LMFDB - Embedded newform 1045.6.a.g.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,6,Mod(1,1045)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1045.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:	$167.601091705$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.21689 q^{2} +5.10751 q^{3} -27.0854 q^{4} -25.0000 q^{5} -11.3228 q^{6} +167.053 q^{7} +130.986 q^{8} -216.913 q^{9} +O(q^{10})$	\(q-2.21689 q^{2} +5.10751 q^{3} -27.0854 q^{4} -25.0000 q^{5} -11.3228 q^{6} +167.053 q^{7} +130.986 q^{8} -216.913 q^{9} +55.4222 q^{10} -121.000 q^{11} -138.339 q^{12} -694.498 q^{13} -370.338 q^{14} -127.688 q^{15} +576.352 q^{16} -1055.62 q^{17} +480.873 q^{18} +361.000 q^{19} +677.135 q^{20} +853.225 q^{21} +268.243 q^{22} +297.195 q^{23} +669.011 q^{24} +625.000 q^{25} +1539.62 q^{26} -2349.01 q^{27} -4524.70 q^{28} -1717.08 q^{29} +283.070 q^{30} +4322.56 q^{31} -5469.25 q^{32} -618.009 q^{33} +2340.18 q^{34} -4176.32 q^{35} +5875.19 q^{36} -9932.56 q^{37} -800.297 q^{38} -3547.16 q^{39} -3274.64 q^{40} -2082.39 q^{41} -1891.50 q^{42} -3768.74 q^{43} +3277.33 q^{44} +5422.83 q^{45} -658.847 q^{46} +15797.5 q^{47} +2943.73 q^{48} +11099.7 q^{49} -1385.55 q^{50} -5391.57 q^{51} +18810.8 q^{52} -40050.9 q^{53} +5207.50 q^{54} +3025.00 q^{55} +21881.5 q^{56} +1843.81 q^{57} +3806.58 q^{58} +42046.2 q^{59} +3458.48 q^{60} -6530.42 q^{61} -9582.63 q^{62} -36236.0 q^{63} -6318.56 q^{64} +17362.4 q^{65} +1370.06 q^{66} +63054.4 q^{67} +28591.8 q^{68} +1517.92 q^{69} +9258.44 q^{70} +3471.45 q^{71} -28412.5 q^{72} -41099.9 q^{73} +22019.4 q^{74} +3192.19 q^{75} -9777.83 q^{76} -20213.4 q^{77} +7863.65 q^{78} -86488.5 q^{79} -14408.8 q^{80} +40712.3 q^{81} +4616.42 q^{82} -29025.0 q^{83} -23109.9 q^{84} +26390.4 q^{85} +8354.88 q^{86} -8770.03 q^{87} -15849.3 q^{88} +25134.0 q^{89} -12021.8 q^{90} -116018. q^{91} -8049.64 q^{92} +22077.5 q^{93} -35021.3 q^{94} -9025.00 q^{95} -27934.3 q^{96} +32157.4 q^{97} -24606.7 q^{98} +26246.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9}+O(q^{10}) $ 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9} - 300 q^{10} - 4719 q^{11} + 872 q^{12} - 717 q^{13} + 2647 q^{14} - 675 q^{15} + 15078 q^{16} + 2155 q^{17} + 3293 q^{18} + 14079 q^{19} - 16750 q^{20} + 6891 q^{21} - 1452 q^{22} + 1296 q^{23} - 3138 q^{24} + 24375 q^{25} + 2585 q^{26} + 3846 q^{27} - 20901 q^{28} - 7635 q^{29} - 1725 q^{30} + 9595 q^{31} - 43 q^{32} - 3267 q^{33} - 28383 q^{34} + 6275 q^{35} + 80573 q^{36} - 28965 q^{37} + 4332 q^{38} + 21358 q^{39} - 6750 q^{40} + 19627 q^{41} + 12478 q^{42} + 3711 q^{43} - 81070 q^{44} - 91650 q^{45} + 37459 q^{46} + 38450 q^{47} - 12259 q^{48} + 78758 q^{49} + 7500 q^{50} - 68114 q^{51} - 50322 q^{52} + 20631 q^{53} - 124732 q^{54} + 117975 q^{55} + 94893 q^{56} + 9747 q^{57} - 148140 q^{58} + 170405 q^{59} - 21800 q^{60} - 22345 q^{61} + 246390 q^{62} - 151688 q^{63} + 340312 q^{64} + 17925 q^{65} - 8349 q^{66} - 16408 q^{67} - 32276 q^{68} + 93536 q^{69} - 66175 q^{70} + 119338 q^{71} + 135668 q^{72} - 141606 q^{73} + 71843 q^{74} + 16875 q^{75} + 241870 q^{76} + 30371 q^{77} + 708290 q^{78} + 14727 q^{79} - 376950 q^{80} + 441659 q^{81} - 219870 q^{82} + 384909 q^{83} + 877024 q^{84} - 53875 q^{85} + 250290 q^{86} - 77038 q^{87} - 32670 q^{88} + 443394 q^{89} - 82325 q^{90} - 207088 q^{91} - 237112 q^{92} + 396718 q^{93} + 409516 q^{94} - 351975 q^{95} + 100332 q^{96} - 152942 q^{97} + 895680 q^{98} - 443586 q^{99}+O(q^{100}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9 - 300 * q^10 - 4719 * q^11 + 872 * q^12 - 717 * q^13 + 2647 * q^14 - 675 * q^15 + 15078 * q^16 + 2155 * q^17 + 3293 * q^18 + 14079 * q^19 - 16750 * q^20 + 6891 * q^21 - 1452 * q^22 + 1296 * q^23 - 3138 * q^24 + 24375 * q^25 + 2585 * q^26 + 3846 * q^27 - 20901 * q^28 - 7635 * q^29 - 1725 * q^30 + 9595 * q^31 - 43 * q^32 - 3267 * q^33 - 28383 * q^34 + 6275 * q^35 + 80573 * q^36 - 28965 * q^37 + 4332 * q^38 + 21358 * q^39 - 6750 * q^40 + 19627 * q^41 + 12478 * q^42 + 3711 * q^43 - 81070 * q^44 - 91650 * q^45 + 37459 * q^46 + 38450 * q^47 - 12259 * q^48 + 78758 * q^49 + 7500 * q^50 - 68114 * q^51 - 50322 * q^52 + 20631 * q^53 - 124732 * q^54 + 117975 * q^55 + 94893 * q^56 + 9747 * q^57 - 148140 * q^58 + 170405 * q^59 - 21800 * q^60 - 22345 * q^61 + 246390 * q^62 - 151688 * q^63 + 340312 * q^64 + 17925 * q^65 - 8349 * q^66 - 16408 * q^67 - 32276 * q^68 + 93536 * q^69 - 66175 * q^70 + 119338 * q^71 + 135668 * q^72 - 141606 * q^73 + 71843 * q^74 + 16875 * q^75 + 241870 * q^76 + 30371 * q^77 + 708290 * q^78 + 14727 * q^79 - 376950 * q^80 + 441659 * q^81 - 219870 * q^82 + 384909 * q^83 + 877024 * q^84 - 53875 * q^85 + 250290 * q^86 - 77038 * q^87 - 32670 * q^88 + 443394 * q^89 - 82325 * q^90 - 207088 * q^91 - 237112 * q^92 + 396718 * q^93 + 409516 * q^94 - 351975 * q^95 + 100332 * q^96 - 152942 * q^97 + 895680 * q^98 - 443586 * 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 $

$2$	−2.21689	−0.391894	−0.195947	−	0.980614i	$-0.562778\pi$
$2$	−2.21689	−0.391894	−0.195947	+	0.980614i	$0.562778\pi$
$3$	5.10751	0.327647	0.163824	−	0.986490i	$-0.447617\pi$
$3$	5.10751	0.327647	0.163824	+	0.986490i	$0.447617\pi$
$4$	−27.0854	−0.846419
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−11.3228	−0.128403
$7$	167.053	1.28857	0.644286	−	0.764784i	$-0.277155\pi$
$7$	167.053	1.28857	0.644286	+	0.764784i	$0.277155\pi$
$8$	130.986	0.723601
$9$	−216.913	−0.892647
$10$	55.4222	0.175260
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−138.339	−0.277327
$13$	−694.498	−1.13976	−0.569879	−	0.821729i	$-0.693010\pi$
$13$	−694.498	−1.13976	−0.569879	+	0.821729i	$0.693010\pi$
$14$	−370.338	−0.504984
$15$	−127.688	−0.146528
$16$	576.352	0.562844
$17$	−1055.62	−0.885898	−0.442949	−	0.896547i	$-0.646068\pi$
$17$	−1055.62	−0.885898	−0.442949	+	0.896547i	$0.646068\pi$
$18$	480.873	0.349823
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	677.135	0.378530
$21$	853.225	0.422197
$22$	268.243	0.118161
$23$	297.195	0.117144	0.0585722	−	0.998283i	$-0.481345\pi$
$23$	297.195	0.117144	0.0585722	+	0.998283i	$0.481345\pi$
$24$	669.011	0.237086
$25$	625.000	0.200000
$26$	1539.62	0.446664
$27$	−2349.01	−0.620120
$28$	−4524.70	−1.09067
$29$	−1717.08	−0.379138	−0.189569	−	0.981867i	$-0.560709\pi$
$29$	−1717.08	−0.379138	−0.189569	+	0.981867i	$0.560709\pi$
$30$	283.070	0.0574235
$31$	4322.56	0.807861	0.403931	−	0.914790i	$-0.367644\pi$
$31$	4322.56	0.807861	0.403931	+	0.914790i	$0.367644\pi$
$32$	−5469.25	−0.944176
$33$	−618.009	−0.0987893
$34$	2340.18	0.347178
$35$	−4176.32	−0.576267
$36$	5875.19	0.755554
$37$	−9932.56	−1.19277	−0.596385	−	0.802698i	$-0.703397\pi$
$37$	−9932.56	−1.19277	−0.596385	+	0.802698i	$0.703397\pi$
$38$	−800.297	−0.0899067
$39$	−3547.16	−0.373438
$40$	−3274.64	−0.323604
$41$	−2082.39	−0.193465	−0.0967324	−	0.995310i	$-0.530839\pi$
$41$	−2082.39	−0.193465	−0.0967324	+	0.995310i	$0.530839\pi$
$42$	−1891.50	−0.165457
$43$	−3768.74	−0.310832	−0.155416	−	0.987849i	$-0.549672\pi$
$43$	−3768.74	−0.310832	−0.155416	+	0.987849i	$0.549672\pi$
$44$	3277.33	0.255205
$45$	5422.83	0.399204
$46$	−658.847	−0.0459082
$47$	15797.5	1.04314	0.521571	−	0.853208i	$-0.325346\pi$
$47$	15797.5	1.04314	0.521571	+	0.853208i	$0.325346\pi$
$48$	2943.73	0.184414
$49$	11099.7	0.660420
$50$	−1385.55	−0.0783788
$51$	−5391.57	−0.290262
$52$	18810.8	0.964713
$53$	−40050.9	−1.95850	−0.979248	−	0.202664i	$-0.935040\pi$
$53$	−40050.9	−1.95850	−0.979248	+	0.202664i	$0.935040\pi$
$54$	5207.50	0.243022
$55$	3025.00	0.134840
$56$	21881.5	0.932412
$57$	1843.81	0.0751674
$58$	3806.58	0.148582
$59$	42046.2	1.57252	0.786261	−	0.617895i	$-0.212014\pi$
$59$	42046.2	1.57252	0.786261	+	0.617895i	$0.212014\pi$
$60$	3458.48	0.124024
$61$	−6530.42	−0.224707	−0.112353	−	0.993668i	$-0.535839\pi$
$61$	−6530.42	−0.224707	−0.112353	+	0.993668i	$0.535839\pi$
$62$	−9582.63	−0.316596
$63$	−36236.0	−1.15024
$64$	−6318.56	−0.192827
$65$	17362.4	0.509715
$66$	1370.06	0.0387149
$67$	63054.4	1.71604	0.858021	−	0.513614i	$-0.171694\pi$
$67$	63054.4	1.71604	0.858021	+	0.513614i	$0.171694\pi$
$68$	28591.8	0.749841
$69$	1517.92	0.0383820
$70$	9258.44	0.225836
$71$	3471.45	0.0817269	0.0408635	−	0.999165i	$-0.486989\pi$
$71$	3471.45	0.0817269	0.0408635	+	0.999165i	$0.486989\pi$
$72$	−28412.5	−0.645920
$73$	−41099.9	−0.902681	−0.451340	−	0.892352i	$-0.649054\pi$
$73$	−41099.9	−0.902681	−0.451340	+	0.892352i	$0.649054\pi$
$74$	22019.4	0.467440
$75$	3192.19	0.0655294
$76$	−9777.83	−0.194182
$77$	−20213.4	−0.388519
$78$	7863.65	0.146348
$79$	−86488.5	−1.55916	−0.779580	−	0.626302i	$-0.784568\pi$
$79$	−86488.5	−1.55916	−0.779580	+	0.626302i	$0.784568\pi$
$80$	−14408.8	−0.251712
$81$	40712.3	0.689467
$82$	4616.42	0.0758177
$83$	−29025.0	−0.462463	−0.231231	−	0.972899i	$-0.574275\pi$
$83$	−29025.0	−0.462463	−0.231231	+	0.972899i	$0.574275\pi$
$84$	−23109.9	−0.357356
$85$	26390.4	0.396186
$86$	8354.88	0.121813
$87$	−8770.03	−0.124223
$88$	−15849.3	−0.218174
$89$	25134.0	0.336347	0.168173	−	0.985757i	$-0.446213\pi$
$89$	25134.0	0.336347	0.168173	+	0.985757i	$0.446213\pi$
$90$	−12021.8	−0.156446
$91$	−116018.	−1.46866
$92$	−8049.64	−0.0991532
$93$	22077.5	0.264693
$94$	−35021.3	−0.408801
$95$	−9025.00	−0.102598
$96$	−27934.3	−0.309356
$97$	32157.4	0.347018	0.173509	−	0.984832i	$-0.444489\pi$
$97$	32157.4	0.347018	0.173509	+	0.984832i	$0.444489\pi$
$98$	−24606.7	−0.258815
$99$	26246.5	0.269143
$100$	−16928.4	−0.169284
$101$	−97512.2	−0.951164	−0.475582	−	0.879671i	$-0.657763\pi$
$101$	−97512.2	−0.951164	−0.475582	+	0.879671i	$0.657763\pi$
$102$	11952.5	0.113752
$103$	−173917.	−1.61529	−0.807643	−	0.589672i	$-0.799257\pi$
$103$	−173917.	−1.61529	−0.807643	+	0.589672i	$0.799257\pi$
$104$	−90969.3	−0.824730
$105$	−21330.6	−0.188812
$106$	88788.4	0.767523
$107$	−164433.	−1.38845	−0.694225	−	0.719758i	$-0.744253\pi$
$107$	−164433.	−1.38845	−0.694225	+	0.719758i	$0.744253\pi$
$108$	63624.0	0.524882
$109$	−11684.5	−0.0941981	−0.0470991	−	0.998890i	$-0.514998\pi$
$109$	−11684.5	−0.0941981	−0.0470991	+	0.998890i	$0.514998\pi$
$110$	−6706.09	−0.0528430
$111$	−50730.7	−0.390808
$112$	96281.3	0.725266
$113$	108809.	0.801617	0.400808	−	0.916162i	$-0.368729\pi$
$113$	108809.	0.801617	0.400808	+	0.916162i	$0.368729\pi$
$114$	−4087.52	−0.0294577
$115$	−7429.87	−0.0523885
$116$	46507.9	0.320909
$117$	150646.	1.01740
$118$	−93211.7	−0.616262
$119$	−176344.	−1.14154
$120$	−16725.3	−0.106028
$121$	14641.0	0.0909091
$122$	14477.2	0.0880613
$123$	−10635.8	−0.0633882
$124$	−117078.	−0.683789
$125$	−15625.0	−0.0894427
$126$	80331.1	0.450773
$127$	−228698.	−1.25821	−0.629106	−	0.777320i	$-0.716579\pi$
$127$	−228698.	−1.25821	−0.629106	+	0.777320i	$0.716579\pi$
$128$	189024.	1.01974
$129$	−19248.9	−0.101843
$130$	−38490.6	−0.199754
$131$	212757.	1.08319	0.541595	−	0.840639i	$-0.317821\pi$
$131$	212757.	1.08319	0.541595	+	0.840639i	$0.317821\pi$
$132$	16739.0	0.0836171
$133$	60306.1	0.295619
$134$	−139784.	−0.672507
$135$	58725.3	0.277326
$136$	−138271.	−0.641036
$137$	−90631.1	−0.412549	−0.206275	−	0.978494i	$-0.566134\pi$
$137$	−90631.1	−0.412549	−0.206275	+	0.978494i	$0.566134\pi$
$138$	−3365.07	−0.0150417
$139$	125929.	0.552827	0.276414	−	0.961039i	$-0.410854\pi$
$139$	125929.	0.552827	0.276414	+	0.961039i	$0.410854\pi$
$140$	113117.	0.487764
$141$	80685.9	0.341782
$142$	−7695.82	−0.0320283
$143$	84034.3	0.343650
$144$	−125019.	−0.502421
$145$	42927.1	0.169555
$146$	91114.0	0.353755
$147$	56691.7	0.216385
$148$	269027.	1.00958
$149$	61618.8	0.227378	0.113689	−	0.993516i	$-0.463733\pi$
$149$	61618.8	0.227378	0.113689	+	0.993516i	$0.463733\pi$
$150$	−7076.74	−0.0256806
$151$	−356981.	−1.27410	−0.637050	−	0.770823i	$-0.719845\pi$
$151$	−356981.	−1.27410	−0.637050	+	0.770823i	$0.719845\pi$
$152$	47285.8	0.166005
$153$	228977.	0.790794
$154$	44810.8	0.152258
$155$	−108064.	−0.361286
$156$	96076.2	0.316085
$157$	522970.	1.69327	0.846637	−	0.532170i	$-0.178623\pi$
$157$	522970.	1.69327	0.846637	+	0.532170i	$0.178623\pi$
$158$	191735.	0.611026
$159$	−204561.	−0.641696
$160$	136731.	0.422248
$161$	49647.2	0.150949
$162$	−90254.7	−0.270198
$163$	408712.	1.20489	0.602447	−	0.798159i	$-0.294193\pi$
$163$	408712.	1.20489	0.602447	+	0.798159i	$0.294193\pi$
$164$	56402.3	0.163752
$165$	15450.2	0.0441799
$166$	64345.1	0.181236
$167$	712237.	1.97621	0.988105	−	0.153779i	$-0.0491445\pi$
$167$	712237.	1.97621	0.988105	+	0.153779i	$0.0491445\pi$
$168$	111760.	0.305502
$169$	111034.	0.299048
$170$	−58504.6	−0.155263
$171$	−78305.7	−0.204787
$172$	102078.	0.263094
$173$	−441830.	−1.12238	−0.561190	−	0.827687i	$-0.689656\pi$
$173$	−441830.	−1.12238	−0.561190	+	0.827687i	$0.689656\pi$
$174$	19442.2	0.0486824
$175$	104408.	0.257715
$176$	−69738.6	−0.169704
$177$	214751.	0.515232
$178$	−55719.3	−0.131812
$179$	−27435.4	−0.0639997	−0.0319999	−	0.999488i	$-0.510188\pi$
$179$	−27435.4	−0.0639997	−0.0319999	+	0.999488i	$0.510188\pi$
$180$	−146880.	−0.337894
$181$	−450481.	−1.02207	−0.511035	−	0.859560i	$-0.670738\pi$
$181$	−450481.	−1.02207	−0.511035	+	0.859560i	$0.670738\pi$
$182$	257199.	0.575560
$183$	−33354.2	−0.0736246
$184$	38928.3	0.0847657
$185$	248314.	0.533423
$186$	−48943.4	−0.103732
$187$	127730.	0.267108
$188$	−427882.	−0.882935
$189$	−392409.	−0.799070
$190$	20007.4	0.0402075
$191$	686508.	1.36164	0.680820	−	0.732451i	$-0.261624\pi$
$191$	686508.	1.36164	0.680820	+	0.732451i	$0.261624\pi$
$192$	−32272.1	−0.0631792
$193$	340028.	0.657084	0.328542	−	0.944489i	$-0.393443\pi$
$193$	340028.	0.657084	0.328542	+	0.944489i	$0.393443\pi$
$194$	−71289.4	−0.135994
$195$	88678.9	0.167007
$196$	−300639.	−0.558992
$197$	−188524.	−0.346100	−0.173050	−	0.984913i	$-0.555362\pi$
$197$	−188524.	−0.346100	−0.173050	+	0.984913i	$0.555362\pi$
$198$	−58185.6	−0.105476
$199$	497280.	0.890160	0.445080	−	0.895491i	$-0.353175\pi$
$199$	497280.	0.890160	0.445080	+	0.895491i	$0.353175\pi$
$200$	81866.1	0.144720
$201$	322051.	0.562256
$202$	216174.	0.372756
$203$	−286844.	−0.488546
$204$	146033.	0.245683
$205$	52059.7	0.0865201
$206$	385555.	0.633021
$207$	−64465.5	−0.104569
$208$	−400276.	−0.641506
$209$	−43681.0	−0.0691714
$210$	47287.6	0.0739944
$211$	124732.	0.192874	0.0964368	−	0.995339i	$-0.469255\pi$
$211$	124732.	0.192874	0.0964368	+	0.995339i	$0.469255\pi$
$212$	1.08480e6	1.65771
$213$	17730.5	0.0267776
$214$	364530.	0.544126
$215$	94218.6	0.139008
$216$	−307687.	−0.448720
$217$	722096.	1.04099
$218$	25903.1	0.0369157
$219$	−209918.	−0.295761
$220$	−81933.4	−0.114131
$221$	733123.	1.00971
$222$	112464.	0.153155
$223$	639066.	0.860565	0.430283	−	0.902694i	$-0.358414\pi$
$223$	639066.	0.860565	0.430283	+	0.902694i	$0.358414\pi$
$224$	−913654.	−1.21664
$225$	−135571.	−0.178529
$226$	−241216.	−0.314149
$227$	643854.	0.829322	0.414661	−	0.909976i	$-0.363900\pi$
$227$	643854.	0.829322	0.414661	+	0.909976i	$0.363900\pi$
$228$	−49940.4	−0.0636231
$229$	−466753.	−0.588164	−0.294082	−	0.955780i	$-0.595014\pi$
$229$	−466753.	−0.588164	−0.294082	+	0.955780i	$0.595014\pi$
$230$	16471.2	0.0205308
$231$	−103240.	−0.127297
$232$	−224914.	−0.274344
$233$	1.09238e6	1.31821	0.659106	−	0.752050i	$-0.270935\pi$
$233$	1.09238e6	1.31821	0.659106	+	0.752050i	$0.270935\pi$
$234$	−333965.	−0.398714
$235$	−394937.	−0.466507
$236$	−1.13884e6	−1.33101
$237$	−441741.	−0.510854
$238$	390934.	0.447364
$239$	480474.	0.544095	0.272048	−	0.962284i	$-0.412299\pi$
$239$	480474.	0.544095	0.272048	+	0.962284i	$0.412299\pi$
$240$	−73593.2	−0.0824725
$241$	442551.	0.490818	0.245409	−	0.969420i	$-0.421078\pi$
$241$	442551.	0.490818	0.245409	+	0.969420i	$0.421078\pi$
$242$	−32457.5	−0.0356267
$243$	778749.	0.846022
$244$	176879.	0.190196
$245$	−277492.	−0.295349
$246$	23578.4	0.0248415
$247$	−250714.	−0.261478
$248$	566194.	0.584569
$249$	−148245.	−0.151525
$250$	34638.9	0.0350521
$251$	1.17187e6	1.17407	0.587035	−	0.809561i	$-0.300295\pi$
$251$	1.17187e6	1.17407	0.587035	+	0.809561i	$0.300295\pi$
$252$	981467.	0.973586
$253$	−35960.5	−0.0353203
$254$	506999.	0.493086
$255$	134789.	0.129809
$256$	−216850.	−0.206804
$257$	−1.50762e6	−1.42384	−0.711919	−	0.702262i	$-0.752174\pi$
$257$	−1.50762e6	−1.42384	−0.711919	+	0.702262i	$0.752174\pi$
$258$	42672.7	0.0399117
$259$	−1.65926e6	−1.53697
$260$	−470269.	−0.431433
$261$	372459.	0.338436
$262$	−471657.	−0.424496
$263$	295904.	0.263792	0.131896	−	0.991264i	$-0.457893\pi$
$263$	295904.	0.263792	0.131896	+	0.991264i	$0.457893\pi$
$264$	−80950.3	−0.0714840
$265$	1.00127e6	0.875866
$266$	−133692.	−0.115851
$267$	128372.	0.110203
$268$	−1.70785e6	−1.45249
$269$	327252.	0.275742	0.137871	−	0.990450i	$-0.455974\pi$
$269$	327252.	0.275742	0.137871	+	0.990450i	$0.455974\pi$
$270$	−130187.	−0.108683
$271$	−1.58233e6	−1.30880	−0.654400	−	0.756149i	$-0.727079\pi$
$271$	−1.58233e6	−1.30880	−0.654400	+	0.756149i	$0.727079\pi$
$272$	−608407.	−0.498622
$273$	−592563.	−0.481202
$274$	200919.	0.161676
$275$	−75625.0	−0.0603023
$276$	−41113.6	−0.0324873
$277$	864987.	0.677345	0.338673	−	0.940904i	$-0.390022\pi$
$277$	864987.	0.677345	0.338673	+	0.940904i	$0.390022\pi$
$278$	−279171.	−0.216650
$279$	−937621.	−0.721135
$280$	−547039.	−0.416987
$281$	1.62596e6	1.22841	0.614206	−	0.789146i	$-0.289476\pi$
$281$	1.62596e6	1.22841	0.614206	+	0.789146i	$0.289476\pi$
$282$	−178872.	−0.133943
$283$	1.18280e6	0.877903	0.438952	−	0.898511i	$-0.355350\pi$
$283$	1.18280e6	0.877903	0.438952	+	0.898511i	$0.355350\pi$
$284$	−94025.6	−0.0691752
$285$	−46095.3	−0.0336159
$286$	−186295.	−0.134674
$287$	−347869.	−0.249294
$288$	1.18635e6	0.842816
$289$	−305532.	−0.215185
$290$	−95164.6	−0.0664478
$291$	164245.	0.113699
$292$	1.11321e6	0.764046
$293$	−124541.	−0.0847506	−0.0423753	−	0.999102i	$-0.513493\pi$
$293$	−124541.	−0.0847506	−0.0423753	+	0.999102i	$0.513493\pi$
$294$	−125679.	−0.0847998
$295$	−1.05115e6	−0.703253
$296$	−1.30102e6	−0.863089
$297$	284231.	0.186973
$298$	−136602.	−0.0891079
$299$	−206401.	−0.133516
$300$	−86461.9	−0.0554653
$301$	−629580.	−0.400529
$302$	791388.	0.499312
$303$	−498045.	−0.311646
$304$	208063.	0.129125
$305$	163260.	0.100492
$306$	−507617.	−0.309908
$307$	1.30111e6	0.787896	0.393948	−	0.919133i	$-0.371109\pi$
$307$	1.30111e6	0.787896	0.393948	+	0.919133i	$0.371109\pi$
$308$	547488.	0.328850
$309$	−888284.	−0.529243
$310$	239566.	0.141586
$311$	−525981.	−0.308368	−0.154184	−	0.988042i	$-0.549275\pi$
$311$	−525981.	−0.308368	−0.154184	+	0.988042i	$0.549275\pi$
$312$	−464627.	−0.270220
$313$	2.46944e6	1.42475	0.712374	−	0.701800i	$-0.247620\pi$
$313$	2.46944e6	1.42475	0.712374	+	0.701800i	$0.247620\pi$
$314$	−1.15937e6	−0.663584
$315$	905900.	0.514403
$316$	2.34258e6	1.31970
$317$	2.28395e6	1.27655	0.638277	−	0.769807i	$-0.279648\pi$
$317$	2.28395e6	1.27655	0.638277	+	0.769807i	$0.279648\pi$
$318$	453488.	0.251477
$319$	207767.	0.114314
$320$	157964.	0.0862349
$321$	−839845.	−0.454922
$322$	−110062.	−0.0591560
$323$	−381077.	−0.203239
$324$	−1.10271e6	−0.583578
$325$	−434061.	−0.227952
$326$	−906069.	−0.472191
$327$	−59678.5	−0.0308637
$328$	−272763.	−0.139991
$329$	2.63902e6	1.34416
$330$	−34251.4	−0.0173138
$331$	−358522.	−0.179865	−0.0899324	−	0.995948i	$-0.528665\pi$
$331$	−358522.	−0.179865	−0.0899324	+	0.995948i	$0.528665\pi$
$332$	786153.	0.391437
$333$	2.15450e6	1.06472
$334$	−1.57895e6	−0.774465
$335$	−1.57636e6	−0.767438
$336$	491758.	0.237631
$337$	2.82603e6	1.35551	0.677753	−	0.735289i	$-0.262954\pi$
$337$	2.82603e6	1.35551	0.677753	+	0.735289i	$0.262954\pi$
$338$	−246151.	−0.117195
$339$	555741.	0.262647
$340$	−714795.	−0.335339
$341$	−523030.	−0.243579
$342$	173595.	0.0802550
$343$	−953426.	−0.437574
$344$	−493652.	−0.224918
$345$	−37948.1	−0.0171650
$346$	979488.	0.439854
$347$	2.43524e6	1.08572	0.542861	−	0.839823i	$-0.317341\pi$
$347$	2.43524e6	1.08572	0.542861	+	0.839823i	$0.317341\pi$
$348$	237540.	0.105145
$349$	−1.64518e6	−0.723021	−0.361511	−	0.932368i	$-0.617739\pi$
$349$	−1.64518e6	−0.723021	−0.361511	+	0.932368i	$0.617739\pi$
$350$	−231461.	−0.100997
$351$	1.63138e6	0.706787
$352$	661779.	0.284680
$353$	−2.16374e6	−0.924203	−0.462101	−	0.886827i	$-0.652904\pi$
$353$	−2.16374e6	−0.924203	−0.462101	+	0.886827i	$0.652904\pi$
$354$	−476080.	−0.201916
$355$	−86786.2	−0.0365494
$356$	−680766.	−0.284690
$357$	−900678.	−0.374023
$358$	60821.1	0.0250811
$359$	2.02468e6	0.829124	0.414562	−	0.910021i	$-0.363935\pi$
$359$	2.02468e6	0.829124	0.414562	+	0.910021i	$0.363935\pi$
$360$	710314.	0.288864
$361$	130321.	0.0526316
$362$	998666.	0.400543
$363$	74779.1	0.0297861
$364$	3.14239e6	1.24310
$365$	1.02750e6	0.403691
$366$	73942.5	0.0288530
$367$	−4.64861e6	−1.80160	−0.900800	−	0.434235i	$-0.857019\pi$
$367$	−4.64861e6	−1.80160	−0.900800	+	0.434235i	$0.857019\pi$
$368$	171289.	0.0659340
$369$	451698.	0.172696
$370$	−550484.	−0.209045
$371$	−6.69062e6	−2.52367
$372$	−597979.	−0.224041
$373$	2.91710e6	1.08562	0.542812	−	0.839854i	$-0.317360\pi$
$373$	2.91710e6	1.08562	0.542812	+	0.839854i	$0.317360\pi$
$374$	−283162.	−0.104678
$375$	−79804.9	−0.0293056
$376$	2.06925e6	0.754818
$377$	1.19251e6	0.432125
$378$	869928.	0.313151
$379$	3.31457e6	1.18530	0.592652	−	0.805459i	$-0.298081\pi$
$379$	3.31457e6	1.18530	0.592652	+	0.805459i	$0.298081\pi$
$380$	244446.	0.0868408
$381$	−1.16808e6	−0.412249
$382$	−1.52191e6	−0.533619
$383$	−3.38031e6	−1.17750	−0.588749	−	0.808316i	$-0.700379\pi$
$383$	−3.38031e6	−1.17750	−0.588749	+	0.808316i	$0.700379\pi$
$384$	965440.	0.334116
$385$	505335.	0.173751
$386$	−753803.	−0.257507
$387$	817491.	0.277463
$388$	−870997.	−0.293723
$389$	3.04055e6	1.01877	0.509387	−	0.860537i	$-0.329872\pi$
$389$	3.04055e6	1.01877	0.509387	+	0.860537i	$0.329872\pi$
$390$	−196591.	−0.0654489
$391$	−313723.	−0.103778
$392$	1.45390e6	0.477880
$393$	1.08666e6	0.354904
$394$	417937.	0.135635
$395$	2.16221e6	0.697278
$396$	−710897.	−0.227808
$397$	4.88377e6	1.55517	0.777587	−	0.628775i	$-0.216443\pi$
$397$	4.88377e6	1.55517	0.777587	+	0.628775i	$0.216443\pi$
$398$	−1.10241e6	−0.348849
$399$	308014.	0.0968586
$400$	360220.	0.112569
$401$	2.15241e6	0.668441	0.334221	−	0.942495i	$-0.391527\pi$
$401$	2.15241e6	0.668441	0.334221	+	0.942495i	$0.391527\pi$
$402$	−713951.	−0.220345
$403$	−3.00201e6	−0.920766
$404$	2.64116e6	0.805083
$405$	−1.01781e6	−0.308339
$406$	635901.	0.191458
$407$	1.20184e6	0.359634
$408$	−706219.	−0.210034
$409$	1.11781e6	0.330415	0.165207	−	0.986259i	$-0.447171\pi$
$409$	1.11781e6	0.330415	0.165207	+	0.986259i	$0.447171\pi$
$410$	−115411.	−0.0339067
$411$	−462900.	−0.135171
$412$	4.71062e6	1.36721
$413$	7.02394e6	2.02631
$414$	142913.	0.0409798
$415$	725624.	0.206820
$416$	3.79838e6	1.07613
$417$	643185.	0.181132
$418$	96835.9	0.0271079
$419$	4.71637e6	1.31242	0.656210	−	0.754578i	$-0.272158\pi$
$419$	4.71637e6	1.31242	0.656210	+	0.754578i	$0.272158\pi$
$420$	577748.	0.159814
$421$	6.89616e6	1.89628	0.948140	−	0.317854i	$-0.102962\pi$
$421$	6.89616e6	1.89628	0.948140	+	0.317854i	$0.102962\pi$
$422$	−276518.	−0.0755860
$423$	−3.42669e6	−0.931158
$424$	−5.24610e6	−1.41717
$425$	−659760.	−0.177180
$426$	−39306.5	−0.0104940
$427$	−1.09093e6	−0.289551
$428$	4.45374e6	1.17521
$429$	429206.	0.112596
$430$	−208872.	−0.0544765
$431$	6.70820e6	1.73945	0.869726	−	0.493534i	$-0.164295\pi$
$431$	6.70820e6	1.73945	0.869726	+	0.493534i	$0.164295\pi$
$432$	−1.35386e6	−0.349031
$433$	−5.57132e6	−1.42803	−0.714017	−	0.700128i	$-0.753126\pi$
$433$	−5.57132e6	−1.42803	−0.714017	+	0.700128i	$0.753126\pi$
$434$	−1.60081e6	−0.407957
$435$	219251.	0.0555543
$436$	316478.	0.0797311
$437$	107287.	0.0268748
$438$	465366.	0.115907
$439$	3.82907e6	0.948270	0.474135	−	0.880452i	$-0.342761\pi$
$439$	3.82907e6	0.948270	0.474135	+	0.880452i	$0.342761\pi$
$440$	396232.	0.0975703
$441$	−2.40767e6	−0.589522
$442$	−1.62525e6	−0.395699
$443$	−241299.	−0.0584180	−0.0292090	−	0.999573i	$-0.509299\pi$
$443$	−241299.	−0.0584180	−0.0292090	+	0.999573i	$0.509299\pi$
$444$	1.37406e6	0.330787
$445$	−628351.	−0.150419
$446$	−1.41674e6	−0.337250
$447$	314719.	0.0744996
$448$	−1.05553e6	−0.248472
$449$	705204.	0.165082	0.0825409	−	0.996588i	$-0.473697\pi$
$449$	705204.	0.165082	0.0825409	+	0.996588i	$0.473697\pi$
$450$	300545.	0.0699647
$451$	251969.	0.0583318
$452$	−2.94712e6	−0.678504
$453$	−1.82329e6	−0.417455
$454$	−1.42735e6	−0.325006
$455$	2.90045e6	0.656805
$456$	241513.	0.0543912
$457$	635509.	0.142341	0.0711707	−	0.997464i	$-0.477326\pi$
$457$	635509.	0.142341	0.0711707	+	0.997464i	$0.477326\pi$
$458$	1.03474e6	0.230498
$459$	2.47966e6	0.549363
$460$	201241.	0.0443427
$461$	−3.44619e6	−0.755244	−0.377622	−	0.925960i	$-0.623258\pi$
$461$	−3.44619e6	−0.755244	−0.377622	+	0.925960i	$0.623258\pi$
$462$	228872.	0.0498870
$463$	−6.64563e6	−1.44073	−0.720367	−	0.693593i	$-0.756027\pi$
$463$	−6.64563e6	−1.44073	−0.720367	+	0.693593i	$0.756027\pi$
$464$	−989646.	−0.213395
$465$	−551938.	−0.118374
$466$	−2.42169e6	−0.516599
$467$	3.13876e6	0.665987	0.332994	−	0.942929i	$-0.391941\pi$
$467$	3.13876e6	0.665987	0.332994	+	0.942929i	$0.391941\pi$
$468$	−4.08030e6	−0.861148
$469$	1.05334e7	2.21125
$470$	875532.	0.182821
$471$	2.67107e6	0.554796
$472$	5.50745e6	1.13788
$473$	456018.	0.0937193
$474$	979291.	0.200201
$475$	225625.	0.0458831
$476$	4.77634e6	0.966224
$477$	8.68758e6	1.74825
$478$	−1.06516e6	−0.213228
$479$	−5.23107e6	−1.04172	−0.520861	−	0.853642i	$-0.674389\pi$
$479$	−5.23107e6	−1.04172	−0.520861	+	0.853642i	$0.674389\pi$
$480$	698357.	0.138348
$481$	6.89814e6	1.35947
$482$	−981085.	−0.192349
$483$	253574.	0.0494580
$484$	−396557.	−0.0769472
$485$	−803936.	−0.155191
$486$	−1.72640e6	−0.331551
$487$	−5.01694e6	−0.958554	−0.479277	−	0.877664i	$-0.659101\pi$
$487$	−5.01694e6	−0.958554	−0.479277	+	0.877664i	$0.659101\pi$
$488$	−855392.	−0.162598
$489$	2.08750e6	0.394780
$490$	615168.	0.115745
$491$	7.70578e6	1.44249	0.721245	−	0.692680i	$-0.243570\pi$
$491$	7.70578e6	1.44249	0.721245	+	0.692680i	$0.243570\pi$
$492$	288076.	0.0536530
$493$	1.81258e6	0.335877
$494$	555804.	0.102472
$495$	−656163.	−0.120365
$496$	2.49132e6	0.454700
$497$	579916.	0.105311
$498$	328643.	0.0593816
$499$	7.08266e6	1.27334	0.636671	−	0.771135i	$-0.280311\pi$
$499$	7.08266e6	1.27334	0.636671	+	0.771135i	$0.280311\pi$
$500$	423210.	0.0757060
$501$	3.63776e6	0.647500
$502$	−2.59790e6	−0.460111
$503$	−3.35711e6	−0.591624	−0.295812	−	0.955246i	$-0.595590\pi$
$503$	−3.35711e6	−0.591624	−0.295812	+	0.955246i	$0.595590\pi$
$504$	−4.74640e6	−0.832315
$505$	2.43780e6	0.425374
$506$	79720.5	0.0138418
$507$	567110.	0.0979822
$508$	6.19439e6	1.06497
$509$	−7.08885e6	−1.21278	−0.606389	−	0.795168i	$-0.707382\pi$
$509$	−7.08885e6	−1.21278	−0.606389	+	0.795168i	$0.707382\pi$
$510$	−298813.	−0.0508714
$511$	−6.86587e6	−1.16317
$512$	−5.56802e6	−0.938698
$513$	−847994.	−0.142265
$514$	3.34223e6	0.557994
$515$	4.34793e6	0.722377
$516$	521364.	0.0862020
$517$	−1.91150e6	−0.314519
$518$	3.67840e6	0.602330
$519$	−2.25665e6	−0.367745
$520$	2.27423e6	0.368830
$521$	−6.30133e6	−1.01704	−0.508520	−	0.861050i	$-0.669807\pi$
$521$	−6.30133e6	−1.01704	−0.508520	+	0.861050i	$0.669807\pi$
$522$	−825699.	−0.132631
$523$	−1.02836e7	−1.64396	−0.821980	−	0.569517i	$-0.807130\pi$
$523$	−1.02836e7	−1.64396	−0.821980	+	0.569517i	$0.807130\pi$
$524$	−5.76260e6	−0.916833
$525$	533265.	0.0844394
$526$	−655987.	−0.103379
$527$	−4.56296e6	−0.715682
$528$	−356191.	−0.0556030
$529$	−6.34802e6	−0.986277
$530$	−2.21971e6	−0.343247
$531$	−9.12038e6	−1.40371
$532$	−1.63342e6	−0.250217
$533$	1.44621e6	0.220503
$534$	−284587.	−0.0431879
$535$	4.11083e6	0.620934
$536$	8.25922e6	1.24173
$537$	−140126.	−0.0209693
$538$	−725482.	−0.108062
$539$	−1.34306e6	−0.199124
$540$	−1.59060e6	−0.234734
$541$	4.06145e6	0.596607	0.298303	−	0.954471i	$-0.403579\pi$
$541$	4.06145e6	0.596607	0.298303	+	0.954471i	$0.403579\pi$
$542$	3.50784e6	0.512911
$543$	−2.30084e6	−0.334878
$544$	5.77343e6	0.836443
$545$	292111.	0.0421267
$546$	1.31365e6	0.188580
$547$	−5.10873e6	−0.730037	−0.365019	−	0.931000i	$-0.618937\pi$
$547$	−5.10873e6	−0.730037	−0.365019	+	0.931000i	$0.618937\pi$
$548$	2.45478e6	0.349190
$549$	1.41653e6	0.200584
$550$	167652.	0.0236321
$551$	−619868.	−0.0869801
$552$	198827.	0.0277732
$553$	−1.44482e7	−2.00909
$554$	−1.91758e6	−0.265448
$555$	1.26827e6	0.174774
$556$	−3.41085e6	−0.467924
$557$	−4.24490e6	−0.579735	−0.289868	−	0.957067i	$-0.593611\pi$
$557$	−4.24490e6	−0.579735	−0.289868	+	0.957067i	$0.593611\pi$
$558$	2.07860e6	0.282609
$559$	2.61738e6	0.354273
$560$	−2.40703e6	−0.324349
$561$	652380.	0.0875172
$562$	−3.60457e6	−0.481407
$563$	−2.84784e6	−0.378656	−0.189328	−	0.981914i	$-0.560631\pi$
$563$	−2.84784e6	−0.378656	−0.189328	+	0.981914i	$0.560631\pi$
$564$	−2.18541e6	−0.289291
$565$	−2.72021e6	−0.358494
$566$	−2.62214e6	−0.344045
$567$	6.80111e6	0.888428
$568$	454710.	0.0591376
$569$	−3.06650e6	−0.397066	−0.198533	−	0.980094i	$-0.563618\pi$
$569$	−3.06650e6	−0.397066	−0.198533	+	0.980094i	$0.563618\pi$
$570$	102188.	0.0131739
$571$	573320.	0.0735880	0.0367940	−	0.999323i	$-0.488285\pi$
$571$	573320.	0.0735880	0.0367940	+	0.999323i	$0.488285\pi$
$572$	−2.27610e6	−0.290872
$573$	3.50635e6	0.446137
$574$	771187.	0.0976967
$575$	185747.	0.0234289
$576$	1.37058e6	0.172127
$577$	1.10064e6	0.137628	0.0688138	−	0.997630i	$-0.478079\pi$
$577$	1.10064e6	0.137628	0.0688138	+	0.997630i	$0.478079\pi$
$578$	677330.	0.0843298
$579$	1.73669e6	0.215292
$580$	−1.16270e6	−0.143515
$581$	−4.84871e6	−0.595917
$582$	−364112.	−0.0445581
$583$	4.84616e6	0.590509
$584$	−5.38351e6	−0.653180
$585$	−3.76615e6	−0.454996
$586$	276093.	0.0332133
$587$	3.59942e6	0.431158	0.215579	−	0.976486i	$-0.430836\pi$
$587$	3.59942e6	0.431158	0.215579	+	0.976486i	$0.430836\pi$
$588$	−1.53552e6	−0.183152
$589$	1.56044e6	0.185336
$590$	2.33029e6	0.275601
$591$	−962890.	−0.113399
$592$	−5.72465e6	−0.671344
$593$	1.50782e7	1.76081	0.880404	−	0.474224i	$-0.157271\pi$
$593$	1.50782e7	1.76081	0.880404	+	0.474224i	$0.157271\pi$
$594$	−630107.	−0.0732737
$595$	4.40859e6	0.510514
$596$	−1.66897e6	−0.192457
$597$	2.53986e6	0.291658
$598$	457568.	0.0523242
$599$	−1.36957e7	−1.55961	−0.779805	−	0.626022i	$-0.784682\pi$
$599$	−1.36957e7	−1.55961	−0.779805	+	0.626022i	$0.784682\pi$
$600$	418132.	0.0474171
$601$	−4.78533e6	−0.540413	−0.270207	−	0.962802i	$-0.587092\pi$
$601$	−4.78533e6	−0.540413	−0.270207	+	0.962802i	$0.587092\pi$
$602$	1.39571e6	0.156965
$603$	−1.36773e7	−1.53182
$604$	9.66899e6	1.07842
$605$	−366025.	−0.0406558
$606$	1.10411e6	0.122132
$607$	4.71972e6	0.519929	0.259965	−	0.965618i	$-0.416289\pi$
$607$	4.71972e6	0.519929	0.259965	+	0.965618i	$0.416289\pi$
$608$	−1.97440e6	−0.216609
$609$	−1.46506e6	−0.160071
$610$	−361930.	−0.0393822
$611$	−1.09713e7	−1.18893
$612$	−6.20194e6	−0.669343
$613$	−5.99713e6	−0.644603	−0.322301	−	0.946637i	$-0.604456\pi$
$613$	−5.99713e6	−0.644603	−0.322301	+	0.946637i	$0.604456\pi$
$614$	−2.88442e6	−0.308772
$615$	265896.	0.0283481
$616$	−2.64767e6	−0.281133
$617$	1.60442e7	1.69670	0.848352	−	0.529433i	$-0.177595\pi$
$617$	1.60442e7	1.69670	0.848352	+	0.529433i	$0.177595\pi$
$618$	1.96923e6	0.207407
$619$	1.57316e7	1.65024	0.825121	−	0.564957i	$-0.191107\pi$
$619$	1.57316e7	1.65024	0.825121	+	0.564957i	$0.191107\pi$
$620$	2.92696e6	0.305800
$621$	−698114.	−0.0726436
$622$	1.16604e6	0.120847
$623$	4.19871e6	0.433407
$624$	−2.04441e6	−0.210188
$625$	390625.	0.0400000
$626$	−5.47448e6	−0.558350
$627$	−223101.	−0.0226638
$628$	−1.41648e7	−1.43322
$629$	1.04850e7	1.05667
$630$	−2.00828e6	−0.201592
$631$	−1.12882e7	−1.12863	−0.564314	−	0.825560i	$-0.690859\pi$
$631$	−1.12882e7	−1.12863	−0.564314	+	0.825560i	$0.690859\pi$
$632$	−1.13288e7	−1.12821
$633$	637072.	0.0631945
$634$	−5.06327e6	−0.500274
$635$	5.71746e6	0.562689
$636$	5.54061e6	0.543143
$637$	−7.70870e6	−0.752718
$638$	−460597.	−0.0447991
$639$	−753004.	−0.0729533
$640$	−4.72559e6	−0.456043
$641$	516550.	0.0496555	0.0248277	−	0.999692i	$-0.492096\pi$
$641$	516550.	0.0496555	0.0248277	+	0.999692i	$0.492096\pi$
$642$	1.86184e6	0.178281
$643$	−1.24181e7	−1.18448	−0.592241	−	0.805761i	$-0.701757\pi$
$643$	−1.24181e7	−1.18448	−0.592241	+	0.805761i	$0.701757\pi$
$644$	−1.34472e6	−0.127766
$645$	481223.	0.0455456
$646$	844806.	0.0796481
$647$	−5.23679e6	−0.491818	−0.245909	−	0.969293i	$-0.579086\pi$
$647$	−5.23679e6	−0.491818	−0.245909	+	0.969293i	$0.579086\pi$
$648$	5.33273e6	0.498899
$649$	−5.08759e6	−0.474133
$650$	962265.	0.0893329
$651$	3.68811e6	0.341077
$652$	−1.10701e7	−1.01984
$653$	−1.23881e7	−1.13690	−0.568449	−	0.822718i	$-0.692456\pi$
$653$	−1.23881e7	−1.13690	−0.568449	+	0.822718i	$0.692456\pi$
$654$	132301.	0.0120953
$655$	−5.31891e6	−0.484417
$656$	−1.20019e6	−0.108891
$657$	8.91513e6	0.805775
$658$	−5.85040e6	−0.526770
$659$	−8.19318e6	−0.734918	−0.367459	−	0.930040i	$-0.619772\pi$
$659$	−8.19318e6	−0.734918	−0.367459	+	0.930040i	$0.619772\pi$
$660$	−418476.	−0.0373947
$661$	1.44516e7	1.28651	0.643255	−	0.765652i	$-0.277584\pi$
$661$	1.44516e7	1.28651	0.643255	+	0.765652i	$0.277584\pi$
$662$	794803.	0.0704879
$663$	3.74444e6	0.330828
$664$	−3.80186e6	−0.334638
$665$	−1.50765e6	−0.132205
$666$	−4.77629e6	−0.417259
$667$	−510308.	−0.0444138
$668$	−1.92912e7	−1.67270
$669$	3.26404e6	0.281962
$670$	3.49461e6	0.300754
$671$	790181.	0.0677517
$672$	−4.66650e6	−0.398628
$673$	1.10836e7	0.943288	0.471644	−	0.881789i	$-0.343661\pi$
$673$	1.10836e7	0.943288	0.471644	+	0.881789i	$0.343661\pi$
$674$	−6.26498e6	−0.531215
$675$	−1.46813e6	−0.124024
$676$	−3.00741e6	−0.253120
$677$	9.05575e6	0.759369	0.379684	−	0.925116i	$-0.376033\pi$
$677$	9.05575e6	0.759369	0.379684	+	0.925116i	$0.376033\pi$
$678$	−1.23202e6	−0.102930
$679$	5.37199e6	0.447158
$680$	3.45677e6	0.286680
$681$	3.28849e6	0.271725
$682$	1.15950e6	0.0954573
$683$	−9.30744e6	−0.763447	−0.381723	−	0.924277i	$-0.624669\pi$
$683$	−9.30744e6	−0.763447	−0.381723	+	0.924277i	$0.624669\pi$
$684$	2.12094e6	0.173336
$685$	2.26578e6	0.184498
$686$	2.11364e6	0.171483
$687$	−2.38395e6	−0.192710
$688$	−2.17212e6	−0.174950
$689$	2.78153e7	2.23221
$690$	84126.7	0.00672684
$691$	−1.13500e7	−0.904274	−0.452137	−	0.891948i	$-0.649338\pi$
$691$	−1.13500e7	−0.904274	−0.452137	+	0.891948i	$0.649338\pi$
$692$	1.19671e7	0.950004
$693$	4.38456e6	0.346811
$694$	−5.39866e6	−0.425488
$695$	−3.14823e6	−0.247232
$696$	−1.14875e6	−0.0898881
$697$	2.19820e6	0.171390
$698$	3.64719e6	0.283348
$699$	5.57936e6	0.431908
$700$	−2.82793e6	−0.218134
$701$	4.04935e6	0.311236	0.155618	−	0.987817i	$-0.450263\pi$
$701$	4.04935e6	0.311236	0.155618	+	0.987817i	$0.450263\pi$
$702$	−3.61660e6	−0.276986
$703$	−3.58565e6	−0.273640
$704$	764546.	0.0581396
$705$	−2.01715e6	−0.152850
$706$	4.79676e6	0.362190
$707$	−1.62897e7	−1.22564
$708$	−5.81663e6	−0.436102
$709$	2.37686e7	1.77577	0.887886	−	0.460064i	$-0.152173\pi$
$709$	2.37686e7	1.77577	0.887886	+	0.460064i	$0.152173\pi$
$710$	192395.	0.0143235
$711$	1.87605e7	1.39178
$712$	3.29220e6	0.243381
$713$	1.28464e6	0.0946364
$714$	1.99670e6	0.146578
$715$	−2.10086e6	−0.153685
$716$	743098.	0.0541706
$717$	2.45403e6	0.178271
$718$	−4.48848e6	−0.324929
$719$	9.50844e6	0.685942	0.342971	−	0.939346i	$-0.388567\pi$
$719$	9.50844e6	0.685942	0.342971	+	0.939346i	$0.388567\pi$
$720$	3.12546e6	0.224690
$721$	−2.90534e7	−2.08141
$722$	−288907.	−0.0206260
$723$	2.26033e6	0.160815
$724$	1.22015e7	0.865099
$725$	−1.07318e6	−0.0758275
$726$	−165777.	−0.0116730
$727$	2.35436e7	1.65211	0.826053	−	0.563593i	$-0.190581\pi$
$727$	2.35436e7	1.65211	0.826053	+	0.563593i	$0.190581\pi$
$728$	−1.51967e7	−1.06272
$729$	−5.91563e6	−0.412270
$730$	−2.27785e6	−0.158204
$731$	3.97835e6	0.275365
$732$	903412.	0.0623172
$733$	−3.60251e6	−0.247654	−0.123827	−	0.992304i	$-0.539517\pi$
$733$	−3.60251e6	−0.247654	−0.123827	+	0.992304i	$0.539517\pi$
$734$	1.03055e7	0.706036
$735$	−1.41729e6	−0.0967701
$736$	−1.62543e6	−0.110605
$737$	−7.62958e6	−0.517406
$738$	−1.00136e6	−0.0676785
$739$	−2.52188e7	−1.69868	−0.849342	−	0.527842i	$-0.823001\pi$
$739$	−2.52188e7	−1.69868	−0.849342	+	0.527842i	$0.823001\pi$
$740$	−6.72568e6	−0.451499
$741$	−1.28052e6	−0.0856726
$742$	1.48324e7	0.989009
$743$	4.49539e6	0.298741	0.149371	−	0.988781i	$-0.452275\pi$
$743$	4.49539e6	0.298741	0.149371	+	0.988781i	$0.452275\pi$
$744$	2.89184e6	0.191532
$745$	−1.54047e6	−0.101686
$746$	−6.46688e6	−0.425449
$747$	6.29590e6	0.412816
$748$	−3.45961e6	−0.226085
$749$	−2.74691e7	−1.78912
$750$	176918.	0.0114847
$751$	−2.65956e7	−1.72072	−0.860359	−	0.509688i	$-0.829761\pi$
$751$	−2.65956e7	−1.72072	−0.860359	+	0.509688i	$0.829761\pi$
$752$	9.10492e6	0.587126
$753$	5.98533e6	0.384681
$754$	−2.64367e6	−0.169347
$755$	8.92454e6	0.569795
$756$	1.06286e7	0.676348
$757$	188420.	0.0119505	0.00597527	−	0.999982i	$-0.498098\pi$
$757$	188420.	0.0119505	0.00597527	+	0.999982i	$0.498098\pi$
$758$	−7.34804e6	−0.464514
$759$	−183669.	−0.0115726
$760$	−1.18215e6	−0.0742399
$761$	−2.93146e7	−1.83494	−0.917470	−	0.397806i	$-0.869772\pi$
$761$	−2.93146e7	−1.83494	−0.917470	+	0.397806i	$0.869772\pi$
$762$	2.58950e6	0.161558
$763$	−1.95192e6	−0.121381
$764$	−1.85944e7	−1.15252
$765$	−5.72443e6	−0.353654
$766$	7.49378e6	0.461454
$767$	−2.92010e7	−1.79229
$768$	−1.10757e6	−0.0677589
$769$	5.00452e6	0.305173	0.152587	−	0.988290i	$-0.451240\pi$
$769$	5.00452e6	0.305173	0.152587	+	0.988290i	$0.451240\pi$
$770$	−1.12027e6	−0.0680920
$771$	−7.70021e6	−0.466516
$772$	−9.20978e6	−0.556168
$773$	1.69966e7	1.02309	0.511545	−	0.859256i	$-0.329073\pi$
$773$	1.69966e7	1.02309	0.511545	+	0.859256i	$0.329073\pi$
$774$	−1.81229e6	−0.108736
$775$	2.70160e6	0.161572
$776$	4.21217e6	0.251103
$777$	−8.47470e6	−0.503584
$778$	−6.74056e6	−0.399252
$779$	−751742.	−0.0443839
$780$	−2.40190e6	−0.141358
$781$	−420045.	−0.0246416
$782$	695490.	0.0406700
$783$	4.03345e6	0.235111
$784$	6.39732e6	0.371713
$785$	−1.30742e7	−0.757255
$786$	−2.40900e6	−0.139085
$787$	−8.94279e6	−0.514679	−0.257339	−	0.966321i	$-0.582846\pi$
$787$	−8.94279e6	−0.514679	−0.257339	+	0.966321i	$0.582846\pi$
$788$	5.10626e6	0.292946
$789$	1.51133e6	0.0864307
$790$	−4.79339e6	−0.273259
$791$	1.81768e7	1.03294
$792$	3.43792e6	0.194752
$793$	4.53536e6	0.256111
$794$	−1.08268e7	−0.609464
$795$	5.11401e6	0.286975
$796$	−1.34690e7	−0.753449
$797$	1.60806e7	0.896719	0.448359	−	0.893853i	$-0.352009\pi$
$797$	1.60806e7	0.896719	0.448359	+	0.893853i	$0.352009\pi$
$798$	−682833.	−0.0379583
$799$	−1.66761e7	−0.924117
$800$	−3.41828e6	−0.188835
$801$	−5.45191e6	−0.300239
$802$	−4.77164e6	−0.261958
$803$	4.97309e6	0.272168
$804$	−8.72288e6	−0.475904
$805$	−1.24118e6	−0.0675064
$806$	6.65512e6	0.360843
$807$	1.67145e6	0.0903459
$808$	−1.27727e7	−0.688263
$809$	−3.68316e6	−0.197856	−0.0989281	−	0.995095i	$-0.531541\pi$
$809$	−3.68316e6	−0.197856	−0.0989281	+	0.995095i	$0.531541\pi$
$810$	2.25637e6	0.120836
$811$	−3.02393e7	−1.61443	−0.807215	−	0.590258i	$-0.799026\pi$
$811$	−3.02393e7	−1.61443	−0.807215	+	0.590258i	$0.799026\pi$
$812$	7.76929e6	0.413515
$813$	−8.08176e6	−0.428824
$814$	−2.66434e6	−0.140938
$815$	−1.02178e7	−0.538845
$816$	−3.10744e6	−0.163372
$817$	−1.36052e6	−0.0713097
$818$	−2.47806e6	−0.129488
$819$	2.51658e7	1.31100
$820$	−1.41006e6	−0.0732323
$821$	3.02483e7	1.56618	0.783092	−	0.621906i	$-0.213641\pi$
$821$	3.02483e7	1.56618	0.783092	+	0.621906i	$0.213641\pi$
$822$	1.02620e6	0.0529726
$823$	9.41458e6	0.484508	0.242254	−	0.970213i	$-0.422113\pi$
$823$	9.41458e6	0.484508	0.242254	+	0.970213i	$0.422113\pi$
$824$	−2.27807e7	−1.16882
$825$	−386256.	−0.0197579
$826$	−1.55713e7	−0.794098
$827$	−9.84564e6	−0.500587	−0.250294	−	0.968170i	$-0.580527\pi$
$827$	−9.84564e6	−0.500587	−0.250294	+	0.968170i	$0.580527\pi$
$828$	1.74607e6	0.0885088
$829$	1.54028e7	0.778417	0.389208	−	0.921150i	$-0.372749\pi$
$829$	1.54028e7	0.778417	0.389208	+	0.921150i	$0.372749\pi$
$830$	−1.60863e6	−0.0810514
$831$	4.41793e6	0.221930
$832$	4.38823e6	0.219776
$833$	−1.17170e7	−0.585064
$834$	−1.42587e6	−0.0709847
$835$	−1.78059e7	−0.883788
$836$	1.18312e6	0.0585480
$837$	−1.01537e7	−0.500971
$838$	−1.04557e7	−0.514330
$839$	1.43705e7	0.704800	0.352400	−	0.935849i	$-0.385366\pi$
$839$	1.43705e7	0.704800	0.352400	+	0.935849i	$0.385366\pi$
$840$	−2.79401e6	−0.136625
$841$	−1.75628e7	−0.856255
$842$	−1.52880e7	−0.743141
$843$	8.30461e6	0.402485
$844$	−3.37843e6	−0.163252
$845$	−2.77586e6	−0.133738
$846$	7.59658e6	0.364915
$847$	2.44582e6	0.117143
$848$	−2.30834e7	−1.10233
$849$	6.04119e6	0.287642
$850$	1.46261e6	0.0694356
$851$	−2.95190e6	−0.139726
$852$	−480237.	−0.0226651
$853$	−2.95538e7	−1.39072	−0.695361	−	0.718661i	$-0.744755\pi$
$853$	−2.95538e7	−1.39072	−0.695361	+	0.718661i	$0.744755\pi$
$854$	2.41846e6	0.113473
$855$	1.95764e6	0.0915837
$856$	−2.15384e7	−1.00468
$857$	1.35703e7	0.631155	0.315578	−	0.948900i	$-0.397802\pi$
$857$	1.35703e7	0.631155	0.315578	+	0.948900i	$0.397802\pi$
$858$	−951501.	−0.0441257
$859$	−6.21341e6	−0.287307	−0.143654	−	0.989628i	$-0.545885\pi$
$859$	−6.21341e6	−0.287307	−0.143654	+	0.989628i	$0.545885\pi$
$860$	−2.55195e6	−0.117659
$861$	−1.77674e6	−0.0816803
$862$	−1.48713e7	−0.681681
$863$	−1.24077e7	−0.567106	−0.283553	−	0.958957i	$-0.591513\pi$
$863$	−1.24077e7	−0.567106	−0.283553	+	0.958957i	$0.591513\pi$
$864$	1.28473e7	0.585503
$865$	1.10458e7	0.501944
$866$	1.23510e7	0.559638
$867$	−1.56051e6	−0.0705047
$868$	−1.95583e7	−0.881112
$869$	1.04651e7	0.470105
$870$	−486054.	−0.0217714
$871$	−4.37911e7	−1.95587
$872$	−1.53050e6	−0.0681618
$873$	−6.97538e6	−0.309765
$874$	−237844.	−0.0105321
$875$	−2.61020e6	−0.115253
$876$	5.68573e6	0.250337
$877$	3.56450e7	1.56495	0.782473	−	0.622685i	$-0.213958\pi$
$877$	3.56450e7	1.56495	0.782473	+	0.622685i	$0.213958\pi$
$878$	−8.48862e6	−0.371621
$879$	−636094.	−0.0277683
$880$	1.74347e6	0.0758939
$881$	−2.29895e7	−0.997908	−0.498954	−	0.866628i	$-0.666282\pi$
$881$	−2.29895e7	−0.997908	−0.498954	+	0.866628i	$0.666282\pi$
$882$	5.33753e6	0.231030
$883$	1.64898e6	0.0711729	0.0355864	−	0.999367i	$-0.488670\pi$
$883$	1.64898e6	0.0711729	0.0355864	+	0.999367i	$0.488670\pi$
$884$	−1.98569e7	−0.854637
$885$	−5.36879e6	−0.230419
$886$	534934.	0.0228937
$887$	−2.31782e7	−0.989168	−0.494584	−	0.869130i	$-0.664680\pi$
$887$	−2.31782e7	−0.989168	−0.494584	+	0.869130i	$0.664680\pi$
$888$	−6.64499e6	−0.282789
$889$	−3.82047e7	−1.62130
$890$	1.39298e6	0.0589483
$891$	−4.92619e6	−0.207882
$892$	−1.73094e7	−0.728399
$893$	5.70289e6	0.239313
$894$	−697696.	−0.0291959
$895$	685884.	0.0286215
$896$	3.15769e7	1.31401
$897$	−1.05420e6	−0.0437462
$898$	−1.56336e6	−0.0646945
$899$	−7.42220e6	−0.306290
$900$	3.67199e6	0.151111
$901$	4.22784e7	1.73503
$902$	−558587.	−0.0228599
$903$	−3.21559e6	−0.131232
$904$	1.42524e7	0.580051
$905$	1.12620e7	0.457083
$906$	4.04202e6	0.163598
$907$	2.10215e7	0.848486	0.424243	−	0.905548i	$-0.360540\pi$
$907$	2.10215e7	0.848486	0.424243	+	0.905548i	$0.360540\pi$
$908$	−1.74391e7	−0.701954
$909$	2.11517e7	0.849054
$910$	−6.42997e6	−0.257398
$911$	2.29624e7	0.916688	0.458344	−	0.888775i	$-0.348443\pi$
$911$	2.29624e7	0.916688	0.458344	+	0.888775i	$0.348443\pi$
$912$	1.06269e6	0.0423075
$913$	3.51202e6	0.139438
$914$	−1.40885e6	−0.0557828
$915$	833855.	0.0329259
$916$	1.26422e7	0.497833
$917$	3.55416e7	1.39577
$918$	−5.49712e6	−0.215292
$919$	2.53360e7	0.989576	0.494788	−	0.869014i	$-0.335246\pi$
$919$	2.53360e7	0.989576	0.494788	+	0.869014i	$0.335246\pi$
$920$	−973206.	−0.0379084
$921$	6.64545e6	0.258152
$922$	7.63982e6	0.295976
$923$	−2.41091e6	−0.0931489
$924$	2.79630e6	0.107747
$925$	−6.20785e6	−0.238554
$926$	1.47326e7	0.564615
$927$	3.77249e7	1.44188
$928$	9.39117e6	0.357973
$929$	1.63197e7	0.620401	0.310201	−	0.950671i	$-0.399604\pi$
$929$	1.63197e7	0.620401	0.310201	+	0.950671i	$0.399604\pi$
$930$	1.22358e6	0.0463903
$931$	4.00698e6	0.151511
$932$	−2.95876e7	−1.11576
$933$	−2.68645e6	−0.101036
$934$	−6.95828e6	−0.260996
$935$	−3.19324e6	−0.119454
$936$	1.97325e7	0.736193
$937$	7.24919e6	0.269737	0.134869	−	0.990864i	$-0.456939\pi$
$937$	7.24919e6	0.269737	0.134869	+	0.990864i	$0.456939\pi$
$938$	−2.33514e7	−0.866574
$939$	1.26127e7	0.466814
$940$	1.06970e7	0.394861
$941$	−2.19216e7	−0.807046	−0.403523	−	0.914969i	$-0.632214\pi$
$941$	−2.19216e7	−0.807046	−0.403523	+	0.914969i	$0.632214\pi$
$942$	−5.92147e6	−0.217421
$943$	−618875.	−0.0226633
$944$	2.42334e7	0.885085
$945$	9.81024e6	0.357355
$946$	−1.01094e6	−0.0367281
$947$	5.21396e7	1.88926	0.944632	−	0.328131i	$-0.106419\pi$
$947$	5.21396e7	1.88926	0.944632	+	0.328131i	$0.106419\pi$
$948$	1.19647e7	0.432397
$949$	2.85438e7	1.02884
$950$	−500185.	−0.0179813
$951$	1.16653e7	0.418259
$952$	−2.30985e7	−0.826022
$953$	1.88658e7	0.672888	0.336444	−	0.941704i	$-0.390776\pi$
$953$	1.88658e7	0.672888	0.336444	+	0.941704i	$0.390776\pi$
$954$	−1.92594e7	−0.685128
$955$	−1.71627e7	−0.608944
$956$	−1.30138e7	−0.460533
$957$	1.06117e6	0.0374547
$958$	1.15967e7	0.408245
$959$	−1.51402e7	−0.531600
$960$	806803.	0.0282546
$961$	−9.94463e6	−0.347360
$962$	−1.52924e7	−0.532768
$963$	3.56678e7	1.23940
$964$	−1.19867e7	−0.415438
$965$	−8.50069e6	−0.293857
$966$	−562145.	−0.0193823
$967$	−2.40322e7	−0.826472	−0.413236	−	0.910624i	$-0.635602\pi$
$967$	−2.40322e7	−0.826472	−0.413236	+	0.910624i	$0.635602\pi$
$968$	1.91776e6	0.0657819
$969$	−1.94636e6	−0.0665906
$970$	1.78224e6	0.0608185
$971$	4.84656e7	1.64962	0.824812	−	0.565406i	$-0.191281\pi$
$971$	4.84656e7	1.64962	0.824812	+	0.565406i	$0.191281\pi$
$972$	−2.10927e7	−0.716089
$973$	2.10368e7	0.712358
$974$	1.11220e7	0.375652
$975$	−2.21697e6	−0.0746877
$976$	−3.76382e6	−0.126475
$977$	−3.09267e7	−1.03657	−0.518283	−	0.855209i	$-0.673429\pi$
$977$	−3.09267e7	−1.03657	−0.518283	+	0.855209i	$0.673429\pi$
$978$	−4.62776e6	−0.154712
$979$	−3.04122e6	−0.101412
$980$	7.51598e6	0.249989
$981$	2.53451e6	0.0840857
$982$	−1.70829e7	−0.565303
$983$	2.14564e7	0.708227	0.354113	−	0.935203i	$-0.384783\pi$
$983$	2.14564e7	0.708227	0.354113	+	0.935203i	$0.384783\pi$
$984$	−1.39314e6	−0.0458677
$985$	4.71311e6	0.154781
$986$	−4.01829e6	−0.131628
$987$	1.34788e7	0.440412
$988$	6.79068e6	0.221320
$989$	−1.12005e6	−0.0364122
$990$	1.45464e6	0.0471702
$991$	3.70775e7	1.19930	0.599648	−	0.800264i	$-0.295307\pi$
$991$	3.70775e7	1.19930	0.599648	+	0.800264i	$0.295307\pi$
$992$	−2.36412e7	−0.762763
$993$	−1.83116e6	−0.0589321
$994$	−1.28561e6	−0.0412708
$995$	−1.24320e7	−0.398092
$996$	4.01529e6	0.128253
$997$	2.54703e7	0.811514	0.405757	−	0.913981i	$-0.367008\pi$
$997$	2.54703e7	0.811514	0.405757	+	0.913981i	$0.367008\pi$
$998$	−1.57015e7	−0.499015
$999$	2.33317e7	0.739661

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.g.1.17	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.g.1.17	✓	39	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-2.21689 q^{2} +5.10751 q^{3} -27.0854 q^{4} -25.0000 q^{5} -11.3228 q^{6} +167.053 q^{7} +130.986 q^{8} -216.913 q^{9} +O(q^{10})\)	\(q-2.21689 q^{2} +5.10751 q^{3} -27.0854 q^{4} -25.0000 q^{5} -11.3228 q^{6} +167.053 q^{7} +130.986 q^{8} -216.913 q^{9} +55.4222 q^{10} -121.000 q^{11} -138.339 q^{12} -694.498 q^{13} -370.338 q^{14} -127.688 q^{15} +576.352 q^{16} -1055.62 q^{17} +480.873 q^{18} +361.000 q^{19} +677.135 q^{20} +853.225 q^{21} +268.243 q^{22} +297.195 q^{23} +669.011 q^{24} +625.000 q^{25} +1539.62 q^{26} -2349.01 q^{27} -4524.70 q^{28} -1717.08 q^{29} +283.070 q^{30} +4322.56 q^{31} -5469.25 q^{32} -618.009 q^{33} +2340.18 q^{34} -4176.32 q^{35} +5875.19 q^{36} -9932.56 q^{37} -800.297 q^{38} -3547.16 q^{39} -3274.64 q^{40} -2082.39 q^{41} -1891.50 q^{42} -3768.74 q^{43} +3277.33 q^{44} +5422.83 q^{45} -658.847 q^{46} +15797.5 q^{47} +2943.73 q^{48} +11099.7 q^{49} -1385.55 q^{50} -5391.57 q^{51} +18810.8 q^{52} -40050.9 q^{53} +5207.50 q^{54} +3025.00 q^{55} +21881.5 q^{56} +1843.81 q^{57} +3806.58 q^{58} +42046.2 q^{59} +3458.48 q^{60} -6530.42 q^{61} -9582.63 q^{62} -36236.0 q^{63} -6318.56 q^{64} +17362.4 q^{65} +1370.06 q^{66} +63054.4 q^{67} +28591.8 q^{68} +1517.92 q^{69} +9258.44 q^{70} +3471.45 q^{71} -28412.5 q^{72} -41099.9 q^{73} +22019.4 q^{74} +3192.19 q^{75} -9777.83 q^{76} -20213.4 q^{77} +7863.65 q^{78} -86488.5 q^{79} -14408.8 q^{80} +40712.3 q^{81} +4616.42 q^{82} -29025.0 q^{83} -23109.9 q^{84} +26390.4 q^{85} +8354.88 q^{86} -8770.03 q^{87} -15849.3 q^{88} +25134.0 q^{89} -12021.8 q^{90} -116018. q^{91} -8049.64 q^{92} +22077.5 q^{93} -35021.3 q^{94} -9025.00 q^{95} -27934.3 q^{96} +32157.4 q^{97} -24606.7 q^{98} +26246.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9}+O(q^{10}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9} - 300 q^{10} - 4719 q^{11} + 872 q^{12} - 717 q^{13} + 2647 q^{14} - 675 q^{15} + 15078 q^{16} + 2155 q^{17} + 3293 q^{18} + 14079 q^{19} - 16750 q^{20} + 6891 q^{21} - 1452 q^{22} + 1296 q^{23} - 3138 q^{24} + 24375 q^{25} + 2585 q^{26} + 3846 q^{27} - 20901 q^{28} - 7635 q^{29} - 1725 q^{30} + 9595 q^{31} - 43 q^{32} - 3267 q^{33} - 28383 q^{34} + 6275 q^{35} + 80573 q^{36} - 28965 q^{37} + 4332 q^{38} + 21358 q^{39} - 6750 q^{40} + 19627 q^{41} + 12478 q^{42} + 3711 q^{43} - 81070 q^{44} - 91650 q^{45} + 37459 q^{46} + 38450 q^{47} - 12259 q^{48} + 78758 q^{49} + 7500 q^{50} - 68114 q^{51} - 50322 q^{52} + 20631 q^{53} - 124732 q^{54} + 117975 q^{55} + 94893 q^{56} + 9747 q^{57} - 148140 q^{58} + 170405 q^{59} - 21800 q^{60} - 22345 q^{61} + 246390 q^{62} - 151688 q^{63} + 340312 q^{64} + 17925 q^{65} - 8349 q^{66} - 16408 q^{67} - 32276 q^{68} + 93536 q^{69} - 66175 q^{70} + 119338 q^{71} + 135668 q^{72} - 141606 q^{73} + 71843 q^{74} + 16875 q^{75} + 241870 q^{76} + 30371 q^{77} + 708290 q^{78} + 14727 q^{79} - 376950 q^{80} + 441659 q^{81} - 219870 q^{82} + 384909 q^{83} + 877024 q^{84} - 53875 q^{85} + 250290 q^{86} - 77038 q^{87} - 32670 q^{88} + 443394 q^{89} - 82325 q^{90} - 207088 q^{91} - 237112 q^{92} + 396718 q^{93} + 409516 q^{94} - 351975 q^{95} + 100332 q^{96} - 152942 q^{97} + 895680 q^{98} - 443586 q^{99}+O(q^{100}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9 - 300 * q^10 - 4719 * q^11 + 872 * q^12 - 717 * q^13 + 2647 * q^14 - 675 * q^15 + 15078 * q^16 + 2155 * q^17 + 3293 * q^18 + 14079 * q^19 - 16750 * q^20 + 6891 * q^21 - 1452 * q^22 + 1296 * q^23 - 3138 * q^24 + 24375 * q^25 + 2585 * q^26 + 3846 * q^27 - 20901 * q^28 - 7635 * q^29 - 1725 * q^30 + 9595 * q^31 - 43 * q^32 - 3267 * q^33 - 28383 * q^34 + 6275 * q^35 + 80573 * q^36 - 28965 * q^37 + 4332 * q^38 + 21358 * q^39 - 6750 * q^40 + 19627 * q^41 + 12478 * q^42 + 3711 * q^43 - 81070 * q^44 - 91650 * q^45 + 37459 * q^46 + 38450 * q^47 - 12259 * q^48 + 78758 * q^49 + 7500 * q^50 - 68114 * q^51 - 50322 * q^52 + 20631 * q^53 - 124732 * q^54 + 117975 * q^55 + 94893 * q^56 + 9747 * q^57 - 148140 * q^58 + 170405 * q^59 - 21800 * q^60 - 22345 * q^61 + 246390 * q^62 - 151688 * q^63 + 340312 * q^64 + 17925 * q^65 - 8349 * q^66 - 16408 * q^67 - 32276 * q^68 + 93536 * q^69 - 66175 * q^70 + 119338 * q^71 + 135668 * q^72 - 141606 * q^73 + 71843 * q^74 + 16875 * q^75 + 241870 * q^76 + 30371 * q^77 + 708290 * q^78 + 14727 * q^79 - 376950 * q^80 + 441659 * q^81 - 219870 * q^82 + 384909 * q^83 + 877024 * q^84 - 53875 * q^85 + 250290 * q^86 - 77038 * q^87 - 32670 * q^88 + 443394 * q^89 - 82325 * q^90 - 207088 * q^91 - 237112 * q^92 + 396718 * q^93 + 409516 * q^94 - 351975 * q^95 + 100332 * q^96 - 152942 * q^97 + 895680 * q^98 - 443586 * q^99

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