LMFDB - Embedded newform 27.7.f.a.2.3

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			2.3
Character	$\chi$	$=$	27.2
Dual form			27.7.f.a.14.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.6551 - 2.05510i) q^{2} +(-14.9225 + 22.5015i) q^{3} +(71.4770 + 26.0155i) q^{4} +(105.310 + 125.503i) q^{5} +(220.166 - 231.590i) q^{6} +(-278.603 + 101.403i) q^{7} +(-123.650 - 71.3896i) q^{8} +(-283.637 - 671.559i) q^{9} +O(q^{10})$	\(q+(-11.6551 - 2.05510i) q^{2} +(-14.9225 + 22.5015i) q^{3} +(71.4770 + 26.0155i) q^{4} +(105.310 + 125.503i) q^{5} +(220.166 - 231.590i) q^{6} +(-278.603 + 101.403i) q^{7} +(-123.650 - 71.3896i) q^{8} +(-283.637 - 671.559i) q^{9} +(-969.470 - 1679.17i) q^{10} +(-1207.08 + 1438.54i) q^{11} +(-1652.01 + 1220.13i) q^{12} +(-524.739 - 2975.94i) q^{13} +(3455.54 - 609.304i) q^{14} +(-4395.49 + 496.805i) q^{15} +(-2434.75 - 2043.00i) q^{16} +(3385.84 - 1954.82i) q^{17} +(1925.69 + 8409.97i) q^{18} +(-1016.82 + 1761.19i) q^{19} +(4262.19 + 11710.3i) q^{20} +(1875.73 - 7782.19i) q^{21} +(17025.0 - 14285.6i) q^{22} +(2009.15 - 5520.08i) q^{23} +(3451.55 - 1717.01i) q^{24} +(-1947.66 + 11045.7i) q^{25} +35763.2i q^{26} +(19343.7 + 3639.08i) q^{27} -22551.8 q^{28} +(-38554.4 - 6798.17i) q^{29} +(52250.8 + 3242.90i) q^{30} +(-23238.8 - 8458.24i) q^{31} +(30052.3 + 35815.0i) q^{32} +(-14356.7 - 48627.8i) q^{33} +(-43479.6 + 15825.3i) q^{34} +(-42066.0 - 24286.8i) q^{35} +(-2802.60 - 55380.0i) q^{36} +(-25350.0 - 43907.6i) q^{37} +(15470.6 - 18437.1i) q^{38} +(74793.7 + 32601.1i) q^{39} +(-4061.96 - 23036.5i) q^{40} +(5206.04 - 917.965i) q^{41} +(-37855.0 + 86847.2i) q^{42} +(99078.2 + 83136.5i) q^{43} +(-123703. + 71419.9i) q^{44} +(54413.0 - 106319. i) q^{45} +(-34761.1 + 60208.0i) q^{46} +(-30602.8 - 84080.5i) q^{47} +(82303.1 - 24298.9i) q^{48} +(-22787.2 + 19120.7i) q^{49} +(45400.3 - 124736. i) q^{50} +(-6538.92 + 105357. i) q^{51} +(39913.9 - 226363. i) q^{52} +232123. i q^{53} +(-217973. - 82167.0i) q^{54} -307658. q^{55} +(41688.6 + 7350.82i) q^{56} +(-24455.9 - 49161.4i) q^{57} +(435383. + 158466. i) q^{58} +(15469.2 + 18435.4i) q^{59} +(-327102. - 78840.9i) q^{60} +(54467.4 - 19824.5i) q^{61} +(253468. + 146340. i) q^{62} +(147120. + 158337. i) q^{63} +(-174952. - 303025. i) q^{64} +(318230. - 379252. i) q^{65} +(67393.4 + 596265. i) q^{66} +(-29705.8 - 168470. i) q^{67} +(292865. - 51640.1i) q^{68} +(94228.8 + 127582. i) q^{69} +(440371. + 369515. i) q^{70} +(-329789. + 190404. i) q^{71} +(-12870.5 + 103287. i) q^{72} +(-6046.53 + 10472.9i) q^{73} +(205222. + 563843. i) q^{74} +(-219482. - 208656. i) q^{75} +(-118498. + 99431.3i) q^{76} +(190423. - 523184. i) q^{77} +(-804728. - 533678. i) q^{78} +(-35153.5 + 199366. i) q^{79} -520716. i q^{80} +(-370541. + 380958. i) q^{81} -62563.3 q^{82} +(-752327. - 132656. i) q^{83} +(336530. - 507450. i) q^{84} +(601897. + 219073. i) q^{85} +(-983910. - 1.17258e6i) q^{86} +(728297. - 766086. i) q^{87} +(251953. - 91703.3i) q^{88} +(-771432. - 445387. i) q^{89} +(-852684. + 1.12733e6i) q^{90} +(447965. + 775897. i) q^{91} +(287216. - 342290. i) q^{92} +(537105. - 396691. i) q^{93} +(183884. + 1.04286e6i) q^{94} +(-328116. + 57855.6i) q^{95} +(-1.25435e6 + 141774. i) q^{96} +(-1.15661e6 - 970509. i) q^{97} +(304882. - 176024. i) q^{98} +(1.30844e6 + 402601. i) 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 $

$2$	−11.6551	−	2.05510i	−1.45688	−	0.256888i	−0.611584	−	0.791179i	$-0.709467\pi$
$2$	−11.6551	−	2.05510i	−1.45688	−	0.256888i	−0.845300	+	0.534291i	$0.820579\pi$
$3$	−14.9225	+	22.5015i	−0.552686	+	0.833390i
$3$	−14.9225	+	22.5015i	−0.552686	+	0.833390i
$4$	71.4770	+	26.0155i	1.11683	+	0.406492i
$5$	105.310	+	125.503i	0.842477	+	1.00402i	0.999864	+	0.0164878i	$0.00524846\pi$
$5$	105.310	+	125.503i	0.842477	+	1.00402i	−0.157387	+	0.987537i	$0.550307\pi$
$6$	220.166	−	231.590i	1.01929	−	1.07217i
$7$	−278.603	+	101.403i	−0.812254	+	0.295636i	−0.714555	−	0.699579i	$-0.753371\pi$
$7$	−278.603	+	101.403i	−0.812254	+	0.295636i	−0.0976997	+	0.995216i	$0.531148\pi$
$8$	−123.650	−	71.3896i	−0.241505	−	0.139433i
$9$	−283.637	−	671.559i	−0.389077	−	0.921205i
$10$	−969.470	−	1679.17i	−0.969470	−	1.67917i
$11$	−1207.08	+	1438.54i	−0.906897	+	1.08080i	0.0895004	+	0.995987i	$0.471473\pi$
$11$	−1207.08	+	1438.54i	−0.906897	+	1.08080i	−0.996397	+	0.0848106i	$0.972971\pi$
$12$	−1652.01	+	1220.13i	−0.956022	+	0.706091i
$13$	−524.739	−	2975.94i	−0.238843	−	1.35455i	−0.834366	−	0.551210i	$-0.814166\pi$
$13$	−524.739	−	2975.94i	−0.238843	−	1.35455i	0.595523	−	0.803338i	$-0.296945\pi$
$14$	3455.54	−	609.304i	1.25931	−	0.222050i
$15$	−4395.49	+	496.805i	−1.30237	+	0.147201i
$16$	−2434.75	−	2043.00i	−0.594421	−	0.498779i
$17$	3385.84	−	1954.82i	0.689159	−	0.397886i	−0.114138	−	0.993465i	$-0.536410\pi$
$17$	3385.84	−	1954.82i	0.689159	−	0.397886i	0.803297	+	0.595579i	$0.203077\pi$
$18$	1925.69	+	8409.97i	0.330194	+	1.44204i
$19$	−1016.82	+	1761.19i	−0.148246	+	0.256770i	−0.930579	−	0.366090i	$-0.880696\pi$
$19$	−1016.82	+	1761.19i	−0.148246	+	0.256770i	0.782333	+	0.622860i	$0.214030\pi$
$20$	4262.19	+	11710.3i	0.532774	+	1.46378i
$21$	1875.73	−	7782.19i	0.202541	−	0.840319i
$22$	17025.0	−	14285.6i	1.59889	−	1.34163i
$23$	2009.15	−	5520.08i	0.165131	−	0.453693i	−0.829335	−	0.558751i	$-0.811281\pi$
$23$	2009.15	−	5520.08i	0.165131	−	0.453693i	0.994466	+	0.105058i	$0.0335029\pi$
$24$	3451.55	−	1717.01i	0.249678	−	0.124205i
$25$	−1947.66	+	11045.7i	−0.124650	+	0.706927i
$26$			35763.2i			2.03478i
$27$	19343.7	+	3639.08i	0.982760	+	0.184884i
$28$	−22551.8			−1.02732
$29$	−38554.4	−	6798.17i	−1.58081	−	0.278739i	−0.686820	−	0.726828i	$-0.740994\pi$
$29$	−38554.4	−	6798.17i	−1.58081	−	0.278739i	−0.893989	+	0.448088i	$0.852105\pi$
$30$	52250.8	+	3242.90i	1.93522	+	0.120108i
$31$	−23238.8	−	8458.24i	−0.780061	−	0.283919i	−0.0788632	−	0.996885i	$-0.525129\pi$
$31$	−23238.8	−	8458.24i	−0.780061	−	0.283919i	−0.701198	+	0.712966i	$0.747351\pi$
$32$	30052.3	+	35815.0i	0.917124	+	1.09299i
$33$	−14356.7	−	48627.8i	−0.399497	−	1.35314i
$34$	−43479.6	+	15825.3i	−1.10624	+	0.402638i
$35$	−42066.0	−	24286.8i	−0.981132	−	0.566457i
$36$	−2802.60	−	55380.0i	−0.0600694	−	1.18699i
$37$	−25350.0	−	43907.6i	−0.500465	−	0.866831i	−1.00000		0.000536843i	$-0.999829\pi$
$37$	−25350.0	−	43907.6i	−0.500465	−	0.866831i	0.499535	−	0.866294i	$-0.333504\pi$
$38$	15470.6	−	18437.1i	0.281939	−	0.336002i
$39$	74793.7	+	32601.1i	1.26087	+	0.549590i
$40$	−4061.96	−	23036.5i	−0.0634681	−	0.359946i
$41$	5206.04	−	917.965i	0.0755363	−	0.0133191i	−0.135752	−	0.990743i	$-0.543345\pi$
$41$	5206.04	−	917.965i	0.0755363	−	0.0133191i	0.211289	+	0.977424i	$0.432234\pi$
$42$	−37855.0	+	86847.2i	−0.510947	+	1.17222i
$43$	99078.2	+	83136.5i	1.24616	+	1.04565i	0.997017	+	0.0771829i	$0.0245925\pi$
$43$	99078.2	+	83136.5i	1.24616	+	1.04565i	0.249140	+	0.968467i	$0.419852\pi$
$44$	−123703.	+	71419.9i	−1.45218	+	0.838419i
$45$	54413.0	−	106319.i	0.597125	−	1.16674i
$46$	−34761.1	+	60208.0i	−0.357125	+	0.618558i
$47$	−30602.8	−	84080.5i	−0.294759	−	0.809845i	−0.995354	−	0.0962852i	$-0.969304\pi$
$47$	−30602.8	−	84080.5i	−0.294759	−	0.809845i	0.700594	−	0.713560i	$-0.252918\pi$
$48$	82303.1	−	24298.9i	0.744205	−	0.219717i
$49$	−22787.2	+	19120.7i	−0.193688	+	0.162524i
$50$	45400.3	−	124736.i	0.363202	−	0.997890i
$51$	−6538.92	+	105357.i	−0.0492941	+	0.794245i
$52$	39913.9	−	226363.i	0.283867	−	1.60989i
$53$			232123.i			1.55916i	0.626303	+	0.779580i	$0.284567\pi$
$53$			232123.i			1.55916i	−0.626303	+	0.779580i	$0.715433\pi$
$54$	−217973.	−	82167.0i	−1.38427	−	0.521814i
$55$	−307658.			−1.84919
$56$	41688.6	+	7350.82i	0.237385	+	0.0418573i
$57$	−24455.9	−	49161.4i	−0.132056	−	0.265460i
$58$	435383.	+	158466.i	2.23145	+	0.812182i
$59$	15469.2	+	18435.4i	0.0753201	+	0.0897630i	0.802389	−	0.596802i	$-0.203562\pi$
$59$	15469.2	+	18435.4i	0.0753201	+	0.0897630i	−0.727069	+	0.686565i	$0.759118\pi$
$60$	−327102.	−	78840.9i	−1.51436	−	0.365004i
$61$	54467.4	−	19824.5i	0.239964	−	0.0873399i	−0.219239	−	0.975671i	$-0.570357\pi$
$61$	54467.4	−	19824.5i	0.239964	−	0.0873399i	0.459203	+	0.888331i	$0.348135\pi$
$62$	253468.	+	146340.i	1.06352	+	0.614026i
$63$	147120.	+	158337.i	0.588371	+	0.633228i
$64$	−174952.	−	303025.i	−0.667388	−	1.15595i
$65$	318230.	−	379252.i	1.15878	−	1.38098i
$66$	67393.4	+	596265.i	0.234415	+	2.07399i
$67$	−29705.8	−	168470.i	−0.0987681	−	0.560141i	−0.993527	−	0.113593i	$-0.963764\pi$
$67$	−29705.8	−	168470.i	−0.0987681	−	0.560141i	0.894759	−	0.446549i	$-0.147347\pi$
$68$	292865.	−	51640.1i	0.931411	−	0.164233i
$69$	94228.8	+	127582.i	0.286838	+	0.388368i
$70$	440371.	+	369515.i	1.28388	+	1.07730i
$71$	−329789.	+	190404.i	−0.921428	+	0.531987i	−0.884090	−	0.467316i	$-0.845221\pi$
$71$	−329789.	+	190404.i	−0.921428	+	0.531987i	−0.0373375	+	0.999303i	$0.511888\pi$
$72$	−12870.5	+	103287.i	−0.0344823	+	0.276726i
$73$	−6046.53	+	10472.9i	−0.0155431	+	0.0269214i	−0.873692	−	0.486479i	$-0.838281\pi$
$73$	−6046.53	+	10472.9i	−0.0155431	+	0.0269214i	0.858149	+	0.513400i	$0.171614\pi$
$74$	205222.	+	563843.i	0.506441	+	1.39144i
$75$	−219482.	−	208656.i	−0.520254	−	0.494591i
$76$	−118498.	+	99431.3i	−0.269941	+	0.226507i
$77$	190423.	−	523184.i	0.417108	−	1.14599i
$78$	−804728.	−	533678.i	−1.69576	−	1.12459i
$79$	−35153.5	+	199366.i	−0.0712997	+	0.404361i	0.928181	+	0.372130i	$0.121372\pi$
$79$	−35153.5	+	199366.i	−0.0712997	+	0.404361i	−0.999480	+	0.0322310i	$0.989739\pi$
$80$		−	520716.i		−	1.01702i
$81$	−370541.	+	380958.i	−0.697238	+	0.716840i
$82$	−62563.3			−0.113469
$83$	−752327.	−	132656.i	−1.31575	−	0.232002i	−0.528655	−	0.848837i	$-0.677303\pi$
$83$	−752327.	−	132656.i	−1.31575	−	0.232002i	−0.787092	+	0.616835i	$0.788414\pi$
$84$	336530.	−	507450.i	0.567787	−	0.856161i
$85$	601897.	+	219073.i	0.980089	+	0.356723i
$86$	−983910.	−	1.17258e6i	−1.54689	−	1.84351i
$87$	728297.	−	766086.i	1.10599	−	1.16337i
$88$	251953.	−	91703.3i	0.369718	−	0.134567i
$89$	−771432.	−	445387.i	−1.09428	−	0.631782i	−0.159566	−	0.987187i	$-0.551009\pi$
$89$	−771432.	−	445387.i	−1.09428	−	0.631782i	−0.934712	+	0.355405i	$0.884343\pi$
$90$	−852684.	+	1.12733e6i	−1.16966	+	1.54641i
$91$	447965.	+	775897.i	0.594456	+	1.02963i
$92$	287216.	−	342290.i	0.368846	−	0.439573i
$93$	537105.	−	396691.i	0.667744	−	0.493177i
$94$	183884.	+	1.04286e6i	0.221391	+	1.25557i
$95$	−328116.	+	57855.6i	−0.382698	+	0.0674799i
$96$	−1.25435e6	+	141774.i	−1.41776	+	0.160244i
$97$	−1.15661e6	−	970509.i	−1.26728	−	1.06337i	−0.994867	−	0.101189i	$-0.967735\pi$
$97$	−1.15661e6	−	970509.i	−1.26728	−	1.06337i	−0.272408	−	0.962182i	$-0.587820\pi$
$98$	304882.	−	176024.i	0.323931	−	0.187022i
$99$	1.30844e6	+	402601.i	1.34849	+	0.414925i
$100$	−426574.	+	738847.i	−0.426574	+	0.738847i
$101$	606966.	+	1.66762e6i	0.589115	+	1.61858i	0.772126	+	0.635469i	$0.219193\pi$
$101$	606966.	+	1.66762e6i	0.589115	+	1.61858i	−0.183011	+	0.983111i	$0.558584\pi$
$102$	292732.	−	1.21451e6i	0.275848	−	1.14446i
$103$	−1.28048e6	+	1.07445e6i	−1.17182	+	0.983277i	−0.999998	−	0.00184986i	$-0.999411\pi$
$103$	−1.28048e6	+	1.07445e6i	−1.17182	+	0.983277i	−0.171826	+	0.985127i	$0.554967\pi$
$104$	−147567.	+	405438.i	−0.131187	+	0.360433i
$105$	1.17422e6	−	584129.i	1.01434	−	0.504593i
$106$	477037.	−	2.70541e6i	0.400530	−	2.27152i
$107$			1.37002e6i			1.11835i	0.829051	+	0.559173i	$0.188881\pi$
$107$			1.37002e6i			1.11835i	−0.829051	+	0.559173i	$0.811119\pi$
$108$	1.28796e6	+	763346.i	1.02242	+	0.605969i
$109$	−113872.			−0.0879302			−0.0439651	−	0.999033i	$-0.513999\pi$
$109$	−113872.			−0.0879302			−0.0439651	+	0.999033i	$0.513999\pi$
$110$	3.58578e6	+	632270.i	2.69405	+	0.475034i
$111$	1.36627e6	+	84796.6i	0.999007	+	0.0620026i
$112$	885496.	+	322294.i	0.630278	+	0.229403i
$113$	657697.	+	783813.i	0.455817	+	0.543221i	0.944185	−	0.329416i	$-0.106852\pi$
$113$	657697.	+	783813.i	0.455817	+	0.543221i	−0.488368	+	0.872638i	$0.662408\pi$
$114$	184003.	+	623239.i	0.124197	+	0.420669i
$115$	904370.	−	329164.i	0.594638	−	0.216431i
$116$	−2.57889e6	−	1.48892e6i	−1.65219	−	0.953891i
$117$	−1.84969e6	+	1.19648e6i	−1.15489	+	0.747048i
$118$	−142408.	−	246657.i	−0.0866736	−	0.150123i
$119$	−745081.	+	887954.i	−0.442143	+	0.526926i
$120$	578971.	+	252362.i	0.335053	+	0.146043i
$121$	−304732.	−	1.72822e6i	−0.172013	−	0.975535i
$122$	−675563.	+	119120.i	−0.372037	+	0.0656002i
$123$	−57031.6	+	130842.i	−0.0306479	+	0.0703125i
$124$	−1.44100e6	−	1.20914e6i	−0.755784	−	0.634178i
$125$	625544.	−	361158.i	0.320278	−	0.184913i
$126$	−1.38930e6	−	2.14777e6i	−0.694521	−	1.07369i
$127$	1.26866e6	−	2.19739e6i	0.619349	−	1.07274i	−0.370256	−	0.928930i	$-0.620730\pi$
$127$	1.26866e6	−	2.19739e6i	0.619349	−	1.07274i	0.989605	−	0.143814i	$-0.0459366\pi$
$128$	392935.	+	1.07958e6i	0.187366	+	0.514784i
$129$	−3.34919e6	+	988806.i	−1.56017	+	0.460619i
$130$	−4.48840e6	+	3.76621e6i	−2.04297	+	1.71425i
$131$	−180261.	+	495262.i	−0.0801839	+	0.220303i	−0.973306	−	0.229511i	$-0.926287\pi$
$131$	−180261.	+	495262.i	−0.0801839	+	0.220303i	0.893122	+	0.449814i	$0.148510\pi$
$132$	238902.	−	3.84927e6i	0.103872	−	1.67362i
$133$	104700.	−	593782.i	0.0445031	−	0.252390i
$134$			2.02458e6i			0.841434i
$135$	1.58036e6	+	2.81092e6i	0.642324	+	1.14248i
$136$	−558214.			−0.221914
$137$	671094.	+	118332.i	0.260989	+	0.0460194i	0.302611	−	0.953114i	$-0.402142\pi$
$137$	671094.	+	118332.i	0.260989	+	0.0460194i	−0.0416226	+	0.999133i	$0.513253\pi$
$138$	−836049.	−	1.68063e6i	−0.318122	−	0.639493i
$139$	2.69369e6	+	980425.i	1.00301	+	0.365065i	0.790743	−	0.612148i	$-0.209694\pi$
$139$	2.69369e6	+	980425.i	1.00301	+	0.365065i	0.212264	+	0.977212i	$0.431916\pi$
$140$	−2.37492e6	−	2.83032e6i	−0.865496	−	1.03146i
$141$	2.34861e6	+	566083.i	0.837826	+	0.201940i
$142$	4.23502e6	−	1.54142e6i	1.47907	−	0.538339i
$143$	4.91442e6	+	2.83734e6i	1.68060	+	0.970294i
$144$	−681407.	+	2.21455e6i	−0.228202	+	0.741647i
$145$	−3.20695e6	−	5.55460e6i	−1.05193	−	1.82200i
$146$	91995.7	−	109636.i	0.0295603	−	0.0352286i
$147$	−90203.3	−	798076.i	−0.0283969	−	0.251242i
$148$	−669668.	−	3.79788e6i	−0.206573	−	1.17154i
$149$	−3.23960e6	+	571229.i	−0.979337	+	0.172684i	−0.640330	−	0.768100i	$-0.721202\pi$
$149$	−3.23960e6	+	571229.i	−0.979337	+	0.172684i	−0.339008	+	0.940784i	$0.610091\pi$
$150$	2.12927e6	+	2.88296e6i	0.630895	+	0.854209i
$151$	−1.69849e6	−	1.42520e6i	−0.493324	−	0.413948i	0.361892	−	0.932220i	$-0.382131\pi$
$151$	−1.69849e6	−	1.42520e6i	−0.493324	−	0.413948i	−0.855216	+	0.518272i	$0.826575\pi$
$152$	251461.	−	145181.i	0.0716044	−	0.0413408i
$153$	−2.27312e6	−	1.71933e6i	−0.634671	−	0.480049i
$154$	−3.29460e6	+	5.70641e6i	−0.902070	+	1.56243i
$155$	−1.38574e6	−	3.80728e6i	−0.372122	−	1.02240i
$156$	4.49790e6	+	4.27603e6i	1.18477	+	1.12633i
$157$	393440.	−	330135.i	0.101667	−	0.0853086i	−0.590537	−	0.807010i	$-0.701084\pi$
$157$	393440.	−	330135.i	0.101667	−	0.0853086i	0.692204	+	0.721702i	$0.256640\pi$
$158$	819434.	−	2.25138e6i	0.207751	−	0.570791i
$159$	−5.22312e6	−	3.46386e6i	−1.29939	−	0.861726i
$160$	−1.33009e6	+	7.54332e6i	−0.324729	+	1.84163i
$161$			1.74165e6i			0.417333i
$162$	5.10159e6	−	3.67859e6i	1.19994	−	0.865240i
$163$	−2.82365e6			−0.652000			−0.326000	−	0.945370i	$-0.605701\pi$
$163$	−2.82365e6			−0.652000			−0.326000	+	0.945370i	$0.605701\pi$
$164$	395994.	+	69824.4i	0.0897753	+	0.0158298i
$165$	4.59104e6	−	6.92278e6i	1.02202	−	1.54109i
$166$	8.49581e6	+	3.09222e6i	1.85729	+	0.675999i
$167$	1.49643e6	+	1.78337e6i	0.321297	+	0.382907i	0.902383	−	0.430936i	$-0.141816\pi$
$167$	1.49643e6	+	1.78337e6i	0.321297	+	0.382907i	−0.581086	+	0.813842i	$0.697372\pi$
$168$	−787503.	+	828363.i	−0.166083	+	0.174700i
$169$	−4.04517e6	+	1.47232e6i	−0.838064	+	0.305030i
$170$	−6.56494e6	−	3.79027e6i	−1.33624	−	0.771477i
$171$	1.47115e6	+	183317.i	0.294217	+	0.0366619i
$172$	4.91898e6	+	8.51992e6i	0.966696	+	1.67437i
$173$	−3.01810e6	+	3.59683e6i	−0.582902	+	0.694675i	−0.974225	−	0.225578i	$-0.927573\pi$
$173$	−3.01810e6	+	3.59683e6i	−0.582902	+	0.694675i	0.391323	+	0.920253i	$0.372017\pi$
$174$	−1.00627e7	+	7.43206e6i	−1.91016	+	1.41079i
$175$	−577449.	−	3.27488e6i	−0.107746	−	0.611056i
$176$	5.87787e6	−	1.03643e6i	1.07816	−	0.190108i
$177$	−645664.	+	72976.8i	−0.116436	+	0.0131603i
$178$	8.07579e6	+	6.77639e6i	1.43194	+	1.20154i
$179$	−2.82878e6	+	1.63319e6i	−0.493219	+	0.284760i	−0.725909	−	0.687791i	$-0.758581\pi$
$179$	−2.82878e6	+	1.63319e6i	−0.493219	+	0.284760i	0.232690	+	0.972551i	$0.425247\pi$
$180$	6.65522e6	−	6.18378e6i	1.14116	−	1.06032i
$181$	4.64911e6	−	8.05250e6i	0.784033	−	1.35799i	−0.145542	−	0.989352i	$-0.546493\pi$
$181$	4.64911e6	−	8.05250e6i	0.784033	−	1.35799i	0.929575	−	0.368633i	$-0.120174\pi$
$182$	−3.62651e6	−	9.96376e6i	−0.601554	−	1.65276i
$183$	−366709.	+	1.52143e6i	−0.0598367	+	0.248255i
$184$	−642508.	+	539129.i	−0.103140	+	0.0865444i
$185$	2.84093e6	−	7.80540e6i	0.448689	−	1.23276i
$186$	−7.07524e6	+	3.51965e6i	−1.09952	+	0.546967i
$187$	−1.27490e6	+	7.23029e6i	−0.194962	+	1.10568i
$188$		−	6.80598e6i		−	1.02428i
$189$	−5.75822e6	+	947654.i	−0.852910	+	0.140367i
$190$	3.94311e6			0.574881
$191$	−9.32643e6	−	1.64450e6i	−1.33849	−	0.236012i	−0.541855	−	0.840472i	$-0.682278\pi$
$191$	−9.32643e6	−	1.64450e6i	−1.33849	−	0.236012i	−0.796636	+	0.604460i	$0.793389\pi$
$192$	9.42926e6	+	585219.i	1.33221	+	0.0826827i
$193$	4.12080e6	+	1.49985e6i	0.573205	+	0.208630i	0.612327	−	0.790605i	$-0.290234\pi$
$193$	4.12080e6	+	1.49985e6i	0.573205	+	0.208630i	−0.0391215	+	0.999234i	$0.512456\pi$
$194$	1.14859e7	+	1.36883e7i	1.57311	+	1.87476i
$195$	3.78495e6	+	1.28201e7i	0.510454	+	1.72896i
$196$	−2.12620e6	+	773873.i	−0.282381	+	0.102778i
$197$	−2.04389e6	−	1.18004e6i	−0.267337	−	0.154347i	0.360340	−	0.932821i	$-0.382661\pi$
$197$	−2.04389e6	−	1.18004e6i	−0.267337	−	0.154347i	−0.627677	+	0.778474i	$0.715994\pi$
$198$	−1.44226e7	−	7.38132e6i	−1.85800	−	0.950908i
$199$	1.28636e6	+	2.22805e6i	0.163232	+	0.282726i	0.936026	−	0.351931i	$-0.114475\pi$
$199$	1.28636e6	+	2.22805e6i	0.163232	+	0.282726i	−0.772794	+	0.634657i	$0.781142\pi$
$200$	1.02938e6	−	1.22677e6i	0.128673	−	0.153346i
$201$	4.23411e6	+	1.84557e6i	0.521404	+	0.227270i
$202$	−3.64709e6	−	2.06837e7i	−0.442479	−	2.50942i
$203$	1.14307e7	−	2.01555e6i	1.36642	−	0.240938i
$204$	−3.20831e6	+	7.36052e6i	−0.377907	+	0.866997i
$205$	663453.	+	556704.i	0.0770103	+	0.0646193i
$206$	1.71323e7	−	9.89131e6i	1.95981	−	1.13149i
$207$	−4.27693e6	+	216441.i	−0.482193	+	0.0244022i
$208$	−4.80224e6	+	8.31772e6i	−0.533646	+	0.924303i
$209$	−1.30616e6	−	3.58863e6i	−0.143072	−	0.393088i
$210$	−1.48861e7	+	4.39492e6i	−1.60740	+	0.474562i
$211$	2.69833e6	−	2.26417e6i	0.287242	−	0.241024i	−0.487769	−	0.872973i	$-0.662189\pi$
$211$	2.69833e6	−	2.26417e6i	0.287242	−	0.241024i	0.775010	+	0.631949i	$0.217745\pi$
$212$	−6.03880e6	+	1.65915e7i	−0.633787	+	1.74131i
$213$	636906.	−	1.02621e7i	0.0659078	−	1.06193i
$214$	2.81554e6	−	1.59677e7i	0.287290	−	1.62930i
$215$			2.11897e7i			2.13211i
$216$	−2.13206e6	−	1.83091e6i	−0.211562	−	0.181679i
$217$	7.33210e6			0.717545
$218$	1.32719e6	+	234019.i	0.128104	+	0.0225882i
$219$	−145427.	−	292338.i	−0.0138456	−	0.0278326i
$220$	−2.19905e7	−	8.00389e6i	−2.06522	−	0.751680i
$221$	−7.59410e6	−	9.05030e6i	−0.703558	−	0.838468i
$222$	−1.57498e7	−	3.79615e6i	−1.43951	−	0.346964i
$223$	−1.79904e7	+	6.54796e6i	−1.62228	+	0.590462i	−0.983815	−	0.179189i	$-0.942653\pi$
$223$	−1.79904e7	+	6.54796e6i	−1.62228	+	0.590462i	−0.638465	+	0.769651i	$0.720430\pi$
$224$	−1.20044e7	−	6.93076e6i	−1.06806	−	0.616648i
$225$	7.97029e6	−	1.82501e6i	0.699724	−	0.160221i
$226$	−6.05469e6	−	1.04870e7i	−0.524526	−	0.908505i
$227$	5.22111e6	−	6.22228e6i	0.446360	−	0.531951i	−0.495208	−	0.868775i	$-0.664908\pi$
$227$	5.22111e6	−	6.22228e6i	0.446360	−	0.531951i	0.941568	+	0.336823i	$0.109353\pi$
$228$	−469073.	−	4.15014e6i	−0.0395764	−	0.350153i
$229$	1.72056e6	+	9.75780e6i	0.143273	+	0.812541i	0.968738	+	0.248088i	$0.0798021\pi$
$229$	1.72056e6	+	9.75780e6i	0.143273	+	0.812541i	−0.825465	+	0.564454i	$0.809087\pi$
$230$	−1.12170e7	+	1.97785e6i	−0.921917	+	0.162559i
$231$	8.93084e6	+	1.20920e7i	0.724530	+	0.980988i
$232$	4.28194e6	+	3.59298e6i	0.342907	+	0.287733i
$233$	1.19411e7	−	6.89418e6i	0.944008	−	0.545023i	0.0527936	−	0.998605i	$-0.483187\pi$
$233$	1.19411e7	−	6.89418e6i	0.944008	−	0.545023i	0.891214	+	0.453582i	$0.149854\pi$
$234$	2.40171e7	−	1.01438e7i	1.87445	−	0.791685i
$235$	7.32960e6	−	1.26952e7i	0.564776	−	0.978221i
$236$	626083.	+	1.72015e6i	0.0476317	+	0.130867i
$237$	−3.96145e6	−	3.76604e6i	−0.297584	−	0.282905i
$238$	1.05088e7	−	8.81795e6i	0.779512	−	0.654089i
$239$	−4.33375e6	+	1.19069e7i	−0.317446	+	0.872176i	0.673653	+	0.739048i	$0.264724\pi$
$239$	−4.33375e6	+	1.19069e7i	−0.317446	+	0.872176i	−0.991099	+	0.133128i	$0.957498\pi$
$240$	1.17169e7	+	7.77039e6i	0.847577	+	0.562094i
$241$	−2.54431e6	+	1.44295e7i	−0.181769	+	1.03086i	0.748269	+	0.663396i	$0.230885\pi$
$241$	−2.54431e6	+	1.44295e7i	−0.181769	+	1.03086i	−0.930037	+	0.367465i	$0.880226\pi$
$242$			2.07688e7i			1.46543i
$243$	−3.04273e6	−	1.40226e7i	−0.212053	−	0.977258i
$244$	4.40891e6			0.303502
$245$	−4.79942e6	−	846268.i	−0.326355	−	0.0575453i
$246$	933602.	−	1.40777e6i	0.0627128	−	0.0945641i
$247$	5.77476e6	+	2.10184e6i	0.383215	+	0.139479i
$248$	2.26966e6	+	2.70487e6i	0.148801	+	0.177334i
$249$	1.42116e7	−	1.49489e7i	0.920542	−	0.968306i
$250$	−8.03298e6	+	2.92376e6i	−0.514110	+	0.187121i
$251$	7.49534e6	+	4.32743e6i	0.473991	+	0.273659i	0.717909	−	0.696137i	$-0.245099\pi$
$251$	7.49534e6	+	4.32743e6i	0.473991	+	0.273659i	−0.243918	+	0.969796i	$0.578433\pi$
$252$	6.39653e6	+	1.51449e7i	0.399708	+	0.946375i
$253$	5.51567e6	+	9.55342e6i	0.340594	+	0.589926i
$254$	−1.93022e7	+	2.30035e7i	−1.17789	+	1.40376i
$255$	−1.39113e7	+	1.02745e7i	−0.838970	+	0.619640i
$256$	1.52761e6	+	8.66350e6i	0.0910525	+	0.516385i
$257$	−3.39471e6	+	598579.i	−0.199988	+	0.0352632i	−0.272745	−	0.962086i	$-0.587931\pi$
$257$	−3.39471e6	+	598579.i	−0.199988	+	0.0352632i	0.0727569	+	0.997350i	$0.476820\pi$
$258$	4.10672e7	−	4.64166e6i	2.39131	−	0.270280i
$259$	1.15150e7	+	9.66221e6i	0.662772	+	0.556131i
$260$	3.26126e7	−	1.88289e7i	1.85552	−	1.07128i
$261$	6.37007e6	+	2.78197e7i	0.358280	+	1.56470i
$262$	3.11877e6	−	5.40186e6i	0.173412	−	0.300358i
$263$	6282.27	+	17260.4i	0.000345342	+	0.000948820i	0.939865	−	0.341546i	$-0.110950\pi$
$263$	6282.27	+	17260.4i	0.000345342	+	0.000948820i	−0.939520	+	0.342495i	$0.888728\pi$
$264$	−1.69630e6	+	7.03776e6i	−0.0921917	+	0.382493i
$265$	−2.91322e7	+	2.44448e7i	−1.56544	+	1.31356i
$266$	−2.44057e6	+	6.70540e6i	−0.129672	+	0.356270i
$267$	2.15336e7	−	1.07121e7i	1.13131	−	0.562783i
$268$	2.25955e6	−	1.28145e7i	0.117386	−	0.665731i
$269$		−	2.27506e7i		−	1.16879i	−0.811470	−	0.584395i	$-0.801332\pi$
$269$		−	2.27506e7i		−	1.16879i	0.811470	−	0.584395i	$-0.198668\pi$
$270$	−1.26425e7	−	3.60093e7i	−0.642304	−	1.82946i
$271$	−1.16101e7			−0.583347			−0.291673	−	0.956518i	$-0.594212\pi$
$271$	−1.16101e7			−0.583347			−0.291673	+	0.956518i	$0.594212\pi$
$272$	−1.22374e7	−	2.15778e6i	−0.608108	−	0.107226i
$273$	−2.41436e7	−	1.49845e6i	−1.18663	−	0.0736471i
$274$	−7.57847e6	−	2.75834e6i	−0.368409	−	0.134090i
$275$	−1.35388e7	−	1.61349e7i	−0.651000	−	0.775832i
$276$	3.41607e6	+	1.15706e7i	0.162480	+	0.550338i
$277$	1.95997e7	−	7.13372e6i	0.922170	−	0.335642i	0.163068	−	0.986615i	$-0.447861\pi$
$277$	1.95997e7	−	7.13372e6i	0.922170	−	0.335642i	0.759101	+	0.650972i	$0.225639\pi$
$278$	−2.93803e7	−	1.69627e7i	−1.36748	−	0.789518i
$279$	911189.	+	1.80053e7i	0.0419562	+	0.829063i
$280$	3.46765e6	+	6.00615e6i	0.157965	+	0.273604i
$281$	1.54318e7	−	1.83909e7i	0.695501	−	0.828866i	−0.296508	−	0.955030i	$-0.595822\pi$
$281$	1.54318e7	−	1.83909e7i	0.695501	−	0.828866i	0.992009	+	0.126165i	$0.0402667\pi$
$282$	−2.62099e7	−	1.14244e7i	−1.16874	−	0.509431i
$283$	−2.58961e6	−	1.46864e7i	−0.114255	−	0.647971i	−0.987116	−	0.160003i	$-0.948849\pi$
$283$	−2.58961e6	−	1.46864e7i	−0.114255	−	0.647971i	0.872862	−	0.487968i	$-0.162262\pi$
$284$	−2.85258e7	+	5.02987e6i	−1.24533	+	0.219584i
$285$	3.59447e6	−	8.24645e6i	0.155275	−	0.356232i
$286$	−5.14469e7	−	4.31691e7i	−2.19918	−	1.84533i
$287$	−1.35734e6	+	783658.i	−0.0574171	+	0.0331498i
$288$	1.55279e7	−	3.03404e7i	0.650033	−	1.27012i
$289$	−4.42617e6	+	7.66636e6i	−0.183373	+	0.317611i
$290$	2.59620e7	+	7.13299e7i	1.06450	+	2.92468i
$291$	3.90974e7	−	1.15430e7i	1.58661	−	0.468425i
$292$	−704646.	+	591268.i	−0.0283023	+	0.0237485i
$293$	−3.19857e6	+	8.78799e6i	−0.127161	+	0.349371i	−0.986893	−	0.161373i	$-0.948408\pi$
$293$	−3.19857e6	+	8.78799e6i	−0.127161	+	0.349371i	0.859733	+	0.510744i	$0.170630\pi$
$294$	−588804.	+	9.48702e6i	−0.0231701	+	0.373326i
$295$	−684652.	+	3.88286e6i	−0.0266688	+	0.151246i
$296$			7.23892e6i			0.279125i
$297$	−2.85843e7	+	2.34340e7i	−1.09108	+	0.894494i
$298$	3.89317e7			1.47114
$299$	−1.74817e7	−	3.08250e6i	−0.653990	−	0.115316i
$300$	−1.02596e7	−	2.06240e7i	−0.379987	−	0.763853i
$301$	−3.60338e7	−	1.31152e7i	−1.32133	−	0.480925i
$302$	1.68671e7	+	2.01014e7i	0.612378	+	0.729804i
$303$	−4.65816e7	−	1.12275e7i	−1.67450	−	0.403604i
$304$	6.07381e6	−	2.21068e6i	0.216192	−	0.0786876i
$305$	8.22397e6	+	4.74811e6i	0.289856	+	0.167348i
$306$	2.29600e7	+	2.47105e7i	0.801324	+	0.862415i
$307$	8.08826e6	+	1.40093e7i	0.279538	+	0.484173i	0.971270	−	0.237981i	$-0.0764855\pi$
$307$	8.08826e6	+	1.40093e7i	0.279538	+	0.484173i	−0.691732	+	0.722154i	$0.743152\pi$
$308$	2.72218e7	−	3.24417e7i	0.931676	−	1.11033i
$309$	−5.06880e6	−	4.48464e7i	−0.171803	−	1.52003i
$310$	8.32650e6	+	4.72219e7i	0.279497	+	1.58511i
$311$	−511467.	+	90185.5i	−0.0170034	+	0.00299817i	−0.182143	−	0.983272i	$-0.558304\pi$
$311$	−511467.	+	90185.5i	−0.0170034	+	0.00299817i	0.165140	+	0.986270i	$0.447192\pi$
$312$	−6.92089e6	−	9.37064e6i	−0.227876	−	0.308536i
$313$	−5.27970e6	−	4.43020e6i	−0.172178	−	0.144474i	0.552627	−	0.833429i	$-0.313625\pi$
$313$	−5.27970e6	−	4.43020e6i	−0.172178	−	0.144474i	−0.724804	+	0.688955i	$0.758070\pi$
$314$	−5.26403e6	+	3.03919e6i	−0.170032	+	0.0981678i
$315$	−4.37854e6	+	3.51385e7i	−0.140087	+	1.12422i
$316$	−7.69927e6	+	1.33355e7i	−0.243999	+	0.422619i
$317$	−5.97604e6	−	1.64190e7i	−0.187601	−	0.515431i	0.809861	−	0.586621i	$-0.199542\pi$
$317$	−5.97604e6	−	1.64190e7i	−0.187601	−	0.515431i	−0.997463	+	0.0711908i	$0.977320\pi$
$318$	5.37573e7	+	5.11056e7i	1.67169	+	1.58923i
$319$	5.63176e7	−	4.72561e7i	1.73489	−	1.45575i
$320$	1.96065e7	−	5.38685e7i	0.598344	−	1.64394i
$321$	−3.08276e7	−	2.04442e7i	−0.932018	−	0.618094i
$322$	3.57927e6	−	2.02990e7i	0.107208	−	0.608006i
$323$			7.95080e6i			0.235941i
$324$	−3.63960e7	+	1.75899e7i	−1.07009	+	0.517165i
$325$	3.38935e7			0.987339
$326$	3.29098e7	+	5.80289e6i	0.949889	+	0.167491i
$327$	1.69926e6	−	2.56230e6i	0.0485978	−	0.0732801i
$328$	−709262.	−	258150.i	−0.0200995	−	0.00731562i
$329$	1.70521e7	+	2.03219e7i	0.478839	+	0.570659i
$330$	−6.77359e7	+	7.12505e7i	−1.88485	+	1.98265i
$331$	5.34215e6	−	1.94439e6i	0.147310	−	0.0536165i	−0.267313	−	0.963610i	$-0.586136\pi$
$331$	5.34215e6	−	1.94439e6i	0.147310	−	0.0536165i	0.414623	+	0.909993i	$0.363913\pi$
$332$	−5.03230e7	−	2.90540e7i	−1.37516	−	0.793947i
$333$	−2.22963e7	+	2.94779e7i	−0.603809	+	0.798295i
$334$	−1.37760e7	−	2.38607e7i	−0.369728	−	0.640388i
$335$	1.80152e7	−	2.14697e7i	0.479186	−	0.571072i
$336$	−2.04659e7	+	1.51156e7i	−0.539528	+	0.398480i
$337$	1.15936e7	+	6.57505e7i	0.302920	+	1.71795i	0.633137	+	0.774040i	$0.281767\pi$
$337$	1.15936e7	+	6.57505e7i	0.302920	+	1.71795i	−0.330216	+	0.943905i	$0.607122\pi$
$338$	5.01726e7	−	8.84678e6i	1.29932	−	0.229105i
$339$	−2.74515e7	+	3.10273e6i	−0.704639	+	0.0796424i
$340$	3.73225e7	+	3.13173e7i	0.949586	+	0.796797i
$341$	4.02186e7	−	2.32202e7i	1.01429	−	0.585603i
$342$	−1.67696e7	−	5.15994e6i	−0.419223	−	0.128993i
$343$	2.18502e7	−	3.78456e7i	0.541468	−	0.937849i
$344$	−6.31598e6	−	1.73530e7i	−0.155155	−	0.426285i
$345$	−6.08879e6	+	2.52617e7i	−0.148277	+	0.615183i
$346$	4.25681e7	−	3.57188e7i	1.02767	−	0.862321i
$347$	−3.97115e6	+	1.09106e7i	−0.0950447	+	0.261133i	−0.978100	−	0.208136i	$-0.933260\pi$
$347$	−3.97115e6	+	1.09106e7i	−0.0950447	+	0.261133i	0.883055	+	0.469269i	$0.155483\pi$
$348$	7.19866e7	−	3.58105e7i	1.70810	−	0.849714i
$349$	−6.21300e6	+	3.52357e7i	−0.146159	+	0.828908i	0.820271	+	0.571976i	$0.193823\pi$
$349$	−6.21300e6	+	3.52357e7i	−0.146159	+	0.828908i	−0.966429	+	0.256932i	$0.917288\pi$
$350$			3.93557e7i			0.917917i
$351$	679301.	−	5.94752e7i	0.0157087	−	1.37536i
$352$	−8.77969e7			−2.01303
$353$	3.54503e7	+	6.25084e6i	0.805926	+	0.142107i	0.561409	−	0.827538i	$-0.310259\pi$
$353$	3.54503e7	+	6.25084e6i	0.805926	+	0.142107i	0.244517	+	0.969645i	$0.421371\pi$
$354$	7.67524e6	+	476357.i	0.173014	+	0.0107380i
$355$	−5.86262e7	−	2.13382e7i	−1.31041	−	0.476950i
$356$	−4.35527e7	−	5.19041e7i	−0.965307	−	1.15041i
$357$	−8.86182e6	−	3.00160e7i	−0.194768	−	0.659702i
$358$	3.63260e7	−	1.32216e7i	0.791714	−	0.288160i
$359$	−2.77987e7	−	1.60496e7i	−0.600817	−	0.346882i	0.168546	−	0.985694i	$-0.446093\pi$
$359$	−2.77987e7	−	1.60496e7i	−0.600817	−	0.346882i	−0.769363	+	0.638812i	$0.779426\pi$
$360$	−1.43183e7	+	9.26186e6i	−0.306890	+	0.198514i
$361$	2.14551e7	+	3.71613e7i	0.456046	+	0.789895i
$362$	−7.07345e7	+	8.42981e7i	−1.49110	+	1.77702i
$363$	4.34350e7	+	1.89325e7i	0.908070	+	0.395810i
$364$	1.18338e7	+	6.71129e7i	0.245369	+	1.39156i
$365$	−1.95114e6	+	344038.i	−0.0401245	+	0.00707503i
$366$	7.40072e6	−	1.69788e7i	0.150949	−	0.346308i
$367$	4.51275e6	+	3.78665e6i	0.0912942	+	0.0766050i	0.687293	−	0.726381i	$-0.258799\pi$
$367$	4.51275e6	+	3.78665e6i	0.0912942	+	0.0766050i	−0.595998	+	0.802986i	$0.703244\pi$
$368$	−1.61693e7	+	9.33534e6i	−0.324450	+	0.187321i
$369$	−2.09309e6	−	3.23579e6i	−0.0416591	−	0.0644023i
$370$	−4.91522e7	+	8.51341e7i	−0.970371	+	1.68073i
$371$	−2.35380e7	−	6.46703e7i	−0.460945	−	1.26643i
$372$	4.87108e7	−	1.43812e7i	0.946229	−	0.279362i
$373$	1.07780e7	−	9.04382e6i	0.207688	−	0.174271i	−0.533010	−	0.846109i	$-0.678939\pi$
$373$	1.07780e7	−	9.04382e6i	0.207688	−	0.174271i	0.740698	+	0.671838i	$0.234495\pi$
$374$	2.97180e7	−	8.16495e7i	0.568074	−	1.56077i
$375$	−1.20808e6	+	1.94651e7i	−0.0229088	+	0.369115i
$376$	−2.21843e6	+	1.25813e7i	−0.0417332	+	0.236681i
$377$			1.18303e8i			2.20786i
$378$	6.90601e7	+	788775.i	1.27865	+	0.0146042i
$379$	−8.01683e7			−1.47260			−0.736300	−	0.676655i	$-0.763429\pi$
$379$	−8.01683e7			−1.47260			−0.736300	+	0.676655i	$0.763429\pi$
$380$	−2.49579e7	−	4.40075e6i	−0.454838	−	0.0802002i
$381$	3.05130e7	+	6.13374e7i	0.551708	+	1.10905i
$382$	1.05321e8	+	3.83336e7i	1.88940	+	0.687685i
$383$	−1.79645e7	−	2.14093e7i	−0.319756	−	0.381071i	0.582092	−	0.813123i	$-0.302234\pi$
$383$	−1.79645e7	−	2.14093e7i	−0.319756	−	0.381071i	−0.901849	+	0.432052i	$0.857790\pi$
$384$	−3.01558e7	−	7.26842e6i	−0.532571	−	0.128365i
$385$	8.57147e7	−	3.11976e7i	1.50201	−	0.546687i
$386$	−4.49459e7	−	2.59496e7i	−0.781499	−	0.451199i
$387$	2.77288e7	−	9.01174e7i	0.478407	−	1.55481i
$388$	−5.74226e7	−	9.94589e7i	−0.983078	−	1.70274i
$389$	−5.29675e6	+	6.31242e6i	−0.0899831	+	0.107238i	−0.809157	−	0.587592i	$-0.800076\pi$
$389$	−5.29675e6	+	6.31242e6i	−0.0899831	+	0.107238i	0.719174	+	0.694830i	$0.244520\pi$
$390$	−1.77674e7	−	1.57197e8i	−0.299522	−	2.65003i
$391$	−3.98810e6	−	2.26176e7i	−0.0667169	−	0.378370i
$392$	4.18267e6	−	737517.i	0.0694377	−	0.0122437i
$393$	−8.45421e6	−	1.14467e7i	−0.139282	−	0.188583i
$394$	2.13966e7	+	1.79539e7i	0.349830	+	0.293542i
$395$	−2.87230e7	+	1.65832e7i	−0.466057	+	0.269078i
$396$	8.30494e7	+	6.28164e7i	1.33737	+	1.01155i
$397$	5.05724e6	−	8.75940e6i	0.0808244	−	0.139992i	−0.822780	−	0.568360i	$-0.807578\pi$
$397$	5.05724e6	−	8.75940e6i	0.0808244	−	0.139992i	0.903604	+	0.428368i	$0.140911\pi$
$398$	−1.04138e7	−	2.86117e7i	−0.165181	−	0.453831i
$399$	1.17986e7	+	1.12166e7i	0.185743	+	0.176581i
$400$	2.73085e7	−	2.29145e7i	0.426695	−	0.358040i
$401$	1.17935e7	−	3.24025e7i	0.182899	−	0.502510i	−0.814030	−	0.580823i	$-0.802731\pi$
$401$	1.17935e7	−	3.24025e7i	0.182899	−	0.502510i	0.996929	+	0.0783124i	$0.0249532\pi$
$402$	−4.55561e7	−	3.02118e7i	−0.701242	−	0.465048i
$403$	−1.29769e7	+	7.35958e7i	−0.198270	+	1.12444i
$404$			1.34987e8i			2.04715i
$405$	−8.68329e7	−	6.38551e6i	−1.30713	−	0.0961237i
$406$	−1.37368e8			−2.05262
$407$	9.37624e7	+	1.65328e7i	1.39074	+	0.245225i
$408$	8.32996e6	−	1.25607e7i	0.122649	−	0.184941i
$409$	−1.36965e7	−	4.98513e6i	−0.200189	−	0.0728629i	0.239980	−	0.970778i	$-0.422859\pi$
$409$	−1.36965e7	−	4.98513e6i	−0.200189	−	0.0728629i	−0.440169	+	0.897915i	$0.645081\pi$
$410$	−6.58852e6	−	7.85189e6i	−0.0955952	−	0.113926i
$411$	−1.26771e7	+	1.33348e7i	−0.182597	+	0.192071i
$412$	−1.19478e8	+	4.34863e7i	−1.70842	+	0.621815i
$413$	−6.17917e6	−	3.56755e6i	−0.0877163	−	0.0506430i
$414$	5.02927e7	+	6.26690e6i	0.708768	+	0.0883184i
$415$	−6.25786e7	−	1.08389e8i	−0.875551	−	1.51650i
$416$	9.08137e7	−	1.08228e8i	1.26145	−	1.50334i
$417$	−6.22577e7	+	4.59818e7i	−0.858589	+	0.634130i
$418$	7.84833e6	+	4.45101e7i	0.107460	+	0.609438i
$419$	−4.96918e7	+	8.76200e6i	−0.675527	+	0.119114i	−0.500879	−	0.865517i	$-0.666990\pi$
$419$	−4.96918e7	+	8.76200e6i	−0.675527	+	0.119114i	−0.174648	+	0.984631i	$0.555879\pi$
$420$	9.91263e7	−	1.12038e7i	1.33795	−	0.151223i
$421$	−6.05266e7	−	5.07878e7i	−0.811148	−	0.680634i	0.139734	−	0.990189i	$-0.455375\pi$
$421$	−6.05266e7	−	5.07878e7i	−0.811148	−	0.680634i	−0.950881	+	0.309556i	$0.899820\pi$
$422$	−3.61023e7	+	2.08437e7i	−0.480394	+	0.277356i
$423$	−4.77849e7	+	4.43999e7i	−0.631349	+	0.586626i
$424$	1.65712e7	−	2.87021e7i	0.217398	−	0.376545i
$425$	1.49979e7	+	4.12064e7i	0.195373	+	0.536782i
$426$	−2.85128e7	+	1.18296e8i	−0.368817	+	1.53018i
$427$	−1.31645e7	+	1.10463e7i	−0.169091	+	0.141884i
$428$	−3.56418e7	+	9.79251e7i	−0.454599	+	1.24900i
$429$	−1.37180e8	+	6.82417e7i	−1.73748	+	0.864326i
$430$	4.35470e7	−	2.46968e8i	0.547713	−	3.10624i
$431$			1.37040e7i			0.171165i	0.996331	+	0.0855823i	$0.0272751\pi$
$431$			1.37040e7i			0.171165i	−0.996331	+	0.0855823i	$0.972725\pi$
$432$	−3.96624e7	−	4.83793e7i	−0.491957	−	0.600079i
$433$	1.08168e8			1.33240			0.666198	−	0.745775i	$-0.267920\pi$
$433$	1.08168e8			1.33240			0.666198	+	0.745775i	$0.267920\pi$
$434$	−8.54562e7	−	1.50682e7i	−1.04538	−	0.184329i
$435$	1.72843e8	+	1.07273e7i	2.09983	+	0.130324i
$436$	−8.13925e6	−	2.96244e6i	−0.0982030	−	0.0357430i
$437$	7.67896e6	+	9.15143e6i	0.0920149	+	0.109659i
$438$	1.09417e6	+	3.70609e6i	0.0130216	+	0.0441056i
$439$	1.08152e8	−	3.93641e7i	1.27832	−	0.465272i	0.388446	−	0.921471i	$-0.373012\pi$
$439$	1.08152e8	−	3.93641e7i	1.27832	−	0.465272i	0.889877	+	0.456200i	$0.150790\pi$
$440$	3.80421e7	+	2.19636e7i	0.446587	+	0.257837i
$441$	1.93040e7	+	9.87959e6i	0.225077	+	0.115192i
$442$	6.99106e7	+	1.21089e8i	0.809610	+	1.40229i
$443$	−6.04106e7	+	7.19946e7i	−0.694868	+	0.828111i	−0.991935	−	0.126745i	$-0.959547\pi$
$443$	−6.04106e7	+	7.19946e7i	−0.694868	+	0.828111i	0.297068	+	0.954856i	$0.403991\pi$
$444$	9.54512e7	+	4.16053e7i	1.09052	+	0.475335i
$445$	−2.53418e7	−	1.43721e8i	−0.287579	−	1.63094i
$446$	2.23136e8	−	3.93449e7i	2.51516	−	0.443490i
$447$	3.54894e7	−	8.14201e7i	0.397353	−	0.911610i
$448$	7.94699e7	+	6.66832e7i	0.883830	+	0.741622i
$449$	8.76760e7	−	5.06198e7i	0.968594	−	0.559218i	0.0697867	−	0.997562i	$-0.477768\pi$
$449$	8.76760e7	−	5.06198e7i	0.968594	−	0.559218i	0.898807	+	0.438344i	$0.144435\pi$
$450$	−9.66449e7	+	4.89088e6i	−1.06058	+	0.0536723i
$451$	−4.96357e6	+	8.59716e6i	−0.0541084	+	0.0937185i
$452$	2.66189e7	+	7.31349e7i	0.288254	+	0.791971i
$453$	5.74150e7	−	1.69510e7i	0.617633	−	0.182348i
$454$	−7.36399e7	+	6.17912e7i	−0.786947	+	0.660327i
$455$	−5.02026e7	+	1.37930e8i	−0.532956	+	1.46429i
$456$	−485635.	+	7.82472e6i	−0.00512171	+	0.0825228i
$457$	−1.00092e7	+	5.67650e7i	−0.104870	+	0.594747i	0.886402	+	0.462916i	$0.153197\pi$
$457$	−1.00092e7	+	5.67650e7i	−0.104870	+	0.594747i	−0.991272	+	0.131831i	$0.957914\pi$
$458$		−	1.17264e8i		−	1.22058i
$459$	7.26083e7	−	2.54920e7i	0.750841	−	0.263612i
$460$	7.32051e7			0.752086
$461$	1.89903e8	+	3.34850e7i	1.93834	+	0.341781i	0.999992	−	0.00391883i	$-0.00124740\pi$
$461$	1.89903e8	+	3.34850e7i	1.93834	+	0.341781i	0.938345	+	0.345700i	$0.112359\pi$
$462$	−7.92393e7	−	1.59287e8i	−0.803553	−	1.61531i
$463$	−1.10816e8	−	4.03338e7i	−1.11650	−	0.406374i	−0.283128	−	0.959082i	$-0.591372\pi$
$463$	−1.10816e8	−	4.03338e7i	−1.11650	−	0.406374i	−0.833375	+	0.552708i	$0.813594\pi$
$464$	7.99815e7	+	9.53183e7i	0.800637	+	0.954162i
$465$	1.06348e8	+	2.56330e7i	1.05772	+	0.254941i
$466$	−1.53342e8	+	5.58121e7i	−1.51532	+	0.551532i
$467$	4.10735e7	+	2.37138e7i	0.403284	+	0.232836i	0.687900	−	0.725805i	$-0.258533\pi$
$467$	4.10735e7	+	2.37138e7i	0.403284	+	0.232836i	−0.284616	+	0.958642i	$0.591866\pi$
$468$	−1.63337e8	+	3.74004e7i	−1.59348	+	0.364871i
$469$	2.53595e7	+	4.39240e7i	0.245823	+	0.425778i
$470$	−1.11517e8	+	1.32901e8i	−1.07411	+	1.28007i
$471$	1.55743e6	+	1.37794e7i	0.0149055	+	0.131877i
$472$	−596670.	−	3.38389e6i	−0.00567425	−	0.0321803i
$473$	−2.39191e8	+	4.21758e7i	−2.26027	+	0.398547i
$474$	3.84314e7	+	5.20347e7i	0.360870	+	0.488605i
$475$	−1.74732e7	−	1.46617e7i	−0.163039	−	0.136806i
$476$	−7.63568e7	+	4.40846e7i	−0.707989	+	0.408758i
$477$	1.55884e8	−	6.58387e7i	1.43631	−	0.606633i
$478$	7.49801e7	−	1.29869e8i	0.686534	−	1.18911i
$479$	6.81579e6	+	1.87262e7i	0.0620169	+	0.170390i	0.966831	−	0.255417i	$-0.0822126\pi$
$479$	6.81579e6	+	1.87262e7i	0.0620169	+	0.170390i	−0.904814	+	0.425807i	$0.859990\pi$
$480$	−1.49888e8	−	1.42494e8i	−1.35532	−	1.28847i
$481$	−1.17364e8	+	9.84803e7i	−1.05463	+	0.884941i
$482$	5.93083e7	−	1.62948e8i	0.529632	−	1.45515i
$483$	−3.91897e7	−	2.59898e7i	−0.347801	−	0.230654i
$484$	2.31792e7	−	1.31456e8i	0.204438	−	1.15943i
$485$		−	2.47362e8i		−	2.16824i
$486$	6.64539e6	+	1.69687e8i	0.0578911	+	1.47823i
$487$	1.57853e8			1.36667			0.683337	−	0.730103i	$-0.260528\pi$
$487$	1.57853e8			1.36667			0.683337	+	0.730103i	$0.260528\pi$
$488$	−8.15018e6	−	1.43710e6i	−0.0701306	−	0.0123659i
$489$	4.21359e7	−	6.35364e7i	0.360351	−	0.543370i
$490$	5.41985e7	+	1.97266e7i	0.460679	+	0.167674i
$491$	−4.24775e7	−	5.06227e7i	−0.358851	−	0.427662i	0.556170	−	0.831069i	$-0.312270\pi$
$491$	−4.24775e7	−	5.06227e7i	−0.358851	−	0.427662i	−0.915021	+	0.403407i	$0.867826\pi$
$492$	−7.48038e6	+	7.86851e6i	−0.0628099	+	0.0660689i
$493$	−1.43828e8	+	5.23491e7i	−1.20034	+	0.436887i
$494$	−6.29858e7	−	3.63648e7i	−0.522470	−	0.301648i
$495$	8.72634e7	+	2.06611e8i	0.719476	+	1.70348i
$496$	3.93005e7	+	6.80705e7i	0.322072	+	0.557846i
$497$	7.25728e7	−	8.64888e7i	0.591159	−	0.704516i
$498$	−1.96358e8	+	1.45025e8i	−1.58987	+	1.17423i
$499$	1.08438e6	+	6.14981e6i	0.00872728	+	0.0494949i	0.988860	−	0.148846i	$-0.0475558\pi$
$499$	1.08438e6	+	6.14981e6i	0.00872728	+	0.0494949i	−0.980133	+	0.198341i	$0.936445\pi$
$500$	5.41077e7	−	9.54065e6i	0.432862	−	0.0763252i
$501$	−6.24591e7	+	7.05950e6i	−0.496687	+	0.0561385i
$502$	−7.84654e7	−	6.58403e7i	−0.620250	−	0.520452i
$503$	−9.70884e7	+	5.60540e7i	−0.762893	+	0.440456i	−0.830333	−	0.557267i	$-0.811850\pi$
$503$	−9.70884e7	+	5.60540e7i	−0.762893	+	0.440456i	0.0674406	+	0.997723i	$0.478517\pi$
$504$	−6.88792e6	−	3.00813e7i	−0.0538017	−	0.234966i
$505$	−1.45373e8	+	2.51793e8i	−1.12878	+	1.95510i
$506$	−4.46523e7	−	1.22681e8i	−0.344661	−	0.946948i
$507$	2.72346e7	−	1.12993e8i	0.208977	−	0.867019i
$508$	1.47847e8	−	1.24058e8i	1.12777	−	0.946310i
$509$	−2.46384e7	+	6.76935e7i	−0.186835	+	0.513326i	−0.997379	−	0.0723520i	$-0.976950\pi$
$509$	−2.46384e7	+	6.76935e7i	−0.186835	+	0.513326i	0.810544	+	0.585678i	$0.199172\pi$
$510$	1.83252e8	−	9.11608e7i	1.38146	−	0.687223i
$511$	622597.	−	3.53092e6i	0.00466599	−	0.0264622i
$512$		−	1.77641e8i		−	1.32353i
$513$	−2.60782e7	+	3.03675e7i	−0.193163	+	0.224935i
$514$	4.07957e7			0.300418
$515$	−2.69695e8	−	4.75544e7i	−1.97447	−	0.348152i
$516$	−2.65115e8	−	1.64541e7i	−1.92968	−	0.119764i
$517$	1.57893e8	+	5.74685e7i	1.14259	+	0.415870i
$518$	−1.14351e8	−	1.36278e8i	−0.822718	−	0.980477i
$519$	−3.58966e7	−	1.21586e8i	−0.256774	−	0.869721i
$520$	−6.64239e7	+	2.41763e7i	−0.472405	+	0.171941i
$521$	7.96330e7	+	4.59761e7i	0.563093	+	0.325102i	0.754386	−	0.656431i	$-0.227935\pi$
$521$	7.96330e7	+	4.59761e7i	0.563093	+	0.325102i	−0.191293	+	0.981533i	$0.561268\pi$
$522$	−1.70713e7	−	3.37332e8i	−0.120020	−	2.37163i
$523$	1.03067e7	+	1.78518e7i	0.0720469	+	0.124789i	0.899798	−	0.436306i	$-0.143714\pi$
$523$	1.03067e7	+	1.78518e7i	0.0720469	+	0.124789i	−0.827751	+	0.561095i	$0.810380\pi$
$524$	−2.57690e7	+	3.07103e7i	−0.179103	+	0.213447i
$525$	8.23068e7	+	3.58759e7i	0.568797	+	0.247928i
$526$	−37748.4	−	214082.i	−0.000259383	−	0.00147103i
$527$	−9.52172e7	+	1.67894e7i	−0.650554	+	0.114710i
$528$	−6.43914e7	+	1.47727e8i	−0.437448	+	1.00360i
$529$	8.69674e7	+	7.29743e7i	0.587475	+	0.492950i
$530$	3.89774e8	−	2.25036e8i	2.61810	−	1.51156i
$531$	7.99284e6	−	1.56174e7i	0.0533848	−	0.104310i
$532$	2.29312e7	−	3.97179e7i	0.152297	−	0.263786i
$533$	−5.46363e6	−	1.50112e7i	−0.0360827	−	0.0991365i
$534$	−2.72990e8	+	8.05967e7i	−1.79276	+	0.529290i
$535$	−1.71942e8	+	1.44276e8i	−1.12285	+	0.942180i
$536$	−8.35386e6	+	2.29520e7i	−0.0542491	+	0.149048i
$537$	5.46308e6	−	8.80232e7i	0.0352789	−	0.568426i
$538$	−4.67549e7	+	2.65160e8i	−0.300248	+	1.70279i
$539$		−	5.58606e7i		−	0.356730i
$540$	3.98319e7	+	2.42030e8i	0.252958	+	1.53705i
$541$	1.00142e8			0.632445			0.316223	−	0.948685i	$-0.397585\pi$
$541$	1.00142e8			0.632445			0.316223	+	0.948685i	$0.397585\pi$
$542$	1.35316e8	+	2.38599e7i	0.849869	+	0.149855i
$543$	1.11817e8	+	2.24776e8i	0.698407	+	1.40394i
$544$	1.71764e8	+	6.25170e7i	1.06693	+	0.388330i
$545$	−1.19918e7	−	1.42913e7i	−0.0740792	−	0.0882841i
$546$	2.78316e8	+	6.70823e7i	1.70986	+	0.412126i
$547$	2.80869e8	−	1.02228e8i	1.71610	−	0.624609i	0.718609	−	0.695415i	$-0.244779\pi$
$547$	2.80869e8	−	1.02228e8i	1.71610	−	0.624609i	0.997490	+	0.0708058i	$0.0225570\pi$
$548$	4.48894e7	+	2.59169e7i	0.272773	+	0.157486i
$549$	−2.87623e7	−	3.09551e7i	−0.173823	−	0.187075i
$550$	1.24637e8	+	2.15877e8i	0.749130	+	1.29753i
$551$	5.11758e7	−	6.09889e7i	0.305921	−	0.364583i
$552$	−2.54337e6	−	2.25026e7i	−0.0151214	−	0.133787i
$553$	−1.04224e7	−	5.91086e7i	−0.0616303	−	0.349523i
$554$	−2.43097e8	+	4.28645e7i	−1.42972	+	0.252098i
$555$	1.33239e8	+	1.80401e8i	0.779388	+	1.05526i
$556$	1.67031e8	+	1.40156e8i	0.971791	+	0.815429i
$557$	4.39967e7	−	2.54015e7i	0.254598	−	0.146992i	−0.367270	−	0.930114i	$-0.619707\pi$
$557$	4.39967e7	−	2.54015e7i	0.254598	−	0.146992i	0.621868	+	0.783122i	$0.286374\pi$
$558$	2.63828e7	−	2.11726e8i	0.151851	−	1.21863i
$559$	1.95419e8	−	3.38476e8i	1.11875	−	1.93773i
$560$	5.28023e7	+	1.45073e8i	0.300669	+	0.826082i
$561$	−1.43668e8	−	1.36581e8i	−0.813713	−	0.773575i
$562$	−2.17654e8	+	1.82633e8i	−1.22619	+	1.02890i
$563$	−1.29132e7	+	3.54786e7i	−0.0723615	+	0.198811i	−0.970601	−	0.240695i	$-0.922625\pi$
$563$	−1.29132e7	+	3.54786e7i	−0.0723615	+	0.198811i	0.898239	+	0.439507i	$0.144847\pi$
$564$	1.53145e8	+	1.01562e8i	0.853621	+	0.566103i
$565$	−2.91091e7	+	1.65086e8i	−0.161393	+	0.915303i
$566$			1.76493e8i			0.973370i
$567$	6.46035e7	−	1.43710e8i	0.354411	−	0.788385i
$568$	5.43714e7			0.296706
$569$	−2.82238e8	−	4.97661e7i	−1.53207	−	0.270145i	−0.656906	−	0.753973i	$-0.728135\pi$
$569$	−2.82238e8	−	4.97661e7i	−1.53207	−	0.270145i	−0.875163	+	0.483827i	$0.839246\pi$
$570$	−5.88411e7	+	8.87260e7i	−0.317729	+	0.479100i
$571$	−2.95532e8	−	1.07565e8i	−1.58743	−	0.577779i	−0.610630	−	0.791916i	$-0.709084\pi$
$571$	−2.95532e8	−	1.07565e8i	−1.58743	−	0.577779i	−0.976804	+	0.214137i	$0.931306\pi$
$572$	2.77453e8	+	3.30656e8i	1.48252	+	1.76680i
$573$	1.76178e8	−	1.85319e8i	0.936455	−	0.985044i
$574$	1.74303e7	−	6.34413e6i	0.0921659	−	0.0335456i
$575$	5.70603e7	+	3.29438e7i	0.300144	+	0.173288i
$576$	−1.53877e8	+	2.03440e8i	−0.805202	+	1.06456i
$577$	−1.24001e8	−	2.14776e8i	−0.645501	−	1.11804i	−0.984185	−	0.177141i	$-0.943315\pi$
$577$	−1.24001e8	−	2.14776e8i	−0.645501	−	1.11804i	0.338684	−	0.940900i	$-0.390018\pi$
$578$	6.73426e7	−	8.02558e7i	0.348744	−	0.415616i
$579$	−9.52417e7	+	7.03428e7i	−0.490672	+	0.362397i
$580$	−8.47175e7	−	4.80457e8i	−0.434200	−	2.46247i
$581$	2.23052e8	−	3.93302e7i	1.13731	−	0.200538i
$582$	−4.79406e8	+	5.41853e7i	−2.43184	+	0.274860i
$583$	−3.33919e8	−	2.80191e8i	−1.68514	−	1.41400i
$584$	1.49531e6	−	863319.i	0.00750747	−	0.00433444i
$585$	−3.44952e8	−	1.06140e8i	−1.72302	−	0.530167i
$586$	5.53398e7	−	9.58513e7i	0.275007	−	0.476327i
$587$	3.26098e7	+	8.95946e7i	0.161225	+	0.442963i	0.993831	−	0.110903i	$-0.0353743\pi$
$587$	3.26098e7	+	8.95946e7i	0.161225	+	0.442963i	−0.832606	+	0.553866i	$0.813152\pi$
$588$	1.43149e7	−	5.93908e7i	0.0704136	−	0.292137i
$589$	3.85263e7	−	3.23274e7i	0.188543	−	0.158207i
$590$	1.59593e7	−	4.38479e7i	0.0777068	−	0.213498i
$591$	5.70528e7	−	2.83815e7i	0.276385	−	0.137491i
$592$	−2.79820e7	+	1.58694e8i	−0.134870	+	0.764884i
$593$			1.05515e8i			0.506001i	0.967466	+	0.253001i	$0.0814175\pi$
$593$			1.05515e8i			0.506001i	−0.967466	+	0.253001i	$0.918582\pi$
$594$	3.81312e8	−	2.14382e8i	1.81937	−	1.02289i
$595$	−1.89905e8			−0.901542
$596$	−2.46418e8	−	4.34501e7i	−1.16395	−	0.205235i
$597$	−6.93302e7	−	4.30292e6i	−0.325836	−	0.0202228i
$598$	1.97416e8	+	7.18536e7i	0.923165	+	0.336004i
$599$	7.18758e7	+	8.56582e7i	0.334428	+	0.398555i	0.906884	−	0.421380i	$-0.138454\pi$
$599$	7.18758e7	+	8.56582e7i	0.334428	+	0.398555i	−0.572457	+	0.819935i	$0.694010\pi$
$600$	1.22432e7	+	4.14691e7i	0.0566815	+	0.191986i
$601$	−1.42266e7	+	5.17805e6i	−0.0655355	+	0.0238530i	−0.374580	−	0.927195i	$-0.622213\pi$
$601$	−1.42266e7	+	5.17805e6i	−0.0655355	+	0.0238530i	0.309044	+	0.951048i	$0.399991\pi$
$602$	3.93024e8	+	2.26912e8i	1.80148	+	1.04009i
$603$	−1.04712e8	+	6.77335e7i	−0.477577	+	0.308924i
$604$	−8.43257e7	−	1.46056e8i	−0.382692	−	0.662842i
$605$	1.84806e8	−	2.20243e8i	0.834544	−	0.994571i
$606$	5.19838e8	+	2.26587e8i	2.33588	+	1.01816i
$607$	−6.47759e7	−	3.67363e8i	−0.289633	−	1.64259i	−0.688252	−	0.725472i	$-0.741622\pi$
$607$	−6.47759e7	−	3.67363e8i	−0.289633	−	1.64259i	0.398619	−	0.917117i	$-0.369490\pi$
$608$	−9.36347e7	+	1.65103e7i	−0.416607	+	0.0734590i
$609$	−1.25222e8	+	2.87286e8i	−0.554409	+	1.27193i
$610$	−8.60932e7	−	7.22408e7i	−0.379297	−	0.318268i
$611$	−2.34160e8	+	1.35193e8i	−1.02657	+	0.592692i
$612$	−1.17747e8	−	1.82029e8i	−0.513683	−	0.794121i
$613$	−1.22519e8	+	2.12210e8i	−0.531892	+	0.921264i	0.467415	+	0.884038i	$0.345185\pi$
$613$	−1.22519e8	+	2.12210e8i	−0.531892	+	0.921264i	−0.999307	+	0.0372260i	$0.988148\pi$
$614$	−6.54788e7	−	1.79901e8i	−0.282876	−	0.777194i
$615$	−2.24271e7	+	6.62130e6i	−0.0964156	+	0.0284654i
$616$	−6.08958e7	+	5.10977e7i	−0.260523	+	0.218604i
$617$	−5.41124e7	+	1.48673e8i	−0.230378	+	0.632958i	−0.999985	−	0.00556003i	$-0.998230\pi$
$617$	−5.41124e7	+	1.48673e8i	−0.230378	+	0.632958i	0.769607	+	0.638518i	$0.220452\pi$
$618$	−3.30867e7	+	5.33105e8i	−0.140181	+	2.25864i
$619$	1.28033e7	−	7.26111e7i	0.0539821	−	0.306148i	−0.945847	−	0.324612i	$-0.894766\pi$
$619$	1.28033e7	−	7.26111e7i	0.0539821	−	0.306148i	0.999830	+	0.0184637i	$0.00587753\pi$
$620$		−	3.08183e8i		−	1.29311i
$621$	5.89523e7	−	9.94673e7i	0.246165	−	0.415342i
$622$	6.14653e6			0.0255422
$623$	2.60087e8	+	4.58604e7i	1.07561	+	0.189659i
$624$	−1.15500e8	−	2.32179e8i	−0.475366	−	0.955584i
$625$	2.75885e8	+	1.00414e8i	1.13003	+	0.411296i
$626$	5.24308e7	+	6.24846e7i	0.213729	+	0.254713i
$627$	1.00241e8	+	2.41609e7i	0.406670	+	0.0980192i
$628$	3.67105e7	−	1.33615e7i	0.148222	−	0.0539483i
$629$	−1.71662e8	−	9.91093e7i	−0.689800	−	0.398256i
$630$	1.23245e8	−	4.00543e8i	0.492889	−	1.60187i
$631$	1.04505e8	+	1.81008e8i	0.415958	+	0.720461i	0.995529	−	0.0944612i	$-0.0301128\pi$
$631$	1.04505e8	+	1.81008e8i	0.415958	+	0.720461i	−0.579570	+	0.814922i	$0.696779\pi$
$632$	1.85794e7	−	2.21420e7i	0.0736004	−	0.0877135i
$633$	1.06813e7	+	9.45035e7i	0.0421129	+	0.372595i
$634$	3.59084e7	+	2.03647e8i	0.140906	+	0.799115i
$635$	4.09382e8	−	7.21850e7i	1.59885	−	0.281920i
$636$	−2.83219e8	−	3.83469e8i	−1.10091	−	1.49059i
$637$	6.88596e7	+	5.77800e7i	0.266407	+	0.223542i
$638$	−7.53502e8	+	4.35035e8i	−2.90150	+	1.67518i
$639$	2.21408e8	+	1.67467e8i	0.848575	+	0.641840i
$640$	−9.41109e7	+	1.63005e8i	−0.359005	+	0.621814i
$641$	−9.59614e7	−	2.63652e8i	−0.364353	−	1.00105i	−0.977473	−	0.211062i	$-0.932308\pi$
$641$	−9.59614e7	−	2.63652e8i	−0.364353	−	1.00105i	0.613120	−	0.789990i	$-0.289914\pi$
$642$	3.17283e8	+	3.01632e8i	1.19906	+	1.13992i
$643$	2.78780e8	−	2.33925e8i	1.04865	−	0.879919i	0.0556964	−	0.998448i	$-0.482262\pi$
$643$	2.78780e8	−	2.33925e8i	1.04865	−	0.879919i	0.992951	+	0.118528i	$0.0378177\pi$
$644$	−4.53099e7	+	1.24488e8i	−0.169643	+	0.466089i
$645$	−4.76800e8	−	3.16204e8i	−1.77688	−	1.17839i
$646$	1.63397e7	−	9.26672e7i	0.0606104	−	0.343739i
$647$			2.28878e8i			0.845066i	0.906348	+	0.422533i	$0.138859\pi$
$647$			2.28878e8i			0.845066i	−0.906348	+	0.422533i	$0.861141\pi$
$648$	7.30140e7	−	2.06528e7i	0.268337	−	0.0759023i
$649$	−4.51926e7			−0.165323
$650$	−3.95032e8	−	6.96547e7i	−1.43844	−	0.253636i
$651$	−1.09413e8	+	1.64983e8i	−0.396577	+	0.597995i
$652$	−2.01826e8	−	7.34587e7i	−0.728173	−	0.265033i
$653$	−3.20818e7	−	3.82337e7i	−0.115218	−	0.137311i	0.705353	−	0.708856i	$-0.250789\pi$
$653$	−3.20818e7	−	3.82337e7i	−0.115218	−	0.137311i	−0.820571	+	0.571545i	$0.806344\pi$
$654$	−2.50708e7	+	2.63716e7i	−0.0896261	+	0.0942765i
$655$	−8.11401e7	+	2.95326e7i	−0.288743	+	0.105094i
$656$	−1.45508e7	−	8.40091e6i	−0.0515437	−	0.0297588i
$657$	8.74819e6	+	1.09010e6i	0.0308476	+	0.00384387i
$658$	−1.56980e8	−	2.71897e8i	−0.551018	−	0.954392i
$659$	−1.82386e8	+	2.17360e8i	−0.637289	+	0.759491i	−0.983939	−	0.178503i	$-0.942875\pi$
$659$	−1.82386e8	+	2.17360e8i	−0.637289	+	0.759491i	0.346650	+	0.937994i	$0.387319\pi$
$660$	5.08254e8	−	3.75382e8i	1.76786	−	1.30569i
$661$	−4.65854e7	−	2.64199e8i	−0.161304	−	0.914802i	−0.952794	−	0.303619i	$-0.901805\pi$
$661$	−4.65854e7	−	2.64199e8i	−0.161304	−	0.914802i	0.791489	−	0.611183i	$-0.209306\pi$
$662$	−6.62591e7	+	1.16833e7i	−0.228387	+	0.0402708i
$663$	3.16969e8	−	3.58257e7i	1.08762	−	0.122929i
$664$	8.35553e7	+	7.01112e7i	0.285410	+	0.239488i
$665$	8.55473e7	−	4.93908e7i	0.290898	−	0.167950i
$666$	3.20445e8	−	2.97746e8i	1.08475	−	1.00791i
$667$	−1.14988e8	+	1.99165e8i	−0.387502	+	0.671174i
$668$	6.05649e7	+	1.66401e8i	0.203185	+	0.558246i
$669$	1.21123e8	−	5.02523e8i	0.404526	−	1.67833i
$670$	−2.54091e8	+	2.13207e8i	−0.844820	+	0.708888i
$671$	−3.72281e7	+	1.02283e8i	−0.123226	+	0.338561i
$672$	3.35089e8	−	1.66694e8i	1.10421	−	0.549302i
$673$	−8.67258e7	+	4.91847e8i	−0.284514	+	1.61356i	0.422504	+	0.906361i	$0.361151\pi$
$673$	−8.67258e7	+	4.91847e8i	−0.284514	+	1.61356i	−0.707017	+	0.707196i	$0.749960\pi$
$674$		−	7.90153e8i		−	2.58066i
$675$	−7.78712e7	+	2.06577e8i	−0.253201	+	0.671694i
$676$	−3.27440e8			−1.05997
$677$	−3.37312e8	−	5.94773e7i	−1.08709	−	0.191684i	−0.398743	−	0.917063i	$-0.630553\pi$
$677$	−3.37312e8	−	5.94773e7i	−1.08709	−	0.191684i	−0.688349	+	0.725379i	$0.741664\pi$
$678$	3.26325e8	+	2.02531e7i	1.04704	+	0.0649835i
$679$	4.20648e8	+	1.53103e8i	1.34372	+	0.489075i
$680$	−5.87853e7	−	7.00576e7i	−0.186957	−	0.222807i
$681$	6.20986e7	+	2.10335e8i	0.196626	+	0.665994i
$682$	−5.16471e8	+	1.87980e8i	−1.62814	+	0.592596i
$683$	2.08388e8	+	1.20313e8i	0.654050	+	0.377616i	0.790006	−	0.613099i	$-0.210077\pi$
$683$	2.08388e8	+	1.20313e8i	0.654050	+	0.377616i	−0.135956	+	0.990715i	$0.543411\pi$
$684$	1.00384e8	+	5.13757e7i	0.313688	+	0.160542i
$685$	5.58216e7	+	9.66859e7i	0.173672	+	0.300809i
$686$	−3.32442e8	+	3.96189e8i	−1.02978	+	1.22724i
$687$	−2.45241e8	−	1.06896e8i	−0.756349	−	0.329678i
$688$	−7.13830e7	−	4.04833e8i	−0.219194	−	1.24311i
$689$	6.90785e8	−	1.21804e8i	2.11196	−	0.372395i
$690$	1.22881e8	−	2.81913e8i	0.374056	−	0.858161i
$691$	1.52910e8	+	1.28306e8i	0.463447	+	0.388879i	0.844398	−	0.535717i	$-0.179959\pi$
$691$	1.52910e8	+	1.28306e8i	0.463447	+	0.388879i	−0.380950	+	0.924596i	$0.624403\pi$
$692$	−3.09298e8	+	1.78573e8i	−0.933382	+	0.538888i
$693$	−4.05360e8	+	2.05139e7i	−1.21798	+	0.0616381i
$694$	6.87066e7	−	1.19003e8i	0.205551	−	0.356025i
$695$	1.60626e8	+	4.41315e8i	0.478476	+	1.31460i
$696$	−1.44745e8	+	4.27340e7i	−0.429314	+	0.126749i
$697$	1.58324e7	−	1.32849e7i	0.0467571	−	0.0392339i
$698$	1.44826e8	−	3.97906e8i	0.425873	−	1.17008i
$699$	−2.30612e7	+	3.71571e8i	−0.0675229	+	1.08795i
$700$	4.39233e7	−	2.49101e8i	0.128056	−	0.726243i
$701$			1.63750e8i			0.475364i	0.971343	+	0.237682i	$0.0763876\pi$
$701$			1.63750e8i			0.475364i	−0.971343	+	0.237682i	$0.923612\pi$
$702$	−1.30145e8	+	6.91792e8i	−0.376198	+	1.99970i
$703$	1.03106e8			0.296768
$704$	6.47095e8	+	1.14100e8i	1.85460	+	0.327016i
$705$	1.76286e8	+	3.54372e8i	0.503096	+	1.01133i
$706$	−4.00329e8	−	1.45708e8i	−1.13764	−	0.414066i
$707$	−3.38205e8	−	4.03057e8i	−0.957023	−	1.14054i
$708$	−4.80487e7	−	1.15811e7i	−0.135388	−	0.0326325i
$709$	4.36303e8	−	1.58801e8i	1.22419	−	0.445570i	0.352588	−	0.935779i	$-0.385302\pi$
$709$	4.36303e8	−	1.58801e8i	1.22419	−	0.445570i	0.871605	+	0.490209i	$0.163080\pi$
$710$	6.39441e8	+	3.69181e8i	1.78659	+	1.03149i
$711$	1.43857e8	−	3.29398e7i	0.400240	−	0.0916458i
$712$	6.35919e7	+	1.10144e8i	0.176182	+	0.305157i
$713$	−9.33803e7	+	1.11286e8i	−0.257624	+	0.307025i
$714$	4.15992e7	+	3.68050e8i	0.114285	+	1.01114i
$715$	1.61440e8	+	9.15574e8i	0.441666	+	2.50481i
$716$	−2.44681e8	+	4.31439e7i	−0.666594	+	0.117538i
$717$	−2.03252e8	−	2.75196e8i	−0.551415	−	0.746596i
$718$	2.91013e8	+	2.44189e8i	0.786211	+	0.659709i
$719$	−1.75569e8	+	1.01365e8i	−0.472347	+	0.272710i	−0.717222	−	0.696845i	$-0.754586\pi$
$719$	−1.75569e8	+	1.01365e8i	−0.472347	+	0.272710i	0.244875	+	0.969555i	$0.421253\pi$
$720$	−3.49691e8	+	1.47694e8i	−0.936887	+	0.395700i
$721$	2.47794e8	−	4.29192e8i	0.661127	−	1.14511i
$722$	−1.73690e8	−	4.77210e8i	−0.461492	−	1.26794i
$723$	−2.86718e8	−	2.72575e8i	−0.758648	−	0.721226i
$724$	5.41795e8	−	4.54620e8i	1.42764	−	1.19793i
$725$	1.50182e8	−	4.12621e8i	0.394097	−	1.08277i
$726$	−4.67330e8	−	3.09923e8i	−1.22127	−	0.809923i
$727$	−4.37455e7	+	2.48093e8i	−0.113849	+	0.645672i	0.873464	+	0.486888i	$0.161868\pi$
$727$	−4.37455e7	+	2.48093e8i	−0.113849	+	0.645672i	−0.987313	+	0.158783i	$0.949243\pi$
$728$		−	1.27920e8i		−	0.331547i
$729$	3.60935e8	+	1.40786e8i	0.931636	+	0.363394i
$730$	2.34477e7			0.0602743
$731$	4.97980e8	+	8.78073e7i	1.27485	+	0.224791i
$732$	−6.57920e7	+	9.92072e7i	−0.167741	+	0.252936i
$733$	9.49802e7	+	3.45700e7i	0.241169	+	0.0877783i	0.459777	−	0.888034i	$-0.347929\pi$
$733$	9.49802e7	+	3.45700e7i	0.241169	+	0.0877783i	−0.218608	+	0.975813i	$0.570152\pi$
$734$	−4.48145e7	−	5.34079e7i	−0.113326	−	0.135057i
$735$	9.06618e7	−	9.53659e7i	0.228330	−	0.240177i
$736$	2.58081e8	−	9.39339e7i	0.647326	−	0.235607i
$737$	2.78208e8	+	1.60623e8i	0.694972	+	0.401242i
$738$	1.77453e7	+	4.20149e7i	0.0441483	+	0.104528i
$739$	−2.20037e8	−	3.81116e8i	−0.545209	−	0.944330i	−0.998594	−	0.0530151i	$-0.983117\pi$
$739$	−2.20037e8	−	3.81116e8i	−0.545209	−	0.944330i	0.453384	−	0.891315i	$-0.350216\pi$
$740$	4.06123e8	−	4.83998e8i	1.00222	−	1.19440i
$741$	−1.33469e8	+	9.85761e7i	−0.328038	+	0.242280i
$742$	1.41434e8	+	8.02110e8i	0.346211	+	1.96346i
$743$	−5.51772e8	+	9.72923e7i	−1.34522	+	0.237198i	−0.799448	−	0.600736i	$-0.794874\pi$
$743$	−5.51772e8	+	9.72923e7i	−1.34522	+	0.237198i	−0.545772	+	0.837934i	$0.683763\pi$
$744$	−9.47328e7	+	1.07073e7i	−0.230028	+	0.0259992i
$745$	−4.12852e8	−	3.46424e8i	−0.998448	−	0.837797i
$746$	−1.44205e8	+	8.32565e7i	−0.347346	+	0.200540i
$747$	1.24302e8	+	5.42858e8i	0.298206	+	1.30234i
$748$	−2.79225e8	+	4.83633e8i	−0.667191	+	1.15561i
$749$	−1.38925e8	−	3.81693e8i	−0.330624	−	0.908381i
$750$	5.40830e7	−	2.24384e8i	0.128197	−	0.531873i
$751$	−5.96122e7	+	5.00205e7i	−0.140739	+	0.118094i	−0.710439	−	0.703758i	$-0.751504\pi$
$751$	−5.96122e7	+	5.00205e7i	−0.140739	+	0.118094i	0.569700	+	0.821853i	$0.307059\pi$
$752$	−9.72661e7	+	2.67237e8i	−0.228722	+	0.628409i
$753$	−2.09223e8	+	1.04080e8i	−0.490032	+	0.243772i
$754$	2.43125e8	−	1.37883e9i	0.567172	−	3.21659i
$755$		−	3.63254e8i		−	0.844052i
$756$	−4.36235e8	−	8.20677e7i	−1.00961	−	0.189936i
$757$	−3.50351e8			−0.807636			−0.403818	−	0.914839i	$-0.632317\pi$
$757$	−3.50351e8			−0.807636			−0.403818	+	0.914839i	$0.632317\pi$
$758$	9.34368e8	+	1.64754e8i	2.14541	+	0.378294i
$759$	−2.97274e8	−	1.84501e7i	−0.679879	−	0.0421962i

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)

\(f(q)\)	\(=\)	\(q+(-11.6551 - 2.05510i) q^{2} +(-14.9225 + 22.5015i) q^{3} +(71.4770 + 26.0155i) q^{4} +(105.310 + 125.503i) q^{5} +(220.166 - 231.590i) q^{6} +(-278.603 + 101.403i) q^{7} +(-123.650 - 71.3896i) q^{8} +(-283.637 - 671.559i) q^{9} +O(q^{10})\)	\(q+(-11.6551 - 2.05510i) q^{2} +(-14.9225 + 22.5015i) q^{3} +(71.4770 + 26.0155i) q^{4} +(105.310 + 125.503i) q^{5} +(220.166 - 231.590i) q^{6} +(-278.603 + 101.403i) q^{7} +(-123.650 - 71.3896i) q^{8} +(-283.637 - 671.559i) q^{9} +(-969.470 - 1679.17i) q^{10} +(-1207.08 + 1438.54i) q^{11} +(-1652.01 + 1220.13i) q^{12} +(-524.739 - 2975.94i) q^{13} +(3455.54 - 609.304i) q^{14} +(-4395.49 + 496.805i) q^{15} +(-2434.75 - 2043.00i) q^{16} +(3385.84 - 1954.82i) q^{17} +(1925.69 + 8409.97i) q^{18} +(-1016.82 + 1761.19i) q^{19} +(4262.19 + 11710.3i) q^{20} +(1875.73 - 7782.19i) q^{21} +(17025.0 - 14285.6i) q^{22} +(2009.15 - 5520.08i) q^{23} +(3451.55 - 1717.01i) q^{24} +(-1947.66 + 11045.7i) q^{25} +35763.2i q^{26} +(19343.7 + 3639.08i) q^{27} -22551.8 q^{28} +(-38554.4 - 6798.17i) q^{29} +(52250.8 + 3242.90i) q^{30} +(-23238.8 - 8458.24i) q^{31} +(30052.3 + 35815.0i) q^{32} +(-14356.7 - 48627.8i) q^{33} +(-43479.6 + 15825.3i) q^{34} +(-42066.0 - 24286.8i) q^{35} +(-2802.60 - 55380.0i) q^{36} +(-25350.0 - 43907.6i) q^{37} +(15470.6 - 18437.1i) q^{38} +(74793.7 + 32601.1i) q^{39} +(-4061.96 - 23036.5i) q^{40} +(5206.04 - 917.965i) q^{41} +(-37855.0 + 86847.2i) q^{42} +(99078.2 + 83136.5i) q^{43} +(-123703. + 71419.9i) q^{44} +(54413.0 - 106319. i) q^{45} +(-34761.1 + 60208.0i) q^{46} +(-30602.8 - 84080.5i) q^{47} +(82303.1 - 24298.9i) q^{48} +(-22787.2 + 19120.7i) q^{49} +(45400.3 - 124736. i) q^{50} +(-6538.92 + 105357. i) q^{51} +(39913.9 - 226363. i) q^{52} +232123. i q^{53} +(-217973. - 82167.0i) q^{54} -307658. q^{55} +(41688.6 + 7350.82i) q^{56} +(-24455.9 - 49161.4i) q^{57} +(435383. + 158466. i) q^{58} +(15469.2 + 18435.4i) q^{59} +(-327102. - 78840.9i) q^{60} +(54467.4 - 19824.5i) q^{61} +(253468. + 146340. i) q^{62} +(147120. + 158337. i) q^{63} +(-174952. - 303025. i) q^{64} +(318230. - 379252. i) q^{65} +(67393.4 + 596265. i) q^{66} +(-29705.8 - 168470. i) q^{67} +(292865. - 51640.1i) q^{68} +(94228.8 + 127582. i) q^{69} +(440371. + 369515. i) q^{70} +(-329789. + 190404. i) q^{71} +(-12870.5 + 103287. i) q^{72} +(-6046.53 + 10472.9i) q^{73} +(205222. + 563843. i) q^{74} +(-219482. - 208656. i) q^{75} +(-118498. + 99431.3i) q^{76} +(190423. - 523184. i) q^{77} +(-804728. - 533678. i) q^{78} +(-35153.5 + 199366. i) q^{79} -520716. i q^{80} +(-370541. + 380958. i) q^{81} -62563.3 q^{82} +(-752327. - 132656. i) q^{83} +(336530. - 507450. i) q^{84} +(601897. + 219073. i) q^{85} +(-983910. - 1.17258e6i) q^{86} +(728297. - 766086. i) q^{87} +(251953. - 91703.3i) q^{88} +(-771432. - 445387. i) q^{89} +(-852684. + 1.12733e6i) q^{90} +(447965. + 775897. i) q^{91} +(287216. - 342290. i) q^{92} +(537105. - 396691. i) q^{93} +(183884. + 1.04286e6i) q^{94} +(-328116. + 57855.6i) q^{95} +(-1.25435e6 + 141774. i) q^{96} +(-1.15661e6 - 970509. i) q^{97} +(304882. - 176024. i) q^{98} +(1.30844e6 + 402601. i) 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

Introduction

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