LMFDB - Embedded newform 38.10.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,10,Mod(1,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("38.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	38.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:	$19.5713617742$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4552x + 85948 $ x^3 - x^2 - 4552*x + 85948
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-74.9878$ of defining polynomial
Character	$\chi$	$=$	38.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.0000 q^{2} -224.963 q^{3} +256.000 q^{4} -29.7721 q^{5} +3599.41 q^{6} -3877.06 q^{7} -4096.00 q^{8} +30925.5 q^{9} +O(q^{10})$	\(q-16.0000 q^{2} -224.963 q^{3} +256.000 q^{4} -29.7721 q^{5} +3599.41 q^{6} -3877.06 q^{7} -4096.00 q^{8} +30925.5 q^{9} +476.353 q^{10} +94691.2 q^{11} -57590.6 q^{12} +116254. q^{13} +62033.0 q^{14} +6697.63 q^{15} +65536.0 q^{16} -550301. q^{17} -494809. q^{18} -130321. q^{19} -7621.65 q^{20} +872197. q^{21} -1.51506e6 q^{22} -607233. q^{23} +921450. q^{24} -1.95224e6 q^{25} -1.86006e6 q^{26} -2.52916e6 q^{27} -992527. q^{28} -1.08420e6 q^{29} -107162. q^{30} +9.46211e6 q^{31} -1.04858e6 q^{32} -2.13021e7 q^{33} +8.80481e6 q^{34} +115428. q^{35} +7.91694e6 q^{36} +2.22817e6 q^{37} +2.08514e6 q^{38} -2.61529e7 q^{39} +121946. q^{40} -1.14354e7 q^{41} -1.39551e7 q^{42} -3.39234e7 q^{43} +2.42410e7 q^{44} -920718. q^{45} +9.71573e6 q^{46} +2.77418e7 q^{47} -1.47432e7 q^{48} -2.53220e7 q^{49} +3.12358e7 q^{50} +1.23798e8 q^{51} +2.97610e7 q^{52} +4.29059e7 q^{53} +4.04666e7 q^{54} -2.81916e6 q^{55} +1.58804e7 q^{56} +2.93175e7 q^{57} +1.73473e7 q^{58} +3.61119e7 q^{59} +1.71459e6 q^{60} -8.02045e7 q^{61} -1.51394e8 q^{62} -1.19900e8 q^{63} +1.67772e7 q^{64} -3.46112e6 q^{65} +3.40833e8 q^{66} -3.40610e7 q^{67} -1.40877e8 q^{68} +1.36605e8 q^{69} -1.84685e6 q^{70} -7.82674e7 q^{71} -1.26671e8 q^{72} -4.18115e8 q^{73} -3.56507e7 q^{74} +4.39182e8 q^{75} -3.33622e7 q^{76} -3.67124e8 q^{77} +4.18446e8 q^{78} -2.06527e8 q^{79} -1.95114e6 q^{80} -3.97386e7 q^{81} +1.82966e8 q^{82} +2.39444e8 q^{83} +2.23282e8 q^{84} +1.63836e7 q^{85} +5.42774e8 q^{86} +2.43906e8 q^{87} -3.87855e8 q^{88} -1.41585e8 q^{89} +1.47315e7 q^{90} -4.50723e8 q^{91} -1.55452e8 q^{92} -2.12863e9 q^{93} -4.43869e8 q^{94} +3.87993e6 q^{95} +2.35891e8 q^{96} -2.72163e8 q^{97} +4.05152e8 q^{98} +2.92838e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 48 q^{2} + 3 q^{3} + 768 q^{4} + 486 q^{5} - 48 q^{6} - 13317 q^{7} - 12288 q^{8} + 22896 q^{9}+O(q^{10}) $ 3 * q - 48 * q^2 + 3 * q^3 + 768 * q^4 + 486 * q^5 - 48 * q^6 - 13317 * q^7 - 12288 * q^8 + 22896 * q^9	\( 3 q - 48 q^{2} + 3 q^{3} + 768 q^{4} + 486 q^{5} - 48 q^{6} - 13317 q^{7} - 12288 q^{8} + 22896 q^{9} - 7776 q^{10} + 55968 q^{11} + 768 q^{12} + 158181 q^{13} + 213072 q^{14} + 135660 q^{15} + 196608 q^{16} - 629091 q^{17} - 366336 q^{18} - 390963 q^{19} + 124416 q^{20} - 873405 q^{21} - 895488 q^{22} - 924627 q^{23} - 12288 q^{24} - 4805517 q^{25} - 2530896 q^{26} - 6711147 q^{27} - 3409152 q^{28} - 9839019 q^{29} - 2170560 q^{30} + 1364628 q^{31} - 3145728 q^{32} - 30339114 q^{33} + 10065456 q^{34} - 11097570 q^{35} + 5861376 q^{36} - 2289090 q^{37} + 6255408 q^{38} - 18481557 q^{39} - 1990656 q^{40} - 12899580 q^{41} + 13974480 q^{42} - 22378638 q^{43} + 14327808 q^{44} + 13005630 q^{45} + 14794032 q^{46} + 58896366 q^{47} + 196608 q^{48} + 22294974 q^{49} + 76888272 q^{50} + 85869585 q^{51} + 40494336 q^{52} + 8770629 q^{53} + 107378352 q^{54} - 73415802 q^{55} + 54546432 q^{56} - 390963 q^{57} + 157424304 q^{58} + 16426299 q^{59} + 34728960 q^{60} - 126843780 q^{61} - 21834048 q^{62} - 234650088 q^{63} + 50331648 q^{64} + 45269952 q^{65} + 485425824 q^{66} - 288075309 q^{67} - 161047296 q^{68} + 323371803 q^{69} + 177561120 q^{70} + 78122274 q^{71} - 93782016 q^{72} - 557941845 q^{73} + 36625440 q^{74} + 150154413 q^{75} - 100086528 q^{76} + 394013736 q^{77} + 295704912 q^{78} - 320222022 q^{79} + 31850496 q^{80} - 346127013 q^{81} + 206393280 q^{82} + 430491462 q^{83} - 223591680 q^{84} - 383428242 q^{85} + 358058208 q^{86} - 1044099345 q^{87} - 229244928 q^{88} + 437689644 q^{89} - 208090080 q^{90} - 1010450187 q^{91} - 236704512 q^{92} - 2684851332 q^{93} - 942341856 q^{94} - 63336006 q^{95} - 3145728 q^{96} - 384952146 q^{97} - 356719584 q^{98} + 2029897422 q^{99}+O(q^{100}) \) 3 * q - 48 * q^2 + 3 * q^3 + 768 * q^4 + 486 * q^5 - 48 * q^6 - 13317 * q^7 - 12288 * q^8 + 22896 * q^9 - 7776 * q^10 + 55968 * q^11 + 768 * q^12 + 158181 * q^13 + 213072 * q^14 + 135660 * q^15 + 196608 * q^16 - 629091 * q^17 - 366336 * q^18 - 390963 * q^19 + 124416 * q^20 - 873405 * q^21 - 895488 * q^22 - 924627 * q^23 - 12288 * q^24 - 4805517 * q^25 - 2530896 * q^26 - 6711147 * q^27 - 3409152 * q^28 - 9839019 * q^29 - 2170560 * q^30 + 1364628 * q^31 - 3145728 * q^32 - 30339114 * q^33 + 10065456 * q^34 - 11097570 * q^35 + 5861376 * q^36 - 2289090 * q^37 + 6255408 * q^38 - 18481557 * q^39 - 1990656 * q^40 - 12899580 * q^41 + 13974480 * q^42 - 22378638 * q^43 + 14327808 * q^44 + 13005630 * q^45 + 14794032 * q^46 + 58896366 * q^47 + 196608 * q^48 + 22294974 * q^49 + 76888272 * q^50 + 85869585 * q^51 + 40494336 * q^52 + 8770629 * q^53 + 107378352 * q^54 - 73415802 * q^55 + 54546432 * q^56 - 390963 * q^57 + 157424304 * q^58 + 16426299 * q^59 + 34728960 * q^60 - 126843780 * q^61 - 21834048 * q^62 - 234650088 * q^63 + 50331648 * q^64 + 45269952 * q^65 + 485425824 * q^66 - 288075309 * q^67 - 161047296 * q^68 + 323371803 * q^69 + 177561120 * q^70 + 78122274 * q^71 - 93782016 * q^72 - 557941845 * q^73 + 36625440 * q^74 + 150154413 * q^75 - 100086528 * q^76 + 394013736 * q^77 + 295704912 * q^78 - 320222022 * q^79 + 31850496 * q^80 - 346127013 * q^81 + 206393280 * q^82 + 430491462 * q^83 - 223591680 * q^84 - 383428242 * q^85 + 358058208 * q^86 - 1044099345 * q^87 - 229244928 * q^88 + 437689644 * q^89 - 208090080 * q^90 - 1010450187 * q^91 - 236704512 * q^92 - 2684851332 * q^93 - 942341856 * q^94 - 63336006 * q^95 - 3145728 * q^96 - 384952146 * q^97 - 356719584 * q^98 + 2029897422 * 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 $

$2$	−16.0000	−0.707107
$2$	−16.0000	−0.707107
$3$	−224.963	−1.60349	−0.801745	−	0.597666i	$-0.796095\pi$
$3$	−224.963	−1.60349	−0.801745	+	0.597666i	$0.796095\pi$
$4$	256.000	0.500000
$5$	−29.7721	−0.0213032	−0.0106516	−	0.999943i	$-0.503391\pi$
$5$	−29.7721	−0.0213032	−0.0106516	+	0.999943i	$0.503391\pi$
$6$	3599.41	1.13384
$7$	−3877.06	−0.610325	−0.305163	−	0.952300i	$-0.598711\pi$
$7$	−3877.06	−0.610325	−0.305163	+	0.952300i	$0.598711\pi$
$8$	−4096.00	−0.353553
$9$	30925.5	1.57118
$10$	476.353	0.0150636
$11$	94691.2	1.95004	0.975018	−	0.222125i	$-0.0712994\pi$
$11$	94691.2	1.95004	0.975018	+	0.222125i	$0.0712994\pi$
$12$	−57590.6	−0.801745
$13$	116254.	1.12892	0.564459	−	0.825461i	$-0.309085\pi$
$13$	116254.	1.12892	0.564459	+	0.825461i	$0.309085\pi$
$14$	62033.0	0.431565
$15$	6697.63	0.0341594
$16$	65536.0	0.250000
$17$	−550301.	−1.59801	−0.799006	−	0.601323i	$-0.794641\pi$
$17$	−550301.	−1.59801	−0.799006	+	0.601323i	$0.794641\pi$
$18$	−494809.	−1.11099
$19$	−130321.	−0.229416
$19$	−130321.	−0.229416
$20$	−7621.65	−0.0106516
$21$	872197.	0.978650
$22$	−1.51506e6	−1.37888
$23$	−607233.	−0.452460	−0.226230	−	0.974074i	$-0.572640\pi$
$23$	−607233.	−0.452460	−0.226230	+	0.974074i	$0.572640\pi$
$24$	921450.	0.566919
$25$	−1.95224e6	−0.999546
$26$	−1.86006e6	−0.798266
$27$	−2.52916e6	−0.915882
$28$	−992527.	−0.305163
$29$	−1.08420e6	−0.284656	−0.142328	−	0.989820i	$-0.545459\pi$
$29$	−1.08420e6	−0.284656	−0.142328	+	0.989820i	$0.545459\pi$
$30$	−107162.	−0.0241544
$31$	9.46211e6	1.84018	0.920090	−	0.391707i	$-0.128115\pi$
$31$	9.46211e6	1.84018	0.920090	+	0.391707i	$0.128115\pi$
$32$	−1.04858e6	−0.176777
$33$	−2.13021e7	−3.12686
$34$	8.80481e6	1.12997
$35$	115428.	0.0130019
$36$	7.91694e6	0.785590
$37$	2.22817e6	0.195452	0.0977261	−	0.995213i	$-0.468843\pi$
$37$	2.22817e6	0.195452	0.0977261	+	0.995213i	$0.468843\pi$
$38$	2.08514e6	0.162221
$39$	−2.61529e7	−1.81021
$40$	121946.	0.00753181
$41$	−1.14354e7	−0.632008	−0.316004	−	0.948758i	$-0.602341\pi$
$41$	−1.14354e7	−0.632008	−0.316004	+	0.948758i	$0.602341\pi$
$42$	−1.39551e7	−0.692010
$43$	−3.39234e7	−1.51318	−0.756591	−	0.653889i	$-0.773136\pi$
$43$	−3.39234e7	−1.51318	−0.756591	+	0.653889i	$0.773136\pi$
$44$	2.42410e7	0.975018
$45$	−920718.	−0.0334711
$46$	9.71573e6	0.319938
$47$	2.77418e7	0.829267	0.414633	−	0.909989i	$-0.363910\pi$
$47$	2.77418e7	0.829267	0.414633	+	0.909989i	$0.363910\pi$
$48$	−1.47432e7	−0.400873
$49$	−2.53220e7	−0.627503
$50$	3.12358e7	0.706786
$51$	1.23798e8	2.56240
$52$	2.97610e7	0.564459
$53$	4.29059e7	0.746923	0.373462	−	0.927646i	$-0.378171\pi$
$53$	4.29059e7	0.746923	0.373462	+	0.927646i	$0.378171\pi$
$54$	4.04666e7	0.647627
$55$	−2.81916e6	−0.0415420
$56$	1.58804e7	0.215783
$57$	2.93175e7	0.367866
$58$	1.73473e7	0.201282
$59$	3.61119e7	0.387986	0.193993	−	0.981003i	$-0.437856\pi$
$59$	3.61119e7	0.387986	0.193993	+	0.981003i	$0.437856\pi$
$60$	1.71459e6	0.0170797
$61$	−8.02045e7	−0.741676	−0.370838	−	0.928697i	$-0.620930\pi$
$61$	−8.02045e7	−0.741676	−0.370838	+	0.928697i	$0.620930\pi$
$62$	−1.51394e8	−1.30120
$63$	−1.19900e8	−0.958931
$64$	1.67772e7	0.125000
$65$	−3.46112e6	−0.0240495
$66$	3.40833e8	2.21103
$67$	−3.40610e7	−0.206500	−0.103250	−	0.994655i	$-0.532924\pi$
$67$	−3.40610e7	−0.206500	−0.103250	+	0.994655i	$0.532924\pi$
$68$	−1.40877e8	−0.799006
$69$	1.36605e8	0.725515
$70$	−1.84685e6	−0.00919371
$71$	−7.82674e7	−0.365526	−0.182763	−	0.983157i	$-0.558504\pi$
$71$	−7.82674e7	−0.365526	−0.182763	+	0.983157i	$0.558504\pi$
$72$	−1.26671e8	−0.555496
$73$	−4.18115e8	−1.72323	−0.861614	−	0.507564i	$-0.830546\pi$
$73$	−4.18115e8	−1.72323	−0.861614	+	0.507564i	$0.830546\pi$
$74$	−3.56507e7	−0.138206
$75$	4.39182e8	1.60276
$76$	−3.33622e7	−0.114708
$77$	−3.67124e8	−1.19016
$78$	4.18446e8	1.28001
$79$	−2.06527e8	−0.596560	−0.298280	−	0.954478i	$-0.596413\pi$
$79$	−2.06527e8	−0.596560	−0.298280	+	0.954478i	$0.596413\pi$
$80$	−1.95114e6	−0.00532579
$81$	−3.97386e7	−0.102572
$82$	1.82966e8	0.446897
$83$	2.39444e8	0.553798	0.276899	−	0.960899i	$-0.410693\pi$
$83$	2.39444e8	0.553798	0.276899	+	0.960899i	$0.410693\pi$
$84$	2.23282e8	0.489325
$85$	1.63836e7	0.0340427
$86$	5.42774e8	1.06998
$87$	2.43906e8	0.456443
$88$	−3.87855e8	−0.689442
$89$	−1.41585e8	−0.239201	−0.119601	−	0.992822i	$-0.538161\pi$
$89$	−1.41585e8	−0.239201	−0.119601	+	0.992822i	$0.538161\pi$
$90$	1.47315e7	0.0236677
$91$	−4.50723e8	−0.689007
$92$	−1.55452e8	−0.226230
$93$	−2.12863e9	−2.95071
$94$	−4.43869e8	−0.586380
$95$	3.87993e6	0.00488728
$96$	2.35891e8	0.283460
$97$	−2.72163e8	−0.312145	−0.156072	−	0.987746i	$-0.549883\pi$
$97$	−2.72163e8	−0.312145	−0.156072	+	0.987746i	$0.549883\pi$
$98$	4.05152e8	0.443712
$99$	2.92838e9	3.06386
$100$	−4.99773e8	−0.499773
$101$	2.46838e7	0.0236029	0.0118015	−	0.999930i	$-0.496243\pi$
$101$	2.46838e7	0.0236029	0.0118015	+	0.999930i	$0.496243\pi$
$102$	−1.98076e9	−1.81189
$103$	4.19496e8	0.367249	0.183624	−	0.982996i	$-0.441217\pi$
$103$	4.19496e8	0.367249	0.183624	+	0.982996i	$0.441217\pi$
$104$	−4.76176e8	−0.399133
$105$	−2.59671e7	−0.0208484
$106$	−6.86495e8	−0.528155
$107$	−1.20059e9	−0.885456	−0.442728	−	0.896656i	$-0.645989\pi$
$107$	−1.20059e9	−0.885456	−0.442728	+	0.896656i	$0.645989\pi$
$108$	−6.47465e8	−0.457941
$109$	−2.14232e9	−1.45367	−0.726835	−	0.686812i	$-0.759010\pi$
$109$	−2.14232e9	−1.45367	−0.726835	+	0.686812i	$0.759010\pi$
$110$	4.51065e7	0.0293746
$111$	−5.01257e8	−0.313406
$112$	−2.54087e8	−0.152581
$113$	1.14926e9	0.663081	0.331541	−	0.943441i	$-0.392432\pi$
$113$	1.14926e9	0.663081	0.331541	+	0.943441i	$0.392432\pi$
$114$	−4.69079e8	−0.260120
$115$	1.80786e7	0.00963883
$116$	−2.77556e8	−0.142328
$117$	3.59522e9	1.77373
$118$	−5.77790e8	−0.274347
$119$	2.13355e9	0.975307
$120$	−2.74335e7	−0.0120772
$121$	6.60848e9	2.80264
$122$	1.28327e9	0.524444
$123$	2.57254e9	1.01342
$124$	2.42230e9	0.920090
$125$	1.16271e8	0.0425967
$126$	1.91840e9	0.678067
$127$	−5.38555e9	−1.83702	−0.918509	−	0.395400i	$-0.870606\pi$
$127$	−5.38555e9	−1.83702	−0.918509	+	0.395400i	$0.870606\pi$
$128$	−2.68435e8	−0.0883883
$129$	7.63152e9	2.42637
$130$	5.53779e7	0.0170056
$131$	7.78212e8	0.230875	0.115437	−	0.993315i	$-0.463173\pi$
$131$	7.78212e8	0.230875	0.115437	+	0.993315i	$0.463173\pi$
$132$	−5.45333e9	−1.56343
$133$	5.05262e8	0.140018
$134$	5.44976e8	0.146018
$135$	7.52984e7	0.0195112
$136$	2.25403e9	0.564983
$137$	−5.83844e9	−1.41597	−0.707985	−	0.706227i	$-0.750396\pi$
$137$	−5.83844e9	−1.41597	−0.707985	+	0.706227i	$0.750396\pi$
$138$	−2.18568e9	−0.513017
$139$	−3.15999e9	−0.717991	−0.358996	−	0.933339i	$-0.616881\pi$
$139$	−3.15999e9	−0.717991	−0.358996	+	0.933339i	$0.616881\pi$
$140$	2.95496e7	0.00650093
$141$	−6.24089e9	−1.32972
$142$	1.25228e9	0.258466
$143$	1.10082e10	2.20143
$144$	2.02674e9	0.392795
$145$	3.22790e7	0.00606407
$146$	6.68984e9	1.21851
$147$	5.69653e9	1.00620
$148$	5.70412e8	0.0977261
$149$	−9.00025e9	−1.49595	−0.747974	−	0.663728i	$-0.768973\pi$
$149$	−9.00025e9	−1.49595	−0.747974	+	0.663728i	$0.768973\pi$
$150$	−7.02692e9	−1.13332
$151$	−9.48059e9	−1.48402	−0.742009	−	0.670390i	$-0.766127\pi$
$151$	−9.48059e9	−1.48402	−0.742009	+	0.670390i	$0.766127\pi$
$152$	5.33795e8	0.0811107
$153$	−1.70184e10	−2.51077
$154$	5.87398e9	0.841568
$155$	−2.81707e8	−0.0392017
$156$	−6.69514e9	−0.905105
$157$	1.08311e10	1.42274	0.711371	−	0.702817i	$-0.248075\pi$
$157$	1.08311e10	1.42274	0.711371	+	0.702817i	$0.248075\pi$
$158$	3.30443e9	0.421832
$159$	−9.65227e9	−1.19768
$160$	3.12183e7	0.00376590
$161$	2.35428e9	0.276148
$162$	6.35818e8	0.0725296
$163$	−1.38943e10	−1.54167	−0.770835	−	0.637035i	$-0.780160\pi$
$163$	−1.38943e10	−1.54167	−0.770835	+	0.637035i	$0.780160\pi$
$164$	−2.92745e9	−0.316004
$165$	6.34207e8	0.0666121
$166$	−3.83110e9	−0.391595
$167$	1.34476e10	1.33789	0.668947	−	0.743310i	$-0.266745\pi$
$167$	1.34476e10	1.33789	0.668947	+	0.743310i	$0.266745\pi$
$168$	−3.57252e9	−0.346005
$169$	2.91047e9	0.274456
$170$	−2.62138e8	−0.0240718
$171$	−4.03025e9	−0.360454
$172$	−8.68438e9	−0.756591
$173$	1.52267e10	1.29240	0.646202	−	0.763166i	$-0.276356\pi$
$173$	1.52267e10	1.29240	0.646202	+	0.763166i	$0.276356\pi$
$174$	−3.90250e9	−0.322754
$175$	7.56895e9	0.610048
$176$	6.20568e9	0.487509
$177$	−8.12385e9	−0.622132
$178$	2.26537e9	0.169141
$179$	−9.10867e9	−0.663157	−0.331579	−	0.943428i	$-0.607581\pi$
$179$	−9.10867e9	−0.663157	−0.331579	+	0.943428i	$0.607581\pi$
$180$	−2.35704e8	−0.0167356
$181$	−1.29332e10	−0.895676	−0.447838	−	0.894115i	$-0.647806\pi$
$181$	−1.29332e10	−0.895676	−0.447838	+	0.894115i	$0.647806\pi$
$182$	7.21157e9	0.487202
$183$	1.80431e10	1.18927
$184$	2.48723e9	0.159969
$185$	−6.63373e7	−0.00416375
$186$	3.40581e10	2.08647
$187$	−5.21087e10	−3.11618
$188$	7.10190e9	0.414633
$189$	9.80571e9	0.558986
$190$	−6.20789e7	−0.00345583
$191$	2.35959e10	1.28288	0.641441	−	0.767172i	$-0.278337\pi$
$191$	2.35959e10	1.28288	0.641441	+	0.767172i	$0.278337\pi$
$192$	−3.77426e9	−0.200436
$193$	−2.46742e9	−0.128007	−0.0640036	−	0.997950i	$-0.520387\pi$
$193$	−2.46742e9	−0.128007	−0.0640036	+	0.997950i	$0.520387\pi$
$194$	4.35461e9	0.220720
$195$	7.78626e8	0.0385632
$196$	−6.48244e9	−0.313752
$197$	−1.98294e10	−0.938019	−0.469010	−	0.883193i	$-0.655389\pi$
$197$	−1.98294e10	−0.938019	−0.469010	+	0.883193i	$0.655389\pi$
$198$	−4.68540e10	−2.16648
$199$	9.78581e9	0.442342	0.221171	−	0.975235i	$-0.429012\pi$
$199$	9.78581e9	0.442342	0.221171	+	0.975235i	$0.429012\pi$
$200$	7.99637e9	0.353393
$201$	7.66248e9	0.331121
$202$	−3.94941e8	−0.0166898
$203$	4.20353e9	0.173733
$204$	3.16922e10	1.28120
$205$	3.40454e8	0.0134638
$206$	−6.71193e9	−0.259684
$207$	−1.87790e10	−0.710896
$208$	7.61882e9	0.282230
$209$	−1.23403e10	−0.447369
$210$	4.15474e8	0.0147420
$211$	4.66257e10	1.61940	0.809700	−	0.586844i	$-0.199630\pi$
$211$	4.66257e10	1.61940	0.809700	+	0.586844i	$0.199630\pi$
$212$	1.09839e10	0.373462
$213$	1.76073e10	0.586117
$214$	1.92094e10	0.626112
$215$	1.00997e9	0.0322356
$216$	1.03594e10	0.323813
$217$	−3.66852e10	−1.12311
$218$	3.42772e10	1.02790
$219$	9.40606e10	2.76318
$220$	−7.21704e8	−0.0207710
$221$	−6.39746e10	−1.80403
$222$	8.02011e9	0.221611
$223$	1.26747e10	0.343215	0.171608	−	0.985165i	$-0.445104\pi$
$223$	1.26747e10	0.343215	0.171608	+	0.985165i	$0.445104\pi$
$224$	4.06539e9	0.107891
$225$	−6.03740e10	−1.57047
$226$	−1.83882e10	−0.468869
$227$	−8.67099e9	−0.216747	−0.108373	−	0.994110i	$-0.534564\pi$
$227$	−8.67099e9	−0.216747	−0.108373	+	0.994110i	$0.534564\pi$
$228$	7.50527e9	0.183933
$229$	1.20906e10	0.290527	0.145264	−	0.989393i	$-0.453597\pi$
$229$	1.20906e10	0.290527	0.145264	+	0.989393i	$0.453597\pi$
$230$	−2.89258e8	−0.00681568
$231$	8.25894e10	1.90840
$232$	4.44090e9	0.100641
$233$	−1.20185e10	−0.267146	−0.133573	−	0.991039i	$-0.542645\pi$
$233$	−1.20185e10	−0.267146	−0.133573	+	0.991039i	$0.542645\pi$
$234$	−5.75235e10	−1.25422
$235$	−8.25931e8	−0.0176660
$236$	9.24464e9	0.193993
$237$	4.64609e10	0.956578
$238$	−3.41368e10	−0.689646
$239$	8.07294e10	1.60045	0.800224	−	0.599702i	$-0.204714\pi$
$239$	8.07294e10	1.60045	0.800224	+	0.599702i	$0.204714\pi$
$240$	4.38936e8	0.00853986
$241$	−7.10466e10	−1.35665	−0.678323	−	0.734764i	$-0.737293\pi$
$241$	−7.10466e10	−1.35665	−0.678323	+	0.734764i	$0.737293\pi$
$242$	−1.05736e11	−1.98177
$243$	5.87212e10	1.08036
$244$	−2.05323e10	−0.370838
$245$	7.53889e8	0.0133678
$246$	−4.11606e10	−0.716595
$247$	−1.51503e10	−0.258992
$248$	−3.87568e10	−0.650602
$249$	−5.38660e10	−0.888010
$250$	−1.86033e9	−0.0301204
$251$	−3.85839e10	−0.613585	−0.306793	−	0.951776i	$-0.599256\pi$
$251$	−3.85839e10	−0.613585	−0.306793	+	0.951776i	$0.599256\pi$
$252$	−3.06944e10	−0.479466
$253$	−5.74996e10	−0.882313
$254$	8.61688e10	1.29897
$255$	−3.68571e9	−0.0545872
$256$	4.29497e9	0.0625000
$257$	4.54081e10	0.649283	0.324641	−	0.945837i	$-0.394756\pi$
$257$	4.54081e10	0.649283	0.324641	+	0.945837i	$0.394756\pi$
$258$	−1.22104e11	−1.71570
$259$	−8.63875e9	−0.119289
$260$	−8.86047e8	−0.0120248
$261$	−3.35296e10	−0.447246
$262$	−1.24514e10	−0.163253
$263$	8.96206e10	1.15507	0.577533	−	0.816367i	$-0.304015\pi$
$263$	8.96206e10	1.15507	0.577533	+	0.816367i	$0.304015\pi$
$264$	8.72533e10	1.10551
$265$	−1.27740e9	−0.0159118
$266$	−8.08420e9	−0.0990078
$267$	3.18515e10	0.383557
$268$	−8.71962e9	−0.103250
$269$	1.06495e11	1.24006	0.620029	−	0.784579i	$-0.287121\pi$
$269$	1.06495e11	1.24006	0.620029	+	0.784579i	$0.287121\pi$
$270$	−1.20477e9	−0.0137965
$271$	−1.03501e11	−1.16569	−0.582843	−	0.812585i	$-0.698060\pi$
$271$	−1.03501e11	−1.16569	−0.582843	+	0.812585i	$0.698060\pi$
$272$	−3.60645e10	−0.399503
$273$	1.01396e11	1.10482
$274$	9.34150e10	1.00124
$275$	−1.84860e11	−1.94915
$276$	3.49709e10	0.362758
$277$	−1.83159e11	−1.86926	−0.934630	−	0.355622i	$-0.884269\pi$
$277$	−1.83159e11	−1.86926	−0.934630	+	0.355622i	$0.884269\pi$
$278$	5.05598e10	0.507696
$279$	2.92621e11	2.89125
$280$	−4.72794e8	−0.00459685
$281$	−1.83624e10	−0.175692	−0.0878460	−	0.996134i	$-0.527998\pi$
$281$	−1.83624e10	−0.175692	−0.0878460	+	0.996134i	$0.527998\pi$
$282$	9.98542e10	0.940255
$283$	−1.55840e11	−1.44424	−0.722121	−	0.691767i	$-0.756833\pi$
$283$	−1.55840e11	−1.44424	−0.722121	+	0.691767i	$0.756833\pi$
$284$	−2.00364e10	−0.182763
$285$	−8.72842e8	−0.00783671
$286$	−1.76132e11	−1.55665
$287$	4.43356e10	0.385730
$288$	−3.24278e10	−0.277748
$289$	1.84243e11	1.55364
$290$	−5.16465e8	−0.00428795
$291$	6.12267e10	0.500521
$292$	−1.07037e11	−0.861614
$293$	−2.02272e11	−1.60336	−0.801682	−	0.597750i	$-0.796061\pi$
$293$	−2.02272e11	−1.60336	−0.801682	+	0.597750i	$0.796061\pi$
$294$	−9.11444e10	−0.711487
$295$	−1.07513e9	−0.00826533
$296$	−9.12658e9	−0.0691028
$297$	−2.39489e11	−1.78600
$298$	1.44004e11	1.05779
$299$	−7.05932e10	−0.510790
$300$	1.12431e11	0.801381
$301$	1.31523e11	0.923533
$302$	1.51689e11	1.04936
$303$	−5.55296e9	−0.0378471
$304$	−8.54072e9	−0.0573539
$305$	2.38786e9	0.0158001
$306$	2.72294e11	1.77538
$307$	4.22712e10	0.271595	0.135797	−	0.990737i	$-0.456640\pi$
$307$	4.22712e10	0.271595	0.135797	+	0.990737i	$0.456640\pi$
$308$	−9.39836e10	−0.595078
$309$	−9.43712e10	−0.588880
$310$	4.50731e9	0.0277198
$311$	−3.53010e10	−0.213976	−0.106988	−	0.994260i	$-0.534121\pi$
$311$	−3.53010e10	−0.213976	−0.106988	+	0.994260i	$0.534121\pi$
$312$	1.07122e11	0.640006
$313$	6.24548e10	0.367804	0.183902	−	0.982945i	$-0.441127\pi$
$313$	6.24548e10	0.367804	0.183902	+	0.982945i	$0.441127\pi$
$314$	−1.73298e11	−1.00603
$315$	3.56968e9	0.0204283
$316$	−5.28708e10	−0.298280
$317$	−1.80523e11	−1.00407	−0.502036	−	0.864847i	$-0.667415\pi$
$317$	−1.80523e11	−1.00407	−0.502036	+	0.864847i	$0.667415\pi$
$318$	1.54436e11	0.846891
$319$	−1.02665e11	−0.555089
$320$	−4.99493e8	−0.00266290
$321$	2.70088e11	1.41982
$322$	−3.76685e10	−0.195266
$323$	7.17158e10	0.366609
$324$	−1.01731e10	−0.0512861
$325$	−2.26955e11	−1.12841
$326$	2.22308e11	1.09012
$327$	4.81945e11	2.33095
$328$	4.68392e10	0.223448
$329$	−1.07557e11	−0.506122
$330$	−1.01473e10	−0.0471019
$331$	1.69131e11	0.774459	0.387229	−	0.921983i	$-0.373432\pi$
$331$	1.69131e11	0.774459	0.387229	+	0.921983i	$0.373432\pi$
$332$	6.12975e10	0.276899
$333$	6.89074e10	0.307091
$334$	−2.15162e11	−0.946034
$335$	1.01407e9	0.00439911
$336$	5.71603e10	0.244663
$337$	2.32014e11	0.979897	0.489949	−	0.871751i	$-0.337016\pi$
$337$	2.32014e11	0.979897	0.489949	+	0.871751i	$0.337016\pi$
$338$	−4.65676e10	−0.194070
$339$	−2.58542e11	−1.06324
$340$	4.19420e9	0.0170214
$341$	8.95979e11	3.58842
$342$	6.44840e10	0.254879
$343$	2.54628e11	0.993306
$344$	1.38950e11	0.534990
$345$	−4.06702e9	−0.0154558
$346$	−2.43627e11	−0.913868
$347$	−1.87750e11	−0.695180	−0.347590	−	0.937647i	$-0.613000\pi$
$347$	−1.87750e11	−0.695180	−0.347590	+	0.937647i	$0.613000\pi$
$348$	6.24400e10	0.228221
$349$	−3.73374e11	−1.34719	−0.673596	−	0.739100i	$-0.735251\pi$
$349$	−3.73374e11	−1.34719	−0.673596	+	0.739100i	$0.735251\pi$
$350$	−1.21103e11	−0.431369
$351$	−2.94025e11	−1.03396
$352$	−9.92910e10	−0.344721
$353$	1.72004e11	0.589592	0.294796	−	0.955560i	$-0.404748\pi$
$353$	1.72004e11	0.589592	0.294796	+	0.955560i	$0.404748\pi$
$354$	1.29982e11	0.439913
$355$	2.33018e9	0.00778686
$356$	−3.62459e10	−0.119601
$357$	−4.79971e11	−1.56390
$358$	1.45739e11	0.468923
$359$	3.21201e11	1.02059	0.510296	−	0.859999i	$-0.329536\pi$
$359$	3.21201e11	1.02059	0.510296	+	0.859999i	$0.329536\pi$
$360$	3.77126e9	0.0118338
$361$	1.69836e10	0.0526316
$362$	2.06931e11	0.633339
$363$	−1.48667e12	−4.49401
$364$	−1.15385e11	−0.344504
$365$	1.24482e10	0.0367102
$366$	−2.88689e11	−0.840941
$367$	−2.03145e11	−0.584533	−0.292267	−	0.956337i	$-0.594409\pi$
$367$	−2.03145e11	−0.584533	−0.292267	+	0.956337i	$0.594409\pi$
$368$	−3.97956e10	−0.113115
$369$	−3.53645e11	−0.992998
$370$	1.06140e9	0.00294422
$371$	−1.66349e11	−0.455866
$372$	−5.44929e11	−1.47536
$373$	−1.35486e11	−0.362413	−0.181207	−	0.983445i	$-0.558000\pi$
$373$	−1.35486e11	−0.362413	−0.181207	+	0.983445i	$0.558000\pi$
$374$	8.33739e11	2.20347
$375$	−2.61567e10	−0.0683033
$376$	−1.13630e11	−0.293190
$377$	−1.26043e11	−0.321353
$378$	−1.56891e11	−0.395263
$379$	−4.76186e11	−1.18550	−0.592749	−	0.805387i	$-0.701957\pi$
$379$	−4.76186e11	−1.18550	−0.592749	+	0.805387i	$0.701957\pi$
$380$	9.93262e8	0.00244364
$381$	1.21155e12	2.94564
$382$	−3.77535e11	−0.907135
$383$	−5.64867e10	−0.134138	−0.0670690	−	0.997748i	$-0.521365\pi$
$383$	−5.64867e10	−0.134138	−0.0670690	+	0.997748i	$0.521365\pi$
$384$	6.03882e10	0.141730
$385$	1.09300e10	0.0253541
$386$	3.94786e10	0.0905148
$387$	−1.04910e12	−2.37748
$388$	−6.96737e10	−0.156072
$389$	−8.32936e11	−1.84433	−0.922164	−	0.386799i	$-0.873581\pi$
$389$	−8.32936e11	−1.84433	−0.922164	+	0.386799i	$0.873581\pi$
$390$	−1.24580e10	−0.0272683
$391$	3.34161e11	0.723037
$392$	1.03719e11	0.221856
$393$	−1.75069e11	−0.370206
$394$	3.17271e11	0.663280
$395$	6.14873e9	0.0127086
$396$	7.49665e11	1.53193
$397$	7.78652e11	1.57321	0.786604	−	0.617457i	$-0.211837\pi$
$397$	7.78652e11	1.57321	0.786604	+	0.617457i	$0.211837\pi$
$398$	−1.56573e11	−0.312783
$399$	−1.13666e11	−0.224518
$400$	−1.27942e11	−0.249887
$401$	6.15050e11	1.18785	0.593924	−	0.804521i	$-0.297578\pi$
$401$	6.15050e11	1.18785	0.593924	+	0.804521i	$0.297578\pi$
$402$	−1.22600e11	−0.234138
$403$	1.10001e12	2.07741
$404$	6.31906e9	0.0118015
$405$	1.18310e9	0.00218512
$406$	−6.72564e10	−0.122848
$407$	2.10988e11	0.381139
$408$	−5.07075e11	−0.905944
$409$	−4.81450e11	−0.850740	−0.425370	−	0.905020i	$-0.639856\pi$
$409$	−4.81450e11	−0.850740	−0.425370	+	0.905020i	$0.639856\pi$
$410$	−5.44727e9	−0.00952032
$411$	1.31344e12	2.27050
$412$	1.07391e11	0.183624
$413$	−1.40008e11	−0.236798
$414$	3.00464e11	0.502680
$415$	−7.12873e9	−0.0117977
$416$	−1.21901e11	−0.199566
$417$	7.10882e11	1.15129
$418$	1.97444e11	0.316338
$419$	8.19161e11	1.29839	0.649197	−	0.760621i	$-0.275105\pi$
$419$	8.19161e11	1.29839	0.649197	+	0.760621i	$0.275105\pi$
$420$	−6.64758e9	−0.0104242
$421$	6.94486e11	1.07744	0.538721	−	0.842484i	$-0.318908\pi$
$421$	6.94486e11	1.07744	0.538721	+	0.842484i	$0.318908\pi$
$422$	−7.46011e11	−1.14509
$423$	8.57930e11	1.30293
$424$	−1.75743e11	−0.264077
$425$	1.07432e12	1.59729
$426$	−2.81717e11	−0.414447
$427$	3.10958e11	0.452664
$428$	−3.07350e11	−0.442728
$429$	−2.47645e12	−3.52997
$430$	−1.61595e10	−0.0227940
$431$	−7.43104e10	−0.103729	−0.0518647	−	0.998654i	$-0.516516\pi$
$431$	−7.43104e10	−0.103729	−0.0518647	+	0.998654i	$0.516516\pi$
$432$	−1.65751e11	−0.228971
$433$	−3.08150e11	−0.421276	−0.210638	−	0.977564i	$-0.567554\pi$
$433$	−3.08150e11	−0.421276	−0.210638	+	0.977564i	$0.567554\pi$
$434$	5.86963e11	0.794157
$435$	−7.26160e9	−0.00972368
$436$	−5.48435e11	−0.726835
$437$	7.91352e10	0.103801
$438$	−1.50497e12	−1.95386
$439$	−6.71351e11	−0.862699	−0.431349	−	0.902185i	$-0.641962\pi$
$439$	−6.71351e11	−0.862699	−0.431349	+	0.902185i	$0.641962\pi$
$440$	1.15473e10	0.0146873
$441$	−7.83097e11	−0.985921
$442$	1.02359e12	1.27564
$443$	−1.45158e11	−0.179070	−0.0895351	−	0.995984i	$-0.528538\pi$
$443$	−1.45158e11	−0.179070	−0.0895351	+	0.995984i	$0.528538\pi$
$444$	−1.28322e11	−0.156703
$445$	4.21529e9	0.00509575
$446$	−2.02796e11	−0.242690
$447$	2.02473e12	2.39874
$448$	−6.50463e10	−0.0762907
$449$	−5.02014e11	−0.582918	−0.291459	−	0.956583i	$-0.594141\pi$
$449$	−5.02014e11	−0.582918	−0.291459	+	0.956583i	$0.594141\pi$
$450$	9.65985e11	1.11049
$451$	−1.08283e12	−1.23244
$452$	2.94212e11	0.331541
$453$	2.13279e12	2.37961
$454$	1.38736e11	0.153263
$455$	1.34190e10	0.0146780
$456$	−1.20084e11	−0.130060
$457$	5.43252e11	0.582610	0.291305	−	0.956630i	$-0.405910\pi$
$457$	5.43252e11	0.582610	0.291305	+	0.956630i	$0.405910\pi$
$458$	−1.93449e11	−0.205434
$459$	1.39180e12	1.46359
$460$	4.62812e9	0.00481942
$461$	1.09534e12	1.12952	0.564761	−	0.825254i	$-0.308968\pi$
$461$	1.09534e12	1.12952	0.564761	+	0.825254i	$0.308968\pi$
$462$	−1.32143e12	−1.34945
$463$	−3.62358e11	−0.366457	−0.183229	−	0.983070i	$-0.558655\pi$
$463$	−3.62358e11	−0.366457	−0.183229	+	0.983070i	$0.558655\pi$
$464$	−7.10544e10	−0.0711640
$465$	6.33737e10	0.0628595
$466$	1.92296e11	0.188901
$467$	−7.13338e11	−0.694016	−0.347008	−	0.937862i	$-0.612802\pi$
$467$	−7.13338e11	−0.694016	−0.347008	+	0.937862i	$0.612802\pi$
$468$	9.20375e11	0.886867
$469$	1.32057e11	0.126032
$470$	1.32149e10	0.0124918
$471$	−2.43661e12	−2.28135
$472$	−1.47914e11	−0.137174
$473$	−3.21225e12	−2.95076
$474$	−7.43375e11	−0.676403
$475$	2.54418e11	0.229312
$476$	5.46189e11	0.487654
$477$	1.32689e12	1.17355
$478$	−1.29167e12	−1.13169
$479$	−8.78996e11	−0.762917	−0.381458	−	0.924386i	$-0.624578\pi$
$479$	−8.78996e11	−0.762917	−0.381458	+	0.924386i	$0.624578\pi$
$480$	−7.02298e9	−0.00603859
$481$	2.59033e11	0.220650
$482$	1.13675e12	0.959294
$483$	−5.29627e11	−0.442800
$484$	1.69177e12	1.40132
$485$	8.10286e9	0.00664968
$486$	−9.39540e11	−0.763927
$487$	−4.24117e11	−0.341668	−0.170834	−	0.985300i	$-0.554646\pi$
$487$	−4.24117e11	−0.341668	−0.170834	+	0.985300i	$0.554646\pi$
$488$	3.28518e11	0.262222
$489$	3.12570e12	2.47205
$490$	−1.20622e10	−0.00945247
$491$	−2.08268e12	−1.61717	−0.808586	−	0.588378i	$-0.799767\pi$
$491$	−2.08268e12	−1.61717	−0.808586	+	0.588378i	$0.799767\pi$
$492$	6.58569e11	0.506709
$493$	5.96639e11	0.454884
$494$	2.42405e11	0.183135
$495$	−8.71839e10	−0.0652699
$496$	6.20109e11	0.460045
$497$	3.03447e11	0.223090
$498$	8.61857e11	0.627918
$499$	1.54074e11	0.111244	0.0556221	−	0.998452i	$-0.482286\pi$
$499$	1.54074e11	0.111244	0.0556221	+	0.998452i	$0.482286\pi$
$500$	2.97653e10	0.0212983
$501$	−3.02523e12	−2.14530
$502$	6.17343e11	0.433870
$503$	−1.61031e12	−1.12164	−0.560820	−	0.827937i	$-0.689514\pi$
$503$	−1.61031e12	−1.12164	−0.560820	+	0.827937i	$0.689514\pi$
$504$	4.91111e11	0.339033
$505$	−7.34889e8	−0.000502818 0
$506$	9.19994e11	0.623890
$507$	−6.54750e11	−0.440088
$508$	−1.37870e12	−0.918509
$509$	−1.07496e12	−0.709845	−0.354923	−	0.934896i	$-0.615493\pi$
$509$	−1.07496e12	−0.709845	−0.354923	+	0.934896i	$0.615493\pi$
$510$	5.89714e10	0.0385990
$511$	1.62106e12	1.05173
$512$	−6.87195e10	−0.0441942
$513$	3.29603e11	0.210118
$514$	−7.26529e11	−0.459112
$515$	−1.24893e10	−0.00782356
$516$	1.95367e12	1.21319
$517$	2.62691e12	1.61710
$518$	1.38220e11	0.0843503
$519$	−3.42545e12	−2.07236
$520$	1.41768e10	0.00850280
$521$	−2.07103e12	−1.23145	−0.615723	−	0.787962i	$-0.711136\pi$
$521$	−2.07103e12	−1.23145	−0.615723	+	0.787962i	$0.711136\pi$
$522$	5.36474e11	0.316251
$523$	3.04903e12	1.78199	0.890993	−	0.454017i	$-0.150010\pi$
$523$	3.04903e12	1.78199	0.890993	+	0.454017i	$0.150010\pi$
$524$	1.99222e11	0.115437
$525$	−1.70274e12	−0.978206
$526$	−1.43393e12	−0.816755
$527$	−5.20701e12	−2.94063
$528$	−1.39605e12	−0.781716
$529$	−1.43242e12	−0.795280
$530$	2.04384e10	0.0112514
$531$	1.11678e12	0.609596
$532$	1.29347e11	0.0700091
$533$	−1.32940e12	−0.713485
$534$	−5.09625e11	−0.271216
$535$	3.57440e10	0.0188630
$536$	1.39514e11	0.0730089
$537$	2.04912e12	1.06337
$538$	−1.70391e12	−0.876854
$539$	−2.39777e12	−1.22365
$540$	1.92764e10	0.00975560
$541$	2.86768e12	1.43927	0.719636	−	0.694352i	$-0.244309\pi$
$541$	2.86768e12	1.43927	0.719636	+	0.694352i	$0.244309\pi$
$542$	1.65601e12	0.824265
$543$	2.90949e12	1.43621
$544$	5.77032e11	0.282491
$545$	6.37815e10	0.0309678
$546$	−1.62234e12	−0.781223
$547$	4.57575e11	0.218534	0.109267	−	0.994012i	$-0.465150\pi$
$547$	4.57575e11	0.218534	0.109267	+	0.994012i	$0.465150\pi$
$548$	−1.49464e12	−0.707985
$549$	−2.48037e12	−1.16531
$550$	2.95776e12	1.37826
$551$	1.41295e11	0.0653045
$552$	−5.59535e11	−0.256508
$553$	8.00716e11	0.364096
$554$	2.93055e12	1.32177
$555$	1.49235e10	0.00667654
$556$	−8.08958e11	−0.358996
$557$	7.14893e11	0.314697	0.157348	−	0.987543i	$-0.449705\pi$
$557$	7.14893e11	0.314697	0.157348	+	0.987543i	$0.449705\pi$
$558$	−4.68193e12	−2.04443
$559$	−3.94373e12	−1.70826
$560$	7.56470e9	0.00325047
$561$	1.17225e13	4.99677
$562$	2.93799e11	0.124233
$563$	2.55851e12	1.07325	0.536624	−	0.843821i	$-0.319699\pi$
$563$	2.55851e12	1.07325	0.536624	+	0.843821i	$0.319699\pi$
$564$	−1.59767e12	−0.664861
$565$	−3.42160e10	−0.0141257
$566$	2.49344e12	1.02123
$567$	1.54069e11	0.0626025
$568$	3.20583e11	0.129233
$569$	3.15681e12	1.26254	0.631268	−	0.775565i	$-0.282535\pi$
$569$	3.15681e12	1.26254	0.631268	+	0.775565i	$0.282535\pi$
$570$	1.39655e10	0.00554139
$571$	−8.86733e11	−0.349084	−0.174542	−	0.984650i	$-0.555845\pi$
$571$	−8.86733e11	−0.349084	−0.174542	+	0.984650i	$0.555845\pi$
$572$	2.81811e12	1.10072
$573$	−5.30822e12	−2.05709
$574$	−7.09369e11	−0.272752
$575$	1.18546e12	0.452255
$576$	5.18845e11	0.196398
$577$	1.13748e12	0.427221	0.213611	−	0.976919i	$-0.431478\pi$
$577$	1.13748e12	0.427221	0.213611	+	0.976919i	$0.431478\pi$
$578$	−2.94789e12	−1.09859
$579$	5.55078e11	0.205258
$580$	8.26343e9	0.00303204
$581$	−9.28337e11	−0.337997
$582$	−9.79627e11	−0.353922
$583$	4.06282e12	1.45653
$584$	1.71260e12	0.609253
$585$	−1.07037e11	−0.0377862
$586$	3.23636e12	1.13375
$587$	−5.20397e12	−1.80910	−0.904551	−	0.426365i	$-0.859794\pi$
$587$	−5.20397e12	−1.80910	−0.904551	+	0.426365i	$0.859794\pi$
$588$	1.45831e12	0.503098
$589$	−1.23311e12	−0.422166
$590$	1.72020e10	0.00584447
$591$	4.46089e12	1.50410
$592$	1.46025e11	0.0488631
$593$	−1.91948e12	−0.637436	−0.318718	−	0.947850i	$-0.603252\pi$
$593$	−1.91948e12	−0.637436	−0.318718	+	0.947850i	$0.603252\pi$
$594$	3.83183e12	1.26290
$595$	−6.35202e10	−0.0207771
$596$	−2.30406e12	−0.747974
$597$	−2.20145e12	−0.709291
$598$	1.12949e12	0.361183
$599$	1.62980e12	0.517265	0.258633	−	0.965976i	$-0.416728\pi$
$599$	1.62980e12	0.517265	0.258633	+	0.965976i	$0.416728\pi$
$600$	−1.79889e12	−0.566662
$601$	1.69905e12	0.531216	0.265608	−	0.964081i	$-0.414427\pi$
$601$	1.69905e12	0.531216	0.265608	+	0.964081i	$0.414427\pi$
$602$	−2.10437e12	−0.653036
$603$	−1.05336e12	−0.324449
$604$	−2.42703e12	−0.742009
$605$	−1.96748e11	−0.0597051
$606$	8.88473e10	0.0267619
$607$	−3.55697e12	−1.06348	−0.531741	−	0.846907i	$-0.678462\pi$
$607$	−3.55697e12	−1.06348	−0.531741	+	0.846907i	$0.678462\pi$
$608$	1.36651e11	0.0405554
$609$	−9.45640e11	−0.278579
$610$	−3.82057e10	−0.0111723
$611$	3.22509e12	0.936174
$612$	−4.35670e12	−1.25538
$613$	6.14032e12	1.75638	0.878191	−	0.478310i	$-0.158750\pi$
$613$	6.14032e12	1.75638	0.878191	+	0.478310i	$0.158750\pi$
$614$	−6.76339e11	−0.192047
$615$	−7.65898e10	−0.0215890
$616$	1.50374e12	0.420784
$617$	1.88764e12	0.524369	0.262184	−	0.965018i	$-0.415557\pi$
$617$	1.88764e12	0.524369	0.262184	+	0.965018i	$0.415557\pi$
$618$	1.50994e12	0.416401
$619$	−3.52678e12	−0.965540	−0.482770	−	0.875747i	$-0.660369\pi$
$619$	−3.52678e12	−0.965540	−0.482770	+	0.875747i	$0.660369\pi$
$620$	−7.21169e10	−0.0196008
$621$	1.53579e12	0.414400
$622$	5.64817e11	0.151304
$623$	5.48935e11	0.145991
$624$	−1.71396e12	−0.452552
$625$	3.80950e12	0.998639
$626$	−9.99276e11	−0.260077
$627$	2.77611e12	0.717352
$628$	2.77277e12	0.711371
$629$	−1.22616e12	−0.312335
$630$	−5.71149e10	−0.0144450
$631$	−4.93291e12	−1.23871	−0.619357	−	0.785110i	$-0.712606\pi$
$631$	−4.93291e12	−1.23871	−0.619357	+	0.785110i	$0.712606\pi$
$632$	8.45933e11	0.210916
$633$	−1.04891e13	−2.59669
$634$	2.88836e12	0.709986
$635$	1.60339e11	0.0391343
$636$	−2.47098e12	−0.598842
$637$	−2.94378e12	−0.708400
$638$	1.64263e12	0.392507
$639$	−2.42046e12	−0.574307
$640$	7.99188e9	0.00188295
$641$	−4.83996e10	−0.0113235	−0.00566175	−	0.999984i	$-0.501802\pi$
$641$	−4.83996e10	−0.0113235	−0.00566175	+	0.999984i	$0.501802\pi$
$642$	−4.32141e12	−1.00396
$643$	5.71104e12	1.31755	0.658773	−	0.752341i	$-0.271076\pi$
$643$	5.71104e12	1.31755	0.658773	+	0.752341i	$0.271076\pi$
$644$	6.02695e11	0.138074
$645$	−2.27206e11	−0.0516894
$646$	−1.14745e12	−0.259232
$647$	−1.34938e12	−0.302738	−0.151369	−	0.988477i	$-0.548368\pi$
$647$	−1.34938e12	−0.302738	−0.151369	+	0.988477i	$0.548368\pi$
$648$	1.62769e11	0.0362648
$649$	3.41948e12	0.756587
$650$	3.63129e12	0.797903
$651$	8.25282e12	1.80089
$652$	−3.55693e12	−0.770835
$653$	−1.24337e12	−0.267604	−0.133802	−	0.991008i	$-0.542719\pi$
$653$	−1.24337e12	−0.267604	−0.133802	+	0.991008i	$0.542719\pi$
$654$	−7.71111e12	−1.64823
$655$	−2.31690e10	−0.00491837
$656$	−7.49427e11	−0.158002
$657$	−1.29304e13	−2.70750
$658$	1.72091e12	0.357883
$659$	1.11305e11	0.0229896	0.0114948	−	0.999934i	$-0.496341\pi$
$659$	1.11305e11	0.0229896	0.0114948	+	0.999934i	$0.496341\pi$
$660$	1.62357e11	0.0333061
$661$	−1.31890e12	−0.268724	−0.134362	−	0.990932i	$-0.542898\pi$
$661$	−1.31890e12	−0.268724	−0.134362	+	0.990932i	$0.542898\pi$
$662$	−2.70610e12	−0.547625
$663$	1.43920e13	2.89274
$664$	−9.80761e11	−0.195797
$665$	−1.50427e10	−0.00298283
$666$	−1.10252e12	−0.217146
$667$	6.58365e11	0.128795
$668$	3.44260e12	0.668947
$669$	−2.85135e12	−0.550342
$670$	−1.62251e10	−0.00311064
$671$	−7.59466e12	−1.44630
$672$	−9.14564e11	−0.173003
$673$	1.23317e11	0.0231716	0.0115858	−	0.999933i	$-0.496312\pi$
$673$	1.23317e11	0.0231716	0.0115858	+	0.999933i	$0.496312\pi$
$674$	−3.71223e12	−0.692892
$675$	4.93753e12	0.915467
$676$	7.45081e11	0.137228
$677$	3.11864e12	0.570580	0.285290	−	0.958441i	$-0.407910\pi$
$677$	3.11864e12	0.570580	0.285290	+	0.958441i	$0.407910\pi$
$678$	4.13668e12	0.751827
$679$	1.05519e12	0.190510
$680$	−6.71073e10	−0.0120359
$681$	1.95066e12	0.347551
$682$	−1.43357e13	−2.53739
$683$	−8.66927e12	−1.52437	−0.762184	−	0.647361i	$-0.775873\pi$
$683$	−8.66927e12	−1.52437	−0.762184	+	0.647361i	$0.775873\pi$
$684$	−1.03174e12	−0.180227
$685$	1.73823e11	0.0301647
$686$	−4.07405e12	−0.702374
$687$	−2.71993e12	−0.465857
$688$	−2.22320e12	−0.378295
$689$	4.98798e12	0.843215
$690$	6.50724e10	0.0109289
$691$	3.95421e12	0.659794	0.329897	−	0.944017i	$-0.392986\pi$
$691$	3.95421e12	0.659794	0.329897	+	0.944017i	$0.392986\pi$
$692$	3.89803e12	0.646202
$693$	−1.13535e13	−1.86995
$694$	3.00400e12	0.491566
$695$	9.40795e10	0.0152955
$696$	−9.99041e11	−0.161377
$697$	6.29289e12	1.00996
$698$	5.97398e12	0.952609
$699$	2.70373e12	0.428366
$700$	1.93765e12	0.305024
$701$	−2.51457e12	−0.393308	−0.196654	−	0.980473i	$-0.563008\pi$
$701$	−2.51457e12	−0.393308	−0.196654	+	0.980473i	$0.563008\pi$
$702$	4.70440e12	0.731117
$703$	−2.90377e11	−0.0448398
$704$	1.58866e12	0.243755
$705$	1.85804e11	0.0283273
$706$	−2.75206e12	−0.416904
$707$	−9.57006e10	−0.0144055
$708$	−2.07971e12	−0.311066
$709$	5.41710e12	0.805116	0.402558	−	0.915394i	$-0.368121\pi$
$709$	5.41710e12	0.805116	0.402558	+	0.915394i	$0.368121\pi$
$710$	−3.72829e10	−0.00550614
$711$	−6.38695e12	−0.937303
$712$	5.79934e11	0.0845704
$713$	−5.74571e12	−0.832608
$714$	7.67953e12	1.10584
$715$	−3.27738e11	−0.0468975
$716$	−2.33182e12	−0.331579
$717$	−1.81612e13	−2.56630
$718$	−5.13922e12	−0.721667
$719$	5.47307e12	0.763749	0.381875	−	0.924214i	$-0.375279\pi$
$719$	5.47307e12	0.763749	0.381875	+	0.924214i	$0.375279\pi$
$720$	−6.03402e10	−0.00836778
$721$	−1.62641e12	−0.224141
$722$	−2.71737e11	−0.0372161
$723$	1.59829e13	2.17537
$724$	−3.31089e12	−0.447838
$725$	2.11663e12	0.284527
$726$	2.37867e13	3.17774
$727$	−6.58387e12	−0.874130	−0.437065	−	0.899430i	$-0.643982\pi$
$727$	−6.58387e12	−0.874130	−0.437065	+	0.899430i	$0.643982\pi$
$728$	1.84616e12	0.243601
$729$	−1.24280e13	−1.62977
$730$	−1.99170e11	−0.0259580
$731$	1.86681e13	2.41808
$732$	4.61903e12	0.594635
$733$	−7.78589e12	−0.996186	−0.498093	−	0.867124i	$-0.665966\pi$
$733$	−7.78589e12	−0.996186	−0.498093	+	0.867124i	$0.665966\pi$
$734$	3.25032e12	0.413328
$735$	−1.69598e11	−0.0214351
$736$	6.36730e11	0.0799844
$737$	−3.22528e12	−0.402683
$738$	5.65831e12	0.702156
$739$	5.19811e12	0.641129	0.320564	−	0.947227i	$-0.396127\pi$
$739$	5.19811e12	0.641129	0.320564	+	0.947227i	$0.396127\pi$
$740$	−1.69823e10	−0.00208188
$741$	3.40827e12	0.415290
$742$	2.66158e12	0.322346
$743$	3.53870e12	0.425985	0.212992	−	0.977054i	$-0.431679\pi$
$743$	3.53870e12	0.425985	0.212992	+	0.977054i	$0.431679\pi$
$744$	8.71886e12	1.04323
$745$	2.67956e11	0.0318684
$746$	2.16777e12	0.256265
$747$	7.40492e12	0.870117
$748$	−1.33398e13	−1.55809
$749$	4.65475e12	0.540416
$750$	4.18507e11	0.0482978
$751$	−3.87336e12	−0.444332	−0.222166	−	0.975009i	$-0.571313\pi$
$751$	−3.87336e12	−0.444332	−0.222166	+	0.975009i	$0.571313\pi$
$752$	1.81809e12	0.207317
$753$	8.67998e12	0.983878
$754$	2.01669e12	0.227231
$755$	2.82257e11	0.0316143
$756$	2.51026e12	0.279493
$757$	−9.51395e12	−1.05300	−0.526501	−	0.850174i	$-0.676496\pi$
$757$	−9.51395e12	−1.05300	−0.526501	+	0.850174i	$0.676496\pi$
$758$	7.61898e12	0.838273
$759$	1.29353e13	1.41478
$760$	−1.58922e10	−0.00172792
$761$	1.62715e13	1.75872	0.879361	−	0.476155i	$-0.157970\pi$
$761$	1.62715e13	1.75872	0.879361	+	0.476155i	$0.157970\pi$
$762$	−1.93848e13	−2.08288
$763$	8.30592e12	0.887212
$764$	6.04056e12	0.641441
$765$	5.06672e11	0.0534873
$766$	9.03787e11	0.0948499
$767$	4.19815e12	0.438004
$768$	−9.66211e11	−0.100218
$769$	−1.34242e13	−1.38427	−0.692134	−	0.721769i	$-0.743329\pi$
$769$	−1.34242e13	−1.38427	−0.692134	+	0.721769i	$0.743329\pi$
$770$	−1.74881e11	−0.0179281
$771$	−1.02152e13	−1.04112
$772$	−6.31658e11	−0.0640036
$773$	3.00352e12	0.302568	0.151284	−	0.988490i	$-0.451659\pi$
$773$	3.00352e12	0.302568	0.151284	+	0.988490i	$0.451659\pi$
$774$	1.67856e13	1.68113
$775$	−1.84723e13	−1.83934
$776$	1.11478e12	0.110360
$777$	1.94340e12	0.191279
$778$	1.33270e13	1.30414
$779$	1.49027e12	0.144992
$780$	1.99328e11	0.0192816
$781$	−7.41123e12	−0.712789
$782$	−5.34657e12	−0.511264
$783$	2.74213e12	0.260711
$784$	−1.65950e12	−0.156876
$785$	−3.22466e11	−0.0303089
$786$	2.80111e12	0.261775
$787$	−6.34566e12	−0.589645	−0.294823	−	0.955552i	$-0.595261\pi$
$787$	−6.34566e12	−0.589645	−0.294823	+	0.955552i	$0.595261\pi$
$788$	−5.07633e12	−0.469010
$789$	−2.01614e13	−1.85214
$790$	−9.83797e10	−0.00898635
$791$	−4.45577e12	−0.404695
$792$	−1.19946e13	−1.08324
$793$	−9.32409e12	−0.837292
$794$	−1.24584e13	−1.11243
$795$	2.87368e11	0.0255145
$796$	2.50517e12	0.221171
$797$	2.44679e12	0.214800	0.107400	−	0.994216i	$-0.465747\pi$
$797$	2.44679e12	0.214800	0.107400	+	0.994216i	$0.465747\pi$
$798$	1.81865e12	0.158758
$799$	−1.52663e13	−1.32518
$800$	2.04707e12	0.176696
$801$	−4.37861e12	−0.375828
$802$	−9.84081e12	−0.839936
$803$	−3.95918e13	−3.36036
$804$	1.96160e12	0.165561
$805$	−7.00918e10	−0.00588282
$806$	−1.76001e13	−1.46895
$807$	−2.39574e13	−1.98842
$808$	−1.01105e11	−0.00834490
$809$	−7.69731e12	−0.631787	−0.315893	−	0.948795i	$-0.602304\pi$
$809$	−7.69731e12	−0.631787	−0.315893	+	0.948795i	$0.602304\pi$
$810$	−1.89296e10	−0.00154511
$811$	1.78237e13	1.44679	0.723393	−	0.690437i	$-0.242582\pi$
$811$	1.78237e13	1.44679	0.723393	+	0.690437i	$0.242582\pi$
$812$	1.07610e12	0.0868663
$813$	2.32839e13	1.86917
$814$	−3.37581e12	−0.269506
$815$	4.13661e11	0.0328424
$816$	8.11320e12	0.640599
$817$	4.42093e12	0.347148
$818$	7.70321e12	0.601564
$819$	−1.39389e13	−1.08255
$820$	8.71563e10	0.00673188
$821$	1.19782e13	0.920129	0.460065	−	0.887885i	$-0.347826\pi$
$821$	1.19782e13	0.920129	0.460065	+	0.887885i	$0.347826\pi$
$822$	−2.10150e13	−1.60548
$823$	1.96218e13	1.49087	0.745436	−	0.666577i	$-0.232241\pi$
$823$	1.96218e13	1.49087	0.745436	+	0.666577i	$0.232241\pi$
$824$	−1.71826e12	−0.129842
$825$	4.15867e13	3.12544
$826$	2.24013e12	0.167441
$827$	2.04561e13	1.52071	0.760356	−	0.649506i	$-0.225024\pi$
$827$	2.04561e13	1.52071	0.760356	+	0.649506i	$0.225024\pi$
$828$	−4.80743e12	−0.355448
$829$	1.49619e12	0.110025	0.0550124	−	0.998486i	$-0.482480\pi$
$829$	1.49619e12	0.110025	0.0550124	+	0.998486i	$0.482480\pi$
$830$	1.14060e11	0.00834221
$831$	4.12041e13	2.99734
$832$	1.95042e12	0.141115
$833$	1.39347e13	1.00276
$834$	−1.13741e13	−0.814086
$835$	−4.00364e11	−0.0285014
$836$	−3.15911e12	−0.223684
$837$	−2.39312e13	−1.68539
$838$	−1.31066e13	−0.918103
$839$	−1.54764e13	−1.07830	−0.539152	−	0.842208i	$-0.681255\pi$
$839$	−1.54764e13	−1.07830	−0.539152	+	0.842208i	$0.681255\pi$
$840$	1.06361e11	0.00737101
$841$	−1.33316e13	−0.918971
$842$	−1.11118e13	−0.761867
$843$	4.13088e12	0.281720
$844$	1.19362e13	0.809700
$845$	−8.66508e10	−0.00584679
$846$	−1.37269e13	−0.921309
$847$	−2.56215e13	−1.71052
$848$	2.81188e12	0.186731
$849$	3.50583e13	2.31583
$850$	−1.71891e13	−1.12945
$851$	−1.35302e12	−0.0884343
$852$	4.50747e12	0.293059
$853$	1.11975e13	0.724187	0.362093	−	0.932142i	$-0.382062\pi$
$853$	1.11975e13	0.724187	0.362093	+	0.932142i	$0.382062\pi$
$854$	−4.97532e12	−0.320082
$855$	1.19989e11	0.00767880
$856$	4.91761e12	0.313056
$857$	1.00823e13	0.638480	0.319240	−	0.947674i	$-0.396572\pi$
$857$	1.00823e13	0.638480	0.319240	+	0.947674i	$0.396572\pi$
$858$	3.96232e13	2.49607
$859$	−1.52768e13	−0.957330	−0.478665	−	0.877998i	$-0.658879\pi$
$859$	−1.52768e13	−0.957330	−0.478665	+	0.877998i	$0.658879\pi$
$860$	2.58552e11	0.0161178
$861$	−9.97388e12	−0.618514
$862$	1.18897e12	0.0733478
$863$	2.17931e13	1.33743	0.668715	−	0.743519i	$-0.266845\pi$
$863$	2.17931e13	1.33743	0.668715	+	0.743519i	$0.266845\pi$
$864$	2.65202e12	0.161907
$865$	−4.53331e11	−0.0275323
$866$	4.93040e12	0.297887
$867$	−4.14480e13	−2.49125
$868$	−9.39140e12	−0.561554
$869$	−1.95563e13	−1.16331
$870$	1.16186e11	0.00687568
$871$	−3.95973e12	−0.233122
$872$	8.77496e12	0.513950
$873$	−8.41679e12	−0.490436
$874$	−1.26616e12	−0.0733987
$875$	−4.50789e11	−0.0259978
$876$	2.40795e13	1.38159
$877$	−1.53433e13	−0.875834	−0.437917	−	0.899015i	$-0.644284\pi$
$877$	−1.53433e13	−0.875834	−0.437917	+	0.899015i	$0.644284\pi$
$878$	1.07416e13	0.610020
$879$	4.55039e13	2.57098
$880$	−1.84756e11	−0.0103855
$881$	1.24857e13	0.698268	0.349134	−	0.937073i	$-0.386476\pi$
$881$	1.24857e13	0.698268	0.349134	+	0.937073i	$0.386476\pi$
$882$	1.25296e13	0.697151
$883$	−8.63145e12	−0.477816	−0.238908	−	0.971042i	$-0.576789\pi$
$883$	−8.63145e12	−0.477816	−0.238908	+	0.971042i	$0.576789\pi$
$884$	−1.63775e13	−0.902013
$885$	2.41864e11	0.0132534
$886$	2.32252e12	0.126622
$887$	1.58662e13	0.860630	0.430315	−	0.902679i	$-0.358403\pi$
$887$	1.58662e13	0.860630	0.430315	+	0.902679i	$0.358403\pi$
$888$	2.05315e12	0.110806
$889$	2.08801e13	1.12118
$890$	−6.74447e10	−0.00360324
$891$	−3.76290e12	−0.200020
$892$	3.24473e12	0.171608
$893$	−3.61534e12	−0.190247
$894$	−3.23956e13	−1.69616
$895$	2.71184e11	0.0141274
$896$	1.04074e12	0.0539456
$897$	1.58809e13	0.819047
$898$	8.03223e12	0.412185
$899$	−1.02589e13	−0.523818
$900$	−1.54558e13	−0.785234
$901$	−2.36112e13	−1.19359
$902$	1.73252e13	0.871465
$903$	−2.95879e13	−1.48088
$904$	−4.70739e12	−0.234435
$905$	3.85047e11	0.0190807
$906$	−3.41246e13	−1.68264
$907$	−7.27437e12	−0.356913	−0.178457	−	0.983948i	$-0.557110\pi$
$907$	−7.27437e12	−0.356913	−0.178457	+	0.983948i	$0.557110\pi$
$908$	−2.21977e12	−0.108373
$909$	7.63361e11	0.0370845
$910$	−2.14704e11	−0.0103789
$911$	−1.44443e13	−0.694809	−0.347404	−	0.937715i	$-0.612937\pi$
$911$	−1.44443e13	−0.694809	−0.347404	+	0.937715i	$0.612937\pi$
$912$	1.92135e12	0.0919665
$913$	2.26732e13	1.07993
$914$	−8.69203e12	−0.411968
$915$	−5.37180e11	−0.0253352
$916$	3.09518e12	0.145264
$917$	−3.01717e12	−0.140909
$918$	−2.22688e13	−1.03492
$919$	3.25751e13	1.50649	0.753243	−	0.657742i	$-0.228488\pi$
$919$	3.25751e13	1.50649	0.753243	+	0.657742i	$0.228488\pi$
$920$	−7.40499e10	−0.00340784
$921$	−9.50946e12	−0.435500
$922$	−1.75254e13	−0.798693
$923$	−9.09889e12	−0.412649
$924$	2.11429e13	0.954202
$925$	−4.34992e12	−0.195364
$926$	5.79773e12	0.259124
$927$	1.29731e13	0.577014
$928$	1.13687e12	0.0503205
$929$	2.37994e13	1.04832	0.524162	−	0.851618i	$-0.324378\pi$
$929$	2.37994e13	1.04832	0.524162	+	0.851618i	$0.324378\pi$
$930$	−1.01398e12	−0.0444484
$931$	3.29999e12	0.143959
$932$	−3.07674e12	−0.133573
$933$	7.94144e12	0.343109
$934$	1.14134e13	0.490743
$935$	1.55138e12	0.0663846
$936$	−1.47260e13	−0.627110
$937$	2.51191e13	1.06458	0.532288	−	0.846564i	$-0.321333\pi$
$937$	2.51191e13	1.06458	0.532288	+	0.846564i	$0.321333\pi$
$938$	−2.11291e12	−0.0891184
$939$	−1.40500e13	−0.589770
$940$	−2.11438e11	−0.00883301
$941$	3.51030e13	1.45945	0.729727	−	0.683738i	$-0.239647\pi$
$941$	3.51030e13	1.45945	0.729727	+	0.683738i	$0.239647\pi$
$942$	3.89858e13	1.61316
$943$	6.94393e12	0.285958
$944$	2.36663e12	0.0969965
$945$	−2.91937e11	−0.0119082
$946$	5.13959e13	2.08650
$947$	1.99074e13	0.804342	0.402171	−	0.915565i	$-0.368256\pi$
$947$	1.99074e13	0.804342	0.402171	+	0.915565i	$0.368256\pi$
$948$	1.18940e13	0.478289
$949$	−4.86075e13	−1.94538
$950$	−4.07068e12	−0.162148
$951$	4.06110e13	1.61002
$952$	−8.73902e12	−0.344823
$953$	−3.87813e13	−1.52301	−0.761507	−	0.648157i	$-0.775540\pi$
$953$	−3.87813e13	−1.52301	−0.761507	+	0.648157i	$0.775540\pi$
$954$	−2.12302e13	−0.829826
$955$	−7.02500e11	−0.0273295
$956$	2.06667e13	0.800224
$957$	2.30958e13	0.890080
$958$	1.40639e13	0.539464
$959$	2.26360e13	0.864203
$960$	1.12368e11	0.00426993
$961$	6.30919e13	2.38626
$962$	−4.14454e12	−0.156023
$963$	−3.71288e13	−1.39121
$964$	−1.81879e13	−0.678323
$965$	7.34601e10	0.00272696
$966$	8.47403e12	0.313107
$967$	−4.34453e13	−1.59780	−0.798902	−	0.601461i	$-0.794586\pi$
$967$	−4.34453e13	−1.59780	−0.798902	+	0.601461i	$0.794586\pi$
$968$	−2.70683e13	−0.990883
$969$	−1.61334e13	−0.587854
$970$	−1.29646e11	−0.00470203
$971$	−5.73513e12	−0.207041	−0.103521	−	0.994627i	$-0.533011\pi$
$971$	−5.73513e12	−0.207041	−0.103521	+	0.994627i	$0.533011\pi$
$972$	1.50326e13	0.540178
$973$	1.22515e13	0.438208
$974$	6.78586e12	0.241596
$975$	5.10567e13	1.80939
$976$	−5.25628e12	−0.185419
$977$	−3.70030e13	−1.29931	−0.649653	−	0.760231i	$-0.725086\pi$
$977$	−3.70030e13	−1.29931	−0.649653	+	0.760231i	$0.725086\pi$
$978$	−5.00112e13	−1.74800
$979$	−1.34069e13	−0.466451
$980$	1.92996e11	0.00668390
$981$	−6.62525e13	−2.28398
$982$	3.33229e13	1.14351
$983$	3.20343e13	1.09427	0.547135	−	0.837044i	$-0.315718\pi$
$983$	3.20343e13	1.09427	0.547135	+	0.837044i	$0.315718\pi$
$984$	−1.05371e13	−0.358297
$985$	5.90363e11	0.0199828
$986$	−9.54622e12	−0.321651
$987$	2.41963e13	0.811562
$988$	−3.87848e12	−0.129496
$989$	2.05994e13	0.684654
$990$	1.39494e12	0.0461528
$991$	3.94471e13	1.29922	0.649611	−	0.760267i	$-0.274932\pi$
$991$	3.94471e13	1.29922	0.649611	+	0.760267i	$0.274932\pi$
$992$	−9.92174e12	−0.325301
$993$	−3.80484e13	−1.24184
$994$	−4.85516e12	−0.157748
$995$	−2.91344e11	−0.00942329
$996$	−1.37897e13	−0.444005
$997$	4.33100e13	1.38823	0.694113	−	0.719866i	$-0.255797\pi$
$997$	4.33100e13	1.38823	0.694113	+	0.719866i	$0.255797\pi$
$998$	−2.46518e12	−0.0786615
$999$	−5.63540e12	−0.179011

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.a.c.1.1	✓	3
3.2	odd	2		342.10.a.e.1.2		3
4.3	odd	2		304.10.a.c.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.a.c.1.1	✓	3	1.1	even	1	trivial
304.10.a.c.1.3		3	4.3	odd	2
342.10.a.e.1.2		3	3.2	odd	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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	38.a (trivial)

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} -224.963 q^{3} +256.000 q^{4} -29.7721 q^{5} +3599.41 q^{6} -3877.06 q^{7} -4096.00 q^{8} +30925.5 q^{9} +O(q^{10})\)	\(q-16.0000 q^{2} -224.963 q^{3} +256.000 q^{4} -29.7721 q^{5} +3599.41 q^{6} -3877.06 q^{7} -4096.00 q^{8} +30925.5 q^{9} +476.353 q^{10} +94691.2 q^{11} -57590.6 q^{12} +116254. q^{13} +62033.0 q^{14} +6697.63 q^{15} +65536.0 q^{16} -550301. q^{17} -494809. q^{18} -130321. q^{19} -7621.65 q^{20} +872197. q^{21} -1.51506e6 q^{22} -607233. q^{23} +921450. q^{24} -1.95224e6 q^{25} -1.86006e6 q^{26} -2.52916e6 q^{27} -992527. q^{28} -1.08420e6 q^{29} -107162. q^{30} +9.46211e6 q^{31} -1.04858e6 q^{32} -2.13021e7 q^{33} +8.80481e6 q^{34} +115428. q^{35} +7.91694e6 q^{36} +2.22817e6 q^{37} +2.08514e6 q^{38} -2.61529e7 q^{39} +121946. q^{40} -1.14354e7 q^{41} -1.39551e7 q^{42} -3.39234e7 q^{43} +2.42410e7 q^{44} -920718. q^{45} +9.71573e6 q^{46} +2.77418e7 q^{47} -1.47432e7 q^{48} -2.53220e7 q^{49} +3.12358e7 q^{50} +1.23798e8 q^{51} +2.97610e7 q^{52} +4.29059e7 q^{53} +4.04666e7 q^{54} -2.81916e6 q^{55} +1.58804e7 q^{56} +2.93175e7 q^{57} +1.73473e7 q^{58} +3.61119e7 q^{59} +1.71459e6 q^{60} -8.02045e7 q^{61} -1.51394e8 q^{62} -1.19900e8 q^{63} +1.67772e7 q^{64} -3.46112e6 q^{65} +3.40833e8 q^{66} -3.40610e7 q^{67} -1.40877e8 q^{68} +1.36605e8 q^{69} -1.84685e6 q^{70} -7.82674e7 q^{71} -1.26671e8 q^{72} -4.18115e8 q^{73} -3.56507e7 q^{74} +4.39182e8 q^{75} -3.33622e7 q^{76} -3.67124e8 q^{77} +4.18446e8 q^{78} -2.06527e8 q^{79} -1.95114e6 q^{80} -3.97386e7 q^{81} +1.82966e8 q^{82} +2.39444e8 q^{83} +2.23282e8 q^{84} +1.63836e7 q^{85} +5.42774e8 q^{86} +2.43906e8 q^{87} -3.87855e8 q^{88} -1.41585e8 q^{89} +1.47315e7 q^{90} -4.50723e8 q^{91} -1.55452e8 q^{92} -2.12863e9 q^{93} -4.43869e8 q^{94} +3.87993e6 q^{95} +2.35891e8 q^{96} -2.72163e8 q^{97} +4.05152e8 q^{98} +2.92838e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 48 q^{2} + 3 q^{3} + 768 q^{4} + 486 q^{5} - 48 q^{6} - 13317 q^{7} - 12288 q^{8} + 22896 q^{9}+O(q^{10}) \) 3 * q - 48 * q^2 + 3 * q^3 + 768 * q^4 + 486 * q^5 - 48 * q^6 - 13317 * q^7 - 12288 * q^8 + 22896 * q^9	\( 3 q - 48 q^{2} + 3 q^{3} + 768 q^{4} + 486 q^{5} - 48 q^{6} - 13317 q^{7} - 12288 q^{8} + 22896 q^{9} - 7776 q^{10} + 55968 q^{11} + 768 q^{12} + 158181 q^{13} + 213072 q^{14} + 135660 q^{15} + 196608 q^{16} - 629091 q^{17} - 366336 q^{18} - 390963 q^{19} + 124416 q^{20} - 873405 q^{21} - 895488 q^{22} - 924627 q^{23} - 12288 q^{24} - 4805517 q^{25} - 2530896 q^{26} - 6711147 q^{27} - 3409152 q^{28} - 9839019 q^{29} - 2170560 q^{30} + 1364628 q^{31} - 3145728 q^{32} - 30339114 q^{33} + 10065456 q^{34} - 11097570 q^{35} + 5861376 q^{36} - 2289090 q^{37} + 6255408 q^{38} - 18481557 q^{39} - 1990656 q^{40} - 12899580 q^{41} + 13974480 q^{42} - 22378638 q^{43} + 14327808 q^{44} + 13005630 q^{45} + 14794032 q^{46} + 58896366 q^{47} + 196608 q^{48} + 22294974 q^{49} + 76888272 q^{50} + 85869585 q^{51} + 40494336 q^{52} + 8770629 q^{53} + 107378352 q^{54} - 73415802 q^{55} + 54546432 q^{56} - 390963 q^{57} + 157424304 q^{58} + 16426299 q^{59} + 34728960 q^{60} - 126843780 q^{61} - 21834048 q^{62} - 234650088 q^{63} + 50331648 q^{64} + 45269952 q^{65} + 485425824 q^{66} - 288075309 q^{67} - 161047296 q^{68} + 323371803 q^{69} + 177561120 q^{70} + 78122274 q^{71} - 93782016 q^{72} - 557941845 q^{73} + 36625440 q^{74} + 150154413 q^{75} - 100086528 q^{76} + 394013736 q^{77} + 295704912 q^{78} - 320222022 q^{79} + 31850496 q^{80} - 346127013 q^{81} + 206393280 q^{82} + 430491462 q^{83} - 223591680 q^{84} - 383428242 q^{85} + 358058208 q^{86} - 1044099345 q^{87} - 229244928 q^{88} + 437689644 q^{89} - 208090080 q^{90} - 1010450187 q^{91} - 236704512 q^{92} - 2684851332 q^{93} - 942341856 q^{94} - 63336006 q^{95} - 3145728 q^{96} - 384952146 q^{97} - 356719584 q^{98} + 2029897422 q^{99}+O(q^{100}) \) 3 * q - 48 * q^2 + 3 * q^3 + 768 * q^4 + 486 * q^5 - 48 * q^6 - 13317 * q^7 - 12288 * q^8 + 22896 * q^9 - 7776 * q^10 + 55968 * q^11 + 768 * q^12 + 158181 * q^13 + 213072 * q^14 + 135660 * q^15 + 196608 * q^16 - 629091 * q^17 - 366336 * q^18 - 390963 * q^19 + 124416 * q^20 - 873405 * q^21 - 895488 * q^22 - 924627 * q^23 - 12288 * q^24 - 4805517 * q^25 - 2530896 * q^26 - 6711147 * q^27 - 3409152 * q^28 - 9839019 * q^29 - 2170560 * q^30 + 1364628 * q^31 - 3145728 * q^32 - 30339114 * q^33 + 10065456 * q^34 - 11097570 * q^35 + 5861376 * q^36 - 2289090 * q^37 + 6255408 * q^38 - 18481557 * q^39 - 1990656 * q^40 - 12899580 * q^41 + 13974480 * q^42 - 22378638 * q^43 + 14327808 * q^44 + 13005630 * q^45 + 14794032 * q^46 + 58896366 * q^47 + 196608 * q^48 + 22294974 * q^49 + 76888272 * q^50 + 85869585 * q^51 + 40494336 * q^52 + 8770629 * q^53 + 107378352 * q^54 - 73415802 * q^55 + 54546432 * q^56 - 390963 * q^57 + 157424304 * q^58 + 16426299 * q^59 + 34728960 * q^60 - 126843780 * q^61 - 21834048 * q^62 - 234650088 * q^63 + 50331648 * q^64 + 45269952 * q^65 + 485425824 * q^66 - 288075309 * q^67 - 161047296 * q^68 + 323371803 * q^69 + 177561120 * q^70 + 78122274 * q^71 - 93782016 * q^72 - 557941845 * q^73 + 36625440 * q^74 + 150154413 * q^75 - 100086528 * q^76 + 394013736 * q^77 + 295704912 * q^78 - 320222022 * q^79 + 31850496 * q^80 - 346127013 * q^81 + 206393280 * q^82 + 430491462 * q^83 - 223591680 * q^84 - 383428242 * q^85 + 358058208 * q^86 - 1044099345 * q^87 - 229244928 * q^88 + 437689644 * q^89 - 208090080 * q^90 - 1010450187 * q^91 - 236704512 * q^92 - 2684851332 * q^93 - 942341856 * q^94 - 63336006 * q^95 - 3145728 * q^96 - 384952146 * q^97 - 356719584 * q^98 + 2029897422 * q^99

Introduction

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