LMFDB - Embedded newform 74.6.f.a.33.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,6,Mod(7,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, 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("74.7");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	74.f (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:	$11.8684026662$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			33.4
Character	$\chi$	$=$	74.33
Dual form			74.6.f.a.9.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.694593 - 3.93923i) q^{2} +(0.515998 + 2.92637i) q^{3} +(-15.0351 - 5.47232i) q^{4} +(33.8915 - 28.4384i) q^{5} +11.8861 q^{6} +(-11.2213 + 9.41575i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(220.048 - 80.0909i) q^{9} +O(q^{10})$	\(q+(0.694593 - 3.93923i) q^{2} +(0.515998 + 2.92637i) q^{3} +(-15.0351 - 5.47232i) q^{4} +(33.8915 - 28.4384i) q^{5} +11.8861 q^{6} +(-11.2213 + 9.41575i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(220.048 - 80.0909i) q^{9} +(-88.4845 - 153.260i) q^{10} +(126.586 - 219.253i) q^{11} +(8.25596 - 46.8219i) q^{12} +(-946.880 - 344.636i) q^{13} +(29.2966 + 50.7432i) q^{14} +(100.709 + 84.5050i) q^{15} +(196.107 + 164.554i) q^{16} +(964.220 - 350.948i) q^{17} +(-162.653 - 922.450i) q^{18} +(-439.618 - 2493.20i) q^{19} +(-665.186 + 242.108i) q^{20} +(-33.3441 - 27.9790i) q^{21} +(-775.763 - 650.943i) q^{22} +(-1219.97 - 2113.06i) q^{23} +(-178.708 - 65.0443i) q^{24} +(-202.756 + 1149.89i) q^{25} +(-2015.30 + 3490.60i) q^{26} +(708.959 + 1227.95i) q^{27} +(220.238 - 80.1602i) q^{28} +(632.504 - 1095.53i) q^{29} +(402.836 - 338.020i) q^{30} -7998.38 q^{31} +(784.430 - 658.215i) q^{32} +(706.934 + 257.303i) q^{33} +(-712.723 - 4042.05i) q^{34} +(-112.537 + 638.228i) q^{35} -3746.72 q^{36} +(7096.28 - 4357.38i) q^{37} -10126.6 q^{38} +(519.944 - 2948.75i) q^{39} +(491.685 + 2788.49i) q^{40} +(8289.16 + 3017.01i) q^{41} +(-133.376 + 111.916i) q^{42} +19330.7 q^{43} +(-3103.05 + 2603.77i) q^{44} +(5180.11 - 8972.21i) q^{45} +(-9171.20 + 3338.04i) q^{46} +(-2374.82 - 4113.30i) q^{47} +(-380.354 + 658.792i) q^{48} +(-2881.24 + 16340.4i) q^{49} +(4388.83 + 1597.40i) q^{50} +(1524.54 + 2640.58i) q^{51} +(12350.5 + 10363.3i) q^{52} +(27725.7 + 23264.6i) q^{53} +(5329.63 - 1939.82i) q^{54} +(-1945.01 - 11030.7i) q^{55} +(-162.794 - 923.249i) q^{56} +(7069.17 - 2572.97i) q^{57} +(-3876.21 - 3252.53i) q^{58} +(27777.9 + 23308.4i) q^{59} +(-1051.73 - 1821.65i) q^{60} +(-34588.9 - 12589.3i) q^{61} +(-5555.62 + 31507.5i) q^{62} +(-1715.10 + 2970.64i) q^{63} +(-2048.00 - 3547.24i) q^{64} +(-41892.1 + 15247.5i) q^{65} +(1504.61 - 2606.05i) q^{66} +(28240.9 - 23696.9i) q^{67} -16417.6 q^{68} +(5554.08 - 4660.43i) q^{69} +(2435.96 + 886.617i) q^{70} +(664.085 + 3766.21i) q^{71} +(-2602.45 + 14759.2i) q^{72} +28350.6 q^{73} +(-12235.7 - 30980.5i) q^{74} -3469.61 q^{75} +(-7033.89 + 39891.1i) q^{76} +(643.981 + 3652.20i) q^{77} +(-11254.7 - 4096.36i) q^{78} +(-63789.4 + 53525.7i) q^{79} +11326.0 q^{80} +(40362.9 - 33868.5i) q^{81} +(17642.3 - 30557.3i) q^{82} +(-75351.0 + 27425.5i) q^{83} +(348.221 + 603.137i) q^{84} +(22698.5 - 39315.0i) q^{85} +(13426.9 - 76147.9i) q^{86} +(3532.29 + 1285.65i) q^{87} +(8101.49 + 14032.2i) q^{88} +(-975.442 - 818.493i) q^{89} +(-31745.5 - 26637.7i) q^{90} +(13870.2 - 5048.33i) q^{91} +(6779.08 + 38446.1i) q^{92} +(-4127.15 - 23406.2i) q^{93} +(-17852.8 + 6497.88i) q^{94} +(-85801.7 - 71996.2i) q^{95} +(2330.94 + 1955.89i) q^{96} +(17608.0 + 30498.0i) q^{97} +(62367.1 + 22699.8i) q^{98} +(10294.8 - 58384.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 3 q^{3} - 72 q^{5} + 114 q^{7} - 1536 q^{8} - 93 q^{9}+O(q^{10}) $ 48 * q - 3 * q^3 - 72 * q^5 + 114 * q^7 - 1536 * q^8 - 93 * q^9	\( 48 q - 3 q^{3} - 72 q^{5} + 114 q^{7} - 1536 q^{8} - 93 q^{9} - 648 q^{10} - 9 q^{11} - 48 q^{12} + 288 q^{13} - 660 q^{14} - 3678 q^{15} - 2475 q^{17} + 744 q^{18} + 945 q^{19} - 1152 q^{20} - 2073 q^{21} - 60 q^{22} - 5739 q^{23} - 192 q^{24} - 3834 q^{25} - 5304 q^{26} - 1077 q^{27} - 5232 q^{28} - 11640 q^{29} - 14712 q^{30} - 20394 q^{31} - 62013 q^{33} + 7812 q^{34} + 27999 q^{35} + 62208 q^{36} + 13605 q^{37} + 60696 q^{38} + 25590 q^{39} + 9216 q^{40} - 18267 q^{41} - 8292 q^{42} + 2208 q^{43} - 240 q^{44} - 48132 q^{45} - 40308 q^{46} - 663 q^{47} + 58326 q^{49} + 61776 q^{50} + 8748 q^{51} - 31536 q^{52} + 20940 q^{53} + 37836 q^{54} - 158868 q^{55} + 13632 q^{56} + 164910 q^{57} - 28068 q^{58} + 111258 q^{59} - 31824 q^{60} + 88758 q^{61} + 116100 q^{62} - 202488 q^{63} - 98304 q^{64} + 155997 q^{65} - 53532 q^{66} + 52503 q^{67} + 32544 q^{68} + 298758 q^{69} - 5760 q^{70} + 160434 q^{71} + 11904 q^{72} - 477210 q^{73} + 8844 q^{74} + 808230 q^{75} + 15120 q^{76} - 510765 q^{77} + 26004 q^{78} - 378768 q^{79} + 82944 q^{80} + 55476 q^{81} - 149064 q^{82} - 230082 q^{83} - 42336 q^{84} + 55653 q^{85} - 149904 q^{86} - 453051 q^{87} - 576 q^{88} + 492789 q^{89} + 12276 q^{90} + 220839 q^{91} + 176160 q^{92} - 109767 q^{93} - 6768 q^{94} - 630843 q^{95} + 6144 q^{96} - 632190 q^{97} - 194628 q^{98} - 414765 q^{99}+O(q^{100}) \) 48 * q - 3 * q^3 - 72 * q^5 + 114 * q^7 - 1536 * q^8 - 93 * q^9 - 648 * q^10 - 9 * q^11 - 48 * q^12 + 288 * q^13 - 660 * q^14 - 3678 * q^15 - 2475 * q^17 + 744 * q^18 + 945 * q^19 - 1152 * q^20 - 2073 * q^21 - 60 * q^22 - 5739 * q^23 - 192 * q^24 - 3834 * q^25 - 5304 * q^26 - 1077 * q^27 - 5232 * q^28 - 11640 * q^29 - 14712 * q^30 - 20394 * q^31 - 62013 * q^33 + 7812 * q^34 + 27999 * q^35 + 62208 * q^36 + 13605 * q^37 + 60696 * q^38 + 25590 * q^39 + 9216 * q^40 - 18267 * q^41 - 8292 * q^42 + 2208 * q^43 - 240 * q^44 - 48132 * q^45 - 40308 * q^46 - 663 * q^47 + 58326 * q^49 + 61776 * q^50 + 8748 * q^51 - 31536 * q^52 + 20940 * q^53 + 37836 * q^54 - 158868 * q^55 + 13632 * q^56 + 164910 * q^57 - 28068 * q^58 + 111258 * q^59 - 31824 * q^60 + 88758 * q^61 + 116100 * q^62 - 202488 * q^63 - 98304 * q^64 + 155997 * q^65 - 53532 * q^66 + 52503 * q^67 + 32544 * q^68 + 298758 * q^69 - 5760 * q^70 + 160434 * q^71 + 11904 * q^72 - 477210 * q^73 + 8844 * q^74 + 808230 * q^75 + 15120 * q^76 - 510765 * q^77 + 26004 * q^78 - 378768 * q^79 + 82944 * q^80 + 55476 * q^81 - 149064 * q^82 - 230082 * q^83 - 42336 * q^84 + 55653 * q^85 - 149904 * q^86 - 453051 * q^87 - 576 * q^88 + 492789 * q^89 + 12276 * q^90 + 220839 * q^91 + 176160 * q^92 - 109767 * q^93 - 6768 * q^94 - 630843 * q^95 + 6144 * q^96 - 632190 * q^97 - 194628 * q^98 - 414765 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	0.694593	−	3.93923i	0.122788	−	0.696364i
$2$	0.694593	−	3.93923i	0.122788	−	0.696364i
$3$	0.515998	+	2.92637i	0.0331013	+	0.187727i	0.996875	−	0.0789943i	$-0.0251709\pi$
$3$	0.515998	+	2.92637i	0.0331013	+	0.187727i	−0.963774	+	0.266721i	$0.914060\pi$
$4$	−15.0351	−	5.47232i	−0.469846	−	0.171010i
$5$	33.8915	−	28.4384i	0.606270	−	0.508721i	−0.287184	−	0.957875i	$-0.592719\pi$
$5$	33.8915	−	28.4384i	0.606270	−	0.508721i	0.893454	+	0.449154i	$0.148275\pi$
$6$	11.8861			0.134791
$7$	−11.2213	+	9.41575i	−0.0865558	+	0.0726290i	−0.685039	−	0.728506i	$-0.740215\pi$
$7$	−11.2213	+	9.41575i	−0.0865558	+	0.0726290i	0.598483	+	0.801135i	$0.295770\pi$
$8$	−32.0000	+	55.4256i	−0.176777	+	0.306186i
$9$	220.048	−	80.0909i	0.905547	−	0.329592i
$10$	−88.4845	−	153.260i	−0.279812	−	0.484649i
$11$	126.586	−	219.253i	0.315430	−	0.546341i	−0.664099	−	0.747645i	$-0.731184\pi$
$11$	126.586	−	219.253i	0.315430	−	0.546341i	0.979529	+	0.201304i	$0.0645178\pi$
$12$	8.25596	−	46.8219i	0.0165506	−	0.0938633i
$13$	−946.880	−	344.636i	−1.55395	−	0.565591i	−0.584609	−	0.811316i	$-0.698752\pi$
$13$	−946.880	−	344.636i	−1.55395	−	0.565591i	−0.969340	+	0.245725i	$0.920974\pi$
$14$	29.2966	+	50.7432i	0.0399482	+	0.0691923i
$15$	100.709	+	84.5050i	0.115569	+	0.0969737i
$16$	196.107	+	164.554i	0.191511	+	0.160697i
$17$	964.220	−	350.948i	0.809196	−	0.294523i	0.0959046	−	0.995391i	$-0.469426\pi$
$17$	964.220	−	350.948i	0.809196	−	0.294523i	0.713292	+	0.700867i	$0.247203\pi$
$18$	−162.653	−	922.450i	−0.118326	−	0.671060i
$19$	−439.618	−	2493.20i	−0.279377	−	1.58443i	−0.724704	−	0.689060i	$-0.758024\pi$
$19$	−439.618	−	2493.20i	−0.279377	−	1.58443i	0.445327	−	0.895368i	$-0.353087\pi$
$20$	−665.186	+	242.108i	−0.371850	+	0.135342i
$21$	−33.3441	−	27.9790i	−0.0164995	−	0.0138447i
$22$	−775.763	−	650.943i	−0.341722	−	0.286738i
$23$	−1219.97	−	2113.06i	−0.480874	−	0.832897i	0.518886	−	0.854844i	$-0.326347\pi$
$23$	−1219.97	−	2113.06i	−0.480874	−	0.832897i	−0.999759	+	0.0219463i	$0.993014\pi$
$24$	−178.708	−	65.0443i	−0.0633308	−	0.0230505i
$25$	−202.756	+	1149.89i	−0.0648819	+	0.367963i
$26$	−2015.30	+	3490.60i	−0.584663	+	1.01267i
$27$	708.959	+	1227.95i	0.187159	+	0.324169i
$28$	220.238	−	80.1602i	0.0530882	−	0.0193225i
$29$	632.504	−	1095.53i	0.139659	−	0.241896i	−0.787709	−	0.616048i	$-0.788733\pi$
$29$	632.504	−	1095.53i	0.139659	−	0.241896i	0.927367	+	0.374152i	$0.122066\pi$
$30$	402.836	−	338.020i	0.0817195	−	0.0685708i
$31$	−7998.38			−1.49485			−0.747426	−	0.664346i	$-0.768710\pi$
$31$	−7998.38			−1.49485			−0.747426	+	0.664346i	$0.768710\pi$
$32$	784.430	−	658.215i	0.135419	−	0.113630i
$33$	706.934	+	257.303i	0.113004	+	0.0411301i
$34$	−712.723	−	4042.05i	−0.105736	−	0.599659i
$35$	−112.537	+	638.228i	−0.0155283	+	0.0880655i
$36$	−3746.72			−0.481832
$37$	7096.28	−	4357.38i	0.852171	−	0.523264i
$37$	7096.28	−	4357.38i	0.852171	−	0.523264i
$38$	−10126.6			−1.13764
$39$	519.944	−	2948.75i	0.0547388	−	0.310439i
$40$	491.685	+	2788.49i	0.0485889	+	0.275562i
$41$	8289.16	+	3017.01i	0.770107	+	0.280296i	0.697041	−	0.717031i	$-0.254500\pi$
$41$	8289.16	+	3017.01i	0.770107	+	0.280296i	0.0730655	+	0.997327i	$0.476722\pi$
$42$	−133.376	+	111.916i	−0.0116669	+	0.00978970i
$43$	19330.7			1.59432			0.797160	−	0.603768i	$-0.206335\pi$
$43$	19330.7			1.59432			0.797160	+	0.603768i	$0.206335\pi$
$44$	−3103.05	+	2603.77i	−0.241634	+	0.202755i
$45$	5180.11	−	8972.21i	0.381336	−	0.660493i
$46$	−9171.20	+	3338.04i	−0.639045	+	0.232593i
$47$	−2374.82	−	4113.30i	−0.156814	−	0.271610i	0.776904	−	0.629619i	$-0.216789\pi$
$47$	−2374.82	−	4113.30i	−0.156814	−	0.271610i	−0.933718	+	0.358009i	$0.883456\pi$
$48$	−380.354	+	658.792i	−0.0238278	+	0.0412710i
$49$	−2881.24	+	16340.4i	−0.171431	+	0.972235i
$50$	4388.83	+	1597.40i	0.248270	+	0.0903628i
$51$	1524.54	+	2640.58i	0.0820753	+	0.142159i
$52$	12350.5	+	10363.3i	0.633395	+	0.531482i
$53$	27725.7	+	23264.6i	1.35579	+	1.13764i	0.977258	+	0.212056i	$0.0680159\pi$
$53$	27725.7	+	23264.6i	1.35579	+	1.13764i	0.378533	+	0.925588i	$0.376429\pi$
$54$	5329.63	−	1939.82i	0.248721	−	0.0905270i
$55$	−1945.01	−	11030.7i	−0.0866993	−	0.491696i
$56$	−162.794	−	923.249i	−0.00693693	−	0.0393413i
$57$	7069.17	−	2572.97i	0.288192	−	0.104893i
$58$	−3876.21	−	3252.53i	−0.151299	−	0.126955i
$59$	27777.9	+	23308.4i	1.03889	+	0.871731i	0.991882	−	0.127163i	$-0.0405872\pi$
$59$	27777.9	+	23308.4i	1.03889	+	0.871731i	0.0470073	+	0.998895i	$0.485032\pi$
$60$	−1051.73	−	1821.65i	−0.0377161	−	0.0653262i
$61$	−34588.9	−	12589.3i	−1.19018	−	0.433190i	−0.330393	−	0.943843i	$-0.607181\pi$
$61$	−34588.9	−	12589.3i	−1.19018	−	0.433190i	−0.859787	+	0.510654i	$0.829403\pi$
$62$	−5555.62	+	31507.5i	−0.183549	+	1.04096i
$63$	−1715.10	+	2970.64i	−0.0544424	+	0.0942970i
$64$	−2048.00	−	3547.24i	−0.0625000	−	0.108253i
$65$	−41892.1	+	15247.5i	−1.22984	+	0.447625i
$66$	1504.61	−	2606.05i	0.0425170	−	0.0736417i
$67$	28240.9	−	23696.9i	0.768584	−	0.644919i	−0.171762	−	0.985139i	$-0.554946\pi$
$67$	28240.9	−	23696.9i	0.768584	−	0.644919i	0.940346	+	0.340220i	$0.110501\pi$
$68$	−16417.6			−0.430564
$69$	5554.08	−	4660.43i	0.140440	−	0.117843i
$70$	2435.96	+	886.617i	0.0594190	+	0.0216267i
$71$	664.085	+	3766.21i	0.0156343	+	0.0886664i	0.991627	−	0.129139i	$-0.0412213\pi$
$71$	664.085	+	3766.21i	0.0156343	+	0.0886664i	−0.975992	+	0.217805i	$0.930110\pi$
$72$	−2602.45	+	14759.2i	−0.0591630	+	0.335530i
$73$	28350.6			0.622665			0.311332	−	0.950301i	$-0.399225\pi$
$73$	28350.6			0.622665			0.311332	+	0.950301i	$0.399225\pi$
$74$	−12235.7	−	30980.5i	−0.259746	−	0.657672i
$75$	−3469.61			−0.0712242
$76$	−7033.89	+	39891.1i	−0.139689	+	0.792214i
$77$	643.981	+	3652.20i	0.0123779	+	0.0701984i
$78$	−11254.7	−	4096.36i	−0.209458	−	0.0762363i
$79$	−63789.4	+	53525.7i	−1.14996	+	0.964927i	−0.999719	−	0.0237230i	$-0.992448\pi$
$79$	−63789.4	+	53525.7i	−1.14996	+	0.964927i	−0.150237	+	0.988650i	$0.548004\pi$
$80$	11326.0			0.197857
$81$	40362.9	−	33868.5i	0.683549	−	0.573565i
$82$	17642.3	−	30557.3i	0.289748	−	0.501858i
$83$	−75351.0	+	27425.5i	−1.20059	+	0.436978i	−0.863429	−	0.504470i	$-0.831688\pi$
$83$	−75351.0	+	27425.5i	−1.20059	+	0.436978i	−0.337158	+	0.941448i	$0.609466\pi$
$84$	348.221	+	603.137i	0.00538464	+	0.00932647i
$85$	22698.5	−	39315.0i	0.340761	−	0.590216i
$86$	13426.9	−	76147.9i	0.195763	−	1.11023i
$87$	3532.29	+	1285.65i	0.0500332	+	0.0182106i
$88$	8101.49	+	14032.2i	0.111521	+	0.193161i
$89$	−975.442	−	818.493i	−0.0130535	−	0.0109532i	0.636238	−	0.771493i	$-0.280490\pi$
$89$	−975.442	−	818.493i	−0.0130535	−	0.0109532i	−0.649291	+	0.760540i	$0.724934\pi$
$90$	−31745.5	−	26637.7i	−0.413120	−	0.346649i
$91$	13870.2	−	5048.33i	0.175582	−	0.0639064i
$92$	6779.08	+	38446.1i	0.0835028	+	0.473568i
$93$	−4127.15	−	23406.2i	−0.0494815	−	0.280623i
$94$	−17852.8	+	6497.88i	−0.208394	+	0.0758494i
$95$	−85801.7	−	71996.2i	−0.975410	−	0.818466i
$96$	2330.94	+	1955.89i	0.0258139	+	0.0216604i
$97$	17608.0	+	30498.0i	0.190012	+	0.329110i	0.945254	−	0.326336i	$-0.105814\pi$
$97$	17608.0	+	30498.0i	0.190012	+	0.329110i	−0.755242	+	0.655446i	$0.772481\pi$
$98$	62367.1	+	22699.8i	0.655980	+	0.238757i
$99$	10294.8	−	58384.6i	0.105567	−	0.598701i
$100$	9340.99	−	16179.1i	0.0934099	−	0.161791i
$101$	−5165.67	−	8947.20i	−0.0503875	−	0.0872737i	0.839732	−	0.543002i	$-0.182712\pi$
$101$	−5165.67	−	8947.20i	−0.0503875	−	0.0872737i	−0.890119	+	0.455728i	$0.849379\pi$
$102$	11460.8	−	4171.38i	0.109072	−	0.0396990i
$103$	13587.3	−	23533.8i	0.126194	−	0.218575i	−0.796005	−	0.605290i	$-0.793057\pi$
$103$	13587.3	−	23533.8i	0.126194	−	0.218575i	0.922199	+	0.386715i	$0.126390\pi$
$104$	49401.8	−	41453.1i	0.447878	−	0.375814i
$105$	−1925.76			−0.0170463
$106$	110903.	−	93058.5i	0.958689	−	0.804435i
$107$	−146851.	−	53449.5i	−1.23999	−	0.451319i	−0.362982	−	0.931796i	$-0.618242\pi$
$107$	−146851.	−	53449.5i	−1.23999	−	0.451319i	−0.877008	+	0.480477i	$0.840464\pi$
$108$	−3939.50	−	22342.0i	−0.0324999	−	0.184316i
$109$	−12406.6	+	70361.1i	−0.100020	+	0.567240i	0.893073	+	0.449911i	$0.148544\pi$
$109$	−12406.6	+	70361.1i	−0.100020	+	0.567240i	−0.993093	+	0.117329i	$0.962567\pi$
$110$	−44803.5			−0.353045
$111$	16413.0	+	18517.9i	0.126439	+	0.142654i
$112$	−3749.97			−0.0282476
$113$	40374.8	−	228977.i	0.297450	−	1.68693i	−0.359622	−	0.933098i	$-0.617094\pi$
$113$	40374.8	−	228977.i	0.297450	−	1.68693i	0.657072	−	0.753827i	$-0.271795\pi$
$114$	−5225.32	−	29634.3i	−0.0376574	−	0.213566i
$115$	−101439.	−	36920.6i	−0.715251	−	0.260330i
$116$	−15504.8	+	13010.1i	−0.106985	+	0.0897710i
$117$	−235961.			−1.59359
$118$	111112.	−	93233.7i	0.734606	−	0.616407i
$119$	−7515.33	+	13016.9i	−0.0486497	+	0.0842638i
$120$	−7906.43	+	2877.71i	−0.0501219	+	0.0182429i
$121$	48477.5	+	83965.6i	0.301007	+	0.521360i
$122$	−73617.5	+	127509.i	−0.447797	+	0.775608i
$123$	−4551.69	+	25813.9i	−0.0271275	+	0.153848i
$124$	120256.	+	43769.7i	0.702350	+	0.255635i
$125$	94957.7	+	164471.i	0.543569	+	0.941490i
$126$	10510.7	+	8819.55i	0.0589802	+	0.0494903i
$127$	221989.	+	186271.i	1.22130	+	1.02479i	0.998756	+	0.0498692i	$0.0158805\pi$
$127$	221989.	+	186271.i	1.22130	+	1.02479i	0.222544	+	0.974923i	$0.428564\pi$
$128$	−15395.9	+	5603.66i	−0.0830579	+	0.0302306i
$129$	9974.58	+	56568.6i	0.0527740	+	0.299296i
$130$	30965.4	+	175613.i	0.160701	+	0.911380i
$131$	−184133.	+	67018.9i	−0.937462	+	0.341208i	−0.765163	−	0.643837i	$-0.777342\pi$
$131$	−184133.	+	67018.9i	−0.937462	+	0.341208i	−0.172299	+	0.985045i	$0.555119\pi$
$132$	−9220.76	−	7737.14i	−0.0460608	−	0.0386496i
$133$	28408.4	+	23837.5i	0.139257	+	0.116851i
$134$	−73731.8	−	127707.i	−0.354726	−	0.614403i
$135$	58948.6	+	21455.5i	0.278381	+	0.101322i
$136$	−11403.6	+	64672.8i	−0.0528681	+	0.299830i
$137$	−80627.1	+	139650.i	−0.367011	+	0.635682i	−0.989097	−	0.147267i	$-0.952952\pi$
$137$	−80627.1	+	139650.i	−0.367011	+	0.635682i	0.622085	+	0.782949i	$0.286286\pi$
$138$	−14500.7	−	25115.9i	−0.0648172	−	0.112267i
$139$	99596.9	−	36250.3i	0.437229	−	0.159138i	−0.114021	−	0.993478i	$-0.536373\pi$
$139$	99596.9	−	36250.3i	0.437229	−	0.159138i	0.551250	+	0.834340i	$0.314151\pi$
$140$	5184.59	−	8979.97i	0.0223560	−	0.0387218i
$141$	10811.6	−	9072.04i	0.0457977	−	0.0384288i
$142$	15297.2			0.0636638
$143$	−195424.	+	163980.i	−0.799168	+	0.670582i
$144$	56332.3	+	20503.3i	0.226387	+	0.0823980i
$145$	−9718.53	−	55116.5i	−0.0383867	−	0.217702i
$146$	19692.1	−	111679.i	0.0764557	−	0.433602i
$147$	−49304.6			−0.188189
$148$	−130538.	+	26680.4i	−0.489873	+	0.100124i
$149$	487609.			1.79931			0.899656	−	0.436600i	$-0.143817\pi$
$149$	487609.			1.79931			0.899656	+	0.436600i	$0.143817\pi$
$150$	−2409.97	+	13667.6i	−0.00874546	+	0.0495980i
$151$	−11811.7	−	66987.4i	−0.0421570	−	0.239084i	0.956447	−	0.291906i	$-0.0942895\pi$
$151$	−11811.7	−	66987.4i	−0.0421570	−	0.239084i	−0.998604	+	0.0528221i	$0.983178\pi$
$152$	152255.	+	55416.2i	0.534517	+	0.194548i
$153$	184067.	−	154451.i	0.635693	−	0.533410i
$154$	14834.1			0.0504035
$155$	−271077.	+	227461.i	−0.906283	+	0.760462i
$156$	−23953.9	+	41489.4i	−0.0788071	+	0.136498i
$157$	67395.3	−	24529.9i	0.218213	−	0.0794230i	−0.230600	−	0.973049i	$-0.574069\pi$
$157$	67395.3	−	24529.9i	0.218213	−	0.0794230i	0.448813	+	0.893626i	$0.351847\pi$
$158$	166542.	+	288460.i	0.530740	+	0.919269i
$159$	−53774.5	+	93140.1i	−0.168688	+	0.292176i
$160$	7866.97	−	44615.8i	0.0242945	−	0.137781i
$161$	33585.6	+	12224.2i	0.102115	+	0.0371668i
$162$	−105380.	−	182523.i	−0.315479	−	0.546426i
$163$	−41250.6	−	34613.3i	−0.121608	−	0.102041i	0.579956	−	0.814648i	$-0.303070\pi$
$163$	−41250.6	−	34613.3i	−0.121608	−	0.102041i	−0.701563	+	0.712607i	$0.747514\pi$
$164$	−108118.	−	90721.9i	−0.313898	−	0.263392i
$165$	31276.3	−	11383.7i	0.0894347	−	0.0325516i
$166$	55697.2	+	315875.i	0.156878	+	0.889702i
$167$	16788.3	+	95211.0i	0.0465817	+	0.264178i	0.999200	−	0.0399903i	$-0.0127327\pi$
$167$	16788.3	+	95211.0i	0.0465817	+	0.264178i	−0.952618	+	0.304168i	$0.901622\pi$
$168$	2617.77	−	952.789i	0.00715579	−	0.00260449i
$169$	493381.	+	413995.i	1.32882	+	1.11501i
$170$	−139105.	−	116723.i	−0.369164	−	0.309765i
$171$	−296419.	−	513413.i	−0.775204	−	1.34269i
$172$	−290638.	−	105784.i	−0.749085	−	0.272645i
$173$	60792.2	−	344769.i	0.154430	−	0.875817i	−0.804875	−	0.593445i	$-0.797768\pi$
$173$	60792.2	−	344769.i	0.154430	−	0.875817i	0.959305	−	0.282372i	$-0.0911214\pi$
$174$	7517.98	−	13021.5i	0.0188247	−	0.0326053i
$175$	−8551.86	−	14812.3i	−0.0211089	−	0.0365617i
$176$	60903.3	−	22167.0i	0.148204	−	0.0539418i
$177$	−53875.7	+	93315.4i	−0.129259	+	0.223883i
$178$	−3901.77	+	3273.97i	−0.00923021	+	0.00774507i
$179$	−22927.9			−0.0534850			−0.0267425	−	0.999642i	$-0.508513\pi$
$179$	−22927.9			−0.0534850			−0.0267425	+	0.999642i	$0.508513\pi$
$180$	−126982.	+	106551.i	−0.292120	+	0.245118i
$181$	659544.	+	240054.i	1.49640	+	0.544645i	0.955125	−	0.296202i	$-0.0957201\pi$
$181$	659544.	+	240054.i	1.49640	+	0.544645i	0.541274	+	0.840847i	$0.317942\pi$
$182$	−10252.4	−	58144.4i	−0.0229429	−	0.130116i
$183$	18993.2	−	107716.i	0.0419248	−	0.237768i
$184$	156157.			0.340029
$185$	116587.	−	349485.i	0.250450	−	0.750756i
$186$	−95069.2			−0.201492
$187$	45110.3	−	255833.i	0.0943348	−	0.534999i
$188$	13196.2	+	74839.6i	0.0272305	+	0.154432i
$189$	−19517.5	−	7103.79i	−0.0397438	−	0.0144656i
$190$	−343207.	+	287985.i	−0.689719	+	0.578743i
$191$	−534401.			−1.05995			−0.529973	−	0.848014i	$-0.677798\pi$
$191$	−534401.			−1.05995			−0.529973	+	0.848014i	$0.677798\pi$
$192$	9323.77	−	7823.57i	0.0182532	−	0.0153162i
$193$	208511.	−	361151.i	0.402935	−	0.697905i	−0.591143	−	0.806567i	$-0.701323\pi$
$193$	208511.	−	361151.i	0.402935	−	0.697905i	0.994079	+	0.108662i	$0.0346566\pi$
$194$	132369.	−	48178.3i	0.252512	−	0.0919068i
$195$	−66236.0	−	114724.i	−0.124740	−	0.216057i
$196$	132739.	−	229911.i	0.246808	−	0.427484i
$197$	−15289.9	+	86713.2i	−0.0280697	+	0.159191i	−0.995621	−	0.0934844i	$-0.970199\pi$
$197$	−15289.9	+	86713.2i	−0.0280697	+	0.159191i	0.967551	+	0.252676i	$0.0813106\pi$
$198$	−222840.	−	81107.0i	−0.403952	−	0.147026i
$199$	20394.2	+	35323.9i	0.0365069	+	0.0632318i	0.883702	−	0.468051i	$-0.155044\pi$
$199$	20394.2	+	35323.9i	0.0365069	+	0.0632318i	−0.847195	+	0.531283i	$0.821710\pi$
$200$	−57244.9	−	48034.2i	−0.101196	−	0.0849133i
$201$	83918.2	+	70415.7i	0.146510	+	0.122936i
$202$	−38833.1	+	14134.1i	−0.0669613	+	0.0243719i
$203$	3217.74	+	18248.7i	0.00548038	+	0.0310808i
$204$	−8471.46	−	48044.0i	−0.0142522	−	0.0808284i
$205$	366731.	−	133479.i	0.609485	−	0.221834i
$206$	−83267.6	−	69869.8i	−0.136712	−	0.114715i
$207$	−437689.	−	367265.i	−0.709970	−	0.595736i
$208$	−128979.	−	223398.i	−0.206710	−	0.358032i
$209$	−602291.	−	219216.i	−0.953763	−	0.347141i
$210$	−1337.62	+	7586.01i	−0.00209307	+	0.0118704i
$211$	−208295.	+	360778.i	−0.322087	+	0.557871i	−0.980919	−	0.194419i	$-0.937718\pi$
$211$	−208295.	+	360778.i	−0.322087	+	0.557871i	0.658831	+	0.752291i	$0.271051\pi$
$212$	−289547.	−	501509.i	−0.442465	−	0.766372i
$213$	−10678.7	+	3886.71i	−0.0161275	+	0.00586994i
$214$	−312552.	+	541355.i	−0.466538	+	0.808068i
$215$	655145.	−	549732.i	0.966588	−	0.811064i
$216$	−90746.7			−0.132342
$217$	89751.9	−	75310.8i	0.129388	−	0.108569i
$218$	268551.	+	97744.6i	0.382724	+	0.139300i
$219$	14628.8	+	82964.2i	0.0206110	+	0.116891i
$220$	−31120.2	+	176491.i	−0.0433497	+	0.245848i
$221$	−1.03395e6			−1.42403
$222$	84346.8	−	51792.0i	0.114865	−	0.0705310i
$223$	200328.			0.269761			0.134881	−	0.990862i	$-0.456935\pi$
$223$	200328.			0.269761			0.134881	+	0.990862i	$0.456935\pi$
$224$	−2604.70	+	14772.0i	−0.00346847	+	0.0196707i
$225$	47479.3	+	269269.i	0.0625242	+	0.354593i
$226$	−873950.	−	318092.i	−1.13819	−	0.414268i
$227$	537941.	−	451386.i	0.692899	−	0.581411i	−0.226845	−	0.973931i	$-0.572841\pi$
$227$	537941.	−	451386.i	0.692899	−	0.581411i	0.919744	+	0.392520i	$0.128396\pi$
$228$	−120366.			−0.153344
$229$	297062.	−	249265.i	0.374334	−	0.314103i	−0.436140	−	0.899879i	$-0.643655\pi$
$229$	297062.	−	249265.i	0.374334	−	0.314103i	0.810473	+	0.585776i	$0.199210\pi$
$230$	−215897.	+	373945.i	−0.269109	+	0.466110i
$231$	−10355.4	+	3769.05i	−0.0127684	+	0.00464731i
$232$	40480.3	+	70113.9i	0.0493769	+	0.0855232i
$233$	318992.	−	552510.i	0.384937	−	0.666730i	−0.606824	−	0.794837i	$-0.707557\pi$
$233$	318992.	−	552510.i	0.384937	−	0.666730i	0.991760	+	0.128106i	$0.0408899\pi$
$234$	−163897.	+	929506.i	−0.195673	+	1.10972i
$235$	−197462.	−	71870.2i	−0.233245	−	0.0848944i
$236$	−290092.	−	502453.i	−0.339043	−	0.587240i
$237$	−189551.	−	159052.i	−0.219208	−	0.183937i
$238$	46056.6	+	38646.1i	0.0527047	+	0.0442245i
$239$	−711927.	+	259120.i	−0.806196	+	0.293431i	−0.712051	−	0.702127i	$-0.752234\pi$
$239$	−711927.	+	259120.i	−0.806196	+	0.293431i	−0.0941442	+	0.995559i	$0.530011\pi$
$240$	5844.20	+	33144.1i	0.00654933	+	0.0371431i
$241$	86175.6	+	488726.i	0.0955745	+	0.542030i	0.994570	+	0.104072i	$0.0331871\pi$
$241$	86175.6	+	488726.i	0.0955745	+	0.542030i	−0.898995	+	0.437958i	$0.855702\pi$
$242$	364432.	−	132642.i	0.400017	−	0.145594i
$243$	383882.	+	322116.i	0.417045	+	0.349942i
$244$	451154.	+	378563.i	0.485122	+	0.407065i
$245$	367043.	+	635737.i	0.390663	+	0.676647i
$246$	98525.4	+	35860.3i	0.103803	+	0.0377812i
$247$	−442980.	+	2.51227e6i	−0.462000	+	2.62013i
$248$	255948.	−	443315.i	0.264255	−	0.457703i
$249$	−119138.	−	206353.i	−0.121773	−	0.210918i
$250$	713848.	−	259819.i	0.722363	−	0.262919i
$251$	243002.	−	420892.i	0.243459	−	0.421683i	−0.718238	−	0.695797i	$-0.755051\pi$
$251$	243002.	−	420892.i	0.243459	−	0.421683i	0.961697	+	0.274114i	$0.0883846\pi$
$252$	42042.9	−	35278.2i	0.0417053	−	0.0349949i
$253$	−617726.			−0.606728
$254$	887956.	−	745084.i	0.863589	−	0.724637i
$255$	126763.	+	46137.8i	0.122079	+	0.0444331i
$256$	11380.2	+	64540.4i	0.0108530	+	0.0615505i
$257$	103204.	−	585296.i	0.0974679	−	0.552768i	−0.896495	−	0.443053i	$-0.853895\pi$
$257$	103204.	−	585296.i	0.0974679	−	0.552768i	0.993963	−	0.109715i	$-0.0349937\pi$
$258$	229765.			0.214899
$259$	−38601.2	+	115712.i	−0.0357562	+	0.107184i
$260$	713290.			0.654384
$261$	51439.3	−	291727.i	0.0467406	−	0.265079i
$262$	136106.	+	771893.i	0.122496	+	0.694711i
$263$	−1.06142e6	−	386326.i	−0.946235	−	0.344401i	−0.177610	−	0.984101i	$-0.556837\pi$
$263$	−1.06142e6	−	386326.i	−0.946235	−	0.344401i	−0.768625	+	0.639700i	$0.779059\pi$
$264$	−36883.0	+	30948.5i	−0.0325699	+	0.0273294i
$265$	1.60127e6			1.40072
$266$	113634.	−	95349.8i	0.0984696	−	0.0826258i
$267$	1891.89	−	3276.85i	0.00162412	−	0.00281305i
$268$	−554282.	+	201742.i	−0.471404	+	0.171577i
$269$	−33369.3	−	57797.2i	−0.0281168	−	0.0486997i	0.851625	−	0.524152i	$-0.175618\pi$
$269$	−33369.3	−	57797.2i	−0.0281168	−	0.0486997i	−0.879741	+	0.475452i	$0.842284\pi$
$270$	125464.	−	217309.i	0.104739	−	0.181413i
$271$	300811.	−	1.70598e6i	0.248811	−	1.41108i	−0.562661	−	0.826688i	$-0.690222\pi$
$271$	300811.	−	1.70598e6i	0.248811	−	1.41108i	0.811472	−	0.584391i	$-0.198666\pi$
$272$	246840.	+	89842.6i	0.202299	+	0.0736309i
$273$	21930.3	+	37984.4i	0.0178089	+	0.0308459i
$274$	494111.	+	414609.i	0.397602	+	0.333628i
$275$	226450.	+	190014.i	0.180568	+	0.151514i
$276$	−109009.	+	39676.2i	−0.0861373	+	0.0313514i
$277$	224416.	+	1.27273e6i	0.175733	+	0.996633i	0.937294	+	0.348540i	$0.113322\pi$
$277$	224416.	+	1.27273e6i	0.175733	+	0.996633i	−0.761561	+	0.648094i	$0.775567\pi$
$278$	−73619.1	−	417515.i	−0.0571319	−	0.324011i
$279$	−1.76003e6	+	640598.i	−1.35366	+	0.492691i
$280$	−31773.0	−	26660.7i	−0.0242194	−	0.0203225i
$281$	497443.	+	417404.i	0.375818	+	0.315349i	0.811058	−	0.584966i	$-0.198892\pi$
$281$	497443.	+	417404.i	0.375818	+	0.315349i	−0.435240	+	0.900314i	$0.643337\pi$
$282$	−28227.2	−	48890.9i	−0.0211371	−	0.0366105i
$283$	620932.	+	226001.i	0.460869	+	0.167743i	0.562012	−	0.827129i	$-0.310028\pi$
$283$	620932.	+	226001.i	0.460869	+	0.167743i	−0.101142	+	0.994872i	$0.532250\pi$
$284$	10625.4	−	60259.4i	0.00781714	−	0.0443332i
$285$	166414.	−	288237.i	0.121361	−	0.210203i
$286$	510216.	+	883720.i	0.368841	+	0.638851i
$287$	−121422.	+	44194.0i	−0.0870148	+	0.0316708i
$288$	119895.	−	207664.i	0.0851766	−	0.147530i
$289$	−281117.	+	235885.i	−0.197990	+	0.166133i
$290$	−223867.			−0.156313
$291$	−80162.6	+	67264.4i	−0.0554931	+	0.0465643i
$292$	−426253.	−	155143.i	−0.292557	−	0.106482i
$293$	358790.	+	2.03480e6i	0.244158	+	1.38469i	0.822439	+	0.568854i	$0.192613\pi$
$293$	358790.	+	2.03480e6i	0.244158	+	1.38469i	−0.578280	+	0.815838i	$0.696276\pi$
$294$	−34246.6	+	194222.i	−0.0231073	+	0.131048i
$295$	1.60429e6			1.07332
$296$	14429.2	+	532752.i	0.00957224	+	0.353424i
$297$	358977.			0.236143
$298$	338690.	−	1.92081e6i	0.220934	−	1.25298i
$299$	426933.	+	2.42126e6i	0.276173	+	1.56626i
$300$	52165.9	+	18986.8i	0.0334644	+	0.0121801i
$301$	−216914.	+	182013.i	−0.137998	+	0.115794i
$302$	−272083.			−0.171666
$303$	23517.3	−	19733.4i	0.0147157	−	0.0123480i
$304$	324052.	−	561275.i	0.201109	−	0.348331i
$305$	−1.53029e6	+	556981.i	−0.941943	+	0.342839i
$306$	−480565.	−	832363.i	−0.293392	−	0.508170i
$307$	5173.69	−	8961.10i	0.00313296	−	0.00542644i	−0.864455	−	0.502711i	$-0.832336\pi$
$307$	5173.69	−	8961.10i	0.00313296	−	0.00542644i	0.867588	+	0.497284i	$0.165669\pi$
$308$	10303.7	−	58435.1i	0.00618894	−	0.0350992i
$309$	75879.7	+	27618.0i	0.0452095	+	0.0164549i
$310$	707733.	+	1.22583e6i	0.418278	+	0.724479i
$311$	−1.76651e6	−	1.48227e6i	−1.03565	−	0.869016i	−0.0441400	−	0.999025i	$-0.514055\pi$
$311$	−1.76651e6	−	1.48227e6i	−1.03565	−	0.869016i	−0.991513	+	0.130009i	$0.958499\pi$
$312$	146798.	+	123178.i	0.0853757	+	0.0716387i
$313$	−2.06540e6	+	751745.i	−1.19164	+	0.433720i	−0.860298	−	0.509792i	$-0.829723\pi$
$313$	−2.06540e6	+	751745.i	−1.19164	+	0.433720i	−0.331339	+	0.943512i	$0.607500\pi$
$314$	−49816.6	−	282524.i	−0.0285135	−	0.161708i
$315$	26352.8	+	149454.i	0.0149641	+	0.0848655i
$316$	1.25199e6	−	455687.i	0.705315	−	0.256713i
$317$	−1.06849e6	−	896572.i	−0.597205	−	0.501115i	0.293341	−	0.956008i	$-0.405233\pi$
$317$	−1.06849e6	−	896572.i	−0.597205	−	0.501115i	−0.890546	+	0.454893i	$0.849677\pi$
$318$	329549.	+	276524.i	0.182748	+	0.153344i
$319$	−160132.	−	277357.i	−0.0881053	−	0.152603i
$320$	−170288.	−	61979.6i	−0.0929625	−	0.0338356i
$321$	80638.0	−	457321.i	0.0436794	−	0.247718i
$322$	71482.2	−	123811.i	0.0384201	−	0.0665455i
$323$	−1.29887e6	−	2.24971e6i	−0.692722	−	1.19983i
$324$	−792198.	+	288337.i	−0.419248	+	0.152594i
$325$	588277.	−	1.01893e6i	0.308940	−	0.535099i
$326$	−165002.	+	138453.i	−0.0859896	+	0.0721538i
$327$	−212304.			−0.109797
$328$	−432473.	+	362888.i	−0.221960	+	0.186246i
$329$	65378.2	+	23795.7i	0.0332999	+	0.0121202i
$330$	−23118.5	−	131112.i	−0.0116863	−	0.0662760i
$331$	−534550.	+	3.03158e6i	−0.268175	+	1.52090i	0.491664	+	0.870785i	$0.336389\pi$
$331$	−534550.	+	3.03158e6i	−0.268175	+	1.52090i	−0.759839	+	0.650111i	$0.774722\pi$
$332$	1.28299e6			0.638819
$333$	1.21254e6	−	1.52718e6i	0.599217	−	0.754709i
$334$	386719.			0.189684
$335$	283225.	−	1.60625e6i	0.137886	−	0.781990i
$336$	−1934.97	−	10973.8i	−0.000935033	−	0.00530284i
$337$	703120.	+	255915.i	0.337252	+	0.122750i	0.505094	−	0.863064i	$-0.331458\pi$
$337$	703120.	+	255915.i	0.337252	+	0.122750i	−0.167842	+	0.985814i	$0.553680\pi$
$338$	1.97352e6	−	1.65598e6i	0.939616	−	0.788431i
$339$	690905.			0.326527
$340$	−556418.	+	466891.i	−0.261038	+	0.219037i
$341$	−1.01248e6	+	1.75367e6i	−0.471521	+	0.816699i
$342$	−2.22834e6	+	811051.i	−1.03019	+	0.374958i
$343$	−244623.	−	423699.i	−0.112269	−	0.194456i
$344$	−618581.	+	1.07141e6i	−0.281839	+	0.488159i
$345$	55701.3	−	315898.i	0.0251952	−	0.142889i
$346$	−1.31590e6	−	478949.i	−0.590926	−	0.215079i
$347$	−529149.	−	916514.i	−0.235915	−	0.408616i	0.723624	−	0.690195i	$-0.242475\pi$
$347$	−529149.	−	916514.i	−0.235915	−	0.408616i	−0.959538	+	0.281579i	$0.909142\pi$
$348$	−46072.8	−	38659.7i	−0.0203937	−	0.0171124i
$349$	−1.29298e6	−	1.08494e6i	−0.568237	−	0.476807i	0.312824	−	0.949811i	$-0.398725\pi$
$349$	−1.29298e6	−	1.08494e6i	−0.568237	−	0.476807i	−0.881060	+	0.473004i	$0.843170\pi$
$350$	−64288.9	+	23399.3i	−0.0280521	+	0.0102101i
$351$	−248102.	−	1.40706e6i	−0.107489	−	0.609598i
$352$	−45017.9	−	255309.i	−0.0193655	−	0.109827i
$353$	817749.	−	297636.i	0.349288	−	0.127130i	−0.161417	−	0.986886i	$-0.551607\pi$
$353$	817749.	−	297636.i	0.349288	−	0.127130i	0.510705	+	0.859756i	$0.329384\pi$
$354$	330169.	+	277045.i	0.140032	+	0.117501i
$355$	129612.	+	108757.i	0.0545850	+	0.0458023i
$356$	10186.8	+	17644.0i	0.00426003	+	0.00737859i
$357$	−41970.2	−	15275.9i	−0.0174289	−	0.00634361i
$358$	−15925.6	+	90318.4i	−0.00656731	+	0.0372450i
$359$	−603697.	+	1.04563e6i	−0.247220	+	0.428197i	−0.962753	−	0.270381i	$-0.912850\pi$
$359$	−603697.	+	1.04563e6i	−0.247220	+	0.428197i	0.715534	+	0.698578i	$0.246184\pi$
$360$	331527.	+	574221.i	0.134822	+	0.233519i
$361$	−3.69599e6	+	1.34523e6i	−1.49267	+	0.543287i
$362$	1.40374e6	−	2.43136e6i	0.563011	−	0.975163i
$363$	−220700.	+	185189.i	−0.0879095	+	0.0737648i
$364$	−236166.			−0.0934250
$365$	960843.	−	806243.i	0.377503	−	0.316763i
$366$	−411126.	−	149638.i	−0.160425	−	0.0583899i
$367$	−714600.	−	4.05270e6i	−0.276948	−	1.57065i	−0.732706	−	0.680545i	$-0.761743\pi$
$367$	−714600.	−	4.05270e6i	−0.276948	−	1.57065i	0.455758	−	0.890104i	$-0.349368\pi$
$368$	108465.	−	615137.i	0.0417514	−	0.236784i
$369$	2.06565e6			0.789751
$370$	−1.29572e6	−	702013.i	−0.492048	−	0.266588i
$371$	−530171.			−0.199977
$372$	−66034.4	+	374500.i	−0.0247407	+	0.140312i
$373$	−879707.	−	4.98907e6i	−0.327391	−	1.85672i	−0.492314	−	0.870418i	$-0.663849\pi$
$373$	−879707.	−	4.98907e6i	−0.327391	−	1.85672i	0.164923	−	0.986306i	$-0.447262\pi$
$374$	−976453.	−	355400.i	−0.360971	−	0.131383i
$375$	−432306.	+	362748.i	−0.158750	+	0.133207i
$376$	303976.			0.110884
$377$	−976464.	+	819351.i	−0.353837	+	0.296904i
$378$	−41540.2	+	71949.7i	−0.0149534	+	0.0259000i
$379$	4.61095e6	−	1.67825e6i	1.64889	−	0.600148i	0.660332	−	0.750974i	$-0.270416\pi$
$379$	4.61095e6	−	1.67825e6i	1.64889	−	0.600148i	0.988560	+	0.150826i	$0.0481935\pi$
$380$	896050.	+	1.55200e6i	0.318327	+	0.551358i
$381$	−430552.	+	745737.i	−0.151954	+	0.263192i
$382$	−371191.	+	2.10513e6i	−0.130148	+	0.738109i
$383$	4.36879e6	+	1.59011e6i	1.52182	+	0.553898i	0.961603	−	0.274446i	$-0.0884943\pi$
$383$	4.36879e6	+	1.59011e6i	1.52182	+	0.553898i	0.560220	+	0.828344i	$0.310717\pi$
$384$	−24342.6	−	42162.7i	−0.00842441	−	0.0145915i
$385$	125688.	+	105465.i	0.0432157	+	0.0362623i
$386$	−1.27783e6	−	1.07223e6i	−0.436520	−	0.366284i
$387$	4.25367e6	−	1.54821e6i	1.44373	−	0.525475i
$388$	−97843.1	−	554896.i	−0.0329952	−	0.187125i
$389$	787755.	+	4.46758e6i	0.263947	+	1.49692i	0.772016	+	0.635603i	$0.219248\pi$
$389$	787755.	+	4.46758e6i	0.263947	+	1.49692i	−0.508069	+	0.861317i	$0.669640\pi$
$390$	−497932.	+	181232.i	−0.165771	+	0.0603356i
$391$	−1.91790e6	−	1.60931e6i	−0.634429	−	0.532349i
$392$	−813474.	−	682586.i	−0.267380	−	0.224358i
$393$	−291134.	−	504260.i	−0.0950850	−	0.164692i
$394$	330963.	+	120461.i	0.107409	+	0.0390935i
$395$	−639738.	+	3.62813e6i	−0.206305	+	1.17001i
$396$	−474282.	+	821480.i	−0.151984	+	0.263244i
$397$	−2.12567e6	−	3.68176e6i	−0.676891	−	1.17241i	−0.975912	−	0.218163i	$-0.929994\pi$
$397$	−2.12567e6	−	3.68176e6i	−0.676891	−	1.17241i	0.299021	−	0.954246i	$-0.403340\pi$
$398$	153315.	−	55802.0i	0.0485150	−	0.0176580i
$399$	−55098.5	+	95433.5i	−0.0173264	+	0.0300102i
$400$	−228980.	+	192137.i	−0.0715562	+	0.0600427i
$401$	−795755.			−0.247126			−0.123563	−	0.992337i	$-0.539432\pi$
$401$	−795755.			−0.247126			−0.123563	+	0.992337i	$0.539432\pi$
$402$	335673.	−	281663.i	0.103598	−	0.0869290i
$403$	7.57351e6	+	2.75653e6i	2.32292	+	0.845474i
$404$	28704.3	+	162790.i	0.00874970	+	0.0496220i
$405$	404795.	−	2.29571e6i	0.122630	−	0.695471i
$406$	74120.9			0.0223165
$407$	−57079.2	−	2.10746e6i	−0.0170802	−	0.630629i
$408$	−195141.			−0.0580360
$409$	1.02069e6	−	5.78865e6i	0.301709	−	1.71107i	−0.336898	−	0.941541i	$-0.609378\pi$
$409$	1.02069e6	−	5.78865e6i	0.301709	−	1.71107i	0.638607	−	0.769533i	$-0.279511\pi$
$410$	−271077.	−	1.53735e6i	−0.0796402	−	0.451662i
$411$	−450271.	−	163885.i	−0.131483	−	0.0478559i
$412$	−333071.	+	279479.i	−0.0966703	+	0.0811160i
$413$	−531169.			−0.153235
$414$	−1.75076e6	+	1.46906e6i	−0.502025	+	0.421249i
$415$	−1.77382e6	+	3.07235e6i	−0.505580	+	0.875691i
$416$	−969605.	+	352907.i	−0.274702	+	0.0999833i
$417$	157474.	+	272752.i	0.0443473	+	0.0768119i
$418$	−1.28189e6	+	2.22030e6i	−0.358847	+	0.621542i
$419$	−1.23227e6	+	6.98858e6i	−0.342904	+	1.94470i	−0.0153199	+	0.999883i	$0.504877\pi$
$419$	−1.23227e6	+	6.98858e6i	−0.342904	+	1.94470i	−0.327584	+	0.944822i	$0.606234\pi$
$420$	28954.0	+	10538.4i	0.00800912	+	0.00291508i
$421$	3.25121e6	+	5.63126e6i	0.894004	+	1.54846i	0.835032	+	0.550201i	$0.185449\pi$
$421$	3.25121e6	+	5.63126e6i	0.894004	+	1.54846i	0.0589723	+	0.998260i	$0.481218\pi$
$422$	1.27651e6	+	1.07112e6i	0.348933	+	0.292790i
$423$	−852011.	−	714922.i	−0.231523	−	0.194271i
$424$	−2.17668e6	+	792246.i	−0.588003	+	0.214016i
$425$	208048.	+	1.17990e6i	0.0558716	+	0.316864i
$426$	7893.35	+	44765.4i	0.00210735	+	0.0119514i
$427$	506669.	−	184412.i	0.134479	−	0.0489464i
$428$	1.91543e6	+	1.60723e6i	0.505425	+	0.424102i
$429$	−580705.	−	487270.i	−0.152340	−	0.127828i
$430$	−1.71046e6	−	2.96261e6i	−0.446111	−	0.772686i
$431$	3.40276e6	+	1.23851e6i	0.882346	+	0.321148i	0.743156	−	0.669118i	$-0.233328\pi$
$431$	3.40276e6	+	1.23851e6i	0.882346	+	0.321148i	0.139190	+	0.990266i	$0.455550\pi$
$432$	−63032.0	+	357472.i	−0.0162499	+	0.0921580i
$433$	725719.	−	1.25698e6i	0.186015	−	0.322188i	−0.757903	−	0.652367i	$-0.773776\pi$
$433$	725719.	−	1.25698e6i	0.186015	−	0.322188i	0.943918	+	0.330179i	$0.107109\pi$
$434$	−234326.	−	405864.i	−0.0597166	−	0.103432i
$435$	156277.	−	56880.0i	0.0395978	−	0.0144124i
$436$	571572.	−	989993.i	0.143998	−	0.249411i
$437$	−4.73194e6	+	3.97057e6i	−1.18532	+	0.994602i
$438$	336976.			0.0839293
$439$	−150960.	+	126671.i	−0.0373854	+	0.0313700i	−0.661289	−	0.750131i	$-0.729990\pi$
$439$	−150960.	+	126671.i	−0.0373854	+	0.0313700i	0.623904	+	0.781501i	$0.285546\pi$
$440$	673625.	+	245179.i	0.165877	+	0.0603743i
$441$	674701.	+	3.82642e6i	0.165202	+	0.936907i
$442$	−718174.	+	4.07297e6i	−0.174853	+	0.991643i
$443$	5.09465e6			1.23340			0.616702	−	0.787197i	$-0.288468\pi$
$443$	5.09465e6			1.23340			0.616702	+	0.787197i	$0.288468\pi$
$444$	−145434.	−	368236.i	−0.0350113	−	0.0886479i
$445$	−56335.8			−0.0134860
$446$	139147.	−	789139.i	0.0331234	−	0.187852i
$447$	251605.	+	1.42692e6i	0.0595595	+	0.337779i
$448$	56381.0	+	20521.0i	0.0132721	+	0.00483063i
$449$	100022.	−	83928.1i	0.0234141	−	0.0196468i	−0.631005	−	0.775778i	$-0.717357\pi$
$449$	100022.	−	83928.1i	0.0234141	−	0.0196468i	0.654420	+	0.756132i	$0.272913\pi$
$450$	1.09369e6			0.254603
$451$	1.71078e6	−	1.43551e6i	0.396052	−	0.332327i
$452$	−1.86008e6	+	3.22175e6i	−0.428237	+	0.741729i
$453$	189935.	−	69130.7i	0.0434870	−	0.0158280i
$454$	−1.40446e6	−	2.43260e6i	−0.319795	−	0.553900i
$455$	326515.	−	565541.i	0.0739393	−	0.128067i
$456$	−83605.1	+	474148.i	−0.0188287	+	0.106783i
$457$	−5.22433e6	−	1.90150e6i	−1.17015	−	0.425898i	−0.317435	−	0.948280i	$-0.602821\pi$
$457$	−5.22433e6	−	1.90150e6i	−1.17015	−	0.425898i	−0.852712	+	0.522382i	$0.825044\pi$
$458$	−775574.	−	1.34333e6i	−0.172767	−	0.299241i
$459$	1.11454e6	+	935209.i	0.246924	+	0.207194i
$460$	1.32310e6	+	1.11021e6i	0.291539	+	0.244630i
$461$	−5.82962e6	+	2.12181e6i	−1.27758	+	0.465001i	−0.889631	−	0.456680i	$-0.849038\pi$
$461$	−5.82962e6	+	2.12181e6i	−1.27758	+	0.465001i	−0.387949	+	0.921681i	$0.626816\pi$
$462$	7654.39	+	43410.2i	0.00166842	+	0.00946208i
$463$	117505.	+	666404.i	0.0254744	+	0.144473i	0.994892	−	0.100944i	$-0.0321863\pi$
$463$	117505.	+	666404.i	0.0254744	+	0.144473i	−0.969418	+	0.245417i	$0.921075\pi$
$464$	304312.	−	110761.i	0.0656182	−	0.0238831i
$465$	−805510.	−	675903.i	−0.172758	−	0.144961i
$466$	−1.95489e6	−	1.64035e6i	−0.417021	−	0.349923i
$467$	−279166.	−	483529.i	−0.0592338	−	0.102596i	0.834888	−	0.550420i	$-0.185532\pi$
$467$	−279166.	−	483529.i	−0.0592338	−	0.102596i	−0.894122	+	0.447824i	$0.852199\pi$
$468$	3.54770e6	+	1.29126e6i	0.748741	+	0.272520i
$469$	−93774.0	+	531819.i	−0.0196857	+	0.111643i
$470$	−420269.	+	727927.i	−0.0877571	+	0.152000i
$471$	106559.	+	184566.i	0.0221329	+	0.0383354i
$472$	−2.18078e6	+	793738.i	−0.450564	+	0.163992i
$473$	2.44699e6	−	4.23831e6i	0.502897	−	0.871043i
$474$	−758204.	+	636209.i	−0.155003	+	0.130063i
$475$	2.95603e6			0.601138
$476$	184226.	−	154584.i	0.0372679	−	0.0312714i
$477$	7.96426e6	+	2.89876e6i	1.60269	+	0.583332i
$478$	526235.	+	2.98443e6i	0.105344	+	0.597436i
$479$	589845.	−	3.34518e6i	0.117462	−	0.666162i	−0.868039	−	0.496496i	$-0.834620\pi$
$479$	589845.	−	3.34518e6i	0.117462	−	0.666162i	0.985502	−	0.169667i	$-0.0542691\pi$
$480$	134622.			0.0266693
$481$	−8.22104e6	+	1.68028e6i	−1.62018	+	0.331145i
$482$	1.98506e6			0.389186
$483$	−18442.3	+	104592.i	−0.00359706	+	0.0203999i
$484$	−269377.	−	1.52771e6i	−0.0522694	−	0.296434i
$485$	1.46407e6	+	532879.i	0.282624	+	0.102867i
$486$	1.53553e6	−	1.28846e6i	0.294895	−	0.247446i
$487$	−733660.			−0.140176			−0.0700878	−	0.997541i	$-0.522328\pi$
$487$	−733660.			−0.140176			−0.0700878	+	0.997541i	$0.522328\pi$
$488$	1.80462e6	−	1.51425e6i	0.343033	−	0.287839i
$489$	80006.2	−	138575.i	0.0151304	−	0.0262067i
$490$	2.75926e6	−	1.00429e6i	0.519162	−	0.188959i
$491$	−2.89772e6	−	5.01901e6i	−0.542442	−	0.939537i	−0.998763	−	0.0497219i	$-0.984167\pi$
$491$	−2.89772e6	−	5.01901e6i	−0.542442	−	0.939537i	0.456321	−	0.889815i	$-0.349167\pi$
$492$	209697.	−	363206.i	0.0390553	−	0.0676457i
$493$	225400.	−	1.27831e6i	0.0417673	−	0.236874i
$494$	9.58870e6	+	3.49000e6i	1.76784	+	0.643441i
$495$	−1.31146e6	−	2.27151e6i	−0.240570	−	0.416679i
$496$	−1.56854e6	−	1.31616e6i	−0.286281	−	0.240218i
$497$	−42913.6	−	36008.8i	−0.00779298	−	0.00653909i
$498$	−895626.	+	325981.i	−0.161828	+	0.0589005i
$499$	−1.46000e6	−	8.28007e6i	−0.262483	−	1.48862i	−0.776107	−	0.630601i	$-0.782808\pi$
$499$	−1.46000e6	−	8.28007e6i	−0.262483	−	1.48862i	0.513624	−	0.858016i	$-0.328303\pi$
$500$	−527655.	−	2.99248e6i	−0.0943898	−	0.535311i
$501$	−269960.	+	98257.4i	−0.0480513	+	0.0174892i
$502$	−1.48920e6	−	1.24959e6i	−0.263751	−	0.221314i
$503$	3.88877e6	+	3.26306e6i	0.685318	+	0.575050i	0.917555	−	0.397609i	$-0.130160\pi$
$503$	3.88877e6	+	3.26306e6i	0.685318	+	0.575050i	−0.232237	+	0.972659i	$0.574604\pi$
$504$	−109766.	−	190121.i	−0.0192483	−	0.0333390i
$505$	−429516.	−	156331.i	−0.0749464	−	0.0272783i
$506$	−429068.	+	2.43336e6i	−0.0744988	+	0.422504i
$507$	−956920.	+	1.65743e6i	−0.165332	+	0.286363i
$508$	−2.31829e6	−	4.01539e6i	−0.398573	−	0.690349i
$509$	−2.12344e6	+	772870.i	−0.363284	+	0.132225i	−0.517212	−	0.855858i	$-0.673030\pi$
$509$	−2.12344e6	+	772870.i	−0.363284	+	0.132225i	0.153928	+	0.988082i	$0.450808\pi$
$510$	269796.	−	467300.i	0.0459314	−	0.0795555i
$511$	−318129.	+	266942.i	−0.0538953	+	0.0452235i
$512$	262144.			0.0441942
$513$	2.74986e6	−	2.30740e6i	0.461335	−	0.387106i
$514$	−2.23393e6	−	813085.i	−0.372960	−	0.135746i
$515$	−208771.	−	1.18400e6i	−0.0346858	−	0.196713i
$516$	159593.	−	905098.i	0.0263870	−	0.149648i
$517$	−1.20247e6			−0.197856
$518$	429004.	+	232432.i	0.0702485	+	0.0380602i
$519$	1.04029e6			0.169526
$520$	495446.	−	2.80981e6i	0.0803504	−	0.455690i
$521$	935764.	+	5.30698e6i	0.151033	+	0.856551i	0.962323	+	0.271908i	$0.0876545\pi$
$521$	935764.	+	5.30698e6i	0.151033	+	0.856551i	−0.811290	+	0.584644i	$0.801234\pi$
$522$	−1.11345e6	−	405263.i	−0.178852	−	0.0650969i
$523$	3.53049e6	−	2.96243e6i	0.564392	−	0.473581i	−0.315388	−	0.948963i	$-0.602135\pi$
$523$	3.53049e6	−	2.96243e6i	0.564392	−	0.473581i	0.879779	+	0.475382i	$0.157690\pi$
$524$	3.13520e6			0.498813
$525$	38933.4	−	32669.0i	0.00616487	−	0.00517294i
$526$	−2.25908e6	+	3.91285e6i	−0.356015	+	0.616636i
$527$	−7.71220e6	+	2.80701e6i	−1.20963	+	0.440269i
$528$	96294.8	+	166787.i	0.0150320	+	0.0260363i
$529$	241500.	−	418291.i	0.0375213	−	0.0649889i
$530$	1.11223e6	−	6.30779e6i	0.171991	−	0.975410i
$531$	7.97926e6	+	2.90421e6i	1.22808	+	0.446984i
$532$	−296676.	−	513858.i	−0.0454468	−	0.0787162i
$533$	−6.80907e6	−	5.71349e6i	−1.03817	−	0.871130i
$534$	−11594.2	−	9728.65i	−0.00175949	−	0.00147639i
$535$	−6.49703e6	+	2.36472e6i	−0.981364	+	0.357187i
$536$	409708.	+	2.32357e6i	0.0615975	+	0.349337i
$537$	−11830.8	−	67095.5i	−0.00177042	−	0.0100406i
$538$	−250855.	+	91303.7i	−0.0373651	+	0.0135998i
$539$	3.21795e6	+	2.70018e6i	0.477098	+	0.400332i
$540$	−768886.	−	645172.i	−0.113469	−	0.0952119i
$541$	−2.32707e6	−	4.03061e6i	−0.341835	−	0.592076i	0.642938	−	0.765918i	$-0.277715\pi$
$541$	−2.32707e6	−	4.03061e6i	−0.341835	−	0.592076i	−0.984774	+	0.173842i	$0.944382\pi$
$542$	−6.51132e6	−	2.36993e6i	−0.952074	−	0.346526i
$543$	−362164.	+	2.05394e6i	−0.0527116	+	0.298942i
$544$	525364.	−	909957.i	0.0761138	−	0.131833i
$545$	1.58048e6	+	2.73747e6i	0.227928	+	0.394782i
$546$	164862.	−	60004.8i	0.0236667	−	0.00861399i
$547$	1.38570e6	−	2.40010e6i	0.198016	−	0.342973i	−0.749869	−	0.661586i	$-0.769884\pi$
$547$	1.38570e6	−	2.40010e6i	0.198016	−	0.342973i	0.947885	+	0.318613i	$0.103217\pi$
$548$	1.97645e6	−	1.65843e6i	0.281147	−	0.235910i
$549$	−8.61951e6			−1.22054
$550$	905800.	−	760056.i	0.127681	−	0.107137i
$551$	−3.00943e6	−	1.09534e6i	−0.422285	−	0.153699i
$552$	80576.5	+	456972.i	0.0112554	+	0.0638325i
$553$	211813.	−	1.20125e6i	0.0294537	−	0.167040i
$554$	5.16944e6			0.715598
$555$	1.08288e6	+	160844.i	0.149227	+	0.0221652i
$556$	−1.69582e6			−0.232645
$557$	1.56102e6	−	8.85300e6i	0.213192	−	1.20907i	−0.670824	−	0.741617i	$-0.734059\pi$
$557$	1.56102e6	−	8.85300e6i	0.213192	−	1.20907i	0.884016	−	0.467457i	$-0.154830\pi$
$558$	1.30096e6	+	7.37811e6i	0.176880	+	1.00314i
$559$	−1.83038e7	−	6.66204e6i	−2.47749	−	0.901733i
$560$	−127092.	+	106643.i	−0.0171257	+	0.0143702i
$561$	771940.			0.103556
$562$	1.98977e6	−	1.66962e6i	0.265743	−	0.222985i
$563$	−1.95367e6	+	3.38386e6i	−0.259765	+	0.449927i	−0.966179	−	0.257873i	$-0.916979\pi$
$563$	−1.95367e6	+	3.38386e6i	−0.259765	+	0.449927i	0.706414	+	0.707799i	$0.250312\pi$
$564$	−212199.	+	77234.1i	−0.0280896	+	0.0102238i
$565$	−5.14337e6	−	8.90858e6i	−0.677839	−	1.17405i
$566$	1.32156e6	−	2.28902e6i	0.173399	−	0.300336i
$567$	−134025.	+	760093.i	−0.0175077	+	0.0992908i
$568$	−229995.	−	83711.5i	−0.0299122	−	0.0108871i
$569$	−1.44563e6	−	2.50391e6i	−0.187187	−	0.324218i	0.757124	−	0.653271i	$-0.226604\pi$
$569$	−1.44563e6	−	2.50391e6i	−0.187187	−	0.324218i	−0.944311	+	0.329053i	$0.893270\pi$
$570$	−1.01984e6	−	855751.i	−0.131476	−	0.110321i
$571$	540067.	+	453170.i	0.0693198	+	0.0581662i	0.676789	−	0.736177i	$-0.263371\pi$
$571$	540067.	+	453170.i	0.0693198	+	0.0581662i	−0.607469	+	0.794343i	$0.707815\pi$
$572$	3.83557e6	−	1.39603e6i	0.490162	−	0.178405i
$573$	−275750.	−	1.56385e6i	−0.0350856	−	0.198980i
$574$	89751.6	+	509007.i	0.0113701	+	0.0644828i
$575$	2.67713e6	−	974395.i	0.337676	−	0.122904i
$576$	−734760.	−	616537.i	−0.0922761	−	0.0774288i
$577$	3.05907e6	+	2.56686e6i	0.382516	+	0.320969i	0.813689	−	0.581300i	$-0.197456\pi$
$577$	3.05907e6	+	2.56686e6i	0.382516	+	0.320969i	−0.431173	+	0.902269i	$0.641900\pi$
$578$	733944.	+	1.27123e6i	0.0913784	+	0.158272i
$579$	1.16445e6	+	423826.i	0.144353	+	0.0525402i
$580$	−155497.	+	881865.i	−0.0191933	+	0.108851i
$581$	587301.	−	1.01724e6i	0.0721806	−	0.125020i
$582$	209290.	+	362500.i	0.0256118	+	0.0443610i
$583$	8.61052e6	−	3.13397e6i	1.04920	−	0.381877i
$584$	−907218.	+	1.57135e6i	−0.110073	+	0.190651i
$585$	−7.99708e6	+	6.71035e6i	−0.966144	+	0.810691i
$586$	8.26477e6			0.994229
$587$	−1.12178e7	+	9.41282e6i	−1.34373	+	1.12752i	−0.363075	+	0.931760i	$0.618273\pi$
$587$	−1.12178e7	+	9.41282e6i	−1.34373	+	1.12752i	−0.980652	+	0.195761i	$0.937282\pi$
$588$	741299.	+	269811.i	0.0884199	+	0.0321822i
$589$	3.51623e6	+	1.99415e7i	0.417628	+	2.36848i
$590$	1.11433e6	−	6.31966e6i	0.131790	−	0.747418i
$591$	−261644.			−0.0308136
$592$	2.10866e6	+	313206.i	0.247287	+	0.0367304i
$593$	2.48966e6			0.290739			0.145369	−	0.989377i	$-0.453563\pi$
$593$	2.48966e6			0.290739			0.145369	+	0.989377i	$0.453563\pi$
$594$	249342.	−	1.41409e6i	0.0289955	−	0.164441i
$595$	115474.	+	654887.i	0.0133719	+	0.0758358i
$596$	−7.33125e6	−	2.66836e6i	−0.845400	−	0.307700i
$597$	−92847.3	+	77908.1i	−0.0106619	+	0.00894637i
$598$	9.83444e6			1.12460
$599$	−1.05919e6	+	888762.i	−0.120616	+	0.101209i	−0.701101	−	0.713062i	$-0.747308\pi$
$599$	−1.05919e6	+	888762.i	−0.120616	+	0.101209i	0.580485	+	0.814271i	$0.302863\pi$
$600$	111028.	−	192305.i	0.0125908	−	0.0218079i
$601$	−1.21481e7	+	4.42155e6i	−1.37190	+	0.499331i	−0.919713	−	0.392591i	$-0.871579\pi$
$601$	−1.21481e7	+	4.42155e6i	−1.37190	+	0.499331i	−0.452188	+	0.891923i	$0.649356\pi$
$602$	566323.	+	980900.i	0.0636902	+	0.110315i
$603$	4.31644e6	−	7.47630e6i	0.483429	−	0.837324i
$604$	−188987.	+	1.07180e6i	−0.0210785	+	0.119542i
$605$	4.03082e6	+	1.46710e6i	0.447719	+	0.162956i
$606$	−61399.4	−	106347.i	−0.00679176	−	0.0117637i
$607$	6.00044e6	+	5.03496e6i	0.661015	+	0.554657i	0.910391	−	0.413750i	$-0.135781\pi$
$607$	6.00044e6	+	5.03496e6i	0.661015	+	0.554657i	−0.249376	+	0.968407i	$0.580226\pi$
$608$	−1.98591e6	−	1.66637e6i	−0.217871	−	0.182816i
$609$	−51742.1	+	18832.6i	−0.00565329	+	0.00205763i
$610$	1.13115e6	+	6.41505e6i	0.123082	+	0.698032i
$611$	831073.	+	4.71325e6i	0.0900609	+	0.510761i
$612$	−3.61267e6	+	1.31490e6i	−0.389896	+	0.141911i
$613$	9.45189e6	+	7.93108e6i	1.01594	+	0.852474i	0.989112	−	0.147166i	$-0.0470152\pi$
$613$	9.45189e6	+	7.93108e6i	1.01594	+	0.852474i	0.0268270	+	0.999640i	$0.491460\pi$
$614$	−31706.2	−	26604.7i	−0.00339409	−	0.00284798i
$615$	579842.	+	1.00432e6i	0.0618189	+	0.107074i
$616$	−223033.	−	81177.2i	−0.0236819	−	0.00861951i
$617$	−2.46024e6	+	1.39527e7i	−0.260174	+	1.47552i	0.522258	+	0.852787i	$0.325090\pi$
$617$	−2.46024e6	+	1.39527e7i	−0.260174	+	1.47552i	−0.782433	+	0.622735i	$0.786021\pi$
$618$	161499.	−	279725.i	0.0170098	−	0.0294618i
$619$	−7.80691e6	−	1.35220e7i	−0.818941	−	1.41845i	−0.906463	−	0.422285i	$-0.861228\pi$
$619$	−7.80691e6	−	1.35220e7i	−0.818941	−	1.41845i	0.0875219	−	0.996163i	$-0.472105\pi$
$620$	5.32041e6	−	1.93647e6i	0.555861	−	0.202317i
$621$	1.72982e6	−	2.99614e6i	0.180000	−	0.311769i
$622$	−7.06602e6	+	5.92910e6i	−0.732317	+	0.614487i
$623$	18652.4			0.00192537
$624$	587193.	−	492713.i	0.0603697	−	0.0506562i
$625$	4.46679e6	+	1.62578e6i	0.457399	+	0.166480i
$626$	1.52668e6	+	8.65825e6i	0.155709	+	0.883069i
$627$	330726.	−	1.87564e6i	0.0335969	−	0.190537i
$628$	−1.14753e6			−0.116109
$629$	5.31317e6	−	6.69189e6i	0.535460	−	0.674407i
$630$	607038.			0.0609347
$631$	1.15141e6	−	6.52996e6i	0.115121	−	0.652886i	−0.871569	−	0.490273i	$-0.836897\pi$
$631$	1.15141e6	−	6.52996e6i	0.115121	−	0.652886i	0.986690	−	0.162612i	$-0.0519920\pi$
$632$	−925433.	−	5.24839e6i	−0.0921621	−	0.522677i
$633$	−1.16325e6	−	423388.i	−0.115389	−	0.0419981i
$634$	−4.27397e6	+	3.58629e6i	−0.422288	+	0.354342i
$635$	1.28208e7			1.26177
$636$	1.31820e6	−	1.10610e6i	0.129222	−	0.108430i
$637$	8.35967e6	−	1.44794e7i	0.816282	−	1.41384i
$638$	−1.20380e6	+	438147.i	−0.117085	+	0.0426156i
$639$	447770.	+	775560.i	0.0433813	+	0.0751386i
$640$	−362432.	+	627751.i	−0.0349766	+	0.0605812i
$641$	−1.64060e6	+	9.30433e6i	−0.157710	+	0.894417i	0.798557	+	0.601920i	$0.205597\pi$
$641$	−1.64060e6	+	9.30433e6i	−0.157710	+	0.894417i	−0.956266	+	0.292497i	$0.905514\pi$
$642$	−1.74548e6	−	635303.i	−0.167139	−	0.0608336i
$643$	4.85839e6	+	8.41499e6i	0.463410	+	0.802650i	0.999128	−	0.0417472i	$-0.0132924\pi$
$643$	4.85839e6	+	8.41499e6i	0.463410	+	0.802650i	−0.535718	+	0.844397i	$0.679959\pi$
$644$	−438068.	−	367583.i	−0.0416224	−	0.0349253i
$645$	1.94677e6	+	1.63354e6i	0.184254	+	0.154607i
$646$	−9.76430e6	+	3.55392e6i	−0.920577	+	0.335063i
$647$	−357028.	−	2.02481e6i	−0.0335306	−	0.190162i	0.963442	−	0.267918i	$-0.0863356\pi$
$647$	−357028.	−	2.02481e6i	−0.0335306	−	0.190162i	−0.996972	+	0.0777561i	$0.975224\pi$
$648$	585569.	+	3.32093e6i	0.0547824	+	0.310686i
$649$	8.62673e6	−	3.13987e6i	0.803960	−	0.292618i
$650$	−3.60517e6	−	3.02510e6i	−0.334690	−	0.280838i
$651$	266699.	+	223787.i	0.0246643	+	0.0206958i
$652$	430790.	+	746151.i	0.0396869	+	0.0687397i
$653$	9.26165e6	+	3.37096e6i	0.849973	+	0.309365i	0.730029	−	0.683416i	$-0.239506\pi$
$653$	9.26165e6	+	3.37096e6i	0.849973	+	0.309365i	0.119944	+	0.992781i	$0.461729\pi$
$654$	−147465.	+	836316.i	−0.0134817	+	0.0764585i
$655$	−4.33464e6	+	7.50782e6i	−0.394775	+	0.683771i
$656$	1.12911e6	+	1.95567e6i	0.102441	+	0.177434i
$657$	6.23848e6	−	2.27062e6i	0.563852	−	0.205225i
$658$	139148.	−	241012.i	0.0125289	−	0.0217007i
$659$	19732.6	−	16557.6i	0.00176999	−	0.00148520i	−0.641902	−	0.766787i	$-0.721854\pi$
$659$	19732.6	−	16557.6i	0.00176999	−	0.00148520i	0.643672	+	0.765301i	$0.277410\pi$
$660$	−532537.			−0.0475872
$661$	−6.72498e6	+	5.64292e6i	−0.598669	+	0.502343i	−0.891018	−	0.453969i	$-0.850008\pi$
$661$	−6.72498e6	+	5.64292e6i	−0.598669	+	0.502343i	0.292348	+	0.956312i	$0.405563\pi$
$662$	1.15708e7	+	4.21143e6i	1.02617	+	0.373495i
$663$	−533516.	−	3.02572e6i	−0.0471372	−	0.267328i
$664$	891156.	−	5.05399e6i	0.0784392	−	0.444851i
$665$	1.64070e6			0.143872
$666$	−5.17369e6	−	5.83723e6i	−0.451976	−	0.509942i
$667$	−3.08655e6			−0.268633
$668$	268612.	−	1.52338e6i	0.0232908	−	0.132089i
$669$	103369.	+	586234.i	0.00892945	+	0.0506414i
$670$	−6.13066e6	−	2.23138e6i	−0.527619	−	0.192038i
$671$	−7.13872e6	+	5.99010e6i	−0.612088	+	0.513603i
$672$	−44572.3			−0.00380752
$673$	8.82326e6	−	7.40359e6i	0.750916	−	0.630093i	−0.184829	−	0.982771i	$-0.559173\pi$
$673$	8.82326e6	−	7.40359e6i	0.750916	−	0.630093i	0.935745	+	0.352678i	$0.114729\pi$
$674$	1.49649e6	−	2.59200e6i	0.126889	−	0.219778i
$675$	−1.55575e6	+	566247.i	−0.131426	+	0.0478350i
$676$	−5.15250e6	−	8.92439e6i	−0.433662	−	0.751125i
$677$	−356494.	+	617465.i	−0.0298937	+	0.0517775i	−0.880585	−	0.473888i	$-0.842850\pi$
$677$	−356494.	+	617465.i	−0.0298937	+	0.0517775i	0.850691	+	0.525665i	$0.176184\pi$
$678$	479897.	−	2.72163e6i	0.0400935	−	0.227382i
$679$	−484745.	−	176433.i	−0.0403496	−	0.0146860i
$680$	1.45271e6	+	2.51616e6i	0.120477	+	0.208673i
$681$	1.59850e6	+	1.34130e6i	0.132082	+	0.110830i
$682$	6.20485e6	+	5.20649e6i	0.510823	+	0.428631i
$683$	1.23485e7	−	4.49447e6i	1.01289	−	0.368661i	0.218346	−	0.975871i	$-0.429934\pi$
$683$	1.23485e7	−	4.49447e6i	1.01289	−	0.368661i	0.794541	+	0.607211i	$0.207712\pi$
$684$	1.64713e6	+	9.34131e6i	0.134613	+	0.763427i
$685$	1.23885e6	+	7.02586e6i	0.100877	+	0.572101i
$686$	−1.83896e6	+	669327.i	−0.149198	+	0.0543035i
$687$	882724.	+	740694.i	0.0713564	+	0.0598752i
$688$	3.79088e6	+	3.18093e6i	0.305330	+	0.256202i
$689$	−1.82351e7	−	3.15841e7i	−1.46339	−	2.53466i
$690$	−1.20570e6	−	438841.i	−0.0964092	−	0.0350901i
$691$	−2.46805e6	+	1.39970e7i	−0.196634	+	1.11517i	0.713439	+	0.700718i	$0.247137\pi$
$691$	−2.46805e6	+	1.39970e7i	−0.196634	+	1.11517i	−0.910073	+	0.414449i	$0.863974\pi$
$692$	−2.80070e6	+	4.85096e6i	−0.222332	+	0.385090i
$693$	434214.	+	752081.i	0.0343456	+	0.0594883i
$694$	−3.97790e6	+	1.44784e6i	−0.313513	+	0.114109i
$695$	2.34459e6	−	4.06095e6i	0.184122	−	0.318908i
$696$	−184291.	+	154639.i	−0.0144206	+	0.0121003i
$697$	9.05139e6			0.705721
$698$	−5.17193e6	+	4.33977e6i	−0.401804	+	0.337154i
$699$	1.78145e6	+	648393.i	0.137905	+	0.0501933i
$700$	47520.5	+	269502.i	0.00366552	+	0.0207882i
$701$	2.14816e6	−	1.21828e7i	0.165109	−	0.936381i	−0.783842	−	0.620960i	$-0.786743\pi$
$701$	2.14816e6	−	1.21828e7i	0.165109	−	0.936381i	0.948952	−	0.315422i	$-0.102146\pi$
$702$	−5.71505e6			−0.437701
$703$	−1.39834e7	−	1.57768e7i	−1.06715	−	1.20402i
$704$	−1.03699e6			−0.0788576
$705$	108429.	−	614931.i	0.00821622	−	0.0465965i
$706$	−604456.	−	3.42804e6i	−0.0456408	−	0.258842i
$707$	142210.	+	51760.1i	0.0106999	+	0.00389446i
$708$	1.32068e6	−	1.10818e6i	0.0990179	−	0.0830859i
$709$	1.24606e7			0.930947			0.465474	−	0.885062i	$-0.345884\pi$
$709$	1.24606e7			0.930947			0.465474	+	0.885062i	$0.345884\pi$
$710$	518447.	−	435029.i	0.0385974	−	0.0323871i
$711$	−9.74981e6	+	1.68872e7i	−0.723306	+	1.25280i
$712$	76579.7	−	27872.7i	0.00566126	−	0.00206053i
$713$	9.75782e6	+	1.69010e7i	0.718834	+	1.24506i
$714$	−89327.6	+	154720.i	−0.00655752	+	0.0113580i
$715$	−1.95989e6	+	1.11151e7i	−0.143373	+	0.813107i
$716$	344723.	+	125469.i	0.0251297	+	0.00914647i
$717$	−1.12563e6	−	1.94965e6i	−0.0817710	−	0.141631i
$718$	3.69967e6	+	3.10439e6i	0.267826	+	0.224732i
$719$	7.18279e6	+	6.02708e6i	0.518169	+	0.434795i	0.863993	−	0.503504i	$-0.167956\pi$
$719$	7.18279e6	+	6.02708e6i	0.518169	+	0.434795i	−0.345824	+	0.938299i	$0.612401\pi$
$720$	2.49227e6	−	907111.i	0.179169	−	0.0652122i
$721$	69122.6	+	392014.i	0.00495201	+	0.0280843i
$722$	2.73197e6	+	1.54938e7i	0.195044	+	1.10615i
$723$	−1.38573e6	+	504363.i	−0.0985898	+	0.0358838i
$724$	−8.60264e6	−	7.21848e6i	−0.609938	−	0.511799i
$725$	1.13149e6	+	949432.i	0.0799476	+	0.0670840i
$726$	576207.	+	998019.i	0.0405730	+	0.0702744i
$727$	−2.07358e7	−	7.54723e6i	−1.45508	−	0.529604i	−0.511072	−	0.859538i	$-0.670751\pi$
$727$	−2.07358e7	−	7.54723e6i	−1.45508	−	0.529604i	−0.944004	+	0.329934i	$0.892974\pi$
$728$	−164039.	+	930310.i	−0.0114714	+	0.0650578i
$729$	5.65729e6	−	9.79871e6i	0.394266	−	0.682889i
$730$	−2.50858e6	−	4.34499e6i	−0.174229	−	0.301774i
$731$	1.86390e7	−	6.78405e6i	1.29012	−	0.469565i
$732$	−875022.	+	1.51558e6i	−0.0603589	+	0.104545i
$733$	−7.33764e6	+	6.15701e6i	−0.504425	+	0.423263i	−0.859162	−	0.511703i	$-0.829015\pi$
$733$	−7.33764e6	+	6.15701e6i	−0.504425	+	0.423263i	0.354737	+	0.934966i	$0.384570\pi$
$734$	−1.64609e7			−1.12775
$735$	−1.67101e6	+	1.40214e6i	−0.114093	+	0.0957357i
$736$	−2.34783e6	−	854539.i	−0.159761	−	0.0581484i
$737$	−1.62073e6	−	9.19160e6i	−0.109911	−	0.623336i
$738$	1.43478e6	−	8.13706e6i	0.0969718	−	0.549954i
$739$	4.01007e6			0.270110			0.135055	−	0.990838i	$-0.456879\pi$
$739$	4.01007e6			0.270110			0.135055	+	0.990838i	$0.456879\pi$
$740$	−3.66539e6	+	4.61653e6i	−0.246060	+	0.309911i
$741$	−7.58039e6			−0.507161
$742$	−368253.	+	2.08847e6i	−0.0245548	+	0.139257i
$743$	−2.84417e6	−	1.61301e7i	−0.189009	−	1.07192i	−0.920695	−	0.390283i	$-0.872377\pi$
$743$	−2.84417e6	−	1.61301e7i	−0.189009	−	1.07192i	0.731686	−	0.681642i	$-0.238734\pi$
$744$	1.42937e6	+	520249.i	0.0946702	+	0.0344571i
$745$	1.65258e7	−	1.38668e7i	1.09087	−	0.915347i
$746$	−2.02641e7			−1.33316
$747$	−1.43843e7	+	1.20699e7i	−0.943164	+	0.791409i
$748$	−2.07824e6	+	3.59962e6i	−0.135813	+	0.235235i
$749$	2.15112e6	−	782944.i	0.140107	−	0.0509949i
$750$	1.12867e6	+	1.95492e6i	0.0732680	+	0.126904i
$751$	−6.87606e6	+	1.19097e7i	−0.444877	+	0.770549i	−0.998044	−	0.0625215i	$-0.980086\pi$
$751$	−6.87606e6	+	1.19097e7i	−0.444877	+	0.770549i	0.553167	+	0.833070i	$0.313419\pi$
$752$	211140.	−	1.19743e6i	0.0136152	−	0.0772159i
$753$	1.35707e6	+	493934.i	0.0872200	+	0.0317455i
$754$	2.54937e6	+	4.41563e6i	0.163307	+	0.282856i
$755$	−2.30533e6	−	1.93440e6i	−0.147186	−	0.123503i
$756$	254573.	+	213612.i	0.0161997	+	0.0135932i
$757$	−1.49920e7	+	5.45664e6i	−0.950866	+	0.346087i	−0.770448	−	0.637503i	$-0.779967\pi$
$757$	−1.49920e7	+	5.45664e6i	−0.950866	+	0.346087i	−0.180418	+	0.983590i	$0.557745\pi$
$758$	−3.40827e6	−	1.93293e7i	−0.215457	−	1.22192i
$759$	−318745.	−	1.80769e6i	−0.0200835	−	0.113899i
$760$	6.73609e6	−	2.45174e6i	0.423033	−	0.153971i
$761$	−7.67300e6	−	6.43841e6i	−0.480290	−	0.403011i	0.370241	−	0.928936i	$-0.379275\pi$
$761$	−7.67300e6	−	6.43841e6i	−0.480290	−	0.403011i	−0.850531	+	0.525924i	$0.823719\pi$
$762$	2.63857e6	+	2.21403e6i	0.164620	+	0.138132i
$763$	−523285.	−	906357.i	−0.0325407	−	0.0563622i
$764$	8.03476e6	+	2.92441e6i	0.498012	+	0.181261i
$765$	1.84599e6	−	1.04691e7i	0.114045	−	0.646780i
$766$	9.29833e6	−	1.61052e7i	0.572576	−	0.991731i
$767$	−1.82694e7	−	3.16435e7i	−1.12134	−	1.94221i
$768$	−182997.	+	66605.4i	−0.0111954	+	0.00407480i
$769$	593232.	−	1.02751e6i	0.0361750	−	0.0626569i	−0.847371	−	0.531001i	$-0.821816\pi$
$769$	593232.	−	1.02751e6i	0.0361750	−	0.0626569i	0.883546	+	0.468344i	$0.155149\pi$
$770$	502752.	−	421859.i	0.0305581	−	0.0256413i
$771$	1.76605e6			0.106996
$772$	−5.11132e6	+	4.28890e6i	−0.308666	+	0.259002i
$773$	5.37369e6	+	1.95586e6i	0.323463	+	0.117731i	0.498648	−	0.866805i	$-0.333830\pi$
$773$	5.37369e6	+	1.95586e6i	0.323463	+	0.117731i	−0.175185	+	0.984536i	$0.556052\pi$
$774$	−3.14419e6	−	1.78316e7i	−0.188650	−	1.06989i
$775$	1.62172e6	−	9.19722e6i	0.0969887	−	0.550050i
$776$	−2.25382e6			−0.134359
$777$	−358534.	−	53254.3i	−0.0213048	−	0.00316448i
$778$	1.81460e7			1.07481
$779$	3.87793e6	−	2.19928e7i	0.228958	−	1.29849i
$780$	368056.	+	2.08735e6i	0.0216610	+	0.122845i
$781$	909817.	+	331146.i	0.0533736	+	0.0194264i
$782$	−7.67158e6	+	6.43722e6i	−0.448609	+	0.376428i
$783$	1.79368e6			0.104554
$784$	−3.25390e6	+	2.73034e6i	−0.189066	+	0.158645i
$785$	1.58654e6	−	2.74797e6i	0.0918918	−	0.159161i
$786$	−2.18861e6	+	796591.i	−0.126361	+	0.0459916i
$787$	7.04986e6	+	1.22107e7i	0.405736	+	0.702755i	0.994407	−	0.105617i	$-0.0336819\pi$
$787$	7.04986e6	+	1.22107e7i	0.405736	+	0.702755i	−0.588671	+	0.808373i	$0.700349\pi$
$788$	704407.	−	1.22007e6i	0.0404118	−	0.0699953i
$789$	582841.	−	3.30546e6i	0.0333317	−	0.189034i
$790$	1.38477e7	+	5.04015e6i	0.789423	+	0.287327i
$791$	1.70293e6	+	2.94957e6i	0.0967736	+	0.167617i
$792$	2.90657e6	+	2.43890e6i	0.164652	+	0.138160i
$793$	2.84128e7	+	2.38412e7i	1.60447	+	1.34631i
$794$	−1.59798e7	+	5.81616e6i	−0.899538	+	0.327405i
$795$	826254.	+	4.68592e6i	0.0463656	+	0.262952i
$796$	−113326.	−	642701.i	−0.00633936	−	0.0359523i
$797$	−2.94312e7	+	1.07121e7i	−1.64120	+	0.597348i	−0.987248	−	0.159187i	$-0.949113\pi$
$797$	−2.94312e7	+	1.07121e7i	−1.64120	+	0.597348i	−0.653953	+	0.756536i	$0.726890\pi$
$798$	337663.	+	283333.i	0.0187705	+	0.0157504i
$799$	−3.73340e6	−	3.13269e6i	−0.206889	−	0.173600i
$800$	597824.	+	1.03546e6i	0.0330254	+	0.0572017i
$801$	−280198.	−	101984.i	−0.0154306	−	0.00561629i
$802$	−552726.	+	3.13466e6i	−0.0303441	+	0.172090i
$803$	3.58878e6	−	6.21595e6i	0.196407	−	0.340188i
$804$	−876380.	−	1.51793e6i	−0.0478137	−	0.0828157i
$805$	1.48590e6	−	540825.i	0.0808167	−	0.0294149i
$806$	1.61191e7	−	2.79191e7i	0.873984	−	1.51379i
$807$	151918.	−	127474.i	0.00821153	−	0.00689029i
$808$	661205.			0.0356294
$809$	−2.59756e7	+	2.17961e7i	−1.39539	+	1.17087i	−0.432281	+	0.901739i	$0.642291\pi$
$809$	−2.59756e7	+	2.17961e7i	−1.39539	+	1.17087i	−0.963104	+	0.269129i	$0.913264\pi$
$810$	−8.76216e6	−	3.18916e6i	−0.469244	−	0.170791i
$811$	3.63455e6	+	2.06125e7i	0.194043	+	1.10047i	0.913775	+	0.406221i	$0.133154\pi$
$811$	3.63455e6	+	2.06125e7i	0.194043	+	1.10047i	−0.719732	+	0.694252i	$0.755735\pi$
$812$	51483.8	−	291979.i	0.00274019	−	0.0155404i
$813$	5.14755e6			0.273133
$814$	−8.34144e6	−	1.23898e6i	−0.441245	−	0.0655396i
$815$	−2.38239e6			−0.125637
$816$	−135543.	+	768705.i	−0.00712612	+	0.0404142i
$817$	−8.49810e6	−	4.81951e7i	−0.445417	−	2.52609i
$818$	−2.20939e7	−	8.04151e6i	−1.15448	−	0.420198i
$819$	2.64778e6	−	2.22175e6i	0.137934	−	0.115741i
$820$	−6.24427e6			−0.324300
$821$	1.01356e7	−	8.50477e6i	0.524797	−	0.440357i	−0.341503	−	0.939881i	$-0.610936\pi$
$821$	1.01356e7	−	8.50477e6i	0.524797	−	0.440357i	0.866300	+	0.499524i	$0.166492\pi$
$822$	−958338.	+	1.65989e6i	−0.0494697	+	0.0856840i
$823$	−1.82523e7	+	6.64328e6i	−0.939327	+	0.341887i	−0.765900	−	0.642960i	$-0.777706\pi$
$823$	−1.82523e7	+	6.64328e6i	−0.939327	+	0.341887i	−0.173427	+	0.984847i	$0.555484\pi$
$824$	869585.	+	1.50617e6i	0.0446164	+	0.0772778i
$825$	−439204.	+	760723.i	−0.0224663	+	0.0389127i
$826$	−368946.	+	2.09240e6i	−0.0188154	+	0.106707i
$827$	2.45353e7	+	8.93012e6i	1.24746	+	0.454039i	0.879544	−	0.475818i	$-0.157848\pi$
$827$	2.45353e7	+	8.93012e6i	1.24746	+	0.454039i	0.367919	+	0.929858i	$0.380070\pi$
$828$	4.57090e6	+	7.91703e6i	0.231700	+	0.401316i
$829$	2.75968e7	+	2.31565e7i	1.39467	+	1.17027i	0.963406	+	0.268047i	$0.0863783\pi$
$829$	2.75968e7	+	2.31565e7i	1.39467	+	1.17027i	0.431268	+	0.902224i	$0.358066\pi$
$830$	1.08706e7	+	9.12154e6i	0.547721	+	0.459592i
$831$	−3.60867e6	+	1.31345e6i	−0.181278	+	0.0659797i
$832$	716703.	+	4.06463e6i	0.0358948	+	0.203569i
$833$	2.95645e6	+	1.67669e7i	0.147624	+	0.837220i
$834$	1.18381e6	−	430873.i	0.0589343	−	0.0214503i
$835$	3.27663e6	+	2.74942e6i	0.162634	+	0.136466i
$836$	7.85587e6	+	6.59186e6i	0.388757	+	0.326206i
$837$	−5.67052e6	−	9.82163e6i	−0.279775	−	0.484585i
$838$	2.66737e7	+	9.70843e6i	1.31212	+	0.477572i
$839$	1.08663e6	−	6.16261e6i	0.0532940	−	0.302245i	−0.946496	−	0.322714i	$-0.895405\pi$
$839$	1.08663e6	−	6.16261e6i	0.0532940	−	0.302245i	0.999790	+	0.0204688i	$0.00651587\pi$
$840$	61624.3	−	106736.i	0.00301338	−	0.00521933i
$841$	9.45545e6	+	1.63773e7i	0.460991	+	0.798460i
$842$	2.44411e7	−	8.89583e6i	1.18807	−	0.432421i
$843$	−964799.	+	1.67108e6i	−0.0467593	+	0.0809895i
$844$	5.10603e6	−	4.28447e6i	0.246733	−	0.207034i
$845$	2.84948e7			1.37285
$846$	−3.40804e6	+	2.85969e6i	−0.163712	+	0.137370i
$847$	−1.33458e6	−	485746.i	−0.0639198	−	0.0232649i
$848$	1.60894e6	+	9.12473e6i	0.0768332	+	0.435743i
$849$	−340962.	+	1.93369e6i	−0.0162344	+	0.0920700i
$850$	4.79241e6			0.227513
$851$	−1.78647e7	−	9.67896e6i	−0.845611	−	0.458147i
$852$	181824.			0.00858128
$853$	2.97240e6	−	1.68573e7i	0.139873	−	0.793260i	−0.831469	−	0.555572i	$-0.812499\pi$
$853$	2.97240e6	−	1.68573e7i	0.139873	−	0.793260i	0.971342	−	0.237688i	$-0.0763895\pi$
$854$	−374515.	−	2.12398e6i	−0.0175721	−	0.0996564i
$855$	−2.46467e7	−	8.97068e6i	−1.15304	−	0.419672i
$856$	7.66171e6	−	6.42894e6i	0.357389	−	0.299885i
$857$	2.75790e7			1.28271			0.641353	−	0.767246i	$-0.278373\pi$
$857$	2.75790e7			1.28271			0.641353	+	0.767246i	$0.278373\pi$
$858$	−2.32282e6	+	1.94908e6i	−0.107720	+	0.0903881i
$859$	−6.06801e6	+	1.05101e7i	−0.280585	+	0.485987i	−0.971529	−	0.236921i	$-0.923862\pi$
$859$	−6.06801e6	+	1.05101e7i	−0.280585	+	0.485987i	0.690944	+	0.722908i	$0.257195\pi$
$860$	−1.28585e7	+	4.68010e6i	−0.592848	+	0.215779i
$861$	−191982.	−	332522.i	−0.00882575	−	0.0152867i
$862$	7.24229e6	−	1.25440e7i	0.331977	−	0.575001i
$863$	−2.69490e6	+	1.52836e7i	−0.123173	+	0.698550i	0.859203	+	0.511635i	$0.170960\pi$
$863$	−2.69490e6	+	1.52836e7i	−0.123173	+	0.698550i	−0.982376	+	0.186915i	$0.940151\pi$
$864$	1.36438e6	+	496595.i	0.0621802	+	0.0226318i
$865$	−7.74434e6	−	1.34136e7i	−0.351920	−	0.609544i
$866$	−4.44747e6	−	3.73187e6i	−0.201520	−	0.169095i
$867$	−835342.	−	700935.i	−0.0377413	−	0.0316687i
$868$	−1.76155e6	+	641152.i	−0.0793590	+	0.0288843i
$869$	3.66083e6	+	2.07616e7i	0.164449	+	0.932635i
$870$	−115515.	−	655118.i	−0.00517416	−	0.0293441i
$871$	−3.49076e7	+	1.27053e7i	−1.55910	+	0.567466i
$872$	−3.50280e6	−	2.93920e6i	−0.156000	−	0.130899i
$873$	6.31721e6	+	5.30077e6i	0.280537	+	0.235398i
$874$	1.23542e7	+	2.13981e7i	0.547062	+	0.947540i
$875$	−2.61417e6	−	951479.i	−0.115428	−	0.0420125i
$876$	234061.	−	1.32743e6i	0.0103055	−	0.0584454i
$877$	−2.70951e6	+	4.69301e6i	−0.118957	+	0.206040i	−0.919355	−	0.393430i	$-0.871289\pi$
$877$	−2.70951e6	+	4.69301e6i	−0.118957	+	0.206040i	0.800397	+	0.599470i	$0.204622\pi$
$878$	394129.	+	682652.i	0.0172545	+	0.0298857i
$879$	−5.76945e6	+	2.09991e6i	−0.251862	+	0.0916701i
$880$	1.43371e6	−	2.48326e6i	0.0624102	−	0.108098i
$881$	−2.98998e7	+	2.50889e7i	−1.29786	+	1.08904i	−0.307354	+	0.951595i	$0.599444\pi$
$881$	−2.98998e7	+	2.50889e7i	−1.29786	+	1.08904i	−0.990510	+	0.137442i	$0.956112\pi$
$882$	1.55418e7			0.672713
$883$	2.07472e7	−	1.74090e7i	0.895485	−	0.751401i	−0.0738175	−	0.997272i	$-0.523518\pi$
$883$	2.07472e7	−	1.74090e7i	0.895485	−	0.751401i	0.969303	+	0.245870i	$0.0790738\pi$
$884$	1.55455e7	+	5.65811e6i	0.669075	+	0.243523i
$885$	827809.	+	4.69474e6i	0.0355281	+	0.201490i
$886$	3.53871e6	−	2.00690e7i	0.151447	−	0.858898i
$887$	−2.91540e7			−1.24420			−0.622098	−	0.782939i	$-0.713719\pi$
$887$	−2.91540e7			−1.24420			−0.622098	+	0.782939i	$0.713719\pi$
$888$	−1.55158e6	+	317124.i	−0.0660302	+	0.0134957i
$889$	−4.24487e6			−0.180140
$890$	−39130.5	+	221920.i	−0.00165592	+	0.00939120i
$891$	−2.31640e6	−	1.31370e7i	−0.0977505	−	0.554371i
$892$	−3.01195e6	−	1.09626e6i	−0.126746	−	0.0461319i
$893$	−9.21126e6	+	7.72916e6i	−0.386536	+	0.324342i
$894$	5.79575e6			0.242530
$895$	−777062.	+	652032.i	−0.0324264	+	0.0272089i
$896$	119999.	−	207844.i	0.00499353	−	0.00864904i
$897$	−6.86520e6	+	2.49873e6i	−0.284886	+	0.103690i
$898$	−261138.	−	452304.i	−0.0108063	−	0.0187171i
$899$	−5.05901e6	+	8.76246e6i	−0.208769	+	0.361599i
$900$	759670.	−	4.30830e6i	0.0312621	−	0.177296i
$901$	3.48983e7	+	1.27020e7i	1.43216	+	0.521265i
$902$	−4.46653e6	−	7.73625e6i	−0.182790	−	0.316602i
$903$	−644563.	−	540853.i	−0.0263055	−	0.0220729i
$904$	1.13992e7	+	9.56507e6i	0.463931	+	0.389284i
$905$	2.91797e7	−	1.06205e7i	1.18429	−	0.431048i
$906$	−140394.	−	796215.i	−0.00568236	−	0.0322263i
$907$	5.77363e6	+	3.27439e7i	0.233040	+	1.32164i	0.846702	+	0.532068i	$0.178585\pi$
$907$	5.77363e6	+	3.27439e7i	0.233040	+	1.32164i	−0.613661	+	0.789569i	$0.710304\pi$
$908$	−1.05581e7	+	3.84284e6i	−0.424983	+	0.154681i
$909$	−1.85328e6	−	1.55509e6i	−0.0743930	−	0.0624231i
$910$	−2.00100e6	−	1.67904e6i	−0.0801021	−	0.0672137i
$911$	6.53393e6	+	1.13171e7i	0.260843	+	0.451793i	0.966466	−	0.256794i	$-0.0826662\pi$
$911$	6.53393e6	+	1.13171e7i	0.260843	+	0.451793i	−0.705623	+	0.708587i	$0.749333\pi$
$912$	1.80971e6	+	658680.i	0.0720479	+	0.0262233i
$913$	−3.52524e6	+	1.99926e7i	−0.139963	+	0.793767i
$914$	−1.11192e7	+	1.92591e7i	−0.440260	+	0.762553i
$915$	−2.41956e6	−	4.19080e6i	−0.0955396	−	0.165479i
$916$	−5.83041e6	+	2.12210e6i	−0.229594	+	0.0835654i
$917$	1.43517e6	−	2.48579e6i	0.0563612	−	0.0976204i
$918$	4.45816e6	−	3.74084e6i	0.174602	−	0.146508i
$919$	−2.65761e7			−1.03801			−0.519006	−	0.854771i	$-0.673698\pi$
$919$	−2.65761e7			−1.03801			−0.519006	+	0.854771i	$0.673698\pi$
$920$	5.29239e6	−	4.44084e6i	0.206149	−	0.172980i
$921$	28893.1	+	10516.2i	0.00112239	+	0.000408518i
$922$	4.30908e6	+	2.44380e7i	0.166939	+	0.946757i
$923$	669164.	−	3.79502e6i	0.0258540	−	0.146626i
$924$	176319.			0.00679392
$925$	3.57167e6	+	9.04340e6i	0.137251	+	0.347518i
$926$	2.70674e6			0.103733
$927$	1.10500e6	−	6.26679e6i	0.0422342	−	0.239522i
$928$	−224938.	−	1.27569e6i	−0.00857420	−	0.0486267i
$929$	−4.47222e7	−	1.62775e7i	−1.70014	−	0.618799i	−0.704295	−	0.709907i	$-0.748737\pi$
$929$	−4.47222e7	−	1.62775e7i	−1.70014	−	0.618799i	−0.995841	+	0.0911080i	$0.970959\pi$
$930$	−3.22204e6	+	2.70361e6i	−0.122158	+	0.102503i
$931$	4.20064e7			1.58833
$932$	−7.81958e6	+	6.56140e6i	−0.294879	+	0.247433i
$933$	3.42617e6	−	5.93430e6i	0.128856	−	0.223185i
$934$	−2.09864e6	+	763842.i	−0.0787173	+	0.0286508i
$935$	−5.74662e6	−	9.95344e6i	−0.214973	−	0.372344i
$936$	7.55076e6	−	1.30783e7i	0.281709	−	0.487935i
$937$	−4.52416e6	+	2.56578e7i	−0.168341	+	0.954708i	0.777212	+	0.629239i	$0.216633\pi$
$937$	−4.52416e6	+	2.56578e7i	−0.168341	+	0.954708i	−0.945553	+	0.325469i	$0.894478\pi$
$938$	2.02982e6	+	738795.i	0.0753270	+	0.0274168i
$939$	−3.26563e6	−	5.65623e6i	−0.120866	−	0.209345i
$940$	2.57556e6	+	2.16115e6i	0.0950717	+	0.0797746i
$941$	−4.58666e6	−	3.84867e6i	−0.168858	−	0.141689i	0.554442	−	0.832222i	$-0.312932\pi$
$941$	−4.58666e6	−	3.84867e6i	−0.168858	−	0.141689i	−0.723301	+	0.690533i	$0.757376\pi$
$942$	801064.	−	291564.i	0.0294131	−	0.0107055i
$943$	−3.73745e6	−	2.11961e7i	−0.136866	−	0.776207i
$944$	1.61196e6	+	9.14190e6i	0.0588743	+	0.333893i
$945$	−863498.	+	314287.i	−0.0314544	+	0.0114485i
$946$	−1.49960e7	−	1.25831e7i	−0.544814	−	0.457153i
$947$	1.84798e7	+	1.55064e7i	0.669611	+	0.561871i	0.912950	−	0.408071i	$-0.133798\pi$
$947$	1.84798e7	+	1.55064e7i	0.669611	+	0.561871i	−0.243339	+	0.969941i	$0.578243\pi$
$948$	1.97953e6	+	3.42865e6i	0.0715388	+	0.123909i
$949$	−2.68446e7	−	9.77062e6i	−0.967589	−	0.352174i
$950$	2.05323e6	−	1.16445e7i	0.0738124	−	0.418611i
$951$	2.07236e6	−	3.58943e6i	0.0743043	−	0.128699i
$952$	−480981.	−	833083.i	−0.0172003	−	0.0297918i
$953$	−5.69723e6	+	2.07362e6i	−0.203204	+	0.0739600i	−0.441617	−	0.897204i	$-0.645595\pi$
$953$	−5.69723e6	+	2.07362e6i	−0.203204	+	0.0739600i	0.238413	+	0.971164i	$0.423373\pi$
$954$	1.69508e7	−	2.93596e7i	0.603002	−	1.04443i
$955$	−1.81117e7	+	1.51975e7i	−0.642614	+	0.539217i
$956$	1.21219e7			0.428968
$957$	729021.	−	611721.i	0.0257312	−	0.0215911i
$958$	−1.27677e7	−	4.64707e6i	−0.449469	−	0.163593i
$959$	−410174.	−	2.32621e6i	−0.0144020	−	0.0816776i
$960$	93507.2	−	530306.i	0.00327466	−	0.0185715i
$961$	3.53450e7			1.23458
$962$	908724.	+	3.35517e7i	0.0316588	+	1.16890i
$963$	−3.65951e7			−1.27162
$964$	1.37881e6	−	7.81962e6i	0.0477872	−	0.271015i
$965$	−3.20381e6	−	1.81697e7i	−0.110751	−	0.628100i
$966$	399201.	+	145297.i	0.0137641	+	0.00500973i
$967$	1.34066e7	−	1.12495e7i	0.461056	−	0.386872i	−0.382463	−	0.923971i	$-0.624924\pi$
$967$	1.34066e7	−	1.12495e7i	0.461056	−	0.386872i	0.843519	+	0.537099i	$0.180480\pi$
$968$	−6.20513e6			−0.212844
$969$	5.91326e6	−	4.96182e6i	0.202310	−	0.169758i
$970$	3.11607e6	−	5.39719e6i	0.106335	−	0.184178i
$971$	−1.70741e7	+	6.21448e6i	−0.581153	+	0.211523i	−0.615834	−	0.787876i	$-0.711181\pi$
$971$	−1.70741e7	+	6.21448e6i	−0.581153	+	0.211523i	0.0346807	+	0.999398i	$0.488959\pi$
$972$	−4.00898e6	−	6.94376e6i	−0.136103	−	0.235738i
$973$	−776278.	+	1.34455e6i	−0.0262867	+	0.0455298i
$974$	−509595.	+	2.89005e6i	−0.0172118	+	0.0976132i
$975$	3.28530e6	+	1.19575e6i	0.110679	+	0.0402838i
$976$	−4.71152e6	−	8.16059e6i	−0.158320	−	0.274219i
$977$	2.85615e7	+	2.39659e7i	0.957292	+	0.803263i	0.980510	−	0.196467i	$-0.0629469\pi$
$977$	2.85615e7	+	2.39659e7i	0.957292	+	0.803263i	−0.0232185	+	0.999730i	$0.507391\pi$
$978$	−490306.	−	411416.i	−0.0163916	−	0.0137542i
$979$	−302934.	+	110259.i	−0.0101016	+	0.00367670i
$980$	−2.03956e6	−	1.15669e7i	−0.0678378	−	0.384728i
$981$	2.90525e6	+	1.64765e7i	0.0963852	+	0.546628i
$982$	−2.17838e7	+	7.92864e6i	−0.720865	+	0.262373i
$983$	2.47969e7	+	2.08071e7i	0.818492	+	0.686796i	0.952618	−	0.304168i	$-0.0983785\pi$
$983$	2.47969e7	+	2.08071e7i	0.818492	+	0.686796i	−0.134127	+	0.990964i	$0.542823\pi$
$984$	−1.28510e6	−	1.07833e6i	−0.0423105	−	0.0355027i
$985$	1.94778e6	+	3.37366e6i	0.0639662	+	0.110793i
$986$	−4.87899e6	−	1.77581e6i	−0.159822	−	0.0581706i
$987$	−35900.1	+	203599.i	−0.00117301	+	0.00665248i
$988$	2.04082e7	−	3.53480e7i	0.665138	−	1.15205i
$989$	−2.35829e7	−	4.08468e7i	−0.766666	−	1.32790i
$990$	−9.85892e6	+	3.58836e6i	−0.319699	+	0.116361i
$991$	5.72972e6	−	9.92416e6i	0.185331	−	0.321003i	−0.758357	−	0.651840i	$-0.773997\pi$
$991$	5.72972e6	−	9.92416e6i	0.185331	−	0.321003i	0.943688	+	0.330836i	$0.107331\pi$
$992$	−6.27417e6	+	5.26465e6i	−0.202431	+	0.169860i
$993$	−9.14736e6			−0.294390
$994$	−171654.	+	144035.i	−0.00551047	+	0.00462383i
$995$	1.69575e6	+	617201.i	0.0543004	+	0.0197637i
$996$	662020.	+	3.75450e6i	0.0211457	+	0.119923i
$997$	2.60856e6	−	1.47939e7i	0.0831119	−	0.471351i	−0.914636	−	0.404278i	$-0.867523\pi$
$997$	2.60856e6	−	1.47939e7i	0.0831119	−	0.471351i	0.997748	−	0.0670731i	$-0.0213661\pi$
$998$	−3.36312e7			−1.06885
$999$	1.03816e7	+	5.62470e6i	0.329118	+	0.178314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.f.a.33.4	yes	48
37.9	even	9	inner	74.6.f.a.9.4	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.f.a.9.4	✓	48	37.9	even	9	inner
74.6.f.a.33.4	yes	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	74.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.694593 - 3.93923i) q^{2} +(0.515998 + 2.92637i) q^{3} +(-15.0351 - 5.47232i) q^{4} +(33.8915 - 28.4384i) q^{5} +11.8861 q^{6} +(-11.2213 + 9.41575i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(220.048 - 80.0909i) q^{9} +O(q^{10})\)	\(q+(0.694593 - 3.93923i) q^{2} +(0.515998 + 2.92637i) q^{3} +(-15.0351 - 5.47232i) q^{4} +(33.8915 - 28.4384i) q^{5} +11.8861 q^{6} +(-11.2213 + 9.41575i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(220.048 - 80.0909i) q^{9} +(-88.4845 - 153.260i) q^{10} +(126.586 - 219.253i) q^{11} +(8.25596 - 46.8219i) q^{12} +(-946.880 - 344.636i) q^{13} +(29.2966 + 50.7432i) q^{14} +(100.709 + 84.5050i) q^{15} +(196.107 + 164.554i) q^{16} +(964.220 - 350.948i) q^{17} +(-162.653 - 922.450i) q^{18} +(-439.618 - 2493.20i) q^{19} +(-665.186 + 242.108i) q^{20} +(-33.3441 - 27.9790i) q^{21} +(-775.763 - 650.943i) q^{22} +(-1219.97 - 2113.06i) q^{23} +(-178.708 - 65.0443i) q^{24} +(-202.756 + 1149.89i) q^{25} +(-2015.30 + 3490.60i) q^{26} +(708.959 + 1227.95i) q^{27} +(220.238 - 80.1602i) q^{28} +(632.504 - 1095.53i) q^{29} +(402.836 - 338.020i) q^{30} -7998.38 q^{31} +(784.430 - 658.215i) q^{32} +(706.934 + 257.303i) q^{33} +(-712.723 - 4042.05i) q^{34} +(-112.537 + 638.228i) q^{35} -3746.72 q^{36} +(7096.28 - 4357.38i) q^{37} -10126.6 q^{38} +(519.944 - 2948.75i) q^{39} +(491.685 + 2788.49i) q^{40} +(8289.16 + 3017.01i) q^{41} +(-133.376 + 111.916i) q^{42} +19330.7 q^{43} +(-3103.05 + 2603.77i) q^{44} +(5180.11 - 8972.21i) q^{45} +(-9171.20 + 3338.04i) q^{46} +(-2374.82 - 4113.30i) q^{47} +(-380.354 + 658.792i) q^{48} +(-2881.24 + 16340.4i) q^{49} +(4388.83 + 1597.40i) q^{50} +(1524.54 + 2640.58i) q^{51} +(12350.5 + 10363.3i) q^{52} +(27725.7 + 23264.6i) q^{53} +(5329.63 - 1939.82i) q^{54} +(-1945.01 - 11030.7i) q^{55} +(-162.794 - 923.249i) q^{56} +(7069.17 - 2572.97i) q^{57} +(-3876.21 - 3252.53i) q^{58} +(27777.9 + 23308.4i) q^{59} +(-1051.73 - 1821.65i) q^{60} +(-34588.9 - 12589.3i) q^{61} +(-5555.62 + 31507.5i) q^{62} +(-1715.10 + 2970.64i) q^{63} +(-2048.00 - 3547.24i) q^{64} +(-41892.1 + 15247.5i) q^{65} +(1504.61 - 2606.05i) q^{66} +(28240.9 - 23696.9i) q^{67} -16417.6 q^{68} +(5554.08 - 4660.43i) q^{69} +(2435.96 + 886.617i) q^{70} +(664.085 + 3766.21i) q^{71} +(-2602.45 + 14759.2i) q^{72} +28350.6 q^{73} +(-12235.7 - 30980.5i) q^{74} -3469.61 q^{75} +(-7033.89 + 39891.1i) q^{76} +(643.981 + 3652.20i) q^{77} +(-11254.7 - 4096.36i) q^{78} +(-63789.4 + 53525.7i) q^{79} +11326.0 q^{80} +(40362.9 - 33868.5i) q^{81} +(17642.3 - 30557.3i) q^{82} +(-75351.0 + 27425.5i) q^{83} +(348.221 + 603.137i) q^{84} +(22698.5 - 39315.0i) q^{85} +(13426.9 - 76147.9i) q^{86} +(3532.29 + 1285.65i) q^{87} +(8101.49 + 14032.2i) q^{88} +(-975.442 - 818.493i) q^{89} +(-31745.5 - 26637.7i) q^{90} +(13870.2 - 5048.33i) q^{91} +(6779.08 + 38446.1i) q^{92} +(-4127.15 - 23406.2i) q^{93} +(-17852.8 + 6497.88i) q^{94} +(-85801.7 - 71996.2i) q^{95} +(2330.94 + 1955.89i) q^{96} +(17608.0 + 30498.0i) q^{97} +(62367.1 + 22699.8i) q^{98} +(10294.8 - 58384.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 3 q^{3} - 72 q^{5} + 114 q^{7} - 1536 q^{8} - 93 q^{9}+O(q^{10}) \) 48 * q - 3 * q^3 - 72 * q^5 + 114 * q^7 - 1536 * q^8 - 93 * q^9	\( 48 q - 3 q^{3} - 72 q^{5} + 114 q^{7} - 1536 q^{8} - 93 q^{9} - 648 q^{10} - 9 q^{11} - 48 q^{12} + 288 q^{13} - 660 q^{14} - 3678 q^{15} - 2475 q^{17} + 744 q^{18} + 945 q^{19} - 1152 q^{20} - 2073 q^{21} - 60 q^{22} - 5739 q^{23} - 192 q^{24} - 3834 q^{25} - 5304 q^{26} - 1077 q^{27} - 5232 q^{28} - 11640 q^{29} - 14712 q^{30} - 20394 q^{31} - 62013 q^{33} + 7812 q^{34} + 27999 q^{35} + 62208 q^{36} + 13605 q^{37} + 60696 q^{38} + 25590 q^{39} + 9216 q^{40} - 18267 q^{41} - 8292 q^{42} + 2208 q^{43} - 240 q^{44} - 48132 q^{45} - 40308 q^{46} - 663 q^{47} + 58326 q^{49} + 61776 q^{50} + 8748 q^{51} - 31536 q^{52} + 20940 q^{53} + 37836 q^{54} - 158868 q^{55} + 13632 q^{56} + 164910 q^{57} - 28068 q^{58} + 111258 q^{59} - 31824 q^{60} + 88758 q^{61} + 116100 q^{62} - 202488 q^{63} - 98304 q^{64} + 155997 q^{65} - 53532 q^{66} + 52503 q^{67} + 32544 q^{68} + 298758 q^{69} - 5760 q^{70} + 160434 q^{71} + 11904 q^{72} - 477210 q^{73} + 8844 q^{74} + 808230 q^{75} + 15120 q^{76} - 510765 q^{77} + 26004 q^{78} - 378768 q^{79} + 82944 q^{80} + 55476 q^{81} - 149064 q^{82} - 230082 q^{83} - 42336 q^{84} + 55653 q^{85} - 149904 q^{86} - 453051 q^{87} - 576 q^{88} + 492789 q^{89} + 12276 q^{90} + 220839 q^{91} + 176160 q^{92} - 109767 q^{93} - 6768 q^{94} - 630843 q^{95} + 6144 q^{96} - 632190 q^{97} - 194628 q^{98} - 414765 q^{99}+O(q^{100}) \) 48 * q - 3 * q^3 - 72 * q^5 + 114 * q^7 - 1536 * q^8 - 93 * q^9 - 648 * q^10 - 9 * q^11 - 48 * q^12 + 288 * q^13 - 660 * q^14 - 3678 * q^15 - 2475 * q^17 + 744 * q^18 + 945 * q^19 - 1152 * q^20 - 2073 * q^21 - 60 * q^22 - 5739 * q^23 - 192 * q^24 - 3834 * q^25 - 5304 * q^26 - 1077 * q^27 - 5232 * q^28 - 11640 * q^29 - 14712 * q^30 - 20394 * q^31 - 62013 * q^33 + 7812 * q^34 + 27999 * q^35 + 62208 * q^36 + 13605 * q^37 + 60696 * q^38 + 25590 * q^39 + 9216 * q^40 - 18267 * q^41 - 8292 * q^42 + 2208 * q^43 - 240 * q^44 - 48132 * q^45 - 40308 * q^46 - 663 * q^47 + 58326 * q^49 + 61776 * q^50 + 8748 * q^51 - 31536 * q^52 + 20940 * q^53 + 37836 * q^54 - 158868 * q^55 + 13632 * q^56 + 164910 * q^57 - 28068 * q^58 + 111258 * q^59 - 31824 * q^60 + 88758 * q^61 + 116100 * q^62 - 202488 * q^63 - 98304 * q^64 + 155997 * q^65 - 53532 * q^66 + 52503 * q^67 + 32544 * q^68 + 298758 * q^69 - 5760 * q^70 + 160434 * q^71 + 11904 * q^72 - 477210 * q^73 + 8844 * q^74 + 808230 * q^75 + 15120 * q^76 - 510765 * q^77 + 26004 * q^78 - 378768 * q^79 + 82944 * q^80 + 55476 * q^81 - 149064 * q^82 - 230082 * q^83 - 42336 * q^84 + 55653 * q^85 - 149904 * q^86 - 453051 * q^87 - 576 * q^88 + 492789 * q^89 + 12276 * q^90 + 220839 * q^91 + 176160 * q^92 - 109767 * q^93 - 6768 * q^94 - 630843 * q^95 + 6144 * q^96 - 632190 * q^97 - 194628 * q^98 - 414765 * q^99

Introduction

L-functions

Modular forms

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