LMFDB - Embedded newform 1045.6.a.h.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$167.601091705$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-6.98489 q^{2} -3.88370 q^{3} +16.7886 q^{4} +25.0000 q^{5} +27.1272 q^{6} +123.805 q^{7} +106.250 q^{8} -227.917 q^{9} +O(q^{10})$	\(q-6.98489 q^{2} -3.88370 q^{3} +16.7886 q^{4} +25.0000 q^{5} +27.1272 q^{6} +123.805 q^{7} +106.250 q^{8} -227.917 q^{9} -174.622 q^{10} +121.000 q^{11} -65.2020 q^{12} +951.650 q^{13} -864.765 q^{14} -97.0925 q^{15} -1279.38 q^{16} -517.237 q^{17} +1591.97 q^{18} +361.000 q^{19} +419.716 q^{20} -480.822 q^{21} -845.171 q^{22} -3167.77 q^{23} -412.642 q^{24} +625.000 q^{25} -6647.16 q^{26} +1828.90 q^{27} +2078.52 q^{28} +5578.60 q^{29} +678.180 q^{30} +7694.65 q^{31} +5536.32 q^{32} -469.928 q^{33} +3612.84 q^{34} +3095.13 q^{35} -3826.41 q^{36} -8284.65 q^{37} -2521.54 q^{38} -3695.92 q^{39} +2656.24 q^{40} +3423.88 q^{41} +3358.49 q^{42} +1400.97 q^{43} +2031.42 q^{44} -5697.92 q^{45} +22126.5 q^{46} +4790.26 q^{47} +4968.72 q^{48} -1479.28 q^{49} -4365.55 q^{50} +2008.80 q^{51} +15976.9 q^{52} +28653.7 q^{53} -12774.7 q^{54} +3025.00 q^{55} +13154.3 q^{56} -1402.02 q^{57} -38965.8 q^{58} +5788.32 q^{59} -1630.05 q^{60} +19822.4 q^{61} -53746.2 q^{62} -28217.3 q^{63} +2269.54 q^{64} +23791.2 q^{65} +3282.39 q^{66} +59597.5 q^{67} -8683.70 q^{68} +12302.7 q^{69} -21619.1 q^{70} +36113.4 q^{71} -24216.1 q^{72} -73235.6 q^{73} +57867.4 q^{74} -2427.31 q^{75} +6060.69 q^{76} +14980.4 q^{77} +25815.6 q^{78} -109266. q^{79} -31984.5 q^{80} +48280.9 q^{81} -23915.4 q^{82} +12319.4 q^{83} -8072.35 q^{84} -12930.9 q^{85} -9785.64 q^{86} -21665.6 q^{87} +12856.2 q^{88} +85859.3 q^{89} +39799.3 q^{90} +117819. q^{91} -53182.5 q^{92} -29883.7 q^{93} -33459.4 q^{94} +9025.00 q^{95} -21501.4 q^{96} +17941.4 q^{97} +10332.6 q^{98} -27577.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9}+O(q^{10}) $ 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + 600 q^{10} + 4840 q^{11} + 2312 q^{12} + 2661 q^{13} + 395 q^{14} + 1575 q^{15} + 15974 q^{16} + 8249 q^{17} + 7225 q^{18} + 14440 q^{19} + 17250 q^{20} + 6845 q^{21} + 2904 q^{22} + 13948 q^{23} + 9740 q^{24} + 25000 q^{25} + 11581 q^{26} + 27864 q^{27} + 37879 q^{28} + 12965 q^{29} + 9125 q^{30} + 4411 q^{31} + 30751 q^{32} + 7623 q^{33} - 17739 q^{34} + 20975 q^{35} + 71345 q^{36} + 5729 q^{37} + 8664 q^{38} - 23560 q^{39} + 21150 q^{40} + 34059 q^{41} + 48528 q^{42} + 68593 q^{43} + 83490 q^{44} + 88875 q^{45} + 43829 q^{46} + 91592 q^{47} + 26539 q^{48} + 152447 q^{49} + 15000 q^{50} - 23170 q^{51} + 46798 q^{52} + 24361 q^{53} + 136436 q^{54} + 121000 q^{55} - 35393 q^{56} + 22743 q^{57} + 77722 q^{58} + 212881 q^{59} + 57800 q^{60} + 137627 q^{61} + 82606 q^{62} + 243832 q^{63} + 259580 q^{64} + 66525 q^{65} + 44165 q^{66} + 78752 q^{67} + 565000 q^{68} + 46134 q^{69} + 9875 q^{70} + 28888 q^{71} - 65574 q^{72} + 291074 q^{73} + 151963 q^{74} + 39375 q^{75} + 249090 q^{76} + 101519 q^{77} - 136222 q^{78} + 87079 q^{79} + 399350 q^{80} + 471360 q^{81} - 74882 q^{82} + 346989 q^{83} - 159196 q^{84} + 206225 q^{85} - 207742 q^{86} + 294612 q^{87} + 102366 q^{88} + 126718 q^{89} + 180625 q^{90} - 239900 q^{91} + 274196 q^{92} + 321654 q^{93} - 418108 q^{94} + 361000 q^{95} + 342154 q^{96} + 137404 q^{97} - 89356 q^{98} + 430155 q^{99}+O(q^{100}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9 + 600 * q^10 + 4840 * q^11 + 2312 * q^12 + 2661 * q^13 + 395 * q^14 + 1575 * q^15 + 15974 * q^16 + 8249 * q^17 + 7225 * q^18 + 14440 * q^19 + 17250 * q^20 + 6845 * q^21 + 2904 * q^22 + 13948 * q^23 + 9740 * q^24 + 25000 * q^25 + 11581 * q^26 + 27864 * q^27 + 37879 * q^28 + 12965 * q^29 + 9125 * q^30 + 4411 * q^31 + 30751 * q^32 + 7623 * q^33 - 17739 * q^34 + 20975 * q^35 + 71345 * q^36 + 5729 * q^37 + 8664 * q^38 - 23560 * q^39 + 21150 * q^40 + 34059 * q^41 + 48528 * q^42 + 68593 * q^43 + 83490 * q^44 + 88875 * q^45 + 43829 * q^46 + 91592 * q^47 + 26539 * q^48 + 152447 * q^49 + 15000 * q^50 - 23170 * q^51 + 46798 * q^52 + 24361 * q^53 + 136436 * q^54 + 121000 * q^55 - 35393 * q^56 + 22743 * q^57 + 77722 * q^58 + 212881 * q^59 + 57800 * q^60 + 137627 * q^61 + 82606 * q^62 + 243832 * q^63 + 259580 * q^64 + 66525 * q^65 + 44165 * q^66 + 78752 * q^67 + 565000 * q^68 + 46134 * q^69 + 9875 * q^70 + 28888 * q^71 - 65574 * q^72 + 291074 * q^73 + 151963 * q^74 + 39375 * q^75 + 249090 * q^76 + 101519 * q^77 - 136222 * q^78 + 87079 * q^79 + 399350 * q^80 + 471360 * q^81 - 74882 * q^82 + 346989 * q^83 - 159196 * q^84 + 206225 * q^85 - 207742 * q^86 + 294612 * q^87 + 102366 * q^88 + 126718 * q^89 + 180625 * q^90 - 239900 * q^91 + 274196 * q^92 + 321654 * q^93 - 418108 * q^94 + 361000 * q^95 + 342154 * q^96 + 137404 * q^97 - 89356 * q^98 + 430155 * 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 $

$2$	−6.98489	−1.23477	−0.617383	−	0.786663i	$-0.711807\pi$
$2$	−6.98489	−1.23477	−0.617383	+	0.786663i	$0.711807\pi$
$3$	−3.88370	−0.249140	−0.124570	−	0.992211i	$-0.539755\pi$
$3$	−3.88370	−0.249140	−0.124570	+	0.992211i	$0.539755\pi$
$4$	16.7886	0.524645
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	27.1272	0.307629
$7$	123.805	0.954979	0.477489	−	0.878638i	$-0.341547\pi$
$7$	123.805	0.954979	0.477489	+	0.878638i	$0.341547\pi$
$8$	106.250	0.586952
$9$	−227.917	−0.937929
$10$	−174.622	−0.552204
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−65.2020	−0.130710
$13$	951.650	1.56178	0.780888	−	0.624671i	$-0.214767\pi$
$13$	951.650	1.56178	0.780888	+	0.624671i	$0.214767\pi$
$14$	−864.765	−1.17917
$15$	−97.0925	−0.111419
$16$	−1279.38	−1.24939
$17$	−517.237	−0.434078	−0.217039	−	0.976163i	$-0.569640\pi$
$17$	−517.237	−0.434078	−0.217039	+	0.976163i	$0.569640\pi$
$18$	1591.97	1.15812
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	419.716	0.234628
$21$	−480.822	−0.237923
$22$	−845.171	−0.372296
$23$	−3167.77	−1.24863	−0.624315	−	0.781172i	$-0.714622\pi$
$23$	−3167.77	−1.24863	−0.624315	+	0.781172i	$0.714622\pi$
$24$	−412.642	−0.146233
$25$	625.000	0.200000
$26$	−6647.16	−1.92843
$27$	1828.90	0.482815
$28$	2078.52	0.501024
$29$	5578.60	1.23177	0.615885	−	0.787836i	$-0.288798\pi$
$29$	5578.60	1.23177	0.615885	+	0.787836i	$0.288798\pi$
$30$	678.180	0.137576
$31$	7694.65	1.43808	0.719042	−	0.694966i	$-0.244581\pi$
$31$	7694.65	1.43808	0.719042	+	0.694966i	$0.244581\pi$
$32$	5536.32	0.955754
$33$	−469.928	−0.0751184
$34$	3612.84	0.535984
$35$	3095.13	0.427079
$36$	−3826.41	−0.492080
$37$	−8284.65	−0.994878	−0.497439	−	0.867499i	$-0.665726\pi$
$37$	−8284.65	−0.994878	−0.497439	+	0.867499i	$0.665726\pi$
$38$	−2521.54	−0.283275
$39$	−3695.92	−0.389100
$40$	2656.24	0.262493
$41$	3423.88	0.318096	0.159048	−	0.987271i	$-0.449157\pi$
$41$	3423.88	0.318096	0.159048	+	0.987271i	$0.449157\pi$
$42$	3358.49	0.293779
$43$	1400.97	0.115547	0.0577735	−	0.998330i	$-0.481600\pi$
$43$	1400.97	0.115547	0.0577735	+	0.998330i	$0.481600\pi$
$44$	2031.42	0.158186
$45$	−5697.92	−0.419455
$46$	22126.5	1.54177
$47$	4790.26	0.316311	0.158156	−	0.987414i	$-0.449445\pi$
$47$	4790.26	0.316311	0.158156	+	0.987414i	$0.449445\pi$
$48$	4968.72	0.311273
$49$	−1479.28	−0.0880159
$50$	−4365.55	−0.246953
$51$	2008.80	0.108146
$52$	15976.9	0.819377
$53$	28653.7	1.40117	0.700585	−	0.713569i	$-0.252922\pi$
$53$	28653.7	1.40117	0.700585	+	0.713569i	$0.252922\pi$
$54$	−12774.7	−0.596163
$55$	3025.00	0.134840
$56$	13154.3	0.560527
$57$	−1402.02	−0.0571565
$58$	−38965.8	−1.52095
$59$	5788.32	0.216482	0.108241	−	0.994125i	$-0.465478\pi$
$59$	5788.32	0.216482	0.108241	+	0.994125i	$0.465478\pi$
$60$	−1630.05	−0.0584552
$61$	19822.4	0.682074	0.341037	−	0.940050i	$-0.389222\pi$
$61$	19822.4	0.682074	0.341037	+	0.940050i	$0.389222\pi$
$62$	−53746.2	−1.77570
$63$	−28217.3	−0.895703
$64$	2269.54	0.0692609
$65$	23791.2	0.698447
$66$	3282.39	0.0927536
$67$	59597.5	1.62196	0.810981	−	0.585072i	$-0.198934\pi$
$67$	59597.5	1.62196	0.810981	+	0.585072i	$0.198934\pi$
$68$	−8683.70	−0.227737
$69$	12302.7	0.311083
$70$	−21619.1	−0.527343
$71$	36113.4	0.850203	0.425101	−	0.905146i	$-0.360238\pi$
$71$	36113.4	0.850203	0.425101	+	0.905146i	$0.360238\pi$
$72$	−24216.1	−0.550520
$73$	−73235.6	−1.60848	−0.804239	−	0.594306i	$-0.797427\pi$
$73$	−73235.6	−1.60848	−0.804239	+	0.594306i	$0.797427\pi$
$74$	57867.4	1.22844
$75$	−2427.31	−0.0498279
$76$	6060.69	0.120362
$77$	14980.4	0.287937
$78$	25815.6	0.480447
$79$	−109266.	−1.96978	−0.984888	−	0.173190i	$-0.944593\pi$
$79$	−109266.	−1.96978	−0.984888	+	0.173190i	$0.944593\pi$
$80$	−31984.5	−0.558745
$81$	48280.9	0.817641
$82$	−23915.4	−0.392774
$83$	12319.4	0.196288	0.0981440	−	0.995172i	$-0.468709\pi$
$83$	12319.4	0.196288	0.0981440	+	0.995172i	$0.468709\pi$
$84$	−8072.35	−0.124825
$85$	−12930.9	−0.194125
$86$	−9785.64	−0.142673
$87$	−21665.6	−0.306883
$88$	12856.2	0.176973
$89$	85859.3	1.14898	0.574490	−	0.818512i	$-0.305201\pi$
$89$	85859.3	1.14898	0.574490	+	0.818512i	$0.305201\pi$
$90$	39799.3	0.517928
$91$	117819.	1.49146
$92$	−53182.5	−0.655088
$93$	−29883.7	−0.358284
$94$	−33459.4	−0.390570
$95$	9025.00	0.102598
$96$	−21501.4	−0.238116
$97$	17941.4	0.193610	0.0968050	−	0.995303i	$-0.469138\pi$
$97$	17941.4	0.193610	0.0968050	+	0.995303i	$0.469138\pi$
$98$	10332.6	0.108679
$99$	−27577.9	−0.282796
$100$	10492.9	0.104929
$101$	70739.1	0.690011	0.345006	−	0.938601i	$-0.387877\pi$
$101$	70739.1	0.690011	0.345006	+	0.938601i	$0.387877\pi$
$102$	−14031.2	−0.133535
$103$	71203.4	0.661314	0.330657	−	0.943751i	$-0.392730\pi$
$103$	71203.4	0.661314	0.330657	+	0.943751i	$0.392730\pi$
$104$	101112.	0.916688
$105$	−12020.6	−0.106402
$106$	−200143.	−1.73012
$107$	69047.8	0.583029	0.291514	−	0.956566i	$-0.405841\pi$
$107$	69047.8	0.583029	0.291514	+	0.956566i	$0.405841\pi$
$108$	30704.7	0.253306
$109$	−44429.0	−0.358179	−0.179090	−	0.983833i	$-0.557315\pi$
$109$	−44429.0	−0.358179	−0.179090	+	0.983833i	$0.557315\pi$
$110$	−21129.3	−0.166496
$111$	32175.1	0.247864
$112$	−158394.	−1.19314
$113$	−107473.	−0.791777	−0.395888	−	0.918299i	$-0.629563\pi$
$113$	−107473.	−0.791777	−0.395888	+	0.918299i	$0.629563\pi$
$114$	9792.92	0.0705749
$115$	−79194.3	−0.558405
$116$	93657.0	0.646242
$117$	−216897.	−1.46484
$118$	−40430.8	−0.267305
$119$	−64036.6	−0.414535
$120$	−10316.1	−0.0653974
$121$	14641.0	0.0909091
$122$	−138457.	−0.842201
$123$	−13297.3	−0.0792504
$124$	129183.	0.754483
$125$	15625.0	0.0894427
$126$	197094.	1.10598
$127$	−210725.	−1.15933	−0.579663	−	0.814856i	$-0.696816\pi$
$127$	−210725.	−1.15933	−0.579663	+	0.814856i	$0.696816\pi$
$128$	−193015.	−1.04128
$129$	−5440.97	−0.0287874
$130$	−166179.	−0.862418
$131$	−321047.	−1.63452	−0.817261	−	0.576268i	$-0.804509\pi$
$131$	−321047.	−1.63452	−0.817261	+	0.576268i	$0.804509\pi$
$132$	−7889.45	−0.0394105
$133$	44693.7	0.219087
$134$	−416282.	−2.00274
$135$	45722.5	0.215921
$136$	−54956.3	−0.254783
$137$	−316103.	−1.43889	−0.719445	−	0.694550i	$-0.755604\pi$
$137$	−316103.	−1.43889	−0.719445	+	0.694550i	$0.755604\pi$
$138$	−85932.8	−0.384115
$139$	−235632.	−1.03442	−0.517211	−	0.855858i	$-0.673030\pi$
$139$	−235632.	−1.03442	−0.517211	+	0.855858i	$0.673030\pi$
$140$	51963.0	0.224065
$141$	−18603.9	−0.0788056
$142$	−252248.	−1.04980
$143$	115150.	0.470893
$144$	291592.	1.17184
$145$	139465.	0.550865
$146$	511542.	1.98609
$147$	5745.09	0.0219282
$148$	−139088.	−0.521958
$149$	301573.	1.11283	0.556413	−	0.830906i	$-0.312177\pi$
$149$	301573.	1.11283	0.556413	+	0.830906i	$0.312177\pi$
$150$	16954.5	0.0615258
$151$	364106.	1.29953	0.649763	−	0.760137i	$-0.274868\pi$
$151$	364106.	1.29953	0.649763	+	0.760137i	$0.274868\pi$
$152$	38356.1	0.134656
$153$	117887.	0.407134
$154$	−104637.	−0.355534
$155$	192366.	0.643131
$156$	−62049.5	−0.204139
$157$	−381142.	−1.23407	−0.617033	−	0.786937i	$-0.711665\pi$
$157$	−381142.	−1.23407	−0.617033	+	0.786937i	$0.711665\pi$
$158$	763210.	2.43221
$159$	−111282.	−0.349087
$160$	138408.	0.427426
$161$	−392186.	−1.19242
$162$	−337237.	−1.00959
$163$	−66067.6	−0.194769	−0.0973845	−	0.995247i	$-0.531048\pi$
$163$	−66067.6	−0.194769	−0.0973845	+	0.995247i	$0.531048\pi$
$164$	57482.2	0.166888
$165$	−11748.2	−0.0335940
$166$	−86049.5	−0.242370
$167$	176059.	0.488501	0.244251	−	0.969712i	$-0.421458\pi$
$167$	176059.	0.488501	0.244251	+	0.969712i	$0.421458\pi$
$168$	−51087.2	−0.139649
$169$	534344.	1.43914
$170$	90321.1	0.239699
$171$	−82278.0	−0.215176
$172$	23520.4	0.0606212
$173$	−119022.	−0.302351	−0.151175	−	0.988507i	$-0.548306\pi$
$173$	−119022.	−0.302351	−0.151175	+	0.988507i	$0.548306\pi$
$174$	151332.	0.378928
$175$	77378.2	0.190996
$176$	−154805.	−0.376706
$177$	−22480.1	−0.0539343
$178$	−599717.	−1.41872
$179$	−277375.	−0.647044	−0.323522	−	0.946221i	$-0.604867\pi$
$179$	−277375.	−0.647044	−0.323522	+	0.946221i	$0.604867\pi$
$180$	−95660.3	−0.220065
$181$	448881.	1.01844	0.509219	−	0.860637i	$-0.329934\pi$
$181$	448881.	1.01844	0.509219	+	0.860637i	$0.329934\pi$
$182$	−822953.	−1.84161
$183$	−76984.2	−0.169932
$184$	−336575.	−0.732887
$185$	−207116.	−0.444923
$186$	208734.	0.442396
$187$	−62585.7	−0.130879
$188$	80421.9	0.165951
$189$	226427.	0.461078
$190$	−63038.6	−0.126684
$191$	−681220.	−1.35115	−0.675576	−	0.737291i	$-0.736105\pi$
$191$	−681220.	−1.35115	−0.675576	+	0.737291i	$0.736105\pi$
$192$	−8814.22	−0.0172556
$193$	797459.	1.54104	0.770522	−	0.637413i	$-0.219996\pi$
$193$	797459.	1.54104	0.770522	+	0.637413i	$0.219996\pi$
$194$	−125319.	−0.239063
$195$	−92398.1	−0.174011
$196$	−24835.1	−0.0461770
$197$	−183040.	−0.336031	−0.168016	−	0.985784i	$-0.553736\pi$
$197$	−183040.	−0.336031	−0.168016	+	0.985784i	$0.553736\pi$
$198$	192629.	0.349187
$199$	−72289.3	−0.129402	−0.0647010	−	0.997905i	$-0.520609\pi$
$199$	−72289.3	−0.129402	−0.0647010	+	0.997905i	$0.520609\pi$
$200$	66406.1	0.117390
$201$	−231459.	−0.404095
$202$	−494104.	−0.852001
$203$	690659.	1.17631
$204$	33724.9	0.0567382
$205$	85596.9	0.142257
$206$	−497348.	−0.816567
$207$	721988.	1.17113
$208$	−1.21752e6	−1.95127
$209$	43681.0	0.0691714
$210$	83962.2	0.131382
$211$	−1.09027e6	−1.68588	−0.842941	−	0.538005i	$-0.819178\pi$
$211$	−1.09027e6	−1.68588	−0.842941	+	0.538005i	$0.819178\pi$
$212$	481056.	0.735117
$213$	−140254.	−0.211819
$214$	−482291.	−0.719904
$215$	35024.4	0.0516742
$216$	194320.	0.283389
$217$	952637.	1.37334
$218$	310332.	0.442267
$219$	284425.	0.400736
$220$	50785.6	0.0707431
$221$	−492229.	−0.677932
$222$	−224740.	−0.306053
$223$	−204245.	−0.275036	−0.137518	−	0.990499i	$-0.543912\pi$
$223$	−204245.	−0.275036	−0.137518	+	0.990499i	$0.543912\pi$
$224$	685425.	0.912725
$225$	−142448.	−0.187586
$226$	750686.	0.977658
$227$	1.44015e6	1.85499	0.927496	−	0.373833i	$-0.121957\pi$
$227$	1.44015e6	1.85499	0.927496	+	0.373833i	$0.121957\pi$
$228$	−23537.9	−0.0299869
$229$	−746076.	−0.940144	−0.470072	−	0.882628i	$-0.655772\pi$
$229$	−746076.	−0.940144	−0.470072	+	0.882628i	$0.655772\pi$
$230$	553163.	0.689499
$231$	−58179.5	−0.0717365
$232$	592724.	0.722990
$233$	−166863.	−0.201358	−0.100679	−	0.994919i	$-0.532102\pi$
$233$	−166863.	−0.201358	−0.100679	+	0.994919i	$0.532102\pi$
$234$	1.51500e6	1.80873
$235$	119756.	0.141459
$236$	97178.0	0.113576
$237$	424356.	0.490749
$238$	447289.	0.511853
$239$	194385.	0.220125	0.110062	−	0.993925i	$-0.464895\pi$
$239$	194385.	0.220125	0.110062	+	0.993925i	$0.464895\pi$
$240$	124218.	0.139206
$241$	242121.	0.268528	0.134264	−	0.990946i	$-0.457133\pi$
$241$	242121.	0.268528	0.134264	+	0.990946i	$0.457133\pi$
$242$	−102266.	−0.112251
$243$	−631931.	−0.686522
$244$	332791.	0.357846
$245$	−36982.1	−0.0393619
$246$	92880.3	0.0978556
$247$	343546.	0.358296
$248$	817554.	0.844087
$249$	−47844.8	−0.0489031
$250$	−109139.	−0.110441
$251$	285795.	0.286332	0.143166	−	0.989699i	$-0.454272\pi$
$251$	285795.	0.286332	0.143166	+	0.989699i	$0.454272\pi$
$252$	−473729.	−0.469926
$253$	−383300.	−0.376476
$254$	1.47189e6	1.43150
$255$	50219.9	0.0483643
$256$	1.27556e6	1.21647
$257$	167621.	0.158305	0.0791525	−	0.996863i	$-0.474779\pi$
$257$	167621.	0.158305	0.0791525	+	0.996863i	$0.474779\pi$
$258$	38004.5	0.0355456
$259$	−1.02568e6	−0.950088
$260$	399422.	0.366437
$261$	−1.27146e6	−1.15531
$262$	2.24248e6	2.01825
$263$	345126.	0.307673	0.153836	−	0.988096i	$-0.450837\pi$
$263$	345126.	0.307673	0.153836	+	0.988096i	$0.450837\pi$
$264$	−49929.7	−0.0440909
$265$	716342.	0.626623
$266$	−312180.	−0.270521
$267$	−333452.	−0.286256
$268$	1.00056e6	0.850954
$269$	1.26503e6	1.06591	0.532956	−	0.846143i	$-0.321081\pi$
$269$	1.26503e6	1.06591	0.532956	+	0.846143i	$0.321081\pi$
$270$	−319367.	−0.266612
$271$	1.02776e6	0.850096	0.425048	−	0.905171i	$-0.360257\pi$
$271$	1.02776e6	0.850096	0.425048	+	0.905171i	$0.360257\pi$
$272$	661742.	0.542333
$273$	−457574.	−0.371582
$274$	2.20794e6	1.77669
$275$	75625.0	0.0603023
$276$	206545.	0.163208
$277$	−797584.	−0.624564	−0.312282	−	0.949989i	$-0.601093\pi$
$277$	−797584.	−0.624564	−0.312282	+	0.949989i	$0.601093\pi$
$278$	1.64586e6	1.27727
$279$	−1.75374e6	−1.34882
$280$	328857.	0.250675
$281$	−239823.	−0.181186	−0.0905929	−	0.995888i	$-0.528876\pi$
$281$	−239823.	−0.181186	−0.0905929	+	0.995888i	$0.528876\pi$
$282$	129946.	0.0973064
$283$	1.75755e6	1.30449	0.652247	−	0.758007i	$-0.273827\pi$
$283$	1.75755e6	1.30449	0.652247	+	0.758007i	$0.273827\pi$
$284$	606294.	0.446054
$285$	−35050.4	−0.0255612
$286$	−804307.	−0.581442
$287$	423894.	0.303775
$288$	−1.26182e6	−0.896430
$289$	−1.15232e6	−0.811577
$290$	−974146.	−0.680188
$291$	−69679.2	−0.0482359
$292$	−1.22953e6	−0.843879
$293$	−2.29399e6	−1.56107	−0.780537	−	0.625110i	$-0.785054\pi$
$293$	−2.29399e6	−1.56107	−0.780537	+	0.625110i	$0.785054\pi$
$294$	−40128.8	−0.0270762
$295$	144708.	0.0968139
$296$	−880242.	−0.583946
$297$	221297.	0.145574
$298$	−2.10646e6	−1.37408
$299$	−3.01461e6	−1.95008
$300$	−40751.3	−0.0261419
$301$	173448.	0.110345
$302$	−2.54324e6	−1.60461
$303$	−274730.	−0.171909
$304$	−461855.	−0.286630
$305$	495560.	0.305033
$306$	−823428.	−0.502715
$307$	2.93267e6	1.77590	0.887948	−	0.459945i	$-0.152131\pi$
$307$	2.93267e6	1.77590	0.887948	+	0.459945i	$0.152131\pi$
$308$	251501.	0.151065
$309$	−276533.	−0.164759
$310$	−1.34366e6	−0.794116
$311$	−263120.	−0.154260	−0.0771299	−	0.997021i	$-0.524576\pi$
$311$	−263120.	−0.154260	−0.0771299	+	0.997021i	$0.524576\pi$
$312$	−392691.	−0.228383
$313$	3.04552e6	1.75712	0.878558	−	0.477635i	$-0.158506\pi$
$313$	3.04552e6	1.75712	0.878558	+	0.477635i	$0.158506\pi$
$314$	2.66224e6	1.52378
$315$	−705432.	−0.400570
$316$	−1.83442e6	−1.03343
$317$	−362904.	−0.202835	−0.101418	−	0.994844i	$-0.532338\pi$
$317$	−362904.	−0.202835	−0.101418	+	0.994844i	$0.532338\pi$
$318$	777295.	0.431040
$319$	675010.	0.371393
$320$	56738.5	0.0309744
$321$	−268161.	−0.145256
$322$	2.73938e6	1.47235
$323$	−186723.	−0.0995843
$324$	810570.	0.428971
$325$	594781.	0.312355
$326$	461475.	0.240494
$327$	172549.	0.0892366
$328$	363786.	0.186707
$329$	593059.	0.302070
$330$	82059.8	0.0414807
$331$	−231296.	−0.116037	−0.0580187	−	0.998315i	$-0.518478\pi$
$331$	−231296.	−0.116037	−0.0580187	+	0.998315i	$0.518478\pi$
$332$	206826.	0.102981
$333$	1.88821e6	0.933126
$334$	−1.22975e6	−0.603184
$335$	1.48994e6	0.725364
$336$	615154.	0.297259
$337$	876405.	0.420368	0.210184	−	0.977662i	$-0.432594\pi$
$337$	876405.	0.420368	0.210184	+	0.977662i	$0.432594\pi$
$338$	−3.73233e6	−1.77700
$339$	417393.	0.197263
$340$	−217093.	−0.101847
$341$	931052.	0.433599
$342$	574702.	0.265692
$343$	−2.26394e6	−1.03903
$344$	148853.	0.0678206
$345$	307567.	0.139121
$346$	831353.	0.373332
$347$	3.59776e6	1.60402	0.802009	−	0.597313i	$-0.203765\pi$
$347$	3.59776e6	1.60402	0.802009	+	0.597313i	$0.203765\pi$
$348$	−363736.	−0.161004
$349$	−3.45127e6	−1.51675	−0.758377	−	0.651817i	$-0.774007\pi$
$349$	−3.45127e6	−1.51675	−0.758377	+	0.651817i	$0.774007\pi$
$350$	−540478.	−0.235835
$351$	1.74047e6	0.754049
$352$	669895.	0.288171
$353$	2.57118e6	1.09823	0.549117	−	0.835745i	$-0.314964\pi$
$353$	2.57118e6	1.09823	0.549117	+	0.835745i	$0.314964\pi$
$354$	157021.	0.0665962
$355$	902835.	0.380222
$356$	1.44146e6	0.602806
$357$	248699.	0.103277
$358$	1.93743e6	0.798948
$359$	2.23456e6	0.915073	0.457536	−	0.889191i	$-0.348732\pi$
$359$	2.23456e6	0.915073	0.457536	+	0.889191i	$0.348732\pi$
$360$	−605402.	−0.246200
$361$	130321.	0.0526316
$362$	−3.13538e6	−1.25753
$363$	−56861.3	−0.0226491
$364$	1.97802e6	0.782488
$365$	−1.83089e6	−0.719333
$366$	537726.	0.209826
$367$	2.79154e6	1.08188	0.540939	−	0.841062i	$-0.318069\pi$
$367$	2.79154e6	1.08188	0.540939	+	0.841062i	$0.318069\pi$
$368$	4.05278e6	1.56003
$369$	−780359.	−0.298352
$370$	1.44668e6	0.549376
$371$	3.54748e6	1.33809
$372$	−501706.	−0.187972
$373$	29973.8	0.0111550	0.00557750	−	0.999984i	$-0.498225\pi$
$373$	29973.8	0.0111550	0.00557750	+	0.999984i	$0.498225\pi$
$374$	437154.	0.161605
$375$	−60682.8	−0.0222837
$376$	508964.	0.185659
$377$	5.30887e6	1.92375
$378$	−1.58157e6	−0.569323
$379$	−4.38294e6	−1.56735	−0.783677	−	0.621168i	$-0.786658\pi$
$379$	−4.38294e6	−1.56735	−0.783677	+	0.621168i	$0.786658\pi$
$380$	151517.	0.0538274
$381$	818391.	0.288834
$382$	4.75824e6	1.66835
$383$	4.37696e6	1.52467	0.762334	−	0.647184i	$-0.224053\pi$
$383$	4.37696e6	1.52467	0.762334	+	0.647184i	$0.224053\pi$
$384$	749612.	0.259423
$385$	374511.	0.128769
$386$	−5.57016e6	−1.90283
$387$	−319306.	−0.108375
$388$	301212.	0.101576
$389$	1.18185e6	0.395993	0.197997	−	0.980203i	$-0.436556\pi$
$389$	1.18185e6	0.395993	0.197997	+	0.980203i	$0.436556\pi$
$390$	645390.	0.214863
$391$	1.63849e6	0.542003
$392$	−157173.	−0.0516611
$393$	1.24685e6	0.407224
$394$	1.27851e6	0.414920
$395$	−2.73165e6	−0.880911
$396$	−462996.	−0.148368
$397$	649750.	0.206904	0.103452	−	0.994634i	$-0.467011\pi$
$397$	649750.	0.206904	0.103452	+	0.994634i	$0.467011\pi$
$398$	504932.	0.159781
$399$	−173577.	−0.0545833
$400$	−799611.	−0.249879
$401$	2.23774e6	0.694942	0.347471	−	0.937691i	$-0.387040\pi$
$401$	2.23774e6	0.694942	0.347471	+	0.937691i	$0.387040\pi$
$402$	1.61671e6	0.498963
$403$	7.32261e6	2.24597
$404$	1.18761e6	0.362011
$405$	1.20702e6	0.365660
$406$	−4.82417e6	−1.45247
$407$	−1.00244e6	−0.299967
$408$	213434.	0.0634765
$409$	1.65685e6	0.489751	0.244876	−	0.969554i	$-0.421253\pi$
$409$	1.65685e6	0.489751	0.244876	+	0.969554i	$0.421253\pi$
$410$	−597885.	−0.175654
$411$	1.22765e6	0.358484
$412$	1.19541e6	0.346955
$413$	716624.	0.206736
$414$	−5.04301e6	−1.44607
$415$	307985.	0.0877827
$416$	5.26864e6	1.49267
$417$	915125.	0.257715
$418$	−305107.	−0.0854105
$419$	721624.	0.200806	0.100403	−	0.994947i	$-0.467987\pi$
$419$	721624.	0.200806	0.100403	+	0.994947i	$0.467987\pi$
$420$	−201809.	−0.0558234
$421$	1.75150e6	0.481619	0.240810	−	0.970572i	$-0.422587\pi$
$421$	1.75150e6	0.481619	0.240810	+	0.970572i	$0.422587\pi$
$422$	7.61540e6	2.08167
$423$	−1.09178e6	−0.296677
$424$	3.04445e6	0.822420
$425$	−323273.	−0.0868155
$426$	979656.	0.261547
$427$	2.45411e6	0.651366
$428$	1.15922e6	0.305883
$429$	−447207.	−0.117318
$430$	−244641.	−0.0638055
$431$	5.59085e6	1.44972	0.724861	−	0.688895i	$-0.241904\pi$
$431$	5.59085e6	1.44972	0.724861	+	0.688895i	$0.241904\pi$
$432$	−2.33986e6	−0.603225
$433$	4.21253e6	1.07975	0.539875	−	0.841745i	$-0.318471\pi$
$433$	4.21253e6	1.07975	0.539875	+	0.841745i	$0.318471\pi$
$434$	−6.65406e6	−1.69575
$435$	−541640.	−0.137242
$436$	−745902.	−0.187917
$437$	−1.14357e6	−0.286456
$438$	−1.98668e6	−0.494814
$439$	5.30842e6	1.31463	0.657315	−	0.753616i	$-0.271692\pi$
$439$	5.30842e6	1.31463	0.657315	+	0.753616i	$0.271692\pi$
$440$	321405.	0.0791446
$441$	337153.	0.0825527
$442$	3.43816e6	0.837087
$443$	−2.94057e6	−0.711905	−0.355952	−	0.934504i	$-0.615843\pi$
$443$	−2.94057e6	−0.711905	−0.355952	+	0.934504i	$0.615843\pi$
$444$	540176.	0.130040
$445$	2.14648e6	0.513839
$446$	1.42663e6	0.339605
$447$	−1.17122e6	−0.277249
$448$	280981.	0.0661427
$449$	1.58930e6	0.372041	0.186020	−	0.982546i	$-0.440441\pi$
$449$	1.58930e6	0.372041	0.186020	+	0.982546i	$0.440441\pi$
$450$	994983.	0.231624
$451$	414289.	0.0959096
$452$	−1.80432e6	−0.415401
$453$	−1.41408e6	−0.323764
$454$	−1.00593e7	−2.29048
$455$	2.94548e6	0.667002
$456$	−148964.	−0.0335482
$457$	−2.98769e6	−0.669184	−0.334592	−	0.942363i	$-0.608598\pi$
$457$	−2.98769e6	−0.669184	−0.334592	+	0.942363i	$0.608598\pi$
$458$	5.21126e6	1.16086
$459$	−945976.	−0.209579
$460$	−1.32956e6	−0.292964
$461$	5.26844e6	1.15460	0.577298	−	0.816534i	$-0.304107\pi$
$461$	5.26844e6	1.15460	0.577298	+	0.816534i	$0.304107\pi$
$462$	406377.	0.0885777
$463$	5.41446e6	1.17382	0.586911	−	0.809651i	$-0.300344\pi$
$463$	5.41446e6	1.17382	0.586911	+	0.809651i	$0.300344\pi$
$464$	−7.13713e6	−1.53897
$465$	−747093.	−0.160229
$466$	1.16552e6	0.248630
$467$	−3.05243e6	−0.647670	−0.323835	−	0.946114i	$-0.604972\pi$
$467$	−3.05243e6	−0.647670	−0.323835	+	0.946114i	$0.604972\pi$
$468$	−3.64140e6	−0.768518
$469$	7.37848e6	1.54894
$470$	−836485.	−0.174668
$471$	1.48024e6	0.307455
$472$	615007.	0.127065
$473$	169518.	0.0348388
$474$	−2.96408e6	−0.605960
$475$	225625.	0.0458831
$476$	−1.07509e6	−0.217484
$477$	−6.53066e6	−1.31420
$478$	−1.35776e6	−0.271802
$479$	−8.87454e6	−1.76729	−0.883644	−	0.468160i	$-0.844917\pi$
$479$	−8.87454e6	−1.76729	−0.883644	+	0.468160i	$0.844917\pi$
$480$	−537535.	−0.106489
$481$	−7.88409e6	−1.55378
$482$	−1.69119e6	−0.331570
$483$	1.52313e6	0.297078
$484$	245802.	0.0476950
$485$	448536.	0.0865851
$486$	4.41397e6	0.847693
$487$	−6.19013e6	−1.18271	−0.591354	−	0.806412i	$-0.701406\pi$
$487$	−6.19013e6	−1.18271	−0.591354	+	0.806412i	$0.701406\pi$
$488$	2.10612e6	0.400345
$489$	256587.	0.0485246
$490$	258316.	0.0486027
$491$	3.30249e6	0.618212	0.309106	−	0.951028i	$-0.399970\pi$
$491$	3.30249e6	0.618212	0.309106	+	0.951028i	$0.399970\pi$
$492$	−223244.	−0.0415783
$493$	−2.88546e6	−0.534684
$494$	−2.39963e6	−0.442411
$495$	−689448.	−0.126470
$496$	−9.84436e6	−1.79673
$497$	4.47102e6	0.811925
$498$	334191.	0.0603839
$499$	−566277.	−0.101807	−0.0509035	−	0.998704i	$-0.516210\pi$
$499$	−566277.	−0.101807	−0.0509035	+	0.998704i	$0.516210\pi$
$500$	262322.	0.0469256
$501$	−683759.	−0.121705
$502$	−1.99625e6	−0.353553
$503$	−2.63666e6	−0.464660	−0.232330	−	0.972637i	$-0.574635\pi$
$503$	−2.63666e6	−0.464660	−0.232330	+	0.972637i	$0.574635\pi$
$504$	−2.99808e6	−0.525735
$505$	1.76848e6	0.308582
$506$	2.67731e6	0.464860
$507$	−2.07523e6	−0.358548
$508$	−3.53778e6	−0.608235
$509$	7.45994e6	1.27627	0.638133	−	0.769926i	$-0.279707\pi$
$509$	7.45994e6	1.27627	0.638133	+	0.769926i	$0.279707\pi$
$510$	−350780.	−0.0597186
$511$	−9.06695e6	−1.53606
$512$	−2.73317e6	−0.460778
$513$	660233.	0.110765
$514$	−1.17081e6	−0.195469
$515$	1.78008e6	0.295749
$516$	−91346.3	−0.0151031
$517$	579621.	0.0953714
$518$	7.16428e6	1.17313
$519$	462245.	0.0753275
$520$	2.52781e6	0.409955
$521$	8.04703e6	1.29880	0.649399	−	0.760448i	$-0.275021\pi$
$521$	8.04703e6	1.29880	0.649399	+	0.760448i	$0.275021\pi$
$522$	8.88097e6	1.42654
$523$	−1.12164e7	−1.79308	−0.896541	−	0.442961i	$-0.853928\pi$
$523$	−1.12164e7	−1.79308	−0.896541	+	0.442961i	$0.853928\pi$
$524$	−5.38994e6	−0.857543
$525$	−300514.	−0.0475846
$526$	−2.41067e6	−0.379903
$527$	−3.97996e6	−0.624240
$528$	601216.	0.0938524
$529$	3.59843e6	0.559079
$530$	−5.00357e6	−0.773732
$531$	−1.31926e6	−0.203045
$532$	750345.	0.114943
$533$	3.25833e6	0.496795
$534$	2.32912e6	0.353459
$535$	1.72619e6	0.260738
$536$	6.33221e6	0.952015
$537$	1.07724e6	0.161204
$538$	−8.83611e6	−1.31615
$539$	−178993.	−0.0265378
$540$	767618.	0.113282
$541$	−4.08167e6	−0.599577	−0.299788	−	0.954006i	$-0.596916\pi$
$541$	−4.08167e6	−0.599577	−0.299788	+	0.954006i	$0.596916\pi$
$542$	−7.17878e6	−1.04967
$543$	−1.74332e6	−0.253733
$544$	−2.86359e6	−0.414872
$545$	−1.11073e6	−0.160183
$546$	3.19610e6	0.458817
$547$	4.38546e6	0.626681	0.313341	−	0.949641i	$-0.398552\pi$
$547$	4.38546e6	0.626681	0.313341	+	0.949641i	$0.398552\pi$
$548$	−5.30694e6	−0.754906
$549$	−4.51786e6	−0.639737
$550$	−528232.	−0.0744591
$551$	2.01387e6	0.282588
$552$	1.30716e6	0.182591
$553$	−1.35277e7	−1.88109
$554$	5.57103e6	0.771190
$555$	804378.	0.110848
$556$	−3.95594e6	−0.542704
$557$	6.05312e6	0.826687	0.413344	−	0.910575i	$-0.364361\pi$
$557$	6.05312e6	0.826687	0.413344	+	0.910575i	$0.364361\pi$
$558$	1.22497e7	1.66548
$559$	1.33324e6	0.180459
$560$	−3.95984e6	−0.533590
$561$	243064.	0.0326072
$562$	1.67513e6	0.223722
$563$	3.87002e6	0.514567	0.257284	−	0.966336i	$-0.417173\pi$
$563$	3.87002e6	0.514567	0.257284	+	0.966336i	$0.417173\pi$
$564$	−312335.	−0.0413449
$565$	−2.68682e6	−0.354093
$566$	−1.22763e7	−1.61074
$567$	5.97742e6	0.780830
$568$	3.83704e6	0.499028
$569$	−1.19092e7	−1.54207	−0.771033	−	0.636795i	$-0.780260\pi$
$569$	−1.19092e7	−1.54207	−0.771033	+	0.636795i	$0.780260\pi$
$570$	244823.	0.0315621
$571$	−5.99201e6	−0.769099	−0.384550	−	0.923104i	$-0.625643\pi$
$571$	−5.99201e6	−0.769099	−0.384550	+	0.923104i	$0.625643\pi$
$572$	1.93320e6	0.247052
$573$	2.64566e6	0.336625
$574$	−2.96085e6	−0.375091
$575$	−1.97986e6	−0.249726
$576$	−517267.	−0.0649619
$577$	−7.63283e6	−0.954434	−0.477217	−	0.878785i	$-0.658354\pi$
$577$	−7.63283e6	−0.954434	−0.477217	+	0.878785i	$0.658354\pi$
$578$	8.04884e6	1.00211
$579$	−3.09709e6	−0.383935
$580$	2.34142e6	0.289008
$581$	1.52520e6	0.187451
$582$	486701.	0.0595601
$583$	3.46710e6	0.422469
$584$	−7.78126e6	−0.944100
$585$	−5.42242e6	−0.655094
$586$	1.60233e7	1.92756
$587$	−1.17109e7	−1.40280	−0.701401	−	0.712767i	$-0.747442\pi$
$587$	−1.17109e7	−1.40280	−0.701401	+	0.712767i	$0.747442\pi$
$588$	96452.2	0.0115045
$589$	2.77777e6	0.329919
$590$	−1.01077e6	−0.119542
$591$	710871.	0.0837187
$592$	1.05992e7	1.24299
$593$	1.07896e7	1.26000	0.629999	−	0.776596i	$-0.283055\pi$
$593$	1.07896e7	1.26000	0.629999	+	0.776596i	$0.283055\pi$
$594$	−1.54573e6	−0.179750
$595$	−1.60092e6	−0.185386
$596$	5.06300e6	0.583838
$597$	280750.	0.0322392
$598$	2.10567e7	2.40789
$599$	−7.89443e6	−0.898988	−0.449494	−	0.893283i	$-0.648396\pi$
$599$	−7.89443e6	−0.898988	−0.449494	+	0.893283i	$0.648396\pi$
$600$	−257901.	−0.0292466
$601$	−1.50210e7	−1.69634	−0.848170	−	0.529724i	$-0.822295\pi$
$601$	−1.50210e7	−1.69634	−0.848170	+	0.529724i	$0.822295\pi$
$602$	−1.21151e6	−0.136250
$603$	−1.35833e7	−1.52129
$604$	6.11284e6	0.681790
$605$	366025.	0.0406558
$606$	1.91895e6	0.212267
$607$	5.98630e6	0.659457	0.329728	−	0.944076i	$-0.393043\pi$
$607$	5.98630e6	0.659457	0.329728	+	0.944076i	$0.393043\pi$
$608$	1.99861e6	0.219265
$609$	−2.68231e6	−0.293067
$610$	−3.46143e6	−0.376644
$611$	4.55865e6	0.494007
$612$	1.97916e6	0.213601
$613$	1.17656e7	1.26463	0.632314	−	0.774713i	$-0.282105\pi$
$613$	1.17656e7	1.26463	0.632314	+	0.774713i	$0.282105\pi$
$614$	−2.04844e7	−2.19281
$615$	−332433.	−0.0354418
$616$	1.59167e6	0.169005
$617$	1.15013e7	1.21628	0.608139	−	0.793831i	$-0.291916\pi$
$617$	1.15013e7	1.21628	0.608139	+	0.793831i	$0.291916\pi$
$618$	1.93155e6	0.203439
$619$	−1.92045e6	−0.201455	−0.100727	−	0.994914i	$-0.532117\pi$
$619$	−1.92045e6	−0.201455	−0.100727	+	0.994914i	$0.532117\pi$
$620$	3.22956e6	0.337415
$621$	−5.79354e6	−0.602858
$622$	1.83786e6	0.190475
$623$	1.06298e7	1.09725
$624$	4.72848e6	0.486139
$625$	390625.	0.0400000
$626$	−2.12726e7	−2.16963
$627$	−169644.	−0.0172333
$628$	−6.39886e6	−0.647446
$629$	4.28513e6	0.431855
$630$	4.92736e6	0.494610
$631$	1.61846e7	1.61819	0.809095	−	0.587678i	$-0.199958\pi$
$631$	1.61846e7	1.61819	0.809095	+	0.587678i	$0.199958\pi$
$632$	−1.16095e7	−1.15616
$633$	4.23428e6	0.420020
$634$	2.53484e6	0.250454
$635$	−5.26811e6	−0.518467
$636$	−1.86828e6	−0.183147
$637$	−1.40776e6	−0.137461
$638$	−4.71487e6	−0.458583
$639$	−8.23085e6	−0.797430
$640$	−4.82537e6	−0.465672
$641$	−1.49719e6	−0.143923	−0.0719615	−	0.997407i	$-0.522926\pi$
$641$	−1.49719e6	−0.143923	−0.0719615	+	0.997407i	$0.522926\pi$
$642$	1.87307e6	0.179357
$643$	8.19022e6	0.781210	0.390605	−	0.920558i	$-0.372266\pi$
$643$	8.19022e6	0.781210	0.390605	+	0.920558i	$0.372266\pi$
$644$	−6.58427e6	−0.625595
$645$	−136024.	−0.0128741
$646$	1.30424e6	0.122963
$647$	−1.24419e7	−1.16849	−0.584247	−	0.811576i	$-0.698610\pi$
$647$	−1.24419e7	−1.16849	−0.584247	+	0.811576i	$0.698610\pi$
$648$	5.12983e6	0.479916
$649$	700387.	0.0652719
$650$	−4.15448e6	−0.385685
$651$	−3.69976e6	−0.342153
$652$	−1.10918e6	−0.102184
$653$	7.28797e6	0.668842	0.334421	−	0.942424i	$-0.391459\pi$
$653$	7.28797e6	0.668842	0.334421	+	0.942424i	$0.391459\pi$
$654$	−1.20524e6	−0.110186
$655$	−8.02618e6	−0.730980
$656$	−4.38043e6	−0.397427
$657$	1.66916e7	1.50864
$658$	−4.14245e6	−0.372986
$659$	−6.60381e6	−0.592354	−0.296177	−	0.955133i	$-0.595712\pi$
$659$	−6.60381e6	−0.592354	−0.296177	+	0.955133i	$0.595712\pi$
$660$	−197236.	−0.0176249
$661$	−1.51636e7	−1.34989	−0.674944	−	0.737869i	$-0.735832\pi$
$661$	−1.51636e7	−1.34989	−0.674944	+	0.737869i	$0.735832\pi$
$662$	1.61558e6	0.143279
$663$	1.91167e6	0.168900
$664$	1.30893e6	0.115212
$665$	1.11734e6	0.0979787
$666$	−1.31889e7	−1.15219
$667$	−1.76717e7	−1.53803
$668$	2.95578e6	0.256290
$669$	793227.	0.0685223
$670$	−1.04070e7	−0.895654
$671$	2.39851e6	0.205653
$672$	−2.66199e6	−0.227396
$673$	−1.25043e7	−1.06420	−0.532100	−	0.846681i	$-0.678597\pi$
$673$	−1.25043e7	−1.06420	−0.532100	+	0.846681i	$0.678597\pi$
$674$	−6.12159e6	−0.519056
$675$	1.14306e6	0.0965630
$676$	8.97090e6	0.755039
$677$	3.79643e6	0.318349	0.159175	−	0.987250i	$-0.449117\pi$
$677$	3.79643e6	0.318349	0.159175	+	0.987250i	$0.449117\pi$
$678$	−2.91544e6	−0.243573
$679$	2.22124e6	0.184893
$680$	−1.37391e6	−0.113942
$681$	−5.59310e6	−0.462152
$682$	−6.50329e6	−0.535393
$683$	4.56570e6	0.374503	0.187252	−	0.982312i	$-0.440042\pi$
$683$	4.56570e6	0.374503	0.187252	+	0.982312i	$0.440042\pi$
$684$	−1.38133e6	−0.112891
$685$	−7.90258e6	−0.643491
$686$	1.58133e7	1.28296
$687$	2.89754e6	0.234227
$688$	−1.79238e6	−0.144364
$689$	2.72683e7	2.18831
$690$	−2.14832e6	−0.171781
$691$	5.23077e6	0.416745	0.208373	−	0.978050i	$-0.433183\pi$
$691$	5.23077e6	0.416745	0.208373	+	0.978050i	$0.433183\pi$
$692$	−1.99821e6	−0.158627
$693$	−3.41429e6	−0.270064
$694$	−2.51300e7	−1.98058
$695$	−5.89081e6	−0.462607
$696$	−2.30196e6	−0.180126
$697$	−1.77096e6	−0.138079
$698$	2.41067e7	1.87283
$699$	648045.	0.0501663
$700$	1.29907e6	0.100205
$701$	726058.	0.0558054	0.0279027	−	0.999611i	$-0.491117\pi$
$701$	726058.	0.0558054	0.0279027	+	0.999611i	$0.491117\pi$
$702$	−1.21570e7	−0.931073
$703$	−2.99076e6	−0.228241
$704$	274615.	0.0208830
$705$	−465098.	−0.0352429
$706$	−1.79594e7	−1.35606
$707$	8.75786e6	0.658946
$708$	−377410.	−0.0282964
$709$	1.23991e7	0.926350	0.463175	−	0.886267i	$-0.346710\pi$
$709$	1.23991e7	0.926350	0.463175	+	0.886267i	$0.346710\pi$
$710$	−6.30620e6	−0.469485
$711$	2.49035e7	1.84751
$712$	9.12252e6	0.674396
$713$	−2.43749e7	−1.79564
$714$	−1.73714e6	−0.127523
$715$	2.87874e6	0.210590
$716$	−4.65674e6	−0.339468
$717$	−754935.	−0.0548418
$718$	−1.56081e7	−1.12990
$719$	−2.21865e7	−1.60054	−0.800270	−	0.599640i	$-0.795310\pi$
$719$	−2.21865e7	−1.60054	−0.800270	+	0.599640i	$0.795310\pi$
$720$	7.28980e6	0.524064
$721$	8.81535e6	0.631541
$722$	−910277.	−0.0649876
$723$	−940327.	−0.0669011
$724$	7.53609e6	0.534318
$725$	3.48662e6	0.246354
$726$	397170.	0.0279663
$727$	−1.48634e7	−1.04299	−0.521496	−	0.853254i	$-0.674626\pi$
$727$	−1.48634e7	−1.04299	−0.521496	+	0.853254i	$0.674626\pi$
$728$	1.25182e7	0.875417
$729$	−9.27802e6	−0.646601
$730$	1.27886e7	0.888208
$731$	−724636.	−0.0501564
$732$	−1.29246e6	−0.0891537
$733$	1.62318e7	1.11585	0.557927	−	0.829890i	$-0.311597\pi$
$733$	1.62318e7	1.11585	0.557927	+	0.829890i	$0.311597\pi$
$734$	−1.94986e7	−1.33587
$735$	143627.	0.00980661
$736$	−1.75378e7	−1.19338
$737$	7.21130e6	0.489040
$738$	5.45072e6	0.368394
$739$	−2.51267e6	−0.169248	−0.0846242	−	0.996413i	$-0.526969\pi$
$739$	−2.51267e6	−0.169248	−0.0846242	+	0.996413i	$0.526969\pi$
$740$	−3.47720e6	−0.233427
$741$	−1.33423e6	−0.0892657
$742$	−2.47787e7	−1.65222
$743$	−8.00202e6	−0.531775	−0.265887	−	0.964004i	$-0.585665\pi$
$743$	−8.00202e6	−0.531775	−0.265887	+	0.964004i	$0.585665\pi$
$744$	−3.17514e6	−0.210295
$745$	7.53933e6	0.497671
$746$	−209364.	−0.0137738
$747$	−2.80780e6	−0.184104
$748$	−1.05073e6	−0.0686651
$749$	8.54847e6	0.556780
$750$	423863.	0.0275152
$751$	−1.10636e7	−0.715810	−0.357905	−	0.933758i	$-0.616509\pi$
$751$	−1.10636e7	−0.715810	−0.357905	+	0.933758i	$0.616509\pi$
$752$	−6.12855e6	−0.395197
$753$	−1.10994e6	−0.0713367
$754$	−3.70818e7	−2.37538
$755$	9.10264e6	0.581166
$756$	3.80140e6	0.241902
$757$	−1.42402e7	−0.903185	−0.451593	−	0.892224i	$-0.649144\pi$
$757$	−1.42402e7	−0.903185	−0.451593	+	0.892224i	$0.649144\pi$
$758$	3.06143e7	1.93531
$759$	1.48862e6	0.0937952
$760$	958904.	0.0602200
$761$	1.86828e6	0.116944	0.0584722	−	0.998289i	$-0.481377\pi$
$761$	1.86828e6	0.116944	0.0584722	+	0.998289i	$0.481377\pi$
$762$	−5.71637e6	−0.356642
$763$	−5.50054e6	−0.342054
$764$	−1.14367e7	−0.708874
$765$	2.94718e6	0.182076
$766$	−3.05725e7	−1.88261
$767$	5.50845e6	0.338097
$768$	−4.95390e6	−0.303071
$769$	1.45878e6	0.0889558	0.0444779	−	0.999010i	$-0.485838\pi$
$769$	1.45878e6	0.0889558	0.0444779	+	0.999010i	$0.485838\pi$
$770$	−2.61591e6	−0.159000
$771$	−650989.	−0.0394400
$772$	1.33882e7	0.808500
$773$	3.14550e7	1.89340	0.946698	−	0.322123i	$-0.104397\pi$
$773$	3.14550e7	1.89340	0.946698	+	0.322123i	$0.104397\pi$
$774$	2.23031e6	0.133818
$775$	4.80915e6	0.287617
$776$	1.90627e6	0.113640
$777$	3.98345e6	0.236704
$778$	−8.25508e6	−0.488959
$779$	1.23602e6	0.0729763
$780$	−1.55124e6	−0.0912939
$781$	4.36972e6	0.256346
$782$	−1.14447e7	−0.669246
$783$	1.02027e7	0.594717
$784$	1.89256e6	0.109966
$785$	−9.52856e6	−0.551891
$786$	−8.70912e6	−0.502826
$787$	1.58210e7	0.910534	0.455267	−	0.890355i	$-0.349544\pi$
$787$	1.58210e7	0.910534	0.455267	+	0.890355i	$0.349544\pi$
$788$	−3.07298e6	−0.176297
$789$	−1.34037e6	−0.0766534
$790$	1.90803e7	1.08772
$791$	−1.33057e7	−0.756130
$792$	−2.93015e6	−0.165988
$793$	1.88640e7	1.06525
$794$	−4.53843e6	−0.255478
$795$	−2.78206e6	−0.156116
$796$	−1.21364e6	−0.0678901
$797$	2.10522e7	1.17395	0.586977	−	0.809604i	$-0.300318\pi$
$797$	2.10522e7	1.17395	0.586977	+	0.809604i	$0.300318\pi$
$798$	1.21241e6	0.0673975
$799$	−2.47770e6	−0.137304
$800$	3.46020e6	0.191151
$801$	−1.95688e7	−1.07766
$802$	−1.56304e7	−0.858091
$803$	−8.86151e6	−0.484974
$804$	−3.88588e6	−0.212006
$805$	−9.80466e6	−0.533265
$806$	−5.11476e7	−2.77324
$807$	−4.91301e6	−0.265561
$808$	7.51601e6	0.405003
$809$	2.24633e7	1.20671	0.603354	−	0.797474i	$-0.293831\pi$
$809$	2.24633e7	1.20671	0.603354	+	0.797474i	$0.293831\pi$
$810$	−8.43091e6	−0.451504
$811$	5.10964e6	0.272796	0.136398	−	0.990654i	$-0.456447\pi$
$811$	5.10964e6	0.272796	0.136398	+	0.990654i	$0.456447\pi$
$812$	1.15952e7	0.617147
$813$	−3.99151e6	−0.211793
$814$	7.00195e6	0.370389
$815$	−1.65169e6	−0.0871033
$816$	−2.57001e6	−0.135117
$817$	505752.	0.0265083
$818$	−1.15729e7	−0.604728
$819$	−2.68530e7	−1.39889
$820$	1.43706e6	0.0746344
$821$	2.14761e7	1.11198	0.555992	−	0.831188i	$-0.312339\pi$
$821$	2.14761e7	1.11198	0.555992	+	0.831188i	$0.312339\pi$
$822$	−8.57500e6	−0.442644
$823$	1.82523e7	0.939329	0.469664	−	0.882845i	$-0.344375\pi$
$823$	1.82523e7	0.939329	0.469664	+	0.882845i	$0.344375\pi$
$824$	7.56534e6	0.388160
$825$	−293705.	−0.0150237
$826$	−5.00554e6	−0.255270
$827$	−3.71952e6	−0.189114	−0.0945568	−	0.995519i	$-0.530143\pi$
$827$	−3.71952e6	−0.189114	−0.0945568	+	0.995519i	$0.530143\pi$
$828$	1.21212e7	0.614426
$829$	1.00633e7	0.508576	0.254288	−	0.967128i	$-0.418159\pi$
$829$	1.00633e7	0.508576	0.254288	+	0.967128i	$0.418159\pi$
$830$	−2.15124e6	−0.108391
$831$	3.09758e6	0.155604
$832$	2.15981e6	0.108170
$833$	765140.	0.0382057
$834$	−6.39205e6	−0.318218
$835$	4.40146e6	0.218464
$836$	733344.	0.0362904
$837$	1.40727e7	0.694329
$838$	−5.04046e6	−0.247948
$839$	−2.09654e7	−1.02825	−0.514124	−	0.857716i	$-0.671883\pi$
$839$	−2.09654e7	−1.02825	−0.514124	+	0.857716i	$0.671883\pi$
$840$	−1.27718e6	−0.0624531
$841$	1.06096e7	0.517259
$842$	−1.22340e7	−0.594687
$843$	931400.	0.0451406
$844$	−1.83041e7	−0.884489
$845$	1.33586e7	0.643605
$846$	7.62596e6	0.366327
$847$	1.81263e6	0.0868162
$848$	−3.66589e7	−1.75061
$849$	−6.82580e6	−0.325001
$850$	2.25803e6	0.107197
$851$	2.62439e7	1.24224
$852$	−2.35467e6	−0.111130
$853$	−1.69305e7	−0.796703	−0.398352	−	0.917233i	$-0.630418\pi$
$853$	−1.69305e7	−0.796703	−0.398352	+	0.917233i	$0.630418\pi$
$854$	−1.71417e7	−0.804284
$855$	−2.05695e6	−0.0962295
$856$	7.33630e6	0.342210
$857$	−3.15364e7	−1.46676	−0.733381	−	0.679818i	$-0.762059\pi$
$857$	−3.15364e7	−1.46676	−0.733381	+	0.679818i	$0.762059\pi$
$858$	3.12369e6	0.144860
$859$	−1.30486e7	−0.603364	−0.301682	−	0.953409i	$-0.597548\pi$
$859$	−1.30486e7	−0.603364	−0.301682	+	0.953409i	$0.597548\pi$
$860$	588011.	0.0271106
$861$	−1.64628e6	−0.0756824
$862$	−3.90514e7	−1.79007
$863$	1.90527e7	0.870823	0.435411	−	0.900232i	$-0.356603\pi$
$863$	1.90527e7	0.870823	0.435411	+	0.900232i	$0.356603\pi$
$864$	1.01254e7	0.461452
$865$	−2.97554e6	−0.135215
$866$	−2.94241e7	−1.33324
$867$	4.47528e6	0.202196
$868$	1.59935e7	0.720515
$869$	−1.32212e7	−0.593910
$870$	3.78329e6	0.169462
$871$	5.67159e7	2.53314
$872$	−4.72057e6	−0.210234
$873$	−4.08916e6	−0.181593
$874$	7.98767e6	0.353705
$875$	1.93446e6	0.0854159
$876$	4.77511e6	0.210244
$877$	−3.72328e7	−1.63466	−0.817328	−	0.576173i	$-0.804545\pi$
$877$	−3.72328e7	−1.63466	−0.817328	+	0.576173i	$0.804545\pi$
$878$	−3.70787e7	−1.62326
$879$	8.90919e6	0.388925
$880$	−3.87012e6	−0.168468
$881$	2.26816e7	0.984541	0.492271	−	0.870442i	$-0.336167\pi$
$881$	2.26816e7	0.984541	0.492271	+	0.870442i	$0.336167\pi$
$882$	−2.35498e6	−0.101933
$883$	−3.38426e7	−1.46070	−0.730352	−	0.683071i	$-0.760644\pi$
$883$	−3.38426e7	−1.46070	−0.730352	+	0.683071i	$0.760644\pi$
$884$	−8.26384e6	−0.355673
$885$	−562003.	−0.0241202
$886$	2.05395e7	0.879035
$887$	2.29689e7	0.980237	0.490118	−	0.871656i	$-0.336954\pi$
$887$	2.29689e7	0.980237	0.490118	+	0.871656i	$0.336954\pi$
$888$	3.41860e6	0.145484
$889$	−2.60888e7	−1.10713
$890$	−1.49929e7	−0.634470
$891$	5.84199e6	0.246528
$892$	−3.42899e6	−0.144296
$893$	1.72928e6	0.0725667
$894$	8.18084e6	0.342337
$895$	−6.93436e6	−0.289367
$896$	−2.38962e7	−0.994395
$897$	1.17078e7	0.485843
$898$	−1.11011e7	−0.459383
$899$	4.29253e7	1.77139
$900$	−2.39151e6	−0.0984159
$901$	−1.48208e7	−0.608217
$902$	−2.89376e6	−0.118426
$903$	−673620.	−0.0274913
$904$	−1.14190e7	−0.464735
$905$	1.12220e7	0.455459
$906$	9.87717e6	0.399772
$907$	2.17023e7	0.875968	0.437984	−	0.898983i	$-0.355693\pi$
$907$	2.17023e7	0.875968	0.437984	+	0.898983i	$0.355693\pi$
$908$	2.41781e7	0.973212
$909$	−1.61226e7	−0.647182
$910$	−2.05738e7	−0.823591
$911$	2.37016e7	0.946197	0.473099	−	0.881010i	$-0.343135\pi$
$911$	2.37016e7	0.946197	0.473099	+	0.881010i	$0.343135\pi$
$912$	1.79371e6	0.0714110
$913$	1.49065e6	0.0591831
$914$	2.08687e7	0.826284
$915$	−1.92461e6	−0.0759957
$916$	−1.25256e7	−0.493241
$917$	−3.97473e7	−1.56093
$918$	6.60753e6	0.258781
$919$	1.95881e7	0.765076	0.382538	−	0.923940i	$-0.375050\pi$
$919$	1.95881e7	0.765076	0.382538	+	0.923940i	$0.375050\pi$
$920$	−8.41437e6	−0.327757
$921$	−1.13896e7	−0.442446
$922$	−3.67995e7	−1.42565
$923$	3.43673e7	1.32783
$924$	−976754.	−0.0376362
$925$	−5.17791e6	−0.198976
$926$	−3.78194e7	−1.44939
$927$	−1.62285e7	−0.620266
$928$	3.08849e7	1.17727
$929$	1.85313e7	0.704478	0.352239	−	0.935910i	$-0.385420\pi$
$929$	1.85313e7	0.704478	0.352239	+	0.935910i	$0.385420\pi$
$930$	5.21836e6	0.197846
$931$	−534021.	−0.0201922
$932$	−2.80139e6	−0.105641
$933$	1.02188e6	0.0384322
$934$	2.13209e7	0.799720
$935$	−1.56464e6	−0.0585310
$936$	−2.30452e7	−0.859788
$937$	−4.36087e6	−0.162265	−0.0811324	−	0.996703i	$-0.525854\pi$
$937$	−4.36087e6	−0.162265	−0.0811324	+	0.996703i	$0.525854\pi$
$938$	−5.15378e7	−1.91258
$939$	−1.18279e7	−0.437767
$940$	2.01055e6	0.0742155
$941$	−1.17176e7	−0.431383	−0.215692	−	0.976462i	$-0.569201\pi$
$941$	−1.17176e7	−0.431383	−0.215692	+	0.976462i	$0.569201\pi$
$942$	−1.03393e7	−0.379634
$943$	−1.08461e7	−0.397185
$944$	−7.40545e6	−0.270471
$945$	5.66068e6	0.206200
$946$	−1.18406e6	−0.0430177
$947$	5.25412e7	1.90382	0.951909	−	0.306382i	$-0.0991185\pi$
$947$	5.25412e7	1.90382	0.951909	+	0.306382i	$0.0991185\pi$
$948$	7.12436e6	0.257469
$949$	−6.96946e7	−2.51208
$950$	−1.57596e6	−0.0566549
$951$	1.40941e6	0.0505343
$952$	−6.80387e6	−0.243312
$953$	4.26992e7	1.52296	0.761478	−	0.648191i	$-0.224474\pi$
$953$	4.26992e7	1.52296	0.761478	+	0.648191i	$0.224474\pi$
$954$	4.56159e7	1.62273
$955$	−1.70305e7	−0.604253
$956$	3.26346e6	0.115487
$957$	−2.62154e6	−0.0925287
$958$	6.19877e7	2.18218
$959$	−3.91352e7	−1.37411
$960$	−220356.	−0.00771696
$961$	3.05784e7	1.06809
$962$	5.50694e7	1.91855
$963$	−1.57371e7	−0.546840
$964$	4.06488e6	0.140882
$965$	1.99365e7	0.689176
$966$	−1.06389e7	−0.366822
$967$	−2.64143e7	−0.908391	−0.454196	−	0.890902i	$-0.650073\pi$
$967$	−2.64143e7	−0.908391	−0.454196	+	0.890902i	$0.650073\pi$
$968$	1.55560e6	0.0533593
$969$	725175.	0.0248104
$970$	−3.13297e6	−0.106912
$971$	4.05408e7	1.37989	0.689945	−	0.723862i	$-0.257635\pi$
$971$	4.05408e7	1.37989	0.689945	+	0.723862i	$0.257635\pi$
$972$	−1.06093e7	−0.360180
$973$	−2.91725e7	−0.987851
$974$	4.32373e7	1.46037
$975$	−2.30995e6	−0.0778200
$976$	−2.53603e7	−0.852178
$977$	2.59650e7	0.870265	0.435133	−	0.900366i	$-0.356701\pi$
$977$	2.59650e7	0.870265	0.435133	+	0.900366i	$0.356701\pi$
$978$	−1.79223e6	−0.0599165
$979$	1.03890e7	0.346430
$980$	−620878.	−0.0206510
$981$	1.01261e7	0.335947
$982$	−2.30675e7	−0.763346
$983$	944035.	0.0311605	0.0155802	−	0.999879i	$-0.495040\pi$
$983$	944035.	0.0311605	0.0155802	+	0.999879i	$0.495040\pi$
$984$	−1.41284e6	−0.0465162
$985$	−4.57599e6	−0.150278
$986$	2.01546e7	0.660209
$987$	−2.30326e6	−0.0752577
$988$	5.76766e6	0.187978
$989$	−4.43796e6	−0.144276
$990$	4.81572e6	0.156161
$991$	1.25889e7	0.407197	0.203599	−	0.979054i	$-0.434736\pi$
$991$	1.25889e7	0.407197	0.203599	+	0.979054i	$0.434736\pi$
$992$	4.26000e7	1.37446
$993$	898285.	0.0289095
$994$	−3.12296e7	−1.00254
$995$	−1.80723e6	−0.0578704
$996$	−803249.	−0.0256568
$997$	1.11731e7	0.355989	0.177995	−	0.984031i	$-0.443039\pi$
$997$	1.11731e7	0.355989	0.177995	+	0.984031i	$0.443039\pi$
$998$	3.95538e6	0.125708
$999$	−1.51518e7	−0.480342

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.h.1.9	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.h.1.9	✓	40	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)

\(f(q)\)	\(=\)	\(q-6.98489 q^{2} -3.88370 q^{3} +16.7886 q^{4} +25.0000 q^{5} +27.1272 q^{6} +123.805 q^{7} +106.250 q^{8} -227.917 q^{9} +O(q^{10})\)	\(q-6.98489 q^{2} -3.88370 q^{3} +16.7886 q^{4} +25.0000 q^{5} +27.1272 q^{6} +123.805 q^{7} +106.250 q^{8} -227.917 q^{9} -174.622 q^{10} +121.000 q^{11} -65.2020 q^{12} +951.650 q^{13} -864.765 q^{14} -97.0925 q^{15} -1279.38 q^{16} -517.237 q^{17} +1591.97 q^{18} +361.000 q^{19} +419.716 q^{20} -480.822 q^{21} -845.171 q^{22} -3167.77 q^{23} -412.642 q^{24} +625.000 q^{25} -6647.16 q^{26} +1828.90 q^{27} +2078.52 q^{28} +5578.60 q^{29} +678.180 q^{30} +7694.65 q^{31} +5536.32 q^{32} -469.928 q^{33} +3612.84 q^{34} +3095.13 q^{35} -3826.41 q^{36} -8284.65 q^{37} -2521.54 q^{38} -3695.92 q^{39} +2656.24 q^{40} +3423.88 q^{41} +3358.49 q^{42} +1400.97 q^{43} +2031.42 q^{44} -5697.92 q^{45} +22126.5 q^{46} +4790.26 q^{47} +4968.72 q^{48} -1479.28 q^{49} -4365.55 q^{50} +2008.80 q^{51} +15976.9 q^{52} +28653.7 q^{53} -12774.7 q^{54} +3025.00 q^{55} +13154.3 q^{56} -1402.02 q^{57} -38965.8 q^{58} +5788.32 q^{59} -1630.05 q^{60} +19822.4 q^{61} -53746.2 q^{62} -28217.3 q^{63} +2269.54 q^{64} +23791.2 q^{65} +3282.39 q^{66} +59597.5 q^{67} -8683.70 q^{68} +12302.7 q^{69} -21619.1 q^{70} +36113.4 q^{71} -24216.1 q^{72} -73235.6 q^{73} +57867.4 q^{74} -2427.31 q^{75} +6060.69 q^{76} +14980.4 q^{77} +25815.6 q^{78} -109266. q^{79} -31984.5 q^{80} +48280.9 q^{81} -23915.4 q^{82} +12319.4 q^{83} -8072.35 q^{84} -12930.9 q^{85} -9785.64 q^{86} -21665.6 q^{87} +12856.2 q^{88} +85859.3 q^{89} +39799.3 q^{90} +117819. q^{91} -53182.5 q^{92} -29883.7 q^{93} -33459.4 q^{94} +9025.00 q^{95} -21501.4 q^{96} +17941.4 q^{97} +10332.6 q^{98} -27577.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9}+O(q^{10}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + 600 q^{10} + 4840 q^{11} + 2312 q^{12} + 2661 q^{13} + 395 q^{14} + 1575 q^{15} + 15974 q^{16} + 8249 q^{17} + 7225 q^{18} + 14440 q^{19} + 17250 q^{20} + 6845 q^{21} + 2904 q^{22} + 13948 q^{23} + 9740 q^{24} + 25000 q^{25} + 11581 q^{26} + 27864 q^{27} + 37879 q^{28} + 12965 q^{29} + 9125 q^{30} + 4411 q^{31} + 30751 q^{32} + 7623 q^{33} - 17739 q^{34} + 20975 q^{35} + 71345 q^{36} + 5729 q^{37} + 8664 q^{38} - 23560 q^{39} + 21150 q^{40} + 34059 q^{41} + 48528 q^{42} + 68593 q^{43} + 83490 q^{44} + 88875 q^{45} + 43829 q^{46} + 91592 q^{47} + 26539 q^{48} + 152447 q^{49} + 15000 q^{50} - 23170 q^{51} + 46798 q^{52} + 24361 q^{53} + 136436 q^{54} + 121000 q^{55} - 35393 q^{56} + 22743 q^{57} + 77722 q^{58} + 212881 q^{59} + 57800 q^{60} + 137627 q^{61} + 82606 q^{62} + 243832 q^{63} + 259580 q^{64} + 66525 q^{65} + 44165 q^{66} + 78752 q^{67} + 565000 q^{68} + 46134 q^{69} + 9875 q^{70} + 28888 q^{71} - 65574 q^{72} + 291074 q^{73} + 151963 q^{74} + 39375 q^{75} + 249090 q^{76} + 101519 q^{77} - 136222 q^{78} + 87079 q^{79} + 399350 q^{80} + 471360 q^{81} - 74882 q^{82} + 346989 q^{83} - 159196 q^{84} + 206225 q^{85} - 207742 q^{86} + 294612 q^{87} + 102366 q^{88} + 126718 q^{89} + 180625 q^{90} - 239900 q^{91} + 274196 q^{92} + 321654 q^{93} - 418108 q^{94} + 361000 q^{95} + 342154 q^{96} + 137404 q^{97} - 89356 q^{98} + 430155 q^{99}+O(q^{100}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9 + 600 * q^10 + 4840 * q^11 + 2312 * q^12 + 2661 * q^13 + 395 * q^14 + 1575 * q^15 + 15974 * q^16 + 8249 * q^17 + 7225 * q^18 + 14440 * q^19 + 17250 * q^20 + 6845 * q^21 + 2904 * q^22 + 13948 * q^23 + 9740 * q^24 + 25000 * q^25 + 11581 * q^26 + 27864 * q^27 + 37879 * q^28 + 12965 * q^29 + 9125 * q^30 + 4411 * q^31 + 30751 * q^32 + 7623 * q^33 - 17739 * q^34 + 20975 * q^35 + 71345 * q^36 + 5729 * q^37 + 8664 * q^38 - 23560 * q^39 + 21150 * q^40 + 34059 * q^41 + 48528 * q^42 + 68593 * q^43 + 83490 * q^44 + 88875 * q^45 + 43829 * q^46 + 91592 * q^47 + 26539 * q^48 + 152447 * q^49 + 15000 * q^50 - 23170 * q^51 + 46798 * q^52 + 24361 * q^53 + 136436 * q^54 + 121000 * q^55 - 35393 * q^56 + 22743 * q^57 + 77722 * q^58 + 212881 * q^59 + 57800 * q^60 + 137627 * q^61 + 82606 * q^62 + 243832 * q^63 + 259580 * q^64 + 66525 * q^65 + 44165 * q^66 + 78752 * q^67 + 565000 * q^68 + 46134 * q^69 + 9875 * q^70 + 28888 * q^71 - 65574 * q^72 + 291074 * q^73 + 151963 * q^74 + 39375 * q^75 + 249090 * q^76 + 101519 * q^77 - 136222 * q^78 + 87079 * q^79 + 399350 * q^80 + 471360 * q^81 - 74882 * q^82 + 346989 * q^83 - 159196 * q^84 + 206225 * q^85 - 207742 * q^86 + 294612 * q^87 + 102366 * q^88 + 126718 * q^89 + 180625 * q^90 - 239900 * q^91 + 274196 * q^92 + 321654 * q^93 - 418108 * q^94 + 361000 * q^95 + 342154 * q^96 + 137404 * q^97 - 89356 * q^98 + 430155 * q^99

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