LMFDB - Embedded newform 1045.6.a.h.1.6

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			1.6
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.31261 q^{2} +15.2747 q^{3} +37.0994 q^{4} +25.0000 q^{5} -126.972 q^{6} +144.510 q^{7} -42.3897 q^{8} -9.68428 q^{9} +O(q^{10})$	\(q-8.31261 q^{2} +15.2747 q^{3} +37.0994 q^{4} +25.0000 q^{5} -126.972 q^{6} +144.510 q^{7} -42.3897 q^{8} -9.68428 q^{9} -207.815 q^{10} +121.000 q^{11} +566.682 q^{12} +149.654 q^{13} -1201.26 q^{14} +381.867 q^{15} -834.813 q^{16} -452.531 q^{17} +80.5016 q^{18} +361.000 q^{19} +927.486 q^{20} +2207.35 q^{21} -1005.83 q^{22} -1575.85 q^{23} -647.489 q^{24} +625.000 q^{25} -1244.01 q^{26} -3859.67 q^{27} +5361.25 q^{28} -5580.10 q^{29} -3174.31 q^{30} +3526.60 q^{31} +8295.95 q^{32} +1848.24 q^{33} +3761.71 q^{34} +3612.76 q^{35} -359.281 q^{36} +5395.86 q^{37} -3000.85 q^{38} +2285.91 q^{39} -1059.74 q^{40} -4224.89 q^{41} -18348.8 q^{42} -15854.9 q^{43} +4489.03 q^{44} -242.107 q^{45} +13099.4 q^{46} +22176.7 q^{47} -12751.5 q^{48} +4076.23 q^{49} -5195.38 q^{50} -6912.27 q^{51} +5552.07 q^{52} +14449.2 q^{53} +32083.9 q^{54} +3025.00 q^{55} -6125.75 q^{56} +5514.16 q^{57} +46385.2 q^{58} +49782.6 q^{59} +14167.0 q^{60} -17737.8 q^{61} -29315.3 q^{62} -1399.48 q^{63} -42246.9 q^{64} +3741.34 q^{65} -15363.7 q^{66} -62411.1 q^{67} -16788.7 q^{68} -24070.6 q^{69} -30031.4 q^{70} +24103.8 q^{71} +410.514 q^{72} +54609.0 q^{73} -44853.7 q^{74} +9546.67 q^{75} +13392.9 q^{76} +17485.7 q^{77} -19001.9 q^{78} +96336.6 q^{79} -20870.3 q^{80} -56601.9 q^{81} +35119.8 q^{82} +66485.2 q^{83} +81891.4 q^{84} -11313.3 q^{85} +131795. q^{86} -85234.3 q^{87} -5129.15 q^{88} +105074. q^{89} +2012.54 q^{90} +21626.5 q^{91} -58463.1 q^{92} +53867.7 q^{93} -184346. q^{94} +9025.00 q^{95} +126718. q^{96} +25518.1 q^{97} -33884.1 q^{98} -1171.80 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−8.31261	−1.46948	−0.734738	−	0.678351i	$-0.762695\pi$
$2$	−8.31261	−1.46948	−0.734738	+	0.678351i	$0.762695\pi$
$3$	15.2747	0.979871	0.489935	−	0.871759i	$-0.337020\pi$
$3$	15.2747	0.979871	0.489935	+	0.871759i	$0.337020\pi$
$4$	37.0994	1.15936
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−126.972	−1.43990
$7$	144.510	1.11469	0.557345	−	0.830281i	$-0.311820\pi$
$7$	144.510	1.11469	0.557345	+	0.830281i	$0.311820\pi$
$8$	−42.3897	−0.234172
$9$	−9.68428	−0.0398530
$10$	−207.815	−0.657169
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	566.682	1.13602
$13$	149.654	0.245601	0.122800	−	0.992431i	$-0.460813\pi$
$13$	149.654	0.245601	0.122800	+	0.992431i	$0.460813\pi$
$14$	−1201.26	−1.63801
$15$	381.867	0.438212
$16$	−834.813	−0.815248
$17$	−452.531	−0.379775	−0.189887	−	0.981806i	$-0.560812\pi$
$17$	−452.531	−0.379775	−0.189887	+	0.981806i	$0.560812\pi$
$18$	80.5016	0.0585630
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	927.486	0.518480
$21$	2207.35	1.09225
$22$	−1005.83	−0.443063
$23$	−1575.85	−0.621147	−0.310574	−	0.950549i	$-0.600521\pi$
$23$	−1575.85	−0.621147	−0.310574	+	0.950549i	$0.600521\pi$
$24$	−647.489	−0.229458
$25$	625.000	0.200000
$26$	−1244.01	−0.360904
$27$	−3859.67	−1.01892
$28$	5361.25	1.29232
$29$	−5580.10	−1.23210	−0.616052	−	0.787706i	$-0.711269\pi$
$29$	−5580.10	−1.23210	−0.616052	+	0.787706i	$0.711269\pi$
$30$	−3174.31	−0.643941
$31$	3526.60	0.659101	0.329551	−	0.944138i	$-0.393103\pi$
$31$	3526.60	0.659101	0.329551	+	0.944138i	$0.393103\pi$
$32$	8295.95	1.43216
$33$	1848.24	0.295442
$34$	3761.71	0.558070
$35$	3612.76	0.498504
$36$	−359.281	−0.0462039
$37$	5395.86	0.647973	0.323986	−	0.946062i	$-0.394977\pi$
$37$	5395.86	0.647973	0.323986	+	0.946062i	$0.394977\pi$
$38$	−3000.85	−0.337121
$39$	2285.91	0.240657
$40$	−1059.74	−0.104725
$41$	−4224.89	−0.392514	−0.196257	−	0.980552i	$-0.562879\pi$
$41$	−4224.89	−0.392514	−0.196257	+	0.980552i	$0.562879\pi$
$42$	−18348.8	−1.60504
$43$	−15854.9	−1.30765	−0.653826	−	0.756645i	$-0.726837\pi$
$43$	−15854.9	−1.30765	−0.653826	+	0.756645i	$0.726837\pi$
$44$	4489.03	0.349559
$45$	−242.107	−0.0178228
$46$	13099.4	0.912761
$47$	22176.7	1.46437	0.732187	−	0.681104i	$-0.238500\pi$
$47$	22176.7	1.46437	0.732187	+	0.681104i	$0.238500\pi$
$48$	−12751.5	−0.798837
$49$	4076.23	0.242532
$50$	−5195.38	−0.293895
$51$	−6912.27	−0.372130
$52$	5552.07	0.284739
$53$	14449.2	0.706570	0.353285	−	0.935516i	$-0.385065\pi$
$53$	14449.2	0.706570	0.353285	+	0.935516i	$0.385065\pi$
$54$	32083.9	1.49728
$55$	3025.00	0.134840
$56$	−6125.75	−0.261029
$57$	5514.16	0.224798
$58$	46385.2	1.81055
$59$	49782.6	1.86186	0.930931	−	0.365195i	$-0.118998\pi$
$59$	49782.6	1.86186	0.930931	+	0.365195i	$0.118998\pi$
$60$	14167.0	0.508044
$61$	−17737.8	−0.610345	−0.305172	−	0.952297i	$-0.598714\pi$
$61$	−17737.8	−0.610345	−0.305172	+	0.952297i	$0.598714\pi$
$62$	−29315.3	−0.968533
$63$	−1399.48	−0.0444237
$64$	−42246.9	−1.28927
$65$	3741.34	0.109836
$66$	−15363.7	−0.434145
$67$	−62411.1	−1.69854	−0.849268	−	0.527962i	$-0.822956\pi$
$67$	−62411.1	−1.69854	−0.849268	+	0.527962i	$0.822956\pi$
$68$	−16788.7	−0.440295
$69$	−24070.6	−0.608644
$70$	−30031.4	−0.732540
$71$	24103.8	0.567466	0.283733	−	0.958903i	$-0.408427\pi$
$71$	24103.8	0.567466	0.283733	+	0.958903i	$0.408427\pi$
$72$	410.514	0.00933246
$73$	54609.0	1.19938	0.599690	−	0.800232i	$-0.295290\pi$
$73$	54609.0	1.19938	0.599690	+	0.800232i	$0.295290\pi$
$74$	−44853.7	−0.952180
$75$	9546.67	0.195974
$76$	13392.9	0.265975
$77$	17485.7	0.336091
$78$	−19001.9	−0.353639
$79$	96336.6	1.73670	0.868348	−	0.495955i	$-0.165182\pi$
$79$	96336.6	1.73670	0.868348	+	0.495955i	$0.165182\pi$
$80$	−20870.3	−0.364590
$81$	−56601.9	−0.958559
$82$	35119.8	0.576790
$83$	66485.2	1.05933	0.529663	−	0.848208i	$-0.322318\pi$
$83$	66485.2	1.05933	0.529663	+	0.848208i	$0.322318\pi$
$84$	81891.4	1.26631
$85$	−11313.3	−0.169840
$86$	131795.	1.92156
$87$	−85234.3	−1.20730
$88$	−5129.15	−0.0706055
$89$	105074.	1.40611	0.703054	−	0.711137i	$-0.251819\pi$
$89$	105074.	1.40611	0.703054	+	0.711137i	$0.251819\pi$
$90$	2012.54	0.0261902
$91$	21626.5	0.273768
$92$	−58463.1	−0.720132
$93$	53867.7	0.645834
$94$	−184346.	−2.15186
$95$	9025.00	0.102598
$96$	126718.	1.40333
$97$	25518.1	0.275372	0.137686	−	0.990476i	$-0.456034\pi$
$97$	25518.1	0.275372	0.137686	+	0.990476i	$0.456034\pi$
$98$	−33884.1	−0.356395
$99$	−1171.80	−0.0120161
$100$	23187.2	0.231872
$101$	100631.	0.981587	0.490793	−	0.871276i	$-0.336707\pi$
$101$	100631.	0.981587	0.490793	+	0.871276i	$0.336707\pi$
$102$	57458.9	0.546836
$103$	24206.2	0.224820	0.112410	−	0.993662i	$-0.464143\pi$
$103$	24206.2	0.224820	0.112410	+	0.993662i	$0.464143\pi$
$104$	−6343.78	−0.0575128
$105$	55183.7	0.488470
$106$	−120111.	−1.03829
$107$	−92293.9	−0.779316	−0.389658	−	0.920960i	$-0.627407\pi$
$107$	−92293.9	−0.779316	−0.389658	+	0.920960i	$0.627407\pi$
$108$	−143192.	−1.18129
$109$	93300.8	0.752176	0.376088	−	0.926584i	$-0.377269\pi$
$109$	93300.8	0.752176	0.376088	+	0.926584i	$0.377269\pi$
$110$	−25145.6	−0.198144
$111$	82420.1	0.634930
$112$	−120639.	−0.908748
$113$	23320.1	0.171804	0.0859022	−	0.996304i	$-0.472623\pi$
$113$	23320.1	0.171804	0.0859022	+	0.996304i	$0.472623\pi$
$114$	−45837.0	−0.330335
$115$	−39396.2	−0.277786
$116$	−207019.	−1.42845
$117$	−1449.29	−0.00978792
$118$	−413823.	−2.73596
$119$	−65395.4	−0.423331
$120$	−16187.2	−0.102617
$121$	14641.0	0.0909091
$122$	147447.	0.896886
$123$	−64533.8	−0.384613
$124$	130835.	0.764134
$125$	15625.0	0.0894427
$126$	11633.3	0.0652795
$127$	280340.	1.54233	0.771163	−	0.636638i	$-0.219676\pi$
$127$	280340.	1.54233	0.771163	+	0.636638i	$0.219676\pi$
$128$	85711.7	0.462397
$129$	−242178.	−1.28133
$130$	−31100.3	−0.161401
$131$	128045.	0.651907	0.325954	−	0.945386i	$-0.394315\pi$
$131$	128045.	0.651907	0.325954	+	0.945386i	$0.394315\pi$
$132$	68568.5	0.342523
$133$	52168.2	0.255727
$134$	518799.	2.49596
$135$	−96491.8	−0.455676
$136$	19182.6	0.0889327
$137$	112674.	0.512889	0.256444	−	0.966559i	$-0.417449\pi$
$137$	112674.	0.512889	0.256444	+	0.966559i	$0.417449\pi$
$138$	200089.	0.894388
$139$	395995.	1.73841	0.869206	−	0.494450i	$-0.164630\pi$
$139$	395995.	1.73841	0.869206	+	0.494450i	$0.164630\pi$
$140$	134031.	0.577945
$141$	338742.	1.43490
$142$	−200366.	−0.833877
$143$	18108.1	0.0740513
$144$	8084.57	0.0324901
$145$	−139503.	−0.551014
$146$	−453943.	−1.76246
$147$	62263.1	0.237650
$148$	200184.	0.751232
$149$	79551.2	0.293549	0.146775	−	0.989170i	$-0.453111\pi$
$149$	79551.2	0.293549	0.146775	+	0.989170i	$0.453111\pi$
$150$	−79357.7	−0.287979
$151$	−91458.6	−0.326424	−0.163212	−	0.986591i	$-0.552185\pi$
$151$	−91458.6	−0.326424	−0.163212	+	0.986591i	$0.552185\pi$
$152$	−15302.7	−0.0537228
$153$	4382.44	0.0151352
$154$	−145352.	−0.493878
$155$	88165.0	0.294759
$156$	84806.1	0.279007
$157$	−73827.6	−0.239039	−0.119520	−	0.992832i	$-0.538135\pi$
$157$	−73827.6	−0.239039	−0.119520	+	0.992832i	$0.538135\pi$
$158$	−800809.	−2.55203
$159$	220707.	0.692347
$160$	207399.	0.640481
$161$	−227726.	−0.692386
$162$	470510.	1.40858
$163$	−433854.	−1.27901	−0.639506	−	0.768786i	$-0.720861\pi$
$163$	−433854.	−1.27901	−0.639506	+	0.768786i	$0.720861\pi$
$164$	−156741.	−0.455065
$165$	46205.9	0.132126
$166$	−552665.	−1.55665
$167$	−180245.	−0.500116	−0.250058	−	0.968231i	$-0.580450\pi$
$167$	−180245.	−0.500116	−0.250058	+	0.968231i	$0.580450\pi$
$168$	−93568.8	−0.255775
$169$	−348897.	−0.939680
$170$	94042.8	0.249576
$171$	−3496.02	−0.00914291
$172$	−588207.	−1.51604
$173$	106434.	0.270374	0.135187	−	0.990820i	$-0.456836\pi$
$173$	106434.	0.270374	0.135187	+	0.990820i	$0.456836\pi$
$174$	708519.	1.77410
$175$	90319.0	0.222938
$176$	−101012.	−0.245806
$177$	760413.	1.82438
$178$	−873435.	−2.06624
$179$	−731309.	−1.70596	−0.852979	−	0.521945i	$-0.825207\pi$
$179$	−731309.	−1.70596	−0.852979	+	0.521945i	$0.825207\pi$
$180$	−8982.03	−0.0206630
$181$	281300.	0.638224	0.319112	−	0.947717i	$-0.396615\pi$
$181$	281300.	0.638224	0.319112	+	0.947717i	$0.396615\pi$
$182$	−179773.	−0.402296
$183$	−270939.	−0.598059
$184$	66799.7	0.145455
$185$	134897.	0.289782
$186$	−447781.	−0.949037
$187$	−54756.3	−0.114506
$188$	822743.	1.69773
$189$	−557762.	−1.13578
$190$	−75021.3	−0.150765
$191$	547618.	1.08616	0.543080	−	0.839681i	$-0.317258\pi$
$191$	547618.	1.08616	0.543080	+	0.839681i	$0.317258\pi$
$192$	−645308.	−1.26332
$193$	−972944.	−1.88016	−0.940080	−	0.340955i	$-0.889250\pi$
$193$	−972944.	−1.88016	−0.940080	+	0.340955i	$0.889250\pi$
$194$	−212122.	−0.404652
$195$	57147.8	0.107625
$196$	151226.	0.281181
$197$	−204818.	−0.376012	−0.188006	−	0.982168i	$-0.560203\pi$
$197$	−204818.	−0.376012	−0.188006	+	0.982168i	$0.560203\pi$
$198$	9740.70	0.0176574
$199$	568694.	1.01800	0.508998	−	0.860768i	$-0.330016\pi$
$199$	568694.	1.01800	0.508998	+	0.860768i	$0.330016\pi$
$200$	−26493.5	−0.0468344
$201$	−953309.	−1.66435
$202$	−836507.	−1.44242
$203$	−806383.	−1.37341
$204$	−256441.	−0.431432
$205$	−105622.	−0.175538
$206$	−201217.	−0.330367
$207$	15261.0	0.0247546
$208$	−124933.	−0.200225
$209$	43681.0	0.0691714
$210$	−458721.	−0.717794
$211$	726034.	1.12267	0.561334	−	0.827590i	$-0.310288\pi$
$211$	726034.	1.12267	0.561334	+	0.827590i	$0.310288\pi$
$212$	536058.	0.819167
$213$	368178.	0.556044
$214$	767203.	1.14519
$215$	−396372.	−0.584800
$216$	163610.	0.238603
$217$	509630.	0.734693
$218$	−775573.	−1.10530
$219$	834135.	1.17524
$220$	112226.	0.156328
$221$	−67723.0	−0.0932729
$222$	−685126.	−0.933013
$223$	−147290.	−0.198340	−0.0991701	−	0.995070i	$-0.531619\pi$
$223$	−147290.	−0.198340	−0.0991701	+	0.995070i	$0.531619\pi$
$224$	1.19885e6	1.59641
$225$	−6052.67	−0.00797060
$226$	−193851.	−0.252462
$227$	−607005.	−0.781858	−0.390929	−	0.920421i	$-0.627846\pi$
$227$	−607005.	−0.781858	−0.390929	+	0.920421i	$0.627846\pi$
$228$	204572.	0.260621
$229$	−958368.	−1.20766	−0.603829	−	0.797114i	$-0.706359\pi$
$229$	−958368.	−1.20766	−0.603829	+	0.797114i	$0.706359\pi$
$230$	327485.	0.408199
$231$	267089.	0.329326
$232$	236539.	0.288524
$233$	−1.04327e6	−1.25895	−0.629473	−	0.777023i	$-0.716729\pi$
$233$	−1.04327e6	−1.25895	−0.629473	+	0.777023i	$0.716729\pi$
$234$	12047.4	0.0143831
$235$	554417.	0.654888
$236$	1.84691e6	2.15856
$237$	1.47151e6	1.70174
$238$	543606.	0.622074
$239$	−1.09616e6	−1.24131	−0.620656	−	0.784083i	$-0.713134\pi$
$239$	−1.09616e6	−1.24131	−0.620656	+	0.784083i	$0.713134\pi$
$240$	−318788.	−0.357251
$241$	230699.	0.255860	0.127930	−	0.991783i	$-0.459167\pi$
$241$	230699.	0.255860	0.127930	+	0.991783i	$0.459167\pi$
$242$	−121705.	−0.133589
$243$	73323.7	0.0796579
$244$	−658062.	−0.707608
$245$	101906.	0.108464
$246$	536444.	0.565180
$247$	54025.0	0.0563446
$248$	−149492.	−0.154343
$249$	1.01554e6	1.03800
$250$	−129884.	−0.131434
$251$	288735.	0.289277	0.144639	−	0.989485i	$-0.453798\pi$
$251$	288735.	0.289277	0.144639	+	0.989485i	$0.453798\pi$
$252$	−51919.9	−0.0515030
$253$	−190678.	−0.187283
$254$	−2.33036e6	−2.26641
$255$	−172807.	−0.166422
$256$	639413.	0.609792
$257$	90953.1	0.0858984	0.0429492	−	0.999077i	$-0.486325\pi$
$257$	90953.1	0.0858984	0.0429492	+	0.999077i	$0.486325\pi$
$258$	2.01313e6	1.88288
$259$	779758.	0.722288
$260$	138802.	0.127339
$261$	54039.3	0.0491030
$262$	−1.06439e6	−0.957961
$263$	1.23506e6	1.10103	0.550513	−	0.834827i	$-0.314432\pi$
$263$	1.23506e6	1.10103	0.550513	+	0.834827i	$0.314432\pi$
$264$	−78346.1	−0.0691843
$265$	361231.	0.315988
$266$	−433654.	−0.375785
$267$	1.60496e6	1.37780
$268$	−2.31542e6	−1.96921
$269$	−1.69081e6	−1.42467	−0.712333	−	0.701842i	$-0.752361\pi$
$269$	−1.69081e6	−1.42467	−0.712333	+	0.701842i	$0.752361\pi$
$270$	802098.	0.669604
$271$	348850.	0.288546	0.144273	−	0.989538i	$-0.453916\pi$
$271$	348850.	0.288546	0.144273	+	0.989538i	$0.453916\pi$
$272$	377779.	0.309610
$273$	330338.	0.268258
$274$	−936616.	−0.753677
$275$	75625.0	0.0603023
$276$	−893005.	−0.705636
$277$	2.13406e6	1.67112	0.835558	−	0.549402i	$-0.185145\pi$
$277$	2.13406e6	1.67112	0.835558	+	0.549402i	$0.185145\pi$
$278$	−3.29175e6	−2.55455
$279$	−34152.6	−0.0262672
$280$	−153144.	−0.116736
$281$	2.25004e6	1.69990	0.849951	−	0.526861i	$-0.176631\pi$
$281$	2.25004e6	1.69990	0.849951	+	0.526861i	$0.176631\pi$
$282$	−2.81583e6	−2.10855
$283$	−660311.	−0.490097	−0.245049	−	0.969511i	$-0.578804\pi$
$283$	−660311.	−0.490097	−0.245049	+	0.969511i	$0.578804\pi$
$284$	894238.	0.657896
$285$	137854.	0.100533
$286$	−150526.	−0.108817
$287$	−610540.	−0.437532
$288$	−80340.3	−0.0570758
$289$	−1.21507e6	−0.855771
$290$	1.15963e6	0.809701
$291$	389781.	0.269829
$292$	2.02596e6	1.39051
$293$	2.63719e6	1.79462	0.897308	−	0.441404i	$-0.145519\pi$
$293$	2.63719e6	1.79462	0.897308	+	0.441404i	$0.145519\pi$
$294$	−517569.	−0.349221
$295$	1.24457e6	0.832650
$296$	−228729.	−0.151737
$297$	−467020.	−0.307216
$298$	−661278.	−0.431363
$299$	−235832.	−0.152554
$300$	354176.	0.227204
$301$	−2.29119e6	−1.45762
$302$	760260.	0.479672
$303$	1.53711e6	0.961828
$304$	−301368.	−0.187031
$305$	−443445.	−0.272954
$306$	−36429.5	−0.0222408
$307$	2.14150e6	1.29680	0.648398	−	0.761302i	$-0.275439\pi$
$307$	2.14150e6	1.29680	0.648398	+	0.761302i	$0.275439\pi$
$308$	648712.	0.389650
$309$	369743.	0.220294
$310$	−732881.	−0.433141
$311$	−921264.	−0.540111	−0.270056	−	0.962845i	$-0.587042\pi$
$311$	−921264.	−0.540111	−0.270056	+	0.962845i	$0.587042\pi$
$312$	−96899.1	−0.0563551
$313$	998692.	0.576197	0.288098	−	0.957601i	$-0.406977\pi$
$313$	998692.	0.576197	0.288098	+	0.957601i	$0.406977\pi$
$314$	613700.	0.351263
$315$	−34987.0	−0.0198669
$316$	3.57404e6	2.01345
$317$	2.99484e6	1.67389	0.836943	−	0.547290i	$-0.184341\pi$
$317$	2.99484e6	1.67389	0.836943	+	0.547290i	$0.184341\pi$
$318$	−1.83465e6	−1.01739
$319$	−675193.	−0.371493
$320$	−1.05617e6	−0.576581
$321$	−1.40976e6	−0.763629
$322$	1.89300e6	1.01744
$323$	−163364.	−0.0871263
$324$	−2.09990e6	−1.11131
$325$	93533.6	0.0491201
$326$	3.60646e6	1.87948
$327$	1.42514e6	0.737035
$328$	179092.	0.0919159
$329$	3.20476e6	1.63232
$330$	−384091.	−0.194156
$331$	−1.78229e6	−0.894147	−0.447074	−	0.894497i	$-0.647534\pi$
$331$	−1.78229e6	−0.894147	−0.447074	+	0.894497i	$0.647534\pi$
$332$	2.46656e6	1.22814
$333$	−52255.1	−0.0258237
$334$	1.49830e6	0.734909
$335$	−1.56028e6	−0.759608
$336$	−1.84272e6	−0.890455
$337$	2.70277e6	1.29639	0.648193	−	0.761476i	$-0.275525\pi$
$337$	2.70277e6	1.29639	0.648193	+	0.761476i	$0.275525\pi$
$338$	2.90024e6	1.38084
$339$	356207.	0.168346
$340$	−419716.	−0.196906
$341$	426719.	0.198727
$342$	29061.1	0.0134353
$343$	−1.83973e6	−0.844341
$344$	672084.	0.306215
$345$	−601764.	−0.272194
$346$	−884745.	−0.397308
$347$	3.39115e6	1.51190	0.755950	−	0.654629i	$-0.227175\pi$
$347$	3.39115e6	1.51190	0.755950	+	0.654629i	$0.227175\pi$
$348$	−3.16214e6	−1.39970
$349$	1.56020e6	0.685673	0.342836	−	0.939395i	$-0.388612\pi$
$349$	1.56020e6	0.685673	0.342836	+	0.939395i	$0.388612\pi$
$350$	−750786.	−0.327602
$351$	−577614.	−0.250248
$352$	1.00381e6	0.431812
$353$	−1.40388e6	−0.599645	−0.299823	−	0.953995i	$-0.596927\pi$
$353$	−1.40388e6	−0.599645	−0.299823	+	0.953995i	$0.596927\pi$
$354$	−6.32102e6	−2.68089
$355$	602595.	0.253779
$356$	3.89817e6	1.63018
$357$	−998894.	−0.414810
$358$	6.07909e6	2.50686
$359$	−3.48587e6	−1.42750	−0.713748	−	0.700403i	$-0.753004\pi$
$359$	−3.48587e6	−1.42750	−0.713748	+	0.700403i	$0.753004\pi$
$360$	10262.8	0.00417360
$361$	130321.	0.0526316
$362$	−2.33834e6	−0.937855
$363$	223637.	0.0890792
$364$	802332.	0.317395
$365$	1.36522e6	0.536379
$366$	2.25221e6	0.878833
$367$	−15817.2	−0.00613006	−0.00306503	−	0.999995i	$-0.500976\pi$
$367$	−15817.2	−0.00613006	−0.00306503	+	0.999995i	$0.500976\pi$
$368$	1.31554e6	0.506389
$369$	40915.0	0.0156429
$370$	−1.12134e6	−0.425828
$371$	2.08806e6	0.787606
$372$	1.99846e6	0.748753
$373$	3.63458e6	1.35264	0.676320	−	0.736608i	$-0.263574\pi$
$373$	3.63458e6	1.35264	0.676320	+	0.736608i	$0.263574\pi$
$374$	455167.	0.168264
$375$	238667.	0.0876423
$376$	−940063.	−0.342916
$377$	−835084.	−0.302605
$378$	4.63646e6	1.66900
$379$	−211476.	−0.0756246	−0.0378123	−	0.999285i	$-0.512039\pi$
$379$	−211476.	−0.0756246	−0.0378123	+	0.999285i	$0.512039\pi$
$380$	334822.	0.118948
$381$	4.28210e6	1.51128
$382$	−4.55213e6	−1.59609
$383$	4.71850e6	1.64364	0.821821	−	0.569745i	$-0.192958\pi$
$383$	4.71850e6	1.64364	0.821821	+	0.569745i	$0.192958\pi$
$384$	1.30922e6	0.453090
$385$	437144.	0.150305
$386$	8.08770e6	2.76285
$387$	153543.	0.0521138
$388$	946708.	0.319254
$389$	587350.	0.196799	0.0983995	−	0.995147i	$-0.468628\pi$
$389$	587350.	0.196799	0.0983995	+	0.995147i	$0.468628\pi$
$390$	−475047.	−0.158152
$391$	713120.	0.235896
$392$	−172790.	−0.0567942
$393$	1.95585e6	0.638785
$394$	1.70257e6	0.552541
$395$	2.40842e6	0.776674
$396$	−43473.0	−0.0139310
$397$	5.04581e6	1.60677	0.803387	−	0.595458i	$-0.203029\pi$
$397$	5.04581e6	1.60677	0.803387	+	0.595458i	$0.203029\pi$
$398$	−4.72733e6	−1.49592
$399$	796853.	0.250580
$400$	−521758.	−0.163050
$401$	1.36117e6	0.422720	0.211360	−	0.977408i	$-0.432211\pi$
$401$	1.36117e6	0.422720	0.211360	+	0.977408i	$0.432211\pi$
$402$	7.92448e6	2.44571
$403$	527769.	0.161876
$404$	3.73336e6	1.13801
$405$	−1.41505e6	−0.428680
$406$	6.70314e6	2.01820
$407$	652899.	0.195371
$408$	293009.	0.0871425
$409$	−5.49039e6	−1.62291	−0.811456	−	0.584413i	$-0.801325\pi$
$409$	−5.49039e6	−1.62291	−0.811456	+	0.584413i	$0.801325\pi$
$410$	877996.	0.257948
$411$	1.72106e6	0.502565
$412$	898038.	0.260646
$413$	7.19410e6	2.07540
$414$	−126858.	−0.0363763
$415$	1.66213e6	0.473745
$416$	1.24152e6	0.351739
$417$	6.04870e6	1.70342
$418$	−363103.	−0.101646
$419$	3.51298e6	0.977554	0.488777	−	0.872409i	$-0.337443\pi$
$419$	3.51298e6	0.977554	0.488777	+	0.872409i	$0.337443\pi$
$420$	2.04728e6	0.566311
$421$	−6.10129e6	−1.67771	−0.838854	−	0.544357i	$-0.816774\pi$
$421$	−6.10129e6	−1.67771	−0.838854	+	0.544357i	$0.816774\pi$
$422$	−6.03524e6	−1.64973
$423$	−214765.	−0.0583597
$424$	−612498.	−0.165459
$425$	−282832.	−0.0759550
$426$	−3.06052e6	−0.817092
$427$	−2.56329e6	−0.680345
$428$	−3.42405e6	−0.903506
$429$	276595.	0.0725608
$430$	3.29489e6	0.859348
$431$	5.19260e6	1.34645	0.673227	−	0.739436i	$-0.264908\pi$
$431$	5.19260e6	1.34645	0.673227	+	0.739436i	$0.264908\pi$
$432$	3.22210e6	0.830673
$433$	−519112.	−0.133058	−0.0665290	−	0.997784i	$-0.521193\pi$
$433$	−519112.	−0.133058	−0.0665290	+	0.997784i	$0.521193\pi$
$434$	−4.23636e6	−1.07961
$435$	−2.13086e6	−0.539922
$436$	3.46141e6	0.872041
$437$	−568881.	−0.142501
$438$	−6.93383e6	−1.72698
$439$	−5.78615e6	−1.43294	−0.716471	−	0.697617i	$-0.754244\pi$
$439$	−5.78615e6	−1.43294	−0.716471	+	0.697617i	$0.754244\pi$
$440$	−128229.	−0.0315758
$441$	−39475.4	−0.00966562
$442$	562955.	0.137062
$443$	−213703.	−0.0517369	−0.0258685	−	0.999665i	$-0.508235\pi$
$443$	−213703.	−0.0517369	−0.0258685	+	0.999665i	$0.508235\pi$
$444$	3.05774e6	0.736110
$445$	2.62684e6	0.628830
$446$	1.22436e6	0.291456
$447$	1.21512e6	0.287640
$448$	−6.10512e6	−1.43714
$449$	−4.31652e6	−1.01046	−0.505228	−	0.862986i	$-0.668592\pi$
$449$	−4.31652e6	−1.01046	−0.505228	+	0.862986i	$0.668592\pi$
$450$	50313.5	0.0117126
$451$	−511212.	−0.118348
$452$	865163.	0.199183
$453$	−1.39700e6	−0.319854
$454$	5.04580e6	1.14892
$455$	540663.	0.122433
$456$	−233743.	−0.0526414
$457$	1.25282e6	0.280607	0.140304	−	0.990109i	$-0.455192\pi$
$457$	1.25282e6	0.280607	0.140304	+	0.990109i	$0.455192\pi$
$458$	7.96654e6	1.77462
$459$	1.74662e6	0.386961
$460$	−1.46158e6	−0.322053
$461$	8.27626e6	1.81377	0.906885	−	0.421379i	$-0.138454\pi$
$461$	8.27626e6	1.81377	0.906885	+	0.421379i	$0.138454\pi$
$462$	−2.22021e6	−0.483937
$463$	−5.96762e6	−1.29374	−0.646872	−	0.762599i	$-0.723923\pi$
$463$	−5.96762e6	−1.29374	−0.646872	+	0.762599i	$0.723923\pi$
$464$	4.65835e6	1.00447
$465$	1.34669e6	0.288826
$466$	8.67229e6	1.84999
$467$	−704565.	−0.149496	−0.0747479	−	0.997202i	$-0.523815\pi$
$467$	−704565.	−0.149496	−0.0747479	+	0.997202i	$0.523815\pi$
$468$	−53767.8	−0.0113477
$469$	−9.01904e6	−1.89334
$470$	−4.60865e6	−0.962342
$471$	−1.12769e6	−0.234228
$472$	−2.11027e6	−0.435996
$473$	−1.91844e6	−0.394272
$474$	−1.22321e7	−2.50066
$475$	225625.	0.0458831
$476$	−2.42613e6	−0.490792
$477$	−139930.	−0.0281589
$478$	9.11199e6	1.82408
$479$	7.25452e6	1.44467	0.722337	−	0.691542i	$-0.243068\pi$
$479$	7.25452e6	1.44467	0.722337	+	0.691542i	$0.243068\pi$
$480$	3.16795e6	0.627588
$481$	807511.	0.159142
$482$	−1.91771e6	−0.375980
$483$	−3.47845e6	−0.678449
$484$	543173.	0.105396
$485$	637953.	0.123150
$486$	−609511.	−0.117055
$487$	−7.13952e6	−1.36410	−0.682051	−	0.731305i	$-0.738912\pi$
$487$	−7.13952e6	−1.36410	−0.682051	+	0.731305i	$0.738912\pi$
$488$	751900.	0.142926
$489$	−6.62698e6	−1.25327
$490$	−847103.	−0.159385
$491$	7.44840e6	1.39431	0.697155	−	0.716921i	$-0.254449\pi$
$491$	7.44840e6	1.39431	0.697155	+	0.716921i	$0.254449\pi$
$492$	−2.39417e6	−0.445905
$493$	2.52517e6	0.467922
$494$	−449089.	−0.0827970
$495$	−29294.9	−0.00537378
$496$	−2.94405e6	−0.537331
$497$	3.48325e6	0.632548
$498$	−8.44178e6	−1.52532
$499$	4.35232e6	0.782473	0.391237	−	0.920290i	$-0.372047\pi$
$499$	4.35232e6	0.782473	0.391237	+	0.920290i	$0.372047\pi$
$500$	579679.	0.103696
$501$	−2.75318e6	−0.490049
$502$	−2.40014e6	−0.425086
$503$	6.91716e6	1.21901	0.609506	−	0.792782i	$-0.291368\pi$
$503$	6.91716e6	1.21901	0.609506	+	0.792782i	$0.291368\pi$
$504$	59323.4	0.0104028
$505$	2.51578e6	0.438979
$506$	1.58503e6	0.275208
$507$	−5.32928e6	−0.920765
$508$	1.04005e7	1.78811
$509$	−2.06370e6	−0.353063	−0.176531	−	0.984295i	$-0.556488\pi$
$509$	−2.06370e6	−0.353063	−0.176531	+	0.984295i	$0.556488\pi$
$510$	1.43647e6	0.244553
$511$	7.89156e6	1.33694
$512$	−8.05797e6	−1.35847
$513$	−1.39334e6	−0.233757
$514$	−756058.	−0.126226
$515$	605156.	0.100542
$516$	−8.98468e6	−1.48552
$517$	2.68338e6	0.441525
$518$	−6.48182e6	−1.06138
$519$	1.62575e6	0.264932
$520$	−158594.	−0.0257205
$521$	−5.58895e6	−0.902061	−0.451030	−	0.892509i	$-0.648943\pi$
$521$	−5.58895e6	−0.902061	−0.451030	+	0.892509i	$0.648943\pi$
$522$	−449207.	−0.0721557
$523$	−8.76544e6	−1.40126	−0.700631	−	0.713523i	$-0.747098\pi$
$523$	−8.76544e6	−1.40126	−0.700631	+	0.713523i	$0.747098\pi$
$524$	4.75041e6	0.755793
$525$	1.37959e6	0.218450
$526$	−1.02665e7	−1.61793
$527$	−1.59590e6	−0.250310
$528$	−1.54293e6	−0.240859
$529$	−3.95305e6	−0.614176
$530$	−3.00277e6	−0.464336
$531$	−482109.	−0.0742008
$532$	1.93541e6	0.296479
$533$	−632271.	−0.0964018
$534$	−1.33414e7	−2.02465
$535$	−2.30735e6	−0.348521
$536$	2.64559e6	0.397750
$537$	−1.11705e7	−1.67162
$538$	1.40550e7	2.09351
$539$	493224.	0.0731261
$540$	−3.57979e6	−0.528291
$541$	5800.67	0.000852088 0	0.000426044	−	1.00000i	$-0.499864\pi$
$541$	5800.67	0.000852088 0	0.000426044		1.00000i	$0.499864\pi$
$542$	−2.89985e6	−0.424011
$543$	4.29677e6	0.625378
$544$	−3.75417e6	−0.543898
$545$	2.33252e6	0.336383
$546$	−2.74597e6	−0.394198
$547$	−8.46675e6	−1.20990	−0.604948	−	0.796265i	$-0.706806\pi$
$547$	−8.46675e6	−1.20990	−0.604948	+	0.796265i	$0.706806\pi$
$548$	4.18015e6	0.594621
$549$	171778.	0.0243241
$550$	−628641.	−0.0886127
$551$	−2.01442e6	−0.282664
$552$	1.02034e6	0.142528
$553$	1.39216e7	1.93588
$554$	−1.77396e7	−2.45566
$555$	2.06050e6	0.283949
$556$	1.46912e7	2.01544
$557$	4.43885e6	0.606223	0.303111	−	0.952955i	$-0.401975\pi$
$557$	4.43885e6	0.606223	0.303111	+	0.952955i	$0.401975\pi$
$558$	283897.	0.0385990
$559$	−2.37274e6	−0.321160
$560$	−3.01598e6	−0.406404
$561$	−836384.	−0.112201
$562$	−1.87037e7	−2.49796
$563$	−1.60757e6	−0.213746	−0.106873	−	0.994273i	$-0.534084\pi$
$563$	−1.60757e6	−0.213746	−0.106873	+	0.994273i	$0.534084\pi$
$564$	1.25671e7	1.66356
$565$	583003.	0.0768333
$566$	5.48890e6	0.720186
$567$	−8.17956e6	−1.06850
$568$	−1.02175e6	−0.132885
$569$	1.39520e7	1.80657	0.903285	−	0.429041i	$-0.141149\pi$
$569$	1.39520e7	1.80657	0.903285	+	0.429041i	$0.141149\pi$
$570$	−1.14593e6	−0.147730
$571$	−7.79325e6	−1.00030	−0.500148	−	0.865940i	$-0.666721\pi$
$571$	−7.79325e6	−1.00030	−0.500148	+	0.865940i	$0.666721\pi$
$572$	671801.	0.0858520
$573$	8.36469e6	1.06430
$574$	5.07518e6	0.642942
$575$	−984905.	−0.124229
$576$	409131.	0.0513814
$577$	−1.07957e6	−0.134994	−0.0674968	−	0.997719i	$-0.521501\pi$
$577$	−1.07957e6	−0.134994	−0.0674968	+	0.997719i	$0.521501\pi$
$578$	1.01004e7	1.25753
$579$	−1.48614e7	−1.84231
$580$	−5.17547e6	−0.638822
$581$	9.60780e6	1.18082
$582$	−3.24010e6	−0.396507
$583$	1.74836e6	0.213039
$584$	−2.31486e6	−0.280861
$585$	−36232.2	−0.00437729
$586$	−2.19219e7	−2.63715
$587$	−1.78108e6	−0.213348	−0.106674	−	0.994294i	$-0.534020\pi$
$587$	−1.78108e6	−0.213348	−0.106674	+	0.994294i	$0.534020\pi$
$588$	2.30993e6	0.275521
$589$	1.27310e6	0.151208
$590$	−1.03456e7	−1.22356
$591$	−3.12853e6	−0.368444
$592$	−4.50454e6	−0.528258
$593$	−1.18103e6	−0.137919	−0.0689594	−	0.997619i	$-0.521968\pi$
$593$	−1.18103e6	−0.137919	−0.0689594	+	0.997619i	$0.521968\pi$
$594$	3.88216e6	0.451447
$595$	−1.63489e6	−0.189319
$596$	2.95131e6	0.340329
$597$	8.68661e6	0.997504
$598$	1.96038e6	0.224175
$599$	−9.12577e6	−1.03921	−0.519604	−	0.854407i	$-0.673921\pi$
$599$	−9.12577e6	−1.03921	−0.519604	+	0.854407i	$0.673921\pi$
$600$	−404680.	−0.0458917
$601$	−5.83983e6	−0.659498	−0.329749	−	0.944069i	$-0.606964\pi$
$601$	−5.83983e6	−0.659498	−0.329749	+	0.944069i	$0.606964\pi$
$602$	1.90458e7	2.14194
$603$	604406.	0.0676917
$604$	−3.39306e6	−0.378442
$605$	366025.	0.0406558
$606$	−1.27774e7	−1.41338
$607$	−3.12003e6	−0.343706	−0.171853	−	0.985123i	$-0.554975\pi$
$607$	−3.12003e6	−0.343706	−0.171853	+	0.985123i	$0.554975\pi$
$608$	2.99484e6	0.328560
$609$	−1.23172e7	−1.34577
$610$	3.68618e6	0.401100
$611$	3.31883e6	0.359651
$612$	162586.	0.0175471
$613$	1.55349e7	1.66977	0.834884	−	0.550426i	$-0.185535\pi$
$613$	1.55349e7	1.66977	0.834884	+	0.550426i	$0.185535\pi$
$614$	−1.78014e7	−1.90561
$615$	−1.61335e6	−0.172004
$616$	−741215.	−0.0787032
$617$	6.56019e6	0.693751	0.346875	−	0.937911i	$-0.387243\pi$
$617$	6.56019e6	0.693751	0.346875	+	0.937911i	$0.387243\pi$
$618$	−3.07352e6	−0.323717
$619$	−5.92966e6	−0.622019	−0.311009	−	0.950407i	$-0.600667\pi$
$619$	−5.92966e6	−0.622019	−0.311009	+	0.950407i	$0.600667\pi$
$620$	3.27087e6	0.341731
$621$	6.08225e6	0.632901
$622$	7.65811e6	0.793680
$623$	1.51842e7	1.56737
$624$	−1.90831e6	−0.196195
$625$	390625.	0.0400000
$626$	−8.30174e6	−0.846707
$627$	667213.	0.0677791
$628$	−2.73896e6	−0.277132
$629$	−2.44180e6	−0.246084
$630$	290833.	0.0291939
$631$	1.18834e7	1.18813	0.594067	−	0.804415i	$-0.297521\pi$
$631$	1.18834e7	1.18813	0.594067	+	0.804415i	$0.297521\pi$
$632$	−4.08368e6	−0.406686
$633$	1.10899e7	1.10007
$634$	−2.48950e7	−2.45973
$635$	7.00850e6	0.689749
$636$	8.18812e6	0.802678
$637$	610024.	0.0595660
$638$	5.61261e6	0.545900
$639$	−233428.	−0.0226152
$640$	2.14279e6	0.206790
$641$	3.81827e6	0.367047	0.183523	−	0.983015i	$-0.441250\pi$
$641$	3.81827e6	0.367047	0.183523	+	0.983015i	$0.441250\pi$
$642$	1.17188e7	1.12213
$643$	6.27799e6	0.598816	0.299408	−	0.954125i	$-0.403211\pi$
$643$	6.27799e6	0.598816	0.299408	+	0.954125i	$0.403211\pi$
$644$	−8.44852e6	−0.802723
$645$	−6.05446e6	−0.573028
$646$	1.35798e6	0.128030
$647$	−1.77005e7	−1.66235	−0.831177	−	0.556008i	$-0.812333\pi$
$647$	−1.77005e7	−1.66235	−0.831177	+	0.556008i	$0.812333\pi$
$648$	2.39934e6	0.224468
$649$	6.02369e6	0.561373
$650$	−777508.	−0.0721808
$651$	7.78444e6	0.719904
$652$	−1.60957e7	−1.48283
$653$	−1.03655e7	−0.951281	−0.475640	−	0.879640i	$-0.657784\pi$
$653$	−1.03655e7	−0.951281	−0.475640	+	0.879640i	$0.657784\pi$
$654$	−1.18466e7	−1.08305
$655$	3.20113e6	0.291542
$656$	3.52699e6	0.319996
$657$	−528849.	−0.0477989
$658$	−2.66399e7	−2.39866
$659$	−8.65946e6	−0.776743	−0.388372	−	0.921503i	$-0.626962\pi$
$659$	−8.65946e6	−0.776743	−0.388372	+	0.921503i	$0.626962\pi$
$660$	1.71421e6	0.153181
$661$	−6.44121e6	−0.573408	−0.286704	−	0.958019i	$-0.592560\pi$
$661$	−6.44121e6	−0.573408	−0.286704	+	0.958019i	$0.592560\pi$
$662$	1.48155e7	1.31393
$663$	−1.03445e6	−0.0913954
$664$	−2.81829e6	−0.248065
$665$	1.30421e6	0.114365
$666$	434376.	0.0379472
$667$	8.79339e6	0.765318
$668$	−6.68697e6	−0.579814
$669$	−2.24981e6	−0.194348
$670$	1.29700e7	1.11623
$671$	−2.14627e6	−0.184026
$672$	1.83120e7	1.56428
$673$	−2.42363e6	−0.206267	−0.103133	−	0.994668i	$-0.532887\pi$
$673$	−2.42363e6	−0.206267	−0.103133	+	0.994668i	$0.532887\pi$
$674$	−2.24671e7	−1.90501
$675$	−2.41229e6	−0.203784
$676$	−1.29439e7	−1.08943
$677$	3.74875e6	0.314351	0.157176	−	0.987571i	$-0.449761\pi$
$677$	3.74875e6	0.314351	0.157176	+	0.987571i	$0.449761\pi$
$678$	−2.96101e6	−0.247381
$679$	3.68763e6	0.306954
$680$	479566.	0.0397719
$681$	−9.27181e6	−0.766120
$682$	−3.54715e6	−0.292024
$683$	−143822.	−0.0117971	−0.00589853	−	0.999983i	$-0.501878\pi$
$683$	−143822.	−0.0117971	−0.00589853	+	0.999983i	$0.501878\pi$
$684$	−129701.	−0.0105999
$685$	2.81685e6	0.229371
$686$	1.52929e7	1.24074
$687$	−1.46388e7	−1.18335
$688$	1.32359e7	1.06606
$689$	2.16238e6	0.173534
$690$	5.00223e6	0.399982
$691$	−1.67134e7	−1.33159	−0.665796	−	0.746134i	$-0.731908\pi$
$691$	−1.67134e7	−1.33159	−0.665796	+	0.746134i	$0.731908\pi$
$692$	3.94865e6	0.313461
$693$	−169337.	−0.0133943
$694$	−2.81893e7	−2.22170
$695$	9.89988e6	0.777442
$696$	3.61305e6	0.282717
$697$	1.91189e6	0.149067
$698$	−1.29693e7	−1.00758
$699$	−1.59356e7	−1.23360
$700$	3.35078e6	0.258465
$701$	−1.21856e7	−0.936596	−0.468298	−	0.883570i	$-0.655133\pi$
$701$	−1.21856e7	−0.936596	−0.468298	+	0.883570i	$0.655133\pi$
$702$	4.80148e6	0.367733
$703$	1.94791e6	0.148655
$704$	−5.11188e6	−0.388731
$705$	8.46854e6	0.641706
$706$	1.16699e7	0.881164
$707$	1.45422e7	1.09416
$708$	2.82109e7	2.11511
$709$	2.51606e7	1.87977	0.939886	−	0.341487i	$-0.110931\pi$
$709$	2.51606e7	1.87977	0.939886	+	0.341487i	$0.110931\pi$
$710$	−5.00914e6	−0.372921
$711$	−932951.	−0.0692125
$712$	−4.45403e6	−0.329271
$713$	−5.55739e6	−0.409399
$714$	8.30341e6	0.609552
$715$	452703.	0.0331168
$716$	−2.71312e7	−1.97782
$717$	−1.67436e7	−1.21633
$718$	2.89767e7	2.09767
$719$	2.18874e7	1.57897	0.789483	−	0.613772i	$-0.210349\pi$
$719$	2.18874e7	1.57897	0.789483	+	0.613772i	$0.210349\pi$
$720$	202114.	0.0145300
$721$	3.49805e6	0.250604
$722$	−1.08331e6	−0.0773408
$723$	3.52385e6	0.250710
$724$	1.04361e7	0.739930
$725$	−3.48756e6	−0.246421
$726$	−1.85900e6	−0.130900
$727$	−8.87194e6	−0.622562	−0.311281	−	0.950318i	$-0.600758\pi$
$727$	−8.87194e6	−0.622562	−0.311281	+	0.950318i	$0.600758\pi$
$728$	−916741.	−0.0641089
$729$	1.48743e7	1.03661
$730$	−1.13486e7	−0.788196
$731$	7.17483e6	0.496613
$732$	−1.00517e7	−0.693364
$733$	−5.23841e6	−0.360114	−0.180057	−	0.983656i	$-0.557628\pi$
$733$	−5.23841e6	−0.360114	−0.180057	+	0.983656i	$0.557628\pi$
$734$	131482.	0.00900797
$735$	1.55658e6	0.106280
$736$	−1.30732e7	−0.889581
$737$	−7.55174e6	−0.512128
$738$	−340110.	−0.0229868
$739$	−1.17409e7	−0.790842	−0.395421	−	0.918500i	$-0.629401\pi$
$739$	−1.17409e7	−0.790842	−0.395421	+	0.918500i	$0.629401\pi$
$740$	5.00459e6	0.335961
$741$	825215.	0.0552105
$742$	−1.73572e7	−1.15737
$743$	−1.41556e6	−0.0940708	−0.0470354	−	0.998893i	$-0.514977\pi$
$743$	−1.41556e6	−0.0940708	−0.0470354	+	0.998893i	$0.514977\pi$
$744$	−2.28343e6	−0.151236
$745$	1.98878e6	0.131279
$746$	−3.02128e7	−1.98767
$747$	−643861.	−0.0422173
$748$	−2.03143e6	−0.132754
$749$	−1.33374e7	−0.868695
$750$	−1.98394e6	−0.128788
$751$	1.50124e7	0.971296	0.485648	−	0.874155i	$-0.338584\pi$
$751$	1.50124e7	0.971296	0.485648	+	0.874155i	$0.338584\pi$
$752$	−1.85134e7	−1.19383
$753$	4.41033e6	0.283454
$754$	6.94172e6	0.444671
$755$	−2.28647e6	−0.145981
$756$	−2.06927e7	−1.31678
$757$	1.82652e7	1.15847	0.579234	−	0.815161i	$-0.303352\pi$
$757$	1.82652e7	1.15847	0.579234	+	0.815161i	$0.303352\pi$
$758$	1.75792e6	0.111128
$759$	−2.91254e6	−0.183513
$760$	−382567.	−0.0240256
$761$	6.48329e6	0.405820	0.202910	−	0.979197i	$-0.434960\pi$
$761$	6.48329e6	0.405820	0.202910	+	0.979197i	$0.434960\pi$
$762$	−3.55955e7	−2.22079
$763$	1.34829e7	0.838442
$764$	2.03163e7	1.25925
$765$	109561.	0.00676865
$766$	−3.92231e7	−2.41529
$767$	7.45015e6	0.457274
$768$	9.76683e6	0.597517
$769$	−2.97931e7	−1.81677	−0.908385	−	0.418134i	$-0.862684\pi$
$769$	−2.97931e7	−1.81677	−0.908385	+	0.418134i	$0.862684\pi$
$770$	−3.63380e6	−0.220869
$771$	1.38928e6	0.0841693
$772$	−3.60957e7	−2.17978
$773$	−1.89506e7	−1.14071	−0.570354	−	0.821399i	$-0.693194\pi$
$773$	−1.89506e7	−1.14071	−0.570354	+	0.821399i	$0.693194\pi$
$774$	−1.27634e6	−0.0765800
$775$	2.20413e6	0.131820
$776$	−1.08170e6	−0.0644844
$777$	1.19106e7	0.707749
$778$	−4.88241e6	−0.289191
$779$	−1.52518e6	−0.0900490
$780$	2.12015e6	0.124776
$781$	2.91656e6	0.171097
$782$	−5.92789e6	−0.346644
$783$	2.15374e7	1.25542
$784$	−3.40289e6	−0.197724
$785$	−1.84569e6	−0.106902
$786$	−1.62582e7	−0.938678
$787$	−1.20848e7	−0.695509	−0.347755	−	0.937586i	$-0.613056\pi$
$787$	−1.20848e7	−0.695509	−0.347755	+	0.937586i	$0.613056\pi$
$788$	−7.59863e6	−0.435933
$789$	1.88651e7	1.07886
$790$	−2.00202e7	−1.14130
$791$	3.37000e6	0.191509
$792$	49672.1	0.00281384
$793$	−2.65453e6	−0.149901
$794$	−4.19438e7	−2.36111
$795$	5.51768e6	0.309627
$796$	2.10982e7	1.18022
$797$	3.27584e7	1.82674	0.913369	−	0.407132i	$-0.133471\pi$
$797$	3.27584e7	1.82674	0.913369	+	0.407132i	$0.133471\pi$
$798$	−6.62392e6	−0.368221
$799$	−1.00356e7	−0.556132
$800$	5.18497e6	0.286432
$801$	−1.01756e6	−0.0560376
$802$	−1.13149e7	−0.621177
$803$	6.60769e6	0.361627
$804$	−3.53672e7	−1.92957
$805$	−5.69316e6	−0.309645
$806$	−4.38714e6	−0.237872
$807$	−2.58265e7	−1.39599
$808$	−4.26572e6	−0.229860
$809$	−418811.	−0.0224981	−0.0112491	−	0.999937i	$-0.503581\pi$
$809$	−418811.	−0.0224981	−0.0112491	+	0.999937i	$0.503581\pi$
$810$	1.17627e7	0.629935
$811$	−1.53182e7	−0.817816	−0.408908	−	0.912576i	$-0.634090\pi$
$811$	−1.53182e7	−0.817816	−0.408908	+	0.912576i	$0.634090\pi$
$812$	−2.99163e7	−1.59228
$813$	5.32857e6	0.282738
$814$	−5.42730e6	−0.287093
$815$	−1.08463e7	−0.571992
$816$	5.77045e6	0.303378
$817$	−5.72361e6	−0.299996
$818$	4.56395e7	2.38483
$819$	−209437.	−0.0109105
$820$	−3.91853e6	−0.203511
$821$	5.86110e6	0.303474	0.151737	−	0.988421i	$-0.451513\pi$
$821$	5.86110e6	0.303474	0.151737	+	0.988421i	$0.451513\pi$
$822$	−1.43065e7	−0.738506
$823$	−6.79481e6	−0.349685	−0.174843	−	0.984596i	$-0.555942\pi$
$823$	−6.79481e6	−0.349685	−0.174843	+	0.984596i	$0.555942\pi$
$824$	−1.02609e6	−0.0526465
$825$	1.15515e6	0.0590884
$826$	−5.98017e7	−3.04975
$827$	2.02224e7	1.02818	0.514089	−	0.857737i	$-0.328130\pi$
$827$	2.02224e7	1.02818	0.514089	+	0.857737i	$0.328130\pi$
$828$	566173.	0.0286994
$829$	−2.39427e7	−1.21000	−0.605001	−	0.796225i	$-0.706827\pi$
$829$	−2.39427e7	−1.21000	−0.605001	+	0.796225i	$0.706827\pi$
$830$	−1.38166e7	−0.696157
$831$	3.25970e7	1.63748
$832$	−6.32241e6	−0.316646
$833$	−1.84462e6	−0.0921075
$834$	−5.02805e7	−2.50313
$835$	−4.50611e6	−0.223659
$836$	1.62054e6	0.0801944
$837$	−1.36115e7	−0.671573
$838$	−2.92020e7	−1.43649
$839$	−2.67950e7	−1.31416	−0.657082	−	0.753819i	$-0.728209\pi$
$839$	−2.67950e7	−1.31416	−0.657082	+	0.753819i	$0.728209\pi$
$840$	−2.33922e6	−0.114386
$841$	1.06264e7	0.518080
$842$	5.07176e7	2.46535
$843$	3.43686e7	1.66569
$844$	2.69355e7	1.30157
$845$	−8.72242e6	−0.420238
$846$	1.78526e6	0.0857581
$847$	2.11578e6	0.101335
$848$	−1.20624e7	−0.576029
$849$	−1.00860e7	−0.480232
$850$	2.35107e6	0.111614
$851$	−8.50306e6	−0.402487
$852$	1.36592e7	0.644653
$853$	−7.25689e6	−0.341490	−0.170745	−	0.985315i	$-0.554617\pi$
$853$	−7.25689e6	−0.341490	−0.170745	+	0.985315i	$0.554617\pi$
$854$	2.13077e7	0.999749
$855$	−87400.6	−0.00408883
$856$	3.91231e6	0.182494
$857$	1.49956e7	0.697447	0.348724	−	0.937226i	$-0.386615\pi$
$857$	1.49956e7	0.697447	0.348724	+	0.937226i	$0.386615\pi$
$858$	−2.29923e6	−0.106626
$859$	−1.18741e7	−0.549058	−0.274529	−	0.961579i	$-0.588522\pi$
$859$	−1.18741e7	−0.549058	−0.274529	+	0.961579i	$0.588522\pi$
$860$	−1.47052e7	−0.677992
$861$	−9.32580e6	−0.428724
$862$	−4.31640e7	−1.97858
$863$	2.95825e7	1.35210	0.676049	−	0.736857i	$-0.263691\pi$
$863$	2.95825e7	1.35210	0.676049	+	0.736857i	$0.263691\pi$
$864$	−3.20196e7	−1.45926
$865$	2.66085e6	0.120915
$866$	4.31517e6	0.195526
$867$	−1.85598e7	−0.838545
$868$	1.89070e7	0.851772
$869$	1.16567e7	0.523634
$870$	1.77130e7	0.793402
$871$	−9.34005e6	−0.417161
$872$	−3.95499e6	−0.176139
$873$	−247125.	−0.0109744
$874$	4.72889e6	0.209402
$875$	2.25797e6	0.0997008
$876$	3.09459e7	1.36252
$877$	3.83287e7	1.68277	0.841385	−	0.540437i	$-0.181741\pi$
$877$	3.83287e7	1.68277	0.841385	+	0.540437i	$0.181741\pi$
$878$	4.80980e7	2.10567
$879$	4.02822e7	1.75849
$880$	−2.52531e6	−0.109928
$881$	4.55924e7	1.97903	0.989516	−	0.144421i	$-0.0461318\pi$
$881$	4.55924e7	1.97903	0.989516	+	0.144421i	$0.0461318\pi$
$882$	328143.	0.0142034
$883$	−2.86236e7	−1.23544	−0.617721	−	0.786397i	$-0.711944\pi$
$883$	−2.86236e7	−1.23544	−0.617721	+	0.786397i	$0.711944\pi$
$884$	−2.51249e6	−0.108137
$885$	1.90103e7	0.815890
$886$	1.77643e6	0.0760261
$887$	2.58691e7	1.10401	0.552004	−	0.833841i	$-0.313863\pi$
$887$	2.58691e7	1.10401	0.552004	+	0.833841i	$0.313863\pi$
$888$	−3.49376e6	−0.148683
$889$	4.05120e7	1.71921
$890$	−2.18359e7	−0.924051
$891$	−6.84883e6	−0.289016
$892$	−5.46437e6	−0.229947
$893$	8.00578e6	0.335950
$894$	−1.01008e7	−0.422680
$895$	−1.82827e7	−0.762928
$896$	1.23862e7	0.515429
$897$	−3.60225e6	−0.149483
$898$	3.58815e7	1.48484
$899$	−1.96788e7	−0.812081
$900$	−224551.	−0.00924078
$901$	−6.53873e6	−0.268337
$902$	4.24950e6	0.173909
$903$	−3.49973e7	−1.42828
$904$	−988532.	−0.0402318
$905$	7.03250e6	0.285423
$906$	1.16127e7	0.470017
$907$	2.21374e7	0.893530	0.446765	−	0.894651i	$-0.352576\pi$
$907$	2.21374e7	0.893530	0.446765	+	0.894651i	$0.352576\pi$
$908$	−2.25196e7	−0.906453
$909$	−974540.	−0.0391192
$910$	−4.49432e6	−0.179912
$911$	3.19542e7	1.27565	0.637826	−	0.770180i	$-0.279834\pi$
$911$	3.19542e7	1.27565	0.637826	+	0.770180i	$0.279834\pi$
$912$	−4.60329e6	−0.183266
$913$	8.04471e6	0.319399
$914$	−1.04142e7	−0.412345
$915$	−6.77348e6	−0.267460
$916$	−3.55549e7	−1.40011
$917$	1.85039e7	0.726674
$918$	−1.45190e7	−0.568629
$919$	1.36287e7	0.532312	0.266156	−	0.963930i	$-0.414246\pi$
$919$	1.36287e7	0.532312	0.266156	+	0.963930i	$0.414246\pi$
$920$	1.66999e6	0.0650496
$921$	3.27107e7	1.27069
$922$	−6.87973e7	−2.66529
$923$	3.60723e6	0.139370
$924$	9.90886e6	0.381807
$925$	3.37241e6	0.129595
$926$	4.96064e7	1.90112
$927$	−234420.	−0.00895974
$928$	−4.62922e7	−1.76457
$929$	−3.24341e7	−1.23300	−0.616500	−	0.787355i	$-0.711450\pi$
$929$	−3.24341e7	−1.23300	−0.616500	+	0.787355i	$0.711450\pi$
$930$	−1.11945e7	−0.424422
$931$	1.47152e6	0.0556406
$932$	−3.87047e7	−1.45957
$933$	−1.40720e7	−0.529239
$934$	5.85677e6	0.219680
$935$	−1.36891e6	−0.0512088
$936$	61434.9	0.00229206
$937$	6.00578e6	0.223471	0.111735	−	0.993738i	$-0.464359\pi$
$937$	6.00578e6	0.223471	0.111735	+	0.993738i	$0.464359\pi$
$938$	7.49718e7	2.78222
$939$	1.52547e7	0.564599
$940$	2.05686e7	0.759249
$941$	−1.83774e7	−0.676565	−0.338283	−	0.941045i	$-0.609846\pi$
$941$	−1.83774e7	−0.676565	−0.338283	+	0.941045i	$0.609846\pi$
$942$	9.37406e6	0.344192
$943$	6.65778e6	0.243809
$944$	−4.15592e7	−1.51788
$945$	−1.39441e7	−0.507937
$946$	1.59472e7	0.579373
$947$	4.10164e6	0.148622	0.0743109	−	0.997235i	$-0.476324\pi$
$947$	4.10164e6	0.148622	0.0743109	+	0.997235i	$0.476324\pi$
$948$	5.45922e7	1.97292
$949$	8.17244e6	0.294569
$950$	−1.87553e6	−0.0674242
$951$	4.57453e7	1.64019
$952$	2.77209e6	0.0991323
$953$	−4.42519e7	−1.57834	−0.789169	−	0.614176i	$-0.789488\pi$
$953$	−4.42519e7	−1.57834	−0.789169	+	0.614176i	$0.789488\pi$
$954$	1.16319e6	0.0413788
$955$	1.36904e7	0.485746
$956$	−4.06671e7	−1.43912
$957$	−1.03133e7	−0.364015
$958$	−6.03039e7	−2.12291
$959$	1.62826e7	0.571711
$960$	−1.61327e7	−0.564975
$961$	−1.61922e7	−0.565585
$962$	−6.71253e6	−0.233856
$963$	893800.	0.0310581
$964$	8.55880e6	0.296634
$965$	−2.43236e7	−0.840833
$966$	2.89150e7	0.996964
$967$	−3.43048e7	−1.17975	−0.589873	−	0.807496i	$-0.700822\pi$
$967$	−3.43048e7	−1.17975	−0.589873	+	0.807496i	$0.700822\pi$
$968$	−620627.	−0.0212884
$969$	−2.49533e6	−0.0853725
$970$	−5.30305e6	−0.180966
$971$	−1.83942e6	−0.0626085	−0.0313043	−	0.999510i	$-0.509966\pi$
$971$	−1.83942e6	−0.0626085	−0.0313043	+	0.999510i	$0.509966\pi$
$972$	2.72027e6	0.0923520
$973$	5.72254e7	1.93779
$974$	5.93480e7	2.00451
$975$	1.42870e6	0.0481314
$976$	1.48078e7	0.497582
$977$	−3.31525e6	−0.111117	−0.0555585	−	0.998455i	$-0.517694\pi$
$977$	−3.31525e6	−0.111117	−0.0555585	+	0.998455i	$0.517694\pi$
$978$	5.50875e7	1.84164
$979$	1.27139e7	0.423957
$980$	3.78065e6	0.125748
$981$	−903551.	−0.0299765
$982$	−6.19156e7	−2.04890
$983$	3.31695e7	1.09485	0.547426	−	0.836854i	$-0.315608\pi$
$983$	3.31695e7	1.09485	0.547426	+	0.836854i	$0.315608\pi$
$984$	2.73557e6	0.0900657
$985$	−5.12045e6	−0.168158
$986$	−2.09907e7	−0.687600
$987$	4.89517e7	1.59946
$988$	2.00430e6	0.0653236
$989$	2.49849e7	0.812244
$990$	243517.	0.00789663
$991$	−4.41671e7	−1.42861	−0.714307	−	0.699832i	$-0.753258\pi$
$991$	−4.41671e7	−1.42861	−0.714307	+	0.699832i	$0.753258\pi$
$992$	2.92565e7	0.943937
$993$	−2.72239e7	−0.876149
$994$	−2.89549e7	−0.929514
$995$	1.42173e7	0.455261
$996$	3.76760e7	1.20342
$997$	−3.02212e6	−0.0962883	−0.0481441	−	0.998840i	$-0.515331\pi$
$997$	−3.02212e6	−0.0962883	−0.0481441	+	0.998840i	$0.515331\pi$
$998$	−3.61791e7	−1.14982
$999$	−2.08263e7	−0.660233

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.h.1.6	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.h.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-8.31261 q^{2} +15.2747 q^{3} +37.0994 q^{4} +25.0000 q^{5} -126.972 q^{6} +144.510 q^{7} -42.3897 q^{8} -9.68428 q^{9} +O(q^{10})\)	\(q-8.31261 q^{2} +15.2747 q^{3} +37.0994 q^{4} +25.0000 q^{5} -126.972 q^{6} +144.510 q^{7} -42.3897 q^{8} -9.68428 q^{9} -207.815 q^{10} +121.000 q^{11} +566.682 q^{12} +149.654 q^{13} -1201.26 q^{14} +381.867 q^{15} -834.813 q^{16} -452.531 q^{17} +80.5016 q^{18} +361.000 q^{19} +927.486 q^{20} +2207.35 q^{21} -1005.83 q^{22} -1575.85 q^{23} -647.489 q^{24} +625.000 q^{25} -1244.01 q^{26} -3859.67 q^{27} +5361.25 q^{28} -5580.10 q^{29} -3174.31 q^{30} +3526.60 q^{31} +8295.95 q^{32} +1848.24 q^{33} +3761.71 q^{34} +3612.76 q^{35} -359.281 q^{36} +5395.86 q^{37} -3000.85 q^{38} +2285.91 q^{39} -1059.74 q^{40} -4224.89 q^{41} -18348.8 q^{42} -15854.9 q^{43} +4489.03 q^{44} -242.107 q^{45} +13099.4 q^{46} +22176.7 q^{47} -12751.5 q^{48} +4076.23 q^{49} -5195.38 q^{50} -6912.27 q^{51} +5552.07 q^{52} +14449.2 q^{53} +32083.9 q^{54} +3025.00 q^{55} -6125.75 q^{56} +5514.16 q^{57} +46385.2 q^{58} +49782.6 q^{59} +14167.0 q^{60} -17737.8 q^{61} -29315.3 q^{62} -1399.48 q^{63} -42246.9 q^{64} +3741.34 q^{65} -15363.7 q^{66} -62411.1 q^{67} -16788.7 q^{68} -24070.6 q^{69} -30031.4 q^{70} +24103.8 q^{71} +410.514 q^{72} +54609.0 q^{73} -44853.7 q^{74} +9546.67 q^{75} +13392.9 q^{76} +17485.7 q^{77} -19001.9 q^{78} +96336.6 q^{79} -20870.3 q^{80} -56601.9 q^{81} +35119.8 q^{82} +66485.2 q^{83} +81891.4 q^{84} -11313.3 q^{85} +131795. q^{86} -85234.3 q^{87} -5129.15 q^{88} +105074. q^{89} +2012.54 q^{90} +21626.5 q^{91} -58463.1 q^{92} +53867.7 q^{93} -184346. q^{94} +9025.00 q^{95} +126718. q^{96} +25518.1 q^{97} -33884.1 q^{98} -1171.80 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more