LMFDB - Embedded newform 1045.6.a.b.1.14

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:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-3.50600 q^{2} -5.81498 q^{3} -19.7080 q^{4} +25.0000 q^{5} +20.3873 q^{6} +29.7384 q^{7} +181.288 q^{8} -209.186 q^{9} +O(q^{10})$	\(q-3.50600 q^{2} -5.81498 q^{3} -19.7080 q^{4} +25.0000 q^{5} +20.3873 q^{6} +29.7384 q^{7} +181.288 q^{8} -209.186 q^{9} -87.6500 q^{10} -121.000 q^{11} +114.601 q^{12} -731.724 q^{13} -104.263 q^{14} -145.374 q^{15} -4.94035 q^{16} +1078.39 q^{17} +733.406 q^{18} +361.000 q^{19} -492.699 q^{20} -172.928 q^{21} +424.226 q^{22} -1423.82 q^{23} -1054.19 q^{24} +625.000 q^{25} +2565.42 q^{26} +2629.45 q^{27} -586.083 q^{28} +2026.23 q^{29} +509.683 q^{30} +6106.80 q^{31} -5783.90 q^{32} +703.612 q^{33} -3780.82 q^{34} +743.459 q^{35} +4122.63 q^{36} -11555.5 q^{37} -1265.67 q^{38} +4254.96 q^{39} +4532.20 q^{40} +5304.12 q^{41} +606.285 q^{42} -9772.75 q^{43} +2384.67 q^{44} -5229.65 q^{45} +4991.91 q^{46} +21201.7 q^{47} +28.7281 q^{48} -15922.6 q^{49} -2191.25 q^{50} -6270.79 q^{51} +14420.8 q^{52} -1317.49 q^{53} -9218.85 q^{54} -3025.00 q^{55} +5391.21 q^{56} -2099.21 q^{57} -7103.96 q^{58} -35475.1 q^{59} +2865.04 q^{60} +1651.81 q^{61} -21410.4 q^{62} -6220.85 q^{63} +20436.4 q^{64} -18293.1 q^{65} -2466.86 q^{66} +59508.8 q^{67} -21252.8 q^{68} +8279.48 q^{69} -2606.57 q^{70} -24118.6 q^{71} -37922.9 q^{72} -24055.2 q^{73} +40513.5 q^{74} -3634.36 q^{75} -7114.58 q^{76} -3598.34 q^{77} -14917.9 q^{78} +47068.7 q^{79} -123.509 q^{80} +35542.0 q^{81} -18596.2 q^{82} +116176. q^{83} +3408.06 q^{84} +26959.6 q^{85} +34263.3 q^{86} -11782.5 q^{87} -21935.9 q^{88} -16974.5 q^{89} +18335.1 q^{90} -21760.3 q^{91} +28060.6 q^{92} -35510.9 q^{93} -74333.0 q^{94} +9025.00 q^{95} +33633.2 q^{96} -132392. q^{97} +55824.7 q^{98} +25311.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9}+O(q^{10}) $ 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9	\( 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9} - 200 q^{10} - 4356 q^{11} - 2008 q^{12} - 43 q^{13} - 1937 q^{14} - 1575 q^{15} + 3612 q^{16} - 2431 q^{17} - 6225 q^{18} + 12996 q^{19} + 13000 q^{20} + 2863 q^{21} + 968 q^{22} - 11444 q^{23} - 6210 q^{24} + 22500 q^{25} - 6339 q^{26} - 12960 q^{27} - 1083 q^{28} - 873 q^{29} + 125 q^{30} - 1405 q^{31} - 14283 q^{32} + 7623 q^{33} + 19937 q^{34} - 12725 q^{35} - 1169 q^{36} - 22729 q^{37} - 2888 q^{38} + 3710 q^{39} - 17250 q^{40} - 17043 q^{41} - 39996 q^{42} - 42231 q^{43} - 62920 q^{44} + 48375 q^{45} + 50947 q^{46} - 72440 q^{47} + 42475 q^{48} + 54119 q^{49} - 5000 q^{50} - 114970 q^{51} + 16786 q^{52} - 67603 q^{53} - 26080 q^{54} - 108900 q^{55} - 216071 q^{56} - 22743 q^{57} - 115746 q^{58} - 247439 q^{59} - 50200 q^{60} - 66627 q^{61} - 262438 q^{62} - 226118 q^{63} + 1078 q^{64} - 1075 q^{65} - 605 q^{66} - 189550 q^{67} - 140936 q^{68} - 65684 q^{69} - 48425 q^{70} - 320146 q^{71} - 509978 q^{72} - 55266 q^{73} - 63309 q^{74} - 39375 q^{75} + 187720 q^{76} + 61589 q^{77} - 284264 q^{78} - 1033 q^{79} + 90300 q^{80} - 58588 q^{81} - 328242 q^{82} - 451983 q^{83} + 43932 q^{84} - 60775 q^{85} - 44142 q^{86} - 457510 q^{87} + 83490 q^{88} + 13940 q^{89} - 155625 q^{90} - 211732 q^{91} - 735304 q^{92} + 4486 q^{93} + 152164 q^{94} + 324900 q^{95} + 195996 q^{96} - 234346 q^{97} - 58328 q^{98} - 234135 q^{99}+O(q^{100}) \) 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9 - 200 * q^10 - 4356 * q^11 - 2008 * q^12 - 43 * q^13 - 1937 * q^14 - 1575 * q^15 + 3612 * q^16 - 2431 * q^17 - 6225 * q^18 + 12996 * q^19 + 13000 * q^20 + 2863 * q^21 + 968 * q^22 - 11444 * q^23 - 6210 * q^24 + 22500 * q^25 - 6339 * q^26 - 12960 * q^27 - 1083 * q^28 - 873 * q^29 + 125 * q^30 - 1405 * q^31 - 14283 * q^32 + 7623 * q^33 + 19937 * q^34 - 12725 * q^35 - 1169 * q^36 - 22729 * q^37 - 2888 * q^38 + 3710 * q^39 - 17250 * q^40 - 17043 * q^41 - 39996 * q^42 - 42231 * q^43 - 62920 * q^44 + 48375 * q^45 + 50947 * q^46 - 72440 * q^47 + 42475 * q^48 + 54119 * q^49 - 5000 * q^50 - 114970 * q^51 + 16786 * q^52 - 67603 * q^53 - 26080 * q^54 - 108900 * q^55 - 216071 * q^56 - 22743 * q^57 - 115746 * q^58 - 247439 * q^59 - 50200 * q^60 - 66627 * q^61 - 262438 * q^62 - 226118 * q^63 + 1078 * q^64 - 1075 * q^65 - 605 * q^66 - 189550 * q^67 - 140936 * q^68 - 65684 * q^69 - 48425 * q^70 - 320146 * q^71 - 509978 * q^72 - 55266 * q^73 - 63309 * q^74 - 39375 * q^75 + 187720 * q^76 + 61589 * q^77 - 284264 * q^78 - 1033 * q^79 + 90300 * q^80 - 58588 * q^81 - 328242 * q^82 - 451983 * q^83 + 43932 * q^84 - 60775 * q^85 - 44142 * q^86 - 457510 * q^87 + 83490 * q^88 + 13940 * q^89 - 155625 * q^90 - 211732 * q^91 - 735304 * q^92 + 4486 * q^93 + 152164 * q^94 + 324900 * q^95 + 195996 * q^96 - 234346 * q^97 - 58328 * q^98 - 234135 * 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 $

$2$	−3.50600	−0.619779	−0.309889	−	0.950773i	$-0.600292\pi$
$2$	−3.50600	−0.619779	−0.309889	+	0.950773i	$0.600292\pi$
$3$	−5.81498	−0.373031	−0.186516	−	0.982452i	$-0.559719\pi$
$3$	−5.81498	−0.373031	−0.186516	+	0.982452i	$0.559719\pi$
$4$	−19.7080	−0.615874
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	20.3873	0.231197
$7$	29.7384	0.229389	0.114694	−	0.993401i	$-0.463411\pi$
$7$	29.7384	0.229389	0.114694	+	0.993401i	$0.463411\pi$
$8$	181.288	1.00148
$9$	−209.186	−0.860848
$10$	−87.6500	−0.277173
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	114.601	0.229740
$13$	−731.724	−1.20085	−0.600425	−	0.799681i	$-0.705002\pi$
$13$	−731.724	−1.20085	−0.600425	+	0.799681i	$0.705002\pi$
$14$	−104.263	−0.142170
$15$	−145.374	−0.166825
$16$	−4.94035	−0.00482456
$17$	1078.39	0.905007	0.452503	−	0.891763i	$-0.350531\pi$
$17$	1078.39	0.905007	0.452503	+	0.891763i	$0.350531\pi$
$18$	733.406	0.533535
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−492.699	−0.275427
$21$	−172.928	−0.0855691
$22$	424.226	0.186870
$23$	−1423.82	−0.561223	−0.280612	−	0.959821i	$-0.590537\pi$
$23$	−1423.82	−0.561223	−0.280612	+	0.959821i	$0.590537\pi$
$24$	−1054.19	−0.373585
$25$	625.000	0.200000
$26$	2565.42	0.744262
$27$	2629.45	0.694154
$28$	−586.083	−0.141275
$29$	2026.23	0.447398	0.223699	−	0.974658i	$-0.428187\pi$
$29$	2026.23	0.447398	0.223699	+	0.974658i	$0.428187\pi$
$30$	509.683	0.103394
$31$	6106.80	1.14133	0.570663	−	0.821184i	$-0.306686\pi$
$31$	6106.80	1.14133	0.570663	+	0.821184i	$0.306686\pi$
$32$	−5783.90	−0.998494
$33$	703.612	0.112473
$34$	−3780.82	−0.560904
$35$	743.459	0.102586
$36$	4122.63	0.530174
$37$	−11555.5	−1.38766	−0.693831	−	0.720138i	$-0.744079\pi$
$37$	−11555.5	−1.38766	−0.693831	+	0.720138i	$0.744079\pi$
$38$	−1265.67	−0.142187
$39$	4254.96	0.447955
$40$	4532.20	0.447878
$41$	5304.12	0.492781	0.246390	−	0.969171i	$-0.420755\pi$
$41$	5304.12	0.492781	0.246390	+	0.969171i	$0.420755\pi$
$42$	606.285	0.0530339
$43$	−9772.75	−0.806020	−0.403010	−	0.915196i	$-0.632036\pi$
$43$	−9772.75	−0.806020	−0.403010	+	0.915196i	$0.632036\pi$
$44$	2384.67	0.185693
$45$	−5229.65	−0.384983
$46$	4991.91	0.347834
$47$	21201.7	1.39999	0.699996	−	0.714147i	$-0.253185\pi$
$47$	21201.7	1.39999	0.699996	+	0.714147i	$0.253185\pi$
$48$	28.7281	0.00179971
$49$	−15922.6	−0.947381
$50$	−2191.25	−0.123956
$51$	−6270.79	−0.337596
$52$	14420.8	0.739573
$53$	−1317.49	−0.0644256	−0.0322128	−	0.999481i	$-0.510255\pi$
$53$	−1317.49	−0.0644256	−0.0322128	+	0.999481i	$0.510255\pi$
$54$	−9218.85	−0.430222
$55$	−3025.00	−0.134840
$56$	5391.21	0.229729
$57$	−2099.21	−0.0855792
$58$	−7103.96	−0.277288
$59$	−35475.1	−1.32676	−0.663382	−	0.748281i	$-0.730880\pi$
$59$	−35475.1	−1.32676	−0.663382	+	0.748281i	$0.730880\pi$
$60$	2865.04	0.102743
$61$	1651.81	0.0568376	0.0284188	−	0.999596i	$-0.490953\pi$
$61$	1651.81	0.0568376	0.0284188	+	0.999596i	$0.490953\pi$
$62$	−21410.4	−0.707370
$63$	−6220.85	−0.197469
$64$	20436.4	0.623670
$65$	−18293.1	−0.537037
$66$	−2466.86	−0.0697084
$67$	59508.8	1.61955	0.809774	−	0.586742i	$-0.199590\pi$
$67$	59508.8	1.61955	0.809774	+	0.586742i	$0.199590\pi$
$68$	−21252.8	−0.557370
$69$	8279.48	0.209354
$70$	−2606.57	−0.0635804
$71$	−24118.6	−0.567815	−0.283907	−	0.958852i	$-0.591631\pi$
$71$	−24118.6	−0.567815	−0.283907	+	0.958852i	$0.591631\pi$
$72$	−37922.9	−0.862126
$73$	−24055.2	−0.528327	−0.264163	−	0.964478i	$-0.585096\pi$
$73$	−24055.2	−0.528327	−0.264163	+	0.964478i	$0.585096\pi$
$74$	40513.5	0.860043
$75$	−3634.36	−0.0746062
$76$	−7114.58	−0.141291
$77$	−3598.34	−0.0691633
$78$	−14917.9	−0.277633
$79$	47068.7	0.848525	0.424262	−	0.905539i	$-0.360533\pi$
$79$	47068.7	0.848525	0.424262	+	0.905539i	$0.360533\pi$
$80$	−123.509	−0.00215761
$81$	35542.0	0.601907
$82$	−18596.2	−0.305415
$83$	116176.	1.85107	0.925533	−	0.378667i	$-0.123618\pi$
$83$	116176.	1.85107	0.925533	+	0.378667i	$0.123618\pi$
$84$	3408.06	0.0526998
$85$	26959.6	0.404731
$86$	34263.3	0.499554
$87$	−11782.5	−0.166893
$88$	−21935.9	−0.301959
$89$	−16974.5	−0.227154	−0.113577	−	0.993529i	$-0.536231\pi$
$89$	−16974.5	−0.227154	−0.113577	+	0.993529i	$0.536231\pi$
$90$	18335.1	0.238604
$91$	−21760.3	−0.275461
$92$	28060.6	0.345643
$93$	−35510.9	−0.425750
$94$	−74333.0	−0.867685
$95$	9025.00	0.102598
$96$	33633.2	0.372469
$97$	−132392.	−1.42868	−0.714338	−	0.699801i	$-0.753272\pi$
$97$	−132392.	−1.42868	−0.714338	+	0.699801i	$0.753272\pi$
$98$	55824.7	0.587167
$99$	25311.5	0.259555
$100$	−12317.5	−0.123175
$101$	40533.0	0.395371	0.197686	−	0.980265i	$-0.436657\pi$
$101$	40533.0	0.395371	0.197686	+	0.980265i	$0.436657\pi$
$102$	21985.4	0.209235
$103$	184248.	1.71124	0.855618	−	0.517608i	$-0.173177\pi$
$103$	184248.	1.71124	0.855618	+	0.517608i	$0.173177\pi$
$104$	−132653.	−1.20263
$105$	−4323.20	−0.0382677
$106$	4619.12	0.0399296
$107$	167446.	1.41389	0.706943	−	0.707271i	$-0.250074\pi$
$107$	167446.	1.41389	0.706943	+	0.707271i	$0.250074\pi$
$108$	−51821.2	−0.427512
$109$	−59463.8	−0.479387	−0.239693	−	0.970849i	$-0.577047\pi$
$109$	−59463.8	−0.479387	−0.239693	+	0.970849i	$0.577047\pi$
$110$	10605.6	0.0835710
$111$	67194.9	0.517641
$112$	−146.918	−0.00110670
$113$	231227.	1.70350	0.851751	−	0.523947i	$-0.175541\pi$
$113$	231227.	1.70350	0.851751	+	0.523947i	$0.175541\pi$
$114$	7359.82	0.0530402
$115$	−35595.5	−0.250987
$116$	−39932.9	−0.275541
$117$	153066.	1.03375
$118$	124376.	0.822301
$119$	32069.4	0.207598
$120$	−26354.7	−0.167072
$121$	14641.0	0.0909091
$122$	−5791.24	−0.0352267
$123$	−30843.4	−0.183823
$124$	−120353.	−0.702913
$125$	15625.0	0.0894427
$126$	21810.3	0.122387
$127$	74539.0	0.410086	0.205043	−	0.978753i	$-0.434267\pi$
$127$	74539.0	0.410086	0.205043	+	0.978753i	$0.434267\pi$
$128$	113435.	0.611957
$129$	56828.3	0.300670
$130$	64135.6	0.332844
$131$	−55709.1	−0.283627	−0.141814	−	0.989893i	$-0.545293\pi$
$131$	−55709.1	−0.283627	−0.141814	+	0.989893i	$0.545293\pi$
$132$	−13866.8	−0.0692693
$133$	10735.5	0.0526254
$134$	−208638.	−1.00376
$135$	65736.3	0.310435
$136$	195498.	0.906350
$137$	383380.	1.74513	0.872564	−	0.488499i	$-0.162455\pi$
$137$	383380.	1.74513	0.872564	+	0.488499i	$0.162455\pi$
$138$	−29027.9	−0.129753
$139$	−120339.	−0.528286	−0.264143	−	0.964484i	$-0.585089\pi$
$139$	−120339.	−0.528286	−0.264143	+	0.964484i	$0.585089\pi$
$140$	−14652.1	−0.0631799
$141$	−123287.	−0.522240
$142$	84559.9	0.351920
$143$	88538.6	0.362070
$144$	1033.45	0.00415322
$145$	50655.8	0.200082
$146$	84337.6	0.327446
$147$	92589.8	0.353402
$148$	227735.	0.854625
$149$	44407.0	0.163865	0.0819324	−	0.996638i	$-0.473891\pi$
$149$	44407.0	0.163865	0.0819324	+	0.996638i	$0.473891\pi$
$150$	12742.1	0.0462393
$151$	−30894.2	−0.110264	−0.0551320	−	0.998479i	$-0.517558\pi$
$151$	−30894.2	−0.110264	−0.0551320	+	0.998479i	$0.517558\pi$
$152$	65445.0	0.229756
$153$	−225583.	−0.779073
$154$	12615.8	0.0428659
$155$	152670.	0.510417
$156$	−83856.6	−0.275884
$157$	−45209.4	−0.146379	−0.0731896	−	0.997318i	$-0.523318\pi$
$157$	−45209.4	−0.146379	−0.0731896	+	0.997318i	$0.523318\pi$
$158$	−165023.	−0.525898
$159$	7661.19	0.0240327
$160$	−144597.	−0.446540
$161$	−42342.1	−0.128738
$162$	−124610.	−0.373049
$163$	−495759.	−1.46151	−0.730754	−	0.682641i	$-0.760831\pi$
$163$	−495759.	−1.46151	−0.730754	+	0.682641i	$0.760831\pi$
$164$	−104534.	−0.303491
$165$	17590.3	0.0502995
$166$	−407313.	−1.14725
$167$	−664867.	−1.84478	−0.922388	−	0.386265i	$-0.873765\pi$
$167$	−664867.	−1.84478	−0.922388	+	0.386265i	$0.873765\pi$
$168$	−31349.8	−0.0856961
$169$	164127.	0.442042
$170$	−94520.5	−0.250844
$171$	−75516.2	−0.197492
$172$	192601.	0.496407
$173$	−114062.	−0.289753	−0.144876	−	0.989450i	$-0.546278\pi$
$173$	−114062.	−0.289753	−0.144876	+	0.989450i	$0.546278\pi$
$174$	41309.4	0.103437
$175$	18586.5	0.0458777
$176$	597.783	0.00145466
$177$	206287.	0.494924
$178$	59512.4	0.140785
$179$	−339774.	−0.792606	−0.396303	−	0.918120i	$-0.629707\pi$
$179$	−339774.	−0.792606	−0.396303	+	0.918120i	$0.629707\pi$
$180$	103066.	0.237101
$181$	−243582.	−0.552648	−0.276324	−	0.961065i	$-0.589116\pi$
$181$	−243582.	−0.552648	−0.276324	+	0.961065i	$0.589116\pi$
$182$	76291.5	0.170725
$183$	−9605.24	−0.0212022
$184$	−258122.	−0.562056
$185$	−288887.	−0.620581
$186$	124501.	0.263871
$187$	−130485.	−0.272870
$188$	−417842.	−0.862219
$189$	78195.6	0.159231
$190$	−31641.6	−0.0635880
$191$	−1346.54	−0.00267077	−0.00133539	−	0.999999i	$-0.500425\pi$
$191$	−1346.54	−0.00267077	−0.00133539	+	0.999999i	$0.500425\pi$
$192$	−118837.	−0.232648
$193$	−558556.	−1.07938	−0.539689	−	0.841864i	$-0.681458\pi$
$193$	−558556.	−1.07938	−0.539689	+	0.841864i	$0.681458\pi$
$194$	464168.	0.885463
$195$	106374.	0.200331
$196$	313803.	0.583468
$197$	−411780.	−0.755961	−0.377981	−	0.925814i	$-0.623381\pi$
$197$	−411780.	−0.755961	−0.377981	+	0.925814i	$0.623381\pi$
$198$	−88742.1	−0.160867
$199$	860913.	1.54108	0.770542	−	0.637389i	$-0.219986\pi$
$199$	860913.	1.54108	0.770542	+	0.637389i	$0.219986\pi$
$200$	113305.	0.200297
$201$	−346042.	−0.604142
$202$	−142109.	−0.245043
$203$	60256.8	0.102628
$204$	123585.	0.207916
$205$	132603.	0.220378
$206$	−645974.	−1.06059
$207$	297843.	0.483128
$208$	3614.98	0.00579358
$209$	−43681.0	−0.0691714
$210$	15157.1	0.0237175
$211$	468885.	0.725037	0.362518	−	0.931977i	$-0.381917\pi$
$211$	468885.	0.725037	0.362518	+	0.931977i	$0.381917\pi$
$212$	25965.1	0.0396781
$213$	140249.	0.211813
$214$	−587064.	−0.876296
$215$	−244319.	−0.360463
$216$	476688.	0.695185
$217$	181606.	0.261807
$218$	208480.	0.297114
$219$	139881.	0.197082
$220$	59616.6	0.0830445
$221$	−789081.	−1.08678
$222$	−235585.	−0.320823
$223$	−1.00733e6	−1.35647	−0.678234	−	0.734846i	$-0.737255\pi$
$223$	−1.00733e6	−1.35647	−0.678234	+	0.734846i	$0.737255\pi$
$224$	−172004.	−0.229043
$225$	−130741.	−0.172170
$226$	−810682.	−1.05579
$227$	1.09080e6	1.40502	0.702510	−	0.711674i	$-0.252063\pi$
$227$	1.09080e6	1.40502	0.702510	+	0.711674i	$0.252063\pi$
$228$	41371.1	0.0527060
$229$	−10726.7	−0.0135169	−0.00675846	−	0.999977i	$-0.502151\pi$
$229$	−10726.7	−0.0135169	−0.00675846	+	0.999977i	$0.502151\pi$
$230$	124798.	0.155556
$231$	20924.3	0.0258000
$232$	367331.	0.448062
$233$	−550224.	−0.663972	−0.331986	−	0.943284i	$-0.607719\pi$
$233$	−550224.	−0.663972	−0.331986	+	0.943284i	$0.607719\pi$
$234$	−536651.	−0.640696
$235$	530042.	0.626095
$236$	699143.	0.817120
$237$	−273704.	−0.316526
$238$	−112435.	−0.128665
$239$	881026.	0.997686	0.498843	−	0.866692i	$-0.333758\pi$
$239$	881026.	0.997686	0.498843	+	0.866692i	$0.333758\pi$
$240$	718.201	0.000804856 0
$241$	−214202.	−0.237564	−0.118782	−	0.992920i	$-0.537899\pi$
$241$	−214202.	−0.237564	−0.118782	+	0.992920i	$0.537899\pi$
$242$	−51331.3	−0.0563435
$243$	−845633.	−0.918684
$244$	−32553.8	−0.0350048
$245$	−398066.	−0.423682
$246$	108137.	0.113929
$247$	−264152.	−0.275494
$248$	1.10709e6	1.14302
$249$	−675562.	−0.690505
$250$	−54781.2	−0.0554347
$251$	517709.	0.518683	0.259341	−	0.965786i	$-0.416495\pi$
$251$	517709.	0.518683	0.259341	+	0.965786i	$0.416495\pi$
$252$	122600.	0.121616
$253$	172282.	0.169215
$254$	−261334.	−0.254162
$255$	−156770.	−0.150977
$256$	−1.05167e6	−1.00295
$257$	1.84040e6	1.73812	0.869060	−	0.494707i	$-0.164725\pi$
$257$	1.84040e6	1.73812	0.869060	+	0.494707i	$0.164725\pi$
$258$	−199240.	−0.186349
$259$	−343641.	−0.318314
$260$	360520.	0.330747
$261$	−423859.	−0.385141
$262$	195316.	0.175786
$263$	−1.73887e6	−1.55017	−0.775083	−	0.631859i	$-0.782292\pi$
$263$	−1.73887e6	−1.55017	−0.775083	+	0.631859i	$0.782292\pi$
$264$	127557.	0.112640
$265$	−32937.3	−0.0288120
$266$	−37638.8	−0.0326161
$267$	98706.1	0.0847356
$268$	−1.17280e6	−0.997438
$269$	−1.81892e6	−1.53262	−0.766309	−	0.642473i	$-0.777909\pi$
$269$	−1.81892e6	−1.53262	−0.766309	+	0.642473i	$0.777909\pi$
$270$	−230471.	−0.192401
$271$	−1.63246e6	−1.35026	−0.675132	−	0.737697i	$-0.735913\pi$
$271$	−1.63246e6	−1.35026	−0.675132	+	0.737697i	$0.735913\pi$
$272$	−5327.61	−0.00436626
$273$	126536.	0.102756
$274$	−1.34413e6	−1.08159
$275$	−75625.0	−0.0603023
$276$	−163172.	−0.128936
$277$	−1.09522e6	−0.857638	−0.428819	−	0.903391i	$-0.641070\pi$
$277$	−1.09522e6	−0.857638	−0.428819	+	0.903391i	$0.641070\pi$
$278$	421908.	0.327420
$279$	−1.27746e6	−0.982508
$280$	134780.	0.102738
$281$	872509.	0.659180	0.329590	−	0.944124i	$-0.393089\pi$
$281$	872509.	0.659180	0.329590	+	0.944124i	$0.393089\pi$
$282$	432245.	0.323673
$283$	−2.05461e6	−1.52498	−0.762489	−	0.647001i	$-0.776023\pi$
$283$	−2.05461e6	−1.52498	−0.762489	+	0.647001i	$0.776023\pi$
$284$	475329.	0.349703
$285$	−52480.2	−0.0382722
$286$	−310416.	−0.224403
$287$	157736.	0.113038
$288$	1.20991e6	0.859552
$289$	−256941.	−0.180963
$290$	−177599.	−0.124007
$291$	769859.	0.532941
$292$	474080.	0.325383
$293$	948695.	0.645591	0.322795	−	0.946469i	$-0.395377\pi$
$293$	948695.	0.645591	0.322795	+	0.946469i	$0.395377\pi$
$294$	−324619.	−0.219031
$295$	−886878.	−0.593347
$296$	−2.09487e6	−1.38972
$297$	−318164.	−0.209295
$298$	−155691.	−0.101560
$299$	1.04184e6	0.673945
$300$	71625.9	0.0459480
$301$	−290626.	−0.184892
$302$	108315.	0.0683393
$303$	−235698.	−0.147486
$304$	−1783.47	−0.00110683
$305$	41295.3	0.0254185
$306$	790894.	0.482853
$307$	−1.71413e6	−1.03800	−0.519001	−	0.854774i	$-0.673696\pi$
$307$	−1.71413e6	−1.03800	−0.519001	+	0.854774i	$0.673696\pi$
$308$	70916.0	0.0425959
$309$	−1.07140e6	−0.638344
$310$	−535261.	−0.316345
$311$	2.27509e6	1.33382	0.666909	−	0.745139i	$-0.267617\pi$
$311$	2.27509e6	1.33382	0.666909	+	0.745139i	$0.267617\pi$
$312$	771373.	0.448620
$313$	161184.	0.0929955	0.0464977	−	0.998918i	$-0.485194\pi$
$313$	161184.	0.0929955	0.0464977	+	0.998918i	$0.485194\pi$
$314$	158504.	0.0907228
$315$	−155521.	−0.0883107
$316$	−927629.	−0.522585
$317$	2.03352e6	1.13658	0.568291	−	0.822828i	$-0.307605\pi$
$317$	2.03352e6	1.13658	0.568291	+	0.822828i	$0.307605\pi$
$318$	−26860.1	−0.0148950
$319$	−245174.	−0.134895
$320$	510911.	0.278914
$321$	−973692.	−0.527423
$322$	148451.	0.0797892
$323$	389297.	0.207623
$324$	−700461.	−0.370699
$325$	−457328.	−0.240170
$326$	1.73813e6	0.905812
$327$	345781.	0.178826
$328$	961574.	0.493512
$329$	630503.	0.321142
$330$	−61671.6	−0.0311746
$331$	−1.99142e6	−0.999063	−0.499531	−	0.866296i	$-0.666494\pi$
$331$	−1.99142e6	−0.999063	−0.499531	+	0.866296i	$0.666494\pi$
$332$	−2.28960e6	−1.14002
$333$	2.41725e6	1.19457
$334$	2.33102e6	1.14335
$335$	1.48772e6	0.724284
$336$	854.325	0.000412834 0
$337$	−1.51438e6	−0.726376	−0.363188	−	0.931716i	$-0.618312\pi$
$337$	−1.51438e6	−0.726376	−0.363188	+	0.931716i	$0.618312\pi$
$338$	−575429.	−0.273968
$339$	−1.34458e6	−0.635459
$340$	−531320.	−0.249264
$341$	−738923.	−0.344123
$342$	264759.	0.122401
$343$	−973325.	−0.446707
$344$	−1.77168e6	−0.807216
$345$	206987.	0.0936258
$346$	399903.	0.179582
$347$	−3.91853e6	−1.74703	−0.873513	−	0.486802i	$-0.838163\pi$
$347$	−3.91853e6	−1.74703	−0.873513	+	0.486802i	$0.838163\pi$
$348$	232209.	0.102785
$349$	1.50076e6	0.659550	0.329775	−	0.944060i	$-0.393027\pi$
$349$	1.50076e6	0.659550	0.329775	+	0.944060i	$0.393027\pi$
$350$	−65164.1	−0.0284340
$351$	−1.92403e6	−0.833575
$352$	699852.	0.301057
$353$	−2.02924e6	−0.866754	−0.433377	−	0.901213i	$-0.642678\pi$
$353$	−2.02924e6	−0.866754	−0.433377	+	0.901213i	$0.642678\pi$
$354$	−723242.	−0.306744
$355$	−602966.	−0.253934
$356$	334532.	0.139898
$357$	−186483.	−0.0774406
$358$	1.19125e6	0.491241
$359$	1.79617e6	0.735549	0.367774	−	0.929915i	$-0.380120\pi$
$359$	1.79617e6	0.735549	0.367774	+	0.929915i	$0.380120\pi$
$360$	−948073.	−0.385554
$361$	130321.	0.0526316
$362$	853997.	0.342519
$363$	−85137.1	−0.0339119
$364$	428851.	0.169650
$365$	−601381.	−0.236275
$366$	33676.0	0.0131407
$367$	2512.52	0.000973743 0	0.000486871	−	1.00000i	$-0.499845\pi$
$367$	2512.52	0.000973743 0	0.000486871		1.00000i	$0.499845\pi$
$368$	7034.18	0.00270766
$369$	−1.10955e6	−0.424209
$370$	1.01284e6	0.384623
$371$	−39180.1	−0.0147785
$372$	699849.	0.262209
$373$	−2.09462e6	−0.779530	−0.389765	−	0.920914i	$-0.627444\pi$
$373$	−2.09462e6	−0.779530	−0.389765	+	0.920914i	$0.627444\pi$
$374$	457479.	0.169119
$375$	−90859.0	−0.0333649
$376$	3.84361e6	1.40207
$377$	−1.48264e6	−0.537258
$378$	−274154.	−0.0986880
$379$	−582857.	−0.208432	−0.104216	−	0.994555i	$-0.533233\pi$
$379$	−582857.	−0.208432	−0.104216	+	0.994555i	$0.533233\pi$
$380$	−177864.	−0.0631874
$381$	−433443.	−0.152975
$382$	4720.98	0.00165529
$383$	−2.90219e6	−1.01095	−0.505475	−	0.862841i	$-0.668683\pi$
$383$	−2.90219e6	−1.01095	−0.505475	+	0.862841i	$0.668683\pi$
$384$	−659620.	−0.228279
$385$	−89958.5	−0.0309308
$386$	1.95830e6	0.668976
$387$	2.04432e6	0.693860
$388$	2.60919e6	0.879885
$389$	1.27175e6	0.426117	0.213059	−	0.977039i	$-0.431657\pi$
$389$	1.27175e6	0.426117	0.213059	+	0.977039i	$0.431657\pi$
$390$	−372947.	−0.124161
$391$	−1.53543e6	−0.507911
$392$	−2.88658e6	−0.948787
$393$	323947.	0.105802
$394$	1.44370e6	0.468529
$395$	1.17672e6	0.379472
$396$	−498839.	−0.159853
$397$	−660230.	−0.210242	−0.105121	−	0.994459i	$-0.533523\pi$
$397$	−660230.	−0.210242	−0.105121	+	0.994459i	$0.533523\pi$
$398$	−3.01836e6	−0.955131
$399$	−62427.0	−0.0196309
$400$	−3087.72	−0.000964913 0
$401$	−4.03032e6	−1.25164	−0.625820	−	0.779968i	$-0.715235\pi$
$401$	−4.03032e6	−1.25164	−0.625820	+	0.779968i	$0.715235\pi$
$402$	1.21322e6	0.374434
$403$	−4.46850e6	−1.37056
$404$	−798823.	−0.243499
$405$	888550.	0.269181
$406$	−211260.	−0.0636066
$407$	1.39821e6	0.418396
$408$	−1.13682e6	−0.338097
$409$	−3.66727e6	−1.08401	−0.542007	−	0.840374i	$-0.682336\pi$
$409$	−3.66727e6	−1.08401	−0.542007	+	0.840374i	$0.682336\pi$
$410$	−464906.	−0.136586
$411$	−2.22934e6	−0.650987
$412$	−3.63116e6	−1.05391
$413$	−1.05497e6	−0.304345
$414$	−1.04424e6	−0.299432
$415$	2.90440e6	0.827822
$416$	4.23222e6	1.19904
$417$	699768.	0.197067
$418$	153146.	0.0428710
$419$	2.48346e6	0.691069	0.345534	−	0.938406i	$-0.387698\pi$
$419$	2.48346e6	0.691069	0.345534	+	0.938406i	$0.387698\pi$
$420$	85201.5	0.0235681
$421$	−2.24679e6	−0.617813	−0.308906	−	0.951092i	$-0.599963\pi$
$421$	−2.24679e6	−0.617813	−0.308906	+	0.951092i	$0.599963\pi$
$422$	−1.64391e6	−0.449362
$423$	−4.43509e6	−1.20518
$424$	−238846.	−0.0645212
$425$	673991.	0.181001
$426$	−491714.	−0.131277
$427$	49122.1	0.0130379
$428$	−3.30001e6	−0.870775
$429$	−514850.	−0.135063
$430$	856581.	0.223407
$431$	−5.49572e6	−1.42505	−0.712527	−	0.701645i	$-0.752449\pi$
$431$	−5.49572e6	−1.42505	−0.712527	+	0.701645i	$0.752449\pi$
$432$	−12990.4	−0.00334899
$433$	1.87816e6	0.481407	0.240704	−	0.970599i	$-0.422622\pi$
$433$	1.87816e6	0.481407	0.240704	+	0.970599i	$0.422622\pi$
$434$	−636711.	−0.162263
$435$	−294562.	−0.0746369
$436$	1.17191e6	0.295242
$437$	−513999.	−0.128753
$438$	−490422.	−0.122147
$439$	5.88982e6	1.45861	0.729307	−	0.684187i	$-0.239843\pi$
$439$	5.88982e6	1.45861	0.729307	+	0.684187i	$0.239843\pi$
$440$	−548396.	−0.135040
$441$	3.33079e6	0.815551
$442$	2.76652e6	0.673562
$443$	−618058.	−0.149630	−0.0748152	−	0.997197i	$-0.523837\pi$
$443$	−618058.	−0.149630	−0.0748152	+	0.997197i	$0.523837\pi$
$444$	−1.32428e6	−0.318802
$445$	−424361.	−0.101586
$446$	3.53170e6	0.840711
$447$	−258226.	−0.0611267
$448$	607746.	0.143063
$449$	−1.59643e6	−0.373708	−0.186854	−	0.982388i	$-0.559829\pi$
$449$	−1.59643e6	−0.373708	−0.186854	+	0.982388i	$0.559829\pi$
$450$	458379.	0.106707
$451$	−641799.	−0.148579
$452$	−4.55702e6	−1.04914
$453$	179649.	0.0411319
$454$	−3.82436e6	−0.870801
$455$	−544007.	−0.123190
$456$	−380561.	−0.0857062
$457$	−2.53227e6	−0.567177	−0.283589	−	0.958946i	$-0.591525\pi$
$457$	−2.53227e6	−0.567177	−0.283589	+	0.958946i	$0.591525\pi$
$458$	37607.8	0.00837750
$459$	2.83556e6	0.628214
$460$	701515.	0.154576
$461$	−5.27078e6	−1.15511	−0.577554	−	0.816353i	$-0.695993\pi$
$461$	−5.27078e6	−1.15511	−0.577554	+	0.816353i	$0.695993\pi$
$462$	−73360.5	−0.0159903
$463$	−3.46604e6	−0.751418	−0.375709	−	0.926738i	$-0.622601\pi$
$463$	−3.46604e6	−0.751418	−0.375709	+	0.926738i	$0.622601\pi$
$464$	−10010.3	−0.00215850
$465$	−887773.	−0.190401
$466$	1.92908e6	0.411516
$467$	7.40137e6	1.57044	0.785218	−	0.619220i	$-0.212551\pi$
$467$	7.40137e6	1.57044	0.785218	+	0.619220i	$0.212551\pi$
$468$	−3.01663e6	−0.636660
$469$	1.76969e6	0.371506
$470$	−1.85833e6	−0.388041
$471$	262892.	0.0546040
$472$	−6.43122e6	−1.32873
$473$	1.18250e6	0.243024
$474$	959604.	0.196176
$475$	225625.	0.0458831
$476$	−632023.	−0.127854
$477$	275601.	0.0554606
$478$	−3.08887e6	−0.618344
$479$	1.43313e6	0.285395	0.142698	−	0.989766i	$-0.454422\pi$
$479$	1.43313e6	0.285395	0.142698	+	0.989766i	$0.454422\pi$
$480$	840831.	0.166573
$481$	8.45542e6	1.66637
$482$	750992.	0.147237
$483$	246218.	0.0480234
$484$	−288544.	−0.0559886
$485$	−3.30981e6	−0.638924
$486$	2.96479e6	0.569381
$487$	−1.40801e6	−0.269019	−0.134510	−	0.990912i	$-0.542946\pi$
$487$	−1.40801e6	−0.269019	−0.134510	+	0.990912i	$0.542946\pi$
$488$	299453.	0.0569220
$489$	2.88283e6	0.545188
$490$	1.39562e6	0.262589
$491$	−2.63536e6	−0.493328	−0.246664	−	0.969101i	$-0.579334\pi$
$491$	−2.63536e6	−0.493328	−0.246664	+	0.969101i	$0.579334\pi$
$492$	607860.	0.113212
$493$	2.18506e6	0.404898
$494$	926118.	0.170745
$495$	632788.	0.116077
$496$	−30169.8	−0.00550640
$497$	−717248.	−0.130250
$498$	2.36852e6	0.427960
$499$	−3.12953e6	−0.562637	−0.281318	−	0.959615i	$-0.590772\pi$
$499$	−3.12953e6	−0.562637	−0.281318	+	0.959615i	$0.590772\pi$
$500$	−307937.	−0.0550855
$501$	3.86619e6	0.688159
$502$	−1.81509e6	−0.321468
$503$	2.89627e6	0.510410	0.255205	−	0.966887i	$-0.417857\pi$
$503$	2.89627e6	0.510410	0.255205	+	0.966887i	$0.417857\pi$
$504$	−1.12777e6	−0.197762
$505$	1.01332e6	0.176815
$506$	−604021.	−0.104876
$507$	−954395.	−0.164895
$508$	−1.46901e6	−0.252561
$509$	−1.02891e7	−1.76029	−0.880145	−	0.474706i	$-0.842555\pi$
$509$	−1.02891e7	−1.76029	−0.880145	+	0.474706i	$0.842555\pi$
$510$	549634.	0.0935726
$511$	−715363.	−0.121192
$512$	57234.6	0.00964903
$513$	949232.	0.159250
$514$	−6.45244e6	−1.07725
$515$	4.60620e6	0.765288
$516$	−1.11997e6	−0.185175
$517$	−2.56540e6	−0.422113
$518$	1.20480e6	0.197284
$519$	663270.	0.108087
$520$	−3.31632e6	−0.537834
$521$	3.49667e6	0.564366	0.282183	−	0.959361i	$-0.408941\pi$
$521$	3.49667e6	0.564366	0.282183	+	0.959361i	$0.408941\pi$
$522$	1.48605e6	0.238702
$523$	495628.	0.0792323	0.0396161	−	0.999215i	$-0.487386\pi$
$523$	495628.	0.0792323	0.0396161	+	0.999215i	$0.487386\pi$
$524$	1.09791e6	0.174679
$525$	−108080.	−0.0171138
$526$	6.09648e6	0.960760
$527$	6.58549e6	1.03291
$528$	−3476.09	−0.000542634 0
$529$	−4.40908e6	−0.685029
$530$	115478.	0.0178571
$531$	7.42090e6	1.14214
$532$	−211576.	−0.0324106
$533$	−3.88115e6	−0.591756
$534$	−346063.	−0.0525173
$535$	4.18614e6	0.632309
$536$	1.07882e7	1.62195
$537$	1.97578e6	0.295667
$538$	6.37714e6	0.949884
$539$	1.92664e6	0.285646
$540$	−1.29553e6	−0.191189
$541$	−9.79685e6	−1.43911	−0.719554	−	0.694437i	$-0.755654\pi$
$541$	−9.79685e6	−1.43911	−0.719554	+	0.694437i	$0.755654\pi$
$542$	5.72339e6	0.836865
$543$	1.41642e6	0.206155
$544$	−6.23727e6	−0.903644
$545$	−1.48659e6	−0.214388
$546$	−443633.	−0.0636858
$547$	−1.26976e7	−1.81448	−0.907239	−	0.420615i	$-0.861814\pi$
$547$	−1.26976e7	−1.81448	−0.907239	+	0.420615i	$0.861814\pi$
$548$	−7.55564e6	−1.07478
$549$	−345536.	−0.0489285
$550$	265141.	0.0373741
$551$	731469.	0.102640
$552$	1.50097e6	0.209664
$553$	1.39975e6	0.194642
$554$	3.83986e6	0.531546
$555$	1.67987e6	0.231496
$556$	2.37164e6	0.325358
$557$	−1.04532e7	−1.42761	−0.713807	−	0.700342i	$-0.753031\pi$
$557$	−1.04532e7	−1.42761	−0.713807	+	0.700342i	$0.753031\pi$
$558$	4.47877e6	0.608938
$559$	7.15096e6	0.967909
$560$	−3672.95	−0.000494931 0
$561$	758766.	0.101789
$562$	−3.05902e6	−0.408546
$563$	2.96651e6	0.394434	0.197217	−	0.980360i	$-0.436810\pi$
$563$	2.96651e6	0.394434	0.197217	+	0.980360i	$0.436810\pi$
$564$	2.42974e6	0.321634
$565$	5.78068e6	0.761829
$566$	7.20346e6	0.945149
$567$	1.05696e6	0.138071
$568$	−4.37242e6	−0.568658
$569$	−1.16344e6	−0.150648	−0.0753239	−	0.997159i	$-0.523999\pi$
$569$	−1.16344e6	−0.150648	−0.0753239	+	0.997159i	$0.523999\pi$
$570$	183995.	0.0237203
$571$	1.18517e7	1.52121	0.760605	−	0.649215i	$-0.224902\pi$
$571$	1.18517e7	1.52121	0.760605	+	0.649215i	$0.224902\pi$
$572$	−1.74492e6	−0.222990
$573$	7830.12	0.000996281 0
$574$	−553022.	−0.0700587
$575$	−889888.	−0.112245
$576$	−4.27501e6	−0.536885
$577$	−7.78810e6	−0.973850	−0.486925	−	0.873444i	$-0.661881\pi$
$577$	−7.78810e6	−0.973850	−0.486925	+	0.873444i	$0.661881\pi$
$578$	900836.	0.112157
$579$	3.24799e6	0.402642
$580$	−998322.	−0.123226
$581$	3.45489e6	0.424613
$582$	−2.69913e6	−0.330305
$583$	159417.	0.0194250
$584$	−4.36093e6	−0.529111
$585$	3.82666e6	0.462307
$586$	−3.32612e6	−0.400124
$587$	−3.47855e6	−0.416680	−0.208340	−	0.978056i	$-0.566806\pi$
$587$	−3.47855e6	−0.416680	−0.208340	+	0.978056i	$0.566806\pi$
$588$	−1.82476e6	−0.217651
$589$	2.20456e6	0.261838
$590$	3.10939e6	0.367744
$591$	2.39449e6	0.281997
$592$	57088.2	0.00669486
$593$	−93731.7	−0.0109459	−0.00547293	−	0.999985i	$-0.501742\pi$
$593$	−93731.7	−0.0109459	−0.00547293	+	0.999985i	$0.501742\pi$
$594$	1.11548e6	0.129717
$595$	801735.	0.0928408
$596$	−875172.	−0.100920
$597$	−5.00619e6	−0.574872
$598$	−3.65270e6	−0.417697
$599$	1.17835e7	1.34186	0.670930	−	0.741521i	$-0.265895\pi$
$599$	1.17835e7	1.34186	0.670930	+	0.741521i	$0.265895\pi$
$600$	−658866.	−0.0747170
$601$	9.52217e6	1.07535	0.537675	−	0.843152i	$-0.319303\pi$
$601$	9.52217e6	1.07535	0.537675	+	0.843152i	$0.319303\pi$
$602$	1.01893e6	0.114592
$603$	−1.24484e7	−1.39418
$604$	608862.	0.0679088
$605$	366025.	0.0406558
$606$	826358.	0.0914086
$607$	−2.89191e6	−0.318576	−0.159288	−	0.987232i	$-0.550920\pi$
$607$	−2.89191e6	−0.318576	−0.159288	+	0.987232i	$0.550920\pi$
$608$	−2.08799e6	−0.229070
$609$	−350392.	−0.0382834
$610$	−144781.	−0.0157539
$611$	−1.55138e7	−1.68118
$612$	4.44579e6	0.479811
$613$	−6.95341e6	−0.747389	−0.373694	−	0.927552i	$-0.621909\pi$
$613$	−6.95341e6	−0.747389	−0.373694	+	0.927552i	$0.621909\pi$
$614$	6.00974e6	0.643331
$615$	−771084.	−0.0822079
$616$	−652336.	−0.0692660
$617$	1.55160e6	0.164084	0.0820421	−	0.996629i	$-0.473856\pi$
$617$	1.55160e6	0.164084	0.0820421	+	0.996629i	$0.473856\pi$
$618$	3.75632e6	0.395632
$619$	−9.01017e6	−0.945162	−0.472581	−	0.881287i	$-0.656678\pi$
$619$	−9.01017e6	−0.945162	−0.472581	+	0.881287i	$0.656678\pi$
$620$	−3.00882e6	−0.314352
$621$	−3.74387e6	−0.389575
$622$	−7.97645e6	−0.826673
$623$	−504792.	−0.0521066
$624$	−21021.0	−0.00216119
$625$	390625.	0.0400000
$626$	−565112.	−0.0576366
$627$	254004.	0.0258031
$628$	890986.	0.0901512
$629$	−1.24613e7	−1.25584
$630$	545257.	0.0547331
$631$	9.33125e6	0.932967	0.466484	−	0.884530i	$-0.345521\pi$
$631$	9.33125e6	0.932967	0.466484	+	0.884530i	$0.345521\pi$
$632$	8.53299e6	0.849784
$633$	−2.72656e6	−0.270461
$634$	−7.12952e6	−0.704429
$635$	1.86348e6	0.183396
$636$	−150987.	−0.0148011
$637$	1.16510e7	1.13766
$638$	859579.	0.0836054
$639$	5.04528e6	0.488802
$640$	2.83587e6	0.273675
$641$	1.42045e7	1.36546	0.682732	−	0.730669i	$-0.260792\pi$
$641$	1.42045e7	1.36546	0.682732	+	0.730669i	$0.260792\pi$
$642$	3.41376e6	0.326886
$643$	4.18161e6	0.398856	0.199428	−	0.979912i	$-0.436092\pi$
$643$	4.18161e6	0.398856	0.199428	+	0.979912i	$0.436092\pi$
$644$	834477.	0.0792866
$645$	1.42071e6	0.134464
$646$	−1.36488e6	−0.128680
$647$	−4.67441e6	−0.439001	−0.219501	−	0.975612i	$-0.570443\pi$
$647$	−4.67441e6	−0.439001	−0.219501	+	0.975612i	$0.570443\pi$
$648$	6.44334e6	0.602800
$649$	4.29249e6	0.400035
$650$	1.60339e6	0.148852
$651$	−1.05604e6	−0.0976622
$652$	9.77040e6	0.900105
$653$	−1.40794e7	−1.29211	−0.646055	−	0.763291i	$-0.723583\pi$
$653$	−1.40794e7	−1.29211	−0.646055	+	0.763291i	$0.723583\pi$
$654$	−1.21231e6	−0.110833
$655$	−1.39273e6	−0.126842
$656$	−26204.2	−0.00237745
$657$	5.03202e6	0.454809
$658$	−2.21054e6	−0.199037
$659$	−7.75740e6	−0.695830	−0.347915	−	0.937526i	$-0.613110\pi$
$659$	−7.75740e6	−0.695830	−0.347915	+	0.937526i	$0.613110\pi$
$660$	−346669.	−0.0309782
$661$	−9.33990e6	−0.831454	−0.415727	−	0.909489i	$-0.636473\pi$
$661$	−9.33990e6	−0.831454	−0.415727	+	0.909489i	$0.636473\pi$
$662$	6.98191e6	0.619198
$663$	4.58849e6	0.405402
$664$	2.10614e7	1.85381
$665$	268389.	0.0235348
$666$	−8.47486e6	−0.740367
$667$	−2.88499e6	−0.251090
$668$	1.31032e7	1.13615
$669$	5.85761e6	0.506005
$670$	−5.21594e6	−0.448896
$671$	−199869.	−0.0171372
$672$	1.00020e6	0.0854402
$673$	−1.70984e7	−1.45519	−0.727593	−	0.686009i	$-0.759361\pi$
$673$	−1.70984e7	−1.45519	−0.727593	+	0.686009i	$0.759361\pi$
$674$	5.30943e6	0.450192
$675$	1.64341e6	0.138831
$676$	−3.23461e6	−0.272242
$677$	590788.	0.0495405	0.0247702	−	0.999693i	$-0.492115\pi$
$677$	590788.	0.0495405	0.0247702	+	0.999693i	$0.492115\pi$
$678$	4.71410e6	0.393844
$679$	−3.93713e6	−0.327722
$680$	4.88746e6	0.405332
$681$	−6.34301e6	−0.524116
$682$	2.59066e6	0.213280
$683$	−9.14079e6	−0.749777	−0.374888	−	0.927070i	$-0.622319\pi$
$683$	−9.14079e6	−0.749777	−0.374888	+	0.927070i	$0.622319\pi$
$684$	1.48827e6	0.121630
$685$	9.58449e6	0.780445
$686$	3.41248e6	0.276860
$687$	62375.6	0.00504223
$688$	48280.9	0.00388869
$689$	964041.	0.0773655
$690$	−725696.	−0.0580273
$691$	−5.73386e6	−0.456827	−0.228414	−	0.973564i	$-0.573354\pi$
$691$	−5.73386e6	−0.456827	−0.228414	+	0.973564i	$0.573354\pi$
$692$	2.24794e6	0.178451
$693$	752723.	0.0595391
$694$	1.37383e7	1.08277
$695$	−3.00847e6	−0.236257
$696$	−2.13602e6	−0.167141
$697$	5.71989e6	0.445970
$698$	−5.26166e6	−0.408775
$699$	3.19954e6	0.247682
$700$	−366302.	−0.0282549
$701$	−1.08537e7	−0.834221	−0.417111	−	0.908856i	$-0.636957\pi$
$701$	−1.08537e7	−0.834221	−0.417111	+	0.908856i	$0.636957\pi$
$702$	6.74566e6	0.516632
$703$	−4.17153e6	−0.318352
$704$	−2.47281e6	−0.188044
$705$	−3.08218e6	−0.233553
$706$	7.11450e6	0.537196
$707$	1.20538e6	0.0906937
$708$	−4.06550e6	−0.304811
$709$	2.25056e7	1.68141	0.840706	−	0.541491i	$-0.182140\pi$
$709$	2.25056e7	1.68141	0.840706	+	0.541491i	$0.182140\pi$
$710$	2.11400e6	0.157383
$711$	−9.84612e6	−0.730451
$712$	−3.07727e6	−0.227491
$713$	−8.69499e6	−0.640539
$714$	653809.	0.0479960
$715$	2.21347e6	0.161923
$716$	6.69626e6	0.488146
$717$	−5.12315e6	−0.372168
$718$	−6.29737e6	−0.455878
$719$	1.79294e7	1.29343	0.646716	−	0.762731i	$-0.276142\pi$
$719$	1.79294e7	1.29343	0.646716	+	0.762731i	$0.276142\pi$
$720$	25836.3	0.00185737
$721$	5.47924e6	0.392538
$722$	−456905.	−0.0326199
$723$	1.24558e6	0.0886188
$724$	4.80050e6	0.340361
$725$	1.26639e6	0.0894795
$726$	298491.	0.0210179
$727$	1.23546e7	0.866950	0.433475	−	0.901166i	$-0.357287\pi$
$727$	1.23546e7	0.866950	0.433475	+	0.901166i	$0.357287\pi$
$728$	−3.94488e6	−0.275870
$729$	−3.71937e6	−0.259209
$730$	2.10844e6	0.146438
$731$	−1.05388e7	−0.729453
$732$	189300.	0.0130579
$733$	−225502.	−0.0155021	−0.00775104	−	0.999970i	$-0.502467\pi$
$733$	−225502.	−0.0155021	−0.00775104	+	0.999970i	$0.502467\pi$
$734$	−8808.89	−0.000603505 0
$735$	2.31474e6	0.158046
$736$	8.23523e6	0.560378
$737$	−7.20056e6	−0.488312
$738$	3.89007e6	0.262916
$739$	6.53929e6	0.440473	0.220236	−	0.975447i	$-0.429317\pi$
$739$	6.53929e6	0.440473	0.220236	+	0.975447i	$0.429317\pi$
$740$	5.69338e6	0.382200
$741$	1.53604e6	0.102768
$742$	137365.	0.00915940
$743$	2.28763e7	1.52024	0.760122	−	0.649781i	$-0.225139\pi$
$743$	2.28763e7	1.52024	0.760122	+	0.649781i	$0.225139\pi$
$744$	−6.43771e6	−0.426382
$745$	1.11018e6	0.0732826
$746$	7.34373e6	0.483136
$747$	−2.43024e7	−1.59349
$748$	2.57159e6	0.168053
$749$	4.97955e6	0.324329
$750$	318552.	0.0206789
$751$	6.54537e6	0.423482	0.211741	−	0.977326i	$-0.432087\pi$
$751$	6.54537e6	0.423482	0.211741	+	0.977326i	$0.432087\pi$
$752$	−104744.	−0.00675435
$753$	−3.01047e6	−0.193485
$754$	5.19814e6	0.332981
$755$	−772354.	−0.0493116
$756$	−1.54108e6	−0.0980663
$757$	2.21668e7	1.40593	0.702965	−	0.711224i	$-0.251859\pi$
$757$	2.21668e7	1.40593	0.702965	+	0.711224i	$0.251859\pi$
$758$	2.04350e6	0.129182
$759$	−1.00182e6	−0.0631225
$760$	1.63612e6	0.102750
$761$	2.80670e7	1.75685	0.878424	−	0.477881i	$-0.158595\pi$
$761$	2.80670e7	1.75685	0.878424	+	0.477881i	$0.158595\pi$
$762$	1.51965e6	0.0948105
$763$	−1.76835e6	−0.109966
$764$	26537.6	0.00164486
$765$	−5.63958e6	−0.348412
$766$	1.01751e7	0.626565
$767$	2.59580e7	1.59325
$768$	6.11542e6	0.374131
$769$	−8.43693e6	−0.514480	−0.257240	−	0.966348i	$-0.582813\pi$
$769$	−8.43693e6	−0.514480	−0.257240	+	0.966348i	$0.582813\pi$
$770$	315394.	0.0191702
$771$	−1.07019e7	−0.648372
$772$	1.10080e7	0.664761
$773$	2.25419e7	1.35688	0.678440	−	0.734656i	$-0.262656\pi$
$773$	2.25419e7	1.35688	0.678440	+	0.734656i	$0.262656\pi$
$774$	−7.16739e6	−0.430040
$775$	3.81675e6	0.228265
$776$	−2.40012e7	−1.43080
$777$	1.99827e6	0.118741
$778$	−4.45877e6	−0.264098
$779$	1.91479e6	0.113052
$780$	−2.09642e6	−0.123379
$781$	2.91835e6	0.171203
$782$	5.38321e6	0.314792
$783$	5.32787e6	0.310563
$784$	78663.4	0.00457070
$785$	−1.13024e6	−0.0654628
$786$	−1.13576e6	−0.0655737
$787$	3.26311e7	1.87800	0.938998	−	0.343922i	$-0.111755\pi$
$787$	3.26311e7	1.87800	0.938998	+	0.343922i	$0.111755\pi$
$788$	8.11535e6	0.465577
$789$	1.01115e7	0.578260
$790$	−4.12557e6	−0.235189
$791$	6.87631e6	0.390764
$792$	4.58867e6	0.259941
$793$	−1.20867e6	−0.0682534
$794$	2.31477e6	0.130303
$795$	191530.	0.0107478
$796$	−1.69668e7	−0.949114
$797$	−6.90386e6	−0.384987	−0.192493	−	0.981298i	$-0.561657\pi$
$797$	−6.90386e6	−0.384987	−0.192493	+	0.981298i	$0.561657\pi$
$798$	218869.	0.0121668
$799$	2.28636e7	1.26700
$800$	−3.61494e6	−0.199699
$801$	3.55082e6	0.195545
$802$	1.41303e7	0.775739
$803$	2.91068e6	0.159297
$804$	6.81979e6	0.372075
$805$	−1.05855e6	−0.0575735
$806$	1.56665e7	0.849445
$807$	1.05770e7	0.571714
$808$	7.34815e6	0.395958
$809$	3.11674e6	0.167428	0.0837142	−	0.996490i	$-0.473322\pi$
$809$	3.11674e6	0.167428	0.0837142	+	0.996490i	$0.473322\pi$
$810$	−3.11525e6	−0.166833
$811$	−1.10702e7	−0.591020	−0.295510	−	0.955340i	$-0.595490\pi$
$811$	−1.10702e7	−0.591020	−0.295510	+	0.955340i	$0.595490\pi$
$812$	−1.18754e6	−0.0632059
$813$	9.49271e6	0.503691
$814$	−4.90213e6	−0.259313
$815$	−1.23940e7	−0.653606
$816$	30979.9	0.00162875
$817$	−3.52796e6	−0.184914
$818$	1.28575e7	0.671849
$819$	4.55194e6	0.237130
$820$	−2.61334e6	−0.135725
$821$	−9.95728e6	−0.515564	−0.257782	−	0.966203i	$-0.582992\pi$
$821$	−9.95728e6	−0.515564	−0.257782	+	0.966203i	$0.582992\pi$
$822$	7.81607e6	0.403468
$823$	1.34663e7	0.693027	0.346514	−	0.938045i	$-0.387365\pi$
$823$	1.34663e7	0.693027	0.346514	+	0.938045i	$0.387365\pi$
$824$	3.34020e7	1.71378
$825$	439758.	0.0224946
$826$	3.69873e6	0.188626
$827$	1.37073e7	0.696927	0.348463	−	0.937322i	$-0.386704\pi$
$827$	1.37073e7	0.696927	0.348463	+	0.937322i	$0.386704\pi$
$828$	−5.86989e6	−0.297546
$829$	−2.40658e6	−0.121623	−0.0608113	−	0.998149i	$-0.519369\pi$
$829$	−2.40658e6	−0.121623	−0.0608113	+	0.998149i	$0.519369\pi$
$830$	−1.01828e7	−0.513066
$831$	6.36871e6	0.319925
$832$	−1.49538e7	−0.748935
$833$	−1.71707e7	−0.857386
$834$	−2.45338e6	−0.122138
$835$	−1.66217e7	−0.825009
$836$	860864.	0.0426009
$837$	1.60575e7	0.792256
$838$	−8.70699e6	−0.428310
$839$	−3.76307e7	−1.84560	−0.922799	−	0.385282i	$-0.874104\pi$
$839$	−3.76307e7	−1.84560	−0.922799	+	0.385282i	$0.874104\pi$
$840$	−783744.	−0.0383245
$841$	−1.64055e7	−0.799835
$842$	7.87723e6	0.382907
$843$	−5.07362e6	−0.245895
$844$	−9.24077e6	−0.446532
$845$	4.10318e6	0.197687
$846$	1.55494e7	0.746945
$847$	435399.	0.0208535
$848$	6508.88	0.000310825 0
$849$	1.19475e7	0.568864
$850$	−2.36301e6	−0.112181
$851$	1.64529e7	0.778788
$852$	−2.76403e6	−0.130450
$853$	−2.12913e7	−1.00191	−0.500955	−	0.865473i	$-0.667018\pi$
$853$	−2.12913e7	−1.00191	−0.500955	+	0.865473i	$0.667018\pi$
$854$	−172222.	−0.00808061
$855$	−1.88790e6	−0.0883211
$856$	3.03559e7	1.41598
$857$	−1.11706e7	−0.519547	−0.259773	−	0.965670i	$-0.583648\pi$
$857$	−1.11706e7	−0.519547	−0.259773	+	0.965670i	$0.583648\pi$
$858$	1.80506e6	0.0837094
$859$	2.43447e7	1.12570	0.562848	−	0.826561i	$-0.309706\pi$
$859$	2.43447e7	1.12570	0.562848	+	0.826561i	$0.309706\pi$
$860$	4.81503e6	0.222000
$861$	−917231.	−0.0421668
$862$	1.92680e7	0.883218
$863$	−1.07299e7	−0.490421	−0.245211	−	0.969470i	$-0.578857\pi$
$863$	−1.07299e7	−0.490421	−0.245211	+	0.969470i	$0.578857\pi$
$864$	−1.52085e7	−0.693109
$865$	−2.85156e6	−0.129581
$866$	−6.58482e6	−0.298366
$867$	1.49411e6	0.0675047
$868$	−3.57909e6	−0.161240
$869$	−5.69531e6	−0.255840
$870$	1.03273e6	0.0462584
$871$	−4.35440e7	−1.94484
$872$	−1.07801e7	−0.480099
$873$	2.76947e7	1.22987
$874$	1.80208e6	0.0797986
$875$	464662.	0.0205171
$876$	−2.75677e6	−0.121378
$877$	−3.70496e6	−0.162662	−0.0813308	−	0.996687i	$-0.525917\pi$
$877$	−3.70496e6	−0.162662	−0.0813308	+	0.996687i	$0.525917\pi$
$878$	−2.06497e7	−0.904018
$879$	−5.51664e6	−0.240825
$880$	14944.6	0.000650544 0
$881$	2.71371e7	1.17794	0.588970	−	0.808155i	$-0.299534\pi$
$881$	2.71371e7	1.17794	0.588970	+	0.808155i	$0.299534\pi$
$882$	−1.16777e7	−0.505461
$883$	−3.09770e7	−1.33702	−0.668509	−	0.743704i	$-0.733067\pi$
$883$	−3.09770e7	−1.33702	−0.668509	+	0.743704i	$0.733067\pi$
$884$	1.55512e7	0.669318
$885$	5.15718e6	0.221337
$886$	2.16691e6	0.0927377
$887$	−7.17442e6	−0.306181	−0.153090	−	0.988212i	$-0.548923\pi$
$887$	−7.17442e6	−0.306181	−0.153090	+	0.988212i	$0.548923\pi$
$888$	1.21816e7	0.518410
$889$	2.21667e6	0.0940690
$890$	1.48781e6	0.0629611
$891$	−4.30058e6	−0.181482
$892$	1.98524e7	0.835414
$893$	7.65380e6	0.321180
$894$	905339.	0.0378850
$895$	−8.49435e6	−0.354464
$896$	3.37336e6	0.140376
$897$	−6.05830e6	−0.251402
$898$	5.59707e6	0.231617
$899$	1.23738e7	0.510627
$900$	2.57665e6	0.106035
$901$	−1.42076e6	−0.0583056
$902$	2.25014e6	0.0920861
$903$	1.68998e6	0.0689704
$904$	4.19187e7	1.70603
$905$	−6.08954e6	−0.247152
$906$	−629849.	−0.0254927
$907$	−1.76196e7	−0.711179	−0.355590	−	0.934642i	$-0.615720\pi$
$907$	−1.76196e7	−0.711179	−0.355590	+	0.934642i	$0.615720\pi$
$908$	−2.14976e7	−0.865315
$909$	−8.47894e6	−0.340355
$910$	1.90729e6	0.0763506
$911$	−6.90833e6	−0.275789	−0.137895	−	0.990447i	$-0.544034\pi$
$911$	−6.90833e6	−0.275789	−0.137895	+	0.990447i	$0.544034\pi$
$912$	10370.8	0.000412882 0
$913$	−1.40573e7	−0.558117
$914$	8.87812e6	0.351524
$915$	−240131.	−0.00948190
$916$	211402.	0.00832473
$917$	−1.65670e6	−0.0650609
$918$	−9.94148e6	−0.389354
$919$	4.51984e6	0.176537	0.0882683	−	0.996097i	$-0.471867\pi$
$919$	4.51984e6	0.176537	0.0882683	+	0.996097i	$0.471867\pi$
$920$	−6.45304e6	−0.251359
$921$	9.96763e6	0.387207
$922$	1.84793e7	0.715911
$923$	1.76482e7	0.681861
$924$	−412375.	−0.0158896
$925$	−7.22218e6	−0.277532
$926$	1.21519e7	0.465713
$927$	−3.85421e7	−1.47311
$928$	−1.17195e7	−0.446724
$929$	1.04523e7	0.397348	0.198674	−	0.980066i	$-0.436337\pi$
$929$	1.04523e7	0.397348	0.198674	+	0.980066i	$0.436337\pi$
$930$	3.11253e6	0.118007
$931$	−5.74807e6	−0.217344
$932$	1.08438e7	0.408923
$933$	−1.32296e7	−0.497556
$934$	−2.59492e7	−0.973322
$935$	−3.26212e6	−0.122031
$936$	2.77491e7	1.03528
$937$	7.01724e6	0.261106	0.130553	−	0.991441i	$-0.458325\pi$
$937$	7.01724e6	0.261106	0.130553	+	0.991441i	$0.458325\pi$
$938$	−6.20454e6	−0.230252
$939$	−937283.	−0.0346902
$940$	−1.04461e7	−0.385596
$941$	−6.71608e6	−0.247253	−0.123626	−	0.992329i	$-0.539452\pi$
$941$	−6.71608e6	−0.247253	−0.123626	+	0.992329i	$0.539452\pi$
$942$	−921698.	−0.0338424
$943$	−7.55212e6	−0.276560
$944$	175260.	0.00640106
$945$	1.95489e6	0.0712103
$946$	−4.14585e6	−0.150621
$947$	5.06237e7	1.83433	0.917167	−	0.398502i	$-0.130470\pi$
$947$	5.06237e7	1.83433	0.917167	+	0.398502i	$0.130470\pi$
$948$	5.39414e6	0.194940
$949$	1.76018e7	0.634441
$950$	−791041.	−0.0284374
$951$	−1.18249e7	−0.423980
$952$	5.81380e6	0.207906
$953$	−8.21131e6	−0.292874	−0.146437	−	0.989220i	$-0.546780\pi$
$953$	−8.21131e6	−0.292874	−0.146437	+	0.989220i	$0.546780\pi$
$954$	−966256.	−0.0343733
$955$	−33663.6	−0.00119441
$956$	−1.73632e7	−0.614449
$957$	1.42568e6	0.0503202
$958$	−5.02455e6	−0.176882
$959$	1.14011e7	0.400313
$960$	−2.97093e6	−0.104044
$961$	8.66390e6	0.302625
$962$	−2.96447e7	−1.03278
$963$	−3.50273e7	−1.21714
$964$	4.22149e6	0.146310
$965$	−1.39639e7	−0.482713
$966$	−863241.	−0.0297639
$967$	−3.68335e6	−0.126671	−0.0633355	−	0.997992i	$-0.520174\pi$
$967$	−3.68335e6	−0.126671	−0.0633355	+	0.997992i	$0.520174\pi$
$968$	2.65424e6	0.0910441
$969$	−2.26376e6	−0.0774497
$970$	1.16042e7	0.395991
$971$	−5.27346e7	−1.79493	−0.897466	−	0.441084i	$-0.854594\pi$
$971$	−5.27346e7	−1.79493	−0.897466	+	0.441084i	$0.854594\pi$
$972$	1.66657e7	0.565794
$973$	−3.57868e6	−0.121183
$974$	4.93648e6	0.166732
$975$	2.65935e6	0.0895909
$976$	−8160.53	−0.000274217 0
$977$	−3.47125e7	−1.16346	−0.581728	−	0.813383i	$-0.697623\pi$
$977$	−3.47125e7	−1.16346	−0.581728	+	0.813383i	$0.697623\pi$
$978$	−1.01072e7	−0.337896
$979$	2.05391e6	0.0684896
$980$	7.84507e6	0.260935
$981$	1.24390e7	0.412679
$982$	9.23956e6	0.305754
$983$	−2.11865e7	−0.699318	−0.349659	−	0.936877i	$-0.613703\pi$
$983$	−2.11865e7	−0.699318	−0.349659	+	0.936877i	$0.613703\pi$
$984$	−5.59153e6	−0.184095
$985$	−1.02945e7	−0.338076
$986$	−7.66081e6	−0.250947
$987$	−3.66636e6	−0.119796
$988$	5.20591e6	0.169670
$989$	1.39146e7	0.452357
$990$	−2.21855e6	−0.0719419
$991$	2.12483e7	0.687291	0.343645	−	0.939099i	$-0.388338\pi$
$991$	2.12483e7	0.687291	0.343645	+	0.939099i	$0.388338\pi$
$992$	−3.53211e7	−1.13961
$993$	1.15801e7	0.372681
$994$	2.51467e6	0.0807263
$995$	2.15228e7	0.689194
$996$	1.33140e7	0.425264
$997$	2.71864e6	0.0866190	0.0433095	−	0.999062i	$-0.486210\pi$
$997$	2.71864e6	0.0866190	0.0433095	+	0.999062i	$0.486210\pi$
$998$	1.09721e7	0.348710
$999$	−3.03846e7	−0.963251

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.b.1.14	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.b.1.14	✓	36	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)

\(f(q)\)	\(=\)	\(q-3.50600 q^{2} -5.81498 q^{3} -19.7080 q^{4} +25.0000 q^{5} +20.3873 q^{6} +29.7384 q^{7} +181.288 q^{8} -209.186 q^{9} +O(q^{10})\)	\(q-3.50600 q^{2} -5.81498 q^{3} -19.7080 q^{4} +25.0000 q^{5} +20.3873 q^{6} +29.7384 q^{7} +181.288 q^{8} -209.186 q^{9} -87.6500 q^{10} -121.000 q^{11} +114.601 q^{12} -731.724 q^{13} -104.263 q^{14} -145.374 q^{15} -4.94035 q^{16} +1078.39 q^{17} +733.406 q^{18} +361.000 q^{19} -492.699 q^{20} -172.928 q^{21} +424.226 q^{22} -1423.82 q^{23} -1054.19 q^{24} +625.000 q^{25} +2565.42 q^{26} +2629.45 q^{27} -586.083 q^{28} +2026.23 q^{29} +509.683 q^{30} +6106.80 q^{31} -5783.90 q^{32} +703.612 q^{33} -3780.82 q^{34} +743.459 q^{35} +4122.63 q^{36} -11555.5 q^{37} -1265.67 q^{38} +4254.96 q^{39} +4532.20 q^{40} +5304.12 q^{41} +606.285 q^{42} -9772.75 q^{43} +2384.67 q^{44} -5229.65 q^{45} +4991.91 q^{46} +21201.7 q^{47} +28.7281 q^{48} -15922.6 q^{49} -2191.25 q^{50} -6270.79 q^{51} +14420.8 q^{52} -1317.49 q^{53} -9218.85 q^{54} -3025.00 q^{55} +5391.21 q^{56} -2099.21 q^{57} -7103.96 q^{58} -35475.1 q^{59} +2865.04 q^{60} +1651.81 q^{61} -21410.4 q^{62} -6220.85 q^{63} +20436.4 q^{64} -18293.1 q^{65} -2466.86 q^{66} +59508.8 q^{67} -21252.8 q^{68} +8279.48 q^{69} -2606.57 q^{70} -24118.6 q^{71} -37922.9 q^{72} -24055.2 q^{73} +40513.5 q^{74} -3634.36 q^{75} -7114.58 q^{76} -3598.34 q^{77} -14917.9 q^{78} +47068.7 q^{79} -123.509 q^{80} +35542.0 q^{81} -18596.2 q^{82} +116176. q^{83} +3408.06 q^{84} +26959.6 q^{85} +34263.3 q^{86} -11782.5 q^{87} -21935.9 q^{88} -16974.5 q^{89} +18335.1 q^{90} -21760.3 q^{91} +28060.6 q^{92} -35510.9 q^{93} -74333.0 q^{94} +9025.00 q^{95} +33633.2 q^{96} -132392. q^{97} +55824.7 q^{98} +25311.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9}+O(q^{10}) \) 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9	\( 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9} - 200 q^{10} - 4356 q^{11} - 2008 q^{12} - 43 q^{13} - 1937 q^{14} - 1575 q^{15} + 3612 q^{16} - 2431 q^{17} - 6225 q^{18} + 12996 q^{19} + 13000 q^{20} + 2863 q^{21} + 968 q^{22} - 11444 q^{23} - 6210 q^{24} + 22500 q^{25} - 6339 q^{26} - 12960 q^{27} - 1083 q^{28} - 873 q^{29} + 125 q^{30} - 1405 q^{31} - 14283 q^{32} + 7623 q^{33} + 19937 q^{34} - 12725 q^{35} - 1169 q^{36} - 22729 q^{37} - 2888 q^{38} + 3710 q^{39} - 17250 q^{40} - 17043 q^{41} - 39996 q^{42} - 42231 q^{43} - 62920 q^{44} + 48375 q^{45} + 50947 q^{46} - 72440 q^{47} + 42475 q^{48} + 54119 q^{49} - 5000 q^{50} - 114970 q^{51} + 16786 q^{52} - 67603 q^{53} - 26080 q^{54} - 108900 q^{55} - 216071 q^{56} - 22743 q^{57} - 115746 q^{58} - 247439 q^{59} - 50200 q^{60} - 66627 q^{61} - 262438 q^{62} - 226118 q^{63} + 1078 q^{64} - 1075 q^{65} - 605 q^{66} - 189550 q^{67} - 140936 q^{68} - 65684 q^{69} - 48425 q^{70} - 320146 q^{71} - 509978 q^{72} - 55266 q^{73} - 63309 q^{74} - 39375 q^{75} + 187720 q^{76} + 61589 q^{77} - 284264 q^{78} - 1033 q^{79} + 90300 q^{80} - 58588 q^{81} - 328242 q^{82} - 451983 q^{83} + 43932 q^{84} - 60775 q^{85} - 44142 q^{86} - 457510 q^{87} + 83490 q^{88} + 13940 q^{89} - 155625 q^{90} - 211732 q^{91} - 735304 q^{92} + 4486 q^{93} + 152164 q^{94} + 324900 q^{95} + 195996 q^{96} - 234346 q^{97} - 58328 q^{98} - 234135 q^{99}+O(q^{100}) \) 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9 - 200 * q^10 - 4356 * q^11 - 2008 * q^12 - 43 * q^13 - 1937 * q^14 - 1575 * q^15 + 3612 * q^16 - 2431 * q^17 - 6225 * q^18 + 12996 * q^19 + 13000 * q^20 + 2863 * q^21 + 968 * q^22 - 11444 * q^23 - 6210 * q^24 + 22500 * q^25 - 6339 * q^26 - 12960 * q^27 - 1083 * q^28 - 873 * q^29 + 125 * q^30 - 1405 * q^31 - 14283 * q^32 + 7623 * q^33 + 19937 * q^34 - 12725 * q^35 - 1169 * q^36 - 22729 * q^37 - 2888 * q^38 + 3710 * q^39 - 17250 * q^40 - 17043 * q^41 - 39996 * q^42 - 42231 * q^43 - 62920 * q^44 + 48375 * q^45 + 50947 * q^46 - 72440 * q^47 + 42475 * q^48 + 54119 * q^49 - 5000 * q^50 - 114970 * q^51 + 16786 * q^52 - 67603 * q^53 - 26080 * q^54 - 108900 * q^55 - 216071 * q^56 - 22743 * q^57 - 115746 * q^58 - 247439 * q^59 - 50200 * q^60 - 66627 * q^61 - 262438 * q^62 - 226118 * q^63 + 1078 * q^64 - 1075 * q^65 - 605 * q^66 - 189550 * q^67 - 140936 * q^68 - 65684 * q^69 - 48425 * q^70 - 320146 * q^71 - 509978 * q^72 - 55266 * q^73 - 63309 * q^74 - 39375 * q^75 + 187720 * q^76 + 61589 * q^77 - 284264 * q^78 - 1033 * q^79 + 90300 * q^80 - 58588 * q^81 - 328242 * q^82 - 451983 * q^83 + 43932 * q^84 - 60775 * q^85 - 44142 * q^86 - 457510 * q^87 + 83490 * q^88 + 13940 * q^89 - 155625 * q^90 - 211732 * q^91 - 735304 * q^92 + 4486 * q^93 + 152164 * q^94 + 324900 * q^95 + 195996 * q^96 - 234346 * q^97 - 58328 * q^98 - 234135 * q^99

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