LMFDB - Embedded newform 983.6.a.b.1.12

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			1.12
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.3513 q^{2} +9.89991 q^{3} +75.1501 q^{4} +97.3083 q^{5} -102.477 q^{6} -91.6942 q^{7} -446.662 q^{8} -144.992 q^{9} +O(q^{10})$	\(q-10.3513 q^{2} +9.89991 q^{3} +75.1501 q^{4} +97.3083 q^{5} -102.477 q^{6} -91.6942 q^{7} -446.662 q^{8} -144.992 q^{9} -1007.27 q^{10} +86.2506 q^{11} +743.979 q^{12} -925.561 q^{13} +949.157 q^{14} +963.343 q^{15} +2218.74 q^{16} +730.431 q^{17} +1500.86 q^{18} +1788.50 q^{19} +7312.73 q^{20} -907.764 q^{21} -892.809 q^{22} +209.428 q^{23} -4421.91 q^{24} +6343.91 q^{25} +9580.79 q^{26} -3841.08 q^{27} -6890.83 q^{28} -8852.68 q^{29} -9971.89 q^{30} -5071.42 q^{31} -8673.75 q^{32} +853.873 q^{33} -7560.93 q^{34} -8922.61 q^{35} -10896.2 q^{36} -12607.3 q^{37} -18513.4 q^{38} -9162.97 q^{39} -43463.9 q^{40} +19585.5 q^{41} +9396.57 q^{42} +19167.9 q^{43} +6481.75 q^{44} -14108.9 q^{45} -2167.86 q^{46} +10941.2 q^{47} +21965.3 q^{48} -8399.17 q^{49} -65667.9 q^{50} +7231.19 q^{51} -69556.1 q^{52} +21316.9 q^{53} +39760.3 q^{54} +8392.90 q^{55} +40956.3 q^{56} +17706.0 q^{57} +91637.1 q^{58} -5118.72 q^{59} +72395.4 q^{60} +4813.59 q^{61} +52496.0 q^{62} +13294.9 q^{63} +18785.2 q^{64} -90064.8 q^{65} -8838.73 q^{66} -21436.0 q^{67} +54892.0 q^{68} +2073.32 q^{69} +92360.9 q^{70} +30547.7 q^{71} +64762.3 q^{72} -51142.8 q^{73} +130502. q^{74} +62804.1 q^{75} +134406. q^{76} -7908.68 q^{77} +94849.0 q^{78} -49898.2 q^{79} +215902. q^{80} -2793.33 q^{81} -202736. q^{82} +74032.9 q^{83} -68218.6 q^{84} +71077.0 q^{85} -198413. q^{86} -87640.7 q^{87} -38524.9 q^{88} -40436.2 q^{89} +146046. q^{90} +84868.6 q^{91} +15738.6 q^{92} -50206.6 q^{93} -113256. q^{94} +174036. q^{95} -85869.3 q^{96} +61393.7 q^{97} +86942.7 q^{98} -12505.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9}+O(q^{10}) $ 218 * q + 35 * q^2 + 70 * q^3 + 3685 * q^4 + 253 * q^5 + 529 * q^6 + 1567 * q^7 + 1695 * q^8 + 19812 * q^9	\( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9} + 2133 q^{10} + 1752 q^{11} + 3512 q^{12} + 5990 q^{13} + 2319 q^{14} + 4639 q^{15} + 66105 q^{16} + 10656 q^{17} + 11911 q^{18} + 11511 q^{19} + 10012 q^{20} + 12225 q^{21} + 19401 q^{22} + 9767 q^{23} + 21725 q^{24} + 185207 q^{25} + 7708 q^{26} + 23764 q^{27} + 77808 q^{28} + 25772 q^{29} + 15736 q^{30} + 35900 q^{31} + 60155 q^{32} + 70026 q^{33} + 17236 q^{34} + 28782 q^{35} + 382874 q^{36} + 126082 q^{37} + 62164 q^{38} + 54264 q^{39} + 102846 q^{40} + 70480 q^{41} + 102244 q^{42} + 137413 q^{43} + 116278 q^{44} + 93481 q^{45} + 126122 q^{46} + 63218 q^{47} + 124701 q^{48} + 732031 q^{49} + 131089 q^{50} + 109902 q^{51} + 229519 q^{52} + 102608 q^{53} + 149130 q^{54} + 167596 q^{55} + 87868 q^{56} + 408318 q^{57} + 304579 q^{58} + 67460 q^{59} + 150523 q^{60} + 195132 q^{61} + 132294 q^{62} + 374425 q^{63} + 1296639 q^{64} + 347092 q^{65} + 147397 q^{66} + 381238 q^{67} + 296321 q^{68} + 139362 q^{69} + 325675 q^{70} + 147818 q^{71} + 646059 q^{72} + 961992 q^{73} + 167410 q^{74} + 167324 q^{75} + 504875 q^{76} + 284328 q^{77} + 284295 q^{78} + 285792 q^{79} + 444932 q^{80} + 1980282 q^{81} + 336676 q^{82} + 276734 q^{83} + 378474 q^{84} + 1021245 q^{85} + 156051 q^{86} + 500457 q^{87} + 1068101 q^{88} + 398983 q^{89} + 463961 q^{90} + 273517 q^{91} + 577884 q^{92} + 967833 q^{93} + 224775 q^{94} + 482817 q^{95} + 780445 q^{96} + 1636277 q^{97} + 495958 q^{98} + 627643 q^{99}+O(q^{100}) \) 218 * q + 35 * q^2 + 70 * q^3 + 3685 * q^4 + 253 * q^5 + 529 * q^6 + 1567 * q^7 + 1695 * q^8 + 19812 * q^9 + 2133 * q^10 + 1752 * q^11 + 3512 * q^12 + 5990 * q^13 + 2319 * q^14 + 4639 * q^15 + 66105 * q^16 + 10656 * q^17 + 11911 * q^18 + 11511 * q^19 + 10012 * q^20 + 12225 * q^21 + 19401 * q^22 + 9767 * q^23 + 21725 * q^24 + 185207 * q^25 + 7708 * q^26 + 23764 * q^27 + 77808 * q^28 + 25772 * q^29 + 15736 * q^30 + 35900 * q^31 + 60155 * q^32 + 70026 * q^33 + 17236 * q^34 + 28782 * q^35 + 382874 * q^36 + 126082 * q^37 + 62164 * q^38 + 54264 * q^39 + 102846 * q^40 + 70480 * q^41 + 102244 * q^42 + 137413 * q^43 + 116278 * q^44 + 93481 * q^45 + 126122 * q^46 + 63218 * q^47 + 124701 * q^48 + 732031 * q^49 + 131089 * q^50 + 109902 * q^51 + 229519 * q^52 + 102608 * q^53 + 149130 * q^54 + 167596 * q^55 + 87868 * q^56 + 408318 * q^57 + 304579 * q^58 + 67460 * q^59 + 150523 * q^60 + 195132 * q^61 + 132294 * q^62 + 374425 * q^63 + 1296639 * q^64 + 347092 * q^65 + 147397 * q^66 + 381238 * q^67 + 296321 * q^68 + 139362 * q^69 + 325675 * q^70 + 147818 * q^71 + 646059 * q^72 + 961992 * q^73 + 167410 * q^74 + 167324 * q^75 + 504875 * q^76 + 284328 * q^77 + 284295 * q^78 + 285792 * q^79 + 444932 * q^80 + 1980282 * q^81 + 336676 * q^82 + 276734 * q^83 + 378474 * q^84 + 1021245 * q^85 + 156051 * q^86 + 500457 * q^87 + 1068101 * q^88 + 398983 * q^89 + 463961 * q^90 + 273517 * q^91 + 577884 * q^92 + 967833 * q^93 + 224775 * q^94 + 482817 * q^95 + 780445 * q^96 + 1636277 * q^97 + 495958 * q^98 + 627643 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−10.3513	−1.82987	−0.914937	−	0.403596i	$-0.867760\pi$
$2$	−10.3513	−1.82987	−0.914937	+	0.403596i	$0.867760\pi$
$3$	9.89991	0.635079	0.317540	−	0.948245i	$-0.397143\pi$
$3$	9.89991	0.635079	0.317540	+	0.948245i	$0.397143\pi$
$4$	75.1501	2.34844
$5$	97.3083	1.74070	0.870352	−	0.492430i	$-0.163891\pi$
$5$	97.3083	1.74070	0.870352	+	0.492430i	$0.163891\pi$
$6$	−102.477	−1.16212
$7$	−91.6942	−0.707289	−0.353644	−	0.935380i	$-0.615058\pi$
$7$	−91.6942	−0.707289	−0.353644	+	0.935380i	$0.615058\pi$
$8$	−446.662	−2.46748
$9$	−144.992	−0.596674
$10$	−1007.27	−3.18527
$11$	86.2506	0.214922	0.107461	−	0.994209i	$-0.465728\pi$
$11$	86.2506	0.214922	0.107461	+	0.994209i	$0.465728\pi$
$12$	743.979	1.49145
$13$	−925.561	−1.51896	−0.759481	−	0.650530i	$-0.774547\pi$
$13$	−925.561	−1.51896	−0.759481	+	0.650530i	$0.774547\pi$
$14$	949.157	1.29425
$15$	963.343	1.10549
$16$	2218.74	2.16674
$17$	730.431	0.612995	0.306497	−	0.951872i	$-0.400843\pi$
$17$	730.431	0.612995	0.306497	+	0.951872i	$0.400843\pi$
$18$	1500.86	1.09184
$19$	1788.50	1.13659	0.568297	−	0.822824i	$-0.307603\pi$
$19$	1788.50	1.13659	0.568297	+	0.822824i	$0.307603\pi$
$20$	7312.73	4.08794
$21$	−907.764	−0.449184
$22$	−892.809	−0.393280
$23$	209.428	0.0825498	0.0412749	−	0.999148i	$-0.486858\pi$
$23$	209.428	0.0825498	0.0412749	+	0.999148i	$0.486858\pi$
$24$	−4421.91	−1.56705
$25$	6343.91	2.03005
$26$	9580.79	2.77951
$27$	−3841.08	−1.01401
$28$	−6890.83	−1.66103
$29$	−8852.68	−1.95470	−0.977349	−	0.211632i	$-0.932122\pi$
$29$	−8852.68	−1.95470	−0.977349	+	0.211632i	$0.932122\pi$
$30$	−9971.89	−2.02290
$31$	−5071.42	−0.947820	−0.473910	−	0.880573i	$-0.657158\pi$
$31$	−5071.42	−0.947820	−0.473910	+	0.880573i	$0.657158\pi$
$32$	−8673.75	−1.49738
$33$	853.873	0.136492
$34$	−7560.93	−1.12170
$35$	−8922.61	−1.23118
$36$	−10896.2	−1.40126
$37$	−12607.3	−1.51397	−0.756986	−	0.653431i	$-0.773329\pi$
$37$	−12607.3	−1.51397	−0.756986	+	0.653431i	$0.773329\pi$
$38$	−18513.4	−2.07982
$39$	−9162.97	−0.964661
$40$	−43463.9	−4.29515
$41$	19585.5	1.81960	0.909799	−	0.415048i	$-0.136235\pi$
$41$	19585.5	1.81960	0.909799	+	0.415048i	$0.136235\pi$
$42$	9396.57	0.821951
$43$	19167.9	1.58089	0.790446	−	0.612531i	$-0.209849\pi$
$43$	19167.9	1.58089	0.790446	+	0.612531i	$0.209849\pi$
$44$	6481.75	0.504732
$45$	−14108.9	−1.03863
$46$	−2167.86	−0.151056
$47$	10941.2	0.722471	0.361235	−	0.932475i	$-0.382355\pi$
$47$	10941.2	0.722471	0.361235	+	0.932475i	$0.382355\pi$
$48$	21965.3	1.37605
$49$	−8399.17	−0.499743
$50$	−65667.9	−3.71474
$51$	7231.19	0.389300
$52$	−69556.1	−3.56719
$53$	21316.9	1.04240	0.521199	−	0.853435i	$-0.325485\pi$
$53$	21316.9	1.04240	0.521199	+	0.853435i	$0.325485\pi$
$54$	39760.3	1.85552
$55$	8392.90	0.374115
$56$	40956.3	1.74522
$57$	17706.0	0.721827
$58$	91637.1	3.57685
$59$	−5118.72	−0.191439	−0.0957197	−	0.995408i	$-0.530515\pi$
$59$	−5118.72	−0.191439	−0.0957197	+	0.995408i	$0.530515\pi$
$60$	72395.4	2.59617
$61$	4813.59	0.165632	0.0828161	−	0.996565i	$-0.473609\pi$
$61$	4813.59	0.165632	0.0828161	+	0.996565i	$0.473609\pi$
$62$	52496.0	1.73439
$63$	13294.9	0.422021
$64$	18785.2	0.573279
$65$	−90064.8	−2.64406
$66$	−8838.73	−0.249764
$67$	−21436.0	−0.583387	−0.291694	−	0.956512i	$-0.594219\pi$
$67$	−21436.0	−0.583387	−0.291694	+	0.956512i	$0.594219\pi$
$68$	54892.0	1.43958
$69$	2073.32	0.0524257
$70$	92360.9	2.25291
$71$	30547.7	0.719171	0.359585	−	0.933112i	$-0.382918\pi$
$71$	30547.7	0.719171	0.359585	+	0.933112i	$0.382918\pi$
$72$	64762.3	1.47228
$73$	−51142.8	−1.12325	−0.561626	−	0.827391i	$-0.689824\pi$
$73$	−51142.8	−1.12325	−0.561626	+	0.827391i	$0.689824\pi$
$74$	130502.	2.77038
$75$	62804.1	1.28924
$76$	134406.	2.66922
$77$	−7908.68	−0.152012
$78$	94849.0	1.76521
$79$	−49898.2	−0.899533	−0.449767	−	0.893146i	$-0.648493\pi$
$79$	−49898.2	−0.899533	−0.449767	+	0.893146i	$0.648493\pi$
$80$	215902.	3.77165
$81$	−2793.33	−0.0473054
$82$	−202736.	−3.32964
$83$	74032.9	1.17959	0.589793	−	0.807554i	$-0.299209\pi$
$83$	74032.9	1.17959	0.589793	+	0.807554i	$0.299209\pi$
$84$	−68218.6	−1.05488
$85$	71077.0	1.06704
$86$	−198413.	−2.89284
$87$	−87640.7	−1.24139
$88$	−38524.9	−0.530315
$89$	−40436.2	−0.541123	−0.270561	−	0.962703i	$-0.587209\pi$
$89$	−40436.2	−0.541123	−0.270561	+	0.962703i	$0.587209\pi$
$90$	146046.	1.90057
$91$	84868.6	1.07434
$92$	15738.6	0.193863
$93$	−50206.6	−0.601941
$94$	−113256.	−1.32203
$95$	174036.	1.97847
$96$	−85869.3	−0.950955
$97$	61393.7	0.662514	0.331257	−	0.943541i	$-0.392527\pi$
$97$	61393.7	0.662514	0.331257	+	0.943541i	$0.392527\pi$
$98$	86942.7	0.914466
$99$	−12505.6	−0.128238
$100$	476746.	4.76746
$101$	136600.	1.33243	0.666217	−	0.745758i	$-0.267912\pi$
$101$	136600.	1.33243	0.666217	+	0.745758i	$0.267912\pi$
$102$	−74852.5	−0.712371
$103$	−12636.5	−0.117363	−0.0586816	−	0.998277i	$-0.518690\pi$
$103$	−12636.5	−0.117363	−0.0586816	+	0.998277i	$0.518690\pi$
$104$	413413.	3.74801
$105$	−88333.0	−0.781897
$106$	−220658.	−1.90746
$107$	194457.	1.64197	0.820985	−	0.570950i	$-0.193425\pi$
$107$	194457.	1.64197	0.820985	+	0.570950i	$0.193425\pi$
$108$	−288658.	−2.38135
$109$	230942.	1.86182	0.930908	−	0.365253i	$-0.119018\pi$
$109$	230942.	1.86182	0.930908	+	0.365253i	$0.119018\pi$
$110$	−86877.8	−0.684584
$111$	−124811.	−0.961493
$112$	−203446.	−1.53251
$113$	68509.5	0.504725	0.252363	−	0.967633i	$-0.418792\pi$
$113$	68509.5	0.504725	0.252363	+	0.967633i	$0.418792\pi$
$114$	−183281.	−1.32085
$115$	20379.1	0.143695
$116$	−665280.	−4.59050
$117$	134199.	0.906325
$118$	52985.6	0.350310
$119$	−66976.3	−0.433564
$120$	−430288.	−2.72776
$121$	−153612.	−0.953809
$122$	−49827.1	−0.303086
$123$	193895.	1.15559
$124$	−381118.	−2.22590
$125$	313227.	1.79301
$126$	−137620.	−0.772246
$127$	−18421.9	−0.101350	−0.0506751	−	0.998715i	$-0.516137\pi$
$127$	−18421.9	−0.101350	−0.0506751	+	0.998715i	$0.516137\pi$
$128$	83108.0	0.448351
$129$	189760.	1.00399
$130$	932291.	4.83830
$131$	225310.	1.14710	0.573552	−	0.819169i	$-0.305565\pi$
$131$	225310.	1.14710	0.573552	+	0.819169i	$0.305565\pi$
$132$	64168.7	0.320545
$133$	−163995.	−0.803900
$134$	221891.	1.06753
$135$	−373769.	−1.76510
$136$	−326255.	−1.51255
$137$	−190919.	−0.869056	−0.434528	−	0.900658i	$-0.643085\pi$
$137$	−190919.	−0.869056	−0.434528	+	0.900658i	$0.643085\pi$
$138$	−21461.6	−0.0959324
$139$	52871.6	0.232105	0.116053	−	0.993243i	$-0.462976\pi$
$139$	52871.6	0.232105	0.116053	+	0.993243i	$0.462976\pi$
$140$	−670535.	−2.89136
$141$	108317.	0.458826
$142$	−316209.	−1.31599
$143$	−79830.2	−0.326458
$144$	−321699.	−1.29284
$145$	−861440.	−3.40255
$146$	529396.	2.05541
$147$	−83151.0	−0.317376
$148$	−947441.	−3.55548
$149$	187424.	0.691606	0.345803	−	0.938307i	$-0.387606\pi$
$149$	187424.	0.691606	0.345803	+	0.938307i	$0.387606\pi$
$150$	−650106.	−2.35915
$151$	−296286.	−1.05747	−0.528735	−	0.848787i	$-0.677334\pi$
$151$	−296286.	−1.05747	−0.528735	+	0.848787i	$0.677334\pi$
$152$	−798855.	−2.80452
$153$	−105907.	−0.365758
$154$	81865.4	0.278163
$155$	−493492.	−1.64987
$156$	−688598.	−2.26545
$157$	490488.	1.58810	0.794052	−	0.607849i	$-0.207968\pi$
$157$	490488.	1.58810	0.794052	+	0.607849i	$0.207968\pi$
$158$	516513.	1.64603
$159$	211035.	0.662005
$160$	−844028.	−2.60649
$161$	−19203.4	−0.0583865
$162$	28914.7	0.0865629
$163$	524144.	1.54519	0.772595	−	0.634899i	$-0.218958\pi$
$163$	524144.	1.54519	0.772595	+	0.634899i	$0.218958\pi$
$164$	1.47186e6	4.27322
$165$	83089.0	0.237593
$166$	−766340.	−2.15849
$167$	159795.	0.443375	0.221688	−	0.975118i	$-0.428843\pi$
$167$	159795.	0.443375	0.221688	+	0.975118i	$0.428843\pi$
$168$	405463.	1.10835
$169$	485371.	1.30724
$170$	−735742.	−1.95255
$171$	−259318.	−0.678176
$172$	1.44047e6	3.71263
$173$	−50370.2	−0.127955	−0.0639777	−	0.997951i	$-0.520379\pi$
$173$	−50370.2	−0.127955	−0.0639777	+	0.997951i	$0.520379\pi$
$174$	907198.	2.27159
$175$	−581700.	−1.43583
$176$	191368.	0.465679
$177$	−50674.8	−0.121579
$178$	418569.	0.990186
$179$	−72514.7	−0.169158	−0.0845792	−	0.996417i	$-0.526955\pi$
$179$	−72514.7	−0.169158	−0.0845792	+	0.996417i	$0.526955\pi$
$180$	−1.06029e6	−2.43917
$181$	19033.4	0.0431837	0.0215918	−	0.999767i	$-0.493127\pi$
$181$	19033.4	0.0431837	0.0215918	+	0.999767i	$0.493127\pi$
$182$	−878503.	−1.96592
$183$	47654.1	0.105190
$184$	−93543.6	−0.203690
$185$	−1.22680e6	−2.63538
$186$	519706.	1.10148
$187$	63000.1	0.131746
$188$	822233.	1.69668
$189$	352205.	0.717201
$190$	−1.80151e6	−3.62036
$191$	40097.4	0.0795304	0.0397652	−	0.999209i	$-0.487339\pi$
$191$	40097.4	0.0795304	0.0397652	+	0.999209i	$0.487339\pi$
$192$	185972.	0.364077
$193$	392495.	0.758474	0.379237	−	0.925300i	$-0.376187\pi$
$193$	392495.	0.758474	0.379237	+	0.925300i	$0.376187\pi$
$194$	−635507.	−1.21232
$195$	−891633.	−1.67919
$196$	−631199.	−1.17362
$197$	−397111.	−0.729032	−0.364516	−	0.931197i	$-0.618766\pi$
$197$	−397111.	−0.729032	−0.364516	+	0.931197i	$0.618766\pi$
$198$	129450.	0.234660
$199$	−1.04030e6	−1.86220	−0.931102	−	0.364758i	$-0.881152\pi$
$199$	−1.04030e6	−1.86220	−0.931102	+	0.364758i	$0.881152\pi$
$200$	−2.83358e6	−5.00911
$201$	−212215.	−0.370497
$202$	−1.41399e6	−2.43819
$203$	811740.	1.38254
$204$	543425.	0.914249
$205$	1.90584e6	3.16738
$206$	130804.	0.214760
$207$	−30365.4	−0.0492554
$208$	−2.05358e6	−3.29119
$209$	154259.	0.244279
$210$	914364.	1.43077
$211$	518297.	0.801443	0.400722	−	0.916200i	$-0.368759\pi$
$211$	518297.	0.801443	0.400722	+	0.916200i	$0.368759\pi$
$212$	1.60197e6	2.44801
$213$	302419.	0.456731
$214$	−2.01289e6	−3.00460
$215$	1.86519e6	2.75187
$216$	1.71566e6	2.50206
$217$	465020.	0.670382
$218$	−2.39056e6	−3.40689
$219$	−506309.	−0.713354
$220$	630728.	0.878588
$221$	−676058.	−0.931115
$222$	1.29196e6	1.75941
$223$	932739.	1.25602	0.628012	−	0.778204i	$-0.283869\pi$
$223$	932739.	1.25602	0.628012	+	0.778204i	$0.283869\pi$
$224$	795332.	1.05908
$225$	−919815.	−1.21128
$226$	−709165.	−0.923584
$227$	526981.	0.678782	0.339391	−	0.940645i	$-0.389779\pi$
$227$	526981.	0.678782	0.339391	+	0.940645i	$0.389779\pi$
$228$	1.33061e6	1.69517
$229$	−12487.2	−0.0157353	−0.00786767	−	0.999969i	$-0.502504\pi$
$229$	−12487.2	−0.0157353	−0.00786767	+	0.999969i	$0.502504\pi$
$230$	−210951.	−0.262943
$231$	−78295.2	−0.0965396
$232$	3.95415e6	4.82318
$233$	−297799.	−0.359363	−0.179682	−	0.983725i	$-0.557507\pi$
$233$	−297799.	−0.359363	−0.179682	+	0.983725i	$0.557507\pi$
$234$	−1.38914e6	−1.65846
$235$	1.06467e6	1.25761
$236$	−384672.	−0.449584
$237$	−493987.	−0.571275
$238$	693294.	0.793368
$239$	1.14707e6	1.29896	0.649482	−	0.760377i	$-0.274986\pi$
$239$	1.14707e6	1.29896	0.649482	+	0.760377i	$0.274986\pi$
$240$	2.13741e6	2.39530
$241$	638908.	0.708591	0.354295	−	0.935134i	$-0.384721\pi$
$241$	638908.	0.708591	0.354295	+	0.935134i	$0.384721\pi$
$242$	1.59009e6	1.74535
$243$	905729.	0.983972
$244$	361742.	0.388977
$245$	−817310.	−0.869904
$246$	−2.00707e6	−2.11458
$247$	−1.65537e6	−1.72644
$248$	2.26521e6	2.33873
$249$	732919.	0.749131
$250$	−3.24231e6	−3.28099
$251$	210034.	0.210429	0.105214	−	0.994450i	$-0.466447\pi$
$251$	210034.	0.210429	0.105214	+	0.994450i	$0.466447\pi$
$252$	999115.	0.991092
$253$	18063.3	0.0177418
$254$	190691.	0.185458
$255$	703655.	0.677656
$256$	−1.46141e6	−1.39370
$257$	1.36675e6	1.29079	0.645397	−	0.763847i	$-0.276692\pi$
$257$	1.36675e6	1.29079	0.645397	+	0.763847i	$0.276692\pi$
$258$	−1.96427e6	−1.83718
$259$	1.15602e6	1.07082
$260$	−6.76838e6	−6.20943
$261$	1.28357e6	1.16632
$262$	−2.33226e6	−2.09906
$263$	341338.	0.304295	0.152148	−	0.988358i	$-0.451381\pi$
$263$	341338.	0.304295	0.152148	+	0.988358i	$0.451381\pi$
$264$	−381392.	−0.336792
$265$	2.07431e6	1.81451
$266$	1.69757e6	1.47104
$267$	−400315.	−0.343656
$268$	−1.61092e6	−1.37005
$269$	−1.88270e6	−1.58635	−0.793176	−	0.608992i	$-0.791574\pi$
$269$	−1.88270e6	−1.58635	−0.793176	+	0.608992i	$0.791574\pi$
$270$	3.86901e6	3.22991
$271$	−2.11279e6	−1.74756	−0.873780	−	0.486321i	$-0.838339\pi$
$271$	−2.11279e6	−1.74756	−0.873780	+	0.486321i	$0.838339\pi$
$272$	1.62064e6	1.32820
$273$	840191.	0.682294
$274$	1.97627e6	1.59026
$275$	547166.	0.436302
$276$	155810.	0.123119
$277$	−205260.	−0.160733	−0.0803667	−	0.996765i	$-0.525609\pi$
$277$	−205260.	−0.160733	−0.0803667	+	0.996765i	$0.525609\pi$
$278$	−547292.	−0.424724
$279$	735315.	0.565540
$280$	3.98539e6	3.03791
$281$	−1.23813e6	−0.935410	−0.467705	−	0.883885i	$-0.654919\pi$
$281$	−1.23813e6	−0.935410	−0.467705	+	0.883885i	$0.654919\pi$
$282$	−1.12122e6	−0.839594
$283$	213076.	0.158150	0.0790748	−	0.996869i	$-0.474803\pi$
$283$	213076.	0.158150	0.0790748	+	0.996869i	$0.474803\pi$
$284$	2.29566e6	1.68893
$285$	1.72294e6	1.25649
$286$	826350.	0.597377
$287$	−1.79588e6	−1.28698
$288$	1.25762e6	0.893448
$289$	−886328.	−0.624238
$290$	8.91705e6	6.22625
$291$	607792.	0.420749
$292$	−3.84339e6	−2.63789
$293$	−1.88647e6	−1.28375	−0.641876	−	0.766809i	$-0.721844\pi$
$293$	−1.88647e6	−1.28375	−0.641876	+	0.766809i	$0.721844\pi$
$294$	860724.	0.580759
$295$	−498094.	−0.333239
$296$	5.63120e6	3.73570
$297$	−331296.	−0.217934
$298$	−1.94009e6	−1.26555
$299$	−193839.	−0.125390
$300$	4.71974e6	3.02771
$301$	−1.75758e6	−1.11815
$302$	3.06695e6	1.93504
$303$	1.35232e6	0.846202
$304$	3.96822e6	2.46270
$305$	468402.	0.288317
$306$	1.09627e6	0.669292
$307$	96227.7	0.0582712	0.0291356	−	0.999575i	$-0.490725\pi$
$307$	96227.7	0.0582712	0.0291356	+	0.999575i	$0.490725\pi$
$308$	−594339.	−0.356991
$309$	−125100.	−0.0745350
$310$	5.10830e6	3.01906
$311$	1.54914e6	0.908217	0.454108	−	0.890946i	$-0.349958\pi$
$311$	1.54914e6	0.908217	0.454108	+	0.890946i	$0.349958\pi$
$312$	4.09275e6	2.38028
$313$	1.27505e6	0.735641	0.367821	−	0.929897i	$-0.380104\pi$
$313$	1.27505e6	0.735641	0.367821	+	0.929897i	$0.380104\pi$
$314$	−5.07720e6	−2.90603
$315$	1.29371e6	0.734614
$316$	−3.74986e6	−2.11250
$317$	−1.89703e6	−1.06029	−0.530146	−	0.847906i	$-0.677863\pi$
$317$	−1.89703e6	−1.06029	−0.530146	+	0.847906i	$0.677863\pi$
$318$	−2.18449e6	−1.21139
$319$	−763549.	−0.420108
$320$	1.82796e6	0.997909
$321$	1.92511e6	1.04278
$322$	198781.	0.106840
$323$	1.30638e6	0.696726
$324$	−209919.	−0.111094
$325$	−5.87168e6	−3.08357
$326$	−5.42560e6	−2.82751
$327$	2.28630e6	1.18240
$328$	−8.74811e6	−4.48982
$329$	−1.00324e6	−0.510995
$330$	−860082.	−0.434765
$331$	2.97886e6	1.49444	0.747222	−	0.664574i	$-0.231387\pi$
$331$	2.97886e6	1.49444	0.747222	+	0.664574i	$0.231387\pi$
$332$	5.56358e6	2.77019
$333$	1.82796e6	0.903349
$334$	−1.65409e6	−0.811321
$335$	−2.08590e6	−1.01550
$336$	−2.01409e6	−0.973265
$337$	3.04959e6	1.46274	0.731370	−	0.681981i	$-0.238881\pi$
$337$	3.04959e6	1.46274	0.731370	+	0.681981i	$0.238881\pi$
$338$	−5.02423e6	−2.39209
$339$	678238.	0.320540
$340$	5.34145e6	2.50589
$341$	−437414.	−0.203707
$342$	2.68429e6	1.24098
$343$	2.31126e6	1.06075
$344$	−8.56154e6	−3.90082
$345$	201751.	0.0912576
$346$	521399.	0.234142
$347$	1.67073e6	0.744872	0.372436	−	0.928058i	$-0.378523\pi$
$347$	1.67073e6	0.744872	0.372436	+	0.928058i	$0.378523\pi$
$348$	−6.58621e6	−2.91533
$349$	−969584.	−0.426110	−0.213055	−	0.977040i	$-0.568341\pi$
$349$	−969584.	−0.426110	−0.213055	+	0.977040i	$0.568341\pi$
$350$	6.02137e6	2.62739
$351$	3.55516e6	1.54025
$352$	−748116.	−0.321820
$353$	−1.11676e6	−0.477006	−0.238503	−	0.971142i	$-0.576657\pi$
$353$	−1.11676e6	−0.477006	−0.238503	+	0.971142i	$0.576657\pi$
$354$	524552.	0.222475
$355$	2.97254e6	1.25186
$356$	−3.03879e6	−1.27079
$357$	−663059.	−0.275348
$358$	750624.	0.309539
$359$	2.15357e6	0.881907	0.440954	−	0.897530i	$-0.354640\pi$
$359$	2.15357e6	0.881907	0.440954	+	0.897530i	$0.354640\pi$
$360$	6.30191e6	2.56281
$361$	722638.	0.291845
$362$	−197021.	−0.0790208
$363$	−1.52074e6	−0.605744
$364$	6.37789e6	2.52304
$365$	−4.97662e6	−1.95525
$366$	−493284.	−0.192484
$367$	1.16003e6	0.449577	0.224788	−	0.974408i	$-0.427831\pi$
$367$	1.16003e6	0.449577	0.224788	+	0.974408i	$0.427831\pi$
$368$	464667.	0.178864
$369$	−2.83974e6	−1.08571
$370$	1.26990e7	4.82241
$371$	−1.95463e6	−0.737276
$372$	−3.77303e6	−1.41362
$373$	3.83484e6	1.42717	0.713584	−	0.700570i	$-0.247071\pi$
$373$	3.83484e6	1.42717	0.713584	+	0.700570i	$0.247071\pi$
$374$	−652135.	−0.241079
$375$	3.10091e6	1.13871
$376$	−4.88701e6	−1.78268
$377$	8.19370e6	2.96911
$378$	−3.64579e6	−1.31239
$379$	−1.27943e6	−0.457530	−0.228765	−	0.973482i	$-0.573469\pi$
$379$	−1.27943e6	−0.457530	−0.228765	+	0.973482i	$0.573469\pi$
$380$	1.30788e7	4.64633
$381$	−182375.	−0.0643655
$382$	−415062.	−0.145531
$383$	−2.61032e6	−0.909279	−0.454639	−	0.890676i	$-0.650232\pi$
$383$	−2.61032e6	−0.909279	−0.454639	+	0.890676i	$0.650232\pi$
$384$	822762.	0.284738
$385$	−769581.	−0.264608
$386$	−4.06284e6	−1.38791
$387$	−2.77918e6	−0.943278
$388$	4.61375e6	1.55587
$389$	3.23947e6	1.08543	0.542713	−	0.839918i	$-0.317397\pi$
$389$	3.23947e6	1.08543	0.542713	+	0.839918i	$0.317397\pi$
$390$	9.22959e6	3.07271
$391$	152973.	0.0506026
$392$	3.75159e6	1.23311
$393$	2.23055e6	0.728502
$394$	4.11063e6	1.33404
$395$	−4.85551e6	−1.56582
$396$	−939801.	−0.301160
$397$	−480849.	−0.153120	−0.0765601	−	0.997065i	$-0.524394\pi$
$397$	−480849.	−0.153120	−0.0765601	+	0.997065i	$0.524394\pi$
$398$	1.07685e7	3.40760
$399$	−1.62354e6	−0.510540
$400$	1.40755e7	4.39859
$401$	−2.23084e6	−0.692799	−0.346400	−	0.938087i	$-0.612596\pi$
$401$	−2.23084e6	−0.692799	−0.346400	+	0.938087i	$0.612596\pi$
$402$	2.19670e6	0.677964
$403$	4.69391e6	1.43970
$404$	1.02655e7	3.12915
$405$	−271815.	−0.0823446
$406$	−8.40259e6	−2.52987
$407$	−1.08739e6	−0.325386
$408$	−3.22990e6	−0.960591
$409$	−935103.	−0.276408	−0.138204	−	0.990404i	$-0.544133\pi$
$409$	−935103.	−0.276408	−0.138204	+	0.990404i	$0.544133\pi$
$410$	−1.97279e7	−5.79592
$411$	−1.89008e6	−0.551919
$412$	−949632.	−0.275621
$413$	469357.	0.135403
$414$	314323.	0.0901311
$415$	7.20402e6	2.05331
$416$	8.02808e6	2.27446
$417$	523424.	0.147405
$418$	−1.59679e6	−0.447000
$419$	−4.19907e6	−1.16847	−0.584236	−	0.811584i	$-0.698606\pi$
$419$	−4.19907e6	−1.16847	−0.584236	+	0.811584i	$0.698606\pi$
$420$	−6.63824e6	−1.83624
$421$	2.45532e6	0.675154	0.337577	−	0.941298i	$-0.390393\pi$
$421$	2.45532e6	0.675154	0.337577	+	0.941298i	$0.390393\pi$
$422$	−5.36507e6	−1.46654
$423$	−1.58638e6	−0.431080
$424$	−9.52142e6	−2.57210
$425$	4.63379e6	1.24441
$426$	−3.13044e6	−0.835760
$427$	−441378.	−0.117150
$428$	1.46135e7	3.85607
$429$	−790312.	−0.207327
$430$	−1.93072e7	−5.03557
$431$	−2.20493e6	−0.571743	−0.285871	−	0.958268i	$-0.592283\pi$
$431$	−2.20493e6	−0.571743	−0.285871	+	0.958268i	$0.592283\pi$
$432$	−8.52236e6	−2.19710
$433$	3.32787e6	0.852996	0.426498	−	0.904488i	$-0.359747\pi$
$433$	3.32787e6	0.852996	0.426498	+	0.904488i	$0.359747\pi$
$434$	−4.81358e6	−1.22672
$435$	−8.52817e6	−2.16089
$436$	1.73553e7	4.37237
$437$	374563.	0.0938256
$438$	5.24097e6	1.30535
$439$	5.34298e6	1.32319	0.661595	−	0.749861i	$-0.269880\pi$
$439$	5.34298e6	1.32319	0.661595	+	0.749861i	$0.269880\pi$
$440$	−3.74879e6	−0.923122
$441$	1.21781e6	0.298184
$442$	6.99811e6	1.70382
$443$	−75196.4	−0.0182049	−0.00910244	−	0.999959i	$-0.502897\pi$
$443$	−75196.4	−0.0182049	−0.00910244	+	0.999959i	$0.502897\pi$
$444$	−9.37958e6	−2.25801
$445$	−3.93478e6	−0.941934
$446$	−9.65509e6	−2.29837
$447$	1.85548e6	0.439225
$448$	−1.72249e6	−0.405474
$449$	−5.89672e6	−1.38037	−0.690183	−	0.723635i	$-0.742470\pi$
$449$	−5.89672e6	−1.38037	−0.690183	+	0.723635i	$0.742470\pi$
$450$	9.52132e6	2.21649
$451$	1.68926e6	0.391072
$452$	5.14850e6	1.18532
$453$	−2.93320e6	−0.671577
$454$	−5.45496e6	−1.24209
$455$	8.25842e6	1.87012
$456$	−7.90859e6	−1.78109
$457$	−6.65678e6	−1.49099	−0.745493	−	0.666513i	$-0.767786\pi$
$457$	−6.65678e6	−1.49099	−0.745493	+	0.666513i	$0.767786\pi$
$458$	129259.	0.0287937
$459$	−2.80564e6	−0.621586
$460$	1.53149e6	0.337459
$461$	−2.28176e6	−0.500056	−0.250028	−	0.968239i	$-0.580440\pi$
$461$	−2.28176e6	−0.500056	−0.250028	+	0.968239i	$0.580440\pi$
$462$	810460.	0.176655
$463$	−6.83892e6	−1.48264	−0.741318	−	0.671153i	$-0.765799\pi$
$463$	−6.83892e6	−1.48264	−0.741318	+	0.671153i	$0.765799\pi$
$464$	−1.96418e7	−4.23532
$465$	−4.88552e6	−1.04780
$466$	3.08262e6	0.657590
$467$	4.12083e6	0.874365	0.437182	−	0.899373i	$-0.355976\pi$
$467$	4.12083e6	0.874365	0.437182	+	0.899373i	$0.355976\pi$
$468$	1.00851e7	2.12845
$469$	1.96556e6	0.412623
$470$	−1.10208e7	−2.30126
$471$	4.85578e6	1.00857
$472$	2.28633e6	0.472373
$473$	1.65324e6	0.339768
$474$	5.11343e6	1.04536
$475$	1.13461e7	2.30734
$476$	−5.03328e6	−1.01820
$477$	−3.09077e6	−0.621972
$478$	−1.18738e7	−2.37694
$479$	7.59191e6	1.51186	0.755931	−	0.654651i	$-0.227185\pi$
$479$	7.59191e6	1.51186	0.755931	+	0.654651i	$0.227185\pi$
$480$	−8.35580e6	−1.65533
$481$	1.16688e7	2.29967
$482$	−6.61355e6	−1.29663
$483$	−190112.	−0.0370801
$484$	−1.15440e7	−2.23996
$485$	5.97412e6	1.15324
$486$	−9.37551e6	−1.80055
$487$	1.43047e6	0.273310	0.136655	−	0.990619i	$-0.456365\pi$
$487$	1.43047e6	0.273310	0.136655	+	0.990619i	$0.456365\pi$
$488$	−2.15005e6	−0.408694
$489$	5.18898e6	0.981318
$490$	8.46025e6	1.59182
$491$	−5.86936e6	−1.09872	−0.549360	−	0.835586i	$-0.685128\pi$
$491$	−5.86936e6	−1.09872	−0.549360	+	0.835586i	$0.685128\pi$
$492$	1.45712e7	2.71384
$493$	−6.46627e6	−1.19822
$494$	1.71353e7	3.15917
$495$	−1.21690e6	−0.223225
$496$	−1.12522e7	−2.05368
$497$	−2.80104e6	−0.508661
$498$	−7.58669e6	−1.37082
$499$	6.64983e6	1.19553	0.597763	−	0.801673i	$-0.296056\pi$
$499$	6.64983e6	1.19553	0.597763	+	0.801673i	$0.296056\pi$
$500$	2.35390e7	4.21079
$501$	1.58195e6	0.281578
$502$	−2.17413e6	−0.385058
$503$	−5.69999e6	−1.00451	−0.502254	−	0.864720i	$-0.667496\pi$
$503$	−5.69999e6	−1.00451	−0.502254	+	0.864720i	$0.667496\pi$
$504$	−5.93833e6	−1.04133
$505$	1.32923e7	2.31938
$506$	−186980.	−0.0324652
$507$	4.80512e6	0.830204
$508$	−1.38441e6	−0.238015
$509$	−8.14602e6	−1.39364	−0.696821	−	0.717245i	$-0.745403\pi$
$509$	−8.14602e6	−1.39364	−0.696821	+	0.717245i	$0.745403\pi$
$510$	−7.28377e6	−1.24003
$511$	4.68949e6	0.794463
$512$	1.24680e7	2.10195
$513$	−6.86978e6	−1.15252
$514$	−1.41477e7	−2.36199
$515$	−1.22963e6	−0.204295
$516$	1.42605e7	2.35782
$517$	943685.	0.155275
$518$	−1.19663e7	−1.95946
$519$	−498661.	−0.0812619
$520$	4.02285e7	6.52417
$521$	6.07951e6	0.981238	0.490619	−	0.871374i	$-0.336771\pi$
$521$	6.07951e6	0.981238	0.490619	+	0.871374i	$0.336771\pi$
$522$	−1.32866e7	−2.13422
$523$	−2.35517e6	−0.376503	−0.188252	−	0.982121i	$-0.560282\pi$
$523$	−2.35517e6	−0.376503	−0.188252	+	0.982121i	$0.560282\pi$
$524$	1.69321e7	2.69391
$525$	−5.75877e6	−0.911867
$526$	−3.53330e6	−0.556822
$527$	−3.70432e6	−0.581008
$528$	1.89452e6	0.295743
$529$	−6.39248e6	−0.993186
$530$	−2.14719e7	−3.32032
$531$	742172.	0.114227
$532$	−1.23243e7	−1.88791
$533$	−1.81276e7	−2.76390
$534$	4.14379e6	0.628847
$535$	1.89223e7	2.85818
$536$	9.57465e6	1.43950
$537$	−717889.	−0.107429
$538$	1.94884e7	2.90283
$539$	−724434.	−0.107406
$540$	−2.80888e7	−4.14523
$541$	−1.29234e6	−0.189838	−0.0949191	−	0.995485i	$-0.530259\pi$
$541$	−1.29234e6	−0.189838	−0.0949191	+	0.995485i	$0.530259\pi$
$542$	2.18702e7	3.19782
$543$	188429.	0.0274251
$544$	−6.33557e6	−0.917886
$545$	2.24726e7	3.24087
$546$	−8.69710e6	−1.24851
$547$	4.51214e6	0.644783	0.322392	−	0.946606i	$-0.395513\pi$
$547$	4.51214e6	0.644783	0.322392	+	0.946606i	$0.395513\pi$
$548$	−1.43476e7	−2.04093
$549$	−697932.	−0.0988284
$550$	−5.66390e6	−0.798379
$551$	−1.58330e7	−2.22170
$552$	−926073.	−0.129359
$553$	4.57538e6	0.636230
$554$	2.12472e6	0.294122
$555$	−1.21452e7	−1.67367
$556$	3.97331e6	0.545086
$557$	1.14344e7	1.56162	0.780812	−	0.624766i	$-0.214806\pi$
$557$	1.14344e7	1.56162	0.780812	+	0.624766i	$0.214806\pi$
$558$	−7.61150e6	−1.03487
$559$	−1.77410e7	−2.40131
$560$	−1.97969e7	−2.66765
$561$	623695.	0.0836691
$562$	1.28163e7	1.71168
$563$	8.78262e6	1.16776	0.583879	−	0.811841i	$-0.301534\pi$
$563$	8.78262e6	1.16776	0.583879	+	0.811841i	$0.301534\pi$
$564$	8.14003e6	1.07753
$565$	6.66655e6	0.878577
$566$	−2.20562e6	−0.289394
$567$	256133.	0.0334585
$568$	−1.36445e7	−1.77454
$569$	−1.06469e7	−1.37861	−0.689307	−	0.724469i	$-0.742085\pi$
$569$	−1.06469e7	−1.37861	−0.689307	+	0.724469i	$0.742085\pi$
$570$	−1.78347e7	−2.29921
$571$	1.01674e7	1.30503	0.652514	−	0.757777i	$-0.273714\pi$
$571$	1.01674e7	1.30503	0.652514	+	0.757777i	$0.273714\pi$
$572$	−5.99925e6	−0.766668
$573$	396961.	0.0505081
$574$	1.85898e7	2.35502
$575$	1.32859e6	0.167580
$576$	−2.72370e6	−0.342061
$577$	1.41106e7	1.76444	0.882218	−	0.470842i	$-0.156050\pi$
$577$	1.41106e7	1.76444	0.882218	+	0.470842i	$0.156050\pi$
$578$	9.17468e6	1.14228
$579$	3.88566e6	0.481691
$580$	−6.47373e7	−7.99070
$581$	−6.78839e6	−0.834308
$582$	−6.29146e6	−0.769917
$583$	1.83859e6	0.224034
$584$	2.28435e7	2.77160
$585$	1.30587e7	1.57764
$586$	1.95275e7	2.34911
$587$	2.45523e6	0.294101	0.147051	−	0.989129i	$-0.453022\pi$
$587$	2.45523e6	0.294101	0.147051	+	0.989129i	$0.453022\pi$
$588$	−6.24881e6	−0.745340
$589$	−9.07025e6	−1.07729
$590$	5.15594e6	0.609786
$591$	−3.93137e6	−0.462993
$592$	−2.79723e7	−3.28038
$593$	1.11436e7	1.30133	0.650664	−	0.759366i	$-0.274491\pi$
$593$	1.11436e7	1.30133	0.650664	+	0.759366i	$0.274491\pi$
$594$	3.42935e6	0.398792
$595$	−6.51735e6	−0.754707
$596$	1.40849e7	1.62420
$597$	−1.02989e7	−1.18265
$598$	2.00649e6	0.229448
$599$	−5.27820e6	−0.601062	−0.300531	−	0.953772i	$-0.597164\pi$
$599$	−5.27820e6	−0.601062	−0.300531	+	0.953772i	$0.597164\pi$
$600$	−2.80522e7	−3.18118
$601$	1.05592e7	1.19246	0.596230	−	0.802814i	$-0.296665\pi$
$601$	1.05592e7	1.19246	0.596230	+	0.802814i	$0.296665\pi$
$602$	1.81933e7	2.04607
$603$	3.10805e6	0.348092
$604$	−2.22659e7	−2.48341
$605$	−1.49477e7	−1.66030
$606$	−1.39984e7	−1.54844
$607$	−1.54544e7	−1.70247	−0.851237	−	0.524782i	$-0.824147\pi$
$607$	−1.54544e7	−1.70247	−0.851237	+	0.524782i	$0.824147\pi$
$608$	−1.55130e7	−1.70191
$609$	8.03614e6	0.878020
$610$	−4.84859e6	−0.527583
$611$	−1.01267e7	−1.09741
$612$	−7.95889e6	−0.858962
$613$	1.36980e7	1.47233	0.736167	−	0.676800i	$-0.236634\pi$
$613$	1.36980e7	1.47233	0.736167	+	0.676800i	$0.236634\pi$
$614$	−996085.	−0.106629
$615$	1.88676e7	2.01154
$616$	3.53251e6	0.375086
$617$	−4.10310e6	−0.433910	−0.216955	−	0.976182i	$-0.569612\pi$
$617$	−4.10310e6	−0.433910	−0.216955	+	0.976182i	$0.569612\pi$
$618$	1.29495e6	0.136390
$619$	1.29804e7	1.36164	0.680818	−	0.732453i	$-0.261625\pi$
$619$	1.29804e7	1.36164	0.680818	+	0.732453i	$0.261625\pi$
$620$	−3.70860e7	−3.87463
$621$	−804432.	−0.0837067
$622$	−1.60357e7	−1.66192
$623$	3.70777e6	0.382730
$624$	−2.03302e7	−2.09017
$625$	1.06548e7	1.09106
$626$	−1.31985e7	−1.34613
$627$	1.52715e6	0.155136
$628$	3.68602e7	3.72957
$629$	−9.20876e6	−0.928057
$630$	−1.33916e7	−1.34425
$631$	−7.46894e6	−0.746768	−0.373384	−	0.927677i	$-0.621803\pi$
$631$	−7.46894e6	−0.746768	−0.373384	+	0.927677i	$0.621803\pi$
$632$	2.22876e7	2.21958
$633$	5.13109e6	0.508980
$634$	1.96368e7	1.94020
$635$	−1.79260e6	−0.176421
$636$	1.58593e7	1.55468
$637$	7.77395e6	0.759090
$638$	7.90376e6	0.768744
$639$	−4.42916e6	−0.429111
$640$	8.08710e6	0.780446
$641$	1.84821e7	1.77667	0.888333	−	0.459199i	$-0.151864\pi$
$641$	1.84821e7	1.77667	0.888333	+	0.459199i	$0.151864\pi$
$642$	−1.99275e7	−1.90816
$643$	1.21329e7	1.15728	0.578640	−	0.815583i	$-0.303584\pi$
$643$	1.21329e7	1.15728	0.578640	+	0.815583i	$0.303584\pi$
$644$	−1.44314e6	−0.137117
$645$	1.84652e7	1.74765
$646$	−1.35227e7	−1.27492
$647$	−1.27920e7	−1.20137	−0.600685	−	0.799486i	$-0.705106\pi$
$647$	−1.27920e7	−1.20137	−0.600685	+	0.799486i	$0.705106\pi$
$648$	1.24768e6	0.116725
$649$	−441493.	−0.0411445
$650$	6.07797e7	5.64255
$651$	4.60366e6	0.425746
$652$	3.93895e7	3.62879
$653$	−1.23363e7	−1.13214	−0.566071	−	0.824357i	$-0.691537\pi$
$653$	−1.23363e7	−1.13214	−0.566071	+	0.824357i	$0.691537\pi$
$654$	−2.36663e7	−2.16365
$655$	2.19246e7	1.99677
$656$	4.34552e7	3.94259
$657$	7.41529e6	0.670215
$658$	1.03849e7	0.935058
$659$	−4.68960e6	−0.420652	−0.210326	−	0.977631i	$-0.567452\pi$
$659$	−4.68960e6	−0.420652	−0.210326	+	0.977631i	$0.567452\pi$
$660$	6.24415e6	0.557973
$661$	−5.96023e6	−0.530591	−0.265295	−	0.964167i	$-0.585469\pi$
$661$	−5.96023e6	−0.530591	−0.265295	+	0.964167i	$0.585469\pi$
$662$	−3.08352e7	−2.73465
$663$	−6.69291e6	−0.591332
$664$	−3.30677e7	−2.91061
$665$	−1.59581e7	−1.39935
$666$	−1.89218e7	−1.65301
$667$	−1.85400e6	−0.161360
$668$	1.20086e7	1.04124
$669$	9.23402e6	0.797675
$670$	2.15919e7	1.85825
$671$	415175.	0.0355980
$672$	7.87372e6	0.672599
$673$	−539129.	−0.0458833	−0.0229417	−	0.999737i	$-0.507303\pi$
$673$	−539129.	−0.0458833	−0.0229417	+	0.999737i	$0.507303\pi$
$674$	−3.15674e7	−2.67663
$675$	−2.43675e7	−2.05850
$676$	3.64757e7	3.06999
$677$	1.49760e7	1.25581	0.627904	−	0.778291i	$-0.283913\pi$
$677$	1.49760e7	1.25581	0.627904	+	0.778291i	$0.283913\pi$
$678$	−7.02067e6	−0.586549
$679$	−5.62945e6	−0.468588
$680$	−3.17474e7	−2.63291
$681$	5.21706e6	0.431080
$682$	4.52781e6	0.372759
$683$	−1.03543e7	−0.849316	−0.424658	−	0.905354i	$-0.639606\pi$
$683$	−1.03543e7	−0.849316	−0.424658	+	0.905354i	$0.639606\pi$
$684$	−1.94878e7	−1.59266
$685$	−1.85780e7	−1.51277
$686$	−2.39246e7	−1.94104
$687$	−123622.	−0.00999319
$688$	4.25285e7	3.42538
$689$	−1.97301e7	−1.58336
$690$	−2.08840e6	−0.166990
$691$	1.40792e7	1.12172	0.560858	−	0.827912i	$-0.310471\pi$
$691$	1.40792e7	1.12172	0.560858	+	0.827912i	$0.310471\pi$
$692$	−3.78533e6	−0.300496
$693$	1.14669e6	0.0907016
$694$	−1.72943e7	−1.36302
$695$	5.14485e6	0.404027
$696$	3.91457e7	3.06310
$697$	1.43059e7	1.11540
$698$	1.00365e7	0.779729
$699$	−2.94818e6	−0.228224
$700$	−4.37148e7	−3.37197
$701$	1.96448e7	1.50991	0.754956	−	0.655776i	$-0.227658\pi$
$701$	1.96448e7	1.50991	0.754956	+	0.655776i	$0.227658\pi$
$702$	−3.68006e7	−2.81846
$703$	−2.25482e7	−1.72077
$704$	1.62024e6	0.123210
$705$	1.05401e7	0.798681
$706$	1.15600e7	0.872861
$707$	−1.25254e7	−0.942416
$708$	−3.80822e6	−0.285522
$709$	1.82623e7	1.36439	0.682196	−	0.731170i	$-0.261025\pi$
$709$	1.82623e7	1.36439	0.682196	+	0.731170i	$0.261025\pi$
$710$	−3.07698e7	−2.29075
$711$	7.23483e6	0.536728
$712$	1.80613e7	1.33521
$713$	−1.06210e6	−0.0782423
$714$	6.86354e6	0.503852
$715$	−7.76815e6	−0.568267
$716$	−5.44949e6	−0.397259
$717$	1.13559e7	0.824944
$718$	−2.22923e7	−1.61378
$719$	2.32032e7	1.67388	0.836942	−	0.547292i	$-0.184341\pi$
$719$	2.32032e7	1.67388	0.836942	+	0.547292i	$0.184341\pi$
$720$	−3.13040e7	−2.25045
$721$	1.15869e6	0.0830097
$722$	−7.48027e6	−0.534040
$723$	6.32512e6	0.450011
$724$	1.43036e6	0.101414
$725$	−5.61606e7	−3.96814
$726$	1.57417e7	1.10844
$727$	−1.43185e7	−1.00476	−0.502380	−	0.864647i	$-0.667542\pi$
$727$	−1.43185e7	−1.00476	−0.502380	+	0.864647i	$0.667542\pi$
$728$	−3.79075e7	−2.65092
$729$	9.64542e6	0.672206
$730$	5.15146e7	3.57786
$731$	1.40008e7	0.969079
$732$	3.58121e6	0.247032
$733$	−1.85225e6	−0.127333	−0.0636663	−	0.997971i	$-0.520279\pi$
$733$	−1.85225e6	−0.127333	−0.0636663	+	0.997971i	$0.520279\pi$
$734$	−1.20079e7	−0.822669
$735$	−8.09129e6	−0.552458
$736$	−1.81653e6	−0.123608
$737$	−1.84887e6	−0.125383
$738$	2.93951e7	1.98671
$739$	1.02577e7	0.690937	0.345469	−	0.938430i	$-0.387720\pi$
$739$	1.02577e7	0.690937	0.345469	+	0.938430i	$0.387720\pi$
$740$	−9.21939e7	−6.18903
$741$	−1.63880e7	−1.09643
$742$	2.02331e7	1.34912
$743$	−1.99742e7	−1.32738	−0.663692	−	0.748006i	$-0.731011\pi$
$743$	−1.99742e7	−1.32738	−0.663692	+	0.748006i	$0.731011\pi$
$744$	2.24254e7	1.48528
$745$	1.82379e7	1.20388
$746$	−3.96957e7	−2.61154
$747$	−1.07342e7	−0.703829
$748$	4.73447e6	0.309398
$749$	−1.78306e7	−1.16135
$750$	−3.20986e7	−2.08369
$751$	−2.85670e7	−1.84827	−0.924134	−	0.382068i	$-0.875212\pi$
$751$	−2.85670e7	−1.84827	−0.924134	+	0.382068i	$0.875212\pi$
$752$	2.42757e7	1.56540
$753$	2.07931e6	0.133639
$754$	−8.48157e7	−5.43310
$755$	−2.88311e7	−1.84074
$756$	2.64683e7	1.68431
$757$	1.70903e7	1.08395	0.541976	−	0.840394i	$-0.317677\pi$
$757$	1.70903e7	1.08395	0.541976	+	0.840394i	$0.317677\pi$
$758$	1.32438e7	0.837222
$759$	178825.	0.0112674
$760$	−7.77352e7	−4.88184
$761$	2.98641e7	1.86934	0.934670	−	0.355516i	$-0.115695\pi$
$761$	2.98641e7	1.86934	0.934670	+	0.355516i	$0.115695\pi$
$762$	1.88782e6	0.117781
$763$	−2.11760e7	−1.31684
$764$	3.01333e6	0.186773
$765$	−1.03056e7	−0.636677
$766$	2.70203e7	1.66387
$767$	4.73769e6	0.290789
$768$	−1.44678e7	−0.885113
$769$	−8.19216e6	−0.499554	−0.249777	−	0.968303i	$-0.580357\pi$
$769$	−8.19216e6	−0.499554	−0.249777	+	0.968303i	$0.580357\pi$
$770$	7.96619e6	0.484199
$771$	1.35307e7	0.819756
$772$	2.94960e7	1.78123
$773$	1.85708e7	1.11785	0.558923	−	0.829220i	$-0.311215\pi$
$773$	1.85708e7	1.11785	0.558923	+	0.829220i	$0.311215\pi$
$774$	2.87683e7	1.72608
$775$	−3.21727e7	−1.92412
$776$	−2.74222e7	−1.63474
$777$	1.14445e7	0.680053
$778$	−3.35329e7	−1.98620
$779$	3.50287e7	2.06814
$780$	−6.70064e7	−3.94348
$781$	2.63476e6	0.154566
$782$	−1.58347e6	−0.0925964
$783$	3.40039e7	1.98209
$784$	−1.86356e7	−1.08281
$785$	4.77285e7	2.76442
$786$	−2.30892e7	−1.33307
$787$	−2.37391e7	−1.36624	−0.683120	−	0.730306i	$-0.739377\pi$
$787$	−2.37391e7	−1.36624	−0.683120	+	0.730306i	$0.739377\pi$
$788$	−2.98430e7	−1.71209
$789$	3.37921e6	0.193252
$790$	5.02610e7	2.86526
$791$	−6.28193e6	−0.356986
$792$	5.58579e6	0.316426
$793$	−4.45527e6	−0.251589
$794$	4.97743e6	0.280191
$795$	2.05355e7	1.15236
$796$	−7.81790e7	−4.37328
$797$	−5.13376e6	−0.286279	−0.143140	−	0.989703i	$-0.545720\pi$
$797$	−5.13376e6	−0.286279	−0.143140	+	0.989703i	$0.545720\pi$
$798$	1.68058e7	0.934225
$799$	7.99179e6	0.442871
$800$	−5.50255e7	−3.03976
$801$	5.86292e6	0.322874
$802$	2.30922e7	1.26774
$803$	−4.41110e6	−0.241411
$804$	−1.59480e7	−0.870091
$805$	−1.86865e6	−0.101634
$806$	−4.85883e7	−2.63447
$807$	−1.86385e7	−1.00746
$808$	−6.10138e7	−3.28776
$809$	−1.00281e7	−0.538699	−0.269349	−	0.963043i	$-0.586809\pi$
$809$	−1.00281e7	−0.538699	−0.269349	+	0.963043i	$0.586809\pi$
$810$	2.81364e6	0.150680
$811$	1.92699e7	1.02879	0.514395	−	0.857553i	$-0.328016\pi$
$811$	1.92699e7	1.02879	0.514395	+	0.857553i	$0.328016\pi$
$812$	6.10023e7	3.24681
$813$	−2.09164e7	−1.10984
$814$	1.12559e7	0.595415
$815$	5.10036e7	2.68972
$816$	1.60441e7	0.843512
$817$	3.42817e7	1.79683
$818$	9.67956e6	0.505793
$819$	−1.23053e7	−0.641034
$820$	1.43224e8	7.43842
$821$	9.47671e6	0.490681	0.245341	−	0.969437i	$-0.421100\pi$
$821$	9.47671e6	0.490681	0.245341	+	0.969437i	$0.421100\pi$
$822$	1.95649e7	1.00994
$823$	−1.60946e7	−0.828286	−0.414143	−	0.910212i	$-0.635919\pi$
$823$	−1.60946e7	−0.828286	−0.414143	+	0.910212i	$0.635919\pi$
$824$	5.64422e6	0.289592
$825$	5.41689e6	0.277087
$826$	−4.85847e6	−0.247770
$827$	−2.47387e7	−1.25781	−0.628903	−	0.777483i	$-0.716496\pi$
$827$	−2.47387e7	−1.25781	−0.628903	+	0.777483i	$0.716496\pi$
$828$	−2.28197e6	−0.115673
$829$	−1.75465e7	−0.886758	−0.443379	−	0.896334i	$-0.646220\pi$
$829$	−1.75465e7	−0.886758	−0.443379	+	0.896334i	$0.646220\pi$
$830$	−7.45712e7	−3.75730
$831$	−2.03206e6	−0.102078
$832$	−1.73869e7	−0.870788
$833$	−6.13501e6	−0.306340
$834$	−5.41814e6	−0.269733
$835$	1.55494e7	0.771785
$836$	1.15926e7	0.573675
$837$	1.94798e7	0.961103
$838$	4.34660e7	2.13816
$839$	−8.59262e6	−0.421426	−0.210713	−	0.977548i	$-0.567578\pi$
$839$	−8.59262e6	−0.421426	−0.210713	+	0.977548i	$0.567578\pi$
$840$	3.94550e7	1.92932
$841$	5.78588e7	2.82085
$842$	−2.54158e7	−1.23545
$843$	−1.22574e7	−0.594059
$844$	3.89501e7	1.88214
$845$	4.72306e7	2.27553
$846$	1.64212e7	0.788822
$847$	1.40853e7	0.674618
$848$	4.72966e7	2.25860
$849$	2.10943e6	0.100437
$850$	−4.79659e7	−2.27712
$851$	−2.64033e6	−0.124978
$852$	2.27268e7	1.07261
$853$	−2.71691e7	−1.27851	−0.639253	−	0.768996i	$-0.720756\pi$
$853$	−2.71691e7	−1.27851	−0.639253	+	0.768996i	$0.720756\pi$
$854$	4.56886e6	0.214369
$855$	−2.52338e7	−1.18050
$856$	−8.68567e7	−4.05153
$857$	2.40775e7	1.11985	0.559925	−	0.828544i	$-0.310830\pi$
$857$	2.40775e7	1.11985	0.559925	+	0.828544i	$0.310830\pi$
$858$	8.18078e6	0.379382
$859$	−2.69852e7	−1.24779	−0.623897	−	0.781506i	$-0.714452\pi$
$859$	−2.69852e7	−1.24779	−0.623897	+	0.781506i	$0.714452\pi$
$860$	1.40169e8	6.46260
$861$	−1.77790e7	−0.817335
$862$	2.28239e7	1.04622
$863$	−811714.	−0.0371002	−0.0185501	−	0.999828i	$-0.505905\pi$
$863$	−811714.	−0.0371002	−0.0185501	+	0.999828i	$0.505905\pi$
$864$	3.33166e7	1.51836
$865$	−4.90144e6	−0.222733
$866$	−3.44479e7	−1.56088
$867$	−8.77456e6	−0.396440
$868$	3.49463e7	1.57435
$869$	−4.30375e6	−0.193329
$870$	8.82780e7	3.95416
$871$	1.98403e7	0.886143
$872$	−1.03153e8	−4.59399
$873$	−8.90159e6	−0.395305
$874$	−3.87723e6	−0.171689
$875$	−2.87211e7	−1.26818
$876$	−3.80492e7	−1.67527
$877$	3.73654e7	1.64048	0.820240	−	0.572020i	$-0.193840\pi$
$877$	3.73654e7	1.64048	0.820240	+	0.572020i	$0.193840\pi$
$878$	−5.53070e7	−2.42127
$879$	−1.86759e7	−0.815284
$880$	1.86217e7	0.810610
$881$	−1.20263e7	−0.522028	−0.261014	−	0.965335i	$-0.584057\pi$
$881$	−1.20263e7	−0.522028	−0.261014	+	0.965335i	$0.584057\pi$
$882$	−1.26060e7	−0.545639
$883$	1.27920e7	0.552124	0.276062	−	0.961140i	$-0.410971\pi$
$883$	1.27920e7	0.552124	0.276062	+	0.961140i	$0.410971\pi$
$884$	−5.08059e7	−2.18667
$885$	−4.93108e6	−0.211633
$886$	778383.	0.0333126
$887$	9.15100e6	0.390535	0.195267	−	0.980750i	$-0.437443\pi$
$887$	9.15100e6	0.390535	0.195267	+	0.980750i	$0.437443\pi$
$888$	5.57484e7	2.37246
$889$	1.68918e6	0.0716839
$890$	4.07302e7	1.72362
$891$	−240927.	−0.0101670
$892$	7.00954e7	2.94970
$893$	1.95683e7	0.821156
$894$	−1.92067e7	−0.803727
$895$	−7.05628e6	−0.294455
$896$	−7.62052e6	−0.317114
$897$	−1.91899e6	−0.0796326
$898$	6.10389e7	2.52590
$899$	4.48957e7	1.85270
$900$	−6.91243e7	−2.84462
$901$	1.55705e7	0.638984
$902$	−1.74861e7	−0.715612
$903$	−1.73999e7	−0.710112
$904$	−3.06006e7	−1.24540
$905$	1.85211e6	0.0751700
$906$	3.03625e7	1.22890
$907$	1.63543e7	0.660105	0.330053	−	0.943963i	$-0.392934\pi$
$907$	1.63543e7	0.660105	0.330053	+	0.943963i	$0.392934\pi$
$908$	3.96027e7	1.59408
$909$	−1.98058e7	−0.795030
$910$	−8.54857e7	−3.42208
$911$	2.39341e7	0.955478	0.477739	−	0.878502i	$-0.341457\pi$
$911$	2.39341e7	0.955478	0.477739	+	0.878502i	$0.341457\pi$
$912$	3.92850e7	1.56401
$913$	6.38539e6	0.253519
$914$	6.89065e7	2.72832
$915$	4.63714e6	0.183104
$916$	−938415.	−0.0369536
$917$	−2.06597e7	−0.811334
$918$	2.90422e7	1.13742
$919$	−4.64439e7	−1.81401	−0.907005	−	0.421119i	$-0.861637\pi$
$919$	−4.64439e7	−1.81401	−0.907005	+	0.421119i	$0.861637\pi$
$920$	−9.10258e6	−0.354564
$921$	952645.	0.0370069
$922$	2.36193e7	0.915040
$923$	−2.82737e7	−1.09239
$924$	−5.88390e6	−0.226718
$925$	−7.99796e7	−3.07344
$926$	7.07919e7	2.71304
$927$	1.83218e6	0.0700277
$928$	7.67859e7	2.92693
$929$	−4.70441e6	−0.178840	−0.0894202	−	0.995994i	$-0.528501\pi$
$929$	−4.70441e6	−0.178840	−0.0894202	+	0.995994i	$0.528501\pi$
$930$	5.05717e7	1.91734
$931$	−1.50219e7	−0.568004
$932$	−2.23797e7	−0.843944
$933$	1.53363e7	0.576790
$934$	−4.26561e7	−1.59998
$935$	6.13043e6	0.229331
$936$	−5.99415e7	−2.23634
$937$	5.69399e6	0.211869	0.105935	−	0.994373i	$-0.466217\pi$
$937$	5.69399e6	0.211869	0.105935	+	0.994373i	$0.466217\pi$
$938$	−2.03462e7	−0.755049
$939$	1.26229e7	0.467190
$940$	8.00101e7	2.95342
$941$	−2.12741e7	−0.783209	−0.391604	−	0.920134i	$-0.628080\pi$
$941$	−2.12741e7	−0.783209	−0.391604	+	0.920134i	$0.628080\pi$
$942$	−5.02638e7	−1.84556
$943$	4.10177e6	0.150208
$944$	−1.13571e7	−0.414799
$945$	3.42725e7	1.24844
$946$	−1.71132e7	−0.621734
$947$	5.34008e7	1.93497	0.967483	−	0.252938i	$-0.0813967\pi$
$947$	5.34008e7	1.93497	0.967483	+	0.252938i	$0.0813967\pi$
$948$	−3.71232e7	−1.34161
$949$	4.73358e7	1.70618
$950$	−1.17447e8	−4.22215
$951$	−1.87804e7	−0.673370
$952$	2.99157e7	1.06981
$953$	−1.57880e7	−0.563113	−0.281556	−	0.959545i	$-0.590851\pi$
$953$	−1.57880e7	−0.563113	−0.281556	+	0.959545i	$0.590851\pi$
$954$	3.19936e7	1.13813
$955$	3.90181e6	0.138439
$956$	8.62028e7	3.05054
$957$	−7.55907e6	−0.266802
$958$	−7.85864e7	−2.76652
$959$	1.75062e7	0.614674
$960$	1.80966e7	0.633751
$961$	−2.90981e6	−0.101638
$962$	−1.20788e8	−4.20810
$963$	−2.81947e7	−0.979721
$964$	4.80140e7	1.66408
$965$	3.81930e7	1.32028
$966$	1.96791e6	0.0678519
$967$	1.96962e7	0.677355	0.338677	−	0.940903i	$-0.390020\pi$
$967$	1.96962e7	0.677355	0.338677	+	0.940903i	$0.390020\pi$
$968$	6.86125e7	2.35350
$969$	1.29330e7	0.442476
$970$	−6.18401e7	−2.11029
$971$	−2.80394e7	−0.954378	−0.477189	−	0.878801i	$-0.658344\pi$
$971$	−2.80394e7	−0.954378	−0.477189	+	0.878801i	$0.658344\pi$
$972$	6.80657e7	2.31080
$973$	−4.84802e6	−0.164166
$974$	−1.48072e7	−0.500123
$975$	−5.81290e7	−1.95831
$976$	1.06801e7	0.358881
$977$	−2.51738e7	−0.843749	−0.421874	−	0.906654i	$-0.638628\pi$
$977$	−2.51738e7	−0.843749	−0.421874	+	0.906654i	$0.638628\pi$
$978$	−5.37129e7	−1.79569
$979$	−3.48765e6	−0.116299
$980$	−6.14209e7	−2.04292
$981$	−3.34847e7	−1.11090
$982$	6.07557e7	2.01052
$983$	966289.	0.0318950
$983$	966289.	0.0318950
$984$	−8.66054e7	−2.85139
$985$	−3.86422e7	−1.26903
$986$	6.69345e7	2.19259
$987$	−9.93202e6	−0.324523
$988$	−1.24401e8	−4.05445
$989$	4.01429e6	0.130502
$990$	1.25966e7	0.408474
$991$	−3.57203e7	−1.15540	−0.577698	−	0.816250i	$-0.696049\pi$
$991$	−3.57203e7	−1.15540	−0.577698	+	0.816250i	$0.696049\pi$
$992$	4.39883e7	1.41925
$993$	2.94904e7	0.949091
$994$	2.89945e7	0.930787
$995$	−1.01230e8	−3.24155
$996$	5.50790e7	1.75929
$997$	4.03325e7	1.28504	0.642522	−	0.766268i	$-0.277888\pi$
$997$	4.03325e7	1.28504	0.642522	+	0.766268i	$0.277888\pi$
$998$	−6.88346e7	−2.18766
$999$	4.84257e7	1.53519

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.6.a.b.1.12	✓	218

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.6.a.b.1.12	✓	218	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-10.3513 q^{2} +9.89991 q^{3} +75.1501 q^{4} +97.3083 q^{5} -102.477 q^{6} -91.6942 q^{7} -446.662 q^{8} -144.992 q^{9} +O(q^{10})\)	\(q-10.3513 q^{2} +9.89991 q^{3} +75.1501 q^{4} +97.3083 q^{5} -102.477 q^{6} -91.6942 q^{7} -446.662 q^{8} -144.992 q^{9} -1007.27 q^{10} +86.2506 q^{11} +743.979 q^{12} -925.561 q^{13} +949.157 q^{14} +963.343 q^{15} +2218.74 q^{16} +730.431 q^{17} +1500.86 q^{18} +1788.50 q^{19} +7312.73 q^{20} -907.764 q^{21} -892.809 q^{22} +209.428 q^{23} -4421.91 q^{24} +6343.91 q^{25} +9580.79 q^{26} -3841.08 q^{27} -6890.83 q^{28} -8852.68 q^{29} -9971.89 q^{30} -5071.42 q^{31} -8673.75 q^{32} +853.873 q^{33} -7560.93 q^{34} -8922.61 q^{35} -10896.2 q^{36} -12607.3 q^{37} -18513.4 q^{38} -9162.97 q^{39} -43463.9 q^{40} +19585.5 q^{41} +9396.57 q^{42} +19167.9 q^{43} +6481.75 q^{44} -14108.9 q^{45} -2167.86 q^{46} +10941.2 q^{47} +21965.3 q^{48} -8399.17 q^{49} -65667.9 q^{50} +7231.19 q^{51} -69556.1 q^{52} +21316.9 q^{53} +39760.3 q^{54} +8392.90 q^{55} +40956.3 q^{56} +17706.0 q^{57} +91637.1 q^{58} -5118.72 q^{59} +72395.4 q^{60} +4813.59 q^{61} +52496.0 q^{62} +13294.9 q^{63} +18785.2 q^{64} -90064.8 q^{65} -8838.73 q^{66} -21436.0 q^{67} +54892.0 q^{68} +2073.32 q^{69} +92360.9 q^{70} +30547.7 q^{71} +64762.3 q^{72} -51142.8 q^{73} +130502. q^{74} +62804.1 q^{75} +134406. q^{76} -7908.68 q^{77} +94849.0 q^{78} -49898.2 q^{79} +215902. q^{80} -2793.33 q^{81} -202736. q^{82} +74032.9 q^{83} -68218.6 q^{84} +71077.0 q^{85} -198413. q^{86} -87640.7 q^{87} -38524.9 q^{88} -40436.2 q^{89} +146046. q^{90} +84868.6 q^{91} +15738.6 q^{92} -50206.6 q^{93} -113256. q^{94} +174036. q^{95} -85869.3 q^{96} +61393.7 q^{97} +86942.7 q^{98} -12505.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9}+O(q^{10}) \) 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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