LMFDB - Embedded newform 37.6.c.a.10.3

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			10.3
Character	$\chi$	$=$	37.10
Dual form			37.6.c.a.26.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.72321 + 6.44878i) q^{2} +(5.98171 + 10.3606i) q^{3} +(-11.7245 - 20.3075i) q^{4} +(37.3727 + 64.7314i) q^{5} -89.0845 q^{6} +(68.5781 + 118.781i) q^{7} -63.6740 q^{8} +(49.9383 - 86.4957i) q^{9} +O(q^{10})$	\(q+(-3.72321 + 6.44878i) q^{2} +(5.98171 + 10.3606i) q^{3} +(-11.7245 - 20.3075i) q^{4} +(37.3727 + 64.7314i) q^{5} -89.0845 q^{6} +(68.5781 + 118.781i) q^{7} -63.6740 q^{8} +(49.9383 - 86.4957i) q^{9} -556.584 q^{10} +109.599 q^{11} +(140.265 - 242.947i) q^{12} +(-500.749 - 867.323i) q^{13} -1021.32 q^{14} +(-447.105 + 774.408i) q^{15} +(612.256 - 1060.46i) q^{16} +(-451.495 + 782.012i) q^{17} +(371.861 + 644.082i) q^{18} +(425.074 + 736.250i) q^{19} +(876.353 - 1517.89i) q^{20} +(-820.429 + 1421.02i) q^{21} +(-408.058 + 706.777i) q^{22} +1603.10 q^{23} +(-380.879 - 659.702i) q^{24} +(-1230.93 + 2132.04i) q^{25} +7457.56 q^{26} +4101.98 q^{27} +(1608.09 - 2785.29i) q^{28} +6170.70 q^{29} +(-3329.33 - 5766.56i) q^{30} -8274.52 q^{31} +(3540.33 + 6132.02i) q^{32} +(655.586 + 1135.51i) q^{33} +(-3362.02 - 5823.18i) q^{34} +(-5125.89 + 8878.31i) q^{35} -2342.01 q^{36} +(2858.72 + 7821.23i) q^{37} -6330.56 q^{38} +(5990.67 - 10376.1i) q^{39} +(-2379.67 - 4121.70i) q^{40} +(-3993.80 - 6917.46i) q^{41} +(-6109.25 - 10581.5i) q^{42} -3863.20 q^{43} +(-1284.99 - 2225.67i) q^{44} +7465.31 q^{45} +(-5968.67 + 10338.0i) q^{46} +17227.1 q^{47} +14649.3 q^{48} +(-1002.41 + 1736.23i) q^{49} +(-9166.03 - 15876.0i) q^{50} -10802.8 q^{51} +(-11742.1 + 20337.9i) q^{52} +(-14229.0 + 24645.4i) q^{53} +(-15272.5 + 26452.7i) q^{54} +(4095.99 + 7094.46i) q^{55} +(-4366.64 - 7563.24i) q^{56} +(-5085.34 + 8808.07i) q^{57} +(-22974.8 + 39793.5i) q^{58} +(13590.4 - 23539.3i) q^{59} +20968.4 q^{60} +(-11246.2 - 19479.0i) q^{61} +(30807.7 - 53360.6i) q^{62} +13698.7 q^{63} -13541.1 q^{64} +(37428.6 - 64828.3i) q^{65} -9763.53 q^{66} +(27223.3 + 47152.2i) q^{67} +21174.2 q^{68} +(9589.28 + 16609.1i) q^{69} +(-38169.5 - 66111.5i) q^{70} +(-299.223 - 518.269i) q^{71} +(-3179.77 + 5507.52i) q^{72} +7985.79 q^{73} +(-61081.0 - 10684.8i) q^{74} -29452.3 q^{75} +(9967.59 - 17264.4i) q^{76} +(7516.06 + 13018.2i) q^{77} +(44609.0 + 77265.0i) q^{78} +(-6652.05 - 11521.7i) q^{79} +91526.5 q^{80} +(12401.8 + 21480.6i) q^{81} +59478.9 q^{82} +(560.254 - 970.388i) q^{83} +38476.5 q^{84} -67494.3 q^{85} +(14383.5 - 24913.0i) q^{86} +(36911.3 + 63932.3i) q^{87} -6978.57 q^{88} +(-40782.4 + 70637.3i) q^{89} +(-27794.9 + 48142.1i) q^{90} +(68680.8 - 118959. i) q^{91} +(-18795.6 - 32554.9i) q^{92} +(-49495.8 - 85729.2i) q^{93} +(-64139.9 + 111094. i) q^{94} +(-31772.3 + 55031.3i) q^{95} +(-42354.4 + 73360.0i) q^{96} -106769. q^{97} +(-7464.38 - 12928.7i) q^{98} +(5473.16 - 9479.80i) 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 $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

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

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 $

$2$	−3.72321	+	6.44878i	−0.658176	+	1.13999i	0.322911	+	0.946429i	$0.395338\pi$
$2$	−3.72321	+	6.44878i	−0.658176	+	1.13999i	−0.981087	+	0.193565i	$0.937995\pi$
$3$	5.98171	+	10.3606i	0.383727	+	0.664634i	0.991592	−	0.129406i	$-0.0413071\pi$
$3$	5.98171	+	10.3606i	0.383727	+	0.664634i	−0.607865	+	0.794041i	$0.707974\pi$
$4$	−11.7245	−	20.3075i	−0.366391	−	0.634608i
$5$	37.3727	+	64.7314i	0.668543	+	1.15795i	0.978312	+	0.207138i	$0.0664149\pi$
$5$	37.3727	+	64.7314i	0.668543	+	1.15795i	−0.309769	+	0.950812i	$0.600252\pi$
$6$	−89.0845			−1.01024
$7$	68.5781	+	118.781i	0.528981	+	0.916223i	0.999429	+	0.0337946i	$0.0107592\pi$
$7$	68.5781	+	118.781i	0.528981	+	0.916223i	−0.470447	+	0.882428i	$0.655907\pi$
$8$	−63.6740			−0.351752
$9$	49.9383	−	86.4957i	0.205507	−	0.355949i
$10$	−556.584			−1.76007
$11$	109.599			0.273101			0.136550	−	0.990633i	$-0.456398\pi$
$11$	109.599			0.273101			0.136550	+	0.990633i	$0.456398\pi$
$12$	140.265	−	242.947i	0.281188	−	0.487032i
$13$	−500.749	−	867.323i	−0.821791	−	1.42338i	−0.904347	−	0.426798i	$-0.859642\pi$
$13$	−500.749	−	867.323i	−0.821791	−	1.42338i	0.0825555	−	0.996586i	$-0.473692\pi$
$14$	−1021.32			−1.39265
$15$	−447.105	+	774.408i	−0.513075	+	0.888673i
$16$	612.256	−	1060.46i	0.597906	−	1.03560i
$17$	−451.495	+	782.012i	−0.378905	+	0.656283i	−0.990903	−	0.134576i	$-0.957033\pi$
$17$	−451.495	+	782.012i	−0.378905	+	0.656283i	0.611998	+	0.790859i	$0.290366\pi$
$18$	371.861	+	644.082i	0.270520	+	0.468555i
$19$	425.074	+	736.250i	0.270135	+	0.467888i	0.968896	−	0.247467i	$-0.0795983\pi$
$19$	425.074	+	736.250i	0.270135	+	0.467888i	−0.698761	+	0.715355i	$0.746265\pi$
$20$	876.353	−	1517.89i	0.489896	−	0.848525i
$21$	−820.429	+	1421.02i	−0.405969	+	0.703158i
$22$	−408.058	+	706.777i	−0.179748	+	0.311333i
$23$	1603.10			0.631890			0.315945	−	0.948778i	$-0.397679\pi$
$23$	1603.10			0.631890			0.315945	+	0.948778i	$0.397679\pi$
$24$	−380.879	−	659.702i	−0.134977	−	0.233787i
$25$	−1230.93	+	2132.04i	−0.393898	+	0.682252i
$26$	7457.56			2.16353
$27$	4101.98			1.08289
$28$	1608.09	−	2785.29i	0.387628	−	0.671392i
$29$	6170.70			1.36251			0.681254	−	0.732047i	$-0.261435\pi$
$29$	6170.70			1.36251			0.681254	+	0.732047i	$0.261435\pi$
$30$	−3329.33	−	5766.56i	−0.675388	−	1.16981i
$31$	−8274.52			−1.54646			−0.773230	−	0.634126i	$-0.781360\pi$
$31$	−8274.52			−1.54646			−0.773230	+	0.634126i	$0.781360\pi$
$32$	3540.33	+	6132.02i	0.611179	+	1.05859i
$33$	655.586	+	1135.51i	0.104796	+	0.181512i
$34$	−3362.02	−	5823.18i	−0.498773	−	0.863900i
$35$	−5125.89	+	8878.31i	−0.707293	+	1.22507i
$36$	−2342.01			−0.301184
$37$	2858.72	+	7821.23i	0.343295	+	0.939227i
$37$	2858.72	+	7821.23i	0.343295	+	0.939227i
$38$	−6330.56			−0.711186
$39$	5990.67	−	10376.1i	0.630687	−	1.09238i
$40$	−2379.67	−	4121.70i	−0.235161	−	0.407311i
$41$	−3993.80	−	6917.46i	−0.371045	−	0.642668i	0.618682	−	0.785642i	$-0.287667\pi$
$41$	−3993.80	−	6917.46i	−0.371045	−	0.642668i	−0.989727	+	0.142973i	$0.954334\pi$
$42$	−6109.25	−	10581.5i	−0.534398	−	0.925604i
$43$	−3863.20			−0.318623			−0.159311	−	0.987228i	$-0.550927\pi$
$43$	−3863.20			−0.318623			−0.159311	+	0.987228i	$0.550927\pi$
$44$	−1284.99	−	2225.67i	−0.100062	−	0.173312i
$45$	7465.31			0.549562
$46$	−5968.67	+	10338.0i	−0.415895	+	0.720351i
$47$	17227.1			1.13754			0.568770	−	0.822497i	$-0.307420\pi$
$47$	17227.1			1.13754			0.568770	+	0.822497i	$0.307420\pi$
$48$	14649.3			0.917731
$49$	−1002.41	+	1736.23i	−0.0596426	+	0.103304i
$50$	−9166.03	−	15876.0i	−0.518509	−	0.898083i
$51$	−10802.8			−0.581584
$52$	−11742.1	+	20337.9i	−0.602194	+	1.04303i
$53$	−14229.0	+	24645.4i	−0.695803	+	1.20517i	0.274106	+	0.961699i	$0.411618\pi$
$53$	−14229.0	+	24645.4i	−0.695803	+	1.20517i	−0.969909	+	0.243467i	$0.921715\pi$
$54$	−15272.5	+	26452.7i	−0.712731	+	1.23449i
$55$	4095.99	+	7094.46i	0.182579	+	0.316237i
$56$	−4366.64	−	7563.24i	−0.186070	−	0.322283i
$57$	−5085.34	+	8808.07i	−0.207316	+	0.359082i
$58$	−22974.8	+	39793.5i	−0.896771	+	1.55325i
$59$	13590.4	−	23539.3i	0.508280	−	0.880368i	−0.491674	−	0.870780i	$-0.663615\pi$
$59$	13590.4	−	23539.3i	0.508280	−	0.880368i	0.999954	−	0.00958803i	$-0.00305201\pi$
$60$	20968.4			0.751945
$61$	−11246.2	−	19479.0i	−0.386974	−	0.670258i	0.605067	−	0.796174i	$-0.293146\pi$
$61$	−11246.2	−	19479.0i	−0.386974	−	0.670258i	−0.992041	+	0.125916i	$0.959813\pi$
$62$	30807.7	−	53360.6i	1.01784	−	1.76296i
$63$	13698.7			0.434838
$64$	−13541.1			−0.413241
$65$	37428.6	−	64828.3i	1.09881	−	1.90319i
$66$	−9763.53			−0.275897
$67$	27223.3	+	47152.2i	0.740891	+	1.28326i	0.952090	+	0.305818i	$0.0989298\pi$
$67$	27223.3	+	47152.2i	0.740891	+	1.28326i	−0.211199	+	0.977443i	$0.567737\pi$
$68$	21174.2			0.555310
$69$	9589.28	+	16609.1i	0.242473	+	0.419976i
$70$	−38169.5	−	66111.5i	−0.931047	−	1.61262i
$71$	−299.223	−	518.269i	−0.00704447	−	0.0122014i	0.862482	−	0.506088i	$-0.168909\pi$
$71$	−299.223	−	518.269i	−0.00704447	−	0.0122014i	−0.869526	+	0.493887i	$0.835576\pi$
$72$	−3179.77	+	5507.52i	−0.0722877	+	0.125206i
$73$	7985.79			0.175392			0.0876962	−	0.996147i	$-0.472050\pi$
$73$	7985.79			0.175392			0.0876962	+	0.996147i	$0.472050\pi$
$74$	−61081.0	−	10684.8i	−1.29666	−	0.226822i
$75$	−29452.3			−0.604597
$76$	9967.59	−	17264.4i	0.197950	−	0.342860i
$77$	7516.06	+	13018.2i	0.144465	+	0.250221i
$78$	44609.0	+	77265.0i	0.830206	+	1.43796i
$79$	−6652.05	−	11521.7i	−0.119919	−	0.207706i	0.799816	−	0.600245i	$-0.204930\pi$
$79$	−6652.05	−	11521.7i	−0.119919	−	0.207706i	−0.919735	+	0.392539i	$0.871597\pi$
$80$	91526.5			1.59890
$81$	12401.8	+	21480.6i	0.210026	+	0.363776i
$82$	59478.9			0.976851
$83$	560.254	−	970.388i	0.00892667	−	0.0154614i	−0.861528	−	0.507711i	$-0.830492\pi$
$83$	560.254	−	970.388i	0.00892667	−	0.0154614i	0.870454	+	0.492249i	$0.163825\pi$
$84$	38476.5			0.594974
$85$	−67494.3			−1.01326
$86$	14383.5	−	24913.0i	0.209710	−	0.363228i
$87$	36911.3	+	63932.3i	0.522831	+	0.905570i
$88$	−6978.57			−0.0960638
$89$	−40782.4	+	70637.3i	−0.545756	+	0.945276i	0.452803	+	0.891610i	$0.350424\pi$
$89$	−40782.4	+	70637.3i	−0.545756	+	0.945276i	−0.998559	+	0.0536659i	$0.982909\pi$
$90$	−27794.9	+	48142.1i	−0.361708	+	0.626497i
$91$	68680.8	−	118959.i	0.869425	−	1.50589i
$92$	−18795.6	−	32554.9i	−0.231519	−	0.401002i
$93$	−49495.8	−	85729.2i	−0.593418	−	1.02783i
$94$	−64139.9	+	111094.i	−0.748701	+	1.29679i
$95$	−31772.3	+	55031.3i	−0.361194	+	0.625606i
$96$	−42354.4	+	73360.0i	−0.469051	+	0.812421i
$97$	−106769.			−1.15217			−0.576086	−	0.817389i	$-0.695421\pi$
$97$	−106769.			−1.15217			−0.576086	+	0.817389i	$0.695421\pi$
$98$	−7464.38	−	12928.7i	−0.0785107	−	0.135984i
$99$	5473.16	−	9479.80i	0.0561242	−	0.0972100i
$100$	57728.3			0.577283
$101$	101362.			0.988720			0.494360	−	0.869257i	$-0.335403\pi$
$101$	101362.			0.988720			0.494360	+	0.869257i	$0.335403\pi$
$102$	40221.2	−	69665.2i	0.382785	−	0.663003i
$103$	−26367.6			−0.244893			−0.122447	−	0.992475i	$-0.539074\pi$
$103$	−26367.6			−0.244893			−0.122447	+	0.992475i	$0.539074\pi$
$104$	31884.7	+	55225.9i	0.289067	+	0.500679i
$105$	−122646.			−1.08563
$106$	−105955.	−	183520.i	−0.915921	−	1.58642i
$107$	−64698.4	−	112061.i	−0.546304	−	0.946226i	−0.998524	−	0.0543197i	$-0.982701\pi$
$107$	−64698.4	−	112061.i	−0.546304	−	0.946226i	0.452220	−	0.891907i	$-0.350632\pi$
$108$	−48093.7	−	83300.7i	−0.396761	−	0.687210i
$109$	−68593.9	+	118808.i	−0.552993	+	0.957811i	0.445064	+	0.895499i	$0.353181\pi$
$109$	−68593.9	+	118808.i	−0.552993	+	0.957811i	−0.998057	+	0.0623125i	$0.980152\pi$
$110$	−61000.8			−0.480678
$111$	−63932.8	+	76402.5i	−0.492511	+	0.588573i
$112$	167949.			1.26512
$113$	91671.3	−	158779.i	0.675363	−	1.16976i	−0.301000	−	0.953624i	$-0.597320\pi$
$113$	91671.3	−	158779.i	0.675363	−	1.16976i	0.976363	−	0.216139i	$-0.0693463\pi$
$114$	−37867.6	−	65588.5i	−0.272901	−	0.472678i
$115$	59912.2	+	103771.i	0.422445	+	0.731696i
$116$	−72348.5	−	125311.i	−0.499211	−	0.864659i
$117$	−100026.			−0.675537
$118$	101200.	+	175284.i	0.669076	+	1.15887i
$119$	−123851.			−0.801735
$120$	28468.9	−	49309.6i	0.180475	−	0.312593i
$121$	−149039.			−0.925416
$122$	167488.			1.01879
$123$	47779.5	−	82756.4i	0.284760	−	0.493218i
$124$	97014.8	+	168035.i	0.566609	+	0.981396i
$125$	49566.3			0.283734
$126$	−51003.1	+	88339.9i	−0.286200	+	0.495713i
$127$	123977.	−	214735.i	0.682075	−	1.18139i	−0.292271	−	0.956336i	$-0.594411\pi$
$127$	123977.	−	214735.i	0.682075	−	1.18139i	0.974346	−	0.225054i	$-0.0722558\pi$
$128$	−62874.2	+	108901.i	−0.339194	+	0.587501i
$129$	−23108.6	−	40025.2i	−0.122264	−	0.211768i
$130$	278709.	+	482738.i	1.44641	+	2.50526i
$131$	102855.	−	178149.i	0.523655	−	0.906998i	−0.475965	−	0.879464i	$-0.657901\pi$
$131$	102855.	−	178149.i	0.523655	−	0.906998i	0.999621	−	0.0275338i	$-0.00876539\pi$
$132$	15372.9	−	26626.6i	0.0767928	−	0.133009i
$133$	−58301.6	+	100981.i	−0.285793	+	0.495008i
$134$	−405432.			−1.95055
$135$	153302.	+	265526.i	0.723957	+	1.25393i
$136$	28748.5	−	49793.8i	0.133281	−	0.230849i
$137$	394541.			1.79594			0.897968	−	0.440061i	$-0.145043\pi$
$137$	394541.			1.79594			0.897968	+	0.440061i	$0.145043\pi$
$138$	−142812.			−0.638360
$139$	200077.	−	346543.i	0.878333	−	1.52132i	0.0251637	−	0.999683i	$-0.491989\pi$
$139$	200077.	−	346543.i	0.878333	−	1.52132i	0.853169	−	0.521634i	$-0.174677\pi$
$140$	240395.			1.03658
$141$	103047.	+	178483.i	0.436504	+	0.756048i
$142$	4456.27			0.0185460
$143$	−54881.3	−	95057.3i	−0.224432	−	0.388727i
$144$	−61150.0	−	105915.i	−0.245748	−	0.425649i
$145$	230615.	+	399438.i	0.910895	+	1.57772i
$146$	−29732.7	+	51498.6i	−0.115439	+	0.199946i
$147$	−23984.6			−0.0915459
$148$	125312.	−	149754.i	0.470261	−	0.561983i
$149$	−194164.			−0.716478			−0.358239	−	0.933630i	$-0.616623\pi$
$149$	−194164.			−0.716478			−0.358239	+	0.933630i	$0.616623\pi$
$150$	109657.	−	189931.i	0.397931	−	0.689237i
$151$	−92492.6	−	160202.i	−0.330114	−	0.571775i	0.652420	−	0.757858i	$-0.273754\pi$
$151$	−92492.6	−	160202.i	−0.330114	−	0.571775i	−0.982534	+	0.186083i	$0.940421\pi$
$152$	−27066.2	−	46880.0i	−0.0950206	−	0.164581i
$153$	45093.8	+	78104.7i	0.155736	+	0.269742i
$154$	−111935.			−0.380334
$155$	−309241.	−	535621.i	−1.03387	−	1.79072i
$156$	−280951.			−0.924313
$157$	222505.	−	385390.i	0.720428	−	1.24782i	−0.240400	−	0.970674i	$-0.577279\pi$
$157$	222505.	−	385390.i	0.720428	−	1.24782i	0.960828	−	0.277145i	$-0.0893881\pi$
$158$	99067.8			0.315711
$159$	−340456.			−1.06799
$160$	−264623.	+	458340.i	−0.817198	+	1.41543i
$161$	109938.	+	190418.i	0.334258	+	0.578952i
$162$	−184698.			−0.552936
$163$	303173.	−	525111.i	0.893761	−	1.54804i	0.0584298	−	0.998292i	$-0.481391\pi$
$163$	303173.	−	525111.i	0.893761	−	1.54804i	0.835331	−	0.549747i	$-0.185276\pi$
$164$	−93650.7	+	162208.i	−0.271895	+	0.470936i
$165$	−49002.0	+	84874.0i	−0.140121	+	0.242697i
$166$	4171.88	+	7225.91i	0.0117506	+	0.0203527i
$167$	111361.	+	192883.i	0.308989	+	0.535185i	0.978141	−	0.207940i	$-0.0666760\pi$
$167$	111361.	+	192883.i	0.308989	+	0.535185i	−0.669152	+	0.743125i	$0.733343\pi$
$168$	52239.9	−	90482.2i	0.142800	−	0.247338i
$169$	−315852.	+	547072.i	−0.850682	+	1.47343i
$170$	251295.	−	435256.i	0.666901	−	1.15511i
$171$	84910.0			0.222059
$172$	45294.2	+	78451.9i	0.116741	+	0.202201i
$173$	−238493.	+	413082.i	−0.605844	+	1.04935i	0.386074	+	0.922468i	$0.373831\pi$
$173$	−238493.	+	413082.i	−0.605844	+	1.04935i	−0.991918	+	0.126884i	$0.959502\pi$
$174$	−549714.			−1.37646
$175$	−337660.			−0.833459
$176$	67102.3	−	116225.i	0.163289	−	0.282824i
$177$	325176.			0.780163
$178$	−303683.	−	525994.i	−0.718406	−	1.24432i
$179$	−619427.			−1.44496			−0.722482	−	0.691389i	$-0.756999\pi$
$179$	−619427.			−1.44496			−0.722482	+	0.691389i	$0.756999\pi$
$180$	−87527.2	−	151602.i	−0.201355	−	0.348756i
$181$	19050.9	+	32997.1i	0.0432234	+	0.0748650i	0.886828	−	0.462100i	$-0.152904\pi$
$181$	19050.9	+	32997.1i	0.0432234	+	0.0748650i	−0.843604	+	0.536965i	$0.819571\pi$
$182$	511426.	+	885815.i	1.14447	+	1.98228i
$183$	134543.	−	233035.i	0.296984	−	0.514392i
$184$	−102076.			−0.222269
$185$	−399441.	+	477349.i	−0.858070	+	1.02543i
$186$	737132.			1.56229
$187$	−49483.2	+	85707.4i	−0.103479	+	0.179231i
$188$	−201979.	−	349838.i	−0.416785	−	0.721892i
$189$	281306.	+	487236.i	0.572828	+	0.992167i
$190$	−236590.	−	409786.i	−0.475458	−	0.823517i
$191$	361821.			0.717646			0.358823	−	0.933406i	$-0.383178\pi$
$191$	361821.			0.717646			0.358823	+	0.933406i	$0.383178\pi$
$192$	−80998.7	−	140294.i	−0.158572	−	0.274654i
$193$	−628955.			−1.21542			−0.607710	−	0.794159i	$-0.707912\pi$
$193$	−628955.			−1.21542			−0.607710	+	0.794159i	$0.707912\pi$
$194$	397525.	−	688533.i	0.758332	−	1.31347i
$195$	895549.			1.68656
$196$	47011.3			0.0874101
$197$	−169729.	+	293980.i	−0.311596	+	0.539700i	−0.978708	−	0.205258i	$-0.934197\pi$
$197$	−169729.	+	293980.i	−0.311596	+	0.539700i	0.667112	+	0.744957i	$0.267530\pi$
$198$	40755.4	+	70590.5i	0.0738793	+	0.127963i
$199$	290334.			0.519715			0.259858	−	0.965647i	$-0.416324\pi$
$199$	290334.			0.519715			0.259858	+	0.965647i	$0.416324\pi$
$200$	78378.3	−	135755.i	0.138555	−	0.239984i
$201$	−325684.	+	564102.i	−0.568600	+	0.984843i
$202$	−377393.	+	653663.i	−0.650751	+	1.12713i
$203$	423175.	+	732960.i	0.720742	+	1.24836i
$204$	126658.	+	219378.i	0.213087	+	0.369078i
$205$	298518.	−	517048.i	0.496118	−	0.859302i
$206$	98171.8	−	170039.i	0.161183	−	0.279177i
$207$	80056.1	−	138661.i	0.129858	−	0.224921i
$208$	−1.22635e6			−1.96542
$209$	46587.5	+	80692.0i	0.0737741	+	0.127780i
$210$	456638.	−	790920.i	0.714535	−	1.23761i
$211$	−529229.			−0.818348			−0.409174	−	0.912456i	$-0.634183\pi$
$211$	−529229.			−0.818348			−0.409174	+	0.912456i	$0.634183\pi$
$212$	667315.			1.01974
$213$	3579.72	−	6200.27i	0.00540631	−	0.00936400i
$214$	963543.			1.43826
$215$	−144378.	−	250070.i	−0.213013	−	0.368949i
$216$	−261189.			−0.380908
$217$	−567451.	−	982854.i	−0.818049	−	1.41690i
$218$	−510778.	−	884694.i	−0.727933	−	1.26082i
$219$	47768.7	+	82737.8i	0.0673028	+	0.116572i
$220$	96047.0	−	166358.i	0.133791	−	0.231733i
$221$	904342.			1.24552
$222$	−254668.	−	696751.i	−0.346811	−	0.948844i
$223$	1.13045e6			1.52227			0.761133	−	0.648596i	$-0.224644\pi$
$223$	1.13045e6			1.52227			0.761133	+	0.648596i	$0.224644\pi$
$224$	−485578.	+	841045.i	−0.646604	+	1.11995i
$225$	122941.	+	212941.i	0.161898	+	0.280416i
$226$	682622.	+	1.18234e6i	0.889015	+	1.53982i
$227$	259486.	+	449444.i	0.334234	+	0.578910i	0.983337	−	0.181790i	$-0.0581892\pi$
$227$	259486.	+	449444.i	0.334234	+	0.578910i	−0.649104	+	0.760700i	$0.724856\pi$
$228$	238493.			0.303835
$229$	−595006.	−	1.03058e6i	−0.749778	−	1.29865i	−0.947929	−	0.318481i	$-0.896827\pi$
$229$	−595006.	−	1.03058e6i	−0.749778	−	1.29865i	0.198152	−	0.980171i	$-0.436506\pi$
$230$	−892261.			−1.11217
$231$	−89917.8	+	155742.i	−0.110870	+	0.192033i
$232$	−392913.			−0.479266
$233$	−576730.			−0.695958			−0.347979	−	0.937502i	$-0.613132\pi$
$233$	−576730.			−0.695958			−0.347979	+	0.937502i	$0.613132\pi$
$234$	372418.	−	645047.i	0.444622	−	0.770108i
$235$	643821.	+	1.11513e6i	0.760494	+	1.31721i
$236$	−637365.			−0.744918
$237$	79581.3	−	137839.i	0.0920322	−	0.159405i
$238$	461122.	−	798686.i	0.527683	−	0.913974i
$239$	−661163.	+	1.14517e6i	−0.748710	+	1.29680i	0.199731	+	0.979851i	$0.435993\pi$
$239$	−661163.	+	1.14517e6i	−0.748710	+	1.29680i	−0.948441	+	0.316953i	$0.897340\pi$
$240$	547485.	+	948272.i	0.613542	+	1.06269i
$241$	13099.4	+	22688.7i	0.0145280	+	0.0251633i	0.873198	−	0.487366i	$-0.162042\pi$
$241$	13099.4	+	22688.7i	0.0145280	+	0.0251633i	−0.858670	+	0.512529i	$0.828709\pi$
$242$	554903.	−	961121.i	0.609087	−	1.05497i
$243$	350022.	−	606256.i	0.380259	−	0.658628i
$244$	−263713.	+	456764.i	−0.283568	+	0.491154i
$245$	−149851.			−0.159494
$246$	355785.	+	616238.i	0.374844	+	0.649249i
$247$	425711.	−	737353.i	0.443989	−	0.769012i
$248$	526872.			0.543971
$249$	13405.1			0.0137016
$250$	−184546.	+	319642.i	−0.186747	+	0.323455i
$251$	263915.			0.264411			0.132206	−	0.991222i	$-0.457794\pi$
$251$	263915.			0.264411			0.132206	+	0.991222i	$0.457794\pi$
$252$	−160611.	−	278186.i	−0.159321	−	0.275952i
$253$	175697.			0.172570
$254$	923185.	+	1.59900e6i	0.897851	+	1.55512i
$255$	−403731.	−	699283.i	−0.388814	−	0.673445i
$256$	−684845.	−	1.18619e6i	−0.653119	−	1.13123i
$257$	−230401.	+	399066.i	−0.217596	+	0.376887i	−0.954073	−	0.299576i	$-0.903155\pi$
$257$	−230401.	+	399066.i	−0.217596	+	0.376887i	0.736476	+	0.676463i	$0.236488\pi$
$258$	344152.			0.321885
$259$	−732966.	+	875927.i	−0.678945	+	0.811369i
$260$	−1.75533e6			−1.61037
$261$	308154.	−	533739.i	0.280006	−	0.484984i
$262$	765898.	+	1.32657e6i	0.689315	+	1.19393i
$263$	−93126.7	−	161300.i	−0.0830204	−	0.143796i	0.821526	−	0.570172i	$-0.193123\pi$
$263$	−93126.7	−	161300.i	−0.0830204	−	0.143796i	−0.904546	+	0.426376i	$0.859790\pi$
$264$	−41743.8	−	72302.4i	−0.0368623	−	0.0638473i
$265$	−2.12711e6			−1.86070
$266$	−434138.	−	751948.i	−0.376204	−	0.651604i
$267$	−975795.			−0.837684
$268$	638361.	−	1.10567e6i	0.542912	−	0.940351i
$269$	709920.			0.598176			0.299088	−	0.954226i	$-0.403318\pi$
$269$	709920.			0.598176			0.299088	+	0.954226i	$0.403318\pi$
$270$	−2.28310e6			−1.90596
$271$	1.04702e6	−	1.81350e6i	0.866030	−	1.50001i	9.67472e−6	−	1.00000i	$-0.499997\pi$
$271$	1.04702e6	−	1.81350e6i	0.866030	−	1.50001i	0.866021	−	0.500008i	$-0.166670\pi$
$272$	552861.	+	957583.i	0.453100	+	0.784791i
$273$	1.64331e6			1.33449
$274$	−1.46896e6	+	2.54431e6i	−1.18204	+	2.04736i
$275$	−134908.	+	233668.i	−0.107574	+	0.186323i
$276$	224860.	−	389468.i	0.177680	−	0.307751i
$277$	−294780.	−	510574.i	−0.230833	−	0.399815i	0.727220	−	0.686404i	$-0.240812\pi$
$277$	−294780.	−	510574.i	−0.230833	−	0.399815i	−0.958054	+	0.286589i	$0.907479\pi$
$278$	1.48985e6	+	2.58050e6i	1.15620	+	2.00259i
$279$	−413216.	+	715710.i	−0.317809	+	0.550461i
$280$	326386.	−	565317.i	0.248792	−	0.430920i
$281$	−544179.	+	942545.i	−0.411127	+	0.712092i	−0.995013	−	0.0997430i	$-0.968198\pi$
$281$	−544179.	+	942545.i	−0.411127	+	0.712092i	0.583887	+	0.811835i	$0.301531\pi$
$282$	−1.53466e6			−1.14919
$283$	−824873.	−	1.42872e6i	−0.612239	−	1.06043i	−0.990862	−	0.134878i	$-0.956936\pi$
$283$	−824873.	−	1.42872e6i	−0.612239	−	1.06043i	0.378623	−	0.925551i	$-0.376398\pi$
$284$	−7016.48	+	12152.9i	−0.00516207	+	0.00894096i
$285$	−760211.			−0.554399
$286$	817338.			0.590863
$287$	547774.	−	948772.i	0.392551	−	0.679919i
$288$	707191.			0.502407
$289$	302233.	+	523483.i	0.212862	+	0.368687i
$290$	−3.43451e6			−2.39812
$291$	−638664.	−	1.10620e6i	−0.442120	−	0.765774i
$292$	−93629.6	−	162171.i	−0.0642622	−	0.111305i
$293$	−1.38563e6	−	2.39998e6i	−0.942925	−	1.63319i	−0.759853	−	0.650095i	$-0.774729\pi$
$293$	−1.38563e6	−	2.39998e6i	−0.942925	−	1.63319i	−0.183072	−	0.983100i	$-0.558604\pi$
$294$	89299.5	−	154671.i	0.0602533	−	0.104362i
$295$	2.03164e6			1.35923
$296$	−182026.	−	498009.i	−0.120755	−	0.330375i
$297$	449571.			0.295738
$298$	722912.	−	1.25212e6i	0.471569	−	0.816781i
$299$	−802751.	−	1.39041e6i	−0.519282	−	0.899422i
$300$	345314.	+	598102.i	0.221519	+	0.383682i
$301$	−264931.	−	458874.i	−0.168545	−	0.291929i
$302$	1.37748e6			0.869093
$303$	606320.	+	1.05018e6i	0.379398	+	0.657137i
$304$	1.04102e6			0.646062
$305$	840602.	−	1.45596e6i	0.517417	−	0.896192i
$306$	−671574.			−0.410006
$307$	−570556.			−0.345503			−0.172752	−	0.984965i	$-0.555266\pi$
$307$	−570556.			−0.345503			−0.172752	+	0.984965i	$0.555266\pi$
$308$	176244.	−	305264.i	0.105862	−	0.183358i
$309$	−157723.	−	273184.i	−0.0939721	−	0.162764i
$310$	4.60547e6			2.72189
$311$	566906.	−	981909.i	0.332361	−	0.575666i	−0.650613	−	0.759409i	$-0.725488\pi$
$311$	566906.	−	981909.i	0.332361	−	0.575666i	0.982974	+	0.183743i	$0.0588215\pi$
$312$	−381450.	+	660690.i	−0.221846	+	0.384248i
$313$	−1.30960e6	+	2.26830e6i	−0.755578	+	1.30870i	0.189508	+	0.981879i	$0.439311\pi$
$313$	−1.30960e6	+	2.26830e6i	−0.755578	+	1.30870i	−0.945086	+	0.326821i	$0.894023\pi$
$314$	1.65686e6	+	2.86977e6i	0.948337	+	1.64257i
$315$	511957.	+	886735.i	0.290708	+	0.503521i
$316$	−155984.	+	270173.i	−0.0878745	+	0.152203i
$317$	−503207.	+	871580.i	−0.281254	+	0.487146i	−0.971694	−	0.236244i	$-0.924084\pi$
$317$	−503207.	+	871580.i	−0.281254	+	0.487146i	0.690440	+	0.723390i	$0.257417\pi$
$318$	1.26759e6	−	2.19553e6i	0.702927	−	1.21751i
$319$	676299.			0.372102
$320$	−506066.	−	876532.i	−0.276269	−	0.478512i
$321$	774015.	−	1.34063e6i	0.419263	−	0.726185i
$322$	−1.63728e6			−0.880002
$323$	−767676.			−0.409422
$324$	290811.	−	503699.i	0.153903	−	0.266568i
$325$	2.46555e6			1.29481
$326$	2.25755e6	+	3.91019e6i	1.17650	+	2.03776i
$327$	−1.64124e6			−0.848792
$328$	254301.	+	440462.i	0.130516	+	0.226060i
$329$	1.18140e6	+	2.04624e6i	0.601737	+	1.04224i
$330$	−364889.	−	632007.i	−0.184449	−	0.319475i
$331$	−560906.	+	971518.i	−0.281397	+	0.487395i	−0.971729	−	0.236098i	$-0.924131\pi$
$331$	−560906.	+	971518.i	−0.281397	+	0.487395i	0.690332	+	0.723493i	$0.257465\pi$
$332$	−26274.8			−0.0130826
$333$	819262.	+	143312.i	0.404867	+	0.0708224i
$334$	−1.65848e6			−0.813477
$335$	−2.03482e6	+	3.52441e6i	−0.990634	+	1.71583i
$336$	1.00462e6	+	1.74006e6i	0.485462	+	0.840846i
$337$	1.27159e6	+	2.20246e6i	0.609920	+	1.05641i	0.991253	+	0.131975i	$0.0421317\pi$
$337$	1.27159e6	+	2.20246e6i	0.609920	+	1.05641i	−0.381333	+	0.924438i	$0.624535\pi$
$338$	−2.35197e6	−	4.07373e6i	−1.11980	−	1.93955i
$339$	2.19340e6			1.03662
$340$	791338.	+	1.37064e6i	0.371248	+	0.643021i
$341$	−906875.			−0.422339
$342$	−316137.	+	547566.i	−0.146154	+	0.253146i
$343$	2.03021e6			0.931763
$344$	245986.			0.112076
$345$	−716754.	+	1.24145e6i	−0.324207	+	0.561543i
$346$	−1.77592e6	−	3.07598e6i	−0.797504	−	1.38132i
$347$	−3.76843e6			−1.68011			−0.840054	−	0.542503i	$-0.817477\pi$
$347$	−3.76843e6			−1.68011			−0.840054	+	0.542503i	$0.817477\pi$
$348$	865535.	−	1.49915e6i	0.383122	−	0.663586i
$349$	463188.	−	802266.i	0.203561	−	0.352578i	−0.746112	−	0.665820i	$-0.768082\pi$
$349$	463188.	−	802266.i	0.203561	−	0.352578i	0.949673	+	0.313242i	$0.101415\pi$
$350$	1.25718e6	−	2.17749e6i	0.548563	−	0.950139i
$351$	−2.05406e6	−	3.55774e6i	−0.889909	−	1.54137i
$352$	388014.	+	672061.i	0.166913	+	0.289103i
$353$	−738994.	+	1.27997e6i	−0.315649	+	0.546720i	−0.979575	−	0.201078i	$-0.935555\pi$
$353$	−738994.	+	1.27997e6i	−0.315649	+	0.546720i	0.663926	+	0.747798i	$0.268889\pi$
$354$	−1.21070e6	+	2.09699e6i	−0.513485	+	0.889382i
$355$	22365.5	−	38738.2i	0.00941906	−	0.0163143i
$356$	1.91262e6			0.799840
$357$	−740839.	−	1.28317e6i	−0.307647	−	0.532861i
$358$	2.30625e6	−	3.99455e6i	0.951041	−	1.64725i
$359$	2.53101e6			1.03647			0.518236	−	0.855238i	$-0.326589\pi$
$359$	2.53101e6			1.03647			0.518236	+	0.855238i	$0.326589\pi$
$360$	−475346.			−0.193310
$361$	876673.	−	1.51844e6i	0.354054	−	0.613240i
$362$	−283721.			−0.113794
$363$	−891509.	−	1.54414e6i	−0.355107	−	0.615063i
$364$	−3.22100e6			−1.27420
$365$	298450.	+	516931.i	0.117257	+	0.203096i
$366$	1.00186e6	+	1.73528e6i	0.390936	+	0.677121i
$367$	157079.	+	272069.i	0.0608771	+	0.105442i	0.894858	−	0.446352i	$-0.147277\pi$
$367$	157079.	+	272069.i	0.0608771	+	0.105442i	−0.833981	+	0.551794i	$0.813944\pi$
$368$	981508.	−	1.70002e6i	0.377811	−	0.654387i
$369$	−797773.			−0.305010
$370$	−1.59112e6	−	4.35318e6i	−0.604226	−	1.65311i
$371$	−3.90320e6			−1.47227
$372$	−1.16063e6	+	2.01027e6i	−0.434847	+	0.753176i
$373$	1.46343e6	+	2.53473e6i	0.544627	+	0.943322i	0.998630	+	0.0523221i	$0.0166623\pi$
$373$	1.46343e6	+	2.53473e6i	0.544627	+	0.943322i	−0.454003	+	0.891000i	$0.650004\pi$
$374$	−368472.	−	638212.i	−0.136215	−	0.235932i
$375$	296491.	+	513538.i	0.108876	+	0.188580i
$376$	−1.09692e6			−0.400132
$377$	−3.08997e6	−	5.35199e6i	−1.11970	−	1.93937i
$378$	−4.18944e6			−1.50809
$379$	−1.25165e6	+	2.16793e6i	−0.447596	+	0.775259i	−0.998229	−	0.0594886i	$-0.981053\pi$
$379$	−1.25165e6	+	2.16793e6i	−0.447596	+	0.775259i	0.550633	+	0.834747i	$0.314386\pi$
$380$	1.49006e6			0.529353
$381$	2.96638e6			1.04692
$382$	−1.34713e6	+	2.33330e6i	−0.472337	+	0.818112i
$383$	156866.	+	271700.i	0.0546427	+	0.0946439i	0.892053	−	0.451931i	$-0.149265\pi$
$383$	156866.	+	271700.i	0.0546427	+	0.0946439i	−0.837410	+	0.546575i	$0.815931\pi$
$384$	−1.50438e6			−0.520631
$385$	−561790.	+	973049.i	−0.193162	+	0.334567i
$386$	2.34173e6	−	4.05599e6i	0.799960	−	1.38557i
$387$	−192922.	+	334150.i	−0.0654793	+	0.113413i
$388$	1.25182e6	+	2.16822e6i	0.422146	+	0.731178i
$389$	704617.	+	1.22043e6i	0.236091	+	0.408921i	0.959589	−	0.281405i	$-0.0908003\pi$
$389$	704617.	+	1.22043e6i	0.236091	+	0.408921i	−0.723498	+	0.690326i	$0.757467\pi$
$390$	−3.33431e6	+	5.77520e6i	−1.11006	+	1.92267i
$391$	−723792.	+	1.25364e6i	−0.239426	+	0.414699i
$392$	63827.6	−	110553.i	0.0209794	−	0.0363374i
$393$	2.46099e6			0.803763
$394$	−1.26387e6	−	2.18910e6i	−0.410170	−	0.710435i
$395$	497210.	−	861193.i	0.160342	−	0.277720i
$396$	−256681.			−0.0822537
$397$	−321237.			−0.102294			−0.0511468	−	0.998691i	$-0.516288\pi$
$397$	−321237.			−0.102294			−0.0511468	+	0.998691i	$0.516288\pi$
$398$	−1.08097e6	+	1.87230e6i	−0.342064	+	0.592472i
$399$	−1.39497e6			−0.438666
$400$	1.50729e6	+	2.61070e6i	0.471028	+	0.815845i
$401$	−713774.			−0.221666			−0.110833	−	0.993839i	$-0.535352\pi$
$401$	−713774.			−0.221666			−0.110833	+	0.993839i	$0.535352\pi$
$402$	−2.42518e6	−	4.20053e6i	−0.748477	−	1.29640i
$403$	4.14346e6	+	7.17668e6i	1.27087	+	2.20121i
$404$	−1.18842e6	−	2.05841e6i	−0.362258	−	0.627450i
$405$	−926978.	+	1.60557e6i	−0.280823	+	0.486399i
$406$	−6.30227e6			−1.89750
$407$	313312.	+	857195.i	0.0937543	+	0.256504i
$408$	687860.			0.204574
$409$	2.33760e6	−	4.04884e6i	0.690974	−	1.19680i	−0.280545	−	0.959841i	$-0.590515\pi$
$409$	2.33760e6	−	4.04884e6i	0.690974	−	1.19680i	0.971519	−	0.236962i	$-0.0761516\pi$
$410$	2.22288e6	+	3.85015e6i	0.653066	+	1.13114i
$411$	2.36003e6	+	4.08769e6i	0.689149	+	1.19364i
$412$	309147.	+	535458.i	0.0897268	+	0.155411i
$413$	3.72803e6			1.07548
$414$	596131.	+	1.03253e6i	0.170939	+	0.296075i
$415$	83752.7			0.0238714
$416$	3.54563e6	−	6.14121e6i	1.00452	−	1.73988i
$417$	4.78720e6			1.34816
$418$	−693820.			−0.194225
$419$	1.07716e6	−	1.86569e6i	0.299740	−	0.519165i	−0.676336	−	0.736593i	$-0.736433\pi$
$419$	1.07716e6	−	1.86569e6i	0.299740	−	0.519165i	0.976076	+	0.217428i	$0.0697668\pi$
$420$	1.43797e6	+	2.49064e6i	0.397765	+	0.688949i
$421$	−2.94380e6			−0.809473			−0.404737	−	0.914433i	$-0.632637\pi$
$421$	−2.94380e6			−0.809473			−0.404737	+	0.914433i	$0.632637\pi$
$422$	1.97043e6	−	3.41289e6i	0.538617	−	0.932912i
$423$	860290.	−	1.49007e6i	0.233773	−	0.404906i
$424$	906020.	−	1.56927e6i	0.244750	−	0.423920i
$425$	−1.11152e6	−	1.92521e6i	−0.298500	−	0.517017i
$426$	26656.1	+	46169.7i	0.00711660	+	0.0123263i
$427$	1.54249e6	−	2.67167e6i	0.409404	−	0.709108i
$428$	−1.51712e6	+	2.62772e6i	−0.400322	+	0.693378i
$429$	656568.	−	1.13721e6i	0.172241	−	0.298330i
$430$	2.15020e6			0.560799
$431$	440476.	+	762926.i	0.114217	+	0.197829i	0.917466	−	0.397814i	$-0.130231\pi$
$431$	440476.	+	762926.i	0.114217	+	0.197829i	−0.803250	+	0.595642i	$0.796898\pi$
$432$	2.51146e6	−	4.34998e6i	0.647466	−	1.12144i
$433$	−2.76675e6			−0.709171			−0.354585	−	0.935024i	$-0.615378\pi$
$433$	−2.76675e6			−0.709171			−0.354585	+	0.935024i	$0.615378\pi$
$434$	8.45095e6			2.15368
$435$	−2.75895e6	+	4.77864e6i	−0.699070	+	1.21082i
$436$	3.21692e6			0.810447
$437$	681437.	+	1.18028e6i	0.170696	+	0.295653i
$438$	−711410.			−0.177188
$439$	−1.24929e6	−	2.16384e6i	−0.309388	−	0.535875i	0.668841	−	0.743406i	$-0.266791\pi$
$439$	−1.24929e6	−	2.16384e6i	−0.309388	−	0.535875i	−0.978229	+	0.207530i	$0.933457\pi$
$440$	−260808.	−	451732.i	−0.0642227	−	0.111237i
$441$	100118.	+	173409.i	0.0245140	+	0.0424595i
$442$	−3.36705e6	+	5.83191e6i	−0.819774	+	1.41989i
$443$	−4.67141e6			−1.13094			−0.565469	−	0.824770i	$-0.691305\pi$
$443$	−4.67141e6			−1.13094			−0.565469	+	0.824770i	$0.691305\pi$
$444$	2.30112e6	+	402530.i	0.553965	+	0.0969038i
$445$	−6.09659e6			−1.45944
$446$	−4.20891e6	+	7.29004e6i	−1.00192	+	1.73537i
$447$	−1.16143e6	−	2.01166e6i	−0.274932	−	0.476196i
$448$	−928621.	−	1.60842e6i	−0.218597	−	0.378620i
$449$	−1.03883e6	−	1.79931e6i	−0.243181	−	0.421202i	0.718438	−	0.695592i	$-0.244858\pi$
$449$	−1.03883e6	−	1.79931e6i	−0.243181	−	0.421202i	−0.961619	+	0.274389i	$0.911524\pi$
$450$	−1.83094e6			−0.426230
$451$	−437714.	−	758143.i	−0.101333	−	0.175513i
$452$	−4.29921e6			−0.989788
$453$	1.10653e6	−	1.91656e6i	0.253347	−	0.438811i
$454$	−3.86449e6			−0.879938
$455$	1.02671e7			2.32499
$456$	323804.	−	560845.i	0.0729239	−	0.126308i
$457$	−1.86249e6	−	3.22593e6i	−0.417161	−	0.722544i	0.578491	−	0.815688i	$-0.303642\pi$
$457$	−1.86249e6	−	3.22593e6i	−0.417161	−	0.722544i	−0.995653	+	0.0931441i	$0.970308\pi$
$458$	8.86131e6			1.97394
$459$	−1.85202e6	+	3.20780e6i	−0.410312	+	0.710681i
$460$	1.40488e6	−	2.43333e6i	0.309560	−	0.536174i
$461$	3.49947e6	−	6.06125e6i	0.766919	−	1.32834i	−0.172307	−	0.985043i	$-0.555122\pi$
$461$	3.49947e6	−	6.06125e6i	0.766919	−	1.32834i	0.939226	−	0.343299i	$-0.111545\pi$
$462$	−669565.	−	1.15972e6i	−0.145944	−	0.252783i
$463$	2.26860e6	+	3.92934e6i	0.491820	+	0.851857i	0.999956	−	0.00941969i	$-0.00299842\pi$
$463$	2.26860e6	+	3.92934e6i	0.491820	+	0.851857i	−0.508136	+	0.861277i	$0.669665\pi$
$464$	3.77805e6	−	6.54377e6i	0.814652	−	1.41102i
$465$	3.69958e6	−	6.40786e6i	0.793451	−	1.37430i
$466$	2.14729e6	−	3.71921e6i	0.458063	−	0.793388i
$467$	1.48204e6			0.314462			0.157231	−	0.987562i	$-0.449743\pi$
$467$	1.48204e6			0.314462			0.157231	+	0.987562i	$0.449743\pi$
$468$	1.17276e6	+	2.03128e6i	0.247511	+	0.428701i
$469$	−3.73385e6	+	6.46722e6i	−0.783835	+	1.35764i
$470$	−9.58831e6			−2.00215
$471$	5.32384e6			1.10579
$472$	−865357.	+	1.49884e6i	−0.178789	+	0.309671i
$473$	−423401.			−0.0870161
$474$	592595.	+	1.02640e6i	0.121147	+	0.209832i
$475$	−2.09295e6			−0.425623
$476$	1.45209e6	+	2.51509e6i	0.293749	+	0.508788i
$477$	1.42115e6	+	2.46150e6i	0.285985	+	0.495341i
$478$	−4.92329e6	−	8.52739e6i	−0.985566	−	1.70705i
$479$	−4.36853e6	+	7.56652e6i	−0.869955	+	1.50681i	−0.00791439	+	0.999969i	$0.502519\pi$
$479$	−4.36853e6	+	7.56652e6i	−0.869955	+	1.50681i	−0.862041	+	0.506838i	$0.830814\pi$
$480$	−6.33159e6			−1.25432
$481$	5.35203e6	−	6.39591e6i	1.05476	−	1.26049i
$482$	−195086.			−0.0382480
$483$	−1.31523e6	+	2.27805e6i	−0.256527	+	0.444319i
$484$	1.74741e6	+	3.02661e6i	0.339064	+	0.587277i
$485$	−3.99026e6	−	6.91133e6i	−0.770277	−	1.33416i
$486$	2.60641e6	+	4.51443e6i	0.500555	+	0.866986i
$487$	−417837.			−0.0798333			−0.0399166	−	0.999203i	$-0.512709\pi$
$487$	−417837.			−0.0798333			−0.0399166	+	0.999203i	$0.512709\pi$
$488$	716091.	+	1.24031e6i	0.136119	+	0.235765i
$489$	7.25397e6			1.37184
$490$	557928.	−	966359.i	0.104975	−	0.181823i
$491$	−9.94641e6			−1.86193			−0.930963	−	0.365113i	$-0.881030\pi$
$491$	−9.94641e6			−1.86193			−0.930963	+	0.365113i	$0.881030\pi$
$492$	−2.24076e6			−0.417334
$493$	−2.78604e6	+	4.82556e6i	−0.516262	+	0.894192i
$494$	3.17002e6	+	5.49064e6i	0.584446	+	1.01229i
$495$	818187.			0.150086
$496$	−5.06613e6	+	8.77479e6i	−0.924638	+	1.60152i
$497$	41040.2	−	71083.8i	0.00745279	−	0.0129086i
$498$	−49910.0	+	86446.6i	−0.00901807	+	0.0156198i
$499$	−832750.	−	1.44237e6i	−0.149714	−	0.259313i	0.781408	−	0.624021i	$-0.214502\pi$
$499$	−832750.	−	1.44237e6i	−0.149714	−	0.259313i	−0.931122	+	0.364708i	$0.881169\pi$
$500$	−581141.	−	1.00657e6i	−0.103958	−	0.180060i
$501$	−1.33226e6	+	2.30755e6i	−0.237135	+	0.410729i
$502$	−982610.	+	1.70193e6i	−0.174029	+	0.301427i
$503$	1.61756e6	−	2.80170e6i	0.285063	−	0.493743i	−0.687562	−	0.726126i	$-0.741319\pi$
$503$	1.61756e6	−	2.80170e6i	0.285063	−	0.493743i	0.972624	+	0.232383i	$0.0746522\pi$
$504$	−872250.			−0.152955
$505$	3.78818e6	+	6.56132e6i	0.661001	+	1.14489i
$506$	−654158.	+	1.13303e6i	−0.113581	+	0.196728i
$507$	−7.55735e6			−1.30572
$508$	−5.81429e6			−0.999626
$509$	1.81451e6	−	3.14283e6i	0.310431	−	0.537683i	−0.668025	−	0.744139i	$-0.732860\pi$
$509$	1.81451e6	−	3.14283e6i	0.310431	−	0.537683i	0.978456	+	0.206457i	$0.0661932\pi$
$510$	6.01270e6			1.02363
$511$	547650.	+	948558.i	0.0927793	+	0.160698i
$512$	6.17532e6			1.04108
$513$	1.74365e6	+	3.02008e6i	0.292526	+	0.506670i
$514$	−1.71566e6	−	2.97161e6i	−0.286433	−	0.496117i
$515$	−985426.	−	1.70681e6i	−0.163722	−	0.283574i
$516$	−541874.	+	938553.i	−0.0895929	+	0.155180i
$517$	1.88806e6			0.310663
$518$	−2.91968e6	−	7.98799e6i	−0.478091	−	1.30802i
$519$	−5.70639e6			−0.929914
$520$	−2.38323e6	+	4.12787e6i	−0.386507	+	0.669450i
$521$	1.81862e6	+	3.14995e6i	0.293528	+	0.508405i	0.974641	−	0.223773i	$-0.0718374\pi$
$521$	1.81862e6	+	3.14995e6i	0.293528	+	0.508405i	−0.681114	+	0.732178i	$0.738504\pi$
$522$	2.29464e6	+	3.97444e6i	0.368586	+	0.638410i
$523$	2.01957e6	+	3.49799e6i	0.322853	+	0.559197i	0.981075	−	0.193626i	$-0.0620249\pi$
$523$	2.01957e6	+	3.49799e6i	0.322853	+	0.559197i	−0.658223	+	0.752823i	$0.728692\pi$
$524$	−4.82368e6			−0.767451
$525$	−2.01978e6	−	3.49837e6i	−0.319821	−	0.553946i
$526$	1.38692e6			0.218568
$527$	3.73591e6	−	6.47078e6i	0.585962	−	1.01492i
$528$	1.60555e6			0.250633
$529$	−3.86641e6			−0.600715
$530$	7.91967e6	−	1.37173e7i	1.22466	−	2.12118i
$531$	−1.35737e6	−	2.35103e6i	−0.208911	−	0.361844i
$532$	2.73423e6			0.418848
$533$	−3.99978e6	+	6.92782e6i	−0.609843	+	1.05628i
$534$	3.63308e6	−	6.29269e6i	0.551344	−	0.954955i
$535$	4.83591e6	−	8.37604e6i	0.730455	−	1.26519i
$536$	−1.73342e6	−	3.00237e6i	−0.260610	−	0.451390i
$537$	−3.70523e6	−	6.41765e6i	−0.554472	−	0.960373i
$538$	−2.64318e6	+	4.57812e6i	−0.393705	+	0.681917i
$539$	−109863.	+	190288.i	−0.0162884	+	0.0282124i
$540$	3.59478e6	−	6.22634e6i	0.530503	−	0.918858i
$541$	878973.			0.129117			0.0645584	−	0.997914i	$-0.479436\pi$
$541$	878973.			0.129117			0.0645584	+	0.997914i	$0.479436\pi$
$542$	7.79656e6	+	1.35040e7i	1.14000	+	1.97454i
$543$	−227914.	+	394758.i	−0.0331719	+	0.0574555i
$544$	−6.39376e6			−0.926315
$545$	−1.02541e7			−1.47880
$546$	−6.11840e6	+	1.05974e7i	−0.878327	+	1.52131i
$547$	9.89740e6			1.41434			0.707168	−	0.707046i	$-0.249972\pi$
$547$	9.89740e6			1.41434			0.707168	+	0.707046i	$0.249972\pi$
$548$	−4.62580e6	−	8.01213e6i	−0.658015	−	1.13972i
$549$	−2.24647e6			−0.318104
$550$	−1.00458e6	−	1.73999e6i	−0.141605	−	0.245267i
$551$	2.62301e6	+	4.54318e6i	0.368061	+	0.637501i
$552$	−610588.	−	1.05757e6i	−0.0852904	−	0.147727i
$553$	912370.	−	1.58027e6i	0.126870	−	0.219745i
$554$	4.39011e6			0.607716
$555$	−7.33498e6	−	1.28309e6i	−1.01080	−	0.176817i
$556$	−9.38321e6			−1.28725
$557$	−2.31127e6	+	4.00323e6i	−0.315655	+	0.546730i	−0.979576	−	0.201072i	$-0.935557\pi$
$557$	−2.31127e6	+	4.00323e6i	−0.315655	+	0.546730i	0.663922	+	0.747802i	$0.268891\pi$
$558$	−3.07697e6	−	5.32947e6i	−0.418349	−	0.724601i
$559$	1.93450e6	+	3.35064e6i	0.261841	+	0.453522i
$560$	6.27672e6	+	1.08716e7i	0.845790	+	1.46495i
$561$	−1.18398e6			−0.158831
$562$	−4.05218e6	−	7.01858e6i	−0.541187	−	0.937364i
$563$	−4.28739e6			−0.570061			−0.285031	−	0.958518i	$-0.592004\pi$
$563$	−4.28739e6			−0.570061			−0.285031	+	0.958518i	$0.592004\pi$
$564$	2.41636e6	−	4.18526e6i	0.319863	−	0.554019i
$565$	1.37040e7			1.80604
$566$	1.22847e7			1.61184
$567$	−1.70099e6	+	2.94620e6i	−0.222200	+	0.384861i
$568$	19052.7	+	33000.2i	0.00247791	+	0.00429186i
$569$	−3.18086e6			−0.411874			−0.205937	−	0.978565i	$-0.566024\pi$
$569$	−3.18086e6			−0.411874			−0.205937	+	0.978565i	$0.566024\pi$
$570$	2.83042e6	−	4.90244e6i	0.364892	−	0.632011i
$571$	−1.92158e6	+	3.32827e6i	−0.246642	+	0.427197i	−0.962592	−	0.270955i	$-0.912661\pi$
$571$	−1.92158e6	+	3.32827e6i	−0.246642	+	0.427197i	0.715950	+	0.698152i	$0.245994\pi$
$572$	−1.28691e6	+	2.22900e6i	−0.164460	+	0.284853i
$573$	2.16431e6	+	3.74869e6i	0.275380	+	0.476972i
$574$	4.07895e6	+	7.06495e6i	0.516736	+	0.895013i
$575$	−1.97331e6	+	3.41787e6i	−0.248900	+	0.431108i
$576$	−676218.	+	1.17124e6i	−0.0849240	+	0.147093i
$577$	6.62376e6	−	1.14727e7i	0.828257	−	1.43458i	−0.0711471	−	0.997466i	$-0.522666\pi$
$577$	6.62376e6	−	1.14727e7i	0.828257	−	1.43458i	0.899404	−	0.437118i	$-0.144001\pi$
$578$	−4.50110e6			−0.560402
$579$	−3.76223e6	−	6.51637e6i	−0.466389	−	0.807810i
$580$	5.40771e6	−	9.36643e6i	0.667488	−	1.15612i
$581$	153685.			0.0188882
$582$	9.51151e6			1.16397
$583$	−1.55948e6	+	2.70110e6i	−0.190024	+	0.329132i
$584$	−508487.			−0.0616947
$585$	−3.73825e6	−	6.47483e6i	−0.451625	−	0.782238i
$586$	2.06359e7			2.48244
$587$	3.67927e6	+	6.37268e6i	0.440724	+	0.763356i	0.997743	−	0.0671436i	$-0.0213886\pi$
$587$	3.67927e6	+	6.37268e6i	0.440724	+	0.763356i	−0.557020	+	0.830499i	$0.688055\pi$
$588$	281208.	+	487066.i	0.0335416	+	0.0580958i
$589$	−3.51729e6	−	6.09212e6i	−0.417753	−	0.723570i
$590$	−7.56423e6	+	1.31016e7i	−0.894612	+	1.54951i
$591$	−4.06109e6			−0.478270
$592$	1.00444e7	+	1.75704e6i	1.17793	+	0.206052i
$593$	7.62393e6			0.890312			0.445156	−	0.895453i	$-0.353148\pi$
$593$	7.62393e6			0.890312			0.445156	+	0.895453i	$0.353148\pi$
$594$	−1.67384e6	+	2.89918e6i	−0.194647	+	0.337139i
$595$	−4.62863e6	−	8.01702e6i	−0.535994	−	0.928369i
$596$	2.27648e6	+	3.94298e6i	0.262511	+	0.454683i
$597$	1.73669e6	+	3.00804e6i	0.199429	+	0.345421i
$598$	1.19552e7			1.36711
$599$	3.89362e6	+	6.74394e6i	0.443390	+	0.767975i	0.997939	−	0.0641770i	$-0.0204422\pi$
$599$	3.89362e6	+	6.74394e6i	0.443390	+	0.767975i	−0.554548	+	0.832152i	$0.687109\pi$
$600$	1.87535e6			0.212668
$601$	−1.74108e6	+	3.01565e6i	−0.196623	+	0.340560i	−0.947431	−	0.319959i	$-0.896331\pi$
$601$	−1.74108e6	+	3.01565e6i	−0.196623	+	0.340560i	0.750809	+	0.660520i	$0.229664\pi$
$602$	3.94557e6			0.443730
$603$	5.43795e6			0.609034
$604$	−2.16886e6	+	3.75658e6i	−0.241902	+	0.418987i
$605$	−5.56999e6	−	9.64751e6i	−0.618680	−	1.07159i
$606$	−9.02982e6			−0.998843
$607$	1.11203e6	−	1.92609e6i	0.122502	−	0.212180i	−0.798251	−	0.602324i	$-0.794241\pi$
$607$	1.11203e6	−	1.92609e6i	0.122502	−	0.212180i	0.920754	+	0.390144i	$0.127575\pi$
$608$	−3.00980e6	+	5.21313e6i	−0.330202	+	0.571926i
$609$	−5.06262e6	+	8.76871e6i	−0.553136	+	0.958060i
$610$	6.25946e6	+	1.08417e7i	0.681103	+	1.17970i
$611$	−8.62643e6	−	1.49414e7i	−0.934820	−	1.61916i
$612$	1.05741e6	−	1.83148e6i	0.114120	−	0.197662i
$613$	4.54968e6	−	7.88028e6i	0.489023	−	0.847013i	−0.510897	−	0.859642i	$-0.670687\pi$
$613$	4.54968e6	−	7.88028e6i	0.489023	−	0.847013i	0.999920	+	0.0126286i	$0.00401993\pi$
$614$	2.12430e6	−	3.67939e6i	0.227402	−	0.393872i
$615$	7.14258e6			0.761496
$616$	−478577.	−	828920.i	−0.0508160	−	0.0880158i
$617$	−4.62699e6	+	8.01417e6i	−0.489311	+	0.847512i	−0.999924	−	0.0122986i	$-0.996085\pi$
$617$	−4.62699e6	+	8.01417e6i	−0.489311	+	0.847512i	0.510613	+	0.859811i	$0.329418\pi$
$618$	2.34894e6			0.247401
$619$	−1.30748e6			−0.137154			−0.0685770	−	0.997646i	$-0.521846\pi$
$619$	−1.30748e6			−0.137154			−0.0685770	+	0.997646i	$0.521846\pi$
$620$	−7.25140e6	+	1.25598e7i	−0.757605	+	1.31221i
$621$	6.57588e6			0.684266
$622$	4.22141e6	+	7.31170e6i	0.437504	+	0.757779i
$623$	−1.11871e7			−1.15478
$624$	−7.33564e6	−	1.27057e7i	−0.754183	−	1.30628i
$625$	5.69909e6	+	9.87111e6i	0.583587	+	1.01080i
$626$	−9.75186e6	−	1.68907e7i	−0.994607	−	1.72271i
$627$	−557346.	+	965352.i	−0.0566182	+	0.0980656i
$628$	−1.04351e7			−1.05583
$629$	−7.40700e6	−	1.29569e6i	−0.746476	−	0.130579i
$630$	−7.62448e6			−0.765348
$631$	−2.77482e6	+	4.80612e6i	−0.277435	+	0.480531i	−0.970747	−	0.240107i	$-0.922818\pi$
$631$	−2.77482e6	+	4.80612e6i	−0.277435	+	0.480531i	0.693312	+	0.720638i	$0.256151\pi$
$632$	423562.	+	733632.i	0.0421818	+	0.0730610i
$633$	−3.16570e6	−	5.48315e6i	−0.314022	−	0.543902i
$634$	−3.74709e6	−	6.49014e6i	−0.370229	−	0.641256i
$635$	1.85334e7			1.82399
$636$	3.99169e6	+	6.91380e6i	0.391303	+	0.677757i
$637$	2.00783e6			0.196055
$638$	−2.51800e6	+	4.36131e6i	−0.244909	+	0.424194i
$639$	−59770.7			−0.00579076
$640$	−9.39911e6			−0.907062
$641$	−1.29283e6	+	2.23925e6i	−0.124279	+	0.215257i	−0.921451	−	0.388495i	$-0.872995\pi$
$641$	−1.29283e6	+	2.23925e6i	−0.124279	+	0.215257i	0.797172	+	0.603752i	$0.206328\pi$
$642$	5.76363e6	+	9.98290e6i	0.551898	+	0.955915i
$643$	−6.34970e6			−0.605656			−0.302828	−	0.953045i	$-0.597931\pi$
$643$	−6.34970e6			−0.605656			−0.302828	+	0.953045i	$0.597931\pi$
$644$	2.57793e6	−	4.46511e6i	0.244938	−	0.424246i
$645$	1.72726e6	−	2.99170e6i	0.163477	−	0.283151i
$646$	2.85821e6	−	4.95057e6i	0.269472	−	0.466739i
$647$	6.28321e6	+	1.08828e7i	0.590093	+	1.02207i	0.994219	+	0.107368i	$0.0342424\pi$
$647$	6.28321e6	+	1.08828e7i	0.590093	+	1.02207i	−0.404126	+	0.914703i	$0.632424\pi$
$648$	−789673.	−	1.36775e6i	−0.0738771	−	0.127959i
$649$	1.48949e6	−	2.57988e6i	0.138812	−	0.240429i
$650$	−9.17975e6	+	1.58998e7i	−0.852212	+	1.47607i
$651$	6.78866e6	−	1.17583e7i	0.627814	−	1.08741i
$652$	−1.42182e7			−1.30986
$653$	−4.79044e6	−	8.29728e6i	−0.439635	−	0.761470i	0.558026	−	0.829823i	$-0.311559\pi$
$653$	−4.79044e6	−	8.29728e6i	−0.439635	−	0.761470i	−0.997661	+	0.0683533i	$0.978225\pi$
$654$	6.11066e6	−	1.05840e7i	0.558655	−	0.967618i
$655$	1.53758e7			1.40034
$656$	−9.78090e6			−0.887400
$657$	398797.	−	690736.i	0.0360444	−	0.0624308i
$658$	−1.75944e7			−1.58420
$659$	−5.89761e6	−	1.02150e7i	−0.529008	−	0.916269i	−0.999428	−	0.0338259i	$-0.989231\pi$
$659$	−5.89761e6	−	1.02150e7i	−0.529008	−	0.916269i	0.470420	−	0.882443i	$-0.344102\pi$
$660$	2.29810e6			0.205357
$661$	−4.60678e6	−	7.97918e6i	−0.410104	−	0.710321i	0.584797	−	0.811180i	$-0.301174\pi$
$661$	−4.60678e6	−	7.97918e6i	−0.410104	−	0.710321i	−0.994901	+	0.100859i	$0.967841\pi$
$662$	−4.17674e6	−	7.23432e6i	−0.370418	−	0.641583i
$663$	5.40951e6	+	9.36955e6i	0.477941	+	0.827818i
$664$	−35673.6	+	61788.5i	−0.00313998	+	0.00543860i
$665$	−8.71554e6			−0.764259
$666$	−3.97447e6	+	4.74967e6i	−0.347211	+	0.414933i
$667$	9.89225e6			0.860955
$668$	2.61132e6	−	4.52293e6i	0.226422	−	0.392174i
$669$	6.76204e6	+	1.17122e7i	0.584134	+	1.01175i
$670$	−1.51521e7	−	2.62442e7i	−1.30402	−	2.25863i
$671$	−1.23257e6	−	2.13487e6i	−0.105683	−	0.183048i
$672$	−1.16183e7			−0.992478
$673$	−2.18919e6	−	3.79179e6i	−0.186314	−	0.322706i	0.757704	−	0.652598i	$-0.226321\pi$
$673$	−2.18919e6	−	3.79179e6i	−0.186314	−	0.322706i	−0.944019	+	0.329892i	$0.892988\pi$
$674$	−1.89376e7			−1.60574
$675$	−5.04925e6	+	8.74556e6i	−0.426548	+	0.738803i
$676$	1.48129e7			1.24673
$677$	−2.07011e7			−1.73589			−0.867943	−	0.496664i	$-0.834558\pi$
$677$	−2.07011e7			−1.73589			−0.867943	+	0.496664i	$0.834558\pi$
$678$	−8.16649e6	+	1.41448e7i	−0.682278	+	1.18174i
$679$	−7.32205e6	−	1.26822e7i	−0.609478	−	1.05565i
$680$	4.29763e6			0.356415
$681$	−3.10435e6	+	5.37688e6i	−0.256509	+	0.444286i
$682$	3.37648e6	−	5.84824e6i	0.277974	−	0.481465i
$683$	218580.	−	378591.i	0.0179291	−	0.0310541i	−0.856922	−	0.515447i	$-0.827626\pi$
$683$	218580.	−	378591.i	0.0179291	−	0.0310541i	0.874851	+	0.484393i	$0.160959\pi$
$684$	−995529.	−	1.72431e6i	−0.0813605	−	0.140920i
$685$	1.47451e7	+	2.55392e7i	1.20066	+	2.07960i
$686$	−7.55889e6	+	1.30924e7i	−0.613264	+	1.06220i
$687$	7.11830e6	−	1.23293e7i	0.575420	−	0.996656i
$688$	−2.36527e6	+	4.09677e6i	−0.190506	+	0.329967i
$689$	2.85007e7			2.28722
$690$	−5.33725e6	−	9.24438e6i	−0.426771	−	0.739188i
$691$	−5.22193e6	+	9.04464e6i	−0.416041	+	0.720604i	−0.995537	−	0.0943712i	$-0.969916\pi$
$691$	−5.22193e6	+	9.04464e6i	−0.416041	+	0.720604i	0.579496	+	0.814975i	$0.303249\pi$
$692$	1.11849e7			0.887904
$693$	1.50136e6			0.118755
$694$	1.40307e7	−	2.43018e7i	1.10581	−	1.91531i
$695$	2.99096e7			2.34881
$696$	−2.35029e6	−	4.07082e6i	−0.183907	−	0.318536i
$697$	7.21271e6			0.562363
$698$	3.44909e6	+	5.97400e6i	0.267958	+	0.464116i
$699$	−3.44983e6	−	5.97529e6i	−0.267058	−	0.462557i
$700$	3.95890e6	+	6.85702e6i	0.305372	+	0.528920i
$701$	−118233.	+	204786.i	−0.00908752	+	0.0157400i	−0.870533	−	0.492109i	$-0.836226\pi$
$701$	−118233.	+	204786.i	−0.00908752	+	0.0157400i	0.861446	+	0.507849i	$0.169559\pi$
$702$	3.05908e7			2.34287
$703$	−4.54321e6	+	5.42934e6i	−0.346717	+	0.414342i
$704$	−1.48408e6			−0.112856
$705$	−7.70230e6	+	1.33408e7i	−0.583644	+	1.01090i
$706$	−5.50285e6	−	9.53122e6i	−0.415505	−	0.719675i
$707$	6.95124e6	+	1.20399e7i	0.523014	+	0.905887i
$708$	−3.81254e6	−	6.60350e6i	−0.285845	−	0.495098i
$709$	−2.49486e6			−0.186394			−0.0931968	−	0.995648i	$-0.529709\pi$
$709$	−2.49486e6			−0.186394			−0.0931968	+	0.995648i	$0.529709\pi$
$710$	166543.	+	288460.i	0.0123988	+	0.0214753i
$711$	−1.32877e6			−0.0985769
$712$	2.59678e6	−	4.49775e6i	0.191971	−	0.332503i
$713$	−1.32649e7			−0.977192
$714$	1.10332e7			0.809944
$715$	4.10212e6	−	7.10509e6i	0.300085	−	0.519762i
$716$	7.26248e6	+	1.25790e7i	0.529422	+	0.916987i
$717$	−1.58195e7			−1.14920
$718$	−9.42346e6	+	1.63219e7i	−0.682181	+	1.18157i
$719$	−1.44882e6	+	2.50944e6i	−0.104518	+	0.181031i	−0.913541	−	0.406746i	$-0.866663\pi$
$719$	−1.44882e6	+	2.50944e6i	−0.104518	+	0.181031i	0.809023	+	0.587777i	$0.199997\pi$
$720$	4.57068e6	−	7.91665e6i	0.328586	−	0.569128i
$721$	−1.80824e6	−	3.13196e6i	−0.129544	−	0.224377i
$722$	6.52807e6	+	1.13069e7i	0.466060	+	0.807239i
$723$	−156713.	+	271435.i	−0.0111496	+	0.0193117i
$724$	446725.	−	773750.i	0.0316733	−	0.0548598i
$725$	−7.59571e6	+	1.31562e7i	−0.536690	+	0.929574i
$726$	1.32771e7			0.934891
$727$	−4.84691e6	−	8.39509e6i	−0.340117	−	0.589100i	0.644337	−	0.764742i	$-0.277133\pi$
$727$	−4.84691e6	−	8.39509e6i	−0.340117	−	0.589100i	−0.984454	+	0.175641i	$0.943800\pi$
$728$	−4.37318e6	+	7.57457e6i	−0.305822	+	0.529699i
$729$	1.44022e7			1.00371
$730$	−4.44477e6			−0.308704
$731$	1.74422e6	−	3.02107e6i	0.120728	−	0.209107i
$732$	−6.30981e6			−0.435250
$733$	1.43081e7	+	2.47824e7i	0.983609	+	1.70366i	0.647960	+	0.761675i	$0.275623\pi$
$733$	1.43081e7	+	2.47824e7i	0.983609	+	1.70366i	0.335650	+	0.941987i	$0.391044\pi$
$734$	−2.33936e6			−0.160271
$735$	−896368.	−	1.55255e6i	−0.0612023	−	0.106006i
$736$	5.67550e6	+	9.83025e6i	0.386198	+	0.668914i
$737$	2.98364e6	+	5.16781e6i	0.202338	+	0.350460i
$738$	2.97027e6	−	5.14467e6i	0.200750	−	0.347709i
$739$	−2.30773e7			−1.55444			−0.777218	−	0.629231i	$-0.783370\pi$
$739$	−2.30773e7			−1.55444			−0.777218	+	0.629231i	$0.783370\pi$
$740$	1.43770e7	+	2.51494e6i	0.965137	+	0.168829i
$741$	1.01859e7			0.681483
$742$	1.45324e7	−	2.51709e7i	0.969011	−	1.67838i
$743$	3.01340e6	+	5.21937e6i	0.200256	+	0.346853i	0.948611	−	0.316445i	$-0.102489\pi$
$743$	3.01340e6	+	5.21937e6i	0.200256	+	0.346853i	−0.748355	+	0.663299i	$0.769156\pi$
$744$	3.15159e6	+	5.45872e6i	0.208736	+	0.361542i
$745$	−7.25642e6	−	1.25685e7i	−0.478996	−	0.829646i
$746$	−2.17946e7			−1.43384
$747$	−55956.2	−	96919.1i	−0.00366899	−	0.00635489i
$748$	2.32067e6			0.151656
$749$	8.87379e6	−	1.53699e7i	0.577969	−	1.00107i
$750$	−4.41559e6			−0.286639
$751$	−262815.			−0.0170040			−0.00850199	−	0.999964i	$-0.502706\pi$
$751$	−262815.			−0.0170040			−0.00850199	+	0.999964i	$0.502706\pi$
$752$	1.05474e7	−	1.82686e7i	0.680142	−	1.17804i
$753$	1.57866e6	+	2.73433e6i	0.101462	+	0.175737i
$754$	4.60184e7			2.94783
$755$	6.91339e6	−	1.19743e7i	0.441391	−	0.764512i
$756$	6.59635e6	−	1.14252e7i	0.419758	−	0.727043i
$757$	−1.15820e7	+	2.00606e7i	−0.734588	+	1.27234i	0.220317	+	0.975428i	$0.429291\pi$
$757$	−1.15820e7	+	2.00606e7i	−0.734588	+	1.27234i	−0.954904	+	0.296914i	$0.904042\pi$
$758$	−9.32033e6	−	1.61433e7i	−0.589194	−	1.02051i
$759$	1.05097e6	+	1.82034e6i	0.0662196	+	0.114696i
$760$	2.02307e6	−	3.50406e6i	0.127051	−	0.220058i
$761$	−1.00618e7	+	1.74275e7i	−0.629814	+	1.09087i	0.357775	+	0.933808i	$0.383536\pi$
$761$	−1.00618e7	+	1.74275e7i	−0.629814	+	1.09087i	−0.987589	+	0.157062i	$0.949798\pi$
$762$	−1.10444e7	+	1.91295e7i	−0.689059	+	1.19349i
$763$	−1.88162e7			−1.17009
$764$	−4.24217e6	−	7.34766e6i	−0.262939	−	0.455424i
$765$	−3.37055e6	+	5.83796e6i	−0.208232	+	0.360668i
$766$	−2.33618e6			−0.143858
$767$	−2.72216e7			−1.67080
$768$	8.19308e6	−	1.41908e7i	0.501238	−	0.868170i
$769$	−1.47176e7			−0.897475			−0.448737	−	0.893664i	$-0.648126\pi$
$769$	−1.47176e7			−0.897475			−0.448737	+	0.893664i	$0.648126\pi$
$770$	−4.18332e6	−	7.24573e6i	−0.254270	−	0.440408i
$771$	−5.51276e6			−0.333990
$772$	7.37419e6	+	1.27725e7i	0.445319	+	0.771315i
$773$	−297475.	−	515242.i	−0.0179061	−	0.0310144i	0.856933	−	0.515427i	$-0.172367\pi$
$773$	−297475.	−	515242.i	−0.0179061	−	0.0310144i	−0.874840	+	0.484413i	$0.839033\pi$
$774$	−1.43658e6	−	2.48822e6i	−0.0861938	−	0.149292i
$775$	1.01854e7	−	1.76416e7i	0.609148	−	1.05508i
$776$	6.79843e6			0.405279
$777$	−1.34595e7	−	2.35444e6i	−0.799793	−	0.139906i
$778$	−1.04937e7			−0.621558
$779$	3.39532e6	−	5.88087e6i	0.200464	−	0.347214i
$780$	−1.04999e7	−	1.81863e7i	−0.617942	−	1.07031i
$781$	−32794.3	−	56801.5i	−0.00192385	−	0.00333221i
$782$	−5.38965e6	−	9.33515e6i	−0.315169	−	0.545889i
$783$	2.53121e7			1.47545
$784$	1.22747e6	+	2.12604e6i	0.0713214	+	0.123532i
$785$	3.32624e7			1.92655
$786$	−9.16276e6	+	1.58704e7i	−0.529017	+	0.916285i
$787$	−2.51111e7			−1.44521			−0.722603	−	0.691263i	$-0.757054\pi$
$787$	−2.51111e7			−1.44521			−0.722603	+	0.691263i	$0.757054\pi$
$788$	7.95998e6			0.456664
$789$	1.11411e6	−	1.92970e6i	0.0637143	−	0.110356i
$790$	3.70243e6	+	6.41279e6i	0.211066	+	0.365578i
$791$	2.51466e7			1.42902
$792$	−348498.	+	603616.i	−0.0197418	+	0.0341938i
$793$	−1.12631e7	+	1.95082e7i	−0.636023	+	1.10163i
$794$	1.19603e6	−	2.07158e6i	0.0673272	−	0.116614i
$795$	−1.27238e7	−	2.20382e7i	−0.713999	−	1.23668i
$796$	−3.40403e6	−	5.89595e6i	−0.190419	−	0.329816i
$797$	9.69690e6	−	1.67955e7i	0.540738	−	0.936586i	−0.458124	−	0.888888i	$-0.651478\pi$
$797$	9.69690e6	−	1.67955e7i	0.540738	−	0.936586i	0.998862	−	0.0476974i	$-0.0151883\pi$
$798$	5.19377e6	−	8.99587e6i	0.288719	−	0.500076i
$799$	−7.77793e6	+	1.34718e7i	−0.431020	+	0.746548i
$800$	−1.74316e7			−0.962969
$801$	4.07321e6	+	7.05501e6i	0.224314	+	0.388523i
$802$	2.65753e6	−	4.60297e6i	0.145896	−	0.252698i
$803$	875231.			0.0478998
$804$	1.52740e7			0.833320
$805$	−8.21732e6	+	1.42328e7i	−0.446931	+	0.774108i
$806$	−6.17078e7			−3.34582
$807$	4.24654e6	+	7.35522e6i	0.229536	+	0.397568i
$808$	−6.45414e6			−0.347784
$809$	−4.94235e6	−	8.56040e6i	−0.265499	−	0.459857i	0.702195	−	0.711984i	$-0.252203\pi$
$809$	−4.94235e6	−	8.56040e6i	−0.265499	−	0.459857i	−0.967694	+	0.252127i	$0.918870\pi$
$810$	−6.90266e6	−	1.19558e7i	−0.369661	−	0.640272i
$811$	−7.13770e6	−	1.23629e7i	−0.381071	−	0.660035i	0.610144	−	0.792290i	$-0.291111\pi$
$811$	−7.13770e6	−	1.23629e7i	−0.381071	−	0.660035i	−0.991216	+	0.132255i	$0.957778\pi$
$812$	9.92304e6	−	1.71872e7i	0.528147	−	0.914777i
$813$	2.50520e7			1.32928
$814$	−6.69439e6	−	1.17103e6i	−0.354120	−	0.0619453i
$815$	4.53215e7			2.39007
$816$	−6.61411e6	+	1.14560e7i	−0.347733	+	0.602291i
$817$	−1.64215e6	−	2.84429e6i	−0.0860711	−	0.149080i
$818$	1.74067e7	+	3.01493e7i	0.909566	+	1.57541i
$819$	−6.85961e6	−	1.18812e7i	−0.357346	−	0.618942i
$820$	−1.39999e7			−0.727094
$821$	9.95517e6	+	1.72429e7i	0.515455	+	0.892794i	0.999839	+	0.0179388i	$0.00571040\pi$
$821$	9.95517e6	+	1.72429e7i	0.515455	+	0.892794i	−0.484384	+	0.874855i	$0.660956\pi$
$822$	−3.51475e7			−1.81432
$823$	−1.04435e7	+	1.80886e7i	−0.537460	+	0.930908i	0.461580	+	0.887098i	$0.347283\pi$
$823$	−1.04435e7	+	1.80886e7i	−0.537460	+	0.930908i	−0.999040	+	0.0438091i	$0.986051\pi$
$824$	1.67893e6			0.0861418
$825$	−3.22793e6			−0.165116
$826$	−1.38802e7	+	2.40412e7i	−0.707858	+	1.22605i
$827$	3.87641e6	+	6.71414e6i	0.197091	+	0.341371i	0.947584	−	0.319507i	$-0.103517\pi$
$827$	3.87641e6	+	6.71414e6i	0.197091	+	0.341371i	−0.750493	+	0.660878i	$0.770184\pi$
$828$	−3.75448e6			−0.190315
$829$	5.05608e6	−	8.75738e6i	0.255521	−	0.442576i	−0.709516	−	0.704690i	$-0.751086\pi$
$829$	5.05608e6	−	8.75738e6i	0.255521	−	0.442576i	0.965037	+	0.262114i	$0.0844195\pi$
$830$	−311829.	+	540103.i	−0.0157116	+	0.0272133i
$831$	3.52658e6	−	6.10821e6i	0.177154	−	0.306840i
$832$	6.78067e6	+	1.17445e7i	0.339598	+	0.588200i
$833$	−905169.	−	1.56780e6i	−0.0451978	−	0.0782849i
$834$	−1.78237e7	+	3.08716e7i	−0.887326	+	1.53689i
$835$	−8.32374e6	+	1.44171e7i	−0.413145	+	0.715587i
$836$	1.09243e6	−	1.89215e6i	0.0540604	−	0.0936353i
$837$	−3.39419e7			−1.67464
$838$	8.02096e6	+	1.38927e7i	0.394563	+	0.683403i
$839$	3.71674e6	−	6.43758e6i	0.182288	−	0.315731i	−0.760372	−	0.649488i	$-0.774983\pi$
$839$	3.71674e6	−	6.43758e6i	0.182288	−	0.315731i	0.942659	+	0.333757i	$0.108316\pi$
$840$	7.80938e6			0.381873
$841$	1.75664e7			0.856430
$842$	1.09604e7	−	1.89839e7i	0.532776	−	0.922795i
$843$	−1.30205e7			−0.631041
$844$	6.20496e6	+	1.07473e7i	0.299835	+	0.519330i
$845$	−4.72170e7			−2.27487
$846$	6.40607e6	+	1.10956e7i	0.307727	+	0.532999i
$847$	−1.02208e7	−	1.77030e7i	−0.489528	−	0.847887i
$848$	1.74236e7	+	3.01786e7i	0.832050	+	1.44115i
$849$	9.86830e6	−	1.70924e7i	0.469865	−	0.813830i
$850$	1.65537e7			0.785863
$851$	4.58282e6	+	1.25382e7i	0.216925	+	0.593488i
$852$	−167882.			−0.00792329
$853$	1.68356e7	−	2.91601e7i	0.792239	−	1.37220i	−0.132338	−	0.991205i	$-0.542249\pi$
$853$	1.68356e7	−	2.91601e7i	0.792239	−	1.37220i	0.924578	−	0.380994i	$-0.124418\pi$
$854$	1.14860e7	+	1.98943e7i	0.538920	+	0.933436i
$855$	3.17331e6	+	5.49634e6i	0.148456	+	0.257133i
$856$	4.11961e6	+	7.13537e6i	0.192164	+	0.332837i
$857$	−2.39811e7			−1.11537			−0.557684	−	0.830054i	$-0.688310\pi$
$857$	−2.39811e7			−1.11537			−0.557684	+	0.830054i	$0.688310\pi$
$858$	4.88908e6	+	8.46813e6i	0.226730	+	0.392708i
$859$	2.77323e7			1.28234			0.641170	−	0.767399i	$-0.278449\pi$
$859$	2.77323e7			1.28234			0.641170	+	0.767399i	$0.278449\pi$
$860$	−3.38553e6	+	5.86391e6i	−0.156092	+	0.270359i
$861$	1.31065e7			0.602530
$862$	−6.55993e6			−0.300698
$863$	5.14162e6	−	8.90555e6i	0.235003	−	0.407037i	−0.724271	−	0.689516i	$-0.757823\pi$
$863$	5.14162e6	−	8.90555e6i	0.235003	−	0.407037i	0.959274	+	0.282479i	$0.0911567\pi$
$864$	1.45223e7	+	2.51534e7i	0.661839	+	1.14634i
$865$	−3.56525e7			−1.62013
$866$	1.03012e7	−	1.78422e7i	0.466759	−	0.808450i
$867$	−3.61574e6	+	6.26265e6i	−0.163361	+	0.282950i
$868$	−1.33062e7	+	2.30470e7i	−0.599452	+	1.03828i
$869$	−729055.	−	1.26276e6i	−0.0327500	−	0.0567246i
$870$	−2.05443e7	−	3.55837e7i	−0.920222	−	1.59387i
$871$	2.72641e7	−	4.72228e7i	1.21772	−	2.10915i
$872$	4.36765e6	−	7.56498e6i	0.194516	−	0.336912i
$873$	−5.33188e6	+	9.23509e6i	−0.236780	+	0.410115i
$874$	−1.01485e7			−0.449391
$875$	3.39917e6	+	5.88753e6i	0.150090	+	0.259964i
$876$	1.12013e6	−	1.94012e6i	0.0493183	−	0.0854218i
$877$	−3.53599e7			−1.55243			−0.776215	−	0.630469i	$-0.782863\pi$
$877$	−3.53599e7			−1.55243			−0.776215	+	0.630469i	$0.782863\pi$
$878$	1.86055e7			0.814526
$879$	1.65768e7	−	2.87119e7i	0.723651	−	1.25340i
$880$	1.00312e7			0.436662
$881$	−2.21031e6	−	3.82838e6i	−0.0959432	−	0.166179i	0.814059	−	0.580783i	$-0.197253\pi$
$881$	−2.21031e6	−	3.82838e6i	−0.0959432	−	0.166179i	−0.910002	+	0.414604i	$0.863920\pi$
$882$	−1.49103e6			−0.0645381
$883$	−79211.4	−	137198.i	−0.00341890	−	0.00592170i	0.864311	−	0.502958i	$-0.167755\pi$
$883$	−79211.4	−	137198.i	−0.00341890	−	0.00592170i	−0.867730	+	0.497036i	$0.834422\pi$
$884$	−1.06030e7	−	1.83649e7i	−0.456349	−	0.790420i
$885$	1.21527e7	+	2.10491e7i	0.521572	+	0.903390i
$886$	1.73926e7	−	3.01249e7i	0.744356	−	1.28926i
$887$	−1.18319e7			−0.504948			−0.252474	−	0.967604i	$-0.581244\pi$
$887$	−1.18319e7			−0.504948			−0.252474	+	0.967604i	$0.581244\pi$
$888$	4.07085e6	−	4.86485e6i	0.173242	−	0.207032i
$889$	3.40085e7			1.44322
$890$	2.26989e7	−	3.93156e7i	0.960570	−	1.66376i
$891$	1.35922e6	+	2.35424e6i	0.0573583	+	0.0993474i
$892$	−1.32540e7	−	2.29566e7i	−0.557745	−	0.966042i
$893$	7.32278e6	+	1.26834e7i	0.307289	+	0.532241i
$894$	1.72970e7			0.723814
$895$	−2.31496e7	−	4.00963e7i	−0.966020	−	1.67320i
$896$	−1.72472e7			−0.717709
$897$	9.60365e6	−	1.66340e7i	0.398525	−	0.690265i
$898$	1.54712e7			0.640224
$899$	−5.10596e7			−2.10707
$900$	2.88286e6	−	4.99325e6i	0.118636	−	0.205484i
$901$	−1.28487e7	−	2.22546e7i	−0.527287	−	0.913287i
$902$	6.51880e6			0.266779
$903$	3.16948e6	−	5.48971e6i	0.129351	−	0.224042i
$904$	−5.83707e6	+	1.01101e7i	−0.237560	+	0.411467i
$905$	−1.42396e6	+	2.46638e6i	−0.0577933	+	0.100101i
$906$	8.23966e6	+	1.42715e7i	0.333494	+	0.577629i
$907$	1.55757e6	+	2.69779e6i	0.0628680	+	0.108890i	0.895746	−	0.444566i	$-0.146642\pi$
$907$	1.55757e6	+	2.69779e6i	0.0628680	+	0.108890i	−0.832878	+	0.553456i	$0.813309\pi$
$908$	6.08471e6	−	1.05390e7i	0.244921	−	0.424215i
$909$	5.06186e6	−	8.76740e6i	0.203189	−	0.351934i
$910$	−3.82267e7	+	6.62105e7i	−1.53025	+	2.65047i
$911$	3.63298e7			1.45033			0.725166	−	0.688574i	$-0.241763\pi$
$911$	3.63298e7			1.45033			0.725166	+	0.688574i	$0.241763\pi$
$912$	6.22706e6	+	1.07856e7i	0.247911	+	0.429395i
$913$	61403.0	−	106353.i	0.00243788	−	0.00422253i
$914$	2.77378e7			1.09826
$915$	2.01129e7			0.794187
$916$	−1.39523e7	+	2.41661e7i	−0.549424	+	0.951630i
$917$	2.82143e7			1.10802
$918$	−1.37909e7	−	2.38866e7i	−0.540115	−	0.935507i
$919$	1.06565e7			0.416221			0.208111	−	0.978105i	$-0.433269\pi$
$919$	1.06565e7			0.416221			0.208111	+	0.978105i	$0.433269\pi$
$920$	−3.81484e6	−	6.60750e6i	−0.148596	−	0.257376i
$921$	−3.41290e6	−	5.91132e6i	−0.132579	−	0.229633i
$922$	2.60585e7	+	4.51346e7i	1.00954	+	1.74857i
$923$	−299671.	+	519045.i	−0.0115782	+	0.0200540i
$924$	4.21697e6			0.162488
$925$	−2.01940e7	−	3.53250e6i	−0.776013	−	0.135746i
$926$	−3.37859e7			−1.29482
$927$	−1.31675e6	+	2.28068e6i	−0.0503274	+	0.0871696i
$928$	2.18463e7	+	3.78389e7i	0.832737	+	1.44234i
$929$	1.42701e7	+	2.47166e7i	0.542487	+	0.939614i	0.998760	+	0.0497749i	$0.0158504\pi$
$929$	1.42701e7	+	2.47166e7i	0.542487	+	0.939614i	−0.456274	+	0.889839i	$0.650816\pi$
$930$	2.75486e7	+	4.77156e7i	1.04446	+	1.80906i
$931$	−1.70440e6			−0.0644462
$932$	6.76188e6	+	1.17119e7i	0.254993	+	0.441661i
$933$	1.35643e7			0.510143
$934$	−5.51794e6	+	9.55736e6i	−0.206971	+	0.358485i
$935$	−7.39727e6			−0.276721
$936$	6.36906e6			0.237622
$937$	−6.36721e6	+	1.10283e7i	−0.236919	+	0.410356i	−0.959829	−	0.280587i	$-0.909471\pi$
$937$	−6.36721e6	+	1.10283e7i	−0.236919	+	0.410356i	0.722910	+	0.690943i	$0.242804\pi$
$938$	−2.78038e7	−	4.81576e7i	−1.03180	−	1.78713i
$939$	−3.13347e7			−1.15974
$940$	1.50970e7	−	2.61487e7i	0.557276	−	0.965231i
$941$	9.19992e6	−	1.59347e7i	0.338696	−	0.586639i	−0.645492	−	0.763767i	$-0.723348\pi$
$941$	9.19992e6	−	1.59347e7i	0.338696	−	0.586639i	0.984188	+	0.177129i	$0.0566809\pi$
$942$	−1.98218e7	+	3.43323e7i	−0.727805	+	1.26060i
$943$	−6.40246e6	−	1.10894e7i	−0.234459	−	0.406095i
$944$	−1.66417e7	−	2.88242e7i	−0.607808	−	1.05275i
$945$	−2.10263e7	+	3.64186e7i	−0.765920	+	1.32661i
$946$	1.57641e6	−	2.73042e6i	0.0572719	−	0.0991978i
$947$	−5.76924e6	+	9.99262e6i	−0.209047	+	0.362080i	−0.951415	−	0.307913i	$-0.900369\pi$
$947$	−5.76924e6	+	9.99262e6i	−0.209047	+	0.362080i	0.742368	+	0.669993i	$0.233703\pi$
$948$	−3.73221e6			−0.134879
$949$	−3.99888e6	−	6.92626e6i	−0.144136	−	0.249651i
$950$	7.79249e6	−	1.34970e7i	0.280135	−	0.485208i
$951$	−1.20402e7			−0.431699
$952$	7.88606e6			0.282012
$953$	1.13786e7	−	1.97084e7i	0.405843	−	0.702941i	−0.588576	−	0.808442i	$-0.700311\pi$
$953$	1.13786e7	−	1.97084e7i	0.405843	−	0.702941i	0.994419	+	0.105501i	$0.0336446\pi$
$954$	−2.11649e7			−0.752915
$955$	1.35222e7	+	2.34211e7i	0.479777	+	0.830998i
$956$	3.10073e7			1.09728
$957$	4.04543e6	+	7.00688e6i	0.142786	+	0.247312i
$958$	−3.25299e7	−	5.63435e7i	−1.14517	−	1.98349i
$959$	2.70569e7	+	4.68639e7i	0.950017	+	1.64548i
$960$	6.05428e6	−	1.04863e7i	0.212024	−	0.367236i
$961$	3.98386e7			1.39154
$962$	2.13191e7	+	5.83273e7i	0.742731	+	2.03205i
$963$	−1.29237e7			−0.449078
$964$	307167.	−	532029.i	0.0106459	−	0.0184392i
$965$	−2.35057e7	−	4.07131e7i	−0.812560	−	1.40739i
$966$	−9.79374e6	−	1.69633e7i	−0.337680	−	0.584880i
$967$	−2.03990e7	−	3.53320e7i	−0.701523	−	1.21507i	−0.967932	−	0.251213i	$-0.919171\pi$
$967$	−2.03990e7	−	3.53320e7i	−0.701523	−	1.21507i	0.266409	−	0.963860i	$-0.414163\pi$
$968$	9.48991e6			0.325517
$969$	−4.59201e6	−	7.95360e6i	−0.157106	−	0.272116i
$970$	5.94262e7			2.02791
$971$	−2.23085e7	+	3.86395e7i	−0.759316	+	1.31517i	0.183884	+	0.982948i	$0.441133\pi$
$971$	−2.23085e7	+	3.86395e7i	−0.759316	+	1.31517i	−0.943200	+	0.332226i	$0.892200\pi$
$972$	−1.64154e7			−0.557294
$973$	5.48835e7			1.85849
$974$	1.55569e6	−	2.69454e6i	0.0525444	−	0.0910095i
$975$	1.47482e7	+	2.55447e7i	0.496853	+	0.860574i
$976$	−2.75422e7			−0.925496
$977$	−2.27921e6	+	3.94770e6i	−0.0763919	+	0.132315i	−0.901691	−	0.432382i	$-0.857673\pi$
$977$	−2.27921e6	+	3.94770e6i	−0.0763919	+	0.132315i	0.825299	+	0.564696i	$0.191007\pi$
$978$	−2.70080e7	+	4.67792e7i	−0.902912	+	1.56389i
$979$	−4.46969e6	+	7.74174e6i	−0.149046	+	0.258156i
$980$	1.75694e6	+	3.04310e6i	0.0584374	+	0.101217i
$981$	6.85093e6	+	1.18662e7i	0.227288	+	0.393675i
$982$	3.70325e7	−	6.41422e7i	1.22548	−	2.12259i
$983$	2.34078e7	−	4.05435e7i	0.772639	−	1.33825i	−0.163473	−	0.986548i	$-0.552270\pi$
$983$	2.34078e7	−	4.05435e7i	0.772639	−	1.33825i	0.936112	−	0.351702i	$-0.114397\pi$
$984$	−3.04231e6	+	5.26943e6i	−0.100165	+	0.173491i
$985$	−2.53730e7			−0.833260
$986$	−2.07460e7	−	3.59331e7i	−0.679582	−	1.17707i
$987$	−1.41336e7	+	2.44801e7i	−0.461805	+	0.799871i
$988$	−1.99650e7			−0.650695
$989$	−6.19311e6			−0.201334
$990$	−3.04628e6	+	5.27631e6i	−0.0987828	+	0.171097i
$991$	4.15013e7			1.34239			0.671193	−	0.741283i	$-0.265782\pi$
$991$	4.15013e7			1.34239			0.671193	+	0.741283i	$0.265782\pi$
$992$	−2.92945e7	−	5.07396e7i	−0.945164	−	1.63707i
$993$	−1.34207e7			−0.431919
$994$	305602.	+	529319.i	0.00981049	+	0.0169923i
$995$	1.08506e7	+	1.87937e7i	0.347452	+	0.601804i
$996$	−157168.	−	272224.i	−0.00502015	−	0.00869516i
$997$	−7.01062e6	+	1.21428e7i	−0.223367	+	0.386883i	−0.955828	−	0.293926i	$-0.905038\pi$
$997$	−7.01062e6	+	1.21428e7i	−0.223367	+	0.386883i	0.732461	+	0.680809i	$0.238371\pi$
$998$	1.24020e7			0.394154
$999$	1.17264e7	+	3.20825e7i	0.371751	+	1.01708i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.6.c.a.10.3	✓	30
37.26	even	3	inner	37.6.c.a.26.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.6.c.a.10.3	✓	30	1.1	even	1	trivial
37.6.c.a.26.3	yes	30	37.26	even	3	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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	37.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.72321 + 6.44878i) q^{2} +(5.98171 + 10.3606i) q^{3} +(-11.7245 - 20.3075i) q^{4} +(37.3727 + 64.7314i) q^{5} -89.0845 q^{6} +(68.5781 + 118.781i) q^{7} -63.6740 q^{8} +(49.9383 - 86.4957i) q^{9} +O(q^{10})\)	\(q+(-3.72321 + 6.44878i) q^{2} +(5.98171 + 10.3606i) q^{3} +(-11.7245 - 20.3075i) q^{4} +(37.3727 + 64.7314i) q^{5} -89.0845 q^{6} +(68.5781 + 118.781i) q^{7} -63.6740 q^{8} +(49.9383 - 86.4957i) q^{9} -556.584 q^{10} +109.599 q^{11} +(140.265 - 242.947i) q^{12} +(-500.749 - 867.323i) q^{13} -1021.32 q^{14} +(-447.105 + 774.408i) q^{15} +(612.256 - 1060.46i) q^{16} +(-451.495 + 782.012i) q^{17} +(371.861 + 644.082i) q^{18} +(425.074 + 736.250i) q^{19} +(876.353 - 1517.89i) q^{20} +(-820.429 + 1421.02i) q^{21} +(-408.058 + 706.777i) q^{22} +1603.10 q^{23} +(-380.879 - 659.702i) q^{24} +(-1230.93 + 2132.04i) q^{25} +7457.56 q^{26} +4101.98 q^{27} +(1608.09 - 2785.29i) q^{28} +6170.70 q^{29} +(-3329.33 - 5766.56i) q^{30} -8274.52 q^{31} +(3540.33 + 6132.02i) q^{32} +(655.586 + 1135.51i) q^{33} +(-3362.02 - 5823.18i) q^{34} +(-5125.89 + 8878.31i) q^{35} -2342.01 q^{36} +(2858.72 + 7821.23i) q^{37} -6330.56 q^{38} +(5990.67 - 10376.1i) q^{39} +(-2379.67 - 4121.70i) q^{40} +(-3993.80 - 6917.46i) q^{41} +(-6109.25 - 10581.5i) q^{42} -3863.20 q^{43} +(-1284.99 - 2225.67i) q^{44} +7465.31 q^{45} +(-5968.67 + 10338.0i) q^{46} +17227.1 q^{47} +14649.3 q^{48} +(-1002.41 + 1736.23i) q^{49} +(-9166.03 - 15876.0i) q^{50} -10802.8 q^{51} +(-11742.1 + 20337.9i) q^{52} +(-14229.0 + 24645.4i) q^{53} +(-15272.5 + 26452.7i) q^{54} +(4095.99 + 7094.46i) q^{55} +(-4366.64 - 7563.24i) q^{56} +(-5085.34 + 8808.07i) q^{57} +(-22974.8 + 39793.5i) q^{58} +(13590.4 - 23539.3i) q^{59} +20968.4 q^{60} +(-11246.2 - 19479.0i) q^{61} +(30807.7 - 53360.6i) q^{62} +13698.7 q^{63} -13541.1 q^{64} +(37428.6 - 64828.3i) q^{65} -9763.53 q^{66} +(27223.3 + 47152.2i) q^{67} +21174.2 q^{68} +(9589.28 + 16609.1i) q^{69} +(-38169.5 - 66111.5i) q^{70} +(-299.223 - 518.269i) q^{71} +(-3179.77 + 5507.52i) q^{72} +7985.79 q^{73} +(-61081.0 - 10684.8i) q^{74} -29452.3 q^{75} +(9967.59 - 17264.4i) q^{76} +(7516.06 + 13018.2i) q^{77} +(44609.0 + 77265.0i) q^{78} +(-6652.05 - 11521.7i) q^{79} +91526.5 q^{80} +(12401.8 + 21480.6i) q^{81} +59478.9 q^{82} +(560.254 - 970.388i) q^{83} +38476.5 q^{84} -67494.3 q^{85} +(14383.5 - 24913.0i) q^{86} +(36911.3 + 63932.3i) q^{87} -6978.57 q^{88} +(-40782.4 + 70637.3i) q^{89} +(-27794.9 + 48142.1i) q^{90} +(68680.8 - 118959. i) q^{91} +(-18795.6 - 32554.9i) q^{92} +(-49495.8 - 85729.2i) q^{93} +(-64139.9 + 111094. i) q^{94} +(-31772.3 + 55031.3i) q^{95} +(-42354.4 + 73360.0i) q^{96} -106769. q^{97} +(-7464.38 - 12928.7i) q^{98} +(5473.16 - 9479.80i) 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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