LMFDB - Embedded newform 43.6.c.a.36.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,6,Mod(6,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, 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("43.6");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	43.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:	$6.89650425196$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			36.1
Character	$\chi$	$=$	43.36
Dual form			43.6.c.a.6.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.9797 q^{2} +(8.65096 + 14.9839i) q^{3} +88.5548 q^{4} +(-5.02316 - 8.70037i) q^{5} +(-94.9853 - 164.519i) q^{6} +(36.4175 - 63.0770i) q^{7} -620.957 q^{8} +(-28.1782 + 48.8060i) q^{9} +O(q^{10})$	\(q-10.9797 q^{2} +(8.65096 + 14.9839i) q^{3} +88.5548 q^{4} +(-5.02316 - 8.70037i) q^{5} +(-94.9853 - 164.519i) q^{6} +(36.4175 - 63.0770i) q^{7} -620.957 q^{8} +(-28.1782 + 48.8060i) q^{9} +(55.1531 + 95.5279i) q^{10} +500.662 q^{11} +(766.084 + 1326.90i) q^{12} +(376.594 - 652.280i) q^{13} +(-399.855 + 692.570i) q^{14} +(86.9104 - 150.533i) q^{15} +3984.20 q^{16} +(-829.023 + 1435.91i) q^{17} +(309.389 - 535.877i) q^{18} +(1131.01 + 1958.96i) q^{19} +(-444.825 - 770.460i) q^{20} +1260.19 q^{21} -5497.15 q^{22} +(20.0997 + 34.8138i) q^{23} +(-5371.88 - 9304.36i) q^{24} +(1512.04 - 2618.92i) q^{25} +(-4134.90 + 7161.86i) q^{26} +3229.29 q^{27} +(3224.95 - 5585.78i) q^{28} +(-638.786 + 1106.41i) q^{29} +(-954.254 + 1652.82i) q^{30} +(2826.10 + 4894.95i) q^{31} -23874.9 q^{32} +(4331.21 + 7501.88i) q^{33} +(9102.46 - 15765.9i) q^{34} -731.725 q^{35} +(-2495.31 + 4322.01i) q^{36} +(1526.84 + 2644.57i) q^{37} +(-12418.2 - 21508.9i) q^{38} +13031.6 q^{39} +(3119.17 + 5402.56i) q^{40} -2618.84 q^{41} -13836.5 q^{42} +(-12059.1 - 1259.13i) q^{43} +44336.1 q^{44} +566.174 q^{45} +(-220.690 - 382.246i) q^{46} +21065.7 q^{47} +(34467.2 + 59698.9i) q^{48} +(5751.03 + 9961.07i) q^{49} +(-16601.8 + 28755.1i) q^{50} -28687.4 q^{51} +(33349.2 - 57762.5i) q^{52} +(-17059.7 - 29548.2i) q^{53} -35456.8 q^{54} +(-2514.91 - 4355.95i) q^{55} +(-22613.7 + 39168.2i) q^{56} +(-19568.6 + 33893.8i) q^{57} +(7013.71 - 12148.1i) q^{58} +17442.8 q^{59} +(7696.33 - 13330.4i) q^{60} +(448.086 - 776.108i) q^{61} +(-31029.9 - 53745.3i) q^{62} +(2052.36 + 3554.79i) q^{63} +134646. q^{64} -7566.77 q^{65} +(-47555.6 - 82368.7i) q^{66} +(-20575.5 - 35637.9i) q^{67} +(-73414.0 + 127157. i) q^{68} +(-347.764 + 602.345i) q^{69} +8034.16 q^{70} +(10965.4 - 18992.6i) q^{71} +(17497.4 - 30306.4i) q^{72} +(-19444.9 + 33679.6i) q^{73} +(-16764.3 - 29036.7i) q^{74} +52322.2 q^{75} +(100156. + 173475. i) q^{76} +(18232.9 - 31580.3i) q^{77} -143084. q^{78} +(45994.2 - 79664.2i) q^{79} +(-20013.3 - 34664.0i) q^{80} +(34783.8 + 60247.3i) q^{81} +28754.2 q^{82} +(39178.2 + 67858.7i) q^{83} +111596. q^{84} +16657.3 q^{85} +(132406. + 13824.9i) q^{86} -22104.4 q^{87} -310890. q^{88} +(-28420.5 - 49225.7i) q^{89} -6216.44 q^{90} +(-27429.2 - 47508.8i) q^{91} +(1779.93 + 3082.93i) q^{92} +(-48897.0 + 84692.1i) q^{93} -231296. q^{94} +(11362.5 - 19680.4i) q^{95} +(-206541. - 357739. i) q^{96} -331.126 q^{97} +(-63144.8 - 109370. i) q^{98} +(-14107.7 + 24435.3i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9}+O(q^{10}) $ 34 * q - 14 * q^2 - 14 * q^3 + 454 * q^4 + 71 * q^5 + 15 * q^6 + 225 * q^7 - 936 * q^8 - 1011 * q^9	\( 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9} - 317 q^{10} + 1326 q^{11} - 648 q^{12} + 1006 q^{13} - 1272 q^{14} + 683 q^{15} + 3574 q^{16} + 200 q^{17} + 1861 q^{18} + 3361 q^{19} + 3825 q^{20} - 1320 q^{21} - 8768 q^{22} + 560 q^{23} - 7382 q^{24} - 3232 q^{25} - 3201 q^{26} - 122 q^{27} + 13934 q^{28} + 8887 q^{29} - 19449 q^{30} - 6749 q^{31} - 19086 q^{32} + 7106 q^{33} + 8423 q^{34} + 31118 q^{35} - 14112 q^{36} - 4514 q^{37} + 7072 q^{38} - 5404 q^{39} - 18519 q^{40} - 28996 q^{41} + 58118 q^{42} - 14998 q^{43} + 71050 q^{44} - 92096 q^{45} + 20052 q^{46} - 10742 q^{47} + 32927 q^{48} + 7472 q^{49} + 20362 q^{50} + 20250 q^{51} + 59532 q^{52} - 50572 q^{53} - 230084 q^{54} + 38544 q^{55} - 40355 q^{56} - 18087 q^{57} - 33436 q^{58} + 112654 q^{59} + 134093 q^{60} - 20120 q^{61} - 31491 q^{62} + 188227 q^{63} + 125164 q^{64} - 36578 q^{65} + 8803 q^{66} - 73824 q^{67} - 128456 q^{68} + 8005 q^{69} - 141610 q^{70} + 142842 q^{71} + 98466 q^{72} - 91624 q^{73} - 99720 q^{74} + 298358 q^{75} + 258288 q^{76} + 68051 q^{77} - 201116 q^{78} + 99734 q^{79} - 31261 q^{80} - 28441 q^{81} - 147772 q^{82} - 47340 q^{83} - 624232 q^{84} - 71734 q^{85} - 115526 q^{86} - 215924 q^{87} - 720684 q^{88} + 60402 q^{89} + 676108 q^{90} + 164172 q^{91} + 78997 q^{92} - 40793 q^{93} - 341874 q^{94} + 123541 q^{95} - 442140 q^{96} + 318476 q^{97} + 217473 q^{98} - 134770 q^{99}+O(q^{100}) \) 34 * q - 14 * q^2 - 14 * q^3 + 454 * q^4 + 71 * q^5 + 15 * q^6 + 225 * q^7 - 936 * q^8 - 1011 * q^9 - 317 * q^10 + 1326 * q^11 - 648 * q^12 + 1006 * q^13 - 1272 * q^14 + 683 * q^15 + 3574 * q^16 + 200 * q^17 + 1861 * q^18 + 3361 * q^19 + 3825 * q^20 - 1320 * q^21 - 8768 * q^22 + 560 * q^23 - 7382 * q^24 - 3232 * q^25 - 3201 * q^26 - 122 * q^27 + 13934 * q^28 + 8887 * q^29 - 19449 * q^30 - 6749 * q^31 - 19086 * q^32 + 7106 * q^33 + 8423 * q^34 + 31118 * q^35 - 14112 * q^36 - 4514 * q^37 + 7072 * q^38 - 5404 * q^39 - 18519 * q^40 - 28996 * q^41 + 58118 * q^42 - 14998 * q^43 + 71050 * q^44 - 92096 * q^45 + 20052 * q^46 - 10742 * q^47 + 32927 * q^48 + 7472 * q^49 + 20362 * q^50 + 20250 * q^51 + 59532 * q^52 - 50572 * q^53 - 230084 * q^54 + 38544 * q^55 - 40355 * q^56 - 18087 * q^57 - 33436 * q^58 + 112654 * q^59 + 134093 * q^60 - 20120 * q^61 - 31491 * q^62 + 188227 * q^63 + 125164 * q^64 - 36578 * q^65 + 8803 * q^66 - 73824 * q^67 - 128456 * q^68 + 8005 * q^69 - 141610 * q^70 + 142842 * q^71 + 98466 * q^72 - 91624 * q^73 - 99720 * q^74 + 298358 * q^75 + 258288 * q^76 + 68051 * q^77 - 201116 * q^78 + 99734 * q^79 - 31261 * q^80 - 28441 * q^81 - 147772 * q^82 - 47340 * q^83 - 624232 * q^84 - 71734 * q^85 - 115526 * q^86 - 215924 * q^87 - 720684 * q^88 + 60402 * q^89 + 676108 * q^90 + 164172 * q^91 + 78997 * q^92 - 40793 * q^93 - 341874 * q^94 + 123541 * q^95 - 442140 * q^96 + 318476 * q^97 + 217473 * q^98 - 134770 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

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

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 $

$2$	−10.9797			−1.94096			−0.970482	−	0.241175i	$-0.922467\pi$
$2$	−10.9797			−1.94096			−0.970482	+	0.241175i	$0.922467\pi$
$3$	8.65096	+	14.9839i	0.554959	+	0.961218i	0.997907	+	0.0646700i	$0.0205995\pi$
$3$	8.65096	+	14.9839i	0.554959	+	0.961218i	−0.442947	+	0.896548i	$0.646067\pi$
$4$	88.5548			2.76734
$5$	−5.02316	−	8.70037i	−0.0898571	−	0.155637i	0.817594	−	0.575796i	$-0.195308\pi$
$5$	−5.02316	−	8.70037i	−0.0898571	−	0.155637i	−0.907451	+	0.420159i	$0.861974\pi$
$6$	−94.9853	−	164.519i	−1.07716	−	1.86569i
$7$	36.4175	−	63.0770i	0.280909	−	0.486549i	−0.690700	−	0.723141i	$-0.742697\pi$
$7$	36.4175	−	63.0770i	0.280909	−	0.486549i	0.971609	+	0.236593i	$0.0760308\pi$
$8$	−620.957			−3.43034
$9$	−28.1782	+	48.8060i	−0.115959	+	0.200848i
$10$	55.1531	+	95.5279i	0.174409	+	0.302086i
$11$	500.662			1.24757			0.623783	−	0.781598i	$-0.285595\pi$
$11$	500.662			1.24757			0.623783	+	0.781598i	$0.285595\pi$
$12$	766.084	+	1326.90i	1.53576	+	2.66001i
$13$	376.594	−	652.280i	0.618037	−	1.07047i	−0.371806	−	0.928310i	$-0.621261\pi$
$13$	376.594	−	652.280i	0.618037	−	1.07047i	0.989843	−	0.142162i	$-0.0454053\pi$
$14$	−399.855	+	692.570i	−0.545234	+	0.944373i
$15$	86.9104	−	150.533i	0.0997340	−	0.172744i
$16$	3984.20			3.89082
$17$	−829.023	+	1435.91i	−0.695736	+	1.20505i	0.274196	+	0.961674i	$0.411588\pi$
$17$	−829.023	+	1435.91i	−0.695736	+	1.20505i	−0.969932	+	0.243376i	$0.921745\pi$
$18$	309.389	−	535.877i	0.225073	−	0.389838i
$19$	1131.01	+	1958.96i	0.718755	+	1.24492i	0.961493	+	0.274829i	$0.0886211\pi$
$19$	1131.01	+	1958.96i	0.718755	+	1.24492i	−0.242738	+	0.970092i	$0.578046\pi$
$20$	−444.825	−	770.460i	−0.248665	−	0.430700i
$21$	1260.19			0.623572
$22$	−5497.15			−2.42148
$23$	20.0997	+	34.8138i	0.00792265	+	0.0137224i	0.869960	−	0.493123i	$-0.164145\pi$
$23$	20.0997	+	34.8138i	0.00792265	+	0.0137224i	−0.862037	+	0.506846i	$0.830811\pi$
$24$	−5371.88	−	9304.36i	−1.90370	−	3.29730i
$25$	1512.04	−	2618.92i	0.483851	−	0.838055i
$26$	−4134.90	+	7161.86i	−1.19959	+	2.07775i
$27$	3229.29			0.852507
$28$	3224.95	−	5585.78i	0.777370	−	1.34644i
$29$	−638.786	+	1106.41i	−0.141046	+	0.244299i	−0.927891	−	0.372852i	$-0.878380\pi$
$29$	−638.786	+	1106.41i	−0.141046	+	0.244299i	0.786845	+	0.617151i	$0.211713\pi$
$30$	−954.254	+	1652.82i	−0.193580	+	0.335291i
$31$	2826.10	+	4894.95i	0.528182	+	0.914838i	0.999460	+	0.0328537i	$0.0104595\pi$
$31$	2826.10	+	4894.95i	0.528182	+	0.914838i	−0.471278	+	0.881985i	$0.656207\pi$
$32$	−23874.9			−4.12160
$33$	4331.21	+	7501.88i	0.692348	+	1.19918i
$34$	9102.46	−	15765.9i	1.35040	−	2.33896i
$35$	−731.725			−0.100967
$36$	−2495.31	+	4322.01i	−0.320899	+	0.555813i
$37$	1526.84	+	2644.57i	0.183354	+	0.317578i	0.943021	−	0.332734i	$-0.107971\pi$
$37$	1526.84	+	2644.57i	0.183354	+	0.317578i	−0.759667	+	0.650313i	$0.774638\pi$
$38$	−12418.2	−	21508.9i	−1.39508	−	2.41634i
$39$	13031.6			1.37194
$40$	3119.17	+	5402.56i	0.308240	+	0.533888i
$41$	−2618.84			−0.243304			−0.121652	−	0.992573i	$-0.538819\pi$
$41$	−2618.84			−0.243304			−0.121652	+	0.992573i	$0.538819\pi$
$42$	−13836.5			−1.21033
$43$	−12059.1	−	1259.13i	−0.994593	−	0.103848i
$43$	−12059.1	−	1259.13i	−0.994593	−	0.103848i
$44$	44336.1			3.45243
$45$	566.174			0.0416791
$46$	−220.690	−	382.246i	−0.0153776	−	0.0266347i
$47$	21065.7			1.39101			0.695506	−	0.718520i	$-0.255180\pi$
$47$	21065.7			1.39101			0.695506	+	0.718520i	$0.255180\pi$
$48$	34467.2	+	59698.9i	2.15925	+	3.73993i
$49$	5751.03	+	9961.07i	0.342180	+	0.592674i
$50$	−16601.8	+	28755.1i	−0.939138	+	1.62663i
$51$	−28687.4			−1.54442
$52$	33349.2	−	57762.5i	1.71032	−	2.96236i
$53$	−17059.7	−	29548.2i	−0.834221	−	1.44491i	−0.894663	−	0.446741i	$-0.852585\pi$
$53$	−17059.7	−	29548.2i	−0.834221	−	1.44491i	0.0604429	−	0.998172i	$-0.480749\pi$
$54$	−35456.8			−1.65469
$55$	−2514.91	−	4355.95i	−0.112103	−	0.194167i
$56$	−22613.7	+	39168.2i	−0.963612	+	1.66903i
$57$	−19568.6	+	33893.8i	−0.797760	+	1.38176i
$58$	7013.71	−	12148.1i	0.273765	−	0.474175i
$59$	17442.8			0.652358			0.326179	−	0.945308i	$-0.394239\pi$
$59$	17442.8			0.652358			0.326179	+	0.945308i	$0.394239\pi$
$60$	7696.33	−	13330.4i	0.275998	−	0.478042i
$61$	448.086	−	776.108i	0.0154183	−	0.0267053i	−0.858213	−	0.513293i	$-0.828425\pi$
$61$	448.086	−	776.108i	0.0154183	−	0.0267053i	0.873632	+	0.486588i	$0.161759\pi$
$62$	−31029.9	−	53745.3i	−1.02518	−	1.77567i
$63$	2052.36	+	3554.79i	0.0651481	+	0.112840i
$64$	134646.			4.10906
$65$	−7566.77			−0.222140
$66$	−47555.6	−	82368.7i	−1.34382	−	2.32757i
$67$	−20575.5	−	35637.9i	−0.559970	−	0.969896i	−0.997498	−	0.0706912i	$-0.977480\pi$
$67$	−20575.5	−	35637.9i	−0.559970	−	0.969896i	0.437529	−	0.899204i	$-0.355854\pi$
$68$	−73414.0	+	127157.i	−1.92534	+	3.33478i
$69$	−347.764	+	602.345i	−0.00879350	+	0.0152308i
$70$	8034.16			0.195972
$71$	10965.4	−	18992.6i	0.258153	−	0.447135i	−0.707594	−	0.706619i	$-0.750219\pi$
$71$	10965.4	−	18992.6i	0.258153	−	0.447135i	0.965747	+	0.259485i	$0.0835527\pi$
$72$	17497.4	−	30306.4i	0.397780	−	0.688975i
$73$	−19444.9	+	33679.6i	−0.427070	+	0.739707i	−0.996611	−	0.0822557i	$-0.973788\pi$
$73$	−19444.9	+	33679.6i	−0.427070	+	0.739707i	0.569541	+	0.821963i	$0.307121\pi$
$74$	−16764.3	−	29036.7i	−0.355883	−	0.616408i
$75$	52322.2			1.07407
$76$	100156.	+	173475.i	1.98904	+	3.44512i
$77$	18232.9	−	31580.3i	0.350452	−	0.607001i
$78$	−143084.			−2.66289
$79$	45994.2	−	79664.2i	0.829154	−	1.43614i	−0.0695491	−	0.997579i	$-0.522156\pi$
$79$	45994.2	−	79664.2i	0.829154	−	1.43614i	0.898703	−	0.438558i	$-0.144511\pi$
$80$	−20013.3	−	34664.0i	−0.349618	−	0.605556i
$81$	34783.8	+	60247.3i	0.589066	+	1.02029i
$82$	28754.2			0.472244
$83$	39178.2	+	67858.7i	0.624237	+	1.08121i	0.988688	+	0.149988i	$0.0479235\pi$
$83$	39178.2	+	67858.7i	0.624237	+	1.08121i	−0.364450	+	0.931223i	$0.618743\pi$
$84$	111596.			1.72563
$85$	16657.3			0.250067
$86$	132406.	+	13824.9i	1.93047	+	0.201566i
$87$	−22104.4			−0.313099
$88$	−310890.			−4.27957
$89$	−28420.5	−	49225.7i	−0.380326	−	0.658744i	0.610783	−	0.791798i	$-0.290855\pi$
$89$	−28420.5	−	49225.7i	−0.380326	−	0.658744i	−0.991109	+	0.133054i	$0.957522\pi$
$90$	−6216.44			−0.0808976
$91$	−27429.2	−	47508.8i	−0.347224	−	0.601410i
$92$	1779.93	+	3082.93i	0.0219247	+	0.0379746i
$93$	−48897.0	+	84692.1i	−0.586239	+	1.01540i
$94$	−231296.			−2.69990
$95$	11362.5	−	19680.4i	0.129170	−	0.223730i
$96$	−206541.	−	357739.i	−2.28732	−	3.96176i
$97$	−331.126			−0.00357325			−0.00178663	−	0.999998i	$-0.500569\pi$
$97$	−331.126			−0.00357325			−0.00178663	+	0.999998i	$0.500569\pi$
$98$	−63144.8	−	109370.i	−0.664159	−	1.15036i
$99$	−14107.7	+	24435.3i	−0.144667	+	0.250571i
$100$	133898.	−	231918.i	1.33898	−	2.31918i
$101$	37817.0	−	65501.0i	0.368879	−	0.638917i	−0.620511	−	0.784197i	$-0.713075\pi$
$101$	37817.0	−	65501.0i	0.368879	−	0.638917i	0.989391	+	0.145280i	$0.0464083\pi$
$102$	314980.			2.99766
$103$	−47711.9	+	82639.4i	−0.443132	+	0.767528i	−0.997920	−	0.0644642i	$-0.979466\pi$
$103$	−47711.9	+	82639.4i	−0.443132	+	0.767528i	0.554788	+	0.831992i	$0.312800\pi$
$104$	−233849.	+	405038.i	−2.12008	+	3.67208i
$105$	−6330.12	−	10964.1i	−0.0560324	−	0.0970509i
$106$	187311.	+	324432.i	1.61919	+	2.80452i
$107$	−67921.9			−0.573522			−0.286761	−	0.958002i	$-0.592579\pi$
$107$	−67921.9			−0.573522			−0.286761	+	0.958002i	$0.592579\pi$
$108$	285969.			2.35918
$109$	30174.0	+	52263.0i	0.243258	+	0.421335i	0.961640	−	0.274313i	$-0.0884505\pi$
$109$	30174.0	+	52263.0i	0.243258	+	0.421335i	−0.718382	+	0.695648i	$0.755117\pi$
$110$	27613.1	+	47827.2i	0.217587	+	0.376872i
$111$	−26417.3	+	45756.1i	−0.203508	+	0.352486i
$112$	145095.	−	251312.i	1.09297	−	1.89307i
$113$	−49345.3			−0.363538			−0.181769	−	0.983341i	$-0.558182\pi$
$113$	−49345.3			−0.363538			−0.181769	+	0.983341i	$0.558182\pi$
$114$	214858.	−	372145.i	1.54842	−	2.68195i
$115$	201.928	−	349.750i	0.00142381	−	0.00246612i
$116$	−56567.6	+	97977.9i	−0.390322	+	0.676057i
$117$	21223.4	+	36760.1i	0.143335	+	0.248263i
$118$	−191517.			−1.26620
$119$	60382.0	+	104585.i	0.390877	+	0.677019i
$120$	−53967.6	+	93474.7i	−0.342121	+	0.592572i
$121$	89611.9			0.556419
$122$	−4919.87	+	8521.47i	−0.0299264	+	0.0518340i
$123$	−22655.5	−	39240.4i	−0.135024	−	0.233868i
$124$	250265.	+	433472.i	1.46166	+	2.53167i
$125$	−61775.6			−0.353624
$126$	−22534.4	−	39030.7i	−0.126450	−	0.219018i
$127$	−122729.			−0.675206			−0.337603	−	0.941289i	$-0.609616\pi$
$127$	−122729.			−0.675206			−0.337603	+	0.941289i	$0.609616\pi$
$128$	−714379.			−3.85393
$129$	−85456.5	−	191586.i	−0.452138	−	1.01365i
$130$	83081.2			0.431166
$131$	−134688.			−0.685727			−0.342863	−	0.939385i	$-0.611397\pi$
$131$	−134688.			−0.685727			−0.342863	+	0.939385i	$0.611397\pi$
$132$	383549.	+	664327.i	1.91596	+	3.31854i
$133$	164754.			0.807619
$134$	225914.	+	391295.i	1.08688	+	1.88253i
$135$	−16221.3	−	28096.1i	−0.0766038	−	0.132682i
$136$	514788.	−	891639.i	2.38661	−	4.13373i
$137$	282687.			1.28678			0.643391	−	0.765538i	$-0.277527\pi$
$137$	282687.			1.28678			0.643391	+	0.765538i	$0.277527\pi$
$138$	3818.36	−	6613.59i	0.0170679	−	0.0295624i
$139$	−208305.	−	360795.i	−0.914457	−	1.58389i	−0.807694	−	0.589602i	$-0.799285\pi$
$139$	−208305.	−	360795.i	−0.914457	−	1.58389i	−0.106764	−	0.994284i	$-0.534049\pi$
$140$	−64797.8			−0.279409
$141$	182238.	+	315646.i	0.771955	+	1.33707i
$142$	−120397.	+	208534.i	−0.501066	+	0.867872i
$143$	188546.	−	326572.i	0.771042	−	1.33548i
$144$	−112267.	+	194453.i	−0.451178	+	0.781462i
$145$	12834.9			0.0506959
$146$	213500.	−	369793.i	0.828927	−	1.43574i
$147$	−99503.8	+	172346.i	−0.379792	+	0.657820i
$148$	135209.	+	234189.i	0.507402	+	0.878846i
$149$	49843.7	+	86331.8i	0.183927	+	0.318570i	0.943214	−	0.332185i	$-0.107786\pi$
$149$	49843.7	+	86331.8i	0.183927	+	0.318570i	−0.759288	+	0.650755i	$0.774452\pi$
$150$	−574485.			−2.08473
$151$	−538696.			−1.92265			−0.961327	−	0.275409i	$-0.911187\pi$
$151$	−538696.			−1.92265			−0.961327	+	0.275409i	$0.911187\pi$
$152$	−702307.	−	1.21643e6i	−2.46557	−	4.27050i
$153$	−46720.7	−	80922.6i	−0.161354	−	0.279474i
$154$	−200193.	+	346744.i	−0.680215	+	1.17817i
$155$	28392.0	−	49176.3i	0.0949218	−	0.164409i
$156$	1.15401e6			3.79663
$157$	24542.7	−	42509.2i	0.0794645	−	0.137637i	−0.823555	−	0.567237i	$-0.808012\pi$
$157$	24542.7	−	42509.2i	0.0794645	−	0.137637i	0.903019	+	0.429601i	$0.141346\pi$
$158$	−505004.	+	874693.i	−1.60936	+	2.78749i
$159$	295165.	−	511241.i	0.925917	−	1.60373i
$160$	119927.	+	207720.i	0.370355	+	0.641474i
$161$	2927.93			0.00890218
$162$	−381917.	−	661500.i	−1.14336	−	1.98035i
$163$	−267536.	+	463386.i	−0.788703	+	1.36607i	0.138059	+	0.990424i	$0.455914\pi$
$163$	−267536.	+	463386.i	−0.788703	+	1.36607i	−0.926762	+	0.375649i	$0.877420\pi$
$164$	−231911.			−0.673305
$165$	43512.7	−	75366.3i	0.124425	−	0.215510i
$166$	−430167.	−	745071.i	−1.21162	−	2.09859i
$167$	−2529.34	−	4380.94i	−0.00701803	−	0.0121556i	0.862495	−	0.506065i	$-0.168901\pi$
$167$	−2529.34	−	4380.94i	−0.00701803	−	0.0121556i	−0.869513	+	0.493910i	$0.835567\pi$
$168$	−782522.			−2.13906
$169$	−97999.3	−	169740.i	−0.263941	−	0.457159i
$170$	−182893.			−0.485371
$171$	−127479.			−0.333386
$172$	−1.06790e6	−	111502.i	−2.75238	−	0.287384i
$173$	−313445.			−0.796244			−0.398122	−	0.917332i	$-0.630338\pi$
$173$	−313445.			−0.796244			−0.398122	+	0.917332i	$0.630338\pi$
$174$	242701.			0.607713
$175$	−110129.	−	190749.i	−0.271836	−	0.470834i
$176$	1.99474e6			4.85405
$177$	150897.	+	261361.i	0.362032	+	0.627058i
$178$	312050.	+	540486.i	0.738199	+	1.27860i
$179$	108557.	−	188026.i	0.253236	−	0.438617i	−0.711179	−	0.703011i	$-0.751839\pi$
$179$	108557.	−	188026.i	0.253236	−	0.438617i	0.964415	+	0.264394i	$0.0851719\pi$
$180$	50137.4			0.115340
$181$	−192913.	+	334134.i	−0.437687	+	0.758097i	−0.997511	−	0.0705153i	$-0.977536\pi$
$181$	−192913.	+	334134.i	−0.437687	+	0.758097i	0.559823	+	0.828612i	$0.310869\pi$
$182$	301166.	+	521635.i	0.673950	+	1.16732i
$183$	15505.5			0.0342261
$184$	−12481.1	−	21617.9i	−0.0271774	−	0.0470726i
$185$	15339.2	−	26568.2i	0.0329513	−	0.0570733i
$186$	536877.	−	929898.i	1.13787	−	1.97085i
$187$	−415061.	+	718906.i	−0.867976	+	1.50338i
$188$	1.86547e6			3.84940
$189$	117603.	−	203694.i	0.239477	−	0.414786i
$190$	−124757.	+	216085.i	−0.250715	+	0.434251i
$191$	−146123.	−	253092.i	−0.289824	−	0.501991i	0.683943	−	0.729535i	$-0.260264\pi$
$191$	−146123.	−	253092.i	−0.289824	−	0.501991i	−0.973768	+	0.227545i	$0.926930\pi$
$192$	1.16481e6	+	2.01752e6i	2.28036	+	3.94970i
$193$	159495.			0.308216			0.154108	−	0.988054i	$-0.450750\pi$
$193$	159495.			0.308216			0.154108	+	0.988054i	$0.450750\pi$
$194$	3635.68			0.00693555
$195$	−65459.8	−	113380.i	−0.123279	−	0.213525i
$196$	509281.	+	882100.i	0.946929	+	1.64013i
$197$	335011.	−	580255.i	0.615025	−	1.06525i	−0.375355	−	0.926881i	$-0.622479\pi$
$197$	335011.	−	580255.i	0.615025	−	1.06525i	0.990380	−	0.138374i	$-0.0441875\pi$
$198$	154899.	−	268294.i	0.280793	−	0.486348i
$199$	−209704.			−0.375383			−0.187692	−	0.982228i	$-0.560101\pi$
$199$	−209704.			−0.375383			−0.187692	+	0.982228i	$0.560101\pi$
$200$	−938910.	+	1.62624e6i	−1.65977	+	2.87481i
$201$	355996.	−	616604.i	0.621520	−	1.07651i
$202$	−415221.	+	719185.i	−0.715981	+	1.24012i
$203$	46526.0	+	80585.5i	0.0792421	+	0.137251i
$204$	−2.54041e6			−4.27393
$205$	13154.9	+	22784.9i	0.0218626	+	0.0378671i
$206$	523864.	−	907360.i	0.860104	−	1.48974i
$207$	−2265.49			−0.00367483
$208$	1.50043e6	−	2.59881e6i	2.40467	−	4.16502i
$209$	566252.	+	980778.i	0.896694	+	1.55312i
$210$	69503.1	+	120383.i	0.108757	+	0.188372i
$211$	12638.9			0.0195435			0.00977177	−	0.999952i	$-0.496890\pi$
$211$	12638.9			0.0195435			0.00977177	+	0.999952i	$0.496890\pi$
$212$	−1.51072e6	−	2.61664e6i	−2.30857	−	3.99856i
$213$	379444.			0.573058
$214$	745765.			1.11319
$215$	49620.2	+	111244.i	0.0732086	+	0.164127i
$216$	−2.00525e6			−2.92439
$217$	411679.			0.593484
$218$	−331303.	−	573834.i	−0.472155	−	0.817796i
$219$	−672869.			−0.948026
$220$	−222707.	−	385740.i	−0.310226	−	0.537327i
$221$	624410.	+	1.08151e6i	0.859982	+	1.48953i
$222$	290055.	−	502391.i	0.395001	−	0.684162i
$223$	−280171.			−0.377278			−0.188639	−	0.982047i	$-0.560408\pi$
$223$	−280171.			−0.377278			−0.188639	+	0.982047i	$0.560408\pi$
$224$	−869464.	+	1.50596e6i	−1.15780	+	2.00536i
$225$	85212.7	+	147593.i	0.112214	+	0.194361i
$226$	541798.			0.705613
$227$	−259056.	−	448698.i	−0.333679	−	0.577950i	0.649551	−	0.760318i	$-0.274957\pi$
$227$	−259056.	−	448698.i	−0.333679	−	0.577950i	−0.983230	+	0.182369i	$0.941624\pi$
$228$	−1.73289e6	+	3.00146e6i	−2.20767	+	3.82380i
$229$	109788.	−	190158.i	0.138346	−	0.239622i	−0.788525	−	0.615003i	$-0.789155\pi$
$229$	109788.	−	190158.i	0.138346	−	0.239622i	0.926871	+	0.375381i	$0.122488\pi$
$230$	−2217.12	+	3840.17i	−0.00276357	+	0.00478664i
$231$	630928.			0.777947
$232$	396659.	−	687033.i	0.483835	−	0.838027i
$233$	−466639.	+	808242.i	−0.563107	+	0.975330i	0.434116	+	0.900857i	$0.357061\pi$
$233$	−466639.	+	808242.i	−0.563107	+	0.975330i	−0.997223	+	0.0744733i	$0.976272\pi$
$234$	−233028.	−	403616.i	−0.278207	−	0.481869i
$235$	−105816.	−	183279.i	−0.124992	−	0.216493i
$236$	1.54464e6			1.80529
$237$	1.59157e6			1.84059
$238$	−662979.	−	1.14831e6i	−0.758678	−	1.31407i
$239$	−373296.	−	646567.i	−0.422725	−	0.732181i	0.573480	−	0.819220i	$-0.305593\pi$
$239$	−373296.	−	646567.i	−0.422725	−	0.732181i	−0.996205	+	0.0870383i	$0.972260\pi$
$240$	346268.	−	599754.i	0.388047	−	0.672118i
$241$	−563630.	+	976236.i	−0.625103	+	1.08271i	0.363418	+	0.931626i	$0.381610\pi$
$241$	−563630.	+	976236.i	−0.625103	+	1.08271i	−0.988521	+	0.151084i	$0.951724\pi$
$242$	−983916.			−1.07999
$243$	−209467.	+	362807.i	−0.227562	+	0.394149i
$244$	39680.2	−	68728.1i	0.0426677	−	0.0739026i
$245$	57776.7	−	100072.i	0.0614947	−	0.106512i
$246$	248751.	+	430850.i	0.262076	+	0.453929i
$247$	1.70372e6			1.77687
$248$	−1.75489e6	−	3.03956e6i	−1.81184	−	3.13820i
$249$	−677859.	+	1.17409e6i	−0.692853	+	1.20006i
$250$	678280.			0.686371
$251$	−440706.	+	763326.i	−0.441535	+	0.764761i	−0.997804	−	0.0662417i	$-0.978899\pi$
$251$	−440706.	+	763326.i	−0.441535	+	0.764761i	0.556269	+	0.831002i	$0.312232\pi$
$252$	181746.	+	314794.i	0.180287	+	0.312266i
$253$	10063.2	+	17429.9i	0.00988403	+	0.0171196i
$254$	1.34753e6			1.31055
$255$	144101.	+	249591.i	0.138777	+	0.240369i
$256$	3.53504e6			3.37127
$257$	585552.			0.553009			0.276505	−	0.961013i	$-0.410824\pi$
$257$	585552.			0.553009			0.276505	+	0.961013i	$0.410824\pi$
$258$	938290.	+	2.10356e6i	0.877583	+	1.96746i
$259$	222416.			0.206023
$260$	−670074.			−0.614737
$261$	−35999.6	−	62353.2i	−0.0327112	−	0.0566575i
$262$	1.47884e6			1.33097
$263$	21088.5	+	36526.4i	0.0187999	+	0.0325625i	0.875272	−	0.483630i	$-0.160682\pi$
$263$	21088.5	+	36526.4i	0.0187999	+	0.0325625i	−0.856472	+	0.516193i	$0.827349\pi$
$264$	−2.68950e6	−	4.65835e6i	−2.37499	−	4.11360i
$265$	−171387.	+	296851.i	−0.149921	+	0.259671i
$266$	−1.80896e6			−1.56756
$267$	491729.	−	851699.i	0.422131	−	0.731152i
$268$	−1.82206e6	−	3.15591e6i	−1.54962	−	2.68403i
$269$	124175.			0.104629			0.0523147	−	0.998631i	$-0.483340\pi$
$269$	124175.			0.104629			0.0523147	+	0.998631i	$0.483340\pi$
$270$	178105.	+	308488.i	0.148685	+	0.257530i
$271$	23151.5	−	40099.6i	0.0191495	−	0.0331678i	−0.856292	−	0.516492i	$-0.827237\pi$
$271$	23151.5	−	40099.6i	0.0191495	−	0.0331678i	0.875441	+	0.483324i	$0.160571\pi$
$272$	−3.30300e6	+	5.72096e6i	−2.70698	+	4.68863i
$273$	474578.	−	821994.i	0.385391	−	0.667517i
$274$	−3.10383e6			−2.49760
$275$	757019.	−	1.31120e6i	0.603636	−	1.04553i
$276$	−30796.2	+	53340.5i	−0.0243346	+	0.0421487i
$277$	558590.	+	967507.i	0.437415	+	0.757626i	0.997489	−	0.0708170i	$-0.0225606\pi$
$277$	558590.	+	967507.i	0.437415	+	0.757626i	−0.560074	+	0.828443i	$0.689227\pi$
$278$	2.28714e6	+	3.96144e6i	1.77493	+	3.07427i
$279$	−318537.			−0.244991
$280$	454370.			0.346350
$281$	−493131.	−	854128.i	−0.372560	−	0.645293i	0.617399	−	0.786651i	$-0.288187\pi$
$281$	−493131.	−	854128.i	−0.372560	−	0.645293i	−0.989959	+	0.141358i	$0.954853\pi$
$282$	−2.00093e6	−	3.46571e6i	−1.49834	−	2.59520i
$283$	−204863.	+	354834.i	−0.152054	+	0.263365i	−0.931982	−	0.362503i	$-0.881922\pi$
$283$	−204863.	+	354834.i	−0.152054	+	0.263365i	0.779928	+	0.625869i	$0.215255\pi$
$284$	971037.	−	1.68188e6i	0.714397	−	1.23737i
$285$	393185.			0.286737
$286$	−2.07019e6	+	3.58568e6i	−1.49656	+	2.59213i
$287$	−95371.7	+	165189.i	−0.0683463	+	0.118379i
$288$	672750.	−	1.16524e6i	0.477939	−	0.827814i
$289$	−664631.	−	1.15117e6i	−0.468097	−	0.810768i
$290$	−140924.			−0.0983988
$291$	−2864.56	−	4961.56i	−0.00198301	−	0.00343467i
$292$	−1.72194e6	+	2.98249e6i	−1.18185	+	2.04702i
$293$	−224494.			−0.152769			−0.0763844	−	0.997078i	$-0.524338\pi$
$293$	−224494.			−0.152769			−0.0763844	+	0.997078i	$0.524338\pi$
$294$	1.09253e6	−	1.89231e6i	0.737163	−	1.27680i
$295$	−87617.9	−	151759.i	−0.0586189	−	0.101531i
$296$	−948105.	−	1.64217e6i	−0.628966	−	1.08940i
$297$	1.61679e6			1.06356
$298$	−547271.	−	947901.i	−0.356995	−	0.618333i
$299$	30277.7			0.0195860
$300$	4.63339e6			2.97232
$301$	−518587.	+	714801.i	−0.329917	+	0.454746i
$302$	5.91474e6			3.73180
$303$	1.30861e6			0.818852
$304$	4.50616e6	+	7.80489e6i	2.79655	+	4.84376i
$305$	−9003.24			−0.00554178
$306$	512981.	+	888510.i	0.313183	+	0.542449i
$307$	−936168.	−	1.62149e6i	−0.566902	−	0.981903i	−0.996870	−	0.0790590i	$-0.974808\pi$
$307$	−936168.	−	1.62149e6i	−0.566902	−	0.981903i	0.429968	−	0.902844i	$-0.358525\pi$
$308$	1.61461e6	−	2.79659e6i	0.969820	−	1.67978i
$309$	−1.65101e6			−0.983682
$310$	−311736.	+	539943.i	−0.184240	+	0.319113i
$311$	−166912.	−	289099.i	−0.0978555	−	0.169491i	0.812941	−	0.582346i	$-0.197865\pi$
$311$	−166912.	−	289099.i	−0.0978555	−	0.169491i	−0.910797	+	0.412855i	$0.864532\pi$
$312$	−8.09206e6			−4.70623
$313$	−1.50992e6	−	2.61526e6i	−0.871151	−	1.50888i	−0.860807	−	0.508931i	$-0.830041\pi$
$313$	−1.50992e6	−	2.61526e6i	−0.871151	−	1.50888i	−0.0103440	−	0.999946i	$-0.503293\pi$
$314$	−269473.	+	466740.i	−0.154238	+	0.267148i
$315$	20618.7	−	35712.6i	0.0117080	−	0.0202789i
$316$	4.07301e6	−	7.05465e6i	2.29455	−	3.97427i
$317$	−2.97812e6			−1.66454			−0.832269	−	0.554371i	$-0.812959\pi$
$317$	−2.97812e6			−1.66454			−0.832269	+	0.554371i	$0.812959\pi$
$318$	−3.24084e6	+	5.61329e6i	−1.79717	+	3.11279i
$319$	−319816.	+	553938.i	−0.175964	+	0.304779i
$320$	−676347.	−	1.17147e6i	−0.369228	−	0.639522i
$321$	−587589.	−	1.01773e6i	−0.318282	−	0.551280i
$322$	−32147.9			−0.0172788
$323$	−3.75052e6			−2.00025
$324$	3.08027e6	+	5.33519e6i	1.63015	+	2.82349i
$325$	−1.13885e6	−	1.97254e6i	−0.598077	−	1.03590i
$326$	2.93748e6	−	5.08786e6i	1.53084	−	2.65150i
$327$	−522069.	+	904250.i	−0.269997	+	0.467648i
$328$	1.62619e6			0.834615
$329$	767161.	−	1.32876e6i	0.390748	−	0.676795i
$330$	−477759.	+	827503.i	−0.241504	+	0.418297i
$331$	−906110.	+	1.56943e6i	−0.454581	+	0.787357i	−0.998664	−	0.0516745i	$-0.983544\pi$
$331$	−906110.	+	1.56943e6i	−0.454581	+	0.787357i	0.544083	+	0.839031i	$0.316877\pi$
$332$	3.46942e6	+	6.00922e6i	1.72748	+	2.99208i
$333$	−172094.			−0.0850465
$334$	27771.5	+	48101.6i	0.0136217	+	0.0235936i
$335$	−206709.	+	358030.i	−0.100634	+	0.174304i
$336$	5.02084e6			2.42621
$337$	−486844.	+	843239.i	−0.233515	+	0.404460i	−0.958840	−	0.283946i	$-0.908356\pi$
$337$	−486844.	+	843239.i	−0.233515	+	0.404460i	0.725325	+	0.688407i	$0.241690\pi$
$338$	1.07601e6	+	1.86370e6i	0.512299	+	0.887328i
$339$	−426884.	−	739384.i	−0.201749	−	0.349439i
$340$	1.47508e6			0.692020
$341$	1.41492e6	+	2.45072e6i	0.658942	+	1.14132i
$342$	1.39968e6			0.647090
$343$	2.06189e6			0.946304
$344$	7.48822e6	+	781867.i	3.41179	+	0.356235i
$345$	6987.50			0.00316063
$346$	3.44155e6			1.54548
$347$	−1.60766e6	−	2.78454e6i	−0.716753	−	1.24145i	−0.962280	−	0.272062i	$-0.912294\pi$
$347$	−1.60766e6	−	2.78454e6i	−0.716753	−	1.24145i	0.245527	−	0.969390i	$-0.421039\pi$
$348$	−1.95745e6			−0.866450
$349$	746288.	+	1.29261e6i	0.327977	+	0.568072i	0.982110	−	0.188307i	$-0.0603000\pi$
$349$	746288.	+	1.29261e6i	0.327977	+	0.568072i	−0.654134	+	0.756379i	$0.726967\pi$
$350$	1.20919e6	+	2.09438e6i	0.527624	+	0.913872i
$351$	1.21613e6	−	2.10640e6i	0.526881	−	0.912586i
$352$	−1.19533e7			−5.14197
$353$	−1.81167e6	+	3.13790e6i	−0.773822	+	1.34030i	0.161631	+	0.986851i	$0.448324\pi$
$353$	−1.81167e6	+	3.13790e6i	−0.773822	+	1.34030i	−0.935454	+	0.353449i	$0.885009\pi$
$354$	−1.65681e6	−	2.86968e6i	−0.702691	−	1.21710i
$355$	−220323.			−0.0927876
$356$	−2.51677e6	−	4.35917e6i	−1.05249	−	1.82297i
$357$	−1.04472e6	+	1.80952e6i	−0.433841	+	0.751435i
$358$	−1.19193e6	+	2.06448e6i	−0.491521	+	0.851339i
$359$	551097.	−	954528.i	0.225679	−	0.390888i	−0.730844	−	0.682545i	$-0.760873\pi$
$359$	551097.	−	954528.i	0.225679	−	0.390888i	0.956523	+	0.291657i	$0.0942065\pi$
$360$	−351570.			−0.142973
$361$	−1.32030e6	+	2.28683e6i	−0.533218	+	0.923560i
$362$	2.11813e6	−	3.66871e6i	0.849535	−	1.47144i
$363$	775229.	+	1.34274e6i	0.308790	+	0.534840i
$364$	−2.42899e6	−	4.20714e6i	−0.960888	−	1.66431i
$365$	390700.			0.153501
$366$	−170246.			−0.0664317
$367$	−1.06747e6	−	1.84891e6i	−0.413704	−	0.716557i	0.581587	−	0.813484i	$-0.302432\pi$
$367$	−1.06747e6	−	1.84891e6i	−0.413704	−	0.716557i	−0.995291	+	0.0969272i	$0.969099\pi$
$368$	80081.4	+	138705.i	0.0308256	+	0.0533916i
$369$	73794.1	−	127815.i	0.0282134	−	0.0488671i
$370$	−168420.	+	291712.i	−0.0639572	+	0.110777i
$371$	−2.48508e6			−0.937360
$372$	−4.33006e6	+	7.49989e6i	−1.62232	+	2.80994i
$373$	2.18818e6	−	3.79004e6i	0.814350	−	1.41050i	−0.0954433	−	0.995435i	$-0.530427\pi$
$373$	2.18818e6	−	3.79004e6i	0.814350	−	1.41050i	0.909794	−	0.415061i	$-0.136240\pi$
$374$	4.55726e6	−	7.89341e6i	1.68471	−	2.91800i
$375$	−534418.	−	925639.i	−0.196247	−	0.339910i
$376$	−1.30809e7			−4.77164
$377$	481126.	+	833334.i	0.174343	+	0.301971i
$378$	−1.29125e6	+	2.23651e6i	−0.464816	+	0.805085i
$379$	147627.			0.0527918			0.0263959	−	0.999652i	$-0.491597\pi$
$379$	147627.			0.0527918			0.0263959	+	0.999652i	$0.491597\pi$
$380$	1.00620e6	−	1.74279e6i	0.357458	−	0.619136i
$381$	−1.06172e6	−	1.83895e6i	−0.374712	−	0.649020i
$382$	1.60439e6	+	2.77889e6i	0.562539	+	0.974345i
$383$	4.70208e6			1.63792			0.818961	−	0.573850i	$-0.194551\pi$
$383$	4.70208e6			1.63792			0.818961	+	0.573850i	$0.194551\pi$
$384$	−6.18006e6	−	1.07042e7i	−2.13877	−	3.70446i
$385$	−366347.			−0.125962
$386$	−1.75122e6			−0.598236
$387$	401258.	−	553079.i	0.136190	−	0.187720i
$388$	−29322.8			−0.00988840
$389$	1.57266e6			0.526941			0.263471	−	0.964667i	$-0.415133\pi$
$389$	1.57266e6			0.526941			0.263471	+	0.964667i	$0.415133\pi$
$390$	718732.	+	1.24488e6i	0.239279	+	0.414444i
$391$	−66652.6			−0.0220483
$392$	−3.57114e6	−	6.18540e6i	−1.17379	−	2.03307i
$393$	−1.16518e6	−	2.01815e6i	−0.380550	−	0.659133i
$394$	−3.67833e6	+	6.37105e6i	−1.19374	+	2.06762i
$395$	−924145.			−0.298021
$396$	−1.24931e6	+	2.16387e6i	−0.400343	+	0.693414i
$397$	2.57403e6	+	4.45835e6i	0.819666	+	1.41970i	0.905928	+	0.423431i	$0.139174\pi$
$397$	2.57403e6	+	4.45835e6i	0.819666	+	1.41970i	−0.0862623	+	0.996272i	$0.527492\pi$
$398$	2.30250e6			0.728605
$399$	1.42528e6	+	2.46866e6i	0.448196	+	0.776298i
$400$	6.02425e6	−	1.04343e7i	1.88258	−	3.26072i
$401$	567285.	−	982566.i	0.176173	−	0.305141i	−0.764393	−	0.644750i	$-0.776961\pi$
$401$	567285.	−	982566.i	0.176173	−	0.305141i	0.940567	+	0.339609i	$0.110295\pi$
$402$	−3.90875e6	+	6.77015e6i	−1.20635	+	2.08946i
$403$	4.25717e6			1.30575
$404$	3.34888e6	−	5.80043e6i	1.02081	−	1.76810i
$405$	349449.	−	605264.i	0.105864	−	0.183361i
$406$	−510844.	−	884808.i	−0.153806	−	0.266400i
$407$	764433.	+	1.32404e6i	0.228746	+	0.396200i
$408$	1.78136e7			5.29788
$409$	−2.05089e6			−0.606224			−0.303112	−	0.952955i	$-0.598026\pi$
$409$	−2.05089e6			−0.606224			−0.303112	+	0.952955i	$0.598026\pi$
$410$	−144437.	−	250172.i	−0.0424345	−	0.0734987i
$411$	2.44552e6	+	4.23576e6i	0.714111	+	1.23688i
$412$	−4.22512e6	+	7.31812e6i	−1.22630	+	2.12401i
$413$	635223.	−	1.10024e6i	0.183253	−	0.317404i
$414$	24874.5			0.00713270
$415$	393597.	−	681731.i	0.112184	−	0.194309i
$416$	−8.99113e6	+	1.55731e7i	−2.54731	+	4.41206i
$417$	3.60408e6	−	6.24245e6i	1.01497	−	1.75798i
$418$	−6.21731e6	−	1.07687e7i	−1.74045	−	3.01455i
$419$	2.20325e6			0.613096			0.306548	−	0.951855i	$-0.400826\pi$
$419$	2.20325e6			0.613096			0.306548	+	0.951855i	$0.400826\pi$
$420$	−560563.	−	970923.i	−0.155060	−	0.268573i
$421$	−1.61280e6	+	2.79345e6i	−0.443481	+	0.768131i	−0.997945	−	0.0640765i	$-0.979590\pi$
$421$	−1.61280e6	+	2.79345e6i	−0.443481	+	0.768131i	0.554464	+	0.832207i	$0.312923\pi$
$422$	−138772.			−0.0379333
$423$	−593592.	+	1.02813e6i	−0.161301	+	0.279382i
$424$	1.05933e7	+	1.83482e7i	2.86166	+	4.95654i
$425$	2.50703e6	+	4.34230e6i	0.673266	+	1.16613i
$426$	−4.16620e6			−1.11228
$427$	−32636.4	−	56527.9i	−0.00866228	−	0.0150035i
$428$	−6.01481e6			−1.58713
$429$	6.52443e6			1.71159
$430$	−544817.	−	1.22143e6i	−0.142095	−	0.318565i
$431$	−2.60589e6			−0.675713			−0.337857	−	0.941198i	$-0.609702\pi$
$431$	−2.60589e6			−0.675713			−0.337857	+	0.941198i	$0.609702\pi$
$432$	1.28662e7			3.31695
$433$	−493922.	−	855498.i	−0.126601	−	0.219280i	0.795756	−	0.605617i	$-0.207074\pi$
$433$	−493922.	−	855498.i	−0.126601	−	0.219280i	−0.922358	+	0.386337i	$0.873740\pi$
$434$	−4.52013e6			−1.15193
$435$	111034.	+	192317.i	0.0281341	+	0.0487298i
$436$	2.67206e6	+	4.62814e6i	0.673177	+	1.16598i
$437$	−45465.8	+	78749.2i	−0.0113889	+	0.0197261i
$438$	7.38793e6			1.84008
$439$	−1.34500e6	+	2.32962e6i	−0.333091	+	0.576930i	−0.983116	−	0.182982i	$-0.941425\pi$
$439$	−1.34500e6	+	2.32962e6i	−0.333091	+	0.576930i	0.650026	+	0.759912i	$0.274758\pi$
$440$	1.56165e6	+	2.70486e6i	0.384550	+	0.666060i
$441$	−648213.			−0.158716
$442$	−6.85586e6	−	1.18747e7i	−1.66919	−	2.89113i
$443$	−3.25280e6	+	5.63402e6i	−0.787496	+	1.36398i	0.140001	+	0.990151i	$0.455289\pi$
$443$	−3.25280e6	+	5.63402e6i	−0.787496	+	1.36398i	−0.927497	+	0.373831i	$0.878044\pi$
$444$	−2.33938e6	+	4.05193e6i	−0.563175	+	0.975448i
$445$	−285521.	+	494537.i	−0.0683500	+	0.118386i
$446$	3.07621e6			0.732282
$447$	−862391.	+	1.49371e6i	−0.204144	+	0.353587i
$448$	4.90346e6	−	8.49305e6i	1.15427	−	1.99926i
$449$	−3.36046e6	−	5.82048e6i	−0.786651	−	1.36252i	−0.928008	−	0.372561i	$-0.878480\pi$
$449$	−3.36046e6	−	5.82048e6i	−0.786651	−	1.36252i	0.141356	−	0.989959i	$-0.454854\pi$
$450$	−935614.	−	1.62053e6i	−0.217804	−	0.377247i
$451$	−1.31116e6			−0.303538
$452$	−4.36976e6			−1.00603
$453$	−4.66024e6	−	8.07176e6i	−1.06699	−	1.84809i
$454$	2.84437e6	+	4.92659e6i	0.647659	+	1.12178i
$455$	−275563.	+	477289.i	−0.0624012	+	0.108082i
$456$	1.21513e7	−	2.10466e7i	2.73658	−	4.73990i
$457$	4.09315e6			0.916785			0.458393	−	0.888750i	$-0.348425\pi$
$457$	4.09315e6			0.916785			0.458393	+	0.888750i	$0.348425\pi$
$458$	−1.20544e6	+	2.08789e6i	−0.268524	+	0.465097i
$459$	−2.67716e6	+	4.63698e6i	−0.593120	+	1.02731i
$460$	17881.7	−	30972.1i	0.00394017	−	0.00682458i
$461$	1.23734e6	+	2.14314e6i	0.271168	+	0.469676i	0.969161	−	0.246428i	$-0.0792568\pi$
$461$	1.23734e6	+	2.14314e6i	0.271168	+	0.469676i	−0.697993	+	0.716104i	$0.745924\pi$
$462$	−6.92743e6			−1.50997
$463$	−190639.	−	330196.i	−0.0413294	−	0.0715846i	0.844621	−	0.535365i	$-0.179826\pi$
$463$	−190639.	−	330196.i	−0.0413294	−	0.0715846i	−0.885950	+	0.463780i	$0.846493\pi$
$464$	−2.54505e6	+	4.40816e6i	−0.548784	+	0.950522i
$465$	982470.			0.210711
$466$	5.12358e6	−	8.87429e6i	1.09297	−	1.89308i
$467$	−84316.9	−	146041.i	−0.0178905	−	0.0309873i	0.856942	−	0.515414i	$-0.172362\pi$
$467$	−84316.9	−	146041.i	−0.0178905	−	0.0309873i	−0.874832	+	0.484426i	$0.839028\pi$
$468$	1.87944e6	+	3.25528e6i	0.396655	+	0.687027i
$469$	−2.99724e6			−0.629202
$470$	1.16184e6	+	2.01236e6i	0.242605	+	0.420205i
$471$	849272.			0.176398
$472$	−1.08312e7			−2.23781
$473$	−6.03756e6	−	630400.i	−1.24082	−	0.129558i
$474$	−1.74751e7			−3.57251
$475$	6.84049e6			1.39108
$476$	5.34712e6	+	9.26147e6i	1.08169	+	1.87354i
$477$	1.92284e6			0.386943
$478$	4.09869e6	+	7.09914e6i	0.820494	+	1.42114i
$479$	2.90428e6	+	5.03036e6i	0.578362	+	1.00175i	0.995667	+	0.0929866i	$0.0296414\pi$
$479$	2.90428e6	+	5.03036e6i	0.578362	+	1.00175i	−0.417305	+	0.908767i	$0.637025\pi$
$480$	−2.07497e6	+	3.59396e6i	−0.411064	+	0.711984i
$481$	2.30000e6			0.453278
$482$	6.18851e6	−	1.07188e7i	1.21330	−	2.10150i
$483$	25329.4	+	43871.8i	0.00494035	+	0.00855693i
$484$	7.93556e6			1.53980
$485$	1663.30	+	2880.92i	0.000321082	+	0.000556130i
$486$	2.29989e6	−	3.98353e6i	0.441689	−	0.765028i
$487$	4.77091e6	−	8.26346e6i	0.911546	−	1.57884i	0.0996661	−	0.995021i	$-0.468223\pi$
$487$	4.77091e6	−	8.26346e6i	0.911546	−	1.57884i	0.811880	−	0.583824i	$-0.198444\pi$
$488$	−278242.	+	481930.i	−0.0528900	+	0.0916082i
$489$	−9.25778e6			−1.75079
$490$	−634373.	+	1.09877e6i	−0.119359	+	0.206736i
$491$	−704101.	+	1.21954e6i	−0.131805	+	0.228293i	−0.924372	−	0.381491i	$-0.875411\pi$
$491$	−704101.	+	1.21954e6i	−0.131805	+	0.228293i	0.792567	+	0.609784i	$0.208744\pi$
$492$	−2.00625e6	−	3.47493e6i	−0.373657	−	0.647192i
$493$	−1.05914e6	−	1.83448e6i	−0.196261	−	0.339935i
$494$	−1.87064e7			−3.44884
$495$	283462.			0.0519974
$496$	1.12598e7	+	1.95025e7i	2.05506	+	3.55947i
$497$	−798664.	−	1.38333e6i	−0.145035	−	0.251208i
$498$	7.44272e6	−	1.28912e7i	1.34480	−	2.32926i
$499$	−2.03319e6	+	3.52159e6i	−0.365533	+	0.633122i	−0.988862	−	0.148838i	$-0.952447\pi$
$499$	−2.03319e6	+	3.52159e6i	−0.365533	+	0.633122i	0.623328	+	0.781960i	$0.285780\pi$
$500$	−5.47052e6			−0.978597
$501$	43762.4	−	75798.7i	0.00778945	−	0.0134917i
$502$	4.83884e6	−	8.38112e6i	0.857003	−	1.48437i
$503$	−351293.	+	608457.i	−0.0619083	+	0.107228i	−0.895318	−	0.445427i	$-0.853052\pi$
$503$	−351293.	+	608457.i	−0.0619083	+	0.107228i	0.833410	+	0.552655i	$0.186385\pi$
$504$	−1.27443e6	−	2.20737e6i	−0.223480	−	0.387079i
$505$	−759845.			−0.132586
$506$	−110491.	−	191376.i	−0.0191845	−	0.0332286i
$507$	1.69558e6	−	2.93682e6i	0.292953	−	0.507409i
$508$	−1.08682e7			−1.86852
$509$	−4.42953e6	+	7.67218e6i	−0.757815	+	1.31257i	0.186147	+	0.982522i	$0.440400\pi$
$509$	−4.42953e6	+	7.67218e6i	−0.757815	+	1.31257i	−0.943962	+	0.330053i	$0.892933\pi$
$510$	−1.58220e6	−	2.74045e6i	−0.269361	−	0.466547i
$511$	1.41627e6	+	2.45306e6i	0.239936	+	0.415581i
$512$	−1.59537e7			−2.68959
$513$	3.65235e6	+	6.32606e6i	0.612744	+	1.06130i
$514$	−6.42921e6			−1.07337
$515$	958658.			0.159274
$516$	−7.56758e6	−	1.69658e7i	−1.25122	−	2.80512i
$517$	1.05468e7			1.73538
$518$	−2.44207e6			−0.399883
$519$	−2.71160e6	−	4.69663e6i	−0.441883	−	0.765364i
$520$	4.69864e6			0.762016
$521$	−3.79348e6	−	6.57049e6i	−0.612270	−	1.06048i	−0.990857	−	0.134917i	$-0.956923\pi$
$521$	−3.79348e6	−	6.57049e6i	−0.612270	−	1.06048i	0.378587	−	0.925566i	$-0.376410\pi$
$522$	395267.	+	684622.i	0.0634913	+	0.109970i
$523$	5.16090e6	−	8.93895e6i	0.825033	−	1.42900i	−0.0768605	−	0.997042i	$-0.524490\pi$
$523$	5.16090e6	−	8.93895e6i	0.825033	−	1.42900i	0.901894	−	0.431958i	$-0.142177\pi$
$524$	−1.19273e7			−1.89764
$525$	1.90545e6	−	3.30033e6i	0.301716	−	0.522588i
$526$	−231547.	−	401050.i	−0.0364900	−	0.0632026i
$527$	−9.37162e6			−1.46990
$528$	1.72564e7	+	2.98890e7i	2.69380	+	4.66580i
$529$	3.21736e6	−	5.57264e6i	0.499874	−	0.865808i
$530$	1.88179e6	−	3.25935e6i	0.290992	−	0.504012i
$531$	−491505.	+	851312.i	−0.0756470	+	0.131025i
$532$	1.45897e7			2.23495
$533$	−986239.	+	1.70822e6i	−0.150371	+	0.260450i
$534$	−5.39905e6	+	9.35144e6i	−0.819341	+	1.41914i
$535$	341183.	+	590946.i	0.0515350	+	0.0892613i
$536$	1.27765e7	+	2.21296e7i	1.92088	+	3.32707i
$537$	3.75648e6			0.562142
$538$	−1.36341e6			−0.203082
$539$	2.87932e6	+	4.98713e6i	0.426892	+	0.739399i
$540$	−1.43647e6	−	2.48804e6i	−0.211989	−	0.367175i
$541$	−1.59418e6	+	2.76121e6i	−0.234178	+	0.405607i	−0.959033	−	0.283293i	$-0.908573\pi$
$541$	−1.59418e6	+	2.76121e6i	−0.234178	+	0.405607i	0.724856	+	0.688901i	$0.241906\pi$
$542$	−254198.	+	440284.i	−0.0371684	+	0.0643776i
$543$	−6.67551e6			−0.971594
$544$	1.97928e7	−	3.42822e7i	2.86755	−	4.96674i
$545$	303138.	−	525051.i	0.0437169	−	0.0757199i
$546$	−5.21075e6	+	9.02529e6i	−0.748029	+	1.29563i
$547$	4.90549e6	+	8.49655e6i	0.700993	+	1.21416i	0.968118	+	0.250494i	$0.0805929\pi$
$547$	4.90549e6	+	8.49655e6i	0.700993	+	1.21416i	−0.267125	+	0.963662i	$0.586074\pi$
$548$	2.50333e7			3.56096
$549$	25252.5	+	43738.6i	0.00357580	+	0.00619346i
$550$	−8.31188e6	+	1.43966e7i	−1.17164	+	2.02933i
$551$	−2.88988e6			−0.405510
$552$	215947.	−	374030.i	0.0301647	−	0.0522468i
$553$	−3.34999e6	−	5.80235e6i	−0.465833	−	0.806847i
$554$	−6.13318e6	−	1.06230e7i	−0.849007	−	1.47052i
$555$	530794.			0.0731465
$556$	−1.84464e7	−	3.19502e7i	−2.53061	−	4.38315i
$557$	−4.05122e6			−0.553283			−0.276642	−	0.960973i	$-0.589222\pi$
$557$	−4.05122e6			−0.553283			−0.276642	+	0.960973i	$0.589222\pi$
$558$	3.49746e6			0.475518
$559$	−5.36271e6	+	7.39176e6i	−0.725863	+	1.00050i
$560$	−2.91534e6			−0.392843
$561$	−1.43627e7			−1.92677
$562$	5.41445e6	+	9.37810e6i	0.723125	+	1.25249i
$563$	966125.			0.128458			0.0642292	−	0.997935i	$-0.479541\pi$
$563$	966125.			0.128458			0.0642292	+	0.997935i	$0.479541\pi$
$564$	1.61381e7	+	2.79520e7i	2.13626	+	3.70011i
$565$	247869.	+	429322.i	0.0326664	+	0.0565799i
$566$	2.24935e6	−	3.89598e6i	0.295131	−	0.511183i
$567$	5.06696e6			0.661896
$568$	−6.80903e6	+	1.17936e7i	−0.885553	+	1.53382i
$569$	−1.79077e6	−	3.10170e6i	−0.231877	−	0.401624i	0.726483	−	0.687184i	$-0.241154\pi$
$569$	−1.79077e6	−	3.10170e6i	−0.231877	−	0.401624i	−0.958361	+	0.285561i	$0.907820\pi$
$570$	−4.31707e6			−0.556547
$571$	1.70131e6	+	2.94676e6i	0.218371	+	0.378229i	0.954310	−	0.298819i	$-0.0965925\pi$
$571$	1.70131e6	+	2.94676e6i	0.218371	+	0.378229i	−0.735939	+	0.677047i	$0.763259\pi$
$572$	1.66967e7	−	2.89195e7i	2.13373	−	3.69574i
$573$	2.52821e6	−	4.37898e6i	0.321681	−	0.557169i
$574$	1.04716e6	−	1.81373e6i	0.132658	−	0.229770i
$575$	121566.			0.0153335
$576$	−3.79406e6	+	6.57151e6i	−0.476484	+	0.825295i
$577$	1.39626e6	−	2.41840e6i	0.174594	−	0.302405i	−0.765427	−	0.643523i	$-0.777472\pi$
$577$	1.39626e6	−	2.41840e6i	0.174594	−	0.302405i	0.940021	+	0.341118i	$0.110806\pi$
$578$	7.29748e6	+	1.26396e7i	0.908559	+	1.57367i
$579$	1.37979e6	+	2.38986e6i	0.171047	+	0.296263i
$580$	1.13659e6			0.140293
$581$	5.70710e6			0.701415
$582$	31452.1	+	54476.6i	0.00384895	+	0.00666657i
$583$	−8.54113e6	−	1.47937e7i	−1.04074	−	1.80262i
$584$	1.20745e7	−	2.09136e7i	1.46499	−	2.53745i
$585$	213218.	−	369304.i	0.0257593	−	0.0446163i
$586$	2.46488e6			0.296519
$587$	4.37350e6	−	7.57513e6i	0.523883	−	0.907392i	−0.475731	−	0.879591i	$-0.657816\pi$
$587$	4.37350e6	−	7.57513e6i	0.523883	−	0.907392i	0.999613	−	0.0278007i	$-0.00885039\pi$
$588$	−8.81154e6	+	1.52620e7i	−1.05101	+	1.82041i
$589$	−6.39268e6	+	1.10724e7i	−0.759267	+	1.31509i
$590$	962023.	+	1.66627e6i	0.113777	+	0.197068i
$591$	1.15926e7			1.36526
$592$	6.08325e6	+	1.05365e7i	0.713397	+	1.23564i
$593$	−3.70637e6	+	6.41962e6i	−0.432824	+	0.749674i	−0.997115	−	0.0759023i	$-0.975816\pi$
$593$	−3.70637e6	+	6.41962e6i	−0.432824	+	0.749674i	0.564291	+	0.825576i	$0.309150\pi$
$594$	−1.77519e7			−2.06433
$595$	606617.	−	1.05069e6i	0.0702461	−	0.121670i
$596$	4.41390e6	+	7.64510e6i	0.508987	+	0.881591i
$597$	−1.81414e6	−	3.14219e6i	−0.208322	−	0.360825i
$598$	−332442.			−0.0380157
$599$	5.05365e6	+	8.75318e6i	0.575491	+	0.996779i	0.995988	+	0.0894854i	$0.0285223\pi$
$599$	5.05365e6	+	8.75318e6i	0.575491	+	0.996779i	−0.420497	+	0.907294i	$0.638144\pi$
$600$	−3.24899e7			−3.68443
$601$	−4.17965e6			−0.472013			−0.236006	−	0.971752i	$-0.575839\pi$
$601$	−4.17965e6			−0.472013			−0.236006	+	0.971752i	$0.575839\pi$
$602$	5.69395e6	−	7.84833e6i	0.640357	−	0.882645i
$603$	2.31912e6			0.259735
$604$	−4.77041e7			−5.32063
$605$	−450135.	−	779657.i	−0.0499982	−	0.0865994i
$606$	−1.43683e7			−1.58936
$607$	2.91717e6	+	5.05268e6i	0.321358	+	0.556609i	0.980769	−	0.195174i	$-0.0625272\pi$
$607$	2.91717e6	+	5.05268e6i	0.321358	+	0.556609i	−0.659410	+	0.751783i	$0.729194\pi$
$608$	−2.70026e7	−	4.67699e7i	−2.96242	−	5.13107i
$609$	−804990.	+	1.39428e6i	−0.0879523	+	0.152338i
$610$	98853.3			0.0107564
$611$	7.93321e6	−	1.37407e7i	0.859698	−	1.48904i
$612$	−4.13734e6	−	7.16609e6i	−0.446522	−	0.773399i
$613$	1.63198e7			1.75414			0.877070	−	0.480362i	$-0.159495\pi$
$613$	1.63198e7			1.75414			0.877070	+	0.480362i	$0.159495\pi$
$614$	1.02789e7	+	1.78036e7i	1.10034	+	1.90584i
$615$	−227604.	+	394222.i	−0.0242657	+	0.0420294i
$616$	−1.13219e7	+	1.96100e7i	−1.20217	+	2.08222i
$617$	−2.65640e6	+	4.60101e6i	−0.280918	+	0.486565i	−0.971611	−	0.236583i	$-0.923972\pi$
$617$	−2.65640e6	+	4.60101e6i	−0.280918	+	0.486565i	0.690693	+	0.723148i	$0.257306\pi$
$618$	1.81277e7			1.90929
$619$	7.23199e6	−	1.25262e7i	0.758632	−	1.31399i	−0.184917	−	0.982754i	$-0.559202\pi$
$619$	7.23199e6	−	1.25262e7i	0.758632	−	1.31399i	0.943548	−	0.331234i	$-0.107465\pi$
$620$	2.51424e6	−	4.35480e6i	0.262681	−	0.454976i
$621$	64907.9	+	112424.i	0.00675412	+	0.0116985i
$622$	1.83265e6	+	3.17424e6i	0.189934	+	0.328975i
$623$	−4.14001e6			−0.427348
$624$	5.19205e7			5.33798
$625$	−4.41480e6	−	7.64666e6i	−0.452076	−	0.783018i
$626$	1.65786e7	+	2.87149e7i	1.69087	+	2.92868i
$627$	−9.79725e6	+	1.69693e7i	−0.995257	+	1.72384i
$628$	2.17337e6	−	3.76440e6i	0.219905	−	0.380887i
$629$	−5.06315e6			−0.510264
$630$	−226388.	+	392115.i	−0.0227249	+	0.0393606i
$631$	3.93843e6	−	6.82156e6i	0.393776	−	0.682040i	−0.599168	−	0.800623i	$-0.704502\pi$
$631$	3.93843e6	−	6.82156e6i	0.393776	−	0.682040i	0.992944	+	0.118583i	$0.0378352\pi$
$632$	−2.85604e7	+	4.94681e7i	−2.84428	+	4.92643i
$633$	109339.	+	189380.i	0.0108459	+	0.0187856i
$634$	3.26990e7			3.23081
$635$	616486.	+	1.06778e6i	0.0606721	+	0.105087i
$636$	2.61383e7	−	4.52728e7i	2.56232	−	4.43808i
$637$	8.66320e6			0.845921
$638$	3.51150e6	−	6.08210e6i	0.341540	−	0.591564i
$639$	617968.	+	1.07035e6i	0.0598706	+	0.103699i
$640$	3.58844e6	+	6.21536e6i	0.346303	+	0.599814i
$641$	−1.62760e7			−1.56460			−0.782301	−	0.622901i	$-0.785954\pi$
$641$	−1.62760e7			−1.56460			−0.782301	+	0.622901i	$0.785954\pi$
$642$	6.45158e6	+	1.11745e7i	0.617773	+	1.07001i
$643$	1.26517e7			1.20676			0.603382	−	0.797452i	$-0.293819\pi$
$643$	1.26517e7			1.20676			0.603382	+	0.797452i	$0.293819\pi$
$644$	259282.			0.0246353
$645$	−1.23761e6	+	1.70587e6i	−0.117134	+	0.161453i
$646$	4.11798e7			3.88242
$647$	1.68252e7			1.58015			0.790075	−	0.613010i	$-0.210041\pi$
$647$	1.68252e7			1.58015			0.790075	+	0.613010i	$0.210041\pi$
$648$	−2.15992e7	−	3.74110e7i	−2.02070	−	3.49995i
$649$	8.73295e6			0.813859
$650$	1.25042e7	+	2.16580e7i	1.16084	+	2.01064i
$651$	3.56142e6	+	6.16856e6i	0.329360	+	0.570468i
$652$	−2.36916e7	+	4.10351e7i	−2.18261	+	3.78039i
$653$	−1.56294e7			−1.43436			−0.717180	−	0.696888i	$-0.754567\pi$
$653$	−1.56294e7			−1.43436			−0.717180	+	0.696888i	$0.754567\pi$
$654$	5.73218e6	−	9.92843e6i	0.524054	−	0.907687i
$655$	676560.	+	1.17184e6i	0.0616174	+	0.106724i
$656$	−1.04340e7			−0.946653
$657$	−1.09584e6	−	1.89806e6i	−0.0990456	−	0.171552i
$658$	−8.42323e6	+	1.45895e7i	−0.758427	+	1.31363i
$659$	−457666.	+	792700.i	−0.0410520	+	0.0711042i	−0.885821	−	0.464026i	$-0.846404\pi$
$659$	−457666.	+	792700.i	−0.0410520	+	0.0711042i	0.844769	+	0.535131i	$0.179738\pi$
$660$	3.85326e6	−	6.67405e6i	0.344325	−	0.596389i
$661$	−8.73256e6			−0.777389			−0.388694	−	0.921367i	$-0.627074\pi$
$661$	−8.73256e6			−0.777389			−0.388694	+	0.921367i	$0.627074\pi$
$662$	9.94885e6	−	1.72319e7i	0.882324	−	1.52823i
$663$	−1.08035e7	+	1.87122e7i	−0.954510	+	1.65326i
$664$	−2.43280e7	−	4.21374e7i	−2.14135	−	3.70892i
$665$	−827586.	−	1.43342e6i	−0.0725703	−	0.125695i
$666$	1.88955e6			0.165072
$667$	−51357.7			−0.00446983
$668$	−223985.	−	387953.i	−0.0194213	−	0.0336386i
$669$	−2.42375e6	−	4.19806e6i	−0.209374	−	0.362646i
$670$	2.26961e6	−	3.93108e6i	0.195328	−	0.338318i
$671$	224340.	−	388568.i	0.0192354	−	0.0333166i
$672$	−3.00868e7			−2.57012
$673$	−3.97823e6	+	6.89050e6i	−0.338573	+	0.586426i	−0.984165	−	0.177257i	$-0.943278\pi$
$673$	−3.97823e6	+	6.89050e6i	−0.338573	+	0.586426i	0.645591	+	0.763683i	$0.276611\pi$
$674$	5.34542e6	−	9.25855e6i	0.453244	−	0.785042i
$675$	4.88281e6	−	8.45727e6i	0.412487	−	0.714448i
$676$	−8.67831e6	−	1.50313e7i	−0.730413	−	1.26511i
$677$	7.91314e6			0.663555			0.331778	−	0.943358i	$-0.392352\pi$
$677$	7.91314e6			0.663555			0.331778	+	0.943358i	$0.392352\pi$
$678$	4.68708e6	+	8.11825e6i	0.391586	+	0.678248i
$679$	−12058.8	+	20886.4i	−0.00100376	+	0.00173856i
$680$	−1.03435e7			−0.857815
$681$	4.48217e6	−	7.76334e6i	0.370357	−	0.641477i
$682$	−1.55355e7	−	2.69083e7i	−1.27898	−	2.21526i
$683$	−6.47217e6	−	1.12101e7i	−0.530882	−	0.919515i	−0.999351	−	0.0360349i	$-0.988527\pi$
$683$	−6.47217e6	−	1.12101e7i	−0.530882	−	0.919515i	0.468468	−	0.883480i	$-0.344806\pi$
$684$	−1.12888e7			−0.922591
$685$	−1.41998e6	−	2.45948e6i	−0.115626	−	0.200271i
$686$	−2.26391e7			−1.83674
$687$	3.79908e6			0.307105
$688$	−4.80461e7	−	5.01663e6i	−3.86978	−	0.404056i
$689$	−2.56983e7			−2.06232
$690$	−76721.0			−0.00613467
$691$	−1.25765e6	−	2.17831e6i	−0.100199	−	0.173550i	0.811568	−	0.584259i	$-0.198615\pi$
$691$	−1.25765e6	−	2.17831e6i	−0.100199	−	0.173550i	−0.911767	+	0.410709i	$0.865281\pi$
$692$	−2.77571e7			−2.20348
$693$	1.02754e6	+	1.77975e6i	0.0812765	+	0.140775i
$694$	1.76516e7	+	3.05736e7i	1.39119	+	2.40961i
$695$	−2.09270e6	+	3.62467e6i	−0.164341	+	0.284647i
$696$	1.37259e7			1.07403
$697$	2.17108e6	−	3.76042e6i	0.169275	−	0.293194i
$698$	−8.19405e6	−	1.41925e7i	−0.636590	−	1.10261i
$699$	−1.61475e7			−1.25001
$700$	−9.75247e6	−	1.68918e7i	−0.752263	−	1.30296i
$701$	−9.67939e6	+	1.67652e7i	−0.743966	+	1.28859i	0.206711	+	0.978402i	$0.433724\pi$
$701$	−9.67939e6	+	1.67652e7i	−0.743966	+	1.28859i	−0.950676	+	0.310184i	$0.899609\pi$
$702$	−1.33528e7	+	2.31278e7i	−1.02266	+	1.77129i
$703$	−3.45374e6	+	5.98205e6i	−0.263573	+	0.456522i
$704$	6.74120e7			5.12632
$705$	1.83083e6	−	3.17108e6i	0.138731	−	0.240290i
$706$	1.98916e7	−	3.44533e7i	1.50196	−	2.60147i
$707$	−2.75441e6	−	4.77077e6i	−0.207243	−	0.358955i
$708$	1.33626e7	+	2.31448e7i	1.00186	+	1.73528i
$709$	2.02872e7			1.51568			0.757838	−	0.652442i	$-0.226256\pi$
$709$	2.02872e7			1.51568			0.757838	+	0.652442i	$0.226256\pi$
$710$	2.41910e6			0.180097
$711$	2.59206e6	+	4.48958e6i	0.192296	+	0.333067i
$712$	1.76479e7	+	3.05671e7i	1.30465	+	2.25972i
$713$	−113608.	+	196775.i	−0.00836921	+	0.0144959i
$714$	1.14708e7	−	1.98680e7i	0.842070	−	1.45851i
$715$	−3.78840e6			−0.277134
$716$	9.61324e6	−	1.66506e7i	0.700789	−	1.21380i
$717$	6.45873e6	−	1.11868e7i	0.469190	−	0.812662i
$718$	−6.05090e6	+	1.04805e7i	−0.438035	+	0.758699i
$719$	2.06802e6	+	3.58192e6i	0.149188	+	0.258401i	0.930927	−	0.365204i	$-0.119001\pi$
$719$	2.06802e6	+	3.58192e6i	0.149188	+	0.258401i	−0.781740	+	0.623605i	$0.785667\pi$
$720$	2.25575e6			0.162166
$721$	3.47510e6	+	6.01905e6i	0.248960	+	0.431211i
$722$	1.44966e7	−	2.51088e7i	1.03496	−	1.79260i
$723$	−1.95038e7			−1.38763
$724$	−1.70833e7	+	2.95892e7i	−1.21123	+	2.09791i
$725$	1.93173e6	+	3.34586e6i	0.136490	+	0.236408i
$726$	−8.51181e6	−	1.47429e7i	−0.599350	−	1.03810i
$727$	−2.55897e7			−1.79568			−0.897841	−	0.440319i	$-0.854865\pi$
$727$	−2.55897e7			−1.79568			−0.897841	+	0.440319i	$0.854865\pi$
$728$	1.70324e7	+	2.95010e7i	1.19110	+	2.06304i
$729$	9.65656e6			0.672982
$730$	−4.28979e6			−0.297940
$731$	1.18053e7	−	1.62720e7i	0.817117	−	1.12628i
$732$	1.37309e6			0.0947153
$733$	−4.15702e6			−0.285774			−0.142887	−	0.989739i	$-0.545638\pi$
$733$	−4.15702e6			−0.285774			−0.142887	+	0.989739i	$0.545638\pi$
$734$	1.17205e7	+	2.03006e7i	0.802985	+	1.39081i
$735$	1.99929e6			0.136508
$736$	−479879.	−	831174.i	−0.0326540	−	0.0565584i
$737$	−1.03014e7	−	1.78426e7i	−0.698599	−	1.21001i
$738$	−810240.	+	1.40338e6i	−0.0547612	+	0.0948492i
$739$	2.19214e6			0.147658			0.0738290	−	0.997271i	$-0.476478\pi$
$739$	2.19214e6			0.147658			0.0738290	+	0.997271i	$0.476478\pi$
$740$	1.35836e6	−	2.35274e6i	0.0911873	−	0.157941i
$741$	1.47388e7	+	2.55284e7i	0.986091	+	1.70796i
$742$	2.72856e7			1.81938
$743$	−9.13301e6	−	1.58188e7i	−0.606935	−	1.05124i	−0.991743	−	0.128245i	$-0.959066\pi$
$743$	−9.13301e6	−	1.58188e7i	−0.606935	−	1.05124i	0.384808	−	0.922997i	$-0.374268\pi$
$744$	3.03630e7	−	5.25902e7i	2.01100	−	3.48315i
$745$	500746.	−	867318.i	0.0330542	−	0.0572516i
$746$	−2.40257e7	+	4.16137e7i	−1.58062	+	2.73772i
$747$	−4.41588e6			−0.289545
$748$	−3.67556e7	+	6.36626e7i	−2.40198	+	4.16036i
$749$	−2.47355e6	+	4.28431e6i	−0.161108	+	0.279046i
$750$	5.86777e6	+	1.01633e7i	0.380908	+	0.659752i
$751$	−1.14127e7	−	1.97674e7i	−0.738395	−	1.27894i	−0.953218	−	0.302285i	$-0.902250\pi$
$751$	−1.14127e7	−	1.97674e7i	−0.738395	−	1.27894i	0.214822	−	0.976653i	$-0.431083\pi$
$752$	8.39299e7			5.41218
$753$	−1.52501e7			−0.980135
$754$	−5.28264e6	−	9.14980e6i	−0.338394	−	0.586115i
$755$	2.70596e6	+	4.68686e6i	0.172764	+	0.299236i
$756$	1.04143e7	−	1.80381e7i	0.662714	−	1.14785i
$757$	2.80633e6	−	4.86071e6i	0.177992	−	0.308290i	−0.763201	−	0.646161i	$-0.776373\pi$
$757$	2.80633e6	−	4.86071e6i	0.177992	−	0.308290i	0.941193	+	0.337871i	$0.109707\pi$
$758$	−1.62090e6			−0.102467
$759$	−174112.	+	301571.i	−0.0109705	+	0.0190014i
$760$	−7.05560e6	+	1.22207e7i	−0.443098	+	0.767469i
$761$	2.35036e6	−	4.07094e6i	0.147120	−	0.254820i	−0.783042	−	0.621969i	$-0.786333\pi$
$761$	2.35036e6	−	4.07094e6i	0.147120	−	0.254820i	0.930162	+	0.367149i	$0.119666\pi$
$762$	1.16574e7	+	2.01912e7i	0.727302	+	1.25972i
$763$	4.39546e6			0.273333
$764$	−1.29399e7	−	2.24125e7i	−0.802042	−	1.38918i
$765$	−469371.	+	812975.i	−0.0289977	+	0.0502254i
$766$	−5.16276e7			−3.17914
$767$	6.56884e6	−	1.13776e7i	0.403181	−	0.698331i
$768$	3.05814e7	+	5.29686e7i	1.87092	+	3.24053i
$769$	−5.12371e6	−	8.87453e6i	−0.312442	−	0.541165i	0.666449	−	0.745551i	$-0.267814\pi$
$769$	−5.12371e6	−	8.87453e6i	−0.312442	−	0.541165i	−0.978890	+	0.204386i	$0.934480\pi$
$770$	4.02240e6			0.244488
$771$	5.06558e6	+	8.77385e6i	0.306898	+	0.531562i
$772$	1.41241e7			0.852937
$773$	2.01869e7			1.21512			0.607562	−	0.794272i	$-0.292147\pi$
$773$	2.01869e7			1.21512			0.607562	+	0.794272i	$0.292147\pi$
$774$	−4.40571e6	+	6.07266e6i	−0.264340	+	0.364357i
$775$	1.70927e7			1.02225
$776$	205615.			0.0122575
$777$	1.92411e6	+	3.33265e6i	0.114334	+	0.198033i
$778$	−1.72675e7			−1.02277
$779$	−2.96192e6	−	5.13020e6i	−0.174876	−	0.302894i
$780$	−5.79678e6	−	1.00403e7i	−0.341154	−	0.590896i
$781$	5.48995e6	−	9.50887e6i	0.322063	−	0.557830i
$782$	731828.			0.0427949
$783$	−2.06283e6	+	3.57292e6i	−0.120243	+	0.208266i
$784$	2.29132e7	+	3.96869e7i	1.33136	+	2.30599i
$785$	−493128.			−0.0285618
$786$	1.27934e7	+	2.21588e7i	0.738634	+	1.27935i
$787$	1.42806e7	−	2.47348e7i	0.821884	−	1.42354i	−0.0823943	−	0.996600i	$-0.526257\pi$
$787$	1.42806e7	−	2.47348e7i	0.821884	−	1.42354i	0.904278	−	0.426944i	$-0.140410\pi$
$788$	2.96668e7	−	5.13844e7i	1.70198	−	2.94792i
$789$	−364872.	+	631976.i	−0.0208664	+	0.0361417i
$790$	1.01469e7			0.578448
$791$	−1.79703e6	+	3.11255e6i	−0.102121	+	0.176879i
$792$	8.76031e6	−	1.51733e7i	0.496257	−	0.859542i
$793$	−337493.	−	584555.i	−0.0190582	−	0.0330098i
$794$	−2.82622e7	−	4.89515e7i	−1.59094	−	2.75559i
$795$	−5.93065e6			−0.332801
$796$	−1.85703e7			−1.03881
$797$	1.65647e7	+	2.86909e7i	0.923715	+	1.59992i	0.793614	+	0.608421i	$0.208197\pi$
$797$	1.65647e7	+	2.86909e7i	0.923715	+	1.59992i	0.130101	+	0.991501i	$0.458470\pi$
$798$	−1.56492e7	−	2.71052e7i	−0.869931	−	1.50676i
$799$	−1.74639e7	+	3.02484e7i	−0.967777	+	1.67624i
$800$	−3.60997e7	+	6.25264e7i	−1.99424	+	3.45413i
$801$	3.20335e6			0.176410
$802$	−6.22864e6	+	1.07883e7i	−0.341946	+	0.592268i
$803$	−9.73534e6	+	1.68621e7i	−0.532798	+	0.922833i
$804$	3.15252e7	−	5.46032e7i	1.71996	−	2.97905i
$805$	−14707.5	−	25474.1i	−0.000799924	−	0.00138551i
$806$	−4.67427e7			−2.53440
$807$	1.07423e6	+	1.86063e6i	0.0580651	+	0.100572i
$808$	−2.34828e7	+	4.06734e7i	−1.26538	+	2.19170i
$809$	2.47179e7			1.32782			0.663912	−	0.747811i	$-0.268895\pi$
$809$	2.47179e7			1.32782			0.663912	+	0.747811i	$0.268895\pi$
$810$	−3.83686e6	+	6.64564e6i	−0.205477	+	0.355897i
$811$	−9.71928e6	−	1.68343e7i	−0.518898	−	0.898758i	−0.999759	−	0.0219609i	$-0.993009\pi$
$811$	−9.71928e6	−	1.68343e7i	−0.518898	−	0.898758i	0.480861	−	0.876797i	$-0.340324\pi$
$812$	4.12010e6	+	7.13623e6i	0.219290	+	0.379821i
$813$	801132.			0.0425087
$814$	−8.39328e6	−	1.45376e7i	−0.443987	−	0.769009i
$815$	5.37551e6			0.283482
$816$	−1.14296e8			−6.00906
$817$	−1.11724e7	−	2.50475e7i	−0.585586	−	1.31283i
$818$	2.25182e7			1.17666
$819$	3.09162e6			0.161056
$820$	1.16493e6	+	2.01771e6i	0.0605012	+	0.104791i
$821$	3.17753e7			1.64525			0.822626	−	0.568583i	$-0.192508\pi$
$821$	3.17753e7			1.64525			0.822626	+	0.568583i	$0.192508\pi$
$822$	−2.68511e7	−	4.65075e7i	−1.38606	−	2.40073i
$823$	1.03903e7	+	1.79965e7i	0.534720	+	0.926163i	0.999177	+	0.0405668i	$0.0129164\pi$
$823$	1.03903e7	+	1.79965e7i	0.534720	+	0.926163i	−0.464457	+	0.885596i	$0.653750\pi$
$824$	2.96271e7	−	5.13156e7i	1.52009	−	2.63288i
$825$	2.61958e7			1.33997
$826$	−6.97459e6	+	1.20803e7i	−0.355687	+	0.616069i
$827$	1.19335e7	+	2.06694e7i	0.606742	+	1.05091i	0.991774	+	0.128005i	$0.0408573\pi$
$827$	1.19335e7	+	2.06694e7i	0.606742	+	1.05091i	−0.385031	+	0.922903i	$0.625809\pi$
$828$	−200620.			−0.0101695
$829$	−543558.	−	941470.i	−0.0274701	−	0.0475795i	0.851964	−	0.523601i	$-0.175412\pi$
$829$	−543558.	−	941470.i	−0.0274701	−	0.0475795i	−0.879434	+	0.476022i	$0.842078\pi$
$830$	−4.32160e6	+	7.48523e6i	−0.217746	+	0.377146i
$831$	−9.66468e6	+	1.67397e7i	−0.485495	+	0.840903i
$832$	5.07067e7	−	8.78266e7i	2.53955	−	4.39863i
$833$	−1.90709e7			−0.952269
$834$	−3.95719e7	+	6.85405e7i	−1.97003	+	3.41218i
$835$	−25410.5	+	44012.4i	−0.00126124	+	0.00218453i
$836$	5.01444e7	+	8.68526e7i	2.48146	+	4.29801i
$837$	9.12632e6	+	1.58072e7i	0.450279	+	0.779906i
$838$	−2.41911e7			−1.19000
$839$	−1.63778e7			−0.803250			−0.401625	−	0.915804i	$-0.631555\pi$
$839$	−1.63778e7			−0.803250			−0.401625	+	0.915804i	$0.631555\pi$
$840$	3.93074e6	+	6.80824e6i	0.192210	+	0.332917i
$841$	9.43948e6	+	1.63497e7i	0.460212	+	0.797111i
$842$	1.77081e7	−	3.06713e7i	0.860780	−	1.49091i
$843$	8.53211e6	−	1.47780e7i	0.413511	−	0.716223i
$844$	1.11924e6			0.0540836
$845$	−984533.	+	1.70526e6i	−0.0474339	+	0.0821579i
$846$	6.51749e6	−	1.12886e7i	0.313079	−	0.542269i
$847$	3.26344e6	−	5.65245e6i	0.156303	−	0.270725i
$848$	−6.79691e7	−	1.17726e8i	−3.24580	−	5.62190i
$849$	−7.08906e6			−0.337535
$850$	−2.75265e7	−	4.76773e7i	−1.30678	−	2.26342i
$851$	−61378.3	+	106310.i	−0.00290530	+	0.00503213i
$852$	3.36016e7			1.58585
$853$	−1.26391e7	+	2.18915e7i	−0.594761	+	1.03016i	0.398820	+	0.917029i	$0.369420\pi$
$853$	−1.26391e7	+	2.18915e7i	−0.594761	+	1.03016i	−0.993581	+	0.113126i	$0.963913\pi$
$854$	358339.	+	620662.i	0.0168132	+	0.0291213i
$855$	640346.	+	1.10911e6i	0.0299571	+	0.0518872i
$856$	4.21766e7			1.96738
$857$	5.73535e6	+	9.93392e6i	0.266752	+	0.462028i	0.968021	−	0.250868i	$-0.0807161\pi$
$857$	5.73535e6	+	9.93392e6i	0.266752	+	0.462028i	−0.701269	+	0.712897i	$0.747383\pi$
$858$	−7.16366e7			−3.32213
$859$	−1.05011e7			−0.485570			−0.242785	−	0.970080i	$-0.578061\pi$
$859$	−1.05011e7			−0.485570			−0.242785	+	0.970080i	$0.578061\pi$
$860$	4.39410e6	+	9.85118e6i	0.202593	+	0.454195i
$861$	−3.30023e6			−0.151718
$862$	2.86120e7			1.31153
$863$	−5.85029e6	−	1.01330e7i	−0.267393	−	0.463139i	0.700795	−	0.713363i	$-0.252829\pi$
$863$	−5.85029e6	−	1.01330e7i	−0.267393	−	0.463139i	−0.968188	+	0.250224i	$0.919496\pi$
$864$	−7.70990e7			−3.51370
$865$	1.57449e6	+	2.72709e6i	0.0715482	+	0.123925i
$866$	5.42313e6	+	9.39314e6i	0.245729	+	0.425614i
$867$	1.14994e7	−	1.99175e7i	0.519549	−	0.899886i
$868$	3.64561e7			1.64237
$869$	2.30276e7	−	3.98849e7i	1.03442	−	1.79167i
$870$	−1.21913e6	−	2.11159e6i	−0.0546073	−	0.0945827i
$871$	−3.09945e7			−1.38433
$872$	−1.87368e7	−	3.24531e7i	−0.834457	−	1.44532i
$873$	9330.51	−	16160.9i	0.000414352	−	0.000717680i
$874$	499203.	−	864646.i	0.0221054	−	0.0382877i
$875$	−2.24971e6	+	3.89662e6i	−0.0993362	+	0.172055i
$876$	−5.95858e7			−2.62351
$877$	−419021.	+	725766.i	−0.0183966	+	0.0318638i	−0.875077	−	0.483983i	$-0.839189\pi$
$877$	−419021.	+	725766.i	−0.0183966	+	0.0318638i	0.856681	+	0.515847i	$0.172523\pi$
$878$	1.47678e7	−	2.55786e7i	0.646517	−	1.11980i
$879$	−1.94208e6	−	3.36379e6i	−0.0847805	−	0.146844i
$880$	−1.00199e7	−	1.73550e7i	−0.436171	−	0.755470i
$881$	−3.69163e7			−1.60243			−0.801213	−	0.598379i	$-0.795812\pi$
$881$	−3.69163e7			−1.60243			−0.801213	+	0.598379i	$0.795812\pi$
$882$	7.11721e6			0.308062
$883$	1.24749e7	+	2.16072e7i	0.538438	+	0.932602i	0.998988	+	0.0449681i	$0.0143186\pi$
$883$	1.24749e7	+	2.16072e7i	0.538438	+	0.932602i	−0.460551	+	0.887633i	$0.652348\pi$
$884$	5.52945e7	+	9.57729e7i	2.37986	+	4.12204i
$885$	1.51596e6	−	2.62572e6i	0.0650623	−	0.112691i
$886$	3.57149e7	−	6.18601e7i	1.52850	−	2.64744i
$887$	1.02677e7			0.438191			0.219096	−	0.975703i	$-0.429689\pi$
$887$	1.02677e7			0.438191			0.219096	+	0.975703i	$0.429689\pi$
$888$	1.64040e7	−	2.84126e7i	0.698101	−	1.20915i
$889$	−4.46947e6	+	7.74136e6i	−0.189671	+	0.328521i
$890$	3.13495e6	−	5.42990e6i	0.132665	−	0.229782i
$891$	1.74149e7	+	3.01635e7i	0.734899	+	1.27288i
$892$	−2.48105e7			−1.04406
$893$	2.38254e7	+	4.12668e7i	0.999797	+	1.73170i
$894$	9.46884e6	−	1.64005e7i	0.396235	−	0.686299i
$895$	−2.18120e6			−0.0910201
$896$	−2.60159e7	+	4.50609e7i	−1.08260	+	1.87512i
$897$	261931.	+	453679.i	0.0108694	+	0.0188264i
$898$	3.68969e7	+	6.39074e7i	1.52686	+	2.64460i
$899$	−7.22110e6			−0.297992
$900$	7.54600e6	+	1.30701e7i	0.310535	+	0.537862i
$901$	5.65714e7			2.32159
$902$	1.43961e7			0.589156
$903$	−1.51968e7	−	1.58674e6i	−0.620200	−	0.0647570i
$904$	3.06413e7			1.24706
$905$	3.87612e6			0.157317
$906$	5.11682e7	+	8.86259e7i	2.07100	+	3.58707i
$907$	1.41953e7			0.572962			0.286481	−	0.958086i	$-0.407514\pi$
$907$	1.41953e7			0.572962			0.286481	+	0.958086i	$0.407514\pi$
$908$	−2.29407e7	−	3.97344e7i	−0.923403	−	1.59938i
$909$	2.13123e6	+	3.69140e6i	0.0855501	+	0.148177i
$910$	3.02561e6	−	5.24052e6i	0.121118	−	0.209783i
$911$	−1.46693e7			−0.585615			−0.292808	−	0.956171i	$-0.594590\pi$
$911$	−1.46693e7			−0.585615			−0.292808	+	0.956171i	$0.594590\pi$
$912$	−7.79651e7	+	1.35040e8i	−3.10394	+	5.37618i
$913$	1.96151e7	+	3.39743e7i	0.778777	+	1.34888i
$914$	−4.49418e7			−1.77945
$915$	−77886.6	−	134904.i	−0.00307546	−	0.00532685i
$916$	9.72224e6	−	1.68394e7i	0.382849	−	0.663114i
$917$	−4.90501e6	+	8.49573e6i	−0.192627	+	0.333639i
$918$	2.93945e7	−	5.09128e7i	1.15122	−	1.99398i
$919$	−4.28459e7			−1.67348			−0.836739	−	0.547601i	$-0.815541\pi$
$919$	−4.28459e7			−1.67348			−0.836739	+	0.547601i	$0.815541\pi$
$920$	−125389.	+	217180.i	−0.00488416	+	0.00845961i
$921$	1.61975e7	−	2.80549e7i	0.629215	−	1.08983i
$922$	−1.35857e7	−	2.35312e7i	−0.526327	−	0.911625i
$923$	−8.25899e6	−	1.43050e7i	−0.319097	−	0.552692i
$924$	5.58717e7			2.15284
$925$	9.23457e6			0.354864
$926$	2.09317e6	+	3.62547e6i	0.0802188	+	0.138943i
$927$	−2.68887e6	−	4.65725e6i	−0.102771	−	0.178004i
$928$	1.52509e7	−	2.64154e7i	0.581335	−	1.00690i
$929$	8.68346e6	−	1.50402e7i	0.330106	−	0.571761i	−0.652426	−	0.757852i	$-0.726249\pi$
$929$	8.68346e6	−	1.50402e7i	0.330106	−	0.571761i	0.982532	+	0.186092i	$0.0595821\pi$
$930$	−1.07873e7			−0.408982
$931$	−1.30089e7	+	2.25321e7i	−0.491888	+	0.851975i
$932$	−4.13231e7	+	7.15737e7i	−1.55831	+	2.69907i
$933$	2.88789e6	−	5.00197e6i	0.108612	−	0.188121i
$934$	925778.	+	1.60350e6i	0.0347248	+	0.0601451i
$935$	8.33967e6			0.311975
$936$	−1.31789e7	−	2.28264e7i	−0.491686	−	0.851625i
$937$	−7.81450e6	+	1.35351e7i	−0.290772	+	0.503632i	−0.973992	−	0.226580i	$-0.927245\pi$
$937$	−7.81450e6	+	1.35351e7i	−0.290772	+	0.503632i	0.683221	+	0.730212i	$0.260579\pi$
$938$	3.29090e7			1.22126
$939$	2.61245e7	−	4.52490e7i	0.966907	−	1.67473i
$940$	−9.37055e6	−	1.62303e7i	−0.345896	−	0.599109i
$941$	1.02564e6	+	1.77647e6i	0.0377592	+	0.0654009i	0.884287	−	0.466943i	$-0.154645\pi$
$941$	1.02564e6	+	1.77647e6i	0.0377592	+	0.0654009i	−0.846528	+	0.532344i	$0.821311\pi$
$942$	−9.32479e6			−0.342383
$943$	−52638.0	−	91171.7i	−0.00192761	−	0.00333873i
$944$	6.94955e7			2.53821
$945$	−2.36296e6			−0.0860748
$946$	6.62909e7	+	6.92163e6i	2.40839	+	0.251467i
$947$	−3.01915e7			−1.09398			−0.546991	−	0.837138i	$-0.684227\pi$
$947$	−3.01915e7			−1.09398			−0.546991	+	0.837138i	$0.684227\pi$
$948$	1.40942e8			5.09352
$949$	1.46457e7	+	2.53671e7i	0.527891	+	0.914333i
$950$	−7.51068e7			−2.70004
$951$	−2.57636e7	−	4.46238e7i	−0.923751	−	1.59998i
$952$	−3.74946e7	−	6.49426e7i	−1.34084	−	2.32240i
$953$	6.69422e6	−	1.15947e7i	0.238763	−	0.413550i	−0.721596	−	0.692314i	$-0.756591\pi$
$953$	6.69422e6	−	1.15947e7i	0.238763	−	0.413550i	0.960360	+	0.278764i	$0.0899246\pi$
$954$	−2.11123e7			−0.751042
$955$	−1.46800e6	+	2.54265e6i	−0.0520855	+	0.0902148i
$956$	−3.30571e7	−	5.72566e7i	−1.16982	−	2.02619i
$957$	−1.10669e7			−0.390611
$958$	−3.18883e7	−	5.52321e7i	−1.12258	−	1.94437i
$959$	1.02948e7	−	1.78311e7i	0.361468	−	0.626082i
$960$	1.17021e7	−	2.02686e7i	0.409813	−	0.709817i
$961$	−1.65914e6	+	2.87372e6i	−0.0579529	+	0.100377i
$962$	−2.52534e7			−0.879796
$963$	1.91391e6	−	3.31500e6i	0.0665053	−	0.115191i
$964$	−4.99121e7	+	8.64504e7i	−1.72987	+	2.99622i
$965$	−801172.	−	1.38767e6i	−0.0276954	−	0.0479698i
$966$	−278111.	−	481702.i	−0.00958903	−	0.0166087i
$967$	8.15640e6			0.280500			0.140250	−	0.990116i	$-0.455209\pi$
$967$	8.15640e6			0.280500			0.140250	+	0.990116i	$0.455209\pi$
$968$	−5.56452e7			−1.90871
$969$	−3.24456e7	−	5.61974e7i	−1.11006	−	1.92268i
$970$	−18262.6	−	31631.8i	−0.000623208	−	0.00107943i
$971$	−1.58889e7	+	2.75204e7i	−0.540812	+	0.936714i	0.458046	+	0.888929i	$0.348550\pi$
$971$	−1.58889e7	+	2.75204e7i	−0.540812	+	0.936714i	−0.998858	+	0.0477851i	$0.984784\pi$
$972$	−1.85493e7	+	3.21283e7i	−0.629741	+	1.09074i
$973$	−3.03439e7			−1.02752
$974$	−5.23834e7	+	9.07307e7i	−1.76928	+	3.06448i
$975$	1.97042e7	−	3.41287e7i	0.663816	−	1.14976i
$976$	1.78526e6	−	3.09217e6i	0.0599899	−	0.103906i
$977$	2.49221e7	+	4.31663e7i	0.835311	+	1.44680i	0.893777	+	0.448511i	$0.148046\pi$
$977$	2.49221e7	+	4.31663e7i	0.835311	+	1.44680i	−0.0584663	+	0.998289i	$0.518621\pi$
$978$	1.01648e8			3.39822
$979$	−1.42291e7	−	2.46455e7i	−0.474482	−	0.821827i
$980$	5.11640e6	−	8.86187e6i	0.170176	−	0.294754i
$981$	−3.40100e6			−0.112832
$982$	7.73085e6	−	1.33902e7i	0.255828	−	0.443108i
$983$	6.95688e6	+	1.20497e7i	0.229631	+	0.397733i	0.957699	−	0.287773i	$-0.0929147\pi$
$983$	6.95688e6	+	1.20497e7i	0.229631	+	0.397733i	−0.728068	+	0.685505i	$0.759581\pi$
$984$	1.40681e7	+	2.43666e7i	0.463177	+	0.802247i
$985$	−6.73125e6			−0.221057
$986$	1.16291e7	+	2.01421e7i	0.380936	+	0.659801i
$987$	2.65467e7			0.867396
$988$	1.50873e8			4.91720
$989$	−198551.	−	445132.i	−0.00645476	−	0.0144710i
$990$	−3.11234e6			−0.100925
$991$	−4.44803e7			−1.43874			−0.719372	−	0.694625i	$-0.755570\pi$
$991$	−4.44803e7			−1.43874			−0.719372	+	0.694625i	$0.755570\pi$
$992$	−6.74729e7	−	1.16866e8i	−2.17696	−	3.77060i
$993$	−3.13549e7			−1.00909
$994$	8.76913e6	+	1.51886e7i	0.281508	+	0.487586i
$995$	1.05338e6	+	1.82451e6i	0.0337308	+	0.0584235i
$996$	−6.00277e7	+	1.03971e8i	−1.91736	+	3.32096i
$997$	−3.38451e7			−1.07835			−0.539173	−	0.842195i	$-0.681263\pi$
$997$	−3.38451e7			−1.07835			−0.539173	+	0.842195i	$0.681263\pi$
$998$	2.23239e7	−	3.86662e7i	0.709487	−	1.22887i
$999$	4.93062e6	+	8.54009e6i	0.156311	+	0.270738i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.c.a.36.1	yes	34
43.6	even	3	inner	43.6.c.a.6.1	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.c.a.6.1	✓	34	43.6	even	3	inner
43.6.c.a.36.1	yes	34	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-10.9797 q^{2} +(8.65096 + 14.9839i) q^{3} +88.5548 q^{4} +(-5.02316 - 8.70037i) q^{5} +(-94.9853 - 164.519i) q^{6} +(36.4175 - 63.0770i) q^{7} -620.957 q^{8} +(-28.1782 + 48.8060i) q^{9} +O(q^{10})\)	\(q-10.9797 q^{2} +(8.65096 + 14.9839i) q^{3} +88.5548 q^{4} +(-5.02316 - 8.70037i) q^{5} +(-94.9853 - 164.519i) q^{6} +(36.4175 - 63.0770i) q^{7} -620.957 q^{8} +(-28.1782 + 48.8060i) q^{9} +(55.1531 + 95.5279i) q^{10} +500.662 q^{11} +(766.084 + 1326.90i) q^{12} +(376.594 - 652.280i) q^{13} +(-399.855 + 692.570i) q^{14} +(86.9104 - 150.533i) q^{15} +3984.20 q^{16} +(-829.023 + 1435.91i) q^{17} +(309.389 - 535.877i) q^{18} +(1131.01 + 1958.96i) q^{19} +(-444.825 - 770.460i) q^{20} +1260.19 q^{21} -5497.15 q^{22} +(20.0997 + 34.8138i) q^{23} +(-5371.88 - 9304.36i) q^{24} +(1512.04 - 2618.92i) q^{25} +(-4134.90 + 7161.86i) q^{26} +3229.29 q^{27} +(3224.95 - 5585.78i) q^{28} +(-638.786 + 1106.41i) q^{29} +(-954.254 + 1652.82i) q^{30} +(2826.10 + 4894.95i) q^{31} -23874.9 q^{32} +(4331.21 + 7501.88i) q^{33} +(9102.46 - 15765.9i) q^{34} -731.725 q^{35} +(-2495.31 + 4322.01i) q^{36} +(1526.84 + 2644.57i) q^{37} +(-12418.2 - 21508.9i) q^{38} +13031.6 q^{39} +(3119.17 + 5402.56i) q^{40} -2618.84 q^{41} -13836.5 q^{42} +(-12059.1 - 1259.13i) q^{43} +44336.1 q^{44} +566.174 q^{45} +(-220.690 - 382.246i) q^{46} +21065.7 q^{47} +(34467.2 + 59698.9i) q^{48} +(5751.03 + 9961.07i) q^{49} +(-16601.8 + 28755.1i) q^{50} -28687.4 q^{51} +(33349.2 - 57762.5i) q^{52} +(-17059.7 - 29548.2i) q^{53} -35456.8 q^{54} +(-2514.91 - 4355.95i) q^{55} +(-22613.7 + 39168.2i) q^{56} +(-19568.6 + 33893.8i) q^{57} +(7013.71 - 12148.1i) q^{58} +17442.8 q^{59} +(7696.33 - 13330.4i) q^{60} +(448.086 - 776.108i) q^{61} +(-31029.9 - 53745.3i) q^{62} +(2052.36 + 3554.79i) q^{63} +134646. q^{64} -7566.77 q^{65} +(-47555.6 - 82368.7i) q^{66} +(-20575.5 - 35637.9i) q^{67} +(-73414.0 + 127157. i) q^{68} +(-347.764 + 602.345i) q^{69} +8034.16 q^{70} +(10965.4 - 18992.6i) q^{71} +(17497.4 - 30306.4i) q^{72} +(-19444.9 + 33679.6i) q^{73} +(-16764.3 - 29036.7i) q^{74} +52322.2 q^{75} +(100156. + 173475. i) q^{76} +(18232.9 - 31580.3i) q^{77} -143084. q^{78} +(45994.2 - 79664.2i) q^{79} +(-20013.3 - 34664.0i) q^{80} +(34783.8 + 60247.3i) q^{81} +28754.2 q^{82} +(39178.2 + 67858.7i) q^{83} +111596. q^{84} +16657.3 q^{85} +(132406. + 13824.9i) q^{86} -22104.4 q^{87} -310890. q^{88} +(-28420.5 - 49225.7i) q^{89} -6216.44 q^{90} +(-27429.2 - 47508.8i) q^{91} +(1779.93 + 3082.93i) q^{92} +(-48897.0 + 84692.1i) q^{93} -231296. q^{94} +(11362.5 - 19680.4i) q^{95} +(-206541. - 357739. i) q^{96} -331.126 q^{97} +(-63144.8 - 109370. i) q^{98} +(-14107.7 + 24435.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9}+O(q^{10}) \) 34 * q - 14 * q^2 - 14 * q^3 + 454 * q^4 + 71 * q^5 + 15 * q^6 + 225 * q^7 - 936 * q^8 - 1011 * q^9	\( 34 q - 14 q^{2} - 14 q^{3} + 454 q^{4} + 71 q^{5} + 15 q^{6} + 225 q^{7} - 936 q^{8} - 1011 q^{9} - 317 q^{10} + 1326 q^{11} - 648 q^{12} + 1006 q^{13} - 1272 q^{14} + 683 q^{15} + 3574 q^{16} + 200 q^{17} + 1861 q^{18} + 3361 q^{19} + 3825 q^{20} - 1320 q^{21} - 8768 q^{22} + 560 q^{23} - 7382 q^{24} - 3232 q^{25} - 3201 q^{26} - 122 q^{27} + 13934 q^{28} + 8887 q^{29} - 19449 q^{30} - 6749 q^{31} - 19086 q^{32} + 7106 q^{33} + 8423 q^{34} + 31118 q^{35} - 14112 q^{36} - 4514 q^{37} + 7072 q^{38} - 5404 q^{39} - 18519 q^{40} - 28996 q^{41} + 58118 q^{42} - 14998 q^{43} + 71050 q^{44} - 92096 q^{45} + 20052 q^{46} - 10742 q^{47} + 32927 q^{48} + 7472 q^{49} + 20362 q^{50} + 20250 q^{51} + 59532 q^{52} - 50572 q^{53} - 230084 q^{54} + 38544 q^{55} - 40355 q^{56} - 18087 q^{57} - 33436 q^{58} + 112654 q^{59} + 134093 q^{60} - 20120 q^{61} - 31491 q^{62} + 188227 q^{63} + 125164 q^{64} - 36578 q^{65} + 8803 q^{66} - 73824 q^{67} - 128456 q^{68} + 8005 q^{69} - 141610 q^{70} + 142842 q^{71} + 98466 q^{72} - 91624 q^{73} - 99720 q^{74} + 298358 q^{75} + 258288 q^{76} + 68051 q^{77} - 201116 q^{78} + 99734 q^{79} - 31261 q^{80} - 28441 q^{81} - 147772 q^{82} - 47340 q^{83} - 624232 q^{84} - 71734 q^{85} - 115526 q^{86} - 215924 q^{87} - 720684 q^{88} + 60402 q^{89} + 676108 q^{90} + 164172 q^{91} + 78997 q^{92} - 40793 q^{93} - 341874 q^{94} + 123541 q^{95} - 442140 q^{96} + 318476 q^{97} + 217473 q^{98} - 134770 q^{99}+O(q^{100}) \) 34 * q - 14 * q^2 - 14 * q^3 + 454 * q^4 + 71 * q^5 + 15 * q^6 + 225 * q^7 - 936 * q^8 - 1011 * q^9 - 317 * q^10 + 1326 * q^11 - 648 * q^12 + 1006 * q^13 - 1272 * q^14 + 683 * q^15 + 3574 * q^16 + 200 * q^17 + 1861 * q^18 + 3361 * q^19 + 3825 * q^20 - 1320 * q^21 - 8768 * q^22 + 560 * q^23 - 7382 * q^24 - 3232 * q^25 - 3201 * q^26 - 122 * q^27 + 13934 * q^28 + 8887 * q^29 - 19449 * q^30 - 6749 * q^31 - 19086 * q^32 + 7106 * q^33 + 8423 * q^34 + 31118 * q^35 - 14112 * q^36 - 4514 * q^37 + 7072 * q^38 - 5404 * q^39 - 18519 * q^40 - 28996 * q^41 + 58118 * q^42 - 14998 * q^43 + 71050 * q^44 - 92096 * q^45 + 20052 * q^46 - 10742 * q^47 + 32927 * q^48 + 7472 * q^49 + 20362 * q^50 + 20250 * q^51 + 59532 * q^52 - 50572 * q^53 - 230084 * q^54 + 38544 * q^55 - 40355 * q^56 - 18087 * q^57 - 33436 * q^58 + 112654 * q^59 + 134093 * q^60 - 20120 * q^61 - 31491 * q^62 + 188227 * q^63 + 125164 * q^64 - 36578 * q^65 + 8803 * q^66 - 73824 * q^67 - 128456 * q^68 + 8005 * q^69 - 141610 * q^70 + 142842 * q^71 + 98466 * q^72 - 91624 * q^73 - 99720 * q^74 + 298358 * q^75 + 258288 * q^76 + 68051 * q^77 - 201116 * q^78 + 99734 * q^79 - 31261 * q^80 - 28441 * q^81 - 147772 * q^82 - 47340 * q^83 - 624232 * q^84 - 71734 * q^85 - 115526 * q^86 - 215924 * q^87 - 720684 * q^88 + 60402 * q^89 + 676108 * q^90 + 164172 * q^91 + 78997 * q^92 - 40793 * q^93 - 341874 * q^94 + 123541 * q^95 - 442140 * q^96 + 318476 * q^97 + 217473 * q^98 - 134770 * q^99

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