LMFDB - Embedded newform 49.6.c.d.30.2

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			30.2
Root			$2.13746 + 0.656712i$ of defining polynomial
Character	$\chi$	$=$	49.30
Dual form			49.6.c.d.18.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.362541 + 0.627940i) q^{2} +(9.82475 + 17.0170i) q^{3} +(15.7371 + 27.2575i) q^{4} +(-23.3746 + 40.4860i) q^{5} -14.2475 q^{6} -46.0241 q^{8} +(-71.5515 + 123.931i) q^{9} +O(q^{10})$	\(q+(-0.362541 + 0.627940i) q^{2} +(9.82475 + 17.0170i) q^{3} +(15.7371 + 27.2575i) q^{4} +(-23.3746 + 40.4860i) q^{5} -14.2475 q^{6} -46.0241 q^{8} +(-71.5515 + 123.931i) q^{9} +(-16.9485 - 29.3557i) q^{10} +(-333.045 - 576.851i) q^{11} +(-309.227 + 535.596i) q^{12} +650.640 q^{13} -918.598 q^{15} +(-486.902 + 843.340i) q^{16} +(593.447 + 1027.88i) q^{17} +(-51.8808 - 89.8601i) q^{18} +(-782.526 + 1355.37i) q^{19} -1471.40 q^{20} +482.970 q^{22} +(550.076 - 952.760i) q^{23} +(-452.175 - 783.191i) q^{24} +(469.757 + 813.644i) q^{25} +(-235.884 + 408.563i) q^{26} +1962.93 q^{27} +2396.72 q^{29} +(333.030 - 576.825i) q^{30} +(-1024.23 - 1774.01i) q^{31} +(-1089.43 - 1886.95i) q^{32} +(6544.17 - 11334.8i) q^{33} -860.596 q^{34} -4504.06 q^{36} +(-538.772 + 933.181i) q^{37} +(-567.396 - 982.759i) q^{38} +(6392.37 + 11071.9i) q^{39} +(1075.79 - 1863.33i) q^{40} -1098.21 q^{41} +16564.3 q^{43} +(10482.3 - 18155.9i) q^{44} +(-3344.97 - 5793.66i) q^{45} +(398.851 + 690.830i) q^{46} +(-4149.19 + 7186.62i) q^{47} -19134.8 q^{48} -681.226 q^{50} +(-11660.9 + 20197.3i) q^{51} +(10239.2 + 17734.8i) q^{52} +(-2759.59 - 4779.75i) q^{53} +(-711.642 + 1232.60i) q^{54} +31139.1 q^{55} -30752.5 q^{57} +(-868.911 + 1505.00i) q^{58} +(-7115.21 - 12323.9i) q^{59} +(-14456.1 - 25038.7i) q^{60} +(-7117.37 + 12327.7i) q^{61} +1485.30 q^{62} -29581.9 q^{64} +(-15208.4 + 26341.8i) q^{65} +(4745.06 + 8218.69i) q^{66} +(-9865.22 - 17087.1i) q^{67} +(-18678.3 + 32351.8i) q^{68} +21617.5 q^{69} +64562.7 q^{71} +(3293.09 - 5703.80i) q^{72} +(14283.5 + 24739.7i) q^{73} +(-390.655 - 676.634i) q^{74} +(-9230.50 + 15987.7i) q^{75} -49258.8 q^{76} -9270.00 q^{78} +(15316.7 - 26529.3i) q^{79} +(-22762.3 - 39425.4i) q^{80} +(36672.3 + 63518.3i) q^{81} +(398.146 - 689.610i) q^{82} +675.946 q^{83} -55486.3 q^{85} +(-6005.25 + 10401.4i) q^{86} +(23547.2 + 40784.9i) q^{87} +(15328.1 + 26549.0i) q^{88} +(62985.7 - 109094. i) q^{89} +4850.76 q^{90} +34626.5 q^{92} +(20125.6 - 34858.5i) q^{93} +(-3008.51 - 5210.89i) q^{94} +(-36582.4 - 63362.6i) q^{95} +(21406.8 - 37077.6i) q^{96} +22906.8 q^{97} +95319.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 9 q^{2} - 6 q^{3} - 5 q^{4} - 18 q^{5} + 396 q^{6} - 18 q^{8} - 558 q^{9}+O(q^{10}) $ 4 * q - 9 * q^2 - 6 * q^3 - 5 * q^4 - 18 * q^5 + 396 * q^6 - 18 * q^8 - 558 * q^9	\( 4 q - 9 q^{2} - 6 q^{3} - 5 q^{4} - 18 q^{5} + 396 q^{6} - 18 q^{8} - 558 q^{9} + 204 q^{10} - 396 q^{11} - 1554 q^{12} + 700 q^{13} - 3312 q^{15} - 113 q^{16} + 1800 q^{17} - 3537 q^{18} - 3266 q^{19} - 5040 q^{20} - 3504 q^{22} - 2088 q^{23} - 1854 q^{24} + 3238 q^{25} + 2016 q^{26} + 12744 q^{27} + 13392 q^{29} + 6768 q^{30} - 20 q^{31} + 6129 q^{32} + 20016 q^{33} - 11868 q^{34} + 21258 q^{36} - 6232 q^{37} - 15210 q^{38} + 20496 q^{39} + 3216 q^{40} + 12096 q^{41} - 6040 q^{43} + 30816 q^{44} + 5238 q^{45} - 25584 q^{46} + 11700 q^{47} - 82428 q^{48} - 39402 q^{50} - 7596 q^{51} + 31444 q^{52} - 9468 q^{53} - 37908 q^{54} + 77808 q^{55} + 25752 q^{57} - 37314 q^{58} - 43938 q^{59} - 2016 q^{60} - 64754 q^{61} - 30600 q^{62} - 141566 q^{64} - 39060 q^{65} + 66816 q^{66} - 24784 q^{67} - 14994 q^{68} + 206784 q^{69} + 194832 q^{71} - 8775 q^{72} + 17452 q^{73} - 43434 q^{74} + 40494 q^{75} + 25564 q^{76} - 146160 q^{78} - 51256 q^{79} - 70272 q^{80} + 61074 q^{81} - 58338 q^{82} - 235116 q^{83} - 75720 q^{85} + 150048 q^{86} - 63180 q^{87} + 40656 q^{88} + 84276 q^{89} - 187704 q^{90} + 301824 q^{92} + 92280 q^{93} + 159468 q^{94} - 24264 q^{95} + 255906 q^{96} - 41552 q^{97} - 33480 q^{99}+O(q^{100}) \) 4 * q - 9 * q^2 - 6 * q^3 - 5 * q^4 - 18 * q^5 + 396 * q^6 - 18 * q^8 - 558 * q^9 + 204 * q^10 - 396 * q^11 - 1554 * q^12 + 700 * q^13 - 3312 * q^15 - 113 * q^16 + 1800 * q^17 - 3537 * q^18 - 3266 * q^19 - 5040 * q^20 - 3504 * q^22 - 2088 * q^23 - 1854 * q^24 + 3238 * q^25 + 2016 * q^26 + 12744 * q^27 + 13392 * q^29 + 6768 * q^30 - 20 * q^31 + 6129 * q^32 + 20016 * q^33 - 11868 * q^34 + 21258 * q^36 - 6232 * q^37 - 15210 * q^38 + 20496 * q^39 + 3216 * q^40 + 12096 * q^41 - 6040 * q^43 + 30816 * q^44 + 5238 * q^45 - 25584 * q^46 + 11700 * q^47 - 82428 * q^48 - 39402 * q^50 - 7596 * q^51 + 31444 * q^52 - 9468 * q^53 - 37908 * q^54 + 77808 * q^55 + 25752 * q^57 - 37314 * q^58 - 43938 * q^59 - 2016 * q^60 - 64754 * q^61 - 30600 * q^62 - 141566 * q^64 - 39060 * q^65 + 66816 * q^66 - 24784 * q^67 - 14994 * q^68 + 206784 * q^69 + 194832 * q^71 - 8775 * q^72 + 17452 * q^73 - 43434 * q^74 + 40494 * q^75 + 25564 * q^76 - 146160 * q^78 - 51256 * q^79 - 70272 * q^80 + 61074 * q^81 - 58338 * q^82 - 235116 * q^83 - 75720 * q^85 + 150048 * q^86 - 63180 * q^87 + 40656 * q^88 + 84276 * q^89 - 187704 * q^90 + 301824 * q^92 + 92280 * q^93 + 159468 * q^94 - 24264 * q^95 + 255906 * q^96 - 41552 * q^97 - 33480 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.362541	+	0.627940i	−0.0640889	+	0.111005i	−0.896289	−	0.443470i	$-0.853747\pi$
$2$	−0.362541	+	0.627940i	−0.0640889	+	0.111005i	0.832201	+	0.554475i	$0.187081\pi$
$3$	9.82475	+	17.0170i	0.630258	+	1.09164i	0.987499	+	0.157627i	$0.0503843\pi$
$3$	9.82475	+	17.0170i	0.630258	+	1.09164i	−0.357241	+	0.934012i	$0.616282\pi$
$4$	15.7371	+	27.2575i	0.491785	+	0.851797i
$5$	−23.3746	+	40.4860i	−0.418137	+	0.724235i	−0.995752	−	0.0920744i	$-0.970650\pi$
$5$	−23.3746	+	40.4860i	−0.418137	+	0.724235i	0.577615	+	0.816309i	$0.303984\pi$
$6$	−14.2475			−0.161570
$7$		0			0
$7$		0			0
$8$	−46.0241			−0.254250
$9$	−71.5515	+	123.931i	−0.294451	+	0.510003i
$10$	−16.9485	−	29.3557i	−0.0535959	−	0.0928308i
$11$	−333.045	−	576.851i	−0.829891	−	1.43741i	−0.898123	−	0.439744i	$-0.855069\pi$
$11$	−333.045	−	576.851i	−0.829891	−	1.43741i	0.0682323	−	0.997669i	$-0.478264\pi$
$12$	−309.227	+	535.596i	−0.619903	+	1.07370i
$13$	650.640			1.06778			0.533890	−	0.845554i	$-0.320729\pi$
$13$	650.640			1.06778			0.533890	+	0.845554i	$0.320729\pi$
$14$		0			0
$15$	−918.598			−1.05414
$16$	−486.902	+	843.340i	−0.475491	+	0.823574i
$17$	593.447	+	1027.88i	0.498035	+	0.862621i	0.999997	−	0.00226795i	$-0.000721910\pi$
$17$	593.447	+	1027.88i	0.498035	+	0.862621i	−0.501963	+	0.864889i	$0.667389\pi$
$18$	−51.8808	−	89.8601i	−0.0377420	−	0.0653711i
$19$	−782.526	+	1355.37i	−0.497296	+	0.861341i	−0.999995	−	0.00311994i	$-0.999007\pi$
$19$	−782.526	+	1355.37i	−0.497296	+	0.861341i	0.502700	+	0.864461i	$0.332340\pi$
$20$	−1471.40			−0.822535
$21$		0			0
$22$	482.970			0.212747
$23$	550.076	−	952.760i	0.216822	−	0.375547i	−0.737013	−	0.675879i	$-0.763764\pi$
$23$	550.076	−	952.760i	0.216822	−	0.375547i	0.953835	+	0.300332i	$0.0970975\pi$
$24$	−452.175	−	783.191i	−0.160243	−	0.277549i
$25$	469.757	+	813.644i	0.150322	+	0.260366i
$26$	−235.884	+	408.563i	−0.0684329	+	0.118529i
$27$	1962.93			0.518197
$28$		0			0
$29$	2396.72			0.529203			0.264602	−	0.964358i	$-0.414760\pi$
$29$	2396.72			0.529203			0.264602	+	0.964358i	$0.414760\pi$
$30$	333.030	−	576.825i	0.0675585	−	0.117015i
$31$	−1024.23	−	1774.01i	−0.191422	−	0.331553i	0.754300	−	0.656530i	$-0.227977\pi$
$31$	−1024.23	−	1774.01i	−0.191422	−	0.331553i	−0.945722	+	0.324977i	$0.894643\pi$
$32$	−1089.43	−	1886.95i	−0.188072	−	0.325750i
$33$	6544.17	−	11334.8i	1.04609	−	1.81188i
$34$	−860.596			−0.127674
$35$		0			0
$36$	−4504.06			−0.579226
$37$	−538.772	+	933.181i	−0.0646995	+	0.112063i	−0.896561	−	0.442921i	$-0.853942\pi$
$37$	−538.772	+	933.181i	−0.0646995	+	0.112063i	0.831861	+	0.554984i	$0.187276\pi$
$38$	−567.396	−	982.759i	−0.0637422	−	0.110405i
$39$	6392.37	+	11071.9i	0.672977	+	1.16563i
$40$	1075.79	−	1863.33i	0.106311	−	0.184136i
$41$	−1098.21			−0.102029			−0.0510147	−	0.998698i	$-0.516246\pi$
$41$	−1098.21			−0.102029			−0.0510147	+	0.998698i	$0.516246\pi$
$42$		0			0
$43$	16564.3			1.36616			0.683081	−	0.730343i	$-0.260640\pi$
$43$	16564.3			1.36616			0.683081	+	0.730343i	$0.260640\pi$
$44$	10482.3	−	18155.9i	0.816256	−	1.41380i
$45$	−3344.97	−	5793.66i	−0.246242	−	0.426503i
$46$	398.851	+	690.830i	0.0277918	+	0.0481367i
$47$	−4149.19	+	7186.62i	−0.273980	+	0.474548i	−0.969877	−	0.243594i	$-0.921674\pi$
$47$	−4149.19	+	7186.62i	−0.273980	+	0.474548i	0.695897	+	0.718141i	$0.255007\pi$
$48$	−19134.8			−1.19873
$49$		0			0
$50$	−681.226			−0.0385360
$51$	−11660.9	+	20197.3i	−0.627781	+	1.08735i
$52$	10239.2	+	17734.8i	0.525119	+	0.909532i
$53$	−2759.59	−	4779.75i	−0.134944	−	0.233731i	0.790632	−	0.612292i	$-0.209752\pi$
$53$	−2759.59	−	4779.75i	−0.134944	−	0.233731i	−0.925576	+	0.378561i	$0.876419\pi$
$54$	−711.642	+	1232.60i	−0.0332106	+	0.0575225i
$55$	31139.1			1.38803
$56$		0			0
$57$	−30752.5			−1.25370
$58$	−868.911	+	1505.00i	−0.0339160	+	0.0587443i
$59$	−7115.21	−	12323.9i	−0.266108	−	0.460912i	0.701745	−	0.712428i	$-0.252404\pi$
$59$	−7115.21	−	12323.9i	−0.266108	−	0.460912i	−0.967853	+	0.251515i	$0.919071\pi$
$60$	−14456.1	−	25038.7i	−0.518409	−	0.897911i
$61$	−7117.37	+	12327.7i	−0.244904	+	0.424186i	−0.962105	−	0.272681i	$-0.912090\pi$
$61$	−7117.37	+	12327.7i	−0.244904	+	0.424186i	0.717201	+	0.696866i	$0.245423\pi$
$62$	1485.30			0.0490721
$63$		0			0
$64$	−29581.9			−0.902768
$65$	−15208.4	+	26341.8i	−0.446479	+	0.773324i
$66$	4745.06	+	8218.69i	0.134086	+	0.232243i
$67$	−9865.22	−	17087.1i	−0.268485	−	0.465029i	0.699986	−	0.714157i	$-0.253190\pi$
$67$	−9865.22	−	17087.1i	−0.268485	−	0.465029i	−0.968471	+	0.249127i	$0.919856\pi$
$68$	−18678.3	+	32351.8i	−0.489852	+	0.848449i
$69$	21617.5			0.546615
$70$		0			0
$71$	64562.7			1.51997			0.759986	−	0.649940i	$-0.225206\pi$
$71$	64562.7			1.51997			0.759986	+	0.649940i	$0.225206\pi$
$72$	3293.09	−	5703.80i	0.0748639	−	0.129668i
$73$	14283.5	+	24739.7i	0.313709	+	0.543360i	0.979162	−	0.203080i	$-0.0650950\pi$
$73$	14283.5	+	24739.7i	0.313709	+	0.543360i	−0.665453	+	0.746440i	$0.731762\pi$
$74$	−390.655	−	676.634i	−0.00829304	−	0.0143640i
$75$	−9230.50	+	15987.7i	−0.189484	+	0.328196i
$76$	−49258.8			−0.978251
$77$		0			0
$78$	−9270.00			−0.172521
$79$	15316.7	−	26529.3i	0.276119	−	0.478253i	−0.694297	−	0.719688i	$-0.744285\pi$
$79$	15316.7	−	26529.3i	0.276119	−	0.478253i	0.970417	+	0.241435i	$0.0776181\pi$
$80$	−22762.3	−	39425.4i	−0.397641	−	0.688734i
$81$	36672.3	+	63518.3i	0.621048	+	1.07569i
$82$	398.146	−	689.610i	0.00653895	−	0.0113258i
$83$	675.946			0.0107700			0.00538501	−	0.999986i	$-0.498286\pi$
$83$	675.946			0.0107700			0.00538501	+	0.999986i	$0.498286\pi$
$84$		0			0
$85$	−55486.3			−0.832987
$86$	−6005.25	+	10401.4i	−0.0875557	+	0.151651i
$87$	23547.2	+	40784.9i	0.333535	+	0.577699i
$88$	15328.1	+	26549.0i	0.210999	+	0.365462i
$89$	62985.7	−	109094.i	0.842882	−	1.45991i	−0.0445658	−	0.999006i	$-0.514190\pi$
$89$	62985.7	−	109094.i	0.842882	−	1.45991i	0.887448	−	0.460908i	$-0.152476\pi$
$90$	4850.76			0.0631254
$91$		0			0
$92$	34626.5			0.426520
$93$	20125.6	−	34858.5i	0.241291	−	0.417928i
$94$	−3008.51	−	5210.89i	−0.0351182	−	0.0608264i
$95$	−36582.4	−	63362.6i	−0.415876	−	0.720318i
$96$	21406.8	−	37077.6i	0.237068	−	0.410614i
$97$	22906.8			0.247192			0.123596	−	0.992333i	$-0.460557\pi$
$97$	22906.8			0.247192			0.123596	+	0.992333i	$0.460557\pi$
$98$		0			0
$99$	95319.4			0.977447
$100$	−14785.3	+	25608.8i	−0.147853	+	0.256088i
$101$	−90737.0	−	157161.i	−0.885077	−	1.53300i	−0.845625	−	0.533777i	$-0.820772\pi$
$101$	−90737.0	−	157161.i	−0.885077	−	1.53300i	−0.0394521	−	0.999221i	$-0.512561\pi$
$102$	−8455.14	−	14644.7i	−0.0804675	−	0.139374i
$103$	32386.0	−	56094.2i	0.300791	−	0.520985i	−0.675525	−	0.737338i	$-0.736083\pi$
$103$	32386.0	−	56094.2i	0.300791	−	0.520985i	0.976315	+	0.216353i	$0.0694161\pi$
$104$	−29945.1			−0.271483
$105$		0			0
$106$	4001.86			0.0345938
$107$	74084.9	−	128319.i	0.625562	−	1.08350i	−0.362870	−	0.931840i	$-0.618203\pi$
$107$	74084.9	−	128319.i	0.625562	−	1.08350i	0.988432	−	0.151665i	$-0.0484635\pi$
$108$	30890.8	+	53504.5i	0.254842	+	0.441398i
$109$	55647.2	+	96383.8i	0.448618	+	0.777030i	0.998296	−	0.0583467i	$-0.0185829\pi$
$109$	55647.2	+	96383.8i	0.448618	+	0.777030i	−0.549678	+	0.835377i	$0.685250\pi$
$110$	−11289.2	+	19553.5i	−0.0889575	+	0.154079i
$111$	−21173.2			−0.163110
$112$		0			0
$113$	−43175.5			−0.318084			−0.159042	−	0.987272i	$-0.550840\pi$
$113$	−43175.5			−0.318084			−0.159042	+	0.987272i	$0.550840\pi$
$114$	11149.0	−	19310.7i	0.0803481	−	0.139167i
$115$	25715.6	+	44540.8i	0.181323	+	0.314060i
$116$	37717.5	+	65328.6i	0.260254	+	0.450774i
$117$	−46554.2	+	80634.3i	−0.314409	+	0.544572i
$118$	10318.2			0.0682182
$119$		0			0
$120$	42277.6			0.268014
$121$	−141312.	+	244760.i	−0.877438	+	1.51977i
$122$	−5160.69	−	8938.57i	−0.0313912	−	0.0543711i
$123$	−10789.6	−	18688.2i	−0.0643049	−	0.111379i
$124$	32236.8	−	55835.8i	0.188277	−	0.326106i
$125$	−190013.			−1.08770
$126$		0			0
$127$	−131449.			−0.723182			−0.361591	−	0.932337i	$-0.617766\pi$
$127$	−131449.			−0.723182			−0.361591	+	0.932337i	$0.617766\pi$
$128$	45586.4	−	78958.0i	0.245929	−	0.425962i
$129$	162740.	+	281874.i	0.861034	+	1.49136i
$130$	−11027.4	−	19100.0i	−0.0572287	−	0.0991230i
$131$	−174729.	+	302639.i	−0.889582	+	1.54080i	−0.0492126	+	0.998788i	$0.515671\pi$
$131$	−174729.	+	302639.i	−0.889582	+	1.54080i	−0.840370	+	0.542014i	$0.817662\pi$
$132$	411946.			2.05781
$133$		0			0
$134$	14306.2			0.0688276
$135$	−45882.6	+	79471.0i	−0.216677	+	0.375296i
$136$	−27312.9	−	47307.2i	−0.126625	−	0.219321i
$137$	−193217.	−	334662.i	−0.879516	−	1.52337i	−0.851873	−	0.523749i	$-0.824533\pi$
$137$	−193217.	−	334662.i	−0.879516	−	1.52337i	−0.0276435	−	0.999618i	$-0.508800\pi$
$138$	−7837.22	+	13574.5i	−0.0350320	+	0.0606771i
$139$	−17289.3			−0.0758997			−0.0379498	−	0.999280i	$-0.512083\pi$
$139$	−17289.3			−0.0758997			−0.0379498	+	0.999280i	$0.512083\pi$
$140$		0			0
$141$	−163059.			−0.690713
$142$	−23406.6	+	40541.5i	−0.0974133	+	0.168725i
$143$	−216692.	−	375322.i	−0.886142	−	1.53484i
$144$	−69677.2	−	120684.i	−0.280017	−	0.485004i
$145$	−56022.4	+	97033.6i	−0.221280	+	0.383268i
$146$	−20713.4			−0.0804210
$147$		0			0
$148$	−33914.9			−0.127273
$149$	56085.3	−	97142.6i	0.206959	−	0.358463i	−0.743796	−	0.668406i	$-0.766977\pi$
$149$	56085.3	−	97142.6i	0.206959	−	0.358463i	0.950755	+	0.309943i	$0.100310\pi$
$150$	−6692.88	−	11592.4i	−0.0242876	−	0.0420674i
$151$	−15247.7	−	26409.8i	−0.0544205	−	0.0942590i	0.837532	−	0.546389i	$-0.183998\pi$
$151$	−15247.7	−	26409.8i	−0.0544205	−	0.0942590i	−0.891952	+	0.452130i	$0.850664\pi$
$152$	36015.0	−	62379.9i	0.126437	−	0.218996i
$153$	−169848.			−0.586586
$154$		0			0
$155$	95763.6			0.320163
$156$	−201195.	+	348480.i	−0.661921	+	1.14648i
$157$	261754.	+	453372.i	0.847510	+	1.46793i	0.883424	+	0.468575i	$0.155232\pi$
$157$	261754.	+	453372.i	0.847510	+	1.46793i	−0.0359139	+	0.999355i	$0.511434\pi$
$158$	11105.9	+	19235.9i	0.0353924	+	0.0613014i
$159$	54224.6	−	93919.8i	0.170100	−	0.294621i
$160$	101860.			0.314560
$161$		0			0
$162$	−53180.9			−0.159209
$163$	219823.	−	380744.i	0.648043	−	1.12244i	−0.335547	−	0.942024i	$-0.608921\pi$
$163$	219823.	−	380744.i	0.648043	−	1.12244i	0.983590	−	0.180420i	$-0.0577457\pi$
$164$	−17282.7	−	29934.5i	−0.0501766	−	0.0869084i
$165$	305934.	+	529894.i	0.874819	+	1.51523i
$166$	−245.058	+	424.454i	−0.000690239	+	0.00119553i
$167$	−279353.			−0.775107			−0.387554	−	0.921847i	$-0.626680\pi$
$167$	−279353.			−0.775107			−0.387554	+	0.921847i	$0.626680\pi$
$168$		0			0
$169$	52038.8			0.140156
$170$	20116.1	−	34842.1i	0.0533852	−	0.0924659i
$171$	−111982.	−	193958.i	−0.292858	−	0.507245i
$172$	260675.	+	451502.i	0.671858	+	1.16369i
$173$	49849.7	−	86342.2i	0.126633	−	0.219335i	−0.795737	−	0.605642i	$-0.792916\pi$
$173$	49849.7	−	86342.2i	0.126633	−	0.219335i	0.922370	+	0.386307i	$0.126250\pi$
$174$	−34147.3			−0.0855034
$175$		0			0
$176$	648641.			1.57842
$177$	139810.	−	242159.i	0.335433	−	0.580987i
$178$	45669.8	+	79102.5i	0.108039	+	0.187129i
$179$	−164990.	−	285771.i	−0.384880	−	0.666631i	0.606873	−	0.794799i	$-0.292424\pi$
$179$	−164990.	−	285771.i	−0.384880	−	0.666631i	−0.991753	+	0.128168i	$0.959090\pi$
$180$	105281.	−	182351.i	0.242196	−	0.419496i
$181$	505810.			1.14760			0.573800	−	0.818995i	$-0.305469\pi$
$181$	505810.			1.14760			0.573800	+	0.818995i	$0.305469\pi$
$182$		0			0
$183$	−279706.			−0.617410
$184$	−25316.8	+	43849.9i	−0.0551269	+	0.0954826i
$185$	−25187.2	−	43625.4i	−0.0541066	−	0.0937153i
$186$	14592.7	+	25275.3i	0.0309281	+	0.0535690i
$187$	395289.	−	684660.i	0.826629	−	1.43176i
$188$	−261186.			−0.538958
$189$		0			0
$190$	53050.6			0.106612
$191$	31917.8	−	55283.2i	0.0633067	−	0.109650i	−0.832635	−	0.553822i	$-0.813169\pi$
$191$	31917.8	−	55283.2i	0.0633067	−	0.109650i	0.895942	+	0.444172i	$0.146502\pi$
$192$	−290635.	−	503394.i	−0.568977	−	0.985497i
$193$	−234677.	−	406473.i	−0.453501	−	0.785486i	0.545100	−	0.838371i	$-0.316492\pi$
$193$	−234677.	−	406473.i	−0.453501	−	0.785486i	−0.998601	+	0.0528848i	$0.983158\pi$
$194$	−8304.65	+	14384.1i	−0.0158423	+	0.0274396i
$195$	−597676.			−1.12559
$196$		0			0
$197$	268021.			0.492043			0.246021	−	0.969264i	$-0.420877\pi$
$197$	268021.			0.492043			0.246021	+	0.969264i	$0.420877\pi$
$198$	−34557.2	+	59854.9i	−0.0626435	+	0.108502i
$199$	−302584.	−	524090.i	−0.541642	−	0.938152i	−0.998810	−	0.0487715i	$-0.984469\pi$
$199$	−302584.	−	524090.i	−0.541642	−	0.938152i	0.457168	−	0.889381i	$-0.348864\pi$
$200$	−21620.2	−	37447.2i	−0.0382194	−	0.0661979i
$201$	193847.	−	335752.i	0.338429	−	0.586177i
$202$	131584.			0.226894
$203$		0			0
$204$	−734039.			−1.23493
$205$	25670.2	−	44462.1i	0.0426623	−	0.0738933i
$206$	23482.5	+	40673.0i	0.0385547	+	0.0667787i
$207$	78717.6	+	136343.i	0.127687	+	0.221160i
$208$	−316798.	+	548710.i	−0.507720	+	0.879396i
$209$	1.04246e6			1.65080
$210$		0			0
$211$	335389.			0.518612			0.259306	−	0.965795i	$-0.416506\pi$
$211$	335389.			0.518612			0.259306	+	0.965795i	$0.416506\pi$
$212$	86856.1	−	150439.i	0.132727	−	0.229891i
$213$	634312.	+	1.09866e6i	0.957974	+	1.65926i
$214$	53717.7	+	93041.8i	0.0801831	+	0.138881i
$215$	−387184.	+	670622.i	−0.571243	+	0.989422i
$216$	−90341.9			−0.131751
$217$		0			0
$218$	−80697.7			−0.115006
$219$	−280663.	+	486123.i	−0.395435	+	0.684914i
$220$	490041.	+	848775.i	0.682614	+	1.18232i
$221$	386120.	+	668779.i	0.531792	+	0.921090i
$222$	7676.17	−	13295.5i	0.0104535	−	0.0181060i
$223$	−1.02526e6			−1.38061			−0.690305	−	0.723518i	$-0.742524\pi$
$223$	−1.02526e6			−1.38061			−0.690305	+	0.723518i	$0.742524\pi$
$224$		0			0
$225$	−134447.			−0.177050
$226$	15652.9	−	27111.6i	0.0203856	−	0.0353089i
$227$	−252113.	−	436673.i	−0.324736	−	0.562460i	0.656723	−	0.754132i	$-0.271942\pi$
$227$	−252113.	−	436673.i	−0.324736	−	0.562460i	−0.981459	+	0.191672i	$0.938609\pi$
$228$	−483956.	−	838236.i	−0.616550	−	1.06790i
$229$	−559696.	+	969422.i	−0.705283	+	1.22159i	0.261306	+	0.965256i	$0.415847\pi$
$229$	−559696.	+	969422.i	−0.705283	+	1.22159i	−0.966589	+	0.256331i	$0.917486\pi$
$230$	−37291.9			−0.0464831
$231$		0			0
$232$	−110307.			−0.134550
$233$	−385352.	+	667448.i	−0.465015	+	0.805430i	−0.999202	−	0.0399362i	$-0.987285\pi$
$233$	−385352.	+	667448.i	−0.465015	+	0.805430i	0.534187	+	0.845366i	$0.320618\pi$
$234$	−33755.7	−	58466.5i	−0.0403002	−	0.0698020i
$235$	−193971.	−	335968.i	−0.229123	−	0.396852i
$236$	223946.	−	387886.i	0.261736	−	0.453340i
$237$	601930.			0.696106
$238$		0			0
$239$	−171646.			−0.194374			−0.0971871	−	0.995266i	$-0.530985\pi$
$239$	−171646.			−0.194374			−0.0971871	+	0.995266i	$0.530985\pi$
$240$	447268.	−	774690.i	0.501233	−	0.868160i
$241$	−191890.	−	332363.i	−0.212818	−	0.368612i	0.739777	−	0.672852i	$-0.234931\pi$
$241$	−191890.	−	332363.i	−0.212818	−	0.368612i	−0.952595	+	0.304240i	$0.901598\pi$
$242$	−102463.	−	177471.i	−0.112468	−	0.194800i
$243$	−482096.	+	835016.i	−0.523743	+	0.907150i
$244$	−448028.			−0.481760
$245$		0			0
$246$	15646.8			0.0164849
$247$	−509142.	+	881860.i	−0.531003	+	0.919724i
$248$	47139.1	+	81647.4i	0.0486690	+	0.0842972i
$249$	6641.00	+	11502.6i	0.00678790	+	0.0117570i
$250$	68887.5	−	119317.i	0.0697092	−	0.120740i
$251$	1.57046e6			1.57342			0.786708	−	0.617325i	$-0.211784\pi$
$251$	1.57046e6			1.57342			0.786708	+	0.617325i	$0.211784\pi$
$252$		0			0
$253$	−732801.			−0.719755
$254$	47655.7	−	82542.1i	0.0463479	−	0.0802770i
$255$	−545139.	−	944209.i	−0.524997	−	0.909322i
$256$	−440257.	−	762547.i	−0.419861	−	0.727221i
$257$	395328.	−	684728.i	0.373357	−	0.646674i	−0.616722	−	0.787181i	$-0.711540\pi$
$257$	395328.	−	684728.i	0.373357	−	0.646674i	0.990080	+	0.140507i	$0.0448732\pi$
$258$	−236000.			−0.220731
$259$		0			0
$260$	−957348.			−0.878287
$261$	−171489.	+	297028.i	−0.155824	+	0.269895i
$262$	−126693.	−	219438.i	−0.114025	−	0.197496i
$263$	−232208.	−	402196.i	−0.207008	−	0.358549i	0.743762	−	0.668444i	$-0.233039\pi$
$263$	−232208.	−	402196.i	−0.207008	−	0.358549i	−0.950771	+	0.309895i	$0.899706\pi$
$264$	−301189.	+	521675.i	−0.265968	+	0.460670i
$265$	258017.			0.225701
$266$		0			0
$267$	2.47527e6			2.12493
$268$	310500.	−	537803.i	0.264074	−	0.457389i
$269$	999794.	+	1.73169e6i	0.842422	+	1.45912i	0.887841	+	0.460150i	$0.152204\pi$
$269$	999794.	+	1.73169e6i	0.842422	+	1.45912i	−0.0454190	+	0.998968i	$0.514462\pi$
$270$	−33268.7	−	57623.1i	−0.0277732	−	0.0481046i
$271$	806482.	−	1.39687e6i	0.667070	−	1.15540i	−0.311650	−	0.950197i	$-0.600882\pi$
$271$	806482.	−	1.39687e6i	0.667070	−	1.15540i	0.978720	−	0.205202i	$-0.0657851\pi$
$272$	−1.15580e6			−0.947243
$273$		0			0
$274$	280197.			0.225469
$275$	312901.	−	541960.i	0.249502	−	0.432151i
$276$	340197.	+	589238.i	0.268817	+	0.465605i
$277$	1.04060e6	+	1.80237e6i	0.814860	+	1.41138i	0.909429	+	0.415860i	$0.136519\pi$
$277$	1.04060e6	+	1.80237e6i	0.814860	+	1.41138i	−0.0945690	+	0.995518i	$0.530147\pi$
$278$	6268.08	−	10856.6i	0.00486432	−	0.00842526i
$279$	293140.			0.225457
$280$		0			0
$281$	−982035.			−0.741927			−0.370964	−	0.928647i	$-0.620973\pi$
$281$	−982035.			−0.741927			−0.370964	+	0.928647i	$0.620973\pi$
$282$	59115.7	−	102391.i	0.0442670	−	0.0766727i
$283$	−698109.	−	1.20916e6i	−0.518152	−	0.897466i	−0.999778	−	0.0210885i	$-0.993287\pi$
$283$	−698109.	−	1.20916e6i	−0.518152	−	0.897466i	0.481626	−	0.876377i	$-0.340047\pi$
$284$	1.01603e6	+	1.75982e6i	0.747500	+	1.29471i
$285$	718827.	−	1.24504e6i	0.524218	−	0.907972i
$286$	314240.			0.227167
$287$		0			0
$288$	311801.			0.221512
$289$	5570.16	−	9647.80i	0.00392304	−	0.00679491i
$290$	−40620.8	−	70357.4i	−0.0283631	−	0.0491264i
$291$	225053.	+	389804.i	0.155795	+	0.269845i
$292$	−449562.	+	778664.i	−0.308555	+	0.534433i
$293$	−2.56205e6			−1.74348			−0.871742	−	0.489965i	$-0.837010\pi$
$293$	−2.56205e6			−1.74348			−0.871742	+	0.489965i	$0.837010\pi$
$294$		0			0
$295$	665260.			0.445078
$296$	24796.5	−	42948.8i	0.0164498	−	0.0284919i
$297$	−653743.	−	1.13232e6i	−0.430047	−	0.744863i
$298$	40666.5	+	70436.4i	0.0265275	+	0.0459470i
$299$	357902.	−	619904.i	0.231518	−	0.401002i
$300$	−581046.			−0.372741
$301$		0			0
$302$	22111.7			0.0139510
$303$	1.78294e6	−	3.08814e6i	1.11565	−	1.93237i
$304$	−762027.	−	1.31987e6i	−0.472919	−	0.819119i
$305$	−332731.	−	576308.i	−0.204807	−	0.354736i
$306$	61576.9	−	106654.i	0.0375937	−	0.0651141i
$307$	884855.			0.535829			0.267915	−	0.963443i	$-0.413666\pi$
$307$	884855.			0.535829			0.267915	+	0.963443i	$0.413666\pi$
$308$		0			0
$309$	1.27274e6			0.758303
$310$	−34718.3	+	60133.8i	−0.0205189	+	0.0355398i
$311$	900601.	+	1.55989e6i	0.527997	+	0.914517i	0.999467	+	0.0326354i	$0.0103900\pi$
$311$	900601.	+	1.55989e6i	0.527997	+	0.914517i	−0.471471	+	0.881882i	$0.656277\pi$
$312$	−294203.	−	509575.i	−0.171104	−	0.296361i
$313$	475183.	−	823041.i	0.274158	−	0.474855i	−0.695765	−	0.718270i	$-0.744934\pi$
$313$	475183.	−	823041.i	0.274158	−	0.474855i	0.969922	+	0.243415i	$0.0782677\pi$
$314$	−379587.			−0.217264
$315$		0			0
$316$	964162.			0.543166
$317$	−1.52139e6	+	2.63512e6i	−0.850338	+	1.47283i	0.0305662	+	0.999533i	$0.490269\pi$
$317$	−1.52139e6	+	2.63512e6i	−0.850338	+	1.47283i	−0.880904	+	0.473295i	$0.843064\pi$
$318$	39317.3	+	68099.6i	0.0218030	+	0.0377639i
$319$	−798216.	−	1.38255e6i	−0.439181	−	0.760684i
$320$	691465.	−	1.19765e6i	0.377481	−	0.653816i
$321$	2.91146e6			1.57706
$322$		0			0
$323$	−1.85755e6			−0.990682
$324$	−1.15423e6	+	1.99919e6i	−0.610845	+	1.05801i
$325$	305643.	+	529389.i	0.160511	+	0.278014i
$326$	159390.	+	276071.i	0.0830647	+	0.143872i
$327$	−1.09344e6	+	1.89389e6i	−0.565491	+	0.979459i
$328$	50544.1			0.0259409
$329$		0			0
$330$	−443655.			−0.224265
$331$	1.09808e6	−	1.90193e6i	0.550889	−	0.954167i	−0.447322	−	0.894373i	$-0.647622\pi$
$331$	1.09808e6	−	1.90193e6i	0.550889	−	0.954167i	0.998211	−	0.0597944i	$-0.0190445\pi$
$332$	10637.5	+	18424.6i	0.00529654	+	0.00917388i
$333$	−77099.9	−	133541.i	−0.0381016	−	0.0659939i
$334$	101277.	−	175417.i	0.0496757	−	0.0860409i
$335$	922382.			0.449054
$336$		0			0
$337$	−2.41491e6			−1.15832			−0.579158	−	0.815216i	$-0.696618\pi$
$337$	−2.41491e6			−1.15832			−0.579158	+	0.815216i	$0.696618\pi$
$338$	−18866.2	+	32677.3i	−0.00898242	+	0.0155580i
$339$	−424189.	−	734716.i	−0.200475	−	0.347233i
$340$	−873195.	−	1.51242e6i	−0.409651	−	0.709536i
$341$	−682228.	+	1.18165e6i	−0.317719	+	0.550306i
$342$	162392.			0.0750757
$343$		0			0
$344$	−762357.			−0.347346
$345$	−505299.	+	875204.i	−0.228560	+	0.395878i
$346$	36145.2	+	62605.3i	0.0162315	+	0.0281139i
$347$	544166.	+	942523.i	0.242609	+	0.420212i	0.961457	−	0.274956i	$-0.0886633\pi$
$347$	544166.	+	942523.i	0.242609	+	0.420212i	−0.718847	+	0.695168i	$0.755330\pi$
$348$	−741130.	+	1.28368e6i	−0.328055	+	0.568208i
$349$	−2.79267e6			−1.22731			−0.613657	−	0.789573i	$-0.710302\pi$
$349$	−2.79267e6			−1.22731			−0.613657	+	0.789573i	$0.710302\pi$
$350$		0			0
$351$	1.27716e6			0.553321
$352$	−725658.	+	1.25688e6i	−0.312159	+	0.540675i
$353$	1.26567e6	+	2.19221e6i	0.540610	+	0.936364i	0.998869	+	0.0475454i	$0.0151399\pi$
$353$	1.26567e6	+	2.19221e6i	0.540610	+	0.936364i	−0.458259	+	0.888819i	$0.651527\pi$
$354$	101374.	+	175585.i	0.0429951	+	0.0744697i
$355$	−1.50913e6	+	2.61388e6i	−0.635557	+	1.10082i
$356$	3.96485e6			1.65807
$357$		0			0
$358$	239263.			0.0986661
$359$	−545141.	+	944211.i	−0.223240	+	0.386663i	−0.955790	−	0.294050i	$-0.904997\pi$
$359$	−545141.	+	944211.i	−0.223240	+	0.386663i	0.732550	+	0.680713i	$0.238330\pi$
$360$	153949.	+	266648.i	0.0626068	+	0.108438i
$361$	13356.4	+	23134.0i	0.00539414	+	0.00934292i
$362$	−183377.	+	317618.i	−0.0735484	+	0.127390i
$363$	−5.55343e6			−2.21205
$364$		0			0
$365$	−1.33548e6			−0.524694
$366$	101405.	−	175638.i	0.0395691	−	0.0685357i
$367$	94035.2	+	162874.i	0.0364439	+	0.0631227i	0.883672	−	0.468106i	$-0.155064\pi$
$367$	94035.2	+	162874.i	0.0364439	+	0.0631227i	−0.847228	+	0.531229i	$0.821730\pi$
$368$	535667.	+	927803.i	0.206194	+	0.357138i
$369$	78578.5	−	136102.i	0.0300426	−	0.0520354i
$370$	36525.6			0.0138705
$371$		0			0
$372$	1.26687e6			0.474653
$373$	896856.	−	1.55340e6i	0.333772	−	0.578111i	−0.649476	−	0.760382i	$-0.725012\pi$
$373$	896856.	−	1.55340e6i	0.333772	−	0.578111i	0.983248	+	0.182271i	$0.0583450\pi$
$374$	286617.	+	496435.i	0.105955	+	0.183520i
$375$	−1.86683e6	−	3.23344e6i	−0.685529	−	1.18737i
$376$	190963.	−	330757.i	0.0696594	−	0.120654i
$377$	1.55940e6			0.565073
$378$		0			0
$379$	3.58806e6			1.28310			0.641551	−	0.767080i	$-0.278291\pi$
$379$	3.58806e6			1.28310			0.641551	+	0.767080i	$0.278291\pi$
$380$	1.15140e6	−	1.99429e6i	0.409043	−	0.708483i
$381$	−1.29145e6	−	2.23686e6i	−0.455791	−	0.789454i
$382$	23143.0	+	40084.9i	0.00811450	+	0.0140547i
$383$	−1.71228e6	+	2.96576e6i	−0.596457	+	1.03309i	0.396883	+	0.917869i	$0.370092\pi$
$383$	−1.71228e6	+	2.96576e6i	−0.596457	+	1.03309i	−0.993340	+	0.115224i	$0.963241\pi$
$384$	1.79150e6			0.619996
$385$		0			0
$386$	340321.			0.116257
$387$	−1.18520e6	+	2.05283e6i	−0.402267	+	0.696747i
$388$	360487.	+	624381.i	0.121565	+	0.210557i
$389$	−4312.64	−	7469.70i	−0.00144500	−	0.00250282i	0.865302	−	0.501251i	$-0.167127\pi$
$389$	−4312.64	−	7469.70i	−0.00144500	−	0.00250282i	−0.866747	+	0.498748i	$0.833793\pi$
$390$	216682.	−	375305.i	0.0721377	−	0.124946i
$391$	1.30576e6			0.431940
$392$		0			0
$393$	−6.86667e6			−2.24267
$394$	−97168.7	+	168301.i	−0.0315345	+	0.0546193i
$395$	716042.	+	1.24022e6i	0.230912	+	0.399951i
$396$	1.50005e6	+	2.59817e6i	0.480694	+	0.832587i
$397$	628547.	−	1.08868e6i	0.200153	−	0.346675i	−0.748425	−	0.663220i	$-0.769189\pi$
$397$	628547.	−	1.08868e6i	0.200153	−	0.346675i	0.948578	+	0.316545i	$0.102523\pi$
$398$	438796.			0.138853
$399$		0			0
$400$	−914904.			−0.285908
$401$	−713351.	+	1.23556e6i	−0.221535	+	0.383710i	−0.955274	−	0.295721i	$-0.904440\pi$
$401$	−713351.	+	1.23556e6i	−0.221535	+	0.383710i	0.733739	+	0.679431i	$0.237773\pi$
$402$	140555.	+	243448.i	0.0433791	+	0.0751348i
$403$	−666403.	−	1.15424e6i	−0.204397	−	0.354026i
$404$	2.85588e6	−	4.94653e6i	0.870536	−	1.50781i
$405$	−3.42880e6			−1.03873
$406$		0			0
$407$	717741.			0.214774
$408$	536684.	−	929564.i	0.159613	−	0.276458i
$409$	−1.53264e6	−	2.65462e6i	−0.453036	−	0.784682i	0.545537	−	0.838087i	$-0.316326\pi$
$409$	−1.53264e6	−	2.65462e6i	−0.453036	−	0.784682i	−0.998573	+	0.0534050i	$0.982993\pi$
$410$	18613.0	+	32238.7i	0.00546836	+	0.00947148i
$411$	3.79662e6	−	6.57593e6i	1.10864	−	1.92023i
$412$	2.03865e6			0.591698
$413$		0			0
$414$	−114154.			−0.0327332
$415$	−15800.0	+	27366.3i	−0.00450335	+	0.00780003i
$416$	−708826.	−	1.22772e6i	−0.200820	−	0.347830i
$417$	−169863.	−	294211.i	−0.0478364	−	0.0828550i
$418$	−377937.	+	654605.i	−0.105798	+	0.183248i
$419$	248240.			0.0690776			0.0345388	−	0.999403i	$-0.489004\pi$
$419$	248240.			0.0690776			0.0345388	+	0.999403i	$0.489004\pi$
$420$		0			0
$421$	5.96280e6			1.63963			0.819814	−	0.572630i	$-0.194077\pi$
$421$	5.96280e6			1.63963			0.819814	+	0.572630i	$0.194077\pi$
$422$	−121592.	+	210604.i	−0.0332373	+	0.0575687i
$423$	−593762.	−	1.02843e6i	−0.161347	−	0.279462i
$424$	127008.	+	219984.i	0.0343096	+	0.0594259i
$425$	−557552.	+	965709.i	−0.149732	+	0.259343i
$426$	−919857.			−0.245582
$427$		0			0
$428$	4.66353e6			1.23057
$429$	4.25789e6	−	7.37489e6i	1.11700	−	1.93469i
$430$	−280740.	−	486256.i	−0.0732206	−	0.126822i
$431$	2.46769e6	+	4.27417e6i	0.639879	+	1.10830i	0.985459	+	0.169913i	$0.0543488\pi$
$431$	2.46769e6	+	4.27417e6i	0.639879	+	1.10830i	−0.345580	+	0.938389i	$0.612318\pi$
$432$	−955754.	+	1.65541e6i	−0.246398	+	0.426773i
$433$	−4.15513e6			−1.06504			−0.532519	−	0.846418i	$-0.678755\pi$
$433$	−4.15513e6			−1.06504			−0.532519	+	0.846418i	$0.678755\pi$
$434$		0			0
$435$	−2.20162e6			−0.557853
$436$	−1.75145e6	+	3.03361e6i	−0.441248	+	0.764264i
$437$	860898.	+	1.49112e6i	0.215649	+	0.373516i
$438$	−203504.	−	352480.i	−0.0506860	−	0.0877907i
$439$	−113977.	+	197415.i	−0.0282265	+	0.0488898i	−0.879794	−	0.475356i	$-0.842319\pi$
$439$	−113977.	+	197415.i	−0.0282265	+	0.0488898i	0.851567	+	0.524246i	$0.175653\pi$
$440$	−1.43315e6			−0.352907
$441$		0			0
$442$	−559938.			−0.136328
$443$	992309.	−	1.71873e6i	0.240236	−	0.416101i	−0.720546	−	0.693408i	$-0.756109\pi$
$443$	992309.	−	1.71873e6i	0.240236	−	0.416101i	0.960781	+	0.277307i	$0.0894419\pi$
$444$	−333206.	−	577129.i	−0.0802149	−	0.138936i
$445$	2.94453e6	+	5.10007e6i	0.704881	+	1.22089i
$446$	371698.	−	643801.i	0.0884817	−	0.153255i
$447$	2.20410e6			0.521749
$448$		0			0
$449$	2.61077e6			0.611157			0.305579	−	0.952167i	$-0.401150\pi$
$449$	2.61077e6			0.611157			0.305579	+	0.952167i	$0.401150\pi$
$450$	48742.7	−	84424.9i	0.0113469	−	0.0196535i
$451$	365753.	+	633503.i	0.0846733	+	0.146659i
$452$	−679459.	−	1.17686e6i	−0.156429	−	0.270943i
$453$	299610.	−	518940.i	0.0685979	−	0.118815i
$454$	365606.			0.0832480
$455$		0			0
$456$	1.41536e6			0.318752
$457$	2.04958e6	−	3.54998e6i	0.459066	−	0.795126i	−0.539846	−	0.841764i	$-0.681517\pi$
$457$	2.04958e6	−	3.54998e6i	0.459066	−	0.795126i	0.998912	+	0.0466383i	$0.0148508\pi$
$458$	−405826.	−	702911.i	−0.0904016	−	0.156580i
$459$	1.16489e6	+	2.01765e6i	0.258080	+	0.447008i
$460$	−809380.	+	1.40189e6i	−0.178344	+	0.308900i
$461$	2.62378e6			0.575009			0.287505	−	0.957779i	$-0.407174\pi$
$461$	2.62378e6			0.575009			0.287505	+	0.957779i	$0.407174\pi$
$462$		0			0
$463$	−4.28563e6			−0.929100			−0.464550	−	0.885547i	$-0.653784\pi$
$463$	−4.28563e6			−0.929100			−0.464550	+	0.885547i	$0.653784\pi$
$464$	−1.16697e6	+	2.02125e6i	−0.251631	+	0.435838i
$465$	940853.	+	1.62961e6i	0.201785	+	0.349502i
$466$	−279412.	−	483955.i	−0.0596046	−	0.103238i
$467$	495059.	−	857467.i	0.105042	−	0.181939i	−0.808713	−	0.588203i	$-0.799835\pi$
$467$	495059.	−	857467.i	0.105042	−	0.181939i	0.913756	+	0.406264i	$0.133169\pi$
$468$	−2.93052e6			−0.618486
$469$		0			0
$470$	281291.			0.0587369
$471$	−5.14334e6	+	8.90853e6i	−1.06830	+	1.85035i
$472$	327471.	+	567197.i	0.0676578	+	0.117187i
$473$	−5.51666e6	−	9.55513e6i	−1.13377	−	1.96374i
$474$	−218225.	+	377976.i	−0.0446127	+	0.0772714i
$475$	−1.47039e6			−0.299019
$476$		0			0
$477$	789812.			0.158938
$478$	62228.7	−	107783.i	0.0124572	−	0.0215765i
$479$	1.28988e6	+	2.23414e6i	0.256868	+	0.444909i	0.965401	−	0.260769i	$-0.0839760\pi$
$479$	1.28988e6	+	2.23414e6i	0.256868	+	0.444909i	−0.708533	+	0.705678i	$0.750643\pi$
$480$	1.00075e6	+	1.73335e6i	0.198254	+	0.343386i
$481$	−350547.	+	607165.i	−0.0690849	+	0.119659i
$482$	278272.			0.0545571
$483$		0			0
$484$	−8.89540e6			−1.72604
$485$	−535436.	+	927403.i	−0.103360	+	0.179025i
$486$	−349560.	−	605455.i	−0.0671322	−	0.116276i
$487$	−1.60737e6	−	2.78404e6i	−0.307109	−	0.531929i	0.670619	−	0.741802i	$-0.266028\pi$
$487$	−1.60737e6	−	2.78404e6i	−0.307109	−	0.531929i	−0.977729	+	0.209873i	$0.932695\pi$
$488$	327571.	−	567369.i	0.0622666	−	0.107849i
$489$	8.63882e6			1.63374
$490$		0			0
$491$	−7.86108e6			−1.47156			−0.735781	−	0.677220i	$-0.763185\pi$
$491$	−7.86108e6			−1.47156			−0.735781	+	0.677220i	$0.763185\pi$
$492$	339596.	−	588197.i	0.0632484	−	0.109549i
$493$	1.42233e6	+	2.46354e6i	0.263562	+	0.456502i
$494$	−369170.	−	639422.i	−0.0680627	−	0.117888i
$495$	−2.22805e6	+	3.85910e6i	−0.408707	+	0.707902i
$496$	1.99480e6			0.364078
$497$		0			0
$498$	−9630.55			−0.00174011
$499$	676912.	−	1.17245e6i	0.121697	−	0.210786i	−0.798740	−	0.601677i	$-0.794500\pi$
$499$	676912.	−	1.17245e6i	0.121697	−	0.210786i	0.920437	+	0.390891i	$0.127833\pi$
$500$	−2.99025e6	−	5.17927e6i	−0.534913	−	0.926496i
$501$	−2.74457e6	−	4.75374e6i	−0.488517	−	0.846137i
$502$	−569358.	+	986157.i	−0.100838	+	0.174657i
$503$	−3.85775e6			−0.679851			−0.339926	−	0.940452i	$-0.610402\pi$
$503$	−3.85775e6			−0.679851			−0.339926	+	0.940452i	$0.610402\pi$
$504$		0			0
$505$	8.48376e6			1.48034
$506$	265671.	−	460155.i	0.0461283	−	0.0798965i
$507$	511269.	+	885543.i	0.0883343	+	0.152999i
$508$	−2.06863e6	−	3.58297e6i	−0.355650	−	0.616004i
$509$	−5.30301e6	+	9.18509e6i	−0.907253	+	1.57141i	−0.0893888	+	0.995997i	$0.528491\pi$
$509$	−5.30301e6	+	9.18509e6i	−0.907253	+	1.57141i	−0.817864	+	0.575411i	$0.804842\pi$
$510$	790542.			0.134586
$511$		0			0
$512$	3.55598e6			0.599493
$513$	−1.53604e6	+	2.66050e6i	−0.257697	+	0.446344i
$514$	286646.	+	496485.i	0.0478561	+	0.0828892i
$515$	1.51402e6	+	2.62236e6i	0.251544	+	0.435686i
$516$	−5.12213e6	+	8.87178e6i	−0.846888	+	1.46685i
$517$	5.52747e6			0.909495
$518$		0			0
$519$	1.95904e6			0.319246
$520$	699954.	−	1.21236e6i	0.113517	−	0.196617i
$521$	−4.58994e6	−	7.95002e6i	−0.740821	−	1.28314i	−0.952122	−	0.305718i	$-0.901104\pi$
$521$	−4.58994e6	−	7.95002e6i	−0.740821	−	1.28314i	0.211302	−	0.977421i	$-0.432230\pi$
$522$	−124344.	−	215370.i	−0.0199732	−	0.0345946i
$523$	4.52793e6	−	7.84260e6i	0.723844	−	1.25373i	−0.235604	−	0.971849i	$-0.575707\pi$
$523$	4.52793e6	−	7.84260e6i	0.723844	−	1.25373i	0.959448	−	0.281886i	$-0.0909599\pi$
$524$	−1.09989e7			−1.74993
$525$		0			0
$526$	336740.			0.0530677
$527$	1.21565e6	−	2.10557e6i	0.190670	−	0.330250i
$528$	6.37274e6	+	1.10379e7i	0.994813	+	1.72307i
$529$	2.61300e6	+	4.52585e6i	0.405976	+	0.703172i
$530$	−93541.9	+	162019.i	−0.0144649	+	0.0250540i
$531$	2.03642e6			0.313422
$532$		0			0
$533$	−714539.			−0.108945
$534$	−897390.	+	1.55432e6i	−0.136185	+	0.235879i
$535$	3.46341e6	+	5.99880e6i	0.523141	+	0.906108i
$536$	454038.	+	786416.i	0.0682622	+	0.118234i
$537$	3.24197e6	−	5.61526e6i	0.485147	−	0.840300i
$538$	−1.44987e6			−0.215960
$539$		0			0
$540$	−2.88824e6			−0.426235
$541$	−6.08917e6	+	1.05467e7i	−0.894468	+	1.54926i	−0.0600061	+	0.998198i	$0.519112\pi$
$541$	−6.08917e6	+	1.05467e7i	−0.894468	+	1.54926i	−0.834462	+	0.551066i	$0.814221\pi$
$542$	584766.	+	1.01284e6i	0.0855035	+	0.148096i
$543$	4.96945e6	+	8.60735e6i	0.723284	+	1.25277i
$544$	1.29304e6	−	2.23961e6i	0.187333	−	0.324470i
$545$	−5.20292e6			−0.750336
$546$		0			0
$547$	−9.00451e6			−1.28674			−0.643372	−	0.765554i	$-0.722465\pi$
$547$	−9.00451e6			−1.28674			−0.643372	+	0.765554i	$0.722465\pi$
$548$	6.08136e6	−	1.05332e7i	0.865066	−	1.49834i
$549$	−1.01852e6	−	1.76412e6i	−0.144224	−	0.249803i
$550$	226879.	+	392966.i	0.0319807	+	0.0553921i
$551$	−1.87550e6	+	3.24845e6i	−0.263170	+	0.455825i
$552$	−994924.			−0.138977
$553$		0			0
$554$	−1.50904e6			−0.208894
$555$	494915.	−	857218.i	0.0682022	−	0.118130i
$556$	−272084.	−	471263.i	−0.0373263	−	0.0646511i
$557$	−772303.	−	1.33767e6i	−0.105475	−	0.182688i	0.808457	−	0.588555i	$-0.200303\pi$
$557$	−772303.	−	1.33767e6i	−0.105475	−	0.182688i	−0.913932	+	0.405867i	$0.866970\pi$
$558$	−106275.	+	184074.i	−0.0144493	+	0.0250269i
$559$	1.07774e7			1.45876
$560$		0			0
$561$	1.55345e7			2.08396
$562$	356028.	−	616659.i	0.0475493	−	0.0823578i
$563$	−5.93738e6	−	1.02838e7i	−0.789449	−	1.36737i	−0.926305	−	0.376775i	$-0.877033\pi$
$563$	−5.93738e6	−	1.02838e7i	−0.789449	−	1.36737i	0.136856	−	0.990591i	$-0.456300\pi$
$564$	−2.56608e6	−	4.44459e6i	−0.339682	−	0.588347i
$565$	1.00921e6	−	1.74800e6i	0.133003	−	0.230367i
$566$	1.01237e6			0.132831
$567$		0			0
$568$	−2.97144e6			−0.386452
$569$	771542.	−	1.33635e6i	0.0999031	−	0.173037i	−0.811741	−	0.584017i	$-0.801480\pi$
$569$	771542.	−	1.33635e6i	0.0999031	−	0.173037i	0.911644	+	0.410980i	$0.134813\pi$
$570$	521209.	+	902760.i	0.0671931	+	0.116382i
$571$	3.50906e6	+	6.07787e6i	0.450402	+	0.780119i	0.998411	−	0.0563532i	$-0.0179473\pi$
$571$	3.50906e6	+	6.07787e6i	0.450402	+	0.780119i	−0.548009	+	0.836473i	$0.684614\pi$
$572$	6.82022e6	−	1.18130e7i	0.871583	−	1.50963i
$573$	1.25434e6			0.159598
$574$		0			0
$575$	1.03361e6			0.130373
$576$	2.11663e6	−	3.66611e6i	0.265821	−	0.460415i
$577$	−2.68772e6	−	4.65526e6i	−0.336081	−	0.582109i	0.647611	−	0.761971i	$-0.275768\pi$
$577$	−2.68772e6	−	4.65526e6i	−0.336081	−	0.582109i	−0.983692	+	0.179862i	$0.942435\pi$
$578$	4038.83	+	6995.46i	0.000502847	+	0.000870957i
$579$	4.61129e6	−	7.98700e6i	0.571645	−	0.990118i
$580$	−3.52652e6			−0.435288
$581$		0			0
$582$	−326365.			−0.0399389
$583$	−1.83814e6	+	3.18374e6i	−0.223978	+	0.387942i
$584$	−657384.	−	1.13862e6i	−0.0797604	−	0.138149i
$585$	−2.17637e6	−	3.76959e6i	−0.262932	−	0.455412i
$586$	928848.	−	1.60881e6i	0.111738	−	0.193536i
$587$	2.06682e6			0.247575			0.123788	−	0.992309i	$-0.460496\pi$
$587$	2.06682e6			0.247575			0.123788	+	0.992309i	$0.460496\pi$
$588$		0			0
$589$	3.20594e6			0.380774
$590$	−241184.	+	417744.i	−0.0285246	+	0.0494060i
$591$	2.63324e6	+	4.56090e6i	0.310114	+	0.537133i
$592$	−524659.	−	908736.i	−0.0615280	−	0.106570i
$593$	−2.73473e6	+	4.73670e6i	−0.319358	+	0.553145i	−0.980354	−	0.197245i	$-0.936801\pi$
$593$	−2.73473e6	+	4.73670e6i	−0.319358	+	0.553145i	0.660996	+	0.750389i	$0.270134\pi$
$594$	948035.			0.110245
$595$		0			0
$596$	3.53049e6			0.407117
$597$	5.94562e6	−	1.02981e7i	0.682749	−	1.18256i
$598$	259508.	+	449481.i	0.0296755	+	0.0513995i
$599$	−5.49716e6	−	9.52137e6i	−0.625996	−	1.08426i	−0.988347	−	0.152216i	$-0.951359\pi$
$599$	−5.49716e6	−	9.52137e6i	−0.625996	−	1.08426i	0.362351	−	0.932042i	$-0.381974\pi$
$600$	424825.	−	735819.i	0.0481762	−	0.0834436i
$601$	−1.58788e7			−1.79322			−0.896608	−	0.442826i	$-0.853976\pi$
$601$	−1.58788e7			−1.79322			−0.896608	+	0.442826i	$0.853976\pi$
$602$		0			0
$603$	2.82348e6			0.316222
$604$	479910.	−	831229.i	0.0535264	−	0.0927104i
$605$	−6.60623e6	−	1.14423e7i	−0.733779	−	1.27094i
$606$	1.29278e6	+	2.23916e6i	0.143002	+	0.247687i
$607$	2.66631e6	−	4.61818e6i	0.293724	−	0.508744i	−0.680964	−	0.732317i	$-0.738439\pi$
$607$	2.66631e6	−	4.61818e6i	0.293724	−	0.508744i	0.974687	+	0.223573i	$0.0717722\pi$
$608$	3.41003e6			0.374110
$609$		0			0
$610$	482516.			0.0525033
$611$	−2.69963e6	+	4.67590e6i	−0.292551	+	0.506713i
$612$	−2.67292e6	−	4.62963e6i	−0.288474	−	0.499652i
$613$	4.45919e6	+	7.72355e6i	0.479297	+	0.830167i	0.999718	−	0.0237428i	$-0.00755827\pi$
$613$	4.45919e6	+	7.72355e6i	0.479297	+	0.830167i	−0.520421	+	0.853910i	$0.674225\pi$
$614$	−320797.	+	555636.i	−0.0343407	+	0.0594798i
$615$	1.00881e6			0.107553
$616$		0			0
$617$	9.63586e6			1.01901			0.509504	−	0.860468i	$-0.329829\pi$
$617$	9.63586e6			1.01901			0.509504	+	0.860468i	$0.329829\pi$
$618$	−461420.	+	799203.i	−0.0485988	+	0.0841756i
$619$	6.08735e6	+	1.05436e7i	0.638560	+	1.10602i	0.985749	+	0.168224i	$0.0538031\pi$
$619$	6.08735e6	+	1.05436e7i	0.638560	+	1.10602i	−0.347189	+	0.937795i	$0.612864\pi$
$620$	1.50704e6	+	2.61028e6i	0.157451	+	0.272714i
$621$	1.07976e6	−	1.87020e6i	0.112356	−	0.194607i
$622$	−1.30602e6			−0.135355
$623$		0			0
$624$	−1.24498e7			−1.27998
$625$	2.97348e6	−	5.15021e6i	0.304484	−	0.527382i
$626$	344547.	+	596773.i	0.0351409	+	0.0608658i
$627$	1.02420e7	+	1.77396e7i	1.04043	+	1.80208i
$628$	−8.23852e6	+	1.42695e7i	−0.833586	+	1.44381i
$629$	−1.27893e6			−0.128890
$630$		0			0
$631$	−1.30854e7			−1.30832			−0.654161	−	0.756356i	$-0.726978\pi$
$631$	−1.30854e7			−1.30832			−0.654161	+	0.756356i	$0.726978\pi$
$632$	−704936.	+	1.22099e6i	−0.0702033	+	0.121596i
$633$	3.29512e6	+	5.70731e6i	0.326860	+	0.566138i
$634$	−1.10313e6	−	1.91068e6i	−0.108994	−	0.188784i
$635$	3.07256e6	−	5.32184e6i	0.302389	−	0.523754i
$636$	3.41336e6			0.334610
$637$		0			0
$638$	1.15754e6			0.112586
$639$	−4.61955e6	+	8.00130e6i	−0.447557	+	0.775191i
$640$	2.13113e6	+	3.69122e6i	0.205665	+	0.356222i
$641$	220554.	+	382010.i	0.0212016	+	0.0367223i	0.876432	−	0.481526i	$-0.159917\pi$
$641$	220554.	+	382010.i	0.0212016	+	0.0367223i	−0.855230	+	0.518249i	$0.826584\pi$
$642$	−1.05553e6	+	1.82822e6i	−0.101072	+	0.175062i
$643$	4.18888e6			0.399550			0.199775	−	0.979842i	$-0.435979\pi$
$643$	4.18888e6			0.399550			0.199775	+	0.979842i	$0.435979\pi$
$644$		0			0
$645$	−1.52159e7			−1.44012
$646$	673439.	−	1.16643e6i	0.0634917	−	0.109971i
$647$	9.39109e6	+	1.62658e7i	0.881973	+	1.52762i	0.849145	+	0.528161i	$0.177118\pi$
$647$	9.39109e6	+	1.62658e7i	0.881973	+	1.52762i	0.0328282	+	0.999461i	$0.489549\pi$
$648$	−1.68781e6	−	2.92337e6i	−0.157901	−	0.273493i
$649$	−4.73937e6	+	8.20883e6i	−0.441681	+	0.765014i
$650$	−443233.			−0.0411480
$651$		0			0
$652$	1.38375e7			1.27479
$653$	758666.	−	1.31405e6i	0.0696254	−	0.120595i	−0.829111	−	0.559084i	$-0.811153\pi$
$653$	758666.	−	1.31405e6i	0.0696254	−	0.120595i	0.898736	+	0.438489i	$0.144486\pi$
$654$	−792835.	−	1.37323e6i	−0.0724833	−	0.125545i
$655$	−8.16842e6	−	1.41481e7i	−0.743935	−	1.28853i
$656$	534721.	−	926164.i	0.0485141	−	0.0840288i
$657$	−4.08802e6			−0.369487
$658$		0			0
$659$	1.84809e7			1.65772			0.828859	−	0.559458i	$-0.188991\pi$
$659$	1.84809e7			1.65772			0.828859	+	0.559458i	$0.188991\pi$
$660$	−9.62906e6	+	1.66780e7i	−0.860446	+	1.49034i
$661$	−5.19762e6	−	9.00254e6i	−0.462702	−	0.801423i	0.536393	−	0.843968i	$-0.319787\pi$
$661$	−5.19762e6	−	9.00254e6i	−0.462702	−	0.801423i	−0.999095	+	0.0425457i	$0.986453\pi$
$662$	796199.	+	1.37906e6i	0.0706117	+	0.122303i
$663$	−7.58707e6	+	1.31412e7i	−0.670332	+	1.16105i
$664$	−31109.8			−0.00273828
$665$		0			0
$666$	111808.			0.00976756
$667$	1.31838e6	−	2.28350e6i	0.114743	−	0.198741i
$668$	−4.39621e6	−	7.61446e6i	−0.381186	−	0.660234i
$669$	−1.00729e7	−	1.74468e7i	−0.870141	−	1.50713i
$670$	−334402.	+	579200.i	−0.0287794	+	0.0498473i
$671$	9.48162e6			0.812973
$672$		0			0
$673$	−1.10398e7			−0.939556			−0.469778	−	0.882785i	$-0.655666\pi$
$673$	−1.10398e7			−0.939556			−0.469778	+	0.882785i	$0.655666\pi$
$674$	875506.	−	1.51642e6i	0.0742351	−	0.128579i
$675$	922099.	+	1.59712e6i	0.0778966	+	0.134921i
$676$	818942.	+	1.41845e6i	0.0689265	+	0.119384i
$677$	−4.11743e6	+	7.13159e6i	−0.345266	+	0.598019i	−0.985402	−	0.170243i	$-0.945545\pi$
$677$	−4.11743e6	+	7.13159e6i	−0.345266	+	0.598019i	0.640136	+	0.768262i	$0.278878\pi$
$678$	615144.			0.0513928
$679$		0			0
$680$	2.55371e6			0.211787
$681$	4.95390e6	−	8.58041e6i	0.409335	−	0.708990i
$682$	−494671.	−	856796.i	−0.0407245	−	0.0705369i
$683$	−9.92184e6	−	1.71851e7i	−0.813842	−	1.40962i	−0.910156	−	0.414265i	$-0.864039\pi$
$683$	−9.92184e6	−	1.71851e7i	−0.813842	−	1.40962i	0.0963137	−	0.995351i	$-0.469295\pi$
$684$	3.52454e6	−	6.10469e6i	0.288046	−	0.498911i
$685$	1.80655e7			1.47103
$686$		0			0
$687$	−2.19955e7			−1.77804
$688$	−8.06520e6	+	1.39693e7i	−0.649597	+	1.12514i
$689$	−1.79550e6	−	3.10990e6i	−0.144091	−	0.249573i
$690$	−366384.	−	634595.i	−0.0292963	−	0.0507428i
$691$	−1.18509e6	+	2.05264e6i	−0.0944185	+	0.163538i	−0.909366	−	0.415997i	$-0.863433\pi$
$691$	−1.18509e6	+	2.05264e6i	−0.0944185	+	0.163538i	0.814947	+	0.579535i	$0.196766\pi$
$692$	3.13796e6			0.249105
$693$		0			0
$694$	−789131.			−0.0621943
$695$	404130.	−	699973.i	0.0317365	−	0.0549692i
$696$	−1.08374e6	−	1.87709e6i	−0.0848010	−	0.146880i
$697$	−651729.	−	1.12883e6i	−0.0508142	−	0.0880128i
$698$	1.01246e6	−	1.75363e6i	0.0786571	−	0.136238i
$699$	−1.51439e7			−1.17232
$700$		0			0
$701$	−1.56833e7			−1.20543			−0.602714	−	0.797957i	$-0.705914\pi$
$701$	−1.56833e7			−1.20543			−0.602714	+	0.797957i	$0.705914\pi$
$702$	−463023.	+	801979.i	−0.0354617	+	0.0614214i
$703$	−843206.	−	1.46048e6i	−0.0643496	−	0.111457i
$704$	9.85210e6	+	1.70643e7i	0.749199	+	1.29765i
$705$	3.81144e6	−	6.60161e6i	0.288813	−	0.500239i
$706$	−1.83543e6			−0.138588
$707$		0			0
$708$	8.80085e6			0.659844
$709$	−1.84272e6	+	3.19169e6i	−0.137671	+	0.238454i	−0.926615	−	0.376012i	$-0.877295\pi$
$709$	−1.84272e6	+	3.19169e6i	−0.137671	+	0.238454i	0.788943	+	0.614466i	$0.210628\pi$
$710$	−1.09424e6	−	1.89528e6i	−0.0814642	−	0.141100i
$711$	2.19186e6	+	3.79642e6i	0.162607	+	0.281644i
$712$	−2.89886e6	+	5.02097e6i	−0.214302	+	0.371183i
$713$	−2.25361e6			−0.166018
$714$		0			0
$715$	2.02604e7			1.48212
$716$	5.19294e6	−	8.99443e6i	0.378556	−	0.655679i
$717$	−1.68638e6	−	2.92089e6i	−0.122506	−	0.212187i
$718$	−395272.	−	684631.i	−0.0286144	−	0.0495616i
$719$	−7.82134e6	+	1.35470e7i	−0.564233	+	0.977281i	0.432887	+	0.901448i	$0.357495\pi$
$719$	−7.82134e6	+	1.35470e7i	−0.564233	+	0.977281i	−0.997121	+	0.0758329i	$0.975838\pi$
$720$	6.51470e6			0.468342
$721$		0			0
$722$	−19369.0			−0.00138282
$723$	3.77054e6	−	6.53076e6i	0.268261	−	0.464642i
$724$	7.95999e6	+	1.37871e7i	0.564373	+	0.977523i
$725$	1.12588e6	+	1.95008e6i	0.0795511	+	0.137787i
$726$	2.01335e6	−	3.48722e6i	0.141768	−	0.245549i
$727$	−1.85908e7			−1.30456			−0.652279	−	0.757979i	$-0.726187\pi$
$727$	−1.85908e7			−1.30456			−0.652279	+	0.757979i	$0.726187\pi$
$728$		0			0
$729$	−1.12318e6			−0.0782767
$730$	484167.	−	838603.i	0.0336270	−	0.0582437i
$731$	9.83003e6	+	1.70261e7i	0.680396	+	1.17848i
$732$	−4.40176e6	−	7.62408e6i	−0.303633	−	0.525908i
$733$	1.24733e7	−	2.16044e7i	0.857476	−	1.48519i	−0.0168533	−	0.999858i	$-0.505365\pi$
$733$	1.24733e7	−	2.16044e7i	0.857476	−	1.48519i	0.874329	−	0.485334i	$-0.161302\pi$
$734$	−136367.			−0.00934260
$735$		0			0
$736$	−2.39708e6			−0.163113
$737$	−6.57112e6	+	1.13815e7i	−0.445626	+	0.771847i
$738$	56975.9	+	98685.2i	0.00385080	+	0.00666978i
$739$	1.21472e7	+	2.10396e7i	0.818211	+	1.41718i	0.906999	+	0.421133i	$0.138367\pi$
$739$	1.21472e7	+	2.10396e7i	0.818211	+	1.41718i	−0.0887878	+	0.996051i	$0.528299\pi$
$740$	792747.	−	1.37308e6i	0.0532176	−	0.0921756i
$741$	−2.00088e7			−1.33868
$742$		0			0
$743$	4.16541e6			0.276812			0.138406	−	0.990376i	$-0.455802\pi$
$743$	4.16541e6			0.276812			0.138406	+	0.990376i	$0.455802\pi$
$744$	−926261.	+	1.60433e6i	−0.0613481	+	0.106258i
$745$	2.62194e6	+	4.54134e6i	0.173074	+	0.299773i
$746$	650295.	+	1.12634e6i	0.0427822	+	0.0741009i
$747$	−48365.0	+	83770.6i	−0.00317124	+	0.00549275i
$748$	2.48828e7			1.62610
$749$		0			0
$750$	2.70721e6			0.175739
$751$	1.18217e7	−	2.04758e7i	0.764858	−	1.32477i	−0.175464	−	0.984486i	$-0.556142\pi$
$751$	1.18217e7	−	2.04758e7i	0.764858	−	1.32477i	0.940322	−	0.340287i	$-0.110524\pi$
$752$	−4.04051e6	−	6.99836e6i	−0.260550	−	0.451286i
$753$	1.54294e7	+	2.67245e7i	0.991659	+	1.71760i
$754$	−565348.	+	979211.i	−0.0362149	+	0.0627260i
$755$	1.42564e6			0.0910209
$756$		0			0
$757$	1.50108e7			0.952062			0.476031	−	0.879429i	$-0.342075\pi$
$757$	1.50108e7			0.952062			0.476031	+	0.879429i	$0.342075\pi$
$758$	−1.30082e6	+	2.25308e6i	−0.0822326	+	0.142431i
$759$	−7.19958e6	−	1.24700e7i	−0.453631	−	0.785712i
$760$	1.68367e6	+	2.91621e6i	0.105736	+	0.183141i
$761$	1.46096e6	−	2.53045e6i	0.0914483	−	0.158393i	−0.816672	−	0.577101i	$-0.804184\pi$
$761$	1.46096e6	−	2.53045e6i	0.0914483	−	0.158393i	0.908121	+	0.418708i	$0.137517\pi$
$762$	1.87282e6			0.116845
$763$		0			0
$764$	2.00918e6			0.124533
$765$	3.97013e6	−	6.87646e6i	0.245274	−	0.424826i
$766$	−1.24155e6	−	2.15042e6i	−0.0764525	−	0.132420i
$767$	−4.62944e6	−	8.01842e6i	−0.284145	−	0.492153i
$768$	8.65082e6	−	1.49837e7i	0.529242	−	0.916674i
$769$	−1.42847e7			−0.871073			−0.435536	−	0.900171i	$-0.643441\pi$
$769$	−1.42847e7			−0.871073			−0.435536	+	0.900171i	$0.643441\pi$
$770$		0			0
$771$	1.55360e7			0.941246
$772$	7.38630e6	−	1.27934e7i	0.446050	−	0.772581i
$773$	−5.45062e6	−	9.44075e6i	−0.328093	−	0.568274i	0.654040	−	0.756460i	$-0.273073\pi$
$773$	−5.45062e6	−	9.44075e6i	−0.328093	−	0.568274i	−0.982133	+	0.188186i	$0.939739\pi$
$774$	−859369.	−	1.48847e6i	−0.0515617	−	0.0893074i
$775$	962277.	−	1.66671e6i	0.0575501	−	0.0996797i
$776$	−1.05426e6			−0.0628485
$777$		0			0
$778$	6254.04			0.000370434
$779$	859377.	−	1.48849e6i	0.0507388	−	0.0878822i
$780$	−9.40571e6	−	1.62912e7i	−0.553548	−	0.958772i
$781$	−2.15023e7	−	3.72430e7i	−1.26141	−	2.18483i
$782$	−473394.	+	819942.i	−0.0276825	+	0.0479475i
$783$	4.70459e6			0.274231
$784$		0			0
$785$	−2.44736e7			−1.41750
$786$	2.48945e6	−	4.31186e6i	0.143730	−	0.248948i
$787$	−1.28225e7	−	2.22092e7i	−0.737963	−	1.27819i	−0.953411	−	0.301675i	$-0.902454\pi$
$787$	−1.28225e7	−	2.22092e7i	−0.737963	−	1.27819i	0.215448	−	0.976515i	$-0.430879\pi$
$788$	4.21788e6	+	7.30558e6i	0.241979	+	0.419121i
$789$	4.56277e6	−	7.90296e6i	0.260937	−	0.451957i
$790$	−1.03838e6			−0.0591955
$791$		0			0
$792$	−4.38699e6			−0.248516
$793$	−4.63085e6	+	8.02086e6i	−0.261503	+	0.452937i
$794$	455749.	+	789380.i	0.0256551	+	0.0444360i
$795$	2.53496e6	+	4.39067e6i	0.142250	+	0.246384i
$796$	9.52359e6	−	1.64953e7i	0.532743	−	0.922739i
$797$	−7.73086e6			−0.431104			−0.215552	−	0.976492i	$-0.569155\pi$
$797$	−7.73086e6			−0.431104			−0.215552	+	0.976492i	$0.569155\pi$
$798$		0			0
$799$	−9.84931e6			−0.545807
$800$	1.02354e6	−	1.77282e6i	0.0565429	−	0.0979352i
$801$	9.01344e6	+	1.56117e7i	0.496374	+	0.859745i
$802$	−517239.	−	895883.i	−0.0283959	−	0.0491831i
$803$	9.51408e6	−	1.64789e7i	0.520688	−	0.901859i
$804$	1.22024e7			0.665738
$805$		0			0
$806$	966395.			0.0523983
$807$	−1.96455e7	+	3.40269e7i	−1.06189	+	1.83924i
$808$	4.17609e6	+	7.23320e6i	0.225031	+	0.389764i
$809$	9.39055e6	+	1.62649e7i	0.504452	+	0.873736i	0.999987	+	0.00514815i	$0.00163871\pi$
$809$	9.39055e6	+	1.62649e7i	0.504452	+	0.873736i	−0.495535	+	0.868588i	$0.665028\pi$
$810$	1.24308e6	−	2.15308e6i	0.0665713	−	0.115305i
$811$	9.00729e6			0.480886			0.240443	−	0.970663i	$-0.422707\pi$
$811$	9.00729e6			0.480886			0.240443	+	0.970663i	$0.422707\pi$
$812$		0			0
$813$	3.16939e7			1.68170
$814$	−260211.	+	450699.i	−0.0137646	+	0.0238410i
$815$	1.02765e7	+	1.77995e7i	0.541942	+	0.938671i
$816$	−1.13555e7	−	1.96683e7i	−0.597008	−	1.03405i
$817$	−1.29620e7	+	2.24508e7i	−0.679386	+	1.17673i
$818$	2.22259e6			0.116138
$819$		0			0
$820$	1.61590e6			0.0839228
$821$	4.63982e6	−	8.03641e6i	0.240239	−	0.416106i	−0.720543	−	0.693410i	$-0.756107\pi$
$821$	4.63982e6	−	8.03641e6i	0.240239	−	0.416106i	0.960782	+	0.277304i	$0.0894408\pi$
$822$	2.75286e6	+	4.76810e6i	0.142104	+	0.246131i
$823$	5.41541e6	+	9.37976e6i	0.278697	+	0.482717i	0.971061	−	0.238831i	$-0.0767643\pi$
$823$	5.41541e6	+	9.37976e6i	0.278697	+	0.482717i	−0.692364	+	0.721548i	$0.743431\pi$
$824$	−1.49054e6	+	2.58169e6i	−0.0764759	+	0.132460i
$825$	1.22967e7			0.629004
$826$		0			0
$827$	−2.05230e7			−1.04346			−0.521731	−	0.853110i	$-0.674714\pi$
$827$	−2.05230e7			−1.04346			−0.521731	+	0.853110i	$0.674714\pi$
$828$	−2.47758e6	+	4.29129e6i	−0.125589	+	0.217526i
$829$	−7.11080e6	−	1.23163e7i	−0.359362	−	0.622433i	0.628492	−	0.777816i	$-0.283672\pi$
$829$	−7.11080e6	−	1.23163e7i	−0.359362	−	0.622433i	−0.987854	+	0.155382i	$0.950339\pi$
$830$	−11456.3	−	19842.9i	−0.000577229	−	0.000999791i
$831$	−2.04472e7	+	3.54156e7i	−1.02714	+	1.77907i
$832$	−1.92472e7			−0.963958
$833$		0			0
$834$	246329.			0.0122631
$835$	6.52975e6	−	1.13099e7i	0.324101	−	0.561360i
$836$	1.64054e7	+	2.84150e7i	0.811841	+	1.40615i
$837$	−2.01048e6	−	3.48226e6i	−0.0991944	−	0.171810i
$838$	−89997.4	+	155880.i	−0.00442710	+	0.00766797i
$839$	9.29934e6			0.456087			0.228043	−	0.973651i	$-0.426767\pi$
$839$	9.29934e6			0.456087			0.228043	+	0.973651i	$0.426767\pi$
$840$		0			0
$841$	−1.47669e7			−0.719944
$842$	−2.16176e6	+	3.74428e6i	−0.105082	+	0.182007i
$843$	−9.64825e6	−	1.67113e7i	−0.467606	−	0.809917i
$844$	5.27806e6	+	9.14187e6i	0.255046	+	0.441752i
$845$	−1.21639e6	+	2.10684e6i	−0.0586043	+	0.101506i
$846$	861053.			0.0413623
$847$		0			0
$848$	5.37461e6			0.256659
$849$	1.37175e7	−	2.37594e7i	0.653139	−	1.13127i
$850$	−404271.	−	700219.i	−0.0191922	−	0.0332419i
$851$	592732.	+	1.02664e6i	0.0280566	+	0.0485954i
$852$	−1.99645e7	+	3.45795e7i	−0.942235	+	1.63200i
$853$	3.07436e6			0.144671			0.0723357	−	0.997380i	$-0.476955\pi$
$853$	3.07436e6			0.144671			0.0723357	+	0.997380i	$0.476955\pi$
$854$		0			0
$855$	1.04701e7			0.489819
$856$	−3.40969e6	+	5.90576e6i	−0.159049	+	0.275481i
$857$	1.72917e7	+	2.99502e7i	0.804242	+	1.39299i	0.916802	+	0.399343i	$0.130762\pi$
$857$	1.72917e7	+	2.99502e7i	0.804242	+	1.39299i	−0.112560	+	0.993645i	$0.535905\pi$
$858$	3.08733e6	+	5.34740e6i	0.143174	+	0.247985i
$859$	8.15112e6	−	1.41182e7i	0.376907	−	0.652822i	−0.613703	−	0.789537i	$-0.710321\pi$
$859$	8.15112e6	−	1.41182e7i	0.376907	−	0.652822i	0.990611	+	0.136714i	$0.0436542\pi$
$860$	−2.43726e7			−1.12372
$861$		0			0
$862$	−3.57856e6			−0.164036
$863$	−1.28481e7	+	2.22536e7i	−0.587235	+	1.01712i	0.407357	+	0.913269i	$0.366450\pi$
$863$	−1.28481e7	+	2.22536e7i	−0.587235	+	1.01712i	−0.994593	+	0.103852i	$0.966883\pi$
$864$	−2.13847e6	−	3.70394e6i	−0.0974584	−	0.168803i
$865$	2.33043e6	+	4.03643e6i	0.105900	+	0.183424i
$866$	1.50641e6	−	2.60917e6i	0.0682571	−	0.118225i
$867$	218902.			0.00989012
$868$		0			0
$869$	−2.04046e7			−0.916596
$870$	798179.	−	1.38249e6i	0.0357522	−	0.0619246i
$871$	−6.41870e6	−	1.11175e7i	−0.286683	−	0.496549i
$872$	−2.56111e6	−	4.43598e6i	−0.114061	−	0.197560i
$873$	−1.63901e6	+	2.83885e6i	−0.0727858	+	0.126069i
$874$	−1.24844e6			−0.0552829
$875$		0			0
$876$	−1.76673e7			−0.777877
$877$	−1.65030e7	+	2.85840e7i	−0.724542	+	1.25494i	0.234620	+	0.972087i	$0.424615\pi$
$877$	−1.65030e7	+	2.85840e7i	−0.724542	+	1.25494i	−0.959162	+	0.282857i	$0.908718\pi$
$878$	−82643.1	−	143142.i	−0.00361801	−	0.00626658i
$879$	−2.51715e7	−	4.35983e7i	−1.09885	−	1.90326i
$880$	−1.51617e7	+	2.62609e7i	−0.659997	+	1.14315i
$881$	−2.26705e6			−0.0984060			−0.0492030	−	0.998789i	$-0.515668\pi$
$881$	−2.26705e6			−0.0984060			−0.0492030	+	0.998789i	$0.515668\pi$
$882$		0			0
$883$	1.97779e7			0.853649			0.426825	−	0.904334i	$-0.359632\pi$
$883$	1.97779e7			0.853649			0.426825	+	0.904334i	$0.359632\pi$
$884$	−1.21528e7	+	2.10493e7i	−0.523055	+	0.905957i
$885$	6.53602e6	+	1.13207e7i	0.280514	+	0.485865i
$886$	719506.	+	1.24622e6i	0.0307929	+	0.0533348i
$887$	−18234.1	+	31582.4i	−0.000778173	+	0.00134783i	−0.866414	−	0.499326i	$-0.833581\pi$
$887$	−18234.1	+	31582.4i	−0.000778173	+	0.00134783i	0.865636	+	0.500674i	$0.166914\pi$
$888$	974478.			0.0414705
$889$		0			0
$890$	−4.27005e6			−0.180700
$891$	2.44270e7	−	4.23089e7i	1.03080	−	1.78541i
$892$	−1.61346e7	−	2.79460e7i	−0.678964	−	1.17600i
$893$	−6.49370e6	−	1.12474e7i	−0.272498	−	0.471981i
$894$	−799076.	+	1.38404e6i	−0.0334383	+	0.0579169i
$895$	1.54263e7			0.643730
$896$		0			0
$897$	1.40652e7			0.583665
$898$	−946513.	+	1.63941e6i	−0.0391684	+	0.0678416i
$899$	−2.45479e6	−	4.25182e6i	−0.101301	−	0.175459i
$900$	−2.11582e6	−	3.66470e6i	−0.0870706	−	0.150811i
$901$	3.27534e6	−	5.67306e6i	0.134414	−	0.232812i
$902$	−530403.			−0.0217065
$903$		0			0
$904$	1.98711e6			0.0808727
$905$	−1.18231e7	+	2.04782e7i	−0.479855	+	0.831132i
$906$	217242.	+	376274.i	0.00879272	+	0.0152294i
$907$	−8.11488e6	−	1.40554e7i	−0.327540	−	0.567315i	0.654483	−	0.756076i	$-0.272886\pi$
$907$	−8.11488e6	−	1.40554e7i	−0.327540	−	0.567315i	−0.982023	+	0.188761i	$0.939553\pi$
$908$	7.93508e6	−	1.37440e7i	0.319401	−	0.553219i
$909$	2.59695e7			1.04245
$910$		0			0
$911$	−2.61699e7			−1.04474			−0.522368	−	0.852720i	$-0.674951\pi$
$911$	−2.61699e7			−1.04474			−0.522368	+	0.852720i	$0.674951\pi$
$912$	1.49735e7	−	2.59348e7i	0.596122	−	1.03251i
$913$	−225120.	−	389920.i	−0.00893795	−	0.0154810i
$914$	1.48612e6	+	2.57403e6i	0.0588420	+	0.101917i
$915$	6.53801e6	−	1.13242e7i	0.258162	−	0.447150i
$916$	−3.52320e7			−1.38739
$917$		0			0
$918$	−1.68929e6			−0.0661602
$919$	−2.02986e6	+	3.51583e6i	−0.0792826	+	0.137322i	−0.902941	−	0.429765i	$-0.858596\pi$
$919$	−2.02986e6	+	3.51583e6i	−0.0792826	+	0.137322i	0.823658	+	0.567087i	$0.191930\pi$
$920$	−1.18354e6	−	2.04995e6i	−0.0461012	−	0.0798497i
$921$	8.69348e6	+	1.50576e7i	0.337711	+	0.584932i
$922$	−951228.	+	1.64758e6i	−0.0368517	+	0.0638290i
$923$	4.20070e7			1.62300
$924$		0			0
$925$	−1.01237e6			−0.0389031
$926$	1.55372e6	−	2.69112e6i	0.0595450	−	0.103135i
$927$	4.63454e6	+	8.02725e6i	0.177136	+	0.306809i
$928$	−2.61106e6	−	4.52249e6i	−0.0995284	−	0.172388i
$929$	1.84759e6	−	3.20012e6i	0.0702370	−	0.121654i	−0.828768	−	0.559592i	$-0.810958\pi$
$929$	1.84759e6	−	3.20012e6i	0.0702370	−	0.121654i	0.899005	+	0.437938i	$0.144291\pi$
$930$	−1.36439e6			−0.0517288
$931$		0			0
$932$	−2.42573e7			−0.914751
$933$	−1.76964e7	+	3.06510e7i	−0.665548	+	1.15276i
$934$	358959.	+	621735.i	0.0134641	+	0.0233205i
$935$	1.84794e7	+	3.20073e7i	0.691289	+	1.19735i
$936$	2.14262e6	−	3.71112e6i	0.0799383	−	0.138457i
$937$	1.91384e7			0.712126			0.356063	−	0.934462i	$-0.384119\pi$
$937$	1.91384e7			0.712126			0.356063	+	0.934462i	$0.384119\pi$
$938$		0			0
$939$	1.86742e7			0.691160
$940$	6.10511e6	−	1.05744e7i	0.225358	−	0.390332i
$941$	6.04770e6	+	1.04749e7i	0.222647	+	0.385636i	0.955611	−	0.294632i	$-0.0951970\pi$
$941$	6.04770e6	+	1.04749e7i	0.222647	+	0.385636i	−0.732964	+	0.680267i	$0.761864\pi$
$942$	−3.72935e6	−	6.45942e6i	−0.136932	−	0.237174i
$943$	−604099.	+	1.04633e6i	−0.0221222	+	0.0383168i
$944$	1.38577e7			0.506127
$945$		0			0
$946$	8.00007e6			0.290647
$947$	9.79843e6	−	1.69714e7i	0.355044	−	0.614953i	−0.632082	−	0.774902i	$-0.717799\pi$
$947$	9.79843e6	−	1.69714e7i	0.355044	−	0.614953i	0.987125	+	0.159948i	$0.0511327\pi$
$948$	9.47266e6	+	1.64071e7i	0.342335	+	0.592941i
$949$	9.29340e6	+	1.60966e7i	0.334972	+	0.580189i
$950$	533077.	−	923316.i	0.0191638	−	0.0331926i
$951$	−5.97890e7			−2.14373
$952$		0			0
$953$	4.23265e7			1.50966			0.754832	−	0.655918i	$-0.227718\pi$
$953$	4.23265e7			1.50966			0.754832	+	0.655918i	$0.227718\pi$
$954$	−286339.	+	495954.i	−0.0101862	+	0.0176429i
$955$	1.49213e6	+	2.58445e6i	0.0529418	+	0.0916978i
$956$	−2.70121e6	−	4.67864e6i	−0.0955904	−	0.165567i
$957$	1.56845e7	−	2.71664e7i	0.553595	−	0.958854i
$958$	−1.87054e6			−0.0658496
$959$		0			0
$960$	2.71739e7			0.951642
$961$	1.22165e7	−	2.11596e7i	0.426715	−	0.739092i
$962$	−254175.	−	440245.i	−0.00885515	−	0.0153376i
$963$	1.06018e7	+	1.83628e7i	0.368394	+	0.638077i
$964$	6.03959e6	−	1.04609e7i	0.209322	−	0.362556i
$965$	2.19419e7			0.758502
$966$		0			0
$967$	1.39211e6			0.0478749			0.0239375	−	0.999713i	$-0.492380\pi$
$967$	1.39211e6			0.0478749			0.0239375	+	0.999713i	$0.492380\pi$
$968$	6.50377e6	−	1.12649e7i	0.223088	−	0.386400i
$969$	−1.82500e7	−	3.16099e7i	−0.624385	−	1.08147i
$970$	−388236.	−	672444.i	−0.0132485	−	0.0229470i
$971$	2.20938e7	−	3.82676e7i	0.752009	−	1.30252i	−0.194839	−	0.980835i	$-0.562418\pi$
$971$	2.20938e7	−	3.82676e7i	0.752009	−	1.30252i	0.946848	−	0.321682i	$-0.104248\pi$
$972$	−3.03473e7			−1.03028
$973$		0			0
$974$	2.33095e6			0.0787292
$975$	−6.00573e6	+	1.04022e7i	−0.202327	+	0.350441i
$976$	−6.93093e6	−	1.20047e7i	−0.232899	−	0.403392i
$977$	2.80229e7	+	4.85370e7i	0.939239	+	1.62681i	0.766895	+	0.641773i	$0.221801\pi$
$977$	2.80229e7	+	4.85370e7i	0.939239	+	1.62681i	0.172344	+	0.985037i	$0.444866\pi$
$978$	−3.13193e6	+	5.42466e6i	−0.104704	+	0.181353i
$979$	−8.39082e7			−2.79800
$980$		0			0
$981$	−1.59266e7			−0.528384
$982$	2.84997e6	−	4.93629e6i	0.0943107	−	0.163351i
$983$	−2.50280e7	−	4.33498e7i	−0.826118	−	1.43088i	−0.901062	−	0.433691i	$-0.857211\pi$
$983$	−2.50280e7	−	4.33498e7i	−0.826118	−	1.43088i	0.0749434	−	0.997188i	$-0.476122\pi$
$984$	496583.	+	860107.i	0.0163495	+	0.0283182i
$985$	−6.26488e6	+	1.08511e7i	−0.205742	+	0.356355i
$986$	−2.06261e6			−0.0675654
$987$		0			0
$988$	−3.20497e7			−1.04456
$989$	9.11163e6	−	1.57818e7i	0.296214	−	0.513058i
$990$	−1.61552e6	−	2.79817e6i	−0.0523872	−	0.0907372i
$991$	−7.95578e6	−	1.37798e7i	−0.257335	−	0.445717i	0.708192	−	0.706020i	$-0.249511\pi$
$991$	−7.95578e6	−	1.37798e7i	−0.257335	−	0.445717i	−0.965527	+	0.260303i	$0.916178\pi$
$992$	−2.23165e6	+	3.86533e6i	−0.0720023	+	0.124712i
$993$	4.31534e7			1.38881
$994$		0			0
$995$	2.82911e7			0.905924
$996$	−209021.	+	362034.i	−0.00667638	+	0.0115638i
$997$	2.12997e7	+	3.68922e7i	0.678635	+	1.17543i	0.975392	+	0.220477i	$0.0707615\pi$
$997$	2.12997e7	+	3.68922e7i	0.678635	+	1.17543i	−0.296757	+	0.954953i	$0.595905\pi$
$998$	490817.	+	850120.i	0.0155989	+	0.0270181i
$999$	−1.05757e6	+	1.83177e6i	−0.0335271	+	0.0580706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.6.c.d.30.2		4
7.2	even	3		49.6.a.f.1.1		2
7.3	odd	6		49.6.c.e.18.2		4
7.4	even	3	inner	49.6.c.d.18.2		4
7.5	odd	6		7.6.a.b.1.1	✓	2
7.6	odd	2		49.6.c.e.30.2		4
21.2	odd	6		441.6.a.l.1.2		2
21.5	even	6		63.6.a.f.1.2		2
28.19	even	6		112.6.a.h.1.1		2
28.23	odd	6		784.6.a.v.1.2		2
35.12	even	12		175.6.b.c.99.3		4
35.19	odd	6		175.6.a.c.1.2		2
35.33	even	12		175.6.b.c.99.2		4
56.5	odd	6		448.6.a.w.1.1		2
56.19	even	6		448.6.a.u.1.2		2
77.54	even	6		847.6.a.c.1.2		2
84.47	odd	6		1008.6.a.bq.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.6.a.b.1.1	✓	2	7.5	odd	6
49.6.a.f.1.1		2	7.2	even	3
49.6.c.d.18.2		4	7.4	even	3	inner
49.6.c.d.30.2		4	1.1	even	1	trivial
49.6.c.e.18.2		4	7.3	odd	6
49.6.c.e.30.2		4	7.6	odd	2
63.6.a.f.1.2		2	21.5	even	6
112.6.a.h.1.1		2	28.19	even	6
175.6.a.c.1.2		2	35.19	odd	6
175.6.b.c.99.2		4	35.33	even	12
175.6.b.c.99.3		4	35.12	even	12
441.6.a.l.1.2		2	21.2	odd	6
448.6.a.u.1.2		2	56.19	even	6
448.6.a.w.1.1		2	56.5	odd	6
784.6.a.v.1.2		2	28.23	odd	6
847.6.a.c.1.2		2	77.54	even	6
1008.6.a.bq.1.2		2	84.47	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.362541 + 0.627940i) q^{2} +(9.82475 + 17.0170i) q^{3} +(15.7371 + 27.2575i) q^{4} +(-23.3746 + 40.4860i) q^{5} -14.2475 q^{6} -46.0241 q^{8} +(-71.5515 + 123.931i) q^{9} +O(q^{10})\)	\(q+(-0.362541 + 0.627940i) q^{2} +(9.82475 + 17.0170i) q^{3} +(15.7371 + 27.2575i) q^{4} +(-23.3746 + 40.4860i) q^{5} -14.2475 q^{6} -46.0241 q^{8} +(-71.5515 + 123.931i) q^{9} +(-16.9485 - 29.3557i) q^{10} +(-333.045 - 576.851i) q^{11} +(-309.227 + 535.596i) q^{12} +650.640 q^{13} -918.598 q^{15} +(-486.902 + 843.340i) q^{16} +(593.447 + 1027.88i) q^{17} +(-51.8808 - 89.8601i) q^{18} +(-782.526 + 1355.37i) q^{19} -1471.40 q^{20} +482.970 q^{22} +(550.076 - 952.760i) q^{23} +(-452.175 - 783.191i) q^{24} +(469.757 + 813.644i) q^{25} +(-235.884 + 408.563i) q^{26} +1962.93 q^{27} +2396.72 q^{29} +(333.030 - 576.825i) q^{30} +(-1024.23 - 1774.01i) q^{31} +(-1089.43 - 1886.95i) q^{32} +(6544.17 - 11334.8i) q^{33} -860.596 q^{34} -4504.06 q^{36} +(-538.772 + 933.181i) q^{37} +(-567.396 - 982.759i) q^{38} +(6392.37 + 11071.9i) q^{39} +(1075.79 - 1863.33i) q^{40} -1098.21 q^{41} +16564.3 q^{43} +(10482.3 - 18155.9i) q^{44} +(-3344.97 - 5793.66i) q^{45} +(398.851 + 690.830i) q^{46} +(-4149.19 + 7186.62i) q^{47} -19134.8 q^{48} -681.226 q^{50} +(-11660.9 + 20197.3i) q^{51} +(10239.2 + 17734.8i) q^{52} +(-2759.59 - 4779.75i) q^{53} +(-711.642 + 1232.60i) q^{54} +31139.1 q^{55} -30752.5 q^{57} +(-868.911 + 1505.00i) q^{58} +(-7115.21 - 12323.9i) q^{59} +(-14456.1 - 25038.7i) q^{60} +(-7117.37 + 12327.7i) q^{61} +1485.30 q^{62} -29581.9 q^{64} +(-15208.4 + 26341.8i) q^{65} +(4745.06 + 8218.69i) q^{66} +(-9865.22 - 17087.1i) q^{67} +(-18678.3 + 32351.8i) q^{68} +21617.5 q^{69} +64562.7 q^{71} +(3293.09 - 5703.80i) q^{72} +(14283.5 + 24739.7i) q^{73} +(-390.655 - 676.634i) q^{74} +(-9230.50 + 15987.7i) q^{75} -49258.8 q^{76} -9270.00 q^{78} +(15316.7 - 26529.3i) q^{79} +(-22762.3 - 39425.4i) q^{80} +(36672.3 + 63518.3i) q^{81} +(398.146 - 689.610i) q^{82} +675.946 q^{83} -55486.3 q^{85} +(-6005.25 + 10401.4i) q^{86} +(23547.2 + 40784.9i) q^{87} +(15328.1 + 26549.0i) q^{88} +(62985.7 - 109094. i) q^{89} +4850.76 q^{90} +34626.5 q^{92} +(20125.6 - 34858.5i) q^{93} +(-3008.51 - 5210.89i) q^{94} +(-36582.4 - 63362.6i) q^{95} +(21406.8 - 37077.6i) q^{96} +22906.8 q^{97} +95319.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 9 q^{2} - 6 q^{3} - 5 q^{4} - 18 q^{5} + 396 q^{6} - 18 q^{8} - 558 q^{9}+O(q^{10}) \) 4 * q - 9 * q^2 - 6 * q^3 - 5 * q^4 - 18 * q^5 + 396 * q^6 - 18 * q^8 - 558 * q^9	\( 4 q - 9 q^{2} - 6 q^{3} - 5 q^{4} - 18 q^{5} + 396 q^{6} - 18 q^{8} - 558 q^{9} + 204 q^{10} - 396 q^{11} - 1554 q^{12} + 700 q^{13} - 3312 q^{15} - 113 q^{16} + 1800 q^{17} - 3537 q^{18} - 3266 q^{19} - 5040 q^{20} - 3504 q^{22} - 2088 q^{23} - 1854 q^{24} + 3238 q^{25} + 2016 q^{26} + 12744 q^{27} + 13392 q^{29} + 6768 q^{30} - 20 q^{31} + 6129 q^{32} + 20016 q^{33} - 11868 q^{34} + 21258 q^{36} - 6232 q^{37} - 15210 q^{38} + 20496 q^{39} + 3216 q^{40} + 12096 q^{41} - 6040 q^{43} + 30816 q^{44} + 5238 q^{45} - 25584 q^{46} + 11700 q^{47} - 82428 q^{48} - 39402 q^{50} - 7596 q^{51} + 31444 q^{52} - 9468 q^{53} - 37908 q^{54} + 77808 q^{55} + 25752 q^{57} - 37314 q^{58} - 43938 q^{59} - 2016 q^{60} - 64754 q^{61} - 30600 q^{62} - 141566 q^{64} - 39060 q^{65} + 66816 q^{66} - 24784 q^{67} - 14994 q^{68} + 206784 q^{69} + 194832 q^{71} - 8775 q^{72} + 17452 q^{73} - 43434 q^{74} + 40494 q^{75} + 25564 q^{76} - 146160 q^{78} - 51256 q^{79} - 70272 q^{80} + 61074 q^{81} - 58338 q^{82} - 235116 q^{83} - 75720 q^{85} + 150048 q^{86} - 63180 q^{87} + 40656 q^{88} + 84276 q^{89} - 187704 q^{90} + 301824 q^{92} + 92280 q^{93} + 159468 q^{94} - 24264 q^{95} + 255906 q^{96} - 41552 q^{97} - 33480 q^{99}+O(q^{100}) \) 4 * q - 9 * q^2 - 6 * q^3 - 5 * q^4 - 18 * q^5 + 396 * q^6 - 18 * q^8 - 558 * q^9 + 204 * q^10 - 396 * q^11 - 1554 * q^12 + 700 * q^13 - 3312 * q^15 - 113 * q^16 + 1800 * q^17 - 3537 * q^18 - 3266 * q^19 - 5040 * q^20 - 3504 * q^22 - 2088 * q^23 - 1854 * q^24 + 3238 * q^25 + 2016 * q^26 + 12744 * q^27 + 13392 * q^29 + 6768 * q^30 - 20 * q^31 + 6129 * q^32 + 20016 * q^33 - 11868 * q^34 + 21258 * q^36 - 6232 * q^37 - 15210 * q^38 + 20496 * q^39 + 3216 * q^40 + 12096 * q^41 - 6040 * q^43 + 30816 * q^44 + 5238 * q^45 - 25584 * q^46 + 11700 * q^47 - 82428 * q^48 - 39402 * q^50 - 7596 * q^51 + 31444 * q^52 - 9468 * q^53 - 37908 * q^54 + 77808 * q^55 + 25752 * q^57 - 37314 * q^58 - 43938 * q^59 - 2016 * q^60 - 64754 * q^61 - 30600 * q^62 - 141566 * q^64 - 39060 * q^65 + 66816 * q^66 - 24784 * q^67 - 14994 * q^68 + 206784 * q^69 + 194832 * q^71 - 8775 * q^72 + 17452 * q^73 - 43434 * q^74 + 40494 * q^75 + 25564 * q^76 - 146160 * q^78 - 51256 * q^79 - 70272 * q^80 + 61074 * q^81 - 58338 * q^82 - 235116 * q^83 - 75720 * q^85 + 150048 * q^86 - 63180 * q^87 + 40656 * q^88 + 84276 * q^89 - 187704 * q^90 + 301824 * q^92 + 92280 * q^93 + 159468 * q^94 - 24264 * q^95 + 255906 * q^96 - 41552 * q^97 - 33480 * q^99

Introduction

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