LMFDB - Embedded newform 37.6.c.a.26.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,6,Mod(10,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("37.10");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	37.c (of order $3$, 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:	$5.93420133308$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			26.9
Character	$\chi$	$=$	37.26
Dual form			37.6.c.a.10.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.684514 + 1.18561i) q^{2} +(-2.47268 + 4.28281i) q^{3} +(15.0629 - 26.0897i) q^{4} +(-49.2630 + 85.3260i) q^{5} -6.77035 q^{6} +(-21.8515 + 37.8479i) q^{7} +85.0519 q^{8} +(109.272 + 189.264i) q^{9} +O(q^{10})$	\(q+(0.684514 + 1.18561i) q^{2} +(-2.47268 + 4.28281i) q^{3} +(15.0629 - 26.0897i) q^{4} +(-49.2630 + 85.3260i) q^{5} -6.77035 q^{6} +(-21.8515 + 37.8479i) q^{7} +85.0519 q^{8} +(109.272 + 189.264i) q^{9} -134.885 q^{10} -339.990 q^{11} +(74.4915 + 129.023i) q^{12} +(-523.635 + 906.962i) q^{13} -59.8307 q^{14} +(-243.624 - 421.968i) q^{15} +(-423.793 - 734.031i) q^{16} +(594.708 + 1030.06i) q^{17} +(-149.596 + 259.108i) q^{18} +(1357.04 - 2350.46i) q^{19} +(1484.08 + 2570.51i) q^{20} +(-108.064 - 187.172i) q^{21} +(-232.728 - 403.096i) q^{22} +1408.08 q^{23} +(-210.307 + 364.262i) q^{24} +(-3291.18 - 5700.50i) q^{25} -1433.74 q^{26} -2282.50 q^{27} +(658.293 + 1140.20i) q^{28} +4866.38 q^{29} +(333.528 - 577.687i) q^{30} +564.433 q^{31} +(1941.02 - 3361.94i) q^{32} +(840.687 - 1456.11i) q^{33} +(-814.172 + 1410.19i) q^{34} +(-2152.94 - 3729.00i) q^{35} +6583.78 q^{36} +(8298.91 - 687.024i) q^{37} +3715.65 q^{38} +(-2589.57 - 4485.26i) q^{39} +(-4189.91 + 7257.14i) q^{40} +(-4744.67 + 8218.02i) q^{41} +(147.942 - 256.244i) q^{42} -18551.2 q^{43} +(-5121.22 + 8870.22i) q^{44} -21532.2 q^{45} +(963.849 + 1669.44i) q^{46} +3095.29 q^{47} +4191.62 q^{48} +(7448.52 + 12901.2i) q^{49} +(4505.72 - 7804.14i) q^{50} -5882.10 q^{51} +(15774.9 + 27322.9i) q^{52} +(2674.36 + 4632.13i) q^{53} +(-1562.40 - 2706.16i) q^{54} +(16748.9 - 29010.0i) q^{55} +(-1858.51 + 3219.04i) q^{56} +(6711.06 + 11623.9i) q^{57} +(3331.11 + 5769.65i) q^{58} +(9411.45 + 16301.1i) q^{59} -14678.7 q^{60} +(7339.78 - 12712.9i) q^{61} +(386.362 + 669.199i) q^{62} -9551.00 q^{63} -21808.1 q^{64} +(-51591.6 - 89359.3i) q^{65} +2301.85 q^{66} +(-27244.4 + 47188.6i) q^{67} +35832.0 q^{68} +(-3481.73 + 6030.53i) q^{69} +(2947.44 - 5105.11i) q^{70} +(25044.2 - 43377.8i) q^{71} +(9293.77 + 16097.3i) q^{72} +39593.9 q^{73} +(6495.27 + 9369.02i) q^{74} +32552.2 q^{75} +(-40881.8 - 70809.4i) q^{76} +(7429.29 - 12867.9i) q^{77} +(3545.19 - 6140.45i) q^{78} +(29418.8 - 50954.9i) q^{79} +83509.2 q^{80} +(-20909.1 + 36215.6i) q^{81} -12991.2 q^{82} +(43070.0 + 74599.4i) q^{83} -6511.01 q^{84} -117188. q^{85} +(-12698.5 - 21994.5i) q^{86} +(-12033.0 + 20841.8i) q^{87} -28916.8 q^{88} +(8332.95 + 14433.1i) q^{89} +(-14739.1 - 25528.9i) q^{90} +(-22884.4 - 39637.0i) q^{91} +(21209.7 - 36736.3i) q^{92} +(-1395.66 + 2417.36i) q^{93} +(2118.77 + 3669.82i) q^{94} +(133704. + 231581. i) q^{95} +(9599.04 + 16626.0i) q^{96} -27920.3 q^{97} +(-10197.2 + 17662.1i) q^{98} +(-37151.2 - 64347.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 4 q^{2} + 16 q^{3} - 230 q^{4} - 51 q^{5} + 60 q^{6} + 50 q^{7} + 24 q^{8} - 1085 q^{9}+O(q^{10}) $ 30 * q - 4 * q^2 + 16 * q^3 - 230 * q^4 - 51 * q^5 + 60 * q^6 + 50 * q^7 + 24 * q^8 - 1085 * q^9	\( 30 q - 4 q^{2} + 16 q^{3} - 230 q^{4} - 51 q^{5} + 60 q^{6} + 50 q^{7} + 24 q^{8} - 1085 q^{9} - 44 q^{10} - 1556 q^{11} + 708 q^{12} - 888 q^{13} + 1888 q^{14} + 1020 q^{15} - 4566 q^{16} - 437 q^{17} - 7302 q^{18} + 4358 q^{19} - 1204 q^{20} + 2354 q^{21} + 7958 q^{22} + 2824 q^{23} + 13824 q^{24} - 620 q^{25} - 17604 q^{26} - 32 q^{27} + 11414 q^{28} + 16954 q^{29} + 15994 q^{30} - 4548 q^{31} - 9148 q^{32} - 680 q^{33} - 4576 q^{34} + 11606 q^{35} + 5828 q^{36} + 12449 q^{37} - 84560 q^{38} + 13468 q^{39} - 23018 q^{40} + 32319 q^{41} + 26750 q^{42} - 49916 q^{43} + 12034 q^{44} + 81730 q^{45} + 5300 q^{46} - 57476 q^{47} - 14944 q^{48} - 52069 q^{49} - 19224 q^{50} - 78336 q^{51} + 1316 q^{52} + 65784 q^{53} + 72114 q^{54} - 24742 q^{55} - 81130 q^{56} - 3762 q^{57} - 73868 q^{58} - 49372 q^{59} - 288608 q^{60} + 137725 q^{61} + 118854 q^{62} - 81596 q^{63} + 427612 q^{64} + 35600 q^{65} + 289576 q^{66} + 64042 q^{67} - 60500 q^{68} - 141544 q^{69} + 5200 q^{70} + 136206 q^{71} - 294660 q^{72} - 270556 q^{73} + 133162 q^{74} - 240592 q^{75} + 209502 q^{76} + 152148 q^{77} + 152814 q^{78} - 61886 q^{79} + 264936 q^{80} - 104975 q^{81} - 28160 q^{82} + 202892 q^{83} - 197912 q^{84} + 576930 q^{85} + 154822 q^{86} - 312 q^{87} - 884284 q^{88} - 12065 q^{89} - 312764 q^{90} + 206252 q^{91} - 291924 q^{92} - 60752 q^{93} - 116814 q^{94} + 506 q^{95} + 81968 q^{96} + 132062 q^{97} + 249798 q^{98} + 289874 q^{99}+O(q^{100}) \) 30 * q - 4 * q^2 + 16 * q^3 - 230 * q^4 - 51 * q^5 + 60 * q^6 + 50 * q^7 + 24 * q^8 - 1085 * q^9 - 44 * q^10 - 1556 * q^11 + 708 * q^12 - 888 * q^13 + 1888 * q^14 + 1020 * q^15 - 4566 * q^16 - 437 * q^17 - 7302 * q^18 + 4358 * q^19 - 1204 * q^20 + 2354 * q^21 + 7958 * q^22 + 2824 * q^23 + 13824 * q^24 - 620 * q^25 - 17604 * q^26 - 32 * q^27 + 11414 * q^28 + 16954 * q^29 + 15994 * q^30 - 4548 * q^31 - 9148 * q^32 - 680 * q^33 - 4576 * q^34 + 11606 * q^35 + 5828 * q^36 + 12449 * q^37 - 84560 * q^38 + 13468 * q^39 - 23018 * q^40 + 32319 * q^41 + 26750 * q^42 - 49916 * q^43 + 12034 * q^44 + 81730 * q^45 + 5300 * q^46 - 57476 * q^47 - 14944 * q^48 - 52069 * q^49 - 19224 * q^50 - 78336 * q^51 + 1316 * q^52 + 65784 * q^53 + 72114 * q^54 - 24742 * q^55 - 81130 * q^56 - 3762 * q^57 - 73868 * q^58 - 49372 * q^59 - 288608 * q^60 + 137725 * q^61 + 118854 * q^62 - 81596 * q^63 + 427612 * q^64 + 35600 * q^65 + 289576 * q^66 + 64042 * q^67 - 60500 * q^68 - 141544 * q^69 + 5200 * q^70 + 136206 * q^71 - 294660 * q^72 - 270556 * q^73 + 133162 * q^74 - 240592 * q^75 + 209502 * q^76 + 152148 * q^77 + 152814 * q^78 - 61886 * q^79 + 264936 * q^80 - 104975 * q^81 - 28160 * q^82 + 202892 * q^83 - 197912 * q^84 + 576930 * q^85 + 154822 * q^86 - 312 * q^87 - 884284 * q^88 - 12065 * q^89 - 312764 * q^90 + 206252 * q^91 - 291924 * q^92 - 60752 * q^93 - 116814 * q^94 + 506 * q^95 + 81968 * q^96 + 132062 * q^97 + 249798 * q^98 + 289874 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.684514	+	1.18561i	0.121006	+	0.209589i	0.920165	−	0.391531i	$-0.128055\pi$
$2$	0.684514	+	1.18561i	0.121006	+	0.209589i	−0.799159	+	0.601120i	$0.794721\pi$
$3$	−2.47268	+	4.28281i	−0.158623	+	0.274743i	−0.934372	−	0.356298i	$-0.884039\pi$
$3$	−2.47268	+	4.28281i	−0.158623	+	0.274743i	0.775750	+	0.631041i	$0.217372\pi$
$4$	15.0629	−	26.0897i	0.470715	−	0.815302i
$5$	−49.2630	+	85.3260i	−0.881243	+	1.52636i	−0.0312831	+	0.999511i	$0.509959\pi$
$5$	−49.2630	+	85.3260i	−0.881243	+	1.52636i	−0.849960	+	0.526847i	$0.823374\pi$
$6$	−6.77035			−0.0767773
$7$	−21.8515	+	37.8479i	−0.168553	+	0.291942i	−0.937911	−	0.346875i	$-0.887243\pi$
$7$	−21.8515	+	37.8479i	−0.168553	+	0.291942i	0.769358	+	0.638817i	$0.220576\pi$
$8$	85.0519			0.469850
$9$	109.272	+	189.264i	0.449678	+	0.778865i
$10$	−134.885			−0.426543
$11$	−339.990			−0.847196			−0.423598	−	0.905850i	$-0.639233\pi$
$11$	−339.990			−0.847196			−0.423598	+	0.905850i	$0.639233\pi$
$12$	74.4915	+	129.023i	0.149332	+	0.258651i
$13$	−523.635	+	906.962i	−0.859350	+	1.48844i	0.0131996	+	0.999913i	$0.495798\pi$
$13$	−523.635	+	906.962i	−0.859350	+	1.48844i	−0.872550	+	0.488525i	$0.837535\pi$
$14$	−59.8307			−0.0815838
$15$	−243.624	−	421.968i	−0.279570	−	0.484230i
$16$	−423.793	−	734.031i	−0.413860	−	0.716827i
$17$	594.708	+	1030.06i	0.499093	+	0.864454i	0.999999	−	0.00104740i	$-0.000333399\pi$
$17$	594.708	+	1030.06i	0.499093	+	0.864454i	−0.500907	+	0.865501i	$0.667000\pi$
$18$	−149.596	+	259.108i	−0.108828	+	0.188495i
$19$	1357.04	−	2350.46i	0.862399	−	1.49372i	−0.00720776	−	0.999974i	$-0.502294\pi$
$19$	1357.04	−	2350.46i	0.862399	−	1.49372i	0.869607	−	0.493745i	$-0.164372\pi$
$20$	1484.08	+	2570.51i	0.829629	+	1.43696i
$21$	−108.064	−	187.172i	−0.0534727	−	0.0926174i
$22$	−232.728	−	403.096i	−0.102516	−	0.177563i
$23$	1408.08			0.555018			0.277509	−	0.960723i	$-0.410491\pi$
$23$	1408.08			0.555018			0.277509	+	0.960723i	$0.410491\pi$
$24$	−210.307	+	364.262i	−0.0745289	+	0.129088i
$25$	−3291.18	−	5700.50i	−1.05318	−	1.82416i
$26$	−1433.74			−0.415947
$27$	−2282.50			−0.602562
$28$	658.293	+	1140.20i	0.158681	+	0.274843i
$29$	4866.38			1.07451			0.537256	−	0.843419i	$-0.319461\pi$
$29$	4866.38			1.07451			0.537256	+	0.843419i	$0.319461\pi$
$30$	333.528	−	577.687i	0.0676595	−	0.117190i
$31$	564.433			0.105489			0.0527446	−	0.998608i	$-0.483203\pi$
$31$	564.433			0.105489			0.0527446	+	0.998608i	$0.483203\pi$
$32$	1941.02	−	3361.94i	0.335084	−	0.580383i
$33$	840.687	−	1456.11i	0.134385	−	0.232761i
$34$	−814.172	+	1410.19i	−0.120787	+	0.209208i
$35$	−2152.94	−	3729.00i	−0.297072	−	0.514544i
$36$	6583.78			0.846680
$37$	8298.91	−	687.024i	0.996591	−	0.0825026i
$37$	8298.91	−	687.024i	0.996591	−	0.0825026i
$38$	3715.65			0.417422
$39$	−2589.57	−	4485.26i	−0.272625	−	0.472200i
$40$	−4189.91	+	7257.14i	−0.414052	+	0.717159i
$41$	−4744.67	+	8218.02i	−0.440805	+	0.763497i	−0.997749	−	0.0670528i	$-0.978640\pi$
$41$	−4744.67	+	8218.02i	−0.440805	+	0.763497i	0.556944	+	0.830550i	$0.311974\pi$
$42$	147.942	−	256.244i	0.0129410	−	0.0224145i
$43$	−18551.2			−1.53003			−0.765015	−	0.644013i	$-0.777268\pi$
$43$	−18551.2			−1.53003			−0.765015	+	0.644013i	$0.777268\pi$
$44$	−5121.22	+	8870.22i	−0.398788	+	0.690721i
$45$	−21532.2			−1.58510
$46$	963.849	+	1669.44i	0.0671606	+	0.116326i
$47$	3095.29			0.204389			0.102194	−	0.994764i	$-0.467414\pi$
$47$	3095.29			0.204389			0.102194	+	0.994764i	$0.467414\pi$
$48$	4191.62			0.262591
$49$	7448.52	+	12901.2i	0.443180	+	0.767610i
$50$	4505.72	−	7804.14i	0.254882	−	0.441469i
$51$	−5882.10			−0.316670
$52$	15774.9	+	27322.9i	0.809018	+	1.40126i
$53$	2674.36	+	4632.13i	0.130777	+	0.226512i	0.923976	−	0.382450i	$-0.124920\pi$
$53$	2674.36	+	4632.13i	0.130777	+	0.226512i	−0.793199	+	0.608962i	$0.791586\pi$
$54$	−1562.40	−	2706.16i	−0.0729137	−	0.126290i
$55$	16748.9	−	29010.0i	0.746586	−	1.29312i
$56$	−1858.51	+	3219.04i	−0.0791946	+	0.137169i
$57$	6711.06	+	11623.9i	0.273592	+	0.473876i
$58$	3331.11	+	5769.65i	0.130023	+	0.225206i
$59$	9411.45	+	16301.1i	0.351987	+	0.609659i	0.986597	−	0.163173i	$-0.0521729\pi$
$59$	9411.45	+	16301.1i	0.351987	+	0.609659i	−0.634611	+	0.772832i	$0.718840\pi$
$60$	−14678.7			−0.526392
$61$	7339.78	−	12712.9i	0.252557	−	0.437441i	−0.711672	−	0.702511i	$-0.752062\pi$
$61$	7339.78	−	12712.9i	0.252557	−	0.437441i	0.964229	+	0.265071i	$0.0853953\pi$
$62$	386.362	+	669.199i	0.0127648	+	0.0221093i
$63$	−9551.00			−0.303178
$64$	−21808.1			−0.665531
$65$	−51591.6	−	89359.3i	−1.51459	−	2.62335i
$66$	2301.85			0.0650455
$67$	−27244.4	+	47188.6i	−0.741463	+	1.28425i	0.210366	+	0.977623i	$0.432535\pi$
$67$	−27244.4	+	47188.6i	−0.741463	+	1.28425i	−0.951829	+	0.306629i	$0.900799\pi$
$68$	35832.0			0.939722
$69$	−3481.73	+	6030.53i	−0.0880384	+	0.152487i
$70$	2947.44	−	5105.11i	0.0718951	−	0.124526i
$71$	25044.2	−	43377.8i	0.589605	−	1.02123i	−0.404679	−	0.914459i	$-0.632617\pi$
$71$	25044.2	−	43377.8i	0.589605	−	1.02123i	0.994284	−	0.106767i	$-0.0340500\pi$
$72$	9293.77	+	16097.3i	0.211281	+	0.365950i
$73$	39593.9			0.869602			0.434801	−	0.900527i	$-0.356819\pi$
$73$	39593.9			0.869602			0.434801	+	0.900527i	$0.356819\pi$
$74$	6495.27	+	9369.02i	0.137885	+	0.198891i
$75$	32552.2			0.668232
$76$	−40881.8	−	70809.4i	−0.811888	−	1.40623i
$77$	7429.29	−	12867.9i	0.142797	−	0.247332i
$78$	3545.19	−	6140.45i	0.0659786	−	0.114278i
$79$	29418.8	−	50954.9i	0.530344	−	0.918583i	−0.469029	−	0.883183i	$-0.655396\pi$
$79$	29418.8	−	50954.9i	0.530344	−	0.918583i	0.999373	−	0.0354001i	$-0.0112706\pi$
$80$	83509.2			1.45885
$81$	−20909.1	+	36215.6i	−0.354098	+	0.613315i
$82$	−12991.2			−0.213361
$83$	43070.0	+	74599.4i	0.686245	+	1.18861i	0.973044	+	0.230621i	$0.0740756\pi$
$83$	43070.0	+	74599.4i	0.686245	+	1.18861i	−0.286799	+	0.957991i	$0.592591\pi$
$84$	−6511.01			−0.100682
$85$	−117188.			−1.75929
$86$	−12698.5	−	21994.5i	−0.185143	−	0.320677i
$87$	−12033.0	+	20841.8i	−0.170442	+	0.295214i
$88$	−28916.8			−0.398055
$89$	8332.95	+	14433.1i	0.111513	+	0.193145i	0.916380	−	0.400309i	$-0.131097\pi$
$89$	8332.95	+	14433.1i	0.111513	+	0.193145i	−0.804868	+	0.593454i	$0.797764\pi$
$90$	−14739.1	−	25528.9i	−0.191807	−	0.332220i
$91$	−22884.4	−	39637.0i	−0.289692	−	0.501761i
$92$	21209.7	−	36736.3i	0.261255	−	0.452507i
$93$	−1395.66	+	2417.36i	−0.0167330	+	0.0289824i
$94$	2118.77	+	3669.82i	0.0247323	+	0.0428376i
$95$	133704.	+	231581.i	1.51997	+	2.63266i
$96$	9599.04	+	16626.0i	0.106304	+	0.184124i
$97$	−27920.3			−0.301294			−0.150647	−	0.988588i	$-0.548136\pi$
$97$	−27920.3			−0.301294			−0.150647	+	0.988588i	$0.548136\pi$
$98$	−10197.2	+	17662.1i	−0.107255	+	0.185771i
$99$	−37151.2	−	64347.8i	−0.380965	−	0.659851i
$100$	−198299.			−1.98299
$101$	−22177.8			−0.216329			−0.108165	−	0.994133i	$-0.534497\pi$
$101$	−22177.8			−0.216329			−0.108165	+	0.994133i	$0.534497\pi$
$102$	−4026.38	−	6973.89i	−0.0383190	−	0.0663704i
$103$	150643.			1.39912			0.699559	−	0.714575i	$-0.253380\pi$
$103$	150643.			1.39912			0.699559	+	0.714575i	$0.253380\pi$
$104$	−44536.2	+	77138.9i	−0.403766	+	0.699343i
$105$	21294.2			0.188490
$106$	−3661.28	+	6341.52i	−0.0316496	+	0.0548187i
$107$	39040.2	−	67619.6i	0.329650	−	0.570970i	−0.652793	−	0.757537i	$-0.726403\pi$
$107$	39040.2	−	67619.6i	0.329650	−	0.570970i	0.982442	+	0.186567i	$0.0597360\pi$
$108$	−34381.0	+	59549.7i	−0.283635	+	0.491270i
$109$	36490.6	+	63203.6i	0.294181	+	0.509537i	0.974794	−	0.223106i	$-0.0716197\pi$
$109$	36490.6	+	63203.6i	0.294181	+	0.509537i	−0.680613	+	0.732643i	$0.738286\pi$
$110$	45859.5			0.361366
$111$	−17578.2	+	37241.5i	−0.135415	+	0.286893i
$112$	37042.1			0.279029
$113$	−42713.2	−	73981.5i	−0.314678	−	0.545038i	0.664691	−	0.747118i	$-0.268563\pi$
$113$	−42713.2	−	73981.5i	−0.314678	−	0.545038i	−0.979369	+	0.202080i	$0.935230\pi$
$114$	−9187.63	+	15913.4i	−0.0662127	+	0.114684i
$115$	−69366.1	+	120146.i	−0.489106	+	0.847156i
$116$	73301.8	−	126962.i	0.505789	−	0.876052i
$117$	−228874.			−1.54572
$118$	−12884.5	+	22316.7i	−0.0851851	+	0.147545i
$119$	−51981.0			−0.336494
$120$	−20720.7	−	35889.2i	−0.131356	−	0.227516i
$121$	−45458.0			−0.282258
$122$	20096.7			0.122244
$123$	−23464.2	−	40641.1i	−0.139843	−	0.242216i
$124$	8501.98	−	14725.9i	0.0496553	−	0.0860056i
$125$	340640.			1.94994
$126$	−6537.80	−	11323.8i	−0.0366864	−	0.0635427i
$127$	48085.4	+	83286.4i	0.264548	+	0.458210i	0.967445	−	0.253081i	$-0.0814440\pi$
$127$	48085.4	+	83286.4i	0.264548	+	0.458210i	−0.702897	+	0.711291i	$0.748111\pi$
$128$	−77040.5	−	133438.i	−0.415618	−	0.719871i
$129$	45871.1	−	79451.1i	0.242697	−	0.420364i
$130$	70630.4	−	122335.i	0.366550	−	0.634883i
$131$	64950.2	+	112497.i	0.330675	+	0.572747i	0.982644	−	0.185499i	$-0.0593901\pi$
$131$	64950.2	+	112497.i	0.330675	+	0.572747i	−0.651969	+	0.758246i	$0.726057\pi$
$132$	−25326.3	−	43866.5i	−0.126514	−	0.219128i
$133$	59306.7	+	102722.i	0.290720	+	0.503541i
$134$	−74596.6			−0.358886
$135$	112443.	−	194757.i	0.531004	−	0.919725i
$136$	50581.0	+	87608.9i	0.234499	+	0.406164i
$137$	163292.			0.743300			0.371650	−	0.928373i	$-0.378792\pi$
$137$	163292.			0.743300			0.371650	+	0.928373i	$0.378792\pi$
$138$	−9533.17			−0.0426128
$139$	−94437.2	−	163570.i	−0.414578	−	0.718070i	0.580806	−	0.814042i	$-0.302737\pi$
$139$	−94437.2	−	163570.i	−0.414578	−	0.718070i	−0.995384	+	0.0959722i	$0.969404\pi$
$140$	−129718.			−0.559345
$141$	−7653.67	+	13256.5i	−0.0324207	+	0.0561543i
$142$	68572.4			0.285383
$143$	178030.	−	308358.i	0.728038	−	1.26100i
$144$	92617.1	−	160418.i	0.372207	−	0.644682i
$145$	−239733.	+	415229.i	−0.946907	+	1.64009i
$146$	27102.6	+	46943.0i	0.105227	+	0.182259i
$147$	−73671.4			−0.281194
$148$	107081.	−	226864.i	0.401846	−	0.851358i
$149$	−307061.			−1.13308			−0.566539	−	0.824035i	$-0.691718\pi$
$149$	−307061.			−1.13308			−0.566539	+	0.824035i	$0.691718\pi$
$150$	22282.5	+	38594.4i	0.0808602	+	0.140054i
$151$	41841.5	−	72471.7i	0.149336	−	0.258658i	−0.781646	−	0.623722i	$-0.785620\pi$
$151$	41841.5	−	72471.7i	0.149336	−	0.258658i	0.930982	+	0.365064i	$0.118953\pi$
$152$	115419.	−	199911.i	0.405198	−	0.701824i
$153$	−129969.	+	225114.i	−0.448862	+	0.777451i
$154$	20341.8			0.0691175
$155$	−27805.6	+	48160.8i	−0.0929616	+	0.161014i
$156$	−156025.			−0.513315
$157$	−54261.5	−	93983.7i	−0.175688	−	0.304301i	0.764711	−	0.644373i	$-0.222882\pi$
$157$	−54261.5	−	93983.7i	−0.175688	−	0.304301i	−0.940399	+	0.340072i	$0.889548\pi$
$158$	80550.4			0.256700
$159$	−26451.4			−0.0829767
$160$	191240.	+	331238.i	0.590581	+	1.02292i
$161$	−30768.6	+	53292.8i	−0.0935499	+	0.162033i
$162$	−57250.3			−0.171392
$163$	−43054.7	−	74572.8i	−0.126926	−	0.219843i	0.795558	−	0.605877i	$-0.207178\pi$
$163$	−43054.7	−	74572.8i	−0.126926	−	0.219843i	−0.922484	+	0.386035i	$0.873844\pi$
$164$	142937.	+	247574.i	0.414987	+	0.718779i
$165$	82829.5	+	143465.i	0.236851	+	0.410238i
$166$	−58964.0	+	102129.i	−0.166080	+	0.287659i
$167$	32440.0	−	56187.7i	0.0900097	−	0.155901i	−0.817505	−	0.575921i	$-0.804644\pi$
$167$	32440.0	−	56187.7i	0.0900097	−	0.155901i	0.907515	+	0.420020i	$0.137977\pi$
$168$	−9191.03	−	15919.3i	−0.0251241	−	0.0435163i
$169$	−362740.	−	628285.i	−0.976965	−	1.69215i
$170$	−80217.0	−	138940.i	−0.212885	−	0.368727i
$171$	593144.			1.55121
$172$	−279434.	+	483994.i	−0.720208	+	1.24744i
$173$	44966.8	+	77884.8i	0.114229	+	0.197851i	0.917471	−	0.397802i	$-0.130227\pi$
$173$	44966.8	+	77884.8i	0.114229	+	0.197851i	−0.803242	+	0.595653i	$0.796894\pi$
$174$	−32947.1			−0.0824982
$175$	287669.			0.710066
$176$	144085.	+	249563.i	0.350621	+	0.607293i
$177$	−93086.1			−0.223332
$178$	−11408.0	+	19759.3i	−0.0269874	+	0.0467436i
$179$	−790485.			−1.84400			−0.922000	−	0.387190i	$-0.873446\pi$
$179$	−790485.			−1.84400			−0.922000	+	0.387190i	$0.873446\pi$
$180$	−324337.	+	561768.i	−0.746131	+	1.29234i
$181$	27592.6	−	47791.9i	0.0626032	−	0.108432i	−0.833025	−	0.553235i	$-0.813393\pi$
$181$	27592.6	−	47791.9i	0.0626032	−	0.108432i	0.895628	+	0.444803i	$0.146726\pi$
$182$	31329.4	−	54264.2i	0.0701090	−	0.121432i
$183$	36297.9	+	62869.9i	0.0801224	+	0.138776i
$184$	119760.			0.260775
$185$	−350208.	+	741958.i	−0.752310	+	1.59386i
$186$	−3821.41			−0.00809917
$187$	−202194.	−	350211.i	−0.422829	−	0.732362i
$188$	46624.0	−	80755.1i	0.0962088	−	0.166638i
$189$	49876.1	−	86388.0i	0.101564	−	0.175913i
$190$	−183044.	+	317041.i	−0.367851	+	0.637136i
$191$	529061.			1.04935			0.524677	−	0.851301i	$-0.324186\pi$
$191$	529061.			1.04935			0.524677	+	0.851301i	$0.324186\pi$
$192$	53924.6	−	93400.2i	0.105568	−	0.182850i
$193$	408009.			0.788454			0.394227	−	0.919013i	$-0.371012\pi$
$193$	408009.			0.788454			0.394227	+	0.919013i	$0.371012\pi$
$194$	−19111.8	−	33102.6i	−0.0364584	−	0.0631478i
$195$	510279.			0.960995
$196$	448785.			0.834446
$197$	−194132.	−	336246.i	−0.356394	−	0.617293i	0.630961	−	0.775814i	$-0.282661\pi$
$197$	−194132.	−	336246.i	−0.356394	−	0.617293i	−0.987356	+	0.158521i	$0.949327\pi$
$198$	50861.1	−	88094.0i	0.0921983	−	0.159692i
$199$	−427354.			−0.764989			−0.382495	−	0.923958i	$-0.624935\pi$
$199$	−427354.			−0.764989			−0.382495	+	0.923958i	$0.624935\pi$
$200$	−279922.	−	484838.i	−0.494836	−	0.857081i
$201$	−134733.	−	233365.i	−0.235226	−	0.407423i
$202$	−15181.0	−	26294.3i	−0.0261772	−	0.0453402i
$203$	−106338.	+	184183.i	−0.181112	+	0.313696i
$204$	−88601.3	+	153462.i	−0.149061	+	0.258182i
$205$	−467474.	−	809688.i	−0.776913	−	1.34565i
$206$	103117.	+	178604.i	0.169302	+	0.293240i
$207$	153863.	+	266498.i	0.249579	+	0.432284i
$208$	887651.			1.42260
$209$	−461379.	+	799132.i	−0.730621	+	1.26547i
$210$	14576.2	+	25246.7i	0.0228084	+	0.0395053i
$211$	74721.7			0.115542			0.0577711	−	0.998330i	$-0.481601\pi$
$211$	74721.7			0.115542			0.0577711	+	0.998330i	$0.481601\pi$
$212$	161134.			0.246234
$213$	123853.	+	214519.i	0.187050	+	0.323979i
$214$	106894.			0.159559
$215$	913885.	−	1.58290e6i	1.34833	−	2.33537i
$216$	−194131.			−0.283114
$217$	−12333.7	+	21362.6i	−0.0177805	+	0.0307967i
$218$	−49956.7	+	86527.5i	−0.0711955	+	0.123314i
$219$	−97903.1	+	169573.i	−0.137939	+	0.238917i
$220$	−504574.	−	873947.i	−0.702858	−	1.21739i
$221$	−1.24564e6			−1.71558
$222$	−56186.5	+	4651.39i	−0.0765156	+	0.00633433i
$223$	177377.			0.238856			0.119428	−	0.992843i	$-0.461894\pi$
$223$	177377.			0.238856			0.119428	+	0.992843i	$0.461894\pi$
$224$	84828.2	+	146927.i	0.112959	+	0.195651i
$225$	719266.	−	1.24581e6i	0.947182	−	1.64057i
$226$	58475.6	−	101283.i	0.0761560	−	0.131906i
$227$	−258214.	+	447240.i	−0.332595	+	0.576071i	−0.983020	−	0.183500i	$-0.941257\pi$
$227$	−258214.	+	447240.i	−0.332595	+	0.576071i	0.650425	+	0.759570i	$0.274591\pi$
$228$	404351.			0.515136
$229$	111008.	−	192272.i	0.139883	−	0.242285i	−0.787569	−	0.616227i	$-0.788661\pi$
$229$	111008.	−	192272.i	0.139883	−	0.242285i	0.927452	+	0.373941i	$0.121994\pi$
$230$	−189928.			−0.236739
$231$	36740.6	+	63636.5i	0.0453018	+	0.0784651i
$232$	413895.			0.504860
$233$	530582.			0.640269			0.320134	−	0.947372i	$-0.396272\pi$
$233$	530582.			0.640269			0.320134	+	0.947372i	$0.396272\pi$
$234$	−156667.	−	271356.i	−0.187042	−	0.323966i
$235$	−152483.	+	264109.i	−0.180116	+	0.311970i
$236$	567054.			0.662742
$237$	145487.	+	251991.i	0.168249	+	0.291416i
$238$	−35581.8	−	61629.4i	−0.0407179	−	0.0705254i
$239$	501940.	+	869386.i	0.568404	+	0.984505i	0.996724	+	0.0808775i	$0.0257723\pi$
$239$	501940.	+	869386.i	0.568404	+	0.984505i	−0.428320	+	0.903627i	$0.640894\pi$
$240$	−206492.	+	357654.i	−0.231406	+	0.400807i
$241$	551083.	−	954504.i	0.611187	−	1.05861i	−0.379853	−	0.925047i	$-0.624026\pi$
$241$	551083.	−	954504.i	0.611187	−	1.05861i	0.991041	−	0.133561i	$-0.0426411\pi$
$242$	−31116.6	−	53895.6i	−0.0341550	−	0.0591582i
$243$	−380727.	−	659439.i	−0.413617	−	0.716405i
$244$	−221117.	−	382985.i	−0.237764	−	0.411820i
$245$	−1.46775e6			−1.56220
$246$	32123.1	−	55638.8i	0.0338438	−	0.0586193i
$247$	1.42119e6	+	2.46157e6i	1.48221	+	2.56726i
$248$	48006.1			0.0495641
$249$	−425994.			−0.435416
$250$	233173.	+	403868.i	0.235955	+	0.408686i
$251$	−243215.			−0.243672			−0.121836	−	0.992550i	$-0.538878\pi$
$251$	−243215.			−0.243672			−0.121836	+	0.992550i	$0.538878\pi$
$252$	−143866.	+	249183.i	−0.142710	+	0.247182i
$253$	−478732.			−0.470209
$254$	−65830.3	+	114021.i	−0.0640238	+	0.110892i
$255$	289770.	−	501896.i	0.279063	−	0.483351i
$256$	−243460.	+	421684.i	−0.232181	+	0.402150i
$257$	−668377.	−	1.15766e6i	−0.631232	−	1.09333i	−0.987300	−	0.158866i	$-0.949216\pi$
$257$	−668377.	−	1.15766e6i	−0.631232	−	1.09333i	0.356068	−	0.934460i	$-0.384117\pi$
$258$	125598.			0.117472
$259$	−155341.	+	329109.i	−0.143892	+	0.304853i
$260$	−3.10847e6			−2.85177
$261$	531758.	+	921032.i	0.483184	+	0.836900i
$262$	−88918.6	+	154012.i	−0.0800275	+	0.138612i
$263$	247329.	−	428387.i	0.220489	−	0.381897i	−0.734468	−	0.678643i	$-0.762568\pi$
$263$	247329.	−	428387.i	0.220489	−	0.381897i	0.954956	+	0.296746i	$0.0959015\pi$
$264$	71502.1	−	123845.i	0.0631406	−	0.109363i
$265$	−526988.			−0.460985
$266$	−81192.6	+	140630.i	−0.0703578	+	0.121863i
$267$	−82419.0			−0.0707537
$268$	820757.	+	1.42159e6i	0.698036	+	1.20903i
$269$	−764022.			−0.643762			−0.321881	−	0.946780i	$-0.604315\pi$
$269$	−764022.			−0.643762			−0.321881	+	0.946780i	$0.604315\pi$
$270$	307875.			0.257019
$271$	649285.	+	1.12459e6i	0.537047	+	0.930192i	0.999061	+	0.0433197i	$0.0137934\pi$
$271$	649285.	+	1.12459e6i	0.537047	+	0.930192i	−0.462015	+	0.886872i	$0.652873\pi$
$272$	504066.	−	873067.i	0.413109	−	0.715526i
$273$	226344.			0.183807
$274$	111776.	+	193601.i	0.0899438	+	0.155787i
$275$	1.11897e6	+	1.93811e6i	0.892249	+	1.54542i
$276$	104890.	+	181674.i	0.0828820	+	0.143556i
$277$	124682.	−	215956.i	0.0976351	−	0.169109i	−0.813070	−	0.582166i	$-0.802206\pi$
$277$	124682.	−	215956.i	0.0976351	−	0.169109i	0.910705	+	0.413057i	$0.135539\pi$
$278$	129287.	−	223932.i	0.100333	−	0.173782i
$279$	61676.5	+	106827.i	0.0474361	+	0.0821618i
$280$	−183112.	−	317159.i	−0.139579	−	0.241759i
$281$	808604.	+	1.40054e6i	0.610900	+	1.05811i	0.991089	+	0.133201i	$0.0425256\pi$
$281$	808604.	+	1.40054e6i	0.610900	+	1.05811i	−0.380189	+	0.924909i	$0.624141\pi$
$282$	−20956.2			−0.0156924
$283$	1.11212e6	−	1.92624e6i	0.825438	−	1.42970i	−0.0761461	−	0.997097i	$-0.524262\pi$
$283$	1.11212e6	−	1.92624e6i	0.825438	−	1.42970i	0.901584	−	0.432604i	$-0.142405\pi$
$284$	−754476.	−	1.30679e6i	−0.555072	−	0.961413i
$285$	−1.32243e6			−0.964405
$286$	487458.			0.352388
$287$	−207357.	−	359152.i	−0.148598	−	0.257379i
$288$	848392.			0.602720
$289$	2574.28	−	4458.79i	0.00181306	−	0.00314031i
$290$	−656402.			−0.458326
$291$	69038.0	−	119577.i	0.0477920	−	0.0827782i
$292$	596397.	−	1.03299e6i	0.409335	−	0.708989i
$293$	−716059.	+	1.24025e6i	−0.487282	+	0.843996i	−0.999893	−	0.0146243i	$-0.995345\pi$
$293$	−716059.	+	1.24025e6i	−0.487282	+	0.843996i	0.512612	+	0.858621i	$0.328678\pi$
$294$	−50429.1	−	87345.8i	−0.0340262	−	0.0589350i
$295$	−1.85454e6			−1.24074
$296$	705839.	−	58432.7i	0.468248	−	0.0387638i
$297$	776027.			0.510488
$298$	−210188.	−	364056.i	−0.137109	−	0.237480i
$299$	−737318.	+	1.27707e6i	−0.476955	+	0.826110i
$300$	490330.	−	849277.i	0.314547	−	0.544811i
$301$	405371.	−	702123.i	0.257891	−	0.446680i
$302$	114565.			0.0722824
$303$	54838.8	−	94983.5i	0.0343148	−	0.0594349i
$304$	−2.30041e6			−1.42765
$305$	723159.	+	1.25255e6i	0.445127	+	0.770983i
$306$	−355864.			−0.217260
$307$	−263641.			−0.159649			−0.0798245	−	0.996809i	$-0.525436\pi$
$307$	−263641.			−0.159649			−0.0798245	+	0.996809i	$0.525436\pi$
$308$	−223813.	−	387655.i	−0.134434	−	0.232846i
$309$	−372491.	+	645174.i	−0.221932	+	0.384398i
$310$	−76133.4			−0.0449957
$311$	−1.26348e6	−	2.18841e6i	−0.740743	−	1.28300i	−0.952158	−	0.305607i	$-0.901141\pi$
$311$	−1.26348e6	−	2.18841e6i	−0.740743	−	1.28300i	0.211415	−	0.977396i	$-0.432193\pi$
$312$	−220248.	−	381480.i	−0.128093	−	0.221863i
$313$	139059.	+	240857.i	0.0802301	+	0.138963i	0.903349	−	0.428907i	$-0.141101\pi$
$313$	139059.	+	240857.i	0.0802301	+	0.138963i	−0.823119	+	0.567869i	$0.807768\pi$
$314$	74285.6	−	128666.i	0.0425187	−	0.0736446i
$315$	470511.	−	814949.i	0.267174	−	0.462758i
$316$	−886265.	−	1.53506e6i	−0.499282	−	0.864781i
$317$	411987.	+	713582.i	0.230269	+	0.398838i	0.957887	−	0.287145i	$-0.0927061\pi$
$317$	411987.	+	713582.i	0.230269	+	0.398838i	−0.727618	+	0.685982i	$0.759373\pi$
$318$	−18106.4	−	31361.2i	−0.0100407	−	0.0173910i
$319$	−1.65452e6			−0.910323
$320$	1.07433e6	−	1.86080e6i	0.586495	−	1.01584i
$321$	193068.	+	334404.i	0.104580	+	0.181138i
$322$	−84246.2			−0.0452804
$323$	3.22817e6			1.72167
$324$	629903.	+	1.09102e6i	0.333358	+	0.577393i
$325$	6.89351e6			3.62020
$326$	58943.0	−	102092.i	0.0307177	−	0.0532046i
$327$	−360919.			−0.186655
$328$	−403544.	+	698958.i	−0.207112	+	0.358729i
$329$	−67636.7	+	117150.i	−0.0344503	+	0.0596697i
$330$	−113396.	+	196408.i	−0.0573209	+	0.0992826i
$331$	−554501.	−	960423.i	−0.278184	−	0.481829i	0.692750	−	0.721178i	$-0.256399\pi$
$331$	−554501.	−	960423.i	−0.278184	−	0.481829i	−0.970933	+	0.239350i	$0.923066\pi$
$332$	2.59503e6			1.29210
$333$	1.03687e6	+	1.49561e6i	0.512403	+	0.739110i
$334$	88822.5			0.0435669
$335$	−2.68428e6	−	4.64930e6i	−1.30682	−	2.26348i
$336$	−91593.3	+	158644.i	−0.0442604	+	0.0766613i
$337$	956999.	−	1.65757e6i	0.459025	−	0.795055i	−0.539884	−	0.841739i	$-0.681532\pi$
$337$	956999.	−	1.65757e6i	0.459025	−	0.795055i	0.998910	+	0.0466839i	$0.0148654\pi$
$338$	496602.	−	860140.i	0.236438	−	0.409522i
$339$	422465.			0.199660
$340$	−1.76519e6	+	3.05740e6i	−0.828123	+	1.43435i
$341$	−191901.			−0.0893700
$342$	406015.	+	703239.i	0.187706	+	0.325115i
$343$	−1.38556e6			−0.635903
$344$	−1.57781e6			−0.718884
$345$	−343041.	−	594164.i	−0.155167	−	0.268756i
$346$	−61560.8	+	106626.i	−0.0276448	+	0.0478823i
$347$	−1.32025e6			−0.588615			−0.294308	−	0.955711i	$-0.595089\pi$
$347$	−1.32025e6			−0.588615			−0.294308	+	0.955711i	$0.595089\pi$
$348$	362504.	+	627876.i	0.160459	+	0.277924i
$349$	−258449.	−	447647.i	−0.113583	−	0.196731i	0.803630	−	0.595130i	$-0.202899\pi$
$349$	−258449.	−	447647.i	−0.113583	−	0.196731i	−0.917212	+	0.398399i	$0.869566\pi$
$350$	196914.	+	341065.i	0.0859223	+	0.148822i
$351$	1.19520e6	−	2.07014e6i	0.517812	−	0.896876i
$352$	−659925.	+	1.14302e6i	−0.283882	+	0.491698i
$353$	1.95078e6	+	3.37884e6i	0.833241	+	1.44322i	0.895455	+	0.445153i	$0.146851\pi$
$353$	1.95078e6	+	3.37884e6i	0.833241	+	1.44322i	−0.0622140	+	0.998063i	$0.519816\pi$
$354$	−63718.8	−	110364.i	−0.0270246	−	0.0468080i
$355$	2.46750e6	+	4.27384e6i	1.03917	+	1.79990i
$356$	502073.			0.209963
$357$	128533.	−	222625.i	0.0533756	−	0.0924493i
$358$	−541098.	−	937209.i	−0.223135	−	0.386482i
$359$	−4.78385e6			−1.95903			−0.979515	−	0.201370i	$-0.935461\pi$
$359$	−4.78385e6			−1.95903			−0.979515	+	0.201370i	$0.935461\pi$
$360$	−1.83135e6			−0.744760
$361$	−2.44506e6	−	4.23497e6i	−0.987464	−	1.71034i
$362$	75550.2			0.0303015
$363$	112403.	−	194688.i	0.0447726	−	0.0775484i
$364$	−1.37882e6			−0.545450
$365$	−1.95051e6	+	3.37838e6i	−0.766331	+	1.32732i
$366$	−49692.9	+	86070.6i	−0.0193906	+	0.0335855i
$367$	123879.	−	214565.i	0.0480102	−	0.0831562i	−0.841022	−	0.541002i	$-0.818045\pi$
$367$	123879.	−	214565.i	0.0480102	−	0.0831562i	0.889032	+	0.457845i	$0.151379\pi$
$368$	−596733.	−	1.03357e6i	−0.229700	−	0.397852i
$369$	−2.07383e6			−0.792881
$370$	−1.11940e6	+	92669.1i	−0.425089	+	0.0351909i
$371$	−233755.			−0.0881712
$372$	42045.4	+	72824.8i	0.0157529	+	0.0272849i
$373$	917087.	−	1.58844e6i	0.341302	−	0.591152i	−0.643373	−	0.765553i	$-0.722466\pi$
$373$	917087.	−	1.58844e6i	0.341302	−	0.591152i	0.984675	+	0.174401i	$0.0557989\pi$
$374$	276810.	−	479449.i	0.102330	−	0.177241i
$375$	−842296.	+	1.45890e6i	−0.309305	+	0.535732i
$376$	263260.			0.0960320
$377$	−2.54821e6	+	4.41363e6i	−0.923382	+	1.59935i
$378$	136564.			0.0491593
$379$	2.35307e6	+	4.07564e6i	0.841468	+	1.45746i	0.888654	+	0.458579i	$0.151641\pi$
$379$	2.35307e6	+	4.07564e6i	0.841468	+	1.45746i	−0.0471860	+	0.998886i	$0.515025\pi$
$380$	8.05584e6			2.86188
$381$	−475600.			−0.167853
$382$	362150.	+	627262.i	0.126978	+	0.219933i
$383$	1.24088e6	−	2.14927e6i	0.432248	−	0.748675i	−0.564819	−	0.825215i	$-0.691054\pi$
$383$	1.24088e6	−	2.14927e6i	0.432248	−	0.748675i	0.997067	+	0.0765401i	$0.0243873\pi$
$384$	761987.			0.263706
$385$	731978.	+	1.26782e6i	0.251679	+	0.435920i
$386$	279288.	+	483741.i	0.0954078	+	0.165251i
$387$	−2.02712e6	−	3.51107e6i	−0.688020	−	1.19169i
$388$	−420559.	+	728430.i	−0.141823	+	0.245645i
$389$	2.93239e6	−	5.07904e6i	0.982533	−	1.70180i	0.330109	−	0.943943i	$-0.392914\pi$
$389$	2.93239e6	−	5.07904e6i	0.982533	−	1.70180i	0.652424	−	0.757854i	$-0.273752\pi$
$390$	349293.	+	604994.i	0.116286	+	0.201414i
$391$	837394.	+	1.45041e6i	0.277005	+	0.479787i
$392$	633511.	+	1.09727e6i	0.208228	+	0.360662i
$393$	−642405.			−0.209811
$394$	265772.	−	460330.i	0.0862518	−	0.149392i
$395$	2.89852e6	+	5.02038e6i	0.934724	+	1.61899i
$396$	−2.23842e6			−0.717304
$397$	−1.93079e6			−0.614837			−0.307418	−	0.951574i	$-0.599465\pi$
$397$	−1.93079e6			−0.614837			−0.307418	+	0.951574i	$0.599465\pi$
$398$	−292530.	−	506677.i	−0.0925684	−	0.160333i
$399$	−586587.			−0.184459
$400$	−2.78956e6	+	4.83166e6i	−0.871738	+	1.50989i
$401$	4.04409e6			1.25591			0.627957	−	0.778248i	$-0.283892\pi$
$401$	4.04409e6			1.25591			0.627957	+	0.778248i	$0.283892\pi$
$402$	184454.	−	319483.i	0.0569276	−	0.0986014i
$403$	−295557.	+	511919.i	−0.0906521	+	0.157014i
$404$	−334062.	+	578612.i	−0.101830	+	0.176374i
$405$	−2.06009e6	−	3.56818e6i	−0.624092	−	1.08096i
$406$	−291159.			−0.0876628
$407$	−2.82155e6	+	233581.i	−0.844308	+	0.0698959i
$408$	−500284.			−0.148787
$409$	−1.72521e6	−	2.98816e6i	−0.509958	−	0.883273i	−0.999933	−	0.0115369i	$-0.996328\pi$
$409$	−1.72521e6	−	2.98816e6i	−0.509958	−	0.883273i	0.489976	−	0.871736i	$-0.337006\pi$
$410$	639985.	−	1.10849e6i	0.188023	−	0.325665i
$411$	−403770.	+	699350.i	−0.117904	+	0.204216i
$412$	2.26911e6	−	3.93021e6i	0.658586	−	1.14070i
$413$	−822617.			−0.237314
$414$	−210643.	+	364844.i	−0.0604012	+	0.104618i
$415$	−8.48702e6			−2.41900
$416$	2.03277e6	+	3.52086e6i	0.575909	+	0.997504i
$417$	934053.			0.263046
$418$	−1.26328e6			−0.353639
$419$	−380573.	−	659172.i	−0.105902	−	0.183427i	0.808204	−	0.588902i	$-0.200440\pi$
$419$	−380573.	−	659172.i	−0.105902	−	0.183427i	−0.914106	+	0.405475i	$0.867106\pi$
$420$	320752.	−	555558.i	0.0887249	−	0.153676i
$421$	2.94008e6			0.808451			0.404226	−	0.914659i	$-0.367541\pi$
$421$	2.94008e6			0.808451			0.404226	+	0.914659i	$0.367541\pi$
$422$	51148.0	+	88591.0i	0.0139813	+	0.0242163i
$423$	338227.	+	585827.i	0.0919090	+	0.159191i
$424$	227460.	+	393972.i	0.0614455	+	0.106427i
$425$	3.91458e6	−	6.78026e6i	1.05127	−	1.82085i
$426$	−169558.	+	293683.i	−0.0452683	+	0.0784070i
$427$	320771.	+	555591.i	0.0851383	+	0.147464i
$428$	−1.17612e6	−	2.03709e6i	−0.310342	−	0.537528i
$429$	880426.	+	1.52494e6i	0.230967	+	0.400046i
$430$	2.50227e6			0.652624
$431$	−1.31893e6	+	2.28445e6i	−0.342001	+	0.592363i	−0.984804	−	0.173668i	$-0.944438\pi$
$431$	−1.31893e6	+	2.28445e6i	−0.342001	+	0.592363i	0.642803	+	0.766031i	$0.277771\pi$
$432$	967308.	+	1.67543e6i	0.249376	+	0.431933i
$433$	1.16452e6			0.298487			0.149244	−	0.988800i	$-0.452316\pi$
$433$	1.16452e6			0.298487			0.149244	+	0.988800i	$0.452316\pi$
$434$	−33770.4			−0.00860620
$435$	−1.18557e6	−	2.05346e6i	−0.300402	−	0.520311i
$436$	2.19862e6			0.553902
$437$	1.91082e6	−	3.30963e6i	0.478647	−	0.829040i
$438$	−268064.			−0.0667657
$439$	2.34381e6	−	4.05960e6i	0.580445	−	1.00536i	−0.414982	−	0.909830i	$-0.636212\pi$
$439$	2.34381e6	−	4.05960e6i	0.580445	−	1.00536i	0.995427	−	0.0955302i	$-0.0304547\pi$
$440$	1.42453e6	−	2.46735e6i	0.350783	−	0.607575i
$441$	−1.62783e6	+	2.81948e6i	−0.398576	+	0.690354i
$442$	−852657.	−	1.47685e6i	−0.207596	−	0.359567i
$443$	1.37568e6			0.333049			0.166524	−	0.986037i	$-0.446746\pi$
$443$	1.37568e6			0.333049			0.166524	+	0.986037i	$0.446746\pi$
$444$	706840.	+	1.01957e6i	0.170163	+	0.245449i
$445$	−1.64202e6			−0.393079
$446$	121417.	+	210301.i	0.0289031	+	0.0500616i
$447$	759266.	−	1.31509e6i	0.179732	−	0.311305i
$448$	476541.	−	825393.i	0.112177	−	0.194297i
$449$	−2.77963e6	+	4.81445e6i	−0.650684	+	1.12702i	0.332273	+	0.943183i	$0.392185\pi$
$449$	−2.77963e6	+	4.81445e6i	−0.650684	+	1.12702i	−0.982957	+	0.183835i	$0.941149\pi$
$450$	1.96939e6			0.458459
$451$	1.61314e6	−	2.79404e6i	0.373449	−	0.646832i
$452$	−2.57354e6			−0.592495
$453$	206922.	+	358399.i	0.0473763	+	0.0820581i
$454$	−707005.			−0.160984
$455$	4.50942e6			1.02116
$456$	570788.	+	988634.i	0.128547	+	0.222650i
$457$	3.65756e6	−	6.33508e6i	0.819221	−	1.41893i	−0.0870357	−	0.996205i	$-0.527739\pi$
$457$	3.65756e6	−	6.33508e6i	0.819221	−	1.41893i	0.906257	−	0.422727i	$-0.138927\pi$
$458$	303947.			0.0677071
$459$	−1.35742e6	−	2.35112e6i	−0.300734	−	0.520887i
$460$	2.08971e6	+	3.61948e6i	0.460459	+	0.797538i
$461$	−1.23171e6	−	2.13339e6i	−0.269934	−	0.467539i	0.698911	−	0.715209i	$-0.253668\pi$
$461$	−1.23171e6	−	2.13339e6i	−0.269934	−	0.467539i	−0.968844	+	0.247670i	$0.920335\pi$
$462$	−50298.9	+	87120.2i	−0.0109636	+	0.0189895i
$463$	2.58424e6	−	4.47603e6i	0.560248	−	0.970377i	−0.437227	−	0.899351i	$-0.644039\pi$
$463$	2.58424e6	−	4.47603e6i	0.560248	−	0.970377i	0.997474	−	0.0710260i	$-0.0226273\pi$
$464$	−2.06234e6	−	3.57208e6i	−0.444698	−	0.770240i
$465$	−137509.	−	238173.i	−0.0294916	−	0.0510810i
$466$	363191.	+	629065.i	0.0774765	+	0.134193i
$467$	−4.13950e6			−0.878325			−0.439163	−	0.898408i	$-0.644725\pi$
$467$	−4.13950e6			−0.878325			−0.439163	+	0.898408i	$0.644725\pi$
$468$	−3.44750e6	+	5.97124e6i	−0.727595	+	1.26023i
$469$	−1.19066e6	−	2.06229e6i	−0.249952	−	0.432929i
$470$	−417508.			−0.0871806
$471$	536686.			0.111473
$472$	800462.	+	1.38644e6i	0.165381	+	0.286448i
$473$	6.30720e6			1.29624
$474$	−199176.	+	344983.i	−0.0407184	+	0.0705263i
$475$	−1.78651e7			−3.63304
$476$	−782984.	+	1.35617e6i	−0.158393	+	0.274344i
$477$	−584464.	+	1.01232e6i	−0.117615	+	0.203715i
$478$	−687170.	+	1.19021e6i	−0.137561	+	0.238262i
$479$	3.40359e6	+	5.89520e6i	0.677796	+	1.17398i	0.975643	+	0.219363i	$0.0703980\pi$
$479$	3.40359e6	+	5.89520e6i	0.677796	+	1.17398i	−0.297847	+	0.954614i	$0.596269\pi$
$480$	−1.89151e6			−0.374719
$481$	−3.72250e6	+	7.88655e6i	−0.733620	+	1.55426i
$482$	1.50890e6			0.295830
$483$	−152162.	−	263553.i	−0.0296783	−	0.0514043i
$484$	−684728.	+	1.18598e6i	−0.132863	+	0.230126i
$485$	1.37543e6	−	2.38232e6i	0.265513	−	0.459882i
$486$	521226.	−	902791.i	0.100100	−	0.173379i
$487$	313113.			0.0598244			0.0299122	−	0.999553i	$-0.490477\pi$
$487$	313113.			0.0598244			0.0299122	+	0.999553i	$0.490477\pi$
$488$	624263.	−	1.08125e6i	0.118664	−	0.205532i
$489$	425842.			0.0805335
$490$	−1.00469e6	−	1.74018e6i	−0.189035	−	0.327419i
$491$	−453024.			−0.0848042			−0.0424021	−	0.999101i	$-0.513501\pi$
$491$	−453024.			−0.0848042			−0.0424021	+	0.999101i	$0.513501\pi$
$492$	−1.41375e6			−0.263306
$493$	2.89408e6	+	5.01269e6i	0.536281	+	0.928866i
$494$	−1.94564e6	+	3.36995e6i	−0.358712	+	0.621307i
$495$	7.32072e6			1.34289
$496$	−239203.	−	414311.i	−0.0436578	−	0.0756175i
$497$	1.09451e6	+	1.89574e6i	0.198759	+	0.344261i
$498$	−291599.	−	505064.i	−0.0526881	−	0.0912584i
$499$	113855.	−	197203.i	0.0204693	−	0.0354538i	−0.855609	−	0.517622i	$-0.826817\pi$
$499$	113855.	−	197203.i	0.0204693	−	0.0354538i	0.876079	+	0.482168i	$0.160151\pi$
$500$	5.13103e6	−	8.88720e6i	0.917866	−	1.58979i
$501$	160428.	+	277869.i	0.0285552	+	0.0494590i
$502$	−166484.	−	288359.i	−0.0294859	−	0.0510710i
$503$	469421.	+	813061.i	0.0827261	+	0.143286i	0.904420	−	0.426643i	$-0.140304\pi$
$503$	469421.	+	813061.i	0.0827261	+	0.143286i	−0.821694	+	0.569929i	$0.806971\pi$
$504$	−812331.			−0.142448
$505$	1.09255e6	−	1.89235e6i	0.190639	−	0.330196i
$506$	−327699.	−	567591.i	−0.0568982	−	0.0985505i
$507$	3.58777e6			0.619876
$508$	2.89722e6			0.498106
$509$	5.35276e6	+	9.27126e6i	0.915764	+	1.58615i	0.805778	+	0.592217i	$0.201747\pi$
$509$	5.35276e6	+	9.27126e6i	0.915764	+	1.58615i	0.109986	+	0.993933i	$0.464919\pi$
$510$	793406.			0.135073
$511$	−865185.	+	1.49855e6i	−0.146574	+	0.253874i
$512$	−5.59720e6			−0.943617
$513$	−3.09744e6	+	5.36493e6i	−0.519649	+	0.900058i
$514$	915028.	−	1.58487e6i	0.152766	−	0.264598i
$515$	−7.42110e6	+	1.28537e7i	−1.23296	+	2.13556i
$516$	−1.38190e6	−	2.39353e6i	−0.228483	−	0.395744i
$517$	−1.05237e6			−0.173157
$518$	−496530.	+	41105.1i	−0.0813057	+	0.00673087i
$519$	−444755.			−0.0724773
$520$	−4.38797e6	−	7.60018e6i	−0.711631	−	1.23258i
$521$	2.32178e6	−	4.02143e6i	0.374737	−	0.649063i	−0.615551	−	0.788097i	$-0.711067\pi$
$521$	2.32178e6	−	4.02143e6i	0.374737	−	0.649063i	0.990288	+	0.139034i	$0.0443998\pi$
$522$	−727992.	+	1.26092e6i	−0.116937	+	0.202540i
$523$	−4.16878e6	+	7.22054e6i	−0.666431	+	1.15429i	0.312464	+	0.949929i	$0.398846\pi$
$523$	−4.16878e6	+	7.22054e6i	−0.666431	+	1.15429i	−0.978895	+	0.204363i	$0.934488\pi$
$524$	3.91335e6			0.622616
$525$	−711315.	+	1.23203e6i	−0.112633	+	0.195085i
$526$	677202.			0.106722
$527$	335672.	+	581401.i	0.0526489	+	0.0911905i
$528$	−1.42511e6			−0.222466
$529$	−4.45366e6			−0.691955
$530$	−360731.	−	624804.i	−0.0557820	−	0.0966172i
$531$	−2.05681e6	+	3.56250e6i	−0.316561	+	0.548300i
$532$	3.57332e6			0.547385
$533$	−4.96895e6	−	8.60648e6i	−0.757612	−	1.31222i
$534$	−56417.0	−	97717.1i	−0.00856163	−	0.0148292i
$535$	3.84647e6	+	6.66229e6i	0.581003	+	1.00633i
$536$	−2.31719e6	+	4.01348e6i	−0.348377	+	0.603406i
$537$	1.95462e6	−	3.38550e6i	0.292500	−	0.506626i
$538$	−522984.	−	905835.i	−0.0778991	−	0.134925i
$539$	−2.53242e6	−	4.38628e6i	−0.375460	−	0.650316i
$540$	−3.38743e6	−	5.86719e6i	−0.499903	−	0.865857i
$541$	5.06199e6			0.743581			0.371790	−	0.928317i	$-0.378744\pi$
$541$	5.06199e6			0.743581			0.371790	+	0.928317i	$0.378744\pi$
$542$	−888889.	+	1.53960e6i	−0.129972	+	0.225118i
$543$	136456.	+	236348.i	0.0198606	+	0.0343996i
$544$	4.61735e6			0.668952
$545$	−7.19055e6			−1.03698
$546$	154936.	+	268356.i	0.0222418	+	0.0385239i
$547$	−6.80524e6			−0.972467			−0.486234	−	0.873829i	$-0.661630\pi$
$547$	−6.80524e6			−0.972467			−0.486234	+	0.873829i	$0.661630\pi$
$548$	2.45965e6	−	4.26024e6i	0.349882	−	0.606014i
$549$	3.20812e6			0.454276
$550$	−1.53190e6	+	2.65333e6i	−0.215935	+	0.374011i
$551$	6.60387e6	−	1.14382e7i	0.926658	−	1.60502i
$552$	−296128.	+	512908.i	−0.0413649	+	0.0716460i
$553$	1.28569e6	+	2.22688e6i	0.178782	+	0.309660i
$554$	341388.			0.0472578
$555$	−2.31171e6	−	3.33450e6i	−0.318568	−	0.459514i
$556$	−5.68998e6			−0.780592
$557$	6.68795e6	+	1.15839e7i	0.913388	+	1.58203i	0.809245	+	0.587472i	$0.199877\pi$
$557$	6.68795e6	+	1.15839e7i	0.913388	+	1.58203i	0.104143	+	0.994562i	$0.466790\pi$
$558$	−84436.9	+	146249.i	−0.0114801	+	0.0198842i
$559$	9.71403e6	−	1.68252e7i	1.31483	−	2.27735i
$560$	−1.82480e6	+	3.16065e6i	−0.245893	+	0.425899i
$561$	1.99985e6			0.268281
$562$	−1.10700e6	+	1.91738e6i	−0.147845	+	0.256076i
$563$	2.78302e6			0.370037			0.185018	−	0.982735i	$-0.440766\pi$
$563$	2.78302e6			0.370037			0.185018	+	0.982735i	$0.440766\pi$
$564$	230573.	+	399364.i	0.0305218	+	0.0528653i
$565$	8.41673e6			1.10923
$566$	3.04504e6			0.399532
$567$	−913791.	−	1.58273e6i	−0.119368	−	0.206752i
$568$	2.13006e6	−	3.68937e6i	0.277026	−	0.479823i
$569$	2.97313e6			0.384975			0.192488	−	0.981299i	$-0.438344\pi$
$569$	2.97313e6			0.384975			0.192488	+	0.981299i	$0.438344\pi$
$570$	−905220.	−	1.56789e6i	−0.116699	−	0.202128i
$571$	4.26817e6	+	7.39269e6i	0.547837	+	0.948882i	0.998422	+	0.0561486i	$0.0178820\pi$
$571$	4.26817e6	+	7.39269e6i	0.547837	+	0.948882i	−0.450585	+	0.892733i	$0.648785\pi$
$572$	−5.36330e6	−	9.28951e6i	−0.685397	−	1.18714i
$573$	−1.30820e6	+	2.26587e6i	−0.166452	+	0.288303i
$574$	283877.	−	491690.i	0.0359626	−	0.0622890i
$575$	−4.63424e6	−	8.02674e6i	−0.584533	−	1.01244i
$576$	−2.38301e6	−	4.12750e6i	−0.299275	−	0.518359i
$577$	2.70917e6	+	4.69243e6i	0.338764	+	0.586757i	0.984201	−	0.177057i	$-0.0566578\pi$
$577$	2.70917e6	+	4.69243e6i	0.338764	+	0.586757i	−0.645436	+	0.763814i	$0.723324\pi$
$578$	7048.54			0.000877565
$579$	−1.00888e6	+	1.74743e6i	−0.125067	+	0.216622i
$580$	7.22213e6	+	1.25091e7i	0.891446	+	1.54403i
$581$	−3.76458e6			−0.462675
$582$	189030.			0.0231325
$583$	−909256.	−	1.57488e6i	−0.110794	−	0.191900i
$584$	3.36753e6			0.408583
$585$	1.12750e7	−	1.95289e7i	1.36216	−	2.35933i
$586$	−1.96061e6			−0.235856
$587$	−2.08780e6	+	3.61617e6i	−0.250088	+	0.433166i	−0.963550	−	0.267529i	$-0.913793\pi$
$587$	−2.08780e6	+	3.61617e6i	−0.250088	+	0.433166i	0.713462	+	0.700694i	$0.247126\pi$
$588$	−1.10970e6	+	1.92206e6i	−0.132362	+	0.229258i
$589$	765957.	−	1.32668e6i	0.0909737	−	0.157571i
$590$	−1.26946e6	−	2.19877e6i	−0.150138	−	0.260046i
$591$	1.92010e6			0.226129
$592$	−4.02132e6	−	5.80050e6i	−0.471589	−	0.680239i
$593$	−1.20172e7			−1.40335			−0.701676	−	0.712496i	$-0.747565\pi$
$593$	−1.20172e7			−1.40335			−0.701676	+	0.712496i	$0.747565\pi$
$594$	531202.	+	920068.i	0.0617722	+	0.106993i
$595$	2.56074e6	−	4.43533e6i	0.296533	−	0.513610i
$596$	−4.62523e6	+	8.01113e6i	−0.533356	+	0.923801i
$597$	1.05671e6	−	1.83028e6i	0.121345	−	0.210175i
$598$	−2.01882e6			−0.230858
$599$	−387917.	+	671891.i	−0.0441745	+	0.0765124i	−0.887267	−	0.461256i	$-0.847399\pi$
$599$	−387917.	+	671891.i	−0.0441745	+	0.0765124i	0.843093	+	0.537768i	$0.180732\pi$
$600$	2.76863e6			0.313969
$601$	73097.2	+	126608.i	0.00825495	+	0.0142980i	0.870123	−	0.492834i	$-0.164039\pi$
$601$	73097.2	+	126608.i	0.00825495	+	0.0142980i	−0.861868	+	0.507132i	$0.830706\pi$
$602$	1.10993e6			0.124826
$603$	−1.19081e7			−1.33368
$604$	−1.26051e6	−	2.18326e6i	−0.140590	−	0.243508i
$605$	2.23940e6	−	3.87875e6i	0.248738	−	0.430827i
$606$	150152.			0.0166092
$607$	6.62670e6	+	1.14778e7i	0.730005	+	1.26441i	0.956880	+	0.290482i	$0.0938157\pi$
$607$	6.62670e6	+	1.14778e7i	0.730005	+	1.26441i	−0.226875	+	0.973924i	$0.572851\pi$
$608$	−5.26807e6	−	9.12456e6i	−0.577953	−	1.00104i
$609$	−525880.	−	910851.i	−0.0574570	−	0.0995185i
$610$	−990026.	+	1.71477e6i	−0.107726	+	0.186587i
$611$	−1.62080e6	+	2.80731e6i	−0.175641	+	0.304220i
$612$	3.91543e6	+	6.78172e6i	0.422572	+	0.731916i
$613$	−3.53183e6	−	6.11731e6i	−0.379619	−	0.657520i	0.611387	−	0.791331i	$-0.290612\pi$
$613$	−3.53183e6	−	6.11731e6i	−0.379619	−	0.657520i	−0.991007	+	0.133811i	$0.957278\pi$
$614$	−180466.	−	312576.i	−0.0193185	−	0.0334606i
$615$	4.62366e6			0.492944
$616$	631875.	−	1.09444e6i	0.0670934	−	0.116209i
$617$	8.33613e6	+	1.44386e7i	0.881560	+	1.52691i	0.849607	+	0.527417i	$0.176839\pi$
$617$	8.33613e6	+	1.44386e7i	0.881560	+	1.52691i	0.0319528	+	0.999489i	$0.489827\pi$
$618$	−1.01990e6			−0.107421
$619$	1.76322e7			1.84961			0.924803	−	0.380447i	$-0.124230\pi$
$619$	1.76322e7			1.84961			0.924803	+	0.380447i	$0.124230\pi$
$620$	837666.	+	1.45088e6i	0.0875168	+	0.151584i
$621$	−3.21394e6			−0.334433
$622$	1.72974e6	−	2.99600e6i	0.179269	−	0.310503i
$623$	−728350.			−0.0751831
$624$	−2.19488e6	+	3.80164e6i	−0.225657	+	0.390850i
$625$	−6.49602e6	+	1.12514e7i	−0.665192	+	1.15215i
$626$	−190375.	+	329740.i	−0.0194167	+	0.0336307i
$627$	−2.28169e6	−	3.95200e6i	−0.231786	−	0.401466i
$628$	−3.26934e6			−0.330796
$629$	5.64311e6	+	8.13983e6i	0.568711	+	0.820330i
$630$	1.28829e6			0.129319
$631$	−4.14758e6	−	7.18381e6i	−0.414688	−	0.718260i	0.580708	−	0.814112i	$-0.302776\pi$
$631$	−4.14758e6	−	7.18381e6i	−0.414688	−	0.718260i	−0.995396	+	0.0958520i	$0.969442\pi$
$632$	2.50213e6	−	4.33381e6i	0.249182	−	0.431596i
$633$	−184763.	+	320019.i	−0.0183276	+	0.0317444i
$634$	−564022.	+	976915.i	−0.0557279	+	0.0965236i
$635$	−9.47532e6			−0.932523
$636$	−398434.	+	690109.i	−0.0390584	+	0.0676511i
$637$	−1.56012e7			−1.52339
$638$	−1.13254e6	−	1.96162e6i	−0.110155	−	0.190794i
$639$	1.09465e7			1.06053
$640$	1.51810e7			1.46504
$641$	−8.13948e6	−	1.40980e7i	−0.782441	−	1.35523i	−0.930516	−	0.366251i	$-0.880641\pi$
$641$	−8.13948e6	−	1.40980e7i	−0.782441	−	1.35523i	0.148075	−	0.988976i	$-0.452692\pi$
$642$	−264316.	+	457808.i	−0.0253096	+	0.0438375i
$643$	−1.06133e7			−1.01233			−0.506166	−	0.862436i	$-0.668938\pi$
$643$	−1.06133e7			−1.01233			−0.506166	+	0.862436i	$0.668938\pi$
$644$	926928.	+	1.60549e6i	0.0880707	+	0.152543i
$645$	4.51950e6	+	7.82800e6i	0.427751	+	0.740886i
$646$	2.20972e6	+	3.82736e6i	0.208332	+	0.360842i
$647$	−2.66970e6	+	4.62405e6i	−0.250727	+	0.434272i	−0.963726	−	0.266893i	$-0.914003\pi$
$647$	−2.66970e6	+	4.62405e6i	−0.250727	+	0.434272i	0.712999	+	0.701165i	$0.247336\pi$
$648$	−1.77836e6	+	3.08021e6i	−0.166373	+	0.288166i
$649$	−3.19979e6	−	5.54221e6i	−0.298202	−	0.516501i
$650$	4.71871e6	+	8.17304e6i	0.438066	+	0.758753i
$651$	−60994.7	−	105646.i	−0.00564079	−	0.00977013i
$652$	−2.59411e6			−0.238984
$653$	−3.50495e6	+	6.07075e6i	−0.321661	+	0.557134i	−0.980831	−	0.194861i	$-0.937575\pi$
$653$	−3.50495e6	+	6.07075e6i	−0.321661	+	0.557134i	0.659170	+	0.751994i	$0.270908\pi$
$654$	−247054.	−	427910.i	−0.0225864	−	0.0391209i
$655$	−1.27986e7			−1.16562
$656$	8.04304e6			0.729727
$657$	4.32649e6	+	7.49369e6i	0.391041	+	0.677302i
$658$	−185193.			−0.0166748
$659$	−7.80237e6	+	1.35141e7i	−0.699863	+	1.21220i	0.268651	+	0.963238i	$0.413422\pi$
$659$	−7.80237e6	+	1.35141e7i	−0.699863	+	1.21220i	−0.968514	+	0.248961i	$0.919911\pi$
$660$	4.99060e6			0.445957
$661$	6.86671e6	−	1.18935e7i	0.611287	−	1.05878i	−0.379737	−	0.925095i	$-0.623985\pi$
$661$	6.86671e6	−	1.18935e7i	0.611287	−	1.05878i	0.991024	−	0.133686i	$-0.0426812\pi$
$662$	759127.	−	1.31485e6i	0.0673239	−	0.116608i
$663$	3.08007e6	−	5.33484e6i	0.272130	−	0.471343i
$664$	3.66318e6	+	6.34482e6i	0.322432	+	0.558469i
$665$	−1.16865e7			−1.02478
$666$	−1.06347e6	+	2.25309e6i	−0.0929052	+	0.196831i
$667$	6.85225e6			0.596373
$668$	−977279.	−	1.69270e6i	−0.0847378	−	0.146770i
$669$	−438598.	+	759675.i	−0.0378880	+	0.0656239i
$670$	3.67485e6	−	6.36503e6i	0.316266	−	0.547789i
$671$	−2.49545e6	+	4.32225e6i	−0.213965	+	0.370598i
$672$	−839014.			−0.0716714
$673$	1.51040e6	−	2.61609e6i	0.128545	−	0.222646i	−0.794568	−	0.607175i	$-0.792303\pi$
$673$	1.51040e6	−	2.61609e6i	0.128545	−	0.222646i	0.923113	+	0.384529i	$0.125636\pi$
$674$	2.62032e6			0.222180
$675$	7.51213e6	+	1.30114e7i	0.634605	+	1.09917i
$676$	−2.18557e7			−1.83949
$677$	−5.63262e6			−0.472323			−0.236162	−	0.971714i	$-0.575889\pi$
$677$	−5.63262e6			−0.472323			−0.236162	+	0.971714i	$0.575889\pi$
$678$	289184.	+	500881.i	0.0241601	+	0.0418466i
$679$	610100.	−	1.05672e6i	0.0507839	−	0.0879604i
$680$	−9.96709e6			−0.826601
$681$	−1.27696e6	−	2.21176e6i	−0.105514	−	0.182756i
$682$	−131359.	−	227521.i	−0.0108143	−	0.0187310i
$683$	1.06483e6	+	1.84434e6i	0.0873429	+	0.151282i	0.906387	−	0.422448i	$-0.138829\pi$
$683$	1.06483e6	+	1.84434e6i	0.0873429	+	0.151282i	−0.819044	+	0.573730i	$0.805496\pi$
$684$	8.93445e6	−	1.54749e7i	0.730176	−	1.26470i
$685$	−8.04426e6	+	1.39331e7i	−0.655028	+	1.13454i
$686$	−948437.	−	1.64274e6i	−0.0769482	−	0.133278i
$687$	548976.	+	950855.i	0.0443774	+	0.0768639i
$688$	7.86185e6	+	1.36171e7i	0.633218	+	1.09677i
$689$	−5.60156e6			−0.449532
$690$	469633.	−	813428.i	0.0375522	−	0.0650423i
$691$	−6.31430e6	−	1.09367e7i	−0.503072	−	0.871347i	−0.999994	−	0.00355105i	$-0.998870\pi$
$691$	−6.31430e6	−	1.09367e7i	−0.503072	−	0.871347i	0.496922	−	0.867795i	$-0.334464\pi$
$692$	2.70932e6			0.215077
$693$	3.24724e6			0.256851
$694$	−903728.	−	1.56530e6i	−0.0712261	−	0.123367i
$695$	1.86090e7			1.46137
$696$	−1.02343e6	+	1.77264e6i	−0.0800822	+	0.138706i
$697$	−1.12868e7			−0.880011
$698$	353824.	−	612842.i	0.0274884	−	0.0476113i
$699$	−1.31196e6	+	2.27238e6i	−0.101561	+	0.175909i
$700$	4.33313e6	−	7.50520e6i	0.334239	−	0.578918i
$701$	−1.07790e7	−	1.86698e7i	−0.828483	−	1.43497i	−0.899228	−	0.437480i	$-0.855871\pi$
$701$	−1.07790e7	−	1.86698e7i	−0.828483	−	1.43497i	0.0707453	−	0.997494i	$-0.477462\pi$
$702$	3.27252e6			0.250634
$703$	9.64712e6	−	2.04386e7i	0.736223	−	1.55978i
$704$	7.41454e6			0.563836
$705$	−754085.	−	1.30611e6i	−0.0571410	−	0.0989711i
$706$	−2.67067e6	+	4.62573e6i	−0.201655	+	0.349276i
$707$	484619.	−	839385.i	0.0364630	−	0.0631557i
$708$	−1.40215e6	+	2.42859e6i	−0.105126	+	0.182083i
$709$	1.75735e7			1.31293			0.656465	−	0.754356i	$-0.272051\pi$
$709$	1.75735e7			1.31293			0.656465	+	0.754356i	$0.272051\pi$
$710$	−3.37808e6	+	5.85101e6i	−0.251492	+	0.435597i
$711$	1.28586e7			0.953935
$712$	708733.	+	1.22756e6i	0.0523942	+	0.0907494i
$713$	794765.			0.0585484
$714$	351930.			0.0258351
$715$	1.75406e7	+	3.03813e7i	1.28316	+	2.22249i
$716$	−1.19070e7	+	2.06235e7i	−0.867999	+	1.50342i
$717$	−4.96456e6			−0.360647
$718$	−3.27461e6	−	5.67179e6i	−0.237055	−	0.410591i
$719$	−1.16001e7	−	2.00919e7i	−0.836833	−	1.44944i	−0.892529	−	0.450990i	$-0.851071\pi$
$719$	−1.16001e7	−	2.00919e7i	−0.836833	−	1.44944i	0.0556958	−	0.998448i	$-0.482262\pi$
$720$	9.12519e6	+	1.58053e7i	0.656010	+	1.13624i
$721$	−3.29177e6	+	5.70151e6i	−0.235826	+	0.408462i
$722$	3.34736e6	−	5.79779e6i	0.238978	−	0.413923i
$723$	2.72531e6	+	4.72037e6i	0.193896	+	0.335838i
$724$	−831249.	−	1.43977e6i	−0.0589366	−	0.102081i
$725$	−1.60162e7	−	2.77408e7i	−1.13165	−	1.96008i
$726$	307766.			0.0216710
$727$	1.36924e7	−	2.37159e7i	0.960820	−	1.66419i	0.240371	−	0.970681i	$-0.422731\pi$
$727$	1.36924e7	−	2.37159e7i	0.960820	−	1.66419i	0.720449	−	0.693508i	$-0.243936\pi$
$728$	−1.94636e6	−	3.37120e6i	−0.136112	−	0.235753i
$729$	−6.39616e6			−0.445759
$730$	−5.34061e6			−0.370923
$731$	−1.10325e7	−	1.91089e7i	−0.763627	−	1.32264i
$732$	2.18701e6			0.150859
$733$	−6.70320e6	+	1.16103e7i	−0.460810	+	0.798146i	−0.999002	−	0.0446762i	$-0.985774\pi$
$733$	−6.70320e6	+	1.16103e7i	−0.460810	+	0.798146i	0.538191	+	0.842823i	$0.319108\pi$
$734$	339189.			0.0232381
$735$	3.62927e6	−	6.28608e6i	0.247800	−	0.429202i
$736$	2.73310e6	−	4.73387e6i	0.185978	−	0.322123i
$737$	9.26280e6	−	1.60436e7i	0.628165	−	1.08801i
$738$	−1.41957e6	−	2.45877e6i	−0.0959435	−	0.166179i
$739$	1.76268e7			1.18730			0.593651	−	0.804723i	$-0.297686\pi$
$739$	1.76268e7			1.18730			0.593651	+	0.804723i	$0.297686\pi$
$740$	1.40823e7	+	2.03128e7i	0.945353	+	1.36361i
$741$	−1.40566e7			−0.940446
$742$	−160009.	−	277144.i	−0.0106693	−	0.0184797i
$743$	−1.12976e6	+	1.95681e6i	−0.0750785	+	0.130040i	−0.901120	−	0.433569i	$-0.857254\pi$
$743$	−1.12976e6	+	1.95681e6i	−0.0750785	+	0.130040i	0.826042	+	0.563609i	$0.190587\pi$
$744$	−118704.	+	205601.i	−0.00786199	+	0.0136174i
$745$	1.51268e7	−	2.62003e7i	0.998517	−	1.72948i
$746$	2.51104e6			0.165198
$747$	−9.41265e6	+	1.63032e7i	−0.617178	+	1.06898i
$748$	−1.21825e7			−0.796129
$749$	1.70618e6	+	2.95518e6i	0.111127	+	0.192477i
$750$	−2.30625e6			−0.149711
$751$	2.50338e7			1.61967			0.809837	−	0.586655i	$-0.199555\pi$
$751$	2.50338e7			1.61967			0.809837	+	0.586655i	$0.199555\pi$
$752$	−1.31176e6	−	2.27204e6i	−0.0845883	−	0.146511i
$753$	601394.	−	1.04165e6i	0.0386520	−	0.0669472i
$754$	−6.97714e6			−0.446940
$755$	4.12248e6	+	7.14034e6i	0.263203	+	0.455881i
$756$	−1.50256e6	−	2.60250e6i	−0.0956150	−	0.165610i
$757$	−4.89896e6	−	8.48525e6i	−0.310716	−	0.538177i	0.667801	−	0.744340i	$-0.267236\pi$
$757$	−4.89896e6	−	8.48525e6i	−0.310716	−	0.538177i	−0.978518	+	0.206163i	$0.933902\pi$
$758$	−3.22142e6	+	5.57967e6i	−0.203646	+	0.352724i
$759$	1.18375e6	−	2.05032e6i	0.0745858	−	0.129186i
$760$	1.13717e7	+	1.96964e7i	0.714156	+	1.23695i
$761$	9.05189e6	+	1.56783e7i	0.566601	+	0.981382i	0.996899	+	0.0786949i	$0.0250753\pi$
$761$	9.05189e6	+	1.56783e7i	0.566601	+	0.981382i	−0.430298	+	0.902687i	$0.641591\pi$
$762$	−325555.	−	563878.i	−0.0203113	−	0.0351801i
$763$	−3.18950e6			−0.198340
$764$	7.96918e6	−	1.38030e7i	0.493947	−	0.855541i
$765$	−1.28054e7	−	2.21795e7i	−0.791112	−	1.37025i
$766$	3.39760e6			0.209218
$767$	−1.97126e7			−1.20992
$768$	−1.20400e6	−	2.08538e6i	−0.0736584	−	0.127580i
$769$	−2.72742e6			−0.166317			−0.0831584	−	0.996536i	$-0.526501\pi$
$769$	−2.72742e6			−0.166317			−0.0831584	+	0.996536i	$0.526501\pi$
$770$	−1.00210e6	+	1.73569e6i	−0.0609093	+	0.105498i
$771$	6.61074e6			0.400511
$772$	6.14579e6	−	1.06448e7i	0.371137	−	0.642828i
$773$	−1.61246e6	+	2.79286e6i	−0.0970598	+	0.168112i	−0.910466	−	0.413583i	$-0.864277\pi$
$773$	−1.61246e6	+	2.79286e6i	−0.0970598	+	0.168112i	0.813407	+	0.581695i	$0.197610\pi$
$774$	2.77518e6	−	4.80675e6i	0.166509	−	0.288403i
$775$	−1.85765e6	−	3.21755e6i	−0.111099	−	0.192429i
$776$	−2.37467e6			−0.141563
$777$	−1.02540e6	−	1.47908e6i	−0.0609315	−	0.0878900i
$778$	8.02904e6			0.475570
$779$	1.28774e7	+	2.23043e7i	0.760300	+	1.31688i
$780$	7.68627e6	−	1.33130e7i	0.452355	−	0.783502i
$781$	−8.51477e6	+	1.47480e7i	−0.499511	+	0.865179i
$782$	−1.14642e6	+	1.98565e6i	−0.0670387	+	0.116114i
$783$	−1.11075e7			−0.647460
$784$	6.31326e6	−	1.09349e7i	0.366829	−	0.635367i
$785$	1.06923e7			0.619296
$786$	−439735.	−	761644.i	−0.0253884	−	0.0439740i
$787$	−2.49843e7			−1.43790			−0.718952	−	0.695060i	$-0.755378\pi$
$787$	−2.49843e7			−1.43790			−0.718952	+	0.695060i	$0.755378\pi$
$788$	−1.16967e7			−0.671040
$789$	1.22313e6	+	2.11853e6i	0.0699490	+	0.121155i
$790$	−3.96815e6	+	6.87305e6i	−0.226215	+	0.391815i
$791$	3.73340e6			0.212160
$792$	−3.15979e6	−	5.47291e6i	−0.178997	−	0.310031i
$793$	7.68673e6	+	1.33138e7i	0.434069	+	0.751830i
$794$	−1.32166e6	−	2.28918e6i	−0.0743990	−	0.128863i
$795$	1.30308e6	−	2.25699e6i	0.0731226	−	0.126652i
$796$	−6.43719e6	+	1.11495e7i	−0.360092	+	0.623698i
$797$	7.78733e6	+	1.34881e7i	0.434253	+	0.752148i	0.997234	−	0.0743214i	$-0.0236791\pi$
$797$	7.78733e6	+	1.34881e7i	0.434253	+	0.752148i	−0.562981	+	0.826470i	$0.690346\pi$
$798$	−401527.	−	695465.i	−0.0223207	−	0.0386606i
$799$	1.84079e6	+	3.18835e6i	0.102009	+	0.176684i
$800$	−2.55530e7			−1.41161
$801$	−1.82111e6	+	3.15426e6i	−0.100289	+	0.173706i
$802$	2.76824e6	+	4.79473e6i	0.151973	+	0.263225i
$803$	−1.34615e7			−0.736724
$804$	−8.11789e6			−0.442897
$805$	−3.03151e6	−	5.25073e6i	−0.164880	−	0.285581i
$806$	−809251.			−0.0438779
$807$	1.88919e6	−	3.27216e6i	0.102115	−	0.176869i
$808$	−1.88627e6			−0.101642
$809$	695396.	−	1.20446e6i	0.0373560	−	0.0647026i	−0.846743	−	0.532002i	$-0.821440\pi$
$809$	695396.	−	1.20446e6i	0.0373560	−	0.0647026i	0.884099	+	0.467300i	$0.154773\pi$
$810$	2.82032e6	−	4.88494e6i	0.151038	−	0.261605i
$811$	−5.34587e6	+	9.25931e6i	−0.285408	+	0.494341i	−0.972708	−	0.232033i	$-0.925462\pi$
$811$	−5.34587e6	+	9.25931e6i	−0.285408	+	0.494341i	0.687300	+	0.726374i	$0.258796\pi$
$812$	3.20351e6	+	5.54864e6i	0.170505	+	0.295322i
$813$	−6.42190e6			−0.340751
$814$	−2.20832e6	−	3.18537e6i	−0.116816	−	0.168500i
$815$	8.48400e6			0.447411
$816$	2.49279e6	+	4.31764e6i	0.131057	+	0.226997i
$817$	−2.51746e7	+	4.36038e7i	−1.31950	+	2.28543i
$818$	2.36187e6	−	4.09087e6i	0.123416	−	0.213763i
$819$	5.00124e6	−	8.66240e6i	0.260536	−	0.451262i
$820$	−2.81660e7			−1.46282
$821$	−6.09794e6	+	1.05619e7i	−0.315737	+	0.546872i	−0.979594	−	0.200987i	$-0.935585\pi$
$821$	−6.09794e6	+	1.05619e7i	−0.315737	+	0.546872i	0.663857	+	0.747859i	$0.268918\pi$
$822$	−1.10554e6			−0.0570686
$823$	7.85586e6	+	1.36068e7i	0.404291	+	0.700253i	0.994239	−	0.107189i	$-0.0341849\pi$
$823$	7.85586e6	+	1.36068e7i	0.404291	+	0.700253i	−0.589948	+	0.807442i	$0.700852\pi$
$824$	1.28124e7			0.657376
$825$	−1.10674e7			−0.566124
$826$	−563093.	−	975306.i	−0.0287164	−	0.0497383i
$827$	1.88268e7	−	3.26090e7i	0.957222	−	1.65796i	0.228023	−	0.973656i	$-0.426774\pi$
$827$	1.88268e7	−	3.26090e7i	0.957222	−	1.65796i	0.729199	−	0.684302i	$-0.239893\pi$
$828$	9.27048e6			0.469922
$829$	1.34171e7	+	2.32391e7i	0.678067	+	1.17445i	0.975562	+	0.219723i	$0.0705153\pi$
$829$	1.34171e7	+	2.32391e7i	0.678067	+	1.17445i	−0.297495	+	0.954723i	$0.596151\pi$
$830$	−5.80949e6	−	1.00623e7i	−0.292713	−	0.506994i
$831$	616600.	+	1.06798e6i	0.0309743	+	0.0536490i
$832$	1.14195e7	−	1.97792e7i	0.571925	−	0.990602i
$833$	−8.85939e6	+	1.53449e7i	−0.442376	+	0.766217i
$834$	639373.	+	1.10743e6i	0.0318302	+	0.0551315i
$835$	3.19618e6	+	5.53594e6i	0.158641	+	0.274774i
$836$	1.38994e7	+	2.40745e7i	0.687829	+	1.19135i
$837$	−1.28832e6			−0.0635637
$838$	521016.	−	902426.i	0.0256295	−	0.0443917i
$839$	−3.39576e6	−	5.88163e6i	−0.166545	−	0.288465i	0.770658	−	0.637249i	$-0.219928\pi$
$839$	−3.39576e6	−	5.88163e6i	−0.166545	−	0.288465i	−0.937203	+	0.348785i	$0.886594\pi$
$840$	1.81111e6			0.0885619
$841$	3.17055e6			0.154577
$842$	2.01253e6	+	3.48580e6i	0.0978276	+	0.169442i
$843$	−7.99769e6			−0.387611
$844$	1.12552e6	−	1.94946e6i	0.0543874	−	0.0942018i
$845$	7.14787e7			3.44378
$846$	−463043.	+	802014.i	−0.0222431	+	0.0385262i
$847$	993326.	−	1.72049e6i	0.0475755	−	0.0824032i
$848$	2.26675e6	−	3.92613e6i	0.108247	−	0.187489i
$849$	5.49983e6	+	9.52598e6i	0.261866	+	0.453566i
$850$	1.07184e7			0.508839
$851$	1.16855e7	−	967383.i	0.553126	−	0.0457904i
$852$	7.46232e6			0.352188
$853$	−1.46354e7	−	2.53492e7i	−0.688702	−	1.19287i	−0.972258	−	0.233911i	$-0.924848\pi$
$853$	−1.46354e7	−	2.53492e7i	−0.688702	−	1.19287i	0.283556	−	0.958956i	$-0.408486\pi$
$854$	−439144.	+	760620.i	−0.0206045	+	0.0356881i
$855$	−2.92200e7	+	5.06106e7i	−1.36699	+	2.36770i
$856$	3.32045e6	−	5.75118e6i	0.154886	−	0.268270i
$857$	−6.84774e6			−0.318489			−0.159245	−	0.987239i	$-0.550906\pi$
$857$	−6.84774e6			−0.318489			−0.159245	+	0.987239i	$0.550906\pi$
$858$	−1.20533e6	+	2.08769e6i	−0.0558968	+	0.0968161i
$859$	1.46671e7			0.678207			0.339103	−	0.940749i	$-0.389876\pi$
$859$	1.46671e7			0.678207			0.339103	+	0.940749i	$0.389876\pi$
$860$	−2.75315e7	−	4.76859e7i	−1.26936	−	2.19859i
$861$	2.05091e6			0.0942841
$862$	−3.61129e6			−0.165537
$863$	−7.84326e6	−	1.35849e7i	−0.358484	−	0.620912i	0.629224	−	0.777224i	$-0.283373\pi$
$863$	−7.84326e6	−	1.35849e7i	−0.358484	−	0.620912i	−0.987708	+	0.156312i	$0.950040\pi$
$864$	−4.43037e6	+	7.67363e6i	−0.201909	+	0.349717i
$865$	−8.86079e6			−0.402654
$866$	797128.	+	1.38067e6i	0.0361188	+	0.0625596i
$867$	12730.8	+	22050.4i	0.000575185	+	0.000996249i
$868$	371562.	+	643565.i	0.0167391	+	0.0289930i
$869$	−1.00021e7	+	1.73241e7i	−0.449306	+	0.778220i
$870$	1.62307e6	−	2.81125e6i	0.0727010	−	0.125922i
$871$	−2.85322e7	−	4.94192e7i	−1.27435	−	2.20724i
$872$	3.10360e6	+	5.37559e6i	0.138221	+	0.239406i
$873$	−3.05089e6	−	5.28430e6i	−0.135485	−	0.234667i
$874$	5.23192e6			0.231677
$875$	−7.44351e6	+	1.28925e7i	−0.328668	+	0.569270i
$876$	2.94940e6	+	5.10852e6i	0.129860	+	0.224923i
$877$	1.30627e7			0.573500			0.286750	−	0.958005i	$-0.407425\pi$
$877$	1.30627e7			0.573500			0.286750	+	0.958005i	$0.407425\pi$
$878$	6.41748e6			0.280950
$879$	−3.54118e6	−	6.13350e6i	−0.154588	−	0.267754i
$880$	−2.83923e7			−1.23593
$881$	−3.51299e6	+	6.08467e6i	−0.152488	+	0.264118i	−0.932142	−	0.362094i	$-0.882062\pi$
$881$	−3.51299e6	+	6.08467e6i	−0.152488	+	0.264118i	0.779653	+	0.626211i	$0.215395\pi$
$882$	−4.45708e6			−0.192921
$883$	−1.30909e7	+	2.26741e7i	−0.565025	+	0.978652i	0.432022	+	0.901863i	$0.357800\pi$
$883$	−1.30909e7	+	2.26741e7i	−0.565025	+	0.978652i	−0.997047	+	0.0767894i	$0.975533\pi$
$884$	−1.87629e7	+	3.24983e7i	−0.807550	+	1.39872i
$885$	4.58570e6	−	7.94267e6i	0.196810	−	0.340885i
$886$	941672.	+	1.63102e6i	0.0403009	+	0.0698033i
$887$	1.67972e7			0.716848			0.358424	−	0.933559i	$-0.383314\pi$
$887$	1.67972e7			0.716848			0.358424	+	0.933559i	$0.383314\pi$
$888$	−1.49506e6	+	3.16746e6i	−0.0636247	+	0.134797i
$889$	−4.20295e6			−0.178361
$890$	−1.12399e6	−	1.94681e6i	−0.0475649	−	0.0823849i
$891$	7.10888e6	−	1.23129e7i	0.299990	−	0.519598i
$892$	2.67182e6	−	4.62772e6i	0.112433	−	0.194740i
$893$	4.20043e6	−	7.27535e6i	0.176264	−	0.305299i
$894$	2.07891e6			0.0869946
$895$	3.89416e7	−	6.74489e7i	1.62501	−	2.81460i
$896$	6.73380e6			0.280214
$897$	−3.64631e6	−	6.31559e6i	−0.151312	−	0.262080i
$898$	−7.61077e6			−0.314947
$899$	2.74675e6			0.113349
$900$	−2.16684e7	−	3.75308e7i	−0.891705	−	1.54448i
$901$	−3.18093e6	+	5.50953e6i	−0.130539	+	0.226101i
$902$	4.41687e6			0.180758
$903$	2.00471e6	+	3.47226e6i	0.0818148	+	0.141707i
$904$	−3.63284e6	−	6.29227e6i	−0.147851	−	0.256086i
$905$	2.71859e6	+	4.70874e6i	0.110337	+	0.191110i
$906$	−283282.	+	490659.i	−0.0114656	+	0.0198591i
$907$	−8.12855e6	+	1.40791e7i	−0.328091	+	0.568271i	−0.982133	−	0.188187i	$-0.939739\pi$
$907$	−8.12855e6	+	1.40791e7i	−0.328091	+	0.568271i	0.654042	+	0.756459i	$0.273072\pi$
$908$	7.77889e6	+	1.34734e7i	0.313114	+	0.542330i
$909$	−2.42341e6	−	4.19747e6i	−0.0972785	−	0.168491i
$910$	3.08676e6	+	5.34643e6i	0.123566	+	0.214023i
$911$	3.99805e7			1.59607			0.798036	−	0.602610i	$-0.205873\pi$
$911$	3.99805e7			1.59607			0.798036	+	0.602610i	$0.205873\pi$
$912$	5.68820e6	−	9.85224e6i	0.226458	−	0.392237i
$913$	−1.46433e7	−	2.53630e7i	−0.581384	−	1.00699i
$914$	1.00146e7			0.396523
$915$	−7.15258e6			−0.282429
$916$	−3.34421e6	−	5.79234e6i	−0.131691	−	0.228095i
$917$	−5.67704e6			−0.222945
$918$	1.85835e6	−	3.21875e6i	0.0727814	−	0.126061i
$919$	−2.99128e6			−0.116834			−0.0584168	−	0.998292i	$-0.518605\pi$
$919$	−2.99128e6			−0.116834			−0.0584168	+	0.998292i	$0.518605\pi$
$920$	−5.89972e6	+	1.02186e7i	−0.229806	+	0.398036i
$921$	651900.	−	1.12912e6i	0.0253240	−	0.0438624i
$922$	1.68625e6	−	2.92067e6i	0.0653273	−	0.113150i
$923$	2.62280e7	+	4.54283e7i	1.01335	+	1.75518i
$924$	2.21368e6			0.0852970
$925$	−3.12296e7	−	4.50468e7i	−1.20009	−	1.73105i
$926$	7.07579e6			0.271174
$927$	1.64610e7	+	2.85112e7i	0.629152	+	1.08972i
$928$	9.44573e6	−	1.63605e7i	0.360052	−	0.623629i
$929$	2.11401e7	−	3.66158e7i	0.803652	−	1.39197i	−0.113545	−	0.993533i	$-0.536221\pi$
$929$	2.11401e7	−	3.66158e7i	0.803652	−	1.39197i	0.917197	−	0.398433i	$-0.130446\pi$
$930$	188254.	−	326065.i	0.00713734	−	0.0123622i
$931$	4.04317e7			1.52879
$932$	7.99209e6	−	1.38427e7i	0.301384	−	0.522013i
$933$	1.24967e7			0.469994
$934$	−2.83354e6	−	4.90784e6i	−0.106283	−	0.184087i
$935$	3.98428e7			1.49046
$936$	−1.94662e7			−0.726258
$937$	5.97758e6	+	1.03535e7i	0.222421	+	0.385245i	0.955543	−	0.294853i	$-0.0952706\pi$
$937$	5.97758e6	+	1.03535e7i	0.222421	+	0.385245i	−0.733121	+	0.680098i	$0.761937\pi$
$938$	1.63005e6	−	2.82333e6i	0.0604914	−	0.104774i
$939$	−1.37539e6			−0.0509053
$940$	4.59367e6	+	7.95647e6i	0.169567	+	0.293698i
$941$	1.07858e7	+	1.86816e7i	0.397082	+	0.687765i	0.993364	−	0.115009i	$-0.0366897\pi$
$941$	1.07858e7	+	1.86816e7i	0.397082	+	0.687765i	−0.596283	+	0.802774i	$0.703356\pi$
$942$	367369.	+	636303.i	0.0134889	+	0.0233634i
$943$	−6.68087e6	+	1.15716e7i	−0.244655	+	0.423754i
$944$	7.97701e6	−	1.38166e7i	0.291347	−	0.504627i
$945$	4.91409e6	+	8.51146e6i	0.179004	+	0.310045i
$946$	4.31737e6	+	7.47790e6i	0.156852	+	0.271676i
$947$	−2.67679e7	−	4.63634e7i	−0.969929	−	1.67997i	−0.695746	−	0.718288i	$-0.744926\pi$
$947$	−2.67679e7	−	4.63634e7i	−0.969929	−	1.67997i	−0.274183	−	0.961678i	$-0.588407\pi$
$948$	8.76581e6			0.316790
$949$	−2.07327e7	+	3.59101e7i	−0.747293	+	1.29435i
$950$	−1.22289e7	−	2.11810e7i	−0.439620	−	0.761445i
$951$	−4.07485e6			−0.146104
$952$	−4.42109e6			−0.158102
$953$	−1.48390e6	−	2.57020e6i	−0.0529266	−	0.0916715i	0.838348	−	0.545135i	$-0.183522\pi$
$953$	−1.48390e6	−	2.57020e6i	−0.0529266	−	0.0916715i	−0.891275	+	0.453463i	$0.850188\pi$
$954$	−1.60030e6			−0.0569285
$955$	−2.60631e7	+	4.51427e7i	−0.924737	+	1.60169i
$956$	3.02427e7			1.07023
$957$	4.09111e6	−	7.08600e6i	0.144398	−	0.250105i
$958$	−4.65962e6	+	8.07069e6i	−0.164035	+	0.284117i
$959$	−3.56818e6	+	6.18027e6i	−0.125285	+	0.217001i
$960$	5.31298e6	+	9.20234e6i	0.186063	+	0.322270i
$961$	−2.83106e7			−0.988872
$962$	−1.18985e7	+	985015.i	−0.414529	+	0.0343167i
$963$	1.70640e7			0.592944
$964$	−1.66018e7	−	2.87551e7i	−0.575390	−	0.996605i
$965$	−2.00997e7	+	3.48138e7i	−0.694819	+	1.20346i
$966$	208314.	−	360811.i	0.00718251	−	0.0124405i
$967$	−1.83136e7	+	3.17201e7i	−0.629807	+	1.09086i	0.357783	+	0.933805i	$0.383533\pi$
$967$	−1.83136e7	+	3.17201e7i	−0.629807	+	1.09086i	−0.987590	+	0.157053i	$0.949801\pi$
$968$	−3.86629e6			−0.132619
$969$	−7.98223e6	+	1.38256e7i	−0.273096	+	0.473016i
$970$	3.76602e6			0.128515
$971$	−2.33925e7	−	4.05170e7i	−0.796212	−	1.37908i	−0.922067	−	0.387031i	$-0.873501\pi$
$971$	−2.33925e7	−	4.05170e7i	−0.796212	−	1.37908i	0.125855	−	0.992049i	$-0.459833\pi$
$972$	−2.29394e7			−0.778783
$973$	8.25438e6			0.279513
$974$	214330.	+	371230.i	0.00723912	+	0.0125385i
$975$	−1.70455e7	+	2.95236e7i	−0.574246	+	0.994623i
$976$	−1.24422e7			−0.418093
$977$	−2.64643e7	−	4.58375e7i	−0.887001	−	1.53633i	−0.843403	−	0.537282i	$-0.819451\pi$
$977$	−2.64643e7	−	4.58375e7i	−0.887001	−	1.53633i	−0.0435982	−	0.999049i	$-0.513882\pi$
$978$	291495.	+	504884.i	0.00974505	+	0.0168789i
$979$	−2.83312e6	−	4.90710e6i	−0.0944730	−	0.163632i
$980$	−2.21085e7	+	3.82930e7i	−0.735349	+	1.27366i
$981$	−7.97478e6	+	1.38127e7i	−0.264573	+	0.458255i
$982$	−310101.	−	537111.i	−0.0102618	−	0.0177740i
$983$	−1.30178e6	−	2.25475e6i	−0.0429689	−	0.0744243i	0.843741	−	0.536750i	$-0.180348\pi$
$983$	−1.30178e6	−	2.25475e6i	−0.0429689	−	0.0744243i	−0.886710	+	0.462326i	$0.847015\pi$
$984$	−1.99567e6	−	3.45661e6i	−0.0657055	−	0.113805i
$985$	3.82540e7			1.25628
$986$	−3.96207e6	+	6.86251e6i	−0.129787	+	0.224797i
$987$	−334489.	−	579351.i	−0.0109292	−	0.0189299i
$988$	8.56286e7			2.79079
$989$	−2.61215e7			−0.849194
$990$	5.01114e6	+	8.67955e6i	0.162498	+	0.281455i
$991$	−5.40729e7			−1.74902			−0.874511	−	0.485005i	$-0.838818\pi$
$991$	−5.40729e7			−1.74902			−0.874511	+	0.485005i	$0.838818\pi$
$992$	1.09557e6	−	1.89759e6i	0.0353478	−	0.0612241i
$993$	5.48442e6			0.176505
$994$	−1.49841e6	+	2.59533e6i	−0.0481022	+	0.0833155i
$995$	2.10527e7	−	3.64644e7i	0.674142	−	1.16765i
$996$	−6.41669e6	+	1.11140e7i	−0.204957	+	0.354996i
$997$	1.56517e7	+	2.71095e7i	0.498681	+	0.863742i	0.999999	−	0.00152182i	$-0.000484410\pi$
$997$	1.56517e7	+	2.71095e7i	0.498681	+	0.863742i	−0.501317	+	0.865263i	$0.667151\pi$
$998$	311743.			0.00990763
$999$	−1.89423e7	+	1.56813e6i	−0.600508	+	0.0497129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.6.c.a.26.9	yes	30
37.10	even	3	inner	37.6.c.a.10.9	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.6.c.a.10.9	✓	30	37.10	even	3	inner
37.6.c.a.26.9	yes	30	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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	37.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.684514 + 1.18561i) q^{2} +(-2.47268 + 4.28281i) q^{3} +(15.0629 - 26.0897i) q^{4} +(-49.2630 + 85.3260i) q^{5} -6.77035 q^{6} +(-21.8515 + 37.8479i) q^{7} +85.0519 q^{8} +(109.272 + 189.264i) q^{9} +O(q^{10})\)	\(q+(0.684514 + 1.18561i) q^{2} +(-2.47268 + 4.28281i) q^{3} +(15.0629 - 26.0897i) q^{4} +(-49.2630 + 85.3260i) q^{5} -6.77035 q^{6} +(-21.8515 + 37.8479i) q^{7} +85.0519 q^{8} +(109.272 + 189.264i) q^{9} -134.885 q^{10} -339.990 q^{11} +(74.4915 + 129.023i) q^{12} +(-523.635 + 906.962i) q^{13} -59.8307 q^{14} +(-243.624 - 421.968i) q^{15} +(-423.793 - 734.031i) q^{16} +(594.708 + 1030.06i) q^{17} +(-149.596 + 259.108i) q^{18} +(1357.04 - 2350.46i) q^{19} +(1484.08 + 2570.51i) q^{20} +(-108.064 - 187.172i) q^{21} +(-232.728 - 403.096i) q^{22} +1408.08 q^{23} +(-210.307 + 364.262i) q^{24} +(-3291.18 - 5700.50i) q^{25} -1433.74 q^{26} -2282.50 q^{27} +(658.293 + 1140.20i) q^{28} +4866.38 q^{29} +(333.528 - 577.687i) q^{30} +564.433 q^{31} +(1941.02 - 3361.94i) q^{32} +(840.687 - 1456.11i) q^{33} +(-814.172 + 1410.19i) q^{34} +(-2152.94 - 3729.00i) q^{35} +6583.78 q^{36} +(8298.91 - 687.024i) q^{37} +3715.65 q^{38} +(-2589.57 - 4485.26i) q^{39} +(-4189.91 + 7257.14i) q^{40} +(-4744.67 + 8218.02i) q^{41} +(147.942 - 256.244i) q^{42} -18551.2 q^{43} +(-5121.22 + 8870.22i) q^{44} -21532.2 q^{45} +(963.849 + 1669.44i) q^{46} +3095.29 q^{47} +4191.62 q^{48} +(7448.52 + 12901.2i) q^{49} +(4505.72 - 7804.14i) q^{50} -5882.10 q^{51} +(15774.9 + 27322.9i) q^{52} +(2674.36 + 4632.13i) q^{53} +(-1562.40 - 2706.16i) q^{54} +(16748.9 - 29010.0i) q^{55} +(-1858.51 + 3219.04i) q^{56} +(6711.06 + 11623.9i) q^{57} +(3331.11 + 5769.65i) q^{58} +(9411.45 + 16301.1i) q^{59} -14678.7 q^{60} +(7339.78 - 12712.9i) q^{61} +(386.362 + 669.199i) q^{62} -9551.00 q^{63} -21808.1 q^{64} +(-51591.6 - 89359.3i) q^{65} +2301.85 q^{66} +(-27244.4 + 47188.6i) q^{67} +35832.0 q^{68} +(-3481.73 + 6030.53i) q^{69} +(2947.44 - 5105.11i) q^{70} +(25044.2 - 43377.8i) q^{71} +(9293.77 + 16097.3i) q^{72} +39593.9 q^{73} +(6495.27 + 9369.02i) q^{74} +32552.2 q^{75} +(-40881.8 - 70809.4i) q^{76} +(7429.29 - 12867.9i) q^{77} +(3545.19 - 6140.45i) q^{78} +(29418.8 - 50954.9i) q^{79} +83509.2 q^{80} +(-20909.1 + 36215.6i) q^{81} -12991.2 q^{82} +(43070.0 + 74599.4i) q^{83} -6511.01 q^{84} -117188. q^{85} +(-12698.5 - 21994.5i) q^{86} +(-12033.0 + 20841.8i) q^{87} -28916.8 q^{88} +(8332.95 + 14433.1i) q^{89} +(-14739.1 - 25528.9i) q^{90} +(-22884.4 - 39637.0i) q^{91} +(21209.7 - 36736.3i) q^{92} +(-1395.66 + 2417.36i) q^{93} +(2118.77 + 3669.82i) q^{94} +(133704. + 231581. i) q^{95} +(9599.04 + 16626.0i) q^{96} -27920.3 q^{97} +(-10197.2 + 17662.1i) q^{98} +(-37151.2 - 64347.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 4 q^{2} + 16 q^{3} - 230 q^{4} - 51 q^{5} + 60 q^{6} + 50 q^{7} + 24 q^{8} - 1085 q^{9}+O(q^{10}) \) 30 * q - 4 * q^2 + 16 * q^3 - 230 * q^4 - 51 * q^5 + 60 * q^6 + 50 * q^7 + 24 * q^8 - 1085 * q^9	\( 30 q - 4 q^{2} + 16 q^{3} - 230 q^{4} - 51 q^{5} + 60 q^{6} + 50 q^{7} + 24 q^{8} - 1085 q^{9} - 44 q^{10} - 1556 q^{11} + 708 q^{12} - 888 q^{13} + 1888 q^{14} + 1020 q^{15} - 4566 q^{16} - 437 q^{17} - 7302 q^{18} + 4358 q^{19} - 1204 q^{20} + 2354 q^{21} + 7958 q^{22} + 2824 q^{23} + 13824 q^{24} - 620 q^{25} - 17604 q^{26} - 32 q^{27} + 11414 q^{28} + 16954 q^{29} + 15994 q^{30} - 4548 q^{31} - 9148 q^{32} - 680 q^{33} - 4576 q^{34} + 11606 q^{35} + 5828 q^{36} + 12449 q^{37} - 84560 q^{38} + 13468 q^{39} - 23018 q^{40} + 32319 q^{41} + 26750 q^{42} - 49916 q^{43} + 12034 q^{44} + 81730 q^{45} + 5300 q^{46} - 57476 q^{47} - 14944 q^{48} - 52069 q^{49} - 19224 q^{50} - 78336 q^{51} + 1316 q^{52} + 65784 q^{53} + 72114 q^{54} - 24742 q^{55} - 81130 q^{56} - 3762 q^{57} - 73868 q^{58} - 49372 q^{59} - 288608 q^{60} + 137725 q^{61} + 118854 q^{62} - 81596 q^{63} + 427612 q^{64} + 35600 q^{65} + 289576 q^{66} + 64042 q^{67} - 60500 q^{68} - 141544 q^{69} + 5200 q^{70} + 136206 q^{71} - 294660 q^{72} - 270556 q^{73} + 133162 q^{74} - 240592 q^{75} + 209502 q^{76} + 152148 q^{77} + 152814 q^{78} - 61886 q^{79} + 264936 q^{80} - 104975 q^{81} - 28160 q^{82} + 202892 q^{83} - 197912 q^{84} + 576930 q^{85} + 154822 q^{86} - 312 q^{87} - 884284 q^{88} - 12065 q^{89} - 312764 q^{90} + 206252 q^{91} - 291924 q^{92} - 60752 q^{93} - 116814 q^{94} + 506 q^{95} + 81968 q^{96} + 132062 q^{97} + 249798 q^{98} + 289874 q^{99}+O(q^{100}) \) 30 * q - 4 * q^2 + 16 * q^3 - 230 * q^4 - 51 * q^5 + 60 * q^6 + 50 * q^7 + 24 * q^8 - 1085 * q^9 - 44 * q^10 - 1556 * q^11 + 708 * q^12 - 888 * q^13 + 1888 * q^14 + 1020 * q^15 - 4566 * q^16 - 437 * q^17 - 7302 * q^18 + 4358 * q^19 - 1204 * q^20 + 2354 * q^21 + 7958 * q^22 + 2824 * q^23 + 13824 * q^24 - 620 * q^25 - 17604 * q^26 - 32 * q^27 + 11414 * q^28 + 16954 * q^29 + 15994 * q^30 - 4548 * q^31 - 9148 * q^32 - 680 * q^33 - 4576 * q^34 + 11606 * q^35 + 5828 * q^36 + 12449 * q^37 - 84560 * q^38 + 13468 * q^39 - 23018 * q^40 + 32319 * q^41 + 26750 * q^42 - 49916 * q^43 + 12034 * q^44 + 81730 * q^45 + 5300 * q^46 - 57476 * q^47 - 14944 * q^48 - 52069 * q^49 - 19224 * q^50 - 78336 * q^51 + 1316 * q^52 + 65784 * q^53 + 72114 * q^54 - 24742 * q^55 - 81130 * q^56 - 3762 * q^57 - 73868 * q^58 - 49372 * q^59 - 288608 * q^60 + 137725 * q^61 + 118854 * q^62 - 81596 * q^63 + 427612 * q^64 + 35600 * q^65 + 289576 * q^66 + 64042 * q^67 - 60500 * q^68 - 141544 * q^69 + 5200 * q^70 + 136206 * q^71 - 294660 * q^72 - 270556 * q^73 + 133162 * q^74 - 240592 * q^75 + 209502 * q^76 + 152148 * q^77 + 152814 * q^78 - 61886 * q^79 + 264936 * q^80 - 104975 * q^81 - 28160 * q^82 + 202892 * q^83 - 197912 * q^84 + 576930 * q^85 + 154822 * q^86 - 312 * q^87 - 884284 * q^88 - 12065 * q^89 - 312764 * q^90 + 206252 * q^91 - 291924 * q^92 - 60752 * q^93 - 116814 * q^94 + 506 * q^95 + 81968 * q^96 + 132062 * q^97 + 249798 * q^98 + 289874 * q^99

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