LMFDB - Embedded newform 29.6.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,6,Mod(1,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	29.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:	$4.65113077458$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 184x^{5} + 584x^{4} + 10145x^{3} - 34491x^{2} - 149754x + 524902 $ x^7 - 3x^6 - 184x^5 + 584x^4 + 10145x^3 - 34491x^2 - 149754x + 524902
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$3.60554$ of defining polynomial
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.60554 q^{2} -13.2844 q^{3} -25.2112 q^{4} +69.0035 q^{5} +34.6131 q^{6} +156.573 q^{7} +149.066 q^{8} -66.5241 q^{9} +O(q^{10})$	\(q-2.60554 q^{2} -13.2844 q^{3} -25.2112 q^{4} +69.0035 q^{5} +34.6131 q^{6} +156.573 q^{7} +149.066 q^{8} -66.5241 q^{9} -179.792 q^{10} +424.515 q^{11} +334.916 q^{12} +44.7757 q^{13} -407.958 q^{14} -916.672 q^{15} +418.359 q^{16} +1380.18 q^{17} +173.331 q^{18} -1119.92 q^{19} -1739.66 q^{20} -2079.98 q^{21} -1106.09 q^{22} -39.2926 q^{23} -1980.26 q^{24} +1636.49 q^{25} -116.665 q^{26} +4111.85 q^{27} -3947.39 q^{28} +841.000 q^{29} +2388.43 q^{30} +8689.59 q^{31} -5860.17 q^{32} -5639.44 q^{33} -3596.13 q^{34} +10804.1 q^{35} +1677.15 q^{36} +2453.17 q^{37} +2918.00 q^{38} -594.820 q^{39} +10286.1 q^{40} -12411.4 q^{41} +5419.48 q^{42} +21380.8 q^{43} -10702.5 q^{44} -4590.40 q^{45} +102.378 q^{46} -7829.13 q^{47} -5557.66 q^{48} +7708.15 q^{49} -4263.94 q^{50} -18334.9 q^{51} -1128.85 q^{52} -33959.8 q^{53} -10713.6 q^{54} +29293.1 q^{55} +23339.7 q^{56} +14877.5 q^{57} -2191.26 q^{58} -27038.1 q^{59} +23110.4 q^{60} +7571.94 q^{61} -22641.1 q^{62} -10415.9 q^{63} +1881.42 q^{64} +3089.68 q^{65} +14693.8 q^{66} -54383.1 q^{67} -34796.0 q^{68} +521.979 q^{69} -28150.5 q^{70} +80884.6 q^{71} -9916.48 q^{72} -45517.8 q^{73} -6391.83 q^{74} -21739.8 q^{75} +28234.5 q^{76} +66467.7 q^{77} +1549.83 q^{78} +68029.7 q^{79} +28868.3 q^{80} -38458.2 q^{81} +32338.4 q^{82} +32492.4 q^{83} +52438.8 q^{84} +95237.5 q^{85} -55708.5 q^{86} -11172.2 q^{87} +63280.8 q^{88} -31236.8 q^{89} +11960.5 q^{90} +7010.68 q^{91} +990.611 q^{92} -115436. q^{93} +20399.1 q^{94} -77278.5 q^{95} +77848.9 q^{96} -108828. q^{97} -20083.9 q^{98} -28240.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 4 q^{2} + 26 q^{3} + 154 q^{4} + 32 q^{5} + 22 q^{6} + 184 q^{7} + 942 q^{8} + 1005 q^{9}+O(q^{10}) $ 7 * q + 4 * q^2 + 26 * q^3 + 154 * q^4 + 32 * q^5 + 22 * q^6 + 184 * q^7 + 942 * q^8 + 1005 * q^9	\( 7 q + 4 q^{2} + 26 q^{3} + 154 q^{4} + 32 q^{5} + 22 q^{6} + 184 q^{7} + 942 q^{8} + 1005 q^{9} + 922 q^{10} + 1106 q^{11} + 214 q^{12} + 408 q^{13} - 2008 q^{14} - 614 q^{15} + 242 q^{16} - 874 q^{17} - 5598 q^{18} + 4288 q^{19} - 6350 q^{20} - 4200 q^{21} - 6114 q^{22} - 4532 q^{23} - 4318 q^{24} + 5527 q^{25} - 19806 q^{26} + 5942 q^{27} - 496 q^{28} + 5887 q^{29} - 16734 q^{30} + 7794 q^{31} + 7898 q^{32} + 34410 q^{33} + 20840 q^{34} + 7088 q^{35} - 572 q^{36} + 5086 q^{37} + 23732 q^{38} + 33394 q^{39} + 22906 q^{40} + 19826 q^{41} - 55440 q^{42} + 19498 q^{43} - 6074 q^{44} + 7854 q^{45} - 12404 q^{46} + 14278 q^{47} - 16406 q^{48} + 38431 q^{49} - 41066 q^{50} + 23892 q^{51} - 34302 q^{52} - 58644 q^{53} - 31194 q^{54} - 25574 q^{55} - 79560 q^{56} - 88540 q^{57} + 3364 q^{58} + 12888 q^{59} - 180822 q^{60} + 102866 q^{61} - 42654 q^{62} - 88632 q^{63} - 10170 q^{64} - 149206 q^{65} + 7710 q^{66} + 102996 q^{67} + 85100 q^{68} - 107244 q^{69} + 349480 q^{70} - 51596 q^{71} + 135568 q^{72} - 17566 q^{73} + 12132 q^{74} + 39356 q^{75} + 360740 q^{76} - 94104 q^{77} + 46386 q^{78} + 212058 q^{79} + 142510 q^{80} - 128285 q^{81} + 201924 q^{82} - 122928 q^{83} - 12328 q^{84} - 109336 q^{85} - 63290 q^{86} + 21866 q^{87} + 136666 q^{88} - 66510 q^{89} + 56084 q^{90} + 194368 q^{91} - 110108 q^{92} - 474274 q^{93} + 438926 q^{94} - 131676 q^{95} - 117018 q^{96} - 118182 q^{97} - 29132 q^{98} + 300668 q^{99}+O(q^{100}) \) 7 * q + 4 * q^2 + 26 * q^3 + 154 * q^4 + 32 * q^5 + 22 * q^6 + 184 * q^7 + 942 * q^8 + 1005 * q^9 + 922 * q^10 + 1106 * q^11 + 214 * q^12 + 408 * q^13 - 2008 * q^14 - 614 * q^15 + 242 * q^16 - 874 * q^17 - 5598 * q^18 + 4288 * q^19 - 6350 * q^20 - 4200 * q^21 - 6114 * q^22 - 4532 * q^23 - 4318 * q^24 + 5527 * q^25 - 19806 * q^26 + 5942 * q^27 - 496 * q^28 + 5887 * q^29 - 16734 * q^30 + 7794 * q^31 + 7898 * q^32 + 34410 * q^33 + 20840 * q^34 + 7088 * q^35 - 572 * q^36 + 5086 * q^37 + 23732 * q^38 + 33394 * q^39 + 22906 * q^40 + 19826 * q^41 - 55440 * q^42 + 19498 * q^43 - 6074 * q^44 + 7854 * q^45 - 12404 * q^46 + 14278 * q^47 - 16406 * q^48 + 38431 * q^49 - 41066 * q^50 + 23892 * q^51 - 34302 * q^52 - 58644 * q^53 - 31194 * q^54 - 25574 * q^55 - 79560 * q^56 - 88540 * q^57 + 3364 * q^58 + 12888 * q^59 - 180822 * q^60 + 102866 * q^61 - 42654 * q^62 - 88632 * q^63 - 10170 * q^64 - 149206 * q^65 + 7710 * q^66 + 102996 * q^67 + 85100 * q^68 - 107244 * q^69 + 349480 * q^70 - 51596 * q^71 + 135568 * q^72 - 17566 * q^73 + 12132 * q^74 + 39356 * q^75 + 360740 * q^76 - 94104 * q^77 + 46386 * q^78 + 212058 * q^79 + 142510 * q^80 - 128285 * q^81 + 201924 * q^82 - 122928 * q^83 - 12328 * q^84 - 109336 * q^85 - 63290 * q^86 + 21866 * q^87 + 136666 * q^88 - 66510 * q^89 + 56084 * q^90 + 194368 * q^91 - 110108 * q^92 - 474274 * q^93 + 438926 * q^94 - 131676 * q^95 - 117018 * q^96 - 118182 * q^97 - 29132 * q^98 + 300668 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.60554	−0.460599	−0.230300	−	0.973120i	$-0.573971\pi$
$2$	−2.60554	−0.460599	−0.230300	+	0.973120i	$0.573971\pi$
$3$	−13.2844	−0.852196	−0.426098	−	0.904677i	$-0.640112\pi$
$3$	−13.2844	−0.852196	−0.426098	+	0.904677i	$0.640112\pi$
$4$	−25.2112	−0.787849
$5$	69.0035	1.23437	0.617186	−	0.786817i	$-0.288272\pi$
$5$	69.0035	1.23437	0.617186	+	0.786817i	$0.288272\pi$
$6$	34.6131	0.392521
$7$	156.573	1.20774	0.603868	−	0.797084i	$-0.293625\pi$
$7$	156.573	1.20774	0.603868	+	0.797084i	$0.293625\pi$
$8$	149.066	0.823481
$9$	−66.5241	−0.273762
$10$	−179.792	−0.568551
$11$	424.515	1.05782	0.528910	−	0.848678i	$-0.322601\pi$
$11$	424.515	1.05782	0.528910	+	0.848678i	$0.322601\pi$
$12$	334.916	0.671401
$13$	44.7757	0.0734826	0.0367413	−	0.999325i	$-0.488302\pi$
$13$	44.7757	0.0734826	0.0367413	+	0.999325i	$0.488302\pi$
$14$	−407.958	−0.556282
$15$	−916.672	−1.05193
$16$	418.359	0.408554
$17$	1380.18	1.15828	0.579141	−	0.815227i	$-0.303388\pi$
$17$	1380.18	1.15828	0.579141	+	0.815227i	$0.303388\pi$
$18$	173.331	0.126094
$19$	−1119.92	−0.711710	−0.355855	−	0.934541i	$-0.615810\pi$
$19$	−1119.92	−0.711710	−0.355855	+	0.934541i	$0.615810\pi$
$20$	−1739.66	−0.972499
$21$	−2079.98	−1.02923
$22$	−1106.09	−0.487231
$23$	−39.2926	−0.0154878	−0.00774392	−	0.999970i	$-0.502465\pi$
$23$	−39.2926	−0.0154878	−0.00774392	+	0.999970i	$0.502465\pi$
$24$	−1980.26	−0.701768
$25$	1636.49	0.523676
$26$	−116.665	−0.0338460
$27$	4111.85	1.08549
$28$	−3947.39	−0.951513
$29$	841.000	0.185695
$29$	841.000	0.185695
$30$	2388.43	0.484517
$31$	8689.59	1.62403	0.812016	−	0.583635i	$-0.198370\pi$
$31$	8689.59	1.62403	0.812016	+	0.583635i	$0.198370\pi$
$32$	−5860.17	−1.01166
$33$	−5639.44	−0.901470
$34$	−3596.13	−0.533504
$35$	10804.1	1.49080
$36$	1677.15	0.215683
$37$	2453.17	0.294593	0.147297	−	0.989092i	$-0.452943\pi$
$37$	2453.17	0.294593	0.147297	+	0.989092i	$0.452943\pi$
$38$	2918.00	0.327813
$39$	−594.820	−0.0626216
$40$	10286.1	1.01648
$41$	−12411.4	−1.15308	−0.576542	−	0.817068i	$-0.695598\pi$
$41$	−12411.4	−1.15308	−0.576542	+	0.817068i	$0.695598\pi$
$42$	5419.48	0.474062
$43$	21380.8	1.76341	0.881703	−	0.471805i	$-0.156397\pi$
$43$	21380.8	1.76341	0.881703	+	0.471805i	$0.156397\pi$
$44$	−10702.5	−0.833402
$45$	−4590.40	−0.337924
$46$	102.378	0.00713369
$47$	−7829.13	−0.516974	−0.258487	−	0.966015i	$-0.583224\pi$
$47$	−7829.13	−0.516974	−0.258487	+	0.966015i	$0.583224\pi$
$48$	−5557.66	−0.348168
$49$	7708.15	0.458627
$50$	−4263.94	−0.241205
$51$	−18334.9	−0.987084
$52$	−1128.85	−0.0578931
$53$	−33959.8	−1.66064	−0.830321	−	0.557285i	$-0.811843\pi$
$53$	−33959.8	−1.66064	−0.830321	+	0.557285i	$0.811843\pi$
$54$	−10713.6	−0.499978
$55$	29293.1	1.30574
$56$	23339.7	0.994548
$57$	14877.5	0.606517
$58$	−2191.26	−0.0855311
$59$	−27038.1	−1.01122	−0.505611	−	0.862761i	$-0.668733\pi$
$59$	−27038.1	−1.01122	−0.505611	+	0.862761i	$0.668733\pi$
$60$	23110.4	0.828760
$61$	7571.94	0.260545	0.130272	−	0.991478i	$-0.458415\pi$
$61$	7571.94	0.260545	0.130272	+	0.991478i	$0.458415\pi$
$62$	−22641.1	−0.748028
$63$	−10415.9	−0.330632
$64$	1881.42	0.0574163
$65$	3089.68	0.0907049
$66$	14693.8	0.415216
$67$	−54383.1	−1.48005	−0.740025	−	0.672579i	$-0.765187\pi$
$67$	−54383.1	−1.48005	−0.740025	+	0.672579i	$0.765187\pi$
$68$	−34796.0	−0.912551
$69$	521.979	0.0131987
$70$	−28150.5	−0.686660
$71$	80884.6	1.90423	0.952116	−	0.305736i	$-0.0989026\pi$
$71$	80884.6	1.90423	0.952116	+	0.305736i	$0.0989026\pi$
$72$	−9916.48	−0.225438
$73$	−45517.8	−0.999711	−0.499855	−	0.866109i	$-0.666614\pi$
$73$	−45517.8	−0.999711	−0.499855	+	0.866109i	$0.666614\pi$
$74$	−6391.83	−0.135689
$75$	−21739.8	−0.446275
$76$	28234.5	0.560720
$77$	66467.7	1.27757
$78$	1549.83	0.0288434
$79$	68029.7	1.22640	0.613198	−	0.789929i	$-0.289883\pi$
$79$	68029.7	1.22640	0.613198	+	0.789929i	$0.289883\pi$
$80$	28868.3	0.504308
$81$	−38458.2	−0.651293
$82$	32338.4	0.531109
$83$	32492.4	0.517710	0.258855	−	0.965916i	$-0.416655\pi$
$83$	32492.4	0.517710	0.258855	+	0.965916i	$0.416655\pi$
$84$	52438.8	0.810876
$85$	95237.5	1.42975
$86$	−55708.5	−0.812223
$87$	−11172.2	−0.158249
$88$	63280.8	0.871095
$89$	−31236.8	−0.418015	−0.209007	−	0.977914i	$-0.567023\pi$
$89$	−31236.8	−0.418015	−0.209007	+	0.977914i	$0.567023\pi$
$90$	11960.5	0.155647
$91$	7010.68	0.0887476
$92$	990.611	0.0122021
$93$	−115436.	−1.38399
$94$	20399.1	0.238118
$95$	−77278.5	−0.878516
$96$	77848.9	0.862133
$97$	−108828.	−1.17439	−0.587195	−	0.809445i	$-0.699768\pi$
$97$	−108828.	−1.17439	−0.587195	+	0.809445i	$0.699768\pi$
$98$	−20083.9	−0.211243
$99$	−28240.5	−0.289591
$100$	−41257.8	−0.412578
$101$	−14528.5	−0.141715	−0.0708577	−	0.997486i	$-0.522574\pi$
$101$	−14528.5	−0.141715	−0.0708577	+	0.997486i	$0.522574\pi$
$102$	47772.5	0.454650
$103$	−87479.6	−0.812482	−0.406241	−	0.913766i	$-0.633161\pi$
$103$	−87479.6	−0.812482	−0.406241	+	0.913766i	$0.633161\pi$
$104$	6674.54	0.0605115
$105$	−143526.	−1.27045
$106$	88483.8	0.764890
$107$	−74225.7	−0.626750	−0.313375	−	0.949629i	$-0.601460\pi$
$107$	−74225.7	−0.626750	−0.313375	+	0.949629i	$0.601460\pi$
$108$	−103664.	−0.855205
$109$	204798.	1.65105	0.825524	−	0.564368i	$-0.190880\pi$
$109$	204798.	1.65105	0.825524	+	0.564368i	$0.190880\pi$
$110$	−76324.3	−0.601424
$111$	−32588.9	−0.251051
$112$	65503.8	0.493425
$113$	−26924.6	−0.198359	−0.0991797	−	0.995070i	$-0.531622\pi$
$113$	−26924.6	−0.198359	−0.0991797	+	0.995070i	$0.531622\pi$
$114$	−38763.9	−0.279361
$115$	−2711.33	−0.0191178
$116$	−21202.6	−0.146300
$117$	−2978.67	−0.0201167
$118$	70449.0	0.465768
$119$	216100.	1.39890
$120$	−136645.	−0.866243
$121$	19162.3	0.118983
$122$	−19729.0	−0.120007
$123$	164878.	0.982653
$124$	−219074.	−1.27949
$125$	−102713.	−0.587961
$126$	27139.0	0.152289
$127$	191030.	1.05098	0.525488	−	0.850801i	$-0.323883\pi$
$127$	191030.	1.05098	0.525488	+	0.850801i	$0.323883\pi$
$128$	182623.	0.985215
$129$	−284031.	−1.50277
$130$	−8050.30	−0.0417786
$131$	−22077.2	−0.112400	−0.0562000	−	0.998420i	$-0.517898\pi$
$131$	−22077.2	−0.112400	−0.0562000	+	0.998420i	$0.517898\pi$
$132$	142177.	0.710222
$133$	−175349.	−0.859558
$134$	141697.	0.681710
$135$	283732.	1.33991
$136$	205739.	0.953824
$137$	−6340.64	−0.0288623	−0.0144312	−	0.999896i	$-0.504594\pi$
$137$	−6340.64	−0.0288623	−0.0144312	+	0.999896i	$0.504594\pi$
$138$	−1360.04	−0.00607930
$139$	249492.	1.09526	0.547632	−	0.836719i	$-0.315529\pi$
$139$	249492.	1.09526	0.547632	+	0.836719i	$0.315529\pi$
$140$	−272384.	−1.17452
$141$	104005.	0.440563
$142$	−210748.	−0.877088
$143$	19008.0	0.0777313
$144$	−27831.0	−0.111846
$145$	58032.0	0.229217
$146$	118599.	0.460466
$147$	−102398.	−0.390840
$148$	−61847.2	−0.232095
$149$	165499.	0.610703	0.305352	−	0.952240i	$-0.401226\pi$
$149$	165499.	0.610703	0.305352	+	0.952240i	$0.401226\pi$
$150$	56644.0	0.205554
$151$	−327632.	−1.16935	−0.584675	−	0.811268i	$-0.698778\pi$
$151$	−327632.	−1.16935	−0.584675	+	0.811268i	$0.698778\pi$
$152$	−166942.	−0.586080
$153$	−91815.5	−0.317093
$154$	−173184.	−0.588446
$155$	599612.	2.00466
$156$	14996.1	0.0493363
$157$	488239.	1.58082	0.790411	−	0.612577i	$-0.209867\pi$
$157$	488239.	1.58082	0.790411	+	0.612577i	$0.209867\pi$
$158$	−177254.	−0.564877
$159$	451137.	1.41519
$160$	−404372.	−1.24877
$161$	−6152.16	−0.0187052
$162$	100204.	0.299985
$163$	−367092.	−1.08220	−0.541098	−	0.840959i	$-0.681991\pi$
$163$	−367092.	−1.08220	−0.541098	+	0.840959i	$0.681991\pi$
$164$	312905.	0.908455
$165$	−389141.	−1.11275
$166$	−84660.3	−0.238457
$167$	−28263.6	−0.0784216	−0.0392108	−	0.999231i	$-0.512484\pi$
$167$	−28263.6	−0.0784216	−0.0392108	+	0.999231i	$0.512484\pi$
$168$	−310055.	−0.847550
$169$	−369288.	−0.994600
$170$	−248145.	−0.658543
$171$	74501.7	0.194839
$172$	−539034.	−1.38930
$173$	−535363.	−1.35998	−0.679991	−	0.733220i	$-0.738016\pi$
$173$	−535363.	−1.35998	−0.679991	+	0.733220i	$0.738016\pi$
$174$	29109.6	0.0728893
$175$	256230.	0.632463
$176$	177600.	0.432176
$177$	359186.	0.861760
$178$	81388.8	0.192537
$179$	−636787.	−1.48546	−0.742731	−	0.669589i	$-0.766470\pi$
$179$	−636787.	−1.48546	−0.742731	+	0.669589i	$0.766470\pi$
$180$	115729.	0.266233
$181$	330095.	0.748931	0.374466	−	0.927241i	$-0.377826\pi$
$181$	330095.	0.748931	0.374466	+	0.927241i	$0.377826\pi$
$182$	−18266.6	−0.0408771
$183$	−100589.	−0.222035
$184$	−5857.19	−0.0127540
$185$	169277.	0.363638
$186$	300774.	0.637467
$187$	585909.	1.22525
$188$	197381.	0.407297
$189$	643805.	1.31099
$190$	201352.	0.404644
$191$	−362442.	−0.718878	−0.359439	−	0.933169i	$-0.617032\pi$
$191$	−362442.	−0.718878	−0.359439	+	0.933169i	$0.617032\pi$
$192$	−24993.5	−0.0489299
$193$	−516560.	−0.998224	−0.499112	−	0.866538i	$-0.666340\pi$
$193$	−516560.	−0.998224	−0.499112	+	0.866538i	$0.666340\pi$
$194$	283557.	0.540923
$195$	−41044.7	−0.0772984
$196$	−194331.	−0.361329
$197$	−792893.	−1.45562	−0.727812	−	0.685777i	$-0.759462\pi$
$197$	−792893.	−1.45562	−0.727812	+	0.685777i	$0.759462\pi$
$198$	73581.8	0.133385
$199$	−778535.	−1.39362	−0.696812	−	0.717254i	$-0.745399\pi$
$199$	−778535.	−1.39362	−0.696812	+	0.717254i	$0.745399\pi$
$200$	243945.	0.431238
$201$	722448.	1.26129
$202$	37854.6	0.0652740
$203$	131678.	0.224271
$204$	462245.	0.777673
$205$	−856430.	−1.42333
$206$	227932.	0.374229
$207$	2613.90	0.00423998
$208$	18732.3	0.0300216
$209$	−475423.	−0.752861
$210$	373964.	0.585169
$211$	−387183.	−0.598702	−0.299351	−	0.954143i	$-0.596770\pi$
$211$	−387183.	−0.598702	−0.299351	+	0.954143i	$0.596770\pi$
$212$	856167.	1.30833
$213$	−1.07451e6	−1.62278
$214$	193398.	0.288681
$215$	1.47535e6	2.17670
$216$	612937.	0.893885
$217$	1.36056e6	1.96140
$218$	−533610.	−0.760471
$219$	604678.	0.851950
$220$	−738512.	−1.02873
$221$	61798.7	0.0851136
$222$	84911.8	0.115634
$223$	8549.70	0.0115130	0.00575650	−	0.999983i	$-0.498168\pi$
$223$	8549.70	0.0115130	0.00575650	+	0.999983i	$0.498168\pi$
$224$	−917544.	−1.22182
$225$	−108866.	−0.143362
$226$	70153.1	0.0913642
$227$	1.04011e6	1.33972	0.669860	−	0.742487i	$-0.266354\pi$
$227$	1.04011e6	1.33972	0.669860	+	0.742487i	$0.266354\pi$
$228$	−375079.	−0.477843
$229$	1.28049e6	1.61357	0.806784	−	0.590846i	$-0.201206\pi$
$229$	1.28049e6	1.61357	0.806784	+	0.590846i	$0.201206\pi$
$230$	7064.48	0.00880563
$231$	−882985.	−1.08874
$232$	125365.	0.152917
$233$	−292352.	−0.352790	−0.176395	−	0.984320i	$-0.556444\pi$
$233$	−292352.	−0.352790	−0.176395	+	0.984320i	$0.556444\pi$
$234$	7761.04	0.00926574
$235$	−540237.	−0.638139
$236$	681663.	0.796690
$237$	−903735.	−1.04513
$238$	−563057.	−0.644332
$239$	113590.	0.128631	0.0643153	−	0.997930i	$-0.479514\pi$
$239$	113590.	0.128631	0.0643153	+	0.997930i	$0.479514\pi$
$240$	−383498.	−0.429769
$241$	−1.37805e6	−1.52835	−0.764175	−	0.645009i	$-0.776854\pi$
$241$	−1.37805e6	−1.52835	−0.764175	+	0.645009i	$0.776854\pi$
$242$	−49928.1	−0.0548033
$243$	−488284.	−0.530466
$244$	−190897.	−0.205270
$245$	531889.	0.566117
$246$	−429597.	−0.452609
$247$	−50145.3	−0.0522983
$248$	1.29532e6	1.33736
$249$	−431643.	−0.441191
$250$	267622.	0.270814
$251$	1.27582e6	1.27822	0.639112	−	0.769114i	$-0.279302\pi$
$251$	1.27582e6	1.27822	0.639112	+	0.769114i	$0.279302\pi$
$252$	262596.	0.260488
$253$	−16680.3	−0.0163834
$254$	−497738.	−0.484079
$255$	−1.26518e6	−1.21843
$256$	−536038.	−0.511205
$257$	−1.11414e6	−1.05223	−0.526113	−	0.850415i	$-0.676351\pi$
$257$	−1.11414e6	−1.05223	−0.526113	+	0.850415i	$0.676351\pi$
$258$	740055.	0.692174
$259$	384100.	0.355791
$260$	−77894.5	−0.0714617
$261$	−55946.8	−0.0508363
$262$	57523.1	0.0517713
$263$	−1.03806e6	−0.925411	−0.462706	−	0.886512i	$-0.653121\pi$
$263$	−1.03806e6	−0.925411	−0.462706	+	0.886512i	$0.653121\pi$
$264$	−840649.	−0.742344
$265$	−2.34335e6	−2.04985
$266$	456880.	0.395912
$267$	414963.	0.356231
$268$	1.37106e6	1.16606
$269$	−1.16582e6	−0.982311	−0.491156	−	0.871072i	$-0.663425\pi$
$269$	−1.16582e6	−0.982311	−0.491156	+	0.871072i	$0.663425\pi$
$270$	−739276.	−0.617159
$271$	832152.	0.688302	0.344151	−	0.938914i	$-0.388167\pi$
$271$	832152.	0.688302	0.344151	+	0.938914i	$0.388167\pi$
$272$	577412.	0.473221
$273$	−93132.8	−0.0756303
$274$	16520.8	0.0132940
$275$	694714.	0.553955
$276$	−13159.7	−0.0103986
$277$	2.13903e6	1.67501	0.837505	−	0.546430i	$-0.184014\pi$
$277$	2.13903e6	1.67501	0.837505	+	0.546430i	$0.184014\pi$
$278$	−650061.	−0.504478
$279$	−578067.	−0.444598
$280$	1.61052e6	1.22764
$281$	1.77750e6	1.34290	0.671451	−	0.741049i	$-0.265671\pi$
$281$	1.77750e6	1.34290	0.671451	+	0.741049i	$0.265671\pi$
$282$	−270990.	−0.202923
$283$	20776.4	0.0154207	0.00771034	−	0.999970i	$-0.497546\pi$
$283$	20776.4	0.0154207	0.00771034	+	0.999970i	$0.497546\pi$
$284$	−2.03919e6	−1.50025
$285$	1.02660e6	0.748668
$286$	−49526.1	−0.0358030
$287$	−1.94329e6	−1.39262
$288$	389842.	0.276954
$289$	485050.	0.341619
$290$	−151205.	−0.105577
$291$	1.44572e6	1.00081
$292$	1.14756e6	0.787621
$293$	1.38379e6	0.941674	0.470837	−	0.882220i	$-0.343952\pi$
$293$	1.38379e6	0.941674	0.470837	+	0.882220i	$0.343952\pi$
$294$	266803.	0.180021
$295$	−1.86573e6	−1.24823
$296$	365684.	0.242592
$297$	1.74554e6	1.14826
$298$	−431215.	−0.281289
$299$	−1759.35	−0.00113809
$300$	548085.	0.351597
$301$	3.34766e6	2.12973
$302$	853660.	0.538602
$303$	193003.	0.120769
$304$	−468529.	−0.290772
$305$	522490.	0.321609
$306$	239229.	0.146053
$307$	−1.26345e6	−0.765089	−0.382545	−	0.923937i	$-0.624952\pi$
$307$	−1.26345e6	−0.765089	−0.382545	+	0.923937i	$0.624952\pi$
$308$	−1.67573e6	−1.00653
$309$	1.16212e6	0.692394
$310$	−1.56231e6	−0.923345
$311$	1.68822e6	0.989754	0.494877	−	0.868963i	$-0.335213\pi$
$311$	1.68822e6	0.989754	0.494877	+	0.868963i	$0.335213\pi$
$312$	−88667.4	−0.0515677
$313$	1.69210e6	0.976259	0.488130	−	0.872771i	$-0.337679\pi$
$313$	1.69210e6	0.976259	0.488130	+	0.872771i	$0.337679\pi$
$314$	−1.27213e6	−0.728125
$315$	−718733.	−0.408123
$316$	−1.71511e6	−0.966214
$317$	−2.57763e6	−1.44070	−0.720349	−	0.693612i	$-0.756018\pi$
$317$	−2.57763e6	−1.44070	−0.720349	+	0.693612i	$0.756018\pi$
$318$	−1.17546e6	−0.651836
$319$	357017.	0.196432
$320$	129824.	0.0708731
$321$	986045.	0.534114
$322$	16029.7	0.00861561
$323$	−1.54570e6	−0.824362
$324$	969575.	0.513120
$325$	73275.0	0.0384811
$326$	956474.	0.498459
$327$	−2.72062e6	−1.40702
$328$	−1.85012e6	−0.949543
$329$	−1.22583e6	−0.624368
$330$	1.01392e6	0.512532
$331$	−224640.	−0.112698	−0.0563492	−	0.998411i	$-0.517946\pi$
$331$	−224640.	−0.112698	−0.0563492	+	0.998411i	$0.517946\pi$
$332$	−819171.	−0.407877
$333$	−163195.	−0.0806484
$334$	73641.9	0.0361209
$335$	−3.75262e6	−1.82693
$336$	−870180.	−0.420495
$337$	1.90186e6	0.912230	0.456115	−	0.889921i	$-0.349241\pi$
$337$	1.90186e6	0.912230	0.456115	+	0.889921i	$0.349241\pi$
$338$	962196.	0.458112
$339$	357678.	0.169041
$340$	−2.40105e6	−1.12643
$341$	3.68886e6	1.71793
$342$	−194117.	−0.0897427
$343$	−1.42464e6	−0.653836
$344$	3.18715e6	1.45213
$345$	36018.4	0.0162921
$346$	1.39491e6	0.626407
$347$	898305.	0.400498	0.200249	−	0.979745i	$-0.435825\pi$
$347$	898305.	0.400498	0.200249	+	0.979745i	$0.435825\pi$
$348$	281664.	0.124676
$349$	2.92758e6	1.28660	0.643302	−	0.765612i	$-0.277564\pi$
$349$	2.92758e6	1.28660	0.643302	+	0.765612i	$0.277564\pi$
$350$	−667618.	−0.291312
$351$	184111.	0.0797650
$352$	−2.48773e6	−1.07015
$353$	−1.12843e6	−0.481989	−0.240994	−	0.970526i	$-0.577474\pi$
$353$	−1.12843e6	−0.481989	−0.240994	+	0.970526i	$0.577474\pi$
$354$	−935875.	−0.396926
$355$	5.58132e6	2.35053
$356$	787516.	0.329332
$357$	−2.87076e6	−1.19214
$358$	1.65918e6	0.684203
$359$	−2.10775e6	−0.863145	−0.431572	−	0.902078i	$-0.642041\pi$
$359$	−2.10775e6	−0.863145	−0.431572	+	0.902078i	$0.642041\pi$
$360$	−684272.	−0.278274
$361$	−1.22188e6	−0.493468
$362$	−860075.	−0.344957
$363$	−254560.	−0.101397
$364$	−176747.	−0.0699196
$365$	−3.14089e6	−1.23402
$366$	262088.	0.102269
$367$	−973174.	−0.377160	−0.188580	−	0.982058i	$-0.560388\pi$
$367$	−973174.	−0.377160	−0.188580	+	0.982058i	$0.560388\pi$
$368$	−16438.4	−0.00632762
$369$	825656.	0.315670
$370$	−441059.	−0.167491
$371$	−5.31720e6	−2.00562
$372$	2.91028e6	1.09038
$373$	2.56625e6	0.955053	0.477527	−	0.878617i	$-0.341533\pi$
$373$	2.56625e6	0.955053	0.477527	+	0.878617i	$0.341533\pi$
$374$	−1.52661e6	−0.564351
$375$	1.36448e6	0.501058
$376$	−1.16706e6	−0.425718
$377$	37656.4	0.0136454
$378$	−1.67746e6	−0.603841
$379$	207947.	0.0743627	0.0371813	−	0.999309i	$-0.488162\pi$
$379$	207947.	0.0743627	0.0371813	+	0.999309i	$0.488162\pi$
$380$	1.94828e6	0.692137
$381$	−2.53773e6	−0.895638
$382$	944358.	0.331115
$383$	−2.32617e6	−0.810297	−0.405148	−	0.914251i	$-0.632780\pi$
$383$	−2.32617e6	−0.810297	−0.405148	+	0.914251i	$0.632780\pi$
$384$	−2.42604e6	−0.839596
$385$	4.58651e6	1.57699
$386$	1.34592e6	0.459781
$387$	−1.42234e6	−0.482753
$388$	2.74369e6	0.925242
$389$	4.27508e6	1.43242	0.716210	−	0.697885i	$-0.245875\pi$
$389$	4.27508e6	1.43242	0.716210	+	0.697885i	$0.245875\pi$
$390$	106944.	0.0356036
$391$	−54231.0	−0.0179393
$392$	1.14902e6	0.377671
$393$	293283.	0.0957868
$394$	2.06592e6	0.670459
$395$	4.69429e6	1.51383
$396$	711976.	0.228153
$397$	492916.	0.156963	0.0784813	−	0.996916i	$-0.474993\pi$
$397$	492916.	0.156963	0.0784813	+	0.996916i	$0.474993\pi$
$398$	2.02851e6	0.641902
$399$	2.32942e6	0.732512
$400$	684640.	0.213950
$401$	−3.49748e6	−1.08616	−0.543081	−	0.839680i	$-0.682742\pi$
$401$	−3.49748e6	−1.08616	−0.543081	+	0.839680i	$0.682742\pi$
$402$	−1.88237e6	−0.580951
$403$	389083.	0.119338
$404$	366280.	0.111650
$405$	−2.65375e6	−0.803938
$406$	−343093.	−0.103299
$407$	1.04141e6	0.311627
$408$	−2.73312e6	−0.812845
$409$	1.71915e6	0.508165	0.254082	−	0.967183i	$-0.418227\pi$
$409$	1.71915e6	0.508165	0.254082	+	0.967183i	$0.418227\pi$
$410$	2.23146e6	0.655587
$411$	84231.7	0.0245964
$412$	2.20546e6	0.640113
$413$	−4.23345e6	−1.22129
$414$	−6810.64	−0.00195293
$415$	2.24209e6	0.639047
$416$	−262393.	−0.0743394
$417$	−3.31435e6	−0.933381
$418$	1.23874e6	0.346767
$419$	1.14391e6	0.318314	0.159157	−	0.987253i	$-0.449122\pi$
$419$	1.14391e6	0.318314	0.159157	+	0.987253i	$0.449122\pi$
$420$	3.61846e6	1.00092
$421$	−2.31765e6	−0.637298	−0.318649	−	0.947873i	$-0.603229\pi$
$421$	−2.31765e6	−0.637298	−0.318649	+	0.947873i	$0.603229\pi$
$422$	1.00882e6	0.275761
$423$	520826.	0.141528
$424$	−5.06226e6	−1.36751
$425$	2.25865e6	0.606565
$426$	2.79967e6	0.747451
$427$	1.18556e6	0.314669
$428$	1.87131e6	0.493784
$429$	−252510.	−0.0662423
$430$	−3.84408e6	−1.00259
$431$	−5.72610e6	−1.48479	−0.742396	−	0.669961i	$-0.766311\pi$
$431$	−5.72610e6	−1.48479	−0.742396	+	0.669961i	$0.766311\pi$
$432$	1.72023e6	0.443483
$433$	−67453.3	−0.0172895	−0.00864477	−	0.999963i	$-0.502752\pi$
$433$	−67453.3	−0.0172895	−0.00864477	+	0.999963i	$0.502752\pi$
$434$	−3.54498e6	−0.903421
$435$	−770921.	−0.195338
$436$	−5.16319e6	−1.30078
$437$	44004.6	0.0110229
$438$	−1.57551e6	−0.392407
$439$	1.55199e6	0.384352	0.192176	−	0.981361i	$-0.438446\pi$
$439$	1.55199e6	0.384352	0.192176	+	0.981361i	$0.438446\pi$
$440$	4.36660e6	1.07526
$441$	−512777.	−0.125555
$442$	−161019.	−0.0392032
$443$	401094.	0.0971040	0.0485520	−	0.998821i	$-0.484539\pi$
$443$	401094.	0.0971040	0.0485520	+	0.998821i	$0.484539\pi$
$444$	821604.	0.197790
$445$	−2.15545e6	−0.515986
$446$	−22276.6	−0.00530288
$447$	−2.19856e6	−0.520439
$448$	294579.	0.0693437
$449$	−954898.	−0.223533	−0.111766	−	0.993735i	$-0.535651\pi$
$449$	−954898.	−0.223533	−0.111766	+	0.993735i	$0.535651\pi$
$450$	283655.	0.0660326
$451$	−5.26882e6	−1.21975
$452$	678800.	0.156277
$453$	4.35241e6	0.996516
$454$	−2.71005e6	−0.617074
$455$	483762.	0.109548
$456$	2.21773e6	0.499455
$457$	−5.90509e6	−1.32262	−0.661312	−	0.750111i	$-0.730000\pi$
$457$	−5.90509e6	−1.32262	−0.661312	+	0.750111i	$0.730000\pi$
$458$	−3.33637e6	−0.743208
$459$	5.67511e6	1.25731
$460$	68355.7	0.0150619
$461$	2.77060e6	0.607185	0.303593	−	0.952802i	$-0.401814\pi$
$461$	2.77060e6	0.607185	0.303593	+	0.952802i	$0.401814\pi$
$462$	2.30065e6	0.501472
$463$	7.56792e6	1.64068	0.820340	−	0.571876i	$-0.193784\pi$
$463$	7.56792e6	1.64068	0.820340	+	0.571876i	$0.193784\pi$
$464$	351840.	0.0758665
$465$	−7.96550e6	−1.70837
$466$	761734.	0.162495
$467$	−83488.4	−0.0177147	−0.00885736	−	0.999961i	$-0.502819\pi$
$467$	−83488.4	−0.0177147	−0.00885736	+	0.999961i	$0.502819\pi$
$468$	75095.6	0.0158489
$469$	−8.51493e6	−1.78751
$470$	1.40761e6	0.293926
$471$	−6.48597e6	−1.34717
$472$	−4.03047e6	−0.832723
$473$	9.07647e6	1.86537
$474$	2.35472e6	0.481386
$475$	−1.83274e6	−0.372706
$476$	−5.44812e6	−1.10212
$477$	2.25915e6	0.454620
$478$	−295963.	−0.0592472
$479$	−4.76766e6	−0.949438	−0.474719	−	0.880137i	$-0.657450\pi$
$479$	−4.76766e6	−0.949438	−0.474719	+	0.880137i	$0.657450\pi$
$480$	5.37185e6	1.06419
$481$	109842.	0.0216475
$482$	3.59057e6	0.703957
$483$	81728.0	0.0159405
$484$	−483103.	−0.0937404
$485$	−7.50954e6	−1.44964
$486$	1.27225e6	0.244332
$487$	2.06622e6	0.394779	0.197389	−	0.980325i	$-0.436754\pi$
$487$	2.06622e6	0.394779	0.197389	+	0.980325i	$0.436754\pi$
$488$	1.12872e6	0.214554
$489$	4.87661e6	0.922244
$490$	−1.38586e6	−0.260753
$491$	−1.66699e6	−0.312053	−0.156027	−	0.987753i	$-0.549869\pi$
$491$	−1.66699e6	−0.312053	−0.156027	+	0.987753i	$0.549869\pi$
$492$	−4.15677e6	−0.774182
$493$	1.16073e6	0.215088
$494$	130656.	0.0240886
$495$	−1.94869e6	−0.357463
$496$	3.63537e6	0.663505
$497$	1.26644e7	2.29981
$498$	1.12466e6	0.203212
$499$	6.36495e6	1.14431	0.572155	−	0.820146i	$-0.306108\pi$
$499$	6.36495e6	1.14431	0.572155	+	0.820146i	$0.306108\pi$
$500$	2.58950e6	0.463224
$501$	375465.	0.0668306
$502$	−3.32421e6	−0.588748
$503$	−1.35276e6	−0.238397	−0.119198	−	0.992870i	$-0.538032\pi$
$503$	−1.35276e6	−0.238397	−0.119198	+	0.992870i	$0.538032\pi$
$504$	−1.55265e6	−0.272269
$505$	−1.00252e6	−0.174930
$506$	43461.2	0.00754616
$507$	4.90578e6	0.847595
$508$	−4.81610e6	−0.828010
$509$	1.44004e6	0.246365	0.123183	−	0.992384i	$-0.460690\pi$
$509$	1.44004e6	0.246365	0.123183	+	0.992384i	$0.460690\pi$
$510$	3.29647e6	0.561208
$511$	−7.12687e6	−1.20739
$512$	−4.44727e6	−0.749754
$513$	−4.60494e6	−0.772558
$514$	2.90295e6	0.484654
$515$	−6.03640e6	−1.00291
$516$	7.16076e6	1.18395
$517$	−3.32358e6	−0.546865
$518$	−1.00079e6	−0.163877
$519$	7.11199e6	1.15897
$520$	460567.	0.0746938
$521$	8.34425e6	1.34677	0.673384	−	0.739293i	$-0.264840\pi$
$521$	8.34425e6	1.34677	0.673384	+	0.739293i	$0.264840\pi$
$522$	145772.	0.0234151
$523$	1.03665e7	1.65721	0.828605	−	0.559834i	$-0.189135\pi$
$523$	1.03665e7	1.65721	0.828605	+	0.559834i	$0.189135\pi$
$524$	556592.	0.0885542
$525$	−3.40387e6	−0.538982
$526$	2.70472e6	0.426244
$527$	1.19932e7	1.88109
$528$	−2.35931e6	−0.368299
$529$	−6.43480e6	−0.999760
$530$	6.10569e6	0.944160
$531$	1.79869e6	0.276834
$532$	4.42076e6	0.677202
$533$	−555729.	−0.0847315
$534$	−1.08120e6	−0.164080
$535$	−5.12183e6	−0.773644
$536$	−8.10667e6	−1.21879
$537$	8.45935e6	1.26591
$538$	3.03758e6	0.452452
$539$	3.27223e6	0.485145
$540$	−7.15321e6	−1.05564
$541$	−9.78616e6	−1.43754	−0.718769	−	0.695249i	$-0.755294\pi$
$541$	−9.78616e6	−1.43754	−0.718769	+	0.695249i	$0.755294\pi$
$542$	−2.16821e6	−0.317031
$543$	−4.38512e6	−0.638236
$544$	−8.08810e6	−1.17179
$545$	1.41318e7	2.03801
$546$	242661.	0.0348353
$547$	2.04011e6	0.291532	0.145766	−	0.989319i	$-0.453435\pi$
$547$	2.04011e6	0.291532	0.145766	+	0.989319i	$0.453435\pi$
$548$	159855.	0.0227392
$549$	−503716.	−0.0713272
$550$	−1.81011e6	−0.255151
$551$	−941853.	−0.132161
$552$	77809.4	0.0108689
$553$	1.06516e7	1.48116
$554$	−5.57333e6	−0.771508
$555$	−2.24875e6	−0.309891
$556$	−6.28997e6	−0.862903
$557$	−8.15249e6	−1.11340	−0.556701	−	0.830713i	$-0.687933\pi$
$557$	−8.15249e6	−1.11340	−0.556701	+	0.830713i	$0.687933\pi$
$558$	1.50618e6	0.204781
$559$	957340.	0.129580
$560$	4.51999e6	0.609071
$561$	−7.78346e6	−1.04416
$562$	−4.63136e6	−0.618539
$563$	−4.27446e6	−0.568342	−0.284171	−	0.958774i	$-0.591718\pi$
$563$	−4.27446e6	−0.568342	−0.284171	+	0.958774i	$0.591718\pi$
$564$	−2.62210e6	−0.347097
$565$	−1.85789e6	−0.244850
$566$	−54133.7	−0.00710275
$567$	−6.02152e6	−0.786590
$568$	1.20571e7	1.56810
$569$	−3.51332e6	−0.454922	−0.227461	−	0.973787i	$-0.573042\pi$
$569$	−3.51332e6	−0.454922	−0.227461	+	0.973787i	$0.573042\pi$
$570$	−2.67485e6	−0.344836
$571$	−7.11024e6	−0.912628	−0.456314	−	0.889819i	$-0.650831\pi$
$571$	−7.11024e6	−0.912628	−0.456314	+	0.889819i	$0.650831\pi$
$572$	−479213.	−0.0612405
$573$	4.81484e6	0.612625
$574$	5.06332e6	0.641440
$575$	−64301.9	−0.00811062
$576$	−125160.	−0.0157184
$577$	−1.32589e7	−1.65793	−0.828966	−	0.559299i	$-0.811070\pi$
$577$	−1.32589e7	−1.65793	−0.828966	+	0.559299i	$0.811070\pi$
$578$	−1.26382e6	−0.157349
$579$	6.86221e6	0.850682
$580$	−1.46305e6	−0.180588
$581$	5.08744e6	0.625257
$582$	−3.76689e6	−0.460973
$583$	−1.44165e7	−1.75666
$584$	−6.78516e6	−0.823243
$585$	−205538.	−0.0248315
$586$	−3.60552e6	−0.433734
$587$	−9.82358e6	−1.17672	−0.588362	−	0.808598i	$-0.700227\pi$
$587$	−9.82358e6	−1.17672	−0.588362	+	0.808598i	$0.700227\pi$
$588$	2.58158e6	0.307923
$589$	−9.73165e6	−1.15584
$590$	4.86123e6	0.574932
$591$	1.05331e7	1.24048
$592$	1.02630e6	0.120357
$593$	8.17963e6	0.955206	0.477603	−	0.878576i	$-0.341506\pi$
$593$	8.17963e6	0.955206	0.477603	+	0.878576i	$0.341506\pi$
$594$	−4.54809e6	−0.528887
$595$	1.49116e7	1.72676
$596$	−4.17243e6	−0.481142
$597$	1.03424e7	1.18764
$598$	4584.07	0.000524202 0
$599$	747490.	0.0851213	0.0425607	−	0.999094i	$-0.486448\pi$
$599$	747490.	0.0851213	0.0425607	+	0.999094i	$0.486448\pi$
$600$	−3.24067e6	−0.367499
$601$	1.37632e6	0.155430	0.0777148	−	0.996976i	$-0.475238\pi$
$601$	1.37632e6	0.155430	0.0777148	+	0.996976i	$0.475238\pi$
$602$	−8.72246e6	−0.980952
$603$	3.61778e6	0.405181
$604$	8.25999e6	0.921271
$605$	1.32227e6	0.146869
$606$	−502877.	−0.0556263
$607$	−2.75873e6	−0.303905	−0.151952	−	0.988388i	$-0.548556\pi$
$607$	−2.75873e6	−0.303905	−0.151952	+	0.988388i	$0.548556\pi$
$608$	6.56292e6	0.720009
$609$	−1.74927e6	−0.191123
$610$	−1.36137e6	−0.148133
$611$	−350555.	−0.0379886
$612$	2.31477e6	0.249822
$613$	1.10862e7	1.19161	0.595803	−	0.803130i	$-0.296834\pi$
$613$	1.10862e7	1.19161	0.595803	+	0.803130i	$0.296834\pi$
$614$	3.29197e6	0.352399
$615$	1.13772e7	1.21296
$616$	9.90808e6	1.05205
$617$	−7.02914e6	−0.743343	−0.371672	−	0.928364i	$-0.621215\pi$
$617$	−7.02914e6	−0.743343	−0.371672	+	0.928364i	$0.621215\pi$
$618$	−3.02794e6	−0.318916
$619$	1.81382e7	1.90269	0.951346	−	0.308125i	$-0.0997014\pi$
$619$	1.81382e7	1.90269	0.951346	+	0.308125i	$0.0997014\pi$
$620$	−1.51169e7	−1.57937
$621$	−161565.	−0.0168120
$622$	−4.39872e6	−0.455880
$623$	−4.89085e6	−0.504852
$624$	−248848.	−0.0255843
$625$	−1.22016e7	−1.24944
$626$	−4.40884e6	−0.449664
$627$	6.31573e6	0.641585
$628$	−1.23091e7	−1.24545
$629$	3.38582e6	0.341222
$630$	1.87269e6	0.187981
$631$	9.99631e6	0.999462	0.499731	−	0.866181i	$-0.333432\pi$
$631$	9.99631e6	0.999462	0.499731	+	0.866181i	$0.333432\pi$
$632$	1.01409e7	1.00991
$633$	5.14351e6	0.510211
$634$	6.71613e6	0.663584
$635$	1.31818e7	1.29730
$636$	−1.13737e7	−1.11496
$637$	345138.	0.0337011
$638$	−930224.	−0.0904765
$639$	−5.38077e6	−0.521306
$640$	1.26016e7	1.21612
$641$	−4.79480e6	−0.460920	−0.230460	−	0.973082i	$-0.574023\pi$
$641$	−4.79480e6	−0.460920	−0.230460	+	0.973082i	$0.574023\pi$
$642$	−2.56918e6	−0.246013
$643$	3.22638e6	0.307743	0.153872	−	0.988091i	$-0.450826\pi$
$643$	3.22638e6	0.307743	0.153872	+	0.988091i	$0.450826\pi$
$644$	155103.	0.0147369
$645$	−1.95992e7	−1.85498
$646$	4.02738e6	0.379700
$647$	−4.53776e6	−0.426168	−0.213084	−	0.977034i	$-0.568351\pi$
$647$	−4.53776e6	−0.426168	−0.213084	+	0.977034i	$0.568351\pi$
$648$	−5.73281e6	−0.536327
$649$	−1.14781e7	−1.06969
$650$	−190921.	−0.0177243
$651$	−1.80742e7	−1.67150
$652$	9.25482e6	0.852607
$653$	6.66746e6	0.611896	0.305948	−	0.952048i	$-0.401027\pi$
$653$	6.66746e6	0.611896	0.305948	+	0.952048i	$0.401027\pi$
$654$	7.08870e6	0.648070
$655$	−1.52341e6	−0.138743
$656$	−5.19242e6	−0.471096
$657$	3.02803e6	0.273683
$658$	3.19395e6	0.287583
$659$	8.72288e6	0.782431	0.391216	−	0.920299i	$-0.372055\pi$
$659$	8.72288e6	0.782431	0.391216	+	0.920299i	$0.372055\pi$
$660$	9.81070e6	0.876678
$661$	2.10399e7	1.87301	0.936503	−	0.350660i	$-0.114043\pi$
$661$	2.10399e7	1.87301	0.936503	+	0.350660i	$0.114043\pi$
$662$	585310.	0.0519088
$663$	−820961.	−0.0725335
$664$	4.84351e6	0.426325
$665$	−1.20997e7	−1.06102
$666$	425211.	0.0371466
$667$	−33045.1	−0.00287602
$668$	712557.	0.0617843
$669$	−113578.	−0.00981134
$670$	9.77762e6	0.841484
$671$	3.21440e6	0.275609
$672$	1.21890e7	1.04123
$673$	−1.88610e6	−0.160519	−0.0802595	−	0.996774i	$-0.525575\pi$
$673$	−1.88610e6	−0.160519	−0.0802595	+	0.996774i	$0.525575\pi$
$674$	−4.95538e6	−0.420172
$675$	6.72899e6	0.568448
$676$	9.31018e6	0.783594
$677$	−2.14561e7	−1.79920	−0.899599	−	0.436718i	$-0.856141\pi$
$677$	−2.14561e7	−1.79920	−0.899599	+	0.436718i	$0.856141\pi$
$678$	−931944.	−0.0778602
$679$	−1.70396e7	−1.41835
$680$	1.41967e7	1.17737
$681$	−1.38172e7	−1.14170
$682$	−9.61149e6	−0.791279
$683$	−4.69314e6	−0.384957	−0.192478	−	0.981301i	$-0.561653\pi$
$683$	−4.69314e6	−0.384957	−0.192478	+	0.981301i	$0.561653\pi$
$684$	−1.87827e6	−0.153504
$685$	−437526.	−0.0356269
$686$	3.71195e6	0.301156
$687$	−1.70106e7	−1.37508
$688$	8.94484e6	0.720446
$689$	−1.52058e6	−0.122028
$690$	−93847.5	−0.00750412
$691$	3.70802e6	0.295425	0.147712	−	0.989030i	$-0.452809\pi$
$691$	3.70802e6	0.295425	0.147712	+	0.989030i	$0.452809\pi$
$692$	1.34971e7	1.07146
$693$	−4.42170e6	−0.349749
$694$	−2.34057e6	−0.184469
$695$	1.72158e7	1.35197
$696$	−1.66540e6	−0.130315
$697$	−1.71300e7	−1.33560
$698$	−7.62793e6	−0.592609
$699$	3.88372e6	0.300646
$700$	−6.45986e6	−0.498285
$701$	−3.16175e6	−0.243014	−0.121507	−	0.992591i	$-0.538773\pi$
$701$	−3.16175e6	−0.243014	−0.121507	+	0.992591i	$0.538773\pi$
$702$	−479709.	−0.0367397
$703$	−2.74735e6	−0.209665
$704$	798690.	0.0607361
$705$	7.17674e6	0.543819
$706$	2.94017e6	0.222004
$707$	−2.27477e6	−0.171155
$708$	−9.05550e6	−0.678937
$709$	−5.99901e6	−0.448192	−0.224096	−	0.974567i	$-0.571943\pi$
$709$	−5.99901e6	−0.448192	−0.224096	+	0.974567i	$0.571943\pi$
$710$	−1.45424e7	−1.08265
$711$	−4.52561e6	−0.335740
$712$	−4.65635e6	−0.344228
$713$	−341436.	−0.0251528
$714$	7.47988e6	0.549097
$715$	1.31162e6	0.0959494
$716$	1.60541e7	1.17032
$717$	−1.50898e6	−0.109619
$718$	5.49184e6	0.397564
$719$	−2.15426e7	−1.55409	−0.777043	−	0.629448i	$-0.783281\pi$
$719$	−2.15426e7	−1.55409	−0.777043	+	0.629448i	$0.783281\pi$
$720$	−1.92043e6	−0.138060
$721$	−1.36970e7	−0.981264
$722$	3.18365e6	0.227291
$723$	1.83066e7	1.30245
$724$	−8.32207e6	−0.590044
$725$	1.37629e6	0.0972442
$726$	663267.	0.0467032
$727$	−4.94167e6	−0.346767	−0.173383	−	0.984854i	$-0.555470\pi$
$727$	−4.94167e6	−0.346767	−0.173383	+	0.984854i	$0.555470\pi$
$728$	1.04505e6	0.0730820
$729$	1.58319e7	1.10335
$730$	8.18372e6	0.568387
$731$	2.95094e7	2.04252
$732$	2.53596e6	0.174930
$733$	1.91206e7	1.31444	0.657221	−	0.753698i	$-0.271732\pi$
$733$	1.91206e7	1.31444	0.657221	+	0.753698i	$0.271732\pi$
$734$	2.53564e6	0.173719
$735$	−7.06584e6	−0.482443
$736$	230261.	0.0156684
$737$	−2.30864e7	−1.56563
$738$	−2.15128e6	−0.145397
$739$	−1.92016e7	−1.29338	−0.646690	−	0.762753i	$-0.723847\pi$
$739$	−1.92016e7	−1.29338	−0.646690	+	0.762753i	$0.723847\pi$
$740$	−4.26767e6	−0.286492
$741$	666151.	0.0445684
$742$	1.38542e7	0.923786
$743$	9.70419e6	0.644893	0.322446	−	0.946588i	$-0.395495\pi$
$743$	9.70419e6	0.644893	0.322446	+	0.946588i	$0.395495\pi$
$744$	−1.72076e7	−1.13969
$745$	1.14200e7	0.753836
$746$	−6.68648e6	−0.439897
$747$	−2.16153e6	−0.141729
$748$	−1.47714e7	−0.965315
$749$	−1.16217e7	−0.756949
$750$	−3.55520e6	−0.230787
$751$	−2.24807e7	−1.45449	−0.727245	−	0.686378i	$-0.759200\pi$
$751$	−2.24807e7	−1.45449	−0.727245	+	0.686378i	$0.759200\pi$
$752$	−3.27539e6	−0.211212
$753$	−1.69486e7	−1.08930
$754$	−98115.3	−0.00628505
$755$	−2.26078e7	−1.44341
$756$	−1.62311e7	−1.03286
$757$	7.45377e6	0.472755	0.236378	−	0.971661i	$-0.424040\pi$
$757$	7.45377e6	0.472755	0.236378	+	0.971661i	$0.424040\pi$
$758$	−541815.	−0.0342514
$759$	221588.	0.0139618
$760$	−1.15196e7	−0.723441
$761$	9.48283e6	0.593576	0.296788	−	0.954943i	$-0.404085\pi$
$761$	9.48283e6	0.593576	0.296788	+	0.954943i	$0.404085\pi$
$762$	6.61216e6	0.412530
$763$	3.20659e7	1.99403
$764$	9.13758e6	0.566367
$765$	−6.33559e6	−0.391411
$766$	6.06093e6	0.373222
$767$	−1.21065e6	−0.0743073
$768$	7.12095e6	0.435647
$769$	5.22835e6	0.318823	0.159411	−	0.987212i	$-0.449040\pi$
$769$	5.22835e6	0.318823	0.159411	+	0.987212i	$0.449040\pi$
$770$	−1.19503e7	−0.726362
$771$	1.48008e7	0.896702
$772$	1.30231e7	0.786449
$773$	1.23031e7	0.740569	0.370284	−	0.928918i	$-0.379260\pi$
$773$	1.23031e7	0.740569	0.370284	+	0.928918i	$0.379260\pi$
$774$	3.70596e6	0.222356
$775$	1.42204e7	0.850467
$776$	−1.62226e7	−0.967089
$777$	−5.10255e6	−0.303204
$778$	−1.11389e7	−0.659771
$779$	1.38998e7	0.820661
$780$	1.03478e6	0.0608994
$781$	3.43368e7	2.01433
$782$	141301.	0.00826283
$783$	3.45807e6	0.201571
$784$	3.22477e6	0.187374
$785$	3.36902e7	1.95132
$786$	−764162.	−0.0441193
$787$	2.91098e6	0.167534	0.0837668	−	0.996485i	$-0.473305\pi$
$787$	2.91098e6	0.167534	0.0837668	+	0.996485i	$0.473305\pi$
$788$	1.99897e7	1.14681
$789$	1.37901e7	0.788632
$790$	−1.22312e7	−0.697268
$791$	−4.21567e6	−0.239566
$792$	−4.20970e6	−0.238472
$793$	339039.	0.0191455
$794$	−1.28431e6	−0.0722968
$795$	3.11300e7	1.74688
$796$	1.96278e7	1.09796
$797$	1.69340e7	0.944311	0.472155	−	0.881515i	$-0.343476\pi$
$797$	1.69340e7	0.944311	0.472155	+	0.881515i	$0.343476\pi$
$798$	−6.06939e6	−0.337394
$799$	−1.08056e7	−0.598802
$800$	−9.59009e6	−0.529783
$801$	2.07800e6	0.114436
$802$	9.11284e6	0.500285
$803$	−1.93230e7	−1.05751
$804$	−1.82137e7	−0.993708
$805$	−424521.	−0.0230892
$806$	−1.01377e6	−0.0549670
$807$	1.54872e7	0.837122
$808$	−2.16571e6	−0.116700
$809$	−1.81296e7	−0.973906	−0.486953	−	0.873428i	$-0.661892\pi$
$809$	−1.81296e7	−0.973906	−0.486953	+	0.873428i	$0.661892\pi$
$810$	6.91446e6	0.370293
$811$	1.09329e7	0.583690	0.291845	−	0.956466i	$-0.405731\pi$
$811$	1.09329e7	0.583690	0.291845	+	0.956466i	$0.405731\pi$
$812$	−3.31975e6	−0.176692
$813$	−1.10547e7	−0.586569
$814$	−2.71343e6	−0.143535
$815$	−2.53307e7	−1.33583
$816$	−7.67059e6	−0.403277
$817$	−2.39448e7	−1.25503
$818$	−4.47931e6	−0.234060
$819$	−466379.	−0.0242957
$820$	2.15916e7	1.12137
$821$	6.96673e6	0.360721	0.180360	−	0.983601i	$-0.442274\pi$
$821$	6.96673e6	0.360721	0.180360	+	0.983601i	$0.442274\pi$
$822$	−219469.	−0.0113291
$823$	1.15448e7	0.594137	0.297069	−	0.954856i	$-0.403991\pi$
$823$	1.15448e7	0.594137	0.297069	+	0.954856i	$0.403991\pi$
$824$	−1.30402e7	−0.669064
$825$	−9.22888e6	−0.472078
$826$	1.10304e7	0.562525
$827$	−2.42560e7	−1.23326	−0.616630	−	0.787253i	$-0.711503\pi$
$827$	−2.42560e7	−1.23326	−0.616630	+	0.787253i	$0.711503\pi$
$828$	−65899.5	−0.00334046
$829$	−1.36048e7	−0.687554	−0.343777	−	0.939051i	$-0.611706\pi$
$829$	−1.36048e7	−0.687554	−0.343777	+	0.939051i	$0.611706\pi$
$830$	−5.84186e6	−0.294345
$831$	−2.84158e7	−1.42744
$832$	84241.8	0.00421910
$833$	1.06387e7	0.531220
$834$	8.63569e6	0.429914
$835$	−1.95029e6	−0.0968015
$836$	1.19860e7	0.593141
$837$	3.57303e7	1.76288
$838$	−2.98049e6	−0.146615
$839$	1.57970e7	0.774766	0.387383	−	0.921919i	$-0.373379\pi$
$839$	1.57970e7	0.774766	0.387383	+	0.921919i	$0.373379\pi$
$840$	−2.13949e7	−1.04619
$841$	707281.	0.0344828
$842$	6.03874e6	0.293539
$843$	−2.36131e7	−1.14442
$844$	9.76134e6	0.471686
$845$	−2.54822e7	−1.22771
$846$	−1.35703e6	−0.0651875
$847$	3.00030e6	0.143700
$848$	−1.42074e7	−0.678462
$849$	−276002.	−0.0131414
$850$	−5.88502e6	−0.279383
$851$	−96391.3	−0.00456262
$852$	2.70895e7	1.27850
$853$	−3.60400e7	−1.69594	−0.847972	−	0.530040i	$-0.822177\pi$
$853$	−3.60400e7	−1.69594	−0.847972	+	0.530040i	$0.822177\pi$
$854$	−3.08903e6	−0.144936
$855$	5.14088e6	0.240504
$856$	−1.10645e7	−0.516117
$857$	1.85334e7	0.861993	0.430997	−	0.902354i	$-0.358162\pi$
$857$	1.85334e7	0.861993	0.430997	+	0.902354i	$0.358162\pi$
$858$	657926.	0.0305112
$859$	3.51982e7	1.62756	0.813780	−	0.581173i	$-0.197406\pi$
$859$	3.51982e7	1.62756	0.813780	+	0.581173i	$0.197406\pi$
$860$	−3.71953e7	−1.71491
$861$	2.58155e7	1.18679
$862$	1.49196e7	0.683894
$863$	−9.59020e6	−0.438329	−0.219165	−	0.975688i	$-0.570333\pi$
$863$	−9.59020e6	−0.438329	−0.219165	+	0.975688i	$0.570333\pi$
$864$	−2.40961e7	−1.09815
$865$	−3.69420e7	−1.67873
$866$	175752.	0.00796355
$867$	−6.44361e6	−0.291126
$868$	−3.43012e7	−1.54529
$869$	2.88796e7	1.29731
$870$	2.00867e6	0.0899725
$871$	−2.43504e6	−0.108758
$872$	3.05284e7	1.35961
$873$	7.23971e6	0.321503
$874$	−114656.	−0.00507712
$875$	−1.60820e7	−0.710102
$876$	−1.52446e7	−0.671207
$877$	1.52437e7	0.669254	0.334627	−	0.942351i	$-0.391390\pi$
$877$	1.52437e7	0.669254	0.334627	+	0.942351i	$0.391390\pi$
$878$	−4.04379e6	−0.177032
$879$	−1.83828e7	−0.802491
$880$	1.22550e7	0.533467
$881$	2.35127e7	1.02062	0.510308	−	0.859992i	$-0.329531\pi$
$881$	2.35127e7	1.02062	0.510308	+	0.859992i	$0.329531\pi$
$882$	1.33606e6	0.0578303
$883$	−1.58265e7	−0.683100	−0.341550	−	0.939864i	$-0.610952\pi$
$883$	−1.58265e7	−0.683100	−0.341550	+	0.939864i	$0.610952\pi$
$884$	−1.55802e6	−0.0670566
$885$	2.47851e7	1.06373
$886$	−1.04507e6	−0.0447260
$887$	−1.12033e7	−0.478120	−0.239060	−	0.971005i	$-0.576839\pi$
$887$	−1.12033e7	−0.478120	−0.239060	+	0.971005i	$0.576839\pi$
$888$	−4.85790e6	−0.206736
$889$	2.99102e7	1.26930
$890$	5.61612e6	0.237663
$891$	−1.63261e7	−0.688950
$892$	−215548.	−0.00907050
$893$	8.76800e6	0.367936
$894$	5.72844e6	0.239714
$895$	−4.39406e7	−1.83362
$896$	2.85939e7	1.18988
$897$	23372.0	0.000969873 0
$898$	2.48803e6	0.102959
$899$	7.30794e6	0.301575
$900$	2.74463e6	0.112948
$901$	−4.68708e7	−1.92349
$902$	1.37281e7	0.561818
$903$	−4.44717e7	−1.81495
$904$	−4.01354e6	−0.163345
$905$	2.27777e7	0.924460
$906$	−1.13404e7	−0.458994
$907$	−8.02468e6	−0.323899	−0.161949	−	0.986799i	$-0.551778\pi$
$907$	−8.02468e6	−0.323899	−0.161949	+	0.986799i	$0.551778\pi$
$908$	−2.62223e7	−1.05550
$909$	966495.	0.0387963
$910$	−1.26046e6	−0.0504575
$911$	4.20753e7	1.67970	0.839849	−	0.542821i	$-0.182644\pi$
$911$	4.20753e7	1.67970	0.839849	+	0.542821i	$0.182644\pi$
$912$	6.22414e6	0.247795
$913$	1.37935e7	0.547644
$914$	1.53860e7	0.609199
$915$	−6.94098e6	−0.274074
$916$	−3.22826e7	−1.27125
$917$	−3.45670e6	−0.135750
$918$	−1.47867e7	−0.579116
$919$	−7.55486e6	−0.295078	−0.147539	−	0.989056i	$-0.547135\pi$
$919$	−7.55486e6	−0.295078	−0.147539	+	0.989056i	$0.547135\pi$
$920$	−404167.	−0.0157431
$921$	1.67842e7	0.652006
$922$	−7.21891e6	−0.279669
$923$	3.62167e6	0.139928
$924$	2.22611e7	0.857761
$925$	4.01458e6	0.154272
$926$	−1.97185e7	−0.755696
$927$	5.81950e6	0.222427
$928$	−4.92840e6	−0.187861
$929$	4.76631e7	1.81194	0.905968	−	0.423345i	$-0.139144\pi$
$929$	4.76631e7	1.81194	0.905968	+	0.423345i	$0.139144\pi$
$930$	2.07544e7	0.786871
$931$	−8.63251e6	−0.326410
$932$	7.37052e6	0.277945
$933$	−2.24270e7	−0.843465
$934$	217533.	0.00815938
$935$	4.04298e7	1.51242
$936$	−444018.	−0.0165657
$937$	−1.03068e7	−0.383509	−0.191755	−	0.981443i	$-0.561418\pi$
$937$	−1.03068e7	−0.383509	−0.191755	+	0.981443i	$0.561418\pi$
$938$	2.21860e7	0.823326
$939$	−2.24786e7	−0.831964
$940$	1.36200e7	0.502757
$941$	7.70159e6	0.283535	0.141767	−	0.989900i	$-0.454722\pi$
$941$	7.70159e6	0.283535	0.141767	+	0.989900i	$0.454722\pi$
$942$	1.68995e7	0.620506
$943$	487676.	0.0178588
$944$	−1.13117e7	−0.413139
$945$	4.44248e7	1.61825
$946$	−2.36491e7	−0.859186
$947$	4.62960e7	1.67752	0.838762	−	0.544499i	$-0.183280\pi$
$947$	4.62960e7	1.67752	0.838762	+	0.544499i	$0.183280\pi$
$948$	2.27842e7	0.823404
$949$	−2.03809e6	−0.0734613
$950$	4.77527e6	0.171668
$951$	3.42424e7	1.22776
$952$	3.22131e7	1.15197
$953$	−4.81628e7	−1.71783	−0.858913	−	0.512122i	$-0.828860\pi$
$953$	−4.81628e7	−1.71783	−0.858913	+	0.512122i	$0.828860\pi$
$954$	−5.88630e6	−0.209398
$955$	−2.50098e7	−0.887364
$956$	−2.86373e6	−0.101341
$957$	−4.74277e6	−0.167399
$958$	1.24223e7	0.437310
$959$	−992774.	−0.0348581
$960$	−1.72464e6	−0.0603978
$961$	4.68797e7	1.63748
$962$	−286199.	−0.00997081
$963$	4.93779e6	0.171580
$964$	3.47423e7	1.20411
$965$	−3.56445e7	−1.23218
$966$	−212946.	−0.00734219
$967$	−2.74247e7	−0.943139	−0.471569	−	0.881829i	$-0.656312\pi$
$967$	−2.74247e7	−0.943139	−0.471569	+	0.881829i	$0.656312\pi$
$968$	2.85645e6	0.0979801
$969$	2.05337e7	0.702518
$970$	1.95664e7	0.667701
$971$	−4.56502e7	−1.55380	−0.776899	−	0.629626i	$-0.783208\pi$
$971$	−4.56502e7	−1.55380	−0.776899	+	0.629626i	$0.783208\pi$
$972$	1.23102e7	0.417927
$973$	3.90637e7	1.32279
$974$	−5.38362e6	−0.181835
$975$	−973416.	−0.0327934
$976$	3.16779e6	0.106447
$977$	−3.33875e7	−1.11904	−0.559522	−	0.828815i	$-0.689015\pi$
$977$	−3.33875e7	−1.11904	−0.559522	+	0.828815i	$0.689015\pi$
$978$	−1.27062e7	−0.424785
$979$	−1.32605e7	−0.442185
$980$	−1.34095e7	−0.446014
$981$	−1.36240e7	−0.451993
$982$	4.34341e6	0.143731
$983$	−1.08502e6	−0.0358141	−0.0179071	−	0.999840i	$-0.505700\pi$
$983$	−1.08502e6	−0.0358141	−0.0179071	+	0.999840i	$0.505700\pi$
$984$	2.45777e7	0.809196
$985$	−5.47124e7	−1.79678
$986$	−3.02434e6	−0.0990692
$987$	1.62845e7	0.532084
$988$	1.26422e6	0.0412031
$989$	−840106.	−0.0273114
$990$	5.07740e6	0.164647
$991$	2.69598e7	0.872031	0.436016	−	0.899939i	$-0.356389\pi$
$991$	2.69598e7	0.872031	0.436016	+	0.899939i	$0.356389\pi$
$992$	−5.09224e7	−1.64297
$993$	2.98422e6	0.0960412
$994$	−3.29975e7	−1.05929
$995$	−5.37217e7	−1.72025
$996$	1.08822e7	0.347591
$997$	−1.98023e7	−0.630924	−0.315462	−	0.948938i	$-0.602159\pi$
$997$	−1.98023e7	−0.630924	−0.315462	+	0.948938i	$0.602159\pi$
$998$	−1.65841e7	−0.527068
$999$	1.00871e7	0.319780

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.6.a.b.1.4	✓	7
3.2	odd	2		261.6.a.e.1.4		7
4.3	odd	2		464.6.a.k.1.5		7
5.4	even	2		725.6.a.b.1.4		7
29.28	even	2		841.6.a.b.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.6.a.b.1.4	✓	7	1.1	even	1	trivial
261.6.a.e.1.4		7	3.2	odd	2
464.6.a.k.1.5		7	4.3	odd	2
725.6.a.b.1.4		7	5.4	even	2
841.6.a.b.1.4		7	29.28	even	2

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q-2.60554 q^{2} -13.2844 q^{3} -25.2112 q^{4} +69.0035 q^{5} +34.6131 q^{6} +156.573 q^{7} +149.066 q^{8} -66.5241 q^{9} +O(q^{10})\)	\(q-2.60554 q^{2} -13.2844 q^{3} -25.2112 q^{4} +69.0035 q^{5} +34.6131 q^{6} +156.573 q^{7} +149.066 q^{8} -66.5241 q^{9} -179.792 q^{10} +424.515 q^{11} +334.916 q^{12} +44.7757 q^{13} -407.958 q^{14} -916.672 q^{15} +418.359 q^{16} +1380.18 q^{17} +173.331 q^{18} -1119.92 q^{19} -1739.66 q^{20} -2079.98 q^{21} -1106.09 q^{22} -39.2926 q^{23} -1980.26 q^{24} +1636.49 q^{25} -116.665 q^{26} +4111.85 q^{27} -3947.39 q^{28} +841.000 q^{29} +2388.43 q^{30} +8689.59 q^{31} -5860.17 q^{32} -5639.44 q^{33} -3596.13 q^{34} +10804.1 q^{35} +1677.15 q^{36} +2453.17 q^{37} +2918.00 q^{38} -594.820 q^{39} +10286.1 q^{40} -12411.4 q^{41} +5419.48 q^{42} +21380.8 q^{43} -10702.5 q^{44} -4590.40 q^{45} +102.378 q^{46} -7829.13 q^{47} -5557.66 q^{48} +7708.15 q^{49} -4263.94 q^{50} -18334.9 q^{51} -1128.85 q^{52} -33959.8 q^{53} -10713.6 q^{54} +29293.1 q^{55} +23339.7 q^{56} +14877.5 q^{57} -2191.26 q^{58} -27038.1 q^{59} +23110.4 q^{60} +7571.94 q^{61} -22641.1 q^{62} -10415.9 q^{63} +1881.42 q^{64} +3089.68 q^{65} +14693.8 q^{66} -54383.1 q^{67} -34796.0 q^{68} +521.979 q^{69} -28150.5 q^{70} +80884.6 q^{71} -9916.48 q^{72} -45517.8 q^{73} -6391.83 q^{74} -21739.8 q^{75} +28234.5 q^{76} +66467.7 q^{77} +1549.83 q^{78} +68029.7 q^{79} +28868.3 q^{80} -38458.2 q^{81} +32338.4 q^{82} +32492.4 q^{83} +52438.8 q^{84} +95237.5 q^{85} -55708.5 q^{86} -11172.2 q^{87} +63280.8 q^{88} -31236.8 q^{89} +11960.5 q^{90} +7010.68 q^{91} +990.611 q^{92} -115436. q^{93} +20399.1 q^{94} -77278.5 q^{95} +77848.9 q^{96} -108828. q^{97} -20083.9 q^{98} -28240.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4 q^{2} + 26 q^{3} + 154 q^{4} + 32 q^{5} + 22 q^{6} + 184 q^{7} + 942 q^{8} + 1005 q^{9}+O(q^{10}) \) 7 * q + 4 * q^2 + 26 * q^3 + 154 * q^4 + 32 * q^5 + 22 * q^6 + 184 * q^7 + 942 * q^8 + 1005 * q^9	\( 7 q + 4 q^{2} + 26 q^{3} + 154 q^{4} + 32 q^{5} + 22 q^{6} + 184 q^{7} + 942 q^{8} + 1005 q^{9} + 922 q^{10} + 1106 q^{11} + 214 q^{12} + 408 q^{13} - 2008 q^{14} - 614 q^{15} + 242 q^{16} - 874 q^{17} - 5598 q^{18} + 4288 q^{19} - 6350 q^{20} - 4200 q^{21} - 6114 q^{22} - 4532 q^{23} - 4318 q^{24} + 5527 q^{25} - 19806 q^{26} + 5942 q^{27} - 496 q^{28} + 5887 q^{29} - 16734 q^{30} + 7794 q^{31} + 7898 q^{32} + 34410 q^{33} + 20840 q^{34} + 7088 q^{35} - 572 q^{36} + 5086 q^{37} + 23732 q^{38} + 33394 q^{39} + 22906 q^{40} + 19826 q^{41} - 55440 q^{42} + 19498 q^{43} - 6074 q^{44} + 7854 q^{45} - 12404 q^{46} + 14278 q^{47} - 16406 q^{48} + 38431 q^{49} - 41066 q^{50} + 23892 q^{51} - 34302 q^{52} - 58644 q^{53} - 31194 q^{54} - 25574 q^{55} - 79560 q^{56} - 88540 q^{57} + 3364 q^{58} + 12888 q^{59} - 180822 q^{60} + 102866 q^{61} - 42654 q^{62} - 88632 q^{63} - 10170 q^{64} - 149206 q^{65} + 7710 q^{66} + 102996 q^{67} + 85100 q^{68} - 107244 q^{69} + 349480 q^{70} - 51596 q^{71} + 135568 q^{72} - 17566 q^{73} + 12132 q^{74} + 39356 q^{75} + 360740 q^{76} - 94104 q^{77} + 46386 q^{78} + 212058 q^{79} + 142510 q^{80} - 128285 q^{81} + 201924 q^{82} - 122928 q^{83} - 12328 q^{84} - 109336 q^{85} - 63290 q^{86} + 21866 q^{87} + 136666 q^{88} - 66510 q^{89} + 56084 q^{90} + 194368 q^{91} - 110108 q^{92} - 474274 q^{93} + 438926 q^{94} - 131676 q^{95} - 117018 q^{96} - 118182 q^{97} - 29132 q^{98} + 300668 q^{99}+O(q^{100}) \) 7 * q + 4 * q^2 + 26 * q^3 + 154 * q^4 + 32 * q^5 + 22 * q^6 + 184 * q^7 + 942 * q^8 + 1005 * q^9 + 922 * q^10 + 1106 * q^11 + 214 * q^12 + 408 * q^13 - 2008 * q^14 - 614 * q^15 + 242 * q^16 - 874 * q^17 - 5598 * q^18 + 4288 * q^19 - 6350 * q^20 - 4200 * q^21 - 6114 * q^22 - 4532 * q^23 - 4318 * q^24 + 5527 * q^25 - 19806 * q^26 + 5942 * q^27 - 496 * q^28 + 5887 * q^29 - 16734 * q^30 + 7794 * q^31 + 7898 * q^32 + 34410 * q^33 + 20840 * q^34 + 7088 * q^35 - 572 * q^36 + 5086 * q^37 + 23732 * q^38 + 33394 * q^39 + 22906 * q^40 + 19826 * q^41 - 55440 * q^42 + 19498 * q^43 - 6074 * q^44 + 7854 * q^45 - 12404 * q^46 + 14278 * q^47 - 16406 * q^48 + 38431 * q^49 - 41066 * q^50 + 23892 * q^51 - 34302 * q^52 - 58644 * q^53 - 31194 * q^54 - 25574 * q^55 - 79560 * q^56 - 88540 * q^57 + 3364 * q^58 + 12888 * q^59 - 180822 * q^60 + 102866 * q^61 - 42654 * q^62 - 88632 * q^63 - 10170 * q^64 - 149206 * q^65 + 7710 * q^66 + 102996 * q^67 + 85100 * q^68 - 107244 * q^69 + 349480 * q^70 - 51596 * q^71 + 135568 * q^72 - 17566 * q^73 + 12132 * q^74 + 39356 * q^75 + 360740 * q^76 - 94104 * q^77 + 46386 * q^78 + 212058 * q^79 + 142510 * q^80 - 128285 * q^81 + 201924 * q^82 - 122928 * q^83 - 12328 * q^84 - 109336 * q^85 - 63290 * q^86 + 21866 * q^87 + 136666 * q^88 - 66510 * q^89 + 56084 * q^90 + 194368 * q^91 - 110108 * q^92 - 474274 * q^93 + 438926 * q^94 - 131676 * q^95 - 117018 * q^96 - 118182 * q^97 - 29132 * q^98 + 300668 * q^99

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