LMFDB - Embedded newform 54.9.f.a.5.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,9,Mod(5,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("54.5");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	54.f (of order $18$, degree $6$, 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:	$21.9984449433$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.15
Character	$\chi$	$=$	54.5
Dual form			54.9.f.a.11.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.27231 + 8.66680i) q^{2} +(-64.9711 - 48.3711i) q^{3} +(-22.2270 + 126.055i) q^{4} +(-403.520 - 1108.66i) q^{5} +(-53.2671 - 914.861i) q^{6} +(-619.994 - 3516.16i) q^{7} +(-1254.14 + 724.077i) q^{8} +(1881.48 + 6285.44i) q^{9} +O(q^{10})$	\(q+(7.27231 + 8.66680i) q^{2} +(-64.9711 - 48.3711i) q^{3} +(-22.2270 + 126.055i) q^{4} +(-403.520 - 1108.66i) q^{5} +(-53.2671 - 914.861i) q^{6} +(-619.994 - 3516.16i) q^{7} +(-1254.14 + 724.077i) q^{8} +(1881.48 + 6285.44i) q^{9} +(6674.03 - 11559.8i) q^{10} +(-7111.83 + 19539.6i) q^{11} +(7541.55 - 7114.81i) q^{12} +(21672.4 + 18185.3i) q^{13} +(25965.1 - 30944.0i) q^{14} +(-27410.0 + 91549.6i) q^{15} +(-15395.9 - 5603.66i) q^{16} +(-60165.8 - 34736.7i) q^{17} +(-40792.0 + 62016.1i) q^{18} +(-73359.7 - 127063. i) q^{19} +(148722. - 26223.7i) q^{20} +(-129799. + 258439. i) q^{21} +(-221065. + 80461.2i) q^{22} +(307696. + 54255.1i) q^{23} +(116507. + 13620.0i) q^{24} +(-767065. + 643644. i) q^{25} +320079. i q^{26} +(181792. - 499381. i) q^{27} +457012. q^{28} +(237865. + 283476. i) q^{29} +(-992777. + 428220. i) q^{30} +(-87415.1 + 495756. i) q^{31} +(-63398.2 - 174185. i) q^{32} +(1.40721e6 - 925501. i) q^{33} +(-136488. - 774061. i) q^{34} +(-3.64805e6 + 2.10620e6i) q^{35} +(-834133. + 97464.0i) q^{36} +(-145676. + 252317. i) q^{37} +(567733. - 1.55983e6i) q^{38} +(-528435. - 2.22983e6i) q^{39} +(1.30883e6 + 1.09824e6i) q^{40} +(-234042. + 278920. i) q^{41} +(-3.18377e6 + 754504. i) q^{42} +(871132. + 317066. i) q^{43} +(-2.30500e6 - 1.33079e6i) q^{44} +(6.20921e6 - 4.62222e6i) q^{45} +(1.76744e6 + 3.06130e6i) q^{46} +(-3.13064e6 + 552016. i) q^{47} +(729234. + 1.10879e6i) q^{48} +(-6.56186e6 + 2.38832e6i) q^{49} +(-1.11567e7 - 1.96722e6i) q^{50} +(2.22878e6 + 5.16717e6i) q^{51} +(-2.77406e6 + 2.32772e6i) q^{52} +1.14459e7i q^{53} +(5.65008e6 - 2.05610e6i) q^{54} +2.45325e7 q^{55} +(3.32353e6 + 3.96083e6i) q^{56} +(-1.37990e6 + 1.18039e7i) q^{57} +(-727006. + 4.12305e6i) q^{58} +(4.51633e6 + 1.24085e7i) q^{59} +(-1.09311e7 - 5.49005e6i) q^{60} +(-2.27513e6 - 1.29029e7i) q^{61} +(-4.93233e6 + 2.84768e6i) q^{62} +(2.09341e7 - 1.05125e7i) q^{63} +(1.04858e6 - 1.81619e6i) q^{64} +(1.14161e7 - 3.13654e7i) q^{65} +(1.82548e7 + 5.46552e6i) q^{66} +(-2.05319e7 - 1.72283e7i) q^{67} +(5.71605e6 - 6.81213e6i) q^{68} +(-1.73669e7 - 1.84086e7i) q^{69} +(-4.47838e7 - 1.63000e7i) q^{70} +(-1.61147e7 - 9.30384e6i) q^{71} +(-6.91078e6 - 6.52048e6i) q^{72} +(-1.09027e7 - 1.88841e7i) q^{73} +(-3.24618e6 + 572390. i) q^{74} +(8.09708e7 - 4.71447e6i) q^{75} +(1.76475e7 - 6.42317e6i) q^{76} +(7.31136e7 + 1.28919e7i) q^{77} +(1.54826e7 - 2.07959e7i) q^{78} +(1.58339e7 - 1.32863e7i) q^{79} +1.93301e7i q^{80} +(-3.59668e7 + 2.36518e7i) q^{81} -4.11937e6 q^{82} +(8.05015e6 + 9.59380e6i) q^{83} +(-2.96925e7 - 2.21062e7i) q^{84} +(-1.42332e7 + 8.07204e7i) q^{85} +(3.58719e6 + 9.85574e6i) q^{86} +(-1.74227e6 - 2.99235e7i) q^{87} +(-5.22895e6 - 2.96549e7i) q^{88} +(-6.09197e7 + 3.51720e7i) q^{89} +(8.52152e7 + 2.01998e7i) q^{90} +(5.05056e7 - 8.74783e7i) q^{91} +(-1.36783e7 + 3.75808e7i) q^{92} +(2.96597e7 - 2.79814e7i) q^{93} +(-2.75512e7 - 2.31182e7i) q^{94} +(-1.11267e8 + 1.32603e8i) q^{95} +(-4.30647e6 + 1.43836e7i) q^{96} +(1.24118e8 + 4.51752e7i) q^{97} +(-6.84190e7 - 3.95017e7i) q^{98} +(-1.36196e8 - 7.93770e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9}+O(q^{10}) $ 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9	\( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25} - 4137588 q^{27} - 2856132 q^{29} - 861696 q^{30} - 1841490 q^{31} + 10547334 q^{33} - 661248 q^{34} - 12450834 q^{35} - 5104128 q^{36} + 14063616 q^{38} + 4239102 q^{39} - 15673536 q^{41} - 11028480 q^{42} - 4412520 q^{43} - 12558942 q^{45} + 15173838 q^{47} + 3440640 q^{48} - 11347488 q^{49} - 27744768 q^{50} - 3281850 q^{51} + 16379136 q^{54} + 12091392 q^{56} - 13553658 q^{57} - 86547168 q^{59} - 26125056 q^{60} - 34059456 q^{61} + 108329070 q^{63} + 150994944 q^{64} + 22190346 q^{65} + 152091648 q^{66} + 167100948 q^{67} + 13411584 q^{68} - 40190130 q^{69} - 118080000 q^{70} - 251437608 q^{71} - 60948480 q^{72} + 15265278 q^{73} + 41902848 q^{74} + 138868662 q^{75} + 67995648 q^{76} + 564911586 q^{77} + 201203712 q^{78} + 137535768 q^{79} - 23838948 q^{81} - 482857578 q^{83} - 128300544 q^{84} - 343215000 q^{85} - 46237824 q^{86} + 34353810 q^{87} + 47480832 q^{88} + 375969762 q^{89} + 452712960 q^{90} - 155093598 q^{91} + 97042176 q^{92} + 285095622 q^{93} - 70995456 q^{94} - 966996432 q^{95} - 88080384 q^{96} - 484917300 q^{97} - 234233856 q^{98} + 26756370 q^{99}+O(q^{100}) \) 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9 - 45756 * q^11 - 21504 * q^12 + 94464 * q^14 - 70002 * q^15 - 182784 * q^18 - 225792 * q^20 - 2071668 * q^21 + 185472 * q^22 + 552996 * q^23 - 1015182 * q^25 - 4137588 * q^27 - 2856132 * q^29 - 861696 * q^30 - 1841490 * q^31 + 10547334 * q^33 - 661248 * q^34 - 12450834 * q^35 - 5104128 * q^36 + 14063616 * q^38 + 4239102 * q^39 - 15673536 * q^41 - 11028480 * q^42 - 4412520 * q^43 - 12558942 * q^45 + 15173838 * q^47 + 3440640 * q^48 - 11347488 * q^49 - 27744768 * q^50 - 3281850 * q^51 + 16379136 * q^54 + 12091392 * q^56 - 13553658 * q^57 - 86547168 * q^59 - 26125056 * q^60 - 34059456 * q^61 + 108329070 * q^63 + 150994944 * q^64 + 22190346 * q^65 + 152091648 * q^66 + 167100948 * q^67 + 13411584 * q^68 - 40190130 * q^69 - 118080000 * q^70 - 251437608 * q^71 - 60948480 * q^72 + 15265278 * q^73 + 41902848 * q^74 + 138868662 * q^75 + 67995648 * q^76 + 564911586 * q^77 + 201203712 * q^78 + 137535768 * q^79 - 23838948 * q^81 - 482857578 * q^83 - 128300544 * q^84 - 343215000 * q^85 - 46237824 * q^86 + 34353810 * q^87 + 47480832 * q^88 + 375969762 * q^89 + 452712960 * q^90 - 155093598 * q^91 + 97042176 * q^92 + 285095622 * q^93 - 70995456 * q^94 - 966996432 * q^95 - 88080384 * q^96 - 484917300 * q^97 - 234233856 * q^98 + 26756370 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	7.27231	+	8.66680i	0.454519	+	0.541675i
$2$	7.27231	+	8.66680i	0.454519	+	0.541675i
$3$	−64.9711	−	48.3711i	−0.802112	−	0.597174i
$3$	−64.9711	−	48.3711i	−0.802112	−	0.597174i
$4$	−22.2270	+	126.055i	−0.0868241	+	0.492404i
$5$	−403.520	−	1108.66i	−0.645632	−	1.77386i	−0.633266	−	0.773934i	$-0.718286\pi$
$5$	−403.520	−	1108.66i	−0.645632	−	1.77386i	−0.0123658	−	0.999924i	$-0.503936\pi$
$6$	−53.2671	−	914.861i	−0.0411012	−	0.705911i
$7$	−619.994	−	3516.16i	−0.258223	−	1.46446i	−0.787661	−	0.616108i	$-0.788708\pi$
$7$	−619.994	−	3516.16i	−0.258223	−	1.46446i	0.529438	−	0.848349i	$-0.322403\pi$
$8$	−1254.14	+	724.077i	−0.306186	+	0.176777i
$9$	1881.48	+	6285.44i	0.286767	+	0.958000i
$10$	6674.03	−	11559.8i	0.667403	−	1.15598i
$11$	−7111.83	+	19539.6i	−0.485747	+	1.33458i	0.418750	+	0.908102i	$0.362468\pi$
$11$	−7111.83	+	19539.6i	−0.485747	+	1.33458i	−0.904498	+	0.426479i	$0.859754\pi$
$12$	7541.55	−	7114.81i	0.363693	−	0.343114i
$13$	21672.4	+	18185.3i	0.758810	+	0.636717i	0.937817	−	0.347131i	$-0.112844\pi$
$13$	21672.4	+	18185.3i	0.758810	+	0.636717i	−0.179007	+	0.983848i	$0.557288\pi$
$14$	25965.1	−	30944.0i	0.675893	−	0.805497i
$15$	−27410.0	+	91549.6i	−0.541433	+	1.80839i
$16$	−15395.9	−	5603.66i	−0.234923	−	0.0855050i
$17$	−60165.8	−	34736.7i	−0.720367	−	0.415904i	0.0945207	−	0.995523i	$-0.469868\pi$
$17$	−60165.8	−	34736.7i	−0.720367	−	0.415904i	−0.814888	+	0.579619i	$0.803201\pi$
$18$	−40792.0	+	62016.1i	−0.388584	+	0.590764i
$19$	−73359.7	−	127063.i	−0.562915	−	0.974998i	−0.997240	−	0.0742417i	$-0.976346\pi$
$19$	−73359.7	−	127063.i	−0.562915	−	0.974998i	0.434325	−	0.900756i	$-0.356987\pi$
$20$	148722.	−	26223.7i	0.929511	−	0.163898i
$21$	−129799.	+	258439.i	−0.667412	+	1.32886i
$22$	−221065.	+	80461.2i	−0.943691	+	0.343475i
$23$	307696.	+	54255.1i	1.09954	+	0.193878i	0.693840	−	0.720129i	$-0.255917\pi$
$23$	307696.	+	54255.1i	1.09954	+	0.193878i	0.405698	+	0.914007i	$0.367029\pi$
$24$	116507.	+	13620.0i	0.351162	+	0.0410517i
$25$	−767065.	+	643644.i	−1.96369	+	1.64773i
$26$			320079.i			0.700429i
$27$	181792.	−	499381.i	0.342074	−	0.939673i
$28$	457012.			0.743524
$29$	237865.	+	283476.i	0.336309	+	0.400797i	0.907522	−	0.420005i	$-0.137972\pi$
$29$	237865.	+	283476.i	0.336309	+	0.400797i	−0.571213	+	0.820802i	$0.693527\pi$
$30$	−992777.	+	428220.i	−1.22565	+	0.528666i
$31$	−87415.1	+	495756.i	−0.0946542	+	0.536811i	0.900199	+	0.435480i	$0.143421\pi$
$31$	−87415.1	+	495756.i	−0.0946542	+	0.536811i	−0.994853	+	0.101331i	$0.967690\pi$
$32$	−63398.2	−	174185.i	−0.0604612	−	0.166116i
$33$	1.40721e6	−	925501.i	1.18660	−	0.780407i
$34$	−136488.	−	774061.i	−0.102136	−	0.579242i
$35$	−3.64805e6	+	2.10620e6i	−2.43102	+	1.40355i
$36$	−834133.	+	97464.0i	−0.496621	+	0.0580275i
$37$	−145676.	+	252317.i	−0.0777284	+	0.134630i	−0.902270	−	0.431173i	$-0.858100\pi$
$37$	−145676.	+	252317.i	−0.0777284	+	0.134630i	0.824541	+	0.565802i	$0.191433\pi$
$38$	567733.	−	1.55983e6i	0.272276	−	0.748073i
$39$	−528435.	−	2.22983e6i	−0.228420	−	0.963860i
$40$	1.30883e6	+	1.09824e6i	0.511260	+	0.428998i
$41$	−234042.	+	278920.i	−0.0828243	+	0.0987062i	−0.805865	−	0.592099i	$-0.798299\pi$
$41$	−234042.	+	278920.i	−0.0828243	+	0.0987062i	0.723041	+	0.690805i	$0.242744\pi$
$42$	−3.18377e6	+	754504.i	−1.02316	+	0.242474i
$43$	871132.	+	317066.i	0.254806	+	0.0927419i	0.466265	−	0.884645i	$-0.345599\pi$
$43$	871132.	+	317066.i	0.254806	+	0.0927419i	−0.211459	+	0.977387i	$0.567821\pi$
$44$	−2.30500e6	−	1.33079e6i	−0.614978	−	0.355058i
$45$	6.20921e6	−	4.62222e6i	1.51421	−	1.12720i
$46$	1.76744e6	+	3.06130e6i	0.394742	+	0.683714i
$47$	−3.13064e6	+	552016.i	−0.641567	+	0.113126i	−0.484961	−	0.874536i	$-0.661166\pi$
$47$	−3.13064e6	+	552016.i	−0.641567	+	0.113126i	−0.156606	+	0.987661i	$0.550055\pi$
$48$	729234.	+	1.10879e6i	0.137373	+	0.208875i
$49$	−6.56186e6	+	2.38832e6i	−1.13826	+	0.414294i
$50$	−1.11567e7	−	1.96722e6i	−1.78507	−	0.314756i
$51$	2.22878e6	+	5.16717e6i	0.329448	+	0.763786i
$52$	−2.77406e6	+	2.32772e6i	−0.379405	+	0.318359i
$53$			1.14459e7i			1.45059i	0.688438	+	0.725295i	$0.258297\pi$
$53$			1.14459e7i			1.45059i	−0.688438	+	0.725295i	$0.741703\pi$
$54$	5.65008e6	−	2.05610e6i	0.664477	−	0.241807i
$55$	2.45325e7			2.68097
$56$	3.32353e6	+	3.96083e6i	0.337946	+	0.402749i
$57$	−1.37990e6	+	1.18039e7i	−0.130722	+	1.11822i
$58$	−727006.	+	4.12305e6i	−0.0642430	+	0.364340i
$59$	4.51633e6	+	1.24085e7i	0.372716	+	1.02403i	0.974307	+	0.225224i	$0.0723115\pi$
$59$	4.51633e6	+	1.24085e7i	0.372716	+	1.02403i	−0.601591	+	0.798804i	$0.705466\pi$
$60$	−1.09311e7	−	5.49005e6i	−0.843447	−	0.423615i
$61$	−2.27513e6	−	1.29029e7i	−0.164318	−	0.931896i	−0.949764	−	0.312966i	$-0.898678\pi$
$61$	−2.27513e6	−	1.29029e7i	−0.164318	−	0.931896i	0.785446	−	0.618930i	$-0.212434\pi$
$62$	−4.93233e6	+	2.84768e6i	−0.333799	+	0.192719i
$63$	2.09341e7	−	1.05125e7i	1.32890	−	0.667336i
$64$	1.04858e6	−	1.81619e6i	0.0625000	−	0.108253i
$65$	1.14161e7	−	3.13654e7i	0.639534	−	1.75711i
$66$	1.82548e7	+	5.46552e6i	0.962060	+	0.288042i
$67$	−2.05319e7	−	1.72283e7i	−1.01889	−	0.854953i	−0.0294057	−	0.999568i	$-0.509361\pi$
$67$	−2.05319e7	−	1.72283e7i	−1.01889	−	0.854953i	−0.989488	+	0.144614i	$0.953806\pi$
$68$	5.71605e6	−	6.81213e6i	0.267338	−	0.318601i
$69$	−1.73669e7	−	1.84086e7i	−0.766173	−	0.812127i
$70$	−4.47838e7	−	1.63000e7i	−1.86522	−	0.678883i
$71$	−1.61147e7	−	9.30384e6i	−0.634147	−	0.366125i	0.148210	−	0.988956i	$-0.452649\pi$
$71$	−1.61147e7	−	9.30384e6i	−0.634147	−	0.366125i	−0.782356	+	0.622831i	$0.785982\pi$
$72$	−6.91078e6	−	6.52048e6i	−0.257156	−	0.242633i
$73$	−1.09027e7	−	1.88841e7i	−0.383923	−	0.664974i	0.607696	−	0.794170i	$-0.292094\pi$
$73$	−1.09027e7	−	1.88841e7i	−0.383923	−	0.664974i	−0.991619	+	0.129195i	$0.958761\pi$
$74$	−3.24618e6	+	572390.i	−0.108255	+	0.0190882i
$75$	8.09708e7	−	4.71447e6i	2.55908	−	0.149000i
$76$	1.76475e7	−	6.42317e6i	0.528967	−	0.192528i
$77$	7.31136e7	+	1.28919e7i	2.07987	+	0.366737i
$78$	1.54826e7	−	2.07959e7i	0.418278	−	0.561822i
$79$	1.58339e7	−	1.32863e7i	0.406519	−	0.341110i	−0.416488	−	0.909141i	$-0.636739\pi$
$79$	1.58339e7	−	1.32863e7i	0.406519	−	0.341110i	0.823007	+	0.568031i	$0.192295\pi$
$80$			1.93301e7i			0.471925i
$81$	−3.59668e7	+	2.36518e7i	−0.835530	+	0.549445i
$82$	−4.11937e6			−0.0911120
$83$	8.05015e6	+	9.59380e6i	0.169626	+	0.202152i	0.844160	−	0.536092i	$-0.180100\pi$
$83$	8.05015e6	+	9.59380e6i	0.169626	+	0.202152i	−0.674534	+	0.738244i	$0.735655\pi$
$84$	−2.96925e7	−	2.21062e7i	−0.596390	−	0.444013i
$85$	−1.42332e7	+	8.07204e7i	−0.272663	+	1.54635i
$86$	3.58719e6	+	9.85574e6i	0.0655785	+	0.180175i
$87$	−1.74227e6	−	2.99235e7i	−0.0304116	−	0.522319i
$88$	−5.22895e6	−	2.96549e7i	−0.0871935	−	0.494499i
$89$	−6.09197e7	+	3.51720e7i	−0.970952	+	0.560579i	−0.899526	−	0.436867i	$-0.856088\pi$
$89$	−6.09197e7	+	3.51720e7i	−0.970952	+	0.560579i	−0.0714257	+	0.997446i	$0.522755\pi$
$90$	8.52152e7	+	2.01998e7i	1.29881	+	0.307877i
$91$	5.05056e7	−	8.74783e7i	0.736502	−	1.27566i
$92$	−1.36783e7	+	3.75808e7i	−0.190933	+	0.524584i
$93$	2.96597e7	−	2.79814e7i	0.396493	−	0.374057i
$94$	−2.75512e7	−	2.31182e7i	−0.352882	−	0.296103i
$95$	−1.11267e8	+	1.32603e8i	−1.36607	+	1.62802i
$96$	−4.30647e6	+	1.43836e7i	−0.0507034	+	0.169349i
$97$	1.24118e8	+	4.51752e7i	1.40200	+	0.510286i	0.928771	−	0.370655i	$-0.120867\pi$
$97$	1.24118e8	+	4.51752e7i	1.40200	+	0.510286i	0.473227	+	0.880940i	$0.343089\pi$
$98$	−6.84190e7	−	3.95017e7i	−0.741775	−	0.428264i
$99$	−1.36196e8	−	7.93770e6i	−1.41782	−	0.0826331i
$100$	−6.40853e7	−	1.10999e8i	−0.640853	−	1.10999i
$101$	−3.06605e7	+	5.40627e6i	−0.294641	+	0.0519532i	−0.319015	−	0.947750i	$-0.603352\pi$
$101$	−3.06605e7	+	5.40627e6i	−0.294641	+	0.0519532i	0.0243736	+	0.999703i	$0.492241\pi$
$102$	−2.85744e7	+	5.68936e7i	−0.263983	+	0.525609i
$103$	−2.82433e7	+	1.02797e7i	−0.250938	+	0.0913340i	−0.464427	−	0.885612i	$-0.653740\pi$
$103$	−2.82433e7	+	1.02797e7i	−0.250938	+	0.0913340i	0.213489	+	0.976946i	$0.431517\pi$
$104$	−4.03477e7	−	7.11439e6i	−0.344894	−	0.0608141i
$105$	3.38897e8	+	3.96179e7i	2.78812	+	0.325938i
$106$	−9.91990e7	+	8.32378e7i	−0.785749	+	0.659322i
$107$		−	9.00804e7i		−	0.687219i	−0.939113	−	0.343610i	$-0.888350\pi$
$107$		−	9.00804e7i		−	0.687219i	0.939113	−	0.343610i	$-0.111650\pi$
$108$	5.89090e7	+	3.40156e7i	0.432998	+	0.250025i
$109$	−2.59330e8			−1.83716			−0.918581	−	0.395233i	$-0.870664\pi$
$109$	−2.59330e8			−1.83716			−0.918581	+	0.395233i	$0.870664\pi$
$110$	1.78408e8	+	2.12619e8i	1.21855	+	1.45221i
$111$	2.16696e7	−	9.34685e6i	0.142744	−	0.0615706i
$112$	−1.01580e7	+	5.76088e7i	−0.0645558	+	0.366114i
$113$	2.88346e7	+	7.92225e7i	0.176848	+	0.485887i	0.996169	−	0.0874488i	$-0.0278714\pi$
$113$	2.88346e7	+	7.92225e7i	0.176848	+	0.485887i	−0.819321	+	0.573335i	$0.805649\pi$
$114$	−1.12337e8	+	7.38822e7i	−0.665126	+	0.437442i
$115$	−6.40108e7	−	3.63023e8i	−0.365984	−	2.07560i
$116$	−4.10207e7	+	2.36833e7i	−0.226554	+	0.130801i
$117$	−7.35264e7	+	1.70436e8i	−0.392374	+	0.909530i
$118$	−7.46981e7	+	1.29381e8i	−0.385284	+	0.667332i
$119$	−8.48375e7	+	2.33089e8i	−0.423058	+	1.16234i
$120$	−3.19130e7	−	1.34663e8i	−0.153901	−	0.649416i
$121$	−1.67009e8	−	1.40137e8i	−0.779109	−	0.653750i
$122$	9.52813e7	−	1.13552e8i	0.430099	−	0.512572i
$123$	2.86976e7	−	6.80088e6i	0.125379	−	0.0297129i
$124$	−6.05497e7	−	2.20383e7i	−0.256109	−	0.0932162i
$125$	6.23989e8	+	3.60260e8i	2.55586	+	1.47563i
$126$	2.43349e8	+	1.04982e8i	0.965490	+	0.416516i
$127$	−8.13092e7	−	1.40832e8i	−0.312554	−	0.541359i	0.666361	−	0.745630i	$-0.267851\pi$
$127$	−8.13092e7	−	1.40832e8i	−0.312554	−	0.541359i	−0.978914	+	0.204270i	$0.934518\pi$
$128$	2.33661e7	−	4.12008e6i	0.0870455	−	0.0153485i
$129$	−4.12615e7	−	6.27377e7i	−0.149000	−	0.226553i
$130$	3.54859e8	−	1.29158e8i	1.24246	−	0.452219i
$131$	−4.53723e8	−	8.00036e7i	−1.54065	−	0.271659i	−0.662142	−	0.749378i	$-0.730353\pi$
$131$	−4.53723e8	−	8.00036e7i	−1.54065	−	0.271659i	−0.878513	+	0.477719i	$0.841464\pi$
$132$	8.53863e7	+	1.97958e8i	0.281250	+	0.652045i
$133$	−4.01290e8	+	3.36723e8i	−1.28248	+	1.07613i
$134$		−	3.03235e8i		−	0.940503i
$135$	−6.27001e8	−	35846.9i	−1.88770	−	0.000107924i
$136$	1.00608e8			0.294089
$137$	3.46205e7	+	4.12591e7i	0.0982768	+	0.117122i	0.812941	−	0.582346i	$-0.197865\pi$
$137$	3.46205e7	+	4.12591e7i	0.0982768	+	0.117122i	−0.714664	+	0.699467i	$0.753421\pi$
$138$	3.32458e7	−	2.84389e8i	0.0916685	−	0.784145i
$139$	8.28764e7	−	4.70016e8i	0.222010	−	1.25908i	−0.646310	−	0.763075i	$-0.723689\pi$
$139$	8.28764e7	−	4.70016e8i	0.222010	−	1.25908i	0.868320	−	0.496005i	$-0.165200\pi$
$140$	−1.84413e8	−	5.06671e8i	−0.480043	−	1.31891i
$141$	2.30103e8	+	1.15567e8i	0.582164	+	0.292388i
$142$	−3.65568e7	−	2.07324e8i	−0.0899113	−	0.509912i
$143$	−5.09463e8	+	2.94139e8i	−1.21834	+	0.703409i
$144$	6.25439e6	−	1.07313e8i	0.0145457	−	0.249576i
$145$	2.18296e8	−	3.78100e8i	0.493826	−	0.855331i
$146$	8.43767e7	−	2.31823e8i	0.185700	−	0.510205i
$147$	5.41856e8	+	1.62232e8i	1.16042	+	0.347431i
$148$	−2.85680e7	−	2.39714e7i	−0.0595434	−	0.0499628i
$149$	−5.93254e8	+	7.07012e8i	−1.20364	+	1.43444i	−0.332706	+	0.943030i	$0.607962\pi$
$149$	−5.93254e8	+	7.07012e8i	−1.20364	+	1.43444i	−0.870930	+	0.491407i	$0.836483\pi$
$150$	6.29704e8	+	6.67473e8i	1.24386	+	1.31847i
$151$	2.59549e8	+	9.44682e7i	0.499243	+	0.181710i	0.579353	−	0.815076i	$-0.303305\pi$
$151$	2.59549e8	+	9.44682e7i	0.499243	+	0.181710i	−0.0801106	+	0.996786i	$0.525527\pi$
$152$	1.84006e8	+	1.06236e8i	0.344714	+	0.199021i
$153$	1.05135e8	−	4.43525e8i	0.191859	−	0.809379i
$154$	4.19974e8	+	7.27416e8i	0.746688	+	1.29330i
$155$	5.84899e8	−	1.03133e8i	1.01334	−	0.178679i
$156$	2.92828e8	−	1.70497e7i	0.494441	−	0.0287884i
$157$	−2.30048e8	+	8.37305e7i	−0.378634	+	0.137811i	−0.524324	−	0.851519i	$-0.675682\pi$
$157$	−2.30048e8	+	8.37305e7i	−0.378634	+	0.137811i	0.145690	+	0.989330i	$0.453460\pi$
$158$	2.30299e8	+	4.06079e7i	0.369542	+	0.0651602i
$159$	5.53648e8	−	7.43649e8i	0.866255	−	1.16354i
$160$	−1.67530e8	+	1.40574e8i	−0.255630	+	0.214499i
$161$		−	1.11555e9i		−	1.66029i
$162$	−4.66548e8	−	1.39714e8i	−0.677385	−	0.202852i
$163$	1.74452e8			0.247130			0.123565	−	0.992336i	$-0.460567\pi$
$163$	1.74452e8			0.247130			0.123565	+	0.992336i	$0.460567\pi$
$164$	−2.99573e7	−	3.57018e7i	−0.0414122	−	0.0493531i
$165$	−1.59391e9	−	1.18667e9i	−2.15044	−	1.60101i
$166$	−2.46043e7	+	1.39538e8i	−0.0324026	+	0.183764i
$167$	1.04322e8	+	2.86622e8i	0.134125	+	0.368505i	0.988514	−	0.151128i	$-0.0482907\pi$
$167$	1.04322e8	+	2.86622e8i	0.134125	+	0.368505i	−0.854389	+	0.519634i	$0.826068\pi$
$168$	−2.43437e7	−	4.18102e8i	−0.0305597	−	0.524862i
$169$	−2.66286e6	−	1.51018e7i	−0.00326438	−	0.0185132i
$170$	−8.03096e8	+	4.63668e8i	−0.961550	+	0.555151i
$171$	6.60621e8	−	7.00163e8i	0.772623	−	0.818870i
$172$	−5.93305e7	+	1.02764e8i	−0.0677898	+	0.117415i
$173$	−5.10806e7	+	1.40343e8i	−0.0570259	+	0.156677i	−0.964934	−	0.262491i	$-0.915456\pi$
$173$	−5.10806e7	+	1.40343e8i	−0.0570259	+	0.156677i	0.907909	+	0.419168i	$0.137678\pi$
$174$	2.46671e8	−	2.32713e8i	0.269105	−	0.253877i
$175$	2.73873e9	+	2.29807e9i	2.92010	+	2.45025i
$176$	2.18986e8	−	2.60978e8i	0.228227	−	0.271990i
$177$	3.06783e8	−	1.02465e9i	0.312563	−	1.04396i
$178$	−7.47856e8	−	2.72197e8i	−0.744969	−	0.271146i
$179$	−5.22458e8	−	3.01641e8i	−0.508908	−	0.293818i	0.223477	−	0.974709i	$-0.428259\pi$
$179$	−5.22458e8	−	3.01641e8i	−0.508908	−	0.293818i	−0.732385	+	0.680891i	$0.761593\pi$
$180$	4.44644e8	+	8.85443e8i	0.423567	+	0.843471i
$181$	4.34304e7	+	7.52236e7i	0.0404650	+	0.0700874i	0.885549	−	0.464547i	$-0.153783\pi$
$181$	4.34304e7	+	7.52236e7i	0.0404650	+	0.0700874i	−0.845084	+	0.534634i	$0.820449\pi$
$182$	1.12545e9	−	1.98447e8i	1.02575	−	0.180867i
$183$	−4.76309e8	+	9.48364e8i	−0.424702	+	0.845611i
$184$	−4.25178e8	+	1.54752e8i	−0.370937	+	0.135010i
$185$	3.38517e8	+	5.96898e7i	0.288998	+	0.0509581i
$186$	4.58204e8	+	5.35652e7i	0.382831	+	0.0447539i
$187$	1.10663e9	−	9.28573e8i	0.904974	−	0.759363i
$188$		−	4.06904e8i		−	0.325732i
$189$	−1.86861e9	−	3.29597e8i	−1.46444	−	0.258307i
$190$	−1.95842e9			−1.50277
$191$	−6.09831e8	−	7.26768e8i	−0.458222	−	0.546087i	0.486620	−	0.873614i	$-0.338230\pi$
$191$	−6.09831e8	−	7.26768e8i	−0.458222	−	0.546087i	−0.944842	+	0.327526i	$0.893785\pi$
$192$	−1.55978e8	+	6.72788e7i	−0.114778	+	0.0495078i
$193$	−4.01671e8	+	2.27799e9i	−0.289495	+	1.64181i	0.399278	+	0.916830i	$0.369261\pi$
$193$	−4.01671e8	+	2.27799e9i	−0.289495	+	1.64181i	−0.688773	+	0.724977i	$0.741850\pi$
$194$	5.11099e8	+	1.40423e9i	0.360826	+	0.991362i
$195$	−2.25890e9	+	1.48564e9i	−1.56228	+	1.02748i
$196$	−1.55211e8	−	8.80243e8i	−0.105171	−	0.596456i
$197$	−1.56540e9	+	9.03783e8i	−1.03935	+	0.600066i	−0.919648	−	0.392744i	$-0.871526\pi$
$197$	−1.56540e9	+	9.03783e8i	−1.03935	+	0.600066i	−0.119698	+	0.992810i	$0.538193\pi$
$198$	−9.21663e8	−	1.23811e9i	−0.599669	−	0.805559i
$199$	7.28901e8	−	1.26249e9i	0.464789	−	0.805039i	−0.534403	−	0.845230i	$-0.679463\pi$
$199$	7.28901e8	−	1.26249e9i	0.464789	−	0.805039i	0.999192	+	0.0401912i	$0.0127967\pi$
$200$	4.95958e8	−	1.36263e9i	0.309974	−	0.851646i
$201$	5.00626e8	+	2.11249e9i	0.306711	+	1.29423i
$202$	−2.69828e8	−	2.26412e8i	−0.162062	−	0.135986i
$203$	8.49273e8	−	1.01212e9i	0.500107	−	0.596005i
$204$	−7.00888e8	+	1.66099e8i	−0.404695	+	0.0959064i
$205$	4.03668e8	+	1.46923e8i	0.228565	+	0.0831908i
$206$	−2.94487e8	−	1.70022e8i	−0.163530	−	0.0944139i
$207$	2.37905e8	+	2.03608e9i	0.129575	+	1.10896i
$208$	−2.31762e8	−	4.01424e8i	−0.123819	−	0.214462i
$209$	3.00447e9	−	5.29770e8i	1.57465	−	0.277653i
$210$	2.12120e9	+	3.22527e9i	1.09070	+	1.65840i
$211$	−9.43369e8	+	3.43358e8i	−0.475940	+	0.173228i	−0.568841	−	0.822447i	$-0.692608\pi$
$211$	−9.43369e8	+	3.43358e8i	−0.475940	+	0.173228i	0.0929015	+	0.995675i	$0.470386\pi$
$212$	−1.44281e9	−	2.54407e8i	−0.714276	−	0.125946i
$213$	5.96954e8	+	1.38397e9i	0.290016	+	0.672369i
$214$	7.80709e8	−	6.55093e8i	0.372250	−	0.312354i
$215$		−	1.09373e9i		−	0.511867i
$216$	1.33598e8	+	7.57924e8i	0.0613740	+	0.348186i
$217$	1.79735e9			0.810578
$218$	−1.88593e9	−	2.24757e9i	−0.835026	−	0.995145i
$219$	−2.05082e8	+	1.75430e9i	−0.0891560	+	0.762653i
$220$	−5.45284e8	+	3.09246e9i	−0.232773	+	1.32012i
$221$	−6.72238e8	−	1.84696e9i	−0.281808	−	0.774262i
$222$	2.38595e8	+	1.19833e8i	0.0982312	+	0.0493359i
$223$	−8.25156e8	−	4.67969e9i	−0.333670	−	1.89233i	−0.439990	−	0.898003i	$-0.645018\pi$
$223$	−8.25156e8	−	4.67969e9i	−0.333670	−	1.89233i	0.106320	−	0.994332i	$-0.466093\pi$
$224$	−5.73156e8	+	3.30912e8i	−0.227657	+	0.131438i
$225$	−5.48880e9	−	3.61034e9i	−2.14165	−	1.40870i
$226$	−4.76912e8	+	8.26035e8i	−0.182812	+	0.316639i
$227$	−4.56931e8	+	1.25541e9i	−0.172087	+	0.472804i	−0.995514	−	0.0946179i	$-0.969837\pi$
$227$	−4.56931e8	+	1.25541e9i	−0.172087	+	0.472804i	0.823427	+	0.567422i	$0.192059\pi$
$228$	−1.45727e9	−	4.36309e8i	−0.539264	−	0.161456i
$229$	2.30538e9	+	1.93444e9i	0.838302	+	0.703419i	0.957181	−	0.289490i	$-0.0934856\pi$
$229$	2.30538e9	+	1.93444e9i	0.838302	+	0.703419i	−0.118879	+	0.992909i	$0.537930\pi$
$230$	2.68075e9	−	3.19479e9i	0.957953	−	1.14164i
$231$	−4.12668e9	−	4.37419e9i	−1.44928	−	1.53621i
$232$	−5.03574e8	−	1.83286e8i	−0.173825	−	0.0632670i
$233$	2.36299e9	+	1.36427e9i	0.801748	+	0.462890i	0.844082	−	0.536214i	$-0.180146\pi$
$233$	2.36299e9	+	1.36427e9i	0.801748	+	0.462890i	−0.0423339	+	0.999104i	$0.513479\pi$
$234$	−2.01184e9	+	6.02221e8i	−0.671011	+	0.200860i
$235$	1.87527e9	+	3.24807e9i	0.614884	+	1.06501i
$236$	−1.66455e9	+	2.93504e8i	−0.536596	+	0.0946164i
$237$	−1.67142e9	+	9.73171e7i	−0.529776	+	0.0308458i
$238$	−2.63710e9	+	9.59827e8i	−0.821900	+	0.299147i
$239$	2.49289e9	+	4.39564e8i	0.764033	+	0.134720i	0.542068	−	0.840335i	$-0.317642\pi$
$239$	2.49289e9	+	4.39564e8i	0.764033	+	0.134720i	0.221965	+	0.975055i	$0.428753\pi$
$240$	9.35015e8	−	1.25589e9i	0.281821	−	0.378537i
$241$	−5.06110e8	+	4.24677e8i	−0.150030	+	0.125890i	−0.714713	−	0.699418i	$-0.753443\pi$
$241$	−5.06110e8	+	4.24677e8i	−0.150030	+	0.125890i	0.564683	+	0.825308i	$0.308998\pi$
$242$		−	2.46656e9i		−	0.719167i
$243$	3.48087e9	+	2.03070e8i	0.998303	+	0.0582400i
$244$	1.67705e9			0.473136
$245$	5.29568e9	+	6.31114e9i	1.46980	+	1.75164i
$246$	2.67640e8	+	1.99258e8i	0.0730820	+	0.0544097i
$247$	7.20792e8	−	4.08782e9i	0.193652	−	1.09826i
$248$	−2.49335e8	−	6.85042e8i	−0.0659138	−	0.181097i
$249$	−5.89645e7	−	1.01271e9i	−0.0153389	−	0.263445i
$250$	1.41554e9	+	8.02792e9i	0.362378	+	2.05515i
$251$	−5.20114e9	+	3.00288e9i	−1.31040	+	0.756560i	−0.982162	−	0.188036i	$-0.939788\pi$
$251$	−5.20114e9	+	3.00288e9i	−1.31040	+	0.756560i	−0.328237	+	0.944595i	$0.606455\pi$
$252$	8.59857e8	+	2.87252e9i	0.213218	+	0.712297i
$253$	−3.24840e9	+	5.62640e9i	−0.792844	+	1.37325i
$254$	6.29255e8	−	1.72886e9i	0.151179	−	0.415361i
$255$	4.82928e9	−	4.55602e9i	1.14215	−	1.07752i
$256$	2.05633e8	+	1.72547e8i	0.0478778	+	0.0401742i
$257$	−2.57408e9	+	3.06767e9i	−0.590051	+	0.703196i	−0.975616	−	0.219485i	$-0.929562\pi$
$257$	−2.57408e9	+	3.06767e9i	−0.590051	+	0.703196i	0.385565	+	0.922681i	$0.374007\pi$
$258$	2.43669e8	−	8.13854e8i	0.0549947	−	0.183682i
$259$	9.77507e8	+	3.55783e8i	0.217230	+	0.0790654i
$260$	3.70004e9	+	2.13622e9i	0.809679	+	0.467468i
$261$	−1.33424e9	+	2.02844e9i	−0.287522	+	0.437119i
$262$	−2.60624e9	−	4.51414e9i	−0.553107	−	0.958009i
$263$	6.30787e9	−	1.11225e9i	1.31844	−	0.232476i	0.530213	−	0.847864i	$-0.322112\pi$
$263$	6.30787e9	−	1.11225e9i	1.31844	−	0.232476i	0.788224	+	0.615388i	$0.211001\pi$
$264$	−1.09471e9	+	2.17964e9i	−0.225363	+	0.448713i
$265$	1.26896e10	−	4.61863e9i	2.57314	−	0.936547i
$266$	−5.83662e9	−	1.02915e9i	−1.16583	−	0.205567i
$267$	5.65933e9	+	6.61590e8i	1.11358	+	0.130180i
$268$	2.62808e9	−	2.20522e9i	0.509447	−	0.427477i
$269$			8.48182e9i			1.61987i	0.586520	+	0.809935i	$0.300497\pi$
$269$			8.48182e9i			1.61987i	−0.586520	+	0.809935i	$0.699503\pi$
$270$	−4.55943e9	−	5.43435e9i	−0.857938	−	1.02257i
$271$	−9.12337e9			−1.69152			−0.845762	−	0.533561i	$-0.820853\pi$
$271$	−9.12337e9			−1.69152			−0.845762	+	0.533561i	$0.820853\pi$
$272$	7.31655e8	+	8.71952e8i	0.133669	+	0.159301i
$273$	−7.51283e9	+	3.24055e9i	−1.35255	+	0.583402i
$274$	−1.05813e8	+	6.00098e8i	−0.0187732	+	0.106468i
$275$	−7.12131e9	−	1.95656e10i	−1.24517	−	3.42108i
$276$	2.70652e9	−	1.78003e9i	0.466417	−	0.306755i
$277$	1.24378e8	+	7.05385e8i	0.0211264	+	0.119814i	0.993547	−	0.113420i	$-0.0361805\pi$
$277$	1.24378e8	+	7.05385e8i	0.0211264	+	0.119814i	−0.972421	+	0.233234i	$0.925069\pi$
$278$	4.67624e9	−	2.69983e9i	0.782920	−	0.452019i
$279$	−3.28051e9	+	3.83310e8i	−0.541409	+	0.0632607i
$280$	3.05011e9	−	5.28294e9i	0.496230	−	0.859496i
$281$	2.57457e9	−	7.07358e9i	0.412933	−	1.13452i	−0.542690	−	0.839933i	$-0.682594\pi$
$281$	2.57457e9	−	7.07358e9i	0.412933	−	1.13452i	0.955623	−	0.294591i	$-0.0951835\pi$
$282$	6.71778e8	+	2.83470e9i	0.106226	+	0.448240i
$283$	−5.06818e9	−	4.25271e9i	−0.790144	−	0.663010i	0.155637	−	0.987814i	$-0.450257\pi$
$283$	−5.06818e9	−	4.25271e9i	−0.790144	−	0.663010i	−0.945781	+	0.324804i	$0.894701\pi$
$284$	1.53098e9	−	1.82455e9i	0.235340	−	0.280468i
$285$	1.36433e10	−	3.23325e9i	2.06795	−	0.490073i
$286$	−6.25422e9	−	2.27635e9i	−0.934779	−	0.340232i
$287$	1.12583e9	+	6.50000e8i	0.165938	+	0.0958045i
$288$	9.75547e8	−	7.26210e8i	0.141801	−	0.105558i
$289$	−1.07460e9	−	1.86126e9i	−0.154048	−	0.266818i
$290$	4.86443e9	−	8.57730e8i	0.687765	−	0.121272i
$291$	−5.87890e9	−	8.93880e9i	−0.819830	−	1.24654i
$292$	2.62278e9	−	9.54613e8i	0.360770	−	0.131309i
$293$	−4.63379e9	−	8.17062e8i	−0.628732	−	0.110862i	−0.149803	−	0.988716i	$-0.547864\pi$
$293$	−4.63379e9	−	8.17062e8i	−0.628732	−	0.110862i	−0.478929	+	0.877853i	$0.658975\pi$
$294$	2.53451e9	+	5.87597e9i	0.339239	+	0.786484i
$295$	1.19344e10	−	1.00142e10i	1.57584	−	1.32229i
$296$		−	4.21921e8i		−	0.0549623i
$297$	8.46482e9	+	7.10365e9i	1.08791	+	0.912969i
$298$	−1.04419e10			−1.32408
$299$	5.68185e9	+	6.77137e9i	0.710895	+	0.847211i
$300$	−1.20545e9	+	1.03116e10i	−0.148821	+	1.27304i
$301$	5.74759e8	−	3.25962e9i	0.0700196	−	0.397101i
$302$	1.06879e9	+	2.93646e9i	0.128488	+	0.353018i
$303$	2.25355e9	+	1.13183e9i	0.267360	+	0.134280i
$304$	4.17424e8	+	2.36733e9i	0.0488746	+	0.277182i
$305$	−1.33869e10	+	7.72891e9i	−1.54696	+	0.893139i
$306$	4.60852e9	−	2.31426e9i	0.525624	−	0.263953i
$307$	−4.97885e9	+	8.62363e9i	−0.560500	+	0.970815i	0.436953	+	0.899485i	$0.356058\pi$
$307$	−4.97885e9	+	8.62363e9i	−0.560500	+	0.970815i	−0.997453	+	0.0713303i	$0.977276\pi$
$308$	−3.25019e9	+	8.92982e9i	−0.361165	+	0.992293i
$309$	2.33224e9	+	6.98275e8i	0.255823	+	0.0765936i
$310$	5.14741e9	+	4.31919e9i	0.557368	+	0.467687i
$311$	8.94373e9	−	1.06587e10i	0.956042	−	1.13937i	−0.0341165	−	0.999418i	$-0.510862\pi$
$311$	8.94373e9	−	1.06587e10i	0.956042	−	1.13937i	0.990159	−	0.139949i	$-0.0446938\pi$
$312$	2.27730e9	+	2.41389e9i	0.240327	+	0.254741i
$313$	6.60843e9	+	2.40527e9i	0.688527	+	0.250603i	0.662505	−	0.749058i	$-0.269494\pi$
$313$	6.60843e9	+	2.40527e9i	0.688527	+	0.250603i	0.0260227	+	0.999661i	$0.491716\pi$
$314$	−2.39865e9	−	1.38486e9i	−0.246745	−	0.142459i
$315$	−2.01021e10	−	1.89668e10i	−2.04174	−	1.92643i
$316$	1.32286e9	+	2.29127e9i	0.132668	+	0.229788i
$317$	−1.39217e10	+	2.45478e9i	−1.37866	+	0.243094i	−0.813344	−	0.581783i	$-0.802355\pi$
$317$	−1.39217e10	+	2.45478e9i	−1.37866	+	0.243094i	−0.565312	+	0.824877i	$0.691244\pi$
$318$	1.04714e10	−	6.09687e8i	1.02399	−	0.0596209i
$319$	−7.23066e9	+	2.63175e9i	−0.698257	+	0.254145i
$320$	−2.43666e9	−	4.29648e8i	−0.232378	−	0.0409745i
$321$	−4.35729e9	+	5.85262e9i	−0.410389	+	0.551227i
$322$	9.66822e9	−	8.11260e9i	0.899338	−	0.754634i
$323$			1.01931e10i			0.936475i
$324$	−2.18201e9	−	5.05952e9i	−0.198005	−	0.459123i
$325$	−2.83290e10			−2.53920
$326$	1.26867e9	+	1.51194e9i	0.112325	+	0.133864i
$327$	1.68490e10	+	1.25441e10i	1.47361	+	1.09711i
$328$	9.15611e7	−	5.19269e8i	0.00791071	−	0.0448639i
$329$	3.88196e9	+	1.06656e10i	0.331335	+	0.910335i
$330$	−1.30678e9	−	2.24439e10i	−0.110191	−	1.89253i
$331$	−9.90353e8	−	5.61657e9i	−0.0825045	−	0.467907i	−0.997867	−	0.0652762i	$-0.979207\pi$
$331$	−9.90353e8	−	5.61657e9i	−0.0825045	−	0.467907i	0.915363	−	0.402630i	$-0.131904\pi$
$332$	−1.38828e9	+	8.01524e8i	−0.114268	+	0.0659727i
$333$	−1.86001e9	−	4.40906e8i	−0.151265	−	0.0358566i
$334$	−1.72544e9	+	2.98854e9i	−0.138648	+	0.240145i
$335$	−1.08153e10	+	2.97148e10i	−0.858736	+	2.35936i
$336$	3.44657e9	−	3.25155e9i	0.270415	−	0.255114i
$337$	4.96748e9	+	4.16821e9i	0.385138	+	0.323169i	0.814715	−	0.579861i	$-0.196893\pi$
$337$	4.96748e9	+	4.16821e9i	0.385138	+	0.323169i	−0.429578	+	0.903030i	$0.641338\pi$
$338$	1.11519e8	−	1.32904e8i	0.00854443	−	0.0101829i
$339$	1.95866e9	−	6.54193e9i	0.148307	−	0.495345i
$340$	−9.85888e9	−	3.58834e9i	−0.737755	−	0.268521i
$341$	−9.06519e9	−	5.23379e9i	−0.670439	−	0.387078i
$342$	1.08724e10	+	6.33662e8i	0.794734	+	0.0463184i
$343$	2.17470e9	+	3.76669e9i	0.157117	+	0.272135i
$344$	−1.32210e9	+	2.33122e8i	−0.0944128	+	0.0166475i
$345$	−1.34010e10	+	2.66823e10i	−0.945933	+	1.88342i
$346$	−1.58780e9	+	5.77911e8i	−0.110788	+	0.0403234i
$347$	−1.60939e10	−	2.83779e9i	−1.11005	−	0.195732i	−0.411583	−	0.911372i	$-0.635024\pi$
$347$	−1.60939e10	−	2.83779e9i	−1.11005	−	0.195732i	−0.698469	+	0.715640i	$0.746135\pi$
$348$	3.81075e9	+	4.45486e8i	0.259832	+	0.0303751i
$349$	−4.67414e9	+	3.92207e9i	−0.315065	+	0.264371i	−0.786582	−	0.617486i	$-0.788151\pi$
$349$	−4.67414e9	+	3.92207e9i	−0.315065	+	0.264371i	0.471517	+	0.881857i	$0.343707\pi$
$350$			4.04484e10i			2.69543i
$351$	1.30212e10	−	7.51683e9i	0.857875	−	0.495229i
$352$	3.85438e9			0.251064
$353$	−1.64262e10	−	1.95760e10i	−1.05789	−	1.26074i	−0.964211	−	0.265137i	$-0.914583\pi$
$353$	−1.64262e10	−	1.95760e10i	−1.05789	−	1.26074i	−0.0936756	−	0.995603i	$-0.529862\pi$
$354$	1.11115e10	−	4.79278e9i	0.707554	−	0.305193i
$355$	−3.81220e9	+	2.16201e10i	−0.240028	+	1.36127i
$356$	−3.07956e9	−	8.46102e9i	−0.191729	−	0.526772i
$357$	1.67868e10	−	1.10404e10i	1.03346	−	0.679690i
$358$	−1.18521e9	−	6.72167e9i	−0.0721546	−	0.409209i
$359$	2.05685e10	−	1.18752e10i	1.23830	−	0.714932i	0.269552	−	0.962986i	$-0.413125\pi$
$359$	2.05685e10	−	1.18752e10i	1.23830	−	0.714932i	0.968746	+	0.248054i	$0.0797912\pi$
$360$	−4.44037e9	+	1.02929e10i	−0.264368	+	0.612810i
$361$	−2.27151e9	+	3.93436e9i	−0.133747	+	0.231657i
$362$	−3.36109e8	+	9.23452e8i	−0.0195725	+	0.0537750i
$363$	4.07216e9	+	1.71833e10i	0.234530	+	0.989645i
$364$	9.90453e9	+	8.31088e9i	0.564194	+	0.473415i
$365$	−1.65366e10	+	1.97076e10i	−0.931697	+	1.11035i
$366$	−1.16832e10	+	2.76872e9i	−0.651082	+	0.154296i
$367$	1.71033e10	+	6.22509e9i	0.942791	+	0.343148i	0.767267	−	0.641327i	$-0.221616\pi$
$367$	1.71033e10	+	6.22509e9i	0.942791	+	0.343148i	0.175524	+	0.984475i	$0.443838\pi$
$368$	−4.43323e9	−	2.55953e9i	−0.241729	−	0.139563i
$369$	−2.19348e9	−	9.46274e8i	−0.118312	−	0.0510401i
$370$	1.94449e9	+	3.36795e9i	0.103752	+	0.179704i
$371$	4.02455e10	−	7.09636e9i	2.12433	−	0.374576i
$372$	2.86796e9	+	4.36071e9i	0.149762	+	0.227712i
$373$	3.50818e9	−	1.27687e9i	0.181237	−	0.0659648i	−0.249808	−	0.968295i	$-0.580367\pi$
$373$	3.50818e9	−	1.27687e9i	0.181237	−	0.0659648i	0.431045	+	0.902331i	$0.358145\pi$
$374$	1.60955e10	+	2.83807e9i	0.822657	+	0.145057i
$375$	−2.31151e10	−	5.35895e10i	−1.16888	−	2.70991i
$376$	3.52656e9	−	2.95913e9i	0.176441	−	0.148052i
$377$			1.04692e10i			0.518262i
$378$	−1.07326e10	−	1.85918e10i	−0.525699	−	0.910658i
$379$	−2.74450e9			−0.133017			−0.0665083	−	0.997786i	$-0.521186\pi$
$379$	−2.74450e9			−0.133017			−0.0665083	+	0.997786i	$0.521186\pi$
$380$	−1.42422e10	−	1.69732e10i	−0.683036	−	0.814011i
$381$	−1.52944e9	+	1.30830e10i	−0.0725824	+	0.620880i
$382$	1.86388e9	−	1.05706e10i	0.0875313	−	0.496415i
$383$	−1.40771e9	−	3.86765e9i	−0.0654211	−	0.179743i	0.902675	−	0.430324i	$-0.141601\pi$
$383$	−1.40771e9	−	3.86765e9i	−0.0654211	−	0.179743i	−0.968096	+	0.250581i	$0.919378\pi$
$384$	−1.71741e9	−	8.62558e8i	−0.0789860	−	0.0396701i
$385$	−1.52100e10	−	8.62604e10i	−0.692289	−	3.92617i
$386$	−2.26639e10	+	1.30850e10i	−1.02091	+	0.589421i
$387$	−3.53886e8	+	6.07200e9i	−0.0157768	+	0.270700i
$388$	−8.45334e9	+	1.46416e10i	−0.372994	+	0.646044i
$389$	5.62862e9	−	1.54645e10i	0.245812	−	0.675363i	−0.754017	−	0.656855i	$-0.771886\pi$
$389$	5.62862e9	−	1.54645e10i	0.245812	−	0.675363i	0.999829	−	0.0185080i	$-0.00589162\pi$
$390$	−2.93031e10	−	8.77338e9i	−1.26665	−	0.379235i
$391$	−1.66281e10	−	1.39526e10i	−0.711436	−	0.596966i
$392$	6.50015e9	−	7.74658e9i	0.275283	−	0.328069i
$393$	2.56090e10	+	2.71450e10i	1.07355	+	1.13794i
$394$	−1.92170e10	−	6.99441e9i	−0.797444	−	0.290246i
$395$	−2.11193e10	−	1.21932e10i	−0.867542	−	0.500876i
$396$	4.02781e9	−	1.69918e10i	0.163790	−	0.690968i
$397$	−1.35537e10	−	2.34757e10i	−0.545626	−	0.945052i	−0.998567	−	0.0535118i	$-0.982959\pi$
$397$	−1.35537e10	−	2.34757e10i	−0.545626	−	0.945052i	0.452941	−	0.891540i	$-0.350375\pi$
$398$	1.62426e10	−	2.86400e9i	0.647325	−	0.114141i
$399$	4.23599e10	−	2.46637e9i	1.67133	−	0.0973122i
$400$	1.54164e10	−	5.61113e9i	0.602205	−	0.219185i
$401$	4.60831e10	+	8.12569e9i	1.78223	+	0.314255i	0.965038	−	0.262109i	$-0.0844179\pi$
$401$	4.60831e10	+	8.12569e9i	1.78223	+	0.314255i	0.817193	+	0.576364i	$0.195529\pi$
$402$	−1.46678e10	+	1.97015e10i	−0.561644	+	0.754388i
$403$	−1.09100e10	+	9.15454e9i	−0.413621	+	0.347069i
$404$		−	3.98509e9i		−	0.149593i
$405$	4.07352e10	+	3.03310e10i	1.51408	+	1.12737i
$406$	1.49481e10			0.550150
$407$	−3.89416e9	−	4.64088e9i	−0.141918	−	0.169131i
$408$	−6.53663e9	−	4.86653e9i	−0.235892	−	0.175622i
$409$	−3.32787e9	+	1.88733e10i	−0.118925	+	0.674458i	0.865807	+	0.500379i	$0.166806\pi$
$409$	−3.32787e9	+	1.88733e10i	−0.118925	+	0.674458i	−0.984732	+	0.174079i	$0.944305\pi$
$410$	1.66225e9	+	4.56699e9i	0.0588248	+	0.161620i
$411$	−2.53583e8	−	4.35528e9i	−0.00888694	−	0.152633i
$412$	−6.68052e8	−	3.78871e9i	−0.0231858	−	0.131493i
$413$	4.08303e10	−	2.35734e10i	1.40340	−	0.810254i
$414$	−1.59162e10	+	1.68689e10i	−0.541799	+	0.574230i
$415$	7.38788e9	−	1.27962e10i	0.249073	−	0.431408i
$416$	1.79361e9	−	4.92791e9i	0.0598902	−	0.164547i
$417$	−2.81197e10	+	2.65286e10i	−0.929966	+	0.877344i
$418$	2.64409e10	+	2.21865e10i	0.866106	+	0.726749i
$419$	6.07589e9	−	7.24097e9i	0.197131	−	0.234931i	−0.658419	−	0.752651i	$-0.728775\pi$
$419$	6.07589e9	−	7.24097e9i	0.197131	−	0.234931i	0.855550	+	0.517720i	$0.173219\pi$
$420$	−1.25267e10	+	4.18392e10i	−0.402569	+	1.34458i
$421$	3.84286e8	+	1.39869e8i	0.0122328	+	0.00445238i	0.348129	−	0.937447i	$-0.386817\pi$
$421$	3.84286e8	+	1.39869e8i	0.0122328	+	0.00445238i	−0.335896	+	0.941899i	$0.609039\pi$
$422$	−9.83629e9	−	5.67899e9i	−0.310157	−	0.179069i
$423$	−9.35989e9	−	1.86389e10i	−0.292354	−	0.582181i
$424$	−8.28768e9	−	1.43547e10i	−0.256431	−	0.444151i
$425$	6.85092e10	−	1.20800e10i	2.09987	−	0.370264i
$426$	−7.65334e9	+	1.52383e10i	−0.232387	+	0.462699i
$427$	−4.39580e10	+	1.59994e10i	−1.32229	+	0.481274i
$428$	1.13551e10	+	2.00221e9i	0.338389	+	0.0596672i
$429$	4.73282e10	+	5.53278e9i	1.39730	+	0.163348i
$430$	9.47917e9	−	7.95397e9i	0.277266	−	0.232654i
$431$			5.75877e10i			1.66886i	0.551112	+	0.834431i	$0.314204\pi$
$431$			5.75877e10i			1.66886i	−0.551112	+	0.834431i	$0.685796\pi$
$432$	−5.59722e9	+	6.66973e9i	−0.160708	+	0.191502i
$433$	1.24460e10			0.354061			0.177031	−	0.984205i	$-0.443351\pi$
$433$	1.24460e10			0.354061			0.177031	+	0.984205i	$0.443351\pi$
$434$	1.30709e10	+	1.55773e10i	0.368424	+	0.439070i
$435$	−3.24720e10	+	1.40063e10i	−0.906885	+	0.391171i
$436$	5.76413e9	−	3.26900e10i	0.159510	−	0.904626i
$437$	−1.56787e10	−	4.30768e10i	−0.429916	−	1.18118i
$438$	−1.66956e10	+	1.09804e10i	−0.453633	+	0.298347i
$439$	1.10370e10	+	6.25938e10i	0.297161	+	1.68528i	0.658287	+	0.752767i	$0.271281\pi$
$439$	1.10370e10	+	6.25938e10i	0.297161	+	1.68528i	−0.361126	+	0.932517i	$0.617608\pi$
$440$	−3.07672e10	+	1.77635e10i	−0.820876	+	0.473933i
$441$	−2.73576e10	−	3.67506e10i	−0.723309	−	0.971650i
$442$	1.11185e10	−	1.92578e10i	0.291311	−	0.504566i
$443$	5.80627e8	−	1.59526e9i	0.0150759	−	0.0414206i	−0.931926	−	0.362647i	$-0.881873\pi$
$443$	5.80627e8	−	1.59526e9i	0.0150759	−	0.0414206i	0.947002	+	0.321227i	$0.104095\pi$
$444$	6.96572e8	+	2.93932e9i	0.0179240	+	0.0756336i
$445$	6.35761e10	+	5.33467e10i	1.62127	+	1.36040i
$446$	3.45572e10	−	4.11837e10i	0.873371	−	1.04084i
$447$	7.27432e10	−	1.72390e10i	1.82206	−	0.431799i
$448$	−7.03612e9	−	2.56094e9i	−0.174671	−	0.0635751i
$449$	−1.74274e10	−	1.00617e10i	−0.428793	−	0.247564i	0.270039	−	0.962849i	$-0.412963\pi$
$449$	−1.74274e10	−	1.00617e10i	−0.428793	−	0.247564i	−0.698832	+	0.715286i	$0.746297\pi$
$450$	−8.62616e9	−	7.38259e10i	−0.210362	−	1.80036i
$451$	−3.78552e9	−	6.55671e9i	−0.0914996	−	0.158482i
$452$	−1.06273e10	+	1.87389e9i	−0.254607	+	0.0448941i
$453$	−1.22937e10	−	1.86924e10i	−0.291936	−	0.443886i
$454$	−1.42033e10	+	5.16959e9i	−0.334323	+	0.121684i
$455$	−1.17364e11	−	2.06944e10i	−2.73835	−	0.482845i
$456$	−6.81633e9	−	1.58029e10i	−0.157649	−	0.365491i
$457$	−3.31169e10	+	2.77884e10i	−0.759250	+	0.637087i	−0.937932	−	0.346820i	$-0.887261\pi$
$457$	−3.31169e10	+	2.77884e10i	−0.759250	+	0.637087i	0.178681	+	0.983907i	$0.442817\pi$
$458$			3.40482e10i			0.773805i
$459$	−2.82845e10	+	2.37308e10i	−0.637233	+	0.534640i
$460$	4.71838e10			1.05381
$461$	−2.06419e9	−	2.46000e9i	−0.0457031	−	0.0544668i	0.742709	−	0.669615i	$-0.233541\pi$
$461$	−2.06419e9	−	2.46000e9i	−0.0457031	−	0.0544668i	−0.788412	+	0.615148i	$0.789096\pi$
$462$	7.89975e9	−	6.75755e10i	0.173399	−	1.48327i
$463$	1.48840e10	−	8.44114e10i	0.323889	−	1.83687i	−0.193482	−	0.981104i	$-0.561978\pi$
$463$	1.48840e10	−	8.44114e10i	0.323889	−	1.83687i	0.517371	−	0.855761i	$-0.326911\pi$
$464$	−2.07364e9	−	5.69729e9i	−0.0447365	−	0.122913i
$465$	−4.29902e10	−	2.15915e10i	−0.919512	−	0.461818i
$466$	5.36051e9	+	3.04010e10i	0.113674	+	0.644679i
$467$	2.62009e10	−	1.51271e10i	0.550870	−	0.318045i	−0.198603	−	0.980080i	$-0.563640\pi$
$467$	2.62009e10	−	1.51271e10i	0.550870	−	0.318045i	0.749473	+	0.662035i	$0.230307\pi$
$468$	−1.98501e10	−	1.30567e10i	−0.413788	−	0.272175i
$469$	−4.78478e10	+	8.28747e10i	−0.988940	+	1.71290i
$470$	−1.45128e10	+	3.98736e10i	−0.297413	+	0.817136i
$471$	1.89966e10	+	5.68760e9i	0.386004	+	0.115570i
$472$	−1.46488e10	−	1.22918e10i	−0.295145	−	0.247656i
$473$	−1.23907e10	+	1.47666e10i	−0.247543	+	0.295010i
$474$	−1.29985e10	−	1.37781e10i	−0.257502	−	0.272946i
$475$	1.38055e11	+	5.02479e10i	2.71192	+	0.987059i
$476$	−2.74965e10	−	1.58751e10i	−0.535610	−	0.309235i
$477$	−7.19422e10	+	2.15351e10i	−1.38967	+	0.415981i
$478$	1.43195e10	+	2.48021e10i	0.274294	+	0.475091i
$479$	3.95522e10	−	6.97412e9i	0.751326	−	0.132479i	0.215145	−	0.976582i	$-0.430978\pi$
$479$	3.95522e10	−	6.97412e9i	0.751326	−	0.132479i	0.536181	+	0.844103i	$0.319866\pi$
$480$	1.76843e10	−	1.02966e9i	0.333137	−	0.0193967i
$481$	−7.74560e9	+	2.81917e9i	−0.144702	+	0.0526672i
$482$	−7.36119e9	−	1.29798e9i	−0.136383	−	0.0240480i
$483$	−5.39602e10	+	7.24782e10i	−0.991482	+	1.33174i
$484$	2.13772e10	−	1.79376e10i	0.389555	−	0.326875i
$485$		−	1.55834e11i		−	2.81640i
$486$	2.35540e10	+	3.16448e10i	0.422201	+	0.567227i
$487$	2.34837e10			0.417494			0.208747	−	0.977970i	$-0.433061\pi$
$487$	2.34837e10			0.417494			0.208747	+	0.977970i	$0.433061\pi$
$488$	1.21960e10	+	1.45346e10i	0.215049	+	0.256286i
$489$	−1.13343e10	−	8.43843e9i	−0.198226	−	0.147580i
$490$	−1.61856e10	+	9.17932e10i	−0.280766	+	1.59230i
$491$	−2.15639e10	−	5.92462e10i	−0.371023	−	1.01938i	−0.974967	−	0.222350i	$-0.928627\pi$
$491$	−2.15639e10	−	5.92462e10i	−0.371023	−	1.01938i	0.603944	−	0.797027i	$-0.293595\pi$
$492$	2.19427e8	+	3.76865e9i	0.00374481	+	0.0643170i
$493$	−4.46428e9	−	2.53182e10i	−0.0755725	−	0.428593i
$494$	4.06701e10	−	2.34809e10i	0.682917	−	0.394282i
$495$	4.61574e10	+	1.54198e11i	0.768813	+	2.56837i
$496$	4.12388e9	−	7.14278e9i	0.0681365	−	0.118016i
$497$	−2.27228e10	+	6.24303e10i	−0.372423	+	1.02322i
$498$	8.34818e9	−	7.87580e9i	0.135730	−	0.128049i
$499$	8.60985e9	+	7.22452e9i	0.138865	+	0.116522i	0.709574	−	0.704630i	$-0.248887\pi$
$499$	8.60985e9	+	7.22452e9i	0.138865	+	0.116522i	−0.570709	+	0.821152i	$0.693332\pi$
$500$	−5.92822e10	+	7.06497e10i	−0.948515	+	1.13040i
$501$	7.08632e9	−	2.36683e10i	0.112479	−	0.375678i
$502$	−6.38497e10	−	2.32394e10i	−1.00541	−	0.365940i
$503$	−3.14479e10	−	1.81565e10i	−0.491270	−	0.283635i	0.233831	−	0.972277i	$-0.424874\pi$
$503$	−3.14479e10	−	1.81565e10i	−0.491270	−	0.283635i	−0.725101	+	0.688643i	$0.758207\pi$
$504$	−1.86424e10	+	2.83421e10i	−0.288922	+	0.439248i
$505$	1.83658e10	+	3.18106e10i	0.282387	+	0.489109i
$506$	−7.23863e10	+	1.27637e10i	−1.10422	+	0.194703i
$507$	−5.57482e8	+	1.10999e9i	−0.00843722	+	0.0167991i
$508$	1.95599e10	−	7.11920e9i	0.293705	−	0.106900i
$509$	2.76640e10	+	4.87791e9i	0.412140	+	0.0726713i	0.375874	−	0.926671i	$-0.377343\pi$
$509$	2.76640e10	+	4.87791e9i	0.412140	+	0.0726713i	0.0362657	+	0.999342i	$0.488454\pi$
$510$	7.46061e10	+	8.72165e9i	1.10279	+	0.128919i
$511$	−5.96399e10	+	5.00438e10i	−0.874688	+	0.733951i
$512$			3.03700e9i			0.0441942i
$513$	−7.67889e10	+	1.35354e10i	−1.10874	+	0.195435i
$514$	−4.53064e10			−0.649093
$515$	2.27935e10	+	2.71642e10i	0.324027	+	0.386161i
$516$	8.82555e9	−	3.80677e9i	0.124492	−	0.0536980i
$517$	1.14784e10	−	6.50973e10i	0.160664	−	0.911173i
$518$	4.02523e9	+	1.10592e10i	0.0559077	+	0.153605i
$519$	1.01073e10	−	6.64740e9i	0.139305	−	0.0916183i
$520$	8.39365e9	+	4.76027e10i	0.114799	+	0.651056i
$521$	4.22873e10	−	2.44146e10i	0.573930	−	0.331358i	−0.184788	−	0.982778i	$-0.559160\pi$
$521$	4.22873e10	−	2.44146e10i	0.573930	−	0.331358i	0.758717	+	0.651420i	$0.225826\pi$
$522$	−2.72831e10	+	3.18788e9i	−0.367461	+	0.0429358i
$523$	−2.02984e10	+	3.51578e10i	−0.271303	+	0.469911i	−0.969196	−	0.246292i	$-0.920788\pi$
$523$	−2.02984e10	+	3.51578e10i	−0.271303	+	0.469911i	0.697893	+	0.716202i	$0.254121\pi$
$524$	2.01698e10	−	5.54160e10i	0.267532	−	0.735038i
$525$	−6.67783e10	−	2.81784e11i	−0.879018	−	3.70918i
$526$	5.55124e10	+	4.65804e10i	0.725182	+	0.608500i
$527$	2.24803e10	−	2.67910e10i	0.291448	−	0.347334i
$528$	−2.68516e10	+	6.36339e9i	−0.345489	+	0.0818753i
$529$	1.81449e10	+	6.60419e9i	0.231703	+	0.0843328i
$530$	1.32311e11	+	7.63900e10i	1.67685	+	0.968128i
$531$	−6.94957e10	+	5.17335e10i	−0.874137	+	0.650719i
$532$	−3.35262e10	−	5.80691e10i	−0.418541	−	0.724935i
$533$	−1.01445e10	+	1.78875e9i	−0.125696	+	0.0221636i
$534$	3.54225e10	+	5.38595e10i	0.435627	+	0.662365i
$535$	−9.98687e10	+	3.63492e10i	−1.21903	+	0.443690i
$536$	3.82244e10	+	6.73999e9i	0.463107	+	0.0816583i
$537$	1.93539e10	+	4.48698e10i	0.232741	+	0.539582i
$538$	−7.35103e10	+	6.16824e10i	−0.877443	+	0.736262i
$539$		−	1.45201e11i		−	1.72034i
$540$	1.39408e10	−	7.90360e10i	0.163951	−	0.929502i
$541$	−3.72829e10			−0.435232			−0.217616	−	0.976034i	$-0.569828\pi$
$541$	−3.72829e10			−0.435232			−0.217616	+	0.976034i	$0.569828\pi$
$542$	−6.63480e10	−	7.90704e10i	−0.768830	−	0.916256i
$543$	8.16931e8	−	6.98813e9i	0.00939693	−	0.0803826i
$544$	−2.23622e9	+	1.26822e10i	−0.0255340	+	0.144810i
$545$	1.04645e11	+	2.87510e11i	1.18613	+	3.25886i
$546$	−8.27208e10	−	4.15459e10i	−0.930774	−	0.467474i
$547$	1.83639e9	+	1.04147e10i	0.0205124	+	0.116332i	0.993345	−	0.115179i	$-0.0367442\pi$
$547$	1.83639e9	+	1.04147e10i	0.0205124	+	0.116332i	−0.972832	+	0.231511i	$0.925633\pi$
$548$	−5.97044e9	+	3.44703e9i	−0.0662040	+	0.0382229i
$549$	7.68197e10	−	3.85766e10i	0.845636	−	0.424654i
$550$	1.17783e11	−	2.04006e11i	1.28716	−	2.22943i
$551$	1.85696e10	−	5.10195e10i	0.201463	−	0.553515i
$552$	3.51098e10	+	1.05119e10i	0.378157	+	0.113221i
$553$	−5.65336e10	−	4.74373e10i	−0.604514	−	0.507247i
$554$	−5.20891e9	+	6.20774e9i	−0.0552978	+	0.0659014i
$555$	−1.91066e10	−	2.02526e10i	−0.201378	−	0.213456i
$556$	5.74059e10	+	2.08940e10i	0.600700	+	0.218637i
$557$	7.68419e10	+	4.43647e10i	0.798320	+	0.460910i	0.842883	−	0.538096i	$-0.180856\pi$
$557$	7.68419e10	+	4.43647e10i	0.798320	+	0.460910i	−0.0445633	+	0.999007i	$0.514190\pi$
$558$	−2.71790e10	−	2.56440e10i	−0.280347	−	0.264514i
$559$	1.31136e10	+	2.27134e10i	0.134299	+	0.232613i
$560$	6.79676e10	−	1.19845e10i	0.691114	−	0.121862i
$561$	−1.16815e11	+	6.80147e9i	−1.17936	+	0.0686675i
$562$	8.00284e10	−	2.91279e10i	0.802230	−	0.291988i
$563$	−7.70494e10	−	1.35859e10i	−0.766895	−	0.135224i	−0.223503	−	0.974703i	$-0.571749\pi$
$563$	−7.70494e10	−	1.35859e10i	−0.766895	−	0.135224i	−0.543392	+	0.839479i	$0.682860\pi$
$564$	−1.96824e10	+	2.64370e10i	−0.194519	+	0.261273i
$565$	7.61956e10	−	6.39357e10i	0.747715	−	0.627407i
$566$		−	7.48520e10i		−	0.729353i
$567$	1.05463e11	+	1.11801e11i	1.02039	+	1.08172i
$568$	2.69468e10			0.258889
$569$	−8.29038e10	−	9.88009e10i	−0.790907	−	0.942566i	0.208464	−	0.978030i	$-0.433154\pi$
$569$	−8.29038e10	−	9.88009e10i	−0.790907	−	0.942566i	−0.999371	+	0.0354639i	$0.988709\pi$
$570$	1.27241e11	+	9.47308e10i	1.20539	+	0.897412i
$571$	−1.64935e10	+	9.35391e10i	−0.155156	+	0.879932i	0.803488	+	0.595321i	$0.202975\pi$
$571$	−1.64935e10	+	9.35391e10i	−0.155156	+	0.879932i	−0.958643	+	0.284610i	$0.908136\pi$
$572$	−2.57539e10	−	7.07584e10i	−0.240580	−	0.660988i
$573$	4.46679e9	+	7.67170e10i	0.0414359	+	0.711661i
$574$	2.55399e9	+	1.44844e10i	0.0235272	+	0.133430i
$575$	−2.70944e11	+	1.56429e11i	−2.47861	+	1.43103i
$576$	1.33884e10	+	3.17365e9i	0.121630	+	0.0288316i
$577$	2.82164e10	−	4.88722e10i	0.254565	−	0.440919i	−0.710212	−	0.703987i	$-0.751401\pi$
$577$	2.82164e10	−	4.88722e10i	0.254565	−	0.440919i	0.964777	+	0.263068i	$0.0847345\pi$
$578$	8.31635e9	−	2.28490e10i	0.0745112	−	0.204718i
$579$	1.36286e11	−	1.28574e11i	1.21265	−	1.14403i
$580$	4.28094e10	+	3.59214e10i	0.378292	+	0.317425i
$581$	2.87423e10	−	3.42537e10i	0.252242	−	0.300610i
$582$	3.47176e10	−	1.15957e11i	0.302593	−	1.01066i
$583$	−2.23647e11	−	8.14010e10i	−1.93593	−	0.704621i
$584$	2.73471e10	+	1.57889e10i	0.235104	+	0.135737i
$585$	2.18625e11	+	1.27418e10i	1.86671	+	0.108795i
$586$	−2.66170e10	−	4.61021e10i	−0.225720	−	0.390958i
$587$	−7.37473e10	+	1.30036e10i	−0.621146	+	0.109525i	−0.475360	−	0.879791i	$-0.657682\pi$
$587$	−7.37473e10	+	1.30036e10i	−0.621146	+	0.109525i	−0.145786	+	0.989316i	$0.546571\pi$
$588$	−3.24941e10	+	6.46980e10i	−0.271829	+	0.541230i
$589$	6.94048e10	−	2.52613e10i	0.576672	−	0.209891i
$590$	1.73582e11	+	3.06071e10i	1.43250	+	0.252589i
$591$	1.45423e11	+	1.70003e10i	1.19202	+	0.139350i
$592$	3.65671e9	−	3.06834e9i	0.0297717	−	0.0249814i
$593$		−	1.47101e11i		−	1.18958i	−0.803879	−	0.594792i	$-0.797234\pi$
$593$		−	1.47101e11i		−	1.18958i	0.803879	−	0.594792i	$-0.202766\pi$
$594$	−7.14781e6	+	1.25023e11i	−5.74152e−5	+	1.00425i
$595$	2.92651e11			2.33497
$596$	−7.59364e10	−	9.04975e10i	−0.601818	−	0.717219i
$597$	−1.08426e11	+	4.67678e10i	−0.853561	+	0.368171i
$598$	−1.73659e10	+	9.84870e10i	−0.135798	+	0.770148i
$599$	3.51461e10	+	9.65630e10i	0.273004	+	0.750073i	0.998111	+	0.0614366i	$0.0195682\pi$
$599$	3.51461e10	+	9.65630e10i	0.273004	+	0.750073i	−0.725107	+	0.688637i	$0.758210\pi$
$600$	−9.81350e10	+	6.45417e10i	−0.757215	+	0.498007i
$601$	−5.61852e9	−	3.18642e10i	−0.0430649	−	0.244233i	0.955675	−	0.294425i	$-0.0951280\pi$
$601$	−5.61852e9	−	3.18642e10i	−0.0430649	−	0.244233i	−0.998740	+	0.0501913i	$0.984017\pi$
$602$	3.24303e10	−	1.87237e10i	0.246925	−	0.142562i
$603$	6.96571e10	−	1.61466e11i	0.526861	−	1.22127i
$604$	−1.76772e10	+	3.06178e10i	−0.132821	+	0.230052i
$605$	−8.79733e10	+	2.41705e11i	−0.656643	+	1.80411i
$606$	6.57918e9	+	2.77621e10i	0.0487845	+	0.205855i
$607$	−1.30725e11	−	1.09691e11i	−0.962947	−	0.808009i	0.0184826	−	0.999829i	$-0.494116\pi$
$607$	−1.30725e11	−	1.09691e11i	−0.962947	−	0.808009i	−0.981430	+	0.191820i	$0.938561\pi$
$608$	−1.74815e10	+	2.08337e10i	−0.127928	+	0.152459i
$609$	−1.04136e11	+	2.46785e10i	−0.757061	+	0.179411i
$610$	−1.64338e11	−	5.98143e10i	−1.18692	−	0.432002i
$611$	−7.78870e10	−	4.49681e10i	−0.558856	−	0.322656i
$612$	5.35719e10	+	2.31111e10i	0.381884	+	0.164746i
$613$	5.88892e10	+	1.01999e11i	0.417056	+	0.722362i	0.995642	−	0.0932596i	$-0.0297287\pi$
$613$	5.88892e10	+	1.01999e11i	0.417056	+	0.722362i	−0.578586	+	0.815621i	$0.696395\pi$
$614$	−1.10947e11	+	1.95630e10i	−0.780625	+	0.137645i
$615$	−1.91199e10	−	2.90716e10i	−0.133655	−	0.203221i
$616$	−1.01029e11	+	3.67717e10i	−0.701657	+	0.255382i
$617$	−4.85126e10	−	8.55409e9i	−0.334745	−	0.0590246i	0.00374940	−	0.999993i	$-0.498807\pi$
$617$	−4.85126e10	−	8.55409e9i	−0.334745	−	0.0590246i	−0.338494	+	0.940968i	$0.609918\pi$
$618$	1.09090e10	+	2.52911e10i	0.0747876	+	0.173386i
$619$	1.87779e11	−	1.57565e11i	1.27904	−	1.07324i	0.285664	−	0.958330i	$-0.407786\pi$
$619$	1.87779e11	−	1.57565e11i	1.27904	−	1.07324i	0.993376	−	0.114912i	$-0.0366587\pi$
$620$			7.60220e10i			0.514485i
$621$	8.30306e10	−	1.43794e11i	0.558305	−	0.966886i
$622$	1.57419e11			1.05171
$623$	1.61440e11	+	1.92397e11i	1.07167	+	1.27716i
$624$	−4.35947e9	+	3.72915e10i	−0.0287538	+	0.245964i
$625$	7.96931e10	−	4.51962e11i	0.522276	−	2.96198i
$626$	2.72126e10	+	7.47659e10i	0.177203	+	0.486862i
$627$	−2.20829e11	−	1.10910e11i	−1.42885	−	0.717630i
$628$	−5.44142e9	−	3.08598e10i	−0.0349843	−	0.198406i
$629$	1.75294e10	−	1.01206e10i	0.111986	−	0.0646551i
$630$	1.81928e10	−	3.12154e11i	0.115488	−	1.98156i
$631$	3.55027e10	−	6.14924e10i	0.223946	−	0.387886i	−0.732057	−	0.681244i	$-0.761439\pi$
$631$	3.55027e10	−	6.14924e10i	0.223946	−	0.387886i	0.956003	+	0.293358i	$0.0947727\pi$
$632$	−1.02377e10	+	2.81278e10i	−0.0641702	+	0.176306i
$633$	7.79003e10	+	2.33234e10i	0.485204	+	0.145271i
$634$	−1.22518e11	−	1.02805e11i	−0.758304	−	0.636293i
$635$	−1.23325e11	+	1.46973e11i	−0.758500	+	0.903945i
$636$	8.14351e10	+	8.63194e10i	0.497718	+	0.527570i
$637$	−1.85643e11	−	6.75686e10i	−1.12751	−	0.410381i
$638$	−7.53924e10	−	4.35278e10i	−0.455035	−	0.262715i
$639$	2.81593e10	−	1.18793e11i	0.168896	−	0.712505i
$640$	−1.39965e10	−	2.42426e10i	−0.0834254	−	0.144497i
$641$	3.18593e11	−	5.61766e10i	1.88714	−	0.332754i	0.893847	−	0.448371i	$-0.147996\pi$
$641$	3.18593e11	−	5.61766e10i	1.88714	−	0.332754i	0.993294	+	0.115617i	$0.0368847\pi$
$642$	−8.24111e10	+	4.79832e9i	−0.485116	+	0.0282455i
$643$	−2.94973e11	+	1.07362e11i	−1.72559	+	0.628065i	−0.998301	−	0.0582613i	$-0.981444\pi$
$643$	−2.94973e11	+	1.07362e11i	−1.72559	+	0.628065i	−0.727294	+	0.686326i	$0.759222\pi$
$644$	1.40621e11	+	2.47952e10i	0.817533	+	0.144153i
$645$	−5.29051e10	+	7.10610e10i	−0.305674	+	0.410575i
$646$	−8.83416e10	+	7.41274e10i	−0.507265	+	0.425646i
$647$			7.30069e10i			0.416627i	0.978062	+	0.208313i	$0.0667974\pi$
$647$			7.30069e10i			0.416627i	−0.978062	+	0.208313i	$0.933203\pi$
$648$	2.79816e10	−	5.57054e10i	0.158699	−	0.315935i
$649$	−2.74577e11			−1.54769
$650$	−2.06017e11	−	2.45522e11i	−1.15412	−	1.37542i
$651$	−1.16776e11	−	8.69400e10i	−0.650174	−	0.484056i
$652$	−3.87754e9	+	2.19906e10i	−0.0214568	+	0.121688i
$653$	2.47064e10	+	6.78803e10i	0.135880	+	0.373328i	0.988906	−	0.148540i	$-0.0474574\pi$
$653$	2.47064e10	+	6.78803e10i	0.135880	+	0.373328i	−0.853026	+	0.521868i	$0.825235\pi$
$654$	1.38138e10	+	2.37251e11i	0.0755095	+	1.29687i
$655$	9.43892e10	+	5.35308e11i	0.512811	+	2.90829i
$656$	5.16626e9	−	2.98274e9i	0.0278972	−	0.0161065i
$657$	9.81816e10	−	1.04059e11i	0.526949	−	0.558491i
$658$	−6.42058e10	+	1.11208e11i	−0.342508	+	0.593241i
$659$	−1.64466e7	+	4.51866e7i	−8.72034e−5	+	0.000239589i	−0.939736	−	0.341900i	$-0.888929\pi$
$659$	−1.64466e7	+	4.51866e7i	−8.72034e−5	+	0.000239589i	0.939649	+	0.342140i	$0.111152\pi$
$660$	1.85013e11	−	1.74544e11i	0.975051	−	0.919878i
$661$	−1.05443e11	−	8.84770e10i	−0.552346	−	0.463473i	0.323389	−	0.946266i	$-0.395178\pi$
$661$	−1.05443e11	−	8.84770e10i	−0.552346	−	0.463473i	−0.875734	+	0.482793i	$0.839622\pi$
$662$	4.14755e10	−	4.94286e10i	0.215953	−	0.257363i
$663$	−4.56634e10	+	1.52516e11i	−0.236327	+	0.789334i
$664$	−1.70427e10	−	6.20302e9i	−0.0876728	−	0.0319103i
$665$	5.35240e11	+	3.09021e11i	2.73692	+	1.58016i
$666$	−9.70534e9	−	1.93268e10i	−0.0493303	−	0.0982340i
$667$	5.78100e10	+	1.00130e11i	0.292078	+	0.505895i
$668$	−3.84490e10	+	6.77960e9i	−0.193099	+	0.0340485i
$669$	−1.72751e11	+	3.43958e11i	−0.862412	+	1.71712i
$670$	−3.36185e11	+	1.22361e11i	−1.66832	+	0.607218i
$671$	2.68297e11	+	4.73081e10i	1.32351	+	0.233370i
$672$	5.32451e10	+	6.22449e9i	0.261098	+	0.0305230i
$673$	2.50644e10	−	2.10315e10i	0.122179	−	0.102520i	−0.579651	−	0.814865i	$-0.696811\pi$
$673$	2.50644e10	−	2.10315e10i	0.122179	−	0.102520i	0.701830	+	0.712345i	$0.252367\pi$
$674$			7.33646e10i			0.355506i
$675$	1.81977e11	+	5.00067e11i	0.876601	+	2.40887i
$676$	1.96285e9			0.00939941
$677$	−1.46754e11	−	1.74894e11i	−0.698609	−	0.832570i	0.293759	−	0.955880i	$-0.405094\pi$
$677$	−1.46754e11	−	1.74894e11i	−0.698609	−	0.832570i	−0.992368	+	0.123309i	$0.960649\pi$
$678$	7.09417e10	−	3.05996e10i	0.335724	−	0.144810i
$679$	8.18910e10	−	4.64427e11i	0.385263	−	2.18493i
$680$	−4.05974e10	−	1.11541e11i	−0.189873	−	0.521671i
$681$	9.04127e10	−	5.94629e10i	0.420379	−	0.276476i
$682$	−2.05646e10	−	1.16628e11i	−0.0950569	−	0.539095i
$683$	1.67591e11	−	9.67586e10i	0.770136	−	0.444638i	−0.0627870	−	0.998027i	$-0.519999\pi$
$683$	1.67591e11	−	9.67586e10i	0.770136	−	0.444638i	0.832923	+	0.553389i	$0.186666\pi$
$684$	7.35758e10	+	9.88373e10i	0.336133	+	0.451540i
$685$	3.17723e10	−	5.50312e10i	0.144307	−	0.249947i
$686$	−1.68301e10	+	4.62403e10i	−0.0759958	+	0.208797i
$687$	−5.62119e10	−	2.37197e11i	−0.252349	−	1.06483i
$688$	−1.16352e10	−	9.76305e9i	−0.0519300	−	0.0435745i
$689$	−2.08146e11	+	2.48059e11i	−0.923616	+	1.10072i
$690$	−3.28706e11	+	7.78982e10i	−1.45015	+	0.343662i
$691$	5.94387e10	+	2.16339e10i	0.260709	+	0.0948905i	0.469068	−	0.883162i	$-0.344590\pi$
$691$	5.94387e10	+	2.16339e10i	0.260709	+	0.0948905i	−0.208359	+	0.978053i	$0.566812\pi$
$692$	−1.65556e10	−	9.55838e9i	−0.0721973	−	0.0416831i
$693$	5.65303e10	+	4.83807e11i	0.245103	+	2.09768i
$694$	−9.24453e10	−	1.60120e11i	−0.398517	−	0.690252i
$695$	−5.54530e11	+	9.77787e10i	−2.37676	+	0.419088i
$696$	2.38520e10	+	3.62667e10i	0.101645	+	0.154551i
$697$	2.37701e10	−	8.65160e9i	0.100716	−	0.0366577i
$698$	−6.79836e10	−	1.19873e10i	−0.286406	−	0.0505011i
$699$	−8.75346e10	−	2.02939e11i	−0.366666	−	0.850072i
$700$	−3.50558e11	+	2.94153e11i	−1.46005	+	1.22513i
$701$		−	1.58336e11i		−	0.655705i	−0.944729	−	0.327853i	$-0.893675\pi$
$701$		−	1.58336e11i		−	0.655705i	0.944729	−	0.327853i	$-0.106325\pi$
$702$	1.59841e11	+	5.81879e10i	0.658174	+	0.239598i
$703$	4.27468e10			0.175018
$704$	2.80303e10	+	3.34052e10i	0.114113	+	0.135995i
$705$	3.52741e10	−	3.01740e11i	0.142791	−	1.22145i
$706$	5.02048e10	−	2.84726e11i	0.202082	−	1.14606i
$707$	3.80187e10	+	1.04455e11i	0.152167	+	0.418074i
$708$	1.22344e11	+	6.14466e10i	0.486913	+	0.244548i
$709$	−3.97548e10	−	2.25461e11i	−0.157327	−	0.892248i	−0.956627	−	0.291315i	$-0.905907\pi$
$709$	−3.97548e10	−	2.25461e11i	−0.157327	−	0.892248i	0.799300	−	0.600933i	$-0.205204\pi$
$710$	−2.15100e11	+	1.24188e11i	−0.846462	+	0.488705i
$711$	1.13301e11	+	7.45256e10i	0.443360	+	0.291626i
$712$	5.09345e10	−	8.82212e10i	0.198195	−	0.343283i
$713$	−5.37946e10	+	1.47799e11i	−0.208152	+	0.571892i
$714$	2.17763e11	+	6.51986e10i	0.837899	+	0.250868i
$715$	5.31678e11	+	4.46131e11i	2.03435	+	1.70702i
$716$	4.96362e10	−	5.91541e10i	0.188863	−	0.225078i
$717$	−1.40704e11	−	1.49143e11i	−0.532389	−	0.564321i
$718$	2.52501e11	+	9.19028e10i	0.950091	+	0.345805i
$719$	−2.89629e11	−	1.67217e11i	−1.08374	−	0.625699i	−0.151840	−	0.988405i	$-0.548520\pi$
$719$	−2.89629e11	−	1.67217e11i	−1.08374	−	0.625699i	−0.931904	+	0.362706i	$0.881853\pi$
$720$	−1.21498e11	+	3.63690e10i	−0.452104	+	0.135332i
$721$	5.36559e10	+	9.29347e10i	0.198553	+	0.343904i
$722$	−5.06175e10	+	8.92522e9i	−0.186274	+	0.0328451i
$723$	5.34246e10	−	3.11061e9i	0.195519	−	0.0113839i
$724$	−1.04477e10	+	3.80264e9i	−0.0380246	+	0.0138398i
$725$	−3.64916e11	−	6.43445e10i	−1.32081	−	0.232895i
$726$	−1.19310e11	+	1.60255e11i	−0.429467	+	0.576852i
$727$	−8.38588e10	+	7.03659e10i	−0.300200	+	0.251898i	−0.780428	−	0.625246i	$-0.784999\pi$
$727$	−8.38588e10	+	7.03659e10i	−0.300200	+	0.251898i	0.480227	+	0.877144i	$0.340554\pi$
$728$			1.46280e11i			0.520786i
$729$	−2.16333e11	−	1.81567e11i	−0.765971	−	0.642875i
$730$	−2.91061e11			−1.02493
$731$	−4.13985e10	−	4.93368e10i	−0.144982	−	0.172783i
$732$	−1.08960e11	−	8.11206e10i	−0.379508	−	0.282544i
$733$	3.01580e10	−	1.71034e11i	0.104469	−	0.592472i	−0.886962	−	0.461842i	$-0.847189\pi$
$733$	3.01580e10	−	1.71034e11i	0.104469	−	0.592472i	0.991431	−	0.130630i	$-0.0417001\pi$
$734$	7.04288e10	+	1.93502e11i	0.242642	+	0.666654i
$735$	−3.87890e10	−	6.66199e11i	−0.132910	−	2.28273i
$736$	−1.00569e10	−	5.70357e10i	−0.0342732	−	0.194373i
$737$	4.82652e11	−	2.78659e11i	1.63593	−	0.944504i
$738$	−7.75050e9	−	2.58921e10i	−0.0261279	−	0.0872853i
$739$	−8.85257e10	+	1.53331e11i	−0.296819	+	0.514106i	−0.975406	−	0.220414i	$-0.929259\pi$
$739$	−8.85257e10	+	1.53331e11i	−0.296819	+	0.514106i	0.678587	+	0.734520i	$0.262593\pi$
$740$	−1.50484e10	+	4.13452e10i	−0.0501839	+	0.137879i
$741$	−2.44563e11	+	2.30724e11i	−0.811180	+	0.765280i
$742$	3.54180e11	+	2.97193e11i	1.16845	+	0.980443i
$743$	−1.57917e11	+	1.88198e11i	−0.518172	+	0.617533i	−0.960148	−	0.279494i	$-0.909833\pi$
$743$	−1.57917e11	+	1.88198e11i	−0.518172	+	0.617533i	0.441975	+	0.897027i	$0.354278\pi$
$744$	−1.69367e10	+	5.65685e10i	−0.0552760	+	0.184622i
$745$	1.02323e12	+	3.72424e11i	3.32159	+	1.20896i
$746$	3.65790e10	+	2.11189e10i	0.118107	+	0.0681892i
$747$	−4.51551e10	+	6.86492e10i	−0.145019	+	0.220472i
$748$	9.24546e10	+	1.60136e11i	0.295340	+	0.511544i
$749$	−3.16737e11	+	5.58493e10i	−1.00640	+	0.177456i
$750$	2.96350e11	−	5.90054e11i	0.936613	−	1.86486i
$751$	−4.87697e10	+	1.77507e10i	−0.153317	+	0.0558029i	−0.417539	−	0.908659i	$-0.637107\pi$
$751$	−4.87697e10	+	1.77507e10i	−0.153317	+	0.0558029i	0.264222	+	0.964462i	$0.414885\pi$
$752$	5.12924e10	+	9.04424e9i	0.160392	+	0.0282814i
$753$	4.83176e11	+	5.64845e10i	1.50288	+	0.175691i
$754$	−9.07348e10	+	7.61356e10i	−0.280730	+	0.235560i
$755$		−	3.25872e11i		−	1.00290i
$756$

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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	54.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(7.27231 + 8.66680i) q^{2} +(-64.9711 - 48.3711i) q^{3} +(-22.2270 + 126.055i) q^{4} +(-403.520 - 1108.66i) q^{5} +(-53.2671 - 914.861i) q^{6} +(-619.994 - 3516.16i) q^{7} +(-1254.14 + 724.077i) q^{8} +(1881.48 + 6285.44i) q^{9} +O(q^{10})\)	\(q+(7.27231 + 8.66680i) q^{2} +(-64.9711 - 48.3711i) q^{3} +(-22.2270 + 126.055i) q^{4} +(-403.520 - 1108.66i) q^{5} +(-53.2671 - 914.861i) q^{6} +(-619.994 - 3516.16i) q^{7} +(-1254.14 + 724.077i) q^{8} +(1881.48 + 6285.44i) q^{9} +(6674.03 - 11559.8i) q^{10} +(-7111.83 + 19539.6i) q^{11} +(7541.55 - 7114.81i) q^{12} +(21672.4 + 18185.3i) q^{13} +(25965.1 - 30944.0i) q^{14} +(-27410.0 + 91549.6i) q^{15} +(-15395.9 - 5603.66i) q^{16} +(-60165.8 - 34736.7i) q^{17} +(-40792.0 + 62016.1i) q^{18} +(-73359.7 - 127063. i) q^{19} +(148722. - 26223.7i) q^{20} +(-129799. + 258439. i) q^{21} +(-221065. + 80461.2i) q^{22} +(307696. + 54255.1i) q^{23} +(116507. + 13620.0i) q^{24} +(-767065. + 643644. i) q^{25} +320079. i q^{26} +(181792. - 499381. i) q^{27} +457012. q^{28} +(237865. + 283476. i) q^{29} +(-992777. + 428220. i) q^{30} +(-87415.1 + 495756. i) q^{31} +(-63398.2 - 174185. i) q^{32} +(1.40721e6 - 925501. i) q^{33} +(-136488. - 774061. i) q^{34} +(-3.64805e6 + 2.10620e6i) q^{35} +(-834133. + 97464.0i) q^{36} +(-145676. + 252317. i) q^{37} +(567733. - 1.55983e6i) q^{38} +(-528435. - 2.22983e6i) q^{39} +(1.30883e6 + 1.09824e6i) q^{40} +(-234042. + 278920. i) q^{41} +(-3.18377e6 + 754504. i) q^{42} +(871132. + 317066. i) q^{43} +(-2.30500e6 - 1.33079e6i) q^{44} +(6.20921e6 - 4.62222e6i) q^{45} +(1.76744e6 + 3.06130e6i) q^{46} +(-3.13064e6 + 552016. i) q^{47} +(729234. + 1.10879e6i) q^{48} +(-6.56186e6 + 2.38832e6i) q^{49} +(-1.11567e7 - 1.96722e6i) q^{50} +(2.22878e6 + 5.16717e6i) q^{51} +(-2.77406e6 + 2.32772e6i) q^{52} +1.14459e7i q^{53} +(5.65008e6 - 2.05610e6i) q^{54} +2.45325e7 q^{55} +(3.32353e6 + 3.96083e6i) q^{56} +(-1.37990e6 + 1.18039e7i) q^{57} +(-727006. + 4.12305e6i) q^{58} +(4.51633e6 + 1.24085e7i) q^{59} +(-1.09311e7 - 5.49005e6i) q^{60} +(-2.27513e6 - 1.29029e7i) q^{61} +(-4.93233e6 + 2.84768e6i) q^{62} +(2.09341e7 - 1.05125e7i) q^{63} +(1.04858e6 - 1.81619e6i) q^{64} +(1.14161e7 - 3.13654e7i) q^{65} +(1.82548e7 + 5.46552e6i) q^{66} +(-2.05319e7 - 1.72283e7i) q^{67} +(5.71605e6 - 6.81213e6i) q^{68} +(-1.73669e7 - 1.84086e7i) q^{69} +(-4.47838e7 - 1.63000e7i) q^{70} +(-1.61147e7 - 9.30384e6i) q^{71} +(-6.91078e6 - 6.52048e6i) q^{72} +(-1.09027e7 - 1.88841e7i) q^{73} +(-3.24618e6 + 572390. i) q^{74} +(8.09708e7 - 4.71447e6i) q^{75} +(1.76475e7 - 6.42317e6i) q^{76} +(7.31136e7 + 1.28919e7i) q^{77} +(1.54826e7 - 2.07959e7i) q^{78} +(1.58339e7 - 1.32863e7i) q^{79} +1.93301e7i q^{80} +(-3.59668e7 + 2.36518e7i) q^{81} -4.11937e6 q^{82} +(8.05015e6 + 9.59380e6i) q^{83} +(-2.96925e7 - 2.21062e7i) q^{84} +(-1.42332e7 + 8.07204e7i) q^{85} +(3.58719e6 + 9.85574e6i) q^{86} +(-1.74227e6 - 2.99235e7i) q^{87} +(-5.22895e6 - 2.96549e7i) q^{88} +(-6.09197e7 + 3.51720e7i) q^{89} +(8.52152e7 + 2.01998e7i) q^{90} +(5.05056e7 - 8.74783e7i) q^{91} +(-1.36783e7 + 3.75808e7i) q^{92} +(2.96597e7 - 2.79814e7i) q^{93} +(-2.75512e7 - 2.31182e7i) q^{94} +(-1.11267e8 + 1.32603e8i) q^{95} +(-4.30647e6 + 1.43836e7i) q^{96} +(1.24118e8 + 4.51752e7i) q^{97} +(-6.84190e7 - 3.95017e7i) q^{98} +(-1.36196e8 - 7.93770e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9}+O(q^{10}) \) 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9	\( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25} - 4137588 q^{27} - 2856132 q^{29} - 861696 q^{30} - 1841490 q^{31} + 10547334 q^{33} - 661248 q^{34} - 12450834 q^{35} - 5104128 q^{36} + 14063616 q^{38} + 4239102 q^{39} - 15673536 q^{41} - 11028480 q^{42} - 4412520 q^{43} - 12558942 q^{45} + 15173838 q^{47} + 3440640 q^{48} - 11347488 q^{49} - 27744768 q^{50} - 3281850 q^{51} + 16379136 q^{54} + 12091392 q^{56} - 13553658 q^{57} - 86547168 q^{59} - 26125056 q^{60} - 34059456 q^{61} + 108329070 q^{63} + 150994944 q^{64} + 22190346 q^{65} + 152091648 q^{66} + 167100948 q^{67} + 13411584 q^{68} - 40190130 q^{69} - 118080000 q^{70} - 251437608 q^{71} - 60948480 q^{72} + 15265278 q^{73} + 41902848 q^{74} + 138868662 q^{75} + 67995648 q^{76} + 564911586 q^{77} + 201203712 q^{78} + 137535768 q^{79} - 23838948 q^{81} - 482857578 q^{83} - 128300544 q^{84} - 343215000 q^{85} - 46237824 q^{86} + 34353810 q^{87} + 47480832 q^{88} + 375969762 q^{89} + 452712960 q^{90} - 155093598 q^{91} + 97042176 q^{92} + 285095622 q^{93} - 70995456 q^{94} - 966996432 q^{95} - 88080384 q^{96} - 484917300 q^{97} - 234233856 q^{98} + 26756370 q^{99}+O(q^{100}) \) 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9 - 45756 * q^11 - 21504 * q^12 + 94464 * q^14 - 70002 * q^15 - 182784 * q^18 - 225792 * q^20 - 2071668 * q^21 + 185472 * q^22 + 552996 * q^23 - 1015182 * q^25 - 4137588 * q^27 - 2856132 * q^29 - 861696 * q^30 - 1841490 * q^31 + 10547334 * q^33 - 661248 * q^34 - 12450834 * q^35 - 5104128 * q^36 + 14063616 * q^38 + 4239102 * q^39 - 15673536 * q^41 - 11028480 * q^42 - 4412520 * q^43 - 12558942 * q^45 + 15173838 * q^47 + 3440640 * q^48 - 11347488 * q^49 - 27744768 * q^50 - 3281850 * q^51 + 16379136 * q^54 + 12091392 * q^56 - 13553658 * q^57 - 86547168 * q^59 - 26125056 * q^60 - 34059456 * q^61 + 108329070 * q^63 + 150994944 * q^64 + 22190346 * q^65 + 152091648 * q^66 + 167100948 * q^67 + 13411584 * q^68 - 40190130 * q^69 - 118080000 * q^70 - 251437608 * q^71 - 60948480 * q^72 + 15265278 * q^73 + 41902848 * q^74 + 138868662 * q^75 + 67995648 * q^76 + 564911586 * q^77 + 201203712 * q^78 + 137535768 * q^79 - 23838948 * q^81 - 482857578 * q^83 - 128300544 * q^84 - 343215000 * q^85 - 46237824 * q^86 + 34353810 * q^87 + 47480832 * q^88 + 375969762 * q^89 + 452712960 * q^90 - 155093598 * q^91 + 97042176 * q^92 + 285095622 * q^93 - 70995456 * q^94 - 966996432 * q^95 - 88080384 * q^96 - 484917300 * q^97 - 234233856 * q^98 + 26756370 * q^99

Introduction

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