LMFDB - Embedded newform 9.9.d.a.5.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,9,Mod(2,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("9.2");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	9.d (of order $6$, degree $2$, 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:	$3.66640749055$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 427 x^{12} - 1362 x^{11} + 135762 x^{10} - 371244 x^{9} + 18261508 x^{8} + \cdots + 872385888256 $ x^14 - x^13 + 427x^12 - 1362x^11 + 135762x^10 - 371244x^9 + 18261508x^8 - 29352736x^7 + 1757083840x^6 - 1434930432x^5 + 61638378240x^4 + 183604924416x^3 + 1254910111744x^2 + 1078377512960x + 872385888256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{21} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.5
Root			$-2.00397 + 3.47098i$ of defining polynomial
Character	$\chi$	$=$	9.5
Dual form			9.9.d.a.2.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.01192 - 3.47098i) q^{2} +(-29.7082 + 75.3553i) q^{3} +(-103.905 + 179.968i) q^{4} +(331.396 + 191.331i) q^{5} +(82.9534 + 556.147i) q^{6} +(467.516 + 809.762i) q^{7} +3219.75i q^{8} +(-4795.84 - 4477.35i) q^{9} +O(q^{10})$	\(q+(6.01192 - 3.47098i) q^{2} +(-29.7082 + 75.3553i) q^{3} +(-103.905 + 179.968i) q^{4} +(331.396 + 191.331i) q^{5} +(82.9534 + 556.147i) q^{6} +(467.516 + 809.762i) q^{7} +3219.75i q^{8} +(-4795.84 - 4477.35i) q^{9} +2656.43 q^{10} +(4890.10 - 2823.30i) q^{11} +(-10474.7 - 13176.3i) q^{12} +(17663.1 - 30593.3i) q^{13} +(5621.34 + 3245.48i) q^{14} +(-24263.0 + 19288.3i) q^{15} +(-15423.9 - 26714.9i) q^{16} +152914. i q^{17} +(-44373.0 - 10271.2i) q^{18} +191248. q^{19} +(-68867.1 + 39760.4i) q^{20} +(-74908.9 + 11173.2i) q^{21} +(19599.3 - 33947.0i) q^{22} +(132313. + 76390.7i) q^{23} +(-242625. - 95653.1i) q^{24} +(-122097. - 211478. i) q^{25} -245233. i q^{26} +(479868. - 228378. i) q^{27} -194308. q^{28} +(401612. - 231871. i) q^{29} +(-78918.0 + 200176. i) q^{30} +(-393956. + 682351. i) q^{31} +(-899280. - 519200. i) q^{32} +(67474.4 + 452371. i) q^{33} +(530763. + 919308. i) q^{34} +357802. i q^{35} +(1.30409e6 - 397881. i) q^{36} -1.10561e6 q^{37} +(1.14977e6 - 663818. i) q^{38} +(1.78063e6 + 2.23988e6i) q^{39} +(-616039. + 1.06701e6i) q^{40} +(-3.14915e6 - 1.81816e6i) q^{41} +(-411564. + 327180. i) q^{42} +(-1.51318e6 - 2.62091e6i) q^{43} +1.17342e6i q^{44} +(-732664. - 2.40137e6i) q^{45} +1.06060e6 q^{46} +(4.75308e6 - 2.74419e6i) q^{47} +(2.47133e6 - 368617. i) q^{48} +(2.44526e6 - 4.23531e6i) q^{49} +(-1.46808e6 - 847594. i) q^{50} +(-1.15229e7 - 4.54281e6i) q^{51} +(3.67054e6 + 6.35757e6i) q^{52} +1.41381e7i q^{53} +(2.09223e6 - 3.03860e6i) q^{54} +2.16075e6 q^{55} +(-2.60723e6 + 1.50528e6i) q^{56} +(-5.68163e6 + 1.44115e7i) q^{57} +(1.60964e6 - 2.78797e6i) q^{58} +(7.58082e6 + 4.37679e6i) q^{59} +(-950238. - 6.37071e6i) q^{60} +(-3.47102e6 - 6.01198e6i) q^{61} +5.46965e6i q^{62} +(1.38345e6 - 5.97672e6i) q^{63} +688484. q^{64} +(1.17069e7 - 6.75900e6i) q^{65} +(1.97582e6 + 2.48541e6i) q^{66} +(7.08899e6 - 1.22785e7i) q^{67} +(-2.75197e7 - 1.58885e7i) q^{68} +(-9.68722e6 + 7.70102e6i) q^{69} +(1.24193e6 + 2.15108e6i) q^{70} -7.97888e6i q^{71} +(1.44159e7 - 1.54414e7i) q^{72} -4.61414e6 q^{73} +(-6.64682e6 + 3.83754e6i) q^{74} +(1.95633e7 - 2.91801e6i) q^{75} +(-1.98715e7 + 3.44184e7i) q^{76} +(4.57241e6 + 2.63988e6i) q^{77} +(1.84796e7 + 7.28544e6i) q^{78} +(-1.37621e6 - 2.38366e6i) q^{79} -1.18043e7i q^{80} +(2.95344e6 + 4.29453e7i) q^{81} -2.52433e7 q^{82} +(3.52291e7 - 2.03395e7i) q^{83} +(5.77256e6 - 1.46422e7i) q^{84} +(-2.92573e7 + 5.06751e7i) q^{85} +(-1.81943e7 - 1.05045e7i) q^{86} +(5.54150e6 + 3.71520e7i) q^{87} +(9.09033e6 + 1.57449e7i) q^{88} -2.90621e7i q^{89} +(-1.27398e7 - 1.18938e7i) q^{90} +3.30311e7 q^{91} +(-2.74958e7 + 1.58747e7i) q^{92} +(-3.97150e7 - 4.99581e7i) q^{93} +(1.90501e7 - 3.29957e7i) q^{94} +(6.33787e7 + 3.65917e7i) q^{95} +(6.58405e7 - 5.23410e7i) q^{96} +(-4.58061e7 - 7.93386e7i) q^{97} -3.39498e7i q^{98} +(-3.60931e7 - 8.35459e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 3 q^{2} - 93 q^{3} + 767 q^{4} + 438 q^{5} - 2259 q^{6} + 922 q^{7} + 17973 q^{9}+O(q^{10}) $ 14 * q - 3 * q^2 - 93 * q^3 + 767 * q^4 + 438 * q^5 - 2259 * q^6 + 922 * q^7 + 17973 * q^9	\( 14 q - 3 q^{2} - 93 q^{3} + 767 q^{4} + 438 q^{5} - 2259 q^{6} + 922 q^{7} + 17973 q^{9} - 516 q^{10} - 28677 q^{11} - 55110 q^{12} + 1684 q^{13} + 120966 q^{14} - 75276 q^{15} - 65281 q^{16} + 243324 q^{18} - 269630 q^{19} + 539454 q^{20} + 354054 q^{21} + 61311 q^{22} - 1000452 q^{23} - 1125513 q^{24} + 65177 q^{25} - 524826 q^{27} + 1075708 q^{28} + 3797682 q^{29} + 2372562 q^{30} - 164132 q^{31} - 8461881 q^{32} - 5761521 q^{33} + 654993 q^{34} + 12958047 q^{36} - 1671668 q^{37} + 10967691 q^{38} + 3383976 q^{39} + 613326 q^{40} - 10239447 q^{41} - 35844228 q^{42} + 791815 q^{43} + 27631638 q^{45} + 1189536 q^{46} + 31148628 q^{47} + 17088189 q^{48} - 4826637 q^{49} - 63849453 q^{50} - 47946573 q^{51} - 5552720 q^{52} + 36967995 q^{54} + 8107476 q^{55} + 116638674 q^{56} + 37276797 q^{57} + 14211822 q^{58} - 83493795 q^{59} - 109012050 q^{60} - 5255600 q^{61} + 38322432 q^{63} - 26813830 q^{64} + 69232992 q^{65} + 36133866 q^{66} - 8288855 q^{67} - 77746743 q^{68} - 62108640 q^{69} + 27813756 q^{70} + 88821171 q^{72} - 36721682 q^{73} - 10383450 q^{74} + 13792011 q^{75} - 42822959 q^{76} + 56158710 q^{77} + 27355140 q^{78} - 32771822 q^{79} - 16336971 q^{81} + 236099418 q^{82} - 198915996 q^{83} - 187060614 q^{84} + 97486146 q^{85} + 146190669 q^{86} + 114294006 q^{87} + 24955827 q^{88} - 222035850 q^{90} - 201514504 q^{91} - 295365804 q^{92} + 94187784 q^{93} - 36698244 q^{94} + 386813838 q^{95} + 768275928 q^{96} + 127049161 q^{97} - 511060752 q^{99}+O(q^{100}) \) 14 * q - 3 * q^2 - 93 * q^3 + 767 * q^4 + 438 * q^5 - 2259 * q^6 + 922 * q^7 + 17973 * q^9 - 516 * q^10 - 28677 * q^11 - 55110 * q^12 + 1684 * q^13 + 120966 * q^14 - 75276 * q^15 - 65281 * q^16 + 243324 * q^18 - 269630 * q^19 + 539454 * q^20 + 354054 * q^21 + 61311 * q^22 - 1000452 * q^23 - 1125513 * q^24 + 65177 * q^25 - 524826 * q^27 + 1075708 * q^28 + 3797682 * q^29 + 2372562 * q^30 - 164132 * q^31 - 8461881 * q^32 - 5761521 * q^33 + 654993 * q^34 + 12958047 * q^36 - 1671668 * q^37 + 10967691 * q^38 + 3383976 * q^39 + 613326 * q^40 - 10239447 * q^41 - 35844228 * q^42 + 791815 * q^43 + 27631638 * q^45 + 1189536 * q^46 + 31148628 * q^47 + 17088189 * q^48 - 4826637 * q^49 - 63849453 * q^50 - 47946573 * q^51 - 5552720 * q^52 + 36967995 * q^54 + 8107476 * q^55 + 116638674 * q^56 + 37276797 * q^57 + 14211822 * q^58 - 83493795 * q^59 - 109012050 * q^60 - 5255600 * q^61 + 38322432 * q^63 - 26813830 * q^64 + 69232992 * q^65 + 36133866 * q^66 - 8288855 * q^67 - 77746743 * q^68 - 62108640 * q^69 + 27813756 * q^70 + 88821171 * q^72 - 36721682 * q^73 - 10383450 * q^74 + 13792011 * q^75 - 42822959 * q^76 + 56158710 * q^77 + 27355140 * q^78 - 32771822 * q^79 - 16336971 * q^81 + 236099418 * q^82 - 198915996 * q^83 - 187060614 * q^84 + 97486146 * q^85 + 146190669 * q^86 + 114294006 * q^87 + 24955827 * q^88 - 222035850 * q^90 - 201514504 * q^91 - 295365804 * q^92 + 94187784 * q^93 - 36698244 * q^94 + 386813838 * q^95 + 768275928 * q^96 + 127049161 * q^97 - 511060752 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	6.01192	−	3.47098i	0.375745	−	0.216937i	−0.300220	−	0.953870i	$-0.597060\pi$
$2$	6.01192	−	3.47098i	0.375745	−	0.216937i	0.675965	+	0.736933i	$0.263727\pi$
$3$	−29.7082	+	75.3553i	−0.366768	+	0.930312i
$3$	−29.7082	+	75.3553i	−0.366768	+	0.930312i
$4$	−103.905	+	179.968i	−0.405877	+	0.703000i
$5$	331.396	+	191.331i	0.530233	+	0.306130i	0.741111	−	0.671382i	$-0.234299\pi$
$5$	331.396	+	191.331i	0.530233	+	0.306130i	−0.210878	+	0.977512i	$0.567632\pi$
$6$	82.9534	+	556.147i	0.0640072	+	0.429126i
$7$	467.516	+	809.762i	0.194717	+	0.337260i	0.946808	−	0.321800i	$-0.104288\pi$
$7$	467.516	+	809.762i	0.194717	+	0.337260i	−0.752091	+	0.659060i	$0.770954\pi$
$8$			3219.75i			0.786071i
$9$	−4795.84	−	4477.35i	−0.730962	−	0.682418i
$10$	2656.43			0.265643
$11$	4890.10	−	2823.30i	0.334001	−	0.192835i	−0.323615	−	0.946189i	$-0.604898\pi$
$11$	4890.10	−	2823.30i	0.334001	−	0.192835i	0.657616	+	0.753353i	$0.271565\pi$
$12$	−10474.7	−	13176.3i	−0.505146	−	0.635431i
$13$	17663.1	−	30593.3i	0.618433	−	1.07116i	−0.371339	−	0.928497i	$-0.621101\pi$
$13$	17663.1	−	30593.3i	0.618433	−	1.07116i	0.989772	−	0.142660i	$-0.0455654\pi$
$14$	5621.34	+	3245.48i	0.146328	+	0.0844826i
$15$	−24263.0	+	19288.3i	−0.479270	+	0.381004i
$16$	−15423.9	−	26714.9i	−0.235350	−	0.407637i
$17$			152914.i			1.83085i	0.402491	+	0.915424i	$0.368144\pi$
$17$			152914.i			1.83085i	−0.402491	+	0.915424i	$0.631856\pi$
$18$	−44373.0	−	10271.2i	−0.422697	−	0.0978431i
$19$	191248.			1.46751			0.733756	−	0.679413i	$-0.237766\pi$
$19$	191248.			1.46751			0.733756	+	0.679413i	$0.237766\pi$
$20$	−68867.1	+	39760.4i	−0.430419	+	0.248503i
$21$	−74908.9	+	11173.2i	−0.385173	+	0.0574515i
$22$	19599.3	−	33947.0i	0.0836661	−	0.144914i
$23$	132313.	+	76390.7i	0.472814	+	0.272979i	0.717417	−	0.696644i	$-0.245324\pi$
$23$	132313.	+	76390.7i	0.472814	+	0.272979i	−0.244603	+	0.969623i	$0.578658\pi$
$24$	−242625.	−	95653.1i	−0.731292	−	0.288306i
$25$	−122097.	−	211478.i	−0.312568	−	0.541384i
$26$		−	245233.i		−	0.536643i
$27$	479868.	−	228378.i	0.902956	−	0.429733i
$28$	−194308.			−0.316125
$29$	401612.	−	231871.i	0.567825	−	0.327834i	−0.188455	−	0.982082i	$-0.560348\pi$
$29$	401612.	−	231871.i	0.567825	−	0.327834i	0.756280	+	0.654248i	$0.227015\pi$
$30$	−78918.0	+	200176.i	−0.0974296	+	0.247131i
$31$	−393956.	+	682351.i	−0.426580	+	0.738858i	−0.996567	−	0.0827958i	$-0.973615\pi$
$31$	−393956.	+	682351.i	−0.426580	+	0.738858i	0.569987	+	0.821654i	$0.306948\pi$
$32$	−899280.	−	519200.i	−0.857621	−	0.495147i
$33$	67474.4	+	452371.i	0.0568962	+	0.381451i
$34$	530763.	+	919308.i	0.397178	+	0.687932i
$35$			357802.i			0.238435i
$36$	1.30409e6	−	397881.i	0.776421	−	0.236888i
$37$	−1.10561e6			−0.589921			−0.294960	−	0.955509i	$-0.595306\pi$
$37$	−1.10561e6			−0.589921			−0.294960	+	0.955509i	$0.595306\pi$
$38$	1.14977e6	−	663818.i	0.551410	−	0.318357i
$39$	1.78063e6	+	2.23988e6i	0.769689	+	0.968202i
$40$	−616039.	+	1.06701e6i	−0.240640	+	0.416801i
$41$	−3.14915e6	−	1.81816e6i	−1.11444	−	0.643425i	−0.174468	−	0.984663i	$-0.555820\pi$
$41$	−3.14915e6	−	1.81816e6i	−1.11444	−	0.643425i	−0.939977	+	0.341238i	$0.889154\pi$
$42$	−411564.	+	327180.i	−0.132264	+	0.105145i
$43$	−1.51318e6	−	2.62091e6i	−0.442607	−	0.766617i	0.555275	−	0.831667i	$-0.312613\pi$
$43$	−1.51318e6	−	2.62091e6i	−0.442607	−	0.766617i	−0.997882	+	0.0650494i	$0.979280\pi$
$44$			1.17342e6i			0.313070i
$45$	−732664.	−	2.40137e6i	−0.178671	−	0.585611i
$46$	1.06060e6			0.236876
$47$	4.75308e6	−	2.74419e6i	0.974055	−	0.562371i	0.0735846	−	0.997289i	$-0.476556\pi$
$47$	4.75308e6	−	2.74419e6i	0.974055	−	0.562371i	0.900470	+	0.434918i	$0.143223\pi$
$48$	2.47133e6	−	368617.i	0.465549	−	0.0694400i
$49$	2.44526e6	−	4.23531e6i	0.424170	−	0.734685i
$50$	−1.46808e6	−	847594.i	−0.234892	−	0.135615i
$51$	−1.15229e7	−	4.54281e6i	−1.70326	−	0.671497i
$52$	3.67054e6	+	6.35757e6i	0.502015	+	0.869516i
$53$			1.41381e7i			1.79179i	0.444269	+	0.895894i	$0.353464\pi$
$53$			1.41381e7i			1.79179i	−0.444269	+	0.895894i	$0.646536\pi$
$54$	2.09223e6	−	3.03860e6i	0.246056	−	0.357354i
$55$	2.16075e6			0.236131
$56$	−2.60723e6	+	1.50528e6i	−0.265111	+	0.153062i
$57$	−5.68163e6	+	1.44115e7i	−0.538237	+	1.36524i
$58$	1.60964e6	−	2.78797e6i	0.142238	−	0.246364i
$59$	7.58082e6	+	4.37679e6i	0.625617	+	0.361200i	0.779052	−	0.626959i	$-0.215701\pi$
$59$	7.58082e6	+	4.37679e6i	0.625617	+	0.361200i	−0.153436	+	0.988159i	$0.549034\pi$
$60$	−950238.	−	6.37071e6i	−0.0733208	−	0.491567i
$61$	−3.47102e6	−	6.01198e6i	−0.250690	−	0.434209i	0.713026	−	0.701138i	$-0.247324\pi$
$61$	−3.47102e6	−	6.01198e6i	−0.250690	−	0.434209i	−0.963716	+	0.266929i	$0.913991\pi$
$62$			5.46965e6i			0.370163i
$63$	1.38345e6	−	5.97672e6i	0.0878217	−	0.379403i
$64$	688484.			0.0410368
$65$	1.17069e7	−	6.75900e6i	0.655827	−	0.378642i
$66$	1.97582e6	+	2.48541e6i	0.104129	+	0.130985i
$67$	7.08899e6	−	1.22785e7i	0.351791	−	0.609321i	−0.634772	−	0.772700i	$-0.718906\pi$
$67$	7.08899e6	−	1.22785e7i	0.351791	−	0.609321i	0.986563	+	0.163379i	$0.0522393\pi$
$68$	−2.75197e7	−	1.58885e7i	−1.28709	−	0.743099i
$69$	−9.68722e6	+	7.70102e6i	−0.427369	+	0.339744i
$70$	1.24193e6	+	2.15108e6i	0.0517254	+	0.0895909i
$71$		−	7.97888e6i		−	0.313985i	−0.987600	−	0.156992i	$-0.949820\pi$
$71$		−	7.97888e6i		−	0.313985i	0.987600	−	0.156992i	$-0.0501798\pi$
$72$	1.44159e7	−	1.54414e7i	0.536430	−	0.574588i
$73$	−4.61414e6			−0.162480			−0.0812399	−	0.996695i	$-0.525888\pi$
$73$	−4.61414e6			−0.162480			−0.0812399	+	0.996695i	$0.525888\pi$
$74$	−6.64682e6	+	3.83754e6i	−0.221660	+	0.127975i
$75$	1.95633e7	−	2.91801e6i	0.618297	−	0.0922235i
$76$	−1.98715e7	+	3.44184e7i	−0.595630	+	1.03166i
$77$	4.57241e6	+	2.63988e6i	0.130071	+	0.0750968i
$78$	1.84796e7	+	7.28544e6i	0.499245	+	0.196824i
$79$	−1.37621e6	−	2.38366e6i	−0.0353326	−	0.0611979i	0.847818	−	0.530287i	$-0.177916\pi$
$79$	−1.37621e6	−	2.38366e6i	−0.0353326	−	0.0611979i	−0.883151	+	0.469089i	$0.844582\pi$
$80$		−	1.18043e7i		−	0.288191i
$81$	2.95344e6	+	4.29453e7i	0.0686102	+	0.997644i
$82$	−2.52433e7			−0.558329
$83$	3.52291e7	−	2.03395e7i	0.742316	−	0.428577i	−0.0805945	−	0.996747i	$-0.525682\pi$
$83$	3.52291e7	−	2.03395e7i	0.742316	−	0.428577i	0.822911	+	0.568170i	$0.192349\pi$
$84$	5.77256e6	−	1.46422e7i	0.115945	−	0.294095i
$85$	−2.92573e7	+	5.06751e7i	−0.560478	+	0.970776i
$86$	−1.81943e7	−	1.05045e7i	−0.332614	−	0.192035i
$87$	5.54150e6	+	3.71520e7i	0.0967275	+	0.648493i
$88$	9.09033e6	+	1.57449e7i	0.151582	+	0.262548i
$89$		−	2.90621e7i		−	0.463199i	−0.972811	−	0.231599i	$-0.925604\pi$
$89$		−	2.90621e7i		−	0.463199i	0.972811	−	0.231599i	$-0.0743958\pi$
$90$	−1.27398e7	−	1.18938e7i	−0.194175	−	0.181280i
$91$	3.30311e7			0.481678
$92$	−2.74958e7	+	1.58747e7i	−0.383808	+	0.221592i
$93$	−3.97150e7	−	4.99581e7i	−0.530913	−	0.667843i
$94$	1.90501e7	−	3.29957e7i	0.243997	−	0.422616i
$95$	6.33787e7	+	3.65917e7i	0.778124	+	0.449250i
$96$	6.58405e7	−	5.23410e7i	0.775190	−	0.616250i
$97$	−4.58061e7	−	7.93386e7i	−0.517412	−	0.896185i	−0.999795	−	0.0202242i	$-0.993562\pi$
$97$	−4.58061e7	−	7.93386e7i	−0.517412	−	0.896185i	0.482383	−	0.875960i	$-0.339771\pi$
$98$		−	3.39498e7i		−	0.368072i
$99$	−3.60931e7	−	8.35459e6i	−0.375736	−	0.0869729i
$100$	5.07458e7			0.507458
$101$	−1.61684e8	+	9.33484e7i	−1.55375	+	0.897060i	−0.555922	+	0.831235i	$0.687635\pi$
$101$	−1.61684e8	+	9.33484e7i	−1.55375	+	0.897060i	−0.997831	+	0.0658252i	$0.979032\pi$
$102$	−8.50428e7	+	1.26848e7i	−0.785664	+	0.117188i
$103$	8.19171e7	−	1.41885e8i	0.727823	−	1.26063i	−0.229979	−	0.973196i	$-0.573866\pi$
$103$	8.19171e7	−	1.41885e8i	0.727823	−	1.26063i	0.957802	−	0.287430i	$-0.0928010\pi$
$104$	9.85028e7	+	5.68706e7i	0.842006	+	0.486132i
$105$	−2.69623e7	−	1.06297e7i	−0.221819	−	0.0874506i
$106$	4.90730e7	+	8.49969e7i	0.388704	+	0.673255i
$107$		−	1.15537e7i		−	0.0881427i	−0.999028	−	0.0440714i	$-0.985967\pi$
$107$		−	1.15537e7i		−	0.0881427i	0.999028	−	0.0440714i	$-0.0140329\pi$
$108$	−8.75976e6	+	1.10090e8i	−0.0643869	+	0.809197i
$109$	−5.79498e7			−0.410531			−0.205265	−	0.978706i	$-0.565806\pi$
$109$	−5.79498e7			−0.410531			−0.205265	+	0.978706i	$0.565806\pi$
$110$	1.29902e7	−	7.49992e6i	0.0887251	−	0.0512255i
$111$	3.28456e7	−	8.33133e7i	0.216364	−	0.548810i
$112$	1.44218e7	−	2.49793e7i	0.0916532	−	0.158748i
$113$	1.35905e8	+	7.84647e7i	0.833530	+	0.481239i	0.855060	−	0.518529i	$-0.173520\pi$
$113$	1.35905e8	+	7.84647e7i	0.833530	+	0.481239i	−0.0215297	+	0.999768i	$0.506854\pi$
$114$	1.58646e7	+	1.06362e8i	0.0939314	+	0.629747i
$115$	2.92319e7	+	5.06311e7i	0.167134	+	0.289485i
$116$			9.63696e7i			0.532241i
$117$	−2.21686e8	+	6.76370e7i	−1.18303	+	0.360945i
$118$	6.07671e7			0.313430
$119$	−1.23824e8	+	7.14899e7i	−0.617472	+	0.356498i
$120$	−6.21035e7	−	7.81208e7i	−0.299496	−	0.376740i
$121$	−9.12374e7	+	1.58028e8i	−0.425629	+	0.737211i
$122$	−4.17350e7	−	2.40957e7i	−0.188391	−	0.108768i
$123$	2.30564e8	−	1.83291e8i	1.00733	−	0.800793i
$124$	−8.18675e7	−	1.41799e8i	−0.346278	−	0.599771i
$125$		−	2.42922e8i		−	0.995007i
$126$	−1.24279e7	−	4.07335e7i	−0.0493078	−	0.161611i
$127$	3.23373e7			0.124305			0.0621525	−	0.998067i	$-0.480203\pi$
$127$	3.23373e7			0.124305			0.0621525	+	0.998067i	$0.480203\pi$
$128$	2.34355e8	−	1.35305e8i	0.873040	−	0.504050i
$129$	2.42454e8	−	3.61637e7i	0.875527	−	0.130591i
$130$	4.69207e7	−	8.12691e7i	0.164283	−	0.284546i
$131$	−2.30428e8	−	1.33038e8i	−0.782438	−	0.451741i	0.0548557	−	0.998494i	$-0.482530\pi$
$131$	−2.30428e8	−	1.33038e8i	−0.782438	−	0.451741i	−0.837294	+	0.546754i	$0.815863\pi$
$132$	−8.84231e7	−	3.48601e7i	−0.291253	−	0.114824i
$133$	8.94114e7	+	1.54865e8i	0.285750	+	0.494933i
$134$		−	9.84231e7i		−	0.305266i
$135$	2.02722e8	+	1.61304e7i	0.610332	+	0.0485634i
$136$	−4.92345e8			−1.43918
$137$	4.61911e7	−	2.66685e7i	0.131122	−	0.0757034i	−0.433004	−	0.901392i	$-0.642546\pi$
$137$	4.61911e7	−	2.66685e7i	0.131122	−	0.0757034i	0.564126	+	0.825689i	$0.309213\pi$
$138$	−3.15087e7	+	7.99221e7i	−0.0868788	+	0.220369i
$139$	−2.03300e8	+	3.52126e8i	−0.544601	+	0.943277i	0.454031	+	0.890986i	$0.349986\pi$
$139$	−2.03300e8	+	3.52126e8i	−0.544601	+	0.943277i	−0.998632	+	0.0522909i	$0.983348\pi$
$140$	−6.43929e7	−	3.71773e7i	−0.167620	−	0.0967755i
$141$	6.55837e7	+	4.39694e8i	0.165928	+	1.11243i
$142$	−2.76946e7	−	4.79684e7i	−0.0681148	−	0.117978i
$143$		−	1.99473e8i		−	0.477023i
$144$	−4.56416e7	+	1.97179e8i	−0.106148	+	0.458574i
$145$	1.77456e8			0.401439
$146$	−2.77398e7	+	1.60156e7i	−0.0610510	+	0.0352478i
$147$	2.46509e8	+	3.10087e8i	0.527914	+	0.664070i
$148$	1.14878e8	−	1.98974e8i	0.239435	−	0.414714i
$149$	−4.39611e7	−	2.53810e7i	−0.0891915	−	0.0514948i	0.454741	−	0.890624i	$-0.349732\pi$
$149$	−4.39611e7	−	2.53810e7i	−0.0891915	−	0.0514948i	−0.543932	+	0.839129i	$0.683065\pi$
$150$	1.07485e8	−	8.54467e7i	0.212315	−	0.168784i
$151$	1.20269e8	+	2.08312e8i	0.231337	+	0.400688i	0.958202	−	0.286093i	$-0.0923566\pi$
$151$	1.20269e8	+	2.08312e8i	0.231337	+	0.400688i	−0.726865	+	0.686781i	$0.759023\pi$
$152$			6.15769e8i			1.15357i
$153$	6.84650e8	−	7.33352e8i	1.24940	−	1.33828i
$154$	3.66519e7			0.0651649
$155$	−2.61110e8	+	1.50752e8i	−0.452374	+	0.261178i
$156$	−5.88122e8	+	8.77227e7i	−0.993045	+	0.148120i
$157$	−8.71150e6	+	1.50888e7i	−0.0143382	+	0.0248345i	−0.873105	−	0.487531i	$-0.837897\pi$
$157$	−8.71150e6	+	1.50888e7i	−0.0143382	+	0.0248345i	0.858767	+	0.512366i	$0.171231\pi$
$158$	−1.65473e7	−	9.55359e6i	−0.0265521	−	0.0153299i
$159$	−1.06538e9	−	4.20017e8i	−1.66692	−	0.657171i
$160$	−1.98678e8	−	3.44121e8i	−0.303159	−	0.525087i
$161$			1.42856e8i			0.212615i
$162$	1.66818e8	+	2.47932e8i	0.242205	+	0.359976i
$163$	5.31250e8			0.752573			0.376286	−	0.926503i	$-0.377201\pi$
$163$	5.31250e8			0.752573			0.376286	+	0.926503i	$0.377201\pi$
$164$	6.54423e8	−	3.77831e8i	0.904655	−	0.522303i
$165$	−6.41920e7	+	1.62824e8i	−0.0866054	+	0.219676i
$166$	1.41196e8	−	2.44559e8i	0.185948	−	0.322071i
$167$	−4.73822e7	−	2.73561e7i	−0.0609185	−	0.0351713i	0.469231	−	0.883075i	$-0.344531\pi$
$167$	−4.73822e7	−	2.73561e7i	−0.0609185	−	0.0351713i	−0.530150	+	0.847904i	$0.677864\pi$
$168$	−3.59749e7	−	2.41188e8i	−0.0451609	−	0.302774i
$169$	−2.16102e8	−	3.74300e8i	−0.264918	−	0.458852i
$170$			4.06207e8i			0.486353i
$171$	−9.17193e8	−	8.56282e8i	−1.07270	−	1.00146i
$172$	6.28907e8			0.718576
$173$	5.38684e8	−	3.11009e8i	0.601381	−	0.347207i	−0.168204	−	0.985752i	$-0.553797\pi$
$173$	5.38684e8	−	3.11009e8i	0.601381	−	0.347207i	0.769584	+	0.638545i	$0.220463\pi$
$174$	1.62269e8	+	2.04121e8i	0.177027	+	0.222684i
$175$	1.14165e8	−	1.97739e8i	0.121725	−	0.210834i
$176$	−1.50849e8	−	8.70925e7i	−0.157214	−	0.0907675i
$177$	−5.55027e8	+	4.41228e8i	−0.565485	+	0.449542i
$178$	−1.00874e8	−	1.74719e8i	−0.100485	−	0.174045i
$179$			1.35171e9i			1.31665i	0.752732	+	0.658327i	$0.228736\pi$
$179$			1.35171e9i			1.31665i	−0.752732	+	0.658327i	$0.771264\pi$
$180$	5.08297e8	+	1.17657e8i	0.484203	+	0.112080i
$181$	−5.83247e8			−0.543423			−0.271712	−	0.962379i	$-0.587590\pi$
$181$	−5.83247e8			−0.543423			−0.271712	+	0.962379i	$0.587590\pi$
$182$	1.98580e8	−	1.14650e8i	0.180988	−	0.104494i
$183$	5.56153e8	−	8.29543e7i	0.495895	−	0.0739664i
$184$	−2.45959e8	+	4.26013e8i	−0.214581	+	0.371665i
$185$	−3.66393e8	−	2.11537e8i	−0.312796	−	0.180593i
$186$	−4.12167e8	−	1.62494e8i	−0.344367	−	0.135764i
$187$	4.31723e8	+	7.47767e8i	0.353052	+	0.611504i
$188$			1.14053e9i			0.913013i
$189$	4.09278e8	+	2.81808e8i	0.320753	+	0.220855i
$190$	5.08037e8			0.389835
$191$	−9.46339e8	+	5.46369e8i	−0.711071	+	0.410537i	−0.811458	−	0.584411i	$-0.801326\pi$
$191$	−9.46339e8	+	5.46369e8i	−0.711071	+	0.410537i	0.100386	+	0.994949i	$0.467992\pi$
$192$	−2.04537e7	+	5.18809e7i	−0.0150510	+	0.0381771i
$193$	5.59017e8	−	9.68245e8i	0.402898	−	0.697840i	−0.591176	−	0.806543i	$-0.701336\pi$
$193$	5.59017e8	−	9.68245e8i	0.402898	−	0.697840i	0.994074	+	0.108702i	$0.0346695\pi$
$194$	−5.50766e8	−	3.17985e8i	−0.388830	−	0.224491i
$195$	1.61534e8	+	1.08298e9i	0.111719	+	0.748998i
$196$	5.08147e8	+	8.80136e8i	0.344322	+	0.596383i
$197$		−	2.60813e9i		−	1.73167i	−0.500332	−	0.865834i	$-0.666789\pi$
$197$		−	2.60813e9i		−	1.73167i	0.500332	−	0.865834i	$-0.333211\pi$
$198$	−2.45987e8	+	7.50514e7i	−0.160049	+	0.0488312i
$199$	−1.55526e9			−0.991722			−0.495861	−	0.868402i	$-0.665147\pi$
$199$	−1.55526e9			−0.991722			−0.495861	+	0.868402i	$0.665147\pi$
$200$	6.80907e8	−	3.93122e8i	0.425567	−	0.245701i
$201$	7.14648e8	+	8.98966e8i	0.437832	+	0.550756i
$202$	−6.48022e8	+	1.12241e9i	−0.389210	+	0.674132i
$203$	3.75520e8	+	2.16806e8i	0.221131	+	0.127670i
$204$	2.01484e9	−	1.60173e9i	1.16338	−	0.924846i
$205$	−6.95744e8	−	1.20506e9i	−0.393944	−	0.682331i
$206$		−	1.13733e9i		−	0.631565i
$207$	−2.92522e8	−	9.58767e8i	−0.159323	−	0.522194i
$208$	−1.08973e9			−0.582192
$209$	9.35221e8	−	5.39950e8i	0.490150	−	0.282988i
$210$	−1.98991e8	+	2.96809e7i	−0.102319	+	0.0152616i
$211$	−1.01997e8	+	1.76664e8i	−0.0514586	+	0.0891289i	−0.890607	−	0.454773i	$-0.849720\pi$
$211$	−1.01997e8	+	1.76664e8i	−0.0514586	+	0.0891289i	0.839149	+	0.543902i	$0.183054\pi$
$212$	−2.54440e9	−	1.46901e9i	−1.25963	−	0.727245i
$213$	6.01251e8	+	2.37039e8i	0.292104	+	0.115160i
$214$	−4.01028e7	−	6.94600e7i	−0.0191214	−	0.0331192i
$215$		−	1.15808e9i		−	0.541981i
$216$	7.35319e8	+	1.54505e9i	0.337801	+	0.709788i
$217$	−7.36722e8			−0.332250
$218$	−3.48390e8	+	2.01143e8i	−0.154255	+	0.0890591i
$219$	1.37078e8	−	3.47700e8i	0.0595925	−	0.151157i
$220$	−2.24511e8	+	3.88865e8i	−0.0958402	+	0.166000i
$221$	4.67815e9	+	2.70093e9i	1.96113	+	1.13226i
$222$	−9.17138e7	−	6.14880e8i	−0.0377592	−	0.253150i
$223$	9.72435e8	+	1.68431e9i	0.393225	+	0.681086i	0.992873	−	0.119178i	$-0.0380260\pi$
$223$	9.72435e8	+	1.68431e9i	0.393225	+	0.681086i	−0.599648	+	0.800264i	$0.704693\pi$
$224$		−	9.70937e8i		−	0.385655i
$225$	−3.61304e8	+	1.56089e9i	−0.140975	+	0.609034i
$226$	1.08940e9			0.417593
$227$	−3.66729e9	+	2.11731e9i	−1.38115	+	0.797409i	−0.992296	−	0.123890i	$-0.960463\pi$
$227$	−3.66729e9	+	2.11731e9i	−1.38115	+	0.797409i	−0.388856	+	0.921298i	$0.627130\pi$
$228$	−2.00326e9	−	2.51993e9i	−0.741308	−	0.932502i
$229$	−2.55548e8	+	4.42621e8i	−0.0929244	+	0.160950i	−0.908740	−	0.417362i	$-0.862955\pi$
$229$	−2.55548e8	+	4.42621e8i	−0.0929244	+	0.160950i	0.815816	+	0.578311i	$0.196288\pi$
$230$	3.51480e8	+	2.02927e8i	0.125600	+	0.0725151i
$231$	−3.34767e8	+	2.66129e8i	−0.117570	+	0.0934639i
$232$	7.46565e8	+	1.29309e9i	0.257701	+	0.446351i
$233$			3.64332e8i			0.123616i	0.998088	+	0.0618079i	$0.0196866\pi$
$233$			3.64332e8i			0.123616i	−0.998088	+	0.0618079i	$0.980313\pi$
$234$	−1.09799e9	+	1.17610e9i	−0.366215	+	0.392265i
$235$	2.10020e9			0.688635
$236$	−1.57536e9	+	9.09537e8i	−0.507847	+	0.293206i
$237$	2.20506e8	−	3.28901e7i	0.0698920	−	0.0104249i
$238$	−4.96280e8	+	8.59583e8i	−0.154675	+	0.267904i
$239$	2.95288e9	+	1.70485e9i	0.905012	+	0.522509i	0.878823	−	0.477148i	$-0.158329\pi$
$239$	2.95288e9	+	1.70485e9i	0.905012	+	0.522509i	0.0261894	+	0.999657i	$0.491663\pi$
$240$	8.89515e8	+	3.50685e8i	0.268107	+	0.105699i
$241$	−2.22976e9	−	3.86206e9i	−0.660982	−	1.14485i	−0.980358	−	0.197226i	$-0.936807\pi$
$241$	−2.22976e9	−	3.86206e9i	−0.660982	−	1.14485i	0.319376	−	0.947628i	$-0.396527\pi$
$242$			1.26673e9i			0.369338i
$243$	−3.32390e9	−	1.05327e9i	−0.953284	−	0.302075i
$244$	1.44262e9			0.406998
$245$	1.62070e9	−	9.35709e8i	0.449818	−	0.259703i
$246$	7.49934e8	−	1.90222e9i	0.204778	−	0.519421i
$247$	3.37802e9	−	5.85090e9i	0.907558	−	1.57194i
$248$	−2.19700e9	−	1.26844e9i	−0.580795	−	0.335322i
$249$	4.86096e8	+	3.25895e9i	0.126452	+	0.847774i
$250$	−8.43177e8	−	1.46043e9i	−0.215853	−	0.373869i
$251$		−	1.16420e8i		−	0.0293313i	−0.999892	−	0.0146657i	$-0.995332\pi$
$251$		−	1.16420e8i		−	0.0293313i	0.999892	−	0.0146657i	$-0.00466839\pi$
$252$	9.31871e8	+	8.69985e8i	0.231075	+	0.215730i
$253$	8.62697e8			0.210560
$254$	1.94409e8	−	1.12242e8i	0.0467070	−	0.0269663i
$255$	−2.94946e9	−	3.71016e9i	−0.697559	−	0.877470i
$256$	8.51156e8	−	1.47425e9i	0.198175	−	0.343250i
$257$	1.46373e9	+	8.45087e8i	0.335529	+	0.193717i	0.658293	−	0.752762i	$-0.271279\pi$
$257$	1.46373e9	+	8.45087e8i	0.335529	+	0.193717i	−0.322764	+	0.946479i	$0.604612\pi$
$258$	1.33209e9	−	1.05897e9i	0.300645	−	0.239003i
$259$	−5.16889e8	−	8.95278e8i	−0.114868	−	0.198957i
$260$			2.80916e9i			0.614729i
$261$	−2.96423e9	−	6.86140e8i	−0.638778	−	0.147860i
$262$	−1.84709e9			−0.391996
$263$	−5.09081e9	+	2.93918e9i	−1.06406	+	0.614333i	−0.926551	−	0.376169i	$-0.877241\pi$
$263$	−5.09081e9	+	2.93918e9i	−1.06406	+	0.614333i	−0.137504	+	0.990501i	$0.543908\pi$
$264$	−1.45652e9	+	2.17251e8i	−0.299848	+	0.0447245i
$265$	−2.70506e9	+	4.68529e9i	−0.548520	+	0.950065i
$266$	1.07507e9	+	6.20691e8i	0.214738	+	0.123979i
$267$	2.18999e9	+	8.63385e8i	0.430919	+	0.169887i
$268$	1.47316e9	+	2.55158e9i	0.285568	+	0.494619i
$269$		−	5.55830e9i		−	1.06153i	−0.847518	−	0.530766i	$-0.821904\pi$
$269$		−	5.55830e9i		−	1.06153i	0.847518	−	0.530766i	$-0.178096\pi$
$270$	1.27474e9	−	6.06670e8i	0.239864	−	0.114156i
$271$	4.93438e9			0.914862			0.457431	−	0.889245i	$-0.348770\pi$
$271$	4.93438e9			0.914862			0.457431	+	0.889245i	$0.348770\pi$
$272$	4.08509e9	−	2.35853e9i	0.746322	−	0.430889i
$273$	−9.81295e8	+	2.48907e9i	−0.176664	+	0.448111i
$274$	1.85132e8	−	3.20657e8i	0.0328457	−	0.0568904i
$275$	−1.19413e9	−	6.89434e8i	−0.208796	−	0.120549i
$276$	−3.79391e8	−	2.54356e9i	−0.0653808	−	0.438335i
$277$	1.81493e9	+	3.14355e9i	0.308277	+	0.533951i	0.977985	−	0.208673i	$-0.0669145\pi$
$277$	1.81493e9	+	3.14355e9i	0.308277	+	0.533951i	−0.669709	+	0.742624i	$0.733581\pi$
$278$			2.82261e9i			0.472576i
$279$	4.94447e9	−	1.50857e9i	0.816024	−	0.248971i
$280$	−1.15203e9			−0.187427
$281$	6.06878e8	−	3.50381e8i	0.0973366	−	0.0561973i	−0.450542	−	0.892755i	$-0.648769\pi$
$281$	6.06878e8	−	3.50381e8i	0.0973366	−	0.0561973i	0.547878	+	0.836558i	$0.315436\pi$
$282$	1.92046e9	+	2.41577e9i	0.303674	+	0.381996i
$283$	−3.91197e9	+	6.77574e9i	−0.609888	+	1.05636i	0.381370	+	0.924422i	$0.375452\pi$
$283$	−3.91197e9	+	6.77574e9i	−0.609888	+	1.05636i	−0.991258	+	0.131935i	$0.957881\pi$
$284$	1.43594e9	+	8.29042e8i	0.220731	+	0.127439i
$285$	−4.64025e9	+	3.68884e9i	−0.703334	+	0.559127i
$286$	−6.92367e8	−	1.19921e9i	−0.103484	−	0.179239i
$287$		−	3.40009e9i		−	0.501144i
$288$	1.98817e9	+	6.51639e9i	0.288990	+	0.947190i
$289$	−1.64070e10			−2.35200
$290$	1.06685e9	−	6.15949e8i	0.150839	−	0.0870868i
$291$	7.33940e9	−	1.09473e9i	1.02350	−	0.152663i
$292$	4.79430e8	−	8.30397e8i	0.0659468	−	0.114223i
$293$	−7.18343e9	−	4.14736e9i	−0.974679	−	0.562731i	−0.0740196	−	0.997257i	$-0.523583\pi$
$293$	−7.18343e9	−	4.14736e9i	−0.974679	−	0.562731i	−0.900660	+	0.434526i	$0.856916\pi$
$294$	2.55830e9	+	1.00859e9i	0.342422	+	0.134997i
$295$	1.67483e9	+	2.90090e9i	0.221148	+	0.383040i
$296$		−	3.55977e9i		−	0.463720i
$297$	1.70182e9	−	2.47160e9i	0.218720	−	0.317653i
$298$	−3.52388e8			−0.0446844
$299$	4.67409e9	−	2.69859e9i	0.584807	−	0.337638i
$300$	−1.50757e9	+	3.82396e9i	−0.186119	+	0.472094i
$301$	1.41488e9	−	2.45064e9i	0.172366	−	0.298547i
$302$	1.44609e9	+	8.34902e8i	0.173848	+	0.100371i
$303$	−2.23094e9	−	1.49570e10i	−0.264678	−	1.77449i
$304$	−2.94978e9	−	5.10917e9i	−0.345378	−	0.598213i
$305$		−	2.65646e9i		−	0.306976i
$306$	1.57061e9	−	6.78526e9i	0.179136	−	0.773893i
$307$	1.48989e10			1.67726			0.838629	−	0.544702i	$-0.183357\pi$
$307$	1.48989e10			1.67726			0.838629	+	0.544702i	$0.183357\pi$
$308$	−9.50188e8	+	5.48591e8i	−0.105586	+	0.0609601i
$309$	8.25814e9	+	1.03880e10i	0.905833	+	1.13946i
$310$	−1.04652e9	+	1.81262e9i	−0.113318	+	0.196273i
$311$	−1.09865e10	−	6.34304e9i	−1.17440	−	0.678041i	−0.219688	−	0.975570i	$-0.570504\pi$
$311$	−1.09865e10	−	6.34304e9i	−1.17440	−	0.678041i	−0.954713	+	0.297529i	$0.903837\pi$
$312$	−7.21185e9	+	5.73318e9i	−0.761076	+	0.605030i
$313$	−1.59338e9	−	2.75982e9i	−0.166013	−	0.287543i	0.771002	−	0.636833i	$-0.219756\pi$
$313$	−1.59338e9	−	2.75982e9i	−0.166013	−	0.287543i	−0.937015	+	0.349290i	$0.886423\pi$
$314$			1.20950e8i			0.0124419i
$315$	1.60200e9	−	1.71596e9i	0.162713	−	0.174287i
$316$	5.71977e8			0.0573628
$317$	1.29666e9	−	7.48628e8i	0.128407	−	0.0741360i	−0.434420	−	0.900710i	$-0.643047\pi$
$317$	1.29666e9	−	7.48628e8i	0.128407	−	0.0741360i	0.562828	+	0.826574i	$0.309713\pi$
$318$	−7.86284e9	+	1.17280e9i	−0.768902	+	0.114687i
$319$	1.30928e9	−	2.26774e9i	0.126436	−	0.218993i
$320$	2.28161e8	+	1.31729e8i	0.0217591	+	0.0125626i
$321$	8.70633e8	+	3.43241e8i	0.0820002	+	0.0323280i
$322$	4.95850e8	+	8.58837e8i	0.0461239	+	0.0798890i
$323$			2.92445e10i			2.68679i
$324$	−8.03565e9	−	3.93068e9i	−0.729190	−	0.356688i
$325$	−8.62643e9			−0.773210
$326$	3.19383e9	−	1.84396e9i	0.282775	−	0.163260i
$327$	1.72159e9	−	4.36682e9i	0.150570	−	0.381922i
$328$	5.85403e9	−	1.01395e10i	0.505778	−	0.876033i
$329$	4.44428e9	+	2.56591e9i	0.379331	+	0.219007i
$330$	1.79241e8	+	1.20169e9i	0.0151141	+	0.101330i
$331$	9.32077e9	+	1.61441e10i	0.776497	+	1.34493i	0.933949	+	0.357406i	$0.116339\pi$
$331$	9.32077e9	+	1.61441e10i	0.776497	+	1.34493i	−0.157452	+	0.987527i	$0.550328\pi$
$332$			8.45348e9i			0.695798i
$333$	5.30231e9	+	4.95018e9i	0.431209	+	0.402573i
$334$	−3.79811e8			−0.0305198
$335$	4.69852e9	−	2.71269e9i	0.373063	−	0.215388i
$336$	1.45388e9	+	1.82885e9i	0.114070	+	0.143490i
$337$	−3.21138e8	+	5.56228e8i	−0.0248985	+	0.0431254i	−0.878206	−	0.478282i	$-0.841260\pi$
$337$	−3.21138e8	+	5.56228e8i	−0.0248985	+	0.0431254i	0.853308	+	0.521408i	$0.174593\pi$
$338$	−2.59838e9	−	1.50017e9i	−0.199083	−	0.114941i
$339$	−9.95023e9	+	7.91010e9i	−0.753415	+	0.598940i
$340$	−6.07993e9	−	1.05308e10i	−0.454970	−	0.788032i
$341$			4.44902e9i			0.329039i
$342$	−8.48623e9	−	1.96434e9i	−0.620313	−	0.143586i
$343$	9.96307e9			0.719808
$344$	8.43867e9	−	4.87207e9i	0.602616	−	0.347920i
$345$	−4.68375e9	+	6.98616e8i	−0.330611	+	0.0493131i
$346$	2.15902e9	−	3.73952e9i	0.150644	−	0.260923i
$347$	8.51548e8	+	4.91642e8i	0.0587342	+	0.0339102i	0.529080	−	0.848572i	$-0.322537\pi$
$347$	8.51548e8	+	4.91642e8i	0.0587342	+	0.0339102i	−0.470345	+	0.882482i	$0.655871\pi$
$348$	−7.26196e9	−	2.86297e9i	−0.495150	−	0.195209i
$349$	−1.27190e9	−	2.20299e9i	−0.0857334	−	0.148495i	0.819970	−	0.572406i	$-0.193990\pi$
$349$	−1.27190e9	−	2.20299e9i	−0.0857334	−	0.148495i	−0.905703	+	0.423912i	$0.860657\pi$
$350$		−	1.58506e9i		−	0.105626i
$351$	1.48910e9	−	1.87146e10i	0.0981059	−	1.23297i
$352$	−5.86343e9			−0.381928
$353$	−5.61563e9	+	3.24219e9i	−0.361660	+	0.208804i	−0.669808	−	0.742534i	$-0.733624\pi$
$353$	−5.61563e9	+	3.24219e9i	−0.361660	+	0.208804i	0.308149	+	0.951338i	$0.400290\pi$
$354$	−1.80528e9	+	4.57912e9i	−0.114956	+	0.291588i
$355$	1.52661e9	−	2.64417e9i	0.0961203	−	0.166485i
$356$	5.23025e9	+	3.01969e9i	0.325629	+	0.188002i
$357$	−1.70854e9	−	1.14546e10i	−0.105185	−	0.705194i
$358$	4.69177e9	+	8.12638e9i	0.285630	+	0.494726i
$359$		−	1.35812e10i		−	0.817639i	−0.912615	−	0.408820i	$-0.865940\pi$
$359$		−	1.35812e10i		−	0.817639i	0.912615	−	0.408820i	$-0.134060\pi$
$360$	7.73180e9	−	2.35899e9i	0.460332	−	0.140448i
$361$	1.95921e10			1.15359
$362$	−3.50643e9	+	2.02444e9i	−0.204189	+	0.117888i
$363$	−9.19772e9	−	1.15699e10i	−0.529729	−	0.666354i
$364$	−3.43208e9	+	5.94453e9i	−0.195502	+	0.338620i
$365$	−1.52911e9	−	8.82830e8i	−0.0861522	−	0.0497400i
$366$	3.05561e9	−	2.42911e9i	0.170284	−	0.135370i
$367$	−1.66185e10	−	2.87842e10i	−0.916070	−	1.58668i	−0.805327	−	0.592831i	$-0.798010\pi$
$367$	−1.66185e10	−	2.87842e10i	−0.916070	−	1.58668i	−0.110744	−	0.993849i	$-0.535323\pi$
$368$		−	4.71296e9i		−	0.256982i
$369$	6.96228e9	+	2.28195e10i	0.375531	+	1.23084i
$370$	−2.93697e9			−0.156709
$371$	−1.14485e10	+	6.60977e9i	−0.604299	+	0.348892i
$372$	1.31174e10	−	1.95656e9i	0.684978	−	0.102170i
$373$	−6.90080e9	+	1.19525e10i	−0.356504	+	0.617482i	−0.987374	−	0.158406i	$-0.949365\pi$
$373$	−6.90080e9	+	1.19525e10i	−0.356504	+	0.617482i	0.630870	+	0.775888i	$0.282698\pi$
$374$	5.19097e9	+	2.99701e9i	0.265315	+	0.153180i
$375$	1.83054e10	+	7.21678e9i	0.925668	+	0.364937i
$376$	8.83560e9	+	1.53037e10i	0.442063	+	0.765676i
$377$		−	1.63822e10i		−	0.810972i
$378$	3.43870e9	+	2.73613e8i	0.168433	+	0.0134020i
$379$	−2.14968e10			−1.04188			−0.520938	−	0.853594i	$-0.674418\pi$
$379$	−2.14968e10			−1.04188			−0.520938	+	0.853594i	$0.674418\pi$
$380$	−1.31707e10	+	7.60408e9i	−0.631645	+	0.364681i
$381$	−9.60684e8	+	2.43679e9i	−0.0455912	+	0.115643i
$382$	−3.79288e9	+	6.56945e9i	−0.178121	+	0.308515i
$383$	−1.44304e10	−	8.33139e9i	−0.670630	−	0.387189i	0.125685	−	0.992070i	$-0.459887\pi$
$383$	−1.44304e10	−	8.33139e9i	−0.670630	−	0.387189i	−0.796315	+	0.604882i	$0.793220\pi$
$384$	3.23366e9	+	2.16795e10i	0.148720	+	0.997069i
$385$	1.01018e9	+	1.74969e9i	0.0459788	+	0.0796376i
$386$		−	7.76135e9i		−	0.349613i
$387$	−4.47774e9	+	1.93445e10i	−0.199625	+	0.862411i
$388$	1.90379e10			0.840023
$389$	2.09033e10	−	1.20686e10i	0.912888	−	0.527056i	0.0315287	−	0.999503i	$-0.489962\pi$
$389$	2.09033e10	−	1.20686e10i	0.912888	−	0.527056i	0.881359	+	0.472447i	$0.156629\pi$
$390$	4.73012e9	+	5.95009e9i	0.204463	+	0.257197i
$391$	−1.16812e10	+	2.02325e10i	−0.499783	+	0.865650i
$392$	1.36366e10	+	7.87311e9i	0.577514	+	0.333428i
$393$	1.68707e10	−	1.34116e10i	0.707233	−	0.562227i
$394$	−9.05278e9	−	1.56799e10i	−0.375662	−	0.650666i
$395$		−	1.05325e9i		−	0.0432655i
$396$	5.25379e9	−	5.62752e9i	0.213645	−	0.228842i
$397$	−3.25313e10			−1.30960			−0.654801	−	0.755801i	$-0.727248\pi$
$397$	−3.25313e10			−1.30960			−0.654801	+	0.755801i	$0.727248\pi$
$398$	−9.35008e9	+	5.39827e9i	−0.372635	+	0.215141i
$399$	−1.43262e10	+	2.13685e9i	−0.565247	+	0.0843107i
$400$	−3.76642e9	+	6.52363e9i	−0.147126	+	0.254829i
$401$	8.68342e9	+	5.01338e9i	0.335825	+	0.193889i	0.658424	−	0.752647i	$-0.271223\pi$
$401$	8.68342e9	+	5.01338e9i	0.335825	+	0.193889i	−0.322599	+	0.946536i	$0.604557\pi$
$402$	7.41670e9	+	2.92398e9i	0.283992	+	0.111962i
$403$	1.39169e10	+	2.41048e10i	0.527622	+	0.913868i
$404$		−	3.87973e10i		−	1.45638i
$405$	−7.23802e9	+	1.47970e10i	−0.269030	+	0.549987i
$406$	3.01013e9			0.110785
$407$	−5.40653e9	+	3.12146e9i	−0.197034	+	0.113758i
$408$	1.46267e10	−	3.71008e10i	0.527845	−	1.33888i
$409$	1.86745e10	−	3.23451e10i	0.667352	−	1.15589i	−0.311289	−	0.950315i	$-0.600761\pi$
$409$	1.86745e10	−	3.23451e10i	0.667352	−	1.15589i	0.978642	−	0.205573i	$-0.0659059\pi$
$410$	−8.36552e9	−	4.82983e9i	−0.296045	−	0.170922i
$411$	6.37352e8	+	4.27302e9i	0.0223363	+	0.149750i
$412$	1.70231e10	+	2.94849e10i	0.590813	+	1.02332i
$413$			8.18488e9i			0.281327i
$414$	−5.08649e9	−	4.74869e9i	−0.173148	−	0.161649i
$415$	1.55664e10			0.524801
$416$	−3.17681e10	+	1.83413e10i	−1.06076	+	0.612431i
$417$	−2.04949e10	−	2.57808e10i	−0.677800	−	0.852613i
$418$	3.74832e9	−	6.49227e9i	0.122781	−	0.212663i
$419$	1.53553e10	+	8.86539e9i	0.498198	+	0.287635i	0.727969	−	0.685610i	$-0.240464\pi$
$419$	1.53553e10	+	8.86539e9i	0.498198	+	0.287635i	−0.229771	+	0.973245i	$0.573798\pi$
$420$	4.71451e9	−	3.74788e9i	0.151509	−	0.120445i
$421$	−1.92354e10	−	3.33166e10i	−0.612311	−	1.06055i	−0.990850	−	0.134968i	$-0.956907\pi$
$421$	−1.92354e10	−	3.33166e10i	−0.612311	−	1.06055i	0.378539	−	0.925585i	$-0.376426\pi$
$422$			1.41612e9i			0.0446530i
$423$	−3.50817e10	−	8.12048e9i	−1.09577	−	0.253641i
$424$	−4.55210e10			−1.40847
$425$	3.23380e10	−	1.86704e10i	0.991192	−	0.572265i
$426$	4.43743e9	−	6.61875e8i	0.134739	−	0.0200973i
$427$	3.24552e9	−	5.62140e9i	0.0976275	−	0.169096i
$428$	2.07930e9	+	1.20048e9i	0.0619643	+	0.0357751i
$429$	1.50313e10	+	5.92598e9i	0.443780	+	0.174957i
$430$	−4.01967e9	−	6.96228e9i	−0.117576	−	0.203647i
$431$			2.36204e10i			0.684508i	0.939608	+	0.342254i	$0.111190\pi$
$431$			2.36204e10i			0.684508i	−0.939608	+	0.342254i	$0.888810\pi$
$432$	−1.35025e10	−	9.29716e9i	−0.387686	−	0.266941i
$433$	4.85864e10			1.38218			0.691088	−	0.722770i	$-0.257132\pi$
$433$	4.85864e10			1.38218			0.691088	+	0.722770i	$0.257132\pi$
$434$	−4.42912e9	+	2.55715e9i	−0.124841	+	0.0720772i
$435$	−5.27192e9	+	1.33723e10i	−0.147235	+	0.373464i
$436$	6.02125e9	−	1.04291e10i	0.166625	−	0.288603i
$437$	2.53045e10	+	1.46095e10i	0.693860	+	0.400600i
$438$	−3.82759e8	−	2.56614e9i	−0.0103999	−	0.0697243i
$439$	−1.45910e9	−	2.52723e9i	−0.0392849	−	0.0680434i	0.845714	−	0.533636i	$-0.179175\pi$
$439$	−1.45910e9	−	2.52723e9i	−0.0392849	−	0.0680434i	−0.884999	+	0.465592i	$0.845841\pi$
$440$			6.95706e9i			0.185616i
$441$	−3.06900e10	+	9.36360e9i	−0.811415	+	0.247565i
$442$	3.74996e10			0.982511
$443$	−6.94159e9	+	4.00773e9i	−0.180237	+	0.104060i	−0.587404	−	0.809294i	$-0.699850\pi$
$443$	−6.94159e9	+	4.00773e9i	−0.180237	+	0.104060i	0.407167	+	0.913354i	$0.366517\pi$
$444$	1.15809e10	+	1.45678e10i	0.297996	+	0.374854i
$445$	5.56050e9	−	9.63107e9i	0.141799	−	0.245603i
$446$	1.16924e10	+	6.75061e9i	0.295505	+	0.170610i
$447$	3.21860e9	−	2.55868e9i	0.0806189	−	0.0640893i
$448$	3.21877e8	+	5.57508e8i	0.00799058	+	0.0138401i
$449$			5.34461e9i			0.131501i	0.997836	+	0.0657507i	$0.0209442\pi$
$449$			5.34461e9i			0.131501i	−0.997836	+	0.0657507i	$0.979056\pi$
$450$	3.24568e9	+	1.06380e10i	0.0791510	+	0.259424i
$451$	−2.05329e10			−0.496300
$452$	−2.82423e10	+	1.63057e10i	−0.676622	+	0.390648i
$453$	−1.92704e10	+	2.87432e9i	−0.457612	+	0.0682562i
$454$	−1.46983e10	+	2.54582e10i	−0.345974	+	0.599245i
$455$	1.09464e10	+	6.31988e9i	0.255402	+	0.147456i
$456$	−4.64015e10	−	1.82934e10i	−1.07318	−	0.423093i
$457$	1.77423e10	+	3.07305e10i	0.406766	+	0.704539i	0.994525	−	0.104497i	$-0.0333231\pi$
$457$	1.77423e10	+	3.07305e10i	0.406766	+	0.704539i	−0.587759	+	0.809036i	$0.699990\pi$
$458$			3.54801e9i			0.0806348i
$459$	3.49222e10	+	7.33786e10i	0.786776	+	1.65317i
$460$	−1.21493e10			−0.271344
$461$	−4.25420e10	+	2.45616e10i	−0.941920	+	0.543818i	−0.890562	−	0.454863i	$-0.849688\pi$
$461$	−4.25420e10	+	2.45616e10i	−0.941920	+	0.543818i	−0.0513583	+	0.998680i	$0.516355\pi$
$462$	−1.08886e9	+	2.76192e9i	−0.0239004	+	0.0606237i
$463$	3.87860e10	−	6.71794e10i	0.844017	−	1.46188i	−0.0424548	−	0.999098i	$-0.513518\pi$
$463$	3.87860e10	−	6.71794e10i	0.844017	−	1.46188i	0.886472	−	0.462782i	$-0.153149\pi$
$464$	−1.23888e10	−	7.15268e9i	−0.267274	−	0.154311i
$465$	−3.60284e9	−	2.41546e10i	−0.0770608	−	0.516641i
$466$	1.26459e9	+	2.19034e9i	0.0268168	+	0.0464480i
$467$			4.39387e10i			0.923803i	0.886931	+	0.461901i	$0.152833\pi$
$467$			4.39387e10i			0.923803i	−0.886931	+	0.461901i	$0.847167\pi$
$468$	1.08617e10	−	4.69242e10i	0.226420	−	0.978168i
$469$	1.32569e10			0.274000
$470$	1.26262e10	−	7.28976e9i	0.258751	−	0.149390i
$471$	−8.78214e8	−	1.10472e9i	−0.0178450	−	0.0224475i
$472$	−1.40922e10	+	2.44083e10i	−0.283929	+	0.491779i
$473$	−1.47993e10	−	8.54435e9i	−0.295662	−	0.170700i
$474$	1.21151e9	−	9.63107e8i	0.0240000	−	0.0190792i
$475$	−2.33508e10	−	4.04447e10i	−0.458698	−	0.794488i
$476$		−	2.97125e10i		−	0.578777i
$477$	6.33010e10	−	6.78039e10i	1.22275	−	1.30973i
$478$	2.36700e10			0.453405
$479$	8.49436e10	−	4.90422e10i	1.61357	−	0.931597i	0.625040	−	0.780592i	$-0.285082\pi$
$479$	8.49436e10	−	4.90422e10i	1.61357	−	0.931597i	0.988533	−	0.151005i	$-0.0482509\pi$
$480$	3.18337e10	−	4.74824e9i	0.599684	−	0.0894473i
$481$	−1.95284e10	+	3.38242e10i	−0.364826	+	0.631898i
$482$	−2.68103e10	−	1.54789e10i	−0.496722	−	0.286782i
$483$	−1.07649e10	−	4.24399e9i	−0.197798	−	0.0779805i
$484$	−1.89600e10	−	3.28396e10i	−0.345506	−	0.598434i
$485$		−	3.50566e10i		−	0.633582i
$486$	−2.36389e10	+	5.20501e9i	−0.423723	+	0.0932988i
$487$	−7.42528e10			−1.32007			−0.660035	−	0.751235i	$-0.729459\pi$
$487$	−7.42528e10			−1.32007			−0.660035	+	0.751235i	$0.729459\pi$
$488$	1.93571e10	−	1.11758e10i	0.341319	−	0.197061i
$489$	−1.57825e10	+	4.00325e10i	−0.276020	+	0.700128i
$490$	6.49567e9	−	1.12508e10i	0.112678	−	0.195164i
$491$	−7.06291e10	−	4.07777e10i	−1.21523	−	0.701612i	−0.251335	−	0.967900i	$-0.580869\pi$
$491$	−7.06291e10	−	4.07777e10i	−1.21523	−	0.701612i	−0.963894	+	0.266288i	$0.914203\pi$
$492$	9.02982e9	+	6.05389e10i	0.154106	+	1.03318i
$493$	3.54563e10	+	6.14121e10i	0.600213	+	1.03960i
$494$		−	4.69002e10i		−	0.787530i
$495$	−1.03626e10	−	9.67441e9i	−0.172603	−	0.161140i
$496$	2.43053e10			0.401582
$497$	6.46099e9	−	3.73026e9i	0.105895	−	0.0611383i
$498$	1.42341e10	+	1.79053e10i	0.231427	+	0.291115i
$499$	−5.69859e10	+	9.87025e10i	−0.919106	+	1.59194i	−0.118330	+	0.992974i	$0.537754\pi$
$499$	−5.69859e10	+	9.87025e10i	−0.919106	+	1.59194i	−0.800776	+	0.598964i	$0.795579\pi$
$500$	4.37181e10	+	2.52407e10i	0.699490	+	0.403851i
$501$	3.46907e9	−	2.75780e9i	0.0550633	−	0.0437735i
$502$	−4.04091e8	−	6.99906e8i	−0.00636303	−	0.0110211i
$503$			9.75128e8i			0.0152331i	0.999971	+	0.00761657i	$0.00242445\pi$
$503$			9.75128e8i			0.0152331i	−0.999971	+	0.00761657i	$0.997576\pi$
$504$	1.92435e10	+	4.45437e9i	0.298238	+	0.0690341i
$505$	−7.14419e10			−1.09847
$506$	5.18646e9	−	2.99441e9i	0.0791169	−	0.0456782i
$507$	3.46255e10	−	5.16464e9i	0.524039	−	0.0781643i
$508$	−3.35999e9	+	5.81968e9i	−0.0504526	+	0.0873864i
$509$	−3.54831e10	−	2.04862e10i	−0.528628	−	0.305204i	0.211829	−	0.977307i	$-0.432058\pi$
$509$	−3.54831e10	−	2.04862e10i	−0.528628	−	0.305204i	−0.740458	+	0.672103i	$0.765391\pi$
$510$	−3.06098e10	−	1.20677e10i	−0.452460	−	0.178379i
$511$	−2.15719e9	−	3.73635e9i	−0.0316376	−	0.0547980i
$512$			5.74587e10i			0.836134i
$513$	9.17736e10	−	4.36767e10i	1.32510	−	0.630639i
$514$	1.17331e10			0.168098
$515$	5.42940e10	−	3.13466e10i	0.771832	−	0.445617i
$516$	−1.86837e10	+	4.73914e10i	−0.263551	+	0.668500i
$517$	1.54954e10	−	2.68387e10i	0.216890	−	0.375664i
$518$	−6.21499e9	−	3.58823e9i	−0.0863220	−	0.0498380i
$519$	7.43284e9	+	4.98322e10i	0.102444	+	0.686816i
$520$	2.17623e10	+	3.76934e10i	0.297640	+	0.515527i
$521$			1.06574e11i			1.44644i	0.690617	+	0.723221i	$0.257339\pi$
$521$			1.06574e11i			1.44644i	−0.690617	+	0.723221i	$0.742661\pi$
$522$	−2.02023e10	+	6.16377e9i	−0.272094	+	0.0830165i
$523$	6.45167e10			0.862314			0.431157	−	0.902277i	$-0.358105\pi$
$523$	6.45167e10			0.862314			0.431157	+	0.902277i	$0.358105\pi$
$524$	4.78850e10	−	2.76464e10i	0.635147	−	0.366702i
$525$	1.15091e10	+	1.44774e10i	0.151496	+	0.190569i
$526$	−2.04037e10	+	3.53403e10i	−0.266542	+	0.461665i
$527$	−1.04341e11	−	6.02414e10i	−1.35274	−	0.781003i
$528$	1.10443e10	−	8.77988e9i	0.142103	−	0.112967i
$529$	−2.74844e10	−	4.76044e10i	−0.350965	−	0.607889i
$530$			3.75568e10i			0.475976i
$531$	−1.67600e10	−	5.49324e10i	−0.210812	−	0.690956i
$532$	−3.71610e10			−0.463917
$533$	−1.11247e11	+	6.42287e10i	−1.37842	+	0.795830i
$534$	1.61628e10	−	2.41080e9i	0.198770	−	0.0296481i
$535$	2.21059e9	−	3.82885e9i	0.0269832	−	0.0467362i
$536$	3.95337e10	+	2.28248e10i	0.478969	+	0.276533i
$537$	−1.01859e11	−	4.01570e10i	−1.22490	−	0.482907i
$538$	−1.92928e10	−	3.34161e10i	−0.230285	−	0.398866i
$539$		−	2.76148e10i		−	0.327180i
$540$	−2.39667e10	+	3.48074e10i	−0.281860	+	0.409352i
$541$	1.30431e11			1.52262			0.761308	−	0.648390i	$-0.224557\pi$
$541$	1.30431e11			1.52262			0.761308	+	0.648390i	$0.224557\pi$
$542$	2.96651e10	−	1.71272e10i	0.343755	−	0.198467i
$543$	1.73272e10	−	4.39507e10i	0.199310	−	0.505553i
$544$	7.93930e10	−	1.37513e11i	0.906540	−	1.57017i
$545$	−1.92043e10	−	1.10876e10i	−0.217677	−	0.125676i
$546$	2.74004e9	+	1.83701e10i	0.0308309	+	0.206701i
$547$	1.26081e10	+	2.18378e10i	0.140831	+	0.243927i	0.927810	−	0.373053i	$-0.121689\pi$
$547$	1.26081e10	+	2.18378e10i	0.140831	+	0.243927i	−0.786979	+	0.616980i	$0.788356\pi$
$548$			1.10839e10i			0.122905i
$549$	−1.02713e10	+	4.43735e10i	−0.113067	+	0.488466i
$550$	−9.57206e9			−0.104606
$551$	7.68073e10	−	4.43447e10i	0.833289	−	0.481100i
$552$	−2.47953e10	−	3.11904e10i	−0.267063	−	0.335942i
$553$	1.28680e9	−	2.22880e9i	0.0137597	−	0.0238326i
$554$	2.18224e10	+	1.25992e10i	0.231667	+	0.133753i
$555$	2.68254e10	−	2.13253e10i	0.282731	−	0.224762i
$556$	−4.22476e10	−	7.31750e10i	−0.442082	−	0.765709i
$557$		−	2.17570e10i		−	0.226037i	−0.993593	−	0.113018i	$-0.963948\pi$
$557$		−	2.17570e10i		−	0.226037i	0.993593	−	0.113018i	$-0.0360519\pi$
$558$	2.44895e10	−	2.62316e10i	0.252606	−	0.270575i
$559$	−1.06910e11			−1.09489
$560$	9.55866e9	−	5.51869e9i	0.0971952	−	0.0561157i
$561$	−6.91739e10	+	1.03178e10i	−0.698379	+	0.104168i
$562$	2.43233e9	−	4.21293e9i	0.0243825	−	0.0422317i
$563$	1.19979e11	+	6.92701e10i	1.19419	+	0.689465i	0.959254	−	0.282546i	$-0.0911791\pi$
$563$	1.19979e11	+	6.92701e10i	1.19419	+	0.689465i	0.234935	+	0.972011i	$0.424512\pi$
$564$	−8.59453e10	−	3.38833e10i	−0.849388	−	0.334865i
$565$	3.00255e10	+	5.20058e10i	0.294644	+	0.510338i
$566$			5.43136e10i			0.529228i
$567$	−3.33947e10	+	2.24692e10i	−0.323106	+	0.217398i
$568$	2.56900e10			0.246814
$569$	−1.37998e11	+	7.96731e10i	−1.31651	+	0.760086i	−0.983165	−	0.182720i	$-0.941510\pi$
$569$	−1.37998e11	+	7.96731e10i	−1.31651	+	0.760086i	−0.333343	+	0.942806i	$0.608177\pi$
$570$	−1.50929e10	+	3.82833e10i	−0.142979	+	0.362668i
$571$	4.81604e10	−	8.34163e10i	0.453050	−	0.784705i	−0.545524	−	0.838095i	$-0.683669\pi$
$571$	4.81604e10	−	8.34163e10i	0.453050	−	0.784705i	0.998574	+	0.0533899i	$0.0170026\pi$
$572$	3.58987e10	+	2.07261e10i	0.335347	+	0.193613i
$573$	−1.30577e10	−	8.75433e10i	−0.121129	−	0.812091i
$574$	−1.18016e10	−	2.04410e10i	−0.108716	−	0.188302i
$575$		−	3.73083e10i		−	0.341299i
$576$	−3.30186e9	−	3.08258e9i	−0.0299964	−	0.0280043i
$577$	1.43893e11			1.29819			0.649093	−	0.760709i	$-0.275149\pi$
$577$	1.43893e11			1.29819			0.649093	+	0.760709i	$0.275149\pi$
$578$	−9.86376e10	+	5.69484e10i	−0.883754	+	0.510235i
$579$	5.63550e10	+	7.08897e10i	0.501439	+	0.630767i
$580$	−1.84385e10	+	3.19365e10i	−0.162935	+	0.282212i
$581$	3.29403e10	+	1.90181e10i	0.289084	+	0.166903i
$582$	4.03241e10	−	3.20564e10i	0.351458	−	0.279397i
$583$	3.99160e10	+	6.91366e10i	0.345520	+	0.598458i
$584$		−	1.48564e10i		−	0.127721i
$585$	−8.64069e10	−	2.00009e10i	−0.737777	−	0.170776i
$586$	−5.75817e10			−0.488308
$587$	4.33157e10	−	2.50083e10i	0.364832	−	0.210636i	−0.306366	−	0.951914i	$-0.599113\pi$
$587$	4.33157e10	−	2.50083e10i	0.364832	−	0.210636i	0.671198	+	0.741278i	$0.265780\pi$
$588$	−8.14191e10	+	1.21442e10i	−0.681109	+	0.101592i
$589$	−7.53431e10	+	1.30498e11i	−0.626011	+	1.08428i
$590$	2.01380e10	+	1.16267e10i	0.166191	+	0.0959504i
$591$	1.96537e11	+	7.74830e10i	1.61099	+	0.635121i
$592$	1.70527e10	+	2.95362e10i	0.138838	+	0.240474i
$593$			1.28923e9i			0.0104258i	0.999986	+	0.00521291i	$0.00165933\pi$
$593$			1.28923e9i			0.0104258i	−0.999986	+	0.00521291i	$0.998341\pi$
$594$	1.65233e9	−	2.07661e10i	0.0132725	−	0.166805i
$595$	−5.47130e10			−0.436539
$596$	9.13552e9	−	5.27439e9i	0.0724016	−	0.0418011i
$597$	4.62040e10	−	1.17197e11i	0.363732	−	0.922611i
$598$	1.87335e10	−	3.24474e10i	0.146492	−	0.253732i
$599$	1.08459e11	+	6.26186e10i	0.842474	+	0.486403i	0.858105	−	0.513475i	$-0.171642\pi$
$599$	1.08459e11	+	6.26186e10i	0.842474	+	0.486403i	−0.0156302	+	0.999878i	$0.504975\pi$
$600$	9.39525e9	+	6.29889e10i	0.0724943	+	0.486025i
$601$	6.08247e10	+	1.05351e11i	0.466211	+	0.807500i	0.999255	−	0.0385866i	$-0.0122856\pi$
$601$	6.08247e10	+	1.05351e11i	0.466211	+	0.807500i	−0.533045	+	0.846087i	$0.678952\pi$
$602$		−	1.96440e10i		−	0.149570i
$603$	−8.89728e10	+	2.71458e10i	−0.672958	+	0.205321i
$604$	−4.99859e10			−0.375578
$605$	−6.04714e10	+	3.49132e10i	−0.451365	+	0.260596i
$606$	−6.53277e10	−	8.21766e10i	−0.484403	−	0.609337i
$607$	1.53955e10	−	2.66659e10i	0.113407	−	0.196427i	−0.803735	−	0.594988i	$-0.797157\pi$
$607$	1.53955e10	−	2.66659e10i	0.113407	−	0.196427i	0.917142	+	0.398561i	$0.130490\pi$
$608$	−1.71985e11	−	9.92957e10i	−1.25857	−	0.726635i
$609$	−2.74935e10	+	2.18565e10i	−0.199876	+	0.158895i
$610$	−9.22053e9	−	1.59704e10i	−0.0665943	−	0.115345i
$611$		−	1.93883e11i		−	1.39115i
$612$	6.08416e10	+	1.99414e11i	0.433706	+	1.42151i
$613$	−1.12498e11			−0.796714			−0.398357	−	0.917230i	$-0.630419\pi$
$613$	−1.12498e11			−0.796714			−0.398357	+	0.917230i	$0.630419\pi$
$614$	8.95709e10	−	5.17138e10i	0.630222	−	0.363859i
$615$	1.11477e11	−	1.66277e10i	0.779267	−	0.116233i
$616$	−8.49975e9	+	1.47220e10i	−0.0590314	+	0.102245i
$617$	−4.32410e10	−	2.49652e10i	−0.298370	−	0.172264i	0.343340	−	0.939211i	$-0.388442\pi$
$617$	−4.32410e10	−	2.49652e10i	−0.298370	−	0.172264i	−0.641710	+	0.766947i	$0.721775\pi$
$618$	8.57040e10	+	3.37881e10i	0.587553	+	0.231638i
$619$	−7.20206e10	−	1.24743e11i	−0.490562	−	0.849678i	0.509379	−	0.860542i	$-0.329875\pi$
$619$	−7.20206e10	−	1.24743e11i	−0.490562	−	0.849678i	−0.999941	+	0.0108640i	$0.996542\pi$
$620$		−	6.26553e10i		−	0.424025i
$621$	8.09385e10	+	6.44019e9i	0.544238	+	0.0433044i
$622$	−8.80663e10			−0.588367
$623$	2.35334e10	−	1.35870e10i	0.156219	−	0.0901928i
$624$	3.23740e10	−	8.21170e10i	0.213529	−	0.541620i
$625$	−1.21560e9	+	2.10547e9i	−0.00796653	+	0.0137984i
$626$	−1.91586e10	−	1.10612e10i	−0.124757	−	0.0720286i
$627$	1.29043e10	+	8.65148e10i	0.0834959	+	0.559784i
$628$	−1.81033e9	−	3.13558e9i	−0.0116391	−	0.0201595i
$629$		−	1.69063e11i		−	1.08005i
$630$	3.67505e9	−	1.58768e10i	0.0233293	−	0.100786i
$631$	2.70159e10			0.170412			0.0852062	−	0.996363i	$-0.472845\pi$
$631$	2.70159e10			0.170412			0.0852062	+	0.996363i	$0.472845\pi$
$632$	7.67479e9	−	4.43104e9i	0.0481059	−	0.0277739i
$633$	−1.02824e10	−	1.29344e10i	−0.0640443	−	0.0805622i
$634$	5.19695e9	−	9.00138e9i	0.0321656	−	0.0557124i
$635$	1.07164e10	+	6.18714e9i	0.0659107	+	0.0380535i
$636$	1.86287e11	−	1.48092e11i	1.13856	−	0.905115i
$637$	−8.63815e10	−	1.49617e11i	−0.524642	−	0.908706i
$638$		−	1.81780e10i		−	0.109714i
$639$	−3.57242e10	+	3.82654e10i	−0.214269	+	0.229511i
$640$	1.03552e11			0.617220
$641$	−1.66097e11	+	9.58963e10i	−0.983853	+	0.568028i	−0.903431	−	0.428733i	$-0.858960\pi$
$641$	−1.66097e11	+	9.58963e10i	−0.983853	+	0.568028i	−0.0804218	+	0.996761i	$0.525627\pi$
$642$	6.42556e9	−	9.58420e8i	0.0378243	−	0.00564177i
$643$	−7.50236e10	+	1.29945e11i	−0.438888	+	0.760177i	−0.997604	−	0.0691825i	$-0.977961\pi$
$643$	−7.50236e10	+	1.29945e11i	−0.438888	+	0.760177i	0.558716	+	0.829359i	$0.311294\pi$
$644$	−2.57094e10	−	1.48433e10i	−0.149468	−	0.0862955i
$645$	8.72674e10	+	3.44045e10i	0.504212	+	0.198782i
$646$	1.01507e11	+	1.75816e11i	0.582863	+	1.00955i
$647$			1.42232e10i			0.0811672i	0.999176	+	0.0405836i	$0.0129217\pi$
$647$			1.42232e10i			0.0811672i	−0.999176	+	0.0405836i	$0.987078\pi$
$648$	−1.38273e11	+	9.50934e9i	−0.784219	+	0.0539325i
$649$	4.94280e10			0.278609
$650$	−5.18614e10	+	2.99422e10i	−0.290530	+	0.167738i
$651$	2.18867e10	−	5.55159e10i	0.121859	−	0.309096i
$652$	−5.51993e10	+	9.56080e10i	−0.305452	+	0.529058i
$653$	1.64751e11	+	9.51189e10i	0.906097	+	0.523135i	0.879173	−	0.476502i	$-0.158096\pi$
$653$	1.64751e11	+	9.51189e10i	0.906097	+	0.523135i	0.0269236	+	0.999637i	$0.491429\pi$
$654$	−4.80713e9	−	3.22286e10i	−0.0262770	−	0.176169i
$655$	−5.09086e10	−	8.81762e10i	−0.276583	−	0.479056i
$656$			1.12173e11i			0.605719i
$657$	2.21287e10	+	2.06591e10i	0.118767	+	0.110879i
$658$	3.56249e10			0.190042
$659$	−3.84135e10	+	2.21780e10i	−0.203677	+	0.117593i	−0.598370	−	0.801220i	$-0.704185\pi$
$659$	−3.84135e10	+	2.21780e10i	−0.203677	+	0.117593i	0.394692	+	0.918813i	$0.370851\pi$
$660$	−2.26332e10	−	2.84706e10i	−0.119281	−	0.150045i
$661$	−7.71408e9	+	1.33612e10i	−0.0404090	+	0.0699905i	−0.885523	−	0.464596i	$-0.846199\pi$
$661$	−7.71408e9	+	1.33612e10i	−0.0404090	+	0.0699905i	0.845114	+	0.534587i	$0.179533\pi$
$662$	1.12071e11	+	6.47045e10i	0.583530	+	0.336901i
$663$	−3.42509e11	+	2.72284e11i	−1.77263	+	1.40918i
$664$	6.54881e10	+	1.13429e11i	0.336892	+	0.583514i
$665$			6.84288e10i			0.349907i
$666$	4.90591e10	+	1.13559e10i	0.249358	+	0.0577196i
$667$	7.08510e10			0.357967
$668$	9.84645e9	−	5.68485e9i	0.0494509	−	0.0285505i
$669$	−1.55811e11	+	2.32403e10i	−0.777845	+	0.116021i
$670$	1.88314e10	−	3.26170e10i	0.0934511	−	0.161862i
$671$	−3.39473e10	−	1.95995e10i	−0.167462	−	0.0966840i
$672$	7.31653e10	+	2.88448e10i	0.358780	+	0.141446i
$673$	−6.47962e9	−	1.12230e10i	−0.0315856	−	0.0547079i	0.849800	−	0.527104i	$-0.176722\pi$
$673$	−6.47962e9	−	1.12230e10i	−0.0315856	−	0.0547079i	−0.881386	+	0.472397i	$0.843389\pi$
$674$			4.45866e9i			0.0216055i
$675$	−1.06887e11	−	7.35974e10i	−0.514886	−	0.354525i
$676$	8.98159e10			0.430097
$677$	1.18359e11	−	6.83344e10i	0.563437	−	0.325301i	−0.191087	−	0.981573i	$-0.561201\pi$
$677$	1.18359e11	−	6.83344e10i	0.563437	−	0.325301i	0.754524	+	0.656273i	$0.227868\pi$
$678$	−3.23641e10	+	8.20920e10i	−0.153160	+	0.388492i
$679$	4.28302e10	−	7.41841e10i	0.201498	−	0.349005i
$680$	−1.63161e11	−	9.42011e10i	−0.763099	−	0.440576i
$681$	−5.06018e10	−	3.39251e11i	−0.235276	−	1.57737i
$682$	1.54425e10	+	2.67472e10i	0.0713806	+	0.123635i
$683$			6.40947e10i			0.294537i	0.989097	+	0.147268i	$0.0470481\pi$
$683$			6.40947e10i			0.294537i	−0.989097	+	0.147268i	$0.952952\pi$
$684$	2.49404e11	−	7.60938e10i	1.13941	−	0.347636i
$685$	2.04101e10			0.0927005
$686$	5.98972e10	−	3.45816e10i	0.270464	−	0.156153i
$687$	−2.57620e10	−	3.24064e10i	−0.115652	−	0.145480i
$688$	−4.66783e10	+	8.08492e10i	−0.208335	+	0.360846i
$689$	4.32530e11	+	2.49721e11i	1.91929	+	1.10810i
$690$	−2.57335e10	+	2.04573e10i	−0.113528	+	0.0902508i
$691$	−1.99280e11	−	3.45164e11i	−0.874082	−	1.51395i	−0.857738	−	0.514088i	$-0.828131\pi$
$691$	−1.99280e11	−	3.45164e11i	−0.874082	−	1.51395i	−0.0163441	−	0.999866i	$-0.505203\pi$
$692$			1.29261e11i			0.563694i
$693$	−1.01089e10	−	3.31327e10i	−0.0438298	−	0.143656i
$694$	6.82592e9			0.0294255
$695$	−1.34746e11	+	7.77954e10i	−0.577531	+	0.333438i
$696$	−1.19620e11	+	1.78422e10i	−0.509762	+	0.0760347i
$697$	2.78023e11	−	4.81550e11i	1.17801	−	2.04038i
$698$	−1.52931e10	−	8.82947e9i	−0.0644278	−	0.0371974i
$699$	−2.74544e10	−	1.08237e10i	−0.115001	−	0.0453384i
$700$	2.37245e10	+	4.10920e10i	0.0988108	+	0.171145i
$701$		−	1.78042e11i		−	0.737312i	−0.929566	−	0.368656i	$-0.879818\pi$
$701$		−	1.78042e11i		−	0.737312i	0.929566	−	0.368656i	$-0.120182\pi$
$702$	−5.60057e10	−	1.17679e11i	−0.230613	−	0.484565i
$703$	−2.11445e11			−0.865716
$704$	3.36676e9	−	1.94380e9i	0.0137063	−	0.00791336i
$705$	−6.23932e10	+	1.58261e11i	−0.252570	+	0.640645i
$706$	−2.25072e10	+	3.89835e10i	−0.0905945	+	0.156914i
$707$	−1.51180e11	−	8.72838e10i	−0.605085	−	0.349346i
$708$	−2.17371e10	−	1.45733e11i	−0.0865105	−	0.579995i
$709$	1.35665e11	+	2.34979e11i	0.536887	+	0.929916i	0.999069	+	0.0431311i	$0.0137333\pi$
$709$	1.35665e11	+	2.34979e11i	0.536887	+	0.929916i	−0.462182	+	0.886785i	$0.652933\pi$
$710$		−	2.11954e10i		−	0.0834080i
$711$	−4.07241e9	+	1.75934e10i	−0.0159358	+	0.0688449i
$712$	9.35727e10			0.364107
$713$	−1.04251e11	+	6.01891e10i	−0.403386	+	0.232895i
$714$	−5.00305e10	−	6.29341e10i	−0.192505	−	0.242155i
$715$	3.81654e10	−	6.61044e10i	0.146031	−	0.252933i
$716$	−2.43265e11	−	1.40449e11i	−0.925608	−	0.534400i
$717$	−2.16194e11	+	1.71867e11i	−0.818027	+	0.650304i
$718$	−4.71403e10	−	8.16494e10i	−0.177376	−	0.307224i
$719$			5.27584e11i			1.97413i	0.160318	+	0.987065i	$0.448748\pi$
$719$			5.27584e11i			1.97413i	−0.160318	+	0.987065i	$0.551252\pi$
$720$	−5.28519e10	+	5.66115e10i	−0.196667	+	0.210656i
$721$	1.53190e11			0.566879
$722$	1.17786e11	−	6.80039e10i	0.433456	−	0.250256i
$723$	3.57269e11	−	5.32892e10i	1.30750	−	0.195023i
$724$	6.06020e10	−	1.04966e11i	0.220563	−	0.382026i
$725$	−9.80712e10	−	5.66214e10i	−0.354968	−	0.204941i
$726$	−9.54551e10	−	3.76324e10i	−0.343600	−	0.135461i
$727$	1.58907e11	+	2.75236e11i	0.568861	+	0.985297i	0.996679	+	0.0814316i	$0.0259492\pi$
$727$	1.58907e11	+	2.75236e11i	0.568861	+	0.985297i	−0.427818	+	0.903865i	$0.640717\pi$
$728$			1.06352e11i			0.378633i
$729$	1.78117e11	−	2.19182e11i	0.630659	−	0.776060i
$730$	−1.22572e10			−0.0431617
$731$	4.00775e11	−	2.31387e11i	1.40356	−	0.810345i
$732$	−4.28577e10	+	1.08709e11i	−0.149274	+	0.378635i
$733$	−1.28841e11	+	2.23159e11i	−0.446312	+	0.773035i	−0.998143	−	0.0609213i	$-0.980596\pi$
$733$	−1.28841e11	+	2.23159e11i	−0.446312	+	0.773035i	0.551831	+	0.833956i	$0.313929\pi$
$734$	−1.99819e11	−	1.15365e11i	−0.688418	−	0.397458i
$735$	2.23626e10	+	1.49926e11i	0.0766255	+	0.513722i
$736$	−7.93241e10	−	1.37393e11i	−0.270330	−	0.468225i
$737$		−	8.00575e10i		−	0.271351i
$738$	1.21063e11	+	1.13023e11i	0.408117	+	0.381014i
$739$	−4.59849e10			−0.154183			−0.0770917	−	0.997024i	$-0.524563\pi$
$739$	−4.59849e10			−0.154183			−0.0770917	+	0.997024i	$0.524563\pi$
$740$	7.61399e10	−	4.39594e10i	0.253913	−	0.146597i
$741$	3.40541e11	+	4.28372e11i	1.12953	+	1.42085i
$742$	−4.58848e10	+	7.94749e10i	−0.151375	+	0.262189i
$743$	−1.15801e11	−	6.68579e10i	−0.379978	−	0.219380i	0.297831	−	0.954619i	$-0.403737\pi$
$743$	−1.15801e11	−	6.68579e10i	−0.379978	−	0.219380i	−0.677809	+	0.735238i	$0.737070\pi$
$744$	1.60852e11	−	1.27872e11i	0.524972	−	0.417335i
$745$	−9.71235e9	−	1.68223e10i	−0.0315282	−	0.0546085i
$746$			9.58102e10i			0.309355i
$747$	−2.60020e11	−	6.01878e10i	−0.835073	−	0.193297i
$748$	−1.79432e11			−0.573183
$749$	9.35575e9	−	5.40155e9i	0.0297270	−	0.0171629i
$750$	1.35100e11	−	2.01512e10i	0.426983	−	0.0636877i
$751$	−2.37013e11	+	4.10519e11i	−0.745097	+	1.29055i	0.205052	+	0.978751i	$0.434264\pi$
$751$	−2.37013e11	+	4.10519e11i	−0.745097	+	1.29055i	−0.950149	+	0.311795i	$0.899070\pi$
$752$	−1.46622e11	−	8.46520e10i	−0.458487	−	0.264707i
$753$	8.77284e9	+	3.45862e9i	0.0272873	+	0.0107578i
$754$	−5.68623e10	−	9.84883e10i	−0.175930	−	0.304719i
$755$			9.20448e10i			0.283277i
$756$	−9.32423e10	+	4.43757e10i	−0.285447	+	0.135849i
$757$	−2.39444e11			−0.729157			−0.364578	−	0.931173i	$-0.618787\pi$
$757$	−2.39444e11			−0.729157			−0.364578	+	0.931173i	$0.618787\pi$
$758$	−1.29237e11	+	7.46149e10i	−0.391480	+	0.226021i
$759$	−2.56292e10	+	6.50088e10i	−0.0772268	+	0.195887i
$760$	−1.17816e11	+	2.04063e11i	−0.353142	+	0.611661i
$761$	2.06197e11	+	1.19048e11i	0.614814	+	0.354963i	0.774847	−	0.632149i	$-0.217827\pi$
$761$	2.06197e11	+	1.19048e11i	0.614814	+	0.354963i	−0.160033	+	0.987112i	$0.551160\pi$
$762$	2.68249e9	+	1.79843e10i	0.00795642	+	0.0533425i
$763$	−2.70925e10	−	4.69255e10i	−0.0799375	−	0.138456i
$764$		−	2.27081e11i		−	0.666511i
$765$	3.67203e11	−	1.12035e11i	1.07216	−	0.327120i
$766$	−1.15673e11			−0.335981
$767$	2.67801e11	−	1.54615e11i	0.773804	−	0.446756i
$768$	8.58058e10	+	1.07936e11i	0.246645	+	0.310258i
$769$	8.28677e10	−	1.43531e11i	0.236963	−	0.410431i	−0.722879	−	0.690975i	$-0.757181\pi$
$769$	8.28677e10	−	1.43531e11i	0.236963	−	0.410431i	0.959841	+	0.280544i	$0.0905148\pi$
$770$	1.21463e10	+	7.01267e9i	0.0345526	+	0.0199490i
$771$	−1.07167e11	+	8.51940e10i	−0.303279	+	0.241097i
$772$	1.16169e11	+	2.01210e11i	0.327054	+	0.566475i
$773$		−	6.52654e11i		−	1.82795i	−0.405766	−	0.913977i	$-0.632995\pi$
$773$		−	6.52654e11i		−	1.82795i	0.405766	−	0.913977i	$-0.367005\pi$
$774$	4.02247e10	+	1.31840e11i	0.112080	+	0.367353i
$775$	1.92403e11			0.533342
$776$	2.55450e11	−	1.47484e11i	0.704465	−	0.406723i
$777$	8.28198e10	−	1.23532e10i	0.227222	−	0.0338918i
$778$	8.37795e10	−	1.45110e11i	0.228675	−	0.396077i
$779$	−6.02268e11	−	3.47720e11i	−1.63546	−	0.944234i
$780$	−2.11685e11	−	8.34553e10i	−0.571890	−	0.225463i
$781$	−2.25268e10	−	3.90176e10i	−0.0605474	−	0.104871i
$782$			1.62181e11i			0.433685i
$783$	1.39766e11	−	2.02986e11i	0.371840	−	0.540032i
$784$	−1.50861e11			−0.399313
$785$	−5.77391e9	+	3.33357e9i	−0.0152052	+	0.00877871i
$786$	5.48737e10	−	1.39188e11i	0.143772	−	0.364679i
$787$	−3.84551e9	+	6.66061e9i	−0.0100243	+	0.0173626i	−0.870994	−	0.491294i	$-0.836524\pi$
$787$	−3.84551e9	+	6.66061e9i	−0.0100243	+	0.0173626i	0.860970	+	0.508656i	$0.169858\pi$
$788$	4.69380e11	+	2.70997e11i	1.21736	+	0.702844i
$789$	−7.02438e10	−	4.70938e11i	−0.181259	−	1.21522i
$790$	−3.65581e9	−	6.33204e9i	−0.00938587	−	0.0162568i
$791$			1.46734e11i			0.374822i
$792$	2.68997e10	−	1.16211e11i	0.0683669	−	0.295355i
$793$	−2.45235e11			−0.620141
$794$	−1.95576e11	+	1.12916e11i	−0.492077	+	0.284101i
$795$	−2.72699e11	−	3.43032e11i	−0.682677	−	0.858749i
$796$	1.61598e11	−	2.79896e11i	0.402517	−	0.697180i
$797$	−3.40517e11	−	1.96598e11i	−0.843928	−	0.487242i	0.0146694	−	0.999892i	$-0.495330\pi$
$797$	−3.40517e11	−	1.96598e11i	−0.843928	−	0.487242i	−0.858598	+	0.512650i	$0.828664\pi$
$798$	−7.87107e10	+	6.25724e10i	−0.194099	+	0.154302i
$799$	4.19626e11	+	7.26813e11i	1.02961	+	1.78335i
$800$			2.53571e11i			0.619070i
$801$	−1.30121e11	+	1.39377e11i	−0.316095	+	0.338581i
$802$	6.96054e10			0.168246
$803$	−2.25636e10	+	1.30271e10i	−0.0542684	+	0.0313319i
$804$	−2.36040e11	+	3.52071e10i	−0.564887	+	0.0842571i
$805$	−2.73328e10	+	4.73417e10i	−0.0650879	+	0.112736i
$806$	1.67335e11	+	9.66108e10i	0.396503	+	0.228921i
$807$	4.18848e11	+	1.65127e11i	0.987557	+	0.389337i
$808$	−3.00558e11	−	5.20582e11i	−0.705153	−	1.22136i
$809$			2.82726e10i			0.0660043i	0.999455	+	0.0330021i	$0.0105068\pi$
$809$			2.82726e10i			0.0660043i	−0.999455	+	0.0330021i	$0.989493\pi$
$810$	7.84563e9	+	1.14081e11i	0.0182258	+	0.265017i
$811$	3.13486e11			0.724661			0.362330	−	0.932050i	$-0.381981\pi$
$811$	3.13486e11			0.724661			0.362330	+	0.932050i	$0.381981\pi$
$812$	−7.80364e10	+	4.50543e10i	−0.179504	+	0.103636i
$813$	−1.46592e11	+	3.71832e11i	−0.335543	+	0.851107i
$814$	−2.16691e10	+	3.75320e10i	−0.0493564	+	0.0854877i
$815$	1.76054e11	+	1.01645e11i	0.399039	+	0.230385i
$816$	5.63667e10	+	3.77901e11i	0.127134	+	0.852349i
$817$	−2.89393e11	−	5.01243e11i	−0.649531	−	1.12502i
$818$		−	2.59275e11i		−	0.579092i
$819$	−1.58412e11	−	1.47892e11i	−0.352088	−	0.328706i
$820$	2.89164e11			0.639571
$821$	−4.79842e11	+	2.77037e11i	−1.05615	+	0.609769i	−0.924365	−	0.381509i	$-0.875404\pi$
$821$	−4.79842e11	+	2.77037e11i	−1.05615	+	0.609769i	−0.131786	+	0.991278i	$0.542071\pi$
$822$	1.86633e10	+	2.34768e10i	0.0408791	+	0.0514223i
$823$	1.04720e11	−	1.81381e11i	0.228261	−	0.395359i	−0.729032	−	0.684480i	$-0.760029\pi$
$823$	1.04720e11	−	1.81381e11i	0.228261	−	0.395359i	0.957293	+	0.289120i	$0.0933628\pi$
$824$	4.56833e11	+	2.63752e11i	0.990942	+	0.572121i
$825$	8.74282e10	−	6.95025e10i	0.188728	−	0.150032i
$826$	2.84096e10	+	4.92069e10i	0.0610302	+	0.105707i
$827$			3.89638e11i			0.832990i	0.909138	+	0.416495i	$0.136742\pi$
$827$			3.89638e11i			0.832990i	−0.909138	+	0.416495i	$0.863258\pi$
$828$	2.02942e11	+	4.69756e10i	0.431768	+	0.0999427i
$829$	2.80930e11			0.594813			0.297406	−	0.954751i	$-0.403878\pi$
$829$	2.80930e11			0.594813			0.297406	+	0.954751i	$0.403878\pi$
$830$	9.35837e10	−	5.40306e10i	0.197191	−	0.113849i
$831$	−2.90801e11	+	4.33752e10i	−0.609807	+	0.0909572i
$832$	1.21607e10	−	2.10630e10i	0.0253785	−	0.0439569i
$833$	6.47639e11	+	3.73915e11i	1.34510	+	0.776591i
$834$	−2.12698e11	−	8.38547e10i	−0.439643	−	0.173326i
$835$	−1.04682e10	−	1.81314e10i	−0.0215340	−	0.0372980i
$836$			2.24413e11i			0.459434i
$837$	−3.32128e10	+	4.17409e11i	−0.0676711	+	0.850472i
$838$	1.23087e11			0.249594
$839$	−7.79523e11	+	4.50058e11i	−1.57319	+	0.908281i	−0.577414	+	0.816451i	$0.695938\pi$
$839$	−7.79523e11	+	4.50058e11i	−1.57319	+	0.908281i	−0.995775	+	0.0918295i	$0.970729\pi$
$840$	3.42249e10	−	8.68118e10i	0.0687424	−	0.174366i
$841$	−1.42595e11	+	2.46982e11i	−0.285050	+	0.493721i
$842$	−2.31283e11	−	1.33531e11i	−0.460145	−	0.265665i
$843$	8.37379e9	+	5.61407e10i	0.0165810	+	0.111165i
$844$	−2.11959e10	−	3.67124e10i	−0.0417717	−	0.0723508i
$845$		−	1.65388e11i		−	0.324398i
$846$	−2.39094e11	+	7.29483e10i	−0.466754	+	0.142408i
$847$	−1.70620e11			−0.331509
$848$	3.77697e11	−	2.18064e11i	0.730399	−	0.421696i
$849$	−3.94370e11	−	4.96083e11i	−0.759055	−	0.954825i
$850$	1.29609e11	−	2.24490e11i	0.248290	−	0.430052i
$851$	−1.46286e11	−	8.44581e10i	−0.278922	−	0.161036i
$852$	−1.05132e11	+	8.35765e10i	−0.199516	+	0.158608i
$853$	7.98028e10	+	1.38222e11i	0.150738	+	0.261085i	0.931499	−	0.363744i	$-0.118502\pi$
$853$	7.98028e10	+	1.38222e11i	0.150738	+	0.261085i	−0.780761	+	0.624830i	$0.785168\pi$
$854$		−	4.50605e10i		−	0.0847159i
$855$	−1.40120e11	−	4.59256e11i	−0.262202	−	0.859390i
$856$	3.72000e10			0.0692865
$857$	−1.34558e11	+	7.76871e10i	−0.249452	+	0.144021i	−0.619513	−	0.784986i	$-0.712670\pi$
$857$	−1.34558e11	+	7.76871e10i	−0.249452	+	0.144021i	0.370062	+	0.929007i	$0.379337\pi$
$858$	1.10936e11	−	1.65469e10i	0.204703	−	0.0305329i
$859$	2.08291e11	−	3.60771e11i	0.382559	−	0.662612i	−0.608868	−	0.793271i	$-0.708376\pi$
$859$	2.08291e11	−	3.60771e11i	0.382559	−	0.662612i	0.991427	+	0.130660i	$0.0417095\pi$
$860$	2.08417e11	+	1.20330e11i	0.381013	+	0.219978i
$861$	2.56214e11	+	1.01011e11i	0.466220	+	0.183804i
$862$	8.19861e10	+	1.42004e11i	0.148495	+	0.257200i
$863$		−	3.88147e11i		−	0.699766i	−0.936793	−	0.349883i	$-0.886221\pi$
$863$		−	3.88147e11i		−	0.699766i	0.936793	−	0.349883i	$-0.113779\pi$
$864$	−5.50109e11	−	4.37716e10i	−0.987175	−	0.0785484i
$865$	2.38023e11			0.425163
$866$	2.92098e11	−	1.68643e11i	0.519346	−	0.299845i
$867$	4.87423e11	−	1.23635e12i	0.862641	−	2.18810i
$868$	7.65488e10	−	1.32586e11i	0.134853	−	0.233572i
$869$	−1.34596e10	−	7.77091e9i	−0.0236022	−	0.0136268i
$870$	1.47206e10	+	9.86919e10i	0.0256950	+	0.172268i
$871$	−2.50427e11	−	4.33752e11i	−0.435119	−	0.753648i
$872$		−	1.86584e11i		−	0.322707i
$873$	−1.35547e11	+	5.85585e11i	−0.233364	+	1.00817i
$874$	2.02838e11			0.347619
$875$	1.96709e11	−	1.13570e11i	0.335576	−	0.193745i
$876$	4.83318e10	+	6.07972e10i	0.0820761	+	0.103245i
$877$	−2.87925e11	+	4.98700e11i	−0.486722	+	0.843026i	−0.999883	−	0.0152653i	$-0.995141\pi$
$877$	−2.87925e11	+	4.98700e11i	−0.486722	+	0.843026i	0.513162	+	0.858292i	$0.328474\pi$
$878$	−1.75439e10	−	1.01290e10i	−0.0295222	−	0.0170447i
$879$	5.25933e11	−	4.18099e11i	0.880997	−	0.700364i
$880$	−3.33271e10	−	5.77242e10i	−0.0555733	−	0.0962558i
$881$		−	3.11023e11i		−	0.516284i	−0.966107	−	0.258142i	$-0.916890\pi$
$881$		−	3.11023e11i		−	0.516284i	0.966107	−	0.258142i	$-0.0831102\pi$
$882$	−1.52005e11	+	1.62818e11i	−0.251179	+	0.269047i
$883$	3.94761e11			0.649368			0.324684	−	0.945822i	$-0.394742\pi$
$883$	3.94761e11			0.649368			0.324684	+	0.945822i	$0.394742\pi$
$884$	−9.72163e11	+	5.61278e11i	−1.59195	+	0.919114i
$885$	−2.68355e11	+	4.00270e10i	−0.437457	+	0.0652500i
$886$	−2.78215e10	+	4.81883e10i	−0.0451488	+	0.0782000i
$887$	−9.38596e10	−	5.41899e10i	−0.151630	−	0.0875435i	0.422265	−	0.906472i	$-0.361235\pi$
$887$	−9.38596e10	−	5.41899e10i	−0.151630	−	0.0875435i	−0.573895	+	0.818929i	$0.694568\pi$
$888$	2.68248e11	+	1.05755e11i	0.431404	+	0.170078i
$889$	1.51182e10	+	2.61855e10i	0.0242043	+	0.0419231i
$890$		−	7.72016e10i		−	0.123046i
$891$	1.35690e11	+	2.01668e11i	0.215297	+	0.319983i
$892$	−4.04162e11			−0.638404
$893$	9.09014e11	−	5.24820e11i	1.42944	−	0.825286i
$894$	1.04688e10	−	2.65543e10i	0.0163888	−	0.0415704i
$895$	−2.58625e11	+	4.47951e11i	−0.403068	+	0.698134i
$896$	2.19129e11	+	1.26514e11i	0.339992	+	0.196294i
$897$	6.44938e10	+	4.32388e11i	0.0996204	+	0.667888i
$898$	1.85511e10	+	3.21314e10i	0.0285275	+	0.0494110i
$899$			3.65387e11i			0.559389i
$900$	−2.43369e11	−	2.27206e11i	−0.370932	−	0.346298i
$901$	−2.16191e12			−3.28049
$902$	−1.23442e11	+	7.12695e10i	−0.186482	+	0.107666i
$903$	1.42635e11	+	1.79423e11i	0.214524	+	0.269852i
$904$	−2.52637e11	+	4.37579e11i	−0.378288	+	0.655214i
$905$	−1.93286e11	−	1.11593e11i	−0.288141	−	0.166358i
$906$	−1.05875e11	+	8.41673e10i	−0.157138	+	0.124920i
$907$	4.57478e11	+	7.92375e11i	0.675991	+	1.17085i	0.976178	+	0.216970i	$0.0696175\pi$
$907$	4.57478e11	+	7.92375e11i	0.675991	+	1.17085i	−0.300187	+	0.953880i	$0.597049\pi$
$908$		−	8.79992e11i		−	1.29460i
$909$	1.19336e12	+	2.76232e11i	1.74790	+	0.404593i
$910$	8.77448e10			0.127955
$911$	−7.18063e10	+	4.14574e10i	−0.104253	+	0.0601905i	−0.551220	−	0.834360i	$-0.685837\pi$
$911$	−7.18063e10	+	4.14574e10i	−0.104253	+	0.0601905i	0.446967	+	0.894550i	$0.352504\pi$
$912$	4.72635e11	−	7.04970e10i	0.683199	−	0.101904i
$913$	1.14849e11	−	1.98925e11i	0.165289	−	0.286290i
$914$	2.13330e11	+	1.23166e11i	0.305681	+	0.176485i
$915$	2.00178e11	+	7.89188e10i	0.285583	+	0.112589i
$916$	−5.31051e10	−	9.19807e10i	−0.0754318	−	0.130652i
$917$		−	2.48789e11i		−	0.351847i
$918$	4.64646e11	+	3.19932e11i	0.654261	+	0.450492i
$919$	1.16192e12			1.62898			0.814488	−	0.580180i	$-0.197018\pi$
$919$	1.16192e12			1.62898			0.814488	+	0.580180i	$0.197018\pi$
$920$	−1.63019e11	+	9.41193e10i	−0.227556	+	0.131379i
$921$	−4.42620e11	+	1.12271e12i	−0.615166	+	1.56037i
$922$	−1.70506e11	+	2.95325e11i	−0.235948	+	0.408674i
$923$	−2.44100e11	−	1.40931e11i	−0.336327	−	0.194179i
$924$	−1.31108e10	−	8.78993e10i	−0.0179863	−	0.120586i
$925$	1.34991e11	+	2.33812e11i	0.184391	+	0.319374i
$926$		−	5.38503e11i		−	0.732393i
$927$	−1.02813e12	+	3.13684e11i	−1.39228	+	0.424790i
$928$	−4.81548e11			−0.649304
$929$	−4.03658e11	+	2.33052e11i	−0.541939	+	0.312889i	−0.745864	−	0.666098i	$-0.767963\pi$
$929$	−4.03658e11	+	2.33052e11i	−0.541939	+	0.312889i	0.203925	+	0.978986i	$0.434630\pi$
$930$	−1.05500e11	−	1.32710e11i	−0.141033	−	0.177408i
$931$	4.67650e11	−	8.09993e11i	0.622475	−	1.07816i
$932$	−6.55682e10	−	3.78558e10i	−0.0869019	−	0.0501728i
$933$	8.04370e11	−	6.39448e11i	1.06152	−	0.843876i
$934$	1.52510e11	+	2.64156e11i	0.200407	+	0.347114i
$935$			3.30409e11i			0.432320i
$936$	−2.17774e11	−	7.13773e11i	−0.283728	−	0.929944i
$937$	1.53650e11			0.199331			0.0996653	−	0.995021i	$-0.468223\pi$
$937$	1.53650e11			0.199331			0.0996653	+	0.995021i	$0.468223\pi$
$938$	7.96993e10	−	4.60144e10i	0.102954	−	0.0594405i
$939$	2.55303e11	−	3.80804e10i	0.328393	−	0.0489822i
$940$	−2.18220e11	+	3.77968e11i	−0.279501	+	0.484110i
$941$	1.35458e11	+	7.82067e10i	0.172761	+	0.0997437i	0.583887	−	0.811835i	$-0.301531\pi$
$941$	1.35458e11	+	7.82067e10i	0.172761	+	0.0997437i	−0.411126	+	0.911579i	$0.634864\pi$
$942$	−9.11421e9	−	3.59321e9i	−0.0115749	−	0.00456330i
$943$	−2.77782e11	−	4.81132e11i	−0.351283	−	0.608440i
$944$		−	2.70028e11i		−	0.340033i
$945$	8.17141e10	+	1.71698e11i	0.102464	+	0.215297i
$946$	−1.18629e11			−0.148125
$947$	2.57065e11	−	1.48417e11i	0.319627	−	0.184537i	−0.331599	−	0.943420i	$-0.607588\pi$
$947$	2.57065e11	−	1.48417e11i	0.319627	−	0.184537i	0.651226	+	0.758883i	$0.274255\pi$
$948$	−1.69924e10	+	4.31015e10i	−0.0210389	+	0.0533653i
$949$	−8.14998e10	+	1.41162e11i	−0.100483	+	0.174041i
$950$	−2.80766e11	−	1.62100e11i	−0.344707	−	0.199017i
$951$	1.78915e10	+	1.19951e11i	0.0218739	+	0.146650i
$952$	−2.30179e11	−	3.98682e11i	−0.280233	−	0.485377i
$953$			4.43879e11i			0.538138i	0.963121	+	0.269069i	$0.0867159\pi$
$953$			4.43879e11i			0.538138i	−0.963121	+	0.269069i	$0.913284\pi$
$954$	1.45215e11	−	6.27349e11i	0.175314	−	0.757383i
$955$	−4.18150e11			−0.502712
$956$	−6.13636e11	+	3.54283e11i	−0.734648	+	0.424149i
$957$	1.31990e11	+	1.66032e11i	0.157360	+	0.197945i
$958$	3.40450e11	−	5.89676e11i	0.404195	−	0.700086i
$959$	4.31902e10	+	2.49359e10i	0.0510635	+	0.0294815i
$960$	−1.67047e10	+	1.32797e10i	−0.0196677	+	0.0156352i
$961$	1.16044e11	+	2.00993e11i	0.136059	+	0.235661i
$962$			2.71131e11i			0.316577i
$963$	−5.17300e10	+	5.54098e10i	−0.0601502	+	0.0644290i
$964$	9.26728e11			1.07311
$965$	3.70512e11	−	2.13915e11i	0.427260	−	0.246679i
$966$	−7.94487e10	+	1.18504e10i	−0.0912385	+	0.0136089i
$967$	3.44613e11	−	5.96888e11i	0.394118	−	0.682632i	−0.598870	−	0.800846i	$-0.704383\pi$
$967$	3.44613e11	−	5.96888e11i	0.394118	−	0.682632i	0.992988	+	0.118214i	$0.0377168\pi$
$968$	−5.08809e11	−	2.93761e11i	−0.579500	−	0.334575i
$969$	−2.20373e12	−	8.68802e11i	−2.49955	−	0.985430i
$970$	−1.21681e11	−	2.10758e11i	−0.137447	−	0.238065i
$971$			4.89136e11i			0.550241i	0.961410	+	0.275121i	$0.0887178\pi$
$971$			4.89136e11i			0.550241i	−0.961410	+	0.275121i	$0.911282\pi$
$972$	5.34923e11	−	4.88755e11i	0.599275	−	0.547553i
$973$	−3.80185e11			−0.424173
$974$	−4.46402e11	+	2.57730e11i	−0.496010	+	0.286371i
$975$	2.56276e11	−	6.50047e11i	0.283589	−	0.719327i
$976$	−1.07073e11	+	1.85456e11i	−0.118000	+	0.204382i
$977$	6.26502e11	+	3.61711e11i	0.687614	+	0.396994i	0.802717	−	0.596360i	$-0.203387\pi$
$977$	6.26502e11	+	3.61711e11i	0.687614	+	0.396994i	−0.115104	+	0.993353i	$0.536720\pi$
$978$	4.40690e10	+	2.95453e11i	0.0481701	+	0.322948i
$979$	−8.20512e10	−	1.42117e11i	−0.0893211	−	0.154709i
$980$			3.88898e11i			0.421630i
$981$	2.77918e11	+	2.59461e11i	0.300082	+	0.280154i
$982$	−5.66156e11			−0.608821
$983$	1.39027e12	−	8.02670e11i	1.48896	−	0.859653i	0.489042	−	0.872260i	$-0.337346\pi$
$983$	1.39027e12	−	8.02670e11i	1.48896	−	0.859653i	0.999921	+	0.0126073i	$0.00401312\pi$
$984$	5.90151e11	+	7.42359e11i	0.629481	+	0.791833i
$985$	4.99018e11	−	8.64324e11i	0.530116	−	0.918188i
$986$	4.26321e11	+	2.46137e11i	0.451055	+	0.260416i
$987$	−3.25386e11	+	2.58671e11i	−0.342871	+	0.272571i
$988$	7.01983e11	+	1.21587e12i	0.736714	+	1.27603i
$989$		−	4.62373e11i		−	0.483289i
$990$	−9.58789e10	−	2.21934e10i	−0.0998118	−	0.0231038i
$991$	8.39412e11			0.870323			0.435162	−	0.900352i	$-0.356691\pi$
$991$	8.39412e11			0.870323			0.435162	+	0.900352i	$0.356691\pi$
$992$	7.08553e11	−	4.09083e11i	0.731688	−	0.422440i
$993$	−1.49344e12	+	2.22758e11i	−1.53600	+	0.229106i
$994$	2.58953e10	−	4.48520e10i	0.0265262	−	0.0459448i
$995$	−5.15406e11	−	2.97570e11i	−0.525844	−	0.303596i
$996$	−6.37014e11	−	2.51138e11i	−0.647309	−	0.255197i
$997$	−7.28767e11	−	1.26226e12i	−0.737578	−	1.27752i	−0.953583	−	0.301130i	$-0.902636\pi$
$997$	−7.28767e11	−	1.26226e12i	−0.737578	−	1.27752i	0.216005	−	0.976392i	$-0.430697\pi$
$998$			7.91189e11i			0.797550i
$999$	−5.30545e11	+	2.52496e11i	−0.532672	+	0.253508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.9.d.a.5.5	yes	14
3.2	odd	2		27.9.d.a.17.3		14
4.3	odd	2		144.9.q.a.113.4		14
9.2	odd	6	inner	9.9.d.a.2.5	✓	14
9.4	even	3		81.9.b.a.80.9		14
9.5	odd	6		81.9.b.a.80.6		14
9.7	even	3		27.9.d.a.8.3		14
12.11	even	2		432.9.q.a.17.3		14
36.7	odd	6		432.9.q.a.305.3		14
36.11	even	6		144.9.q.a.65.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.9.d.a.2.5	✓	14	9.2	odd	6	inner
9.9.d.a.5.5	yes	14	1.1	even	1	trivial
27.9.d.a.8.3		14	9.7	even	3
27.9.d.a.17.3		14	3.2	odd	2
81.9.b.a.80.6		14	9.5	odd	6
81.9.b.a.80.9		14	9.4	even	3
144.9.q.a.65.4		14	36.11	even	6
144.9.q.a.113.4		14	4.3	odd	2
432.9.q.a.17.3		14	12.11	even	2
432.9.q.a.305.3		14	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(6.01192 - 3.47098i) q^{2} +(-29.7082 + 75.3553i) q^{3} +(-103.905 + 179.968i) q^{4} +(331.396 + 191.331i) q^{5} +(82.9534 + 556.147i) q^{6} +(467.516 + 809.762i) q^{7} +3219.75i q^{8} +(-4795.84 - 4477.35i) q^{9} +O(q^{10})\)	\(q+(6.01192 - 3.47098i) q^{2} +(-29.7082 + 75.3553i) q^{3} +(-103.905 + 179.968i) q^{4} +(331.396 + 191.331i) q^{5} +(82.9534 + 556.147i) q^{6} +(467.516 + 809.762i) q^{7} +3219.75i q^{8} +(-4795.84 - 4477.35i) q^{9} +2656.43 q^{10} +(4890.10 - 2823.30i) q^{11} +(-10474.7 - 13176.3i) q^{12} +(17663.1 - 30593.3i) q^{13} +(5621.34 + 3245.48i) q^{14} +(-24263.0 + 19288.3i) q^{15} +(-15423.9 - 26714.9i) q^{16} +152914. i q^{17} +(-44373.0 - 10271.2i) q^{18} +191248. q^{19} +(-68867.1 + 39760.4i) q^{20} +(-74908.9 + 11173.2i) q^{21} +(19599.3 - 33947.0i) q^{22} +(132313. + 76390.7i) q^{23} +(-242625. - 95653.1i) q^{24} +(-122097. - 211478. i) q^{25} -245233. i q^{26} +(479868. - 228378. i) q^{27} -194308. q^{28} +(401612. - 231871. i) q^{29} +(-78918.0 + 200176. i) q^{30} +(-393956. + 682351. i) q^{31} +(-899280. - 519200. i) q^{32} +(67474.4 + 452371. i) q^{33} +(530763. + 919308. i) q^{34} +357802. i q^{35} +(1.30409e6 - 397881. i) q^{36} -1.10561e6 q^{37} +(1.14977e6 - 663818. i) q^{38} +(1.78063e6 + 2.23988e6i) q^{39} +(-616039. + 1.06701e6i) q^{40} +(-3.14915e6 - 1.81816e6i) q^{41} +(-411564. + 327180. i) q^{42} +(-1.51318e6 - 2.62091e6i) q^{43} +1.17342e6i q^{44} +(-732664. - 2.40137e6i) q^{45} +1.06060e6 q^{46} +(4.75308e6 - 2.74419e6i) q^{47} +(2.47133e6 - 368617. i) q^{48} +(2.44526e6 - 4.23531e6i) q^{49} +(-1.46808e6 - 847594. i) q^{50} +(-1.15229e7 - 4.54281e6i) q^{51} +(3.67054e6 + 6.35757e6i) q^{52} +1.41381e7i q^{53} +(2.09223e6 - 3.03860e6i) q^{54} +2.16075e6 q^{55} +(-2.60723e6 + 1.50528e6i) q^{56} +(-5.68163e6 + 1.44115e7i) q^{57} +(1.60964e6 - 2.78797e6i) q^{58} +(7.58082e6 + 4.37679e6i) q^{59} +(-950238. - 6.37071e6i) q^{60} +(-3.47102e6 - 6.01198e6i) q^{61} +5.46965e6i q^{62} +(1.38345e6 - 5.97672e6i) q^{63} +688484. q^{64} +(1.17069e7 - 6.75900e6i) q^{65} +(1.97582e6 + 2.48541e6i) q^{66} +(7.08899e6 - 1.22785e7i) q^{67} +(-2.75197e7 - 1.58885e7i) q^{68} +(-9.68722e6 + 7.70102e6i) q^{69} +(1.24193e6 + 2.15108e6i) q^{70} -7.97888e6i q^{71} +(1.44159e7 - 1.54414e7i) q^{72} -4.61414e6 q^{73} +(-6.64682e6 + 3.83754e6i) q^{74} +(1.95633e7 - 2.91801e6i) q^{75} +(-1.98715e7 + 3.44184e7i) q^{76} +(4.57241e6 + 2.63988e6i) q^{77} +(1.84796e7 + 7.28544e6i) q^{78} +(-1.37621e6 - 2.38366e6i) q^{79} -1.18043e7i q^{80} +(2.95344e6 + 4.29453e7i) q^{81} -2.52433e7 q^{82} +(3.52291e7 - 2.03395e7i) q^{83} +(5.77256e6 - 1.46422e7i) q^{84} +(-2.92573e7 + 5.06751e7i) q^{85} +(-1.81943e7 - 1.05045e7i) q^{86} +(5.54150e6 + 3.71520e7i) q^{87} +(9.09033e6 + 1.57449e7i) q^{88} -2.90621e7i q^{89} +(-1.27398e7 - 1.18938e7i) q^{90} +3.30311e7 q^{91} +(-2.74958e7 + 1.58747e7i) q^{92} +(-3.97150e7 - 4.99581e7i) q^{93} +(1.90501e7 - 3.29957e7i) q^{94} +(6.33787e7 + 3.65917e7i) q^{95} +(6.58405e7 - 5.23410e7i) q^{96} +(-4.58061e7 - 7.93386e7i) q^{97} -3.39498e7i q^{98} +(-3.60931e7 - 8.35459e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{2} - 93 q^{3} + 767 q^{4} + 438 q^{5} - 2259 q^{6} + 922 q^{7} + 17973 q^{9}+O(q^{10}) \) 14 * q - 3 * q^2 - 93 * q^3 + 767 * q^4 + 438 * q^5 - 2259 * q^6 + 922 * q^7 + 17973 * q^9	\( 14 q - 3 q^{2} - 93 q^{3} + 767 q^{4} + 438 q^{5} - 2259 q^{6} + 922 q^{7} + 17973 q^{9} - 516 q^{10} - 28677 q^{11} - 55110 q^{12} + 1684 q^{13} + 120966 q^{14} - 75276 q^{15} - 65281 q^{16} + 243324 q^{18} - 269630 q^{19} + 539454 q^{20} + 354054 q^{21} + 61311 q^{22} - 1000452 q^{23} - 1125513 q^{24} + 65177 q^{25} - 524826 q^{27} + 1075708 q^{28} + 3797682 q^{29} + 2372562 q^{30} - 164132 q^{31} - 8461881 q^{32} - 5761521 q^{33} + 654993 q^{34} + 12958047 q^{36} - 1671668 q^{37} + 10967691 q^{38} + 3383976 q^{39} + 613326 q^{40} - 10239447 q^{41} - 35844228 q^{42} + 791815 q^{43} + 27631638 q^{45} + 1189536 q^{46} + 31148628 q^{47} + 17088189 q^{48} - 4826637 q^{49} - 63849453 q^{50} - 47946573 q^{51} - 5552720 q^{52} + 36967995 q^{54} + 8107476 q^{55} + 116638674 q^{56} + 37276797 q^{57} + 14211822 q^{58} - 83493795 q^{59} - 109012050 q^{60} - 5255600 q^{61} + 38322432 q^{63} - 26813830 q^{64} + 69232992 q^{65} + 36133866 q^{66} - 8288855 q^{67} - 77746743 q^{68} - 62108640 q^{69} + 27813756 q^{70} + 88821171 q^{72} - 36721682 q^{73} - 10383450 q^{74} + 13792011 q^{75} - 42822959 q^{76} + 56158710 q^{77} + 27355140 q^{78} - 32771822 q^{79} - 16336971 q^{81} + 236099418 q^{82} - 198915996 q^{83} - 187060614 q^{84} + 97486146 q^{85} + 146190669 q^{86} + 114294006 q^{87} + 24955827 q^{88} - 222035850 q^{90} - 201514504 q^{91} - 295365804 q^{92} + 94187784 q^{93} - 36698244 q^{94} + 386813838 q^{95} + 768275928 q^{96} + 127049161 q^{97} - 511060752 q^{99}+O(q^{100}) \) 14 * q - 3 * q^2 - 93 * q^3 + 767 * q^4 + 438 * q^5 - 2259 * q^6 + 922 * q^7 + 17973 * q^9 - 516 * q^10 - 28677 * q^11 - 55110 * q^12 + 1684 * q^13 + 120966 * q^14 - 75276 * q^15 - 65281 * q^16 + 243324 * q^18 - 269630 * q^19 + 539454 * q^20 + 354054 * q^21 + 61311 * q^22 - 1000452 * q^23 - 1125513 * q^24 + 65177 * q^25 - 524826 * q^27 + 1075708 * q^28 + 3797682 * q^29 + 2372562 * q^30 - 164132 * q^31 - 8461881 * q^32 - 5761521 * q^33 + 654993 * q^34 + 12958047 * q^36 - 1671668 * q^37 + 10967691 * q^38 + 3383976 * q^39 + 613326 * q^40 - 10239447 * q^41 - 35844228 * q^42 + 791815 * q^43 + 27631638 * q^45 + 1189536 * q^46 + 31148628 * q^47 + 17088189 * q^48 - 4826637 * q^49 - 63849453 * q^50 - 47946573 * q^51 - 5552720 * q^52 + 36967995 * q^54 + 8107476 * q^55 + 116638674 * q^56 + 37276797 * q^57 + 14211822 * q^58 - 83493795 * q^59 - 109012050 * q^60 - 5255600 * q^61 + 38322432 * q^63 - 26813830 * q^64 + 69232992 * q^65 + 36133866 * q^66 - 8288855 * q^67 - 77746743 * q^68 - 62108640 * q^69 + 27813756 * q^70 + 88821171 * q^72 - 36721682 * q^73 - 10383450 * q^74 + 13792011 * q^75 - 42822959 * q^76 + 56158710 * q^77 + 27355140 * q^78 - 32771822 * q^79 - 16336971 * q^81 + 236099418 * q^82 - 198915996 * q^83 - 187060614 * q^84 + 97486146 * q^85 + 146190669 * q^86 + 114294006 * q^87 + 24955827 * q^88 - 222035850 * q^90 - 201514504 * q^91 - 295365804 * q^92 + 94187784 * q^93 - 36698244 * q^94 + 386813838 * q^95 + 768275928 * q^96 + 127049161 * q^97 - 511060752 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more