LMFDB - Embedded newform 49.6.c.h.18.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,6,Mod(18,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, 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("49.18");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	49.c (of order $3$, degree $2$, not 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:	$7.85880717084$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.54095201243136.19
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 102x^{6} + 320x^{5} + 4283x^{4} - 9104x^{3} - 85298x^{2} + 89904x + 714364 $ x^8 - 4x^7 - 102x^6 + 320x^5 + 4283x^4 - 9104x^3 - 85298x^2 + 89904*x + 714364
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			18.1
Root			$-4.10797 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	49.18
Dual form			49.6.c.h.30.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40754 - 2.43792i) q^{2} +(-3.27401 + 5.67075i) q^{3} +(12.0377 - 20.8499i) q^{4} +(22.9955 + 39.8294i) q^{5} +18.4331 q^{6} -157.856 q^{8} +(100.062 + 173.312i) q^{9} +O(q^{10})$	\(q+(-1.40754 - 2.43792i) q^{2} +(-3.27401 + 5.67075i) q^{3} +(12.0377 - 20.8499i) q^{4} +(22.9955 + 39.8294i) q^{5} +18.4331 q^{6} -157.856 q^{8} +(100.062 + 173.312i) q^{9} +(64.7341 - 112.123i) q^{10} +(275.890 - 477.856i) q^{11} +(78.8229 + 136.525i) q^{12} +1094.10 q^{13} -301.150 q^{15} +(-163.017 - 282.354i) q^{16} +(590.357 - 1022.53i) q^{17} +(281.681 - 487.886i) q^{18} +(583.063 + 1009.89i) q^{19} +1107.25 q^{20} -1553.30 q^{22} +(-22.1925 - 38.4386i) q^{23} +(516.823 - 895.163i) q^{24} +(504.912 - 874.533i) q^{25} +(-1539.98 - 2667.33i) q^{26} -2901.58 q^{27} +3329.02 q^{29} +(423.880 + 734.181i) q^{30} +(-4392.01 + 7607.18i) q^{31} +(-2984.61 + 5169.49i) q^{32} +(1806.53 + 3129.01i) q^{33} -3323.80 q^{34} +4818.05 q^{36} +(1278.56 + 2214.53i) q^{37} +(1641.37 - 2842.93i) q^{38} +(-3582.08 + 6204.35i) q^{39} +(-3629.99 - 6287.32i) q^{40} -12761.3 q^{41} -96.7714 q^{43} +(-6642.16 - 11504.6i) q^{44} +(-4601.94 + 7970.80i) q^{45} +(-62.4736 + 108.207i) q^{46} +(-3839.58 - 6650.34i) q^{47} +2134.88 q^{48} -2842.73 q^{50} +(3865.67 + 6695.53i) q^{51} +(13170.4 - 22811.8i) q^{52} +(5976.67 - 10351.9i) q^{53} +(4084.08 + 7073.83i) q^{54} +25377.0 q^{55} -7635.81 q^{57} +(-4685.71 - 8115.89i) q^{58} +(-4928.62 + 8536.62i) q^{59} +(-3625.15 + 6278.94i) q^{60} +(19258.9 + 33357.5i) q^{61} +24727.6 q^{62} +6370.65 q^{64} +(25159.4 + 43577.3i) q^{65} +(5085.53 - 8808.39i) q^{66} +(33774.5 - 58499.1i) q^{67} +(-14213.1 - 24617.7i) q^{68} +290.634 q^{69} -61374.6 q^{71} +(-15795.4 - 27358.4i) q^{72} +(-925.199 + 1602.49i) q^{73} +(3599.24 - 6234.07i) q^{74} +(3306.17 + 5726.45i) q^{75} +28074.9 q^{76} +20167.7 q^{78} +(4.26456 + 7.38644i) q^{79} +(7497.34 - 12985.8i) q^{80} +(-14815.2 + 25660.7i) q^{81} +(17961.9 + 31111.0i) q^{82} -95039.3 q^{83} +54302.3 q^{85} +(136.209 + 235.921i) q^{86} +(-10899.2 + 18878.0i) q^{87} +(-43551.0 + 75432.6i) q^{88} +(-26802.8 - 46423.8i) q^{89} +25909.6 q^{90} -1068.59 q^{92} +(-28758.9 - 49811.9i) q^{93} +(-10808.7 + 18721.2i) q^{94} +(-26815.7 + 46446.1i) q^{95} +(-19543.2 - 33849.9i) q^{96} +3110.79 q^{97} +110424. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 10 q^{2} - 10 q^{4} - 540 q^{8} - 220 q^{9}+O(q^{10}) $ 8 * q + 10 * q^2 - 10 * q^4 - 540 * q^8 - 220 * q^9	$ 8 q + 10 q^{2} - 10 q^{4} - 540 q^{8} - 220 q^{9} + 1952 q^{11} - 8192 q^{15} + 1566 q^{16} + 5974 q^{18} + 7048 q^{22} + 7136 q^{23} - 2764 q^{25} - 6704 q^{29} - 25608 q^{30} - 27810 q^{32} + 55340 q^{36} + 9208 q^{37} - 2464 q^{39} + 40896 q^{43} - 1900 q^{44} - 56712 q^{46} - 86140 q^{50} + 67408 q^{51} + 102920 q^{53} - 31152 q^{57} - 96972 q^{58} + 87080 q^{60} - 80636 q^{64} + 63168 q^{65} + 22896 q^{67} - 307648 q^{71} - 77358 q^{72} - 17596 q^{74} + 266112 q^{78} + 90688 q^{79} + 17204 q^{81} + 545312 q^{85} + 161860 q^{86} - 154812 q^{88} - 424400 q^{92} - 247760 q^{93} - 108224 q^{95} - 84544 q^{99}+O(q^{100}) $ 8 * q + 10 * q^2 - 10 * q^4 - 540 * q^8 - 220 * q^9 + 1952 * q^11 - 8192 * q^15 + 1566 * q^16 + 5974 * q^18 + 7048 * q^22 + 7136 * q^23 - 2764 * q^25 - 6704 * q^29 - 25608 * q^30 - 27810 * q^32 + 55340 * q^36 + 9208 * q^37 - 2464 * q^39 + 40896 * q^43 - 1900 * q^44 - 56712 * q^46 - 86140 * q^50 + 67408 * q^51 + 102920 * q^53 - 31152 * q^57 - 96972 * q^58 + 87080 * q^60 - 80636 * q^64 + 63168 * q^65 + 22896 * q^67 - 307648 * q^71 - 77358 * q^72 - 17596 * q^74 + 266112 * q^78 + 90688 * q^79 + 17204 * q^81 + 545312 * q^85 + 161860 * q^86 - 154812 * q^88 - 424400 * q^92 - 247760 * q^93 - 108224 * q^95 - 84544 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.40754	−	2.43792i	−0.248820	−	0.430968i	0.714379	−	0.699759i	$-0.246709\pi$
$2$	−1.40754	−	2.43792i	−0.248820	−	0.430968i	−0.963199	+	0.268791i	$0.913376\pi$
$3$	−3.27401	+	5.67075i	−0.210028	+	0.363779i	−0.951723	−	0.306958i	$-0.900689\pi$
$3$	−3.27401	+	5.67075i	−0.210028	+	0.363779i	0.741695	+	0.670737i	$0.234022\pi$
$4$	12.0377	−	20.8499i	0.376178	−	0.651559i
$5$	22.9955	+	39.8294i	0.411356	+	0.712490i	0.995038	−	0.0994921i	$-0.0317218\pi$
$5$	22.9955	+	39.8294i	0.411356	+	0.712490i	−0.583682	+	0.811982i	$0.698388\pi$
$6$	18.4331			0.209036
$7$		0			0
$7$		0			0
$8$	−157.856			−0.872041
$9$	100.062	+	173.312i	0.411777	+	0.713218i
$10$	64.7341	−	112.123i	0.204707	−	0.354563i
$11$	275.890	−	477.856i	0.687472	−	1.19074i	−0.285181	−	0.958474i	$-0.592054\pi$
$11$	275.890	−	477.856i	0.687472	−	1.19074i	0.972653	−	0.232263i	$-0.0746129\pi$
$12$	78.8229	+	136.525i	0.158015	+	0.273691i
$13$	1094.10			1.79555			0.897776	−	0.440453i	$-0.145182\pi$
$13$	1094.10			1.79555			0.897776	+	0.440453i	$0.145182\pi$
$14$		0			0
$15$	−301.150			−0.345585
$16$	−163.017	−	282.354i	−0.159197	−	0.275737i
$17$	590.357	−	1022.53i	0.495442	−	0.858130i	−0.504545	−	0.863386i	$-0.668340\pi$
$17$	590.357	−	1022.53i	0.495442	−	0.858130i	0.999986	+	0.00525555i	$0.00167290\pi$
$18$	281.681	−	487.886i	0.204916	−	0.354925i
$19$	583.063	+	1009.89i	0.370537	+	0.641789i	0.989648	−	0.143514i	$-0.0458404\pi$
$19$	583.063	+	1009.89i	0.370537	+	0.641789i	−0.619111	+	0.785303i	$0.712507\pi$
$20$	1107.25			0.618972
$21$		0			0
$22$	−1553.30			−0.684226
$23$	−22.1925	−	38.4386i	−0.00874757	−	0.0151512i	0.861618	−	0.507556i	$-0.169451\pi$
$23$	−22.1925	−	38.4386i	−0.00874757	−	0.0151512i	−0.870366	+	0.492405i	$0.836118\pi$
$24$	516.823	−	895.163i	0.183153	−	0.317230i
$25$	504.912	−	874.533i	0.161572	−	0.279850i
$26$	−1539.98	−	2667.33i	−0.446768	−	0.773826i
$27$	−2901.58			−0.765993
$28$		0			0
$29$	3329.02			0.735057			0.367529	−	0.930012i	$-0.380204\pi$
$29$	3329.02			0.735057			0.367529	+	0.930012i	$0.380204\pi$
$30$	423.880	+	734.181i	0.0859883	+	0.148936i
$31$	−4392.01	+	7607.18i	−0.820841	+	1.42174i	0.0842165	+	0.996447i	$0.473161\pi$
$31$	−4392.01	+	7607.18i	−0.820841	+	1.42174i	−0.905057	+	0.425290i	$0.860172\pi$
$32$	−2984.61	+	5169.49i	−0.515243	+	0.892427i
$33$	1806.53	+	3129.01i	0.288776	+	0.500175i
$34$	−3323.80			−0.493102
$35$		0			0
$36$	4818.05			0.619605
$37$	1278.56	+	2214.53i	0.153539	+	0.265937i	0.932526	−	0.361103i	$-0.117600\pi$
$37$	1278.56	+	2214.53i	0.153539	+	0.265937i	−0.778987	+	0.627040i	$0.784266\pi$
$38$	1641.37	−	2842.93i	0.184394	−	0.319379i
$39$	−3582.08	+	6204.35i	−0.377115	+	0.653183i
$40$	−3629.99	−	6287.32i	−0.358720	−	0.621321i
$41$	−12761.3			−1.18559			−0.592794	−	0.805354i	$-0.701975\pi$
$41$	−12761.3			−1.18559			−0.592794	+	0.805354i	$0.701975\pi$
$42$		0			0
$43$	−96.7714			−0.00798135			−0.00399067	−	0.999992i	$-0.501270\pi$
$43$	−96.7714			−0.00798135			−0.00399067	+	0.999992i	$0.501270\pi$
$44$	−6642.16	−	11504.6i	−0.517223	−	0.895857i
$45$	−4601.94	+	7970.80i	−0.338774	+	0.586774i
$46$	−62.4736	+	108.207i	−0.00435313	+	0.00753985i
$47$	−3839.58	−	6650.34i	−0.253535	−	0.439136i	0.710961	−	0.703231i	$-0.248260\pi$
$47$	−3839.58	−	6650.34i	−0.253535	−	0.439136i	−0.964497	+	0.264095i	$0.914927\pi$
$48$	2134.88			0.133743
$49$		0			0
$50$	−2842.73			−0.160809
$51$	3865.67	+	6695.53i	0.208113	+	0.360462i
$52$	13170.4	−	22811.8i	0.675446	−	1.16991i
$53$	5976.67	−	10351.9i	0.292260	−	0.506209i	−0.682084	−	0.731274i	$-0.738926\pi$
$53$	5976.67	−	10351.9i	0.292260	−	0.506209i	0.974344	+	0.225065i	$0.0722594\pi$
$54$	4084.08	+	7073.83i	0.190594	+	0.330119i
$55$	25377.0			1.13118
$56$		0			0
$57$	−7635.81			−0.311292
$58$	−4685.71	−	8115.89i	−0.182897	−	0.316786i
$59$	−4928.62	+	8536.62i	−0.184330	+	0.319268i	−0.943350	−	0.331798i	$-0.892345\pi$
$59$	−4928.62	+	8536.62i	−0.184330	+	0.319268i	0.759021	+	0.651066i	$0.225678\pi$
$60$	−3625.15	+	6278.94i	−0.130001	+	0.225169i
$61$	19258.9	+	33357.5i	0.662686	+	1.14781i	0.979907	+	0.199454i	$0.0639169\pi$
$61$	19258.9	+	33357.5i	0.662686	+	1.14781i	−0.317221	+	0.948352i	$0.602750\pi$
$62$	24727.6			0.816965
$63$		0			0
$64$	6370.65			0.194417
$65$	25159.4	+	43577.3i	0.738612	+	1.27931i
$66$	5085.53	−	8808.39i	0.143706	−	0.248907i
$67$	33774.5	−	58499.1i	0.919182	−	1.59207i	0.118521	−	0.992952i	$-0.462185\pi$
$67$	33774.5	−	58499.1i	0.919182	−	1.59207i	0.800661	−	0.599118i	$-0.204482\pi$
$68$	−14213.1	−	24617.7i	−0.372748	−	0.645619i
$69$	290.634			0.00734893
$70$		0			0
$71$	−61374.6			−1.44492			−0.722458	−	0.691415i	$-0.756988\pi$
$71$	−61374.6			−1.44492			−0.722458	+	0.691415i	$0.756988\pi$
$72$	−15795.4	−	27358.4i	−0.359086	−	0.621955i
$73$	−925.199	+	1602.49i	−0.0203202	+	0.0351956i	−0.876007	−	0.482299i	$-0.839802\pi$
$73$	−925.199	+	1602.49i	−0.0203202	+	0.0351956i	0.855686	+	0.517495i	$0.173135\pi$
$74$	3599.24	−	6234.07i	0.0764068	−	0.132340i
$75$	3306.17	+	5726.45i	0.0678691	+	0.117553i
$76$	28074.9			0.557551
$77$		0			0
$78$	20167.7			0.375335
$79$	4.26456	+	7.38644i	7.68788e−5	+	0.000133158i	0.866064	−	0.499933i	$-0.166642\pi$
$79$	4.26456	+	7.38644i	7.68788e−5	+	0.000133158i	−0.865987	+	0.500067i	$0.833309\pi$
$80$	7497.34	−	12985.8i	0.130973	−	0.226852i
$81$	−14815.2	+	25660.7i	−0.250897	+	0.434566i
$82$	17961.9	+	31111.0i	0.294998	+	0.510951i
$83$	−95039.3			−1.51429			−0.757143	−	0.653249i	$-0.773405\pi$
$83$	−95039.3			−1.51429			−0.757143	+	0.653249i	$0.773405\pi$
$84$		0			0
$85$	54302.3			0.815212
$86$	136.209	+	235.921i	0.00198592	+	0.00343971i
$87$	−10899.2	+	18878.0i	−0.154382	+	0.267398i
$88$	−43551.0	+	75432.6i	−0.599503	+	1.03837i
$89$	−26802.8	−	46423.8i	−0.358678	−	0.621249i	0.629062	−	0.777355i	$-0.283439\pi$
$89$	−26802.8	−	46423.8i	−0.358678	−	0.621249i	−0.987740	+	0.156106i	$0.950106\pi$
$90$	25909.6			0.337175
$91$		0			0
$92$	−1068.59			−0.0131626
$93$	−28758.9	−	49811.9i	−0.344798	−	0.597208i
$94$	−10808.7	+	18721.2i	−0.126169	+	0.218531i
$95$	−26815.7	+	46446.1i	−0.304846	+	0.528008i
$96$	−19543.2	−	33849.9i	−0.216431	−	0.374869i
$97$	3110.79			0.0335693			0.0167846	−	0.999859i	$-0.494657\pi$
$97$	3110.79			0.0335693			0.0167846	+	0.999859i	$0.494657\pi$
$98$		0			0
$99$	110424.			1.13234
$100$	−12155.9	−	21054.7i	−0.121559	−	0.210547i
$101$	−10918.0	+	18910.4i	−0.106497	+	0.184458i	−0.914349	−	0.404927i	$-0.867297\pi$
$101$	−10918.0	+	18910.4i	−0.106497	+	0.184458i	0.807852	+	0.589386i	$0.200630\pi$
$102$	10882.1	−	18848.4i	0.103565	−	0.179380i
$103$	−32670.7	−	56587.3i	−0.303435	−	0.525565i	0.673477	−	0.739208i	$-0.264800\pi$
$103$	−32670.7	−	56587.3i	−0.303435	−	0.525565i	−0.976912	+	0.213644i	$0.931467\pi$
$104$	−172710.			−1.56579
$105$		0			0
$106$	−33649.5			−0.290880
$107$	54478.7	+	94359.8i	0.460010	+	0.796760i	0.998961	−	0.0455767i	$-0.0145125\pi$
$107$	54478.7	+	94359.8i	0.460010	+	0.796760i	−0.538951	+	0.842337i	$0.681179\pi$
$108$	−34928.3	+	60497.6i	−0.288150	+	0.499090i
$109$	−43364.3	+	75109.2i	−0.349596	+	0.605518i	−0.986178	−	0.165691i	$-0.947014\pi$
$109$	−43364.3	+	75109.2i	−0.349596	+	0.605518i	0.636582	+	0.771209i	$0.280348\pi$
$110$	−35719.0	−	61867.2i	−0.281461	−	0.487504i
$111$	−16744.1			−0.128989
$112$		0			0
$113$	−101496.			−0.747746			−0.373873	−	0.927480i	$-0.621970\pi$
$113$	−101496.			−0.747746			−0.373873	+	0.927480i	$0.621970\pi$
$114$	10747.7	+	18615.5i	0.0774556	+	0.134157i
$115$	1020.66	−	1767.83i	0.00719674	−	0.0124651i
$116$	40073.7	−	69409.6i	0.276512	−	0.478933i
$117$	109477.	+	189620.i	0.739366	+	1.28062i
$118$	27748.9			0.183459
$119$		0			0
$120$	47538.4			0.301364
$121$	−71705.6	−	124198.i	−0.445235	−	0.771170i
$122$	54215.3	−	93903.7i	0.329779	−	0.571193i
$123$	41780.5	−	72365.9i	0.249006	−	0.431292i
$124$	105739.	+	183146.i	0.617564	+	1.06965i
$125$	190165.			1.08857
$126$		0			0
$127$	−3094.61			−0.0170253			−0.00851267	−	0.999964i	$-0.502710\pi$
$127$	−3094.61			−0.0170253			−0.00851267	+	0.999964i	$0.502710\pi$
$128$	86540.5	+	149892.i	0.466868	+	0.808639i
$129$	316.830	−	548.766i	0.00167630	−	0.00290344i
$130$	70825.4	−	122673.i	0.367562	−	0.636636i
$131$	−126715.	−	219478.i	−0.645136	−	1.11741i	−0.984270	−	0.176671i	$-0.943467\pi$
$131$	−126715.	−	219478.i	−0.645136	−	1.11741i	0.339134	−	0.940738i	$-0.389866\pi$
$132$	86986.0			0.434525
$133$		0			0
$134$	−190155.			−0.914842
$135$	−66723.3	−	115568.i	−0.315096	−	0.545763i
$136$	−93191.6	+	161413.i	−0.432045	+	0.748324i
$137$	48576.4	−	84136.9i	0.221118	−	0.382988i	−0.734030	−	0.679117i	$-0.762363\pi$
$137$	48576.4	−	84136.9i	0.221118	−	0.382988i	0.955148	+	0.296130i	$0.0956960\pi$
$138$	−409.078	−	708.544i	−0.00182856	−	0.00316715i
$139$	210308.			0.923249			0.461624	−	0.887076i	$-0.347267\pi$
$139$	210308.			0.923249			0.461624	+	0.887076i	$0.347267\pi$
$140$		0			0
$141$	50283.2			0.212998
$142$	86387.0	+	149627.i	0.359524	+	0.622713i
$143$	301851.	−	522822.i	1.23439	−	2.13803i
$144$	32623.6	−	56505.8i	0.131107	−	0.227084i
$145$	76552.5	+	132593.i	0.302370	+	0.523721i
$146$	5209.01			0.0202243
$147$		0			0
$148$	61563.7			0.231031
$149$	−70203.2	−	121595.i	−0.259055	−	0.448696i	0.706934	−	0.707279i	$-0.250078\pi$
$149$	−70203.2	−	121595.i	−0.259055	−	0.448696i	−0.965989	+	0.258584i	$0.916744\pi$
$150$	9307.11	−	16120.4i	0.0337743	−	0.0584988i
$151$	−59847.9	+	103660.i	−0.213603	+	0.369971i	−0.952839	−	0.303475i	$-0.901853\pi$
$151$	−59847.9	+	103660.i	−0.213603	+	0.369971i	0.739237	+	0.673446i	$0.235186\pi$
$152$	−92040.1	−	159418.i	−0.323123	−	0.559666i
$153$	236289.			0.816045
$154$		0			0
$155$	−403986.			−1.35063
$156$	86240.0	+	149372.i	0.283725	+	0.491426i
$157$	−48808.4	+	84538.7i	−0.158032	+	0.273720i	−0.934159	−	0.356857i	$-0.883848\pi$
$157$	−48808.4	+	84538.7i	−0.158032	+	0.273720i	0.776127	+	0.630577i	$0.217182\pi$
$158$	12.0051	−	20.7934i	3.82579e−5	−	6.62647e-5i
$159$	39135.3	+	67784.3i	0.122765	+	0.212636i
$160$	−274530.			−0.847794
$161$		0			0
$162$	83411.8			0.249712
$163$	−91339.0	−	158204.i	−0.269270	−	0.466389i	0.699404	−	0.714727i	$-0.253449\pi$
$163$	−91339.0	−	158204.i	−0.269270	−	0.466389i	−0.968673	+	0.248338i	$0.920116\pi$
$164$	−153616.	+	266071.i	−0.445992	+	0.772481i
$165$	−83084.4	+	143906.i	−0.237580	+	0.411501i
$166$	133771.	+	231699.i	0.376784	+	0.652609i
$167$	−451674.			−1.25324			−0.626619	−	0.779326i	$-0.715562\pi$
$167$	−451674.			−1.25324			−0.626619	+	0.779326i	$0.715562\pi$
$168$		0			0
$169$	825757.			2.22400
$170$	−76432.5	−	132385.i	−0.202841	−	0.351331i
$171$	−116685.	+	202104.i	−0.305157	+	0.528547i
$172$	−1164.90	+	2017.67i	−0.00300240	+	0.00520031i
$173$	−185824.	−	321856.i	−0.472047	−	0.817610i	0.527441	−	0.849592i	$-0.323152\pi$
$173$	−185824.	−	321856.i	−0.472047	−	0.817610i	−0.999488	+	0.0319815i	$0.989818\pi$
$174$	61364.2			0.153653
$175$		0			0
$176$	−179900.			−0.437773
$177$	−32272.7	−	55897.9i	−0.0774287	−	0.134110i
$178$	−75451.8	+	130686.i	−0.178492	+	0.309158i
$179$	−42501.7	+	73615.1i	−0.0991457	+	0.171725i	−0.911331	−	0.411674i	$-0.864944\pi$
$179$	−42501.7	+	73615.1i	−0.0991457	+	0.171725i	0.812186	+	0.583399i	$0.198278\pi$
$180$	110794.	+	191900.i	0.254878	+	0.441462i
$181$	−379442.			−0.860892			−0.430446	−	0.902616i	$-0.641644\pi$
$181$	−379442.			−0.860892			−0.430446	+	0.902616i	$0.641644\pi$
$182$		0			0
$183$	−252216.			−0.556730
$184$	3503.23	+	6067.77i	0.00762824	+	0.0132125i
$185$	−58802.4	+	101849.i	−0.126318	+	0.218789i
$186$	−80958.5	+	140224.i	−0.171585	+	0.297194i
$187$	−325748.	−	564212.i	−0.681204	−	1.17988i
$188$	−184878.			−0.381497
$189$		0			0
$190$	150976.			0.303406
$191$	461098.	+	798645.i	0.914555	+	1.58406i	0.807552	+	0.589796i	$0.200792\pi$
$191$	461098.	+	798645.i	0.914555	+	1.58406i	0.107003	+	0.994259i	$0.465875\pi$
$192$	−20857.6	+	36126.4i	−0.0408329	+	0.0707247i
$193$	−252553.	+	437435.i	−0.488045	+	0.845319i	−0.999905	−	0.0137498i	$-0.995623\pi$
$193$	−252553.	+	437435.i	−0.488045	+	0.845319i	0.511860	+	0.859069i	$0.328956\pi$
$194$	−4378.55	−	7583.88i	−0.00835269	−	0.0144673i
$195$	−329488.			−0.620516
$196$		0			0
$197$	251505.			0.461723			0.230861	−	0.972987i	$-0.425846\pi$
$197$	251505.			0.461723			0.230861	+	0.972987i	$0.425846\pi$
$198$	−155426.	−	269206.i	−0.281748	−	0.488002i
$199$	104017.	−	180162.i	0.186196	−	0.322501i	−0.757783	−	0.652507i	$-0.773717\pi$
$199$	104017.	−	180162.i	0.186196	−	0.322501i	0.943979	+	0.330006i	$0.107051\pi$
$200$	−79703.5	+	138050.i	−0.140897	+	0.244041i
$201$	221156.	+	383053.i	0.386107	+	0.668757i
$202$	61469.7			0.105994
$203$		0			0
$204$	186135.			0.313150
$205$	−293452.	−	508274.i	−0.487700	−	0.844720i
$206$	−91970.5	+	159297.i	−0.151001	+	0.261542i
$207$	4441.25	−	7692.47i	0.00720409	−	0.0124779i
$208$	−178357.	−	308923.i	−0.285846	−	0.495100i
$209$	643446.			1.01893
$210$		0			0
$211$	−640577.			−0.990525			−0.495262	−	0.868744i	$-0.664928\pi$
$211$	−640577.			−0.990525			−0.495262	+	0.868744i	$0.664928\pi$
$212$	−143890.	−	249225.i	−0.219883	−	0.380849i
$213$	200941.	−	348040.i	0.303472	−	0.525630i
$214$	153361.	−	265630.i	0.228919	−	0.396499i
$215$	−2225.31	−	3854.35i	−0.00328318	−	0.00568663i
$216$	458032.			0.667977
$217$		0			0
$218$	244148.			0.347945
$219$	−6058.22	−	10493.1i	−0.00853561	−	0.0147841i
$220$	305480.	−	529107.i	0.425526	−	0.737033i
$221$	645909.	−	1.11875e6i	0.889591	−	1.54082i
$222$	23567.9	+	40820.8i	0.0320951	+	0.0555903i
$223$	390135.			0.525354			0.262677	−	0.964884i	$-0.415395\pi$
$223$	390135.			0.525354			0.262677	+	0.964884i	$0.415395\pi$
$224$		0			0
$225$	202089.			0.266126
$226$	142860.	+	247440.i	0.186054	+	0.322255i
$227$	−145676.	+	252319.i	−0.187639	+	0.325001i	−0.944463	−	0.328618i	$-0.893417\pi$
$227$	−145676.	+	252319.i	−0.187639	+	0.325001i	0.756823	+	0.653620i	$0.226750\pi$
$228$	−91917.5	+	159206.i	−0.117101	+	0.202825i
$229$	615202.	+	1.06556e6i	0.775227	+	1.34273i	0.934667	+	0.355526i	$0.115698\pi$
$229$	615202.	+	1.06556e6i	0.775227	+	1.34273i	−0.159439	+	0.987208i	$0.550969\pi$
$230$	−5746.45			−0.00716276
$231$		0			0
$232$	−525506.			−0.641000
$233$	−57139.3	−	98968.1i	−0.0689517	−	0.119428i	0.829488	−	0.558524i	$-0.188632\pi$
$233$	−57139.3	−	98968.1i	−0.0689517	−	0.119428i	−0.898440	+	0.439096i	$0.855299\pi$
$234$	308187.	−	533795.i	0.367938	−	0.637287i
$235$	176586.	−	305856.i	0.208587	−	0.361283i
$236$	118658.	+	205522.i	0.138681	+	0.240203i
$237$	−55.8489			−6.45867e−5
$238$		0			0
$239$	−1.14782e6			−1.29981			−0.649906	−	0.760014i	$-0.725192\pi$
$239$	−1.14782e6			−1.29981			−0.649906	+	0.760014i	$0.725192\pi$
$240$	49092.7	+	85031.1i	0.0550160	+	0.0952905i
$241$	−406354.	+	703825.i	−0.450673	+	0.780589i	−0.998428	−	0.0560501i	$-0.982149\pi$
$241$	−406354.	+	703825.i	−0.450673	+	0.780589i	0.547755	+	0.836639i	$0.315483\pi$
$242$	−201856.	+	349626.i	−0.221567	+	0.383764i
$243$	−449552.	−	778647.i	−0.488387	−	0.845912i
$244$	927332.			0.997150
$245$		0			0
$246$	−235230.			−0.247831
$247$	637928.	+	1.10492e6i	0.665318	+	1.15236i
$248$	693306.	−	1.20084e6i	0.715806	−	1.23981i
$249$	311159.	−	538944.i	0.318042	−	0.550865i
$250$	−267664.	−	463608.i	−0.270857	−	0.469138i
$251$	−406772.			−0.407537			−0.203768	−	0.979019i	$-0.565319\pi$
$251$	−406772.			−0.407537			−0.203768	+	0.979019i	$0.565319\pi$
$252$		0			0
$253$	−24490.8			−0.0240548
$254$	4355.77	+	7544.41i	0.00423624	+	0.00733738i
$255$	−177786.	+	307935.i	−0.171217	+	0.296557i
$256$	345548.	−	598507.i	0.329540	−	0.570781i
$257$	848562.	+	1.46975e6i	0.801403	+	1.38807i	0.918693	+	0.394973i	$0.129246\pi$
$257$	848562.	+	1.46975e6i	0.801403	+	1.38807i	−0.117290	+	0.993098i	$0.537421\pi$
$258$	−1783.80			−0.00166839
$259$		0			0
$260$	1.21144e6			1.11140
$261$	333107.	+	576959.i	0.302679	+	0.524256i
$262$	−356713.	+	617846.i	−0.321045	+	0.556067i
$263$	−102847.	+	178136.i	−0.0916859	+	0.158805i	−0.908221	−	0.418492i	$-0.862559\pi$
$263$	−102847.	+	178136.i	−0.0916859	+	0.158805i	0.816535	+	0.577296i	$0.195892\pi$
$264$	−285173.	−	493934.i	−0.251825	−	0.436173i
$265$	549746.			0.480892
$266$		0			0
$267$	351010.			0.301330
$268$	−813133.	−	1.40839e6i	−0.691551	−	1.19780i
$269$	−867123.	+	1.50190e6i	−0.730635	+	1.26550i	0.225978	+	0.974132i	$0.427442\pi$
$269$	−867123.	+	1.50190e6i	−0.730635	+	1.26550i	−0.956612	+	0.291364i	$0.905891\pi$
$270$	−187831.	+	325333.i	−0.156804	+	0.271593i
$271$	−184521.	−	319600.i	−0.152624	−	0.264352i	0.779567	−	0.626318i	$-0.215439\pi$
$271$	−184521.	−	319600.i	−0.152624	−	0.264352i	−0.932191	+	0.361966i	$0.882106\pi$
$272$	−384954.			−0.315491
$273$		0			0
$274$	−273492.			−0.220074
$275$	−278601.	−	482550.i	−0.222152	−	0.384779i
$276$	3498.56	−	6059.69i	0.00276450	−	0.00478826i
$277$	−613835.	+	1.06319e6i	−0.480676	+	0.832554i	−0.999754	−	0.0221720i	$-0.992942\pi$
$277$	−613835.	+	1.06319e6i	−0.480676	+	0.832554i	0.519079	+	0.854727i	$0.326275\pi$
$278$	−296016.	−	512715.i	−0.229722	−	0.397891i
$279$	−1.75789e6			−1.35201
$280$		0			0
$281$	2.00671e6			1.51607			0.758035	−	0.652214i	$-0.226159\pi$
$281$	2.00671e6			1.51607			0.758035	+	0.652214i	$0.226159\pi$
$282$	−70775.4	−	122587.i	−0.0529980	−	0.0917953i
$283$	892905.	−	1.54656e6i	0.662734	−	1.14789i	−0.317160	−	0.948372i	$-0.602729\pi$
$283$	892905.	−	1.54656e6i	0.662734	−	1.14789i	0.979894	−	0.199517i	$-0.0639374\pi$
$284$	−738808.	+	1.27965e6i	−0.543545	+	0.941448i
$285$	−175589.	−	304130.i	−0.128052	−	0.221793i
$286$	−1.69947e6			−1.22856
$287$		0			0
$288$	−1.19458e6			−0.848660
$289$	12885.4	+	22318.1i	0.00907513	+	0.0157186i
$290$	215501.	−	373258.i	0.150471	−	0.260624i
$291$	−10184.8	+	17640.5i	−0.00705047	+	0.0122118i
$292$	22274.5	+	38580.6i	0.0152880	+	0.0264796i
$293$	853248.			0.580639			0.290319	−	0.956930i	$-0.406238\pi$
$293$	853248.			0.580639			0.290319	+	0.956930i	$0.406238\pi$
$294$		0			0
$295$	−453345.			−0.303301
$296$	−201829.	−	349578.i	−0.133892	−	0.231908i
$297$	−800518.	+	1.38654e6i	−0.526599	+	0.912096i
$298$	−197627.	+	342300.i	−0.128916	+	0.223289i
$299$	−24280.8	−	42055.6i	−0.0157067	−	0.0272048i
$300$	159194.			0.102123
$301$		0			0
$302$	336952.			0.212594
$303$	−71490.9	−	123826.i	−0.0447347	−	0.0774827i
$304$	190099.	−	329261.i	0.117977	−	0.204341i
$305$	−885739.	+	1.53414e6i	−0.545200	+	0.944315i
$306$	−332585.	−	576054.i	−0.203048	−	0.351690i
$307$	−1.96068e6			−1.18730			−0.593652	−	0.804722i	$-0.702314\pi$
$307$	−1.96068e6			−1.18730			−0.593652	+	0.804722i	$0.702314\pi$
$308$		0			0
$309$	427857.			0.254919
$310$	568625.	+	984888.i	0.336064	+	0.582080i
$311$	−431802.	+	747903.i	−0.253153	+	0.438474i	−0.964392	−	0.264476i	$-0.914801\pi$
$311$	−431802.	+	747903.i	−0.253153	+	0.438474i	0.711239	+	0.702950i	$0.248134\pi$
$312$	565454.	−	979396.i	0.328860	−	0.569602i
$313$	−550235.	−	953035.i	−0.317459	−	0.549855i	0.662498	−	0.749063i	$-0.269496\pi$
$313$	−550235.	−	953035.i	−0.317459	−	0.549855i	−0.979957	+	0.199209i	$0.936163\pi$
$314$	274799.			0.157286
$315$		0			0
$316$	205.342			0.000115680
$317$	−747954.	−	1.29549e6i	−0.418048	−	0.724081i	0.577695	−	0.816253i	$-0.303952\pi$
$317$	−747954.	−	1.29549e6i	−0.418048	−	0.724081i	−0.995743	+	0.0921719i	$0.970619\pi$
$318$	110169.	−	190818.i	0.0610929	−	0.105816i
$319$	918444.	−	1.59079e6i	0.505331	−	0.875259i
$320$	146496.	+	253739.i	0.0799746	+	0.138520i
$321$	−713454.			−0.386459
$322$		0			0
$323$	1.37686e6			0.734318
$324$	356682.	+	617791.i	0.188764	+	0.326948i
$325$	552423.	−	956824.i	0.290110	−	0.502486i
$326$	−257126.	+	445355.i	−0.133999	+	0.232093i
$327$	−283950.	−	491816.i	−0.146850	−	0.254351i
$328$	2.01445e6			1.03388
$329$		0			0
$330$	467777.			0.236458
$331$	1.37008e6	+	2.37304e6i	0.687345	+	1.19052i	0.972694	+	0.232093i	$0.0745573\pi$
$331$	1.37008e6	+	2.37304e6i	0.687345	+	1.19052i	−0.285348	+	0.958424i	$0.592109\pi$
$332$	−1.14405e6	+	1.98156e6i	−0.569640	+	0.986646i
$333$	−255870.	+	443180.i	−0.126447	+	0.219013i
$334$	635747.	+	1.10115e6i	0.311830	+	0.540106i
$335$	3.10665e6			1.51245
$336$		0			0
$337$	−2.31353e6			−1.10968			−0.554842	−	0.831956i	$-0.687221\pi$
$337$	−2.31353e6			−1.10968			−0.554842	+	0.831956i	$0.687221\pi$
$338$	−1.16228e6	−	2.01313e6i	−0.553376	−	0.958475i
$339$	332300.	−	575560.i	0.157047	−	0.272014i
$340$	653674.	−	1.13220e6i	0.306665	−	0.531159i
$341$	2.42343e6	+	4.19750e6i	1.12861	+	1.95481i
$342$	656951.			0.303716
$343$		0			0
$344$	15276.0			0.00696006
$345$	6683.29	+	11575.8i	0.00302303	+	0.00523604i
$346$	−523107.	+	906048.i	−0.234909	+	0.406875i
$347$	1.52963e6	−	2.64940e6i	0.681966	−	1.18120i	−0.292414	−	0.956292i	$-0.594459\pi$
$347$	1.52963e6	−	2.64940e6i	0.681966	−	1.18120i	0.974380	−	0.224908i	$-0.0722081\pi$
$348$	262403.	+	454495.i	0.116150	+	0.201178i
$349$	−210232.			−0.0923921			−0.0461961	−	0.998932i	$-0.514710\pi$
$349$	−210232.			−0.0923921			−0.0461961	+	0.998932i	$0.514710\pi$
$350$		0			0
$351$	−3.17461e6			−1.37538
$352$	1.64685e6	+	2.85243e6i	0.708430	+	1.22704i
$353$	1.88395e6	−	3.26310e6i	0.804697	−	1.39378i	−0.111798	−	0.993731i	$-0.535661\pi$
$353$	1.88395e6	−	3.26310e6i	0.804697	−	1.39378i	0.916495	−	0.400045i	$-0.131006\pi$
$354$	−90850.0	+	157357.i	−0.0385316	+	0.0667386i
$355$	−1.41134e6	−	2.44451e6i	−0.594376	−	1.02949i
$356$	−1.29057e6			−0.539707
$357$		0			0
$358$	239291.			0.0986776
$359$	−503608.	−	872275.i	−0.206232	−	0.357205i	0.744292	−	0.667854i	$-0.232787\pi$
$359$	−503608.	−	872275.i	−0.206232	−	0.357205i	−0.950525	+	0.310649i	$0.899454\pi$
$360$	726446.	−	1.25824e6i	0.295425	−	0.511691i
$361$	558124.	−	966700.i	0.225405	−	0.390412i
$362$	534078.	+	925050.i	0.214207	+	0.371017i
$363$	939058.			0.374047
$364$		0			0
$365$	−85101.8			−0.0334354
$366$	355003.	+	614883.i	0.138525	+	0.239933i
$367$	763248.	−	1.32198e6i	0.295802	−	0.512343i	−0.679369	−	0.733796i	$-0.737747\pi$
$367$	763248.	−	1.32198e6i	0.295802	−	0.512343i	0.975171	+	0.221453i	$0.0710799\pi$
$368$	−7235.54	+	12532.3i	−0.00278517	+	0.00482405i
$369$	−1.27691e6	−	2.21168e6i	−0.488198	−	0.845583i
$370$	331066.			0.125722
$371$		0			0
$372$	−1.38476e6			−0.518822
$373$	−2.43149e6	−	4.21146e6i	−0.904898	−	1.56733i	−0.821054	−	0.570850i	$-0.806614\pi$
$373$	−2.43149e6	−	4.21146e6i	−0.904898	−	1.56733i	−0.0838438	−	0.996479i	$-0.526720\pi$
$374$	−917004.	+	1.58830e6i	−0.338994	+	0.587155i
$375$	−622601.	+	1.07838e6i	−0.228629	+	0.395997i
$376$	606101.	+	1.04980e6i	0.221093	+	0.382945i
$377$	3.64227e6			1.31983
$378$		0			0
$379$	630878.			0.225604			0.112802	−	0.993617i	$-0.464017\pi$
$379$	630878.			0.225604			0.112802	+	0.993617i	$0.464017\pi$
$380$	645597.	+	1.11821e6i	0.229352	+	0.397249i
$381$	10131.8	−	17548.7i	0.00357579	−	0.00619346i
$382$	1.29802e6	−	2.24824e6i	0.455118	−	0.788288i
$383$	−282822.	−	489862.i	−0.0985182	−	0.170639i	0.812553	−	0.582887i	$-0.198077\pi$
$383$	−282822.	−	489862.i	−0.0985182	−	0.170639i	−0.911072	+	0.412248i	$0.864744\pi$
$384$	−1.13334e6			−0.392221
$385$		0			0
$386$	1.42191e6			0.485741
$387$	−9683.12	−	16771.7i	−0.00328653	−	0.00569244i
$388$	37446.7	−	64859.7i	0.0126280	−	0.0218723i
$389$	−296106.	+	512870.i	−0.0992140	+	0.171844i	−0.911360	−	0.411611i	$-0.864966\pi$
$389$	−296106.	+	512870.i	−0.0992140	+	0.171844i	0.812146	+	0.583455i	$0.198300\pi$
$390$	463766.	+	803266.i	0.154396	+	0.267423i
$391$	−52406.1			−0.0173356
$392$		0			0
$393$	1.65947e6			0.541986
$394$	−354003.	−	613151.i	−0.114886	−	0.198988i
$395$	−196.132	+	339.710i	−6.32492e−5	+	0.000109551i
$396$	1.32925e6	−	2.30233e6i	0.425961	−	0.737786i
$397$	−671558.	−	1.16317e6i	−0.213849	−	0.370397i	0.739067	−	0.673632i	$-0.235267\pi$
$397$	−671558.	−	1.16317e6i	−0.213849	−	0.370397i	−0.952916	+	0.303235i	$0.901933\pi$
$398$	−585629.			−0.185317
$399$		0			0
$400$	−329238.			−0.102887
$401$	1.84358e6	+	3.19318e6i	0.572534	+	0.991658i	0.996305	+	0.0858884i	$0.0273729\pi$
$401$	1.84358e6	+	3.19318e6i	0.572534	+	0.991658i	−0.423771	+	0.905769i	$0.639294\pi$
$402$	622569.	−	1.07832e6i	0.192142	−	0.332800i
$403$	−4.80529e6	+	8.32300e6i	−1.47386	+	2.55280i
$404$	262854.	+	455276.i	0.0801236	+	0.138778i
$405$	−1.36273e6			−0.412832
$406$		0			0
$407$	1.41097e6			0.422214
$408$	−610220.	−	1.05693e6i	−0.181483	−	0.314338i
$409$	−728151.	+	1.26119e6i	−0.215235	+	0.372798i	−0.953345	−	0.301882i	$-0.902385\pi$
$409$	−728151.	+	1.26119e6i	−0.215235	+	0.372798i	0.738110	+	0.674680i	$0.235718\pi$
$410$	−826089.	+	1.43083e6i	−0.242698	+	0.420366i
$411$	318079.	+	550929.i	0.0928818	+	0.160876i
$412$	−1.57312e6			−0.456582
$413$		0			0
$414$	−25004.9			−0.00717008
$415$	−2.18548e6	−	3.78536e6i	−0.622911	−	1.07891i
$416$	−3.26545e6	+	5.65593e6i	−0.925145	+	1.60240i
$417$	−688550.	+	1.19260e6i	−0.193908	+	0.335858i
$418$	−905674.	−	1.56867e6i	−0.253531	−	0.439129i
$419$	−2.92192e6			−0.813080			−0.406540	−	0.913633i	$-0.633265\pi$
$419$	−2.92192e6			−0.813080			−0.406540	+	0.913633i	$0.633265\pi$
$420$		0			0
$421$	2.01999e6			0.555450			0.277725	−	0.960661i	$-0.410420\pi$
$421$	2.01999e6			0.555450			0.277725	+	0.960661i	$0.410420\pi$
$422$	901636.	+	1.56168e6i	0.246462	+	0.426885i
$423$	768389.	−	1.33089e6i	0.208800	−	0.361652i
$424$	−943454.	+	1.63411e6i	−0.254863	+	0.441435i
$425$	−596156.	−	1.03257e6i	−0.160099	−	0.277299i
$426$	−1.13133e6			−0.302040
$427$		0			0
$428$	2.62319e6			0.692182
$429$	1.97653e6	+	3.42344e6i	0.518513	+	0.898090i
$430$	−6264.41	+	10850.3i	−0.00163384	+	0.00282989i
$431$	2.71900e6	−	4.70944e6i	0.705043	−	1.22117i	−0.261633	−	0.965167i	$-0.584261\pi$
$431$	2.71900e6	−	4.70944e6i	0.705043	−	1.22117i	0.966676	−	0.256003i	$-0.0824057\pi$
$432$	473008.	+	819274.i	0.121944	+	0.211213i
$433$	−3.77335e6			−0.967179			−0.483590	−	0.875295i	$-0.660667\pi$
$433$	−3.77335e6			−0.967179			−0.483590	+	0.875295i	$0.660667\pi$
$434$		0			0
$435$	−1.00253e6			−0.254025
$436$	1.04401e6	+	1.80828e6i	0.263020	+	0.455565i
$437$	25879.3	−	44824.3i	0.00648260	−	0.0112282i
$438$	−17054.3	+	29539.0i	−0.00424766	+	0.00735716i
$439$	−1.17575e6	−	2.03646e6i	−0.291175	−	0.504330i	0.682913	−	0.730500i	$-0.260713\pi$
$439$	−1.17575e6	−	2.03646e6i	−0.291175	−	0.504330i	−0.974088	+	0.226170i	$0.927379\pi$
$440$	−4.00591e6			−0.986439
$441$		0			0
$442$	−3.63656e6			−0.885391
$443$	−2.40188e6	−	4.16019e6i	−0.581491	−	1.00717i	−0.995303	−	0.0968092i	$-0.969136\pi$
$443$	−2.40188e6	−	4.16019e6i	−0.581491	−	1.00717i	0.413812	−	0.910362i	$-0.364197\pi$
$444$	−201560.	+	349112.i	−0.0485229	+	0.0840441i
$445$	1.23269e6	−	2.13508e6i	0.295089	−	0.511110i
$446$	−549129.	−	951119.i	−0.130718	−	0.226411i
$447$	919383.			0.217634
$448$		0			0
$449$	−2.76805e6			−0.647975			−0.323987	−	0.946061i	$-0.605024\pi$
$449$	−2.76805e6			−0.647975			−0.323987	+	0.946061i	$0.605024\pi$
$450$	−284448.	−	492679.i	−0.0662174	−	0.114692i
$451$	−3.52071e6	+	6.09805e6i	−0.815059	+	1.41172i
$452$	−1.22178e6	+	2.11619e6i	−0.281285	+	0.487201i
$453$	−391885.	−	678765.i	−0.0897249	−	0.155408i
$454$	820179.			0.186754
$455$		0			0
$456$	1.20536e6			0.271459
$457$	−120783.	−	209203.i	−0.0270530	−	0.0468573i	0.852182	−	0.523246i	$-0.175279\pi$
$457$	−120783.	−	209203.i	−0.0270530	−	0.0468573i	−0.879235	+	0.476388i	$0.841946\pi$
$458$	1.73184e6	−	2.99963e6i	0.385784	−	0.668197i
$459$	−1.71297e6	+	2.96695e6i	−0.379505	+	0.657322i
$460$	−24572.7	−	42561.2i	−0.00541450	−	0.00937819i
$461$	990579.			0.217088			0.108544	−	0.994092i	$-0.465381\pi$
$461$	990579.			0.217088			0.108544	+	0.994092i	$0.465381\pi$
$462$		0			0
$463$	6.20488e6			1.34518			0.672591	−	0.740014i	$-0.265181\pi$
$463$	6.20488e6			1.34518			0.672591	+	0.740014i	$0.265181\pi$
$464$	−542688.	−	939963.i	−0.117019	−	0.202682i
$465$	1.32265e6	−	2.29090e6i	0.283670	−	0.491331i
$466$	−160851.	+	278602.i	−0.0343131	+	0.0594320i
$467$	3.44249e6	+	5.96256e6i	0.730432	+	1.26515i	0.956699	+	0.291080i	$0.0940147\pi$
$467$	3.44249e6	+	5.96256e6i	0.730432	+	1.26515i	−0.226266	+	0.974066i	$0.572652\pi$
$468$	5.27141e6			1.11253
$469$		0			0
$470$	−994206.			−0.207602
$471$	−319598.	−	553561.i	−0.0663823	−	0.114978i
$472$	778014.	−	1.34756e6i	0.160743	−	0.278415i
$473$	−26698.3	+	46242.8i	−0.00548695	+	0.00950368i
$474$	78.6093	+	136.155i	1.60705e−5	+	2.78348e-5i
$475$	1.17758e6			0.239473
$476$		0			0
$477$	2.39214e6			0.481383
$478$	1.61561e6	+	2.79831e6i	0.323419	+	0.560178i
$479$	2.70644e6	−	4.68769e6i	0.538963	−	0.933512i	−0.459997	−	0.887921i	$-0.652149\pi$
$479$	2.70644e6	−	4.68769e6i	0.538963	−	0.933512i	0.998960	−	0.0455914i	$-0.0145172\pi$
$480$	898814.	−	1.55679e6i	0.178060	−	0.308409i
$481$	1.39887e6	+	2.42292e6i	0.275686	+	0.477503i
$482$	2.28783e6			0.448545
$483$		0			0
$484$	−3.45268e6			−0.669950
$485$	71534.3	+	123901.i	0.0138089	+	0.0239178i
$486$	−1.26552e6	+	2.19195e6i	−0.243041	+	0.420959i
$487$	1.50521e6	−	2.60711e6i	0.287591	−	0.498122i	−0.685643	−	0.727938i	$-0.740479\pi$
$487$	1.50521e6	−	2.60711e6i	0.287591	−	0.498122i	0.973234	+	0.229815i	$0.0738122\pi$
$488$	−3.04014e6	−	5.26568e6i	−0.577889	−	1.00093i
$489$	1.19618e6			0.226216
$490$		0			0
$491$	−7.24498e6			−1.35623			−0.678115	−	0.734956i	$-0.737203\pi$
$491$	−7.24498e6			−1.35623			−0.678115	+	0.734956i	$0.737203\pi$
$492$	−1.00588e6	−	1.74224e6i	−0.187341	−	0.324485i
$493$	1.96531e6	−	3.40402e6i	0.364178	−	0.630775i
$494$	1.79581e6	−	3.11044e6i	0.331088	−	0.573462i
$495$	2.53927e6	+	4.39814e6i	0.465795	+	0.806781i
$496$	2.86389e6			0.522700
$497$		0			0
$498$	−1.75187e6			−0.316540
$499$	2.56394e6	+	4.44088e6i	0.460953	+	0.798394i	0.999009	−	0.0445152i	$-0.0141743\pi$
$499$	2.56394e6	+	4.44088e6i	0.460953	+	0.798394i	−0.538056	+	0.842909i	$0.680841\pi$
$500$	2.28914e6	−	3.96491e6i	0.409495	−	0.709265i
$501$	1.47878e6	−	2.56133e6i	0.263215	−	0.455901i
$502$	572546.	+	991679.i	0.101403	+	0.175635i
$503$	1.05978e7			1.86766			0.933830	−	0.357718i	$-0.116445\pi$
$503$	1.05978e7			1.86766			0.933830	+	0.357718i	$0.116445\pi$
$504$		0			0
$505$	−1.00426e6			−0.175233
$506$	34471.7	+	59706.8i	0.00598531	+	0.0103669i
$507$	−2.70354e6	+	4.68266e6i	−0.467103	+	0.809045i
$508$	−37251.9	+	64522.1i	−0.00640455	+	0.0110930i
$509$	−4.39420e6	−	7.61097e6i	−0.751770	−	1.30210i	−0.946964	−	0.321340i	$-0.895867\pi$
$509$	−4.39420e6	−	7.61097e6i	−0.751770	−	1.30210i	0.195194	−	0.980765i	$-0.437466\pi$
$510$	1.00096e6			0.170409
$511$		0			0
$512$	3.59310e6			0.605752
$513$	−1.69180e6	−	2.93029e6i	−0.283829	−	0.491606i
$514$	2.38877e6	−	4.13746e6i	0.398810	−	0.690759i
$515$	1.50256e6	−	2.60251e6i	0.249640	−	0.432389i
$516$	−7627.81	−	13211.8i	−0.00126118	−	0.00218442i
$517$	−4.23721e6			−0.697194
$518$		0			0
$519$	2.43355e6			0.396572
$520$	−3.97156e6	−	6.87895e6i	−0.644099	−	1.11561i
$521$	−81066.4	+	140411.i	−0.0130842	+	0.0226625i	−0.872493	−	0.488626i	$-0.837498\pi$
$521$	−81066.4	+	140411.i	−0.0130842	+	0.0226625i	0.859409	+	0.511288i	$0.170832\pi$
$522$	937721.	−	1.62418e6i	0.150625	−	0.260890i
$523$	3.57422e6	+	6.19073e6i	0.571383	+	0.989664i	0.996424	+	0.0844904i	$0.0269262\pi$
$523$	3.57422e6	+	6.19073e6i	0.571383	+	0.989664i	−0.425041	+	0.905174i	$0.639740\pi$
$524$	−6.10144e6			−0.970743
$525$		0			0
$526$	579044.			0.0912530
$527$	5.18571e6	+	8.98191e6i	0.813357	+	1.40878i
$528$	588993.	−	1.02017e6i	0.0919445	−	0.159252i
$529$	3.21719e6	−	5.57233e6i	0.499847	−	0.865760i
$530$	−773788.	−	1.34024e6i	−0.119655	−	0.207249i
$531$	−1.97267e6			−0.303611
$532$		0			0
$533$	−1.39621e7			−2.12879
$534$	−494060.	−	855737.i	−0.0749767	−	0.129863i
$535$	−2.50553e6	+	4.33971e6i	−0.378456	+	0.655505i
$536$	−5.33151e6	+	9.23445e6i	−0.801564	+	1.38835i
$537$	−278302.	−	482033.i	−0.0416467	−	0.0721342i
$538$	4.88203e6			0.727185
$539$		0			0
$540$	−3.21278e6			−0.474129
$541$	2.41802e6	+	4.18813e6i	0.355195	+	0.615216i	0.987151	−	0.159788i	$-0.0510811\pi$
$541$	2.41802e6	+	4.18813e6i	0.355195	+	0.615216i	−0.631956	+	0.775004i	$0.717748\pi$
$542$	−519440.	+	899696.i	−0.0759516	+	0.131552i
$543$	1.24230e6	−	2.15172e6i	0.180811	−	0.313174i
$544$	3.52397e6	+	6.10369e6i	0.510546	+	0.884291i
$545$	−3.98874e6			−0.575234
$546$		0			0
$547$	9.98777e6			1.42725			0.713626	−	0.700527i	$-0.247052\pi$
$547$	9.98777e6			1.42725			0.713626	+	0.700527i	$0.247052\pi$
$548$	−1.16950e6	−	2.02563e6i	−0.166359	−	0.288143i
$549$	−3.85417e6	+	6.67561e6i	−0.545757	+	0.945279i
$550$	−784281.	+	1.35841e6i	−0.110552	+	0.191481i
$551$	1.94103e6	+	3.36196e6i	0.272366	+	0.471751i
$552$	−45878.4			−0.00640856
$553$		0			0
$554$	3.45598e6			0.478406
$555$	−385039.	−	666907.i	−0.0530606	−	0.0919037i
$556$	2.53162e6	−	4.38490e6i	0.347305	−	0.601551i
$557$	−873096.	+	1.51225e6i	−0.119241	+	0.206531i	−0.919467	−	0.393167i	$-0.871379\pi$
$557$	−873096.	+	1.51225e6i	−0.119241	+	0.206531i	0.800226	+	0.599698i	$0.204713\pi$
$558$	2.47429e6	+	4.28560e6i	0.336407	+	0.582674i
$559$	−105877.			−0.0143309
$560$		0			0
$561$	4.26600e6			0.572287
$562$	−2.82452e6	−	4.89221e6i	−0.377228	−	0.653378i
$563$	377609.	−	654038.i	0.0502078	−	0.0869625i	−0.839829	−	0.542851i	$-0.817345\pi$
$563$	377609.	−	654038.i	0.0502078	−	0.0869625i	0.890037	+	0.455888i	$0.150678\pi$
$564$	605293.	−	1.04840e6i	0.0801250	−	0.138781i
$565$	−2.33396e6	−	4.04254e6i	−0.307590	−	0.532762i
$566$	−5.02719e6			−0.659605
$567$		0			0
$568$	9.68836e6			1.26003
$569$	2.19767e6	+	3.80648e6i	0.284565	+	0.492882i	0.972504	−	0.232888i	$-0.0748174\pi$
$569$	2.19767e6	+	3.80648e6i	0.284565	+	0.492882i	−0.687938	+	0.725769i	$0.741484\pi$
$570$	−494297.	+	856148.i	−0.0637237	+	0.110373i
$571$	−5.80520e6	+	1.00549e7i	−0.745121	+	1.29059i	0.205018	+	0.978758i	$0.434275\pi$
$571$	−5.80520e6	+	1.00549e7i	−0.745121	+	1.29059i	−0.950138	+	0.311829i	$0.899059\pi$
$572$	−7.26718e6	−	1.25871e7i	−0.928700	−	1.60856i
$573$	−6.03855e6			−0.768327
$574$		0			0
$575$	−44821.1			−0.00565344
$576$	637458.	+	1.10411e6i	0.0800563	+	0.138662i
$577$	−5.33214e6	+	9.23554e6i	−0.666748	+	1.15484i	0.312060	+	0.950062i	$0.398981\pi$
$577$	−5.33214e6	+	9.23554e6i	−0.666748	+	1.15484i	−0.978808	+	0.204779i	$0.934352\pi$
$578$	36273.3	−	62827.2i	0.00451614	−	0.00782218i
$579$	−1.65372e6	−	2.86433e6i	−0.205006	−	0.355081i
$580$	3.68606e6			0.454980
$581$		0			0
$582$	57341.7			0.00701719
$583$	−3.29781e6	−	5.71197e6i	−0.401841	−	0.696009i
$584$	146049.	−	252963.i	0.0177201	−	0.0306920i
$585$	−5.03498e6	+	8.72084e6i	−0.608286	+	1.05358i
$586$	−1.20098e6	−	2.08015e6i	−0.144474	−	0.250237i
$587$	−1.39482e7			−1.67079			−0.835396	−	0.549648i	$-0.814762\pi$
$587$	−1.39482e7			−1.67079			−0.835396	+	0.549648i	$0.814762\pi$
$588$		0			0
$589$	−1.02433e7			−1.21661
$590$	638099.	+	1.10522e6i	0.0754672	+	0.130713i
$591$	−823430.	+	1.42622e6i	−0.0969746	+	0.167965i
$592$	416856.	−	722015.i	0.0488857	−	0.0846724i
$593$	−5.89663e6	−	1.02133e7i	−0.688600	−	1.19269i	−0.972291	−	0.233774i	$-0.924892\pi$
$593$	−5.89663e6	−	1.02133e7i	−0.688600	−	1.19269i	0.283691	−	0.958916i	$-0.408441\pi$
$594$	4.50703e6			0.524113
$595$		0			0
$596$	−3.38033e6			−0.389802
$597$	681102.	+	1.17970e6i	0.0782125	+	0.135468i
$598$	−68352.3	+	118390.i	−0.00781628	+	0.0135382i
$599$	2.19029e6	−	3.79369e6i	0.249421	−	0.432011i	−0.713944	−	0.700203i	$-0.753093\pi$
$599$	2.19029e6	−	3.79369e6i	0.249421	−	0.432011i	0.963365	+	0.268192i	$0.0864262\pi$
$600$	−521899.	−	903956.i	−0.0591846	−	0.102511i
$601$	688570.			0.0777610			0.0388805	−	0.999244i	$-0.487621\pi$
$601$	688570.			0.0777610			0.0388805	+	0.999244i	$0.487621\pi$
$602$		0			0
$603$	1.35181e7			1.51399
$604$	1.44086e6	+	2.49564e6i	0.160705	+	0.278349i
$605$	3.29781e6	−	5.71198e6i	0.366301	−	0.634451i
$606$	−201252.	+	348579.i	−0.0222617	+	0.0385584i
$607$	4.68660e6	+	8.11742e6i	0.516281	+	0.894224i	0.999821	+	0.0189023i	$0.00601715\pi$
$607$	4.68660e6	+	8.11742e6i	0.516281	+	0.894224i	−0.483541	+	0.875322i	$0.660650\pi$
$608$	−6.96085e6			−0.763666
$609$		0			0
$610$	4.98684e6			0.542626
$611$	−4.20087e6	−	7.27612e6i	−0.455236	−	0.788492i
$612$	2.84437e6	−	4.92659e6i	0.306978	−	0.531701i
$613$	1.08342e6	−	1.87655e6i	0.116452	−	0.201701i	−0.801907	−	0.597449i	$-0.796181\pi$
$613$	1.08342e6	−	1.87655e6i	0.116452	−	0.201701i	0.918359	+	0.395748i	$0.129515\pi$
$614$	2.75974e6	+	4.78000e6i	0.295424	+	0.511690i
$615$	3.84306e6			0.409722
$616$		0			0
$617$	−5.07951e6			−0.537166			−0.268583	−	0.963256i	$-0.586555\pi$
$617$	−5.07951e6			−0.537166			−0.268583	+	0.963256i	$0.586555\pi$
$618$	−602224.	−	1.04308e6i	−0.0634288	−	0.109862i
$619$	1.09517e6	−	1.89689e6i	0.114883	−	0.198983i	−0.802850	−	0.596181i	$-0.796684\pi$
$619$	1.09517e6	−	1.89689e6i	0.114883	−	0.198983i	0.917733	+	0.397198i	$0.130017\pi$
$620$	−4.86306e6	+	8.42306e6i	−0.508078	+	0.880016i
$621$	64393.4	+	111533.i	0.00670058	+	0.0116057i
$622$	2.43111e6			0.251958
$623$		0			0
$624$	2.33577e6			0.240142
$625$	2.79509e6	+	4.84124e6i	0.286217	+	0.495743i
$626$	−1.54895e6	+	2.68286e6i	−0.157980	+	0.273629i
$627$	−2.10665e6	+	3.64882e6i	−0.214005	+	0.370667i
$628$	1.17508e6	+	2.03530e6i	0.118896	+	0.205935i
$629$	3.01923e6			0.304278
$630$		0			0
$631$	−7.18693e6			−0.718572			−0.359286	−	0.933228i	$-0.616980\pi$
$631$	−7.18693e6			−0.718572			−0.359286	+	0.933228i	$0.616980\pi$
$632$	−673.188	−	1166.00i	−6.70415e−5	−	0.000116119i
$633$	2.09725e6	−	3.63255e6i	0.208038	−	0.360332i
$634$	−2.10554e6	+	3.64691e6i	−0.208037	+	0.360331i
$635$	−71162.1	−	123256.i	−0.00700349	−	0.0121304i
$636$	1.88439e6			0.184726
$637$		0			0
$638$	−5.17097e6			−0.502945
$639$	−6.14125e6	−	1.06370e7i	−0.594983	−	1.03054i
$640$	−3.98009e6	+	6.89371e6i	−0.384098	+	0.665278i
$641$	8.82500e6	−	1.52854e7i	0.848340	−	1.46937i	−0.0343490	−	0.999410i	$-0.510936\pi$
$641$	8.82500e6	−	1.52854e7i	0.848340	−	1.46937i	0.882689	−	0.469958i	$-0.155731\pi$
$642$	1.00421e6	+	1.73935e6i	0.0961586	+	0.166552i
$643$	898309.			0.0856837			0.0428419	−	0.999082i	$-0.486359\pi$
$643$	898309.			0.0856837			0.0428419	+	0.999082i	$0.486359\pi$
$644$		0			0
$645$	29142.7			0.00275823
$646$	−1.93798e6	−	3.35669e6i	−0.182713	−	0.316468i
$647$	693210.	−	1.20068e6i	0.0651035	−	0.112763i	−0.831636	−	0.555321i	$-0.812596\pi$
$647$	693210.	−	1.20068e6i	0.0651035	−	0.112763i	0.896740	+	0.442558i	$0.145929\pi$
$648$	2.33867e6	−	4.05070e6i	0.218792	−	0.378959i
$649$	2.71952e6	+	4.71034e6i	0.253443	+	0.438976i
$650$	−3.11022e6			−0.288741
$651$		0			0
$652$	−4.39804e6			−0.405173
$653$	8.77125e6	+	1.51923e7i	0.804968	+	1.39425i	0.916313	+	0.400464i	$0.131151\pi$
$653$	8.77125e6	+	1.51923e7i	0.804968	+	1.39425i	−0.111345	+	0.993782i	$0.535516\pi$
$654$	−799341.	+	1.38450e6i	−0.0730782	+	0.126575i
$655$	5.82778e6	−	1.00940e7i	0.530762	−	0.919307i
$656$	2.08031e6	+	3.60320e6i	0.188742	+	0.326910i
$657$	−370308.			−0.0334696
$658$		0			0
$659$	9.87522e6			0.885795			0.442898	−	0.896572i	$-0.353950\pi$
$659$	9.87522e6			0.885795			0.442898	+	0.896572i	$0.353950\pi$
$660$	2.00029e6	+	3.46460e6i	0.178744	+	0.309595i
$661$	4.03396e6	−	6.98702e6i	0.359110	−	0.621997i	−0.628702	−	0.777646i	$-0.716414\pi$
$661$	4.03396e6	−	6.98702e6i	0.359110	−	0.621997i	0.987812	+	0.155649i	$0.0497468\pi$
$662$	3.85687e6	−	6.68029e6i	0.342050	−	0.592448i
$663$	4.22942e6	+	7.32557e6i	0.373677	+	0.647228i
$664$	1.50025e7			1.32052
$665$		0			0
$666$	1.44059e6			0.125850
$667$	−73879.3	−	127963.i	−0.00642996	−	0.0111370i
$668$	−5.43710e6	+	9.41734e6i	−0.471440	+	0.816558i
$669$	−1.27730e6	+	2.21236e6i	−0.110339	+	0.191113i
$670$	−4.37272e6	−	7.57377e6i	−0.376326	−	0.651816i
$671$	2.12534e7			1.82231
$672$		0			0
$673$	−1.12772e7			−0.959762			−0.479881	−	0.877334i	$-0.659320\pi$
$673$	−1.12772e7			−0.959762			−0.479881	+	0.877334i	$0.659320\pi$
$674$	3.25637e6	+	5.64020e6i	0.276111	+	0.478239i
$675$	−1.46504e6	+	2.53753e6i	−0.123763	+	0.214364i
$676$	9.94020e6	−	1.72169e7i	0.836621	−	1.44907i
$677$	−2.60186e6	−	4.50655e6i	−0.218179	−	0.377897i	0.736073	−	0.676903i	$-0.236678\pi$
$677$	−2.60186e6	−	4.50655e6i	−0.218179	−	0.377897i	−0.954251	+	0.299006i	$0.903345\pi$
$678$	−1.87090e6			−0.156306
$679$		0			0
$680$	−8.57196e6			−0.710899
$681$	−953891.	−	1.65219e6i	−0.0788190	−	0.136518i
$682$	6.82212e6	−	1.18163e7i	0.561640	−	0.972790i
$683$	−3.02957e6	+	5.24737e6i	−0.248502	+	0.430418i	−0.963110	−	0.269107i	$-0.913272\pi$
$683$	−3.02957e6	+	5.24737e6i	−0.248502	+	0.430418i	0.714608	+	0.699525i	$0.246605\pi$
$684$	2.80922e6	+	4.86572e6i	0.229586	+	0.397655i
$685$	4.46816e6			0.363833
$686$		0			0
$687$	−8.05671e6			−0.651277
$688$	15775.4	+	27323.8i	0.00127060	+	0.00220075i
$689$	6.53906e6	−	1.13260e7i	0.524768	−	0.908924i
$690$	18813.9	−	32586.7i	0.00150438	−	0.00260566i
$691$	−3.68249e6	−	6.37826e6i	−0.293391	−	0.508168i	0.681219	−	0.732080i	$-0.261450\pi$
$691$	−3.68249e6	−	6.37826e6i	−0.293391	−	0.508168i	−0.974609	+	0.223912i	$0.928117\pi$
$692$	−8.94754e6			−0.710295
$693$		0			0
$694$	−8.61204e6			−0.678746
$695$	4.83614e6	+	8.37644e6i	0.379784	+	0.657806i
$696$	1.72051e6	−	2.98001e6i	0.134628	−	0.233182i
$697$	−7.53370e6	+	1.30488e7i	−0.587390	+	1.01739i
$698$	295909.	+	512529.i	0.0229890	+	0.0398181i
$699$	748298.			0.0579271
$700$		0			0
$701$	7.80919e6			0.600221			0.300110	−	0.953904i	$-0.402977\pi$
$701$	7.80919e6			0.600221			0.300110	+	0.953904i	$0.402977\pi$
$702$	4.46838e6	+	7.73946e6i	0.342222	+	0.592745i
$703$	−1.49096e6	+	2.58243e6i	−0.113783	+	0.197079i
$704$	1.75760e6	−	3.04426e6i	0.133656	−	0.231499i
$705$	1.15629e6	+	2.00275e6i	0.0876180	+	0.151759i
$706$	−1.06069e7			−0.800898
$707$		0			0
$708$	−1.55395e6			−0.116508
$709$	−8.78251e6	−	1.52118e7i	−0.656150	−	1.13649i	−0.981604	−	0.190927i	$-0.938851\pi$
$709$	−8.78251e6	−	1.52118e7i	−0.656150	−	1.13649i	0.325454	−	0.945558i	$-0.394483\pi$
$710$	−3.97303e6	+	6.88149e6i	−0.295785	+	0.512314i
$711$	−853.439	+	1478.20i	−6.33138e−5	+	0.000109663i
$712$	4.23099e6	+	7.32829e6i	0.312782	+	0.541755i
$713$	389879.			0.0287214
$714$		0			0
$715$	2.77649e7			2.03110
$716$	1.02324e6	+	1.77231e6i	0.0745928	+	0.129198i
$717$	3.75799e6	−	6.50902e6i	0.272997	−	0.472844i
$718$	−1.41769e6	+	2.45552e6i	−0.102629	+	0.177759i
$719$	4.04610e6	+	7.00805e6i	0.291887	+	0.505563i	0.974256	−	0.225445i	$-0.0723836\pi$
$719$	4.04610e6	+	7.00805e6i	0.291887	+	0.505563i	−0.682369	+	0.731008i	$0.739050\pi$
$720$	3.00079e6			0.215727
$721$		0			0
$722$	−3.14232e6			−0.224341
$723$	−2.66081e6	−	4.60866e6i	−0.189308	−	0.327890i
$724$	−4.56760e6	+	7.91131e6i	−0.323848	+	0.560922i
$725$	1.68086e6	−	2.91133e6i	0.118764	−	0.205706i
$726$	−1.32176e6	−	2.28935e6i	−0.0930702	−	0.161202i
$727$	1.51986e7			1.06652			0.533258	−	0.845952i	$-0.320967\pi$
$727$	1.51986e7			1.06652			0.533258	+	0.845952i	$0.320967\pi$
$728$		0			0
$729$	−1.31285e6			−0.0914944
$730$	119784.	+	207472.i	0.00831938	+	0.0144096i
$731$	−57129.7	+	98951.6i	−0.00395429	+	0.00684903i
$732$	−3.03609e6	+	5.25866e6i	−0.209429	+	0.362742i
$733$	−2.91701e6	−	5.05241e6i	−0.200530	−	0.347327i	0.748170	−	0.663507i	$-0.230933\pi$
$733$	−2.91701e6	−	5.05241e6i	−0.200530	−	0.347327i	−0.948699	+	0.316180i	$0.897600\pi$
$734$	−4.29720e6			−0.294405
$735$		0			0
$736$	264944.			0.0180285
$737$	−1.86361e7	−	3.22787e7i	−1.26382	−	2.18901i
$738$	−3.59461e6	+	6.22604e6i	−0.242946	+	0.420796i
$739$	−3.23860e6	+	5.60941e6i	−0.218145	+	0.377838i	−0.954241	−	0.299039i	$-0.903334\pi$
$739$	−3.23860e6	+	5.60941e6i	−0.218145	+	0.377838i	0.736096	+	0.676877i	$0.236667\pi$
$740$	1.41569e6	+	2.45205e6i	0.0950361	+	0.164607i
$741$	−8.35433e6			−0.558941
$742$		0			0
$743$	−1.50899e7			−1.00280			−0.501401	−	0.865215i	$-0.667182\pi$
$743$	−1.50899e7			−1.00280			−0.501401	+	0.865215i	$0.667182\pi$
$744$	4.53978e6	+	7.86312e6i	0.300678	+	0.520790i
$745$	3.22872e6	−	5.59230e6i	0.213127	−	0.369148i
$746$	−6.84481e6	+	1.18556e7i	−0.450313	+	0.779965i
$747$	−9.50979e6	−	1.64714e7i	−0.623548	−	1.08002i
$748$	−1.56850e7			−1.02502
$749$		0			0
$750$	3.50534e6			0.227550
$751$	1.06998e6	+	1.85327e6i	0.0692273	+	0.119905i	0.898561	−	0.438848i	$-0.144613\pi$
$751$	1.06998e6	+	1.85327e6i	0.0692273	+	0.119905i	−0.829334	+	0.558753i	$0.811280\pi$
$752$	−1.25184e6	+	2.16824e6i	−0.0807240	+	0.139818i
$753$	1.33177e6	−	2.30670e6i	0.0855940	−	0.148253i
$754$	−5.12663e6	−	8.87958e6i	−0.328400	−	0.568806i
$755$	−5.50494e6			−0.351467
$756$		0			0
$757$	2.10943e7			1.33791			0.668954	−	0.743304i	$-0.266742\pi$
$757$	2.10943e7			1.33791			0.668954	+	0.743304i	$0.266742\pi$
$758$	−887984.	−	1.53803e6i	−0.0561348	−	0.0972283i
$759$	80183.2	−	138881.i	0.00505218	−	0.00875063i
$760$	4.23302e6	−	7.33181e6i	0.265838	−	0.460444i
$761$	−4.89979e6	−	8.48669e6i	−0.306701	−	0.531222i	0.670937	−	0.741514i	$-0.265892\pi$
$761$	−4.89979e6	−	8.48669e6i	−0.306701	−	0.531222i	−0.977639	+	0.210292i	$0.932559\pi$
$762$	−57043.3			−0.00355891
$763$		0			0
$764$	2.22022e7			1.37614
$765$	5.43358e6	+	9.41124e6i	0.335686	+	0.581424i
$766$	−796165.	+	1.37900e6i	−0.0490265	+	0.0849164i
$767$	−5.39239e6	+	9.33990e6i	−0.330973	+	0.573263i
$768$	2.26265e6	+	3.91903e6i	0.138425	+	0.239759i
$769$	−3.23493e7			−1.97265			−0.986323	−	0.164825i	$-0.947294\pi$
$769$	−3.23493e7			−1.97265			−0.986323	+	0.164825i	$0.947294\pi$
$770$		0			0
$771$	−1.11128e7			−0.673267
$772$	6.08031e6	+	1.05314e7i	0.367183	+	0.635980i
$773$	−4.59856e6	+	7.96495e6i	−0.276805	+	0.479440i	−0.970589	−	0.240743i	$-0.922609\pi$
$773$	−4.59856e6	+	7.96495e6i	−0.276805	+	0.479440i	0.693784	+	0.720183i	$0.255942\pi$
$774$	−27258.7	+	47213.4i	−0.00163551	+	0.00283278i
$775$	4.43515e6	+	7.68191e6i	0.265249	+	0.459425i
$776$	−491058.			−0.0292738
$777$		0			0
$778$	1.66712e6			0.0987456
$779$	−7.44062e6	−	1.28875e7i	−0.439304	−	0.760898i
$780$	−3.96627e6	+	6.86978e6i	−0.233424	+	0.404302i
$781$	−1.69327e7	+	2.93282e7i	−0.993339	+	1.72051i
$782$	73763.5	+	127762.i	0.00431345	+	0.00747111i
$783$	−9.65941e6			−0.563049
$784$		0			0
$785$	−4.48950e6			−0.260030
$786$	−2.33576e6	−	4.04566e6i	−0.134857	−	0.233579i
$787$	−7.34749e6	+	1.27262e7i	−0.422866	+	0.732425i	−0.996218	−	0.0868838i	$-0.972309\pi$
$787$	−7.34749e6	+	1.27262e7i	−0.422866	+	0.732425i	0.573353	+	0.819309i	$0.305642\pi$
$788$	3.02754e6	−	5.24385e6i	0.173690	−	0.300839i
$789$	−673444.	−	1.16644e6i	−0.0385132	−	0.0667068i
$790$	1104.25			6.29506e−5
$791$		0			0
$792$	−1.74312e7			−0.987446
$793$	2.10712e7	+	3.64963e7i	1.18989	+	2.06094i
$794$	−1.89048e6	+	3.27442e6i	−0.106420	+	0.184324i
$795$	−1.79987e6	+	3.11747e6i	−0.101001	+	0.174938i
$796$	−2.50424e6	−	4.33747e6i	−0.140085	−	0.242635i
$797$	2.33344e7			1.30122			0.650610	−	0.759412i	$-0.274513\pi$
$797$	2.33344e7			1.30122			0.650610	+	0.759412i	$0.274513\pi$
$798$		0			0
$799$	−9.06688e6			−0.502448
$800$	3.01392e6	+	5.22027e6i	0.166497	+	0.288382i
$801$	5.36387e6	−	9.29050e6i	0.295391	−	0.511632i
$802$	5.18981e6	−	8.98902e6i	0.284915	−	0.493488i
$803$	510507.	+	884225.i	0.0279391	+	0.0483920i
$804$	1.06488e7			0.580980
$805$		0			0
$806$	2.70545e7			1.46690
$807$	−5.67794e6	−	9.83448e6i	−0.306907	−	0.531578i
$808$	1.72347e6	−	2.98513e6i	0.0928698	−	0.160855i
$809$	−846503.	+	1.46619e6i	−0.0454734	+	0.0787622i	−0.887866	−	0.460102i	$-0.847813\pi$
$809$	−846503.	+	1.46619e6i	−0.0454734	+	0.0787622i	0.842393	+	0.538864i	$0.181146\pi$
$810$	1.91810e6	+	3.32224e6i	0.102721	+	0.177918i
$811$	−2.12400e7			−1.13397			−0.566987	−	0.823727i	$-0.691891\pi$
$811$	−2.12400e7			−1.13397			−0.566987	+	0.823727i	$0.691891\pi$
$812$		0			0
$813$	2.41649e6			0.128221
$814$	−1.98599e6	−	3.43984e6i	−0.105055	−	0.181961i
$815$	4.20078e6	−	7.27596e6i	0.221532	−	0.383704i
$816$	1.26034e6	−	2.18298e6i	0.0662618	−	0.114769i
$817$	−56423.9	−	97729.0i	−0.00295738	−	0.00512234i
$818$	4.09960e6			0.214219
$819$		0			0
$820$	−1.41299e7			−0.733847
$821$	−4.36775e6	−	7.56517e6i	−0.226152	−	0.391706i	0.730513	−	0.682899i	$-0.239281\pi$
$821$	−4.36775e6	−	7.56517e6i	−0.226152	−	0.391706i	−0.956664	+	0.291193i	$0.905948\pi$
$822$	895416.	−	1.55091e6i	0.0462217	−	0.0800583i
$823$	1.63982e7	−	2.84025e7i	0.843910	−	1.46170i	−0.0426542	−	0.999090i	$-0.513581\pi$
$823$	1.63982e7	−	2.84025e7i	0.843910	−	1.46170i	0.886564	−	0.462605i	$-0.153085\pi$
$824$	5.15728e6	+	8.93266e6i	0.264608	+	0.458314i
$825$	3.64856e6			0.186632
$826$		0			0
$827$	1.31248e7			0.667311			0.333656	−	0.942695i	$-0.391718\pi$
$827$	1.31248e7			0.667311			0.333656	+	0.942695i	$0.391718\pi$
$828$	−106925.	−	185199.i	−0.00542004	−	0.00938778i
$829$	−1.02701e7	+	1.77884e7i	−0.519026	+	0.898979i	0.480730	+	0.876869i	$0.340372\pi$
$829$	−1.02701e7	+	1.77884e7i	−0.519026	+	0.898979i	−0.999756	+	0.0221101i	$0.992962\pi$
$830$	−6.15228e6	+	1.06561e7i	−0.309985	+	0.536910i
$831$	−4.01940e6	−	6.96180e6i	−0.201910	−	0.349719i
$832$	6.97012e6			0.349085
$833$		0			0
$834$	3.87664e6			0.192992
$835$	−1.03865e7	−	1.79899e7i	−0.515528	−	0.892920i
$836$	7.74560e6	−	1.34158e7i	0.383300	−	0.663896i
$837$	1.27438e7	−	2.20728e7i	0.628758	−	1.08904i
$838$	4.11271e6	+	7.12343e6i	0.202310	+	0.350412i
$839$	2.83736e7			1.39159			0.695793	−	0.718243i	$-0.255053\pi$
$839$	2.83736e7			1.39159			0.695793	+	0.718243i	$0.255053\pi$
$840$		0			0
$841$	−9.42879e6			−0.459691
$842$	−2.84322e6	−	4.92459e6i	−0.138207	−	0.239381i
$843$	−6.56999e6	+	1.13796e7i	−0.318417	+	0.551514i
$844$	−7.71106e6	+	1.33560e7i	−0.372613	+	0.645385i
$845$	1.89887e7	+	3.28894e7i	0.914859	+	1.58458i
$846$	−4.32614e6			−0.207814
$847$		0			0
$848$	−3.89720e6			−0.186107
$849$	5.84676e6	+	1.01269e7i	0.278385	+	0.482177i
$850$	−1.67822e6	+	2.90677e6i	−0.0796714	+	0.137995i
$851$	56749.1	−	98292.3i	0.00268618	−	0.00465260i
$852$	−4.83772e6	−	8.37919e6i	−0.228319	−	0.395460i
$853$	1.02093e7			0.480424			0.240212	−	0.970720i	$-0.422783\pi$
$853$	1.02093e7			0.480424			0.240212	+	0.970720i	$0.422783\pi$
$854$		0			0
$855$	−1.07329e7			−0.502113
$856$	−8.59980e6	−	1.48953e7i	−0.401147	−	0.694808i
$857$	4.16603e6	−	7.21577e6i	0.193763	−	0.335607i	−0.752732	−	0.658328i	$-0.771264\pi$
$857$	4.16603e6	−	7.21577e6i	0.193763	−	0.335607i	0.946494	+	0.322721i	$0.104597\pi$
$858$	5.56406e6	−	9.63724e6i	0.258032	−	0.446925i
$859$	−1.56383e7	−	2.70863e7i	−0.723113	−	1.25247i	−0.959746	−	0.280870i	$-0.909377\pi$
$859$	−1.56383e7	−	2.70863e7i	−0.723113	−	1.25247i	0.236633	−	0.971599i	$-0.423956\pi$
$860$	−107150.			−0.00494023
$861$		0			0
$862$	−1.53084e7			−0.701714
$863$	1.86787e7	+	3.23524e7i	0.853726	+	1.47870i	0.877822	+	0.478988i	$0.158996\pi$
$863$	1.86787e7	+	3.23524e7i	0.853726	+	1.47870i	−0.0240955	+	0.999710i	$0.507671\pi$
$864$	8.66007e6	−	1.49997e7i	0.394673	−	0.683593i
$865$	8.54622e6	−	1.48025e7i	0.388360	−	0.672658i
$866$	5.31112e6	+	9.19913e6i	0.240653	+	0.416823i
$867$	−168747.			−0.00762411
$868$		0			0
$869$	4706.21			0.000211408
$870$	1.41110e6	+	2.44410e6i	0.0632063	+	0.109477i
$871$	3.69526e7	−	6.40037e7i	1.65044	−	2.85864i
$872$	6.84533e6	−	1.18565e7i	0.304862	−	0.528036i
$873$	311271.	+	539138.i	0.0138230	+	0.0239422i
$874$	−145704.			−0.00645199
$875$		0			0
$876$	−291708.			−0.0128436
$877$	−19498.3	−	33772.1i	−0.000856049	−	0.00148272i	0.865597	−	0.500741i	$-0.166939\pi$
$877$	−19498.3	−	33772.1i	−0.000856049	−	0.00148272i	−0.866453	+	0.499258i	$0.833606\pi$
$878$	−3.30982e6	+	5.73278e6i	−0.144900	+	0.250974i
$879$	−2.79354e6	+	4.83855e6i	−0.121950	+	0.211224i
$880$	−4.13689e6	−	7.16530e6i	−0.180081	−	0.311909i
$881$	3.15554e7			1.36973			0.684864	−	0.728671i	$-0.259862\pi$
$881$	3.15554e7			1.36973			0.684864	+	0.728671i	$0.259862\pi$
$882$		0			0
$883$	−3.42253e7			−1.47722			−0.738611	−	0.674132i	$-0.764518\pi$
$883$	−3.42253e7			−1.47722			−0.738611	+	0.674132i	$0.764518\pi$
$884$	−1.55505e7	−	2.69342e7i	−0.669288	−	1.15924i
$885$	1.48425e6	−	2.57080e6i	0.0637016	−	0.110334i
$886$	−6.76148e6	+	1.17112e7i	−0.289373	+	0.501208i
$887$	1.34943e7	+	2.33728e7i	0.575892	+	0.997474i	0.995944	+	0.0899741i	$0.0286784\pi$
$887$	1.34943e7	+	2.33728e7i	0.575892	+	0.997474i	−0.420052	+	0.907500i	$0.637988\pi$
$888$	2.64316e6			0.112484
$889$		0			0
$890$	−6.94022e6			−0.293696
$891$	8.17475e6	+	1.41591e7i	0.344969	+	0.597504i
$892$	4.69632e6	−	8.13426e6i	0.197627	−	0.342299i
$893$	4.47743e6	−	7.75514e6i	0.187888	−	0.325432i
$894$	−1.29407e6	−	2.24139e6i	−0.0541517	−	0.0937935i
$895$	−3.90940e6			−0.163137
$896$		0			0
$897$	317982.			0.0131954
$898$	3.89613e6	+	6.74830e6i	0.161229	+	0.279257i
$899$	−1.46211e7	+	2.53244e7i	−0.603365	+	1.04506i
$900$	2.43269e6	−	4.21354e6i	0.100111	−	0.173397i
$901$	−7.05673e6	−	1.22226e7i	−0.289595	−	0.501594i
$902$	1.98221e7			0.811211
$903$		0			0
$904$	1.60218e7			0.652065
$905$	−8.72546e6	−	1.51129e7i	−0.354133	−	0.613377i
$906$	−1.10318e6	+	1.91077e6i	−0.0446506	+	0.0773372i
$907$	−9.60513e6	+	1.66366e7i	−0.387690	+	0.671499i	−0.992138	−	0.125145i	$-0.960060\pi$
$907$	−9.60513e6	+	1.66366e7i	−0.387690	+	0.671499i	0.604448	+	0.796644i	$0.293394\pi$
$908$	3.50721e6	+	6.07467e6i	0.141172	+	0.244516i
$909$	−4.36988e6			−0.175412
$910$		0			0
$911$	2.86013e7			1.14180			0.570899	−	0.821020i	$-0.306595\pi$
$911$	2.86013e7			1.14180			0.570899	+	0.821020i	$0.306595\pi$
$912$	1.24477e6	+	2.15601e6i	0.0495567	+	0.0858347i
$913$	−2.62204e7	+	4.54151e7i	−1.04103	+	1.80311i
$914$	−340014.	+	588921.i	−0.0134627	+	0.0233180i
$915$	−5.79983e6	−	1.00456e7i	−0.229014	−	0.396664i
$916$	2.96224e7			1.16649
$917$		0			0
$918$	9.64426e6			0.377713
$919$	2.10877e7	+	3.65249e7i	0.823645	+	1.42660i	0.902950	+	0.429745i	$0.141396\pi$
$919$	2.10877e7	+	3.65249e7i	0.823645	+	1.42660i	−0.0793054	+	0.996850i	$0.525270\pi$
$920$	−161117.	+	279063.i	−0.00627585	+	0.0108701i
$921$	6.41930e6	−	1.11185e7i	0.249367	−	0.431916i
$922$	−1.39428e6	−	2.41496e6i	−0.0540159	−	0.0935582i
$923$	−6.71498e7			−2.59442
$924$		0			0
$925$	2.58224e6			0.0992299
$926$	−8.73360e6	−	1.51270e7i	−0.334708	−	0.579731i
$927$	6.53818e6	−	1.13245e7i	0.249895	−	0.432831i
$928$	−9.93580e6	+	1.72093e7i	−0.378733	+	0.655985i
$929$	1.50943e7	+	2.61441e7i	0.573817	+	0.993881i	0.996169	+	0.0874487i	$0.0278714\pi$
$929$	1.50943e7	+	2.61441e7i	0.573817	+	0.993881i	−0.422352	+	0.906432i	$0.638795\pi$
$930$	−7.44673e6			−0.282331
$931$		0			0
$932$	−2.75130e6			−0.103752
$933$	−2.82745e6	−	4.89728e6i	−0.106338	−	0.184184i
$934$	9.69085e6	−	1.67850e7i	0.363492	−	0.629586i
$935$	1.49815e7	−	2.59487e7i	0.560436	−	0.970703i
$936$	−1.72817e7	−	2.99328e7i	−0.644758	−	1.11675i
$937$	−3.64068e6			−0.135467			−0.0677335	−	0.997703i	$-0.521577\pi$
$937$	−3.64068e6			−0.135467			−0.0677335	+	0.997703i	$0.521577\pi$
$938$		0			0
$939$	7.20589e6			0.266701
$940$	−4.25138e6	−	7.36360e6i	−0.156931	−	0.271813i
$941$	−9.43004e6	+	1.63333e7i	−0.347168	+	0.601312i	−0.985745	−	0.168245i	$-0.946190\pi$
$941$	−9.43004e6	+	1.63333e7i	−0.347168	+	0.601312i	0.638577	+	0.769558i	$0.279523\pi$
$942$	−899693.	+	1.55831e6i	−0.0330344	+	0.0572173i
$943$	283205.	+	490525.i	0.0103710	+	0.0179631i
$944$	3.21380e6			0.117379
$945$		0			0
$946$	150315.			0.00546104
$947$	9.10858e6	+	1.57765e7i	0.330047	+	0.571658i	0.982521	−	0.186153i	$-0.0596021\pi$
$947$	9.10858e6	+	1.57765e7i	0.330047	+	0.571658i	−0.652474	+	0.757811i	$0.726269\pi$
$948$	−672.291	+	1164.44i	−2.42961e−5	+	4.20821e-5i
$949$	−1.01226e6	+	1.75328e6i	−0.0364860	+	0.0631956i
$950$	−1.65749e6	−	2.87085e6i	−0.0595856	−	0.103205i
$951$	9.79522e6			0.351207
$952$		0			0
$953$	2.76898e7			0.987616			0.493808	−	0.869571i	$-0.335604\pi$
$953$	2.76898e7			0.987616			0.493808	+	0.869571i	$0.335604\pi$
$954$	−3.36703e6	−	5.83186e6i	−0.119778	−	0.207461i
$955$	−2.12064e7	+	3.67305e7i	−0.752416	+	1.30322i
$956$	−1.38171e7	+	2.39320e7i	−0.488960	+	0.846904i
$957$	6.01399e6	+	1.04165e7i	0.212267	+	0.367657i
$958$	−1.52376e7			−0.536419
$959$		0			0
$960$	−1.91852e6			−0.0671875
$961$	−2.42649e7	−	4.20280e7i	−0.847559	−	1.46801i
$962$	3.93793e6	−	6.82069e6i	0.137192	−	0.237624i
$963$	−1.09025e7	+	1.88836e7i	−0.378843	+	0.656175i
$964$	9.78311e6	+	1.69449e7i	0.339066	+	0.587280i
$965$	−2.32304e7			−0.803042
$966$		0			0
$967$	−2.44768e7			−0.841761			−0.420881	−	0.907116i	$-0.638279\pi$
$967$	−2.44768e7			−0.841761			−0.420881	+	0.907116i	$0.638279\pi$
$968$	1.13192e7	+	1.96054e7i	0.388263	+	0.672492i
$969$	−4.50786e6	+	7.80784e6i	−0.154227	+	0.267129i
$970$	201374.	−	348791.i	0.00687187	−	0.0119024i
$971$	−4.75076e6	−	8.22855e6i	−0.161702	−	0.280076i	0.773777	−	0.633458i	$-0.218365\pi$
$971$	−4.75076e6	−	8.22855e6i	−0.161702	−	0.280076i	−0.935479	+	0.353382i	$0.885032\pi$
$972$	−2.16463e7			−0.734881
$973$		0			0
$974$	−8.47457e6			−0.286233
$975$	3.61727e6	+	6.26530e6i	0.121862	+	0.211072i
$976$	6.27908e6	−	1.08757e7i	0.210995	−	0.365454i
$977$	−2.34506e7	+	4.06176e7i	−0.785991	+	1.36138i	0.142414	+	0.989807i	$0.454514\pi$
$977$	−2.34506e7	+	4.06176e7i	−0.785991	+	1.36138i	−0.928405	+	0.371570i	$0.878820\pi$
$978$	−1.68366e6	−	2.91619e6i	−0.0562870	−	0.0974920i
$979$	−2.95785e7			−0.986325
$980$		0			0
$981$	−1.73564e7			−0.575822
$982$	1.01976e7	+	1.76627e7i	0.337457	+	0.584492i
$983$	−1.17691e7	+	2.03847e7i	−0.388473	+	0.672854i	−0.992244	−	0.124303i	$-0.960330\pi$
$983$	−1.17691e7	+	2.03847e7i	−0.388473	+	0.672854i	0.603772	+	0.797157i	$0.293664\pi$
$984$	−6.59531e6	+	1.14234e7i	−0.217144	+	0.376104i
$985$	5.78349e6	+	1.00173e7i	0.189933	+	0.328973i
$986$	−1.10650e7			−0.362458
$987$		0			0
$988$	3.07167e7			1.00111
$989$	2147.60	+	3719.76i	6.98174e−5	+	0.000120927i
$990$	7.14822e6	−	1.23811e7i	0.231798	−	0.401486i
$991$	1.32052e7	−	2.28721e7i	0.427130	−	0.739812i	−0.569486	−	0.822001i	$-0.692858\pi$
$991$	1.32052e7	−	2.28721e7i	0.427130	−	0.739812i	0.996617	+	0.0821892i	$0.0261912\pi$
$992$	−2.62168e7	−	4.54089e7i	−0.845865	−	1.46508i
$993$	−1.79426e7			−0.577446
$994$		0			0
$995$	9.56766e6			0.306371
$996$	−7.49127e6	−	1.29753e7i	−0.239280	−	0.414446i
$997$	9.75818e6	−	1.69017e7i	0.310907	−	0.538507i	−0.667652	−	0.744474i	$-0.732700\pi$
$997$	9.75818e6	−	1.69017e7i	0.310907	−	0.538507i	0.978559	+	0.205966i	$0.0660338\pi$
$998$	7.21768e6	−	1.25014e7i	0.229388	−	0.397312i
$999$	−3.70985e6	−	6.42565e6i	−0.117610	−	0.203706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.6.c.h.18.1		8
7.2	even	3	inner	49.6.c.h.30.1		8
7.3	odd	6		49.6.a.g.1.3	✓	4
7.4	even	3		49.6.a.g.1.4	yes	4
7.5	odd	6	inner	49.6.c.h.30.2		8
7.6	odd	2	inner	49.6.c.h.18.2		8
21.11	odd	6		441.6.a.z.1.2		4
21.17	even	6		441.6.a.z.1.1		4
28.3	even	6		784.6.a.bf.1.3		4
28.11	odd	6		784.6.a.bf.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.6.a.g.1.3	✓	4	7.3	odd	6
49.6.a.g.1.4	yes	4	7.4	even	3
49.6.c.h.18.1		8	1.1	even	1	trivial
49.6.c.h.18.2		8	7.6	odd	2	inner
49.6.c.h.30.1		8	7.2	even	3	inner
49.6.c.h.30.2		8	7.5	odd	6	inner
441.6.a.z.1.1		4	21.17	even	6
441.6.a.z.1.2		4	21.11	odd	6
784.6.a.bf.1.2		4	28.11	odd	6
784.6.a.bf.1.3		4	28.3	even	6

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	49.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.40754 - 2.43792i) q^{2} +(-3.27401 + 5.67075i) q^{3} +(12.0377 - 20.8499i) q^{4} +(22.9955 + 39.8294i) q^{5} +18.4331 q^{6} -157.856 q^{8} +(100.062 + 173.312i) q^{9} +O(q^{10})\)	\(q+(-1.40754 - 2.43792i) q^{2} +(-3.27401 + 5.67075i) q^{3} +(12.0377 - 20.8499i) q^{4} +(22.9955 + 39.8294i) q^{5} +18.4331 q^{6} -157.856 q^{8} +(100.062 + 173.312i) q^{9} +(64.7341 - 112.123i) q^{10} +(275.890 - 477.856i) q^{11} +(78.8229 + 136.525i) q^{12} +1094.10 q^{13} -301.150 q^{15} +(-163.017 - 282.354i) q^{16} +(590.357 - 1022.53i) q^{17} +(281.681 - 487.886i) q^{18} +(583.063 + 1009.89i) q^{19} +1107.25 q^{20} -1553.30 q^{22} +(-22.1925 - 38.4386i) q^{23} +(516.823 - 895.163i) q^{24} +(504.912 - 874.533i) q^{25} +(-1539.98 - 2667.33i) q^{26} -2901.58 q^{27} +3329.02 q^{29} +(423.880 + 734.181i) q^{30} +(-4392.01 + 7607.18i) q^{31} +(-2984.61 + 5169.49i) q^{32} +(1806.53 + 3129.01i) q^{33} -3323.80 q^{34} +4818.05 q^{36} +(1278.56 + 2214.53i) q^{37} +(1641.37 - 2842.93i) q^{38} +(-3582.08 + 6204.35i) q^{39} +(-3629.99 - 6287.32i) q^{40} -12761.3 q^{41} -96.7714 q^{43} +(-6642.16 - 11504.6i) q^{44} +(-4601.94 + 7970.80i) q^{45} +(-62.4736 + 108.207i) q^{46} +(-3839.58 - 6650.34i) q^{47} +2134.88 q^{48} -2842.73 q^{50} +(3865.67 + 6695.53i) q^{51} +(13170.4 - 22811.8i) q^{52} +(5976.67 - 10351.9i) q^{53} +(4084.08 + 7073.83i) q^{54} +25377.0 q^{55} -7635.81 q^{57} +(-4685.71 - 8115.89i) q^{58} +(-4928.62 + 8536.62i) q^{59} +(-3625.15 + 6278.94i) q^{60} +(19258.9 + 33357.5i) q^{61} +24727.6 q^{62} +6370.65 q^{64} +(25159.4 + 43577.3i) q^{65} +(5085.53 - 8808.39i) q^{66} +(33774.5 - 58499.1i) q^{67} +(-14213.1 - 24617.7i) q^{68} +290.634 q^{69} -61374.6 q^{71} +(-15795.4 - 27358.4i) q^{72} +(-925.199 + 1602.49i) q^{73} +(3599.24 - 6234.07i) q^{74} +(3306.17 + 5726.45i) q^{75} +28074.9 q^{76} +20167.7 q^{78} +(4.26456 + 7.38644i) q^{79} +(7497.34 - 12985.8i) q^{80} +(-14815.2 + 25660.7i) q^{81} +(17961.9 + 31111.0i) q^{82} -95039.3 q^{83} +54302.3 q^{85} +(136.209 + 235.921i) q^{86} +(-10899.2 + 18878.0i) q^{87} +(-43551.0 + 75432.6i) q^{88} +(-26802.8 - 46423.8i) q^{89} +25909.6 q^{90} -1068.59 q^{92} +(-28758.9 - 49811.9i) q^{93} +(-10808.7 + 18721.2i) q^{94} +(-26815.7 + 46446.1i) q^{95} +(-19543.2 - 33849.9i) q^{96} +3110.79 q^{97} +110424. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 10 q^{2} - 10 q^{4} - 540 q^{8} - 220 q^{9}+O(q^{10}) \) 8 * q + 10 * q^2 - 10 * q^4 - 540 * q^8 - 220 * q^9	\( 8 q + 10 q^{2} - 10 q^{4} - 540 q^{8} - 220 q^{9} + 1952 q^{11} - 8192 q^{15} + 1566 q^{16} + 5974 q^{18} + 7048 q^{22} + 7136 q^{23} - 2764 q^{25} - 6704 q^{29} - 25608 q^{30} - 27810 q^{32} + 55340 q^{36} + 9208 q^{37} - 2464 q^{39} + 40896 q^{43} - 1900 q^{44} - 56712 q^{46} - 86140 q^{50} + 67408 q^{51} + 102920 q^{53} - 31152 q^{57} - 96972 q^{58} + 87080 q^{60} - 80636 q^{64} + 63168 q^{65} + 22896 q^{67} - 307648 q^{71} - 77358 q^{72} - 17596 q^{74} + 266112 q^{78} + 90688 q^{79} + 17204 q^{81} + 545312 q^{85} + 161860 q^{86} - 154812 q^{88} - 424400 q^{92} - 247760 q^{93} - 108224 q^{95} - 84544 q^{99}+O(q^{100}) \) 8 * q + 10 * q^2 - 10 * q^4 - 540 * q^8 - 220 * q^9 + 1952 * q^11 - 8192 * q^15 + 1566 * q^16 + 5974 * q^18 + 7048 * q^22 + 7136 * q^23 - 2764 * q^25 - 6704 * q^29 - 25608 * q^30 - 27810 * q^32 + 55340 * q^36 + 9208 * q^37 - 2464 * q^39 + 40896 * q^43 - 1900 * q^44 - 56712 * q^46 - 86140 * q^50 + 67408 * q^51 + 102920 * q^53 - 31152 * q^57 - 96972 * q^58 + 87080 * q^60 - 80636 * q^64 + 63168 * q^65 + 22896 * q^67 - 307648 * q^71 - 77358 * q^72 - 17596 * q^74 + 266112 * q^78 + 90688 * q^79 + 17204 * q^81 + 545312 * q^85 + 161860 * q^86 - 154812 * q^88 - 424400 * q^92 - 247760 * q^93 - 108224 * q^95 - 84544 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more