LMFDB - Embedded newform 49.6.c.e.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.e.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	$-0.949616\pi$
$3$	−9.82475	−	17.0170i	−0.630258	−	1.09164i	0.357241	−	0.934012i	$-0.383718\pi$
$4$	15.7371	+	27.2575i	0.491785	+	0.851797i
$5$	23.3746	−	40.4860i	0.418137	−	0.724235i	−0.577615	−	0.816309i	$-0.696016\pi$
$5$	23.3746	−	40.4860i	0.418137	−	0.724235i	0.995752	+	0.0920744i	$0.0293498\pi$
$6$	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	$-0.679271\pi$
$13$	−650.640			−1.06778			−0.533890	+	0.845554i	$0.679271\pi$
$14$		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	0.501963	−	0.864889i	$-0.332611\pi$
$17$	−593.447	−	1027.88i	−0.498035	−	0.862621i	−0.999997	+	0.00226795i	$0.999278\pi$
$18$	−51.8808	−	89.8601i	−0.0377420	−	0.0653711i
$19$	782.526	−	1355.37i	0.497296	−	0.861341i	−0.502700	−	0.864461i	$-0.667660\pi$
$19$	782.526	−	1355.37i	0.497296	−	0.861341i	0.999995	+	0.00311994i	$0.000993110\pi$
$20$	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	0.945722	−	0.324977i	$-0.105357\pi$
$31$	1024.23	+	1774.01i	0.191422	+	0.331553i	−0.754300	+	0.656530i	$0.772023\pi$
$32$	−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	$-0.483754\pi$
$41$	1098.21			0.102029			0.0510147	+	0.998698i	$0.483754\pi$
$42$		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	−0.695897	−	0.718141i	$-0.744993\pi$
$47$	4149.19	−	7186.62i	0.273980	−	0.474548i	0.969877	+	0.243594i	$0.0783264\pi$
$48$	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	0.967853	−	0.251515i	$-0.0809289\pi$
$59$	7115.21	+	12323.9i	0.266108	+	0.460912i	−0.701745	+	0.712428i	$0.747596\pi$
$60$	−14456.1	−	25038.7i	−0.518409	−	0.897911i
$61$	7117.37	−	12327.7i	0.244904	−	0.424186i	−0.717201	−	0.696866i	$-0.754577\pi$
$61$	7117.37	−	12327.7i	0.244904	−	0.424186i	0.962105	+	0.272681i	$0.0879103\pi$
$62$	−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	0.665453	−	0.746440i	$-0.268238\pi$
$73$	−14283.5	−	24739.7i	−0.313709	−	0.543360i	−0.979162	+	0.203080i	$0.934905\pi$
$74$	−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	$-0.501714\pi$
$83$	−675.946			−0.0107700			−0.00538501	+	0.999986i	$0.501714\pi$
$84$		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	$0.485810\pi$
$89$	−62985.7	+	109094.i	−0.842882	+	1.45991i	−0.887448	+	0.460908i	$0.847524\pi$
$90$	−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	$-0.539443\pi$
$97$	−22906.8			−0.247192			−0.123596	+	0.992333i	$0.539443\pi$
$98$		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	$0.179228\pi$
$101$	90737.0	+	157161.i	0.885077	+	1.53300i	0.0394521	+	0.999221i	$0.487439\pi$
$102$	−8455.14	−	14644.7i	−0.0804675	−	0.139374i
$103$	−32386.0	+	56094.2i	−0.300791	+	0.520985i	−0.976315	−	0.216353i	$-0.930584\pi$
$103$	−32386.0	+	56094.2i	−0.300791	+	0.520985i	0.675525	+	0.737338i	$0.263917\pi$
$104$	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	$-0.484329\pi$
$131$	174729.	−	302639.i	0.889582	−	1.54080i	0.840370	−	0.542014i	$-0.182338\pi$
$132$	−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	$-0.487917\pi$
$139$	17289.3			0.0758997			0.0379498	+	0.999280i	$0.487917\pi$
$140$		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	$-0.844768\pi$
$157$	−261754.	−	453372.i	−0.847510	−	1.46793i	0.0359139	−	0.999355i	$-0.488566\pi$
$158$	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	$-0.373320\pi$
$167$	279353.			0.775107			0.387554	+	0.921847i	$0.373320\pi$
$168$		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	−0.922370	−	0.386307i	$-0.873750\pi$
$173$	−49849.7	+	86342.2i	−0.126633	+	0.219335i	0.795737	+	0.605642i	$0.207084\pi$
$174$	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	$-0.694531\pi$
$181$	−505810.			−1.14760			−0.573800	+	0.818995i	$0.694531\pi$
$182$		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	$0.0155306\pi$
$199$	302584.	+	524090.i	0.541642	+	0.938152i	−0.457168	+	0.889381i	$0.651136\pi$
$200$	−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	$-0.257476\pi$
$223$	1.02526e6			1.38061			0.690305	+	0.723518i	$0.257476\pi$
$224$		0			0
$225$	−134447.			−0.177050
$226$	15652.9	−	27111.6i	0.0203856	−	0.0353089i
$227$	252113.	+	436673.i	0.324736	+	0.562460i	0.981459	−	0.191672i	$-0.0613911\pi$
$227$	252113.	+	436673.i	0.324736	+	0.562460i	−0.656723	+	0.754132i	$0.728058\pi$
$228$	−483956.	−	838236.i	−0.616550	−	1.06790i
$229$	559696.	−	969422.i	0.705283	−	1.22159i	−0.261306	−	0.965256i	$-0.584153\pi$
$229$	559696.	−	969422.i	0.705283	−	1.22159i	0.966589	−	0.256331i	$-0.0825136\pi$
$230$	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	0.952595	−	0.304240i	$-0.0984024\pi$
$241$	191890.	+	332363.i	0.212818	+	0.368612i	−0.739777	+	0.672852i	$0.765069\pi$
$242$	−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	$-0.788216\pi$
$251$	−1.57046e6			−1.57342			−0.786708	+	0.617325i	$0.788216\pi$
$252$		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	−0.990080	−	0.140507i	$-0.955127\pi$
$257$	−395328.	+	684728.i	−0.373357	+	0.646674i	0.616722	+	0.787181i	$0.288460\pi$
$258$	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	$-0.847796\pi$
$269$	−999794.	−	1.73169e6i	−0.842422	−	1.45912i	0.0454190	−	0.998968i	$-0.485538\pi$
$270$	−33268.7	−	57623.1i	−0.0277732	−	0.0481046i
$271$	−806482.	+	1.39687e6i	−0.667070	+	1.15540i	0.311650	+	0.950197i	$0.399118\pi$
$271$	−806482.	+	1.39687e6i	−0.667070	+	1.15540i	−0.978720	+	0.205202i	$0.934215\pi$
$272$	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	$0.00671318\pi$
$283$	698109.	+	1.20916e6i	0.518152	+	0.897466i	−0.481626	+	0.876377i	$0.659953\pi$
$284$	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	$-0.162990\pi$
$293$	2.56205e6			1.74348			0.871742	+	0.489965i	$0.162990\pi$
$294$		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	$-0.586334\pi$
$307$	−884855.			−0.535829			−0.267915	+	0.963443i	$0.586334\pi$
$308$		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	$-0.989610\pi$
$311$	−900601.	−	1.55989e6i	−0.527997	−	0.914517i	0.471471	−	0.881882i	$-0.343723\pi$
$312$	−294203.	−	509575.i	−0.171104	−	0.296361i
$313$	−475183.	+	823041.i	−0.274158	+	0.474855i	−0.969922	−	0.243415i	$-0.921732\pi$
$313$	−475183.	+	823041.i	−0.274158	+	0.474855i	0.695765	+	0.718270i	$0.255066\pi$
$314$	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	$-0.289698\pi$
$349$	2.79267e6			1.22731			0.613657	+	0.789573i	$0.289698\pi$
$350$		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	$-0.984860\pi$
$353$	−1.26567e6	−	2.19221e6i	−0.540610	−	0.936364i	0.458259	−	0.888819i	$-0.348473\pi$
$354$	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	0.847228	−	0.531229i	$-0.178270\pi$
$367$	−94035.2	−	162874.i	−0.0364439	−	0.0631227i	−0.883672	+	0.468106i	$0.844936\pi$
$368$	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	$-0.629908\pi$
$383$	1.71228e6	−	2.96576e6i	0.596457	−	1.03309i	0.993340	−	0.115224i	$-0.0367587\pi$
$384$	−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	−0.948578	−	0.316545i	$-0.897477\pi$
$397$	−628547.	+	1.08868e6i	−0.200153	+	0.346675i	0.748425	+	0.663220i	$0.230811\pi$
$398$	−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	0.998573	−	0.0534050i	$-0.0170074\pi$
$409$	1.53264e6	+	2.65462e6i	0.453036	+	0.784682i	−0.545537	+	0.838087i	$0.683674\pi$
$410$	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	$-0.510996\pi$
$419$	−248240.			−0.0690776			−0.0345388	+	0.999403i	$0.510996\pi$
$420$		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	$-0.321245\pi$
$433$	4.15513e6			1.06504			0.532519	+	0.846418i	$0.321245\pi$
$434$		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	−0.851567	−	0.524246i	$-0.824347\pi$
$439$	113977.	−	197415.i	0.0282265	−	0.0488898i	0.879794	+	0.475356i	$0.157681\pi$
$440$	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	$-0.592826\pi$
$461$	−2.62378e6			−0.575009			−0.287505	+	0.957779i	$0.592826\pi$
$462$		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	−0.913756	−	0.406264i	$-0.866831\pi$
$467$	−495059.	+	857467.i	−0.105042	+	0.181939i	0.808713	+	0.588203i	$0.200165\pi$
$468$	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	0.708533	−	0.705678i	$-0.249357\pi$
$479$	−1.28988e6	−	2.23414e6i	−0.256868	−	0.444909i	−0.965401	+	0.260769i	$0.916024\pi$
$480$	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	$-0.389598\pi$
$503$	3.85775e6			0.679851			0.339926	+	0.940452i	$0.389598\pi$
$504$		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	$-0.471509\pi$
$509$	5.30301e6	−	9.18509e6i	0.907253	−	1.57141i	0.817864	−	0.575411i	$-0.195158\pi$
$510$	−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	$0.0988965\pi$
$521$	4.58994e6	+	7.95002e6i	0.740821	+	1.28314i	−0.211302	+	0.977421i	$0.567770\pi$
$522$	−124344.	−	215370.i	−0.0199732	−	0.0345946i
$523$	−4.52793e6	+	7.84260e6i	−0.723844	+	1.25373i	0.235604	+	0.971849i	$0.424293\pi$
$523$	−4.52793e6	+	7.84260e6i	−0.723844	+	1.25373i	−0.959448	+	0.281886i	$0.909040\pi$
$524$	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	$0.122967\pi$
$563$	5.93738e6	+	1.02838e7i	0.789449	+	1.36737i	−0.136856	+	0.990591i	$0.543700\pi$
$564$	−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	0.983692	−	0.179862i	$-0.0575651\pi$
$577$	2.68772e6	+	4.65526e6i	0.336081	+	0.582109i	−0.647611	+	0.761971i	$0.724232\pi$
$578$	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	$-0.539504\pi$
$587$	−2.06682e6			−0.247575			−0.123788	+	0.992309i	$0.539504\pi$
$588$		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	−0.660996	−	0.750389i	$-0.729866\pi$
$593$	2.73473e6	−	4.73670e6i	0.319358	−	0.553145i	0.980354	+	0.197245i	$0.0631993\pi$
$594$	−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	$-0.146024\pi$
$601$	1.58788e7			1.79322			0.896608	+	0.442826i	$0.146024\pi$
$602$		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	−0.974687	−	0.223573i	$-0.928228\pi$
$607$	−2.66631e6	+	4.61818e6i	−0.293724	+	0.508744i	0.680964	+	0.732317i	$0.261561\pi$
$608$	−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	$-0.946197\pi$
$619$	−6.08735e6	−	1.05436e7i	−0.638560	−	1.10602i	0.347189	−	0.937795i	$-0.387136\pi$
$620$	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	$-0.564021\pi$
$643$	−4.18888e6			−0.399550			−0.199775	+	0.979842i	$0.564021\pi$
$644$		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	$-0.822882\pi$
$647$	−9.39109e6	−	1.62658e7i	−0.881973	−	1.52762i	−0.0328282	−	0.999461i	$-0.510451\pi$
$648$	−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	0.999095	−	0.0425457i	$-0.0135468\pi$
$661$	5.19762e6	+	9.00254e6i	0.462702	+	0.801423i	−0.536393	+	0.843968i	$0.680213\pi$
$662$	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	−0.640136	−	0.768262i	$-0.721122\pi$
$677$	4.11743e6	−	7.13159e6i	0.345266	−	0.598019i	0.985402	+	0.170243i	$0.0544553\pi$
$678$	−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	−0.814947	−	0.579535i	$-0.803234\pi$
$691$	1.18509e6	−	2.05264e6i	0.0944185	−	0.163538i	0.909366	+	0.415997i	$0.136567\pi$
$692$	−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	$-0.642505\pi$
$719$	7.82134e6	−	1.35470e7i	0.564233	−	0.977281i	0.997121	−	0.0758329i	$-0.0241616\pi$
$720$	−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	$-0.273813\pi$
$727$	1.85908e7			1.30456			0.652279	+	0.757979i	$0.273813\pi$
$728$		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	$0.494635\pi$
$733$	−1.24733e7	+	2.16044e7i	−0.857476	+	1.48519i	−0.874329	+	0.485334i	$0.838698\pi$
$734$	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	−0.908121	−	0.418708i	$-0.862483\pi$
$761$	−1.46096e6	+	2.53045e6i	−0.0914483	+	0.158393i	0.816672	+	0.577101i	$0.195816\pi$
$762$	−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	$-0.356559\pi$
$769$	1.42847e7			0.871073			0.435536	+	0.900171i	$0.356559\pi$
$770$		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	0.982133	−	0.188186i	$-0.0602607\pi$
$773$	5.45062e6	+	9.44075e6i	0.328093	+	0.568274i	−0.654040	+	0.756460i	$0.726927\pi$
$774$	−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	$0.0975456\pi$
$787$	1.28225e7	+	2.22092e7i	0.737963	+	1.27819i	−0.215448	+	0.976515i	$0.569121\pi$
$788$	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	$-0.430845\pi$
$797$	7.73086e6			0.431104			0.215552	+	0.976492i	$0.430845\pi$
$798$		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	$-0.577293\pi$
$811$	−9.00729e6			−0.480886			−0.240443	+	0.970663i	$0.577293\pi$
$812$		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	0.987854	−	0.155382i	$-0.0496610\pi$
$829$	7.11080e6	+	1.23163e7i	0.359362	+	0.622433i	−0.628492	+	0.777816i	$0.716328\pi$
$830$	−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	$-0.573233\pi$
$839$	−9.29934e6			−0.456087			−0.228043	+	0.973651i	$0.573233\pi$
$840$		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	$-0.523045\pi$
$853$	−3.07436e6			−0.144671			−0.0723357	+	0.997380i	$0.523045\pi$
$854$		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	$-0.869238\pi$
$857$	−1.72917e7	−	2.99502e7i	−0.804242	−	1.39299i	0.112560	−	0.993645i	$-0.464095\pi$
$858$	3.08733e6	+	5.34740e6i	0.143174	+	0.247985i
$859$	−8.15112e6	+	1.41182e7i	−0.376907	+	0.652822i	−0.990611	−	0.136714i	$-0.956346\pi$
$859$	−8.15112e6	+	1.41182e7i	−0.376907	+	0.652822i	0.613703	+	0.789537i	$0.289679\pi$
$860$	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	$-0.484332\pi$
$881$	2.26705e6			0.0984060			0.0492030	+	0.998789i	$0.484332\pi$
$882$		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	−0.865636	−	0.500674i	$-0.833086\pi$
$887$	18234.1	−	31582.4i	0.000778173	−	0.00134783i	0.866414	+	0.499326i	$0.166419\pi$
$888$	−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	−0.899005	−	0.437938i	$-0.855709\pi$
$929$	−1.84759e6	+	3.20012e6i	−0.0702370	+	0.121654i	0.828768	+	0.559592i	$0.189042\pi$
$930$	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	$-0.615881\pi$
$937$	−1.91384e7			−0.712126			−0.356063	+	0.934462i	$0.615881\pi$
$938$		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	0.732964	−	0.680267i	$-0.238136\pi$
$941$	−6.04770e6	−	1.04749e7i	−0.222647	−	0.385636i	−0.955611	+	0.294632i	$0.904803\pi$
$942$	−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	$0.437582\pi$
$971$	−2.20938e7	+	3.82676e7i	−0.752009	+	1.30252i	−0.946848	+	0.321682i	$0.895752\pi$
$972$	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	$0.142789\pi$
$983$	2.50280e7	+	4.33498e7i	0.826118	+	1.43088i	−0.0749434	+	0.997188i	$0.523878\pi$
$984$	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	$-0.929238\pi$
$997$	−2.12997e7	−	3.68922e7i	−0.678635	−	1.17543i	0.296757	−	0.954953i	$-0.404095\pi$
$998$	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.e.30.2		4
7.2	even	3		7.6.a.b.1.1	✓	2
7.3	odd	6		49.6.c.d.18.2		4
7.4	even	3	inner	49.6.c.e.18.2		4
7.5	odd	6		49.6.a.f.1.1		2
7.6	odd	2		49.6.c.d.30.2		4
21.2	odd	6		63.6.a.f.1.2		2
21.5	even	6		441.6.a.l.1.2		2
28.19	even	6		784.6.a.v.1.2		2
28.23	odd	6		112.6.a.h.1.1		2
35.2	odd	12		175.6.b.c.99.3		4
35.9	even	6		175.6.a.c.1.2		2
35.23	odd	12		175.6.b.c.99.2		4
56.37	even	6		448.6.a.w.1.1		2
56.51	odd	6		448.6.a.u.1.2		2
77.65	odd	6		847.6.a.c.1.2		2
84.23	even	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	7.2	even	3
49.6.a.f.1.1		2	7.5	odd	6
49.6.c.d.18.2		4	7.3	odd	6
49.6.c.d.30.2		4	7.6	odd	2
49.6.c.e.18.2		4	7.4	even	3	inner
49.6.c.e.30.2		4	1.1	even	1	trivial
63.6.a.f.1.2		2	21.2	odd	6
112.6.a.h.1.1		2	28.23	odd	6
175.6.a.c.1.2		2	35.9	even	6
175.6.b.c.99.2		4	35.23	odd	12
175.6.b.c.99.3		4	35.2	odd	12
441.6.a.l.1.2		2	21.5	even	6
448.6.a.u.1.2		2	56.51	odd	6
448.6.a.w.1.1		2	56.37	even	6
784.6.a.v.1.2		2	28.19	even	6
847.6.a.c.1.2		2	77.65	odd	6
1008.6.a.bq.1.2		2	84.23	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)

\(f(q)\)	\(=\)	\(q+(-0.362541 + 0.627940i) q^{2} +(-9.82475 - 17.0170i) q^{3} +(15.7371 + 27.2575i) q^{4} +(23.3746 - 40.4860i) q^{5} +14.2475 q^{6} -46.0241 q^{8} +(-71.5515 + 123.931i) q^{9} +O(q^{10})\)	\(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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