LMFDB - Embedded newform 983.6.a.a.1.19

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:	$1$
Dimension:	$191$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q-9.71106 q^{2} -11.8693 q^{3} +62.3048 q^{4} +93.6186 q^{5} +115.264 q^{6} +163.882 q^{7} -294.291 q^{8} -102.119 q^{9} +O(q^{10})$	\(q-9.71106 q^{2} -11.8693 q^{3} +62.3048 q^{4} +93.6186 q^{5} +115.264 q^{6} +163.882 q^{7} -294.291 q^{8} -102.119 q^{9} -909.136 q^{10} -545.959 q^{11} -739.516 q^{12} -332.358 q^{13} -1591.47 q^{14} -1111.19 q^{15} +864.131 q^{16} +1069.21 q^{17} +991.685 q^{18} -819.519 q^{19} +5832.89 q^{20} -1945.17 q^{21} +5301.85 q^{22} +708.289 q^{23} +3493.04 q^{24} +5639.44 q^{25} +3227.55 q^{26} +4096.33 q^{27} +10210.6 q^{28} -3508.76 q^{29} +10790.8 q^{30} +36.5495 q^{31} +1025.70 q^{32} +6480.17 q^{33} -10383.1 q^{34} +15342.4 q^{35} -6362.51 q^{36} +1763.23 q^{37} +7958.40 q^{38} +3944.86 q^{39} -27551.2 q^{40} -11200.9 q^{41} +18889.6 q^{42} -715.650 q^{43} -34015.9 q^{44} -9560.25 q^{45} -6878.24 q^{46} -11990.2 q^{47} -10256.7 q^{48} +10050.3 q^{49} -54765.0 q^{50} -12690.8 q^{51} -20707.5 q^{52} +21283.2 q^{53} -39779.7 q^{54} -51111.9 q^{55} -48229.0 q^{56} +9727.14 q^{57} +34073.8 q^{58} +40008.2 q^{59} -69232.4 q^{60} -17524.9 q^{61} -354.935 q^{62} -16735.5 q^{63} -37612.8 q^{64} -31114.9 q^{65} -62929.3 q^{66} +38139.8 q^{67} +66616.6 q^{68} -8406.91 q^{69} -148991. q^{70} +15432.2 q^{71} +30052.8 q^{72} +8809.92 q^{73} -17122.8 q^{74} -66936.4 q^{75} -51059.9 q^{76} -89472.8 q^{77} -38308.8 q^{78} -45369.0 q^{79} +80898.7 q^{80} -23805.7 q^{81} +108773. q^{82} +54.7297 q^{83} -121193. q^{84} +100098. q^{85} +6949.72 q^{86} +41646.6 q^{87} +160671. q^{88} -128220. q^{89} +92840.2 q^{90} -54467.4 q^{91} +44129.8 q^{92} -433.818 q^{93} +116438. q^{94} -76722.2 q^{95} -12174.3 q^{96} +167635. q^{97} -97598.7 q^{98} +55752.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 191 q - 37 q^{2} - 74 q^{3} + 2821 q^{4} - 247 q^{5} - 335 q^{6} - 1569 q^{7} - 1761 q^{8} + 13251 q^{9}+O(q^{10}) $ 191 * q - 37 * q^2 - 74 * q^3 + 2821 * q^4 - 247 * q^5 - 335 * q^6 - 1569 * q^7 - 1761 * q^8 + 13251 * q^9	\( 191 q - 37 q^{2} - 74 q^{3} + 2821 q^{4} - 247 q^{5} - 335 q^{6} - 1569 q^{7} - 1761 q^{8} + 13251 q^{9} - 2867 q^{10} - 1878 q^{11} - 3400 q^{12} - 6854 q^{13} - 1601 q^{14} - 3461 q^{15} + 38457 q^{16} - 10730 q^{17} - 17249 q^{18} - 5817 q^{19} - 9988 q^{20} - 15999 q^{21} - 20287 q^{22} - 15625 q^{23} - 19747 q^{24} + 67082 q^{25} - 9868 q^{26} - 22892 q^{27} - 72720 q^{28} - 17960 q^{29} - 27464 q^{30} - 25604 q^{31} - 68869 q^{32} - 60654 q^{33} - 42876 q^{34} - 30018 q^{35} + 172922 q^{36} - 114862 q^{37} + 4404 q^{38} - 73500 q^{39} - 137154 q^{40} - 90896 q^{41} - 10652 q^{42} - 121447 q^{43} - 57962 q^{44} - 109019 q^{45} - 136262 q^{46} - 86994 q^{47} - 133347 q^{48} + 278242 q^{49} - 93911 q^{50} - 66966 q^{51} - 284241 q^{52} - 122112 q^{53} - 130806 q^{54} - 134904 q^{55} - 100292 q^{56} - 423426 q^{57} - 307669 q^{58} - 85704 q^{59} - 238277 q^{60} - 206736 q^{61} - 190602 q^{62} - 387623 q^{63} + 411903 q^{64} - 244408 q^{65} - 113963 q^{66} - 337002 q^{67} - 388031 q^{68} - 165342 q^{69} - 183925 q^{70} - 174806 q^{71} - 753621 q^{72} - 1009738 q^{73} - 204958 q^{74} - 282676 q^{75} - 326869 q^{76} - 332288 q^{77} - 591801 q^{78} - 488092 q^{79} - 259068 q^{80} + 385959 q^{81} - 523996 q^{82} - 315720 q^{83} - 750486 q^{84} - 1001755 q^{85} - 287709 q^{86} - 316995 q^{87} - 836923 q^{88} - 298065 q^{89} - 751039 q^{90} - 521459 q^{91} - 640932 q^{92} - 554391 q^{93} - 623481 q^{94} - 491883 q^{95} - 767843 q^{96} - 1468693 q^{97} - 714146 q^{98} - 842507 q^{99}+O(q^{100}) \) 191 * q - 37 * q^2 - 74 * q^3 + 2821 * q^4 - 247 * q^5 - 335 * q^6 - 1569 * q^7 - 1761 * q^8 + 13251 * q^9 - 2867 * q^10 - 1878 * q^11 - 3400 * q^12 - 6854 * q^13 - 1601 * q^14 - 3461 * q^15 + 38457 * q^16 - 10730 * q^17 - 17249 * q^18 - 5817 * q^19 - 9988 * q^20 - 15999 * q^21 - 20287 * q^22 - 15625 * q^23 - 19747 * q^24 + 67082 * q^25 - 9868 * q^26 - 22892 * q^27 - 72720 * q^28 - 17960 * q^29 - 27464 * q^30 - 25604 * q^31 - 68869 * q^32 - 60654 * q^33 - 42876 * q^34 - 30018 * q^35 + 172922 * q^36 - 114862 * q^37 + 4404 * q^38 - 73500 * q^39 - 137154 * q^40 - 90896 * q^41 - 10652 * q^42 - 121447 * q^43 - 57962 * q^44 - 109019 * q^45 - 136262 * q^46 - 86994 * q^47 - 133347 * q^48 + 278242 * q^49 - 93911 * q^50 - 66966 * q^51 - 284241 * q^52 - 122112 * q^53 - 130806 * q^54 - 134904 * q^55 - 100292 * q^56 - 423426 * q^57 - 307669 * q^58 - 85704 * q^59 - 238277 * q^60 - 206736 * q^61 - 190602 * q^62 - 387623 * q^63 + 411903 * q^64 - 244408 * q^65 - 113963 * q^66 - 337002 * q^67 - 388031 * q^68 - 165342 * q^69 - 183925 * q^70 - 174806 * q^71 - 753621 * q^72 - 1009738 * q^73 - 204958 * q^74 - 282676 * q^75 - 326869 * q^76 - 332288 * q^77 - 591801 * q^78 - 488092 * q^79 - 259068 * q^80 + 385959 * q^81 - 523996 * q^82 - 315720 * q^83 - 750486 * q^84 - 1001755 * q^85 - 287709 * q^86 - 316995 * q^87 - 836923 * q^88 - 298065 * q^89 - 751039 * q^90 - 521459 * q^91 - 640932 * q^92 - 554391 * q^93 - 623481 * q^94 - 491883 * q^95 - 767843 * q^96 - 1468693 * q^97 - 714146 * q^98 - 842507 * 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 $

$2$	−9.71106	−1.71669	−0.858345	−	0.513073i	$-0.828507\pi$
$2$	−9.71106	−1.71669	−0.858345	+	0.513073i	$0.828507\pi$
$3$	−11.8693	−0.761418	−0.380709	−	0.924695i	$-0.624320\pi$
$3$	−11.8693	−0.761418	−0.380709	+	0.924695i	$0.624320\pi$
$4$	62.3048	1.94702
$5$	93.6186	1.67470	0.837350	−	0.546667i	$-0.184104\pi$
$5$	93.6186	1.67470	0.837350	+	0.546667i	$0.184104\pi$
$6$	115.264	1.30712
$7$	163.882	1.26411	0.632056	−	0.774922i	$-0.282211\pi$
$7$	163.882	1.26411	0.632056	+	0.774922i	$0.282211\pi$
$8$	−294.291	−1.62575
$9$	−102.119	−0.420243
$10$	−909.136	−2.87494
$11$	−545.959	−1.36044	−0.680219	−	0.733009i	$-0.738115\pi$
$11$	−545.959	−1.36044	−0.680219	+	0.733009i	$0.738115\pi$
$12$	−739.516	−1.48250
$13$	−332.358	−0.545440	−0.272720	−	0.962093i	$-0.587923\pi$
$13$	−332.358	−0.545440	−0.272720	+	0.962093i	$0.587923\pi$
$14$	−1591.47	−2.17009
$15$	−1111.19	−1.27515
$16$	864.131	0.843878
$17$	1069.21	0.897303	0.448651	−	0.893707i	$-0.351905\pi$
$17$	1069.21	0.897303	0.448651	+	0.893707i	$0.351905\pi$
$18$	991.685	0.721427
$19$	−819.519	−0.520805	−0.260402	−	0.965500i	$-0.583855\pi$
$19$	−819.519	−0.520805	−0.260402	+	0.965500i	$0.583855\pi$
$20$	5832.89	3.26068
$21$	−1945.17	−0.962518
$22$	5301.85	2.33545
$23$	708.289	0.279184	0.139592	−	0.990209i	$-0.455421\pi$
$23$	708.289	0.279184	0.139592	+	0.990209i	$0.455421\pi$
$24$	3493.04	1.23787
$25$	5639.44	1.80462
$26$	3227.55	0.936352
$27$	4096.33	1.08140
$28$	10210.6	2.46126
$29$	−3508.76	−0.774744	−0.387372	−	0.921923i	$-0.626617\pi$
$29$	−3508.76	−0.774744	−0.387372	+	0.921923i	$0.626617\pi$
$30$	10790.8	2.18903
$31$	36.5495	0.00683089	0.00341545	−	0.999994i	$-0.498913\pi$
$31$	36.5495	0.00683089	0.00341545	+	0.999994i	$0.498913\pi$
$32$	1025.70	0.177069
$33$	6480.17	1.03586
$34$	−10383.1	−1.54039
$35$	15342.4	2.11701
$36$	−6362.51	−0.818224
$37$	1763.23	0.211741	0.105870	−	0.994380i	$-0.466237\pi$
$37$	1763.23	0.211741	0.105870	+	0.994380i	$0.466237\pi$
$38$	7958.40	0.894060
$39$	3944.86	0.415308
$40$	−27551.2	−2.72264
$41$	−11200.9	−1.04063	−0.520314	−	0.853975i	$-0.674185\pi$
$41$	−11200.9	−1.04063	−0.520314	+	0.853975i	$0.674185\pi$
$42$	18889.6	1.65234
$43$	−715.650	−0.0590241	−0.0295121	−	0.999564i	$-0.509395\pi$
$43$	−715.650	−0.0590241	−0.0295121	+	0.999564i	$0.509395\pi$
$44$	−34015.9	−2.64880
$45$	−9560.25	−0.703782
$46$	−6878.24	−0.479273
$47$	−11990.2	−0.791738	−0.395869	−	0.918307i	$-0.629557\pi$
$47$	−11990.2	−0.791738	−0.395869	+	0.918307i	$0.629557\pi$
$48$	−10256.7	−0.642544
$49$	10050.3	0.597981
$50$	−54765.0	−3.09798
$51$	−12690.8	−0.683222
$52$	−20707.5	−1.06199
$53$	21283.2	1.04075	0.520375	−	0.853938i	$-0.325792\pi$
$53$	21283.2	1.04075	0.520375	+	0.853938i	$0.325792\pi$
$54$	−39779.7	−1.85643
$55$	−51111.9	−2.27833
$56$	−48229.0	−2.05513
$57$	9727.14	0.396550
$58$	34073.8	1.33000
$59$	40008.2	1.49630	0.748151	−	0.663528i	$-0.230942\pi$
$59$	40008.2	1.49630	0.748151	+	0.663528i	$0.230942\pi$
$60$	−69232.4	−2.48274
$61$	−17524.9	−0.603019	−0.301509	−	0.953463i	$-0.597490\pi$
$61$	−17524.9	−0.603019	−0.301509	+	0.953463i	$0.597490\pi$
$62$	−354.935	−0.0117265
$63$	−16735.5	−0.531235
$64$	−37612.8	−1.14785
$65$	−31114.9	−0.913449
$66$	−62929.3	−1.77825
$67$	38139.8	1.03798	0.518992	−	0.854779i	$-0.326307\pi$
$67$	38139.8	1.03798	0.518992	+	0.854779i	$0.326307\pi$
$68$	66616.6	1.74707
$69$	−8406.91	−0.212576
$70$	−148991.	−3.63425
$71$	15432.2	0.363315	0.181657	−	0.983362i	$-0.441854\pi$
$71$	15432.2	0.363315	0.181657	+	0.983362i	$0.441854\pi$
$72$	30052.8	0.683209
$73$	8809.92	0.193493	0.0967465	−	0.995309i	$-0.469156\pi$
$73$	8809.92	0.193493	0.0967465	+	0.995309i	$0.469156\pi$
$74$	−17122.8	−0.363494
$75$	−66936.4	−1.37407
$76$	−51059.9	−1.01402
$77$	−89472.8	−1.71975
$78$	−38308.8	−0.712955
$79$	−45369.0	−0.817883	−0.408942	−	0.912561i	$-0.634102\pi$
$79$	−45369.0	−0.817883	−0.408942	+	0.912561i	$0.634102\pi$
$80$	80898.7	1.41324
$81$	−23805.7	−0.403152
$82$	108773.	1.78643
$83$	54.7297	0.000872023 0	0.000436012	−	1.00000i	$-0.499861\pi$
$83$	54.7297	0.000872023 0	0.000436012		1.00000i	$0.499861\pi$
$84$	−121193.	−1.87404
$85$	100098.	1.50271
$86$	6949.72	0.101326
$87$	41646.6	0.589904
$88$	160671.	2.21173
$89$	−128220.	−1.71586	−0.857929	−	0.513768i	$-0.828249\pi$
$89$	−128220.	−1.71586	−0.857929	+	0.513768i	$0.828249\pi$
$90$	92840.2	1.20817
$91$	−54467.4	−0.689498
$92$	44129.8	0.543579
$93$	−433.818	−0.00520116
$94$	116438.	1.35917
$95$	−76722.2	−0.872192
$96$	−12174.3	−0.134824
$97$	167635.	1.80899	0.904495	−	0.426485i	$-0.140248\pi$
$97$	167635.	1.80899	0.904495	+	0.426485i	$0.140248\pi$
$98$	−97598.7	−1.02655
$99$	55752.9	0.571715
$100$	351364.	3.51364
$101$	−18819.9	−0.183575	−0.0917874	−	0.995779i	$-0.529258\pi$
$101$	−18819.9	−0.183575	−0.0917874	+	0.995779i	$0.529258\pi$
$102$	123241.	1.17288
$103$	−29093.2	−0.270208	−0.135104	−	0.990831i	$-0.543137\pi$
$103$	−29093.2	−0.270208	−0.135104	+	0.990831i	$0.543137\pi$
$104$	97810.0	0.886748
$105$	−182104.	−1.61193
$106$	−206682.	−1.78665
$107$	−3471.06	−0.0293091	−0.0146546	−	0.999893i	$-0.504665\pi$
$107$	−3471.06	−0.0293091	−0.0146546	+	0.999893i	$0.504665\pi$
$108$	255221.	2.10551
$109$	−107336.	−0.865324	−0.432662	−	0.901556i	$-0.642426\pi$
$109$	−107336.	−0.865324	−0.432662	+	0.901556i	$0.642426\pi$
$110$	496351.	3.91118
$111$	−20928.4	−0.161223
$112$	141615.	1.06676
$113$	86764.6	0.639215	0.319607	−	0.947550i	$-0.396449\pi$
$113$	86764.6	0.639215	0.319607	+	0.947550i	$0.396449\pi$
$114$	−94460.9	−0.680753
$115$	66309.0	0.467550
$116$	−218612.	−1.50845
$117$	33940.1	0.229218
$118$	−388522.	−2.56869
$119$	175223.	1.13429
$120$	327014.	2.07306
$121$	137021.	0.850790
$122$	170185.	1.03520
$123$	132948.	0.792352
$124$	2277.21	0.0132999
$125$	235399.	1.34750
$126$	162519.	0.911965
$127$	−246470.	−1.35599	−0.677993	−	0.735068i	$-0.737150\pi$
$127$	−246470.	−1.35599	−0.677993	+	0.735068i	$0.737150\pi$
$128$	332438.	1.79344
$129$	8494.29	0.0449420
$130$	302158.	1.56811
$131$	−99005.1	−0.504056	−0.252028	−	0.967720i	$-0.581098\pi$
$131$	−99005.1	−0.504056	−0.252028	+	0.967720i	$0.581098\pi$
$132$	403745.	2.01685
$133$	−134304.	−0.658356
$134$	−370378.	−1.78190
$135$	383493.	1.81102
$136$	−314658.	−1.45879
$137$	294517.	1.34063	0.670314	−	0.742077i	$-0.266159\pi$
$137$	294517.	1.34063	0.670314	+	0.742077i	$0.266159\pi$
$138$	81640.1	0.364927
$139$	−184420.	−0.809603	−0.404801	−	0.914405i	$-0.632659\pi$
$139$	−184420.	−0.809603	−0.404801	+	0.914405i	$0.632659\pi$
$140$	955904.	4.12187
$141$	142316.	0.602843
$142$	−149863.	−0.623699
$143$	181454.	0.742038
$144$	−88244.3	−0.354634
$145$	−328485.	−1.29746
$146$	−85553.7	−0.332167
$147$	−119290.	−0.455313
$148$	109858.	0.412265
$149$	−503731.	−1.85880	−0.929402	−	0.369070i	$-0.879676\pi$
$149$	−503731.	−1.85880	−0.929402	+	0.369070i	$0.879676\pi$
$150$	650024.	2.35885
$151$	−345730.	−1.23394	−0.616972	−	0.786985i	$-0.711641\pi$
$151$	−345730.	−1.23394	−0.616972	+	0.786985i	$0.711641\pi$
$152$	241177.	0.846697
$153$	−109186.	−0.377085
$154$	868876.	2.95227
$155$	3421.72	0.0114397
$156$	245784.	0.808614
$157$	−163599.	−0.529703	−0.264851	−	0.964289i	$-0.585323\pi$
$157$	−163599.	−0.529703	−0.264851	+	0.964289i	$0.585323\pi$
$158$	440581.	1.40405
$159$	−252617.	−0.792446
$160$	96024.2	0.296538
$161$	116076.	0.352920
$162$	231179.	0.692088
$163$	−431163.	−1.27108	−0.635540	−	0.772068i	$-0.719222\pi$
$163$	−431163.	−1.27108	−0.635540	+	0.772068i	$0.719222\pi$
$164$	−697872.	−2.02613
$165$	606664.	1.73476
$166$	−531.484	−0.00149699
$167$	−99070.0	−0.274885	−0.137443	−	0.990510i	$-0.543888\pi$
$167$	−99070.0	−0.274885	−0.137443	+	0.990510i	$0.543888\pi$
$168$	572446.	1.56481
$169$	−260831.	−0.702495
$170$	−972054.	−2.57969
$171$	83688.6	0.218865
$172$	−44588.4	−0.114921
$173$	−578915.	−1.47062	−0.735309	−	0.677732i	$-0.762963\pi$
$173$	−578915.	−1.47062	−0.735309	+	0.677732i	$0.762963\pi$
$174$	−404433.	−1.01268
$175$	924202.	2.28125
$176$	−471780.	−1.14804
$177$	−474871.	−1.13931
$178$	1.24515e6	2.94560
$179$	487841.	1.13801	0.569005	−	0.822334i	$-0.307329\pi$
$179$	487841.	1.13801	0.569005	+	0.822334i	$0.307329\pi$
$180$	−595649.	−1.37028
$181$	359118.	0.814781	0.407391	−	0.913254i	$-0.366439\pi$
$181$	359118.	0.814781	0.407391	+	0.913254i	$0.366439\pi$
$182$	528936.	1.18365
$183$	208009.	0.459149
$184$	−208443.	−0.453883
$185$	165071.	0.354603
$186$	4212.84	0.00892878
$187$	−583743.	−1.22072
$188$	−747046.	−1.54153
$189$	671314.	1.36701
$190$	745055.	1.49728
$191$	−67280.5	−0.133446	−0.0667230	−	0.997772i	$-0.521254\pi$
$191$	−67280.5	−0.133446	−0.0667230	+	0.997772i	$0.521254\pi$
$192$	446438.	0.873994
$193$	497112.	0.960641	0.480320	−	0.877093i	$-0.340520\pi$
$193$	497112.	0.960641	0.480320	+	0.877093i	$0.340520\pi$
$194$	−1.62792e6	−3.10547
$195$	369312.	0.695516
$196$	626179.	1.16428
$197$	763785.	1.40219	0.701093	−	0.713070i	$-0.252696\pi$
$197$	763785.	1.40219	0.701093	+	0.713070i	$0.252696\pi$
$198$	−541420.	−0.981457
$199$	188961.	0.338251	0.169126	−	0.985595i	$-0.445906\pi$
$199$	188961.	0.338251	0.169126	+	0.985595i	$0.445906\pi$
$200$	−1.65964e6	−2.93386
$201$	−452693.	−0.790340
$202$	182761.	0.315141
$203$	−575022.	−0.979364
$204$	−790694.	−1.33025
$205$	−1.04862e6	−1.74274
$206$	282526.	0.463864
$207$	−72329.9	−0.117325
$208$	−287201.	−0.460285
$209$	447424.	0.708522
$210$	1.76842e6	2.76718
$211$	23706.0	0.0366566	0.0183283	−	0.999832i	$-0.494166\pi$
$211$	23706.0	0.0366566	0.0183283	+	0.999832i	$0.494166\pi$
$212$	1.32604e6	2.02637
$213$	−183170.	−0.276634
$214$	33707.7	0.0503147
$215$	−66998.2	−0.0988478
$216$	−1.20552e6	−1.75808
$217$	5989.80	0.00863502
$218$	1.04235e6	1.48549
$219$	−104568.	−0.147329
$220$	−3.18452e6	−4.43595
$221$	−355359.	−0.489425
$222$	203237.	0.276770
$223$	578728.	0.779314	0.389657	−	0.920960i	$-0.372594\pi$
$223$	578728.	0.779314	0.389657	+	0.920960i	$0.372594\pi$
$224$	168093.	0.223836
$225$	−575895.	−0.758380
$226$	−842577.	−1.09733
$227$	504725.	0.650115	0.325057	−	0.945694i	$-0.394616\pi$
$227$	504725.	0.650115	0.325057	+	0.945694i	$0.394616\pi$
$228$	606047.	0.772092
$229$	2443.41	0.00307898	0.00153949	−	0.999999i	$-0.499510\pi$
$229$	2443.41	0.00307898	0.00153949	+	0.999999i	$0.499510\pi$
$230$	−643931.	−0.802639
$231$	1.06198e6	1.30944
$232$	1.03260e6	1.25954
$233$	361063.	0.435706	0.217853	−	0.975982i	$-0.430095\pi$
$233$	361063.	0.435706	0.217853	+	0.975982i	$0.430095\pi$
$234$	−329594.	−0.393496
$235$	−1.12251e6	−1.32592
$236$	2.49270e6	2.91334
$237$	538499.	0.622751
$238$	−1.70161e6	−1.94723
$239$	−490542.	−0.555496	−0.277748	−	0.960654i	$-0.589588\pi$
$239$	−490542.	−0.555496	−0.277748	+	0.960654i	$0.589588\pi$
$240$	−960214.	−1.07607
$241$	−455553.	−0.505239	−0.252619	−	0.967566i	$-0.581292\pi$
$241$	−455553.	−0.505239	−0.252619	+	0.967566i	$0.581292\pi$
$242$	−1.33062e6	−1.46054
$243$	−712850.	−0.774431
$244$	−1.09188e6	−1.17409
$245$	940891.	1.00144
$246$	−1.29106e6	−1.36022
$247$	272373.	0.284068
$248$	−10756.2	−0.0111053
$249$	−649.605	−0.000663974 0
$250$	−2.28597e6	−2.31324
$251$	715480.	0.716825	0.358412	−	0.933563i	$-0.383318\pi$
$251$	715480.	0.716825	0.358412	+	0.933563i	$0.383318\pi$
$252$	−1.04270e6	−1.03433
$253$	−386697.	−0.379813
$254$	2.39349e6	2.32781
$255$	−1.18809e6	−1.14419
$256$	−2.02472e6	−1.93092
$257$	−864271.	−0.816239	−0.408119	−	0.912929i	$-0.633815\pi$
$257$	−864271.	−0.816239	−0.408119	+	0.912929i	$0.633815\pi$
$258$	−82488.5	−0.0771515
$259$	288962.	0.267664
$260$	−1.93860e6	−1.77851
$261$	358311.	0.325581
$262$	961444.	0.865308
$263$	233202.	0.207894	0.103947	−	0.994583i	$-0.466853\pi$
$263$	233202.	0.207894	0.103947	+	0.994583i	$0.466853\pi$
$264$	−1.90706e6	−1.68405
$265$	1.99250e6	1.74295
$266$	1.30424e6	1.13019
$267$	1.52189e6	1.30648
$268$	2.37629e6	2.02098
$269$	−547497.	−0.461318	−0.230659	−	0.973035i	$-0.574088\pi$
$269$	−547497.	−0.461318	−0.230659	+	0.973035i	$0.574088\pi$
$270$	−3.72412e6	−3.10896
$271$	1.62487e6	1.34399	0.671994	−	0.740556i	$-0.265438\pi$
$271$	1.62487e6	1.34399	0.671994	+	0.740556i	$0.265438\pi$
$272$	923934.	0.757214
$273$	646491.	0.524996
$274$	−2.86007e6	−2.30144
$275$	−3.07891e6	−2.45508
$276$	−523791.	−0.413890
$277$	−2.13079e6	−1.66856	−0.834279	−	0.551342i	$-0.814116\pi$
$277$	−2.13079e6	−1.66856	−0.834279	+	0.551342i	$0.814116\pi$
$278$	1.79092e6	1.38984
$279$	−3732.41	−0.00287064
$280$	−4.51513e6	−3.44172
$281$	−1.38512e6	−1.04646	−0.523230	−	0.852191i	$-0.675273\pi$
$281$	−1.38512e6	−1.04646	−0.523230	+	0.852191i	$0.675273\pi$
$282$	−1.38204e6	−1.03490
$283$	2.40318e6	1.78369	0.891847	−	0.452338i	$-0.149410\pi$
$283$	2.40318e6	1.78369	0.891847	+	0.452338i	$0.149410\pi$
$284$	961502.	0.707383
$285$	910641.	0.664103
$286$	−1.76211e6	−1.27385
$287$	−1.83563e6	−1.31547
$288$	−104743.	−0.0744122
$289$	−276656.	−0.194848
$290$	3.18994e6	2.22734
$291$	−1.98972e6	−1.37740
$292$	548900.	0.376735
$293$	−425493.	−0.289550	−0.144775	−	0.989465i	$-0.546246\pi$
$293$	−425493.	−0.289550	−0.144775	+	0.989465i	$0.546246\pi$
$294$	1.15843e6	0.781631
$295$	3.74551e6	2.50586
$296$	−518904.	−0.344237
$297$	−2.23643e6	−1.47117
$298$	4.89177e6	3.19099
$299$	−235405.	−0.152278
$300$	−4.17046e6	−2.67535
$301$	−117282.	−0.0746132
$302$	3.35741e6	2.11830
$303$	223379.	0.139777
$304$	−708172.	−0.439496
$305$	−1.64066e6	−1.00988
$306$	1.06032e6	0.647339
$307$	−1.58761e6	−0.961385	−0.480692	−	0.876889i	$-0.659615\pi$
$307$	−1.58761e6	−0.961385	−0.480692	+	0.876889i	$0.659615\pi$
$308$	−5.57458e6	−3.34839
$309$	345317.	0.205741
$310$	−33228.5	−0.0196384
$311$	−392950.	−0.230375	−0.115188	−	0.993344i	$-0.536747\pi$
$311$	−392950.	−0.230375	−0.115188	+	0.993344i	$0.536747\pi$
$312$	−1.16094e6	−0.675185
$313$	210182.	0.121265	0.0606323	−	0.998160i	$-0.480688\pi$
$313$	210182.	0.121265	0.0606323	+	0.998160i	$0.480688\pi$
$314$	1.58872e6	0.909335
$315$	−1.56675e6	−0.889659
$316$	−2.82670e6	−1.59244
$317$	1.96823e6	1.10009	0.550043	−	0.835136i	$-0.314611\pi$
$317$	1.96823e6	1.10009	0.550043	+	0.835136i	$0.314611\pi$
$318$	2.45318e6	1.36038
$319$	1.91564e6	1.05399
$320$	−3.52126e6	−1.92231
$321$	41199.1	0.0223165
$322$	−1.12722e6	−0.605855
$323$	−876235.	−0.467320
$324$	−1.48321e6	−0.784947
$325$	−1.87431e6	−0.984314
$326$	4.18705e6	2.18205
$327$	1.27400e6	0.658873
$328$	3.29634e6	1.69180
$329$	−1.96498e6	−1.00085
$330$	−5.89136e6	−2.97804
$331$	151197.	0.0758530	0.0379265	−	0.999281i	$-0.487925\pi$
$331$	151197.	0.0758530	0.0379265	+	0.999281i	$0.487925\pi$
$332$	3409.92	0.00169785
$333$	−180060.	−0.0889827
$334$	962075.	0.471892
$335$	3.57059e6	1.73831
$336$	−1.68088e6	−0.812247
$337$	−1.05955e6	−0.508212	−0.254106	−	0.967176i	$-0.581781\pi$
$337$	−1.05955e6	−0.508212	−0.254106	+	0.967176i	$0.581781\pi$
$338$	2.53295e6	1.20597
$339$	−1.02984e6	−0.486709
$340$	6.23655e6	2.92582
$341$	−19954.6	−0.00929300
$342$	−812705.	−0.375723
$343$	−1.10731e6	−0.508198
$344$	210610.	0.0959583
$345$	−787044.	−0.356001
$346$	5.62189e6	2.52460
$347$	388500.	0.173208	0.0866038	−	0.996243i	$-0.472399\pi$
$347$	388500.	0.173208	0.0866038	+	0.996243i	$0.472399\pi$
$348$	2.59478e6	1.14856
$349$	−3.36309e6	−1.47800	−0.739002	−	0.673704i	$-0.764702\pi$
$349$	−3.36309e6	−1.47800	−0.739002	+	0.673704i	$0.764702\pi$
$350$	−8.97499e6	−3.91619
$351$	−1.36145e6	−0.589838
$352$	−559988.	−0.240892
$353$	1.43654e6	0.613595	0.306797	−	0.951775i	$-0.400743\pi$
$353$	1.43654e6	0.613595	0.306797	+	0.951775i	$0.400743\pi$
$354$	4.61150e6	1.95584
$355$	1.44474e6	0.608443
$356$	−7.98873e6	−3.34082
$357$	−2.07978e6	−0.863670
$358$	−4.73746e6	−1.95361
$359$	1.57767e6	0.646070	0.323035	−	0.946387i	$-0.395297\pi$
$359$	1.57767e6	0.646070	0.323035	+	0.946387i	$0.395297\pi$
$360$	2.81350e6	1.14417
$361$	−1.80449e6	−0.728762
$362$	−3.48742e6	−1.39873
$363$	−1.62634e6	−0.647806
$364$	−3.39358e6	−1.34247
$365$	824773.	0.324043
$366$	−2.01998e6	−0.788216
$367$	−1.29868e6	−0.503311	−0.251656	−	0.967817i	$-0.580975\pi$
$367$	−1.29868e6	−0.503311	−0.251656	+	0.967817i	$0.580975\pi$
$368$	612055.	0.235598
$369$	1.14383e6	0.437317
$370$	−1.60302e6	−0.608743
$371$	3.48793e6	1.31563
$372$	−27028.9	−0.0101268
$373$	−432653.	−0.161016	−0.0805078	−	0.996754i	$-0.525654\pi$
$373$	−432653.	−0.161016	−0.0805078	+	0.996754i	$0.525654\pi$
$374$	5.66876e6	2.09560
$375$	−2.79402e6	−1.02601
$376$	3.52861e6	1.28717
$377$	1.16616e6	0.422577
$378$	−6.51918e6	−2.34673
$379$	−322586.	−0.115358	−0.0576790	−	0.998335i	$-0.518370\pi$
$379$	−322586.	−0.115358	−0.0576790	+	0.998335i	$0.518370\pi$
$380$	−4.78016e6	−1.69818
$381$	2.92544e6	1.03247
$382$	653365.	0.229085
$383$	974779.	0.339554	0.169777	−	0.985482i	$-0.445695\pi$
$383$	974779.	0.339554	0.169777	+	0.985482i	$0.445695\pi$
$384$	−3.94581e6	−1.36555
$385$	−8.37632e6	−2.88006
$386$	−4.82749e6	−1.64912
$387$	73081.6	0.0248045
$388$	1.04445e7	3.52215
$389$	−4.35115e6	−1.45791	−0.728953	−	0.684563i	$-0.759993\pi$
$389$	−4.35115e6	−1.45791	−0.728953	+	0.684563i	$0.759993\pi$
$390$	−3.58642e6	−1.19399
$391$	757307.	0.250513
$392$	−2.95771e6	−0.972165
$393$	1.17512e6	0.383797
$394$	−7.41716e6	−2.40712
$395$	−4.24738e6	−1.36971
$396$	3.47367e6	1.11314
$397$	1.25041e6	0.398177	0.199088	−	0.979982i	$-0.436202\pi$
$397$	1.25041e6	0.398177	0.199088	+	0.979982i	$0.436202\pi$
$398$	−1.83501e6	−0.580672
$399$	1.59410e6	0.501284
$400$	4.87322e6	1.52288
$401$	−3.29892e6	−1.02450	−0.512249	−	0.858837i	$-0.671188\pi$
$401$	−3.29892e6	−1.02450	−0.512249	+	0.858837i	$0.671188\pi$
$402$	4.39613e6	1.35677
$403$	−12147.5	−0.00372585
$404$	−1.17257e6	−0.357425
$405$	−2.22866e6	−0.675159
$406$	5.58407e6	1.68126
$407$	−962652.	−0.288060
$408$	3.73478e6	1.11075
$409$	−2.96289e6	−0.875806	−0.437903	−	0.899022i	$-0.644279\pi$
$409$	−2.96289e6	−0.875806	−0.437903	+	0.899022i	$0.644279\pi$
$410$	1.01832e7	2.99174
$411$	−3.49571e6	−1.02078
$412$	−1.81265e6	−0.526102
$413$	6.55662e6	1.89149
$414$	702400.	0.201411
$415$	5123.72	0.00146038
$416$	−340898.	−0.0965808
$417$	2.18895e6	0.616446
$418$	−4.34496e6	−1.21631
$419$	2.45879e6	0.684205	0.342102	−	0.939663i	$-0.388861\pi$
$419$	2.45879e6	0.684205	0.342102	+	0.939663i	$0.388861\pi$
$420$	−1.13459e7	−3.13846
$421$	347883.	0.0956596	0.0478298	−	0.998856i	$-0.484769\pi$
$421$	347883.	0.0956596	0.0478298	+	0.998856i	$0.484769\pi$
$422$	−230210.	−0.0629280
$423$	1.22443e6	0.332723
$424$	−6.26346e6	−1.69200
$425$	6.02973e6	1.61929
$426$	1.77878e6	0.474895
$427$	−2.87201e6	−0.762283
$428$	−216264.	−0.0570655
$429$	−2.15373e6	−0.565000
$430$	650624.	0.169691
$431$	6.03992e6	1.56617	0.783083	−	0.621917i	$-0.213646\pi$
$431$	6.03992e6	1.56617	0.783083	+	0.621917i	$0.213646\pi$
$432$	3.53977e6	0.912568
$433$	−7.57049e6	−1.94046	−0.970229	−	0.242188i	$-0.922135\pi$
$433$	−7.57049e6	−1.94046	−0.970229	+	0.242188i	$0.922135\pi$
$434$	−58167.4	−0.0148236
$435$	3.89890e6	0.987912
$436$	−6.68753e6	−1.68481
$437$	−580457.	−0.145401
$438$	1.01547e6	0.252918
$439$	4.08472e6	1.01158	0.505790	−	0.862656i	$-0.331201\pi$
$439$	4.08472e6	1.01158	0.505790	+	0.862656i	$0.331201\pi$
$440$	1.50418e7	3.70398
$441$	−1.02632e6	−0.251297
$442$	3.45091e6	0.840191
$443$	−5.05859e6	−1.22467	−0.612337	−	0.790597i	$-0.709770\pi$
$443$	−5.05859e6	−1.22467	−0.612337	+	0.790597i	$0.709770\pi$
$444$	−1.30394e6	−0.313906
$445$	−1.20038e7	−2.87355
$446$	−5.62007e6	−1.33784
$447$	5.97895e6	1.41533
$448$	−6.16405e6	−1.45101
$449$	−1.80555e6	−0.422664	−0.211332	−	0.977414i	$-0.567780\pi$
$449$	−1.80555e6	−0.422664	−0.211332	+	0.977414i	$0.567780\pi$
$450$	5.59255e6	1.30190
$451$	6.11526e6	1.41571
$452$	5.40585e6	1.24457
$453$	4.10359e6	0.939546
$454$	−4.90142e6	−1.11605
$455$	−5.09916e6	−1.15470
$456$	−2.86261e6	−0.644690
$457$	−2.58278e6	−0.578490	−0.289245	−	0.957255i	$-0.593404\pi$
$457$	−2.58278e6	−0.578490	−0.289245	+	0.957255i	$0.593404\pi$
$458$	−23728.1	−0.00528566
$459$	4.37982e6	0.970342
$460$	4.13137e6	0.910331
$461$	−5.71082e6	−1.25154	−0.625772	−	0.780006i	$-0.715216\pi$
$461$	−5.71082e6	−1.25154	−0.625772	+	0.780006i	$0.715216\pi$
$462$	−1.03130e7	−2.24791
$463$	856499.	0.185684	0.0928420	−	0.995681i	$-0.470405\pi$
$463$	856499.	0.185684	0.0928420	+	0.995681i	$0.470405\pi$
$464$	−3.03203e6	−0.653790
$465$	−40613.5	−0.00871039
$466$	−3.50631e6	−0.747972
$467$	−2.53534e6	−0.537953	−0.268977	−	0.963147i	$-0.586685\pi$
$467$	−2.53534e6	−0.537953	−0.268977	+	0.963147i	$0.586685\pi$
$468$	2.11463e6	0.446292
$469$	6.25041e6	1.31213
$470$	1.09007e7	2.27620
$471$	1.94181e6	0.403325
$472$	−1.17741e7	−2.43261
$473$	390716.	0.0802986
$474$	−5.22940e6	−1.06907
$475$	−4.62163e6	−0.939856
$476$	1.09173e7	2.20849
$477$	−2.17342e6	−0.437368
$478$	4.76368e6	0.953615
$479$	−7.56308e6	−1.50612	−0.753061	−	0.657951i	$-0.771423\pi$
$479$	−7.56308e6	−1.50612	−0.753061	+	0.657951i	$0.771423\pi$
$480$	−1.13974e6	−0.225789
$481$	−586023.	−0.115492
$482$	4.42391e6	0.867338
$483$	−1.37774e6	−0.268720
$484$	8.53703e6	1.65651
$485$	1.56938e7	3.02952
$486$	6.92254e6	1.32946
$487$	−8.22075e6	−1.57068	−0.785342	−	0.619062i	$-0.787513\pi$
$487$	−8.22075e6	−1.57068	−0.785342	+	0.619062i	$0.787513\pi$
$488$	5.15743e6	0.980355
$489$	5.11762e6	0.967822
$490$	−9.13706e6	−1.71916
$491$	−2.77033e6	−0.518594	−0.259297	−	0.965798i	$-0.583491\pi$
$491$	−2.77033e6	−0.518594	−0.259297	+	0.965798i	$0.583491\pi$
$492$	8.28327e6	1.54273
$493$	−3.75158e6	−0.695180
$494$	−2.64504e6	−0.487657
$495$	5.21951e6	0.957451
$496$	31583.6	0.00576444
$497$	2.52906e6	0.459271
$498$	6308.35	0.00113984
$499$	−1.31752e6	−0.236867	−0.118434	−	0.992962i	$-0.537787\pi$
$499$	−1.31752e6	−0.236867	−0.118434	+	0.992962i	$0.537787\pi$
$500$	1.46665e7	2.62362
$501$	1.17589e6	0.209302
$502$	−6.94807e6	−1.23057
$503$	8.56863e6	1.51005	0.755025	−	0.655696i	$-0.227625\pi$
$503$	8.56863e6	1.51005	0.755025	+	0.655696i	$0.227625\pi$
$504$	4.92511e6	0.863653
$505$	−1.76189e6	−0.307433
$506$	3.75524e6	0.652021
$507$	3.09589e6	0.534892
$508$	−1.53563e7	−2.64014
$509$	3.81784e6	0.653166	0.326583	−	0.945168i	$-0.394103\pi$
$509$	3.81784e6	0.653166	0.326583	+	0.945168i	$0.394103\pi$
$510$	1.15376e7	1.96422
$511$	1.44379e6	0.244597
$512$	9.02414e6	1.52136
$513$	−3.35702e6	−0.563198
$514$	8.39299e6	1.40123
$515$	−2.72367e6	−0.452518
$516$	529234.	0.0875032
$517$	6.54616e6	1.07711
$518$	−2.80612e6	−0.459497
$519$	6.87134e6	1.11975
$520$	9.15684e6	1.48504
$521$	7.78185e6	1.25600	0.627998	−	0.778215i	$-0.283874\pi$
$521$	7.78185e6	1.25600	0.627998	+	0.778215i	$0.283874\pi$
$522$	−3.47958e6	−0.558922
$523$	−1.61102e6	−0.257542	−0.128771	−	0.991674i	$-0.541103\pi$
$523$	−1.61102e6	−0.257542	−0.128771	+	0.991674i	$0.541103\pi$
$524$	−6.16849e6	−0.981410
$525$	−1.09697e7	−1.73698
$526$	−2.26464e6	−0.356890
$527$	39079.0	0.00612938
$528$	5.59972e6	0.874140
$529$	−5.93467e6	−0.922056
$530$	−1.93493e7	−2.99210
$531$	−4.08561e6	−0.628811
$532$	−8.36780e6	−1.28183
$533$	3.72272e6	0.567600
$534$	−1.47791e7	−2.24283
$535$	−324956.	−0.0490840
$536$	−1.12242e7	−1.68750
$537$	−5.79034e6	−0.866500
$538$	5.31678e6	0.791941
$539$	−5.48703e6	−0.813515
$540$	2.38934e7	3.52610
$541$	8.14152e6	1.19595	0.597974	−	0.801516i	$-0.295973\pi$
$541$	8.14152e6	1.19595	0.597974	+	0.801516i	$0.295973\pi$
$542$	−1.57792e7	−2.30721
$543$	−4.26249e6	−0.620389
$544$	1.09668e6	0.158885
$545$	−1.00486e7	−1.44916
$546$	−6.27812e6	−0.901255
$547$	−3.96600e6	−0.566740	−0.283370	−	0.959011i	$-0.591452\pi$
$547$	−3.96600e6	−0.566740	−0.283370	+	0.959011i	$0.591452\pi$
$548$	1.83498e7	2.61024
$549$	1.78963e6	0.253414
$550$	2.98995e7	4.21460
$551$	2.87549e6	0.403491
$552$	2.47408e6	0.345594
$553$	−7.43515e6	−1.03390
$554$	2.06922e7	2.86440
$555$	−1.95928e6	−0.270001
$556$	−1.14903e7	−1.57632
$557$	−1.12871e7	−1.54151	−0.770754	−	0.637133i	$-0.780120\pi$
$557$	−1.12871e7	−1.54151	−0.770754	+	0.637133i	$0.780120\pi$
$558$	36245.6	0.00492799
$559$	237852.	0.0321942
$560$	1.32578e7	1.78650
$561$	6.92863e6	0.929481
$562$	1.34510e7	1.79645
$563$	1.07135e7	1.42449	0.712245	−	0.701931i	$-0.247679\pi$
$563$	1.07135e7	1.42449	0.712245	+	0.701931i	$0.247679\pi$
$564$	8.86694e6	1.17375
$565$	8.12278e6	1.07049
$566$	−2.33374e7	−3.06205
$567$	−3.90133e6	−0.509630
$568$	−4.54158e6	−0.590658
$569$	2.68116e6	0.347170	0.173585	−	0.984819i	$-0.444465\pi$
$569$	2.68116e6	0.347170	0.173585	+	0.984819i	$0.444465\pi$
$570$	−8.84330e6	−1.14006
$571$	9.15722e6	1.17537	0.587683	−	0.809091i	$-0.300040\pi$
$571$	9.15722e6	1.17537	0.587683	+	0.809091i	$0.300040\pi$
$572$	1.13054e7	1.44476
$573$	798574.	0.101608
$574$	1.78259e7	2.25825
$575$	3.99436e6	0.503822
$576$	3.84098e6	0.482377
$577$	−1.30522e7	−1.63209	−0.816047	−	0.577985i	$-0.803839\pi$
$577$	−1.30522e7	−1.63209	−0.816047	+	0.577985i	$0.803839\pi$
$578$	2.68662e6	0.334493
$579$	−5.90038e6	−0.731449
$580$	−2.04662e7	−2.52619
$581$	8969.21	0.00110234
$582$	1.93223e7	2.36456
$583$	−1.16197e7	−1.41588
$584$	−2.59269e6	−0.314570
$585$	3.17742e6	0.383871
$586$	4.13199e6	0.497067
$587$	−8.60784e6	−1.03110	−0.515548	−	0.856861i	$-0.672412\pi$
$587$	−8.60784e6	−1.03110	−0.515548	+	0.856861i	$0.672412\pi$
$588$	−7.43232e6	−0.886505
$589$	−29953.0	−0.00355756
$590$	−3.63729e7	−4.30178
$591$	−9.06561e6	−1.06765
$592$	1.52366e6	0.178684
$593$	8.51033e6	0.993825	0.496912	−	0.867801i	$-0.334467\pi$
$593$	8.51033e6	0.993825	0.496912	+	0.867801i	$0.334467\pi$
$594$	2.17181e7	2.52555
$595$	1.64042e7	1.89960
$596$	−3.13849e7	−3.61913
$597$	−2.24284e6	−0.257550
$598$	2.28604e6	0.261415
$599$	−1.14596e7	−1.30498	−0.652490	−	0.757797i	$-0.726276\pi$
$599$	−1.14596e7	−1.30498	−0.652490	+	0.757797i	$0.726276\pi$
$600$	1.96988e7	2.23389
$601$	−2.27238e6	−0.256623	−0.128311	−	0.991734i	$-0.540956\pi$
$601$	−2.27238e6	−0.256623	−0.128311	+	0.991734i	$0.540956\pi$
$602$	1.13893e6	0.128088
$603$	−3.89480e6	−0.436206
$604$	−2.15407e7	−2.40252
$605$	1.28277e7	1.42482
$606$	−2.16925e6	−0.239954
$607$	−4.76655e6	−0.525088	−0.262544	−	0.964920i	$-0.584562\pi$
$607$	−4.76655e6	−0.525088	−0.262544	+	0.964920i	$0.584562\pi$
$608$	−840577.	−0.0922186
$609$	6.82512e6	0.745705
$610$	1.59325e7	1.73364
$611$	3.98503e6	0.431846
$612$	−6.80283e6	−0.734194
$613$	1.68421e6	0.181028	0.0905140	−	0.995895i	$-0.471149\pi$
$613$	1.68421e6	0.181028	0.0905140	+	0.995895i	$0.471149\pi$
$614$	1.54174e7	1.65040
$615$	1.24464e7	1.32695
$616$	2.63311e7	2.79587
$617$	−5.57499e6	−0.589564	−0.294782	−	0.955564i	$-0.595247\pi$
$617$	−5.57499e6	−0.589564	−0.294782	+	0.955564i	$0.595247\pi$
$618$	−3.35340e6	−0.353194
$619$	−5.18596e6	−0.544005	−0.272002	−	0.962297i	$-0.587686\pi$
$619$	−5.18596e6	−0.544005	−0.272002	+	0.962297i	$0.587686\pi$
$620$	213189.	0.0222734
$621$	2.90139e6	0.301909
$622$	3.81596e6	0.395483
$623$	−2.10130e7	−2.16904
$624$	3.40888e6	0.350469
$625$	4.41444e6	0.452038
$626$	−2.04109e6	−0.208174
$627$	−5.31062e6	−0.539481
$628$	−1.01930e7	−1.03134
$629$	1.88526e6	0.189996
$630$	1.52148e7	1.52727
$631$	−928772.	−0.0928615	−0.0464308	−	0.998922i	$-0.514785\pi$
$631$	−928772.	−0.0928615	−0.0464308	+	0.998922i	$0.514785\pi$
$632$	1.33517e7	1.32967
$633$	−281374.	−0.0279110
$634$	−1.91136e7	−1.88851
$635$	−2.30742e7	−2.27087
$636$	−1.57392e7	−1.54291
$637$	−3.34028e6	−0.326163
$638$	−1.86029e7	−1.80938
$639$	−1.57593e6	−0.152681
$640$	3.11224e7	3.00347
$641$	1.59391e7	1.53222	0.766108	−	0.642712i	$-0.222191\pi$
$641$	1.59391e7	1.53222	0.766108	+	0.642712i	$0.222191\pi$
$642$	−400087.	−0.0383105
$643$	2.85296e6	0.272125	0.136062	−	0.990700i	$-0.456555\pi$
$643$	2.85296e6	0.272125	0.136062	+	0.990700i	$0.456555\pi$
$644$	7.23207e6	0.687144
$645$	795223.	0.0752644
$646$	8.50917e6	0.802243
$647$	1.17422e7	1.10278	0.551389	−	0.834248i	$-0.314098\pi$
$647$	1.17422e7	1.10278	0.551389	+	0.834248i	$0.314098\pi$
$648$	7.00583e6	0.655423
$649$	−2.18429e7	−2.03563
$650$	1.82016e7	1.68976
$651$	−71094.9	−0.00657485
$652$	−2.68635e7	−2.47482
$653$	4.18026e6	0.383637	0.191818	−	0.981430i	$-0.438562\pi$
$653$	4.18026e6	0.383637	0.191818	+	0.981430i	$0.438562\pi$
$654$	−1.23719e7	−1.13108
$655$	−9.26871e6	−0.844143
$656$	−9.67909e6	−0.878162
$657$	−899662.	−0.0813141
$658$	1.90820e7	1.71814
$659$	−1.21499e6	−0.108983	−0.0544915	−	0.998514i	$-0.517354\pi$
$659$	−1.21499e6	−0.108983	−0.0544915	+	0.998514i	$0.517354\pi$
$660$	3.77981e7	3.37761
$661$	1.68890e7	1.50349	0.751743	−	0.659456i	$-0.229213\pi$
$661$	1.68890e7	1.50349	0.751743	+	0.659456i	$0.229213\pi$
$662$	−1.46828e6	−0.130216
$663$	4.21787e6	0.372657
$664$	−16106.5	−0.00141769
$665$	−1.25734e7	−1.10255
$666$	1.74857e6	0.152756
$667$	−2.48521e6	−0.216296
$668$	−6.17253e6	−0.535208
$669$	−6.86911e6	−0.593384
$670$	−3.46742e7	−2.98414
$671$	9.56788e6	0.820369
$672$	−1.99515e6	−0.170432
$673$	7.89080e6	0.671558	0.335779	−	0.941941i	$-0.391000\pi$
$673$	7.89080e6	0.671558	0.335779	+	0.941941i	$0.391000\pi$
$674$	1.02893e7	0.872442
$675$	2.31010e7	1.95151
$676$	−1.62510e7	−1.36777
$677$	9.13833e6	0.766293	0.383147	−	0.923688i	$-0.374840\pi$
$677$	9.13833e6	0.766293	0.383147	+	0.923688i	$0.374840\pi$
$678$	1.00008e7	0.835529
$679$	2.74724e7	2.28677
$680$	−2.94579e7	−2.44303
$681$	−5.99074e6	−0.495009
$682$	193780.	0.0159532
$683$	−2.08569e7	−1.71080	−0.855399	−	0.517969i	$-0.826688\pi$
$683$	−2.08569e7	−1.71080	−0.855399	+	0.517969i	$0.826688\pi$
$684$	5.21420e6	0.426135
$685$	2.75722e7	2.24515
$686$	1.07531e7	0.872418
$687$	−29001.6	−0.00234439
$688$	−618416.	−0.0498092
$689$	−7.07362e6	−0.567667
$690$	7.64303e6	0.611143
$691$	−2.42165e6	−0.192937	−0.0964687	−	0.995336i	$-0.530755\pi$
$691$	−2.42165e6	−0.192937	−0.0964687	+	0.995336i	$0.530755\pi$
$692$	−3.60692e7	−2.86333
$693$	9.13688e6	0.722712
$694$	−3.77275e6	−0.297344
$695$	−1.72652e7	−1.35584
$696$	−1.22562e7	−0.959034
$697$	−1.19761e7	−0.933758
$698$	3.26592e7	2.53727
$699$	−4.28558e6	−0.331754
$700$	5.75822e7	4.44164
$701$	2.05427e7	1.57893	0.789465	−	0.613796i	$-0.210358\pi$
$701$	2.05427e7	1.57893	0.789465	+	0.613796i	$0.210358\pi$
$702$	1.32211e7	1.01257
$703$	−1.44500e6	−0.110276
$704$	2.05351e7	1.56158
$705$	1.33234e7	1.00958
$706$	−1.39504e7	−1.05335
$707$	−3.08424e6	−0.232059
$708$	−2.95867e7	−2.21827
$709$	−2.96117e6	−0.221232	−0.110616	−	0.993863i	$-0.535282\pi$
$709$	−2.96117e6	−0.221232	−0.110616	+	0.993863i	$0.535282\pi$
$710$	−1.40300e7	−1.04451
$711$	4.63304e6	0.343710
$712$	3.77341e7	2.78955
$713$	25887.6	0.00190708
$714$	2.01969e7	1.48265
$715$	1.69874e7	1.24269
$716$	3.03948e7	2.21573
$717$	5.82240e6	0.422965
$718$	−1.53208e7	−1.10910
$719$	−2.68277e6	−0.193536	−0.0967678	−	0.995307i	$-0.530850\pi$
$719$	−2.68277e6	−0.193536	−0.0967678	+	0.995307i	$0.530850\pi$
$720$	−8.26131e6	−0.593906
$721$	−4.76785e6	−0.341574
$722$	1.75235e7	1.25106
$723$	5.40711e6	0.384698
$724$	2.23748e7	1.58640
$725$	−1.97874e7	−1.39812
$726$	1.57935e7	1.11208
$727$	−2.18780e7	−1.53522	−0.767610	−	0.640917i	$-0.778554\pi$
$727$	−2.18780e7	−1.53522	−0.767610	+	0.640917i	$0.778554\pi$
$728$	1.60293e7	1.12095
$729$	1.42458e7	0.992818
$730$	−8.00942e6	−0.556281
$731$	−765177.	−0.0529625
$732$	1.29599e7	0.893974
$733$	−2.22461e7	−1.52930	−0.764652	−	0.644443i	$-0.777089\pi$
$733$	−2.22461e7	−1.52930	−0.764652	+	0.644443i	$0.777089\pi$
$734$	1.26116e7	0.864030
$735$	−1.11677e7	−0.762513
$736$	726489.	0.0494350
$737$	−2.08228e7	−1.41211
$738$	−1.11078e7	−0.750737
$739$	−2.10742e7	−1.41952	−0.709758	−	0.704445i	$-0.751196\pi$
$739$	−2.10742e7	−1.41952	−0.709758	+	0.704445i	$0.751196\pi$
$740$	1.02847e7	0.690420
$741$	−3.23289e6	−0.216294
$742$	−3.38715e7	−2.25852
$743$	1.47213e7	0.978303	0.489152	−	0.872199i	$-0.337306\pi$
$743$	1.47213e7	0.978303	0.489152	+	0.872199i	$0.337306\pi$
$744$	127669.	0.00845577
$745$	−4.71586e7	−3.11294
$746$	4.20152e6	0.276414
$747$	−5588.95	−0.000366462 0
$748$	−3.63700e7	−2.37678
$749$	−568844.	−0.0370500
$750$	2.71329e7	1.76134
$751$	−5.07710e6	−0.328485	−0.164242	−	0.986420i	$-0.552518\pi$
$751$	−5.07710e6	−0.328485	−0.164242	+	0.986420i	$0.552518\pi$
$752$	−1.03611e7	−0.668130
$753$	−8.49226e6	−0.545803
$754$	−1.13247e7	−0.725433
$755$	−3.23668e7	−2.06649
$756$	4.18261e7	2.66160
$757$	−2.06884e7	−1.31216	−0.656081	−	0.754691i	$-0.727787\pi$
$757$	−2.06884e7	−1.31216	−0.656081	+	0.754691i	$0.727787\pi$
$758$	3.13265e6	0.198034
$759$	4.58983e6	0.289196
$760$	2.25787e7	1.41796
$761$	−4.45675e6	−0.278969	−0.139485	−	0.990224i	$-0.544545\pi$
$761$	−4.45675e6	−0.278969	−0.139485	+	0.990224i	$0.544545\pi$
$762$	−2.84091e7	−1.77243
$763$	−1.75904e7	−1.09387
$764$	−4.19189e6	−0.259822
$765$	−1.02219e7	−0.631505
$766$	−9.46614e6	−0.582909
$767$	−1.32970e7	−0.816144
$768$	2.40320e7	1.47024
$769$	−1.12059e6	−0.0683333	−0.0341667	−	0.999416i	$-0.510878\pi$
$769$	−1.12059e6	−0.0683333	−0.0341667	+	0.999416i	$0.510878\pi$
$770$	8.13430e7	4.94417
$771$	1.02583e7	0.621499
$772$	3.09724e7	1.87039
$773$	2.97600e7	1.79136	0.895682	−	0.444695i	$-0.146688\pi$
$773$	2.97600e7	1.79136	0.895682	+	0.444695i	$0.146688\pi$
$774$	−709700.	−0.0425816
$775$	206119.	0.0123272
$776$	−4.93336e7	−2.94096
$777$	−3.42978e6	−0.203804
$778$	4.22543e7	2.50277
$779$	9.17939e6	0.541964
$780$	2.30099e7	1.35419
$781$	−8.42537e6	−0.494267
$782$	−7.35426e6	−0.430053
$783$	−1.43730e7	−0.837807
$784$	8.68474e6	0.504623
$785$	−1.53159e7	−0.887093
$786$	−1.14117e7	−0.658861
$787$	1.09454e7	0.629932	0.314966	−	0.949103i	$-0.398007\pi$
$787$	1.09454e7	0.629932	0.314966	+	0.949103i	$0.398007\pi$
$788$	4.75874e7	2.73009
$789$	−2.76795e6	−0.158294
$790$	4.12466e7	2.35137
$791$	1.42191e7	0.808039
$792$	−1.64076e7	−0.929463
$793$	5.82453e6	0.328911
$794$	−1.21428e7	−0.683546
$795$	−2.36496e7	−1.32711
$796$	1.17732e7	0.658583
$797$	−1.46737e7	−0.818267	−0.409133	−	0.912475i	$-0.634169\pi$
$797$	−1.46737e7	−0.818267	−0.409133	+	0.912475i	$0.634169\pi$
$798$	−1.54804e7	−0.860549
$799$	−1.28200e7	−0.710429
$800$	5.78435e6	0.319543
$801$	1.30937e7	0.721078
$802$	3.20360e7	1.75875
$803$	−4.80986e6	−0.263235
$804$	−2.82049e7	−1.53881
$805$	1.08668e7	0.591036
$806$	117965.	0.00639612
$807$	6.49842e6	0.351256
$808$	5.53853e6	0.298446
$809$	−2.47274e7	−1.32833	−0.664166	−	0.747585i	$-0.731213\pi$
$809$	−2.47274e7	−1.32833	−0.664166	+	0.747585i	$0.731213\pi$
$810$	2.16427e7	1.15904
$811$	66388.6	0.00354439	0.00177219	−	0.999998i	$-0.499436\pi$
$811$	66388.6	0.00354439	0.00177219	+	0.999998i	$0.499436\pi$
$812$	−3.58266e7	−1.90684
$813$	−1.92861e7	−1.02334
$814$	9.34838e6	0.494510
$815$	−4.03649e7	−2.12868
$816$	−1.09665e7	−0.576556
$817$	586489.	0.0307401
$818$	2.87729e7	1.50349
$819$	5.56216e6	0.289757
$820$	−6.53338e7	−3.39315
$821$	7.67107e6	0.397190	0.198595	−	0.980082i	$-0.436362\pi$
$821$	7.67107e6	0.397190	0.198595	+	0.980082i	$0.436362\pi$
$822$	3.39471e7	1.75236
$823$	3.03661e6	0.156275	0.0781375	−	0.996943i	$-0.475103\pi$
$823$	3.03661e6	0.156275	0.0781375	+	0.996943i	$0.475103\pi$
$824$	8.56189e6	0.439290
$825$	3.65445e7	1.86934
$826$	−6.36718e7	−3.24711
$827$	9.25238e6	0.470424	0.235212	−	0.971944i	$-0.424422\pi$
$827$	9.25238e6	0.470424	0.235212	+	0.971944i	$0.424422\pi$
$828$	−4.50649e6	−0.228435
$829$	−239092.	−0.0120831	−0.00604157	−	0.999982i	$-0.501923\pi$
$829$	−239092.	−0.0120831	−0.00604157	+	0.999982i	$0.501923\pi$
$830$	−49756.8	−0.00250702
$831$	2.52911e7	1.27047
$832$	1.25009e7	0.626084
$833$	1.07458e7	0.536570
$834$	−2.12570e7	−1.05825
$835$	−9.27480e6	−0.460350
$836$	2.78767e7	1.37951
$837$	149719.	0.00738692
$838$	−2.38774e7	−1.17457
$839$	1.29146e7	0.633398	0.316699	−	0.948526i	$-0.397426\pi$
$839$	1.29146e7	0.633398	0.316699	+	0.948526i	$0.397426\pi$
$840$	5.35916e7	2.62059
$841$	−8.19977e6	−0.399771
$842$	−3.37832e6	−0.164218
$843$	1.64405e7	0.796794
$844$	1.47700e6	0.0713712
$845$	−2.44187e7	−1.17647
$846$	−1.18905e7	−0.571182
$847$	2.24552e7	1.07549
$848$	1.83914e7	0.878266
$849$	−2.85241e7	−1.35814
$850$	−5.85550e7	−2.77982
$851$	1.24888e6	0.0591148
$852$	−1.14124e7	−0.538614
$853$	−2.03883e7	−0.959417	−0.479709	−	0.877428i	$-0.659258\pi$
$853$	−2.03883e7	−0.959417	−0.479709	+	0.877428i	$0.659258\pi$
$854$	2.78903e7	1.30860
$855$	7.83481e6	0.366533
$856$	1.02150e6	0.0476492
$857$	−3.38056e7	−1.57230	−0.786152	−	0.618033i	$-0.787930\pi$
$857$	−3.38056e7	−1.57230	−0.786152	+	0.618033i	$0.787930\pi$
$858$	2.09150e7	0.969930
$859$	2.89327e7	1.33785	0.668924	−	0.743331i	$-0.266755\pi$
$859$	2.89327e7	1.33785	0.668924	+	0.743331i	$0.266755\pi$
$860$	−4.17431e6	−0.192459
$861$	2.17877e7	1.00162
$862$	−5.86540e7	−2.68862
$863$	2.70355e7	1.23569	0.617843	−	0.786302i	$-0.288007\pi$
$863$	2.70355e7	1.23569	0.617843	+	0.786302i	$0.288007\pi$
$864$	4.20159e6	0.191483
$865$	−5.41973e7	−2.46284
$866$	7.35175e7	3.33117
$867$	3.28372e6	0.148361
$868$	373193.	0.0168126
$869$	2.47696e7	1.11268
$870$	−3.78624e7	−1.69594
$871$	−1.26760e7	−0.566159
$872$	3.15880e7	1.40680
$873$	−1.71188e7	−0.760216
$874$	5.63685e6	0.249608
$875$	3.85776e7	1.70339
$876$	−6.51508e6	−0.286853
$877$	1.40735e7	0.617878	0.308939	−	0.951082i	$-0.400026\pi$
$877$	1.40735e7	0.617878	0.308939	+	0.951082i	$0.400026\pi$
$878$	−3.96669e7	−1.73657
$879$	5.05031e6	0.220468
$880$	−4.41674e7	−1.92263
$881$	−3.59284e7	−1.55954	−0.779772	−	0.626064i	$-0.784665\pi$
$881$	−3.59284e7	−1.55954	−0.779772	+	0.626064i	$0.784665\pi$
$882$	9.96669e6	0.431400
$883$	1.69917e7	0.733392	0.366696	−	0.930341i	$-0.380489\pi$
$883$	1.69917e7	0.733392	0.366696	+	0.930341i	$0.380489\pi$
$884$	−2.21405e7	−0.952922
$885$	−4.44567e7	−1.90800
$886$	4.91243e7	2.10239
$887$	−2.05204e7	−0.875744	−0.437872	−	0.899037i	$-0.644268\pi$
$887$	−2.05204e7	−0.875744	−0.437872	+	0.899037i	$0.644268\pi$
$888$	6.15904e6	0.262108
$889$	−4.03920e7	−1.71412
$890$	1.16570e8	4.93299
$891$	1.29970e7	0.548464
$892$	3.60575e7	1.51734
$893$	9.82619e6	0.412341
$894$	−5.80620e7	−2.42967
$895$	4.56710e7	1.90582
$896$	5.44805e7	2.26710
$897$	2.79410e6	0.115947
$898$	1.75339e7	0.725582
$899$	−128243.	−0.00529220
$900$	−3.58810e7	−1.47658
$901$	2.27561e7	0.933868
$902$	−5.93857e7	−2.43033
$903$	1.39206e6	0.0568118
$904$	−2.55341e7	−1.03920
$905$	3.36202e7	1.36451
$906$	−3.98502e7	−1.61291
$907$	−2.43427e7	−0.982539	−0.491270	−	0.871008i	$-0.663467\pi$
$907$	−2.43427e7	−0.982539	−0.491270	+	0.871008i	$0.663467\pi$
$908$	3.14468e7	1.26579
$909$	1.92187e6	0.0771461
$910$	4.95183e7	1.98227
$911$	1.82797e7	0.729747	0.364873	−	0.931057i	$-0.381112\pi$
$911$	1.82797e7	0.729747	0.364873	+	0.931057i	$0.381112\pi$
$912$	8.40552e6	0.334640
$913$	−29880.2	−0.00118633
$914$	2.50815e7	0.993088
$915$	1.94735e7	0.768937
$916$	152236.	0.00599485
$917$	−1.62251e7	−0.637184
$918$	−4.25327e7	−1.66578
$919$	−4.29100e7	−1.67598	−0.837991	−	0.545684i	$-0.816270\pi$
$919$	−4.29100e7	−1.67598	−0.837991	+	0.545684i	$0.816270\pi$
$920$	−1.95142e7	−0.760118
$921$	1.88438e7	0.732015
$922$	5.54581e7	2.14851
$923$	−5.12902e6	−0.198167
$924$	6.61665e7	2.54952
$925$	9.94364e6	0.382112
$926$	−8.31752e6	−0.318762
$927$	2.97098e6	0.113553
$928$	−3.59892e6	−0.137184
$929$	2.03163e7	0.772336	0.386168	−	0.922428i	$-0.373799\pi$
$929$	2.03163e7	0.772336	0.386168	+	0.922428i	$0.373799\pi$
$930$	394400.	0.0149530
$931$	−8.23638e6	−0.311431
$932$	2.24960e7	0.848330
$933$	4.66405e6	0.175412
$934$	2.46209e7	0.923499
$935$	−5.46492e7	−2.04435
$936$	−9.98827e6	−0.372650
$937$	−1.11763e7	−0.415862	−0.207931	−	0.978144i	$-0.566673\pi$
$937$	−1.11763e7	−0.415862	−0.207931	+	0.978144i	$0.566673\pi$
$938$	−6.06982e7	−2.25252
$939$	−2.49471e6	−0.0923330
$940$	−6.99374e7	−2.58161
$941$	3.34521e7	1.23154	0.615772	−	0.787925i	$-0.288844\pi$
$941$	3.34521e7	1.23154	0.615772	+	0.787925i	$0.288844\pi$
$942$	−1.88571e7	−0.692384
$943$	−7.93351e6	−0.290527
$944$	3.45724e7	1.26270
$945$	6.28475e7	2.28933
$946$	−3.79427e6	−0.137848
$947$	5.04141e7	1.82674	0.913372	−	0.407127i	$-0.133469\pi$
$947$	5.04141e7	1.82674	0.913372	+	0.407127i	$0.133469\pi$
$948$	3.35511e7	1.21251
$949$	−2.92805e6	−0.105539
$950$	4.48810e7	1.61344
$951$	−2.33615e7	−0.837625
$952$	−5.15668e7	−1.84407
$953$	3.13191e7	1.11706	0.558531	−	0.829483i	$-0.311365\pi$
$953$	3.13191e7	1.11706	0.558531	+	0.829483i	$0.311365\pi$
$954$	2.11062e7	0.750826
$955$	−6.29870e6	−0.223482
$956$	−3.05631e7	−1.08156
$957$	−2.27373e7	−0.802527
$958$	7.34455e7	2.58554
$959$	4.82659e7	1.69471
$960$	4.17949e7	1.46368
$961$	−2.86278e7	−0.999953
$962$	5.69091e6	0.198264
$963$	354462.	0.0123170
$964$	−2.83831e7	−0.983712
$965$	4.65389e7	1.60879
$966$	1.33793e7	0.461309
$967$	−2.43205e7	−0.836384	−0.418192	−	0.908359i	$-0.637336\pi$
$967$	−2.43205e7	−0.836384	−0.418192	+	0.908359i	$0.637336\pi$
$968$	−4.03240e7	−1.38317
$969$	1.04003e7	0.355825
$970$	−1.52403e8	−5.20074
$971$	−7.36629e6	−0.250727	−0.125363	−	0.992111i	$-0.540010\pi$
$971$	−7.36629e6	−0.250727	−0.125363	+	0.992111i	$0.540010\pi$
$972$	−4.44140e7	−1.50784
$973$	−3.02232e7	−1.02343
$974$	7.98322e7	2.69638
$975$	2.22468e7	0.749474
$976$	−1.51438e7	−0.508874
$977$	3.98829e7	1.33675	0.668375	−	0.743824i	$-0.266990\pi$
$977$	3.98829e7	1.33675	0.668375	+	0.743824i	$0.266990\pi$
$978$	−4.96975e7	−1.66145
$979$	7.00030e7	2.33432
$980$	5.86220e7	1.94982
$981$	1.09610e7	0.363646
$982$	2.69028e7	0.890265
$983$	−966289.	−0.0318950
$983$	−966289.	−0.0318950
$984$	−3.91254e7	−1.28816
$985$	7.15045e7	2.34824
$986$	3.64319e7	1.19341
$987$	2.33229e7	0.762062
$988$	1.69702e7	0.553087
$989$	−506887.	−0.0164786
$990$	−5.06870e7	−1.64365
$991$	1.64066e7	0.530683	0.265342	−	0.964154i	$-0.414515\pi$
$991$	1.64066e7	0.530683	0.265342	+	0.964154i	$0.414515\pi$
$992$	37488.7	0.00120954
$993$	−1.79461e6	−0.0577558
$994$	−2.45599e7	−0.788426
$995$	1.76903e7	0.566469
$996$	−40473.5	−0.00129277
$997$	4.44486e7	1.41619	0.708093	−	0.706119i	$-0.249556\pi$
$997$	4.44486e7	1.41619	0.708093	+	0.706119i	$0.249556\pi$
$998$	1.27945e7	0.406627
$999$	7.22278e6	0.228976

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.6.a.a.1.19	✓	191

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.6.a.a.1.19	✓	191	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)

\(f(q)\)	\(=\)	\(q-9.71106 q^{2} -11.8693 q^{3} +62.3048 q^{4} +93.6186 q^{5} +115.264 q^{6} +163.882 q^{7} -294.291 q^{8} -102.119 q^{9} +O(q^{10})\)	\(q-9.71106 q^{2} -11.8693 q^{3} +62.3048 q^{4} +93.6186 q^{5} +115.264 q^{6} +163.882 q^{7} -294.291 q^{8} -102.119 q^{9} -909.136 q^{10} -545.959 q^{11} -739.516 q^{12} -332.358 q^{13} -1591.47 q^{14} -1111.19 q^{15} +864.131 q^{16} +1069.21 q^{17} +991.685 q^{18} -819.519 q^{19} +5832.89 q^{20} -1945.17 q^{21} +5301.85 q^{22} +708.289 q^{23} +3493.04 q^{24} +5639.44 q^{25} +3227.55 q^{26} +4096.33 q^{27} +10210.6 q^{28} -3508.76 q^{29} +10790.8 q^{30} +36.5495 q^{31} +1025.70 q^{32} +6480.17 q^{33} -10383.1 q^{34} +15342.4 q^{35} -6362.51 q^{36} +1763.23 q^{37} +7958.40 q^{38} +3944.86 q^{39} -27551.2 q^{40} -11200.9 q^{41} +18889.6 q^{42} -715.650 q^{43} -34015.9 q^{44} -9560.25 q^{45} -6878.24 q^{46} -11990.2 q^{47} -10256.7 q^{48} +10050.3 q^{49} -54765.0 q^{50} -12690.8 q^{51} -20707.5 q^{52} +21283.2 q^{53} -39779.7 q^{54} -51111.9 q^{55} -48229.0 q^{56} +9727.14 q^{57} +34073.8 q^{58} +40008.2 q^{59} -69232.4 q^{60} -17524.9 q^{61} -354.935 q^{62} -16735.5 q^{63} -37612.8 q^{64} -31114.9 q^{65} -62929.3 q^{66} +38139.8 q^{67} +66616.6 q^{68} -8406.91 q^{69} -148991. q^{70} +15432.2 q^{71} +30052.8 q^{72} +8809.92 q^{73} -17122.8 q^{74} -66936.4 q^{75} -51059.9 q^{76} -89472.8 q^{77} -38308.8 q^{78} -45369.0 q^{79} +80898.7 q^{80} -23805.7 q^{81} +108773. q^{82} +54.7297 q^{83} -121193. q^{84} +100098. q^{85} +6949.72 q^{86} +41646.6 q^{87} +160671. q^{88} -128220. q^{89} +92840.2 q^{90} -54467.4 q^{91} +44129.8 q^{92} -433.818 q^{93} +116438. q^{94} -76722.2 q^{95} -12174.3 q^{96} +167635. q^{97} -97598.7 q^{98} +55752.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 191 q - 37 q^{2} - 74 q^{3} + 2821 q^{4} - 247 q^{5} - 335 q^{6} - 1569 q^{7} - 1761 q^{8} + 13251 q^{9}+O(q^{10}) \) 191 * q - 37 * q^2 - 74 * q^3 + 2821 * q^4 - 247 * q^5 - 335 * q^6 - 1569 * q^7 - 1761 * q^8 + 13251 * q^9	\( 191 q - 37 q^{2} - 74 q^{3} + 2821 q^{4} - 247 q^{5} - 335 q^{6} - 1569 q^{7} - 1761 q^{8} + 13251 q^{9} - 2867 q^{10} - 1878 q^{11} - 3400 q^{12} - 6854 q^{13} - 1601 q^{14} - 3461 q^{15} + 38457 q^{16} - 10730 q^{17} - 17249 q^{18} - 5817 q^{19} - 9988 q^{20} - 15999 q^{21} - 20287 q^{22} - 15625 q^{23} - 19747 q^{24} + 67082 q^{25} - 9868 q^{26} - 22892 q^{27} - 72720 q^{28} - 17960 q^{29} - 27464 q^{30} - 25604 q^{31} - 68869 q^{32} - 60654 q^{33} - 42876 q^{34} - 30018 q^{35} + 172922 q^{36} - 114862 q^{37} + 4404 q^{38} - 73500 q^{39} - 137154 q^{40} - 90896 q^{41} - 10652 q^{42} - 121447 q^{43} - 57962 q^{44} - 109019 q^{45} - 136262 q^{46} - 86994 q^{47} - 133347 q^{48} + 278242 q^{49} - 93911 q^{50} - 66966 q^{51} - 284241 q^{52} - 122112 q^{53} - 130806 q^{54} - 134904 q^{55} - 100292 q^{56} - 423426 q^{57} - 307669 q^{58} - 85704 q^{59} - 238277 q^{60} - 206736 q^{61} - 190602 q^{62} - 387623 q^{63} + 411903 q^{64} - 244408 q^{65} - 113963 q^{66} - 337002 q^{67} - 388031 q^{68} - 165342 q^{69} - 183925 q^{70} - 174806 q^{71} - 753621 q^{72} - 1009738 q^{73} - 204958 q^{74} - 282676 q^{75} - 326869 q^{76} - 332288 q^{77} - 591801 q^{78} - 488092 q^{79} - 259068 q^{80} + 385959 q^{81} - 523996 q^{82} - 315720 q^{83} - 750486 q^{84} - 1001755 q^{85} - 287709 q^{86} - 316995 q^{87} - 836923 q^{88} - 298065 q^{89} - 751039 q^{90} - 521459 q^{91} - 640932 q^{92} - 554391 q^{93} - 623481 q^{94} - 491883 q^{95} - 767843 q^{96} - 1468693 q^{97} - 714146 q^{98} - 842507 q^{99}+O(q^{100}) \) 191 * q - 37 * q^2 - 74 * q^3 + 2821 * q^4 - 247 * q^5 - 335 * q^6 - 1569 * q^7 - 1761 * q^8 + 13251 * q^9 - 2867 * q^10 - 1878 * q^11 - 3400 * q^12 - 6854 * q^13 - 1601 * q^14 - 3461 * q^15 + 38457 * q^16 - 10730 * q^17 - 17249 * q^18 - 5817 * q^19 - 9988 * q^20 - 15999 * q^21 - 20287 * q^22 - 15625 * q^23 - 19747 * q^24 + 67082 * q^25 - 9868 * q^26 - 22892 * q^27 - 72720 * q^28 - 17960 * q^29 - 27464 * q^30 - 25604 * q^31 - 68869 * q^32 - 60654 * q^33 - 42876 * q^34 - 30018 * q^35 + 172922 * q^36 - 114862 * q^37 + 4404 * q^38 - 73500 * q^39 - 137154 * q^40 - 90896 * q^41 - 10652 * q^42 - 121447 * q^43 - 57962 * q^44 - 109019 * q^45 - 136262 * q^46 - 86994 * q^47 - 133347 * q^48 + 278242 * q^49 - 93911 * q^50 - 66966 * q^51 - 284241 * q^52 - 122112 * q^53 - 130806 * q^54 - 134904 * q^55 - 100292 * q^56 - 423426 * q^57 - 307669 * q^58 - 85704 * q^59 - 238277 * q^60 - 206736 * q^61 - 190602 * q^62 - 387623 * q^63 + 411903 * q^64 - 244408 * q^65 - 113963 * q^66 - 337002 * q^67 - 388031 * q^68 - 165342 * q^69 - 183925 * q^70 - 174806 * q^71 - 753621 * q^72 - 1009738 * q^73 - 204958 * q^74 - 282676 * q^75 - 326869 * q^76 - 332288 * q^77 - 591801 * q^78 - 488092 * q^79 - 259068 * q^80 + 385959 * q^81 - 523996 * q^82 - 315720 * q^83 - 750486 * q^84 - 1001755 * q^85 - 287709 * q^86 - 316995 * q^87 - 836923 * q^88 - 298065 * q^89 - 751039 * q^90 - 521459 * q^91 - 640932 * q^92 - 554391 * q^93 - 623481 * q^94 - 491883 * q^95 - 767843 * q^96 - 1468693 * q^97 - 714146 * q^98 - 842507 * q^99

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