LMFDB - Embedded newform 41.6.c.a.9.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [41,6,Mod(9,41)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(41, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

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

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

chi := DirichletCharacter("41.9");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 41 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	41.c (of order $4$, degree $2$, 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:	$6.57573661233$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			9.10
Character	$\chi$	$=$	41.9
Dual form			41.6.c.a.32.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.127223i q^{2} +(14.0147 + 14.0147i) q^{3} +31.9838 q^{4} +90.6024i q^{5} +(-1.78299 + 1.78299i) q^{6} +(-136.937 - 136.937i) q^{7} +8.14022i q^{8} +149.822i q^{9} +O(q^{10})$	\(q+0.127223i q^{2} +(14.0147 + 14.0147i) q^{3} +31.9838 q^{4} +90.6024i q^{5} +(-1.78299 + 1.78299i) q^{6} +(-136.937 - 136.937i) q^{7} +8.14022i q^{8} +149.822i q^{9} -11.5267 q^{10} +(174.701 + 174.701i) q^{11} +(448.243 + 448.243i) q^{12} +(-66.0780 - 66.0780i) q^{13} +(17.4216 - 17.4216i) q^{14} +(-1269.76 + 1269.76i) q^{15} +1022.45 q^{16} +(-640.372 + 640.372i) q^{17} -19.0608 q^{18} +(1317.88 - 1317.88i) q^{19} +2897.81i q^{20} -3838.26i q^{21} +(-22.2260 + 22.2260i) q^{22} +4167.41 q^{23} +(-114.083 + 114.083i) q^{24} -5083.79 q^{25} +(8.40666 - 8.40666i) q^{26} +(1305.86 - 1305.86i) q^{27} +(-4379.77 - 4379.77i) q^{28} +(-2387.92 - 2387.92i) q^{29} +(-161.543 - 161.543i) q^{30} -4921.90 q^{31} +390.566i q^{32} +4896.75i q^{33} +(-81.4702 - 81.4702i) q^{34} +(12406.8 - 12406.8i) q^{35} +4791.88i q^{36} +9781.61 q^{37} +(167.665 + 167.665i) q^{38} -1852.12i q^{39} -737.524 q^{40} +(-9290.86 - 5434.72i) q^{41} +488.316 q^{42} +1544.03i q^{43} +(5587.60 + 5587.60i) q^{44} -13574.2 q^{45} +530.191i q^{46} +(-1531.90 + 1531.90i) q^{47} +(14329.2 + 14329.2i) q^{48} +20696.6i q^{49} -646.776i q^{50} -17949.2 q^{51} +(-2113.43 - 2113.43i) q^{52} +(-6643.24 - 6643.24i) q^{53} +(166.136 + 166.136i) q^{54} +(-15828.3 + 15828.3i) q^{55} +(1114.70 - 1114.70i) q^{56} +36939.3 q^{57} +(303.799 - 303.799i) q^{58} +39010.9 q^{59} +(-40611.8 + 40611.8i) q^{60} -47612.1i q^{61} -626.180i q^{62} +(20516.2 - 20516.2i) q^{63} +32668.6 q^{64} +(5986.83 - 5986.83i) q^{65} -622.980 q^{66} +(-34935.8 + 34935.8i) q^{67} +(-20481.5 + 20481.5i) q^{68} +(58404.9 + 58404.9i) q^{69} +(1578.44 + 1578.44i) q^{70} +(-53185.0 - 53185.0i) q^{71} -1219.58 q^{72} +37779.3i q^{73} +1244.45i q^{74} +(-71247.7 - 71247.7i) q^{75} +(42150.8 - 42150.8i) q^{76} -47846.1i q^{77} +235.633 q^{78} +(-34928.5 - 34928.5i) q^{79} +92636.1i q^{80} +73009.1 q^{81} +(691.422 - 1182.01i) q^{82} -58165.7 q^{83} -122762. i q^{84} +(-58019.2 - 58019.2i) q^{85} -196.436 q^{86} -66931.9i q^{87} +(-1422.10 + 1422.10i) q^{88} +(37358.7 + 37358.7i) q^{89} -1726.96i q^{90} +18097.1i q^{91} +133290. q^{92} +(-68978.8 - 68978.8i) q^{93} +(-194.893 - 194.893i) q^{94} +(119403. + 119403. i) q^{95} +(-5473.66 + 5473.66i) q^{96} +(-89914.2 + 89914.2i) q^{97} -2633.09 q^{98} +(-26174.0 + 26174.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 20 q^{3} - 548 q^{4} - 124 q^{6} - 2 q^{7}+O(q^{10}) $ 34 * q + 20 * q^3 - 548 * q^4 - 124 * q^6 - 2 * q^7	\( 34 q + 20 q^{3} - 548 q^{4} - 124 q^{6} - 2 q^{7} + 1660 q^{10} + 654 q^{11} + 98 q^{12} + 854 q^{13} + 2236 q^{14} - 998 q^{15} + 8828 q^{16} + 1730 q^{17} + 2068 q^{18} + 716 q^{19} - 7750 q^{22} - 8156 q^{23} + 5496 q^{24} - 28870 q^{25} + 11470 q^{26} - 26806 q^{27} - 5942 q^{28} - 19190 q^{29} + 21430 q^{30} - 6376 q^{31} + 4228 q^{34} + 20934 q^{35} + 768 q^{37} - 6552 q^{38} - 47024 q^{40} - 9618 q^{41} + 126236 q^{42} - 57632 q^{44} + 81112 q^{45} + 2372 q^{47} + 88202 q^{48} + 24936 q^{51} + 151982 q^{52} - 94170 q^{53} - 153650 q^{54} - 105662 q^{55} + 8144 q^{56} - 69412 q^{57} - 63094 q^{58} + 87684 q^{59} + 58746 q^{60} - 76328 q^{63} - 109780 q^{64} + 88904 q^{65} - 427468 q^{66} + 212150 q^{67} - 199904 q^{68} + 125672 q^{69} + 113566 q^{70} + 189392 q^{71} + 579216 q^{72} + 199072 q^{75} + 128522 q^{76} - 327232 q^{78} - 28880 q^{79} - 557850 q^{81} - 241122 q^{82} + 384572 q^{83} - 114880 q^{85} - 453980 q^{86} + 338338 q^{88} - 391266 q^{89} + 955316 q^{92} + 394684 q^{93} - 42650 q^{94} - 404378 q^{95} - 254372 q^{96} - 324538 q^{97} - 167276 q^{98} - 685716 q^{99}+O(q^{100}) \) 34 * q + 20 * q^3 - 548 * q^4 - 124 * q^6 - 2 * q^7 + 1660 * q^10 + 654 * q^11 + 98 * q^12 + 854 * q^13 + 2236 * q^14 - 998 * q^15 + 8828 * q^16 + 1730 * q^17 + 2068 * q^18 + 716 * q^19 - 7750 * q^22 - 8156 * q^23 + 5496 * q^24 - 28870 * q^25 + 11470 * q^26 - 26806 * q^27 - 5942 * q^28 - 19190 * q^29 + 21430 * q^30 - 6376 * q^31 + 4228 * q^34 + 20934 * q^35 + 768 * q^37 - 6552 * q^38 - 47024 * q^40 - 9618 * q^41 + 126236 * q^42 - 57632 * q^44 + 81112 * q^45 + 2372 * q^47 + 88202 * q^48 + 24936 * q^51 + 151982 * q^52 - 94170 * q^53 - 153650 * q^54 - 105662 * q^55 + 8144 * q^56 - 69412 * q^57 - 63094 * q^58 + 87684 * q^59 + 58746 * q^60 - 76328 * q^63 - 109780 * q^64 + 88904 * q^65 - 427468 * q^66 + 212150 * q^67 - 199904 * q^68 + 125672 * q^69 + 113566 * q^70 + 189392 * q^71 + 579216 * q^72 + 199072 * q^75 + 128522 * q^76 - 327232 * q^78 - 28880 * q^79 - 557850 * q^81 - 241122 * q^82 + 384572 * q^83 - 114880 * q^85 - 453980 * q^86 + 338338 * q^88 - 391266 * q^89 + 955316 * q^92 + 394684 * q^93 - 42650 * q^94 - 404378 * q^95 - 254372 * q^96 - 324538 * q^97 - 167276 * q^98 - 685716 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/41\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$			0.127223i			0.0224901i	0.999937	+	0.0112450i	$0.00357949\pi$
$2$			0.127223i			0.0224901i	−0.999937	+	0.0112450i	$0.996421\pi$
$3$	14.0147	+	14.0147i	0.899042	+	0.899042i	0.995351	−	0.0963099i	$-0.0307040\pi$
$3$	14.0147	+	14.0147i	0.899042	+	0.899042i	−0.0963099	+	0.995351i	$0.530704\pi$
$4$	31.9838			0.999494
$5$			90.6024i			1.62074i	0.585915	+	0.810372i	$0.300735\pi$
$5$			90.6024i			1.62074i	−0.585915	+	0.810372i	$0.699265\pi$
$6$	−1.78299	+	1.78299i	−0.0202195	+	0.0202195i
$7$	−136.937	−	136.937i	−1.05627	−	1.05627i	−0.998319	−	0.0579542i	$-0.981542\pi$
$7$	−136.937	−	136.937i	−1.05627	−	1.05627i	−0.0579542	−	0.998319i	$-0.518458\pi$
$8$			8.14022i			0.0449688i
$9$			149.822i			0.616551i
$10$	−11.5267			−0.0364507
$11$	174.701	+	174.701i	0.435325	+	0.435325i	0.890435	−	0.455110i	$-0.150400\pi$
$11$	174.701	+	174.701i	0.435325	+	0.435325i	−0.455110	+	0.890435i	$0.650400\pi$
$12$	448.243	+	448.243i	0.898587	+	0.898587i
$13$	−66.0780	−	66.0780i	−0.108442	−	0.108442i	0.650804	−	0.759246i	$-0.274432\pi$
$13$	−66.0780	−	66.0780i	−0.108442	−	0.108442i	−0.759246	+	0.650804i	$0.774432\pi$
$14$	17.4216	−	17.4216i	0.0237557	−	0.0237557i
$15$	−1269.76	+	1269.76i	−1.45712	+	1.45712i
$16$	1022.45			0.998483
$17$	−640.372	+	640.372i	−0.537415	+	0.537415i	−0.922769	−	0.385354i	$-0.874079\pi$
$17$	−640.372	+	640.372i	−0.537415	+	0.537415i	0.385354	+	0.922769i	$0.374079\pi$
$18$	−19.0608			−0.0138663
$19$	1317.88	−	1317.88i	0.837514	−	0.837514i	−0.151017	−	0.988531i	$-0.548255\pi$
$19$	1317.88	−	1317.88i	0.837514	−	0.837514i	0.988531	+	0.151017i	$0.0482549\pi$
$20$			2897.81i			1.61992i
$21$		−	3838.26i		−	1.89927i
$22$	−22.2260	+	22.2260i	−0.00979049	+	0.00979049i
$23$	4167.41			1.64266			0.821328	−	0.570456i	$-0.193234\pi$
$23$	4167.41			1.64266			0.821328	+	0.570456i	$0.193234\pi$
$24$	−114.083	+	114.083i	−0.0404288	+	0.0404288i
$25$	−5083.79			−1.62681
$26$	8.40666	−	8.40666i	0.00243888	−	0.00243888i
$27$	1305.86	−	1305.86i	0.344736	−	0.344736i
$28$	−4379.77	−	4379.77i	−1.05574	−	1.05574i
$29$	−2387.92	−	2387.92i	−0.527261	−	0.527261i	0.392494	−	0.919755i	$-0.371612\pi$
$29$	−2387.92	−	2387.92i	−0.527261	−	0.527261i	−0.919755	+	0.392494i	$0.871612\pi$
$30$	−161.543	−	161.543i	−0.0327707	−	0.0327707i
$31$	−4921.90			−0.919874			−0.459937	−	0.887951i	$-0.652128\pi$
$31$	−4921.90			−0.919874			−0.459937	+	0.887951i	$0.652128\pi$
$32$			390.566i			0.0674248i
$33$			4896.75i			0.782750i
$34$	−81.4702	−	81.4702i	−0.0120865	−	0.0120865i
$35$	12406.8	−	12406.8i	1.71195	−	1.71195i
$36$			4791.88i			0.616239i
$37$	9781.61			1.17464			0.587322	−	0.809354i	$-0.300182\pi$
$37$	9781.61			1.17464			0.587322	+	0.809354i	$0.300182\pi$
$38$	167.665	+	167.665i	0.0188358	+	0.0188358i
$39$		−	1852.12i		−	0.194988i
$40$	−737.524			−0.0728830
$41$	−9290.86	−	5434.72i	−0.863170	−	0.504914i
$41$	−9290.86	−	5434.72i	−0.863170	−	0.504914i
$42$	488.316			0.0427147
$43$			1544.03i			0.127346i	0.997971	+	0.0636728i	$0.0202814\pi$
$43$			1544.03i			0.127346i	−0.997971	+	0.0636728i	$0.979719\pi$
$44$	5587.60	+	5587.60i	0.435105	+	0.435105i
$45$	−13574.2			−0.999272
$46$			530.191i			0.0369435i
$47$	−1531.90	+	1531.90i	−0.101154	+	0.101154i	−0.755873	−	0.654718i	$-0.772787\pi$
$47$	−1531.90	+	1531.90i	−0.101154	+	0.101154i	0.654718	+	0.755873i	$0.272787\pi$
$48$	14329.2	+	14329.2i	0.897678	+	0.897678i
$49$			20696.6i			1.23143i
$50$		−	646.776i		−	0.0365872i
$51$	−17949.2			−0.966317
$52$	−2113.43	−	2113.43i	−0.108387	−	0.108387i
$53$	−6643.24	−	6643.24i	−0.324855	−	0.324855i	0.525771	−	0.850626i	$-0.323777\pi$
$53$	−6643.24	−	6643.24i	−0.324855	−	0.324855i	−0.850626	+	0.525771i	$0.823777\pi$
$54$	166.136	+	166.136i	0.00775315	+	0.00775315i
$55$	−15828.3	+	15828.3i	−0.705550	+	0.705550i
$56$	1114.70	−	1114.70i	0.0474994	−	0.0474994i
$57$	36939.3			1.50592
$58$	303.799	−	303.799i	0.0118581	−	0.0118581i
$59$	39010.9			1.45900			0.729501	−	0.683980i	$-0.239752\pi$
$59$	39010.9			1.45900			0.729501	+	0.683980i	$0.239752\pi$
$60$	−40611.8	+	40611.8i	−1.45638	+	1.45638i
$61$		−	47612.1i		−	1.63830i	−0.573580	−	0.819149i	$-0.694446\pi$
$61$		−	47612.1i		−	1.63830i	0.573580	−	0.819149i	$-0.305554\pi$
$62$		−	626.180i		−	0.0206881i
$63$	20516.2	−	20516.2i	0.651247	−	0.651247i
$64$	32668.6			0.996966
$65$	5986.83	−	5986.83i	0.175757	−	0.175757i
$66$	−622.980			−0.0176041
$67$	−34935.8	+	34935.8i	−0.950787	+	0.950787i	−0.998845	−	0.0480574i	$-0.984697\pi$
$67$	−34935.8	+	34935.8i	−0.950787	+	0.950787i	0.0480574	+	0.998845i	$0.484697\pi$
$68$	−20481.5	+	20481.5i	−0.537143	+	0.537143i
$69$	58404.9	+	58404.9i	1.47682	+	1.47682i
$70$	1578.44	+	1578.44i	0.0385019	+	0.0385019i
$71$	−53185.0	−	53185.0i	−1.25211	−	1.25211i	−0.954771	−	0.297341i	$-0.903900\pi$
$71$	−53185.0	−	53185.0i	−1.25211	−	1.25211i	−0.297341	−	0.954771i	$-0.596100\pi$
$72$	−1219.58			−0.0277256
$73$			37779.3i			0.829749i	0.909879	+	0.414875i	$0.136175\pi$
$73$			37779.3i			0.829749i	−0.909879	+	0.414875i	$0.863825\pi$
$74$			1244.45i			0.0264178i
$75$	−71247.7	−	71247.7i	−1.46257	−	1.46257i
$76$	42150.8	−	42150.8i	0.837090	−	0.837090i
$77$		−	47846.1i		−	0.919644i
$78$	235.633			0.00438531
$79$	−34928.5	−	34928.5i	−0.629669	−	0.629669i	0.318316	−	0.947985i	$-0.396883\pi$
$79$	−34928.5	−	34928.5i	−0.629669	−	0.629669i	−0.947985	+	0.318316i	$0.896883\pi$
$80$			92636.1i			1.61829i
$81$	73009.1			1.23642
$82$	691.422	−	1182.01i	0.0113556	−	0.0194128i
$83$	−58165.7			−0.926770			−0.463385	−	0.886157i	$-0.653365\pi$
$83$	−58165.7			−0.926770			−0.463385	+	0.886157i	$0.653365\pi$
$84$		−	122762.i		−	1.89831i
$85$	−58019.2	−	58019.2i	−0.871013	−	0.871013i
$86$	−196.436			−0.00286401
$87$		−	66931.9i		−	0.948058i
$88$	−1422.10	+	1422.10i	−0.0195760	+	0.0195760i
$89$	37358.7	+	37358.7i	0.499938	+	0.499938i	0.911419	−	0.411480i	$-0.134988\pi$
$89$	37358.7	+	37358.7i	0.499938	+	0.499938i	−0.411480	+	0.911419i	$0.634988\pi$
$90$		−	1726.96i		−	0.0224737i
$91$			18097.1i			0.229090i
$92$	133290.			1.64183
$93$	−68978.8	−	68978.8i	−0.827005	−	0.827005i
$94$	−194.893	−	194.893i	−0.00227497	−	0.00227497i
$95$	119403.	+	119403.i	1.35740	+	1.35740i
$96$	−5473.66	+	5473.66i	−0.0606177	+	0.0606177i
$97$	−89914.2	+	89914.2i	−0.970284	+	0.970284i	−0.999571	−	0.0292870i	$-0.990676\pi$
$97$	−89914.2	+	89914.2i	−0.970284	+	0.970284i	0.0292870	+	0.999571i	$0.490676\pi$
$98$	−2633.09			−0.0276949
$99$	−26174.0	+	26174.0i	−0.268400	+	0.268400i
$100$	−162599.			−1.62599
$101$	−17987.7	+	17987.7i	−0.175458	+	0.175458i	−0.789373	−	0.613914i	$-0.789594\pi$
$101$	−17987.7	+	17987.7i	−0.175458	+	0.175458i	0.613914	+	0.789373i	$0.289594\pi$
$102$		−	2283.56i		−	0.0217326i
$103$			70016.8i			0.650293i	0.945664	+	0.325147i	$0.105414\pi$
$103$			70016.8i			0.650293i	−0.945664	+	0.325147i	$0.894586\pi$
$104$	537.890	−	537.890i	0.00487652	−	0.00487652i
$105$	347755.			3.07823
$106$	845.174	−	845.174i	0.00730603	−	0.00730603i
$107$	−48210.6			−0.407083			−0.203542	−	0.979066i	$-0.565245\pi$
$107$	−48210.6			−0.407083			−0.203542	+	0.979066i	$0.565245\pi$
$108$	41766.4	−	41766.4i	0.344562	−	0.344562i
$109$	−61736.3	+	61736.3i	−0.497707	+	0.497707i	−0.910724	−	0.413016i	$-0.864475\pi$
$109$	−61736.3	+	61736.3i	−0.497707	+	0.497707i	0.413016	+	0.910724i	$0.364475\pi$
$110$	−2013.73	−	2013.73i	−0.0158679	−	0.0158679i
$111$	137086.	+	137086.i	1.05605	+	1.05605i
$112$	−140011.	−	140011.i	−1.05467	−	1.05467i
$113$	−15004.7			−0.110543			−0.0552715	−	0.998471i	$-0.517602\pi$
$113$	−15004.7			−0.110543			−0.0552715	+	0.998471i	$0.517602\pi$
$114$			4699.54i			0.0338683i
$115$			377577.i			2.66233i
$116$	−76374.9	−	76374.9i	−0.526994	−	0.526994i
$117$	9899.94	−	9899.94i	0.0668603	−	0.0668603i
$118$			4963.09i			0.0328131i
$119$	175382.			1.13532
$120$	−10336.2	−	10336.2i	−0.0655248	−	0.0655248i
$121$		−	100010.i		−	0.620985i
$122$	6057.37			0.0368455
$123$	−54042.5	−	206374.i	−0.322087	−	1.22996i
$124$	−157421.			−0.919409
$125$		−	177471.i		−	1.01590i
$126$	2610.14	+	2610.14i	0.0146466	+	0.0146466i
$127$	−145505.			−0.800514			−0.400257	−	0.916403i	$-0.631079\pi$
$127$	−145505.			−0.800514			−0.400257	+	0.916403i	$0.631079\pi$
$128$			16654.3i			0.0898467i
$129$	−21639.0	+	21639.0i	−0.114489	+	0.114489i
$130$	761.663	+	761.663i	0.00395280	+	0.00395280i
$131$			337967.i			1.72066i	0.509735	+	0.860331i	$0.329743\pi$
$131$			337967.i			1.72066i	−0.509735	+	0.860331i	$0.670257\pi$
$132$			156617.i			0.782354i
$133$	−360934.			−1.76929
$134$	−4444.64	−	4444.64i	−0.0213833	−	0.0213833i
$135$	118314.	+	118314.i	0.558729	+	0.558729i
$136$	−5212.77	−	5212.77i	−0.0241669	−	0.0241669i
$137$	80407.1	−	80407.1i	0.366010	−	0.366010i	−0.500010	−	0.866020i	$-0.666670\pi$
$137$	80407.1	−	80407.1i	0.366010	−	0.366010i	0.866020	+	0.500010i	$0.166670\pi$
$138$	−7430.46	+	7430.46i	−0.0332137	+	0.0332137i
$139$	445249.			1.95464			0.977319	−	0.211774i	$-0.0679240\pi$
$139$	445249.			1.95464			0.977319	+	0.211774i	$0.0679240\pi$
$140$	396818.	−	396818.i	1.71108	−	1.71108i
$141$	−42938.0			−0.181884
$142$	6766.36	−	6766.36i	0.0281601	−	0.0281601i
$143$		−	23087.8i		−	0.0944152i
$144$			153185.i			0.615616i
$145$	216352.	−	216352.i	0.854555	−	0.854555i
$146$	−4806.41			−0.0186611
$147$	−290056.	+	290056.i	−1.10710	+	1.10710i
$148$	312853.			1.17405
$149$	−110883.	+	110883.i	−0.409167	+	0.409167i	−0.881448	−	0.472281i	$-0.843431\pi$
$149$	−110883.	+	110883.i	−0.409167	+	0.409167i	0.472281	+	0.881448i	$0.343431\pi$
$150$	9064.35	−	9064.35i	0.0328934	−	0.0328934i
$151$	−205636.	−	205636.i	−0.733933	−	0.733933i	0.237463	−	0.971396i	$-0.423684\pi$
$151$	−205636.	−	205636.i	−0.733933	−	0.733933i	−0.971396	+	0.237463i	$0.923684\pi$
$152$	10727.8	+	10727.8i	0.0376620	+	0.0376620i
$153$	−95941.8	−	95941.8i	−0.331344	−	0.331344i
$154$	6087.13			0.0206829
$155$		−	445936.i		−	1.49088i
$156$		−	59238.0i		−	0.194890i
$157$	−105840.	−	105840.i	−0.342690	−	0.342690i	0.514688	−	0.857378i	$-0.327908\pi$
$157$	−105840.	−	105840.i	−0.342690	−	0.342690i	−0.857378	+	0.514688i	$0.827908\pi$
$158$	4443.72	−	4443.72i	0.0141613	−	0.0141613i
$159$		−	186206.i		−	0.584117i
$160$	−35386.2			−0.109278
$161$	−570674.	−	570674.i	−1.73509	−	1.73509i
$162$			9288.45i			0.0278071i
$163$	−469926.			−1.38535			−0.692676	−	0.721248i	$-0.743569\pi$
$163$	−469926.			−1.38535			−0.692676	+	0.721248i	$0.743569\pi$
$164$	−297157.	−	173823.i	−0.862733	−	0.504659i
$165$	−443657.			−1.26864
$166$		−	7400.03i		−	0.0208431i
$167$	483125.	+	483125.i	1.34050	+	1.34050i	0.895557	+	0.444948i	$0.146778\pi$
$167$	483125.	+	483125.i	1.34050	+	1.34050i	0.444948	+	0.895557i	$0.353222\pi$
$168$	31244.3			0.0854078
$169$		−	362560.i		−	0.976481i
$170$	7381.39	−	7381.39i	0.0195892	−	0.0195892i
$171$	197447.	+	197447.i	0.516370	+	0.516370i
$172$			49383.9i			0.127281i
$173$		−	44116.0i		−	0.112068i	−0.998429	−	0.0560339i	$-0.982155\pi$
$173$		−	44116.0i		−	0.112068i	0.998429	−	0.0560339i	$-0.0178455\pi$
$174$	8515.29			0.0213219
$175$	696160.	+	696160.i	1.71836	+	1.71836i
$176$	178622.	+	178622.i	0.434664	+	0.434664i
$177$	546725.	+	546725.i	1.31170	+	1.31170i
$178$	−4752.89	+	4752.89i	−0.0112437	+	0.0112437i
$179$	154212.	−	154212.i	0.359737	−	0.359737i	−0.503979	−	0.863716i	$-0.668131\pi$
$179$	154212.	−	154212.i	0.359737	−	0.359737i	0.863716	+	0.503979i	$0.168131\pi$
$180$	−434156.			−0.998767
$181$	20765.2	−	20765.2i	0.0471130	−	0.0471130i	−0.683158	−	0.730271i	$-0.739394\pi$
$181$	20765.2	−	20765.2i	0.0471130	−	0.0471130i	0.730271	+	0.683158i	$0.239394\pi$
$182$	−2302.37			−0.00515224
$183$	667268.	−	667268.i	1.47290	−	1.47290i
$184$			33923.7i			0.0738683i
$185$			886237.i			1.90380i
$186$	8775.70	−	8775.70i	0.0185994	−	0.0185994i
$187$	−223747.			−0.467900
$188$	−48995.9	+	48995.9i	−0.101103	+	0.101103i
$189$	−357641.			−0.728272
$190$	−15190.8	+	15190.8i	−0.0305280	+	0.0305280i
$191$	−98344.1	+	98344.1i	−0.195059	+	0.195059i	−0.797878	−	0.602819i	$-0.794044\pi$
$191$	−98344.1	+	98344.1i	−0.195059	+	0.195059i	0.602819	+	0.797878i	$0.294044\pi$
$192$	457840.	+	457840.i	0.896314	+	0.896314i
$193$	−107375.	−	107375.i	−0.207497	−	0.207497i	0.595706	−	0.803203i	$-0.296872\pi$
$193$	−107375.	−	107375.i	−0.207497	−	0.207497i	−0.803203	+	0.595706i	$0.796872\pi$
$194$	−11439.2	−	11439.2i	−0.0218218	−	0.0218218i
$195$	167807.			0.316026
$196$			661956.i			1.23080i
$197$		−	221487.i		−	0.406615i	−0.979115	−	0.203307i	$-0.934831\pi$
$197$		−	221487.i		−	0.406615i	0.979115	−	0.203307i	$-0.0651691\pi$
$198$	−3329.94	−	3329.94i	−0.00603634	−	0.00603634i
$199$	68076.6	−	68076.6i	0.121861	−	0.121861i	−0.643546	−	0.765407i	$-0.722538\pi$
$199$	68076.6	−	68076.6i	0.121861	−	0.121861i	0.765407	+	0.643546i	$0.222538\pi$
$200$		−	41383.2i		−	0.0731559i
$201$	−979227.			−1.70959
$202$	−2288.46	−	2288.46i	−0.00394607	−	0.00394607i
$203$			653991.i			1.11386i
$204$	−574084.			−0.965829
$205$	492398.	−	841774.i	0.818337	−	1.39898i
$206$	−8907.76			−0.0146252
$207$			624370.i			1.01278i
$208$	−67561.3	−	67561.3i	−0.108278	−	0.108278i
$209$	460470.			0.729181
$210$			44242.6i			0.0692296i
$211$	244315.	−	244315.i	0.377785	−	0.377785i	−0.492518	−	0.870302i	$-0.663923\pi$
$211$	244315.	−	244315.i	0.377785	−	0.377785i	0.870302	+	0.492518i	$0.163923\pi$
$212$	−212476.	−	212476.i	−0.324691	−	0.324691i
$213$		−	1.49074e6i		−	2.25140i
$214$		−	6133.51i		−	0.00915534i
$215$	−139893.			−0.206395
$216$	10630.0	+	10630.0i	0.0155024	+	0.0155024i
$217$	673991.	+	673991.i	0.971639	+	0.971639i
$218$	−7854.28	−	7854.28i	−0.0111935	−	0.0111935i
$219$	−529465.	+	529465.i	−0.745979	+	0.745979i
$220$	−506250.	+	506250.i	−0.705193	+	0.705193i
$221$	84629.1			0.116557
$222$	−17440.5	+	17440.5i	−0.0237507	+	0.0237507i
$223$	−883416.			−1.18961			−0.594803	−	0.803872i	$-0.702770\pi$
$223$	−883416.			−1.18961			−0.594803	+	0.803872i	$0.702770\pi$
$224$	53483.0	−	53483.0i	0.0712190	−	0.0712190i
$225$		−	761664.i		−	1.00301i
$226$		−	1908.95i		−	0.00248612i
$227$	−871192.	+	871192.i	−1.12215	+	1.12215i	−0.130728	+	0.991418i	$0.541731\pi$
$227$	−871192.	+	871192.i	−1.12215	+	1.12215i	−0.991418	+	0.130728i	$0.958269\pi$
$228$	1.18146e6			1.50516
$229$	1.02386e6	−	1.02386e6i	1.29019	−	1.29019i	0.355518	−	0.934669i	$-0.384304\pi$
$229$	1.02386e6	−	1.02386e6i	1.29019	−	1.29019i	0.934669	−	0.355518i	$-0.115696\pi$
$230$	−48036.6			−0.0598760
$231$	670547.	−	670547.i	0.826798	−	0.826798i
$232$	19438.2	−	19438.2i	0.0237103	−	0.0237103i
$233$	−272172.	−	272172.i	−0.328438	−	0.328438i	0.523554	−	0.851992i	$-0.324606\pi$
$233$	−272172.	−	272172.i	−0.328438	−	0.328438i	−0.851992	+	0.523554i	$0.824606\pi$
$234$	1259.50	+	1259.50i	0.00150369	+	0.00150369i
$235$	−138793.	−	138793.i	−0.163945	−	0.163945i
$236$	1.24772e6			1.45826
$237$		−	979024.i		−	1.13220i
$238$			22312.6i			0.0255333i
$239$	65400.5	+	65400.5i	0.0740605	+	0.0740605i	0.743167	−	0.669106i	$-0.233323\pi$
$239$	65400.5	+	65400.5i	0.0740605	+	0.0740605i	−0.669106	+	0.743167i	$0.733323\pi$
$240$	−1.29826e6	+	1.29826e6i	−1.45491	+	1.45491i
$241$			1.20325e6i			1.33448i	0.744843	+	0.667240i	$0.232525\pi$
$241$			1.20325e6i			1.33448i	−0.744843	+	0.667240i	$0.767475\pi$
$242$	12723.6			0.0139660
$243$	705875.	+	705875.i	0.766853	+	0.766853i
$244$		−	1.52282e6i		−	1.63747i
$245$	−1.87516e6			−1.99583
$246$	26255.6	−	6875.46i	0.0276620	−	0.00724376i
$247$	−174166.			−0.181644
$248$		−	40065.4i		−	0.0413657i
$249$	−815173.	−	815173.i	−0.833205	−	0.833205i
$250$	22578.4			0.0228478
$251$			176006.i			0.176337i	0.996106	+	0.0881683i	$0.0281013\pi$
$251$			176006.i			0.176337i	−0.996106	+	0.0881683i	$0.971899\pi$
$252$	656186.	−	656186.i	0.650917	−	0.650917i
$253$	728050.	+	728050.i	0.715089	+	0.715089i
$254$		−	18511.6i		−	0.0180036i
$255$		−	1.62624e6i		−	1.56615i
$256$	1.04328e6			0.994946
$257$	182604.	+	182604.i	0.172456	+	0.172456i	0.788058	−	0.615601i	$-0.211087\pi$
$257$	182604.	+	182604.i	0.172456	+	0.172456i	−0.615601	+	0.788058i	$0.711087\pi$
$258$	−2752.99	−	2752.99i	−0.00257487	−	0.00257487i
$259$	−1.33947e6	−	1.33947e6i	−1.24074	−	1.24074i
$260$	191482.	−	191482.i	0.175668	−	0.175668i
$261$	357763.	−	357763.i	0.325083	−	0.325083i
$262$	−42997.2			−0.0386979
$263$	439385.	−	439385.i	0.391702	−	0.391702i	−0.483592	−	0.875294i	$-0.660668\pi$
$263$	439385.	−	439385.i	0.391702	−	0.391702i	0.875294	+	0.483592i	$0.160668\pi$
$264$	−39860.6			−0.0351993
$265$	601893.	−	601893.i	0.526508	−	0.526508i
$266$		−	45919.1i		−	0.0397914i
$267$			1.04714e6i			0.898930i
$268$	−1.11738e6	+	1.11738e6i	−0.950306	+	0.950306i
$269$	−1.65744e6			−1.39655			−0.698277	−	0.715828i	$-0.746050\pi$
$269$	−1.65744e6			−1.39655			−0.698277	+	0.715828i	$0.746050\pi$
$270$	−15052.3	+	15052.3i	−0.0125659	+	0.0125659i
$271$	−477414.			−0.394886			−0.197443	−	0.980314i	$-0.563264\pi$
$271$	−477414.			−0.394886			−0.197443	+	0.980314i	$0.563264\pi$
$272$	−654746.	+	654746.i	−0.536600	+	0.536600i
$273$	−253625.	+	253625.i	−0.205961	+	0.205961i
$274$	10229.6	+	10229.6i	0.00823160	+	0.00823160i
$275$	−888143.	−	888143.i	−0.708192	−	0.708192i
$276$	1.86801e6	+	1.86801e6i	1.47607	+	1.47607i
$277$	1.48311e6			1.16138			0.580691	−	0.814124i	$-0.302782\pi$
$277$	1.48311e6			1.16138			0.580691	+	0.814124i	$0.302782\pi$
$278$			56646.0i			0.0439600i
$279$		−	737409.i		−	0.567150i
$280$	100994.	+	100994.i	0.0769843	+	0.0769843i
$281$	1.25310e6	−	1.25310e6i	0.946714	−	0.946714i	−0.0519360	−	0.998650i	$-0.516539\pi$
$281$	1.25310e6	−	1.25310e6i	0.946714	−	0.946714i	0.998650	+	0.0519360i	$0.0165392\pi$
$282$		−	5462.71i		−	0.00409059i
$283$	1.84658e6			1.37057			0.685285	−	0.728275i	$-0.259678\pi$
$283$	1.84658e6			1.37057			0.685285	+	0.728275i	$0.259678\pi$
$284$	−1.70106e6	−	1.70106e6i	−1.25148	−	1.25148i
$285$			3.34679e6i			2.44071i
$286$	2937.30			0.00212341
$287$	528049.	+	2.01648e6i	0.378416	+	1.44507i
$288$	−58515.4			−0.0415708
$289$			599704.i			0.422370i
$290$	27524.9	+	27524.9i	0.0192190	+	0.0192190i
$291$	−2.52024e6			−1.74465
$292$			1.20833e6i			0.829330i
$293$	25777.6	−	25777.6i	0.0175418	−	0.0175418i	−0.698281	−	0.715823i	$-0.746052\pi$
$293$	25777.6	−	25777.6i	0.0175418	−	0.0175418i	0.715823	+	0.698281i	$0.246052\pi$
$294$	−36901.9	−	36901.9i	−0.0248989	−	0.0248989i
$295$			3.53448e6i			2.36467i
$296$			79624.5i			0.0528223i
$297$	456269.			0.300144
$298$	−14106.9	−	14106.9i	−0.00920219	−	0.00920219i
$299$	−275374.	−	275374.i	−0.178133	−	0.178133i
$300$	−2.27877e6	−	2.27877e6i	−1.46183	−	1.46183i
$301$	211435.	−	211435.i	0.134512	−	0.134512i
$302$	26161.6	−	26161.6i	0.0165062	−	0.0165062i
$303$	−504185.			−0.315488
$304$	1.34746e6	−	1.34746e6i	0.836243	−	0.836243i
$305$	4.31377e6			2.65526
$306$	12206.0	−	12206.0i	0.00745196	−	0.00745196i
$307$			774866.i			0.469224i	0.972089	+	0.234612i	$0.0753820\pi$
$307$			774866.i			0.469224i	−0.972089	+	0.234612i	$0.924618\pi$
$308$		−	1.53030e6i		−	0.919179i
$309$	−981262.	+	981262.i	−0.584640	+	0.584640i
$310$	56733.4			0.0335301
$311$	−372059.	+	372059.i	−0.218128	+	0.218128i	−0.807709	−	0.589581i	$-0.799293\pi$
$311$	−372059.	+	372059.i	−0.218128	+	0.218128i	0.589581	+	0.807709i	$0.299293\pi$
$312$	15076.7			0.00876839
$313$	1.53103e6	−	1.53103e6i	0.883330	−	0.883330i	−0.110542	−	0.993871i	$-0.535259\pi$
$313$	1.53103e6	−	1.53103e6i	0.883330	−	0.883330i	0.993871	+	0.110542i	$0.0352586\pi$
$314$	13465.3	−	13465.3i	0.00770713	−	0.00770713i
$315$	1.85882e6	+	1.85882e6i	1.05550	+	1.05550i
$316$	−1.11715e6	−	1.11715e6i	−0.629351	−	0.629351i
$317$	102608.	+	102608.i	0.0573498	+	0.0573498i	0.735200	−	0.677850i	$-0.237088\pi$
$317$	102608.	+	102608.i	0.0573498	+	0.0573498i	−0.677850	+	0.735200i	$0.737088\pi$
$318$	23689.7			0.0131368
$319$		−	834344.i		−	0.459059i
$320$			2.95985e6i			1.61583i
$321$	−675656.	−	675656.i	−0.365985	−	0.365985i
$322$	72602.9	−	72602.9i	0.0390224	−	0.0390224i
$323$			1.68787e6i			0.900185i
$324$	2.33511e6			1.23579
$325$	335927.	+	335927.i	0.176415	+	0.176415i
$326$		−	59785.5i		−	0.0311567i
$327$	−1.73043e6			−0.894919
$328$	44239.8	−	75629.7i	0.0227054	−	0.0388157i
$329$	419547.			0.213693
$330$		−	56443.5i		−	0.0285318i
$331$	730608.	+	730608.i	0.366534	+	0.366534i	0.866212	−	0.499677i	$-0.166548\pi$
$331$	730608.	+	730608.i	0.366534	+	0.366534i	−0.499677	+	0.866212i	$0.666548\pi$
$332$	−1.86036e6			−0.926301
$333$			1.46550e6i			0.724228i
$334$	−61464.7	+	61464.7i	−0.0301481	+	0.0301481i
$335$	−3.16526e6	−	3.16526e6i	−1.54098	−	1.54098i
$336$		−	3.92441e6i		−	1.89639i
$337$			331091.i			0.158808i	0.996843	+	0.0794039i	$0.0253017\pi$
$337$			331091.i			0.158808i	−0.996843	+	0.0794039i	$0.974698\pi$
$338$	46126.1			0.0219611
$339$	−210286.	−	210286.i	−0.0993827	−	0.0993827i
$340$	−1.85568e6	−	1.85568e6i	−0.870572	−	0.870572i
$341$	−859860.	−	859860.i	−0.400444	−	0.400444i
$342$	−25119.9	+	25119.9i	−0.0116132	+	0.0116132i
$343$	532631.	−	532631.i	0.244451	−	0.244451i
$344$	−12568.7			−0.00572658
$345$	−5.29162e6	+	5.29162e6i	−2.39354	+	2.39354i
$346$	5612.57			0.00252041
$347$	779469.	−	779469.i	0.347516	−	0.347516i	−0.511667	−	0.859184i	$-0.670972\pi$
$347$	779469.	−	779469.i	0.347516	−	0.347516i	0.859184	+	0.511667i	$0.170972\pi$
$348$		−	2.14074e6i		−	0.947579i
$349$		−	2.80104e6i		−	1.23099i	−0.788139	−	0.615497i	$-0.788955\pi$
$349$		−	2.80104e6i		−	1.23099i	0.788139	−	0.615497i	$-0.211045\pi$
$350$	−88567.7	+	88567.7i	−0.0386461	+	0.0386461i
$351$	−172577.			−0.0747680
$352$	−68232.2	+	68232.2i	−0.0293517	+	0.0293517i
$353$	−1.35597e6			−0.579178			−0.289589	−	0.957151i	$-0.593519\pi$
$353$	−1.35597e6			−0.579178			−0.289589	+	0.957151i	$0.593519\pi$
$354$	−69556.1	+	69556.1i	−0.0295003	+	0.0295003i
$355$	4.81869e6	−	4.81869e6i	2.02935	−	2.02935i
$356$	1.19487e6	+	1.19487e6i	0.499685	+	0.499685i
$357$	2.45791e6	+	2.45791e6i	1.02070	+	1.02070i
$358$	19619.3	+	19619.3i	0.00809053	+	0.00809053i
$359$	−414706.			−0.169826			−0.0849130	−	0.996388i	$-0.527061\pi$
$359$	−414706.			−0.169826			−0.0849130	+	0.996388i	$0.527061\pi$
$360$		−	110497.i		−	0.0449361i
$361$		−	997518.i		−	0.402859i
$362$	2641.82	+	2641.82i	0.00105958	+	0.00105958i
$363$	1.40161e6	−	1.40161e6i	0.558291	−	0.558291i
$364$			578814.i			0.228974i
$365$	−3.42290e6			−1.34481
$366$	84892.0	+	84892.0i	0.0331256	+	0.0331256i
$367$			291371.i			0.112923i	0.998405	+	0.0564613i	$0.0179818\pi$
$367$			291371.i			0.112923i	−0.998405	+	0.0564613i	$0.982018\pi$
$368$	4.26095e6			1.64016
$369$	814240.	−	1.39197e6i	0.311305	−	0.532188i
$370$	−112750.			−0.0428166
$371$			1.81941e6i			0.686272i
$372$	−2.20620e6	−	2.20620e6i	−0.826587	−	0.826587i
$373$	−1.00111e6			−0.372573			−0.186286	−	0.982495i	$-0.559645\pi$
$373$	−1.00111e6			−0.372573			−0.186286	+	0.982495i	$0.559645\pi$
$374$		−	28465.8i		−	0.0105231i
$375$	2.48720e6	−	2.48720e6i	0.913340	−	0.913340i
$376$	−12470.0	−	12470.0i	−0.00454879	−	0.00454879i
$377$			315579.i			0.114355i
$378$		−	45500.3i		−	0.0163789i
$379$	3.94147e6			1.40948			0.704742	−	0.709464i	$-0.251063\pi$
$379$	3.94147e6			1.40948			0.704742	+	0.709464i	$0.251063\pi$
$380$	3.81897e6	+	3.81897e6i	1.35671	+	1.35671i
$381$	−2.03921e6	−	2.03921e6i	−0.719696	−	0.719696i
$382$	−12511.7	−	12511.7i	−0.00438689	−	0.00438689i
$383$	−1.63277e6	+	1.63277e6i	−0.568758	+	0.568758i	−0.931780	−	0.363023i	$-0.881745\pi$
$383$	−1.63277e6	+	1.63277e6i	−0.568758	+	0.568758i	0.363023	+	0.931780i	$0.381745\pi$
$384$	−233405.	+	233405.i	−0.0807759	+	0.0807759i
$385$	4.33497e6			1.49051
$386$	13660.6	−	13660.6i	0.00466662	−	0.00466662i
$387$	−231329.			−0.0785151
$388$	−2.87580e6	+	2.87580e6i	−0.969793	+	0.969793i
$389$		−	26701.2i		−	0.00894658i	−0.999990	−	0.00447329i	$-0.998576\pi$
$389$		−	26701.2i		−	0.00894658i	0.999990	−	0.00447329i	$-0.00142390\pi$
$390$			21348.9i			0.00710746i
$391$	−2.66869e6	+	2.66869e6i	−0.882789	+	0.882789i
$392$	−168475.			−0.0553758
$393$	−4.73649e6	+	4.73649e6i	−1.54695	+	1.54695i
$394$	28178.3			0.00914480
$395$	3.16461e6	−	3.16461e6i	1.02053	−	1.02053i
$396$	−837145.	+	837145.i	−0.268264	+	0.268264i
$397$	431492.	+	431492.i	0.137403	+	0.137403i	0.772463	−	0.635060i	$-0.219025\pi$
$397$	431492.	+	431492.i	0.137403	+	0.137403i	−0.635060	+	0.772463i	$0.719025\pi$
$398$	8660.92	+	8660.92i	0.00274067	+	0.00274067i
$399$	−5.05837e6	−	5.05837e6i	−1.59066	−	1.59066i
$400$	−5.19790e6			−1.62435
$401$		−	3.00497e6i		−	0.933210i	−0.884466	−	0.466605i	$-0.845477\pi$
$401$		−	3.00497e6i		−	0.933210i	0.884466	−	0.466605i	$-0.154523\pi$
$402$		−	124580.i		−	0.0384489i
$403$	325229.	+	325229.i	0.0997533	+	0.0997533i
$404$	−575317.	+	575317.i	−0.175369	+	0.175369i
$405$			6.61480e6i			2.00391i
$406$	−83202.8			−0.0250509
$407$	1.70886e6	+	1.70886e6i	0.511351	+	0.511351i
$408$		−	146111.i		−	0.0434541i
$409$	−1.58145e6			−0.467463			−0.233731	−	0.972301i	$-0.575094\pi$
$409$	−1.58145e6			−0.467463			−0.233731	+	0.972301i	$0.575094\pi$
$410$	107093.	+	62644.5i	0.0314631	+	0.0184045i
$411$	2.25376e6			0.658116
$412$			2.23940e6i			0.649964i
$413$	−5.34204e6	−	5.34204e6i	−1.54111	−	1.54111i
$414$	−79434.3			−0.0227776
$415$		−	5.26995e6i		−	1.50206i
$416$	25807.8	−	25807.8i	0.00731170	−	0.00731170i
$417$	6.24002e6	+	6.24002e6i	1.75730	+	1.75730i
$418$			58582.4i			0.0163993i
$419$			6.47911e6i			1.80294i	0.432845	+	0.901468i	$0.357510\pi$
$419$			6.47911e6i			1.80294i	−0.432845	+	0.901468i	$0.642490\pi$
$420$	1.11225e7			3.07667
$421$	−1.81683e6	−	1.81683e6i	−0.499585	−	0.499585i	0.411724	−	0.911309i	$-0.364927\pi$
$421$	−1.81683e6	−	1.81683e6i	−0.499585	−	0.499585i	−0.911309	+	0.411724i	$0.864927\pi$
$422$	31082.6	+	31082.6i	0.00849642	+	0.00849642i
$423$	−229512.	−	229512.i	−0.0623669	−	0.0623669i
$424$	54077.4	−	54077.4i	0.0146084	−	0.0146084i
$425$	3.25552e6	−	3.25552e6i	0.874274	−	0.874274i
$426$	189657.			0.0506342
$427$	−6.51987e6	+	6.51987e6i	−1.73049	+	1.73049i
$428$	−1.54196e6			−0.406877
$429$	323568.	−	323568.i	0.0848832	−	0.0848832i
$430$		−	17797.6i		−	0.00464183i
$431$		−	832983.i		−	0.215995i	−0.994151	−	0.107997i	$-0.965556\pi$
$431$		−	832983.i		−	0.215995i	0.994151	−	0.107997i	$-0.0344438\pi$
$432$	1.33517e6	−	1.33517e6i	0.344213	−	0.344213i
$433$	555656.			0.142425			0.0712125	−	0.997461i	$-0.477313\pi$
$433$	555656.			0.142425			0.0712125	+	0.997461i	$0.477313\pi$
$434$	−85747.3	+	85747.3i	−0.0218522	+	0.0218522i
$435$	6.06419e6			1.53656
$436$	−1.97456e6	+	1.97456e6i	−0.497456	+	0.497456i
$437$	5.49215e6	−	5.49215e6i	1.37575	−	1.37575i
$438$	−67360.2	−	67360.2i	−0.0167771	−	0.0167771i
$439$	2.46473e6	+	2.46473e6i	0.610390	+	0.610390i	0.943048	−	0.332657i	$-0.107945\pi$
$439$	2.46473e6	+	2.46473e6i	0.610390	+	0.610390i	−0.332657	+	0.943048i	$0.607945\pi$
$440$	−128846.	−	128846.i	−0.0317278	−	0.0317278i
$441$	−3.10081e6			−0.759238
$442$			10766.8i			0.00262138i
$443$			430798.i			0.104295i	0.998639	+	0.0521476i	$0.0166066\pi$
$443$			430798.i			0.104295i	−0.998639	+	0.0521476i	$0.983393\pi$
$444$	4.38453e6	+	4.38453e6i	1.05552	+	1.05552i
$445$	−3.38478e6	+	3.38478e6i	−0.810272	+	0.810272i
$446$		−	112391.i		−	0.0267543i
$447$	−3.10798e6			−0.735715
$448$	−4.47355e6	−	4.47355e6i	−1.05307	−	1.05307i
$449$			648533.i			0.151816i	0.997115	+	0.0759078i	$0.0241855\pi$
$449$			648533.i			0.151816i	−0.997115	+	0.0759078i	$0.975815\pi$
$450$	96901.3			0.0225579
$451$	−673671.	−	2.57257e6i	−0.155958	−	0.595561i
$452$	−479908.			−0.110487
$453$		−	5.76384e6i		−	1.31967i
$454$	−110836.	−	110836.i	−0.0252372	−	0.0252372i
$455$	−1.63964e6			−0.371296
$456$			300694.i			0.0677194i
$457$	−5.83418e6	+	5.83418e6i	−1.30674	+	1.30674i	−0.382988	+	0.923753i	$0.625105\pi$
$457$	−5.83418e6	+	5.83418e6i	−1.30674	+	1.30674i	−0.923753	+	0.382988i	$0.874895\pi$
$458$	130259.	+	130259.i	0.0290164	+	0.0290164i
$459$			1.67247e6i			0.370533i
$460$			1.20764e7i			2.66098i
$461$	−2.32262e6			−0.509009			−0.254505	−	0.967072i	$-0.581912\pi$
$461$	−2.32262e6			−0.509009			−0.254505	+	0.967072i	$0.581912\pi$
$462$	85309.2	+	85309.2i	0.0185948	+	0.0185948i
$463$	−2.57068e6	−	2.57068e6i	−0.557308	−	0.557308i	0.371232	−	0.928540i	$-0.378935\pi$
$463$	−2.57068e6	−	2.57068e6i	−0.557308	−	0.557308i	−0.928540	+	0.371232i	$0.878935\pi$
$464$	−2.44152e6	−	2.44152e6i	−0.526461	−	0.526461i
$465$	6.24964e6	−	6.24964e6i	1.34036	−	1.34036i
$466$	34626.6	−	34626.6i	0.00738661	−	0.00738661i
$467$	3.64734e6			0.773898			0.386949	−	0.922101i	$-0.373529\pi$
$467$	3.64734e6			0.773898			0.386949	+	0.922101i	$0.373529\pi$
$468$	316638.	−	316638.i	0.0668264	−	0.0668264i
$469$	9.56801e6			2.00858
$470$	17657.7	−	17657.7i	0.00368715	−	0.00368715i
$471$		−	2.96663e6i		−	0.616185i
$472$			317557.i			0.0656096i
$473$	−269743.	+	269743.i	−0.0554367	+	0.0554367i
$474$	124554.			0.0254632
$475$	−6.69983e6	+	6.69983e6i	−1.36248	+	1.36248i
$476$	5.60937e6			1.13474
$477$	995303.	−	995303.i	0.200290	−	0.200290i
$478$	−8320.46	+	8320.46i	−0.00166563	+	0.00166563i
$479$	3.15232e6	+	3.15232e6i	0.627757	+	0.627757i	0.947503	−	0.319746i	$-0.103598\pi$
$479$	3.15232e6	+	3.15232e6i	0.627757	+	0.627757i	−0.319746	+	0.947503i	$0.603598\pi$
$480$	−495926.	−	495926.i	−0.0982458	−	0.0982458i
$481$	−646350.	−	646350.i	−0.127381	−	0.127381i
$482$	−153081.			−0.0300126
$483$		−	1.59956e7i		−	3.11984i
$484$		−	3.19871e6i		−	0.620671i
$485$	−8.14644e6	−	8.14644e6i	−1.57258	−	1.57258i
$486$	−89803.7	+	89803.7i	−0.0172466	+	0.0172466i
$487$		−	3.72388e6i		−	0.711497i	−0.934582	−	0.355749i	$-0.884226\pi$
$487$		−	3.72388e6i		−	0.711497i	0.934582	−	0.355749i	$-0.115774\pi$
$488$	387574.			0.0736724
$489$	−6.58586e6	−	6.58586e6i	−1.24549	−	1.24549i
$490$		−	238564.i		−	0.0448864i
$491$	1.48238e6			0.277496			0.138748	−	0.990328i	$-0.455692\pi$
$491$	1.48238e6			0.277496			0.138748	+	0.990328i	$0.455692\pi$
$492$	−1.72849e6	−	6.60063e6i	−0.321924	−	1.22934i
$493$	3.05832e6			0.566716
$494$		−	22157.9i		−	0.00408519i
$495$	−2.37143e6	−	2.37143e6i	−0.435008	−	0.435008i
$496$	−5.03238e6			−0.918479
$497$			1.45660e7i			2.64515i
$498$	103709.	−	103709.i	0.0187388	−	0.0187388i
$499$	−7.24072e6	−	7.24072e6i	−1.30176	−	1.30176i	−0.927206	−	0.374553i	$-0.877796\pi$
$499$	−7.24072e6	−	7.24072e6i	−1.30176	−	1.30176i	−0.374553	−	0.927206i	$-0.622204\pi$
$500$		−	5.67620e6i		−	1.01539i
$501$			1.35417e7i			2.41034i
$502$	−22392.0			−0.00396583
$503$	5.73763e6	+	5.73763e6i	1.01114	+	1.01114i	0.999937	+	0.0112051i	$0.00356677\pi$
$503$	5.73763e6	+	5.73763e6i	1.01114	+	1.01114i	0.0112051	+	0.999937i	$0.496433\pi$
$504$	167007.	+	167007.i	0.0292858	+	0.0292858i
$505$	−1.62973e6	−	1.62973e6i	−0.284373	−	0.284373i
$506$	−92624.9	+	92624.9i	−0.0160824	+	0.0160824i
$507$	5.08116e6	−	5.08116e6i	0.877897	−	0.877897i
$508$	−4.65381e6			−0.800110
$509$	5.20793e6	−	5.20793e6i	0.890986	−	0.890986i	−0.103630	−	0.994616i	$-0.533046\pi$
$509$	5.20793e6	−	5.20793e6i	0.890986	−	0.890986i	0.994616	+	0.103630i	$0.0330458\pi$
$510$	206896.			0.0352229
$511$	5.17339e6	−	5.17339e6i	0.876442	−	0.876442i
$512$			665667.i			0.112223i
$513$		−	3.44193e6i		−	0.577443i
$514$	−23231.5	+	23231.5i	−0.00387855	+	0.00387855i
$515$	−6.34369e6			−1.05396
$516$	−692099.	+	692099.i	−0.114431	+	0.114431i
$517$	−535247.			−0.0880700
$518$	170411.	−	170411.i	0.0279045	−	0.0279045i
$519$	618271.	−	618271.i	0.100754	−	0.100754i
$520$	48734.1	+	48734.1i	0.00790360	+	0.00790360i
$521$	2.65221e6	+	2.65221e6i	0.428069	+	0.428069i	0.887970	−	0.459901i	$-0.152115\pi$
$521$	2.65221e6	+	2.65221e6i	0.428069	+	0.428069i	−0.459901	+	0.887970i	$0.652115\pi$
$522$	45515.8	+	45515.8i	0.00731115	+	0.00731115i
$523$	3.28892e6			0.525773			0.262887	−	0.964827i	$-0.415325\pi$
$523$	3.28892e6			0.525773			0.262887	+	0.964827i	$0.415325\pi$
$524$			1.08095e7i			1.71979i
$525$			1.95129e7i			3.08975i
$526$	55899.9	+	55899.9i	0.00880941	+	0.00880941i
$527$	3.15185e6	−	3.15185e6i	0.494354	−	0.494354i
$528$			5.00666e6i			0.781562i
$529$	1.09310e7			1.69832
$530$	76574.8	+	76574.8i	0.0118412	+	0.0118412i
$531$			5.84469e6i			0.899550i
$532$	−1.15440e7			−1.76839
$533$	254806.	+	973037.i	0.0388501	+	0.148358i
$534$	−133220.			−0.0202170
$535$		−	4.36799e6i		−	0.659778i
$536$	−284385.	−	284385.i	−0.0427558	−	0.0427558i
$537$	4.32246e6			0.646838
$538$		−	210865.i		−	0.0314086i
$539$	−3.61571e6	+	3.61571e6i	−0.536071	+	0.536071i
$540$	3.78413e6	+	3.78413e6i	0.558447	+	0.558447i
$541$		−	1.97799e6i		−	0.290557i	−0.989391	−	0.145278i	$-0.953592\pi$
$541$		−	1.97799e6i		−	0.290557i	0.989391	−	0.145278i	$-0.0464078\pi$
$542$		−	60738.1i		−	0.00888103i
$543$	582036.			0.0847130
$544$	−250108.	−	250108.i	−0.0362351	−	0.0362351i
$545$	−5.59345e6	−	5.59345e6i	−0.806657	−	0.806657i
$546$	−32266.9	−	32266.9i	−0.00463208	−	0.00463208i
$547$	4.15148e6	−	4.15148e6i	0.593246	−	0.593246i	−0.345261	−	0.938507i	$-0.612210\pi$
$547$	4.15148e6	−	4.15148e6i	0.593246	−	0.593246i	0.938507	+	0.345261i	$0.112210\pi$
$548$	2.57172e6	−	2.57172e6i	0.365825	−	0.365825i
$549$	7.13334e6			1.01010
$550$	112992.	−	112992.i	0.0159273	−	0.0159273i
$551$	−6.29399e6			−0.883176
$552$	−475429.	+	475429.i	−0.0664107	+	0.0664107i
$553$			9.56603e6i			1.33021i
$554$			188686.i			0.0261196i
$555$	−1.24203e7	+	1.24203e7i	−1.71159	+	1.71159i
$556$	1.42408e7			1.95365
$557$	−1.02551e6	+	1.02551e6i	−0.140057	+	0.140057i	−0.773659	−	0.633602i	$-0.781576\pi$
$557$	−1.02551e6	+	1.02551e6i	−0.140057	+	0.140057i	0.633602	+	0.773659i	$0.281576\pi$
$558$	93815.5			0.0127552
$559$	102026.	−	102026.i	0.0138096	−	0.0138096i
$560$	1.26853e7	−	1.26853e7i	1.70935	−	1.70935i
$561$	−3.13574e6	−	3.13574e6i	−0.420662	−	0.420662i
$562$	159423.	+	159423.i	0.0212917	+	0.0212917i
$563$	3.60169e6	+	3.60169e6i	0.478889	+	0.478889i	0.904776	−	0.425887i	$-0.140038\pi$
$563$	3.60169e6	+	3.60169e6i	0.478889	+	0.478889i	−0.425887	+	0.904776i	$0.640038\pi$
$564$	−1.37332e6			−0.181792
$565$		−	1.35946e6i		−	0.179162i
$566$			234927.i			0.0308242i
$567$	−9.99766e6	−	9.99766e6i	−1.30599	−	1.30599i
$568$	432938.	−	432938.i	0.0563060	−	0.0563060i
$569$			1.07623e7i			1.39356i	0.717285	+	0.696780i	$0.245385\pi$
$569$			1.07623e7i			1.39356i	−0.717285	+	0.696780i	$0.754615\pi$
$570$	−425789.			−0.0548918
$571$	1.43844e6	+	1.43844e6i	0.184630	+	0.184630i	0.793370	−	0.608740i	$-0.208325\pi$
$571$	1.43844e6	+	1.43844e6i	0.184630	+	0.184630i	−0.608740	+	0.793370i	$0.708325\pi$
$572$		−	738435.i		−	0.0943675i
$573$	−2.75652e6			−0.350732
$574$	−256543.	+	67180.1i	−0.0324998	+	0.00851061i
$575$	−2.11862e7			−2.67230
$576$			4.89447e6i			0.614681i
$577$	−9.04138e6	−	9.04138e6i	−1.13056	−	1.13056i	−0.990083	−	0.140481i	$-0.955135\pi$
$577$	−9.04138e6	−	9.04138e6i	−1.13056	−	1.13056i	−0.140481	−	0.990083i	$-0.544865\pi$
$578$	−76296.3			−0.00949913
$579$		−	3.00966e6i		−	0.373097i
$580$	6.91975e6	−	6.91975e6i	0.854123	−	0.854123i
$581$	7.96505e6	+	7.96505e6i	0.978922	+	0.978922i
$582$		−	320632.i		−	0.0392374i
$583$		−	2.32116e6i		−	0.282835i
$584$	−307532.			−0.0373128
$585$	896958.	+	896958.i	0.108363	+	0.108363i
$586$	3279.51	+	3279.51i	0.000394516	+	0.000394516i
$587$	2.26518e6	+	2.26518e6i	0.271336	+	0.271336i	0.829638	−	0.558302i	$-0.188547\pi$
$587$	2.26518e6	+	2.26518e6i	0.271336	+	0.271336i	−0.558302	+	0.829638i	$0.688547\pi$
$588$	−9.27710e6	+	9.27710e6i	−1.10654	+	1.10654i
$589$	−6.48647e6	+	6.48647e6i	−0.770407	+	0.770407i
$590$	−449668.			−0.0531817
$591$	3.10407e6	−	3.10407e6i	0.365564	−	0.365564i
$592$	1.00012e7			1.17286
$593$	1.03816e7	−	1.03816e7i	1.21235	−	1.21235i	0.242100	−	0.970251i	$-0.422164\pi$
$593$	1.03816e7	−	1.03816e7i	1.21235	−	1.21235i	0.970251	−	0.242100i	$-0.0778362\pi$
$594$			58048.1i			0.00675028i
$595$			1.58900e7i			1.84006i
$596$	−3.54647e6	+	3.54647e6i	−0.408960	+	0.408960i
$597$	1.90814e6			0.219116
$598$	35034.0	−	35034.0i	0.00400624	−	0.00400624i
$599$	829602.			0.0944720			0.0472360	−	0.998884i	$-0.484959\pi$
$599$	829602.			0.0944720			0.0472360	+	0.998884i	$0.484959\pi$
$600$	579972.	−	579972.i	0.0657702	−	0.0657702i
$601$	−878005.	+	878005.i	−0.0991541	+	0.0991541i	−0.754944	−	0.655790i	$-0.772336\pi$
$601$	−878005.	+	878005.i	−0.0991541	+	0.0991541i	0.655790	+	0.754944i	$0.272336\pi$
$602$	26899.4	+	26899.4i	0.00302518	+	0.00302518i
$603$	−5.23415e6	−	5.23415e6i	−0.586209	−	0.586209i
$604$	−6.57702e6	−	6.57702e6i	−0.733562	−	0.733562i
$605$	9.06116e6			1.00646
$606$		−	64144.0i		−	0.00709536i
$607$		−	4.65129e6i		−	0.512391i	−0.966625	−	0.256195i	$-0.917531\pi$
$607$		−	4.65129e6i		−	0.512391i	0.966625	−	0.256195i	$-0.0824690\pi$
$608$	514719.	+	514719.i	0.0564692	+	0.0564692i
$609$	−9.16547e6	+	9.16547e6i	−1.00141	+	1.00141i
$610$			548812.i			0.0597171i
$611$	202449.			0.0219388
$612$	−3.06858e6	−	3.06858e6i	−0.331177	−	0.331177i
$613$			1.01443e7i			1.09036i	0.838319	+	0.545181i	$0.183539\pi$
$613$			1.01443e7i			1.09036i	−0.838319	+	0.545181i	$0.816461\pi$
$614$	−98580.9			−0.0105529
$615$	1.86980e7	−	4.89638e6i	1.99346	−	0.522020i
$616$	389478.			0.0413553
$617$			1.11572e7i			1.17989i	0.807444	+	0.589945i	$0.200850\pi$
$617$			1.11572e7i			1.17989i	−0.807444	+	0.589945i	$0.799150\pi$
$618$	−124839.	−	124839.i	−0.0131486	−	0.0131486i
$619$	−2.15682e6			−0.226249			−0.113125	−	0.993581i	$-0.536086\pi$
$619$	−2.15682e6			−0.226249			−0.113125	+	0.993581i	$0.536086\pi$
$620$		−	1.42627e7i		−	1.49013i
$621$	5.44205e6	−	5.44205e6i	0.566283	−	0.566283i
$622$	−47334.6	−	47334.6i	−0.00490572	−	0.00490572i
$623$		−	1.02316e7i		−	1.05614i
$624$		−	1.89370e6i		−	0.194692i
$625$	192462.			0.0197081
$626$	194782.	+	194782.i	0.0198662	+	0.0198662i
$627$	6.45333e6	+	6.45333e6i	0.655564	+	0.655564i
$628$	−3.38517e6	−	3.38517e6i	−0.342517	−	0.342517i
$629$	−6.26387e6	+	6.26387e6i	−0.631271	+	0.631271i
$630$	−236485.	+	236485.i	−0.0237384	+	0.0237384i
$631$	1.08975e7			1.08956			0.544782	−	0.838578i	$-0.316612\pi$
$631$	1.08975e7			1.08956			0.544782	+	0.838578i	$0.316612\pi$
$632$	284326.	−	284326.i	0.0283155	−	0.0283155i
$633$	6.84800e6			0.679288
$634$	−13054.1	+	13054.1i	−0.00128980	+	0.00128980i
$635$		−	1.31831e7i		−	1.29743i
$636$		−	5.95556e6i		−	0.583822i
$637$	1.36759e6	−	1.36759e6i	0.133539	−	0.133539i
$638$	106148.			0.0103243
$639$	7.96828e6	−	7.96828e6i	0.771991	−	0.771991i
$640$	−1.50892e6			−0.145618
$641$	951202.	−	951202.i	0.0914382	−	0.0914382i	−0.659908	−	0.751346i	$-0.729405\pi$
$641$	951202.	−	951202.i	0.0914382	−	0.0914382i	0.751346	+	0.659908i	$0.229405\pi$
$642$	85959.1	−	85959.1i	0.00823103	−	0.00823103i
$643$	1.12826e7	+	1.12826e7i	1.07617	+	1.07617i	0.996849	+	0.0793197i	$0.0252748\pi$
$643$	1.12826e7	+	1.12826e7i	1.07617	+	1.07617i	0.0793197	+	0.996849i	$0.474725\pi$
$644$	−1.82523e7	−	1.82523e7i	−1.73422	−	1.73422i
$645$	−1.96055e6	−	1.96055e6i	−0.185557	−	0.185557i
$646$	−214736.			−0.0202453
$647$		−	1.33608e7i		−	1.25479i	−0.778702	−	0.627394i	$-0.784122\pi$
$647$		−	1.33608e7i		−	1.25479i	0.778702	−	0.627394i	$-0.215878\pi$
$648$			594311.i			0.0556002i
$649$	6.81524e6	+	6.81524e6i	0.635140	+	0.635140i
$650$	−42737.7	+	42737.7i	−0.00396760	+	0.00396760i
$651$			1.88915e7i			1.74709i
$652$	−1.50300e7			−1.38465
$653$	3.42273e6	+	3.42273e6i	0.314116	+	0.314116i	0.846502	−	0.532386i	$-0.178704\pi$
$653$	3.42273e6	+	3.42273e6i	0.314116	+	0.314116i	−0.532386	+	0.846502i	$0.678704\pi$
$654$		−	220150.i		−	0.0201268i
$655$	−3.06206e7			−2.78875
$656$	−9.49940e6	−	5.55671e6i	−0.861860	−	0.504148i
$657$	−5.66017e6			−0.511583
$658$			53376.1i			0.00480598i
$659$	7690.56	+	7690.56i	0.000689833	+	0.000689833i	0.707452	−	0.706762i	$-0.249845\pi$
$659$	7690.56	+	7690.56i	0.000689833	+	0.000689833i	−0.706762	+	0.707452i	$0.749845\pi$
$660$	−1.41898e7			−1.26800
$661$		−	4.27321e6i		−	0.380408i	−0.981745	−	0.190204i	$-0.939085\pi$
$661$		−	4.27321e6i		−	0.380408i	0.981745	−	0.190204i	$-0.0609150\pi$
$662$	−92950.3	+	92950.3i	−0.00824339	+	0.00824339i
$663$	1.18605e6	+	1.18605e6i	0.104790	+	0.104790i
$664$		−	473482.i		−	0.0416757i
$665$		−	3.27015e7i		−	2.86756i
$666$	−186446.			−0.0162880
$667$	−9.95146e6	−	9.95146e6i	−0.866108	−	0.866108i
$668$	1.54522e7	+	1.54522e7i	1.33983	+	1.33983i
$669$	−1.23808e7	−	1.23808e7i	−1.06950	−	1.06950i
$670$	402695.	−	402695.i	0.0346569	−	0.0346569i
$671$	8.31788e6	−	8.31788e6i	0.713192	−	0.713192i
$672$	1.49909e6			0.128058
$673$	−457431.	+	457431.i	−0.0389303	+	0.0389303i	−0.726304	−	0.687374i	$-0.758764\pi$
$673$	−457431.	+	457431.i	−0.0389303	+	0.0389303i	0.687374	+	0.726304i	$0.258764\pi$
$674$	−42122.4			−0.00357160
$675$	−6.63872e6	+	6.63872e6i	−0.560822	+	0.560822i
$676$		−	1.15961e7i		−	0.975987i
$677$			9.52996e6i			0.799133i	0.916704	+	0.399567i	$0.130839\pi$
$677$			9.52996e6i			0.799133i	−0.916704	+	0.399567i	$0.869161\pi$
$678$	26753.2	−	26753.2i	0.00223513	−	0.00223513i
$679$	2.46252e7			2.04977
$680$	472290.	−	472290.i	0.0391684	−	0.0391684i
$681$	−2.44189e7			−2.01771
$682$	109394.	−	109394.i	0.00900602	−	0.00900602i
$683$	−1.29328e7	+	1.29328e7i	−1.06082	+	1.06082i	−0.0627887	+	0.998027i	$0.519999\pi$
$683$	−1.29328e7	+	1.29328e7i	−1.06082	+	1.06082i	−0.998027	+	0.0627887i	$0.980001\pi$
$684$	6.31512e6	+	6.31512e6i	0.516109	+	0.516109i
$685$	7.28507e6	+	7.28507e6i	0.593208	+	0.593208i
$686$	67763.0	+	67763.0i	0.00549772	+	0.00549772i
$687$	2.86982e7			2.31986
$688$			1.57868e6i			0.127152i
$689$			877944.i			0.0704562i
$690$	−673217.	−	673217.i	−0.0538310	−	0.0538310i
$691$	−4.41257e6	+	4.41257e6i	−0.351558	+	0.351558i	−0.860689	−	0.509131i	$-0.829967\pi$
$691$	−4.41257e6	+	4.41257e6i	−0.351558	+	0.351558i	0.509131	+	0.860689i	$0.329967\pi$
$692$		−	1.41100e6i		−	0.112011i
$693$	7.16840e6			0.567008
$694$	99166.6	+	99166.6i	0.00781568	+	0.00781568i
$695$			4.03406e7i			3.16797i
$696$	544841.			0.0426331
$697$	9.42985e6	−	2.46936e6i	0.735229	−	0.192532i
$698$	356358.			0.0276852
$699$		−	7.62881e6i		−	0.590559i
$700$	2.22659e7	+	2.22659e7i	1.71749	+	1.71749i
$701$	−9.03490e6			−0.694430			−0.347215	−	0.937786i	$-0.612873\pi$
$701$	−9.03490e6			−0.694430			−0.347215	+	0.937786i	$0.612873\pi$
$702$		−	21955.8i		−	0.00168154i
$703$	1.28910e7	−	1.28910e7i	0.983780	−	0.983780i
$704$	5.70723e6	+	5.70723e6i	0.434004	+	0.434004i
$705$		−	3.89029e6i		−	0.294787i
$706$		−	172510.i		−	0.0130258i
$707$	4.92638e6			0.370663
$708$	1.74863e7	+	1.74863e7i	1.31104	+	1.31104i
$709$	2.57567e6	+	2.57567e6i	0.192431	+	0.192431i	0.796746	−	0.604315i	$-0.206553\pi$
$709$	2.57567e6	+	2.57567e6i	0.192431	+	0.192431i	−0.604315	+	0.796746i	$0.706553\pi$
$710$	613049.	+	613049.i	0.0456404	+	0.0456404i
$711$	5.23306e6	−	5.23306e6i	0.388223	−	0.388223i
$712$	−304108.	+	304108.i	−0.0224816	+	0.0224816i
$713$	−2.05116e7			−1.51104
$714$	−312704.	+	312704.i	−0.0229555	+	0.0229555i
$715$	2.09181e6			0.153023
$716$	4.93229e6	−	4.93229e6i	0.359555	−	0.359555i
$717$			1.83313e6i			0.133167i
$718$		−	52760.2i		−	0.00381940i
$719$	−1.44397e7	+	1.44397e7i	−1.04168	+	1.04168i	−0.0425879	+	0.999093i	$0.513560\pi$
$719$	−1.44397e7	+	1.44397e7i	−1.04168	+	1.04168i	−0.999093	+	0.0425879i	$0.986440\pi$
$720$	−1.38789e7			−0.997756
$721$	9.58790e6	−	9.58790e6i	0.686887	−	0.686887i
$722$	126907.			0.00906033
$723$	−1.68631e7	+	1.68631e7i	−1.19975	+	1.19975i
$724$	664152.	−	664152.i	0.0470891	−	0.0470891i
$725$	1.21397e7	+	1.21397e7i	0.857755	+	0.857755i
$726$	178317.	+	178317.i	0.0125560	+	0.0125560i
$727$	−7.87266e6	−	7.87266e6i	−0.552441	−	0.552441i	0.374704	−	0.927145i	$-0.377744\pi$
$727$	−7.87266e6	−	7.87266e6i	−0.552441	−	0.552441i	−0.927145	+	0.374704i	$0.877744\pi$
$728$	−147314.			−0.0103019
$729$			2.04399e6i			0.142449i
$730$		−	435472.i		−	0.0302449i
$731$	−988752.	−	988752.i	−0.0684374	−	0.0684374i
$732$	2.13418e7	−	2.13418e7i	1.47215	−	1.47215i
$733$			6.30481e6i			0.433423i	0.976236	+	0.216711i	$0.0695331\pi$
$733$			6.30481e6i			0.433423i	−0.976236	+	0.216711i	$0.930467\pi$
$734$	−37069.1			−0.00253964
$735$	−2.62798e7	−	2.62798e7i	−1.79433	−	1.79433i
$736$			1.62765e6i			0.110756i
$737$	−1.22066e7			−0.827802
$738$	177091.	+	103590.i	0.0119690	+	0.00700129i
$739$	−1.05307e7			−0.709325			−0.354662	−	0.934994i	$-0.615404\pi$
$739$	−1.05307e7			−0.709325			−0.354662	+	0.934994i	$0.615404\pi$
$740$			2.83452e7i			1.90283i
$741$	−2.44088e6	−	2.44088e6i	−0.163305	−	0.163305i
$742$	−231471.			−0.0154343
$743$			1.58426e7i			1.05282i	0.850231	+	0.526410i	$0.176462\pi$
$743$			1.58426e7i			1.05282i	−0.850231	+	0.526410i	$0.823538\pi$
$744$	561503.	−	561503.i	0.0371894	−	0.0371894i
$745$	−1.00463e7	−	1.00463e7i	−0.663154	−	0.663154i
$746$		−	127365.i		−	0.00837920i
$747$		−	8.71450e6i		−	0.571401i
$748$	−7.15628e6			−0.467664
$749$	6.60182e6	+	6.60182e6i	0.429991	+	0.429991i
$750$	316429.	+	316429.i	0.0205411	+	0.0205411i
$751$	1.69165e6	+	1.69165e6i	0.109449	+	0.109449i	0.759710	−	0.650262i	$-0.225341\pi$
$751$	1.69165e6	+	1.69165e6i	0.109449	+	0.109449i	−0.650262	+	0.759710i	$0.725341\pi$
$752$	−1.56628e6	+	1.56628e6i	−0.101001	+	0.101001i
$753$	−2.46666e6	+	2.46666e6i	−0.158534	+	0.158534i
$754$	−40148.9			−0.00257185
$755$	1.86311e7	−	1.86311e7i	1.18952	−	1.18952i
$756$	−1.14387e7			−0.727903
$757$	1.36900e7	−	1.36900e7i	0.868286	−	0.868286i	−0.123997	−	0.992283i	$-0.539571\pi$
$757$	1.36900e7	−	1.36900e7i	0.868286	−	0.868286i	0.992283	+	0.123997i	$0.0395713\pi$
$758$			501446.i			0.0316994i
$759$			2.04068e7i			1.28579i
$760$	−971968.	+	971968.i	−0.0610405	+	0.0610405i
$761$	−2.05674e7			−1.28741			−0.643706	−	0.765273i	$-0.722604\pi$
$761$	−2.05674e7			−1.28741			−0.643706	+	0.765273i	$0.722604\pi$
$762$	259434.	−	259434.i	0.0161860	−	0.0161860i
$763$	1.69080e7			1.05143
$764$	−3.14542e6	+	3.14542e6i	−0.194960	+	0.194960i
$765$	8.69256e6	−	8.69256e6i	0.537024	−	0.537024i
$766$	−207726.	−	207726.i	−0.0127914	−	0.0127914i
$767$	−2.57776e6	−	2.57776e6i	−0.158218	−	0.158218i
$768$	1.46212e7	+	1.46212e7i	0.894498	+	0.894498i
$769$	−1.17154e7			−0.714399			−0.357199	−	0.934028i	$-0.616268\pi$
$769$	−1.17154e7			−0.714399			−0.357199	+	0.934028i	$0.616268\pi$
$770$			551509.i			0.0335217i
$771$			5.11828e6i			0.310090i
$772$	−3.43428e6	−	3.43428e6i	−0.207392	−	0.207392i
$773$	2.18830e6	−	2.18830e6i	0.131722	−	0.131722i	−0.638172	−	0.769894i	$-0.720309\pi$
$773$	2.18830e6	−	2.18830e6i	0.131722	−	0.131722i	0.769894	+	0.638172i	$0.220309\pi$
$774$		−	29430.4i		−	0.00176581i
$775$	2.50219e7			1.49646
$776$	−731922.	−	731922.i	−0.0436325	−	0.0436325i
$777$		−	3.75444e7i		−	2.23096i
$778$	3397.02			0.000201210
$779$	−1.94065e7	+	5.08193e6i	−1.14579	+	0.300044i
$780$	5.36710e6			0.315866
$781$		−	1.85829e7i		−	1.09015i
$782$	−339520.	−	339520.i	−0.0198540	−	0.0198540i
$783$	−6.23658e6			−0.363532
$784$			2.11612e7i			1.22956i
$785$	9.58938e6	−	9.58938e6i	0.555413	−	0.555413i
$786$	−602592.	−	602592.i	−0.0347910	−	0.0347910i
$787$			3.36593e7i			1.93717i	0.248673	+	0.968587i	$0.420006\pi$
$787$			3.36593e7i			1.93717i	−0.248673	+	0.968587i	$0.579994\pi$
$788$		−	7.08401e6i		−	0.406409i
$789$	1.23157e7			0.704312
$790$	402611.	+	402611.i	0.0229519	+	0.0229519i
$791$	2.05470e6	+	2.05470e6i	0.116764	+	0.116764i
$792$	−213062.	−	213062.i	−0.0120696	−	0.0120696i
$793$	−3.14612e6	+	3.14612e6i	−0.177661	+	0.177661i
$794$	−54895.8	+	54895.8i	−0.00309021	+	0.00309021i
$795$	1.68707e7			0.946705
$796$	2.17735e6	−	2.17735e6i	0.121799	−	0.121799i
$797$	−2.60311e7			−1.45160			−0.725799	−	0.687906i	$-0.758530\pi$
$797$	−2.60311e7			−1.45160			−0.725799	+	0.687906i	$0.758530\pi$
$798$	643542.	−	643542.i	0.0357742	−	0.0357742i
$799$		−	1.96197e6i		−	0.108724i
$800$		−	1.98556e6i		−	0.109688i
$801$	−5.59715e6	+	5.59715e6i	−0.308238	+	0.308238i
$802$	382302.			0.0209880
$803$	−6.60008e6	+	6.60008e6i	−0.361210	+	0.361210i
$804$	−3.13194e7			−1.70873
$805$	5.17044e7	−	5.17044e7i	2.81214	−	2.81214i
$806$	−41376.7	+	41376.7i	−0.00224346	+	0.00224346i
$807$	−2.32285e7	−	2.32285e7i	−1.25556	−	1.25556i
$808$	−146424.	−	146424.i	−0.00789014	−	0.00789014i
$809$	1.17917e7	+	1.17917e7i	0.633441	+	0.633441i	0.948929	−	0.315488i	$-0.102168\pi$
$809$	1.17917e7	+	1.17917e7i	0.633441	+	0.633441i	−0.315488	+	0.948929i	$0.602168\pi$
$810$	−841556.			−0.0450682
$811$			2.35091e7i			1.25512i	0.778570	+	0.627558i	$0.215945\pi$
$811$			2.35091e7i			1.25512i	−0.778570	+	0.627558i	$0.784055\pi$
$812$			2.09171e7i			1.11330i
$813$	−6.69080e6	−	6.69080e6i	−0.355019	−	0.355019i
$814$	−217406.	+	217406.i	−0.0115003	+	0.0115003i
$815$		−	4.25764e7i		−	2.24530i
$816$	−1.83521e7			−0.964851
$817$	2.03484e6	+	2.03484e6i	0.106654	+	0.106654i
$818$		−	201197.i		−	0.0105133i
$819$	−2.71134e6			−0.141245
$820$	1.57488e7	−	2.69231e7i	0.817923	−	1.39827i
$821$	−447471.			−0.0231690			−0.0115845	−	0.999933i	$-0.503688\pi$
$821$	−447471.			−0.0231690			−0.0115845	+	0.999933i	$0.503688\pi$
$822$			286730.i			0.0148011i
$823$	−1.27619e7	−	1.27619e7i	−0.656774	−	0.656774i	0.297841	−	0.954615i	$-0.403733\pi$
$823$	−1.27619e7	−	1.27619e7i	−0.656774	−	0.656774i	−0.954615	+	0.297841i	$0.903733\pi$
$824$	−569952.			−0.0292429
$825$		−	2.48941e7i		−	1.27339i
$826$	679632.	−	679632.i	0.0346596	−	0.0346596i
$827$	−1.88270e7	−	1.88270e7i	−0.957230	−	0.957230i	0.0418920	−	0.999122i	$-0.486661\pi$
$827$	−1.88270e7	−	1.88270e7i	−0.957230	−	0.957230i	−0.999122	+	0.0418920i	$0.986661\pi$
$828$			1.99697e7i			1.01227i
$829$			2.07174e7i			1.04701i	0.852024	+	0.523503i	$0.175375\pi$
$829$			2.07174e7i			1.04701i	−0.852024	+	0.523503i	$0.824625\pi$
$830$	670460.			0.0337814
$831$	2.07854e7	+	2.07854e7i	1.04413	+	1.04413i
$832$	−2.15868e6	−	2.15868e6i	−0.108113	−	0.108113i
$833$	−1.32535e7	−	1.32535e7i	−0.661788	−	0.661788i
$834$	−793875.	+	793875.i	−0.0395218	+	0.0395218i
$835$	−4.37723e7	+	4.37723e7i	−2.17262	+	2.17262i
$836$	1.47276e7			0.728812
$837$	−6.42731e6	+	6.42731e6i	−0.317114	+	0.317114i
$838$	−824293.			−0.0405482
$839$	1.47890e7	−	1.47890e7i	0.725326	−	0.725326i	−0.244359	−	0.969685i	$-0.578577\pi$
$839$	1.47890e7	−	1.47890e7i	0.725326	−	0.725326i	0.969685	+	0.244359i	$0.0785774\pi$
$840$			2.83081e6i			0.138424i
$841$		−	9.10680e6i		−	0.443992i
$842$	231143.	−	231143.i	0.0112357	−	0.0112357i
$843$	3.51235e7			1.70227
$844$	7.81413e6	−	7.81413e6i	0.377594	−	0.377594i
$845$	3.28488e7			1.58263
$846$	29199.2	−	29199.2i	0.00140264	−	0.00140264i
$847$	−1.36951e7	+	1.36951e7i	−0.655930	+	0.655930i
$848$	−6.79235e6	−	6.79235e6i	−0.324363	−	0.324363i
$849$	2.58792e7	+	2.58792e7i	1.23220	+	1.23220i
$850$	414177.	+	414177.i	0.0196625	+	0.0196625i
$851$	4.07640e7			1.92954
$852$		−	4.76796e7i		−	2.25026i
$853$		−	1.39016e7i		−	0.654171i	−0.944995	−	0.327085i	$-0.893934\pi$
$853$		−	1.39016e7i		−	0.654171i	0.944995	−	0.327085i	$-0.106066\pi$
$854$	−829479.	−	829479.i	−0.0389189	−	0.0389189i
$855$	−1.78892e7	+	1.78892e7i	−0.836904	+	0.836904i
$856$		−	392445.i		−	0.0183060i
$857$	−1.62359e7			−0.755133			−0.377566	−	0.925983i	$-0.623239\pi$
$857$	−1.62359e7			−0.755133			−0.377566	+	0.925983i	$0.623239\pi$
$858$	41165.3	+	41165.3i	0.00190903	+	0.00190903i
$859$		−	3.71501e7i		−	1.71782i	−0.512127	−	0.858910i	$-0.671142\pi$
$859$		−	3.71501e7i		−	1.71782i	0.512127	−	0.858910i	$-0.328858\pi$
$860$	−4.47430e6			−0.206290
$861$	−2.08599e7	+	3.56607e7i	−0.958967	+	1.63939i
$862$	105975.			0.00485774
$863$		−	2.19053e7i		−	1.00120i	−0.865678	−	0.500601i	$-0.833112\pi$
$863$		−	2.19053e7i		−	1.00120i	0.865678	−	0.500601i	$-0.166888\pi$
$864$	510024.	+	510024.i	0.0232438	+	0.0232438i
$865$	3.99701e6			0.181633
$866$			70692.4i			0.00320315i
$867$	−8.40466e6	+	8.40466e6i	−0.379728	+	0.379728i
$868$	2.15568e7	+	2.15568e7i	0.971147	+	0.971147i
$869$		−	1.22041e7i		−	0.548221i
$870$			771506.i			0.0345574i
$871$	4.61697e6			0.206211
$872$	−502547.	−	502547.i	−0.0223813	−	0.0223813i
$873$	−1.34711e7	−	1.34711e7i	−0.598230	−	0.598230i
$874$	698729.	+	698729.i	0.0309407	+	0.0309407i
$875$	−2.43024e7	+	2.43024e7i	−1.07307	+	1.07307i
$876$	−1.69343e7	+	1.69343e7i	−0.745602	+	0.745602i
$877$	−1.41048e7			−0.619254			−0.309627	−	0.950858i	$-0.600204\pi$
$877$	−1.41048e7			−0.619254			−0.309627	+	0.950858i	$0.600204\pi$
$878$	−313571.	+	313571.i	−0.0137277	+	0.0137277i
$879$	722530.			0.0315416
$880$	−1.61836e7	+	1.61836e7i	−0.704480	+	0.704480i
$881$		−	2.99000e7i		−	1.29787i	−0.760844	−	0.648935i	$-0.775215\pi$
$881$		−	2.99000e7i		−	1.29787i	0.760844	−	0.648935i	$-0.224785\pi$
$882$		−	394494.i		−	0.0170753i
$883$	1.48801e7	−	1.48801e7i	0.642250	−	0.642250i	−0.308858	−	0.951108i	$-0.599947\pi$
$883$	1.48801e7	−	1.48801e7i	0.642250	−	0.642250i	0.951108	+	0.308858i	$0.0999469\pi$
$884$	2.70676e6			0.116498
$885$	−4.95346e7	+	4.95346e7i	−2.12594	+	2.12594i
$886$	−54807.5			−0.00234561
$887$	3.40694e6	−	3.40694e6i	0.145397	−	0.145397i	−0.630661	−	0.776058i	$-0.717216\pi$
$887$	3.40694e6	−	3.40694e6i	0.145397	−	0.145397i	0.776058	+	0.630661i	$0.217216\pi$
$888$	−1.11591e6	+	1.11591e6i	−0.0474895	+	0.0474895i
$889$	1.99251e7	+	1.99251e7i	0.845562	+	0.845562i
$890$	−430623.	−	430623.i	−0.0182231	−	0.0182231i
$891$	1.27548e7	+	1.27548e7i	0.538242	+	0.538242i
$892$	−2.82550e7			−1.18900
$893$			4.03771e6i			0.169436i
$894$		−	395408.i		−	0.0165463i
$895$	1.39720e7	+	1.39720e7i	0.583042	+	0.583042i
$896$	2.28060e6	−	2.28060e6i	0.0949026	−	0.0949026i
$897$		−	7.71856e6i		−	0.320299i
$898$	−82508.4			−0.00341435
$899$	1.17531e7	+	1.17531e7i	0.485013	+	0.485013i
$900$		−	2.43609e7i		−	1.00251i
$901$	8.50829e6			0.349165
$902$	327291.	−	85706.6i	0.0133942	−	0.00350750i
$903$	5.92638e6			0.241863
$904$		−	122142.i		−	0.00497099i
$905$	1.88138e6	+	1.88138e6i	0.0763581	+	0.0763581i
$906$	733294.			0.0296796
$907$			1.76275e7i			0.711497i	0.934582	+	0.355749i	$0.115774\pi$
$907$			1.76275e7i			0.711497i	−0.934582	+	0.355749i	$0.884226\pi$
$908$	−2.78640e7	+	2.78640e7i	−1.12158	+	1.12158i
$909$	−2.69496e6	−	2.69496e6i	−0.108179	−	0.108179i
$910$		−	208600.i		−	0.00835047i
$911$			2.01872e7i			0.805898i	0.915222	+	0.402949i	$0.132015\pi$
$911$			2.01872e7i			0.805898i	−0.915222	+	0.402949i	$0.867985\pi$
$912$	3.77685e7			1.50363
$913$	−1.01616e7	−	1.01616e7i	−0.403446	−	0.403446i
$914$	−742243.	−	742243.i	−0.0293887	−	0.0293887i
$915$	6.04561e7	+	6.04561e7i	2.38719	+	2.38719i
$916$	3.27470e7	−	3.27470e7i	1.28954	−	1.28954i
$917$	4.62802e7	−	4.62802e7i	1.81749	−	1.81749i
$918$	−212777.			−0.00833332
$919$	−1.98731e7	+	1.98731e7i	−0.776205	+	0.776205i	−0.979183	−	0.202978i	$-0.934938\pi$
$919$	−1.98731e7	+	1.98731e7i	−0.776205	+	0.776205i	0.202978	+	0.979183i	$0.434938\pi$
$920$	−3.07356e6			−0.119722
$921$	−1.08595e7	+	1.08595e7i	−0.421852	+	0.421852i
$922$		−	295491.i		−	0.0114477i
$923$			7.02872e6i			0.271564i
$924$	2.14467e7	−	2.14467e7i	0.826380	−	0.826380i
$925$	−4.97277e7			−1.91093
$926$	327050.	−	327050.i	0.0125339	−	0.0125339i
$927$	−1.04901e7			−0.400939
$928$	932642.	−	932642.i	0.0355504	−	0.0355504i
$929$	−2.36512e7	+	2.36512e7i	−0.899112	+	0.899112i	−0.995358	−	0.0962457i	$-0.969317\pi$
$929$	−2.36512e7	+	2.36512e7i	−0.899112	+	0.899112i	0.0962457	+	0.995358i	$0.469317\pi$
$930$	795099.	+	795099.i	0.0301449	+	0.0301449i
$931$	2.72756e7	+	2.72756e7i	1.03134	+	1.03134i
$932$	−8.70510e6	−	8.70510e6i	−0.328272	−	0.328272i
$933$	−1.04286e7			−0.392212
$934$			464026.i			0.0174050i
$935$		−	2.02720e7i		−	0.758347i
$936$	80587.8	+	80587.8i	0.00300663	+	0.00300663i
$937$	−5.37215e6	+	5.37215e6i	−0.199894	+	0.199894i	−0.799954	−	0.600061i	$-0.795143\pi$
$937$	−5.37215e6	+	5.37215e6i	−0.199894	+	0.199894i	0.600061	+	0.799954i	$0.295143\pi$
$938$			1.21727e6i			0.0451732i
$939$	4.29138e7			1.58830
$940$	−4.43914e6	−	4.43914e6i	−0.163862	−	0.163862i
$941$			4.50103e7i			1.65706i	0.559946	+	0.828529i	$0.310822\pi$
$941$			4.50103e7i			1.65706i	−0.559946	+	0.828529i	$0.689178\pi$
$942$	377424.			0.0138581
$943$	−3.87188e7	−	2.26487e7i	−1.41789	−	0.829400i
$944$	3.98866e7			1.45679
$945$		−	3.24032e7i		−	1.18034i
$946$	−34317.5	−	34317.5i	−0.00124678	−	0.00124678i
$947$	3.28553e7			1.19050			0.595252	−	0.803539i	$-0.297052\pi$
$947$	3.28553e7			1.19050			0.595252	+	0.803539i	$0.297052\pi$
$948$		−	3.13129e7i		−	1.13163i
$949$	2.49638e6	−	2.49638e6i	0.0899800	−	0.0899800i
$950$	−852374.	−	852374.i	−0.0306423	−	0.0306423i
$951$			2.87603e6i			0.103120i
$952$			1.42764e6i			0.0510538i
$953$	7.01290e6			0.250130			0.125065	−	0.992149i	$-0.460086\pi$
$953$	7.01290e6			0.250130			0.125065	+	0.992149i	$0.460086\pi$
$954$	126626.	+	126626.i	0.00450454	+	0.00450454i
$955$	−8.91021e6	−	8.91021e6i	−0.316140	−	0.316140i
$956$	2.09176e6	+	2.09176e6i	0.0740230	+	0.0740230i
$957$	1.16931e7	−	1.16931e7i	0.412713	−	0.412713i
$958$	−401048.	+	401048.i	−0.0141183	+	0.0141183i
$959$	−2.20214e7			−0.773213
$960$	−4.14814e7	+	4.14814e7i	−1.45270	+	1.45270i
$961$	−4.40406e6			−0.153831
$962$	82230.7	−	82230.7i	0.00286481	−	0.00286481i
$963$		−	7.22301e6i		−	0.250988i
$964$			3.84844e7i			1.33381i
$965$	9.72847e6	−	9.72847e6i	0.336299	−	0.336299i
$966$	2.03501e6			0.0701656
$967$	1.09700e7	−	1.09700e7i	0.377261	−	0.377261i	−0.492852	−	0.870113i	$-0.664046\pi$
$967$	1.09700e7	−	1.09700e7i	0.377261	−	0.377261i	0.870113	+	0.492852i	$0.164046\pi$
$968$	814106.			0.0279250
$969$	−2.36549e7	+	2.36549e7i	−0.809304	+	0.809304i
$970$	1.03642e6	−	1.03642e6i	0.0353675	−	0.0353675i
$971$	−2.74124e7	−	2.74124e7i	−0.933036	−	0.933036i	0.0648589	−	0.997894i	$-0.479340\pi$
$971$	−2.74124e7	−	2.74124e7i	−0.933036	−	0.933036i	−0.997894	+	0.0648589i	$0.979340\pi$
$972$	2.25766e7	+	2.25766e7i	0.766465	+	0.766465i
$973$	−6.09712e7	−	6.09712e7i	−2.06463	−	2.06463i
$974$	473764.			0.0160016
$975$			9.41581e6i			0.317210i
$976$		−	4.86809e7i		−	1.63581i
$977$	2.45113e7	+	2.45113e7i	0.821543	+	0.821543i	0.986329	−	0.164786i	$-0.0526933\pi$
$977$	2.45113e7	+	2.45113e7i	0.821543	+	0.821543i	−0.164786	+	0.986329i	$0.552693\pi$
$978$	837874.	−	837874.i	0.0280112	−	0.0280112i
$979$			1.30532e7i			0.435271i
$980$	−5.99748e7			−1.99482
$981$	−9.24945e6	−	9.24945e6i	−0.306862	−	0.306862i
$982$			188593.i			0.00624090i
$983$	3.65336e7			1.20589			0.602946	−	0.797782i	$-0.293993\pi$
$983$	3.65336e7			1.20589			0.602946	+	0.797782i	$0.293993\pi$
$984$	1.67993e6	−	439918.i	0.0553100	−	0.0144839i
$985$	2.00673e7			0.659019
$986$			389089.i			0.0127455i
$987$	5.87982e6	+	5.87982e6i	0.192119	+	0.192119i
$988$	−5.57049e6			−0.181552
$989$			6.43459e6i			0.209185i
$990$	301701.	−	301701.i	0.00978337	−	0.00978337i
$991$	−9.20786e6	−	9.20786e6i	−0.297834	−	0.297834i	0.542331	−	0.840165i	$-0.317542\pi$
$991$	−9.20786e6	−	9.20786e6i	−0.297834	−	0.297834i	−0.840165	+	0.542331i	$0.817542\pi$
$992$		−	1.92233e6i		−	0.0620223i
$993$			2.04785e7i			0.659059i
$994$	−1.85313e6			−0.0594896
$995$	6.16790e6	+	6.16790e6i	0.197506	+	0.197506i
$996$	−2.60724e7	−	2.60724e7i	−0.832783	−	0.832783i
$997$	−2.95246e7	−	2.95246e7i	−0.940688	−	0.940688i	0.0576485	−	0.998337i	$-0.481640\pi$
$997$	−2.95246e7	−	2.95246e7i	−0.940688	−	0.940688i	−0.998337	+	0.0576485i	$0.981640\pi$
$998$	921188.	−	921188.i	0.0292767	−	0.0292767i
$999$	1.27734e7	−	1.27734e7i	0.404942	−	0.404942i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	41.6.c.a.9.10	✓	34
41.32	even	4	inner	41.6.c.a.32.8	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.6.c.a.9.10	✓	34	1.1	even	1	trivial
41.6.c.a.32.8	yes	34	41.32	even	4	inner

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:	\( N \)	\(=\)	\( 41 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	41.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.127223i q^{2} +(14.0147 + 14.0147i) q^{3} +31.9838 q^{4} +90.6024i q^{5} +(-1.78299 + 1.78299i) q^{6} +(-136.937 - 136.937i) q^{7} +8.14022i q^{8} +149.822i q^{9} +O(q^{10})\)	\(q+0.127223i q^{2} +(14.0147 + 14.0147i) q^{3} +31.9838 q^{4} +90.6024i q^{5} +(-1.78299 + 1.78299i) q^{6} +(-136.937 - 136.937i) q^{7} +8.14022i q^{8} +149.822i q^{9} -11.5267 q^{10} +(174.701 + 174.701i) q^{11} +(448.243 + 448.243i) q^{12} +(-66.0780 - 66.0780i) q^{13} +(17.4216 - 17.4216i) q^{14} +(-1269.76 + 1269.76i) q^{15} +1022.45 q^{16} +(-640.372 + 640.372i) q^{17} -19.0608 q^{18} +(1317.88 - 1317.88i) q^{19} +2897.81i q^{20} -3838.26i q^{21} +(-22.2260 + 22.2260i) q^{22} +4167.41 q^{23} +(-114.083 + 114.083i) q^{24} -5083.79 q^{25} +(8.40666 - 8.40666i) q^{26} +(1305.86 - 1305.86i) q^{27} +(-4379.77 - 4379.77i) q^{28} +(-2387.92 - 2387.92i) q^{29} +(-161.543 - 161.543i) q^{30} -4921.90 q^{31} +390.566i q^{32} +4896.75i q^{33} +(-81.4702 - 81.4702i) q^{34} +(12406.8 - 12406.8i) q^{35} +4791.88i q^{36} +9781.61 q^{37} +(167.665 + 167.665i) q^{38} -1852.12i q^{39} -737.524 q^{40} +(-9290.86 - 5434.72i) q^{41} +488.316 q^{42} +1544.03i q^{43} +(5587.60 + 5587.60i) q^{44} -13574.2 q^{45} +530.191i q^{46} +(-1531.90 + 1531.90i) q^{47} +(14329.2 + 14329.2i) q^{48} +20696.6i q^{49} -646.776i q^{50} -17949.2 q^{51} +(-2113.43 - 2113.43i) q^{52} +(-6643.24 - 6643.24i) q^{53} +(166.136 + 166.136i) q^{54} +(-15828.3 + 15828.3i) q^{55} +(1114.70 - 1114.70i) q^{56} +36939.3 q^{57} +(303.799 - 303.799i) q^{58} +39010.9 q^{59} +(-40611.8 + 40611.8i) q^{60} -47612.1i q^{61} -626.180i q^{62} +(20516.2 - 20516.2i) q^{63} +32668.6 q^{64} +(5986.83 - 5986.83i) q^{65} -622.980 q^{66} +(-34935.8 + 34935.8i) q^{67} +(-20481.5 + 20481.5i) q^{68} +(58404.9 + 58404.9i) q^{69} +(1578.44 + 1578.44i) q^{70} +(-53185.0 - 53185.0i) q^{71} -1219.58 q^{72} +37779.3i q^{73} +1244.45i q^{74} +(-71247.7 - 71247.7i) q^{75} +(42150.8 - 42150.8i) q^{76} -47846.1i q^{77} +235.633 q^{78} +(-34928.5 - 34928.5i) q^{79} +92636.1i q^{80} +73009.1 q^{81} +(691.422 - 1182.01i) q^{82} -58165.7 q^{83} -122762. i q^{84} +(-58019.2 - 58019.2i) q^{85} -196.436 q^{86} -66931.9i q^{87} +(-1422.10 + 1422.10i) q^{88} +(37358.7 + 37358.7i) q^{89} -1726.96i q^{90} +18097.1i q^{91} +133290. q^{92} +(-68978.8 - 68978.8i) q^{93} +(-194.893 - 194.893i) q^{94} +(119403. + 119403. i) q^{95} +(-5473.66 + 5473.66i) q^{96} +(-89914.2 + 89914.2i) q^{97} -2633.09 q^{98} +(-26174.0 + 26174.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 20 q^{3} - 548 q^{4} - 124 q^{6} - 2 q^{7}+O(q^{10}) \) 34 * q + 20 * q^3 - 548 * q^4 - 124 * q^6 - 2 * q^7	\( 34 q + 20 q^{3} - 548 q^{4} - 124 q^{6} - 2 q^{7} + 1660 q^{10} + 654 q^{11} + 98 q^{12} + 854 q^{13} + 2236 q^{14} - 998 q^{15} + 8828 q^{16} + 1730 q^{17} + 2068 q^{18} + 716 q^{19} - 7750 q^{22} - 8156 q^{23} + 5496 q^{24} - 28870 q^{25} + 11470 q^{26} - 26806 q^{27} - 5942 q^{28} - 19190 q^{29} + 21430 q^{30} - 6376 q^{31} + 4228 q^{34} + 20934 q^{35} + 768 q^{37} - 6552 q^{38} - 47024 q^{40} - 9618 q^{41} + 126236 q^{42} - 57632 q^{44} + 81112 q^{45} + 2372 q^{47} + 88202 q^{48} + 24936 q^{51} + 151982 q^{52} - 94170 q^{53} - 153650 q^{54} - 105662 q^{55} + 8144 q^{56} - 69412 q^{57} - 63094 q^{58} + 87684 q^{59} + 58746 q^{60} - 76328 q^{63} - 109780 q^{64} + 88904 q^{65} - 427468 q^{66} + 212150 q^{67} - 199904 q^{68} + 125672 q^{69} + 113566 q^{70} + 189392 q^{71} + 579216 q^{72} + 199072 q^{75} + 128522 q^{76} - 327232 q^{78} - 28880 q^{79} - 557850 q^{81} - 241122 q^{82} + 384572 q^{83} - 114880 q^{85} - 453980 q^{86} + 338338 q^{88} - 391266 q^{89} + 955316 q^{92} + 394684 q^{93} - 42650 q^{94} - 404378 q^{95} - 254372 q^{96} - 324538 q^{97} - 167276 q^{98} - 685716 q^{99}+O(q^{100}) \) 34 * q + 20 * q^3 - 548 * q^4 - 124 * q^6 - 2 * q^7 + 1660 * q^10 + 654 * q^11 + 98 * q^12 + 854 * q^13 + 2236 * q^14 - 998 * q^15 + 8828 * q^16 + 1730 * q^17 + 2068 * q^18 + 716 * q^19 - 7750 * q^22 - 8156 * q^23 + 5496 * q^24 - 28870 * q^25 + 11470 * q^26 - 26806 * q^27 - 5942 * q^28 - 19190 * q^29 + 21430 * q^30 - 6376 * q^31 + 4228 * q^34 + 20934 * q^35 + 768 * q^37 - 6552 * q^38 - 47024 * q^40 - 9618 * q^41 + 126236 * q^42 - 57632 * q^44 + 81112 * q^45 + 2372 * q^47 + 88202 * q^48 + 24936 * q^51 + 151982 * q^52 - 94170 * q^53 - 153650 * q^54 - 105662 * q^55 + 8144 * q^56 - 69412 * q^57 - 63094 * q^58 + 87684 * q^59 + 58746 * q^60 - 76328 * q^63 - 109780 * q^64 + 88904 * q^65 - 427468 * q^66 + 212150 * q^67 - 199904 * q^68 + 125672 * q^69 + 113566 * q^70 + 189392 * q^71 + 579216 * q^72 + 199072 * q^75 + 128522 * q^76 - 327232 * q^78 - 28880 * q^79 - 557850 * q^81 - 241122 * q^82 + 384572 * q^83 - 114880 * q^85 - 453980 * q^86 + 338338 * q^88 - 391266 * q^89 + 955316 * q^92 + 394684 * q^93 - 42650 * q^94 - 404378 * q^95 - 254372 * q^96 - 324538 * q^97 - 167276 * q^98 - 685716 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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