LMFDB - Embedded newform 54.9.f.a.5.2

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			5.2
Character	$\chi$	$=$	54.5
Dual form			54.9.f.a.11.2

$q$-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 $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

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

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
$3$	−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	−0.904996	−	0.425420i	$-0.860126\pi$
$5$	−303.240	−	833.145i	−0.485184	−	1.33303i	0.419812	−	0.907611i	$-0.362096\pi$
$6$	818.128	+	412.886i	0.631272	+	0.318585i
$7$	−11.0691	−	62.7758i	−0.00461019	−	0.0261457i	0.982416	−	0.186706i	$-0.0597811\pi$
$7$	−11.0691	−	62.7758i	−0.00461019	−	0.0261457i	−0.987026	+	0.160560i	$0.948670\pi$
$8$	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	−0.0744041	−	0.997228i	$-0.523705\pi$
$11$	9130.11	−	25084.8i	0.623599	−	1.71332i	0.698003	−	0.716095i	$-0.254072\pi$
$12$	−2371.28	−	10093.2i	−0.114356	−	0.486747i
$13$	18567.5	+	15580.0i	0.650099	+	0.545498i	0.907101	−	0.420913i	$-0.138290\pi$
$13$	18567.5	+	15580.0i	0.650099	+	0.545498i	−0.257002	+	0.966411i	$0.582735\pi$
$14$	−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	0.0329802	−	0.999456i	$-0.489500\pi$
$17$	−68160.2	−	39352.3i	−0.816084	−	0.471166i	−0.849064	+	0.528290i	$0.822834\pi$
$18$	−74086.2	−	4606.01i	−0.705744	−	0.0438768i
$19$	−76941.2	−	133266.i	−0.590398	−	1.02260i	−0.994179	−	0.107743i	$-0.965638\pi$
$19$	−76941.2	−	133266.i	−0.590398	−	1.02260i	0.403781	−	0.914856i	$-0.367696\pi$
$20$	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	0.0761521	−	0.997096i	$-0.475737\pi$
$23$	−54097.6	−	9538.86i	−0.193315	−	0.0340867i	−0.269467	+	0.963009i	$0.586848\pi$
$24$	−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	0.754972	−	0.655757i	$-0.227650\pi$
$29$	−15504.7	−	18477.7i	−0.0219215	−	0.0261250i	−0.776894	+	0.629632i	$0.783206\pi$
$30$	95904.7	−	806822.i	0.118401	−	0.996077i
$31$	−284690.	+	1.61456e6i	−0.308266	+	1.74826i	0.299452	+	0.954111i	$0.403196\pi$
$31$	−284690.	+	1.61456e6i	−0.308266	+	1.74826i	−0.607718	+	0.794153i	$0.707915\pi$
$32$	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	−0.664015	−	0.747720i	$-0.731149\pi$
$37$	591367.	−	1.02428e6i	0.315537	−	0.546526i	0.979551	+	0.201194i	$0.0644820\pi$
$38$	−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	−0.755168	−	0.655531i	$-0.772445\pi$
$41$	60858.7	−	72528.6i	0.0215371	−	0.0256669i	0.776705	+	0.629864i	$0.216889\pi$
$42$	16863.3	−	55928.9i	0.00541933	−	0.0179738i
$43$	−2.97385e6	−	1.08239e6i	−0.869852	−	0.316600i	−0.131745	−	0.991284i	$-0.542058\pi$
$43$	−2.97385e6	−	1.08239e6i	−0.869852	−	0.316600i	−0.738107	+	0.674683i	$0.764280\pi$
$44$	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	−0.721006	−	0.692929i	$-0.756320\pi$
$47$	−5.66791e6	+	999406.i	−1.16153	+	0.204810i	−0.440528	+	0.897739i	$0.645209\pi$
$48$	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	$0.165484\pi$
$53$			7.83964e6i			0.993557i	−0.867877	+	0.496778i	$0.834516\pi$
$54$	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	−0.801445	−	0.598068i	$-0.795935\pi$
$59$	−6.93032e6	−	1.90409e7i	−0.571933	−	1.57137i	0.229512	−	0.973306i	$-0.426287\pi$
$60$	−7.69002e6	+	5.03628e6i	−0.593366	+	0.388602i
$61$	142275.	+	806884.i	0.0102757	+	0.0582763i	0.989514	−	0.144434i	$-0.0461361\pi$
$61$	142275.	+	806884.i	0.0102757	+	0.0582763i	−0.979239	+	0.202710i	$0.935025\pi$
$62$	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	0.370633	−	0.928779i	$-0.379141\pi$
$67$	−9.66601e6	−	8.11075e6i	−0.479676	−	0.402496i	−0.850309	+	0.526283i	$0.823585\pi$
$68$	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	0.997210	−	0.0746471i	$-0.0237830\pi$
$71$	3.63684e7	+	2.09973e7i	1.43117	+	0.826286i	0.433959	+	0.900933i	$0.357116\pi$
$72$	2.22732e6	−	9.23659e6i	0.0828807	−	0.343702i
$73$	−8.83674e6	−	1.53057e7i	−0.311172	−	0.538966i	0.667444	−	0.744660i	$-0.267388\pi$
$73$	−8.83674e6	−	1.53057e7i	−0.311172	−	0.538966i	−0.978616	+	0.205694i	$0.934055\pi$
$74$	−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	−0.966478	−	0.256750i	$-0.917348\pi$
$79$	−3.43327e7	+	2.88086e7i	−0.881455	+	0.739629i	0.0850227	+	0.996379i	$0.472904\pi$
$80$			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	0.980691	+	0.195565i	$0.0626542\pi$
$83$	4.76002e7	+	5.67277e7i	1.00299	+	1.19532i	0.0222992	+	0.999751i	$0.492901\pi$
$84$	−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	−0.183561	−	0.983008i	$-0.558762\pi$
$89$	3.61376e7	−	2.08641e7i	0.575969	−	0.332536i	0.759530	+	0.650472i	$0.225429\pi$
$90$	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	0.0311371	−	0.999515i	$-0.490087\pi$
$97$	−5.20097e7	−	1.89300e7i	−0.587486	−	0.213828i	−0.618624	+	0.785688i	$0.712309\pi$
$98$	−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	−0.365409	−	0.930847i	$-0.619071\pi$
$101$	−4.06266e7	+	7.16356e6i	−0.390413	+	0.0688404i	−0.0250041	+	0.999687i	$0.507960\pi$
$102$	−3.95157e7	−	6.03376e7i	−0.365064	−	0.557426i
$103$	−1.23122e8	+	4.48127e7i	−1.09392	+	0.398155i	−0.825072	−	0.565027i	$-0.808866\pi$
$103$	−1.23122e8	+	4.48127e7i	−1.09392	+	0.398155i	−0.268849	+	0.963182i	$0.586643\pi$
$104$	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	$0.0990519\pi$
$107$			8.02687e7i			0.612366i	−0.951973	+	0.306183i	$0.900948\pi$
$108$	−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	0.906914	+	0.421317i	$0.138432\pi$
$113$	7.87510e7	+	2.16367e8i	0.482995	+	1.32702i	−0.423919	+	0.905700i	$0.639346\pi$
$114$	−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	0.822312	+	0.569036i	$0.192684\pi$
$127$	2.35159e8	+	4.07308e8i	0.903956	+	1.56570i	0.0816437	+	0.996662i	$0.473983\pi$
$128$	−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	−0.293601	−	0.955928i	$-0.594854\pi$
$131$	−2.64002e8	−	4.65507e7i	−0.896442	−	0.158067i	−0.602841	+	0.797861i	$0.705965\pi$
$132$	−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	0.484216	−	0.874948i	$-0.339105\pi$
$137$	−1.62583e8	−	1.93759e8i	−0.461523	−	0.550022i	−0.945739	+	0.324926i	$0.894660\pi$
$138$	−4.03203e7	−	3.01401e7i	−0.111175	−	0.0831053i
$139$	−6.23408e7	+	3.53552e8i	−0.166999	+	0.947096i	0.779981	+	0.625803i	$0.215229\pi$
$139$	−6.23408e7	+	3.53552e8i	−0.166999	+	0.947096i	−0.946980	+	0.321293i	$0.895882\pi$
$140$	−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	−0.966279	−	0.257498i	$-0.917102\pi$
$149$	−2.68573e8	+	3.20073e8i	−0.544900	+	0.649387i	0.421379	+	0.906885i	$0.361546\pi$
$150$	−3.52797e8	+	8.28857e7i	−0.696883	+	0.163725i
$151$	−1.14283e8	−	4.15956e7i	−0.219823	−	0.0800091i	0.229761	−	0.973247i	$-0.426206\pi$
$151$	−1.14283e8	−	4.15956e7i	−0.219823	−	0.0800091i	−0.449584	+	0.893238i	$0.648428\pi$
$152$	−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	−0.269969	−	0.962869i	$-0.587013\pi$
$157$	8.63622e7	−	3.14333e7i	0.142143	−	0.0517357i	0.412112	+	0.911133i	$0.364791\pi$
$158$	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	−0.960365	−	0.278746i	$-0.910081\pi$
$167$	−3.14119e8	−	8.63034e8i	−0.403857	−	1.10959i	0.556508	−	0.830842i	$-0.312141\pi$
$168$	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	−0.999511	−	0.0312832i	$-0.990041\pi$
$173$	−1.91450e8	+	5.26004e8i	−0.213733	+	0.587225i	0.785778	+	0.618509i	$0.212263\pi$
$174$	−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	−0.471903	−	0.881650i	$-0.656433\pi$
$179$	−1.51056e9	−	8.72124e8i	−1.47139	−	0.849505i	−0.999483	+	0.0321448i	$0.989766\pi$
$180$	4.11588e8	−	6.20486e8i	0.392078	−	0.591074i
$181$	−3.38611e8	−	5.86492e8i	−0.315491	−	0.546447i	0.664051	−	0.747688i	$-0.268836\pi$
$181$	−3.38611e8	−	5.86492e8i	−0.315491	−	0.546447i	−0.979542	+	0.201241i	$0.935503\pi$
$182$	−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	−1.00000		0.000881673i	$-0.999719\pi$
$191$	−1.10092e9	−	1.31202e9i	−0.827220	−	0.985842i	0.172780	−	0.984960i	$-0.444725\pi$
$192$	−2.00507e7	+	1.68682e8i	−0.0147545	+	0.124126i
$193$	−3.48843e7	+	1.97839e8i	−0.0251420	+	0.142588i	−0.994795	−	0.101899i	$-0.967508\pi$
$193$	−3.48843e7	+	1.97839e8i	−0.0251420	+	0.142588i	0.969653	+	0.244486i	$0.0786193\pi$
$194$	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	0.603390	−	0.797446i	$-0.293816\pi$
$197$	2.40334e9	−	1.38757e9i	1.59569	−	0.921274i	0.992304	−	0.123828i	$-0.0395170\pi$
$198$	−7.91956e8	+	1.81638e9i	−0.515276	+	1.18181i
$199$	−9.47443e8	+	1.64102e9i	−0.604144	+	1.04641i	0.388042	+	0.921642i	$0.373152\pi$
$199$	−9.47443e8	+	1.64102e9i	−0.604144	+	1.04641i	−0.992186	+	0.124767i	$0.960182\pi$
$200$	−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	−0.0191686	−	0.999816i	$-0.506102\pi$
$211$	1.20675e9	−	4.39220e8i	0.608817	−	0.221591i	0.627986	+	0.778225i	$0.283880\pi$
$212$	−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	0.997176	−	0.0751051i	$-0.0239292\pi$
$223$	8.51929e7	+	4.83153e8i	0.0344496	+	0.195373i	−0.962726	+	0.270478i	$0.912818\pi$
$224$	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	−0.921562	−	0.388231i	$-0.873086\pi$
$227$	9.01326e7	−	2.47637e8i	0.0339452	−	0.0932637i	0.955507	+	0.294967i	$0.0953086\pi$
$228$	−1.16263e9	+	1.09259e9i	−0.430232	+	0.404314i
$229$	2.16367e9	+	1.81554e9i	0.786773	+	0.660181i	0.944944	−	0.327231i	$-0.106116\pi$
$229$	2.16367e9	+	1.81554e9i	0.786773	+	0.660181i	−0.158172	+	0.987412i	$0.550560\pi$
$230$	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	0.381899	−	0.924204i	$-0.375270\pi$
$233$	−6.70615e8	−	3.87179e8i	−0.227536	−	0.131368i	−0.609435	+	0.792836i	$0.708604\pi$
$234$	−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	−0.712484	−	0.701689i	$-0.752430\pi$
$239$	−5.29225e9	−	9.33166e8i	−1.62199	−	0.286001i	−0.909507	+	0.415688i	$0.863541\pi$
$240$	−4.63924e8	−	1.08131e9i	−0.139830	−	0.325916i
$241$	1.38459e9	−	1.16181e9i	0.410444	−	0.344403i	−0.414070	−	0.910245i	$-0.635893\pi$
$241$	1.38459e9	−	1.16181e9i	0.410444	−	0.344403i	0.824514	+	0.565842i	$0.191449\pi$
$242$			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	−0.241522	−	0.970395i	$-0.577647\pi$
$251$	1.89765e9	−	1.09561e9i	0.478104	−	0.276033i	0.719626	+	0.694362i	$0.244313\pi$
$252$	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	−0.998535	−	0.0541052i	$-0.982769\pi$
$257$	−3.36721e9	+	4.01288e9i	−0.771858	+	0.919865i	0.226677	+	0.973970i	$0.427214\pi$
$258$	−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	−0.321814	−	0.946803i	$-0.604293\pi$
$263$	−1.43719e9	+	2.53416e8i	−0.300394	+	0.0529676i	0.0214195	+	0.999771i	$0.493181\pi$
$264$	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	$-0.710584\pi$
$269$		−	8.26288e9i		−	1.57806i	0.614357	−	0.789028i	$-0.289416\pi$
$270$	−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	−0.980754	−	0.195248i	$-0.937449\pi$
$277$	−7.41366e8	−	4.20449e9i	−0.125925	−	0.714159i	0.854828	−	0.518911i	$-0.173662\pi$
$278$	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	−0.163511	−	0.986542i	$-0.552282\pi$
$281$	3.71523e9	−	1.02075e10i	0.595882	−	1.63717i	0.759393	−	0.650632i	$-0.225496\pi$
$282$	−5.04972e9	−	1.52256e9i	−0.798492	−	0.240756i
$283$	−6.88289e9	−	5.77543e9i	−1.07306	−	0.900407i	−0.0777365	−	0.996974i	$-0.524769\pi$
$283$	−6.88289e9	−	5.77543e9i	−1.07306	−	0.900407i	−0.995326	+	0.0965672i	$0.969214\pi$
$284$	−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	0.681760	−	0.731576i	$-0.261215\pi$
$293$	7.90211e9	+	1.39336e9i	1.07219	+	0.189056i	0.390432	+	0.920632i	$0.372326\pi$
$294$	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	0.137442	+	0.990510i	$0.456112\pi$
$307$	−7.00935e9	+	1.21405e10i	−0.789086	+	1.36674i	−0.926528	+	0.376227i	$0.877221\pi$
$308$	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	−0.769148	−	0.639070i	$-0.779319\pi$
$311$	−5.82406e7	+	6.94085e7i	−0.00622565	+	0.00741944i	0.762923	+	0.646490i	$0.223764\pi$
$312$	−2.76779e9	+	6.50260e8i	−0.292088	+	0.0686228i
$313$	−2.49888e8	−	9.09519e7i	−0.0260357	−	0.00947621i	0.328969	−	0.944341i	$-0.393299\pi$
$313$	−2.49888e8	−	9.09519e7i	−0.0260357	−	0.00947621i	−0.355005	+	0.934864i	$0.615521\pi$
$314$	−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	0.194020	−	0.980998i	$-0.437847\pi$
$317$	7.18838e9	−	1.26751e9i	0.711859	−	0.125520i	0.517840	+	0.855478i	$0.326736\pi$
$318$	−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	0.997206	+	0.0747004i	$0.0238000\pi$
$331$	1.02856e9	+	5.83328e9i	0.0856879	+	0.485960i	−0.911518	+	0.411260i	$0.865089\pi$
$332$	−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	0.562215	−	0.826991i	$-0.309949\pi$
$337$	−1.99381e9	−	1.67301e9i	−0.154584	−	0.129712i	−0.716799	+	0.697279i	$0.754394\pi$
$338$	−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	0.340731	−	0.940161i	$-0.389325\pi$
$347$	4.92015e9	+	8.67555e8i	0.339360	+	0.0598383i	−0.00137139	+	0.999999i	$0.500437\pi$
$348$	−1.49733e8	+	2.00307e8i	−0.0102094	+	0.0136578i
$349$	−1.32735e10	+	1.11378e10i	−0.894715	+	0.750755i	−0.969150	−	0.246471i	$-0.920729\pi$
$349$	−1.32735e10	+	1.11378e10i	−0.894715	+	0.750755i	0.0744352	+	0.997226i	$0.476285\pi$
$350$		−	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	0.440674	−	0.897667i	$-0.354739\pi$
$353$	−8.07235e9	−	9.62025e9i	−0.519877	−	0.619566i	−0.960552	+	0.278101i	$0.910295\pi$
$354$	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	−0.520166	−	0.854065i	$-0.674130\pi$
$359$	−6.74486e8	+	3.89415e8i	−0.0406064	+	0.0234441i	0.479559	+	0.877509i	$0.340797\pi$
$360$	−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	0.149084	−	0.988824i	$-0.452367\pi$
$367$	−6.75421e9	−	2.45833e9i	−0.372315	−	0.135511i	−0.521399	+	0.853313i	$0.674590\pi$
$368$	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	0.0879098	−	0.996128i	$-0.471981\pi$
$373$	1.53994e10	−	5.60492e9i	0.795552	−	0.289557i	0.707642	+	0.706571i	$0.249759\pi$
$374$	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	0.899978	−	0.435936i	$-0.143583\pi$
$383$	−1.49891e9	−	4.11823e9i	−0.0696597	−	0.191389i	−0.969637	+	0.244548i	$0.921360\pi$
$384$	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	−0.974640	−	0.223780i	$-0.928160\pi$
$389$	−1.92754e9	+	5.29586e9i	−0.0841791	+	0.231280i	0.890461	+	0.455061i	$0.150382\pi$
$390$	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	0.983667	−	0.180000i	$-0.0576098\pi$
$397$	8.34516e9	+	1.44542e10i	0.335949	+	0.581880i	−0.647718	+	0.761880i	$0.724276\pi$
$398$	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	−0.578627	−	0.815592i	$-0.696411\pi$
$401$	−3.62336e10	−	6.38896e9i	−1.40131	−	0.247088i	−0.822681	+	0.568504i	$0.807523\pi$
$402$	−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	−0.681510	−	0.731809i	$-0.738676\pi$
$409$	5.85385e9	−	3.31988e10i	0.209193	−	1.18639i	0.890703	−	0.454586i	$-0.150213\pi$
$410$	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	−0.773995	−	0.633192i	$-0.781745\pi$
$419$	−4.93771e8	+	5.88453e8i	−0.0160202	+	0.0190922i	0.757975	+	0.652284i	$0.226189\pi$
$420$	4.01277e8	+	4.27000e8i	0.0128958	+	0.0137224i
$421$	2.83636e10	+	1.03235e10i	0.902886	+	0.328624i	0.751409	−	0.659837i	$-0.229375\pi$
$421$	2.83636e10	+	1.03235e10i	0.902886	+	0.328624i	0.151478	+	0.988461i	$0.451597\pi$
$422$	−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	$-0.741305\pi$
$431$		−	5.01152e10i		−	1.45231i	0.687530	−	0.726156i	$-0.258695\pi$
$432$	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	−0.995522	−	0.0945249i	$-0.969867\pi$
$439$	−3.43063e9	−	1.94561e10i	−0.0923668	−	0.523838i	0.903156	−	0.429313i	$-0.141244\pi$
$440$	−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	0.0188697	+	0.999822i	$0.493993\pi$
$443$	−2.45817e10	+	6.75376e10i	−0.638258	+	1.75360i	−0.657128	+	0.753779i	$0.728229\pi$
$444$	−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	0.562676	−	0.826678i	$-0.309772\pi$
$449$	5.20595e9	+	3.00565e9i	0.128090	+	0.0739527i	−0.434586	+	0.900630i	$0.643105\pi$
$450$	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	−0.110427	−	0.993884i	$-0.535222\pi$
$457$	3.70396e10	−	3.10799e10i	0.849183	−	0.712549i	0.959610	+	0.281335i	$0.0907772\pi$
$458$		−	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	−0.998169	−	0.0604837i	$-0.980736\pi$
$461$	−3.99443e10	−	4.76037e10i	−0.884404	−	1.05399i	0.113765	−	0.993508i	$-0.463709\pi$
$462$	−1.24900e9	−	9.33649e8i	−0.0274154	−	0.0204935i
$463$	1.49946e9	−	8.50384e9i	0.0326295	−	0.185051i	−0.964137	−	0.265406i	$-0.914494\pi$
$463$	1.49946e9	−	8.50384e9i	0.0326295	−	0.185051i	0.996766	+	0.0803546i	$0.0256053\pi$
$464$	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	0.0605735	−	0.998164i	$-0.480707\pi$
$467$	4.54365e10	−	2.62328e10i	0.955295	−	0.551540i	0.894722	+	0.446624i	$0.147374\pi$
$468$	−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	0.343968	−	0.938981i	$-0.388229\pi$
$479$	5.20295e10	−	9.17420e9i	0.988343	−	0.174271i	0.644375	+	0.764710i	$0.277118\pi$
$480$	−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	0.865914	−	0.500193i	$-0.166738\pi$
$491$	−6.91237e9	−	1.89916e10i	−0.118933	−	0.326765i	−0.984846	+	0.173428i	$0.944515\pi$
$492$	−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	0.334404	−	0.942430i	$-0.391465\pi$
$499$	−3.32105e10	−	2.78669e10i	−0.535640	−	0.449455i	−0.870044	+	0.492975i	$0.835910\pi$
$500$	−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	−0.144116	−	0.989561i	$-0.546034\pi$
$503$	−6.86967e10	−	3.96621e10i	−1.07316	−	0.619589i	−0.929043	+	0.369972i	$0.879367\pi$
$504$	−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	−0.393733	−	0.919225i	$-0.628817\pi$
$509$	−7.23662e10	−	1.27601e10i	−1.07811	−	0.190101i	−0.684381	+	0.729124i	$0.739928\pi$
$510$	−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	−0.188440	−	0.982085i	$-0.560343\pi$
$521$	4.18393e10	−	2.41559e10i	0.567850	−	0.327848i	0.756290	+	0.654236i	$0.227010\pi$
$522$	1.06357e9	+	1.44036e9i	0.0143247	+	0.0193994i
$523$	−5.01333e10	+	8.68334e10i	−0.670069	+	1.16059i	0.307815	+	0.951446i	$0.400402\pi$
$523$	−5.01333e10	+	8.68334e10i	−0.670069	+	1.16059i	−0.977884	+	0.209147i	$0.932931\pi$
$524$	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	−0.742681	−	0.669646i	$-0.766446\pi$
$547$	−2.45141e10	−	1.39027e11i	−0.273821	−	1.55292i	0.468859	−	0.883273i	$-0.344665\pi$
$548$	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	0.487522	−	0.873111i	$-0.337901\pi$
$557$	−2.39225e9	−	1.38117e9i	−0.0248534	−	0.0143491i	−0.512375	+	0.858762i	$0.671234\pi$
$558$	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	0.420025	−	0.907512i	$-0.362021\pi$
$563$	5.06700e10	+	8.93448e9i	0.504333	+	0.0889274i	0.0843072	+	0.996440i	$0.473132\pi$
$564$	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	0.856554	+	0.516058i	$0.172601\pi$
$569$	1.27466e11	+	1.51908e11i	1.21603	+	1.44921i	0.359479	+	0.933153i	$0.382954\pi$
$570$	−1.14901e11	+	4.92970e10i	−1.08849	+	0.467005i
$571$	−1.53674e10	+	8.71529e10i	−0.144563	+	0.819856i	0.823155	+	0.567817i	$0.192212\pi$
$571$	−1.53674e10	+	8.71529e10i	−0.144563	+	0.819856i	−0.967717	+	0.252038i	$0.918899\pi$
$572$	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	−0.782670	−	0.622437i	$-0.786143\pi$
$577$	1.63726e10	−	2.83581e10i	0.147711	−	0.255843i	0.930381	+	0.366594i	$0.119476\pi$
$578$	−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	−0.314370	−	0.949300i	$-0.601793\pi$
$587$	−3.38496e10	+	5.96859e9i	−0.285102	+	0.0502712i	0.0292682	+	0.999572i	$0.490682\pi$
$588$	−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	$0.154830\pi$
$593$			1.15609e11i			0.934915i	−0.884016	+	0.467457i	$0.845170\pi$
$594$	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	−0.984014	−	0.178090i	$-0.943008\pi$
$599$	−4.43747e10	−	1.21918e11i	−0.344690	−	0.947027i	0.639325	−	0.768937i	$-0.279214\pi$
$600$	−2.60658e9	−	4.63143e10i	−0.0201125	−	0.357363i
$601$	4.05510e10	+	2.29976e11i	0.310816	+	1.76273i	0.594776	+	0.803891i	$0.297241\pi$
$601$	4.05510e10	+	2.29976e11i	0.310816	+	1.76273i	−0.283960	+	0.958836i	$0.591648\pi$
$602$	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	0.00165202	−	0.999999i	$-0.499474\pi$
$607$	−1.33429e11	−	1.11960e11i	−0.982868	−	0.824724i	−0.984520	+	0.175275i	$0.943919\pi$
$608$	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	−0.903119	−	0.429389i	$-0.858729\pi$
$613$	−1.16269e11	−	2.01384e11i	−0.823422	−	1.42621i	0.0796977	−	0.996819i	$-0.474605\pi$
$614$	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	0.0923789	−	0.995724i	$-0.470553\pi$
$617$	−2.33865e10	−	4.12368e9i	−0.161371	−	0.0284540i	−0.253750	+	0.967270i	$0.581664\pi$
$618$	−1.19232e11	−	1.41728e10i	−0.817408	−	0.0971629i
$619$	−1.59321e11	+	1.33686e11i	−1.08520	+	0.910591i	−0.996342	−	0.0854530i	$-0.972766\pi$
$619$	−1.59321e11	+	1.33686e11i	−1.08520	+	0.910591i	−0.0888583	+	0.996044i	$0.528322\pi$
$620$			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	−0.844099	−	0.536187i	$-0.819864\pi$
$631$	6.70620e9	−	1.16155e10i	0.0423018	−	0.0732689i	0.886401	+	0.462918i	$0.153198\pi$
$632$	−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	−0.472023	−	0.881586i	$-0.656476\pi$
$641$	−1.03667e11	+	1.82794e10i	−0.614059	+	0.108275i	−0.142036	+	0.989861i	$0.545365\pi$
$642$	−3.31418e10	+	6.56701e10i	−0.195090	+	0.386569i
$643$	−1.15569e11	+	4.20638e10i	−0.676082	+	0.246074i	−0.657164	−	0.753747i	$-0.728244\pi$
$643$	−1.15569e11	+	4.20638e10i	−0.676082	+	0.246074i	−0.0189174	+	0.999821i	$0.506022\pi$
$644$	−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	$0.197446\pi$
$647$			2.03718e11i			1.16255i	−0.813707	+	0.581276i	$0.802554\pi$
$648$	−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	0.944038	−	0.329837i	$-0.106994\pi$
$653$	1.60879e9	+	4.42011e9i	0.00884803	+	0.0243098i	−0.935190	+	0.354146i	$0.884771\pi$
$654$	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	0.601746	+	0.798687i	$0.294472\pi$
$659$	−7.02732e10	+	1.93074e11i	−0.372604	+	1.02372i	−0.974351	+	0.225035i	$0.927750\pi$
$660$	5.61231e10	+	2.38884e11i	0.295778	+	1.25896i
$661$	1.25081e11	+	1.04955e11i	0.655217	+	0.549792i	0.908649	−	0.417561i	$-0.137115\pi$
$661$	1.25081e11	+	1.04955e11i	0.655217	+	0.549792i	−0.253432	+	0.967353i	$0.581559\pi$
$662$	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	−0.761356	−	0.648335i	$-0.775466\pi$
$673$	−5.23280e10	+	4.39084e10i	−0.255079	+	0.214036i	0.506277	+	0.862371i	$0.331021\pi$
$674$			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	0.263535	−	0.964650i	$-0.415112\pi$
$677$	−1.53815e11	−	1.83309e11i	−0.732222	−	0.872629i	−0.995757	+	0.0920212i	$0.970667\pi$
$678$	−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	−0.00362853	−	0.999993i	$-0.501155\pi$
$683$	1.87272e11	−	1.08121e11i	0.860577	−	0.496854i	0.864205	+	0.503139i	$0.167822\pi$
$684$	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	−0.486776	−	0.873527i	$-0.661827\pi$
$691$	−3.24008e11	−	1.17929e11i	−1.42116	−	0.517260i	−0.934384	+	0.356267i	$0.884049\pi$
$692$	−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	$-0.817598\pi$
$701$		−	2.61847e11i		−	1.08437i	0.840261	−	0.542183i	$-0.182402\pi$
$702$	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	0.894203	+	0.447662i	$0.147743\pi$
$709$	5.23157e10	+	2.96697e11i	0.207037	+	1.17416i	−0.687166	+	0.726500i	$0.741146\pi$
$710$	−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	−0.168688	−	0.985670i	$-0.553953\pi$
$719$	−2.95750e11	−	1.70751e11i	−1.10665	−	0.638923i	−0.937959	+	0.346747i	$0.887286\pi$
$720$	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	−0.418978	−	0.907997i	$-0.637611\pi$
$727$	1.12427e11	−	9.43375e10i	0.402470	−	0.337712i	0.821447	+	0.570284i	$0.193167\pi$
$728$		−	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	0.571781	+	0.820406i	$0.306253\pi$
$733$	−7.10478e10	+	4.02932e11i	−0.246113	+	1.39578i	−0.817894	+	0.575369i	$0.804858\pi$
$734$	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	−0.891410	−	0.453199i	$-0.850283\pi$
$739$	−1.58737e10	+	2.74941e10i	−0.0532231	+	0.0921852i	0.838186	+	0.545384i	$0.183616\pi$
$740$	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	0.00507025	+	0.999987i	$0.498386\pi$
$743$	−2.98847e11	+	3.56152e11i	−0.980605	+	1.16864i	−0.985676	+	0.168653i	$0.946058\pi$
$744$	−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	−0.00407359	−	0.999992i	$-0.501297\pi$
$751$	2.02179e11	−	7.35871e10i	0.635588	−	0.231335i	0.639662	+	0.768657i	$0.279074\pi$
$752$	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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more