LMFDB - Embedded newform 27.7.f.a.2.4

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			2.4
Character	$\chi$	$=$	27.2
Dual form			27.7.f.a.14.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.97059 - 1.75808i) q^{2} +(24.1318 - 12.1101i) q^{3} +(36.1814 + 13.1690i) q^{4} +(60.9980 + 72.6946i) q^{5} +(-261.899 + 78.3191i) q^{6} +(-133.791 + 48.6960i) q^{7} +(223.553 + 129.069i) q^{8} +(435.691 - 584.478i) q^{9} +O(q^{10})$	\(q+(-9.97059 - 1.75808i) q^{2} +(24.1318 - 12.1101i) q^{3} +(36.1814 + 13.1690i) q^{4} +(60.9980 + 72.6946i) q^{5} +(-261.899 + 78.3191i) q^{6} +(-133.791 + 48.6960i) q^{7} +(223.553 + 129.069i) q^{8} +(435.691 - 584.478i) q^{9} +(-480.383 - 832.047i) q^{10} +(1624.00 - 1935.41i) q^{11} +(1032.60 - 120.370i) q^{12} +(-126.490 - 717.362i) q^{13} +(1419.59 - 250.312i) q^{14} +(2352.33 + 1015.56i) q^{15} +(-3889.75 - 3263.89i) q^{16} +(4210.29 - 2430.81i) q^{17} +(-5371.65 + 5061.61i) q^{18} +(62.0141 - 107.412i) q^{19} +(1249.68 + 3433.47i) q^{20} +(-2638.91 + 2795.35i) q^{21} +(-19594.9 + 16442.1i) q^{22} +(-4137.25 + 11367.0i) q^{23} +(6957.79 + 407.407i) q^{24} +(1149.51 - 6519.18i) q^{25} +7374.90i q^{26} +(3435.93 - 19380.8i) q^{27} -5482.03 q^{28} +(22191.9 + 3913.03i) q^{29} +(-21668.7 - 14261.3i) q^{30} +(14120.1 + 5139.28i) q^{31} +(22425.5 + 26725.7i) q^{32} +(15752.1 - 66371.9i) q^{33} +(-46252.6 + 16834.6i) q^{34} +(-11700.9 - 6755.53i) q^{35} +(23460.9 - 15409.6i) q^{36} +(17270.1 + 29912.7i) q^{37} +(-807.155 + 961.930i) q^{38} +(-11739.8 - 15779.5i) q^{39} +(4253.72 + 24124.0i) q^{40} +(-87091.6 + 15356.6i) q^{41} +(31226.0 - 23231.8i) q^{42} +(-4953.54 - 4156.52i) q^{43} +(84246.1 - 48639.5i) q^{44} +(69064.6 - 3979.63i) q^{45} +(61235.0 - 106062. i) q^{46} +(59675.6 + 163957. i) q^{47} +(-133393. - 31658.3i) q^{48} +(-74595.6 + 62593.1i) q^{49} +(-22922.5 + 62979.1i) q^{50} +(72164.6 - 109647. i) q^{51} +(4870.32 - 27620.9i) q^{52} -277335. i q^{53} +(-68331.3 + 187197. i) q^{54} +239755. q^{55} +(-36194.6 - 6382.08i) q^{56} +(195.749 - 3343.04i) q^{57} +(-214387. - 78030.5i) q^{58} +(66748.6 + 79547.9i) q^{59} +(71736.8 + 67722.2i) q^{60} +(-284660. + 103608. i) q^{61} +(-131750. - 76065.9i) q^{62} +(-29829.8 + 99414.4i) q^{63} +(-14123.1 - 24462.0i) q^{64} +(44432.7 - 52952.8i) q^{65} +(-273745. + 634073. i) q^{66} +(-7050.75 - 39986.8i) q^{67} +(184345. - 32505.1i) q^{68} +(37816.2 + 324409. i) q^{69} +(104788. + 87927.9i) q^{70} +(-8731.10 + 5040.90i) q^{71} +(172838. - 74428.0i) q^{72} +(159295. - 275906. i) q^{73} +(-119604. - 328610. i) q^{74} +(-51208.2 - 171240. i) q^{75} +(3658.26 - 3069.64i) q^{76} +(-123031. + 338024. i) q^{77} +(89310.9 + 177970. i) q^{78} +(11705.7 - 66386.4i) q^{79} -481854. i q^{80} +(-151788. - 509303. i) q^{81} +895353. q^{82} +(-975779. - 172056. i) q^{83} +(-132291. + 66388.0i) q^{84} +(433526. + 157790. i) q^{85} +(42082.2 + 50151.7i) q^{86} +(582919. - 174318. i) q^{87} +(612852. - 223060. i) q^{88} +(-169602. - 97919.9i) q^{89} +(-695611. - 81742.1i) q^{90} +(51856.0 + 89817.2i) q^{91} +(-299383. + 356791. i) q^{92} +(402980. - 46975.1i) q^{93} +(-306750. - 1.73967e6i) q^{94} +(11591.0 - 2043.80i) q^{95} +(864820. + 373365. i) q^{96} +(981600. + 823660. i) q^{97} +(853806. - 492945. i) q^{98} +(-423643. - 1.79244e6i) 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 $

$2$	−9.97059	−	1.75808i	−1.24632	−	0.219760i	−0.488700	−	0.872452i	$-0.662529\pi$
$2$	−9.97059	−	1.75808i	−1.24632	−	0.219760i	−0.757624	+	0.652692i	$0.773640\pi$
$3$	24.1318	−	12.1101i	0.893772	−	0.448522i
$3$	24.1318	−	12.1101i	0.893772	−	0.448522i
$4$	36.1814	+	13.1690i	0.565335	+	0.205765i
$5$	60.9980	+	72.6946i	0.487984	+	0.581556i	0.952703	−	0.303901i	$-0.0982893\pi$
$5$	60.9980	+	72.6946i	0.487984	+	0.581556i	−0.464720	+	0.885458i	$0.653845\pi$
$6$	−261.899	+	78.3191i	−1.21250	+	0.362588i
$7$	−133.791	+	48.6960i	−0.390062	+	0.141971i	−0.529604	−	0.848245i	$-0.677659\pi$
$7$	−133.791	+	48.6960i	−0.390062	+	0.141971i	0.139542	+	0.990216i	$0.455437\pi$
$8$	223.553	+	129.069i	0.436628	+	0.252087i
$9$	435.691	−	584.478i	0.597655	−	0.801753i
$10$	−480.383	−	832.047i	−0.480383	−	0.832047i
$11$	1624.00	−	1935.41i	1.22014	−	1.45410i	0.368782	−	0.929516i	$-0.379775\pi$
$11$	1624.00	−	1935.41i	1.22014	−	1.45410i	0.851356	−	0.524588i	$-0.175781\pi$
$12$	1032.60	−	120.370i	0.597570	−	0.0696583i
$13$	−126.490	−	717.362i	−0.0575741	−	0.326519i	0.942394	−	0.334505i	$-0.108569\pi$
$13$	−126.490	−	717.362i	−0.0575741	−	0.326519i	−0.999968	+	0.00798588i	$0.997458\pi$
$14$	1419.59	−	250.312i	0.517343	−	0.0912215i
$15$	2352.33	+	1015.56i	0.696987	+	0.300907i
$16$	−3889.75	−	3263.89i	−0.949645	−	0.796847i
$17$	4210.29	−	2430.81i	0.856968	−	0.494771i	−0.00602755	−	0.999982i	$-0.501919\pi$
$17$	4210.29	−	2430.81i	0.856968	−	0.494771i	0.862996	+	0.505211i	$0.168585\pi$
$18$	−5371.65	+	5061.61i	−0.921065	+	0.867903i
$19$	62.0141	−	107.412i	0.00904127	−	0.0156599i	−0.861469	−	0.507810i	$-0.830455\pi$
$19$	62.0141	−	107.412i	0.00904127	−	0.0156599i	0.870511	+	0.492150i	$0.163789\pi$
$20$	1249.68	+	3433.47i	0.156210	+	0.429184i
$21$	−2638.91	+	2795.35i	−0.284949	+	0.301841i
$22$	−19594.9	+	16442.1i	−1.84024	+	1.54415i
$23$	−4137.25	+	11367.0i	−0.340039	+	0.934249i	0.645344	+	0.763892i	$0.276714\pi$
$23$	−4137.25	+	11367.0i	−0.340039	+	0.934249i	−0.985382	+	0.170357i	$0.945508\pi$
$24$	6957.79	+	407.407i	0.503312	+	0.0294710i
$25$	1149.51	−	6519.18i	0.0735685	−	0.417227i
$26$			7374.90i			0.419601i
$27$	3435.93	−	19380.8i	0.174563	−	0.984646i
$28$	−5482.03			−0.249728
$29$	22191.9	+	3913.03i	0.909915	+	0.160443i	0.608965	−	0.793197i	$-0.291585\pi$
$29$	22191.9	+	3913.03i	0.909915	+	0.160443i	0.300950	+	0.953640i	$0.402696\pi$
$30$	−21668.7	−	14261.3i	−0.802544	−	0.528198i
$31$	14120.1	+	5139.28i	0.473971	+	0.172511i	0.567950	−	0.823063i	$-0.307737\pi$
$31$	14120.1	+	5139.28i	0.473971	+	0.172511i	−0.0939796	+	0.995574i	$0.529959\pi$
$32$	22425.5	+	26725.7i	0.684373	+	0.815604i
$33$	15752.1	−	66371.9i	0.438327	−	1.84690i
$34$	−46252.6	+	16834.6i	−1.17679	+	0.428317i
$35$	−11700.9	−	6755.53i	−0.272908	−	0.157563i
$36$	23460.9	−	15409.6i	0.502848	−	0.330282i
$37$	17270.1	+	29912.7i	0.340950	+	0.590542i	0.984609	−	0.174770i	$-0.0559180\pi$
$37$	17270.1	+	29912.7i	0.340950	+	0.590542i	−0.643660	+	0.765312i	$0.722585\pi$
$38$	−807.155	+	961.930i	−0.0147098	+	0.0175304i
$39$	−11739.8	−	15779.5i	−0.197909	−	0.266010i
$40$	4253.72	+	24124.0i	0.0664643	+	0.376938i
$41$	−87091.6	+	15356.6i	−1.26364	+	0.222815i	−0.765022	−	0.644004i	$-0.777272\pi$
$41$	−87091.6	+	15356.6i	−1.26364	+	0.222815i	−0.498623	+	0.866819i	$0.666161\pi$
$42$	31226.0	−	23231.8i	0.421471	−	0.313571i
$43$	−4953.54	−	4156.52i	−0.0623032	−	0.0522786i	0.611104	−	0.791550i	$-0.290726\pi$
$43$	−4953.54	−	4156.52i	−0.0623032	−	0.0522786i	−0.673408	+	0.739271i	$0.735170\pi$
$44$	84246.1	−	48639.5i	0.988990	−	0.570994i
$45$	69064.6	−	3979.63i	0.757911	−	0.0436722i
$46$	61235.0	−	106062.i	0.629109	−	1.08965i
$47$	59675.6	+	163957.i	0.574782	+	1.57920i	0.796855	+	0.604171i	$0.206496\pi$
$47$	59675.6	+	163957.i	0.574782	+	1.57920i	−0.222072	+	0.975030i	$0.571282\pi$
$48$	−133393.	−	31658.3i	−1.20617	−	0.286262i
$49$	−74595.6	+	62593.1i	−0.634052	+	0.532033i
$50$	−22922.5	+	62979.1i	−0.183380	+	0.503833i
$51$	72164.6	−	109647.i	0.544018	−	0.826582i
$52$	4870.32	−	27620.9i	0.0346375	−	0.196439i
$53$		−	277335.i		−	1.86285i	−0.363938	−	0.931423i	$-0.618568\pi$
$53$		−	277335.i		−	1.86285i	0.363938	−	0.931423i	$-0.381432\pi$
$54$	−68331.3	+	187197.i	−0.433948	+	1.18883i
$55$	239755.			1.44105
$56$	−36194.6	−	6382.08i	−0.206101	−	0.0363411i
$57$	195.749	−	3343.04i	0.00105700	−	0.0180516i
$58$	−214387.	−	78030.5i	−1.09879	−	0.399927i
$59$	66748.6	+	79547.9i	0.325002	+	0.387323i	0.903662	−	0.428247i	$-0.140869\pi$
$59$	66748.6	+	79547.9i	0.325002	+	0.387323i	−0.578660	+	0.815569i	$0.696424\pi$
$60$	71736.8	+	67722.2i	0.332115	+	0.313529i
$61$	−284660.	+	103608.i	−1.25411	+	0.456459i	−0.881789	−	0.471644i	$-0.843661\pi$
$61$	−284660.	+	103608.i	−1.25411	+	0.456459i	−0.372323	+	0.928103i	$0.621439\pi$
$62$	−131750.	−	76065.9i	−0.552809	−	0.319165i
$63$	−29829.8	+	99414.4i	−0.119297	+	0.397583i
$64$	−14123.1	−	24462.0i	−0.0538755	−	0.0933151i
$65$	44432.7	−	52952.8i	0.161794	−	0.192819i
$66$	−273745.	+	634073.i	−0.952171	+	2.20550i
$67$	−7050.75	−	39986.8i	−0.0234429	−	0.132951i	0.970840	−	0.239728i	$-0.0770582\pi$
$67$	−7050.75	−	39986.8i	−0.0234429	−	0.132951i	−0.994283	+	0.106777i	$0.965947\pi$
$68$	184345.	−	32505.1i	0.586280	−	0.103377i
$69$	37816.2	+	324409.i	0.115115	+	0.987520i
$70$	104788.	+	87927.9i	0.305505	+	0.256349i
$71$	−8731.10	+	5040.90i	−0.0243946	+	0.0140842i	−0.512148	−	0.858897i	$-0.671150\pi$
$71$	−8731.10	+	5040.90i	−0.0243946	+	0.0140842i	0.487753	+	0.872982i	$0.337817\pi$
$72$	172838.	−	74428.0i	0.463064	−	0.199406i
$73$	159295.	−	275906.i	0.409480	−	0.709239i	−0.585352	−	0.810779i	$-0.699044\pi$
$73$	159295.	−	275906.i	0.409480	−	0.709239i	0.994831	+	0.101540i	$0.0323770\pi$
$74$	−119604.	−	328610.i	−0.295156	−	0.810934i
$75$	−51208.2	−	171240.i	−0.121382	−	0.405903i
$76$	3658.26	−	3069.64i	0.00833361	−	0.00699273i
$77$	−123031.	+	338024.i	−0.269489	+	0.740415i
$78$	89310.9	+	177970.i	0.188200	+	0.375027i
$79$	11705.7	−	66386.4i	0.0237420	−	0.134647i	−0.970633	−	0.240566i	$-0.922667\pi$
$79$	11705.7	−	66386.4i	0.0237420	−	0.134647i	0.994375	+	0.105918i	$0.0337782\pi$
$80$		−	481854.i		−	0.941121i
$81$	−151788.	−	509303.i	−0.285616	−	0.958344i
$82$	895353.			1.62388
$83$	−975779.	−	172056.i	−1.70654	−	0.300910i	−0.766571	−	0.642160i	$-0.778039\pi$
$83$	−975779.	−	172056.i	−1.70654	−	0.300910i	−0.939973	+	0.341250i	$0.889150\pi$
$84$	−132291.	+	66388.0i	−0.223200	+	0.112009i
$85$	433526.	+	157790.i	0.705924	+	0.256935i
$86$	42082.2	+	50151.7i	0.0661612	+	0.0788479i
$87$	582919.	−	174318.i	0.885218	−	0.264718i
$88$	612852.	−	223060.i	0.899307	−	0.327321i
$89$	−169602.	−	97919.9i	−0.240581	−	0.138900i	0.374863	−	0.927080i	$-0.377690\pi$
$89$	−169602.	−	97919.9i	−0.240581	−	0.138900i	−0.615444	+	0.788181i	$0.711023\pi$
$90$	−695611.	−	81742.1i	−0.954199	−	0.112129i
$91$	51856.0	+	89817.2i	0.0688137	+	0.119189i
$92$	−299383.	+	356791.i	−0.384471	+	0.458195i
$93$	402980.	−	46975.1i	0.500997	−	0.0584008i
$94$	−306750.	−	1.73967e6i	−0.369319	−	2.09451i
$95$	11591.0	−	2043.80i	0.0135191	−	0.00238379i
$96$	864820.	+	373365.i	0.977490	+	0.422007i
$97$	981600.	+	823660.i	1.07552	+	0.902470i	0.995541	−	0.0943259i	$-0.0300696\pi$
$97$	981600.	+	823660.i	1.07552	+	0.902470i	0.0799810	+	0.996796i	$0.474514\pi$
$98$	853806.	−	492945.i	0.907153	−	0.523745i
$99$	−423643.	−	1.79244e6i	−0.436610	−	1.84730i
$100$	127442.	−	220735.i	0.127442	−	0.220735i
$101$	144793.	+	397814.i	0.140534	+	0.386115i	0.989914	−	0.141667i	$-0.0452462\pi$
$101$	144793.	+	397814.i	0.140534	+	0.386115i	−0.849380	+	0.527781i	$0.823024\pi$
$102$	−912291.	+	966372.i	−0.859672	+	0.910634i
$103$	−1.47195e6	+	1.23511e6i	−1.34704	+	1.13030i	−0.367286	+	0.930108i	$0.619713\pi$
$103$	−1.47195e6	+	1.23511e6i	−1.34704	+	1.13030i	−0.979756	+	0.200195i	$0.935842\pi$
$104$	64311.6	−	176695.i	0.0571728	−	0.157081i
$105$	−364175.	−	21324.0i	−0.314588	−	0.0184204i
$106$	−487578.	+	2.76519e6i	−0.409380	+	2.32171i
$107$			1.43594e6i			1.17215i	0.810257	+	0.586075i	$0.199328\pi$
$107$			1.43594e6i			1.17215i	−0.810257	+	0.586075i	$0.800672\pi$
$108$	379542.	−	655977.i	0.301292	−	0.520735i
$109$	−1.85981e6			−1.43611			−0.718057	−	0.695984i	$-0.754968\pi$
$109$	−1.85981e6			−1.43611			−0.718057	+	0.695984i	$0.754968\pi$
$110$	−2.39050e6	−	421509.i	−1.79602	−	0.316686i
$111$	779006.	+	512706.i	0.569603	+	0.374886i
$112$	679352.	+	247264.i	0.483550	+	0.175998i
$113$	1.43022e6	+	1.70447e6i	0.991212	+	1.18128i	0.983426	+	0.181310i	$0.0580338\pi$
$113$	1.43022e6	+	1.70447e6i	0.991212	+	1.18128i	0.00778556	+	0.999970i	$0.497522\pi$
$114$	−7829.06	+	32987.9i	−0.00528439	+	0.0222659i
$115$	−1.07868e6	+	392609.i	−0.709252	+	0.258147i
$116$	751404.	+	433823.i	0.481393	+	0.277932i
$117$	−474393.	−	238617.i	−0.296197	−	0.148986i
$118$	−525671.	−	910489.i	−0.319940	−	0.554152i
$119$	−444928.	+	530245.i	−0.264028	+	0.314656i
$120$	394795.	+	530644.i	0.228469	+	0.307086i
$121$	−800805.	−	4.54159e6i	−0.452033	−	2.56361i
$122$	3.02037e6	−	532573.i	1.66334	−	0.293292i
$123$	−1.91571e6	+	1.42527e6i	−1.02947	+	0.765918i
$124$	443205.	+	371893.i	0.232455	+	0.195053i
$125$	1.82813e6	−	1.05547e6i	0.936000	−	0.540400i
$126$	472200.	−	938777.i	0.236056	−	0.469300i
$127$	−661639.	+	1.14599e6i	−0.323006	+	0.559462i	−0.981107	−	0.193467i	$-0.938027\pi$
$127$	−661639.	+	1.14599e6i	−0.323006	+	0.559462i	0.658101	+	0.752930i	$0.271360\pi$
$128$	−665862.	−	1.82944e6i	−0.317508	−	0.872346i
$129$	−169874.	−	40316.4i	−0.0791330	−	0.0187808i
$130$	−536115.	+	449854.i	−0.244022	+	0.204758i
$131$	93255.3	−	256217.i	0.0414820	−	0.113971i	−0.917222	−	0.398376i	$-0.869574\pi$
$131$	93255.3	−	256217.i	0.0414820	−	0.113971i	0.958704	+	0.284405i	$0.0917961\pi$
$132$	1.44398e6	−	2.19399e6i	0.627828	−	0.953922i
$133$	−3066.43	+	17390.6i	−0.00130340	+	0.00739195i
$134$			411088.i			0.170852i
$135$	1.61846e6	−	932416.i	0.657811	−	0.378973i
$136$	1.25496e6			0.498901
$137$	3.97328e6	+	700596.i	1.54521	+	0.272462i	0.880284	−	0.474447i	$-0.157352\pi$
$137$	3.97328e6	+	700596.i	1.54521	+	0.272462i	0.664926	+	0.746910i	$0.268463\pi$
$138$	193289.	−	3.30103e6i	0.0735480	−	1.25607i
$139$	−2.76811e6	−	1.00751e6i	−1.03071	−	0.375149i	−0.229362	−	0.973341i	$-0.573664\pi$
$139$	−2.76811e6	−	1.00751e6i	−1.03071	−	0.375149i	−0.801353	+	0.598192i	$0.795886\pi$
$140$	−334393.	−	398514.i	−0.121863	−	0.145231i
$141$	3.42562e6	+	3.23392e6i	1.22203	+	1.15364i
$142$	95916.5	−	34910.7i	0.0334987	−	0.0121925i
$143$	−1.59381e6	−	920188.i	−0.545041	−	0.314680i
$144$	−3.60240e6	+	851427.i	−1.20644	+	0.285141i
$145$	1.06921e6	+	1.85192e6i	0.350717	+	0.607460i
$146$	−2.07333e6	+	2.47089e6i	−0.666207	+	0.793954i
$147$	−1.04212e6	+	2.41385e6i	−0.328069	+	0.759902i
$148$	230938.	+	1.30972e6i	0.0712378	+	0.404010i
$149$	938820.	−	165539.i	0.283807	−	0.0500429i	−0.0299325	−	0.999552i	$-0.509529\pi$
$149$	938820.	−	165539.i	0.283807	−	0.0500429i	0.313740	+	0.949509i	$0.398418\pi$
$150$	209521.	+	1.79740e6i	0.0620803	+	0.532562i
$151$	−3.13417e6	−	2.62988e6i	−0.910316	−	0.763846i	0.0618631	−	0.998085i	$-0.480296\pi$
$151$	−3.13417e6	−	2.62988e6i	−0.910316	−	0.763846i	−0.972179	+	0.234239i	$0.924740\pi$
$152$	27726.9	−	16008.1i	0.00789534	−	0.00455838i
$153$	413628.	−	3.51990e6i	0.115488	−	0.982780i
$154$	1.82096e6	−	3.15400e6i	0.498584	−	0.863573i
$155$	487697.	+	1.33994e6i	0.130965	+	0.359823i
$156$	−216963.	−	725524.i	−0.0571494	−	0.191108i
$157$	−2.55010e6	+	2.13979e6i	−0.658960	+	0.552933i	−0.909775	−	0.415102i	$-0.863746\pi$
$157$	−2.55010e6	+	2.13979e6i	−0.658960	+	0.552933i	0.250815	+	0.968035i	$0.419301\pi$
$158$	−233426.	+	641332.i	−0.0591803	+	0.162597i
$159$	−3.35856e6	−	6.69260e6i	−0.835528	−	1.66496i
$160$	−574901.	+	3.26043e6i	−0.140357	+	0.796003i
$161$		−	1.72227e6i		−	0.412691i
$162$	618019.	+	5.34491e6i	0.145364	+	1.25717i
$163$	2.30993e6			0.533380			0.266690	−	0.963782i	$-0.414070\pi$
$163$	2.30993e6			0.533380			0.266690	+	0.963782i	$0.414070\pi$
$164$	−3.35333e6	−	591282.i	−0.760229	−	0.134049i
$165$	5.78573e6	−	2.90346e6i	1.28797	−	0.646344i
$166$	9.42660e6	+	3.43100e6i	2.06078	+	0.750061i
$167$	1.52636e6	+	1.81904e6i	0.327723	+	0.390565i	0.904597	−	0.426268i	$-0.140172\pi$
$167$	1.52636e6	+	1.81904e6i	0.327723	+	0.390565i	−0.576874	+	0.816833i	$0.695727\pi$
$168$	−950730.	+	284309.i	−0.200507	+	0.0599601i
$169$	4.03711e6	−	1.46939e6i	0.836393	−	0.304422i
$170$	−4.04510e6	−	2.33544e6i	−0.823345	−	0.475359i
$171$	−35760.7	−	83044.1i	−0.00715184	−	0.0166081i
$172$	−124489.	−	215622.i	−0.0244651	−	0.0423747i
$173$	3.26555e6	−	3.89174e6i	0.630694	−	0.751632i	−0.352176	−	0.935934i	$-0.614558\pi$
$173$	3.26555e6	−	3.89174e6i	0.630694	−	0.751632i	0.982870	+	0.184302i	$0.0590025\pi$
$174$	−6.11851e6	+	713230.i	−1.16144	+	0.135389i
$175$	163664.	+	928185.i	0.0305379	+	0.173189i
$176$	−1.26339e7	+	2.22770e6i	−2.31740	+	0.408620i
$177$	2.57410e6	+	1.11130e6i	0.464201	+	0.200407i
$178$	1.51888e6	+	1.27449e6i	0.269317	+	0.225984i
$179$	−2.84156e6	+	1.64058e6i	−0.495447	+	0.286047i	−0.726832	−	0.686816i	$-0.759008\pi$
$179$	−2.84156e6	+	1.64058e6i	−0.495447	+	0.286047i	0.231384	+	0.972862i	$0.425675\pi$
$180$	2.55126e6	+	765521.i	0.437459	+	0.131262i
$181$	324598.	−	562220.i	0.0547407	−	0.0948137i	−0.837357	−	0.546657i	$-0.815900\pi$
$181$	324598.	−	562220.i	0.0547407	−	0.0948137i	0.892097	+	0.451843i	$0.149233\pi$
$182$	−359129.	−	986698.i	−0.0595711	−	0.163670i
$183$	−5.61466e6	+	5.94750e6i	−0.916158	+	0.970468i
$184$	−2.39202e6	+	2.00714e6i	−0.383982	+	0.322199i
$185$	−1.12105e6	+	3.08006e6i	−0.177056	+	0.486457i
$186$	−4.10053e6	−	240103.i	−0.637238	−	0.0373129i
$187$	2.13290e6	−	1.20963e7i	0.326171	−	1.84981i
$188$			6.71808e6i			1.01105i
$189$	484070.	+	2.76030e6i	0.0717006	+	0.408856i
$190$	−119162.			−0.0173731
$191$	8.13036e6	+	1.43360e6i	1.16684	+	0.205745i	0.723314	−	0.690519i	$-0.242618\pi$
$191$	8.13036e6	+	1.43360e6i	1.16684	+	0.205745i	0.443522	+	0.896264i	$0.353729\pi$
$192$	−637054.	−	419280.i	−0.0900063	−	0.0592380i
$193$	8.86230e6	+	3.22561e6i	1.23275	+	0.448684i	0.874538	−	0.484957i	$-0.161165\pi$
$193$	8.86230e6	+	3.22561e6i	1.23275	+	0.448684i	0.358211	+	0.933641i	$0.383387\pi$
$194$	−8.33907e6	−	9.93811e6i	−1.14212	−	1.36113i
$195$	430978.	−	1.81593e6i	0.0581235	−	0.244904i
$196$	−3.52326e6	+	1.28236e6i	−0.467925	+	0.170311i
$197$	−4.99084e6	−	2.88146e6i	−0.652792	−	0.376889i	0.136733	−	0.990608i	$-0.456340\pi$
$197$	−4.99084e6	−	2.88146e6i	−0.652792	−	0.376889i	−0.789525	+	0.613718i	$0.789673\pi$
$198$	1.07271e6	+	1.86164e7i	0.138194	+	2.39829i
$199$	1.79973e6	+	3.11723e6i	0.228375	+	0.395557i	0.957327	−	0.289008i	$-0.0933254\pi$
$199$	1.79973e6	+	3.11723e6i	0.228375	+	0.395557i	−0.728952	+	0.684565i	$0.759992\pi$
$200$	1.09840e6	−	1.30902e6i	0.137300	−	0.163627i
$201$	−654392.	−	879570.i	−0.0805842	−	0.108313i
$202$	−744276.	−	4.22100e6i	−0.0902984	−	0.512107i
$203$	−3.15963e6	+	557128.i	−0.377701	+	0.0665989i
$204$	4.05495e6	−	3.01685e6i	0.477634	−	0.355355i
$205$	−6.42876e6	−	5.39437e6i	−0.746217	−	0.626151i
$206$	1.68476e7	−	9.72698e6i	1.92725	−	1.11270i
$207$	4.84120e6	+	7.37063e6i	0.545811	+	0.830986i
$208$	−1.84937e6	+	3.20321e6i	−0.205511	+	0.355955i
$209$	−107175.	−	294460.i	−0.0117396	−	0.0322542i
$210$	3.59355e6	+	852863.i	0.388030	+	0.0920919i
$211$	−8.40990e6	+	7.05675e6i	−0.895249	+	0.751203i	−0.969256	−	0.246055i	$-0.920866\pi$
$211$	−8.40990e6	+	7.05675e6i	−0.895249	+	0.751203i	0.0740074	+	0.997258i	$0.476421\pi$
$212$	3.65221e6	−	1.00344e7i	0.383309	−	1.05313i
$213$	−149652.	+	227381.i	−0.0154861	+	0.0235296i
$214$	2.52449e6	−	1.43171e7i	0.257592	−	1.46088i
$215$		−	613635.i		−	0.0617440i
$216$	3.26956e6	−	3.88917e6i	0.324436	−	0.385918i
$217$	−2.13940e6			−0.209369
$218$	1.85434e7	+	3.26970e6i	1.78986	+	0.315601i
$219$	502816.	−	8.58719e6i	0.0478715	−	0.817559i
$220$	8.67467e6	+	3.15732e6i	0.814676	+	0.296518i
$221$	−2.27633e6	−	2.71283e6i	−0.210891	−	0.251331i
$222$	−6.86577e6	−	6.48154e6i	−0.627524	−	0.592406i
$223$	1.99653e6	−	726678.i	0.180037	−	0.0655280i	−0.250429	−	0.968135i	$-0.580572\pi$
$223$	1.99653e6	−	726678.i	0.180037	−	0.0655280i	0.430466	+	0.902607i	$0.358349\pi$
$224$	−4.30178e6	−	2.48363e6i	−0.382740	−	0.220975i
$225$	−3.30949e6	−	3.51221e6i	−0.290545	−	0.308342i
$226$	−1.12635e7	−	1.95090e7i	−0.975771	−	1.69009i
$227$	121910.	−	145286.i	0.0104222	−	0.0124207i	−0.760808	−	0.648977i	$-0.775197\pi$
$227$	121910.	−	145286.i	0.0104222	−	0.0124207i	0.771230	+	0.636556i	$0.219642\pi$
$228$	51106.8	−	118378.i	0.00431195	−	0.00998772i
$229$	−156615.	−	888210.i	−0.0130415	−	0.0739621i	0.977592	−	0.210507i	$-0.0675114\pi$
$229$	−156615.	−	888210.i	−0.0130415	−	0.0739621i	−0.990634	+	0.136545i	$0.956400\pi$
$230$	1.14453e7	−	2.01812e6i	0.940688	−	0.165869i
$231$	1.12455e6	+	9.64705e6i	0.0912310	+	0.782633i
$232$	4.45603e6	+	3.73905e6i	0.356848	+	0.299431i
$233$	−6.44223e6	+	3.71942e6i	−0.509294	+	0.294041i	−0.732543	−	0.680720i	$-0.761667\pi$
$233$	−6.44223e6	+	3.71942e6i	−0.509294	+	0.294041i	0.223249	+	0.974761i	$0.428334\pi$
$234$	4.31047e6	+	3.21318e6i	0.336416	+	0.250777i
$235$	−8.27872e6	+	1.43392e7i	−0.637910	+	1.10489i
$236$	1.36750e6	+	3.75717e6i	0.104038	+	0.285841i
$237$	−521466.	−	1.74378e6i	−0.0391724	−	0.130993i
$238$	5.36841e6	−	4.50463e6i	0.398213	−	0.334140i
$239$	−2.60021e6	+	7.14402e6i	−0.190465	+	0.523298i	−0.997763	−	0.0668453i	$-0.978707\pi$
$239$	−2.60021e6	+	7.14402e6i	−0.190465	+	0.523298i	0.807298	+	0.590143i	$0.200929\pi$
$240$	−5.83530e6	−	1.16280e7i	−0.422114	−	0.841147i
$241$	−1.52112e6	+	8.62668e6i	−0.108670	+	0.616301i	0.881020	+	0.473079i	$0.156857\pi$
$241$	−1.52112e6	+	8.62668e6i	−0.108670	+	0.616301i	−0.989691	+	0.143222i	$0.954254\pi$
$242$			4.66902e7i			3.29442i
$243$	−9.83064e6	−	1.04523e7i	−0.685114	−	0.728436i
$244$	−1.16638e7			−0.802916
$245$	−9.10036e6	−	1.60464e6i	−0.618814	−	0.109114i
$246$	2.16065e7	−	1.08428e7i	1.45137	−	0.728344i
$247$	−84897.2	−	30900.1i	−0.00563381	−	0.00205054i
$248$	2.49327e6	+	2.97136e6i	0.163461	+	0.194805i
$249$	−2.56310e7	+	7.66476e6i	−1.66022	+	0.496478i
$250$	−2.00831e7	+	7.30965e6i	−1.28532	+	0.467817i
$251$	−2.29316e7	−	1.32396e7i	−1.45015	−	0.837245i	−0.451661	−	0.892189i	$-0.649168\pi$
$251$	−2.29316e7	−	1.32396e7i	−1.45015	−	0.837245i	−0.998489	+	0.0549446i	$0.982502\pi$
$252$	−2.38847e6	+	3.20413e6i	−0.149251	+	0.200220i
$253$	1.52809e7	+	2.64674e7i	0.943601	+	1.63436i
$254$	8.61169e6	−	1.02630e7i	0.525517	−	0.626287i
$255$	1.23726e7	−	1.44227e6i	0.746176	−	0.0869812i
$256$	3.73664e6	+	2.11915e7i	0.222721	+	1.26311i
$257$	6.58651e6	−	1.16138e6i	0.388022	−	0.0684187i	0.0237657	−	0.999718i	$-0.492434\pi$
$257$	6.58651e6	−	1.16138e6i	0.388022	−	0.0684187i	0.364256	+	0.931299i	$0.381323\pi$
$258$	1.62286e6	+	700631.i	0.0944981	+	0.0407972i
$259$	−3.76722e6	−	3.16108e6i	−0.216831	−	0.181943i
$260$	2.30497e6	−	1.33078e6i	0.131143	−	0.0757155i
$261$	1.19559e7	−	1.12658e7i	0.672451	−	0.633638i
$262$	−1.38026e6	+	2.39068e6i	−0.0767463	+	0.132928i
$263$	6.79907e6	+	1.86803e7i	0.373751	+	1.02687i	0.973899	+	0.226983i	$0.0728861\pi$
$263$	6.79907e6	+	1.86803e7i	0.373751	+	1.02687i	−0.600148	+	0.799889i	$0.704892\pi$
$264$	1.20880e7	−	1.28046e7i	0.656964	−	0.695909i
$265$	2.01607e7	−	1.69169e7i	1.08335	−	0.909039i
$266$	61148.1	−	168003.i	0.00324891	−	0.00892632i
$267$	−5.27863e6	−	309086.i	−0.277324	−	0.0162385i
$268$	271478.	−	1.53963e6i	0.0141036	−	0.0799857i
$269$			1.98444e7i			1.01949i	0.860327	+	0.509743i	$0.170260\pi$
$269$			1.98444e7i			1.01949i	−0.860327	+	0.509743i	$0.829740\pi$
$270$	−1.77763e7	+	6.45134e6i	−0.903129	+	0.327762i
$271$	−1.77711e7			−0.892907			−0.446454	−	0.894807i	$-0.647313\pi$
$271$	−1.77711e7			−0.892907			−0.446454	+	0.894807i	$0.647313\pi$
$272$	−2.43108e7	−	4.28666e6i	−1.20807	−	0.213016i
$273$	2.33908e6	+	1.53947e6i	0.114963	+	0.0756631i
$274$	−3.83842e7	−	1.39707e7i	−1.86595	−	0.679152i
$275$	−1.07505e7	−	1.28119e7i	−0.516929	−	0.616051i
$276$	−2.90389e6	+	1.22356e7i	−0.138119	+	0.581966i
$277$	3.51398e7	−	1.27899e7i	1.65333	−	0.601764i	0.664040	−	0.747697i	$-0.268841\pi$
$277$	3.51398e7	−	1.27899e7i	1.65333	−	0.601764i	0.989294	+	0.145933i	$0.0466184\pi$
$278$	2.58284e7	+	1.49120e7i	1.20216	+	0.694068i
$279$	9.15577e6	−	6.01373e6i	0.421582	−	0.276905i
$280$	−1.74385e6	−	3.02044e6i	−0.0794394	−	0.137593i
$281$	2.08127e6	−	2.48036e6i	0.0938014	−	0.111788i	−0.717102	−	0.696968i	$-0.754532\pi$
$281$	2.08127e6	−	2.48036e6i	0.0938014	−	0.111788i	0.810903	+	0.585180i	$0.198976\pi$
$282$	−2.84700e7	−	3.82666e7i	−1.26952	−	1.70637i
$283$	1.44560e6	+	8.19842e6i	0.0637807	+	0.361718i	0.999948	+	0.0101645i	$0.00323551\pi$
$283$	1.44560e6	+	8.19842e6i	0.0637807	+	0.361718i	−0.936168	+	0.351554i	$0.885653\pi$
$284$	−382287.	+	67407.5i	−0.0166892	+	0.00294275i
$285$	254961.	−	189689.i	0.0110138	−	0.00819420i
$286$	1.42735e7	+	1.19769e7i	0.610143	+	0.511971i
$287$	1.09043e7	−	6.29560e6i	0.461266	−	0.266312i
$288$	2.53912e7	−	1.46309e6i	1.06293	−	0.0612481i
$289$	−251115.	+	434944.i	−0.0104035	+	0.0180194i
$290$	−7.40478e6	−	2.03445e7i	−0.303611	−	0.834166i
$291$	3.36624e7	+	7.98915e6i	1.36605	+	0.324207i
$292$	9.39690e6	−	7.88493e6i	0.377430	−	0.316701i
$293$	1.20558e7	−	3.31231e7i	0.479285	−	1.31683i	−0.430816	−	0.902440i	$-0.641774\pi$
$293$	1.20558e7	−	3.31231e7i	0.479285	−	1.31683i	0.910101	−	0.414386i	$-0.136004\pi$
$294$	1.46343e7	−	2.22353e7i	0.575877	−	0.874987i
$295$	−1.71117e6	+	9.70452e6i	−0.0666541	+	0.378014i
$296$			8.91613e6i			0.343796i
$297$	−3.19299e7	−	3.81244e7i	−1.21879	−	1.45524i
$298$	−9.65161e6			−0.364713
$299$	8.67759e6	+	1.53009e6i	0.324628	+	0.0572406i
$300$	402272.	−	6.87008e6i	0.0148990	−	0.254447i
$301$	865147.	+	314888.i	0.0317242	+	0.0115467i
$302$	2.66260e7	+	3.17316e7i	0.966685	+	1.15205i
$303$	8.31168e6	+	7.84653e6i	0.298786	+	0.282065i
$304$	−591798.	+	215397.i	−0.0210646	+	0.00766688i
$305$	−2.48954e7	−	1.43733e7i	−0.877443	−	0.506592i
$306$	−1.03124e7	+	3.43683e7i	−0.359911	+	1.19948i
$307$	−9.02470e6	−	1.56312e7i	−0.311902	−	0.540230i	0.666872	−	0.745172i	$-0.267633\pi$
$307$	−9.02470e6	−	1.56312e7i	−0.311902	−	0.540230i	−0.978774	+	0.204942i	$0.934299\pi$
$308$	−8.90284e6	+	1.06100e7i	−0.304703	+	0.363131i
$309$	−2.05635e7	+	4.76310e7i	−0.696982	+	1.61441i
$310$	−2.50691e6	−	1.42174e7i	−0.0841498	−	0.477237i
$311$	9.81559e6	−	1.73075e6i	0.326314	−	0.0575379i	−0.00809160	−	0.999967i	$-0.502576\pi$
$311$	9.81559e6	−	1.73075e6i	0.326314	−	0.0575379i	0.334405	+	0.942429i	$0.391465\pi$
$312$	−587834.	−	5.04279e6i	−0.0193549	−	0.166038i
$313$	−4.19324e6	−	3.51855e6i	−0.136747	−	0.114744i	0.571849	−	0.820359i	$-0.306226\pi$
$313$	−4.19324e6	−	3.51855e6i	−0.136747	−	0.114744i	−0.708595	+	0.705615i	$0.750671\pi$
$314$	2.91880e7	−	1.68517e7i	0.942790	−	0.544320i
$315$	−9.04645e6	+	3.89561e6i	−0.289432	+	0.124636i
$316$	1.29777e6	−	2.24780e6i	0.0411279	−	0.0712355i
$317$	−4.37930e6	−	1.20320e7i	−0.137476	−	0.377712i	0.851781	−	0.523898i	$-0.175523\pi$
$317$	−4.37930e6	−	1.20320e7i	−0.137476	−	0.377712i	−0.989257	+	0.146185i	$0.953300\pi$
$318$	2.17206e7	+	7.26338e7i	0.675446	+	2.25869i
$319$	4.36131e7	−	3.65957e7i	1.34352	−	1.12735i
$320$	916771.	−	2.51881e6i	0.0279776	−	0.0768679i
$321$	1.73893e7	+	3.46517e7i	0.525736	+	1.04764i
$322$	−3.02790e6	+	1.71721e7i	−0.0906930	+	0.514346i
$323$		−	602978.i		−	0.0178934i
$324$	1.21509e6	−	2.04262e7i	0.0357250	−	0.600555i
$325$	−4.82202e6			−0.140468
$326$	−2.30314e7	−	4.06106e6i	−0.664764	−	0.117216i
$327$	−4.48806e7	+	2.25225e7i	−1.28356	+	0.644129i
$328$	−2.14517e7	−	7.80777e6i	−0.607911	−	0.221261i
$329$	−1.59681e7	−	1.90301e7i	−0.448401	−	0.534384i
$330$	−6.27916e7	+	1.87774e7i	−1.74727	+	0.522508i
$331$	−1.02584e7	+	3.73374e6i	−0.282874	+	0.102958i	−0.479561	−	0.877509i	$-0.659204\pi$
$331$	−1.02584e7	+	3.73374e6i	−0.282874	+	0.102958i	0.196687	+	0.980466i	$0.436982\pi$
$332$	−3.30393e7	−	1.90752e7i	−0.902851	−	0.521262i
$333$	2.50078e7	+	2.93869e6i	0.677240	+	0.0795833i
$334$	−1.20207e7	−	2.08204e7i	−0.322618	−	0.558791i
$335$	2.47674e6	−	2.95167e6i	0.0658789	−	0.0785114i
$336$	1.93884e7	−	2.26009e6i	0.511122	−	0.0595811i
$337$	4.54260e6	+	2.57624e7i	0.118690	+	0.673125i	0.984857	+	0.173370i	$0.0554656\pi$
$337$	4.54260e6	+	2.57624e7i	0.118690	+	0.673125i	−0.866167	+	0.499755i	$0.833423\pi$
$338$	−4.28356e7	+	7.55308e6i	−1.10932	+	0.195602i
$339$	5.51550e7	+	2.38118e7i	1.41575	+	0.611214i
$340$	1.36076e7	+	1.14182e7i	0.346215	+	0.290509i
$341$	3.28777e7	−	1.89819e7i	0.829159	−	0.478715i
$342$	210557.	+	890869.i	0.00526370	+	0.0222708i
$343$	1.53075e7	−	2.65134e7i	0.379334	−	0.657026i
$344$	−570906.	−	1.56855e6i	−0.0140246	−	0.0385321i
$345$	−2.12761e7	+	2.25373e7i	−0.518125	+	0.548839i
$346$	−3.94015e7	+	3.30618e7i	−0.951227	+	0.798175i
$347$	−9.54635e6	+	2.62284e7i	−0.228480	+	0.627745i	−0.999964	−	0.00850455i	$-0.997293\pi$
$347$	−9.54635e6	+	2.62284e7i	−0.228480	+	0.627745i	0.771483	+	0.636250i	$0.219515\pi$
$348$	2.33864e7	+	1.36937e6i	0.554914	+	0.0324925i
$349$	9933.24	−	56334.2i	0.000233676	−	0.00132524i	−0.984691	−	0.174311i	$-0.944230\pi$
$349$	9933.24	−	56334.2i	0.000233676	−	0.00132524i	0.984924	+	0.172986i	$0.0553414\pi$
$350$		−	9.54229e6i		−	0.222561i
$351$	−1.43377e7	−	13322.9i	−0.331556	−	0.000308090i
$352$	8.81444e7			2.02100
$353$	−2.73231e7	−	4.81780e6i	−0.621164	−	0.109528i	−0.145795	−	0.989315i	$-0.546574\pi$
$353$	−2.73231e7	−	4.81780e6i	−0.621164	−	0.109528i	−0.475368	+	0.879787i	$0.657685\pi$
$354$	−2.37115e7	−	1.56058e7i	−0.534502	−	0.351785i
$355$	−899025.	−	327218.i	−0.0200949	−	0.00731396i
$356$	−4.84694e6	−	5.77636e6i	−0.107428	−	0.128028i
$357$	−4.31562e6	+	1.81839e7i	−0.0948502	+	0.399653i
$358$	3.12163e7	−	1.13618e7i	0.680350	−	0.247627i
$359$	−3.18617e7	−	1.83954e7i	−0.688630	−	0.397581i	0.114469	−	0.993427i	$-0.463483\pi$
$359$	−3.18617e7	−	1.83954e7i	−0.688630	−	0.397581i	−0.803099	+	0.595846i	$0.796817\pi$
$360$	1.59533e7	+	8.02441e6i	0.341934	+	0.171991i
$361$	2.35152e7	+	4.07296e7i	0.499837	+	0.865742i
$362$	−4.22486e6	+	5.03500e6i	−0.0890609	+	0.106139i
$363$	−7.43240e7	−	9.98990e7i	−1.55385	−	2.08853i
$364$	693424.	+	3.93260e6i	0.0143779	+	0.0815410i
$365$	2.97735e7	−	5.24987e6i	0.612282	−	0.107962i
$366$	6.64376e7	−	4.94290e7i	1.35510	−	1.00818i
$367$	−5.33099e7	−	4.47324e7i	−1.07847	−	0.904948i	−0.0826816	−	0.996576i	$-0.526348\pi$
$367$	−5.33099e7	−	4.47324e7i	−1.07847	−	0.904948i	−0.995793	+	0.0916281i	$0.970793\pi$
$368$	5.31935e7	−	3.07113e7i	1.06737	−	0.616246i
$369$	−2.89694e7	+	5.75939e7i	−0.576582	+	1.14630i
$370$	1.65925e7	−	2.87391e7i	0.327573	−	0.567373i
$371$	1.35051e7	+	3.71050e7i	0.264470	+	0.726625i
$372$	1.51990e7	+	3.60720e6i	0.295248	+	0.0700715i
$373$	1.18708e7	−	9.96079e6i	0.228746	−	0.191941i	−0.521210	−	0.853429i	$-0.674519\pi$
$373$	1.18708e7	−	9.96079e6i	0.228746	−	0.191941i	0.749956	+	0.661488i	$0.230075\pi$
$374$	−4.25326e7	+	1.16857e8i	−0.813030	+	2.23378i
$375$	3.13342e7	−	4.76092e7i	0.594189	−	0.902811i
$376$	−7.82107e6	+	4.43555e7i	−0.147130	+	0.834418i
$377$		−	1.64146e7i		−	0.306342i
$378$	26364.7	−	2.83728e7i	0.000488144	−	0.525323i
$379$	8.36659e7			1.53685			0.768424	−	0.639941i	$-0.221041\pi$
$379$	8.36659e7			1.53685			0.768424	+	0.639941i	$0.221041\pi$
$380$	446292.	+	78693.4i	0.00813334	+	0.00143413i
$381$	−2.08848e6	+	3.56674e7i	−0.0377620	+	0.644907i
$382$	−7.85441e7	−	2.85877e7i	−1.40904	−	0.512849i
$383$	3.74148e7	+	4.45892e7i	0.665958	+	0.793658i	0.988228	−	0.152990i	$-0.0488901\pi$
$383$	3.74148e7	+	4.45892e7i	0.665958	+	0.793658i	−0.322269	+	0.946648i	$0.604446\pi$
$384$	−3.82232e7	−	3.60841e7i	−0.675046	−	0.637269i
$385$	−3.20771e7	+	1.16751e7i	−0.562099	+	0.204587i
$386$	−8.26915e7	−	4.77419e7i	−1.43780	−	0.830115i
$387$	−4.58761e6	+	1.08428e6i	−0.0791504	+	0.0187072i
$388$	2.46689e7	+	4.27279e7i	0.422333	+	0.731503i
$389$	−4.28033e7	+	5.10110e7i	−0.727158	+	0.866593i	−0.995305	−	0.0967851i	$-0.969144\pi$
$389$	−4.28033e7	+	5.10110e7i	−0.727158	+	0.866593i	0.268148	+	0.963378i	$0.413588\pi$
$390$	−7.48967e6	+	1.73482e7i	−0.126261	+	0.292456i
$391$	1.02120e7	+	5.79152e7i	0.170837	+	0.968863i
$392$	−2.47549e7	+	4.36496e6i	−0.410963	+	0.0724639i
$393$	−852391.	−	7.31232e6i	−0.0140430	−	0.120470i
$394$	4.46957e7	+	3.75042e7i	0.730764	+	0.613184i
$395$	5.53995e6	−	3.19849e6i	0.0898907	−	0.0518984i
$396$	8.27653e6	−	7.04318e7i	0.133279	−	1.13418i
$397$	1.99741e7	−	3.45961e7i	0.319224	−	0.552911i	−0.661103	−	0.750295i	$-0.729911\pi$
$397$	1.99741e7	−	3.45961e7i	0.319224	−	0.552911i	0.980326	+	0.197384i	$0.0632446\pi$
$398$	−1.24640e7	−	3.42447e7i	−0.197701	−	0.543180i
$399$	136603.	+	456801.i	0.00215051	+	0.00719131i
$400$	−2.57492e7	+	2.16061e7i	−0.402330	+	0.337595i
$401$	3.17423e7	−	8.72114e7i	0.492273	−	1.35251i	−0.406322	−	0.913730i	$-0.633189\pi$
$401$	3.17423e7	−	8.72114e7i	0.492273	−	1.35251i	0.898595	−	0.438779i	$-0.144589\pi$
$402$	4.97832e6	+	9.92030e6i	0.0766310	+	0.152703i
$403$	1.90068e6	−	1.07793e7i	0.0290397	−	0.164693i
$404$			1.63002e7i			0.247201i
$405$	2.77648e7	−	4.21006e7i	0.417955	−	0.633758i
$406$	3.24829e7			0.485374
$407$	8.59403e7	+	1.51536e7i	1.27472	+	0.224767i
$408$	3.02846e7	−	1.51977e7i	0.445904	−	0.223768i
$409$	−4.46234e7	−	1.62416e7i	−0.652218	−	0.237388i	−0.00534478	−	0.999986i	$-0.501701\pi$
$409$	−4.46234e7	−	1.62416e7i	−0.652218	−	0.237388i	−0.646873	+	0.762598i	$0.723924\pi$
$410$	5.46147e7	+	6.50873e7i	0.792425	+	0.944375i
$411$	1.04367e8	−	3.12101e7i	1.50327	−	0.449542i
$412$	−6.95224e7	+	2.53041e7i	−0.994106	+	0.361825i
$413$	−1.28040e7	−	7.39242e6i	−0.181760	−	0.104939i
$414$	−3.53114e7	−	8.20008e7i	−0.497639	−	1.15563i
$415$	−4.70130e7	−	8.14289e7i	−0.657770	−	1.13929i
$416$	1.63354e7	−	1.94678e7i	0.226908	−	0.270419i
$417$	−7.90005e7	+	9.20903e6i	−1.08949	+	0.127001i
$418$	550909.	+	3.12436e6i	0.00754311	+	0.0427791i
$419$	6.76442e7	−	1.19275e7i	0.919578	−	0.162146i	0.306228	−	0.951958i	$-0.400933\pi$
$419$	6.76442e7	−	1.19275e7i	0.919578	−	0.162146i	0.613349	+	0.789812i	$0.289822\pi$
$420$	−1.28956e7	−	5.56734e6i	−0.174057	−	0.0751449i
$421$	−1.86100e7	−	1.56156e7i	−0.249402	−	0.209273i	0.509513	−	0.860463i	$-0.329826\pi$
$421$	−1.86100e7	−	1.56156e7i	−0.249402	−	0.209273i	−0.758915	+	0.651190i	$0.774270\pi$
$422$	9.62580e7	−	5.55746e7i	1.28085	−	0.739501i
$423$	1.21830e8	+	3.65556e7i	1.60965	+	0.482985i
$424$	3.57952e7	−	6.19991e7i	0.469599	−	0.813370i
$425$	−1.10071e7	−	3.02418e7i	−0.143386	−	0.393950i
$426$	1.89187e6	−	2.00402e6i	0.0244716	−	0.0259223i
$427$	3.30397e7	−	2.77236e7i	0.424377	−	0.356095i
$428$	−1.89098e7	+	5.19542e7i	−0.241188	+	0.662657i
$429$	−4.96052e7	−	2.90459e6i	−0.628283	−	0.0367886i
$430$	−1.07882e6	+	6.11830e6i	−0.0135689	+	0.0769530i
$431$		−	2.49856e7i		−	0.312074i	−0.987751	−	0.156037i	$-0.950128\pi$
$431$		−	2.49856e7i		−	0.312074i	0.987751	−	0.156037i	$-0.0498720\pi$
$432$	−7.66216e7	+	6.41719e7i	−0.950385	+	0.795964i
$433$	−1.32089e8			−1.62705			−0.813526	−	0.581529i	$-0.802455\pi$
$433$	−1.32089e8			−1.62705			−0.813526	+	0.581529i	$0.802455\pi$
$434$	2.13311e7	+	3.76125e6i	0.260942	+	0.0460111i
$435$	4.82288e7	+	3.17420e7i	0.585921	+	0.385626i
$436$	−6.72905e7	−	2.44918e7i	−0.811885	−	0.295502i
$437$	964380.	+	1.14930e6i	0.0115559	+	0.0137718i
$438$	−2.01104e7	+	8.47354e7i	−0.239330	+	1.00842i
$439$	−8.38973e7	+	3.05361e7i	−0.991641	+	0.360928i	−0.786356	−	0.617774i	$-0.788035\pi$
$439$	−8.38973e7	+	3.05361e7i	−0.991641	+	0.360928i	−0.205286	+	0.978702i	$0.565812\pi$
$440$	5.35980e7	+	3.09448e7i	0.629203	+	0.363270i
$441$	4.08370e6	+	7.08707e7i	0.0476144	+	0.826325i
$442$	1.79270e7	+	3.10505e7i	0.207606	+	0.359585i
$443$	−8.53181e7	+	1.01678e8i	−0.981364	+	1.16954i	0.00415751	+	0.999991i	$0.498677\pi$
$443$	−8.53181e7	+	1.01678e8i	−0.981364	+	1.16954i	−0.985521	+	0.169552i	$0.945768\pi$
$444$	2.14337e7	+	2.88091e7i	0.244878	+	0.329141i
$445$	−3.22715e6	−	1.83021e7i	−0.0366217	−	0.207692i
$446$	−2.11841e7	+	3.73534e6i	−0.238785	+	0.0421042i
$447$	2.06507e7	−	1.53640e7i	0.231213	−	0.172021i
$448$	3.08075e6	+	2.58506e6i	0.0342628	+	0.0287499i
$449$	−3.23233e7	+	1.86619e7i	−0.357089	+	0.206166i	−0.667803	−	0.744338i	$-0.732765\pi$
$449$	−3.23233e7	+	1.86619e7i	−0.357089	+	0.206166i	0.310714	+	0.950504i	$0.399432\pi$
$450$	2.68228e7	+	4.08371e7i	0.294351	+	0.448144i
$451$	−1.11716e8	+	1.93497e8i	−1.21783	+	2.10934i
$452$	2.93012e7	+	8.05044e7i	0.317300	+	0.871775i
$453$	−1.07482e8	−	2.55088e7i	−1.15622	−	0.274407i
$454$	−1.47094e6	+	1.23426e6i	−0.0157191	+	0.0131899i
$455$	−3.36611e6	+	9.24832e6i	−0.0357350	+	0.0981812i
$456$	475241.	−	722082.i	0.00501210	−	0.00761538i
$457$	−1.03006e7	+	5.84174e7i	−0.107923	+	0.612059i	0.882090	+	0.471081i	$0.156136\pi$
$457$	−1.03006e7	+	5.84174e7i	−0.107923	+	0.612059i	−0.990013	+	0.140979i	$0.954975\pi$
$458$			9.13132e6i			0.0950467i
$459$	−3.26448e7	−	8.99507e7i	−0.337579	−	0.930179i
$460$	−4.41985e7			−0.454082
$461$	−2.12064e7	−	3.73926e6i	−0.216453	−	0.0381666i	0.0643697	−	0.997926i	$-0.479496\pi$
$461$	−2.12064e7	−	3.73926e6i	−0.216453	−	0.0381666i	−0.280823	+	0.959760i	$0.590607\pi$
$462$	5.74790e6	−	9.81638e7i	0.0582885	−	0.995463i
$463$	2.25228e7	+	8.19764e6i	0.226924	+	0.0825935i	0.452980	−	0.891521i	$-0.350361\pi$
$463$	2.25228e7	+	8.19764e6i	0.226924	+	0.0825935i	−0.226056	+	0.974114i	$0.572583\pi$
$464$	−7.35492e7	−	8.76526e7i	−0.736248	−	0.877427i
$465$	2.79958e7	+	2.64291e7i	0.278442	+	0.262859i
$466$	7.07719e7	−	2.57589e7i	0.699363	−	0.254547i
$467$	1.47125e8	+	8.49425e7i	1.44456	+	0.834016i	0.998149	−	0.0608139i	$-0.0193696\pi$
$467$	1.47125e8	+	8.49425e7i	1.44456	+	0.834016i	0.446408	+	0.894829i	$0.352703\pi$
$468$	−1.40219e7	−	1.48808e7i	−0.136794	−	0.145174i
$469$	2.89053e6	+	5.00654e6i	0.0280194	+	0.0485310i
$470$	1.07753e8	−	1.28415e8i	1.03785	−	1.23687i
$471$	−3.56256e7	+	8.25191e7i	−0.340957	+	0.789754i
$472$	4.65474e6	+	2.63984e7i	0.0442659	+	0.251045i
$473$	−1.60892e7	+	2.83695e6i	−0.152037	+	0.0268083i
$474$	2.13360e6	+	1.83033e7i	0.0200345	+	0.171868i
$475$	−628950.	−	527751.i	−0.00586861	−	0.00492435i
$476$	−2.30809e7	+	1.33258e7i	−0.214009	+	0.123558i
$477$	−1.62096e8	−	1.20832e8i	−1.49354	−	1.11334i
$478$	3.84854e7	−	6.66587e7i	0.352381	−	0.610342i
$479$	1.09566e7	+	3.01031e7i	0.0996944	+	0.273908i	0.979506	−	0.201414i	$-0.0645537\pi$
$479$	1.09566e7	+	3.01031e7i	0.0996944	+	0.273908i	−0.879812	+	0.475322i	$0.842331\pi$
$480$	2.56107e7	+	8.56422e7i	0.231578	+	0.774398i
$481$	1.92738e7	−	1.61726e7i	0.173193	−	0.145327i
$482$	3.03329e7	−	8.33388e7i	0.270877	−	0.744229i
$483$	−2.08569e7	−	4.15616e7i	−0.185101	−	0.368851i
$484$	3.08337e7	−	1.74867e8i	0.271951	−	1.54231i
$485$			1.21599e8i			1.06587i
$486$	7.96413e7	+	1.21498e8i	0.693793	+	1.05843i
$487$	−2.29636e7			−0.198817			−0.0994085	−	0.995047i	$-0.531695\pi$
$487$	−2.29636e7			−0.198817			−0.0994085	+	0.995047i	$0.531695\pi$
$488$	−7.70091e7	−	1.35788e7i	−0.662647	−	0.116843i
$489$	5.57430e7	−	2.79735e7i	0.476720	−	0.239233i
$490$	8.79148e7	+	3.19984e7i	0.747264	+	0.271982i
$491$	−3.71786e7	−	4.43077e7i	−0.314086	−	0.374313i	0.585787	−	0.810465i	$-0.300786\pi$
$491$	−3.71786e7	−	4.43077e7i	−0.314086	−	0.374313i	−0.899873	+	0.436152i	$0.856341\pi$
$492$	−8.80825e7	+	2.63404e7i	−0.739595	+	0.221171i
$493$	1.02946e8	−	3.74693e7i	0.859150	−	0.312705i
$494$	792150.	+	457348.i	0.00657093	+	0.00379373i
$495$	1.04459e8	−	1.40131e8i	0.861252	−	1.15537i
$496$	−3.81494e7	−	6.60768e7i	−0.312639	−	0.541506i
$497$	922672.	−	1.09960e6i	0.00751585	−	0.00895704i
$498$	2.69031e8	−	3.13608e7i	2.17828	−	0.253921i
$499$	−3.38252e7	−	1.91832e8i	−0.272232	−	1.54390i	−0.747620	−	0.664127i	$-0.768803\pi$
$499$	−3.38252e7	−	1.91832e8i	−0.272232	−	1.54390i	0.475388	−	0.879776i	$-0.342308\pi$
$500$	8.00436e7	−	1.41138e7i	0.640349	−	0.112911i
$501$	5.88627e7	+	2.54125e7i	0.468087	+	0.202085i
$502$	2.05365e8	+	1.72322e8i	1.62336	+	1.36216i
$503$	−1.32381e8	+	7.64301e7i	−1.04021	+	0.600566i	−0.919893	−	0.392170i	$-0.871725\pi$
$503$	−1.32381e8	+	7.64301e7i	−1.04021	+	0.600566i	−0.120318	+	0.992735i	$0.538391\pi$
$504$	−1.94998e7	+	1.83743e7i	−0.152314	+	0.143522i
$505$	−2.00869e7	+	3.47915e7i	−0.155969	+	0.270146i
$506$	−1.05828e8	−	2.90760e8i	−0.816863	−	2.24431i
$507$	7.96284e7	−	8.43488e7i	0.611004	−	0.647225i
$508$	−3.90306e7	+	3.27506e7i	−0.297724	+	0.249820i
$509$	1.62115e7	−	4.45409e7i	0.122934	−	0.337758i	−0.862926	−	0.505330i	$-0.831371\pi$
$509$	1.62115e7	−	4.45409e7i	0.122934	−	0.337758i	0.985860	+	0.167573i	$0.0535929\pi$
$510$	−1.25898e8	−	7.37185e6i	−0.949092	−	0.0555733i
$511$	−7.87667e6	+	4.46708e7i	−0.0590310	+	0.334781i
$512$		−	9.32630e7i		−	0.694864i
$513$	−1.86864e6	−	1.57094e6i	−0.0138412	−	0.0116361i
$514$	−6.77132e7			−0.498636
$515$	−1.79572e8	−	3.16634e7i	−1.31467	−	0.231812i
$516$	−5.61536e6	−	3.69577e6i	−0.0408722	−	0.0269002i
$517$	4.14239e8	+	1.50771e8i	2.99764	+	1.09105i
$518$	3.20040e7	+	3.81409e7i	0.230258	+	0.274411i
$519$	3.16745e7	−	1.33461e8i	0.226573	−	0.954667i
$520$	1.67676e7	−	6.10291e6i	0.119251	−	0.0434037i
$521$	−1.50479e8	−	8.68789e7i	−1.06405	−	0.614330i	−0.137500	−	0.990502i	$-0.543907\pi$
$521$	−1.50479e8	−	8.68789e7i	−1.06405	−	0.614330i	−0.926550	+	0.376172i	$0.877240\pi$
$522$	−1.39014e8	+	9.13073e7i	−0.977340	+	0.641939i
$523$	1.79872e7	+	3.11547e7i	0.125736	+	0.217781i	0.922020	−	0.387142i	$-0.126538\pi$
$523$	1.79872e7	+	3.11547e7i	0.125736	+	0.217781i	−0.796285	+	0.604922i	$0.793204\pi$
$524$	6.74822e6	−	8.04222e6i	0.0469024	−	0.0558961i
$525$	1.51899e7	+	2.04168e7i	0.104973	+	0.141095i
$526$	−3.49492e7	−	1.98207e8i	−0.240148	−	1.36195i
$527$	7.19421e7	−	1.26853e7i	0.491531	−	0.0866702i
$528$	−2.77902e8	+	2.06757e8i	−1.88795	+	1.40462i
$529$	1.31007e6	+	1.09928e6i	0.00884971	+	0.00742579i
$530$	−2.30756e8	+	1.33227e8i	−1.54998	+	0.894879i
$531$	7.55758e7	−	4.35481e6i	0.504776	−	0.0290861i
$532$	−339963.	+	588834.i	−0.00225786	+	0.00391073i
$533$	2.20325e7	+	6.05338e7i	0.145506	+	0.399776i
$534$	5.20877e7	+	1.23620e7i	0.342067	+	0.0811833i
$535$	−1.04385e8	+	8.75891e7i	−0.681672	+	0.571991i
$536$	3.58482e6	−	9.84921e6i	0.0232795	−	0.0639598i
$537$	−4.87045e7	+	7.40017e7i	−0.314519	+	0.477880i
$538$	3.48881e7	−	1.97860e8i	0.224043	−	1.27061i
$539$			2.46025e8i			1.57113i
$540$	7.08372e7	−	1.24227e7i	0.449863	−	0.0788920i
$541$	−1.02622e7			−0.0648111			−0.0324056	−	0.999475i	$-0.510317\pi$
$541$	−1.02622e7			−0.0648111			−0.0324056	+	0.999475i	$0.510317\pi$
$542$	1.77188e8	+	3.12431e7i	1.11285	+	0.196226i
$543$	1.02460e6	−	1.74983e7i	0.00639963	−	0.109294i
$544$	1.59383e8	+	5.80107e7i	0.990023	+	0.360339i
$545$	−1.13445e8	−	1.35198e8i	−0.700800	−	0.835181i
$546$	−2.06154e7	−	1.94617e7i	−0.126653	−	0.119565i
$547$	1.37063e8	−	4.98867e7i	0.837447	−	0.304806i	0.112535	−	0.993648i	$-0.464103\pi$
$547$	1.37063e8	−	4.98867e7i	0.837447	−	0.304806i	0.724911	+	0.688842i	$0.241881\pi$
$548$	1.34533e8	+	7.76725e7i	0.817497	+	0.471982i
$549$	−6.34672e7	+	2.11518e8i	−0.383559	+	1.27829i
$550$	8.46643e7	+	1.46643e8i	0.508876	+	0.881400i
$551$	1.79652e6	−	2.14100e6i	0.0107393	−	0.0127986i
$552$	−3.34171e7	+	7.74036e7i	−0.198679	+	0.460197i
$553$	1.66663e6	+	9.45194e6i	0.00985517	+	0.0558915i
$554$	−3.72851e8	+	6.57436e7i	−2.19283	+	0.386656i
$555$	1.02469e7	+	8.79036e7i	0.0599393	+	0.514195i
$556$	−8.68862e7	−	7.29062e7i	−0.505506	−	0.424170i
$557$	−4.76277e7	+	2.74979e7i	−0.275609	+	0.159123i	−0.631434	−	0.775430i	$-0.717533\pi$
$557$	−4.76277e7	+	2.74979e7i	−0.275609	+	0.159123i	0.355825	+	0.934553i	$0.384200\pi$
$558$	−1.01861e8	+	4.38638e7i	−0.586281	+	0.252466i
$559$	−2.35515e6	+	4.07925e6i	−0.0134829	+	0.0233531i
$560$	2.34644e7	+	6.44678e7i	0.133612	+	0.367095i
$561$	−9.50164e7	−	3.17735e8i	−0.538158	−	1.79960i
$562$	−2.51122e7	+	2.10716e7i	−0.141473	+	0.118710i
$563$	7.37539e7	−	2.02637e8i	0.413295	−	1.13552i	−0.542133	−	0.840293i	$-0.682383\pi$
$563$	7.37539e7	−	2.02637e8i	0.413295	−	1.13552i	0.955428	−	0.295225i	$-0.0953948\pi$
$564$	8.13566e7	+	1.62120e8i	0.453477	+	0.903645i
$565$	−3.66651e7	+	2.07938e8i	−0.203286	+	1.15289i
$566$		−	8.42845e7i		−	0.464835i
$567$	4.51090e7	+	6.07488e7i	0.247465	+	0.333264i
$568$	−2.60249e6			−0.0142018
$569$	1.56179e8	+	2.75386e7i	0.847785	+	0.149487i	0.580631	−	0.814167i	$-0.302806\pi$
$569$	1.56179e8	+	2.75386e7i	0.847785	+	0.149487i	0.267153	+	0.963654i	$0.413917\pi$
$570$	−2.87560e6	+	1.44306e6i	−0.0155276	+	0.00779221i
$571$	−3.79068e7	−	1.37969e7i	−0.203615	−	0.0741096i	0.238200	−	0.971216i	$-0.423443\pi$
$571$	−3.79068e7	−	1.37969e7i	−0.203615	−	0.0741096i	−0.441814	+	0.897107i	$0.645665\pi$
$572$	−4.55485e7	−	5.42826e7i	−0.243381	−	0.290050i
$573$	2.13562e8	−	6.38641e7i	1.13517	−	0.339463i
$574$	−1.19790e8	+	4.36001e7i	−0.633412	+	0.230543i
$575$	6.93478e7	+	4.00379e7i	0.364778	+	0.210605i
$576$	−2.04508e7	−	2.40320e6i	−0.107015	−	0.0125754i
$577$	−3.44340e7	−	5.96414e7i	−0.179250	−	0.310470i	0.762374	−	0.647137i	$-0.224034\pi$
$577$	−3.44340e7	−	5.96414e7i	−0.179250	−	0.310470i	−0.941624	+	0.336667i	$0.890700\pi$
$578$	3.26843e6	−	3.89517e6i	0.0169261	−	0.0201717i
$579$	2.52926e8	−	2.94834e7i	1.30304	−	0.151895i
$580$	1.42975e7	+	8.10854e7i	0.0732786	+	0.415584i
$581$	1.38929e8	−	2.44970e7i	0.708378	−	0.124906i
$582$	−3.21589e8	−	1.38838e8i	−1.63129	−	0.704270i
$583$	−5.36758e8	−	4.50393e8i	−2.70877	−	2.27293i
$584$	7.12216e7	−	4.11198e7i	0.357580	−	0.206449i
$585$	−1.15908e7	−	4.90410e7i	−0.0578959	−	0.244958i
$586$	−1.78437e8	+	3.09062e8i	−0.886731	+	1.53586i
$587$	9.28254e7	+	2.55036e8i	0.458937	+	1.26092i	0.926278	+	0.376841i	$0.122990\pi$
$587$	9.28254e7	+	2.55036e8i	0.458937	+	1.26092i	−0.467341	+	0.884077i	$0.654788\pi$
$588$	−6.94932e7	+	7.36128e7i	−0.341830	+	0.362094i
$589$	1.42766e6	−	1.19795e6i	0.00698681	−	0.00586263i
$590$	3.41227e7	−	9.37514e7i	0.166145	−	0.456480i
$591$	−1.55333e8	−	9.09538e6i	−0.752490	−	0.0440614i
$592$	3.04553e7	−	1.72721e8i	0.146791	−	0.832491i
$593$		−	3.09822e8i		−	1.48576i	−0.669426	−	0.742879i	$-0.733460\pi$
$593$		−	3.09822e8i		−	1.48576i	0.669426	−	0.742879i	$-0.266540\pi$
$594$	2.51334e8	+	4.36258e8i	1.19920	+	2.08154i
$595$	−6.56857e7			−0.311831
$596$	3.61478e7	+	6.37383e6i	0.170743	+	0.0301066i
$597$	8.11808e7	+	5.34295e7i	0.381532	+	0.251107i
$598$	−8.38306e7	−	3.05118e7i	−0.392012	−	0.142681i
$599$	9.08134e7	+	1.08227e8i	0.422542	+	0.503566i	0.934755	−	0.355293i	$-0.115619\pi$
$599$	9.08134e7	+	1.08227e8i	0.422542	+	0.503566i	−0.512213	+	0.858858i	$0.671174\pi$
$600$	1.06540e7	−	4.48907e7i	0.0493240	−	0.207827i
$601$	1.37922e8	−	5.01997e7i	0.635348	−	0.231248i	−0.00420951	−	0.999991i	$-0.501340\pi$
$601$	1.37922e8	−	5.01997e7i	0.635348	−	0.231248i	0.639557	+	0.768743i	$0.279118\pi$
$602$	−8.07242e6	−	4.66061e6i	−0.0370011	−	0.0213626i
$603$	−2.64434e7	−	1.33009e7i	−0.120605	−	0.0606636i
$604$	−7.87660e7	−	1.36427e8i	−0.357460	−	0.619140i
$605$	2.81301e8	−	3.35242e8i	1.27030	−	1.51388i
$606$	−6.90775e7	−	9.28472e7i	−0.310398	−	0.417206i
$607$	1.72497e6	+	9.78277e6i	0.00771284	+	0.0437417i	0.988421	−	0.151735i	$-0.0484859\pi$
$607$	1.72497e6	+	9.78277e6i	0.00771284	+	0.0437417i	−0.980708	+	0.195476i	$0.937375\pi$
$608$	4.26135e6	−	751391.i	0.0189599	−	0.00334314i
$609$	−6.95008e7	+	5.17080e7i	−0.307708	+	0.228932i
$610$	2.22952e8	+	1.87079e8i	0.982249	+	0.824205i
$611$	1.10069e8	−	6.35481e7i	0.482547	−	0.278599i
$612$	6.13191e7	−	1.21908e8i	0.267511	−	0.531836i
$613$	8.53880e7	−	1.47896e8i	0.370694	−	0.642060i	−0.618979	−	0.785408i	$-0.712453\pi$
$613$	8.53880e7	−	1.47896e8i	0.370694	−	0.642060i	0.989672	+	0.143347i	$0.0457866\pi$
$614$	6.25005e7	+	1.71719e8i	0.270009	+	0.741844i
$615$	−2.20464e8	−	5.23231e7i	−0.947790	−	0.224941i
$616$	−7.11321e7	+	5.96869e7i	−0.304315	+	0.255351i
$617$	−9.12853e7	+	2.50804e8i	−0.388638	+	1.06777i	0.578977	+	0.815344i	$0.303452\pi$
$617$	−9.12853e7	+	2.50804e8i	−0.388638	+	1.06777i	−0.967615	+	0.252430i	$0.918770\pi$
$618$	2.88769e8	−	4.38757e8i	1.22345	−	1.85891i
$619$	−2.27041e7	+	1.28761e8i	−0.0957263	+	0.542891i	0.898796	+	0.438367i	$0.144443\pi$
$619$	−2.27041e7	+	1.28761e8i	−0.0957263	+	0.542891i	−0.994522	+	0.104524i	$0.966668\pi$
$620$			5.49033e7i			0.230369i
$621$	2.06086e8	+	1.19239e8i	0.860546	+	0.497903i
$622$	−1.00910e8			−0.419337
$623$	2.74596e7	+	4.84187e6i	0.113561	+	0.0200239i
$624$	−5.83758e6	+	9.96954e7i	−0.0240259	+	0.410319i
$625$	9.10430e7	+	3.31370e7i	0.372912	+	0.135729i
$626$	3.56232e7	+	4.24541e7i	0.145214	+	0.173060i
$627$	−6.15226e6	−	5.80796e6i	−0.0249593	−	0.0235625i
$628$	−1.20445e8	+	4.38385e7i	−0.486307	+	0.177001i
$629$	1.45424e8	+	8.39608e7i	0.584366	+	0.337384i
$630$	9.70472e7	−	2.29371e7i	0.388116	−	0.0917313i
$631$	−1.33783e8	−	2.31719e8i	−0.532492	−	0.922302i	−0.999280	−	0.0379335i	$-0.987922\pi$
$631$	−1.33783e8	−	2.31719e8i	−0.532492	−	0.922302i	0.466789	−	0.884369i	$-0.345411\pi$
$632$	1.11852e7	−	1.33301e7i	0.0443092	−	0.0528057i
$633$	−1.17488e8	+	2.72137e8i	−0.463216	+	1.07294i
$634$	2.25109e7	+	1.27666e8i	0.0883334	+	0.500963i
$635$	−1.23666e8	+	2.18057e7i	−0.482981	+	0.0851625i
$636$	−3.33827e7	−	2.86376e8i	−0.129763	−	1.11318i
$637$	5.43376e7	+	4.55946e7i	0.210224	+	0.176399i
$638$	−4.99186e8	+	2.88205e8i	−1.92221	+	1.10979i
$639$	−857762.	+	7.29941e6i	−0.00328749	+	0.0279760i
$640$	9.23742e7	−	1.59997e8i	0.352380	−	0.610339i
$641$	7.67803e6	+	2.10952e7i	0.0291525	+	0.0800958i	0.953415	−	0.301661i	$-0.0975412\pi$
$641$	7.67803e6	+	2.10952e7i	0.0291525	+	0.0800958i	−0.924263	+	0.381757i	$0.875319\pi$
$642$	−1.12461e8	−	3.76070e8i	−0.425008	−	1.42123i
$643$	−1.35708e8	+	1.13873e8i	−0.510473	+	0.428337i	−0.861295	−	0.508104i	$-0.830346\pi$
$643$	−1.35708e8	+	1.13873e8i	−0.510473	+	0.428337i	0.350823	+	0.936442i	$0.385902\pi$
$644$	2.26805e7	−	6.23143e7i	0.0849173	−	0.233308i
$645$	−7.43118e6	−	1.48081e7i	−0.0276936	−	0.0551850i
$646$	−1.06009e6	+	6.01204e6i	−0.00393227	+	0.0223010i
$647$		−	2.72620e8i		−	1.00657i	−0.864120	−	0.503285i	$-0.832124\pi$
$647$		−	2.72620e8i		−	1.00657i	0.864120	−	0.503285i	$-0.167876\pi$
$648$	3.18023e7	−	1.33448e8i	0.116878	−	0.490440i
$649$	2.62358e8			0.959755
$650$	4.80783e7	+	8.47751e6i	0.175069	+	0.0308694i
$651$	−5.16277e7	+	2.59084e7i	−0.187128	+	0.0939069i
$652$	8.35767e7	+	3.04194e7i	0.301538	+	0.109751i
$653$	−1.80200e8	−	2.14754e8i	−0.647165	−	0.771261i	0.338319	−	0.941031i	$-0.390142\pi$
$653$	−1.80200e8	−	2.14754e8i	−0.647165	−	0.771261i	−0.985484	+	0.169771i	$0.945697\pi$
$654$	4.87082e8	−	1.45659e8i	1.74128	−	0.520718i
$655$	2.43140e7	−	8.84956e6i	0.0865231	−	0.0314918i
$656$	3.88887e8	+	2.24524e8i	1.37756	+	0.795337i
$657$	−9.18579e7	−	2.13314e8i	−0.323907	−	0.752182i
$658$	1.25755e8	+	2.17815e8i	0.441417	+	0.764556i
$659$	−8.48943e7	+	1.01173e8i	−0.296635	+	0.353516i	−0.893690	−	0.448684i	$-0.851893\pi$
$659$	−8.48943e7	+	1.01173e8i	−0.296635	+	0.353516i	0.597055	+	0.802200i	$0.296337\pi$
$660$	2.47571e8	−	2.88592e7i	0.861129	−	0.100381i
$661$	2.92045e7	+	1.65627e8i	0.101122	+	0.573492i	0.992699	+	0.120622i	$0.0384888\pi$
$661$	2.92045e7	+	1.65627e8i	0.101122	+	0.573492i	−0.891576	+	0.452870i	$0.850400\pi$
$662$	1.08846e8	−	1.91925e7i	0.375179	−	0.0661542i
$663$	−8.77847e7	−	3.78989e7i	−0.301216	−	0.130043i
$664$	−1.95932e8	−	1.64406e8i	−0.669269	−	0.561583i
$665$	−1.45125e6	+	837877.i	−0.00493487	+	0.00284915i
$666$	−2.44176e8	−	7.32663e7i	−0.826570	−	0.248017i
$667$	−1.36293e8	+	2.36066e8i	−0.459300	+	0.795530i
$668$	3.12709e7	+	8.59162e7i	0.104909	+	0.288234i
$669$	3.93798e7	−	4.17143e7i	0.131521	−	0.139318i
$670$	−2.98838e7	+	2.50755e7i	−0.0993601	+	0.0833730i
$671$	−2.61765e8	+	7.19193e8i	−0.866450	+	2.38055i
$672$	−1.33887e8	−	7.83963e6i	−0.441194	−	0.0258338i
$673$	4.99732e7	−	2.83412e8i	0.163943	−	0.929765i	−0.786205	−	0.617966i	$-0.787957\pi$
$673$	4.99732e7	−	2.83412e8i	0.163943	−	0.929765i	0.950148	−	0.311800i	$-0.100932\pi$
$674$		−	2.64852e8i		−	0.865015i
$675$	−1.22397e8	−	4.46778e7i	−0.397979	−	0.145271i
$676$	1.65419e8			0.535481
$677$	2.13604e8	+	3.76642e7i	0.688405	+	0.121384i	0.506899	−	0.862005i	$-0.330792\pi$
$677$	2.13604e8	+	3.76642e7i	0.688405	+	0.121384i	0.181506	+	0.983390i	$0.441903\pi$
$678$	−5.08064e8	−	3.34385e8i	−1.63016	−	1.07290i
$679$	−1.71438e8	−	6.23985e7i	−0.547645	−	0.199326i
$680$	7.65503e7	+	9.12291e7i	0.243456	+	0.290139i
$681$	1.18247e6	−	4.98237e6i	0.00374412	−	0.0157759i
$682$	−3.61181e8	+	1.31459e8i	−1.13860	+	0.414417i
$683$	9.37113e7	+	5.41042e7i	0.294124	+	0.169812i	0.639800	−	0.768541i	$-0.279017\pi$
$683$	9.37113e7	+	5.41042e7i	0.294124	+	0.169812i	−0.345676	+	0.938354i	$0.612351\pi$
$684$	−200269.	−	3.47558e6i	−0.000625816	−	0.0108607i
$685$	1.91432e8	+	3.31571e8i	0.595585	+	1.03158i
$686$	−1.99237e8	+	2.37442e8i	−0.617161	+	0.735504i
$687$	−1.45357e7	−	1.95375e7i	−0.0448298	−	0.0602558i
$688$	5.70164e6	+	3.23356e7i	0.0175079	+	0.0992923i
$689$	−1.98950e8	+	3.50802e7i	−0.608255	+	0.107252i
$690$	2.51758e8	−	1.87305e8i	0.766364	−	0.570168i
$691$	−6.99958e6	−	5.87335e6i	−0.0212148	−	0.0178013i	0.632119	−	0.774872i	$-0.282186\pi$
$691$	−6.99958e6	−	5.87335e6i	−0.0212148	−	0.0178013i	−0.653333	+	0.757070i	$0.726630\pi$
$692$	1.69403e8	−	9.78046e7i	0.511213	−	0.295149i
$693$	1.43964e8	+	2.19182e8i	0.432568	+	0.658576i
$694$	1.41294e8	−	2.44729e8i	0.422714	−	0.732162i
$695$	−9.56085e7	−	2.62682e8i	−0.284801	−	0.782485i
$696$	1.52812e8	+	3.62672e7i	0.453243	+	0.107569i
$697$	−3.29352e8	+	2.76359e8i	−0.972661	+	0.816160i
$698$	−198081.	+	544222.i	−0.000582473	+	0.00160033i
$699$	−1.10420e8	+	1.67773e8i	−0.323308	+	0.491235i
$700$	−6.30164e6	+	3.57384e7i	−0.0183721	+	0.104193i
$701$		−	4.78882e8i		−	1.39019i	−0.718918	−	0.695095i	$-0.755362\pi$
$701$		−	4.78882e8i		−	1.39019i	0.718918	−	0.695095i	$-0.244638\pi$
$702$	1.42931e8	+	2.53396e7i	0.413158	+	0.0732469i
$703$	4.28397e6			0.0123305
$704$	−7.02801e7	−	1.23923e7i	−0.201425	−	0.0355167i
$705$	−2.61319e7	+	4.46286e8i	−0.0745769	+	1.27364i
$706$	2.63957e8	+	9.60726e7i	0.750101	+	0.273014i
$707$	−3.87439e7	−	4.61732e7i	−0.109634	−	0.130657i
$708$	7.84999e7	+	7.41068e7i	0.221192	+	0.208813i
$709$	4.01983e8	−	1.46310e8i	1.12790	−	0.410520i	0.290368	−	0.956915i	$-0.406222\pi$
$709$	4.01983e8	−	1.46310e8i	1.12790	−	0.410520i	0.837528	+	0.546395i	$0.184000\pi$
$710$	8.38853e6	+	4.84312e6i	0.0234375	+	0.0135316i
$711$	−3.37013e7	−	3.57657e7i	−0.0937644	−	0.0995079i
$712$	−2.52768e7	−	4.37806e7i	−0.0700296	−	0.121295i
$713$	−1.16836e8	+	1.39240e8i	−0.322337	+	0.384146i
$714$	7.49981e7	−	1.73717e8i	0.206042	−	0.477252i
$715$	−3.03267e7	−	1.71991e8i	−0.0829673	−	0.470531i
$716$	−1.24416e8	+	2.19380e7i	−0.338952	+	0.0597664i
$717$	2.37670e7	+	2.03887e8i	0.0644788	+	0.553137i
$718$	2.85339e8	+	2.39428e8i	0.770883	+	0.646848i
$719$	−5.10332e8	+	2.94640e8i	−1.37299	+	0.792694i	−0.991303	−	0.131599i	$-0.957989\pi$
$719$	−5.10332e8	+	2.94640e8i	−1.37299	+	0.792694i	−0.381683	+	0.924293i	$0.624655\pi$
$720$	−2.81633e8	−	2.09939e8i	−0.754547	−	0.562466i
$721$	1.36789e8	−	2.36925e8i	0.364960	−	0.632129i
$722$	−1.62855e8	−	4.47440e8i	−0.432702	−	1.18884i
$723$	6.77627e7	+	2.26599e8i	0.179298	+	0.599573i
$724$	1.91483e7	−	1.60673e7i	0.0504561	−	0.0423377i
$725$	5.10195e7	−	1.40175e8i	0.133882	−	0.367838i
$726$	5.65423e8	+	1.12672e9i	1.47762	+	2.94446i
$727$	−7.30630e7	+	4.14361e8i	−0.190149	+	1.07839i	0.729010	+	0.684503i	$0.239981\pi$
$727$	−7.30630e7	+	4.14361e8i	−0.190149	+	1.07839i	−0.919159	+	0.393886i	$0.871130\pi$
$728$			2.67719e7i			0.0693882i
$729$	−3.63809e8	−	1.33182e8i	−0.939055	−	0.343766i
$730$	−3.06089e8			−0.786827
$731$	−3.09595e7	−	5.45900e6i	−0.0792579	−	0.0139753i
$732$	−2.81469e8	+	1.41250e8i	−0.717624	+	0.360126i
$733$	−4.50292e8	−	1.63893e8i	−1.14336	−	0.416148i	−0.300233	−	0.953866i	$-0.597064\pi$
$733$	−4.50292e8	−	1.63893e8i	−1.14336	−	0.416148i	−0.843125	+	0.537718i	$0.819287\pi$
$734$	4.52888e8	+	5.39731e8i	1.14526	+	1.36486i
$735$	−2.39041e8	+	7.14834e7i	−0.602018	+	0.180029i
$736$	−3.96571e8	+	1.44340e8i	−0.994690	+	0.362038i
$737$	−8.88414e7	−	5.12926e7i	−0.221928	−	0.128130i
$738$	3.90097e8	−	5.23314e8i	0.970518	−	1.30195i
$739$	5.55849e7	+	9.62759e7i	0.137728	+	0.238553i	0.926636	−	0.375959i	$-0.122687\pi$
$739$	5.55849e7	+	9.62759e7i	0.137728	+	0.238553i	−0.788908	+	0.614511i	$0.789353\pi$
$740$	−8.11224e7	+	9.66779e7i	−0.200192	+	0.238579i
$741$	−2.42293e6	+	282439.i	−0.00595506	+	0.000694177i
$742$	−6.94202e7	−	3.93702e8i	−0.169932	−	0.963730i
$743$	6.73484e8	−	1.18753e8i	1.64195	−	0.289521i	0.725070	−	0.688675i	$-0.241807\pi$
$743$	6.73484e8	−	1.18753e8i	1.64195	−	0.289521i	0.916884	+	0.399154i	$0.130696\pi$
$744$	9.61505e7	+	4.15106e7i	0.233471	+	0.100795i
$745$	6.92999e7	+	5.81495e7i	0.167596	+	0.140630i
$746$	−1.35871e8	+	7.84451e7i	−0.327273	+	0.188951i
$747$	−5.25701e8	+	4.95358e8i	−1.26118	+	1.18839i
$748$	2.36467e8	−	4.09573e8i	0.565022	−	0.978647i
$749$	−6.99243e7	−	1.92116e8i	−0.166411	−	0.457211i
$750$	−3.96121e8	+	4.19603e8i	−0.938954	+	0.994616i
$751$	5.90120e8	−	4.95170e8i	1.39322	−	1.16905i	0.429208	−	0.903206i	$-0.358793\pi$
$751$	5.90120e8	−	4.95170e8i	1.39322	−	1.16905i	0.964015	−	0.265847i	$-0.0856517\pi$
$752$	3.03015e8	−	8.32527e8i	0.712543	−	1.95770i
$753$	−7.13714e8	−	4.17909e7i	−1.67163	−	0.0978807i
$754$	−2.88582e7	+	1.63663e8i	−0.0673218	+	0.381801i
$755$		−	3.88255e8i		−	0.902145i
$756$	−1.88359e7	+	1.06246e8i	−0.0435933	+	0.245894i
$757$	2.98071e8			0.687119			0.343559	−	0.939131i	$-0.388367\pi$
$757$	2.98071e8			0.687119			0.343559	+	0.939131i	$0.388367\pi$
$758$	−8.34198e8	−	1.47092e8i	−1.91541	−	0.337738i
$759$	6.89279e8	+	4.53652e8i	1.57641	+

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)

\(f(q)\)	\(=\)	\(q+(-9.97059 - 1.75808i) q^{2} +(24.1318 - 12.1101i) q^{3} +(36.1814 + 13.1690i) q^{4} +(60.9980 + 72.6946i) q^{5} +(-261.899 + 78.3191i) q^{6} +(-133.791 + 48.6960i) q^{7} +(223.553 + 129.069i) q^{8} +(435.691 - 584.478i) q^{9} +O(q^{10})\)	\(q+(-9.97059 - 1.75808i) q^{2} +(24.1318 - 12.1101i) q^{3} +(36.1814 + 13.1690i) q^{4} +(60.9980 + 72.6946i) q^{5} +(-261.899 + 78.3191i) q^{6} +(-133.791 + 48.6960i) q^{7} +(223.553 + 129.069i) q^{8} +(435.691 - 584.478i) q^{9} +(-480.383 - 832.047i) q^{10} +(1624.00 - 1935.41i) q^{11} +(1032.60 - 120.370i) q^{12} +(-126.490 - 717.362i) q^{13} +(1419.59 - 250.312i) q^{14} +(2352.33 + 1015.56i) q^{15} +(-3889.75 - 3263.89i) q^{16} +(4210.29 - 2430.81i) q^{17} +(-5371.65 + 5061.61i) q^{18} +(62.0141 - 107.412i) q^{19} +(1249.68 + 3433.47i) q^{20} +(-2638.91 + 2795.35i) q^{21} +(-19594.9 + 16442.1i) q^{22} +(-4137.25 + 11367.0i) q^{23} +(6957.79 + 407.407i) q^{24} +(1149.51 - 6519.18i) q^{25} +7374.90i q^{26} +(3435.93 - 19380.8i) q^{27} -5482.03 q^{28} +(22191.9 + 3913.03i) q^{29} +(-21668.7 - 14261.3i) q^{30} +(14120.1 + 5139.28i) q^{31} +(22425.5 + 26725.7i) q^{32} +(15752.1 - 66371.9i) q^{33} +(-46252.6 + 16834.6i) q^{34} +(-11700.9 - 6755.53i) q^{35} +(23460.9 - 15409.6i) q^{36} +(17270.1 + 29912.7i) q^{37} +(-807.155 + 961.930i) q^{38} +(-11739.8 - 15779.5i) q^{39} +(4253.72 + 24124.0i) q^{40} +(-87091.6 + 15356.6i) q^{41} +(31226.0 - 23231.8i) q^{42} +(-4953.54 - 4156.52i) q^{43} +(84246.1 - 48639.5i) q^{44} +(69064.6 - 3979.63i) q^{45} +(61235.0 - 106062. i) q^{46} +(59675.6 + 163957. i) q^{47} +(-133393. - 31658.3i) q^{48} +(-74595.6 + 62593.1i) q^{49} +(-22922.5 + 62979.1i) q^{50} +(72164.6 - 109647. i) q^{51} +(4870.32 - 27620.9i) q^{52} -277335. i q^{53} +(-68331.3 + 187197. i) q^{54} +239755. q^{55} +(-36194.6 - 6382.08i) q^{56} +(195.749 - 3343.04i) q^{57} +(-214387. - 78030.5i) q^{58} +(66748.6 + 79547.9i) q^{59} +(71736.8 + 67722.2i) q^{60} +(-284660. + 103608. i) q^{61} +(-131750. - 76065.9i) q^{62} +(-29829.8 + 99414.4i) q^{63} +(-14123.1 - 24462.0i) q^{64} +(44432.7 - 52952.8i) q^{65} +(-273745. + 634073. i) q^{66} +(-7050.75 - 39986.8i) q^{67} +(184345. - 32505.1i) q^{68} +(37816.2 + 324409. i) q^{69} +(104788. + 87927.9i) q^{70} +(-8731.10 + 5040.90i) q^{71} +(172838. - 74428.0i) q^{72} +(159295. - 275906. i) q^{73} +(-119604. - 328610. i) q^{74} +(-51208.2 - 171240. i) q^{75} +(3658.26 - 3069.64i) q^{76} +(-123031. + 338024. i) q^{77} +(89310.9 + 177970. i) q^{78} +(11705.7 - 66386.4i) q^{79} -481854. i q^{80} +(-151788. - 509303. i) q^{81} +895353. q^{82} +(-975779. - 172056. i) q^{83} +(-132291. + 66388.0i) q^{84} +(433526. + 157790. i) q^{85} +(42082.2 + 50151.7i) q^{86} +(582919. - 174318. i) q^{87} +(612852. - 223060. i) q^{88} +(-169602. - 97919.9i) q^{89} +(-695611. - 81742.1i) q^{90} +(51856.0 + 89817.2i) q^{91} +(-299383. + 356791. i) q^{92} +(402980. - 46975.1i) q^{93} +(-306750. - 1.73967e6i) q^{94} +(11591.0 - 2043.80i) q^{95} +(864820. + 373365. i) q^{96} +(981600. + 823660. i) q^{97} +(853806. - 492945. i) q^{98} +(-423643. - 1.79244e6i) 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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