LMFDB - Embedded newform 147.6.e.l.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(67,147)]

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([0, 4]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("147.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$23.5764215125$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-83})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 20x^{2} - 21x + 441 $ x^4 - x^3 - 20x^2 - 21x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.2
Root			$-3.69493 - 2.71062i$ of defining polynomial
Character	$\chi$	$=$	147.67
Dual form			147.6.e.l.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.69493 + 8.13186i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-28.0848 + 48.6443i) q^{4} +(-35.8645 - 62.1192i) q^{5} -84.5088 q^{6} -226.949 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$	\(q+(4.69493 + 8.13186i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-28.0848 + 48.6443i) q^{4} +(-35.8645 - 62.1192i) q^{5} -84.5088 q^{6} -226.949 q^{8} +(-40.5000 - 70.1481i) q^{9} +(336.763 - 583.291i) q^{10} +(280.305 - 485.503i) q^{11} +(-252.763 - 437.799i) q^{12} -533.509 q^{13} +645.562 q^{15} +(-166.798 - 288.903i) q^{16} +(502.850 - 870.962i) q^{17} +(380.290 - 658.681i) q^{18} +(684.263 + 1185.18i) q^{19} +4028.99 q^{20} +5264.05 q^{22} +(-1614.04 - 2795.60i) q^{23} +(1021.27 - 1768.90i) q^{24} +(-1010.03 + 1749.42i) q^{25} +(-2504.79 - 4338.42i) q^{26} +729.000 q^{27} -753.456 q^{29} +(3030.87 + 5249.62i) q^{30} +(4103.21 - 7106.97i) q^{31} +(-2064.97 + 3576.64i) q^{32} +(2522.75 + 4369.52i) q^{33} +9443.39 q^{34} +4549.74 q^{36} +(1404.33 + 2432.37i) q^{37} +(-6425.14 + 11128.7i) q^{38} +(2400.79 - 4158.29i) q^{39} +(8139.43 + 14097.9i) q^{40} -245.827 q^{41} -17504.5 q^{43} +(15744.6 + 27270.5i) q^{44} +(-2905.03 + 5031.65i) q^{45} +(15155.6 - 26250.3i) q^{46} +(-8172.74 - 14155.6i) q^{47} +3002.37 q^{48} -18968.1 q^{50} +(4525.65 + 7838.66i) q^{51} +(14983.5 - 25952.2i) q^{52} +(14820.8 - 25670.4i) q^{53} +(3422.61 + 5928.13i) q^{54} -40212.0 q^{55} -12316.7 q^{57} +(-3537.43 - 6127.00i) q^{58} +(-5178.05 + 8968.65i) q^{59} +(-18130.5 + 31402.9i) q^{60} +(477.089 + 826.343i) q^{61} +77057.2 q^{62} -49454.8 q^{64} +(19134.0 + 33141.1i) q^{65} +(-23688.2 + 41029.2i) q^{66} +(9907.60 - 17160.5i) q^{67} +(28244.9 + 48921.6i) q^{68} +29052.7 q^{69} +62125.4 q^{71} +(9191.45 + 15920.1i) q^{72} +(13554.8 - 23477.6i) q^{73} +(-13186.5 + 22839.7i) q^{74} +(-9090.27 - 15744.8i) q^{75} -76869.6 q^{76} +45086.2 q^{78} +(-22343.7 - 38700.4i) q^{79} +(-11964.3 + 20722.8i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-1154.14 - 1999.03i) q^{82} -15606.6 q^{83} -72137.9 q^{85} +(-82182.5 - 142344. i) q^{86} +(3390.55 - 5872.61i) q^{87} +(-63615.0 + 110184. i) q^{88} +(6817.66 + 11808.5i) q^{89} -54555.6 q^{90} +181320. q^{92} +(36928.9 + 63962.7i) q^{93} +(76740.9 - 132919. i) q^{94} +(49081.6 - 85011.8i) q^{95} +(-18584.8 - 32189.8i) q^{96} +12919.5 q^{97} -45409.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - 18 q^{3} - 65 q^{4} - 33 q^{5} - 54 q^{6} - 750 q^{8} - 162 q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 - 18 * q^3 - 65 * q^4 - 33 * q^5 - 54 * q^6 - 750 * q^8 - 162 * q^9	\( 4 q + 3 q^{2} - 18 q^{3} - 65 q^{4} - 33 q^{5} - 54 q^{6} - 750 q^{8} - 162 q^{9} + 921 q^{10} + 1137 q^{11} - 585 q^{12} - 1850 q^{13} + 594 q^{15} + 895 q^{16} - 324 q^{17} + 243 q^{18} + 2311 q^{19} + 7374 q^{20} + 3162 q^{22} - 1596 q^{23} + 3375 q^{24} - 395 q^{25} - 2508 q^{26} + 2916 q^{27} - 4434 q^{29} + 8289 q^{30} + 4294 q^{31} - 1017 q^{32} + 10233 q^{33} + 35880 q^{34} + 10530 q^{36} + 19109 q^{37} - 6828 q^{38} + 8325 q^{39} + 10545 q^{40} + 25716 q^{41} - 5542 q^{43} + 36579 q^{44} - 2673 q^{45} + 40740 q^{46} - 23160 q^{47} - 16110 q^{48} - 58704 q^{50} - 2916 q^{51} + 33424 q^{52} + 31653 q^{53} + 2187 q^{54} - 35778 q^{55} - 41598 q^{57} + 2277 q^{58} + 41097 q^{59} - 33183 q^{60} + 42052 q^{61} + 204114 q^{62} - 60062 q^{64} + 23106 q^{65} - 14229 q^{66} - 30763 q^{67} + 44748 q^{68} + 28728 q^{69} + 204192 q^{71} + 30375 q^{72} - 28577 q^{73} + 77784 q^{74} - 3555 q^{75} - 170384 q^{76} + 45144 q^{78} + 18464 q^{79} - 71511 q^{80} - 13122 q^{81} - 86040 q^{82} - 122358 q^{83} - 247272 q^{85} - 258510 q^{86} + 19953 q^{87} - 212565 q^{88} + 29322 q^{89} - 149202 q^{90} + 333816 q^{92} + 38646 q^{93} + 109938 q^{94} + 61662 q^{95} - 9153 q^{96} + 19582 q^{97} - 184194 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 - 18 * q^3 - 65 * q^4 - 33 * q^5 - 54 * q^6 - 750 * q^8 - 162 * q^9 + 921 * q^10 + 1137 * q^11 - 585 * q^12 - 1850 * q^13 + 594 * q^15 + 895 * q^16 - 324 * q^17 + 243 * q^18 + 2311 * q^19 + 7374 * q^20 + 3162 * q^22 - 1596 * q^23 + 3375 * q^24 - 395 * q^25 - 2508 * q^26 + 2916 * q^27 - 4434 * q^29 + 8289 * q^30 + 4294 * q^31 - 1017 * q^32 + 10233 * q^33 + 35880 * q^34 + 10530 * q^36 + 19109 * q^37 - 6828 * q^38 + 8325 * q^39 + 10545 * q^40 + 25716 * q^41 - 5542 * q^43 + 36579 * q^44 - 2673 * q^45 + 40740 * q^46 - 23160 * q^47 - 16110 * q^48 - 58704 * q^50 - 2916 * q^51 + 33424 * q^52 + 31653 * q^53 + 2187 * q^54 - 35778 * q^55 - 41598 * q^57 + 2277 * q^58 + 41097 * q^59 - 33183 * q^60 + 42052 * q^61 + 204114 * q^62 - 60062 * q^64 + 23106 * q^65 - 14229 * q^66 - 30763 * q^67 + 44748 * q^68 + 28728 * q^69 + 204192 * q^71 + 30375 * q^72 - 28577 * q^73 + 77784 * q^74 - 3555 * q^75 - 170384 * q^76 + 45144 * q^78 + 18464 * q^79 - 71511 * q^80 - 13122 * q^81 - 86040 * q^82 - 122358 * q^83 - 247272 * q^85 - 258510 * q^86 + 19953 * q^87 - 212565 * q^88 + 29322 * q^89 - 149202 * q^90 + 333816 * q^92 + 38646 * q^93 + 109938 * q^94 + 61662 * q^95 - 9153 * q^96 + 19582 * q^97 - 184194 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	4.69493	+	8.13186i	0.829955	+	1.43752i	0.898073	+	0.439847i	$0.144967\pi$
$2$	4.69493	+	8.13186i	0.829955	+	1.43752i	−0.0681181	+	0.997677i	$0.521699\pi$
$3$	−4.50000	+	7.79423i	−0.288675	+	0.500000i
$3$	−4.50000	+	7.79423i	−0.288675	+	0.500000i
$4$	−28.0848	+	48.6443i	−0.877650	+	1.52013i
$5$	−35.8645	−	62.1192i	−0.641564	−	1.11122i	−0.985084	−	0.172076i	$-0.944952\pi$
$5$	−35.8645	−	62.1192i	−0.641564	−	1.11122i	0.343519	−	0.939146i	$-0.388381\pi$
$6$	−84.5088			−0.958349
$7$		0			0
$7$		0			0
$8$	−226.949			−1.25373
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$	336.763	−	583.291i	1.06494	−	1.84453i
$11$	280.305	−	485.503i	0.698472	−	1.20979i	−0.270524	−	0.962713i	$-0.587197\pi$
$11$	280.305	−	485.503i	0.698472	−	1.20979i	0.968996	−	0.247076i	$-0.0794698\pi$
$12$	−252.763	−	437.799i	−0.506711	−	0.877650i
$13$	−533.509			−0.875555			−0.437777	−	0.899083i	$-0.644234\pi$
$13$	−533.509			−0.875555			−0.437777	+	0.899083i	$0.644234\pi$
$14$		0			0
$15$	645.562			0.740815
$16$	−166.798	−	288.903i	−0.162889	−	0.282132i
$17$	502.850	−	870.962i	0.422004	−	0.730932i	−0.574132	−	0.818763i	$-0.694660\pi$
$17$	502.850	−	870.962i	0.422004	−	0.730932i	0.996135	+	0.0878311i	$0.0279936\pi$
$18$	380.290	−	658.681i	0.276652	−	0.479175i
$19$	684.263	+	1185.18i	0.434850	+	0.753182i	0.997283	−	0.0736606i	$-0.0234682\pi$
$19$	684.263	+	1185.18i	0.434850	+	0.753182i	−0.562434	+	0.826842i	$0.690135\pi$
$20$	4028.99			2.25228
$21$		0			0
$22$	5264.05			2.31880
$23$	−1614.04	−	2795.60i	−0.636201	−	1.10193i	−0.986259	−	0.165205i	$-0.947171\pi$
$23$	−1614.04	−	2795.60i	−0.636201	−	1.10193i	0.350058	−	0.936728i	$-0.386162\pi$
$24$	1021.27	−	1768.90i	0.361921	−	0.626865i
$25$	−1010.03	+	1749.42i	−0.323209	+	0.559815i
$26$	−2504.79	−	4338.42i	−0.726671	−	1.25863i
$27$	729.000			0.192450
$28$		0			0
$29$	−753.456			−0.166365			−0.0831827	−	0.996534i	$-0.526508\pi$
$29$	−753.456			−0.166365			−0.0831827	+	0.996534i	$0.526508\pi$
$30$	3030.87	+	5249.62i	0.614843	+	1.06494i
$31$	4103.21	−	7106.97i	0.766866	−	1.32825i	−0.172389	−	0.985029i	$-0.555148\pi$
$31$	4103.21	−	7106.97i	0.766866	−	1.32825i	0.939254	−	0.343222i	$-0.111518\pi$
$32$	−2064.97	+	3576.64i	−0.356484	+	0.617448i
$33$	2522.75	+	4369.52i	0.403263	+	0.698472i
$34$	9443.39			1.40098
$35$		0			0
$36$	4549.74			0.585100
$37$	1404.33	+	2432.37i	0.168642	+	0.292096i	0.937943	−	0.346791i	$-0.112729\pi$
$37$	1404.33	+	2432.37i	0.168642	+	0.292096i	−0.769301	+	0.638887i	$0.779395\pi$
$38$	−6425.14	+	11128.7i	−0.721811	+	1.25021i
$39$	2400.79	−	4158.29i	0.252751	−	0.437777i
$40$	8139.43	+	14097.9i	0.804348	+	1.39317i
$41$	−245.827			−0.0228387			−0.0114193	−	0.999935i	$-0.503635\pi$
$41$	−245.827			−0.0228387			−0.0114193	+	0.999935i	$0.503635\pi$
$42$		0			0
$43$	−17504.5			−1.44371			−0.721853	−	0.692047i	$-0.756709\pi$
$43$	−17504.5			−1.44371			−0.721853	+	0.692047i	$0.756709\pi$
$44$	15744.6	+	27270.5i	1.22603	+	2.12354i
$45$	−2905.03	+	5031.65i	−0.213855	+	0.370407i
$46$	15155.6	−	26250.3i	1.05604	−	1.82911i
$47$	−8172.74	−	14155.6i	−0.539663	−	0.934725i	−0.998922	−	0.0464219i	$-0.985218\pi$
$47$	−8172.74	−	14155.6i	−0.539663	−	0.934725i	0.459258	−	0.888303i	$-0.348115\pi$
$48$	3002.37			0.188088
$49$		0			0
$50$	−18968.1			−1.07300
$51$	4525.65	+	7838.66i	0.243644	+	0.422004i
$52$	14983.5	−	25952.2i	0.768430	−	1.33096i
$53$	14820.8	−	25670.4i	0.724741	−	1.25529i	−0.234340	−	0.972155i	$-0.575293\pi$
$53$	14820.8	−	25670.4i	0.724741	−	1.25529i	0.959081	−	0.283133i	$-0.0913739\pi$
$54$	3422.61	+	5928.13i	0.159725	+	0.276652i
$55$	−40212.0			−1.79246
$56$		0			0
$57$	−12316.7			−0.502121
$58$	−3537.43	−	6127.00i	−0.138076	−	0.239154i
$59$	−5178.05	+	8968.65i	−0.193659	+	0.335426i	−0.946460	−	0.322821i	$-0.895369\pi$
$59$	−5178.05	+	8968.65i	−0.193659	+	0.335426i	0.752801	+	0.658248i	$0.228702\pi$
$60$	−18130.5	+	31402.9i	−0.650176	+	1.12614i
$61$	477.089	+	826.343i	0.0164163	+	0.0284339i	0.874117	−	0.485716i	$-0.161441\pi$
$61$	477.089	+	826.343i	0.0164163	+	0.0284339i	−0.857701	+	0.514150i	$0.828108\pi$
$62$	77057.2			2.54586
$63$		0			0
$64$	−49454.8			−1.50924
$65$	19134.0	+	33141.1i	0.561725	+	0.972935i
$66$	−23688.2	+	41029.2i	−0.669380	+	1.15940i
$67$	9907.60	−	17160.5i	0.269638	−	0.467027i	−0.699130	−	0.714994i	$-0.746429\pi$
$67$	9907.60	−	17160.5i	0.269638	−	0.467027i	0.968768	+	0.247967i	$0.0797626\pi$
$68$	28244.9	+	48921.6i	0.740743	+	1.28300i
$69$	29052.7			0.734622
$70$		0			0
$71$	62125.4			1.46259			0.731296	−	0.682060i	$-0.238916\pi$
$71$	62125.4			1.46259			0.731296	+	0.682060i	$0.238916\pi$
$72$	9191.45	+	15920.1i	0.208955	+	0.361921i
$73$	13554.8	−	23477.6i	0.297705	−	0.515641i	−0.677905	−	0.735149i	$-0.737112\pi$
$73$	13554.8	−	23477.6i	0.297705	−	0.515641i	0.975611	+	0.219509i	$0.0704454\pi$
$74$	−13186.5	+	22839.7i	−0.279930	+	0.484853i
$75$	−9090.27	−	15744.8i	−0.186605	−	0.323209i
$76$	−76869.6			−1.52658
$77$		0			0
$78$	45086.2			0.839087
$79$	−22343.7	−	38700.4i	−0.402798	−	0.697666i	0.591265	−	0.806477i	$-0.298629\pi$
$79$	−22343.7	−	38700.4i	−0.402798	−	0.697666i	−0.994062	+	0.108812i	$0.965295\pi$
$80$	−11964.3	+	20722.8i	−0.209008	+	0.362012i
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$	−1154.14	−	1999.03i	−0.0189551	−	0.0328311i
$83$	−15606.6			−0.248665			−0.124332	−	0.992241i	$-0.539679\pi$
$83$	−15606.6			−0.248665			−0.124332	+	0.992241i	$0.539679\pi$
$84$		0			0
$85$	−72137.9			−1.08297
$86$	−82182.5	−	142344.i	−1.19821	−	2.07536i
$87$	3390.55	−	5872.61i	0.0480255	−	0.0831827i
$88$	−63615.0	+	110184.i	−0.875696	+	1.51675i
$89$	6817.66	+	11808.5i	0.0912347	+	0.158023i	0.908031	−	0.418903i	$-0.137585\pi$
$89$	6817.66	+	11808.5i	0.0912347	+	0.158023i	−0.816796	+	0.576926i	$0.804252\pi$
$90$	−54555.6			−0.709959
$91$		0			0
$92$	181320.			2.23345
$93$	36928.9	+	63962.7i	0.442750	+	0.766866i
$94$	76740.9	−	132919.i	0.895793	−	1.55156i
$95$	49081.6	−	85011.8i	0.557968	−	0.966429i
$96$	−18584.8	−	32189.8i	−0.205816	−	0.356484i
$97$	12919.5			0.139417			0.0697086	−	0.997567i	$-0.477793\pi$
$97$	12919.5			0.139417			0.0697086	+	0.997567i	$0.477793\pi$
$98$		0			0
$99$	−45409.4			−0.465648
$100$	−56733.0	−	98264.4i	−0.567330	−	0.982644i
$101$	12571.5	−	21774.4i	0.122626	−	0.212394i	−0.798177	−	0.602424i	$-0.794202\pi$
$101$	12571.5	−	21774.4i	0.122626	−	0.212394i	0.920802	+	0.390029i	$0.127535\pi$
$102$	−42495.3	+	73604.0i	−0.404427	+	0.700488i
$103$	−80376.6	−	139216.i	−0.746511	−	1.29300i	−0.949485	−	0.313811i	$-0.898394\pi$
$103$	−80376.6	−	139216.i	−0.746511	−	1.29300i	0.202974	−	0.979184i	$-0.434939\pi$
$104$	121079.			1.09771
$105$		0			0
$106$	278331.			2.40601
$107$	47187.8	+	81731.6i	0.398446	+	0.690129i	0.993534	−	0.113531i	$-0.0362162\pi$
$107$	47187.8	+	81731.6i	0.398446	+	0.690129i	−0.595088	+	0.803661i	$0.702883\pi$
$108$	−20473.8	+	35461.7i	−0.168904	+	0.292550i
$109$	41696.7	−	72220.9i	0.336152	−	0.582233i	−0.647553	−	0.762020i	$-0.724208\pi$
$109$	41696.7	−	72220.9i	0.336152	−	0.582233i	0.983705	+	0.179788i	$0.0575410\pi$
$110$	−188793.	−	326999.i	−1.48766	−	2.57670i
$111$	−25278.0			−0.194731
$112$		0			0
$113$	−179254.			−1.32060			−0.660301	−	0.751001i	$-0.729571\pi$
$113$	−179254.			−1.32060			−0.660301	+	0.751001i	$0.729571\pi$
$114$	−57826.3	−	100158.i	−0.416738	−	0.721811i
$115$	−115774.	+	200526.i	−0.816328	+	1.41392i
$116$	21160.7	−	36651.3i	0.146011	−	0.252898i
$117$	21607.1	+	37424.6i	0.145926	+	0.252751i
$118$	−97242.5			−0.642911
$119$		0			0
$120$	−146510.			−0.928781
$121$	−76616.4	−	132703.i	−0.475727	−	0.823984i
$122$	−4479.80	+	7759.25i	−0.0272496	+	0.0471976i
$123$	1106.22	−	1916.04i	0.00659295	−	0.0114193i
$124$	230476.	+	399195.i	1.34608	+	2.33148i
$125$	−79256.4			−0.453690
$126$		0			0
$127$	−143674.			−0.790440			−0.395220	−	0.918586i	$-0.629332\pi$
$127$	−143674.			−0.790440			−0.395220	+	0.918586i	$0.629332\pi$
$128$	−166108.	−	287707.i	−0.896117	−	1.55212i
$129$	78770.2	−	136434.i	0.416762	−	0.721853i
$130$	−179666.	+	311191.i	−0.932412	+	1.61498i
$131$	26144.9	+	45284.3i	0.133110	+	0.230553i	0.924874	−	0.380274i	$-0.124170\pi$
$131$	26144.9	+	45284.3i	0.133110	+	0.230553i	−0.791764	+	0.610827i	$0.790837\pi$
$132$	−283403.			−1.41570
$133$		0			0
$134$	186062.			0.895150
$135$	−26145.2	−	45284.9i	−0.123469	−	0.213855i
$136$	−114122.	+	197664.i	−0.529079	+	0.916391i
$137$	−4705.05	+	8149.39i	−0.0214172	+	0.0370957i	−0.876535	−	0.481337i	$-0.840151\pi$
$137$	−4705.05	+	8149.39i	−0.0214172	+	0.0370957i	0.855118	+	0.518433i	$0.173484\pi$
$138$	136401.	+	236253.i	0.609703	+	1.05604i
$139$	−183094.			−0.803781			−0.401890	−	0.915688i	$-0.631647\pi$
$139$	−183094.			−0.803781			−0.401890	+	0.915688i	$0.631647\pi$
$140$		0			0
$141$	147109.			0.623150
$142$	291674.	+	505195.i	1.21389	+	2.10251i
$143$	−149545.	+	259020.i	−0.611551	+	1.05924i
$144$	−13510.7	+	23401.2i	−0.0542964	+	0.0940441i
$145$	27022.3	+	46804.1i	0.106734	+	0.184869i
$146$	254556.			0.988328
$147$		0			0
$148$	−157762.			−0.592034
$149$	83500.8	+	144628.i	0.308123	+	0.533685i	0.977952	−	0.208830i	$-0.0669657\pi$
$149$	83500.8	+	144628.i	0.308123	+	0.533685i	−0.669828	+	0.742516i	$0.733632\pi$
$150$	85356.4	−	147842.i	0.309748	−	0.536499i
$151$	−188132.	+	325855.i	−0.671461	+	1.16300i	0.306029	+	0.952022i	$0.401000\pi$
$151$	−188132.	+	325855.i	−0.671461	+	1.16300i	−0.977490	+	0.210982i	$0.932334\pi$
$152$	−155293.	−	268976.i	−0.545184	−	0.944286i
$153$	−81461.7			−0.281336
$154$		0			0
$155$	−588639.			−1.96797
$156$	134851.	+	233569.i	0.443654	+	0.768430i
$157$	19537.5	−	33840.0i	0.0632587	−	0.109567i	−0.832662	−	0.553782i	$-0.813184\pi$
$157$	19537.5	−	33840.0i	0.0632587	−	0.109567i	0.895920	+	0.444215i	$0.146517\pi$
$158$	209804.	−	363391.i	0.668608	−	1.15806i
$159$	133387.	+	231034.i	0.418429	+	0.724741i
$160$	296237.			0.914829
$161$		0			0
$162$	−61606.9			−0.184434
$163$	238959.	+	413890.i	0.704458	+	1.22016i	0.966887	+	0.255206i	$0.0821433\pi$
$163$	238959.	+	413890.i	0.704458	+	1.22016i	−0.262428	+	0.964951i	$0.584523\pi$
$164$	6904.01	−	11958.1i	0.0200444	−	0.0347178i
$165$	180954.	−	313422.i	0.517439	−	0.896230i
$166$	−73272.1	−	126911.i	−0.206381	−	0.357462i
$167$	−39793.4			−0.110413			−0.0552064	−	0.998475i	$-0.517582\pi$
$167$	−39793.4			−0.110413			−0.0552064	+	0.998475i	$0.517582\pi$
$168$		0			0
$169$	−86661.4			−0.233404
$170$	−338683.	−	586616.i	−0.898816	−	1.55680i
$171$	55425.3	−	95999.5i	0.144950	−	0.251061i
$172$	491610.	−	851494.i	1.26707	−	2.19463i
$173$	24169.1	+	41862.1i	0.0613968	+	0.106342i	0.895090	−	0.445886i	$-0.147111\pi$
$173$	24169.1	+	41862.1i	0.0613968	+	0.106342i	−0.833693	+	0.552228i	$0.813778\pi$
$174$	63673.7			0.159436
$175$		0			0
$176$	−187018.			−0.455094
$177$	−46602.5	−	80717.9i	−0.111809	−	0.193659i
$178$	−64016.9	+	110881.i	−0.151441	+	0.262304i
$179$	71455.3	−	123764.i	0.166687	−	0.288711i	−0.770566	−	0.637360i	$-0.780026\pi$
$179$	71455.3	−	123764.i	0.166687	−	0.288711i	0.937253	+	0.348650i	$0.113360\pi$
$180$	−163174.	−	282626.i	−0.375379	−	0.650176i
$181$	77245.3			0.175257			0.0876285	−	0.996153i	$-0.472071\pi$
$181$	77245.3			0.175257			0.0876285	+	0.996153i	$0.472071\pi$
$182$		0			0
$183$	−8587.61			−0.0189559
$184$	366305.	+	634459.i	0.797625	+	1.38153i
$185$	100731.	−	174472.i	0.216389	−	0.374797i
$186$	−346757.	+	600601.i	−0.734925	+	1.27293i
$187$	−281903.	−	488270.i	−0.589516	−	1.02107i
$188$	918119.			1.89454
$189$		0			0
$190$	921739.			1.85235
$191$	−136027.	−	235606.i	−0.269800	−	0.467307i	0.699010	−	0.715112i	$-0.253624\pi$
$191$	−136027.	−	235606.i	−0.269800	−	0.467307i	−0.968810	+	0.247805i	$0.920291\pi$
$192$	222546.	−	385462.i	0.435680	−	0.754620i
$193$	8016.89	−	13885.7i	0.0154922	−	0.0268333i	−0.858175	−	0.513357i	$-0.828402\pi$
$193$	8016.89	−	13885.7i	0.0154922	−	0.0268333i	0.873668	+	0.486523i	$0.161735\pi$
$194$	60656.2	+	105060.i	0.115710	+	0.200415i
$195$	−344413.			−0.648624
$196$		0			0
$197$	1.03228e6			1.89510			0.947552	−	0.319603i	$-0.103549\pi$
$197$	1.03228e6			1.89510			0.947552	+	0.319603i	$0.103549\pi$
$198$	−213194.	−	369263.i	−0.386467	−	0.669380i
$199$	−440868.	+	763606.i	−0.789180	+	1.36690i	0.137290	+	0.990531i	$0.456161\pi$
$199$	−440868.	+	763606.i	−0.789180	+	1.36690i	−0.926470	+	0.376369i	$0.877173\pi$
$200$	229226.	−	397030.i	0.405217	−	0.701857i
$201$	89168.4	+	154444.i	0.155676	+	0.269638i
$202$	236089.			0.407096
$203$		0			0
$204$	−508408.			−0.855337
$205$	8816.49	+	15270.6i	0.0146525	+	0.0253788i
$206$	754725.	−	1.30722e6i	1.23914	−	2.14626i
$207$	−130737.	+	226443.i	−0.212067	+	0.367311i
$208$	88988.4	+	154132.i	0.142618	+	0.247022i
$209$	767210.			1.21492
$210$		0			0
$211$	−372813.			−0.576480			−0.288240	−	0.957558i	$-0.593070\pi$
$211$	−372813.			−0.576480			−0.288240	+	0.957558i	$0.593070\pi$
$212$	832480.	+	1.44190e6i	1.27214	+	2.20341i
$213$	−279564.	+	484219.i	−0.422214	+	0.731296i
$214$	−443087.	+	767449.i	−0.661385	+	1.14555i
$215$	627791.	+	1.08737e6i	0.926230	+	1.60428i
$216$	−165446.			−0.241280
$217$		0			0
$218$	783054.			1.11596
$219$	121993.	+	211299.i	0.171880	+	0.297705i
$220$	1.12935e6	−	1.95609e6i	1.57315	−	2.72478i
$221$	−268275.	+	464666.i	−0.369487	+	0.639971i
$222$	−118678.	−	205557.i	−0.161618	−	0.279930i
$223$	1.08205e6			1.45708			0.728541	−	0.685002i	$-0.240199\pi$
$223$	1.08205e6			1.45708			0.728541	+	0.685002i	$0.240199\pi$
$224$		0			0
$225$	163625.			0.215473
$226$	−841584.	−	1.45767e6i	−1.09604	−	1.89840i
$227$	276524.	−	478954.i	0.356179	−	0.616921i	−0.631140	−	0.775669i	$-0.717413\pi$
$227$	276524.	−	478954.i	0.356179	−	0.616921i	0.987319	+	0.158748i	$0.0507459\pi$
$228$	345913.	−	599139.i	0.440687	−	0.763292i
$229$	261512.	+	452952.i	0.329536	+	0.570773i	0.982420	−	0.186685i	$-0.0597743\pi$
$229$	261512.	+	452952.i	0.329536	+	0.570773i	−0.652884	+	0.757458i	$0.726441\pi$
$230$	−2.17420e6			−2.71006
$231$		0			0
$232$	170996.			0.208577
$233$	182090.	+	315390.i	0.219734	+	0.380590i	0.954727	−	0.297485i	$-0.0961477\pi$
$233$	182090.	+	315390.i	0.219734	+	0.380590i	−0.734993	+	0.678075i	$0.762814\pi$
$234$	−202888.	+	351412.i	−0.242224	+	0.419544i
$235$	−586223.	+	1.01537e6i	−0.692458	+	1.19937i
$236$	−290849.	−	503766.i	−0.339929	−	0.588774i
$237$	402186.			0.465111
$238$		0			0
$239$	371841.			0.421078			0.210539	−	0.977585i	$-0.432478\pi$
$239$	371841.			0.421078			0.210539	+	0.977585i	$0.432478\pi$
$240$	−107679.	−	186505.i	−0.120671	−	0.209008i
$241$	−855737.	+	1.48218e6i	−0.949069	+	1.64384i	−0.201678	+	0.979452i	$0.564640\pi$
$241$	−855737.	+	1.48218e6i	−0.949069	+	1.64384i	−0.747391	+	0.664384i	$0.768694\pi$
$242$	719417.	−	1.24607e6i	0.789664	−	1.36774i
$243$	−29524.5	−	51137.9i	−0.0320750	−	0.0555556i
$244$	−53595.8			−0.0576310
$245$		0			0
$246$	20774.6			0.0218874
$247$	−365060.	−	632303.i	−0.380735	−	0.659452i
$248$	−931221.	+	1.61292e6i	−0.961443	+	1.66527i
$249$	70229.9	−	121642.i	0.0717833	−	0.124332i
$250$	−372103.	−	644502.i	−0.376542	−	0.652190i
$251$	−58134.1			−0.0582434			−0.0291217	−	0.999576i	$-0.509271\pi$
$251$	−58134.1			−0.0582434			−0.0291217	+	0.999576i	$0.509271\pi$
$252$		0			0
$253$	−1.80969e6			−1.77748
$254$	−674540.	−	1.16834e6i	−0.656030	−	1.13628i
$255$	324621.	−	562260.i	0.312627	−	0.541485i
$256$	768453.	−	1.33100e6i	0.732853	−	1.26934i
$257$	−155920.	−	270061.i	−0.147254	−	0.255052i	0.782957	−	0.622075i	$-0.213710\pi$
$257$	−155920.	−	270061.i	−0.147254	−	0.255052i	−0.930212	+	0.367023i	$0.880377\pi$
$258$	1.47928e6			1.38357
$259$		0			0
$260$	−2.14950e6			−1.97199
$261$	30515.0	+	52853.5i	0.0277276	+	0.0480255i
$262$	−245497.	+	425214.i	−0.220950	+	0.382696i
$263$	−431983.	+	748216.i	−0.385103	+	0.667018i	−0.991783	−	0.127928i	$-0.959167\pi$
$263$	−431983.	+	748216.i	−0.385103	+	0.667018i	0.606681	+	0.794946i	$0.292501\pi$
$264$	−572535.	−	991660.i	−0.505583	−	0.875696i
$265$	−2.12617e6			−1.85987
$266$		0			0
$267$	−122718.			−0.105349
$268$	556506.	+	963896.i	0.473296	+	0.819773i
$269$	−560346.	+	970548.i	−0.472145	+	0.817779i	−0.999492	−	0.0318707i	$-0.989854\pi$
$269$	−560346.	+	970548.i	−0.472145	+	0.817779i	0.527347	+	0.849650i	$0.323187\pi$
$270$	245500.	−	425219.i	0.204948	−	0.354980i
$271$	570058.	+	987369.i	0.471515	+	0.816688i	0.999469	−	0.0325848i	$-0.0103739\pi$
$271$	570058.	+	987369.i	0.471515	+	0.816688i	−0.527954	+	0.849273i	$0.677041\pi$
$272$	−335498.			−0.274959
$273$		0			0
$274$	−88359.6			−0.0711013
$275$	566233.	+	980744.i	0.451506	+	0.782031i
$276$	−815940.	+	1.41325e6i	−0.644741	+	1.11672i
$277$	994005.	−	1.72167e6i	0.778375	−	1.34819i	−0.154502	−	0.987992i	$-0.549377\pi$
$277$	994005.	−	1.72167e6i	0.778375	−	1.34819i	0.932878	−	0.360193i	$-0.117289\pi$
$278$	−859615.	−	1.48890e6i	−0.667102	−	1.15545i
$279$	−664720.			−0.511244
$280$		0			0
$281$	532321.			0.402168			0.201084	−	0.979574i	$-0.435554\pi$
$281$	532321.			0.402168			0.201084	+	0.979574i	$0.435554\pi$
$282$	690668.	+	1.19627e6i	0.517186	+	0.895793i
$283$	1.31237e6	−	2.27308e6i	0.974067	−	1.68713i	0.291087	−	0.956697i	$-0.405983\pi$
$283$	1.31237e6	−	2.27308e6i	0.974067	−	1.68713i	0.682980	−	0.730437i	$-0.260684\pi$
$284$	−1.74478e6	+	3.02205e6i	−1.28364	+	2.22334i
$285$	441734.	+	765106.i	0.322143	+	0.557968i
$286$	−2.80842e6			−2.03024
$287$		0			0
$288$	334526.			0.237656
$289$	204212.	+	353705.i	0.143826	+	0.249113i
$290$	−253736.	+	439484.i	−0.177169	+	0.306866i
$291$	−58137.7	+	100697.i	−0.0402463	+	0.0697086i
$292$	761369.	+	1.31873e6i	0.522562	+	0.905104i
$293$	−609962.			−0.415082			−0.207541	−	0.978226i	$-0.566546\pi$
$293$	−609962.			−0.415082			−0.207541	+	0.978226i	$0.566546\pi$
$294$		0			0
$295$	742834.			0.496978
$296$	−318712.	−	552026.i	−0.211431	−	0.366210i
$297$	204342.	−	353931.i	0.134421	−	0.232824i
$298$	−784061.	+	1.35803e6i	−0.511457	+	0.885870i
$299$	861104.	+	1.49148e6i	0.557029	+	0.964802i
$300$	1.02119e6			0.655096
$301$		0			0
$302$	−3.53307e6			−2.22913
$303$	113143.	+	195970.i	0.0707981	+	0.122626i
$304$	228268.	−	395372.i	0.141665	−	0.245370i
$305$	34221.2	−	59272.8i	0.0210642	−	0.0364843i
$306$	−382457.	−	662436.i	−0.233496	−	0.404427i
$307$	1.34843e6			0.816551			0.408275	−	0.912859i	$-0.366130\pi$
$307$	1.34843e6			0.816551			0.408275	+	0.912859i	$0.366130\pi$
$308$		0			0
$309$	1.44678e6			0.861997
$310$	−2.76362e6	−	4.78673e6i	−1.63333	−	2.82901i
$311$	−1.66530e6	+	2.88439e6i	−0.976320	+	1.69104i	−0.300813	+	0.953683i	$0.597258\pi$
$311$	−1.66530e6	+	2.88439e6i	−0.976320	+	1.69104i	−0.675507	+	0.737353i	$0.736075\pi$
$312$	−544858.	+	943721.i	−0.316881	+	0.548854i
$313$	−1.41835e6	−	2.45666e6i	−0.818320	−	1.41737i	−0.906919	−	0.421305i	$-0.861572\pi$
$313$	−1.41835e6	−	2.45666e6i	−0.818320	−	1.41737i	0.0885991	−	0.996067i	$-0.471761\pi$
$314$	366909.			0.210007
$315$		0			0
$316$	2.51007e6			1.41406
$317$	544195.	+	942574.i	0.304163	+	0.526826i	0.977075	−	0.212897i	$-0.0682899\pi$
$317$	544195.	+	942574.i	0.304163	+	0.526826i	−0.672912	+	0.739723i	$0.734957\pi$
$318$	−1.25249e6	+	2.16938e6i	−0.694555	+	1.20300i
$319$	−211198.	+	365805.i	−0.116202	+	0.201267i
$320$	1.77367e6	+	3.07209e6i	0.968274	+	1.67710i
$321$	−849380.			−0.460086
$322$		0			0
$323$	1.37633e6			0.734033
$324$	−184264.	−	319155.i	−0.0975167	−	0.168904i
$325$	538860.	−	933332.i	0.282988	−	0.490149i
$326$	−2.24380e6	+	3.88637e6i	−1.16934	+	2.02535i
$327$	375271.	+	649988.i	0.194078	+	0.336152i
$328$	55790.4			0.0286335
$329$		0			0
$330$	3.39827e6			1.71780
$331$	−652773.	−	1.13064e6i	−0.327485	−	0.567221i	0.654527	−	0.756039i	$-0.272868\pi$
$331$	−652773.	−	1.13064e6i	−0.327485	−	0.567221i	−0.982012	+	0.188817i	$0.939535\pi$
$332$	438309.	−	759174.i	0.218241	−	0.378004i
$333$	113751.	−	197022.i	0.0562140	−	0.0973654i
$334$	−186827.	−	323594.i	−0.0916376	−	0.158721i
$335$	−1.42133e6			−0.691961
$336$		0			0
$337$	−3.17016e6			−1.52057			−0.760285	−	0.649590i	$-0.774941\pi$
$337$	−3.17016e6			−1.52057			−0.760285	+	0.649590i	$0.774941\pi$
$338$	−406869.	−	704718.i	−0.193715	−	0.335524i
$339$	806641.	−	1.39714e6i	0.381225	−	0.660301i
$340$	2.02598e6	−	3.50910e6i	0.950469	−	1.64626i
$341$	−2.30030e6	−	3.98424e6i	−1.07127	−	1.85549i
$342$	1.04087e6			0.481207
$343$		0			0
$344$	3.97263e6			1.81002
$345$	−1.04196e6	−	1.80473e6i	−0.471307	−	0.816328i
$346$	−226945.	+	393080.i	−0.101913	+	0.176519i
$347$	857958.	−	1.48603e6i	0.382510	−	0.662526i	−0.608911	−	0.793239i	$-0.708393\pi$
$347$	857958.	−	1.48603e6i	0.382510	−	0.662526i	0.991420	+	0.130713i	$0.0417265\pi$
$348$	190446.	+	329862.i	0.0842992	+	0.146011i
$349$	2.95822e6			1.30007			0.650034	−	0.759905i	$-0.274755\pi$
$349$	2.95822e6			1.30007			0.650034	+	0.759905i	$0.274755\pi$
$350$		0			0
$351$	−388928.			−0.168501
$352$	1.15765e6	+	2.00510e6i	0.497988	+	0.862541i
$353$	1.88490e6	−	3.26474e6i	0.805103	−	1.39448i	−0.111119	−	0.993807i	$-0.535443\pi$
$353$	1.88490e6	−	3.26474e6i	0.805103	−	1.39448i	0.916222	−	0.400672i	$-0.131223\pi$
$354$	437591.	−	757930.i	0.185592	−	0.321456i
$355$	−2.22810e6	−	3.85918e6i	−0.938347	−	1.62526i
$356$	−765890.			−0.320289
$357$		0			0
$358$	1.34191e6			0.553371
$359$	−964935.	−	1.67132e6i	−0.395150	−	0.684420i	0.597970	−	0.801518i	$-0.295974\pi$
$359$	−964935.	−	1.67132e6i	−0.395150	−	0.684420i	−0.993120	+	0.117099i	$0.962641\pi$
$360$	659294.	−	1.14193e6i	0.268116	−	0.464391i
$361$	301617.	−	522416.i	0.121811	−	0.210984i
$362$	362662.	+	628148.i	0.145455	+	0.251936i
$363$	1.37909e6			0.549323
$364$		0			0
$365$	−1.94455e6			−0.763988
$366$	−40318.2	−	69833.2i	−0.0157325	−	0.0272496i
$367$	1.18371e6	−	2.05025e6i	0.458754	−	0.794586i	−0.540141	−	0.841575i	$-0.681629\pi$
$367$	1.18371e6	−	2.05025e6i	0.458754	−	0.794586i	0.998895	+	0.0469885i	$0.0149624\pi$
$368$	−538438.	+	932603.i	−0.207260	+	0.358986i
$369$	9956.01	+	17244.3i	0.00380644	+	0.00659295i
$370$	1.89171e6			0.718373
$371$		0			0
$372$	−4.14856e6			−1.55432
$373$	−1.76914e6	−	3.06425e6i	−0.658402	−	1.14039i	−0.981029	−	0.193860i	$-0.937899\pi$
$373$	−1.76914e6	−	3.06425e6i	−0.658402	−	1.14039i	0.322627	−	0.946526i	$-0.395434\pi$
$374$	2.64703e6	−	4.58479e6i	0.978543	−	1.69489i
$375$	356654.	−	617742.i	0.130969	−	0.226845i
$376$	1.85480e6	+	3.21260e6i	0.676592	+	1.17189i
$377$	401975.			0.145662
$378$		0			0
$379$	1.79847e6			0.643139			0.321569	−	0.946886i	$-0.395790\pi$
$379$	1.79847e6			0.643139			0.321569	+	0.946886i	$0.395790\pi$
$380$	2.75689e6	+	4.77508e6i	0.979401	+	1.69637i
$381$	646533.	−	1.11983e6i	0.228180	−	0.395220i
$382$	1.27728e6	−	2.21231e6i	0.447843	−	0.775687i
$383$	1.30407e6	+	2.25872e6i	0.454261	+	0.786802i	0.998645	−	0.0520333i	$-0.0165702\pi$
$383$	1.30407e6	+	2.25872e6i	0.454261	+	0.786802i	−0.544385	+	0.838836i	$0.683237\pi$
$384$	2.98994e6			1.03475
$385$		0			0
$386$	150555.			0.0514313
$387$	708932.	+	1.22791e6i	0.240618	+	0.416762i
$388$	−362841.	+	628460.i	−0.122359	+	0.211933i
$389$	1.41498e6	−	2.45081e6i	0.474106	−	0.821175i	−0.525455	−	0.850821i	$-0.676105\pi$
$389$	1.41498e6	−	2.45081e6i	0.474106	−	0.821175i	0.999560	+	0.0296466i	$0.00943818\pi$
$390$	−1.61700e6	−	2.80072e6i	−0.538328	−	0.932412i
$391$	−3.24648e6			−1.07392
$392$		0			0
$393$	−470609.			−0.153702
$394$	4.84650e6	+	8.39438e6i	1.57285	+	2.72426i
$395$	−1.60269e6	+	2.77594e6i	−0.516841	+	0.895195i
$396$	1.27531e6	−	2.20891e6i	0.408676	−	0.707848i
$397$	−1.21531e6	−	2.10498e6i	−0.387000	−	0.670303i	0.605045	−	0.796191i	$-0.293155\pi$
$397$	−1.21531e6	−	2.10498e6i	−0.387000	−	0.670303i	−0.992044	+	0.125888i	$0.959822\pi$
$398$	−8.27939e6			−2.61993
$399$		0			0
$400$	673885.			0.210589
$401$	1.21592e6	+	2.10604e6i	0.377611	+	0.654041i	0.990714	−	0.135962i	$-0.0434124\pi$
$401$	1.21592e6	+	2.10604e6i	0.377611	+	0.654041i	−0.613103	+	0.790003i	$0.710079\pi$
$402$	−837279.	+	1.45021e6i	−0.258408	+	0.447575i
$403$	−2.18910e6	+	3.79163e6i	−0.671433	+	1.16296i
$404$	706134.	+	1.22306e6i	0.215245	+	0.372816i
$405$	470614.			0.142570
$406$		0			0
$407$	1.57457e6			0.471167
$408$	−1.02709e6	−	1.77898e6i	−0.305464	−	0.529079i
$409$	−2.38733e6	+	4.13497e6i	−0.705674	+	1.22226i	0.260774	+	0.965400i	$0.416022\pi$
$409$	−2.38733e6	+	4.13497e6i	−0.705674	+	1.22226i	−0.966448	+	0.256863i	$0.917311\pi$
$410$	−82785.6	+	143389.i	−0.0243218	+	0.0421266i
$411$	−42345.5	−	73344.5i	−0.0123652	−	0.0214172i
$412$	9.02944e6			2.62070
$413$		0			0
$414$	−2.45521e6			−0.704024
$415$	559725.	+	969472.i	0.159534	+	0.276322i
$416$	1.10168e6	−	1.90817e6i	0.312121	−	0.540609i
$417$	823924.	−	1.42708e6i	0.232032	−	0.401890i
$418$	3.60200e6	+	6.23884e6i	1.00833	+	1.74648i
$419$	457181.			0.127219			0.0636097	−	0.997975i	$-0.479739\pi$
$419$	457181.			0.127219			0.0636097	+	0.997975i	$0.479739\pi$
$420$		0			0
$421$	−1.82396e6			−0.501545			−0.250773	−	0.968046i	$-0.580685\pi$
$421$	−1.82396e6			−0.501545			−0.250773	+	0.968046i	$0.580685\pi$
$422$	−1.75033e6	−	3.03166e6i	−0.478453	−	0.828704i
$423$	−661992.	+	1.14660e6i	−0.179888	+	0.311575i
$424$	−3.36358e6	+	5.82589e6i	−0.908629	+	1.57379i
$425$	1.01579e6	+	1.75939e6i	0.272791	+	0.472488i
$426$	−5.25014e6			−1.40167
$427$		0			0
$428$	−5.30104e6			−1.39879
$429$	−1.34591e6	−	2.33118e6i	−0.353079	−	0.611551i
$430$	−5.89487e6	+	1.02102e7i	−1.53746	+	2.66295i
$431$	1.69124e6	−	2.92932e6i	0.438544	−	0.759580i	−0.559034	−	0.829145i	$-0.688828\pi$
$431$	1.69124e6	−	2.92932e6i	0.438544	−	0.759580i	0.997577	+	0.0695651i	$0.0221612\pi$
$432$	−121596.	−	210611.i	−0.0313480	−	0.0542964i
$433$	285266.			0.0731190			0.0365595	−	0.999331i	$-0.488360\pi$
$433$	285266.			0.0731190			0.0365595	+	0.999331i	$0.488360\pi$
$434$		0			0
$435$	−486402.			−0.123246
$436$	2.34209e6	+	4.05662e6i	0.590048	+	1.02199i
$437$	2.20886e6	−	3.82585e6i	0.553304	−	0.958351i
$438$	−1.14550e6	+	1.98407e6i	−0.285306	+	0.494164i
$439$	2.17610e6	+	3.76911e6i	0.538911	+	0.933421i	0.998963	+	0.0455294i	$0.0144975\pi$
$439$	2.17610e6	+	3.76911e6i	0.538911	+	0.933421i	−0.460052	+	0.887892i	$0.652169\pi$
$440$	9.12610e6			2.24726
$441$		0			0
$442$	−5.03813e6			−1.22663
$443$	2.55280e6	+	4.42158e6i	0.618027	+	1.07045i	0.989845	+	0.142148i	$0.0454010\pi$
$443$	2.55280e6	+	4.42158e6i	0.618027	+	1.07045i	−0.371819	+	0.928305i	$0.621266\pi$
$444$	709927.	−	1.22963e6i	0.170906	−	0.296017i
$445$	489024.	−	847015.i	0.117066	−	0.202764i
$446$	5.08014e6	+	8.79906e6i	1.20931	+	2.09459i
$447$	−1.50301e6			−0.355790
$448$		0			0
$449$	3.04163e6			0.712016			0.356008	−	0.934483i	$-0.384138\pi$
$449$	3.04163e6			0.712016			0.356008	+	0.934483i	$0.384138\pi$
$450$	768208.	+	1.33057e6i	0.178833	+	0.309748i
$451$	−68906.7	+	119350.i	−0.0159522	+	0.0276300i
$452$	5.03430e6	−	8.71966e6i	1.15903	−	2.00749i
$453$	−1.69319e6	−	2.93269e6i	−0.387668	−	0.671461i
$454$	5.19305e6			1.18245
$455$		0			0
$456$	2.79528e6			0.629524
$457$	872162.	+	1.51063e6i	0.195347	+	0.338351i	0.947014	−	0.321192i	$-0.104083\pi$
$457$	872162.	+	1.51063e6i	0.195347	+	0.338351i	−0.751667	+	0.659542i	$0.770750\pi$
$458$	−2.45556e6	+	4.25316e6i	−0.547000	+	0.947432i
$459$	366578.	−	634931.i	0.0812147	−	0.140668i
$460$	−6.50295e6	−	1.12634e7i	−1.43290	−	2.48186i
$461$	6.85701e6			1.50273			0.751367	−	0.659884i	$-0.229395\pi$
$461$	6.85701e6			1.50273			0.751367	+	0.659884i	$0.229395\pi$
$462$		0			0
$463$	5.13844e6			1.11398			0.556992	−	0.830518i	$-0.311955\pi$
$463$	5.13844e6			1.11398			0.556992	+	0.830518i	$0.311955\pi$
$464$	125675.	+	217676.i	0.0270991	+	0.0469370i
$465$	2.64887e6	−	4.58798e6i	0.568105	−	0.983987i
$466$	−1.70980e6	+	2.96147e6i	−0.364738	+	0.631746i
$467$	−2.29085e6	−	3.96788e6i	−0.486077	−	0.841910i	0.513795	−	0.857913i	$-0.328239\pi$
$467$	−2.29085e6	−	3.96788e6i	−0.486077	−	0.841910i	−0.999872	+	0.0160029i	$0.994906\pi$
$468$	−2.42733e6			−0.512287
$469$		0			0
$470$	−1.10091e7			−2.29883
$471$	175838.	+	304560.i	0.0365224	+	0.0632587i
$472$	1.17516e6	−	2.03543e6i	0.242795	−	0.420534i
$473$	−4.90660e6	+	8.49848e6i	−1.00839	+	1.74658i
$474$	1.88824e6	+	3.27052e6i	0.386021	+	0.668608i
$475$	−2.76450e6			−0.562190
$476$		0			0
$477$	−2.40097e6			−0.483161
$478$	1.74577e6	+	3.02376e6i	0.349476	+	0.605310i
$479$	−144261.	+	249868.i	−0.0287284	+	0.0497590i	−0.880032	−	0.474914i	$-0.842479\pi$
$479$	−144261.	+	249868.i	−0.0287284	+	0.0497590i	0.851304	+	0.524673i	$0.175812\pi$
$480$	−1.33307e6	+	2.30894e6i	−0.264088	+	0.457414i
$481$	−749223.	−	1.29769e6i	−0.147655	−	0.255746i
$482$	−1.60705e7			−3.15074
$483$		0			0
$484$	8.60702e6			1.67009
$485$	−463352.	−	802549.i	−0.0894451	−	0.154923i
$486$	277231.	−	480178.i	0.0532416	−	0.0922172i
$487$	3.90842e6	−	6.76959e6i	0.746757	−	1.29342i	−0.202613	−	0.979259i	$-0.564943\pi$
$487$	3.90842e6	−	6.76959e6i	0.746757	−	1.29342i	0.949369	−	0.314162i	$-0.101723\pi$
$488$	−108275.	−	187538.i	−0.0205816	−	0.0356484i
$489$	−4.30127e6			−0.813438
$490$		0			0
$491$	3.14467e6			0.588669			0.294335	−	0.955702i	$-0.404902\pi$
$491$	3.14467e6			0.588669			0.294335	+	0.955702i	$0.404902\pi$
$492$	62136.1	+	107623.i	0.0115726	+	0.0200444i
$493$	−378875.	+	656232.i	−0.0702068	+	0.121602i
$494$	3.42787e6	−	5.93724e6i	0.631985	−	1.09463i
$495$	1.62859e6	+	2.82080e6i	0.298743	+	0.517439i
$496$	−2.73763e6			−0.499656
$497$		0			0
$498$	1.31890e6			0.238308
$499$	−3.36281e6	−	5.82456e6i	−0.604577	−	1.04716i	−0.992118	−	0.125305i	$-0.960009\pi$
$499$	−3.36281e6	−	5.82456e6i	−0.604577	−	1.04716i	0.387541	−	0.921852i	$-0.373324\pi$
$500$	2.22590e6	−	3.85537e6i	0.398181	−	0.689670i
$501$	179070.	−	310159.i	0.0318734	−	0.0552064i
$502$	−272936.	−	472738.i	−0.0483394	−	0.0837262i
$503$	9.45056e6			1.66547			0.832737	−	0.553669i	$-0.186773\pi$
$503$	9.45056e6			1.66547			0.832737	+	0.553669i	$0.186773\pi$
$504$		0			0
$505$	−1.80348e6			−0.314690
$506$	−8.49639e6	−	1.47162e7i	−1.47522	−	2.55516i
$507$	389976.	−	675458.i	0.0673780	−	0.116702i
$508$	4.03506e6	−	6.98892e6i	0.693730	−	1.20158i
$509$	−4.41851e6	−	7.65308e6i	−0.755930	−	1.30931i	−0.944911	−	0.327328i	$-0.893852\pi$
$509$	−4.41851e6	−	7.65308e6i	−0.755930	−	1.30931i	0.188981	−	0.981981i	$-0.439481\pi$
$510$	6.09629e6			1.03786
$511$		0			0
$512$	3.80044e6			0.640707
$513$	498828.	+	863995.i	0.0836869	+	0.144950i
$514$	1.46406e6	−	2.53583e6i	0.244429	−	0.423363i
$515$	−5.76534e6	+	9.98585e6i	−0.957870	+	1.65908i
$516$	4.42449e6	+	7.66345e6i	0.731542	+	1.26707i
$517$	−9.16344e6			−1.50776
$518$		0			0
$519$	−435044.			−0.0708949
$520$	−4.34246e6	−	7.52136e6i	−0.704251	−	1.21980i
$521$	347492.	−	601874.i	0.0560855	−	0.0971430i	−0.836619	−	0.547784i	$-0.815471\pi$
$521$	347492.	−	601874.i	0.0560855	−	0.0971430i	0.892705	+	0.450641i	$0.148805\pi$
$522$	−286531.	+	496287.i	−0.0460252	+	0.0797181i
$523$	1.79105e6	+	3.10219e6i	0.286321	+	0.495923i	0.972929	−	0.231105i	$-0.0742342\pi$
$523$	1.79105e6	+	3.10219e6i	0.286321	+	0.495923i	−0.686607	+	0.727028i	$0.740901\pi$
$524$	−2.93710e6			−0.467294
$525$		0			0
$526$	−8.11252e6			−1.27847
$527$	−4.12660e6	−	7.14748e6i	−0.647240	−	1.12105i
$528$	841580.	−	1.45766e6i	0.131374	−	0.227547i
$529$	−1.99208e6	+	3.45038e6i	−0.309504	+	0.536077i
$530$	−9.98222e6	−	1.72897e7i	−1.54361	−	2.67361i
$531$	838845.			0.129106
$532$		0			0
$533$	131151.			0.0199965
$534$	−576152.	−	997925.i	−0.0874347	−	0.151441i
$535$	3.38473e6	−	5.86253e6i	0.511258	−	0.885525i
$536$	−2.24852e6	+	3.89456e6i	−0.338053	+	0.585526i
$537$	643098.	+	1.11388e6i	0.0962368	+	0.166687i
$538$	−1.05231e7			−1.56744
$539$		0			0
$540$	2.93714e6			0.433451
$541$	2.58423e6	+	4.47602e6i	0.379610	+	0.657504i	0.991005	−	0.133821i	$-0.0427248\pi$
$541$	2.58423e6	+	4.47602e6i	0.379610	+	0.657504i	−0.611395	+	0.791325i	$0.709391\pi$
$542$	−5.35277e6	+	9.27126e6i	−0.782673	+	1.35563i
$543$	−347604.	+	602068.i	−0.0505924	+	0.0876285i
$544$	2.07675e6	+	3.59703e6i	0.300875	+	0.521131i
$545$	−5.98174e6			−0.862653
$546$		0			0
$547$	8.47489e6			1.21106			0.605530	−	0.795822i	$-0.292961\pi$
$547$	8.47489e6			1.21106			0.605530	+	0.795822i	$0.292961\pi$
$548$	−264281.	−	457748.i	−0.0375936	−	0.0651141i
$549$	38644.2	−	66933.8i	0.00547210	−	0.00947795i
$550$	−5.31685e6	+	9.20906e6i	−0.749459	+	1.29810i
$551$	−515562.	−	892980.i	−0.0723439	−	0.125303i
$552$	−6.59349e6			−0.921018
$553$		0			0
$554$	1.86671e7			2.58407
$555$	906583.	+	1.57025e6i	0.124932	+	0.216389i
$556$	5.14217e6	−	8.90649e6i	0.705438	−	1.22186i
$557$	5.21063e6	−	9.02508e6i	0.711627	−	1.23257i	−0.252619	−	0.967566i	$-0.581292\pi$
$557$	5.21063e6	−	9.02508e6i	0.711627	−	1.23257i	0.964246	−	0.265009i	$-0.0853748\pi$
$558$	−3.12082e6	−	5.40541e6i	−0.424309	−	0.734925i
$559$	9.33880e6			1.26404
$560$		0			0
$561$	5.07425e6			0.680714
$562$	2.49921e6	+	4.32876e6i	0.333781	+	0.578126i
$563$	−3.62039e6	+	6.27069e6i	−0.481375	+	0.833767i	−0.999772	−	0.0213739i	$-0.993196\pi$
$563$	−3.62039e6	+	6.27069e6i	−0.481375	+	0.833767i	0.518396	+	0.855141i	$0.326529\pi$
$564$	−4.13154e6	+	7.15603e6i	−0.546907	+	0.947271i
$565$	6.42885e6	+	1.11351e7i	0.847251	+	1.46748i
$566$	2.46459e7			3.23373
$567$		0			0
$568$	−1.40993e7			−1.83369
$569$	−458268.	−	793743.i	−0.0593388	−	0.102778i	0.834830	−	0.550508i	$-0.185566\pi$
$569$	−458268.	−	793743.i	−0.0593388	−	0.102778i	−0.894169	+	0.447730i	$0.852233\pi$
$570$	−4.14782e6	+	7.18424e6i	−0.534728	+	0.926177i
$571$	−5.03538e6	+	8.72154e6i	−0.646312	+	1.11944i	0.337685	+	0.941259i	$0.390356\pi$
$571$	−5.03538e6	+	8.72154e6i	−0.646312	+	1.11944i	−0.983997	+	0.178186i	$0.942977\pi$
$572$	−8.39990e6	−	1.45490e7i	−1.07345	−	1.85928i
$573$	2.44849e6			0.311538
$574$		0			0
$575$	6.52091e6			0.822505
$576$	2.00292e6	+	3.46916e6i	0.251540	+	0.435680i
$577$	5.84987e6	−	1.01323e7i	0.731488	−	1.26697i	−0.224760	−	0.974414i	$-0.572160\pi$
$577$	5.84987e6	−	1.01323e7i	0.731488	−	1.26697i	0.956247	−	0.292560i	$-0.0945070\pi$
$578$	−1.91752e6	+	3.32125e6i	−0.238738	+	0.413506i
$579$	72152.0	+	124971.i	0.00894442	+	0.0154922i
$580$	−3.03567e6			−0.374701
$581$		0			0
$582$	−1.09181e6			−0.133610
$583$	−8.30871e6	−	1.43911e7i	−1.01242	−	1.75357i
$584$	−3.07626e6	+	5.32823e6i	−0.373242	+	0.646474i
$585$	1.54986e6	−	2.68443e6i	0.187242	−	0.324312i
$586$	−2.86373e6	−	4.96013e6i	−0.344499	−	0.596690i
$587$	6.92367e6			0.829357			0.414678	−	0.909968i	$-0.363894\pi$
$587$	6.92367e6			0.829357			0.414678	+	0.909968i	$0.363894\pi$
$588$		0			0
$589$	1.12307e7			1.33389
$590$	3.48756e6	+	6.04062e6i	0.412469	+	0.714417i
$591$	−4.64527e6	+	8.04584e6i	−0.547069	+	0.947552i
$592$	468481.	−	811432.i	0.0549398	−	0.0951586i
$593$	7.88850e6	+	1.36633e7i	0.921208	+	1.59558i	0.797548	+	0.603255i	$0.206130\pi$
$593$	7.88850e6	+	1.36633e7i	0.921208	+	1.59558i	0.123660	+	0.992325i	$0.460537\pi$
$594$	3.83750e6			0.446254
$595$		0			0
$596$	−9.38041e6			−1.08170
$597$	−3.96781e6	−	6.87245e6i	−0.455633	−	0.789180i
$598$	−8.08565e6	+	1.40048e7i	−0.924618	+	1.60148i
$599$	−7.13541e6	+	1.23589e7i	−0.812553	+	1.40738i	0.0985183	+	0.995135i	$0.468590\pi$
$599$	−7.13541e6	+	1.23589e7i	−0.812553	+	1.40738i	−0.911072	+	0.412248i	$0.864744\pi$
$600$	2.06303e6	+	3.57327e6i	0.233952	+	0.405217i
$601$	−7.63222e6			−0.861916			−0.430958	−	0.902372i	$-0.641824\pi$
$601$	−7.63222e6			−0.861916			−0.430958	+	0.902372i	$0.641824\pi$
$602$		0			0
$603$	−1.60503e6			−0.179759
$604$	−1.05673e7	−	1.83031e7i	−1.17862	−	2.04142i
$605$	−5.49562e6	+	9.51869e6i	−0.610419	+	1.05728i
$606$	−1.06240e6	+	1.84013e6i	−0.117518	+	0.203548i
$607$	−1.78017e6	−	3.08335e6i	−0.196106	−	0.339665i	0.751157	−	0.660124i	$-0.229496\pi$
$607$	−1.78017e6	−	3.08335e6i	−0.196106	−	0.339665i	−0.947262	+	0.320459i	$0.896163\pi$
$608$	−5.65194e6			−0.620067
$609$		0			0
$610$	642664.			0.0699294
$611$	4.36023e6	+	7.55214e6i	0.472505	+	0.818402i
$612$	2.28784e6	−	3.96265e6i	0.246914	−	0.427668i
$613$	6.86420e6	−	1.18891e7i	0.737800	−	1.27791i	−0.215683	−	0.976463i	$-0.569198\pi$
$613$	6.86420e6	−	1.18891e7i	0.737800	−	1.27791i	0.953484	−	0.301445i	$-0.0974688\pi$
$614$	6.33080e6	+	1.09653e7i	0.677700	+	1.17381i
$615$	−158697.			−0.0169192
$616$		0			0
$617$	−6.51173e6			−0.688626			−0.344313	−	0.938855i	$-0.611888\pi$
$617$	−6.51173e6			−0.688626			−0.344313	+	0.938855i	$0.611888\pi$
$618$	6.79253e6	+	1.17650e7i	0.715419	+	1.23914i
$619$	4.42555e6	−	7.66527e6i	0.464238	−	0.804083i	−0.534929	−	0.844897i	$-0.679662\pi$
$619$	4.42555e6	−	7.66527e6i	0.464238	−	0.804083i	0.999167	+	0.0408136i	$0.0129950\pi$
$620$	1.65318e7	−	2.86339e7i	1.72719	−	2.99159i
$621$	−1.17663e6	−	2.03799e6i	−0.122437	−	0.212067i
$622$	−3.12739e7			−3.24121
$623$		0			0
$624$	−1.60179e6			−0.164681
$625$	5.99884e6	+	1.03903e7i	0.614281	+	1.06397i
$626$	1.33181e7	−	2.30677e7i	1.35834	−	2.35271i
$627$	−3.45244e6	+	5.97981e6i	−0.350718	+	0.607461i
$628$	1.09741e6	+	1.90078e6i	0.111038	+	0.192323i
$629$	2.82467e6			0.284670
$630$		0			0
$631$	−6.89663e6			−0.689546			−0.344773	−	0.938686i	$-0.612044\pi$
$631$	−6.89663e6			−0.689546			−0.344773	+	0.938686i	$0.612044\pi$
$632$	5.07088e6	+	8.78303e6i	0.504999	+	0.874685i
$633$	1.67766e6	−	2.90579e6i	0.166416	−	0.288240i
$634$	−5.10992e6	+	8.85064e6i	−0.504883	+	0.874483i
$635$	5.15280e6	+	8.92492e6i	0.507118	+	0.878355i
$636$	−1.49846e7			−1.46894
$637$		0			0
$638$	−3.96623e6			−0.385768
$639$	−2.51608e6	−	4.35797e6i	−0.243765	−	0.422214i
$640$	−1.19147e7	+	2.06369e7i	−1.14983	+	1.99157i
$641$	8.33473e6	−	1.44362e7i	0.801210	−	1.38774i	−0.117610	−	0.993060i	$-0.537523\pi$
$641$	8.33473e6	−	1.44362e7i	0.801210	−	1.38774i	0.918820	−	0.394677i	$-0.129144\pi$
$642$	−3.98778e6	−	6.90704e6i	−0.381851	−	0.661385i
$643$	1.28697e7			1.22756			0.613779	−	0.789478i	$-0.289649\pi$
$643$	1.28697e7			1.22756			0.613779	+	0.789478i	$0.289649\pi$
$644$		0			0
$645$	−1.13002e7			−1.06952
$646$	6.46177e6	+	1.11921e7i	0.609214	+	1.05519i
$647$	−5.73656e6	+	9.93601e6i	−0.538754	+	0.933150i	0.460217	+	0.887806i	$0.347772\pi$
$647$	−5.73656e6	+	9.93601e6i	−0.538754	+	0.933150i	−0.998971	+	0.0453435i	$0.985562\pi$
$648$	744507.	−	1.28952e6i	0.0696517	−	0.120640i
$649$	2.90287e6	+	5.02792e6i	0.270530	+	0.468572i
$650$	1.01196e7			0.939467
$651$		0			0
$652$	−2.68445e7			−2.47307
$653$	6.59005e6	+	1.14143e7i	0.604791	+	1.04753i	0.992084	+	0.125573i	$0.0400768\pi$
$653$	6.59005e6	+	1.14143e7i	0.604791	+	1.04753i	−0.387293	+	0.921957i	$0.626590\pi$
$654$	−3.52374e6	+	6.10330e6i	−0.322151	+	0.557982i
$655$	1.87535e6	−	3.24820e6i	0.170797	−	0.295829i
$656$	41003.6	+	71020.4i	0.00372017	+	0.00644352i
$657$	−2.19588e6			−0.198470
$658$		0			0
$659$	−1.13068e7			−1.01421			−0.507104	−	0.861885i	$-0.669284\pi$
$659$	−1.13068e7			−1.01421			−0.507104	+	0.861885i	$0.669284\pi$
$660$	1.01641e7	+	1.76048e7i	0.908260	+	1.57315i
$661$	1.10160e6	−	1.90802e6i	0.0980661	−	0.169856i	−0.812818	−	0.582518i	$-0.802068\pi$
$661$	1.10160e6	−	1.90802e6i	0.0980661	−	0.169856i	0.910884	+	0.412662i	$0.135401\pi$
$662$	6.12945e6	−	1.06165e7i	0.543596	−	0.941536i
$663$	−2.41447e6	−	4.18199e6i	−0.213324	−	0.369487i
$664$	3.54192e6			0.311758
$665$		0			0
$666$	2.13621e6			0.186620
$667$	1.21611e6	+	2.10636e6i	0.105842	+	0.183323i
$668$	1.11759e6	−	1.93572e6i	0.0969038	−	0.167842i
$669$	−4.86921e6	+	8.43372e6i	−0.420623	+	0.728541i
$670$	−6.67303e6	−	1.15580e7i	−0.574296	−	0.994710i
$671$	534922.			0.0458653
$672$		0			0
$673$	−1.89787e7			−1.61521			−0.807606	−	0.589723i	$-0.799237\pi$
$673$	−1.89787e7			−1.61521			−0.807606	+	0.589723i	$0.799237\pi$
$674$	−1.48837e7	−	2.57793e7i	−1.26200	−	2.18586i
$675$	−736312.	+	1.27533e6i	−0.0622017	+	0.107736i
$676$	2.43387e6	−	4.21558e6i	0.204847	−	0.354806i
$677$	−9.82377e6	−	1.70153e7i	−0.823771	−	1.42681i	−0.902855	−	0.429945i	$-0.858533\pi$
$677$	−9.82377e6	−	1.70153e7i	−0.823771	−	1.42681i	0.0790842	−	0.996868i	$-0.474800\pi$
$678$	1.51485e7			1.26560
$679$		0			0
$680$	1.63717e7			1.35775
$681$	2.48872e6	+	4.31059e6i	0.205640	+	0.356179i
$682$	2.15995e7	−	3.74115e7i	1.77821	−	3.07995i
$683$	−8.13523e6	+	1.40906e7i	−0.667295	+	1.15579i	0.311363	+	0.950291i	$0.399215\pi$
$683$	−8.13523e6	+	1.40906e7i	−0.667295	+	1.15579i	−0.978658	+	0.205498i	$0.934119\pi$
$684$	3.11322e6	+	5.39225e6i	0.254431	+	0.440687i
$685$	674978.			0.0549621
$686$		0			0
$687$	−4.70722e6			−0.380515
$688$	2.91972e6	+	5.05711e6i	0.235164	+	0.407316i
$689$	−7.90704e6	+	1.36954e7i	−0.634550	+	1.09907i
$690$	9.78388e6	−	1.69462e7i	0.782327	−	1.35503i
$691$	9.72335e6	+	1.68413e7i	0.774677	+	1.34178i	0.934976	+	0.354712i	$0.115421\pi$
$691$	9.72335e6	+	1.68413e7i	0.774677	+	1.34178i	−0.160299	+	0.987069i	$0.551246\pi$
$692$	−2.71514e6			−0.215539
$693$		0			0
$694$	1.61122e7			1.26986
$695$	6.56659e6	+	1.13737e7i	0.515677	+	0.893179i
$696$	−769484.	+	1.33278e6i	−0.0602111	+	0.104289i
$697$	−123614.	+	214106.i	−0.00963800	+	0.0166935i
$698$	1.38886e7	+	2.40558e7i	1.07900	+	1.86888i
$699$	−3.27763e6			−0.253727
$700$		0			0
$701$	1.49625e7			1.15003			0.575014	−	0.818144i	$-0.304997\pi$
$701$	1.49625e7			1.15003			0.575014	+	0.818144i	$0.304997\pi$
$702$	−1.82599e6	−	3.16271e6i	−0.139848	−	0.242224i
$703$	−1.92187e6	+	3.32877e6i	−0.146668	+	0.254036i
$704$	−1.38624e7	+	2.40104e7i	−1.05416	+	1.82586i
$705$	−5.27601e6	−	9.13831e6i	−0.399791	−	0.692458i
$706$	3.53979e7			2.67280
$707$		0			0
$708$	5.23529e6			0.392516
$709$	−793193.	−	1.37385e6i	−0.0592603	−	0.102642i	0.834873	−	0.550442i	$-0.185541\pi$
$709$	−793193.	−	1.37385e6i	−0.0592603	−	0.102642i	−0.894134	+	0.447800i	$0.852208\pi$
$710$	2.09215e7	−	3.62372e7i	1.55757	−	2.69779i
$711$	−1.80984e6	+	3.13473e6i	−0.134266	+	0.232555i
$712$	−1.54726e6	−	2.67994e6i	−0.114384	−	0.198118i
$713$	−2.64910e7			−1.95152
$714$		0			0
$715$	2.14535e7			1.56940
$716$	4.01362e6	+	6.95179e6i	0.292586	+	0.506774i
$717$	−1.67329e6	+	2.89822e6i	−0.121555	+	0.210539i
$718$	9.06061e6	−	1.56934e7i	0.655913	−	1.13607i
$719$	−9.08376e6	−	1.57335e7i	−0.655305	−	1.13502i	−0.981817	−	0.189829i	$-0.939207\pi$
$719$	−9.08376e6	−	1.57335e7i	−0.655305	−	1.13502i	0.326512	−	0.945193i	$-0.394127\pi$
$720$	1.93822e6			0.139338
$721$		0			0
$722$	5.66429e6			0.404392
$723$	−7.70164e6	−	1.33396e7i	−0.547945	−	0.949069i
$724$	−2.16942e6	+	3.75754e6i	−0.153814	+	0.266414i
$725$	761013.	−	1.31811e6i	0.0537709	−	0.0931339i
$726$	6.47476e6	+	1.12146e7i	0.455913	+	0.789664i
$727$	−1.26903e7			−0.890506			−0.445253	−	0.895405i	$-0.646886\pi$
$727$	−1.26903e7			−0.890506			−0.445253	+	0.895405i	$0.646886\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	−9.12953e6	−	1.58128e7i	−0.634076	−	1.09825i
$731$	−8.80214e6	+	1.52458e7i	−0.609249	+	1.05525i
$732$	241181.	−	417738.i	0.0166366	−	0.0288155i
$733$	−1.55701e6	−	2.69681e6i	−0.107036	−	0.185392i	0.807532	−	0.589824i	$-0.200803\pi$
$733$	−1.55701e6	−	2.69681e6i	−0.107036	−	0.185392i	−0.914568	+	0.404432i	$0.867469\pi$
$734$	2.22298e7			1.52298
$735$		0			0
$736$	1.33318e7			0.907182
$737$	−5.55430e6	−	9.62033e6i	−0.376670	−	0.652411i
$738$	−93485.6	+	161922.i	−0.00631835	+	0.0109437i
$739$	−4.54950e6	+	7.87996e6i	−0.306445	+	0.530778i	−0.977582	−	0.210555i	$-0.932473\pi$
$739$	−4.54950e6	+	7.87996e6i	−0.306445	+	0.530778i	0.671137	+	0.741333i	$0.265806\pi$
$740$	5.65804e6	+	9.80002e6i	0.379828	+	0.657881i
$741$	6.57109e6			0.439634
$742$		0			0
$743$	−8.79218e6			−0.584285			−0.292142	−	0.956375i	$-0.594368\pi$
$743$	−8.79218e6			−0.584285			−0.292142	+	0.956375i	$0.594368\pi$
$744$	−8.38098e6	−	1.45163e7i	−0.555089	−	0.961443i
$745$	5.98943e6	−	1.03740e7i	0.395362	−	0.684787i
$746$	1.66120e7	−	2.87729e7i	1.09289	−	1.89294i
$747$	632069.	+	1.09478e6i	0.0414441	+	0.0717833i
$748$	3.16687e7			2.06955
$749$		0			0
$750$	6.69786e6			0.434793
$751$	1.40459e7	+	2.43282e7i	0.908759	+	1.57402i	0.815790	+	0.578349i	$0.196303\pi$
$751$	1.40459e7	+	2.43282e7i	0.908759	+	1.57402i	0.0929698	+	0.995669i	$0.470364\pi$
$752$	−2.72640e6	+	4.72226e6i	−0.175811	+	0.304513i
$753$	261603.	−	453110.i	0.0168134	−	0.0291217i
$754$	1.88725e6	+	3.26881e6i	0.120893	+	0.209393i
$755$	2.69891e7			1.72314
$756$		0			0
$757$	−4.18815e6			−0.265634			−0.132817	−	0.991141i	$-0.542402\pi$
$757$	−4.18815e6			−0.265634			−0.132817	+	0.991141i	$0.542402\pi$
$758$	8.44369e6	+	1.46249e7i	0.533776	+	0.924527i
$759$	8.14362e6	−	1.41052e7i	0.513113	−	0.888738i
$760$	−1.11390e7	+	1.92934e7i	−0.699541	+	1.21164i
$761$	−196591.	−	340506.i	−0.0123056	−	0.0213139i	0.859807	−	0.510619i	$-0.170584\pi$
$761$	−196591.	−	340506.i	−0.0123056	−	0.0213139i	−0.872113	+	0.489305i	$0.837250\pi$
$762$	1.21417e7			0.757518
$763$		0			0
$764$	1.52812e7			0.947159
$765$	2.92159e6	+	5.06034e6i	0.180495	+	0.312627i
$766$	−1.22451e7	+	2.12091e7i	−0.754031	+	1.30602i
$767$	2.76254e6	−	4.78486e6i	0.169559	−	0.293684i
$768$	6.91607e6	+	1.19790e7i	0.423113	+	0.732853i
$769$	−1.57517e7			−0.960530			−0.480265	−	0.877124i	$-0.659459\pi$
$769$	−1.57517e7			−0.960530			−0.480265	+	0.877124i	$0.659459\pi$
$770$		0			0
$771$	2.80655e6			0.170035
$772$	450306.	+	779952.i	0.0271934	+	0.0471004i
$773$	1.44236e6	−	2.49824e6i	0.0868210	−	0.150378i	−0.819345	−	0.573301i	$-0.805663\pi$
$773$	1.44236e6	−	2.49824e6i	0.0868210	−	0.150378i	0.906166	+	0.422923i	$0.138996\pi$
$774$	−6.65678e6	+	1.15299e7i	−0.399403	+	0.691787i
$775$	8.28873e6	+	1.43565e7i	0.495717	+	0.858606i
$776$	−2.93207e6			−0.174791
$777$		0			0
$778$	2.65729e7			1.57394
$779$	−168211.	−	291349.i	−0.00993139	−	0.0172017i
$780$	9.67276e6	−	1.67537e7i	0.569265	−	0.985995i
$781$	1.74141e7	−	3.01620e7i	1.02158	−	1.76943i
$782$	−1.52420e7	−	2.63999e7i	−0.891303	−	1.54378i
$783$	−549269.			−0.0320170
$784$		0			0
$785$	−2.80281e6			−0.162338
$786$	−2.20948e6	−	3.82693e6i	−0.127565	−	0.220950i
$787$	−1.48933e7	+	2.57960e7i	−0.857145	+	1.48462i	0.0174963	+	0.999847i	$0.494430\pi$
$787$	−1.48933e7	+	2.57960e7i	−0.857145	+	1.48462i	−0.874641	+	0.484771i	$0.838903\pi$
$788$	−2.89914e7	+	5.02146e7i	−1.66324	+	2.88081i
$789$	−3.88784e6	−	6.73394e6i	−0.222339	−	0.385103i
$790$	−3.00981e7			−1.71582
$791$		0			0
$792$	1.03056e7			0.583797
$793$	−254531.	−	440861.i	−0.0143734	−	0.0248954i
$794$	1.14116e7	−	1.97655e7i	0.642385	−	1.11264i
$795$	9.56776e6	−	1.65718e7i	0.536899	−	0.929936i
$796$	−2.47634e7	−	4.28914e7i	−1.38525	−	2.39932i
$797$	−8.11321e6			−0.452425			−0.226213	−	0.974078i	$-0.572634\pi$
$797$	−8.11321e6			−0.452425			−0.226213	+	0.974078i	$0.572634\pi$
$798$		0			0
$799$	−1.64387e7			−0.910960
$800$	−4.17137e6	−	7.22503e6i	−0.230438	−	0.399130i
$801$	552230.	−	956491.i	0.0304116	−	0.0526744i
$802$	−1.14173e7	+	1.97754e7i	−0.626800	+	1.08565i
$803$	−7.59897e6	−	1.31618e7i	−0.415878	−	0.720321i
$804$	−1.00171e7			−0.546515
$805$		0			0
$806$	−4.11107e7			−2.22904
$807$	−5.04311e6	−	8.73493e6i	−0.272593	−	0.472145i
$808$	−2.85308e6	+	4.94169e6i	−0.153740	+	0.266285i
$809$	−55798.5	+	96645.8i	−0.00299744	+	0.00519173i	−0.867520	−	0.497402i	$-0.834287\pi$
$809$	−55798.5	+	96645.8i	−0.00299744	+	0.00519173i	0.864523	+	0.502594i	$0.167621\pi$
$810$	2.20950e6	+	3.82697e6i	0.118327	+	0.204948i
$811$	209250.			0.0111716			0.00558578	−	0.999984i	$-0.498222\pi$
$811$	209250.			0.0111716			0.00558578	+	0.999984i	$0.498222\pi$
$812$		0			0
$813$	−1.02610e7			−0.544459
$814$	7.39248e6	+	1.28042e7i	0.391047	+	0.677314i
$815$	1.71403e7	−	2.96879e7i	0.903910	−	1.56562i
$816$	1.50974e6	−	2.61495e6i	0.0793739	−	0.137480i
$817$	−1.19777e7	−	2.07460e7i	−0.627795	−	1.08737i
$818$	−4.48334e7			−2.34271
$819$		0			0
$820$	−990437.			−0.0514390
$821$	−3.42307e6	−	5.92893e6i	−0.177238	−	0.306986i	0.763695	−	0.645577i	$-0.223383\pi$
$821$	−3.42307e6	−	5.92893e6i	−0.177238	−	0.306986i	−0.940934	+	0.338591i	$0.890050\pi$
$822$	397618.	−	688695.i	0.0205252	−	0.0355506i
$823$	2.80605e6	−	4.86022e6i	0.144409	−	0.250125i	−0.784743	−	0.619821i	$-0.787205\pi$
$823$	2.80605e6	−	4.86022e6i	0.144409	−	0.250125i	0.929152	+	0.369697i	$0.120538\pi$
$824$	1.82414e7	+	3.15950e7i	0.935923	+	1.62107i
$825$	−1.01922e7			−0.521354
$826$		0			0
$827$	−2.15868e7			−1.09755			−0.548776	−	0.835969i	$-0.684906\pi$
$827$	−2.15868e7			−1.09755			−0.548776	+	0.835969i	$0.684906\pi$
$828$	−7.34346e6	−	1.27192e7i	−0.372241	−	0.644741i
$829$	9.62135e6	−	1.66647e7i	0.486239	−	0.842190i	−0.513636	−	0.858008i	$-0.671702\pi$
$829$	9.62135e6	−	1.66647e7i	0.486239	−	0.842190i	0.999875	+	0.0158177i	$0.00503515\pi$
$830$	−5.25574e6	+	9.10321e6i	−0.264813	+	0.458669i
$831$	8.94604e6	+	1.54950e7i	0.449395	+	0.778375i
$832$	2.63846e7			1.32142
$833$		0			0
$834$	1.54731e7			0.770303
$835$	1.42717e6	+	2.47193e6i	0.0708369	+	0.122693i
$836$	−2.15469e7	+	3.73204e7i	−1.06628	+	1.84684i
$837$	2.99124e6	−	5.18098e6i	0.147583	−	0.255622i
$838$	2.14644e6	+	3.71774e6i	0.105586	+	0.182881i
$839$	−2.47678e7			−1.21474			−0.607369	−	0.794420i	$-0.707775\pi$
$839$	−2.47678e7			−1.21474			−0.607369	+	0.794420i	$0.707775\pi$
$840$		0			0
$841$	−1.99435e7			−0.972323
$842$	−8.56337e6	−	1.48322e7i	−0.416260	−	0.720983i
$843$	−2.39544e6	+	4.14903e6i	−0.116096	+	0.201084i
$844$	1.04704e7	−	1.81352e7i	0.505948	−	0.876328i
$845$	3.10807e6	+	5.38333e6i	0.149744	+	0.259364i
$846$	−1.24320e7			−0.597195
$847$		0			0
$848$	−9.88836e6			−0.472210
$849$	1.18113e7	+	2.04578e7i	0.562378	+	0.974067i
$850$	−9.53811e6	+	1.65205e7i	−0.452809	+	0.784288i
$851$	4.53329e6	−	7.85190e6i	0.214580	−	0.371664i
$852$	−1.57030e7	−	2.71984e7i	−0.741112	−	1.28364i
$853$	2.91267e7			1.37062			0.685312	−	0.728250i	$-0.259666\pi$
$853$	2.91267e7			1.37062			0.685312	+	0.728250i	$0.259666\pi$
$854$		0			0
$855$	−7.95121e6			−0.371979
$856$	−1.07092e7	−	1.85489e7i	−0.499544	−	0.865236i
$857$	−1.61293e6	+	2.79367e6i	−0.0750175	+	0.129934i	−0.901094	−	0.433624i	$-0.857235\pi$
$857$	−1.61293e6	+	2.79367e6i	−0.0750175	+	0.129934i	0.826076	+	0.563558i	$0.190568\pi$
$858$	1.26379e7	−	2.18895e7i	0.586079	−	1.01512i
$859$	1.32335e7	+	2.29212e7i	0.611918	+	1.05987i	0.990917	+	0.134476i	$0.0429350\pi$
$859$	1.32335e7	+	2.29212e7i	0.611918	+	1.05987i	−0.378999	+	0.925397i	$0.623732\pi$
$860$	−7.05255e7			−3.25162
$861$		0			0
$862$	3.17611e7			1.45589
$863$	−7.92552e6	−	1.37274e7i	−0.362243	−	0.627424i	0.626086	−	0.779754i	$-0.284656\pi$
$863$	−7.92552e6	−	1.37274e7i	−0.362243	−	0.627424i	−0.988330	+	0.152330i	$0.951322\pi$
$864$	−1.50537e6	+	2.60737e6i	−0.0686053	+	0.118828i
$865$	1.73363e6	−	3.00273e6i	0.0787799	−	0.136451i
$866$	1.33930e6	+	2.31974e6i	0.0606854	+	0.105110i
$867$	−3.67582e6			−0.166076
$868$		0			0
$869$	−2.50522e7			−1.12537
$870$	−2.28363e6	−	3.95536e6i	−0.102289	−	0.177169i
$871$	−5.28579e6	+	9.15526e6i	−0.236083	+	0.408908i
$872$	−9.46305e6	+	1.63905e7i	−0.421444	+	0.729962i
$873$	−523240.	−	906277.i	−0.0232362	−	0.0402463i
$874$	4.14817e7			1.83687
$875$		0			0
$876$	−1.37046e7			−0.603403
$877$	7.45659e6	+	1.29152e7i	0.327372	+	0.567024i	0.981989	−	0.188936i	$-0.0605037\pi$
$877$	7.45659e6	+	1.29152e7i	0.327372	+	0.567024i	−0.654618	+	0.755960i	$0.727170\pi$
$878$	−2.04333e7	+	3.53915e7i	−0.894544	+	1.54940i
$879$	2.74483e6	−	4.75419e6i	0.119824	−	0.207541i
$880$	6.70730e6	+	1.16174e7i	0.291972	+	0.505711i
$881$	3.70679e7			1.60901			0.804504	−	0.593947i	$-0.202431\pi$
$881$	3.70679e7			1.60901			0.804504	+	0.593947i	$0.202431\pi$
$882$		0			0
$883$	1.50440e7			0.649325			0.324663	−	0.945830i	$-0.394749\pi$
$883$	1.50440e7			0.649325			0.324663	+	0.945830i	$0.394749\pi$
$884$	−1.50689e7	−	2.61001e7i	−0.648561	−	1.12334i
$885$	−3.34275e6	+	5.78982e6i	−0.143465	+	0.248489i
$886$	−2.39704e7	+	4.15180e7i	−1.02587	+	1.77686i
$887$	8.90504e6	+	1.54240e7i	0.380038	+	0.658245i	0.991067	−	0.133363i	$-0.0425777\pi$
$887$	8.90504e6	+	1.54240e7i	0.380038	+	0.658245i	−0.611030	+	0.791608i	$0.709244\pi$
$888$	5.73682e6			0.244140
$889$		0			0
$890$	9.18375e6			0.388638
$891$	1.83908e6	+	3.18538e6i	0.0776080	+	0.134421i
$892$	−3.03891e7	+	5.26354e7i	−1.27881	+	2.21496i
$893$	1.11846e7	−	1.93723e7i	0.469345	−	0.812929i
$894$	−7.05655e6	−	1.22223e7i	−0.295290	−	0.511457i
$895$	−1.02508e7			−0.427762
$896$		0			0
$897$	−1.54999e7			−0.643202
$898$	1.42802e7	+	2.47341e7i	0.590941	+	1.02354i
$899$	−3.09159e6	+	5.35479e6i	−0.127580	+	0.220975i
$900$	−4.59537e6	+	7.95941e6i	−0.189110	+	0.327548i
$901$	−1.49053e7	−	2.58168e7i	−0.611687	−	1.05947i
$902$	−1.29405e6			−0.0529583
$903$		0			0
$904$	4.06815e7			1.65568
$905$	−2.77037e6	−	4.79842e6i	−0.112439	−	0.194750i
$906$	1.58988e7	−	2.75376e7i	0.643494	−	1.11456i
$907$	584680.	−	1.01270e6i	0.0235993	−	0.0408753i	−0.853985	−	0.520298i	$-0.825821\pi$
$907$	584680.	−	1.01270e6i	0.0235993	−	0.0408753i	0.877584	+	0.479423i	$0.159154\pi$
$908$	1.55323e7	+	2.69027e7i	0.625202	+	1.08288i
$909$	−2.03658e6			−0.0817506
$910$		0			0
$911$	2.74389e7			1.09539			0.547697	−	0.836677i	$-0.315505\pi$
$911$	2.74389e7			1.09539			0.547697	+	0.836677i	$0.315505\pi$
$912$	2.05441e6	+	3.55835e6i	0.0817901	+	0.141665i
$913$	−4.37462e6	+	7.57707e6i	−0.173685	+	0.300832i
$914$	−8.18948e6	+	1.41846e7i	−0.324258	+	0.561632i
$915$	307991.	+	533455.i	0.0121614	+	0.0210642i
$916$	−2.93781e7			−1.15687
$917$		0			0
$918$	6.88423e6			0.269618
$919$	−5.51091e6	−	9.54518e6i	−0.215246	−	0.372817i	0.738103	−	0.674688i	$-0.235722\pi$
$919$	−5.51091e6	−	9.54518e6i	−0.215246	−	0.372817i	−0.953349	+	0.301872i	$0.902389\pi$
$920$	2.62747e7	−	4.55092e7i	1.02345	−	1.77268i
$921$	−6.06794e6	+	1.05100e7i	−0.235718	+	0.408275i
$922$	3.21932e7	+	5.57602e7i	1.24720	+	2.16022i
$923$	−3.31444e7			−1.28058
$924$		0			0
$925$	−5.67367e6			−0.218027
$926$	2.41246e7	+	4.17851e7i	0.924557	+	1.60138i
$927$	−6.51050e6	+	1.12765e7i	−0.248837	+	0.430998i
$928$	1.55587e6	−	2.69484e6i	0.0593065	−	0.102722i
$929$	2.12526e6	+	3.68105e6i	0.0807927	+	0.139937i	0.903591	−	0.428397i	$-0.140921\pi$
$929$	2.12526e6	+	3.68105e6i	0.0807927	+	0.139937i	−0.822798	+	0.568334i	$0.807588\pi$
$930$	4.97452e7			1.88601
$931$		0			0
$932$	−2.04559e7			−0.771398
$933$	−1.49877e7	−	2.59595e7i	−0.563679	−	0.976320i
$934$	2.15108e7	−	3.72578e7i	0.806844	−	1.39749i
$935$	−2.02206e7	+	3.50232e7i	−0.756425	+	1.31017i
$936$	−4.90372e6	−	8.49349e6i	−0.182951	−	0.316881i
$937$	−3.75738e7			−1.39809			−0.699046	−	0.715077i	$-0.746392\pi$
$937$	−3.75738e7			−1.39809			−0.699046	+	0.715077i	$0.746392\pi$
$938$		0			0
$939$	2.55303e7			0.944915
$940$	−3.29279e7	−	5.70328e7i	−1.21547	−	2.10526i
$941$	3.43521e6	−	5.94997e6i	0.126468	−	0.219049i	−0.795838	−	0.605510i	$-0.792969\pi$
$941$	3.43521e6	−	5.94997e6i	0.126468	−	0.219049i	0.922306	+	0.386461i	$0.126303\pi$
$942$	−1.65109e6	+	2.85977e6i	−0.0606239	+	0.105004i
$943$	396775.	+	687235.i	0.0145300	+	0.0251667i
$944$	3.45476e6			0.126179
$945$		0			0
$946$	−9.21446e7			−3.34767
$947$	1.15462e7	+	1.99985e7i	0.418372	+	0.724641i	0.995776	−	0.0918172i	$-0.0292676\pi$
$947$	1.15462e7	+	1.99985e7i	0.418372	+	0.724641i	−0.577404	+	0.816459i	$0.695934\pi$
$948$	−1.12953e7	+	1.95641e7i	−0.408204	+	0.707031i
$949$	−7.23161e6	+	1.25255e7i	−0.260657	+	0.451471i
$950$	−1.29792e7	−	2.24806e7i	−0.466592	−	0.808162i
$951$	−9.79551e6			−0.351217
$952$		0			0
$953$	−2.95399e7			−1.05360			−0.526802	−	0.849988i	$-0.676609\pi$
$953$	−2.95399e7			−1.05360			−0.526802	+	0.849988i	$0.676609\pi$
$954$	−1.12724e7	−	1.95244e7i	−0.401002	−	0.694555i
$955$	−9.75709e6	+	1.68998e7i	−0.346188	+	0.599615i
$956$	−1.04431e7	+	1.80880e7i	−0.369559	+	0.640096i
$957$	−1.90078e6	−	3.29224e6i	−0.0670890	−	0.116202i
$958$	−2.70919e6			−0.0953730
$959$		0			0
$960$	−3.19261e7			−1.11807
$961$	−1.93581e7	−	3.35292e7i	−0.676166	−	1.17115i
$962$	7.03511e6	−	1.21852e7i	0.245094	−	0.424516i
$963$	3.82221e6	−	6.62026e6i	0.132815	−	0.230043i
$964$	−4.80664e7	−	8.32535e7i	−1.66590	−	2.88543i
$965$	−1.15009e6			−0.0397569
$966$		0			0
$967$	1.49151e7			0.512931			0.256466	−	0.966553i	$-0.417442\pi$
$967$	1.49151e7			0.512931			0.256466	+	0.966553i	$0.417442\pi$
$968$	1.73880e7	+	3.01170e7i	0.596434	+	1.03305i
$969$	−6.19347e6	+	1.07274e7i	−0.211897	+	0.367016i
$970$	4.35081e6	−	7.53582e6i	0.148471	−	0.257159i
$971$	7.74150e6	+	1.34087e7i	0.263498	+	0.456391i	0.967169	−	0.254134i	$-0.0817905\pi$
$971$	7.74150e6	+	1.34087e7i	0.263498	+	0.456391i	−0.703671	+	0.710526i	$0.748457\pi$
$972$	3.31676e6			0.112603
$973$		0			0
$974$	7.33992e7			2.47910
$975$	4.84974e6	+	8.39999e6i	0.163383	+	0.282988i
$976$	159155.	−	275665.i	0.00534807	−	0.00926313i
$977$	1.41714e7	−	2.45455e7i	0.474980	−	0.822690i	−0.524609	−	0.851343i	$-0.675788\pi$
$977$	1.41714e7	−	2.45455e7i	0.474980	−	0.822690i	0.999589	+	0.0286531i	$0.00912183\pi$
$978$	−2.01942e7	−	3.49773e7i	−0.675117	−	1.16934i
$979$	7.64410e6			0.254900
$980$		0			0
$981$	−6.75487e6			−0.224101
$982$	1.47640e7	+	2.55720e7i	0.488569	+	0.846226i
$983$	1.28497e7	−	2.22563e7i	0.424139	−	0.734630i	−0.572201	−	0.820114i	$-0.693910\pi$
$983$	1.28497e7	−	2.22563e7i	0.424139	−	0.734630i	0.996340	+	0.0854834i	$0.0272434\pi$
$984$	−251057.	+	434843.i	−0.00826578	+	0.0143168i
$985$	−3.70223e7	−	6.41245e7i	−1.21583	−	2.10588i
$986$	−7.11518e6			−0.233074
$987$		0			0
$988$	4.10106e7			1.33661
$989$	2.82530e7	+	4.89355e7i	0.918487	+	1.59087i
$990$	−1.52922e7	+	2.64869e7i	−0.495887	+	0.858901i
$991$	−2.23202e7	+	3.86598e7i	−0.721962	+	1.25048i	0.238250	+	0.971204i	$0.423426\pi$
$991$	−2.23202e7	+	3.86598e7i	−0.721962	+	1.25048i	−0.960212	+	0.279271i	$0.909907\pi$
$992$	1.69460e7	+	2.93514e7i	0.546750	+	0.947000i
$993$	1.17499e7			0.378148
$994$		0			0
$995$	6.32461e7			2.02524
$996$	3.94479e6	+	6.83257e6i	0.126001	+	0.218241i
$997$	1.15277e7	−	1.99665e7i	0.367286	−	0.636158i	−0.621854	−	0.783133i	$-0.713620\pi$
$997$	1.15277e7	−	1.99665e7i	0.367286	−	0.636158i	0.989140	+	0.146975i	$0.0469537\pi$
$998$	3.15764e7	−	5.46919e7i	1.00354	−	1.73819i
$999$	1.02376e6	+	1.77320e6i	0.0324551	+	0.0562140i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.e.l.67.2		4
7.2	even	3	inner	147.6.e.l.79.2		4
7.3	odd	6		147.6.a.i.1.1		2
7.4	even	3		147.6.a.k.1.1		2
7.5	odd	6		21.6.e.b.16.2	yes	4
7.6	odd	2		21.6.e.b.4.2	✓	4
21.5	even	6		63.6.e.c.37.1		4
21.11	odd	6		441.6.a.s.1.2		2
21.17	even	6		441.6.a.t.1.2		2
21.20	even	2		63.6.e.c.46.1		4
28.19	even	6		336.6.q.e.289.2		4
28.27	even	2		336.6.q.e.193.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.e.b.4.2	✓	4	7.6	odd	2
21.6.e.b.16.2	yes	4	7.5	odd	6
63.6.e.c.37.1		4	21.5	even	6
63.6.e.c.46.1		4	21.20	even	2
147.6.a.i.1.1		2	7.3	odd	6
147.6.a.k.1.1		2	7.4	even	3
147.6.e.l.67.2		4	1.1	even	1	trivial
147.6.e.l.79.2		4	7.2	even	3	inner
336.6.q.e.193.2		4	28.27	even	2
336.6.q.e.289.2		4	28.19	even	6
441.6.a.s.1.2		2	21.11	odd	6
441.6.a.t.1.2		2	21.17	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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.69493 + 8.13186i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-28.0848 + 48.6443i) q^{4} +(-35.8645 - 62.1192i) q^{5} -84.5088 q^{6} -226.949 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\)	\(q+(4.69493 + 8.13186i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-28.0848 + 48.6443i) q^{4} +(-35.8645 - 62.1192i) q^{5} -84.5088 q^{6} -226.949 q^{8} +(-40.5000 - 70.1481i) q^{9} +(336.763 - 583.291i) q^{10} +(280.305 - 485.503i) q^{11} +(-252.763 - 437.799i) q^{12} -533.509 q^{13} +645.562 q^{15} +(-166.798 - 288.903i) q^{16} +(502.850 - 870.962i) q^{17} +(380.290 - 658.681i) q^{18} +(684.263 + 1185.18i) q^{19} +4028.99 q^{20} +5264.05 q^{22} +(-1614.04 - 2795.60i) q^{23} +(1021.27 - 1768.90i) q^{24} +(-1010.03 + 1749.42i) q^{25} +(-2504.79 - 4338.42i) q^{26} +729.000 q^{27} -753.456 q^{29} +(3030.87 + 5249.62i) q^{30} +(4103.21 - 7106.97i) q^{31} +(-2064.97 + 3576.64i) q^{32} +(2522.75 + 4369.52i) q^{33} +9443.39 q^{34} +4549.74 q^{36} +(1404.33 + 2432.37i) q^{37} +(-6425.14 + 11128.7i) q^{38} +(2400.79 - 4158.29i) q^{39} +(8139.43 + 14097.9i) q^{40} -245.827 q^{41} -17504.5 q^{43} +(15744.6 + 27270.5i) q^{44} +(-2905.03 + 5031.65i) q^{45} +(15155.6 - 26250.3i) q^{46} +(-8172.74 - 14155.6i) q^{47} +3002.37 q^{48} -18968.1 q^{50} +(4525.65 + 7838.66i) q^{51} +(14983.5 - 25952.2i) q^{52} +(14820.8 - 25670.4i) q^{53} +(3422.61 + 5928.13i) q^{54} -40212.0 q^{55} -12316.7 q^{57} +(-3537.43 - 6127.00i) q^{58} +(-5178.05 + 8968.65i) q^{59} +(-18130.5 + 31402.9i) q^{60} +(477.089 + 826.343i) q^{61} +77057.2 q^{62} -49454.8 q^{64} +(19134.0 + 33141.1i) q^{65} +(-23688.2 + 41029.2i) q^{66} +(9907.60 - 17160.5i) q^{67} +(28244.9 + 48921.6i) q^{68} +29052.7 q^{69} +62125.4 q^{71} +(9191.45 + 15920.1i) q^{72} +(13554.8 - 23477.6i) q^{73} +(-13186.5 + 22839.7i) q^{74} +(-9090.27 - 15744.8i) q^{75} -76869.6 q^{76} +45086.2 q^{78} +(-22343.7 - 38700.4i) q^{79} +(-11964.3 + 20722.8i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-1154.14 - 1999.03i) q^{82} -15606.6 q^{83} -72137.9 q^{85} +(-82182.5 - 142344. i) q^{86} +(3390.55 - 5872.61i) q^{87} +(-63615.0 + 110184. i) q^{88} +(6817.66 + 11808.5i) q^{89} -54555.6 q^{90} +181320. q^{92} +(36928.9 + 63962.7i) q^{93} +(76740.9 - 132919. i) q^{94} +(49081.6 - 85011.8i) q^{95} +(-18584.8 - 32189.8i) q^{96} +12919.5 q^{97} -45409.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 18 q^{3} - 65 q^{4} - 33 q^{5} - 54 q^{6} - 750 q^{8} - 162 q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 - 18 * q^3 - 65 * q^4 - 33 * q^5 - 54 * q^6 - 750 * q^8 - 162 * q^9	\( 4 q + 3 q^{2} - 18 q^{3} - 65 q^{4} - 33 q^{5} - 54 q^{6} - 750 q^{8} - 162 q^{9} + 921 q^{10} + 1137 q^{11} - 585 q^{12} - 1850 q^{13} + 594 q^{15} + 895 q^{16} - 324 q^{17} + 243 q^{18} + 2311 q^{19} + 7374 q^{20} + 3162 q^{22} - 1596 q^{23} + 3375 q^{24} - 395 q^{25} - 2508 q^{26} + 2916 q^{27} - 4434 q^{29} + 8289 q^{30} + 4294 q^{31} - 1017 q^{32} + 10233 q^{33} + 35880 q^{34} + 10530 q^{36} + 19109 q^{37} - 6828 q^{38} + 8325 q^{39} + 10545 q^{40} + 25716 q^{41} - 5542 q^{43} + 36579 q^{44} - 2673 q^{45} + 40740 q^{46} - 23160 q^{47} - 16110 q^{48} - 58704 q^{50} - 2916 q^{51} + 33424 q^{52} + 31653 q^{53} + 2187 q^{54} - 35778 q^{55} - 41598 q^{57} + 2277 q^{58} + 41097 q^{59} - 33183 q^{60} + 42052 q^{61} + 204114 q^{62} - 60062 q^{64} + 23106 q^{65} - 14229 q^{66} - 30763 q^{67} + 44748 q^{68} + 28728 q^{69} + 204192 q^{71} + 30375 q^{72} - 28577 q^{73} + 77784 q^{74} - 3555 q^{75} - 170384 q^{76} + 45144 q^{78} + 18464 q^{79} - 71511 q^{80} - 13122 q^{81} - 86040 q^{82} - 122358 q^{83} - 247272 q^{85} - 258510 q^{86} + 19953 q^{87} - 212565 q^{88} + 29322 q^{89} - 149202 q^{90} + 333816 q^{92} + 38646 q^{93} + 109938 q^{94} + 61662 q^{95} - 9153 q^{96} + 19582 q^{97} - 184194 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 - 18 * q^3 - 65 * q^4 - 33 * q^5 - 54 * q^6 - 750 * q^8 - 162 * q^9 + 921 * q^10 + 1137 * q^11 - 585 * q^12 - 1850 * q^13 + 594 * q^15 + 895 * q^16 - 324 * q^17 + 243 * q^18 + 2311 * q^19 + 7374 * q^20 + 3162 * q^22 - 1596 * q^23 + 3375 * q^24 - 395 * q^25 - 2508 * q^26 + 2916 * q^27 - 4434 * q^29 + 8289 * q^30 + 4294 * q^31 - 1017 * q^32 + 10233 * q^33 + 35880 * q^34 + 10530 * q^36 + 19109 * q^37 - 6828 * q^38 + 8325 * q^39 + 10545 * q^40 + 25716 * q^41 - 5542 * q^43 + 36579 * q^44 - 2673 * q^45 + 40740 * q^46 - 23160 * q^47 - 16110 * q^48 - 58704 * q^50 - 2916 * q^51 + 33424 * q^52 + 31653 * q^53 + 2187 * q^54 - 35778 * q^55 - 41598 * q^57 + 2277 * q^58 + 41097 * q^59 - 33183 * q^60 + 42052 * q^61 + 204114 * q^62 - 60062 * q^64 + 23106 * q^65 - 14229 * q^66 - 30763 * q^67 + 44748 * q^68 + 28728 * q^69 + 204192 * q^71 + 30375 * q^72 - 28577 * q^73 + 77784 * q^74 - 3555 * q^75 - 170384 * q^76 + 45144 * q^78 + 18464 * q^79 - 71511 * q^80 - 13122 * q^81 - 86040 * q^82 - 122358 * q^83 - 247272 * q^85 - 258510 * q^86 + 19953 * q^87 - 212565 * q^88 + 29322 * q^89 - 149202 * q^90 + 333816 * q^92 + 38646 * q^93 + 109938 * q^94 + 61662 * q^95 - 9153 * q^96 + 19582 * q^97 - 184194 * q^99

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