LMFDB - Embedded newform 54.9.f.a.11.2

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			11.2
Character	$\chi$	$=$	54.11
Dual form			54.9.f.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.27231 + 8.66680i) q^{2} +(-74.4381 - 31.9369i) q^{3} +(-22.2270 - 126.055i) q^{4} +(-303.240 + 833.145i) q^{5} +(818.128 - 412.886i) q^{6} +(-11.0691 + 62.7758i) q^{7} +(1254.14 + 724.077i) q^{8} +(4521.07 + 4754.64i) q^{9} +O(q^{10})$	\(q+(-7.27231 + 8.66680i) q^{2} +(-74.4381 - 31.9369i) q^{3} +(-22.2270 - 126.055i) q^{4} +(-303.240 + 833.145i) q^{5} +(818.128 - 412.886i) q^{6} +(-11.0691 + 62.7758i) q^{7} +(1254.14 + 724.077i) q^{8} +(4521.07 + 4754.64i) q^{9} +(-5015.45 - 8687.01i) q^{10} +(9130.11 + 25084.8i) q^{11} +(-2371.28 + 10093.2i) q^{12} +(18567.5 - 15580.0i) q^{13} +(-463.568 - 552.458i) q^{14} +(49180.6 - 52333.2i) q^{15} +(-15395.9 + 5603.66i) q^{16} +(-68160.2 + 39352.3i) q^{17} +(-74086.2 + 4606.01i) q^{18} +(-76941.2 + 133266. i) q^{19} +(111762. + 19706.7i) q^{20} +(2828.82 - 4319.40i) q^{21} +(-283802. - 103295. i) q^{22} +(-54097.6 + 9538.86i) q^{23} +(-70231.0 - 93952.2i) q^{24} +(-302939. - 254196. i) q^{25} +274223. i q^{26} +(-184692. - 498316. i) q^{27} +8159.26 q^{28} +(-15504.7 + 18477.7i) q^{29} +(95904.7 + 806822. i) q^{30} +(-284690. - 1.61456e6i) q^{31} +(63398.2 - 174185. i) q^{32} +(121501. - 2.15885e6i) q^{33} +(154623. - 876913. i) q^{34} +(-48944.7 - 28258.2i) q^{35} +(498859. - 675587. i) q^{36} +(591367. + 1.02428e6i) q^{37} +(-595450. - 1.63599e6i) q^{38} +(-1.87970e6 + 566757. i) q^{39} +(-983566. + 825310. i) q^{40} +(60858.7 + 72528.6i) q^{41} +(16863.3 + 55928.9i) q^{42} +(-2.97385e6 + 1.08239e6i) q^{43} +(2.95914e6 - 1.70846e6i) q^{44} +(-5.33227e6 + 2.32491e6i) q^{45} +(310743. - 538223. i) q^{46} +(-5.66791e6 - 999406. i) q^{47} +(1.32501e6 + 74571.7i) q^{48} +(5.41332e6 + 1.97029e6i) q^{49} +(4.40614e6 - 776921. i) q^{50} +(6.33050e6 - 752489. i) q^{51} +(-2.37664e6 - 1.99424e6i) q^{52} -7.83964e6i q^{53} +(5.66194e6 + 2.02322e6i) q^{54} -2.36678e7 q^{55} +(-59336.6 + 70714.7i) q^{56} +(9.98346e6 - 7.46282e6i) q^{57} +(-47388.2 - 268752. i) q^{58} +(-6.93032e6 + 1.90409e7i) q^{59} +(-7.69002e6 - 5.03628e6i) q^{60} +(142275. - 806884. i) q^{61} +(1.60634e7 + 9.27422e6i) q^{62} +(-348520. + 231184. i) q^{63} +(1.04858e6 + 1.81619e6i) q^{64} +(7.34997e6 + 2.01939e7i) q^{65} +(1.78267e7 + 1.67529e7i) q^{66} +(-9.66601e6 + 8.11075e6i) q^{67} +(6.47556e6 + 7.71727e6i) q^{68} +(4.33156e6 + 1.01765e6i) q^{69} +(600850. - 218691. i) q^{70} +(3.63684e7 - 2.09973e7i) q^{71} +(2.22732e6 + 9.23659e6i) q^{72} +(-8.83674e6 + 1.53057e7i) q^{73} +(-1.31778e7 - 2.32361e6i) q^{74} +(1.44320e7 + 2.85968e7i) q^{75} +(1.85091e7 + 6.73675e6i) q^{76} +(-1.67578e6 + 295485. i) q^{77} +(8.75783e6 - 2.04127e7i) q^{78} +(-3.43327e7 - 2.88086e7i) q^{79} -1.45263e7i q^{80} +(-2.16652e6 + 4.29922e7i) q^{81} -1.07117e6 q^{82} +(4.76002e7 - 5.67277e7i) q^{83} +(-607360. - 260581. i) q^{84} +(-1.21173e7 - 6.87204e7i) q^{85} +(1.22459e7 - 3.36453e7i) q^{86} +(1.74426e6 - 880279. i) q^{87} +(-6.71289e6 + 3.80707e7i) q^{88} +(3.61376e7 + 2.08641e7i) q^{89} +(1.86284e7 - 6.31212e7i) q^{90} +(772520. + 1.33804e6i) q^{91} +(2.40485e6 + 6.60727e6i) q^{92} +(-3.03721e7 + 1.29277e8i) q^{93} +(4.98805e7 - 4.18547e7i) q^{94} +(-8.76983e7 - 1.04515e8i) q^{95} +(-1.02822e7 + 1.09413e7i) q^{96} +(-5.20097e7 + 1.89300e7i) q^{97} +(-5.64435e7 + 3.25877e7i) q^{98} +(-7.79912e7 + 1.56820e8i) 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 $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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
$3$	−74.4381	−	31.9369i	−0.918989	−	0.394282i
$3$	−74.4381	−	31.9369i	−0.918989	−	0.394282i
$4$	−22.2270	−	126.055i	−0.0868241	−	0.492404i
$5$	−303.240	+	833.145i	−0.485184	+	1.33303i	0.419812	+	0.907611i	$0.362096\pi$
$5$	−303.240	+	833.145i	−0.485184	+	1.33303i	−0.904996	+	0.425420i	$0.860126\pi$
$6$	818.128	−	412.886i	0.631272	−	0.318585i
$7$	−11.0691	+	62.7758i	−0.00461019	+	0.0261457i	−0.987026	−	0.160560i	$-0.948670\pi$
$7$	−11.0691	+	62.7758i	−0.00461019	+	0.0261457i	0.982416	+	0.186706i	$0.0597811\pi$
$8$	1254.14	+	724.077i	0.306186	+	0.176777i
$9$	4521.07	+	4754.64i	0.689083	+	0.724683i
$10$	−5015.45	−	8687.01i	−0.501545	−	0.868701i
$11$	9130.11	+	25084.8i	0.623599	+	1.71332i	0.698003	+	0.716095i	$0.254072\pi$
$11$	9130.11	+	25084.8i	0.623599	+	1.71332i	−0.0744041	+	0.997228i	$0.523705\pi$
$12$	−2371.28	+	10093.2i	−0.114356	+	0.486747i
$13$	18567.5	−	15580.0i	0.650099	−	0.545498i	−0.257002	−	0.966411i	$-0.582735\pi$
$13$	18567.5	−	15580.0i	0.650099	−	0.545498i	0.907101	+	0.420913i	$0.138290\pi$
$14$	−463.568	−	552.458i	−0.0120670	−	0.0143809i
$15$	49180.6	−	52333.2i	0.971469	−	1.03374i
$16$	−15395.9	+	5603.66i	−0.234923	+	0.0855050i
$17$	−68160.2	+	39352.3i	−0.816084	+	0.471166i	−0.849064	−	0.528290i	$-0.822834\pi$
$17$	−68160.2	+	39352.3i	−0.816084	+	0.471166i	0.0329802	+	0.999456i	$0.489500\pi$
$18$	−74086.2	+	4606.01i	−0.705744	+	0.0438768i
$19$	−76941.2	+	133266.i	−0.590398	+	1.02260i	0.403781	+	0.914856i	$0.367696\pi$
$19$	−76941.2	+	133266.i	−0.590398	+	1.02260i	−0.994179	+	0.107743i	$0.965638\pi$
$20$	111762.	+	19706.7i	0.698515	+	0.123167i
$21$	2828.82	−	4319.40i	0.0145455	−	0.0222099i
$22$	−283802.	−	103295.i	−1.21150	−	0.440951i
$23$	−54097.6	+	9538.86i	−0.193315	+	0.0340867i	−0.269467	−	0.963009i	$-0.586848\pi$
$23$	−54097.6	+	9538.86i	−0.193315	+	0.0340867i	0.0761521	+	0.997096i	$0.475737\pi$
$24$	−70231.0	−	93952.2i	−0.211682	−	0.283180i
$25$	−302939.	−	254196.i	−0.775525	−	0.650743i
$26$			274223.i			0.600082i
$27$	−184692.	−	498316.i	−0.347530	−	0.937669i
$28$	8159.26			0.0132745
$29$	−15504.7	+	18477.7i	−0.0219215	+	0.0261250i	−0.776894	−	0.629632i	$-0.783206\pi$
$29$	−15504.7	+	18477.7i	−0.0219215	+	0.0261250i	0.754972	+	0.655757i	$0.227650\pi$
$30$	95904.7	+	806822.i	0.118401	+	0.996077i
$31$	−284690.	−	1.61456e6i	−0.308266	−	1.74826i	−0.607718	−	0.794153i	$-0.707915\pi$
$31$	−284690.	−	1.61456e6i	−0.308266	−	1.74826i	0.299452	−	0.954111i	$-0.403196\pi$
$32$	63398.2	−	174185.i	0.0604612	−	0.166116i
$33$	121501.	−	2.15885e6i	0.102453	−	1.82040i
$34$	154623.	−	876913.i	0.115707	−	0.656207i
$35$	−48944.7	−	28258.2i	−0.0326162	−	0.0188310i
$36$	498859.	−	675587.i	0.297007	−	0.402227i
$37$	591367.	+	1.02428e6i	0.315537	+	0.546526i	0.979551	−	0.201194i	$-0.0644820\pi$
$37$	591367.	+	1.02428e6i	0.315537	+	0.546526i	−0.664015	+	0.747720i	$0.731149\pi$
$38$	−595450.	−	1.63599e6i	−0.285569	−	0.784595i
$39$	−1.87970e6	+	566757.i	−0.812514	+	0.244984i
$40$	−983566.	+	825310.i	−0.384205	+	0.322387i
$41$	60858.7	+	72528.6i	0.0215371	+	0.0256669i	0.776705	−	0.629864i	$-0.216889\pi$
$41$	60858.7	+	72528.6i	0.0215371	+	0.0256669i	−0.755168	+	0.655531i	$0.772445\pi$
$42$	16863.3	+	55928.9i	0.00541933	+	0.0179738i
$43$	−2.97385e6	+	1.08239e6i	−0.869852	+	0.316600i	−0.738107	−	0.674683i	$-0.764280\pi$
$43$	−2.97385e6	+	1.08239e6i	−0.869852	+	0.316600i	−0.131745	+	0.991284i	$0.542058\pi$
$44$	2.95914e6	−	1.70846e6i	0.789504	−	0.455820i
$45$	−5.33227e6	+	2.32491e6i	−1.30036	+	0.566965i
$46$	310743.	−	538223.i	0.0694017	−	0.120207i
$47$	−5.66791e6	−	999406.i	−1.16153	−	0.204810i	−0.440528	−	0.897739i	$-0.645209\pi$
$47$	−5.66791e6	−	999406.i	−1.16153	−	0.204810i	−0.721006	+	0.692929i	$0.756320\pi$
$48$	1.32501e6	+	74571.7i	0.249605	+	0.0140478i
$49$	5.41332e6	+	1.97029e6i	0.939030	+	0.341779i
$50$	4.40614e6	−	776921.i	0.704982	−	0.124307i
$51$	6.33050e6	−	752489.i	0.935745	−	0.111229i
$52$	−2.37664e6	−	1.99424e6i	−0.325050	−	0.272749i
$53$		−	7.83964e6i		−	0.993557i	−0.867877	−	0.496778i	$-0.834516\pi$
$53$		−	7.83964e6i		−	0.993557i	0.867877	−	0.496778i	$-0.165484\pi$
$54$	5.66194e6	+	2.02322e6i	0.665871	+	0.237940i
$55$	−2.36678e7			−2.58647
$56$	−59336.6	+	70714.7i	−0.00603352	+	0.00719047i
$57$	9.98346e6	−	7.46282e6i	0.945762	−	0.706974i
$58$	−47388.2	−	268752.i	−0.00418753	−	0.0237487i
$59$	−6.93032e6	+	1.90409e7i	−0.571933	+	1.57137i	0.229512	+	0.973306i	$0.426287\pi$
$59$	−6.93032e6	+	1.90409e7i	−0.571933	+	1.57137i	−0.801445	+	0.598068i	$0.795935\pi$
$60$	−7.69002e6	−	5.03628e6i	−0.593366	−	0.388602i
$61$	142275.	−	806884.i	0.0102757	−	0.0582763i	−0.979239	−	0.202710i	$-0.935025\pi$
$61$	142275.	−	806884.i	0.0102757	−	0.0582763i	0.989514	+	0.144434i	$0.0461361\pi$
$62$	1.60634e7	+	9.27422e6i	1.08710	+	0.627640i
$63$	−348520.	+	231184.i	−0.0221241	+	0.0146756i
$64$	1.04858e6	+	1.81619e6i	0.0625000	+	0.108253i
$65$	7.34997e6	+	2.01939e7i	0.411748	+	1.13127i
$66$	1.78267e7	+	1.67529e7i	0.939499	+	0.882903i
$67$	−9.66601e6	+	8.11075e6i	−0.479676	+	0.402496i	−0.850309	−	0.526283i	$-0.823585\pi$
$67$	−9.66601e6	+	8.11075e6i	−0.479676	+	0.402496i	0.370633	+	0.928779i	$0.379141\pi$
$68$	6.47556e6	+	7.71727e6i	0.302860	+	0.360934i
$69$	4.33156e6	+	1.01765e6i	0.191095	+	0.0448955i
$70$	600850.	−	218691.i	0.0250250	−	0.00910835i
$71$	3.63684e7	−	2.09973e7i	1.43117	−	0.826286i	0.433959	−	0.900933i	$-0.357116\pi$
$71$	3.63684e7	−	2.09973e7i	1.43117	−	0.826286i	0.997210	+	0.0746471i	$0.0237830\pi$
$72$	2.22732e6	+	9.23659e6i	0.0828807	+	0.343702i
$73$	−8.83674e6	+	1.53057e7i	−0.311172	+	0.538966i	−0.978616	−	0.205694i	$-0.934055\pi$
$73$	−8.83674e6	+	1.53057e7i	−0.311172	+	0.538966i	0.667444	+	0.744660i	$0.267388\pi$
$74$	−1.31778e7	−	2.32361e6i	−0.439457	−	0.0774882i
$75$	1.44320e7	+	2.85968e7i	0.456123	+	0.903801i
$76$	1.85091e7	+	6.73675e6i	0.554792	+	0.201928i
$77$	−1.67578e6	+	295485.i	−0.0476709	+	0.00840567i
$78$	8.75783e6	−	2.04127e7i	0.236602	−	0.551469i
$79$	−3.43327e7	−	2.88086e7i	−0.881455	−	0.739629i	0.0850227	−	0.996379i	$-0.472904\pi$
$79$	−3.43327e7	−	2.88086e7i	−0.881455	−	0.739629i	−0.966478	+	0.256750i	$0.917348\pi$
$80$		−	1.45263e7i		−	0.354646i
$81$	−2.16652e6	+	4.29922e7i	−0.0503295	+	0.998733i
$82$	−1.07117e6			−0.0236922
$83$	4.76002e7	−	5.67277e7i	1.00299	−	1.19532i	0.0222992	−	0.999751i	$-0.492901\pi$
$83$	4.76002e7	−	5.67277e7i	1.00299	−	1.19532i	0.980691	−	0.195565i	$-0.0626542\pi$
$84$	−607360.	−	260581.i	−0.0121991	−	0.00523390i
$85$	−1.21173e7	−	6.87204e7i	−0.232129	−	1.31647i
$86$	1.22459e7	−	3.36453e7i	0.223870	−	0.615078i
$87$	1.74426e6	−	880279.i	0.0304463	−	0.0153654i
$88$	−6.71289e6	+	3.80707e7i	−0.111938	+	0.634834i
$89$	3.61376e7	+	2.08641e7i	0.575969	+	0.332536i	0.759530	−	0.650472i	$-0.225429\pi$
$89$	3.61376e7	+	2.08641e7i	0.575969	+	0.332536i	−0.183561	+	0.983008i	$0.558762\pi$
$90$	1.86284e7	−	6.31212e7i	0.283926	−	0.962067i
$91$	772520.	+	1.33804e6i	0.0112653	+	0.0195121i
$92$	2.40485e6	+	6.60727e6i	0.0335689	+	0.0922297i
$93$	−3.03721e7	+	1.29277e8i	−0.406016	+	1.72818i
$94$	4.98805e7	−	4.18547e7i	0.638880	−	0.536084i
$95$	−8.76983e7	−	1.04515e8i	−1.07670	−	1.28317i
$96$	−1.02822e7	+	1.09413e7i	−0.121060	+	0.128820i
$97$	−5.20097e7	+	1.89300e7i	−0.587486	+	0.213828i	−0.618624	−	0.785688i	$-0.712309\pi$
$97$	−5.20097e7	+	1.89300e7i	−0.587486	+	0.213828i	0.0311371	+	0.999515i	$0.490087\pi$
$98$	−5.64435e7	+	3.25877e7i	−0.611941	+	0.353304i
$99$	−7.79912e7	+	1.56820e8i	−0.811904	+	1.63253i
$100$	−2.53094e7	+	4.38372e7i	−0.253094	+	0.438372i
$101$	−4.06266e7	−	7.16356e6i	−0.390413	−	0.0688404i	−0.0250041	−	0.999687i	$-0.507960\pi$
$101$	−4.06266e7	−	7.16356e6i	−0.390413	−	0.0688404i	−0.365409	+	0.930847i	$0.619071\pi$
$102$	−3.95157e7	+	6.03376e7i	−0.365064	+	0.557426i
$103$	−1.23122e8	−	4.48127e7i	−1.09392	−	0.398155i	−0.268849	−	0.963182i	$-0.586643\pi$
$103$	−1.23122e8	−	4.48127e7i	−1.09392	−	0.398155i	−0.825072	+	0.565027i	$0.808866\pi$
$104$	3.45673e7	−	6.09515e6i	0.295483	−	0.0521016i
$105$	2.74087e6	+	3.66663e6i	0.0225492	+	0.0301655i
$106$	6.79446e7	+	5.70123e7i	0.538185	+	0.451591i
$107$		−	8.02687e7i		−	0.612366i	−0.951973	−	0.306183i	$-0.900948\pi$
$107$		−	8.02687e7i		−	0.612366i	0.951973	−	0.306183i	$-0.0990519\pi$
$108$	−5.87102e7	+	3.43574e7i	−0.431538	+	0.252538i
$109$	8.96726e7			0.635263			0.317632	−	0.948214i	$-0.397112\pi$
$109$	8.96726e7			0.635263			0.317632	+	0.948214i	$0.397112\pi$
$110$	1.72120e8	−	2.05125e8i	1.17560	−	1.40103i
$111$	−1.13080e7	−	9.51317e7i	−0.0744895	−	0.626662i
$112$	−181355.	−	1.02852e6i	−0.00115255	−	0.00653642i
$113$	7.87510e7	−	2.16367e8i	0.482995	−	1.32702i	−0.423919	−	0.905700i	$-0.639346\pi$
$113$	7.87510e7	−	2.16367e8i	0.482995	−	1.32702i	0.906914	−	0.421317i	$-0.138432\pi$
$114$	−7.92407e6	+	1.40797e8i	−0.0469168	+	0.833629i
$115$	8.45729e6	−	4.79637e7i	0.0483548	−	0.274234i
$116$	2.67384e6	+	1.54374e6i	0.0147674	+	0.00852596i
$117$	1.58022e8	+	1.78436e7i	0.843285	+	0.0952222i
$118$	−1.14624e8	−	1.98535e8i	−0.591219	−	1.02402i
$119$	−1.71590e6	−	4.71440e6i	−0.00855666	−	0.0235092i
$120$	9.95726e7	−	3.00225e7i	0.480192	−	0.144784i
$121$	−3.81678e8	+	3.20266e8i	−1.78056	+	1.49406i
$122$	5.95843e6	+	7.10099e6i	0.0268963	+	0.0320538i
$123$	−2.21387e6	−	7.34253e6i	−0.00967236	−	0.0320793i
$124$	−1.97196e8	+	7.17735e7i	−0.834087	+	0.303583i
$125$	3.71194e6	−	2.14309e6i	0.0152041	−	0.00877809i
$126$	530919.	−	4.70180e6i	0.00210642	−	0.0186544i
$127$	2.35159e8	−	4.07308e8i	0.903956	−	1.56570i	0.0816437	−	0.996662i	$-0.473983\pi$
$127$	2.35159e8	−	4.07308e8i	0.903956	−	1.56570i	0.822312	−	0.569036i	$-0.192684\pi$
$128$	−2.33661e7	−	4.12008e6i	−0.0870455	−	0.0153485i
$129$	2.55936e8	+	1.44042e7i	0.924215	+	0.0520150i
$130$	−2.28467e8	−	8.31554e7i	−0.799928	−	0.291150i
$131$	−2.64002e8	+	4.65507e7i	−0.896442	+	0.158067i	−0.602841	−	0.797861i	$-0.705965\pi$
$131$	−2.64002e8	+	4.65507e7i	−0.896442	+	0.158067i	−0.293601	+	0.955928i	$0.594854\pi$
$132$	−2.74835e8	+	3.26689e7i	−0.905267	+	0.107607i
$133$	−7.51421e6	−	6.30517e6i	−0.0240147	−	0.0201507i
$134$		−	1.42757e8i		−	0.442771i
$135$	4.71175e8	−	2.76588e6i	1.41856	−	0.00832720i
$136$	−1.13976e8			−0.333165
$137$	−1.62583e8	+	1.93759e8i	−0.461523	+	0.550022i	−0.945739	−	0.324926i	$-0.894660\pi$
$137$	−1.62583e8	+	1.93759e8i	−0.461523	+	0.550022i	0.484216	+	0.874948i	$0.339105\pi$
$138$	−4.03203e7	+	3.01401e7i	−0.111175	+	0.0831053i
$139$	−6.23408e7	−	3.53552e8i	−0.166999	−	0.947096i	−0.946980	−	0.321293i	$-0.895882\pi$
$139$	−6.23408e7	−	3.53552e8i	−0.166999	−	0.947096i	0.779981	−	0.625803i	$-0.215229\pi$
$140$	−2.47421e6	+	6.79784e6i	−0.00644057	+	0.0176953i
$141$	3.89991e8	+	2.55409e8i	0.986684	+	0.646190i
$142$	−8.25028e7	+	4.67897e8i	−0.202916	+	1.15079i
$143$	5.60343e8	+	3.23514e8i	1.34002	+	0.773658i
$144$	−9.62495e7	−	4.78676e7i	−0.223846	−	0.111325i
$145$	−1.06930e7	−	1.85208e7i	−0.0241895	−	0.0418975i
$146$	−6.83878e7	−	1.87894e8i	−0.150511	−	0.413525i
$147$	−3.40033e8	−	3.19549e8i	−0.728201	−	0.684334i
$148$	1.15971e8	−	9.73116e7i	0.241715	−	0.202823i
$149$	−2.68573e8	−	3.20073e8i	−0.544900	−	0.649387i	0.421379	−	0.906885i	$-0.361546\pi$
$149$	−2.68573e8	−	3.20073e8i	−0.544900	−	0.649387i	−0.966279	+	0.257498i	$0.917102\pi$
$150$	−3.52797e8	−	8.28857e7i	−0.696883	−	0.163725i
$151$	−1.14283e8	+	4.15956e7i	−0.219823	+	0.0800091i	−0.449584	−	0.893238i	$-0.648428\pi$
$151$	−1.14283e8	+	4.15956e7i	−0.219823	+	0.0800091i	0.229761	+	0.973247i	$0.426206\pi$
$152$	−1.92990e8	+	1.11423e8i	−0.361543	+	0.208737i
$153$	−4.95263e8	−	1.46163e8i	−0.903796	−	0.266729i
$154$	9.62586e6	−	1.66725e7i	0.0171142	−	0.0296427i
$155$	1.43149e9	+	2.52410e8i	2.48006	+	0.437301i
$156$	1.13223e8	+	2.24350e8i	0.191177	+	0.378815i
$157$	8.63622e7	+	3.14333e7i	0.142143	+	0.0517357i	0.412112	−	0.911133i	$-0.364791\pi$
$157$	8.63622e7	+	3.14333e7i	0.142143	+	0.0517357i	−0.269969	+	0.962869i	$0.587013\pi$
$158$	4.99357e8	−	8.80501e7i	0.801277	−	0.141287i
$159$	−2.50374e8	+	5.83568e8i	−0.391742	+	0.913068i
$160$	1.25896e8	+	1.05640e8i	0.192103	+	0.161193i
$161$		−	3.50160e6i		−	0.00521151i
$162$	−3.56849e8	−	3.31429e8i	−0.518113	−	0.481206i
$163$	1.35944e9			1.92580			0.962898	−	0.269866i	$-0.0869793\pi$
$163$	1.35944e9			1.92580			0.962898	+	0.269866i	$0.0869793\pi$
$164$	7.78992e6	−	9.28366e6i	0.0107686	−	0.0128335i
$165$	1.76179e9	+	7.55877e8i	2.37694	+	1.01980i
$166$	1.45484e8	+	8.25083e8i	0.191595	+	1.08659i
$167$	−3.14119e8	+	8.63034e8i	−0.403857	+	1.10959i	0.556508	+	0.830842i	$0.312141\pi$
$167$	−3.14119e8	+	8.63034e8i	−0.403857	+	1.10959i	−0.960365	+	0.278746i	$0.910081\pi$
$168$	6.67531e6	−	3.36884e6i	0.00837982	−	0.00422906i
$169$	−3.96342e7	+	2.24776e8i	−0.0485873	+	0.275552i
$170$	6.83707e8	+	3.94738e8i	0.818605	+	0.472622i
$171$	−9.81489e8	+	2.36678e8i	−1.14789	+	0.276804i
$172$	2.02541e8	+	3.50812e8i	0.231419	+	0.400830i
$173$	−1.91450e8	−	5.26004e8i	−0.213733	−	0.587225i	0.785778	−	0.618509i	$-0.212263\pi$
$173$	−1.91450e8	−	5.26004e8i	−0.213733	−	0.587225i	−0.999511	+	0.0312832i	$0.990041\pi$
$174$	−5.05560e6	+	2.15188e7i	−0.00551539	+	0.0234759i
$175$	1.93106e7	−	1.62035e7i	0.0205894	−	0.0172766i
$176$	−2.81133e8	−	3.35041e8i	−0.292996	−	0.349178i
$177$	1.12399e9	−	1.19604e9i	1.14517	−	1.21857i
$178$	−4.43629e8	+	1.61468e8i	−0.441916	+	0.160844i
$179$	−1.51056e9	+	8.72124e8i	−1.47139	+	0.849505i	−0.999483	−	0.0321448i	$-0.989766\pi$
$179$	−1.51056e9	+	8.72124e8i	−1.47139	+	0.849505i	−0.471903	+	0.881650i	$0.656433\pi$
$180$	4.11588e8	+	6.20486e8i	0.392078	+	0.591074i
$181$	−3.38611e8	+	5.86492e8i	−0.315491	+	0.546447i	−0.979542	−	0.201241i	$-0.935503\pi$
$181$	−3.38611e8	+	5.86492e8i	−0.315491	+	0.546447i	0.664051	+	0.747688i	$0.268836\pi$
$182$	−1.72146e7	−	3.03539e6i	−0.0156895	−	0.00276649i
$183$	−3.63601e7	+	5.55191e7i	−0.0324205	+	0.0495038i
$184$	−7.47527e7	−	2.72078e7i	−0.0652162	−	0.0237368i
$185$	−1.03270e9	+	1.82092e8i	−0.881630	+	0.155455i
$186$	−8.99542e8	−	1.20337e9i	−0.751570	−	1.00542i
$187$	−1.60945e9	−	1.35049e9i	−1.31617	−	1.10440i
$188$			7.36685e8i			0.589726i
$189$	3.33265e7	−	6.07829e6i	0.0261182	−	0.00476359i
$190$	1.54358e9			1.18444
$191$	−1.10092e9	+	1.31202e9i	−0.827220	+	0.985842i	0.172780	+	0.984960i	$0.444725\pi$
$191$	−1.10092e9	+	1.31202e9i	−0.827220	+	0.985842i	−1.00000		0.000881673i	$0.999719\pi$
$192$	−2.00507e7	−	1.68682e8i	−0.0147545	−	0.124126i
$193$	−3.48843e7	−	1.97839e8i	−0.0251420	−	0.142588i	0.969653	−	0.244486i	$-0.0786193\pi$
$193$	−3.48843e7	−	1.97839e8i	−0.0251420	−	0.142588i	−0.994795	+	0.101899i	$0.967508\pi$
$194$	2.14169e8	−	5.88423e8i	0.151199	−	0.415416i
$195$	9.78110e7	−	1.73793e9i	0.0676471	−	1.20197i
$196$	1.28044e8	−	7.26172e8i	0.0867629	−	0.492057i
$197$	2.40334e9	+	1.38757e9i	1.59569	+	0.921274i	0.992304	+	0.123828i	$0.0395170\pi$
$197$	2.40334e9	+	1.38757e9i	1.59569	+	0.921274i	0.603390	+	0.797446i	$0.293816\pi$
$198$	−7.91956e8	−	1.81638e9i	−0.515276	−	1.18181i
$199$	−9.47443e8	−	1.64102e9i	−0.604144	−	1.04641i	−0.992186	−	0.124767i	$-0.960182\pi$
$199$	−9.47443e8	−	1.64102e9i	−0.604144	−	1.04641i	0.388042	−	0.921642i	$-0.373152\pi$
$200$	−1.95870e8	−	5.38149e8i	−0.122419	−	0.336343i
$201$	9.78552e8	−	2.95047e8i	0.599514	−	0.180762i
$202$	3.57534e8	−	3.00007e8i	0.214740	−	0.180188i
$203$	−988333.	−	1.17785e6i	−0.000581995	−	0.000693594i
$204$	−2.35563e8	−	7.81269e8i	−0.136015	−	0.451107i
$205$	−7.88816e7	+	2.87105e7i	−0.0446643	+	0.0162565i
$206$	1.28376e9	−	7.41181e8i	0.712879	−	0.411581i
$207$	−2.89933e8	−	2.14089e8i	−0.157912	−	0.116604i
$208$	−1.98559e8	+	3.43914e8i	−0.106081	+	0.183737i
$209$	−4.04543e9	−	7.13318e8i	−2.12021	−	0.373851i
$210$	−5.17105e7	−	2.91028e6i	−0.0265890	−	0.00149643i
$211$	1.20675e9	+	4.39220e8i	0.608817	+	0.221591i	0.627986	−	0.778225i	$-0.283880\pi$
$211$	1.20675e9	+	4.39220e8i	0.608817	+	0.221591i	−0.0191686	+	0.999816i	$0.506102\pi$
$212$	−9.88229e8	+	1.74251e8i	−0.489231	+	0.0862647i
$213$	−3.37778e9	+	4.01508e8i	−1.64102	+	0.195063i
$214$	6.95673e8	+	5.83739e8i	0.331704	+	0.278332i
$215$		−	2.80587e9i		−	1.31315i
$216$	1.29190e8	−	7.58688e8i	0.0593490	−	0.348537i
$217$	1.04506e8			0.0471307
$218$	−6.52127e8	+	7.77175e8i	−0.288739	+	0.344106i
$219$	1.14661e9	−	8.57109e8i	0.498469	−	0.372614i
$220$	5.26064e8	+	2.98346e9i	0.224568	+	1.27359i
$221$	−6.52455e8	+	1.79261e9i	−0.273515	+	0.751477i
$222$	9.06724e8	+	5.93823e8i	0.373304	+	0.244481i
$223$	8.51929e7	−	4.83153e8i	0.0344496	−	0.195373i	−0.962726	−	0.270478i	$-0.912818\pi$
$223$	8.51929e7	−	4.83153e8i	0.0344496	−	0.195373i	0.997176	+	0.0751051i	$0.0239292\pi$
$224$	1.02328e7	+	5.90793e6i	0.00406447	+	0.00234662i
$225$	−1.60998e8	−	2.58961e9i	−0.0628191	−	1.01042i
$226$	1.30250e9	+	2.25600e9i	0.499282	+	0.864781i
$227$	9.01326e7	+	2.47637e8i	0.0339452	+	0.0932637i	0.955507	−	0.294967i	$-0.0953086\pi$
$227$	9.01326e7	+	2.47637e8i	0.0339452	+	0.0932637i	−0.921562	+	0.388231i	$0.873086\pi$
$228$	−1.16263e9	−	1.09259e9i	−0.430232	−	0.404314i
$229$	2.16367e9	−	1.81554e9i	0.786773	−	0.660181i	−0.158172	−	0.987412i	$-0.550560\pi$
$229$	2.16367e9	−	1.81554e9i	0.786773	−	0.660181i	0.944944	+	0.327231i	$0.106116\pi$
$230$	3.54188e8	+	4.22104e8i	0.126567	+	0.150837i
$231$	1.34179e8	+	3.15237e7i	0.0471233	+	0.0110711i
$232$	−3.28243e7	+	1.19471e7i	−0.0113304	+	0.00412392i
$233$	−6.70615e8	+	3.87179e8i	−0.227536	+	0.131368i	−0.609435	−	0.792836i	$-0.708604\pi$
$233$	−6.70615e8	+	3.87179e8i	−0.227536	+	0.131368i	0.381899	+	0.924204i	$0.375270\pi$
$234$	−1.30383e9	+	1.23978e9i	−0.434869	+	0.413506i
$235$	2.55139e9	−	4.41913e9i	0.836575	−	1.44899i
$236$	2.55425e9	+	4.50383e8i	0.823408	+	0.145189i
$237$	1.63561e9	+	3.24094e9i	0.518425	+	1.02725i
$238$	5.33373e7	+	1.94132e7i	0.0166235	+	0.00605047i
$239$	−5.29225e9	+	9.33166e8i	−1.62199	+	0.286001i	−0.909507	−	0.415688i	$-0.863541\pi$
$239$	−5.29225e9	+	9.33166e8i	−1.62199	+	0.286001i	−0.712484	+	0.701689i	$0.752430\pi$
$240$	−4.63924e8	+	1.08131e9i	−0.139830	+	0.325916i
$241$	1.38459e9	+	1.16181e9i	0.410444	+	0.344403i	0.824514	−	0.565842i	$-0.191449\pi$
$241$	1.38459e9	+	1.16181e9i	0.410444	+	0.344403i	−0.414070	+	0.910245i	$0.635893\pi$
$242$		−	5.63700e9i		−	1.64356i
$243$	1.53431e9	−	3.13106e9i	0.440035	−	0.897981i
$244$	−1.04874e8			−0.0295876
$245$	−3.28307e9	+	3.91261e9i	−0.911204	+	1.08593i
$246$	7.97362e7	+	3.42100e7i	0.0217729	+	0.00934140i
$247$	6.47677e8	+	3.67316e9i	0.174008	+	0.986851i
$248$	8.12024e8	−	2.23102e9i	0.214666	−	0.589789i
$249$	−5.35498e9	+	2.70250e9i	−1.39303	+	0.703022i
$250$	−8.42065e6	+	4.77559e7i	−0.00215569	+	0.0122255i
$251$	1.89765e9	+	1.09561e9i	0.478104	+	0.276033i	0.719626	−	0.694362i	$-0.244313\pi$
$251$	1.89765e9	+	1.09561e9i	0.478104	+	0.276033i	−0.241522	+	0.970395i	$0.577647\pi$
$252$	3.68886e7	+	3.87943e7i	0.00914724	+	0.00961980i
$253$	−7.33197e8	−	1.26993e9i	−0.178953	−	0.309955i
$254$	1.81991e9	+	5.00015e9i	0.437234	+	1.20129i
$255$	−1.29273e9	+	5.50241e9i	−0.305736	+	1.30134i
$256$	2.05633e8	−	1.72547e8i	0.0478778	−	0.0401742i
$257$	−3.36721e9	−	4.01288e9i	−0.771858	−	0.919865i	0.226677	−	0.973970i	$-0.427214\pi$
$257$	−3.36721e9	−	4.01288e9i	−0.771858	−	0.919865i	−0.998535	+	0.0541052i	$0.982769\pi$
$258$	−1.98609e9	+	2.11340e9i	−0.448249	+	0.476982i
$259$	−7.08457e7	+	2.57857e7i	−0.0157440	+	0.00573034i
$260$	2.38218e9	−	1.37535e9i	0.521292	−	0.300968i
$261$	−1.57953e8	+	9.82008e6i	−0.0340381	+	0.00211618i
$262$	1.51646e9	−	2.62658e9i	0.321829	−	0.557425i
$263$	−1.43719e9	−	2.53416e8i	−0.300394	−	0.0529676i	0.0214195	−	0.999771i	$-0.493181\pi$
$263$	−1.43719e9	−	2.53416e8i	−0.300394	−	0.0529676i	−0.321814	+	0.946803i	$0.604293\pi$
$264$	1.71555e9	−	2.61952e9i	0.353174	−	0.539270i
$265$	6.53156e9	+	2.37729e9i	1.32444	+	0.482058i
$266$	1.09291e8	−	1.92710e7i	0.0218303	−	0.00384927i
$267$	−2.02368e9	−	2.70720e9i	−0.398197	−	0.532692i
$268$	1.23725e9	+	1.03818e9i	0.239838	+	0.201248i
$269$			8.26288e9i			1.57806i	0.614357	+	0.789028i	$0.289416\pi$
$269$			8.26288e9i			1.57806i	−0.614357	+	0.789028i	$0.710584\pi$
$270$	−3.40256e9	+	4.10369e9i	−0.640252	+	0.772183i
$271$	6.07080e9			1.12556			0.562780	−	0.826607i	$-0.309732\pi$
$271$	6.07080e9			1.12556			0.562780	+	0.826607i	$0.309732\pi$
$272$	8.28872e8	−	9.87811e8i	0.151430	−	0.180467i
$273$	−1.47720e7	−	1.24273e8i	−0.00265943	−	0.0223732i
$274$	−4.96917e8	−	2.81815e9i	−0.0881620	−	0.499991i
$275$	3.61059e9	−	9.92000e9i	0.631316	−	1.73453i
$276$	3.20030e7	−	5.68636e8i	0.00551511	−	0.0979937i
$277$	−7.41366e8	+	4.20449e9i	−0.125925	+	0.714159i	0.854828	+	0.518911i	$0.173662\pi$
$277$	−7.41366e8	+	4.20449e9i	−0.125925	+	0.714159i	−0.980754	+	0.195248i	$0.937449\pi$
$278$	3.51753e9	+	2.03085e9i	0.588923	+	0.340015i
$279$	6.38954e9	−	8.65314e9i	1.05452	−	1.42809i
$280$	−4.09223e7	−	7.08795e7i	−0.00665776	−	0.0115316i
$281$	3.71523e9	+	1.02075e10i	0.595882	+	1.63717i	0.759393	+	0.650632i	$0.225496\pi$
$281$	3.71523e9	+	1.02075e10i	0.595882	+	1.63717i	−0.163511	+	0.986542i	$0.552282\pi$
$282$	−5.04972e9	+	1.52256e9i	−0.798492	+	0.240756i
$283$	−6.88289e9	+	5.77543e9i	−1.07306	+	0.900407i	−0.995326	−	0.0965672i	$-0.969214\pi$
$283$	−6.88289e9	+	5.77543e9i	−1.07306	+	0.900407i	−0.0777365	+	0.996974i	$0.524769\pi$
$284$	−3.45518e9	−	4.11773e9i	−0.531126	−	0.632972i
$285$	3.19022e9	+	1.05807e10i	0.483550	+	1.60374i
$286$	−6.87882e9	+	2.50369e9i	−1.02813	+	0.374210i
$287$	−5.22669e6	+	3.01763e6i	−0.000770369	+	0.000444773i
$288$	1.11481e9	−	4.86068e8i	0.162044	−	0.0706524i
$289$	−3.90674e8	+	6.76668e8i	−0.0560046	+	0.0970028i
$290$	2.38279e8	+	4.20150e7i	0.0336895	+	0.00594036i
$291$	4.47607e9	+	2.51915e8i	0.624202	+	0.0351303i
$292$	2.12578e9	+	7.73720e8i	0.292406	+	0.106427i
$293$	7.90211e9	−	1.39336e9i	1.07219	−	0.189056i	0.390432	−	0.920632i	$-0.372326\pi$
$293$	7.90211e9	−	1.39336e9i	1.07219	−	0.189056i	0.681760	+	0.731576i	$0.261215\pi$
$294$	5.24229e9	−	6.23137e8i	0.701669	−	0.0834053i
$295$	−1.37623e10	−	1.15479e10i	−1.81720	−	1.52481i
$296$			1.71278e9i			0.223118i
$297$	1.08139e10	−	9.18263e9i	1.38981	−	1.18016i
$298$	4.72715e9			0.599424
$299$	−8.55840e8	+	1.01995e9i	−0.107080	+	0.127613i
$300$	3.28401e9	−	2.45485e9i	0.405433	−	0.303068i
$301$	−3.50303e7	−	1.98667e8i	−0.00426755	−	0.0242025i
$302$	4.70600e8	−	1.29296e9i	0.0565749	−	0.155438i
$303$	2.79539e9	+	1.83073e9i	0.331643	+	0.217197i
$304$	4.37803e8	−	2.48291e9i	0.0512607	−	0.290714i
$305$	6.29108e8	+	3.63215e8i	0.0726985	+	0.0419725i
$306$	4.86847e9	−	3.22941e9i	0.555273	−	0.368330i
$307$	−7.00935e9	−	1.21405e10i	−0.789086	−	1.36674i	−0.926528	−	0.376227i	$-0.877221\pi$
$307$	−7.00935e9	−	1.21405e10i	−0.789086	−	1.36674i	0.137442	−	0.990510i	$-0.456112\pi$
$308$	7.44949e7	+	2.04673e8i	0.00827796	+	0.0227435i
$309$	7.73378e9	+	7.26790e9i	0.848317	+	0.797214i
$310$	−1.25978e10	+	1.05708e10i	−1.36411	+	1.14462i
$311$	−5.82406e7	−	6.94085e7i	−0.00622565	−	0.00741944i	0.762923	−	0.646490i	$-0.223764\pi$
$311$	−5.82406e7	−	6.94085e7i	−0.00622565	−	0.00741944i	−0.769148	+	0.639070i	$0.779319\pi$
$312$	−2.76779e9	−	6.50260e8i	−0.292088	−	0.0686228i
$313$	−2.49888e8	+	9.09519e7i	−0.0260357	+	0.00947621i	−0.355005	−	0.934864i	$-0.615521\pi$
$313$	−2.49888e8	+	9.09519e7i	−0.0260357	+	0.00947621i	0.328969	+	0.944341i	$0.393299\pi$
$314$	−9.00478e8	+	5.19891e8i	−0.0926306	+	0.0534803i
$315$	−8.69248e7	−	3.60472e8i	−0.00882879	−	0.0366125i
$316$	−2.86837e9	+	4.96816e9i	−0.287664	+	0.498249i
$317$	7.18838e9	+	1.26751e9i	0.711859	+	0.125520i	0.517840	−	0.855478i	$-0.326736\pi$
$317$	7.18838e9	+	1.26751e9i	0.711859	+	0.125520i	0.194020	+	0.980998i	$0.437847\pi$
$318$	−3.23688e9	−	6.41383e9i	−0.316532	−	0.627204i
$319$	−6.05069e8	−	2.20227e8i	−0.0584309	−	0.0212671i
$320$	−1.83112e9	+	3.22875e8i	−0.174629	+	0.0307918i
$321$	−2.56353e9	+	5.97505e9i	−0.241445	+	0.562758i
$322$	3.03477e7	+	2.54647e7i	0.00282294	+	0.00236873i
$323$		−	1.21112e10i		−	1.11270i
$324$	5.46755e9	−	6.82484e8i	0.496150	−	0.0619316i
$325$	−9.58519e9			−0.859147
$326$	−9.88629e9	+	1.17820e10i	−0.875312	+	1.04316i
$327$	−6.67506e9	−	2.86386e9i	−0.583800	−	0.250473i
$328$	2.38090e7	+	1.35027e8i	0.00205705	+	0.0116661i
$329$	1.25477e8	−	3.44745e8i	0.0107098	−	0.0294249i
$330$	−1.93633e10	+	9.77212e9i	−1.63277	+	0.824011i
$331$	1.02856e9	−	5.83328e9i	0.0856879	−	0.485960i	−0.911518	−	0.411260i	$-0.865089\pi$
$331$	1.02856e9	−	5.83328e9i	0.0856879	−	0.485960i	0.997206	−	0.0747004i	$-0.0238000\pi$
$332$	−8.20884e9	−	4.73938e9i	−0.675662	−	0.390094i
$333$	−2.19646e9	+	7.44257e9i	−0.178627	+	0.605266i
$334$	−5.19538e9	−	8.99865e9i	−0.417476	−	0.723089i
$335$	−3.82630e9	−	1.05127e10i	−0.303809	−	0.834708i
$336$	−1.93479e7	+	8.23529e7i	−0.00151802	+	0.00646133i
$337$	−1.99381e9	+	1.67301e9i	−0.154584	+	0.129712i	−0.716799	−	0.697279i	$-0.754394\pi$
$337$	−1.99381e9	+	1.67301e9i	−0.154584	+	0.129712i	0.562215	+	0.826991i	$0.309949\pi$
$338$	−1.65986e9	−	1.97815e9i	−0.127176	−	0.151562i
$339$	−1.27721e10	+	1.35909e10i	−0.967086	+	1.02908i
$340$	−8.39325e9	+	3.05489e9i	−0.628079	+	0.228602i
$341$	3.79016e10	−	2.18825e10i	2.80311	−	1.61837i
$342$	5.08646e9	−	1.02276e10i	0.371801	−	0.747598i
$343$	−3.67343e8	+	6.36257e8i	−0.0265397	+	0.0459680i
$344$	−4.51336e9	−	7.95827e8i	−0.322304	−	0.0568310i
$345$	−2.16135e9	+	3.30023e9i	−0.152563	+	0.232952i
$346$	5.95106e9	+	2.16601e9i	0.415231	+	0.151132i
$347$	4.92015e9	−	8.67555e8i	0.339360	−	0.0598383i	−0.00137139	−	0.999999i	$-0.500437\pi$
$347$	4.92015e9	−	8.67555e8i	0.339360	−	0.0598383i	0.340731	+	0.940161i	$0.389325\pi$
$348$	−1.49733e8	−	2.00307e8i	−0.0102094	−	0.0136578i
$349$	−1.32735e10	−	1.11378e10i	−0.894715	−	0.750755i	0.0744352	−	0.997226i	$-0.476285\pi$
$349$	−1.32735e10	−	1.11378e10i	−0.894715	−	0.750755i	−0.969150	+	0.246471i	$0.920729\pi$
$350$			2.85199e8i			0.0190053i
$351$	−1.11930e10	−	6.37497e9i	−0.737426	−	0.420001i
$352$	4.94822e9			0.322313
$353$	−8.07235e9	+	9.62025e9i	−0.519877	+	0.619566i	−0.960552	−	0.278101i	$-0.910295\pi$
$353$	−8.07235e9	+	9.62025e9i	−0.519877	+	0.619566i	0.440674	+	0.897667i	$0.354739\pi$
$354$	2.19183e9	+	1.84393e10i	0.139571	+	1.17417i
$355$	6.46544e9	+	3.66674e10i	0.407085	+	2.30869i
$356$	1.82680e9	−	5.01909e9i	0.113734	−	0.312482i
$357$	−2.28347e7	+	4.05732e8i	−0.00140579	+	0.0249785i
$358$	3.42676e9	−	1.94341e10i	0.208618	−	1.18313i
$359$	−6.74486e8	−	3.89415e8i	−0.0406064	−	0.0234441i	0.479559	−	0.877509i	$-0.340797\pi$
$359$	−6.74486e8	−	3.89415e8i	−0.0406064	−	0.0234441i	−0.520166	+	0.854065i	$0.674130\pi$
$360$	−8.37083e9	−	9.45218e8i	−0.498377	−	0.0562759i
$361$	−3.34811e9	−	5.79910e9i	−0.197139	−	0.341454i
$362$	−2.62052e9	−	7.19983e9i	−0.152600	−	0.419264i
$363$	3.86397e10	−	1.16504e10i	2.22540	−	0.670987i
$364$	1.51497e8	−	1.27121e8i	0.00862975	−	0.00724122i
$365$	−1.00722e10	−	1.20036e10i	−0.567483	−	0.676300i
$366$	−2.16752e8	−	7.18878e8i	−0.0120792	−	0.0400618i
$367$	−6.75421e9	+	2.45833e9i	−0.372315	+	0.135511i	−0.521399	−	0.853313i	$-0.674590\pi$
$367$	−6.75421e9	+	2.45833e9i	−0.372315	+	0.135511i	0.149084	+	0.988824i	$0.452367\pi$
$368$	7.79430e8	−	4.50004e8i	0.0424997	−	0.0245372i
$369$	−6.97008e7	+	6.17268e8i	−0.00375952	+	0.0332942i
$370$	5.93194e9	−	1.02744e10i	0.316512	−	0.548214i
$371$	4.92140e8	+	8.67775e7i	0.0259772	+	0.00458048i
$372$	1.69711e10	+	9.55139e8i	0.886215	+	0.0498764i
$373$	1.53994e10	+	5.60492e9i	0.795552	+	0.289557i	0.707642	−	0.706571i	$-0.249759\pi$
$373$	1.53994e10	+	5.60492e9i	0.795552	+	0.289557i	0.0879098	+	0.996128i	$0.471981\pi$
$374$	2.34089e10	−	4.12762e9i	1.19645	−	0.210966i
$375$	−3.44753e8	+	4.09799e7i	−0.0174335	+	0.00207227i
$376$	−6.38470e9	−	5.35740e9i	−0.319440	−	0.268042i
$377$			5.84648e8i			0.0289420i
$378$	−1.89681e8	+	3.33038e8i	−0.00929090	+	0.0163127i
$379$	−3.06483e9			−0.148542			−0.0742711	−	0.997238i	$-0.523663\pi$
$379$	−3.06483e9			−0.148542			−0.0742711	+	0.997238i	$0.523663\pi$
$380$	−1.12254e10	+	1.33779e10i	−0.538352	+	0.641583i
$381$	−3.05130e10	+	2.28090e10i	−1.44805	+	1.08245i
$382$	−3.36482e9	−	1.90829e10i	−0.158019	−	0.896169i
$383$	−1.49891e9	+	4.11823e9i	−0.0696597	+	0.191389i	−0.969637	−	0.244548i	$-0.921360\pi$
$383$	−1.49891e9	+	4.11823e9i	−0.0696597	+	0.191389i	0.899978	+	0.435936i	$0.143583\pi$
$384$	1.60775e9	+	1.05293e9i	0.0739423	+	0.0484256i
$385$	2.61981e8	−	1.48577e9i	0.0119241	−	0.0676251i
$386$	1.96832e9	+	1.13641e9i	0.0886637	+	0.0511900i
$387$	−1.85914e10	−	9.24602e9i	−0.828835	−	0.412203i
$388$	3.54225e9	+	6.13535e9i	0.156297	+	0.270715i
$389$	−1.92754e9	−	5.29586e9i	−0.0841791	−	0.231280i	0.890461	−	0.455061i	$-0.150382\pi$
$389$	−1.92754e9	−	5.29586e9i	−0.0841791	−	0.231280i	−0.974640	+	0.223780i	$0.928160\pi$
$390$	1.43510e10	+	1.34865e10i	0.620330	+	0.582961i
$391$	3.31192e9	−	2.77903e9i	0.141701	−	0.118901i
$392$	5.36242e9	+	6.39068e9i	0.227100	+	0.270647i
$393$	2.11385e10	+	4.96625e9i	0.886143	+	0.208189i
$394$	−2.95036e10	+	1.07384e10i	−1.22431	+	0.445611i
$395$	3.44128e10	−	1.98682e10i	1.41362	−	0.816151i
$396$	2.15016e10	+	6.34557e9i	0.874358	+	0.258042i
$397$	8.34516e9	−	1.44542e10i	0.335949	−	0.581880i	−0.647718	−	0.761880i	$-0.724276\pi$
$397$	8.34516e9	−	1.44542e10i	0.335949	−	0.581880i	0.983667	+	0.180000i	$0.0576098\pi$
$398$	2.11125e10	+	3.72270e9i	0.841409	+	0.148363i
$399$	3.57976e8	+	7.09326e8i	0.0141242	+	0.0279869i
$400$	6.08846e9	+	2.21602e9i	0.237831	+	0.0865632i
$401$	−3.62336e10	+	6.38896e9i	−1.40131	+	0.247088i	−0.822681	−	0.568504i	$-0.807523\pi$
$401$	−3.62336e10	+	6.38896e9i	−1.40131	+	0.247088i	−0.578627	+	0.815592i	$0.696411\pi$
$402$	−4.55922e9	+	1.06266e10i	−0.174577	+	0.406902i
$403$	−3.04408e10	−	2.55428e10i	−1.15408	−	0.968387i
$404$			5.28042e9i			0.198218i
$405$	−3.51617e10	−	1.48420e10i	−1.30692	−	0.551660i
$406$	1.73956e7			0.000640231
$407$	−2.02945e10	+	2.41861e10i	−0.739607	+	0.881430i
$408$	8.48419e9	+	3.64005e9i	0.306175	+	0.131361i
$409$	5.85385e9	+	3.31988e10i	0.209193	+	1.18639i	0.890703	+	0.454586i	$0.150213\pi$
$409$	5.85385e9	+	3.31988e10i	0.209193	+	1.18639i	−0.681510	+	0.731809i	$0.738676\pi$
$410$	3.24823e8	−	8.92443e8i	0.0114951	−	0.0315824i
$411$	1.82905e10	−	9.23067e9i	0.640999	−	0.323494i
$412$	−2.91226e9	+	1.65162e10i	−0.101074	+	0.573221i
$413$	−1.11860e9	−	6.45821e8i	−0.0384479	−	0.0221979i
$414$	3.96395e9	−	9.55872e8i	0.134936	−	0.0325386i
$415$	3.28281e10	+	5.68600e10i	1.10676	+	1.91697i
$416$	−1.53665e9	−	4.22192e9i	−0.0513100	−	0.140973i
$417$	−6.65081e9	+	2.83087e10i	−0.219953	+	0.936216i
$418$	3.56018e10	−	2.98735e10i	1.16618	−	0.978544i
$419$	−4.93771e8	−	5.88453e8i	−0.0160202	−	0.0190922i	0.757975	−	0.652284i	$-0.226189\pi$
$419$	−4.93771e8	−	5.88453e8i	−0.0160202	−	0.0190922i	−0.773995	+	0.633192i	$0.781745\pi$
$420$	4.01277e8	−	4.27000e8i	0.0128958	−	0.0137224i
$421$	2.83636e10	−	1.03235e10i	0.902886	−	0.328624i	0.151478	−	0.988461i	$-0.451597\pi$
$421$	2.83636e10	−	1.03235e10i	0.902886	−	0.328624i	0.751409	+	0.659837i	$0.229375\pi$
$422$	−1.25825e10	+	7.26450e9i	−0.396750	+	0.229064i
$423$	−2.08732e10	−	3.14673e10i	−0.651971	−	0.982874i
$424$	5.67651e9	−	9.83200e9i	0.175638	−	0.304213i
$425$	3.06516e10	+	5.40470e9i	0.939502	+	0.165659i
$426$	2.10845e10	−	3.21945e10i	0.640214	−	0.977559i
$427$	4.90779e7	+	1.78629e7i	0.00147630	+	0.000537329i
$428$	−1.01183e10	+	1.78413e9i	−0.301531	+	0.0531681i
$429$	−3.13789e10	−	4.19774e10i	−0.926420	−	1.23933i
$430$	2.43180e10	+	2.04052e10i	0.711301	+	0.596852i
$431$			5.01152e10i			1.45231i	0.687530	+	0.726156i	$0.258695\pi$
$431$			5.01152e10i			1.45231i	−0.687530	+	0.726156i	$0.741305\pi$
$432$	5.63589e9	+	6.63708e9i	0.161818	+	0.190565i
$433$	2.41637e10			0.687403			0.343702	−	0.939079i	$-0.388319\pi$
$433$	2.41637e10			0.687403			0.343702	+	0.939079i	$0.388319\pi$
$434$	−7.60003e8	+	9.05737e8i	−0.0214218	+	0.0255295i
$435$	2.04470e8	+	1.72016e9i	0.00571048	+	0.0480409i
$436$	−1.99315e9	−	1.13037e10i	−0.0551561	−	0.312806i
$437$	2.89113e9	−	7.94330e9i	0.0792759	−	0.217809i
$438$	−9.10084e8	+	1.61706e10i	−0.0247278	+	0.439369i
$439$	−3.43063e9	+	1.94561e10i	−0.0923668	+	0.523838i	0.903156	+	0.429313i	$0.141244\pi$
$439$	−3.43063e9	+	1.94561e10i	−0.0923668	+	0.523838i	−0.995522	+	0.0945249i	$0.969867\pi$
$440$	−2.96828e10	−	1.71374e10i	−0.791943	−	0.457228i
$441$	1.51060e10	+	3.46462e10i	0.399388	+	0.916013i
$442$	−1.07913e10	−	1.86911e10i	−0.282738	−	0.489717i
$443$	−2.45817e10	−	6.75376e10i	−0.638258	−	1.75360i	−0.657128	−	0.753779i	$-0.728229\pi$
$443$	−2.45817e10	−	6.75376e10i	−0.638258	−	1.75360i	0.0188697	−	0.999822i	$-0.493993\pi$
$444$	−1.17405e10	+	3.53993e9i	−0.302103	+	0.0910883i
$445$	−2.83411e10	+	2.37810e10i	−0.722732	+	0.606444i
$446$	3.56784e9	+	4.25199e9i	0.0901709	+	0.107461i
$447$	9.76994e9	+	3.24030e10i	0.244716	+	0.811624i
$448$	−1.25619e8	+	4.57217e7i	−0.00311849	+	0.00113504i
$449$	5.20595e9	−	3.00565e9i	0.128090	−	0.0739527i	−0.434586	−	0.900630i	$-0.643105\pi$
$449$	5.20595e9	−	3.00565e9i	0.128090	−	0.0739527i	0.562676	+	0.826678i	$0.309772\pi$
$450$	2.36145e10	+	1.74371e10i	0.575875	+	0.425230i
$451$	−1.26372e9	+	2.18882e9i	−0.0305452	+	0.0529059i
$452$	−2.90246e10	−	5.11781e9i	−0.695364	−	0.122611i
$453$	9.83543e9	+	5.53541e8i	0.233561	+	0.0131449i
$454$	−2.80170e9	−	1.01973e9i	−0.0659474	−	0.0240029i
$455$	−1.34904e9	+	2.37873e8i	−0.0314760	+	0.00555007i
$456$	1.79243e10	−	2.13061e9i	0.414556	−	0.0492770i
$457$	3.70396e10	+	3.10799e10i	0.849183	+	0.712549i	0.959610	−	0.281335i	$-0.0907772\pi$
$457$	3.70396e10	+	3.10799e10i	0.849183	+	0.712549i	−0.110427	+	0.993884i	$0.535222\pi$
$458$			3.19552e10i			0.726240i
$459$	3.21985e10	+	2.66972e10i	0.725412	+	0.601472i
$460$	−6.23406e9			−0.139232
$461$	−3.99443e10	+	4.76037e10i	−0.884404	+	1.05399i	0.113765	+	0.993508i	$0.463709\pi$
$461$	−3.99443e10	+	4.76037e10i	−0.884404	+	1.05399i	−0.998169	+	0.0604837i	$0.980736\pi$
$462$	−1.24900e9	+	9.33649e8i	−0.0274154	+	0.0204935i
$463$	1.49946e9	+	8.50384e9i	0.0326295	+	0.185051i	0.996766	−	0.0803546i	$-0.0256053\pi$
$463$	1.49946e9	+	8.50384e9i	0.0326295	+	0.185051i	−0.964137	+	0.265406i	$0.914494\pi$
$464$	1.35166e8	−	3.71365e8i	0.00291605	−	0.00801178i
$465$	−9.84963e10	−	6.45063e10i	−2.10673	−	1.37972i
$466$	1.52131e9	−	8.62777e9i	0.0322607	−	0.182960i
$467$	4.54365e10	+	2.62328e10i	0.955295	+	0.551540i	0.894722	−	0.446624i	$-0.147374\pi$
$467$	4.54365e10	+	2.62328e10i	0.955295	+	0.551540i	0.0605735	+	0.998164i	$0.480707\pi$
$468$	−1.26307e9	−	2.03161e10i	−0.0263297	−	0.423504i
$469$	−4.02165e8	−	6.96569e8i	−0.00831213	−	0.0143970i
$470$	1.97453e10	+	5.42497e10i	0.404642	+	1.11175i
$471$	−5.42476e9	−	5.09797e9i	−0.110229	−	0.103589i
$472$	−2.24787e10	+	1.88618e10i	−0.452900	+	0.380029i
$473$	−5.43032e10	−	6.47160e10i	−1.08488	−	1.29291i
$474$	−3.99832e10	−	9.39361e9i	−0.792072	−	0.186088i
$475$	5.71843e10	−	2.08134e10i	1.12332	−	0.408854i
$476$	−5.56136e8	+	3.21085e8i	−0.0108331	+	0.00625450i
$477$	3.72747e10	−	3.54436e10i	0.720013	−	0.684643i
$478$	3.03993e10	−	5.26531e10i	0.582307	−	1.00859i
$479$	5.20295e10	+	9.17420e9i	0.988343	+	0.174271i	0.644375	−	0.764710i	$-0.277118\pi$
$479$	5.20295e10	+	9.17420e9i	0.988343	+	0.174271i	0.343968	+	0.938981i	$0.388229\pi$
$480$	−5.99770e9	−	1.18844e10i	−0.112985	−	0.223878i
$481$	2.69384e10	+	9.80478e9i	0.503259	+	0.183171i
$482$	−2.01384e10	+	3.55094e9i	−0.373109	+	0.0657892i
$483$	−1.11830e8	+	2.60653e8i	−0.00205481	+	0.00478932i
$484$	4.88548e10	+	4.09940e10i	0.890278	+	0.747032i
$485$		−	4.90720e10i		−	0.886883i
$486$	1.59784e10	+	3.60676e10i	0.286409	+	0.646506i
$487$	−2.59684e10			−0.461667			−0.230834	−	0.972993i	$-0.574145\pi$
$487$	−2.59684e10			−0.461667			−0.230834	+	0.972993i	$0.574145\pi$
$488$	7.62680e8	−	9.08926e8i	0.0134482	−	0.0160269i
$489$	−1.01194e11	−	4.34163e10i	−1.76979	−	0.759307i
$490$	−1.00343e10	−	5.69074e10i	−0.174062	−	0.987154i
$491$	−6.91237e9	+	1.89916e10i	−0.118933	+	0.326765i	−0.984846	−	0.173428i	$-0.944515\pi$
$491$	−6.91237e9	+	1.89916e10i	−0.118933	+	0.326765i	0.865914	+	0.500193i	$0.166738\pi$
$492$	−8.76358e8	+	4.42273e8i	−0.0149562	+	0.00754796i
$493$	3.29659e8	−	1.86959e9i	0.00558056	−	0.0316489i
$494$	−3.65446e10	−	2.10991e10i	−0.613643	−	0.354287i
$495$	−1.07004e11	−	1.12532e11i	−1.78229	−	1.87437i
$496$	1.34305e10	+	2.32623e10i	0.221904	+	0.384349i
$497$	9.15558e8	+	2.51547e9i	0.0150058	+	0.0412282i
$498$	1.55210e10	−	6.60640e10i	0.252349	−	1.07411i
$499$	−3.32105e10	+	2.78669e10i	−0.535640	+	0.449455i	−0.870044	−	0.492975i	$-0.835910\pi$
$499$	−3.32105e10	+	2.78669e10i	−0.535640	+	0.449455i	0.334404	+	0.942430i	$0.391465\pi$
$500$	−3.52653e8	−	4.20276e8i	−0.00564245	−	0.00672441i
$501$	5.09450e10	−	5.42107e10i	0.808632	−	0.860466i
$502$	−2.32958e10	+	8.47897e9i	−0.366828	+	0.133514i
$503$	−6.86967e10	+	3.96621e10i	−1.07316	+	0.619589i	−0.929043	−	0.369972i	$-0.879367\pi$
$503$	−6.86967e10	+	3.96621e10i	−1.07316	+	0.619589i	−0.144116	+	0.989561i	$0.546034\pi$
$504$	−6.04488e8	+	3.75816e7i	−0.00936841	+	0.000582443i
$505$	1.82879e10	−	3.16755e10i	0.281189	−	0.487033i
$506$	1.63383e10	+	2.88088e9i	0.249233	+	0.0439464i
$507$	1.01289e10	−	1.54661e10i	0.153297	−	0.234072i
$508$	−5.65702e10	−	2.05899e10i	−0.849441	−	0.309171i
$509$	−7.23662e10	+	1.27601e10i	−1.07811	+	0.190101i	−0.684381	−	0.729124i	$-0.739928\pi$
$509$	−7.23662e10	+	1.27601e10i	−1.07811	+	0.190101i	−0.393733	+	0.919225i	$0.628817\pi$
$510$	−3.82872e10	−	5.12191e10i	−0.565943	−	0.757096i
$511$	−8.63012e8	−	7.24153e8i	−0.0126571	−	0.0106205i
$512$			3.03700e9i			0.0441942i
$513$	8.06190e10	+	1.37278e10i	1.16404	+	0.198213i
$514$	5.92663e10			0.849093
$515$	7.46709e10	−	8.89893e10i	1.06151	−	1.26505i
$516$	−3.87297e9	−	3.25823e10i	−0.0546317	−	0.459603i
$517$	−2.66788e10	−	1.51303e11i	−0.373425	−	2.11780i
$518$	2.91732e8	−	8.01528e8i	0.00405196	−	0.0111327i
$519$	−2.54776e9	+	4.52691e10i	−0.0351146	+	0.623925i
$520$	−5.40404e9	+	3.06478e10i	−0.0739104	+	0.419167i
$521$	4.18393e10	+	2.41559e10i	0.567850	+	0.327848i	0.756290	−	0.654236i	$-0.227010\pi$
$521$	4.18393e10	+	2.41559e10i	0.567850	+	0.327848i	−0.188440	+	0.982085i	$0.560343\pi$
$522$	1.06357e9	−	1.44036e9i	0.0143247	−	0.0193994i
$523$	−5.01333e10	−	8.68334e10i	−0.670069	−	1.16059i	−0.977884	−	0.209147i	$-0.932931\pi$
$523$	−5.01333e10	−	8.68334e10i	−0.670069	−	1.16059i	0.307815	−	0.951446i	$-0.400402\pi$
$524$	1.17359e10	+	3.22442e10i	0.155665	+	0.427687i
$525$	−1.95494e9	+	5.89440e8i	−0.0257333	+	0.00775894i
$526$	1.26480e10	−	1.06129e10i	0.165226	−	0.138641i
$527$	8.29411e10	+	9.88454e10i	1.07529	+	1.28149i
$528$	1.02268e10	+	3.39183e10i	0.131585	+	0.436414i
$529$	−7.07527e10	+	2.57519e10i	−0.903484	+	0.328841i
$530$	−6.81030e10	+	3.93193e10i	−0.863104	+	0.498313i
$531$	−1.21865e11	+	5.31341e10i	−1.53286	+	0.668337i
$532$	−6.27783e8	+	1.08735e9i	−0.00783724	+	0.0135745i
$533$	2.25999e9	+	3.98497e8i	0.0280025	+	0.00493760i
$534$	3.81797e10	+	2.14876e9i	0.469534	+	0.0264255i
$535$	6.68754e10	+	2.43407e10i	0.816303	+	0.297110i
$536$	−1.79953e10	+	3.17306e9i	−0.218022	+	0.0384432i
$537$	1.40296e11	−	1.66766e10i	1.68713	−	0.200545i
$538$	−7.16128e10	−	6.00903e10i	−0.854794	−	0.717257i
$539$			1.53781e11i			1.82200i
$540$	−1.08214e10	−	5.93327e10i	−0.127265	−	0.697780i
$541$	−6.57095e10			−0.767077			−0.383538	−	0.923525i	$-0.625295\pi$
$541$	−6.57095e10			−0.767077			−0.383538	+	0.923525i	$0.625295\pi$
$542$	−4.41488e10	+	5.26144e10i	−0.511589	+	0.609688i
$543$	4.39363e10	−	3.28432e10i	0.505387	−	0.377786i
$544$	2.53335e9	+	1.43673e10i	0.0289267	+	0.164052i
$545$	−2.71923e10	+	7.47102e10i	−0.308219	+	0.846826i
$546$	1.18448e9	+	7.75728e8i	0.0133278	+	0.00872849i
$547$	−2.45141e10	+	1.39027e11i	−0.273821	+	1.55292i	0.468859	+	0.883273i	$0.344665\pi$
$547$	−2.45141e10	+	1.39027e11i	−0.273821	+	1.55292i	−0.742681	+	0.669646i	$0.766446\pi$
$548$	2.80381e10	+	1.61878e10i	0.310904	+	0.179501i
$549$	4.47968e9	−	2.97151e9i	0.0493126	−	0.0327106i
$550$	5.97174e10	+	1.03434e11i	0.652605	+	1.13034i
$551$	−1.26951e9	−	3.48795e9i	−0.0137730	−	0.0378411i
$552$	4.69552e9	+	4.41266e9i	0.0505740	+	0.0475275i
$553$	2.18851e9	−	1.83638e9i	0.0234018	−	0.0196364i
$554$	−3.10481e10	−	3.70017e10i	−0.329606	−	0.392810i
$555$	8.26875e10	+	1.94265e10i	0.871502	+	0.204749i
$556$	−4.31815e10	+	1.57168e10i	−0.451854	+	0.164462i
$557$	−2.39225e9	+	1.38117e9i	−0.0248534	+	0.0143491i	−0.512375	−	0.858762i	$-0.671234\pi$
$557$	−2.39225e9	+	1.38117e9i	−0.0248534	+	0.0143491i	0.487522	+	0.873111i	$0.337901\pi$
$558$	2.85283e10	+	1.18305e11i	0.294265	+	1.22030i
$559$	−3.83533e10	+	6.64298e10i	−0.392785	+	0.680324i
$560$	9.11899e8	+	1.60792e8i	0.00927245	+	0.00163498i
$561$	7.66742e10	+	1.51929e11i	0.774101	+	1.53387i
$562$	−1.15485e11	−	4.20330e10i	−1.15766	−	0.421353i
$563$	5.06700e10	−	8.93448e9i	0.504333	−	0.0889274i	0.0843072	−	0.996440i	$-0.473132\pi$
$563$	5.06700e10	−	8.93448e9i	0.504333	−	0.0889274i	0.420025	+	0.907512i	$0.362021\pi$
$564$	2.35274e10	−	5.48374e10i	0.232519	−	0.541952i
$565$	1.56384e11	+	1.31222e11i	1.53461	+	1.28769i
$566$		−	1.01653e11i		−	0.990504i
$567$	−2.67488e9	−	6.11888e8i	−0.0258805	−	0.00592024i
$568$	6.08147e10			0.584272
$569$	1.27466e11	−	1.51908e11i	1.21603	−	1.44921i	0.359479	−	0.933153i	$-0.382954\pi$
$569$	1.27466e11	−	1.51908e11i	1.21603	−	1.44921i	0.856554	−	0.516058i	$-0.172601\pi$
$570$	−1.14901e11	−	4.92970e10i	−1.08849	−	0.467005i
$571$	−1.53674e10	−	8.71529e10i	−0.144563	−	0.819856i	−0.967717	−	0.252038i	$-0.918899\pi$
$571$	−1.53674e10	−	8.71529e10i	−0.144563	−	0.819856i	0.823155	−	0.567817i	$-0.192212\pi$
$572$	2.83260e10	−	7.78250e10i	0.264607	−	0.727001i
$573$	1.23852e11	−	6.25046e10i	1.14891	−	0.579820i
$574$	1.18569e7	−	6.72438e7i	0.000109225	−	0.000619448i
$575$	1.88130e10	+	1.08617e10i	0.172103	+	0.0993635i
$576$	−3.89463e9	+	1.31967e10i	−0.0353815	+	0.119888i
$577$	1.63726e10	+	2.83581e10i	0.147711	+	0.255843i	0.930381	−	0.366594i	$-0.119476\pi$
$577$	1.63726e10	+	2.83581e10i	0.147711	+	0.255843i	−0.782670	+	0.622437i	$0.786143\pi$
$578$	−3.02344e9	−	8.30684e9i	−0.0270888	−	0.0744260i
$579$	−3.72162e9	+	1.58408e10i	−0.0331145	+	0.140950i
$580$	−2.09698e9	+	1.75957e9i	−0.0185303	+	0.0155487i
$581$	3.03424e9	+	3.61606e9i	0.0266284	+	0.0317345i
$582$	−3.47347e10	+	3.69613e10i	−0.302741	+	0.322147i
$583$	1.96656e11	−	7.15768e10i	1.70228	−	0.619581i
$584$	−2.21650e10	+	1.27970e10i	−0.190553	+	0.110016i
$585$	−6.27849e10	+	1.26244e11i	−0.536082	+	1.07793i
$586$	−4.53907e10	+	7.86189e10i	−0.384925	+	0.666710i
$587$	−3.38496e10	−	5.96859e9i	−0.285102	−	0.0502712i	0.0292682	−	0.999572i	$-0.490682\pi$
$587$	−3.38496e10	−	5.96859e9i	−0.285102	−	0.0502712i	−0.314370	+	0.949300i	$0.601793\pi$
$588$	−3.27230e10	+	4.99656e10i	−0.273743	+	0.417986i
$589$	2.37070e11	+	8.62865e10i	1.96977	+	0.716938i
$590$	2.00167e11	−	3.52949e10i	1.65190	−	0.291275i
$591$	−1.34585e11	−	1.80043e11i	−1.10318	−	1.47579i
$592$	−1.48443e10	−	1.24559e10i	−0.120858	−	0.101412i
$593$		−	1.15609e11i		−	0.934915i	−0.884016	−	0.467457i	$-0.845170\pi$
$593$		−	1.15609e11i		−	0.934915i	0.884016	−	0.467457i	$-0.154830\pi$
$594$	9.42169e8	+	1.60501e11i	0.00756803	+	1.28923i
$595$	4.44811e9			0.0354901
$596$	−3.43773e10	+	4.09693e10i	−0.272450	+	0.324693i
$597$	1.81169e10	+	1.52413e11i	0.142622	+	1.19984i
$598$	−2.61578e9	−	1.48348e10i	−0.0204548	−	0.116005i
$599$	−4.43747e10	+	1.21918e11i	−0.344690	+	0.947027i	0.639325	+	0.768937i	$0.279214\pi$
$599$	−4.43747e10	+	1.21918e11i	−0.344690	+	0.947027i	−0.984014	+	0.178090i	$0.943008\pi$
$600$	−2.60658e9	+	4.63143e10i	−0.0201125	+	0.357363i
$601$	4.05510e10	−	2.29976e11i	0.310816	−	1.76273i	−0.283960	−	0.958836i	$-0.591648\pi$
$601$	4.05510e10	−	2.29976e11i	0.310816	−	1.76273i	0.594776	−	0.803891i	$-0.297241\pi$
$602$	1.97656e9	+	1.14117e9i	0.0150496	+	0.00868887i
$603$	−8.22644e10	−	9.28915e9i	−0.622218	−	0.0702597i
$604$	7.78350e9	+	1.34814e10i	0.0584827	+	0.101295i
$605$	−1.51088e11	−	4.15110e11i	−1.12774	−	3.09843i
$606$	−3.61955e10	+	1.09134e10i	−0.268388	+	0.0809228i
$607$	−1.33429e11	+	1.11960e11i	−0.982868	+	0.824724i	−0.984520	−	0.175275i	$-0.943919\pi$
$607$	−1.33429e11	+	1.11960e11i	−0.982868	+	0.824724i	0.00165202	+	0.999999i	$0.499474\pi$
$608$	1.83350e10	+	2.18508e10i	0.134174	+	0.159902i
$609$	3.59528e7	+	1.19241e8i	0.000261375	+	0.000866876i
$610$	−7.72298e9	+	2.81094e9i	−0.0557784	+	0.0203017i
$611$	−1.20810e11	+	6.97494e10i	−0.866835	+	0.500467i
$612$	−7.41639e9	+	6.56793e10i	−0.0528673	+	0.468191i
$613$	−1.16269e11	+	2.01384e11i	−0.823422	+	1.42621i	0.0796977	+	0.996819i	$0.474605\pi$
$613$	−1.16269e11	+	2.01384e11i	−0.823422	+	1.42621i	−0.903119	+	0.429389i	$0.858729\pi$
$614$	1.56194e11	+	2.75412e10i	1.09898	+	0.193780i
$615$	6.78872e9	+	3.82071e8i	0.0474556	+	0.00267081i
$616$	−2.31561e9	−	8.42813e8i	−0.0160821	−	0.00585340i
$617$	−2.33865e10	+	4.12368e9i	−0.161371	+	0.0284540i	−0.253750	−	0.967270i	$-0.581664\pi$
$617$	−2.33865e10	+	4.12368e9i	−0.161371	+	0.0284540i	0.0923789	+	0.995724i	$0.470553\pi$
$618$	−1.19232e11	+	1.41728e10i	−0.817408	+	0.0971629i
$619$	−1.59321e11	−	1.33686e11i	−1.08520	−	0.910591i	−0.0888583	−	0.996044i	$-0.528322\pi$
$619$	−1.59321e11	−	1.33686e11i	−1.08520	−	0.910591i	−0.996342	+	0.0854530i	$0.972766\pi$
$620$		−	1.86057e11i		−	1.25916i
$621$	1.47447e10	+	2.51959e10i	0.0991450	+	0.169420i
$622$	1.02509e9			0.00684860
$623$	−1.70977e9	+	2.03762e9i	−0.0113497	+	0.0135261i
$624$	2.57639e10	−	1.92590e10i	0.169931	−	0.127027i
$625$	−2.61646e10	−	1.48387e11i	−0.171473	−	0.972469i
$626$	1.02900e9	−	2.82716e9i	0.00670069	−	0.0184100i
$627$	2.78353e11	+	1.82296e11i	1.80105	+	1.17953i
$628$	2.04276e9	−	1.15851e10i	0.0131335	−	0.0744836i
$629$	−8.06153e10	−	4.65433e10i	−0.515009	−	0.297341i
$630$	3.75629e9	+	1.86811e9i	0.0238449	+	0.0118588i
$631$	6.70620e9	+	1.16155e10i	0.0423018	+	0.0732689i	0.886401	−	0.462918i	$-0.153198\pi$
$631$	6.70620e9	+	1.16155e10i	0.0423018	+	0.0732689i	−0.844099	+	0.536187i	$0.819864\pi$
$632$	−2.21984e10	−	6.09895e10i	−0.139140	−	0.382285i
$633$	−7.58008e10	−	7.12345e10i	−0.472127	−	0.443686i
$634$	−6.32614e10	+	5.30826e10i	−0.391545	+	0.328545i
$635$	2.68037e11	+	3.19434e11i	1.64854	+	1.96465i
$636$	7.91270e10	+	1.85900e10i	0.483611	+	0.113619i
$637$	1.31209e11	−	4.77561e10i	0.796903	−	0.290049i
$638$	6.30892e9	−	3.64246e9i	0.0380778	−	0.0219842i
$639$	2.64259e11	+	7.79884e10i	1.58499	+	0.467764i
$640$	1.05182e10	−	1.82180e10i	0.0626931	−	0.108588i
$641$	−1.03667e11	−	1.82794e10i	−0.614059	−	0.108275i	−0.142036	−	0.989861i	$-0.545365\pi$
$641$	−1.03667e11	−	1.82794e10i	−0.614059	−	0.108275i	−0.472023	+	0.881586i	$0.656476\pi$
$642$	−3.31418e10	−	6.56701e10i	−0.195090	−	0.386569i
$643$	−1.15569e11	−	4.20638e10i	−0.676082	−	0.246074i	−0.0189174	−	0.999821i	$-0.506022\pi$
$643$	−1.15569e11	−	4.20638e10i	−0.676082	−	0.246074i	−0.657164	+	0.753747i	$0.728244\pi$
$644$	−4.41396e8	+	7.78300e7i	−0.00256617	+	0.000452484i
$645$	−8.96108e10	+	2.08864e11i	−0.517752	+	1.20677i
$646$	1.04966e11	+	8.80768e10i	0.602723	+	0.505745i
$647$		−	2.03718e11i		−	1.16255i	−0.813707	−	0.581276i	$-0.802554\pi$
$647$		−	2.03718e11i		−	1.16255i	0.813707	−	0.581276i	$-0.197446\pi$
$648$	−3.38468e10	+	5.23494e10i	−0.191963	+	0.296901i
$649$	−5.40911e11			−3.04893
$650$	6.97065e10	−	8.30730e10i	0.390499	−	0.465379i
$651$	−7.77926e9	−	3.33761e9i	−0.0433126	−	0.0185828i
$652$	−3.02163e10	−	1.71365e11i	−0.167205	−	0.948269i
$653$	1.60879e9	−	4.42011e9i	0.00884803	−	0.0243098i	−0.935190	−	0.354146i	$-0.884771\pi$
$653$	1.60879e9	−	4.42011e9i	0.00884803	−	0.0243098i	0.944038	+	0.329837i	$0.106994\pi$
$654$	7.33636e10	−	3.70245e10i	0.401024	−	0.202385i
$655$	4.12725e10	−	2.34068e11i	0.224231	−	1.27168i
$656$	−1.34340e9	−	7.75613e8i	−0.00725422	−	0.00418822i
$657$	−1.12725e11	+	2.71826e10i	−0.605003	+	0.145891i
$658$	2.07533e9	+	3.59458e9i	0.0110709	+	0.0191754i
$659$	−7.02732e10	−	1.93074e11i	−0.372604	−	1.02372i	−0.974351	−	0.225035i	$-0.927750\pi$
$659$	−7.02732e10	−	1.93074e11i	−0.372604	−	1.02372i	0.601746	−	0.798687i	$-0.294472\pi$
$660$	5.61231e10	−	2.38884e11i	0.295778	−	1.25896i
$661$	1.25081e11	−	1.04955e11i	0.655217	−	0.549792i	−0.253432	−	0.967353i	$-0.581559\pi$
$661$	1.25081e11	−	1.04955e11i	0.655217	−	0.549792i	0.908649	+	0.417561i	$0.137115\pi$
$662$	4.30758e10	+	5.13358e10i	0.224286	+	0.267293i
$663$	1.05818e11	−	1.12601e11i	0.547652	−	0.582757i
$664$	1.00773e11	−	3.66782e10i	0.518406	−	0.188684i
$665$	7.53173e9	−	4.34845e9i	0.0385131	−	0.0222355i
$666$	−4.85300e10	−	7.31610e10i	−0.246668	−	0.371863i
$667$	6.62508e8	−	1.14750e9i	0.00334725	−	0.00579761i
$668$	1.15772e11	+	2.04137e10i	0.581430	+	0.102522i
$669$	−2.17720e10	+	3.32442e10i	−0.108691	+	0.165963i
$670$	1.18937e11	+	4.32897e10i	0.590227	+	0.214825i
$671$	2.15395e10	−	3.79799e9i	0.106254	−	0.0187354i
$672$	−5.73033e8	−	7.66580e8i	−0.00280997	−	0.00375907i
$673$	−5.23280e10	−	4.39084e10i	−0.255079	−	0.214036i	0.506277	−	0.862371i	$-0.331021\pi$
$673$	−5.23280e10	−	4.39084e10i	−0.255079	−	0.214036i	−0.761356	+	0.648335i	$0.775466\pi$
$674$		−	2.94466e10i		−	0.142691i
$675$	−7.07196e10	+	1.97907e11i	−0.340663	+	0.953338i
$676$	2.92152e10			0.139902
$677$	−1.53815e11	+	1.83309e11i	−0.732222	+	0.872629i	−0.995757	−	0.0920212i	$-0.970667\pi$
$677$	−1.53815e11	+	1.83309e11i	−0.732222	+	0.872629i	0.263535	+	0.964650i	$0.415112\pi$
$678$	−2.49063e10	−	2.09531e11i	−0.117867	−	0.991583i
$679$	−6.12646e8	−	3.47449e9i	−0.00288224	−	0.0163460i
$680$	3.45622e10	−	9.49588e10i	0.161646	−	0.444119i
$681$	1.19946e9	−	2.13122e10i	0.00557694	−	0.0990924i
$682$	−8.59809e10	+	4.87622e11i	−0.397433	+	2.25396i
$683$	1.87272e11	+	1.08121e11i	0.860577	+	0.496854i	0.864205	−	0.503139i	$-0.167822\pi$
$683$	1.87272e11	+	1.08121e11i	0.860577	+	0.496854i	−0.00362853	+	0.999993i	$0.501155\pi$
$684$	5.16500e10	+	1.18461e11i	0.235964	+	0.541193i
$685$	−1.12128e11	−	1.94211e11i	−0.509273	−	0.882087i
$686$	−2.84288e9	−	7.81075e9i	−0.0128370	−	0.0352692i
$687$	−2.19042e11	+	6.60442e10i	−0.983333	+	0.296488i
$688$	3.97198e10	−	3.33289e10i	0.177278	−	0.148754i
$689$	−1.22141e11	−	1.45562e11i	−0.541983	−	0.645911i
$690$	−1.28844e10	−	4.27323e10i	−0.0568417	−	0.188521i
$691$	−3.24008e11	+	1.17929e11i	−1.42116	+	0.517260i	−0.934384	−	0.356267i	$-0.884049\pi$
$691$	−3.24008e11	+	1.17929e11i	−1.42116	+	0.517260i	−0.486776	+	0.873527i	$0.661827\pi$
$692$	−6.20503e10	+	3.58248e10i	−0.270595	+	0.156228i
$693$	−8.98123e9	−	6.63181e9i	−0.0389406	−	0.0287541i
$694$	−2.82619e10	+	4.89511e10i	−0.121833	+	0.211020i
$695$	3.13464e11	+	5.52722e10i	1.34353	+	0.236901i
$696$	2.82493e9	+	1.58988e8i	0.0120385	+	0.000677528i
$697$	−7.00230e9	−	2.54863e9i	−0.0296695	−	0.0107988i
$698$	1.93059e11	−	3.40414e10i	0.813331	−	0.143412i
$699$	6.22846e10	−	7.40359e9i	0.260899	−	0.0310123i
$700$	−2.47176e9	−	2.07405e9i	−0.0102947	−	0.00863829i
$701$			2.61847e11i			1.08437i	0.840261	+	0.542183i	$0.182402\pi$
$701$			2.61847e11i			1.08437i	−0.840261	+	0.542183i	$0.817598\pi$
$702$	1.36650e11	−	5.06468e10i	0.562678	−	0.208547i
$703$	−1.82002e11			−0.745169
$704$	−3.59850e10	+	4.28853e10i	−0.146498	+	0.174589i
$705$	−3.31054e11	+	2.47469e11i	−1.34011	+	1.00176i
$706$	−2.46722e10	−	1.39923e11i	−0.0993090	−	0.563209i
$707$	8.99396e8	−	2.47107e9i	0.00359976	−	0.00989026i
$708$	−1.75750e11	−	1.15100e11i	−0.699458	−	0.458083i
$709$	5.23157e10	−	2.96697e11i	0.207037	−	1.17416i	−0.687166	−	0.726500i	$-0.741146\pi$
$709$	5.23157e10	−	2.96697e11i	0.207037	−	1.17416i	0.894203	−	0.447662i	$-0.147743\pi$
$710$	−3.64808e11	−	2.10622e11i	−1.43559	−	0.828838i
$711$	−1.82463e10	−	2.93486e11i	−0.0713997	−	1.14844i
$712$	3.02144e10	+	5.23328e10i	0.117569	+	0.203636i
$713$	3.08021e10	+	8.46281e10i	0.119185	+	0.327459i
$714$	−3.35033e9	−	3.14851e9i	−0.0128913	−	0.0121147i
$715$	−4.39452e11	+	3.68744e11i	−1.68146	+	1.41092i
$716$	1.43511e11	+	1.71030e11i	0.546052	+	0.650759i
$717$	4.23747e11	+	9.95546e10i	1.60336	+	0.376691i
$718$	8.28005e9	−	3.01369e9i	0.0311555	−	0.0113397i
$719$	−2.95750e11	+	1.70751e11i	−1.10665	+	0.638923i	−0.937959	−	0.346747i	$-0.887286\pi$
$719$	−2.95750e11	+	1.70751e11i	−1.10665	+	0.638923i	−0.168688	+	0.985670i	$0.553953\pi$
$720$	6.90673e10	−	6.56744e10i	0.257005	−	0.244380i
$721$	4.17599e9	−	7.23303e9i	0.0154532	−	0.0267657i
$722$	7.46082e10	+	1.31554e10i	0.274560	+	0.0484124i
$723$	−6.59618e10	−	1.30703e11i	−0.241401	−	0.478333i
$724$	8.14568e10	+	2.96478e10i	0.296465	+	0.107904i
$725$	9.39395e9	−	1.65641e9i	0.0340014	−	0.00599536i
$726$	−1.80028e11	+	4.19608e11i	−0.648029	+	1.51042i
$727$	1.12427e11	+	9.43375e10i	0.402470	+	0.337712i	0.821447	−	0.570284i	$-0.193167\pi$
$727$	1.12427e11	+	9.43375e10i	0.402470	+	0.337712i	−0.418978	+	0.907997i	$0.637611\pi$
$728$			2.23746e9i			0.00796579i
$729$	−2.14207e11	+	1.84070e11i	−0.758445	+	0.651737i
$730$	1.77281e11			0.624267
$731$	1.60104e11	−	1.90804e11i	0.560701	−	0.668218i
$732$	7.80666e9	+	3.34936e9i	0.0271907	+	0.0116659i
$733$	−7.10478e10	−	4.02932e11i	−0.246113	−	1.39578i	−0.817894	−	0.575369i	$-0.804858\pi$
$733$	−7.10478e10	−	4.02932e11i	−0.246113	−	1.39578i	0.571781	−	0.820406i	$-0.306253\pi$
$734$	2.78128e10	−	7.64151e10i	0.0958211	−	0.263266i
$735$	3.69342e11	−	1.86396e11i	1.26555	−	0.638687i
$736$	−1.76816e9	+	1.00277e10i	−0.00602574	+	0.0341737i
$737$	−2.91708e11	−	1.68418e11i	−0.988731	−	0.570844i
$738$	−4.84286e9	−	5.09305e9i	−0.0163259	−	0.0171693i
$739$	−1.58737e10	−	2.74941e10i	−0.0532231	−	0.0921852i	0.838186	−	0.545384i	$-0.183616\pi$
$739$	−1.58737e10	−	2.74941e10i	−0.0532231	−	0.0921852i	−0.891410	+	0.453199i	$0.850283\pi$
$740$	4.59075e10	+	1.26130e11i	0.153093	+	0.420621i
$741$	6.90973e10	−	2.94108e11i	0.229186	−	0.975514i
$742$	−4.33108e9	+	3.63420e9i	−0.0142883	+	0.0119893i
$743$	−2.98847e11	−	3.56152e11i	−0.980605	−	1.16864i	−0.985676	−	0.168653i	$-0.946058\pi$
$743$	−2.98847e11	−	3.56152e11i	−0.980605	−	1.16864i	0.00507025	−	0.999987i	$-0.498386\pi$
$744$	−1.31697e11	+	1.40139e11i	−0.429819	+	0.457371i
$745$	3.48109e11	−	1.26701e11i	1.13003	−	0.411297i
$746$	−1.60566e11	+	9.27028e10i	−0.518440	+	0.299321i
$747$	4.84924e11	−	3.01482e10i	1.55737	−	0.0968231i
$748$	−1.34463e11	+	2.32897e11i	−0.429534	+	0.743975i
$749$	5.03893e9	+	8.88499e8i	0.0160107	+	0.00282312i
$750$	2.15199e9	−	3.28593e9i	0.00680135	−	0.0103852i
$751$	2.02179e11	+	7.35871e10i	0.635588	+	0.231335i	0.639662	−	0.768657i	$-0.279074\pi$
$751$	2.02179e11	+	7.35871e10i	0.635588	+	0.231335i	−0.00407359	+	0.999992i	$0.501297\pi$
$752$	9.28631e10	−	1.63743e10i	0.290383	−	0.0512024i
$753$	−1.06267e11	−	1.42160e11i	−0.330537	−	0.442179i
$754$	−5.06703e9	−	4.25174e9i	−0.0156772	−	0.0131547i
$755$		−	1.07828e11i		−	0.331850i

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)

\(f(q)\)	\(=\)	\(q+(-7.27231 + 8.66680i) q^{2} +(-74.4381 - 31.9369i) q^{3} +(-22.2270 - 126.055i) q^{4} +(-303.240 + 833.145i) q^{5} +(818.128 - 412.886i) q^{6} +(-11.0691 + 62.7758i) q^{7} +(1254.14 + 724.077i) q^{8} +(4521.07 + 4754.64i) q^{9} +O(q^{10})\)	\(q+(-7.27231 + 8.66680i) q^{2} +(-74.4381 - 31.9369i) q^{3} +(-22.2270 - 126.055i) q^{4} +(-303.240 + 833.145i) q^{5} +(818.128 - 412.886i) q^{6} +(-11.0691 + 62.7758i) q^{7} +(1254.14 + 724.077i) q^{8} +(4521.07 + 4754.64i) q^{9} +(-5015.45 - 8687.01i) q^{10} +(9130.11 + 25084.8i) q^{11} +(-2371.28 + 10093.2i) q^{12} +(18567.5 - 15580.0i) q^{13} +(-463.568 - 552.458i) q^{14} +(49180.6 - 52333.2i) q^{15} +(-15395.9 + 5603.66i) q^{16} +(-68160.2 + 39352.3i) q^{17} +(-74086.2 + 4606.01i) q^{18} +(-76941.2 + 133266. i) q^{19} +(111762. + 19706.7i) q^{20} +(2828.82 - 4319.40i) q^{21} +(-283802. - 103295. i) q^{22} +(-54097.6 + 9538.86i) q^{23} +(-70231.0 - 93952.2i) q^{24} +(-302939. - 254196. i) q^{25} +274223. i q^{26} +(-184692. - 498316. i) q^{27} +8159.26 q^{28} +(-15504.7 + 18477.7i) q^{29} +(95904.7 + 806822. i) q^{30} +(-284690. - 1.61456e6i) q^{31} +(63398.2 - 174185. i) q^{32} +(121501. - 2.15885e6i) q^{33} +(154623. - 876913. i) q^{34} +(-48944.7 - 28258.2i) q^{35} +(498859. - 675587. i) q^{36} +(591367. + 1.02428e6i) q^{37} +(-595450. - 1.63599e6i) q^{38} +(-1.87970e6 + 566757. i) q^{39} +(-983566. + 825310. i) q^{40} +(60858.7 + 72528.6i) q^{41} +(16863.3 + 55928.9i) q^{42} +(-2.97385e6 + 1.08239e6i) q^{43} +(2.95914e6 - 1.70846e6i) q^{44} +(-5.33227e6 + 2.32491e6i) q^{45} +(310743. - 538223. i) q^{46} +(-5.66791e6 - 999406. i) q^{47} +(1.32501e6 + 74571.7i) q^{48} +(5.41332e6 + 1.97029e6i) q^{49} +(4.40614e6 - 776921. i) q^{50} +(6.33050e6 - 752489. i) q^{51} +(-2.37664e6 - 1.99424e6i) q^{52} -7.83964e6i q^{53} +(5.66194e6 + 2.02322e6i) q^{54} -2.36678e7 q^{55} +(-59336.6 + 70714.7i) q^{56} +(9.98346e6 - 7.46282e6i) q^{57} +(-47388.2 - 268752. i) q^{58} +(-6.93032e6 + 1.90409e7i) q^{59} +(-7.69002e6 - 5.03628e6i) q^{60} +(142275. - 806884. i) q^{61} +(1.60634e7 + 9.27422e6i) q^{62} +(-348520. + 231184. i) q^{63} +(1.04858e6 + 1.81619e6i) q^{64} +(7.34997e6 + 2.01939e7i) q^{65} +(1.78267e7 + 1.67529e7i) q^{66} +(-9.66601e6 + 8.11075e6i) q^{67} +(6.47556e6 + 7.71727e6i) q^{68} +(4.33156e6 + 1.01765e6i) q^{69} +(600850. - 218691. i) q^{70} +(3.63684e7 - 2.09973e7i) q^{71} +(2.22732e6 + 9.23659e6i) q^{72} +(-8.83674e6 + 1.53057e7i) q^{73} +(-1.31778e7 - 2.32361e6i) q^{74} +(1.44320e7 + 2.85968e7i) q^{75} +(1.85091e7 + 6.73675e6i) q^{76} +(-1.67578e6 + 295485. i) q^{77} +(8.75783e6 - 2.04127e7i) q^{78} +(-3.43327e7 - 2.88086e7i) q^{79} -1.45263e7i q^{80} +(-2.16652e6 + 4.29922e7i) q^{81} -1.07117e6 q^{82} +(4.76002e7 - 5.67277e7i) q^{83} +(-607360. - 260581. i) q^{84} +(-1.21173e7 - 6.87204e7i) q^{85} +(1.22459e7 - 3.36453e7i) q^{86} +(1.74426e6 - 880279. i) q^{87} +(-6.71289e6 + 3.80707e7i) q^{88} +(3.61376e7 + 2.08641e7i) q^{89} +(1.86284e7 - 6.31212e7i) q^{90} +(772520. + 1.33804e6i) q^{91} +(2.40485e6 + 6.60727e6i) q^{92} +(-3.03721e7 + 1.29277e8i) q^{93} +(4.98805e7 - 4.18547e7i) q^{94} +(-8.76983e7 - 1.04515e8i) q^{95} +(-1.02822e7 + 1.09413e7i) q^{96} +(-5.20097e7 + 1.89300e7i) q^{97} +(-5.64435e7 + 3.25877e7i) q^{98} +(-7.79912e7 + 1.56820e8i) 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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