LMFDB - Embedded newform 471.6.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,6,Mod(1,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("471.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	471.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:	$75.5407791319$
Analytic rank:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	471.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.01065 q^{2} -9.00000 q^{3} +32.1705 q^{4} -50.4239 q^{5} +72.0959 q^{6} +130.088 q^{7} -1.36618 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-8.01065 q^{2} -9.00000 q^{3} +32.1705 q^{4} -50.4239 q^{5} +72.0959 q^{6} +130.088 q^{7} -1.36618 q^{8} +81.0000 q^{9} +403.929 q^{10} -543.858 q^{11} -289.535 q^{12} +881.397 q^{13} -1042.09 q^{14} +453.815 q^{15} -1018.51 q^{16} -1152.81 q^{17} -648.863 q^{18} +376.341 q^{19} -1622.17 q^{20} -1170.79 q^{21} +4356.65 q^{22} -2808.90 q^{23} +12.2956 q^{24} -582.428 q^{25} -7060.57 q^{26} -729.000 q^{27} +4185.00 q^{28} +2312.72 q^{29} -3635.36 q^{30} +3813.41 q^{31} +8202.67 q^{32} +4894.72 q^{33} +9234.79 q^{34} -6559.54 q^{35} +2605.81 q^{36} +4805.83 q^{37} -3014.74 q^{38} -7932.57 q^{39} +68.8883 q^{40} +1232.77 q^{41} +9378.79 q^{42} -9646.49 q^{43} -17496.2 q^{44} -4084.34 q^{45} +22501.2 q^{46} +11853.0 q^{47} +9166.62 q^{48} +115.839 q^{49} +4665.63 q^{50} +10375.3 q^{51} +28355.0 q^{52} +1751.99 q^{53} +5839.77 q^{54} +27423.4 q^{55} -177.724 q^{56} -3387.07 q^{57} -18526.4 q^{58} +21914.2 q^{59} +14599.5 q^{60} +23265.5 q^{61} -30547.9 q^{62} +10537.1 q^{63} -33116.3 q^{64} -44443.5 q^{65} -39209.9 q^{66} -12277.7 q^{67} -37086.7 q^{68} +25280.1 q^{69} +52546.2 q^{70} +65912.9 q^{71} -110.661 q^{72} -3780.86 q^{73} -38497.8 q^{74} +5241.85 q^{75} +12107.1 q^{76} -70749.3 q^{77} +63545.1 q^{78} +45943.6 q^{79} +51357.4 q^{80} +6561.00 q^{81} -9875.29 q^{82} -42028.6 q^{83} -37665.0 q^{84} +58129.4 q^{85} +77274.7 q^{86} -20814.5 q^{87} +743.009 q^{88} +39290.8 q^{89} +32718.2 q^{90} +114659. q^{91} -90364.0 q^{92} -34320.7 q^{93} -94950.2 q^{94} -18976.6 q^{95} -73824.1 q^{96} -47667.8 q^{97} -927.945 q^{98} -44052.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 8 q^{2} - 270 q^{3} + 470 q^{4} - 136 q^{5} + 72 q^{6} + 68 q^{7} - 261 q^{8} + 2430 q^{9}+O(q^{10}) $ 30 * q - 8 * q^2 - 270 * q^3 + 470 * q^4 - 136 * q^5 + 72 * q^6 + 68 * q^7 - 261 * q^8 + 2430 * q^9	\( 30 q - 8 q^{2} - 270 q^{3} + 470 q^{4} - 136 q^{5} + 72 q^{6} + 68 q^{7} - 261 q^{8} + 2430 q^{9} - 383 q^{10} - 875 q^{11} - 4230 q^{12} + 101 q^{13} - 2279 q^{14} + 1224 q^{15} + 7454 q^{16} - 4042 q^{17} - 648 q^{18} + 846 q^{19} - 5089 q^{20} - 612 q^{21} - 700 q^{22} - 5902 q^{23} + 2349 q^{24} + 12880 q^{25} - 7567 q^{26} - 21870 q^{27} - 375 q^{28} - 10301 q^{29} + 3447 q^{30} - 4099 q^{31} - 1560 q^{32} + 7875 q^{33} - 3683 q^{34} - 20686 q^{35} + 38070 q^{36} + 8468 q^{37} - 11848 q^{38} - 909 q^{39} - 5132 q^{40} - 47958 q^{41} + 20511 q^{42} + 63916 q^{43} + 3101 q^{44} - 11016 q^{45} + 19654 q^{46} + 8589 q^{47} - 67086 q^{48} + 27834 q^{49} + 121727 q^{50} + 36378 q^{51} + 56510 q^{52} + 10134 q^{53} + 5832 q^{54} - 11473 q^{55} - 68192 q^{56} - 7614 q^{57} + 32006 q^{58} - 64236 q^{59} + 45801 q^{60} - 98194 q^{61} - 67276 q^{62} + 5508 q^{63} + 138849 q^{64} - 155917 q^{65} + 6300 q^{66} + 62323 q^{67} - 117531 q^{68} + 53118 q^{69} - 220939 q^{70} - 179713 q^{71} - 21141 q^{72} - 148343 q^{73} - 214732 q^{74} - 115920 q^{75} - 189758 q^{76} - 142357 q^{77} + 68103 q^{78} + 26916 q^{79} - 463727 q^{80} + 196830 q^{81} - 206514 q^{82} - 89285 q^{83} + 3375 q^{84} - 23932 q^{85} - 477235 q^{86} + 92709 q^{87} - 114708 q^{88} - 474411 q^{89} - 31023 q^{90} + 51305 q^{91} - 1030074 q^{92} + 36891 q^{93} - 485800 q^{94} - 169960 q^{95} + 14040 q^{96} - 169188 q^{97} - 629739 q^{98} - 70875 q^{99}+O(q^{100}) \) 30 * q - 8 * q^2 - 270 * q^3 + 470 * q^4 - 136 * q^5 + 72 * q^6 + 68 * q^7 - 261 * q^8 + 2430 * q^9 - 383 * q^10 - 875 * q^11 - 4230 * q^12 + 101 * q^13 - 2279 * q^14 + 1224 * q^15 + 7454 * q^16 - 4042 * q^17 - 648 * q^18 + 846 * q^19 - 5089 * q^20 - 612 * q^21 - 700 * q^22 - 5902 * q^23 + 2349 * q^24 + 12880 * q^25 - 7567 * q^26 - 21870 * q^27 - 375 * q^28 - 10301 * q^29 + 3447 * q^30 - 4099 * q^31 - 1560 * q^32 + 7875 * q^33 - 3683 * q^34 - 20686 * q^35 + 38070 * q^36 + 8468 * q^37 - 11848 * q^38 - 909 * q^39 - 5132 * q^40 - 47958 * q^41 + 20511 * q^42 + 63916 * q^43 + 3101 * q^44 - 11016 * q^45 + 19654 * q^46 + 8589 * q^47 - 67086 * q^48 + 27834 * q^49 + 121727 * q^50 + 36378 * q^51 + 56510 * q^52 + 10134 * q^53 + 5832 * q^54 - 11473 * q^55 - 68192 * q^56 - 7614 * q^57 + 32006 * q^58 - 64236 * q^59 + 45801 * q^60 - 98194 * q^61 - 67276 * q^62 + 5508 * q^63 + 138849 * q^64 - 155917 * q^65 + 6300 * q^66 + 62323 * q^67 - 117531 * q^68 + 53118 * q^69 - 220939 * q^70 - 179713 * q^71 - 21141 * q^72 - 148343 * q^73 - 214732 * q^74 - 115920 * q^75 - 189758 * q^76 - 142357 * q^77 + 68103 * q^78 + 26916 * q^79 - 463727 * q^80 + 196830 * q^81 - 206514 * q^82 - 89285 * q^83 + 3375 * q^84 - 23932 * q^85 - 477235 * q^86 + 92709 * q^87 - 114708 * q^88 - 474411 * q^89 - 31023 * q^90 + 51305 * q^91 - 1030074 * q^92 + 36891 * q^93 - 485800 * q^94 - 169960 * q^95 + 14040 * q^96 - 169188 * q^97 - 629739 * q^98 - 70875 * 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 $

$2$	−8.01065	−1.41610	−0.708048	−	0.706164i	$-0.750424\pi$
$2$	−8.01065	−1.41610	−0.708048	+	0.706164i	$0.750424\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	32.1705	1.00533
$5$	−50.4239	−0.902011	−0.451005	−	0.892521i	$-0.648934\pi$
$5$	−50.4239	−0.902011	−0.451005	+	0.892521i	$0.648934\pi$
$6$	72.0959	0.817584
$7$	130.088	1.00344	0.501720	−	0.865030i	$-0.332701\pi$
$7$	130.088	1.00344	0.501720	+	0.865030i	$0.332701\pi$
$8$	−1.36618	−0.00754716
$9$	81.0000	0.333333
$10$	403.929	1.27733
$11$	−543.858	−1.35520	−0.677600	−	0.735430i	$-0.736980\pi$
$11$	−543.858	−1.35520	−0.677600	+	0.735430i	$0.736980\pi$
$12$	−289.535	−0.580427
$13$	881.397	1.44648	0.723241	−	0.690595i	$-0.242651\pi$
$13$	881.397	1.44648	0.723241	+	0.690595i	$0.242651\pi$
$14$	−1042.09	−1.42097
$15$	453.815	0.520776
$16$	−1018.51	−0.994642
$17$	−1152.81	−0.967469	−0.483734	−	0.875215i	$-0.660720\pi$
$17$	−1152.81	−0.967469	−0.483734	+	0.875215i	$0.660720\pi$
$18$	−648.863	−0.472032
$19$	376.341	0.239165	0.119582	−	0.992824i	$-0.461844\pi$
$19$	376.341	0.239165	0.119582	+	0.992824i	$0.461844\pi$
$20$	−1622.17	−0.906818
$21$	−1170.79	−0.579336
$22$	4356.65	1.91909
$23$	−2808.90	−1.10718	−0.553589	−	0.832790i	$-0.686742\pi$
$23$	−2808.90	−1.10718	−0.553589	+	0.832790i	$0.686742\pi$
$24$	12.2956	0.00435736
$25$	−582.428	−0.186377
$26$	−7060.57	−2.04836
$27$	−729.000	−0.192450
$28$	4185.00	1.00879
$29$	2312.72	0.510656	0.255328	−	0.966855i	$-0.417817\pi$
$29$	2312.72	0.510656	0.255328	+	0.966855i	$0.417817\pi$
$30$	−3635.36	−0.737469
$31$	3813.41	0.712705	0.356352	−	0.934352i	$-0.384020\pi$
$31$	3813.41	0.712705	0.356352	+	0.934352i	$0.384020\pi$
$32$	8202.67	1.41606
$33$	4894.72	0.782425
$34$	9234.79	1.37003
$35$	−6559.54	−0.905114
$36$	2605.81	0.335110
$37$	4805.83	0.577117	0.288558	−	0.957462i	$-0.406824\pi$
$37$	4805.83	0.577117	0.288558	+	0.957462i	$0.406824\pi$
$38$	−3014.74	−0.338681
$39$	−7932.57	−0.835127
$40$	68.8883	0.00680762
$41$	1232.77	0.114531	0.0572654	−	0.998359i	$-0.481762\pi$
$41$	1232.77	0.114531	0.0572654	+	0.998359i	$0.481762\pi$
$42$	9378.79	0.820396
$43$	−9646.49	−0.795606	−0.397803	−	0.917471i	$-0.630227\pi$
$43$	−9646.49	−0.795606	−0.397803	+	0.917471i	$0.630227\pi$
$44$	−17496.2	−1.36242
$45$	−4084.34	−0.300670
$46$	22501.2	1.56787
$47$	11853.0	0.782678	0.391339	−	0.920247i	$-0.372012\pi$
$47$	11853.0	0.782678	0.391339	+	0.920247i	$0.372012\pi$
$48$	9166.62	0.574257
$49$	115.839	0.00689230
$50$	4665.63	0.263928
$51$	10375.3	0.558568
$52$	28355.0	1.45419
$53$	1751.99	0.0856725	0.0428363	−	0.999082i	$-0.486361\pi$
$53$	1751.99	0.0856725	0.0428363	+	0.999082i	$0.486361\pi$
$54$	5839.77	0.272528
$55$	27423.4	1.22241
$56$	−177.724	−0.00757313
$57$	−3387.07	−0.138082
$58$	−18526.4	−0.723138
$59$	21914.2	0.819589	0.409794	−	0.912178i	$-0.365600\pi$
$59$	21914.2	0.819589	0.409794	+	0.912178i	$0.365600\pi$
$60$	14599.5	0.523552
$61$	23265.5	0.800548	0.400274	−	0.916395i	$-0.368915\pi$
$61$	23265.5	0.800548	0.400274	+	0.916395i	$0.368915\pi$
$62$	−30547.9	−1.00926
$63$	10537.1	0.334480
$64$	−33116.3	−1.01063
$65$	−44443.5	−1.30474
$66$	−39209.9	−1.10799
$67$	−12277.7	−0.334140	−0.167070	−	0.985945i	$-0.553431\pi$
$67$	−12277.7	−0.334140	−0.167070	+	0.985945i	$0.553431\pi$
$68$	−37086.7	−0.972625
$69$	25280.1	0.639229
$70$	52546.2	1.28173
$71$	65912.9	1.55176	0.775880	−	0.630881i	$-0.217306\pi$
$71$	65912.9	1.55176	0.775880	+	0.630881i	$0.217306\pi$
$72$	−110.661	−0.00251572
$73$	−3780.86	−0.0830392	−0.0415196	−	0.999138i	$-0.513220\pi$
$73$	−3780.86	−0.0830392	−0.0415196	+	0.999138i	$0.513220\pi$
$74$	−38497.8	−0.817253
$75$	5241.85	0.107605
$76$	12107.1	0.240440
$77$	−70749.3	−1.35986
$78$	63545.1	1.18262
$79$	45943.6	0.828242	0.414121	−	0.910222i	$-0.364089\pi$
$79$	45943.6	0.828242	0.414121	+	0.910222i	$0.364089\pi$
$80$	51357.4	0.897178
$81$	6561.00	0.111111
$82$	−9875.29	−0.162187
$83$	−42028.6	−0.669654	−0.334827	−	0.942280i	$-0.608678\pi$
$83$	−42028.6	−0.669654	−0.334827	+	0.942280i	$0.608678\pi$
$84$	−37665.0	−0.582424
$85$	58129.4	0.872667
$86$	77274.7	1.12666
$87$	−20814.5	−0.294827
$88$	743.009	0.0102279
$89$	39290.8	0.525795	0.262897	−	0.964824i	$-0.415322\pi$
$89$	39290.8	0.525795	0.262897	+	0.964824i	$0.415322\pi$
$90$	32718.2	0.425778
$91$	114659.	1.45146
$92$	−90364.0	−1.11308
$93$	−34320.7	−0.411480
$94$	−94950.2	−1.10835
$95$	−18976.6	−0.215729
$96$	−73824.1	−0.817561
$97$	−47667.8	−0.514394	−0.257197	−	0.966359i	$-0.582799\pi$
$97$	−47667.8	−0.514394	−0.257197	+	0.966359i	$0.582799\pi$
$98$	−927.945	−0.00976016
$99$	−44052.5	−0.451733
$100$	−18737.0	−0.187370
$101$	−56384.0	−0.549987	−0.274994	−	0.961446i	$-0.588676\pi$
$101$	−56384.0	−0.549987	−0.274994	+	0.961446i	$0.588676\pi$
$102$	−83113.1	−0.790987
$103$	176480.	1.63909	0.819545	−	0.573015i	$-0.194226\pi$
$103$	176480.	1.63909	0.819545	+	0.573015i	$0.194226\pi$
$104$	−1204.15	−0.0109168
$105$	59035.8	0.522568
$106$	−14034.6	−0.121321
$107$	71931.0	0.607375	0.303687	−	0.952772i	$-0.401782\pi$
$107$	71931.0	0.607375	0.303687	+	0.952772i	$0.401782\pi$
$108$	−23452.3	−0.193476
$109$	−142324.	−1.14739	−0.573696	−	0.819068i	$-0.694491\pi$
$109$	−142324.	−1.14739	−0.573696	+	0.819068i	$0.694491\pi$
$110$	−219680.	−1.73104
$111$	−43252.4	−0.333199
$112$	−132496.	−0.998064
$113$	137208.	1.01084	0.505421	−	0.862873i	$-0.331337\pi$
$113$	137208.	1.01084	0.505421	+	0.862873i	$0.331337\pi$
$114$	27132.6	0.195537
$115$	141636.	0.998686
$116$	74401.5	0.513377
$117$	71393.2	0.482161
$118$	−175547.	−1.16062
$119$	−149967.	−0.970797
$120$	−619.994	−0.00393038
$121$	134730.	0.836568
$122$	−186372.	−1.13365
$123$	−11094.9	−0.0661244
$124$	122680.	0.716503
$125$	186943.	1.07012
$126$	−84409.1	−0.473656
$127$	−284159.	−1.56334	−0.781669	−	0.623694i	$-0.785631\pi$
$127$	−284159.	−1.56334	−0.781669	+	0.623694i	$0.785631\pi$
$128$	2797.90	0.0150941
$129$	86818.4	0.459344
$130$	356021.	1.84764
$131$	39819.3	0.202729	0.101364	−	0.994849i	$-0.467679\pi$
$131$	39819.3	0.202729	0.101364	+	0.994849i	$0.467679\pi$
$132$	157466.	0.786595
$133$	48957.4	0.239988
$134$	98352.0	0.473175
$135$	36759.0	0.173592
$136$	1574.95	0.00730164
$137$	−288640.	−1.31388	−0.656939	−	0.753944i	$-0.728149\pi$
$137$	−288640.	−1.31388	−0.656939	+	0.753944i	$0.728149\pi$
$138$	−202510.	−0.905210
$139$	287463.	1.26196	0.630979	−	0.775800i	$-0.282653\pi$
$139$	287463.	1.26196	0.630979	+	0.775800i	$0.282653\pi$
$140$	−211024.	−0.909938
$141$	−106677.	−0.451879
$142$	−528005.	−2.19744
$143$	−479355.	−1.96027
$144$	−82499.6	−0.331547
$145$	−116616.	−0.460617
$146$	30287.1	0.117592
$147$	−1042.55	−0.00397927
$148$	154606.	0.580193
$149$	−246867.	−0.910956	−0.455478	−	0.890247i	$-0.650532\pi$
$149$	−246867.	−0.910956	−0.455478	+	0.890247i	$0.650532\pi$
$150$	−41990.6	−0.152379
$151$	−231949.	−0.827848	−0.413924	−	0.910311i	$-0.635842\pi$
$151$	−231949.	−0.827848	−0.413924	+	0.910311i	$0.635842\pi$
$152$	−514.150	−0.00180502
$153$	−93377.9	−0.322490
$154$	566748.	1.92570
$155$	−192287.	−0.642867
$156$	−255195.	−0.839578
$157$	−24649.0	−0.0798087
$157$	−24649.0	−0.0798087
$158$	−368038.	−1.17287
$159$	−15767.9	−0.0494631
$160$	−413611.	−1.27730
$161$	−365404.	−1.11099
$162$	−52557.9	−0.157344
$163$	−132246.	−0.389865	−0.194933	−	0.980817i	$-0.562449\pi$
$163$	−132246.	−0.389865	−0.194933	+	0.980817i	$0.562449\pi$
$164$	39658.9	0.115141
$165$	−246811.	−0.705756
$166$	336677.	0.948294
$167$	−499847.	−1.38690	−0.693452	−	0.720503i	$-0.743911\pi$
$167$	−499847.	−1.38690	−0.693452	+	0.720503i	$0.743911\pi$
$168$	1599.51	0.00437235
$169$	405568.	1.09231
$170$	−465654.	−1.23578
$171$	30483.6	0.0797216
$172$	−310333.	−0.799847
$173$	183603.	0.466406	0.233203	−	0.972428i	$-0.425079\pi$
$173$	183603.	0.466406	0.233203	+	0.972428i	$0.425079\pi$
$174$	166738.	0.417504
$175$	−75766.8	−0.187018
$176$	553926.	1.34794
$177$	−197228.	−0.473190
$178$	−314745.	−0.744576
$179$	−675753.	−1.57636	−0.788180	−	0.615445i	$-0.788976\pi$
$179$	−675753.	−1.57636	−0.788180	+	0.615445i	$0.788976\pi$
$180$	−131395.	−0.302273
$181$	−135576.	−0.307601	−0.153801	−	0.988102i	$-0.549151\pi$
$181$	−135576.	−0.307601	−0.153801	+	0.988102i	$0.549151\pi$
$182$	−918494.	−2.05541
$183$	−209389.	−0.462197
$184$	3837.47	0.00835605
$185$	−242329.	−0.520566
$186$	274931.	0.582696
$187$	626967.	1.31111
$188$	381317.	0.786849
$189$	−94834.0	−0.193112
$190$	152015.	0.305494
$191$	−435271.	−0.863329	−0.431665	−	0.902034i	$-0.642074\pi$
$191$	−435271.	−0.863329	−0.431665	+	0.902034i	$0.642074\pi$
$192$	298047.	0.583488
$193$	114292.	0.220862	0.110431	−	0.993884i	$-0.464777\pi$
$193$	114292.	0.220862	0.110431	+	0.993884i	$0.464777\pi$
$194$	381850.	0.728431
$195$	399992.	0.753294
$196$	3726.60	0.00692903
$197$	−350757.	−0.643933	−0.321967	−	0.946751i	$-0.604344\pi$
$197$	−350757.	−0.643933	−0.321967	+	0.946751i	$0.604344\pi$
$198$	352889.	0.639698
$199$	−317648.	−0.568609	−0.284304	−	0.958734i	$-0.591763\pi$
$199$	−317648.	−0.568609	−0.284304	+	0.958734i	$0.591763\pi$
$200$	795.703	0.00140662
$201$	110499.	0.192916
$202$	451673.	0.778835
$203$	300857.	0.512412
$204$	333780.	0.561545
$205$	−62161.1	−0.103308
$206$	−1.41372e6	−2.32111
$207$	−227521.	−0.369059
$208$	−897715.	−1.43873
$209$	−204676.	−0.324116
$210$	−472916.	−0.740006
$211$	−868366.	−1.34275	−0.671377	−	0.741116i	$-0.734297\pi$
$211$	−868366.	−1.34275	−0.671377	+	0.741116i	$0.734297\pi$
$212$	56362.4	0.0861291
$213$	−593216.	−0.895909
$214$	−576215.	−0.860102
$215$	486414.	0.717645
$216$	995.947	0.00145245
$217$	496078.	0.715156
$218$	1.14011e6	1.62482
$219$	34027.7	0.0479427
$220$	882227.	1.22892
$221$	−1.01609e6	−1.39943
$222$	346480.	0.471841
$223$	110563.	0.148884	0.0744422	−	0.997225i	$-0.476282\pi$
$223$	110563.	0.148884	0.0744422	+	0.997225i	$0.476282\pi$
$224$	1.06707e6	1.42093
$225$	−47176.7	−0.0621256
$226$	−1.09913e6	−1.43145
$227$	482629.	0.621654	0.310827	−	0.950467i	$-0.399394\pi$
$227$	482629.	0.621654	0.310827	+	0.950467i	$0.399394\pi$
$228$	−108964.	−0.138818
$229$	264468.	0.333260	0.166630	−	0.986019i	$-0.446711\pi$
$229$	264468.	0.333260	0.166630	+	0.986019i	$0.446711\pi$
$230$	−1.13460e6	−1.41424
$231$	636743.	0.785117
$232$	−3159.60	−0.00385400
$233$	1.35835e6	1.63916	0.819581	−	0.572963i	$-0.194206\pi$
$233$	1.35835e6	1.63916	0.819581	+	0.572963i	$0.194206\pi$
$234$	−571906.	−0.682786
$235$	−597674.	−0.705984
$236$	704992.	0.823957
$237$	−413493.	−0.478186
$238$	1.20133e6	1.37474
$239$	188728.	0.213718	0.106859	−	0.994274i	$-0.465921\pi$
$239$	188728.	0.213718	0.106859	+	0.994274i	$0.465921\pi$
$240$	−462217.	−0.517986
$241$	−186252.	−0.206565	−0.103283	−	0.994652i	$-0.532935\pi$
$241$	−186252.	−0.206565	−0.103283	+	0.994652i	$0.532935\pi$
$242$	−1.07928e6	−1.18466
$243$	−59049.0	−0.0641500
$244$	748463.	0.804815
$245$	−5841.05	−0.00621693
$246$	88877.6	0.0936385
$247$	331706.	0.345948
$248$	−5209.82	−0.00537890
$249$	378258.	0.386625
$250$	−1.49754e6	−1.51540
$251$	1.47025e6	1.47301	0.736505	−	0.676432i	$-0.236475\pi$
$251$	1.47025e6	1.47301	0.736505	+	0.676432i	$0.236475\pi$
$252$	338985.	0.336263
$253$	1.52764e6	1.50045
$254$	2.27630e6	2.21384
$255$	−523165.	−0.503835
$256$	1.03731e6	0.989256
$257$	−1.28684e6	−1.21532	−0.607660	−	0.794197i	$-0.707892\pi$
$257$	−1.28684e6	−1.21532	−0.607660	+	0.794197i	$0.707892\pi$
$258$	−695472.	−0.650475
$259$	625180.	0.579102
$260$	−1.42977e6	−1.31170
$261$	187330.	0.170219
$262$	−318979.	−0.287084
$263$	1.28504e6	1.14559	0.572794	−	0.819699i	$-0.305859\pi$
$263$	1.28504e6	1.14559	0.572794	+	0.819699i	$0.305859\pi$
$264$	−6687.08	−0.00590509
$265$	−88342.2	−0.0772775
$266$	−392181.	−0.339846
$267$	−353618.	−0.303568
$268$	−394979.	−0.335921
$269$	−213282.	−0.179711	−0.0898553	−	0.995955i	$-0.528640\pi$
$269$	−213282.	−0.179711	−0.0898553	+	0.995955i	$0.528640\pi$
$270$	−294464.	−0.245823
$271$	1.14006e6	0.942981	0.471490	−	0.881871i	$-0.343716\pi$
$271$	1.14006e6	0.942981	0.471490	+	0.881871i	$0.343716\pi$
$272$	1.17416e6	0.962285
$273$	−1.03193e6	−0.838000
$274$	2.31219e6	1.86058
$275$	316758.	0.252578
$276$	813276.	0.642636
$277$	597548.	0.467922	0.233961	−	0.972246i	$-0.424831\pi$
$277$	597548.	0.467922	0.233961	+	0.972246i	$0.424831\pi$
$278$	−2.30277e6	−1.78705
$279$	308886.	0.237568
$280$	8961.52	0.00683104
$281$	151453.	0.114423	0.0572113	−	0.998362i	$-0.481779\pi$
$281$	151453.	0.114423	0.0572113	+	0.998362i	$0.481779\pi$
$282$	854551.	0.639905
$283$	785823.	0.583255	0.291628	−	0.956532i	$-0.405803\pi$
$283$	785823.	0.583255	0.291628	+	0.956532i	$0.405803\pi$
$284$	2.12045e6	1.56003
$285$	170789.	0.124551
$286$	3.83994e6	2.77594
$287$	160368.	0.114925
$288$	664417.	0.472019
$289$	−90876.9	−0.0640042
$290$	934174.	0.652278
$291$	429010.	0.296985
$292$	−121632.	−0.0834818
$293$	−2.00010e6	−1.36108	−0.680538	−	0.732713i	$-0.738254\pi$
$293$	−2.00010e6	−1.36108	−0.680538	+	0.732713i	$0.738254\pi$
$294$	8351.51	0.00563503
$295$	−1.10500e6	−0.739278
$296$	−6565.64	−0.00435559
$297$	396472.	0.260808
$298$	1.97757e6	1.29000
$299$	−2.47576e6	−1.60151
$300$	168633.	0.108178
$301$	−1.25489e6	−0.798343
$302$	1.85807e6	1.17231
$303$	507456.	0.317535
$304$	−383308.	−0.237884
$305$	−1.17314e6	−0.722103
$306$	748018.	0.456676
$307$	1.55974e6	0.944511	0.472255	−	0.881462i	$-0.343440\pi$
$307$	1.55974e6	0.944511	0.472255	+	0.881462i	$0.343440\pi$
$308$	−2.27604e6	−1.36711
$309$	−1.58832e6	−0.946329
$310$	1.54035e6	0.910362
$311$	−201859.	−0.118344	−0.0591721	−	0.998248i	$-0.518846\pi$
$311$	−201859.	−0.118344	−0.0591721	+	0.998248i	$0.518846\pi$
$312$	10837.3	0.00630284
$313$	602644.	0.347696	0.173848	−	0.984772i	$-0.444380\pi$
$313$	602644.	0.347696	0.173848	+	0.984772i	$0.444380\pi$
$314$	197455.	0.113017
$315$	−531323.	−0.301705
$316$	1.47803e6	0.832657
$317$	−167035.	−0.0933594	−0.0466797	−	0.998910i	$-0.514864\pi$
$317$	−167035.	−0.0933594	−0.0466797	+	0.998910i	$0.514864\pi$
$318$	126311.	0.0700445
$319$	−1.25779e6	−0.692041
$320$	1.66986e6	0.911599
$321$	−647379.	−0.350668
$322$	2.92713e6	1.57326
$323$	−433851.	−0.231385
$324$	211071.	0.111703
$325$	−513350.	−0.269591
$326$	1.05938e6	0.552087
$327$	1.28092e6	0.662447
$328$	−1684.19	−0.000864383 0
$329$	1.54193e6	0.785371
$330$	1.97712e6	0.999419
$331$	−3.16373e6	−1.58719	−0.793596	−	0.608445i	$-0.791794\pi$
$331$	−3.16373e6	−1.58719	−0.793596	+	0.608445i	$0.791794\pi$
$332$	−1.35208e6	−0.673222
$333$	389272.	0.192372
$334$	4.00410e6	1.96399
$335$	619088.	0.301398
$336$	1.19247e6	0.576232
$337$	862985.	0.413932	0.206966	−	0.978348i	$-0.433641\pi$
$337$	862985.	0.413932	0.206966	+	0.978348i	$0.433641\pi$
$338$	−3.24886e6	−1.54682
$339$	−1.23487e6	−0.583610
$340$	1.87005e6	0.877318
$341$	−2.07395e6	−0.965858
$342$	−244194.	−0.112894
$343$	−2.17132e6	−0.996524
$344$	13178.9	0.00600457
$345$	−1.27472e6	−0.576592
$346$	−1.47078e6	−0.660476
$347$	−594390.	−0.265001	−0.132501	−	0.991183i	$-0.542301\pi$
$347$	−594390.	−0.265001	−0.132501	+	0.991183i	$0.542301\pi$
$348$	−669613.	−0.296398
$349$	−708488.	−0.311364	−0.155682	−	0.987807i	$-0.549758\pi$
$349$	−708488.	−0.311364	−0.155682	+	0.987807i	$0.549758\pi$
$350$	606941.	0.264836
$351$	−642538.	−0.278376
$352$	−4.46109e6	−1.91904
$353$	−4.42524e6	−1.89017	−0.945084	−	0.326827i	$-0.894020\pi$
$353$	−4.42524e6	−1.89017	−0.945084	+	0.326827i	$0.894020\pi$
$354$	1.57992e6	0.670082
$355$	−3.32359e6	−1.39970
$356$	1.26401e6	0.528597
$357$	1.34970e6	0.560490
$358$	5.41322e6	2.23228
$359$	−1.66754e6	−0.682872	−0.341436	−	0.939905i	$-0.610913\pi$
$359$	−1.66754e6	−0.682872	−0.341436	+	0.939905i	$0.610913\pi$
$360$	5579.95	0.00226921
$361$	−2.33447e6	−0.942800
$362$	1.08606e6	0.435593
$363$	−1.21257e6	−0.482993
$364$	3.68864e6	1.45919
$365$	190646.	0.0749023
$366$	1.67735e6	0.654515
$367$	−1.61412e6	−0.625562	−0.312781	−	0.949825i	$-0.601261\pi$
$367$	−1.61412e6	−0.625562	−0.312781	+	0.949825i	$0.601261\pi$
$368$	2.86091e6	1.10125
$369$	99854.4	0.0381769
$370$	1.94121e6	0.737171
$371$	227912.	0.0859673
$372$	−1.10412e6	−0.413673
$373$	161337.	0.0600431	0.0300216	−	0.999549i	$-0.490442\pi$
$373$	161337.	0.0600431	0.0300216	+	0.999549i	$0.490442\pi$
$374$	−5.02241e6	−1.85666
$375$	−1.68249e6	−0.617837
$376$	−16193.3	−0.00590700
$377$	2.03842e6	0.738654
$378$	759682.	0.273465
$379$	−4.76876e6	−1.70533	−0.852663	−	0.522462i	$-0.825014\pi$
$379$	−4.76876e6	−1.70533	−0.852663	+	0.522462i	$0.825014\pi$
$380$	−610487.	−0.216879
$381$	2.55743e6	0.902593
$382$	3.48681e6	1.22256
$383$	−3.60084e6	−1.25432	−0.627159	−	0.778892i	$-0.715782\pi$
$383$	−3.60084e6	−1.25432	−0.627159	+	0.778892i	$0.715782\pi$
$384$	−25181.1	−0.00871459
$385$	3.56745e6	1.22661
$386$	−915550.	−0.312762
$387$	−781366.	−0.265202
$388$	−1.53350e6	−0.517135
$389$	3.19249e6	1.06968	0.534842	−	0.844952i	$-0.320371\pi$
$389$	3.19249e6	1.06968	0.534842	+	0.844952i	$0.320371\pi$
$390$	−3.20419e6	−1.06674
$391$	3.23814e6	1.07116
$392$	−158.257	−5.20173e−5 0
$393$	−358374.	−0.117046
$394$	2.80979e6	0.911871
$395$	−2.31666e6	−0.747083
$396$	−1.41719e6	−0.454141
$397$	−965266.	−0.307377	−0.153688	−	0.988119i	$-0.549115\pi$
$397$	−965266.	−0.307377	−0.153688	+	0.988119i	$0.549115\pi$
$398$	2.54457e6	0.805205
$399$	−440616.	−0.138557
$400$	593211.	0.185378
$401$	1.22115e6	0.379234	0.189617	−	0.981858i	$-0.439275\pi$
$401$	1.22115e6	0.379234	0.189617	+	0.981858i	$0.439275\pi$
$402$	−885168.	−0.273187
$403$	3.36113e6	1.03091
$404$	−1.81391e6	−0.552919
$405$	−330831.	−0.100223
$406$	−2.41006e6	−0.725625
$407$	−2.61369e6	−0.782109
$408$	−14174.6	−0.00421561
$409$	−289200.	−0.0854850	−0.0427425	−	0.999086i	$-0.513610\pi$
$409$	−289200.	−0.0854850	−0.0427425	+	0.999086i	$0.513610\pi$
$410$	497951.	0.146294
$411$	2.59776e6	0.758568
$412$	5.67746e6	1.64783
$413$	2.85077e6	0.822408
$414$	1.82259e6	0.522623
$415$	2.11925e6	0.604035
$416$	7.22981e6	2.04830
$417$	−2.58717e6	−0.728592
$418$	1.63959e6	0.458980
$419$	6.51026e6	1.81160	0.905802	−	0.423701i	$-0.139269\pi$
$419$	6.51026e6	1.81160	0.905802	+	0.423701i	$0.139269\pi$
$420$	1.89922e6	0.525353
$421$	3.87989e6	1.06688	0.533439	−	0.845839i	$-0.320900\pi$
$421$	3.87989e6	1.06688	0.533439	+	0.845839i	$0.320900\pi$
$422$	6.95617e6	1.90147
$423$	960092.	0.260893
$424$	−2393.54	−0.000646585 0
$425$	671431.	0.180314
$426$	4.75205e6	1.26869
$427$	3.02656e6	0.803302
$428$	2.31406e6	0.610612
$429$	4.31419e6	1.13176
$430$	−3.89649e6	−1.01626
$431$	−7.38490e6	−1.91492	−0.957462	−	0.288561i	$-0.906823\pi$
$431$	−7.38490e6	−1.91492	−0.957462	+	0.288561i	$0.906823\pi$
$432$	742496.	0.191419
$433$	270737.	0.0693951	0.0346975	−	0.999398i	$-0.488953\pi$
$433$	270737.	0.0693951	0.0346975	+	0.999398i	$0.488953\pi$
$434$	−3.97391e6	−1.01273
$435$	1.04955e6	0.265937
$436$	−4.57864e6	−1.15351
$437$	−1.05711e6	−0.264798
$438$	−272584.	−0.0678915
$439$	1.83338e6	0.454037	0.227018	−	0.973890i	$-0.427102\pi$
$439$	1.83338e6	0.454037	0.227018	+	0.973890i	$0.427102\pi$
$440$	−37465.4	−0.00922569
$441$	9382.95	0.00229743
$442$	8.13952e6	1.98172
$443$	787815.	0.190728	0.0953641	−	0.995442i	$-0.469598\pi$
$443$	787815.	0.190728	0.0953641	+	0.995442i	$0.469598\pi$
$444$	−1.39145e6	−0.334974
$445$	−1.98120e6	−0.474273
$446$	−885684.	−0.210835
$447$	2.22180e6	0.525941
$448$	−4.30803e6	−1.01411
$449$	−2.43718e6	−0.570521	−0.285261	−	0.958450i	$-0.592080\pi$
$449$	−2.43718e6	−0.570521	−0.285261	+	0.958450i	$0.592080\pi$
$450$	377916.	0.0879759
$451$	−670451.	−0.155212
$452$	4.41406e6	1.01623
$453$	2.08754e6	0.477958
$454$	−3.86617e6	−0.880322
$455$	−5.78156e6	−1.30923
$456$	4627.35	0.00104213
$457$	−5.84362e6	−1.30886	−0.654428	−	0.756125i	$-0.727090\pi$
$457$	−5.84362e6	−1.30886	−0.654428	+	0.756125i	$0.727090\pi$
$458$	−2.11856e6	−0.471929
$459$	840401.	0.186189
$460$	4.55651e6	1.00401
$461$	−3.47871e6	−0.762371	−0.381185	−	0.924499i	$-0.624484\pi$
$461$	−3.47871e6	−0.762371	−0.381185	+	0.924499i	$0.624484\pi$
$462$	−5.10073e6	−1.11180
$463$	−1.57539e6	−0.341535	−0.170768	−	0.985311i	$-0.554625\pi$
$463$	−1.57539e6	−0.341535	−0.170768	+	0.985311i	$0.554625\pi$
$464$	−2.35554e6	−0.507920
$465$	1.73058e6	0.371159
$466$	−1.08813e7	−2.32121
$467$	−5.67553e6	−1.20424	−0.602121	−	0.798405i	$-0.705678\pi$
$467$	−5.67553e6	−1.20424	−0.602121	+	0.798405i	$0.705678\pi$
$468$	2.29676e6	0.484731
$469$	−1.59717e6	−0.335290
$470$	4.78776e6	0.999741
$471$	221841.	0.0460776
$472$	−29938.8	−0.00618557
$473$	5.24632e6	1.07821
$474$	3.31235e6	0.677158
$475$	−219191.	−0.0445748
$476$	−4.82452e6	−0.975971
$477$	141911.	0.0285575
$478$	−1.51183e6	−0.302645
$479$	−6.98669e6	−1.39134	−0.695669	−	0.718362i	$-0.744892\pi$
$479$	−6.98669e6	−1.39134	−0.695669	+	0.718362i	$0.744892\pi$
$480$	3.72250e6	0.737448
$481$	4.23584e6	0.834790
$482$	1.49200e6	0.292517
$483$	3.28864e6	0.641428
$484$	4.33434e6	0.841027
$485$	2.40360e6	0.463989
$486$	473021.	0.0908426
$487$	2.29336e6	0.438177	0.219089	−	0.975705i	$-0.429692\pi$
$487$	2.29336e6	0.438177	0.219089	+	0.975705i	$0.429692\pi$
$488$	−31784.9	−0.00604187
$489$	1.19022e6	0.225089
$490$	46790.6	0.00880377
$491$	−4.04531e6	−0.757265	−0.378632	−	0.925547i	$-0.623606\pi$
$491$	−4.04531e6	−0.757265	−0.378632	+	0.925547i	$0.623606\pi$
$492$	−356930.	−0.0664768
$493$	−2.66614e6	−0.494043
$494$	−2.65718e6	−0.489896
$495$	2.22130e6	0.407468
$496$	−3.88401e6	−0.708886
$497$	8.57446e6	1.55710
$498$	−3.03009e6	−0.547498
$499$	−6.10078e6	−1.09682	−0.548408	−	0.836211i	$-0.684766\pi$
$499$	−6.10078e6	−1.09682	−0.548408	+	0.836211i	$0.684766\pi$
$500$	6.01406e6	1.07583
$501$	4.49863e6	0.800729
$502$	−1.17776e7	−2.08592
$503$	553552.	0.0975526	0.0487763	−	0.998810i	$-0.484468\pi$
$503$	553552.	0.0975526	0.0487763	+	0.998810i	$0.484468\pi$
$504$	−14395.6	−0.00252438
$505$	2.84310e6	0.496094
$506$	−1.22374e7	−2.12478
$507$	−3.65011e6	−0.630647
$508$	−9.14156e6	−1.57167
$509$	−7.90065e6	−1.35166	−0.675831	−	0.737056i	$-0.736215\pi$
$509$	−7.90065e6	−1.35166	−0.675831	+	0.737056i	$0.736215\pi$
$510$	4.19089e6	0.713478
$511$	−491844.	−0.0833249
$512$	−8.39906e6	−1.41598
$513$	−274353.	−0.0460273
$514$	1.03084e7	1.72101
$515$	−8.89882e6	−1.47848
$516$	2.79300e6	0.461792
$517$	−6.44634e6	−1.06069
$518$	−5.00810e6	−0.820065
$519$	−1.65242e6	−0.269279
$520$	60717.9	0.00984710
$521$	−2.40957e6	−0.388906	−0.194453	−	0.980912i	$-0.562293\pi$
$521$	−2.40957e6	−0.388906	−0.194453	+	0.980912i	$0.562293\pi$
$522$	−1.50064e6	−0.241046
$523$	3.61719e6	0.578252	0.289126	−	0.957291i	$-0.406635\pi$
$523$	3.61719e6	0.578252	0.289126	+	0.957291i	$0.406635\pi$
$524$	1.28101e6	0.203809
$525$	681901.	0.107975
$526$	−1.02940e7	−1.62226
$527$	−4.39616e6	−0.689519
$528$	−4.98534e6	−0.778233
$529$	1.45360e6	0.225842
$530$	707678.	0.109432
$531$	1.77505e6	0.273196
$532$	1.57499e6	0.241267
$533$	1.08656e6	0.165667
$534$	2.83271e6	0.429881
$535$	−3.62705e6	−0.547859
$536$	16773.5	0.00252181
$537$	6.08177e6	0.910111
$538$	1.70853e6	0.254488
$539$	−62999.9	−0.00934045
$540$	1.18256e6	0.174517
$541$	505392.	0.0742395	0.0371198	−	0.999311i	$-0.488182\pi$
$541$	505392.	0.0742395	0.0371198	+	0.999311i	$0.488182\pi$
$542$	−9.13259e6	−1.33535
$543$	1.22019e6	0.177594
$544$	−9.45616e6	−1.36999
$545$	7.17654e6	1.03496
$546$	8.26644e6	1.18669
$547$	−1.05410e7	−1.50630	−0.753152	−	0.657847i	$-0.771467\pi$
$547$	−1.05410e7	−1.50630	−0.753152	+	0.657847i	$0.771467\pi$
$548$	−9.28570e6	−1.32088
$549$	1.88450e6	0.266849
$550$	−2.53744e6	−0.357675
$551$	870371.	0.122131
$552$	−34537.3	−0.00482437
$553$	5.97670e6	0.831092
$554$	−4.78675e6	−0.662623
$555$	2.18096e6	0.300549
$556$	9.24784e6	1.26868
$557$	−7.63355e6	−1.04253	−0.521265	−	0.853395i	$-0.674540\pi$
$557$	−7.63355e6	−1.04253	−0.521265	+	0.853395i	$0.674540\pi$
$558$	−2.47438e6	−0.336420
$559$	−8.50239e6	−1.15083
$560$	6.68098e6	0.900264
$561$	−5.64270e6	−0.756972
$562$	−1.21324e6	−0.162033
$563$	1.07078e7	1.42374	0.711869	−	0.702312i	$-0.247849\pi$
$563$	1.07078e7	1.42374	0.711869	+	0.702312i	$0.247849\pi$
$564$	−3.43185e6	−0.454288
$565$	−6.91857e6	−0.911791
$566$	−6.29495e6	−0.825946
$567$	853506.	0.111493
$568$	−90049.0	−0.0117114
$569$	5.44680e6	0.705278	0.352639	−	0.935759i	$-0.385284\pi$
$569$	5.44680e6	0.705278	0.352639	+	0.935759i	$0.385284\pi$
$570$	−1.36813e6	−0.176377
$571$	−3.64813e6	−0.468252	−0.234126	−	0.972206i	$-0.575223\pi$
$571$	−3.64813e6	−0.468252	−0.234126	+	0.972206i	$0.575223\pi$
$572$	−1.54211e7	−1.97072
$573$	3.91744e6	0.498443
$574$	−1.28466e6	−0.162745
$575$	1.63598e6	0.206352
$576$	−2.68242e6	−0.336877
$577$	−996401.	−0.124593	−0.0622967	−	0.998058i	$-0.519842\pi$
$577$	−996401.	−0.124593	−0.0622967	+	0.998058i	$0.519842\pi$
$578$	727983.	0.0906362
$579$	−1.02862e6	−0.127515
$580$	−3.75161e6	−0.463072
$581$	−5.46741e6	−0.671957
$582$	−3.43665e6	−0.420560
$583$	−952833.	−0.116103
$584$	5165.34	0.000626710 0
$585$	−3.59992e6	−0.434914
$586$	1.60221e7	1.92741
$587$	7.17752e6	0.859764	0.429882	−	0.902885i	$-0.358555\pi$
$587$	7.17752e6	0.859764	0.429882	+	0.902885i	$0.358555\pi$
$588$	−33539.4	−0.00400048
$589$	1.43514e6	0.170454
$590$	8.85178e6	1.04689
$591$	3.15681e6	0.371775
$592$	−4.89480e6	−0.574025
$593$	1.60087e7	1.86948	0.934739	−	0.355334i	$-0.115633\pi$
$593$	1.60087e7	1.86948	0.934739	+	0.355334i	$0.115633\pi$
$594$	−3.17600e6	−0.369330
$595$	7.56193e6	0.875669
$596$	−7.94184e6	−0.915811
$597$	2.85883e6	0.328286
$598$	1.98324e7	2.26790
$599$	−1.24030e6	−0.141241	−0.0706205	−	0.997503i	$-0.522498\pi$
$599$	−1.24030e6	−0.141241	−0.0706205	+	0.997503i	$0.522498\pi$
$600$	−7161.32	−0.000812111 0
$601$	−1.51872e6	−0.171511	−0.0857554	−	0.996316i	$-0.527330\pi$
$601$	−1.51872e6	−0.171511	−0.0857554	+	0.996316i	$0.527330\pi$
$602$	1.00525e7	1.13053
$603$	−994490.	−0.111380
$604$	−7.46194e6	−0.832260
$605$	−6.79362e6	−0.754593
$606$	−4.06506e6	−0.449661
$607$	−1.65820e7	−1.82669	−0.913345	−	0.407186i	$-0.866510\pi$
$607$	−1.65820e7	−1.82669	−0.913345	+	0.407186i	$0.866510\pi$
$608$	3.08700e6	0.338671
$609$	−2.70771e6	−0.295841
$610$	9.39759e6	1.02257
$611$	1.04472e7	1.13213
$612$	−3.00402e6	−0.324208
$613$	−1.45006e7	−1.55860	−0.779298	−	0.626654i	$-0.784424\pi$
$613$	−1.45006e7	−1.55860	−0.779298	+	0.626654i	$0.784424\pi$
$614$	−1.24946e7	−1.33752
$615$	559450.	0.0596449
$616$	96656.4	0.0102631
$617$	1.93473e6	0.204601	0.102301	−	0.994754i	$-0.467380\pi$
$617$	1.93473e6	0.204601	0.102301	+	0.994754i	$0.467380\pi$
$618$	1.27235e7	1.34009
$619$	2.04727e6	0.214758	0.107379	−	0.994218i	$-0.465754\pi$
$619$	2.04727e6	0.214758	0.107379	+	0.994218i	$0.465754\pi$
$620$	−6.18598e6	−0.646293
$621$	2.04769e6	0.213076
$622$	1.61702e6	0.167587
$623$	5.11126e6	0.527604
$624$	8.07943e6	0.830653
$625$	−7.60632e6	−0.778887
$626$	−4.82757e6	−0.492372
$627$	1.84208e6	0.187129
$628$	−792972.	−0.0802340
$629$	−5.54023e6	−0.558343
$630$	4.25624e6	0.427243
$631$	−1.25862e7	−1.25840	−0.629202	−	0.777242i	$-0.716618\pi$
$631$	−1.25862e7	−1.25840	−0.629202	+	0.777242i	$0.716618\pi$
$632$	−62767.3	−0.00625088
$633$	7.81529e6	0.775239
$634$	1.33806e6	0.132206
$635$	1.43284e7	1.41015
$636$	−507262.	−0.0497267
$637$	102100.	0.00996959
$638$	1.00757e7	0.979996
$639$	5.33894e6	0.517253
$640$	−141081.	−0.0136150
$641$	167068.	0.0160601	0.00803004	−	0.999968i	$-0.497444\pi$
$641$	167068.	0.0160601	0.00803004	+	0.999968i	$0.497444\pi$
$642$	5.18593e6	0.496580
$643$	−818867.	−0.0781063	−0.0390531	−	0.999237i	$-0.512434\pi$
$643$	−818867.	−0.0781063	−0.0390531	+	0.999237i	$0.512434\pi$
$644$	−1.17553e7	−1.11691
$645$	−4.37773e6	−0.414333
$646$	3.47543e6	0.327663
$647$	1.96572e7	1.84613	0.923064	−	0.384647i	$-0.125677\pi$
$647$	1.96572e7	1.84613	0.923064	+	0.384647i	$0.125677\pi$
$648$	−8963.52	−0.000838573 0
$649$	−1.19182e7	−1.11071
$650$	4.11227e6	0.381767
$651$	−4.46471e6	−0.412896
$652$	−4.25444e6	−0.391943
$653$	1.87341e6	0.171929	0.0859647	−	0.996298i	$-0.472603\pi$
$653$	1.87341e6	0.171929	0.0859647	+	0.996298i	$0.472603\pi$
$654$	−1.02610e7	−0.938089
$655$	−2.00785e6	−0.182864
$656$	−1.25559e6	−0.113917
$657$	−306250.	−0.0276797
$658$	−1.23519e7	−1.11216
$659$	−1.16592e7	−1.04581	−0.522907	−	0.852390i	$-0.675153\pi$
$659$	−1.16592e7	−1.04581	−0.522907	+	0.852390i	$0.675153\pi$
$660$	−7.94004e6	−0.709517
$661$	−4.42372e6	−0.393808	−0.196904	−	0.980423i	$-0.563089\pi$
$661$	−4.42372e6	−0.393808	−0.196904	+	0.980423i	$0.563089\pi$
$662$	2.53435e7	2.24762
$663$	9.14478e6	0.807959
$664$	57418.8	0.00505398
$665$	−2.46862e6	−0.216471
$666$	−3.11832e6	−0.272418
$667$	−6.49621e6	−0.565386
$668$	−1.60804e7	−1.39430
$669$	−995070.	−0.0859584
$670$	−4.95930e6	−0.426808
$671$	−1.26531e7	−1.08490
$672$	−9.60361e6	−0.820373
$673$	−1.21247e7	−1.03189	−0.515945	−	0.856621i	$-0.672559\pi$
$673$	−1.21247e7	−1.03189	−0.515945	+	0.856621i	$0.672559\pi$
$674$	−6.91307e6	−0.586167
$675$	424590.	0.0358683
$676$	1.30473e7	1.09813
$677$	652613.	0.0547248	0.0273624	−	0.999626i	$-0.491289\pi$
$677$	652613.	0.0547248	0.0273624	+	0.999626i	$0.491289\pi$
$678$	9.89214e6	0.826449
$679$	−6.20100e6	−0.516163
$680$	−79415.4	−0.00658616
$681$	−4.34366e6	−0.358912
$682$	1.66137e7	1.36775
$683$	−1.42720e7	−1.17067	−0.585335	−	0.810791i	$-0.699037\pi$
$683$	−1.42720e7	−1.17067	−0.585335	+	0.810791i	$0.699037\pi$
$684$	980675.	0.0801465
$685$	1.45544e7	1.18513
$686$	1.73937e7	1.41117
$687$	−2.38021e6	−0.192408
$688$	9.82508e6	0.791344
$689$	1.54420e6	0.123924
$690$	1.02114e7	0.816509
$691$	8.45754e6	0.673828	0.336914	−	0.941535i	$-0.390617\pi$
$691$	8.45754e6	0.673828	0.336914	+	0.941535i	$0.390617\pi$
$692$	5.90660e6	0.468891
$693$	−5.73069e6	−0.453288
$694$	4.76145e6	0.375267
$695$	−1.44950e7	−1.13830
$696$	28436.4	0.00222511
$697$	−1.42115e6	−0.110805
$698$	5.67545e6	0.440922
$699$	−1.22252e7	−0.946371
$700$	−2.43746e6	−0.188015
$701$	−503720.	−0.0387164	−0.0193582	−	0.999813i	$-0.506162\pi$
$701$	−503720.	−0.0387164	−0.0193582	+	0.999813i	$0.506162\pi$
$702$	5.14715e6	0.394207
$703$	1.80863e6	0.138026
$704$	1.80106e7	1.36961
$705$	5.37907e6	0.407600
$706$	3.54491e7	2.67666
$707$	−7.33488e6	−0.551880
$708$	−6.34493e6	−0.475712
$709$	−5.32900e6	−0.398135	−0.199067	−	0.979986i	$-0.563791\pi$
$709$	−5.32900e6	−0.398135	−0.199067	+	0.979986i	$0.563791\pi$
$710$	2.66241e7	1.98212
$711$	3.72143e6	0.276081
$712$	−53678.4	−0.00396826
$713$	−1.07115e7	−0.789091
$714$	−1.08120e7	−0.793708
$715$	2.41709e7	1.76819
$716$	−2.17393e7	−1.58476
$717$	−1.69855e6	−0.123390
$718$	1.33580e7	0.967012
$719$	−1.30821e7	−0.943749	−0.471875	−	0.881666i	$-0.656423\pi$
$719$	−1.30821e7	−0.943749	−0.471875	+	0.881666i	$0.656423\pi$
$720$	4.15995e6	0.299059
$721$	2.29579e7	1.64473
$722$	1.87006e7	1.33510
$723$	1.67627e6	0.119261
$724$	−4.36157e6	−0.309241
$725$	−1.34699e6	−0.0951744
$726$	9.71349e6	0.683965
$727$	2.00785e7	1.40895	0.704475	−	0.709729i	$-0.251183\pi$
$727$	2.00785e7	1.40895	0.704475	+	0.709729i	$0.251183\pi$
$728$	−156645.	−0.0109544
$729$	531441.	0.0370370
$730$	−1.52720e6	−0.106069
$731$	1.11206e7	0.769724
$732$	−6.73617e6	−0.464660
$733$	2.37956e7	1.63582	0.817911	−	0.575344i	$-0.195132\pi$
$733$	2.37956e7	1.63582	0.817911	+	0.575344i	$0.195132\pi$
$734$	1.29301e7	0.885856
$735$	52569.5	0.00358935
$736$	−2.30405e7	−1.56783
$737$	6.67730e6	0.452827
$738$	−799899.	−0.0540622
$739$	−1.28052e7	−0.862532	−0.431266	−	0.902225i	$-0.641933\pi$
$739$	−1.28052e7	−0.862532	−0.431266	+	0.902225i	$0.641933\pi$
$740$	−7.79585e6	−0.523340
$741$	−2.98535e6	−0.199733
$742$	−1.82573e6	−0.121738
$743$	2.47381e7	1.64397	0.821987	−	0.569506i	$-0.192866\pi$
$743$	2.47381e7	1.64397	0.821987	+	0.569506i	$0.192866\pi$
$744$	46888.3	0.00310551
$745$	1.24480e7	0.821692
$746$	−1.29242e6	−0.0850268
$747$	−3.40432e6	−0.223218
$748$	2.01699e7	1.31810
$749$	9.35735e6	0.609464
$750$	1.34778e7	0.874916
$751$	−9.84535e6	−0.636988	−0.318494	−	0.947925i	$-0.603177\pi$
$751$	−9.84535e6	−0.636988	−0.318494	+	0.947925i	$0.603177\pi$
$752$	−1.20724e7	−0.778485
$753$	−1.32322e7	−0.850443
$754$	−1.63291e7	−1.04601
$755$	1.16958e7	0.746728
$756$	−3.05086e6	−0.194141
$757$	−2.16698e7	−1.37441	−0.687205	−	0.726464i	$-0.741162\pi$
$757$	−2.16698e7	−1.37441	−0.687205	+	0.726464i	$0.741162\pi$
$758$	3.82009e7	2.41491
$759$	−1.37488e7	−0.866284
$760$	25925.5	0.00162814
$761$	9.62217e6	0.602298	0.301149	−	0.953577i	$-0.402630\pi$
$761$	9.62217e6	0.602298	0.301149	+	0.953577i	$0.402630\pi$
$762$	−2.04867e7	−1.27816
$763$	−1.85146e7	−1.15134
$764$	−1.40029e7	−0.867930
$765$	4.70848e6	0.290889
$766$	2.88451e7	1.77623
$767$	1.93151e7	1.18552
$768$	−9.33579e6	−0.571147
$769$	−2.41984e7	−1.47561	−0.737804	−	0.675015i	$-0.764137\pi$
$769$	−2.41984e7	−1.47561	−0.737804	+	0.675015i	$0.764137\pi$
$770$	−2.85776e7	−1.73700
$771$	1.15815e7	0.701666
$772$	3.67682e6	0.222039
$773$	2.12900e7	1.28152	0.640761	−	0.767740i	$-0.278619\pi$
$773$	2.12900e7	1.28152	0.640761	+	0.767740i	$0.278619\pi$
$774$	6.25925e6	0.375552
$775$	−2.22104e6	−0.132832
$776$	65122.9	0.00388221
$777$	−5.62662e6	−0.334345
$778$	−2.55739e7	−1.51478
$779$	463942.	0.0273918
$780$	1.28679e7	0.757308
$781$	−3.58472e7	−2.10295
$782$	−2.59396e7	−1.51687
$783$	−1.68597e6	−0.0982757
$784$	−117983.	−0.00685537
$785$	1.24290e6	0.0719883
$786$	2.87081e6	0.165748
$787$	2.77630e7	1.59782	0.798912	−	0.601448i	$-0.205409\pi$
$787$	2.77630e7	1.59782	0.798912	+	0.601448i	$0.205409\pi$
$788$	−1.12840e7	−0.647365
$789$	−1.15654e7	−0.661406
$790$	1.85579e7	1.05794
$791$	1.78491e7	1.01432
$792$	60183.7	0.00340931
$793$	2.05061e7	1.15798
$794$	7.73241e6	0.435275
$795$	795079.	0.0446162
$796$	−1.02189e7	−0.571639
$797$	197775.	0.0110287	0.00551436	−	0.999985i	$-0.498245\pi$
$797$	197775.	0.0110287	0.00551436	+	0.999985i	$0.498245\pi$
$798$	3.52962e6	0.196210
$799$	−1.36643e7	−0.757217
$800$	−4.77747e6	−0.263920
$801$	3.18256e6	0.175265
$802$	−9.78218e6	−0.537031
$803$	2.05625e6	0.112535
$804$	3.55481e6	0.193944
$805$	1.84251e7	1.00212
$806$	−2.69248e7	−1.45987
$807$	1.91954e6	0.103756
$808$	77030.9	0.00415084
$809$	−2.30614e7	−1.23884	−0.619418	−	0.785061i	$-0.712631\pi$
$809$	−2.30614e7	−1.23884	−0.619418	+	0.785061i	$0.712631\pi$
$810$	2.65017e6	0.141926
$811$	2.91077e7	1.55402	0.777009	−	0.629489i	$-0.216736\pi$
$811$	2.91077e7	1.55402	0.777009	+	0.629489i	$0.216736\pi$
$812$	9.67872e6	0.515143
$813$	−1.02605e7	−0.544430
$814$	2.09373e7	1.10754
$815$	6.66838e6	0.351663
$816$	−1.05674e7	−0.555576
$817$	−3.63037e6	−0.190281
$818$	2.31668e6	0.121055
$819$	9.28738e6	0.483820
$820$	−1.99976e6	−0.103859
$821$	−1.84168e6	−0.0953578	−0.0476789	−	0.998863i	$-0.515182\pi$
$821$	−1.84168e6	−0.0953578	−0.0476789	+	0.998863i	$0.515182\pi$
$822$	−2.08097e7	−1.07421
$823$	−2.10114e7	−1.08132	−0.540660	−	0.841241i	$-0.681826\pi$
$823$	−2.10114e7	−1.08132	−0.540660	+	0.841241i	$0.681826\pi$
$824$	−241104.	−0.0123705
$825$	−2.85082e6	−0.145826
$826$	−2.28365e7	−1.16461
$827$	2.55214e7	1.29760	0.648801	−	0.760958i	$-0.275271\pi$
$827$	2.55214e7	1.29760	0.648801	+	0.760958i	$0.275271\pi$
$828$	−7.31948e6	−0.371026
$829$	−3.43311e7	−1.73501	−0.867503	−	0.497433i	$-0.834276\pi$
$829$	−3.43311e7	−1.73501	−0.867503	+	0.497433i	$0.834276\pi$
$830$	−1.69766e7	−0.855371
$831$	−5.37794e6	−0.270155
$832$	−2.91886e7	−1.46186
$833$	−133541.	−0.00666809
$834$	2.07249e7	1.03176
$835$	2.52043e7	1.25100
$836$	−6.58454e6	−0.325844
$837$	−2.77998e6	−0.137160
$838$	−5.21514e7	−2.56541
$839$	−2.31108e7	−1.13347	−0.566735	−	0.823900i	$-0.691794\pi$
$839$	−2.31108e7	−1.13347	−0.566735	+	0.823900i	$0.691794\pi$
$840$	−80653.7	−0.00394390
$841$	−1.51625e7	−0.739231
$842$	−3.10805e7	−1.51080
$843$	−1.36308e6	−0.0660619
$844$	−2.79358e7	−1.34991
$845$	−2.04503e7	−0.985277
$846$	−7.69096e6	−0.369449
$847$	1.75267e7	0.839446
$848$	−1.78442e6	−0.0852135
$849$	−7.07241e6	−0.336743
$850$	−5.37860e6	−0.255342
$851$	−1.34991e7	−0.638971
$852$	−1.90841e7	−0.900684
$853$	−2.49666e7	−1.17486	−0.587432	−	0.809274i	$-0.699861\pi$
$853$	−2.49666e7	−1.17486	−0.587432	+	0.809274i	$0.699861\pi$
$854$	−2.42447e7	−1.13755
$855$	−1.53710e6	−0.0719098
$856$	−98270.9	−0.00458396
$857$	−1.83322e7	−0.852632	−0.426316	−	0.904574i	$-0.640189\pi$
$857$	−1.83322e7	−0.852632	−0.426316	+	0.904574i	$0.640189\pi$
$858$	−3.45595e7	−1.60269
$859$	4.08002e7	1.88660	0.943298	−	0.331946i	$-0.107705\pi$
$859$	4.08002e7	1.88660	0.943298	+	0.331946i	$0.107705\pi$
$860$	1.56482e7	0.721470
$861$	−1.44332e6	−0.0663519
$862$	5.91578e7	2.71172
$863$	3.42668e7	1.56620	0.783100	−	0.621896i	$-0.213637\pi$
$863$	3.42668e7	1.56620	0.783100	+	0.621896i	$0.213637\pi$
$864$	−5.97975e6	−0.272520
$865$	−9.25797e6	−0.420703
$866$	−2.16878e6	−0.0982701
$867$	817892.	0.0369529
$868$	1.59591e7	0.718968
$869$	−2.49868e7	−1.12243
$870$	−8.40756e6	−0.376593
$871$	−1.08215e7	−0.483328
$872$	194441.	0.00865956
$873$	−3.86109e6	−0.171465
$874$	8.46811e6	0.374980
$875$	2.43190e7	1.07381
$876$	1.09469e6	0.0481982
$877$	3.49651e7	1.53509	0.767547	−	0.640992i	$-0.221477\pi$
$877$	3.49651e7	1.53509	0.767547	+	0.640992i	$0.221477\pi$
$878$	−1.46866e7	−0.642960
$879$	1.80009e7	0.785817
$880$	−2.79311e7	−1.21586
$881$	−3.60062e7	−1.56292	−0.781461	−	0.623954i	$-0.785525\pi$
$881$	−3.60062e7	−1.56292	−0.781461	+	0.623954i	$0.785525\pi$
$882$	−75163.6	−0.00325339
$883$	−2.04032e6	−0.0880638	−0.0440319	−	0.999030i	$-0.514020\pi$
$883$	−2.04032e6	−0.0880638	−0.0440319	+	0.999030i	$0.514020\pi$
$884$	−3.26881e7	−1.40689
$885$	9.94501e6	0.426822
$886$	−6.31091e6	−0.270090
$887$	−1.23778e7	−0.528242	−0.264121	−	0.964490i	$-0.585082\pi$
$887$	−1.23778e7	−0.528242	−0.264121	+	0.964490i	$0.585082\pi$
$888$	59090.7	0.00251470
$889$	−3.69657e7	−1.56872
$890$	1.58707e7	0.671616
$891$	−3.56825e6	−0.150578
$892$	3.55688e6	0.149678
$893$	4.46077e6	0.187189
$894$	−1.77981e7	−0.744783
$895$	3.40741e7	1.42189
$896$	363973.	0.0151460
$897$	2.22818e7	0.924634
$898$	1.95234e7	0.807913
$899$	8.81936e6	0.363947
$900$	−1.51770e6	−0.0624567
$901$	−2.01972e6	−0.0828855
$902$	5.37075e6	0.219796
$903$	1.12940e7	0.460924
$904$	−187451.	−0.00762899
$905$	6.83630e6	0.277460
$906$	−1.67226e7	−0.676835
$907$	3.18709e7	1.28640	0.643199	−	0.765699i	$-0.277607\pi$
$907$	3.18709e7	1.28640	0.643199	+	0.765699i	$0.277607\pi$
$908$	1.55264e7	0.624967
$909$	−4.56711e6	−0.183329
$910$	4.63140e7	1.85400
$911$	1.92955e7	0.770301	0.385150	−	0.922854i	$-0.374150\pi$
$911$	1.92955e7	0.770301	0.385150	+	0.922854i	$0.374150\pi$
$912$	3.44978e6	0.137342
$913$	2.28576e7	0.907515
$914$	4.68112e7	1.85347
$915$	1.05582e7	0.416906
$916$	8.50807e6	0.335037
$917$	5.18001e6	0.203426
$918$	−6.73216e6	−0.263662
$919$	−1.22903e7	−0.480035	−0.240017	−	0.970769i	$-0.577153\pi$
$919$	−1.22903e7	−0.480035	−0.240017	+	0.970769i	$0.577153\pi$
$920$	−193501.	−0.00753724
$921$	−1.40377e7	−0.545314
$922$	2.78668e7	1.07959
$923$	5.80954e7	2.24459
$924$	2.04844e7	0.789301
$925$	−2.79905e6	−0.107561
$926$	1.26199e7	0.483647
$927$	1.42949e7	0.546363
$928$	1.89705e7	0.723117
$929$	3.75326e7	1.42682	0.713411	−	0.700746i	$-0.247149\pi$
$929$	3.75326e7	1.42682	0.713411	+	0.700746i	$0.247149\pi$
$930$	−1.38631e7	−0.525598
$931$	43594.9	0.00164840
$932$	4.36989e7	1.64790
$933$	1.81673e6	0.0683260
$934$	4.54647e7	1.70532
$935$	−3.16141e7	−1.18264
$936$	−97536.1	−0.00363895
$937$	−1.81510e7	−0.675384	−0.337692	−	0.941257i	$-0.609646\pi$
$937$	−1.81510e7	−0.675384	−0.337692	+	0.941257i	$0.609646\pi$
$938$	1.27944e7	0.474802
$939$	−5.42380e6	−0.200743
$940$	−1.92275e7	−0.709747
$941$	−2.06931e7	−0.761820	−0.380910	−	0.924612i	$-0.624389\pi$
$941$	−2.06931e7	−0.761820	−0.380910	+	0.924612i	$0.624389\pi$
$942$	−1.77709e6	−0.0652503
$943$	−3.46273e6	−0.126806
$944$	−2.23199e7	−0.815197
$945$	4.78190e6	0.174189
$946$	−4.20264e7	−1.52684
$947$	3.21751e7	1.16585	0.582927	−	0.812524i	$-0.301907\pi$
$947$	3.21751e7	1.16585	0.582927	+	0.812524i	$0.301907\pi$
$948$	−1.33023e7	−0.480735
$949$	−3.33244e6	−0.120115
$950$	1.75587e6	0.0631223
$951$	1.50331e6	0.0539011
$952$	204882.	0.00732676
$953$	−4.74547e7	−1.69257	−0.846286	−	0.532728i	$-0.821167\pi$
$953$	−4.74547e7	−1.69257	−0.846286	+	0.532728i	$0.821167\pi$
$954$	−1.13680e6	−0.0404402
$955$	2.19481e7	0.778732
$956$	6.07148e6	0.214857
$957$	1.13201e7	0.399550
$958$	5.59679e7	1.97027
$959$	−3.75485e7	−1.31840
$960$	−1.50287e7	−0.526312
$961$	−1.40870e7	−0.492052
$962$	−3.39319e7	−1.18214
$963$	5.82641e6	0.202458
$964$	−5.99182e6	−0.207666
$965$	−5.76303e6	−0.199220
$966$	−2.63441e7	−0.908325
$967$	2.00999e6	0.0691238	0.0345619	−	0.999403i	$-0.488996\pi$
$967$	2.00999e6	0.0691238	0.0345619	+	0.999403i	$0.488996\pi$
$968$	−184066.	−0.00631371
$969$	3.90466e6	0.133590
$970$	−1.92544e7	−0.657053
$971$	−1.73673e7	−0.591131	−0.295565	−	0.955323i	$-0.595508\pi$
$971$	−1.73673e7	−0.591131	−0.295565	+	0.955323i	$0.595508\pi$
$972$	−1.89964e6	−0.0644919
$973$	3.73954e7	1.26630
$974$	−1.83713e7	−0.620501
$975$	4.62015e6	0.155648
$976$	−2.36962e7	−0.796259
$977$	−9.02178e6	−0.302382	−0.151191	−	0.988505i	$-0.548311\pi$
$977$	−9.02178e6	−0.302382	−0.151191	+	0.988505i	$0.548311\pi$
$978$	−9.53441e6	−0.318747
$979$	−2.13686e7	−0.712557
$980$	−187910.	−0.00625006
$981$	−1.15282e7	−0.382464
$982$	3.24056e7	1.07236
$983$	−140546.	−0.00463912	−0.00231956	−	0.999997i	$-0.500738\pi$
$983$	−140546.	−0.00463912	−0.00231956	+	0.999997i	$0.500738\pi$
$984$	15157.7	0.000499052 0
$985$	1.76865e7	0.580834
$986$	2.13575e7	0.699613
$987$	−1.38774e7	−0.453434
$988$	1.06712e7	0.347792
$989$	2.70961e7	0.880878
$990$	−1.77940e7	−0.577015
$991$	−2.19130e6	−0.0708790	−0.0354395	−	0.999372i	$-0.511283\pi$
$991$	−2.19130e6	−0.0708790	−0.0354395	+	0.999372i	$0.511283\pi$
$992$	3.12802e7	1.00923
$993$	2.84736e7	0.916366
$994$	−6.86871e7	−2.20500
$995$	1.60171e7	0.512891
$996$	1.21688e7	0.388685
$997$	−4.42434e7	−1.40965	−0.704823	−	0.709383i	$-0.748974\pi$
$997$	−4.42434e7	−1.40965	−0.704823	+	0.709383i	$0.748974\pi$
$998$	4.88712e7	1.55320
$999$	−3.50345e6	−0.111066

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.6.a.b.1.5	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.6.a.b.1.5	✓	30	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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	471.a (trivial)

\(f(q)\)	\(=\)	\(q-8.01065 q^{2} -9.00000 q^{3} +32.1705 q^{4} -50.4239 q^{5} +72.0959 q^{6} +130.088 q^{7} -1.36618 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-8.01065 q^{2} -9.00000 q^{3} +32.1705 q^{4} -50.4239 q^{5} +72.0959 q^{6} +130.088 q^{7} -1.36618 q^{8} +81.0000 q^{9} +403.929 q^{10} -543.858 q^{11} -289.535 q^{12} +881.397 q^{13} -1042.09 q^{14} +453.815 q^{15} -1018.51 q^{16} -1152.81 q^{17} -648.863 q^{18} +376.341 q^{19} -1622.17 q^{20} -1170.79 q^{21} +4356.65 q^{22} -2808.90 q^{23} +12.2956 q^{24} -582.428 q^{25} -7060.57 q^{26} -729.000 q^{27} +4185.00 q^{28} +2312.72 q^{29} -3635.36 q^{30} +3813.41 q^{31} +8202.67 q^{32} +4894.72 q^{33} +9234.79 q^{34} -6559.54 q^{35} +2605.81 q^{36} +4805.83 q^{37} -3014.74 q^{38} -7932.57 q^{39} +68.8883 q^{40} +1232.77 q^{41} +9378.79 q^{42} -9646.49 q^{43} -17496.2 q^{44} -4084.34 q^{45} +22501.2 q^{46} +11853.0 q^{47} +9166.62 q^{48} +115.839 q^{49} +4665.63 q^{50} +10375.3 q^{51} +28355.0 q^{52} +1751.99 q^{53} +5839.77 q^{54} +27423.4 q^{55} -177.724 q^{56} -3387.07 q^{57} -18526.4 q^{58} +21914.2 q^{59} +14599.5 q^{60} +23265.5 q^{61} -30547.9 q^{62} +10537.1 q^{63} -33116.3 q^{64} -44443.5 q^{65} -39209.9 q^{66} -12277.7 q^{67} -37086.7 q^{68} +25280.1 q^{69} +52546.2 q^{70} +65912.9 q^{71} -110.661 q^{72} -3780.86 q^{73} -38497.8 q^{74} +5241.85 q^{75} +12107.1 q^{76} -70749.3 q^{77} +63545.1 q^{78} +45943.6 q^{79} +51357.4 q^{80} +6561.00 q^{81} -9875.29 q^{82} -42028.6 q^{83} -37665.0 q^{84} +58129.4 q^{85} +77274.7 q^{86} -20814.5 q^{87} +743.009 q^{88} +39290.8 q^{89} +32718.2 q^{90} +114659. q^{91} -90364.0 q^{92} -34320.7 q^{93} -94950.2 q^{94} -18976.6 q^{95} -73824.1 q^{96} -47667.8 q^{97} -927.945 q^{98} -44052.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 8 q^{2} - 270 q^{3} + 470 q^{4} - 136 q^{5} + 72 q^{6} + 68 q^{7} - 261 q^{8} + 2430 q^{9}+O(q^{10}) \) 30 * q - 8 * q^2 - 270 * q^3 + 470 * q^4 - 136 * q^5 + 72 * q^6 + 68 * q^7 - 261 * q^8 + 2430 * q^9	\( 30 q - 8 q^{2} - 270 q^{3} + 470 q^{4} - 136 q^{5} + 72 q^{6} + 68 q^{7} - 261 q^{8} + 2430 q^{9} - 383 q^{10} - 875 q^{11} - 4230 q^{12} + 101 q^{13} - 2279 q^{14} + 1224 q^{15} + 7454 q^{16} - 4042 q^{17} - 648 q^{18} + 846 q^{19} - 5089 q^{20} - 612 q^{21} - 700 q^{22} - 5902 q^{23} + 2349 q^{24} + 12880 q^{25} - 7567 q^{26} - 21870 q^{27} - 375 q^{28} - 10301 q^{29} + 3447 q^{30} - 4099 q^{31} - 1560 q^{32} + 7875 q^{33} - 3683 q^{34} - 20686 q^{35} + 38070 q^{36} + 8468 q^{37} - 11848 q^{38} - 909 q^{39} - 5132 q^{40} - 47958 q^{41} + 20511 q^{42} + 63916 q^{43} + 3101 q^{44} - 11016 q^{45} + 19654 q^{46} + 8589 q^{47} - 67086 q^{48} + 27834 q^{49} + 121727 q^{50} + 36378 q^{51} + 56510 q^{52} + 10134 q^{53} + 5832 q^{54} - 11473 q^{55} - 68192 q^{56} - 7614 q^{57} + 32006 q^{58} - 64236 q^{59} + 45801 q^{60} - 98194 q^{61} - 67276 q^{62} + 5508 q^{63} + 138849 q^{64} - 155917 q^{65} + 6300 q^{66} + 62323 q^{67} - 117531 q^{68} + 53118 q^{69} - 220939 q^{70} - 179713 q^{71} - 21141 q^{72} - 148343 q^{73} - 214732 q^{74} - 115920 q^{75} - 189758 q^{76} - 142357 q^{77} + 68103 q^{78} + 26916 q^{79} - 463727 q^{80} + 196830 q^{81} - 206514 q^{82} - 89285 q^{83} + 3375 q^{84} - 23932 q^{85} - 477235 q^{86} + 92709 q^{87} - 114708 q^{88} - 474411 q^{89} - 31023 q^{90} + 51305 q^{91} - 1030074 q^{92} + 36891 q^{93} - 485800 q^{94} - 169960 q^{95} + 14040 q^{96} - 169188 q^{97} - 629739 q^{98} - 70875 q^{99}+O(q^{100}) \) 30 * q - 8 * q^2 - 270 * q^3 + 470 * q^4 - 136 * q^5 + 72 * q^6 + 68 * q^7 - 261 * q^8 + 2430 * q^9 - 383 * q^10 - 875 * q^11 - 4230 * q^12 + 101 * q^13 - 2279 * q^14 + 1224 * q^15 + 7454 * q^16 - 4042 * q^17 - 648 * q^18 + 846 * q^19 - 5089 * q^20 - 612 * q^21 - 700 * q^22 - 5902 * q^23 + 2349 * q^24 + 12880 * q^25 - 7567 * q^26 - 21870 * q^27 - 375 * q^28 - 10301 * q^29 + 3447 * q^30 - 4099 * q^31 - 1560 * q^32 + 7875 * q^33 - 3683 * q^34 - 20686 * q^35 + 38070 * q^36 + 8468 * q^37 - 11848 * q^38 - 909 * q^39 - 5132 * q^40 - 47958 * q^41 + 20511 * q^42 + 63916 * q^43 + 3101 * q^44 - 11016 * q^45 + 19654 * q^46 + 8589 * q^47 - 67086 * q^48 + 27834 * q^49 + 121727 * q^50 + 36378 * q^51 + 56510 * q^52 + 10134 * q^53 + 5832 * q^54 - 11473 * q^55 - 68192 * q^56 - 7614 * q^57 + 32006 * q^58 - 64236 * q^59 + 45801 * q^60 - 98194 * q^61 - 67276 * q^62 + 5508 * q^63 + 138849 * q^64 - 155917 * q^65 + 6300 * q^66 + 62323 * q^67 - 117531 * q^68 + 53118 * q^69 - 220939 * q^70 - 179713 * q^71 - 21141 * q^72 - 148343 * q^73 - 214732 * q^74 - 115920 * q^75 - 189758 * q^76 - 142357 * q^77 + 68103 * q^78 + 26916 * q^79 - 463727 * q^80 + 196830 * q^81 - 206514 * q^82 - 89285 * q^83 + 3375 * q^84 - 23932 * q^85 - 477235 * q^86 + 92709 * q^87 - 114708 * q^88 - 474411 * q^89 - 31023 * q^90 + 51305 * q^91 - 1030074 * q^92 + 36891 * q^93 - 485800 * q^94 - 169960 * q^95 + 14040 * q^96 - 169188 * q^97 - 629739 * q^98 - 70875 * q^99

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