LMFDB - Embedded newform 1045.6.a.e.1.16

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			1.16
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67362 q^{2} -11.1309 q^{3} -24.8518 q^{4} +25.0000 q^{5} +29.7598 q^{6} +158.866 q^{7} +152.000 q^{8} -119.103 q^{9} +O(q^{10})$	\(q-2.67362 q^{2} -11.1309 q^{3} -24.8518 q^{4} +25.0000 q^{5} +29.7598 q^{6} +158.866 q^{7} +152.000 q^{8} -119.103 q^{9} -66.8405 q^{10} +121.000 q^{11} +276.623 q^{12} +28.0995 q^{13} -424.746 q^{14} -278.273 q^{15} +388.867 q^{16} +594.756 q^{17} +318.435 q^{18} -361.000 q^{19} -621.294 q^{20} -1768.32 q^{21} -323.508 q^{22} -639.193 q^{23} -1691.90 q^{24} +625.000 q^{25} -75.1273 q^{26} +4030.53 q^{27} -3948.09 q^{28} +1512.48 q^{29} +743.995 q^{30} -3791.35 q^{31} -5903.68 q^{32} -1346.84 q^{33} -1590.15 q^{34} +3971.64 q^{35} +2959.91 q^{36} -14890.2 q^{37} +965.176 q^{38} -312.773 q^{39} +3800.00 q^{40} -17630.9 q^{41} +4727.81 q^{42} +16177.1 q^{43} -3007.06 q^{44} -2977.57 q^{45} +1708.96 q^{46} +9812.98 q^{47} -4328.44 q^{48} +8431.27 q^{49} -1671.01 q^{50} -6620.18 q^{51} -698.321 q^{52} -3001.00 q^{53} -10776.1 q^{54} +3025.00 q^{55} +24147.6 q^{56} +4018.26 q^{57} -4043.80 q^{58} -38382.2 q^{59} +6915.57 q^{60} -19545.8 q^{61} +10136.6 q^{62} -18921.3 q^{63} +3340.45 q^{64} +702.487 q^{65} +3600.94 q^{66} -12987.1 q^{67} -14780.7 q^{68} +7114.80 q^{69} -10618.6 q^{70} +59486.4 q^{71} -18103.6 q^{72} +81674.0 q^{73} +39810.6 q^{74} -6956.82 q^{75} +8971.49 q^{76} +19222.7 q^{77} +836.235 q^{78} -82205.5 q^{79} +9721.66 q^{80} -15921.5 q^{81} +47138.3 q^{82} +55610.5 q^{83} +43945.8 q^{84} +14868.9 q^{85} -43251.3 q^{86} -16835.3 q^{87} +18392.0 q^{88} +570.416 q^{89} +7960.89 q^{90} +4464.04 q^{91} +15885.1 q^{92} +42201.2 q^{93} -26236.2 q^{94} -9025.00 q^{95} +65713.3 q^{96} +177715. q^{97} -22542.0 q^{98} -14411.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.67362	−0.472633	−0.236317	−	0.971676i	$-0.575940\pi$
$2$	−2.67362	−0.472633	−0.236317	+	0.971676i	$0.575940\pi$
$3$	−11.1309	−0.714048	−0.357024	−	0.934095i	$-0.616209\pi$
$3$	−11.1309	−0.714048	−0.357024	+	0.934095i	$0.616209\pi$
$4$	−24.8518	−0.776618
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	29.7598	0.337483
$7$	158.866	1.22542	0.612710	−	0.790308i	$-0.290080\pi$
$7$	158.866	1.22542	0.612710	+	0.790308i	$0.290080\pi$
$8$	152.000	0.839689
$9$	−119.103	−0.490135
$10$	−66.8405	−0.211368
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	276.623	0.554543
$13$	28.0995	0.0461147	0.0230574	−	0.999734i	$-0.492660\pi$
$13$	28.0995	0.0461147	0.0230574	+	0.999734i	$0.492660\pi$
$14$	−424.746	−0.579174
$15$	−278.273	−0.319332
$16$	388.867	0.379753
$17$	594.756	0.499133	0.249567	−	0.968358i	$-0.419712\pi$
$17$	594.756	0.499133	0.249567	+	0.968358i	$0.419712\pi$
$18$	318.435	0.231654
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−621.294	−0.347314
$21$	−1768.32	−0.875009
$22$	−323.508	−0.142504
$23$	−639.193	−0.251949	−0.125974	−	0.992033i	$-0.540206\pi$
$23$	−639.193	−0.251949	−0.125974	+	0.992033i	$0.540206\pi$
$24$	−1691.90	−0.599579
$25$	625.000	0.200000
$26$	−75.1273	−0.0217954
$27$	4030.53	1.06403
$28$	−3948.09	−0.951682
$29$	1512.48	0.333960	0.166980	−	0.985960i	$-0.446598\pi$
$29$	1512.48	0.333960	0.166980	+	0.985960i	$0.446598\pi$
$30$	743.995	0.150927
$31$	−3791.35	−0.708581	−0.354290	−	0.935135i	$-0.615278\pi$
$31$	−3791.35	−0.708581	−0.354290	+	0.935135i	$0.615278\pi$
$32$	−5903.68	−1.01917
$33$	−1346.84	−0.215294
$34$	−1590.15	−0.235907
$35$	3971.64	0.548024
$36$	2959.91	0.380647
$37$	−14890.2	−1.78811	−0.894057	−	0.447953i	$-0.852153\pi$
$37$	−14890.2	−1.78811	−0.894057	+	0.447953i	$0.852153\pi$
$38$	965.176	0.108430
$39$	−312.773	−0.0329282
$40$	3800.00	0.375520
$41$	−17630.9	−1.63800	−0.819002	−	0.573791i	$-0.805472\pi$
$41$	−17630.9	−1.63800	−0.819002	+	0.573791i	$0.805472\pi$
$42$	4727.81	0.413558
$43$	16177.1	1.33422	0.667112	−	0.744958i	$-0.267530\pi$
$43$	16177.1	1.33422	0.667112	+	0.744958i	$0.267530\pi$
$44$	−3007.06	−0.234159
$45$	−2977.57	−0.219195
$46$	1708.96	0.119079
$47$	9812.98	0.647972	0.323986	−	0.946062i	$-0.394977\pi$
$47$	9812.98	0.647972	0.323986	+	0.946062i	$0.394977\pi$
$48$	−4328.44	−0.271162
$49$	8431.27	0.501652
$50$	−1671.01	−0.0945267
$51$	−6620.18	−0.356405
$52$	−698.321	−0.0358135
$53$	−3001.00	−0.146749	−0.0733747	−	0.997304i	$-0.523377\pi$
$53$	−3001.00	−0.146749	−0.0733747	+	0.997304i	$0.523377\pi$
$54$	−10776.1	−0.502895
$55$	3025.00	0.134840
$56$	24147.6	1.02897
$57$	4018.26	0.163814
$58$	−4043.80	−0.157841
$59$	−38382.2	−1.43549	−0.717745	−	0.696306i	$-0.754826\pi$
$59$	−38382.2	−1.43549	−0.717745	+	0.696306i	$0.754826\pi$
$60$	6915.57	0.247999
$61$	−19545.8	−0.672557	−0.336279	−	0.941763i	$-0.609168\pi$
$61$	−19545.8	−0.672557	−0.336279	+	0.941763i	$0.609168\pi$
$62$	10136.6	0.334899
$63$	−18921.3	−0.600621
$64$	3340.45	0.101943
$65$	702.487	0.0206231
$66$	3600.94	0.101755
$67$	−12987.1	−0.353447	−0.176724	−	0.984261i	$-0.556550\pi$
$67$	−12987.1	−0.353447	−0.176724	+	0.984261i	$0.556550\pi$
$68$	−14780.7	−0.387636
$69$	7114.80	0.179904
$70$	−10618.6	−0.259015
$71$	59486.4	1.40046	0.700232	−	0.713915i	$-0.253080\pi$
$71$	59486.4	1.40046	0.700232	+	0.713915i	$0.253080\pi$
$72$	−18103.6	−0.411561
$73$	81674.0	1.79381	0.896906	−	0.442221i	$-0.145809\pi$
$73$	81674.0	1.79381	0.896906	+	0.442221i	$0.145809\pi$
$74$	39810.6	0.845123
$75$	−6956.82	−0.142810
$76$	8971.49	0.178168
$77$	19222.7	0.369478
$78$	836.235	0.0155629
$79$	−82205.5	−1.48195	−0.740974	−	0.671533i	$-0.765636\pi$
$79$	−82205.5	−1.48195	−0.740974	+	0.671533i	$0.765636\pi$
$80$	9721.66	0.169830
$81$	−15921.5	−0.269633
$82$	47138.3	0.774175
$83$	55610.5	0.886057	0.443028	−	0.896508i	$-0.353904\pi$
$83$	55610.5	0.886057	0.443028	+	0.896508i	$0.353904\pi$
$84$	43945.8	0.679547
$85$	14868.9	0.223219
$86$	−43251.3	−0.630599
$87$	−16835.3	−0.238464
$88$	18392.0	0.253176
$89$	570.416	0.00763338	0.00381669	−	0.999993i	$-0.498785\pi$
$89$	570.416	0.00763338	0.00381669	+	0.999993i	$0.498785\pi$
$90$	7960.89	0.103599
$91$	4464.04	0.0565099
$92$	15885.1	0.195668
$93$	42201.2	0.505961
$94$	−26236.2	−0.306253
$95$	−9025.00	−0.102598
$96$	65713.3	0.727739
$97$	177715.	1.91777	0.958884	−	0.283799i	$-0.0915949\pi$
$97$	177715.	1.91777	0.958884	+	0.283799i	$0.0915949\pi$
$98$	−22542.0	−0.237098
$99$	−14411.4	−0.147781
$100$	−15532.4	−0.155324
$101$	30127.1	0.293869	0.146935	−	0.989146i	$-0.453059\pi$
$101$	30127.1	0.293869	0.146935	+	0.989146i	$0.453059\pi$
$102$	17699.8	0.168449
$103$	−6069.97	−0.0563759	−0.0281879	−	0.999603i	$-0.508974\pi$
$103$	−6069.97	−0.0563759	−0.0281879	+	0.999603i	$0.508974\pi$
$104$	4271.12	0.0387220
$105$	−44208.0	−0.391316
$106$	8023.53	0.0693587
$107$	69323.3	0.585356	0.292678	−	0.956211i	$-0.405454\pi$
$107$	69323.3	0.585356	0.292678	+	0.956211i	$0.405454\pi$
$108$	−100166.	−0.826343
$109$	−153955.	−1.24116	−0.620578	−	0.784144i	$-0.713102\pi$
$109$	−153955.	−1.24116	−0.620578	+	0.784144i	$0.713102\pi$
$110$	−8087.70	−0.0637299
$111$	165741.	1.27680
$112$	61777.5	0.465356
$113$	−153923.	−1.13398	−0.566992	−	0.823724i	$-0.691893\pi$
$113$	−153923.	−1.13398	−0.566992	+	0.823724i	$0.691893\pi$
$114$	−10743.3	−0.0774239
$115$	−15979.8	−0.112675
$116$	−37587.8	−0.259359
$117$	−3346.73	−0.0226024
$118$	102619.	0.678461
$119$	94486.3	0.611648
$120$	−42297.4	−0.268140
$121$	14641.0	0.0909091
$122$	52258.0	0.317873
$123$	196248.	1.16961
$124$	94221.7	0.550296
$125$	15625.0	0.0894427
$126$	50588.4	0.283873
$127$	282905.	1.55643	0.778217	−	0.627996i	$-0.216124\pi$
$127$	282905.	1.55643	0.778217	+	0.627996i	$0.216124\pi$
$128$	179987.	0.970991
$129$	−180066.	−0.952700
$130$	−1878.18	−0.00974719
$131$	376340.	1.91603	0.958014	−	0.286720i	$-0.0925650\pi$
$131$	376340.	1.91603	0.958014	+	0.286720i	$0.0925650\pi$
$132$	33471.4	0.167201
$133$	−57350.5	−0.281130
$134$	34722.5	0.167051
$135$	100763.	0.475848
$136$	90402.9	0.419117
$137$	206452.	0.939759	0.469880	−	0.882730i	$-0.344297\pi$
$137$	206452.	0.939759	0.469880	+	0.882730i	$0.344297\pi$
$138$	−19022.3	−0.0850284
$139$	−256355.	−1.12539	−0.562697	−	0.826664i	$-0.690236\pi$
$139$	−256355.	−1.12539	−0.562697	+	0.826664i	$0.690236\pi$
$140$	−98702.2	−0.425605
$141$	−109227.	−0.462683
$142$	−159044.	−0.661906
$143$	3400.04	0.0139041
$144$	−46315.1	−0.186130
$145$	37812.0	0.149352
$146$	−218365.	−0.847816
$147$	−93847.7	−0.358204
$148$	370047.	1.38868
$149$	−135691.	−0.500708	−0.250354	−	0.968154i	$-0.580547\pi$
$149$	−135691.	−0.500708	−0.250354	+	0.968154i	$0.580547\pi$
$150$	18599.9	0.0674966
$151$	−97450.0	−0.347808	−0.173904	−	0.984763i	$-0.555638\pi$
$151$	−97450.0	−0.347808	−0.173904	+	0.984763i	$0.555638\pi$
$152$	−54872.0	−0.192638
$153$	−70837.1	−0.244643
$154$	−51394.3	−0.174628
$155$	−94783.7	−0.316887
$156$	7772.96	0.0255726
$157$	287217.	0.929954	0.464977	−	0.885323i	$-0.346063\pi$
$157$	287217.	0.929954	0.464977	+	0.885323i	$0.346063\pi$
$158$	219786.	0.700418
$159$	33403.9	0.104786
$160$	−147592.	−0.455788
$161$	−101546.	−0.308743
$162$	42568.2	0.127438
$163$	−19331.6	−0.0569901	−0.0284951	−	0.999594i	$-0.509071\pi$
$163$	−19331.6	−0.0569901	−0.0284951	+	0.999594i	$0.509071\pi$
$164$	438159.	1.27210
$165$	−33671.0	−0.0962823
$166$	−148681.	−0.418780
$167$	317091.	0.879819	0.439909	−	0.898042i	$-0.355011\pi$
$167$	317091.	0.879819	0.439909	+	0.898042i	$0.355011\pi$
$168$	−268784.	−0.734735
$169$	−370503.	−0.997873
$170$	−39753.8	−0.105501
$171$	42996.1	0.112445
$172$	−402029.	−1.03618
$173$	−588624.	−1.49528	−0.747640	−	0.664104i	$-0.768813\pi$
$173$	−588624.	−1.49528	−0.747640	+	0.664104i	$0.768813\pi$
$174$	45011.1	0.112706
$175$	99291.0	0.245084
$176$	47052.9	0.114500
$177$	427229.	1.02501
$178$	−1525.07	−0.00360779
$179$	−129454.	−0.301982	−0.150991	−	0.988535i	$-0.548247\pi$
$179$	−129454.	−0.301982	−0.150991	+	0.988535i	$0.548247\pi$
$180$	73997.9	0.170231
$181$	−856115.	−1.94239	−0.971194	−	0.238292i	$-0.923412\pi$
$181$	−856115.	−1.94239	−0.971194	+	0.238292i	$0.923412\pi$
$182$	−11935.1	−0.0267085
$183$	217563.	0.480238
$184$	−97157.2	−0.211559
$185$	−372254.	−0.799669
$186$	−112830.	−0.239134
$187$	71965.5	0.150494
$188$	−243870.	−0.503226
$189$	640313.	1.30388
$190$	24129.4	0.0484912
$191$	−924734.	−1.83414	−0.917072	−	0.398722i	$-0.869454\pi$
$191$	−924734.	−1.83414	−0.917072	+	0.398722i	$0.869454\pi$
$192$	−37182.3	−0.0727919
$193$	−835323.	−1.61421	−0.807107	−	0.590405i	$-0.798968\pi$
$193$	−835323.	−1.61421	−0.807107	+	0.590405i	$0.798968\pi$
$194$	−475143.	−0.906401
$195$	−7819.32	−0.0147259
$196$	−209532.	−0.389592
$197$	−239783.	−0.440204	−0.220102	−	0.975477i	$-0.570639\pi$
$197$	−239783.	−0.440204	−0.220102	+	0.975477i	$0.570639\pi$
$198$	38530.7	0.0698464
$199$	−29003.5	−0.0519180	−0.0259590	−	0.999663i	$-0.508264\pi$
$199$	−29003.5	−0.0519180	−0.0259590	+	0.999663i	$0.508264\pi$
$200$	95000.0	0.167938
$201$	144558.	0.252378
$202$	−80548.4	−0.138892
$203$	240281.	0.409241
$204$	164523.	0.276791
$205$	−440773.	−0.732537
$206$	16228.8	0.0266451
$207$	76129.6	0.123489
$208$	10926.9	0.0175122
$209$	−43681.0	−0.0691714
$210$	118195.	0.184949
$211$	713199.	1.10282	0.551410	−	0.834234i	$-0.314090\pi$
$211$	713199.	1.10282	0.551410	+	0.834234i	$0.314090\pi$
$212$	74580.2	0.113968
$213$	−662138.	−0.999999
$214$	−185344.	−0.276659
$215$	404427.	0.596683
$216$	612641.	0.893453
$217$	−602314.	−0.868308
$218$	411616.	0.586612
$219$	−909107.	−1.28087
$220$	−75176.6	−0.104719
$221$	16712.3	0.0230174
$222$	−443129.	−0.603459
$223$	527793.	0.710725	0.355363	−	0.934728i	$-0.384357\pi$
$223$	527793.	0.710725	0.355363	+	0.934728i	$0.384357\pi$
$224$	−937891.	−1.24891
$225$	−74439.2	−0.0980270
$226$	411531.	0.535958
$227$	−1.40705e6	−1.81236	−0.906181	−	0.422890i	$-0.861016\pi$
$227$	−1.40705e6	−1.81236	−0.906181	+	0.422890i	$0.861016\pi$
$228$	−99860.8	−0.127221
$229$	−33615.3	−0.0423592	−0.0211796	−	0.999776i	$-0.506742\pi$
$229$	−33615.3	−0.0423592	−0.0211796	+	0.999776i	$0.506742\pi$
$230$	42723.9	0.0532539
$231$	−213967.	−0.263825
$232$	229897.	0.280423
$233$	−1.32292e6	−1.59641	−0.798205	−	0.602385i	$-0.794217\pi$
$233$	−1.32292e6	−1.59641	−0.798205	+	0.602385i	$0.794217\pi$
$234$	8947.87	0.0106827
$235$	245324.	0.289782
$236$	953866.	1.11483
$237$	915022.	1.05818
$238$	−252620.	−0.289085
$239$	633228.	0.717077	0.358538	−	0.933515i	$-0.383275\pi$
$239$	633228.	0.717077	0.358538	+	0.933515i	$0.383275\pi$
$240$	−108211.	−0.121267
$241$	1.03481e6	1.14768	0.573839	−	0.818968i	$-0.305454\pi$
$241$	1.03481e6	1.14768	0.573839	+	0.818968i	$0.305454\pi$
$242$	−39144.4	−0.0429667
$243$	−802198.	−0.871498
$244$	485748.	0.522320
$245$	210782.	0.224346
$246$	−524692.	−0.552799
$247$	−10143.9	−0.0105794
$248$	−576284.	−0.594987
$249$	−618996.	−0.632688
$250$	−41775.3	−0.0422736
$251$	−1.05570e6	−1.05769	−0.528844	−	0.848719i	$-0.677374\pi$
$251$	−1.05570e6	−1.05769	−0.528844	+	0.848719i	$0.677374\pi$
$252$	470228.	0.466453
$253$	−77342.3	−0.0759654
$254$	−756379.	−0.735623
$255$	−165504.	−0.159389
$256$	−588110.	−0.560866
$257$	266463.	0.251654	0.125827	−	0.992052i	$-0.459842\pi$
$257$	266463.	0.251654	0.125827	+	0.992052i	$0.459842\pi$
$258$	481427.	0.450278
$259$	−2.36554e6	−2.19119
$260$	−17458.0	−0.0160163
$261$	−180141.	−0.163686
$262$	−1.00619e6	−0.905579
$263$	−29997.0	−0.0267416	−0.0133708	−	0.999911i	$-0.504256\pi$
$263$	−29997.0	−0.0267416	−0.0133708	+	0.999911i	$0.504256\pi$
$264$	−204720.	−0.180780
$265$	−75025.0	−0.0656284
$266$	153333.	0.132872
$267$	−6349.25	−0.00545060
$268$	322752.	0.274493
$269$	−832965.	−0.701853	−0.350927	−	0.936403i	$-0.614133\pi$
$269$	−832965.	−0.701853	−0.350927	+	0.936403i	$0.614133\pi$
$270$	−269403.	−0.224902
$271$	261551.	0.216339	0.108169	−	0.994132i	$-0.465501\pi$
$271$	261551.	0.216339	0.108169	+	0.994132i	$0.465501\pi$
$272$	231281.	0.189547
$273$	−49688.8	−0.0403508
$274$	−551973.	−0.444162
$275$	75625.0	0.0603023
$276$	−176815.	−0.139716
$277$	1.32909e6	1.04077	0.520386	−	0.853931i	$-0.325788\pi$
$277$	1.32909e6	1.04077	0.520386	+	0.853931i	$0.325788\pi$
$278$	685395.	0.531898
$279$	451560.	0.347300
$280$	603689.	0.460170
$281$	1.88953e6	1.42754	0.713769	−	0.700381i	$-0.246987\pi$
$281$	1.88953e6	1.42754	0.713769	+	0.700381i	$0.246987\pi$
$282$	292032.	0.218680
$283$	−77783.1	−0.0577323	−0.0288662	−	0.999583i	$-0.509190\pi$
$283$	−77783.1	−0.0577323	−0.0288662	+	0.999583i	$0.509190\pi$
$284$	−1.47834e6	−1.08763
$285$	100456.	0.0732598
$286$	−9090.40	−0.00657155
$287$	−2.80094e6	−2.00724
$288$	703145.	0.499532
$289$	−1.06612e6	−0.750866
$290$	−101095.	−0.0705885
$291$	−1.97814e6	−1.36938
$292$	−2.02974e6	−1.39311
$293$	1.89833e6	1.29182	0.645911	−	0.763413i	$-0.276478\pi$
$293$	1.89833e6	1.29182	0.645911	+	0.763413i	$0.276478\pi$
$294$	250913.	0.169299
$295$	−959556.	−0.641971
$296$	−2.26330e6	−1.50146
$297$	487695.	0.320817
$298$	362785.	0.236651
$299$	−17961.0	−0.0116185
$300$	172889.	0.110909
$301$	2.56998e6	1.63498
$302$	260544.	0.164386
$303$	−335342.	−0.209837
$304$	−140381.	−0.0871212
$305$	−488645.	−0.300777
$306$	189391.	0.115626
$307$	1.71376e6	1.03778	0.518890	−	0.854841i	$-0.326346\pi$
$307$	1.71376e6	1.03778	0.518890	+	0.854841i	$0.326346\pi$
$308$	−477719.	−0.286943
$309$	67564.3	0.0402551
$310$	253415.	0.149771
$311$	−2.61114e6	−1.53084	−0.765419	−	0.643533i	$-0.777468\pi$
$311$	−2.61114e6	−1.53084	−0.765419	+	0.643533i	$0.777468\pi$
$312$	−47541.4	−0.0276494
$313$	−669005.	−0.385983	−0.192992	−	0.981200i	$-0.561819\pi$
$313$	−669005.	−0.385983	−0.192992	+	0.981200i	$0.561819\pi$
$314$	−767910.	−0.439527
$315$	−473033.	−0.268606
$316$	2.04295e6	1.15091
$317$	634933.	0.354879	0.177439	−	0.984132i	$-0.443219\pi$
$317$	634933.	0.354879	0.177439	+	0.984132i	$0.443219\pi$
$318$	−89309.2	−0.0495255
$319$	183010.	0.100693
$320$	83511.4	0.0455901
$321$	−771632.	−0.417972
$322$	271494.	0.145922
$323$	−214707.	−0.114509
$324$	395679.	0.209402
$325$	17562.2	0.00922295
$326$	51685.4	0.0269355
$327$	1.71366e6	0.886246
$328$	−2.67990e6	−1.37541
$329$	1.55894e6	0.794037
$330$	90023.4	0.0455062
$331$	−1.15522e6	−0.579556	−0.289778	−	0.957094i	$-0.593582\pi$
$331$	−1.15522e6	−0.579556	−0.289778	+	0.957094i	$0.593582\pi$
$332$	−1.38202e6	−0.688127
$333$	1.77346e6	0.876417
$334$	−847781.	−0.415832
$335$	−324677.	−0.158066
$336$	−687640.	−0.332287
$337$	−1.25587e6	−0.602381	−0.301190	−	0.953564i	$-0.597384\pi$
$337$	−1.25587e6	−0.602381	−0.301190	+	0.953564i	$0.597384\pi$
$338$	990585.	0.471628
$339$	1.71330e6	0.809719
$340$	−369518.	−0.173356
$341$	−458753.	−0.213645
$342$	−114955.	−0.0531451
$343$	−1.33062e6	−0.610685
$344$	2.45891e6	1.12033
$345$	177870.	0.0804553
$346$	1.57376e6	0.706720
$347$	4.26053e6	1.89950	0.949751	−	0.313007i	$-0.101336\pi$
$347$	4.26053e6	1.89950	0.949751	+	0.313007i	$0.101336\pi$
$348$	418387.	0.185195
$349$	−2.87443e6	−1.26325	−0.631624	−	0.775275i	$-0.717612\pi$
$349$	−2.87443e6	−1.26325	−0.631624	+	0.775275i	$0.717612\pi$
$350$	−265466.	−0.115835
$351$	113256.	0.0490674
$352$	−714345.	−0.307292
$353$	635946.	0.271634	0.135817	−	0.990734i	$-0.456634\pi$
$353$	635946.	0.271634	0.135817	+	0.990734i	$0.456634\pi$
$354$	−1.14225e6	−0.484454
$355$	1.48716e6	0.626307
$356$	−14175.8	−0.00592822
$357$	−1.05172e6	−0.436746
$358$	346110.	0.142727
$359$	1.44032e6	0.589823	0.294911	−	0.955525i	$-0.404710\pi$
$359$	1.44032e6	0.589823	0.294911	+	0.955525i	$0.404710\pi$
$360$	−452590.	−0.184056
$361$	130321.	0.0526316
$362$	2.28893e6	0.918037
$363$	−162968.	−0.0649135
$364$	−110939.	−0.0438866
$365$	2.04185e6	0.802217
$366$	−581680.	−0.226977
$367$	−3.62473e6	−1.40479	−0.702394	−	0.711788i	$-0.747885\pi$
$367$	−3.62473e6	−1.40479	−0.702394	+	0.711788i	$0.747885\pi$
$368$	−248561.	−0.0956782
$369$	2.09989e6	0.802843
$370$	995266.	0.377950
$371$	−476756.	−0.179830
$372$	−1.04877e6	−0.392938
$373$	847535.	0.315417	0.157709	−	0.987486i	$-0.449589\pi$
$373$	847535.	0.315417	0.157709	+	0.987486i	$0.449589\pi$
$374$	−192408.	−0.0711287
$375$	−173921.	−0.0638664
$376$	1.49157e6	0.544095
$377$	42499.9	0.0154005
$378$	−1.71195e6	−0.616258
$379$	−362494.	−0.129629	−0.0648146	−	0.997897i	$-0.520646\pi$
$379$	−362494.	−0.129629	−0.0648146	+	0.997897i	$0.520646\pi$
$380$	224287.	0.0796793
$381$	−3.14899e6	−1.11137
$382$	2.47239e6	0.866878
$383$	1.29459e6	0.450959	0.225479	−	0.974248i	$-0.427605\pi$
$383$	1.29459e6	0.450959	0.225479	+	0.974248i	$0.427605\pi$
$384$	−2.00342e6	−0.693335
$385$	480568.	0.165235
$386$	2.23333e6	0.762932
$387$	−1.92673e6	−0.653950
$388$	−4.41654e6	−1.48937
$389$	−2.58538e6	−0.866265	−0.433133	−	0.901330i	$-0.642592\pi$
$389$	−2.58538e6	−0.866265	−0.433133	+	0.901330i	$0.642592\pi$
$390$	20905.9	0.00695996
$391$	−380164.	−0.125756
$392$	1.28155e6	0.421232
$393$	−4.18901e6	−1.36814
$394$	641089.	0.208055
$395$	−2.05514e6	−0.662748
$396$	358150.	0.114770
$397$	−5.22858e6	−1.66497	−0.832487	−	0.554045i	$-0.813083\pi$
$397$	−5.22858e6	−1.66497	−0.832487	+	0.554045i	$0.813083\pi$
$398$	77544.3	0.0245382
$399$	638363.	0.200741
$400$	243042.	0.0759505
$401$	397814.	0.123543	0.0617717	−	0.998090i	$-0.480325\pi$
$401$	397814.	0.123543	0.0617717	+	0.998090i	$0.480325\pi$
$402$	−386493.	−0.119283
$403$	−106535.	−0.0326760
$404$	−748712.	−0.228224
$405$	−398039.	−0.120583
$406$	−642420.	−0.193421
$407$	−1.80171e6	−0.539137
$408$	−1.00627e6	−0.299270
$409$	−203039.	−0.0600164	−0.0300082	−	0.999550i	$-0.509553\pi$
$409$	−203039.	−0.0600164	−0.0300082	+	0.999550i	$0.509553\pi$
$410$	1.17846e6	0.346222
$411$	−2.29799e6	−0.671034
$412$	150849.	0.0437825
$413$	−6.09762e6	−1.75908
$414$	−203542.	−0.0583650
$415$	1.39026e6	0.396257
$416$	−165890.	−0.0469989
$417$	2.85346e6	0.803585
$418$	116786.	0.0326927
$419$	−2.49172e6	−0.693368	−0.346684	−	0.937982i	$-0.612692\pi$
$419$	−2.49172e6	−0.693368	−0.346684	+	0.937982i	$0.612692\pi$
$420$	1.09865e6	0.303903
$421$	−5.53097e6	−1.52089	−0.760443	−	0.649405i	$-0.775018\pi$
$421$	−5.53097e6	−1.52089	−0.760443	+	0.649405i	$0.775018\pi$
$422$	−1.90682e6	−0.521230
$423$	−1.16875e6	−0.317594
$424$	−456152.	−0.123224
$425$	371723.	0.0998267
$426$	1.77030e6	0.472633
$427$	−3.10516e6	−0.824164
$428$	−1.72281e6	−0.454598
$429$	−37845.5	−0.00992821
$430$	−1.08128e6	−0.282012
$431$	3.55697e6	0.922331	0.461166	−	0.887314i	$-0.347431\pi$
$431$	3.55697e6	0.922331	0.461166	+	0.887314i	$0.347431\pi$
$432$	1.56734e6	0.404067
$433$	−7.50301e6	−1.92316	−0.961581	−	0.274521i	$-0.911481\pi$
$433$	−7.50301e6	−1.92316	−0.961581	+	0.274521i	$0.911481\pi$
$434$	1.61036e6	0.410392
$435$	−420882.	−0.106644
$436$	3.82605e6	0.963904
$437$	230749.	0.0578010
$438$	2.43060e6	0.605381
$439$	4.06166e6	1.00587	0.502935	−	0.864324i	$-0.332254\pi$
$439$	4.06166e6	1.00587	0.502935	+	0.864324i	$0.332254\pi$
$440$	459800.	0.113224
$441$	−1.00419e6	−0.245877
$442$	−44682.4	−0.0108788
$443$	−2.71980e6	−0.658457	−0.329229	−	0.944250i	$-0.606789\pi$
$443$	−2.71980e6	−0.658457	−0.329229	+	0.944250i	$0.606789\pi$
$444$	−4.11896e6	−0.991586
$445$	14260.4	0.00341375
$446$	−1.41112e6	−0.335913
$447$	1.51036e6	0.357530
$448$	530683.	0.124922
$449$	−6.34599e6	−1.48554	−0.742768	−	0.669549i	$-0.766488\pi$
$449$	−6.34599e6	−1.48554	−0.742768	+	0.669549i	$0.766488\pi$
$450$	199022.	0.0463308
$451$	−2.13334e6	−0.493877
$452$	3.82525e6	0.880671
$453$	1.08471e6	0.248352
$454$	3.76192e6	0.856583
$455$	111601.	0.0252720
$456$	610775.	0.137553
$457$	−2.19014e6	−0.490548	−0.245274	−	0.969454i	$-0.578878\pi$
$457$	−2.19014e6	−0.490548	−0.245274	+	0.969454i	$0.578878\pi$
$458$	89874.5	0.0200204
$459$	2.39718e6	0.531092
$460$	397127.	0.0875053
$461$	6.76629e6	1.48285	0.741427	−	0.671034i	$-0.234149\pi$
$461$	6.76629e6	1.48285	0.741427	+	0.671034i	$0.234149\pi$
$462$	572065.	0.124693
$463$	2.15006e6	0.466120	0.233060	−	0.972462i	$-0.425126\pi$
$463$	2.15006e6	0.466120	0.233060	+	0.972462i	$0.425126\pi$
$464$	588153.	0.126822
$465$	1.05503e6	0.226273
$466$	3.53699e6	0.754517
$467$	−7.09945e6	−1.50637	−0.753186	−	0.657807i	$-0.771484\pi$
$467$	−7.09945e6	−1.50637	−0.753186	+	0.657807i	$0.771484\pi$
$468$	83172.0	0.0175535
$469$	−2.06320e6	−0.433121
$470$	−655904.	−0.136961
$471$	−3.19699e6	−0.664032
$472$	−5.83410e6	−1.20537
$473$	1.95743e6	0.402284
$474$	−2.44642e6	−0.500133
$475$	−225625.	−0.0458831
$476$	−2.34815e6	−0.475016
$477$	357428.	0.0719270
$478$	−1.69301e6	−0.338914
$479$	4.84801e6	0.965439	0.482719	−	0.875775i	$-0.339649\pi$
$479$	4.84801e6	0.965439	0.482719	+	0.875775i	$0.339649\pi$
$480$	1.64283e6	0.325455
$481$	−418406.	−0.0824584
$482$	−2.76670e6	−0.542431
$483$	1.13030e6	0.220457
$484$	−363855.	−0.0706016
$485$	4.44289e6	0.857652
$486$	2.14477e6	0.411899
$487$	−154249.	−0.0294713	−0.0147357	−	0.999891i	$-0.504691\pi$
$487$	−154249.	−0.0294713	−0.0147357	+	0.999891i	$0.504691\pi$
$488$	−2.97096e6	−0.564739
$489$	215179.	0.0406937
$490$	−563550.	−0.106033
$491$	6.62749e6	1.24064	0.620319	−	0.784350i	$-0.287003\pi$
$491$	6.62749e6	1.24064	0.620319	+	0.784350i	$0.287003\pi$
$492$	−4.87711e6	−0.908343
$493$	899557.	0.166691
$494$	27120.9	0.00500020
$495$	−360286.	−0.0660898
$496$	−1.47433e6	−0.269085
$497$	9.45034e6	1.71616
$498$	1.65496e6	0.299029
$499$	−1.03494e6	−0.186065	−0.0930327	−	0.995663i	$-0.529656\pi$
$499$	−1.03494e6	−0.186065	−0.0930327	+	0.995663i	$0.529656\pi$
$500$	−388309.	−0.0694628
$501$	−3.52952e6	−0.628233
$502$	2.82255e6	0.499899
$503$	−8.58314e6	−1.51261	−0.756304	−	0.654221i	$-0.772997\pi$
$503$	−8.58314e6	−1.51261	−0.756304	+	0.654221i	$0.772997\pi$
$504$	−2.87604e6	−0.504335
$505$	753178.	0.131422
$506$	206784.	0.0359038
$507$	4.12404e6	0.712530
$508$	−7.03068e6	−1.20875
$509$	8.64511e6	1.47903	0.739514	−	0.673141i	$-0.235056\pi$
$509$	8.64511e6	1.47903	0.739514	+	0.673141i	$0.235056\pi$
$510$	442496.	0.0753327
$511$	1.29752e7	2.19817
$512$	−4.18719e6	−0.705907
$513$	−1.45502e6	−0.244105
$514$	−712420.	−0.118940
$515$	−151749.	−0.0252121
$516$	4.47495e6	0.739884
$517$	1.18737e6	0.195371
$518$	6.32454e6	1.03563
$519$	6.55192e6	1.06770
$520$	106778.	0.0173170
$521$	1.26022e6	0.203400	0.101700	−	0.994815i	$-0.467572\pi$
$521$	1.26022e6	0.203400	0.101700	+	0.994815i	$0.467572\pi$
$522$	481627.	0.0773633
$523$	−602649.	−0.0963408	−0.0481704	−	0.998839i	$-0.515339\pi$
$523$	−602649.	−0.0963408	−0.0481704	+	0.998839i	$0.515339\pi$
$524$	−9.35271e6	−1.48802
$525$	−1.10520e6	−0.175002
$526$	80200.5	0.0126390
$527$	−2.25493e6	−0.353676
$528$	−523741.	−0.0817583
$529$	−6.02778e6	−0.936522
$530$	200588.	0.0310182
$531$	4.57143e6	0.703584
$532$	1.42526e6	0.218331
$533$	−495419.	−0.0755361
$534$	16975.5	0.00257614
$535$	1.73308e6	0.261779
$536$	−1.97404e6	−0.296786
$537$	1.44094e6	0.215630
$538$	2.22703e6	0.331719
$539$	1.02018e6	0.151254
$540$	−2.50415e6	−0.369552
$541$	1.09584e7	1.60973	0.804864	−	0.593459i	$-0.202238\pi$
$541$	1.09584e7	1.60973	0.804864	+	0.593459i	$0.202238\pi$
$542$	−699289.	−0.102249
$543$	9.52934e6	1.38696
$544$	−3.51125e6	−0.508703
$545$	−3.84887e6	−0.555062
$546$	132849.	0.0190711
$547$	3.59304e6	0.513444	0.256722	−	0.966485i	$-0.417358\pi$
$547$	3.59304e6	0.513444	0.256722	+	0.966485i	$0.417358\pi$
$548$	−5.13068e6	−0.729834
$549$	2.32796e6	0.329644
$550$	−202192.	−0.0285009
$551$	−546005.	−0.0766157
$552$	1.08145e6	0.151063
$553$	−1.30596e7	−1.81601
$554$	−3.55348e6	−0.491903
$555$	4.14353e6	0.571002
$556$	6.37087e6	0.874000
$557$	−5.25528e6	−0.717724	−0.358862	−	0.933391i	$-0.616835\pi$
$557$	−5.25528e6	−0.717724	−0.358862	+	0.933391i	$0.616835\pi$
$558$	−1.20730e6	−0.164146
$559$	454567.	0.0615274
$560$	1.54444e6	0.208114
$561$	−801041.	−0.107460
$562$	−5.05188e6	−0.674702
$563$	−584052.	−0.0776570	−0.0388285	−	0.999246i	$-0.512363\pi$
$563$	−584052.	−0.0776570	−0.0388285	+	0.999246i	$0.512363\pi$
$564$	2.71449e6	0.359328
$565$	−3.84807e6	−0.507133
$566$	207962.	0.0272862
$567$	−2.52939e6	−0.330413
$568$	9.04193e6	1.17595
$569$	−1.19839e7	−1.55173	−0.775865	−	0.630899i	$-0.782686\pi$
$569$	−1.19839e7	−1.55173	−0.775865	+	0.630899i	$0.782686\pi$
$570$	−268582.	−0.0346250
$571$	−1.05126e7	−1.34933	−0.674666	−	0.738123i	$-0.735712\pi$
$571$	−1.05126e7	−1.34933	−0.674666	+	0.738123i	$0.735712\pi$
$572$	−84496.9	−0.0107982
$573$	1.02931e7	1.30967
$574$	7.48865e6	0.948689
$575$	−399495.	−0.0503897
$576$	−397857.	−0.0499656
$577$	1.03475e7	1.29389	0.646943	−	0.762539i	$-0.276047\pi$
$577$	1.03475e7	1.29389	0.646943	+	0.762539i	$0.276047\pi$
$578$	2.85040e6	0.354884
$579$	9.29791e6	1.15263
$580$	−939695.	−0.115989
$581$	8.83459e6	1.08579
$582$	5.28878e6	0.647214
$583$	−363121.	−0.0442466
$584$	1.24144e7	1.50624
$585$	−83668.1	−0.0101081
$586$	−5.07541e6	−0.610558
$587$	−4.22037e6	−0.505540	−0.252770	−	0.967526i	$-0.581342\pi$
$587$	−4.22037e6	−0.505540	−0.252770	+	0.967526i	$0.581342\pi$
$588$	2.33228e6	0.278188
$589$	1.36868e6	0.162560
$590$	2.56549e6	0.303417
$591$	2.66901e6	0.314327
$592$	−5.79029e6	−0.679041
$593$	−5.08018e6	−0.593256	−0.296628	−	0.954993i	$-0.595862\pi$
$593$	−5.08018e6	−0.593256	−0.296628	+	0.954993i	$0.595862\pi$
$594$	−1.30391e6	−0.151629
$595$	2.36216e6	0.273537
$596$	3.37216e6	0.388859
$597$	322835.	0.0370719
$598$	48020.8	0.00549132
$599$	−3.89596e6	−0.443657	−0.221829	−	0.975086i	$-0.571203\pi$
$599$	−3.89596e6	−0.443657	−0.221829	+	0.975086i	$0.571203\pi$
$600$	−1.05744e6	−0.119916
$601$	−1.58068e7	−1.78508	−0.892540	−	0.450968i	$-0.851079\pi$
$601$	−1.58068e7	−1.78508	−0.892540	+	0.450968i	$0.851079\pi$
$602$	−6.87114e6	−0.772748
$603$	1.54680e6	0.173237
$604$	2.42180e6	0.270114
$605$	366025.	0.0406558
$606$	896578.	0.0991759
$607$	−1.64787e7	−1.81531	−0.907656	−	0.419714i	$-0.862130\pi$
$607$	−1.64787e7	−1.81531	−0.907656	+	0.419714i	$0.862130\pi$
$608$	2.13123e6	0.233814
$609$	−2.67455e6	−0.292218
$610$	1.30645e6	0.142157
$611$	275740.	0.0298811
$612$	1.76043e6	0.189994
$613$	3.38216e6	0.363533	0.181766	−	0.983342i	$-0.441819\pi$
$613$	3.38216e6	0.363533	0.181766	+	0.983342i	$0.441819\pi$
$614$	−4.58195e6	−0.490489
$615$	4.90620e6	0.523067
$616$	2.92185e6	0.310246
$617$	1.21583e7	1.28575	0.642877	−	0.765969i	$-0.277740\pi$
$617$	1.21583e7	1.28575	0.642877	+	0.765969i	$0.277740\pi$
$618$	−180641.	−0.0190259
$619$	1.37467e7	1.44202	0.721012	−	0.692923i	$-0.243677\pi$
$619$	1.37467e7	1.44202	0.721012	+	0.692923i	$0.243677\pi$
$620$	2.35554e6	0.246100
$621$	−2.57629e6	−0.268081
$622$	6.98119e6	0.723525
$623$	90619.5	0.00935409
$624$	−121627.	−0.0125046
$625$	390625.	0.0400000
$626$	1.78866e6	0.182429
$627$	486209.	0.0493918
$628$	−7.13786e6	−0.722219
$629$	−8.85602e6	−0.892508
$630$	1.26471e6	0.126952
$631$	−1.20626e7	−1.20605	−0.603027	−	0.797721i	$-0.706039\pi$
$631$	−1.20626e7	−1.20605	−0.603027	+	0.797721i	$0.706039\pi$
$632$	−1.24952e7	−1.24438
$633$	−7.93856e6	−0.787467
$634$	−1.69757e6	−0.167727
$635$	7.07261e6	0.696058
$636$	−830145.	−0.0813788
$637$	236914.	0.0231336
$638$	−489299.	−0.0475908
$639$	−7.08500e6	−0.686416
$640$	4.49967e6	0.434240
$641$	−3.79722e6	−0.365023	−0.182512	−	0.983204i	$-0.558423\pi$
$641$	−3.79722e6	−0.365023	−0.182512	+	0.983204i	$0.558423\pi$
$642$	2.06305e6	0.197548
$643$	−2.83957e6	−0.270847	−0.135424	−	0.990788i	$-0.543240\pi$
$643$	−2.83957e6	−0.270847	−0.135424	+	0.990788i	$0.543240\pi$
$644$	2.52359e6	0.239775
$645$	−4.50164e6	−0.426061
$646$	574044.	0.0541208
$647$	1.09611e7	1.02943	0.514713	−	0.857363i	$-0.327899\pi$
$647$	1.09611e7	1.02943	0.514713	+	0.857363i	$0.327899\pi$
$648$	−2.42007e6	−0.226408
$649$	−4.64425e6	−0.432817
$650$	−46954.5	−0.00435907
$651$	6.70431e6	0.620014
$652$	480425.	0.0442596
$653$	−1.71212e7	−1.57127	−0.785636	−	0.618689i	$-0.787664\pi$
$653$	−1.71212e7	−1.57127	−0.785636	+	0.618689i	$0.787664\pi$
$654$	−4.58166e6	−0.418870
$655$	9.40850e6	0.856874
$656$	−6.85607e6	−0.622036
$657$	−9.72761e6	−0.879210
$658$	−4.16802e6	−0.375289
$659$	−7.46322e6	−0.669442	−0.334721	−	0.942317i	$-0.608642\pi$
$659$	−7.46322e6	−0.669442	−0.334721	+	0.942317i	$0.608642\pi$
$660$	836784.	0.0747745
$661$	−1.66639e7	−1.48345	−0.741725	−	0.670704i	$-0.765992\pi$
$661$	−1.66639e7	−1.48345	−0.741725	+	0.670704i	$0.765992\pi$
$662$	3.08862e6	0.273918
$663$	−186024.	−0.0164355
$664$	8.45279e6	0.744012
$665$	−1.43376e6	−0.125725
$666$	−4.74156e6	−0.414224
$667$	−966766.	−0.0841408
$668$	−7.88028e6	−0.683283
$669$	−5.87482e6	−0.507492
$670$	868063.	0.0747075
$671$	−2.36504e6	−0.202784
$672$	1.04396e7	0.891785
$673$	5.00754e6	0.426174	0.213087	−	0.977033i	$-0.431648\pi$
$673$	5.00754e6	0.426174	0.213087	+	0.977033i	$0.431648\pi$
$674$	3.35773e6	0.284705
$675$	2.51908e6	0.212806
$676$	9.20766e6	0.774966
$677$	3.94204e6	0.330559	0.165280	−	0.986247i	$-0.447147\pi$
$677$	3.94204e6	0.330559	0.165280	+	0.986247i	$0.447147\pi$
$678$	−4.58071e6	−0.382700
$679$	2.82329e7	2.35007
$680$	2.26007e6	0.187435
$681$	1.56618e7	1.29411
$682$	1.22653e6	0.100976
$683$	−1.59045e7	−1.30458	−0.652288	−	0.757971i	$-0.726191\pi$
$683$	−1.59045e7	−1.30458	−0.652288	+	0.757971i	$0.726191\pi$
$684$	−1.06853e6	−0.0873265
$685$	5.16129e6	0.420273
$686$	3.55756e6	0.288630
$687$	374169.	0.0302465
$688$	6.29072e6	0.506675
$689$	−84326.6	−0.00676731
$690$	−475556.	−0.0380259
$691$	1.43372e7	1.14227	0.571136	−	0.820856i	$-0.306503\pi$
$691$	1.43372e7	1.14227	0.571136	+	0.820856i	$0.306503\pi$
$692$	1.46283e7	1.16126
$693$	−2.28948e6	−0.181094
$694$	−1.13910e7	−0.897768
$695$	−6.40887e6	−0.503291
$696$	−2.55896e6	−0.200235
$697$	−1.04861e7	−0.817582
$698$	7.68514e6	0.597054
$699$	1.47253e7	1.13991
$700$	−2.46756e6	−0.190336
$701$	1.26604e7	0.973087	0.486544	−	0.873656i	$-0.338257\pi$
$701$	1.26604e7	0.973087	0.486544	+	0.873656i	$0.338257\pi$
$702$	−302803.	−0.0231909
$703$	5.37535e6	0.410222
$704$	404195.	0.0307368
$705$	−2.73068e6	−0.206918
$706$	−1.70028e6	−0.128383
$707$	4.78616e6	0.360113
$708$	−1.06174e7	−0.796040
$709$	−6.92115e6	−0.517086	−0.258543	−	0.966000i	$-0.583242\pi$
$709$	−6.92115e6	−0.517086	−0.258543	+	0.966000i	$0.583242\pi$
$710$	−3.97610e6	−0.296013
$711$	9.79090e6	0.726355
$712$	86703.2	0.00640966
$713$	2.42340e6	0.178526
$714$	2.81189e6	0.206421
$715$	85000.9	0.00621811
$716$	3.21715e6	0.234525
$717$	−7.04841e6	−0.512027
$718$	−3.85085e6	−0.278770
$719$	2.41883e6	0.174495	0.0872474	−	0.996187i	$-0.472193\pi$
$719$	2.41883e6	0.174495	0.0872474	+	0.996187i	$0.472193\pi$
$720$	−1.15788e6	−0.0832399
$721$	−964309.	−0.0690841
$722$	−348429.	−0.0248754
$723$	−1.15184e7	−0.819497
$724$	2.12760e7	1.50849
$725$	945300.	0.0667920
$726$	435713.	0.0306803
$727$	5.05767e6	0.354907	0.177454	−	0.984129i	$-0.443214\pi$
$727$	5.05767e6	0.354907	0.177454	+	0.984129i	$0.443214\pi$
$728$	678534.	0.0474507
$729$	1.27981e7	0.891924
$730$	−5.45913e6	−0.379155
$731$	9.62141e6	0.665956
$732$	−5.40682e6	−0.372961
$733$	9.13123e6	0.627725	0.313862	−	0.949469i	$-0.398377\pi$
$733$	9.13123e6	0.627725	0.313862	+	0.949469i	$0.398377\pi$
$734$	9.69115e6	0.663950
$735$	−2.34619e6	−0.160194
$736$	3.77359e6	0.256779
$737$	−1.57144e6	−0.106568
$738$	−5.61430e6	−0.379450
$739$	3.39513e6	0.228689	0.114345	−	0.993441i	$-0.463523\pi$
$739$	3.39513e6	0.228689	0.114345	+	0.993441i	$0.463523\pi$
$740$	9.25117e6	0.621037
$741$	112911.	0.00755424
$742$	1.27466e6	0.0849935
$743$	1.86005e6	0.123610	0.0618048	−	0.998088i	$-0.480314\pi$
$743$	1.86005e6	0.123610	0.0618048	+	0.998088i	$0.480314\pi$
$744$	6.41457e6	0.424850
$745$	−3.39227e6	−0.223924
$746$	−2.26599e6	−0.149077
$747$	−6.62337e6	−0.434287
$748$	−1.78847e6	−0.116877
$749$	1.10131e7	0.717306
$750$	464997.	0.0301854
$751$	−1.86820e7	−1.20871	−0.604357	−	0.796714i	$-0.706570\pi$
$751$	−1.86820e7	−1.20871	−0.604357	+	0.796714i	$0.706570\pi$
$752$	3.81594e6	0.246069
$753$	1.17509e7	0.755240
$754$	−113629.	−0.00727879
$755$	−2.43625e6	−0.155544
$756$	−1.59129e7	−1.01262
$757$	1.97502e6	0.125266	0.0626329	−	0.998037i	$-0.480050\pi$
$757$	1.97502e6	0.125266	0.0626329	+	0.998037i	$0.480050\pi$
$758$	969172.	0.0612671
$759$	860890.	0.0542430
$760$	−1.37180e6	−0.0861503
$761$	3.55322e6	0.222413	0.111207	−	0.993797i	$-0.464528\pi$
$761$	3.55322e6	0.222413	0.111207	+	0.993797i	$0.464528\pi$
$762$	8.41919e6	0.525270
$763$	−2.44581e7	−1.52094
$764$	2.29813e7	1.42443
$765$	−1.77093e6	−0.109408
$766$	−3.46125e6	−0.213138
$767$	−1.07852e6	−0.0661973
$768$	6.54620e6	0.400485
$769$	9.17919e6	0.559743	0.279872	−	0.960037i	$-0.409708\pi$
$769$	9.17919e6	0.559743	0.279872	+	0.960037i	$0.409708\pi$
$770$	−1.28486e6	−0.0780958
$771$	−2.96597e6	−0.179693
$772$	2.07592e7	1.25363
$773$	2.53792e7	1.52767	0.763836	−	0.645411i	$-0.223314\pi$
$773$	2.53792e7	1.52767	0.763836	+	0.645411i	$0.223314\pi$
$774$	5.15135e6	0.309079
$775$	−2.36959e6	−0.141716
$776$	2.70127e7	1.61033
$777$	2.63306e7	1.56462
$778$	6.91233e6	0.409426
$779$	6.36475e6	0.375784
$780$	194324.	0.0114364
$781$	7.19786e6	0.422256
$782$	1.01641e6	0.0594365
$783$	6.09610e6	0.355343
$784$	3.27864e6	0.190504
$785$	7.18043e6	0.415888
$786$	1.11998e7	0.646627
$787$	283893.	0.0163387	0.00816936	−	0.999967i	$-0.497400\pi$
$787$	283893.	0.0163387	0.00816936	+	0.999967i	$0.497400\pi$
$788$	5.95904e6	0.341870
$789$	333894.	0.0190948
$790$	5.49465e6	0.313237
$791$	−2.44530e7	−1.38961
$792$	−2.19054e6	−0.124090
$793$	−549227.	−0.0310148
$794$	1.39792e7	0.786922
$795$	835097.	0.0468618
$796$	720788.	0.0403204
$797$	−2.82009e7	−1.57259	−0.786297	−	0.617848i	$-0.788005\pi$
$797$	−2.82009e7	−1.57259	−0.786297	+	0.617848i	$0.788005\pi$
$798$	−1.70674e6	−0.0948768
$799$	5.83633e6	0.323424
$800$	−3.68980e6	−0.203835
$801$	−67938.1	−0.00374138
$802$	−1.06360e6	−0.0583907
$803$	9.88256e6	0.540855
$804$	−3.59252e6	−0.196002
$805$	−2.53864e6	−0.138074
$806$	284834.	0.0154438
$807$	9.27166e6	0.501157
$808$	4.57932e6	0.246759
$809$	−1.71962e6	−0.0923762	−0.0461881	−	0.998933i	$-0.514707\pi$
$809$	−1.71962e6	−0.0923762	−0.0461881	+	0.998933i	$0.514707\pi$
$810$	1.06420e6	0.0569918
$811$	1.21851e6	0.0650542	0.0325271	−	0.999471i	$-0.489644\pi$
$811$	1.21851e6	0.0650542	0.0325271	+	0.999471i	$0.489644\pi$
$812$	−5.97141e6	−0.317824
$813$	−2.91131e6	−0.154476
$814$	4.81709e6	0.254814
$815$	−483291.	−0.0254868
$816$	−2.57437e6	−0.135346
$817$	−5.83992e6	−0.306092
$818$	542848.	0.0283658
$819$	−531679.	−0.0276975
$820$	1.09540e7	0.568902
$821$	3.22411e7	1.66937	0.834685	−	0.550728i	$-0.185650\pi$
$821$	3.22411e7	1.66937	0.834685	+	0.550728i	$0.185650\pi$
$822$	6.14396e6	0.317153
$823$	−2.01097e7	−1.03492	−0.517459	−	0.855708i	$-0.673122\pi$
$823$	−2.01097e7	−1.03492	−0.517459	+	0.855708i	$0.673122\pi$
$824$	−922635.	−0.0473382
$825$	−841775.	−0.0430587
$826$	1.63027e7	0.831399
$827$	−3.73414e7	−1.89857	−0.949285	−	0.314416i	$-0.898191\pi$
$827$	−3.73414e7	−1.89857	−0.949285	+	0.314416i	$0.898191\pi$
$828$	−1.89196e6	−0.0959036
$829$	3.50927e6	0.177350	0.0886749	−	0.996061i	$-0.471737\pi$
$829$	3.50927e6	0.177350	0.0886749	+	0.996061i	$0.471737\pi$
$830$	−3.71703e6	−0.187284
$831$	−1.47940e7	−0.743161
$832$	93865.0	0.00470106
$833$	5.01455e6	0.250391
$834$	−7.62907e6	−0.379801
$835$	7.92728e6	0.393467
$836$	1.08555e6	0.0537198
$837$	−1.52812e7	−0.753950
$838$	6.66190e6	0.327709
$839$	1.89274e7	0.928297	0.464149	−	0.885757i	$-0.346360\pi$
$839$	1.89274e7	0.928297	0.464149	+	0.885757i	$0.346360\pi$
$840$	−6.71961e6	−0.328583
$841$	−1.82236e7	−0.888471
$842$	1.47877e7	0.718821
$843$	−2.10322e7	−1.01933
$844$	−1.77243e7	−0.856470
$845$	−9.26259e6	−0.446263
$846$	3.12480e6	0.150105
$847$	2.32595e6	0.111402
$848$	−1.16699e6	−0.0557285
$849$	865797.	0.0412237
$850$	−993844.	−0.0471814
$851$	9.51769e6	0.450513
$852$	1.64553e7	0.776617
$853$	2.87561e7	1.35319	0.676594	−	0.736356i	$-0.263455\pi$
$853$	2.87561e7	1.35319	0.676594	+	0.736356i	$0.263455\pi$
$854$	8.30200e6	0.389528
$855$	1.07490e6	0.0502868
$856$	1.05371e7	0.491517
$857$	−8.55019e6	−0.397671	−0.198835	−	0.980033i	$-0.563716\pi$
$857$	−8.55019e6	−0.397671	−0.198835	+	0.980033i	$0.563716\pi$
$858$	101184.	0.00469241
$859$	−3.49252e7	−1.61494	−0.807470	−	0.589908i	$-0.799164\pi$
$859$	−3.49252e7	−1.61494	−0.807470	+	0.589908i	$0.799164\pi$
$860$	−1.00507e7	−0.463395
$861$	3.11771e7	1.43327
$862$	−9.50998e6	−0.435925
$863$	2.26606e7	1.03572	0.517861	−	0.855465i	$-0.326728\pi$
$863$	2.26606e7	1.03572	0.517861	+	0.855465i	$0.326728\pi$
$864$	−2.37950e7	−1.08443
$865$	−1.47156e7	−0.668710
$866$	2.00602e7	0.908951
$867$	1.18669e7	0.536155
$868$	1.49686e7	0.674344
$869$	−9.94687e6	−0.446824
$870$	1.12528e6	0.0504036
$871$	−364930.	−0.0162991
$872$	−2.34011e7	−1.04219
$873$	−2.11664e7	−0.939965
$874$	−616933.	−0.0273187
$875$	2.48227e6	0.109605
$876$	2.25929e7	0.994745
$877$	2.01643e7	0.885285	0.442643	−	0.896698i	$-0.354041\pi$
$877$	2.01643e7	0.885285	0.442643	+	0.896698i	$0.354041\pi$
$878$	−1.08593e7	−0.475408
$879$	−2.11301e7	−0.922423
$880$	1.17632e6	0.0512058
$881$	−3.96160e7	−1.71961	−0.859807	−	0.510619i	$-0.829416\pi$
$881$	−3.96160e7	−1.71961	−0.859807	+	0.510619i	$0.829416\pi$
$882$	2.68481e6	0.116210
$883$	7.11110e6	0.306927	0.153463	−	0.988154i	$-0.450957\pi$
$883$	7.11110e6	0.306927	0.153463	+	0.988154i	$0.450957\pi$
$884$	−415331.	−0.0178757
$885$	1.06807e7	0.458398
$886$	7.27171e6	0.311209
$887$	2.98367e7	1.27333	0.636666	−	0.771140i	$-0.280313\pi$
$887$	2.98367e7	1.27333	0.636666	+	0.771140i	$0.280313\pi$
$888$	2.51926e7	1.07212
$889$	4.49438e7	1.90728
$890$	−38126.9	−0.00161345
$891$	−1.92651e6	−0.0812974
$892$	−1.31166e7	−0.551962
$893$	−3.54248e6	−0.148655
$894$	−4.03813e6	−0.168981
$895$	−3.23634e6	−0.135051
$896$	2.85937e7	1.18987
$897$	199922.	0.00829621
$898$	1.69667e7	0.702114
$899$	−5.73434e6	−0.236638
$900$	1.84995e6	0.0761295
$901$	−1.78486e6	−0.0732475
$902$	5.70373e6	0.233423
$903$	−2.86062e7	−1.16746
$904$	−2.33962e7	−0.952193
$905$	−2.14029e7	−0.868662
$906$	−2.90009e6	−0.117379
$907$	3.92822e7	1.58554	0.792771	−	0.609519i	$-0.208637\pi$
$907$	3.92822e7	1.58554	0.792771	+	0.609519i	$0.208637\pi$
$908$	3.49677e7	1.40751
$909$	−3.58822e6	−0.144036
$910$	−298378.	−0.0119444
$911$	−2.22436e7	−0.887992	−0.443996	−	0.896029i	$-0.646440\pi$
$911$	−2.22436e7	−0.887992	−0.443996	+	0.896029i	$0.646440\pi$
$912$	1.56257e6	0.0622088
$913$	6.72887e6	0.267156
$914$	5.85560e6	0.231849
$915$	5.43907e6	0.214769
$916$	835399.	0.0328969
$917$	5.97875e7	2.34794
$918$	−6.40916e6	−0.251012
$919$	−1.46287e7	−0.571371	−0.285685	−	0.958323i	$-0.592221\pi$
$919$	−1.46287e7	−0.571371	−0.285685	+	0.958323i	$0.592221\pi$
$920$	−2.42893e6	−0.0946118
$921$	−1.90758e7	−0.741025
$922$	−1.80905e7	−0.700846
$923$	1.67154e6	0.0645820
$924$	5.31745e6	0.204891
$925$	−9.30636e6	−0.357623
$926$	−5.74843e6	−0.220304
$927$	722950.	0.0276318
$928$	−8.92920e6	−0.340363
$929$	4.05045e6	0.153980	0.0769899	−	0.997032i	$-0.475469\pi$
$929$	4.05045e6	0.153980	0.0769899	+	0.997032i	$0.475469\pi$
$930$	−2.82074e6	−0.106944
$931$	−3.04369e6	−0.115087
$932$	3.28770e7	1.23980
$933$	2.90644e7	1.09309
$934$	1.89812e7	0.711962
$935$	1.79914e6	0.0673031
$936$	−508702.	−0.0189790
$937$	−1.70019e6	−0.0632629	−0.0316315	−	0.999500i	$-0.510070\pi$
$937$	−1.70019e6	−0.0632629	−0.0316315	+	0.999500i	$0.510070\pi$
$938$	5.51621e6	0.204708
$939$	7.44664e6	0.275611
$940$	−6.09674e6	−0.225050
$941$	−1.56899e7	−0.577626	−0.288813	−	0.957386i	$-0.593261\pi$
$941$	−1.56899e7	−0.577626	−0.288813	+	0.957386i	$0.593261\pi$
$942$	8.54753e6	0.313844
$943$	1.12695e7	0.412693
$944$	−1.49256e7	−0.545131
$945$	1.60078e7	0.583113
$946$	−5.23341e6	−0.190133
$947$	−4.35051e7	−1.57640	−0.788198	−	0.615422i	$-0.788986\pi$
$947$	−4.35051e7	−1.57640	−0.788198	+	0.615422i	$0.788986\pi$
$948$	−2.27399e7	−0.821804
$949$	2.29500e6	0.0827212
$950$	603235.	0.0216859
$951$	−7.06738e6	−0.253400
$952$	1.43619e7	0.513594
$953$	−4.16326e7	−1.48491	−0.742457	−	0.669894i	$-0.766339\pi$
$953$	−4.16326e7	−1.48491	−0.742457	+	0.669894i	$0.766339\pi$
$954$	−955625.	−0.0339951
$955$	−2.31183e7	−0.820254
$956$	−1.57368e7	−0.556894
$957$	−2.03707e6	−0.0718995
$958$	−1.29617e7	−0.456299
$959$	3.27980e7	1.15160
$960$	−929558.	−0.0325535
$961$	−1.42548e7	−0.497913
$962$	1.11866e6	0.0389726
$963$	−8.25660e6	−0.286903
$964$	−2.57170e7	−0.891306
$965$	−2.08831e7	−0.721898
$966$	−3.02198e6	−0.104195
$967$	−1.70617e7	−0.586752	−0.293376	−	0.955997i	$-0.594779\pi$
$967$	−1.70617e7	−0.586752	−0.293376	+	0.955997i	$0.594779\pi$
$968$	2.22543e6	0.0763354
$969$	2.38988e6	0.0817650
$970$	−1.18786e7	−0.405355
$971$	2.08041e7	0.708112	0.354056	−	0.935224i	$-0.384802\pi$
$971$	2.08041e7	0.708112	0.354056	+	0.935224i	$0.384802\pi$
$972$	1.99360e7	0.676820
$973$	−4.07259e7	−1.37908
$974$	412403.	0.0139291
$975$	−195483.	−0.00658563
$976$	−7.60071e6	−0.255405
$977$	−5.47220e7	−1.83411	−0.917056	−	0.398758i	$-0.869441\pi$
$977$	−5.47220e7	−1.83411	−0.917056	+	0.398758i	$0.869441\pi$
$978$	−575306.	−0.0192332
$979$	69020.3	0.00230155
$980$	−5.23830e6	−0.174231
$981$	1.83364e7	0.608334
$982$	−1.77194e7	−0.586367
$983$	−1.24829e7	−0.412033	−0.206016	−	0.978549i	$-0.566050\pi$
$983$	−1.24829e7	−0.412033	−0.206016	+	0.978549i	$0.566050\pi$
$984$	2.98297e7	0.982112
$985$	−5.99459e6	−0.196865
$986$	−2.40507e6	−0.0787836
$987$	−1.73525e7	−0.566981
$988$	252094.	0.00821619
$989$	−1.03403e7	−0.336156
$990$	963267.	0.0312362
$991$	5.11779e7	1.65538	0.827691	−	0.561184i	$-0.189654\pi$
$991$	5.11779e7	1.65538	0.827691	+	0.561184i	$0.189654\pi$
$992$	2.23829e7	0.722166
$993$	1.28587e7	0.413831
$994$	−2.52666e7	−0.811113
$995$	−725087.	−0.0232184
$996$	1.53831e7	0.491356
$997$	3.84645e7	1.22552	0.612762	−	0.790268i	$-0.290059\pi$
$997$	3.84645e7	1.22552	0.612762	+	0.790268i	$0.290059\pi$
$998$	2.76705e6	0.0879408
$999$	−6.00153e7	−1.90260

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.e.1.16	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.e.1.16	✓	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)

\(f(q)\)	\(=\)	\(q-2.67362 q^{2} -11.1309 q^{3} -24.8518 q^{4} +25.0000 q^{5} +29.7598 q^{6} +158.866 q^{7} +152.000 q^{8} -119.103 q^{9} +O(q^{10})\)	\(q-2.67362 q^{2} -11.1309 q^{3} -24.8518 q^{4} +25.0000 q^{5} +29.7598 q^{6} +158.866 q^{7} +152.000 q^{8} -119.103 q^{9} -66.8405 q^{10} +121.000 q^{11} +276.623 q^{12} +28.0995 q^{13} -424.746 q^{14} -278.273 q^{15} +388.867 q^{16} +594.756 q^{17} +318.435 q^{18} -361.000 q^{19} -621.294 q^{20} -1768.32 q^{21} -323.508 q^{22} -639.193 q^{23} -1691.90 q^{24} +625.000 q^{25} -75.1273 q^{26} +4030.53 q^{27} -3948.09 q^{28} +1512.48 q^{29} +743.995 q^{30} -3791.35 q^{31} -5903.68 q^{32} -1346.84 q^{33} -1590.15 q^{34} +3971.64 q^{35} +2959.91 q^{36} -14890.2 q^{37} +965.176 q^{38} -312.773 q^{39} +3800.00 q^{40} -17630.9 q^{41} +4727.81 q^{42} +16177.1 q^{43} -3007.06 q^{44} -2977.57 q^{45} +1708.96 q^{46} +9812.98 q^{47} -4328.44 q^{48} +8431.27 q^{49} -1671.01 q^{50} -6620.18 q^{51} -698.321 q^{52} -3001.00 q^{53} -10776.1 q^{54} +3025.00 q^{55} +24147.6 q^{56} +4018.26 q^{57} -4043.80 q^{58} -38382.2 q^{59} +6915.57 q^{60} -19545.8 q^{61} +10136.6 q^{62} -18921.3 q^{63} +3340.45 q^{64} +702.487 q^{65} +3600.94 q^{66} -12987.1 q^{67} -14780.7 q^{68} +7114.80 q^{69} -10618.6 q^{70} +59486.4 q^{71} -18103.6 q^{72} +81674.0 q^{73} +39810.6 q^{74} -6956.82 q^{75} +8971.49 q^{76} +19222.7 q^{77} +836.235 q^{78} -82205.5 q^{79} +9721.66 q^{80} -15921.5 q^{81} +47138.3 q^{82} +55610.5 q^{83} +43945.8 q^{84} +14868.9 q^{85} -43251.3 q^{86} -16835.3 q^{87} +18392.0 q^{88} +570.416 q^{89} +7960.89 q^{90} +4464.04 q^{91} +15885.1 q^{92} +42201.2 q^{93} -26236.2 q^{94} -9025.00 q^{95} +65713.3 q^{96} +177715. q^{97} -22542.0 q^{98} -14411.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 24 q^{2} - 63 q^{3} + 594 q^{4} + 950 q^{5} - 67 q^{6} - 729 q^{7} - 1272 q^{8} + 3029 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more