LMFDB - Embedded newform 983.6.a.b.1.17

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			1.17
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)

$f(q)$	$=$	$q-9.77516 q^{2} -29.0216 q^{3} +63.5537 q^{4} -38.6585 q^{5} +283.690 q^{6} +235.286 q^{7} -308.442 q^{8} +599.250 q^{9} +O(q^{10})$	\(q-9.77516 q^{2} -29.0216 q^{3} +63.5537 q^{4} -38.6585 q^{5} +283.690 q^{6} +235.286 q^{7} -308.442 q^{8} +599.250 q^{9} +377.893 q^{10} -624.207 q^{11} -1844.43 q^{12} -530.110 q^{13} -2299.96 q^{14} +1121.93 q^{15} +981.354 q^{16} +771.018 q^{17} -5857.77 q^{18} +1343.02 q^{19} -2456.89 q^{20} -6828.36 q^{21} +6101.72 q^{22} -3775.26 q^{23} +8951.48 q^{24} -1630.52 q^{25} +5181.91 q^{26} -10338.9 q^{27} +14953.3 q^{28} -6319.31 q^{29} -10967.0 q^{30} -2041.95 q^{31} +277.264 q^{32} +18115.5 q^{33} -7536.83 q^{34} -9095.80 q^{35} +38084.6 q^{36} -10685.2 q^{37} -13128.2 q^{38} +15384.6 q^{39} +11923.9 q^{40} +16245.5 q^{41} +66748.3 q^{42} +13628.6 q^{43} -39670.7 q^{44} -23166.1 q^{45} +36903.7 q^{46} +5621.69 q^{47} -28480.4 q^{48} +38552.4 q^{49} +15938.6 q^{50} -22376.1 q^{51} -33690.5 q^{52} -18077.3 q^{53} +101065. q^{54} +24130.9 q^{55} -72572.1 q^{56} -38976.5 q^{57} +61772.2 q^{58} -38250.1 q^{59} +71302.8 q^{60} +16161.4 q^{61} +19960.4 q^{62} +140995. q^{63} -34113.6 q^{64} +20493.3 q^{65} -177081. q^{66} -24831.6 q^{67} +49001.1 q^{68} +109564. q^{69} +88912.9 q^{70} +32033.3 q^{71} -184834. q^{72} +64927.0 q^{73} +104449. q^{74} +47320.2 q^{75} +85353.9 q^{76} -146867. q^{77} -150387. q^{78} -105869. q^{79} -37937.7 q^{80} +154434. q^{81} -158803. q^{82} +60180.3 q^{83} -433968. q^{84} -29806.4 q^{85} -133222. q^{86} +183396. q^{87} +192532. q^{88} -128882. q^{89} +226453. q^{90} -124727. q^{91} -239932. q^{92} +59260.7 q^{93} -54952.9 q^{94} -51919.2 q^{95} -8046.63 q^{96} -21230.1 q^{97} -376856. q^{98} -374056. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−9.77516	−1.72802	−0.864010	−	0.503475i	$-0.832055\pi$
$2$	−9.77516	−1.72802	−0.864010	+	0.503475i	$0.832055\pi$
$3$	−29.0216	−1.86173	−0.930867	−	0.365359i	$-0.880946\pi$
$3$	−29.0216	−1.86173	−0.930867	+	0.365359i	$0.880946\pi$
$4$	63.5537	1.98605
$5$	−38.6585	−0.691545	−0.345772	−	0.938318i	$-0.612383\pi$
$5$	−38.6585	−0.691545	−0.345772	+	0.938318i	$0.612383\pi$
$6$	283.690	3.21711
$7$	235.286	1.81489	0.907446	−	0.420169i	$-0.138029\pi$
$7$	235.286	1.81489	0.907446	+	0.420169i	$0.138029\pi$
$8$	−308.442	−1.70392
$9$	599.250	2.46605
$10$	377.893	1.19500
$11$	−624.207	−1.55542	−0.777709	−	0.628625i	$-0.783618\pi$
$11$	−624.207	−1.55542	−0.777709	+	0.628625i	$0.783618\pi$
$12$	−1844.43	−3.69750
$13$	−530.110	−0.869977	−0.434989	−	0.900436i	$-0.643248\pi$
$13$	−530.110	−0.869977	−0.434989	+	0.900436i	$0.643248\pi$
$14$	−2299.96	−3.13617
$15$	1121.93	1.28747
$16$	981.354	0.958354
$17$	771.018	0.647057	0.323528	−	0.946218i	$-0.395131\pi$
$17$	771.018	0.647057	0.323528	+	0.946218i	$0.395131\pi$
$18$	−5857.77	−4.26139
$19$	1343.02	0.853490	0.426745	−	0.904372i	$-0.359660\pi$
$19$	1343.02	0.853490	0.426745	+	0.904372i	$0.359660\pi$
$20$	−2456.89	−1.37344
$21$	−6828.36	−3.37884
$22$	6101.72	2.68779
$23$	−3775.26	−1.48808	−0.744041	−	0.668134i	$-0.767093\pi$
$23$	−3775.26	−1.48808	−0.744041	+	0.668134i	$0.767093\pi$
$24$	8951.48	3.17224
$25$	−1630.52	−0.521766
$26$	5181.91	1.50334
$27$	−10338.9	−2.72940
$28$	14953.3	3.60447
$29$	−6319.31	−1.39532	−0.697661	−	0.716428i	$-0.745776\pi$
$29$	−6319.31	−1.39532	−0.697661	+	0.716428i	$0.745776\pi$
$30$	−10967.0	−2.22478
$31$	−2041.95	−0.381629	−0.190815	−	0.981626i	$-0.561113\pi$
$31$	−2041.95	−0.381629	−0.190815	+	0.981626i	$0.561113\pi$
$32$	277.264	0.0478651
$33$	18115.5	2.89577
$34$	−7536.83	−1.11813
$35$	−9095.80	−1.25508
$36$	38084.6	4.89771
$37$	−10685.2	−1.28315	−0.641576	−	0.767059i	$-0.721719\pi$
$37$	−10685.2	−1.28315	−0.641576	+	0.767059i	$0.721719\pi$
$38$	−13128.2	−1.47485
$39$	15384.6	1.61967
$40$	11923.9	1.17834
$41$	16245.5	1.50930	0.754648	−	0.656130i	$-0.227808\pi$
$41$	16245.5	1.50930	0.754648	+	0.656130i	$0.227808\pi$
$42$	66748.3	5.83871
$43$	13628.6	1.12404	0.562018	−	0.827125i	$-0.310025\pi$
$43$	13628.6	1.12404	0.562018	+	0.827125i	$0.310025\pi$
$44$	−39670.7	−3.08914
$45$	−23166.1	−1.70538
$46$	36903.7	2.57144
$47$	5621.69	0.371212	0.185606	−	0.982624i	$-0.440575\pi$
$47$	5621.69	0.371212	0.185606	+	0.982624i	$0.440575\pi$
$48$	−28480.4	−1.78420
$49$	38552.4	2.29383
$50$	15938.6	0.901622
$51$	−22376.1	−1.20465
$52$	−33690.5	−1.72782
$53$	−18077.3	−0.883982	−0.441991	−	0.897019i	$-0.645728\pi$
$53$	−18077.3	−0.883982	−0.441991	+	0.897019i	$0.645728\pi$
$54$	101065.	4.71645
$55$	24130.9	1.07564
$56$	−72572.1	−3.09243
$57$	−38976.5	−1.58897
$58$	61772.2	2.41114
$59$	−38250.1	−1.43055	−0.715275	−	0.698843i	$-0.753698\pi$
$59$	−38250.1	−1.43055	−0.715275	+	0.698843i	$0.753698\pi$
$60$	71302.8	2.55699
$61$	16161.4	0.556102	0.278051	−	0.960566i	$-0.410312\pi$
$61$	16161.4	0.556102	0.278051	+	0.960566i	$0.410312\pi$
$62$	19960.4	0.659463
$63$	140995.	4.47562
$64$	−34113.6	−1.04107
$65$	20493.3	0.601628
$66$	−177081.	−5.00395
$67$	−24831.6	−0.675799	−0.337899	−	0.941182i	$-0.609716\pi$
$67$	−24831.6	−0.675799	−0.337899	+	0.941182i	$0.609716\pi$
$68$	49001.1	1.28509
$69$	109564.	2.77041
$70$	88912.9	2.16880
$71$	32033.3	0.754146	0.377073	−	0.926183i	$-0.376931\pi$
$71$	32033.3	0.754146	0.377073	+	0.926183i	$0.376931\pi$
$72$	−184834.	−4.20195
$73$	64927.0	1.42600	0.712998	−	0.701166i	$-0.247337\pi$
$73$	64927.0	1.42600	0.712998	+	0.701166i	$0.247337\pi$
$74$	104449.	2.21731
$75$	47320.2	0.971389
$76$	85353.9	1.69508
$77$	−146867.	−2.82291
$78$	−150387.	−2.79881
$79$	−105869.	−1.90853	−0.954267	−	0.298957i	$-0.903361\pi$
$79$	−105869.	−1.90853	−0.954267	+	0.298957i	$0.903361\pi$
$80$	−37937.7	−0.662744
$81$	154434.	2.61536
$82$	−158803.	−2.60809
$83$	60180.3	0.958868	0.479434	−	0.877578i	$-0.340842\pi$
$83$	60180.3	0.958868	0.479434	+	0.877578i	$0.340842\pi$
$84$	−433968.	−6.71056
$85$	−29806.4	−0.447469
$86$	−133222.	−1.94236
$87$	183396.	2.59772
$88$	192532.	2.65031
$89$	−128882.	−1.72471	−0.862355	−	0.506303i	$-0.831012\pi$
$89$	−128882.	−1.72471	−0.862355	+	0.506303i	$0.831012\pi$
$90$	226453.	2.94694
$91$	−124727.	−1.57891
$92$	−239932.	−2.95541
$93$	59260.7	0.710492
$94$	−54952.9	−0.641462
$95$	−51919.2	−0.590227
$96$	−8046.63	−0.0891120
$97$	−21230.1	−0.229099	−0.114549	−	0.993418i	$-0.536542\pi$
$97$	−21230.1	−0.229099	−0.114549	+	0.993418i	$0.536542\pi$
$98$	−376856.	−3.96379
$99$	−374056.	−3.83574
$100$	−103625.	−1.03625
$101$	−113755.	−1.10960	−0.554802	−	0.831983i	$-0.687206\pi$
$101$	−113755.	−1.10960	−0.554802	+	0.831983i	$0.687206\pi$
$102$	218730.	2.08165
$103$	−46306.2	−0.430077	−0.215039	−	0.976606i	$-0.568988\pi$
$103$	−46306.2	−0.430077	−0.215039	+	0.976606i	$0.568988\pi$
$104$	163508.	1.48237
$105$	263974.	2.33662
$106$	176708.	1.52754
$107$	−33095.8	−0.279456	−0.139728	−	0.990190i	$-0.544623\pi$
$107$	−33095.8	−0.279456	−0.139728	+	0.990190i	$0.544623\pi$
$108$	−657078.	−5.42073
$109$	48363.1	0.389896	0.194948	−	0.980814i	$-0.437546\pi$
$109$	48363.1	0.389896	0.194948	+	0.980814i	$0.437546\pi$
$110$	−235884.	−1.85873
$111$	310101.	2.38889
$112$	230899.	1.73931
$113$	−125659.	−0.925758	−0.462879	−	0.886421i	$-0.653184\pi$
$113$	−125659.	−0.925758	−0.462879	+	0.886421i	$0.653184\pi$
$114$	381002.	2.74577
$115$	145946.	1.02908
$116$	−401615.	−2.77118
$117$	−317669.	−2.14541
$118$	373901.	2.47202
$119$	181410.	1.17434
$120$	−346051.	−2.19375
$121$	228583.	1.41932
$122$	−157980.	−0.960955
$123$	−471471.	−2.80991
$124$	−129774.	−0.757936
$125$	183841.	1.05237
$126$	−1.37825e6	−7.73395
$127$	19835.7	0.109128	0.0545642	−	0.998510i	$-0.482623\pi$
$127$	19835.7	0.109128	0.0545642	+	0.998510i	$0.482623\pi$
$128$	324594.	1.75112
$129$	−395523.	−2.09266
$130$	−200325.	−1.03963
$131$	195914.	0.997439	0.498719	−	0.866764i	$-0.333804\pi$
$131$	195914.	0.997439	0.498719	+	0.866764i	$0.333804\pi$
$132$	1.15130e6	5.75116
$133$	315994.	1.54899
$134$	242733.	1.16779
$135$	399688.	1.88750
$136$	−237815.	−1.10253
$137$	−297054.	−1.35218	−0.676088	−	0.736820i	$-0.736326\pi$
$137$	−297054.	−1.35218	−0.676088	+	0.736820i	$0.736326\pi$
$138$	−1.07100e6	−4.78733
$139$	67216.1	0.295078	0.147539	−	0.989056i	$-0.452865\pi$
$139$	67216.1	0.295078	0.147539	+	0.989056i	$0.452865\pi$
$140$	−578072.	−2.49265
$141$	−163150.	−0.691098
$142$	−313130.	−1.30318
$143$	330899.	1.35318
$144$	588077.	2.36335
$145$	244295.	0.964928
$146$	−634672.	−2.46415
$147$	−1.11885e6	−4.27050
$148$	−679084.	−2.54841
$149$	13690.9	0.0505203	0.0252602	−	0.999681i	$-0.491959\pi$
$149$	13690.9	0.0505203	0.0252602	+	0.999681i	$0.491959\pi$
$150$	−462562.	−1.67858
$151$	−53387.8	−0.190546	−0.0952730	−	0.995451i	$-0.530372\pi$
$151$	−53387.8	−0.190546	−0.0952730	+	0.995451i	$0.530372\pi$
$152$	−414244.	−1.45428
$153$	462033.	1.59568
$154$	1.43565e6	4.87805
$155$	78939.0	0.263914
$156$	977750.	3.21674
$157$	98746.6	0.319722	0.159861	−	0.987139i	$-0.448895\pi$
$157$	98746.6	0.319722	0.159861	+	0.987139i	$0.448895\pi$
$158$	1.03488e6	3.29798
$159$	524631.	1.64574
$160$	−10718.6	−0.0331008
$161$	−888265.	−2.70071
$162$	−1.50962e6	−4.51939
$163$	−462925.	−1.36471	−0.682357	−	0.731019i	$-0.739045\pi$
$163$	−462925.	−1.36471	−0.682357	+	0.731019i	$0.739045\pi$
$164$	1.03246e6	2.99754
$165$	−700317.	−2.00256
$166$	−588272.	−1.65694
$167$	−137707.	−0.382090	−0.191045	−	0.981581i	$-0.561188\pi$
$167$	−137707.	−0.382090	−0.191045	+	0.981581i	$0.561188\pi$
$168$	2.10616e6	5.75728
$169$	−90276.1	−0.243140
$170$	291363.	0.773235
$171$	804805.	2.10475
$172$	866148.	2.23239
$173$	27940.5	0.0709772	0.0354886	−	0.999370i	$-0.488701\pi$
$173$	27940.5	0.0709772	0.0354886	+	0.999370i	$0.488701\pi$
$174$	−1.79273e6	−4.48891
$175$	−383638.	−0.946949
$176$	−612568.	−1.49064
$177$	1.11008e6	2.66330
$178$	1.25984e6	2.98033
$179$	146981.	0.342868	0.171434	−	0.985196i	$-0.445160\pi$
$179$	146981.	0.342868	0.171434	+	0.985196i	$0.445160\pi$
$180$	−1.47229e6	−3.38698
$181$	13387.3	0.0303737	0.0151868	−	0.999885i	$-0.495166\pi$
$181$	13387.3	0.0303737	0.0151868	+	0.999885i	$0.495166\pi$
$182$	1.21923e6	2.72840
$183$	−469029.	−1.03531
$184$	1.16445e6	2.53557
$185$	413074.	0.887357
$186$	−579283.	−1.22774
$187$	−481275.	−1.00644
$188$	357279.	0.737247
$189$	−2.43261e6	−4.95356
$190$	507518.	1.01992
$191$	−680778.	−1.35028	−0.675138	−	0.737692i	$-0.735916\pi$
$191$	−680778.	−1.35028	−0.675138	+	0.737692i	$0.735916\pi$
$192$	990031.	1.93819
$193$	537971.	1.03960	0.519799	−	0.854288i	$-0.326007\pi$
$193$	537971.	1.03960	0.519799	+	0.854288i	$0.326007\pi$
$194$	207528.	0.395888
$195$	−594747.	−1.12007
$196$	2.45015e6	4.55567
$197$	145857.	0.267769	0.133885	−	0.990997i	$-0.457255\pi$
$197$	145857.	0.267769	0.133885	+	0.990997i	$0.457255\pi$
$198$	3.65646e6	6.62823
$199$	990489.	1.77303	0.886516	−	0.462697i	$-0.153118\pi$
$199$	990489.	1.77303	0.886516	+	0.462697i	$0.153118\pi$
$200$	502921.	0.889047
$201$	720651.	1.25816
$202$	1.11197e6	1.91742
$203$	−1.48684e6	−2.53236
$204$	−1.42209e6	−2.39249
$205$	−628028.	−1.04375
$206$	452651.	0.743182
$207$	−2.26232e6	−3.66969
$208$	−520226.	−0.833746
$209$	−838323.	−1.32753
$210$	−2.58039e6	−4.03773
$211$	−592766.	−0.916594	−0.458297	−	0.888799i	$-0.651540\pi$
$211$	−592766.	−0.916594	−0.458297	+	0.888799i	$0.651540\pi$
$212$	−1.14888e6	−1.75564
$213$	−929656.	−1.40402
$214$	323517.	0.482906
$215$	−526862.	−0.777321
$216$	3.18897e6	4.65067
$217$	−480443.	−0.692616
$218$	−472757.	−0.673747
$219$	−1.88428e6	−2.65483
$220$	1.53361e6	2.13628
$221$	−408725.	−0.562925
$222$	−3.03129e6	−4.12805
$223$	532982.	0.717712	0.358856	−	0.933393i	$-0.383167\pi$
$223$	532982.	0.717712	0.358856	+	0.933393i	$0.383167\pi$
$224$	65236.3	0.0868699
$225$	−977089.	−1.28670
$226$	1.22834e6	1.59973
$227$	714971.	0.920924	0.460462	−	0.887680i	$-0.347684\pi$
$227$	714971.	0.920924	0.460462	+	0.887680i	$0.347684\pi$
$228$	−2.47710e6	−3.15578
$229$	−898284.	−1.13194	−0.565972	−	0.824424i	$-0.691499\pi$
$229$	−898284.	−1.13194	−0.565972	+	0.824424i	$0.691499\pi$
$230$	−1.42664e6	−1.77826
$231$	4.26231e6	5.25551
$232$	1.94914e6	2.37752
$233$	−532515.	−0.642601	−0.321301	−	0.946977i	$-0.604120\pi$
$233$	−532515.	−0.642601	−0.321301	+	0.946977i	$0.604120\pi$
$234$	3.10526e6	3.70731
$235$	−217326.	−0.256710
$236$	−2.43094e6	−2.84115
$237$	3.07247e6	3.55318
$238$	−1.77331e6	−2.02928
$239$	−1.49346e6	−1.69122	−0.845610	−	0.533801i	$-0.820763\pi$
$239$	−1.49346e6	−1.69122	−0.845610	+	0.533801i	$0.820763\pi$
$240$	1.10101e6	1.23385
$241$	351687.	0.390044	0.195022	−	0.980799i	$-0.437522\pi$
$241$	351687.	0.390044	0.195022	+	0.980799i	$0.437522\pi$
$242$	−2.23444e6	−2.45262
$243$	−1.96956e6	−2.13970
$244$	1.02712e6	1.10445
$245$	−1.49038e6	−1.58629
$246$	4.60870e6	4.85557
$247$	−711949.	−0.742517
$248$	629825.	0.650266
$249$	−1.74652e6	−1.78516
$250$	−1.79708e6	−1.81851
$251$	−1.21049e6	−1.21276	−0.606381	−	0.795175i	$-0.707379\pi$
$251$	−1.21049e6	−1.21276	−0.606381	+	0.795175i	$0.707379\pi$
$252$	8.96076e6	8.88881
$253$	2.35654e6	2.31459
$254$	−193897.	−0.188576
$255$	865029.	0.833067
$256$	−2.08132e6	−1.98490
$257$	1.56850e6	1.48133	0.740663	−	0.671877i	$-0.234512\pi$
$257$	1.56850e6	1.48133	0.740663	+	0.671877i	$0.234512\pi$
$258$	3.86630e6	3.61615
$259$	−2.51408e6	−2.32878
$260$	1.30242e6	1.19487
$261$	−3.78685e6	−3.44094
$262$	−1.91509e6	−1.72359
$263$	−41986.9	−0.0374304	−0.0187152	−	0.999825i	$-0.505958\pi$
$263$	−41986.9	−0.0374304	−0.0187152	+	0.999825i	$0.505958\pi$
$264$	−5.58757e6	−4.93416
$265$	698841.	0.611313
$266$	−3.08889e6	−2.67669
$267$	3.74035e6	3.21095
$268$	−1.57814e6	−1.34217
$269$	−2.09867e6	−1.76833	−0.884167	−	0.467171i	$-0.845273\pi$
$269$	−2.09867e6	−1.76833	−0.884167	+	0.467171i	$0.845273\pi$
$270$	−3.90701e6	−3.26164
$271$	1.09532e6	0.905976	0.452988	−	0.891517i	$-0.350358\pi$
$271$	1.09532e6	0.905976	0.452988	+	0.891517i	$0.350358\pi$
$272$	756642.	0.620109
$273$	3.61978e6	2.93952
$274$	2.90375e6	2.33659
$275$	1.01778e6	0.811564
$276$	6.96319e6	5.50219
$277$	1.54564e6	1.21034	0.605172	−	0.796094i	$-0.293104\pi$
$277$	1.54564e6	1.21034	0.605172	+	0.796094i	$0.293104\pi$
$278$	−657048.	−0.509900
$279$	−1.22364e6	−0.941118
$280$	2.80553e6	2.13855
$281$	−1.21348e6	−0.916783	−0.458391	−	0.888750i	$-0.651574\pi$
$281$	−1.21348e6	−0.916783	−0.458391	+	0.888750i	$0.651574\pi$
$282$	1.59482e6	1.19423
$283$	−800310.	−0.594008	−0.297004	−	0.954876i	$-0.595987\pi$
$283$	−800310.	−0.594008	−0.297004	+	0.954876i	$0.595987\pi$
$284$	2.03583e6	1.49777
$285$	1.50677e6	1.09884
$286$	−3.23459e6	−2.33832
$287$	3.82234e6	2.73921
$288$	166151.	0.118038
$289$	−825388.	−0.581317
$290$	−2.38802e6	−1.66741
$291$	616131.	0.426521
$292$	4.12635e6	2.83210
$293$	−2.28362e6	−1.55401	−0.777006	−	0.629494i	$-0.783262\pi$
$293$	−2.28362e6	−1.55401	−0.777006	+	0.629494i	$0.783262\pi$
$294$	1.09370e7	7.37952
$295$	1.47869e6	0.989289
$296$	3.29577e6	2.18639
$297$	6.45364e6	4.24535
$298$	−133831.	−0.0873001
$299$	2.00130e6	1.29460
$300$	3.00737e6	1.92923
$301$	3.20662e6	2.04000
$302$	521874.	0.329267
$303$	3.30135e6	2.06579
$304$	1.31798e6	0.817945
$305$	−624776.	−0.384569
$306$	−4.51645e6	−2.75736
$307$	1.15505e6	0.699447	0.349724	−	0.936853i	$-0.386276\pi$
$307$	1.15505e6	0.699447	0.349724	+	0.936853i	$0.386276\pi$
$308$	−9.33395e6	−5.60646
$309$	1.34388e6	0.800689
$310$	−771641.	−0.456048
$311$	2.32383e6	1.36240	0.681199	−	0.732098i	$-0.261459\pi$
$311$	2.32383e6	1.36240	0.681199	+	0.732098i	$0.261459\pi$
$312$	−4.74527e6	−2.75978
$313$	−1.05611e6	−0.609323	−0.304661	−	0.952461i	$-0.598543\pi$
$313$	−1.05611e6	−0.609323	−0.304661	+	0.952461i	$0.598543\pi$
$314$	−965264.	−0.552487
$315$	−5.45066e6	−3.09509
$316$	−6.72835e6	−3.79045
$317$	864859.	0.483390	0.241695	−	0.970352i	$-0.422297\pi$
$317$	864859.	0.483390	0.241695	+	0.970352i	$0.422297\pi$
$318$	−5.12835e6	−2.84387
$319$	3.94456e6	2.17031
$320$	1.31878e6	0.719943
$321$	960493.	0.520273
$322$	8.68293e6	4.66688
$323$	1.03549e6	0.552257
$324$	9.81486e6	5.19424
$325$	864355.	0.453924
$326$	4.52516e6	2.35825
$327$	−1.40357e6	−0.725882
$328$	−5.01081e6	−2.57172
$329$	1.32270e6	0.673710
$330$	6.84571e6	3.46046
$331$	−2.55723e6	−1.28292	−0.641461	−	0.767155i	$-0.721671\pi$
$331$	−2.55723e6	−1.28292	−0.641461	+	0.767155i	$0.721671\pi$
$332$	3.82468e6	1.90436
$333$	−6.40311e6	−3.16432
$334$	1.34611e6	0.660259
$335$	959952.	0.467345
$336$	−6.70104e6	−3.23813
$337$	−2.66774e6	−1.27959	−0.639793	−	0.768547i	$-0.720980\pi$
$337$	−2.66774e6	−1.27959	−0.639793	+	0.768547i	$0.720980\pi$
$338$	882463.	0.420150
$339$	3.64682e6	1.72351
$340$	−1.89431e6	−0.888697
$341$	1.27460e6	0.593593
$342$	−7.86710e6	−3.63705
$343$	5.11640e6	2.34817
$344$	−4.20364e6	−1.91527
$345$	−4.23558e6	−1.91586
$346$	−273123.	−0.122650
$347$	−34362.5	−0.0153201	−0.00766003	−	0.999971i	$-0.502438\pi$
$347$	−34362.5	−0.0153201	−0.00766003	+	0.999971i	$0.502438\pi$
$348$	1.16555e7	5.15921
$349$	−4.14118e6	−1.81996	−0.909978	−	0.414656i	$-0.863902\pi$
$349$	−4.14118e6	−1.81996	−0.909978	+	0.414656i	$0.863902\pi$
$350$	3.75012e6	1.63635
$351$	5.48078e6	2.37451
$352$	−173070.	−0.0744502
$353$	−1.57353e6	−0.672108	−0.336054	−	0.941843i	$-0.609092\pi$
$353$	−1.57353e6	−0.672108	−0.336054	+	0.941843i	$0.609092\pi$
$354$	−1.08512e7	−4.60224
$355$	−1.23836e6	−0.521526
$356$	−8.19091e6	−3.42537
$357$	−5.26479e6	−2.18630
$358$	−1.43676e6	−0.592483
$359$	−501946.	−0.205552	−0.102776	−	0.994705i	$-0.532772\pi$
$359$	−501946.	−0.205552	−0.102776	+	0.994705i	$0.532772\pi$
$360$	7.14542e6	2.90584
$361$	−672396.	−0.271555
$362$	−130863.	−0.0524864
$363$	−6.63385e6	−2.64240
$364$	−7.92689e6	−3.13581
$365$	−2.50998e6	−0.986140
$366$	4.58483e6	1.78904
$367$	−2.54328e6	−0.985664	−0.492832	−	0.870125i	$-0.664038\pi$
$367$	−2.54328e6	−0.985664	−0.492832	+	0.870125i	$0.664038\pi$
$368$	−3.70487e6	−1.42611
$369$	9.73514e6	3.72200
$370$	−4.03786e6	−1.53337
$371$	−4.25333e6	−1.60433
$372$	3.76624e6	1.41108
$373$	4.98406e6	1.85486	0.927429	−	0.373999i	$-0.122014\pi$
$373$	4.98406e6	1.85486	0.927429	+	0.373999i	$0.122014\pi$
$374$	4.70454e6	1.73915
$375$	−5.33536e6	−1.95923
$376$	−1.73397e6	−0.632516
$377$	3.34993e6	1.21390
$378$	2.37791e7	8.55985
$379$	−2.28746e6	−0.818005	−0.409002	−	0.912533i	$-0.634123\pi$
$379$	−2.28746e6	−0.818005	−0.409002	+	0.912533i	$0.634123\pi$
$380$	−3.29966e6	−1.17222
$381$	−575662.	−0.203168
$382$	6.65472e6	2.33330
$383$	−320412.	−0.111612	−0.0558061	−	0.998442i	$-0.517773\pi$
$383$	−320412.	−0.111612	−0.0558061	+	0.998442i	$0.517773\pi$
$384$	−9.42021e6	−3.26011
$385$	5.67767e6	1.95217
$386$	−5.25875e6	−1.79645
$387$	8.16695e6	2.77193
$388$	−1.34925e6	−0.455003
$389$	−88522.5	−0.0296606	−0.0148303	−	0.999890i	$-0.504721\pi$
$389$	−88522.5	−0.0296606	−0.0148303	+	0.999890i	$0.504721\pi$
$390$	5.81374e6	1.93551
$391$	−2.91079e6	−0.962874
$392$	−1.18912e7	−3.90851
$393$	−5.68571e6	−1.85696
$394$	−1.42577e6	−0.462711
$395$	4.09273e6	1.31984
$396$	−2.37727e7	−7.61798
$397$	−2.14606e6	−0.683386	−0.341693	−	0.939812i	$-0.611000\pi$
$397$	−2.14606e6	−0.683386	−0.341693	+	0.939812i	$0.611000\pi$
$398$	−9.68218e6	−3.06384
$399$	−9.17063e6	−2.88381
$400$	−1.60012e6	−0.500036
$401$	3.56906e6	1.10839	0.554195	−	0.832387i	$-0.313026\pi$
$401$	3.56906e6	1.10839	0.554195	+	0.832387i	$0.313026\pi$
$402$	−7.04448e6	−2.17412
$403$	1.08246e6	0.332009
$404$	−7.22956e6	−2.20373
$405$	−5.97020e6	−1.80864
$406$	1.45341e7	4.37597
$407$	6.66978e6	1.99584
$408$	6.90175e6	2.05262
$409$	348490.	0.103011	0.0515053	−	0.998673i	$-0.483598\pi$
$409$	348490.	0.103011	0.0515053	+	0.998673i	$0.483598\pi$
$410$	6.13908e6	1.80361
$411$	8.62096e6	2.51739
$412$	−2.94293e6	−0.854156
$413$	−8.99971e6	−2.59629
$414$	2.21146e7	6.34129
$415$	−2.32648e6	−0.663100
$416$	−146981.	−0.0416415
$417$	−1.95072e6	−0.549356
$418$	8.19473e6	2.29400
$419$	5.59777e6	1.55769	0.778843	−	0.627219i	$-0.215807\pi$
$419$	5.59777e6	1.55769	0.778843	+	0.627219i	$0.215807\pi$
$420$	1.67765e7	4.64066
$421$	−1.42420e6	−0.391621	−0.195811	−	0.980642i	$-0.562734\pi$
$421$	−1.42420e6	−0.391621	−0.195811	+	0.980642i	$0.562734\pi$
$422$	5.79438e6	1.58389
$423$	3.36880e6	0.915429
$424$	5.57580e6	1.50623
$425$	−1.25716e6	−0.337612
$426$	9.08753e6	2.42617
$427$	3.80255e6	1.00926
$428$	−2.10336e6	−0.555015
$429$	−9.60319e6	−2.51926
$430$	5.15016e6	1.34323
$431$	−4.76665e6	−1.23601	−0.618003	−	0.786176i	$-0.712058\pi$
$431$	−4.76665e6	−1.23601	−0.618003	+	0.786176i	$0.712058\pi$
$432$	−1.01462e7	−2.61573
$433$	6.57306e6	1.68480	0.842398	−	0.538855i	$-0.181143\pi$
$433$	6.57306e6	1.68480	0.842398	+	0.538855i	$0.181143\pi$
$434$	4.69641e6	1.19685
$435$	−7.08982e6	−1.79644
$436$	3.07366e6	0.774353
$437$	−5.07025e6	−1.27006
$438$	1.84192e7	4.58759
$439$	−7.26461e6	−1.79908	−0.899541	−	0.436837i	$-0.856099\pi$
$439$	−7.26461e6	−1.79908	−0.899541	+	0.436837i	$0.856099\pi$
$440$	−7.44300e6	−1.83280
$441$	2.31026e7	5.65671
$442$	3.99535e6	0.972745
$443$	−329900.	−0.0798681	−0.0399341	−	0.999202i	$-0.512715\pi$
$443$	−329900.	−0.0798681	−0.0399341	+	0.999202i	$0.512715\pi$
$444$	1.97081e7	4.74446
$445$	4.98238e6	1.19271
$446$	−5.20998e6	−1.24022
$447$	−397331.	−0.0940554
$448$	−8.02646e6	−1.88942
$449$	4.78756e6	1.12072	0.560362	−	0.828248i	$-0.310662\pi$
$449$	4.78756e6	1.12072	0.560362	+	0.828248i	$0.310662\pi$
$450$	9.55120e6	2.22345
$451$	−1.01406e7	−2.34759
$452$	−7.98609e6	−1.83860
$453$	1.54940e6	0.354746
$454$	−6.98895e6	−1.59137
$455$	4.82178e6	1.09189
$456$	1.20220e7	2.70748
$457$	2.27176e6	0.508829	0.254415	−	0.967095i	$-0.418117\pi$
$457$	2.27176e6	0.508829	0.254415	+	0.967095i	$0.418117\pi$
$458$	8.78087e6	1.95602
$459$	−7.97151e6	−1.76607
$460$	9.27540e6	2.04380
$461$	−2.74925e6	−0.602507	−0.301254	−	0.953544i	$-0.597405\pi$
$461$	−2.74925e6	−0.602507	−0.301254	+	0.953544i	$0.597405\pi$
$462$	−4.16648e7	−9.08163
$463$	−3.53960e6	−0.767364	−0.383682	−	0.923465i	$-0.625344\pi$
$463$	−3.53960e6	−0.767364	−0.383682	+	0.923465i	$0.625344\pi$
$464$	−6.20148e6	−1.33721
$465$	−2.29093e6	−0.491337
$466$	5.20541e6	1.11043
$467$	2.15889e6	0.458078	0.229039	−	0.973417i	$-0.426442\pi$
$467$	2.15889e6	0.458078	0.229039	+	0.973417i	$0.426442\pi$
$468$	−2.01890e7	−4.26089
$469$	−5.84252e6	−1.22650
$470$	2.12440e6	0.443600
$471$	−2.86578e6	−0.595238
$472$	1.17980e7	2.43754
$473$	−8.50707e6	−1.74834
$474$	−3.00339e7	−6.13997
$475$	−2.18982e6	−0.445322
$476$	1.15293e7	2.33230
$477$	−1.08328e7	−2.17995
$478$	1.45988e7	2.92246
$479$	−3.37164e6	−0.671432	−0.335716	−	0.941963i	$-0.608978\pi$
$479$	−3.37164e6	−0.671432	−0.335716	+	0.941963i	$0.608978\pi$
$480$	311071.	0.0616249
$481$	5.66433e6	1.11631
$482$	−3.43779e6	−0.674003
$483$	2.57788e7	5.02800
$484$	1.45273e7	2.81885
$485$	820725.	0.158432
$486$	1.92527e7	3.69745
$487$	−7.09633e6	−1.35585	−0.677925	−	0.735131i	$-0.737121\pi$
$487$	−7.09633e6	−1.35585	−0.677925	+	0.735131i	$0.737121\pi$
$488$	−4.98486e6	−0.947553
$489$	1.34348e7	2.54073
$490$	1.45687e7	2.74114
$491$	1.03704e6	0.194130	0.0970652	−	0.995278i	$-0.469054\pi$
$491$	1.03704e6	0.194130	0.0970652	+	0.995278i	$0.469054\pi$
$492$	−2.99637e7	−5.58062
$493$	−4.87230e6	−0.902853
$494$	6.95941e6	1.28308
$495$	1.44605e7	2.65258
$496$	−2.00388e6	−0.365736
$497$	7.53698e6	1.36869
$498$	1.70726e7	3.08479
$499$	−1.03777e7	−1.86574	−0.932869	−	0.360217i	$-0.882703\pi$
$499$	−1.03777e7	−1.86574	−0.932869	+	0.360217i	$0.882703\pi$
$500$	1.16838e7	2.09006
$501$	3.99647e6	0.711349
$502$	1.18327e7	2.09568
$503$	−6.89058e6	−1.21433	−0.607163	−	0.794577i	$-0.707693\pi$
$503$	−6.89058e6	−1.21433	−0.607163	+	0.794577i	$0.707693\pi$
$504$	−4.34889e7	−7.62609
$505$	4.39761e6	0.767340
$506$	−2.30356e7	−3.99966
$507$	2.61995e6	0.452661
$508$	1.26063e6	0.216735
$509$	−4.64224e6	−0.794205	−0.397103	−	0.917774i	$-0.629984\pi$
$509$	−4.64224e6	−0.794205	−0.397103	+	0.917774i	$0.629984\pi$
$510$	−8.45579e6	−1.43956
$511$	1.52764e7	2.58803
$512$	9.95821e6	1.67883
$513$	−1.38854e7	−2.32951
$514$	−1.53323e7	−2.55976
$515$	1.79013e6	0.297418
$516$	−2.51370e7	−4.15612
$517$	−3.50910e6	−0.577390
$518$	2.45755e7	4.02418
$519$	−810876.	−0.132141
$520$	−6.32100e6	−1.02513
$521$	−7.13891e6	−1.15223	−0.576113	−	0.817370i	$-0.695431\pi$
$521$	−7.13891e6	−1.15223	−0.576113	+	0.817370i	$0.695431\pi$
$522$	3.70170e7	5.94601
$523$	−3.66384e6	−0.585709	−0.292854	−	0.956157i	$-0.594605\pi$
$523$	−3.66384e6	−0.585709	−0.292854	+	0.956157i	$0.594605\pi$
$524$	1.24510e7	1.98097
$525$	1.11338e7	1.76297
$526$	410429.	0.0646805
$527$	−1.57438e6	−0.246936
$528$	1.77777e7	2.77517
$529$	7.81623e6	1.21439
$530$	−6.83128e6	−1.05636
$531$	−2.29214e7	−3.52781
$532$	2.00826e7	3.07638
$533$	−8.61193e6	−1.31305
$534$	−3.65625e7	−5.54859
$535$	1.27944e6	0.193257
$536$	7.65911e6	1.15151
$537$	−4.26560e6	−0.638329
$538$	2.05149e7	3.05572
$539$	−2.40647e7	−3.56787
$540$	2.54017e7	3.74867
$541$	4.35982e6	0.640435	0.320217	−	0.947344i	$-0.396244\pi$
$541$	4.35982e6	0.640435	0.320217	+	0.947344i	$0.396244\pi$
$542$	−1.07069e7	−1.56554
$543$	−388521.	−0.0565477
$544$	213776.	0.0309714
$545$	−1.86965e6	−0.269630
$546$	−3.53840e7	−5.07955
$547$	−1.74501e6	−0.249362	−0.124681	−	0.992197i	$-0.539791\pi$
$547$	−1.74501e6	−0.249362	−0.124681	+	0.992197i	$0.539791\pi$
$548$	−1.88789e7	−2.68550
$549$	9.68473e6	1.37138
$550$	−9.94897e6	−1.40240
$551$	−8.48696e6	−1.19089
$552$	−3.37941e7	−4.72056
$553$	−2.49094e7	−3.46378
$554$	−1.51089e7	−2.09150
$555$	−1.19880e7	−1.65202
$556$	4.27183e6	0.586040
$557$	1.40973e6	0.192529	0.0962647	−	0.995356i	$-0.469310\pi$
$557$	1.40973e6	0.192529	0.0962647	+	0.995356i	$0.469310\pi$
$558$	1.19613e7	1.62627
$559$	−7.22466e6	−0.977886
$560$	−8.92621e6	−1.20281
$561$	1.39673e7	1.87373
$562$	1.18619e7	1.58422
$563$	8.95869e6	1.19117	0.595585	−	0.803293i	$-0.296920\pi$
$563$	8.95869e6	1.19117	0.595585	+	0.803293i	$0.296920\pi$
$564$	−1.03688e7	−1.37256
$565$	4.85779e6	0.640203
$566$	7.82316e6	1.02646
$567$	3.63362e7	4.74659
$568$	−9.88042e6	−1.28500
$569$	−6.28938e6	−0.814380	−0.407190	−	0.913343i	$-0.633491\pi$
$569$	−6.28938e6	−0.814380	−0.407190	+	0.913343i	$0.633491\pi$
$570$	−1.47290e7	−1.89883
$571$	−8.03994e6	−1.03196	−0.515980	−	0.856601i	$-0.672572\pi$
$571$	−8.03994e6	−1.03196	−0.515980	+	0.856601i	$0.672572\pi$
$572$	2.10298e7	2.68748
$573$	1.97572e7	2.51385
$574$	−3.73640e7	−4.73341
$575$	6.15563e6	0.776431
$576$	−2.04426e7	−2.56732
$577$	4.76595e6	0.595950	0.297975	−	0.954574i	$-0.403689\pi$
$577$	4.76595e6	0.595950	0.297975	+	0.954574i	$0.403689\pi$
$578$	8.06829e6	1.00453
$579$	−1.56128e7	−1.93546
$580$	1.55259e7	1.91640
$581$	1.41596e7	1.74024
$582$	−6.02278e6	−0.737037
$583$	1.12840e7	1.37496
$584$	−2.00262e7	−2.42978
$585$	1.22806e7	1.48365
$586$	2.23227e7	2.68536
$587$	1.24637e7	1.49297	0.746486	−	0.665401i	$-0.231739\pi$
$587$	1.24637e7	1.49297	0.746486	+	0.665401i	$0.231739\pi$
$588$	−7.11072e7	−8.48145
$589$	−2.74239e6	−0.325717
$590$	−1.44545e7	−1.70951
$591$	−4.23299e6	−0.498515
$592$	−1.04860e7	−1.22971
$593$	8.31370e6	0.970863	0.485431	−	0.874275i	$-0.338663\pi$
$593$	8.31370e6	0.970863	0.485431	+	0.874275i	$0.338663\pi$
$594$	−6.30853e7	−7.33605
$595$	−7.01303e6	−0.812107
$596$	870107.	0.100336
$597$	−2.87455e7	−3.30091
$598$	−1.95631e7	−2.23709
$599$	1.49149e7	1.69845	0.849224	−	0.528032i	$-0.177070\pi$
$599$	1.49149e7	1.69845	0.849224	+	0.528032i	$0.177070\pi$
$600$	−1.45955e7	−1.65517
$601$	5.55504e6	0.627337	0.313669	−	0.949533i	$-0.398442\pi$
$601$	5.55504e6	0.627337	0.313669	+	0.949533i	$0.398442\pi$
$602$	−3.13452e7	−3.52517
$603$	−1.48803e7	−1.66655
$604$	−3.39299e6	−0.378434
$605$	−8.83670e6	−0.981526
$606$	−3.22712e7	−3.56972
$607$	800456.	0.0881792	0.0440896	−	0.999028i	$-0.485961\pi$
$607$	800456.	0.0881792	0.0440896	+	0.999028i	$0.485961\pi$
$608$	372371.	0.0408524
$609$	4.31505e7	4.71458
$610$	6.10728e6	0.664543
$611$	−2.98012e6	−0.322946
$612$	2.93639e7	3.16910
$613$	7.03532e6	0.756193	0.378096	−	0.925766i	$-0.376579\pi$
$613$	7.03532e6	0.756193	0.378096	+	0.925766i	$0.376579\pi$
$614$	−1.12908e7	−1.20866
$615$	1.82264e7	1.94318
$616$	4.53000e7	4.81002
$617$	7.84863e6	0.830005	0.415003	−	0.909820i	$-0.363781\pi$
$617$	7.84863e6	0.830005	0.415003	+	0.909820i	$0.363781\pi$
$618$	−1.31366e7	−1.38361
$619$	−1.00331e6	−0.105247	−0.0526234	−	0.998614i	$-0.516758\pi$
$619$	−1.00331e6	−0.105247	−0.0526234	+	0.998614i	$0.516758\pi$
$620$	5.01686e6	0.524147
$621$	3.90322e7	4.06157
$622$	−2.27159e7	−2.35425
$623$	−3.03240e7	−3.13016
$624$	1.50978e7	1.55221
$625$	−2.01166e6	−0.205994
$626$	1.03236e7	1.05292
$627$	2.43294e7	2.47151
$628$	6.27571e6	0.634986
$629$	−8.23848e6	−0.830272
$630$	5.32811e7	5.34837
$631$	−8.31526e6	−0.831385	−0.415693	−	0.909505i	$-0.636461\pi$
$631$	−8.31526e6	−0.831385	−0.415693	+	0.909505i	$0.636461\pi$
$632$	3.26544e7	3.25199
$633$	1.72030e7	1.70645
$634$	−8.45414e6	−0.835307
$635$	−766818.	−0.0754671
$636$	3.33422e7	3.26853
$637$	−2.04370e7	−1.99558
$638$	−3.85587e7	−3.75034
$639$	1.91960e7	1.85976
$640$	−1.25483e7	−1.21098
$641$	−277066.	−0.0266341	−0.0133171	−	0.999911i	$-0.504239\pi$
$641$	−277066.	−0.0266341	−0.0133171	+	0.999911i	$0.504239\pi$
$642$	−9.38897e6	−0.899042
$643$	1.91774e7	1.82920	0.914600	−	0.404359i	$-0.132505\pi$
$643$	1.91774e7	1.82920	0.914600	+	0.404359i	$0.132505\pi$
$644$	−5.64525e7	−5.36375
$645$	1.52903e7	1.44716
$646$	−1.01221e7	−0.954310
$647$	4.60517e6	0.432499	0.216250	−	0.976338i	$-0.430618\pi$
$647$	4.60517e6	0.432499	0.216250	+	0.976338i	$0.430618\pi$
$648$	−4.76340e7	−4.45636
$649$	2.38760e7	2.22510
$650$	−8.44920e6	−0.784391
$651$	1.39432e7	1.28947
$652$	−2.94206e7	−2.71039
$653$	5.51960e6	0.506553	0.253276	−	0.967394i	$-0.418492\pi$
$653$	5.51960e6	0.506553	0.253276	+	0.967394i	$0.418492\pi$
$654$	1.37202e7	1.25434
$655$	−7.57373e6	−0.689773
$656$	1.59426e7	1.44644
$657$	3.89076e7	3.51658
$658$	−1.29296e7	−1.16418
$659$	1.58096e7	1.41810	0.709049	−	0.705159i	$-0.249124\pi$
$659$	1.58096e7	1.41810	0.709049	+	0.705159i	$0.249124\pi$
$660$	−4.45077e7	−3.97718
$661$	7.44603e6	0.662859	0.331429	−	0.943480i	$-0.392469\pi$
$661$	7.44603e6	0.662859	0.331429	+	0.943480i	$0.392469\pi$
$662$	2.49974e7	2.21692
$663$	1.18618e7	1.04802
$664$	−1.85621e7	−1.63383
$665$	−1.22158e7	−1.07120
$666$	6.25914e7	5.46801
$667$	2.38570e7	2.07635
$668$	−8.75180e6	−0.758850
$669$	−1.54680e7	−1.33619
$670$	−9.38369e6	−0.807582
$671$	−1.00881e7	−0.864971
$672$	−1.89326e6	−0.161729
$673$	−3.23941e6	−0.275695	−0.137847	−	0.990453i	$-0.544018\pi$
$673$	−3.23941e6	−0.275695	−0.137847	+	0.990453i	$0.544018\pi$
$674$	2.60776e7	2.21115
$675$	1.68578e7	1.42411
$676$	−5.73738e6	−0.482888
$677$	2.41450e6	0.202467	0.101234	−	0.994863i	$-0.467721\pi$
$677$	2.41450e6	0.202467	0.101234	+	0.994863i	$0.467721\pi$
$678$	−3.56482e7	−2.97827
$679$	−4.99515e6	−0.415790
$680$	9.19357e6	0.762451
$681$	−2.07496e7	−1.71451
$682$	−1.24594e7	−1.02574
$683$	−1.22726e7	−1.00667	−0.503334	−	0.864092i	$-0.667893\pi$
$683$	−1.22726e7	−1.00667	−0.503334	+	0.864092i	$0.667893\pi$
$684$	5.11484e7	4.18015
$685$	1.14837e7	0.935091
$686$	−5.00136e7	−4.05768
$687$	2.60696e7	2.10738
$688$	1.33745e7	1.07722
$689$	9.58296e6	0.769044
$690$	4.14034e7	3.31065
$691$	−2.17798e7	−1.73524	−0.867618	−	0.497232i	$-0.834350\pi$
$691$	−2.17798e7	−1.73524	−0.867618	+	0.497232i	$0.834350\pi$
$692$	1.77572e6	0.140964
$693$	−8.80102e7	−6.96145
$694$	335899.	0.0264734
$695$	−2.59848e6	−0.204059
$696$	−5.65671e7	−4.42630
$697$	1.25256e7	0.976600
$698$	4.04807e7	3.14492
$699$	1.54544e7	1.19635
$700$	−2.43816e7	−1.88069
$701$	−2.68648e6	−0.206485	−0.103242	−	0.994656i	$-0.532922\pi$
$701$	−2.68648e6	−0.206485	−0.103242	+	0.994656i	$0.532922\pi$
$702$	−5.35755e7	−4.10320
$703$	−1.43504e7	−1.09516
$704$	2.12940e7	1.61929
$705$	6.30715e6	0.477925
$706$	1.53815e7	1.16142
$707$	−2.67650e7	−2.01381
$708$	7.05496e7	5.28946
$709$	1.07907e7	0.806187	0.403094	−	0.915159i	$-0.367935\pi$
$709$	1.07907e7	0.806187	0.403094	+	0.915159i	$0.367935\pi$
$710$	1.21052e7	0.901207
$711$	−6.34418e7	−4.70654
$712$	3.97526e7	2.93877
$713$	7.70891e6	0.567896
$714$	5.14642e7	3.77798
$715$	−1.27921e7	−0.935783
$716$	9.34116e6	0.680955
$717$	4.33427e7	3.14860
$718$	4.90660e6	0.355197
$719$	−1.54858e7	−1.11715	−0.558576	−	0.829453i	$-0.688652\pi$
$719$	−1.54858e7	−1.11715	−0.558576	+	0.829453i	$0.688652\pi$
$720$	−2.27342e7	−1.63436
$721$	−1.08952e7	−0.780543
$722$	6.57278e6	0.469252
$723$	−1.02065e7	−0.726157
$724$	850815.	0.0603238
$725$	1.03037e7	0.728032
$726$	6.48469e7	4.56612
$727$	−6.09629e6	−0.427789	−0.213895	−	0.976857i	$-0.568615\pi$
$727$	−6.09629e6	−0.427789	−0.213895	+	0.976857i	$0.568615\pi$
$728$	3.84712e7	2.69034
$729$	1.96321e7	1.36820
$730$	2.45355e7	1.70407
$731$	1.05079e7	0.727315
$732$	−2.98085e7	−2.05619
$733$	8.54574e6	0.587476	0.293738	−	0.955886i	$-0.405101\pi$
$733$	8.54574e6	0.587476	0.293738	+	0.955886i	$0.405101\pi$
$734$	2.48609e7	1.70325
$735$	4.32532e7	2.95324
$736$	−1.04674e6	−0.0712272
$737$	1.55001e7	1.05115
$738$	−9.51626e7	−6.43169
$739$	1.60166e6	0.107884	0.0539422	−	0.998544i	$-0.482821\pi$
$739$	1.60166e6	0.107884	0.0539422	+	0.998544i	$0.482821\pi$
$740$	2.62524e7	1.76234
$741$	2.06619e7	1.38237
$742$	4.15770e7	2.77232
$743$	−2.28963e6	−0.152157	−0.0760787	−	0.997102i	$-0.524240\pi$
$743$	−2.28963e6	−0.152157	−0.0760787	+	0.997102i	$0.524240\pi$
$744$	−1.82785e7	−1.21062
$745$	−529270.	−0.0349371
$746$	−4.87199e7	−3.20523
$747$	3.60631e7	2.36462
$748$	−3.05868e7	−1.99885
$749$	−7.78698e6	−0.507183
$750$	5.21540e7	3.38559
$751$	2.24581e7	1.45303	0.726514	−	0.687152i	$-0.241139\pi$
$751$	2.24581e7	1.45303	0.726514	+	0.687152i	$0.241139\pi$
$752$	5.51687e6	0.355753
$753$	3.51302e7	2.25784
$754$	−3.27461e7	−2.09764
$755$	2.06389e6	0.131771
$756$	−1.54601e8	−9.83803
$757$	6.29447e6	0.399226	0.199613	−	0.979875i	$-0.436031\pi$
$757$	6.29447e6	0.399226	0.199613	+	0.979875i	$0.436031\pi$
$758$	2.23603e7	1.41353
$759$	−6.83905e7	−4.30915
$760$	1.60141e7	1.00570
$761$	−2.97279e6	−0.186081	−0.0930407	−	0.995662i	$-0.529659\pi$
$761$	−2.97279e6	−0.186081	−0.0930407	+	0.995662i	$0.529659\pi$
$762$	5.62719e6	0.351078
$763$	1.13792e7	0.707618
$764$	−4.32660e7	−2.68172
$765$	−1.78615e7	−1.10348
$766$	3.13208e6	0.192868
$767$	2.02768e7	1.24455
$768$	6.04031e7	3.69535
$769$	376102.	0.0229346	0.0114673	−	0.999934i	$-0.496350\pi$
$769$	376102.	0.0229346	0.0114673	+	0.999934i	$0.496350\pi$
$770$	−5.55001e7	−3.37339
$771$	−4.55202e7	−2.75783
$772$	3.41901e7	2.06470
$773$	−1.21332e6	−0.0730342	−0.0365171	−	0.999333i	$-0.511626\pi$
$773$	−1.21332e6	−0.0730342	−0.0365171	+	0.999333i	$0.511626\pi$
$774$	−7.98332e7	−4.78995
$775$	3.32945e6	0.199121
$776$	6.54827e6	0.390366
$777$	7.29624e7	4.33557
$778$	865322.	0.0512541
$779$	2.18181e7	1.28817
$780$	−3.77984e7	−2.22452
$781$	−1.99954e7	−1.17301
$782$	2.84535e7	1.66387
$783$	6.53349e7	3.80839
$784$	3.78336e7	2.19830
$785$	−3.81740e6	−0.221102
$786$	5.55788e7	3.20887
$787$	−9.23780e6	−0.531657	−0.265829	−	0.964020i	$-0.585646\pi$
$787$	−9.23780e6	−0.531657	−0.265829	+	0.964020i	$0.585646\pi$
$788$	9.26974e6	0.531804
$789$	1.21853e6	0.0696854
$790$	−4.00070e7	−2.28070
$791$	−2.95658e7	−1.68015
$792$	1.15375e8	6.53579
$793$	−8.56732e6	−0.483796
$794$	2.09781e7	1.18090
$795$	−2.02815e7	−1.13810
$796$	6.29492e7	3.52134
$797$	2.50781e7	1.39846	0.699228	−	0.714899i	$-0.253527\pi$
$797$	2.50781e7	1.39846	0.699228	+	0.714899i	$0.253527\pi$
$798$	8.96443e7	4.98328
$799$	4.33443e6	0.240195
$800$	−452084.	−0.0249744
$801$	−7.72324e7	−4.25322
$802$	−3.48881e7	−1.91532
$803$	−4.05279e7	−2.21802
$804$	4.58000e7	2.49877
$805$	3.43390e7	1.86766
$806$	−1.05812e7	−0.573718
$807$	6.09068e7	3.29217
$808$	3.50869e7	1.89067
$809$	3.65330e7	1.96252	0.981259	−	0.192693i	$-0.0617222\pi$
$809$	3.65330e7	1.96252	0.981259	+	0.192693i	$0.0617222\pi$
$810$	5.83596e7	3.12536
$811$	−2.94912e6	−0.157449	−0.0787246	−	0.996896i	$-0.525085\pi$
$811$	−2.94912e6	−0.157449	−0.0787246	+	0.996896i	$0.525085\pi$
$812$	−9.44944e7	−5.02940
$813$	−3.17878e7	−1.68669
$814$	−6.51981e7	−3.44885
$815$	1.78960e7	0.943760
$816$	−2.19589e7	−1.15448
$817$	1.83035e7	0.959353
$818$	−3.40654e6	−0.178004
$819$	−7.47430e7	−3.89368
$820$	−3.99135e7	−2.07293
$821$	−3.56581e7	−1.84629	−0.923145	−	0.384451i	$-0.874391\pi$
$821$	−3.56581e7	−1.84629	−0.923145	+	0.384451i	$0.874391\pi$
$822$	−8.42712e7	−4.35011
$823$	1.69202e7	0.870773	0.435387	−	0.900244i	$-0.356612\pi$
$823$	1.69202e7	0.870773	0.435387	+	0.900244i	$0.356612\pi$
$824$	1.42828e7	0.732817
$825$	−2.95376e7	−1.51092
$826$	8.79736e7	4.48644
$827$	2.92756e6	0.148848	0.0744239	−	0.997227i	$-0.476288\pi$
$827$	2.92756e6	0.148848	0.0744239	+	0.997227i	$0.476288\pi$
$828$	−1.43779e8	−7.28819
$829$	3.38413e6	0.171025	0.0855126	−	0.996337i	$-0.472747\pi$
$829$	3.38413e6	0.171025	0.0855126	+	0.996337i	$0.472747\pi$
$830$	2.27417e7	1.14585
$831$	−4.48569e7	−2.25334
$832$	1.80840e7	0.905703
$833$	2.97246e7	1.48424
$834$	1.90686e7	0.949298
$835$	5.32355e6	0.264232
$836$	−5.32785e7	−2.63655
$837$	2.11116e7	1.04162
$838$	−5.47191e7	−2.69171
$839$	−8.70695e6	−0.427033	−0.213516	−	0.976940i	$-0.568492\pi$
$839$	−8.70695e6	−0.427033	−0.213516	+	0.976940i	$0.568492\pi$
$840$	−8.14209e7	−3.98142
$841$	1.94225e7	0.946924
$842$	1.39218e7	0.676729
$843$	3.52170e7	1.70680
$844$	−3.76724e7	−1.82040
$845$	3.48994e6	0.168142
$846$	−3.29306e7	−1.58188
$847$	5.37825e7	2.57592
$848$	−1.77402e7	−0.847168
$849$	2.32262e7	1.10588
$850$	1.22889e7	0.583401
$851$	4.03394e7	1.90944
$852$	−5.90831e7	−2.78846
$853$	−1.76930e6	−0.0832584	−0.0416292	−	0.999133i	$-0.513255\pi$
$853$	−1.76930e6	−0.0832584	−0.0416292	+	0.999133i	$0.513255\pi$
$854$	−3.71705e7	−1.74403
$855$	−3.11126e7	−1.45553
$856$	1.02082e7	0.476171
$857$	3.47080e7	1.61428	0.807139	−	0.590362i	$-0.201015\pi$
$857$	3.47080e7	1.61428	0.807139	+	0.590362i	$0.201015\pi$
$858$	9.38727e7	4.35332
$859$	1.99164e7	0.920934	0.460467	−	0.887677i	$-0.347682\pi$
$859$	1.99164e7	0.920934	0.460467	+	0.887677i	$0.347682\pi$
$860$	−3.34840e7	−1.54380
$861$	−1.10930e8	−5.09968
$862$	4.65948e7	2.13584
$863$	−1.79703e7	−0.821351	−0.410675	−	0.911782i	$-0.634707\pi$
$863$	−1.79703e7	−0.821351	−0.410675	+	0.911782i	$0.634707\pi$
$864$	−2.86662e6	−0.130643
$865$	−1.08014e6	−0.0490839
$866$	−6.42527e7	−2.91136
$867$	2.39540e7	1.08226
$868$	−3.05339e7	−1.37557
$869$	6.60840e7	2.96857
$870$	6.93041e7	3.10428
$871$	1.31635e7	0.587930
$872$	−1.49172e7	−0.664351
$873$	−1.27222e7	−0.564970
$874$	4.95625e7	2.19470
$875$	4.32553e7	1.90994
$876$	−1.19753e8	−5.27262
$877$	−3.20795e7	−1.40841	−0.704204	−	0.709997i	$-0.748696\pi$
$877$	−3.20795e7	−1.40841	−0.704204	+	0.709997i	$0.748696\pi$
$878$	7.10127e7	3.10885
$879$	6.62741e7	2.89315
$880$	2.36810e7	1.03084
$881$	−2.57477e7	−1.11763	−0.558816	−	0.829291i	$-0.688744\pi$
$881$	−2.57477e7	−1.11763	−0.558816	+	0.829291i	$0.688744\pi$
$882$	−2.25831e8	−9.77490
$883$	−3.36302e7	−1.45154	−0.725768	−	0.687940i	$-0.758515\pi$
$883$	−3.36302e7	−1.45154	−0.725768	+	0.687940i	$0.758515\pi$
$884$	−2.59760e7	−1.11800
$885$	−4.29140e7	−1.84179
$886$	3.22483e6	0.138014
$887$	2.80435e7	1.19680	0.598402	−	0.801196i	$-0.295802\pi$
$887$	2.80435e7	1.19680	0.598402	+	0.801196i	$0.295802\pi$
$888$	−9.56483e7	−4.07047
$889$	4.66705e6	0.198056
$890$	−4.87035e7	−2.06103
$891$	−9.63989e7	−4.06797
$892$	3.38730e7	1.42541
$893$	7.55005e6	0.316826
$894$	3.88397e6	0.162530
$895$	−5.68205e6	−0.237109
$896$	7.63723e7	3.17809
$897$	−5.80809e7	−2.41020
$898$	−4.67992e7	−1.93663
$899$	1.29037e7	0.532496
$900$	−6.20976e7	−2.55546
$901$	−1.39379e7	−0.571987
$902$	9.91257e7	4.05667
$903$	−9.30610e7	−3.79794
$904$	3.87586e7	1.57742
$905$	−517535.	−0.0210048
$906$	−1.51456e7	−0.613008
$907$	−1.71810e7	−0.693473	−0.346736	−	0.937963i	$-0.612710\pi$
$907$	−1.71810e7	−0.693473	−0.346736	+	0.937963i	$0.612710\pi$
$908$	4.54390e7	1.82900
$909$	−6.81679e7	−2.73634
$910$	−4.71337e7	−1.88681
$911$	−1.15446e7	−0.460875	−0.230438	−	0.973087i	$-0.574016\pi$
$911$	−1.15446e7	−0.460875	−0.230438	+	0.973087i	$0.574016\pi$
$912$	−3.82498e7	−1.52280
$913$	−3.75650e7	−1.49144
$914$	−2.22068e7	−0.879267
$915$	1.81320e7	0.715966
$916$	−5.70893e7	−2.24810
$917$	4.60957e7	1.81024
$918$	7.79228e7	3.05181
$919$	−7.06892e6	−0.276099	−0.138049	−	0.990425i	$-0.544083\pi$
$919$	−7.06892e6	−0.276099	−0.138049	+	0.990425i	$0.544083\pi$
$920$	−4.50159e7	−1.75346
$921$	−3.35213e7	−1.30218
$922$	2.68744e7	1.04114
$923$	−1.69812e7	−0.656090
$924$	2.70886e8	10.4377
$925$	1.74224e7	0.669505
$926$	3.46001e7	1.32602
$927$	−2.77490e7	−1.06059
$928$	−1.75212e6	−0.0667872
$929$	−3.62334e7	−1.37743	−0.688715	−	0.725032i	$-0.741825\pi$
$929$	−3.62334e7	−1.37743	−0.688715	+	0.725032i	$0.741825\pi$
$930$	2.23942e7	0.849041
$931$	5.17767e7	1.95776
$932$	−3.38433e7	−1.27624
$933$	−6.74413e7	−2.53642
$934$	−2.11035e7	−0.791568
$935$	1.86054e7	0.696001
$936$	9.79825e7	3.65560
$937$	2.16287e7	0.804787	0.402393	−	0.915467i	$-0.368178\pi$
$937$	2.16287e7	0.804787	0.402393	+	0.915467i	$0.368178\pi$
$938$	5.71116e7	2.11942
$939$	3.06499e7	1.13440
$940$	−1.38119e7	−0.509840
$941$	4.65423e7	1.71346	0.856729	−	0.515767i	$-0.172493\pi$
$941$	4.65423e7	1.71346	0.856729	+	0.515767i	$0.172493\pi$
$942$	2.80135e7	1.02858
$943$	−6.13311e7	−2.24596
$944$	−3.75369e7	−1.37097
$945$	9.40410e7	3.42561
$946$	8.31579e7	3.02118
$947$	−1.73630e7	−0.629142	−0.314571	−	0.949234i	$-0.601861\pi$
$947$	−1.73630e7	−0.629142	−0.314571	+	0.949234i	$0.601861\pi$
$948$	1.95267e8	7.05680
$949$	−3.44185e7	−1.24058
$950$	2.14058e7	0.769525
$951$	−2.50996e7	−0.899943
$952$	−5.59544e7	−2.00098
$953$	3.47646e7	1.23995	0.619976	−	0.784621i	$-0.287142\pi$
$953$	3.47646e7	1.23995	0.619976	+	0.784621i	$0.287142\pi$
$954$	1.05893e8	3.76699
$955$	2.63179e7	0.933776
$956$	−9.49152e7	−3.35885
$957$	−1.14477e8	−4.04054
$958$	3.29583e7	1.16025
$959$	−6.98925e7	−2.45405
$960$	−3.82731e7	−1.34034
$961$	−2.44596e7	−0.854359
$962$	−5.53697e7	−1.92901
$963$	−1.98327e7	−0.689154
$964$	2.23510e7	0.774647
$965$	−2.07972e7	−0.718929
$966$	−2.51992e8	−8.68848
$967$	1.83535e7	0.631181	0.315590	−	0.948896i	$-0.397797\pi$
$967$	1.83535e7	0.631181	0.315590	+	0.948896i	$0.397797\pi$
$968$	−7.05048e7	−2.41841
$969$	−3.00516e7	−1.02815
$970$	−8.02272e6	−0.273774
$971$	4.62712e7	1.57493	0.787467	−	0.616357i	$-0.211392\pi$
$971$	4.62712e7	1.57493	0.787467	+	0.616357i	$0.211392\pi$
$972$	−1.25173e8	−4.24956
$973$	1.58150e7	0.535534
$974$	6.93678e7	2.34294
$975$	−2.50849e7	−0.845086
$976$	1.58601e7	0.532942
$977$	−4.48832e7	−1.50434	−0.752172	−	0.658967i	$-0.770994\pi$
$977$	−4.48832e7	−1.50434	−0.752172	+	0.658967i	$0.770994\pi$
$978$	−1.31327e8	−4.39044
$979$	8.04489e7	2.68265
$980$	−9.47192e7	−3.15045
$981$	2.89816e7	0.961502
$982$	−1.01373e7	−0.335461
$983$	966289.	0.0318950
$983$	966289.	0.0318950
$984$	1.45422e8	4.78785
$985$	−5.63861e6	−0.185175
$986$	4.76275e7	1.56015
$987$	−3.83869e7	−1.25427
$988$	−4.52470e7	−1.47468
$989$	−5.14515e7	−1.67266
$990$	−1.41353e8	−4.58372
$991$	−7.34483e6	−0.237573	−0.118787	−	0.992920i	$-0.537900\pi$
$991$	−7.34483e6	−0.237573	−0.118787	+	0.992920i	$0.537900\pi$
$992$	−566161.	−0.0182667
$993$	7.42149e7	2.38846
$994$	−7.36752e7	−2.36513
$995$	−3.82908e7	−1.22613
$996$	−1.10998e8	−3.54542
$997$	−1.94449e7	−0.619539	−0.309770	−	0.950812i	$-0.600252\pi$
$997$	−1.94449e7	−0.619539	−0.309770	+	0.950812i	$0.600252\pi$
$998$	1.01444e8	3.22403
$999$	1.10474e8	3.50223

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.6.a.b.1.17	✓	218

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.6.a.b.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-9.77516 q^{2} -29.0216 q^{3} +63.5537 q^{4} -38.6585 q^{5} +283.690 q^{6} +235.286 q^{7} -308.442 q^{8} +599.250 q^{9} +O(q^{10})\)	\(q-9.77516 q^{2} -29.0216 q^{3} +63.5537 q^{4} -38.6585 q^{5} +283.690 q^{6} +235.286 q^{7} -308.442 q^{8} +599.250 q^{9} +377.893 q^{10} -624.207 q^{11} -1844.43 q^{12} -530.110 q^{13} -2299.96 q^{14} +1121.93 q^{15} +981.354 q^{16} +771.018 q^{17} -5857.77 q^{18} +1343.02 q^{19} -2456.89 q^{20} -6828.36 q^{21} +6101.72 q^{22} -3775.26 q^{23} +8951.48 q^{24} -1630.52 q^{25} +5181.91 q^{26} -10338.9 q^{27} +14953.3 q^{28} -6319.31 q^{29} -10967.0 q^{30} -2041.95 q^{31} +277.264 q^{32} +18115.5 q^{33} -7536.83 q^{34} -9095.80 q^{35} +38084.6 q^{36} -10685.2 q^{37} -13128.2 q^{38} +15384.6 q^{39} +11923.9 q^{40} +16245.5 q^{41} +66748.3 q^{42} +13628.6 q^{43} -39670.7 q^{44} -23166.1 q^{45} +36903.7 q^{46} +5621.69 q^{47} -28480.4 q^{48} +38552.4 q^{49} +15938.6 q^{50} -22376.1 q^{51} -33690.5 q^{52} -18077.3 q^{53} +101065. q^{54} +24130.9 q^{55} -72572.1 q^{56} -38976.5 q^{57} +61772.2 q^{58} -38250.1 q^{59} +71302.8 q^{60} +16161.4 q^{61} +19960.4 q^{62} +140995. q^{63} -34113.6 q^{64} +20493.3 q^{65} -177081. q^{66} -24831.6 q^{67} +49001.1 q^{68} +109564. q^{69} +88912.9 q^{70} +32033.3 q^{71} -184834. q^{72} +64927.0 q^{73} +104449. q^{74} +47320.2 q^{75} +85353.9 q^{76} -146867. q^{77} -150387. q^{78} -105869. q^{79} -37937.7 q^{80} +154434. q^{81} -158803. q^{82} +60180.3 q^{83} -433968. q^{84} -29806.4 q^{85} -133222. q^{86} +183396. q^{87} +192532. q^{88} -128882. q^{89} +226453. q^{90} -124727. q^{91} -239932. q^{92} +59260.7 q^{93} -54952.9 q^{94} -51919.2 q^{95} -8046.63 q^{96} -21230.1 q^{97} -376856. q^{98} -374056. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9}+O(q^{10}) \) 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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