LMFDB - Embedded newform 27.7.f.a.2.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,7,Mod(2,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("27.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	27.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:	$6.21146025774$
Analytic rank:	$0$
Dimension:	$102$
Relative dimension:	$17$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			2.8
Character	$\chi$	$=$	27.2
Dual form			27.7.f.a.14.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.18396 - 0.385091i) q^{2} +(-26.6089 - 4.57871i) q^{3} +(-55.5189 - 20.2072i) q^{4} +(71.1763 + 84.8246i) q^{5} +(56.3496 + 20.2466i) q^{6} +(318.690 - 115.994i) q^{7} +(236.384 + 136.476i) q^{8} +(687.071 + 243.669i) q^{9} +O(q^{10})$	\(q+(-2.18396 - 0.385091i) q^{2} +(-26.6089 - 4.57871i) q^{3} +(-55.5189 - 20.2072i) q^{4} +(71.1763 + 84.8246i) q^{5} +(56.3496 + 20.2466i) q^{6} +(318.690 - 115.994i) q^{7} +(236.384 + 136.476i) q^{8} +(687.071 + 243.669i) q^{9} +(-122.781 - 212.663i) q^{10} +(27.8912 - 33.2395i) q^{11} +(1384.78 + 791.899i) q^{12} +(248.990 + 1412.09i) q^{13} +(-740.673 + 130.601i) q^{14} +(-1505.54 - 2582.99i) q^{15} +(2432.91 + 2041.45i) q^{16} +(7299.99 - 4214.65i) q^{17} +(-1406.70 - 796.748i) q^{18} +(-4970.99 + 8610.00i) q^{19} +(-2237.56 - 6147.65i) q^{20} +(-9011.09 + 1627.28i) q^{21} +(-73.7135 + 61.8529i) q^{22} +(-926.465 + 2545.44i) q^{23} +(-5665.04 - 4713.83i) q^{24} +(584.106 - 3312.63i) q^{25} -3179.84i q^{26} +(-17166.5 - 9629.68i) q^{27} -20037.2 q^{28} +(17906.8 + 3157.45i) q^{29} +(2293.35 + 6220.90i) q^{30} +(22689.5 + 8258.29i) q^{31} +(-15756.1 - 18777.4i) q^{32} +(-894.349 + 756.761i) q^{33} +(-17565.9 + 6393.46i) q^{34} +(32522.2 + 18776.7i) q^{35} +(-33221.6 - 27412.1i) q^{36} +(36855.3 + 63835.3i) q^{37} +(14172.1 - 16889.6i) q^{38} +(-159.793 - 38714.3i) q^{39} +(5248.38 + 29765.1i) q^{40} +(93500.0 - 16486.6i) q^{41} +(20306.5 - 83.8148i) q^{42} +(29000.0 + 24333.9i) q^{43} +(-2220.17 + 1281.81i) q^{44} +(28234.0 + 75624.0i) q^{45} +(3003.59 - 5202.36i) q^{46} +(-25819.3 - 70937.9i) q^{47} +(-55389.9 - 65460.5i) q^{48} +(-2015.75 + 1691.42i) q^{49} +(-2551.33 + 7009.71i) q^{50} +(-213543. + 78722.8i) q^{51} +(14710.8 - 83429.3i) q^{52} +148857. i q^{53} +(33782.7 + 27641.5i) q^{54} +4804.71 q^{55} +(91163.6 + 16074.6i) q^{56} +(171695. - 206342. i) q^{57} +(-37891.7 - 13791.5i) q^{58} +(-140576. - 167532. i) q^{59} +(31390.8 + 173827. i) q^{60} +(-153655. + 55925.7i) q^{61} +(-46372.7 - 26773.3i) q^{62} +(247226. - 2040.88i) q^{63} +(-74450.3 - 128952. i) q^{64} +(-102058. + 121628. i) q^{65} +(2244.64 - 1308.33i) q^{66} +(-50843.2 - 288346. i) q^{67} +(-490454. + 86480.3i) q^{68} +(36307.1 - 63489.4i) q^{69} +(-63796.5 - 53531.6i) q^{70} +(-192070. + 110892. i) q^{71} +(129157. + 151369. i) q^{72} +(-265411. + 459706. i) q^{73} +(-55908.1 - 153606. i) q^{74} +(-30710.0 + 85471.1i) q^{75} +(449969. - 377568. i) q^{76} +(5033.08 - 13828.3i) q^{77} +(-14559.6 + 84612.1i) q^{78} +(140976. - 799517. i) q^{79} +351673. i q^{80} +(412692. + 334836. i) q^{81} -210549. q^{82} +(763363. + 134602. i) q^{83} +(533169. + 91744.7i) q^{84} +(877092. + 319235. i) q^{85} +(-53964.1 - 64311.9i) q^{86} +(-462023. - 166006. i) q^{87} +(11129.4 - 4050.78i) q^{88} +(718568. + 414866. i) q^{89} +(-32539.8 - 176032. i) q^{90} +(243144. + 421138. i) q^{91} +(102873. - 122599. i) q^{92} +(-565930. - 323633. i) q^{93} +(29070.7 + 164868. i) q^{94} +(-1.08416e6 + 191166. i) q^{95} +(333276. + 571788. i) q^{96} +(-961565. - 806849. i) q^{97} +(5053.67 - 2917.74i) q^{98} +(27262.7 - 16041.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) $ 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	−2.18396	−	0.385091i	−0.272995	−	0.0481364i	0.0354747	−	0.999371i	$-0.488706\pi$
$2$	−2.18396	−	0.385091i	−0.272995	−	0.0481364i	−0.308470	+	0.951234i	$0.599817\pi$
$3$	−26.6089	−	4.57871i	−0.985516	−	0.169582i
$3$	−26.6089	−	4.57871i	−0.985516	−	0.169582i
$4$	−55.5189	−	20.2072i	−0.867484	−	0.315738i
$5$	71.1763	+	84.8246i	0.569410	+	0.678597i	0.971510	−	0.236999i	$-0.0761639\pi$
$5$	71.1763	+	84.8246i	0.569410	+	0.678597i	−0.402100	+	0.915596i	$0.631719\pi$
$6$	56.3496	+	20.2466i	0.260878	+	0.0937341i
$7$	318.690	−	115.994i	0.929124	−	0.338174i	0.167262	−	0.985912i	$-0.446507\pi$
$7$	318.690	−	115.994i	0.929124	−	0.338174i	0.761862	+	0.647739i	$0.224285\pi$
$8$	236.384	+	136.476i	0.461688	+	0.266555i
$9$	687.071	+	243.669i	0.942484	+	0.334251i
$10$	−122.781	−	212.663i	−0.122781	−	0.212663i
$11$	27.8912	−	33.2395i	0.0209551	−	0.0249733i	−0.755465	−	0.655189i	$-0.772589\pi$
$11$	27.8912	−	33.2395i	0.0209551	−	0.0249733i	0.776420	+	0.630216i	$0.217033\pi$
$12$	1384.78	+	791.899i	0.801376	+	0.458275i
$13$	248.990	+	1412.09i	0.113332	+	0.642737i	0.987563	+	0.157226i	$0.0502552\pi$
$13$	248.990	+	1412.09i	0.113332	+	0.642737i	−0.874231	+	0.485511i	$0.838634\pi$
$14$	−740.673	+	130.601i	−0.269925	+	0.0475950i
$15$	−1505.54	−	2582.99i	−0.446085	−	0.765329i
$16$	2432.91	+	2041.45i	0.593972	+	0.498401i
$17$	7299.99	−	4214.65i	1.48585	−	0.857857i	0.485981	−	0.873969i	$-0.338462\pi$
$17$	7299.99	−	4214.65i	1.48585	−	0.857857i	0.999870	+	0.0161127i	$0.00512906\pi$
$18$	−1406.70	−	796.748i	−0.241204	−	0.136617i
$19$	−4970.99	+	8610.00i	−0.724740	+	1.25529i	0.234342	+	0.972154i	$0.424707\pi$
$19$	−4970.99	+	8610.00i	−0.724740	+	1.25529i	−0.959081	+	0.283131i	$0.908627\pi$
$20$	−2237.56	−	6147.65i	−0.279695	−	0.768456i
$21$	−9011.09	+	1627.28i	−0.973015	+	0.175713i
$22$	−73.7135	+	61.8529i	−0.00692275	+	0.00580888i
$23$	−926.465	+	2545.44i	−0.0761457	+	0.209209i	−0.971925	−	0.235290i	$-0.924396\pi$
$23$	−926.465	+	2545.44i	−0.0761457	+	0.209209i	0.895779	+	0.444499i	$0.146618\pi$
$24$	−5665.04	−	4713.83i	−0.409798	−	0.340989i
$25$	584.106	−	3312.63i	0.0373828	−	0.212008i
$26$		−	3179.84i		−	0.180919i
$27$	−17166.5	−	9629.68i	−0.872150	−	0.489238i
$28$	−20037.2			−0.912775
$29$	17906.8	+	3157.45i	0.734215	+	0.129462i	0.528240	−	0.849095i	$-0.322852\pi$
$29$	17906.8	+	3157.45i	0.734215	+	0.129462i	0.205975	+	0.978557i	$0.433963\pi$
$30$	2293.35	+	6220.90i	0.0849387	+	0.230404i
$31$	22689.5	+	8258.29i	0.761621	+	0.277208i	0.693487	−	0.720469i	$-0.256073\pi$
$31$	22689.5	+	8258.29i	0.761621	+	0.277208i	0.0681339	+	0.997676i	$0.478295\pi$
$32$	−15756.1	−	18777.4i	−0.480837	−	0.573039i
$33$	−894.349	+	756.761i	−0.0248866	+	0.0210580i
$34$	−17565.9	+	6393.46i	−0.446924	+	0.162667i
$35$	32522.2	+	18776.7i	0.758536	+	0.437941i
$36$	−33221.6	−	27412.1i	−0.712053	−	0.587536i
$37$	36855.3	+	63835.3i	0.727604	+	1.26025i	0.957893	+	0.287125i	$0.0926994\pi$
$37$	36855.3	+	63835.3i	0.727604	+	1.26025i	−0.230289	+	0.973122i	$0.573967\pi$
$38$	14172.1	−	16889.6i	0.258275	−	0.307800i
$39$	−159.793	−	38714.3i	−0.00269379	−	0.652647i
$40$	5248.38	+	29765.1i	0.0820060	+	0.465079i
$41$	93500.0	−	16486.6i	1.35663	−	0.239210i	0.552423	−	0.833564i	$-0.313703\pi$
$41$	93500.0	−	16486.6i	1.35663	−	0.239210i	0.804203	+	0.594354i	$0.202592\pi$
$42$	20306.5	−	83.8148i	0.274086	−	0.00113129i
$43$	29000.0	+	24333.9i	0.364748	+	0.306060i	0.806680	−	0.590989i	$-0.201262\pi$
$43$	29000.0	+	24333.9i	0.364748	+	0.306060i	−0.441932	+	0.897049i	$0.645707\pi$
$44$	−2220.17	+	1281.81i	−0.0260632	+	0.0150476i
$45$	28234.0	+	75624.0i	0.309838	+	0.829892i
$46$	3003.59	−	5202.36i	0.0308579	−	0.0534475i
$47$	−25819.3	−	70937.9i	−0.248686	−	0.683258i	−0.999735	−	0.0230121i	$-0.992674\pi$
$47$	−25819.3	−	70937.9i	−0.248686	−	0.683258i	0.751050	−	0.660246i	$-0.229548\pi$
$48$	−55389.9	−	65460.5i	−0.500849	−	0.591910i
$49$	−2015.75	+	1691.42i	−0.0171336	+	0.0143768i
$50$	−2551.33	+	7009.71i	−0.0204106	+	0.0560777i
$51$	−213543.	+	78722.8i	−1.60981	+	0.593458i
$52$	14710.8	−	83429.3i	0.104623	−	0.593347i
$53$			148857.i			0.999868i	0.866064	+	0.499934i	$0.166642\pi$
$53$			148857.i			0.999868i	−0.866064	+	0.499934i	$0.833358\pi$
$54$	33782.7	+	27641.5i	0.214542	+	0.175542i
$55$	4804.71			0.0288788
$56$	91163.6	+	16074.6i	0.519107	+	0.0915326i
$57$	171695.	−	206342.i	0.927116	−	1.11420i
$58$	−37891.7	−	13791.5i	−0.194205	−	0.0706848i
$59$	−140576.	−	167532.i	−0.684473	−	0.815723i	0.306203	−	0.951966i	$-0.400941\pi$
$59$	−140576.	−	167532.i	−0.684473	−	0.815723i	−0.990675	+	0.136244i	$0.956497\pi$
$60$	31390.8	+	173827.i	0.145328	+	0.804757i
$61$	−153655.	+	55925.7i	−0.676949	+	0.246389i	−0.657537	−	0.753422i	$-0.728402\pi$
$61$	−153655.	+	55925.7i	−0.676949	+	0.246389i	−0.0194122	+	0.999812i	$0.506179\pi$
$62$	−46372.7	−	26773.3i	−0.194575	−	0.112338i
$63$	247226.	−	2040.88i	0.988720	−	0.00816200i
$64$	−74450.3	−	128952.i	−0.284006	−	0.491912i
$65$	−102058.	+	121628.i	−0.371627	+	0.442887i
$66$	2244.64	−	1308.33i	0.00780756	−	0.00455077i
$67$	−50843.2	−	288346.i	−0.169048	−	0.958716i	−0.944792	−	0.327670i	$-0.893737\pi$
$67$	−50843.2	−	288346.i	−0.169048	−	0.958716i	0.775745	−	0.631047i	$-0.217374\pi$
$68$	−490454.	+	86480.3i	−1.55981	+	0.275037i
$69$	36307.1	−	63489.4i	0.110521	−	0.193265i
$70$	−63796.5	−	53531.6i	−0.185996	−	0.156069i
$71$	−192070.	+	110892.i	−0.536642	+	0.309830i	−0.743717	−	0.668495i	$-0.766939\pi$
$71$	−192070.	+	110892.i	−0.536642	+	0.309830i	0.207075	+	0.978325i	$0.433606\pi$
$72$	129157.	+	151369.i	0.346037	+	0.405544i
$73$	−265411.	+	459706.i	−0.682261	+	1.18171i	0.292028	+	0.956410i	$0.405670\pi$
$73$	−265411.	+	459706.i	−0.682261	+	1.18171i	−0.974289	+	0.225301i	$0.927663\pi$
$74$	−55908.1	−	153606.i	−0.137968	−	0.379065i
$75$	−30710.0	+	85471.1i	−0.0727941	+	0.202598i
$76$	449969.	−	377568.i	1.02504	−	0.860112i
$77$	5033.08	−	13828.3i	0.0110246	−	0.0302898i
$78$	−14559.6	+	84612.1i	−0.0306806	+	0.178299i
$79$	140976.	−	799517.i	0.285933	−	1.62161i	−0.415999	−	0.909365i	$-0.636568\pi$
$79$	140976.	−	799517.i	0.285933	−	1.62161i	0.701932	−	0.712244i	$-0.252321\pi$
$80$			351673.i			0.686862i
$81$	412692.	+	334836.i	0.776552	+	0.630053i
$82$	−210549.			−0.381867
$83$	763363.	+	134602.i	1.33505	+	0.235405i	0.795195	−	0.606354i	$-0.207368\pi$
$83$	763363.	+	134602.i	1.33505	+	0.235405i	0.539854	+	0.841759i	$0.318480\pi$
$84$	533169.	+	91744.7i	0.899554	+	0.154790i
$85$	877092.	+	319235.i	1.42820	+	0.519821i
$86$	−53964.1	−	64311.9i	−0.0848417	−	0.101110i
$87$	−462023.	−	166006.i	−0.701626	−	0.252096i
$88$	11129.4	−	4050.78i	0.0163315	−	0.00594417i
$89$	718568.	+	414866.i	1.01929	+	0.588488i	0.913898	−	0.405943i	$-0.133057\pi$
$89$	718568.	+	414866.i	1.01929	+	0.588488i	0.105392	+	0.994431i	$0.466390\pi$
$90$	−32539.8	−	176032.i	−0.0446362	−	0.241471i
$91$	243144.	+	421138.i	0.322656	+	0.558857i
$92$	102873.	−	122599.i	0.132110	−	0.157443i
$93$	−565930.	−	323633.i	−0.703581	−	0.402350i
$94$	29070.7	+	164868.i	0.0350003	+	0.198497i
$95$	−1.08416e6	+	191166.i	−1.26451	+	0.222967i
$96$	333276.	+	571788.i	0.376696	+	0.646281i
$97$	−961565.	−	806849.i	−1.05357	−	0.884051i	−0.0601060	−	0.998192i	$-0.519144\pi$
$97$	−961565.	−	806849.i	−1.05357	−	0.884051i	−0.993465	+	0.114141i	$0.963588\pi$
$98$	5053.67	−	2917.74i	0.00536943	−	0.00310004i
$99$	27262.7	−	16041.6i	0.0280972	−	0.0165327i
$100$	−99368.1	+	172111.i	−0.0993681	+	0.172111i
$101$	−575585.	−	1.58141e6i	−0.558657	−	1.53490i	−0.821588	−	0.570082i	$-0.806911\pi$
$101$	−575585.	−	1.58141e6i	−0.558657	−	1.53490i	0.262931	−	0.964815i	$-0.415311\pi$
$102$	496684.	−	89694.0i	0.468036	−	0.0845207i
$103$	−196018.	+	164479.i	−0.179384	+	0.150521i	−0.728059	−	0.685515i	$-0.759577\pi$
$103$	−196018.	+	164479.i	−0.179384	+	0.150521i	0.548674	+	0.836036i	$0.315133\pi$
$104$	−133860.	+	367778.i	−0.119001	+	0.326953i
$105$	−779409.	−	648539.i	−0.673283	−	0.560232i
$106$	57323.6	−	325098.i	0.0481300	−	0.272959i
$107$			1.50113e6i			1.22537i	0.790329	+	0.612683i	$0.209910\pi$
$107$			1.50113e6i			1.22537i	−0.790329	+	0.612683i	$0.790090\pi$
$108$	758478.	+	881518.i	0.602105	+	0.699777i
$109$	−877376.			−0.677496			−0.338748	−	0.940877i	$-0.610003\pi$
$109$	−877376.			−0.677496			−0.338748	+	0.940877i	$0.610003\pi$
$110$	−10493.3	−	1850.25i	−0.00788377	−	0.00139012i
$111$	−688397.	−	1.86734e6i	−0.503350	−	1.36538i
$112$	1.01214e6	+	368388.i	0.720420	+	0.262211i
$113$	−53300.7	−	63521.3i	−0.0369400	−	0.0440234i	0.747258	−	0.664534i	$-0.231370\pi$
$113$	−53300.7	−	63521.3i	−0.0369400	−	0.0440234i	−0.784198	+	0.620510i	$0.786925\pi$
$114$	−454436.	+	384525.i	−0.306732	+	0.259543i
$115$	−281858.	+	102588.i	−0.185326	+	0.0674533i
$116$	−930361.	−	537144.i	−0.596043	−	0.344126i
$117$	−173010.	+	1.03088e6i	−0.108022	+	0.643651i
$118$	242498.	+	420018.i	0.147592	+	0.255636i
$119$	1.83756e6	−	2.18992e6i	1.09044	−	1.29953i
$120$	−3368.22	−	816047.i	−0.00194920	−	0.472250i
$121$	307301.	+	1.74279e6i	0.173464	+	0.983761i
$122$	357112.	−	62968.4i	0.196664	−	0.0346772i
$123$	−2.56342e6	+	10580.5i	−1.37754	+	0.00568579i
$124$	−1.09282e6	−	916983.i	−0.573169	−	0.480946i
$125$	1.82093e6	−	1.05132e6i	0.932318	−	0.538274i
$126$	−540718.	−	90747.4i	−0.270308	−	0.0453652i
$127$	−895415.	+	1.55090e6i	−0.437133	+	0.757136i	−0.997467	−	0.0711304i	$-0.977339\pi$
$127$	−895415.	+	1.55090e6i	−0.437133	+	0.757136i	0.560334	+	0.828267i	$0.310673\pi$
$128$	649491.	+	1.78446e6i	0.309701	+	0.850897i
$129$	−660242.	−	780282.i	−0.307563	−	0.363482i
$130$	269728.	−	226329.i	0.122771	−	0.103017i
$131$	693563.	−	1.90555e6i	0.308512	−	0.847630i	−0.684435	−	0.729074i	$-0.739951\pi$
$131$	693563.	−	1.90555e6i	0.308512	−	0.847630i	0.992947	−	0.118556i	$-0.0378266\pi$
$132$	64945.4	−	23942.2i	0.0282375	−	0.0104098i
$133$	−585498.	+	3.32052e6i	−0.248869	+	1.41140i
$134$			649316.i			0.269862i
$135$	−405016.	−	2.14155e6i	−0.164616	−	0.870415i
$136$	2.30080e6			0.914666
$137$	2.59708e6	+	457935.i	1.01000	+	0.178091i	0.654082	−	0.756424i	$-0.273055\pi$
$137$	2.59708e6	+	457935.i	1.01000	+	0.178091i	0.355923	+	0.934515i	$0.384166\pi$
$138$	−103742.	+	124677.i	−0.0394747	+	0.0474404i
$139$	1.31198e6	+	477521.i	0.488520	+	0.177807i	0.574523	−	0.818488i	$-0.305187\pi$
$139$	1.31198e6	+	477521.i	0.488520	+	0.177807i	−0.0860037	+	0.996295i	$0.527410\pi$
$140$	−1.42617e6	−	1.69965e6i	−0.519743	−	0.619406i
$141$	362219.	+	2.00580e6i	0.129215	+	0.715534i
$142$	462176.	−	168218.i	0.161415	−	0.0587501i
$143$	53881.8	+	31108.7i	0.0184261	+	0.0106383i
$144$	1.17414e6	+	1.99545e6i	0.393217	+	0.668271i
$145$	1.00671e6	+	1.74367e6i	0.330217	+	0.571952i
$146$	756676.	−	901771.i	0.243137	−	0.289759i
$147$	61381.5	−	35777.3i	0.0193235	−	0.0112630i
$148$	−756233.	−	4.28881e6i	−0.233276	−	1.32298i
$149$	556174.	−	98068.5i	0.168133	−	0.0296463i	−0.0889481	−	0.996036i	$-0.528351\pi$
$149$	556174.	−	98068.5i	0.168133	−	0.0296463i	0.257081	+	0.966390i	$0.417239\pi$
$150$	99983.6	−	174839.i	0.0296248	−	0.0518042i
$151$	834813.	+	700491.i	0.242470	+	0.203457i	0.755922	−	0.654662i	$-0.227189\pi$
$151$	834813.	+	700491.i	0.242470	+	0.203457i	−0.513452	+	0.858118i	$0.671633\pi$
$152$	−2.35013e6	+	1.35685e6i	−0.669207	+	0.386367i
$153$	6.04259e6	−	1.11698e6i	1.68713	−	0.311868i
$154$	−16317.2	+	28262.2i	−0.00446769	+	0.00773826i
$155$	914445.	+	2.51242e6i	0.245563	+	0.674678i
$156$	−773439.	+	2.15261e6i	−0.203729	+	0.567011i
$157$	−762066.	+	639449.i	−0.196922	+	0.165237i	−0.735917	−	0.677072i	$-0.763249\pi$
$157$	−762066.	+	639449.i	−0.196922	+	0.165237i	0.538995	+	0.842309i	$0.318804\pi$
$158$	−615773.	+	1.69182e6i	−0.156117	+	0.428927i
$159$	681575.	−	3.96093e6i	0.169560	−	0.985386i
$160$	471323.	−	2.67300e6i	0.115069	−	0.652589i
$161$			918670.i			0.220131i
$162$	−772359.	−	890192.i	−0.181666	−	0.209382i
$163$	−4.92801e6			−1.13791			−0.568956	−	0.822368i	$-0.692653\pi$
$163$	−4.92801e6			−1.13791			−0.568956	+	0.822368i	$0.692653\pi$
$164$	−5.52417e6	−	974060.i	−1.25238	−	0.220828i
$165$	−127848.	−	21999.4i	−0.0284605	−	0.00489733i
$166$	−1.61532e6	−	587928.i	−0.353130	−	0.128529i
$167$	−290372.	−	346052.i	−0.0623455	−	0.0743005i	0.733970	−	0.679182i	$-0.237665\pi$
$167$	−290372.	−	346052.i	−0.0623455	−	0.0743005i	−0.796316	+	0.604881i	$0.793221\pi$
$168$	−2.35216e6	−	845140.i	−0.496066	−	0.178238i
$169$	2.60371e6	−	947672.i	0.539426	−	0.196335i
$170$	−1.79260e6	−	1.03496e6i	−0.364868	−	0.210657i
$171$	−5.51342e6	+	4.70441e6i	−1.10264	+	0.940841i
$172$	−1.11833e6	−	1.93700e6i	−0.219778	−	0.380667i
$173$	−2.88075e6	+	3.43314e6i	−0.556374	+	0.663061i	−0.968775	−	0.247942i	$-0.920246\pi$
$173$	−2.88075e6	+	3.43314e6i	−0.556374	+	0.663061i	0.412401	+	0.911002i	$0.364690\pi$
$174$	945111.	+	540471.i	0.179405	+	0.102595i
$175$	−198095.	−	1.12345e6i	−0.0369624	−	0.209624i
$176$	135714.	−	23930.0i	0.0248935	−	0.00438939i
$177$	2.97350e6	+	5.10151e6i	0.536227	+	0.919982i
$178$	−1.40956e6	−	1.18276e6i	−0.249933	−	0.209719i
$179$	7.74388e6	−	4.47093e6i	1.35020	−	0.779541i	0.361926	−	0.932207i	$-0.382119\pi$
$179$	7.74388e6	−	4.47093e6i	1.35020	−	0.779541i	0.988278	+	0.152666i	$0.0487858\pi$
$180$	−39369.4	−	4.76909e6i	−0.00675059	−	0.817746i
$181$	4.00732e6	−	6.94088e6i	0.675800	−	1.17052i	−0.300434	−	0.953803i	$-0.597131\pi$
$181$	4.00732e6	−	6.94088e6i	0.675800	−	1.17052i	0.976234	−	0.216718i	$-0.0695352\pi$
$182$	−368841.	−	1.01338e6i	−0.0611821	−	0.168096i
$183$	4.34465e6	−	784583.i	0.708928	−	0.128022i
$184$	−566394.	+	475261.i	−0.0909212	+	0.0762920i
$185$	−2.79158e6	+	7.66979e6i	−0.440894	+	1.21135i
$186$	1.11134e6	+	924735.i	0.172706	+	0.143707i
$187$	63512.8	−	360199.i	0.00971263	−	0.0550831i
$188$			4.46013e6i			0.671234i
$189$	−6.58778e6	−	1.07767e6i	−0.975783	−	0.159625i
$190$	2.44137e6			0.355937
$191$	−9.14248e6	−	1.61207e6i	−1.31209	−	0.231357i	−0.526538	−	0.850151i	$-0.676510\pi$
$191$	−9.14248e6	−	1.61207e6i	−1.31209	−	0.231357i	−0.785553	+	0.618794i	$0.787621\pi$
$192$	1.39061e6	+	3.77216e6i	0.196473	+	0.532949i
$193$	−2.87707e6	−	1.04717e6i	−0.400201	−	0.145661i	0.134075	−	0.990971i	$-0.457194\pi$
$193$	−2.87707e6	−	1.04717e6i	−0.400201	−	0.145661i	−0.534276	+	0.845310i	$0.679416\pi$
$194$	1.78931e6	+	2.13242e6i	0.245064	+	0.292056i
$195$	3.27255e6	−	2.76910e6i	0.441350	−	0.373452i
$196$	146091.	−	53172.9i	0.0194024	−	0.00706191i
$197$	−9.01118e6	−	5.20261e6i	−1.17865	−	0.680491i	−0.222945	−	0.974831i	$-0.571567\pi$
$197$	−9.01118e6	−	5.20261e6i	−1.17865	−	0.680491i	−0.955701	+	0.294340i	$0.904900\pi$
$198$	−65718.0	+	24535.6i	−0.00846621	+	0.00316083i
$199$	−4.00988e6	−	6.94532e6i	−0.508830	−	0.881319i	−0.999948	−	0.0102257i	$-0.996745\pi$
$199$	−4.00988e6	−	6.94532e6i	−0.508830	−	0.881319i	0.491118	−	0.871093i	$-0.336588\pi$
$200$	590169.	−	703336.i	0.0737712	−	0.0879171i
$201$	32629.4	+	7.90539e6i	0.00401810	+	0.973498i
$202$	648068.	+	3.67538e6i	0.0786261	+	0.445911i
$203$	6.07294e6	−	1.07082e6i	0.725957	−	0.128006i
$204$	1.34464e7	−	55500.0i	1.58386	−	0.00653736i
$205$	8.05345e6	+	6.75764e6i	0.934803	+	0.784393i
$206$	491435.	−	283730.i	0.0562166	−	0.0324567i
$207$	−1.25679e6	+	1.52315e6i	−0.141694	+	0.171724i
$208$	−2.27695e6	+	3.94379e6i	−0.253025	+	0.438252i
$209$	147545.	+	405376.i	0.0161616	+	0.0444037i
$210$	1.45245e6	+	1.71652e6i	0.156835	+	0.185350i
$211$	−4.05691e6	+	3.40415e6i	−0.431865	+	0.362378i	−0.832655	−	0.553792i	$-0.813180\pi$
$211$	−4.05691e6	+	3.40415e6i	−0.431865	+	0.362378i	0.400790	+	0.916170i	$0.368736\pi$
$212$	3.00800e6	−	8.26440e6i	0.315696	−	0.867369i
$213$	5.61852e6	−	2.07128e6i	0.581411	−	0.214338i
$214$	578070.	−	3.27840e6i	0.0589846	−	0.334518i
$215$			4.19191e6i			0.421790i
$216$	−2.74367e6	−	4.61913e6i	−0.272252	−	0.458352i
$217$	8.18881e6			0.801385
$218$	1.91615e6	+	337870.i	0.184953	+	0.0326122i
$219$	9.16717e6	−	1.10170e7i	0.872776	−	1.04890i
$220$	−266753.	−	97090.0i	−0.0250519	−	0.00911815i
$221$	7.76910e6	+	9.25885e6i	0.719770	+	0.857789i
$222$	784336.	+	4.34329e6i	0.0716875	+	0.396972i
$223$	−6.18122e6	+	2.24978e6i	−0.557390	+	0.202873i	−0.605327	−	0.795977i	$-0.706958\pi$
$223$	−6.18122e6	+	2.24978e6i	−0.557390	+	0.202873i	0.0479368	+	0.998850i	$0.484735\pi$
$224$	−7.19935e6	−	4.15655e6i	−0.640544	−	0.369818i
$225$	1.20851e6	−	2.13368e6i	0.106097	−	0.187319i
$226$	91945.0	+	159253.i	0.00796531	+	0.0137963i
$227$	−7.96730e6	+	9.49506e6i	−0.681136	+	0.811746i	−0.990253	−	0.139278i	$-0.955522\pi$
$227$	−7.96730e6	+	9.49506e6i	−0.681136	+	0.811746i	0.309117	+	0.951024i	$0.399966\pi$
$228$	−1.37020e7	+	7.98642e6i	−1.15605	+	0.673825i
$229$	−1.74391e6	−	9.89022e6i	−0.145217	−	0.823568i	−0.967192	−	0.254045i	$-0.918239\pi$
$229$	−1.74391e6	−	9.89022e6i	−0.145217	−	0.823568i	0.821975	−	0.569523i	$-0.192872\pi$
$230$	655072.	−	115507.i	0.0538401	−	0.00949346i
$231$	−197241.	+	344911.i	−0.0160015	+	0.0279815i
$232$	3.80196e6	+	3.19022e6i	0.304469	+	0.255480i
$233$	1.65003e7	−	9.52644e6i	1.30444	−	0.753118i	0.323276	−	0.946305i	$-0.395216\pi$
$233$	1.65003e7	−	9.52644e6i	1.30444	−	0.753118i	0.981162	+	0.193187i	$0.0618823\pi$
$234$	774829.	−	2.18477e6i	0.0604725	−	0.170513i
$235$	4.17956e6	−	7.23920e6i	0.322052	−	0.557811i
$236$	4.41928e6	+	1.21419e7i	0.336214	+	0.923740i
$237$	−7.41199e6	+	2.06288e7i	−0.556788	+	1.54963i
$238$	−4.85647e6	+	4.07506e6i	−0.360238	+	0.302276i
$239$	4.77432e6	−	1.31173e7i	0.349718	−	0.960843i	−0.632741	−	0.774364i	$-0.718070\pi$
$239$	4.77432e6	−	1.31173e7i	0.349718	−	0.960843i	0.982459	−	0.186479i	$-0.0597076\pi$
$240$	1.61021e6	−	9.35765e6i	0.116479	−	0.676914i
$241$	−2.32803e6	+	1.32029e7i	−0.166317	+	0.943233i	0.781378	+	0.624058i	$0.214517\pi$
$241$	−2.32803e6	+	1.32029e7i	−0.166317	+	0.943233i	−0.947696	+	0.319176i	$0.896594\pi$
$242$		−	3.92453e6i		−	0.276912i
$243$	−9.44816e6	−	1.07992e7i	−0.658459	−	0.752617i
$244$	9.66085e6			0.665037
$245$	−286947.	−	50596.6i	−0.0195121	−	0.00344051i
$246$	5.60248e6	+	964043.i	0.376336	+	0.0647577i
$247$	−1.33959e7	−	4.87569e6i	−0.888955	−	0.323553i
$248$	4.23637e6	+	5.04870e6i	0.277740	+	0.330998i
$249$	−1.96960e7	−	7.07683e6i	−1.27579	−	0.458396i
$250$	−4.38170e6	+	1.59481e6i	−0.280429	+	0.102068i
$251$	−2.23324e7	−	1.28936e7i	−1.41226	−	0.815367i	−0.416656	−	0.909064i	$-0.636798\pi$
$251$	−2.23324e7	−	1.28936e7i	−1.41226	−	0.815367i	−0.995601	+	0.0936975i	$0.970131\pi$
$252$	−1.37670e7	−	4.88246e6i	−0.860275	−	0.305096i
$253$	58768.8	+	101791.i	0.00362899	+	0.00628559i
$254$	2.55279e6	−	3.04230e6i	0.155781	−	0.185652i
$255$	−2.18768e7	−	1.25105e7i	−1.31936	−	0.754489i
$256$	923524.	+	5.23757e6i	0.0550463	+	0.312183i
$257$	2.18415e6	−	385124.i	0.128671	−	0.0226883i	−0.108941	−	0.994048i	$-0.534746\pi$
$257$	2.18415e6	−	385124.i	0.128671	−	0.0226883i	0.237613	+	0.971360i	$0.423635\pi$
$258$	1.14146e6	+	1.95836e6i	0.0664664	+	0.114034i
$259$	1.91499e7	+	1.60687e7i	1.10222	+	0.924870i
$260$	8.12392e6	−	4.69035e6i	0.462217	−	0.266861i
$261$	1.15338e7	+	6.53272e6i	0.648713	+	0.367428i
$262$	−2.24852e6	+	3.89456e6i	−0.125024	+	0.216548i
$263$	−4.28425e6	−	1.17709e7i	−0.235509	−	0.647056i	−0.999997	−	0.00241771i	$-0.999230\pi$
$263$	−4.28425e6	−	1.17709e7i	−0.235509	−	0.647056i	0.764488	−	0.644638i	$-0.222992\pi$
$264$	−314690.	+	56828.6i	−0.0171029	+	0.00308855i
$265$	−1.26268e7	+	1.05951e7i	−0.678507	+	0.569335i
$266$	2.55741e6	−	7.02641e6i	0.135880	−	0.373326i
$267$	−1.72208e7	−	1.43293e7i	−0.904731	−	0.752818i
$268$	−3.00392e6	+	1.70361e7i	−0.156057	+	0.885045i
$269$			1.15113e6i			0.0591379i	0.999563	+	0.0295689i	$0.00941346\pi$
$269$			1.15113e6i			0.0591379i	−0.999563	+	0.0295689i	$0.990587\pi$
$270$	59847.4	+	4.83302e6i	0.00304056	+	0.245543i
$271$	−1.75441e7			−0.881500			−0.440750	−	0.897630i	$-0.645287\pi$
$271$	−1.75441e7			−0.881500			−0.440750	+	0.897630i	$0.645287\pi$
$272$	2.63642e7	+	4.64872e6i	1.31011	+	0.231008i
$273$	−4.54154e6	−	1.23193e7i	−0.223211	−	0.605479i
$274$	−5.49557e6	−	2.00022e6i	−0.267153	−	0.0972359i
$275$	−93818.6	−	111809.i	−0.00451119	−	0.00537622i
$276$	−3.29868e6	+	2.79120e6i	−0.156896	+	0.132759i
$277$	1.46203e7	−	5.32137e6i	0.687889	−	0.250371i	0.0256578	−	0.999671i	$-0.491832\pi$
$277$	1.46203e7	−	5.32137e6i	0.687889	−	0.250371i	0.662231	+	0.749300i	$0.269610\pi$
$278$	−2.68142e6	−	1.54812e6i	−0.124804	−	0.0720558i
$279$	1.35770e7	+	1.12028e7i	0.625159	+	0.515837i
$280$	5.12516e6	+	8.87704e6i	0.233471	+	0.404384i
$281$	−1.38170e7	+	1.64664e7i	−0.622722	+	0.742131i	−0.981536	−	0.191278i	$-0.938737\pi$
$281$	−1.38170e7	+	1.64664e7i	−0.622722	+	0.742131i	0.358814	+	0.933409i	$0.383181\pi$
$282$	−18656.5	−	4.52007e6i	−0.000831924	−	0.201557i
$283$	3.73753e6	+	2.11966e7i	0.164902	+	0.935203i	0.949166	+	0.314776i	$0.101930\pi$
$283$	3.73753e6	+	2.11966e7i	0.164902	+	0.935203i	−0.784264	+	0.620427i	$0.786959\pi$
$284$	1.29043e7	−	2.27538e6i	0.563353	−	0.0993344i
$285$	2.97235e7	−	122684.i	1.28400	−	0.00529970i
$286$	−105696.	−	88689.5i	−0.00451815	−	0.00379118i
$287$	2.78852e7	−	1.60995e7i	1.17958	−	0.681031i
$288$	−6.25007e6	−	1.67406e7i	−0.261642	−	0.700801i
$289$	2.34578e7	−	4.06300e7i	0.971836	−	1.68327i
$290$	−1.52714e6	−	4.19577e6i	−0.0626158	−	0.172035i
$291$	2.18919e7	+	2.58721e7i	0.888392	+	1.04991i
$292$	2.40247e7	−	2.01591e7i	0.964962	−	0.809699i
$293$	−1.52102e7	+	4.17896e7i	−0.604688	+	1.66137i	0.136960	+	0.990577i	$0.456267\pi$
$293$	−1.52102e7	+	4.17896e7i	−0.604688	+	1.66137i	−0.741648	+	0.670790i	$0.765955\pi$
$294$	−147832.	+	54498.6i	−0.00581738	+	0.00214458i
$295$	4.20516e6	−	2.38486e7i	0.163801	−	0.928961i
$296$			2.01195e7i			0.775787i
$297$	−798881.	+	302023.i	−0.0304939	+	0.0115284i
$298$	−1.25243e6			−0.0473264
$299$	−3.82508e6	−	674465.i	−0.143096	−	0.0252317i
$300$	3.43212e6	−	4.12470e6i	0.127116	−	0.152767i
$301$	1.20646e7	+	4.39115e6i	0.442398	+	0.161020i
$302$	−1.55344e6	−	1.85132e6i	−0.0563994	−	0.0672142i
$303$	8.07489e6	+	4.47150e7i	0.290274	+	1.60740i
$304$	−2.96709e7	+	1.07993e7i	−1.05611	+	0.384393i
$305$	−1.56804e7	−	9.05310e6i	−0.552661	−	0.319079i
$306$	−1.36269e7	+	112492.i	−0.475590	+	0.00392605i
$307$	−564777.	−	978223.i	−0.0195192	−	0.0338082i	0.856101	−	0.516809i	$-0.172880\pi$
$307$	−564777.	−	978223.i	−0.0195192	−	0.0338082i	−0.875620	+	0.483001i	$0.839547\pi$
$308$	−558863.	+	666026.i	−0.0191273	+	0.0227950i
$309$	5.96894e6	−	3.47909e6i	0.202312	−	0.117921i
$310$	−1.02960e6	−	5.83916e6i	−0.0345608	−	0.196004i
$311$	−1.09505e7	+	1.93087e6i	−0.364044	+	0.0641908i	−0.352678	−	0.935745i	$-0.614729\pi$
$311$	−1.09505e7	+	1.93087e6i	−0.364044	+	0.0641908i	−0.0113658	+	0.999935i	$0.503618\pi$
$312$	5.24582e6	−	9.17326e6i	0.172723	−	0.302037i
$313$	−4.57348e7	−	3.83761e7i	−1.49147	−	1.25149i	−0.892768	−	0.450517i	$-0.851240\pi$
$313$	−4.57348e7	−	3.83761e7i	−1.49147	−	1.25149i	−0.598700	−	0.800973i	$-0.704316\pi$
$314$	1.91057e6	−	1.10307e6i	0.0617125	−	0.0356297i
$315$	1.77698e7	+	2.08256e7i	0.568526	+	0.666294i
$316$	−2.39829e7	+	4.15396e7i	−0.760046	+	1.31644i
$317$	−1.45968e7	−	4.01043e7i	−0.458226	−	1.25897i	−0.926805	−	0.375543i	$-0.877456\pi$
$317$	−1.45968e7	−	4.01043e7i	−0.458226	−	1.25897i	0.468579	−	0.883422i	$-0.344766\pi$
$318$	−3.01385e6	+	8.38805e6i	−0.0937217	+	0.260843i
$319$	604393.	−	507146.i	0.0186186	−	0.0156229i
$320$	5.63918e6	−	1.54935e7i	0.172094	−	0.472825i
$321$	6.87322e6	−	3.99434e7i	0.207800	−	1.20762i
$322$	353771.	−	2.00634e6i	0.0105963	−	0.0600947i
$323$			8.38039e7i			2.48689i
$324$	−1.61461e7	−	2.69291e7i	−0.474714	−	0.791748i
$325$	4.82318e6			0.140502
$326$	1.07626e7	+	1.89773e6i	0.310644	+	0.0547750i
$327$	2.33461e7	+	4.01725e6i	0.667683	+	0.114891i
$328$	2.43519e7	+	8.86338e6i	0.690100	+	0.251176i
$329$	−1.64567e7	−	1.96123e7i	−0.462120	−	0.550733i
$330$	270744.	+	97279.0i	0.00753384	+	0.00270693i
$331$	5.82852e7	−	2.12141e7i	1.60722	−	0.584979i	0.626330	−	0.779558i	$-0.284556\pi$
$331$	5.82852e7	−	2.12141e7i	1.60722	−	0.584979i	0.980887	+	0.194579i	$0.0623340\pi$
$332$	−3.96612e7	−	2.28984e7i	−1.08381	−	0.625736i
$333$	9.76751e6	+	5.28399e7i	0.264516	+	1.43096i
$334$	500899.	+	867582.i	0.0134434	+	0.0232847i
$335$	2.08400e7	−	2.48362e7i	0.554324	−	0.660618i
$336$	−2.52452e7	−	1.44367e7i	−0.665519	−	0.380584i
$337$	579840.	+	3.28844e6i	0.0151502	+	0.0859211i	0.991445	−	0.130522i	$-0.0416654\pi$
$337$	579840.	+	3.28844e6i	0.0151502	+	0.0859211i	−0.976295	+	0.216443i	$0.930554\pi$
$338$	−6.05133e6	+	1.06701e6i	−0.156711	+	0.0276324i
$339$	1.12743e6	+	1.93428e6i	0.0289394	+	0.0496502i
$340$	−4.22443e7	−	3.54472e7i	−1.07481	−	0.901873i
$341$	907338.	−	523852.i	0.0228826	−	0.0132113i
$342$	1.38527e7	−	8.15106e6i	0.346303	−	0.203768i
$343$	−2.03961e7	+	3.53271e7i	−0.505434	+	0.875438i
$344$	3.53414e6	+	9.70997e6i	0.0868177	+	0.238530i
$345$	7.96967e6	−	1.43921e6i	0.194081	−	0.0350483i
$346$	7.61351e6	−	6.38849e6i	0.183805	−	0.154230i
$347$	−9.61851e6	+	2.64266e7i	−0.230207	+	0.632489i	−0.999983	−	0.00582501i	$-0.998146\pi$
$347$	−9.61851e6	+	2.64266e7i	−0.230207	+	0.632489i	0.769776	+	0.638314i	$0.220368\pi$
$348$	2.22965e7	+	1.85527e7i	0.529053	+	0.440220i
$349$	1.94804e6	−	1.10479e7i	0.0458271	−	0.259898i	−0.953283	−	0.302079i	$-0.902319\pi$
$349$	1.94804e6	−	1.10479e7i	0.0458271	−	0.259898i	0.999110	+	0.0421807i	$0.0134305\pi$
$350$			2.52986e6i			0.0590055i
$351$	9.32371e6	−	2.66384e7i	0.215609	−	0.616009i
$352$	−1.06360e6			−0.0243867
$353$	−5.55789e7	−	9.80006e6i	−1.26353	−	0.222795i	−0.498558	−	0.866856i	$-0.666137\pi$
$353$	−5.55789e7	−	9.80006e6i	−1.26353	−	0.222795i	−0.764974	+	0.644062i	$0.777248\pi$
$354$	−4.52946e6	−	1.22866e7i	−0.102103	−	0.276962i
$355$	−2.30772e7	−	8.39940e6i	−0.515819	−	0.187743i
$356$	−3.15109e7	−	3.75532e7i	−0.698410	−	0.832333i
$357$	−5.89225e7	+	4.98577e7i	−1.29502	+	1.09579i
$358$	−1.86340e7	+	6.78223e6i	−0.406123	+	0.147817i
$359$	3.98907e7	+	2.30309e7i	0.862160	+	0.497768i	0.864735	−	0.502228i	$-0.167486\pi$
$359$	3.98907e7	+	2.30309e7i	0.862160	+	0.497768i	−0.00257486	+	0.999997i	$0.500820\pi$
$360$	−3.64682e6	+	2.17296e7i	−0.0781640	+	0.465740i
$361$	−2.58985e7	−	4.48575e7i	−0.550495	−	0.953485i
$362$	−1.14247e7	+	1.36154e7i	−0.240835	+	0.287015i
$363$	−197215.	−	4.77809e7i	−0.00412307	−	0.998929i
$364$	−4.98907e6	−	2.82944e7i	−0.103446	−	0.586674i
$365$	−5.78853e7	+	1.02067e7i	−1.19039	+	0.209898i
$366$	−9.79068e6	+	40410.9i	−0.199696	+	0.000824243i
$367$	2.15514e7	+	1.80838e7i	0.435991	+	0.365840i	0.834207	−	0.551452i	$-0.185926\pi$
$367$	2.15514e7	+	1.80838e7i	0.435991	+	0.365840i	−0.398215	+	0.917292i	$0.630370\pi$
$368$	−7.45040e6	+	4.30149e6i	−0.149498	+	0.0863129i
$369$	6.82584e7	+	1.14556e7i	1.35855	+	0.228003i
$370$	9.05025e6	−	1.56755e7i	0.178672	−	0.309468i
$371$	1.72665e7	+	4.74393e7i	0.338129	+	0.929002i
$372$	2.48801e7	+	2.94036e7i	0.483308	+	0.571179i
$373$	5.43484e7	−	4.56037e7i	1.04727	−	0.878766i	0.0544687	−	0.998515i	$-0.482653\pi$
$373$	5.43484e7	−	4.56037e7i	1.04727	−	0.878766i	0.992804	+	0.119749i	$0.0382090\pi$
$374$	−277419.	+	762202.i	−0.00530299	+	0.0145699i
$375$	−5.32668e7	+	1.96369e7i	−1.01010	+	0.372374i
$376$	3.57808e6	−	2.02923e7i	0.0673111	−	0.381740i
$377$			2.60722e7i			0.486579i
$378$	1.39724e7	+	4.89049e6i	0.258700	+	0.0905475i
$379$	−2.73515e7			−0.502416			−0.251208	−	0.967933i	$-0.580828\pi$
$379$	−2.73515e7			−0.502416			−0.251208	+	0.967933i	$0.580828\pi$
$380$	6.40542e7	+	1.12945e7i	1.16734	+	0.205833i
$381$	3.09272e7	−	3.71681e7i	0.559198	−	0.672040i
$382$	1.93460e7	+	7.04137e6i	0.347057	+	0.126319i
$383$	1.60698e7	+	1.91512e7i	0.286031	+	0.340878i	0.889859	−	0.456237i	$-0.150803\pi$
$383$	1.60698e7	+	1.91512e7i	0.286031	+	0.340878i	−0.603828	+	0.797115i	$0.706358\pi$
$384$	−9.11172e6	−	5.04564e7i	−0.160919	−	0.891093i
$385$	1.53121e6	−	557316.i	0.0268320	−	0.00976606i
$386$	5.88015e6	+	3.39491e6i	0.102241	+	0.0590290i
$387$	1.39956e7	+	2.37855e7i	0.241468	+	0.410374i
$388$	3.70809e7	+	6.42260e7i	0.634827	+	1.09955i
$389$	5.54722e7	−	6.61092e7i	0.942381	−	1.12309i	−0.0498597	−	0.998756i	$-0.515877\pi$
$389$	5.54722e7	−	6.61092e7i	0.942381	−	1.12309i	0.992241	−	0.124330i	$-0.0396781\pi$
$390$	−8.21348e6	+	4.78736e6i	−0.138463	+	0.0807054i
$391$	3.96496e6	+	2.24864e7i	0.0663298	+	0.376175i
$392$	−707330.	+	124721.i	−0.0117426	+	0.00207054i
$393$	−2.71799e7	+	4.75290e7i	−0.447786	+	0.783035i
$394$	1.76766e7	+	1.48324e7i	0.289008	+	0.242506i
$395$	7.78528e7	−	4.49483e7i	1.26323	−	0.729327i
$396$	−1.83775e6	+	339711.i	−0.0295938	+	0.00547046i
$397$	−2.16049e7	+	3.74208e7i	−0.345288	+	0.598056i	−0.985406	−	0.170221i	$-0.945552\pi$
$397$	−2.16049e7	+	3.74208e7i	−0.345288	+	0.598056i	0.640118	+	0.768276i	$0.278885\pi$
$398$	6.08284e6	+	1.67125e7i	0.0964844	+	0.265089i
$399$	3.07832e7	−	8.56747e7i	0.484613	−	1.34876i
$400$	8.18366e6	−	6.86690e6i	0.127870	−	0.107295i
$401$	1.72225e7	−	4.73185e7i	0.267094	−	0.733835i	−0.731551	−	0.681787i	$-0.761203\pi$
$401$	1.72225e7	−	4.73185e7i	0.267094	−	0.733835i	0.998645	−	0.0520475i	$-0.0165747\pi$
$402$	2.97303e6	−	1.72776e7i	0.0457637	−	0.265953i
$403$	−6.01202e6	+	3.40959e7i	−0.0918555	+	0.520939i
$404$			9.94290e7i			1.50789i
$405$	971508.	+	5.88388e7i	0.0146245	+	0.885724i
$406$	−1.36754e7			−0.204344
$407$	3.14979e6	+	555393.i	0.0467195	+	0.00823791i
$408$	−6.12219e7	−	1.05347e7i	−0.901418	−	0.155111i
$409$	−5.79103e6	−	2.10776e6i	−0.0846420	−	0.0308072i	0.299352	−	0.954143i	$-0.403229\pi$
$409$	−5.79103e6	−	2.10776e6i	−0.0846420	−	0.0308072i	−0.383994	+	0.923336i	$0.625452\pi$
$410$	−1.49861e7	−	1.78597e7i	−0.217439	−	0.259133i
$411$	−6.70088e7	−	2.40764e7i	−0.965175	−	0.346790i
$412$	1.42064e7	−	5.17070e6i	0.203138	−	0.0739363i
$413$	−6.42329e7	−	3.70849e7i	−0.911816	−	0.526437i
$414$	3.33133e6	−	2.84251e6i	0.0469480	−	0.0400591i
$415$	4.29158e7	+	7.43324e7i	0.600445	+	1.04000i
$416$	2.25923e7	−	2.69244e7i	0.313819	−	0.373995i
$417$	−3.27239e7	−	1.87135e7i	−0.451291	−	0.258075i
$418$	−166125.	−	942143.i	−0.00227461	−	0.0129000i
$419$	1.02171e7	−	1.80155e6i	0.138895	−	0.0244908i	−0.103769	−	0.994601i	$-0.533090\pi$
$419$	1.02171e7	−	1.80155e6i	0.138895	−	0.0244908i	0.242663	+	0.970111i	$0.421979\pi$
$420$	3.01668e7	+	5.17559e7i	0.407175	+	0.698573i
$421$	9.22556e6	+	7.74116e6i	0.123636	+	0.103743i	0.702509	−	0.711674i	$-0.252063\pi$
$421$	9.22556e6	+	7.74116e6i	0.123636	+	0.103743i	−0.578873	+	0.815418i	$0.696507\pi$
$422$	1.01710e7	−	5.87225e6i	0.135340	−	0.0781389i
$423$	−454285.	−	5.50307e7i	−0.00600215	−	0.727083i
$424$	−2.03155e7	+	3.51875e7i	−0.266520	+	0.461627i
$425$	−9.69761e6	−	2.66440e7i	−0.126328	−	0.347082i
$426$	−1.30682e7	+	2.35994e6i	−0.169040	+	0.0305262i
$427$	−4.24811e7	+	3.56459e7i	−0.545648	+	0.457853i
$428$	3.03336e7	−	8.33409e7i	0.386895	−	1.06298i
$429$	−1.29130e6	−	1.07448e6i	−0.0163552	−	0.0136090i
$430$	1.61427e6	−	9.15496e6i	0.0203034	−	0.115147i
$431$		−	1.33928e7i		−	0.167278i	−0.996496	−	0.0836392i	$-0.973346\pi$
$431$		−	1.33928e7i		−	0.167278i	0.996496	−	0.0836392i	$-0.0266543\pi$
$432$	−2.21061e7	−	5.84728e7i	−0.274195	−	0.725275i
$433$	1.45081e7			0.178709			0.0893546	−	0.996000i	$-0.471520\pi$
$433$	1.45081e7			0.178709			0.0893546	+	0.996000i	$0.471520\pi$
$434$	−1.78840e7	−	3.15343e6i	−0.218774	−	0.0385758i
$435$	−1.88037e7	−	5.10066e7i	−0.228441	−	0.619667i
$436$	4.87110e7	+	1.77294e7i	0.587716	+	0.213911i
$437$	−1.73108e7	−	2.06302e7i	−0.207431	−	0.247206i
$438$	−2.42633e7	+	2.05306e7i	−0.288753	+	0.244331i
$439$	−1.21991e8	+	4.44012e7i	−1.44190	+	0.524809i	−0.940317	−	0.340300i	$-0.889471\pi$
$439$	−1.21991e8	+	4.44012e7i	−1.44190	+	0.524809i	−0.501583	+	0.865109i	$0.667249\pi$
$440$	1.13576e6	+	655730.i	0.0133330	+	0.00769781i
$441$	−1.79711e6	+	670946.i	−0.0209536	+	0.00782297i
$442$	−1.34019e7	−	2.32128e7i	−0.155203	−	0.268819i
$443$	3.77626e7	−	4.50037e7i	0.434360	−	0.517651i	−0.503815	−	0.863812i	$-0.668071\pi$
$443$	3.77626e7	−	4.50037e7i	0.434360	−	0.517651i	0.938175	+	0.346161i	$0.112515\pi$
$444$	485324.	+	1.17583e8i	0.00554476	+	1.34337i
$445$	1.59542e7	+	9.04808e7i	0.181049	+	1.02678i
$446$	1.43659e7	−	2.53309e6i	0.161930	−	0.0285527i
$447$	−1.52482e7	+	62936.9i	−0.170725	+	0.000704665i
$448$	−3.86841e7	−	3.24598e7i	−0.430228	−	0.361004i
$449$	1.84690e7	−	1.06631e7i	0.204035	−	0.117800i	−0.394501	−	0.918895i	$-0.629083\pi$
$449$	1.84690e7	−	1.06631e7i	0.204035	−	0.117800i	0.598536	+	0.801096i	$0.295749\pi$
$450$	−3.46100e6	+	4.19449e6i	−0.0379807	+	0.0460301i
$451$	2.05982e6	−	3.56772e6i	0.0224543	−	0.0388921i
$452$	1.67561e6	+	4.60369e6i	0.0181450	+	0.0498530i
$453$	−1.90061e7	−	2.24617e7i	−0.204456	−	0.241628i
$454$	2.10567e7	−	1.76687e7i	0.225021	−	0.188815i
$455$	−1.84168e7	+	5.05997e7i	−0.195515	+	0.537172i
$456$	6.87469e7	−	2.53437e7i	0.725035	−	0.267285i
$457$	1.20494e7	−	6.83356e7i	0.126246	−	0.715976i	−0.854314	−	0.519757i	$-0.826023\pi$
$457$	1.20494e7	−	6.83356e7i	0.126246	−	0.715976i	0.980560	−	0.196219i	$-0.0628664\pi$
$458$			2.22714e7i			0.231820i
$459$	−1.65901e8	+	2.05436e6i	−1.71558	+	0.0212441i
$460$	1.77215e7			0.182065
$461$	−2.38197e7	−	4.20005e6i	−0.243127	−	0.0428698i	0.0507568	−	0.998711i	$-0.483837\pi$
$461$	−2.38197e7	−	4.20005e6i	−0.243127	−	0.0428698i	−0.293884	+	0.955841i	$0.594948\pi$
$462$	563587.	−	677315.i	0.00571525	−	0.00686854i
$463$	9.74758e6	+	3.54783e6i	0.0982096	+	0.0357454i	0.390658	−	0.920536i	$-0.372248\pi$
$463$	9.74758e6	+	3.54783e6i	0.0982096	+	0.0357454i	−0.292448	+	0.956281i	$0.594470\pi$
$464$	3.71197e7	+	4.42376e7i	0.371579	+	0.442830i
$465$	−1.28288e7	−	7.10397e7i	−0.127593	−	0.706549i
$466$	−3.97045e7	+	1.44512e7i	−0.392357	+	0.142806i
$467$	6.31951e7	+	3.64857e7i	0.620487	+	0.358238i	0.777059	−	0.629428i	$-0.216711\pi$
$467$	6.31951e7	+	3.64857e7i	0.620487	+	0.358238i	−0.156571	+	0.987667i	$0.550044\pi$
$468$	3.04366e7	−	5.37373e7i	0.296933	−	0.524249i
$469$	−4.96495e7	−	8.59955e7i	−0.481279	−	0.833599i
$470$	−1.19157e7	+	1.42006e7i	−0.114770	+	0.136777i
$471$	2.32056e7	−	1.35258e7i	0.222091	−	0.129449i
$472$	−1.03658e7	−	5.87873e7i	−0.0985772	−	0.559059i
$473$	1.61769e6	−	285243.i	0.0152866	−	0.00269545i
$474$	2.41314e7	−	4.21981e7i	0.226594	−	0.396240i
$475$	2.56182e7	+	2.14962e7i	0.239038	+	0.200577i
$476$	−1.46271e8	+	8.44499e7i	−1.35625	+	0.783030i
$477$	−3.62720e7	+	1.02276e8i	−0.334207	+	0.942359i
$478$	−1.54783e7	+	2.68092e7i	−0.141723	+	0.245471i
$479$	−1.39415e7	−	3.83039e7i	−0.126854	−	0.348527i	0.859966	−	0.510351i	$-0.170485\pi$
$479$	−1.39415e7	−	3.83039e7i	−0.126854	−	0.348527i	−0.986820	+	0.161824i	$0.948262\pi$
$480$	−2.47803e7	+	6.89677e7i	−0.224070	+	0.623623i
$481$	−8.09647e7	+	6.79375e7i	−0.727546	+	0.610484i
$482$	1.01687e7	−	2.79381e7i	0.0908076	−	0.249492i
$483$	4.20632e6	−	2.44448e7i	0.0373303	−	0.216943i
$484$	1.81560e7	−	1.02968e8i	0.160134	−	0.908166i
$485$		−	1.38993e8i		−	1.21834i
$486$	1.64757e7	+	2.72235e7i	0.143528	+	0.237156i
$487$	−1.41045e7			−0.122115			−0.0610577	−	0.998134i	$-0.519447\pi$
$487$	−1.41045e7			−0.122115			−0.0610577	+	0.998134i	$0.519447\pi$
$488$	−4.39540e7	−	7.75028e6i	−0.378216	−	0.0666896i
$489$	1.31129e8	+	2.25639e7i	1.12143	+	0.192969i
$490$	607197.	+	221002.i	0.00516109	+	0.00187848i
$491$	1.01486e8	+	1.20946e8i	0.857358	+	1.02176i	0.999491	+	0.0319120i	$0.0101596\pi$
$491$	1.01486e8	+	1.20946e8i	0.857358	+	1.02176i	−0.142133	+	0.989848i	$0.545396\pi$
$492$	1.42532e8	+	5.12123e7i	1.19679	+	0.430010i
$493$	1.44027e8	−	5.24214e7i	1.20199	−	0.437490i
$494$	2.73784e7	+	1.58069e7i	0.227105	+	0.131119i
$495$	3.30118e6	+	1.17076e6i	0.0272178	+	0.00965279i
$496$	3.83425e7	+	6.64111e7i	0.314221	+	0.544247i
$497$	−4.83480e7	+	5.76189e7i	−0.393831	+	0.469349i
$498$	4.02900e7	+	2.30402e7i	0.326219	+	0.186552i
$499$	−2.12369e6	−	1.20440e7i	−0.0170919	−	0.0969328i	0.975068	−	0.221904i	$-0.0712272\pi$
$499$	−2.12369e6	−	1.20440e7i	−0.0170919	−	0.0969328i	−0.992160	+	0.124971i	$0.960116\pi$
$500$	−1.22341e8	+	2.15719e7i	−0.978725	+	0.172576i
$501$	6.14201e6	+	1.05376e7i	0.0488425	+	0.0837970i
$502$	4.38078e7	+	3.67591e7i	0.346290	+	0.290572i
$503$	1.12962e8	−	6.52185e7i	0.887620	−	0.512468i	0.0144569	−	0.999895i	$-0.495398\pi$
$503$	1.12962e8	−	6.52185e7i	0.887620	−	0.512468i	0.873163	+	0.487428i	$0.162065\pi$
$504$	5.87189e7	+	3.32581e7i	0.458655	+	0.259780i
$505$	9.31741e7	−	1.61382e8i	0.723471	−	1.25309i
$506$	−89150.1	−	244938.i	−0.000688129	−	0.00189062i
$507$	−7.36210e7	+	1.32949e7i	−0.564908	+	0.102014i
$508$	8.10520e7	−	6.80107e7i	0.618262	−	0.518784i
$509$	−8.78811e7	+	2.41451e8i	−0.666411	+	1.83095i	−0.121244	+	0.992623i	$0.538688\pi$
$509$	−8.78811e7	+	2.41451e8i	−0.666411	+	1.83095i	−0.545167	+	0.838327i	$0.683534\pi$
$510$	4.29603e7	+	3.57469e7i	0.323860	+	0.269481i
$511$	−3.12609e7	+	1.77289e8i	−0.234282	+	1.32868i
$512$		−	1.33329e8i		−	0.993380i
$513$	1.68246e8	−	9.99349e7i	1.24622	−	0.740227i
$514$	−4.91839e6			−0.0362188
$515$	−2.79037e7	−	4.92017e6i	−0.204287	−	0.0360212i
$516$	2.08886e7	+	5.66621e7i	0.152041	+	0.412424i
$517$	−3.07807e6	−	1.12032e6i	−0.0222744	−	0.00810723i
$518$	−3.56347e7	−	4.24677e7i	−0.256380	−	0.305541i
$519$	9.23730e7	−	7.81621e7i	0.660759	−	0.559106i
$520$	−4.07242e7	+	1.48224e7i	−0.289630	+	0.105417i
$521$	−3.64559e7	−	2.10478e7i	−0.257783	−	0.148831i	0.365540	−	0.930796i	$-0.380884\pi$
$521$	−3.64559e7	−	2.10478e7i	−0.257783	−	0.148831i	−0.623323	+	0.781965i	$0.714218\pi$
$522$	−2.26737e7	−	1.87088e7i	−0.159409	−	0.131533i
$523$	−8.97239e7	−	1.55406e8i	−0.627196	−	1.08633i	−0.988112	−	0.153737i	$-0.950869\pi$
$523$	−8.97239e7	−	1.55406e8i	−0.627196	−	1.08633i	0.360916	−	0.932598i	$-0.382464\pi$
$524$	−7.70118e7	+	9.17791e7i	−0.535258	+	0.637896i
$525$	127130.	+	3.08009e7i	0.000878561	+	0.212856i
$526$	4.82377e6	+	2.73569e7i	0.0331458	+	0.187979i
$527$	2.00439e8	−	3.53427e7i	1.36946	−	0.241473i
$528$	−3.72076e6	+	15357.4i	−0.0252773	+	0.000104332i
$529$	1.07781e8	+	9.04391e7i	0.728074	+	0.610927i
$530$	3.16564e7	−	1.82768e7i	0.212635	−	0.122765i
$531$	−5.57634e7	−	1.49361e8i	−0.372448	−	0.997592i
$532$	9.96048e7	−	1.72521e8i	0.661524	−	1.14579i
$533$	4.65612e7	+	1.27926e8i	0.307498	+	0.844843i
$534$	3.20914e7	+	3.79261e7i	0.210749	+	0.249066i
$535$	−1.27332e8	+	1.06845e8i	−0.831529	+	0.697736i
$536$	2.73339e7	−	7.50994e7i	0.177504	−	0.487688i
$537$	−2.26527e8	+	8.35097e7i	−1.46284	+	0.539280i
$538$	443288.	−	2.51401e6i	0.00284668	−	0.0161443i
$539$			114178.i			0.000729150i
$540$	−2.07887e7	+	1.27081e8i	−0.132022	+	0.807046i
$541$	4.03807e7			0.255025			0.127512	−	0.991837i	$-0.459301\pi$
$541$	4.03807e7			0.255025			0.127512	+	0.991837i	$0.459301\pi$
$542$	3.83155e7	+	6.75606e6i	0.240645	+	0.0424322i
$543$	−1.38411e8	+	1.66341e8i	−0.864511	+	1.03896i
$544$	−1.94159e8	−	7.06681e7i	−1.20604	−	0.438962i
$545$	−6.24484e7	−	7.44231e7i	−0.385773	−	0.459746i
$546$	5.17447e6	+	2.86538e7i	0.0317898	+	0.176037i
$547$	7.61986e7	−	2.77340e7i	0.465570	−	0.169454i	−0.0985745	−	0.995130i	$-0.531428\pi$
$547$	7.61986e7	−	2.77340e7i	0.465570	−	0.169454i	0.564145	+	0.825676i	$0.309206\pi$
$548$	−1.34934e8	−	7.79039e7i	−0.819933	−	0.473388i
$549$	−1.19199e8	+	984001.i	−0.720370	+	0.00594674i
$550$	161839.	+	280314.i	0.000972739	+	0.00168483i
$551$	−1.16200e8	+	1.38482e8i	−0.694626	+	0.827823i
$552$	1.72472e7	−	1.00528e7i	0.102542	−	0.0597684i
$553$	−4.78111e7	−	2.71150e8i	−0.282718	−	1.60337i
$554$	−3.39794e7	+	5.99149e6i	−0.199842	+	0.0352375i
$555$	1.09399e8	−	1.91303e8i	0.639931	−	1.11903i
$556$	−6.31902e7	−	5.30229e7i	−0.367642	−	0.308489i
$557$	−2.35182e8	+	1.35783e8i	−1.36094	+	0.785739i	−0.989749	−	0.142817i	$-0.954384\pi$
$557$	−2.35182e8	+	1.35783e8i	−1.36094	+	0.785739i	−0.371191	+	0.928557i	$0.621050\pi$
$558$	−2.53375e7	−	2.96947e7i	−0.145835	−	0.170914i
$559$	−2.71410e7	+	4.70096e7i	−0.155378	+	0.269123i
$560$	4.07918e7	+	1.12075e8i	0.232279	+	0.638180i
$561$	−3.33926e6	+	9.29371e6i	−0.0189130	+	0.0526381i
$562$	3.65168e7	−	3.06412e7i	0.205723	−	0.172622i
$563$	1.28801e7	−	3.53877e7i	0.0721761	−	0.198302i	−0.898359	−	0.439262i	$-0.855240\pi$
$563$	1.28801e7	−	3.53877e7i	0.0721761	−	0.198302i	0.970535	+	0.240960i	$0.0774622\pi$
$564$	2.04217e7	−	1.18679e8i	0.113829	−	0.661512i
$565$	1.59442e6	−	9.04241e6i	0.00884011	−	0.0501348i
$566$		−	4.77317e7i		−	0.263243i
$567$	1.70359e8	+	5.88393e7i	0.934581	+	0.322789i
$568$	−6.05364e7			−0.330348
$569$	1.04168e7	+	1.83677e6i	0.0565457	+	0.00997053i	0.201849	−	0.979417i	$-0.435305\pi$
$569$	1.04168e7	+	1.83677e6i	0.0565457	+	0.00997053i	−0.145304	+	0.989387i	$0.546416\pi$
$570$	−6.49622e7	−	1.11783e7i	−0.350781	−	0.0603604i
$571$	−1.00683e8	−	3.66457e7i	−0.540816	−	0.196841i	0.0571455	−	0.998366i	$-0.481800\pi$
$571$	−1.00683e8	−	3.66457e7i	−0.540816	−	0.196841i	−0.597961	+	0.801525i	$0.704022\pi$
$572$	−2.36284e6	−	2.81593e6i	−0.0126254	−	0.0150464i
$573$	2.35891e8	+	8.47562e7i	1.25385	+	0.450513i
$574$	−6.70998e7	+	2.44223e7i	−0.354802	+	0.129137i
$575$	7.89095e6	+	4.55584e6i	0.0415074	+	0.0239643i
$576$	−1.97311e7	−	1.06740e8i	−0.103248	−	0.558548i
$577$	3.63819e7	+	6.30153e7i	0.189390	+	0.328034i	0.945047	−	0.326934i	$-0.106015\pi$
$577$	3.63819e7	+	6.30153e7i	0.189390	+	0.328034i	−0.755657	+	0.654968i	$0.772682\pi$
$578$	−6.68770e7	+	7.97009e7i	−0.346333	+	0.412743i
$579$	7.17611e7	+	4.10373e7i	0.369703	+	0.211419i
$580$	−2.06566e7	−	1.17149e8i	−0.105870	−	0.600421i
$581$	2.58889e8	−	4.56491e7i	1.32003	−	0.232758i
$582$	−3.78479e7	−	6.49340e7i	−0.191987	−	0.329385i
$583$	4.94794e6	+	4.15181e6i	0.0249700	+	0.0209523i
$584$	−1.25478e8	+	7.24447e7i	−0.629983	+	0.363721i
$585$	−9.97581e7	+	5.86986e7i	−0.498288	+	0.293198i
$586$	4.93112e7	−	8.54095e7i	0.245049	−	0.424437i
$587$	−1.05031e8	−	2.88571e8i	−0.519282	−	1.42672i	−0.871313	−	0.490728i	$-0.836731\pi$
$587$	−1.05031e8	−	2.88571e8i	−0.519282	−	1.42672i	0.352030	−	0.935989i	$-0.385491\pi$
$588$	−4.13080e6	+	745964.i	−0.0203190	+	0.00366932i
$589$	−1.83893e8	+	1.54305e8i	−0.899952	+	0.755149i
$590$	−1.83678e7	+	5.04651e7i	−0.0894336	+	0.245717i
$591$	2.15957e8	+	1.79696e8i	1.04617	+	0.870512i
$592$	−4.06511e7	+	2.30544e8i	−0.195933	+	1.11119i
$593$		−	2.65451e8i		−	1.27298i	−0.771286	−	0.636489i	$-0.780386\pi$
$593$		−	2.65451e8i		−	1.27298i	0.771286	−	0.636489i	$-0.219614\pi$
$594$	1.86103e6	−	351963.i	0.00887960	−	0.00167934i
$595$	3.16549e8			1.50276
$596$	−3.28599e7	−	5.79409e6i	−0.155213	−	0.0273682i
$597$	7.48981e7	+	2.03168e8i	0.352004	+	0.954842i
$598$	8.09408e6	+	2.94601e6i	0.0378499	+	0.0137762i
$599$	4.10633e7	+	4.89373e7i	0.191061	+	0.227698i	0.853068	−	0.521800i	$-0.174739\pi$
$599$	4.10633e7	+	4.89373e7i	0.191061	+	0.227698i	−0.662006	+	0.749498i	$0.730295\pi$
$600$	−1.89242e7	+	1.60128e7i	−0.0876118	+	0.0741334i
$601$	6.90264e7	−	2.51236e7i	0.317974	−	0.115733i	−0.178102	−	0.984012i	$-0.556996\pi$
$601$	6.90264e7	−	2.51236e7i	0.317974	−	0.115733i	0.496076	+	0.868279i	$0.334774\pi$
$602$	−2.46576e7	−	1.42360e7i	−0.113021	−	0.0652529i
$603$	3.53283e7	−	2.10503e8i	0.161128	−	0.960079i
$604$	−3.21929e7	−	5.57598e7i	−0.146100	−	0.253052i
$605$	−1.25959e8	+	1.50112e8i	−0.568805	+	0.677875i
$606$	−415907.	−	1.00765e8i	−0.00186887	−	0.452786i
$607$	5.94566e7	+	3.37195e8i	0.265848	+	1.50770i	0.766609	+	0.642115i	$0.221943\pi$
$607$	5.94566e7	+	3.37195e8i	0.265848	+	1.50770i	−0.500760	+	0.865586i	$0.666946\pi$
$608$	2.39996e8	−	4.23178e7i	1.06781	−	0.188284i
$609$	−1.66498e8	+	687217.i	−0.737150	+	0.00304258i
$610$	3.07592e7	+	2.58100e7i	0.135514	+	0.113710i
$611$	9.37421e7	−	5.41221e7i	0.410971	−	0.237274i
$612$	−3.58049e8	−	6.00905e7i	−1.56203	−	0.262151i
$613$	−5.45698e7	+	9.45176e7i	−0.236903	+	0.410328i	−0.959824	−	0.280603i	$-0.909466\pi$
$613$	−5.45698e7	+	9.45176e7i	−0.236903	+	0.410328i	0.722921	+	0.690931i	$0.242799\pi$
$614$	856745.	+	2.35389e6i	0.00370123	+	0.0101691i
$615$	−1.83352e8	−	2.16688e8i	−0.788245	−	0.931558i
$616$	3.07697e6	−	2.58189e6i	0.0131638	−	0.0110457i
$617$	7.18699e7	−	1.97461e8i	0.305979	−	0.840670i	−0.687451	−	0.726230i	$-0.741271\pi$
$617$	7.18699e7	−	1.97461e8i	0.305979	−	0.840670i	0.993430	−	0.114439i	$-0.0365072\pi$
$618$	−1.43757e7	+	5.29962e6i	−0.0609064	+	0.0224532i
$619$	−5.85565e7	+	3.32090e8i	−0.246890	+	1.40018i	0.569172	+	0.822218i	$0.307264\pi$
$619$	−5.85565e7	+	3.32090e8i	−0.246890	+	1.40018i	−0.816062	+	0.577964i	$0.803847\pi$
$620$		−	1.57965e8i		−	0.662806i
$621$	4.04160e7	−	3.47748e7i	0.168763	−	0.145208i
$622$	2.46591e7			0.102472
$623$	2.77122e8	+	4.88641e7i	1.14606	+	0.202081i
$624$	7.86447e7	−	9.45147e7i	0.323680	−	0.388996i
$625$	1.69396e8	+	6.16551e7i	0.693847	+	0.252539i
$626$	8.51047e7	+	1.01424e8i	0.346921	+	0.413444i
$627$	−2.06991e6	−	1.14622e7i	−0.00839748	−	0.0465013i
$628$	5.52306e7	−	2.01023e7i	0.222998	−	0.0811646i
$629$	5.38087e8	+	3.10664e8i	2.16222	+	1.24836i
$630$	−3.07887e7	−	5.23253e7i	−0.123132	−	0.209262i
$631$	−8.09313e7	−	1.40177e8i	−0.322128	−	0.557942i	0.658799	−	0.752319i	$-0.271065\pi$
$631$	−8.09313e7	−	1.40177e8i	−0.322128	−	0.557942i	−0.980927	+	0.194377i	$0.937731\pi$
$632$	1.42440e8	−	1.69753e8i	0.564261	−	0.672460i
$633$	1.23537e8	−	7.20054e7i	0.487063	−	0.283893i
$634$	1.64350e7	+	9.32073e7i	0.0644913	+	0.365748i
$635$	−1.95287e8	+	3.44344e7i	−0.762698	+	0.134484i
$636$	−1.17880e8	+	2.06134e8i	−0.458214	+	0.801269i
$637$	−2.89034e6	−	2.42528e6i	−0.0111823	−	0.00938305i
$638$	−1.51527e6	+	874840.i	−0.00583481	+	0.00336873i
$639$	−1.58987e8	+	2.93889e7i	−0.609337	+	0.112637i
$640$	−1.05138e8	+	1.82104e8i	−0.401069	+	0.694672i
$641$	−5.69038e7	−	1.56342e8i	−0.216057	−	0.593610i	0.783560	−	0.621317i	$-0.213402\pi$
$641$	−5.69038e7	−	1.56342e8i	−0.216057	−	0.593610i	−0.999616	+	0.0277063i	$0.991180\pi$
$642$	−3.03927e7	+	8.45878e7i	−0.114859	+	0.319671i
$643$	−1.05069e8	+	8.81632e7i	−0.395222	+	0.331630i	−0.818643	−	0.574302i	$-0.805273\pi$
$643$	−1.05069e8	+	8.81632e7i	−0.395222	+	0.331630i	0.423422	+	0.905933i	$0.360829\pi$
$644$	1.85638e7	−	5.10036e7i	0.0695038	−	0.190960i
$645$	1.91936e7	−	1.11542e8i	0.0715280	−	0.415681i
$646$	3.22721e7	−	1.83024e8i	0.119710	−	0.678908i
$647$		−	2.63341e8i		−	0.972311i	−0.873872	−	0.486156i	$-0.838399\pi$
$647$		−	2.63341e8i		−	0.972311i	0.873872	−	0.486156i	$-0.161601\pi$
$648$	5.18565e7	+	1.35473e8i	0.190580	+	0.497882i
$649$	−9.48953e6			−0.0347145
$650$	−1.05336e7	−	1.85736e6i	−0.0383564	−	0.00676327i
$651$	−2.17895e8	−	3.74942e7i	−0.789778	−	0.135900i
$652$	2.73598e8	+	9.95815e7i	0.987120	+	0.359282i
$653$	9.44334e7	+	1.12541e8i	0.339145	+	0.404178i	0.908480	−	0.417928i	$-0.137244\pi$
$653$	9.44334e7	+	1.12541e8i	0.339145	+	0.404178i	−0.569335	+	0.822106i	$0.692799\pi$
$654$	−4.94398e7	−	1.77639e7i	−0.176744	−	0.0635045i
$655$	2.11003e8	−	7.67987e7i	0.750869	−	0.273294i
$656$	2.61134e8	+	1.50766e8i	0.925020	+	0.534061i
$657$	−2.94372e8	+	2.51178e8i	−1.03801	+	0.885697i
$658$	2.83882e7	+	4.91698e7i	0.0996460	+	0.172592i
$659$	9.73541e7	−	1.16022e8i	0.340172	−	0.405401i	−0.568654	−	0.822577i	$-0.692536\pi$
$659$	9.73541e7	−	1.16022e8i	0.340172	−	0.405401i	0.908826	+	0.417176i	$0.136980\pi$
$660$	6.65346e6	+	3.80485e6i	0.0231428	+	0.0132344i
$661$	−3.20427e7	−	1.81723e8i	−0.110949	−	0.629224i	−0.988676	−	0.150063i	$-0.952052\pi$
$661$	−3.20427e7	−	1.81723e8i	−0.110949	−	0.629224i	0.877727	−	0.479161i	$-0.159059\pi$
$662$	−1.35462e8	+	2.38856e7i	−0.466921	+	0.0823307i
$663$	−1.64334e8	−	2.81941e8i	−0.563880	−	0.967425i
$664$	1.62077e8	+	1.35999e8i	0.553627	+	0.464548i
$665$	−3.23335e8	+	1.86678e8i	−1.09948	+	0.634787i
$666$	−983692.	−	1.19161e8i	−0.00332994	−	0.403379i
$667$	−2.46271e7	+	4.26553e7i	−0.0829918	+	0.143746i
$668$	9.12839e6	+	2.50800e7i	0.0306242	+	0.0841393i
$669$	1.74777e8	−	3.15622e7i	0.583721	−	0.105412i
$670$	−5.50779e7	+	4.62159e7i	−0.183127	+	0.153662i
$671$	−2.42667e6	+	6.66723e6i	−0.00803237	+	0.0220688i
$672$	1.72535e8	+	1.43565e8i	0.568552	+	0.473087i
$673$	3.45516e7	−	1.95952e8i	0.113350	−	0.642842i	−0.874203	−	0.485560i	$-0.838616\pi$
$673$	3.45516e7	−	1.95952e8i	0.113350	−	0.642842i	0.987554	−	0.157282i	$-0.0502732\pi$
$674$		−	7.40510e6i		−	0.0241853i
$675$	−4.19267e7	+	5.12416e7i	−0.136326	+	0.166614i
$676$	−1.63705e8			−0.529934
$677$	−4.57829e8	−	8.07276e7i	−1.47549	−	0.260169i	−0.622718	−	0.782446i	$-0.713972\pi$
$677$	−4.57829e8	−	8.07276e7i	−1.47549	−	0.260169i	−0.852776	+	0.522277i	$0.825083\pi$
$678$	−1.71738e6	−	4.65855e6i	−0.00551034	−	0.0149473i
$679$	−4.00030e8	−	1.45599e8i	−1.27786	−	0.465103i
$680$	1.63762e8	+	1.95164e8i	0.520820	+	0.620689i
$681$	2.55477e8	−	2.16174e8i	0.808928	−	0.684481i
$682$	−2.18332e6	+	794663.i	−0.00688278	+	0.00250513i
$683$	4.65585e7	+	2.68806e7i	0.146129	+	0.0843677i	0.571282	−	0.820754i	$-0.306446\pi$
$683$	4.65585e7	+	2.68806e7i	0.146129	+	0.0843677i	−0.425153	+	0.905122i	$0.639780\pi$
$684$	4.01162e8	−	1.49773e8i	1.25358	−	0.468020i
$685$	1.46006e8	+	2.52890e8i	0.454255	+	0.786793i
$686$	5.81484e7	−	6.92985e7i	0.180121	−	0.214660i
$687$	1.11918e6	+	2.71153e8i	0.00345168	+	0.836266i
$688$	2.08779e7	+	1.18404e8i	0.0641093	+	0.363582i
$689$	−2.10200e8	+	3.70640e7i	−0.642652	+	0.113317i
$690$	−1.79596e7	+	74128.2i	−0.0546702	+	0.000225651i
$691$	−3.21966e8	−	2.70161e8i	−0.975833	−	0.818821i	0.00762268	−	0.999971i	$-0.497574\pi$
$691$	−3.21966e8	−	2.70161e8i	−0.975833	−	0.818821i	−0.983455	+	0.181150i	$0.942018\pi$
$692$	2.29310e8	−	1.32392e8i	0.691999	−	0.399526i
$693$	6.82761e6	−	8.27459e6i	0.0205149	−	0.0248626i
$694$	3.11831e7	−	5.40107e7i	0.0932911	−	0.161585i
$695$	5.28762e7	+	1.45276e8i	0.157509	+	0.432752i
$696$	−8.65589e7	−	1.02296e8i	−0.256734	−	0.303412i
$697$	6.13064e8	−	5.14422e8i	1.81054	−	1.51922i
$698$	−8.50888e6	+	2.33780e7i	−0.0250211	+	0.0687449i
$699$	−4.82674e8	+	1.77938e8i	−1.41326	+	0.521001i
$700$	−1.17039e7	+	6.63759e7i	−0.0341221	+	0.193516i
$701$		−	4.04803e7i		−	0.117514i	−0.998272	−	0.0587571i	$-0.981286\pi$
$701$		−	4.04803e7i		−	0.117514i	0.998272	−	0.0587571i	$-0.0187137\pi$
$702$	−3.06208e7	+	5.45868e7i	−0.0885126	+	0.157789i
$703$	−7.32829e8			−2.10929
$704$	−6.36280e6	−	1.12193e6i	−0.0182360	−	0.00321550i
$705$	−1.44360e8	+	1.73490e8i	−0.411982	+	0.495117i
$706$	1.17608e8	+	4.28059e7i	0.334213	+	0.121644i
$707$	−3.66866e8	−	4.37214e8i	−1.03812	−	1.23719i
$708$	−6.19982e7	−	3.43317e8i	−0.174695	−	0.967377i
$709$	−3.50199e8	+	1.27462e8i	−0.982599	+	0.357637i	−0.782850	−	0.622210i	$-0.786235\pi$
$709$	−3.50199e8	+	1.27462e8i	−0.982599	+	0.357637i	−0.199749	+	0.979847i	$0.564013\pi$
$710$	4.71650e7	+	2.72307e7i	0.131779	+	0.0760824i
$711$	2.91678e8	−	5.14973e8i	0.811513	−	1.43277i
$712$	1.13239e8	+	1.96135e8i	0.313729	+	0.543395i
$713$	−4.20420e7	+	5.01037e7i	−0.115988	+	0.138230i
$714$	1.47884e8	−	8.61967e7i	0.406281	−	0.236808i
$715$	1.19633e6	+	6.78470e6i	0.00327289	+	0.0185615i
$716$	−5.20277e8	+	9.17389e7i	−1.41741	+	0.249928i
$717$	−1.87100e8	+	3.27178e8i	−0.507594	+	0.887620i
$718$	−7.82506e7	−	6.56600e7i	−0.211405	−	0.177389i
$719$	−4.82422e8	+	2.78526e8i	−1.29790	+	0.749341i	−0.980040	−	0.198798i	$-0.936296\pi$
$719$	−4.82422e8	+	2.78526e8i	−1.29790	+	0.749341i	−0.317856	+	0.948139i	$0.602963\pi$
$720$	−8.56920e7	+	2.41624e8i	−0.229585	+	0.647356i
$721$	−4.33905e7	+	7.51545e7i	−0.115768	+	0.200516i
$722$	3.92871e7	+	1.07940e8i	0.104385	+	0.286795i
$723$	1.22399e8	−	3.40656e8i	0.323864	−	0.901367i
$724$	−3.62738e8	+	3.04374e8i	−0.955824	+	0.802031i
$725$	2.09189e7	−	5.74742e7i	0.0548940	−	0.150820i
$726$	−1.79693e7	+	1.04427e8i	−0.0469592	+	0.272901i
$727$	1.05447e8	−	5.98020e8i	0.274430	−	1.55637i	−0.466337	−	0.884607i	$-0.654427\pi$
$727$	1.05447e8	−	5.98020e8i	0.274430	−	1.55637i	0.740767	−	0.671762i	$-0.234462\pi$
$728$			1.32734e8i			0.344023i
$729$	2.01959e8	+	3.30616e8i	0.521291	+	0.853379i
$730$	1.30350e8			0.335074
$731$	3.14259e8	+	5.54123e7i	0.804517	+	0.141858i
$732$	−2.57065e8	−	4.42342e7i	−0.655405	−	0.112778i
$733$	3.79891e8	+	1.38269e8i	0.964599	+	0.351085i	0.775834	−	0.630937i	$-0.217329\pi$
$733$	3.79891e8	+	1.38269e8i	0.964599	+	0.351085i	0.188765	+	0.982022i	$0.439551\pi$
$734$	−4.01035e7	−	4.77935e7i	−0.101413	−	0.120860i
$735$	7.40370e6	+	2.66017e6i	0.0186460	+	0.00669958i
$736$	6.23941e7	−	2.27096e7i	0.156498	−	0.0569608i
$737$	−1.10026e7	−	6.35233e6i	−0.0274847	−	0.0158683i
$738$	−1.44662e8	−	5.13043e7i	−0.359903	−	0.127639i
$739$	2.36685e7	+	4.09950e7i	0.0586459	+	0.101578i	0.893858	−	0.448351i	$-0.147988\pi$
$739$	2.36685e7	+	4.09950e7i	0.0586459	+	0.101578i	−0.835212	+	0.549928i	$0.814655\pi$
$740$	3.09971e8	−	3.69409e8i	0.764937	−	0.911616i
$741$	3.34125e8	+	1.91073e8i	0.821210	+	0.469617i
$742$	−1.94409e7	−	1.10255e8i	−0.0475887	−	0.269889i
$743$	2.18569e8	−	3.85397e7i	0.532872	−	0.0939596i	0.0992635	−	0.995061i	$-0.468351\pi$
$743$	2.18569e8	−	3.85397e7i	0.532872	−	0.0939596i	0.433608	+	0.901102i	$0.357240\pi$
$744$	−8.96086e7	−	1.53738e8i	−0.217586	−	0.373303i
$745$	4.79050e7	+	4.01971e7i	0.115854	+	0.0972133i
$746$	−1.36256e8	+	7.86675e7i	−0.328201	+	0.189487i
$747$	4.91686e8	+	2.78489e8i	1.17958	+	0.668107i
$748$	−1.08048e7	+	1.87145e7i	−0.0258174	+	0.0447170i
$749$	1.74121e8	+	4.78393e8i	0.414386	+	1.13852i
$750$	1.23894e8	−	2.23736e7i	0.293676	−	0.0530337i
$751$	5.79606e8	−	4.86347e8i	1.36840	−	1.14822i	0.395112	−	0.918633i	$-0.370706\pi$
$751$	5.79606e8	−	4.86347e8i	1.36840	−	1.14822i	0.973287	−	0.229590i	$-0.0737386\pi$
$752$	8.20004e7	−	2.25294e8i	0.192825	−	0.529781i
$753$	5.35204e8	+	4.45338e8i	1.25353	+	1.04305i
$754$	1.00402e7	−	5.69406e7i	0.0234221	−	0.132834i
$755$			1.20671e8i			0.280390i
$756$	3.43970e8	+	1.92952e8i	0.796076	+	0.446564i
$757$	4.73188e8			1.09080			0.545401	−	0.838175i	$-0.316377\pi$
$757$	4.73188e8			1.09080			0.545401	+	0.838175i	$0.316377\pi$
$758$	5.97346e7	+	1.05328e7i	0.137157	+	0.0241845i
$759$	−1.09771e6	−	2.97762e6i	−0.00251050

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.18396 - 0.385091i) q^{2} +(-26.6089 - 4.57871i) q^{3} +(-55.5189 - 20.2072i) q^{4} +(71.1763 + 84.8246i) q^{5} +(56.3496 + 20.2466i) q^{6} +(318.690 - 115.994i) q^{7} +(236.384 + 136.476i) q^{8} +(687.071 + 243.669i) q^{9} +O(q^{10})\)	\(q+(-2.18396 - 0.385091i) q^{2} +(-26.6089 - 4.57871i) q^{3} +(-55.5189 - 20.2072i) q^{4} +(71.1763 + 84.8246i) q^{5} +(56.3496 + 20.2466i) q^{6} +(318.690 - 115.994i) q^{7} +(236.384 + 136.476i) q^{8} +(687.071 + 243.669i) q^{9} +(-122.781 - 212.663i) q^{10} +(27.8912 - 33.2395i) q^{11} +(1384.78 + 791.899i) q^{12} +(248.990 + 1412.09i) q^{13} +(-740.673 + 130.601i) q^{14} +(-1505.54 - 2582.99i) q^{15} +(2432.91 + 2041.45i) q^{16} +(7299.99 - 4214.65i) q^{17} +(-1406.70 - 796.748i) q^{18} +(-4970.99 + 8610.00i) q^{19} +(-2237.56 - 6147.65i) q^{20} +(-9011.09 + 1627.28i) q^{21} +(-73.7135 + 61.8529i) q^{22} +(-926.465 + 2545.44i) q^{23} +(-5665.04 - 4713.83i) q^{24} +(584.106 - 3312.63i) q^{25} -3179.84i q^{26} +(-17166.5 - 9629.68i) q^{27} -20037.2 q^{28} +(17906.8 + 3157.45i) q^{29} +(2293.35 + 6220.90i) q^{30} +(22689.5 + 8258.29i) q^{31} +(-15756.1 - 18777.4i) q^{32} +(-894.349 + 756.761i) q^{33} +(-17565.9 + 6393.46i) q^{34} +(32522.2 + 18776.7i) q^{35} +(-33221.6 - 27412.1i) q^{36} +(36855.3 + 63835.3i) q^{37} +(14172.1 - 16889.6i) q^{38} +(-159.793 - 38714.3i) q^{39} +(5248.38 + 29765.1i) q^{40} +(93500.0 - 16486.6i) q^{41} +(20306.5 - 83.8148i) q^{42} +(29000.0 + 24333.9i) q^{43} +(-2220.17 + 1281.81i) q^{44} +(28234.0 + 75624.0i) q^{45} +(3003.59 - 5202.36i) q^{46} +(-25819.3 - 70937.9i) q^{47} +(-55389.9 - 65460.5i) q^{48} +(-2015.75 + 1691.42i) q^{49} +(-2551.33 + 7009.71i) q^{50} +(-213543. + 78722.8i) q^{51} +(14710.8 - 83429.3i) q^{52} +148857. i q^{53} +(33782.7 + 27641.5i) q^{54} +4804.71 q^{55} +(91163.6 + 16074.6i) q^{56} +(171695. - 206342. i) q^{57} +(-37891.7 - 13791.5i) q^{58} +(-140576. - 167532. i) q^{59} +(31390.8 + 173827. i) q^{60} +(-153655. + 55925.7i) q^{61} +(-46372.7 - 26773.3i) q^{62} +(247226. - 2040.88i) q^{63} +(-74450.3 - 128952. i) q^{64} +(-102058. + 121628. i) q^{65} +(2244.64 - 1308.33i) q^{66} +(-50843.2 - 288346. i) q^{67} +(-490454. + 86480.3i) q^{68} +(36307.1 - 63489.4i) q^{69} +(-63796.5 - 53531.6i) q^{70} +(-192070. + 110892. i) q^{71} +(129157. + 151369. i) q^{72} +(-265411. + 459706. i) q^{73} +(-55908.1 - 153606. i) q^{74} +(-30710.0 + 85471.1i) q^{75} +(449969. - 377568. i) q^{76} +(5033.08 - 13828.3i) q^{77} +(-14559.6 + 84612.1i) q^{78} +(140976. - 799517. i) q^{79} +351673. i q^{80} +(412692. + 334836. i) q^{81} -210549. q^{82} +(763363. + 134602. i) q^{83} +(533169. + 91744.7i) q^{84} +(877092. + 319235. i) q^{85} +(-53964.1 - 64311.9i) q^{86} +(-462023. - 166006. i) q^{87} +(11129.4 - 4050.78i) q^{88} +(718568. + 414866. i) q^{89} +(-32539.8 - 176032. i) q^{90} +(243144. + 421138. i) q^{91} +(102873. - 122599. i) q^{92} +(-565930. - 323633. i) q^{93} +(29070.7 + 164868. i) q^{94} +(-1.08416e6 + 191166. i) q^{95} +(333276. + 571788. i) q^{96} +(-961565. - 806849. i) q^{97} +(5053.67 - 2917.74i) q^{98} +(27262.7 - 16041.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9}+O(q^{10}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9	\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} - 3 q^{10} - 492 q^{11} + 3549 q^{12} - 6 q^{13} - 12183 q^{14} - 7974 q^{15} - 198 q^{16} - 9 q^{17} + 40995 q^{18} - 3 q^{19} - 19767 q^{20} - 2406 q^{21} - 10806 q^{22} + 14466 q^{23} + 35352 q^{24} - 15990 q^{25} + 64548 q^{27} - 12 q^{28} - 45690 q^{29} - 186003 q^{30} + 18354 q^{31} - 140544 q^{32} - 78804 q^{33} - 82278 q^{34} + 268263 q^{35} + 412632 q^{36} - 3 q^{37} + 28428 q^{38} + 126402 q^{39} - 34593 q^{40} + 234948 q^{41} - 466074 q^{42} + 148764 q^{43} - 1222785 q^{44} - 646578 q^{45} - 3 q^{46} + 517098 q^{47} + 1608681 q^{48} - 311262 q^{49} + 1710663 q^{50} + 825291 q^{51} - 213057 q^{52} - 1089018 q^{54} - 12 q^{55} - 3167925 q^{56} - 1657317 q^{57} + 663789 q^{58} - 230802 q^{59} - 168786 q^{60} - 51414 q^{61} + 1777536 q^{62} + 1460250 q^{63} + 983037 q^{64} + 2264754 q^{65} + 1054197 q^{66} - 845052 q^{67} - 3979053 q^{68} - 3558150 q^{69} - 835251 q^{70} - 427689 q^{71} - 419292 q^{72} - 257043 q^{73} + 2458185 q^{74} + 3429390 q^{75} + 2759802 q^{76} + 5459610 q^{77} + 5939316 q^{78} + 662682 q^{79} - 3002958 q^{81} - 12 q^{82} - 4926426 q^{83} - 10132716 q^{84} - 2530881 q^{85} - 6700758 q^{86} - 3444642 q^{87} - 2860230 q^{88} + 5907321 q^{89} + 5189148 q^{90} - 451443 q^{91} + 712473 q^{92} - 2952102 q^{93} + 7395807 q^{94} - 2179119 q^{95} + 809838 q^{96} + 272208 q^{97} + 1179270 q^{98} + 1743822 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 210 * q^5 - 342 * q^6 - 6 * q^7 - 9 * q^8 + 1242 * q^9 - 3 * q^10 - 492 * q^11 + 3549 * q^12 - 6 * q^13 - 12183 * q^14 - 7974 * q^15 - 198 * q^16 - 9 * q^17 + 40995 * q^18 - 3 * q^19 - 19767 * q^20 - 2406 * q^21 - 10806 * q^22 + 14466 * q^23 + 35352 * q^24 - 15990 * q^25 + 64548 * q^27 - 12 * q^28 - 45690 * q^29 - 186003 * q^30 + 18354 * q^31 - 140544 * q^32 - 78804 * q^33 - 82278 * q^34 + 268263 * q^35 + 412632 * q^36 - 3 * q^37 + 28428 * q^38 + 126402 * q^39 - 34593 * q^40 + 234948 * q^41 - 466074 * q^42 + 148764 * q^43 - 1222785 * q^44 - 646578 * q^45 - 3 * q^46 + 517098 * q^47 + 1608681 * q^48 - 311262 * q^49 + 1710663 * q^50 + 825291 * q^51 - 213057 * q^52 - 1089018 * q^54 - 12 * q^55 - 3167925 * q^56 - 1657317 * q^57 + 663789 * q^58 - 230802 * q^59 - 168786 * q^60 - 51414 * q^61 + 1777536 * q^62 + 1460250 * q^63 + 983037 * q^64 + 2264754 * q^65 + 1054197 * q^66 - 845052 * q^67 - 3979053 * q^68 - 3558150 * q^69 - 835251 * q^70 - 427689 * q^71 - 419292 * q^72 - 257043 * q^73 + 2458185 * q^74 + 3429390 * q^75 + 2759802 * q^76 + 5459610 * q^77 + 5939316 * q^78 + 662682 * q^79 - 3002958 * q^81 - 12 * q^82 - 4926426 * q^83 - 10132716 * q^84 - 2530881 * q^85 - 6700758 * q^86 - 3444642 * q^87 - 2860230 * q^88 + 5907321 * q^89 + 5189148 * q^90 - 451443 * q^91 + 712473 * q^92 - 2952102 * q^93 + 7395807 * q^94 - 2179119 * q^95 + 809838 * q^96 + 272208 * q^97 + 1179270 * q^98 + 1743822 * q^99

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