644.i	0.311973	−	0.311973i	−0.533700	−	0.845674i	$-0.679199\pi$
$907$	256644.	−	256644.i	0.311973	−	0.311973i	0.845674	+	0.533700i	$0.179199\pi$
$908$	1.18208e6	+	1.18208e6i	1.43375	+	1.43375i
$909$		−	5112.29i		−	0.00618711i
$910$	−133878.	+	252843.i	−0.161668	+	0.305329i
$911$	−143826.			−0.173301			−0.0866506	−	0.996239i	$-0.527616\pi$
$911$	−143826.			−0.173301			−0.0866506	+	0.996239i	$0.527616\pi$
$912$	−446220.	+	446220.i	−0.536487	+	0.536487i
$913$	25124.4	+	25124.4i	0.0301408	+	0.0301408i
$914$		−	1.48312e6i		−	1.77535i
$915$	−376182.	−	199184.i	−0.449320	−	0.237910i
$916$	2.53801e6			3.02485
$917$	−419249.	+	419249.i	−0.498578	+	0.498578i
$918$	15833.6	+	15833.6i	0.0187886	+	0.0187886i
$919$			993411.i			1.17625i	0.808772	+	0.588123i	$0.200133\pi$
$919$			993411.i			1.17625i	−0.808772	+	0.588123i	$0.799867\pi$
$920$	786113.	+	2.55541e6i	0.928772	+	3.01916i
$921$	−620486.			−0.731497
$922$	−1.03869e6	+	1.03869e6i	−1.22187	+	1.22187i
$923$	−118525.	−	118525.i	−0.139125	−	0.139125i
$924$			395991.i			0.463812i
$925$	−97704.7	+	512116.i	−0.114191	+	0.598528i
$926$	1.57582e6			1.83775
$927$	−386935.	+	386935.i	−0.450276	+	0.450276i
$928$	367330.	+	367330.i	0.426541	+	0.426541i
$929$			1.39909e6i			1.62112i	0.585658	+	0.810558i	$0.300836\pi$
$929$			1.39909e6i			1.62112i	−0.585658	+	0.810558i	$0.699164\pi$
$930$	1.18942e6	−	365897.i	1.37521	−	0.423051i
$931$	180338.			0.208059
$932$	629168.	−	629168.i	0.724327	−	0.724327i
$933$	−343456.	−	343456.i	−0.394556	−	0.394556i
$934$		−	1.00570e6i		−	1.15286i
$935$	10616.9	−	20051.3i	0.0121444	−	0.0229361i
$936$	−105187.			−0.120063
$937$	482443.	−	482443.i	0.549499	−	0.549499i	−0.376797	−	0.926296i	$-0.622975\pi$
$937$	482443.	−	482443.i	0.549499	−	0.549499i	0.926296	+	0.376797i	$0.122975\pi$
$938$	1.32961e6	+	1.32961e6i	1.51119	+	1.51119i
$939$			51289.3i			0.0581696i
$940$	545237.	+	288697.i	0.617063	+	0.326728i
$941$	494897.			0.558902			0.279451	−	0.960160i	$-0.409848\pi$
$941$	494897.			0.558902			0.279451	+	0.960160i	$0.409848\pi$
$942$	−782738.	+	782738.i	−0.882094	+	0.882094i
$943$	−1.06356e6	−	1.06356e6i	−1.19602	−	1.19602i
$944$		−	996871.i		−	1.11865i
$945$	−56236.5	−	182808.i	−0.0629731	−	0.204706i
$946$	−272864.			−0.304905
$947$	−1.05460e6	+	1.05460e6i	−1.17595	+	1.17595i	−0.195183	+	0.980767i	$0.562530\pi$
$947$	−1.05460e6	+	1.05460e6i	−1.17595	+	1.17595i	−0.980767	+	0.195183i	$0.937470\pi$
$948$	821123.	+	821123.i	0.913675	+	0.913675i
$949$			185735.i			0.206235i
$950$	−1.37482e6	−	262296.i	−1.52334	−	0.290633i
$951$	−304201.			−0.336357
$952$	−114246.	+	114246.i	−0.126058	+	0.126058i
$953$	−319054.	−	319054.i	−0.351300	−	0.351300i	0.509293	−	0.860593i	$-0.329907\pi$
$953$	−319054.	−	319054.i	−0.351300	−	0.351300i	−0.860593	+	0.509293i	$0.829907\pi$
$954$		−	611275.i		−	0.671645i
$955$	194242.	−	59753.9i	0.212979	−	0.0655178i
$956$	−3.55229e6			−3.88681
$957$	−122479.	+	122479.i	−0.133733	+	0.133733i
$958$	−627599.	−	627599.i	−0.683835	−	0.683835i
$959$		−	261221.i		−	0.284034i
$960$	102702.	−	193964.i	0.111439	−	0.210465i
$961$	891397.			0.965216
$962$	123785.	−	123785.i	0.133758	−	0.133758i
$963$	−10369.8	−	10369.8i	−0.0111819	−	0.0111819i
$964$		−	2.39885e6i		−	2.58136i
$965$	890361.	+	471436.i	0.956118	+	0.506254i
$966$	1.63236e6			1.74929
$967$	−1.01810e6	+	1.01810e6i	−1.08877	+	1.08877i	−0.0931182	+	0.995655i	$0.529683\pi$
$967$	−1.01810e6	+	1.01810e6i	−1.08877	+	1.08877i	−0.995655	+	0.0931182i	$0.970317\pi$
$968$	−1.21400e6	−	1.21400e6i	−1.29559	−	1.29559i
$969$		−	36729.8i		−	0.0391175i
$970$	−915395.	−	2.97567e6i	−0.972893	−	3.16258i
$971$	610675.			0.647696			0.323848	−	0.946109i	$-0.395023\pi$
$971$	610675.			0.647696			0.323848	+	0.946109i	$0.395023\pi$
$972$	92579.6	−	92579.6i	0.0979902	−	0.0979902i
$973$	−235061.	−	235061.i	−0.248287	−	0.248287i
$974$		−	1.06762e6i		−	1.12538i
$975$	−53871.6	−	79273.9i	−0.0566696	−	0.0833914i
$976$	1.26362e6			1.32653
$977$	−90031.7	+	90031.7i	−0.0943206	+	0.0943206i	−0.752693	−	0.658372i	$-0.771245\pi$
$977$	−90031.7	+	90031.7i	−0.0943206	+	0.0943206i	0.658372	+	0.752693i	$0.271245\pi$
$978$	146070.	+	146070.i	0.152715	+	0.152715i
$979$		−	75075.1i		−	0.0783305i
$980$	472939.	−	145488.i	0.492439	−	0.151487i
$981$	380827.			0.395722
$982$	−930662.	+	930662.i	−0.965093	+	0.965093i
$983$	406452.	+	406452.i	0.420632	+	0.420632i	0.885421	−	0.464790i	$-0.153870\pi$
$983$	406452.	+	406452.i	0.420632	+	0.420632i	−0.464790	+	0.885421i	$0.653870\pi$
$984$		−	1.27342e6i		−	1.31517i
$985$	246649.	−	465824.i	0.254218	−	0.480120i
$986$	−131584.			−0.135347
$987$	143054.	−	143054.i	0.146848	−	0.146848i
$988$	227158.	+	227158.i	0.232709	+	0.232709i
$989$			768879.i			0.786078i
$990$	−171513.	−	90814.2i	−0.174995	−	0.0926581i
$991$	−563990.			−0.574281			−0.287140	−	0.957889i	$-0.592705\pi$
$991$	−563990.			−0.574281			−0.287140	+	0.957889i	$0.592705\pi$
$992$	−600246.	+	600246.i	−0.609967	+	0.609967i
$993$	−242056.	−	242056.i	−0.245481	−	0.245481i
$994$			2.20229e6i			2.22896i
$995$	−28450.3	−	92483.3i	−0.0287369	−	0.0934151i
$996$	157825.			0.159095
$997$	49988.1	−	49988.1i	0.0502894	−	0.0502894i	−0.681515	−	0.731804i	$-0.738679\pi$
$997$	49988.1	−	49988.1i	0.0502894	−	0.0502894i	0.731804	+	0.681515i	$0.238679\pi$
$998$	2.42596e6	+	2.42596e6i	2.43569	+	2.43569i
$999$			117030.i			0.117264i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.5.f.a.13.1	yes	8
3.2	odd	2		45.5.g.e.28.4		8
4.3	odd	2		240.5.bg.c.193.3		8
5.2	odd	4	inner	15.5.f.a.7.1	✓	8
5.3	odd	4		75.5.f.e.7.4		8
5.4	even	2		75.5.f.e.43.4		8
15.2	even	4		45.5.g.e.37.4		8
15.8	even	4		225.5.g.m.82.1		8
15.14	odd	2		225.5.g.m.118.1		8
20.7	even	4		240.5.bg.c.97.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.5.f.a.7.1	✓	8	5.2	odd	4	inner
15.5.f.a.13.1	yes	8	1.1	even	1	trivial
45.5.g.e.28.4		8	3.2	odd	2
45.5.g.e.37.4		8	15.2	even	4
75.5.f.e.7.4		8	5.3	odd	4
75.5.f.e.43.4		8	5.4	even	2
225.5.g.m.82.1		8	15.8	even	4
225.5.g.m.118.1		8	15.14	odd	2
240.5.bg.c.97.3		8	20.7	even	4
240.5.bg.c.193.3		8	4.3	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	15.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.02811 + 5.02811i) q^{2} +(-3.67423 - 3.67423i) q^{3} -34.5637i q^{4} +(-23.8949 + 7.35070i) q^{5} +36.9489 q^{6} +(-38.5593 + 38.5593i) q^{7} +(93.3405 + 93.3405i) q^{8} +27.0000i q^{9} +O(q^{10})\)	\(q+(-5.02811 + 5.02811i) q^{2} +(-3.67423 - 3.67423i) q^{3} -34.5637i q^{4} +(-23.8949 + 7.35070i) q^{5} +36.9489 q^{6} +(-38.5593 + 38.5593i) q^{7} +(93.3405 + 93.3405i) q^{8} +27.0000i q^{9} +(83.1861 - 157.106i) q^{10} -40.4333 q^{11} +(-126.995 + 126.995i) q^{12} +(20.8688 + 20.8688i) q^{13} -387.760i q^{14} +(114.804 + 60.7873i) q^{15} -385.633 q^{16} +(15.8713 - 15.8713i) q^{17} +(-135.759 - 135.759i) q^{18} +314.926i q^{19} +(254.068 + 825.898i) q^{20} +283.352 q^{21} +(203.303 - 203.303i) q^{22} +(-572.869 - 572.869i) q^{23} -685.910i q^{24} +(516.934 - 351.289i) q^{25} -209.862 q^{26} +(99.2043 - 99.2043i) q^{27} +(1332.75 + 1332.75i) q^{28} +824.433i q^{29} +(-882.891 + 271.600i) q^{30} -1347.19 q^{31} +(445.555 - 445.555i) q^{32} +(148.561 + 148.561i) q^{33} +159.606i q^{34} +(637.933 - 1204.81i) q^{35} +933.221 q^{36} +(-589.843 + 589.843i) q^{37} +(-1583.48 - 1583.48i) q^{38} -153.354i q^{39} +(-2916.48 - 1544.25i) q^{40} +1856.55 q^{41} +(-1424.72 + 1424.72i) q^{42} +(-671.078 - 671.078i) q^{43} +1397.53i q^{44} +(-198.469 - 645.163i) q^{45} +5760.90 q^{46} +(504.865 - 504.865i) q^{47} +(1416.91 + 1416.91i) q^{48} -572.636i q^{49} +(-832.883 + 4365.52i) q^{50} -116.630 q^{51} +(721.305 - 721.305i) q^{52} +(2251.32 + 2251.32i) q^{53} +997.620i q^{54} +(966.151 - 297.213i) q^{55} -7198.29 q^{56} +(1157.11 - 1157.11i) q^{57} +(-4145.34 - 4145.34i) q^{58} +2585.03i q^{59} +(2101.04 - 3968.05i) q^{60} -3276.74 q^{61} +(6773.81 - 6773.81i) q^{62} +(-1041.10 - 1041.10i) q^{63} -1689.53i q^{64} +(-652.060 - 345.259i) q^{65} -1493.97 q^{66} +(-3428.94 + 3428.94i) q^{67} +(-548.573 - 548.573i) q^{68} +4209.71i q^{69} +(2850.31 + 9265.50i) q^{70} -5679.51 q^{71} +(-2520.19 + 2520.19i) q^{72} +(4450.06 + 4450.06i) q^{73} -5931.59i q^{74} +(-3190.06 - 608.620i) q^{75} +10885.0 q^{76} +(1559.08 - 1559.08i) q^{77} +(771.081 + 771.081i) q^{78} -6465.77i q^{79} +(9214.66 - 2834.67i) q^{80} -729.000 q^{81} +(-9334.92 + 9334.92i) q^{82} +(-621.380 - 621.380i) q^{83} -9793.70i q^{84} +(-262.579 + 495.910i) q^{85} +6748.50 q^{86} +(3029.16 - 3029.16i) q^{87} +(-3774.07 - 3774.07i) q^{88} +1856.76i q^{89} +(4241.87 + 2246.02i) q^{90} -1609.37 q^{91} +(-19800.5 + 19800.5i) q^{92} +(4949.89 + 4949.89i) q^{93} +5077.03i q^{94} +(-2314.93 - 7525.13i) q^{95} -3274.14 q^{96} +(12383.5 - 12383.5i) q^{97} +(2879.27 + 2879.27i) q^{98} -1091.70i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 84 q^{5} + 36 q^{6} + 20 q^{7} + 180 q^{8}+O(q^{10}) \) 8 * q - 84 * q^5 + 36 * q^6 + 20 * q^7 + 180 * q^8	\( 8 q - 84 q^{5} + 36 q^{6} + 20 q^{7} + 180 q^{8} + 104 q^{10} - 288 q^{11} - 360 q^{12} - 340 q^{13} + 144 q^{15} + 620 q^{16} + 900 q^{17} + 564 q^{20} + 792 q^{21} - 1100 q^{22} - 1560 q^{23} - 1204 q^{25} - 3024 q^{26} + 3580 q^{28} - 2664 q^{30} - 512 q^{31} + 4980 q^{32} + 2700 q^{33} + 6600 q^{35} + 2484 q^{36} - 3820 q^{37} - 7680 q^{38} - 2952 q^{40} - 2712 q^{41} - 7380 q^{42} - 1240 q^{43} - 1944 q^{45} + 13528 q^{46} + 4800 q^{47} + 3600 q^{48} + 3744 q^{50} + 6264 q^{51} - 1240 q^{52} + 1020 q^{53} - 3644 q^{55} - 30720 q^{56} - 5400 q^{57} + 2340 q^{58} - 1044 q^{60} - 4760 q^{61} + 28680 q^{62} + 540 q^{63} - 1212 q^{65} + 10008 q^{66} - 8920 q^{67} - 1920 q^{68} + 7380 q^{70} + 7536 q^{71} - 4860 q^{72} + 11600 q^{73} - 5976 q^{75} + 4344 q^{76} - 360 q^{77} - 4680 q^{78} + 10644 q^{80} - 5832 q^{81} - 27200 q^{82} - 32400 q^{83} - 15628 q^{85} + 14592 q^{86} + 10620 q^{87} - 14340 q^{88} + 8964 q^{90} + 16528 q^{91} - 31800 q^{92} + 14040 q^{93} + 18864 q^{95} - 4068 q^{96} + 58640 q^{97} + 46440 q^{98}+O(q^{100}) \) 8 * q - 84 * q^5 + 36 * q^6 + 20 * q^7 + 180 * q^8 + 104 * q^10 - 288 * q^11 - 360 * q^12 - 340 * q^13 + 144 * q^15 + 620 * q^16 + 900 * q^17 + 564 * q^20 + 792 * q^21 - 1100 * q^22 - 1560 * q^23 - 1204 * q^25 - 3024 * q^26 + 3580 * q^28 - 2664 * q^30 - 512 * q^31 + 4980 * q^32 + 2700 * q^33 + 6600 * q^35 + 2484 * q^36 - 3820 * q^37 - 7680 * q^38 - 2952 * q^40 - 2712 * q^41 - 7380 * q^42 - 1240 * q^43 - 1944 * q^45 + 13528 * q^46 + 4800 * q^47 + 3600 * q^48 + 3744 * q^50 + 6264 * q^51 - 1240 * q^52 + 1020 * q^53 - 3644 * q^55 - 30720 * q^56 - 5400 * q^57 + 2340 * q^58 - 1044 * q^60 - 4760 * q^61 + 28680 * q^62 + 540 * q^63 - 1212 * q^65 + 10008 * q^66 - 8920 * q^67 - 1920 * q^68 + 7380 * q^70 + 7536 * q^71 - 4860 * q^72 + 11600 * q^73 - 5976 * q^75 + 4344 * q^76 - 360 * q^77 - 4680 * q^78 + 10644 * q^80 - 5832 * q^81 - 27200 * q^82 - 32400 * q^83 - 15628 * q^85 + 14592 * q^86 + 10620 * q^87 - 14340 * q^88 + 8964 * q^90 + 16528 * q^91 - 31800 * q^92 + 14040 * q^93 + 18864 * q^95 - 4068 * q^96 + 58640 * q^97 + 46440 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more