LMFDB - Embedded newform 39.6.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,6,Mod(1,39)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(39, 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("39.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	39.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:	$6.25496897271$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.125308.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 55x - 78 $ x^3 - 55*x - 78
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.47673$ of defining polynomial
Character	$\chi$	$=$	39.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.47673 q^{2} -9.00000 q^{3} -29.8193 q^{4} +6.18613 q^{5} +13.2906 q^{6} +190.614 q^{7} +91.2906 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-1.47673 q^{2} -9.00000 q^{3} -29.8193 q^{4} +6.18613 q^{5} +13.2906 q^{6} +190.614 q^{7} +91.2906 q^{8} +81.0000 q^{9} -9.13526 q^{10} +141.200 q^{11} +268.373 q^{12} +169.000 q^{13} -281.485 q^{14} -55.6751 q^{15} +819.404 q^{16} +1854.72 q^{17} -119.615 q^{18} -2091.51 q^{19} -184.466 q^{20} -1715.52 q^{21} -208.515 q^{22} +4682.44 q^{23} -821.615 q^{24} -3086.73 q^{25} -249.568 q^{26} -729.000 q^{27} -5683.95 q^{28} -2483.38 q^{29} +82.2174 q^{30} +4629.17 q^{31} -4131.34 q^{32} -1270.80 q^{33} -2738.93 q^{34} +1179.16 q^{35} -2415.36 q^{36} +1013.68 q^{37} +3088.61 q^{38} -1521.00 q^{39} +564.735 q^{40} +14283.8 q^{41} +2533.37 q^{42} -625.799 q^{43} -4210.49 q^{44} +501.076 q^{45} -6914.72 q^{46} +9057.59 q^{47} -7374.64 q^{48} +19526.5 q^{49} +4558.28 q^{50} -16692.5 q^{51} -5039.45 q^{52} +31642.2 q^{53} +1076.54 q^{54} +873.483 q^{55} +17401.2 q^{56} +18823.6 q^{57} +3667.29 q^{58} -25952.5 q^{59} +1660.19 q^{60} -4735.49 q^{61} -6836.05 q^{62} +15439.7 q^{63} -20120.0 q^{64} +1045.46 q^{65} +1876.64 q^{66} +19717.3 q^{67} -55306.3 q^{68} -42142.0 q^{69} -1741.30 q^{70} -27169.0 q^{71} +7394.54 q^{72} -13688.2 q^{73} -1496.94 q^{74} +27780.6 q^{75} +62367.4 q^{76} +26914.7 q^{77} +2246.11 q^{78} -75281.6 q^{79} +5068.94 q^{80} +6561.00 q^{81} -21093.4 q^{82} -104809. q^{83} +51155.6 q^{84} +11473.5 q^{85} +924.139 q^{86} +22350.4 q^{87} +12890.3 q^{88} +4771.10 q^{89} -739.956 q^{90} +32213.7 q^{91} -139627. q^{92} -41662.5 q^{93} -13375.6 q^{94} -12938.4 q^{95} +37182.1 q^{96} +34879.0 q^{97} -28835.5 q^{98} +11437.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 27 q^{3} + 14 q^{4} + 54 q^{5} + 84 q^{7} + 234 q^{8} + 243 q^{9}+O(q^{10}) $ 3 * q - 27 * q^3 + 14 * q^4 + 54 * q^5 + 84 * q^7 + 234 * q^8 + 243 * q^9	\( 3 q - 27 q^{3} + 14 q^{4} + 54 q^{5} + 84 q^{7} + 234 q^{8} + 243 q^{9} + 880 q^{10} + 876 q^{11} - 126 q^{12} + 507 q^{13} + 1896 q^{14} - 486 q^{15} - 1438 q^{16} + 102 q^{17} - 16 q^{19} + 2124 q^{20} - 756 q^{21} - 2776 q^{22} - 2106 q^{24} - 1363 q^{25} - 2187 q^{27} - 4688 q^{28} + 9666 q^{29} - 7920 q^{30} - 10196 q^{31} - 8502 q^{32} - 7884 q^{33} - 23552 q^{34} + 16680 q^{35} + 1134 q^{36} + 11818 q^{37} - 8040 q^{38} - 4563 q^{39} - 3708 q^{40} + 35490 q^{41} - 17064 q^{42} + 2780 q^{43} + 7296 q^{44} + 4374 q^{45} - 12576 q^{46} + 25728 q^{47} + 12942 q^{48} + 39291 q^{49} + 46656 q^{50} - 918 q^{51} + 2366 q^{52} + 36786 q^{53} - 6440 q^{55} - 10512 q^{56} + 144 q^{57} + 4720 q^{58} - 27516 q^{59} - 19116 q^{60} + 45994 q^{61} - 14280 q^{62} + 6804 q^{63} - 39462 q^{64} + 9126 q^{65} + 24984 q^{66} - 42536 q^{67} - 122532 q^{68} + 18128 q^{70} - 54432 q^{71} + 18954 q^{72} + 27846 q^{73} - 80928 q^{74} + 12267 q^{75} + 89144 q^{76} - 78000 q^{77} - 80568 q^{79} - 33996 q^{80} + 19683 q^{81} + 13344 q^{82} + 24012 q^{83} + 42192 q^{84} - 186580 q^{85} - 117840 q^{86} - 86994 q^{87} + 93312 q^{88} + 117450 q^{89} + 71280 q^{90} + 14196 q^{91} - 245472 q^{92} + 91764 q^{93} - 21864 q^{94} - 64608 q^{95} + 76518 q^{96} - 20930 q^{97} - 254784 q^{98} + 70956 q^{99}+O(q^{100}) \) 3 * q - 27 * q^3 + 14 * q^4 + 54 * q^5 + 84 * q^7 + 234 * q^8 + 243 * q^9 + 880 * q^10 + 876 * q^11 - 126 * q^12 + 507 * q^13 + 1896 * q^14 - 486 * q^15 - 1438 * q^16 + 102 * q^17 - 16 * q^19 + 2124 * q^20 - 756 * q^21 - 2776 * q^22 - 2106 * q^24 - 1363 * q^25 - 2187 * q^27 - 4688 * q^28 + 9666 * q^29 - 7920 * q^30 - 10196 * q^31 - 8502 * q^32 - 7884 * q^33 - 23552 * q^34 + 16680 * q^35 + 1134 * q^36 + 11818 * q^37 - 8040 * q^38 - 4563 * q^39 - 3708 * q^40 + 35490 * q^41 - 17064 * q^42 + 2780 * q^43 + 7296 * q^44 + 4374 * q^45 - 12576 * q^46 + 25728 * q^47 + 12942 * q^48 + 39291 * q^49 + 46656 * q^50 - 918 * q^51 + 2366 * q^52 + 36786 * q^53 - 6440 * q^55 - 10512 * q^56 + 144 * q^57 + 4720 * q^58 - 27516 * q^59 - 19116 * q^60 + 45994 * q^61 - 14280 * q^62 + 6804 * q^63 - 39462 * q^64 + 9126 * q^65 + 24984 * q^66 - 42536 * q^67 - 122532 * q^68 + 18128 * q^70 - 54432 * q^71 + 18954 * q^72 + 27846 * q^73 - 80928 * q^74 + 12267 * q^75 + 89144 * q^76 - 78000 * q^77 - 80568 * q^79 - 33996 * q^80 + 19683 * q^81 + 13344 * q^82 + 24012 * q^83 + 42192 * q^84 - 186580 * q^85 - 117840 * q^86 - 86994 * q^87 + 93312 * q^88 + 117450 * q^89 + 71280 * q^90 + 14196 * q^91 - 245472 * q^92 + 91764 * q^93 - 21864 * q^94 - 64608 * q^95 + 76518 * q^96 - 20930 * q^97 - 254784 * q^98 + 70956 * 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 $

$2$	−1.47673	−0.261052	−0.130526	−	0.991445i	$-0.541667\pi$
$2$	−1.47673	−0.261052	−0.130526	+	0.991445i	$0.541667\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−29.8193	−0.931852
$5$	6.18613	0.110661	0.0553304	−	0.998468i	$-0.482379\pi$
$5$	6.18613	0.110661	0.0553304	+	0.998468i	$0.482379\pi$
$6$	13.2906	0.150719
$7$	190.614	1.47031	0.735154	−	0.677900i	$-0.237110\pi$
$7$	190.614	1.47031	0.735154	+	0.677900i	$0.237110\pi$
$8$	91.2906	0.504314
$9$	81.0000	0.333333
$10$	−9.13526	−0.0288882
$11$	141.200	0.351847	0.175924	−	0.984404i	$-0.443709\pi$
$11$	141.200	0.351847	0.175924	+	0.984404i	$0.443709\pi$
$12$	268.373	0.538005
$13$	169.000	0.277350
$13$	169.000	0.277350
$14$	−281.485	−0.383827
$15$	−55.6751	−0.0638900
$16$	819.404	0.800199
$17$	1854.72	1.55652	0.778262	−	0.627940i	$-0.216102\pi$
$17$	1854.72	1.55652	0.778262	+	0.627940i	$0.216102\pi$
$18$	−119.615	−0.0870174
$19$	−2091.51	−1.32916	−0.664579	−	0.747218i	$-0.731389\pi$
$19$	−2091.51	−1.32916	−0.664579	+	0.747218i	$0.731389\pi$
$20$	−184.466	−0.103119
$21$	−1715.52	−0.848883
$22$	−208.515	−0.0918505
$23$	4682.44	1.84566	0.922832	−	0.385203i	$-0.125868\pi$
$23$	4682.44	1.84566	0.922832	+	0.385203i	$0.125868\pi$
$24$	−821.615	−0.291166
$25$	−3086.73	−0.987754
$26$	−249.568	−0.0724028
$27$	−729.000	−0.192450
$28$	−5683.95	−1.37011
$29$	−2483.38	−0.548337	−0.274169	−	0.961682i	$-0.588403\pi$
$29$	−2483.38	−0.548337	−0.274169	+	0.961682i	$0.588403\pi$
$30$	82.2174	0.0166786
$31$	4629.17	0.865164	0.432582	−	0.901595i	$-0.357603\pi$
$31$	4629.17	0.865164	0.432582	+	0.901595i	$0.357603\pi$
$32$	−4131.34	−0.713208
$33$	−1270.80	−0.203139
$34$	−2738.93	−0.406334
$35$	1179.16	0.162706
$36$	−2415.36	−0.310617
$37$	1013.68	0.121730	0.0608650	−	0.998146i	$-0.480614\pi$
$37$	1013.68	0.121730	0.0608650	+	0.998146i	$0.480614\pi$
$38$	3088.61	0.346980
$39$	−1521.00	−0.160128
$40$	564.735	0.0558078
$41$	14283.8	1.32704	0.663520	−	0.748159i	$-0.269062\pi$
$41$	14283.8	1.32704	0.663520	+	0.748159i	$0.269062\pi$
$42$	2533.37	0.221603
$43$	−625.799	−0.0516135	−0.0258068	−	0.999667i	$-0.508215\pi$
$43$	−625.799	−0.0516135	−0.0258068	+	0.999667i	$0.508215\pi$
$44$	−4210.49	−0.327869
$45$	501.076	0.0368869
$46$	−6914.72	−0.481815
$47$	9057.59	0.598092	0.299046	−	0.954239i	$-0.403332\pi$
$47$	9057.59	0.598092	0.299046	+	0.954239i	$0.403332\pi$
$48$	−7374.64	−0.461995
$49$	19526.5	1.16181
$50$	4558.28	0.257855
$51$	−16692.5	−0.898659
$52$	−5039.45	−0.258449
$53$	31642.2	1.54731	0.773654	−	0.633608i	$-0.218427\pi$
$53$	31642.2	1.54731	0.773654	+	0.633608i	$0.218427\pi$
$54$	1076.54	0.0502395
$55$	873.483	0.0389357
$56$	17401.2	0.741498
$57$	18823.6	0.767390
$58$	3667.29	0.143145
$59$	−25952.5	−0.970618	−0.485309	−	0.874343i	$-0.661293\pi$
$59$	−25952.5	−0.970618	−0.485309	+	0.874343i	$0.661293\pi$
$60$	1660.19	0.0595360
$61$	−4735.49	−0.162945	−0.0814724	−	0.996676i	$-0.525962\pi$
$61$	−4735.49	−0.162945	−0.0814724	+	0.996676i	$0.525962\pi$
$62$	−6836.05	−0.225853
$63$	15439.7	0.490103
$64$	−20120.0	−0.614015
$65$	1045.46	0.0306918
$66$	1876.64	0.0530299
$67$	19717.3	0.536611	0.268306	−	0.963334i	$-0.413536\pi$
$67$	19717.3	0.536611	0.268306	+	0.963334i	$0.413536\pi$
$68$	−55306.3	−1.45045
$69$	−42142.0	−1.06559
$70$	−1741.30	−0.0424746
$71$	−27169.0	−0.639629	−0.319815	−	0.947480i	$-0.603621\pi$
$71$	−27169.0	−0.639629	−0.319815	+	0.947480i	$0.603621\pi$
$72$	7394.54	0.168105
$73$	−13688.2	−0.300634	−0.150317	−	0.988638i	$-0.548029\pi$
$73$	−13688.2	−0.300634	−0.150317	+	0.988638i	$0.548029\pi$
$74$	−1496.94	−0.0317779
$75$	27780.6	0.570280
$76$	62367.4	1.23858
$77$	26914.7	0.517324
$78$	2246.11	0.0418018
$79$	−75281.6	−1.35713	−0.678564	−	0.734541i	$-0.737397\pi$
$79$	−75281.6	−1.35713	−0.678564	+	0.734541i	$0.737397\pi$
$80$	5068.94	0.0885507
$81$	6561.00	0.111111
$82$	−21093.4	−0.346427
$83$	−104809.	−1.66995	−0.834974	−	0.550289i	$-0.814517\pi$
$83$	−104809.	−1.66995	−0.834974	+	0.550289i	$0.814517\pi$
$84$	51155.6	0.791033
$85$	11473.5	0.172246
$86$	924.139	0.0134738
$87$	22350.4	0.316583
$88$	12890.3	0.177442
$89$	4771.10	0.0638475	0.0319237	−	0.999490i	$-0.489837\pi$
$89$	4771.10	0.0638475	0.0319237	+	0.999490i	$0.489837\pi$
$90$	−739.956	−0.00962941
$91$	32213.7	0.407790
$92$	−139627.	−1.71989
$93$	−41662.5	−0.499503
$94$	−13375.6	−0.156133
$95$	−12938.4	−0.147086
$96$	37182.1	0.411771
$97$	34879.0	0.376387	0.188194	−	0.982132i	$-0.439737\pi$
$97$	34879.0	0.376387	0.188194	+	0.982132i	$0.439737\pi$
$98$	−28835.5	−0.303293
$99$	11437.2	0.117282
$100$	92044.0	0.920440
$101$	123059.	1.20036	0.600179	−	0.799865i	$-0.295096\pi$
$101$	123059.	1.20036	0.600179	+	0.799865i	$0.295096\pi$
$102$	24650.3	0.234597
$103$	−70651.4	−0.656187	−0.328094	−	0.944645i	$-0.606406\pi$
$103$	−70651.4	−0.656187	−0.328094	+	0.944645i	$0.606406\pi$
$104$	15428.1	0.139872
$105$	−10612.4	−0.0939381
$106$	−46727.1	−0.403928
$107$	−51075.5	−0.431274	−0.215637	−	0.976474i	$-0.569183\pi$
$107$	−51075.5	−0.431274	−0.215637	+	0.976474i	$0.569183\pi$
$108$	21738.2	0.179335
$109$	172935.	1.39418	0.697088	−	0.716985i	$-0.254479\pi$
$109$	172935.	1.39418	0.697088	+	0.716985i	$0.254479\pi$
$110$	−1289.90	−0.0101642
$111$	−9123.15	−0.0702809
$112$	156190.	1.17654
$113$	15198.7	0.111972	0.0559860	−	0.998432i	$-0.482170\pi$
$113$	15198.7	0.111972	0.0559860	+	0.998432i	$0.482170\pi$
$114$	−27797.5	−0.200329
$115$	28966.2	0.204243
$116$	74052.4	0.510969
$117$	13689.0	0.0924500
$118$	38324.9	0.253382
$119$	353534.	2.28857
$120$	−5082.62	−0.0322207
$121$	−141113.	−0.876204
$122$	6993.06	0.0425371
$123$	−128554.	−0.766167
$124$	−138038.	−0.806205
$125$	−38426.6	−0.219966
$126$	−22800.3	−0.127942
$127$	82441.7	0.453563	0.226781	−	0.973946i	$-0.427180\pi$
$127$	82441.7	0.453563	0.226781	+	0.973946i	$0.427180\pi$
$128$	161915.	0.873498
$129$	5632.19	0.0297991
$130$	−1543.86	−0.00801216
$131$	−301955.	−1.53732	−0.768658	−	0.639660i	$-0.779075\pi$
$131$	−301955.	−1.53732	−0.768658	+	0.639660i	$0.779075\pi$
$132$	37894.4	0.189296
$133$	−398671.	−1.95427
$134$	−29117.2	−0.140084
$135$	−4509.69	−0.0212967
$136$	169318.	0.784977
$137$	−387921.	−1.76580	−0.882900	−	0.469562i	$-0.844412\pi$
$137$	−387921.	−1.76580	−0.882900	+	0.469562i	$0.844412\pi$
$138$	62232.5	0.278176
$139$	−215864.	−0.947640	−0.473820	−	0.880622i	$-0.657125\pi$
$139$	−215864.	−0.947640	−0.473820	+	0.880622i	$0.657125\pi$
$140$	−35161.7	−0.151617
$141$	−81518.3	−0.345309
$142$	40121.4	0.166977
$143$	23862.9	0.0975849
$144$	66371.7	0.266733
$145$	−15362.5	−0.0606794
$146$	20213.8	0.0784813
$147$	−175739.	−0.670770
$148$	−30227.3	−0.113434
$149$	306915.	1.13254	0.566268	−	0.824221i	$-0.308387\pi$
$149$	306915.	1.13254	0.566268	+	0.824221i	$0.308387\pi$
$150$	−41024.5	−0.148873
$151$	188241.	0.671851	0.335925	−	0.941889i	$-0.390951\pi$
$151$	188241.	0.671851	0.335925	+	0.941889i	$0.390951\pi$
$152$	−190935.	−0.670313
$153$	150232.	0.518841
$154$	−39745.9	−0.135049
$155$	28636.6	0.0957398
$156$	45355.1	0.149216
$157$	5384.05	0.0174325	0.00871626	−	0.999962i	$-0.497225\pi$
$157$	5384.05	0.0174325	0.00871626	+	0.999962i	$0.497225\pi$
$158$	111171.	0.354281
$159$	−284780.	−0.893339
$160$	−25557.0	−0.0789242
$161$	892536.	2.71370
$162$	−9688.85	−0.0290058
$163$	−650379.	−1.91733	−0.958666	−	0.284533i	$-0.908162\pi$
$163$	−650379.	−1.91733	−0.958666	+	0.284533i	$0.908162\pi$
$164$	−425932.	−1.23660
$165$	−7861.35	−0.0224795
$166$	154775.	0.435944
$167$	235868.	0.654452	0.327226	−	0.944946i	$-0.393886\pi$
$167$	235868.	0.654452	0.327226	+	0.944946i	$0.393886\pi$
$168$	−156611.	−0.428104
$169$	28561.0	0.0769231
$170$	−16943.3	−0.0449652
$171$	−169413.	−0.443053
$172$	18660.9	0.0480962
$173$	332282.	0.844096	0.422048	−	0.906574i	$-0.361311\pi$
$173$	332282.	0.844096	0.422048	+	0.906574i	$0.361311\pi$
$174$	−33005.6	−0.0826446
$175$	−588373.	−1.45230
$176$	115700.	0.281548
$177$	233572.	0.560387
$178$	−7045.65	−0.0166675
$179$	612970.	1.42990	0.714952	−	0.699174i	$-0.246449\pi$
$179$	612970.	1.42990	0.714952	+	0.699174i	$0.246449\pi$
$180$	−14941.7	−0.0343732
$181$	138097.	0.313319	0.156659	−	0.987653i	$-0.449927\pi$
$181$	138097.	0.313319	0.156659	+	0.987653i	$0.449927\pi$
$182$	−47571.0	−0.106455
$183$	42619.4	0.0940762
$184$	427463.	0.930794
$185$	6270.77	0.0134707
$186$	61524.4	0.130396
$187$	261887.	0.547658
$188$	−270091.	−0.557333
$189$	−138957.	−0.282961
$190$	19106.5	0.0383970
$191$	94267.9	0.186974	0.0934868	−	0.995621i	$-0.470199\pi$
$191$	94267.9	0.186974	0.0934868	+	0.995621i	$0.470199\pi$
$192$	181080.	0.354502
$193$	1.03276e6	1.99574	0.997870	−	0.0652281i	$-0.0207775\pi$
$193$	1.03276e6	1.99574	0.997870	+	0.0652281i	$0.0207775\pi$
$194$	−51507.1	−0.0982568
$195$	−9409.10	−0.0177199
$196$	−582266.	−1.08263
$197$	−157331.	−0.288834	−0.144417	−	0.989517i	$-0.546131\pi$
$197$	−157331.	−0.288834	−0.144417	+	0.989517i	$0.546131\pi$
$198$	−16889.7	−0.0306168
$199$	510479.	0.913788	0.456894	−	0.889521i	$-0.348962\pi$
$199$	510479.	0.913788	0.456894	+	0.889521i	$0.348962\pi$
$200$	−281790.	−0.498138
$201$	−177455.	−0.309813
$202$	−181726.	−0.313356
$203$	−473365.	−0.806225
$204$	497757.	0.837417
$205$	88361.4	0.146851
$206$	104333.	0.171299
$207$	379278.	0.615221
$208$	138479.	0.221935
$209$	−295322.	−0.467660
$210$	15671.7	0.0245227
$211$	−442016.	−0.683490	−0.341745	−	0.939793i	$-0.611018\pi$
$211$	−442016.	−0.683490	−0.341745	+	0.939793i	$0.611018\pi$
$212$	−943546.	−1.44186
$213$	244521.	0.369290
$214$	75424.9	0.112585
$215$	−3871.27	−0.00571160
$216$	−66550.9	−0.0970553
$217$	882382.	1.27206
$218$	−255380.	−0.363953
$219$	123194.	0.173571
$220$	−26046.6	−0.0362823
$221$	313447.	0.431702
$222$	13472.5	0.0183470
$223$	−972760.	−1.30992	−0.654958	−	0.755665i	$-0.727314\pi$
$223$	−972760.	−1.30992	−0.654958	+	0.755665i	$0.727314\pi$
$224$	−787490.	−1.04864
$225$	−250025.	−0.329251
$226$	−22444.4	−0.0292305
$227$	257972.	0.332283	0.166141	−	0.986102i	$-0.446869\pi$
$227$	257972.	0.332283	0.166141	+	0.986102i	$0.446869\pi$
$228$	−561306.	−0.715093
$229$	133806.	0.168612	0.0843060	−	0.996440i	$-0.473133\pi$
$229$	133806.	0.168612	0.0843060	+	0.996440i	$0.473133\pi$
$230$	−42775.3	−0.0533180
$231$	−242232.	−0.298677
$232$	−226709.	−0.276534
$233$	−1.62143e6	−1.95663	−0.978317	−	0.207112i	$-0.933594\pi$
$233$	−1.62143e6	−1.95663	−0.978317	+	0.207112i	$0.933594\pi$
$234$	−20215.0	−0.0241343
$235$	56031.4	0.0661853
$236$	773883.	0.904472
$237$	677534.	0.783538
$238$	−522076.	−0.597436
$239$	−811498.	−0.918952	−0.459476	−	0.888190i	$-0.651963\pi$
$239$	−811498.	−0.918952	−0.459476	+	0.888190i	$0.651963\pi$
$240$	−45620.4	−0.0511248
$241$	252994.	0.280587	0.140294	−	0.990110i	$-0.455195\pi$
$241$	252994.	0.280587	0.140294	+	0.990110i	$0.455195\pi$
$242$	208387.	0.228735
$243$	−59049.0	−0.0641500
$244$	141209.	0.151840
$245$	120793.	0.128567
$246$	189840.	0.200010
$247$	−353466.	−0.368642
$248$	422599.	0.436315
$249$	943280.	0.964145
$250$	56745.8	0.0574227
$251$	959107.	0.960910	0.480455	−	0.877019i	$-0.340471\pi$
$251$	959107.	0.960910	0.480455	+	0.877019i	$0.340471\pi$
$252$	−460400.	−0.456703
$253$	661162.	0.649392
$254$	−121744.	−0.118404
$255$	−103262.	−0.0994464
$256$	404736.	0.385986
$257$	−424311.	−0.400730	−0.200365	−	0.979721i	$-0.564213\pi$
$257$	−424311.	−0.400730	−0.200365	+	0.979721i	$0.564213\pi$
$258$	−8317.25	−0.00777912
$259$	193222.	0.178981
$260$	−31174.7	−0.0286002
$261$	−201153.	−0.182779
$262$	445907.	0.401320
$263$	−1.63733e6	−1.45964	−0.729822	−	0.683638i	$-0.760397\pi$
$263$	−1.63733e6	−1.45964	−0.729822	+	0.683638i	$0.760397\pi$
$264$	−116012.	−0.102446
$265$	195743.	0.171226
$266$	588731.	0.510167
$267$	−42939.9	−0.0368624
$268$	−587954.	−0.500042
$269$	−1.32752e6	−1.11857	−0.559283	−	0.828977i	$-0.688923\pi$
$269$	−1.32752e6	−1.11857	−0.559283	+	0.828977i	$0.688923\pi$
$270$	6659.61	0.00555955
$271$	105128.	0.0869547	0.0434774	−	0.999054i	$-0.486156\pi$
$271$	105128.	0.0869547	0.0434774	+	0.999054i	$0.486156\pi$
$272$	1.51976e6	1.24553
$273$	−289923.	−0.235438
$274$	572856.	0.460966
$275$	−435848.	−0.347539
$276$	1.25664e6	0.992976
$277$	−1.28791e6	−1.00852	−0.504260	−	0.863552i	$-0.668235\pi$
$277$	−1.28791e6	−1.00852	−0.504260	+	0.863552i	$0.668235\pi$
$278$	318774.	0.247383
$279$	374963.	0.288388
$280$	107646.	0.0820547
$281$	−297907.	−0.225068	−0.112534	−	0.993648i	$-0.535897\pi$
$281$	−297907.	−0.225068	−0.112534	+	0.993648i	$0.535897\pi$
$282$	120381.	0.0901435
$283$	−925425.	−0.686871	−0.343435	−	0.939176i	$-0.611591\pi$
$283$	−925425.	−0.686871	−0.343435	+	0.939176i	$0.611591\pi$
$284$	810160.	0.596039
$285$	116445.	0.0849199
$286$	−35239.1	−0.0254747
$287$	2.72268e6	1.95116
$288$	−334639.	−0.237736
$289$	2.02012e6	1.42277
$290$	22686.3	0.0158405
$291$	−313911.	−0.217307
$292$	408171.	0.280147
$293$	2.14512e6	1.45976	0.729880	−	0.683575i	$-0.239576\pi$
$293$	2.14512e6	1.45976	0.729880	+	0.683575i	$0.239576\pi$
$294$	259519.	0.175106
$295$	−160545.	−0.107409
$296$	92539.8	0.0613902
$297$	−102935.	−0.0677130
$298$	−453231.	−0.295651
$299$	791332.	0.511895
$300$	−828396.	−0.531417
$301$	−119286.	−0.0758879
$302$	−277983.	−0.175388
$303$	−1.10753e6	−0.693028
$304$	−1.71379e6	−1.06359
$305$	−29294.3	−0.0180316
$306$	−221853.	−0.135445
$307$	2.53446e6	1.53475	0.767377	−	0.641196i	$-0.221562\pi$
$307$	2.53446e6	1.53475	0.767377	+	0.641196i	$0.221562\pi$
$308$	−802576.	−0.482069
$309$	635863.	0.378850
$310$	−42288.7	−0.0249931
$311$	−1.40549e6	−0.824001	−0.412000	−	0.911184i	$-0.635170\pi$
$311$	−1.40549e6	−0.824001	−0.412000	+	0.911184i	$0.635170\pi$
$312$	−138853.	−0.0807549
$313$	−3.05827e6	−1.76447	−0.882236	−	0.470808i	$-0.843962\pi$
$313$	−3.05827e6	−1.76447	−0.882236	+	0.470808i	$0.843962\pi$
$314$	−7950.81	−0.00455080
$315$	95511.9	0.0542352
$316$	2.24484e6	1.26464
$317$	543899.	0.303997	0.151999	−	0.988381i	$-0.451429\pi$
$317$	543899.	0.303997	0.151999	+	0.988381i	$0.451429\pi$
$318$	420544.	0.233208
$319$	−350654.	−0.192931
$320$	−124465.	−0.0679474
$321$	459679.	0.248996
$322$	−1.31804e6	−0.708416
$323$	−3.87917e6	−2.06887
$324$	−195644.	−0.103539
$325$	−521658.	−0.273954
$326$	960437.	0.500524
$327$	−1.55642e6	−0.804928
$328$	1.30398e6	0.669245
$329$	1.72650e6	0.879380
$330$	11609.1	0.00586833
$331$	−3.20780e6	−1.60930	−0.804650	−	0.593749i	$-0.797647\pi$
$331$	−3.20780e6	−1.60930	−0.804650	+	0.593749i	$0.797647\pi$
$332$	3.12532e6	1.55614
$333$	82108.3	0.0405767
$334$	−348314.	−0.170846
$335$	121974.	0.0593818
$336$	−1.40571e6	−0.679276
$337$	1.89691e6	0.909855	0.454928	−	0.890528i	$-0.349665\pi$
$337$	1.89691e6	0.909855	0.454928	+	0.890528i	$0.349665\pi$
$338$	−42177.0	−0.0200809
$339$	−136788.	−0.0646471
$340$	−342132.	−0.160508
$341$	653640.	0.304406
$342$	250177.	0.115660
$343$	518376.	0.237908
$344$	−57129.6	−0.0260294
$345$	−260696.	−0.117920
$346$	−490692.	−0.220353
$347$	−1.45684e6	−0.649512	−0.324756	−	0.945798i	$-0.605282\pi$
$347$	−1.45684e6	−0.649512	−0.324756	+	0.945798i	$0.605282\pi$
$348$	−666472.	−0.295008
$349$	−3.62193e6	−1.59176	−0.795878	−	0.605457i	$-0.792990\pi$
$349$	−3.62193e6	−1.59176	−0.795878	+	0.605457i	$0.792990\pi$
$350$	868870.	0.379127
$351$	−123201.	−0.0533761
$352$	−583347.	−0.250940
$353$	−1.74392e6	−0.744888	−0.372444	−	0.928055i	$-0.621480\pi$
$353$	−1.74392e6	−0.744888	−0.372444	+	0.928055i	$0.621480\pi$
$354$	−344924.	−0.146290
$355$	−168071.	−0.0707819
$356$	−142271.	−0.0594964
$357$	−3.18181e6	−1.32131
$358$	−905194.	−0.373279
$359$	−2.52775e6	−1.03514	−0.517569	−	0.855641i	$-0.673163\pi$
$359$	−2.52775e6	−1.03514	−0.517569	+	0.855641i	$0.673163\pi$
$360$	45743.6	0.0186026
$361$	1.89833e6	0.766661
$362$	−203932.	−0.0817926
$363$	1.27002e6	0.505876
$364$	−960588.	−0.380000
$365$	−84676.8	−0.0332684
$366$	−62937.5	−0.0245588
$367$	1.53298e6	0.594116	0.297058	−	0.954859i	$-0.403994\pi$
$367$	1.53298e6	0.594116	0.297058	+	0.954859i	$0.403994\pi$
$368$	3.83681e6	1.47690
$369$	1.15699e6	0.442347
$370$	−9260.26	−0.00351657
$371$	6.03143e6	2.27502
$372$	1.24234e6	0.465463
$373$	−331711.	−0.123449	−0.0617246	−	0.998093i	$-0.519660\pi$
$373$	−331711.	−0.123449	−0.0617246	+	0.998093i	$0.519660\pi$
$374$	−386737.	−0.142967
$375$	345839.	0.126998
$376$	826873.	0.301626
$377$	−419691.	−0.152081
$378$	205203.	0.0738676
$379$	−3.12182e6	−1.11638	−0.558188	−	0.829715i	$-0.688503\pi$
$379$	−3.12182e6	−1.11638	−0.558188	+	0.829715i	$0.688503\pi$
$380$	385812.	0.137062
$381$	−741975.	−0.261865
$382$	−139209.	−0.0488099
$383$	2.43441e6	0.848003	0.424001	−	0.905662i	$-0.360625\pi$
$383$	2.43441e6	0.848003	0.424001	+	0.905662i	$0.360625\pi$
$384$	−1.45723e6	−0.504314
$385$	166498.	0.0572475
$386$	−1.52510e6	−0.520992
$387$	−50689.7	−0.0172045
$388$	−1.04007e6	−0.350737
$389$	−5.21717e6	−1.74808	−0.874039	−	0.485857i	$-0.838508\pi$
$389$	−5.21717e6	−1.74808	−0.874039	+	0.485857i	$0.838508\pi$
$390$	13894.7	0.00462582
$391$	8.68461e6	2.87282
$392$	1.78259e6	0.585916
$393$	2.71759e6	0.887570
$394$	232336.	0.0754008
$395$	−465701.	−0.150181
$396$	−341050.	−0.109290
$397$	4.19247e6	1.33504	0.667519	−	0.744593i	$-0.267356\pi$
$397$	4.19247e6	1.33504	0.667519	+	0.744593i	$0.267356\pi$
$398$	−753842.	−0.238546
$399$	3.58804e6	1.12830
$400$	−2.52928e6	−0.790400
$401$	730988.	0.227012	0.113506	−	0.993537i	$-0.463792\pi$
$401$	730988.	0.227012	0.113506	+	0.993537i	$0.463792\pi$
$402$	262054.	0.0808773
$403$	782329.	0.239953
$404$	−3.66954e6	−1.11856
$405$	40587.2	0.0122956
$406$	699034.	0.210467
$407$	143132.	0.0428304
$408$	−1.52387e6	−0.453207
$409$	5.26806e6	1.55719	0.778596	−	0.627525i	$-0.215932\pi$
$409$	5.26806e6	1.55719	0.778596	+	0.627525i	$0.215932\pi$
$410$	−130486.	−0.0383359
$411$	3.49129e6	1.01948
$412$	2.10677e6	0.611469
$413$	−4.94689e6	−1.42711
$414$	−560092.	−0.160605
$415$	−648361.	−0.184798
$416$	−698197.	−0.197808
$417$	1.94278e6	0.547120
$418$	436113.	0.122084
$419$	2.12251e6	0.590630	0.295315	−	0.955400i	$-0.404575\pi$
$419$	2.12251e6	0.590630	0.295315	+	0.955400i	$0.404575\pi$
$420$	316455.	0.0875364
$421$	−2.85481e6	−0.785005	−0.392502	−	0.919751i	$-0.628391\pi$
$421$	−2.85481e6	−0.785005	−0.392502	+	0.919751i	$0.628391\pi$
$422$	652741.	0.178427
$423$	733665.	0.199364
$424$	2.88863e6	0.780329
$425$	−5.72502e6	−1.53746
$426$	−361093.	−0.0964040
$427$	−902648.	−0.239579
$428$	1.52303e6	0.401883
$429$	−214766.	−0.0563406
$430$	5716.84	0.00149102
$431$	5.25703e6	1.36316	0.681581	−	0.731743i	$-0.261293\pi$
$431$	5.25703e6	1.36316	0.681581	+	0.731743i	$0.261293\pi$
$432$	−597346.	−0.153998
$433$	−3.05346e6	−0.782659	−0.391329	−	0.920251i	$-0.627985\pi$
$433$	−3.05346e6	−0.782659	−0.391329	+	0.920251i	$0.627985\pi$
$434$	−1.30304e6	−0.332074
$435$	138262.	0.0350333
$436$	−5.15681e6	−1.29917
$437$	−9.79338e6	−2.45318
$438$	−181924.	−0.0453112
$439$	−2.76642e6	−0.685105	−0.342552	−	0.939499i	$-0.611291\pi$
$439$	−2.76642e6	−0.685105	−0.342552	+	0.939499i	$0.611291\pi$
$440$	79740.8	0.0196358
$441$	1.58165e6	0.387269
$442$	−462879.	−0.112697
$443$	2.38712e6	0.577915	0.288958	−	0.957342i	$-0.406691\pi$
$443$	2.38712e6	0.577915	0.288958	+	0.957342i	$0.406691\pi$
$444$	272046.	0.0654914
$445$	29514.7	0.00706541
$446$	1.43651e6	0.341956
$447$	−2.76223e6	−0.653870
$448$	−3.83515e6	−0.902792
$449$	88547.7	0.0207282	0.0103641	−	0.999946i	$-0.496701\pi$
$449$	88547.7	0.0207282	0.0103641	+	0.999946i	$0.496701\pi$
$450$	369221.	0.0859518
$451$	2.01688e6	0.466915
$452$	−453213.	−0.104341
$453$	−1.69417e6	−0.387893
$454$	−380956.	−0.0867431
$455$	199278.	0.0451264
$456$	1.71842e6	0.387005
$457$	−5.82616e6	−1.30494	−0.652472	−	0.757812i	$-0.726268\pi$
$457$	−5.82616e6	−1.30494	−0.652472	+	0.757812i	$0.726268\pi$
$458$	−197597.	−0.0440165
$459$	−1.35209e6	−0.299553
$460$	−863750.	−0.190324
$461$	4.32111e6	0.946984	0.473492	−	0.880798i	$-0.342993\pi$
$461$	4.32111e6	0.946984	0.473492	+	0.880798i	$0.342993\pi$
$462$	357713.	0.0779703
$463$	5.57763e6	1.20920	0.604599	−	0.796530i	$-0.293333\pi$
$463$	5.57763e6	1.20920	0.604599	+	0.796530i	$0.293333\pi$
$464$	−2.03489e6	−0.438779
$465$	−257730.	−0.0552754
$466$	2.39443e6	0.510784
$467$	1.95457e6	0.414724	0.207362	−	0.978264i	$-0.433512\pi$
$467$	1.95457e6	0.414724	0.207362	+	0.978264i	$0.433512\pi$
$468$	−408196.	−0.0861497
$469$	3.75838e6	0.788984
$470$	−82743.5	−0.0172778
$471$	−48456.5	−0.0100647
$472$	−2.36922e6	−0.489496
$473$	−88363.0	−0.0181601
$474$	−1.00054e6	−0.204544
$475$	6.45594e6	1.31288
$476$	−1.05421e7	−2.13261
$477$	2.56302e6	0.515769
$478$	1.19837e6	0.239894
$479$	3.03700e6	0.604793	0.302396	−	0.953182i	$-0.402213\pi$
$479$	3.03700e6	0.604793	0.302396	+	0.953182i	$0.402213\pi$
$480$	230013.	0.0455669
$481$	171312.	0.0337619
$482$	−373605.	−0.0732480
$483$	−8.03283e6	−1.56675
$484$	4.20790e6	0.816492
$485$	215766.	0.0416513
$486$	87199.7	0.0167465
$487$	−8.37573e6	−1.60030	−0.800148	−	0.599803i	$-0.795246\pi$
$487$	−8.37573e6	−1.60030	−0.800148	+	0.599803i	$0.795246\pi$
$488$	−432306.	−0.0821753
$489$	5.85341e6	1.10697
$490$	−178380.	−0.0335626
$491$	−1.40343e6	−0.262716	−0.131358	−	0.991335i	$-0.541934\pi$
$491$	−1.40343e6	−0.262716	−0.131358	+	0.991335i	$0.541934\pi$
$492$	3.83339e6	0.713954
$493$	−4.60596e6	−0.853500
$494$	521975.	0.0962348
$495$	70752.1	0.0129786
$496$	3.79316e6	0.692304
$497$	−5.17878e6	−0.940452
$498$	−1.39297e6	−0.251692
$499$	−2.14531e6	−0.385691	−0.192845	−	0.981229i	$-0.561772\pi$
$499$	−2.14531e6	−0.385691	−0.192845	+	0.981229i	$0.561772\pi$
$500$	1.14585e6	0.204976
$501$	−2.12281e6	−0.377848
$502$	−1.41635e6	−0.250848
$503$	5.55969e6	0.979785	0.489892	−	0.871783i	$-0.337036\pi$
$503$	5.55969e6	0.979785	0.489892	+	0.871783i	$0.337036\pi$
$504$	1.40950e6	0.247166
$505$	761261.	0.132833
$506$	−976361.	−0.169525
$507$	−257049.	−0.0444116
$508$	−2.45835e6	−0.422653
$509$	−1.12359e6	−0.192227	−0.0961136	−	0.995370i	$-0.530641\pi$
$509$	−1.12359e6	−0.192227	−0.0961136	+	0.995370i	$0.530641\pi$
$510$	152490.	0.0259607
$511$	−2.60915e6	−0.442025
$512$	−5.77896e6	−0.974260
$513$	1.52471e6	0.255797
$514$	626594.	0.104611
$515$	−437059.	−0.0726142
$516$	−167948.	−0.0277683
$517$	1.27893e6	0.210437
$518$	−285337.	−0.0467233
$519$	−2.99054e6	−0.487339
$520$	95440.3	0.0154783
$521$	−3.76416e6	−0.607538	−0.303769	−	0.952746i	$-0.598245\pi$
$521$	−3.76416e6	−0.607538	−0.303769	+	0.952746i	$0.598245\pi$
$522$	297050.	0.0477149
$523$	591216.	0.0945131	0.0472565	−	0.998883i	$-0.484952\pi$
$523$	591216.	0.0945131	0.0472565	+	0.998883i	$0.484952\pi$
$524$	9.00406e6	1.43255
$525$	5.29536e6	0.838488
$526$	2.41790e6	0.381043
$527$	8.58580e6	1.34665
$528$	−1.04130e6	−0.162552
$529$	1.54889e7	2.40648
$530$	−289060.	−0.0446990
$531$	−2.10215e6	−0.323539
$532$	1.18881e7	1.82109
$533$	2.41396e6	0.368055
$534$	63410.9	0.00962300
$535$	−315959.	−0.0477251
$536$	1.80000e6	0.270621
$537$	−5.51673e6	−0.825555
$538$	1.96040e6	0.292004
$539$	2.75715e6	0.408779
$540$	134475.	0.0198453
$541$	−5.87874e6	−0.863557	−0.431778	−	0.901980i	$-0.642114\pi$
$541$	−5.87874e6	−0.863557	−0.431778	+	0.901980i	$0.642114\pi$
$542$	−155245.	−0.0226997
$543$	−1.24287e6	−0.180895
$544$	−7.66248e6	−1.11012
$545$	1.06980e6	0.154281
$546$	428139.	0.0614616
$547$	−9.43385e6	−1.34810	−0.674048	−	0.738688i	$-0.735446\pi$
$547$	−9.43385e6	−1.34810	−0.674048	+	0.738688i	$0.735446\pi$
$548$	1.15675e7	1.64546
$549$	−383575.	−0.0543149
$550$	643631.	0.0907257
$551$	5.19401e6	0.728826
$552$	−3.84717e6	−0.537394
$553$	−1.43497e7	−1.99540
$554$	1.90189e6	0.263276
$555$	−56437.0	−0.00777734
$556$	6.43690e6	0.883060
$557$	9.68718e6	1.32300	0.661499	−	0.749946i	$-0.269921\pi$
$557$	9.68718e6	1.32300	0.661499	+	0.749946i	$0.269921\pi$
$558$	−553720.	−0.0752843
$559$	−105760.	−0.0143150
$560$	966208.	0.130197
$561$	−2.35698e6	−0.316191
$562$	439929.	0.0587546
$563$	1.16995e7	1.55560	0.777800	−	0.628512i	$-0.216336\pi$
$563$	1.16995e7	1.55560	0.777800	+	0.628512i	$0.216336\pi$
$564$	2.43081e6	0.321776
$565$	94020.9	0.0123909
$566$	1.36661e6	0.179309
$567$	1.25062e6	0.163368
$568$	−2.48028e6	−0.322574
$569$	1.47102e6	0.190475	0.0952373	−	0.995455i	$-0.469639\pi$
$569$	1.47102e6	0.190475	0.0952373	+	0.995455i	$0.469639\pi$
$570$	−171959.	−0.0221685
$571$	−5.53198e6	−0.710052	−0.355026	−	0.934856i	$-0.615528\pi$
$571$	−5.53198e6	−0.710052	−0.355026	+	0.934856i	$0.615528\pi$
$572$	−711573.	−0.0909346
$573$	−848411.	−0.107949
$574$	−4.02068e6	−0.509354
$575$	−1.44534e7	−1.82306
$576$	−1.62972e6	−0.204672
$577$	1.46652e7	1.83378	0.916891	−	0.399138i	$-0.130691\pi$
$577$	1.46652e7	1.83378	0.916891	+	0.399138i	$0.130691\pi$
$578$	−2.98319e6	−0.371416
$579$	−9.29480e6	−1.15224
$580$	458098.	0.0565442
$581$	−1.99780e7	−2.45534
$582$	463564.	0.0567286
$583$	4.46789e6	0.544416
$584$	−1.24960e6	−0.151614
$585$	84681.9	0.0102306
$586$	−3.16777e6	−0.381074
$587$	4.66463e6	0.558756	0.279378	−	0.960181i	$-0.409872\pi$
$587$	4.66463e6	0.558756	0.279378	+	0.960181i	$0.409872\pi$
$588$	5.24039e6	0.625058
$589$	−9.68196e6	−1.14994
$590$	237083.	0.0280395
$591$	1.41598e6	0.166759
$592$	830616.	0.0974084
$593$	9.26934e6	1.08246	0.541230	−	0.840875i	$-0.317959\pi$
$593$	9.26934e6	1.08246	0.541230	+	0.840875i	$0.317959\pi$
$594$	152008.	0.0176766
$595$	2.18701e6	0.253255
$596$	−9.15197e6	−1.05536
$597$	−4.59431e6	−0.527576
$598$	−1.16859e6	−0.133631
$599$	4.96013e6	0.564840	0.282420	−	0.959291i	$-0.408863\pi$
$599$	4.96013e6	0.564840	0.282420	+	0.959291i	$0.408863\pi$
$600$	2.53611e6	0.287600
$601$	−7.53100e6	−0.850485	−0.425243	−	0.905079i	$-0.639811\pi$
$601$	−7.53100e6	−0.850485	−0.425243	+	0.905079i	$0.639811\pi$
$602$	176153.	0.0198107
$603$	1.59710e6	0.178870
$604$	−5.61322e6	−0.626065
$605$	−872946.	−0.0969614
$606$	1.63553e6	0.180916
$607$	−1.70472e7	−1.87794	−0.938970	−	0.343999i	$-0.888218\pi$
$607$	−1.70472e7	−1.87794	−0.938970	+	0.343999i	$0.888218\pi$
$608$	8.64075e6	0.947966
$609$	4.26029e6	0.465474
$610$	43259.9	0.00470719
$611$	1.53073e6	0.165881
$612$	−4.47981e6	−0.483483
$613$	−5.65370e6	−0.607689	−0.303845	−	0.952722i	$-0.598270\pi$
$613$	−5.65370e6	−0.607689	−0.303845	+	0.952722i	$0.598270\pi$
$614$	−3.74272e6	−0.400651
$615$	−795252.	−0.0847846
$616$	2.45706e6	0.260894
$617$	−5.06541e6	−0.535676	−0.267838	−	0.963464i	$-0.586309\pi$
$617$	−5.06541e6	−0.535676	−0.267838	+	0.963464i	$0.586309\pi$
$618$	−939000.	−0.0988996
$619$	8.67695e6	0.910208	0.455104	−	0.890438i	$-0.349602\pi$
$619$	8.67695e6	0.910208	0.455104	+	0.890438i	$0.349602\pi$
$620$	−853923.	−0.0892153
$621$	−3.41350e6	−0.355198
$622$	2.07554e6	0.215107
$623$	909437.	0.0938755
$624$	−1.24631e6	−0.128134
$625$	9.40833e6	0.963413
$626$	4.51625e6	0.460619
$627$	2.65790e6	0.270004
$628$	−160548.	−0.0162445
$629$	1.88010e6	0.189476
$630$	−141046.	−0.0141582
$631$	−1.39822e7	−1.39798	−0.698992	−	0.715129i	$-0.746368\pi$
$631$	−1.39822e7	−1.39798	−0.698992	+	0.715129i	$0.746368\pi$
$632$	−6.87250e6	−0.684419
$633$	3.97815e6	0.394613
$634$	−803194.	−0.0793592
$635$	509995.	0.0501916
$636$	8.49192e6	0.832459
$637$	3.29998e6	0.322228
$638$	517822.	0.0503650
$639$	−2.20069e6	−0.213210
$640$	1.00163e6	0.0966620
$641$	1.51645e6	0.145775	0.0728876	−	0.997340i	$-0.476779\pi$
$641$	1.51645e6	0.145775	0.0728876	+	0.997340i	$0.476779\pi$
$642$	−678824.	−0.0650009
$643$	1.42916e7	1.36318	0.681589	−	0.731735i	$-0.261289\pi$
$643$	1.42916e7	1.36318	0.681589	+	0.731735i	$0.261289\pi$
$644$	−2.66148e7	−2.52876
$645$	34841.4	0.00329759
$646$	5.72850e6	0.540082
$647$	1.98547e6	0.186468	0.0932338	−	0.995644i	$-0.470280\pi$
$647$	1.98547e6	0.186468	0.0932338	+	0.995644i	$0.470280\pi$
$648$	598958.	0.0560349
$649$	−3.66450e6	−0.341509
$650$	770350.	0.0715162
$651$	−7.94144e6	−0.734423
$652$	1.93938e7	1.78667
$653$	−1.55847e7	−1.43027	−0.715133	−	0.698989i	$-0.753634\pi$
$653$	−1.55847e7	−1.43027	−0.715133	+	0.698989i	$0.753634\pi$
$654$	2.29842e6	0.210128
$655$	−1.86793e6	−0.170121
$656$	1.17042e7	1.06190
$657$	−1.10874e6	−0.100211
$658$	−2.54958e6	−0.229564
$659$	−75439.4	−0.00676682	−0.00338341	−	0.999994i	$-0.501077\pi$
$659$	−75439.4	−0.00676682	−0.00338341	+	0.999994i	$0.501077\pi$
$660$	234420.	0.0209476
$661$	3.11557e6	0.277353	0.138677	−	0.990338i	$-0.455715\pi$
$661$	3.11557e6	0.277353	0.138677	+	0.990338i	$0.455715\pi$
$662$	4.73707e6	0.420111
$663$	−2.82103e6	−0.249243
$664$	−9.56807e6	−0.842179
$665$	−2.46623e6	−0.216261
$666$	−121252.	−0.0105926
$667$	−1.16283e7	−1.01205
$668$	−7.03341e6	−0.609853
$669$	8.75484e6	0.756280
$670$	−180122.	−0.0155018
$671$	−668653.	−0.0573316
$672$	7.08741e6	0.605430
$673$	1.40632e7	1.19687	0.598435	−	0.801172i	$-0.295790\pi$
$673$	1.40632e7	1.19687	0.598435	+	0.801172i	$0.295790\pi$
$674$	−2.80123e6	−0.237520
$675$	2.25023e6	0.190093
$676$	−851668.	−0.0716809
$677$	−6.04060e6	−0.506533	−0.253267	−	0.967396i	$-0.581505\pi$
$677$	−6.04060e6	−0.506533	−0.253267	+	0.967396i	$0.581505\pi$
$678$	202000.	0.0168763
$679$	6.64842e6	0.553406
$680$	1.04742e6	0.0868662
$681$	−2.32175e6	−0.191843
$682$	−965253.	−0.0794658
$683$	1.32539e7	1.08716	0.543578	−	0.839359i	$-0.317069\pi$
$683$	1.32539e7	1.08716	0.543578	+	0.839359i	$0.317069\pi$
$684$	5.05176e6	0.412859
$685$	−2.39973e6	−0.195405
$686$	−765503.	−0.0621064
$687$	−1.20426e6	−0.0973482
$688$	−512782.	−0.0413011
$689$	5.34753e6	0.429146
$690$	384978.	0.0307832
$691$	459579.	0.0366155	0.0183077	−	0.999832i	$-0.494172\pi$
$691$	459579.	0.0366155	0.0183077	+	0.999832i	$0.494172\pi$
$692$	−9.90840e6	−0.786572
$693$	2.18009e6	0.172441
$694$	2.15136e6	0.169557
$695$	−1.33536e6	−0.104867
$696$	2.04038e6	0.159657
$697$	2.64924e7	2.06557
$698$	5.34863e6	0.415531
$699$	1.45929e7	1.12966
$700$	1.75448e7	1.35333
$701$	−1.53638e7	−1.18087	−0.590437	−	0.807083i	$-0.701045\pi$
$701$	−1.53638e7	−1.18087	−0.590437	+	0.807083i	$0.701045\pi$
$702$	181935.	0.0139339
$703$	−2.12013e6	−0.161799
$704$	−2.84096e6	−0.216039
$705$	−504282.	−0.0382121
$706$	2.57531e6	0.194455
$707$	2.34568e7	1.76490
$708$	−6.96495e6	−0.522197
$709$	7.38149e6	0.551478	0.275739	−	0.961232i	$-0.411077\pi$
$709$	7.38149e6	0.551478	0.275739	+	0.961232i	$0.411077\pi$
$710$	248196.	0.0184778
$711$	−6.09781e6	−0.452376
$712$	435557.	0.0321992
$713$	2.16758e7	1.59680
$714$	4.69869e6	0.344930
$715$	147619.	0.0107988
$716$	−1.82783e7	−1.33246
$717$	7.30349e6	0.530557
$718$	3.73282e6	0.270225
$719$	−2.47769e7	−1.78741	−0.893707	−	0.448651i	$-0.851904\pi$
$719$	−2.47769e7	−1.78741	−0.893707	+	0.448651i	$0.851904\pi$
$720$	410584.	0.0295169
$721$	−1.34671e7	−0.964798
$722$	−2.80332e6	−0.200138
$723$	−2.27695e6	−0.161997
$724$	−4.11794e6	−0.291967
$725$	7.66552e6	0.541622
$726$	−1.87548e6	−0.132060
$727$	1.24758e7	0.875452	0.437726	−	0.899108i	$-0.355784\pi$
$727$	1.24758e7	0.875452	0.437726	+	0.899108i	$0.355784\pi$
$728$	2.94081e6	0.205654
$729$	531441.	0.0370370
$730$	125045.	0.00868480
$731$	−1.16068e6	−0.0803377
$732$	−1.27088e6	−0.0876650
$733$	2.67161e6	0.183659	0.0918296	−	0.995775i	$-0.470728\pi$
$733$	2.67161e6	0.183659	0.0918296	+	0.995775i	$0.470728\pi$
$734$	−2.26380e6	−0.155095
$735$	−1.08714e6	−0.0742280
$736$	−1.93448e7	−1.31634
$737$	2.78409e6	0.188805
$738$	−1.70856e6	−0.115476
$739$	−1.53282e7	−1.03248	−0.516239	−	0.856445i	$-0.672668\pi$
$739$	−1.53282e7	−1.03248	−0.516239	+	0.856445i	$0.672668\pi$
$740$	−186990.	−0.0125527
$741$	3.18119e6	0.212836
$742$	−8.90681e6	−0.593899
$743$	−9.13987e6	−0.607391	−0.303695	−	0.952769i	$-0.598220\pi$
$743$	−9.13987e6	−0.607391	−0.303695	+	0.952769i	$0.598220\pi$
$744$	−3.80340e6	−0.251906
$745$	1.89861e6	0.125327
$746$	489849.	0.0322267
$747$	−8.48952e6	−0.556649
$748$	−7.80927e6	−0.510336
$749$	−9.73567e6	−0.634105
$750$	−510712.	−0.0331530
$751$	−1.95912e6	−0.126754	−0.0633769	−	0.997990i	$-0.520187\pi$
$751$	−1.95912e6	−0.126754	−0.0633769	+	0.997990i	$0.520187\pi$
$752$	7.42183e6	0.478593
$753$	−8.63196e6	−0.554782
$754$	619771.	0.0397012
$755$	1.16449e6	0.0743475
$756$	4.14360e6	0.263678
$757$	−1.81437e7	−1.15076	−0.575382	−	0.817885i	$-0.695147\pi$
$757$	−1.81437e7	−1.15076	−0.575382	+	0.817885i	$0.695147\pi$
$758$	4.61010e6	0.291432
$759$	−5.95046e6	−0.374926
$760$	−1.18115e6	−0.0741774
$761$	1.52710e7	0.955883	0.477941	−	0.878392i	$-0.341383\pi$
$761$	1.52710e7	0.955883	0.477941	+	0.878392i	$0.341383\pi$
$762$	1.09570e6	0.0683603
$763$	3.29638e7	2.04987
$764$	−2.81100e6	−0.174232
$765$	929355.	0.0574154
$766$	−3.59498e6	−0.221373
$767$	−4.38596e6	−0.269201
$768$	−3.64262e6	−0.222849
$769$	1.54324e7	0.941062	0.470531	−	0.882384i	$-0.344062\pi$
$769$	1.54324e7	0.941062	0.470531	+	0.882384i	$0.344062\pi$
$770$	−245873.	−0.0149446
$771$	3.81880e6	0.231361
$772$	−3.07960e7	−1.85973
$773$	342144.	0.0205949	0.0102975	−	0.999947i	$-0.496722\pi$
$773$	342144.	0.0205949	0.0102975	+	0.999947i	$0.496722\pi$
$774$	74855.2	0.00449128
$775$	−1.42890e7	−0.854570
$776$	3.18413e6	0.189818
$777$	−1.73900e6	−0.103335
$778$	7.70437e6	0.456339
$779$	−2.98747e7	−1.76385
$780$	280572.	0.0165123
$781$	−3.83628e6	−0.225052
$782$	−1.28249e7	−0.749956
$783$	1.81038e6	0.105528
$784$	1.60001e7	0.929678
$785$	33306.4	0.00192910
$786$	−4.01316e6	−0.231702
$787$	−2.07885e7	−1.19643	−0.598213	−	0.801337i	$-0.704122\pi$
$787$	−2.07885e7	−1.19643	−0.598213	+	0.801337i	$0.704122\pi$
$788$	4.69149e6	0.269151
$789$	1.47360e7	0.842725
$790$	687717.	0.0392050
$791$	2.89707e6	0.164633
$792$	1.04411e6	0.0591472
$793$	−800298.	−0.0451927
$794$	−6.19116e6	−0.348515
$795$	−1.76168e6	−0.0988576
$796$	−1.52221e7	−0.851515
$797$	−2.31380e7	−1.29027	−0.645133	−	0.764070i	$-0.723198\pi$
$797$	−2.31380e7	−1.29027	−0.645133	+	0.764070i	$0.723198\pi$
$798$	−5.29857e6	−0.294545
$799$	1.67993e7	0.930944
$800$	1.27523e7	0.704474
$801$	386459.	0.0212825
$802$	−1.07948e6	−0.0592621
$803$	−1.93278e6	−0.105777
$804$	5.29159e6	0.288699
$805$	5.52134e6	0.300300
$806$	−1.15529e6	−0.0626404
$807$	1.19477e7	0.645804
$808$	1.12342e7	0.605358
$809$	1.89827e7	1.01973	0.509866	−	0.860254i	$-0.329695\pi$
$809$	1.89827e7	1.01973	0.509866	+	0.860254i	$0.329695\pi$
$810$	−59936.5	−0.00320980
$811$	−1.05961e7	−0.565712	−0.282856	−	0.959162i	$-0.591282\pi$
$811$	−1.05961e7	−0.565712	−0.282856	+	0.959162i	$0.591282\pi$
$812$	1.41154e7	0.751282
$813$	−946148.	−0.0502033
$814$	−211369.	−0.0111810
$815$	−4.02333e6	−0.212174
$816$	−1.36779e7	−0.719107
$817$	1.30887e6	0.0686025
$818$	−7.77952e6	−0.406508
$819$	2.60931e6	0.135930
$820$	−2.63487e6	−0.136844
$821$	1.09767e7	0.568346	0.284173	−	0.958773i	$-0.408281\pi$
$821$	1.09767e7	0.568346	0.284173	+	0.958773i	$0.408281\pi$
$822$	−5.15570e6	−0.266139
$823$	−1.13830e7	−0.585810	−0.292905	−	0.956142i	$-0.594622\pi$
$823$	−1.13830e7	−0.585810	−0.292905	+	0.956142i	$0.594622\pi$
$824$	−6.44981e6	−0.330925
$825$	3.92263e6	0.200651
$826$	7.30524e6	0.372550
$827$	9.41841e6	0.478866	0.239433	−	0.970913i	$-0.423039\pi$
$827$	9.41841e6	0.478866	0.239433	+	0.970913i	$0.423039\pi$
$828$	−1.13098e7	−0.573295
$829$	1.04972e7	0.530502	0.265251	−	0.964179i	$-0.414545\pi$
$829$	1.04972e7	0.530502	0.265251	+	0.964179i	$0.414545\pi$
$830$	957457.	0.0482419
$831$	1.15911e7	0.582269
$832$	−3.40029e6	−0.170297
$833$	3.62162e7	1.80838
$834$	−2.86896e6	−0.142827
$835$	1.45911e6	0.0724222
$836$	8.80629e6	0.435790
$837$	−3.37466e6	−0.166501
$838$	−3.13439e6	−0.154185
$839$	−6.67378e6	−0.327316	−0.163658	−	0.986517i	$-0.552329\pi$
$839$	−6.67378e6	−0.327316	−0.163658	+	0.986517i	$0.552329\pi$
$840$	−968816.	−0.0473743
$841$	−1.43440e7	−0.699327
$842$	4.21580e6	0.204927
$843$	2.68116e6	0.129943
$844$	1.31806e7	0.636912
$845$	176682.	0.00851237
$846$	−1.08343e6	−0.0520444
$847$	−2.68981e7	−1.28829
$848$	2.59277e7	1.23815
$849$	8.32882e6	0.396565
$850$	8.45433e6	0.401358
$851$	4.74651e6	0.224673
$852$	−7.29144e6	−0.344124
$853$	3.58582e6	0.168739	0.0843695	−	0.996435i	$-0.473112\pi$
$853$	3.58582e6	0.168739	0.0843695	+	0.996435i	$0.473112\pi$
$854$	1.33297e6	0.0625426
$855$	−1.04801e6	−0.0490286
$856$	−4.66271e6	−0.217497
$857$	1.55304e7	0.722321	0.361160	−	0.932504i	$-0.382381\pi$
$857$	1.55304e7	0.722321	0.361160	+	0.932504i	$0.382381\pi$
$858$	317152.	0.0147078
$859$	3.10835e7	1.43730	0.718649	−	0.695373i	$-0.244761\pi$
$859$	3.10835e7	1.43730	0.718649	+	0.695373i	$0.244761\pi$
$860$	115438.	0.00532236
$861$	−2.45042e7	−1.12650
$862$	−7.76324e6	−0.355856
$863$	3.59926e7	1.64508	0.822539	−	0.568708i	$-0.192557\pi$
$863$	3.59926e7	1.64508	0.822539	+	0.568708i	$0.192557\pi$
$864$	3.01175e6	0.137257
$865$	2.05554e6	0.0934083
$866$	4.50915e6	0.204315
$867$	−1.81811e7	−0.821434
$868$	−2.63120e7	−1.18537
$869$	−1.06298e7	−0.477502
$870$	−204177.	−0.00914551
$871$	3.33222e6	0.148829
$872$	1.57874e7	0.703103
$873$	2.82520e6	0.125462
$874$	1.44622e7	0.640408
$875$	−7.32462e6	−0.323419
$876$	−3.67354e6	−0.161743
$877$	−1.74870e7	−0.767746	−0.383873	−	0.923386i	$-0.625410\pi$
$877$	−1.74870e7	−0.767746	−0.383873	+	0.923386i	$0.625410\pi$
$878$	4.08527e6	0.178848
$879$	−1.93060e7	−0.842793
$880$	715736.	0.0311563
$881$	1.52380e7	0.661437	0.330719	−	0.943729i	$-0.392709\pi$
$881$	1.52380e7	0.661437	0.330719	+	0.943729i	$0.392709\pi$
$882$	−2.33567e6	−0.101098
$883$	−3.22630e7	−1.39252	−0.696262	−	0.717787i	$-0.745155\pi$
$883$	−3.22630e7	−1.39252	−0.696262	+	0.717787i	$0.745155\pi$
$884$	−9.34677e6	−0.402282
$885$	1.44491e6	0.0620128
$886$	−3.52514e6	−0.150866
$887$	2.82559e7	1.20587	0.602934	−	0.797791i	$-0.293998\pi$
$887$	2.82559e7	1.20587	0.602934	+	0.797791i	$0.293998\pi$
$888$	−832858.	−0.0354437
$889$	1.57145e7	0.666877
$890$	−43585.3	−0.00184444
$891$	926416.	0.0390941
$892$	2.90070e7	1.22065
$893$	−1.89441e7	−0.794959
$894$	4.07908e6	0.170694
$895$	3.79191e6	0.158234
$896$	3.08632e7	1.28431
$897$	−7.12199e6	−0.295543
$898$	−130761.	−0.00541114
$899$	−1.14960e7	−0.474402
$900$	7.45557e6	0.306813
$901$	5.86873e7	2.40842
$902$	−2.97839e6	−0.121889
$903$	1.07357e6	0.0438139
$904$	1.38750e6	0.0564691
$905$	854283.	0.0346721
$906$	2.50184e6	0.101260
$907$	−1.87244e7	−0.755771	−0.377885	−	0.925852i	$-0.623349\pi$
$907$	−1.87244e7	−0.755771	−0.377885	+	0.925852i	$0.623349\pi$
$908$	−7.69253e6	−0.309638
$909$	9.96781e6	0.400120
$910$	−294281.	−0.0117803
$911$	−1.24649e7	−0.497616	−0.248808	−	0.968553i	$-0.580039\pi$
$911$	−1.24649e7	−0.497616	−0.248808	+	0.968553i	$0.580039\pi$
$912$	1.54242e7	0.614065
$913$	−1.47991e7	−0.587567
$914$	8.60370e6	0.340659
$915$	263649.	0.0104105
$916$	−3.99001e6	−0.157121
$917$	−5.75566e7	−2.26033
$918$	1.99668e6	0.0781990
$919$	−3.05164e7	−1.19191	−0.595956	−	0.803017i	$-0.703227\pi$
$919$	−3.05164e7	−1.19191	−0.595956	+	0.803017i	$0.703227\pi$
$920$	2.64434e6	0.103002
$921$	−2.28101e7	−0.886091
$922$	−6.38113e6	−0.247212
$923$	−4.59157e6	−0.177401
$924$	7.22319e6	0.278323
$925$	−3.12897e6	−0.120239
$926$	−8.23668e6	−0.315664
$927$	−5.72276e6	−0.218729
$928$	1.02597e7	0.391078
$929$	−1.89467e7	−0.720267	−0.360134	−	0.932901i	$-0.617269\pi$
$929$	−1.89467e7	−0.720267	−0.360134	+	0.932901i	$0.617269\pi$
$930$	380598.	0.0144298
$931$	−4.08400e7	−1.54423
$932$	4.83500e7	1.82329
$933$	1.26494e7	0.475737
$934$	−2.88638e6	−0.108265
$935$	1.62007e6	0.0606043
$936$	1.24968e6	0.0466239
$937$	6.77539e6	0.252107	0.126054	−	0.992023i	$-0.459769\pi$
$937$	6.77539e6	0.252107	0.126054	+	0.992023i	$0.459769\pi$
$938$	−5.55013e6	−0.205966
$939$	2.75244e7	1.01872
$940$	−1.67081e6	−0.0616749
$941$	−4.09175e7	−1.50638	−0.753190	−	0.657802i	$-0.771486\pi$
$941$	−4.09175e7	−1.50638	−0.753190	+	0.657802i	$0.771486\pi$
$942$	71557.3	0.00262740
$943$	6.68830e7	2.44927
$944$	−2.12656e7	−0.776688
$945$	−859607.	−0.0313127
$946$	130489.	0.00474073
$947$	−3.30315e7	−1.19689	−0.598445	−	0.801164i	$-0.704214\pi$
$947$	−3.30315e7	−1.19689	−0.598445	+	0.801164i	$0.704214\pi$
$948$	−2.02036e7	−0.730142
$949$	−2.31330e6	−0.0833810
$950$	−9.53371e6	−0.342731
$951$	−4.89509e6	−0.175513
$952$	3.22744e7	1.15416
$953$	7.16060e6	0.255398	0.127699	−	0.991813i	$-0.459241\pi$
$953$	7.16060e6	0.255398	0.127699	+	0.991813i	$0.459241\pi$
$954$	−3.78489e6	−0.134643
$955$	583153.	0.0206906
$956$	2.41983e7	0.856327
$957$	3.15588e6	0.111389
$958$	−4.48485e6	−0.157883
$959$	−7.39429e7	−2.59627
$960$	1.12019e6	0.0392294
$961$	−7.19996e6	−0.251491
$962$	−252983.	−0.00881361
$963$	−4.13711e6	−0.143758
$964$	−7.54410e6	−0.261466
$965$	6.38875e6	0.220850
$966$	1.18623e7	0.409004
$967$	5.72729e6	0.196962	0.0984812	−	0.995139i	$-0.468602\pi$
$967$	5.72729e6	0.196962	0.0984812	+	0.995139i	$0.468602\pi$
$968$	−1.28823e7	−0.441882
$969$	3.49125e7	1.19446
$970$	−318629.	−0.0108732
$971$	1.19944e7	0.408254	0.204127	−	0.978944i	$-0.434564\pi$
$971$	1.19944e7	0.408254	0.204127	+	0.978944i	$0.434564\pi$
$972$	1.76080e6	0.0597783
$973$	−4.11466e7	−1.39332
$974$	1.23687e7	0.417761
$975$	4.69492e6	0.158167
$976$	−3.88028e6	−0.130388
$977$	−2.39435e7	−0.802512	−0.401256	−	0.915966i	$-0.631426\pi$
$977$	−2.39435e7	−0.802512	−0.401256	+	0.915966i	$0.631426\pi$
$978$	−8.64393e6	−0.288978
$979$	673682.	0.0224646
$980$	−3.60197e6	−0.119805
$981$	1.40078e7	0.464726
$982$	2.07249e6	0.0685826
$983$	5.44669e7	1.79783	0.898915	−	0.438123i	$-0.144357\pi$
$983$	5.44669e7	1.79783	0.898915	+	0.438123i	$0.144357\pi$
$984$	−1.17358e7	−0.386389
$985$	−973270.	−0.0319626
$986$	6.80178e6	0.222808
$987$	−1.55385e7	−0.507710
$988$	1.05401e7	0.343520
$989$	−2.93027e6	−0.0952613
$990$	−104482.	−0.00338808
$991$	1.99942e7	0.646724	0.323362	−	0.946275i	$-0.395187\pi$
$991$	1.99942e7	0.646724	0.323362	+	0.946275i	$0.395187\pi$
$992$	−1.91247e7	−0.617042
$993$	2.88702e7	0.929130
$994$	7.64769e6	0.245507
$995$	3.15789e6	0.101120
$996$	−2.81279e7	−0.898440
$997$	5.61651e6	0.178949	0.0894744	−	0.995989i	$-0.471481\pi$
$997$	5.61651e6	0.178949	0.0894744	+	0.995989i	$0.471481\pi$
$998$	3.16806e6	0.100685
$999$	−738975.	−0.0234270

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.6.a.c.1.2	✓	3
3.2	odd	2		117.6.a.e.1.2		3
4.3	odd	2		624.6.a.t.1.2		3
5.4	even	2		975.6.a.d.1.2		3
13.12	even	2		507.6.a.d.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.6.a.c.1.2	✓	3	1.1	even	1	trivial
117.6.a.e.1.2		3	3.2	odd	2
507.6.a.d.1.2		3	13.12	even	2
624.6.a.t.1.2		3	4.3	odd	2
975.6.a.d.1.2		3	5.4	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:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	39.a (trivial)

\(f(q)\)	\(=\)	\(q-1.47673 q^{2} -9.00000 q^{3} -29.8193 q^{4} +6.18613 q^{5} +13.2906 q^{6} +190.614 q^{7} +91.2906 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-1.47673 q^{2} -9.00000 q^{3} -29.8193 q^{4} +6.18613 q^{5} +13.2906 q^{6} +190.614 q^{7} +91.2906 q^{8} +81.0000 q^{9} -9.13526 q^{10} +141.200 q^{11} +268.373 q^{12} +169.000 q^{13} -281.485 q^{14} -55.6751 q^{15} +819.404 q^{16} +1854.72 q^{17} -119.615 q^{18} -2091.51 q^{19} -184.466 q^{20} -1715.52 q^{21} -208.515 q^{22} +4682.44 q^{23} -821.615 q^{24} -3086.73 q^{25} -249.568 q^{26} -729.000 q^{27} -5683.95 q^{28} -2483.38 q^{29} +82.2174 q^{30} +4629.17 q^{31} -4131.34 q^{32} -1270.80 q^{33} -2738.93 q^{34} +1179.16 q^{35} -2415.36 q^{36} +1013.68 q^{37} +3088.61 q^{38} -1521.00 q^{39} +564.735 q^{40} +14283.8 q^{41} +2533.37 q^{42} -625.799 q^{43} -4210.49 q^{44} +501.076 q^{45} -6914.72 q^{46} +9057.59 q^{47} -7374.64 q^{48} +19526.5 q^{49} +4558.28 q^{50} -16692.5 q^{51} -5039.45 q^{52} +31642.2 q^{53} +1076.54 q^{54} +873.483 q^{55} +17401.2 q^{56} +18823.6 q^{57} +3667.29 q^{58} -25952.5 q^{59} +1660.19 q^{60} -4735.49 q^{61} -6836.05 q^{62} +15439.7 q^{63} -20120.0 q^{64} +1045.46 q^{65} +1876.64 q^{66} +19717.3 q^{67} -55306.3 q^{68} -42142.0 q^{69} -1741.30 q^{70} -27169.0 q^{71} +7394.54 q^{72} -13688.2 q^{73} -1496.94 q^{74} +27780.6 q^{75} +62367.4 q^{76} +26914.7 q^{77} +2246.11 q^{78} -75281.6 q^{79} +5068.94 q^{80} +6561.00 q^{81} -21093.4 q^{82} -104809. q^{83} +51155.6 q^{84} +11473.5 q^{85} +924.139 q^{86} +22350.4 q^{87} +12890.3 q^{88} +4771.10 q^{89} -739.956 q^{90} +32213.7 q^{91} -139627. q^{92} -41662.5 q^{93} -13375.6 q^{94} -12938.4 q^{95} +37182.1 q^{96} +34879.0 q^{97} -28835.5 q^{98} +11437.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 27 q^{3} + 14 q^{4} + 54 q^{5} + 84 q^{7} + 234 q^{8} + 243 q^{9}+O(q^{10}) \) 3 * q - 27 * q^3 + 14 * q^4 + 54 * q^5 + 84 * q^7 + 234 * q^8 + 243 * q^9	\( 3 q - 27 q^{3} + 14 q^{4} + 54 q^{5} + 84 q^{7} + 234 q^{8} + 243 q^{9} + 880 q^{10} + 876 q^{11} - 126 q^{12} + 507 q^{13} + 1896 q^{14} - 486 q^{15} - 1438 q^{16} + 102 q^{17} - 16 q^{19} + 2124 q^{20} - 756 q^{21} - 2776 q^{22} - 2106 q^{24} - 1363 q^{25} - 2187 q^{27} - 4688 q^{28} + 9666 q^{29} - 7920 q^{30} - 10196 q^{31} - 8502 q^{32} - 7884 q^{33} - 23552 q^{34} + 16680 q^{35} + 1134 q^{36} + 11818 q^{37} - 8040 q^{38} - 4563 q^{39} - 3708 q^{40} + 35490 q^{41} - 17064 q^{42} + 2780 q^{43} + 7296 q^{44} + 4374 q^{45} - 12576 q^{46} + 25728 q^{47} + 12942 q^{48} + 39291 q^{49} + 46656 q^{50} - 918 q^{51} + 2366 q^{52} + 36786 q^{53} - 6440 q^{55} - 10512 q^{56} + 144 q^{57} + 4720 q^{58} - 27516 q^{59} - 19116 q^{60} + 45994 q^{61} - 14280 q^{62} + 6804 q^{63} - 39462 q^{64} + 9126 q^{65} + 24984 q^{66} - 42536 q^{67} - 122532 q^{68} + 18128 q^{70} - 54432 q^{71} + 18954 q^{72} + 27846 q^{73} - 80928 q^{74} + 12267 q^{75} + 89144 q^{76} - 78000 q^{77} - 80568 q^{79} - 33996 q^{80} + 19683 q^{81} + 13344 q^{82} + 24012 q^{83} + 42192 q^{84} - 186580 q^{85} - 117840 q^{86} - 86994 q^{87} + 93312 q^{88} + 117450 q^{89} + 71280 q^{90} + 14196 q^{91} - 245472 q^{92} + 91764 q^{93} - 21864 q^{94} - 64608 q^{95} + 76518 q^{96} - 20930 q^{97} - 254784 q^{98} + 70956 q^{99}+O(q^{100}) \) 3 * q - 27 * q^3 + 14 * q^4 + 54 * q^5 + 84 * q^7 + 234 * q^8 + 243 * q^9 + 880 * q^10 + 876 * q^11 - 126 * q^12 + 507 * q^13 + 1896 * q^14 - 486 * q^15 - 1438 * q^16 + 102 * q^17 - 16 * q^19 + 2124 * q^20 - 756 * q^21 - 2776 * q^22 - 2106 * q^24 - 1363 * q^25 - 2187 * q^27 - 4688 * q^28 + 9666 * q^29 - 7920 * q^30 - 10196 * q^31 - 8502 * q^32 - 7884 * q^33 - 23552 * q^34 + 16680 * q^35 + 1134 * q^36 + 11818 * q^37 - 8040 * q^38 - 4563 * q^39 - 3708 * q^40 + 35490 * q^41 - 17064 * q^42 + 2780 * q^43 + 7296 * q^44 + 4374 * q^45 - 12576 * q^46 + 25728 * q^47 + 12942 * q^48 + 39291 * q^49 + 46656 * q^50 - 918 * q^51 + 2366 * q^52 + 36786 * q^53 - 6440 * q^55 - 10512 * q^56 + 144 * q^57 + 4720 * q^58 - 27516 * q^59 - 19116 * q^60 + 45994 * q^61 - 14280 * q^62 + 6804 * q^63 - 39462 * q^64 + 9126 * q^65 + 24984 * q^66 - 42536 * q^67 - 122532 * q^68 + 18128 * q^70 - 54432 * q^71 + 18954 * q^72 + 27846 * q^73 - 80928 * q^74 + 12267 * q^75 + 89144 * q^76 - 78000 * q^77 - 80568 * q^79 - 33996 * q^80 + 19683 * q^81 + 13344 * q^82 + 24012 * q^83 + 42192 * q^84 - 186580 * q^85 - 117840 * q^86 - 86994 * q^87 + 93312 * q^88 + 117450 * q^89 + 71280 * q^90 + 14196 * q^91 - 245472 * q^92 + 91764 * q^93 - 21864 * q^94 - 64608 * q^95 + 76518 * q^96 - 20930 * q^97 - 254784 * q^98 + 70956 * q^99

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