LMFDB - Embedded newform 38.6.e.b.23.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,6,Mod(5,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	38.e (of order $9$, 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:	$6.09458515289$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			23.5
Character	$\chi$	$=$	38.23
Dual form			38.6.e.b.5.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.75877 - 1.36808i) q^{2} +(4.41021 + 25.0115i) q^{3} +(12.2567 + 10.2846i) q^{4} +(-71.5678 + 60.0525i) q^{5} +(17.6408 - 100.046i) q^{6} +(91.0882 - 157.769i) q^{7} +(-32.0000 - 55.4256i) q^{8} +(-377.781 + 137.501i) q^{9} +O(q^{10})$	\(q+(-3.75877 - 1.36808i) q^{2} +(4.41021 + 25.0115i) q^{3} +(12.2567 + 10.2846i) q^{4} +(-71.5678 + 60.0525i) q^{5} +(17.6408 - 100.046i) q^{6} +(91.0882 - 157.769i) q^{7} +(-32.0000 - 55.4256i) q^{8} +(-377.781 + 137.501i) q^{9} +(351.164 - 127.813i) q^{10} +(-198.935 - 344.565i) q^{11} +(-203.179 + 351.916i) q^{12} +(-119.944 + 680.234i) q^{13} +(-558.221 + 468.403i) q^{14} +(-1817.63 - 1525.18i) q^{15} +(44.4539 + 252.111i) q^{16} +(-1158.23 - 421.562i) q^{17} +1608.11 q^{18} +(785.549 + 1363.46i) q^{19} -1494.80 q^{20} +(4347.77 + 1582.46i) q^{21} +(276.357 + 1567.30i) q^{22} +(216.010 + 181.254i) q^{23} +(1245.15 - 1044.81i) q^{24} +(972.994 - 5518.13i) q^{25} +(1381.45 - 2392.75i) q^{26} +(-2019.43 - 3497.75i) q^{27} +(2739.04 - 996.928i) q^{28} +(-4078.07 + 1484.30i) q^{29} +(4745.50 + 8219.45i) q^{30} +(-1343.51 + 2327.02i) q^{31} +(177.816 - 1008.44i) q^{32} +(7740.75 - 6495.26i) q^{33} +(3776.80 + 3169.11i) q^{34} +(2955.47 + 16761.3i) q^{35} +(-6044.50 - 2200.02i) q^{36} -3855.72 q^{37} +(-1087.38 - 6199.61i) q^{38} -17542.7 q^{39} +(5618.62 + 2045.01i) q^{40} +(3396.47 + 19262.3i) q^{41} +(-14177.3 - 11896.2i) q^{42} +(-284.262 + 238.524i) q^{43} +(1105.43 - 6269.19i) q^{44} +(18779.7 - 32527.4i) q^{45} +(-563.962 - 976.811i) q^{46} +(-12719.0 + 4629.35i) q^{47} +(-6109.62 + 2223.72i) q^{48} +(-8190.64 - 14186.6i) q^{49} +(-11206.5 + 19410.2i) q^{50} +(5435.86 - 30828.3i) q^{51} +(-8466.04 + 7103.85i) q^{52} +(4309.46 + 3616.06i) q^{53} +(2805.36 + 15910.0i) q^{54} +(34929.3 + 12713.2i) q^{55} -11659.3 q^{56} +(-30637.7 + 25660.9i) q^{57} +17359.2 q^{58} +(28278.6 + 10292.6i) q^{59} +(-6592.39 - 37387.3i) q^{60} +(1693.96 + 1421.40i) q^{61} +(8233.48 - 6908.71i) q^{62} +(-12717.9 + 72127.1i) q^{63} +(-2048.00 + 3547.24i) q^{64} +(-32265.6 - 55885.7i) q^{65} +(-37981.7 + 13824.2i) q^{66} +(-249.987 + 90.9880i) q^{67} +(-9860.51 - 17078.9i) q^{68} +(-3580.79 + 6202.11i) q^{69} +(11821.9 - 67045.2i) q^{70} +(17075.9 - 14328.4i) q^{71} +(19710.1 + 16538.7i) q^{72} +(9670.88 + 54846.3i) q^{73} +(14492.8 + 5274.93i) q^{74} +142308. q^{75} +(-4394.35 + 24790.5i) q^{76} -72482.4 q^{77} +(65938.8 + 23999.8i) q^{78} +(-9821.32 - 55699.5i) q^{79} +(-18321.4 - 15373.4i) q^{80} +(3741.21 - 3139.25i) q^{81} +(13585.9 - 77049.4i) q^{82} +(-42577.7 + 73746.7i) q^{83} +(37014.4 + 64110.9i) q^{84} +(108208. - 39384.5i) q^{85} +(1394.80 - 507.664i) q^{86} +(-55109.7 - 95452.8i) q^{87} +(-12731.8 + 22052.1i) q^{88} +(3768.14 - 21370.2i) q^{89} +(-115089. + 96570.8i) q^{90} +(96394.6 + 80884.7i) q^{91} +(783.448 + 4443.16i) q^{92} +(-64127.4 - 23340.5i) q^{93} +54141.2 q^{94} +(-138099. - 50405.3i) q^{95} +26006.9 q^{96} +(-104831. - 38155.4i) q^{97} +(11378.3 + 64529.6i) q^{98} +(122532. + 102816. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 15 q^{3} + 60 q^{6} - 84 q^{7} - 960 q^{8} - 345 q^{9}+O(q^{10}) $ 30 * q + 15 * q^3 + 60 * q^6 - 84 * q^7 - 960 * q^8 - 345 * q^9	\( 30 q + 15 q^{3} + 60 q^{6} - 84 q^{7} - 960 q^{8} - 345 q^{9} - 126 q^{11} - 2610 q^{13} - 864 q^{14} - 5160 q^{15} + 1902 q^{17} + 17016 q^{18} - 2400 q^{19} + 3456 q^{20} - 6426 q^{21} + 216 q^{22} - 3306 q^{23} + 960 q^{24} - 18060 q^{25} + 456 q^{26} + 13017 q^{27} + 6048 q^{28} + 5988 q^{29} - 6840 q^{31} + 51867 q^{33} - 10752 q^{34} + 24408 q^{35} - 5520 q^{36} - 8556 q^{37} + 2772 q^{38} + 9912 q^{39} - 40527 q^{41} + 27432 q^{42} + 3678 q^{43} + 864 q^{44} - 31770 q^{45} - 15744 q^{46} - 133740 q^{47} - 7680 q^{48} - 63777 q^{49} - 107580 q^{50} + 45657 q^{51} + 5760 q^{52} - 64626 q^{53} + 1476 q^{54} + 142056 q^{55} + 10752 q^{56} + 232824 q^{57} + 117264 q^{58} + 169041 q^{59} - 56640 q^{60} + 61698 q^{61} - 101616 q^{62} - 188064 q^{63} - 61440 q^{64} - 80646 q^{65} - 173772 q^{66} - 72129 q^{67} - 65904 q^{68} - 124224 q^{69} + 97632 q^{70} + 417828 q^{71} + 44160 q^{72} + 239082 q^{73} - 116112 q^{74} - 174960 q^{75} + 6912 q^{76} + 242436 q^{77} + 336624 q^{78} - 145740 q^{79} + 14781 q^{81} - 162108 q^{82} - 201630 q^{83} - 54528 q^{84} - 46512 q^{85} - 75720 q^{86} - 376512 q^{87} - 8064 q^{88} + 416928 q^{89} + 560640 q^{90} - 380316 q^{91} + 269376 q^{92} - 205146 q^{93} + 5616 q^{94} + 708168 q^{95} + 858363 q^{97} + 308328 q^{98} - 1068531 q^{99}+O(q^{100}) \) 30 * q + 15 * q^3 + 60 * q^6 - 84 * q^7 - 960 * q^8 - 345 * q^9 - 126 * q^11 - 2610 * q^13 - 864 * q^14 - 5160 * q^15 + 1902 * q^17 + 17016 * q^18 - 2400 * q^19 + 3456 * q^20 - 6426 * q^21 + 216 * q^22 - 3306 * q^23 + 960 * q^24 - 18060 * q^25 + 456 * q^26 + 13017 * q^27 + 6048 * q^28 + 5988 * q^29 - 6840 * q^31 + 51867 * q^33 - 10752 * q^34 + 24408 * q^35 - 5520 * q^36 - 8556 * q^37 + 2772 * q^38 + 9912 * q^39 - 40527 * q^41 + 27432 * q^42 + 3678 * q^43 + 864 * q^44 - 31770 * q^45 - 15744 * q^46 - 133740 * q^47 - 7680 * q^48 - 63777 * q^49 - 107580 * q^50 + 45657 * q^51 + 5760 * q^52 - 64626 * q^53 + 1476 * q^54 + 142056 * q^55 + 10752 * q^56 + 232824 * q^57 + 117264 * q^58 + 169041 * q^59 - 56640 * q^60 + 61698 * q^61 - 101616 * q^62 - 188064 * q^63 - 61440 * q^64 - 80646 * q^65 - 173772 * q^66 - 72129 * q^67 - 65904 * q^68 - 124224 * q^69 + 97632 * q^70 + 417828 * q^71 + 44160 * q^72 + 239082 * q^73 - 116112 * q^74 - 174960 * q^75 + 6912 * q^76 + 242436 * q^77 + 336624 * q^78 - 145740 * q^79 + 14781 * q^81 - 162108 * q^82 - 201630 * q^83 - 54528 * q^84 - 46512 * q^85 - 75720 * q^86 - 376512 * q^87 - 8064 * q^88 + 416928 * q^89 + 560640 * q^90 - 380316 * q^91 + 269376 * q^92 - 205146 * q^93 + 5616 * q^94 + 708168 * q^95 + 858363 * q^97 + 308328 * q^98 - 1068531 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−3.75877	−	1.36808i	−0.664463	−	0.241845i
$2$	−3.75877	−	1.36808i	−0.664463	−	0.241845i
$3$	4.41021	+	25.0115i	0.282915	+	1.60449i	0.712640	+	0.701530i	$0.247499\pi$
$3$	4.41021	+	25.0115i	0.282915	+	1.60449i	−0.429725	+	0.902960i	$0.641389\pi$
$4$	12.2567	+	10.2846i	0.383022	+	0.321394i
$5$	−71.5678	+	60.0525i	−1.28024	+	1.07425i	−0.287033	+	0.957921i	$0.592669\pi$
$5$	−71.5678	+	60.0525i	−1.28024	+	1.07425i	−0.993210	+	0.116331i	$0.962887\pi$
$6$	17.6408	−	100.046i	0.200051	−	1.13455i
$7$	91.0882	−	157.769i	0.702615	−	1.21696i	−0.264931	−	0.964267i	$-0.585349\pi$
$7$	91.0882	−	157.769i	0.702615	−	1.21696i	0.967545	−	0.252697i	$-0.0813176\pi$
$8$	−32.0000	−	55.4256i	−0.176777	−	0.306186i
$9$	−377.781	+	137.501i	−1.55466	+	0.565848i
$10$	351.164	−	127.813i	1.11048	−	0.404180i
$11$	−198.935	−	344.565i	−0.495711	−	0.858597i	0.504277	−	0.863542i	$-0.331759\pi$
$11$	−198.935	−	344.565i	−0.495711	−	0.858597i	−0.999988	+	0.00494549i	$0.998426\pi$
$12$	−203.179	+	351.916i	−0.407311	+	0.705482i
$13$	−119.944	+	680.234i	−0.196842	+	1.11635i	0.712928	+	0.701237i	$0.247368\pi$
$13$	−119.944	+	680.234i	−0.196842	+	1.11635i	−0.909771	+	0.415111i	$0.863743\pi$
$14$	−558.221	+	468.403i	−0.761178	+	0.638704i
$15$	−1817.63	−	1525.18i	−2.08583	−	1.75022i
$16$	44.4539	+	252.111i	0.0434120	+	0.246202i
$17$	−1158.23	−	421.562i	−0.972015	−	0.353785i	−0.193284	−	0.981143i	$-0.561914\pi$
$17$	−1158.23	−	421.562i	−0.972015	−	0.353785i	−0.778731	+	0.627358i	$0.784136\pi$
$18$	1608.11			1.16986
$19$	785.549	+	1363.46i	0.499217	+	0.866477i
$19$	785.549	+	1363.46i	0.499217	+	0.866477i
$20$	−1494.80			−0.835620
$21$	4347.77	+	1582.46i	2.15139	+	0.783041i
$22$	276.357	+	1567.30i	0.121735	+	0.690391i
$23$	216.010	+	181.254i	0.0851441	+	0.0714444i	0.684366	−	0.729138i	$-0.260079\pi$
$23$	216.010	+	181.254i	0.0851441	+	0.0714444i	−0.599222	+	0.800583i	$0.704523\pi$
$24$	1245.15	−	1044.81i	0.441260	−	0.370261i
$25$	972.994	−	5518.13i	0.311358	−	1.76580i
$26$	1381.45	−	2392.75i	0.400777	−	0.694167i
$27$	−2019.43	−	3497.75i	−0.533112	−	0.923377i
$28$	2739.04	−	996.928i	0.660242	−	0.240308i
$29$	−4078.07	+	1484.30i	−0.900451	+	0.327737i	−0.750433	−	0.660946i	$-0.770155\pi$
$29$	−4078.07	+	1484.30i	−0.900451	+	0.327737i	−0.150017	+	0.988683i	$0.547933\pi$
$30$	4745.50	+	8219.45i	0.962674	+	1.66740i
$31$	−1343.51	+	2327.02i	−0.251093	+	0.434906i	−0.963827	−	0.266528i	$-0.914123\pi$
$31$	−1343.51	+	2327.02i	−0.251093	+	0.434906i	0.712734	+	0.701435i	$0.247457\pi$
$32$	177.816	−	1008.44i	0.0306970	−	0.174091i
$33$	7740.75	−	6495.26i	1.23737	−	1.03827i
$34$	3776.80	+	3169.11i	0.560307	+	0.470154i
$35$	2955.47	+	16761.3i	0.407808	+	2.31280i
$36$	−6044.50	−	2200.02i	−0.777328	−	0.282924i
$37$	−3855.72			−0.463021			−0.231511	−	0.972832i	$-0.574367\pi$
$37$	−3855.72			−0.463021			−0.231511	+	0.972832i	$0.574367\pi$
$38$	−1087.38	−	6199.61i	−0.122158	−	0.696475i
$39$	−17542.7			−1.84686
$40$	5618.62	+	2045.01i	0.555238	+	0.202090i
$41$	3396.47	+	19262.3i	0.315550	+	1.78957i	0.569118	+	0.822256i	$0.307285\pi$
$41$	3396.47	+	19262.3i	0.315550	+	1.78957i	−0.253568	+	0.967318i	$0.581604\pi$
$42$	−14177.3	−	11896.2i	−1.24014	−	1.04060i
$43$	−284.262	+	238.524i	−0.0234449	+	0.0196726i	−0.654435	−	0.756118i	$-0.727093\pi$
$43$	−284.262	+	238.524i	−0.0234449	+	0.0196726i	0.630990	+	0.775791i	$0.282649\pi$
$44$	1105.43	−	6269.19i	0.0860793	−	0.488180i
$45$	18779.7	−	32527.4i	1.38247	−	2.39451i
$46$	−563.962	−	976.811i	−0.0392966	−	0.0680638i
$47$	−12719.0	+	4629.35i	−0.839865	+	0.305686i	−0.725901	−	0.687799i	$-0.758577\pi$
$47$	−12719.0	+	4629.35i	−0.839865	+	0.305686i	−0.113964	+	0.993485i	$0.536355\pi$
$48$	−6109.62	+	2223.72i	−0.382747	+	0.139308i
$49$	−8190.64	−	14186.6i	−0.487335	−	0.844089i
$50$	−11206.5	+	19410.2i	−0.633936	+	1.09801i
$51$	5435.86	−	30828.3i	0.292646	−	1.65968i
$52$	−8466.04	+	7103.85i	−0.434182	+	0.364322i
$53$	4309.46	+	3616.06i	0.210733	+	0.176826i	0.742045	−	0.670350i	$-0.233856\pi$
$53$	4309.46	+	3616.06i	0.210733	+	0.176826i	−0.531312	+	0.847176i	$0.678301\pi$
$54$	2805.36	+	15910.0i	0.130919	+	0.742480i
$55$	34929.3	+	12713.2i	1.55698	+	0.566694i
$56$	−11659.3			−0.496824
$57$	−30637.7	+	25660.9i	−1.24902	+	1.04613i
$58$	17359.2			0.677578
$59$	28278.6	+	10292.6i	1.05762	+	0.384941i	0.811533	−	0.584307i	$-0.198634\pi$
$59$	28278.6	+	10292.6i	1.05762	+	0.384941i	0.246085	+	0.969248i	$0.420856\pi$
$60$	−6592.39	−	37387.3i	−0.236409	−	1.34074i
$61$	1693.96	+	1421.40i	0.0582878	+	0.0489092i	0.671466	−	0.741035i	$-0.265665\pi$
$61$	1693.96	+	1421.40i	0.0582878	+	0.0489092i	−0.613178	+	0.789944i	$0.710109\pi$
$62$	8233.48	−	6908.71i	0.272022	−	0.228254i
$63$	−12717.9	+	72127.1i	−0.403706	+	2.28953i
$64$	−2048.00	+	3547.24i	−0.0625000	+	0.108253i
$65$	−32265.6	−	55885.7i	−0.947233	−	1.64066i
$66$	−37981.7	+	13824.2i	−1.07328	+	0.390644i
$67$	−249.987	+	90.9880i	−0.00680348	+	0.00247626i	−0.345420	−	0.938448i	$-0.612263\pi$
$67$	−249.987	+	90.9880i	−0.00680348	+	0.00247626i	0.338616	+	0.940925i	$0.390041\pi$
$68$	−9860.51	−	17078.9i	−0.258599	−	0.447907i
$69$	−3580.79	+	6202.11i	−0.0905433	+	0.156826i
$70$	11821.9	−	67045.2i	0.288364	−	1.63539i
$71$	17075.9	−	14328.4i	0.402011	−	0.337327i	−0.419260	−	0.907866i	$-0.637710\pi$
$71$	17075.9	−	14328.4i	0.402011	−	0.337327i	0.821270	+	0.570539i	$0.193266\pi$
$72$	19710.1	+	16538.7i	0.448082	+	0.375985i
$73$	9670.88	+	54846.3i	0.212402	+	1.20459i	0.885358	+	0.464909i	$0.153913\pi$
$73$	9670.88	+	54846.3i	0.212402	+	1.20459i	−0.672956	+	0.739682i	$0.734976\pi$
$74$	14492.8	+	5274.93i	0.307661	+	0.111979i
$75$	142308.			2.92130
$76$	−4394.35	+	24790.5i	−0.0872692	+	0.492325i
$77$	−72482.4			−1.39318
$78$	65938.8	+	23999.8i	1.22717	+	0.446653i
$79$	−9821.32	−	55699.5i	−0.177052	−	1.00411i	−0.935748	−	0.352669i	$-0.885274\pi$
$79$	−9821.32	−	55699.5i	−0.177052	−	1.00411i	0.758696	−	0.651445i	$-0.225837\pi$
$80$	−18321.4	−	15373.4i	−0.320061	−	0.268563i
$81$	3741.21	−	3139.25i	0.0633577	−	0.0531634i
$82$	13585.9	−	77049.4i	0.223128	−	1.26542i
$83$	−42577.7	+	73746.7i	−0.678401	+	1.17503i	0.297061	+	0.954859i	$0.403994\pi$
$83$	−42577.7	+	73746.7i	−0.678401	+	1.17503i	−0.975462	+	0.220167i	$0.929340\pi$
$84$	37014.4	+	64110.9i	0.572365	+	0.991365i
$85$	108208.	−	39384.5i	1.62447	−	0.591259i
$86$	1394.80	−	507.664i	0.0203360	−	0.00740168i
$87$	−55109.7	−	95452.8i	−0.780602	−	1.35204i
$88$	−12731.8	+	22052.1i	−0.175260	+	0.303560i
$89$	3768.14	−	21370.2i	0.0504257	−	0.285978i	−0.949159	−	0.314797i	$-0.898064\pi$
$89$	3768.14	−	21370.2i	0.0504257	−	0.285978i	0.999585	+	0.0288189i	$0.00917462\pi$
$90$	−115089.	+	96570.8i	−1.49770	+	1.25672i
$91$	96394.6	+	80884.7i	1.22025	+	1.02391i
$92$	783.448	+	4443.16i	0.00965030	+	0.0547296i
$93$	−64127.4	−	23340.5i	−0.768841	−	0.279835i
$94$	54141.2			0.631988
$95$	−138099.	−	50405.3i	−1.56993	−	0.573017i
$96$	26006.9			0.288012
$97$	−104831.	−	38155.4i	−1.13125	−	0.411743i	−0.292507	−	0.956263i	$-0.594490\pi$
$97$	−104831.	−	38155.4i	−1.13125	−	0.411743i	−0.838748	+	0.544520i	$0.816712\pi$
$98$	11378.3	+	64529.6i	0.119678	+	0.678725i
$99$	122532.	+	102816.i	1.25650	+	1.05432i
$100$	68677.4	−	57627.2i	0.686774	−	0.576272i
$101$	26663.9	−	151218.i	0.260088	−	1.47503i	−0.522579	−	0.852591i	$-0.675030\pi$
$101$	26663.9	−	151218.i	0.260088	−	1.47503i	0.782667	−	0.622441i	$-0.213859\pi$
$102$	−62607.8	+	108440.i	−0.595837	+	1.03202i
$103$	9004.54	+	15596.3i	0.0836312	+	0.144854i	0.904807	−	0.425822i	$-0.140015\pi$
$103$	9004.54	+	15596.3i	0.0836312	+	0.144854i	−0.821176	+	0.570675i	$0.806682\pi$
$104$	41540.6	−	15119.5i	0.376608	−	0.137074i
$105$	−406191.	+	147842.i	−3.59548	+	1.30865i
$106$	−11251.2	−	19487.6i	−0.0972599	−	0.168459i
$107$	−19122.0	+	33120.2i	−0.161463	+	0.279662i	−0.935394	−	0.353608i	$-0.884955\pi$
$107$	−19122.0	+	33120.2i	−0.161463	+	0.279662i	0.773931	+	0.633270i	$0.218288\pi$
$108$	11221.4	−	63639.9i	0.0925739	−	0.525013i
$109$	116484.	−	97741.7i	0.939074	−	0.787977i	−0.0383498	−	0.999264i	$-0.512210\pi$
$109$	116484.	−	97741.7i	0.939074	−	0.787977i	0.977424	+	0.211288i	$0.0677657\pi$
$110$	−113898.	−	95572.1i	−0.897503	−	0.753095i
$111$	−17004.5	−	96437.4i	−0.130996	−	0.742913i
$112$	43824.6	+	15950.9i	0.330121	+	0.120154i
$113$	235307.			1.73356			0.866782	−	0.498688i	$-0.166185\pi$
$113$	235307.			1.73356			0.866782	+	0.498688i	$0.166185\pi$
$114$	150266.	−	54538.6i	1.08293	−	0.393045i
$115$	−26344.1			−0.185754
$116$	−65249.2	−	23748.8i	−0.450225	−	0.163869i
$117$	−48220.5	−	273472.i	−0.325662	−	1.84692i
$118$	−92211.8	−	77374.9i	−0.609651	−	0.511558i
$119$	−172011.	+	144334.i	−1.11350	+	0.934333i
$120$	−26369.5	+	149549.i	−0.167167	+	0.948049i
$121$	1375.58	−	2382.58i	0.00854127	−	0.0147939i
$122$	−4422.60	−	7660.17i	−0.0269016	−	0.0465950i
$123$	−466802.	+	169902.i	−2.78208	+	1.01259i
$124$	−40399.4	+	14704.2i	−0.235950	+	0.0858790i
$125$	115765.	+	200512.i	0.662680	+	1.14780i
$126$	146480.	−	253710.i	0.821960	−	1.42368i
$127$	−18207.2	+	103258.i	−0.100169	+	0.568088i	0.892871	+	0.450313i	$0.148687\pi$
$127$	−18207.2	+	103258.i	−0.100169	+	0.568088i	−0.993040	+	0.117776i	$0.962424\pi$
$128$	12550.9	−	10531.4i	0.0677094	−	0.0568149i
$129$	−7219.51	−	6057.89i	−0.0381974	−	0.0320514i
$130$	44823.0	+	254204.i	0.232617	+	1.31924i
$131$	255660.	+	93052.8i	1.30162	+	0.473752i	0.897525	−	0.440964i	$-0.145363\pi$
$131$	255660.	+	93052.8i	1.30162	+	0.473752i	0.404098	+	0.914716i	$0.367585\pi$
$132$	161677.			0.807633
$133$	286666.	+	259.134i	1.40523	+	0.00127027i
$134$	1064.12			0.00511953
$135$	354574.	+	129055.i	1.67445	+	0.609451i
$136$	13698.1	+	77685.7i	0.0635057	+	0.360158i
$137$	63506.5	+	53288.3i	0.289079	+	0.242566i	0.775781	−	0.631002i	$-0.217356\pi$
$137$	63506.5	+	53288.3i	0.289079	+	0.242566i	−0.486702	+	0.873568i	$0.661800\pi$
$138$	21944.4	−	18413.5i	0.0980901	−	0.0823073i
$139$	−15639.2	+	88694.2i	−0.0686557	+	0.389366i	0.931045	+	0.364904i	$0.118898\pi$
$139$	−15639.2	+	88694.2i	−0.0686557	+	0.389366i	−0.999701	+	0.0244617i	$0.992213\pi$
$140$	−136159.	+	235834.i	−0.587119	+	1.01692i
$141$	−171881.	−	297706.i	−0.728080	−	1.26107i
$142$	−83786.7	+	30495.9i	−0.348702	+	0.126917i
$143$	258245.	−	93993.7i	1.05607	−	0.384378i
$144$	−51459.4	−	89130.3i	−0.206804	−	0.358195i
$145$	202723.	−	351126.i	0.800724	−	1.38689i
$146$	38683.5	−	219385.i	0.150191	−	0.851775i
$147$	318706.	−	267426.i	1.21646	−	1.02073i
$148$	−47258.4	−	39654.5i	−0.177347	−	0.148812i
$149$	13171.4	+	74698.5i	0.0486032	+	0.275642i	0.999418	−	0.0341181i	$-0.0108622\pi$
$149$	13171.4	+	74698.5i	0.0486032	+	0.275642i	−0.950815	+	0.309761i	$0.899751\pi$
$150$	−534903.	−	194689.i	−1.94109	−	0.706500i
$151$	−321781.			−1.14847			−0.574233	−	0.818692i	$-0.694700\pi$
$151$	−321781.			−1.14847			−0.574233	+	0.818692i	$0.694700\pi$
$152$	50432.8	−	87170.1i	0.177053	−	0.306026i
$153$	495523.			1.71134
$154$	272445.	+	99161.8i	0.925713	+	0.336932i
$155$	−43591.6	−	247220.i	−0.145738	−	0.826523i
$156$	−215015.	−	180419.i	−0.707388	−	0.593569i
$157$	−127737.	+	107184.i	−0.413586	+	0.347040i	−0.825717	−	0.564085i	$-0.809229\pi$
$157$	−127737.	+	107184.i	−0.413586	+	0.347040i	0.412131	+	0.911125i	$0.364785\pi$
$158$	−39285.3	+	222798.i	−0.125195	+	0.710016i
$159$	−71437.7	+	123734.i	−0.224096	+	0.388146i
$160$	47833.7	+	82850.3i	0.147718	+	0.255855i
$161$	48272.3	−	17569.7i	0.146769	−	0.0534194i
$162$	−18357.1	+	6681.44i	−0.0549562	+	0.0200024i
$163$	305358.	+	528896.i	0.900203	+	1.55920i	0.827231	+	0.561863i	$0.189915\pi$
$163$	305358.	+	528896.i	0.900203	+	1.55920i	0.0729720	+	0.997334i	$0.476752\pi$
$164$	−156476.	+	271024.i	−0.454295	+	0.786862i
$165$	−163932.	+	929703.i	−0.468763	+	2.65848i
$166$	260931.	−	218947.i	0.734946	−	0.616693i
$167$	−23512.5	−	19729.3i	−0.0652390	−	0.0547420i	0.609585	−	0.792721i	$-0.291336\pi$
$167$	−23512.5	−	19729.3i	−0.0652390	−	0.0547420i	−0.674824	+	0.737979i	$0.735781\pi$
$168$	−51419.9	−	291617.i	−0.140559	−	0.797149i
$169$	−99430.0	−	36189.5i	−0.267794	−	0.0974690i
$170$	−460610.			−1.22239
$171$	−484242.	−	407074.i	−1.26640	−	1.06459i
$172$	−5937.25			−0.0153026
$173$	9027.06	+	3285.58i	0.0229314	+	0.00834635i	0.353460	−	0.935449i	$-0.385005\pi$
$173$	9027.06	+	3285.58i	0.0229314	+	0.00834635i	−0.330529	+	0.943796i	$0.607227\pi$
$174$	76557.6	+	434180.i	0.191697	+	1.08717i
$175$	−781963.	−	656145.i	−1.93015	−	1.61959i
$176$	78025.1	−	65470.8i	0.189868	−	0.159318i
$177$	−132719.	+	752684.i	−0.318419	+	1.80584i
$178$	−43399.7	+	75170.4i	−0.102668	+	0.177827i
$179$	−260394.	−	451016.i	−0.607433	−	1.05211i	−0.991662	−	0.128867i	$-0.958866\pi$
$179$	−260394.	−	451016.i	−0.607433	−	1.05211i	0.384229	−	0.923238i	$-0.374467\pi$
$180$	564708.	−	205537.i	1.29910	−	0.472834i
$181$	−243019.	+	88451.8i	−0.551371	+	0.200683i	−0.602656	−	0.798001i	$-0.705891\pi$
$181$	−243019.	+	88451.8i	−0.551371	+	0.200683i	0.0512843	+	0.998684i	$0.483669\pi$
$182$	−251669.	−	435903.i	−0.563184	−	0.975464i
$183$	−28080.6	+	48637.1i	−0.0619839	+	0.107359i
$184$	3133.79	−	17772.6i	0.00682379	−	0.0386996i
$185$	275945.	−	231546.i	0.592780	−	0.497401i
$186$	209109.	+	175463.i	0.443190	+	0.371880i
$187$	85156.9	+	482949.i	0.178080	+	1.00994i
$188$	−203504.	−	74069.6i	−0.419932	−	0.152843i
$189$	−735784.			−1.49829
$190$	450124.	+	378393.i	0.904582	+	0.760429i
$191$	423915.			0.840805			0.420402	−	0.907338i	$-0.361889\pi$
$191$	423915.			0.840805			0.420402	+	0.907338i	$0.361889\pi$
$192$	−97754.0	−	35579.5i	−0.191373	−	0.0696542i
$193$	−88691.6	−	502995.i	−0.171391	−	0.972009i	−0.942227	−	0.334975i	$-0.891272\pi$
$193$	−88691.6	−	502995.i	−0.171391	−	0.972009i	0.770836	−	0.637034i	$-0.219839\pi$
$194$	341836.	+	286835.i	0.652099	+	0.547176i
$195$	1.25549e6	−	1.05348e6i	2.36443	−	1.98399i
$196$	45513.3	−	258118.i	0.0846248	−	0.479931i
$197$	−366400.	+	634623.i	−0.672650	+	1.16506i	0.304499	+	0.952513i	$0.401511\pi$
$197$	−366400.	+	634623.i	−0.672650	+	1.16506i	−0.977150	+	0.212552i	$0.931823\pi$
$198$	−319908.	−	554097.i	−0.579912	−	1.00444i
$199$	345017.	−	125576.i	0.617601	−	0.224789i	−0.0142246	−	0.999899i	$-0.504528\pi$
$199$	345017.	−	125576.i	0.617601	−	0.224789i	0.631826	+	0.775110i	$0.282306\pi$
$200$	−336981.	+	122651.i	−0.595705	+	0.216819i
$201$	−3378.24	−	5851.29i	−0.00589795	−	0.0102155i
$202$	−307102.	+	531917.i	−0.529547	+	0.917203i
$203$	−137288.	+	778597.i	−0.233825	+	1.32609i
$204$	383683.	−	321948.i	0.645501	−	0.541639i
$205$	−1.39983e6	−	1.17460e6i	−2.32643	−	1.95211i
$206$	−12509.0	−	70941.9i	−0.0205378	−	0.116476i
$207$	−106527.	−	38772.7i	−0.172796	−	0.0628927i
$208$	−176826.			−0.283392
$209$	313526.	−	541911.i	0.496487	−	0.858148i
$210$	1.72904e6			2.70556
$211$	921289.	+	335322.i	1.42459	+	0.518508i	0.935376	−	0.353655i	$-0.115061\pi$
$211$	921289.	+	335322.i	1.42459	+	0.518508i	0.489214	+	0.872164i	$0.337284\pi$
$212$	15630.0	+	88642.1i	0.0238847	+	0.135457i
$213$	433683.	+	363903.i	0.654973	+	0.549587i
$214$	117186.	−	98330.9i	0.174921	−	0.146776i
$215$	6020.03	−	34141.3i	0.00888184	−	0.0503714i
$216$	−129243.	+	223856.i	−0.188484	+	0.326463i
$217$	244755.	+	423928.i	0.352844	+	0.611143i
$218$	−571555.	+	208029.i	−0.814548	+	0.296471i
$219$	−1.32914e6	+	483767.i	−1.87266	+	0.681594i
$220$	297368.	+	515056.i	0.414226	+	0.717460i
$221$	425683.	−	737304.i	0.586280	−	1.01547i
$222$	−68018.1	+	385750.i	−0.0926279	+	0.525319i
$223$	−420654.	+	352971.i	−0.566452	+	0.475309i	−0.880466	−	0.474109i	$-0.842770\pi$
$223$	−420654.	+	352971.i	−0.566452	+	0.475309i	0.314015	+	0.949418i	$0.398326\pi$
$224$	−142905.	−	119911.i	−0.190294	−	0.159676i
$225$	391169.	+	2.21843e6i	0.515120	+	2.92139i
$226$	−884467.	−	321920.i	−1.15189	−	0.419253i
$227$	497072.			0.640257			0.320129	−	0.947374i	$-0.396274\pi$
$227$	497072.			0.640257			0.320129	+	0.947374i	$0.396274\pi$
$228$	−639429.	−	578.018i	−0.814621	−	0.000736384i
$229$	352557.			0.444263			0.222132	−	0.975017i	$-0.428699\pi$
$229$	352557.			0.444263			0.222132	+	0.975017i	$0.428699\pi$
$230$	99021.5	+	36040.9i	0.123427	+	0.0449237i
$231$	−319662.	−	1.81290e6i	−0.394150	−	2.23534i
$232$	212766.	+	178532.i	0.259527	+	0.217769i
$233$	−630507.	+	529058.i	−0.760852	+	0.638430i	−0.938348	−	0.345691i	$-0.887645\pi$
$233$	−630507.	+	529058.i	−0.760852	+	0.638430i	0.177497	+	0.984121i	$0.443200\pi$
$234$	−192882.	+	1.09389e6i	−0.230278	+	1.30597i
$235$	632269.	−	1.09512e6i	0.746848	−	1.29358i
$236$	240748.	+	416988.i	0.281373	+	0.487353i
$237$	1.34981e6	−	491292.i	1.56100	−	0.568158i
$238$	844010.	−	307195.i	0.965840	−	0.351537i
$239$	−584303.	−	1.01204e6i	−0.661673	−	1.14605i	−0.980176	−	0.198130i	$-0.936513\pi$
$239$	−584303.	−	1.01204e6i	−0.661673	−	1.14605i	0.318502	−	0.947922i	$-0.396820\pi$
$240$	303712.	−	526045.i	0.340357	−	0.589515i
$241$	−30924.1	+	175379.i	−0.0342969	+	0.194507i	−0.997142	−	0.0755458i	$-0.975930\pi$
$241$	−30924.1	+	175379.i	−0.0342969	+	0.194507i	0.962845	+	0.270053i	$0.0870412\pi$
$242$	−8430.05	+	7073.65i	−0.00925319	+	0.00776435i
$243$	−656811.	−	551129.i	−0.713550	−	0.598740i
$244$	6143.82	+	34843.3i	0.00660638	+	0.0374666i
$245$	1.43813e6	+	523435.i	1.53067	+	0.557119i
$246$	1.98704e6			2.09348
$247$	−1.02169e6	+	370819.i	−1.06556	+	0.386741i
$248$	171969.			0.177550
$249$	−2.03229e6	−	739694.i	−2.07725	−	0.756056i
$250$	−160820.	−	912054.i	−0.162738	−	0.922934i
$251$	−189012.	−	158600.i	−0.189368	−	0.158898i	0.543175	−	0.839620i	$-0.317222\pi$
$251$	−189012.	−	158600.i	−0.189368	−	0.158898i	−0.732543	+	0.680721i	$0.761667\pi$
$252$	−897679.	+	753242.i	−0.890470	+	0.747193i
$253$	19481.9	−	110487.i	0.0191350	−	0.108520i
$254$	209703.	−	363216.i	0.203948	−	0.353248i
$255$	1.46228e6	+	2.53275e6i	1.40826	+	2.43917i
$256$	−61583.7	+	22414.6i	−0.0587308	+	0.0213763i
$257$	1.03030e6	−	375000.i	0.973044	−	0.354159i	0.193912	−	0.981019i	$-0.437882\pi$
$257$	1.03030e6	−	375000.i	0.973044	−	0.354159i	0.779132	+	0.626860i	$0.215660\pi$
$258$	18848.8	+	32647.1i	0.0176293	+	0.0305348i
$259$	−351211.	+	608315.i	−0.325326	+	0.563480i
$260$	179292.	−	1.01681e6i	0.164485	−	0.932842i
$261$	1.33653e6	−	1.12148e6i	1.21444	−	1.01904i
$262$	−833665.	−	699528.i	−0.750306	−	0.629582i
$263$	−130573.	−	740514.i	−0.116403	−	0.660152i	−0.986046	−	0.166472i	$-0.946762\pi$
$263$	−130573.	−	740514.i	−0.116403	−	0.660152i	0.869644	−	0.493680i	$-0.164349\pi$
$264$	−607708.	−	221188.i	−0.536642	−	0.195322i
$265$	−525572.			−0.459745
$266$	−1.07716e6	−	393156.i	−0.933415	−	0.340691i
$267$	551119.			0.473115
$268$	−3999.80	−	1455.81i	−0.00340174	−	0.00123813i
$269$	279875.	+	1.58725e6i	0.235821	+	1.33741i	0.840877	+	0.541226i	$0.182040\pi$
$269$	279875.	+	1.58725e6i	0.235821	+	1.33741i	−0.605056	+	0.796183i	$0.706849\pi$
$270$	−1.15621e6	−	970173.i	−0.965220	−	0.809915i
$271$	−1.20159e6	+	1.00825e6i	−0.993878	+	0.833962i	−0.986124	−	0.166008i	$-0.946912\pi$
$271$	−1.20159e6	+	1.00825e6i	−0.993878	+	0.833962i	−0.00775321	+	0.999970i	$0.502468\pi$
$272$	54792.3	−	310743.i	0.0449053	−	0.254671i
$273$	−1.59793e6	+	2.76770e6i	−1.29763	+	2.24756i
$274$	−165804.	−	287180.i	−0.133419	−	0.231089i
$275$	−2.09491e6	+	762486.i	−1.67045	+	0.607995i
$276$	−107675.	+	39190.5i	−0.0850828	+	0.0309676i
$277$	−91674.8	−	158785.i	−0.0717878	−	0.124340i	0.827897	−	0.560880i	$-0.189537\pi$
$277$	−91674.8	−	158785.i	−0.0717878	−	0.124340i	−0.899685	+	0.436540i	$0.856204\pi$
$278$	180125.	−	311985.i	0.139785	−	0.242115i
$279$	187583.	−	1.06384e6i	0.144273	−	0.818210i
$280$	834430.	−	700170.i	0.636055	−	0.533714i
$281$	1.76856e6	+	1.48400e6i	1.33615	+	1.12116i	0.982597	+	0.185748i	$0.0594708\pi$
$281$	1.76856e6	+	1.48400e6i	1.33615	+	1.12116i	0.353552	+	0.935415i	$0.384974\pi$
$282$	238774.	+	1.35415e6i	0.178799	+	1.01402i
$283$	−2.18330e6	−	794655.i	−1.62049	−	0.589811i	−0.637016	−	0.770851i	$-0.719831\pi$
$283$	−2.18330e6	−	794655.i	−1.62049	−	0.589811i	−0.983476	+	0.181040i	$0.942054\pi$
$284$	356656.			0.262394
$285$	651669.	−	3.67636e6i	0.475242	−	2.68106i
$286$	−1.09928e6			−0.794679
$287$	3.34839e6	+	1.21871e6i	2.39956	+	0.873367i
$288$	71486.6	+	405421.i	0.0507859	+	0.288021i
$289$	76111.9	+	63865.5i	0.0536053	+	0.0449802i
$290$	−1.24236e6	+	1.04246e6i	−0.867465	+	0.727889i
$291$	491998.	−	2.79026e6i	0.340589	−	1.93158i
$292$	−445539.	+	771696.i	−0.305794	+	0.529650i
$293$	−515337.	−	892590.i	−0.350689	−	0.607412i	0.635681	−	0.771952i	$-0.280719\pi$
$293$	−515337.	−	892590.i	−0.350689	−	0.607412i	−0.986370	+	0.164540i	$0.947386\pi$
$294$	−1.56380e6	+	569178.i	−1.05515	+	0.384043i
$295$	−2.64193e6	+	961586.i	−1.76753	+	0.643329i
$296$	123383.	+	213706.i	0.0818514	+	0.141771i
$297$	−803467.	+	1.39165e6i	−0.528539	+	0.915456i
$298$	52685.4	−	298794.i	0.0343676	−	0.194909i
$299$	−149204.	+	125197.i	−0.0965167	+	0.0809872i
$300$	1.74423e6	+	1.46358e6i	1.11892	+	0.938887i
$301$	11738.9	+	66574.6i	0.00746812	+	0.0423538i
$302$	1.20950e6	+	440223.i	0.763113	+	0.277751i
$303$	3.89980e6			2.44026
$304$	−308821.	+	258656.i	−0.191656	+	0.160524i
$305$	−206591.			−0.127163
$306$	−1.86256e6	−	677916.i	−1.13712	−	0.413878i
$307$	292135.	+	1.65678e6i	0.176904	+	1.00327i	0.935923	+	0.352203i	$0.114567\pi$
$307$	292135.	+	1.65678e6i	0.176904	+	1.00327i	−0.759020	+	0.651068i	$0.774321\pi$
$308$	−888396.	−	745453.i	−0.533617	−	0.447758i
$309$	−350376.	+	294000.i	−0.208756	+	0.175167i
$310$	−174367.	+	988882.i	−0.103053	+	0.584440i
$311$	346830.	−	600727.i	0.203337	−	0.352190i	−0.746265	−	0.665649i	$-0.768155\pi$
$311$	346830.	−	600727.i	0.203337	−	0.352190i	0.949602	+	0.313460i	$0.101488\pi$
$312$	561365.	+	972313.i	0.326482	+	0.565483i
$313$	1.43212e6	−	521248.i	0.826262	−	0.300735i	0.105938	−	0.994373i	$-0.466215\pi$
$313$	1.43212e6	−	521248.i	0.826262	−	0.300735i	0.720324	+	0.693638i	$0.243993\pi$
$314$	626768.	−	228125.i	0.358743	−	0.130572i
$315$	−3.42122e6	−	5.92572e6i	−1.94269	−	3.36484i
$316$	452470.	−	783701.i	0.254901	−	0.441502i
$317$	260136.	−	1.47531e6i	0.145396	−	0.824582i	−0.821652	−	0.569989i	$-0.806947\pi$
$317$	260136.	−	1.47531e6i	0.145396	−	0.824582i	0.967048	−	0.254593i	$-0.0819415\pi$
$318$	437795.	−	367354.i	0.242775	−	0.203712i
$319$	1.32271e6	+	1.10988e6i	0.727757	+	0.610661i
$320$	−66449.8	−	376856.i	−0.0362760	−	0.205731i
$321$	−912719.	−	332202.i	−0.494395	−	0.179945i
$322$	−205481.			−0.110442
$323$	−335067.	−	1.91035e6i	−0.178700	−	1.01884i
$324$	78140.8			0.0413538
$325$	3.63691e6	+	1.32373e6i	1.90996	+	0.695168i
$326$	−424199.	−	2.40575e6i	−0.221068	−	1.25374i
$327$	2.95839e6	+	2.48238e6i	1.52998	+	1.28380i
$328$	958941.	−	804647.i	0.492161	−	0.412972i
$329$	−428184.	+	2.42835e6i	−0.218093	+	1.23686i
$330$	1.88809e6	−	3.27027e6i	0.954416	−	1.65310i
$331$	−255612.	−	442733.i	−0.128236	−	0.222112i	0.794757	−	0.606928i	$-0.207598\pi$
$331$	−255612.	−	442733.i	−0.128236	−	0.222112i	−0.922993	+	0.384816i	$0.874265\pi$
$332$	−1.28032e6	+	465997.i	−0.637489	+	0.232027i
$333$	1.45662e6	−	530166.i	0.719838	−	0.262000i
$334$	61386.7	+	106325.i	0.0301098	+	0.0521518i
$335$	12427.0	−	21524.2i	0.00604998	−	0.0104789i
$336$	−205680.	+	1.16647e6i	−0.0993901	+	0.563669i
$337$	−3.17454e6	+	2.66375e6i	−1.52267	+	1.27767i	−0.690163	+	0.723654i	$0.742461\pi$
$337$	−3.17454e6	+	2.66375e6i	−1.52267	+	1.27767i	−0.832505	+	0.554017i	$0.813094\pi$
$338$	324224.	+	272056.i	0.154367	+	0.129529i
$339$	1.03775e6	+	5.88540e6i	0.490451	+	2.78148i
$340$	1.73133e6	+	630151.i	0.812235	+	0.295629i
$341$	1.06908e6			0.497879
$342$	1.26325e6	+	2.19258e6i	0.584013	+	1.01366i
$343$	77557.5			0.0355950
$344$	22316.7	+	8122.63i	0.0101680	+	0.00370084i
$345$	−116183.	−	658907.i	−0.0525527	−	0.298041i
$346$	−29435.7	−	24699.5i	−0.0132186	−	0.0110917i
$347$	−2.48041e6	+	2.08131e6i	−1.10586	+	0.927927i	−0.997805	−	0.0662174i	$-0.978907\pi$
$347$	−2.48041e6	+	2.08131e6i	−1.10586	+	0.927927i	−0.108056	+	0.994145i	$0.534462\pi$
$348$	306230.	−	1.73672e6i	0.135550	−	0.768743i
$349$	1.11303e6	−	1.92783e6i	0.489153	−	0.847238i	−0.510769	−	0.859718i	$-0.670639\pi$
$349$	1.11303e6	−	1.92783e6i	0.489153	−	0.847238i	0.999922	+	0.0124799i	$0.00397257\pi$
$350$	2.04156e6	+	3.53609e6i	0.890825	+	1.54295i
$351$	2.62150e6	−	954149.i	1.13575	−	0.413379i
$352$	−382848.	+	139345.i	−0.164691	+	0.0599426i
$353$	532415.	+	922171.i	0.227412	+	0.393890i	0.957040	−	0.289955i	$-0.0936402\pi$
$353$	532415.	+	922171.i	0.227412	+	0.393890i	−0.729628	+	0.683844i	$0.760307\pi$
$354$	1.52859e6	−	2.64760e6i	0.648311	−	1.12291i
$355$	−361629.	+	2.05090e6i	−0.152297	+	0.863721i
$356$	265969.	−	223174.i	0.111226	−	0.0933295i
$357$	−4.36862e6	−	3.66571e6i	−1.81415	−	1.52226i
$358$	361736.	+	2.05150e6i	0.149171	+	0.845990i
$359$	−742235.	−	270151.i	−0.303952	−	0.110630i	0.185541	−	0.982636i	$-0.440596\pi$
$359$	−742235.	−	270151.i	−0.303952	−	0.110630i	−0.489494	+	0.872007i	$0.662818\pi$
$360$	−2.40380e6			−0.977557
$361$	−1.24192e6	+	2.14212e6i	−0.501565	+	0.865120i
$362$	1.03446e6			0.414900
$363$	65658.5	+	23897.7i	0.0261532	+	0.00951897i
$364$	349614.	+	1.98276e6i	0.138304	+	0.784363i
$365$	−3.98578e6	−	3.34447e6i	−1.56596	−	1.31400i
$366$	172088.	−	144399.i	0.0671503	−	0.0563458i
$367$	625710.	−	3.54858e6i	0.242498	−	1.37527i	−0.583734	−	0.811945i	$-0.698409\pi$
$367$	625710.	−	3.54858e6i	0.242498	−	1.37527i	0.826232	−	0.563330i	$-0.190480\pi$
$368$	−36093.6	+	62515.9i	−0.0138935	+	0.0240642i
$369$	−3.93172e6	−	6.80993e6i	−1.50320	−	2.60362i
$370$	−1.35399e6	+	492811.i	−0.514174	+	0.187144i
$371$	963045.	−	350520.i	0.363255	−	0.132214i
$372$	−545944.	−	945603.i	−0.204546	−	0.354284i
$373$	−861755.	+	1.49260e6i	−0.320709	+	0.555485i	−0.980635	−	0.195846i	$-0.937255\pi$
$373$	−861755.	+	1.49260e6i	−0.320709	+	0.555485i	0.659925	+	0.751331i	$0.270588\pi$
$374$	340628.	−	1.93180e6i	0.125922	−	0.714138i
$375$	−4.50455e6	+	3.77977e6i	−1.65414	+	1.38799i
$376$	663593.	+	556821.i	0.242065	+	0.203117i
$377$	−520530.	−	2.95207e6i	−0.188622	−	1.06973i
$378$	2.76564e6	+	1.00661e6i	0.995558	+	0.362353i
$379$	1.34133e6			0.479666			0.239833	−	0.970814i	$-0.422907\pi$
$379$	1.34133e6			0.479666			0.239833	+	0.970814i	$0.422907\pi$
$380$	−1.17424e6	−	2.03810e6i	−0.417155	−	0.724045i
$381$	−2.66295e6			−0.939832
$382$	−1.59340e6	−	579950.i	−0.558684	−	0.203344i
$383$	−183285.	−	1.03946e6i	−0.0638456	−	0.362086i	−0.999946	−	0.0103545i	$-0.996704\pi$
$383$	−183285.	−	1.03946e6i	−0.0638456	−	0.362086i	0.936101	−	0.351732i	$-0.114407\pi$
$384$	318759.	+	267471.i	0.110315	+	0.0925653i
$385$	5.18740e6	−	4.35275e6i	1.78360	−	1.49662i
$386$	−354766.	+	2.01198e6i	−0.121192	+	0.687314i
$387$	74591.5	−	129196.i	0.0253170	−	0.0438503i
$388$	−892471.	−	1.54580e6i	−0.300964	−	0.521285i
$389$	3.05224e6	−	1.11092e6i	1.02269	−	0.372229i	0.224397	−	0.974498i	$-0.427959\pi$
$389$	3.05224e6	−	1.11092e6i	1.02269	−	0.372229i	0.798293	+	0.602269i	$0.205736\pi$
$390$	−6.16034e6	+	2.24218e6i	−2.05089	+	0.746464i
$391$	−173780.	−	300996.i	−0.0574854	−	0.0995677i
$392$	−524201.	+	907942.i	−0.172299	+	0.298430i
$393$	−1.19988e6	+	6.80484e6i	−0.391882	+	2.22247i
$394$	2.24543e6	−	1.88414e6i	0.728716	−	0.611465i
$395$	4.04778e6	+	3.39649e6i	1.30534	+	1.09531i
$396$	444411.	+	2.52038e6i	0.142412	+	0.807659i
$397$	−5.69014e6	−	2.07104e6i	−1.81195	−	0.659496i	−0.996772	−	0.0802876i	$-0.974416\pi$
$397$	−5.69014e6	−	2.07104e6i	−1.81195	−	0.659496i	−0.815179	−	0.579209i	$-0.803362\pi$
$398$	−1.46864e6			−0.464737
$399$	1.25777e6	+	7.17110e6i	0.395522	+	2.25504i
$400$	1.43443e6			0.448260
$401$	−713025.	−	259520.i	−0.221434	−	0.0805953i	0.228921	−	0.973445i	$-0.426480\pi$
$401$	−713025.	−	259520.i	−0.221434	−	0.0805953i	−0.450355	+	0.892850i	$0.648702\pi$
$402$	4693.01	+	26615.4i	0.00144839	+	0.00821424i
$403$	−1.42177e6	−	1.19301e6i	−0.436081	−	0.365915i
$404$	1.88203e6	−	1.57921e6i	0.573685	−	0.481379i
$405$	−79230.4	+	449338.i	−0.0240024	+	0.136124i
$406$	1.58122e6	−	2.73875e6i	0.476076	−	0.824588i
$407$	767036.	+	1.32854e6i	0.229525	+	0.397548i
$408$	−1.88263e6	+	685220.i	−0.559904	+	0.203788i
$409$	2.80119e6	−	1.01955e6i	0.828007	−	0.301370i	0.106967	−	0.994263i	$-0.465886\pi$
$409$	2.80119e6	−	1.01955e6i	0.828007	−	0.301370i	0.721041	+	0.692893i	$0.243664\pi$
$410$	3.65470e6	+	6.33012e6i	1.07372	+	1.85974i
$411$	−1.05274e6	+	1.82341e6i	−0.307410	+	0.532450i
$412$	−50035.9	+	283768.i	−0.0145224	+	0.0823607i
$413$	4.19971e6	−	3.52397e6i	1.21156	−	1.01662i
$414$	347367.	+	291476.i	0.0996065	+	0.0835798i
$415$	−1.38148e6	−	7.83478e6i	−0.393754	−	2.23309i
$416$	664649.	+	241912.i	0.188304	+	0.0685370i
$417$	−2.28735e6			−0.644158
$418$	−1.91985e6	+	1.60799e6i	−0.537436	+	0.450135i
$419$	−4.92084e6			−1.36932			−0.684658	−	0.728864i	$-0.740049\pi$
$419$	−4.92084e6			−1.36932			−0.684658	+	0.728864i	$0.740049\pi$
$420$	−6.49906e6	−	2.36546e6i	−1.79774	−	0.654324i
$421$	121190.	+	687305.i	0.0333244	+	0.188992i	0.996926	−	0.0783508i	$-0.0249654\pi$
$421$	121190.	+	687305.i	0.0333244	+	0.188992i	−0.963601	+	0.267343i	$0.913854\pi$
$422$	−3.00417e6	−	2.52080e6i	−0.821189	−	0.689059i
$423$	4.16847e6	−	3.49776e6i	1.13273	−	0.950472i
$424$	62520.0	−	354568.i	0.0168890	−	0.0957823i
$425$	−3.45318e6	+	5.98109e6i	−0.927358	+	1.60623i
$426$	−1.13227e6	−	1.96114e6i	−0.302290	−	0.523582i
$427$	378552.	−	137782.i	0.100475	−	0.0365698i
$428$	−575000.	+	209283.i	−0.151726	+	0.0552236i
$429$	3.48984e6	+	6.04458e6i	0.915508	+	1.58571i
$430$	−69336.0	+	120093.i	−0.0180837	+	0.0313219i
$431$	600219.	−	3.40401e6i	0.155638	−	0.882668i	−0.802562	−	0.596569i	$-0.796530\pi$
$431$	600219.	−	3.40401e6i	0.155638	−	0.882668i	0.958200	−	0.286099i	$-0.0923587\pi$
$432$	792049.	−	664608.i	0.204194	−	0.171339i
$433$	−4.32864e6	−	3.63216e6i	−1.10951	−	0.930990i	−0.111483	−	0.993766i	$-0.535560\pi$
$433$	−4.32864e6	−	3.63216e6i	−1.10951	−	0.930990i	−0.998028	+	0.0627763i	$0.980005\pi$
$434$	−340010.	−	1.92829e6i	−0.0866498	−	0.491415i
$435$	9.67626e6	+	3.52187e6i	2.45180	+	0.892380i
$436$	2.43294e6			0.612937
$437$	−77445.3	+	436904.i	−0.0193995	+	0.109442i
$438$	5.65776e6			1.40916
$439$	6.82988e6	+	2.48587e6i	1.69142	+	0.615627i	0.994803	−	0.101815i	$-0.0324650\pi$
$439$	6.82988e6	+	2.48587e6i	1.69142	+	0.615627i	0.696618	+	0.717442i	$0.254687\pi$
$440$	−413099.	−	2.34280e6i	−0.101724	−	0.576904i
$441$	5.04494e6	+	4.23321e6i	1.23526	+	1.03651i
$442$	−2.60874e6	+	2.18899e6i	−0.635147	+	0.532952i
$443$	−314818.	+	1.78542e6i	−0.0762168	+	0.432247i	0.922692	+	0.385539i	$0.125984\pi$
$443$	−314818.	+	1.78542e6i	−0.0762168	+	0.432247i	−0.998909	+	0.0467085i	$0.985127\pi$
$444$	783401.	−	1.35689e6i	0.188593	−	0.326653i
$445$	1.01365e6	+	1.75570e6i	0.242655	+	0.420292i
$446$	2.06403e6	−	751247.i	0.491337	−	0.178832i
$447$	−1.81023e6	+	658871.i	−0.428515	+	0.155967i
$448$	373097.	+	646224.i	0.0878268	+	0.152121i
$449$	−1.38034e6	+	2.39082e6i	−0.323126	+	0.559670i	−0.981131	−	0.193343i	$-0.938067\pi$
$449$	−1.38034e6	+	2.39082e6i	−0.323126	+	0.559670i	0.658006	+	0.753013i	$0.271400\pi$
$450$	1.56468e6	−	8.87373e6i	0.364245	−	2.06574i
$451$	5.96145e6	−	5.00225e6i	1.38010	−	1.15804i
$452$	2.88410e6	+	2.42004e6i	0.663993	+	0.557156i
$453$	−1.41912e6	−	8.04824e6i	−0.324918	−	1.84270i
$454$	−1.86838e6	−	680034.i	−0.425427	−	0.154843i
$455$	−1.17561e7			−2.66216
$456$	2.40268e6	+	876963.i	0.541107	+	0.197501i
$457$	7.69236e6			1.72294			0.861468	−	0.507812i	$-0.169546\pi$
$457$	7.69236e6			1.72294			0.861468	+	0.507812i	$0.169546\pi$
$458$	−1.32518e6	−	482326.i	−0.295197	−	0.107443i
$459$	864446.	+	4.90251e6i	0.191516	+	1.08614i
$460$	−322892.	−	270939.i	−0.0711481	−	0.0597003i
$461$	−4.45160e6	+	3.73534e6i	−0.975583	+	0.818611i	−0.983417	−	0.181358i	$-0.941951\pi$
$461$	−4.45160e6	+	3.73534e6i	−0.975583	+	0.818611i	0.00783434	+	0.999969i	$0.497506\pi$
$462$	−1.27865e6	+	7.25158e6i	−0.278706	+	1.58062i
$463$	−2.02656e6	+	3.51010e6i	−0.439346	+	0.760969i	−0.997639	−	0.0686746i	$-0.978123\pi$
$463$	−2.02656e6	+	3.51010e6i	−0.439346	+	0.760969i	0.558293	+	0.829644i	$0.311456\pi$
$464$	−555494.	−	962143.i	−0.119780	−	0.207465i
$465$	5.99111e6	−	2.18059e6i	1.28492	−	0.467672i
$466$	3.09372e6	−	1.12602e6i	0.659959	−	0.240205i
$467$	−3.02813e6	−	5.24487e6i	−0.642513	−	1.11286i	−0.984870	−	0.173295i	$-0.944559\pi$
$467$	−3.02813e6	−	5.24487e6i	−0.642513	−	1.11286i	0.342357	−	0.939570i	$-0.388775\pi$
$468$	2.22152e6	−	3.84779e6i	0.468853	−	0.812077i
$469$	−8415.79	+	47728.3i	−0.00176670	+	0.0100195i
$470$	−3.87477e6	+	3.25132e6i	−0.809098	+	0.678914i
$471$	−3.24417e6	−	2.72218e6i	−0.673832	−	0.565412i
$472$	−334444.	−	1.89672e6i	−0.0690984	−	0.391876i
$473$	138737.	+	50496.0i	0.0285127	+	0.0103778i
$474$	−5.74577e6			−1.17463
$475$	8.28806e6	−	3.00812e6i	1.68546	−	0.611733i
$476$	−3.59271e6			−0.726782
$477$	−2.12524e6	−	773526.i	−0.427674	−	0.155661i
$478$	811706.	+	4.60341e6i	0.162491	+	0.921531i
$479$	3.05657e6	+	2.56477e6i	0.608690	+	0.510752i	0.894226	−	0.447617i	$-0.147727\pi$
$479$	3.05657e6	+	2.56477e6i	0.608690	+	0.510752i	−0.285536	+	0.958368i	$0.592171\pi$
$480$	−1.86126e6	+	1.56178e6i	−0.368726	+	0.309397i
$481$	462468.	−	2.62279e6i	0.0911422	−	0.516893i
$482$	356170.	−	616904.i	0.0698296	−	0.120948i
$483$	652336.	+	1.12988e6i	0.127234	+	0.220376i
$484$	41363.9	−	15055.2i	0.00802617	−	0.00292129i
$485$	9.79385e6	−	3.56467e6i	1.89060	−	0.688121i
$486$	1.71481e6	+	2.97014e6i	0.329326	+	0.570409i
$487$	−3.78689e6	+	6.55908e6i	−0.723535	+	1.25320i	0.236039	+	0.971744i	$0.424151\pi$
$487$	−3.78689e6	+	6.55908e6i	−0.723535	+	1.25320i	−0.959574	+	0.281456i	$0.909183\pi$
$488$	24575.3	−	139373.i	0.00467142	−	0.0264929i
$489$	−1.18818e7	+	9.97001e6i	−2.24703	+	1.88549i
$490$	−4.68949e6	−	3.93495e6i	−0.882338	−	0.740370i
$491$	−265158.	−	1.50379e6i	−0.0496365	−	0.281503i	0.949879	−	0.312617i	$-0.101206\pi$
$491$	−265158.	−	1.50379e6i	−0.0496365	−	0.281503i	−0.999516	+	0.0311141i	$0.990094\pi$
$492$	−7.46882e6	−	2.71843e6i	−1.39104	−	0.506297i
$493$	5.34907e6			0.991200
$494$	4.34761e6	+	3930.06i	0.801554	+	0.000724572i
$495$	−1.49437e7			−2.74123
$496$	−646391.	−	235267.i	−0.117975	−	0.0429395i
$497$	−705167.	−	3.99920e6i	−0.128056	−	0.726243i
$498$	6.62696e6	+	5.56068e6i	1.19741	+	1.00474i
$499$	1.11992e6	−	939722.i	0.201342	−	0.168946i	−0.536542	−	0.843874i	$-0.680270\pi$
$499$	1.11992e6	−	939722.i	0.201342	−	0.168946i	0.737884	+	0.674928i	$0.235825\pi$
$500$	−643279.	+	3.64822e6i	−0.115073	+	0.652613i
$501$	389765.	−	675094.i	0.0693760	−	0.120163i
$502$	493476.	+	854726.i	0.0873991	+	0.151380i
$503$	−7.01217e6	+	2.55222e6i	−1.23576	+	0.449778i	−0.875565	−	0.483100i	$-0.839511\pi$
$503$	−7.01217e6	+	2.55222e6i	−1.23576	+	0.449778i	−0.360191	+	0.932879i	$0.617288\pi$
$504$	4.40466e6	−	1.60317e6i	0.772389	−	0.281127i
$505$	7.17277e6	+	1.24236e7i	1.25158	+	2.16780i
$506$	−224383.	+	388643.i	−0.0389596	+	0.0674799i
$507$	466649.	−	2.64650e6i	0.0806251	−	0.457248i
$508$	−1.28513e6	+	1.07835e6i	−0.220947	+	0.185397i
$509$	−3.22046e6	−	2.70228e6i	−0.550964	−	0.462314i	0.324303	−	0.945953i	$-0.394870\pi$
$509$	−3.22046e6	−	2.70228e6i	−0.550964	−	0.462314i	−0.875267	+	0.483640i	$0.839315\pi$
$510$	−2.03138e6	−	1.15206e7i	−0.345833	−	1.96132i
$511$	9.53397e6	+	3.47008e6i	1.61518	+	0.587878i
$512$	262144.			0.0441942
$513$	3.18267e6	−	5.50105e6i	0.533947	−	0.922895i
$514$	−4.38571e6			−0.732203
$515$	−1.58103e6	−	575449.i	−0.262678	−	0.0956068i
$516$	−26184.5	−	148500.i	−0.00432932	−	0.0245528i
$517$	4.12536e6	+	3.46159e6i	0.678791	+	0.569573i
$518$	2.15234e6	−	1.80603e6i	0.352442	−	0.295734i
$519$	−42366.2	+	240271.i	−0.00690400	+	0.0391545i
$520$	−2.06500e6	+	3.57669e6i	−0.334897	+	0.580059i
$521$	−3.03872e6	−	5.26322e6i	−0.490452	−	0.849487i	0.509488	−	0.860478i	$-0.329835\pi$
$521$	−3.03872e6	−	5.26322e6i	−0.490452	−	0.849487i	−0.999940	+	0.0109905i	$0.996502\pi$
$522$	−6.55797e6	+	2.38691e6i	−1.05340	+	0.383406i
$523$	−4.53079e6	+	1.64907e6i	−0.724302	+	0.263624i	−0.677751	−	0.735291i	$-0.737045\pi$
$523$	−4.53079e6	+	1.64907e6i	−0.724302	+	0.263624i	−0.0465512	+	0.998916i	$0.514823\pi$
$524$	2.17655e6	+	3.76989e6i	0.346290	+	0.599791i
$525$	1.29626e7	−	2.24518e7i	2.05255	−	3.55511i
$526$	−522291.	+	2.96206e6i	−0.0823091	+	0.466798i
$527$	2.53707e6	−	2.12886e6i	0.397930	−	0.333903i
$528$	1.98163e6	+	1.66279e6i	0.309341	+	0.259568i
$529$	−1.10385e6	−	6.26026e6i	−0.171503	−	0.972642i
$530$	1.97550e6	+	719025.i	0.305484	+	0.111187i
$531$	−1.20984e7			−1.86205
$532$	3.51092e6	+	2.95142e6i	0.537826	+	0.452118i
$533$	−1.35103e7			−2.05990
$534$	−2.07153e6	−	753975.i	−0.314368	−	0.114420i
$535$	−620435.	−	3.51866e6i	−0.0937156	−	0.531487i
$536$	13042.7	+	10944.1i	0.00196089	+	0.00164539i
$537$	1.01322e7	−	8.50193e6i	1.51624	−	1.27228i
$538$	1.11950e6	−	6.34899e6i	0.166751	−	0.945691i
$539$	−3.25880e6	+	5.64441e6i	−0.483154	+	0.836848i
$540$	3.01864e6	+	5.22844e6i	0.445479	+	0.771592i
$541$	−1.02131e7	+	3.71727e6i	−1.50026	+	0.546049i	−0.956127	−	0.292952i	$-0.905362\pi$
$541$	−1.02131e7	+	3.71727e6i	−1.50026	+	0.546049i	−0.544130	+	0.839001i	$0.683140\pi$
$542$	5.89587e6	−	2.14592e6i	0.862084	−	0.313773i
$543$	−3.28408e6	−	5.68819e6i	−0.477985	−	0.827894i
$544$	−631073.	+	1.09305e6i	−0.0914286	+	0.158359i
$545$	−2.46687e6	+	1.39903e7i	−0.355758	+	2.01760i
$546$	9.79268e6	−	8.21704e6i	1.40579	−	1.17960i
$547$	3.11294e6	+	2.61207e6i	0.444839	+	0.373264i	0.837517	−	0.546412i	$-0.184007\pi$
$547$	3.11294e6	+	2.61207e6i	0.444839	+	0.373264i	−0.392678	+	0.919676i	$0.628451\pi$
$548$	230332.	+	1.30628e6i	0.0327645	+	0.185816i
$549$	−835388.	−	304056.i	−0.118293	−	0.0430550i
$550$	8.91744e6			1.25700
$551$	−5.22730e6	−	4.39428e6i	−0.733497	−	0.616608i
$552$	458341.			0.0640237
$553$	−9.68228e6	−	3.52406e6i	−1.34637	−	0.490039i
$554$	127353.	+	722256.i	0.0176293	+	0.0999809i
$555$	7.00828e6	+	5.88065e6i	0.965782	+	0.810387i
$556$	−1.10387e6	+	926256.i	−0.151436	+	0.127070i
$557$	1.79534e6	−	1.01819e7i	0.245194	−	1.39056i	−0.574848	−	0.818260i	$-0.694939\pi$
$557$	1.79534e6	−	1.01819e7i	0.245194	−	1.39056i	0.820042	−	0.572304i	$-0.193950\pi$
$558$	−2.16050e6	+	3.74209e6i	−0.293744	+	0.508779i
$559$	−128157.	−	221974.i	−0.0173465	−	0.0300450i
$560$	−4.09432e6	+	1.49021e6i	−0.551711	+	0.200806i
$561$	−1.17037e7	+	4.25981e6i	−1.57006	+	0.571456i
$562$	−4.61739e6	−	7.99756e6i	−0.616675	−	1.06811i
$563$	−4.77797e6	+	8.27569e6i	−0.635291	+	1.10036i	0.351163	+	0.936314i	$0.385786\pi$
$563$	−4.77797e6	+	8.27569e6i	−0.635291	+	1.10036i	−0.986453	+	0.164041i	$0.947547\pi$
$564$	955096.	−	5.41662e6i	0.126430	−	0.717019i
$565$	−1.68404e7	+	1.41308e7i	−2.21938	+	1.86228i
$566$	7.11936e6	+	5.97385e6i	0.934114	+	0.783815i
$567$	−154497.	−	876197.i	−0.0201819	−	0.114457i
$568$	−1.34059e6	−	487934.i	−0.174351	−	0.0634586i
$569$	5.49168e6			0.711089			0.355545	−	0.934659i	$-0.384295\pi$
$569$	5.49168e6			0.711089			0.355545	+	0.934659i	$0.384295\pi$
$570$	−7.47904e6	+	1.29271e7i	−0.964181	+	1.66653i
$571$	7.79290e6			1.00025			0.500125	−	0.865953i	$-0.333287\pi$
$571$	7.79290e6			1.00025			0.500125	+	0.865953i	$0.333287\pi$
$572$	4.13193e6	+	1.50390e6i	0.528035	+	0.192189i
$573$	1.86955e6	+	1.06028e7i	0.237876	+	1.34906i
$574$	−1.09185e7	−	9.16173e6i	−1.38320	−	1.16064i
$575$	1.21036e6	−	1.01561e6i	0.152667	−	0.128103i
$576$	285946.	−	1.62168e6i	0.0359111	−	0.203662i
$577$	1.87425e6	−	3.24630e6i	0.234363	−	0.405929i	−0.724724	−	0.689039i	$-0.758033\pi$
$577$	1.87425e6	−	3.24630e6i	0.234363	−	0.405929i	0.959087	+	0.283110i	$0.0913662\pi$
$578$	−198714.	−	344183.i	−0.0247405	−	0.0428519i
$579$	1.21895e7	−	4.43662e6i	1.51109	−	0.549992i
$580$	6.09591e6	−	2.21873e6i	0.752434	−	0.273864i
$581$	7.75665e6	+	1.34349e7i	0.953309	+	1.65118i
$582$	−5.66660e6	+	9.81484e6i	−0.693450	+	1.20109i
$583$	388668.	−	2.20425e6i	0.0473596	−	0.268589i
$584$	2.73042e6	−	2.29109e6i	0.331282	−	0.277978i
$585$	1.98737e7	+	1.66760e7i	2.40098	+	2.01466i
$586$	715899.	+	4.06006e6i	0.0861207	+	0.488415i
$587$	5.37343e6	+	1.95577e6i	0.643660	+	0.234273i	0.643166	−	0.765727i	$-0.277621\pi$
$587$	5.37343e6	+	1.95577e6i	0.643660	+	0.234273i	0.000493919		1.00000i	$0.499843\pi$
$588$	6.65666e6			0.793986
$589$	−4.22818e6	−	3822.10i	−0.502186	−	0.000453956i
$590$	1.12460e7			1.33004
$591$	−1.74888e7	−	6.36539e6i	−2.05964	−	0.749647i
$592$	−171402.	−	972068.i	−0.0201007	−	0.113997i
$593$	3.82253e6	+	3.20749e6i	0.446390	+	0.374566i	0.838094	−	0.545525i	$-0.183670\pi$
$593$	3.82253e6	+	3.20749e6i	0.446390	+	0.374566i	−0.391704	+	0.920091i	$0.628114\pi$
$594$	4.92393e6	−	4.13167e6i	0.572593	−	0.480463i
$595$	3.64280e6	−	2.06594e7i	0.421836	−	2.39235i
$596$	−606807.	+	1.05102e6i	−0.0699737	+	0.121198i
$597$	4.66245e6	+	8.07559e6i	0.535400	+	0.927339i
$598$	732104.	−	266464.i	0.0837181	−	0.0304709i
$599$	1.16806e7	−	4.25139e6i	1.33014	−	0.484132i	0.423448	−	0.905920i	$-0.360820\pi$
$599$	1.16806e7	−	4.25139e6i	1.33014	−	0.484132i	0.906694	+	0.421788i	$0.138597\pi$
$600$	−4.55385e6	−	7.88750e6i	−0.516417	−	0.894461i
$601$	1.34088e6	−	2.32247e6i	0.151427	−	0.262279i	−0.780325	−	0.625374i	$-0.784947\pi$
$601$	1.34088e6	−	2.32247e6i	0.151427	−	0.262279i	0.931752	+	0.363095i	$0.118280\pi$
$602$	46955.6	−	266299.i	0.00528076	−	0.0299487i
$603$	81929.6	−	68747.1i	0.00917588	−	0.00769947i
$604$	−3.94398e6	−	3.30939e6i	−0.439888	−	0.369110i
$605$	44632.4	+	253123.i	0.00495749	+	0.0281153i
$606$	−1.46584e7	−	5.33524e6i	−1.62146	−	0.590163i
$607$	−4.21605e6			−0.464444			−0.232222	−	0.972663i	$-0.574600\pi$
$607$	−4.21605e6			−0.464444			−0.232222	+	0.972663i	$0.574600\pi$
$608$	1.51465e6	−	549738.i	0.166170	−	0.0603110i
$609$	−2.00794e7			−2.19385
$610$	776528.	+	282633.i	0.0844954	+	0.0307538i
$611$	−1.62347e6	−	9.20717e6i	−0.175931	−	0.997753i
$612$	6.07349e6	+	5.09626e6i	0.655480	+	0.550013i
$613$	−6.87125e6	+	5.76566e6i	−0.738558	+	0.619724i	−0.932450	−	0.361299i	$-0.882333\pi$
$613$	−6.87125e6	+	5.76566e6i	−0.738558	+	0.619724i	0.193892	+	0.981023i	$0.437889\pi$
$614$	1.16854e6	−	6.62711e6i	0.125090	−	0.709420i
$615$	2.32049e7	−	4.01921e7i	2.47396	−	4.28502i
$616$	2.31944e6	+	4.01738e6i	0.246281	+	0.426571i
$617$	1.28712e7	−	4.68472e6i	1.36115	−	0.495416i	0.444737	−	0.895661i	$-0.353297\pi$
$617$	1.28712e7	−	4.68472e6i	1.36115	−	0.495416i	0.916408	+	0.400245i	$0.131075\pi$
$618$	1.71920e6	−	625737.i	0.181074	−	0.0659054i
$619$	−683721.	−	1.18424e6i	−0.0717219	−	0.124226i	0.827934	−	0.560825i	$-0.189516\pi$
$619$	−683721.	−	1.18424e6i	−0.0717219	−	0.124226i	−0.899656	+	0.436599i	$0.856183\pi$
$620$	2.00827e6	−	3.47843e6i	0.209818	−	0.363416i
$621$	197764.	−	1.12158e6i	0.0205788	−	0.116708i
$622$	−2.12550e6	+	1.78350e6i	−0.220285	+	0.184841i
$623$	−3.02833e6	−	2.54107e6i	−0.312595	−	0.262299i
$624$	−779840.	−	4.42269e6i	−0.0801759	−	0.454700i
$625$	−3.87214e6	−	1.40934e6i	−0.396507	−	0.144317i
$626$	−6.09611e6			−0.621752
$627$	1.49367e7	+	5.45182e6i	1.51735	+	0.553825i
$628$	−2.66797e6			−0.269949
$629$	4.46581e6	+	1.62542e6i	0.450064	+	0.163810i
$630$	4.75270e6	+	2.69539e7i	0.477078	+	2.70564i
$631$	5.65734e6	+	4.74707e6i	0.565639	+	0.474627i	0.880195	−	0.474612i	$-0.157411\pi$
$631$	5.65734e6	+	4.74707e6i	0.565639	+	0.474627i	−0.314557	+	0.949239i	$0.601856\pi$
$632$	−2.77290e6	+	2.32674e6i	−0.276147	+	0.231715i
$633$	−4.32384e6	+	2.45217e7i	−0.428904	+	2.43243i
$634$	−2.99613e6	+	5.18945e6i	−0.296031	+	0.512741i
$635$	−4.89787e6	−	8.48336e6i	−0.482029	−	0.834899i
$636$	−2.14814e6	+	781860.i	−0.210582	+	0.0766454i
$637$	1.06326e7	−	3.86996e6i	1.03822	−	0.377883i
$638$	−3.45334e6	−	5.98136e6i	−0.335883	−	0.581766i
$639$	−4.48078e6	+	7.76095e6i	−0.434112	+	0.751904i
$640$	−265799.	+	1.50742e6i	−0.0256510	+	0.145474i
$641$	−1.52523e6	+	1.27982e6i	−0.146619	+	0.123028i	−0.713147	−	0.701014i	$-0.752731\pi$
$641$	−1.52523e6	+	1.27982e6i	−0.146619	+	0.123028i	0.566528	+	0.824043i	$0.308286\pi$
$642$	2.97622e6	+	2.49735e6i	0.284989	+	0.239134i
$643$	3.03365e6	+	1.72047e7i	0.289360	+	1.64104i	0.689283	+	0.724492i	$0.257926\pi$
$643$	3.03365e6	+	1.72047e7i	0.289360	+	1.64104i	−0.399923	+	0.916549i	$0.630963\pi$
$644$	772357.	+	281115.i	0.0733844	+	0.0267097i
$645$	880476.			0.0833332
$646$	−1.35408e6	+	7.63898e6i	−0.127662	+	0.720202i
$647$	1.46630e7			1.37709			0.688544	−	0.725195i	$-0.258250\pi$
$647$	1.46630e7			1.37709			0.688544	+	0.725195i	$0.258250\pi$
$648$	−293713.	−	106903.i	−0.0274781	−	0.0100012i
$649$	−2.07914e6	−	1.17914e7i	−0.193763	−	1.09889i
$650$	−1.18593e7	−	9.95117e6i	−1.10097	−	0.923827i
$651$	−9.52367e6	+	7.99131e6i	−0.880748	+	0.739036i
$652$	−1.69680e6	+	9.62300e6i	−0.156319	+	0.886526i
$653$	4.66959e6	−	8.08796e6i	0.428544	−	0.742260i	−0.568200	−	0.822891i	$-0.692360\pi$
$653$	4.66959e6	−	8.08796e6i	0.428544	−	0.742260i	0.996744	+	0.0806303i	$0.0256933\pi$
$654$	−7.72380e6	−	1.33780e7i	−0.706133	−	1.22306i
$655$	−2.38851e7	+	8.69347e6i	−2.17532	+	0.791753i
$656$	−4.70526e6	+	1.71257e6i	−0.426898	+	0.155378i
$657$	−1.11949e7	−	1.93901e7i	−1.01183	−	1.75254i
$658$	4.93163e6	−	8.54183e6i	0.444044	−	0.769106i
$659$	542640.	−	3.07747e6i	0.0486742	−	0.276045i	−0.950751	−	0.309957i	$-0.899685\pi$
$659$	542640.	−	3.07747e6i	0.0486742	−	0.276045i	0.999425	+	0.0339118i	$0.0107965\pi$
$660$	−1.15709e7	+	9.70912e6i	−1.03397	+	0.867601i
$661$	5.66697e6	+	4.75515e6i	0.504484	+	0.423312i	0.859183	−	0.511668i	$-0.170972\pi$
$661$	5.66697e6	+	4.75515e6i	0.504484	+	0.423312i	−0.354699	+	0.934980i	$0.615417\pi$
$662$	355093.	+	2.01383e6i	0.0314917	+	0.178599i
$663$	2.03185e7	+	7.39531e6i	1.79518	+	0.653390i
$664$	5.44994e6			0.479702
$665$	−2.05316e7	+	1.71965e7i	−1.80040	+	1.50794i
$666$	−6.20040e6			−0.541669
$667$	−1.14994e6	−	418544.i	−0.100083	−	0.0364272i
$668$	−85277.6	−	483633.i	−0.00739424	−	0.0419348i
$669$	−1.06835e7	−	8.96452e6i	−0.922887	−	0.774394i
$670$	−76157.0	+	63903.3i	−0.00655425	+	0.00549967i
$671$	152777.	−	866442.i	0.0130994	−	0.0742905i
$672$	2.36892e6	−	4.10310e6i	0.202361	−	0.350500i
$673$	−3.27104e6	−	5.66561e6i	−0.278386	−	0.482179i	0.692597	−	0.721324i	$-0.256466\pi$
$673$	−3.27104e6	−	5.66561e6i	−0.278386	−	0.482179i	−0.970984	+	0.239145i	$0.923133\pi$
$674$	1.55766e7	−	5.66941e6i	1.32075	−	0.480716i
$675$	−2.12659e7	+	7.74016e6i	−1.79649	+	0.653868i
$676$	−846489.	−	1.46616e6i	−0.0712450	−	0.123400i
$677$	−4.01356e6	+	6.95170e6i	−0.336557	+	0.582934i	−0.983783	−	0.179365i	$-0.942596\pi$
$677$	−4.01356e6	+	6.95170e6i	−0.336557	+	0.582934i	0.647226	+	0.762298i	$0.275929\pi$
$678$	4.15102e6	−	2.35416e7i	0.346801	−	1.96681i
$679$	−1.55686e7	+	1.30636e7i	−1.29591	+	1.08740i
$680$	−5.64556e6	−	4.73719e6i	−0.468204	−	0.392869i
$681$	2.19219e6	+	1.24325e7i	0.181138	+	1.02729i
$682$	−4.01842e6	−	1.46259e6i	−0.330822	−	0.120409i
$683$	4.90962e6			0.402714			0.201357	−	0.979518i	$-0.435465\pi$
$683$	4.90962e6			0.402714			0.201357	+	0.979518i	$0.435465\pi$
$684$	−1.74862e6	−	9.96963e6i	−0.142908	−	0.814777i
$685$	−7.74511e6			−0.630669
$686$	−291521.	−	106105.i	−0.0236515	−	0.00860846i
$687$	1.55485e6	+	8.81799e6i	0.125689	+	0.712816i
$688$	−72771.1	−	61062.2i	−0.00586122	−	0.00491815i
$689$	−2.97666e6	+	2.49771e6i	−0.238881	+	0.200445i
$690$	−464732.	+	2.63563e6i	−0.0371604	+	0.210747i
$691$	−4.39173e6	+	7.60670e6i	−0.349897	+	0.606040i	−0.986231	−	0.165374i	$-0.947117\pi$
$691$	−4.39173e6	+	7.60670e6i	−0.349897	+	0.606040i	0.636333	+	0.771414i	$0.280450\pi$
$692$	76851.1	+	133110.i	0.00610078	+	0.0105669i
$693$	2.73825e7	−	9.96641e6i	2.16591	−	0.788326i
$694$	1.21707e7	−	4.42978e6i	0.959218	−	0.349127i
$695$	−4.20705e6	−	7.28682e6i	−0.330381	−	0.572237i
$696$	−3.52702e6	+	6.10898e6i	−0.275985	+	0.478019i
$697$	4.18637e6	−	2.37421e7i	0.326404	−	1.85113i
$698$	−6.82107e6	+	5.72356e6i	−0.529924	+	0.444659i
$699$	−1.60132e7	−	1.34367e7i	−1.23961	−	1.04016i
$700$	−2.83611e6	−	1.60844e7i	−0.218765	−	1.24068i
$701$	2.14762e7	+	7.81670e6i	1.65068	+	0.600798i	0.988858	−	0.148865i	$-0.0475619\pi$
$701$	2.14762e7	+	7.81670e6i	1.65068	+	0.600798i	0.661820	+	0.749662i	$0.269784\pi$
$702$	−1.11590e7			−0.854637
$703$	−3.02886e6	−	5.25710e6i	−0.231148	−	0.401197i
$704$	1.62967e6			0.123928
$705$	3.01791e7	+	1.09843e7i	2.28683	+	0.832337i
$706$	−739624.	−	4.19461e6i	−0.0558469	−	0.316724i
$707$	−2.14289e7	−	1.79810e7i	−1.61232	−	1.35290i
$708$	−9.36775e6	+	7.86048e6i	−0.702348	+	0.589340i
$709$	−1.40143e6	+	7.94790e6i	−0.104702	+	0.593796i	0.886637	+	0.462467i	$0.153036\pi$
$709$	−1.40143e6	+	7.94790e6i	−0.104702	+	0.593796i	−0.991339	+	0.131329i	$0.958076\pi$
$710$	4.16508e6	−	7.21413e6i	0.310082	−	0.537079i
$711$	1.13690e7	+	1.96918e7i	0.843432	+	1.46087i
$712$	−1.30504e6	+	474994.i	−0.0964767	+	0.0351146i
$713$	−711992.	+	259144.i	−0.0524507	+	0.0190905i
$714$	1.14057e7	+	1.97552e7i	0.837288	+	1.45023i
$715$	−1.28375e7	+	2.22352e7i	−0.939108	+	1.62658i
$716$	1.44694e6	−	8.20602e6i	0.105480	−	0.598205i
$717$	2.27358e7	−	1.90776e7i	1.65163	−	1.38588i
$718$	2.42030e6	+	2.03087e6i	0.175210	+	0.147019i
$719$	−4.17538e6	−	2.36797e7i	−0.301213	−	1.70826i	−0.640816	−	0.767695i	$-0.721404\pi$
$719$	−4.17538e6	−	2.36797e7i	−0.301213	−	1.70826i	0.339603	−	0.940569i	$-0.389707\pi$
$720$	9.03533e6	+	3.28859e6i	0.649550	+	0.236417i
$721$	3.28083e6			0.235042
$722$	7.59871e6	−	6.35270e6i	0.542496	−	0.453539i
$723$	−4.52289e6			−0.321788
$724$	−3.88831e6	−	1.41523e6i	−0.275686	−	0.100341i
$725$	4.22260e6	+	2.39475e7i	0.298356	+	1.69206i
$726$	−214101.	−	179652.i	−0.0150757	−	0.0126500i
$727$	4.82701e6	−	4.05034e6i	0.338721	−	0.284221i	−0.457521	−	0.889199i	$-0.651263\pi$
$727$	4.82701e6	−	4.05034e6i	0.338721	−	0.284221i	0.796242	+	0.604978i	$0.206818\pi$
$728$	1.39846e6	−	7.93104e6i	0.0977959	−	0.554628i
$729$	1.14813e7	−	1.98862e7i	0.800152	−	1.38590i
$730$	1.04061e7	+	1.80239e7i	0.722740	+	1.25182i
$731$	429794.	−	156432.i	0.0297486	−	0.0108276i
$732$	−844389.	+	307332.i	−0.0582458	+	0.0211997i
$733$	−9.20180e6	−	1.59380e7i	−0.632576	−	1.09565i	−0.987023	−	0.160578i	$-0.948664\pi$
$733$	−9.20180e6	−	1.59380e7i	−0.632576	−	1.09565i	0.354447	−	0.935076i	$-0.384669\pi$
$734$	−7.20664e6	+	1.24823e7i	−0.493734	+	0.855172i
$735$	−6.74948e6	+	3.82782e7i	−0.460842	+	2.61356i
$736$	221194.	−	185604.i	0.0150515	−	0.0126297i
$737$	81082.4	+	68036.2i	0.00549867	+	0.00461393i
$738$	5.46188e6	+	3.09759e7i	0.369149	+	2.09355i
$739$	1.91984e6	+	698765.i	0.129316	+	0.0470674i	0.405868	−	0.913932i	$-0.366969\pi$
$739$	1.91984e6	+	698765.i	0.129316	+	0.0470674i	−0.276551	+	0.960999i	$0.589192\pi$
$740$	5.76353e6			0.386910
$741$	−1.37806e7	−	2.39186e7i	−0.921983	−	1.60026i
$742$	−4.09940e6			−0.273345
$743$	2.00671e7	+	7.30384e6i	1.33356	+	0.485377i	0.907780	−	0.419448i	$-0.137776\pi$
$743$	2.00671e7	+	7.30384e6i	1.33356	+	0.485377i	0.425784	+	0.904825i	$0.359998\pi$
$744$	758417.	+	4.30120e6i	0.0502315	+	0.284877i
$745$	−5.42848e6	−	4.55503e6i	−0.358333	−	0.300677i
$746$	5.28114e6	−	4.43140e6i	0.347441	−	0.291537i
$747$	5.94479e6	−	3.37146e7i	0.389794	−	2.21063i
$748$	−3.92319e6	+	6.79517e6i	−0.256381	+	0.444065i
$749$	3.48357e6	+	6.03372e6i	0.226892	+	0.392989i
$750$	2.21026e7	−	8.04469e6i	1.43480	−	0.522223i
$751$	7.86870e6	−	2.86397e6i	0.509100	−	0.185297i	−0.0746824	−	0.997207i	$-0.523794\pi$
$751$	7.86870e6	−	2.86397e6i	0.509100	−	0.185297i	0.583783	+	0.811910i	$0.301572\pi$
$752$	−1.73252e6	−	3.00081e6i	−0.111721	−	0.193506i
$753$	3.13325e6	−	5.42695e6i	0.201376	−	0.348793i
$754$	−2.08212e6	+	1.18083e7i	−0.133376	+	0.756413i
$755$	2.30292e7	−	1.93238e7i	1.47032	−	1.23374i
$756$	−9.01829e6	−	7.56724e6i	−0.573878	−	0.481541i
$757$	−282321.	−	1.60112e6i	−0.0179062	−	0.101551i	0.974545	−	0.224193i	$-0.0719745\pi$
$757$	−282321.	−	1.60112e6i	−0.0179062	−	0.101551i	−0.992451	+	0.122642i	$0.960863\pi$
$758$	−5.04176e6	−	1.83505e6i	−0.318720	−	0.116005i
$759$	2.84937e6			0.179533
$760$	1.62542e6	+	9.26719e6i	0.102078	+	0.581988i
$761$	−5.87944e6			−0.368022			−0.184011	−	0.982924i	$-0.558908\pi$
$761$	−5.87944e6			−0.368022			−0.184011	+	0.982924i	$0.558908\pi$
$762$	1.00094e7	+	3.64313e6i	0.624483	+	0.227293i
$763$	−4.81033e6	−	2.72807e7i	−0.299132	−	1.69646i
$764$	5.19580e6	+	4.35979e6i	0.322047	+	0.270229i
$765$	−3.54635e7	+	2.97574e7i	−2.19093	+	1.83841i
$766$	−733141.	+	4.15785e6i	−0.0451456	+	0.256034i
$767$	−1.03932e7	+	1.80015e7i	−0.637912	+	1.10490i
$768$	−832221.	−	1.44145e6i	−0.0509138	−	0.0881853i
$769$	2.06056e6	−	749982.i	0.125652	−	0.0457336i	−0.278429	−	0.960457i	$-0.589814\pi$
$769$	2.06056e6	−	749982.i	0.125652	−	0.0457336i	0.404081	+	0.914723i	$0.367591\pi$
$770$	−2.54532e7	+	9.26420e6i	−1.54709	+	0.563094i
$771$	1.39232e7	+	2.41156e7i	0.843533	+	1.46104i
$772$	4.08604e6	−	7.07722e6i	0.246751	−	0.427385i
$773$	−2.60836e6	+	1.47927e7i	−0.157007	+	0.890430i	0.799921	+	0.600105i	$0.204874\pi$
$773$	−2.60836e6	+	1.47927e7i	−0.157007	+	0.890430i	−0.956928	+	0.290325i	$0.906237\pi$
$774$	−457123.	+	383572.i	−0.0274272	+	0.0230141i
$775$	1.15336e7	+	9.67781e6i	0.689778	+	0.578792i
$776$	1.23981e6	+	7.03130e6i	0.0739094	+	0.419161i
$777$	−1.67638e7	−	6.10152e6i	−0.996138	−	0.362565i
$778$	−1.29925e7			−0.769562
$779$	−2.35953e7	+	1.97625e7i	−1.39310	+	1.16680i
$780$	2.62228e7			1.54327
$781$	−8.33404e6	−	3.03334e6i	−0.488909	−	0.177948i
$782$	241413.	+	1.36912e6i	0.0141170	+	0.0800616i
$783$	1.34271e7	+	1.12666e7i	0.782666	+	0.656735i
$784$	3.21249e6	−	2.69560e6i	0.186660	−	0.156626i
$785$	2.70517e6	−	1.53418e7i	0.156683	−	0.888592i
$786$	1.38196e7	−	2.39363e7i	0.797885	−	1.38198i
$787$	1.10649e7	+	1.91650e7i	0.636812	+	1.10299i	0.986128	+	0.165986i	$0.0530806\pi$
$787$	1.10649e7	+	1.91650e7i	0.636812	+	1.10299i	−0.349316	+	0.937005i	$0.613586\pi$
$788$	−1.10177e7	+	4.01011e6i	−0.632085	+	0.230060i
$789$	1.79455e7	−	6.53164e6i	1.02628	−	0.373534i
$790$	−1.05680e7	−	1.83043e7i	−0.602456	−	1.04348i
$791$	2.14337e7	−	3.71243e7i	1.21803	−	2.10968i
$792$	1.77764e6	−	1.00815e7i	0.100701	−	0.571101i
$793$	−1.17006e6	+	981798.i	−0.0660732	+	0.0554420i
$794$	1.85546e7	+	1.55691e7i	1.04448	+	0.876422i
$795$	−2.31788e6	−	1.31454e7i	−0.130069	−	0.737657i
$796$	5.52028e6	+	2.00922e6i	0.308801	+	0.112394i
$797$	1.03614e6			0.0577791			0.0288895	−	0.999583i	$-0.490803\pi$
$797$	1.03614e6			0.0577791			0.0288895	+	0.999583i	$0.490803\pi$
$798$	5.08295e6	−	2.86752e7i	0.282559	−	1.59404i
$799$	1.66831e7			0.924508
$800$	−5.39170e6	−	1.96242e6i	−0.297852	−	0.108409i
$801$	1.51489e6	+	8.59137e6i	0.0834257	+	0.473131i
$802$	2.32505e6	+	1.95095e6i	0.127643	+	0.107105i
$803$	1.69742e7	−	1.42431e7i	0.928968	−	0.779497i
$804$	18772.0	−	106461.i	0.00102417	−	0.00580834i
$805$	−2.39964e6	+	4.15630e6i	−0.130514	+	0.226056i
$806$	3.71198e6	+	6.42934e6i	0.201265	+	0.348601i
$807$	−3.84652e7	+	1.40002e7i	−2.07914	+	0.756746i
$808$	−9.23462e6	+	3.36113e6i	−0.497612	+	0.181116i
$809$	1.57596e7	+	2.72965e7i	0.846593	+	1.46634i	0.884231	+	0.467050i	$0.154683\pi$
$809$	1.57596e7	+	2.72965e7i	0.846593	+	1.46634i	−0.0376384	+	0.999291i	$0.511984\pi$
$810$	912540.	−	1.58056e6i	0.0488696	−	0.0846447i
$811$	−2.52997e6	+	1.43482e7i	−0.135072	+	0.766029i	0.839738	+	0.542991i	$0.182708\pi$
$811$	−2.52997e6	+	1.43482e7i	−0.135072	+	0.766029i	−0.974810	+	0.223038i	$0.928403\pi$
$812$	−9.69026e6	+	8.13109e6i	−0.515757	+	0.432772i
$813$	−3.05172e7	−	2.56070e7i	−1.61927	−	1.35873i
$814$	−1.06555e6	−	6.04306e6i	−0.0563657	−	0.319666i
$815$	−5.36153e7	−	1.95144e7i	−2.82745	−	1.02911i
$816$	8.01379e6			0.421321
$817$	−548519.	−	200206.i	−0.0287499	−	0.0104936i
$818$	−1.19239e7			−0.623065
$819$	−4.75378e7	−	1.73024e7i	−2.47645	−	0.901354i
$820$	−5.07705e6	−	2.87934e7i	−0.263680	−	1.49540i
$821$	1.57556e7	+	1.32205e7i	0.815787	+	0.684527i	0.951982	−	0.306155i	$-0.0990427\pi$
$821$	1.57556e7	+	1.32205e7i	0.815787	+	0.684527i	−0.136194	+	0.990682i	$0.543487\pi$
$822$	6.45159e6	−	5.41353e6i	0.333033	−	0.279448i
$823$	−1.79175e6	+	1.01615e7i	−0.0922099	+	0.522949i	0.903357	+	0.428890i	$0.141095\pi$
$823$	−1.79175e6	+	1.01615e7i	−0.0922099	+	0.522949i	−0.995567	+	0.0940586i	$0.970016\pi$
$824$	576291.	−	998165.i	0.0295681	−	0.0512135i
$825$	−2.83100e7	−	4.90343e7i	−1.44812	−	2.50822i
$826$	−2.06068e7	+	7.50027e6i	−1.05090	+	0.382496i
$827$	1.09383e7	−	3.98120e6i	0.556140	−	0.202418i	−0.0486324	−	0.998817i	$-0.515486\pi$
$827$	1.09383e7	−	3.98120e6i	0.556140	−	0.202418i	0.604772	+	0.796398i	$0.293264\pi$
$828$	−906911.	−	1.57082e6i	−0.0459715	−	0.0796250i
$829$	3.21588e6	−	5.57008e6i	0.162523	−	0.281498i	−0.773250	−	0.634101i	$-0.781370\pi$
$829$	3.21588e6	−	5.57008e6i	0.162523	−	0.281498i	0.935773	+	0.352604i	$0.114704\pi$
$830$	−5.52593e6	+	3.13391e7i	−0.278426	+	1.57903i
$831$	3.56716e6	−	2.99320e6i	0.179193	−	0.150360i
$832$	−2.16731e6	−	1.81859e6i	−0.108546	−	0.0910806i
$833$	3.50612e6	+	1.98842e7i	0.175071	+	0.992878i
$834$	8.59762e6	+	3.12928e6i	0.428019	+	0.155786i
$835$	2.86753e6			0.142329
$836$	9.41614e6	−	3.41756e6i	0.465969	−	0.169122i
$837$	1.08524e7			0.535443
$838$	1.84963e7	+	6.73210e6i	0.909860	+	0.331162i
$839$	1.80456e6	+	1.02342e7i	0.0885046	+	0.501934i	0.996545	+	0.0830523i	$0.0264669\pi$
$839$	1.80456e6	+	1.02342e7i	0.0885046	+	0.501934i	−0.908041	+	0.418882i	$0.862422\pi$
$840$	2.11923e7	+	1.77825e7i	1.03629	+	0.869549i
$841$	−1.28491e6	+	1.07817e6i	−0.0626447	+	0.0525651i
$842$	484761.	−	2.74922e6i	0.0235639	−	0.133638i
$843$	−2.93174e7	+	5.07793e7i	−1.42088	+	2.46103i
$844$	7.84333e6	+	1.35850e7i	0.379004	+	0.656455i
$845$	9.28926e6	−	3.38101e6i	0.447547	−	0.162894i
$846$	−2.04535e7	+	7.44448e6i	−0.982523	+	0.357609i
$847$	−250598.	−	434049.i	−0.0120024	−	0.0207889i
$848$	−720076.	+	1.24721e6i	−0.0343866	+	0.0595593i
$849$	1.02467e7	−	5.81122e7i	0.487884	−	2.76693i
$850$	2.11623e7	−	1.77573e7i	1.00465	−	0.843004i
$851$	−832874.	−	698864.i	−0.0394235	−	0.0330803i
$852$	1.57293e6	+	8.92051e6i	0.0742351	+	0.421008i
$853$	−3.68896e7	−	1.34267e7i	−1.73592	−	0.631825i	−0.736901	−	0.676001i	$-0.763712\pi$
$853$	−3.68896e7	−	1.34267e7i	−1.73592	−	0.631825i	−0.999024	+	0.0441756i	$0.985934\pi$
$854$	−1.61139e6			−0.0756059
$855$	5.91020e7	+	53425.8i	2.76495	+	0.00249940i
$856$	2.44761e6			0.114172
$857$	−2.81715e7	−	1.02536e7i	−1.31026	−	0.476896i	−0.409935	−	0.912115i	$-0.634449\pi$
$857$	−2.81715e7	−	1.02536e7i	−1.31026	−	0.476896i	−0.900325	+	0.435219i	$0.856671\pi$
$858$	−4.84804e6	−	2.74946e7i	−0.224827	−	1.27505i
$859$	1.41398e7	+	1.18647e7i	0.653823	+	0.548623i	0.908228	−	0.418475i	$-0.137435\pi$
$859$	1.41398e7	+	1.18647e7i	0.653823	+	0.548623i	−0.254405	+	0.967098i	$0.581880\pi$
$860$	424916.	−	356546.i	0.0195910	−	0.0164388i
$861$	−1.57148e7	+	8.91231e7i	−0.722439	+	4.09715i
$862$	−6.91304e6	+	1.19737e7i	−0.316884	+	0.548860i
$863$	1.41254e6	+	2.44659e6i	0.0645614	+	0.111824i	0.896499	−	0.443045i	$-0.146102\pi$
$863$	1.41254e6	+	2.44659e6i	0.0645614	+	0.111824i	−0.831938	+	0.554869i	$0.812768\pi$
$864$	−3.88637e6	+	1.41452e6i	−0.177117	+	0.0644652i
$865$	−843354.	+	306956.i	−0.0383239	+	0.0139488i
$866$	1.13013e7	+	1.95744e7i	0.512074	+	0.886938i
$867$	−1.26170e6	+	2.18534e6i	−0.0570046	+	0.0987348i
$868$	−1.36004e6	+	7.71317e6i	−0.0612707	+	0.347483i
$869$	−1.72383e7	+	1.44646e7i	−0.774362	+	0.649767i
$870$	−3.15526e7	−	2.64758e7i	−1.41331	−	1.18591i
$871$	−31908.7	−	180963.i	−0.00142516	−	0.00808249i
$872$	−9.14488e6	−	3.32846e6i	−0.407274	−	0.148236i
$873$	4.48496e7			1.99170
$874$	888819.	−	1.53627e6i	0.0393582	−	0.0680282i
$875$	4.21795e7			1.86244
$876$	−2.12662e7	−	7.74027e6i	−0.936332	−	0.340797i
$877$	−2.41157e6	−	1.36767e7i	−0.105877	−	0.600458i	−0.990866	−	0.134847i	$-0.956946\pi$
$877$	−2.41157e6	−	1.36767e7i	−0.105877	−	0.600458i	0.884989	−	0.465611i	$-0.154165\pi$
$878$	−2.22711e7	−	1.86877e7i	−0.975001	−	0.818123i
$879$	2.00523e7	−	1.68259e7i	0.875371	−	0.734523i
$880$	−1.65240e6	+	9.37120e6i	−0.0719296	+	0.407933i
$881$	−1.03189e7	+	1.78729e7i	−0.447915	+	0.775811i	−0.998250	−	0.0591325i	$-0.981167\pi$
$881$	−1.03189e7	+	1.78729e7i	−0.447915	+	0.775811i	0.550335	+	0.834944i	$0.314500\pi$
$882$	−1.31714e7	−	2.28135e7i	−0.570113	−	0.987464i
$883$	1.56603e7	−	5.69988e6i	0.675925	−	0.246017i	0.0188280	−	0.999823i	$-0.494006\pi$
$883$	1.56603e7	−	5.69988e6i	0.675925	−	0.246017i	0.657097	+	0.753806i	$0.271784\pi$
$884$	1.28004e7	−	4.65895e6i	0.550923	−	0.200520i
$885$	−3.57022e7	−	6.18380e7i	−1.53228	−	2.65398i
$886$	3.62593e6	−	6.28030e6i	0.155180	−	0.268780i
$887$	−4.21757e6	+	2.39190e7i	−0.179992	+	1.02078i	0.752231	+	0.658900i	$0.228978\pi$
$887$	−4.21757e6	+	2.39190e7i	−0.179992	+	1.02078i	−0.932223	+	0.361885i	$0.882133\pi$
$888$	−4.80096e6	+	4.02848e6i	−0.204313	+	0.171439i
$889$	1.46326e7	+	1.22782e7i	0.620963	+	0.521050i
$890$	−1.40815e6	−	7.98604e6i	−0.0595903	−	0.337953i
$891$	−1.82593e6	−	664584.i	−0.0770531	−	0.0280450i
$892$	−8.78600e6			−0.369725
$893$	−1.63033e7	−	1.37053e7i	−0.684144	−	0.575120i
$894$	7.70564e6			0.322452
$895$	4.57205e7	+	1.66409e7i	1.90789	+	0.694415i
$896$	−518302.	−	2.93943e6i	−0.0215681	−	0.122319i
$897$	−3.78939e6	−	3.17968e6i	−0.157249	−	0.131948i
$898$	8.45923e6	−	7.09814e6i	0.350058	−	0.293734i
$899$	2.02492e6	−	1.14839e7i	0.0835621	−	0.473904i
$900$	−1.80212e7	+	3.12137e7i	−0.741615	+	1.28451i
$901$	−3.46695e6	−	6.00494e6i	−0.142277	−	0.246432i
$902$	−2.92512e7	+	1.06466e7i	−1.19709	+	0.435706i
$903$	−1.61336e6	+	587216.i	−0.0658434	+	0.0239651i
$904$	−7.52984e6	−	1.30421e7i	−0.306454	−	0.530793i
$905$	1.20806e7	−	2.09242e7i	0.490306	−	0.849235i
$906$	−5.67649e6	+	3.21929e7i	−0.229752	+	1.30299i
$907$	2.86275e7	−	2.40214e7i	1.15549	−	0.969571i	0.155656	−	0.987811i	$-0.450251\pi$
$907$	2.86275e7	−	2.40214e7i	1.15549	−	0.969571i	0.999834	+	0.0182406i	$0.00580650\pi$
$908$	6.09246e6	+	5.11218e6i	0.245233	+	0.205775i
$909$	1.07196e7	+	6.07938e7i	0.430297	+	2.44034i
$910$	4.41884e7	+	1.60833e7i	1.76891	+	0.643829i
$911$	−2.05225e7			−0.819285			−0.409642	−	0.912246i	$-0.634347\pi$
$911$	−2.05225e7			−0.819285			−0.409642	+	0.912246i	$0.634347\pi$
$912$	−7.83136e6	−	6.58336e6i	−0.311781	−	0.262096i
$913$	3.38807e7			1.34516
$914$	−2.89138e7	−	1.05238e7i	−1.14483	−	0.416683i
$915$	−911109.	−	5.16716e6i	−0.0359764	−	0.204032i
$916$	4.32119e6	+	3.62591e6i	0.170163	+	0.142784i
$917$	3.79685e7	−	3.18594e7i	1.49108	−	1.25116i
$918$	3.45778e6	−	1.96101e7i	0.135423	−	0.768019i
$919$	−4.85432e6	+	8.40793e6i	−0.189601	+	0.328398i	−0.945117	−	0.326732i	$-0.894053\pi$
$919$	−4.85432e6	+	8.40793e6i	−0.189601	+	0.328398i	0.755516	+	0.655130i	$0.227386\pi$
$920$	843012.	+	1.46014e6i	0.0328370	+	0.0568754i
$921$	−4.01502e7	+	1.46135e7i	−1.55969	+	0.567681i
$922$	2.18428e7	−	7.95013e6i	0.846216	−	0.307997i
$923$	7.69850e6	+	1.33342e7i	0.297442	+	0.515184i
$924$	1.47269e7	−	2.55077e7i	0.567455	−	0.982861i
$925$	−3.75159e6	+	2.12763e7i	−0.144165	+	0.817603i
$926$	1.24195e7	−	1.04212e7i	0.475965	−	0.399382i
$927$	−5.54626e6	−	4.65386e6i	−0.211983	−	0.177875i
$928$	771684.	+	4.37644e6i	0.0294150	+	0.166821i
$929$	−2.24337e7	−	8.16521e6i	−0.852829	−	0.310404i	−0.121636	−	0.992575i	$-0.538814\pi$
$929$	−2.24337e7	−	8.16521e6i	−0.852829	−	0.310404i	−0.731193	+	0.682170i	$0.761036\pi$
$930$	−2.55024e7			−0.966884
$931$	1.29087e7	−	2.23118e7i	0.488098	−	0.843648i
$932$	−1.31691e7			−0.496611
$933$	1.65547e7	+	6.02542e6i	0.622612	+	0.226612i
$934$	4.20663e6	+	2.38570e7i	0.157785	+	0.894846i
$935$	−3.50968e7	−	2.94497e7i	−1.31292	−	1.10167i
$936$	−1.36143e7	+	1.14237e7i	−0.507932	+	0.426205i
$937$	5.54122e6	−	3.14258e7i	0.206185	−	1.16933i	−0.689380	−	0.724400i	$-0.742117\pi$
$937$	5.54122e6	−	3.14258e7i	0.206185	−	1.16933i	0.895565	−	0.444931i	$-0.146772\pi$
$938$	96929.2	−	167886.i	0.00359706	−	0.00623029i
$939$	1.93531e7	+	3.35206e7i	0.716288	+	1.24065i
$940$	1.90124e7	−	6.91996e6i	0.701807	−	0.255437i
$941$	−1.64295e7	+	5.97986e6i	−0.604854	+	0.220149i	−0.626250	−	0.779622i	$-0.715411\pi$
$941$	−1.64295e7	+	5.97986e6i	−0.604854	+	0.220149i	0.0213959	+	0.999771i	$0.493189\pi$
$942$	8.46993e6	+	1.46704e7i	0.310995	+	0.538658i
$943$	−2.75771e6	+	4.77649e6i	−0.100988	+	0.174916i
$944$	−1.33777e6	+	7.58690e6i	−0.0488599	+	0.277098i
$945$	5.26584e7	−	4.41857e7i	1.91818	−	1.60954i
$946$	−452396.	−	379606.i	−0.0164358	−	0.0137913i
$947$	−153533.	−	870731.i	−0.00556324	−	0.0315507i	0.981900	−	0.189401i	$-0.0606547\pi$
$947$	−153533.	−	870731.i	−0.00556324	−	0.0315507i	−0.987463	+	0.157851i	$0.949544\pi$
$948$	2.15970e7	+	7.86068e6i	0.780501	+	0.284079i
$949$	−3.84682e7			−1.38655
$950$	−3.52683e7	−	31881.1i	−1.26787	−	0.00114610i
$951$	3.80469e7			1.36417
$952$	1.35042e7	+	4.91511e6i	0.482920	+	0.175769i
$953$	125838.	+	713661.i	0.00448826	+	0.0254542i	0.986970	−	0.160907i	$-0.0514418\pi$
$953$	125838.	+	713661.i	0.00448826	+	0.0254542i	−0.982481	+	0.186361i	$0.940331\pi$
$954$	6.93006e6	+	5.81501e6i	0.246528	+	0.206861i
$955$	−3.03386e7	+	2.54571e7i	−1.07643	+	0.903236i
$956$	3.24682e6	−	1.84136e7i	0.114898	−	0.651621i
$957$	−2.19264e7	+	3.79777e7i	−0.773906	+	1.34044i
$958$	−7.98015e6	−	1.38220e7i	−0.280929	−	0.486584i
$959$	1.41920e7	−	5.16545e6i	0.498306	−	0.181368i
$960$	9.13268e6	−	3.32402e6i	0.319831	−	0.116409i
$961$	1.07046e7	+	1.85408e7i	0.373904	+	0.647621i
$962$	−5.32650e6	+	9.22577e6i	−0.185568	+	0.321414i
$963$	2.66985e6	−	1.51415e7i	0.0927730	−	0.526142i
$964$	−2.18273e6	+	1.83153e6i	−0.0756499	+	0.0634778i
$965$	3.65536e7	+	3.06721e7i	1.26361	+	1.06029i
$966$	−906215.	−	5.13940e6i	−0.0312456	−	0.177202i
$967$	1.67471e7	+	6.09544e6i	0.575934	+	0.209623i	0.613532	−	0.789670i	$-0.289748\pi$
$967$	1.67471e7	+	6.09544e6i	0.575934	+	0.209623i	−0.0375975	+	0.999293i	$0.511970\pi$
$968$	−176074.			−0.00603959
$969$	4.63032e7	−	1.68056e7i	1.58417	−	0.574969i
$970$	−4.16896e7			−1.42265
$971$	1.35287e7	+	4.92406e6i	0.460479	+	0.167601i	0.561834	−	0.827250i	$-0.310096\pi$
$971$	1.35287e7	+	4.92406e6i	0.460479	+	0.167601i	−0.101356	+	0.994850i	$0.532318\pi$
$972$	−2.38219e6	−	1.35101e7i	−0.0808743	−	0.458661i
$973$	1.25687e7	+	1.05464e7i	0.425606	+	0.357126i
$974$	2.32074e7	−	1.94733e7i	0.783842	−	0.657722i
$975$	−1.70689e7	+	9.68026e7i	−0.575035	+	3.26118i
$976$	−283047.	+	490251.i	−0.00951116	+	0.0164738i
$977$	3.63560e6	+	6.29705e6i	0.121854	+	0.211058i	0.920499	−	0.390745i	$-0.127783\pi$
$977$	3.63560e6	+	6.29705e6i	0.121854	+	0.211058i	−0.798645	+	0.601803i	$0.794449\pi$
$978$	5.83007e7	−	2.12197e7i	1.94907	−	0.709402i
$979$	−8.11302e6	+	2.95290e6i	−0.270536	+	0.0984672i
$980$	1.22434e7	+	2.12062e7i	0.407227	+	0.705337i
$981$	−3.05659e7	+	5.29416e7i	−1.01406	+	1.75641i
$982$	−1.06063e6	+	6.01515e6i	−0.0350983	+	0.199053i
$983$	−2.32329e7	+	1.94947e7i	−0.766866	+	0.643477i	−0.939904	−	0.341438i	$-0.889086\pi$
$983$	−2.32329e7	+	1.94947e7i	−0.766866	+	0.643477i	0.173038	+	0.984915i	$0.444642\pi$
$984$	2.43546e7	+	2.04359e7i	0.801849	+	0.672831i
$985$	−1.18883e7	−	6.74217e7i	−0.390417	−	2.21416i
$986$	−2.01059e7	−	7.31796e6i	−0.658616	−	0.239717i
$987$	−6.26252e7			−2.04624
$988$	−1.63363e7	−	5.96265e6i	−0.532428	−	0.194333i
$989$	−104637.			−0.00340169
$990$	5.61700e7	+	2.04442e7i	1.82145	+	0.662952i
$991$	−8.04912e6	−	4.56488e7i	−0.260354	−	1.47654i	−0.781946	−	0.623346i	$-0.785773\pi$
$991$	−8.04912e6	−	4.56488e7i	−0.260354	−	1.47654i	0.521592	−	0.853195i	$-0.325338\pi$
$992$	2.10777e6	+	1.76863e6i	0.0680055	+	0.0570634i
$993$	9.94613e6	−	8.34579e6i	0.320097	−	0.268593i
$994$	−2.82067e6	+	1.59968e7i	−0.0905495	+	0.513532i
$995$	−1.71510e7	+	2.97064e7i	−0.549201	+	0.951243i
$996$	−1.73018e7	−	2.99676e7i	−0.552640	−	0.957200i
$997$	−8.07373e6	+	2.93860e6i	−0.257239	+	0.0936272i	−0.467421	−	0.884035i	$-0.654817\pi$
$997$	−8.07373e6	+	2.93860e6i	−0.257239	+	0.0936272i	0.210182	+	0.977662i	$0.432594\pi$
$998$	−5.49513e6	+	2.00006e6i	−0.174643	+	0.0635649i
$999$	7.78634e6	+	1.34863e7i	0.246842	+	0.427543i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.6.e.b.23.5	yes	30
19.5	even	9	inner	38.6.e.b.5.5	✓	30
19.9	even	9		722.6.a.r.1.13		15
19.10	odd	18		722.6.a.q.1.3		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.e.b.5.5	✓	30	19.5	even	9	inner
38.6.e.b.23.5	yes	30	1.1	even	1	trivial
722.6.a.q.1.3		15	19.10	odd	18
722.6.a.r.1.13		15	19.9	even	9

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.75877 - 1.36808i) q^{2} +(4.41021 + 25.0115i) q^{3} +(12.2567 + 10.2846i) q^{4} +(-71.5678 + 60.0525i) q^{5} +(17.6408 - 100.046i) q^{6} +(91.0882 - 157.769i) q^{7} +(-32.0000 - 55.4256i) q^{8} +(-377.781 + 137.501i) q^{9} +O(q^{10})\)	\(q+(-3.75877 - 1.36808i) q^{2} +(4.41021 + 25.0115i) q^{3} +(12.2567 + 10.2846i) q^{4} +(-71.5678 + 60.0525i) q^{5} +(17.6408 - 100.046i) q^{6} +(91.0882 - 157.769i) q^{7} +(-32.0000 - 55.4256i) q^{8} +(-377.781 + 137.501i) q^{9} +(351.164 - 127.813i) q^{10} +(-198.935 - 344.565i) q^{11} +(-203.179 + 351.916i) q^{12} +(-119.944 + 680.234i) q^{13} +(-558.221 + 468.403i) q^{14} +(-1817.63 - 1525.18i) q^{15} +(44.4539 + 252.111i) q^{16} +(-1158.23 - 421.562i) q^{17} +1608.11 q^{18} +(785.549 + 1363.46i) q^{19} -1494.80 q^{20} +(4347.77 + 1582.46i) q^{21} +(276.357 + 1567.30i) q^{22} +(216.010 + 181.254i) q^{23} +(1245.15 - 1044.81i) q^{24} +(972.994 - 5518.13i) q^{25} +(1381.45 - 2392.75i) q^{26} +(-2019.43 - 3497.75i) q^{27} +(2739.04 - 996.928i) q^{28} +(-4078.07 + 1484.30i) q^{29} +(4745.50 + 8219.45i) q^{30} +(-1343.51 + 2327.02i) q^{31} +(177.816 - 1008.44i) q^{32} +(7740.75 - 6495.26i) q^{33} +(3776.80 + 3169.11i) q^{34} +(2955.47 + 16761.3i) q^{35} +(-6044.50 - 2200.02i) q^{36} -3855.72 q^{37} +(-1087.38 - 6199.61i) q^{38} -17542.7 q^{39} +(5618.62 + 2045.01i) q^{40} +(3396.47 + 19262.3i) q^{41} +(-14177.3 - 11896.2i) q^{42} +(-284.262 + 238.524i) q^{43} +(1105.43 - 6269.19i) q^{44} +(18779.7 - 32527.4i) q^{45} +(-563.962 - 976.811i) q^{46} +(-12719.0 + 4629.35i) q^{47} +(-6109.62 + 2223.72i) q^{48} +(-8190.64 - 14186.6i) q^{49} +(-11206.5 + 19410.2i) q^{50} +(5435.86 - 30828.3i) q^{51} +(-8466.04 + 7103.85i) q^{52} +(4309.46 + 3616.06i) q^{53} +(2805.36 + 15910.0i) q^{54} +(34929.3 + 12713.2i) q^{55} -11659.3 q^{56} +(-30637.7 + 25660.9i) q^{57} +17359.2 q^{58} +(28278.6 + 10292.6i) q^{59} +(-6592.39 - 37387.3i) q^{60} +(1693.96 + 1421.40i) q^{61} +(8233.48 - 6908.71i) q^{62} +(-12717.9 + 72127.1i) q^{63} +(-2048.00 + 3547.24i) q^{64} +(-32265.6 - 55885.7i) q^{65} +(-37981.7 + 13824.2i) q^{66} +(-249.987 + 90.9880i) q^{67} +(-9860.51 - 17078.9i) q^{68} +(-3580.79 + 6202.11i) q^{69} +(11821.9 - 67045.2i) q^{70} +(17075.9 - 14328.4i) q^{71} +(19710.1 + 16538.7i) q^{72} +(9670.88 + 54846.3i) q^{73} +(14492.8 + 5274.93i) q^{74} +142308. q^{75} +(-4394.35 + 24790.5i) q^{76} -72482.4 q^{77} +(65938.8 + 23999.8i) q^{78} +(-9821.32 - 55699.5i) q^{79} +(-18321.4 - 15373.4i) q^{80} +(3741.21 - 3139.25i) q^{81} +(13585.9 - 77049.4i) q^{82} +(-42577.7 + 73746.7i) q^{83} +(37014.4 + 64110.9i) q^{84} +(108208. - 39384.5i) q^{85} +(1394.80 - 507.664i) q^{86} +(-55109.7 - 95452.8i) q^{87} +(-12731.8 + 22052.1i) q^{88} +(3768.14 - 21370.2i) q^{89} +(-115089. + 96570.8i) q^{90} +(96394.6 + 80884.7i) q^{91} +(783.448 + 4443.16i) q^{92} +(-64127.4 - 23340.5i) q^{93} +54141.2 q^{94} +(-138099. - 50405.3i) q^{95} +26006.9 q^{96} +(-104831. - 38155.4i) q^{97} +(11378.3 + 64529.6i) q^{98} +(122532. + 102816. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 15 q^{3} + 60 q^{6} - 84 q^{7} - 960 q^{8} - 345 q^{9}+O(q^{10}) \) 30 * q + 15 * q^3 + 60 * q^6 - 84 * q^7 - 960 * q^8 - 345 * q^9	\( 30 q + 15 q^{3} + 60 q^{6} - 84 q^{7} - 960 q^{8} - 345 q^{9} - 126 q^{11} - 2610 q^{13} - 864 q^{14} - 5160 q^{15} + 1902 q^{17} + 17016 q^{18} - 2400 q^{19} + 3456 q^{20} - 6426 q^{21} + 216 q^{22} - 3306 q^{23} + 960 q^{24} - 18060 q^{25} + 456 q^{26} + 13017 q^{27} + 6048 q^{28} + 5988 q^{29} - 6840 q^{31} + 51867 q^{33} - 10752 q^{34} + 24408 q^{35} - 5520 q^{36} - 8556 q^{37} + 2772 q^{38} + 9912 q^{39} - 40527 q^{41} + 27432 q^{42} + 3678 q^{43} + 864 q^{44} - 31770 q^{45} - 15744 q^{46} - 133740 q^{47} - 7680 q^{48} - 63777 q^{49} - 107580 q^{50} + 45657 q^{51} + 5760 q^{52} - 64626 q^{53} + 1476 q^{54} + 142056 q^{55} + 10752 q^{56} + 232824 q^{57} + 117264 q^{58} + 169041 q^{59} - 56640 q^{60} + 61698 q^{61} - 101616 q^{62} - 188064 q^{63} - 61440 q^{64} - 80646 q^{65} - 173772 q^{66} - 72129 q^{67} - 65904 q^{68} - 124224 q^{69} + 97632 q^{70} + 417828 q^{71} + 44160 q^{72} + 239082 q^{73} - 116112 q^{74} - 174960 q^{75} + 6912 q^{76} + 242436 q^{77} + 336624 q^{78} - 145740 q^{79} + 14781 q^{81} - 162108 q^{82} - 201630 q^{83} - 54528 q^{84} - 46512 q^{85} - 75720 q^{86} - 376512 q^{87} - 8064 q^{88} + 416928 q^{89} + 560640 q^{90} - 380316 q^{91} + 269376 q^{92} - 205146 q^{93} + 5616 q^{94} + 708168 q^{95} + 858363 q^{97} + 308328 q^{98} - 1068531 q^{99}+O(q^{100}) \) 30 * q + 15 * q^3 + 60 * q^6 - 84 * q^7 - 960 * q^8 - 345 * q^9 - 126 * q^11 - 2610 * q^13 - 864 * q^14 - 5160 * q^15 + 1902 * q^17 + 17016 * q^18 - 2400 * q^19 + 3456 * q^20 - 6426 * q^21 + 216 * q^22 - 3306 * q^23 + 960 * q^24 - 18060 * q^25 + 456 * q^26 + 13017 * q^27 + 6048 * q^28 + 5988 * q^29 - 6840 * q^31 + 51867 * q^33 - 10752 * q^34 + 24408 * q^35 - 5520 * q^36 - 8556 * q^37 + 2772 * q^38 + 9912 * q^39 - 40527 * q^41 + 27432 * q^42 + 3678 * q^43 + 864 * q^44 - 31770 * q^45 - 15744 * q^46 - 133740 * q^47 - 7680 * q^48 - 63777 * q^49 - 107580 * q^50 + 45657 * q^51 + 5760 * q^52 - 64626 * q^53 + 1476 * q^54 + 142056 * q^55 + 10752 * q^56 + 232824 * q^57 + 117264 * q^58 + 169041 * q^59 - 56640 * q^60 + 61698 * q^61 - 101616 * q^62 - 188064 * q^63 - 61440 * q^64 - 80646 * q^65 - 173772 * q^66 - 72129 * q^67 - 65904 * q^68 - 124224 * q^69 + 97632 * q^70 + 417828 * q^71 + 44160 * q^72 + 239082 * q^73 - 116112 * q^74 - 174960 * q^75 + 6912 * q^76 + 242436 * q^77 + 336624 * q^78 - 145740 * q^79 + 14781 * q^81 - 162108 * q^82 - 201630 * q^83 - 54528 * q^84 - 46512 * q^85 - 75720 * q^86 - 376512 * q^87 - 8064 * q^88 + 416928 * q^89 + 560640 * q^90 - 380316 * q^91 + 269376 * q^92 - 205146 * q^93 + 5616 * q^94 + 708168 * q^95 + 858363 * q^97 + 308328 * q^98 - 1068531 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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