LMFDB - Embedded newform 1045.6.a.e.1.8

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			1.8
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)

$f(q)$	$=$	$q-8.25643 q^{2} -6.02271 q^{3} +36.1686 q^{4} +25.0000 q^{5} +49.7261 q^{6} +24.7368 q^{7} -34.4178 q^{8} -206.727 q^{9} +O(q^{10})$	\(q-8.25643 q^{2} -6.02271 q^{3} +36.1686 q^{4} +25.0000 q^{5} +49.7261 q^{6} +24.7368 q^{7} -34.4178 q^{8} -206.727 q^{9} -206.411 q^{10} +121.000 q^{11} -217.833 q^{12} -594.926 q^{13} -204.237 q^{14} -150.568 q^{15} -873.227 q^{16} +1805.24 q^{17} +1706.83 q^{18} -361.000 q^{19} +904.215 q^{20} -148.982 q^{21} -999.028 q^{22} -2409.07 q^{23} +207.289 q^{24} +625.000 q^{25} +4911.96 q^{26} +2708.58 q^{27} +894.694 q^{28} +5092.49 q^{29} +1243.15 q^{30} -4902.68 q^{31} +8311.11 q^{32} -728.748 q^{33} -14904.8 q^{34} +618.419 q^{35} -7477.03 q^{36} +5403.60 q^{37} +2980.57 q^{38} +3583.07 q^{39} -860.445 q^{40} +14545.0 q^{41} +1230.06 q^{42} -8138.22 q^{43} +4376.40 q^{44} -5168.17 q^{45} +19890.3 q^{46} -15608.1 q^{47} +5259.20 q^{48} -16195.1 q^{49} -5160.27 q^{50} -10872.4 q^{51} -21517.6 q^{52} +31803.3 q^{53} -22363.2 q^{54} +3025.00 q^{55} -851.385 q^{56} +2174.20 q^{57} -42045.8 q^{58} -14265.3 q^{59} -5445.83 q^{60} -4401.88 q^{61} +40478.6 q^{62} -5113.75 q^{63} -40676.8 q^{64} -14873.1 q^{65} +6016.86 q^{66} -24951.2 q^{67} +65292.9 q^{68} +14509.1 q^{69} -5105.93 q^{70} -54622.2 q^{71} +7115.09 q^{72} -15339.9 q^{73} -44614.4 q^{74} -3764.20 q^{75} -13056.9 q^{76} +2993.15 q^{77} -29583.3 q^{78} +14275.2 q^{79} -21830.7 q^{80} +33921.7 q^{81} -120089. q^{82} -15480.8 q^{83} -5388.49 q^{84} +45130.9 q^{85} +67192.7 q^{86} -30670.6 q^{87} -4164.55 q^{88} +33903.7 q^{89} +42670.7 q^{90} -14716.5 q^{91} -87132.5 q^{92} +29527.4 q^{93} +128867. q^{94} -9025.00 q^{95} -50055.4 q^{96} +96973.2 q^{97} +133714. q^{98} -25014.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−8.25643	−1.45954	−0.729772	−	0.683691i	$-0.760374\pi$
$2$	−8.25643	−1.45954	−0.729772	+	0.683691i	$0.760374\pi$
$3$	−6.02271	−0.386357	−0.193179	−	0.981164i	$-0.561880\pi$
$3$	−6.02271	−0.386357	−0.193179	+	0.981164i	$0.561880\pi$
$4$	36.1686	1.13027
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	49.7261	0.563905
$7$	24.7368	0.190809	0.0954043	−	0.995439i	$-0.469586\pi$
$7$	24.7368	0.190809	0.0954043	+	0.995439i	$0.469586\pi$
$8$	−34.4178	−0.190133
$9$	−206.727	−0.850728
$10$	−206.411	−0.652728
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−217.833	−0.436688
$13$	−594.926	−0.976348	−0.488174	−	0.872746i	$-0.662337\pi$
$13$	−594.926	−0.976348	−0.488174	+	0.872746i	$0.662337\pi$
$14$	−204.237	−0.278493
$15$	−150.568	−0.172784
$16$	−873.227	−0.852761
$17$	1805.24	1.51500	0.757499	−	0.652836i	$-0.226421\pi$
$17$	1805.24	1.51500	0.757499	+	0.652836i	$0.226421\pi$
$18$	1706.83	1.24168
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	904.215	0.505472
$21$	−148.982	−0.0737202
$22$	−999.028	−0.440069
$23$	−2409.07	−0.949574	−0.474787	−	0.880101i	$-0.657475\pi$
$23$	−2409.07	−0.949574	−0.474787	+	0.880101i	$0.657475\pi$
$24$	207.289	0.0734594
$25$	625.000	0.200000
$26$	4911.96	1.42502
$27$	2708.58	0.715042
$28$	894.694	0.215665
$29$	5092.49	1.12444	0.562218	−	0.826989i	$-0.309948\pi$
$29$	5092.49	1.12444	0.562218	+	0.826989i	$0.309948\pi$
$30$	1243.15	0.252186
$31$	−4902.68	−0.916282	−0.458141	−	0.888879i	$-0.651485\pi$
$31$	−4902.68	−0.916282	−0.458141	+	0.888879i	$0.651485\pi$
$32$	8311.11	1.43478
$33$	−728.748	−0.116491
$34$	−14904.8	−2.21121
$35$	618.419	0.0853322
$36$	−7477.03	−0.961552
$37$	5403.60	0.648902	0.324451	−	0.945903i	$-0.394821\pi$
$37$	5403.60	0.648902	0.324451	+	0.945903i	$0.394821\pi$
$38$	2980.57	0.334842
$39$	3583.07	0.377219
$40$	−860.445	−0.0850302
$41$	14545.0	1.35130	0.675652	−	0.737221i	$-0.263862\pi$
$41$	14545.0	1.35130	0.675652	+	0.737221i	$0.263862\pi$
$42$	1230.06	0.107598
$43$	−8138.22	−0.671210	−0.335605	−	0.942003i	$-0.608941\pi$
$43$	−8138.22	−0.671210	−0.335605	+	0.942003i	$0.608941\pi$
$44$	4376.40	0.340789
$45$	−5168.17	−0.380457
$46$	19890.3	1.38595
$47$	−15608.1	−1.03063	−0.515317	−	0.857000i	$-0.672326\pi$
$47$	−15608.1	−1.03063	−0.515317	+	0.857000i	$0.672326\pi$
$48$	5259.20	0.329470
$49$	−16195.1	−0.963592
$50$	−5160.27	−0.291909
$51$	−10872.4	−0.585330
$52$	−21517.6	−1.10354
$53$	31803.3	1.55519	0.777593	−	0.628767i	$-0.216440\pi$
$53$	31803.3	1.55519	0.777593	+	0.628767i	$0.216440\pi$
$54$	−22363.2	−1.04364
$55$	3025.00	0.134840
$56$	−851.385	−0.0362791
$57$	2174.20	0.0886364
$58$	−42045.8	−1.64116
$59$	−14265.3	−0.533521	−0.266761	−	0.963763i	$-0.585953\pi$
$59$	−14265.3	−0.533521	−0.266761	+	0.963763i	$0.585953\pi$
$60$	−5445.83	−0.195293
$61$	−4401.88	−0.151465	−0.0757327	−	0.997128i	$-0.524130\pi$
$61$	−4401.88	−0.151465	−0.0757327	+	0.997128i	$0.524130\pi$
$62$	40478.6	1.33735
$63$	−5113.75	−0.162326
$64$	−40676.8	−1.24136
$65$	−14873.1	−0.436636
$66$	6016.86	0.170024
$67$	−24951.2	−0.679054	−0.339527	−	0.940596i	$-0.610267\pi$
$67$	−24951.2	−0.679054	−0.339527	+	0.940596i	$0.610267\pi$
$68$	65292.9	1.71236
$69$	14509.1	0.366875
$70$	−5105.93	−0.124546
$71$	−54622.2	−1.28595	−0.642974	−	0.765888i	$-0.722300\pi$
$71$	−54622.2	−1.28595	−0.642974	+	0.765888i	$0.722300\pi$
$72$	7115.09	0.161752
$73$	−15339.9	−0.336911	−0.168456	−	0.985709i	$-0.553878\pi$
$73$	−15339.9	−0.336911	−0.168456	+	0.985709i	$0.553878\pi$
$74$	−44614.4	−0.947100
$75$	−3764.20	−0.0772714
$76$	−13056.9	−0.259301
$77$	2993.15	0.0575309
$78$	−29583.3	−0.550568
$79$	14275.2	0.257344	0.128672	−	0.991687i	$-0.458929\pi$
$79$	14275.2	0.257344	0.128672	+	0.991687i	$0.458929\pi$
$80$	−21830.7	−0.381366
$81$	33921.7	0.574466
$82$	−120089.	−1.97229
$83$	−15480.8	−0.246660	−0.123330	−	0.992366i	$-0.539357\pi$
$83$	−15480.8	−0.246660	−0.123330	+	0.992366i	$0.539357\pi$
$84$	−5388.49	−0.0833237
$85$	45130.9	0.677528
$86$	67192.7	0.979661
$87$	−30670.6	−0.434434
$88$	−4164.55	−0.0573273
$89$	33903.7	0.453704	0.226852	−	0.973929i	$-0.427157\pi$
$89$	33903.7	0.453704	0.226852	+	0.973929i	$0.427157\pi$
$90$	42670.7	0.555294
$91$	−14716.5	−0.186295
$92$	−87132.5	−1.07327
$93$	29527.4	0.354012
$94$	128867.	1.50426
$95$	−9025.00	−0.102598
$96$	−50055.4	−0.554336
$97$	96973.2	1.04646	0.523230	−	0.852192i	$-0.324727\pi$
$97$	96973.2	1.04646	0.523230	+	0.852192i	$0.324727\pi$
$98$	133714.	1.40641
$99$	−25014.0	−0.256504
$100$	22605.4	0.226054
$101$	161665.	1.57693	0.788465	−	0.615080i	$-0.210876\pi$
$101$	161665.	1.57693	0.788465	+	0.615080i	$0.210876\pi$
$102$	89767.4	0.854316
$103$	−207368.	−1.92597	−0.962985	−	0.269555i	$-0.913123\pi$
$103$	−207368.	−1.92597	−0.962985	+	0.269555i	$0.913123\pi$
$104$	20476.0	0.185636
$105$	−3724.56	−0.0329687
$106$	−262582.	−2.26986
$107$	57705.1	0.487253	0.243627	−	0.969869i	$-0.421663\pi$
$107$	57705.1	0.487253	0.243627	+	0.969869i	$0.421663\pi$
$108$	97965.4	0.808190
$109$	−222315.	−1.79227	−0.896134	−	0.443783i	$-0.853636\pi$
$109$	−222315.	−1.79227	−0.896134	+	0.443783i	$0.853636\pi$
$110$	−24975.7	−0.196805
$111$	−32544.3	−0.250708
$112$	−21600.8	−0.162714
$113$	75690.2	0.557627	0.278813	−	0.960345i	$-0.410059\pi$
$113$	75690.2	0.557627	0.278813	+	0.960345i	$0.410059\pi$
$114$	−17951.1	−0.129369
$115$	−60226.6	−0.424663
$116$	184188.	1.27092
$117$	122987.	0.830606
$118$	117781.	0.778698
$119$	44655.7	0.289075
$120$	5182.21	0.0328520
$121$	14641.0	0.0909091
$122$	36343.8	0.221071
$123$	−87600.2	−0.522086
$124$	−177323.	−1.03565
$125$	15625.0	0.0894427
$126$	42221.3	0.236922
$127$	282059.	1.55178	0.775890	−	0.630868i	$-0.217301\pi$
$127$	282059.	1.55178	0.775890	+	0.630868i	$0.217301\pi$
$128$	69889.6	0.377040
$129$	49014.2	0.259327
$130$	122799.	0.637289
$131$	383307.	1.95150	0.975751	−	0.218883i	$-0.0702415\pi$
$131$	383307.	1.95150	0.975751	+	0.218883i	$0.0702415\pi$
$132$	−26357.8	−0.131666
$133$	−8929.97	−0.0437745
$134$	206008.	0.991109
$135$	67714.4	0.319777
$136$	−62132.3	−0.288052
$137$	−59281.1	−0.269845	−0.134923	−	0.990856i	$-0.543079\pi$
$137$	−59281.1	−0.269845	−0.134923	+	0.990856i	$0.543079\pi$
$138$	−119793.	−0.535470
$139$	170513.	0.748548	0.374274	−	0.927318i	$-0.377892\pi$
$139$	170513.	0.748548	0.374274	+	0.927318i	$0.377892\pi$
$140$	22367.4	0.0964483
$141$	94002.9	0.398193
$142$	450984.	1.87690
$143$	−71986.0	−0.294380
$144$	180520.	0.725468
$145$	127312.	0.502863
$146$	126653.	0.491737
$147$	97538.4	0.372291
$148$	195441.	0.733433
$149$	308233.	1.13740	0.568700	−	0.822545i	$-0.307447\pi$
$149$	308233.	1.13740	0.568700	+	0.822545i	$0.307447\pi$
$150$	31078.8	0.112781
$151$	−315697.	−1.12675	−0.563375	−	0.826201i	$-0.690497\pi$
$151$	−315697.	−1.12675	−0.563375	+	0.826201i	$0.690497\pi$
$152$	12424.8	0.0436196
$153$	−373191.	−1.28885
$154$	−24712.7	−0.0839689
$155$	−122567.	−0.409774
$156$	129595.	0.426359
$157$	−117678.	−0.381019	−0.190509	−	0.981685i	$-0.561014\pi$
$157$	−117678.	−0.381019	−0.190509	+	0.981685i	$0.561014\pi$
$158$	−117862.	−0.375605
$159$	−191542.	−0.600858
$160$	207778.	0.641651
$161$	−59592.5	−0.181187
$162$	−280072.	−0.838459
$163$	234545.	0.691443	0.345721	−	0.938337i	$-0.387634\pi$
$163$	234545.	0.691443	0.345721	+	0.938337i	$0.387634\pi$
$164$	526071.	1.52734
$165$	−18218.7	−0.0520964
$166$	127816.	0.360011
$167$	−446508.	−1.23891	−0.619453	−	0.785034i	$-0.712646\pi$
$167$	−446508.	−1.23891	−0.619453	+	0.785034i	$0.712646\pi$
$168$	5127.65	0.0140167
$169$	−17356.1	−0.0467451
$170$	−372620.	−0.988882
$171$	74628.4	0.195170
$172$	−294348.	−0.758648
$173$	301836.	0.766754	0.383377	−	0.923592i	$-0.374761\pi$
$173$	301836.	0.766754	0.383377	+	0.923592i	$0.374761\pi$
$174$	253230.	0.634076
$175$	15460.5	0.0381617
$176$	−105661.	−0.257117
$177$	85916.0	0.206130
$178$	−279924.	−0.662201
$179$	−447187.	−1.04317	−0.521586	−	0.853198i	$-0.674660\pi$
$179$	−447187.	−1.04317	−0.521586	+	0.853198i	$0.674660\pi$
$180$	−186926.	−0.430019
$181$	757602.	1.71888	0.859438	−	0.511240i	$-0.170814\pi$
$181$	757602.	1.71888	0.859438	+	0.511240i	$0.170814\pi$
$182$	121506.	0.271906
$183$	26511.3	0.0585198
$184$	82914.7	0.180546
$185$	135090.	0.290198
$186$	−243791.	−0.516697
$187$	218434.	0.456789
$188$	−564522.	−1.16489
$189$	67001.4	0.136436
$190$	74514.3	0.149746
$191$	165240.	0.327742	0.163871	−	0.986482i	$-0.447602\pi$
$191$	165240.	0.327742	0.163871	+	0.986482i	$0.447602\pi$
$192$	244985.	0.479607
$193$	−804494.	−1.55464	−0.777319	−	0.629106i	$-0.783421\pi$
$193$	−804494.	−1.55464	−0.777319	+	0.629106i	$0.783421\pi$
$194$	−800652.	−1.52735
$195$	89576.7	0.168697
$196$	−585754.	−1.08912
$197$	391546.	0.718814	0.359407	−	0.933181i	$-0.382979\pi$
$197$	391546.	0.718814	0.359407	+	0.933181i	$0.382979\pi$
$198$	206526.	0.374379
$199$	427292.	0.764877	0.382439	−	0.923981i	$-0.375084\pi$
$199$	427292.	0.764877	0.382439	+	0.923981i	$0.375084\pi$
$200$	−21511.1	−0.0380267
$201$	150274.	0.262357
$202$	−1.33477e6	−2.30160
$203$	125972.	0.214552
$204$	−393241.	−0.661581
$205$	363624.	0.604322
$206$	1.71212e6	2.81104
$207$	498019.	0.807830
$208$	519506.	0.832591
$209$	−43681.0	−0.0691714
$210$	30751.6	0.0481193
$211$	670895.	1.03741	0.518703	−	0.854955i	$-0.326415\pi$
$211$	670895.	1.03741	0.518703	+	0.854955i	$0.326415\pi$
$212$	1.15028e6	1.75778
$213$	328974.	0.496835
$214$	−476438.	−0.711168
$215$	−203456.	−0.300174
$216$	−93223.2	−0.135953
$217$	−121276.	−0.174834
$218$	1.83553e6	2.61590
$219$	92387.9	0.130168
$220$	109410.	0.152405
$221$	−1.07398e6	−1.47916
$222$	268700.	0.365919
$223$	−713055.	−0.960198	−0.480099	−	0.877214i	$-0.659399\pi$
$223$	−713055.	−0.960198	−0.480099	+	0.877214i	$0.659399\pi$
$224$	205590.	0.273767
$225$	−129204.	−0.170146
$226$	−624931.	−0.813881
$227$	114178.	0.147068	0.0735342	−	0.997293i	$-0.476572\pi$
$227$	114178.	0.147068	0.0735342	+	0.997293i	$0.476572\pi$
$228$	78637.8	0.100183
$229$	1.24817e6	1.57284	0.786421	−	0.617691i	$-0.211932\pi$
$229$	1.24817e6	1.57284	0.786421	+	0.617691i	$0.211932\pi$
$230$	497257.	0.619814
$231$	−18026.9	−0.0222275
$232$	−175272.	−0.213793
$233$	855205.	1.03200	0.516001	−	0.856588i	$-0.327420\pi$
$233$	855205.	1.03200	0.516001	+	0.856588i	$0.327420\pi$
$234$	−1.01544e6	−1.21231
$235$	−390202.	−0.460914
$236$	−515957.	−0.603022
$237$	−85975.3	−0.0994267
$238$	−368697.	−0.421917
$239$	74586.1	0.0844624	0.0422312	−	0.999108i	$-0.486553\pi$
$239$	74586.1	0.0844624	0.0422312	+	0.999108i	$0.486553\pi$
$240$	131480.	0.147344
$241$	576267.	0.639118	0.319559	−	0.947566i	$-0.396465\pi$
$241$	576267.	0.639118	0.319559	+	0.947566i	$0.396465\pi$
$242$	−120882.	−0.132686
$243$	−862484.	−0.936991
$244$	−159210.	−0.171197
$245$	−404877.	−0.430931
$246$	723264.	0.762008
$247$	214768.	0.223990
$248$	168739.	0.174216
$249$	93236.5	0.0952988
$250$	−129007.	−0.130546
$251$	−710360.	−0.711695	−0.355848	−	0.934544i	$-0.615808\pi$
$251$	−710360.	−0.711695	−0.355848	+	0.934544i	$0.615808\pi$
$252$	−184957.	−0.183472
$253$	−291497.	−0.286307
$254$	−2.32880e6	−2.26489
$255$	−271811.	−0.261768
$256$	724619.	0.691051
$257$	−429172.	−0.405321	−0.202660	−	0.979249i	$-0.564959\pi$
$257$	−429172.	−0.405321	−0.202660	+	0.979249i	$0.564959\pi$
$258$	−404682.	−0.378499
$259$	133668.	0.123816
$260$	−537941.	−0.493516
$261$	−1.05275e6	−0.956590
$262$	−3.16475e6	−2.84830
$263$	−1.27530e6	−1.13690	−0.568450	−	0.822718i	$-0.692457\pi$
$263$	−1.27530e6	−1.13690	−0.568450	+	0.822718i	$0.692457\pi$
$264$	25081.9	0.0221488
$265$	795083.	0.695501
$266$	73729.7	0.0638908
$267$	−204192.	−0.175292
$268$	−902449.	−0.767513
$269$	1.80441e6	1.52039	0.760193	−	0.649697i	$-0.225104\pi$
$269$	1.80441e6	1.52039	0.760193	+	0.649697i	$0.225104\pi$
$270$	−559079.	−0.466728
$271$	92554.0	0.0765547	0.0382774	−	0.999267i	$-0.487813\pi$
$271$	92554.0	0.0765547	0.0382774	+	0.999267i	$0.487813\pi$
$272$	−1.57638e6	−1.29193
$273$	88633.5	0.0719766
$274$	489450.	0.393851
$275$	75625.0	0.0603023
$276$	524774.	0.414667
$277$	−1.58532e6	−1.24142	−0.620708	−	0.784042i	$-0.713155\pi$
$277$	−1.58532e6	−1.24142	−0.620708	+	0.784042i	$0.713155\pi$
$278$	−1.40782e6	−1.09254
$279$	1.01352e6	0.779507
$280$	−21284.6	−0.0162245
$281$	−1.72266e6	−1.30147	−0.650736	−	0.759304i	$-0.725539\pi$
$281$	−1.72266e6	−1.30147	−0.650736	+	0.759304i	$0.725539\pi$
$282$	−776128.	−0.581180
$283$	−1.41543e6	−1.05056	−0.525280	−	0.850929i	$-0.676040\pi$
$283$	−1.41543e6	−1.05056	−0.525280	+	0.850929i	$0.676040\pi$
$284$	−1.97561e6	−1.45347
$285$	54355.0	0.0396394
$286$	594348.	0.429660
$287$	359795.	0.257840
$288$	−1.71813e6	−1.22060
$289$	1.83903e6	1.29522
$290$	−1.05114e6	−0.733951
$291$	−584042.	−0.404307
$292$	−554823.	−0.380801
$293$	−2.48897e6	−1.69375	−0.846877	−	0.531790i	$-0.821520\pi$
$293$	−2.48897e6	−1.69375	−0.846877	+	0.531790i	$0.821520\pi$
$294$	−805319.	−0.543375
$295$	−356633.	−0.238598
$296$	−185980.	−0.123378
$297$	327738.	0.215593
$298$	−2.54490e6	−1.66008
$299$	1.43322e6	0.927115
$300$	−136146.	−0.0873375
$301$	−201313.	−0.128073
$302$	2.60653e6	1.64454
$303$	−973661.	−0.609258
$304$	315235.	0.195637
$305$	−110047.	−0.0677374
$306$	3.08123e6	1.88114
$307$	−1.09057e6	−0.660403	−0.330201	−	0.943910i	$-0.607117\pi$
$307$	−1.09057e6	−0.660403	−0.330201	+	0.943910i	$0.607117\pi$
$308$	108258.	0.0650254
$309$	1.24892e6	0.744112
$310$	1.01197e6	0.598083
$311$	79797.3	0.0467829	0.0233915	−	0.999726i	$-0.492554\pi$
$311$	79797.3	0.0467829	0.0233915	+	0.999726i	$0.492554\pi$
$312$	−123321.	−0.0717219
$313$	1.38444e6	0.798757	0.399378	−	0.916786i	$-0.369226\pi$
$313$	1.38444e6	0.798757	0.399378	+	0.916786i	$0.369226\pi$
$314$	971601.	0.556114
$315$	−127844.	−0.0725945
$316$	516313.	0.290868
$317$	−2.72302e6	−1.52196	−0.760980	−	0.648775i	$-0.775281\pi$
$317$	−2.72302e6	−1.52196	−0.760980	+	0.648775i	$0.775281\pi$
$318$	1.58145e6	0.876978
$319$	616191.	0.339030
$320$	−1.01692e6	−0.555152
$321$	−347541.	−0.188254
$322$	492021.	0.264450
$323$	−651691.	−0.347564
$324$	1.22690e6	0.649302
$325$	−371829.	−0.195270
$326$	−1.93650e6	−1.00919
$327$	1.33894e6	0.692456
$328$	−500606.	−0.256928
$329$	−386093.	−0.196654
$330$	150421.	0.0760370
$331$	−1.94582e6	−0.976184	−0.488092	−	0.872792i	$-0.662307\pi$
$331$	−1.94582e6	−0.976184	−0.488092	+	0.872792i	$0.662307\pi$
$332$	−559919.	−0.278792
$333$	−1.11707e6	−0.552039
$334$	3.68656e6	1.80824
$335$	−623780.	−0.303682
$336$	130096.	0.0628657
$337$	−2.69197e6	−1.29120	−0.645602	−	0.763674i	$-0.723393\pi$
$337$	−2.69197e6	−1.29120	−0.645602	+	0.763674i	$0.723393\pi$
$338$	143300.	0.0682266
$339$	−455861.	−0.215443
$340$	1.63232e6	0.765789
$341$	−593224.	−0.276270
$342$	−616164.	−0.284860
$343$	−816365.	−0.374670
$344$	280100.	0.127619
$345$	362728.	0.164071
$346$	−2.49209e6	−1.11911
$347$	3.64087e6	1.62324	0.811619	−	0.584188i	$-0.198587\pi$
$347$	3.64087e6	1.62324	0.811619	+	0.584188i	$0.198587\pi$
$348$	−1.10931e6	−0.491027
$349$	−2.94740e6	−1.29532	−0.647658	−	0.761931i	$-0.724251\pi$
$349$	−2.94740e6	−1.29532	−0.647658	+	0.761931i	$0.724251\pi$
$350$	−127648.	−0.0556987
$351$	−1.61140e6	−0.698130
$352$	1.00564e6	0.432601
$353$	−2.84548e6	−1.21540	−0.607699	−	0.794167i	$-0.707907\pi$
$353$	−2.84548e6	−1.21540	−0.607699	+	0.794167i	$0.707907\pi$
$354$	−709359.	−0.300855
$355$	−1.36556e6	−0.575094
$356$	1.22625e6	0.512807
$357$	−268949.	−0.111686
$358$	3.69216e6	1.52256
$359$	3.40377e6	1.39387	0.696937	−	0.717132i	$-0.254546\pi$
$359$	3.40377e6	1.39387	0.696937	+	0.717132i	$0.254546\pi$
$360$	177877.	0.0723376
$361$	130321.	0.0526316
$362$	−6.25508e6	−2.50877
$363$	−88178.5	−0.0351234
$364$	−532277.	−0.210564
$365$	−383498.	−0.150671
$366$	−218888.	−0.0854122
$367$	−555867.	−0.215430	−0.107715	−	0.994182i	$-0.534353\pi$
$367$	−555867.	−0.215430	−0.107715	+	0.994182i	$0.534353\pi$
$368$	2.10366e6	0.809760
$369$	−3.00684e6	−1.14959
$370$	−1.11536e6	−0.423556
$371$	786711.	0.296743
$372$	1.06797e6	0.400129
$373$	4.81025e6	1.79017	0.895087	−	0.445892i	$-0.147113\pi$
$373$	4.81025e6	1.79017	0.895087	+	0.445892i	$0.147113\pi$
$374$	−1.80348e6	−0.666704
$375$	−94104.9	−0.0345568
$376$	537195.	0.195958
$377$	−3.02965e6	−1.09784
$378$	−553192.	−0.199135
$379$	−4.97286e6	−1.77831	−0.889157	−	0.457602i	$-0.848709\pi$
$379$	−4.97286e6	−1.77831	−0.889157	+	0.457602i	$0.848709\pi$
$380$	−326422.	−0.115963
$381$	−1.69876e6	−0.599542
$382$	−1.36429e6	−0.478354
$383$	−627163.	−0.218466	−0.109233	−	0.994016i	$-0.534839\pi$
$383$	−627163.	−0.218466	−0.109233	+	0.994016i	$0.534839\pi$
$384$	−420925.	−0.145672
$385$	74828.7	0.0257286
$386$	6.64225e6	2.26906
$387$	1.68239e6	0.571017
$388$	3.50738e6	1.18278
$389$	−2.80390e6	−0.939483	−0.469741	−	0.882804i	$-0.655653\pi$
$389$	−2.80390e6	−0.939483	−0.469741	+	0.882804i	$0.655653\pi$
$390$	−739584.	−0.246221
$391$	−4.34894e6	−1.43860
$392$	557399.	0.183211
$393$	−2.30855e6	−0.753977
$394$	−3.23277e6	−1.04914
$395$	356880.	0.115088
$396$	−904720.	−0.289919
$397$	−1.61446e6	−0.514103	−0.257051	−	0.966398i	$-0.582751\pi$
$397$	−1.61446e6	−0.514103	−0.257051	+	0.966398i	$0.582751\pi$
$398$	−3.52790e6	−1.11637
$399$	53782.6	0.0169126
$400$	−545767.	−0.170552
$401$	−3.69627e6	−1.14790	−0.573948	−	0.818892i	$-0.694589\pi$
$401$	−3.69627e6	−1.14790	−0.573948	+	0.818892i	$0.694589\pi$
$402$	−1.24072e6	−0.382922
$403$	2.91673e6	0.894610
$404$	5.84719e6	1.78235
$405$	848042.	0.256909
$406$	−1.04008e6	−0.313148
$407$	653835.	0.195651
$408$	374205.	0.111291
$409$	1.49078e6	0.440663	0.220331	−	0.975425i	$-0.429286\pi$
$409$	1.49078e6	0.440663	0.220331	+	0.975425i	$0.429286\pi$
$410$	−3.00224e6	−0.882034
$411$	357033.	0.104257
$412$	−7.50023e6	−2.17686
$413$	−352878.	−0.101800
$414$	−4.11186e6	−1.17906
$415$	−387020.	−0.110310
$416$	−4.94449e6	−1.40084
$417$	−1.02695e6	−0.289207
$418$	360649.	0.100959
$419$	3.31068e6	0.921260	0.460630	−	0.887592i	$-0.347624\pi$
$419$	3.31068e6	0.921260	0.460630	+	0.887592i	$0.347624\pi$
$420$	−134712.	−0.0372635
$421$	−378392.	−0.104049	−0.0520243	−	0.998646i	$-0.516567\pi$
$421$	−378392.	−0.104049	−0.0520243	+	0.998646i	$0.516567\pi$
$422$	−5.53920e6	−1.51414
$423$	3.22661e6	0.876789
$424$	−1.09460e6	−0.295693
$425$	1.12827e6	0.303000
$426$	−2.71615e6	−0.725153
$427$	−108888.	−0.0289009
$428$	2.08711e6	0.550727
$429$	433551.	0.113736
$430$	1.67982e6	0.438118
$431$	−2.04088e6	−0.529205	−0.264603	−	0.964358i	$-0.585241\pi$
$431$	−2.04088e6	−0.529205	−0.264603	+	0.964358i	$0.585241\pi$
$432$	−2.36520e6	−0.609760
$433$	−6.08566e6	−1.55987	−0.779935	−	0.625861i	$-0.784748\pi$
$433$	−6.08566e6	−1.55987	−0.779935	+	0.625861i	$0.784748\pi$
$434$	1.00131e6	0.255179
$435$	−766765.	−0.194285
$436$	−8.04084e6	−2.02575
$437$	869673.	0.217847
$438$	−762794.	−0.189986
$439$	−4.11914e6	−1.02011	−0.510053	−	0.860143i	$-0.670374\pi$
$439$	−4.11914e6	−1.02011	−0.510053	+	0.860143i	$0.670374\pi$
$440$	−104114.	−0.0256376
$441$	3.34796e6	0.819755
$442$	8.86726e6	2.15891
$443$	−1.40385e6	−0.339870	−0.169935	−	0.985455i	$-0.554356\pi$
$443$	−1.40385e6	−0.339870	−0.169935	+	0.985455i	$0.554356\pi$
$444$	−1.17708e6	−0.283367
$445$	847593.	0.202903
$446$	5.88729e6	1.40145
$447$	−1.85640e6	−0.439442
$448$	−1.00621e6	−0.236862
$449$	7.49006e6	1.75335	0.876677	−	0.481080i	$-0.159755\pi$
$449$	7.49006e6	1.75335	0.876677	+	0.481080i	$0.159755\pi$
$450$	1.06677e6	0.248335
$451$	1.75994e6	0.407434
$452$	2.73761e6	0.630268
$453$	1.90135e6	0.435328
$454$	−942706.	−0.214653
$455$	−367914.	−0.0833139
$456$	−74831.2	−0.0168527
$457$	4.15061e6	0.929655	0.464827	−	0.885401i	$-0.346116\pi$
$457$	4.15061e6	0.929655	0.464827	+	0.885401i	$0.346116\pi$
$458$	−1.03054e7	−2.29563
$459$	4.88962e6	1.08329
$460$	−2.17831e6	−0.479983
$461$	−2.29150e6	−0.502190	−0.251095	−	0.967962i	$-0.580791\pi$
$461$	−2.29150e6	−0.502190	−0.251095	+	0.967962i	$0.580791\pi$
$462$	148838.	0.0324420
$463$	391473.	0.0848690	0.0424345	−	0.999099i	$-0.486489\pi$
$463$	391473.	0.0848690	0.0424345	+	0.999099i	$0.486489\pi$
$464$	−4.44690e6	−0.958876
$465$	738186.	0.158319
$466$	−7.06094e6	−1.50625
$467$	−2.55207e6	−0.541502	−0.270751	−	0.962649i	$-0.587272\pi$
$467$	−2.55207e6	−0.541502	−0.270751	+	0.962649i	$0.587272\pi$
$468$	4.44828e6	0.938809
$469$	−617211.	−0.129569
$470$	3.22167e6	0.672724
$471$	708741.	0.147209
$472$	490981.	0.101440
$473$	−984725.	−0.202377
$474$	709849.	0.145118
$475$	−225625.	−0.0458831
$476$	1.61514e6	0.326732
$477$	−6.57460e6	−1.32304
$478$	−615815.	−0.123277
$479$	−5.07573e6	−1.01079	−0.505393	−	0.862889i	$-0.668653\pi$
$479$	−5.07573e6	−1.01079	−0.505393	+	0.862889i	$0.668653\pi$
$480$	−1.25139e6	−0.247907
$481$	−3.21474e6	−0.633554
$482$	−4.75791e6	−0.932821
$483$	358908.	0.0700028
$484$	529545.	0.102752
$485$	2.42433e6	0.467991
$486$	7.12104e6	1.36758
$487$	−5.58460e6	−1.06701	−0.533507	−	0.845796i	$-0.679126\pi$
$487$	−5.58460e6	−1.06701	−0.533507	+	0.845796i	$0.679126\pi$
$488$	151503.	0.0287986
$489$	−1.41259e6	−0.267144
$490$	3.34284e6	0.628964
$491$	−3.79553e6	−0.710508	−0.355254	−	0.934770i	$-0.615606\pi$
$491$	−3.79553e6	−0.710508	−0.355254	+	0.934770i	$0.615606\pi$
$492$	−3.16838e6	−0.590098
$493$	9.19315e6	1.70352
$494$	−1.77322e6	−0.326923
$495$	−625349.	−0.114712
$496$	4.28115e6	0.781370
$497$	−1.35118e6	−0.245370
$498$	−769800.	−0.139093
$499$	9.99622e6	1.79715	0.898575	−	0.438819i	$-0.144603\pi$
$499$	9.99622e6	1.79715	0.898575	+	0.438819i	$0.144603\pi$
$500$	565134.	0.101094
$501$	2.68919e6	0.478660
$502$	5.86503e6	1.03875
$503$	−26269.3	−0.00462944	−0.00231472	−	0.999997i	$-0.500737\pi$
$503$	−26269.3	−0.00462944	−0.00231472	+	0.999997i	$0.500737\pi$
$504$	176004.	0.0308636
$505$	4.04162e6	0.705224
$506$	2.40672e6	0.417878
$507$	104531.	0.0180603
$508$	1.02017e7	1.75393
$509$	5.94091e6	1.01639	0.508193	−	0.861243i	$-0.330314\pi$
$509$	5.94091e6	1.01639	0.508193	+	0.861243i	$0.330314\pi$
$510$	2.24419e6	0.382062
$511$	−379460.	−0.0642856
$512$	−8.21923e6	−1.38566
$513$	−977796.	−0.164042
$514$	3.54343e6	0.591584
$515$	−5.18421e6	−0.861320
$516$	1.77277e6	0.293109
$517$	−1.88858e6	−0.310748
$518$	−1.10362e6	−0.180715
$519$	−1.81787e6	−0.296241
$520$	511901.	0.0830190
$521$	−8.51929e6	−1.37502	−0.687510	−	0.726175i	$-0.741296\pi$
$521$	−8.51929e6	−1.37502	−0.687510	+	0.726175i	$0.741296\pi$
$522$	8.69199e6	1.39619
$523$	4.55730e6	0.728540	0.364270	−	0.931293i	$-0.381319\pi$
$523$	4.55730e6	0.728540	0.364270	+	0.931293i	$0.381319\pi$
$524$	1.38637e7	2.20572
$525$	−93114.0	−0.0147440
$526$	1.05294e7	1.65936
$527$	−8.85050e6	−1.38817
$528$	636363.	0.0993391
$529$	−632748.	−0.0983086
$530$	−6.56454e6	−1.01511
$531$	2.94903e6	0.453881
$532$	−322985.	−0.0494769
$533$	−8.65318e6	−1.31934
$534$	1.68590e6	0.255846
$535$	1.44263e6	0.217906
$536$	858765.	0.129111
$537$	2.69328e6	0.403037
$538$	−1.48980e7	−2.21907
$539$	−1.95961e6	−0.290534
$540$	2.44914e6	0.361434
$541$	−7.46880e6	−1.09713	−0.548565	−	0.836108i	$-0.684826\pi$
$541$	−7.46880e6	−1.09713	−0.548565	+	0.836108i	$0.684826\pi$
$542$	−764165.	−0.111735
$543$	−4.56282e6	−0.664100
$544$	1.50035e7	2.17368
$545$	−5.55788e6	−0.801527
$546$	−731796.	−0.105053
$547$	5.80818e6	0.829987	0.414994	−	0.909824i	$-0.363784\pi$
$547$	5.80818e6	0.829987	0.414994	+	0.909824i	$0.363784\pi$
$548$	−2.14412e6	−0.304998
$549$	909987.	0.128856
$550$	−624392.	−0.0880138
$551$	−1.83839e6	−0.257963
$552$	−499372.	−0.0697551
$553$	353122.	0.0491034
$554$	1.30891e7	1.81190
$555$	−813608.	−0.112120
$556$	6.16720e6	0.846060
$557$	−9.67920e6	−1.32191	−0.660954	−	0.750426i	$-0.729848\pi$
$557$	−9.67920e6	−1.32191	−0.660954	+	0.750426i	$0.729848\pi$
$558$	−8.36802e6	−1.13773
$559$	4.84164e6	0.655334
$560$	−540020.	−0.0727679
$561$	−1.31556e6	−0.176484
$562$	1.42230e7	1.89955
$563$	−174858.	−0.0232495	−0.0116248	−	0.999932i	$-0.503700\pi$
$563$	−174858.	−0.0232495	−0.0116248	+	0.999932i	$0.503700\pi$
$564$	3.39995e6	0.450065
$565$	1.89226e6	0.249378
$566$	1.16864e7	1.53334
$567$	839112.	0.109613
$568$	1.87998e6	0.244502
$569$	9.40133e6	1.21733	0.608666	−	0.793427i	$-0.291705\pi$
$569$	9.40133e6	1.21733	0.608666	+	0.793427i	$0.291705\pi$
$570$	−448778.	−0.0578555
$571$	4.34985e6	0.558320	0.279160	−	0.960245i	$-0.409944\pi$
$571$	4.34985e6	0.558320	0.279160	+	0.960245i	$0.409944\pi$
$572$	−2.60363e6	−0.332728
$573$	−995194.	−0.126625
$574$	−2.97062e6	−0.376329
$575$	−1.50567e6	−0.189915
$576$	8.40899e6	1.05606
$577$	−1.00200e7	−1.25294	−0.626469	−	0.779447i	$-0.715500\pi$
$577$	−1.00200e7	−1.25294	−0.626469	+	0.779447i	$0.715500\pi$
$578$	−1.51838e7	−1.89043
$579$	4.84524e6	0.600646
$580$	4.60470e6	0.568371
$581$	−382945.	−0.0470648
$582$	4.82210e6	0.590104
$583$	3.84820e6	0.468906
$584$	527966.	0.0640581
$585$	3.07468e6	0.371458
$586$	2.05500e7	2.47211
$587$	−1.26079e7	−1.51025	−0.755123	−	0.655583i	$-0.772423\pi$
$587$	−1.26079e7	−1.51025	−0.755123	+	0.655583i	$0.772423\pi$
$588$	3.52783e6	0.420789
$589$	1.76987e6	0.210210
$590$	2.94452e6	0.348244
$591$	−2.35817e6	−0.277719
$592$	−4.71857e6	−0.553358
$593$	−4.65777e6	−0.543928	−0.271964	−	0.962307i	$-0.587673\pi$
$593$	−4.65777e6	−0.543928	−0.271964	+	0.962307i	$0.587673\pi$
$594$	−2.70594e6	−0.314668
$595$	1.11639e6	0.129278
$596$	1.11483e7	1.28557
$597$	−2.57345e6	−0.295516
$598$	−1.18332e7	−1.35316
$599$	8.53046e6	0.971416	0.485708	−	0.874121i	$-0.338562\pi$
$599$	8.53046e6	0.971416	0.485708	+	0.874121i	$0.338562\pi$
$600$	129555.	0.0146919
$601$	−1.13781e7	−1.28494	−0.642472	−	0.766309i	$-0.722091\pi$
$601$	−1.13781e7	−1.28494	−0.642472	+	0.766309i	$0.722091\pi$
$602$	1.66213e6	0.186928
$603$	5.15808e6	0.577690
$604$	−1.14183e7	−1.27353
$605$	366025.	0.0406558
$606$	8.03896e6	0.889239
$607$	8.15500e6	0.898364	0.449182	−	0.893440i	$-0.351716\pi$
$607$	8.15500e6	0.898364	0.449182	+	0.893440i	$0.351716\pi$
$608$	−3.00031e6	−0.329160
$609$	−758691.	−0.0828937
$610$	908595.	0.0988658
$611$	9.28565e6	1.00626
$612$	−1.34978e7	−1.45675
$613$	332678.	0.0357580	0.0178790	−	0.999840i	$-0.494309\pi$
$613$	332678.	0.0357580	0.0178790	+	0.999840i	$0.494309\pi$
$614$	9.00424e6	0.963887
$615$	−2.19000e6	−0.233484
$616$	−103018.	−0.0109385
$617$	−1.27684e7	−1.35028	−0.675138	−	0.737692i	$-0.735916\pi$
$617$	−1.27684e7	−1.35028	−0.675138	+	0.737692i	$0.735916\pi$
$618$	−1.03116e7	−1.08606
$619$	−3.85513e6	−0.404401	−0.202201	−	0.979344i	$-0.564809\pi$
$619$	−3.85513e6	−0.404401	−0.202201	+	0.979344i	$0.564809\pi$
$620$	−4.43308e6	−0.463155
$621$	−6.52514e6	−0.678986
$622$	−658841.	−0.0682817
$623$	838668.	0.0865706
$624$	−3.12883e6	−0.321678
$625$	390625.	0.0400000
$626$	−1.14306e7	−1.16582
$627$	263078.	0.0267249
$628$	−4.25625e6	−0.430654
$629$	9.75478e6	0.983085
$630$	1.05553e6	0.105955
$631$	1.57288e7	1.57262	0.786309	−	0.617834i	$-0.211990\pi$
$631$	1.57288e7	1.57262	0.786309	+	0.617834i	$0.211990\pi$
$632$	−491320.	−0.0489296
$633$	−4.04061e6	−0.400809
$634$	2.24824e7	2.22137
$635$	7.05147e6	0.693977
$636$	−6.92781e6	−0.679131
$637$	9.63488e6	0.940801
$638$	−5.08754e6	−0.494830
$639$	1.12919e7	1.09399
$640$	1.74724e6	0.168617
$641$	4.26391e6	0.409886	0.204943	−	0.978774i	$-0.434299\pi$
$641$	4.26391e6	0.409886	0.204943	+	0.978774i	$0.434299\pi$
$642$	2.86945e6	0.274765
$643$	−9.51374e6	−0.907453	−0.453726	−	0.891141i	$-0.649906\pi$
$643$	−9.51374e6	−0.907453	−0.453726	+	0.891141i	$0.649906\pi$
$644$	−2.15538e6	−0.204790
$645$	1.22535e6	0.115974
$646$	5.38064e6	0.507286
$647$	1.08189e7	1.01607	0.508034	−	0.861337i	$-0.330372\pi$
$647$	1.08189e7	1.01607	0.508034	+	0.861337i	$0.330372\pi$
$648$	−1.16751e6	−0.109225
$649$	−1.72610e6	−0.160863
$650$	3.06998e6	0.285005
$651$	730413.	0.0675486
$652$	8.48315e6	0.781516
$653$	2.02576e7	1.85911	0.929556	−	0.368681i	$-0.120190\pi$
$653$	2.02576e7	1.85911	0.929556	+	0.368681i	$0.120190\pi$
$654$	−1.10549e7	−1.01067
$655$	9.58269e6	0.872738
$656$	−1.27011e7	−1.15234
$657$	3.17117e6	0.286620
$658$	3.18775e6	0.287025
$659$	991119.	0.0889022	0.0444511	−	0.999012i	$-0.485846\pi$
$659$	991119.	0.0889022	0.0444511	+	0.999012i	$0.485846\pi$
$660$	−658945.	−0.0588829
$661$	1.56196e7	1.39048	0.695241	−	0.718777i	$-0.255298\pi$
$661$	1.56196e7	1.39048	0.695241	+	0.718777i	$0.255298\pi$
$662$	1.60655e7	1.42478
$663$	6.46829e6	0.571486
$664$	532816.	0.0468983
$665$	−223249.	−0.0195765
$666$	9.22300e6	0.805725
$667$	−1.22681e7	−1.06774
$668$	−1.61496e7	−1.40030
$669$	4.29453e6	0.370979
$670$	5.15019e6	0.443237
$671$	−532628.	−0.0456686
$672$	−1.23821e6	−0.105772
$673$	−2.11868e7	−1.80313	−0.901565	−	0.432644i	$-0.857581\pi$
$673$	−2.11868e7	−1.80313	−0.901565	+	0.432644i	$0.857581\pi$
$674$	2.22260e7	1.88457
$675$	1.69286e6	0.143008
$676$	−627748.	−0.0528346
$677$	−1.95250e7	−1.63727	−0.818633	−	0.574317i	$-0.805268\pi$
$677$	−1.95250e7	−1.63727	−0.818633	+	0.574317i	$0.805268\pi$
$678$	3.76378e6	0.314449
$679$	2.39880e6	0.199673
$680$	−1.55331e6	−0.128821
$681$	−687664.	−0.0568209
$682$	4.89791e6	0.403228
$683$	−2.08731e7	−1.71213	−0.856063	−	0.516872i	$-0.827096\pi$
$683$	−2.08731e7	−1.71213	−0.856063	+	0.516872i	$0.827096\pi$
$684$	2.69921e6	0.220595
$685$	−1.48203e6	−0.120679
$686$	6.74026e6	0.546848
$687$	−7.51737e6	−0.607679
$688$	7.10652e6	0.572382
$689$	−1.89206e7	−1.51840
$690$	−2.99484e6	−0.239469
$691$	−1.69969e6	−0.135417	−0.0677087	−	0.997705i	$-0.521569\pi$
$691$	−1.69969e6	−0.135417	−0.0677087	+	0.997705i	$0.521569\pi$
$692$	1.09170e7	0.866638
$693$	−618764.	−0.0489432
$694$	−3.00606e7	−2.36919
$695$	4.26281e6	0.334761
$696$	1.05561e6	0.0826004
$697$	2.62571e7	2.04722
$698$	2.43350e7	1.89057
$699$	−5.15065e6	−0.398721
$700$	559184.	0.0431330
$701$	−2.47511e7	−1.90239	−0.951194	−	0.308594i	$-0.900142\pi$
$701$	−2.47511e7	−1.90239	−0.951194	+	0.308594i	$0.900142\pi$
$702$	1.33044e7	1.01895
$703$	−1.95070e6	−0.148868
$704$	−4.92189e6	−0.374283
$705$	2.35007e6	0.178077
$706$	2.34935e7	1.77393
$707$	3.99907e6	0.300892
$708$	3.10746e6	0.232982
$709$	3.22724e6	0.241110	0.120555	−	0.992707i	$-0.461533\pi$
$709$	3.22724e6	0.241110	0.120555	+	0.992707i	$0.461533\pi$
$710$	1.12746e7	0.839374
$711$	−2.95106e6	−0.218930
$712$	−1.16689e6	−0.0862642
$713$	1.18109e7	0.870078
$714$	2.22056e6	0.163011
$715$	−1.79965e6	−0.131651
$716$	−1.61741e7	−1.17907
$717$	−449211.	−0.0326327
$718$	−2.81030e7	−2.03442
$719$	1.15290e7	0.831708	0.415854	−	0.909431i	$-0.363483\pi$
$719$	1.15290e7	0.831708	0.415854	+	0.909431i	$0.363483\pi$
$720$	4.51299e6	0.324439
$721$	−5.12962e6	−0.367491
$722$	−1.07599e6	−0.0768181
$723$	−3.47069e6	−0.246928
$724$	2.74014e7	1.94279
$725$	3.18280e6	0.224887
$726$	728040.	0.0512641
$727$	−2.67834e6	−0.187945	−0.0939723	−	0.995575i	$-0.529957\pi$
$727$	−2.67834e6	−0.187945	−0.0939723	+	0.995575i	$0.529957\pi$
$728$	506511.	0.0354210
$729$	−3.04847e6	−0.212453
$730$	3.16632e6	0.219912
$731$	−1.46914e7	−1.01688
$732$	958876.	0.0661431
$733$	−1.03216e7	−0.709559	−0.354779	−	0.934950i	$-0.615444\pi$
$733$	−1.03216e7	−0.709559	−0.354779	+	0.934950i	$0.615444\pi$
$734$	4.58947e6	0.314429
$735$	2.43846e6	0.166493
$736$	−2.00220e7	−1.36243
$737$	−3.01909e6	−0.204742
$738$	2.48257e7	1.67788
$739$	−5.68784e6	−0.383121	−0.191561	−	0.981481i	$-0.561355\pi$
$739$	−5.68784e6	−0.383121	−0.191561	+	0.981481i	$0.561355\pi$
$740$	4.88602e6	0.328001
$741$	−1.29349e6	−0.0865400
$742$	−6.49542e6	−0.433109
$743$	−2.60104e7	−1.72852	−0.864261	−	0.503044i	$-0.832213\pi$
$743$	−2.60104e7	−1.72852	−0.864261	+	0.503044i	$0.832213\pi$
$744$	−1.01627e6	−0.0673095
$745$	7.70582e6	0.508660
$746$	−3.97154e7	−2.61284
$747$	3.20030e6	0.209841
$748$	7.90045e6	0.516295
$749$	1.42744e6	0.0929721
$750$	776970.	0.0504372
$751$	−1.41909e7	−0.918144	−0.459072	−	0.888399i	$-0.651818\pi$
$751$	−1.41909e7	−0.918144	−0.459072	+	0.888399i	$0.651818\pi$
$752$	1.36294e7	0.878885
$753$	4.27829e6	0.274969
$754$	2.50141e7	1.60235
$755$	−7.89242e6	−0.503898
$756$	2.42335e6	0.154210
$757$	2.25578e7	1.43073	0.715365	−	0.698751i	$-0.246260\pi$
$757$	2.25578e7	1.43073	0.715365	+	0.698751i	$0.246260\pi$
$758$	4.10581e7	2.59553
$759$	1.75560e6	0.110617
$760$	310621.	0.0195073
$761$	−1.76971e6	−0.110774	−0.0553872	−	0.998465i	$-0.517639\pi$
$761$	−1.76971e6	−0.110774	−0.0553872	+	0.998465i	$0.517639\pi$
$762$	1.40257e7	0.875057
$763$	−5.49936e6	−0.341980
$764$	5.97651e6	0.370437
$765$	−9.32978e6	−0.576392
$766$	5.17812e6	0.318860
$767$	8.48681e6	0.520902
$768$	−4.36417e6	−0.266992
$769$	−2.32876e7	−1.42007	−0.710033	−	0.704169i	$-0.751320\pi$
$769$	−2.32876e7	−1.42007	−0.710033	+	0.704169i	$0.751320\pi$
$770$	−617818.	−0.0375520
$771$	2.58478e6	0.156599
$772$	−2.90974e7	−1.75716
$773$	−2.75836e7	−1.66036	−0.830181	−	0.557494i	$-0.811763\pi$
$773$	−2.75836e7	−1.66036	−0.830181	+	0.557494i	$0.811763\pi$
$774$	−1.38905e7	−0.833425
$775$	−3.06417e6	−0.183256
$776$	−3.33760e6	−0.198967
$777$	−805041.	−0.0478372
$778$	2.31502e7	1.37122
$779$	−5.25073e6	−0.310010
$780$	3.23986e6	0.190673
$781$	−6.60929e6	−0.387728
$782$	3.59067e7	2.09971
$783$	1.37934e7	0.804020
$784$	1.41420e7	0.821714
$785$	−2.94195e6	−0.170397
$786$	1.90604e7	1.10046
$787$	3.32205e6	0.191192	0.0955960	−	0.995420i	$-0.469524\pi$
$787$	3.32205e6	0.191192	0.0955960	+	0.995420i	$0.469524\pi$
$788$	1.41617e7	0.812454
$789$	7.68076e6	0.439250
$790$	−2.94655e6	−0.167976
$791$	1.87233e6	0.106400
$792$	860925.	0.0487700
$793$	2.61879e6	0.147883
$794$	1.33296e7	0.750355
$795$	−4.78855e6	−0.268712
$796$	1.54545e7	0.864517
$797$	2.08736e7	1.16399	0.581997	−	0.813191i	$-0.302271\pi$
$797$	2.08736e7	1.16399	0.581997	+	0.813191i	$0.302271\pi$
$798$	−444053.	−0.0246847
$799$	−2.81763e7	−1.56141
$800$	5.19444e6	0.286955
$801$	−7.00881e6	−0.385979
$802$	3.05180e7	1.67540
$803$	−1.85613e6	−0.101583
$804$	5.43519e6	0.296534
$805$	−1.48981e6	−0.0810292
$806$	−2.40818e7	−1.30572
$807$	−1.08674e7	−0.587412
$808$	−5.56415e6	−0.299827
$809$	1.66436e7	0.894077	0.447038	−	0.894515i	$-0.352479\pi$
$809$	1.66436e7	0.894077	0.447038	+	0.894515i	$0.352479\pi$
$810$	−7.00180e6	−0.374970
$811$	−1.27949e7	−0.683100	−0.341550	−	0.939864i	$-0.610952\pi$
$811$	−1.27949e7	−0.683100	−0.341550	+	0.939864i	$0.610952\pi$
$812$	4.55622e6	0.242502
$813$	−557426.	−0.0295775
$814$	−5.39835e6	−0.285562
$815$	5.86361e6	0.309223
$816$	9.49410e6	0.499147
$817$	2.93790e6	0.153986
$818$	−1.23085e7	−0.643167
$819$	3.04231e6	0.158487
$820$	1.31518e7	0.683046
$821$	2.03567e7	1.05402	0.527010	−	0.849859i	$-0.323313\pi$
$821$	2.03567e7	1.05402	0.527010	+	0.849859i	$0.323313\pi$
$822$	−2.94782e6	−0.152167
$823$	−7.20199e6	−0.370641	−0.185320	−	0.982678i	$-0.559332\pi$
$823$	−7.20199e6	−0.370641	−0.185320	+	0.982678i	$0.559332\pi$
$824$	7.13716e6	0.366191
$825$	−455468.	−0.0232982
$826$	2.91351e6	0.148582
$827$	3.37690e7	1.71694	0.858469	−	0.512866i	$-0.171416\pi$
$827$	3.37690e7	1.71694	0.858469	+	0.512866i	$0.171416\pi$
$828$	1.80126e7	0.913065
$829$	2.79898e6	0.141454	0.0707268	−	0.997496i	$-0.477468\pi$
$829$	2.79898e6	0.141454	0.0707268	+	0.997496i	$0.477468\pi$
$830$	3.19541e6	0.161002
$831$	9.54793e6	0.479630
$832$	2.41997e7	1.21200
$833$	−2.92360e7	−1.45984
$834$	8.47892e6	0.422110
$835$	−1.11627e7	−0.554056
$836$	−1.57988e6	−0.0781823
$837$	−1.32793e7	−0.655180
$838$	−2.73344e7	−1.34462
$839$	3.17640e7	1.55787	0.778934	−	0.627106i	$-0.215761\pi$
$839$	3.17640e7	1.55787	0.778934	+	0.627106i	$0.215761\pi$
$840$	128191.	0.00626845
$841$	5.42228e6	0.264358
$842$	3.12416e6	0.151864
$843$	1.03751e7	0.502833
$844$	2.42653e7	1.17255
$845$	−433904.	−0.0209051
$846$	−2.66403e7	−1.27971
$847$	362171.	0.0173462
$848$	−2.77715e7	−1.32620
$849$	8.52470e6	0.405892
$850$	−9.31551e6	−0.442241
$851$	−1.30176e7	−0.616180
$852$	1.18985e7	0.561558
$853$	2.26751e7	1.06703	0.533514	−	0.845791i	$-0.320871\pi$
$853$	2.26751e7	1.06703	0.533514	+	0.845791i	$0.320871\pi$
$854$	899028.	0.0421821
$855$	1.86571e6	0.0872829
$856$	−1.98608e6	−0.0926431
$857$	−3.15983e7	−1.46964	−0.734820	−	0.678262i	$-0.762734\pi$
$857$	−3.15983e7	−1.46964	−0.734820	+	0.678262i	$0.762734\pi$
$858$	−3.57958e6	−0.166002
$859$	−1.48466e7	−0.686506	−0.343253	−	0.939243i	$-0.611529\pi$
$859$	−1.48466e7	−0.686506	−0.343253	+	0.939243i	$0.611529\pi$
$860$	−7.35871e6	−0.339278
$861$	−2.16694e6	−0.0996185
$862$	1.68504e7	0.772399
$863$	−2.04618e7	−0.935225	−0.467612	−	0.883934i	$-0.654886\pi$
$863$	−2.04618e7	−0.935225	−0.467612	+	0.883934i	$0.654886\pi$
$864$	2.25113e7	1.02593
$865$	7.54590e6	0.342903
$866$	5.02459e7	2.27670
$867$	−1.10759e7	−0.500417
$868$	−4.38640e6	−0.197610
$869$	1.72730e6	0.0775921
$870$	6.33074e6	0.283567
$871$	1.48441e7	0.662992
$872$	7.65160e6	0.340770
$873$	−2.00470e7	−0.890252
$874$	−7.18039e6	−0.317958
$875$	386512.	0.0170664
$876$	3.34154e6	0.147125
$877$	−2.58986e7	−1.13704	−0.568522	−	0.822668i	$-0.692484\pi$
$877$	−2.58986e7	−1.13704	−0.568522	+	0.822668i	$0.692484\pi$
$878$	3.40094e7	1.48889
$879$	1.49903e7	0.654394
$880$	−2.64151e6	−0.114986
$881$	−3.98303e6	−0.172891	−0.0864457	−	0.996257i	$-0.527551\pi$
$881$	−3.98303e6	−0.172891	−0.0864457	+	0.996257i	$0.527551\pi$
$882$	−2.76422e7	−1.19647
$883$	2.17160e7	0.937300	0.468650	−	0.883384i	$-0.344741\pi$
$883$	2.17160e7	0.937300	0.468650	+	0.883384i	$0.344741\pi$
$884$	−3.88445e7	−1.67185
$885$	2.14790e6	0.0921840
$886$	1.15908e7	0.496055
$887$	2.16000e7	0.921816	0.460908	−	0.887448i	$-0.347524\pi$
$887$	2.16000e7	0.921816	0.460908	+	0.887448i	$0.347524\pi$
$888$	1.12010e6	0.0476679
$889$	6.97722e6	0.296093
$890$	−6.99809e6	−0.296145
$891$	4.10452e6	0.173208
$892$	−2.57902e7	−1.08528
$893$	5.63451e6	0.236444
$894$	1.53272e7	0.641386
$895$	−1.11797e7	−0.466521
$896$	1.72884e6	0.0719424
$897$	−8.63184e6	−0.358197
$898$	−6.18411e7	−2.55910
$899$	−2.49668e7	−1.03030
$900$	−4.67314e6	−0.192310
$901$	5.74125e7	2.35611
$902$	−1.45308e7	−0.594667
$903$	1.21245e6	0.0494818
$904$	−2.60509e6	−0.106023
$905$	1.89400e7	0.768705
$906$	−1.56984e7	−0.635380
$907$	−4.09708e7	−1.65370	−0.826850	−	0.562423i	$-0.809869\pi$
$907$	−4.09708e7	−1.65370	−0.826850	+	0.562423i	$0.809869\pi$
$908$	4.12967e6	0.166227
$909$	−3.34205e7	−1.34154
$910$	3.03765e6	0.121600
$911$	−1.18740e7	−0.474025	−0.237013	−	0.971507i	$-0.576168\pi$
$911$	−1.18740e7	−0.474025	−0.237013	+	0.971507i	$0.576168\pi$
$912$	−1.89857e6	−0.0755857
$913$	−1.87318e6	−0.0743708
$914$	−3.42692e7	−1.35687
$915$	662782.	0.0261708
$916$	4.51446e7	1.77773
$917$	9.48178e6	0.372363
$918$	−4.03708e7	−1.58111
$919$	−1.96775e7	−0.768565	−0.384283	−	0.923215i	$-0.625551\pi$
$919$	−1.96775e7	−0.768565	−0.384283	+	0.923215i	$0.625551\pi$
$920$	2.07287e6	0.0807425
$921$	6.56821e6	0.255151
$922$	1.89196e7	0.732969
$923$	3.24962e7	1.25553
$924$	−652007.	−0.0251230
$925$	3.37725e6	0.129780
$926$	−3.23217e6	−0.123870
$927$	4.28686e7	1.63848
$928$	4.23242e7	1.61331
$929$	−4.86550e7	−1.84964	−0.924822	−	0.380399i	$-0.875787\pi$
$929$	−4.86550e7	−1.84964	−0.924822	+	0.380399i	$0.875787\pi$
$930$	−6.09478e6	−0.231074
$931$	5.84643e6	0.221063
$932$	3.09316e7	1.16644
$933$	−480596.	−0.0180749
$934$	2.10710e7	0.790346
$935$	5.46084e6	0.204282
$936$	−4.23295e6	−0.157926
$937$	4.63189e7	1.72349	0.861747	−	0.507339i	$-0.169371\pi$
$937$	4.63189e7	1.72349	0.861747	+	0.507339i	$0.169371\pi$
$938$	5.09596e6	0.189112
$939$	−8.33811e6	−0.308605
$940$	−1.41131e7	−0.520956
$941$	1.38189e7	0.508743	0.254372	−	0.967107i	$-0.418131\pi$
$941$	1.38189e7	0.508743	0.254372	+	0.967107i	$0.418131\pi$
$942$	−5.85167e6	−0.214859
$943$	−3.50398e7	−1.28316
$944$	1.24569e7	0.454966
$945$	1.67504e6	0.0610161
$946$	8.13031e6	0.295379
$947$	−4.31629e7	−1.56400	−0.781998	−	0.623281i	$-0.785799\pi$
$947$	−4.31629e7	−1.56400	−0.781998	+	0.623281i	$0.785799\pi$
$948$	−3.10961e6	−0.112379
$949$	9.12611e6	0.328943
$950$	1.86286e6	0.0669685
$951$	1.64000e7	0.588020
$952$	−1.53695e6	−0.0549627
$953$	−2.15877e7	−0.769971	−0.384986	−	0.922923i	$-0.625794\pi$
$953$	−2.15877e7	−0.769971	−0.384986	+	0.922923i	$0.625794\pi$
$954$	5.42827e7	1.93104
$955$	4.13100e6	0.146571
$956$	2.69768e6	0.0954652
$957$	−3.71114e6	−0.130987
$958$	4.19074e7	1.47529
$959$	−1.46642e6	−0.0514888
$960$	6.12462e6	0.214487
$961$	−4.59288e6	−0.160427
$962$	2.65423e7	0.924699
$963$	−1.19292e7	−0.414520
$964$	2.08428e7	0.722376
$965$	−2.01123e7	−0.695256
$966$	−2.96330e6	−0.102172
$967$	2.36627e7	0.813763	0.406882	−	0.913481i	$-0.366616\pi$
$967$	2.36627e7	0.813763	0.406882	+	0.913481i	$0.366616\pi$
$968$	−503911.	−0.0172848
$969$	3.92495e6	0.134284
$970$	−2.00163e7	−0.683053
$971$	1.06192e7	0.361447	0.180724	−	0.983534i	$-0.442156\pi$
$971$	1.06192e7	0.361447	0.180724	+	0.983534i	$0.442156\pi$
$972$	−3.11949e7	−1.05905
$973$	4.21793e6	0.142829
$974$	4.61089e7	1.55735
$975$	2.23942e6	0.0754438
$976$	3.84384e6	0.129164
$977$	3.36804e7	1.12886	0.564430	−	0.825481i	$-0.309096\pi$
$977$	3.36804e7	1.12886	0.564430	+	0.825481i	$0.309096\pi$
$978$	1.16630e7	0.389908
$979$	4.10235e6	0.136797
$980$	−1.46438e7	−0.487068
$981$	4.59586e7	1.52473
$982$	3.13375e7	1.03702
$983$	−2.98045e7	−0.983780	−0.491890	−	0.870657i	$-0.663694\pi$
$983$	−2.98045e7	−0.983780	−0.491890	+	0.870657i	$0.663694\pi$
$984$	3.01501e6	0.0992660
$985$	9.78864e6	0.321464
$986$	−7.59026e7	−2.48636
$987$	2.32533e6	0.0759786
$988$	7.76787e6	0.253168
$989$	1.96055e7	0.637364
$990$	5.16315e6	0.167427
$991$	−4.07017e7	−1.31652	−0.658261	−	0.752790i	$-0.728708\pi$
$991$	−4.07017e7	−1.31652	−0.658261	+	0.752790i	$0.728708\pi$
$992$	−4.07467e7	−1.31466
$993$	1.17191e7	0.377156
$994$	1.11559e7	0.358128
$995$	1.06823e7	0.342063
$996$	3.37223e6	0.107713
$997$	1.37634e7	0.438519	0.219259	−	0.975667i	$-0.429636\pi$
$997$	1.37634e7	0.438519	0.219259	+	0.975667i	$0.429636\pi$
$998$	−8.25331e7	−2.62302
$999$	1.46361e7	0.463992

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.e.1.8	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.e.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-8.25643 q^{2} -6.02271 q^{3} +36.1686 q^{4} +25.0000 q^{5} +49.7261 q^{6} +24.7368 q^{7} -34.4178 q^{8} -206.727 q^{9} +O(q^{10})\)	\(q-8.25643 q^{2} -6.02271 q^{3} +36.1686 q^{4} +25.0000 q^{5} +49.7261 q^{6} +24.7368 q^{7} -34.4178 q^{8} -206.727 q^{9} -206.411 q^{10} +121.000 q^{11} -217.833 q^{12} -594.926 q^{13} -204.237 q^{14} -150.568 q^{15} -873.227 q^{16} +1805.24 q^{17} +1706.83 q^{18} -361.000 q^{19} +904.215 q^{20} -148.982 q^{21} -999.028 q^{22} -2409.07 q^{23} +207.289 q^{24} +625.000 q^{25} +4911.96 q^{26} +2708.58 q^{27} +894.694 q^{28} +5092.49 q^{29} +1243.15 q^{30} -4902.68 q^{31} +8311.11 q^{32} -728.748 q^{33} -14904.8 q^{34} +618.419 q^{35} -7477.03 q^{36} +5403.60 q^{37} +2980.57 q^{38} +3583.07 q^{39} -860.445 q^{40} +14545.0 q^{41} +1230.06 q^{42} -8138.22 q^{43} +4376.40 q^{44} -5168.17 q^{45} +19890.3 q^{46} -15608.1 q^{47} +5259.20 q^{48} -16195.1 q^{49} -5160.27 q^{50} -10872.4 q^{51} -21517.6 q^{52} +31803.3 q^{53} -22363.2 q^{54} +3025.00 q^{55} -851.385 q^{56} +2174.20 q^{57} -42045.8 q^{58} -14265.3 q^{59} -5445.83 q^{60} -4401.88 q^{61} +40478.6 q^{62} -5113.75 q^{63} -40676.8 q^{64} -14873.1 q^{65} +6016.86 q^{66} -24951.2 q^{67} +65292.9 q^{68} +14509.1 q^{69} -5105.93 q^{70} -54622.2 q^{71} +7115.09 q^{72} -15339.9 q^{73} -44614.4 q^{74} -3764.20 q^{75} -13056.9 q^{76} +2993.15 q^{77} -29583.3 q^{78} +14275.2 q^{79} -21830.7 q^{80} +33921.7 q^{81} -120089. q^{82} -15480.8 q^{83} -5388.49 q^{84} +45130.9 q^{85} +67192.7 q^{86} -30670.6 q^{87} -4164.55 q^{88} +33903.7 q^{89} +42670.7 q^{90} -14716.5 q^{91} -87132.5 q^{92} +29527.4 q^{93} +128867. q^{94} -9025.00 q^{95} -50055.4 q^{96} +96973.2 q^{97} +133714. q^{98} -25014.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9}+O(q^{10}) \) 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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