LMFDB - Embedded newform 983.6.a.b.1.18

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			1.18
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.74643 q^{2} +22.6936 q^{3} +62.9930 q^{4} +3.05529 q^{5} -221.181 q^{6} -41.0311 q^{7} -302.071 q^{8} +271.998 q^{9} +O(q^{10})$	\(q-9.74643 q^{2} +22.6936 q^{3} +62.9930 q^{4} +3.05529 q^{5} -221.181 q^{6} -41.0311 q^{7} -302.071 q^{8} +271.998 q^{9} -29.7782 q^{10} -55.9782 q^{11} +1429.54 q^{12} -740.396 q^{13} +399.907 q^{14} +69.3354 q^{15} +928.340 q^{16} -598.038 q^{17} -2651.01 q^{18} -347.499 q^{19} +192.462 q^{20} -931.142 q^{21} +545.588 q^{22} +1846.32 q^{23} -6855.07 q^{24} -3115.67 q^{25} +7216.22 q^{26} +658.074 q^{27} -2584.67 q^{28} +1996.63 q^{29} -675.773 q^{30} +6199.65 q^{31} +618.266 q^{32} -1270.35 q^{33} +5828.74 q^{34} -125.362 q^{35} +17134.0 q^{36} -11689.4 q^{37} +3386.87 q^{38} -16802.2 q^{39} -922.914 q^{40} +5457.97 q^{41} +9075.31 q^{42} -9431.28 q^{43} -3526.24 q^{44} +831.033 q^{45} -17995.0 q^{46} +1181.18 q^{47} +21067.4 q^{48} -15123.5 q^{49} +30366.6 q^{50} -13571.6 q^{51} -46639.7 q^{52} +5177.85 q^{53} -6413.87 q^{54} -171.030 q^{55} +12394.3 q^{56} -7885.99 q^{57} -19460.1 q^{58} -866.974 q^{59} +4367.64 q^{60} +37586.7 q^{61} -60424.5 q^{62} -11160.4 q^{63} -35732.8 q^{64} -2262.12 q^{65} +12381.3 q^{66} -16626.3 q^{67} -37672.2 q^{68} +41899.6 q^{69} +1221.83 q^{70} -38922.6 q^{71} -82162.8 q^{72} +80659.9 q^{73} +113930. q^{74} -70705.6 q^{75} -21890.0 q^{76} +2296.85 q^{77} +163762. q^{78} +94667.7 q^{79} +2836.35 q^{80} -51161.5 q^{81} -53195.7 q^{82} +29306.0 q^{83} -58655.4 q^{84} -1827.18 q^{85} +91921.4 q^{86} +45310.8 q^{87} +16909.4 q^{88} +35001.9 q^{89} -8099.61 q^{90} +30379.2 q^{91} +116305. q^{92} +140692. q^{93} -11512.3 q^{94} -1061.71 q^{95} +14030.7 q^{96} +173153. q^{97} +147400. q^{98} -15226.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−9.74643	−1.72294	−0.861471	−	0.507806i	$-0.830457\pi$
$2$	−9.74643	−1.72294	−0.861471	+	0.507806i	$0.830457\pi$
$3$	22.6936	1.45579	0.727897	−	0.685687i	$-0.240498\pi$
$3$	22.6936	1.45579	0.727897	+	0.685687i	$0.240498\pi$
$4$	62.9930	1.96853
$5$	3.05529	0.0546547	0.0273273	−	0.999627i	$-0.491300\pi$
$5$	3.05529	0.0546547	0.0273273	+	0.999627i	$0.491300\pi$
$6$	−221.181	−2.50825
$7$	−41.0311	−0.316496	−0.158248	−	0.987399i	$-0.550584\pi$
$7$	−41.0311	−0.316496	−0.158248	+	0.987399i	$0.550584\pi$
$8$	−302.071	−1.66872
$9$	271.998	1.11933
$10$	−29.7782	−0.0941668
$11$	−55.9782	−0.139488	−0.0697441	−	0.997565i	$-0.522218\pi$
$11$	−55.9782	−0.139488	−0.0697441	+	0.997565i	$0.522218\pi$
$12$	1429.54	2.86577
$13$	−740.396	−1.21508	−0.607541	−	0.794288i	$-0.707844\pi$
$13$	−740.396	−1.21508	−0.607541	+	0.794288i	$0.707844\pi$
$14$	399.907	0.545304
$15$	69.3354	0.0795659
$16$	928.340	0.906582
$17$	−598.038	−0.501887	−0.250944	−	0.968002i	$-0.580741\pi$
$17$	−598.038	−0.501887	−0.250944	+	0.968002i	$0.580741\pi$
$18$	−2651.01	−1.92855
$19$	−347.499	−0.220836	−0.110418	−	0.993885i	$-0.535219\pi$
$19$	−347.499	−0.220836	−0.110418	+	0.993885i	$0.535219\pi$
$20$	192.462	0.107589
$21$	−931.142	−0.460752
$22$	545.588	0.240330
$23$	1846.32	0.727759	0.363879	−	0.931446i	$-0.381452\pi$
$23$	1846.32	0.727759	0.363879	+	0.931446i	$0.381452\pi$
$24$	−6855.07	−2.42932
$25$	−3115.67	−0.997013
$26$	7216.22	2.09352
$27$	658.074	0.173726
$28$	−2584.67	−0.623031
$29$	1996.63	0.440863	0.220431	−	0.975402i	$-0.429253\pi$
$29$	1996.63	0.440863	0.220431	+	0.975402i	$0.429253\pi$
$30$	−675.773	−0.137087
$31$	6199.65	1.15868	0.579339	−	0.815087i	$-0.303311\pi$
$31$	6199.65	1.15868	0.579339	+	0.815087i	$0.303311\pi$
$32$	618.266	0.106733
$33$	−1270.35	−0.203066
$34$	5828.74	0.864723
$35$	−125.362	−0.0172980
$36$	17134.0	2.20344
$37$	−11689.4	−1.40375	−0.701875	−	0.712300i	$-0.747653\pi$
$37$	−11689.4	−1.40375	−0.701875	+	0.712300i	$0.747653\pi$
$38$	3386.87	0.380487
$39$	−16802.2	−1.76891
$40$	−922.914	−0.0912035
$41$	5457.97	0.507074	0.253537	−	0.967326i	$-0.418406\pi$
$41$	5457.97	0.507074	0.253537	+	0.967326i	$0.418406\pi$
$42$	9075.31	0.793850
$43$	−9431.28	−0.777857	−0.388928	−	0.921268i	$-0.627155\pi$
$43$	−9431.28	−0.777857	−0.388928	+	0.921268i	$0.627155\pi$
$44$	−3526.24	−0.274587
$45$	831.033	0.0611768
$46$	−17995.0	−1.25389
$47$	1181.18	0.0779958	0.0389979	−	0.999239i	$-0.487583\pi$
$47$	1181.18	0.0779958	0.0389979	+	0.999239i	$0.487583\pi$
$48$	21067.4	1.31980
$49$	−15123.5	−0.899830
$50$	30366.6	1.71780
$51$	−13571.6	−0.730644
$52$	−46639.7	−2.39193
$53$	5177.85	0.253198	0.126599	−	0.991954i	$-0.459594\pi$
$53$	5177.85	0.253198	0.126599	+	0.991954i	$0.459594\pi$
$54$	−6413.87	−0.299320
$55$	−171.030	−0.00762368
$56$	12394.3	0.528143
$57$	−7885.99	−0.321491
$58$	−19460.1	−0.759582
$59$	−866.974	−0.0324247	−0.0162123	−	0.999869i	$-0.505161\pi$
$59$	−866.974	−0.0324247	−0.0162123	+	0.999869i	$0.505161\pi$
$60$	4367.64	0.156628
$61$	37586.7	1.29333	0.646666	−	0.762773i	$-0.276163\pi$
$61$	37586.7	1.29333	0.646666	+	0.762773i	$0.276163\pi$
$62$	−60424.5	−1.99634
$63$	−11160.4	−0.354264
$64$	−35732.8	−1.09048
$65$	−2262.12	−0.0664099
$66$	12381.3	0.349871
$67$	−16626.3	−0.452490	−0.226245	−	0.974070i	$-0.572645\pi$
$67$	−16626.3	−0.452490	−0.226245	+	0.974070i	$0.572645\pi$
$68$	−37672.2	−0.987981
$69$	41899.6	1.05947
$70$	1221.83	0.0298034
$71$	−38922.6	−0.916339	−0.458169	−	0.888865i	$-0.651495\pi$
$71$	−38922.6	−0.916339	−0.458169	+	0.888865i	$0.651495\pi$
$72$	−82162.8	−1.86786
$73$	80659.9	1.77154	0.885769	−	0.464127i	$-0.153632\pi$
$73$	80659.9	1.77154	0.885769	+	0.464127i	$0.153632\pi$
$74$	113930.	2.41858
$75$	−70705.6	−1.45144
$76$	−21890.0	−0.434722
$77$	2296.85	0.0441474
$78$	163762.	3.04773
$79$	94667.7	1.70661	0.853304	−	0.521413i	$-0.174595\pi$
$79$	94667.7	1.70661	0.853304	+	0.521413i	$0.174595\pi$
$80$	2836.35	0.0495489
$81$	−51161.5	−0.866425
$82$	−53195.7	−0.873660
$83$	29306.0	0.466941	0.233470	−	0.972364i	$-0.424992\pi$
$83$	29306.0	0.466941	0.233470	+	0.972364i	$0.424992\pi$
$84$	−58655.4	−0.907005
$85$	−1827.18	−0.0274305
$86$	91921.4	1.34020
$87$	45310.8	0.641805
$88$	16909.4	0.232767
$89$	35001.9	0.468400	0.234200	−	0.972188i	$-0.424753\pi$
$89$	35001.9	0.468400	0.234200	+	0.972188i	$0.424753\pi$
$90$	−8099.61	−0.105404
$91$	30379.2	0.384568
$92$	116305.	1.43262
$93$	140692.	1.68680
$94$	−11512.3	−0.134382
$95$	−1061.71	−0.0120697
$96$	14030.7	0.155382
$97$	173153.	1.86853	0.934265	−	0.356579i	$-0.116057\pi$
$97$	173153.	1.86853	0.934265	+	0.356579i	$0.116057\pi$
$98$	147400.	1.55036
$99$	−15226.0	−0.156134
$100$	−196265.	−1.96265
$101$	−84636.1	−0.825566	−0.412783	−	0.910829i	$-0.635443\pi$
$101$	−84636.1	−0.825566	−0.412783	+	0.910829i	$0.635443\pi$
$102$	132275.	1.25886
$103$	159049.	1.47720	0.738598	−	0.674146i	$-0.235488\pi$
$103$	159049.	1.47720	0.738598	+	0.674146i	$0.235488\pi$
$104$	223652.	2.02763
$105$	−2844.91	−0.0251823
$106$	−50465.6	−0.436245
$107$	178946.	1.51099	0.755496	−	0.655154i	$-0.227396\pi$
$107$	178946.	1.51099	0.755496	+	0.655154i	$0.227396\pi$
$108$	41454.0	0.341985
$109$	−20101.1	−0.162052	−0.0810258	−	0.996712i	$-0.525820\pi$
$109$	−20101.1	−0.162052	−0.0810258	+	0.996712i	$0.525820\pi$
$110$	1666.93	0.0131352
$111$	−265275.	−2.04357
$112$	−38090.8	−0.286929
$113$	183807.	1.35415	0.677074	−	0.735915i	$-0.263248\pi$
$113$	183807.	1.35415	0.677074	+	0.735915i	$0.263248\pi$
$114$	76860.3	0.553911
$115$	5641.04	0.0397754
$116$	125774.	0.867852
$117$	−201386.	−1.36008
$118$	8449.90	0.0558659
$119$	24538.1	0.158845
$120$	−20944.2	−0.132773
$121$	−157917.	−0.980543
$122$	−366337.	−2.22834
$123$	123861.	0.738195
$124$	390534.	2.28089
$125$	−19067.0	−0.109146
$126$	108774.	0.610377
$127$	50388.5	0.277218	0.138609	−	0.990347i	$-0.455737\pi$
$127$	50388.5	0.277218	0.138609	+	0.990347i	$0.455737\pi$
$128$	328483.	1.77210
$129$	−214030.	−1.13240
$130$	22047.6	0.114420
$131$	130551.	0.664662	0.332331	−	0.943163i	$-0.392165\pi$
$131$	130551.	0.664662	0.332331	+	0.943163i	$0.392165\pi$
$132$	−80022.9	−0.399742
$133$	14258.2	0.0698935
$134$	162047.	0.779615
$135$	2010.60	0.00949494
$136$	180650.	0.837511
$137$	11768.8	0.0535712	0.0267856	−	0.999641i	$-0.491473\pi$
$137$	11768.8	0.0535712	0.0267856	+	0.999641i	$0.491473\pi$
$138$	−408372.	−1.82540
$139$	−6571.80	−0.0288501	−0.0144251	−	0.999896i	$-0.504592\pi$
$139$	−6571.80	−0.0288501	−0.0144251	+	0.999896i	$0.504592\pi$
$140$	−7896.91	−0.0340516
$141$	26805.2	0.113546
$142$	379357.	1.57880
$143$	41446.0	0.169490
$144$	252507.	1.01477
$145$	6100.29	0.0240952
$146$	−786146.	−3.05226
$147$	−343205.	−1.30997
$148$	−736353.	−2.76332
$149$	−435597.	−1.60738	−0.803691	−	0.595046i	$-0.797134\pi$
$149$	−435597.	−1.60738	−0.803691	+	0.595046i	$0.797134\pi$
$150$	689127.	2.50076
$151$	373511.	1.33309	0.666547	−	0.745463i	$-0.267771\pi$
$151$	373511.	1.33309	0.666547	+	0.745463i	$0.267771\pi$
$152$	104969.	0.368513
$153$	−162665.	−0.561780
$154$	−22386.1	−0.0760634
$155$	18941.7	0.0633272
$156$	−1.05842e6	−3.48215
$157$	428872.	1.38860	0.694302	−	0.719684i	$-0.255713\pi$
$157$	428872.	1.38860	0.694302	+	0.719684i	$0.255713\pi$
$158$	−922672.	−2.94039
$159$	117504.	0.368604
$160$	1888.98	0.00583347
$161$	−75756.5	−0.230332
$162$	498642.	1.49280
$163$	−242552.	−0.715049	−0.357524	−	0.933904i	$-0.616379\pi$
$163$	−242552.	−0.715049	−0.357524	+	0.933904i	$0.616379\pi$
$164$	343814.	0.998191
$165$	−3881.27	−0.0110985
$166$	−285629.	−0.804512
$167$	−335048.	−0.929641	−0.464821	−	0.885405i	$-0.653881\pi$
$167$	−335048.	−0.929641	−0.464821	+	0.885405i	$0.653881\pi$
$168$	281271.	0.768868
$169$	176893.	0.476424
$170$	17808.5	0.0472611
$171$	−94519.1	−0.247189
$172$	−594105.	−1.53124
$173$	−718455.	−1.82509	−0.912546	−	0.408975i	$-0.865886\pi$
$173$	−718455.	−1.82509	−0.912546	+	0.408975i	$0.865886\pi$
$174$	−441618.	−1.10579
$175$	127839.	0.315550
$176$	−51966.8	−0.126458
$177$	−19674.7	−0.0472036
$178$	−341144.	−0.807026
$179$	−185929.	−0.433726	−0.216863	−	0.976202i	$-0.569582\pi$
$179$	−185929.	−0.433726	−0.216863	+	0.976202i	$0.569582\pi$
$180$	52349.2	0.120428
$181$	−65817.7	−0.149330	−0.0746648	−	0.997209i	$-0.523789\pi$
$181$	−65817.7	−0.149330	−0.0746648	+	0.997209i	$0.523789\pi$
$182$	−296089.	−0.662589
$183$	852977.	1.88282
$184$	−557720.	−1.21443
$185$	−35714.6	−0.0767214
$186$	−1.37125e6	−2.90625
$187$	33477.1	0.0700074
$188$	74406.1	0.153537
$189$	−27001.5	−0.0549836
$190$	10347.9	0.0207954
$191$	561351.	1.11340	0.556700	−	0.830714i	$-0.312067\pi$
$191$	561351.	1.11340	0.556700	+	0.830714i	$0.312067\pi$
$192$	−810904.	−1.58751
$193$	664585.	1.28427	0.642136	−	0.766591i	$-0.278048\pi$
$193$	664585.	1.28427	0.642136	+	0.766591i	$0.278048\pi$
$194$	−1.68762e6	−3.21937
$195$	−51335.6	−0.0966791
$196$	−952671.	−1.77134
$197$	−169985.	−0.312065	−0.156033	−	0.987752i	$-0.549870\pi$
$197$	−169985.	−0.312065	−0.156033	+	0.987752i	$0.549870\pi$
$198$	148399.	0.269010
$199$	917564.	1.64249	0.821247	−	0.570574i	$-0.193279\pi$
$199$	917564.	1.64249	0.821247	+	0.570574i	$0.193279\pi$
$200$	941152.	1.66374
$201$	−377311.	−0.658732
$202$	824900.	1.42240
$203$	−81924.1	−0.139531
$204$	−854916.	−1.43830
$205$	16675.7	0.0277140
$206$	−1.55016e6	−2.54512
$207$	502196.	0.814605
$208$	−687339.	−1.10157
$209$	19452.4	0.0308040
$210$	27727.7	0.0433876
$211$	453475.	0.701209	0.350604	−	0.936524i	$-0.385976\pi$
$211$	453475.	0.701209	0.350604	+	0.936524i	$0.385976\pi$
$212$	326168.	0.498427
$213$	−883293.	−1.33400
$214$	−1.74408e6	−2.60335
$215$	−28815.3	−0.0425135
$216$	−198785.	−0.289901
$217$	−254378.	−0.366717
$218$	195914.	0.279205
$219$	1.83046e6	2.57899
$220$	−10773.7	−0.0150074
$221$	442785.	0.609834
$222$	2.58549e6	3.52095
$223$	−145631.	−0.196106	−0.0980529	−	0.995181i	$-0.531261\pi$
$223$	−145631.	−0.196106	−0.0980529	+	0.995181i	$0.531261\pi$
$224$	−25368.1	−0.0337806
$225$	−847455.	−1.11599
$226$	−1.79146e6	−2.33312
$227$	1.25530e6	1.61690	0.808451	−	0.588563i	$-0.200306\pi$
$227$	1.25530e6	1.61690	0.808451	+	0.588563i	$0.200306\pi$
$228$	−496762.	−0.632865
$229$	−1.37345e6	−1.73071	−0.865354	−	0.501160i	$-0.832907\pi$
$229$	−1.37345e6	−1.73071	−0.865354	+	0.501160i	$0.832907\pi$
$230$	−54980.0	−0.0685307
$231$	52123.7	0.0642695
$232$	−603126.	−0.735678
$233$	−1.22835e6	−1.48229	−0.741145	−	0.671345i	$-0.765717\pi$
$233$	−1.22835e6	−1.48229	−0.741145	+	0.671345i	$0.765717\pi$
$234$	1.96280e6	2.34334
$235$	3608.85	0.00426284
$236$	−54613.2	−0.0638290
$237$	2.14835e6	2.48447
$238$	−239159.	−0.273681
$239$	−1.18252e6	−1.33910	−0.669549	−	0.742768i	$-0.733513\pi$
$239$	−1.18252e6	−1.33910	−0.669549	+	0.742768i	$0.733513\pi$
$240$	64366.8	0.0721330
$241$	1.03873e6	1.15202	0.576012	−	0.817442i	$-0.304608\pi$
$241$	1.03873e6	1.15202	0.576012	+	0.817442i	$0.304608\pi$
$242$	1.53913e6	1.68942
$243$	−1.32095e6	−1.43506
$244$	2.36770e6	2.54596
$245$	−46206.5	−0.0491799
$246$	−1.20720e6	−1.27187
$247$	257287.	0.268333
$248$	−1.87273e6	−1.93351
$249$	665059.	0.679769
$250$	185836.	0.188052
$251$	−1.46795e6	−1.47071	−0.735357	−	0.677680i	$-0.762986\pi$
$251$	−1.46795e6	−1.47071	−0.735357	+	0.677680i	$0.762986\pi$
$252$	−703026.	−0.697380
$253$	−103354.	−0.101514
$254$	−491108.	−0.477631
$255$	−41465.2	−0.0399331
$256$	−2.05809e6	−1.96274
$257$	303624.	0.286750	0.143375	−	0.989668i	$-0.454204\pi$
$257$	303624.	0.286750	0.143375	+	0.989668i	$0.454204\pi$
$258$	2.08602e6	1.95106
$259$	479630.	0.444281
$260$	−142498.	−0.130730
$261$	543081.	0.493473
$262$	−1.27240e6	−1.14517
$263$	1.46908e6	1.30965	0.654826	−	0.755780i	$-0.272742\pi$
$263$	1.46908e6	1.30965	0.654826	+	0.755780i	$0.272742\pi$
$264$	383735.	0.338861
$265$	15819.8	0.0138384
$266$	−138967.	−0.120423
$267$	794318.	0.681893
$268$	−1.04734e6	−0.890741
$269$	1.93047e6	1.62661	0.813304	−	0.581839i	$-0.197666\pi$
$269$	1.93047e6	1.62661	0.813304	+	0.581839i	$0.197666\pi$
$270$	−19596.2	−0.0163592
$271$	−1.85352e6	−1.53311	−0.766557	−	0.642176i	$-0.778032\pi$
$271$	−1.85352e6	−1.53311	−0.766557	+	0.642176i	$0.778032\pi$
$272$	−555183.	−0.455002
$273$	689413.	0.559852
$274$	−114704.	−0.0923001
$275$	174409.	0.139072
$276$	2.63938e6	2.08559
$277$	749234.	0.586702	0.293351	−	0.956005i	$-0.405229\pi$
$277$	749234.	0.586702	0.293351	+	0.956005i	$0.405229\pi$
$278$	64051.6	0.0497071
$279$	1.68629e6	1.29695
$280$	37868.2	0.0288655
$281$	984646.	0.743900	0.371950	−	0.928253i	$-0.378689\pi$
$281$	984646.	0.743900	0.371950	+	0.928253i	$0.378689\pi$
$282$	−261255.	−0.195633
$283$	369421.	0.274192	0.137096	−	0.990558i	$-0.456223\pi$
$283$	369421.	0.274192	0.137096	+	0.990558i	$0.456223\pi$
$284$	−2.45185e6	−1.80384
$285$	−24094.0	−0.0175710
$286$	−403951.	−0.292021
$287$	−223946.	−0.160487
$288$	168167.	0.119470
$289$	−1.06221e6	−0.748109
$290$	−59456.1	−0.0415147
$291$	3.92946e6	2.72019
$292$	5.08101e6	3.48733
$293$	602955.	0.410313	0.205157	−	0.978729i	$-0.434230\pi$
$293$	602955.	0.410313	0.205157	+	0.978729i	$0.434230\pi$
$294$	3.34503e6	2.25700
$295$	−2648.85	−0.00177216
$296$	3.53104e6	2.34247
$297$	−36837.8	−0.0242327
$298$	4.24552e6	2.76943
$299$	−1.36701e6	−0.884287
$300$	−4.45396e6	−2.85721
$301$	386976.	0.246188
$302$	−3.64040e6	−2.29685
$303$	−1.92069e6	−1.20185
$304$	−322597.	−0.200206
$305$	114838.	0.0706866
$306$	1.58541e6	0.967914
$307$	1.26455e6	0.765753	0.382876	−	0.923800i	$-0.374934\pi$
$307$	1.26455e6	0.765753	0.382876	+	0.923800i	$0.374934\pi$
$308$	144685.	0.0869055
$309$	3.60939e6	2.15049
$310$	−184614.	−0.109109
$311$	495618.	0.290567	0.145283	−	0.989390i	$-0.453591\pi$
$311$	495618.	0.290567	0.145283	+	0.989390i	$0.453591\pi$
$312$	5.07547e6	2.95182
$313$	−1.85464e6	−1.07003	−0.535017	−	0.844841i	$-0.679695\pi$
$313$	−1.85464e6	−1.07003	−0.535017	+	0.844841i	$0.679695\pi$
$314$	−4.17997e6	−2.39248
$315$	−34098.2	−0.0193622
$316$	5.96340e6	3.35951
$317$	−663847.	−0.371039	−0.185520	−	0.982641i	$-0.559397\pi$
$317$	−663847.	−0.371039	−0.185520	+	0.982641i	$0.559397\pi$
$318$	−1.14524e6	−0.635083
$319$	−111768.	−0.0614952
$320$	−109174.	−0.0595997
$321$	4.06092e6	2.19969
$322$	738356.	0.396850
$323$	207817.	0.110835
$324$	−3.22282e6	−1.70558
$325$	2.30683e6	1.21145
$326$	2.36402e6	1.23199
$327$	−456165.	−0.235914
$328$	−1.64869e6	−0.846166
$329$	−48465.1	−0.0246853
$330$	37828.6	0.0191221
$331$	−449403.	−0.225458	−0.112729	−	0.993626i	$-0.535959\pi$
$331$	−449403.	−0.225458	−0.112729	+	0.993626i	$0.535959\pi$
$332$	1.84607e6	0.919187
$333$	−3.17951e6	−1.57127
$334$	3.26552e6	1.60172
$335$	−50798.2	−0.0247307
$336$	−864416.	−0.417710
$337$	−2.18462e6	−1.04786	−0.523928	−	0.851762i	$-0.675534\pi$
$337$	−2.18462e6	−1.04786	−0.523928	+	0.851762i	$0.675534\pi$
$338$	−1.72408e6	−0.820851
$339$	4.17124e6	1.97136
$340$	−115099.	−0.0539977
$341$	−347045.	−0.161622
$342$	921224.	0.425892
$343$	1.31014e6	0.601288
$344$	2.84892e6	1.29803
$345$	128015.	0.0579048
$346$	7.00238e6	3.14453
$347$	2.64608e6	1.17972	0.589861	−	0.807505i	$-0.299183\pi$
$347$	2.64608e6	1.17972	0.589861	+	0.807505i	$0.299183\pi$
$348$	2.85426e6	1.26341
$349$	3.54462e6	1.55778	0.778890	−	0.627161i	$-0.215783\pi$
$349$	3.54462e6	1.55778	0.778890	+	0.627161i	$0.215783\pi$
$350$	−1.24598e6	−0.543675
$351$	−487235.	−0.211091
$352$	−34609.4	−0.0148880
$353$	−827731.	−0.353551	−0.176776	−	0.984251i	$-0.556567\pi$
$353$	−827731.	−0.353551	−0.176776	+	0.984251i	$0.556567\pi$
$354$	191758.	0.0813292
$355$	−118920.	−0.0500822
$356$	2.20487e6	0.922059
$357$	556858.	0.231246
$358$	1.81215e6	0.747285
$359$	3.97275e6	1.62688	0.813439	−	0.581650i	$-0.197593\pi$
$359$	3.97275e6	1.62688	0.813439	+	0.581650i	$0.197593\pi$
$360$	−251031.	−0.102087
$361$	−2.35534e6	−0.951232
$362$	641488.	0.257286
$363$	−3.58371e6	−1.42747
$364$	1.91368e6	0.757034
$365$	246439.	0.0968228
$366$	−8.31349e6	−3.24400
$367$	4.04168e6	1.56638	0.783190	−	0.621782i	$-0.213591\pi$
$367$	4.04168e6	1.56638	0.783190	+	0.621782i	$0.213591\pi$
$368$	1.71401e6	0.659773
$369$	1.48456e6	0.567586
$370$	348090.	0.132187
$371$	−212453.	−0.0801360
$372$	8.86262e6	3.32051
$373$	−411407.	−0.153109	−0.0765543	−	0.997065i	$-0.524392\pi$
$373$	−411407.	−0.153109	−0.0765543	+	0.997065i	$0.524392\pi$
$374$	−326282.	−0.120619
$375$	−432699.	−0.158894
$376$	−356800.	−0.130153
$377$	−1.47830e6	−0.535685
$378$	263168.	0.0947335
$379$	−989446.	−0.353830	−0.176915	−	0.984226i	$-0.556612\pi$
$379$	−989446.	−0.353830	−0.176915	+	0.984226i	$0.556612\pi$
$380$	−66880.2	−0.0237596
$381$	1.14349e6	0.403573
$382$	−5.47117e6	−1.91832
$383$	1.53846e6	0.535908	0.267954	−	0.963432i	$-0.413652\pi$
$383$	1.53846e6	0.535908	0.267954	+	0.963432i	$0.413652\pi$
$384$	7.45445e6	2.57981
$385$	7017.53	0.00241286
$386$	−6.47733e6	−2.21273
$387$	−2.56529e6	−0.870682
$388$	1.09074e7	3.67826
$389$	−4.67932e6	−1.56786	−0.783932	−	0.620847i	$-0.786789\pi$
$389$	−4.67932e6	−1.56786	−0.783932	+	0.620847i	$0.786789\pi$
$390$	500339.	0.166572
$391$	−1.10417e6	−0.365253
$392$	4.56836e6	1.50157
$393$	2.96266e6	0.967611
$394$	1.65675e6	0.537670
$395$	289237.	0.0932741
$396$	−959130.	−0.307354
$397$	3.16624e6	1.00825	0.504124	−	0.863631i	$-0.331815\pi$
$397$	3.16624e6	1.00825	0.504124	+	0.863631i	$0.331815\pi$
$398$	−8.94297e6	−2.82992
$399$	323571.	0.101751
$400$	−2.89240e6	−0.903874
$401$	563780.	0.175085	0.0875425	−	0.996161i	$-0.472099\pi$
$401$	563780.	0.175085	0.0875425	+	0.996161i	$0.472099\pi$
$402$	3.67743e6	1.13496
$403$	−4.59019e6	−1.40789
$404$	−5.33148e6	−1.62515
$405$	−156313.	−0.0473542
$406$	798468.	0.240404
$407$	654354.	0.195806
$408$	4.09959e6	1.21924
$409$	3.92288e6	1.15957	0.579784	−	0.814770i	$-0.303137\pi$
$409$	3.92288e6	1.15957	0.579784	+	0.814770i	$0.303137\pi$
$410$	−162528.	−0.0477496
$411$	267077.	0.0779886
$412$	1.00190e7	2.90790
$413$	35572.9	0.0102623
$414$	−4.89462e6	−1.40352
$415$	89538.4	0.0255205
$416$	−457761.	−0.129690
$417$	−149138.	−0.0419998
$418$	−189591.	−0.0530735
$419$	−2.33439e6	−0.649589	−0.324795	−	0.945785i	$-0.605295\pi$
$419$	−2.33439e6	−0.649589	−0.324795	+	0.945785i	$0.605295\pi$
$420$	−179209.	−0.0495720
$421$	−1.34385e6	−0.369526	−0.184763	−	0.982783i	$-0.559152\pi$
$421$	−1.34385e6	−0.369526	−0.184763	+	0.982783i	$0.559152\pi$
$422$	−4.41976e6	−1.20814
$423$	321279.	0.0873034
$424$	−1.56408e6	−0.422517
$425$	1.86329e6	0.500388
$426$	8.60896e6	2.29841
$427$	−1.54222e6	−0.409334
$428$	1.12723e7	2.97443
$429$	940559.	0.246742
$430$	280846.	0.0732483
$431$	7.55823e6	1.95987	0.979934	−	0.199322i	$-0.0638741\pi$
$431$	7.55823e6	1.95987	0.979934	+	0.199322i	$0.0638741\pi$
$432$	610916.	0.157497
$433$	−1.28471e6	−0.329296	−0.164648	−	0.986352i	$-0.552649\pi$
$433$	−1.28471e6	−0.329296	−0.164648	+	0.986352i	$0.552649\pi$
$434$	2.47928e6	0.631832
$435$	138437.	0.0350776
$436$	−1.26623e6	−0.319003
$437$	−641594.	−0.160715
$438$	−1.78405e7	−4.44346
$439$	503146.	0.124604	0.0623021	−	0.998057i	$-0.480156\pi$
$439$	503146.	0.124604	0.0623021	+	0.998057i	$0.480156\pi$
$440$	51663.1	0.0127218
$441$	−4.11355e6	−1.00721
$442$	−4.31557e6	−1.05071
$443$	−6.83400e6	−1.65450	−0.827248	−	0.561837i	$-0.810095\pi$
$443$	−6.83400e6	−1.65450	−0.827248	+	0.561837i	$0.810095\pi$
$444$	−1.67105e7	−4.02283
$445$	106941.	0.0256002
$446$	1.41938e6	0.337879
$447$	−9.88526e6	−2.34002
$448$	1.46615e6	0.345132
$449$	6.72066e6	1.57324	0.786622	−	0.617435i	$-0.211828\pi$
$449$	6.72066e6	1.57324	0.786622	+	0.617435i	$0.211828\pi$
$450$	8.25967e6	1.92279
$451$	−305527.	−0.0707309
$452$	1.15786e7	2.66568
$453$	8.47630e6	1.94071
$454$	−1.22347e7	−2.78583
$455$	92817.3	0.0210184
$456$	2.38213e6	0.536480
$457$	735102.	0.164648	0.0823241	−	0.996606i	$-0.473766\pi$
$457$	735102.	0.164648	0.0823241	+	0.996606i	$0.473766\pi$
$458$	1.33862e7	2.98191
$459$	−393553.	−0.0871910
$460$	355346.	0.0782991
$461$	−4.22061e6	−0.924960	−0.462480	−	0.886630i	$-0.653040\pi$
$461$	−4.22061e6	−0.924960	−0.462480	+	0.886630i	$0.653040\pi$
$462$	−508020.	−0.110733
$463$	4.84850e6	1.05113	0.525563	−	0.850755i	$-0.323855\pi$
$463$	4.84850e6	1.05113	0.525563	+	0.850755i	$0.323855\pi$
$464$	1.85356e6	0.399679
$465$	429855.	0.0921913
$466$	1.19721e7	2.55390
$467$	449112.	0.0952934	0.0476467	−	0.998864i	$-0.484828\pi$
$467$	449112.	0.0952934	0.0476467	+	0.998864i	$0.484828\pi$
$468$	−1.26859e7	−2.67736
$469$	682196.	0.143211
$470$	−35173.4	−0.00734462
$471$	9.73263e6	2.02152
$472$	261888.	0.0541078
$473$	527947.	0.108502
$474$	−2.09387e7	−4.28060
$475$	1.08269e6	0.220176
$476$	1.54573e6	0.312692
$477$	1.40837e6	0.283413
$478$	1.15253e7	2.30719
$479$	−4.37768e6	−0.871776	−0.435888	−	0.900001i	$-0.643566\pi$
$479$	−4.37768e6	−0.871776	−0.435888	+	0.900001i	$0.643566\pi$
$480$	42867.7	0.00849233
$481$	8.65482e6	1.70567
$482$	−1.01239e7	−1.98487
$483$	−1.71919e6	−0.335317
$484$	−9.94769e6	−1.93023
$485$	529032.	0.102124
$486$	1.28746e7	2.47253
$487$	2.92877e6	0.559582	0.279791	−	0.960061i	$-0.409735\pi$
$487$	2.92877e6	0.559582	0.279791	+	0.960061i	$0.409735\pi$
$488$	−1.13539e7	−2.15821
$489$	−5.50437e6	−1.04096
$490$	450349.	0.0847342
$491$	−8.31322e6	−1.55620	−0.778100	−	0.628140i	$-0.783817\pi$
$491$	−8.31322e6	−1.55620	−0.778100	+	0.628140i	$0.783817\pi$
$492$	7.80236e6	1.45316
$493$	−1.19406e6	−0.221264
$494$	−2.50763e6	−0.462323
$495$	−46519.7	−0.00853344
$496$	5.75539e6	1.05044
$497$	1.59704e6	0.290017
$498$	−6.48195e6	−1.17120
$499$	−6.26614e6	−1.12655	−0.563273	−	0.826271i	$-0.690458\pi$
$499$	−6.26614e6	−1.12655	−0.563273	+	0.826271i	$0.690458\pi$
$500$	−1.20109e6	−0.214857
$501$	−7.60343e6	−1.35337
$502$	1.43073e7	2.53396
$503$	9.10030e6	1.60375	0.801873	−	0.597495i	$-0.203837\pi$
$503$	9.10030e6	1.60375	0.801873	+	0.597495i	$0.203837\pi$
$504$	3.37123e6	0.591169
$505$	−258588.	−0.0451210
$506$	1.00733e6	0.174902
$507$	4.01433e6	0.693575
$508$	3.17412e6	0.545713
$509$	1.20688e6	0.206476	0.103238	−	0.994657i	$-0.467080\pi$
$509$	1.20688e6	0.206476	0.103238	+	0.994657i	$0.467080\pi$
$510$	404138.	0.0688025
$511$	−3.30956e6	−0.560684
$512$	9.54755e6	1.60960
$513$	−228680.	−0.0383649
$514$	−2.95925e6	−0.494054
$515$	485941.	0.0807356
$516$	−1.34824e7	−2.22916
$517$	−66120.4	−0.0108795
$518$	−4.67469e6	−0.765470
$519$	−1.63043e7	−2.65696
$520$	683322.	0.110820
$521$	−2.50146e6	−0.403738	−0.201869	−	0.979413i	$-0.564702\pi$
$521$	−2.50146e6	−0.403738	−0.201869	+	0.979413i	$0.564702\pi$
$522$	−5.29310e6	−0.850226
$523$	2.87094e6	0.458955	0.229478	−	0.973314i	$-0.426298\pi$
$523$	2.87094e6	0.458955	0.229478	+	0.973314i	$0.426298\pi$
$524$	8.22378e6	1.30841
$525$	2.90113e6	0.459376
$526$	−1.43183e7	−2.25645
$527$	−3.70763e6	−0.581526
$528$	−1.17931e6	−0.184096
$529$	−3.02744e6	−0.470367
$530$	−154187.	−0.0238428
$531$	−235815.	−0.0362941
$532$	898169.	0.137588
$533$	−4.04106e6	−0.616137
$534$	−7.74177e6	−1.17486
$535$	546731.	0.0825827
$536$	5.02233e6	0.755081
$537$	−4.21940e6	−0.631415
$538$	−1.88152e7	−2.80255
$539$	846584.	0.125516
$540$	126654.	0.0186911
$541$	−1.91451e6	−0.281232	−0.140616	−	0.990064i	$-0.544908\pi$
$541$	−1.91451e6	−0.281232	−0.140616	+	0.990064i	$0.544908\pi$
$542$	1.80652e7	2.64147
$543$	−1.49364e6	−0.217393
$544$	−369746.	−0.0535681
$545$	−61414.6	−0.00885687
$546$	−6.71932e6	−0.964592
$547$	710094.	0.101472	0.0507362	−	0.998712i	$-0.483843\pi$
$547$	710094.	0.101472	0.0507362	+	0.998712i	$0.483843\pi$
$548$	741353.	0.105457
$549$	1.02235e7	1.44767
$550$	−1.69987e6	−0.239612
$551$	−693828.	−0.0973583
$552$	−1.26567e7	−1.76796
$553$	−3.88432e6	−0.540134
$554$	−7.30236e6	−1.01085
$555$	−810492.	−0.111691
$556$	−413977.	−0.0567923
$557$	2.86435e6	0.391191	0.195595	−	0.980685i	$-0.437336\pi$
$557$	2.86435e6	0.391191	0.195595	+	0.980685i	$0.437336\pi$
$558$	−1.64354e7	−2.23457
$559$	6.98288e6	0.945160
$560$	−116378.	−0.0156820
$561$	759715.	0.101916
$562$	−9.59679e6	−1.28170
$563$	8.92937e6	1.18727	0.593635	−	0.804734i	$-0.297692\pi$
$563$	8.92937e6	1.18727	0.593635	+	0.804734i	$0.297692\pi$
$564$	1.68854e6	0.223518
$565$	561584.	0.0740105
$566$	−3.60054e6	−0.472418
$567$	2.09921e6	0.274220
$568$	1.17574e7	1.52912
$569$	−5.51301e6	−0.713852	−0.356926	−	0.934133i	$-0.616175\pi$
$569$	−5.51301e6	−0.713852	−0.356926	+	0.934133i	$0.616175\pi$
$570$	234830.	0.0302738
$571$	1.44967e7	1.86070	0.930352	−	0.366667i	$-0.119501\pi$
$571$	1.44967e7	1.86070	0.930352	+	0.366667i	$0.119501\pi$
$572$	2.61081e6	0.333645
$573$	1.27391e7	1.62088
$574$	2.18268e6	0.276509
$575$	−5.75252e6	−0.725585
$576$	−9.71925e6	−1.22061
$577$	6.70927e6	0.838950	0.419475	−	0.907767i	$-0.362214\pi$
$577$	6.70927e6	0.838950	0.419475	+	0.907767i	$0.362214\pi$
$578$	1.03527e7	1.28895
$579$	1.50818e7	1.86963
$580$	384276.	0.0474322
$581$	−1.20246e6	−0.147785
$582$	−3.82982e7	−4.68674
$583$	−289847.	−0.0353181
$584$	−2.43650e7	−2.95620
$585$	−615293.	−0.0743349
$586$	−5.87666e6	−0.706946
$587$	−5.39945e6	−0.646777	−0.323388	−	0.946266i	$-0.604822\pi$
$587$	−5.39945e6	−0.646777	−0.323388	+	0.946266i	$0.604822\pi$
$588$	−2.16195e7	−2.57871
$589$	−2.15437e6	−0.255878
$590$	25816.9	0.00305333
$591$	−3.85757e6	−0.454303
$592$	−1.08518e7	−1.27261
$593$	−1.15063e7	−1.34369	−0.671847	−	0.740690i	$-0.734499\pi$
$593$	−1.15063e7	−1.34369	−0.671847	+	0.740690i	$0.734499\pi$
$594$	359037.	0.0417516
$595$	74971.1	0.00868163
$596$	−2.74396e7	−3.16418
$597$	2.08228e7	2.39113
$598$	1.33235e7	1.52357
$599$	−2.60459e6	−0.296601	−0.148300	−	0.988942i	$-0.547380\pi$
$599$	−2.60459e6	−0.296601	−0.148300	+	0.988942i	$0.547380\pi$
$600$	2.13581e7	2.42206
$601$	−406696.	−0.0459286	−0.0229643	−	0.999736i	$-0.507310\pi$
$601$	−406696.	−0.0459286	−0.0229643	+	0.999736i	$0.507310\pi$
$602$	−3.77163e6	−0.424168
$603$	−4.52233e6	−0.506488
$604$	2.35286e7	2.62424
$605$	−482483.	−0.0535912
$606$	1.87199e7	2.07073
$607$	1.31326e7	1.44671	0.723353	−	0.690478i	$-0.242600\pi$
$607$	1.31326e7	1.44671	0.723353	+	0.690478i	$0.242600\pi$
$608$	−214847.	−0.0235705
$609$	−1.85915e6	−0.203129
$610$	−1.11926e6	−0.121789
$611$	−874541.	−0.0947713
$612$	−1.02468e7	−1.10588
$613$	−3.14859e6	−0.338427	−0.169214	−	0.985579i	$-0.554123\pi$
$613$	−3.14859e6	−0.338427	−0.169214	+	0.985579i	$0.554123\pi$
$614$	−1.23248e7	−1.31935
$615$	378430.	0.0403458
$616$	−693811.	−0.0736698
$617$	1.33112e7	1.40768	0.703842	−	0.710357i	$-0.251466\pi$
$617$	1.33112e7	1.40768	0.703842	+	0.710357i	$0.251466\pi$
$618$	−3.51787e7	−3.70517
$619$	1.70637e6	0.178997	0.0894986	−	0.995987i	$-0.471474\pi$
$619$	1.70637e6	0.178997	0.0894986	+	0.995987i	$0.471474\pi$
$620$	1.19320e6	0.124661
$621$	1.21501e6	0.126431
$622$	−4.83051e6	−0.500630
$623$	−1.43617e6	−0.148247
$624$	−1.55982e7	−1.60366
$625$	9.67820e6	0.991048
$626$	1.80761e7	1.84361
$627$	441444.	0.0448442
$628$	2.70159e7	2.73351
$629$	6.99073e6	0.704524
$630$	332336.	0.0333600
$631$	1.58625e7	1.58598	0.792990	−	0.609235i	$-0.208523\pi$
$631$	1.58625e7	1.58598	0.792990	+	0.609235i	$0.208523\pi$
$632$	−2.85964e7	−2.84786
$633$	1.02910e7	1.02081
$634$	6.47014e6	0.639279
$635$	153951.	0.0151513
$636$	7.40192e6	0.725607
$637$	1.11973e7	1.09337
$638$	1.08934e6	0.105953
$639$	−1.05869e7	−1.02569
$640$	1.00361e6	0.0968534
$641$	1.27557e7	1.22619	0.613095	−	0.790009i	$-0.289924\pi$
$641$	1.27557e7	1.22619	0.613095	+	0.790009i	$0.289924\pi$
$642$	−3.95795e7	−3.78994
$643$	1.41850e7	1.35301	0.676507	−	0.736436i	$-0.263493\pi$
$643$	1.41850e7	1.35301	0.676507	+	0.736436i	$0.263493\pi$
$644$	−4.77213e6	−0.453417
$645$	−653922.	−0.0618909
$646$	−2.02548e6	−0.190962
$647$	6.71667e6	0.630802	0.315401	−	0.948958i	$-0.397861\pi$
$647$	6.71667e6	0.630802	0.315401	+	0.948958i	$0.397861\pi$
$648$	1.54544e7	1.44582
$649$	48531.6	0.00452286
$650$	−2.24833e7	−2.08726
$651$	−5.77275e6	−0.533864
$652$	−1.52791e7	−1.40760
$653$	−1.22976e7	−1.12860	−0.564299	−	0.825571i	$-0.690853\pi$
$653$	−1.22976e7	−1.12860	−0.564299	+	0.825571i	$0.690853\pi$
$654$	4.44599e6	0.406465
$655$	398870.	0.0363269
$656$	5.06685e6	0.459705
$657$	2.19393e7	1.98294
$658$	472362.	0.0425314
$659$	1.18214e7	1.06037	0.530184	−	0.847883i	$-0.322123\pi$
$659$	1.18214e7	1.06037	0.530184	+	0.847883i	$0.322123\pi$
$660$	−244493.	−0.0218477
$661$	1.13990e7	1.01476	0.507380	−	0.861722i	$-0.330614\pi$
$661$	1.13990e7	1.01476	0.507380	+	0.861722i	$0.330614\pi$
$662$	4.38008e6	0.388452
$663$	1.00484e7	0.887793
$664$	−8.85251e6	−0.779195
$665$	43563.0	0.00382001
$666$	3.09889e7	2.70720
$667$	3.68643e6	0.320842
$668$	−2.11057e7	−1.83003
$669$	−3.30488e6	−0.285490
$670$	495101.	0.0426096
$671$	−2.10404e6	−0.180405
$672$	−575693.	−0.0491776
$673$	1.48196e7	1.26124	0.630619	−	0.776092i	$-0.282801\pi$
$673$	1.48196e7	1.26124	0.630619	+	0.776092i	$0.282801\pi$
$674$	2.12923e7	1.80540
$675$	−2.05034e6	−0.173207
$676$	1.11430e7	0.937855
$677$	993365.	0.0832985	0.0416493	−	0.999132i	$-0.486739\pi$
$677$	993365.	0.0832985	0.0416493	+	0.999132i	$0.486739\pi$
$678$	−4.06547e7	−3.39654
$679$	−7.10465e6	−0.591382
$680$	551938.	0.0457739
$681$	2.84873e7	2.35388
$682$	3.38246e6	0.278465
$683$	−9.80197e6	−0.804010	−0.402005	−	0.915637i	$-0.631687\pi$
$683$	−9.80197e6	−0.804010	−0.402005	+	0.915637i	$0.631687\pi$
$684$	−5.95404e6	−0.486599
$685$	35957.1	0.00292792
$686$	−1.27692e7	−1.03598
$687$	−3.11685e7	−2.51955
$688$	−8.75544e6	−0.705191
$689$	−3.83366e6	−0.307656
$690$	−1.24769e6	−0.0997666
$691$	1.29080e6	0.102841	0.0514203	−	0.998677i	$-0.483625\pi$
$691$	1.29080e6	0.102841	0.0514203	+	0.998677i	$0.483625\pi$
$692$	−4.52576e7	−3.59275
$693$	624738.	0.0494157
$694$	−2.57899e7	−2.03259
$695$	−20078.7	−0.00157679
$696$	−1.36871e7	−1.07100
$697$	−3.26407e6	−0.254494
$698$	−3.45474e7	−2.68396
$699$	−2.78757e7	−2.15791
$700$	8.05297e6	0.621170
$701$	−1.33824e7	−1.02858	−0.514289	−	0.857617i	$-0.671944\pi$
$701$	−1.33824e7	−1.02858	−0.514289	+	0.857617i	$0.671944\pi$
$702$	4.74880e6	0.363699
$703$	4.06207e6	0.309998
$704$	2.00026e6	0.152109
$705$	81897.6	0.00620581
$706$	8.06743e6	0.609149
$707$	3.47271e6	0.261288
$708$	−1.23937e6	−0.0929218
$709$	−9.76035e6	−0.729206	−0.364603	−	0.931163i	$-0.618795\pi$
$709$	−9.76035e6	−0.729206	−0.364603	+	0.931163i	$0.618795\pi$
$710$	1.15904e6	0.0862887
$711$	2.57494e7	1.91027
$712$	−1.05731e7	−0.781629
$713$	1.14465e7	0.843238
$714$	−5.42738e6	−0.398423
$715$	126630.	0.00926339
$716$	−1.17122e7	−0.853803
$717$	−2.68355e7	−1.94945
$718$	−3.87201e7	−2.80302
$719$	−2.06276e7	−1.48808	−0.744039	−	0.668136i	$-0.767092\pi$
$719$	−2.06276e7	−1.48808	−0.744039	+	0.668136i	$0.767092\pi$
$720$	771481.	0.0554618
$721$	−6.52595e6	−0.467526
$722$	2.29562e7	1.63892
$723$	2.35726e7	1.67711
$724$	−4.14605e6	−0.293960
$725$	−6.22085e6	−0.439546
$726$	3.49284e7	2.45945
$727$	1.50252e6	0.105435	0.0527173	−	0.998609i	$-0.483212\pi$
$727$	1.50252e6	0.105435	0.0527173	+	0.998609i	$0.483212\pi$
$728$	−9.17669e6	−0.641738
$729$	−1.75448e7	−1.22273
$730$	−2.40190e6	−0.166820
$731$	5.64026e6	0.390397
$732$	5.37316e7	3.70640
$733$	5.05306e6	0.347372	0.173686	−	0.984801i	$-0.444432\pi$
$733$	5.05306e6	0.347372	0.173686	+	0.984801i	$0.444432\pi$
$734$	−3.93920e7	−2.69878
$735$	−1.04859e6	−0.0715958
$736$	1.14152e6	0.0776761
$737$	930712.	0.0631170
$738$	−1.44691e7	−0.977917
$739$	−1.96785e7	−1.32550	−0.662750	−	0.748841i	$-0.730611\pi$
$739$	−1.96785e7	−1.32550	−0.662750	+	0.748841i	$0.730611\pi$
$740$	−2.24977e6	−0.151029
$741$	5.83875e6	0.390638
$742$	2.07066e6	0.138070
$743$	−1.80646e7	−1.20048	−0.600242	−	0.799818i	$-0.704929\pi$
$743$	−1.80646e7	−1.20048	−0.600242	+	0.799818i	$0.704929\pi$
$744$	−4.24990e7	−2.81480
$745$	−1.33087e6	−0.0878510
$746$	4.00975e6	0.263797
$747$	7.97119e6	0.522663
$748$	2.10882e6	0.137812
$749$	−7.34234e6	−0.478222
$750$	4.21727e6	0.273765
$751$	1.96118e7	1.26887	0.634434	−	0.772977i	$-0.281233\pi$
$751$	1.96118e7	1.26887	0.634434	+	0.772977i	$0.281233\pi$
$752$	1.09654e6	0.0707097
$753$	−3.33131e7	−2.14106
$754$	1.44082e7	0.922954
$755$	1.14118e6	0.0728598
$756$	−1.70090e6	−0.108237
$757$	−1.84651e7	−1.17115	−0.585574	−	0.810619i	$-0.699131\pi$
$757$	−1.84651e7	−1.17115	−0.585574	+	0.810619i	$0.699131\pi$
$758$	9.64357e6	0.609628
$759$	−2.34547e6	−0.147783
$760$	320711.	0.0201410
$761$	8.72068e6	0.545869	0.272935	−	0.962033i	$-0.412006\pi$
$761$	8.72068e6	0.545869	0.272935	+	0.962033i	$0.412006\pi$
$762$	−1.11450e7	−0.695332
$763$	824769.	0.0512886
$764$	3.53612e7	2.19176
$765$	−496989.	−0.0307039
$766$	−1.49945e7	−0.923339
$767$	641904.	0.0393987
$768$	−4.67053e7	−2.85735
$769$	−5.33732e6	−0.325467	−0.162734	−	0.986670i	$-0.552031\pi$
$769$	−5.33732e6	−0.325467	−0.162734	+	0.986670i	$0.552031\pi$
$770$	−68395.9	−0.00415722
$771$	6.89032e6	0.417449
$772$	4.18642e7	2.52813
$773$	1.05197e7	0.633220	0.316610	−	0.948556i	$-0.397455\pi$
$773$	1.05197e7	0.633220	0.316610	+	0.948556i	$0.397455\pi$
$774$	2.50025e7	1.50013
$775$	−1.93160e7	−1.15522
$776$	−5.23045e7	−3.11806
$777$	1.08845e7	0.646781
$778$	4.56067e7	2.70134
$779$	−1.89664e6	−0.111980
$780$	−3.23378e6	−0.190316
$781$	2.17882e6	0.127818
$782$	1.07617e7	0.629310
$783$	1.31393e6	0.0765894
$784$	−1.40397e7	−0.815770
$785$	1.31033e6	0.0758937
$786$	−2.88754e7	−1.66714
$787$	1.46072e7	0.840679	0.420339	−	0.907367i	$-0.361911\pi$
$787$	1.46072e7	0.840679	0.420339	+	0.907367i	$0.361911\pi$
$788$	−1.07079e7	−0.614310
$789$	3.33386e7	1.90658
$790$	−2.81903e6	−0.160706
$791$	−7.54180e6	−0.428582
$792$	4.59933e6	0.260544
$793$	−2.78291e7	−1.57150
$794$	−3.08596e7	−1.73715
$795$	359008.	0.0201459
$796$	5.78001e7	3.23330
$797$	9.69252e6	0.540494	0.270247	−	0.962791i	$-0.412895\pi$
$797$	9.69252e6	0.540494	0.270247	+	0.962791i	$0.412895\pi$
$798$	−3.15366e6	−0.175310
$799$	−706390.	−0.0391451
$800$	−1.92631e6	−0.106415
$801$	9.52046e6	0.524296
$802$	−5.49485e6	−0.301661
$803$	−4.51520e6	−0.247109
$804$	−2.37679e7	−1.29673
$805$	−231458.	−0.0125887
$806$	4.47380e7	2.42571
$807$	4.38093e7	2.36801
$808$	2.55661e7	1.37764
$809$	−2.10086e7	−1.12856	−0.564280	−	0.825583i	$-0.690846\pi$
$809$	−2.10086e7	−1.12856	−0.564280	+	0.825583i	$0.690846\pi$
$810$	1.52350e6	0.0815885
$811$	1.38008e7	0.736803	0.368402	−	0.929667i	$-0.379905\pi$
$811$	1.38008e7	0.736803	0.368402	+	0.929667i	$0.379905\pi$
$812$	−5.16064e6	−0.274671
$813$	−4.20630e7	−2.23190
$814$	−6.37762e6	−0.337363
$815$	−741066.	−0.0390807
$816$	−1.25991e7	−0.662389
$817$	3.27736e6	0.171779
$818$	−3.82341e7	−1.99787
$819$	8.26310e6	0.430460
$820$	1.05045e6	0.0545558
$821$	3.31350e7	1.71565	0.857825	−	0.513942i	$-0.171815\pi$
$821$	3.31350e7	1.71565	0.857825	+	0.513942i	$0.171815\pi$
$822$	−2.60304e6	−0.134370
$823$	−2.46650e7	−1.26935	−0.634676	−	0.772778i	$-0.718866\pi$
$823$	−2.46650e7	−1.26935	−0.634676	+	0.772778i	$0.718866\pi$
$824$	−4.80441e7	−2.46503
$825$	3.95797e6	0.202459
$826$	−346708.	−0.0176813
$827$	1.08100e7	0.549620	0.274810	−	0.961499i	$-0.411385\pi$
$827$	1.08100e7	0.549620	0.274810	+	0.961499i	$0.411385\pi$
$828$	3.16348e7	1.60358
$829$	−1.04001e7	−0.525594	−0.262797	−	0.964851i	$-0.584645\pi$
$829$	−1.04001e7	−0.525594	−0.262797	+	0.964851i	$0.584645\pi$
$830$	−872680.	−0.0439703
$831$	1.70028e7	0.854117
$832$	2.64564e7	1.32502
$833$	9.04440e6	0.451614
$834$	1.45356e6	0.0723632
$835$	−1.02367e6	−0.0508092
$836$	1.22536e6	0.0606386
$837$	4.07983e6	0.201293
$838$	2.27520e7	1.11920
$839$	−5.14350e6	−0.252263	−0.126132	−	0.992014i	$-0.540256\pi$
$839$	−5.14350e6	−0.252263	−0.126132	+	0.992014i	$0.540256\pi$
$840$	859364.	0.0420222
$841$	−1.65246e7	−0.805640
$842$	1.30977e7	0.636671
$843$	2.23451e7	1.08296
$844$	2.85657e7	1.38035
$845$	540459.	0.0260388
$846$	−3.13132e6	−0.150419
$847$	6.47952e6	0.310338
$848$	4.80681e6	0.229545
$849$	8.38348e6	0.399168
$850$	−1.81604e7	−0.862140
$851$	−2.15825e7	−1.02159
$852$	−5.56413e7	−2.62602
$853$	−2.05030e7	−0.964817	−0.482408	−	0.875946i	$-0.660238\pi$
$853$	−2.05030e7	−0.964817	−0.482408	+	0.875946i	$0.660238\pi$
$854$	1.50312e7	0.705259
$855$	−288783.	−0.0135100
$856$	−5.40543e7	−2.52143
$857$	1.19422e7	0.555434	0.277717	−	0.960663i	$-0.410422\pi$
$857$	1.19422e7	0.555434	0.277717	+	0.960663i	$0.410422\pi$
$858$	−9.16709e6	−0.425122
$859$	1.33847e6	0.0618908	0.0309454	−	0.999521i	$-0.490148\pi$
$859$	1.33847e6	0.0618908	0.0309454	+	0.999521i	$0.490148\pi$
$860$	−1.81516e6	−0.0836891
$861$	−5.08214e6	−0.233636
$862$	−7.36658e7	−3.37674
$863$	2.06157e7	0.942261	0.471131	−	0.882063i	$-0.343846\pi$
$863$	2.06157e7	0.942261	0.471131	+	0.882063i	$0.343846\pi$
$864$	406864.	0.0185424
$865$	−2.19509e6	−0.0997497
$866$	1.25214e7	0.567357
$867$	−2.41053e7	−1.08909
$868$	−1.60240e7	−0.721893
$869$	−5.29933e6	−0.238052
$870$	−1.34927e6	−0.0604368
$871$	1.23101e7	0.549813
$872$	6.07196e6	0.270419
$873$	4.70973e7	2.09151
$874$	6.25325e6	0.276903
$875$	782341.	0.0345442
$876$	1.15306e8	5.07683
$877$	−8.34124e6	−0.366211	−0.183106	−	0.983093i	$-0.558615\pi$
$877$	−8.34124e6	−0.366211	−0.183106	+	0.983093i	$0.558615\pi$
$878$	−4.90388e6	−0.214686
$879$	1.36832e7	0.597331
$880$	−158774.	−0.00691149
$881$	3.46027e7	1.50200	0.751001	−	0.660302i	$-0.229572\pi$
$881$	3.46027e7	1.50200	0.751001	+	0.660302i	$0.229572\pi$
$882$	4.00925e7	1.73537
$883$	−7.29959e6	−0.315062	−0.157531	−	0.987514i	$-0.550353\pi$
$883$	−7.29959e6	−0.315062	−0.157531	+	0.987514i	$0.550353\pi$
$884$	2.78923e7	1.20048
$885$	−60112.0	−0.00257990
$886$	6.66071e7	2.85060
$887$	−1.42373e7	−0.607603	−0.303802	−	0.952735i	$-0.598256\pi$
$887$	−1.42373e7	−0.607603	−0.303802	+	0.952735i	$0.598256\pi$
$888$	8.01320e7	3.41015
$889$	−2.06749e6	−0.0877384
$890$	−1.04229e6	−0.0441077
$891$	2.86393e6	0.120856
$892$	−9.17371e6	−0.386040
$893$	−410459.	−0.0172243
$894$	9.63460e7	4.03172
$895$	−568068.	−0.0237051
$896$	−1.34780e7	−0.560861
$897$	−3.10223e7	−1.28734
$898$	−6.55024e7	−2.71061
$899$	1.23784e7	0.510818
$900$	−5.33837e7	−2.19686
$901$	−3.09655e6	−0.127077
$902$	2.97780e6	0.121865
$903$	8.78186e6	0.358399
$904$	−5.55228e7	−2.25970
$905$	−201092.	−0.00816156
$906$	−8.26137e7	−3.34373
$907$	−1.93549e7	−0.781219	−0.390609	−	0.920557i	$-0.627736\pi$
$907$	−1.93549e7	−0.781219	−0.390609	+	0.920557i	$0.627736\pi$
$908$	7.90753e7	3.18292
$909$	−2.30209e7	−0.924085
$910$	−904638.	−0.0362136
$911$	−1.84408e7	−0.736179	−0.368090	−	0.929790i	$-0.619988\pi$
$911$	−1.84408e7	−0.736179	−0.368090	+	0.929790i	$0.619988\pi$
$912$	−7.32088e6	−0.291458
$913$	−1.64050e6	−0.0651327
$914$	−7.16462e6	−0.283679
$915$	2.60609e6	0.102905
$916$	−8.65177e7	−3.40695
$917$	−5.35664e6	−0.210363
$918$	3.83574e6	0.150225
$919$	−2.54845e7	−0.995376	−0.497688	−	0.867356i	$-0.665818\pi$
$919$	−2.54845e7	−0.995376	−0.497688	+	0.867356i	$0.665818\pi$
$920$	−1.70399e6	−0.0663741
$921$	2.86971e7	1.11478
$922$	4.11359e7	1.59365
$923$	2.88181e7	1.11343
$924$	3.28342e6	0.126516
$925$	3.64204e7	1.39956
$926$	−4.72556e7	−1.81103
$927$	4.32611e7	1.65348
$928$	1.23445e6	0.0470548
$929$	−2.94678e6	−0.112023	−0.0560116	−	0.998430i	$-0.517838\pi$
$929$	−2.94678e6	−0.112023	−0.0560116	+	0.998430i	$0.517838\pi$
$930$	−4.18956e6	−0.158840
$931$	5.25538e6	0.198715
$932$	−7.73775e7	−2.91793
$933$	1.12473e7	0.423005
$934$	−4.37725e6	−0.164185
$935$	102282.	0.00382623
$936$	6.08330e7	2.26960
$937$	3.39540e7	1.26340	0.631702	−	0.775211i	$-0.282357\pi$
$937$	3.39540e7	1.26340	0.631702	+	0.775211i	$0.282357\pi$
$938$	−6.64898e6	−0.246745
$939$	−4.20883e7	−1.55775
$940$	227332.	0.00839152
$941$	−1.20890e7	−0.445057	−0.222528	−	0.974926i	$-0.571431\pi$
$941$	−1.20890e7	−0.445057	−0.222528	+	0.974926i	$0.571431\pi$
$942$	−9.48585e7	−3.48296
$943$	1.00772e7	0.369028
$944$	−804847.	−0.0293957
$945$	−82497.3	−0.00300511
$946$	−5.14560e6	−0.186942
$947$	3.80246e7	1.37781	0.688906	−	0.724850i	$-0.258091\pi$
$947$	3.80246e7	1.37781	0.688906	+	0.724850i	$0.258091\pi$
$948$	1.35331e8	4.89075
$949$	−5.97202e7	−2.15256
$950$	−1.05524e7	−0.379351
$951$	−1.50651e7	−0.540156
$952$	−7.41226e6	−0.265069
$953$	−1.56213e7	−0.557166	−0.278583	−	0.960412i	$-0.589865\pi$
$953$	−1.56213e7	−0.557166	−0.278583	+	0.960412i	$0.589865\pi$
$954$	−1.37265e7	−0.488304
$955$	1.71509e6	0.0608525
$956$	−7.44903e7	−2.63606
$957$	−2.53642e6	−0.0895243
$958$	4.26668e7	1.50202
$959$	−482887.	−0.0169551
$960$	−2.47755e6	−0.0867648
$961$	9.80651e6	0.342536
$962$	−8.43536e7	−2.93877
$963$	4.86729e7	1.69130
$964$	6.54329e7	2.26779
$965$	2.03050e6	0.0701914
$966$	1.67559e7	0.577731
$967$	1.73024e7	0.595033	0.297516	−	0.954717i	$-0.403842\pi$
$967$	1.73024e7	0.595033	0.297516	+	0.954717i	$0.403842\pi$
$968$	4.77023e7	1.63625
$969$	4.71612e6	0.161352
$970$	−5.15617e6	−0.175954
$971$	−389922.	−0.0132718	−0.00663590	−	0.999978i	$-0.502112\pi$
$971$	−389922.	−0.0132718	−0.00663590	+	0.999978i	$0.502112\pi$
$972$	−8.32106e7	−2.82496
$973$	269648.	0.00913094
$974$	−2.85451e7	−0.964127
$975$	5.23501e7	1.76362
$976$	3.48933e7	1.17251
$977$	−4.26752e7	−1.43034	−0.715170	−	0.698951i	$-0.753651\pi$
$977$	−4.26752e7	−1.43034	−0.715170	+	0.698951i	$0.753651\pi$
$978$	5.36480e7	1.79352
$979$	−1.95934e6	−0.0653362
$980$	−2.91068e6	−0.0968122
$981$	−5.46746e6	−0.181390
$982$	8.10243e7	2.68124
$983$	966289.	0.0318950
$983$	966289.	0.0318950
$984$	−3.74148e7	−1.23184
$985$	−519354.	−0.0170558
$986$	1.16379e7	0.381224
$987$	−1.09985e6	−0.0359368
$988$	1.62073e7	0.528223
$989$	−1.74132e7	−0.566092
$990$	453402.	0.0147026
$991$	3.30504e7	1.06904	0.534519	−	0.845156i	$-0.320493\pi$
$991$	3.30504e7	1.06904	0.534519	+	0.845156i	$0.320493\pi$
$992$	3.83303e6	0.123670
$993$	−1.01986e7	−0.328221
$994$	−1.55654e7	−0.499683
$995$	2.80342e6	0.0897699
$996$	4.18940e7	1.33815
$997$	−4.72845e7	−1.50654	−0.753271	−	0.657710i	$-0.771525\pi$
$997$	−4.72845e7	−1.50654	−0.753271	+	0.657710i	$0.771525\pi$
$998$	6.10725e7	1.94097
$999$	−7.69252e6	−0.243868

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.6.a.b.1.18	✓	218

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.6.a.b.1.18	✓	218	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-9.74643 q^{2} +22.6936 q^{3} +62.9930 q^{4} +3.05529 q^{5} -221.181 q^{6} -41.0311 q^{7} -302.071 q^{8} +271.998 q^{9} +O(q^{10})\)	\(q-9.74643 q^{2} +22.6936 q^{3} +62.9930 q^{4} +3.05529 q^{5} -221.181 q^{6} -41.0311 q^{7} -302.071 q^{8} +271.998 q^{9} -29.7782 q^{10} -55.9782 q^{11} +1429.54 q^{12} -740.396 q^{13} +399.907 q^{14} +69.3354 q^{15} +928.340 q^{16} -598.038 q^{17} -2651.01 q^{18} -347.499 q^{19} +192.462 q^{20} -931.142 q^{21} +545.588 q^{22} +1846.32 q^{23} -6855.07 q^{24} -3115.67 q^{25} +7216.22 q^{26} +658.074 q^{27} -2584.67 q^{28} +1996.63 q^{29} -675.773 q^{30} +6199.65 q^{31} +618.266 q^{32} -1270.35 q^{33} +5828.74 q^{34} -125.362 q^{35} +17134.0 q^{36} -11689.4 q^{37} +3386.87 q^{38} -16802.2 q^{39} -922.914 q^{40} +5457.97 q^{41} +9075.31 q^{42} -9431.28 q^{43} -3526.24 q^{44} +831.033 q^{45} -17995.0 q^{46} +1181.18 q^{47} +21067.4 q^{48} -15123.5 q^{49} +30366.6 q^{50} -13571.6 q^{51} -46639.7 q^{52} +5177.85 q^{53} -6413.87 q^{54} -171.030 q^{55} +12394.3 q^{56} -7885.99 q^{57} -19460.1 q^{58} -866.974 q^{59} +4367.64 q^{60} +37586.7 q^{61} -60424.5 q^{62} -11160.4 q^{63} -35732.8 q^{64} -2262.12 q^{65} +12381.3 q^{66} -16626.3 q^{67} -37672.2 q^{68} +41899.6 q^{69} +1221.83 q^{70} -38922.6 q^{71} -82162.8 q^{72} +80659.9 q^{73} +113930. q^{74} -70705.6 q^{75} -21890.0 q^{76} +2296.85 q^{77} +163762. q^{78} +94667.7 q^{79} +2836.35 q^{80} -51161.5 q^{81} -53195.7 q^{82} +29306.0 q^{83} -58655.4 q^{84} -1827.18 q^{85} +91921.4 q^{86} +45310.8 q^{87} +16909.4 q^{88} +35001.9 q^{89} -8099.61 q^{90} +30379.2 q^{91} +116305. q^{92} +140692. q^{93} -11512.3 q^{94} -1061.71 q^{95} +14030.7 q^{96} +173153. q^{97} +147400. q^{98} -15226.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9}+O(q^{10}) \) 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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