LMFDB - Embedded newform 1045.6.a.c.1.3

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:	$37$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.5199 q^{2} +0.539776 q^{3} +78.6693 q^{4} -25.0000 q^{5} -5.67841 q^{6} +3.26226 q^{7} -490.959 q^{8} -242.709 q^{9} +O(q^{10})$	\(q-10.5199 q^{2} +0.539776 q^{3} +78.6693 q^{4} -25.0000 q^{5} -5.67841 q^{6} +3.26226 q^{7} -490.959 q^{8} -242.709 q^{9} +262.999 q^{10} -121.000 q^{11} +42.4638 q^{12} +723.636 q^{13} -34.3188 q^{14} -13.4944 q^{15} +2647.44 q^{16} -1175.61 q^{17} +2553.28 q^{18} -361.000 q^{19} -1966.73 q^{20} +1.76089 q^{21} +1272.91 q^{22} -4117.32 q^{23} -265.007 q^{24} +625.000 q^{25} -7612.61 q^{26} -262.174 q^{27} +256.640 q^{28} -1048.15 q^{29} +141.960 q^{30} +9334.21 q^{31} -12140.3 q^{32} -65.3128 q^{33} +12367.4 q^{34} -81.5565 q^{35} -19093.7 q^{36} +5595.99 q^{37} +3797.70 q^{38} +390.601 q^{39} +12274.0 q^{40} +3912.40 q^{41} -18.5245 q^{42} +11344.2 q^{43} -9518.98 q^{44} +6067.72 q^{45} +43314.0 q^{46} +9965.93 q^{47} +1429.02 q^{48} -16796.4 q^{49} -6574.97 q^{50} -634.566 q^{51} +56927.9 q^{52} +21711.7 q^{53} +2758.05 q^{54} +3025.00 q^{55} -1601.64 q^{56} -194.859 q^{57} +11026.5 q^{58} -6076.08 q^{59} -1061.59 q^{60} -15716.1 q^{61} -98195.4 q^{62} -791.779 q^{63} +42996.8 q^{64} -18090.9 q^{65} +687.088 q^{66} -22144.0 q^{67} -92484.5 q^{68} -2222.43 q^{69} +857.970 q^{70} +32464.5 q^{71} +119160. q^{72} +52854.2 q^{73} -58869.5 q^{74} +337.360 q^{75} -28399.6 q^{76} -394.734 q^{77} -4109.10 q^{78} -103297. q^{79} -66186.0 q^{80} +58836.7 q^{81} -41158.2 q^{82} -108422. q^{83} +138.528 q^{84} +29390.3 q^{85} -119340. q^{86} -565.766 q^{87} +59406.0 q^{88} +69175.3 q^{89} -63832.1 q^{90} +2360.69 q^{91} -323907. q^{92} +5038.38 q^{93} -104841. q^{94} +9025.00 q^{95} -6553.02 q^{96} +55854.6 q^{97} +176697. q^{98} +29367.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9}+O(q^{10}) $ 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9	\( 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9} + 300 q^{10} - 4477 q^{11} - 568 q^{12} + 719 q^{13} + 687 q^{14} + 675 q^{15} + 11494 q^{16} + 999 q^{17} - 595 q^{18} - 13357 q^{19} - 14350 q^{20} - 1077 q^{21} + 1452 q^{22} + 5096 q^{23} - 3154 q^{24} + 23125 q^{25} - 10395 q^{26} - 7578 q^{27} + 19863 q^{28} - 7969 q^{29} + 1875 q^{30} + 603 q^{31} - 27809 q^{32} + 3267 q^{33} - 24081 q^{34} - 8425 q^{35} + 59869 q^{36} + 7963 q^{37} + 4332 q^{38} + 86 q^{39} + 17400 q^{40} + 1475 q^{41} - 46542 q^{42} + 38059 q^{43} - 69454 q^{44} - 78500 q^{45} - 3413 q^{46} - 37658 q^{47} - 51317 q^{48} + 39188 q^{49} - 7500 q^{50} - 40262 q^{51} + 25358 q^{52} - 52545 q^{53} + 64732 q^{54} + 111925 q^{55} - 54173 q^{56} + 9747 q^{57} + 105808 q^{58} - 34039 q^{59} + 14200 q^{60} + 30023 q^{61} - 100198 q^{62} + 30376 q^{63} + 160888 q^{64} - 17975 q^{65} + 9075 q^{66} - 45284 q^{67} + 125176 q^{68} + 109244 q^{69} - 17175 q^{70} - 84020 q^{71} - 291176 q^{72} + 24542 q^{73} + 38795 q^{74} - 16875 q^{75} - 207214 q^{76} - 40777 q^{77} + 1042 q^{78} + 49303 q^{79} - 287350 q^{80} + 344453 q^{81} - 286030 q^{82} - 402155 q^{83} - 203270 q^{84} - 24975 q^{85} - 276426 q^{86} + 116994 q^{87} + 84216 q^{88} - 442930 q^{89} + 14875 q^{90} - 93040 q^{91} + 402160 q^{92} - 241950 q^{93} - 170720 q^{94} + 333925 q^{95} - 234384 q^{96} - 87732 q^{97} - 712662 q^{98} - 379940 q^{99}+O(q^{100}) \) 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9 + 300 * q^10 - 4477 * q^11 - 568 * q^12 + 719 * q^13 + 687 * q^14 + 675 * q^15 + 11494 * q^16 + 999 * q^17 - 595 * q^18 - 13357 * q^19 - 14350 * q^20 - 1077 * q^21 + 1452 * q^22 + 5096 * q^23 - 3154 * q^24 + 23125 * q^25 - 10395 * q^26 - 7578 * q^27 + 19863 * q^28 - 7969 * q^29 + 1875 * q^30 + 603 * q^31 - 27809 * q^32 + 3267 * q^33 - 24081 * q^34 - 8425 * q^35 + 59869 * q^36 + 7963 * q^37 + 4332 * q^38 + 86 * q^39 + 17400 * q^40 + 1475 * q^41 - 46542 * q^42 + 38059 * q^43 - 69454 * q^44 - 78500 * q^45 - 3413 * q^46 - 37658 * q^47 - 51317 * q^48 + 39188 * q^49 - 7500 * q^50 - 40262 * q^51 + 25358 * q^52 - 52545 * q^53 + 64732 * q^54 + 111925 * q^55 - 54173 * q^56 + 9747 * q^57 + 105808 * q^58 - 34039 * q^59 + 14200 * q^60 + 30023 * q^61 - 100198 * q^62 + 30376 * q^63 + 160888 * q^64 - 17975 * q^65 + 9075 * q^66 - 45284 * q^67 + 125176 * q^68 + 109244 * q^69 - 17175 * q^70 - 84020 * q^71 - 291176 * q^72 + 24542 * q^73 + 38795 * q^74 - 16875 * q^75 - 207214 * q^76 - 40777 * q^77 + 1042 * q^78 + 49303 * q^79 - 287350 * q^80 + 344453 * q^81 - 286030 * q^82 - 402155 * q^83 - 203270 * q^84 - 24975 * q^85 - 276426 * q^86 + 116994 * q^87 + 84216 * q^88 - 442930 * q^89 + 14875 * q^90 - 93040 * q^91 + 402160 * q^92 - 241950 * q^93 - 170720 * q^94 + 333925 * q^95 - 234384 * q^96 - 87732 * q^97 - 712662 * q^98 - 379940 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−10.5199	−1.85968	−0.929841	−	0.367962i	$-0.880056\pi$
$2$	−10.5199	−1.85968	−0.929841	+	0.367962i	$0.880056\pi$
$3$	0.539776	0.0346266	0.0173133	−	0.999850i	$-0.494489\pi$
$3$	0.539776	0.0346266	0.0173133	+	0.999850i	$0.494489\pi$
$4$	78.6693	2.45842
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−5.67841	−0.0643945
$7$	3.26226	0.0251637	0.0125818	−	0.999921i	$-0.495995\pi$
$7$	3.26226	0.0251637	0.0125818	+	0.999921i	$0.495995\pi$
$8$	−490.959	−2.71219
$9$	−242.709	−0.998801
$10$	262.999	0.831675
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	42.4638	0.0851266
$13$	723.636	1.18758	0.593788	−	0.804621i	$-0.297632\pi$
$13$	723.636	1.18758	0.593788	+	0.804621i	$0.297632\pi$
$14$	−34.3188	−0.0467964
$15$	−13.4944	−0.0154855
$16$	2647.44	2.58539
$17$	−1175.61	−0.986601	−0.493300	−	0.869859i	$-0.664210\pi$
$17$	−1175.61	−0.986601	−0.493300	+	0.869859i	$0.664210\pi$
$18$	2553.28	1.85745
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−1966.73	−1.09944
$21$	1.76089	0.000871332 0
$22$	1272.91	0.560715
$23$	−4117.32	−1.62291	−0.811456	−	0.584413i	$-0.801325\pi$
$23$	−4117.32	−1.62291	−0.811456	+	0.584413i	$0.801325\pi$
$24$	−265.007	−0.0939139
$25$	625.000	0.200000
$26$	−7612.61	−2.20851
$27$	−262.174	−0.0692117
$28$	256.640	0.0618627
$29$	−1048.15	−0.231435	−0.115717	−	0.993282i	$-0.536917\pi$
$29$	−1048.15	−0.231435	−0.115717	+	0.993282i	$0.536917\pi$
$30$	141.960	0.0287981
$31$	9334.21	1.74451	0.872255	−	0.489051i	$-0.162657\pi$
$31$	9334.21	1.74451	0.872255	+	0.489051i	$0.162657\pi$
$32$	−12140.3	−2.09582
$33$	−65.3128	−0.0104403
$34$	12367.4	1.83476
$35$	−81.5565	−0.0112535
$36$	−19093.7	−2.45547
$37$	5595.99	0.672005	0.336002	−	0.941861i	$-0.390925\pi$
$37$	5595.99	0.672005	0.336002	+	0.941861i	$0.390925\pi$
$38$	3797.70	0.426640
$39$	390.601	0.0411218
$40$	12274.0	1.21293
$41$	3912.40	0.363482	0.181741	−	0.983346i	$-0.441827\pi$
$41$	3912.40	0.363482	0.181741	+	0.983346i	$0.441827\pi$
$42$	−18.5245	−0.00162040
$43$	11344.2	0.935625	0.467812	−	0.883828i	$-0.345042\pi$
$43$	11344.2	0.935625	0.467812	+	0.883828i	$0.345042\pi$
$44$	−9518.98	−0.741240
$45$	6067.72	0.446677
$46$	43314.0	3.01810
$47$	9965.93	0.658072	0.329036	−	0.944317i	$-0.393276\pi$
$47$	9965.93	0.658072	0.329036	+	0.944317i	$0.393276\pi$
$48$	1429.02	0.0895234
$49$	−16796.4	−0.999367
$50$	−6574.97	−0.371936
$51$	−634.566	−0.0341626
$52$	56927.9	2.91956
$53$	21711.7	1.06170	0.530852	−	0.847464i	$-0.321872\pi$
$53$	21711.7	1.06170	0.530852	+	0.847464i	$0.321872\pi$
$54$	2758.05	0.128712
$55$	3025.00	0.134840
$56$	−1601.64	−0.0682486
$57$	−194.859	−0.00794389
$58$	11026.5	0.430395
$59$	−6076.08	−0.227244	−0.113622	−	0.993524i	$-0.536245\pi$
$59$	−6076.08	−0.227244	−0.113622	+	0.993524i	$0.536245\pi$
$60$	−1061.59	−0.0380698
$61$	−15716.1	−0.540779	−0.270390	−	0.962751i	$-0.587153\pi$
$61$	−15716.1	−0.540779	−0.270390	+	0.962751i	$0.587153\pi$
$62$	−98195.4	−3.24423
$63$	−791.779	−0.0251335
$64$	42996.8	1.31216
$65$	−18090.9	−0.531101
$66$	687.088	0.0194157
$67$	−22144.0	−0.602654	−0.301327	−	0.953521i	$-0.597430\pi$
$67$	−22144.0	−0.602654	−0.301327	+	0.953521i	$0.597430\pi$
$68$	−92484.5	−2.42547
$69$	−2222.43	−0.0561960
$70$	857.970	0.0209280
$71$	32464.5	0.764299	0.382150	−	0.924100i	$-0.375184\pi$
$71$	32464.5	0.764299	0.382150	+	0.924100i	$0.375184\pi$
$72$	119160.	2.70894
$73$	52854.2	1.16084	0.580420	−	0.814317i	$-0.302888\pi$
$73$	52854.2	1.16084	0.580420	+	0.814317i	$0.302888\pi$
$74$	−58869.5	−1.24972
$75$	337.360	0.00692532
$76$	−28399.6	−0.563999
$77$	−394.734	−0.00758713
$78$	−4109.10	−0.0764734
$79$	−103297.	−1.86217	−0.931086	−	0.364800i	$-0.881137\pi$
$79$	−103297.	−1.86217	−0.931086	+	0.364800i	$0.881137\pi$
$80$	−66186.0	−1.15622
$81$	58836.7	0.996404
$82$	−41158.2	−0.675961
$83$	−108422.	−1.72752	−0.863758	−	0.503908i	$-0.831895\pi$
$83$	−108422.	−1.72752	−0.863758	+	0.503908i	$0.831895\pi$
$84$	138.528	0.00214210
$85$	29390.3	0.441221
$86$	−119340.	−1.73996
$87$	−565.766	−0.00801381
$88$	59406.0	0.817756
$89$	69175.3	0.925713	0.462856	−	0.886433i	$-0.346825\pi$
$89$	69175.3	0.925713	0.462856	+	0.886433i	$0.346825\pi$
$90$	−63832.1	−0.830678
$91$	2360.69	0.0298838
$92$	−323907.	−3.98979
$93$	5038.38	0.0604065
$94$	−104841.	−1.22380
$95$	9025.00	0.102598
$96$	−6553.02	−0.0725710
$97$	55854.6	0.602740	0.301370	−	0.953507i	$-0.402556\pi$
$97$	55854.6	0.602740	0.301370	+	0.953507i	$0.402556\pi$
$98$	176697.	1.85850
$99$	29367.7	0.301150
$100$	49168.3	0.491683
$101$	−189025.	−1.84381	−0.921904	−	0.387419i	$-0.873367\pi$
$101$	−189025.	−1.84381	−0.921904	+	0.387419i	$0.873367\pi$
$102$	6675.60	0.0635316
$103$	112283.	1.04285	0.521423	−	0.853299i	$-0.325402\pi$
$103$	112283.	1.04285	0.521423	+	0.853299i	$0.325402\pi$
$104$	−355275.	−3.22093
$105$	−44.0222	−0.000389672 0
$106$	−228406.	−1.97443
$107$	26500.2	0.223764	0.111882	−	0.993722i	$-0.464312\pi$
$107$	26500.2	0.223764	0.111882	+	0.993722i	$0.464312\pi$
$108$	−20625.0	−0.170151
$109$	173096.	1.39547	0.697736	−	0.716355i	$-0.254191\pi$
$109$	173096.	1.39547	0.697736	+	0.716355i	$0.254191\pi$
$110$	−31822.8	−0.250759
$111$	3020.58	0.0232693
$112$	8636.64	0.0650579
$113$	−136491.	−1.00556	−0.502780	−	0.864414i	$-0.667690\pi$
$113$	−136491.	−1.00556	−0.502780	+	0.864414i	$0.667690\pi$
$114$	2049.91	0.0147731
$115$	102933.	0.725789
$116$	−82457.3	−0.568963
$117$	−175633.	−1.18615
$118$	63920.0	0.422602
$119$	−3835.15	−0.0248265
$120$	6625.19	0.0419996
$121$	14641.0	0.0909091
$122$	165332.	1.00568
$123$	2111.82	0.0125862
$124$	734316.	4.28873
$125$	−15625.0	−0.0894427
$126$	8329.47	0.0467403
$127$	337326.	1.85584	0.927920	−	0.372779i	$-0.121595\pi$
$127$	337326.	1.85584	0.927920	+	0.372779i	$0.121595\pi$
$128$	−63836.0	−0.344382
$129$	6123.31	0.0323975
$130$	190315.	0.987678
$131$	133475.	0.679550	0.339775	−	0.940507i	$-0.389649\pi$
$131$	133475.	0.679550	0.339775	+	0.940507i	$0.389649\pi$
$132$	−5138.11	−0.0256666
$133$	−1177.68	−0.00577294
$134$	232953.	1.12075
$135$	6554.34	0.0309524
$136$	577176.	2.67585
$137$	−97342.3	−0.443099	−0.221549	−	0.975149i	$-0.571111\pi$
$137$	−97342.3	−0.443099	−0.221549	+	0.975149i	$0.571111\pi$
$138$	23379.8	0.104507
$139$	−207441.	−0.910664	−0.455332	−	0.890322i	$-0.650479\pi$
$139$	−207441.	−0.910664	−0.455332	+	0.890322i	$0.650479\pi$
$140$	−6416.00	−0.0276658
$141$	5379.37	0.0227868
$142$	−341525.	−1.42135
$143$	−87559.9	−0.358068
$144$	−642557.	−2.58229
$145$	26203.8	0.103501
$146$	−556023.	−2.15879
$147$	−9066.26	−0.0346047
$148$	440232.	1.65207
$149$	465912.	1.71925	0.859623	−	0.510929i	$-0.170698\pi$
$149$	465912.	1.71925	0.859623	+	0.510929i	$0.170698\pi$
$150$	−3549.01	−0.0128789
$151$	16663.5	0.0594737	0.0297368	−	0.999558i	$-0.490533\pi$
$151$	16663.5	0.0594737	0.0297368	+	0.999558i	$0.490533\pi$
$152$	177236.	0.622219
$153$	285331.	0.985418
$154$	4152.58	0.0141096
$155$	−233355.	−0.780169
$156$	30728.3	0.101094
$157$	−252200.	−0.816576	−0.408288	−	0.912853i	$-0.633874\pi$
$157$	−252200.	−0.816576	−0.408288	+	0.912853i	$0.633874\pi$
$158$	1.08668e6	3.46305
$159$	11719.4	0.0367632
$160$	303507.	0.937277
$161$	−13431.8	−0.0408384
$162$	−618959.	−1.85299
$163$	168288.	0.496117	0.248058	−	0.968745i	$-0.420208\pi$
$163$	168288.	0.496117	0.248058	+	0.968745i	$0.420208\pi$
$164$	307785.	0.893590
$165$	1632.82	0.00466905
$166$	1.14059e6	3.21263
$167$	573254.	1.59058	0.795291	−	0.606227i	$-0.207318\pi$
$167$	573254.	1.59058	0.795291	+	0.606227i	$0.207318\pi$
$168$	−864.523	−0.00236322
$169$	152356.	0.410339
$170$	−309184.	−0.820531
$171$	87617.8	0.229141
$172$	892438.	2.30015
$173$	−486515.	−1.23589	−0.617947	−	0.786220i	$-0.712035\pi$
$173$	−486515.	−1.23589	−0.617947	+	0.786220i	$0.712035\pi$
$174$	5951.83	0.0149031
$175$	2038.91	0.00503273
$176$	−320340.	−0.779525
$177$	−3279.72	−0.00786870
$178$	−727721.	−1.72153
$179$	−436078.	−1.01726	−0.508629	−	0.860986i	$-0.669848\pi$
$179$	−436078.	−1.01726	−0.508629	+	0.860986i	$0.669848\pi$
$180$	477343.	1.09812
$181$	−377906.	−0.857407	−0.428703	−	0.903445i	$-0.641029\pi$
$181$	−377906.	−0.857407	−0.428703	+	0.903445i	$0.641029\pi$
$182$	−24834.3	−0.0555743
$183$	−8483.16	−0.0187254
$184$	2.02143e6	4.40165
$185$	−139900.	−0.300530
$186$	−53003.5	−0.112337
$187$	142249.	0.297471
$188$	784013.	1.61781
$189$	−855.279	−0.00174162
$190$	−94942.5	−0.190799
$191$	468596.	0.929426	0.464713	−	0.885461i	$-0.346157\pi$
$191$	468596.	0.929426	0.464713	+	0.885461i	$0.346157\pi$
$192$	23208.6	0.0454356
$193$	−172718.	−0.333767	−0.166884	−	0.985977i	$-0.553370\pi$
$193$	−172718.	−0.333767	−0.166884	+	0.985977i	$0.553370\pi$
$194$	−587588.	−1.12090
$195$	−9765.02	−0.0183902
$196$	−1.32136e6	−2.45686
$197$	774319.	1.42152	0.710762	−	0.703432i	$-0.248350\pi$
$197$	774319.	1.42152	0.710762	+	0.703432i	$0.248350\pi$
$198$	−308947.	−0.560043
$199$	−651278.	−1.16583	−0.582913	−	0.812535i	$-0.698087\pi$
$199$	−651278.	−1.16583	−0.582913	+	0.812535i	$0.698087\pi$
$200$	−306849.	−0.542438
$201$	−11952.8	−0.0208679
$202$	1.98853e6	3.42889
$203$	−3419.34	−0.00582375
$204$	−49920.9	−0.0839860
$205$	−97809.9	−0.162554
$206$	−1.18121e6	−1.93936
$207$	999310.	1.62097
$208$	1.91578e6	3.07035
$209$	43681.0	0.0691714
$210$	463.111	0.000724665 0
$211$	547373.	0.846402	0.423201	−	0.906036i	$-0.360906\pi$
$211$	547373.	0.846402	0.423201	+	0.906036i	$0.360906\pi$
$212$	1.70804e6	2.61011
$213$	17523.6	0.0264651
$214$	−278781.	−0.416129
$215$	−283604.	−0.418424
$216$	128716.	0.187715
$217$	30450.6	0.0438982
$218$	−1.82096e6	−2.59513
$219$	28529.4	0.0401960
$220$	237975.	0.331493
$221$	−850714.	−1.17166
$222$	−31776.3	−0.0432734
$223$	−1.27215e6	−1.71307	−0.856536	−	0.516087i	$-0.827388\pi$
$223$	−1.27215e6	−1.71307	−0.856536	+	0.516087i	$0.827388\pi$
$224$	−39604.7	−0.0527384
$225$	−151693.	−0.199760
$226$	1.43588e6	1.87002
$227$	1.53309e6	1.97471	0.987353	−	0.158535i	$-0.0506771\pi$
$227$	1.53309e6	1.97471	0.987353	+	0.158535i	$0.0506771\pi$
$228$	−15329.4	−0.0195294
$229$	−1.06517e6	−1.34224	−0.671120	−	0.741349i	$-0.734186\pi$
$229$	−1.06517e6	−1.34224	−0.671120	+	0.741349i	$0.734186\pi$
$230$	−1.08285e6	−1.34974
$231$	−213.068	−0.000262717 0
$232$	514599.	0.627695
$233$	1.37909e6	1.66419	0.832094	−	0.554634i	$-0.187142\pi$
$233$	1.37909e6	1.66419	0.832094	+	0.554634i	$0.187142\pi$
$234$	1.84765e6	2.20587
$235$	−249148.	−0.294299
$236$	−478001.	−0.558661
$237$	−55757.2	−0.0644807
$238$	40345.6	0.0461693
$239$	259501.	0.293863	0.146931	−	0.989147i	$-0.453060\pi$
$239$	259501.	0.293863	0.146931	+	0.989147i	$0.453060\pi$
$240$	−35725.6	−0.0400361
$241$	1.38460e6	1.53561	0.767807	−	0.640681i	$-0.221348\pi$
$241$	1.38460e6	1.53561	0.767807	+	0.640681i	$0.221348\pi$
$242$	−154023.	−0.169062
$243$	95466.8	0.103714
$244$	−1.23637e6	−1.32946
$245$	419909.	0.446930
$246$	−22216.2	−0.0234062
$247$	−261233.	−0.272449
$248$	−4.58271e6	−4.73144
$249$	−58523.5	−0.0598180
$250$	164374.	0.166335
$251$	−570862.	−0.571935	−0.285968	−	0.958239i	$-0.592315\pi$
$251$	−570862.	−0.571935	−0.285968	+	0.958239i	$0.592315\pi$
$252$	−62288.7	−0.0617885
$253$	498196.	0.489327
$254$	−3.54865e6	−3.45127
$255$	15864.2	0.0152780
$256$	−704347.	−0.671718
$257$	1.94988e6	1.84152	0.920759	−	0.390131i	$-0.127570\pi$
$257$	1.94988e6	1.84152	0.920759	+	0.390131i	$0.127570\pi$
$258$	−64416.9	−0.0602491
$259$	18255.6	0.0169101
$260$	−1.42320e6	−1.30567
$261$	254395.	0.231157
$262$	−1.40415e6	−1.26375
$263$	832580.	0.742227	0.371113	−	0.928588i	$-0.378976\pi$
$263$	832580.	0.742227	0.371113	+	0.928588i	$0.378976\pi$
$264$	32065.9	0.0283161
$265$	−542792.	−0.474809
$266$	12389.1	0.0107358
$267$	37339.1	0.0320543
$268$	−1.74205e6	−1.48157
$269$	593453.	0.500041	0.250020	−	0.968241i	$-0.419563\pi$
$269$	593453.	0.500041	0.250020	+	0.968241i	$0.419563\pi$
$270$	−68951.3	−0.0575616
$271$	−1.09745e6	−0.907740	−0.453870	−	0.891068i	$-0.649957\pi$
$271$	−1.09745e6	−0.907740	−0.453870	+	0.891068i	$0.649957\pi$
$272$	−3.11236e6	−2.55075
$273$	1274.24	0.00103477
$274$	1.02404e6	0.824022
$275$	−75625.0	−0.0603023
$276$	−174837.	−0.138153
$277$	1.33447e6	1.04498	0.522491	−	0.852645i	$-0.325003\pi$
$277$	1.33447e6	1.04498	0.522491	+	0.852645i	$0.325003\pi$
$278$	2.18227e6	1.69354
$279$	−2.26549e6	−1.74242
$280$	40040.9	0.0305217
$281$	−1.61230e6	−1.21809	−0.609046	−	0.793135i	$-0.708448\pi$
$281$	−1.61230e6	−1.21809	−0.609046	+	0.793135i	$0.708448\pi$
$282$	−56590.7	−0.0423762
$283$	−2.33395e6	−1.73231	−0.866154	−	0.499777i	$-0.833415\pi$
$283$	−2.33395e6	−1.73231	−0.866154	+	0.499777i	$0.833415\pi$
$284$	2.55396e6	1.87896
$285$	4871.47	0.00355262
$286$	921126.	0.665892
$287$	12763.3	0.00914654
$288$	2.94655e6	2.09330
$289$	−37795.5	−0.0266192
$290$	−275662.	−0.192479
$291$	30148.9	0.0208708
$292$	4.15800e6	2.85383
$293$	−785842.	−0.534769	−0.267384	−	0.963590i	$-0.586159\pi$
$293$	−785842.	−0.534769	−0.267384	+	0.963590i	$0.586159\pi$
$294$	95376.6	0.0643537
$295$	151902.	0.101627
$296$	−2.74740e6	−1.82260
$297$	31723.0	0.0208681
$298$	−4.90137e6	−3.19725
$299$	−2.97944e6	−1.92733
$300$	26539.9	0.0170253
$301$	37007.7	0.0235437
$302$	−175300.	−0.110602
$303$	−102031.	−0.0638448
$304$	−955726.	−0.593129
$305$	392902.	0.241844
$306$	−3.00167e6	−1.83256
$307$	1.40042e6	0.848030	0.424015	−	0.905655i	$-0.360620\pi$
$307$	1.40042e6	0.848030	0.424015	+	0.905655i	$0.360620\pi$
$308$	−31053.4	−0.0186523
$309$	60607.5	0.0361102
$310$	2.45489e6	1.45087
$311$	−2.50986e6	−1.47146	−0.735729	−	0.677276i	$-0.763161\pi$
$311$	−2.50986e6	−1.47146	−0.735729	+	0.677276i	$0.763161\pi$
$312$	−191769.	−0.111530
$313$	653036.	0.376770	0.188385	−	0.982095i	$-0.439675\pi$
$313$	653036.	0.376770	0.188385	+	0.982095i	$0.439675\pi$
$314$	2.65313e6	1.51857
$315$	19794.5	0.0112400
$316$	−8.12630e6	−4.57799
$317$	3.35848e6	1.87713	0.938565	−	0.345101i	$-0.112156\pi$
$317$	3.35848e6	1.87713	0.938565	+	0.345101i	$0.112156\pi$
$318$	−123288.	−0.0683679
$319$	126826.	0.0697803
$320$	−1.07492e6	−0.586815
$321$	14304.2	0.00774818
$322$	141302.	0.0759464
$323$	424396.	0.226342
$324$	4.62864e6	2.44958
$325$	452272.	0.237515
$326$	−1.77038e6	−0.922619
$327$	93433.0	0.0483205
$328$	−1.92082e6	−0.985832
$329$	32511.5	0.0165595
$330$	−17177.2	−0.00868295
$331$	1.93258e6	0.969542	0.484771	−	0.874641i	$-0.338903\pi$
$331$	1.93258e6	0.969542	0.484771	+	0.874641i	$0.338903\pi$
$332$	−8.52948e6	−4.24695
$333$	−1.35819e6	−0.671199
$334$	−6.03061e6	−2.95798
$335$	553599.	0.269515
$336$	4661.85	0.00225273
$337$	−3.43632e6	−1.64823	−0.824116	−	0.566421i	$-0.808327\pi$
$337$	−3.43632e6	−1.64823	−0.824116	+	0.566421i	$0.808327\pi$
$338$	−1.60278e6	−0.763100
$339$	−73674.6	−0.0348192
$340$	2.31211e6	1.08471
$341$	−1.12944e6	−0.525990
$342$	−921735.	−0.426129
$343$	−109623.	−0.0503114
$344$	−5.56952e6	−2.53759
$345$	55560.7	0.0251316
$346$	5.11811e6	2.29837
$347$	−3.26020e6	−1.45352	−0.726759	−	0.686892i	$-0.758974\pi$
$347$	−3.26020e6	−1.45352	−0.726759	+	0.686892i	$0.758974\pi$
$348$	−44508.4	−0.0197013
$349$	−586291.	−0.257662	−0.128831	−	0.991667i	$-0.541122\pi$
$349$	−586291.	−0.257662	−0.128831	+	0.991667i	$0.541122\pi$
$350$	−21449.3	−0.00935928
$351$	−189718.	−0.0821942
$352$	1.46897e6	0.631912
$353$	1.75519e6	0.749702	0.374851	−	0.927085i	$-0.377694\pi$
$353$	1.75519e6	0.749702	0.374851	+	0.927085i	$0.377694\pi$
$354$	34502.4	0.0146333
$355$	−811613.	−0.341805
$356$	5.44197e6	2.27579
$357$	−2070.12	−0.000859657 0
$358$	4.58752e6	1.89178
$359$	−1.11337e6	−0.455936	−0.227968	−	0.973669i	$-0.573208\pi$
$359$	−1.11337e6	−0.455936	−0.227968	+	0.973669i	$0.573208\pi$
$360$	−2.97900e6	−1.21147
$361$	130321.	0.0526316
$362$	3.97555e6	1.59450
$363$	7902.85	0.00314787
$364$	185714.	0.0734667
$365$	−1.32135e6	−0.519143
$366$	89242.4	0.0348232
$367$	4.10647e6	1.59149	0.795744	−	0.605634i	$-0.207080\pi$
$367$	4.10647e6	1.59149	0.795744	+	0.605634i	$0.207080\pi$
$368$	−1.09004e7	−4.19586
$369$	−949572.	−0.363046
$370$	1.47174e6	0.558890
$371$	70829.1	0.0267164
$372$	396366.	0.148504
$373$	1.70667e6	0.635152	0.317576	−	0.948233i	$-0.397131\pi$
$373$	1.70667e6	0.635152	0.317576	+	0.948233i	$0.397131\pi$
$374$	−1.49645e6	−0.553202
$375$	−8433.99	−0.00309710
$376$	−4.89286e6	−1.78482
$377$	−758480.	−0.274847
$378$	8997.49	0.00323886
$379$	−1.58440e6	−0.566589	−0.283294	−	0.959033i	$-0.591427\pi$
$379$	−1.58440e6	−0.566589	−0.283294	+	0.959033i	$0.591427\pi$
$380$	709990.	0.252228
$381$	182080.	0.0642615
$382$	−4.92960e6	−1.72844
$383$	−4.32590e6	−1.50688	−0.753441	−	0.657515i	$-0.771607\pi$
$383$	−4.32590e6	−1.50688	−0.753441	+	0.657515i	$0.771607\pi$
$384$	−34457.1	−0.0119248
$385$	9868.34	0.00339307
$386$	1.81698e6	0.620700
$387$	−2.75333e6	−0.934503
$388$	4.39404e6	1.48178
$389$	−5.30612e6	−1.77788	−0.888941	−	0.458021i	$-0.848558\pi$
$389$	−5.30612e6	−1.77788	−0.888941	+	0.458021i	$0.848558\pi$
$390$	102728.	0.0341999
$391$	4.84037e6	1.60117
$392$	8.24632e6	2.71047
$393$	72046.5	0.0235305
$394$	−8.14579e6	−2.64358
$395$	2.58242e6	0.832789
$396$	2.31034e6	0.740351
$397$	439748.	0.140032	0.0700161	−	0.997546i	$-0.477695\pi$
$397$	439748.	0.140032	0.0700161	+	0.997546i	$0.477695\pi$
$398$	6.85141e6	2.16806
$399$	−635.681	−0.000199897 0
$400$	1.65465e6	0.517078
$401$	−4.29061e6	−1.33247	−0.666237	−	0.745740i	$-0.732096\pi$
$401$	−4.29061e6	−1.33247	−0.666237	+	0.745740i	$0.732096\pi$
$402$	125742.	0.0388076
$403$	6.75457e6	2.07174
$404$	−1.48705e7	−4.53284
$405$	−1.47092e6	−0.445606
$406$	35971.3	0.0108303
$407$	−677115.	−0.202617
$408$	311546.	0.0926555
$409$	−5.38206e6	−1.59089	−0.795445	−	0.606026i	$-0.792763\pi$
$409$	−5.38206e6	−1.59089	−0.795445	+	0.606026i	$0.792763\pi$
$410$	1.02896e6	0.302299
$411$	−52543.0	−0.0153430
$412$	8.83320e6	2.56375
$413$	−19821.7	−0.00571830
$414$	−1.05127e7	−3.01448
$415$	2.71055e6	0.772568
$416$	−8.78513e6	−2.48894
$417$	−111972.	−0.0315332
$418$	−459522.	−0.128637
$419$	3.19052e6	0.887823	0.443911	−	0.896071i	$-0.353591\pi$
$419$	3.19052e6	0.887823	0.443911	+	0.896071i	$0.353591\pi$
$420$	−3463.20	−0.000957975 0
$421$	−2.15476e6	−0.592509	−0.296254	−	0.955109i	$-0.595738\pi$
$421$	−2.15476e6	−0.592509	−0.296254	+	0.955109i	$0.595738\pi$
$422$	−5.75833e6	−1.57404
$423$	−2.41882e6	−0.657283
$424$	−1.06595e7	−2.87954
$425$	−734757.	−0.197320
$426$	−184347.	−0.0492166
$427$	−51270.0	−0.0136080
$428$	2.08475e6	0.550104
$429$	−47262.7	−0.0123987
$430$	2.98350e6	0.778136
$431$	−2.82077e6	−0.731434	−0.365717	−	0.930726i	$-0.619176\pi$
$431$	−2.82077e6	−0.731434	−0.365717	+	0.930726i	$0.619176\pi$
$432$	−694089.	−0.178939
$433$	−4.78088e6	−1.22543	−0.612715	−	0.790304i	$-0.709923\pi$
$433$	−4.78088e6	−1.22543	−0.612715	+	0.790304i	$0.709923\pi$
$434$	−320339.	−0.0816368
$435$	14144.2	0.00358388
$436$	1.36173e7	3.43065
$437$	1.48635e6	0.372322
$438$	−300128.	−0.0747517
$439$	−3.79012e6	−0.938623	−0.469312	−	0.883033i	$-0.655498\pi$
$439$	−3.79012e6	−0.938623	−0.469312	+	0.883033i	$0.655498\pi$
$440$	−1.48515e6	−0.365711
$441$	4.07662e6	0.998169
$442$	8.94947e6	2.17892
$443$	−2.97408e6	−0.720018	−0.360009	−	0.932949i	$-0.617226\pi$
$443$	−2.97408e6	−0.720018	−0.360009	+	0.932949i	$0.617226\pi$
$444$	237627.	0.0572055
$445$	−1.72938e6	−0.413991
$446$	1.33829e7	3.18577
$447$	251488.	0.0595317
$448$	140267.	0.0330187
$449$	−5.83896e6	−1.36685	−0.683423	−	0.730023i	$-0.739510\pi$
$449$	−5.83896e6	−1.36685	−0.683423	+	0.730023i	$0.739510\pi$
$450$	1.59580e6	0.371490
$451$	−473400.	−0.109594
$452$	−1.07377e7	−2.47209
$453$	8994.57	0.00205937
$454$	−1.61280e7	−3.67233
$455$	−59017.2	−0.0133644
$456$	95667.7	0.0215453
$457$	2.40814e6	0.539376	0.269688	−	0.962948i	$-0.413079\pi$
$457$	2.40814e6	0.539376	0.269688	+	0.962948i	$0.413079\pi$
$458$	1.12055e7	2.49614
$459$	308214.	0.0682843
$460$	8.09767e6	1.78429
$461$	−7.44497e6	−1.63159	−0.815794	−	0.578342i	$-0.803700\pi$
$461$	−7.44497e6	−1.63159	−0.815794	+	0.578342i	$0.803700\pi$
$462$	2241.46	0.000488569 0
$463$	−4.71045e6	−1.02120	−0.510599	−	0.859819i	$-0.670576\pi$
$463$	−4.71045e6	−1.02120	−0.510599	+	0.859819i	$0.670576\pi$
$464$	−2.77492e6	−0.598350
$465$	−125960.	−0.0270146
$466$	−1.45079e7	−3.09486
$467$	−5.36120e6	−1.13755	−0.568774	−	0.822494i	$-0.692582\pi$
$467$	−5.36120e6	−1.13755	−0.568774	+	0.822494i	$0.692582\pi$
$468$	−1.38169e7	−2.91606
$469$	−72239.4	−0.0151650
$470$	2.62103e6	0.547302
$471$	−136132.	−0.0282753
$472$	2.98310e6	0.616330
$473$	−1.37264e6	−0.282101
$474$	586562.	0.119914
$475$	−225625.	−0.0458831
$476$	−301709.	−0.0610338
$477$	−5.26961e6	−1.06043
$478$	−2.72994e6	−0.546491
$479$	8.05417e6	1.60392	0.801958	−	0.597380i	$-0.203792\pi$
$479$	8.05417e6	1.60392	0.801958	+	0.597380i	$0.203792\pi$
$480$	163825.	0.0324547
$481$	4.04946e6	0.798058
$482$	−1.45659e7	−2.85575
$483$	−7250.15	−0.00141410
$484$	1.15180e6	0.223492
$485$	−1.39637e6	−0.269553
$486$	−1.00431e6	−0.192875
$487$	−6.12280e6	−1.16984	−0.584921	−	0.811090i	$-0.698875\pi$
$487$	−6.12280e6	−1.16984	−0.584921	+	0.811090i	$0.698875\pi$
$488$	7.71595e6	1.46670
$489$	90837.7	0.0171788
$490$	−4.41742e6	−0.831148
$491$	2.66635e6	0.499130	0.249565	−	0.968358i	$-0.419712\pi$
$491$	2.66635e6	0.499130	0.249565	+	0.968358i	$0.419712\pi$
$492$	166135.	0.0309420
$493$	1.23222e6	0.228334
$494$	2.74815e6	0.506668
$495$	−734194.	−0.134678
$496$	2.47118e7	4.51024
$497$	105908.	0.0192326
$498$	615664.	0.111242
$499$	−1.64976e6	−0.296599	−0.148299	−	0.988943i	$-0.547380\pi$
$499$	−1.64976e6	−0.296599	−0.148299	+	0.988943i	$0.547380\pi$
$500$	−1.22921e6	−0.219887
$501$	309429.	0.0550765
$502$	6.00544e6	1.06362
$503$	−6.41722e6	−1.13091	−0.565454	−	0.824780i	$-0.691299\pi$
$503$	−6.41722e6	−1.13091	−0.565454	+	0.824780i	$0.691299\pi$
$504$	388731.	0.0681667
$505$	4.72562e6	0.824576
$506$	−5.24099e6	−0.909992
$507$	82238.0	0.0142086
$508$	2.65372e7	4.56243
$509$	−486125.	−0.0831674	−0.0415837	−	0.999135i	$-0.513240\pi$
$509$	−486125.	−0.0831674	−0.0415837	+	0.999135i	$0.513240\pi$
$510$	−166890.	−0.0284122
$511$	172424.	0.0292110
$512$	9.45245e6	1.59356
$513$	94644.7	0.0158783
$514$	−2.05127e7	−3.42464
$515$	−2.80707e6	−0.466375
$516$	481716.	0.0796466
$517$	−1.20588e6	−0.198416
$518$	−192048.	−0.0314474
$519$	−262609.	−0.0427948
$520$	8.88188e6	1.44044
$521$	−9.66232e6	−1.55951	−0.779753	−	0.626087i	$-0.784655\pi$
$521$	−9.66232e6	−1.55951	−0.779753	+	0.626087i	$0.784655\pi$
$522$	−2.67623e6	−0.429879
$523$	6.22318e6	0.994851	0.497425	−	0.867507i	$-0.334279\pi$
$523$	6.22318e6	0.994851	0.497425	+	0.867507i	$0.334279\pi$
$524$	1.05004e7	1.67062
$525$	1100.56	0.000174266 0
$526$	−8.75870e6	−1.38031
$527$	−1.09734e7	−1.72113
$528$	−172912.	−0.0269923
$529$	1.05160e7	1.63385
$530$	5.71014e6	0.882993
$531$	1.47472e6	0.226972
$532$	−92647.0	−0.0141923
$533$	2.83115e6	0.431663
$534$	−392806.	−0.0596108
$535$	−662505.	−0.100070
$536$	1.08718e7	1.63451
$537$	−235384.	−0.0352242
$538$	−6.24309e6	−0.929917
$539$	2.03236e6	0.301320
$540$	515625.	0.0760939
$541$	−1.86050e6	−0.273299	−0.136649	−	0.990619i	$-0.543633\pi$
$541$	−1.86050e6	−0.273299	−0.136649	+	0.990619i	$0.543633\pi$
$542$	1.15451e7	1.68811
$543$	−203984.	−0.0296891
$544$	1.42722e7	2.06773
$545$	−4.32740e6	−0.624074
$546$	−13405.0	−0.00192435
$547$	−5.23104e6	−0.747515	−0.373757	−	0.927527i	$-0.621931\pi$
$547$	−5.23104e6	−0.747515	−0.373757	+	0.927527i	$0.621931\pi$
$548$	−7.65785e6	−1.08932
$549$	3.81443e6	0.540131
$550$	795571.	0.112143
$551$	378383.	0.0530948
$552$	1.09112e6	0.152414
$553$	−336982.	−0.0468590
$554$	−1.40385e7	−1.94333
$555$	−75514.4	−0.0104063
$556$	−1.63193e7	−2.23879
$557$	6.80475e6	0.929340	0.464670	−	0.885484i	$-0.346173\pi$
$557$	6.80475e6	0.929340	0.464670	+	0.885484i	$0.346173\pi$
$558$	2.38329e7	3.24034
$559$	8.20905e6	1.11113
$560$	−215916.	−0.0290948
$561$	76782.5	0.0103004
$562$	1.69613e7	2.26526
$563$	9.09920e6	1.20985	0.604926	−	0.796282i	$-0.293203\pi$
$563$	9.09920e6	1.20985	0.604926	+	0.796282i	$0.293203\pi$
$564$	423191.	0.0560194
$565$	3.41228e6	0.449700
$566$	2.45530e7	3.22154
$567$	191941.	0.0250732
$568$	−1.59387e7	−2.07292
$569$	3.37142e6	0.436548	0.218274	−	0.975888i	$-0.429957\pi$
$569$	3.37142e6	0.436548	0.218274	+	0.975888i	$0.429957\pi$
$570$	−51247.7	−0.00660673
$571$	1.19275e7	1.53095	0.765473	−	0.643469i	$-0.222505\pi$
$571$	1.19275e7	1.53095	0.765473	+	0.643469i	$0.222505\pi$
$572$	−6.88828e6	−0.880280
$573$	252937.	0.0321829
$574$	−134269.	−0.0170097
$575$	−2.57333e6	−0.324583
$576$	−1.04357e7	−1.31059
$577$	7.65467e6	0.957166	0.478583	−	0.878042i	$-0.341151\pi$
$577$	7.65467e6	0.957166	0.478583	+	0.878042i	$0.341151\pi$
$578$	397607.	0.0495033
$579$	−93228.8	−0.0115572
$580$	2.06143e6	0.254448
$581$	−353701.	−0.0434706
$582$	−317165.	−0.0388131
$583$	−2.62711e6	−0.320116
$584$	−2.59492e7	−3.14842
$585$	4.39082e6	0.530464
$586$	8.26701e6	0.994500
$587$	756684.	0.0906399	0.0453200	−	0.998973i	$-0.485569\pi$
$587$	756684.	0.0906399	0.0453200	+	0.998973i	$0.485569\pi$
$588$	−713237.	−0.0850727
$589$	−3.36965e6	−0.400218
$590$	−1.59800e6	−0.188993
$591$	417958.	0.0492226
$592$	1.48150e7	1.73740
$593$	6.22886e6	0.727398	0.363699	−	0.931517i	$-0.381514\pi$
$593$	6.22886e6	0.727398	0.363699	+	0.931517i	$0.381514\pi$
$594$	−333724.	−0.0388081
$595$	95878.8	0.0111027
$596$	3.66530e7	4.22662
$597$	−351544.	−0.0403686
$598$	3.13436e7	3.58423
$599$	−9.81727e6	−1.11795	−0.558977	−	0.829183i	$-0.688806\pi$
$599$	−9.81727e6	−1.11795	−0.558977	+	0.829183i	$0.688806\pi$
$600$	−165630.	−0.0187828
$601$	1.11830e7	1.26291	0.631457	−	0.775411i	$-0.282457\pi$
$601$	1.11830e7	1.26291	0.631457	+	0.775411i	$0.282457\pi$
$602$	−389319.	−0.0437838
$603$	5.37453e6	0.601932
$604$	1.31091e6	0.146211
$605$	−366025.	−0.0406558
$606$	1.07336e6	0.118731
$607$	−8.78042e6	−0.967261	−0.483631	−	0.875272i	$-0.660682\pi$
$607$	−8.78042e6	−0.967261	−0.483631	+	0.875272i	$0.660682\pi$
$608$	4.38264e6	0.480813
$609$	−1845.68	−0.000201657 0
$610$	−4.13331e6	−0.449752
$611$	7.21171e6	0.781511
$612$	2.24468e7	2.42257
$613$	1.86969e6	0.200964	0.100482	−	0.994939i	$-0.467961\pi$
$613$	1.86969e6	0.200964	0.100482	+	0.994939i	$0.467961\pi$
$614$	−1.47323e7	−1.57707
$615$	−52795.4	−0.00562870
$616$	193798.	0.0205777
$617$	−6.45003e6	−0.682101	−0.341050	−	0.940045i	$-0.610783\pi$
$617$	−6.45003e6	−0.682101	−0.341050	+	0.940045i	$0.610783\pi$
$618$	−637587.	−0.0671535
$619$	1.48225e7	1.55487	0.777437	−	0.628960i	$-0.216519\pi$
$619$	1.48225e7	1.55487	0.777437	+	0.628960i	$0.216519\pi$
$620$	−1.83579e7	−1.91798
$621$	1.07945e6	0.112325
$622$	2.64036e7	2.73645
$623$	225668.	0.0232943
$624$	1.03409e6	0.106316
$625$	390625.	0.0400000
$626$	−6.86991e6	−0.700672
$627$	23577.9	0.00239517
$628$	−1.98404e7	−2.00748
$629$	−6.57871e6	−0.663001
$630$	−208237.	−0.0209029
$631$	−973837.	−0.0973672	−0.0486836	−	0.998814i	$-0.515503\pi$
$631$	−973837.	−0.0973672	−0.0486836	+	0.998814i	$0.515503\pi$
$632$	5.07145e7	5.05056
$633$	295458.	0.0293081
$634$	−3.53310e7	−3.49087
$635$	−8.43315e6	−0.829957
$636$	921959.	0.0903793
$637$	−1.21544e7	−1.18682
$638$	−1.33421e6	−0.129769
$639$	−7.87942e6	−0.763383
$640$	1.59590e6	0.154012
$641$	−7.22896e6	−0.694914	−0.347457	−	0.937696i	$-0.612955\pi$
$641$	−7.22896e6	−0.694914	−0.347457	+	0.937696i	$0.612955\pi$
$642$	−150479.	−0.0144092
$643$	−1.87993e7	−1.79314	−0.896570	−	0.442901i	$-0.853949\pi$
$643$	−1.87993e7	−1.79314	−0.896570	+	0.442901i	$0.853949\pi$
$644$	−1.05667e6	−0.100398
$645$	−153083.	−0.0144886
$646$	−4.46462e6	−0.420923
$647$	3.23051e6	0.303396	0.151698	−	0.988427i	$-0.451526\pi$
$647$	3.23051e6	0.303396	0.151698	+	0.988427i	$0.451526\pi$
$648$	−2.88864e7	−2.70244
$649$	735205.	0.0685168
$650$	−4.75788e6	−0.441703
$651$	16436.5	0.00152005
$652$	1.32391e7	1.21966
$653$	−7.38717e6	−0.677946	−0.338973	−	0.940796i	$-0.610080\pi$
$653$	−7.38717e6	−0.677946	−0.338973	+	0.940796i	$0.610080\pi$
$654$	−982911.	−0.0898607
$655$	−3.33687e6	−0.303904
$656$	1.03578e7	0.939744
$657$	−1.28282e7	−1.15945
$658$	−342019.	−0.0307954
$659$	1.56873e7	1.40714	0.703568	−	0.710628i	$-0.251589\pi$
$659$	1.56873e7	1.40714	0.703568	+	0.710628i	$0.251589\pi$
$660$	128453.	0.0114785
$661$	2.97714e6	0.265030	0.132515	−	0.991181i	$-0.457695\pi$
$661$	2.97714e6	0.265030	0.132515	+	0.991181i	$0.457695\pi$
$662$	−2.03306e7	−1.80304
$663$	−459195.	−0.0405708
$664$	5.32307e7	4.68535
$665$	29441.9	0.00258174
$666$	1.42881e7	1.24822
$667$	4.31558e6	0.375599
$668$	4.50975e7	3.91031
$669$	−686675.	−0.0593179
$670$	−5.82383e6	−0.501212
$671$	1.90165e6	0.163051
$672$	−21377.7	−0.00182615
$673$	−1.22670e7	−1.04400	−0.522000	−	0.852945i	$-0.674814\pi$
$673$	−1.22670e7	−1.04400	−0.522000	+	0.852945i	$0.674814\pi$
$674$	3.61499e7	3.06519
$675$	−163859.	−0.0138423
$676$	1.19857e7	1.00878
$677$	2.55350e6	0.214124	0.107062	−	0.994252i	$-0.465856\pi$
$677$	2.55350e6	0.214124	0.107062	+	0.994252i	$0.465856\pi$
$678$	775053.	0.0647526
$679$	182212.	0.0151671
$680$	−1.44294e7	−1.19668
$681$	827524.	0.0683774
$682$	1.18816e7	0.978173
$683$	1.33821e6	0.109767	0.0548837	−	0.998493i	$-0.482521\pi$
$683$	1.33821e6	0.109767	0.0548837	+	0.998493i	$0.482521\pi$
$684$	6.89283e6	0.563323
$685$	2.43356e6	0.198160
$686$	1.15323e6	0.0935631
$687$	−574952.	−0.0464772
$688$	3.00330e7	2.41896
$689$	1.57113e7	1.26086
$690$	−584496.	−0.0467368
$691$	2.56244e6	0.204154	0.102077	−	0.994776i	$-0.467451\pi$
$691$	2.56244e6	0.204154	0.102077	+	0.994776i	$0.467451\pi$
$692$	−3.82738e7	−3.03834
$693$	95805.3	0.00757803
$694$	3.42971e7	2.70308
$695$	5.18603e6	0.407261
$696$	277768.	0.0217350
$697$	−4.59946e6	−0.358612
$698$	6.16775e6	0.479169
$699$	744398.	0.0576252
$700$	160400.	0.0123725
$701$	−2.03430e7	−1.56358	−0.781789	−	0.623543i	$-0.785692\pi$
$701$	−2.03430e7	−1.56358	−0.781789	+	0.623543i	$0.785692\pi$
$702$	1.99583e6	0.152855
$703$	−2.02015e6	−0.154169
$704$	−5.20262e6	−0.395631
$705$	−134484.	−0.0101906
$706$	−1.84646e7	−1.39421
$707$	−616649.	−0.0463969
$708$	−258013.	−0.0193445
$709$	−3.24590e6	−0.242504	−0.121252	−	0.992622i	$-0.538691\pi$
$709$	−3.24590e6	−0.242504	−0.121252	+	0.992622i	$0.538691\pi$
$710$	8.53813e6	0.635648
$711$	2.50711e7	1.85994
$712$	−3.39622e7	−2.51071
$713$	−3.84320e7	−2.83119
$714$	21777.6	0.00159869
$715$	2.18900e6	0.160133
$716$	−3.43059e7	−2.50084
$717$	140072.	0.0101755
$718$	1.17126e7	0.847897
$719$	−1.97890e7	−1.42758	−0.713791	−	0.700359i	$-0.753023\pi$
$719$	−1.97890e7	−1.42758	−0.713791	+	0.700359i	$0.753023\pi$
$720$	1.60639e7	1.15484
$721$	366296.	0.0262418
$722$	−1.37097e6	−0.0978780
$723$	747374.	0.0531731
$724$	−2.97296e7	−2.10786
$725$	−655095.	−0.0462870
$726$	−83137.6	−0.00585404
$727$	1.79939e7	1.26267	0.631334	−	0.775511i	$-0.282508\pi$
$727$	1.79939e7	1.26267	0.631334	+	0.775511i	$0.282508\pi$
$728$	−1.15900e6	−0.0810504
$729$	−1.42458e7	−0.992813
$730$	1.39006e7	0.965441
$731$	−1.33363e7	−0.923088
$732$	−667364.	−0.0460347
$733$	−1.29777e7	−0.892149	−0.446075	−	0.894996i	$-0.647178\pi$
$733$	−1.29777e7	−0.892149	−0.446075	+	0.894996i	$0.647178\pi$
$734$	−4.31998e7	−2.95966
$735$	226657.	0.0154757
$736$	4.99854e7	3.40133
$737$	2.67942e6	0.181707
$738$	9.98945e6	0.675151
$739$	−3.92638e6	−0.264473	−0.132236	−	0.991218i	$-0.542216\pi$
$739$	−3.92638e6	−0.264473	−0.132236	+	0.991218i	$0.542216\pi$
$740$	−1.10058e7	−0.738827
$741$	−141007.	−0.00943398
$742$	−745119.	−0.0496839
$743$	−2.31489e7	−1.53836	−0.769180	−	0.639032i	$-0.779335\pi$
$743$	−2.31489e7	−1.53836	−0.769180	+	0.639032i	$0.779335\pi$
$744$	−2.47364e6	−0.163834
$745$	−1.16478e7	−0.768870
$746$	−1.79541e7	−1.18118
$747$	2.63149e7	1.72544
$748$	1.11906e7	0.731308
$749$	86450.6	0.00563071
$750$	88725.2	0.00575962
$751$	−1.13405e7	−0.733722	−0.366861	−	0.930276i	$-0.619568\pi$
$751$	−1.13405e7	−0.733722	−0.366861	+	0.930276i	$0.619568\pi$
$752$	2.63842e7	1.70137
$753$	−308137.	−0.0198042
$754$	7.97917e6	0.511128
$755$	−416588.	−0.0265974
$756$	−67284.2	−0.00428162
$757$	−1.76623e7	−1.12023	−0.560117	−	0.828414i	$-0.689244\pi$
$757$	−1.76623e7	−1.12023	−0.560117	+	0.828414i	$0.689244\pi$
$758$	1.66678e7	1.05367
$759$	268914.	0.0169437
$760$	−4.43090e6	−0.278265
$761$	−4.39319e6	−0.274991	−0.137495	−	0.990502i	$-0.543905\pi$
$761$	−4.39319e6	−0.274991	−0.137495	+	0.990502i	$0.543905\pi$
$762$	−1.91548e6	−0.119506
$763$	564685.	0.0351152
$764$	3.68641e7	2.28492
$765$	−7.13327e6	−0.440692
$766$	4.55082e7	2.80232
$767$	−4.39687e6	−0.269870
$768$	−380189.	−0.0232593
$769$	−1.85557e7	−1.13152	−0.565758	−	0.824572i	$-0.691416\pi$
$769$	−1.85557e7	−1.13152	−0.565758	+	0.824572i	$0.691416\pi$
$770$	−103814.	−0.00631002
$771$	1.05250e6	0.0637656
$772$	−1.35876e7	−0.820538
$773$	1.04698e6	0.0630216	0.0315108	−	0.999503i	$-0.489968\pi$
$773$	1.04698e6	0.0630216	0.0315108	+	0.999503i	$0.489968\pi$
$774$	2.89649e7	1.73788
$775$	5.83388e6	0.348902
$776$	−2.74223e7	−1.63474
$777$	9853.91	0.000585539 0
$778$	5.58201e7	3.30629
$779$	−1.41237e6	−0.0833885
$780$	−768208.	−0.0452108
$781$	−3.92821e6	−0.230445
$782$	−5.09204e7	−2.97766
$783$	274798.	0.0160180
$784$	−4.44674e7	−2.58375
$785$	6.30501e6	0.365184
$786$	−757925.	−0.0437593
$787$	−1.41502e7	−0.814379	−0.407190	−	0.913344i	$-0.633491\pi$
$787$	−1.41502e7	−0.814379	−0.407190	+	0.913344i	$0.633491\pi$
$788$	6.09151e7	3.49470
$789$	449406.	0.0257008
$790$	−2.71670e7	−1.54872
$791$	−445270.	−0.0253036
$792$	−1.44183e7	−0.816775
$793$	−1.13727e7	−0.642217
$794$	−4.62613e6	−0.260415
$795$	−292986.	−0.0164410
$796$	−5.12355e7	−2.86608
$797$	1.47198e7	0.820834	0.410417	−	0.911898i	$-0.365383\pi$
$797$	1.47198e7	0.820834	0.410417	+	0.911898i	$0.365383\pi$
$798$	6687.33	0.000371745 0
$799$	−1.17161e7	−0.649254
$800$	−7.58766e6	−0.419163
$801$	−1.67894e7	−0.924603
$802$	4.51370e7	2.47798
$803$	−6.39536e6	−0.350006
$804$	−940316.	−0.0513019
$805$	335794.	0.0182635
$806$	−7.10577e7	−3.85278
$807$	320331.	0.0173147
$808$	9.28034e7	5.00075
$809$	−8.24774e6	−0.443061	−0.221531	−	0.975153i	$-0.571105\pi$
$809$	−8.24774e6	−0.443061	−0.221531	+	0.975153i	$0.571105\pi$
$810$	1.54740e7	0.828685
$811$	−9.81566e6	−0.524043	−0.262022	−	0.965062i	$-0.584389\pi$
$811$	−9.81566e6	−0.524043	−0.262022	+	0.965062i	$0.584389\pi$
$812$	−268997.	−0.0143172
$813$	−592377.	−0.0314320
$814$	7.12321e6	0.376803
$815$	−4.20720e6	−0.221870
$816$	−1.67998e6	−0.0883238
$817$	−4.09525e6	−0.214647
$818$	5.66190e7	2.95855
$819$	−572960.	−0.0298479
$820$	−7.69464e6	−0.399626
$821$	1.58935e7	0.822926	0.411463	−	0.911427i	$-0.365018\pi$
$821$	1.58935e7	0.822926	0.411463	+	0.911427i	$0.365018\pi$
$822$	552750.	0.0285331
$823$	−1.75791e7	−0.904686	−0.452343	−	0.891844i	$-0.649412\pi$
$823$	−1.75791e7	−0.904686	−0.452343	+	0.891844i	$0.649412\pi$
$824$	−5.51262e7	−2.82839
$825$	−40820.5	−0.00208806
$826$	208524.	0.0106342
$827$	−2.95666e7	−1.50327	−0.751636	−	0.659578i	$-0.770735\pi$
$827$	−2.95666e7	−1.50327	−0.751636	+	0.659578i	$0.770735\pi$
$828$	7.86150e7	3.98501
$829$	−2.32838e7	−1.17670	−0.588352	−	0.808605i	$-0.700223\pi$
$829$	−2.32838e7	−1.17670	−0.588352	+	0.808605i	$0.700223\pi$
$830$	−2.85148e7	−1.43673
$831$	720313.	0.0361842
$832$	3.11141e7	1.55829
$833$	1.97460e7	0.985976
$834$	1.17794e6	0.0586417
$835$	−1.43314e7	−0.711330
$836$	3.43635e6	0.170052
$837$	−2.44718e6	−0.120741
$838$	−3.35641e7	−1.65107
$839$	−6.49106e6	−0.318354	−0.159177	−	0.987250i	$-0.550884\pi$
$839$	−6.49106e6	−0.318354	−0.159177	+	0.987250i	$0.550884\pi$
$840$	21613.1	0.00105686
$841$	−1.94125e7	−0.946438
$842$	2.26680e7	1.10188
$843$	−870281.	−0.0421784
$844$	4.30614e7	2.08081
$845$	−3.80890e6	−0.183509
$846$	2.54458e7	1.22234
$847$	47762.8	0.00228760
$848$	5.74804e7	2.74492
$849$	−1.25981e6	−0.0599840
$850$	7.72960e6	0.366953
$851$	−2.30405e7	−1.09061
$852$	1.37857e6	0.0650622
$853$	−5.06805e6	−0.238489	−0.119245	−	0.992865i	$-0.538047\pi$
$853$	−5.06805e6	−0.238489	−0.119245	+	0.992865i	$0.538047\pi$
$854$	539358.	0.0253065
$855$	−2.19045e6	−0.102475
$856$	−1.30105e7	−0.606890
$857$	−2.66753e7	−1.24067	−0.620336	−	0.784336i	$-0.713004\pi$
$857$	−2.66753e7	−1.24067	−0.620336	+	0.784336i	$0.713004\pi$
$858$	497201.	0.0230576
$859$	3.49525e6	0.161620	0.0808100	−	0.996730i	$-0.474249\pi$
$859$	3.49525e6	0.161620	0.0808100	+	0.996730i	$0.474249\pi$
$860$	−2.23110e7	−1.02866
$861$	6889.29	0.000316714 0
$862$	2.96744e7	1.36023
$863$	2.02694e7	0.926431	0.463215	−	0.886246i	$-0.346696\pi$
$863$	2.02694e7	0.926431	0.463215	+	0.886246i	$0.346696\pi$
$864$	3.18286e6	0.145055
$865$	1.21629e7	0.552708
$866$	5.02947e7	2.27891
$867$	−20401.1	−0.000921734 0
$868$	2.39553e6	0.107920
$869$	1.24989e7	0.561466
$870$	−148796.	−0.00666488
$871$	−1.60242e7	−0.715698
$872$	−8.49830e7	−3.78478
$873$	−1.35564e7	−0.602017
$874$	−1.56364e7	−0.692400
$875$	−50972.8	−0.00225071
$876$	2.24439e6	0.0988184
$877$	1.31167e7	0.575872	0.287936	−	0.957650i	$-0.407031\pi$
$877$	1.31167e7	0.575872	0.287936	+	0.957650i	$0.407031\pi$
$878$	3.98718e7	1.74554
$879$	−424178.	−0.0185172
$880$	8.00851e6	0.348614
$881$	1.22394e7	0.531278	0.265639	−	0.964073i	$-0.414417\pi$
$881$	1.22394e7	0.531278	0.265639	+	0.964073i	$0.414417\pi$
$882$	−4.28858e7	−1.85628
$883$	1.55678e7	0.671933	0.335966	−	0.941874i	$-0.390937\pi$
$883$	1.55678e7	0.671933	0.335966	+	0.941874i	$0.390937\pi$
$884$	−6.69251e7	−2.88044
$885$	81992.9	0.00351899
$886$	3.12872e7	1.33900
$887$	−1.07923e6	−0.0460580	−0.0230290	−	0.999735i	$-0.507331\pi$
$887$	−1.07923e6	−0.0460580	−0.0230290	+	0.999735i	$0.507331\pi$
$888$	−1.48298e6	−0.0631106
$889$	1.10045e6	0.0466997
$890$	1.81930e7	0.769892
$891$	−7.11924e6	−0.300427
$892$	−1.00079e8	−4.21144
$893$	−3.59770e6	−0.150972
$894$	−2.64564e6	−0.110710
$895$	1.09019e7	0.454932
$896$	−208250.	−0.00866592
$897$	−1.60823e6	−0.0667370
$898$	6.14255e7	2.54190
$899$	−9.78367e6	−0.403741
$900$	−1.19336e7	−0.491094
$901$	−2.55245e7	−1.04748
$902$	4.98014e6	0.203810
$903$	19975.8	0.000815240 0
$904$	6.70115e7	2.72727
$905$	9.44764e6	0.383444
$906$	−94622.4	−0.00382978
$907$	9.65999e6	0.389905	0.194952	−	0.980813i	$-0.437545\pi$
$907$	9.65999e6	0.389905	0.194952	+	0.980813i	$0.437545\pi$
$908$	1.20607e8	4.85465
$909$	4.58780e7	1.84160
$910$	620858.	0.0248536
$911$	3.66614e7	1.46357	0.731785	−	0.681535i	$-0.238687\pi$
$911$	3.66614e7	1.46357	0.731785	+	0.681535i	$0.238687\pi$
$912$	−515878.	−0.0205381
$913$	1.31191e7	0.520865
$914$	−2.53335e7	−1.00307
$915$	212079.	0.00837423
$916$	−8.37961e7	−3.29978
$917$	435430.	0.0171000
$918$	−3.24240e6	−0.126987
$919$	−6.57489e6	−0.256803	−0.128401	−	0.991722i	$-0.540985\pi$
$919$	−6.57489e6	−0.256803	−0.128401	+	0.991722i	$0.540985\pi$
$920$	−5.05359e7	−1.96848
$921$	755911.	0.0293644
$922$	7.83207e7	3.03424
$923$	2.34925e7	0.907664
$924$	−16761.9	−0.000645866 0
$925$	3.49749e6	0.134401
$926$	4.95537e7	1.89910
$927$	−2.72520e7	−1.04159
$928$	1.27248e7	0.485045
$929$	−3.67068e7	−1.39543	−0.697715	−	0.716376i	$-0.745800\pi$
$929$	−3.67068e7	−1.39543	−0.697715	+	0.716376i	$0.745800\pi$
$930$	1.32509e6	0.0502386
$931$	6.06349e6	0.229270
$932$	1.08492e8	4.09127
$933$	−1.35476e6	−0.0509516
$934$	5.63995e7	2.11548
$935$	−3.55622e6	−0.133033
$936$	8.62284e7	3.21707
$937$	2.45122e7	0.912081	0.456041	−	0.889959i	$-0.349267\pi$
$937$	2.45122e7	0.912081	0.456041	+	0.889959i	$0.349267\pi$
$938$	759955.	0.0282020
$939$	352493.	0.0130463
$940$	−1.96003e7	−0.723509
$941$	4.03727e6	0.148632	0.0743162	−	0.997235i	$-0.476323\pi$
$941$	4.03727e6	0.148632	0.0743162	+	0.997235i	$0.476323\pi$
$942$	1.43210e6	0.0525830
$943$	−1.61086e7	−0.589900
$944$	−1.60860e7	−0.587516
$945$	21382.0	0.000778876 0
$946$	1.44402e7	0.524619
$947$	−2.76320e7	−1.00124	−0.500619	−	0.865668i	$-0.666894\pi$
$947$	−2.76320e7	−1.00124	−0.500619	+	0.865668i	$0.666894\pi$
$948$	−4.38638e6	−0.158520
$949$	3.82472e7	1.37859
$950$	2.37356e6	0.0853280
$951$	1.81282e6	0.0649987
$952$	1.88290e6	0.0673341
$953$	−3.17893e7	−1.13383	−0.566915	−	0.823776i	$-0.691863\pi$
$953$	−3.17893e7	−1.13383	−0.566915	+	0.823776i	$0.691863\pi$
$954$	5.54360e7	1.97206
$955$	−1.17149e7	−0.415652
$956$	2.04148e7	0.722437
$957$	68457.7	0.00241625
$958$	−8.47294e7	−2.98277
$959$	−317556.	−0.0111500
$960$	−580216.	−0.0203194
$961$	5.84984e7	2.04332
$962$	−4.26001e7	−1.48413
$963$	−6.43183e6	−0.223495
$964$	1.08926e8	3.77518
$965$	4.31794e6	0.149265
$966$	76271.2	0.00262977
$967$	2.18700e7	0.752114	0.376057	−	0.926597i	$-0.377280\pi$
$967$	2.18700e7	0.752114	0.376057	+	0.926597i	$0.377280\pi$
$968$	−7.18812e6	−0.246563
$969$	229078.	0.00783745
$970$	1.46897e7	0.501283
$971$	2.72384e6	0.0927115	0.0463558	−	0.998925i	$-0.485239\pi$
$971$	2.72384e6	0.0927115	0.0463558	+	0.998925i	$0.485239\pi$
$972$	7.51031e6	0.254972
$973$	−676727.	−0.0229156
$974$	6.44115e7	2.17553
$975$	244126.	0.00822435
$976$	−4.16074e7	−1.39813
$977$	−1.84511e7	−0.618423	−0.309211	−	0.950993i	$-0.600065\pi$
$977$	−1.84511e7	−0.618423	−0.309211	+	0.950993i	$0.600065\pi$
$978$	−955608.	−0.0319472
$979$	−8.37021e6	−0.279113
$980$	3.30339e7	1.09874
$981$	−4.20119e7	−1.39380
$982$	−2.80499e7	−0.928222
$983$	−2.23407e7	−0.737416	−0.368708	−	0.929545i	$-0.620200\pi$
$983$	−2.23407e7	−0.737416	−0.368708	+	0.929545i	$0.620200\pi$
$984$	−1.03681e6	−0.0341360
$985$	−1.93580e7	−0.635725
$986$	−1.29629e7	−0.424628
$987$	17548.9	0.000573399 0
$988$	−2.05510e7	−0.669792
$989$	−4.67076e7	−1.51844
$990$	7.72368e6	0.250459
$991$	2.82943e7	0.915197	0.457598	−	0.889159i	$-0.348710\pi$
$991$	2.82943e7	0.915197	0.457598	+	0.889159i	$0.348710\pi$
$992$	−1.13320e8	−3.65617
$993$	1.04316e6	0.0335719
$994$	−1.11414e6	−0.0357664
$995$	1.62819e7	0.521373
$996$	−4.60400e6	−0.147058
$997$	8.44493e6	0.269066	0.134533	−	0.990909i	$-0.457047\pi$
$997$	8.44493e6	0.269066	0.134533	+	0.990909i	$0.457047\pi$
$998$	1.73554e7	0.551579
$999$	−1.46712e6	−0.0465106

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.c.1.3	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.c.1.3	✓	37	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-10.5199 q^{2} +0.539776 q^{3} +78.6693 q^{4} -25.0000 q^{5} -5.67841 q^{6} +3.26226 q^{7} -490.959 q^{8} -242.709 q^{9} +O(q^{10})\)	\(q-10.5199 q^{2} +0.539776 q^{3} +78.6693 q^{4} -25.0000 q^{5} -5.67841 q^{6} +3.26226 q^{7} -490.959 q^{8} -242.709 q^{9} +262.999 q^{10} -121.000 q^{11} +42.4638 q^{12} +723.636 q^{13} -34.3188 q^{14} -13.4944 q^{15} +2647.44 q^{16} -1175.61 q^{17} +2553.28 q^{18} -361.000 q^{19} -1966.73 q^{20} +1.76089 q^{21} +1272.91 q^{22} -4117.32 q^{23} -265.007 q^{24} +625.000 q^{25} -7612.61 q^{26} -262.174 q^{27} +256.640 q^{28} -1048.15 q^{29} +141.960 q^{30} +9334.21 q^{31} -12140.3 q^{32} -65.3128 q^{33} +12367.4 q^{34} -81.5565 q^{35} -19093.7 q^{36} +5595.99 q^{37} +3797.70 q^{38} +390.601 q^{39} +12274.0 q^{40} +3912.40 q^{41} -18.5245 q^{42} +11344.2 q^{43} -9518.98 q^{44} +6067.72 q^{45} +43314.0 q^{46} +9965.93 q^{47} +1429.02 q^{48} -16796.4 q^{49} -6574.97 q^{50} -634.566 q^{51} +56927.9 q^{52} +21711.7 q^{53} +2758.05 q^{54} +3025.00 q^{55} -1601.64 q^{56} -194.859 q^{57} +11026.5 q^{58} -6076.08 q^{59} -1061.59 q^{60} -15716.1 q^{61} -98195.4 q^{62} -791.779 q^{63} +42996.8 q^{64} -18090.9 q^{65} +687.088 q^{66} -22144.0 q^{67} -92484.5 q^{68} -2222.43 q^{69} +857.970 q^{70} +32464.5 q^{71} +119160. q^{72} +52854.2 q^{73} -58869.5 q^{74} +337.360 q^{75} -28399.6 q^{76} -394.734 q^{77} -4109.10 q^{78} -103297. q^{79} -66186.0 q^{80} +58836.7 q^{81} -41158.2 q^{82} -108422. q^{83} +138.528 q^{84} +29390.3 q^{85} -119340. q^{86} -565.766 q^{87} +59406.0 q^{88} +69175.3 q^{89} -63832.1 q^{90} +2360.69 q^{91} -323907. q^{92} +5038.38 q^{93} -104841. q^{94} +9025.00 q^{95} -6553.02 q^{96} +55854.6 q^{97} +176697. q^{98} +29367.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9}+O(q^{10}) \) 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9	\( 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9} + 300 q^{10} - 4477 q^{11} - 568 q^{12} + 719 q^{13} + 687 q^{14} + 675 q^{15} + 11494 q^{16} + 999 q^{17} - 595 q^{18} - 13357 q^{19} - 14350 q^{20} - 1077 q^{21} + 1452 q^{22} + 5096 q^{23} - 3154 q^{24} + 23125 q^{25} - 10395 q^{26} - 7578 q^{27} + 19863 q^{28} - 7969 q^{29} + 1875 q^{30} + 603 q^{31} - 27809 q^{32} + 3267 q^{33} - 24081 q^{34} - 8425 q^{35} + 59869 q^{36} + 7963 q^{37} + 4332 q^{38} + 86 q^{39} + 17400 q^{40} + 1475 q^{41} - 46542 q^{42} + 38059 q^{43} - 69454 q^{44} - 78500 q^{45} - 3413 q^{46} - 37658 q^{47} - 51317 q^{48} + 39188 q^{49} - 7500 q^{50} - 40262 q^{51} + 25358 q^{52} - 52545 q^{53} + 64732 q^{54} + 111925 q^{55} - 54173 q^{56} + 9747 q^{57} + 105808 q^{58} - 34039 q^{59} + 14200 q^{60} + 30023 q^{61} - 100198 q^{62} + 30376 q^{63} + 160888 q^{64} - 17975 q^{65} + 9075 q^{66} - 45284 q^{67} + 125176 q^{68} + 109244 q^{69} - 17175 q^{70} - 84020 q^{71} - 291176 q^{72} + 24542 q^{73} + 38795 q^{74} - 16875 q^{75} - 207214 q^{76} - 40777 q^{77} + 1042 q^{78} + 49303 q^{79} - 287350 q^{80} + 344453 q^{81} - 286030 q^{82} - 402155 q^{83} - 203270 q^{84} - 24975 q^{85} - 276426 q^{86} + 116994 q^{87} + 84216 q^{88} - 442930 q^{89} + 14875 q^{90} - 93040 q^{91} + 402160 q^{92} - 241950 q^{93} - 170720 q^{94} + 333925 q^{95} - 234384 q^{96} - 87732 q^{97} - 712662 q^{98} - 379940 q^{99}+O(q^{100}) \) 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9 + 300 * q^10 - 4477 * q^11 - 568 * q^12 + 719 * q^13 + 687 * q^14 + 675 * q^15 + 11494 * q^16 + 999 * q^17 - 595 * q^18 - 13357 * q^19 - 14350 * q^20 - 1077 * q^21 + 1452 * q^22 + 5096 * q^23 - 3154 * q^24 + 23125 * q^25 - 10395 * q^26 - 7578 * q^27 + 19863 * q^28 - 7969 * q^29 + 1875 * q^30 + 603 * q^31 - 27809 * q^32 + 3267 * q^33 - 24081 * q^34 - 8425 * q^35 + 59869 * q^36 + 7963 * q^37 + 4332 * q^38 + 86 * q^39 + 17400 * q^40 + 1475 * q^41 - 46542 * q^42 + 38059 * q^43 - 69454 * q^44 - 78500 * q^45 - 3413 * q^46 - 37658 * q^47 - 51317 * q^48 + 39188 * q^49 - 7500 * q^50 - 40262 * q^51 + 25358 * q^52 - 52545 * q^53 + 64732 * q^54 + 111925 * q^55 - 54173 * q^56 + 9747 * q^57 + 105808 * q^58 - 34039 * q^59 + 14200 * q^60 + 30023 * q^61 - 100198 * q^62 + 30376 * q^63 + 160888 * q^64 - 17975 * q^65 + 9075 * q^66 - 45284 * q^67 + 125176 * q^68 + 109244 * q^69 - 17175 * q^70 - 84020 * q^71 - 291176 * q^72 + 24542 * q^73 + 38795 * q^74 - 16875 * q^75 - 207214 * q^76 - 40777 * q^77 + 1042 * q^78 + 49303 * q^79 - 287350 * q^80 + 344453 * q^81 - 286030 * q^82 - 402155 * q^83 - 203270 * q^84 - 24975 * q^85 - 276426 * q^86 + 116994 * q^87 + 84216 * q^88 - 442930 * q^89 + 14875 * q^90 - 93040 * q^91 + 402160 * q^92 - 241950 * q^93 - 170720 * q^94 + 333925 * q^95 - 234384 * q^96 - 87732 * q^97 - 712662 * q^98 - 379940 * q^99

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