LMFDB - Embedded newform 21.8.g.b.5.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [21,8,Mod(5,21)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("21.5"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(21, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	21.g (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.56008553517$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.13
Character	$\chi$	$=$	21.5
Dual form			21.8.g.b.17.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(12.6634 + 7.31122i) q^{2} +(44.5268 + 14.2957i) q^{3} +(42.9078 + 74.3185i) q^{4} +(-269.104 + 466.101i) q^{5} +(459.342 + 506.577i) q^{6} +(626.737 - 656.311i) q^{7} -616.838i q^{8} +(1778.27 + 1273.08i) q^{9} +(-6815.54 + 3934.95i) q^{10} +(1644.13 - 949.242i) q^{11} +(848.115 + 3922.56i) q^{12} +431.129i q^{13} +(12735.1 - 3728.92i) q^{14} +(-18645.5 + 16907.0i) q^{15} +(10002.0 - 17324.0i) q^{16} +(-10408.0 - 18027.1i) q^{17} +(13211.2 + 29122.8i) q^{18} +(23102.3 + 13338.1i) q^{19} -46186.6 q^{20} +(37289.0 - 20263.8i) q^{21} +27760.4 q^{22} +(-26678.1 - 15402.6i) q^{23} +(8818.11 - 27465.8i) q^{24} +(-105771. - 183201. i) q^{25} +(-3152.08 + 5459.56i) q^{26} +(60981.1 + 82107.6i) q^{27} +(75668.0 + 18417.3i) q^{28} -40183.4i q^{29} +(-359727. + 77778.2i) q^{30} +(25132.1 - 14510.0i) q^{31} +(184942. - 106777. i) q^{32} +(86778.1 - 18762.7i) q^{33} -304380. i q^{34} +(137250. + 468739. i) q^{35} +(-18311.7 + 186783. i) q^{36} +(-143496. + 248543. i) q^{37} +(195036. + 337812. i) q^{38} +(-6163.27 + 19196.8i) q^{39} +(287509. + 165994. i) q^{40} -309693. q^{41} +(620358. + 16019.1i) q^{42} -47389.8 q^{43} +(141092. + 81459.8i) q^{44} +(-1.07192e6 + 486263. i) q^{45} +(-225223. - 390098. i) q^{46} +(-360027. + 623585. i) q^{47} +(693017. - 628398. i) q^{48} +(-37945.1 - 822668. i) q^{49} -3.09326e6i q^{50} +(-205724. - 951478. i) q^{51} +(-32040.9 + 18498.8i) q^{52} +(-679694. + 392422. i) q^{53} +(171921. + 1.48561e6i) q^{54} +1.02178e6i q^{55} +(-404838. - 386595. i) q^{56} +(837993. + 924165. i) q^{57} +(293790. - 508859. i) q^{58} +(494964. + 857303. i) q^{59} +(-2.05654e6 - 660268. i) q^{60} +(1.30273e6 + 752131. i) q^{61} +424344. q^{62} +(1.95004e6 - 369212. i) q^{63} +562144. q^{64} +(-200950. - 116018. i) q^{65} +(1.23608e6 + 396854. i) q^{66} +(-997379. - 1.72751e6i) q^{67} +(893166. - 1.54701e6i) q^{68} +(-967698. - 1.06721e6i) q^{69} +(-1.68900e6 + 6.93929e6i) q^{70} +672836. i q^{71} +(785284. - 1.09690e6i) q^{72} +(-3.19678e6 + 1.84566e6i) q^{73} +(-3.63430e6 + 2.09827e6i) q^{74} +(-2.09067e6 - 9.66942e6i) q^{75} +2.28924e6i q^{76} +(407442. - 1.67399e6i) q^{77} +(-218400. + 198036. i) q^{78} +(626552. - 1.08522e6i) q^{79} +(5.38317e6 + 9.32393e6i) q^{80} +(1.54151e6 + 4.52775e6i) q^{81} +(-3.92177e6 - 2.26423e6i) q^{82} +4.44416e6 q^{83} +(3.10596e6 + 1.90178e6i) q^{84} +1.12033e7 q^{85} +(-600116. - 346477. i) q^{86} +(574448. - 1.78924e6i) q^{87} +(-585529. - 1.01417e6i) q^{88} +(737221. - 1.27690e6i) q^{89} +(-1.71294e7 - 1.67931e6i) q^{90} +(282955. + 270204. i) q^{91} -2.64356e6i q^{92} +(1.32648e6 - 286805. i) q^{93} +(-9.11834e6 + 5.26447e6i) q^{94} +(-1.24338e7 + 7.17867e6i) q^{95} +(9.76133e6 - 2.11054e6i) q^{96} -8.19557e6i q^{97} +(5.53419e6 - 1.06952e7i) q^{98} +(4.13217e6 + 405106. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 84 q^{3} + 1150 q^{4} + 2464 q^{7} - 3516 q^{9} - 630 q^{10} - 3864 q^{12} + 27576 q^{15} - 19594 q^{16} + 33498 q^{18} - 47880 q^{19} + 151788 q^{21} + 105132 q^{22} - 211554 q^{24} - 331252 q^{25}+ \cdots + 35642232 q^{99}+O(q^{100}) $ 32 * q - 84 * q^3 + 1150 * q^4 + 2464 * q^7 - 3516 * q^9 - 630 * q^10 - 3864 * q^12 + 27576 * q^15 - 19594 * q^16 + 33498 * q^18 - 47880 * q^19 + 151788 * q^21 + 105132 * q^22 - 211554 * q^24 - 331252 * q^25 - 353122 * q^28 - 40662 * q^30 + 628152 * q^31 - 66024 * q^33 - 227244 * q^36 - 618748 * q^37 + 1996104 * q^39 + 1986138 * q^40 + 4274802 * q^42 - 1416064 * q^43 - 4757508 * q^45 - 3492840 * q^46 - 6640312 * q^49 + 677340 * q^51 + 11962272 * q^52 - 6743898 * q^54 - 6279408 * q^57 - 2064342 * q^58 + 7521282 * q^60 + 10948728 * q^61 + 13194636 * q^63 - 589508 * q^64 - 6977250 * q^66 - 1944728 * q^67 - 24852702 * q^70 - 1544472 * q^72 + 13351212 * q^73 - 23106048 * q^75 + 1917432 * q^78 + 7626328 * q^79 + 8703036 * q^81 + 14640192 * q^82 + 15191904 * q^84 + 3418848 * q^85 + 15346296 * q^87 + 12313398 * q^88 + 3988992 * q^91 - 24832104 * q^93 - 51594732 * q^94 - 57374730 * q^96 + 35642232 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	12.6634	+	7.31122i	1.11930	+	0.646226i	0.941221	−	0.337790i	$-0.109679\pi$
$2$	12.6634	+	7.31122i	1.11930	+	0.646226i	0.178076	+	0.984017i	$0.443013\pi$
$3$	44.5268	+	14.2957i	0.952131	+	0.305689i
$3$	44.5268	+	14.2957i	0.952131	+	0.305689i
$4$	42.9078	+	74.3185i	0.335217	+	0.580613i
$5$	−269.104	+	466.101i	−0.962775	+	1.66758i	−0.247297	+	0.968940i	$0.579542\pi$
$5$	−269.104	+	466.101i	−0.962775	+	1.66758i	−0.715478	+	0.698635i	$0.753791\pi$
$6$	459.342	+	506.577i	0.868174	+	0.957449i
$7$	626.737	−	656.311i	0.690625	−	0.723213i
$7$	626.737	−	656.311i	0.690625	−	0.723213i
$8$		−	616.838i		−	0.425948i
$9$	1778.27	+	1273.08i	0.813109	+	0.582112i
$10$	−6815.54	+	3934.95i	−2.15526	+	1.24434i
$11$	1644.13	−	949.242i	0.372446	−	0.215032i	−0.302081	−	0.953282i	$-0.597681\pi$
$11$	1644.13	−	949.242i	0.372446	−	0.215032i	0.674526	+	0.738251i	$0.264348\pi$
$12$	848.115	+	3922.56i	0.141684	+	0.655292i
$13$			431.129i			0.0544259i	0.999630	+	0.0272129i	$0.00866322\pi$
$13$			431.129i			0.0544259i	−0.999630	+	0.0272129i	$0.991337\pi$
$14$	12735.1	−	3728.92i	1.24037	−	0.363191i
$15$	−18645.5	+	16907.0i	−1.42645	+	1.29344i
$16$	10002.0	−	17324.0i	0.610476	−	1.05738i
$17$	−10408.0	−	18027.1i	−0.513801	−	0.889929i	−0.999872	−	0.0160095i	$-0.994904\pi$
$17$	−10408.0	−	18027.1i	−0.513801	−	0.889929i	0.486071	−	0.873919i	$-0.338430\pi$
$18$	13211.2	+	29122.8i	0.533934	+	1.17701i
$19$	23102.3	+	13338.1i	0.772711	+	0.446125i	0.833841	−	0.552005i	$-0.186137\pi$
$19$	23102.3	+	13338.1i	0.772711	+	0.446125i	−0.0611298	+	0.998130i	$0.519470\pi$
$20$	−46186.6			−1.29096
$21$	37289.0	−	20263.8i	0.878644	−	0.477478i
$22$	27760.4			0.555837
$23$	−26678.1	−	15402.6i	−0.457201	−	0.263965i	0.253666	−	0.967292i	$-0.418364\pi$
$23$	−26678.1	−	15402.6i	−0.457201	−	0.263965i	−0.710866	+	0.703327i	$0.751697\pi$
$24$	8818.11	−	27465.8i	0.130208	−	0.405558i
$25$	−105771.	−	183201.i	−1.35387	−	2.34497i
$26$	−3152.08	+	5459.56i	−0.0351714	+	0.0609187i
$27$	60981.1	+	82107.6i	0.596241	+	0.802805i
$28$	75668.0	+	18417.3i	0.651417	+	0.158552i
$29$		−	40183.4i		−	0.305952i	−0.988230	−	0.152976i	$-0.951114\pi$
$29$		−	40183.4i		−	0.305952i	0.988230	−	0.152976i	$-0.0488858\pi$
$30$	−359727.	+	77778.2i	−2.43247	+	0.525937i
$31$	25132.1	−	14510.0i	0.151518	−	0.0874787i	−0.422324	−	0.906445i	$-0.638786\pi$
$31$	25132.1	−	14510.0i	0.151518	−	0.0874787i	0.573842	+	0.818966i	$0.305452\pi$
$32$	184942.	−	106777.i	0.997726	−	0.576038i
$33$	86778.1	−	18762.7i	0.420350	−	0.0908859i
$34$		−	304380.i		−	1.32813i
$35$	137250.	+	468739.i	0.541097	+	1.84796i
$36$	−18311.7	+	186783.i	−0.0654139	+	0.667236i
$37$	−143496.	+	248543.i	−0.465730	+	0.806669i	−0.999234	−	0.0391289i	$-0.987542\pi$
$37$	−143496.	+	248543.i	−0.465730	+	0.806669i	0.533504	+	0.845798i	$0.320875\pi$
$38$	195036.	+	337812.i	0.576596	+	0.998693i
$39$	−6163.27	+	19196.8i	−0.0166374	+	0.0518206i
$40$	287509.	+	165994.i	0.710300	+	0.410092i
$41$	−309693.			−0.701759			−0.350879	−	0.936421i	$-0.614117\pi$
$41$	−309693.			−0.701759			−0.350879	+	0.936421i	$0.614117\pi$
$42$	620358.	+	16019.1i	1.29202	+	0.0333630i
$43$	−47389.8			−0.0908961			−0.0454480	−	0.998967i	$-0.514472\pi$
$43$	−47389.8			−0.0908961			−0.0454480	+	0.998967i	$0.514472\pi$
$44$	141092.	+	81459.8i	0.249700	+	0.144165i
$45$	−1.07192e6	+	486263.i	−1.75356	+	0.795477i
$46$	−225223.	−	390098.i	−0.341162	−	0.590910i
$47$	−360027.	+	623585.i	−0.505816	+	0.876099i	0.494161	+	0.869370i	$0.335475\pi$
$47$	−360027.	+	623585.i	−0.505816	+	0.876099i	−0.999977	+	0.00672904i	$0.997858\pi$
$48$	693017.	−	628398.i	0.904481	−	0.820145i
$49$	−37945.1	−	822668.i	−0.0460755	−	0.998938i
$50$		−	3.09326e6i		−	3.49963i
$51$	−205724.	−	951478.i	−0.217164	−	1.00439i
$52$	−32040.9	+	18498.8i	−0.0316004	+	0.0182445i
$53$	−679694.	+	392422.i	−0.627116	+	0.362066i	−0.779634	−	0.626235i	$-0.784595\pi$
$53$	−679694.	+	392422.i	−0.627116	+	0.362066i	0.152518	+	0.988301i	$0.451262\pi$
$54$	171921.	+	1.48561e6i	0.148577	+	1.28388i
$55$			1.02178e6i			0.828108i
$56$	−404838.	−	386595.i	−0.308051	−	0.294170i
$57$	837993.	+	924165.i	0.599347	+	0.660979i
$58$	293790.	−	508859.i	0.197715	−	0.342452i
$59$	494964.	+	857303.i	0.313756	+	0.543441i	0.979172	−	0.203032i	$-0.0650794\pi$
$59$	494964.	+	857303.i	0.313756	+	0.543441i	−0.665417	+	0.746472i	$0.731746\pi$
$60$	−2.05654e6	−	660268.i	−1.22916	−	0.394631i
$61$	1.30273e6	+	752131.i	0.734852	+	0.424267i	0.820194	−	0.572085i	$-0.193865\pi$
$61$	1.30273e6	+	752131.i	0.734852	+	0.424267i	−0.0853427	+	0.996352i	$0.527199\pi$
$62$	424344.			0.226124
$63$	1.95004e6	−	369212.i	0.982544	−	0.186030i
$64$	562144.			0.268051
$65$	−200950.	−	116018.i	−0.0907592	−	0.0523999i
$66$	1.23608e6	+	396854.i	0.529229	+	0.169913i
$67$	−997379.	−	1.72751e6i	−0.405134	−	0.701712i	0.589203	−	0.807985i	$-0.299442\pi$
$67$	−997379.	−	1.72751e6i	−0.405134	−	0.701712i	−0.994337	+	0.106273i	$0.966108\pi$
$68$	893166.	−	1.54701e6i	0.344470	−	0.596639i
$69$	−967698.	−	1.06721e6i	−0.354624	−	0.391090i
$70$	−1.68900e6	+	6.93929e6i	−0.588553	+	2.41809i
$71$			672836.i			0.223103i	0.993759	+	0.111551i	$0.0355820\pi$
$71$			672836.i			0.223103i	−0.993759	+	0.111551i	$0.964418\pi$
$72$	785284.	−	1.09690e6i	0.247949	−	0.346342i
$73$	−3.19678e6	+	1.84566e6i	−0.961795	+	0.555293i	−0.896725	−	0.442588i	$-0.854060\pi$
$73$	−3.19678e6	+	1.84566e6i	−0.961795	+	0.555293i	−0.0650703	+	0.997881i	$0.520727\pi$
$74$	−3.63430e6	+	2.09827e6i	−1.04258	+	0.601935i
$75$	−2.09067e6	−	9.66942e6i	−0.572231	−	2.64659i
$76$			2.28924e6i			0.598195i
$77$	407442.	−	1.67399e6i	0.101706	−	0.417864i
$78$	−218400.	+	198036.i	−0.0521100	+	0.0472511i
$79$	626552.	−	1.08522e6i	0.142976	−	0.247641i	−0.785640	−	0.618684i	$-0.787666\pi$
$79$	626552.	−	1.08522e6i	0.142976	−	0.247641i	0.928616	+	0.371043i	$0.121000\pi$
$80$	5.38317e6	+	9.32393e6i	1.17550	+	2.03603i
$81$	1.54151e6	+	4.52775e6i	0.322291	+	0.946641i
$82$	−3.92177e6	−	2.26423e6i	−0.785477	−	0.453495i
$83$	4.44416e6			0.853133			0.426566	−	0.904456i	$-0.359723\pi$
$83$	4.44416e6			0.853133			0.426566	+	0.904456i	$0.359723\pi$
$84$	3.10596e6	+	1.90178e6i	0.571767	+	0.350093i
$85$	1.12033e7			1.97870
$86$	−600116.	−	346477.i	−0.101740	−	0.0587395i
$87$	574448.	−	1.78924e6i	0.0935262	−	0.291307i
$88$	−585529.	−	1.01417e6i	−0.0915923	−	0.158642i
$89$	737221.	−	1.27690e6i	0.110849	−	0.191996i	−0.805264	−	0.592917i	$-0.797976\pi$
$89$	737221.	−	1.27690e6i	0.110849	−	0.191996i	0.916113	+	0.400920i	$0.131310\pi$
$90$	−1.71294e7	−	1.67931e6i	−2.47681	−	0.242819i
$91$	282955.	+	270204.i	0.0393615	+	0.0375879i
$92$		−	2.64356e6i		−	0.353942i
$93$	1.32648e6	−	286805.i	0.171006	−	0.0369740i
$94$	−9.11834e6	+	5.26447e6i	−1.13232	+	0.653744i
$95$	−1.24338e7	+	7.17867e6i	−1.48789	+	0.859036i
$96$	9.76133e6	−	2.11054e6i	1.12605	−	0.243470i
$97$		−	8.19557e6i		−	0.911755i	−0.890043	−	0.455877i	$-0.849326\pi$
$97$		−	8.19557e6i		−	0.911755i	0.890043	−	0.455877i	$-0.150674\pi$
$98$	5.53419e6	−	1.06952e7i	0.593968	−	1.14788i
$99$	4.13217e6	+	405106.i	0.428011	+	0.0419610i
$100$	9.07682e6	−	1.57215e7i	0.907682	−	1.57215i
$101$	−6.76207e6	−	1.17123e7i	−0.653063	−	1.13114i	−0.982376	−	0.186917i	$-0.940150\pi$
$101$	−6.76207e6	−	1.17123e7i	−0.653063	−	1.13114i	0.329313	−	0.944221i	$-0.393183\pi$
$102$	4.35130e6	−	1.35530e7i	0.405993	−	1.26455i
$103$	8.19802e6	+	4.73313e6i	0.739228	+	0.426794i	0.821789	−	0.569792i	$-0.192976\pi$
$103$	8.19802e6	+	4.73313e6i	0.739228	+	0.426794i	−0.0825603	+	0.996586i	$0.526310\pi$
$104$	265937.			0.0231826
$105$	−589613.	+	2.28335e7i	−0.0497055	+	1.92491i
$106$	−1.14763e7			−0.935906
$107$	170692.	+	98549.2i	0.0134701	+	0.00777696i	0.506720	−	0.862111i	$-0.330858\pi$
$107$	170692.	+	98549.2i	0.0134701	+	0.00777696i	−0.493250	+	0.869888i	$0.664191\pi$
$108$	−3.48555e6	+	8.05508e6i	−0.266249	+	0.615300i
$109$	924586.	+	1.60143e6i	0.0683840	+	0.118445i	0.898190	−	0.439607i	$-0.144882\pi$
$109$	924586.	+	1.60143e6i	0.0683840	+	0.118445i	−0.829806	+	0.558052i	$0.811549\pi$
$110$	−7.47044e6	+	1.29392e7i	−0.535145	+	0.926899i
$111$	−9.94251e6	+	9.01544e6i	−0.690026	+	0.625686i
$112$	−5.10131e6	−	1.74221e7i	−0.343098	−	1.17175i
$113$		−	1.54177e7i		−	1.00518i	−0.864525	−	0.502590i	$-0.832380\pi$
$113$		−	1.54177e7i		−	1.00518i	0.864525	−	0.502590i	$-0.167620\pi$
$114$	3.85507e6	+	1.78298e7i	0.243706	+	1.12715i
$115$	1.43583e7	−	8.28979e6i	0.880362	−	0.508277i
$116$	2.98637e6	−	1.72418e6i	0.177640	−	0.102561i
$117$	−548861.	+	766663.i	−0.0316820	+	0.0442542i
$118$			1.44752e7i			0.811029i
$119$	−1.83545e7	−	4.46740e6i	−0.998452	−	0.243019i
$120$	1.04289e7	+	1.15013e7i	0.550938	+	0.607592i
$121$	−7.94147e6	+	1.37550e7i	−0.407523	+	0.705850i
$122$	1.09980e7	+	1.90491e7i	0.548345	+	0.949761i
$123$	−1.37896e7	−	4.42726e6i	−0.668167	−	0.214520i
$124$	2.15673e6	+	1.24519e6i	0.101583	+	0.0586488i
$125$	7.18062e7			3.28834
$126$	2.73935e7	+	9.58170e6i	1.21998	+	0.426723i
$127$	−1.74020e7			−0.753853			−0.376926	−	0.926243i	$-0.623019\pi$
$127$	−1.74020e7			−0.753853			−0.376926	+	0.926243i	$0.623019\pi$
$128$	−1.65540e7	−	9.55744e6i	−0.697698	−	0.402816i
$129$	−2.11012e6	−	677468.i	−0.0865450	−	0.0277859i
$130$	−1.69647e6	−	2.93838e6i	−0.0677244	−	0.117302i
$131$	−2.28229e7	+	3.95304e7i	−0.886995	+	1.53632i	−0.0435843	+	0.999050i	$0.513878\pi$
$131$	−2.28229e7	+	3.95304e7i	−0.886995	+	1.53632i	−0.843410	+	0.537270i	$0.819456\pi$
$132$	5.11787e6	+	5.64415e6i	0.193678	+	0.213594i
$133$	2.32330e7	−	6.80280e6i	0.856297	−	0.250730i
$134$		−	2.91682e7i		−	1.04723i
$135$	−5.46807e7	+	6.32790e6i	−1.91278	+	0.221356i
$136$	−1.11198e7	+	6.42003e6i	−0.379063	+	0.218852i
$137$	2.55140e7	−	1.47305e7i	0.847728	−	0.489436i	−0.0121555	−	0.999926i	$-0.503869\pi$
$137$	2.55140e7	−	1.47305e7i	0.847728	−	0.489436i	0.859884	+	0.510490i	$0.170536\pi$
$138$	−4.45176e6	−	2.05895e7i	−0.144197	−	0.666914i
$139$		−	6.02035e7i		−	1.90138i	−0.310136	−	0.950692i	$-0.600375\pi$
$139$		−	6.02035e7i		−	1.90138i	0.310136	−	0.950692i	$-0.399625\pi$
$140$	−2.89468e7	+	3.03128e7i	−0.891565	+	0.933636i
$141$	−2.49454e7	+	2.26194e7i	−0.749417	+	0.679539i
$142$	−4.91925e6	+	8.52039e6i	−0.144175	+	0.249718i
$143$	409246.	+	708834.i	0.0117033	+	0.0202707i
$144$	3.98412e7	−	1.80734e7i	1.11189	−	0.504396i
$145$	1.87295e7	+	1.08135e7i	0.510199	+	0.294563i
$146$	−5.39761e7			−1.43538
$147$	1.00710e7	−	3.71732e7i	0.261494	−	0.965205i
$148$	−2.46284e7			−0.624484
$149$	9.02712e6	+	5.21181e6i	0.223562	+	0.129073i	0.607598	−	0.794244i	$-0.292133\pi$
$149$	9.02712e6	+	5.21181e6i	0.223562	+	0.129073i	−0.384037	+	0.923318i	$0.625466\pi$
$150$	4.42202e7	−	1.37733e8i	1.06980	−	3.33211i
$151$	1.90839e7	+	3.30543e7i	0.451074	+	0.781283i	0.998453	−	0.0556021i	$-0.0177078\pi$
$151$	1.90839e7	+	3.30543e7i	0.451074	+	0.781283i	−0.547379	+	0.836885i	$0.684374\pi$
$152$	8.22746e6	−	1.42504e7i	0.190026	−	0.329135i
$153$	4.44179e6	−	4.53072e7i	0.100262	−	1.02270i
$154$	1.73985e7	−	1.82195e7i	0.383874	−	0.401988i
$155$			1.56188e7i			0.336889i
$156$	−1.69113e6	+	365647.i	−0.0356649	+	0.00771127i
$157$	−4.74464e7	+	2.73932e7i	−0.978486	+	0.564929i	−0.901813	−	0.432127i	$-0.857763\pi$
$157$	−4.74464e7	+	2.73932e7i	−0.978486	+	0.564929i	−0.0766733	+	0.997056i	$0.524430\pi$
$158$	1.58686e7	−	9.16171e6i	0.320065	−	0.184789i
$159$	−3.58745e7	+	7.75660e6i	−0.707776	+	0.153032i
$160$			1.14936e8i			2.21838i
$161$	−2.68290e7	+	7.85573e6i	−0.506657	+	0.148353i
$162$	−1.35826e7	+	6.86071e7i	−0.251004	+	1.26785i
$163$	3.01449e7	−	5.22125e7i	0.545202	−	0.944317i	−0.453393	−	0.891311i	$-0.649786\pi$
$163$	3.01449e7	−	5.22125e7i	0.545202	−	0.944317i	0.998594	−	0.0530060i	$-0.0168802\pi$
$164$	−1.32883e7	−	2.30159e7i	−0.235242	−	0.407451i
$165$	−1.46070e7	+	4.54965e7i	−0.253143	+	0.788468i
$166$	5.62782e7	+	3.24922e7i	0.954909	+	0.551317i
$167$	−3.16225e7			−0.525398			−0.262699	−	0.964878i	$-0.584613\pi$
$167$	−3.16225e7			−0.525398			−0.262699	+	0.964878i	$0.584613\pi$
$168$	−1.24995e7	−	2.30013e7i	−0.203381	−	0.374256i
$169$	6.25626e7			0.997038
$170$	1.41872e8	+	8.19097e7i	2.21475	+	1.27869i
$171$	2.41016e7	+	5.31298e7i	0.368603	+	0.812552i
$172$	−2.03339e6	−	3.52194e6i	−0.0304699	−	0.0527755i
$173$	−1.77562e6	+	3.07546e6i	−0.0260729	+	0.0451595i	−0.878767	−	0.477250i	$-0.841634\pi$
$173$	−1.77562e6	+	3.07546e6i	−0.0260729	+	0.0451595i	0.852695	+	0.522410i	$0.174967\pi$
$174$	2.03560e7	−	1.84579e7i	0.292934	−	0.265620i
$175$	−1.86528e8	−	4.54001e7i	−2.63093	−	0.640358i
$176$		−	3.79774e7i		−	0.525087i
$177$	9.78345e6	+	4.52488e7i	0.132613	+	0.613339i
$178$	1.86714e7	−	1.07800e7i	0.248146	−	0.143267i
$179$	7.62456e7	−	4.40204e7i	0.993641	−	0.573679i	0.0872803	−	0.996184i	$-0.472182\pi$
$179$	7.62456e7	−	4.40204e7i	0.993641	−	0.573679i	0.906361	+	0.422505i	$0.138849\pi$
$180$	−8.21322e7	−	5.87992e7i	−1.04969	−	0.751480i
$181$			1.12564e8i			1.41099i	0.708714	+	0.705496i	$0.249276\pi$
$181$			1.12564e8i			1.41099i	−0.708714	+	0.705496i	$0.750724\pi$
$182$	1.60765e6	+	5.49045e6i	0.0197670	+	0.0675084i
$183$	4.72541e7	+	5.21133e7i	0.569982	+	0.628594i
$184$	−9.50090e6	+	1.64560e7i	−0.112435	+	0.194744i
$185$	−7.72308e7	−	1.33768e8i	−0.896787	−	1.55328i
$186$	1.88947e7	+	6.06627e6i	0.215300	+	0.0691237i
$187$	−3.42242e7	−	1.97593e7i	−0.382726	−	0.220967i
$188$	−6.17919e7			−0.678233
$189$	9.21072e7	+	1.14373e7i	0.992378	+	0.123227i
$190$	−2.09939e8			−2.22053
$191$	−7.36326e7	−	4.25118e7i	−0.764633	−	0.441461i	0.0663235	−	0.997798i	$-0.478873\pi$
$191$	−7.36326e7	−	4.25118e7i	−0.764633	−	0.441461i	−0.830957	+	0.556337i	$0.812206\pi$
$192$	2.50304e7	+	8.03621e6i	0.255220	+	0.0819402i
$193$	9.02429e7	+	1.56305e8i	0.903571	+	1.56503i	0.822824	+	0.568296i	$0.192397\pi$
$193$	9.02429e7	+	1.56305e8i	0.903571	+	1.56503i	0.0807470	+	0.996735i	$0.474269\pi$
$194$	5.99196e7	−	1.03784e8i	0.589200	−	1.02052i
$195$	−7.28909e6	−	8.03864e6i	−0.0703967	−	0.0776357i
$196$	5.95113e7	−	3.81189e7i	0.564551	−	0.361613i
$197$			2.09911e8i			1.95616i	0.208239	+	0.978078i	$0.433227\pi$
$197$			2.09911e8i			1.95616i	−0.208239	+	0.978078i	$0.566773\pi$
$198$	4.93655e7	+	3.53412e7i	0.451955	+	0.323559i
$199$	1.26959e8	−	7.32997e7i	1.14203	−	0.659350i	0.195096	−	0.980784i	$-0.437498\pi$
$199$	1.26959e8	−	7.32997e7i	1.14203	−	0.659350i	0.946932	+	0.321434i	$0.104165\pi$
$200$	−1.13005e8	+	6.52437e7i	−0.998836	+	0.576678i
$201$	−1.97142e7	−	9.11787e7i	−0.171235	−	0.791967i
$202$		−	1.97756e8i		−	1.68811i
$203$	−2.63728e7	−	2.51844e7i	−0.221269	−	0.211298i
$204$	6.18853e7	−	5.61149e7i	0.510366	−	0.462778i
$205$	8.33396e7	−	1.44348e8i	0.675636	−	1.17024i
$206$	6.92099e7	+	1.19875e8i	0.551611	+	0.955418i
$207$	−2.78320e7	−	6.13532e7i	−0.218097	−	0.480774i
$208$	7.46890e6	+	4.31217e6i	0.0575486	+	0.0332257i
$209$	5.06443e7			0.383724
$210$	−1.74407e8	+	2.84839e8i	−1.29956	+	2.12242i
$211$	1.44961e8			1.06233			0.531167	−	0.847267i	$-0.321754\pi$
$211$	1.44961e8			1.06233			0.531167	+	0.847267i	$0.321754\pi$
$212$	−5.83284e7	−	3.36759e7i	−0.420440	−	0.242741i
$213$	−9.61863e6	+	2.99592e7i	−0.0682000	+	0.212423i
$214$	1.44103e6	+	2.49594e6i	0.0100514	+	0.0174095i
$215$	1.27528e7	−	2.20885e7i	0.0875125	−	0.151576i
$216$	5.06471e7	−	3.76155e7i	0.341953	−	0.253968i
$217$	6.22812e6	−	2.55884e7i	0.0413760	−	0.169994i
$218$			2.70394e7i			0.176766i
$219$	−1.68727e8	+	3.64813e7i	−1.08550	+	0.234702i
$220$	−7.59370e7	+	4.38423e7i	−0.480811	+	0.277596i
$221$	7.77202e6	−	4.48718e6i	0.0484352	−	0.0279640i
$222$	−1.91820e8	+	4.14743e7i	−1.17668	+	0.254415i
$223$			1.90116e8i			1.14803i	0.818846	+	0.574013i	$0.194614\pi$
$223$			1.90116e8i			1.14803i	−0.818846	+	0.574013i	$0.805386\pi$
$224$	4.58316e7	−	1.88300e8i	0.272456	−	1.11939i
$225$	4.51398e7	−	4.60436e8i	0.264193	−	2.69482i
$226$	1.12722e8	−	1.95240e8i	0.649575	−	1.12510i
$227$	2.24577e7	+	3.88979e7i	0.127431	+	0.220717i	0.922681	−	0.385565i	$-0.125994\pi$
$227$	2.24577e7	+	3.88979e7i	0.127431	+	0.220717i	−0.795250	+	0.606282i	$0.792660\pi$
$228$	−3.27261e7	+	1.01932e8i	−0.182862	+	0.569560i
$229$	−7.11671e7	−	4.10883e7i	−0.391611	−	0.226097i	0.291247	−	0.956648i	$-0.405930\pi$
$229$	−7.11671e7	−	4.10883e7i	−0.391611	−	0.226097i	−0.682858	+	0.730551i	$0.739263\pi$
$230$	2.42434e8			1.31385
$231$	4.20728e7	−	6.87127e7i	0.224574	−	0.366771i
$232$	−2.47867e7			−0.130320
$233$	−3.15260e7	−	1.82015e7i	−0.163276	−	0.0942676i	0.416135	−	0.909303i	$-0.363384\pi$
$233$	−3.15260e7	−	1.82015e7i	−0.163276	−	0.0942676i	−0.579412	+	0.815035i	$0.696718\pi$
$234$	−1.25557e7	+	5.69572e6i	−0.0640597	+	0.0290598i
$235$	−1.93769e8	−	3.35618e8i	−0.973974	−	1.68697i
$236$	−4.24756e7	+	7.35700e7i	−0.210353	+	0.364341i
$237$	4.34123e7	−	3.93644e7i	0.211833	−	0.192081i
$238$	−1.99768e8	−	1.90766e8i	−0.960519	−	0.917236i
$239$			1.04151e8i			0.493482i	0.969081	+	0.246741i	$0.0793597\pi$
$239$			1.04151e8i			0.493482i	−0.969081	+	0.246741i	$0.920640\pi$
$240$	1.06404e8	+	4.92121e8i	0.496841	+	2.29791i
$241$	−2.43431e8	+	1.40545e8i	−1.12025	+	0.646778i	−0.941465	−	0.337110i	$-0.890551\pi$
$241$	−2.43431e8	+	1.40545e8i	−1.12025	+	0.646778i	−0.178787	+	0.983888i	$0.557217\pi$
$242$	−2.01132e8	+	1.16124e8i	−0.912278	+	0.526704i
$243$	3.91129e6	+	2.23643e8i	0.0174863	+	0.999847i
$244$			1.29089e8i			0.568886i
$245$	3.93658e8	+	2.03697e8i	1.71016	+	0.884918i
$246$	−1.42255e8	−	1.56883e8i	−0.609249	−	0.671899i
$247$	−5.75044e6	+	9.96006e6i	−0.0242807	+	0.0420555i
$248$	−8.95034e6	−	1.55024e7i	−0.0372614	−	0.0645386i
$249$	1.97884e8	+	6.35322e7i	0.812295	+	0.260793i
$250$	9.09311e8	+	5.24991e8i	3.68063	+	2.12501i
$251$	−3.23864e8			−1.29272			−0.646360	−	0.763033i	$-0.723710\pi$
$251$	−3.23864e8			−1.29272			−0.646360	+	0.763033i	$0.723710\pi$
$252$	1.11111e8	+	1.29082e8i	0.437377	+	0.508118i
$253$	−5.84831e7			−0.227043
$254$	−2.20369e8	−	1.27230e8i	−0.843785	−	0.487160i
$255$	4.98846e8	+	1.60158e8i	1.88398	+	0.604866i
$256$	−1.75730e8	−	3.04374e8i	−0.654646	−	1.13388i
$257$	−1.00340e8	+	1.73794e8i	−0.368729	+	0.638657i	−0.989367	−	0.145440i	$-0.953540\pi$
$257$	−1.00340e8	+	1.73794e8i	−0.368729	+	0.638657i	0.620638	+	0.784097i	$0.286874\pi$
$258$	−2.17681e7	−	2.40066e7i	−0.0789136	−	0.0870284i
$259$	7.31870e7	+	2.49949e8i	0.261749	+	0.893928i
$260$		−	1.99124e7i		−	0.0702614i
$261$	5.11567e7	−	7.14569e7i	0.178099	−	0.248773i
$262$	−5.78031e8	+	3.33726e8i	−1.98562	+	1.14640i
$263$	3.72853e8	−	2.15267e8i	1.26384	−	0.729679i	0.290025	−	0.957019i	$-0.406336\pi$
$263$	3.72853e8	−	2.15267e8i	1.26384	−	0.729679i	0.973815	+	0.227340i	$0.0730030\pi$
$264$	−1.15735e7	−	5.35280e7i	−0.0387126	−	0.179047i
$265$		−	4.22408e8i		−	1.39435i
$266$	3.43945e8	+	8.37149e7i	1.12048	+	0.272720i
$267$	5.10802e7	−	4.63174e7i	0.164234	−	0.148920i
$268$	8.55907e7	−	1.48247e8i	0.271616	−	0.470452i
$269$	−1.21334e8	−	2.10157e8i	−0.380058	−	0.658280i	0.611012	−	0.791621i	$-0.290763\pi$
$269$	−1.21334e8	−	2.10157e8i	−0.380058	−	0.658280i	−0.991070	+	0.133342i	$0.957429\pi$
$270$	−7.38708e8	−	3.19650e8i	−2.28402	−	0.988329i
$271$	−1.27614e8	−	7.36782e7i	−0.389500	−	0.224878i	0.292444	−	0.956283i	$-0.405532\pi$
$271$	−1.27614e8	−	7.36782e7i	−0.389500	−	0.224878i	−0.681943	+	0.731405i	$0.738865\pi$
$272$	−4.16403e8			−1.25465
$273$	8.73631e6	+	1.60764e7i	0.0259872	+	0.0478210i
$274$	4.30792e8			1.26515
$275$	−3.47804e8	−	2.00805e8i	−1.00849	−	0.582250i
$276$	3.77915e7	−	1.17709e8i	0.108196	−	0.337000i
$277$	2.57551e8	+	4.46092e8i	0.728089	+	1.26109i	0.957690	+	0.287802i	$0.0929244\pi$
$277$	2.57551e8	+	4.46092e8i	0.728089	+	1.26109i	−0.229602	+	0.973285i	$0.573742\pi$
$278$	4.40161e8	−	7.62381e8i	1.22872	−	2.12821i
$279$	6.31641e7	+	6.19242e6i	0.174123	+	0.0170705i
$280$	2.89136e8	−	8.46612e7i	0.787135	−	0.230479i
$281$		−	3.74214e8i		−	1.00612i	−0.864253	−	0.503058i	$-0.832208\pi$
$281$		−	3.74214e8i		−	1.00612i	0.864253	−	0.503058i	$-0.167792\pi$
$282$	−4.81269e8	+	1.04058e8i	−1.27796	+	0.276313i
$283$	−3.25535e8	+	1.87948e8i	−0.853778	+	0.492929i	−0.861924	−	0.507038i	$-0.830740\pi$
$283$	−3.25535e8	+	1.87948e8i	−0.853778	+	0.492929i	0.00814601	+	0.999967i	$0.497407\pi$
$284$	−5.00042e7	+	2.88699e7i	−0.129536	+	0.0747879i
$285$	−6.56262e8	+	1.41893e8i	−1.67927	+	0.363083i
$286$			1.19683e7i			0.0302519i
$287$	−1.94096e8	+	2.03255e8i	−0.484652	+	0.507522i
$288$	4.64812e8	+	4.55689e7i	1.14658	+	0.112407i
$289$	−1.14821e7	+	1.98876e7i	−0.0279820	+	0.0484663i
$290$	1.58120e8	+	2.73872e8i	0.380709	+	0.659408i
$291$	1.17161e8	−	3.64922e8i	0.278713	−	0.868110i
$292$	−2.74334e8	−	1.58387e8i	−0.644821	−	0.372288i
$293$	1.82974e7			0.0424964			0.0212482	−	0.999774i	$-0.493236\pi$
$293$	1.82974e7			0.0424964			0.0212482	+	0.999774i	$0.493236\pi$
$294$	3.99315e8	−	3.97108e8i	0.916431	−	0.911367i
$295$	−5.32787e8			−1.20830
$296$	1.53311e8	+	8.85140e7i	0.343599	+	0.198377i
$297$	1.78201e8	+	7.71102e7i	0.394696	+	0.170791i
$298$	7.62093e7	+	1.31998e8i	0.166821	+	0.288943i
$299$	6.64050e6	−	1.15017e7i	0.0143665	−	0.0248835i
$300$	6.28911e8	−	5.70269e8i	1.34482	−	1.21943i
$301$	−2.97009e7	+	3.11024e7i	−0.0627751	+	0.0657373i
$302$			5.58106e8i			1.16598i
$303$	−1.33659e8	−	6.18177e8i	−0.276025	−	1.27663i
$304$	4.62140e8	−	2.66817e8i	0.943443	−	0.544697i
$305$	−7.01139e8	+	4.04803e8i	−1.41499	+	0.816947i
$306$	3.87499e8	−	5.41269e8i	0.773118	−	1.07991i
$307$			6.99449e8i			1.37966i	0.723972	+	0.689830i	$0.242315\pi$
$307$			6.99449e8i			1.37966i	−0.723972	+	0.689830i	$0.757685\pi$
$308$	1.41891e8	−	4.15467e7i	0.276711	−	0.0810231i
$309$	2.97368e8	+	3.27947e8i	0.573376	+	0.632338i
$310$	−1.14193e8	+	1.97787e8i	−0.217707	+	0.377079i
$311$	2.11777e8	+	3.66808e8i	0.399224	+	0.691476i	0.993630	−	0.112689i	$-0.0359463\pi$
$311$	2.11777e8	+	3.66808e8i	0.399224	+	0.691476i	−0.594406	+	0.804165i	$0.702613\pi$
$312$	1.18413e7	+	3.80174e6i	0.0220729	+	0.00708666i
$313$	2.91296e8	+	1.68180e8i	0.536944	+	0.310005i	0.743840	−	0.668358i	$-0.233003\pi$
$313$	2.91296e8	+	1.68180e8i	0.536944	+	0.310005i	−0.206895	+	0.978363i	$0.566336\pi$
$314$	−8.01111e8			−1.46029
$315$	−3.52673e8	+	1.00827e9i	−0.635749	+	1.81757i
$316$	1.07536e8			0.191712
$317$	5.98493e8	+	3.45540e8i	1.05524	+	0.609244i	0.924112	−	0.382121i	$-0.124806\pi$
$317$	5.98493e8	+	3.45540e8i	1.05524	+	0.609244i	0.131129	+	0.991365i	$0.458140\pi$
$318$	−5.11003e8	−	1.64061e8i	−0.891105	−	0.286096i
$319$	−3.81438e7	−	6.60669e7i	−0.0657894	−	0.113951i
$320$	−1.51275e8	+	2.62016e8i	−0.258073	+	0.446995i
$321$	6.19155e6	+	6.82823e6i	0.0104480	+	0.0115223i
$322$	−3.97181e8	−	9.66723e7i	−0.662969	−	0.161364i
$323$		−	5.55290e8i		−	0.916877i
$324$	−2.70353e8	+	3.08839e8i	−0.441594	+	0.504457i
$325$	7.89833e7	−	4.56010e7i	0.127627	−	0.0736856i
$326$	7.63474e8	−	4.40792e8i	1.22049	−	0.704647i
$327$	1.82754e7	+	8.45241e7i	0.0289034	+	0.133679i
$328$			1.91031e8i			0.298913i
$329$	1.83624e8	+	6.27114e8i	0.284278	+	0.970869i
$330$	−5.17609e8	+	4.69345e8i	−0.792872	+	0.718942i
$331$	4.28091e8	−	7.41475e8i	0.648840	−	1.12382i	−0.334560	−	0.942374i	$-0.608588\pi$
$331$	4.28091e8	−	7.41475e8i	0.648840	−	1.12382i	0.983400	−	0.181450i	$-0.0580789\pi$
$332$	1.90689e8	+	3.30284e8i	0.285985	+	0.495340i
$333$	−5.71590e8	+	2.59294e8i	−0.848261	+	0.384802i
$334$	−4.00448e8	−	2.31199e8i	−0.588077	−	0.339526i
$335$	1.07359e9			1.56021
$336$	2.19147e7	−	8.48675e8i	0.0315173	−	1.22055i
$337$	−8.30714e8			−1.18235			−0.591176	−	0.806542i	$-0.701336\pi$
$337$	−8.30714e8			−1.18235			−0.591176	+	0.806542i	$0.701336\pi$
$338$	7.92256e8	+	4.57409e8i	1.11598	+	0.644312i
$339$	2.20406e8	−	6.86499e8i	0.307273	−	0.957064i
$340$	4.80709e8	+	8.32612e8i	0.663293	+	1.14886i
$341$	2.75470e7	−	4.77129e7i	0.0376214	−	0.0651621i
$342$	−8.32351e7	+	8.49015e8i	−0.112516	+	1.14769i
$343$	−5.63708e8	−	4.90693e8i	−0.754266	−	0.656569i
$344$			2.92318e7i			0.0387170i
$345$	7.57838e8	−	1.63856e8i	0.993595	−	0.214830i
$346$	−4.49708e7	+	2.59639e7i	−0.0583666	+	0.0336979i
$347$	−9.93989e7	+	5.73880e7i	−0.127711	+	0.0737340i	−0.562495	−	0.826801i	$-0.690158\pi$
$347$	−9.93989e7	+	5.73880e7i	−0.127711	+	0.0737340i	0.434783	+	0.900535i	$0.356825\pi$
$348$	1.57622e8	−	3.40802e7i	0.200488	−	0.0433485i
$349$			2.74148e8i			0.345220i	0.984990	+	0.172610i	$0.0552200\pi$
$349$			2.74148e8i			0.345220i	−0.984990	+	0.172610i	$0.944780\pi$
$350$	−2.03014e9	−	1.93866e9i	−2.53098	−	2.41693i
$351$	−3.53990e7	+	2.62907e7i	−0.0436934	+	0.0324510i
$352$	2.02713e8	−	3.51110e8i	0.247733	−	0.429085i
$353$	−6.24059e8	−	1.08090e9i	−0.755117	−	1.30790i	−0.945316	−	0.326155i	$-0.894247\pi$
$353$	−6.24059e8	−	1.08090e9i	−0.755117	−	1.30790i	0.190199	−	0.981746i	$-0.439087\pi$
$354$	−2.06932e8	+	6.44532e8i	−0.247922	+	0.772206i
$355$	−3.13610e8	−	1.81063e8i	−0.372041	−	0.214798i
$356$	1.26530e8			0.148634
$357$	−7.53400e8	−	4.61308e8i	−0.876369	−	0.536602i
$358$	1.28737e9			1.48291
$359$	5.32474e8	+	3.07424e8i	0.607391	+	0.350677i	0.771943	−	0.635691i	$-0.219285\pi$
$359$	5.32474e8	+	3.07424e8i	0.607391	+	0.350677i	−0.164553	+	0.986368i	$0.552618\pi$
$360$	2.99946e8	+	6.61203e8i	0.338832	+	0.746923i
$361$	−9.11257e7	−	1.57834e8i	−0.101945	−	0.176574i
$362$	−8.22980e8	+	1.42544e9i	−0.911820	+	1.57932i
$363$	−5.50245e8	+	4.98938e8i	−0.603786	+	0.547487i
$364$	−7.94022e6	+	3.26226e7i	−0.00862934	+	0.0354539i
$365$		−	1.98670e9i		−	2.13849i
$366$	2.17386e8	+	1.00542e9i	0.231765	+	1.07192i
$367$	4.65901e8	−	2.68988e8i	0.491997	−	0.284055i	−0.233406	−	0.972379i	$-0.574987\pi$
$367$	4.65901e8	−	2.68988e8i	0.491997	−	0.284055i	0.725403	+	0.688325i	$0.241654\pi$
$368$	−5.33670e8	+	3.08114e8i	−0.558220	+	0.322288i
$369$	−5.50717e8	−	3.94264e8i	−0.570606	−	0.408502i
$370$		−	2.25860e9i		−	2.31811i
$371$	−1.68439e8	+	6.92036e8i	−0.171251	+	0.703590i
$372$	7.82314e7	+	8.62760e7i	0.0787917	+	0.0868940i
$373$	5.39544e8	−	9.34518e8i	0.538327	−	0.932409i	−0.460668	−	0.887573i	$-0.652390\pi$
$373$	5.39544e8	−	9.34518e8i	0.538327	−	0.932409i	0.998994	−	0.0448366i	$-0.0142767\pi$
$374$	−2.88930e8	−	5.00441e8i	−0.285589	−	0.494655i
$375$	3.19730e9	+	1.02652e9i	3.13093	+	1.00521i
$376$	3.84651e8	+	2.22079e8i	0.373173	+	0.215451i
$377$	1.73242e7			0.0166517
$378$	1.08277e9	+	8.18251e8i	1.03113	+	0.779229i
$379$	1.22890e9			1.15952			0.579761	−	0.814787i	$-0.303146\pi$
$379$	1.22890e9			1.15952			0.579761	+	0.814787i	$0.303146\pi$
$380$	−1.06702e9	−	6.16042e8i	−0.997535	−	0.575927i
$381$	−7.74856e8	−	2.48773e8i	−0.717767	−	0.230444i
$382$	−6.21626e8	−	1.07669e9i	−0.570568	−	0.988253i
$383$	5.18994e8	−	8.98924e8i	0.472027	−	0.817574i	−0.527461	−	0.849579i	$-0.676856\pi$
$383$	5.18994e8	−	8.98924e8i	0.472027	−	0.817574i	0.999488	+	0.0320050i	$0.0101893\pi$
$384$	−6.00465e8	−	6.62212e8i	−0.541164	−	0.596812i
$385$	6.70604e8	+	6.40386e8i	0.598899	+	0.571912i
$386$			2.63914e9i			2.33565i
$387$	−8.42718e7	−	6.03309e7i	−0.0739084	−	0.0529117i
$388$	6.09083e8	−	3.51654e8i	0.529377	−	0.305636i
$389$	4.61824e8	−	2.66634e8i	0.397790	−	0.229664i	−0.287740	−	0.957708i	$-0.592904\pi$
$389$	4.61824e8	−	2.66634e8i	0.397790	−	0.229664i	0.685530	+	0.728045i	$0.259571\pi$
$390$	−3.35324e7	−	1.55089e8i	−0.0286246	−	0.132390i
$391$			6.41238e8i			0.542501i
$392$	−5.07453e8	+	2.34060e7i	−0.425495	+	0.0196257i
$393$	−1.58134e9	+	1.43389e9i	−1.31417	+	1.19163i
$394$	−1.53471e9	+	2.65819e9i	−1.26412	+	2.18952i
$395$	3.37215e8	+	5.84073e8i	0.275307	+	0.476845i
$396$	1.47196e8	+	3.24479e8i	0.119114	+	0.262575i
$397$	−9.29738e8	−	5.36785e8i	−0.745751	−	0.430560i	0.0784055	−	0.996922i	$-0.475017\pi$
$397$	−9.29738e8	−	5.36785e8i	−0.745751	−	0.430560i	−0.824157	+	0.566362i	$0.808350\pi$
$398$	2.14364e9			1.70436
$399$	1.13174e9	+	2.92241e7i	0.891953	+	0.0230323i
$400$	−4.23171e9			−3.30602
$401$	−1.98658e9	−	1.14695e9i	−1.53851	−	0.888262i	−0.998926	−	0.0463328i	$-0.985247\pi$
$401$	−1.98658e9	−	1.14695e9i	−1.53851	−	0.888262i	−0.539588	−	0.841929i	$-0.681420\pi$
$402$	4.16979e8	−	1.29877e9i	0.320127	−	0.997103i
$403$	6.25569e6	+	1.08352e7i	0.00476111	+	0.00824648i
$404$	5.80291e8	−	1.00509e9i	0.437836	−	0.758354i
$405$	−2.52522e9	−	4.99935e8i	−1.88889	−	0.373957i
$406$	−1.49841e8	−	5.11738e8i	−0.111119	−	0.379495i
$407$			5.44851e8i			0.400587i
$408$	−5.86908e8	+	1.26898e8i	−0.427819	+	0.0925007i
$409$	1.47920e9	−	8.54019e8i	1.06905	−	0.617214i	0.141126	−	0.989992i	$-0.454928\pi$
$409$	1.47920e9	−	8.54019e8i	1.06905	−	0.617214i	0.927921	+	0.372777i	$0.121594\pi$
$410$	2.11072e9	−	1.21863e9i	1.51247	−	0.873228i
$411$	1.34664e9	−	2.91163e8i	0.956764	−	0.206866i
$412$			8.12353e8i			0.572274i
$413$	8.72869e8	+	2.12453e8i	0.609711	+	0.148401i
$414$	9.61182e7	−	9.80426e8i	0.0665740	−	0.679069i
$415$	−1.19594e9	+	2.07143e9i	−0.821375	+	1.42266i
$416$	4.60345e7	+	7.97340e7i	0.0313514	+	0.0543021i
$417$	8.60648e8	−	2.68067e9i	0.581232	−	1.81037i
$418$	6.41330e8	+	3.70272e8i	0.429501	+	0.247973i
$419$	1.93716e9			1.28652			0.643261	−	0.765647i	$-0.277581\pi$
$419$	1.93716e9			1.28652			0.643261	+	0.765647i	$0.277581\pi$
$420$	−1.72225e9	+	9.35917e8i	−1.13429	+	0.616403i
$421$	2.15401e9			1.40689			0.703447	−	0.710748i	$-0.251643\pi$
$421$	2.15401e9			1.40689			0.703447	+	0.710748i	$0.251643\pi$
$422$	1.83569e9	+	1.05984e9i	1.18907	+	0.686509i
$423$	−1.43410e9	+	6.50559e8i	−0.921271	+	0.417922i
$424$	2.42061e8	+	4.19261e8i	0.154221	+	0.267119i
$425$	−2.20173e9	+	3.81350e9i	−1.39124	+	2.40970i
$426$	−3.40843e8	+	3.09062e8i	−0.213610	+	0.193692i
$427$	1.31010e9	−	3.83607e8i	0.814342	−	0.238446i
$428$			1.69141e7i			0.0104279i
$429$	8.08914e6	+	3.74125e7i	0.00494654	+	0.0228779i
$430$	3.22987e8	−	1.86477e8i	0.195905	−	0.113106i
$431$	−2.52692e9	+	1.45892e9i	−1.52027	+	0.877729i	−0.520557	+	0.853827i	$0.674276\pi$
$431$	−2.52692e9	+	1.45892e9i	−1.52027	+	0.877729i	−0.999714	+	0.0239018i	$0.992391\pi$
$432$	2.03237e9	−	2.35195e8i	1.21286	−	0.140357i
$433$			1.75910e9i			1.04132i	0.853765	+	0.520659i	$0.174314\pi$
$433$			1.75910e9i			1.04132i	−0.853765	+	0.520659i	$0.825686\pi$
$434$	2.65952e8	−	2.78502e8i	0.156167	−	0.163536i
$435$	6.79380e8	+	7.49242e8i	0.395731	+	0.436425i
$436$	−7.93439e7	+	1.37428e8i	−0.0458470	+	0.0794093i
$437$	−4.10883e8	−	7.11669e8i	−0.235523	−	0.407937i
$438$	−2.40338e9	−	7.71624e8i	−1.36667	−	0.438780i
$439$	−1.10932e9	−	6.40468e8i	−0.625795	−	0.361303i	0.153327	−	0.988176i	$-0.451001\pi$
$439$	−1.10932e9	−	6.40468e8i	−0.625795	−	0.361303i	−0.779122	+	0.626873i	$0.784335\pi$
$440$	6.30272e8			0.352731
$441$	9.79845e8	−	1.51123e9i	0.544029	−	0.839066i
$442$	1.31227e8			0.0722844
$443$	−1.15271e9	−	6.65519e8i	−0.629953	−	0.363703i	0.150781	−	0.988567i	$-0.451821\pi$
$443$	−1.15271e9	−	6.65519e8i	−0.629953	−	0.363703i	−0.780734	+	0.624864i	$0.785155\pi$
$444$	−1.09663e9	−	3.52080e8i	−0.594590	−	0.190898i
$445$	3.96778e8	+	6.87239e8i	0.213446	+	0.369699i
$446$	−1.38998e9	+	2.40751e9i	−0.741884	+	1.28498i
$447$	3.27442e8	+	3.61114e8i	0.173404	+	0.191235i
$448$	3.52316e8	−	3.68941e8i	0.185123	−	0.193858i
$449$			9.16466e8i			0.477809i	0.971043	+	0.238905i	$0.0767883\pi$
$449$			9.16466e8i			0.477809i	−0.971043	+	0.238905i	$0.923212\pi$
$450$	3.93797e9	−	5.50066e9i	2.03718	−	2.84558i
$451$	−5.09177e8	+	2.93974e8i	−0.261367	+	0.150900i
$452$	1.14582e9	−	6.61539e8i	0.583621	−	0.336954i
$453$	3.77212e8	+	1.74462e9i	0.190652	+	0.881772i
$454$			6.56773e8i			0.329397i
$455$	−2.02087e8	+	5.91726e7i	−0.100577	+	0.0294497i
$456$	5.70060e8	−	5.16906e8i	0.281542	−	0.255291i
$457$	−3.22049e8	+	5.57805e8i	−0.157839	+	0.273386i	−0.934089	−	0.357040i	$-0.883786\pi$
$457$	−3.22049e8	+	5.57805e8i	−0.157839	+	0.273386i	0.776250	+	0.630425i	$0.217119\pi$
$458$	−6.00811e8	−	1.04064e9i	−0.292219	−	0.506139i
$459$	8.45475e8	−	1.95389e9i	0.408090	−	0.943094i
$460$	1.23217e9	+	7.11393e8i	0.590225	+	0.340767i
$461$	−1.81792e9			−0.864215			−0.432108	−	0.901822i	$-0.642230\pi$
$461$	−1.81792e9			−0.864215			−0.432108	+	0.901822i	$0.642230\pi$
$462$	1.03516e9	−	5.62532e8i	0.488382	−	0.265400i
$463$	−1.41455e9			−0.662348			−0.331174	−	0.943570i	$-0.607445\pi$
$463$	−1.41455e9			−0.662348			−0.331174	+	0.943570i	$0.607445\pi$
$464$	−6.96139e8	−	4.01916e8i	−0.323507	−	0.186777i
$465$	−2.23281e8	+	6.95456e8i	−0.102983	+	0.320763i
$466$	−2.66151e8	−	4.60987e8i	−0.121836	−	0.211027i
$467$	2.04006e9	−	3.53349e9i	0.926902	−	1.60544i	0.138429	−	0.990372i	$-0.455795\pi$
$467$	2.04006e9	−	3.53349e9i	0.926902	−	1.60544i	0.788473	−	0.615069i	$-0.210872\pi$
$468$	−8.05277e7	−	7.89471e6i	−0.0363149	−	0.00356021i
$469$	−1.75888e9	−	4.28104e8i	−0.787283	−	0.191622i
$470$		−	5.66676e9i		−	2.51763i
$471$	−2.50424e9	+	5.41454e8i	−1.10434	+	0.238775i
$472$	5.28817e8	−	3.05313e8i	0.231477	−	0.133644i
$473$	−7.79152e7	+	4.49844e7i	−0.0338539	+	0.0195455i
$474$	8.37548e8	−	1.81090e8i	0.361232	−	0.0781036i
$475$		−	5.64315e9i		−	2.41598i
$476$	−4.55539e8	−	1.55576e9i	−0.193598	−	0.661179i
$477$	−1.70826e9	−	1.67473e8i	−0.720676	−	0.0706531i
$478$	−7.61471e8	+	1.31891e9i	−0.318901	+	0.552353i
$479$	−515988.	−	893717.i	−0.000214519	−	0.000371557i	0.865918	−	0.500186i	$-0.166735\pi$
$479$	−515988.	−	893717.i	−0.000214519	−	0.000371557i	−0.866133	+	0.499814i	$0.833402\pi$
$480$	−1.64308e9	+	5.11772e9i	−0.678134	+	2.11219i
$481$	−1.07154e8	−	6.18654e7i	−0.0439037	−	0.0253478i
$482$	−4.11021e9			−1.67186
$483$	−1.30691e9	−	3.37474e7i	−0.527754	−	0.0136278i
$484$	−1.36300e9			−0.546435
$485$	3.81997e9	+	2.20546e9i	1.52042	+	0.877815i
$486$	−1.58557e9	+	2.86068e9i	−0.626555	+	1.13043i
$487$	4.79628e8	+	8.30739e8i	0.188171	+	0.325922i	0.944640	−	0.328107i	$-0.106411\pi$
$487$	4.79628e8	+	8.30739e8i	0.188171	+	0.325922i	−0.756469	+	0.654029i	$0.773077\pi$
$488$	4.63943e8	−	8.03573e8i	0.180716	−	0.313009i
$489$	2.08867e9	−	1.89391e9i	0.807771	−	0.732452i
$490$	3.49578e9	+	5.45762e9i	1.34232	+	2.09564i
$491$		−	6.85759e8i		−	0.261449i	−0.991419	−	0.130724i	$-0.958270\pi$
$491$		−	6.85759e8i		−	0.261449i	0.991419	−	0.130724i	$-0.0417303\pi$
$492$	−2.62655e8	−	1.21479e9i	−0.0994279	−	0.459857i
$493$	−7.24391e8	+	4.18228e8i	−0.272276	+	0.157199i
$494$	−1.45640e8	+	8.40855e7i	−0.0543547	+	0.0313817i
$495$	−1.30080e9	+	1.81700e9i	−0.482052	+	0.673342i
$496$		−	5.80520e8i		−	0.213615i
$497$	4.41590e8	+	4.21691e8i	0.161351	+	0.154080i
$498$	2.04139e9	+	2.25131e9i	0.740668	+	0.816831i
$499$	1.49005e9	−	2.58084e9i	0.536844	−	0.929841i	−0.462227	−	0.886761i	$-0.652950\pi$
$499$	1.49005e9	−	2.58084e9i	0.536844	−	0.929841i	0.999072	−	0.0430800i	$-0.0137170\pi$
$500$	3.08105e9	+	5.33653e9i	1.10231	+	1.90926i
$501$	−1.40805e9	−	4.52064e8i	−0.500248	−	0.160608i
$502$	−4.10122e9	−	2.36784e9i	−1.44694	−	0.835390i
$503$	2.90478e9			1.01771			0.508856	−	0.860852i	$-0.330069\pi$
$503$	2.90478e9			1.01771			0.508856	+	0.860852i	$0.330069\pi$
$504$	−2.27744e8	−	1.20286e9i	−0.0792392	−	0.418512i
$505$	7.27880e9			2.51501
$506$	−7.40595e8	−	4.27583e8i	−0.254129	−	0.146721i
$507$	2.78571e9	+	8.94374e8i	0.949311	+	0.304783i
$508$	−7.46682e8	−	1.29329e9i	−0.252704	−	0.437697i
$509$	2.50540e8	−	4.33948e8i	0.0842102	−	0.145856i	−0.820844	−	0.571152i	$-0.806497\pi$
$509$	2.50540e8	−	4.33948e8i	0.0842102	−	0.145856i	0.905054	+	0.425296i	$0.139830\pi$
$510$	5.14614e9	+	5.67532e9i	1.71785	+	1.89450i
$511$	−7.92211e8	+	3.25483e9i	−0.262644	+	1.07908i
$512$		−	2.69250e9i		−	0.886567i
$513$	3.13642e8	+	2.71025e9i	0.102571	+	0.886335i
$514$	−2.54129e9	+	1.46721e9i	−0.825435	+	0.476565i
$515$	−4.41224e9	+	2.54741e9i	−1.42342	+	0.821813i
$516$	−4.01920e7	−	1.85889e8i	−0.0128785	−	0.0595635i
$517$			1.36701e9i			0.435066i
$518$	−9.00636e8	+	3.70029e9i	−0.284705	+	1.16972i
$519$	−1.23028e8	+	1.11557e8i	−0.0386296	+	0.0350276i
$520$	−7.15646e7	+	1.23954e8i	−0.0223196	+	0.0386587i
$521$	2.31309e9	+	4.00639e9i	0.716573	+	1.24114i	0.962350	+	0.271814i	$0.0876237\pi$
$521$	2.31309e9	+	4.00639e9i	0.716573	+	1.24114i	−0.245777	+	0.969327i	$0.579043\pi$
$522$	1.17025e9	−	5.30870e8i	0.360109	−	0.163358i
$523$	−3.91578e9	−	2.26078e9i	−1.19691	−	0.691037i	−0.237046	−	0.971498i	$-0.576179\pi$
$523$	−3.91578e9	−	2.26078e9i	−1.19691	−	0.691037i	−0.959865	+	0.280461i	$0.909513\pi$
$524$	−3.91712e9			−1.18934
$525$	−7.65645e9	−	4.68805e9i	−2.30924	−	1.41395i
$526$	6.29545e9			1.88615
$527$	−5.23148e8	−	3.02040e8i	−0.155700	−	0.0898932i
$528$	5.42912e8	−	1.69101e9i	0.160513	−	0.499951i
$529$	−1.22793e9	−	2.12684e9i	−0.360645	−	0.624656i
$530$	3.08832e9	−	5.34913e9i	0.901066	−	1.56069i
$531$	−2.11235e8	+	2.15464e9i	−0.0612259	+	0.624517i
$532$	1.50245e9	+	1.43475e9i	0.432623	+	0.413128i
$533$		−	1.33518e8i		−	0.0381939i
$534$	9.85486e8	−	2.13077e8i	0.280063	−	0.0605538i
$535$	−9.18678e7	+	5.30399e7i	−0.0259373	+	0.0149749i
$536$	−1.06560e9	+	6.15222e8i	−0.298893	+	0.172566i
$537$	4.02427e9	−	8.70107e8i	1.12144	−	0.242473i
$538$		−	3.54840e9i		−	0.982414i
$539$	−8.43298e8	−	1.31656e9i	−0.231964	−	0.362142i
$540$	−2.81651e9	−	3.79227e9i	−0.769721	−	1.03639i
$541$	−5.49428e8	+	9.51638e8i	−0.149183	+	0.258393i	−0.930926	−	0.365208i	$-0.880998\pi$
$541$	−5.49428e8	+	9.51638e8i	−0.149183	+	0.258393i	0.781742	+	0.623601i	$0.214331\pi$
$542$	−1.07735e9	−	1.86603e9i	−0.290644	−	0.503410i
$543$	−1.60918e9	+	5.01211e9i	−0.431324	+	1.34345i
$544$	−3.84975e9	−	2.22265e9i	−1.02526	−	0.591937i
$545$	−9.95238e8			−0.263354
$546$	−6.90628e6	+	2.67454e8i	−0.00181581	+	0.0703195i
$547$	−4.60429e9			−1.20284			−0.601419	−	0.798934i	$-0.705398\pi$
$547$	−4.60429e9			−1.20284			−0.601419	+	0.798934i	$0.705398\pi$
$548$	2.18950e9	+	1.26411e9i	0.568346	+	0.328135i
$549$	1.35908e9	+	2.99597e9i	0.350544	+	0.772741i
$550$	−2.93626e9	−	5.08574e9i	−0.752531	−	1.30342i
$551$	5.35971e8	−	9.28328e8i	0.136493	−	0.236413i
$552$	−6.58295e8	+	5.96913e8i	−0.166584	+	0.151051i
$553$	−3.19558e8	−	1.09136e9i	−0.0803549	−	0.274429i
$554$			7.53205e9i			1.88204i
$555$	−1.52654e9	−	7.06031e9i	−0.379039	−	1.75307i
$556$	4.47423e9	−	2.58320e9i	1.10397	−	0.637377i
$557$	3.59243e9	−	2.07409e9i	0.880837	−	0.508551i	0.00990238	−	0.999951i	$-0.496848\pi$
$557$	3.59243e9	−	2.07409e9i	0.880837	−	0.508551i	0.870934	+	0.491400i	$0.163515\pi$
$558$	7.54598e8	+	5.40223e8i	0.183864	+	0.131630i
$559$		−	2.04311e7i		−	0.00494710i
$560$	9.49323e9	+	2.31061e9i	2.28431	+	0.555993i
$561$	−1.24142e9	−	1.36908e9i	−0.296858	−	0.327384i
$562$	2.73596e9	−	4.73882e9i	0.650179	−	1.12614i
$563$	−3.29882e9	−	5.71373e9i	−0.779075	−	1.34940i	−0.932475	−	0.361234i	$-0.882356\pi$
$563$	−3.29882e9	−	5.71373e9i	−0.779075	−	1.34940i	0.153400	−	0.988164i	$-0.450978\pi$
$564$	−2.75139e9	−	8.83356e8i	−0.645767	−	0.207328i
$565$	7.18620e9	+	4.14895e9i	1.67621	+	0.967763i
$566$	−5.49650e9			−1.27417
$567$	3.93773e9	+	1.82600e9i	0.907206	+	0.420688i
$568$	4.15031e8			0.0950301
$569$	−9.40776e8	−	5.43157e8i	−0.214089	−	0.123604i	0.389122	−	0.921186i	$-0.372779\pi$
$569$	−9.40776e8	−	5.43157e8i	−0.214089	−	0.123604i	−0.603210	+	0.797582i	$0.706112\pi$
$570$	−9.34792e9	−	3.00122e9i	−2.11423	−	0.678790i
$571$	7.54394e8	+	1.30665e9i	0.169579	+	0.293719i	0.938272	−	0.345899i	$-0.112426\pi$
$571$	7.54394e8	+	1.30665e9i	0.169579	+	0.293719i	−0.768693	+	0.639618i	$0.779093\pi$
$572$	−3.51197e7	+	6.08290e7i	−0.00784629	+	0.0135902i
$573$	−2.67089e9	−	2.94554e9i	−0.593082	−	0.654069i
$574$	−3.94396e9	+	1.15482e9i	−0.870443	+	0.254872i
$575$			6.51660e9i			1.42950i
$576$	9.99642e8	+	7.15653e8i	0.217955	+	0.156036i
$577$	6.90685e8	−	3.98767e8i	0.149680	−	0.0864180i	−0.423289	−	0.905995i	$-0.639125\pi$
$577$	6.90685e8	−	3.98767e8i	0.149680	−	0.0864180i	0.572970	+	0.819577i	$0.305791\pi$
$578$	−2.90805e8	+	1.67896e8i	−0.0626404	+	0.0361654i
$579$	1.78374e9	+	8.24985e9i	0.381906	+	1.76633i
$580$			1.85594e9i			0.394971i
$581$	2.78532e9	−	2.91675e9i	0.589194	−	0.616997i
$582$	4.15168e9	−	3.76457e9i	0.872959	−	0.791562i
$583$	−7.45006e8	+	1.29039e9i	−0.155711	+	0.269700i
$584$	1.13847e9	+	1.97190e9i	0.236526	+	0.409675i
$585$	−2.09642e8	−	4.62137e8i	−0.0432945	−	0.0954388i
$586$	2.31707e8	+	1.33776e8i	0.0475661	+	0.0274623i
$587$	−3.14642e9			−0.642072			−0.321036	−	0.947067i	$-0.604031\pi$
$587$	−3.14642e9			−0.642072			−0.321036	+	0.947067i	$0.604031\pi$
$588$	3.19478e9	−	8.46560e8i	0.648068	−	0.171726i
$589$	7.74145e8			0.156106
$590$	−6.74689e9	−	3.89532e9i	−1.35245	−	0.780838i
$591$	−3.00082e9	+	9.34666e9i	−0.597975	+	1.86252i
$592$	2.87051e9	+	4.97187e9i	0.568635	+	0.984904i
$593$	1.02329e9	−	1.77240e9i	0.201516	−	0.349035i	−0.747501	−	0.664260i	$-0.768747\pi$
$593$	1.02329e9	−	1.77240e9i	0.201516	−	0.349035i	0.949017	+	0.315225i	$0.102080\pi$
$594$	1.69286e9	+	2.27934e9i	0.331413	+	0.446229i
$595$	7.02151e9	−	7.35284e9i	1.36654	−	1.43102i
$596$			8.94509e8i			0.173070i
$597$	6.70093e9	−	1.44884e9i	1.28892	−	0.278683i
$598$	1.68183e8	−	9.71003e7i	0.0321608	−	0.0185680i
$599$	4.71997e8	−	2.72508e8i	0.0897316	−	0.0518066i	−0.454463	−	0.890766i	$-0.650169\pi$
$599$	4.71997e8	−	2.72508e8i	0.0897316	−	0.0518066i	0.544194	+	0.838959i	$0.316835\pi$
$600$	−5.96447e9	+	1.28961e9i	−1.12731	+	0.243741i
$601$		−	1.21229e9i		−	0.227796i	−0.993492	−	0.113898i	$-0.963666\pi$
$601$		−	1.21229e9i		−	0.227796i	0.993492	−	0.113898i	$-0.0363336\pi$
$602$	−6.03511e8	+	1.76713e8i	−0.112745	+	0.0330126i
$603$	4.25650e8	−	4.34172e9i	0.0790573	−	0.806402i
$604$	−1.63770e9	+	2.83657e9i	−0.302415	+	0.523799i
$605$	−4.27416e9	−	7.40306e9i	−0.784705	−	1.35915i
$606$	2.82705e9	−	8.80543e9i	0.516035	−	1.60730i
$607$	1.38049e9	+	7.97028e8i	0.250538	+	0.144648i	0.620011	−	0.784593i	$-0.287128\pi$
$607$	1.38049e9	+	7.97028e8i	0.250538	+	0.144648i	−0.369473	+	0.929242i	$0.620462\pi$
$608$	5.69679e9			1.02794
$609$	−8.14269e8	−	1.49840e9i	−0.146086	−	0.268823i
$610$	−1.18384e10			−2.11173
$611$	−2.68846e8	−	1.55218e8i	−0.0476825	−	0.0275295i
$612$	3.55775e9	−	1.61393e9i	0.627402	−	0.284612i
$613$	8.48511e8	+	1.46966e9i	0.148780	+	0.257695i	0.930777	−	0.365587i	$-0.119132\pi$
$613$	8.48511e8	+	1.46966e9i	0.148780	+	0.257695i	−0.781997	+	0.623283i	$0.785799\pi$
$614$	−5.11383e9	+	8.85741e9i	−0.891572	+	1.54425i
$615$	5.77440e9	−	5.23598e9i	1.00102	−	0.907684i
$616$	−1.03258e9	−	2.51326e8i	−0.177988	−	0.0433216i
$617$		−	1.19915e9i		−	0.205530i	−0.994706	−	0.102765i	$-0.967231\pi$
$617$		−	1.19915e9i		−	0.205530i	0.994706	−	0.102765i	$-0.0327690\pi$
$618$	1.36800e9	+	6.32705e9i	0.233145	+	1.07830i
$619$	−5.24316e9	+	3.02714e9i	−0.888538	+	0.512997i	−0.873464	−	0.486889i	$-0.838132\pi$
$619$	−5.24316e9	+	3.02714e9i	−0.888538	+	0.512997i	−0.0150737	+	0.999886i	$0.504798\pi$
$620$	−1.16077e9	+	6.70169e8i	−0.195602	+	0.112931i
$621$	−3.62187e8	−	3.12974e9i	−0.0606894	−	0.524430i
$622$			6.19338e9i			1.03196i
$623$	−3.76003e8	−	1.28413e9i	−0.0622992	−	0.212765i
$624$	2.70921e8	+	2.98780e8i	0.0446371	+	0.0492272i
$625$	−1.10600e10	+	1.91564e10i	−1.81206	+	3.13859i
$626$	2.45920e9	+	4.25946e9i	0.400667	+	0.693975i
$627$	2.25503e9	+	7.23994e8i	0.365356	+	0.117300i
$628$	−4.07164e9	−	2.35076e9i	−0.656011	−	0.378748i
$629$	5.97402e9			0.957170
$630$	−1.18378e10	+	1.01897e10i	−1.88615	+	1.62356i
$631$	−4.25664e8			−0.0674472			−0.0337236	−	0.999431i	$-0.510737\pi$
$631$	−4.25664e8			−0.0674472			−0.0337236	+	0.999431i	$0.510737\pi$
$632$	−6.69405e8	−	3.86481e8i	−0.105482	−	0.0609002i
$633$	6.45463e9	+	2.07231e9i	1.01148	+	0.324744i
$634$	5.05264e9	+	8.75143e9i	0.787419	+	1.36385i
$635$	4.68295e9	−	8.11110e9i	0.725791	−	1.25711i
$636$	−2.11576e9	−	2.33332e9i	−0.326111	−	0.359646i
$637$	3.54676e8	−	1.63592e7i	0.0543681	−	0.00250770i
$638$		−	1.11551e9i		−	0.170060i
$639$	−8.56573e8	+	1.19648e9i	−0.129871	+	0.181407i
$640$	8.90947e9	−	5.14389e9i	1.34345	−	0.775642i
$641$	7.45438e9	−	4.30379e9i	1.11791	−	0.645428i	0.177046	−	0.984203i	$-0.443346\pi$
$641$	7.45438e9	−	4.30379e9i	1.11791	−	0.645428i	0.940868	+	0.338775i	$0.110012\pi$
$642$	2.84834e7	+	1.31736e8i	0.00424833	+	0.0196487i
$643$		−	2.22868e9i		−	0.330605i	−0.986243	−	0.165303i	$-0.947140\pi$
$643$		−	2.22868e9i		−	0.330605i	0.986243	−	0.165303i	$-0.0528601\pi$
$644$	−1.73500e9	−	1.65682e9i	−0.255976	−	0.244441i
$645$	8.83609e8	−	8.01218e8i	0.129659	−	0.117569i
$646$	4.05985e9	−	7.03186e9i	0.592510	−	1.02626i
$647$	−2.39282e9	−	4.14449e9i	−0.347333	−	0.601598i	0.638442	−	0.769670i	$-0.279579\pi$
$647$	−2.39282e9	−	4.14449e9i	−0.347333	−	0.601598i	−0.985775	+	0.168072i	$0.946246\pi$
$648$	2.79289e9	−	9.50862e8i	0.403219	−	0.137279i
$649$	1.62757e9	+	9.39681e8i	0.233714	+	0.134935i
$650$	1.33360e9			0.190470
$651$	6.43122e8	−	1.05034e9i	0.0913608	−	0.149209i
$652$	5.17381e9			0.731044
$653$	−3.97133e9	−	2.29285e9i	−0.558136	−	0.322240i	0.194261	−	0.980950i	$-0.437769\pi$
$653$	−3.97133e9	−	2.29285e9i	−0.558136	−	0.322240i	−0.752397	+	0.658710i	$0.771103\pi$
$654$	−3.86546e8	+	1.20398e9i	−0.0540355	+	0.168305i
$655$	−1.22834e10	−	2.12756e10i	−1.70795	−	2.95826i
$656$	−3.09756e9	+	5.36514e9i	−0.428407	+	0.742023i
$657$	−8.03441e9	−	7.87670e8i	−1.10529	−	0.108359i
$658$	−2.25966e9	+	9.28390e9i	−0.309210	+	1.27040i
$659$			1.15059e10i			1.56610i	0.621956	+	0.783052i	$0.286338\pi$
$659$			1.15059e10i			1.56610i	−0.621956	+	0.783052i	$0.713662\pi$
$660$	−4.00798e9	+	8.66585e8i	−0.542653	+	0.117330i
$661$	3.44053e9	−	1.98639e9i	0.463361	−	0.267522i	−0.250095	−	0.968221i	$-0.580462\pi$
$661$	3.44053e9	−	1.98639e9i	0.463361	−	0.267522i	0.713457	+	0.700699i	$0.247129\pi$
$662$	1.08422e10	−	6.25973e9i	1.45249	−	0.838595i
$663$	4.10210e8	−	8.86934e7i	0.0546649	−	0.0118194i
$664$		−	2.74133e9i		−	0.363390i
$665$	−3.08129e9	+	1.26596e10i	−0.406310	+	1.66934i
$666$	−9.13402e9	−	8.95474e8i	−1.19813	−	0.117461i
$667$	−6.18928e8	+	1.07202e9i	−0.0807607	+	0.139882i
$668$	−1.35685e9	−	2.35014e9i	−0.176123	−	0.305053i
$669$	−2.71783e9	+	8.46525e9i	−0.350939	+	1.09307i
$670$	1.35953e10	+	7.84928e9i	1.74634	+	1.00825i
$671$	2.85582e9			0.364923
$672$	4.73261e9	−	7.72922e9i	0.601601	−	0.982524i
$673$	2.68753e9			0.339861			0.169931	−	0.985456i	$-0.445646\pi$
$673$	2.68753e9			0.339861			0.169931	+	0.985456i	$0.445646\pi$
$674$	−1.05197e10	−	6.07353e9i	−1.32340	−	0.764068i
$675$	8.59216e9	−	1.98564e10i	1.07532	−	2.48506i
$676$	2.68443e9	+	4.64956e9i	0.334224	+	0.578893i
$677$	−3.78037e9	+	6.54778e9i	−0.468245	+	0.811025i	−0.999341	−	0.0362869i	$-0.988447\pi$
$677$	−3.78037e9	+	6.54778e9i	−0.468245	+	0.811025i	0.531096	+	0.847312i	$0.321780\pi$
$678$	7.81023e9	−	7.08198e9i	0.962410	−	0.872672i
$679$	−5.37884e9	−	5.13646e9i	−0.659393	−	0.629680i
$680$		−	6.91062e9i		−	0.842822i
$681$	4.43899e8	+	2.05305e9i	0.0538604	+	0.249106i
$682$	6.97679e8	−	4.02805e8i	0.0842190	−	0.0486239i
$683$	−1.22736e10	+	7.08616e9i	−1.47401	+	0.851018i	−0.999571	−	0.0292726i	$-0.990681\pi$
$683$	−1.22736e10	+	7.08616e9i	−1.47401	+	0.851018i	−0.474435	+	0.880291i	$0.657348\pi$
$684$	−2.91438e9	+	4.07088e9i	−0.348217	+	0.486398i
$685$			1.58561e10i			1.88487i
$686$	−3.55090e9	−	1.03352e10i	−0.419956	−	1.22232i
$687$	−2.58146e9	−	2.84691e9i	−0.303750	−	0.334985i
$688$	−4.73995e8	+	8.20983e8i	−0.0554899	+	0.0961113i
$689$	−1.69184e8	−	2.93036e8i	−0.0197057	−	0.0341313i
$690$	1.07948e10	+	3.46575e9i	1.25096	+	0.401629i
$691$	−7.55947e9	−	4.36446e9i	−0.871602	−	0.503219i	−0.00372142	−	0.999993i	$-0.501185\pi$
$691$	−7.55947e9	−	4.36446e9i	−0.871602	−	0.503219i	−0.867880	+	0.496774i	$0.834518\pi$
$692$	−3.04752e8			−0.0349603
$693$	2.85566e9	−	2.45809e9i	0.325942	−	0.280564i
$694$	−1.67830e9			−0.190596
$695$	2.80609e10	+	1.62010e10i	3.17070	+	1.83061i
$696$	−1.10367e9	−	3.54342e8i	−0.124082	−	0.0398373i
$697$	3.22327e9	+	5.58288e9i	0.360564	+	0.624515i
$698$	−2.00436e9	+	3.47165e9i	−0.223090	+	0.386404i
$699$	−1.14355e9	−	1.26114e9i	−0.126644	−	0.139667i
$700$	−4.62942e9	−	1.58105e10i	−0.510134	−	1.74221i
$701$		−	1.45093e9i		−	0.159086i	−0.996831	−	0.0795432i	$-0.974654\pi$
$701$		−	1.45093e9i		−	0.159086i	0.996831	−	0.0795432i	$-0.0253461\pi$
$702$	−6.40488e8	+	7.41202e7i	−0.0698765	+	0.00808643i
$703$	−6.63018e9	+	3.82794e9i	−0.719750	+	0.415548i
$704$	9.24240e8	−	5.33610e8i	0.0998344	−	0.0576394i
$705$	−3.83004e9	−	1.77141e10i	−0.411663	−	1.90395i
$706$		−	1.82505e10i		−	1.95191i
$707$	−1.19249e10	−	2.90248e9i	−1.26908	−	0.308888i
$708$	−2.94303e9	+	2.66862e9i	−0.311658	+	0.282598i
$709$	7.91772e9	−	1.37139e10i	0.834331	−	1.44510i	−0.0602432	−	0.998184i	$-0.519188\pi$
$709$	7.91772e9	−	1.37139e10i	0.834331	−	1.44510i	0.894574	−	0.446920i	$-0.147479\pi$
$710$	−2.64758e9	−	4.58574e9i	−0.277616	−	0.480845i
$711$	2.49575e9	−	1.13216e9i	0.260410	−	0.118131i
$712$	−7.87643e8	−	4.54746e8i	−0.0817805	−	0.0472160i
$713$	−8.93968e8			−0.0923652
$714$	−6.16789e9	−	1.13500e10i	−0.634151	−	1.16695i
$715$	−4.40518e8			−0.0450705
$716$	6.54307e9	+	3.77764e9i	0.666171	+	0.384614i
$717$	−1.48891e9	+	4.63751e9i	−0.150852	+	0.469860i
$718$	4.49529e9	+	7.78607e9i	0.453234	+	0.785024i
$719$	−7.47727e8	+	1.29510e9i	−0.0750225	+	0.129943i	−0.901096	−	0.433619i	$-0.857236\pi$
$719$	−7.47727e8	+	1.29510e9i	−0.0750225	+	0.129943i	0.826074	+	0.563562i	$0.190570\pi$
$720$	−2.29737e9	+	2.34337e10i	−0.229386	+	2.33979i
$721$	8.24440e9	−	2.41402e9i	0.819192	−	0.239866i
$722$		−	2.66496e9i		−	0.263518i
$723$	−1.28484e10	+	2.77801e9i	−1.26434	+	0.273369i
$724$	−8.36559e9	+	4.82987e9i	−0.819241	+	0.472989i
$725$	−7.36165e9	+	4.25025e9i	−0.717450	+	0.414220i
$726$	−1.06158e10	+	2.29530e9i	−1.02962	+	0.222618i
$727$			1.76815e10i			1.70667i	0.521364	+	0.853334i	$0.325423\pi$
$727$			1.76815e10i			1.70667i	−0.521364	+	0.853334i	$0.674577\pi$
$728$	1.66672e8	−	1.74537e8i	0.0160105	−	0.0167660i
$729$	−3.02297e9	+	1.00140e10i	−0.288993	+	0.957331i
$730$	1.45252e10	−	2.51584e10i	1.38195	−	2.39360i
$731$	4.93231e8	+	8.54302e8i	0.0467025	+	0.0808910i
$732$	−1.84541e9	+	5.74793e9i	−0.173902	+	0.541655i
$733$	−2.58930e9	−	1.49494e9i	−0.242839	−	0.140203i	0.373642	−	0.927573i	$-0.378109\pi$
$733$	−2.58930e9	−	1.49494e9i	−0.242839	−	0.140203i	−0.616481	+	0.787370i	$0.711442\pi$
$734$	7.86652e9			0.734254
$735$	1.46163e10	+	1.46976e10i	1.35779	+	1.36534i
$736$	−6.57854e9			−0.608215
$737$	−3.27965e9	−	1.89351e9i	−0.301781	−	0.174233i
$738$	−4.09141e9	−	9.01913e9i	−0.374693	−	0.825976i
$739$	5.30209e9	+	9.18349e9i	0.483272	+	0.837052i	0.999815	−	0.0192094i	$-0.00611491\pi$
$739$	5.30209e9	+	9.18349e9i	0.483272	+	0.837052i	−0.516544	+	0.856261i	$0.672782\pi$
$740$	6.62761e9	−	1.14794e10i	0.601237	−	1.04137i
$741$	−3.98434e8	+	3.61283e8i	−0.0359744	+	0.0326200i
$742$	−7.19263e9	+	7.53203e9i	−0.646359	+	0.676860i
$743$			6.92790e9i			0.619642i	0.950795	+	0.309821i	$0.100269\pi$
$743$			6.92790e9i			0.619642i	−0.950795	+	0.309821i	$0.899731\pi$
$744$	−1.76912e8	−	8.18225e8i	−0.0157490	−	0.0728396i
$745$	−4.85846e9	+	2.80503e9i	−0.430479	+	0.248537i
$746$	1.36649e10	−	7.88945e9i	1.20510	−	0.695762i
$747$	7.90292e9	+	5.65777e9i	0.693690	+	0.496619i
$748$		−	3.39132e9i		−	0.296287i
$749$	1.71658e8	−	5.02628e7i	0.0149272	−	0.00437079i
$750$	3.29836e10	+	3.63754e10i	2.85485	+	3.14842i
$751$	3.62072e9	−	6.27127e9i	0.311929	−	0.540276i	−0.666851	−	0.745191i	$-0.732358\pi$
$751$	3.62072e9	−	6.27127e9i	0.311929	−	0.540276i	0.978780	+	0.204915i	$0.0656916\pi$
$752$	7.20201e9	+	1.24742e10i	0.617577	+	1.06968i
$753$	−1.44206e10	−	4.62985e9i	−1.23084	−	0.395170i
$754$	2.19384e8	+	1.26661e8i	0.0186382	+	0.0107608i
$755$	−2.05422e10			−1.73713
$756$	3.10212e9	+	7.33602e9i	0.261115	+	0.617496i
$757$	−1.94667e10			−1.63101			−0.815507	−	0.578747i	$-0.803542\pi$
$757$	−1.94667e10			−1.63101			−0.815507	+	0.578747i	$0.803542\pi$
$758$	1.55620e10	+	8.98475e9i	1.29785	+	0.749314i
$759$	−2.60406e9	−	8.36054e8i	−0.216175	−	0.0694046i
$760$	4.42808e9	+	7.66966e9i	0.365904	+	0.633765i
$761$	8.19400e9	−	1.41924e10i	0.673984	−	1.16737i	−0.302780	−	0.953060i	$-0.597915\pi$
$761$	8.19400e9	−	1.41924e10i	0.673984	−	1.16737i	0.976765	−	0.214315i	$-0.0687518\pi$
$762$	−7.99347e9	−	8.81545e9i	−0.654475	−	0.721776i
$763$	1.63051e9	+	3.96859e8i	0.132888	+	0.0323445i
$764$		−	7.29635e9i		−	0.591942i
$765$	1.99225e10	+	1.42627e10i	1.60890	+	1.15182i
$766$	1.31445e10	−	7.58896e9i	1.05668	−	0.610072i
$767$	−3.69608e8	+	2.13393e8i	−0.0295772	+	0.0170764i
$768$	−3.47348e9	−	1.60650e10i	−0.276695	−	1.27972i
$769$		−	1.90743e10i		−	1.51254i	−0.654259	−	0.756270i	$-0.727020\pi$
$769$		−	1.90743e10i		−	1.51254i	0.654259	−	0.756270i	$-0.272980\pi$
$770$	3.81013e9	+	1.30124e10i	0.300761	+	1.02716i
$771$	−6.95230e9	+	6.30405e9i	−0.546309	+	0.495369i
$772$	−7.74425e9	+	1.34134e10i	−0.605785	+	1.04925i
$773$	2.93621e9	+	5.08567e9i	0.228644	+	0.396023i	0.957406	−	0.288744i	$-0.0932376\pi$
$773$	2.93621e9	+	5.08567e9i	0.228644	+	0.396023i	−0.728763	+	0.684766i	$0.759904\pi$
$774$	−6.26075e8	−	1.38012e9i	−0.0485325	−	0.106985i
$775$	−5.31651e9	−	3.06949e9i	−0.410271	−	0.236870i
$776$	−5.05534e9			−0.388360
$777$	−3.14404e8	+	1.21757e10i	−0.0240444	+	0.931150i
$778$	7.79769e9			0.593660
$779$	−7.15462e9	−	4.13072e9i	−0.542257	−	0.313072i
$780$	2.84661e8	−	8.86635e8i	0.0214781	−	0.0668981i
$781$	6.38684e8	+	1.10623e9i	0.0479742	+	0.0830937i
$782$	−4.68823e9	+	8.12025e9i	−0.350579	+	0.607220i
$783$	3.29936e9	−	2.45043e9i	0.245620	−	0.182421i
$784$	−1.46315e10	−	7.57100e9i	−1.08438	−	0.561109i
$785$		−	2.94865e10i		−	2.17560i
$786$	−3.05087e10	+	6.59643e9i	−2.24101	+	0.484540i
$787$	1.02364e10	−	5.91001e9i	0.748579	−	0.432192i	−0.0766013	−	0.997062i	$-0.524407\pi$
$787$	1.02364e10	−	5.91001e9i	0.748579	−	0.432192i	0.825180	+	0.564870i	$0.191074\pi$
$788$	−1.56003e10	+	9.00682e9i	−1.13577	+	0.655737i
$789$	1.96793e10	−	4.25496e9i	1.42640	−	0.308408i
$790$			9.86181e9i			0.711642i
$791$	−1.01188e10	−	9.66282e9i	−0.726960	−	0.694203i
$792$	2.49885e8	−	2.54888e9i	0.0178732	−	0.182310i
$793$	−3.24266e8	+	5.61644e8i	−0.0230911	+	0.0399950i
$794$	−7.84910e9	−	1.35950e10i	−0.556478	−	0.963848i
$795$	6.03860e9	−	1.88085e10i	0.426238	−	1.32761i
$796$	1.08950e10	+	6.29026e9i	0.765655	+	0.442051i
$797$	−1.19819e9			−0.0838345			−0.0419173	−	0.999121i	$-0.513347\pi$
$797$	−1.19819e9			−0.0838345			−0.0419173	+	0.999121i	$0.513347\pi$
$798$	1.41180e10	+	8.64448e9i	0.983476	+	0.602183i
$799$	1.49886e10			1.03955
$800$	−3.91231e10	−	2.25878e10i	−2.70159	−	1.55976i
$801$	2.93658e9	−	1.33214e9i	0.201896	−	0.0915873i
$802$	−1.67713e10	−	2.90487e10i	−1.14804	−	1.98846i
$803$	−3.50396e9	+	6.06903e9i	−0.238811	+	0.413633i
$804$	5.93037e9	−	5.37741e9i	0.402426	−	0.364902i
$805$	3.55822e9	−	1.46190e10i	0.240407	−	0.987719i
$806$			1.82947e8i			0.0123070i
$807$	−2.39829e9	−	1.10922e10i	−0.160636	−	0.742948i
$808$	−7.22457e9	+	4.17110e9i	−0.481806	+	0.278171i
$809$	1.38749e10	−	8.01065e9i	0.921316	−	0.531922i	0.0372616	−	0.999306i	$-0.488137\pi$
$809$	1.38749e10	−	8.01065e9i	0.921316	−	0.531922i	0.884055	+	0.467383i	$0.154803\pi$
$810$	−2.83227e10	−	2.47933e10i	−1.87257	−	1.63922i
$811$			1.85573e10i			1.22164i	0.791770	+	0.610819i	$0.209160\pi$
$811$			1.85573e10i			1.22164i	−0.791770	+	0.610819i	$0.790840\pi$
$812$	7.40069e8	−	3.04060e9i	0.0485094	−	0.199303i
$813$	−4.62898e9	−	5.10498e9i	−0.302112	−	0.333179i
$814$	−3.98352e9	+	6.89966e9i	−0.258870	+	0.448376i
$815$	1.62242e10	+	2.81012e10i	1.04981	+	1.81833i
$816$	−1.85411e10	−	5.95276e9i	−1.19459	−	0.383533i
$817$	−1.09481e9	−	6.32090e8i	−0.0702364	−	0.0405510i
$818$	2.49757e10			1.59544
$819$	1.59178e8	+	8.40720e8i	0.0101249	+	0.0534758i
$820$	1.43037e10			0.905939
$821$	1.22520e10	+	7.07369e9i	0.772690	+	0.446113i	0.833834	−	0.552016i	$-0.186141\pi$
$821$	1.22520e10	+	7.07369e9i	0.772690	+	0.446113i	−0.0611431	+	0.998129i	$0.519475\pi$
$822$	1.91818e10	+	6.15845e9i	1.20459	+	0.386741i
$823$	2.52111e9	+	4.36670e9i	0.157650	+	0.273057i	0.934021	−	0.357219i	$-0.116275\pi$
$823$	2.52111e9	+	4.36670e9i	0.157650	+	0.273057i	−0.776371	+	0.630276i	$0.782942\pi$
$824$	2.91957e9	−	5.05685e9i	0.181792	−	0.314873i
$825$	−1.26160e10	−	1.39133e10i	−0.782225	−	0.862662i
$826$	9.50020e9	+	9.07211e9i	0.586547	+	0.560116i
$827$		−	2.69970e10i		−	1.65976i	−0.557941	−	0.829881i	$-0.688408\pi$
$827$		−	2.69970e10i		−	1.65976i	0.557941	−	0.829881i	$-0.311592\pi$
$828$	3.36547e9	−	4.70097e9i	0.206034	−	0.287794i
$829$	−2.29907e10	+	1.32737e10i	−1.40156	+	0.809191i	−0.994553	−	0.104234i	$-0.966761\pi$
$829$	−2.29907e10	+	1.32737e10i	−1.40156	+	0.809191i	−0.407007	+	0.913425i	$0.633428\pi$
$830$	−3.02894e10	+	1.74876e10i	−1.83873	+	1.06159i
$831$	5.09075e9	+	2.35449e10i	0.307736	+	1.42329i
$832$			2.42356e8i			0.0145889i
$833$	−1.44354e10	+	9.24634e9i	−0.865310	+	0.554259i
$834$	3.04977e10	−	2.76540e10i	1.82048	−	1.65073i
$835$	8.50973e9	−	1.47393e10i	0.505840	−	0.876141i
$836$	2.17304e9	+	3.76381e9i	0.128631	+	0.222795i
$837$	2.72397e9	+	1.17870e9i	0.160569	+	0.0694807i
$838$	2.45311e10	+	1.41630e10i	1.44000	+	0.831385i
$839$	1.50756e10			0.881266			0.440633	−	0.897687i	$-0.354754\pi$
$839$	1.50756e10			0.881266			0.440633	+	0.897687i	$0.354754\pi$
$840$	1.40846e10	+	3.63696e8i	0.819910	+	0.0211720i
$841$	1.56352e10			0.906393
$842$	2.72771e10	+	1.57485e10i	1.57473	+	0.909172i
$843$	5.34964e9	−	1.66626e10i	0.307558	−	0.957955i
$844$	6.21994e9	+	1.07733e10i	0.356113	+	0.616806i
$845$	−1.68358e10	+	2.91605e10i	−0.959923	+	1.66264i
$846$	−2.29169e10	−	2.24671e9i	−1.30125	−	0.127571i
$847$	4.05036e9	+	1.38328e10i	0.229035	+	0.782203i
$848$			1.57001e10i			0.884130i
$849$	−1.71818e10	+	3.71497e9i	−0.963591	+	0.208343i
$850$	−5.57627e10	+	3.21946e10i	−3.11442	+	1.79811i
$851$	7.65640e9	−	4.42043e9i	0.425864	−	0.245873i
$852$	−2.63924e9	+	5.70642e8i	−0.146198	+	0.0316101i
$853$		−	1.92731e10i		−	1.06324i	−0.846984	−	0.531618i	$-0.821584\pi$
$853$		−	1.92731e10i		−	1.06324i	0.846984	−	0.531618i	$-0.178416\pi$
$854$	1.93950e10	+	4.72065e9i	1.06558	+	0.259358i
$855$	−3.12497e10	−	3.06363e9i	−1.70987	−	0.167631i
$856$	6.07889e7	−	1.05289e8i	0.00331258	−	0.00573756i
$857$	6.08570e9	+	1.05407e10i	0.330277	+	0.572056i	0.982566	−	0.185914i	$-0.0595246\pi$
$857$	6.08570e9	+	1.05407e10i	0.330277	+	0.572056i	−0.652289	+	0.757970i	$0.726191\pi$
$858$	−1.71095e8	+	5.32911e8i	−0.00924767	+	0.0288038i
$859$	1.81238e10	+	1.04638e10i	0.975603	+	0.563264i	0.900940	−	0.433944i	$-0.142879\pi$
$859$	1.81238e10	+	1.04638e10i	0.975603	+	0.563264i	0.0746630	+	0.997209i	$0.476212\pi$
$860$	2.18877e9			0.117343
$861$	−1.15481e10	+	6.27556e9i	−0.616596	+	0.335075i
$862$	−4.26659e10			−2.26885
$863$	−1.03063e10	−	5.95032e9i	−0.545838	−	0.315140i	0.201604	−	0.979467i	$-0.435385\pi$
$863$	−1.03063e10	−	5.95032e9i	−0.545838	−	0.315140i	−0.747442	+	0.664328i	$0.768718\pi$
$864$	2.00452e10	+	8.67383e9i	1.05733	+	0.457523i
$865$	−9.55652e8	−	1.65524e9i	−0.0502046	−	0.0869569i
$866$	−1.28612e10	+	2.22762e10i	−0.672928	+	1.16554i
$867$	−7.95567e8	+	7.21386e8i	−0.0414582	+	0.0375925i
$868$	2.16893e9	−	6.35079e8i	0.112571	−	0.0329616i
$869$		−	2.37900e9i		−	0.122977i
$870$	3.12539e9	+	1.44550e10i	0.160912	+	0.744221i
$871$	7.44780e8	−	4.29999e8i	0.0381913	−	0.0220498i
$872$	9.87823e8	−	5.70320e8i	0.0504512	−	0.0291280i
$873$	1.04336e10	−	1.45739e10i	0.530743	−	0.741356i
$874$		−	1.20162e10i		−	0.608804i
$875$	4.50036e10	−	4.71272e10i	2.27101	−	2.37817i
$876$	−9.95095e9	−	1.09742e10i	−0.500150	−	0.551581i
$877$	1.30463e10	−	2.25968e10i	0.653112	−	1.13122i	−0.329251	−	0.944242i	$-0.606796\pi$
$877$	1.30463e10	−	2.25968e10i	0.653112	−	1.13122i	0.982363	−	0.186981i	$-0.0598704\pi$
$878$	−9.36520e9	−	1.62210e10i	−0.466967	−	0.808811i
$879$	8.14724e8	+	2.61573e8i	0.0404622	+	0.0129907i
$880$	1.77013e10	+	1.02199e10i	0.875621	+	0.505540i
$881$	2.60616e10			1.28406			0.642031	−	0.766678i	$-0.278092\pi$
$881$	2.60616e10			1.28406			0.642031	+	0.766678i	$0.278092\pi$
$882$	2.34571e10	−	1.19735e10i	1.15116	−	0.587598i
$883$	−7.75021e9			−0.378836			−0.189418	−	0.981897i	$-0.560660\pi$
$883$	−7.75021e9			−0.378836			−0.189418	+	0.981897i	$0.560660\pi$
$884$	6.66960e8	+	3.85070e8i	0.0324726	+	0.0187481i
$885$	−2.37233e10	−	7.61653e9i	−1.15046	−	0.369365i
$886$	−9.73151e9	−	1.68555e10i	−0.470070	−	0.814185i
$887$	3.45188e9	−	5.97884e9i	0.166082	−	0.287663i	−0.770957	−	0.636887i	$-0.780222\pi$
$887$	3.45188e9	−	5.97884e9i	0.166082	−	0.287663i	0.937039	+	0.349224i	$0.113555\pi$
$888$	5.56107e9	+	6.13292e9i	0.266510	+	0.293915i
$889$	−1.09065e10	+	1.14211e10i	−0.520629	+	0.545197i
$890$			1.16037e10i			0.551737i
$891$	6.83238e9	+	5.98097e9i	0.323594	+	0.283269i
$892$	−1.41291e10	+	8.15746e9i	−0.666559	+	0.384838i
$893$	−1.66349e10	+	9.60416e9i	−0.781700	+	0.451315i
$894$	1.50635e9	+	6.96693e9i	0.0705091	+	0.326107i
$895$			4.73843e10i			2.20929i
$896$	−1.66476e10	+	4.87455e9i	−0.773169	+	0.226390i
$897$	4.60104e8	−	4.17203e8i	0.0212854	−	0.0193007i
$898$	−6.70049e9	+	1.16056e10i	−0.308773	+	0.534810i
$899$	−5.83063e8	−	1.00989e9i	−0.0267643	−	0.0463572i
$900$	3.61558e10	−	1.64016e10i	1.65321	−	0.749957i
$901$	1.41485e10	+	8.16862e9i	0.644425	+	0.372059i
$902$	−8.59722e9			−0.390063
$903$	−1.76712e9	+	9.60298e8i	−0.0798653	+	0.0434009i
$904$	−9.51021e9			−0.428155
$905$	−5.24662e10	−	3.02914e10i	−2.35293	−	1.35847i
$906$	−7.97849e9	+	2.48507e10i	−0.356428	+	1.11017i
$907$	−1.82417e10	−	3.15956e10i	−0.811784	−	1.40605i	−0.911614	−	0.411047i	$-0.865163\pi$
$907$	−1.82417e10	−	3.15956e10i	−0.811784	−	1.40605i	0.0998298	−	0.995005i	$-0.468170\pi$
$908$	−1.92722e9	+	3.33805e9i	−0.0854342	+	0.147976i
$909$	2.88584e9	−	2.94362e10i	0.127438	−	1.29989i
$910$	−2.99173e9	−	7.28175e8i	−0.131607	−	0.0320325i
$911$		−	2.78042e8i		−	0.0121842i	−0.999981	−	0.00609209i	$-0.998061\pi$
$911$		−	2.78042e8i		−	0.0121842i	0.999981	−	0.00609209i	$-0.00193918\pi$
$912$	2.43919e10	−	5.27389e9i	1.06479	−	0.230223i
$913$	7.30680e9	−	4.21858e9i	0.317746	−	0.183451i
$914$	−8.15647e9	+	4.70914e9i	−0.353338	+	0.204000i
$915$	−3.70064e10	+	8.00132e9i	−1.59699	+	0.345293i
$916$		−	7.05204e9i		−	0.303166i
$917$	1.16403e10	+	3.97541e10i	0.498507	+	1.70251i
$918$	2.49919e10	−	1.85614e10i	1.06623	−	0.791883i
$919$	−1.20510e10	+	2.08729e10i	−0.512174	+	0.887112i	0.487726	+	0.872997i	$0.337827\pi$
$919$	−1.20510e10	+	2.08729e10i	−0.512174	+	0.887112i	−0.999900	+	0.0141152i	$0.995507\pi$
$920$	−5.11346e9	−	8.85677e9i	−0.216500	−	0.374988i
$921$	−9.99908e9	+	3.11442e10i	−0.421747	+	1.31362i
$922$	−2.30211e10	−	1.32912e10i	−0.967314	−	0.558479i
$923$	−2.90079e8			−0.0121426
$924$	6.91188e9	+	1.78480e8i	0.288233	+	0.00744284i
$925$	6.07111e10			2.52216
$926$	−1.79131e10	−	1.03421e10i	−0.741364	−	0.428027i
$927$	8.55263e9	+	1.88535e10i	0.352631	+	0.777343i
$928$	−4.29065e9	−	7.43162e9i	−0.176240	−	0.305257i
$929$	9.45594e8	−	1.63782e9i	0.0386945	−	0.0670209i	−0.846030	−	0.533136i	$-0.821013\pi$
$929$	9.45594e8	−	1.63782e9i	0.0386945	−	0.0670209i	0.884724	+	0.466115i	$0.154347\pi$
$930$	−7.91213e9	+	7.17438e9i	−0.322554	+	0.292478i
$931$	1.00962e10	−	1.95116e10i	0.410048	−	0.792446i
$932$		−	3.12395e9i		−	0.126401i
$933$	4.18597e9	+	1.93603e10i	0.168737	+	0.780415i
$934$	5.16682e10	−	2.98306e10i	2.07496	−	1.19798i
$935$	1.84197e10	−	1.06346e10i	0.736957	−	0.425482i
$936$	4.72907e8	+	3.38559e8i	0.0188500	+	0.0134949i
$937$		−	3.00074e9i		−	0.119163i	−0.998223	−	0.0595813i	$-0.981023\pi$
$937$		−	3.00074e9i		−	0.119163i	0.998223	−	0.0595813i	$-0.0189766\pi$
$938$	−1.91434e10	−	1.82808e10i	−0.757373	−	0.723245i
$939$	1.05662e10	+	1.16528e10i	0.416476	+	0.459303i
$940$	1.66284e10	−	2.88013e10i	0.652986	−	1.13101i
$941$	8.56893e7	+	1.48418e8i	0.00335246	+	0.00580662i	0.867697	−	0.497094i	$-0.165600\pi$
$941$	8.56893e7	+	1.48418e8i	0.00335246	+	0.00580662i	−0.864344	+	0.502901i	$0.832266\pi$
$942$	−3.56709e10	−	1.14524e10i	−1.39039	−	0.446394i
$943$	8.26201e9	+	4.77007e9i	0.320845	+	0.185240i
$944$	1.98026e10			0.766161
$945$	−3.01173e10	+	3.98535e10i	−1.16093	+	1.53623i
$946$	−1.31556e9			−0.0505234
$947$	1.86765e10	+	1.07829e10i	0.714613	+	0.412582i	0.812767	−	0.582589i	$-0.197960\pi$
$947$	1.86765e10	+	1.07829e10i	0.714613	+	0.412582i	−0.0981536	+	0.995171i	$0.531294\pi$
$948$	4.78823e9	+	1.53730e9i	0.182535	+	0.0586041i
$949$	−7.95718e8	−	1.37822e9i	−0.0302223	−	0.0523466i
$950$	4.12583e10	−	7.14615e10i	1.56127	−	2.70420i
$951$	2.17093e10	+	2.39417e10i	0.818490	+	0.902656i
$952$	−2.75566e9	+	1.13217e10i	−0.103513	+	0.425288i
$953$			2.27050e10i			0.849760i	0.905250	+	0.424880i	$0.139684\pi$
$953$			2.27050e10i			0.849760i	−0.905250	+	0.424880i	$0.860316\pi$
$954$	−2.04080e10	−	1.46103e10i	−0.760993	−	0.544802i
$955$	3.96296e10	−	2.28802e10i	1.47234	−	0.850056i
$956$	−7.74035e9	+	4.46890e9i	−0.286522	+	0.165424i
$957$	−7.53949e8	−	3.48704e9i	−0.0278068	−	0.128607i
$958$		−	1.50900e7i		−	0.000554510i
$959$	6.32276e9	−	2.59773e10i	0.231495	−	0.951105i
$960$	−1.04815e10	+	9.50415e9i	−0.382361	+	0.346708i
$961$	−1.33352e10	+	2.30973e10i	−0.484695	+	0.839516i
$962$	−9.04623e8	−	1.56685e9i	−0.0327608	−	0.0567434i
$963$	1.78076e8	+	3.92552e8i	0.00642559	+	0.0141646i
$964$	−2.08902e10	−	1.20609e10i	−0.751056	−	0.433622i
$965$	−9.71388e10			−3.47974
$966$	−1.63032e10	−	9.98247e9i	−0.581907	−	0.356302i
$967$	−3.81459e10			−1.35661			−0.678306	−	0.734780i	$-0.737285\pi$
$967$	−3.81459e10			−1.35661			−0.678306	+	0.734780i	$0.737285\pi$
$968$	8.48463e9	+	4.89860e9i	0.300655	+	0.173583i
$969$	7.93823e9	−	2.47253e10i	0.280279	−	0.872988i
$970$	3.22492e10	+	5.58572e10i	1.13453	+	1.96507i
$971$	1.40228e10	−	2.42883e10i	0.491551	−	0.851391i	−0.508402	−	0.861120i	$-0.669764\pi$
$971$	1.40228e10	−	2.42883e10i	0.491551	−	0.851391i	0.999953	+	0.00972902i	$0.00309689\pi$
$972$	−1.64530e10	+	9.88672e9i	−0.574663	+	0.345319i
$973$	−3.95122e10	−	3.77317e10i	−1.37511	−	1.31314i
$974$			1.40266e10i			0.486404i
$975$	4.16877e9	−	9.01349e8i	0.144043	−	0.0311442i
$976$	2.60599e10	−	1.50457e10i	0.897219	−	0.518010i
$977$	2.09543e10	−	1.20980e10i	0.718857	−	0.415032i	−0.0954746	−	0.995432i	$-0.530437\pi$
$977$	2.09543e10	−	1.20980e10i	0.718857	−	0.415032i	0.814332	+	0.580399i	$0.197104\pi$
$978$	4.02964e10	−	8.71268e9i	1.37747	−	0.297828i
$979$		−	2.79920e9i		−	0.0953443i
$980$	1.75256e9	+	3.79963e10i	0.0594814	+	1.28958i
$981$	−3.94584e8	+	4.02484e9i	−0.0133444	+	0.136115i
$982$	5.01373e9	−	8.68404e9i	0.168955	−	0.292639i
$983$	−7.54203e9	−	1.30632e10i	−0.253251	−	0.438643i	0.711168	−	0.703022i	$-0.248166\pi$
$983$	−7.54203e9	−	1.30632e10i	−0.253251	−	0.438643i	−0.964419	+	0.264379i	$0.914833\pi$
$984$	−2.73091e9	+	8.50598e9i	−0.0913743	+	0.284604i
$985$	−9.78398e10	−	5.64878e10i	−3.26204	−	1.88334i
$986$	−1.22310e10			−0.406343
$987$	−7.88829e8	+	3.05484e10i	−0.0261140	+	1.01130i
$988$	−9.86956e8			−0.0325573
$989$	1.26427e9	+	7.29925e8i	0.0415577	+	0.0239934i
$990$	−2.97571e10	+	1.34989e10i	−0.974690	+	0.442155i
$991$	1.84469e10	+	3.19510e10i	0.602096	+	1.04286i	0.992503	+	0.122218i	$0.0390008\pi$
$991$	1.84469e10	+	3.19510e10i	0.602096	+	1.04286i	−0.390408	+	0.920642i	$0.627666\pi$
$992$	3.09866e9	−	5.36704e9i	0.100782	−	0.174560i
$993$	2.96614e10	−	2.68956e10i	0.961321	−	0.871685i
$994$	2.50895e9	+	8.56860e9i	0.0810289	+	0.276731i
$995$			7.89009e10i			2.53922i
$996$	3.76916e9	+	1.74325e10i	0.120875	+	0.559051i
$997$	−3.57225e10	+	2.06244e10i	−1.14158	+	0.659094i	−0.946823	−	0.321756i	$-0.895727\pi$
$997$	−3.57225e10	+	2.06244e10i	−1.14158	+	0.659094i	−0.194762	+	0.980850i	$0.562394\pi$
$998$	3.77381e10	−	2.17881e10i	1.20178	−	0.693846i
$999$	−2.91578e10	+	3.37428e9i	−0.925286	+	0.107078i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.8.g.b.5.13	yes	32
3.2	odd	2	inner	21.8.g.b.5.4	✓	32
7.2	even	3		147.8.c.b.146.31		32
7.3	odd	6	inner	21.8.g.b.17.4	yes	32
7.5	odd	6		147.8.c.b.146.1		32
21.2	odd	6		147.8.c.b.146.2		32
21.5	even	6		147.8.c.b.146.32		32
21.17	even	6	inner	21.8.g.b.17.13	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.8.g.b.5.4	✓	32	3.2	odd	2	inner
21.8.g.b.5.13	yes	32	1.1	even	1	trivial
21.8.g.b.17.4	yes	32	7.3	odd	6	inner
21.8.g.b.17.13	yes	32	21.17	even	6	inner
147.8.c.b.146.1		32	7.5	odd	6
147.8.c.b.146.2		32	21.2	odd	6
147.8.c.b.146.31		32	7.2	even	3
147.8.c.b.146.32		32	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	21.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(12.6634 + 7.31122i) q^{2} +(44.5268 + 14.2957i) q^{3} +(42.9078 + 74.3185i) q^{4} +(-269.104 + 466.101i) q^{5} +(459.342 + 506.577i) q^{6} +(626.737 - 656.311i) q^{7} -616.838i q^{8} +(1778.27 + 1273.08i) q^{9} +(-6815.54 + 3934.95i) q^{10} +(1644.13 - 949.242i) q^{11} +(848.115 + 3922.56i) q^{12} +431.129i q^{13} +(12735.1 - 3728.92i) q^{14} +(-18645.5 + 16907.0i) q^{15} +(10002.0 - 17324.0i) q^{16} +(-10408.0 - 18027.1i) q^{17} +(13211.2 + 29122.8i) q^{18} +(23102.3 + 13338.1i) q^{19} -46186.6 q^{20} +(37289.0 - 20263.8i) q^{21} +27760.4 q^{22} +(-26678.1 - 15402.6i) q^{23} +(8818.11 - 27465.8i) q^{24} +(-105771. - 183201. i) q^{25} +(-3152.08 + 5459.56i) q^{26} +(60981.1 + 82107.6i) q^{27} +(75668.0 + 18417.3i) q^{28} -40183.4i q^{29} +(-359727. + 77778.2i) q^{30} +(25132.1 - 14510.0i) q^{31} +(184942. - 106777. i) q^{32} +(86778.1 - 18762.7i) q^{33} -304380. i q^{34} +(137250. + 468739. i) q^{35} +(-18311.7 + 186783. i) q^{36} +(-143496. + 248543. i) q^{37} +(195036. + 337812. i) q^{38} +(-6163.27 + 19196.8i) q^{39} +(287509. + 165994. i) q^{40} -309693. q^{41} +(620358. + 16019.1i) q^{42} -47389.8 q^{43} +(141092. + 81459.8i) q^{44} +(-1.07192e6 + 486263. i) q^{45} +(-225223. - 390098. i) q^{46} +(-360027. + 623585. i) q^{47} +(693017. - 628398. i) q^{48} +(-37945.1 - 822668. i) q^{49} -3.09326e6i q^{50} +(-205724. - 951478. i) q^{51} +(-32040.9 + 18498.8i) q^{52} +(-679694. + 392422. i) q^{53} +(171921. + 1.48561e6i) q^{54} +1.02178e6i q^{55} +(-404838. - 386595. i) q^{56} +(837993. + 924165. i) q^{57} +(293790. - 508859. i) q^{58} +(494964. + 857303. i) q^{59} +(-2.05654e6 - 660268. i) q^{60} +(1.30273e6 + 752131. i) q^{61} +424344. q^{62} +(1.95004e6 - 369212. i) q^{63} +562144. q^{64} +(-200950. - 116018. i) q^{65} +(1.23608e6 + 396854. i) q^{66} +(-997379. - 1.72751e6i) q^{67} +(893166. - 1.54701e6i) q^{68} +(-967698. - 1.06721e6i) q^{69} +(-1.68900e6 + 6.93929e6i) q^{70} +672836. i q^{71} +(785284. - 1.09690e6i) q^{72} +(-3.19678e6 + 1.84566e6i) q^{73} +(-3.63430e6 + 2.09827e6i) q^{74} +(-2.09067e6 - 9.66942e6i) q^{75} +2.28924e6i q^{76} +(407442. - 1.67399e6i) q^{77} +(-218400. + 198036. i) q^{78} +(626552. - 1.08522e6i) q^{79} +(5.38317e6 + 9.32393e6i) q^{80} +(1.54151e6 + 4.52775e6i) q^{81} +(-3.92177e6 - 2.26423e6i) q^{82} +4.44416e6 q^{83} +(3.10596e6 + 1.90178e6i) q^{84} +1.12033e7 q^{85} +(-600116. - 346477. i) q^{86} +(574448. - 1.78924e6i) q^{87} +(-585529. - 1.01417e6i) q^{88} +(737221. - 1.27690e6i) q^{89} +(-1.71294e7 - 1.67931e6i) q^{90} +(282955. + 270204. i) q^{91} -2.64356e6i q^{92} +(1.32648e6 - 286805. i) q^{93} +(-9.11834e6 + 5.26447e6i) q^{94} +(-1.24338e7 + 7.17867e6i) q^{95} +(9.76133e6 - 2.11054e6i) q^{96} -8.19557e6i q^{97} +(5.53419e6 - 1.06952e7i) q^{98} +(4.13217e6 + 405106. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 84 q^{3} + 1150 q^{4} + 2464 q^{7} - 3516 q^{9} - 630 q^{10} - 3864 q^{12} + 27576 q^{15} - 19594 q^{16} + 33498 q^{18} - 47880 q^{19} + 151788 q^{21} + 105132 q^{22} - 211554 q^{24} - 331252 q^{25}+ \cdots + 35642232 q^{99}+O(q^{100}) \) 32 * q - 84 * q^3 + 1150 * q^4 + 2464 * q^7 - 3516 * q^9 - 630 * q^10 - 3864 * q^12 + 27576 * q^15 - 19594 * q^16 + 33498 * q^18 - 47880 * q^19 + 151788 * q^21 + 105132 * q^22 - 211554 * q^24 - 331252 * q^25 - 353122 * q^28 - 40662 * q^30 + 628152 * q^31 - 66024 * q^33 - 227244 * q^36 - 618748 * q^37 + 1996104 * q^39 + 1986138 * q^40 + 4274802 * q^42 - 1416064 * q^43 - 4757508 * q^45 - 3492840 * q^46 - 6640312 * q^49 + 677340 * q^51 + 11962272 * q^52 - 6743898 * q^54 - 6279408 * q^57 - 2064342 * q^58 + 7521282 * q^60 + 10948728 * q^61 + 13194636 * q^63 - 589508 * q^64 - 6977250 * q^66 - 1944728 * q^67 - 24852702 * q^70 - 1544472 * q^72 + 13351212 * q^73 - 23106048 * q^75 + 1917432 * q^78 + 7626328 * q^79 + 8703036 * q^81 + 14640192 * q^82 + 15191904 * q^84 + 3418848 * q^85 + 15346296 * q^87 + 12313398 * q^88 + 3988992 * q^91 - 24832104 * q^93 - 51594732 * q^94 - 57374730 * q^96 + 35642232 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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