LMFDB - Embedded newform 983.6.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,6,Mod(1,983)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

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

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

chi := DirichletCharacter("983.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	983.a (trivial)

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:	yes
Analytic conductor:	$157.657294876$
Analytic rank:	$0$
Dimension:	$218$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.0849 q^{2} +8.47019 q^{3} +69.7046 q^{4} +6.04415 q^{5} -85.4208 q^{6} -170.780 q^{7} -380.247 q^{8} -171.256 q^{9} +O(q^{10})$	\(q-10.0849 q^{2} +8.47019 q^{3} +69.7046 q^{4} +6.04415 q^{5} -85.4208 q^{6} -170.780 q^{7} -380.247 q^{8} -171.256 q^{9} -60.9545 q^{10} -338.471 q^{11} +590.412 q^{12} -278.750 q^{13} +1722.29 q^{14} +51.1951 q^{15} +1604.19 q^{16} -1679.76 q^{17} +1727.09 q^{18} +2484.22 q^{19} +421.305 q^{20} -1446.54 q^{21} +3413.43 q^{22} +3660.67 q^{23} -3220.76 q^{24} -3088.47 q^{25} +2811.16 q^{26} -3508.83 q^{27} -11904.2 q^{28} +1810.08 q^{29} -516.296 q^{30} -2192.98 q^{31} -4010.15 q^{32} -2866.91 q^{33} +16940.2 q^{34} -1032.22 q^{35} -11937.3 q^{36} -8634.20 q^{37} -25053.0 q^{38} -2361.06 q^{39} -2298.27 q^{40} -16151.0 q^{41} +14588.2 q^{42} -7958.34 q^{43} -23593.0 q^{44} -1035.10 q^{45} -36917.4 q^{46} -400.062 q^{47} +13587.8 q^{48} +12358.8 q^{49} +31146.8 q^{50} -14227.9 q^{51} -19430.2 q^{52} -22212.3 q^{53} +35386.1 q^{54} -2045.77 q^{55} +64938.5 q^{56} +21041.8 q^{57} -18254.4 q^{58} -46812.0 q^{59} +3568.54 q^{60} -26447.5 q^{61} +22116.0 q^{62} +29247.1 q^{63} -10892.2 q^{64} -1684.81 q^{65} +28912.4 q^{66} +43887.6 q^{67} -117087. q^{68} +31006.6 q^{69} +10409.8 q^{70} -55571.6 q^{71} +65119.4 q^{72} -52566.9 q^{73} +87074.8 q^{74} -26159.9 q^{75} +173162. q^{76} +57804.0 q^{77} +23811.0 q^{78} -19184.9 q^{79} +9695.96 q^{80} +11894.7 q^{81} +162880. q^{82} +40850.4 q^{83} -100830. q^{84} -10152.7 q^{85} +80258.9 q^{86} +15331.7 q^{87} +128702. q^{88} -48462.0 q^{89} +10438.8 q^{90} +47604.9 q^{91} +255166. q^{92} -18575.0 q^{93} +4034.57 q^{94} +15015.0 q^{95} -33966.8 q^{96} +18800.4 q^{97} -124637. q^{98} +57965.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9}+O(q^{10}) $ 218 * q + 35 * q^2 + 70 * q^3 + 3685 * q^4 + 253 * q^5 + 529 * q^6 + 1567 * q^7 + 1695 * q^8 + 19812 * q^9	\( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9} + 2133 q^{10} + 1752 q^{11} + 3512 q^{12} + 5990 q^{13} + 2319 q^{14} + 4639 q^{15} + 66105 q^{16} + 10656 q^{17} + 11911 q^{18} + 11511 q^{19} + 10012 q^{20} + 12225 q^{21} + 19401 q^{22} + 9767 q^{23} + 21725 q^{24} + 185207 q^{25} + 7708 q^{26} + 23764 q^{27} + 77808 q^{28} + 25772 q^{29} + 15736 q^{30} + 35900 q^{31} + 60155 q^{32} + 70026 q^{33} + 17236 q^{34} + 28782 q^{35} + 382874 q^{36} + 126082 q^{37} + 62164 q^{38} + 54264 q^{39} + 102846 q^{40} + 70480 q^{41} + 102244 q^{42} + 137413 q^{43} + 116278 q^{44} + 93481 q^{45} + 126122 q^{46} + 63218 q^{47} + 124701 q^{48} + 732031 q^{49} + 131089 q^{50} + 109902 q^{51} + 229519 q^{52} + 102608 q^{53} + 149130 q^{54} + 167596 q^{55} + 87868 q^{56} + 408318 q^{57} + 304579 q^{58} + 67460 q^{59} + 150523 q^{60} + 195132 q^{61} + 132294 q^{62} + 374425 q^{63} + 1296639 q^{64} + 347092 q^{65} + 147397 q^{66} + 381238 q^{67} + 296321 q^{68} + 139362 q^{69} + 325675 q^{70} + 147818 q^{71} + 646059 q^{72} + 961992 q^{73} + 167410 q^{74} + 167324 q^{75} + 504875 q^{76} + 284328 q^{77} + 284295 q^{78} + 285792 q^{79} + 444932 q^{80} + 1980282 q^{81} + 336676 q^{82} + 276734 q^{83} + 378474 q^{84} + 1021245 q^{85} + 156051 q^{86} + 500457 q^{87} + 1068101 q^{88} + 398983 q^{89} + 463961 q^{90} + 273517 q^{91} + 577884 q^{92} + 967833 q^{93} + 224775 q^{94} + 482817 q^{95} + 780445 q^{96} + 1636277 q^{97} + 495958 q^{98} + 627643 q^{99}+O(q^{100}) \) 218 * q + 35 * q^2 + 70 * q^3 + 3685 * q^4 + 253 * q^5 + 529 * q^6 + 1567 * q^7 + 1695 * q^8 + 19812 * q^9 + 2133 * q^10 + 1752 * q^11 + 3512 * q^12 + 5990 * q^13 + 2319 * q^14 + 4639 * q^15 + 66105 * q^16 + 10656 * q^17 + 11911 * q^18 + 11511 * q^19 + 10012 * q^20 + 12225 * q^21 + 19401 * q^22 + 9767 * q^23 + 21725 * q^24 + 185207 * q^25 + 7708 * q^26 + 23764 * q^27 + 77808 * q^28 + 25772 * q^29 + 15736 * q^30 + 35900 * q^31 + 60155 * q^32 + 70026 * q^33 + 17236 * q^34 + 28782 * q^35 + 382874 * q^36 + 126082 * q^37 + 62164 * q^38 + 54264 * q^39 + 102846 * q^40 + 70480 * q^41 + 102244 * q^42 + 137413 * q^43 + 116278 * q^44 + 93481 * q^45 + 126122 * q^46 + 63218 * q^47 + 124701 * q^48 + 732031 * q^49 + 131089 * q^50 + 109902 * q^51 + 229519 * q^52 + 102608 * q^53 + 149130 * q^54 + 167596 * q^55 + 87868 * q^56 + 408318 * q^57 + 304579 * q^58 + 67460 * q^59 + 150523 * q^60 + 195132 * q^61 + 132294 * q^62 + 374425 * q^63 + 1296639 * q^64 + 347092 * q^65 + 147397 * q^66 + 381238 * q^67 + 296321 * q^68 + 139362 * q^69 + 325675 * q^70 + 147818 * q^71 + 646059 * q^72 + 961992 * q^73 + 167410 * q^74 + 167324 * q^75 + 504875 * q^76 + 284328 * q^77 + 284295 * q^78 + 285792 * q^79 + 444932 * q^80 + 1980282 * q^81 + 336676 * q^82 + 276734 * q^83 + 378474 * q^84 + 1021245 * q^85 + 156051 * q^86 + 500457 * q^87 + 1068101 * q^88 + 398983 * q^89 + 463961 * q^90 + 273517 * q^91 + 577884 * q^92 + 967833 * q^93 + 224775 * q^94 + 482817 * q^95 + 780445 * q^96 + 1636277 * q^97 + 495958 * q^98 + 627643 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−10.0849	−1.78277	−0.891385	−	0.453247i	$-0.850266\pi$
$2$	−10.0849	−1.78277	−0.891385	+	0.453247i	$0.850266\pi$
$3$	8.47019	0.543363	0.271682	−	0.962387i	$-0.412420\pi$
$3$	8.47019	0.543363	0.271682	+	0.962387i	$0.412420\pi$
$4$	69.7046	2.17827
$5$	6.04415	0.108121	0.0540605	−	0.998538i	$-0.482784\pi$
$5$	6.04415	0.108121	0.0540605	+	0.998538i	$0.482784\pi$
$6$	−85.4208	−0.968692
$7$	−170.780	−1.31732	−0.658661	−	0.752440i	$-0.728877\pi$
$7$	−170.780	−1.31732	−0.658661	+	0.752440i	$0.728877\pi$
$8$	−380.247	−2.10059
$9$	−171.256	−0.704756
$10$	−60.9545	−0.192755
$11$	−338.471	−0.843411	−0.421705	−	0.906733i	$-0.638568\pi$
$11$	−338.471	−0.843411	−0.421705	+	0.906733i	$0.638568\pi$
$12$	590.412	1.18359
$13$	−278.750	−0.457463	−0.228732	−	0.973490i	$-0.573458\pi$
$13$	−278.750	−0.457463	−0.228732	+	0.973490i	$0.573458\pi$
$14$	1722.29	2.34848
$15$	51.1951	0.0587490
$16$	1604.19	1.56659
$17$	−1679.76	−1.40970	−0.704849	−	0.709357i	$-0.748985\pi$
$17$	−1679.76	−1.40970	−0.704849	+	0.709357i	$0.748985\pi$
$18$	1727.09	1.25642
$19$	2484.22	1.57872	0.789361	−	0.613929i	$-0.210412\pi$
$19$	2484.22	1.57872	0.789361	+	0.613929i	$0.210412\pi$
$20$	421.305	0.235517
$21$	−1446.54	−0.715784
$22$	3413.43	1.50361
$23$	3660.67	1.44292	0.721459	−	0.692457i	$-0.243472\pi$
$23$	3660.67	1.44292	0.721459	+	0.692457i	$0.243472\pi$
$24$	−3220.76	−1.14138
$25$	−3088.47	−0.988310
$26$	2811.16	0.815552
$27$	−3508.83	−0.926302
$28$	−11904.2	−2.86948
$29$	1810.08	0.399671	0.199836	−	0.979829i	$-0.435959\pi$
$29$	1810.08	0.399671	0.199836	+	0.979829i	$0.435959\pi$
$30$	−516.296	−0.104736
$31$	−2192.98	−0.409856	−0.204928	−	0.978777i	$-0.565696\pi$
$31$	−2192.98	−0.409856	−0.204928	+	0.978777i	$0.565696\pi$
$32$	−4010.15	−0.692286
$33$	−2866.91	−0.458278
$34$	16940.2	2.51317
$35$	−1032.22	−0.142430
$36$	−11937.3	−1.53515
$37$	−8634.20	−1.03685	−0.518427	−	0.855122i	$-0.673482\pi$
$37$	−8634.20	−1.03685	−0.518427	+	0.855122i	$0.673482\pi$
$38$	−25053.0	−2.81450
$39$	−2361.06	−0.248569
$40$	−2298.27	−0.227117
$41$	−16151.0	−1.50051	−0.750255	−	0.661149i	$-0.770069\pi$
$41$	−16151.0	−1.50051	−0.750255	+	0.661149i	$0.770069\pi$
$42$	14588.2	1.27608
$43$	−7958.34	−0.656374	−0.328187	−	0.944613i	$-0.606438\pi$
$43$	−7958.34	−0.656374	−0.328187	+	0.944613i	$0.606438\pi$
$44$	−23593.0	−1.83718
$45$	−1035.10	−0.0761990
$46$	−36917.4	−2.57239
$47$	−400.062	−0.0264170	−0.0132085	−	0.999913i	$-0.504205\pi$
$47$	−400.062	−0.0264170	−0.0132085	+	0.999913i	$0.504205\pi$
$48$	13587.8	0.851228
$49$	12358.8	0.735335
$50$	31146.8	1.76193
$51$	−14227.9	−0.765978
$52$	−19430.2	−0.996478
$53$	−22212.3	−1.08619	−0.543093	−	0.839673i	$-0.682747\pi$
$53$	−22212.3	−1.08619	−0.543093	+	0.839673i	$0.682747\pi$
$54$	35386.1	1.65138
$55$	−2045.77	−0.0911904
$56$	64938.5	2.76715
$57$	21041.8	0.857820
$58$	−18254.4	−0.712522
$59$	−46812.0	−1.75076	−0.875380	−	0.483435i	$-0.839389\pi$
$59$	−46812.0	−1.75076	−0.875380	+	0.483435i	$0.839389\pi$
$60$	3568.54	0.127971
$61$	−26447.5	−0.910038	−0.455019	−	0.890482i	$-0.650367\pi$
$61$	−26447.5	−0.910038	−0.455019	+	0.890482i	$0.650367\pi$
$62$	22116.0	0.730679
$63$	29247.1	0.928391
$64$	−10892.2	−0.332403
$65$	−1684.81	−0.0494614
$66$	28912.4	0.817005
$67$	43887.6	1.19441	0.597207	−	0.802087i	$-0.296277\pi$
$67$	43887.6	1.19441	0.597207	+	0.802087i	$0.296277\pi$
$68$	−117087.	−3.07070
$69$	31006.6	0.784028
$70$	10409.8	0.253920
$71$	−55571.6	−1.30830	−0.654150	−	0.756365i	$-0.726973\pi$
$71$	−55571.6	−1.30830	−0.654150	+	0.756365i	$0.726973\pi$
$72$	65119.4	1.48040
$73$	−52566.9	−1.15453	−0.577265	−	0.816557i	$-0.695880\pi$
$73$	−52566.9	−1.15453	−0.577265	+	0.816557i	$0.695880\pi$
$74$	87074.8	1.84847
$75$	−26159.9	−0.537011
$76$	173162.	3.43888
$77$	57804.0	1.11104
$78$	23811.0	0.443141
$79$	−19184.9	−0.345853	−0.172927	−	0.984935i	$-0.555322\pi$
$79$	−19184.9	−0.345853	−0.172927	+	0.984935i	$0.555322\pi$
$80$	9695.96	0.169381
$81$	11894.7	0.201438
$82$	162880.	2.67506
$83$	40850.4	0.650881	0.325440	−	0.945563i	$-0.394487\pi$
$83$	40850.4	0.650881	0.325440	+	0.945563i	$0.394487\pi$
$84$	−100830.	−1.55917
$85$	−10152.7	−0.152418
$86$	80258.9	1.17016
$87$	15331.7	0.217167
$88$	128702.	1.77166
$89$	−48462.0	−0.648525	−0.324262	−	0.945967i	$-0.605116\pi$
$89$	−48462.0	−0.648525	−0.324262	+	0.945967i	$0.605116\pi$
$90$	10438.8	0.135845
$91$	47604.9	0.602626
$92$	255166.	3.14306
$93$	−18575.0	−0.222701
$94$	4034.57	0.0470954
$95$	15015.0	0.170693
$96$	−33966.8	−0.376163
$97$	18800.4	0.202879	0.101439	−	0.994842i	$-0.467655\pi$
$97$	18800.4	0.202879	0.101439	+	0.994842i	$0.467655\pi$
$98$	−124637.	−1.31093
$99$	57965.0	0.594399
$100$	−215281.	−2.15281
$101$	169324.	1.65164	0.825819	−	0.563935i	$-0.190713\pi$
$101$	169324.	1.65164	0.825819	+	0.563935i	$0.190713\pi$
$102$	143487.	1.36556
$103$	−54321.3	−0.504519	−0.252259	−	0.967660i	$-0.581174\pi$
$103$	−54321.3	−0.504519	−0.252259	+	0.967660i	$0.581174\pi$
$104$	105994.	0.960940
$105$	−8743.10	−0.0773913
$106$	224008.	1.93642
$107$	−150477.	−1.27061	−0.635304	−	0.772262i	$-0.719125\pi$
$107$	−150477.	−1.27061	−0.635304	+	0.772262i	$0.719125\pi$
$108$	−244582.	−2.01774
$109$	−122598.	−0.988362	−0.494181	−	0.869359i	$-0.664532\pi$
$109$	−122598.	−0.988362	−0.494181	+	0.869359i	$0.664532\pi$
$110$	20631.3	0.162572
$111$	−73133.3	−0.563388
$112$	−273963.	−2.06370
$113$	−139068.	−1.02455	−0.512273	−	0.858823i	$-0.671196\pi$
$113$	−139068.	−1.02455	−0.512273	+	0.858823i	$0.671196\pi$
$114$	−212204.	−1.52930
$115$	22125.7	0.156010
$116$	126171.	0.870592
$117$	47737.5	0.322400
$118$	472093.	3.12120
$119$	286870.	1.85703
$120$	−19466.8	−0.123407
$121$	−46488.7	−0.288658
$122$	266719.	1.62239
$123$	−136802.	−0.815322
$124$	−152861.	−0.892777
$125$	−37555.1	−0.214978
$126$	−294953.	−1.65511
$127$	248658.	1.36802	0.684012	−	0.729471i	$-0.260234\pi$
$127$	248658.	1.36802	0.684012	+	0.729471i	$0.260234\pi$
$128$	238171.	1.28488
$129$	−67408.7	−0.356650
$130$	16991.0	0.0881783
$131$	−322443.	−1.64163	−0.820813	−	0.571197i	$-0.806479\pi$
$131$	−322443.	−1.64163	−0.820813	+	0.571197i	$0.806479\pi$
$132$	−199837.	−0.998254
$133$	−424255.	−2.07968
$134$	−442601.	−2.12937
$135$	−21207.9	−0.100153
$136$	638725.	2.96119
$137$	206882.	0.941720	0.470860	−	0.882208i	$-0.343944\pi$
$137$	206882.	0.941720	0.470860	+	0.882208i	$0.343944\pi$
$138$	−312698.	−1.39774
$139$	376729.	1.65383	0.826917	−	0.562324i	$-0.190093\pi$
$139$	376729.	1.65383	0.826917	+	0.562324i	$0.190093\pi$
$140$	−71950.5	−0.310251
$141$	−3388.60	−0.0143540
$142$	560433.	2.33240
$143$	94348.6	0.385829
$144$	−274727.	−1.10406
$145$	10940.4	0.0432129
$146$	530130.	2.05826
$147$	104681.	0.399554
$148$	−601844.	−2.25855
$149$	−418035.	−1.54258	−0.771289	−	0.636486i	$-0.780387\pi$
$149$	−418035.	−1.54258	−0.771289	+	0.636486i	$0.780387\pi$
$150$	263819.	0.957368
$151$	−364656.	−1.30149	−0.650745	−	0.759296i	$-0.725543\pi$
$151$	−364656.	−1.30149	−0.650745	+	0.759296i	$0.725543\pi$
$152$	−944615.	−3.31624
$153$	287669.	0.993494
$154$	−582946.	−1.98073
$155$	−13254.7	−0.0443141
$156$	−164577.	−0.541450
$157$	−337613.	−1.09313	−0.546563	−	0.837418i	$-0.684064\pi$
$157$	−337613.	−1.09313	−0.546563	+	0.837418i	$0.684064\pi$
$158$	193477.	0.616576
$159$	−188143.	−0.590193
$160$	−24238.0	−0.0748507
$161$	−625170.	−1.90079
$162$	−119957.	−0.359118
$163$	507461.	1.49601	0.748004	−	0.663695i	$-0.231013\pi$
$163$	507461.	1.49601	0.748004	+	0.663695i	$0.231013\pi$
$164$	−1.12580e6	−3.26852
$165$	−17328.0	−0.0495495
$166$	−411971.	−1.16037
$167$	115943.	0.321703	0.160851	−	0.986979i	$-0.448576\pi$
$167$	115943.	0.321703	0.160851	+	0.986979i	$0.448576\pi$
$168$	550041.	1.50356
$169$	−293592.	−0.790727
$170$	102389.	0.271726
$171$	−425437.	−1.11261
$172$	−554733.	−1.42976
$173$	−390176.	−0.991162	−0.495581	−	0.868562i	$-0.665045\pi$
$173$	−390176.	−0.991162	−0.495581	+	0.868562i	$0.665045\pi$
$174$	−154619.	−0.387158
$175$	527448.	1.30192
$176$	−542971.	−1.32128
$177$	−396506.	−0.951299
$178$	488733.	1.15617
$179$	303489.	0.707963	0.353981	−	0.935253i	$-0.384828\pi$
$179$	303489.	0.707963	0.353981	+	0.935253i	$0.384828\pi$
$180$	−72151.0	−0.165982
$181$	126797.	0.287682	0.143841	−	0.989601i	$-0.454055\pi$
$181$	126797.	0.287682	0.143841	+	0.989601i	$0.454055\pi$
$182$	−480089.	−1.07434
$183$	−224015.	−0.494481
$184$	−1.39196e6	−3.03097
$185$	−52186.4	−0.112106
$186$	187327.	0.397024
$187$	568551.	1.18895
$188$	−27886.2	−0.0575433
$189$	599237.	1.22024
$190$	−151424.	−0.304307
$191$	−170892.	−0.338952	−0.169476	−	0.985534i	$-0.554208\pi$
$191$	−170892.	−0.338952	−0.169476	+	0.985534i	$0.554208\pi$
$192$	−92258.9	−0.180616
$193$	−635170.	−1.22743	−0.613715	−	0.789528i	$-0.710325\pi$
$193$	−635170.	−1.22743	−0.613715	+	0.789528i	$0.710325\pi$
$194$	−189599.	−0.361686
$195$	−14270.6	−0.0268755
$196$	861464.	1.60176
$197$	998262.	1.83265	0.916324	−	0.400437i	$-0.131142\pi$
$197$	998262.	1.83265	0.916324	+	0.400437i	$0.131142\pi$
$198$	−584570.	−1.05968
$199$	471871.	0.844677	0.422339	−	0.906438i	$-0.361209\pi$
$199$	471871.	0.844677	0.422339	+	0.906438i	$0.361209\pi$
$200$	1.17438e6	2.07603
$201$	371737.	0.649001
$202$	−1.70761e6	−2.94449
$203$	−309125.	−0.526496
$204$	−991753.	−1.66851
$205$	−97618.8	−0.162237
$206$	547824.	0.899441
$207$	−626912.	−1.01691
$208$	−447167.	−0.716658
$209$	−840835.	−1.33151
$210$	88173.0	0.137971
$211$	78759.9	0.121786	0.0608932	−	0.998144i	$-0.480605\pi$
$211$	78759.9	0.121786	0.0608932	+	0.998144i	$0.480605\pi$
$212$	−1.54830e6	−2.36601
$213$	−470702.	−0.710882
$214$	1.51754e6	2.26520
$215$	−48101.4	−0.0709679
$216$	1.33422e6	1.94578
$217$	374518.	0.539912
$218$	1.23638e6	1.76202
$219$	−445252.	−0.627329
$220$	−142599.	−0.198637
$221$	468234.	0.644885
$222$	737540.	1.00439
$223$	1.25054e6	1.68397	0.841984	−	0.539502i	$-0.181388\pi$
$223$	1.25054e6	1.68397	0.841984	+	0.539502i	$0.181388\pi$
$224$	684853.	0.911964
$225$	528918.	0.696518
$226$	1.40248e6	1.82653
$227$	12628.0	0.0162656	0.00813281	−	0.999967i	$-0.497411\pi$
$227$	12628.0	0.0162656	0.00813281	+	0.999967i	$0.497411\pi$
$228$	1.46671e6	1.86856
$229$	5039.43	0.00635027	0.00317514	−	0.999995i	$-0.498989\pi$
$229$	5039.43	0.00635027	0.00317514	+	0.999995i	$0.498989\pi$
$230$	−223135.	−0.278130
$231$	489611.	0.603700
$232$	−688277.	−0.839544
$233$	1.24552e6	1.50301	0.751503	−	0.659730i	$-0.229329\pi$
$233$	1.24552e6	1.50301	0.751503	+	0.659730i	$0.229329\pi$
$234$	−481427.	−0.574765
$235$	−2418.04	−0.00285623
$236$	−3.26301e6	−3.81363
$237$	−162500.	−0.187924
$238$	−2.89305e6	−3.31065
$239$	1.37494e6	1.55701	0.778503	−	0.627641i	$-0.215979\pi$
$239$	1.37494e6	1.55701	0.778503	+	0.627641i	$0.215979\pi$
$240$	82126.6	0.0920356
$241$	−951808.	−1.05562	−0.527809	−	0.849363i	$-0.676986\pi$
$241$	−951808.	−1.05562	−0.527809	+	0.849363i	$0.676986\pi$
$242$	468833.	0.514611
$243$	953396.	1.03576
$244$	−1.84351e6	−1.98231
$245$	74698.3	0.0795052
$246$	1.37963e6	1.45353
$247$	−692475.	−0.722207
$248$	833875.	0.860938
$249$	346011.	0.353665
$250$	378739.	0.383257
$251$	−1.00916e6	−1.01106	−0.505530	−	0.862809i	$-0.668703\pi$
$251$	−1.00916e6	−1.01106	−0.505530	+	0.862809i	$0.668703\pi$
$252$	2.03866e6	2.02229
$253$	−1.23903e6	−1.21697
$254$	−2.50769e6	−2.43887
$255$	−85995.8	−0.0828184
$256$	−2.05338e6	−1.95825
$257$	−1.22567e6	−1.15755	−0.578775	−	0.815487i	$-0.696469\pi$
$257$	−1.22567e6	−1.15755	−0.578775	+	0.815487i	$0.696469\pi$
$258$	679808.	0.635824
$259$	1.47455e6	1.36587
$260$	−117439.	−0.107740
$261$	−309987.	−0.281671
$262$	3.25179e6	2.92664
$263$	−468847.	−0.417966	−0.208983	−	0.977919i	$-0.567015\pi$
$263$	−468847.	−0.417966	−0.208983	+	0.977919i	$0.567015\pi$
$264$	1.09013e6	0.962653
$265$	−134254.	−0.117439
$266$	4.27855e6	3.70760
$267$	−410483.	−0.352385
$268$	3.05917e6	2.60176
$269$	−612117.	−0.515768	−0.257884	−	0.966176i	$-0.583025\pi$
$269$	−612117.	−0.515768	−0.257884	+	0.966176i	$0.583025\pi$
$270$	213879.	0.178549
$271$	1.74269e6	1.44144	0.720722	−	0.693225i	$-0.243811\pi$
$271$	1.74269e6	1.44144	0.720722	+	0.693225i	$0.243811\pi$
$272$	−2.69466e6	−2.20842
$273$	403222.	0.327445
$274$	−2.08638e6	−1.67887
$275$	1.04536e6	0.833551
$276$	2.16131e6	1.70783
$277$	509120.	0.398676	0.199338	−	0.979931i	$-0.436121\pi$
$277$	509120.	0.398676	0.199338	+	0.979931i	$0.436121\pi$
$278$	−3.79926e6	−2.94841
$279$	375561.	0.288849
$280$	392498.	0.299187
$281$	−499479.	−0.377356	−0.188678	−	0.982039i	$-0.560420\pi$
$281$	−499479.	−0.377356	−0.188678	+	0.982039i	$0.560420\pi$
$282$	34173.6	0.0255899
$283$	2.42799e6	1.80211	0.901053	−	0.433710i	$-0.142796\pi$
$283$	2.42799e6	1.80211	0.901053	+	0.433710i	$0.142796\pi$
$284$	−3.87360e6	−2.84983
$285$	127180.	0.0927483
$286$	−951493.	−0.687845
$287$	2.75826e6	1.97665
$288$	686762.	0.487893
$289$	1.40175e6	0.987249
$290$	−110333.	−0.0770386
$291$	159243.	0.110237
$292$	−3.66416e6	−2.51488
$293$	−407501.	−0.277306	−0.138653	−	0.990341i	$-0.544277\pi$
$293$	−407501.	−0.277306	−0.138653	+	0.990341i	$0.544277\pi$
$294$	−1.05570e6	−0.712313
$295$	−282939.	−0.189294
$296$	3.28312e6	2.17800
$297$	1.18763e6	0.781253
$298$	4.21583e6	2.75006
$299$	−1.02041e6	−0.660082
$300$	−1.82347e6	−1.16976
$301$	1.35912e6	0.864656
$302$	3.67751e6	2.32026
$303$	1.43421e6	0.897440
$304$	3.98516e6	2.47321
$305$	−159852.	−0.0983942
$306$	−2.90111e6	−1.77117
$307$	2.58736e6	1.56679	0.783395	−	0.621524i	$-0.213486\pi$
$307$	2.58736e6	1.56679	0.783395	+	0.621524i	$0.213486\pi$
$308$	4.02920e6	2.42015
$309$	−460112.	−0.274137
$310$	133672.	0.0790018
$311$	451601.	0.264761	0.132380	−	0.991199i	$-0.457738\pi$
$311$	451601.	0.264761	0.132380	+	0.991199i	$0.457738\pi$
$312$	897787.	0.522140
$313$	1.20643e6	0.696051	0.348025	−	0.937485i	$-0.386852\pi$
$313$	1.20643e6	0.696051	0.348025	+	0.937485i	$0.386852\pi$
$314$	3.40479e6	1.94879
$315$	176774.	0.100379
$316$	−1.33728e6	−0.753361
$317$	−48035.7	−0.0268482	−0.0134241	−	0.999910i	$-0.504273\pi$
$317$	−48035.7	−0.0268482	−0.0134241	+	0.999910i	$0.504273\pi$
$318$	1.89739e6	1.05218
$319$	−612659.	−0.337087
$320$	−65834.0	−0.0359398
$321$	−1.27457e6	−0.690402
$322$	6.30476e6	3.38867
$323$	−4.17290e6	−2.22552
$324$	829117.	0.438787
$325$	860910.	0.452115
$326$	−5.11768e6	−2.66704
$327$	−1.03843e6	−0.537040
$328$	6.14135e6	3.15195
$329$	68322.6	0.0347996
$330$	174751.	0.0883354
$331$	947659.	0.475425	0.237712	−	0.971336i	$-0.423602\pi$
$331$	947659.	0.475425	0.237712	+	0.971336i	$0.423602\pi$
$332$	2.84746e6	1.41779
$333$	1.47866e6	0.730730
$334$	−1.16927e6	−0.573522
$335$	265263.	0.129141
$336$	−2.32052e6	−1.12134
$337$	−2.87391e6	−1.37848	−0.689238	−	0.724535i	$-0.742055\pi$
$337$	−2.87391e6	−1.37848	−0.689238	+	0.724535i	$0.742055\pi$
$338$	2.96083e6	1.40969
$339$	−1.17793e6	−0.556701
$340$	−707694.	−0.332008
$341$	742261.	0.345677
$342$	4.29048e6	1.98354
$343$	759667.	0.348649
$344$	3.02613e6	1.37877
$345$	187409.	0.0847700
$346$	3.93487e6	1.76701
$347$	−3.18008e6	−1.41780	−0.708898	−	0.705311i	$-0.750808\pi$
$347$	−3.18008e6	−1.41780	−0.708898	+	0.705311i	$0.750808\pi$
$348$	1.06869e6	0.473048
$349$	−1.86968e6	−0.821683	−0.410842	−	0.911707i	$-0.634765\pi$
$349$	−1.86968e6	−0.821683	−0.410842	+	0.911707i	$0.634765\pi$
$350$	−5.31925e6	−2.32103
$351$	978085.	0.423749
$352$	1.35732e6	0.583882
$353$	−1.98297e6	−0.846990	−0.423495	−	0.905898i	$-0.639197\pi$
$353$	−1.98297e6	−0.846990	−0.423495	+	0.905898i	$0.639197\pi$
$354$	3.99872e6	1.69595
$355$	−335883.	−0.141455
$356$	−3.37803e6	−1.41266
$357$	2.42985e6	1.00904
$358$	−3.06065e6	−1.26213
$359$	−660940.	−0.270661	−0.135331	−	0.990800i	$-0.543210\pi$
$359$	−660940.	−0.270661	−0.135331	+	0.990800i	$0.543210\pi$
$360$	393592.	0.160062
$361$	3.69524e6	1.49236
$362$	−1.27873e6	−0.512870
$363$	−393768.	−0.156846
$364$	3.31828e6	1.31268
$365$	−317722.	−0.124829
$366$	2.25916e6	0.881546
$367$	4.39363e6	1.70278	0.851389	−	0.524535i	$-0.175761\pi$
$367$	4.39363e6	1.70278	0.851389	+	0.524535i	$0.175761\pi$
$368$	5.87241e6	2.26046
$369$	2.76595e6	1.05749
$370$	526293.	0.199859
$371$	3.79342e6	1.43085
$372$	−1.29476e6	−0.485102
$373$	−3.78772e6	−1.40963	−0.704817	−	0.709389i	$-0.748971\pi$
$373$	−3.78772e6	−1.40963	−0.704817	+	0.709389i	$0.748971\pi$
$374$	−5.73376e6	−2.11963
$375$	−318099.	−0.116811
$376$	152122.	0.0554911
$377$	−504560.	−0.182835
$378$	−6.04323e6	−2.17540
$379$	−3.57838e6	−1.27964	−0.639820	−	0.768525i	$-0.720991\pi$
$379$	−3.57838e6	−1.27964	−0.639820	+	0.768525i	$0.720991\pi$
$380$	1.04661e6	0.371816
$381$	2.10618e6	0.743334
$382$	1.72342e6	0.604274
$383$	1.18255e6	0.411930	0.205965	−	0.978559i	$-0.433967\pi$
$383$	1.18255e6	0.411930	0.205965	+	0.978559i	$0.433967\pi$
$384$	2.01736e6	0.698159
$385$	349376.	0.120127
$386$	6.40561e6	2.18822
$387$	1.36291e6	0.462584
$388$	1.31047e6	0.441925
$389$	3.58591e6	1.20151	0.600753	−	0.799435i	$-0.294868\pi$
$389$	3.58591e6	1.20151	0.600753	+	0.799435i	$0.294868\pi$
$390$	143917.	0.0479128
$391$	−6.14907e6	−2.03408
$392$	−4.69938e6	−1.54463
$393$	−2.73115e6	−0.891999
$394$	−1.00673e7	−3.26719
$395$	−115956.	−0.0373940
$396$	4.04043e6	1.29476
$397$	−398458.	−0.126884	−0.0634420	−	0.997986i	$-0.520208\pi$
$397$	−398458.	−0.126884	−0.0634420	+	0.997986i	$0.520208\pi$
$398$	−4.75876e6	−1.50587
$399$	−3.59352e6	−1.13002
$400$	−4.95449e6	−1.54828
$401$	−1.13914e6	−0.353765	−0.176883	−	0.984232i	$-0.556601\pi$
$401$	−1.13914e6	−0.353765	−0.176883	+	0.984232i	$0.556601\pi$
$402$	−3.74892e6	−1.15702
$403$	611294.	0.187494
$404$	1.18027e7	3.59772
$405$	71893.5	0.0217797
$406$	3.11749e6	0.938621
$407$	2.92242e6	0.874494
$408$	5.41012e6	1.60900
$409$	−845755.	−0.249998	−0.124999	−	0.992157i	$-0.539893\pi$
$409$	−845755.	−0.249998	−0.124999	+	0.992157i	$0.539893\pi$
$410$	984474.	0.289231
$411$	1.75233e6	0.511696
$412$	−3.78645e6	−1.09898
$413$	7.99454e6	2.30631
$414$	6.32233e6	1.81291
$415$	246906.	0.0703739
$416$	1.11783e6	0.316696
$417$	3.19097e6	0.898632
$418$	8.47971e6	2.37378
$419$	5.15618e6	1.43481	0.717403	−	0.696659i	$-0.245331\pi$
$419$	5.15618e6	1.43481	0.717403	+	0.696659i	$0.245331\pi$
$420$	−609435.	−0.168579
$421$	−4.16216e6	−1.14449	−0.572247	−	0.820081i	$-0.693928\pi$
$421$	−4.16216e6	−1.14449	−0.572247	+	0.820081i	$0.693928\pi$
$422$	−794284.	−0.217117
$423$	68513.0	0.0186175
$424$	8.44615e6	2.28162
$425$	5.18790e6	1.39322
$426$	4.74697e6	1.26734
$427$	4.51669e6	1.19881
$428$	−1.04890e7	−2.76773
$429$	799151.	0.209645
$430$	485097.	0.126519
$431$	944642.	0.244948	0.122474	−	0.992472i	$-0.460917\pi$
$431$	944642.	0.244948	0.122474	+	0.992472i	$0.460917\pi$
$432$	−5.62882e6	−1.45114
$433$	−4.20845e6	−1.07870	−0.539352	−	0.842080i	$-0.681331\pi$
$433$	−4.20845e6	−1.07870	−0.539352	+	0.842080i	$0.681331\pi$
$434$	−3.77696e6	−0.962539
$435$	92667.3	0.0234803
$436$	−8.54563e6	−2.15292
$437$	9.09391e6	2.27797
$438$	4.49031e6	1.11838
$439$	4.08621e6	1.01195	0.505976	−	0.862548i	$-0.331133\pi$
$439$	4.08621e6	1.01195	0.505976	+	0.862548i	$0.331133\pi$
$440$	777896.	0.191553
$441$	−2.11651e6	−0.518232
$442$	−4.72208e6	−1.14968
$443$	−10007.8	−0.00242287	−0.00121143	−	0.999999i	$-0.500386\pi$
$443$	−10007.8	−0.00242287	−0.00121143	+	0.999999i	$0.500386\pi$
$444$	−5.09773e6	−1.22721
$445$	−292912.	−0.0701192
$446$	−1.26115e7	−3.00213
$447$	−3.54084e6	−0.838180
$448$	1.86017e6	0.437882
$449$	−4.54076e6	−1.06295	−0.531475	−	0.847074i	$-0.678362\pi$
$449$	−4.54076e6	−1.06295	−0.531475	+	0.847074i	$0.678362\pi$
$450$	−5.33407e6	−1.24173
$451$	5.46663e6	1.26555
$452$	−9.69369e6	−2.23174
$453$	−3.08871e6	−0.707182
$454$	−127352.	−0.0289979
$455$	287731.	0.0651565
$456$	−8.00107e6	−1.80192
$457$	7.19766e6	1.61213	0.806067	−	0.591825i	$-0.201592\pi$
$457$	7.19766e6	1.61213	0.806067	+	0.591825i	$0.201592\pi$
$458$	−50822.0	−0.0113211
$459$	5.89400e6	1.30581
$460$	1.54226e6	0.339831
$461$	587799.	0.128818	0.0644089	−	0.997924i	$-0.479484\pi$
$461$	587799.	0.128818	0.0644089	+	0.997924i	$0.479484\pi$
$462$	−4.93766e6	−1.07626
$463$	2.90442e6	0.629661	0.314830	−	0.949148i	$-0.398052\pi$
$463$	2.90442e6	0.629661	0.314830	+	0.949148i	$0.398052\pi$
$464$	2.90371e6	0.626121
$465$	−112270.	−0.0240786
$466$	−1.25609e7	−2.67951
$467$	−5.38687e6	−1.14300	−0.571498	−	0.820604i	$-0.693637\pi$
$467$	−5.38687e6	−1.14300	−0.571498	+	0.820604i	$0.693637\pi$
$468$	3.32753e6	0.702275
$469$	−7.49512e6	−1.57343
$470$	24385.6	0.00509200
$471$	−2.85965e6	−0.593964
$472$	1.78001e7	3.67762
$473$	2.69366e6	0.553593
$474$	1.63879e6	0.335025
$475$	−7.67243e6	−1.56027
$476$	1.99962e7	4.04510
$477$	3.80399e6	0.765496
$478$	−1.38661e7	−2.77579
$479$	−2.49565e6	−0.496986	−0.248493	−	0.968634i	$-0.579935\pi$
$479$	−2.49565e6	−0.496986	−0.248493	+	0.968634i	$0.579935\pi$
$480$	−205300.	−0.0406711
$481$	2.40678e6	0.474323
$482$	9.59886e6	1.88192
$483$	−5.29531e6	−1.03282
$484$	−3.24048e6	−0.628776
$485$	113632.	0.0219355
$486$	−9.61487e6	−1.84651
$487$	−1.63674e6	−0.312721	−0.156360	−	0.987700i	$-0.549976\pi$
$487$	−1.63674e6	−0.312721	−0.156360	+	0.987700i	$0.549976\pi$
$488$	1.00566e7	1.91161
$489$	4.29829e6	0.812875
$490$	−753323.	−0.141739
$491$	3.79128e6	0.709713	0.354856	−	0.934921i	$-0.384530\pi$
$491$	3.79128e6	0.709713	0.354856	+	0.934921i	$0.384530\pi$
$492$	−9.53572e6	−1.77599
$493$	−3.04051e6	−0.563416
$494$	6.98352e6	1.28753
$495$	350349.	0.0642671
$496$	−3.51796e6	−0.642077
$497$	9.49052e6	1.72345
$498$	−3.48948e6	−0.630503
$499$	−1.02447e7	−1.84182	−0.920908	−	0.389780i	$-0.872551\pi$
$499$	−1.02447e7	−1.84182	−0.920908	+	0.389780i	$0.872551\pi$
$500$	−2.61777e6	−0.468280
$501$	982062.	0.174801
$502$	1.01773e7	1.80249
$503$	−208030.	−0.0366611	−0.0183305	−	0.999832i	$-0.505835\pi$
$503$	−208030.	−0.0366611	−0.0183305	+	0.999832i	$0.505835\pi$
$504$	−1.11211e7	−1.95016
$505$	1.02342e6	0.178577
$506$	1.24955e7	2.16958
$507$	−2.48678e6	−0.429652
$508$	1.73326e7	2.97993
$509$	−4.57080e6	−0.781984	−0.390992	−	0.920394i	$-0.627868\pi$
$509$	−4.57080e6	−0.781984	−0.390992	+	0.920394i	$0.627868\pi$
$510$	867256.	0.147646
$511$	8.97737e6	1.52089
$512$	1.30866e7	2.20623
$513$	−8.71669e6	−1.46237
$514$	1.23607e7	2.06365
$515$	−328326.	−0.0545491
$516$	−4.69870e6	−0.776879
$517$	135409.	0.0222803
$518$	−1.48706e7	−2.43503
$519$	−3.30486e6	−0.538561
$520$	640641.	0.103898
$521$	−1.13224e7	−1.82745	−0.913726	−	0.406331i	$-0.866808\pi$
$521$	−1.13224e7	−1.82745	−0.913726	+	0.406331i	$0.866808\pi$
$522$	3.12618e6	0.502155
$523$	−6.27160e6	−1.00259	−0.501296	−	0.865276i	$-0.667143\pi$
$523$	−6.27160e6	−1.00259	−0.501296	+	0.865276i	$0.667143\pi$
$524$	−2.24758e7	−3.57591
$525$	4.46759e6	0.707416
$526$	4.72826e6	0.745138
$527$	3.68370e6	0.577773
$528$	−4.59907e6	−0.717935
$529$	6.96420e6	1.08201
$530$	1.35394e6	0.209368
$531$	8.01682e6	1.23386
$532$	−2.95725e7	−4.53011
$533$	4.50208e6	0.686428
$534$	4.13967e6	0.628221
$535$	−909508.	−0.137379
$536$	−1.66881e7	−2.50897
$537$	2.57061e6	0.384681
$538$	6.17313e6	0.919495
$539$	−4.18308e6	−0.620189
$540$	−1.47829e6	−0.218160
$541$	1.34480e7	1.97545	0.987723	−	0.156219i	$-0.0499304\pi$
$541$	1.34480e7	1.97545	0.987723	+	0.156219i	$0.0499304\pi$
$542$	−1.75748e7	−2.56976
$543$	1.07399e6	0.156316
$544$	6.73611e6	0.975915
$545$	−740999.	−0.106863
$546$	−4.06645e6	−0.583759
$547$	5.48761e6	0.784178	0.392089	−	0.919927i	$-0.371752\pi$
$547$	5.48761e6	0.784178	0.392089	+	0.919927i	$0.371752\pi$
$548$	1.44207e7	2.05132
$549$	4.52928e6	0.641355
$550$	−1.05423e7	−1.48603
$551$	4.49664e6	0.630970
$552$	−1.17902e7	−1.64692
$553$	3.27639e6	0.455599
$554$	−5.13441e6	−0.710748
$555$	−442029.	−0.0609141
$556$	2.62597e7	3.60250
$557$	−3.00415e6	−0.410284	−0.205142	−	0.978732i	$-0.565766\pi$
$557$	−3.00415e6	−0.410284	−0.205142	+	0.978732i	$0.565766\pi$
$558$	−3.78749e6	−0.514951
$559$	2.21839e6	0.300267
$560$	−1.65587e6	−0.223130
$561$	4.81574e6	0.646034
$562$	5.03719e6	0.672740
$563$	−7.50973e6	−0.998512	−0.499256	−	0.866454i	$-0.666393\pi$
$563$	−7.50973e6	−0.998512	−0.499256	+	0.866454i	$0.666393\pi$
$564$	−236201.	−0.0312669
$565$	−840548.	−0.110775
$566$	−2.44859e7	−3.21274
$567$	−2.03138e6	−0.265359
$568$	2.11309e7	2.74819
$569$	3.17297e6	0.410852	0.205426	−	0.978673i	$-0.434142\pi$
$569$	3.17297e6	0.410852	0.205426	+	0.978673i	$0.434142\pi$
$570$	−1.28259e6	−0.165349
$571$	−4.06825e6	−0.522177	−0.261088	−	0.965315i	$-0.584081\pi$
$571$	−4.06825e6	−0.522177	−0.261088	+	0.965315i	$0.584081\pi$
$572$	6.57653e6	0.840441
$573$	−1.44749e6	−0.184174
$574$	−2.78167e7	−3.52392
$575$	−1.13059e7	−1.42605
$576$	1.86535e6	0.234263
$577$	5.10612e6	0.638486	0.319243	−	0.947673i	$-0.396571\pi$
$577$	5.10612e6	0.638486	0.319243	+	0.947673i	$0.396571\pi$
$578$	−1.41365e7	−1.76004
$579$	−5.38001e6	−0.666940
$580$	762597.	0.0941293
$581$	−6.97643e6	−0.857419
$582$	−1.60594e6	−0.196527
$583$	7.51821e6	0.916100
$584$	1.99884e7	2.42519
$585$	288533.	0.0348582
$586$	4.10959e6	0.494373
$587$	−9.11305e6	−1.09161	−0.545806	−	0.837912i	$-0.683776\pi$
$587$	−9.11305e6	−1.09161	−0.545806	+	0.837912i	$0.683776\pi$
$588$	7.29677e6	0.870337
$589$	−5.44785e6	−0.647049
$590$	2.85340e6	0.337468
$591$	8.45548e6	0.995794
$592$	−1.38509e7	−1.62433
$593$	150511.	0.0175764	0.00878822	−	0.999961i	$-0.497203\pi$
$593$	150511.	0.0175764	0.00878822	+	0.999961i	$0.497203\pi$
$594$	−1.19771e7	−1.39279
$595$	1.73389e6	0.200784
$596$	−2.91390e7	−3.36015
$597$	3.99684e6	0.458967
$598$	1.02907e7	1.17677
$599$	−171303.	−0.0195073	−0.00975366	−	0.999952i	$-0.503105\pi$
$599$	−171303.	−0.0195073	−0.00975366	+	0.999952i	$0.503105\pi$
$600$	9.94722e6	1.12804
$601$	3.16738e6	0.357696	0.178848	−	0.983877i	$-0.442763\pi$
$601$	3.16738e6	0.357696	0.178848	+	0.983877i	$0.442763\pi$
$602$	−1.37066e7	−1.54148
$603$	−7.51601e6	−0.841771
$604$	−2.54182e7	−2.83500
$605$	−280985.	−0.0312100
$606$	−1.44638e7	−1.59993
$607$	−1.43522e7	−1.58106	−0.790528	−	0.612425i	$-0.790194\pi$
$607$	−1.43522e7	−1.58106	−0.790528	+	0.612425i	$0.790194\pi$
$608$	−9.96209e6	−1.09293
$609$	−2.61835e6	−0.286078
$610$	1.61209e6	0.175414
$611$	111517.	0.0120848
$612$	2.00519e7	2.16410
$613$	1.46682e7	1.57662	0.788310	−	0.615278i	$-0.210956\pi$
$613$	1.46682e7	1.57662	0.788310	+	0.615278i	$0.210956\pi$
$614$	−2.60932e7	−2.79323
$615$	−826851.	−0.0881534
$616$	−2.19798e7	−2.33384
$617$	−1.45898e6	−0.154290	−0.0771448	−	0.997020i	$-0.524580\pi$
$617$	−1.45898e6	−0.154290	−0.0771448	+	0.997020i	$0.524580\pi$
$618$	4.64017e6	0.488723
$619$	1.58830e7	1.66612	0.833062	−	0.553180i	$-0.186586\pi$
$619$	1.58830e7	1.66612	0.833062	+	0.553180i	$0.186586\pi$
$620$	−923916.	−0.0965280
$621$	−1.28447e7	−1.33658
$622$	−4.55434e6	−0.472008
$623$	8.27634e6	0.854316
$624$	−3.78759e6	−0.389405
$625$	9.42447e6	0.965066
$626$	−1.21667e7	−1.24090
$627$	−7.12203e6	−0.723494
$628$	−2.35332e7	−2.38112
$629$	1.45034e7	1.46165
$630$	−1.78274e6	−0.178952
$631$	1.53948e7	1.53922	0.769610	−	0.638514i	$-0.220451\pi$
$631$	1.53948e7	1.53922	0.769610	+	0.638514i	$0.220451\pi$
$632$	7.29499e6	0.726494
$633$	667112.	0.0661743
$634$	484433.	0.0478642
$635$	1.50293e6	0.147912
$636$	−1.31144e7	−1.28560
$637$	−3.44501e6	−0.336389
$638$	6.17859e6	0.600949
$639$	9.51696e6	0.922033
$640$	1.43954e6	0.138923
$641$	1.51498e7	1.45634	0.728170	−	0.685397i	$-0.240371\pi$
$641$	1.51498e7	1.45634	0.728170	+	0.685397i	$0.240371\pi$
$642$	1.28539e7	1.23083
$643$	1.68002e7	1.60246	0.801231	−	0.598356i	$-0.204179\pi$
$643$	1.68002e7	1.60246	0.801231	+	0.598356i	$0.204179\pi$
$644$	−4.35772e7	−4.14043
$645$	−407428.	−0.0385613
$646$	4.20832e7	3.96759
$647$	−1.51594e7	−1.42371	−0.711856	−	0.702325i	$-0.752145\pi$
$647$	−1.51594e7	−1.42371	−0.711856	+	0.702325i	$0.752145\pi$
$648$	−4.52293e6	−0.423138
$649$	1.58445e7	1.47661
$650$	−8.68217e6	−0.806018
$651$	3.17224e6	0.293368
$652$	3.53724e7	3.25871
$653$	−6.60100e6	−0.605797	−0.302898	−	0.953023i	$-0.597954\pi$
$653$	−6.60100e6	−0.605797	−0.302898	+	0.953023i	$0.597954\pi$
$654$	1.04724e7	0.957418
$655$	−1.94889e6	−0.177494
$656$	−2.59092e7	−2.35068
$657$	9.00239e6	0.813662
$658$	−689024.	−0.0620397
$659$	−1.28510e7	−1.15272	−0.576360	−	0.817196i	$-0.695527\pi$
$659$	−1.28510e7	−1.15272	−0.576360	+	0.817196i	$0.695527\pi$
$660$	−1.20784e6	−0.107932
$661$	1.41209e6	0.125707	0.0628536	−	0.998023i	$-0.479980\pi$
$661$	1.41209e6	0.125707	0.0628536	+	0.998023i	$0.479980\pi$
$662$	−9.55702e6	−0.847573
$663$	3.96603e6	0.350407
$664$	−1.55332e7	−1.36723
$665$	−2.56426e6	−0.224858
$666$	−1.49121e7	−1.30272
$667$	6.62612e6	0.576693
$668$	8.08179e6	0.700755
$669$	1.05923e7	0.915006
$670$	−2.67515e6	−0.230229
$671$	8.95168e6	0.767535
$672$	5.80084e6	0.495527
$673$	−1.11992e7	−0.953121	−0.476561	−	0.879142i	$-0.658117\pi$
$673$	−1.11992e7	−0.953121	−0.476561	+	0.879142i	$0.658117\pi$
$674$	2.89831e7	2.45751
$675$	1.08369e7	0.915473
$676$	−2.04647e7	−1.72242
$677$	−1.96106e7	−1.64445	−0.822223	−	0.569165i	$-0.807267\pi$
$677$	−1.96106e7	−1.64445	−0.822223	+	0.569165i	$0.807267\pi$
$678$	1.18793e7	0.992469
$679$	−3.21072e6	−0.267257
$680$	3.86055e6	0.320167
$681$	106962.	0.00883814
$682$	−7.48560e6	−0.616263
$683$	−1.49532e7	−1.22654	−0.613272	−	0.789872i	$-0.710147\pi$
$683$	−1.49532e7	−1.22654	−0.613272	+	0.789872i	$0.710147\pi$
$684$	−2.96549e7	−2.42358
$685$	1.25043e6	0.101820
$686$	−7.66115e6	−0.621561
$687$	42684.9	0.00345050
$688$	−1.27667e7	−1.02827
$689$	6.19168e6	0.496890
$690$	−1.88999e6	−0.151125
$691$	−1.28347e7	−1.02257	−0.511284	−	0.859412i	$-0.670830\pi$
$691$	−1.28347e7	−1.02257	−0.511284	+	0.859412i	$0.670830\pi$
$692$	−2.71970e7	−2.15902
$693$	−9.89926e6	−0.783015
$694$	3.20707e7	2.52761
$695$	2.27700e6	0.178814
$696$	−5.82984e6	−0.456177
$697$	2.71298e7	2.11527
$698$	1.88555e7	1.46487
$699$	1.05498e7	0.816678
$700$	3.67656e7	2.83594
$701$	2.20670e7	1.69609	0.848043	−	0.529927i	$-0.177781\pi$
$701$	2.20670e7	1.69609	0.848043	+	0.529927i	$0.177781\pi$
$702$	−9.86386e6	−0.755447
$703$	−2.14492e7	−1.63690
$704$	3.68668e6	0.280352
$705$	−20481.2	−0.00155197
$706$	1.99980e7	1.50999
$707$	−2.89171e7	−2.17574
$708$	−2.76383e7	−2.07219
$709$	−5.50926e6	−0.411603	−0.205801	−	0.978594i	$-0.565980\pi$
$709$	−5.50926e6	−0.411603	−0.205801	+	0.978594i	$0.565980\pi$
$710$	3.38734e6	0.252181
$711$	3.28552e6	0.243742
$712$	1.84275e7	1.36228
$713$	−8.02780e6	−0.591389
$714$	−2.45047e7	−1.79889
$715$	570257.	0.0417163
$716$	2.11546e7	1.54213
$717$	1.16460e7	0.846020
$718$	6.66550e6	0.482527
$719$	−1.50340e7	−1.08456	−0.542279	−	0.840199i	$-0.682438\pi$
$719$	−1.50340e7	−1.08456	−0.542279	+	0.840199i	$0.682438\pi$
$720$	−1.66049e6	−0.119373
$721$	9.27699e6	0.664613
$722$	−3.72660e7	−2.66054
$723$	−8.06200e6	−0.573584
$724$	8.83833e6	0.626648
$725$	−5.59038e6	−0.394999
$726$	3.97110e6	0.279621
$727$	−7.90235e6	−0.554524	−0.277262	−	0.960794i	$-0.589427\pi$
$727$	−7.90235e6	−0.554524	−0.277262	+	0.960794i	$0.589427\pi$
$728$	−1.81016e7	−1.26587
$729$	5.18503e6	0.361354
$730$	3.20419e6	0.222541
$731$	1.33681e7	0.925290
$732$	−1.56149e7	−1.07711
$733$	2.25087e7	1.54736	0.773680	−	0.633576i	$-0.218414\pi$
$733$	2.25087e7	1.54736	0.773680	+	0.633576i	$0.218414\pi$
$734$	−4.43091e7	−3.03566
$735$	632709.	0.0432002
$736$	−1.46799e7	−0.998912
$737$	−1.48547e7	−1.00738
$738$	−2.78942e7	−1.88527
$739$	−1.27127e6	−0.0856299	−0.0428150	−	0.999083i	$-0.513633\pi$
$739$	−1.27127e6	−0.0856299	−0.0428150	+	0.999083i	$0.513633\pi$
$740$	−3.63763e6	−0.244197
$741$	−5.86540e6	−0.392421
$742$	−3.82561e7	−2.55089
$743$	1.06812e7	0.709817	0.354908	−	0.934901i	$-0.384512\pi$
$743$	1.06812e7	0.709817	0.354908	+	0.934901i	$0.384512\pi$
$744$	7.06308e6	0.467802
$745$	−2.52667e6	−0.166785
$746$	3.81987e7	2.51305
$747$	−6.99587e6	−0.458712
$748$	3.96306e7	2.58986
$749$	2.56985e7	1.67380
$750$	3.20799e6	0.208248
$751$	3.09587e6	0.200301	0.100150	−	0.994972i	$-0.468068\pi$
$751$	3.09587e6	0.200301	0.100150	+	0.994972i	$0.468068\pi$
$752$	−641775.	−0.0413846
$753$	−8.54780e6	−0.549372
$754$	5.08842e6	0.325953
$755$	−2.20403e6	−0.140718
$756$	4.17696e7	2.65801
$757$	2.02855e7	1.28661	0.643305	−	0.765610i	$-0.277563\pi$
$757$	2.02855e7	1.28661	0.643305	+	0.765610i	$0.277563\pi$
$758$	3.60875e7	2.28131
$759$	−1.04948e7	−0.661258
$760$	−5.70940e6	−0.358555
$761$	−2.08417e7	−1.30458	−0.652290	−	0.757970i	$-0.726191\pi$
$761$	−2.08417e7	−1.30458	−0.652290	+	0.757970i	$0.726191\pi$
$762$	−2.12406e7	−1.32519
$763$	2.09372e7	1.30199
$764$	−1.19120e7	−0.738329
$765$	1.73872e6	0.107418
$766$	−1.19259e7	−0.734377
$767$	1.30488e7	0.800909
$768$	−1.73925e7	−1.06404
$769$	−9.66503e6	−0.589369	−0.294685	−	0.955595i	$-0.595215\pi$
$769$	−9.66503e6	−0.589369	−0.294685	+	0.955595i	$0.595215\pi$
$770$	−3.52341e6	−0.214159
$771$	−1.03816e7	−0.628970
$772$	−4.42743e7	−2.67367
$773$	−6.44296e6	−0.387826	−0.193913	−	0.981019i	$-0.562118\pi$
$773$	−6.44296e6	−0.387826	−0.193913	+	0.981019i	$0.562118\pi$
$774$	−1.37448e7	−0.824681
$775$	6.77296e6	0.405065
$776$	−7.14877e6	−0.426164
$777$	1.24897e7	0.742164
$778$	−3.61635e7	−2.14201
$779$	−4.01225e7	−2.36889
$780$	−994729.	−0.0585421
$781$	1.88094e7	1.10343
$782$	6.20126e7	3.62630
$783$	−6.35126e6	−0.370216
$784$	1.98258e7	1.15197
$785$	−2.04058e6	−0.118190
$786$	2.75433e7	1.59023
$787$	1.83097e7	1.05377	0.526884	−	0.849937i	$-0.323360\pi$
$787$	1.83097e7	1.05377	0.526884	+	0.849937i	$0.323360\pi$
$788$	6.95835e7	3.99200
$789$	−3.97122e6	−0.227108
$790$	1.16940e6	0.0666649
$791$	2.37500e7	1.34966
$792$	−2.20410e7	−1.24859
$793$	7.37222e6	0.416309
$794$	4.01840e6	0.226205
$795$	−1.13716e6	−0.0638123
$796$	3.28916e7	1.83994
$797$	1.33407e7	0.743931	0.371966	−	0.928246i	$-0.378684\pi$
$797$	1.33407e7	0.743931	0.371966	+	0.928246i	$0.378684\pi$
$798$	3.62402e7	2.01457
$799$	672010.	0.0372399
$800$	1.23852e7	0.684194
$801$	8.29941e6	0.457052
$802$	1.14880e7	0.630682
$803$	1.77923e7	0.973743
$804$	2.59118e7	1.41370
$805$	−3.77862e6	−0.205515
$806$	−6.16482e6	−0.334259
$807$	−5.18475e6	−0.280249
$808$	−6.43849e7	−3.46941
$809$	−1.11251e7	−0.597630	−0.298815	−	0.954311i	$-0.596591\pi$
$809$	−1.11251e7	−0.597630	−0.298815	+	0.954311i	$0.596591\pi$
$810$	−725036.	−0.0388282
$811$	2.52877e7	1.35007	0.675037	−	0.737784i	$-0.264128\pi$
$811$	2.52877e7	1.35007	0.675037	+	0.737784i	$0.264128\pi$
$812$	−2.15475e7	−1.14685
$813$	1.47609e7	0.783227
$814$	−2.94722e7	−1.55902
$815$	3.06717e6	0.161750
$816$	−2.28243e7	−1.19997
$817$	−1.97703e7	−1.03623
$818$	8.52933e6	0.445689
$819$	−8.15261e6	−0.424705
$820$	−6.80449e6	−0.353395
$821$	7.46280e6	0.386406	0.193203	−	0.981159i	$-0.438112\pi$
$821$	7.46280e6	0.386406	0.193203	+	0.981159i	$0.438112\pi$
$822$	−1.76721e7	−0.912237
$823$	−9.34496e6	−0.480925	−0.240463	−	0.970658i	$-0.577299\pi$
$823$	−9.34496e6	−0.480925	−0.240463	+	0.970658i	$0.577299\pi$
$824$	2.06555e7	1.05978
$825$	8.85436e6	0.452921
$826$	−8.06239e7	−4.11163
$827$	−1.06334e7	−0.540642	−0.270321	−	0.962770i	$-0.587130\pi$
$827$	−1.06334e7	−0.540642	−0.270321	+	0.962770i	$0.587130\pi$
$828$	−4.36987e7	−2.21510
$829$	−8.19375e6	−0.414092	−0.207046	−	0.978331i	$-0.566385\pi$
$829$	−8.19375e6	−0.414092	−0.207046	+	0.978331i	$0.566385\pi$
$830$	−2.49002e6	−0.125460
$831$	4.31234e6	0.216626
$832$	3.03619e6	0.152062
$833$	−2.07598e7	−1.03660
$834$	−3.21805e7	−1.60205
$835$	700779.	0.0347828
$836$	−5.86101e7	−2.90039
$837$	7.69480e6	0.379650
$838$	−5.19994e7	−2.55793
$839$	−2.51517e7	−1.23357	−0.616783	−	0.787134i	$-0.711564\pi$
$839$	−2.51517e7	−1.23357	−0.616783	+	0.787134i	$0.711564\pi$
$840$	3.32453e6	0.162567
$841$	−1.72348e7	−0.840263
$842$	4.19748e7	2.04037
$843$	−4.23069e6	−0.205042
$844$	5.48993e6	0.265284
$845$	−1.77451e6	−0.0854943
$846$	−690944.	−0.0331908
$847$	7.93934e6	0.380256
$848$	−3.56327e7	−1.70161
$849$	2.05655e7	0.979198
$850$	−5.23193e7	−2.48379
$851$	−3.16070e7	−1.49610
$852$	−3.28101e7	−1.54849
$853$	5.08435e6	0.239256	0.119628	−	0.992819i	$-0.461830\pi$
$853$	5.08435e6	0.239256	0.119628	+	0.992819i	$0.461830\pi$
$854$	−4.55503e7	−2.13721
$855$	−2.57140e6	−0.120297
$856$	5.72185e7	2.66902
$857$	3.67113e6	0.170745	0.0853726	−	0.996349i	$-0.472792\pi$
$857$	3.67113e6	0.170745	0.0853726	+	0.996349i	$0.472792\pi$
$858$	−8.05933e6	−0.373750
$859$	−4.23557e6	−0.195853	−0.0979263	−	0.995194i	$-0.531221\pi$
$859$	−4.23557e6	−0.195853	−0.0979263	+	0.995194i	$0.531221\pi$
$860$	−3.35289e6	−0.154587
$861$	2.33630e7	1.07404
$862$	−9.52660e6	−0.436686
$863$	6.36869e6	0.291087	0.145544	−	0.989352i	$-0.453507\pi$
$863$	6.36869e6	0.291087	0.145544	+	0.989352i	$0.453507\pi$
$864$	1.40709e7	0.641266
$865$	−2.35828e6	−0.107165
$866$	4.24417e7	1.92308
$867$	1.18731e7	0.536435
$868$	2.61056e7	1.17607
$869$	6.49352e6	0.291696
$870$	−934538.	−0.0418600
$871$	−1.22337e7	−0.546401
$872$	4.66174e7	2.07614
$873$	−3.21967e6	−0.142980
$874$	−9.17110e7	−4.06109
$875$	6.41366e6	0.283195
$876$	−3.10361e7	−1.36649
$877$	3.59515e7	1.57840	0.789201	−	0.614135i	$-0.210495\pi$
$877$	3.59515e7	1.57840	0.789201	+	0.614135i	$0.210495\pi$
$878$	−4.12089e7	−1.80408
$879$	−3.45161e6	−0.150678
$880$	−3.28180e6	−0.142858
$881$	−2.70930e7	−1.17603	−0.588014	−	0.808850i	$-0.700090\pi$
$881$	−2.70930e7	−1.17603	−0.588014	+	0.808850i	$0.700090\pi$
$882$	2.13448e7	0.923889
$883$	263525.	0.0113742	0.00568710	−	0.999984i	$-0.498190\pi$
$883$	263525.	0.0113742	0.00568710	+	0.999984i	$0.498190\pi$
$884$	3.26381e7	1.40473
$885$	−2.39654e6	−0.102855
$886$	100927.	0.00431941
$887$	4.24313e7	1.81083	0.905415	−	0.424527i	$-0.139560\pi$
$887$	4.24313e7	1.81083	0.905415	+	0.424527i	$0.139560\pi$
$888$	2.78087e7	1.18345
$889$	−4.24658e7	−1.80213
$890$	2.95398e6	0.125006
$891$	−4.02601e6	−0.169895
$892$	8.71681e7	3.66814
$893$	−993841.	−0.0417050
$894$	3.57089e7	1.49428
$895$	1.83433e6	0.0765456
$896$	−4.06748e7	−1.69261
$897$	−8.64309e6	−0.358664
$898$	4.57930e7	1.89500
$899$	−3.96948e6	−0.163808
$900$	3.68681e7	1.51720
$901$	3.73114e7	1.53119
$902$	−5.51302e7	−2.25618
$903$	1.15121e7	0.469822
$904$	5.28802e7	2.15215
$905$	766379.	0.0311044
$906$	3.11492e7	1.26074
$907$	1.03649e7	0.418357	0.209179	−	0.977877i	$-0.432921\pi$
$907$	1.03649e7	0.418357	0.209179	+	0.977877i	$0.432921\pi$
$908$	880232.	0.0354309
$909$	−2.89977e7	−1.16400
$910$	−2.90173e6	−0.116159
$911$	−1.89959e6	−0.0758341	−0.0379171	−	0.999281i	$-0.512072\pi$
$911$	−1.89959e6	−0.0758341	−0.0379171	+	0.999281i	$0.512072\pi$
$912$	3.37550e7	1.34385
$913$	−1.38267e7	−0.548960
$914$	−7.25875e7	−2.87406
$915$	−1.35398e6	−0.0534638
$916$	351271.	0.0138326
$917$	5.50667e7	2.16255
$918$	−5.94403e7	−2.32795
$919$	4.23657e7	1.65473	0.827363	−	0.561668i	$-0.189840\pi$
$919$	4.23657e7	1.65473	0.827363	+	0.561668i	$0.189840\pi$
$920$	−8.41321e6	−0.327712
$921$	2.19154e7	0.851336
$922$	−5.92787e6	−0.229653
$923$	1.54906e7	0.598499
$924$	3.41281e7	1.31502
$925$	2.66664e7	1.02473
$926$	−2.92907e7	−1.12254
$927$	9.30285e6	0.355563
$928$	−7.25870e6	−0.276687
$929$	−2.47186e7	−0.939689	−0.469844	−	0.882749i	$-0.655690\pi$
$929$	−2.47186e7	−0.939689	−0.469844	+	0.882749i	$0.655690\pi$
$930$	1.13223e6	0.0429267
$931$	3.07019e7	1.16089
$932$	8.68184e7	3.27395
$933$	3.82515e6	0.143861
$934$	5.43259e7	2.03770
$935$	3.43641e6	0.128551
$936$	−1.81520e7	−0.677229
$937$	6.43909e6	0.239594	0.119797	−	0.992798i	$-0.461776\pi$
$937$	6.43909e6	0.239594	0.119797	+	0.992798i	$0.461776\pi$
$938$	7.55874e7	2.80506
$939$	1.02187e7	0.378208
$940$	−168548.	−0.00622164
$941$	−4.36383e7	−1.60655	−0.803274	−	0.595609i	$-0.796911\pi$
$941$	−4.36383e7	−1.60655	−0.803274	+	0.595609i	$0.796911\pi$
$942$	2.88392e7	1.05890
$943$	−5.91234e7	−2.16511
$944$	−7.50952e7	−2.74273
$945$	3.62188e6	0.131933
$946$	−2.71653e7	−0.986929
$947$	1.86942e7	0.677381	0.338691	−	0.940898i	$-0.390016\pi$
$947$	1.86942e7	0.677381	0.338691	+	0.940898i	$0.390016\pi$
$948$	−1.13270e7	−0.409349
$949$	1.46530e7	0.528155
$950$	7.73755e7	2.78160
$951$	−406871.	−0.0145883
$952$	−1.09081e8	−3.90084
$953$	−1.77335e7	−0.632504	−0.316252	−	0.948675i	$-0.602425\pi$
$953$	−1.77335e7	−0.632504	−0.316252	+	0.948675i	$0.602425\pi$
$954$	−3.83627e7	−1.36470
$955$	−1.03290e6	−0.0366478
$956$	9.58400e7	3.39158
$957$	−5.18934e6	−0.183161
$958$	2.51683e7	0.886012
$959$	−3.53313e7	−1.24055
$960$	−557627.	−0.0195283
$961$	−2.38200e7	−0.832018
$962$	−2.42721e7	−0.845608
$963$	2.57701e7	0.895469
$964$	−6.63455e7	−2.29942
$965$	−3.83906e6	−0.132711
$966$	5.34025e7	1.84128
$967$	1.49629e7	0.514576	0.257288	−	0.966335i	$-0.417171\pi$
$967$	1.49629e7	0.514576	0.257288	+	0.966335i	$0.417171\pi$
$968$	1.76772e7	0.606351
$969$	−3.53453e7	−1.20927
$970$	−1.14597e6	−0.0391059
$971$	3.68661e6	0.125481	0.0627407	−	0.998030i	$-0.480016\pi$
$971$	3.68661e6	0.125481	0.0627407	+	0.998030i	$0.480016\pi$
$972$	6.64561e7	2.25616
$973$	−6.43377e7	−2.17863
$974$	1.65063e7	0.557509
$975$	7.29207e6	0.245663
$976$	−4.24267e7	−1.42566
$977$	−1.89607e7	−0.635505	−0.317752	−	0.948174i	$-0.602928\pi$
$977$	−1.89607e7	−0.635505	−0.317752	+	0.948174i	$0.602928\pi$
$978$	−4.33477e7	−1.44917
$979$	1.64030e7	0.546973
$980$	5.20682e6	0.173184
$981$	2.09956e7	0.696555
$982$	−3.82346e7	−1.26526
$983$	966289.	0.0318950
$983$	966289.	0.0318950
$984$	5.20184e7	1.71265
$985$	6.03365e6	0.198148
$986$	3.06632e7	1.00444
$987$	578705.	0.0189088
$988$	−4.82687e7	−1.57316
$989$	−2.91329e7	−0.947094
$990$	−3.53323e6	−0.114573
$991$	1.66800e7	0.539525	0.269762	−	0.962927i	$-0.413055\pi$
$991$	1.66800e7	0.539525	0.269762	+	0.962927i	$0.413055\pi$
$992$	8.79420e6	0.283738
$993$	8.02685e6	0.258328
$994$	−9.57106e7	−3.07252
$995$	2.85206e6	0.0913274
$996$	2.41186e7	0.770377
$997$	2.98605e7	0.951390	0.475695	−	0.879610i	$-0.342197\pi$
$997$	2.98605e7	0.951390	0.475695	+	0.879610i	$0.342197\pi$
$998$	1.03316e8	3.28354
$999$	3.02959e7	0.960440

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.6.a.b.1.14	✓	218

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.6.a.b.1.14	✓	218	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q-10.0849 q^{2} +8.47019 q^{3} +69.7046 q^{4} +6.04415 q^{5} -85.4208 q^{6} -170.780 q^{7} -380.247 q^{8} -171.256 q^{9} +O(q^{10})\)	\(q-10.0849 q^{2} +8.47019 q^{3} +69.7046 q^{4} +6.04415 q^{5} -85.4208 q^{6} -170.780 q^{7} -380.247 q^{8} -171.256 q^{9} -60.9545 q^{10} -338.471 q^{11} +590.412 q^{12} -278.750 q^{13} +1722.29 q^{14} +51.1951 q^{15} +1604.19 q^{16} -1679.76 q^{17} +1727.09 q^{18} +2484.22 q^{19} +421.305 q^{20} -1446.54 q^{21} +3413.43 q^{22} +3660.67 q^{23} -3220.76 q^{24} -3088.47 q^{25} +2811.16 q^{26} -3508.83 q^{27} -11904.2 q^{28} +1810.08 q^{29} -516.296 q^{30} -2192.98 q^{31} -4010.15 q^{32} -2866.91 q^{33} +16940.2 q^{34} -1032.22 q^{35} -11937.3 q^{36} -8634.20 q^{37} -25053.0 q^{38} -2361.06 q^{39} -2298.27 q^{40} -16151.0 q^{41} +14588.2 q^{42} -7958.34 q^{43} -23593.0 q^{44} -1035.10 q^{45} -36917.4 q^{46} -400.062 q^{47} +13587.8 q^{48} +12358.8 q^{49} +31146.8 q^{50} -14227.9 q^{51} -19430.2 q^{52} -22212.3 q^{53} +35386.1 q^{54} -2045.77 q^{55} +64938.5 q^{56} +21041.8 q^{57} -18254.4 q^{58} -46812.0 q^{59} +3568.54 q^{60} -26447.5 q^{61} +22116.0 q^{62} +29247.1 q^{63} -10892.2 q^{64} -1684.81 q^{65} +28912.4 q^{66} +43887.6 q^{67} -117087. q^{68} +31006.6 q^{69} +10409.8 q^{70} -55571.6 q^{71} +65119.4 q^{72} -52566.9 q^{73} +87074.8 q^{74} -26159.9 q^{75} +173162. q^{76} +57804.0 q^{77} +23811.0 q^{78} -19184.9 q^{79} +9695.96 q^{80} +11894.7 q^{81} +162880. q^{82} +40850.4 q^{83} -100830. q^{84} -10152.7 q^{85} +80258.9 q^{86} +15331.7 q^{87} +128702. q^{88} -48462.0 q^{89} +10438.8 q^{90} +47604.9 q^{91} +255166. q^{92} -18575.0 q^{93} +4034.57 q^{94} +15015.0 q^{95} -33966.8 q^{96} +18800.4 q^{97} -124637. q^{98} +57965.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9}+O(q^{10}) \) 218 * q + 35 * q^2 + 70 * q^3 + 3685 * q^4 + 253 * q^5 + 529 * q^6 + 1567 * q^7 + 1695 * q^8 + 19812 * q^9	\( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9} + 2133 q^{10} + 1752 q^{11} + 3512 q^{12} + 5990 q^{13} + 2319 q^{14} + 4639 q^{15} + 66105 q^{16} + 10656 q^{17} + 11911 q^{18} + 11511 q^{19} + 10012 q^{20} + 12225 q^{21} + 19401 q^{22} + 9767 q^{23} + 21725 q^{24} + 185207 q^{25} + 7708 q^{26} + 23764 q^{27} + 77808 q^{28} + 25772 q^{29} + 15736 q^{30} + 35900 q^{31} + 60155 q^{32} + 70026 q^{33} + 17236 q^{34} + 28782 q^{35} + 382874 q^{36} + 126082 q^{37} + 62164 q^{38} + 54264 q^{39} + 102846 q^{40} + 70480 q^{41} + 102244 q^{42} + 137413 q^{43} + 116278 q^{44} + 93481 q^{45} + 126122 q^{46} + 63218 q^{47} + 124701 q^{48} + 732031 q^{49} + 131089 q^{50} + 109902 q^{51} + 229519 q^{52} + 102608 q^{53} + 149130 q^{54} + 167596 q^{55} + 87868 q^{56} + 408318 q^{57} + 304579 q^{58} + 67460 q^{59} + 150523 q^{60} + 195132 q^{61} + 132294 q^{62} + 374425 q^{63} + 1296639 q^{64} + 347092 q^{65} + 147397 q^{66} + 381238 q^{67} + 296321 q^{68} + 139362 q^{69} + 325675 q^{70} + 147818 q^{71} + 646059 q^{72} + 961992 q^{73} + 167410 q^{74} + 167324 q^{75} + 504875 q^{76} + 284328 q^{77} + 284295 q^{78} + 285792 q^{79} + 444932 q^{80} + 1980282 q^{81} + 336676 q^{82} + 276734 q^{83} + 378474 q^{84} + 1021245 q^{85} + 156051 q^{86} + 500457 q^{87} + 1068101 q^{88} + 398983 q^{89} + 463961 q^{90} + 273517 q^{91} + 577884 q^{92} + 967833 q^{93} + 224775 q^{94} + 482817 q^{95} + 780445 q^{96} + 1636277 q^{97} + 495958 q^{98} + 627643 q^{99}+O(q^{100}) \) 218 * q + 35 * q^2 + 70 * q^3 + 3685 * q^4 + 253 * q^5 + 529 * q^6 + 1567 * q^7 + 1695 * q^8 + 19812 * q^9 + 2133 * q^10 + 1752 * q^11 + 3512 * q^12 + 5990 * q^13 + 2319 * q^14 + 4639 * q^15 + 66105 * q^16 + 10656 * q^17 + 11911 * q^18 + 11511 * q^19 + 10012 * q^20 + 12225 * q^21 + 19401 * q^22 + 9767 * q^23 + 21725 * q^24 + 185207 * q^25 + 7708 * q^26 + 23764 * q^27 + 77808 * q^28 + 25772 * q^29 + 15736 * q^30 + 35900 * q^31 + 60155 * q^32 + 70026 * q^33 + 17236 * q^34 + 28782 * q^35 + 382874 * q^36 + 126082 * q^37 + 62164 * q^38 + 54264 * q^39 + 102846 * q^40 + 70480 * q^41 + 102244 * q^42 + 137413 * q^43 + 116278 * q^44 + 93481 * q^45 + 126122 * q^46 + 63218 * q^47 + 124701 * q^48 + 732031 * q^49 + 131089 * q^50 + 109902 * q^51 + 229519 * q^52 + 102608 * q^53 + 149130 * q^54 + 167596 * q^55 + 87868 * q^56 + 408318 * q^57 + 304579 * q^58 + 67460 * q^59 + 150523 * q^60 + 195132 * q^61 + 132294 * q^62 + 374425 * q^63 + 1296639 * q^64 + 347092 * q^65 + 147397 * q^66 + 381238 * q^67 + 296321 * q^68 + 139362 * q^69 + 325675 * q^70 + 147818 * q^71 + 646059 * q^72 + 961992 * q^73 + 167410 * q^74 + 167324 * q^75 + 504875 * q^76 + 284328 * q^77 + 284295 * q^78 + 285792 * q^79 + 444932 * q^80 + 1980282 * q^81 + 336676 * q^82 + 276734 * q^83 + 378474 * q^84 + 1021245 * q^85 + 156051 * q^86 + 500457 * q^87 + 1068101 * q^88 + 398983 * q^89 + 463961 * q^90 + 273517 * q^91 + 577884 * q^92 + 967833 * q^93 + 224775 * q^94 + 482817 * q^95 + 780445 * q^96 + 1636277 * q^97 + 495958 * q^98 + 627643 * q^99

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