LMFDB - Embedded newform 1045.6.a.e.1.2

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:	$1$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-10.8606 q^{2} +27.1939 q^{3} +85.9518 q^{4} +25.0000 q^{5} -295.341 q^{6} -206.298 q^{7} -585.946 q^{8} +496.509 q^{9} +O(q^{10})$	\(q-10.8606 q^{2} +27.1939 q^{3} +85.9518 q^{4} +25.0000 q^{5} -295.341 q^{6} -206.298 q^{7} -585.946 q^{8} +496.509 q^{9} -271.514 q^{10} +121.000 q^{11} +2337.36 q^{12} -408.237 q^{13} +2240.51 q^{14} +679.848 q^{15} +3613.25 q^{16} +1567.58 q^{17} -5392.36 q^{18} -361.000 q^{19} +2148.79 q^{20} -5610.06 q^{21} -1314.13 q^{22} -2541.47 q^{23} -15934.2 q^{24} +625.000 q^{25} +4433.69 q^{26} +6893.90 q^{27} -17731.7 q^{28} +4581.22 q^{29} -7383.53 q^{30} -4714.60 q^{31} -20491.6 q^{32} +3290.46 q^{33} -17024.8 q^{34} -5157.46 q^{35} +42675.8 q^{36} +490.812 q^{37} +3920.66 q^{38} -11101.6 q^{39} -14648.7 q^{40} -11682.0 q^{41} +60928.4 q^{42} -21163.4 q^{43} +10400.2 q^{44} +12412.7 q^{45} +27601.7 q^{46} +27536.5 q^{47} +98258.4 q^{48} +25752.0 q^{49} -6787.85 q^{50} +42628.6 q^{51} -35088.7 q^{52} +10377.5 q^{53} -74871.6 q^{54} +3025.00 q^{55} +120880. q^{56} -9817.00 q^{57} -49754.6 q^{58} -74.2036 q^{59} +58434.1 q^{60} +47574.4 q^{61} +51203.1 q^{62} -102429. q^{63} +106927. q^{64} -10205.9 q^{65} -35736.3 q^{66} -50141.8 q^{67} +134736. q^{68} -69112.4 q^{69} +56012.9 q^{70} -20052.3 q^{71} -290927. q^{72} +30408.2 q^{73} -5330.49 q^{74} +16996.2 q^{75} -31028.6 q^{76} -24962.1 q^{77} +120569. q^{78} -41210.0 q^{79} +90331.2 q^{80} +66820.3 q^{81} +126873. q^{82} -101109. q^{83} -482194. q^{84} +39189.5 q^{85} +229846. q^{86} +124581. q^{87} -70899.5 q^{88} +37971.6 q^{89} -134809. q^{90} +84218.7 q^{91} -218443. q^{92} -128208. q^{93} -299061. q^{94} -9025.00 q^{95} -557247. q^{96} -149013. q^{97} -279681. q^{98} +60077.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9}+O(q^{10}) $ 38 * q - 24 * q^2 - 63 * q^3 + 594 * q^4 + 950 * q^5 - 67 * q^6 - 729 * q^7 - 1272 * q^8 + 3029 * q^9	\( 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9} - 600 q^{10} + 4598 q^{11} - 2008 q^{12} - 2663 q^{13} - 1565 q^{14} - 1575 q^{15} + 12390 q^{16} - 3311 q^{17} - 6383 q^{18} - 13718 q^{19} + 14850 q^{20} - 8179 q^{21} - 2904 q^{22} - 3412 q^{23} - 4100 q^{24} + 23750 q^{25} - 1399 q^{26} - 31596 q^{27} - 43653 q^{28} - 13633 q^{29} - 1675 q^{30} - 13789 q^{31} - 58603 q^{32} - 7623 q^{33} - 29149 q^{34} - 18225 q^{35} + 50641 q^{36} - 12103 q^{37} + 8664 q^{38} - 50960 q^{39} - 31800 q^{40} - 37885 q^{41} + 51100 q^{42} - 56119 q^{43} + 71874 q^{44} + 75725 q^{45} - 56291 q^{46} - 37532 q^{47} - 113895 q^{48} + 153501 q^{49} - 15000 q^{50} + 32882 q^{51} - 169554 q^{52} - 51511 q^{53} - 175060 q^{54} + 114950 q^{55} - 84247 q^{56} + 22743 q^{57} - 256962 q^{58} - 154267 q^{59} - 50200 q^{60} - 47165 q^{61} + 143002 q^{62} - 358780 q^{63} + 142292 q^{64} - 66575 q^{65} - 8107 q^{66} - 161712 q^{67} - 210188 q^{68} - 124602 q^{69} - 39125 q^{70} + 6118 q^{71} - 327878 q^{72} - 152182 q^{73} - 167349 q^{74} - 39375 q^{75} - 214434 q^{76} - 88209 q^{77} - 216594 q^{78} - 140433 q^{79} + 309750 q^{80} + 382874 q^{81} - 29842 q^{82} - 515287 q^{83} + 29222 q^{84} - 82775 q^{85} + 204974 q^{86} - 106764 q^{87} - 153912 q^{88} - 271610 q^{89} - 159575 q^{90} - 44332 q^{91} + 236348 q^{92} + 25202 q^{93} - 496224 q^{94} - 342950 q^{95} - 275218 q^{96} - 126390 q^{97} - 285506 q^{98} + 366509 q^{99}+O(q^{100}) \) 38 * q - 24 * q^2 - 63 * q^3 + 594 * q^4 + 950 * q^5 - 67 * q^6 - 729 * q^7 - 1272 * q^8 + 3029 * q^9 - 600 * q^10 + 4598 * q^11 - 2008 * q^12 - 2663 * q^13 - 1565 * q^14 - 1575 * q^15 + 12390 * q^16 - 3311 * q^17 - 6383 * q^18 - 13718 * q^19 + 14850 * q^20 - 8179 * q^21 - 2904 * q^22 - 3412 * q^23 - 4100 * q^24 + 23750 * q^25 - 1399 * q^26 - 31596 * q^27 - 43653 * q^28 - 13633 * q^29 - 1675 * q^30 - 13789 * q^31 - 58603 * q^32 - 7623 * q^33 - 29149 * q^34 - 18225 * q^35 + 50641 * q^36 - 12103 * q^37 + 8664 * q^38 - 50960 * q^39 - 31800 * q^40 - 37885 * q^41 + 51100 * q^42 - 56119 * q^43 + 71874 * q^44 + 75725 * q^45 - 56291 * q^46 - 37532 * q^47 - 113895 * q^48 + 153501 * q^49 - 15000 * q^50 + 32882 * q^51 - 169554 * q^52 - 51511 * q^53 - 175060 * q^54 + 114950 * q^55 - 84247 * q^56 + 22743 * q^57 - 256962 * q^58 - 154267 * q^59 - 50200 * q^60 - 47165 * q^61 + 143002 * q^62 - 358780 * q^63 + 142292 * q^64 - 66575 * q^65 - 8107 * q^66 - 161712 * q^67 - 210188 * q^68 - 124602 * q^69 - 39125 * q^70 + 6118 * q^71 - 327878 * q^72 - 152182 * q^73 - 167349 * q^74 - 39375 * q^75 - 214434 * q^76 - 88209 * q^77 - 216594 * q^78 - 140433 * q^79 + 309750 * q^80 + 382874 * q^81 - 29842 * q^82 - 515287 * q^83 + 29222 * q^84 - 82775 * q^85 + 204974 * q^86 - 106764 * q^87 - 153912 * q^88 - 271610 * q^89 - 159575 * q^90 - 44332 * q^91 + 236348 * q^92 + 25202 * q^93 - 496224 * q^94 - 342950 * q^95 - 275218 * q^96 - 126390 * q^97 - 285506 * q^98 + 366509 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−10.8606	−1.91989	−0.959947	−	0.280182i	$-0.909605\pi$
$2$	−10.8606	−1.91989	−0.959947	+	0.280182i	$0.909605\pi$
$3$	27.1939	1.74449	0.872245	−	0.489069i	$-0.162663\pi$
$3$	27.1939	1.74449	0.872245	+	0.489069i	$0.162663\pi$
$4$	85.9518	2.68599
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−295.341	−3.34924
$7$	−206.298	−1.59129	−0.795647	−	0.605760i	$-0.792869\pi$
$7$	−206.298	−1.59129	−0.795647	+	0.605760i	$0.792869\pi$
$8$	−585.946	−3.23693
$9$	496.509	2.04325
$10$	−271.514	−0.858603
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	2337.36	4.68569
$13$	−408.237	−0.669968	−0.334984	−	0.942224i	$-0.608731\pi$
$13$	−408.237	−0.669968	−0.334984	+	0.942224i	$0.608731\pi$
$14$	2240.51	3.05512
$15$	679.848	0.780160
$16$	3613.25	3.52856
$17$	1567.58	1.31555	0.657775	−	0.753214i	$-0.271498\pi$
$17$	1567.58	1.31555	0.657775	+	0.753214i	$0.271498\pi$
$18$	−5392.36	−3.92282
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	2148.79	1.20121
$21$	−5610.06	−2.77600
$22$	−1314.13	−0.578870
$23$	−2541.47	−1.00176	−0.500881	−	0.865516i	$-0.666991\pi$
$23$	−2541.47	−1.00176	−0.500881	+	0.865516i	$0.666991\pi$
$24$	−15934.2	−5.64679
$25$	625.000	0.200000
$26$	4433.69	1.28627
$27$	6893.90	1.81993
$28$	−17731.7	−4.27420
$29$	4581.22	1.01155	0.505773	−	0.862666i	$-0.331207\pi$
$29$	4581.22	1.01155	0.505773	+	0.862666i	$0.331207\pi$
$30$	−7383.53	−1.49782
$31$	−4714.60	−0.881130	−0.440565	−	0.897721i	$-0.645222\pi$
$31$	−4714.60	−0.881130	−0.440565	+	0.897721i	$0.645222\pi$
$32$	−20491.6	−3.53754
$33$	3290.46	0.525984
$34$	−17024.8	−2.52572
$35$	−5157.46	−0.711648
$36$	42675.8	5.48814
$37$	490.812	0.0589401	0.0294700	−	0.999566i	$-0.490618\pi$
$37$	490.812	0.0589401	0.0294700	+	0.999566i	$0.490618\pi$
$38$	3920.66	0.440454
$39$	−11101.6	−1.16875
$40$	−14648.7	−1.44760
$41$	−11682.0	−1.08532	−0.542659	−	0.839953i	$-0.682582\pi$
$41$	−11682.0	−1.08532	−0.542659	+	0.839953i	$0.682582\pi$
$42$	60928.4	5.32962
$43$	−21163.4	−1.74547	−0.872737	−	0.488191i	$-0.837657\pi$
$43$	−21163.4	−1.74547	−0.872737	+	0.488191i	$0.837657\pi$
$44$	10400.2	0.809857
$45$	12412.7	0.913767
$46$	27601.7	1.92328
$47$	27536.5	1.81829	0.909146	−	0.416478i	$-0.136736\pi$
$47$	27536.5	1.81829	0.909146	+	0.416478i	$0.136736\pi$
$48$	98258.4	6.15554
$49$	25752.0	1.53222
$50$	−6787.85	−0.383979
$51$	42628.6	2.29497
$52$	−35088.7	−1.79953
$53$	10377.5	0.507459	0.253730	−	0.967275i	$-0.418343\pi$
$53$	10377.5	0.507459	0.253730	+	0.967275i	$0.418343\pi$
$54$	−74871.6	−3.49408
$55$	3025.00	0.134840
$56$	120880.	5.15090
$57$	−9817.00	−0.400213
$58$	−49754.6	−1.94206
$59$	−74.2036	−0.00277521	−0.00138760	−	0.999999i	$-0.500442\pi$
$59$	−74.2036	−0.00277521	−0.00138760	+	0.999999i	$0.500442\pi$
$60$	58434.1	2.09550
$61$	47574.4	1.63700	0.818500	−	0.574506i	$-0.194806\pi$
$61$	47574.4	1.63700	0.818500	+	0.574506i	$0.194806\pi$
$62$	51203.1	1.69168
$63$	−102429.	−3.25141
$64$	106927.	3.26314
$65$	−10205.9	−0.299619
$66$	−35736.3	−1.00983
$67$	−50141.8	−1.36462	−0.682312	−	0.731061i	$-0.739025\pi$
$67$	−50141.8	−1.36462	−0.682312	+	0.731061i	$0.739025\pi$
$68$	134736.	3.53356
$69$	−69112.4	−1.74756
$70$	56012.9	1.36629
$71$	−20052.3	−0.472084	−0.236042	−	0.971743i	$-0.575850\pi$
$71$	−20052.3	−0.472084	−0.236042	+	0.971743i	$0.575850\pi$
$72$	−290927.	−6.61384
$73$	30408.2	0.667858	0.333929	−	0.942598i	$-0.391625\pi$
$73$	30408.2	0.667858	0.333929	+	0.942598i	$0.391625\pi$
$74$	−5330.49	−0.113159
$75$	16996.2	0.348898
$76$	−31028.6	−0.616209
$77$	−24962.1	−0.479793
$78$	120569.	2.24388
$79$	−41210.0	−0.742907	−0.371454	−	0.928452i	$-0.621141\pi$
$79$	−41210.0	−0.742907	−0.371454	+	0.928452i	$0.621141\pi$
$80$	90331.2	1.57802
$81$	66820.3	1.13161
$82$	126873.	2.08369
$83$	−101109.	−1.61100	−0.805500	−	0.592596i	$-0.798103\pi$
$83$	−101109.	−1.61100	−0.805500	+	0.592596i	$0.798103\pi$
$84$	−482194.	−7.45631
$85$	39189.5	0.588332
$86$	229846.	3.35112
$87$	124581.	1.76463
$88$	−70899.5	−0.975970
$89$	37971.6	0.508140	0.254070	−	0.967186i	$-0.418231\pi$
$89$	37971.6	0.508140	0.254070	+	0.967186i	$0.418231\pi$
$90$	−134809.	−1.75434
$91$	84218.7	1.06612
$92$	−218443.	−2.69073
$93$	−128208.	−1.53712
$94$	−299061.	−3.49093
$95$	−9025.00	−0.102598
$96$	−557247.	−6.17120
$97$	−149013.	−1.60803	−0.804015	−	0.594610i	$-0.797307\pi$
$97$	−149013.	−1.60803	−0.804015	+	0.594610i	$0.797307\pi$
$98$	−279681.	−2.94169
$99$	60077.6	0.616062
$100$	53719.8	0.537198
$101$	−24259.1	−0.236631	−0.118315	−	0.992976i	$-0.537749\pi$
$101$	−24259.1	−0.236631	−0.118315	+	0.992976i	$0.537749\pi$
$102$	−462971.	−4.40609
$103$	−114936.	−1.06749	−0.533743	−	0.845647i	$-0.679215\pi$
$103$	−114936.	−1.06749	−0.533743	+	0.845647i	$0.679215\pi$
$104$	239205.	2.16864
$105$	−140251.	−1.24146
$106$	−112705.	−0.974268
$107$	−118257.	−0.998548	−0.499274	−	0.866444i	$-0.666400\pi$
$107$	−118257.	−0.998548	−0.499274	+	0.866444i	$0.666400\pi$
$108$	592542.	4.88832
$109$	166357.	1.34114	0.670572	−	0.741845i	$-0.266049\pi$
$109$	166357.	1.34114	0.670572	+	0.741845i	$0.266049\pi$
$110$	−32853.2	−0.258878
$111$	13347.1	0.102820
$112$	−745407.	−5.61498
$113$	238291.	1.75555	0.877773	−	0.479076i	$-0.159028\pi$
$113$	238291.	1.75555	0.877773	+	0.479076i	$0.159028\pi$
$114$	106618.	0.768367
$115$	−63536.6	−0.448002
$116$	393764.	2.71701
$117$	−202693.	−1.36891
$118$	805.893	0.00532810
$119$	−323389.	−2.09343
$120$	−398354.	−2.52532
$121$	14641.0	0.0909091
$122$	−516685.	−3.14287
$123$	−317679.	−1.89333
$124$	−405228.	−2.36671
$125$	15625.0	0.0894427
$126$	1.11244e6	6.24235
$127$	140605.	0.773556	0.386778	−	0.922173i	$-0.373588\pi$
$127$	140605.	0.773556	0.386778	+	0.922173i	$0.373588\pi$
$128$	−505550.	−2.72734
$129$	−575514.	−3.04496
$130$	110842.	0.575237
$131$	41443.2	0.210996	0.105498	−	0.994419i	$-0.466356\pi$
$131$	41443.2	0.210996	0.105498	+	0.994419i	$0.466356\pi$
$132$	282821.	1.41279
$133$	74473.7	0.365068
$134$	544568.	2.61993
$135$	172347.	0.813899
$136$	−918518.	−4.25834
$137$	−382748.	−1.74225	−0.871126	−	0.491059i	$-0.836610\pi$
$137$	−382748.	−1.74225	−0.871126	+	0.491059i	$0.836610\pi$
$138$	750599.	3.35514
$139$	−55909.6	−0.245442	−0.122721	−	0.992441i	$-0.539162\pi$
$139$	−55909.6	−0.245442	−0.122721	+	0.992441i	$0.539162\pi$
$140$	−443292.	−1.91148
$141$	748824.	3.17199
$142$	217780.	0.906351
$143$	−49396.7	−0.202003
$144$	1.79401e6	7.20972
$145$	114530.	0.452377
$146$	−330251.	−1.28222
$147$	700297.	2.67294
$148$	42186.2	0.158313
$149$	218115.	0.804860	0.402430	−	0.915451i	$-0.368166\pi$
$149$	218115.	0.804860	0.402430	+	0.915451i	$0.368166\pi$
$150$	−184588.	−0.669847
$151$	−111973.	−0.399640	−0.199820	−	0.979833i	$-0.564036\pi$
$151$	−111973.	−0.399640	−0.199820	+	0.979833i	$0.564036\pi$
$152$	211527.	0.742602
$153$	778318.	2.68799
$154$	271102.	0.921152
$155$	−117865.	−0.394053
$156$	−954199.	−3.13926
$157$	546460.	1.76933	0.884666	−	0.466226i	$-0.154387\pi$
$157$	546460.	1.76933	0.884666	+	0.466226i	$0.154387\pi$
$158$	447563.	1.42630
$159$	282204.	0.885258
$160$	−512291.	−1.58204
$161$	524300.	1.59410
$162$	−725706.	−2.17257
$163$	−224897.	−0.663002	−0.331501	−	0.943455i	$-0.607555\pi$
$163$	−224897.	−0.663002	−0.331501	+	0.943455i	$0.607555\pi$
$164$	−1.00409e6	−2.91515
$165$	82261.6	0.235227
$166$	1.09810e6	3.09295
$167$	−504301.	−1.39926	−0.699630	−	0.714505i	$-0.746652\pi$
$167$	−504301.	−1.39926	−0.699630	+	0.714505i	$0.746652\pi$
$168$	3.28719e6	8.98570
$169$	−204635.	−0.551142
$170$	−425620.	−1.12954
$171$	−179240.	−0.468753
$172$	−1.81903e6	−4.68833
$173$	−564549.	−1.43412	−0.717061	−	0.697010i	$-0.754513\pi$
$173$	−564549.	−1.43412	−0.717061	+	0.697010i	$0.754513\pi$
$174$	−1.35302e6	−3.38791
$175$	−128936.	−0.318259
$176$	437203.	1.06390
$177$	−2017.89	−0.00484132
$178$	−412393.	−0.975575
$179$	−64849.4	−0.151277	−0.0756386	−	0.997135i	$-0.524100\pi$
$179$	−64849.4	−0.151277	−0.0756386	+	0.997135i	$0.524100\pi$
$180$	1.06690e6	2.45437
$181$	37008.4	0.0839662	0.0419831	−	0.999118i	$-0.486632\pi$
$181$	37008.4	0.0839662	0.0419831	+	0.999118i	$0.486632\pi$
$182$	−914662.	−2.04683
$183$	1.29373e6	2.85573
$184$	1.48916e6	3.24263
$185$	12270.3	0.0263588
$186$	1.39241e6	2.95111
$187$	189677.	0.396653
$188$	2.36681e6	4.88392
$189$	−1.42220e6	−2.89605
$190$	98016.6	0.196977
$191$	−660056.	−1.30917	−0.654587	−	0.755987i	$-0.727157\pi$
$191$	−660056.	−1.30917	−0.654587	+	0.755987i	$0.727157\pi$
$192$	2.90775e6	5.69251
$193$	−832746.	−1.60923	−0.804617	−	0.593794i	$-0.797630\pi$
$193$	−832746.	−1.60923	−0.804617	+	0.593794i	$0.797630\pi$
$194$	1.61836e6	3.08725
$195$	−277539.	−0.522682
$196$	2.21343e6	4.11552
$197$	−419852.	−0.770780	−0.385390	−	0.922754i	$-0.625933\pi$
$197$	−419852.	−0.770780	−0.385390	+	0.922754i	$0.625933\pi$
$198$	−652476.	−1.18277
$199$	−397097.	−0.710828	−0.355414	−	0.934709i	$-0.615660\pi$
$199$	−397097.	−0.710828	−0.355414	+	0.934709i	$0.615660\pi$
$200$	−366216.	−0.647385
$201$	−1.36355e6	−2.38057
$202$	263468.	0.454306
$203$	−945097.	−1.60967
$204$	3.66401e6	6.16426
$205$	−292049.	−0.485369
$206$	1.24827e6	2.04946
$207$	−1.26186e6	−2.04685
$208$	−1.47506e6	−2.36403
$209$	−43681.0	−0.0691714
$210$	1.52321e6	2.38348
$211$	139757.	0.216106	0.108053	−	0.994145i	$-0.465538\pi$
$211$	139757.	0.216106	0.108053	+	0.994145i	$0.465538\pi$
$212$	891961.	1.36303
$213$	−545302.	−0.823546
$214$	1.28434e6	1.91711
$215$	−529084.	−0.780600
$216$	−4.03945e6	−5.89099
$217$	972613.	1.40214
$218$	−1.80673e6	−2.57485
$219$	826919.	1.16507
$220$	260004.	0.362179
$221$	−639945.	−0.881377
$222$	−144957.	−0.197404
$223$	501213.	0.674932	0.337466	−	0.941338i	$-0.390430\pi$
$223$	501213.	0.674932	0.337466	+	0.941338i	$0.390430\pi$
$224$	4.22739e6	5.62927
$225$	310318.	0.408649
$226$	−2.58798e6	−3.37046
$227$	435429.	0.560858	0.280429	−	0.959875i	$-0.409523\pi$
$227$	435429.	0.560858	0.280429	+	0.959875i	$0.409523\pi$
$228$	−843789.	−1.07497
$229$	−864868.	−1.08984	−0.544918	−	0.838489i	$-0.683439\pi$
$229$	−864868.	−1.08984	−0.544918	+	0.838489i	$0.683439\pi$
$230$	690044.	0.860116
$231$	−678817.	−0.836995
$232$	−2.68435e6	−3.27430
$233$	332203.	0.400880	0.200440	−	0.979706i	$-0.435763\pi$
$233$	332203.	0.400880	0.200440	+	0.979706i	$0.435763\pi$
$234$	2.20136e6	2.62816
$235$	688412.	0.813165
$236$	−6377.93	−0.00745418
$237$	−1.12066e6	−1.29599
$238$	3.51219e6	4.01916
$239$	367382.	0.416029	0.208014	−	0.978126i	$-0.433300\pi$
$239$	367382.	0.416029	0.208014	+	0.978126i	$0.433300\pi$
$240$	2.45646e6	2.75284
$241$	−583630.	−0.647284	−0.323642	−	0.946180i	$-0.604907\pi$
$241$	−583630.	−0.647284	−0.323642	+	0.946180i	$0.604907\pi$
$242$	−159009.	−0.174536
$243$	141890.	0.154147
$244$	4.08910e6	4.39697
$245$	643799.	0.685228
$246$	3.45017e6	3.63498
$247$	147374.	0.153701
$248$	2.76250e6	2.85215
$249$	−2.74956e6	−2.81037
$250$	−169696.	−0.171721
$251$	−281672.	−0.282201	−0.141101	−	0.989995i	$-0.545064\pi$
$251$	−281672.	−0.282201	−0.141101	+	0.989995i	$0.545064\pi$
$252$	−8.80394e6	−8.73325
$253$	−307517.	−0.302043
$254$	−1.52705e6	−1.48514
$255$	1.06572e6	1.02634
$256$	2.06891e6	1.97306
$257$	−1.19452e6	−1.12813	−0.564067	−	0.825729i	$-0.690764\pi$
$257$	−1.19452e6	−1.12813	−0.564067	+	0.825729i	$0.690764\pi$
$258$	6.25041e6	5.84600
$259$	−101254.	−0.0937910
$260$	−877218.	−0.804774
$261$	2.27461e6	2.06684
$262$	−450096.	−0.405091
$263$	465453.	0.414941	0.207471	−	0.978241i	$-0.433477\pi$
$263$	465453.	0.414941	0.207471	+	0.978241i	$0.433477\pi$
$264$	−1.92803e6	−1.70257
$265$	259436.	0.226943
$266$	−808826.	−0.700892
$267$	1.03260e6	0.886446
$268$	−4.30977e6	−3.66537
$269$	−1.45085e6	−1.22248	−0.611241	−	0.791444i	$-0.709330\pi$
$269$	−1.45085e6	−1.22248	−0.611241	+	0.791444i	$0.709330\pi$
$270$	−1.87179e6	−1.56260
$271$	−572165.	−0.473258	−0.236629	−	0.971600i	$-0.576043\pi$
$271$	−572165.	−0.473258	−0.236629	+	0.971600i	$0.576043\pi$
$272$	5.66406e6	4.64200
$273$	2.29023e6	1.85983
$274$	4.15685e6	3.34494
$275$	75625.0	0.0603023
$276$	−5.94033e6	−4.69395
$277$	2.36440e6	1.85149	0.925747	−	0.378144i	$-0.123438\pi$
$277$	2.36440e6	1.85149	0.925747	+	0.378144i	$0.123438\pi$
$278$	607209.	0.471223
$279$	−2.34084e6	−1.80037
$280$	3.02199e6	2.30355
$281$	246360.	0.186125	0.0930623	−	0.995660i	$-0.470334\pi$
$281$	246360.	0.186125	0.0930623	+	0.995660i	$0.470334\pi$
$282$	−8.13265e6	−6.08989
$283$	−1.24324e6	−0.922760	−0.461380	−	0.887203i	$-0.652646\pi$
$283$	−1.24324e6	−0.922760	−0.461380	+	0.887203i	$0.652646\pi$
$284$	−1.72353e6	−1.26801
$285$	−245425.	−0.178981
$286$	536476.	0.387824
$287$	2.40997e6	1.72706
$288$	−1.01743e7	−7.22806
$289$	1.03745e6	0.730674
$290$	−1.24386e6	−0.868516
$291$	−4.05224e6	−2.80519
$292$	2.61364e6	1.79386
$293$	−32060.4	−0.0218172	−0.0109086	−	0.999940i	$-0.503472\pi$
$293$	−32060.4	−0.0218172	−0.0109086	+	0.999940i	$0.503472\pi$
$294$	−7.60562e6	−5.13176
$295$	−1855.09	−0.00124111
$296$	−287589.	−0.190785
$297$	834161.	0.548730
$298$	−2.36885e6	−1.54525
$299$	1.03752e6	0.671149
$300$	1.46085e6	0.937138
$301$	4.36596e6	2.77756
$302$	1.21608e6	0.767267
$303$	−659700.	−0.412800
$304$	−1.30438e6	−0.809508
$305$	1.18936e6	0.732089
$306$	−8.45296e6	−5.16066
$307$	−1.00441e6	−0.608228	−0.304114	−	0.952636i	$-0.598360\pi$
$307$	−1.00441e6	−0.608228	−0.304114	+	0.952636i	$0.598360\pi$
$308$	−2.14554e6	−1.28872
$309$	−3.12555e6	−1.86222
$310$	1.28008e6	0.756541
$311$	−2.72507e6	−1.59763	−0.798816	−	0.601575i	$-0.794540\pi$
$311$	−2.72507e6	−1.59763	−0.798816	+	0.601575i	$0.794540\pi$
$312$	6.50492e6	3.78317
$313$	1.11018e6	0.640518	0.320259	−	0.947330i	$-0.396230\pi$
$313$	1.11018e6	0.640518	0.320259	+	0.947330i	$0.396230\pi$
$314$	−5.93486e6	−3.39693
$315$	−2.56072e6	−1.45407
$316$	−3.54207e6	−1.99544
$317$	2.00207e6	1.11900	0.559500	−	0.828830i	$-0.310993\pi$
$317$	2.00207e6	1.11900	0.559500	+	0.828830i	$0.310993\pi$
$318$	−3.06489e6	−1.69960
$319$	554327.	0.304993
$320$	2.67316e6	1.45932
$321$	−3.21588e6	−1.74196
$322$	−5.69419e6	−3.06050
$323$	−565897.	−0.301808
$324$	5.74333e6	3.03949
$325$	−255148.	−0.133994
$326$	2.44251e6	1.27289
$327$	4.52390e6	2.33961
$328$	6.84501e6	3.51309
$329$	−5.68073e6	−2.89344
$330$	−893407.	−0.451611
$331$	103312.	0.0518300	0.0259150	−	0.999664i	$-0.491750\pi$
$331$	103312.	0.0518300	0.0259150	+	0.999664i	$0.491750\pi$
$332$	−8.69052e6	−4.32713
$333$	243692.	0.120429
$334$	5.47699e6	2.68643
$335$	−1.25354e6	−0.610278
$336$	−2.02705e7	−9.79528
$337$	−2.05576e6	−0.986046	−0.493023	−	0.870016i	$-0.664108\pi$
$337$	−2.05576e6	−0.986046	−0.493023	+	0.870016i	$0.664108\pi$
$338$	2.22245e6	1.05813
$339$	6.48008e6	3.06253
$340$	3.36841e6	1.58026
$341$	−570466.	−0.265671
$342$	1.94664e6	0.899956
$343$	−1.84533e6	−0.846915
$344$	1.24006e7	5.64997
$345$	−1.72781e6	−0.781535
$346$	6.13132e6	2.75336
$347$	−1.17926e6	−0.525757	−0.262879	−	0.964829i	$-0.584672\pi$
$347$	−1.17926e6	−0.525757	−0.262879	+	0.964829i	$0.584672\pi$
$348$	1.07080e7	4.73979
$349$	4.04136e6	1.77609	0.888043	−	0.459761i	$-0.152065\pi$
$349$	4.04136e6	1.77609	0.888043	+	0.459761i	$0.152065\pi$
$350$	1.40032e6	0.611023
$351$	−2.81435e6	−1.21930
$352$	−2.47949e6	−1.06661
$353$	2.72359e6	1.16334	0.581668	−	0.813426i	$-0.302400\pi$
$353$	2.72359e6	1.16334	0.581668	+	0.813426i	$0.302400\pi$
$354$	21915.4	0.00929482
$355$	−501309.	−0.211122
$356$	3.26372e6	1.36486
$357$	−8.79422e6	−3.65197
$358$	704300.	0.290436
$359$	−1.77817e6	−0.728178	−0.364089	−	0.931364i	$-0.618620\pi$
$359$	−1.77817e6	−0.728178	−0.364089	+	0.931364i	$0.618620\pi$
$360$	−7.27319e6	−2.95780
$361$	130321.	0.0526316
$362$	−401932.	−0.161206
$363$	398146.	0.158590
$364$	7.23874e6	2.86358
$365$	760206.	0.298675
$366$	−1.40507e7	−5.48270
$367$	1.61301e6	0.625131	0.312565	−	0.949896i	$-0.398812\pi$
$367$	1.61301e6	0.625131	0.312565	+	0.949896i	$0.398812\pi$
$368$	−9.18295e6	−3.53478
$369$	−5.80020e6	−2.21757
$370$	−133262.	−0.0506061
$371$	−2.14085e6	−0.807517
$372$	−1.10197e7	−4.12870
$373$	−3.82168e6	−1.42227	−0.711135	−	0.703056i	$-0.751818\pi$
$373$	−3.82168e6	−1.42227	−0.711135	+	0.703056i	$0.751818\pi$
$374$	−2.06000e6	−0.761533
$375$	424905.	0.156032
$376$	−1.61349e7	−5.88568
$377$	−1.87022e6	−0.677704
$378$	1.54459e7	5.56011
$379$	2.49903e6	0.893662	0.446831	−	0.894618i	$-0.352552\pi$
$379$	2.49903e6	0.893662	0.446831	+	0.894618i	$0.352552\pi$
$380$	−775715.	−0.275577
$381$	3.82360e6	1.34946
$382$	7.16857e6	2.51347
$383$	−4.32573e6	−1.50682	−0.753411	−	0.657550i	$-0.771593\pi$
$383$	−4.32573e6	−1.50682	−0.753411	+	0.657550i	$0.771593\pi$
$384$	−1.37479e7	−4.75782
$385$	−624052.	−0.214570
$386$	9.04409e6	3.08956
$387$	−1.05078e7	−3.56643
$388$	−1.28079e7	−4.31915
$389$	3.80671e6	1.27549	0.637743	−	0.770249i	$-0.279868\pi$
$389$	3.80671e6	1.27549	0.637743	+	0.770249i	$0.279868\pi$
$390$	3.01423e6	1.00349
$391$	−3.98395e6	−1.31787
$392$	−1.50893e7	−4.95968
$393$	1.12700e6	0.368081
$394$	4.55983e6	1.47982
$395$	−1.03025e6	−0.332238
$396$	5.16377e6	1.65474
$397$	−3.67790e6	−1.17118	−0.585590	−	0.810608i	$-0.699137\pi$
$397$	−3.67790e6	−1.17118	−0.585590	+	0.810608i	$0.699137\pi$
$398$	4.31270e6	1.36471
$399$	2.02523e6	0.636857
$400$	2.25828e6	0.705713
$401$	−2.67650e6	−0.831201	−0.415600	−	0.909547i	$-0.636429\pi$
$401$	−2.67650e6	−0.831201	−0.415600	+	0.909547i	$0.636429\pi$
$402$	1.48089e7	4.57045
$403$	1.92467e6	0.590330
$404$	−2.08511e6	−0.635589
$405$	1.67051e6	0.506071
$406$	1.02643e7	3.09039
$407$	59388.3	0.0177711
$408$	−2.49781e7	−7.42863
$409$	234395.	0.0692851	0.0346426	−	0.999400i	$-0.488971\pi$
$409$	234395.	0.0692851	0.0346426	+	0.999400i	$0.488971\pi$
$410$	3.17182e6	0.931856
$411$	−1.04084e7	−3.03934
$412$	−9.87893e6	−2.86726
$413$	15308.1	0.00441617
$414$	1.37045e7	3.92973
$415$	−2.52773e6	−0.720461
$416$	8.36544e6	2.37004
$417$	−1.52040e6	−0.428172
$418$	474400.	0.132802
$419$	−472881.	−0.131588	−0.0657941	−	0.997833i	$-0.520958\pi$
$419$	−472881.	−0.131588	−0.0657941	+	0.997833i	$0.520958\pi$
$420$	−1.20549e7	−3.33456
$421$	907027.	0.249411	0.124705	−	0.992194i	$-0.460201\pi$
$421$	907027.	0.249411	0.124705	+	0.992194i	$0.460201\pi$
$422$	−1.51784e6	−0.414900
$423$	1.36721e7	3.71522
$424$	−6.08063e6	−1.64261
$425$	979738.	0.263110
$426$	5.92228e6	1.58112
$427$	−9.81452e6	−2.60495
$428$	−1.01644e7	−2.68209
$429$	−1.34329e6	−0.352392
$430$	5.74615e6	1.49867
$431$	2.24031e6	0.580917	0.290459	−	0.956888i	$-0.406192\pi$
$431$	2.24031e6	0.580917	0.290459	+	0.956888i	$0.406192\pi$
$432$	2.49094e7	6.42175
$433$	−395485.	−0.101370	−0.0506852	−	0.998715i	$-0.516141\pi$
$433$	−395485.	−0.101370	−0.0506852	+	0.998715i	$0.516141\pi$
$434$	−1.05631e7	−2.69196
$435$	3.11453e6	0.789168
$436$	1.42987e7	3.60230
$437$	917469.	0.229820
$438$	−8.98081e6	−2.23681
$439$	−1.73873e6	−0.430596	−0.215298	−	0.976548i	$-0.569072\pi$
$439$	−1.73873e6	−0.430596	−0.215298	+	0.976548i	$0.569072\pi$
$440$	−1.77249e6	−0.436467
$441$	1.27861e7	3.13070
$442$	6.95016e6	1.69215
$443$	−5.52681e6	−1.33803	−0.669015	−	0.743249i	$-0.733284\pi$
$443$	−5.52681e6	−1.33803	−0.669015	+	0.743249i	$0.733284\pi$
$444$	1.14721e6	0.276175
$445$	949289.	0.227247
$446$	−5.44345e6	−1.29580
$447$	5.93140e6	1.40407
$448$	−2.20588e7	−5.19261
$449$	6.53068e6	1.52877	0.764385	−	0.644760i	$-0.223043\pi$
$449$	6.53068e6	1.52877	0.764385	+	0.644760i	$0.223043\pi$
$450$	−3.37023e6	−0.784563
$451$	−1.41352e6	−0.327235
$452$	2.04816e7	4.71538
$453$	−3.04497e6	−0.697169
$454$	−4.72900e6	−1.07679
$455$	2.10547e6	0.476782
$456$	5.75224e6	1.29546
$457$	326134.	0.0730475	0.0365237	−	0.999333i	$-0.488372\pi$
$457$	326134.	0.0730475	0.0365237	+	0.999333i	$0.488372\pi$
$458$	9.39295e6	2.09237
$459$	1.08067e7	2.39421
$460$	−5.46109e6	−1.20333
$461$	2.89122e6	0.633621	0.316810	−	0.948489i	$-0.397388\pi$
$461$	2.89122e6	0.633621	0.316810	+	0.948489i	$0.397388\pi$
$462$	7.37233e6	1.60694
$463$	7.86562e6	1.70522	0.852610	−	0.522548i	$-0.175019\pi$
$463$	7.86562e6	1.70522	0.852610	+	0.522548i	$0.175019\pi$
$464$	1.65531e7	3.56931
$465$	−3.20521e6	−0.687422
$466$	−3.60791e6	−0.769647
$467$	−4.15802e6	−0.882255	−0.441127	−	0.897444i	$-0.645421\pi$
$467$	−4.15802e6	−0.882255	−0.441127	+	0.897444i	$0.645421\pi$
$468$	−1.74219e7	−3.67688
$469$	1.03442e7	2.17152
$470$	−7.47654e6	−1.56119
$471$	1.48604e7	3.08658
$472$	43479.4	0.00898314
$473$	−2.56077e6	−0.526280
$474$	1.21710e7	2.48817
$475$	−225625.	−0.0458831
$476$	−2.77959e7	−5.62293
$477$	5.15250e6	1.03686
$478$	−3.98998e6	−0.798731
$479$	−7.81837e6	−1.55696	−0.778480	−	0.627669i	$-0.784009\pi$
$479$	−7.81837e6	−1.55696	−0.778480	+	0.627669i	$0.784009\pi$
$480$	−1.39312e7	−2.75985
$481$	−200368.	−0.0394880
$482$	6.33854e6	1.24272
$483$	1.42578e7	2.78089
$484$	1.25842e6	0.244181
$485$	−3.72532e6	−0.719132
$486$	−1.54100e6	−0.295946
$487$	−3.61636e6	−0.690955	−0.345477	−	0.938427i	$-0.612283\pi$
$487$	−3.61636e6	−0.690955	−0.345477	+	0.938427i	$0.612283\pi$
$488$	−2.78760e7	−5.29885
$489$	−6.11583e6	−1.15660
$490$	−6.99202e6	−1.31557
$491$	221811.	0.0415221	0.0207610	−	0.999784i	$-0.493391\pi$
$491$	221811.	0.0415221	0.0207610	+	0.999784i	$0.493391\pi$
$492$	−2.73050e7	−5.08546
$493$	7.18143e6	1.33074
$494$	−1.60056e6	−0.295090
$495$	1.50194e6	0.275511
$496$	−1.70350e7	−3.10912
$497$	4.13676e6	0.751224
$498$	2.98617e7	5.39562
$499$	5.72243e6	1.02880	0.514398	−	0.857552i	$-0.328015\pi$
$499$	5.72243e6	1.02880	0.514398	+	0.857552i	$0.328015\pi$
$500$	1.34300e6	0.240242
$501$	−1.37139e7	−2.44100
$502$	3.05911e6	0.541797
$503$	610801.	0.107641	0.0538207	−	0.998551i	$-0.482860\pi$
$503$	610801.	0.107641	0.0538207	+	0.998551i	$0.482860\pi$
$504$	6.00178e7	10.5246
$505$	−606478.	−0.105825
$506$	3.33981e6	0.579890
$507$	−5.56483e6	−0.961462
$508$	1.20852e7	2.07776
$509$	−6.82079e6	−1.16692	−0.583459	−	0.812142i	$-0.698301\pi$
$509$	−6.82079e6	−1.16692	−0.583459	+	0.812142i	$0.698301\pi$
$510$	−1.15743e7	−1.97046
$511$	−6.27317e6	−1.06276
$512$	−6.29189e6	−1.06073
$513$	−2.48870e6	−0.417521
$514$	1.29732e7	2.16590
$515$	−2.87339e6	−0.477394
$516$	−4.94665e7	−8.17875
$517$	3.33191e6	0.548236
$518$	1.09967e6	0.180069
$519$	−1.53523e7	−2.50181
$520$	5.98013e6	0.969845
$521$	−2.41165e6	−0.389242	−0.194621	−	0.980878i	$-0.562348\pi$
$521$	−2.41165e6	−0.389242	−0.194621	+	0.980878i	$0.562348\pi$
$522$	−2.47036e7	−3.96811
$523$	−520796.	−0.0832556	−0.0416278	−	0.999133i	$-0.513254\pi$
$523$	−520796.	−0.0832556	−0.0416278	+	0.999133i	$0.513254\pi$
$524$	3.56212e6	0.566735
$525$	−3.50629e6	−0.555199
$526$	−5.05508e6	−0.796643
$527$	−7.39051e6	−1.15917
$528$	1.18893e7	1.85597
$529$	22705.8	0.00352775
$530$	−2.81762e6	−0.435706
$531$	−36842.8	−0.00567043
$532$	6.40114e6	0.980570
$533$	4.76902e6	0.727128
$534$	−1.12146e7	−1.70188
$535$	−2.95644e6	−0.446564
$536$	2.93804e7	4.41719
$537$	−1.76351e6	−0.263901
$538$	1.57571e7	2.34704
$539$	3.11599e6	0.461981
$540$	1.48136e7	2.18613
$541$	241426.	0.0354643	0.0177322	−	0.999843i	$-0.494355\pi$
$541$	241426.	0.0354643	0.0177322	+	0.999843i	$0.494355\pi$
$542$	6.21403e6	0.908605
$543$	1.00640e6	0.146478
$544$	−3.21223e7	−4.65381
$545$	4.15893e6	0.599778
$546$	−2.48732e7	−3.57068
$547$	9.15785e6	1.30865	0.654327	−	0.756211i	$-0.272952\pi$
$547$	9.15785e6	1.30865	0.654327	+	0.756211i	$0.272952\pi$
$548$	−3.28978e7	−4.67968
$549$	2.36211e7	3.34479
$550$	−821330.	−0.115774
$551$	−1.65382e6	−0.232065
$552$	4.04962e7	5.65674
$553$	8.50155e6	1.18218
$554$	−2.56787e7	−3.55467
$555$	333677.	0.0459827
$556$	−4.80553e6	−0.659256
$557$	9.92387e6	1.35532	0.677662	−	0.735374i	$-0.262993\pi$
$557$	9.92387e6	1.35532	0.677662	+	0.735374i	$0.262993\pi$
$558$	2.54228e7	3.45651
$559$	8.63967e6	1.16941
$560$	−1.86352e7	−2.51110
$561$	5.15807e6	0.691958
$562$	−2.67560e6	−0.357339
$563$	8.17891e6	1.08749	0.543744	−	0.839251i	$-0.317006\pi$
$563$	8.17891e6	1.08749	0.543744	+	0.839251i	$0.317006\pi$
$564$	6.43628e7	8.51995
$565$	5.95729e6	0.785104
$566$	1.35023e7	1.77160
$567$	−1.37849e7	−1.80072
$568$	1.17496e7	1.52810
$569$	−2.14200e6	−0.277357	−0.138678	−	0.990337i	$-0.544285\pi$
$569$	−2.14200e6	−0.277357	−0.138678	+	0.990337i	$0.544285\pi$
$570$	2.66545e6	0.343624
$571$	−5.17031e6	−0.663631	−0.331815	−	0.943344i	$-0.607661\pi$
$571$	−5.17031e6	−0.663631	−0.331815	+	0.943344i	$0.607661\pi$
$572$	−4.24573e6	−0.542579
$573$	−1.79495e7	−2.28384
$574$	−2.61736e7	−3.31577
$575$	−1.58842e6	−0.200352
$576$	5.30900e7	6.66739
$577$	−9.16003e6	−1.14540	−0.572700	−	0.819765i	$-0.694104\pi$
$577$	−9.16003e6	−1.14540	−0.572700	+	0.819765i	$0.694104\pi$
$578$	−1.12673e7	−1.40282
$579$	−2.26456e7	−2.80729
$580$	9.84409e6	1.21508
$581$	2.08587e7	2.56358
$582$	4.40096e7	5.38567
$583$	1.25567e6	0.153005
$584$	−1.78176e7	−2.16181
$585$	−5.06734e6	−0.612195
$586$	348194.	0.0418868
$587$	−5.13979e6	−0.615673	−0.307836	−	0.951439i	$-0.599605\pi$
$587$	−5.13979e6	−0.615673	−0.307836	+	0.951439i	$0.599605\pi$
$588$	6.01918e7	7.17949
$589$	1.70197e6	0.202145
$590$	20147.3	0.00238280
$591$	−1.14174e7	−1.34462
$592$	1.77343e6	0.207974
$593$	−1.43471e7	−1.67543	−0.837716	−	0.546106i	$-0.816110\pi$
$593$	−1.43471e7	−1.67543	−0.837716	+	0.546106i	$0.816110\pi$
$594$	−9.05946e6	−1.05350
$595$	−8.08473e6	−0.936210
$596$	1.87474e7	2.16185
$597$	−1.07986e7	−1.24003
$598$	−1.12681e7	−1.28854
$599$	−8.13507e6	−0.926391	−0.463195	−	0.886256i	$-0.653297\pi$
$599$	−8.13507e6	−0.926391	−0.463195	+	0.886256i	$0.653297\pi$
$600$	−9.95886e6	−1.12936
$601$	1.16339e7	1.31383	0.656917	−	0.753963i	$-0.271860\pi$
$601$	1.16339e7	1.31383	0.656917	+	0.753963i	$0.271860\pi$
$602$	−4.74168e7	−5.33263
$603$	−2.48958e7	−2.78826
$604$	−9.62424e6	−1.07343
$605$	366025.	0.0406558
$606$	7.16471e6	0.792533
$607$	−9.14190e6	−1.00708	−0.503541	−	0.863972i	$-0.667970\pi$
$607$	−9.14190e6	−1.00708	−0.503541	+	0.863972i	$0.667970\pi$
$608$	7.39748e6	0.811567
$609$	−2.57009e7	−2.80805
$610$	−1.29171e7	−1.40553
$611$	−1.12414e7	−1.21820
$612$	6.68978e7	7.21993
$613$	1.03428e7	1.11170	0.555852	−	0.831282i	$-0.312392\pi$
$613$	1.03428e7	1.11170	0.555852	+	0.831282i	$0.312392\pi$
$614$	1.09085e7	1.16773
$615$	−7.94197e6	−0.846721
$616$	1.46264e7	1.55306
$617$	−1.16522e7	−1.23224	−0.616119	−	0.787653i	$-0.711296\pi$
$617$	−1.16522e7	−1.23224	−0.616119	+	0.787653i	$0.711296\pi$
$618$	3.39452e7	3.57526
$619$	1.18202e7	1.23993	0.619965	−	0.784629i	$-0.287147\pi$
$619$	1.18202e7	1.23993	0.619965	+	0.784629i	$0.287147\pi$
$620$	−1.01307e7	−1.05842
$621$	−1.75206e7	−1.82314
$622$	2.95958e7	3.06729
$623$	−7.83347e6	−0.808601
$624$	−4.01127e7	−4.12402
$625$	390625.	0.0400000
$626$	−1.20571e7	−1.22973
$627$	−1.18786e6	−0.120669
$628$	4.69692e7	4.75241
$629$	769387.	0.0775387
$630$	2.78109e7	2.79167
$631$	−4.00568e6	−0.400500	−0.200250	−	0.979745i	$-0.564175\pi$
$631$	−4.00568e6	−0.400500	−0.200250	+	0.979745i	$0.564175\pi$
$632$	2.41468e7	2.40474
$633$	3.80053e6	0.376995
$634$	−2.17436e7	−2.14836
$635$	3.51513e6	0.345945
$636$	2.42559e7	2.37780
$637$	−1.05129e7	−1.02654
$638$	−6.02030e6	−0.585554
$639$	−9.95616e6	−0.964584
$640$	−1.26388e7	−1.21970
$641$	1.12013e7	1.07677	0.538385	−	0.842699i	$-0.319035\pi$
$641$	1.12013e7	1.07677	0.538385	+	0.842699i	$0.319035\pi$
$642$	3.49263e7	3.34437
$643$	−1.24947e7	−1.19178	−0.595892	−	0.803064i	$-0.703201\pi$
$643$	−1.24947e7	−1.19178	−0.595892	+	0.803064i	$0.703201\pi$
$644$	4.50645e7	4.28174
$645$	−1.43879e7	−1.36175
$646$	6.14595e6	0.579439
$647$	−1.73939e7	−1.63356	−0.816781	−	0.576948i	$-0.804243\pi$
$647$	−1.73939e7	−1.63356	−0.816781	+	0.576948i	$0.804243\pi$
$648$	−3.91531e7	−3.66293
$649$	−8978.64	−0.000836756 0
$650$	2.77105e6	0.257254
$651$	2.64491e7	2.44602
$652$	−1.93303e7	−1.78082
$653$	−7.05606e6	−0.647559	−0.323779	−	0.946133i	$-0.604954\pi$
$653$	−7.05606e6	−0.647559	−0.323779	+	0.946133i	$0.604954\pi$
$654$	−4.91321e7	−4.49181
$655$	1.03608e6	0.0943604
$656$	−4.22099e7	−3.82961
$657$	1.50980e7	1.36460
$658$	6.16959e7	5.55509
$659$	−2.04727e7	−1.83637	−0.918186	−	0.396149i	$-0.870346\pi$
$659$	−2.04727e7	−1.83637	−0.918186	+	0.396149i	$0.870346\pi$
$660$	7.07053e6	0.631818
$661$	−4.05521e6	−0.361002	−0.180501	−	0.983575i	$-0.557772\pi$
$661$	−4.05521e6	−0.361002	−0.180501	+	0.983575i	$0.557772\pi$
$662$	−1.12203e6	−0.0995080
$663$	−1.74026e7	−1.53755
$664$	5.92446e7	5.21469
$665$	1.86184e6	0.163263
$666$	−2.64664e6	−0.231211
$667$	−1.16430e7	−1.01333
$668$	−4.33455e7	−3.75840
$669$	1.36299e7	1.17741
$670$	1.36142e7	1.17167
$671$	5.75650e6	0.493574
$672$	1.14959e8	9.82020
$673$	−9.18537e6	−0.781734	−0.390867	−	0.920447i	$-0.627825\pi$
$673$	−9.18537e6	−0.781734	−0.390867	+	0.920447i	$0.627825\pi$
$674$	2.23267e7	1.89310
$675$	4.30868e6	0.363986
$676$	−1.75888e7	−1.48036
$677$	5.98964e6	0.502261	0.251130	−	0.967953i	$-0.419198\pi$
$677$	5.98964e6	0.502261	0.251130	+	0.967953i	$0.419198\pi$
$678$	−7.03773e7	−5.87974
$679$	3.07411e7	2.55885
$680$	−2.29630e7	−1.90439
$681$	1.18410e7	0.978410
$682$	6.19558e6	0.510060
$683$	1.28056e7	1.05038	0.525190	−	0.850985i	$-0.323994\pi$
$683$	1.28056e7	1.05038	0.525190	+	0.850985i	$0.323994\pi$
$684$	−1.54060e7	−1.25907
$685$	−9.56869e6	−0.779159
$686$	2.00414e7	1.62599
$687$	−2.35191e7	−1.90121
$688$	−7.64685e7	−6.15901
$689$	−4.23646e6	−0.339982
$690$	1.87650e7	1.50046
$691$	−6.05307e6	−0.482260	−0.241130	−	0.970493i	$-0.577518\pi$
$691$	−6.05307e6	−0.482260	−0.241130	+	0.970493i	$0.577518\pi$
$692$	−4.85240e7	−3.85204
$693$	−1.23939e7	−0.980336
$694$	1.28074e7	1.00940
$695$	−1.39774e6	−0.109765
$696$	−7.29979e7	−5.71199
$697$	−1.83124e7	−1.42779
$698$	−4.38914e7	−3.40990
$699$	9.03391e6	0.699331
$700$	−1.10823e7	−0.854841
$701$	1.27500e7	0.979973	0.489986	−	0.871730i	$-0.337002\pi$
$701$	1.27500e7	0.979973	0.489986	+	0.871730i	$0.337002\pi$
$702$	3.05654e7	2.34092
$703$	−177183.	−0.0135218
$704$	1.29381e7	0.983873
$705$	1.87206e7	1.41856
$706$	−2.95797e7	−2.23348
$707$	5.00461e6	0.376550
$708$	−173441.	−0.0130037
$709$	−1.87488e7	−1.40074	−0.700372	−	0.713778i	$-0.746982\pi$
$709$	−1.87488e7	−1.40074	−0.700372	+	0.713778i	$0.746982\pi$
$710$	5.44449e6	0.405333
$711$	−2.04611e7	−1.51794
$712$	−2.22493e7	−1.64481
$713$	1.19820e7	0.882683
$714$	9.55101e7	7.01139
$715$	−1.23492e6	−0.0903385
$716$	−5.57392e6	−0.406329
$717$	9.99056e6	0.725758
$718$	1.93119e7	1.39803
$719$	−2.60285e7	−1.87771	−0.938853	−	0.344318i	$-0.888110\pi$
$719$	−2.60285e7	−1.87771	−0.938853	+	0.344318i	$0.888110\pi$
$720$	4.48502e7	3.22429
$721$	2.37110e7	1.69868
$722$	−1.41536e6	−0.101047
$723$	−1.58712e7	−1.12918
$724$	3.18094e6	0.225533
$725$	2.86326e6	0.202309
$726$	−4.32409e6	−0.304476
$727$	1.34044e7	0.940611	0.470306	−	0.882504i	$-0.344144\pi$
$727$	1.34044e7	0.940611	0.470306	+	0.882504i	$0.344144\pi$
$728$	−4.93476e7	−3.45094
$729$	−1.23788e7	−0.862700
$730$	−8.25626e6	−0.573425
$731$	−3.31753e7	−2.29626
$732$	1.11199e8	7.67047
$733$	1.46451e7	1.00677	0.503386	−	0.864062i	$-0.332087\pi$
$733$	1.46451e7	1.00677	0.503386	+	0.864062i	$0.332087\pi$
$734$	−1.75181e7	−1.20018
$735$	1.75074e7	1.19537
$736$	5.20788e7	3.54377
$737$	−6.06716e6	−0.411449
$738$	6.29935e7	4.25750
$739$	1.76852e7	1.19124	0.595619	−	0.803267i	$-0.296907\pi$
$739$	1.76852e7	1.19124	0.595619	+	0.803267i	$0.296907\pi$
$740$	1.05465e6	0.0707996
$741$	4.00767e6	0.268130
$742$	2.32508e7	1.55035
$743$	−1.58234e7	−1.05154	−0.525772	−	0.850625i	$-0.676224\pi$
$743$	−1.58234e7	−1.05154	−0.525772	+	0.850625i	$0.676224\pi$
$744$	7.51232e7	4.97556
$745$	5.45288e6	0.359944
$746$	4.15056e7	2.73061
$747$	−5.02016e7	−3.29167
$748$	1.63031e7	1.06541
$749$	2.43963e7	1.58898
$750$	−4.61470e6	−0.299565
$751$	2.49465e7	1.61402	0.807012	−	0.590535i	$-0.201083\pi$
$751$	2.49465e7	1.61402	0.807012	+	0.590535i	$0.201083\pi$
$752$	9.94961e7	6.41596
$753$	−7.65976e6	−0.492298
$754$	2.03117e7	1.30112
$755$	−2.79931e6	−0.178725
$756$	−1.22240e8	−7.77876
$757$	−2.58220e7	−1.63776	−0.818880	−	0.573964i	$-0.805405\pi$
$757$	−2.58220e7	−1.63776	−0.818880	+	0.573964i	$0.805405\pi$
$758$	−2.71409e7	−1.71574
$759$	−8.36260e6	−0.526911
$760$	5.28817e6	0.332102
$761$	3.62267e6	0.226760	0.113380	−	0.993552i	$-0.463832\pi$
$761$	3.62267e6	0.226760	0.113380	+	0.993552i	$0.463832\pi$
$762$	−4.15264e7	−2.59082
$763$	−3.43192e7	−2.13415
$764$	−5.67329e7	−3.51643
$765$	1.94579e7	1.20211
$766$	4.69798e7	2.89294
$767$	30292.7	0.00185930
$768$	5.62617e7	3.44199
$769$	2.15093e7	1.31163	0.655813	−	0.754923i	$-0.272326\pi$
$769$	2.15093e7	1.31163	0.655813	+	0.754923i	$0.272326\pi$
$770$	6.77756e6	0.411952
$771$	−3.24837e7	−1.96802
$772$	−7.15760e7	−4.32239
$773$	1.80078e7	1.08396	0.541979	−	0.840392i	$-0.317675\pi$
$773$	1.80078e7	1.08396	0.541979	+	0.840392i	$0.317675\pi$
$774$	1.14120e8	6.84717
$775$	−2.94662e6	−0.176226
$776$	8.73134e7	5.20507
$777$	−2.75348e6	−0.163618
$778$	−4.13430e7	−2.44880
$779$	4.21719e6	0.248989
$780$	−2.38550e7	−1.40392
$781$	−2.42633e6	−0.142339
$782$	4.32680e7	2.53017
$783$	3.15824e7	1.84095
$784$	9.30483e7	5.40653
$785$	1.36615e7	0.791269
$786$	−1.22399e7	−0.706677
$787$	−1.27927e6	−0.0736250	−0.0368125	−	0.999322i	$-0.511720\pi$
$787$	−1.27927e6	−0.0736250	−0.0368125	+	0.999322i	$0.511720\pi$
$788$	−3.60870e7	−2.07031
$789$	1.26575e7	0.723861
$790$	1.11891e7	0.637862
$791$	−4.91591e7	−2.79359
$792$	−3.52022e7	−1.99415
$793$	−1.94216e7	−1.09674
$794$	3.99440e7	2.24854
$795$	7.05509e6	0.395899
$796$	−3.41312e7	−1.90928
$797$	837805.	0.0467194	0.0233597	−	0.999727i	$-0.492564\pi$
$797$	837805.	0.0467194	0.0233597	+	0.999727i	$0.492564\pi$
$798$	−2.19951e7	−1.22270
$799$	4.31656e7	2.39206
$800$	−1.28073e7	−0.707508
$801$	1.88532e7	1.03826
$802$	2.90683e7	1.59582
$803$	3.67940e6	0.201367
$804$	−1.17200e8	−6.39420
$805$	1.31075e7	0.712903
$806$	−2.09030e7	−1.13337
$807$	−3.94544e7	−2.13261
$808$	1.42145e7	0.765957
$809$	−2.07886e7	−1.11674	−0.558372	−	0.829590i	$-0.688574\pi$
$809$	−2.07886e7	−1.11674	−0.558372	+	0.829590i	$0.688574\pi$
$810$	−1.81427e7	−0.971602
$811$	−5.89050e6	−0.314485	−0.157243	−	0.987560i	$-0.550260\pi$
$811$	−5.89050e6	−0.314485	−0.157243	+	0.987560i	$0.550260\pi$
$812$	−8.12328e7	−4.32356
$813$	−1.55594e7	−0.825594
$814$	−644990.	−0.0341186
$815$	−5.62243e6	−0.296504
$816$	1.54028e8	8.09793
$817$	7.63997e6	0.400439
$818$	−2.54566e6	−0.133020
$819$	4.18153e7	2.17834
$820$	−2.51022e7	−1.30370
$821$	−2.56535e7	−1.32828	−0.664138	−	0.747610i	$-0.731201\pi$
$821$	−2.56535e7	−1.32828	−0.664138	+	0.747610i	$0.731201\pi$
$822$	1.13041e8	5.83521
$823$	−2.65216e7	−1.36490	−0.682449	−	0.730933i	$-0.739085\pi$
$823$	−2.65216e7	−1.36490	−0.682449	+	0.730933i	$0.739085\pi$
$824$	6.73462e7	3.45537
$825$	2.05654e6	0.105197
$826$	−166254.	−0.00847858
$827$	−1.15781e7	−0.588673	−0.294336	−	0.955702i	$-0.595099\pi$
$827$	−1.15781e7	−0.588673	−0.294336	+	0.955702i	$0.595099\pi$
$828$	−1.08459e8	−5.49782
$829$	1.23572e6	0.0624502	0.0312251	−	0.999512i	$-0.490059\pi$
$829$	1.23572e6	0.0624502	0.0312251	+	0.999512i	$0.490059\pi$
$830$	2.74526e7	1.38321
$831$	6.42974e7	3.22991
$832$	−4.36514e7	−2.18620
$833$	4.03683e7	2.01571
$834$	1.65124e7	0.822044
$835$	−1.26075e7	−0.625768
$836$	−3.75446e6	−0.185794
$837$	−3.25019e7	−1.60360
$838$	5.13576e6	0.252635
$839$	7.88637e6	0.386787	0.193394	−	0.981121i	$-0.438051\pi$
$839$	7.88637e6	0.386787	0.193394	+	0.981121i	$0.438051\pi$
$840$	8.21798e7	4.01853
$841$	476397.	0.0232263
$842$	−9.85082e6	−0.478842
$843$	6.69948e6	0.324693
$844$	1.20123e7	0.580459
$845$	−5.11588e6	−0.246478
$846$	−1.48487e8	−7.13282
$847$	−3.02041e6	−0.144663
$848$	3.74963e7	1.79060
$849$	−3.38086e7	−1.60975
$850$	−1.06405e7	−0.505144
$851$	−1.24738e6	−0.0590440
$852$	−4.68696e7	−2.21204
$853$	4.18337e6	0.196858	0.0984292	−	0.995144i	$-0.468618\pi$
$853$	4.18337e6	0.196858	0.0984292	+	0.995144i	$0.468618\pi$
$854$	1.06591e8	5.00123
$855$	−4.48099e6	−0.209633
$856$	6.92925e7	3.23223
$857$	−1.99149e6	−0.0926243	−0.0463122	−	0.998927i	$-0.514747\pi$
$857$	−1.99149e6	−0.0926243	−0.0463122	+	0.998927i	$0.514747\pi$
$858$	1.45889e7	0.676556
$859$	6.09514e6	0.281839	0.140919	−	0.990021i	$-0.454994\pi$
$859$	6.09514e6	0.281839	0.140919	+	0.990021i	$0.454994\pi$
$860$	−4.54757e7	−2.09668
$861$	6.55366e7	3.01284
$862$	−2.43310e7	−1.11530
$863$	8.49981e6	0.388492	0.194246	−	0.980953i	$-0.437774\pi$
$863$	8.49981e6	0.388492	0.194246	+	0.980953i	$0.437774\pi$
$864$	−1.41267e8	−6.43808
$865$	−1.41137e7	−0.641359
$866$	4.29519e6	0.194620
$867$	2.82124e7	1.27465
$868$	8.35978e7	3.76613
$869$	−4.98641e6	−0.223995
$870$	−3.38255e7	−1.51512
$871$	2.04697e7	0.914255
$872$	−9.74764e7	−4.34118
$873$	−7.39861e7	−3.28560
$874$	−9.96423e6	−0.441230
$875$	−3.22341e6	−0.142330
$876$	7.10752e7	3.12937
$877$	1.76101e7	0.773150	0.386575	−	0.922258i	$-0.373658\pi$
$877$	1.76101e7	0.773150	0.386575	+	0.922258i	$0.373658\pi$
$878$	1.88836e7	0.826699
$879$	−871847.	−0.0380599
$880$	1.09301e7	0.475791
$881$	−1.17321e7	−0.509254	−0.254627	−	0.967039i	$-0.581953\pi$
$881$	−1.17321e7	−0.509254	−0.254627	+	0.967039i	$0.581953\pi$
$882$	−1.38864e8	−6.01061
$883$	−1.78593e7	−0.770839	−0.385419	−	0.922742i	$-0.625943\pi$
$883$	−1.78593e7	−0.770839	−0.385419	+	0.922742i	$0.625943\pi$
$884$	−5.50044e7	−2.36737
$885$	−50447.2	−0.00216510
$886$	6.00243e7	2.56887
$887$	2.45054e7	1.04581	0.522904	−	0.852392i	$-0.324849\pi$
$887$	2.45054e7	1.04581	0.522904	+	0.852392i	$0.324849\pi$
$888$	−7.82068e6	−0.332822
$889$	−2.90066e7	−1.23095
$890$	−1.03098e7	−0.436291
$891$	8.08526e6	0.341193
$892$	4.30801e7	1.81286
$893$	−9.94067e6	−0.417145
$894$	−6.44184e7	−2.69566
$895$	−1.62123e6	−0.0676532
$896$	1.04294e8	4.34000
$897$	2.82143e7	1.17081
$898$	−7.09268e7	−2.93508
$899$	−2.15986e7	−0.891304
$900$	2.66724e7	1.09763
$901$	1.62675e7	0.667588
$902$	1.53516e7	0.628257
$903$	1.18728e8	4.84543
$904$	−1.39626e8	−5.68257
$905$	925211.	0.0375508
$906$	3.30701e7	1.33849
$907$	2.03431e7	0.821105	0.410552	−	0.911837i	$-0.365336\pi$
$907$	2.03431e7	0.821105	0.410552	+	0.911837i	$0.365336\pi$
$908$	3.74259e7	1.50646
$909$	−1.20449e7	−0.483495
$910$	−2.28665e7	−0.915371
$911$	2.86098e7	1.14214	0.571070	−	0.820901i	$-0.306528\pi$
$911$	2.86098e7	1.14214	0.571070	+	0.820901i	$0.306528\pi$
$912$	−3.54713e7	−1.41218
$913$	−1.22342e7	−0.485735
$914$	−3.54199e6	−0.140243
$915$	3.23434e7	1.27712
$916$	−7.43369e7	−2.92729
$917$	−8.54966e6	−0.335757
$918$	−1.17367e8	−4.59664
$919$	2.76381e7	1.07949	0.539746	−	0.841828i	$-0.318520\pi$
$919$	2.76381e7	1.07949	0.539746	+	0.841828i	$0.318520\pi$
$920$	3.72291e7	1.45015
$921$	−2.73139e7	−1.06105
$922$	−3.14003e7	−1.21648
$923$	8.18611e6	0.316281
$924$	−5.83455e7	−2.24816
$925$	306757.	0.0117880
$926$	−8.54250e7	−3.27384
$927$	−5.70666e7	−2.18114
$928$	−9.38766e7	−3.57839
$929$	2.10798e7	0.801361	0.400680	−	0.916218i	$-0.368774\pi$
$929$	2.10798e7	0.801361	0.400680	+	0.916218i	$0.368774\pi$
$930$	3.48103e7	1.31978
$931$	−9.29646e6	−0.351515
$932$	2.85535e7	1.07676
$933$	−7.41054e7	−2.78705
$934$	4.51584e7	1.69384
$935$	4.74193e6	0.177389
$936$	1.18767e8	4.43106
$937$	−4.78560e7	−1.78068	−0.890342	−	0.455292i	$-0.849535\pi$
$937$	−4.78560e7	−1.78068	−0.890342	+	0.455292i	$0.849535\pi$
$938$	−1.12343e8	−4.16908
$939$	3.01901e7	1.11738
$940$	5.91702e7	2.18415
$941$	2.32341e7	0.855366	0.427683	−	0.903929i	$-0.359330\pi$
$941$	2.32341e7	0.855366	0.427683	+	0.903929i	$0.359330\pi$
$942$	−1.61392e8	−5.92591
$943$	2.96893e7	1.08723
$944$	−268116.	−0.00979249
$945$	−3.55550e7	−1.29515
$946$	2.78114e7	1.01040
$947$	1.29421e7	0.468954	0.234477	−	0.972122i	$-0.424662\pi$
$947$	1.29421e7	0.468954	0.234477	+	0.972122i	$0.424662\pi$
$948$	−9.63227e7	−3.48103
$949$	−1.24138e7	−0.447444
$950$	2.45041e6	0.0880908
$951$	5.44440e7	1.95209
$952$	1.89489e8	6.77627
$953$	1.17497e7	0.419079	0.209540	−	0.977800i	$-0.432804\pi$
$953$	1.17497e7	0.419079	0.209540	+	0.977800i	$0.432804\pi$
$954$	−5.59590e7	−1.99067
$955$	−1.65014e7	−0.585480
$956$	3.15772e7	1.11745
$957$	1.50743e7	0.532057
$958$	8.49119e7	2.98920
$959$	7.89602e7	2.77244
$960$	7.26938e7	2.54577
$961$	−6.40174e6	−0.223609
$962$	2.17611e6	0.0758128
$963$	−5.87159e7	−2.04028
$964$	−5.01640e7	−1.73860
$965$	−2.08187e7	−0.719672
$966$	−1.54847e8	−5.33901
$967$	1.70389e7	0.585971	0.292985	−	0.956117i	$-0.405351\pi$
$967$	1.70389e7	0.585971	0.292985	+	0.956117i	$0.405351\pi$
$968$	−8.57884e6	−0.294266
$969$	−1.53889e7	−0.526501
$970$	4.04590e7	1.38066
$971$	4.13436e7	1.40721	0.703607	−	0.710589i	$-0.251572\pi$
$971$	4.13436e7	1.40721	0.703607	+	0.710589i	$0.251572\pi$
$972$	1.21957e7	0.414038
$973$	1.15341e7	0.390571
$974$	3.92757e7	1.32656
$975$	−6.93848e6	−0.233751
$976$	1.71898e8	5.77626
$977$	−2.59627e7	−0.870187	−0.435094	−	0.900385i	$-0.643285\pi$
$977$	−2.59627e7	−0.870187	−0.435094	+	0.900385i	$0.643285\pi$
$978$	6.64214e7	2.22055
$979$	4.59456e6	0.153210
$980$	5.53357e7	1.84052
$981$	8.25978e7	2.74029
$982$	−2.40899e6	−0.0797180
$983$	−2.51752e7	−0.830978	−0.415489	−	0.909598i	$-0.636390\pi$
$983$	−2.51752e7	−0.830978	−0.415489	+	0.909598i	$0.636390\pi$
$984$	1.86143e8	6.12856
$985$	−1.04963e7	−0.344704
$986$	−7.79943e7	−2.55488
$987$	−1.54481e8	−5.04757
$988$	1.26670e7	0.412841
$989$	5.37859e7	1.74855
$990$	−1.63119e7	−0.528952
$991$	4.63976e7	1.50076	0.750381	−	0.661006i	$-0.229870\pi$
$991$	4.63976e7	1.50076	0.750381	+	0.661006i	$0.229870\pi$
$992$	9.66097e7	3.11703
$993$	2.80946e6	0.0904169
$994$	−4.49276e7	−1.44227
$995$	−9.92744e6	−0.317892
$996$	−2.36329e8	−7.54864
$997$	−1.29196e7	−0.411633	−0.205816	−	0.978591i	$-0.565985\pi$
$997$	−1.29196e7	−0.411633	−0.205816	+	0.978591i	$0.565985\pi$
$998$	−6.21488e7	−1.97518
$999$	3.38361e6	0.107267

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.e.1.2	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.e.1.2	✓	38	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)

\(f(q)\)	\(=\)	\(q-10.8606 q^{2} +27.1939 q^{3} +85.9518 q^{4} +25.0000 q^{5} -295.341 q^{6} -206.298 q^{7} -585.946 q^{8} +496.509 q^{9} +O(q^{10})\)	\(q-10.8606 q^{2} +27.1939 q^{3} +85.9518 q^{4} +25.0000 q^{5} -295.341 q^{6} -206.298 q^{7} -585.946 q^{8} +496.509 q^{9} -271.514 q^{10} +121.000 q^{11} +2337.36 q^{12} -408.237 q^{13} +2240.51 q^{14} +679.848 q^{15} +3613.25 q^{16} +1567.58 q^{17} -5392.36 q^{18} -361.000 q^{19} +2148.79 q^{20} -5610.06 q^{21} -1314.13 q^{22} -2541.47 q^{23} -15934.2 q^{24} +625.000 q^{25} +4433.69 q^{26} +6893.90 q^{27} -17731.7 q^{28} +4581.22 q^{29} -7383.53 q^{30} -4714.60 q^{31} -20491.6 q^{32} +3290.46 q^{33} -17024.8 q^{34} -5157.46 q^{35} +42675.8 q^{36} +490.812 q^{37} +3920.66 q^{38} -11101.6 q^{39} -14648.7 q^{40} -11682.0 q^{41} +60928.4 q^{42} -21163.4 q^{43} +10400.2 q^{44} +12412.7 q^{45} +27601.7 q^{46} +27536.5 q^{47} +98258.4 q^{48} +25752.0 q^{49} -6787.85 q^{50} +42628.6 q^{51} -35088.7 q^{52} +10377.5 q^{53} -74871.6 q^{54} +3025.00 q^{55} +120880. q^{56} -9817.00 q^{57} -49754.6 q^{58} -74.2036 q^{59} +58434.1 q^{60} +47574.4 q^{61} +51203.1 q^{62} -102429. q^{63} +106927. q^{64} -10205.9 q^{65} -35736.3 q^{66} -50141.8 q^{67} +134736. q^{68} -69112.4 q^{69} +56012.9 q^{70} -20052.3 q^{71} -290927. q^{72} +30408.2 q^{73} -5330.49 q^{74} +16996.2 q^{75} -31028.6 q^{76} -24962.1 q^{77} +120569. q^{78} -41210.0 q^{79} +90331.2 q^{80} +66820.3 q^{81} +126873. q^{82} -101109. q^{83} -482194. q^{84} +39189.5 q^{85} +229846. q^{86} +124581. q^{87} -70899.5 q^{88} +37971.6 q^{89} -134809. q^{90} +84218.7 q^{91} -218443. q^{92} -128208. q^{93} -299061. q^{94} -9025.00 q^{95} -557247. q^{96} -149013. q^{97} -279681. q^{98} +60077.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9}+O(q^{10}) \) 38 * q - 24 * q^2 - 63 * q^3 + 594 * q^4 + 950 * q^5 - 67 * q^6 - 729 * q^7 - 1272 * q^8 + 3029 * q^9	\( 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9} - 600 q^{10} + 4598 q^{11} - 2008 q^{12} - 2663 q^{13} - 1565 q^{14} - 1575 q^{15} + 12390 q^{16} - 3311 q^{17} - 6383 q^{18} - 13718 q^{19} + 14850 q^{20} - 8179 q^{21} - 2904 q^{22} - 3412 q^{23} - 4100 q^{24} + 23750 q^{25} - 1399 q^{26} - 31596 q^{27} - 43653 q^{28} - 13633 q^{29} - 1675 q^{30} - 13789 q^{31} - 58603 q^{32} - 7623 q^{33} - 29149 q^{34} - 18225 q^{35} + 50641 q^{36} - 12103 q^{37} + 8664 q^{38} - 50960 q^{39} - 31800 q^{40} - 37885 q^{41} + 51100 q^{42} - 56119 q^{43} + 71874 q^{44} + 75725 q^{45} - 56291 q^{46} - 37532 q^{47} - 113895 q^{48} + 153501 q^{49} - 15000 q^{50} + 32882 q^{51} - 169554 q^{52} - 51511 q^{53} - 175060 q^{54} + 114950 q^{55} - 84247 q^{56} + 22743 q^{57} - 256962 q^{58} - 154267 q^{59} - 50200 q^{60} - 47165 q^{61} + 143002 q^{62} - 358780 q^{63} + 142292 q^{64} - 66575 q^{65} - 8107 q^{66} - 161712 q^{67} - 210188 q^{68} - 124602 q^{69} - 39125 q^{70} + 6118 q^{71} - 327878 q^{72} - 152182 q^{73} - 167349 q^{74} - 39375 q^{75} - 214434 q^{76} - 88209 q^{77} - 216594 q^{78} - 140433 q^{79} + 309750 q^{80} + 382874 q^{81} - 29842 q^{82} - 515287 q^{83} + 29222 q^{84} - 82775 q^{85} + 204974 q^{86} - 106764 q^{87} - 153912 q^{88} - 271610 q^{89} - 159575 q^{90} - 44332 q^{91} + 236348 q^{92} + 25202 q^{93} - 496224 q^{94} - 342950 q^{95} - 275218 q^{96} - 126390 q^{97} - 285506 q^{98} + 366509 q^{99}+O(q^{100}) \) 38 * q - 24 * q^2 - 63 * q^3 + 594 * q^4 + 950 * q^5 - 67 * q^6 - 729 * q^7 - 1272 * q^8 + 3029 * q^9 - 600 * q^10 + 4598 * q^11 - 2008 * q^12 - 2663 * q^13 - 1565 * q^14 - 1575 * q^15 + 12390 * q^16 - 3311 * q^17 - 6383 * q^18 - 13718 * q^19 + 14850 * q^20 - 8179 * q^21 - 2904 * q^22 - 3412 * q^23 - 4100 * q^24 + 23750 * q^25 - 1399 * q^26 - 31596 * q^27 - 43653 * q^28 - 13633 * q^29 - 1675 * q^30 - 13789 * q^31 - 58603 * q^32 - 7623 * q^33 - 29149 * q^34 - 18225 * q^35 + 50641 * q^36 - 12103 * q^37 + 8664 * q^38 - 50960 * q^39 - 31800 * q^40 - 37885 * q^41 + 51100 * q^42 - 56119 * q^43 + 71874 * q^44 + 75725 * q^45 - 56291 * q^46 - 37532 * q^47 - 113895 * q^48 + 153501 * q^49 - 15000 * q^50 + 32882 * q^51 - 169554 * q^52 - 51511 * q^53 - 175060 * q^54 + 114950 * q^55 - 84247 * q^56 + 22743 * q^57 - 256962 * q^58 - 154267 * q^59 - 50200 * q^60 - 47165 * q^61 + 143002 * q^62 - 358780 * q^63 + 142292 * q^64 - 66575 * q^65 - 8107 * q^66 - 161712 * q^67 - 210188 * q^68 - 124602 * q^69 - 39125 * q^70 + 6118 * q^71 - 327878 * q^72 - 152182 * q^73 - 167349 * q^74 - 39375 * q^75 - 214434 * q^76 - 88209 * q^77 - 216594 * q^78 - 140433 * q^79 + 309750 * q^80 + 382874 * q^81 - 29842 * q^82 - 515287 * q^83 + 29222 * q^84 - 82775 * q^85 + 204974 * q^86 - 106764 * q^87 - 153912 * q^88 - 271610 * q^89 - 159575 * q^90 - 44332 * q^91 + 236348 * q^92 + 25202 * q^93 - 496224 * q^94 - 342950 * q^95 - 275218 * q^96 - 126390 * q^97 - 285506 * q^98 + 366509 * q^99

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