LMFDB - Embedded newform 38.10.a.d.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:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 34433x^{2} - 2723303x - 48270488 $ x^4 - x^3 - 34433x^2 - 2723303x - 48270488
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-124.888$ 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)

$f(q)$	$=$	$q-16.0000 q^{2} -140.229 q^{3} +256.000 q^{4} +1263.95 q^{5} +2243.67 q^{6} -3487.42 q^{7} -4096.00 q^{8} -18.7042 q^{9} +O(q^{10})$	\(q-16.0000 q^{2} -140.229 q^{3} +256.000 q^{4} +1263.95 q^{5} +2243.67 q^{6} -3487.42 q^{7} -4096.00 q^{8} -18.7042 q^{9} -20223.2 q^{10} -49259.2 q^{11} -35898.7 q^{12} -68065.3 q^{13} +55798.7 q^{14} -177243. q^{15} +65536.0 q^{16} +505716. q^{17} +299.267 q^{18} +130321. q^{19} +323571. q^{20} +489039. q^{21} +788147. q^{22} -585044. q^{23} +574380. q^{24} -355562. q^{25} +1.08905e6 q^{26} +2.76276e6 q^{27} -892779. q^{28} +2.62021e6 q^{29} +2.83588e6 q^{30} +3.53093e6 q^{31} -1.04858e6 q^{32} +6.90759e6 q^{33} -8.09145e6 q^{34} -4.40791e6 q^{35} -4788.27 q^{36} +1.85431e7 q^{37} -2.08514e6 q^{38} +9.54476e6 q^{39} -5.17713e6 q^{40} +2.18141e7 q^{41} -7.82462e6 q^{42} -1.12704e7 q^{43} -1.26104e7 q^{44} -23641.1 q^{45} +9.36070e6 q^{46} +1.54092e7 q^{47} -9.19008e6 q^{48} -2.81915e7 q^{49} +5.68899e6 q^{50} -7.09162e7 q^{51} -1.74247e7 q^{52} +7.05741e6 q^{53} -4.42041e7 q^{54} -6.22611e7 q^{55} +1.42845e7 q^{56} -1.82748e7 q^{57} -4.19234e7 q^{58} +2.90730e7 q^{59} -4.53741e7 q^{60} +1.44284e8 q^{61} -5.64949e7 q^{62} +65229.3 q^{63} +1.67772e7 q^{64} -8.60310e7 q^{65} -1.10521e8 q^{66} +2.65266e7 q^{67} +1.29463e8 q^{68} +8.20404e7 q^{69} +7.05266e7 q^{70} -4.27081e7 q^{71} +76612.3 q^{72} +3.24644e8 q^{73} -2.96689e8 q^{74} +4.98602e7 q^{75} +3.33622e7 q^{76} +1.71787e8 q^{77} -1.52716e8 q^{78} -8.88210e7 q^{79} +8.28341e7 q^{80} -3.87052e8 q^{81} -3.49026e8 q^{82} +6.29830e7 q^{83} +1.25194e8 q^{84} +6.39198e8 q^{85} +1.80326e8 q^{86} -3.67431e8 q^{87} +2.01766e8 q^{88} -4.54329e7 q^{89} +378258. q^{90} +2.37372e8 q^{91} -1.49771e8 q^{92} -4.95140e8 q^{93} -2.46547e8 q^{94} +1.64719e8 q^{95} +1.47041e8 q^{96} +1.64830e9 q^{97} +4.51064e8 q^{98} +921353. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 64 q^{2} + 84 q^{3} + 1024 q^{4} - 1395 q^{5} - 1344 q^{6} + 12307 q^{7} - 16384 q^{8} + 16538 q^{9}+O(q^{10}) $ 4 * q - 64 * q^2 + 84 * q^3 + 1024 * q^4 - 1395 * q^5 - 1344 * q^6 + 12307 * q^7 - 16384 * q^8 + 16538 * q^9	\( 4 q - 64 q^{2} + 84 q^{3} + 1024 q^{4} - 1395 q^{5} - 1344 q^{6} + 12307 q^{7} - 16384 q^{8} + 16538 q^{9} + 22320 q^{10} - 104249 q^{11} + 21504 q^{12} + 120486 q^{13} - 196912 q^{14} - 591090 q^{15} + 262144 q^{16} - 412139 q^{17} - 264608 q^{18} + 521284 q^{19} - 357120 q^{20} + 2437006 q^{21} + 1667984 q^{22} + 3010300 q^{23} - 344064 q^{24} + 9760585 q^{25} - 1927776 q^{26} + 12387978 q^{27} + 3150592 q^{28} + 6153240 q^{29} + 9457440 q^{30} + 12774024 q^{31} - 4194304 q^{32} - 3258022 q^{33} + 6594224 q^{34} + 9823425 q^{35} + 4233728 q^{36} + 20506048 q^{37} - 8340544 q^{38} + 69881444 q^{39} + 5713920 q^{40} + 11620300 q^{41} - 38992096 q^{42} + 7698327 q^{43} - 26687744 q^{44} - 124015815 q^{45} - 48164800 q^{46} - 31581083 q^{47} + 5505024 q^{48} + 18970383 q^{49} - 156169360 q^{50} - 8594812 q^{51} + 30844416 q^{52} + 72549422 q^{53} - 198207648 q^{54} + 21332505 q^{55} - 50409472 q^{56} + 10946964 q^{57} - 98451840 q^{58} - 149234120 q^{59} - 151319040 q^{60} + 129004373 q^{61} - 204384384 q^{62} + 102967551 q^{63} + 67108864 q^{64} + 124691700 q^{65} + 52128352 q^{66} + 132595266 q^{67} - 105507584 q^{68} - 45529972 q^{69} - 157174800 q^{70} - 47138482 q^{71} - 67739648 q^{72} - 39332795 q^{73} - 328096768 q^{74} + 824627010 q^{75} + 133448704 q^{76} - 165933719 q^{77} - 1118103104 q^{78} - 307010840 q^{79} - 91422720 q^{80} + 1305551744 q^{81} - 185924800 q^{82} - 746568232 q^{83} + 623873536 q^{84} - 105005985 q^{85} - 123173232 q^{86} - 82148208 q^{87} + 427003904 q^{88} + 286943482 q^{89} + 1984253040 q^{90} + 3155781114 q^{91} + 770636800 q^{92} + 1151901596 q^{93} + 505297328 q^{94} - 181797795 q^{95} - 88080384 q^{96} + 793519958 q^{97} - 303526128 q^{98} - 1681833809 q^{99}+O(q^{100}) \) 4 * q - 64 * q^2 + 84 * q^3 + 1024 * q^4 - 1395 * q^5 - 1344 * q^6 + 12307 * q^7 - 16384 * q^8 + 16538 * q^9 + 22320 * q^10 - 104249 * q^11 + 21504 * q^12 + 120486 * q^13 - 196912 * q^14 - 591090 * q^15 + 262144 * q^16 - 412139 * q^17 - 264608 * q^18 + 521284 * q^19 - 357120 * q^20 + 2437006 * q^21 + 1667984 * q^22 + 3010300 * q^23 - 344064 * q^24 + 9760585 * q^25 - 1927776 * q^26 + 12387978 * q^27 + 3150592 * q^28 + 6153240 * q^29 + 9457440 * q^30 + 12774024 * q^31 - 4194304 * q^32 - 3258022 * q^33 + 6594224 * q^34 + 9823425 * q^35 + 4233728 * q^36 + 20506048 * q^37 - 8340544 * q^38 + 69881444 * q^39 + 5713920 * q^40 + 11620300 * q^41 - 38992096 * q^42 + 7698327 * q^43 - 26687744 * q^44 - 124015815 * q^45 - 48164800 * q^46 - 31581083 * q^47 + 5505024 * q^48 + 18970383 * q^49 - 156169360 * q^50 - 8594812 * q^51 + 30844416 * q^52 + 72549422 * q^53 - 198207648 * q^54 + 21332505 * q^55 - 50409472 * q^56 + 10946964 * q^57 - 98451840 * q^58 - 149234120 * q^59 - 151319040 * q^60 + 129004373 * q^61 - 204384384 * q^62 + 102967551 * q^63 + 67108864 * q^64 + 124691700 * q^65 + 52128352 * q^66 + 132595266 * q^67 - 105507584 * q^68 - 45529972 * q^69 - 157174800 * q^70 - 47138482 * q^71 - 67739648 * q^72 - 39332795 * q^73 - 328096768 * q^74 + 824627010 * q^75 + 133448704 * q^76 - 165933719 * q^77 - 1118103104 * q^78 - 307010840 * q^79 - 91422720 * q^80 + 1305551744 * q^81 - 185924800 * q^82 - 746568232 * q^83 + 623873536 * q^84 - 105005985 * q^85 - 123173232 * q^86 - 82148208 * q^87 + 427003904 * q^88 + 286943482 * q^89 + 1984253040 * q^90 + 3155781114 * q^91 + 770636800 * q^92 + 1151901596 * q^93 + 505297328 * q^94 - 181797795 * q^95 - 88080384 * q^96 + 793519958 * q^97 - 303526128 * q^98 - 1681833809 * 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
$3$	−140.229	−0.999525	−0.499762	−	0.866163i	$-0.666579\pi$
$3$	−140.229	−0.999525	−0.499762	+	0.866163i	$0.666579\pi$
$4$	256.000	0.500000
$5$	1263.95	0.904407	0.452204	−	0.891915i	$-0.350638\pi$
$5$	1263.95	0.904407	0.452204	+	0.891915i	$0.350638\pi$
$6$	2243.67	0.706771
$7$	−3487.42	−0.548988	−0.274494	−	0.961589i	$-0.588510\pi$
$7$	−3487.42	−0.548988	−0.274494	+	0.961589i	$0.588510\pi$
$8$	−4096.00	−0.353553
$9$	−18.7042	−0.000950271 0
$10$	−20223.2	−0.639512
$11$	−49259.2	−1.01443	−0.507213	−	0.861821i	$-0.669324\pi$
$11$	−49259.2	−1.01443	−0.507213	+	0.861821i	$0.669324\pi$
$12$	−35898.7	−0.499762
$13$	−68065.3	−0.660969	−0.330484	−	0.943811i	$-0.607212\pi$
$13$	−68065.3	−0.660969	−0.330484	+	0.943811i	$0.607212\pi$
$14$	55798.7	0.388193
$15$	−177243.	−0.903977
$16$	65536.0	0.250000
$17$	505716.	1.46854	0.734271	−	0.678857i	$-0.237524\pi$
$17$	505716.	1.46854	0.734271	+	0.678857i	$0.237524\pi$
$18$	299.267	0.000671943 0
$19$	130321.	0.229416
$19$	130321.	0.229416
$20$	323571.	0.452204
$21$	489039.	0.548727
$22$	788147.	0.717307
$23$	−585044.	−0.435926	−0.217963	−	0.975957i	$-0.569941\pi$
$23$	−585044.	−0.435926	−0.217963	+	0.975957i	$0.569941\pi$
$24$	574380.	0.353385
$25$	−355562.	−0.182048
$26$	1.08905e6	0.467375
$27$	2.76276e6	1.00047
$28$	−892779.	−0.274494
$29$	2.62021e6	0.687932	0.343966	−	0.938982i	$-0.388229\pi$
$29$	2.62021e6	0.687932	0.343966	+	0.938982i	$0.388229\pi$
$30$	2.83588e6	0.639209
$31$	3.53093e6	0.686691	0.343345	−	0.939209i	$-0.388440\pi$
$31$	3.53093e6	0.686691	0.343345	+	0.939209i	$0.388440\pi$
$32$	−1.04858e6	−0.176777
$33$	6.90759e6	1.01394
$34$	−8.09145e6	−1.03842
$35$	−4.40791e6	−0.496509
$36$	−4788.27	−0.000475135 0
$37$	1.85431e7	1.62657	0.813287	−	0.581863i	$-0.197676\pi$
$37$	1.85431e7	1.62657	0.813287	+	0.581863i	$0.197676\pi$
$38$	−2.08514e6	−0.162221
$39$	9.54476e6	0.660655
$40$	−5.17713e6	−0.319756
$41$	2.18141e7	1.20562	0.602811	−	0.797884i	$-0.294047\pi$
$41$	2.18141e7	1.20562	0.602811	+	0.797884i	$0.294047\pi$
$42$	−7.82462e6	−0.388009
$43$	−1.12704e7	−0.502725	−0.251362	−	0.967893i	$-0.580879\pi$
$43$	−1.12704e7	−0.502725	−0.251362	+	0.967893i	$0.580879\pi$
$44$	−1.26104e7	−0.507213
$45$	−23641.1	−0.000859432 0
$46$	9.36070e6	0.308246
$47$	1.54092e7	0.460616	0.230308	−	0.973118i	$-0.426027\pi$
$47$	1.54092e7	0.460616	0.230308	+	0.973118i	$0.426027\pi$
$48$	−9.19008e6	−0.249881
$49$	−2.81915e7	−0.698612
$50$	5.68899e6	0.128727
$51$	−7.09162e7	−1.46784
$52$	−1.74247e7	−0.330484
$53$	7.05741e6	0.122858	0.0614291	−	0.998111i	$-0.480434\pi$
$53$	7.05741e6	0.122858	0.0614291	+	0.998111i	$0.480434\pi$
$54$	−4.42041e7	−0.707442
$55$	−6.22611e7	−0.917454
$56$	1.42845e7	0.194097
$57$	−1.82748e7	−0.229307
$58$	−4.19234e7	−0.486442
$59$	2.90730e7	0.312360	0.156180	−	0.987729i	$-0.450082\pi$
$59$	2.90730e7	0.312360	0.156180	+	0.987729i	$0.450082\pi$
$60$	−4.53741e7	−0.451989
$61$	1.44284e8	1.33424	0.667121	−	0.744949i	$-0.267526\pi$
$61$	1.44284e8	1.33424	0.667121	+	0.744949i	$0.267526\pi$
$62$	−5.64949e7	−0.485564
$63$	65229.3	0.000521687 0
$64$	1.67772e7	0.125000
$65$	−8.60310e7	−0.597785
$66$	−1.10521e8	−0.716967
$67$	2.65266e7	0.160822	0.0804110	−	0.996762i	$-0.474377\pi$
$67$	2.65266e7	0.160822	0.0804110	+	0.996762i	$0.474377\pi$
$68$	1.29463e8	0.734271
$69$	8.20404e7	0.435719
$70$	7.05266e7	0.351085
$71$	−4.27081e7	−0.199456	−0.0997281	−	0.995015i	$-0.531797\pi$
$71$	−4.27081e7	−0.199456	−0.0997281	+	0.995015i	$0.531797\pi$
$72$	76612.3	0.000335972 0
$73$	3.24644e8	1.33800	0.668998	−	0.743264i	$-0.266723\pi$
$73$	3.24644e8	1.33800	0.668998	+	0.743264i	$0.266723\pi$
$74$	−2.96689e8	−1.15016
$75$	4.98602e7	0.181961
$76$	3.33622e7	0.114708
$77$	1.71787e8	0.556908
$78$	−1.52716e8	−0.467153
$79$	−8.88210e7	−0.256563	−0.128281	−	0.991738i	$-0.540946\pi$
$79$	−8.88210e7	−0.256563	−0.128281	+	0.991738i	$0.540946\pi$
$80$	8.28341e7	0.226102
$81$	−3.87052e8	−0.999049
$82$	−3.49026e8	−0.852503
$83$	6.29830e7	0.145671	0.0728353	−	0.997344i	$-0.476795\pi$
$83$	6.29830e7	0.145671	0.0728353	+	0.997344i	$0.476795\pi$
$84$	1.25194e8	0.274363
$85$	6.39198e8	1.32816
$86$	1.80326e8	0.355480
$87$	−3.67431e8	−0.687605
$88$	2.01766e8	0.358654
$89$	−4.54329e7	−0.0767565	−0.0383783	−	0.999263i	$-0.512219\pi$
$89$	−4.54329e7	−0.0767565	−0.0383783	+	0.999263i	$0.512219\pi$
$90$	378258.	0.000607710 0
$91$	2.37372e8	0.362864
$92$	−1.49771e8	−0.217963
$93$	−4.95140e8	−0.686365
$94$	−2.46547e8	−0.325705
$95$	1.64719e8	0.207485
$96$	1.47041e8	0.176693
$97$	1.64830e9	1.89044	0.945219	−	0.326438i	$-0.105848\pi$
$97$	1.64830e9	1.89044	0.945219	+	0.326438i	$0.105848\pi$
$98$	4.51064e8	0.493994
$99$	921353.	0.000963980 0
$100$	−9.10238e7	−0.0910238
$101$	−8.97226e8	−0.857938	−0.428969	−	0.903319i	$-0.641123\pi$
$101$	−8.97226e8	−0.857938	−0.428969	+	0.903319i	$0.641123\pi$
$102$	1.13466e9	1.03792
$103$	1.67622e9	1.46745	0.733726	−	0.679445i	$-0.237779\pi$
$103$	1.67622e9	1.46745	0.733726	+	0.679445i	$0.237779\pi$
$104$	2.78796e8	0.233688
$105$	6.18119e8	0.496273
$106$	−1.12919e8	−0.0868738
$107$	3.08053e8	0.227195	0.113597	−	0.993527i	$-0.463763\pi$
$107$	3.08053e8	0.227195	0.113597	+	0.993527i	$0.463763\pi$
$108$	7.07266e8	0.500237
$109$	−1.79569e8	−0.121846	−0.0609230	−	0.998142i	$-0.519404\pi$
$109$	−1.79569e8	−0.121846	−0.0609230	+	0.998142i	$0.519404\pi$
$110$	9.96177e8	0.648738
$111$	−2.60028e9	−1.62580
$112$	−2.28551e8	−0.137247
$113$	−2.30787e9	−1.33155	−0.665776	−	0.746152i	$-0.731899\pi$
$113$	−2.30787e9	−1.33155	−0.665776	+	0.746152i	$0.731899\pi$
$114$	2.92397e8	0.162144
$115$	−7.39465e8	−0.394255
$116$	6.70775e8	0.343966
$117$	1.27311e6	0.000628099 0
$118$	−4.65168e8	−0.220872
$119$	−1.76364e9	−0.806212
$120$	7.25986e8	0.319604
$121$	6.85222e7	0.0290601
$122$	−2.30855e9	−0.943452
$123$	−3.05899e9	−1.20505
$124$	9.03918e8	0.343345
$125$	−2.91806e9	−1.06905
$126$	−1.04367e6	−0.000368889 0
$127$	−4.51313e9	−1.53943	−0.769717	−	0.638385i	$-0.779603\pi$
$127$	−4.51313e9	−1.53943	−0.769717	+	0.638385i	$0.779603\pi$
$128$	−2.68435e8	−0.0883883
$129$	1.58044e9	0.502486
$130$	1.37650e9	0.422698
$131$	−2.53716e9	−0.752708	−0.376354	−	0.926476i	$-0.622822\pi$
$131$	−2.53716e9	−0.752708	−0.376354	+	0.926476i	$0.622822\pi$
$132$	1.76834e9	0.506972
$133$	−4.54484e8	−0.125946
$134$	−4.24426e8	−0.113718
$135$	3.49198e9	0.904836
$136$	−2.07141e9	−0.519208
$137$	4.04090e9	0.980021	0.490010	−	0.871717i	$-0.336993\pi$
$137$	4.04090e9	0.980021	0.490010	+	0.871717i	$0.336993\pi$
$138$	−1.31265e9	−0.308100
$139$	−1.86522e9	−0.423803	−0.211901	−	0.977291i	$-0.567966\pi$
$139$	−1.86522e9	−0.423803	−0.211901	+	0.977291i	$0.567966\pi$
$140$	−1.12843e9	−0.248254
$141$	−2.16082e9	−0.460397
$142$	6.83329e8	0.141037
$143$	3.35284e9	0.670504
$144$	−1.22580e6	−0.000237568 0
$145$	3.31181e9	0.622171
$146$	−5.19431e9	−0.946106
$147$	3.95328e9	0.698280
$148$	4.74702e9	0.813287
$149$	−7.60481e9	−1.26401	−0.632004	−	0.774965i	$-0.717768\pi$
$149$	−7.60481e9	−1.26401	−0.632004	+	0.774965i	$0.717768\pi$
$150$	−7.97763e8	−0.128666
$151$	1.74653e9	0.273388	0.136694	−	0.990613i	$-0.456352\pi$
$151$	1.74653e9	0.273388	0.136694	+	0.990613i	$0.456352\pi$
$152$	−5.33795e8	−0.0811107
$153$	−9.45900e6	−0.00139551
$154$	−2.74860e9	−0.393793
$155$	4.46291e9	0.621048
$156$	2.44346e9	0.330327
$157$	1.06564e10	1.39979	0.699893	−	0.714248i	$-0.253231\pi$
$157$	1.06564e10	1.39979	0.699893	+	0.714248i	$0.253231\pi$
$158$	1.42114e9	0.181417
$159$	−9.89657e8	−0.122800
$160$	−1.32535e9	−0.159878
$161$	2.04029e9	0.239318
$162$	6.19283e9	0.706434
$163$	9.11348e9	1.01121	0.505603	−	0.862766i	$-0.331270\pi$
$163$	9.11348e9	1.01121	0.505603	+	0.862766i	$0.331270\pi$
$164$	5.58442e9	0.602811
$165$	8.73083e9	0.917018
$166$	−1.00773e9	−0.103005
$167$	1.15546e10	1.14956	0.574778	−	0.818309i	$-0.305088\pi$
$167$	1.15546e10	1.14956	0.574778	+	0.818309i	$0.305088\pi$
$168$	−2.00310e9	−0.194004
$169$	−5.97161e9	−0.563120
$170$	−1.02272e10	−0.939151
$171$	−2.43755e6	−0.000218007 0
$172$	−2.88522e9	−0.251362
$173$	−2.52786e9	−0.214558	−0.107279	−	0.994229i	$-0.534214\pi$
$173$	−2.52786e9	−0.214558	−0.107279	+	0.994229i	$0.534214\pi$
$174$	5.87890e9	0.486210
$175$	1.23999e9	0.0999419
$176$	−3.22825e9	−0.253606
$177$	−4.07689e9	−0.312212
$178$	7.26926e8	0.0542751
$179$	−1.73068e10	−1.26002	−0.630009	−	0.776588i	$-0.716949\pi$
$179$	−1.73068e10	−1.26002	−0.630009	+	0.776588i	$0.716949\pi$
$180$	−6.05212e6	−0.000429716 0
$181$	1.08688e10	0.752711	0.376355	−	0.926475i	$-0.377177\pi$
$181$	1.08688e10	0.752711	0.376355	+	0.926475i	$0.377177\pi$
$182$	−3.79796e9	−0.256583
$183$	−2.02329e10	−1.33361
$184$	2.39634e9	0.154123
$185$	2.34375e10	1.47108
$186$	7.92224e9	0.485333
$187$	−2.49112e10	−1.48973
$188$	3.94475e9	0.230308
$189$	−9.63489e9	−0.549248
$190$	−2.63550e9	−0.146714
$191$	−5.33871e9	−0.290259	−0.145130	−	0.989413i	$-0.546360\pi$
$191$	−5.33871e9	−0.290259	−0.145130	+	0.989413i	$0.546360\pi$
$192$	−2.35266e9	−0.124941
$193$	2.75948e10	1.43159	0.715797	−	0.698309i	$-0.246064\pi$
$193$	2.75948e10	1.43159	0.715797	+	0.698309i	$0.246064\pi$
$194$	−2.63727e10	−1.33674
$195$	1.20641e10	0.597501
$196$	−7.21703e9	−0.349306
$197$	−9.61053e9	−0.454621	−0.227310	−	0.973822i	$-0.572993\pi$
$197$	−9.61053e9	−0.454621	−0.227310	+	0.973822i	$0.572993\pi$
$198$	−1.47417e7	−0.000681636 0
$199$	2.88815e10	1.30551	0.652756	−	0.757568i	$-0.273612\pi$
$199$	2.88815e10	1.30551	0.652756	+	0.757568i	$0.273612\pi$
$200$	1.45638e9	0.0643635
$201$	−3.71982e9	−0.160746
$202$	1.43556e10	0.606654
$203$	−9.13778e9	−0.377666
$204$	−1.81546e10	−0.733922
$205$	2.75719e10	1.09037
$206$	−2.68196e10	−1.03765
$207$	1.09428e7	0.000414248 0
$208$	−4.46073e9	−0.165242
$209$	−6.41951e9	−0.232725
$210$	−9.88990e9	−0.350918
$211$	2.26589e10	0.786986	0.393493	−	0.919328i	$-0.371267\pi$
$211$	2.26589e10	0.786986	0.393493	+	0.919328i	$0.371267\pi$
$212$	1.80670e9	0.0614291
$213$	5.98893e9	0.199361
$214$	−4.92884e9	−0.160651
$215$	−1.42452e10	−0.454668
$216$	−1.13163e10	−0.353721
$217$	−1.23138e10	−0.376985
$218$	2.87310e9	0.0861581
$219$	−4.55247e10	−1.33736
$220$	−1.59388e10	−0.458727
$221$	−3.44217e10	−0.970660
$222$	4.16045e10	1.14961
$223$	−5.84566e10	−1.58293	−0.791465	−	0.611214i	$-0.790681\pi$
$223$	−5.84566e10	−1.58293	−0.791465	+	0.611214i	$0.790681\pi$
$224$	3.65682e9	0.0970483
$225$	6.65049e6	0.000172995 0
$226$	3.69259e10	0.941549
$227$	−4.82187e9	−0.120531	−0.0602656	−	0.998182i	$-0.519195\pi$
$227$	−4.82187e9	−0.120531	−0.0602656	+	0.998182i	$0.519195\pi$
$228$	−4.67836e9	−0.114653
$229$	−7.15833e9	−0.172009	−0.0860046	−	0.996295i	$-0.527410\pi$
$229$	−7.15833e9	−0.172009	−0.0860046	+	0.996295i	$0.527410\pi$
$230$	1.18314e10	0.278780
$231$	−2.40897e10	−0.556643
$232$	−1.07324e10	−0.243221
$233$	4.52737e10	1.00634	0.503169	−	0.864188i	$-0.332167\pi$
$233$	4.52737e10	1.00634	0.503169	+	0.864188i	$0.332167\pi$
$234$	−2.03697e7	−0.000444133 0
$235$	1.94764e10	0.416585
$236$	7.44268e9	0.156180
$237$	1.24553e10	0.256441
$238$	2.82183e10	0.570078
$239$	−7.05422e10	−1.39849	−0.699244	−	0.714883i	$-0.746480\pi$
$239$	−7.05422e10	−1.39849	−0.699244	+	0.714883i	$0.746480\pi$
$240$	−1.16158e10	−0.225994
$241$	7.83138e10	1.49542	0.747708	−	0.664028i	$-0.231154\pi$
$241$	7.83138e10	1.49542	0.747708	+	0.664028i	$0.231154\pi$
$242$	−1.09635e9	−0.0205486
$243$	−1.03301e8	−0.00190054
$244$	3.69368e10	0.667121
$245$	−3.56326e10	−0.631830
$246$	4.89438e10	0.852098
$247$	−8.87034e9	−0.151637
$248$	−1.44627e10	−0.242782
$249$	−8.83207e9	−0.145601
$250$	4.66889e10	0.755934
$251$	1.03661e11	1.64848	0.824240	−	0.566241i	$-0.191603\pi$
$251$	1.03661e11	1.64848	0.824240	+	0.566241i	$0.191603\pi$
$252$	1.66987e7	0.000260844 0
$253$	2.88188e10	0.442215
$254$	7.22101e10	1.08854
$255$	−8.96344e10	−1.32753
$256$	4.29497e9	0.0625000
$257$	1.07294e11	1.53419	0.767093	−	0.641536i	$-0.221703\pi$
$257$	1.07294e11	1.53419	0.767093	+	0.641536i	$0.221703\pi$
$258$	−2.52870e10	−0.355311
$259$	−6.46674e10	−0.892969
$260$	−2.20239e10	−0.298892
$261$	−4.90090e7	−0.000653722 0
$262$	4.05945e10	0.532245
$263$	−1.18240e11	−1.52393	−0.761963	−	0.647620i	$-0.775764\pi$
$263$	−1.18240e11	−1.52393	−0.761963	+	0.647620i	$0.775764\pi$
$264$	−2.82935e10	−0.358483
$265$	8.92019e9	0.111114
$266$	7.27174e9	0.0890576
$267$	6.37103e9	0.0767201
$268$	6.79082e9	0.0804110
$269$	1.08142e11	1.25924	0.629620	−	0.776903i	$-0.283211\pi$
$269$	1.08142e11	1.25924	0.629620	+	0.776903i	$0.283211\pi$
$270$	−5.58717e10	−0.639816
$271$	−1.22183e11	−1.37609	−0.688047	−	0.725667i	$-0.741532\pi$
$271$	−1.22183e11	−1.37609	−0.688047	+	0.725667i	$0.741532\pi$
$272$	3.31426e10	0.367135
$273$	−3.32866e10	−0.362691
$274$	−6.46544e10	−0.692979
$275$	1.75147e10	0.184674
$276$	2.10023e10	0.217860
$277$	1.18944e11	1.21390	0.606951	−	0.794740i	$-0.292393\pi$
$277$	1.18944e11	1.21390	0.606951	+	0.794740i	$0.292393\pi$
$278$	2.98436e10	0.299674
$279$	−6.60431e7	−0.000652542 0
$280$	1.80548e10	0.175542
$281$	−4.73680e10	−0.453218	−0.226609	−	0.973986i	$-0.572764\pi$
$281$	−4.73680e10	−0.453218	−0.226609	+	0.973986i	$0.572764\pi$
$282$	3.45731e10	0.325550
$283$	1.59829e11	1.48121	0.740603	−	0.671943i	$-0.234540\pi$
$283$	1.59829e11	1.48121	0.740603	+	0.671943i	$0.234540\pi$
$284$	−1.09333e10	−0.0997281
$285$	−2.30984e10	−0.207387
$286$	−5.36455e10	−0.474118
$287$	−7.60750e10	−0.661871
$288$	1.96128e7	0.000167986 0
$289$	1.37161e11	1.15662
$290$	−5.29890e10	−0.439941
$291$	−2.31140e11	−1.88954
$292$	8.31089e10	0.668998
$293$	1.32731e11	1.05212	0.526062	−	0.850446i	$-0.323668\pi$
$293$	1.32731e11	1.05212	0.526062	+	0.850446i	$0.323668\pi$
$294$	−6.32525e10	−0.493759
$295$	3.67467e10	0.282501
$296$	−7.59524e10	−0.575081
$297$	−1.36091e11	−1.01491
$298$	1.21677e11	0.893789
$299$	3.98212e10	0.288134
$300$	1.27642e10	0.0909805
$301$	3.93045e10	0.275990
$302$	−2.79444e10	−0.193314
$303$	1.25818e11	0.857530
$304$	8.54072e9	0.0573539
$305$	1.82368e11	1.20670
$306$	1.51344e8	0.000986776 0
$307$	2.41951e11	1.55455	0.777274	−	0.629162i	$-0.216602\pi$
$307$	2.41951e11	1.55455	0.777274	+	0.629162i	$0.216602\pi$
$308$	4.39776e10	0.278454
$309$	−2.35056e11	−1.46676
$310$	−7.14065e10	−0.439147
$311$	−1.75276e11	−1.06243	−0.531217	−	0.847236i	$-0.678265\pi$
$311$	−1.75276e11	−1.06243	−0.531217	+	0.847236i	$0.678265\pi$
$312$	−3.90954e10	−0.233577
$313$	−2.56460e11	−1.51032	−0.755161	−	0.655539i	$-0.772442\pi$
$313$	−2.56460e11	−1.51032	−0.755161	+	0.655539i	$0.772442\pi$
$314$	−1.70502e11	−0.989798
$315$	8.24464e7	0.000471818 0
$316$	−2.27382e10	−0.128281
$317$	−2.91020e10	−0.161866	−0.0809331	−	0.996720i	$-0.525790\pi$
$317$	−2.91020e10	−0.161866	−0.0809331	+	0.996720i	$0.525790\pi$
$318$	1.58345e10	0.0868325
$319$	−1.29070e11	−0.697856
$320$	2.12055e10	0.113051
$321$	−4.31980e10	−0.227087
$322$	−3.26447e10	−0.169224
$323$	6.59054e10	0.336907
$324$	−9.90853e10	−0.499524
$325$	2.42014e10	0.120328
$326$	−1.45816e11	−0.715031
$327$	2.51808e10	0.121788
$328$	−8.93508e10	−0.426251
$329$	−5.37382e10	−0.252873
$330$	−1.39693e11	−0.648430
$331$	−1.45683e11	−0.667088	−0.333544	−	0.942734i	$-0.608245\pi$
$331$	−1.45683e11	−0.667088	−0.333544	+	0.942734i	$0.608245\pi$
$332$	1.61236e10	0.0728353
$333$	−3.46833e8	−0.00154569
$334$	−1.84873e11	−0.812859
$335$	3.35283e10	0.145449
$336$	3.20496e10	0.137182
$337$	−4.16729e10	−0.176002	−0.0880012	−	0.996120i	$-0.528048\pi$
$337$	−4.16729e10	−0.176002	−0.0880012	+	0.996120i	$0.528048\pi$
$338$	9.55457e10	0.398186
$339$	3.23631e11	1.33092
$340$	1.63635e11	0.664080
$341$	−1.73931e11	−0.696597
$342$	3.90008e7	0.000154154 0
$343$	2.39045e11	0.932518
$344$	4.61635e10	0.177740
$345$	1.03695e11	0.394067
$346$	4.04457e10	0.151716
$347$	−5.79909e10	−0.214722	−0.107361	−	0.994220i	$-0.534240\pi$
$347$	−5.79909e10	−0.214722	−0.107361	+	0.994220i	$0.534240\pi$
$348$	−9.40624e10	−0.343803
$349$	−1.06762e11	−0.385214	−0.192607	−	0.981276i	$-0.561694\pi$
$349$	−1.06762e11	−0.385214	−0.192607	+	0.981276i	$0.561694\pi$
$350$	−1.98399e10	−0.0706696
$351$	−1.88048e11	−0.661282
$352$	5.16520e10	0.179327
$353$	−4.27202e11	−1.46436	−0.732180	−	0.681112i	$-0.761497\pi$
$353$	−4.27202e11	−1.46436	−0.732180	+	0.681112i	$0.761497\pi$
$354$	6.52302e10	0.220767
$355$	−5.39808e10	−0.180390
$356$	−1.16308e10	−0.0383783
$357$	2.47314e11	0.805828
$358$	2.76908e11	0.890968
$359$	4.29892e11	1.36595	0.682975	−	0.730442i	$-0.260686\pi$
$359$	4.29892e11	1.36595	0.682975	+	0.730442i	$0.260686\pi$
$360$	9.68340e7	0.000303855 0
$361$	1.69836e10	0.0526316
$362$	−1.73901e11	−0.532247
$363$	−9.60883e9	−0.0290463
$364$	6.07673e10	0.181432
$365$	4.10333e11	1.21009
$366$	3.23727e11	0.943004
$367$	1.40582e11	0.404512	0.202256	−	0.979333i	$-0.435173\pi$
$367$	1.40582e11	0.404512	0.202256	+	0.979333i	$0.435173\pi$
$368$	−3.83414e10	−0.108982
$369$	−4.08016e8	−0.00114567
$370$	−3.74999e11	−1.04021
$371$	−2.46121e10	−0.0674476
$372$	−1.26756e11	−0.343182
$373$	4.31647e11	1.15462	0.577310	−	0.816525i	$-0.304102\pi$
$373$	4.31647e11	1.15462	0.577310	+	0.816525i	$0.304102\pi$
$374$	3.98579e11	1.05340
$375$	4.09198e11	1.06854
$376$	−6.31160e10	−0.162852
$377$	−1.78346e11	−0.454702
$378$	1.54158e11	0.388377
$379$	7.16332e11	1.78336	0.891678	−	0.452670i	$-0.149528\pi$
$379$	7.16332e11	1.78336	0.891678	+	0.452670i	$0.149528\pi$
$380$	4.21680e10	0.103743
$381$	6.32874e11	1.53870
$382$	8.54194e10	0.205244
$383$	−1.03271e11	−0.245236	−0.122618	−	0.992454i	$-0.539129\pi$
$383$	−1.03271e11	−0.245236	−0.122618	+	0.992454i	$0.539129\pi$
$384$	3.76426e10	0.0883463
$385$	2.17130e11	0.503671
$386$	−4.41517e11	−1.01229
$387$	2.10803e8	0.000477725 0
$388$	4.21964e11	0.945219
$389$	−3.49935e11	−0.774845	−0.387422	−	0.921902i	$-0.626634\pi$
$389$	−3.49935e11	−0.774845	−0.387422	+	0.921902i	$0.626634\pi$
$390$	−1.93025e11	−0.422497
$391$	−2.95866e11	−0.640176
$392$	1.15473e11	0.246997
$393$	3.55784e11	0.752351
$394$	1.53769e11	0.321466
$395$	−1.12265e11	−0.232037
$396$	2.35866e8	0.000481990 0
$397$	−2.83640e11	−0.573073	−0.286536	−	0.958069i	$-0.592504\pi$
$397$	−2.83640e11	−0.573073	−0.286536	+	0.958069i	$0.592504\pi$
$398$	−4.62104e11	−0.923137
$399$	6.37320e10	0.125887
$400$	−2.33021e10	−0.0455119
$401$	−9.94065e11	−1.91984	−0.959920	−	0.280275i	$-0.909574\pi$
$401$	−9.94065e11	−1.91984	−0.959920	+	0.280275i	$0.909574\pi$
$402$	5.95171e10	0.113664
$403$	−2.40334e11	−0.453881
$404$	−2.29690e11	−0.428969
$405$	−4.89213e11	−0.903547
$406$	1.46204e11	0.267051
$407$	−9.13417e11	−1.65004
$408$	2.90473e11	0.518961
$409$	2.41111e11	0.426051	0.213026	−	0.977047i	$-0.431668\pi$
$409$	2.41111e11	0.426051	0.213026	+	0.977047i	$0.431668\pi$
$410$	−4.41151e11	−0.771010
$411$	−5.66653e11	−0.979555
$412$	4.29113e11	0.733726
$413$	−1.01390e11	−0.171482
$414$	−1.75084e8	−0.000292918 0
$415$	7.96072e10	0.131745
$416$	7.13717e10	0.116844
$417$	2.61559e11	0.423602
$418$	1.02712e11	0.164562
$419$	7.03102e11	1.11444	0.557218	−	0.830366i	$-0.311869\pi$
$419$	7.03102e11	1.11444	0.557218	+	0.830366i	$0.311869\pi$
$420$	1.58238e11	0.248136
$421$	−2.68270e11	−0.416200	−0.208100	−	0.978108i	$-0.566728\pi$
$421$	−2.68270e11	−0.416200	−0.208100	+	0.978108i	$0.566728\pi$
$422$	−3.62542e11	−0.556483
$423$	−2.88216e8	−0.000437710 0
$424$	−2.89071e10	−0.0434369
$425$	−1.79813e11	−0.267344
$426$	−9.58229e10	−0.140970
$427$	−5.03180e11	−0.732483
$428$	7.88615e10	0.113597
$429$	−4.70168e11	−0.670185
$430$	2.27923e11	0.321499
$431$	5.95908e10	0.0831825	0.0415912	−	0.999135i	$-0.486757\pi$
$431$	5.95908e10	0.0831825	0.0415912	+	0.999135i	$0.486757\pi$
$432$	1.81060e11	0.250119
$433$	−1.16290e12	−1.58982	−0.794909	−	0.606729i	$-0.792481\pi$
$433$	−1.16290e12	−1.58982	−0.794909	+	0.606729i	$0.792481\pi$
$434$	1.97021e11	0.266569
$435$	−4.64414e11	−0.621875
$436$	−4.59696e10	−0.0609230
$437$	−7.62435e10	−0.100008
$438$	7.28395e11	0.945657
$439$	−1.32465e12	−1.70220	−0.851100	−	0.525004i	$-0.824064\pi$
$439$	−1.32465e12	−1.70220	−0.851100	+	0.525004i	$0.824064\pi$
$440$	2.55021e11	0.324369
$441$	5.27300e8	0.000663871 0
$442$	5.50747e11	0.686360
$443$	7.48682e11	0.923593	0.461797	−	0.886986i	$-0.347205\pi$
$443$	7.48682e11	0.923593	0.461797	+	0.886986i	$0.347205\pi$
$444$	−6.65673e11	−0.812900
$445$	−5.74248e10	−0.0694192
$446$	9.35306e11	1.11930
$447$	1.06642e12	1.26341
$448$	−5.85091e10	−0.0686235
$449$	8.07450e11	0.937577	0.468788	−	0.883310i	$-0.344691\pi$
$449$	8.07450e11	0.937577	0.468788	+	0.883310i	$0.344691\pi$
$450$	−1.06408e8	−0.000122326 0
$451$	−1.07455e12	−1.22301
$452$	−5.90814e11	−0.665776
$453$	−2.44914e11	−0.273258
$454$	7.71500e10	0.0852284
$455$	3.00026e11	0.328177
$456$	7.48537e10	0.0810722
$457$	−2.09593e11	−0.224778	−0.112389	−	0.993664i	$-0.535850\pi$
$457$	−2.09593e11	−0.224778	−0.112389	+	0.993664i	$0.535850\pi$
$458$	1.14533e11	0.121629
$459$	1.39717e12	1.46924
$460$	−1.89303e11	−0.197127
$461$	1.12823e12	1.16343	0.581717	−	0.813391i	$-0.302381\pi$
$461$	1.12823e12	1.16343	0.581717	+	0.813391i	$0.302381\pi$
$462$	3.85434e11	0.393606
$463$	−9.75512e11	−0.986548	−0.493274	−	0.869874i	$-0.664200\pi$
$463$	−9.75512e11	−0.986548	−0.493274	+	0.869874i	$0.664200\pi$
$464$	1.71718e11	0.171983
$465$	−6.25831e11	−0.620753
$466$	−7.24379e11	−0.711589
$467$	−5.15878e11	−0.501904	−0.250952	−	0.968000i	$-0.580744\pi$
$467$	−5.15878e11	−0.501904	−0.250952	+	0.968000i	$0.580744\pi$
$468$	3.25915e8	0.000314050 0
$469$	−9.25095e10	−0.0882894
$470$	−3.11622e11	−0.294570
$471$	−1.49434e12	−1.39912
$472$	−1.19083e11	−0.110436
$473$	5.55170e11	0.509977
$474$	−1.99285e11	−0.181331
$475$	−4.63372e10	−0.0417646
$476$	−4.51492e11	−0.403106
$477$	−1.32003e8	−0.000116749 0
$478$	1.12868e12	0.988880
$479$	1.89215e12	1.64228	0.821139	−	0.570728i	$-0.193339\pi$
$479$	1.89215e12	1.64228	0.821139	+	0.570728i	$0.193339\pi$
$480$	1.85852e11	0.159802
$481$	−1.26214e12	−1.07511
$482$	−1.25302e12	−1.05742
$483$	−2.86109e11	−0.239204
$484$	1.75417e10	0.0145300
$485$	2.08336e12	1.70973
$486$	1.65282e9	0.00134389
$487$	1.35254e12	1.08960	0.544802	−	0.838565i	$-0.316605\pi$
$487$	1.35254e12	1.08960	0.544802	+	0.838565i	$0.316605\pi$
$488$	−5.90989e11	−0.471726
$489$	−1.27798e12	−1.01073
$490$	5.70122e11	0.446771
$491$	9.23267e11	0.716903	0.358452	−	0.933548i	$-0.383305\pi$
$491$	9.23267e11	0.716903	0.358452	+	0.933548i	$0.383305\pi$
$492$	−7.83100e11	−0.602524
$493$	1.32508e12	1.01026
$494$	1.41925e11	0.107223
$495$	1.16454e9	0.000871830 0
$496$	2.31403e11	0.171673
$497$	1.48941e11	0.109499
$498$	1.41313e11	0.102956
$499$	1.98116e12	1.43043	0.715214	−	0.698905i	$-0.246329\pi$
$499$	1.98116e12	1.43043	0.715214	+	0.698905i	$0.246329\pi$
$500$	−7.47023e11	−0.534526
$501$	−1.62029e12	−1.14901
$502$	−1.65858e12	−1.16565
$503$	2.56937e12	1.78966	0.894830	−	0.446406i	$-0.147296\pi$
$503$	2.56937e12	1.78966	0.894830	+	0.446406i	$0.147296\pi$
$504$	−2.67179e8	−0.000184444 0
$505$	−1.13405e12	−0.775925
$506$	−4.61101e11	−0.312693
$507$	8.37395e11	0.562853
$508$	−1.15536e12	−0.769717
$509$	1.56900e11	0.103608	0.0518040	−	0.998657i	$-0.483503\pi$
$509$	1.56900e11	0.103608	0.0518040	+	0.998657i	$0.483503\pi$
$510$	1.43415e12	0.938705
$511$	−1.13217e12	−0.734544
$512$	−6.87195e10	−0.0441942
$513$	3.60046e11	0.229525
$514$	−1.71671e12	−1.08483
$515$	2.11866e12	1.32717
$516$	4.04592e11	0.251243
$517$	−7.59044e11	−0.467261
$518$	1.03468e12	0.631424
$519$	3.54480e11	0.214456
$520$	3.52383e11	0.211349
$521$	−1.30379e12	−0.775241	−0.387621	−	0.921819i	$-0.626703\pi$
$521$	−1.30379e12	−0.775241	−0.387621	+	0.921819i	$0.626703\pi$
$522$	7.84143e8	0.000462251 0
$523$	2.30458e12	1.34690	0.673449	−	0.739234i	$-0.264812\pi$
$523$	2.30458e12	1.34690	0.673449	+	0.739234i	$0.264812\pi$
$524$	−6.49513e11	−0.376354
$525$	−1.73883e11	−0.0998944
$526$	1.89184e12	1.07758
$527$	1.78565e12	1.00843
$528$	4.52696e11	0.253486
$529$	−1.45888e12	−0.809968
$530$	−1.42723e11	−0.0785693
$531$	−5.43786e8	−0.000296827 0
$532$	−1.16348e11	−0.0629732
$533$	−1.48479e12	−0.796878
$534$	−1.01936e11	−0.0542493
$535$	3.89362e11	0.205476
$536$	−1.08653e11	−0.0568592
$537$	2.42692e12	1.25942
$538$	−1.73027e12	−0.890417
$539$	1.38869e12	0.708691
$540$	8.93947e11	0.452418
$541$	5.93525e11	0.297887	0.148943	−	0.988846i	$-0.452413\pi$
$541$	5.93525e11	0.297887	0.148943	+	0.988846i	$0.452413\pi$
$542$	1.95492e12	0.973045
$543$	−1.52413e12	−0.752353
$544$	−5.30281e11	−0.259604
$545$	−2.26965e11	−0.110198
$546$	5.32585e11	0.256462
$547$	−2.57843e12	−1.23144	−0.615719	−	0.787966i	$-0.711134\pi$
$547$	−2.57843e12	−1.23144	−0.615719	+	0.787966i	$0.711134\pi$
$548$	1.03447e12	0.490010
$549$	−2.69872e9	−0.00126789
$550$	−2.80235e11	−0.130584
$551$	3.41469e11	0.157822
$552$	−3.36037e11	−0.154050
$553$	3.09756e11	0.140850
$554$	−1.90310e12	−0.858358
$555$	−3.28662e12	−1.47039
$556$	−4.77497e11	−0.211901
$557$	−3.49163e12	−1.53702	−0.768510	−	0.639838i	$-0.779001\pi$
$557$	−3.49163e12	−1.53702	−0.768510	+	0.639838i	$0.779001\pi$
$558$	1.05669e9	0.000461417 0
$559$	7.67122e11	0.332285
$560$	−2.88877e11	−0.124127
$561$	3.49328e12	1.48902
$562$	7.57888e11	0.320473
$563$	−1.40676e12	−0.590109	−0.295054	−	0.955480i	$-0.595338\pi$
$563$	−1.40676e12	−0.590109	−0.295054	+	0.955480i	$0.595338\pi$
$564$	−5.53170e11	−0.230199
$565$	−2.91702e12	−1.20427
$566$	−2.55726e12	−1.04737
$567$	1.34981e12	0.548466
$568$	1.74932e11	0.0705184
$569$	2.81635e12	1.12637	0.563185	−	0.826331i	$-0.309576\pi$
$569$	2.81635e12	1.12637	0.563185	+	0.826331i	$0.309576\pi$
$570$	3.69575e11	0.146644
$571$	−1.85246e11	−0.0729266	−0.0364633	−	0.999335i	$-0.511609\pi$
$571$	−1.85246e11	−0.0729266	−0.0364633	+	0.999335i	$0.511609\pi$
$572$	8.58328e11	0.335252
$573$	7.48645e11	0.290121
$574$	1.21720e12	0.468014
$575$	2.08019e11	0.0793593
$576$	−3.13804e8	−0.000118784 0
$577$	−2.36440e12	−0.888034	−0.444017	−	0.896018i	$-0.646447\pi$
$577$	−2.36440e12	−0.888034	−0.444017	+	0.896018i	$0.646447\pi$
$578$	−2.19457e12	−0.817850
$579$	−3.86961e12	−1.43091
$580$	8.47824e11	0.311085
$581$	−2.19648e11	−0.0799714
$582$	3.69823e12	1.33611
$583$	−3.47642e11	−0.124630
$584$	−1.32974e12	−0.473053
$585$	1.60914e9	0.000568058 0
$586$	−2.12369e12	−0.743964
$587$	8.75403e11	0.304324	0.152162	−	0.988356i	$-0.451376\pi$
$587$	8.75403e11	0.304324	0.152162	+	0.988356i	$0.451376\pi$
$588$	1.01204e12	0.349140
$589$	4.60154e11	0.157538
$590$	−5.87947e11	−0.199758
$591$	1.34768e12	0.454405
$592$	1.21524e12	0.406643
$593$	−2.10579e12	−0.699307	−0.349654	−	0.936879i	$-0.613701\pi$
$593$	−2.10579e12	−0.699307	−0.349654	+	0.936879i	$0.613701\pi$
$594$	2.17746e12	0.717648
$595$	−2.22915e12	−0.729144
$596$	−1.94683e12	−0.632004
$597$	−4.05004e12	−1.30489
$598$	−6.37139e11	−0.203741
$599$	5.86647e12	1.86190	0.930950	−	0.365147i	$-0.118981\pi$
$599$	5.86647e12	1.86190	0.930950	+	0.365147i	$0.118981\pi$
$600$	−2.04227e11	−0.0643330
$601$	−8.97472e11	−0.280599	−0.140299	−	0.990109i	$-0.544807\pi$
$601$	−8.97472e11	−0.280599	−0.140299	+	0.990109i	$0.544807\pi$
$602$	−6.28872e11	−0.195154
$603$	−4.96159e8	−0.000152825 0
$604$	4.47111e11	0.136694
$605$	8.66084e10	0.0262822
$606$	−2.01308e12	−0.606365
$607$	−4.20534e12	−1.25734	−0.628669	−	0.777673i	$-0.716400\pi$
$607$	−4.20534e12	−1.25734	−0.628669	+	0.777673i	$0.716400\pi$
$608$	−1.36651e11	−0.0405554
$609$	1.28139e12	0.377487
$610$	−2.91788e12	−0.853265
$611$	−1.04883e12	−0.304453
$612$	−2.42150e9	−0.000697756 0
$613$	4.66333e12	1.33390	0.666951	−	0.745102i	$-0.267599\pi$
$613$	4.66333e12	1.33390	0.666951	+	0.745102i	$0.267599\pi$
$614$	−3.87121e12	−1.09923
$615$	−3.86640e12	−1.08985
$616$	−7.03641e11	−0.196897
$617$	3.80910e12	1.05813	0.529065	−	0.848581i	$-0.322543\pi$
$617$	3.80910e12	1.05813	0.529065	+	0.848581i	$0.322543\pi$
$618$	3.76089e12	1.03715
$619$	−3.62001e12	−0.991063	−0.495532	−	0.868590i	$-0.665027\pi$
$619$	−3.62001e12	−0.991063	−0.495532	+	0.868590i	$0.665027\pi$
$620$	1.14250e12	0.310524
$621$	−1.61633e12	−0.436133
$622$	2.80442e12	0.751254
$623$	1.58443e11	0.0421384
$624$	6.25526e11	0.165164
$625$	−2.99382e12	−0.784811
$626$	4.10336e12	1.06796
$627$	9.00204e11	0.232615
$628$	2.72804e12	0.699893
$629$	9.37752e12	2.38869
$630$	−1.31914e9	−0.000333625 0
$631$	−7.16358e11	−0.179886	−0.0899431	−	0.995947i	$-0.528669\pi$
$631$	−7.16358e11	−0.179886	−0.0899431	+	0.995947i	$0.528669\pi$
$632$	3.63811e11	0.0907086
$633$	−3.17744e12	−0.786612
$634$	4.65632e11	0.114457
$635$	−5.70436e12	−1.39228
$636$	−2.53352e11	−0.0613999
$637$	1.91887e12	0.461761
$638$	2.06511e12	0.493459
$639$	7.98820e8	0.000189537 0
$640$	−3.39288e11	−0.0799391
$641$	−4.92458e12	−1.15215	−0.576074	−	0.817397i	$-0.695416\pi$
$641$	−4.92458e12	−1.15215	−0.576074	+	0.817397i	$0.695416\pi$
$642$	6.91169e11	0.160574
$643$	3.16432e12	0.730013	0.365007	−	0.931005i	$-0.381067\pi$
$643$	3.16432e12	0.730013	0.365007	+	0.931005i	$0.381067\pi$
$644$	5.22315e11	0.119659
$645$	1.99759e12	0.454452
$646$	−1.05449e12	−0.238229
$647$	8.63261e12	1.93675	0.968374	−	0.249504i	$-0.0802677\pi$
$647$	8.63261e12	1.93675	0.968374	+	0.249504i	$0.0802677\pi$
$648$	1.58536e12	0.353217
$649$	−1.43211e12	−0.316866
$650$	−3.87223e11	−0.0850846
$651$	1.72676e12	0.376806
$652$	2.33305e12	0.505603
$653$	−4.53346e12	−0.975710	−0.487855	−	0.872925i	$-0.662220\pi$
$653$	−4.53346e12	−0.975710	−0.487855	+	0.872925i	$0.662220\pi$
$654$	−4.02893e11	−0.0861172
$655$	−3.20684e12	−0.680755
$656$	1.42961e12	0.301405
$657$	−6.07221e9	−0.00127146
$658$	8.59812e11	0.178808
$659$	2.67609e12	0.552734	0.276367	−	0.961052i	$-0.410869\pi$
$659$	2.67609e12	0.552734	0.276367	+	0.961052i	$0.410869\pi$
$660$	2.23509e12	0.458509
$661$	1.23915e12	0.252475	0.126238	−	0.992000i	$-0.459710\pi$
$661$	1.23915e12	0.252475	0.126238	+	0.992000i	$0.459710\pi$
$662$	2.33093e12	0.471703
$663$	4.82694e12	0.970199
$664$	−2.57978e11	−0.0515023
$665$	−5.74444e11	−0.113907
$666$	5.54933e9	0.00109296
$667$	−1.53294e12	−0.299888
$668$	2.95797e12	0.574778
$669$	8.19734e12	1.58218
$670$	−5.36452e11	−0.102848
$671$	−7.10733e12	−1.35349
$672$	−5.12794e11	−0.0970021
$673$	−5.79692e11	−0.108926	−0.0544628	−	0.998516i	$-0.517345\pi$
$673$	−5.79692e11	−0.108926	−0.0544628	+	0.998516i	$0.517345\pi$
$674$	6.66766e11	0.124453
$675$	−9.82331e11	−0.182134
$676$	−1.52873e12	−0.281560
$677$	6.09981e12	1.11601	0.558004	−	0.829838i	$-0.311567\pi$
$677$	6.09981e12	1.11601	0.558004	+	0.829838i	$0.311567\pi$
$678$	−5.17810e12	−0.941102
$679$	−5.74829e12	−1.03783
$680$	−2.61816e12	−0.469575
$681$	6.76168e11	0.120474
$682$	2.78289e12	0.492569
$683$	−1.92035e12	−0.337665	−0.168833	−	0.985645i	$-0.554000\pi$
$683$	−1.92035e12	−0.337665	−0.168833	+	0.985645i	$0.554000\pi$
$684$	−6.24012e8	−0.000109004 0
$685$	5.10748e12	0.886338
$686$	−3.82473e12	−0.659389
$687$	1.00381e12	0.171928
$688$	−7.38615e11	−0.125681
$689$	−4.80365e11	−0.0812054
$690$	−1.65912e12	−0.278648
$691$	−1.22588e12	−0.204549	−0.102275	−	0.994756i	$-0.532612\pi$
$691$	−1.22588e12	−0.204549	−0.102275	+	0.994756i	$0.532612\pi$
$692$	−6.47132e11	−0.107279
$693$	−3.21314e9	−0.000529213 0
$694$	9.27854e11	0.151832
$695$	−2.35754e12	−0.383290
$696$	1.50500e12	0.243105
$697$	1.10318e13	1.77051
$698$	1.70819e12	0.272388
$699$	−6.34870e12	−1.00586
$700$	3.17438e11	0.0499710
$701$	−7.54657e10	−0.0118037	−0.00590186	−	0.999983i	$-0.501879\pi$
$701$	−7.54657e10	−0.0118037	−0.00590186	+	0.999983i	$0.501879\pi$
$702$	3.00877e12	0.467597
$703$	2.41655e12	0.373162
$704$	−8.26432e11	−0.126803
$705$	−2.73116e12	−0.416387
$706$	6.83524e12	1.03546
$707$	3.12900e12	0.470997
$708$	−1.04368e12	−0.156106
$709$	−2.48251e12	−0.368964	−0.184482	−	0.982836i	$-0.559061\pi$
$709$	−2.48251e12	−0.368964	−0.184482	+	0.982836i	$0.559061\pi$
$710$	8.63692e11	0.127555
$711$	1.66132e9	0.000243804 0
$712$	1.86093e11	0.0271375
$713$	−2.06575e12	−0.299347
$714$	−3.95703e12	−0.569807
$715$	4.23782e12	0.606409
$716$	−4.43053e12	−0.630009
$717$	9.89210e12	1.39782
$718$	−6.87828e12	−0.965872
$719$	−5.21696e12	−0.728010	−0.364005	−	0.931397i	$-0.618591\pi$
$719$	−5.21696e12	−0.728010	−0.364005	+	0.931397i	$0.618591\pi$
$720$	−1.54934e9	−0.000214858 0
$721$	−5.84569e12	−0.805614
$722$	−2.71737e11	−0.0372161
$723$	−1.09819e13	−1.49470
$724$	2.78241e12	0.376355
$725$	−9.31648e11	−0.125236
$726$	1.53741e11	0.0205388
$727$	1.23462e13	1.63919	0.819595	−	0.572944i	$-0.194199\pi$
$727$	1.23462e13	1.63919	0.819595	+	0.572944i	$0.194199\pi$
$728$	−9.72277e11	−0.128292
$729$	7.63283e12	1.00095
$730$	−6.56533e12	−0.855665
$731$	−5.69961e12	−0.738273
$732$	−5.17962e12	−0.666804
$733$	−7.23773e12	−0.926050	−0.463025	−	0.886345i	$-0.653236\pi$
$733$	−7.23773e12	−0.926050	−0.463025	+	0.886345i	$0.653236\pi$
$734$	−2.24931e12	−0.286033
$735$	4.99674e12	0.631530
$736$	6.13463e11	0.0770616
$737$	−1.30668e12	−0.163142
$738$	6.52825e9	0.000810109 0
$739$	−1.58616e12	−0.195636	−0.0978179	−	0.995204i	$-0.531186\pi$
$739$	−1.58616e12	−0.195636	−0.0978179	+	0.995204i	$0.531186\pi$
$740$	5.99999e12	0.735542
$741$	1.24388e12	0.151565
$742$	3.93794e11	0.0476927
$743$	−1.32982e13	−1.60082	−0.800408	−	0.599455i	$-0.795384\pi$
$743$	−1.32982e13	−1.60082	−0.800408	+	0.599455i	$0.795384\pi$
$744$	2.02809e12	0.242667
$745$	−9.61208e12	−1.14318
$746$	−6.90636e12	−0.816440
$747$	−1.17805e9	−0.000138426 0
$748$	−6.37726e12	−0.744864
$749$	−1.07431e12	−0.124727
$750$	−6.54716e12	−0.755575
$751$	−7.69495e12	−0.882726	−0.441363	−	0.897329i	$-0.645505\pi$
$751$	−7.69495e12	−0.882726	−0.441363	+	0.897329i	$0.645505\pi$
$752$	1.00986e12	0.115154
$753$	−1.45363e13	−1.64770
$754$	2.85353e12	0.321523
$755$	2.20752e12	0.247254
$756$	−2.46653e12	−0.274624
$757$	1.46042e13	1.61640	0.808198	−	0.588911i	$-0.200443\pi$
$757$	1.46042e13	1.61640	0.808198	+	0.588911i	$0.200443\pi$
$758$	−1.14613e13	−1.26102
$759$	−4.04124e12	−0.442005
$760$	−6.74689e11	−0.0733571
$761$	−2.14254e12	−0.231578	−0.115789	−	0.993274i	$-0.536940\pi$
$761$	−2.14254e12	−0.231578	−0.115789	+	0.993274i	$0.536940\pi$
$762$	−1.01260e13	−1.08803
$763$	6.26231e11	0.0668920
$764$	−1.36671e12	−0.145130
$765$	−1.19557e10	−0.00126211
$766$	1.65234e12	0.173408
$767$	−1.97886e12	−0.206460
$768$	−6.02281e11	−0.0624703
$769$	1.37576e13	1.41865	0.709326	−	0.704881i	$-0.249000\pi$
$769$	1.37576e13	1.41865	0.709326	+	0.704881i	$0.249000\pi$
$770$	−3.47408e12	−0.356149
$771$	−1.50458e13	−1.53346
$772$	7.06428e12	0.715797
$773$	1.78934e13	1.80254	0.901270	−	0.433257i	$-0.142636\pi$
$773$	1.78934e13	1.80254	0.901270	+	0.433257i	$0.142636\pi$
$774$	−3.37285e9	−0.000337802 0
$775$	−1.25546e12	−0.125010
$776$	−6.75142e12	−0.668371
$777$	9.06827e12	0.892545
$778$	5.59897e12	0.547898
$779$	2.84284e12	0.276588
$780$	3.08840e12	0.298750
$781$	2.10377e12	0.202334
$782$	4.73385e12	0.452673
$783$	7.23902e12	0.688259
$784$	−1.84756e12	−0.174653
$785$	1.34691e13	1.26598
$786$	−5.69255e12	−0.531992
$787$	1.90983e13	1.77464	0.887318	−	0.461158i	$-0.152566\pi$
$787$	1.90983e13	1.77464	0.887318	+	0.461158i	$0.152566\pi$
$788$	−2.46030e12	−0.227310
$789$	1.65807e13	1.52320
$790$	1.79624e12	0.164075
$791$	8.04850e12	0.731006
$792$	−3.77386e9	−0.000340818 0
$793$	−9.82076e12	−0.881893
$794$	4.53823e12	0.405224
$795$	−1.25087e12	−0.111061
$796$	7.39367e12	0.652756
$797$	−4.39907e10	−0.00386188	−0.00193094	−	0.999998i	$-0.500615\pi$
$797$	−4.39907e10	−0.00386188	−0.00193094	+	0.999998i	$0.500615\pi$
$798$	−1.01971e12	−0.0890153
$799$	7.79267e12	0.676434
$800$	3.72833e11	0.0321818
$801$	8.49785e8	7.29395e−5 0
$802$	1.59050e13	1.35753
$803$	−1.59917e13	−1.35730
$804$	−9.52273e11	−0.0803728
$805$	2.57882e12	0.216441
$806$	3.84534e12	0.320943
$807$	−1.51647e13	−1.25864
$808$	3.67504e12	0.303327
$809$	−1.85839e13	−1.52535	−0.762675	−	0.646782i	$-0.776114\pi$
$809$	−1.85839e13	−1.52535	−0.762675	+	0.646782i	$0.776114\pi$
$810$	7.82741e12	0.638904
$811$	1.29810e13	1.05369	0.526847	−	0.849960i	$-0.323374\pi$
$811$	1.29810e13	1.05369	0.526847	+	0.849960i	$0.323374\pi$
$812$	−2.33927e12	−0.188833
$813$	1.71336e13	1.37544
$814$	1.46147e13	1.16675
$815$	1.15190e13	0.914543
$816$	−4.64757e12	−0.366961
$817$	−1.46877e12	−0.115333
$818$	−3.85777e12	−0.301264
$819$	−4.43985e9	−0.000344819 0
$820$	7.05842e12	0.545186
$821$	−4.47787e12	−0.343975	−0.171987	−	0.985099i	$-0.555019\pi$
$821$	−4.47787e12	−0.343975	−0.171987	+	0.985099i	$0.555019\pi$
$822$	9.06644e12	0.692650
$823$	1.13315e13	0.860973	0.430487	−	0.902597i	$-0.358342\pi$
$823$	1.13315e13	0.860973	0.430487	+	0.902597i	$0.358342\pi$
$824$	−6.86581e12	−0.518823
$825$	−2.45607e12	−0.184586
$826$	1.62223e12	0.121256
$827$	−1.46669e13	−1.09034	−0.545171	−	0.838325i	$-0.683535\pi$
$827$	−1.46669e13	−1.09034	−0.545171	+	0.838325i	$0.683535\pi$
$828$	2.80135e9	0.000207124 0
$829$	−2.45530e13	−1.80555	−0.902774	−	0.430115i	$-0.858473\pi$
$829$	−2.45530e13	−1.80555	−0.902774	+	0.430115i	$0.858473\pi$
$830$	−1.27371e12	−0.0931581
$831$	−1.66794e13	−1.21332
$832$	−1.14195e12	−0.0826211
$833$	−1.42569e13	−1.02594
$834$	−4.18495e12	−0.299532
$835$	1.46044e13	1.03967
$836$	−1.64339e12	−0.116363
$837$	9.75510e12	0.687017
$838$	−1.12496e13	−0.788025
$839$	8.71743e12	0.607379	0.303689	−	0.952771i	$-0.401781\pi$
$839$	8.71743e12	0.607379	0.303689	+	0.952771i	$0.401781\pi$
$840$	−2.53182e12	−0.175459
$841$	−7.64163e12	−0.526749
$842$	4.29231e12	0.294298
$843$	6.64239e12	0.453002
$844$	5.80067e12	0.393493
$845$	−7.54780e12	−0.509290
$846$	4.61146e9	0.000309508 0
$847$	−2.38965e11	−0.0159536
$848$	4.62514e11	0.0307145
$849$	−2.24127e13	−1.48050
$850$	2.87701e12	0.189041
$851$	−1.08485e13	−0.709066
$852$	1.53317e12	0.0996807
$853$	1.30680e12	0.0845159	0.0422580	−	0.999107i	$-0.486545\pi$
$853$	1.30680e12	0.0845159	0.0422580	+	0.999107i	$0.486545\pi$
$854$	8.05087e12	0.517944
$855$	−3.08093e9	−0.000197167 0
$856$	−1.26178e12	−0.0803254
$857$	−1.57408e12	−0.0996811	−0.0498405	−	0.998757i	$-0.515871\pi$
$857$	−1.57408e12	−0.0996811	−0.0498405	+	0.998757i	$0.515871\pi$
$858$	7.52268e12	0.473893
$859$	1.39034e13	0.871265	0.435633	−	0.900125i	$-0.356525\pi$
$859$	1.39034e13	0.871265	0.435633	+	0.900125i	$0.356525\pi$
$860$	−3.64676e12	−0.227334
$861$	1.06680e13	0.661557
$862$	−9.53453e11	−0.0588189
$863$	2.53344e11	0.0155476	0.00777378	−	0.999970i	$-0.497526\pi$
$863$	2.53344e11	0.0155476	0.00777378	+	0.999970i	$0.497526\pi$
$864$	−2.89696e12	−0.176861
$865$	−3.19508e12	−0.194048
$866$	1.86064e13	1.12417
$867$	−1.92339e13	−1.15607
$868$	−3.15234e12	−0.188492
$869$	4.37525e12	0.260264
$870$	7.43062e12	0.439732
$871$	−1.80554e12	−0.106298
$872$	7.35513e11	0.0430791
$873$	−3.08300e10	−0.00179643
$874$	1.21990e12	0.0707166
$875$	1.01765e13	0.586897
$876$	−1.16543e13	−0.668680
$877$	−4.95849e12	−0.283042	−0.141521	−	0.989935i	$-0.545199\pi$
$877$	−4.95849e12	−0.283042	−0.141521	+	0.989935i	$0.545199\pi$
$878$	2.11944e13	1.20364
$879$	−1.86127e13	−1.05162
$880$	−4.08034e12	−0.229364
$881$	−1.32981e13	−0.743702	−0.371851	−	0.928292i	$-0.621277\pi$
$881$	−1.32981e13	−0.743702	−0.371851	+	0.928292i	$0.621277\pi$
$882$	−8.43679e9	−0.000469428 0
$883$	1.27657e13	0.706677	0.353338	−	0.935496i	$-0.385046\pi$
$883$	1.27657e13	0.706677	0.353338	+	0.935496i	$0.385046\pi$
$884$	−8.81196e12	−0.485330
$885$	−5.15297e12	−0.282366
$886$	−1.19789e13	−0.653079
$887$	1.14862e13	0.623044	0.311522	−	0.950239i	$-0.399161\pi$
$887$	1.14862e13	0.623044	0.311522	+	0.950239i	$0.399161\pi$
$888$	1.06508e13	0.574807
$889$	1.57392e13	0.845131
$890$	9.18797e11	0.0490868
$891$	1.90659e13	1.01346
$892$	−1.49649e13	−0.791465
$893$	2.00814e12	0.105673
$894$	−1.70627e13	−0.893365
$895$	−2.18748e13	−1.13957
$896$	9.36146e11	0.0485241
$897$	−5.58410e12	−0.287997
$898$	−1.29192e13	−0.662967
$899$	9.25179e12	0.472397
$900$	1.70253e9	8.64973e−5 0
$901$	3.56904e12	0.180422
$902$	1.71928e13	0.864801
$903$	−5.51165e12	−0.275859
$904$	9.45303e12	0.470775
$905$	1.37376e13	0.680757
$906$	3.91863e12	0.193222
$907$	1.87998e13	0.922400	0.461200	−	0.887296i	$-0.347419\pi$
$907$	1.87998e13	0.922400	0.461200	+	0.887296i	$0.347419\pi$
$908$	−1.23440e12	−0.0602656
$909$	1.67819e10	0.000815273 0
$910$	−4.80042e12	−0.232056
$911$	−1.56523e12	−0.0752914	−0.0376457	−	0.999291i	$-0.511986\pi$
$911$	−1.56523e12	−0.0752914	−0.0376457	+	0.999291i	$0.511986\pi$
$912$	−1.19766e12	−0.0573267
$913$	−3.10249e12	−0.147772
$914$	3.35349e12	0.158942
$915$	−2.55733e13	−1.20613
$916$	−1.83253e12	−0.0860046
$917$	8.84813e12	0.413228
$918$	−2.23547e13	−1.03891
$919$	2.72891e13	1.26203	0.631014	−	0.775771i	$-0.282639\pi$
$919$	2.72891e13	1.26203	0.631014	+	0.775771i	$0.282639\pi$
$920$	3.02885e12	0.139390
$921$	−3.39286e13	−1.55381
$922$	−1.80516e13	−0.822673
$923$	2.90694e12	0.131834
$924$	−6.16695e12	−0.278321
$925$	−6.59320e12	−0.296114
$926$	1.56082e13	0.697595
$927$	−3.13524e10	−0.00139448
$928$	−2.74749e12	−0.121610
$929$	−3.27413e13	−1.44220	−0.721100	−	0.692831i	$-0.756363\pi$
$929$	−3.27413e13	−1.44220	−0.721100	+	0.692831i	$0.756363\pi$
$930$	1.00133e13	0.438939
$931$	−3.67395e12	−0.160273
$932$	1.15901e13	0.503169
$933$	2.45789e13	1.06193
$934$	8.25404e12	0.354900
$935$	−3.14864e13	−1.34732
$936$	−5.21464e9	−0.000222067 0
$937$	−2.41823e13	−1.02487	−0.512435	−	0.858726i	$-0.671256\pi$
$937$	−2.41823e13	−1.02487	−0.512435	+	0.858726i	$0.671256\pi$
$938$	1.48015e12	0.0624300
$939$	3.59632e13	1.50961
$940$	4.98596e12	0.208292
$941$	7.48541e12	0.311216	0.155608	−	0.987819i	$-0.450266\pi$
$941$	7.48541e12	0.311216	0.155608	+	0.987819i	$0.450266\pi$
$942$	2.39094e13	0.989328
$943$	−1.27622e13	−0.525562
$944$	1.90533e12	0.0780900
$945$	−1.21780e13	−0.496744
$946$	−8.88272e12	−0.360608
$947$	−4.31138e13	−1.74197	−0.870986	−	0.491307i	$-0.836519\pi$
$947$	−4.31138e13	−1.74197	−0.870986	+	0.491307i	$0.836519\pi$
$948$	3.18856e12	0.128220
$949$	−2.20970e13	−0.884374
$950$	7.41394e11	0.0295320
$951$	4.08096e12	0.161789
$952$	7.22388e12	0.285039
$953$	−9.69686e12	−0.380814	−0.190407	−	0.981705i	$-0.560981\pi$
$953$	−9.69686e12	−0.380814	−0.190407	+	0.981705i	$0.560981\pi$
$954$	2.11205e9	8.25537e−5 0
$955$	−6.74785e12	−0.262513
$956$	−1.80588e13	−0.699244
$957$	1.80994e13	0.697525
$958$	−3.02745e13	−1.16127
$959$	−1.40923e13	−0.538019
$960$	−2.97364e12	−0.112997
$961$	−1.39722e13	−0.528456
$962$	2.01942e13	0.760221
$963$	−5.76187e9	−0.000215896 0
$964$	2.00483e13	0.747708
$965$	3.48784e13	1.29474
$966$	4.57774e12	0.169143
$967$	2.84710e13	1.04709	0.523545	−	0.851998i	$-0.324609\pi$
$967$	2.84710e13	1.04709	0.523545	+	0.851998i	$0.324609\pi$
$968$	−2.80667e11	−0.0102743
$969$	−9.24187e12	−0.336746
$970$	−3.33337e13	−1.20896
$971$	3.67091e13	1.32522	0.662609	−	0.748965i	$-0.269449\pi$
$971$	3.67091e13	1.32522	0.662609	+	0.748965i	$0.269449\pi$
$972$	−2.64451e10	−0.000950271 0
$973$	6.50481e12	0.232663
$974$	−2.16406e13	−0.770467
$975$	−3.39375e12	−0.120271
$976$	9.45582e12	0.333561
$977$	−4.89209e13	−1.71778	−0.858892	−	0.512157i	$-0.828847\pi$
$977$	−4.89209e13	−1.71778	−0.858892	+	0.512157i	$0.828847\pi$
$978$	2.04476e13	0.714691
$979$	2.23799e12	0.0778638
$980$	−9.12195e12	−0.315915
$981$	3.35868e9	0.000115787 0
$982$	−1.47723e13	−0.506927
$983$	−1.06278e13	−0.363038	−0.181519	−	0.983387i	$-0.558101\pi$
$983$	−1.06278e13	−0.363038	−0.181519	+	0.983387i	$0.558101\pi$
$984$	1.25296e13	0.426049
$985$	−1.21472e13	−0.411162
$986$	−2.12013e13	−0.714360
$987$	7.53568e12	0.252753
$988$	−2.27081e12	−0.0758183
$989$	6.59366e12	0.219151
$990$	−1.86327e10	−0.000616477 0
$991$	−9.73679e12	−0.320689	−0.160345	−	0.987061i	$-0.551261\pi$
$991$	−9.73679e12	−0.320689	−0.160345	+	0.987061i	$0.551261\pi$
$992$	−3.70245e12	−0.121391
$993$	2.04291e13	0.666771
$994$	−2.38305e12	−0.0774275
$995$	3.65047e13	1.18072
$996$	−2.26101e12	−0.0728007
$997$	1.04996e13	0.336547	0.168273	−	0.985740i	$-0.446181\pi$
$997$	1.04996e13	0.336547	0.168273	+	0.985740i	$0.446181\pi$
$998$	−3.16985e13	−1.01147
$999$	5.12300e13	1.62735

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.a.d.1.1	✓	4
3.2	odd	2		342.10.a.l.1.2		4
4.3	odd	2		304.10.a.e.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.a.d.1.1	✓	4	1.1	even	1	trivial
304.10.a.e.1.4		4	4.3	odd	2
342.10.a.l.1.2		4	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)

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} -140.229 q^{3} +256.000 q^{4} +1263.95 q^{5} +2243.67 q^{6} -3487.42 q^{7} -4096.00 q^{8} -18.7042 q^{9} +O(q^{10})\)	\(q-16.0000 q^{2} -140.229 q^{3} +256.000 q^{4} +1263.95 q^{5} +2243.67 q^{6} -3487.42 q^{7} -4096.00 q^{8} -18.7042 q^{9} -20223.2 q^{10} -49259.2 q^{11} -35898.7 q^{12} -68065.3 q^{13} +55798.7 q^{14} -177243. q^{15} +65536.0 q^{16} +505716. q^{17} +299.267 q^{18} +130321. q^{19} +323571. q^{20} +489039. q^{21} +788147. q^{22} -585044. q^{23} +574380. q^{24} -355562. q^{25} +1.08905e6 q^{26} +2.76276e6 q^{27} -892779. q^{28} +2.62021e6 q^{29} +2.83588e6 q^{30} +3.53093e6 q^{31} -1.04858e6 q^{32} +6.90759e6 q^{33} -8.09145e6 q^{34} -4.40791e6 q^{35} -4788.27 q^{36} +1.85431e7 q^{37} -2.08514e6 q^{38} +9.54476e6 q^{39} -5.17713e6 q^{40} +2.18141e7 q^{41} -7.82462e6 q^{42} -1.12704e7 q^{43} -1.26104e7 q^{44} -23641.1 q^{45} +9.36070e6 q^{46} +1.54092e7 q^{47} -9.19008e6 q^{48} -2.81915e7 q^{49} +5.68899e6 q^{50} -7.09162e7 q^{51} -1.74247e7 q^{52} +7.05741e6 q^{53} -4.42041e7 q^{54} -6.22611e7 q^{55} +1.42845e7 q^{56} -1.82748e7 q^{57} -4.19234e7 q^{58} +2.90730e7 q^{59} -4.53741e7 q^{60} +1.44284e8 q^{61} -5.64949e7 q^{62} +65229.3 q^{63} +1.67772e7 q^{64} -8.60310e7 q^{65} -1.10521e8 q^{66} +2.65266e7 q^{67} +1.29463e8 q^{68} +8.20404e7 q^{69} +7.05266e7 q^{70} -4.27081e7 q^{71} +76612.3 q^{72} +3.24644e8 q^{73} -2.96689e8 q^{74} +4.98602e7 q^{75} +3.33622e7 q^{76} +1.71787e8 q^{77} -1.52716e8 q^{78} -8.88210e7 q^{79} +8.28341e7 q^{80} -3.87052e8 q^{81} -3.49026e8 q^{82} +6.29830e7 q^{83} +1.25194e8 q^{84} +6.39198e8 q^{85} +1.80326e8 q^{86} -3.67431e8 q^{87} +2.01766e8 q^{88} -4.54329e7 q^{89} +378258. q^{90} +2.37372e8 q^{91} -1.49771e8 q^{92} -4.95140e8 q^{93} -2.46547e8 q^{94} +1.64719e8 q^{95} +1.47041e8 q^{96} +1.64830e9 q^{97} +4.51064e8 q^{98} +921353. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 64 q^{2} + 84 q^{3} + 1024 q^{4} - 1395 q^{5} - 1344 q^{6} + 12307 q^{7} - 16384 q^{8} + 16538 q^{9}+O(q^{10}) \) 4 * q - 64 * q^2 + 84 * q^3 + 1024 * q^4 - 1395 * q^5 - 1344 * q^6 + 12307 * q^7 - 16384 * q^8 + 16538 * q^9	\( 4 q - 64 q^{2} + 84 q^{3} + 1024 q^{4} - 1395 q^{5} - 1344 q^{6} + 12307 q^{7} - 16384 q^{8} + 16538 q^{9} + 22320 q^{10} - 104249 q^{11} + 21504 q^{12} + 120486 q^{13} - 196912 q^{14} - 591090 q^{15} + 262144 q^{16} - 412139 q^{17} - 264608 q^{18} + 521284 q^{19} - 357120 q^{20} + 2437006 q^{21} + 1667984 q^{22} + 3010300 q^{23} - 344064 q^{24} + 9760585 q^{25} - 1927776 q^{26} + 12387978 q^{27} + 3150592 q^{28} + 6153240 q^{29} + 9457440 q^{30} + 12774024 q^{31} - 4194304 q^{32} - 3258022 q^{33} + 6594224 q^{34} + 9823425 q^{35} + 4233728 q^{36} + 20506048 q^{37} - 8340544 q^{38} + 69881444 q^{39} + 5713920 q^{40} + 11620300 q^{41} - 38992096 q^{42} + 7698327 q^{43} - 26687744 q^{44} - 124015815 q^{45} - 48164800 q^{46} - 31581083 q^{47} + 5505024 q^{48} + 18970383 q^{49} - 156169360 q^{50} - 8594812 q^{51} + 30844416 q^{52} + 72549422 q^{53} - 198207648 q^{54} + 21332505 q^{55} - 50409472 q^{56} + 10946964 q^{57} - 98451840 q^{58} - 149234120 q^{59} - 151319040 q^{60} + 129004373 q^{61} - 204384384 q^{62} + 102967551 q^{63} + 67108864 q^{64} + 124691700 q^{65} + 52128352 q^{66} + 132595266 q^{67} - 105507584 q^{68} - 45529972 q^{69} - 157174800 q^{70} - 47138482 q^{71} - 67739648 q^{72} - 39332795 q^{73} - 328096768 q^{74} + 824627010 q^{75} + 133448704 q^{76} - 165933719 q^{77} - 1118103104 q^{78} - 307010840 q^{79} - 91422720 q^{80} + 1305551744 q^{81} - 185924800 q^{82} - 746568232 q^{83} + 623873536 q^{84} - 105005985 q^{85} - 123173232 q^{86} - 82148208 q^{87} + 427003904 q^{88} + 286943482 q^{89} + 1984253040 q^{90} + 3155781114 q^{91} + 770636800 q^{92} + 1151901596 q^{93} + 505297328 q^{94} - 181797795 q^{95} - 88080384 q^{96} + 793519958 q^{97} - 303526128 q^{98} - 1681833809 q^{99}+O(q^{100}) \) 4 * q - 64 * q^2 + 84 * q^3 + 1024 * q^4 - 1395 * q^5 - 1344 * q^6 + 12307 * q^7 - 16384 * q^8 + 16538 * q^9 + 22320 * q^10 - 104249 * q^11 + 21504 * q^12 + 120486 * q^13 - 196912 * q^14 - 591090 * q^15 + 262144 * q^16 - 412139 * q^17 - 264608 * q^18 + 521284 * q^19 - 357120 * q^20 + 2437006 * q^21 + 1667984 * q^22 + 3010300 * q^23 - 344064 * q^24 + 9760585 * q^25 - 1927776 * q^26 + 12387978 * q^27 + 3150592 * q^28 + 6153240 * q^29 + 9457440 * q^30 + 12774024 * q^31 - 4194304 * q^32 - 3258022 * q^33 + 6594224 * q^34 + 9823425 * q^35 + 4233728 * q^36 + 20506048 * q^37 - 8340544 * q^38 + 69881444 * q^39 + 5713920 * q^40 + 11620300 * q^41 - 38992096 * q^42 + 7698327 * q^43 - 26687744 * q^44 - 124015815 * q^45 - 48164800 * q^46 - 31581083 * q^47 + 5505024 * q^48 + 18970383 * q^49 - 156169360 * q^50 - 8594812 * q^51 + 30844416 * q^52 + 72549422 * q^53 - 198207648 * q^54 + 21332505 * q^55 - 50409472 * q^56 + 10946964 * q^57 - 98451840 * q^58 - 149234120 * q^59 - 151319040 * q^60 + 129004373 * q^61 - 204384384 * q^62 + 102967551 * q^63 + 67108864 * q^64 + 124691700 * q^65 + 52128352 * q^66 + 132595266 * q^67 - 105507584 * q^68 - 45529972 * q^69 - 157174800 * q^70 - 47138482 * q^71 - 67739648 * q^72 - 39332795 * q^73 - 328096768 * q^74 + 824627010 * q^75 + 133448704 * q^76 - 165933719 * q^77 - 1118103104 * q^78 - 307010840 * q^79 - 91422720 * q^80 + 1305551744 * q^81 - 185924800 * q^82 - 746568232 * q^83 + 623873536 * q^84 - 105005985 * q^85 - 123173232 * q^86 - 82148208 * q^87 + 427003904 * q^88 + 286943482 * q^89 + 1984253040 * q^90 + 3155781114 * q^91 + 770636800 * q^92 + 1151901596 * q^93 + 505297328 * q^94 - 181797795 * q^95 - 88080384 * q^96 + 793519958 * q^97 - 303526128 * q^98 - 1681833809 * q^99

Introduction

L-functions

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