LMFDB - Embedded newform 49.6.c.f.18.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("49.18");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.85880717084$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{37})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 10x^{2} + 9x + 81 $ x^4 - x^3 + 10x^2 + 9x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			18.1
Root			$1.77069 + 3.06693i$ of defining polynomial
Character	$\chi$	$=$	49.18
Dual form			49.6.c.f.30.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.54138 - 6.13385i) q^{2} +(-5.04138 + 8.73193i) q^{3} +(-9.08276 + 15.7318i) q^{4} +(-39.9138 - 69.1328i) q^{5} +71.4138 q^{6} -97.9863 q^{8} +(70.6689 + 122.402i) q^{9} +O(q^{10})$	\(q+(-3.54138 - 6.13385i) q^{2} +(-5.04138 + 8.73193i) q^{3} +(-9.08276 + 15.7318i) q^{4} +(-39.9138 - 69.1328i) q^{5} +71.4138 q^{6} -97.9863 q^{8} +(70.6689 + 122.402i) q^{9} +(-282.700 + 489.651i) q^{10} +(-175.952 + 304.757i) q^{11} +(-91.5793 - 158.620i) q^{12} +291.683 q^{13} +804.883 q^{15} +(637.655 + 1104.45i) q^{16} +(-185.038 + 320.495i) q^{17} +(500.531 - 866.946i) q^{18} +(752.463 + 1303.30i) q^{19} +1450.11 q^{20} +2492.45 q^{22} +(212.855 + 368.676i) q^{23} +(493.986 - 855.609i) q^{24} +(-1623.72 + 2812.37i) q^{25} +(-1032.96 - 1789.14i) q^{26} -3875.19 q^{27} -7783.93 q^{29} +(-2850.40 - 4937.03i) q^{30} +(-1287.59 + 2230.17i) q^{31} +(2948.58 - 5107.09i) q^{32} +(-1774.08 - 3072.80i) q^{33} +2621.16 q^{34} -2567.48 q^{36} +(-369.809 - 640.528i) q^{37} +(5329.51 - 9230.99i) q^{38} +(-1470.48 + 2546.95i) q^{39} +(3911.01 + 6774.06i) q^{40} -7029.84 q^{41} +1835.23 q^{43} +(-3196.26 - 5536.08i) q^{44} +(5641.33 - 9771.08i) q^{45} +(1507.60 - 2611.25i) q^{46} +(-766.342 - 1327.34i) q^{47} -12858.7 q^{48} +23000.9 q^{50} +(-1865.69 - 3231.47i) q^{51} +(-2649.28 + 4588.69i) q^{52} +(4768.73 - 8259.68i) q^{53} +(13723.5 + 23769.8i) q^{54} +28091.6 q^{55} -15173.8 q^{57} +(27565.9 + 47745.5i) q^{58} +(-14837.0 + 25698.5i) q^{59} +(-7310.56 + 12662.3i) q^{60} +(-23255.4 - 40279.5i) q^{61} +18239.4 q^{62} -958.246 q^{64} +(-11642.2 - 20164.8i) q^{65} +(-12565.4 + 21763.9i) q^{66} +(-13373.0 + 23162.8i) q^{67} +(-3361.31 - 5821.95i) q^{68} -4292.34 q^{69} -14388.8 q^{71} +(-6924.59 - 11993.7i) q^{72} +(-35047.6 + 60704.2i) q^{73} +(-2619.27 + 4536.71i) q^{74} +(-16371.6 - 28356.5i) q^{75} -27337.8 q^{76} +20830.2 q^{78} +(13542.9 + 23457.0i) q^{79} +(50902.5 - 88165.7i) q^{80} +(2363.74 - 4094.13i) q^{81} +(24895.3 + 43120.0i) q^{82} +79755.4 q^{83} +29542.2 q^{85} +(-6499.26 - 11257.0i) q^{86} +(39241.8 - 67968.8i) q^{87} +(17240.9 - 29862.1i) q^{88} +(21788.7 + 37739.1i) q^{89} -79912.5 q^{90} -7733.26 q^{92} +(-12982.4 - 22486.2i) q^{93} +(-5427.82 + 9401.25i) q^{94} +(60067.3 - 104040. i) q^{95} +(29729.8 + 51493.6i) q^{96} -103374. q^{97} -49737.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 8 q^{3} - 12 q^{4} - 38 q^{5} + 164 q^{6} + 192 q^{8} + 380 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 8 * q^3 - 12 * q^4 - 38 * q^5 + 164 * q^6 + 192 * q^8 + 380 * q^9	\( 4 q - 2 q^{2} - 8 q^{3} - 12 q^{4} - 38 q^{5} + 164 q^{6} + 192 q^{8} + 380 q^{9} - 778 q^{10} - 424 q^{11} - 196 q^{12} + 1848 q^{13} + 1784 q^{15} + 2064 q^{16} - 2346 q^{17} - 212 q^{18} - 360 q^{19} + 3416 q^{20} + 4252 q^{22} + 12 q^{23} + 1392 q^{24} - 1872 q^{25} + 1148 q^{26} - 5744 q^{27} - 14104 q^{29} - 5258 q^{30} + 3548 q^{31} + 8096 q^{32} - 3398 q^{33} - 14844 q^{34} - 2192 q^{36} - 11090 q^{37} + 20138 q^{38} - 1624 q^{39} + 15936 q^{40} - 7000 q^{41} - 25360 q^{43} - 5948 q^{44} + 1300 q^{45} + 5118 q^{46} - 22956 q^{47} - 22432 q^{48} + 59984 q^{50} + 384 q^{51} - 1400 q^{52} - 3042 q^{53} + 32546 q^{54} + 50152 q^{55} - 38116 q^{57} + 58852 q^{58} - 65808 q^{59} - 14084 q^{60} - 42486 q^{61} + 98724 q^{62} + 70912 q^{64} + 3164 q^{65} - 25894 q^{66} - 42312 q^{67} + 5460 q^{68} - 10308 q^{69} - 4416 q^{71} + 32448 q^{72} - 50506 q^{73} + 47370 q^{74} - 35608 q^{75} - 77672 q^{76} + 55048 q^{78} - 9004 q^{79} + 68816 q^{80} - 51178 q^{81} + 67732 q^{82} + 208656 q^{83} - 106212 q^{85} - 86776 q^{86} + 80008 q^{87} + 20496 q^{88} - 26666 q^{89} - 261304 q^{90} - 20568 q^{92} - 38718 q^{93} + 98034 q^{94} + 198140 q^{95} + 54880 q^{96} - 418264 q^{97} - 133888 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 8 * q^3 - 12 * q^4 - 38 * q^5 + 164 * q^6 + 192 * q^8 + 380 * q^9 - 778 * q^10 - 424 * q^11 - 196 * q^12 + 1848 * q^13 + 1784 * q^15 + 2064 * q^16 - 2346 * q^17 - 212 * q^18 - 360 * q^19 + 3416 * q^20 + 4252 * q^22 + 12 * q^23 + 1392 * q^24 - 1872 * q^25 + 1148 * q^26 - 5744 * q^27 - 14104 * q^29 - 5258 * q^30 + 3548 * q^31 + 8096 * q^32 - 3398 * q^33 - 14844 * q^34 - 2192 * q^36 - 11090 * q^37 + 20138 * q^38 - 1624 * q^39 + 15936 * q^40 - 7000 * q^41 - 25360 * q^43 - 5948 * q^44 + 1300 * q^45 + 5118 * q^46 - 22956 * q^47 - 22432 * q^48 + 59984 * q^50 + 384 * q^51 - 1400 * q^52 - 3042 * q^53 + 32546 * q^54 + 50152 * q^55 - 38116 * q^57 + 58852 * q^58 - 65808 * q^59 - 14084 * q^60 - 42486 * q^61 + 98724 * q^62 + 70912 * q^64 + 3164 * q^65 - 25894 * q^66 - 42312 * q^67 + 5460 * q^68 - 10308 * q^69 - 4416 * q^71 + 32448 * q^72 - 50506 * q^73 + 47370 * q^74 - 35608 * q^75 - 77672 * q^76 + 55048 * q^78 - 9004 * q^79 + 68816 * q^80 - 51178 * q^81 + 67732 * q^82 + 208656 * q^83 - 106212 * q^85 - 86776 * q^86 + 80008 * q^87 + 20496 * q^88 - 26666 * q^89 - 261304 * q^90 - 20568 * q^92 - 38718 * q^93 + 98034 * q^94 + 198140 * q^95 + 54880 * q^96 - 418264 * q^97 - 133888 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−3.54138	−	6.13385i	−0.626034	−	1.08432i	−0.988340	−	0.152263i	$-0.951344\pi$
$2$	−3.54138	−	6.13385i	−0.626034	−	1.08432i	0.362306	−	0.932059i	$-0.381989\pi$
$3$	−5.04138	+	8.73193i	−0.323405	+	0.560153i	−0.981188	−	0.193054i	$-0.938161\pi$
$3$	−5.04138	+	8.73193i	−0.323405	+	0.560153i	0.657783	+	0.753207i	$0.271494\pi$
$4$	−9.08276	+	15.7318i	−0.283836	+	0.491619i
$5$	−39.9138	−	69.1328i	−0.714000	−	1.23668i	−0.963344	−	0.268269i	$-0.913548\pi$
$5$	−39.9138	−	69.1328i	−0.714000	−	1.23668i	0.249344	−	0.968415i	$-0.419785\pi$
$6$	71.4138			0.809849
$7$		0			0
$7$		0			0
$8$	−97.9863			−0.541303
$9$	70.6689	+	122.402i	0.290819	+	0.503713i
$10$	−282.700	+	489.651i	−0.893976	+	1.54841i
$11$	−175.952	+	304.757i	−0.438442	+	0.759403i	−0.997570	−	0.0696781i	$-0.977803\pi$
$11$	−175.952	+	304.757i	−0.438442	+	0.759403i	0.559128	+	0.829082i	$0.311136\pi$
$12$	−91.5793	−	158.620i	−0.183588	−	0.317984i
$13$	291.683			0.478688			0.239344	−	0.970935i	$-0.423068\pi$
$13$	291.683			0.478688			0.239344	+	0.970935i	$0.423068\pi$
$14$		0			0
$15$	804.883			0.923644
$16$	637.655	+	1104.45i	0.622710	+	1.07857i
$17$	−185.038	+	320.495i	−0.155288	+	0.268967i	−0.933164	−	0.359451i	$-0.882964\pi$
$17$	−185.038	+	320.495i	−0.155288	+	0.268967i	0.777876	+	0.628418i	$0.216297\pi$
$18$	500.531	−	866.946i	0.364125	−	0.630682i
$19$	752.463	+	1303.30i	0.478190	+	0.828250i	0.999687	−	0.0250030i	$-0.00795952\pi$
$19$	752.463	+	1303.30i	0.478190	+	0.828250i	−0.521497	+	0.853253i	$0.674626\pi$
$20$	1450.11			0.810637
$21$		0			0
$22$	2492.45			1.09792
$23$	212.855	+	368.676i	0.0839006	+	0.145320i	0.904922	−	0.425577i	$-0.139929\pi$
$23$	212.855	+	368.676i	0.0839006	+	0.145320i	−0.821022	+	0.570897i	$0.806596\pi$
$24$	493.986	−	855.609i	0.175060	−	0.303213i
$25$	−1623.72	+	2812.37i	−0.519592	+	0.899960i
$26$	−1032.96	−	1789.14i	−0.299675	−	0.519052i
$27$	−3875.19			−1.02302
$28$		0			0
$29$	−7783.93			−1.71872			−0.859358	−	0.511374i	$-0.829137\pi$
$29$	−7783.93			−1.71872			−0.859358	+	0.511374i	$0.829137\pi$
$30$	−2850.40	−	4937.03i	−0.578232	−	1.00153i
$31$	−1287.59	+	2230.17i	−0.240643	+	0.416805i	−0.960898	−	0.276904i	$-0.910692\pi$
$31$	−1287.59	+	2230.17i	−0.240643	+	0.416805i	0.720255	+	0.693710i	$0.244025\pi$
$32$	2948.58	−	5107.09i	0.509024	−	0.881655i
$33$	−1774.08	−	3072.80i	−0.283588	−	0.491189i
$34$	2621.16			0.388862
$35$		0			0
$36$	−2567.48			−0.330180
$37$	−369.809	−	640.528i	−0.0444092	−	0.0769190i	0.842966	−	0.537966i	$-0.180807\pi$
$37$	−369.809	−	640.528i	−0.0444092	−	0.0769190i	−0.887376	+	0.461047i	$0.847474\pi$
$38$	5329.51	−	9230.99i	0.598727	−	1.03703i
$39$	−1470.48	+	2546.95i	−0.154810	+	0.268139i
$40$	3911.01	+	6774.06i	0.386490	+	0.669421i
$41$	−7029.84			−0.653109			−0.326554	−	0.945178i	$-0.605888\pi$
$41$	−7029.84			−0.653109			−0.326554	+	0.945178i	$0.605888\pi$
$42$		0			0
$43$	1835.23			0.151363			0.0756816	−	0.997132i	$-0.475887\pi$
$43$	1835.23			0.151363			0.0756816	+	0.997132i	$0.475887\pi$
$44$	−3196.26	−	5536.08i	−0.248891	−	0.431093i
$45$	5641.33	−	9771.08i	0.415289	−	0.719302i
$46$	1507.60	−	2611.25i	0.105049	−	0.181950i
$47$	−766.342	−	1327.34i	−0.0506032	−	0.0876473i	0.839614	−	0.543183i	$-0.182781\pi$
$47$	−766.342	−	1327.34i	−0.0506032	−	0.0876473i	−0.890217	+	0.455536i	$0.849448\pi$
$48$	−12858.7			−0.805550
$49$		0			0
$50$	23000.9			1.30113
$51$	−1865.69	−	3231.47i	−0.100442	−	0.173970i
$52$	−2649.28	+	4588.69i	−0.135869	+	0.235332i
$53$	4768.73	−	8259.68i	0.233192	−	0.403900i	−0.725554	−	0.688165i	$-0.758416\pi$
$53$	4768.73	−	8259.68i	0.233192	−	0.403900i	0.958746	+	0.284265i	$0.0917497\pi$
$54$	13723.5	+	23769.8i	0.640444	+	1.10928i
$55$	28091.6			1.25219
$56$		0			0
$57$	−15173.8			−0.618596
$58$	27565.9	+	47745.5i	1.07597	+	1.86364i
$59$	−14837.0	+	25698.5i	−0.554903	+	0.961120i	0.443008	+	0.896517i	$0.353911\pi$
$59$	−14837.0	+	25698.5i	−0.554903	+	0.961120i	−0.997911	+	0.0646022i	$0.979422\pi$
$60$	−7310.56	+	12662.3i	−0.262164	+	0.454081i
$61$	−23255.4	−	40279.5i	−0.800201	−	1.38599i	−0.919483	−	0.393129i	$-0.871393\pi$
$61$	−23255.4	−	40279.5i	−0.800201	−	1.38599i	0.119282	−	0.992860i	$-0.461941\pi$
$62$	18239.4			0.602602
$63$		0			0
$64$	−958.246			−0.0292434
$65$	−11642.2	−	20164.8i	−0.341783	−	0.591985i
$66$	−12565.4	+	21763.9i	−0.355072	+	0.615002i
$67$	−13373.0	+	23162.8i	−0.363951	+	0.630381i	−0.988607	−	0.150518i	$-0.951906\pi$
$67$	−13373.0	+	23162.8i	−0.363951	+	0.630381i	0.624656	+	0.780900i	$0.285239\pi$
$68$	−3361.31	−	5821.95i	−0.0881527	−	0.152685i
$69$	−4292.34			−0.108535
$70$		0			0
$71$	−14388.8			−0.338748			−0.169374	−	0.985552i	$-0.554175\pi$
$71$	−14388.8			−0.338748			−0.169374	+	0.985552i	$0.554175\pi$
$72$	−6924.59	−	11993.7i	−0.157421	−	0.272661i
$73$	−35047.6	+	60704.2i	−0.769752	+	1.33325i	0.167946	+	0.985796i	$0.446287\pi$
$73$	−35047.6	+	60704.2i	−0.769752	+	1.33325i	−0.937697	+	0.347453i	$0.887047\pi$
$74$	−2619.27	+	4536.71i	−0.0556033	+	0.0963078i
$75$	−16371.6	−	28356.5i	−0.336077	−	0.582102i
$76$	−27337.8			−0.542911
$77$		0			0
$78$	20830.2			0.387665
$79$	13542.9	+	23457.0i	0.244143	+	0.422868i	0.961890	−	0.273436i	$-0.0881601\pi$
$79$	13542.9	+	23457.0i	0.244143	+	0.422868i	−0.717748	+	0.696303i	$0.754827\pi$
$80$	50902.5	−	88165.7i	0.889230	−	1.54019i
$81$	2363.74	−	4094.13i	0.0400302	−	0.0693344i
$82$	24895.3	+	43120.0i	0.408868	+	0.708181i
$83$	79755.4			1.27076			0.635382	−	0.772198i	$-0.280843\pi$
$83$	79755.4			1.27076			0.635382	+	0.772198i	$0.280843\pi$
$84$		0			0
$85$	29542.2			0.443502
$86$	−6499.26	−	11257.0i	−0.0947584	−	0.164126i
$87$	39241.8	−	67968.8i	0.555841	−	0.962745i
$88$	17240.9	−	29862.1i	0.237330	−	0.411067i
$89$	21788.7	+	37739.1i	0.291579	+	0.505029i	0.974183	−	0.225759i	$-0.0724862\pi$
$89$	21788.7	+	37739.1i	0.291579	+	0.505029i	−0.682605	+	0.730788i	$0.739153\pi$
$90$	−79912.5			−1.03994
$91$		0			0
$92$	−7733.26			−0.0952561
$93$	−12982.4	−	22486.2i	−0.155650	−	0.269594i
$94$	−5427.82	+	9401.25i	−0.0633586	+	0.109740i
$95$	60067.3	−	104040.i	0.682856	−	1.18274i
$96$	29729.8	+	51493.6i	0.329241	+	0.570263i
$97$	−103374.			−1.11553			−0.557765	−	0.829999i	$-0.688341\pi$
$97$	−103374.			−1.11553			−0.557765	+	0.829999i	$0.688341\pi$
$98$		0			0
$99$	−49737.3			−0.510028
$100$	−29495.8	−	51088.3i	−0.294958	−	0.510883i
$101$	14350.1	−	24855.1i	0.139975	−	0.242444i	−0.787512	−	0.616300i	$-0.788631\pi$
$101$	14350.1	−	24855.1i	0.139975	−	0.242444i	0.927487	+	0.373855i	$0.121964\pi$
$102$	−13214.2	+	22887.7i	−0.125760	+	0.217822i
$103$	14614.0	+	25312.1i	0.135730	+	0.235091i	0.925876	−	0.377828i	$-0.123329\pi$
$103$	14614.0	+	25312.1i	0.135730	+	0.235091i	−0.790146	+	0.612918i	$0.789995\pi$
$104$	−28580.9			−0.259115
$105$		0			0
$106$	−67551.6			−0.583944
$107$	−43929.2	−	76087.6i	−0.370932	−	0.642472i	0.618778	−	0.785566i	$-0.287628\pi$
$107$	−43929.2	−	76087.6i	−0.370932	−	0.642472i	−0.989709	+	0.143094i	$0.954295\pi$
$108$	35197.4	−	60963.7i	0.290370	−	0.502935i
$109$	−110314.	+	191069.i	−0.889333	+	1.54037i	−0.0486678	+	0.998815i	$0.515498\pi$
$109$	−110314.	+	191069.i	−0.889333	+	1.54037i	−0.840665	+	0.541555i	$0.817836\pi$
$110$	−99483.2	−	172310.i	−0.783913	−	1.35778i
$111$	7457.39			0.0574486
$112$		0			0
$113$	39665.6			0.292225			0.146113	−	0.989268i	$-0.453324\pi$
$113$	39665.6			0.292225			0.146113	+	0.989268i	$0.453324\pi$
$114$	53736.2	+	93073.9i	0.387262	+	0.670758i
$115$	16991.7	−	29430.5i	0.119810	−	0.207517i
$116$	70699.6	−	122455.i	0.487834	−	0.844953i
$117$	20612.9	+	35702.6i	0.139211	+	0.241121i
$118$	210174.			1.38955
$119$		0			0
$120$	−78867.5			−0.499971
$121$	18607.4	+	32229.0i	0.115538	+	0.200117i
$122$	−164712.	+	285290.i	−1.00191	+	1.73535i
$123$	35440.1	−	61384.0i	0.211219	−	0.365841i
$124$	−23389.7	−	40512.2i	−0.136606	−	0.236609i
$125$	9774.87			0.0559546
$126$		0			0
$127$	51740.3			0.284655			0.142328	−	0.989820i	$-0.454541\pi$
$127$	51740.3			0.284655			0.142328	+	0.989820i	$0.454541\pi$
$128$	−90961.0	−	157549.i	−0.490716	−	0.849946i
$129$	−9252.11	+	16025.1i	−0.0489515	+	0.0847866i
$130$	−82458.7	+	142823.i	−0.427935	+	0.741206i
$131$	−83336.9	−	144344.i	−0.424286	−	0.734885i	0.572067	−	0.820207i	$-0.306142\pi$
$131$	−83336.9	−	144344.i	−0.424286	−	0.734885i	−0.996353	+	0.0853215i	$0.972808\pi$
$132$	64454.2			0.321971
$133$		0			0
$134$	189436.			0.911382
$135$	154674.	+	267902.i	0.730435	+	1.26515i
$136$	18131.2	−	31404.1i	0.0840578	−	0.145592i
$137$	−14129.7	+	24473.4i	−0.0643178	+	0.111402i	−0.896391	−	0.443264i	$-0.853820\pi$
$137$	−14129.7	+	24473.4i	−0.0643178	+	0.111402i	0.832073	+	0.554666i	$0.187154\pi$
$138$	15200.8	+	26328.6i	0.0679468	+	0.117687i
$139$	−336393.			−1.47676			−0.738380	−	0.674384i	$-0.764409\pi$
$139$	−336393.			−1.47676			−0.738380	+	0.674384i	$0.764409\pi$
$140$		0			0
$141$	15453.7			0.0654612
$142$	50956.1	+	88258.5i	0.212068	+	0.367312i
$143$	−51322.1	+	88892.4i	−0.209877	+	0.363517i
$144$	−90124.9	+	156101.i	−0.362192	+	0.627334i
$145$	310686.	+	538125.i	1.22716	+	2.12551i
$146$	496467.			1.92756
$147$		0			0
$148$	13435.5			0.0504198
$149$	177691.	+	307769.i	0.655691	+	1.13569i	0.981720	+	0.190330i	$0.0609557\pi$
$149$	177691.	+	307769.i	0.655691	+	1.13569i	−0.326030	+	0.945360i	$0.605711\pi$
$150$	−115956.	+	200842.i	−0.420791	+	0.728832i
$151$	179399.	−	310727.i	0.640290	−	1.10901i	−0.345078	−	0.938574i	$-0.612148\pi$
$151$	179399.	−	310727.i	0.640290	−	1.10901i	0.985368	−	0.170441i	$-0.0545191\pi$
$152$	−73731.0	−	127706.i	−0.258846	−	0.448334i
$153$	−52305.7			−0.180643
$154$		0			0
$155$	205570.			0.687275
$156$	−26712.1	−	46266.7i	−0.0878813	−	0.152215i
$157$	229455.	−	397428.i	0.742932	−	1.28680i	−0.208223	−	0.978081i	$-0.566768\pi$
$157$	229455.	−	397428.i	0.742932	−	1.28680i	0.951155	−	0.308714i	$-0.0998986\pi$
$158$	95921.1	−	166140.i	0.305683	−	0.529459i
$159$	48082.0	+	83280.4i	0.150831	+	0.261246i
$160$	−470756.			−1.45377
$161$		0			0
$162$	−33483.7			−0.100241
$163$	−251220.	−	435126.i	−0.740603	−	1.28276i	−0.952221	−	0.305410i	$-0.901206\pi$
$163$	−251220.	−	435126.i	−0.740603	−	1.28276i	0.211618	−	0.977353i	$-0.432127\pi$
$164$	63850.3	−	110592.i	0.185376	−	0.321081i
$165$	−141621.	+	245294.i	−0.404964	+	0.701418i
$166$	−282444.	−	489208.i	−0.795541	−	1.37792i
$167$	676652.			1.87748			0.938738	−	0.344632i	$-0.111996\pi$
$167$	676652.			1.87748			0.938738	+	0.344632i	$0.111996\pi$
$168$		0			0
$169$	−286214.			−0.770858
$170$	−104620.	−	181208.i	−0.277647	−	0.480900i
$171$	−106351.	+	184206.i	−0.278133	+	0.481741i
$172$	−16669.0	+	28871.5i	−0.0429623	+	0.0744130i
$173$	−124580.	−	215779.i	−0.316470	−	0.548143i	0.663279	−	0.748373i	$-0.269164\pi$
$173$	−124580.	−	215779.i	−0.316470	−	0.548143i	−0.979749	+	0.200230i	$0.935831\pi$
$174$	−555880.			−1.39190
$175$		0			0
$176$	−448786.			−1.09209
$177$	−149598.	−	259112.i	−0.358916	−	0.621661i
$178$	154324.	−	267297.i	0.365076	−	0.632330i
$179$	−69628.9	+	120601.i	−0.162427	+	0.281331i	−0.935738	−	0.352695i	$-0.885265\pi$
$179$	−69628.9	+	120601.i	−0.162427	+	0.281331i	0.773312	+	0.634026i	$0.218599\pi$
$180$	102478.	+	177497.i	0.235748	+	0.408328i
$181$	−306246.			−0.694823			−0.347412	−	0.937713i	$-0.612939\pi$
$181$	−306246.			−0.694823			−0.347412	+	0.937713i	$0.612939\pi$
$182$		0			0
$183$	468957.			1.03516
$184$	−20856.9	−	36125.2i	−0.0454156	−	0.0786622i
$185$	−29521.0	+	51131.8i	−0.0634163	+	0.109840i
$186$	−91951.5	+	159265.i	−0.194884	+	0.337549i
$187$	−65115.4	−	112783.i	−0.136169	−	0.235852i
$188$	27842.0			0.0574521
$189$		0			0
$190$	−850885.			−1.70996
$191$	−113747.	−	197015.i	−0.225609	−	0.390766i	0.730893	−	0.682492i	$-0.239104\pi$
$191$	−113747.	−	197015.i	−0.225609	−	0.390766i	−0.956502	+	0.291726i	$0.905770\pi$
$192$	4830.89	−	8367.34i	0.00945744	−	0.0163808i
$193$	336187.	−	582293.i	0.649663	−	1.12525i	−0.333541	−	0.942736i	$-0.608244\pi$
$193$	336187.	−	582293.i	0.649663	−	1.12525i	0.983203	−	0.182513i	$-0.0584231\pi$
$194$	366086.	+	634079.i	0.698359	+	1.20959i
$195$	234770.			0.442137
$196$		0			0
$197$	−1282.76			−0.00235493			−0.00117747	−	0.999999i	$-0.500375\pi$
$197$	−1282.76			−0.00235493			−0.00117747	+	0.999999i	$0.500375\pi$
$198$	176139.	+	305081.i	0.319295	+	0.553035i
$199$	184449.	−	319475.i	0.330175	−	0.571879i	−0.652371	−	0.757900i	$-0.726226\pi$
$199$	184449.	−	319475.i	0.330175	−	0.571879i	0.982546	+	0.186020i	$0.0595591\pi$
$200$	159103.	−	275574.i	0.281257	−	0.487151i
$201$	−134837.	−	233545.i	−0.235407	−	0.407737i
$202$	−203277.			−0.350517
$203$		0			0
$204$	67782.5			0.114036
$205$	280588.	+	485992.i	0.466320	+	0.807690i
$206$	103507.	−	179280.i	0.169943	−	0.294349i
$207$	−30084.5	+	52107.9i	−0.0487997	+	0.0845236i
$208$	185993.	+	322149.i	0.298084	+	0.516296i
$209$	−529589.			−0.838635
$210$		0			0
$211$	502168.			0.776503			0.388251	−	0.921553i	$-0.373079\pi$
$211$	502168.			0.776503			0.388251	+	0.921553i	$0.373079\pi$
$212$	86626.5	+	150042.i	0.132377	+	0.229283i
$213$	72539.2	−	125642.i	0.109553	−	0.189751i
$214$	−311140.	+	538910.i	−0.464431	+	0.804419i
$215$	−73251.1	−	126875.i	−0.108073	−	0.187188i
$216$	379715.			0.553763
$217$		0			0
$218$	1.56266e6			2.22701
$219$	−353376.	−	612066.i	−0.497883	−	0.862358i
$220$	−255150.	+	441932.i	−0.355417	+	0.615600i
$221$	−53972.3	+	93482.7i	−0.0743344	+	0.128751i
$222$	−26409.5	−	45742.5i	−0.0359647	−	0.0622928i
$223$	1.17328e6			1.57993			0.789967	−	0.613149i	$-0.210098\pi$
$223$	1.17328e6			1.57993			0.789967	+	0.613149i	$0.210098\pi$
$224$		0			0
$225$	−458988.			−0.604428
$226$	−140471.	−	243303.i	−0.182943	−	0.316867i
$227$	−455079.	+	788220.i	−0.586168	+	1.01527i	0.408560	+	0.912731i	$0.366031\pi$
$227$	−455079.	+	788220.i	−0.586168	+	1.01527i	−0.994729	+	0.102542i	$0.967302\pi$
$228$	137820.	−	238711.i	0.175580	−	0.304114i
$229$	260962.	+	452000.i	0.328843	+	0.569573i	0.982283	−	0.187406i	$-0.0600079\pi$
$229$	260962.	+	452000.i	0.328843	+	0.569573i	−0.653439	+	0.756979i	$0.726675\pi$
$230$	−240697.			−0.300020
$231$		0			0
$232$	762719.			0.930346
$233$	521394.	+	903081.i	0.629182	+	1.08977i	0.987716	+	0.156258i	$0.0499432\pi$
$233$	521394.	+	903081.i	0.629182	+	1.08977i	−0.358535	+	0.933516i	$0.616723\pi$
$234$	145996.	−	252873.i	0.174302	−	0.301900i
$235$	−61175.2	+	105959.i	−0.0722613	+	0.125160i
$236$	−269522.	−	466826.i	−0.315003	−	0.545601i
$237$	−273100.			−0.315828
$238$		0			0
$239$	−1.53447e6			−1.73766			−0.868830	−	0.495110i	$-0.835128\pi$
$239$	−1.53447e6			−1.73766			−0.868830	+	0.495110i	$0.835128\pi$
$240$	513238.	+	888954.i	0.575163	+	0.996211i
$241$	−503789.	+	872588.i	−0.558735	+	0.967758i	0.438867	+	0.898552i	$0.355380\pi$
$241$	−503789.	+	872588.i	−0.558735	+	0.967758i	−0.997602	+	0.0692059i	$0.977953\pi$
$242$	131792.	−	228271.i	0.144661	−	0.250560i
$243$	−447002.	−	774231.i	−0.485617	−	0.841114i
$244$	844893.			0.908505
$245$		0			0
$246$	−502028.			−0.528920
$247$	219480.	+	380151.i	0.228904	+	0.396473i
$248$	126166.	−	218526.i	0.130261	−	0.225618i
$249$	−402077.	+	696419.i	−0.410971	+	0.711823i
$250$	−34616.6	−	59957.6i	−0.0350295	−	0.0606729i
$251$	−8511.89			−0.00852789			−0.00426394	−	0.999991i	$-0.501357\pi$
$251$	−8511.89			−0.00852789			−0.00426394	+	0.999991i	$0.501357\pi$
$252$		0			0
$253$	−149809.			−0.147142
$254$	−183232.	−	317367.i	−0.178204	−	0.308658i
$255$	−148934.	+	257961.i	−0.143431	+	0.248429i
$256$	−659587.	+	1.14244e6i	−0.629032	+	1.08951i
$257$	−263766.	−	456856.i	−0.249107	−	0.431466i	0.714171	−	0.699971i	$-0.246804\pi$
$257$	−263766.	−	456856.i	−0.249107	−	0.431466i	−0.963278	+	0.268505i	$0.913470\pi$
$258$	131061.			0.122581
$259$		0			0
$260$	422972.			0.388042
$261$	−550082.	−	952771.i	−0.499835	−	0.865739i
$262$	−590255.	+	1.02235e6i	−0.531235	+	0.920126i
$263$	176042.	−	304914.i	0.156938	−	0.271824i	−0.776825	−	0.629716i	$-0.783171\pi$
$263$	176042.	−	304914.i	0.156938	−	0.271824i	0.933763	+	0.357892i	$0.116504\pi$
$264$	173836.	+	301092.i	0.153507	+	0.265882i
$265$	−761353.			−0.665996
$266$		0			0
$267$	−439380.			−0.377192
$268$	−242928.	−	420764.i	−0.206605	−	0.357850i
$269$	239770.	−	415294.i	0.202029	−	0.349925i	−0.747153	−	0.664652i	$-0.768580\pi$
$269$	239770.	−	415294.i	0.202029	−	0.349925i	0.949182	+	0.314727i	$0.101913\pi$
$270$	1.09552e6	−	1.89749e6i	0.914554	−	1.58405i
$271$	−488805.	−	846636.i	−0.404308	−	0.700283i	0.589932	−	0.807453i	$-0.299154\pi$
$271$	−488805.	−	846636.i	−0.404308	−	0.700283i	−0.994241	+	0.107170i	$0.965821\pi$
$272$	−471961.			−0.386798
$273$		0			0
$274$	200155.			0.161061
$275$	−571395.	−	989684.i	−0.455622	−	0.789160i
$276$	38986.3	−	67526.2i	0.0308063	−	0.0533580i
$277$	−484362.	+	838939.i	−0.379289	+	0.656948i	−0.990959	−	0.134165i	$-0.957165\pi$
$277$	−484362.	+	838939.i	−0.379289	+	0.656948i	0.611670	+	0.791113i	$0.290498\pi$
$278$	1.19130e6	+	2.06339e6i	0.924502	+	1.60128i
$279$	−363970.			−0.279934
$280$		0			0
$281$	−318333.			−0.240501			−0.120250	−	0.992744i	$-0.538370\pi$
$281$	−318333.			−0.240501			−0.120250	+	0.992744i	$0.538370\pi$
$282$	−54727.4	−	94790.6i	−0.0409809	−	0.0709811i
$283$	886051.	−	1.53468e6i	0.657646	−	1.13908i	−0.323577	−	0.946202i	$-0.604885\pi$
$283$	886051.	−	1.53468e6i	0.657646	−	1.13908i	0.981223	−	0.192875i	$-0.0617812\pi$
$284$	130690.	−	226361.i	0.0961491	−	0.166535i
$285$	605644.	+	1.04901e6i	0.441678	+	0.765008i
$286$	727004.			0.525559
$287$		0			0
$288$	833492.			0.592134
$289$	641451.	+	1.11103e6i	0.451771	+	0.782491i
$290$	2.20052e6	−	3.81141e6i	1.53649	−	2.66128i
$291$	521147.	−	902652.i	0.360768	−	0.624868i
$292$	−636657.	−	1.10272e6i	−0.436967	−	0.756849i
$293$	−1.64148e6			−1.11703			−0.558516	−	0.829494i	$-0.688629\pi$
$293$	−1.64148e6			−1.11703			−0.558516	+	0.829494i	$0.688629\pi$
$294$		0			0
$295$	2.36881e6			1.58480
$296$	36236.2	+	62762.9i	0.0240388	+	0.0416365i
$297$	681846.	−	1.18099e6i	0.448534	−	0.776883i
$298$	1.25854e6	−	2.17986e6i	0.820969	−	1.42196i
$299$	62086.2	+	107536.i	0.0401622	+	0.0695629i
$300$	594799.			0.381563
$301$		0			0
$302$	−2.54128e6			−1.60337
$303$	144689.	+	250608.i	0.0905374	+	0.156815i
$304$	−959623.	+	1.66212e6i	−0.595548	+	1.03152i
$305$	−1.85642e6	+	3.21542e6i	−1.14269	+	1.97919i
$306$	185234.	+	320835.i	0.113088	+	0.195875i
$307$	466930.			0.282752			0.141376	−	0.989956i	$-0.454847\pi$
$307$	466930.			0.282752			0.141376	+	0.989956i	$0.454847\pi$
$308$		0			0
$309$	−294698.			−0.175582
$310$	−728002.	−	1.26094e6i	−0.430257	−	0.745228i
$311$	−1.21898e6	+	2.11134e6i	−0.714654	+	1.23782i	0.248439	+	0.968647i	$0.420082\pi$
$311$	−1.21898e6	+	2.11134e6i	−0.714654	+	1.23782i	−0.963093	+	0.269169i	$0.913251\pi$
$312$	144087.	−	249566.i	0.0837990	−	0.145144i
$313$	1.21047e6	+	2.09659e6i	0.698381	+	1.20963i	0.969028	+	0.246953i	$0.0794293\pi$
$313$	1.21047e6	+	2.09659e6i	0.698381	+	1.20963i	−0.270646	+	0.962679i	$0.587237\pi$
$314$	−3.25035e6			−1.86040
$315$		0			0
$316$	−492028.			−0.277186
$317$	−938057.	−	1.62476e6i	−0.524301	−	0.908116i	−0.999600	−	0.0282918i	$-0.990993\pi$
$317$	−938057.	−	1.62476e6i	−0.524301	−	0.908116i	0.475298	−	0.879825i	$-0.342340\pi$
$318$	340553.	−	589856.i	0.188850	−	0.327098i
$319$	1.36960e6	−	2.37221e6i	0.753557	−	1.30520i
$320$	38247.3	+	66246.2i	0.0208798	+	0.0361648i
$321$	885855.			0.479844
$322$		0			0
$323$	−556936.			−0.297029
$324$	42938.7	+	74371.9i	0.0227241	+	0.0393592i
$325$	−473612.	+	820321.i	−0.248722	+	0.430800i
$326$	−1.77933e6	+	3.08190e6i	−0.927285	+	1.60611i
$327$	−1.11227e6	−	1.92651e6i	−0.575229	−	0.996326i
$328$	688828.			0.353530
$329$		0			0
$330$	2.00613e6			1.01408
$331$	541549.	+	937990.i	0.271686	+	0.470575i	0.969294	−	0.245906i	$-0.0790853\pi$
$331$	541549.	+	937990.i	0.271686	+	0.470575i	−0.697607	+	0.716480i	$0.745752\pi$
$332$	−724399.	+	1.25470e6i	−0.360689	+	0.624732i
$333$	52268.0	−	90530.8i	0.0258301	−	0.0447390i
$334$	−2.39628e6	−	4.15048e6i	−1.17536	−	2.03579i
$335$	2.13507e6			1.03944
$336$		0			0
$337$	−2.59465e6			−1.24453			−0.622263	−	0.782809i	$-0.713786\pi$
$337$	−2.59465e6			−1.24453			−0.622263	+	0.782809i	$0.713786\pi$
$338$	1.01359e6	+	1.75560e6i	0.482583	+	0.835859i
$339$	−199969.	+	346357.i	−0.0945071	+	0.163691i
$340$	−268325.	+	464753.i	−0.125882	+	0.218034i
$341$	−453107.	−	784804.i	−0.211016	−	0.365490i
$342$	1.50652e6			0.696484
$343$		0			0
$344$	−179828.			−0.0819333
$345$	171324.	+	296741.i	0.0774943	+	0.134224i
$346$	−882371.	+	1.52831e6i	−0.396242	+	0.686312i
$347$	935255.	−	1.61991e6i	0.416972	−	0.722216i	−0.578662	−	0.815568i	$-0.696425\pi$
$347$	935255.	−	1.61991e6i	0.416972	−	0.722216i	0.995633	+	0.0933518i	$0.0297581\pi$
$348$	712847.	+	1.23469e6i	0.315536	+	0.546524i
$349$	1.61685e6			0.710568			0.355284	−	0.934758i	$-0.384384\pi$
$349$	1.61685e6			0.710568			0.355284	+	0.934758i	$0.384384\pi$
$350$		0			0
$351$	−1.13033e6			−0.489706
$352$	1.03762e6	+	1.79720e6i	0.446354	+	0.773109i
$353$	−289153.	+	500827.i	−0.123507	+	0.213920i	−0.921148	−	0.389212i	$-0.872747\pi$
$353$	−289153.	+	500827.i	−0.123507	+	0.213920i	0.797642	+	0.603132i	$0.206081\pi$
$354$	−1.05957e6	+	1.83523e6i	−0.449387	+	0.778362i
$355$	574310.	+	994734.i	0.241866	+	0.418925i
$356$	−791605.			−0.331042
$357$		0			0
$358$	986330.			0.406738
$359$	984090.	+	1.70449e6i	0.402994	+	0.698006i	0.994086	−	0.108598i	$-0.0346362\pi$
$359$	984090.	+	1.70449e6i	0.402994	+	0.698006i	−0.591092	+	0.806604i	$0.701303\pi$
$360$	−552773.	+	957432.i	−0.224797	+	0.389360i
$361$	105650.	−	182990.i	0.0426677	−	0.0739027i
$362$	1.08453e6	+	1.87847e6i	0.434983	+	0.753412i
$363$	−375229.			−0.149462
$364$		0			0
$365$	5.59553e6			2.19841
$366$	−1.66076e6	−	2.87651e6i	−0.648042	−	1.12244i
$367$	1.08726e6	−	1.88319e6i	0.421375	−	0.729842i	−0.574700	−	0.818364i	$-0.694881\pi$
$367$	1.08726e6	−	1.88319e6i	0.421375	−	0.729842i	0.996074	+	0.0885223i	$0.0282144\pi$
$368$	−271457.	+	470177.i	−0.104491	+	0.180985i
$369$	−496791.	−	860468.i	−0.189936	−	0.328979i
$370$	418180.			0.158803
$371$		0			0
$372$	471666.			0.176716
$373$	−692379.	−	1.19924e6i	−0.257675	−	0.446306i	0.707944	−	0.706269i	$-0.249623\pi$
$373$	−692379.	−	1.19924e6i	−0.257675	−	0.446306i	−0.965619	+	0.259963i	$0.916290\pi$
$374$	−461197.	+	798817.i	−0.170493	+	0.295303i
$375$	−49278.9	+	85353.5i	−0.0180960	+	0.0313432i
$376$	75091.0	+	130061.i	0.0273916	+	0.0474437i
$377$	−2.27044e6			−0.822728
$378$		0			0
$379$	3.37190e6			1.20580			0.602902	−	0.797815i	$-0.294011\pi$
$379$	3.37190e6			1.20580			0.602902	+	0.797815i	$0.294011\pi$
$380$	1.09115e6	+	1.88993e6i	0.387639	+	0.671410i
$381$	−260842.	+	451792.i	−0.0920589	+	0.159451i
$382$	−805642.	+	1.39541e6i	−0.282478	+	0.489265i
$383$	1.64030e6	+	2.84108e6i	0.571382	+	0.989662i	0.996424	+	0.0844886i	$0.0269257\pi$
$383$	1.64030e6	+	2.84108e6i	0.571382	+	0.989662i	−0.425043	+	0.905173i	$0.639741\pi$
$384$	1.83428e6			0.634800
$385$		0			0
$386$	−4.76227e6			−1.62684
$387$	129694.	+	224637.i	0.0440192	+	0.0762435i
$388$	938919.	−	1.62626e6i	0.316628	−	0.548415i
$389$	1.47405e6	−	2.55313e6i	0.493899	−	0.855457i	−0.506077	−	0.862488i	$-0.668905\pi$
$389$	1.47405e6	−	2.55313e6i	0.493899	−	0.855457i	0.999975	+	0.00703108i	$0.00223808\pi$
$390$	−831412.	−	1.44005e6i	−0.276793	−	0.479419i
$391$	−157545.			−0.0521150
$392$		0			0
$393$	1.68053e6			0.548865
$394$	4542.73	+	7868.24i	0.00147427	+	0.00255351i
$395$	1.08110e6	−	1.87251e6i	0.348636	−	0.603855i
$396$	451752.	−	782458.i	0.144765	−	0.250740i
$397$	−34635.1	−	59989.7i	−0.0110291	−	0.0191030i	0.860458	−	0.509521i	$-0.170177\pi$
$397$	−34635.1	−	59989.7i	−0.0110291	−	0.0191030i	−0.871487	+	0.490418i	$0.836844\pi$
$398$	−2.61282e6			−0.826802
$399$		0			0
$400$	−4.14151e6			−1.29422
$401$	1.67393e6	+	2.89933e6i	0.519848	+	0.900404i	0.999734	+	0.0230725i	$0.00734485\pi$
$401$	1.67393e6	+	2.89933e6i	0.519848	+	0.900404i	−0.479886	+	0.877331i	$0.659322\pi$
$402$	−955019.	+	1.65414e6i	−0.294745	+	0.510514i
$403$	−375567.	+	650501.i	−0.115193	+	0.199520i
$404$	260677.	+	451506.i	0.0794602	+	0.137629i
$405$	−377384.			−0.114326
$406$		0			0
$407$	260274.			0.0778834
$408$	182812.	+	316640.i	0.0543694	+	0.0941706i
$409$	1.45608e6	−	2.52201e6i	0.430406	−	0.745485i	−0.566502	−	0.824060i	$-0.691704\pi$
$409$	1.45608e6	−	2.52201e6i	0.430406	−	0.745485i	0.996908	+	0.0785754i	$0.0250371\pi$
$410$	1.98734e6	−	3.44217e6i	0.583864	−	1.01128i
$411$	−142466.	−	246759.i	−0.0416014	−	0.0720557i
$412$	−530940.			−0.154100
$413$		0			0
$414$	426163.			0.122201
$415$	−3.18334e6	−	5.51371e6i	−0.907326	−	1.57153i
$416$	860050.	−	1.48965e6i	0.243663	−	0.422037i
$417$	1.69589e6	−	2.93736e6i	0.477592	−	0.827213i
$418$	1.87547e6	+	3.24842e6i	0.525014	+	0.909350i
$419$	4.62361e6			1.28661			0.643304	−	0.765611i	$-0.277563\pi$
$419$	4.62361e6			1.28661			0.643304	+	0.765611i	$0.277563\pi$
$420$		0			0
$421$	−2.63042e6			−0.723303			−0.361652	−	0.932313i	$-0.617787\pi$
$421$	−2.63042e6			−0.723303			−0.361652	+	0.932313i	$0.617787\pi$
$422$	−1.77837e6	−	3.08023e6i	−0.486117	−	0.841979i
$423$	108313.	−	187604.i	0.0294327	−	0.0509789i
$424$	−467270.	+	809336.i	−0.126227	+	0.218632i
$425$	−600901.	−	1.04079e6i	−0.161373	−	0.279506i
$426$	−1.02756e6			−0.274335
$427$		0			0
$428$	1.59599e6			0.421135
$429$	−517468.	−	896281.i	−0.135750	−	0.235126i
$430$	−518820.	+	898623.i	−0.135315	+	0.234372i
$431$	−3.77064e6	+	6.53094e6i	−0.977736	+	1.69349i	−0.307144	+	0.951663i	$0.599373\pi$
$431$	−3.77064e6	+	6.53094e6i	−0.977736	+	1.69349i	−0.670592	+	0.741826i	$0.733960\pi$
$432$	−2.47103e6	−	4.27996e6i	−0.637044	−	1.10339i
$433$	−5.83558e6			−1.49577			−0.747883	−	0.663830i	$-0.768930\pi$
$433$	−5.83558e6			−1.49577			−0.747883	+	0.663830i	$0.768930\pi$
$434$		0			0
$435$	−6.26516e6			−1.58748
$436$	−2.00391e6	−	3.47088e6i	−0.504850	−	0.874426i
$437$	−320331.	+	554830.i	−0.0802409	+	0.138981i
$438$	−2.50288e6	+	4.33512e6i	−0.623383	+	1.07973i
$439$	84051.9	+	145582.i	0.0208155	+	0.0360535i	0.876246	−	0.481865i	$-0.160040\pi$
$439$	84051.9	+	145582.i	0.0208155	+	0.0360535i	−0.855430	+	0.517918i	$0.826707\pi$
$440$	−2.75259e6			−0.677814
$441$		0			0
$442$	764546.			0.186143
$443$	1.42076e6	+	2.46082e6i	0.343962	+	0.595760i	0.985165	−	0.171612i	$-0.0548975\pi$
$443$	1.42076e6	+	2.46082e6i	0.343962	+	0.595760i	−0.641203	+	0.767372i	$0.721564\pi$
$444$	−67733.7	+	117318.i	−0.0163060	+	0.0282428i
$445$	1.73934e6	−	3.01262e6i	0.416374	−	0.721181i
$446$	−4.15503e6	−	7.19672e6i	−0.989092	−	1.71316i
$447$	−3.58323e6			−0.848214
$448$		0			0
$449$	−1.41567e6			−0.331396			−0.165698	−	0.986177i	$-0.552988\pi$
$449$	−1.41567e6			−0.331396			−0.165698	+	0.986177i	$0.552988\pi$
$450$	1.62545e6	+	2.81536e6i	0.378392	+	0.655395i
$451$	1.23691e6	−	2.14240e6i	0.286350	−	0.495973i
$452$	−360273.	+	624012.i	−0.0829442	+	0.143664i
$453$	1.80883e6	+	3.13299e6i	0.414146	+	0.717321i
$454$	6.44644e6			1.46784
$455$		0			0
$456$	1.48682e6			0.334848
$457$	−778637.	−	1.34864e6i	−0.174399	−	0.302068i	0.765554	−	0.643372i	$-0.222465\pi$
$457$	−778637.	−	1.34864e6i	−0.174399	−	0.302068i	−0.939953	+	0.341303i	$0.889132\pi$
$458$	1.84833e6	−	3.20141e6i	0.411734	−	0.713144i
$459$	717056.	−	1.24198e6i	0.158862	−	0.275158i
$460$	308664.	+	534621.i	0.0680129	+	0.117802i
$461$	4.45345e6			0.975987			0.487994	−	0.872847i	$-0.337729\pi$
$461$	4.45345e6			0.975987			0.487994	+	0.872847i	$0.337729\pi$
$462$		0			0
$463$	4.92263e6			1.06720			0.533599	−	0.845738i	$-0.320839\pi$
$463$	4.92263e6			1.06720			0.533599	+	0.845738i	$0.320839\pi$
$464$	−4.96347e6	−	8.59698e6i	−1.07026	−	1.85375i
$465$	−1.03636e6	+	1.79502e6i	−0.222268	+	0.384980i
$466$	3.69291e6	−	6.39631e6i	0.787778	−	1.36447i
$467$	2.54545e6	+	4.40885e6i	0.540098	+	0.935477i	0.998898	+	0.0469376i	$0.0149462\pi$
$467$	2.54545e6	+	4.40885e6i	0.540098	+	0.935477i	−0.458800	+	0.888540i	$0.651720\pi$
$468$	−748889.			−0.158053
$469$		0			0
$470$	866579.			0.180952
$471$	2.31354e6	+	4.00717e6i	0.480535	+	0.832312i
$472$	1.45383e6	−	2.51810e6i	0.300370	−	0.520257i
$473$	−322912.	+	559301.i	−0.0663639	+	0.114946i
$474$	967150.	+	1.67515e6i	0.197719	+	0.342459i
$475$	−4.88717e6			−0.993856
$476$		0			0
$477$	1.34800e6			0.271266
$478$	5.43416e6	+	9.41224e6i	1.08783	+	1.88418i
$479$	−4.15042e6	+	7.18874e6i	−0.826521	+	1.43158i	0.0742312	+	0.997241i	$0.476350\pi$
$479$	−4.15042e6	+	7.18874e6i	−0.826521	+	1.43158i	−0.900752	+	0.434334i	$0.856984\pi$
$480$	2.37326e6	−	4.11061e6i	0.470157	−	0.814335i
$481$	−107867.	−	186831.i	−0.0212581	−	0.0368202i
$482$	7.13644e6			1.39915
$483$		0			0
$484$	−676028.			−0.131175
$485$	4.12604e6	+	7.14651e6i	0.796488	+	1.37956i
$486$	−3.16601e6	+	5.48369e6i	−0.608025	+	1.05313i
$487$	−4.31701e6	+	7.47727e6i	−0.824822	+	1.42863i	0.0772330	+	0.997013i	$0.475391\pi$
$487$	−4.31701e6	+	7.47727e6i	−0.824822	+	1.42863i	−0.902055	+	0.431621i	$0.857942\pi$
$488$	2.27871e6	+	3.94684e6i	0.433151	+	0.750240i
$489$	5.06599e6			0.958059
$490$		0			0
$491$	95039.5			0.0177910			0.00889550	−	0.999960i	$-0.497168\pi$
$491$	95039.5			0.0177910			0.00889550	+	0.999960i	$0.497168\pi$
$492$	643788.	+	1.11507e6i	0.119903	+	0.207678i
$493$	1.44032e6	−	2.49471e6i	0.266896	−	0.462277i
$494$	1.55453e6	−	2.69252e6i	0.286603	−	0.496411i
$495$	1.98521e6	+	3.43848e6i	0.364160	+	0.630744i
$496$	−3.28415e6			−0.599402
$497$		0			0
$498$	5.69564e6			1.02913
$499$	−1.07102e6	−	1.85506e6i	−0.192551	−	0.333507i	0.753544	−	0.657397i	$-0.228343\pi$
$499$	−1.07102e6	−	1.85506e6i	−0.192551	−	0.333507i	−0.946095	+	0.323890i	$0.895009\pi$
$500$	−88782.9	+	153776.i	−0.0158820	+	0.0275084i
$501$	−3.41126e6	+	5.90848e6i	−0.607185	+	1.05167i
$502$	30143.8	+	52210.7i	0.00533875	+	0.00924698i
$503$	−5.24794e6			−0.924844			−0.462422	−	0.886660i	$-0.653019\pi$
$503$	−5.24794e6			−0.924844			−0.462422	+	0.886660i	$0.653019\pi$
$504$		0			0
$505$	−2.29107e6			−0.399769
$506$	530531.	+	918907.i	0.0921159	+	0.159549i
$507$	1.44292e6	−	2.49920e6i	0.249299	−	0.431799i
$508$	−469945.	+	813968.i	−0.0807956	+	0.139942i
$509$	−5.29453e6	−	9.17040e6i	−0.905802	−	1.56889i	−0.819837	−	0.572596i	$-0.805936\pi$
$509$	−5.29453e6	−	9.17040e6i	−0.905802	−	1.56889i	−0.0859643	−	0.996298i	$-0.527397\pi$
$510$	2.10972e6			0.359170
$511$		0			0
$512$	3.52190e6			0.593747
$513$	−2.91593e6	−	5.05055e6i	−0.489198	−	0.847315i
$514$	−1.86819e6	+	3.23580e6i	−0.311899	+	0.540225i
$515$	1.16660e6	−	2.02061e6i	0.193822	−	0.335709i
$516$	−168069.	−	291105.i	−0.0277885	−	0.0481310i
$517$	539357.			0.0887462
$518$		0			0
$519$	2.51222e6			0.409392
$520$	1.14077e6	+	1.97588e6i	0.185008	+	0.320443i
$521$	−2.27232e6	+	3.93578e6i	−0.366755	+	0.635238i	−0.989056	−	0.147540i	$-0.952865\pi$
$521$	−2.27232e6	+	3.93578e6i	−0.366755	+	0.635238i	0.622301	+	0.782778i	$0.286198\pi$
$522$	−3.89610e6	+	6.74825e6i	−0.625827	+	1.08396i
$523$	−2.63599e6	−	4.56566e6i	−0.421394	−	0.729877i	0.574682	−	0.818377i	$-0.305126\pi$
$523$	−2.63599e6	−	4.56566e6i	−0.421394	−	0.729877i	−0.996076	+	0.0885004i	$0.971793\pi$
$524$	3.02772e6			0.481711
$525$		0			0
$526$	−2.49373e6			−0.392993
$527$	−476504.	−	825330.i	−0.0747378	−	0.129450i
$528$	2.26250e6	−	3.91877e6i	0.353187	−	0.611737i
$529$	3.12756e6	−	5.41709e6i	0.485921	−	0.841641i
$530$	2.69624e6	+	4.67003e6i	0.416936	+	0.722154i
$531$	−4.19407e6			−0.645504
$532$		0			0
$533$	−2.05048e6			−0.312635
$534$	1.55601e6	+	2.69509e6i	0.236135	+	0.408997i
$535$	−3.50676e6	+	6.07389e6i	−0.529690	+	0.917451i
$536$	1.31037e6	−	2.26963e6i	0.197008	−	0.341227i
$537$	−702052.	−	1.21599e6i	−0.105059	−	0.181968i
$538$	−3.39647e6			−0.505908
$539$		0			0
$540$	−5.61945e6			−0.829296
$541$	−2.96723e6	−	5.13939e6i	−0.435871	−	0.754950i	0.561496	−	0.827480i	$-0.310226\pi$
$541$	−2.96723e6	−	5.13939e6i	−0.435871	−	0.754950i	−0.997366	+	0.0725298i	$0.976893\pi$
$542$	−3.46209e6	+	5.99652e6i	−0.506221	+	0.876801i
$543$	1.54390e6	−	2.67412e6i	0.224709	−	0.389208i
$544$	1.09120e6	+	1.89001e6i	0.158091	+	0.273821i
$545$	1.76122e7			2.53994
$546$		0			0
$547$	−8.82017e6			−1.26040			−0.630200	−	0.776433i	$-0.717027\pi$
$547$	−8.82017e6			−1.26040			−0.630200	+	0.776433i	$0.717027\pi$
$548$	−256673.	−	444571.i	−0.0365115	−	0.0632397i
$549$	3.28687e6	−	5.69302e6i	0.465427	−	0.806143i
$550$	−4.04705e6	+	7.00970e6i	−0.570469	+	0.988081i
$551$	−5.85712e6	−	1.01448e7i	−0.821874	−	1.42353i
$552$	420590.			0.0587505
$553$		0			0
$554$	6.86124e6			0.949791
$555$	−297653.	−	515550.i	−0.0410183	−	0.0710458i
$556$	3.05538e6	−	5.29207e6i	0.419158	−	0.726004i
$557$	591120.	−	1.02385e6i	0.0807304	−	0.139829i	−0.822833	−	0.568283i	$-0.807608\pi$
$557$	591120.	−	1.02385e6i	0.0807304	−	0.139829i	0.903564	+	0.428453i	$0.140941\pi$
$558$	1.28896e6	+	2.23254e6i	0.175248	+	0.303538i
$559$	535306.			0.0724556
$560$		0			0
$561$	1.31309e6			0.176151
$562$	1.12734e6	+	1.95261e6i	0.150561	+	0.260780i
$563$	2.03870e6	−	3.53114e6i	0.271071	−	0.469509i	−0.698065	−	0.716034i	$-0.745955\pi$
$563$	2.03870e6	−	3.53114e6i	0.271071	−	0.469509i	0.969136	+	0.246525i	$0.0792888\pi$
$564$	−140362.	+	243114.i	−0.0185803	+	0.0321820i
$565$	−1.58321e6	−	2.74219e6i	−0.208649	−	0.361391i
$566$	−1.25514e7			−1.64684
$567$		0			0
$568$	1.40990e6			0.183366
$569$	−4.08807e6	−	7.08075e6i	−0.529344	−	0.916851i	−0.999414	−	0.0342216i	$-0.989105\pi$
$569$	−4.08807e6	−	7.08075e6i	−0.529344	−	0.916851i	0.470070	−	0.882629i	$-0.344229\pi$
$570$	4.28964e6	−	7.42987e6i	0.553010	−	0.957842i
$571$	−1.65307e6	+	2.86321e6i	−0.212179	+	0.367504i	−0.952396	−	0.304863i	$-0.901389\pi$
$571$	−1.65307e6	+	2.86321e6i	−0.212179	+	0.367504i	0.740217	+	0.672368i	$0.234723\pi$
$572$	−932292.	−	1.61478e6i	−0.119141	−	0.206359i
$573$	2.29377e6			0.291852
$574$		0			0
$575$	−1.38247e6			−0.174376
$576$	−67718.3	−	117291.i	−0.00850452	−	0.0147303i
$577$	−3.57497e6	+	6.19203e6i	−0.447026	+	0.774272i	−0.998191	−	0.0601245i	$-0.980850\pi$
$577$	−3.57497e6	+	6.19203e6i	−0.447026	+	0.774272i	0.551165	+	0.834396i	$0.314184\pi$
$578$	4.54324e6	−	7.86913e6i	0.565648	−	0.979731i
$579$	3.38970e6	+	5.87112e6i	0.420208	+	0.727821i
$580$	−1.12876e7			−1.39325
$581$		0			0
$582$	−7.38232e6			−0.903411
$583$	1.67813e6	+	2.90661e6i	0.204482	+	0.354173i
$584$	3.43418e6	−	5.94818e6i	0.416669	−	0.721692i
$585$	1.64548e6	−	2.85005e6i	0.198794	−	0.344321i
$586$	5.81309e6	+	1.00686e7i	0.699300	+	1.21122i
$587$	−9.69191e6			−1.16095			−0.580476	−	0.814277i	$-0.697133\pi$
$587$	−9.69191e6			−1.16095			−0.580476	+	0.814277i	$0.697133\pi$
$588$		0			0
$589$	−3.87545e6			−0.460292
$590$	−8.38886e6	−	1.45299e7i	−0.992139	−	1.71844i
$591$	6466.87	−	11200.9i	0.000761597	−	0.00131912i
$592$	471621.	−	816872.i	0.0553081	−	0.0957965i
$593$	3.31980e6	+	5.75006e6i	0.387682	+	0.671484i	0.992137	−	0.125154i	$-0.0399426\pi$
$593$	3.31980e6	+	5.75006e6i	0.387682	+	0.671484i	−0.604456	+	0.796639i	$0.706609\pi$
$594$	−9.65871e6			−1.12319
$595$		0			0
$596$	−6.45569e6			−0.744435
$597$	1.85976e6	+	3.22119e6i	0.213560	+	0.369897i
$598$	439742.	−	761655.i	0.0502857	−	0.0870974i
$599$	1.62096e6	−	2.80758e6i	0.184588	−	0.319716i	−0.758849	−	0.651266i	$-0.774238\pi$
$599$	1.62096e6	−	2.80758e6i	0.184588	−	0.319716i	0.943438	+	0.331550i	$0.107572\pi$
$600$	1.60420e6	+	2.77855e6i	0.181919	+	0.315094i
$601$	5.65076e6			0.638147			0.319074	−	0.947730i	$-0.396628\pi$
$601$	5.65076e6			0.638147			0.319074	+	0.947730i	$0.396628\pi$
$602$		0			0
$603$	−3.78023e6			−0.423375
$604$	3.25887e6	+	5.64453e6i	0.363475	+	0.629557i
$605$	1.48539e6	−	2.57277e6i	0.164988	−	0.285767i
$606$	1.02480e6	−	1.77500e6i	0.113359	−	0.196343i
$607$	117837.	+	204100.i	0.0129811	+	0.0224839i	0.872443	−	0.488716i	$-0.162535\pi$
$607$	117837.	+	204100.i	0.0129811	+	0.0224839i	−0.859462	+	0.511200i	$0.829201\pi$
$608$	8.87478e6			0.973641
$609$		0			0
$610$	2.62972e7			2.86144
$611$	−223529.	−	387163.i	−0.0242231	−	0.0419557i
$612$	475080.	−	822863.i	0.0512729	−	0.0888073i
$613$	−394438.	+	683187.i	−0.0423963	+	0.0734325i	−0.886445	−	0.462834i	$-0.846833\pi$
$613$	−394438.	+	683187.i	−0.0423963	+	0.0734325i	0.844049	+	0.536267i	$0.180166\pi$
$614$	−1.65358e6	−	2.86408e6i	−0.177012	−	0.306595i
$615$	−5.65820e6			−0.603240
$616$		0			0
$617$	1.67739e7			1.77387			0.886935	−	0.461894i	$-0.152830\pi$
$617$	1.67739e7			1.77387			0.886935	+	0.461894i	$0.152830\pi$
$618$	1.04364e6	+	1.80763e6i	0.109921	+	0.190388i
$619$	4.11150e6	−	7.12132e6i	0.431294	−	0.747023i	−0.565691	−	0.824617i	$-0.691390\pi$
$619$	4.11150e6	−	7.12132e6i	0.431294	−	0.747023i	0.996985	+	0.0775941i	$0.0247238\pi$
$620$	−1.86714e6	+	3.23399e6i	−0.195074	+	0.337878i
$621$	−824854.	−	1.42869e6i	−0.0858318	−	0.148665i
$622$	1.72675e7			1.78959
$623$		0			0
$624$	−3.75065e6			−0.385607
$625$	4.68399e6	+	8.11290e6i	0.479640	+	0.830761i
$626$	8.57346e6	−	1.48497e7i	0.874420	−	1.51454i
$627$	2.66986e6	−	4.62433e6i	0.271218	−	0.469764i
$628$	4.16818e6	+	7.21949e6i	0.421742	+	0.730479i
$629$	273714.			0.0275849
$630$		0			0
$631$	−5.94507e6			−0.594406			−0.297203	−	0.954814i	$-0.596054\pi$
$631$	−5.94507e6			−0.594406			−0.297203	+	0.954814i	$0.596054\pi$
$632$	−1.32702e6	−	2.29846e6i	−0.132155	−	0.228899i
$633$	−2.53162e6	+	4.38490e6i	−0.251125	+	0.434961i
$634$	−6.64403e6	+	1.15078e7i	−0.656460	+	1.13702i
$635$	−2.06515e6	−	3.57695e6i	−0.203244	−	0.352029i
$636$	−1.74687e6			−0.171245
$637$		0			0
$638$	−1.94011e7			−1.88701
$639$	−1.01684e6	−	1.76122e6i	−0.0985144	−	0.170632i
$640$	−7.26120e6	+	1.25768e7i	−0.700743	+	1.21372i
$641$	5.33804e6	−	9.24576e6i	0.513141	−	0.888786i	−0.486743	−	0.873545i	$-0.661815\pi$
$641$	5.33804e6	−	9.24576e6i	0.513141	−	0.888786i	0.999884	−	0.0152411i	$-0.00485157\pi$
$642$	−3.13715e6	−	5.43371e6i	−0.300399	−	0.520306i
$643$	3.13159e6			0.298701			0.149351	−	0.988784i	$-0.452282\pi$
$643$	3.13159e6			0.298701			0.149351	+	0.988784i	$0.452282\pi$
$644$		0			0
$645$	1.47715e6			0.139806
$646$	1.97232e6	+	3.41616e6i	0.185950	+	0.322075i
$647$	−2.46728e6	+	4.27346e6i	−0.231717	+	0.401346i	−0.958314	−	0.285719i	$-0.907768\pi$
$647$	−2.46728e6	+	4.27346e6i	−0.231717	+	0.401346i	0.726596	+	0.687065i	$0.241101\pi$
$648$	−231615.	+	401168.i	−0.0216685	+	0.0375309i
$649$	−5.22120e6	−	9.04339e6i	−0.486585	−	0.842790i
$650$	6.70897e6			0.622834
$651$		0			0
$652$	9.12710e6			0.840841
$653$	−2.86112e6	−	4.95561e6i	−0.262575	−	0.454793i	0.704351	−	0.709852i	$-0.251238\pi$
$653$	−2.86112e6	−	4.95561e6i	−0.262575	−	0.454793i	−0.966925	+	0.255059i	$0.917905\pi$
$654$	−7.87794e6	+	1.36450e7i	−0.720226	+	1.24747i
$655$	−6.65258e6	+	1.15226e7i	−0.605881	+	1.04942i
$656$	−4.48261e6	−	7.76411e6i	−0.406698	−	0.704421i
$657$	−9.90710e6			−0.895433
$658$		0			0
$659$	362477.			0.0325137			0.0162569	−	0.999868i	$-0.494825\pi$
$659$	362477.			0.0325137			0.0162569	+	0.999868i	$0.494825\pi$
$660$	−2.57261e6	−	4.45590e6i	−0.229887	−	0.398176i
$661$	−9.56053e6	+	1.65593e7i	−0.851096	+	1.47414i	0.0291249	+	0.999576i	$0.490728\pi$
$661$	−9.56053e6	+	1.65593e7i	−0.851096	+	1.47414i	−0.880220	+	0.474565i	$0.842605\pi$
$662$	3.83566e6	−	6.64356e6i	0.340170	−	0.589191i
$663$	−544190.	−	942564.i	−0.0480802	−	0.0832774i
$664$	−7.81494e6			−0.687868
$665$		0			0
$666$	−740404.			−0.0646819
$667$	−1.65685e6	−	2.86975e6i	−0.144201	−	0.249764i
$668$	−6.14587e6	+	1.06450e7i	−0.532896	+	0.923003i
$669$	−5.91495e6	+	1.02450e7i	−0.510958	+	0.885006i
$670$	−7.56111e6	−	1.30962e7i	−0.650727	−	1.12709i
$671$	1.63673e7			1.40337
$672$		0			0
$673$	−573374.			−0.0487978			−0.0243989	−	0.999702i	$-0.507767\pi$
$673$	−573374.			−0.0487978			−0.0243989	+	0.999702i	$0.507767\pi$
$674$	9.18864e6	+	1.59152e7i	0.779115	+	1.34947i
$675$	6.29224e6	−	1.08985e7i	0.531552	−	0.920675i
$676$	2.59962e6	−	4.50267e6i	0.218798	−	0.378968i
$677$	5.84516e6	+	1.01241e7i	0.490146	+	0.848957i	0.999936	−	0.0113419i	$-0.00361030\pi$
$677$	5.84516e6	+	1.01241e7i	0.490146	+	0.848957i	−0.509790	+	0.860299i	$0.670277\pi$
$678$	2.83267e6			0.236659
$679$		0			0
$680$	−2.89473e6			−0.240069
$681$	−4.58846e6	−	7.94744e6i	−0.379139	−	0.656689i
$682$	−3.20925e6	+	5.55858e6i	−0.264206	+	0.457618i
$683$	−9.18370e6	+	1.59066e7i	−0.753297	+	1.30475i	0.192920	+	0.981214i	$0.438204\pi$
$683$	−9.18370e6	+	1.59066e7i	−0.753297	+	1.30475i	−0.946217	+	0.323534i	$0.895129\pi$
$684$	−1.93193e6	−	3.34620e6i	−0.157889	−	0.273471i
$685$	2.25588e6			0.183692
$686$		0			0
$687$	−5.26244e6			−0.425398
$688$	1.17025e6	+	2.02693e6i	0.0942554	+	0.163255i
$689$	1.39096e6	−	2.40921e6i	0.111626	−	0.193342i
$690$	1.21344e6	−	2.10175e6i	0.0970280	−	0.168057i
$691$	1.17806e7	+	2.04045e7i	0.938579	+	1.62567i	0.768125	+	0.640300i	$0.221190\pi$
$691$	1.17806e7	+	2.04045e7i	0.938579	+	1.62567i	0.170454	+	0.985366i	$0.445477\pi$
$692$	4.52612e6			0.359303
$693$		0			0
$694$	−1.32484e7			−1.04415
$695$	1.34267e7	+	2.32558e7i	1.05441	+	1.82629i
$696$	−3.84516e6	+	6.66001e6i	−0.300878	+	0.521137i
$697$	1.30078e6	−	2.25303e6i	0.101420	−	0.175665i
$698$	−5.72587e6	−	9.91750e6i	−0.444839	−	0.770484i
$699$	−1.05142e7			−0.813921
$700$		0			0
$701$	1.32980e7			1.02210			0.511048	−	0.859552i	$-0.329257\pi$
$701$	1.32980e7			1.02210			0.511048	+	0.859552i	$0.329257\pi$
$702$	4.00291e6	+	6.93325e6i	0.306573	+	0.530999i
$703$	556535.	−	963946.i	0.0424721	−	0.0735639i
$704$	168605.	−	292033.i	0.0128215	−	0.0222075i
$705$	−616815.	−	1.06836e6i	−0.0467393	−	0.0809549i
$706$	4.09600e6			0.309277
$707$		0			0
$708$	5.43506e6			0.407494
$709$	3.42677e6	+	5.93533e6i	0.256017	+	0.443434i	0.965171	−	0.261619i	$-0.0842564\pi$
$709$	3.42677e6	+	5.93533e6i	0.256017	+	0.443434i	−0.709154	+	0.705053i	$0.750923\pi$
$710$	4.06770e6	−	7.04547e6i	0.302833	−	0.524522i
$711$	−1.91412e6	+	3.31536e6i	−0.142003	+	0.245956i
$712$	−2.13499e6	−	3.69791e6i	−0.157832	−	0.273374i
$713$	−1.09628e6			−0.0807602
$714$		0			0
$715$	8.19384e6			0.599408
$716$	−1.26485e6	−	2.19078e6i	−0.0922051	−	0.159704i
$717$	7.73587e6	−	1.33989e7i	0.561968	−	0.973357i
$718$	6.97008e6	−	1.20725e7i	0.504576	−	0.873951i
$719$	1.32865e7	+	2.30128e7i	0.958490	+	1.66015i	0.726172	+	0.687513i	$0.241298\pi$
$719$	1.32865e7	+	2.30128e7i	0.958490	+	1.66015i	0.232318	+	0.972640i	$0.425369\pi$
$720$	1.43889e7			1.03442
$721$		0			0
$722$	−1.49658e6			−0.106846
$723$	−5.07958e6	−	8.79810e6i	−0.361395	−	0.625955i
$724$	2.78156e6	−	4.81781e6i	0.197216	−	0.341588i
$725$	1.26390e7	−	2.18913e7i	0.893031	−	1.54678i
$726$	1.32883e6	+	2.30160e6i	0.0935680	+	0.162065i
$727$	−2.16991e6			−0.152267			−0.0761335	−	0.997098i	$-0.524258\pi$
$727$	−2.16991e6			−0.152267			−0.0761335	+	0.997098i	$0.524258\pi$
$728$		0			0
$729$	1.01628e7			0.708264
$730$	−1.98159e7	−	3.43221e7i	−1.37628	−	2.38379i
$731$	−339587.	+	588182.i	−0.0235049	+	0.0407116i
$732$	−4.25943e6	+	7.37755e6i	−0.293815	+	0.508902i
$733$	−8.73265e6	−	1.51254e7i	−0.600324	−	1.03979i	−0.992772	−	0.120018i	$-0.961705\pi$
$733$	−8.73265e6	−	1.51254e7i	−0.600324	−	1.03979i	0.392447	−	0.919774i	$-0.371628\pi$
$734$	−1.54016e7			−1.05518
$735$		0			0
$736$	2.51048e6			0.170829
$737$	−4.70602e6	−	8.15106e6i	−0.319143	−	0.552771i
$738$	−3.51865e6	+	6.09449e6i	−0.237813	+	0.411904i
$739$	6.82304e6	−	1.18178e7i	0.459586	−	0.796026i	−0.539353	−	0.842080i	$-0.681331\pi$
$739$	6.82304e6	−	1.18178e7i	0.459586	−	0.796026i	0.998939	+	0.0460536i	$0.0146645\pi$
$740$	−536264.	−	928836.i	−0.0359997	−	0.0623533i
$741$	−4.42594e6			−0.296114
$742$		0			0
$743$	1.48965e7			0.989944			0.494972	−	0.868909i	$-0.335178\pi$
$743$	1.48965e7			0.989944			0.494972	+	0.868909i	$0.335178\pi$
$744$	1.27210e6	+	2.20334e6i	0.0842538	+	0.145932i
$745$	1.41846e7	−	2.45685e7i	0.936326	−	1.62176i
$746$	−4.90396e6	+	8.49390e6i	−0.322626	+	0.558805i
$747$	5.63623e6	+	9.76224e6i	0.369562	+	0.640100i
$748$	2.36571e6			0.154599
$749$		0			0
$750$	698061.			0.0453148
$751$	1.26731e7	+	2.19505e7i	0.819944	+	1.42019i	0.905723	+	0.423871i	$0.139329\pi$
$751$	1.26731e7	+	2.19505e7i	0.819944	+	1.42019i	−0.0857783	+	0.996314i	$0.527338\pi$
$752$	977324.	−	1.69277e6i	0.0630222	−	0.109158i
$753$	42911.7	−	74325.2i	0.00275796	−	0.00477693i
$754$	8.04049e6	+	1.39265e7i	0.515056	+	0.892102i
$755$	−2.86419e7			−1.82867
$756$		0			0
$757$	−2.66725e7			−1.69170			−0.845852	−	0.533417i	$-0.820908\pi$
$757$	−2.66725e7			−1.69170			−0.845852	+	0.533417i	$0.820908\pi$
$758$	−1.19412e7	−	2.06828e7i	−0.754875	−	1.30748i
$759$	755245.	−	1.30812e6i	0.0475864	−	0.0824221i
$760$	−5.88577e6	+	1.01945e7i	−0.369632	+	0.640221i
$761$	289914.	+	502146.i	0.0181471	+	0.0314318i	0.874956	−	0.484202i	$-0.160890\pi$
$761$	289914.	+	502146.i	0.0181471	+	0.0314318i	−0.856809	+	0.515634i	$0.827557\pi$
$762$	3.69497e6			0.230528
$763$		0			0
$764$	4.13255e6			0.256144
$765$	2.08772e6	+	3.61604e6i	0.128979	+	0.223398i
$766$	1.16179e7	−	2.01227e7i	0.715408	−	1.23912i
$767$	−4.32770e6	+	7.49580e6i	−0.265625	+	0.460076i
$768$	−6.65046e6	−	1.15189e7i	−0.406864	−	0.704708i
$769$	−1.52438e7			−0.929562			−0.464781	−	0.885426i	$-0.653867\pi$
$769$	−1.52438e7			−0.929562			−0.464781	+	0.885426i	$0.653867\pi$
$770$		0			0
$771$	5.31898e6			0.322250
$772$	6.10702e6	+	1.05777e7i	0.368796	+	0.638773i
$773$	−9.74628e6	+	1.68810e7i	−0.586665	+	1.01613i	0.408001	+	0.912982i	$0.366226\pi$
$773$	−9.74628e6	+	1.68810e7i	−0.586665	+	1.01613i	−0.994666	+	0.103152i	$0.967107\pi$
$774$	918592.	−	1.59105e6i	0.0551150	−	0.0954620i
$775$	−4.18138e6	−	7.24236e6i	−0.250072	−	0.433137i
$776$	1.01292e7			0.603839
$777$		0			0
$778$	−2.08807e7			−1.23679
$779$	−5.28969e6	−	9.16201e6i	−0.312311	−	0.540938i
$780$	−2.13236e6	+	3.69336e6i	−0.125495	+	0.217363i
$781$	2.53173e6	−	4.38508e6i	0.148521	−	0.257247i
$782$	557927.	+	966358.i	0.0326257	+	0.0565094i
$783$	3.01642e7			1.75828
$784$		0			0
$785$	−3.66337e7			−2.12181
$786$	−5.95140e6	−	1.03081e7i	−0.343608	−	0.595146i
$787$	6.81384e6	−	1.18019e7i	0.392153	−	0.679228i	−0.600580	−	0.799564i	$-0.705064\pi$
$787$	6.81384e6	−	1.18019e7i	0.392153	−	0.679228i	0.992733	+	0.120336i	$0.0383971\pi$
$788$	11651.0	−	20180.1i	0.000668416	−	0.00115773i
$789$	1.77499e6	+	3.07438e6i	0.101509	+	0.175819i
$790$	−1.53143e7			−0.873031
$791$		0			0
$792$	4.87357e6			0.276080
$793$	−6.78320e6	−	1.17488e7i	−0.383046	−	0.663456i
$794$	−245312.	+	424893.i	−0.0138092	+	0.0239182i
$795$	3.83827e6	−	6.64808e6i	0.215386	−	0.373060i
$796$	3.35061e6	+	5.80343e6i	0.187431	+	0.324640i
$797$	−3.62853e6			−0.202341			−0.101171	−	0.994869i	$-0.532259\pi$
$797$	−3.62853e6			−0.202341			−0.101171	+	0.994869i	$0.532259\pi$
$798$		0			0
$799$	567208.			0.0314323
$800$	9.57537e6	+	1.65850e7i	0.528969	+	0.916202i
$801$	−3.07956e6	+	5.33396e6i	−0.169593	+	0.293744i
$802$	1.18561e7	−	2.05353e7i	0.650885	−	1.12737i
$803$	−1.23334e7	−	2.13620e7i	−0.674983	−	1.16910i
$804$	4.89877e6			0.267268
$805$		0			0
$806$	5.32010e6			0.288458
$807$	2.41754e6	+	4.18731e6i	0.130674	+	0.226335i
$808$	−1.40611e6	+	2.43546e6i	−0.0757691	+	0.131236i
$809$	−1.49390e7	+	2.58751e7i	−0.802509	+	1.38999i	0.115451	+	0.993313i	$0.463169\pi$
$809$	−1.49390e7	+	2.58751e7i	−0.802509	+	1.38999i	−0.917960	+	0.396673i	$0.870165\pi$
$810$	1.33646e6	+	2.31482e6i	0.0715721	+	0.123967i
$811$	1.02643e6			0.0547995			0.0273998	−	0.999625i	$-0.491277\pi$
$811$	1.02643e6			0.0547995			0.0273998	+	0.999625i	$0.491277\pi$
$812$		0			0
$813$	9.85702e6			0.523021
$814$	−921730.	−	1.59648e6i	−0.0487576	−	0.0844507i
$815$	−2.00543e7	+	3.47351e7i	−1.05758	+	1.83178i
$816$	2.37934e6	−	4.12113e6i	0.125092	−	0.216666i
$817$	1.38094e6	+	2.39187e6i	0.0723804	+	0.125367i
$818$	−2.06262e7			−1.07779
$819$		0			0
$820$	−1.01940e7			−0.529434
$821$	5.75312e6	+	9.96470e6i	0.297883	+	0.515948i	0.975651	−	0.219327i	$-0.0703861\pi$
$821$	5.75312e6	+	9.96470e6i	0.297883	+	0.515948i	−0.677768	+	0.735275i	$0.737053\pi$
$822$	−1.00906e6	+	1.74774e6i	−0.0520877	+	0.0902186i
$823$	1.25605e7	−	2.17554e7i	0.646408	−	1.11961i	−0.337566	−	0.941302i	$-0.609604\pi$
$823$	1.25605e7	−	2.17554e7i	0.646408	−	1.11961i	0.983974	−	0.178310i	$-0.0570630\pi$
$824$	−1.43197e6	−	2.48024e6i	−0.0734708	−	0.127255i
$825$	1.15225e7			0.589401
$826$		0			0
$827$	−2.14447e6			−0.109032			−0.0545162	−	0.998513i	$-0.517362\pi$
$827$	−2.14447e6			−0.109032			−0.0545162	+	0.998513i	$0.517362\pi$
$828$	−546501.	−	946568.i	−0.0277023	−	0.0479817i
$829$	409033.	−	708465.i	0.0206715	−	0.0358041i	−0.855505	−	0.517795i	$-0.826753\pi$
$829$	409033.	−	708465.i	0.0206715	−	0.0358041i	0.876176	+	0.481991i	$0.160086\pi$
$830$	−2.25469e7	+	3.90523e7i	−1.13603	+	1.96767i
$831$	−4.88370e6	−	8.45882e6i	−0.245328	−	0.424920i
$832$	−279504.			−0.0139984
$833$		0			0
$834$	−2.40231e7			−1.19595
$835$	−2.70078e7	−	4.67788e7i	−1.34052	−	2.32184i
$836$	4.81013e6	−	8.33138e6i	0.238035	−	0.412289i
$837$	4.98964e6	−	8.64232e6i	0.246182	−	0.426399i
$838$	−1.63740e7	−	2.83606e7i	−0.805460	−	1.39510i
$839$	2.11279e7			1.03622			0.518110	−	0.855314i	$-0.326636\pi$
$839$	2.11279e7			1.03622			0.518110	+	0.855314i	$0.326636\pi$
$840$		0			0
$841$	4.00785e7			1.95398
$842$	9.31533e6	+	1.61346e7i	0.452812	+	0.784294i
$843$	1.60484e6	−	2.77966e6i	0.0777790	−	0.134717i
$844$	−4.56107e6	+	7.90001e6i	−0.220400	+	0.381743i
$845$	1.14239e7	+	1.97868e7i	0.550393	+	0.953308i
$846$	−1.53431e6			−0.0737035
$847$		0			0
$848$	1.21632e7			0.580844
$849$	8.93384e6	+	1.54739e7i	0.425372	+	0.736766i
$850$	−4.25604e6	+	7.37167e6i	−0.202050	+	0.349960i
$851$	157432.	−	272679.i	0.00745191	−	0.0129071i
$852$	1.31771e6	+	2.28235e6i	0.0621902	+	0.107717i
$853$	1.89000e7			0.889386			0.444693	−	0.895683i	$-0.353313\pi$
$853$	1.89000e7			0.889386			0.444693	+	0.895683i	$0.353313\pi$
$854$		0			0
$855$	1.69796e7			0.794349
$856$	4.30446e6	+	7.45554e6i	0.200786	+	0.347772i
$857$	1.86143e7	−	3.22409e7i	0.865753	−	1.49953i	−0.000544054	−	1.00000i	$-0.500173\pi$
$857$	1.86143e7	−	3.22409e7i	0.865753	−	1.49953i	0.866297	−	0.499529i	$-0.166493\pi$
$858$	−3.66511e6	+	6.34815e6i	−0.169968	+	0.294394i
$859$	1.51032e6	+	2.61595e6i	0.0698371	+	0.120961i	0.898829	−	0.438298i	$-0.144419\pi$
$859$	1.51032e6	+	2.61595e6i	0.0698371	+	0.120961i	−0.828992	+	0.559260i	$0.811085\pi$
$860$	2.66129e6			0.122700
$861$		0			0
$862$	5.34131e7			2.44838
$863$	1.35921e7	+	2.35423e7i	0.621242	+	1.07602i	0.989255	+	0.146202i	$0.0467048\pi$
$863$	1.35921e7	+	2.35423e7i	0.621242	+	1.07602i	−0.368013	+	0.929821i	$0.619962\pi$
$864$	−1.14263e7	+	1.97909e7i	−0.520740	+	0.901949i
$865$	−9.94493e6	+	1.72251e7i	−0.451920	+	0.782748i
$866$	2.06660e7	+	3.57946e7i	0.936400	+	1.62189i
$867$	−1.29352e7			−0.584420
$868$		0			0
$869$	−9.53158e6			−0.428169
$870$	2.21873e7	+	3.84295e7i	0.993817	+	1.72134i
$871$	−3.90068e6	+	6.75618e6i	−0.174219	+	0.301756i
$872$	1.08093e7	−	1.87222e7i	0.481399	−	0.833807i
$873$	−7.30532e6	−	1.26532e7i	−0.324417	−	0.561906i
$874$	4.53766e6			0.200934
$875$		0			0
$876$	1.28385e7			0.565269
$877$	−8.69339e6	−	1.50574e7i	−0.381672	−	0.661075i	0.609629	−	0.792687i	$-0.291318\pi$
$877$	−8.69339e6	−	1.50574e7i	−0.381672	−	0.661075i	−0.991301	+	0.131611i	$0.957985\pi$
$878$	595320.	−	1.03112e6i	0.0260624	−	0.0451414i
$879$	8.27531e6	−	1.43333e7i	0.361253	−	0.625709i
$880$	1.79128e7	+	3.10258e7i	0.779751	+	1.35057i
$881$	8.14472e6			0.353538			0.176769	−	0.984252i	$-0.443435\pi$
$881$	8.14472e6			0.353538			0.176769	+	0.984252i	$0.443435\pi$
$882$		0			0
$883$	−3.10298e7			−1.33930			−0.669649	−	0.742678i	$-0.733555\pi$
$883$	−3.10298e7			−1.33930			−0.669649	+	0.742678i	$0.733555\pi$
$884$	−980435.	−	1.69816e6i	−0.0421976	−	0.0730884i
$885$	−1.19421e7	+	2.06843e7i	−0.512533	+	0.887732i
$886$	1.00629e7	−	1.74294e7i	0.430664	−	0.745931i
$887$	−7.35138e6	−	1.27330e7i	−0.313733	−	0.543401i	0.665435	−	0.746456i	$-0.268246\pi$
$887$	−7.35138e6	−	1.27330e7i	−0.313733	−	0.543401i	−0.979167	+	0.203055i	$0.934913\pi$
$888$	−730722.			−0.0310971
$889$		0			0
$890$	−2.46386e7			−1.04266
$891$	831810.	+	1.44074e6i	0.0351018	+	0.0607982i
$892$	−1.06566e7	+	1.84578e7i	−0.448443	+	0.776726i
$893$	1.15329e6	−	1.99755e6i	0.0483959	−	0.0838242i
$894$	1.26896e7	+	2.19790e7i	0.531010	+	0.919737i
$895$	1.11166e7			0.463890
$896$		0			0
$897$	−1.25200e6			−0.0519545
$898$	5.01344e6	+	8.68354e6i	0.207465	+	0.359340i
$899$	1.00225e7	−	1.73595e7i	0.413596	−	0.716370i
$900$	4.16888e6	−	7.22071e6i	0.171559	−	0.297148i
$901$	1.76479e6	+	3.05671e6i	0.0724238	+	0.125442i
$902$	−1.75215e7			−0.717060
$903$		0			0
$904$	−3.88669e6			−0.158183
$905$	1.22235e7	+	2.11716e7i	0.496104	+	0.859277i
$906$	1.28115e7	−	2.21902e7i	0.518538	−	0.898135i
$907$	−6.54701e6	+	1.13398e7i	−0.264256	+	0.457705i	−0.967368	−	0.253374i	$-0.918460\pi$
$907$	−6.54701e6	+	1.13398e7i	−0.264256	+	0.457705i	0.703112	+	0.711079i	$0.251793\pi$
$908$	−8.26675e6	−	1.43184e7i	−0.332752	−	0.576343i
$909$	4.05643e6			0.162830
$910$		0			0
$911$	2.68695e7			1.07266			0.536332	−	0.844007i	$-0.319809\pi$
$911$	2.68695e7			1.07266			0.536332	+	0.844007i	$0.319809\pi$
$912$	−9.67566e6	−	1.67587e7i	−0.385206	−	0.667197i
$913$	−1.40331e7	+	2.43061e7i	−0.557156	+	0.965023i
$914$	−5.51490e6	+	9.55209e6i	−0.218360	+	0.378210i
$915$	−1.87179e7	−	3.24203e7i	−0.739101	−	1.28016i
$916$	−9.48103e6			−0.373351
$917$		0			0
$918$	−1.01575e7			−0.397813
$919$	−636586.	−	1.10260e6i	−0.0248638	−	0.0430654i	0.853326	−	0.521378i	$-0.174582\pi$
$919$	−636586.	−	1.10260e6i	−0.0248638	−	0.0430654i	−0.878190	+	0.478313i	$0.841249\pi$
$920$	−1.66496e6	+	2.88379e6i	−0.0648535	+	0.112330i
$921$	−2.35397e6	+	4.07720e6i	−0.0914435	+	0.158385i
$922$	−1.57714e7	−	2.73168e7i	−0.611001	−	1.05828i
$923$	−4.19695e6			−0.162155
$924$		0			0
$925$	2.40187e6			0.0922986
$926$	−1.74329e7	−	3.01947e7i	−0.668102	−	1.15719i
$927$	−2.06551e6	+	3.57756e6i	−0.0789454	+	0.136737i
$928$	−2.29516e7	+	3.97533e7i	−0.874867	+	1.51531i
$929$	−4.65852e6	−	8.06880e6i	−0.177096	−	0.306740i	0.763789	−	0.645467i	$-0.223337\pi$
$929$	−4.65852e6	−	8.06880e6i	−0.177096	−	0.306740i	−0.940885	+	0.338727i	$0.890004\pi$
$930$	1.46805e7			0.556589
$931$		0			0
$932$	−1.89428e7			−0.714338
$933$	−1.22907e7	−	2.12881e7i	−0.462245	−	0.800631i
$934$	1.80288e7	−	3.12268e7i	0.676239	−	1.17128i
$935$	−5.19801e6	+	9.00322e6i	−0.194450	+	0.336797i
$936$	−2.01978e6	−	3.49837e6i	−0.0753555	−	0.130520i
$937$	−1.18158e7			−0.439657			−0.219829	−	0.975539i	$-0.570550\pi$
$937$	−1.18158e7			−0.439657			−0.219829	+	0.975539i	$0.570550\pi$
$938$		0			0
$939$	−2.44097e7			−0.903439
$940$	−1.11128e6	−	1.92479e6i	−0.0410208	−	0.0710501i
$941$	−1.26765e7	+	2.19563e7i	−0.466685	+	0.808323i	−0.999276	−	0.0380504i	$-0.987885\pi$
$941$	−1.26765e7	+	2.19563e7i	−0.466685	+	0.808323i	0.532591	+	0.846373i	$0.321219\pi$
$942$	1.63863e7	−	2.83819e7i	0.601663	−	1.04211i
$943$	−1.49634e6	−	2.59173e6i	−0.0547962	−	0.0949098i
$944$	−3.78436e7			−1.38217
$945$		0			0
$946$	4.57422e6			0.166184
$947$	−1.32471e7	−	2.29446e7i	−0.480004	−	0.831391i	0.519733	−	0.854329i	$-0.326031\pi$
$947$	−1.32471e7	−	2.29446e7i	−0.480004	−	0.831391i	−0.999737	+	0.0229375i	$0.992698\pi$
$948$	2.48050e6	−	4.29635e6i	0.0896434	−	0.155267i
$949$	−1.02228e7	+	1.77063e7i	−0.368471	+	0.638210i
$950$	1.73073e7	+	2.99772e7i	0.622187	+	1.07766i
$951$	1.89164e7			0.678246
$952$		0			0
$953$	−1.88335e7			−0.671735			−0.335868	−	0.941909i	$-0.609030\pi$
$953$	−1.88335e7			−0.671735			−0.335868	+	0.941909i	$0.609030\pi$
$954$	−4.77380e6	−	8.26846e6i	−0.169822	−	0.294140i
$955$	−9.08015e6	+	1.57273e7i	−0.322170	+	0.558014i
$956$	1.39373e7	−	2.41401e7i	0.493211	−	0.854267i
$957$	1.38093e7	+	2.39184e7i	0.487408	+	0.844215i
$958$	5.87929e7			2.06972
$959$		0			0
$960$	−771276.			−0.0270105
$961$	1.09988e7	+	1.90505e7i	0.384182	+	0.665423i
$962$	−763995.	+	1.32328e6i	−0.0266166	+	0.0461013i
$963$	6.20886e6	−	1.07541e7i	0.215748	−	0.373686i
$964$	−9.15159e6	−	1.58510e7i	−0.317179	−	0.549370i
$965$	−5.36740e7			−1.85544
$966$		0			0
$967$	−3.14956e7			−1.08314			−0.541569	−	0.840656i	$-0.682169\pi$
$967$	−3.14956e7			−1.08314			−0.541569	+	0.840656i	$0.682169\pi$
$968$	−1.82328e6	−	3.15801e6i	−0.0625409	−	0.108324i
$969$	2.80773e6	−	4.86312e6i	0.0960606	−	0.166382i
$970$	2.92238e7	−	5.06171e7i	0.997257	−	1.72730i
$971$	−3.42834e6	−	5.93806e6i	−0.116691	−	0.202114i	0.801764	−	0.597641i	$-0.203895\pi$
$971$	−3.42834e6	−	5.93806e6i	−0.116691	−	0.202114i	−0.918454	+	0.395527i	$0.870562\pi$
$972$	1.62401e7			0.551343
$973$		0			0
$974$	6.11527e7			2.06547
$975$	−4.77532e6	−	8.27110e6i	−0.160876	−	0.278645i
$976$	2.96579e7	−	5.13689e7i	0.996587	−	1.72614i
$977$	−1.40735e7	+	2.43761e7i	−0.471701	+	0.817010i	−0.999476	−	0.0323741i	$-0.989693\pi$
$977$	−1.40735e7	+	2.43761e7i	−0.471701	+	0.817010i	0.527775	+	0.849384i	$0.323027\pi$
$978$	−1.79406e7	−	3.10740e7i	−0.599777	−	1.03884i
$979$	−1.53350e7			−0.511361
$980$		0			0
$981$	−3.11831e7			−1.03454
$982$	−336571.	−	582958.i	−0.0111378	−	0.0192912i
$983$	1.17458e7	−	2.03443e7i	0.387703	−	0.671521i	−0.604437	−	0.796653i	$-0.706602\pi$
$983$	1.17458e7	−	2.03443e7i	0.387703	−	0.671521i	0.992140	+	0.125132i	$0.0399354\pi$
$984$	−3.47264e6	+	6.01480e6i	−0.114333	+	0.198031i
$985$	51199.7	+	88680.5i	0.00168142	+	0.00291231i
$986$	−2.04029e7			−0.668343
$987$		0			0
$988$	−7.97395e6			−0.259885
$989$	390639.	+	676607.i	0.0126995	+	0.0219961i
$990$	1.40607e7	−	2.43539e7i	0.455953	−	0.789734i
$991$	1.07206e6	−	1.85686e6i	0.0346765	−	0.0600615i	−0.848166	−	0.529730i	$-0.822293\pi$
$991$	1.07206e6	−	1.85686e6i	0.0346765	−	0.0600615i	0.882843	+	0.469669i	$0.155627\pi$
$992$	7.59311e6	+	1.31517e7i	0.244986	+	0.424327i
$993$	−1.09206e7			−0.351459
$994$		0			0
$995$	−2.94483e7			−0.942979
$996$	−7.30395e6	−	1.26508e7i	−0.233297	−	0.404082i
$997$	1.25436e7	−	2.17261e7i	0.399654	−	0.692220i	−0.594029	−	0.804443i	$-0.702464\pi$
$997$	1.25436e7	−	2.17261e7i	0.399654	−	0.692220i	0.993683	+	0.112223i	$0.0357971\pi$
$998$	−7.58576e6	+	1.31389e7i	−0.241086	+	0.417574i
$999$	1.43308e6	+	2.48216e6i	0.0454314	+	0.0786895i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.6.c.f.18.1		4
7.2	even	3	inner	49.6.c.f.30.1		4
7.3	odd	6		49.6.a.d.1.2		2
7.4	even	3		49.6.a.e.1.2		2
7.5	odd	6		7.6.c.a.2.1	✓	4
7.6	odd	2		7.6.c.a.4.1	yes	4
21.5	even	6		63.6.e.d.37.2		4
21.11	odd	6		441.6.a.m.1.1		2
21.17	even	6		441.6.a.n.1.1		2
21.20	even	2		63.6.e.d.46.2		4
28.3	even	6		784.6.a.ba.1.2		2
28.11	odd	6		784.6.a.t.1.1		2
28.19	even	6		112.6.i.c.65.1		4
28.27	even	2		112.6.i.c.81.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.6.c.a.2.1	✓	4	7.5	odd	6
7.6.c.a.4.1	yes	4	7.6	odd	2
49.6.a.d.1.2		2	7.3	odd	6
49.6.a.e.1.2		2	7.4	even	3
49.6.c.f.18.1		4	1.1	even	1	trivial
49.6.c.f.30.1		4	7.2	even	3	inner
63.6.e.d.37.2		4	21.5	even	6
63.6.e.d.46.2		4	21.20	even	2
112.6.i.c.65.1		4	28.19	even	6
112.6.i.c.81.1		4	28.27	even	2
441.6.a.m.1.1		2	21.11	odd	6
441.6.a.n.1.1		2	21.17	even	6
784.6.a.t.1.1		2	28.11	odd	6
784.6.a.ba.1.2		2	28.3	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-3.54138 - 6.13385i) q^{2} +(-5.04138 + 8.73193i) q^{3} +(-9.08276 + 15.7318i) q^{4} +(-39.9138 - 69.1328i) q^{5} +71.4138 q^{6} -97.9863 q^{8} +(70.6689 + 122.402i) q^{9} +O(q^{10})\)	\(q+(-3.54138 - 6.13385i) q^{2} +(-5.04138 + 8.73193i) q^{3} +(-9.08276 + 15.7318i) q^{4} +(-39.9138 - 69.1328i) q^{5} +71.4138 q^{6} -97.9863 q^{8} +(70.6689 + 122.402i) q^{9} +(-282.700 + 489.651i) q^{10} +(-175.952 + 304.757i) q^{11} +(-91.5793 - 158.620i) q^{12} +291.683 q^{13} +804.883 q^{15} +(637.655 + 1104.45i) q^{16} +(-185.038 + 320.495i) q^{17} +(500.531 - 866.946i) q^{18} +(752.463 + 1303.30i) q^{19} +1450.11 q^{20} +2492.45 q^{22} +(212.855 + 368.676i) q^{23} +(493.986 - 855.609i) q^{24} +(-1623.72 + 2812.37i) q^{25} +(-1032.96 - 1789.14i) q^{26} -3875.19 q^{27} -7783.93 q^{29} +(-2850.40 - 4937.03i) q^{30} +(-1287.59 + 2230.17i) q^{31} +(2948.58 - 5107.09i) q^{32} +(-1774.08 - 3072.80i) q^{33} +2621.16 q^{34} -2567.48 q^{36} +(-369.809 - 640.528i) q^{37} +(5329.51 - 9230.99i) q^{38} +(-1470.48 + 2546.95i) q^{39} +(3911.01 + 6774.06i) q^{40} -7029.84 q^{41} +1835.23 q^{43} +(-3196.26 - 5536.08i) q^{44} +(5641.33 - 9771.08i) q^{45} +(1507.60 - 2611.25i) q^{46} +(-766.342 - 1327.34i) q^{47} -12858.7 q^{48} +23000.9 q^{50} +(-1865.69 - 3231.47i) q^{51} +(-2649.28 + 4588.69i) q^{52} +(4768.73 - 8259.68i) q^{53} +(13723.5 + 23769.8i) q^{54} +28091.6 q^{55} -15173.8 q^{57} +(27565.9 + 47745.5i) q^{58} +(-14837.0 + 25698.5i) q^{59} +(-7310.56 + 12662.3i) q^{60} +(-23255.4 - 40279.5i) q^{61} +18239.4 q^{62} -958.246 q^{64} +(-11642.2 - 20164.8i) q^{65} +(-12565.4 + 21763.9i) q^{66} +(-13373.0 + 23162.8i) q^{67} +(-3361.31 - 5821.95i) q^{68} -4292.34 q^{69} -14388.8 q^{71} +(-6924.59 - 11993.7i) q^{72} +(-35047.6 + 60704.2i) q^{73} +(-2619.27 + 4536.71i) q^{74} +(-16371.6 - 28356.5i) q^{75} -27337.8 q^{76} +20830.2 q^{78} +(13542.9 + 23457.0i) q^{79} +(50902.5 - 88165.7i) q^{80} +(2363.74 - 4094.13i) q^{81} +(24895.3 + 43120.0i) q^{82} +79755.4 q^{83} +29542.2 q^{85} +(-6499.26 - 11257.0i) q^{86} +(39241.8 - 67968.8i) q^{87} +(17240.9 - 29862.1i) q^{88} +(21788.7 + 37739.1i) q^{89} -79912.5 q^{90} -7733.26 q^{92} +(-12982.4 - 22486.2i) q^{93} +(-5427.82 + 9401.25i) q^{94} +(60067.3 - 104040. i) q^{95} +(29729.8 + 51493.6i) q^{96} -103374. q^{97} -49737.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 8 q^{3} - 12 q^{4} - 38 q^{5} + 164 q^{6} + 192 q^{8} + 380 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 8 * q^3 - 12 * q^4 - 38 * q^5 + 164 * q^6 + 192 * q^8 + 380 * q^9	\( 4 q - 2 q^{2} - 8 q^{3} - 12 q^{4} - 38 q^{5} + 164 q^{6} + 192 q^{8} + 380 q^{9} - 778 q^{10} - 424 q^{11} - 196 q^{12} + 1848 q^{13} + 1784 q^{15} + 2064 q^{16} - 2346 q^{17} - 212 q^{18} - 360 q^{19} + 3416 q^{20} + 4252 q^{22} + 12 q^{23} + 1392 q^{24} - 1872 q^{25} + 1148 q^{26} - 5744 q^{27} - 14104 q^{29} - 5258 q^{30} + 3548 q^{31} + 8096 q^{32} - 3398 q^{33} - 14844 q^{34} - 2192 q^{36} - 11090 q^{37} + 20138 q^{38} - 1624 q^{39} + 15936 q^{40} - 7000 q^{41} - 25360 q^{43} - 5948 q^{44} + 1300 q^{45} + 5118 q^{46} - 22956 q^{47} - 22432 q^{48} + 59984 q^{50} + 384 q^{51} - 1400 q^{52} - 3042 q^{53} + 32546 q^{54} + 50152 q^{55} - 38116 q^{57} + 58852 q^{58} - 65808 q^{59} - 14084 q^{60} - 42486 q^{61} + 98724 q^{62} + 70912 q^{64} + 3164 q^{65} - 25894 q^{66} - 42312 q^{67} + 5460 q^{68} - 10308 q^{69} - 4416 q^{71} + 32448 q^{72} - 50506 q^{73} + 47370 q^{74} - 35608 q^{75} - 77672 q^{76} + 55048 q^{78} - 9004 q^{79} + 68816 q^{80} - 51178 q^{81} + 67732 q^{82} + 208656 q^{83} - 106212 q^{85} - 86776 q^{86} + 80008 q^{87} + 20496 q^{88} - 26666 q^{89} - 261304 q^{90} - 20568 q^{92} - 38718 q^{93} + 98034 q^{94} + 198140 q^{95} + 54880 q^{96} - 418264 q^{97} - 133888 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 8 * q^3 - 12 * q^4 - 38 * q^5 + 164 * q^6 + 192 * q^8 + 380 * q^9 - 778 * q^10 - 424 * q^11 - 196 * q^12 + 1848 * q^13 + 1784 * q^15 + 2064 * q^16 - 2346 * q^17 - 212 * q^18 - 360 * q^19 + 3416 * q^20 + 4252 * q^22 + 12 * q^23 + 1392 * q^24 - 1872 * q^25 + 1148 * q^26 - 5744 * q^27 - 14104 * q^29 - 5258 * q^30 + 3548 * q^31 + 8096 * q^32 - 3398 * q^33 - 14844 * q^34 - 2192 * q^36 - 11090 * q^37 + 20138 * q^38 - 1624 * q^39 + 15936 * q^40 - 7000 * q^41 - 25360 * q^43 - 5948 * q^44 + 1300 * q^45 + 5118 * q^46 - 22956 * q^47 - 22432 * q^48 + 59984 * q^50 + 384 * q^51 - 1400 * q^52 - 3042 * q^53 + 32546 * q^54 + 50152 * q^55 - 38116 * q^57 + 58852 * q^58 - 65808 * q^59 - 14084 * q^60 - 42486 * q^61 + 98724 * q^62 + 70912 * q^64 + 3164 * q^65 - 25894 * q^66 - 42312 * q^67 + 5460 * q^68 - 10308 * q^69 - 4416 * q^71 + 32448 * q^72 - 50506 * q^73 + 47370 * q^74 - 35608 * q^75 - 77672 * q^76 + 55048 * q^78 - 9004 * q^79 + 68816 * q^80 - 51178 * q^81 + 67732 * q^82 + 208656 * q^83 - 106212 * q^85 - 86776 * q^86 + 80008 * q^87 + 20496 * q^88 - 26666 * q^89 - 261304 * q^90 - 20568 * q^92 - 38718 * q^93 + 98034 * q^94 + 198140 * q^95 + 54880 * q^96 - 418264 * q^97 - 133888 * q^99

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