LMFDB - Embedded newform 983.6.a.b.1.5

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			1.5
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)

$f(q)$	$=$	$q-11.0085 q^{2} +27.1723 q^{3} +89.1872 q^{4} -88.2795 q^{5} -299.126 q^{6} +52.5145 q^{7} -629.545 q^{8} +495.333 q^{9} +O(q^{10})$	\(q-11.0085 q^{2} +27.1723 q^{3} +89.1872 q^{4} -88.2795 q^{5} -299.126 q^{6} +52.5145 q^{7} -629.545 q^{8} +495.333 q^{9} +971.825 q^{10} -30.8641 q^{11} +2423.42 q^{12} -126.146 q^{13} -578.107 q^{14} -2398.76 q^{15} +4076.36 q^{16} -1803.13 q^{17} -5452.87 q^{18} +2700.32 q^{19} -7873.40 q^{20} +1426.94 q^{21} +339.768 q^{22} +1696.46 q^{23} -17106.2 q^{24} +4668.27 q^{25} +1388.67 q^{26} +6856.45 q^{27} +4683.62 q^{28} +1094.40 q^{29} +26406.7 q^{30} +2910.53 q^{31} -24729.2 q^{32} -838.649 q^{33} +19849.7 q^{34} -4635.96 q^{35} +44177.3 q^{36} +7936.57 q^{37} -29726.5 q^{38} -3427.66 q^{39} +55576.0 q^{40} +3158.47 q^{41} -15708.5 q^{42} -1448.41 q^{43} -2752.69 q^{44} -43727.7 q^{45} -18675.5 q^{46} -16625.3 q^{47} +110764. q^{48} -14049.2 q^{49} -51390.7 q^{50} -48995.0 q^{51} -11250.6 q^{52} -2683.36 q^{53} -75479.3 q^{54} +2724.67 q^{55} -33060.3 q^{56} +73374.0 q^{57} -12047.7 q^{58} -26541.6 q^{59} -213938. q^{60} -29334.5 q^{61} -32040.6 q^{62} +26012.2 q^{63} +141788. q^{64} +11136.1 q^{65} +9232.27 q^{66} -8181.55 q^{67} -160816. q^{68} +46096.7 q^{69} +51035.0 q^{70} +18993.8 q^{71} -311834. q^{72} +17124.6 q^{73} -87369.7 q^{74} +126848. q^{75} +240834. q^{76} -1620.82 q^{77} +37733.4 q^{78} -42755.6 q^{79} -359859. q^{80} +65939.6 q^{81} -34770.1 q^{82} +115136. q^{83} +127265. q^{84} +159179. q^{85} +15944.8 q^{86} +29737.3 q^{87} +19430.4 q^{88} +63350.4 q^{89} +481377. q^{90} -6624.48 q^{91} +151302. q^{92} +79085.8 q^{93} +183019. q^{94} -238383. q^{95} -671949. q^{96} -179414. q^{97} +154661. q^{98} -15288.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−11.0085	−1.94605	−0.973024	−	0.230706i	$-0.925897\pi$
$2$	−11.0085	−1.94605	−0.973024	+	0.230706i	$0.925897\pi$
$3$	27.1723	1.74310	0.871551	−	0.490305i	$-0.163114\pi$
$3$	27.1723	1.74310	0.871551	+	0.490305i	$0.163114\pi$
$4$	89.1872	2.78710
$5$	−88.2795	−1.57919	−0.789596	−	0.613627i	$-0.789710\pi$
$5$	−88.2795	−1.57919	−0.789596	+	0.613627i	$0.789710\pi$
$6$	−299.126	−3.39216
$7$	52.5145	0.405074	0.202537	−	0.979275i	$-0.435081\pi$
$7$	52.5145	0.405074	0.202537	+	0.979275i	$0.435081\pi$
$8$	−629.545	−3.47778
$9$	495.333	2.03841
$10$	971.825	3.07318
$11$	−30.8641	−0.0769082	−0.0384541	−	0.999260i	$-0.512243\pi$
$11$	−30.8641	−0.0769082	−0.0384541	+	0.999260i	$0.512243\pi$
$12$	2423.42	4.85820
$13$	−126.146	−0.207021	−0.103510	−	0.994628i	$-0.533007\pi$
$13$	−126.146	−0.207021	−0.103510	+	0.994628i	$0.533007\pi$
$14$	−578.107	−0.788293
$15$	−2398.76	−2.75269
$16$	4076.36	3.98082
$17$	−1803.13	−1.51323	−0.756613	−	0.653863i	$-0.773147\pi$
$17$	−1803.13	−1.51323	−0.756613	+	0.653863i	$0.773147\pi$
$18$	−5452.87	−3.96683
$19$	2700.32	1.71606	0.858029	−	0.513602i	$-0.171689\pi$
$19$	2700.32	1.71606	0.858029	+	0.513602i	$0.171689\pi$
$20$	−7873.40	−4.40137
$21$	1426.94	0.706086
$22$	339.768	0.149667
$23$	1696.46	0.668689	0.334344	−	0.942451i	$-0.391485\pi$
$23$	1696.46	0.668689	0.334344	+	0.942451i	$0.391485\pi$
$24$	−17106.2	−6.06213
$25$	4668.27	1.49385
$26$	1388.67	0.402872
$27$	6856.45	1.81005
$28$	4683.62	1.12898
$29$	1094.40	0.241647	0.120823	−	0.992674i	$-0.461447\pi$
$29$	1094.40	0.241647	0.120823	+	0.992674i	$0.461447\pi$
$30$	26406.7	5.35687
$31$	2910.53	0.543961	0.271981	−	0.962303i	$-0.412321\pi$
$31$	2910.53	0.543961	0.271981	+	0.962303i	$0.412321\pi$
$32$	−24729.2	−4.26909
$33$	−838.649	−0.134059
$34$	19849.7	2.94481
$35$	−4635.96	−0.639690
$36$	44177.3	5.68124
$37$	7936.57	0.953078	0.476539	−	0.879153i	$-0.341891\pi$
$37$	7936.57	0.953078	0.476539	+	0.879153i	$0.341891\pi$
$38$	−29726.5	−3.33953
$39$	−3427.66	−0.360858
$40$	55576.0	5.49208
$41$	3158.47	0.293439	0.146719	−	0.989178i	$-0.453129\pi$
$41$	3158.47	0.293439	0.146719	+	0.989178i	$0.453129\pi$
$42$	−15708.5	−1.37408
$43$	−1448.41	−0.119459	−0.0597296	−	0.998215i	$-0.519024\pi$
$43$	−1448.41	−0.119459	−0.0597296	+	0.998215i	$0.519024\pi$
$44$	−2752.69	−0.214351
$45$	−43727.7	−3.21903
$46$	−18675.5	−1.30130
$47$	−16625.3	−1.09780	−0.548901	−	0.835887i	$-0.684954\pi$
$47$	−16625.3	−1.09780	−0.548901	+	0.835887i	$0.684954\pi$
$48$	110764.	6.93898
$49$	−14049.2	−0.835915
$50$	−51390.7	−2.90710
$51$	−48995.0	−2.63771
$52$	−11250.6	−0.576987
$53$	−2683.36	−0.131217	−0.0656083	−	0.997845i	$-0.520899\pi$
$53$	−2683.36	−0.131217	−0.0656083	+	0.997845i	$0.520899\pi$
$54$	−75479.3	−3.52244
$55$	2724.67	0.121453
$56$	−33060.3	−1.40876
$57$	73374.0	2.99126
$58$	−12047.7	−0.470256
$59$	−26541.6	−0.992653	−0.496327	−	0.868136i	$-0.665318\pi$
$59$	−26541.6	−0.992653	−0.496327	+	0.868136i	$0.665318\pi$
$60$	−213938.	−7.67203
$61$	−29334.5	−1.00938	−0.504689	−	0.863301i	$-0.668393\pi$
$61$	−29334.5	−1.00938	−0.504689	+	0.863301i	$0.668393\pi$
$62$	−32040.6	−1.05857
$63$	26012.2	0.825705
$64$	141788.	4.32703
$65$	11136.1	0.326925
$66$	9232.27	0.260885
$67$	−8181.55	−0.222663	−0.111332	−	0.993783i	$-0.535512\pi$
$67$	−8181.55	−0.222663	−0.111332	+	0.993783i	$0.535512\pi$
$68$	−160816.	−4.21751
$69$	46096.7	1.16559
$70$	51035.0	1.24487
$71$	18993.8	0.447163	0.223582	−	0.974685i	$-0.428225\pi$
$71$	18993.8	0.447163	0.223582	+	0.974685i	$0.428225\pi$
$72$	−311834.	−7.08913
$73$	17124.6	0.376108	0.188054	−	0.982159i	$-0.439782\pi$
$73$	17124.6	0.376108	0.188054	+	0.982159i	$0.439782\pi$
$74$	−87369.7	−1.85473
$75$	126848.	2.60393
$76$	240834.	4.78282
$77$	−1620.82	−0.0311535
$78$	37733.4	0.702247
$79$	−42755.6	−0.770771	−0.385386	−	0.922756i	$-0.625932\pi$
$79$	−42755.6	−0.770771	−0.385386	+	0.922756i	$0.625932\pi$
$80$	−359859.	−6.28649
$81$	65939.6	1.11669
$82$	−34770.1	−0.571046
$83$	115136.	1.83449	0.917247	−	0.398320i	$-0.130407\pi$
$83$	115136.	1.83449	0.917247	+	0.398320i	$0.130407\pi$
$84$	127265.	1.96793
$85$	159179.	2.38967
$86$	15944.8	0.232473
$87$	29737.3	0.421215
$88$	19430.4	0.267470
$89$	63350.4	0.847763	0.423882	−	0.905718i	$-0.360667\pi$
$89$	63350.4	0.847763	0.423882	+	0.905718i	$0.360667\pi$
$90$	481377.	6.26439
$91$	−6624.48	−0.0838587
$92$	151302.	1.86370
$93$	79085.8	0.948180
$94$	183019.	2.13638
$95$	−238383.	−2.70998
$96$	−671949.	−7.44146
$97$	−179414.	−1.93610	−0.968050	−	0.250757i	$-0.919321\pi$
$97$	−179414.	−1.93610	−0.968050	+	0.250757i	$0.919321\pi$
$98$	154661.	1.62673
$99$	−15288.0	−0.156770
$100$	416350.	4.16350
$101$	−135726.	−1.32392	−0.661959	−	0.749540i	$-0.730275\pi$
$101$	−135726.	−1.32392	−0.661959	+	0.749540i	$0.730275\pi$
$102$	539362.	5.13310
$103$	72179.6	0.670380	0.335190	−	0.942151i	$-0.391199\pi$
$103$	72179.6	0.670380	0.335190	+	0.942151i	$0.391199\pi$
$104$	79414.4	0.719972
$105$	−125970.	−1.11504
$106$	29539.8	0.255354
$107$	96892.0	0.818141	0.409071	−	0.912503i	$-0.365853\pi$
$107$	96892.0	0.818141	0.409071	+	0.912503i	$0.365853\pi$
$108$	611508.	5.04478
$109$	205954.	1.66037	0.830183	−	0.557491i	$-0.188236\pi$
$109$	205954.	1.66037	0.830183	+	0.557491i	$0.188236\pi$
$110$	−29994.6	−0.236353
$111$	215655.	1.66131
$112$	214068.	1.61253
$113$	69137.3	0.509350	0.254675	−	0.967027i	$-0.418031\pi$
$113$	69137.3	0.509350	0.254675	+	0.967027i	$0.418031\pi$
$114$	−807738.	−5.82114
$115$	−149763.	−1.05599
$116$	97606.4	0.673493
$117$	−62484.0	−0.421992
$118$	292184.	1.93175
$119$	−94690.3	−0.612968
$120$	1.51013e6	9.57326
$121$	−160098.	−0.994085
$122$	322929.	1.96430
$123$	85823.0	0.511494
$124$	259582.	1.51607
$125$	−136239.	−0.779880
$126$	−286355.	−1.60686
$127$	−198460.	−1.09185	−0.545926	−	0.837833i	$-0.683822\pi$
$127$	−198460.	−1.09185	−0.545926	+	0.837833i	$0.683822\pi$
$128$	−769540.	−4.15151
$129$	−39356.6	−0.208230
$130$	−122591.	−0.636212
$131$	−51644.8	−0.262935	−0.131468	−	0.991320i	$-0.541969\pi$
$131$	−51644.8	−0.262935	−0.131468	+	0.991320i	$0.541969\pi$
$132$	−74796.7	−0.373635
$133$	141806.	0.695131
$134$	90066.6	0.433313
$135$	−605284.	−2.85841
$136$	1.13515e6	5.26266
$137$	96775.8	0.440520	0.220260	−	0.975441i	$-0.429309\pi$
$137$	96775.8	0.440520	0.220260	+	0.975441i	$0.429309\pi$
$138$	−507455.	−2.26830
$139$	59857.2	0.262772	0.131386	−	0.991331i	$-0.458057\pi$
$139$	59857.2	0.262772	0.131386	+	0.991331i	$0.458057\pi$
$140$	−413468.	−1.78288
$141$	−451747.	−1.91358
$142$	−209093.	−0.870200
$143$	3893.37	0.0159216
$144$	2.01916e6	8.11454
$145$	−96613.0	−0.381607
$146$	−188516.	−0.731923
$147$	−381749.	−1.45709
$148$	707840.	2.65632
$149$	478599.	1.76606	0.883031	−	0.469315i	$-0.155499\pi$
$149$	478599.	1.76606	0.883031	+	0.469315i	$0.155499\pi$
$150$	−1.39640e6	−5.06737
$151$	337874.	1.20590	0.602951	−	0.797778i	$-0.293991\pi$
$151$	337874.	1.20590	0.602951	+	0.797778i	$0.293991\pi$
$152$	−1.69998e6	−5.96807
$153$	−893147.	−3.08457
$154$	17842.8	0.0606262
$155$	−256940.	−0.859019
$156$	−305704.	−1.00575
$157$	582371.	1.88560	0.942802	−	0.333353i	$-0.108180\pi$
$157$	582371.	1.88560	0.942802	+	0.333353i	$0.108180\pi$
$158$	470676.	1.49996
$159$	−72912.9	−0.228724
$160$	2.18308e6	6.74172
$161$	89088.8	0.270868
$162$	−725896.	−2.17314
$163$	278733.	0.821712	0.410856	−	0.911700i	$-0.365230\pi$
$163$	278733.	0.821712	0.410856	+	0.911700i	$0.365230\pi$
$164$	281695.	0.817844
$165$	74035.5	0.211705
$166$	−1.26748e6	−3.57001
$167$	552485.	1.53295	0.766477	−	0.642272i	$-0.222008\pi$
$167$	552485.	1.53295	0.766477	+	0.642272i	$0.222008\pi$
$168$	−898323.	−2.45561
$169$	−355380.	−0.957142
$170$	−1.75232e6	−4.65042
$171$	1.33756e6	3.49802
$172$	−129179.	−0.332945
$173$	657184.	1.66944	0.834722	−	0.550672i	$-0.185628\pi$
$173$	657184.	1.66944	0.834722	+	0.550672i	$0.185628\pi$
$174$	−327363.	−0.819704
$175$	245152.	0.605119
$176$	−125813.	−0.306158
$177$	−721196.	−1.73030
$178$	−697394.	−1.64979
$179$	−251056.	−0.585650	−0.292825	−	0.956166i	$-0.594595\pi$
$179$	−251056.	−0.585650	−0.292825	+	0.956166i	$0.594595\pi$
$180$	−3.89995e6	−8.97177
$181$	−455537.	−1.03354	−0.516769	−	0.856125i	$-0.672866\pi$
$181$	−455537.	−1.03354	−0.516769	+	0.856125i	$0.672866\pi$
$182$	72925.6	0.163193
$183$	−797085.	−1.75945
$184$	−1.06800e6	−2.32555
$185$	−700636.	−1.50509
$186$	−870616.	−1.84520
$187$	55651.9	0.116379
$188$	−1.48276e6	−3.05969
$189$	360063.	0.733203
$190$	2.62424e6	5.27376
$191$	−833183.	−1.65256	−0.826280	−	0.563260i	$-0.809547\pi$
$191$	−833183.	−1.65256	−0.826280	+	0.563260i	$0.809547\pi$
$192$	3.85271e6	7.54246
$193$	22713.4	0.0438923	0.0219461	−	0.999759i	$-0.493014\pi$
$193$	22713.4	0.0438923	0.0219461	+	0.999759i	$0.493014\pi$
$194$	1.97508e6	3.76774
$195$	302592.	0.569864
$196$	−1.25301e6	−2.32978
$197$	1.01550e6	1.86429	0.932145	−	0.362084i	$-0.117935\pi$
$197$	1.01550e6	1.86429	0.932145	+	0.362084i	$0.117935\pi$
$198$	168298.	0.305082
$199$	−303128.	−0.542618	−0.271309	−	0.962492i	$-0.587456\pi$
$199$	−303128.	−0.542618	−0.271309	+	0.962492i	$0.587456\pi$
$200$	−2.93889e6	−5.19527
$201$	−222311.	−0.388125
$202$	1.49415e6	2.57641
$203$	57471.9	0.0978848
$204$	−4.36973e6	−7.35155
$205$	−278829.	−0.463396
$206$	−794589.	−1.30459
$207$	840312.	1.36306
$208$	−514215.	−0.824113
$209$	−83343.2	−0.131979
$210$	1.38674e6	2.16993
$211$	−938696.	−1.45151	−0.725753	−	0.687955i	$-0.758509\pi$
$211$	−938696.	−1.45151	−0.725753	+	0.687955i	$0.758509\pi$
$212$	−239321.	−0.365714
$213$	516105.	0.779451
$214$	−1.06664e6	−1.59214
$215$	127865.	0.188649
$216$	−4.31645e6	−6.29495
$217$	152845.	0.220345
$218$	−2.26725e6	−3.23115
$219$	465313.	0.655594
$220$	243006.	0.338501
$221$	227456.	0.313269
$222$	−2.37403e6	−3.23299
$223$	896234.	1.20687	0.603433	−	0.797414i	$-0.293799\pi$
$223$	896234.	1.20687	0.603433	+	0.797414i	$0.293799\pi$
$224$	−1.29864e6	−1.72930
$225$	2.31235e6	3.04507
$226$	−761099.	−0.991220
$227$	1.01651e6	1.30933	0.654664	−	0.755920i	$-0.272810\pi$
$227$	1.01651e6	1.30933	0.654664	+	0.755920i	$0.272810\pi$
$228$	6.54402e6	8.33695
$229$	−1.40505e6	−1.77053	−0.885266	−	0.465085i	$-0.846024\pi$
$229$	−1.40505e6	−1.77053	−0.885266	+	0.465085i	$0.846024\pi$
$230$	1.64866e6	2.05500
$231$	−44041.3	−0.0543037
$232$	−688974.	−0.840394
$233$	1.04269e6	1.25824	0.629122	−	0.777307i	$-0.283415\pi$
$233$	1.04269e6	1.25824	0.629122	+	0.777307i	$0.283415\pi$
$234$	687856.	0.821217
$235$	1.46767e6	1.73364
$236$	−2.36717e6	−2.76662
$237$	−1.16177e6	−1.34353
$238$	1.04240e6	1.19287
$239$	−1.25174e6	−1.41749	−0.708747	−	0.705463i	$-0.750739\pi$
$239$	−1.25174e6	−1.41749	−0.708747	+	0.705463i	$0.750739\pi$
$240$	−9.77820e6	−10.9580
$241$	249166.	0.276341	0.138171	−	0.990408i	$-0.455878\pi$
$241$	249166.	0.276341	0.138171	+	0.990408i	$0.455878\pi$
$242$	1.76244e6	1.93454
$243$	125611.	0.136462
$244$	−2.61626e6	−2.81324
$245$	1.24026e6	1.32007
$246$	−944782.	−0.995392
$247$	−340634.	−0.355259
$248$	−1.83231e6	−1.89178
$249$	3.12851e6	3.19771
$250$	1.49979e6	1.51768
$251$	1.57720e6	1.58017	0.790083	−	0.613000i	$-0.210038\pi$
$251$	1.57720e6	1.58017	0.790083	+	0.613000i	$0.210038\pi$
$252$	2.31995e6	2.30132
$253$	−52359.8	−0.0514276
$254$	2.18475e6	2.12480
$255$	4.32526e6	4.16544
$256$	3.93427e6	3.75201
$257$	2.07443e6	1.95914	0.979571	−	0.201097i	$-0.0644508\pi$
$257$	2.07443e6	1.95914	0.979571	+	0.201097i	$0.0644508\pi$
$258$	433257.	0.405225
$259$	416785.	0.386067
$260$	993195.	0.911173
$261$	542092.	0.492574
$262$	568532.	0.511684
$263$	−199253.	−0.177630	−0.0888148	−	0.996048i	$-0.528308\pi$
$263$	−199253.	−0.177630	−0.0888148	+	0.996048i	$0.528308\pi$
$264$	527968.	0.466227
$265$	236886.	0.207216
$266$	−1.56108e6	−1.35276
$267$	1.72138e6	1.47774
$268$	−729689.	−0.620584
$269$	−388770.	−0.327576	−0.163788	−	0.986496i	$-0.552371\pi$
$269$	−388770.	−0.327576	−0.163788	+	0.986496i	$0.552371\pi$
$270$	6.66327e6	5.56261
$271$	1.07282e6	0.887369	0.443684	−	0.896183i	$-0.353671\pi$
$271$	1.07282e6	0.887369	0.443684	+	0.896183i	$0.353671\pi$
$272$	−7.35019e6	−6.02388
$273$	−180002.	−0.146174
$274$	−1.06536e6	−0.857272
$275$	−144082.	−0.114889
$276$	4.11123e6	3.24862
$277$	−1.70416e6	−1.33448	−0.667238	−	0.744844i	$-0.732524\pi$
$277$	−1.70416e6	−1.33448	−0.667238	+	0.744844i	$0.732524\pi$
$278$	−658939.	−0.511367
$279$	1.44168e6	1.10881
$280$	2.91855e6	2.22470
$281$	−249587.	−0.188563	−0.0942815	−	0.995546i	$-0.530055\pi$
$281$	−249587.	−0.188563	−0.0942815	+	0.995546i	$0.530055\pi$
$282$	4.97306e6	3.72392
$283$	−10968.2	−0.00814082	−0.00407041	−	0.999992i	$-0.501296\pi$
$283$	−10968.2	−0.00814082	−0.00407041	+	0.999992i	$0.501296\pi$
$284$	1.69400e6	1.24629
$285$	−6.47742e6	−4.72378
$286$	−42860.2	−0.0309841
$287$	165866.	0.118865
$288$	−1.22492e7	−8.70214
$289$	1.83140e6	1.28985
$290$	1.06357e6	0.742624
$291$	−4.87510e6	−3.37482
$292$	1.52729e6	1.04825
$293$	1.11698e6	0.760111	0.380056	−	0.924964i	$-0.375905\pi$
$293$	1.11698e6	0.760111	0.380056	+	0.924964i	$0.375905\pi$
$294$	4.20249e6	2.83556
$295$	2.34308e6	1.56759
$296$	−4.99643e6	−3.31459
$297$	−211618.	−0.139207
$298$	−5.26866e6	−3.43684
$299$	−214001.	−0.138432
$300$	1.13132e7	7.25741
$301$	−76062.5	−0.0483899
$302$	−3.71949e6	−2.34674
$303$	−3.68800e6	−2.30773
$304$	1.10075e7	6.83132
$305$	2.58963e6	1.59400
$306$	9.83221e6	6.00271
$307$	2.60408e6	1.57692	0.788458	−	0.615089i	$-0.210880\pi$
$307$	2.60408e6	1.57692	0.788458	+	0.615089i	$0.210880\pi$
$308$	−144556.	−0.0868279
$309$	1.96128e6	1.16854
$310$	2.82853e6	1.67169
$311$	−2.06362e6	−1.20984	−0.604921	−	0.796285i	$-0.706795\pi$
$311$	−2.06362e6	−1.20984	−0.604921	+	0.796285i	$0.706795\pi$
$312$	2.15787e6	1.25499
$313$	2.49795e6	1.44120	0.720598	−	0.693353i	$-0.243867\pi$
$313$	2.49795e6	1.44120	0.720598	+	0.693353i	$0.243867\pi$
$314$	−6.41103e6	−3.66947
$315$	−2.29634e6	−1.30395
$316$	−3.81325e6	−2.14822
$317$	−2.36475e6	−1.32171	−0.660856	−	0.750513i	$-0.729806\pi$
$317$	−2.36475e6	−1.32171	−0.660856	+	0.750513i	$0.729806\pi$
$318$	802662.	0.445108
$319$	−33777.7	−0.0185846
$320$	−1.25170e7	−6.83321
$321$	2.63278e6	1.42610
$322$	−980734.	−0.527123
$323$	−4.86902e6	−2.59678
$324$	5.88096e6	3.11233
$325$	−588882.	−0.309257
$326$	−3.06843e6	−1.59909
$327$	5.59624e6	2.89419
$328$	−1.98840e6	−1.02052
$329$	−873069.	−0.444692
$330$	−815020.	−0.411987
$331$	−1.36631e6	−0.685453	−0.342727	−	0.939435i	$-0.611350\pi$
$331$	−1.36631e6	−0.685453	−0.342727	+	0.939435i	$0.611350\pi$
$332$	1.02687e7	5.11292
$333$	3.93124e6	1.94276
$334$	−6.08203e6	−2.98320
$335$	722263.	0.351628
$336$	5.81673e6	2.81080
$337$	3.19910e6	1.53445	0.767226	−	0.641377i	$-0.221636\pi$
$337$	3.19910e6	1.53445	0.767226	+	0.641377i	$0.221636\pi$
$338$	3.91221e6	1.86264
$339$	1.87862e6	0.887850
$340$	1.41967e7	6.66026
$341$	−89831.0	−0.0418351
$342$	−1.47245e7	−6.80732
$343$	−1.62040e6	−0.743682
$344$	911839.	0.415453
$345$	−4.06939e6	−1.84069
$346$	−7.23462e6	−3.24882
$347$	2.03343e6	0.906578	0.453289	−	0.891364i	$-0.350251\pi$
$347$	2.03343e6	0.906578	0.453289	+	0.891364i	$0.350251\pi$
$348$	2.65219e6	1.17397
$349$	1.13392e6	0.498332	0.249166	−	0.968461i	$-0.419844\pi$
$349$	1.13392e6	0.498332	0.249166	+	0.968461i	$0.419844\pi$
$350$	−2.69876e6	−1.17759
$351$	−864911.	−0.374717
$352$	763246.	0.328328
$353$	−856058.	−0.365651	−0.182825	−	0.983145i	$-0.558524\pi$
$353$	−856058.	−0.365651	−0.182825	+	0.983145i	$0.558524\pi$
$354$	7.93929e6	3.36724
$355$	−1.67676e6	−0.706156
$356$	5.65005e6	2.36280
$357$	−2.57295e6	−1.06847
$358$	2.76375e6	1.13970
$359$	−142014.	−0.0581561	−0.0290781	−	0.999577i	$-0.509257\pi$
$359$	−142014.	−0.0581561	−0.0290781	+	0.999577i	$0.509257\pi$
$360$	2.75286e7	11.1951
$361$	4.81565e6	1.94485
$362$	5.01478e6	2.01132
$363$	−4.35024e6	−1.73279
$364$	−590819.	−0.233723
$365$	−1.51175e6	−0.593946
$366$	8.77471e6	3.42397
$367$	169874.	0.0658358	0.0329179	−	0.999458i	$-0.489520\pi$
$367$	169874.	0.0658358	0.0329179	+	0.999458i	$0.489520\pi$
$368$	6.91539e6	2.66193
$369$	1.56450e6	0.598148
$370$	7.71296e6	2.92898
$371$	−140915.	−0.0531525
$372$	7.05344e6	2.64267
$373$	−2.23607e6	−0.832174	−0.416087	−	0.909325i	$-0.636599\pi$
$373$	−2.23607e6	−0.832174	−0.416087	+	0.909325i	$0.636599\pi$
$374$	−612644.	−0.226480
$375$	−3.70193e6	−1.35941
$376$	1.04664e7	3.81792
$377$	−138054.	−0.0500259
$378$	−3.96376e6	−1.42685
$379$	495445.	0.177173	0.0885865	−	0.996068i	$-0.471765\pi$
$379$	495445.	0.177173	0.0885865	+	0.996068i	$0.471765\pi$
$380$	−2.12607e7	−7.55300
$381$	−5.39261e6	−1.90321
$382$	9.17210e6	3.21596
$383$	−3.62027e6	−1.26108	−0.630542	−	0.776155i	$-0.717167\pi$
$383$	−3.62027e6	−1.26108	−0.630542	+	0.776155i	$0.717167\pi$
$384$	−2.09102e7	−7.23651
$385$	143085.	0.0491974
$386$	−250040.	−0.0854164
$387$	−717444.	−0.243507
$388$	−1.60015e7	−5.39610
$389$	2.42198e6	0.811514	0.405757	−	0.913981i	$-0.367008\pi$
$389$	2.42198e6	0.811514	0.405757	+	0.913981i	$0.367008\pi$
$390$	−3.33109e6	−1.10898
$391$	−3.05893e6	−1.01188
$392$	8.84462e6	2.90713
$393$	−1.40331e6	−0.458323
$394$	−1.11791e7	−3.62800
$395$	3.77445e6	1.21720
$396$	−1.36349e6	−0.436934
$397$	1.50859e6	0.480392	0.240196	−	0.970724i	$-0.422788\pi$
$397$	1.50859e6	0.480392	0.240196	+	0.970724i	$0.422788\pi$
$398$	3.33699e6	1.05596
$399$	3.85320e6	1.21168
$400$	1.90296e7	5.94674
$401$	−751603.	−0.233414	−0.116707	−	0.993166i	$-0.537234\pi$
$401$	−751603.	−0.233414	−0.116707	+	0.993166i	$0.537234\pi$
$402$	2.44731e6	0.755309
$403$	−367151.	−0.112611
$404$	−1.21051e7	−3.68989
$405$	−5.82111e6	−1.76347
$406$	−632680.	−0.190488
$407$	−244955.	−0.0732994
$408$	3.08446e7	9.17336
$409$	2.33521e6	0.690268	0.345134	−	0.938553i	$-0.387833\pi$
$409$	2.33521e6	0.690268	0.345134	+	0.938553i	$0.387833\pi$
$410$	3.06949e6	0.901791
$411$	2.62962e6	0.767871
$412$	6.43749e6	1.86842
$413$	−1.39382e6	−0.402098
$414$	−9.25058e6	−2.65258
$415$	−1.01642e7	−2.89702
$416$	3.11948e6	0.883790
$417$	1.62646e6	0.458039
$418$	917484.	0.256837
$419$	6.10416e6	1.69860	0.849299	−	0.527912i	$-0.177025\pi$
$419$	6.10416e6	1.69860	0.849299	+	0.527912i	$0.177025\pi$
$420$	−1.12349e7	−3.10774
$421$	3.55657e6	0.977970	0.488985	−	0.872292i	$-0.337367\pi$
$421$	3.55657e6	0.977970	0.488985	+	0.872292i	$0.337367\pi$
$422$	1.03336e7	2.82470
$423$	−8.23504e6	−2.23777
$424$	1.68930e6	0.456343
$425$	−8.41748e6	−2.26053
$426$	−5.68154e6	−1.51685
$427$	−1.54049e6	−0.408873
$428$	8.64152e6	2.28024
$429$	105792.	0.0277529
$430$	−1.40760e6	−0.367120
$431$	−4.44184e6	−1.15178	−0.575890	−	0.817527i	$-0.695345\pi$
$431$	−4.44184e6	−1.15178	−0.575890	+	0.817527i	$0.695345\pi$
$432$	2.79494e7	7.20548
$433$	2.84016e6	0.727987	0.363993	−	0.931402i	$-0.381413\pi$
$433$	2.84016e6	0.727987	0.363993	+	0.931402i	$0.381413\pi$
$434$	−1.68260e6	−0.428801
$435$	−2.62520e6	−0.665179
$436$	1.83685e7	4.62761
$437$	4.58099e6	1.14751
$438$	−5.12240e6	−1.27582
$439$	2.07290e6	0.513355	0.256678	−	0.966497i	$-0.417372\pi$
$439$	2.07290e6	0.513355	0.256678	+	0.966497i	$0.417372\pi$
$440$	−1.71530e6	−0.422386
$441$	−6.95904e6	−1.70393
$442$	−2.50395e6	−0.609636
$443$	6.55103e6	1.58599	0.792995	−	0.609229i	$-0.208521\pi$
$443$	6.55103e6	1.58599	0.792995	+	0.609229i	$0.208521\pi$
$444$	1.92336e7	4.63024
$445$	−5.59255e6	−1.33878
$446$	−9.86619e6	−2.34862
$447$	1.30046e7	3.07843
$448$	7.44594e6	1.75277
$449$	2.48826e6	0.582478	0.291239	−	0.956650i	$-0.405932\pi$
$449$	2.48826e6	0.582478	0.291239	+	0.956650i	$0.405932\pi$
$450$	−2.54555e7	−5.92584
$451$	−97483.6	−0.0225678
$452$	6.16616e6	1.41961
$453$	9.18080e6	2.10201
$454$	−1.11903e7	−2.54802
$455$	584806.	0.132429
$456$	−4.61922e7	−10.4030
$457$	4.27645e6	0.957840	0.478920	−	0.877859i	$-0.341028\pi$
$457$	4.27645e6	0.957840	0.478920	+	0.877859i	$0.341028\pi$
$458$	1.54675e7	3.44554
$459$	−1.23630e7	−2.73901
$460$	−1.33569e7	−2.94314
$461$	−5.56754e6	−1.22014	−0.610071	−	0.792346i	$-0.708859\pi$
$461$	−5.56754e6	−1.22014	−0.610071	+	0.792346i	$0.708859\pi$
$462$	484828.	0.105678
$463$	−1.59560e6	−0.345917	−0.172958	−	0.984929i	$-0.555333\pi$
$463$	−1.59560e6	−0.345917	−0.172958	+	0.984929i	$0.555333\pi$
$464$	4.46117e6	0.961953
$465$	−6.98165e6	−1.49736
$466$	−1.14784e7	−2.44860
$467$	5.33654e6	1.13232	0.566158	−	0.824297i	$-0.308429\pi$
$467$	5.33654e6	1.13232	0.566158	+	0.824297i	$0.308429\pi$
$468$	−5.57277e6	−1.17613
$469$	−429650.	−0.0901951
$470$	−1.61569e7	−3.37375
$471$	1.58243e7	3.28680
$472$	1.67092e7	3.45223
$473$	44703.9	0.00918739
$474$	1.27893e7	2.61458
$475$	1.26058e7	2.56353
$476$	−8.44516e6	−1.70840
$477$	−1.32915e6	−0.267473
$478$	1.37798e7	2.75851
$479$	−4.11457e6	−0.819380	−0.409690	−	0.912225i	$-0.634363\pi$
$479$	−4.11457e6	−0.819380	−0.409690	+	0.912225i	$0.634363\pi$
$480$	5.93194e7	11.7515
$481$	−1.00116e6	−0.197307
$482$	−2.74294e6	−0.537773
$483$	2.42075e6	0.472151
$484$	−1.42787e7	−2.77061
$485$	1.58386e7	3.05747
$486$	−1.38278e6	−0.265561
$487$	42197.5	0.00806241	0.00403120	−	0.999992i	$-0.498717\pi$
$487$	42197.5	0.00806241	0.00403120	+	0.999992i	$0.498717\pi$
$488$	1.84674e7	3.51040
$489$	7.57381e6	1.43233
$490$	−1.36534e7	−2.56892
$491$	9.69813e6	1.81545	0.907725	−	0.419567i	$-0.137818\pi$
$491$	9.69813e6	1.81545	0.907725	+	0.419567i	$0.137818\pi$
$492$	7.65431e6	1.42559
$493$	−1.97334e6	−0.365666
$494$	3.74987e6	0.691351
$495$	1.34962e6	0.247570
$496$	1.18644e7	2.16541
$497$	997450.	0.181134
$498$	−3.44402e7	−6.22289
$499$	2.24992e6	0.404498	0.202249	−	0.979334i	$-0.435175\pi$
$499$	2.24992e6	0.404498	0.202249	+	0.979334i	$0.435175\pi$
$500$	−1.21508e7	−2.17360
$501$	1.50123e7	2.67209
$502$	−1.73626e7	−3.07508
$503$	−5.03286e6	−0.886942	−0.443471	−	0.896289i	$-0.646253\pi$
$503$	−5.03286e6	−0.886942	−0.443471	+	0.896289i	$0.646253\pi$
$504$	−1.63758e7	−2.87162
$505$	1.19819e7	2.09072
$506$	576403.	0.100081
$507$	−9.65649e6	−1.66840
$508$	−1.77001e7	−3.04310
$509$	2.73635e6	0.468141	0.234071	−	0.972220i	$-0.424795\pi$
$509$	2.73635e6	0.468141	0.234071	+	0.972220i	$0.424795\pi$
$510$	−4.76146e7	−8.10615
$511$	899289.	0.152352
$512$	−1.86851e7	−3.15007
$513$	1.85146e7	3.10615
$514$	−2.28364e7	−3.81258
$515$	−6.37198e6	−1.05866
$516$	−3.51010e6	−0.580357
$517$	513125.	0.0844300
$518$	−4.58818e6	−0.751305
$519$	1.78572e7	2.91001
$520$	−7.01066e6	−1.13697
$521$	−3.57263e6	−0.576626	−0.288313	−	0.957536i	$-0.593094\pi$
$521$	−3.57263e6	−0.576626	−0.288313	+	0.957536i	$0.593094\pi$
$522$	−5.96762e6	−0.958572
$523$	−6.98803e6	−1.11712	−0.558561	−	0.829463i	$-0.688646\pi$
$523$	−6.98803e6	−1.11712	−0.558561	+	0.829463i	$0.688646\pi$
$524$	−4.60606e6	−0.732826
$525$	6.66134e6	1.05478
$526$	2.19348e6	0.345675
$527$	−5.24805e6	−0.823136
$528$	−3.41864e6	−0.533664
$529$	−3.55837e6	−0.552856
$530$	−2.60776e6	−0.403253
$531$	−1.31469e7	−2.02343
$532$	1.26473e7	1.93740
$533$	−398428.	−0.0607479
$534$	−1.89498e7	−2.87575
$535$	−8.55358e6	−1.29200
$536$	5.15066e6	0.774374
$537$	−6.82177e6	−1.02085
$538$	4.27977e6	0.637478
$539$	433617.	0.0642887
$540$	−5.39836e7	−7.96668
$541$	5.82497e6	0.855658	0.427829	−	0.903860i	$-0.359279\pi$
$541$	5.82497e6	0.855658	0.427829	+	0.903860i	$0.359279\pi$
$542$	−1.18102e7	−1.72686
$543$	−1.23780e7	−1.80156
$544$	4.45899e7	6.46010
$545$	−1.81815e7	−2.62204
$546$	1.98155e6	0.284462
$547$	2.35837e6	0.337010	0.168505	−	0.985701i	$-0.446106\pi$
$547$	2.35837e6	0.337010	0.168505	+	0.985701i	$0.446106\pi$
$548$	8.63116e6	1.22777
$549$	−1.45303e7	−2.05752
$550$	1.58613e6	0.223579
$551$	2.95523e6	0.414680
$552$	−2.90199e7	−4.05367
$553$	−2.24529e6	−0.312220
$554$	1.87603e7	2.59695
$555$	−1.90379e7	−2.62353
$556$	5.33850e6	0.732373
$557$	2.56797e6	0.350713	0.175356	−	0.984505i	$-0.443892\pi$
$557$	2.56797e6	0.350713	0.175356	+	0.984505i	$0.443892\pi$
$558$	−1.58708e7	−2.15780
$559$	182710.	0.0247305
$560$	−1.88979e7	−2.54649
$561$	1.51219e6	0.202861
$562$	2.74758e6	0.366953
$563$	−272952.	−0.0362924	−0.0181462	−	0.999835i	$-0.505776\pi$
$563$	−272952.	−0.0362924	−0.0181462	+	0.999835i	$0.505776\pi$
$564$	−4.02900e7	−5.33335
$565$	−6.10341e6	−0.804362
$566$	120743.	0.0158424
$567$	3.46279e6	0.452343
$568$	−1.19575e7	−1.55513
$569$	6.26078e6	0.810676	0.405338	−	0.914167i	$-0.367154\pi$
$569$	6.26078e6	0.810676	0.405338	+	0.914167i	$0.367154\pi$
$570$	7.13067e7	9.19270
$571$	2.20987e6	0.283646	0.141823	−	0.989892i	$-0.454704\pi$
$571$	2.20987e6	0.283646	0.141823	+	0.989892i	$0.454704\pi$
$572$	347239.	0.0443750
$573$	−2.26395e7	−2.88058
$574$	−1.82594e6	−0.231316
$575$	7.91954e6	0.998919
$576$	7.02323e7	8.82024
$577$	1.00866e7	1.26126	0.630628	−	0.776085i	$-0.282797\pi$
$577$	1.00866e7	1.26126	0.630628	+	0.776085i	$0.282797\pi$
$578$	−2.01610e7	−2.51011
$579$	617174.	0.0765087
$580$	−8.61665e6	−1.06358
$581$	6.04632e6	0.743106
$582$	5.36675e7	6.56756
$583$	82819.5	0.0100916
$584$	−1.07807e7	−1.30802
$585$	5.51606e6	0.666407
$586$	−1.22963e7	−1.47921
$587$	−1.07458e6	−0.128720	−0.0643598	−	0.997927i	$-0.520501\pi$
$587$	−1.07458e6	−0.128720	−0.0643598	+	0.997927i	$0.520501\pi$
$588$	−3.40472e7	−4.06104
$589$	7.85938e6	0.933469
$590$	−2.57938e7	−3.05060
$591$	2.75934e7	3.24965
$592$	3.23523e7	3.79404
$593$	−3.13133e6	−0.365673	−0.182836	−	0.983143i	$-0.558528\pi$
$593$	−3.13133e6	−0.365673	−0.182836	+	0.983143i	$0.558528\pi$
$594$	2.32960e6	0.270904
$595$	8.35921e6	0.967995
$596$	4.26849e7	4.92219
$597$	−8.23669e6	−0.945838
$598$	2.35583e6	0.269396
$599$	7.80147e6	0.888402	0.444201	−	0.895927i	$-0.353488\pi$
$599$	7.80147e6	0.888402	0.444201	+	0.895927i	$0.353488\pi$
$600$	−7.98563e7	−9.05589
$601$	9.70561e6	1.09607	0.548033	−	0.836457i	$-0.315377\pi$
$601$	9.70561e6	1.09607	0.548033	+	0.836457i	$0.315377\pi$
$602$	837335.	0.0941690
$603$	−4.05259e6	−0.453878
$604$	3.01340e7	3.36097
$605$	1.41334e7	1.56985
$606$	4.05993e7	4.49094
$607$	1.56543e7	1.72449	0.862246	−	0.506490i	$-0.169057\pi$
$607$	1.56543e7	1.72449	0.862246	+	0.506490i	$0.169057\pi$
$608$	−6.67769e7	−7.32601
$609$	1.56164e6	0.170623
$610$	−2.85080e7	−3.10200
$611$	2.09721e6	0.227268
$612$	−7.96572e7	−8.59700
$613$	1.84483e6	0.198292	0.0991462	−	0.995073i	$-0.468389\pi$
$613$	1.84483e6	0.198292	0.0991462	+	0.995073i	$0.468389\pi$
$614$	−2.86670e7	−3.06875
$615$	−7.57641e6	−0.807747
$616$	1.02038e6	0.108345
$617$	2.79358e6	0.295426	0.147713	−	0.989030i	$-0.452809\pi$
$617$	2.79358e6	0.295426	0.147713	+	0.989030i	$0.452809\pi$
$618$	−2.15908e7	−2.27404
$619$	6.52419e6	0.684385	0.342192	−	0.939630i	$-0.388831\pi$
$619$	6.52419e6	0.684385	0.342192	+	0.939630i	$0.388831\pi$
$620$	−2.29158e7	−2.39417
$621$	1.16317e7	1.21036
$622$	2.27174e7	2.35441
$623$	3.32682e6	0.343407
$624$	−1.39724e7	−1.43651
$625$	−2.56121e6	−0.262268
$626$	−2.74987e7	−2.80464
$627$	−2.26462e6	−0.230053
$628$	5.19400e7	5.25537
$629$	−1.43106e7	−1.44222
$630$	2.52793e7	2.53754
$631$	−1.48062e6	−0.148037	−0.0740183	−	0.997257i	$-0.523582\pi$
$631$	−1.48062e6	−0.148037	−0.0740183	+	0.997257i	$0.523582\pi$
$632$	2.69166e7	2.68057
$633$	−2.55065e7	−2.53012
$634$	2.60323e7	2.57211
$635$	1.75200e7	1.72424
$636$	−6.50290e6	−0.637477
$637$	1.77225e6	0.173052
$638$	371842.	0.0361665
$639$	9.40825e6	0.911500
$640$	6.79346e7	6.55603
$641$	1.57661e7	1.51558	0.757790	−	0.652498i	$-0.226279\pi$
$641$	1.57661e7	1.51558	0.757790	+	0.652498i	$0.226279\pi$
$642$	−2.89829e7	−2.77527
$643$	1.73788e6	0.165765	0.0828825	−	0.996559i	$-0.473587\pi$
$643$	1.73788e6	0.165765	0.0828825	+	0.996559i	$0.473587\pi$
$644$	7.94558e6	0.754937
$645$	3.47438e6	0.328835
$646$	5.36007e7	5.05346
$647$	−8.92631e6	−0.838323	−0.419161	−	0.907912i	$-0.637676\pi$
$647$	−8.92631e6	−0.838323	−0.419161	+	0.907912i	$0.637676\pi$
$648$	−4.15120e7	−3.88361
$649$	819184.	0.0763431
$650$	6.48271e6	0.601829
$651$	4.15315e6	0.384083
$652$	2.48594e7	2.29019
$653$	−8.24306e6	−0.756494	−0.378247	−	0.925705i	$-0.623473\pi$
$653$	−8.24306e6	−0.756494	−0.378247	+	0.925705i	$0.623473\pi$
$654$	−6.16062e7	−5.63223
$655$	4.55918e6	0.415225
$656$	1.28751e7	1.16813
$657$	8.48235e6	0.766660
$658$	9.61119e6	0.865391
$659$	1.73270e7	1.55421	0.777107	−	0.629368i	$-0.216686\pi$
$659$	1.73270e7	1.55421	0.777107	+	0.629368i	$0.216686\pi$
$660$	6.60302e6	0.590042
$661$	9.46218e6	0.842341	0.421170	−	0.906982i	$-0.361619\pi$
$661$	9.46218e6	0.842341	0.421170	+	0.906982i	$0.361619\pi$
$662$	1.50410e7	1.33392
$663$	6.18050e6	0.546060
$664$	−7.24834e7	−6.37996
$665$	−1.25186e7	−1.09774
$666$	−4.32771e7	−3.78070
$667$	1.85660e6	0.161586
$668$	4.92745e7	4.27249
$669$	2.43527e7	2.10369
$670$	−7.95104e6	−0.684285
$671$	905384.	0.0776294
$672$	−3.52871e7	−3.01434
$673$	1.58693e6	0.135058	0.0675290	−	0.997717i	$-0.478488\pi$
$673$	1.58693e6	0.135058	0.0675290	+	0.997717i	$0.478488\pi$
$674$	−3.52173e7	−2.98612
$675$	3.20078e7	2.70393
$676$	−3.16954e7	−2.66765
$677$	3.64454e6	0.305612	0.152806	−	0.988256i	$-0.451169\pi$
$677$	3.64454e6	0.305612	0.152806	+	0.988256i	$0.451169\pi$
$678$	−2.06808e7	−1.72780
$679$	−9.42186e6	−0.784264
$680$	−1.00210e8	−8.31076
$681$	2.76210e7	2.28229
$682$	988905.	0.0814130
$683$	−9.13736e6	−0.749495	−0.374748	−	0.927127i	$-0.622271\pi$
$683$	−9.13736e6	−0.749495	−0.374748	+	0.927127i	$0.622271\pi$
$684$	1.19293e8	9.74934
$685$	−8.54332e6	−0.695665
$686$	1.78382e7	1.44724
$687$	−3.81785e7	−3.08622
$688$	−5.90424e6	−0.475546
$689$	338494.	0.0271646
$690$	4.47979e7	3.58208
$691$	1.81115e7	1.44298	0.721488	−	0.692427i	$-0.243459\pi$
$691$	1.81115e7	1.44298	0.721488	+	0.692427i	$0.243459\pi$
$692$	5.86124e7	4.65291
$693$	−802843.	−0.0635035
$694$	−2.23850e7	−1.76424
$695$	−5.28417e6	−0.414968
$696$	−1.87210e7	−1.46489
$697$	−5.69513e6	−0.444039
$698$	−1.24828e7	−0.969778
$699$	2.83322e7	2.19325
$700$	2.18644e7	1.68653
$701$	−1.33102e7	−1.02304	−0.511518	−	0.859273i	$-0.670917\pi$
$701$	−1.33102e7	−1.02304	−0.511518	+	0.859273i	$0.670917\pi$
$702$	9.52138e6	0.729217
$703$	2.14313e7	1.63554
$704$	−4.37617e6	−0.332784
$705$	3.98800e7	3.02191
$706$	9.42392e6	0.711574
$707$	−7.12762e6	−0.536285
$708$	−6.43215e7	−4.82251
$709$	−2.09133e7	−1.56245	−0.781226	−	0.624249i	$-0.785405\pi$
$709$	−2.09133e7	−1.56245	−0.781226	+	0.624249i	$0.785405\pi$
$710$	1.84587e7	1.37421
$711$	−2.11783e7	−1.57114
$712$	−3.98820e7	−2.94833
$713$	4.93760e6	0.363741
$714$	2.83243e7	2.07929
$715$	−343705.	−0.0251432
$716$	−2.23910e7	−1.63227
$717$	−3.40128e7	−2.47084
$718$	1.56336e6	0.113175
$719$	−8.73488e6	−0.630137	−0.315068	−	0.949069i	$-0.602027\pi$
$719$	−8.73488e6	−0.630137	−0.315068	+	0.949069i	$0.602027\pi$
$720$	−1.78250e8	−12.8144
$721$	3.79048e6	0.271554
$722$	−5.30131e7	−3.78478
$723$	6.77039e6	0.481691
$724$	−4.06280e7	−2.88058
$725$	5.10895e6	0.360983
$726$	4.78896e7	3.37210
$727$	−1.80007e7	−1.26315	−0.631574	−	0.775315i	$-0.717591\pi$
$727$	−1.80007e7	−1.26315	−0.631574	+	0.775315i	$0.717591\pi$
$728$	4.17041e6	0.291642
$729$	−1.26102e7	−0.878826
$730$	1.66421e7	1.15585
$731$	2.61166e6	0.180769
$732$	−7.10898e7	−4.90376
$733$	1.25234e6	0.0860918	0.0430459	−	0.999073i	$-0.486294\pi$
$733$	1.25234e6	0.0860918	0.0430459	+	0.999073i	$0.486294\pi$
$734$	−1.87006e6	−0.128119
$735$	3.37006e7	2.30102
$736$	−4.19521e7	−2.85469
$737$	252516.	0.0171246
$738$	−1.72228e7	−1.16402
$739$	3.67545e6	0.247571	0.123785	−	0.992309i	$-0.460497\pi$
$739$	3.67545e6	0.247571	0.123785	+	0.992309i	$0.460497\pi$
$740$	−6.24878e7	−4.19484
$741$	−9.25580e6	−0.619253
$742$	1.55127e6	0.103437
$743$	4.77871e6	0.317570	0.158785	−	0.987313i	$-0.449242\pi$
$743$	4.77871e6	0.317570	0.158785	+	0.987313i	$0.449242\pi$
$744$	−4.97881e7	−3.29756
$745$	−4.22505e7	−2.78895
$746$	2.46158e7	1.61945
$747$	5.70306e7	3.73944
$748$	4.96344e6	0.324361
$749$	5.08824e6	0.331408
$750$	4.07528e7	2.64548
$751$	−4.55268e6	−0.294556	−0.147278	−	0.989095i	$-0.547051\pi$
$751$	−4.55268e6	−0.294556	−0.147278	+	0.989095i	$0.547051\pi$
$752$	−6.77707e7	−4.37016
$753$	4.28561e7	2.75439
$754$	1.51976e6	0.0973527
$755$	−2.98273e7	−1.90435
$756$	3.21130e7	2.04351
$757$	5.82850e6	0.369672	0.184836	−	0.982769i	$-0.440825\pi$
$757$	5.82850e6	0.369672	0.184836	+	0.982769i	$0.440825\pi$
$758$	−5.45411e6	−0.344787
$759$	−1.42273e6	−0.0896436
$760$	1.50073e8	9.42473
$761$	1.26344e7	0.790848	0.395424	−	0.918499i	$-0.370598\pi$
$761$	1.26344e7	0.790848	0.395424	+	0.918499i	$0.370598\pi$
$762$	5.93646e7	3.70374
$763$	1.08156e7	0.672572
$764$	−7.43093e7	−4.60585
$765$	7.88466e7	4.87112
$766$	3.98537e7	2.45413
$767$	3.34811e6	0.205500
$768$	1.06903e8	6.54014
$769$	−1.22587e7	−0.747532	−0.373766	−	0.927523i	$-0.621934\pi$
$769$	−1.22587e7	−0.747532	−0.373766	+	0.927523i	$0.621934\pi$
$770$	−1.57515e6	−0.0957404
$771$	5.63670e7	3.41499
$772$	2.02574e6	0.122332
$773$	1.09480e7	0.659003	0.329501	−	0.944155i	$-0.393119\pi$
$773$	1.09480e7	0.659003	0.329501	+	0.944155i	$0.393119\pi$
$774$	7.89799e6	0.473875
$775$	1.35872e7	0.812595
$776$	1.12949e8	6.73333
$777$	1.13250e7	0.672955
$778$	−2.66624e7	−1.57925
$779$	8.52891e6	0.503558
$780$	2.69874e7	1.58827
$781$	−586227.	−0.0343905
$782$	3.36742e7	1.96916
$783$	7.50370e6	0.437392
$784$	−5.72697e7	−3.32763
$785$	−5.14114e7	−2.97773
$786$	1.54483e7	0.891917
$787$	−9.68880e6	−0.557613	−0.278807	−	0.960347i	$-0.589939\pi$
$787$	−9.68880e6	−0.557613	−0.278807	+	0.960347i	$0.589939\pi$
$788$	9.05694e7	5.19596
$789$	−5.41415e6	−0.309626
$790$	−4.15510e7	−2.36872
$791$	3.63072e6	0.206325
$792$	9.62450e6	0.545212
$793$	3.70042e6	0.208962
$794$	−1.66073e7	−0.934865
$795$	6.43672e6	0.361199
$796$	−2.70352e7	−1.51233
$797$	−2.29573e7	−1.28019	−0.640097	−	0.768294i	$-0.721106\pi$
$797$	−2.29573e7	−1.28019	−0.640097	+	0.768294i	$0.721106\pi$
$798$	−4.24180e7	−2.35799
$799$	2.99775e7	1.66122
$800$	−1.15443e8	−6.37737
$801$	3.13795e7	1.72809
$802$	8.27402e6	0.454235
$803$	−528535.	−0.0289258
$804$	−1.98273e7	−1.08174
$805$	−7.86472e6	−0.427753
$806$	4.04178e6	0.219147
$807$	−1.05638e7	−0.570998
$808$	8.54460e7	4.60430
$809$	2.77983e7	1.49330	0.746651	−	0.665216i	$-0.231661\pi$
$809$	2.77983e7	1.49330	0.746651	+	0.665216i	$0.231661\pi$
$810$	6.40818e7	3.43180
$811$	−2.15327e7	−1.14960	−0.574800	−	0.818294i	$-0.694920\pi$
$811$	−2.15327e7	−1.14960	−0.574800	+	0.818294i	$0.694920\pi$
$812$	5.12576e6	0.272815
$813$	2.91510e7	1.54677
$814$	2.69659e6	0.142644
$815$	−2.46064e7	−1.29764
$816$	−1.99722e8	−10.5002
$817$	−3.91117e6	−0.204999
$818$	−2.57072e7	−1.34329
$819$	−3.28132e6	−0.170938
$820$	−2.48679e7	−1.29153
$821$	−2.24873e7	−1.16434	−0.582169	−	0.813068i	$-0.697796\pi$
$821$	−2.24873e7	−1.16434	−0.582169	+	0.813068i	$0.697796\pi$
$822$	−2.89482e7	−1.49431
$823$	3.47399e7	1.78784	0.893921	−	0.448225i	$-0.147944\pi$
$823$	3.47399e7	1.78784	0.893921	+	0.448225i	$0.147944\pi$
$824$	−4.54403e7	−2.33143
$825$	−3.91504e6	−0.200263
$826$	1.53439e7	0.782502
$827$	1.68325e7	0.855824	0.427912	−	0.903821i	$-0.359249\pi$
$827$	1.68325e7	0.855824	0.427912	+	0.903821i	$0.359249\pi$
$828$	7.49450e7	3.79898
$829$	−1.74412e7	−0.881433	−0.440716	−	0.897646i	$-0.645276\pi$
$829$	−1.74412e7	−0.881433	−0.440716	+	0.897646i	$0.645276\pi$
$830$	1.11892e8	5.63773
$831$	−4.63059e7	−2.32613
$832$	−1.78859e7	−0.895785
$833$	2.53325e7	1.26493
$834$	−1.79049e7	−0.891366
$835$	−4.87731e7	−2.42083
$836$	−7.43314e6	−0.367838
$837$	1.99559e7	0.984596
$838$	−6.71977e7	−3.30555
$839$	3.46278e6	0.169832	0.0849160	−	0.996388i	$-0.472938\pi$
$839$	3.46278e6	0.169832	0.0849160	+	0.996388i	$0.472938\pi$
$840$	7.93036e7	3.87788
$841$	−1.93134e7	−0.941607
$842$	−3.91525e7	−1.90318
$843$	−6.78185e6	−0.328685
$844$	−8.37197e7	−4.04549
$845$	3.13728e7	1.51151
$846$	9.06555e7	4.35480
$847$	−8.40749e6	−0.402678
$848$	−1.09383e7	−0.522350
$849$	−298030.	−0.0141903
$850$	9.26639e7	4.39909
$851$	1.34641e7	0.637312
$852$	4.60299e7	2.17241
$853$	−9.49288e6	−0.446710	−0.223355	−	0.974737i	$-0.571701\pi$
$853$	−9.49288e6	−0.446710	−0.223355	+	0.974737i	$0.571701\pi$
$854$	1.69585e7	0.795686
$855$	−1.18079e8	−5.52405
$856$	−6.09979e7	−2.84532
$857$	−3.74401e7	−1.74134	−0.870672	−	0.491864i	$-0.836316\pi$
$857$	−3.74401e7	−1.74134	−0.870672	+	0.491864i	$0.836316\pi$
$858$	−1.16461e6	−0.0540085
$859$	2.14199e7	0.990455	0.495227	−	0.868763i	$-0.335085\pi$
$859$	2.14199e7	0.990455	0.495227	+	0.868763i	$0.335085\pi$
$860$	1.14039e7	0.525784
$861$	4.50695e6	0.207193
$862$	4.88980e7	2.24142
$863$	−1.38398e7	−0.632561	−0.316280	−	0.948666i	$-0.602434\pi$
$863$	−1.38398e7	−0.632561	−0.316280	+	0.948666i	$0.602434\pi$
$864$	−1.69555e8	−7.72726
$865$	−5.80159e7	−2.63637
$866$	−3.12659e7	−1.41670
$867$	4.97634e7	2.24834
$868$	1.36318e7	0.614123
$869$	1.31962e6	0.0592786
$870$	2.88995e7	1.29447
$871$	1.03207e6	0.0460959
$872$	−1.29657e8	−5.77439
$873$	−8.88698e7	−3.94656
$874$	−5.04299e7	−2.23310
$875$	−7.15455e6	−0.315909
$876$	4.15000e7	1.82721
$877$	2.44180e7	1.07204	0.536020	−	0.844205i	$-0.319927\pi$
$877$	2.44180e7	1.07204	0.536020	+	0.844205i	$0.319927\pi$
$878$	−2.28196e7	−0.999013
$879$	3.03509e7	1.32495
$880$	1.11068e7	0.483482
$881$	1.35385e7	0.587666	0.293833	−	0.955857i	$-0.405069\pi$
$881$	1.35385e7	0.587666	0.293833	+	0.955857i	$0.405069\pi$
$882$	7.66086e7	3.31594
$883$	−1.15148e7	−0.496998	−0.248499	−	0.968632i	$-0.579937\pi$
$883$	−1.15148e7	−0.496998	−0.248499	+	0.968632i	$0.579937\pi$
$884$	2.02862e7	0.873111
$885$	6.36669e7	2.73247
$886$	−7.21170e7	−3.08641
$887$	4.82708e6	0.206004	0.103002	−	0.994681i	$-0.467155\pi$
$887$	4.82708e6	0.206004	0.103002	+	0.994681i	$0.467155\pi$
$888$	−1.35764e8	−5.77768
$889$	−1.04220e7	−0.442281
$890$	6.15656e7	2.60533
$891$	−2.03517e6	−0.0858828
$892$	7.99326e7	3.36366
$893$	−4.48936e7	−1.88389
$894$	−1.43161e8	−5.99076
$895$	2.21631e7	0.924855
$896$	−4.04120e7	−1.68167
$897$	−5.81489e6	−0.241302
$898$	−2.73920e7	−1.13353
$899$	3.18528e6	0.131446
$900$	2.06232e8	8.48690
$901$	4.83843e6	0.198560
$902$	1.07315e6	0.0439181
$903$	−2.06679e6	−0.0843485
$904$	−4.35251e7	−1.77141
$905$	4.02145e7	1.63216
$906$	−1.01067e8	−4.09061
$907$	−1.19097e7	−0.480710	−0.240355	−	0.970685i	$-0.577264\pi$
$907$	−1.19097e7	−0.480710	−0.240355	+	0.970685i	$0.577264\pi$
$908$	9.06600e7	3.64923
$909$	−6.72298e7	−2.69868
$910$	−6.43784e6	−0.257713
$911$	−1.59962e7	−0.638587	−0.319293	−	0.947656i	$-0.603446\pi$
$911$	−1.59962e7	−0.638587	−0.319293	+	0.947656i	$0.603446\pi$
$912$	2.99099e8	11.9077
$913$	−3.55357e6	−0.141087
$914$	−4.70773e7	−1.86400
$915$	7.03663e7	2.77851
$916$	−1.25313e8	−4.93465
$917$	−2.71210e6	−0.106508
$918$	1.36099e8	5.33024
$919$	−1.46844e7	−0.573544	−0.286772	−	0.957999i	$-0.592582\pi$
$919$	−1.46844e7	−0.573544	−0.286772	+	0.957999i	$0.592582\pi$
$920$	9.42824e7	3.67249
$921$	7.07588e7	2.74873
$922$	6.12902e7	2.37446
$923$	−2.39598e6	−0.0925720
$924$	−3.92792e6	−0.151350
$925$	3.70501e7	1.42375
$926$	1.75652e7	0.673170
$927$	3.57529e7	1.36651
$928$	−2.70636e7	−1.03161
$929$	−3.20826e7	−1.21964	−0.609818	−	0.792541i	$-0.708758\pi$
$929$	−3.20826e7	−1.21964	−0.609818	+	0.792541i	$0.708758\pi$
$930$	7.68576e7	2.91393
$931$	−3.79375e7	−1.43448
$932$	9.29944e7	3.50685
$933$	−5.60732e7	−2.10888
$934$	−5.87474e7	−2.20354
$935$	−4.91292e6	−0.183785
$936$	3.93365e7	1.46760
$937$	−3.86582e7	−1.43844	−0.719222	−	0.694780i	$-0.755502\pi$
$937$	−3.86582e7	−1.43844	−0.719222	+	0.694780i	$0.755502\pi$
$938$	4.72981e6	0.175524
$939$	6.78750e7	2.51215
$940$	1.30898e8	4.83183
$941$	−1.47207e7	−0.541942	−0.270971	−	0.962587i	$-0.587345\pi$
$941$	−1.47207e7	−0.541942	−0.270971	+	0.962587i	$0.587345\pi$
$942$	−1.74202e8	−6.39627
$943$	5.35822e6	0.196219
$944$	−1.08193e8	−3.95158
$945$	−3.17862e7	−1.15787
$946$	−492123.	−0.0178791
$947$	2.52750e7	0.915833	0.457916	−	0.888995i	$-0.348596\pi$
$947$	2.52750e7	0.915833	0.457916	+	0.888995i	$0.348596\pi$
$948$	−1.03615e8	−3.74456
$949$	−2.16019e6	−0.0778621
$950$	−1.38772e8	−4.98875
$951$	−6.42556e7	−2.30388
$952$	5.96118e7	2.13177
$953$	1.85227e7	0.660652	0.330326	−	0.943867i	$-0.392841\pi$
$953$	1.85227e7	0.660652	0.330326	+	0.943867i	$0.392841\pi$
$954$	1.46320e7	0.520515
$955$	7.35530e7	2.60971
$956$	−1.11640e8	−3.95070
$957$	−917817.	−0.0323949
$958$	4.52953e7	1.59455
$959$	5.08214e6	0.178443
$960$	−3.40115e8	−11.9110
$961$	−2.01580e7	−0.704106
$962$	1.10213e7	0.383968
$963$	4.79938e7	1.66770
$964$	2.22224e7	0.770190
$965$	−2.00512e6	−0.0693143
$966$	−2.66488e7	−0.918829
$967$	3.92303e7	1.34914	0.674568	−	0.738213i	$-0.264330\pi$
$967$	3.92303e7	1.34914	0.674568	+	0.738213i	$0.264330\pi$
$968$	1.00789e8	3.45721
$969$	−1.32302e8	−4.52646
$970$	−1.74359e8	−5.94999
$971$	3.09183e7	1.05237	0.526183	−	0.850371i	$-0.323623\pi$
$971$	3.09183e7	1.05237	0.526183	+	0.850371i	$0.323623\pi$
$972$	1.12029e7	0.380332
$973$	3.14338e6	0.106442
$974$	−464532.	−0.0156898
$975$	−1.60013e7	−0.539067
$976$	−1.19578e8	−4.01816
$977$	−6.70144e6	−0.224611	−0.112306	−	0.993674i	$-0.535824\pi$
$977$	−6.70144e6	−0.224611	−0.112306	+	0.993674i	$0.535824\pi$
$978$	−8.33763e7	−2.78738
$979$	−1.95526e6	−0.0651999
$980$	1.10615e8	3.67917
$981$	1.02016e8	3.38450
$982$	−1.06762e8	−3.53295
$983$	966289.	0.0318950
$983$	966289.	0.0318950
$984$	−5.40294e7	−1.77886
$985$	−8.96477e7	−2.94407
$986$	2.17235e7	0.711603
$987$	−2.37233e7	−0.775143
$988$	−3.03802e7	−0.990143
$989$	−2.45717e6	−0.0798811
$990$	−1.48573e7	−0.481783
$991$	−1.45872e7	−0.471834	−0.235917	−	0.971773i	$-0.575809\pi$
$991$	−1.45872e7	−0.471834	−0.235917	+	0.971773i	$0.575809\pi$
$992$	−7.19752e7	−2.32222
$993$	−3.71256e7	−1.19482
$994$	−1.09804e7	−0.352496
$995$	2.67600e7	0.856897
$996$	2.79023e8	8.91233
$997$	3.22481e7	1.02746	0.513732	−	0.857951i	$-0.328263\pi$
$997$	3.22481e7	1.02746	0.513732	+	0.857951i	$0.328263\pi$
$998$	−2.47683e7	−0.787172
$999$	5.44167e7	1.72512

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.6.a.b.1.5	✓	218

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.6.a.b.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-11.0085 q^{2} +27.1723 q^{3} +89.1872 q^{4} -88.2795 q^{5} -299.126 q^{6} +52.5145 q^{7} -629.545 q^{8} +495.333 q^{9} +O(q^{10})\)	\(q-11.0085 q^{2} +27.1723 q^{3} +89.1872 q^{4} -88.2795 q^{5} -299.126 q^{6} +52.5145 q^{7} -629.545 q^{8} +495.333 q^{9} +971.825 q^{10} -30.8641 q^{11} +2423.42 q^{12} -126.146 q^{13} -578.107 q^{14} -2398.76 q^{15} +4076.36 q^{16} -1803.13 q^{17} -5452.87 q^{18} +2700.32 q^{19} -7873.40 q^{20} +1426.94 q^{21} +339.768 q^{22} +1696.46 q^{23} -17106.2 q^{24} +4668.27 q^{25} +1388.67 q^{26} +6856.45 q^{27} +4683.62 q^{28} +1094.40 q^{29} +26406.7 q^{30} +2910.53 q^{31} -24729.2 q^{32} -838.649 q^{33} +19849.7 q^{34} -4635.96 q^{35} +44177.3 q^{36} +7936.57 q^{37} -29726.5 q^{38} -3427.66 q^{39} +55576.0 q^{40} +3158.47 q^{41} -15708.5 q^{42} -1448.41 q^{43} -2752.69 q^{44} -43727.7 q^{45} -18675.5 q^{46} -16625.3 q^{47} +110764. q^{48} -14049.2 q^{49} -51390.7 q^{50} -48995.0 q^{51} -11250.6 q^{52} -2683.36 q^{53} -75479.3 q^{54} +2724.67 q^{55} -33060.3 q^{56} +73374.0 q^{57} -12047.7 q^{58} -26541.6 q^{59} -213938. q^{60} -29334.5 q^{61} -32040.6 q^{62} +26012.2 q^{63} +141788. q^{64} +11136.1 q^{65} +9232.27 q^{66} -8181.55 q^{67} -160816. q^{68} +46096.7 q^{69} +51035.0 q^{70} +18993.8 q^{71} -311834. q^{72} +17124.6 q^{73} -87369.7 q^{74} +126848. q^{75} +240834. q^{76} -1620.82 q^{77} +37733.4 q^{78} -42755.6 q^{79} -359859. q^{80} +65939.6 q^{81} -34770.1 q^{82} +115136. q^{83} +127265. q^{84} +159179. q^{85} +15944.8 q^{86} +29737.3 q^{87} +19430.4 q^{88} +63350.4 q^{89} +481377. q^{90} -6624.48 q^{91} +151302. q^{92} +79085.8 q^{93} +183019. q^{94} -238383. q^{95} -671949. q^{96} -179414. q^{97} +154661. q^{98} -15288.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9}+O(q^{10}) \) 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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