LMFDB - Embedded newform 147.6.e.l.79.2

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			79.2
Root			$-3.69493 + 2.71062i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.6.e.l.67.2

$q$-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} +(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} + 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}+ \cdots - 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

Character values

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

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

Coefficient data

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

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

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

$2$	4.69493	−	8.13186i	0.829955	−	1.43752i	−0.0681181	−	0.997677i	$-0.521699\pi$
$2$	4.69493	−	8.13186i	0.829955	−	1.43752i	0.898073	−	0.439847i	$-0.144967\pi$
$3$	−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	0.343519	+	0.939146i	$0.388381\pi$
$5$	−35.8645	+	62.1192i	−0.641564	+	1.11122i	−0.985084	+	0.172076i	$0.944952\pi$
$6$	−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	0.968996	+	0.247076i	$0.0794698\pi$
$11$	280.305	+	485.503i	0.698472	+	1.20979i	−0.270524	+	0.962713i	$0.587197\pi$
$12$	−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	0.996135	−	0.0878311i	$-0.0279936\pi$
$17$	502.850	+	870.962i	0.422004	+	0.730932i	−0.574132	+	0.818763i	$0.694660\pi$
$18$	380.290	+	658.681i	0.276652	+	0.479175i
$19$	684.263	−	1185.18i	0.434850	−	0.753182i	−0.562434	−	0.826842i	$-0.690135\pi$
$19$	684.263	−	1185.18i	0.434850	−	0.753182i	0.997283	+	0.0736606i	$0.0234682\pi$
$20$	4028.99			2.25228
$21$		0			0
$22$	5264.05			2.31880
$23$	−1614.04	+	2795.60i	−0.636201	+	1.10193i	0.350058	+	0.936728i	$0.386162\pi$
$23$	−1614.04	+	2795.60i	−0.636201	+	1.10193i	−0.986259	+	0.165205i	$0.947171\pi$
$24$	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	0.939254	+	0.343222i	$0.111518\pi$
$31$	4103.21	+	7106.97i	0.766866	+	1.32825i	−0.172389	+	0.985029i	$0.555148\pi$
$32$	−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	−0.769301	−	0.638887i	$-0.779395\pi$
$37$	1404.33	−	2432.37i	0.168642	−	0.292096i	0.937943	+	0.346791i	$0.112729\pi$
$38$	−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	0.459258	+	0.888303i	$0.348115\pi$
$47$	−8172.74	+	14155.6i	−0.539663	+	0.934725i	−0.998922	+	0.0464219i	$0.985218\pi$
$48$	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	0.959081	+	0.283133i	$0.0913739\pi$
$53$	14820.8	+	25670.4i	0.724741	+	1.25529i	−0.234340	+	0.972155i	$0.575293\pi$
$54$	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	0.752801	−	0.658248i	$-0.228702\pi$
$59$	−5178.05	−	8968.65i	−0.193659	−	0.335426i	−0.946460	+	0.322821i	$0.895369\pi$
$60$	−18130.5	−	31402.9i	−0.650176	−	1.12614i
$61$	477.089	−	826.343i	0.0164163	−	0.0284339i	−0.857701	−	0.514150i	$-0.828108\pi$
$61$	477.089	−	826.343i	0.0164163	−	0.0284339i	0.874117	+	0.485716i	$0.161441\pi$
$62$	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	0.968768	−	0.247967i	$-0.0797626\pi$
$67$	9907.60	+	17160.5i	0.269638	+	0.467027i	−0.699130	+	0.714994i	$0.746429\pi$
$68$	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	0.975611	−	0.219509i	$-0.0704454\pi$
$73$	13554.8	+	23477.6i	0.297705	+	0.515641i	−0.677905	+	0.735149i	$0.737112\pi$
$74$	−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	−0.994062	−	0.108812i	$-0.965295\pi$
$79$	−22343.7	+	38700.4i	−0.402798	+	0.697666i	0.591265	+	0.806477i	$0.298629\pi$
$80$	−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	−0.816796	−	0.576926i	$-0.804252\pi$
$89$	6817.66	−	11808.5i	0.0912347	−	0.158023i	0.908031	+	0.418903i	$0.137585\pi$
$90$	−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	0.920802	−	0.390029i	$-0.127535\pi$
$101$	12571.5	+	21774.4i	0.122626	+	0.212394i	−0.798177	+	0.602424i	$0.794202\pi$
$102$	−42495.3	−	73604.0i	−0.404427	−	0.700488i
$103$	−80376.6	+	139216.i	−0.746511	+	1.29300i	0.202974	+	0.979184i	$0.434939\pi$
$103$	−80376.6	+	139216.i	−0.746511	+	1.29300i	−0.949485	+	0.313811i	$0.898394\pi$
$104$	121079.			1.09771
$105$		0			0
$106$	278331.			2.40601
$107$	47187.8	−	81731.6i	0.398446	−	0.690129i	−0.595088	−	0.803661i	$-0.702883\pi$
$107$	47187.8	−	81731.6i	0.398446	−	0.690129i	0.993534	+	0.113531i	$0.0362162\pi$
$108$	−20473.8	−	35461.7i	−0.168904	−	0.292550i
$109$	41696.7	+	72220.9i	0.336152	+	0.582233i	0.983705	−	0.179788i	$-0.0575410\pi$
$109$	41696.7	+	72220.9i	0.336152	+	0.582233i	−0.647553	+	0.762020i	$0.724208\pi$
$110$	−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	−0.791764	−	0.610827i	$-0.790837\pi$
$131$	26144.9	−	45284.3i	0.133110	−	0.230553i	0.924874	+	0.380274i	$0.124170\pi$
$132$	−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	0.855118	−	0.518433i	$-0.173484\pi$
$137$	−4705.05	−	8149.39i	−0.0214172	−	0.0370957i	−0.876535	+	0.481337i	$0.840151\pi$
$138$	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	−0.669828	−	0.742516i	$-0.733632\pi$
$149$	83500.8	−	144628.i	0.308123	−	0.533685i	0.977952	+	0.208830i	$0.0669657\pi$
$150$	85356.4	+	147842.i	0.309748	+	0.536499i
$151$	−188132.	−	325855.i	−0.671461	−	1.16300i	−0.977490	−	0.210982i	$-0.932334\pi$
$151$	−188132.	−	325855.i	−0.671461	−	1.16300i	0.306029	−	0.952022i	$-0.401000\pi$
$152$	−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	0.895920	−	0.444215i	$-0.146517\pi$
$157$	19537.5	+	33840.0i	0.0632587	+	0.109567i	−0.832662	+	0.553782i	$0.813184\pi$
$158$	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	−0.262428	−	0.964951i	$-0.584523\pi$
$163$	238959.	−	413890.i	0.704458	−	1.22016i	0.966887	−	0.255206i	$-0.0821433\pi$
$164$	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	−0.833693	−	0.552228i	$-0.813778\pi$
$173$	24169.1	−	41862.1i	0.0613968	−	0.106342i	0.895090	+	0.445886i	$0.147111\pi$
$174$	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	0.937253	−	0.348650i	$-0.113360\pi$
$179$	71455.3	+	123764.i	0.166687	+	0.288711i	−0.770566	+	0.637360i	$0.780026\pi$
$180$	−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	−0.968810	−	0.247805i	$-0.920291\pi$
$191$	−136027.	+	235606.i	−0.269800	+	0.467307i	0.699010	+	0.715112i	$0.253624\pi$
$192$	222546.	+	385462.i	0.435680	+	0.754620i
$193$	8016.89	+	13885.7i	0.0154922	+	0.0268333i	0.873668	−	0.486523i	$-0.161735\pi$
$193$	8016.89	+	13885.7i	0.0154922	+	0.0268333i	−0.858175	+	0.513357i	$0.828402\pi$
$194$	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	−0.926470	−	0.376369i	$-0.877173\pi$
$199$	−440868.	−	763606.i	−0.789180	−	1.36690i	0.137290	−	0.990531i	$-0.456161\pi$
$200$	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	0.987319	−	0.158748i	$-0.0507459\pi$
$227$	276524.	+	478954.i	0.356179	+	0.616921i	−0.631140	+	0.775669i	$0.717413\pi$
$228$	345913.	+	599139.i	0.440687	+	0.763292i
$229$	261512.	−	452952.i	0.329536	−	0.570773i	−0.652884	−	0.757458i	$-0.726441\pi$
$229$	261512.	−	452952.i	0.329536	−	0.570773i	0.982420	+	0.186685i	$0.0597743\pi$
$230$	−2.17420e6			−2.71006
$231$		0			0
$232$	170996.			0.208577
$233$	182090.	−	315390.i	0.219734	−	0.380590i	−0.734993	−	0.678075i	$-0.762814\pi$
$233$	182090.	−	315390.i	0.219734	−	0.380590i	0.954727	+	0.297485i	$0.0961477\pi$
$234$	−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	−0.747391	−	0.664384i	$-0.768694\pi$
$241$	−855737.	−	1.48218e6i	−0.949069	−	1.64384i	−0.201678	−	0.979452i	$-0.564640\pi$
$242$	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	−0.930212	−	0.367023i	$-0.880377\pi$
$257$	−155920.	+	270061.i	−0.147254	+	0.255052i	0.782957	+	0.622075i	$0.213710\pi$
$258$	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	0.606681	−	0.794946i	$-0.292501\pi$
$263$	−431983.	−	748216.i	−0.385103	−	0.667018i	−0.991783	+	0.127928i	$0.959167\pi$
$264$	−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	0.527347	−	0.849650i	$-0.323187\pi$
$269$	−560346.	−	970548.i	−0.472145	−	0.817779i	−0.999492	+	0.0318707i	$0.989854\pi$
$270$	245500.	+	425219.i	0.204948	+	0.354980i
$271$	570058.	−	987369.i	0.471515	−	0.816688i	−0.527954	−	0.849273i	$-0.677041\pi$
$271$	570058.	−	987369.i	0.471515	−	0.816688i	0.999469	+	0.0325848i	$0.0103739\pi$
$272$	−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	0.932878	+	0.360193i	$0.117289\pi$
$277$	994005.	+	1.72167e6i	0.778375	+	1.34819i	−0.154502	+	0.987992i	$0.549377\pi$
$278$	−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	0.682980	+	0.730437i	$0.260684\pi$
$283$	1.31237e6	+	2.27308e6i	0.974067	+	1.68713i	0.291087	+	0.956697i	$0.405983\pi$
$284$	−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	−0.675507	−	0.737353i	$-0.736075\pi$
$311$	−1.66530e6	−	2.88439e6i	−0.976320	−	1.69104i	−0.300813	−	0.953683i	$-0.597258\pi$
$312$	−544858.	−	943721.i	−0.316881	−	0.548854i
$313$	−1.41835e6	+	2.45666e6i	−0.818320	+	1.41737i	0.0885991	+	0.996067i	$0.471761\pi$
$313$	−1.41835e6	+	2.45666e6i	−0.818320	+	1.41737i	−0.906919	+	0.421305i	$0.861572\pi$
$314$	366909.			0.210007
$315$		0			0
$316$	2.51007e6			1.41406
$317$	544195.	−	942574.i	0.304163	−	0.526826i	−0.672912	−	0.739723i	$-0.734957\pi$
$317$	544195.	−	942574.i	0.304163	−	0.526826i	0.977075	+	0.212897i	$0.0682899\pi$
$318$	−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	−0.982012	−	0.188817i	$-0.939535\pi$
$331$	−652773.	+	1.13064e6i	−0.327485	+	0.567221i	0.654527	+	0.756039i	$0.272868\pi$
$332$	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	0.991420	−	0.130713i	$-0.0417265\pi$
$347$	857958.	+	1.48603e6i	0.382510	+	0.662526i	−0.608911	+	0.793239i	$0.708393\pi$
$348$	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	0.916222	+	0.400672i	$0.131223\pi$
$353$	1.88490e6	+	3.26474e6i	0.805103	+	1.39448i	−0.111119	+	0.993807i	$0.535443\pi$
$354$	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	−0.993120	−	0.117099i	$-0.962641\pi$
$359$	−964935.	+	1.67132e6i	−0.395150	+	0.684420i	0.597970	+	0.801518i	$0.295974\pi$
$360$	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	0.998895	−	0.0469885i	$-0.0149624\pi$
$367$	1.18371e6	+	2.05025e6i	0.458754	+	0.794586i	−0.540141	+	0.841575i	$0.681629\pi$
$368$	−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	0.322627	+	0.946526i	$0.395434\pi$
$373$	−1.76914e6	+	3.06425e6i	−0.658402	+	1.14039i	−0.981029	+	0.193860i	$0.937899\pi$
$374$	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	−0.544385	−	0.838836i	$-0.683237\pi$
$383$	1.30407e6	−	2.25872e6i	0.454261	−	0.786802i	0.998645	+	0.0520333i	$0.0165702\pi$
$384$	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	0.999560	−	0.0296466i	$-0.00943818\pi$
$389$	1.41498e6	+	2.45081e6i	0.474106	+	0.821175i	−0.525455	+	0.850821i	$0.676105\pi$
$390$	−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	−0.992044	−	0.125888i	$-0.959822\pi$
$397$	−1.21531e6	+	2.10498e6i	−0.387000	+	0.670303i	0.605045	+	0.796191i	$0.293155\pi$
$398$	−8.27939e6			−2.61993
$399$		0			0
$400$	673885.			0.210589
$401$	1.21592e6	−	2.10604e6i	0.377611	−	0.654041i	−0.613103	−	0.790003i	$-0.710079\pi$
$401$	1.21592e6	−	2.10604e6i	0.377611	−	0.654041i	0.990714	+	0.135962i	$0.0434124\pi$
$402$	−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	−0.966448	−	0.256863i	$-0.917311\pi$
$409$	−2.38733e6	−	4.13497e6i	−0.705674	−	1.22226i	0.260774	−	0.965400i	$-0.416022\pi$
$410$	−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	0.997577	−	0.0695651i	$-0.0221612\pi$
$431$	1.69124e6	+	2.92932e6i	0.438544	+	0.759580i	−0.559034	+	0.829145i	$0.688828\pi$
$432$	−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	−0.460052	−	0.887892i	$-0.652169\pi$
$439$	2.17610e6	−	3.76911e6i	0.538911	−	0.933421i	0.998963	−	0.0455294i	$-0.0144975\pi$
$440$	9.12610e6			2.24726
$441$		0			0
$442$	−5.03813e6			−1.22663
$443$	2.55280e6	−	4.42158e6i	0.618027	−	1.07045i	−0.371819	−	0.928305i	$-0.621266\pi$
$443$	2.55280e6	−	4.42158e6i	0.618027	−	1.07045i	0.989845	−	0.142148i	$-0.0454010\pi$
$444$	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	−0.751667	−	0.659542i	$-0.770750\pi$
$457$	872162.	−	1.51063e6i	0.195347	−	0.338351i	0.947014	+	0.321192i	$0.104083\pi$
$458$	−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	−0.999872	−	0.0160029i	$-0.994906\pi$
$467$	−2.29085e6	+	3.96788e6i	−0.486077	+	0.841910i	0.513795	+	0.857913i	$0.328239\pi$
$468$	−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	0.851304	−	0.524673i	$-0.175812\pi$
$479$	−144261.	−	249868.i	−0.0287284	−	0.0497590i	−0.880032	+	0.474914i	$0.842479\pi$
$480$	−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	0.949369	+	0.314162i	$0.101723\pi$
$487$	3.90842e6	+	6.76959e6i	0.746757	+	1.29342i	−0.202613	+	0.979259i	$0.564943\pi$
$488$	−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	0.387541	+	0.921852i	$0.373324\pi$
$499$	−3.36281e6	+	5.82456e6i	−0.604577	+	1.04716i	−0.992118	+	0.125305i	$0.960009\pi$
$500$	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	0.188981	+	0.981981i	$0.439481\pi$
$509$	−4.41851e6	+	7.65308e6i	−0.755930	+	1.30931i	−0.944911	+	0.327328i	$0.893852\pi$
$510$	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	0.892705	−	0.450641i	$-0.148805\pi$
$521$	347492.	+	601874.i	0.0560855	+	0.0971430i	−0.836619	+	0.547784i	$0.815471\pi$
$522$	−286531.	−	496287.i	−0.0460252	−	0.0797181i
$523$	1.79105e6	−	3.10219e6i	0.286321	−	0.495923i	−0.686607	−	0.727028i	$-0.740901\pi$
$523$	1.79105e6	−	3.10219e6i	0.286321	−	0.495923i	0.972929	+	0.231105i	$0.0742342\pi$
$524$	−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	−0.611395	−	0.791325i	$-0.709391\pi$
$541$	2.58423e6	−	4.47602e6i	0.379610	−	0.657504i	0.991005	+	0.133821i	$0.0427248\pi$
$542$	−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	0.964246	+	0.265009i	$0.0853748\pi$
$557$	5.21063e6	+	9.02508e6i	0.711627	+	1.23257i	−0.252619	+	0.967566i	$0.581292\pi$
$558$	−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	0.518396	−	0.855141i	$-0.326529\pi$
$563$	−3.62039e6	−	6.27069e6i	−0.481375	−	0.833767i	−0.999772	+	0.0213739i	$0.993196\pi$
$564$	−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	−0.894169	−	0.447730i	$-0.852233\pi$
$569$	−458268.	+	793743.i	−0.0593388	+	0.102778i	0.834830	+	0.550508i	$0.185566\pi$
$570$	−4.14782e6	−	7.18424e6i	−0.534728	−	0.926177i
$571$	−5.03538e6	−	8.72154e6i	−0.646312	−	1.11944i	−0.983997	−	0.178186i	$-0.942977\pi$
$571$	−5.03538e6	−	8.72154e6i	−0.646312	−	1.11944i	0.337685	−	0.941259i	$-0.390356\pi$
$572$	−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	0.956247	+	0.292560i	$0.0945070\pi$
$577$	5.84987e6	+	1.01323e7i	0.731488	+	1.26697i	−0.224760	+	0.974414i	$0.572160\pi$
$578$	−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	0.123660	−	0.992325i	$-0.460537\pi$
$593$	7.88850e6	−	1.36633e7i	0.921208	−	1.59558i	0.797548	−	0.603255i	$-0.206130\pi$
$594$	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	−0.911072	−	0.412248i	$-0.864744\pi$
$599$	−7.13541e6	−	1.23589e7i	−0.812553	−	1.40738i	0.0985183	−	0.995135i	$-0.468590\pi$
$600$	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	−0.947262	−	0.320459i	$-0.896163\pi$
$607$	−1.78017e6	+	3.08335e6i	−0.196106	+	0.339665i	0.751157	+	0.660124i	$0.229496\pi$
$608$	−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	0.953484	+	0.301445i	$0.0974688\pi$
$613$	6.86420e6	+	1.18891e7i	0.737800	+	1.27791i	−0.215683	+	0.976463i	$0.569198\pi$
$614$	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	0.999167	−	0.0408136i	$-0.0129950\pi$
$619$	4.42555e6	+	7.66527e6i	0.464238	+	0.804083i	−0.534929	+	0.844897i	$0.679662\pi$
$620$	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	0.918820	+	0.394677i	$0.129144\pi$
$641$	8.33473e6	+	1.44362e7i	0.801210	+	1.38774i	−0.117610	+	0.993060i	$0.537523\pi$
$642$	−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	−0.998971	−	0.0453435i	$-0.985562\pi$
$647$	−5.73656e6	−	9.93601e6i	−0.538754	−	0.933150i	0.460217	−	0.887806i	$-0.347772\pi$
$648$	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	−0.387293	−	0.921957i	$-0.626590\pi$
$653$	6.59005e6	−	1.14143e7i	0.604791	−	1.04753i	0.992084	−	0.125573i	$-0.0400768\pi$
$654$	−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	0.910884	−	0.412662i	$-0.135401\pi$
$661$	1.10160e6	+	1.90802e6i	0.0980661	+	0.169856i	−0.812818	+	0.582518i	$0.802068\pi$
$662$	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	0.0790842	+	0.996868i	$0.474800\pi$
$677$	−9.82377e6	+	1.70153e7i	−0.823771	+	1.42681i	−0.902855	+	0.429945i	$0.858533\pi$
$678$	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	−0.978658	−	0.205498i	$-0.934119\pi$
$683$	−8.13523e6	−	1.40906e7i	−0.667295	−	1.15579i	0.311363	−	0.950291i	$-0.399215\pi$
$684$	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	−0.160299	−	0.987069i	$-0.551246\pi$
$691$	9.72335e6	−	1.68413e7i	0.774677	−	1.34178i	0.934976	−	0.354712i	$-0.115421\pi$
$692$	−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	−0.894134	−	0.447800i	$-0.852208\pi$
$709$	−793193.	+	1.37385e6i	−0.0592603	+	0.102642i	0.834873	+	0.550442i	$0.185541\pi$
$710$	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	0.326512	+	0.945193i	$0.394127\pi$
$719$	−9.08376e6	+	1.57335e7i	−0.655305	+	1.13502i	−0.981817	+	0.189829i	$0.939207\pi$
$720$	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	−0.914568	−	0.404432i	$-0.867469\pi$
$733$	−1.55701e6	+	2.69681e6i	−0.107036	+	0.185392i	0.807532	+	0.589824i	$0.200803\pi$
$734$	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	0.671137	−	0.741333i	$-0.265806\pi$
$739$	−4.54950e6	−	7.87996e6i	−0.306445	−	0.530778i	−0.977582	+	0.210555i	$0.932473\pi$
$740$	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	0.0929698	−	0.995669i	$-0.470364\pi$
$751$	1.40459e7	−	2.43282e7i	0.908759	−	1.57402i	0.815790	−	0.578349i	$-0.196303\pi$
$752$	−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	−0.872113	−	0.489305i	$-0.837250\pi$
$761$	−196591.	+	340506.i	−0.0123056	+	0.0213139i	0.859807	+	0.510619i	$0.170584\pi$
$762$	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	0.906166	−	0.422923i	$-0.138996\pi$
$773$	1.44236e6	+	2.49824e6i	0.0868210	+	0.150378i	−0.819345	+	0.573301i	$0.805663\pi$
$774$	−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	−0.874641	−	0.484771i	$-0.838903\pi$
$787$	−1.48933e7	−	2.57960e7i	−0.857145	−	1.48462i	0.0174963	−	0.999847i	$-0.494430\pi$
$788$	−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	0.864523	−	0.502594i	$-0.167621\pi$
$809$	−55798.5	−	96645.8i	−0.00299744	−	0.00519173i	−0.867520	+	0.497402i	$0.834287\pi$
$810$	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	−0.940934	−	0.338591i	$-0.890050\pi$
$821$	−3.42307e6	+	5.92893e6i	−0.177238	+	0.306986i	0.763695	+	0.645577i	$0.223383\pi$
$822$	397618.	+	688695.i	0.0205252	+	0.0355506i
$823$	2.80605e6	+	4.86022e6i	0.144409	+	0.250125i	0.929152	−	0.369697i	$-0.120538\pi$
$823$	2.80605e6	+	4.86022e6i	0.144409	+	0.250125i	−0.784743	+	0.619821i	$0.787205\pi$
$824$	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	0.999875	−	0.0158177i	$-0.00503515\pi$
$829$	9.62135e6	+	1.66647e7i	0.486239	+	0.842190i	−0.513636	+	0.858008i	$0.671702\pi$
$830$	−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	0.826076	−	0.563558i	$-0.190568\pi$
$857$	−1.61293e6	−	2.79367e6i	−0.0750175	−	0.129934i	−0.901094	+	0.433624i	$0.857235\pi$
$858$	1.26379e7	+	2.18895e7i	0.586079	+	1.01512i
$859$	1.32335e7	−	2.29212e7i	0.611918	−	1.05987i	−0.378999	−	0.925397i	$-0.623732\pi$
$859$	1.32335e7	−	2.29212e7i	0.611918	−	1.05987i	0.990917	−	0.134476i	$-0.0429350\pi$
$860$	−7.05255e7			−3.25162
$861$		0			0
$862$	3.17611e7			1.45589
$863$	−7.92552e6	+	1.37274e7i	−0.362243	+	0.627424i	−0.988330	−	0.152330i	$-0.951322\pi$
$863$	−7.92552e6	+	1.37274e7i	−0.362243	+	0.627424i	0.626086	+	0.779754i	$0.284656\pi$
$864$	−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	−0.654618	−	0.755960i	$-0.727170\pi$
$877$	7.45659e6	−	1.29152e7i	0.327372	−	0.567024i	0.981989	+	0.188936i	$0.0605037\pi$
$878$	−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	−0.611030	−	0.791608i	$-0.709244\pi$
$887$	8.90504e6	−	1.54240e7i	0.380038	−	0.658245i	0.991067	+	0.133363i	$0.0425777\pi$
$888$	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	0.877584	−	0.479423i	$-0.159154\pi$
$907$	584680.	+	1.01270e6i	0.0235993	+	0.0408753i	−0.853985	+	0.520298i	$0.825821\pi$
$908$	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	−0.953349	−	0.301872i	$-0.902389\pi$
$919$	−5.51091e6	+	9.54518e6i	−0.215246	+	0.372817i	0.738103	+	0.674688i	$0.235722\pi$
$920$	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	−0.822798	−	0.568334i	$-0.807588\pi$
$929$	2.12526e6	−	3.68105e6i	0.0807927	−	0.139937i	0.903591	+	0.428397i	$0.140921\pi$
$930$	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	0.922306	−	0.386461i	$-0.126303\pi$
$941$	3.43521e6	+	5.94997e6i	0.126468	+	0.219049i	−0.795838	+	0.605510i	$0.792969\pi$
$942$	−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	−0.577404	−	0.816459i	$-0.695934\pi$
$947$	1.15462e7	−	1.99985e7i	0.418372	−	0.724641i	0.995776	+	0.0918172i	$0.0292676\pi$
$948$	−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	−0.703671	−	0.710526i	$-0.748457\pi$
$971$	7.74150e6	−	1.34087e7i	0.263498	−	0.456391i	0.967169	+	0.254134i	$0.0817905\pi$
$972$	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	0.999589	−	0.0286531i	$-0.00912183\pi$
$977$	1.41714e7	+	2.45455e7i	0.474980	+	0.822690i	−0.524609	+	0.851343i	$0.675788\pi$
$978$	−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	0.996340	−	0.0854834i	$-0.0272434\pi$
$983$	1.28497e7	+	2.22563e7i	0.424139	+	0.734630i	−0.572201	+	0.820114i	$0.693910\pi$
$984$	−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	−0.960212	−	0.279271i	$-0.909907\pi$
$991$	−2.23202e7	−	3.86598e7i	−0.721962	−	1.25048i	0.238250	−	0.971204i	$-0.423426\pi$
$992$	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	0.989140	−	0.146975i	$-0.0469537\pi$
$997$	1.15277e7	+	1.99665e7i	0.367286	+	0.636158i	−0.621854	+	0.783133i	$0.713620\pi$
$998$	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.79.2		4
7.2	even	3		147.6.a.k.1.1		2
7.3	odd	6		21.6.e.b.4.2	✓	4
7.4	even	3	inner	147.6.e.l.67.2		4
7.5	odd	6		147.6.a.i.1.1		2
7.6	odd	2		21.6.e.b.16.2	yes	4
21.2	odd	6		441.6.a.s.1.2		2
21.5	even	6		441.6.a.t.1.2		2
21.17	even	6		63.6.e.c.46.1		4
21.20	even	2		63.6.e.c.37.1		4
28.3	even	6		336.6.q.e.193.2		4
28.27	even	2		336.6.q.e.289.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.e.b.4.2	✓	4	7.3	odd	6
21.6.e.b.16.2	yes	4	7.6	odd	2
63.6.e.c.37.1		4	21.20	even	2
63.6.e.c.46.1		4	21.17	even	6
147.6.a.i.1.1		2	7.5	odd	6
147.6.a.k.1.1		2	7.2	even	3
147.6.e.l.67.2		4	7.4	even	3	inner
147.6.e.l.79.2		4	1.1	even	1	trivial
336.6.q.e.193.2		4	28.3	even	6
336.6.q.e.289.2		4	28.27	even	2
441.6.a.s.1.2		2	21.2	odd	6
441.6.a.t.1.2		2	21.5	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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 18 q^{3} - 65 q^{4} - 33 q^{5} - 54 q^{6} - 750 q^{8} - 162 q^{9} + 921 q^{10} + 1137 q^{11} - 585 q^{12} - 1850 q^{13} + 594 q^{15} + 895 q^{16} - 324 q^{17} + 243 q^{18} + 2311 q^{19}+ \cdots - 184194 q^{99}+O(q^{100}) \) 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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