LMFDB - Embedded newform 10.12.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,12,Mod(1,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	10.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:	$7.68343180560$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{1969}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 492 $ x^2 - x - 492
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-21.6867$ of defining polynomial
Character	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+32.0000 q^{2} +745.734 q^{3} +1024.00 q^{4} +3125.00 q^{5} +23863.5 q^{6} -71494.9 q^{7} +32768.0 q^{8} +378972. q^{9} +O(q^{10})$	\(q+32.0000 q^{2} +745.734 q^{3} +1024.00 q^{4} +3125.00 q^{5} +23863.5 q^{6} -71494.9 q^{7} +32768.0 q^{8} +378972. q^{9} +100000. q^{10} -345651. q^{11} +763632. q^{12} +1.50956e6 q^{13} -2.28784e6 q^{14} +2.33042e6 q^{15} +1.04858e6 q^{16} -5.39291e6 q^{17} +1.21271e7 q^{18} -1.11633e7 q^{19} +3.20000e6 q^{20} -5.33162e7 q^{21} -1.10608e7 q^{22} -5.27646e6 q^{23} +2.44362e7 q^{24} +9.76562e6 q^{25} +4.83060e7 q^{26} +1.50508e8 q^{27} -7.32108e7 q^{28} -1.86291e7 q^{29} +7.45734e7 q^{30} +7.10448e7 q^{31} +3.35544e7 q^{32} -2.57763e8 q^{33} -1.72573e8 q^{34} -2.23422e8 q^{35} +3.88068e8 q^{36} +3.23164e8 q^{37} -3.57225e8 q^{38} +1.12573e9 q^{39} +1.02400e8 q^{40} -9.11277e8 q^{41} -1.70612e9 q^{42} -1.16431e9 q^{43} -3.53946e8 q^{44} +1.18429e9 q^{45} -1.68847e8 q^{46} +2.81949e8 q^{47} +7.81959e8 q^{48} +3.13420e9 q^{49} +3.12500e8 q^{50} -4.02168e9 q^{51} +1.54579e9 q^{52} +4.05957e9 q^{53} +4.81626e9 q^{54} -1.08016e9 q^{55} -2.34275e9 q^{56} -8.32485e9 q^{57} -5.96132e8 q^{58} +4.89828e9 q^{59} +2.38635e9 q^{60} +1.07565e10 q^{61} +2.27343e9 q^{62} -2.70946e10 q^{63} +1.07374e9 q^{64} +4.71739e9 q^{65} -8.24843e9 q^{66} +3.70812e9 q^{67} -5.52234e9 q^{68} -3.93484e9 q^{69} -7.14949e9 q^{70} +3.45274e9 q^{71} +1.24182e10 q^{72} -2.21136e10 q^{73} +1.03413e10 q^{74} +7.28256e9 q^{75} -1.14312e10 q^{76} +2.47123e10 q^{77} +3.60235e10 q^{78} +7.02672e9 q^{79} +3.27680e9 q^{80} +4.51052e10 q^{81} -2.91609e10 q^{82} +5.55656e10 q^{83} -5.45958e10 q^{84} -1.68528e10 q^{85} -3.72580e10 q^{86} -1.38924e10 q^{87} -1.13263e10 q^{88} -9.29706e9 q^{89} +3.78972e10 q^{90} -1.07926e11 q^{91} -5.40310e9 q^{92} +5.29805e10 q^{93} +9.02235e9 q^{94} -3.48853e10 q^{95} +2.50227e10 q^{96} +4.71888e10 q^{97} +1.00294e11 q^{98} -1.30992e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 64 q^{2} + 604 q^{3} + 2048 q^{4} + 6250 q^{5} + 19328 q^{6} + 14092 q^{7} + 65536 q^{8} + 221914 q^{9}+O(q^{10}) $ 2 * q + 64 * q^2 + 604 * q^3 + 2048 * q^4 + 6250 * q^5 + 19328 * q^6 + 14092 * q^7 + 65536 * q^8 + 221914 * q^9	\( 2 q + 64 q^{2} + 604 q^{3} + 2048 q^{4} + 6250 q^{5} + 19328 q^{6} + 14092 q^{7} + 65536 q^{8} + 221914 q^{9} + 200000 q^{10} + 421584 q^{11} + 618496 q^{12} + 1730524 q^{13} + 450944 q^{14} + 1887500 q^{15} + 2097152 q^{16} - 6323628 q^{17} + 7101248 q^{18} - 28897400 q^{19} + 6400000 q^{20} - 65446816 q^{21} + 13490688 q^{22} - 45236076 q^{23} + 19791872 q^{24} + 19531250 q^{25} + 55376768 q^{26} + 197876440 q^{27} + 14430208 q^{28} + 58226220 q^{29} + 60400000 q^{30} + 41413384 q^{31} + 67108864 q^{32} - 366506832 q^{33} - 202356096 q^{34} + 44037500 q^{35} + 227239936 q^{36} + 377255452 q^{37} - 924716800 q^{38} + 1094415848 q^{39} + 204800000 q^{40} - 785271036 q^{41} - 2094298112 q^{42} - 1452987236 q^{43} + 431702016 q^{44} + 693481250 q^{45} - 1447554432 q^{46} - 1288127748 q^{47} + 633339904 q^{48} + 8481998946 q^{49} + 625000000 q^{50} - 3889762056 q^{51} + 1772056576 q^{52} - 30490836 q^{53} + 6332046080 q^{54} + 1317450000 q^{55} + 461766656 q^{56} - 5811319600 q^{57} + 1863239040 q^{58} + 8677102440 q^{59} + 1932800000 q^{60} + 1115498764 q^{61} + 1325228288 q^{62} - 40536764356 q^{63} + 2147483648 q^{64} + 5407887500 q^{65} - 11728218624 q^{66} - 12673769708 q^{67} - 6475395072 q^{68} + 1728802848 q^{69} + 1409200000 q^{70} + 13799832984 q^{71} + 7271677952 q^{72} - 17842079516 q^{73} + 12072174464 q^{74} + 5898437500 q^{75} - 29590937600 q^{76} + 90377541264 q^{77} + 35021307136 q^{78} - 12636930320 q^{79} + 6553600000 q^{80} + 66213933922 q^{81} - 25128673152 q^{82} + 41986488924 q^{83} - 67017539584 q^{84} - 19761337500 q^{85} - 46495591552 q^{86} - 24785411160 q^{87} + 13814464512 q^{88} + 13208740020 q^{89} + 22191400000 q^{90} - 89014903096 q^{91} - 46321741824 q^{92} + 57180301568 q^{93} - 41220087936 q^{94} - 90304375000 q^{95} + 20266876928 q^{96} - 61787462828 q^{97} + 271423966272 q^{98} - 251492724912 q^{99}+O(q^{100}) \) 2 * q + 64 * q^2 + 604 * q^3 + 2048 * q^4 + 6250 * q^5 + 19328 * q^6 + 14092 * q^7 + 65536 * q^8 + 221914 * q^9 + 200000 * q^10 + 421584 * q^11 + 618496 * q^12 + 1730524 * q^13 + 450944 * q^14 + 1887500 * q^15 + 2097152 * q^16 - 6323628 * q^17 + 7101248 * q^18 - 28897400 * q^19 + 6400000 * q^20 - 65446816 * q^21 + 13490688 * q^22 - 45236076 * q^23 + 19791872 * q^24 + 19531250 * q^25 + 55376768 * q^26 + 197876440 * q^27 + 14430208 * q^28 + 58226220 * q^29 + 60400000 * q^30 + 41413384 * q^31 + 67108864 * q^32 - 366506832 * q^33 - 202356096 * q^34 + 44037500 * q^35 + 227239936 * q^36 + 377255452 * q^37 - 924716800 * q^38 + 1094415848 * q^39 + 204800000 * q^40 - 785271036 * q^41 - 2094298112 * q^42 - 1452987236 * q^43 + 431702016 * q^44 + 693481250 * q^45 - 1447554432 * q^46 - 1288127748 * q^47 + 633339904 * q^48 + 8481998946 * q^49 + 625000000 * q^50 - 3889762056 * q^51 + 1772056576 * q^52 - 30490836 * q^53 + 6332046080 * q^54 + 1317450000 * q^55 + 461766656 * q^56 - 5811319600 * q^57 + 1863239040 * q^58 + 8677102440 * q^59 + 1932800000 * q^60 + 1115498764 * q^61 + 1325228288 * q^62 - 40536764356 * q^63 + 2147483648 * q^64 + 5407887500 * q^65 - 11728218624 * q^66 - 12673769708 * q^67 - 6475395072 * q^68 + 1728802848 * q^69 + 1409200000 * q^70 + 13799832984 * q^71 + 7271677952 * q^72 - 17842079516 * q^73 + 12072174464 * q^74 + 5898437500 * q^75 - 29590937600 * q^76 + 90377541264 * q^77 + 35021307136 * q^78 - 12636930320 * q^79 + 6553600000 * q^80 + 66213933922 * q^81 - 25128673152 * q^82 + 41986488924 * q^83 - 67017539584 * q^84 - 19761337500 * q^85 - 46495591552 * q^86 - 24785411160 * q^87 + 13814464512 * q^88 + 13208740020 * q^89 + 22191400000 * q^90 - 89014903096 * q^91 - 46321741824 * q^92 + 57180301568 * q^93 - 41220087936 * q^94 - 90304375000 * q^95 + 20266876928 * q^96 - 61787462828 * q^97 + 271423966272 * q^98 - 251492724912 * 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 $

$2$	32.0000	0.707107
$2$	32.0000	0.707107
$3$	745.734	1.77181	0.885905	−	0.463867i	$-0.153538\pi$
$3$	745.734	1.77181	0.885905	+	0.463867i	$0.153538\pi$
$4$	1024.00	0.500000
$5$	3125.00	0.447214
$5$	3125.00	0.447214
$6$	23863.5	1.25286
$7$	−71494.9	−1.60782	−0.803908	−	0.594754i	$-0.797249\pi$
$7$	−71494.9	−1.60782	−0.803908	+	0.594754i	$0.797249\pi$
$8$	32768.0	0.353553
$9$	378972.	2.13931
$10$	100000.	0.316228
$11$	−345651.	−0.647109	−0.323555	−	0.946209i	$-0.604878\pi$
$11$	−345651.	−0.647109	−0.323555	+	0.946209i	$0.604878\pi$
$12$	763632.	0.885905
$13$	1.50956e6	1.12762	0.563810	−	0.825904i	$-0.309335\pi$
$13$	1.50956e6	1.12762	0.563810	+	0.825904i	$0.309335\pi$
$14$	−2.28784e6	−1.13690
$15$	2.33042e6	0.792377
$16$	1.04858e6	0.250000
$17$	−5.39291e6	−0.921200	−0.460600	−	0.887608i	$-0.652366\pi$
$17$	−5.39291e6	−0.921200	−0.460600	+	0.887608i	$0.652366\pi$
$18$	1.21271e7	1.51272
$19$	−1.11633e7	−1.03430	−0.517151	−	0.855894i	$-0.673007\pi$
$19$	−1.11633e7	−1.03430	−0.517151	+	0.855894i	$0.673007\pi$
$20$	3.20000e6	0.223607
$21$	−5.33162e7	−2.84874
$22$	−1.10608e7	−0.457575
$23$	−5.27646e6	−0.170938	−0.0854692	−	0.996341i	$-0.527239\pi$
$23$	−5.27646e6	−0.170938	−0.0854692	+	0.996341i	$0.527239\pi$
$24$	2.44362e7	0.626429
$25$	9.76562e6	0.200000
$26$	4.83060e7	0.797348
$27$	1.50508e8	2.01864
$28$	−7.32108e7	−0.803908
$29$	−1.86291e7	−0.168657	−0.0843284	−	0.996438i	$-0.526874\pi$
$29$	−1.86291e7	−0.168657	−0.0843284	+	0.996438i	$0.526874\pi$
$30$	7.45734e7	0.560295
$31$	7.10448e7	0.445700	0.222850	−	0.974853i	$-0.428464\pi$
$31$	7.10448e7	0.445700	0.222850	+	0.974853i	$0.428464\pi$
$32$	3.35544e7	0.176777
$33$	−2.57763e8	−1.14655
$34$	−1.72573e8	−0.651387
$35$	−2.23422e8	−0.719037
$36$	3.88068e8	1.06966
$37$	3.23164e8	0.766150	0.383075	−	0.923717i	$-0.374865\pi$
$37$	3.23164e8	0.766150	0.383075	+	0.923717i	$0.374865\pi$
$38$	−3.57225e8	−0.731362
$39$	1.12573e9	1.99793
$40$	1.02400e8	0.158114
$41$	−9.11277e8	−1.22840	−0.614199	−	0.789151i	$-0.710521\pi$
$41$	−9.11277e8	−1.22840	−0.614199	+	0.789151i	$0.710521\pi$
$42$	−1.70612e9	−2.01437
$43$	−1.16431e9	−1.20779	−0.603897	−	0.797063i	$-0.706386\pi$
$43$	−1.16431e9	−1.20779	−0.603897	+	0.797063i	$0.706386\pi$
$44$	−3.53946e8	−0.323555
$45$	1.18429e9	0.956729
$46$	−1.68847e8	−0.120872
$47$	2.81949e8	0.179321	0.0896606	−	0.995972i	$-0.471422\pi$
$47$	2.81949e8	0.179321	0.0896606	+	0.995972i	$0.471422\pi$
$48$	7.81959e8	0.442952
$49$	3.13420e9	1.58507
$50$	3.12500e8	0.141421
$51$	−4.02168e9	−1.63219
$52$	1.54579e9	0.563810
$53$	4.05957e9	1.33341	0.666704	−	0.745323i	$-0.267705\pi$
$53$	4.05957e9	1.33341	0.666704	+	0.745323i	$0.267705\pi$
$54$	4.81626e9	1.42740
$55$	−1.08016e9	−0.289396
$56$	−2.34275e9	−0.568449
$57$	−8.32485e9	−1.83259
$58$	−5.96132e8	−0.119258
$59$	4.89828e9	0.891986	0.445993	−	0.895036i	$-0.352851\pi$
$59$	4.89828e9	0.891986	0.445993	+	0.895036i	$0.352851\pi$
$60$	2.38635e9	0.396189
$61$	1.07565e10	1.63064	0.815320	−	0.579011i	$-0.196561\pi$
$61$	1.07565e10	1.63064	0.815320	+	0.579011i	$0.196561\pi$
$62$	2.27343e9	0.315158
$63$	−2.70946e10	−3.43962
$64$	1.07374e9	0.125000
$65$	4.71739e9	0.504287
$66$	−8.24843e9	−0.810736
$67$	3.70812e9	0.335539	0.167769	−	0.985826i	$-0.446344\pi$
$67$	3.70812e9	0.335539	0.167769	+	0.985826i	$0.446344\pi$
$68$	−5.52234e9	−0.460600
$69$	−3.93484e9	−0.302870
$70$	−7.14949e9	−0.508436
$71$	3.45274e9	0.227113	0.113557	−	0.993532i	$-0.463776\pi$
$71$	3.45274e9	0.227113	0.113557	+	0.993532i	$0.463776\pi$
$72$	1.24182e10	0.756360
$73$	−2.21136e10	−1.24848	−0.624242	−	0.781231i	$-0.714592\pi$
$73$	−2.21136e10	−1.24848	−0.624242	+	0.781231i	$0.714592\pi$
$74$	1.03413e10	0.541750
$75$	7.28256e9	0.354362
$76$	−1.14312e10	−0.517151
$77$	2.47123e10	1.04043
$78$	3.60235e10	1.41275
$79$	7.02672e9	0.256923	0.128462	−	0.991714i	$-0.458996\pi$
$79$	7.02672e9	0.256923	0.128462	+	0.991714i	$0.458996\pi$
$80$	3.27680e9	0.111803
$81$	4.51052e10	1.43734
$82$	−2.91609e10	−0.868609
$83$	5.55656e10	1.54838	0.774188	−	0.632956i	$-0.218159\pi$
$83$	5.55656e10	1.54838	0.774188	+	0.632956i	$0.218159\pi$
$84$	−5.45958e10	−1.42437
$85$	−1.68528e10	−0.411973
$86$	−3.72580e10	−0.854039
$87$	−1.38924e10	−0.298828
$88$	−1.13263e10	−0.228788
$89$	−9.29706e9	−0.176482	−0.0882410	−	0.996099i	$-0.528125\pi$
$89$	−9.29706e9	−0.176482	−0.0882410	+	0.996099i	$0.528125\pi$
$90$	3.78972e10	0.676509
$91$	−1.07926e11	−1.81301
$92$	−5.40310e9	−0.0854692
$93$	5.29805e10	0.789696
$94$	9.02235e9	0.126799
$95$	−3.48853e10	−0.462554
$96$	2.50227e10	0.313215
$97$	4.71888e10	0.557949	0.278975	−	0.960298i	$-0.410005\pi$
$97$	4.71888e10	0.557949	0.278975	+	0.960298i	$0.410005\pi$
$98$	1.00294e11	1.12081
$99$	−1.30992e11	−1.38437
$100$	1.00000e10	0.100000
$101$	1.61228e11	1.52642	0.763209	−	0.646151i	$-0.223622\pi$
$101$	1.61228e11	1.52642	0.763209	+	0.646151i	$0.223622\pi$
$102$	−1.28694e11	−1.15413
$103$	−1.85579e11	−1.57733	−0.788666	−	0.614822i	$-0.789228\pi$
$103$	−1.85579e11	−1.57733	−0.788666	+	0.614822i	$0.789228\pi$
$104$	4.94654e10	0.398674
$105$	−1.66613e11	−1.27400
$106$	1.29906e11	0.942861
$107$	−5.45807e10	−0.376208	−0.188104	−	0.982149i	$-0.560234\pi$
$107$	−5.45807e10	−0.376208	−0.188104	+	0.982149i	$0.560234\pi$
$108$	1.54120e11	1.00932
$109$	−3.54035e10	−0.220394	−0.110197	−	0.993910i	$-0.535148\pi$
$109$	−3.54035e10	−0.220394	−0.110197	+	0.993910i	$0.535148\pi$
$110$	−3.45651e10	−0.204634
$111$	2.40995e11	1.35747
$112$	−7.49679e10	−0.401954
$113$	1.20314e11	0.614308	0.307154	−	0.951660i	$-0.400623\pi$
$113$	1.20314e11	0.614308	0.307154	+	0.951660i	$0.400623\pi$
$114$	−2.66395e11	−1.29583
$115$	−1.64889e10	−0.0764460
$116$	−1.90762e10	−0.0843284
$117$	5.72083e11	2.41233
$118$	1.56745e11	0.630729
$119$	3.85566e11	1.48112
$120$	7.63632e10	0.280148
$121$	−1.65837e11	−0.581250
$122$	3.44209e11	1.15304
$123$	−6.79571e11	−2.17649
$124$	7.27499e10	0.222850
$125$	3.05176e10	0.0894427
$126$	−8.67028e11	−2.43218
$127$	−5.60687e11	−1.50591	−0.752957	−	0.658070i	$-0.771373\pi$
$127$	−5.60687e11	−1.50591	−0.752957	+	0.658070i	$0.771373\pi$
$128$	3.43597e10	0.0883883
$129$	−8.68267e11	−2.13998
$130$	1.50956e11	0.356585
$131$	4.11999e11	0.933048	0.466524	−	0.884508i	$-0.345506\pi$
$131$	4.11999e11	0.933048	0.466524	+	0.884508i	$0.345506\pi$
$132$	−2.63950e11	−0.573277
$133$	7.98119e11	1.66297
$134$	1.18660e11	0.237262
$135$	4.70338e11	0.902764
$136$	−1.76715e11	−0.325693
$137$	−7.86259e11	−1.39188	−0.695941	−	0.718099i	$-0.745013\pi$
$137$	−7.86259e11	−1.39188	−0.695941	+	0.718099i	$0.745013\pi$
$138$	−1.25915e11	−0.214162
$139$	8.57152e11	1.40112	0.700562	−	0.713592i	$-0.252933\pi$
$139$	8.57152e11	1.40112	0.700562	+	0.713592i	$0.252933\pi$
$140$	−2.28784e11	−0.359518
$141$	2.10259e11	0.317723
$142$	1.10488e11	0.160593
$143$	−5.21782e11	−0.729694
$144$	3.97381e11	0.534828
$145$	−5.82160e10	−0.0754256
$146$	−7.07634e11	−0.882812
$147$	2.33728e12	2.80844
$148$	3.30920e11	0.383075
$149$	−2.38606e11	−0.266168	−0.133084	−	0.991105i	$-0.542488\pi$
$149$	−2.38606e11	−0.266168	−0.133084	+	0.991105i	$0.542488\pi$
$150$	2.33042e11	0.250572
$151$	−9.57309e10	−0.0992382	−0.0496191	−	0.998768i	$-0.515801\pi$
$151$	−9.57309e10	−0.0992382	−0.0496191	+	0.998768i	$0.515801\pi$
$152$	−3.65799e11	−0.365681
$153$	−2.04376e12	−1.97073
$154$	7.90793e11	0.735697
$155$	2.22015e11	0.199323
$156$	1.15275e12	0.998965
$157$	−1.79935e12	−1.50545	−0.752727	−	0.658333i	$-0.771262\pi$
$157$	−1.79935e12	−1.50545	−0.752727	+	0.658333i	$0.771262\pi$
$158$	2.24855e11	0.181672
$159$	3.02736e12	2.36254
$160$	1.04858e11	0.0790569
$161$	3.77240e11	0.274837
$162$	1.44337e12	1.01635
$163$	−2.50619e12	−1.70601	−0.853005	−	0.521903i	$-0.825222\pi$
$163$	−2.50619e12	−1.70601	−0.853005	+	0.521903i	$0.825222\pi$
$164$	−9.33148e11	−0.614199
$165$	−8.05511e11	−0.512755
$166$	1.77810e12	1.09487
$167$	−2.69855e12	−1.60764	−0.803822	−	0.594871i	$-0.797203\pi$
$167$	−2.69855e12	−1.60764	−0.803822	+	0.594871i	$0.797203\pi$
$168$	−1.74707e12	−1.00718
$169$	4.86623e11	0.271529
$170$	−5.39291e11	−0.291309
$171$	−4.23058e12	−2.21269
$172$	−1.19225e12	−0.603897
$173$	3.07796e12	1.51011	0.755057	−	0.655659i	$-0.227609\pi$
$173$	3.07796e12	1.51011	0.755057	+	0.655659i	$0.227609\pi$
$174$	−4.44556e11	−0.211303
$175$	−6.98193e11	−0.321563
$176$	−3.62441e11	−0.161777
$177$	3.65282e12	1.58043
$178$	−2.97506e11	−0.124792
$179$	3.51154e11	0.142826	0.0714128	−	0.997447i	$-0.477249\pi$
$179$	3.51154e11	0.142826	0.0714128	+	0.997447i	$0.477249\pi$
$180$	1.21271e12	0.478364
$181$	6.34106e11	0.242622	0.121311	−	0.992615i	$-0.461290\pi$
$181$	6.34106e11	0.242622	0.121311	+	0.992615i	$0.461290\pi$
$182$	−3.45364e12	−1.28199
$183$	8.02151e12	2.88918
$184$	−1.72899e11	−0.0604359
$185$	1.00989e12	0.342633
$186$	1.69538e12	0.558399
$187$	1.86406e12	0.596117
$188$	2.88715e11	0.0896606
$189$	−1.07606e13	−3.24560
$190$	−1.11633e12	−0.327075
$191$	−2.61584e12	−0.744609	−0.372304	−	0.928111i	$-0.621432\pi$
$191$	−2.61584e12	−0.744609	−0.372304	+	0.928111i	$0.621432\pi$
$192$	8.00726e11	0.221476
$193$	1.59819e12	0.429598	0.214799	−	0.976658i	$-0.431090\pi$
$193$	1.59819e12	0.429598	0.214799	+	0.976658i	$0.431090\pi$
$194$	1.51004e12	0.394530
$195$	3.51792e12	0.893501
$196$	3.20942e12	0.792535
$197$	−6.16281e10	−0.0147984	−0.00739920	−	0.999973i	$-0.502355\pi$
$197$	−6.16281e10	−0.0147984	−0.00739920	+	0.999973i	$0.502355\pi$
$198$	−4.19175e12	−0.978896
$199$	2.36544e12	0.537303	0.268652	−	0.963237i	$-0.413422\pi$
$199$	2.36544e12	0.537303	0.268652	+	0.963237i	$0.413422\pi$
$200$	3.20000e11	0.0707107
$201$	2.76527e12	0.594510
$202$	5.15931e12	1.07934
$203$	1.33189e12	0.271169
$204$	−4.11820e12	−0.816096
$205$	−2.84774e12	−0.549357
$206$	−5.93851e12	−1.11534
$207$	−1.99963e12	−0.365690
$208$	1.58289e12	0.281905
$209$	3.85860e12	0.669307
$210$	−5.33162e12	−0.900852
$211$	5.39734e12	0.888436	0.444218	−	0.895919i	$-0.353482\pi$
$211$	5.39734e12	0.888436	0.444218	+	0.895919i	$0.353482\pi$
$212$	4.15700e12	0.666704
$213$	2.57482e12	0.402402
$214$	−1.74658e12	−0.266020
$215$	−3.63847e12	−0.540142
$216$	4.93185e12	0.713698
$217$	−5.07934e12	−0.716604
$218$	−1.13291e12	−0.155842
$219$	−1.64908e13	−2.21208
$220$	−1.10608e12	−0.144698
$221$	−8.14094e12	−1.03876
$222$	7.71183e12	0.959878
$223$	−9.37124e12	−1.13794	−0.568971	−	0.822357i	$-0.692658\pi$
$223$	−9.37124e12	−1.13794	−0.568971	+	0.822357i	$0.692658\pi$
$224$	−2.39897e12	−0.284224
$225$	3.70090e12	0.427862
$226$	3.85006e12	0.434382
$227$	−6.51561e12	−0.717485	−0.358742	−	0.933437i	$-0.616794\pi$
$227$	−6.51561e12	−0.717485	−0.358742	+	0.933437i	$0.616794\pi$
$228$	−8.52464e12	−0.916294
$229$	−1.74808e12	−0.183429	−0.0917144	−	0.995785i	$-0.529235\pi$
$229$	−1.74808e12	−0.183429	−0.0917144	+	0.995785i	$0.529235\pi$
$230$	−5.27646e11	−0.0540555
$231$	1.84288e13	1.84345
$232$	−6.10440e11	−0.0596292
$233$	8.64493e12	0.824715	0.412358	−	0.911022i	$-0.364705\pi$
$233$	8.64493e12	0.824715	0.412358	+	0.911022i	$0.364705\pi$
$234$	1.83067e13	1.70578
$235$	8.81089e11	0.0801949
$236$	5.01584e12	0.445993
$237$	5.24006e12	0.455219
$238$	1.23381e13	1.04731
$239$	6.71025e12	0.556609	0.278304	−	0.960493i	$-0.410228\pi$
$239$	6.71025e12	0.556609	0.278304	+	0.960493i	$0.410228\pi$
$240$	2.44362e12	0.198094
$241$	−1.20329e13	−0.953404	−0.476702	−	0.879065i	$-0.658168\pi$
$241$	−1.20329e13	−0.953404	−0.476702	+	0.879065i	$0.658168\pi$
$242$	−5.30679e12	−0.411006
$243$	6.97444e12	0.528050
$244$	1.10147e13	0.815320
$245$	9.79438e12	0.708865
$246$	−2.17463e13	−1.53901
$247$	−1.68517e13	−1.16630
$248$	2.32800e12	0.157579
$249$	4.14371e13	2.74343
$250$	9.76562e11	0.0632456
$251$	−2.23212e13	−1.41420	−0.707101	−	0.707113i	$-0.749997\pi$
$251$	−2.23212e13	−1.41420	−0.707101	+	0.707113i	$0.749997\pi$
$252$	−2.77449e13	−1.71981
$253$	1.82381e12	0.110616
$254$	−1.79420e13	−1.06484
$255$	−1.25677e13	−0.729938
$256$	1.09951e12	0.0625000
$257$	1.80055e13	1.00178	0.500890	−	0.865511i	$-0.333006\pi$
$257$	1.80055e13	1.00178	0.500890	+	0.865511i	$0.333006\pi$
$258$	−2.77845e13	−1.51319
$259$	−2.31046e13	−1.23183
$260$	4.83060e12	0.252144
$261$	−7.05993e12	−0.360809
$262$	1.31840e13	0.659765
$263$	1.38894e13	0.680653	0.340326	−	0.940307i	$-0.389462\pi$
$263$	1.38894e13	0.680653	0.340326	+	0.940307i	$0.389462\pi$
$264$	−8.44639e12	−0.405368
$265$	1.26862e13	0.596318
$266$	2.55398e13	1.17590
$267$	−6.93313e12	−0.312693
$268$	3.79711e12	0.167769
$269$	2.71611e13	1.17574	0.587868	−	0.808957i	$-0.299967\pi$
$269$	2.71611e13	1.17574	0.587868	+	0.808957i	$0.299967\pi$
$270$	1.50508e13	0.638351
$271$	−7.24542e12	−0.301115	−0.150558	−	0.988601i	$-0.548107\pi$
$271$	−7.24542e12	−0.301115	−0.150558	+	0.988601i	$0.548107\pi$
$272$	−5.65488e12	−0.230300
$273$	−8.04842e13	−3.21230
$274$	−2.51603e13	−0.984209
$275$	−3.37549e12	−0.129422
$276$	−4.02928e12	−0.151435
$277$	3.97300e13	1.46380	0.731898	−	0.681415i	$-0.238635\pi$
$277$	3.97300e13	1.46380	0.731898	+	0.681415i	$0.238635\pi$
$278$	2.74289e13	0.990744
$279$	2.69240e13	0.953491
$280$	−7.32108e12	−0.254218
$281$	5.95255e12	0.202683	0.101342	−	0.994852i	$-0.467686\pi$
$281$	5.95255e12	0.202683	0.101342	+	0.994852i	$0.467686\pi$
$282$	6.72828e12	0.224664
$283$	−3.85782e13	−1.26333	−0.631665	−	0.775241i	$-0.717628\pi$
$283$	−3.85782e13	−1.26333	−0.631665	+	0.775241i	$0.717628\pi$
$284$	3.53560e12	0.113557
$285$	−2.60152e13	−0.819558
$286$	−1.66970e13	−0.515971
$287$	6.51517e13	1.97504
$288$	1.27162e13	0.378180
$289$	−5.18843e12	−0.151390
$290$	−1.86291e12	−0.0533339
$291$	3.51903e13	0.988580
$292$	−2.26443e13	−0.624242
$293$	−5.32529e13	−1.44069	−0.720346	−	0.693615i	$-0.756017\pi$
$293$	−5.32529e13	−1.44069	−0.720346	+	0.693615i	$0.756017\pi$
$294$	7.47930e13	1.98587
$295$	1.53071e13	0.398908
$296$	1.05895e13	0.270875
$297$	−5.20232e13	−1.30628
$298$	−7.63539e12	−0.188210
$299$	−7.96516e12	−0.192754
$300$	7.45734e12	0.177181
$301$	8.32424e13	1.94191
$302$	−3.06339e12	−0.0701720
$303$	1.20233e14	2.70452
$304$	−1.17056e13	−0.258576
$305$	3.36142e13	0.729244
$306$	−6.54004e13	−1.39352
$307$	−5.74336e13	−1.20200	−0.601001	−	0.799249i	$-0.705231\pi$
$307$	−5.74336e13	−1.20200	−0.601001	+	0.799249i	$0.705231\pi$
$308$	2.53054e13	0.520216
$309$	−1.38392e14	−2.79473
$310$	7.10448e12	0.140943
$311$	−2.58616e13	−0.504050	−0.252025	−	0.967721i	$-0.581097\pi$
$311$	−2.58616e13	−0.504050	−0.252025	+	0.967721i	$0.581097\pi$
$312$	3.68880e13	0.706375
$313$	−3.57307e13	−0.672277	−0.336138	−	0.941813i	$-0.609121\pi$
$313$	−3.57307e13	−0.672277	−0.336138	+	0.941813i	$0.609121\pi$
$314$	−5.75792e13	−1.06452
$315$	−8.46707e13	−1.53824
$316$	7.19536e12	0.128462
$317$	−1.78631e13	−0.313422	−0.156711	−	0.987644i	$-0.550089\pi$
$317$	−1.78631e13	−0.313422	−0.156711	+	0.987644i	$0.550089\pi$
$318$	9.68755e13	1.67057
$319$	6.43917e12	0.109139
$320$	3.35544e12	0.0559017
$321$	−4.07027e13	−0.666570
$322$	1.20717e13	0.194339
$323$	6.02026e13	0.952800
$324$	4.61877e13	0.718669
$325$	1.47418e13	0.225524
$326$	−8.01980e13	−1.20633
$327$	−2.64016e13	−0.390496
$328$	−2.98607e13	−0.434305
$329$	−2.01579e13	−0.288315
$330$	−2.57763e13	−0.362572
$331$	7.78278e13	1.07667	0.538333	−	0.842732i	$-0.319054\pi$
$331$	7.78278e13	1.07667	0.538333	+	0.842732i	$0.319054\pi$
$332$	5.68992e13	0.774188
$333$	1.22470e14	1.63903
$334$	−8.63535e13	−1.13678
$335$	1.15879e13	0.150057
$336$	−5.59061e13	−0.712186
$337$	4.95598e12	0.0621105	0.0310552	−	0.999518i	$-0.490113\pi$
$337$	4.95598e12	0.0621105	0.0310552	+	0.999518i	$0.490113\pi$
$338$	1.55719e13	0.192000
$339$	8.97226e13	1.08844
$340$	−1.72573e13	−0.205987
$341$	−2.45567e13	−0.288417
$342$	−1.35379e14	−1.56461
$343$	−8.27106e13	−0.940684
$344$	−3.81522e13	−0.427019
$345$	−1.22964e13	−0.135448
$346$	9.84948e13	1.06781
$347$	−6.55706e13	−0.699676	−0.349838	−	0.936810i	$-0.613763\pi$
$347$	−6.55706e13	−0.699676	−0.349838	+	0.936810i	$0.613763\pi$
$348$	−1.42258e13	−0.149414
$349$	1.14750e14	1.18635	0.593177	−	0.805072i	$-0.297873\pi$
$349$	1.14750e14	1.18635	0.593177	+	0.805072i	$0.297873\pi$
$350$	−2.23422e13	−0.227379
$351$	2.27202e14	2.27626
$352$	−1.15981e13	−0.114394
$353$	−5.10272e13	−0.495497	−0.247749	−	0.968824i	$-0.579691\pi$
$353$	−5.10272e13	−0.495497	−0.247749	+	0.968824i	$0.579691\pi$
$354$	1.16890e14	1.11753
$355$	1.07898e13	0.101568
$356$	−9.52019e12	−0.0882410
$357$	2.87530e14	2.62426
$358$	1.12369e13	0.100993
$359$	−1.16657e14	−1.03251	−0.516253	−	0.856436i	$-0.672674\pi$
$359$	−1.16657e14	−1.03251	−0.516253	+	0.856436i	$0.672674\pi$
$360$	3.88068e13	0.338255
$361$	8.12884e12	0.0697813
$362$	2.02914e13	0.171559
$363$	−1.23671e14	−1.02986
$364$	−1.10516e14	−0.906503
$365$	−6.91049e13	−0.558339
$366$	2.56688e14	2.04296
$367$	1.44058e14	1.12947	0.564733	−	0.825274i	$-0.308979\pi$
$367$	1.44058e14	1.12947	0.564733	+	0.825274i	$0.308979\pi$
$368$	−5.53277e12	−0.0427346
$369$	−3.45349e14	−2.62793
$370$	3.23164e13	0.242278
$371$	−2.90239e14	−2.14387
$372$	5.42521e13	0.394848
$373$	6.90594e13	0.495250	0.247625	−	0.968856i	$-0.420350\pi$
$373$	6.90594e13	0.495250	0.247625	+	0.968856i	$0.420350\pi$
$374$	5.96500e13	0.421518
$375$	2.27580e13	0.158475
$376$	9.23889e12	0.0633996
$377$	−2.81219e13	−0.190181
$378$	−3.44338e14	−2.29499
$379$	2.28579e14	1.50149	0.750743	−	0.660595i	$-0.229696\pi$
$379$	2.28579e14	1.50149	0.750743	+	0.660595i	$0.229696\pi$
$380$	−3.57225e13	−0.231277
$381$	−4.18123e14	−2.66819
$382$	−8.37070e13	−0.526518
$383$	−7.16725e13	−0.444385	−0.222192	−	0.975003i	$-0.571321\pi$
$383$	−7.16725e13	−0.444385	−0.222192	+	0.975003i	$0.571321\pi$
$384$	2.56232e13	0.156607
$385$	7.72259e13	0.465295
$386$	5.11420e13	0.303772
$387$	−4.41242e14	−2.58385
$388$	4.83214e13	0.278975
$389$	5.31179e13	0.302356	0.151178	−	0.988507i	$-0.451693\pi$
$389$	5.31179e13	0.302356	0.151178	+	0.988507i	$0.451693\pi$
$390$	1.12573e14	0.631801
$391$	2.84555e13	0.157469
$392$	1.02701e14	0.560407
$393$	3.07242e14	1.65318
$394$	−1.97210e12	−0.0104641
$395$	2.19585e13	0.114900
$396$	−1.34136e14	−0.692184
$397$	9.39721e12	0.0478246	0.0239123	−	0.999714i	$-0.492388\pi$
$397$	9.39721e12	0.0478246	0.0239123	+	0.999714i	$0.492388\pi$
$398$	7.56940e13	0.379931
$399$	5.95185e14	2.94646
$400$	1.02400e13	0.0500000
$401$	2.20216e14	1.06061	0.530303	−	0.847808i	$-0.322078\pi$
$401$	2.20216e14	1.06061	0.530303	+	0.847808i	$0.322078\pi$
$402$	8.84887e13	0.420382
$403$	1.07247e14	0.502581
$404$	1.65098e14	0.763209
$405$	1.40954e14	0.642797
$406$	4.26204e13	0.191745
$407$	−1.11702e14	−0.495783
$408$	−1.31782e14	−0.577067
$409$	−3.05103e14	−1.31816	−0.659080	−	0.752072i	$-0.729054\pi$
$409$	−3.05103e14	−1.31816	−0.659080	+	0.752072i	$0.729054\pi$
$410$	−9.11277e13	−0.388454
$411$	−5.86340e14	−2.46615
$412$	−1.90032e14	−0.788666
$413$	−3.50203e14	−1.43415
$414$	−6.39883e13	−0.258582
$415$	1.73642e14	0.692455
$416$	5.06526e13	0.199337
$417$	6.39208e14	2.48253
$418$	1.23475e14	0.473271
$419$	4.21440e14	1.59426	0.797130	−	0.603808i	$-0.206351\pi$
$419$	4.21440e14	1.59426	0.797130	+	0.603808i	$0.206351\pi$
$420$	−1.70612e14	−0.636998
$421$	1.11120e12	0.00409487	0.00204744	−	0.999998i	$-0.499348\pi$
$421$	1.11120e12	0.00409487	0.00204744	+	0.999998i	$0.499348\pi$
$422$	1.72715e14	0.628219
$423$	1.06851e14	0.383624
$424$	1.33024e14	0.471431
$425$	−5.26651e13	−0.184240
$426$	8.23944e13	0.284541
$427$	−7.69037e14	−2.62177
$428$	−5.58907e13	−0.188104
$429$	−3.89110e14	−1.29288
$430$	−1.16431e14	−0.381938
$431$	2.29204e14	0.742332	0.371166	−	0.928567i	$-0.378958\pi$
$431$	2.29204e14	0.742332	0.371166	+	0.928567i	$0.378958\pi$
$432$	1.57819e14	0.504660
$433$	1.54032e14	0.486325	0.243162	−	0.969986i	$-0.421815\pi$
$433$	1.54032e14	0.486325	0.243162	+	0.969986i	$0.421815\pi$
$434$	−1.62539e14	−0.506715
$435$	−4.34137e13	−0.133640
$436$	−3.62531e13	−0.110197
$437$	5.89027e13	0.176802
$438$	−5.27707e14	−1.56417
$439$	−1.25797e14	−0.368227	−0.184114	−	0.982905i	$-0.558941\pi$
$439$	−1.25797e14	−0.368227	−0.184114	+	0.982905i	$0.558941\pi$
$440$	−3.53946e13	−0.102317
$441$	1.18778e15	3.39096
$442$	−2.60510e14	−0.734517
$443$	−1.34623e14	−0.374885	−0.187443	−	0.982276i	$-0.560020\pi$
$443$	−1.34623e14	−0.374885	−0.187443	+	0.982276i	$0.560020\pi$
$444$	2.46779e14	0.678736
$445$	−2.90533e13	−0.0789252
$446$	−2.99880e14	−0.804647
$447$	−1.77937e14	−0.471600
$448$	−7.67671e13	−0.200977
$449$	4.28972e14	1.10937	0.554683	−	0.832062i	$-0.312840\pi$
$449$	4.28972e14	1.10937	0.554683	+	0.832062i	$0.312840\pi$
$450$	1.18429e14	0.302544
$451$	3.14984e14	0.794908
$452$	1.23202e14	0.307154
$453$	−7.13898e13	−0.175831
$454$	−2.08499e14	−0.507338
$455$	−3.37269e14	−0.810801
$456$	−2.72789e14	−0.647917
$457$	−7.89196e14	−1.85202	−0.926011	−	0.377497i	$-0.876785\pi$
$457$	−7.89196e14	−1.85202	−0.926011	+	0.377497i	$0.876785\pi$
$458$	−5.59387e13	−0.129704
$459$	−8.11677e14	−1.85957
$460$	−1.68847e13	−0.0382230
$461$	−6.01739e14	−1.34602	−0.673012	−	0.739632i	$-0.735000\pi$
$461$	−6.01739e14	−1.34602	−0.673012	+	0.739632i	$0.735000\pi$
$462$	5.89721e14	1.30351
$463$	2.36873e14	0.517393	0.258696	−	0.965959i	$-0.416707\pi$
$463$	2.36873e14	0.517393	0.258696	+	0.965959i	$0.416707\pi$
$464$	−1.95341e13	−0.0421642
$465$	1.65564e14	0.353163
$466$	2.76638e14	0.583162
$467$	8.17060e14	1.70220	0.851101	−	0.525002i	$-0.175936\pi$
$467$	8.17060e14	1.70220	0.851101	+	0.525002i	$0.175936\pi$
$468$	5.85813e14	1.20617
$469$	−2.65112e14	−0.539484
$470$	2.81949e13	0.0567063
$471$	−1.34184e15	−2.66738
$472$	1.60507e14	0.315365
$473$	4.02445e14	0.781574
$474$	1.67682e14	0.321889
$475$	−1.09017e14	−0.206860
$476$	3.94819e14	0.740560
$477$	1.53847e15	2.85257
$478$	2.14728e14	0.393582
$479$	2.80917e14	0.509018	0.254509	−	0.967070i	$-0.418086\pi$
$479$	2.80917e14	0.509018	0.254509	+	0.967070i	$0.418086\pi$
$480$	7.81959e13	0.140074
$481$	4.87837e14	0.863927
$482$	−3.85053e14	−0.674159
$483$	2.81321e14	0.486960
$484$	−1.69817e14	−0.290625
$485$	1.47465e14	0.249522
$486$	2.23182e14	0.373387
$487$	−4.06414e14	−0.672294	−0.336147	−	0.941810i	$-0.609124\pi$
$487$	−4.06414e14	−0.672294	−0.336147	+	0.941810i	$0.609124\pi$
$488$	3.52470e14	0.576518
$489$	−1.86895e15	−3.02273
$490$	3.13420e14	0.501243
$491$	1.02479e15	1.62065	0.810324	−	0.585982i	$-0.199291\pi$
$491$	1.02479e15	1.62065	0.810324	+	0.585982i	$0.199291\pi$
$492$	−6.95880e14	−1.08824
$493$	1.00465e14	0.155367
$494$	−5.39255e14	−0.824699
$495$	−4.09350e14	−0.619108
$496$	7.44959e13	0.111425
$497$	−2.46853e14	−0.365156
$498$	1.32599e15	1.93990
$499$	1.01593e14	0.146997	0.0734987	−	0.997295i	$-0.476584\pi$
$499$	1.01593e14	0.146997	0.0734987	+	0.997295i	$0.476584\pi$
$500$	3.12500e13	0.0447214
$501$	−2.01240e15	−2.84844
$502$	−7.14277e14	−0.999991
$503$	9.67924e14	1.34035	0.670174	−	0.742204i	$-0.266220\pi$
$503$	9.67924e14	1.34035	0.670174	+	0.742204i	$0.266220\pi$
$504$	−8.87836e14	−1.21609
$505$	5.03838e14	0.682635
$506$	5.83620e13	0.0782172
$507$	3.62891e14	0.481097
$508$	−5.74143e14	−0.752957
$509$	9.40088e14	1.21961	0.609805	−	0.792552i	$-0.291248\pi$
$509$	9.40088e14	1.21961	0.609805	+	0.792552i	$0.291248\pi$
$510$	−4.02168e14	−0.516144
$511$	1.58101e15	2.00733
$512$	3.51844e13	0.0441942
$513$	−1.68017e15	−2.08789
$514$	5.76175e14	0.708365
$515$	−5.79933e14	−0.705404
$516$	−8.89105e14	−1.06999
$517$	−9.74557e13	−0.116040
$518$	−7.39348e14	−0.871034
$519$	2.29534e15	2.67564
$520$	1.54579e14	0.178293
$521$	−1.00574e15	−1.14783	−0.573916	−	0.818914i	$-0.694576\pi$
$521$	−1.00574e15	−1.14783	−0.573916	+	0.818914i	$0.694576\pi$
$522$	−2.25918e14	−0.255131
$523$	−1.24911e15	−1.39586	−0.697931	−	0.716165i	$-0.745896\pi$
$523$	−1.24911e15	−1.39586	−0.697931	+	0.716165i	$0.745896\pi$
$524$	4.21887e14	0.466524
$525$	−5.20666e14	−0.569749
$526$	4.44460e14	0.481294
$527$	−3.83138e14	−0.410579
$528$	−2.70285e14	−0.286639
$529$	−9.24969e14	−0.970780
$530$	4.05957e14	0.421660
$531$	1.85631e15	1.90823
$532$	8.17274e14	0.831483
$533$	−1.37563e15	−1.38517
$534$	−2.21860e14	−0.221107
$535$	−1.70565e14	−0.168246
$536$	1.21508e14	0.118631
$537$	2.61868e14	0.253060
$538$	8.69155e14	0.831371
$539$	−1.08334e15	−1.02571
$540$	4.81626e14	0.451382
$541$	1.47684e15	1.37009	0.685046	−	0.728500i	$-0.259782\pi$
$541$	1.47684e15	1.37009	0.685046	+	0.728500i	$0.259782\pi$
$542$	−2.31853e14	−0.212921
$543$	4.72874e14	0.429880
$544$	−1.80956e14	−0.162847
$545$	−1.10636e14	−0.0985632
$546$	−2.57550e15	−2.27144
$547$	−2.32000e14	−0.202562	−0.101281	−	0.994858i	$-0.532294\pi$
$547$	−2.32000e14	−0.202562	−0.101281	+	0.994858i	$0.532294\pi$
$548$	−8.05129e14	−0.695941
$549$	4.07643e15	3.48844
$550$	−1.08016e14	−0.0915151
$551$	2.07962e14	0.174442
$552$	−1.28937e14	−0.107081
$553$	−5.02375e14	−0.413085
$554$	1.27136e15	1.03506
$555$	7.53108e14	0.607080
$556$	8.77724e14	0.700562
$557$	2.34238e15	1.85120	0.925602	−	0.378498i	$-0.123559\pi$
$557$	2.34238e15	1.85120	0.925602	+	0.378498i	$0.123559\pi$
$558$	8.61568e14	0.674220
$559$	−1.75760e15	−1.36193
$560$	−2.34275e14	−0.179759
$561$	1.39010e15	1.05621
$562$	1.90482e14	0.143319
$563$	2.32309e15	1.73089	0.865446	−	0.501002i	$-0.167035\pi$
$563$	2.32309e15	1.73089	0.865446	+	0.501002i	$0.167035\pi$
$564$	2.15305e14	0.158862
$565$	3.75983e14	0.274727
$566$	−1.23450e15	−0.893309
$567$	−3.22479e15	−2.31098
$568$	1.13139e14	0.0802967
$569$	−2.48598e14	−0.174735	−0.0873676	−	0.996176i	$-0.527845\pi$
$569$	−2.48598e14	−0.174735	−0.0873676	+	0.996176i	$0.527845\pi$
$570$	−8.32485e14	−0.579515
$571$	−2.44700e15	−1.68708	−0.843540	−	0.537066i	$-0.819533\pi$
$571$	−2.44700e15	−1.68708	−0.843540	+	0.537066i	$0.819533\pi$
$572$	−5.34305e14	−0.364847
$573$	−1.95072e15	−1.31931
$574$	2.08486e15	1.39656
$575$	−5.15280e13	−0.0341877
$576$	4.06919e14	0.267414
$577$	−2.05338e15	−1.33660	−0.668302	−	0.743890i	$-0.732979\pi$
$577$	−2.05338e15	−1.33660	−0.668302	+	0.743890i	$0.732979\pi$
$578$	−1.66030e14	−0.107049
$579$	1.19182e15	0.761166
$580$	−5.96132e13	−0.0377128
$581$	−3.97266e15	−2.48950
$582$	1.12609e15	0.699032
$583$	−1.40319e15	−0.862860
$584$	−7.24617e14	−0.441406
$585$	1.78776e15	1.07883
$586$	−1.70409e15	−1.01872
$587$	3.00291e14	0.177841	0.0889207	−	0.996039i	$-0.471658\pi$
$587$	3.00291e14	0.177841	0.0889207	+	0.996039i	$0.471658\pi$
$588$	2.39338e15	1.40422
$589$	−7.93094e14	−0.460989
$590$	4.89828e14	0.282071
$591$	−4.59582e13	−0.0262200
$592$	3.38862e14	0.191538
$593$	−2.71460e15	−1.52022	−0.760108	−	0.649796i	$-0.774854\pi$
$593$	−2.71460e15	−1.52022	−0.760108	+	0.649796i	$0.774854\pi$
$594$	−1.66474e15	−0.923681
$595$	1.20489e15	0.662377
$596$	−2.44332e14	−0.133084
$597$	1.76399e15	0.951999
$598$	−2.54885e14	−0.136298
$599$	−2.10006e15	−1.11272	−0.556358	−	0.830943i	$-0.687802\pi$
$599$	−2.10006e15	−1.11272	−0.556358	+	0.830943i	$0.687802\pi$
$600$	2.38635e14	0.125286
$601$	2.84187e15	1.47841	0.739204	−	0.673481i	$-0.235202\pi$
$601$	2.84187e15	1.47841	0.739204	+	0.673481i	$0.235202\pi$
$602$	2.66376e15	1.37314
$603$	1.40528e15	0.717821
$604$	−9.80284e13	−0.0496191
$605$	−5.18242e14	−0.259943
$606$	3.84747e15	1.91239
$607$	−3.78069e14	−0.186223	−0.0931114	−	0.995656i	$-0.529681\pi$
$607$	−3.78069e14	−0.186223	−0.0931114	+	0.995656i	$0.529681\pi$
$608$	−3.74578e14	−0.182841
$609$	9.93235e14	0.480460
$610$	1.07565e15	0.515654
$611$	4.25619e14	0.202206
$612$	−2.09281e15	−0.985367
$613$	2.97141e15	1.38653	0.693267	−	0.720681i	$-0.256171\pi$
$613$	2.97141e15	1.38653	0.693267	+	0.720681i	$0.256171\pi$
$614$	−1.83788e15	−0.849943
$615$	−2.12366e15	−0.973355
$616$	8.09772e14	0.367848
$617$	−1.19545e15	−0.538222	−0.269111	−	0.963109i	$-0.586730\pi$
$617$	−1.19545e15	−0.538222	−0.269111	+	0.963109i	$0.586730\pi$
$618$	−4.42855e15	−1.97617
$619$	3.17735e14	0.140529	0.0702645	−	0.997528i	$-0.477616\pi$
$619$	3.17735e14	0.140529	0.0702645	+	0.997528i	$0.477616\pi$
$620$	2.27343e14	0.0996616
$621$	−7.94151e14	−0.345064
$622$	−8.27572e14	−0.356417
$623$	6.64693e14	0.283750
$624$	1.18042e15	0.499482
$625$	9.53674e13	0.0400000
$626$	−1.14338e15	−0.475372
$627$	2.87749e15	1.18588
$628$	−1.84253e15	−0.752727
$629$	−1.74280e15	−0.705778
$630$	−2.70946e15	−1.08770
$631$	−7.14141e14	−0.284199	−0.142099	−	0.989852i	$-0.545385\pi$
$631$	−7.14141e14	−0.284199	−0.142099	+	0.989852i	$0.545385\pi$
$632$	2.30251e14	0.0908361
$633$	4.02498e15	1.57414
$634$	−5.71618e14	−0.221623
$635$	−1.75215e15	−0.673465
$636$	3.10002e15	1.18127
$637$	4.73128e15	1.78736
$638$	2.06054e14	0.0771732
$639$	1.30849e15	0.485866
$640$	1.07374e14	0.0395285
$641$	3.74739e15	1.36776	0.683880	−	0.729594i	$-0.260291\pi$
$641$	3.74739e15	1.36776	0.683880	+	0.729594i	$0.260291\pi$
$642$	−1.30249e15	−0.471336
$643$	3.72691e14	0.133718	0.0668588	−	0.997762i	$-0.478702\pi$
$643$	3.72691e14	0.133718	0.0668588	+	0.997762i	$0.478702\pi$
$644$	3.86294e14	0.137419
$645$	−2.71333e15	−0.957028
$646$	1.92648e15	0.673731
$647$	3.55565e15	1.23295	0.616475	−	0.787374i	$-0.288560\pi$
$647$	3.55565e15	1.23295	0.616475	+	0.787374i	$0.288560\pi$
$648$	1.47801e15	0.508176
$649$	−1.69310e15	−0.577212
$650$	4.71739e14	0.159470
$651$	−3.78784e15	−1.26969
$652$	−2.56633e15	−0.853005
$653$	5.07282e15	1.67196	0.835982	−	0.548757i	$-0.184899\pi$
$653$	5.07282e15	1.67196	0.835982	+	0.548757i	$0.184899\pi$
$654$	−8.44850e14	−0.276123
$655$	1.28750e15	0.417272
$656$	−9.55544e14	−0.307100
$657$	−8.38043e15	−2.67090
$658$	−6.45053e14	−0.203870
$659$	1.66566e15	0.522054	0.261027	−	0.965331i	$-0.415939\pi$
$659$	1.66566e15	0.522054	0.261027	+	0.965331i	$0.415939\pi$
$660$	−8.24843e14	−0.256377
$661$	3.06978e14	0.0946235	0.0473118	−	0.998880i	$-0.484935\pi$
$661$	3.06978e14	0.0946235	0.0473118	+	0.998880i	$0.484935\pi$
$662$	2.49049e15	0.761318
$663$	−6.07098e15	−1.84049
$664$	1.82077e15	0.547433
$665$	2.49412e15	0.743701
$666$	3.91905e15	1.15897
$667$	9.82960e13	0.0288299
$668$	−2.76331e15	−0.803822
$669$	−6.98845e15	−2.01622
$670$	3.70812e14	0.106107
$671$	−3.71800e15	−1.05520
$672$	−1.78900e15	−0.503591
$673$	3.20107e15	0.893742	0.446871	−	0.894599i	$-0.352538\pi$
$673$	3.20107e15	0.893742	0.446871	+	0.894599i	$0.352538\pi$
$674$	1.58591e14	0.0439187
$675$	1.46981e15	0.403728
$676$	4.98302e14	0.135764
$677$	−4.88443e15	−1.32001	−0.660004	−	0.751262i	$-0.729445\pi$
$677$	−4.88443e15	−1.32001	−0.660004	+	0.751262i	$0.729445\pi$
$678$	2.87112e15	0.769642
$679$	−3.37376e15	−0.897079
$680$	−5.52234e14	−0.145655
$681$	−4.85891e15	−1.27125
$682$	−7.85814e14	−0.203941
$683$	3.43048e15	0.883163	0.441582	−	0.897221i	$-0.354418\pi$
$683$	3.43048e15	0.883163	0.441582	+	0.897221i	$0.354418\pi$
$684$	−4.33211e15	−1.10635
$685$	−2.45706e15	−0.622469
$686$	−2.64674e15	−0.665164
$687$	−1.30361e15	−0.325001
$688$	−1.22087e15	−0.301948
$689$	6.12818e15	1.50358
$690$	−3.93484e14	−0.0957761
$691$	1.26067e15	0.304420	0.152210	−	0.988348i	$-0.451361\pi$
$691$	1.26067e15	0.304420	0.152210	+	0.988348i	$0.451361\pi$
$692$	3.15183e15	0.755057
$693$	9.36527e15	2.22581
$694$	−2.09826e15	−0.494746
$695$	2.67860e15	0.626602
$696$	−4.55226e14	−0.105652
$697$	4.91444e15	1.13160
$698$	3.67201e15	0.838879
$699$	6.44682e15	1.46124
$700$	−7.14949e14	−0.160782
$701$	−1.46416e15	−0.326693	−0.163347	−	0.986569i	$-0.552229\pi$
$701$	−1.46416e15	−0.326693	−0.163347	+	0.986569i	$0.552229\pi$
$702$	7.27045e15	1.60956
$703$	−3.60758e15	−0.792431
$704$	−3.71140e14	−0.0808887
$705$	6.57058e14	0.142090
$706$	−1.63287e15	−0.350369
$707$	−1.15270e16	−2.45420
$708$	3.74049e15	0.790215
$709$	−2.00407e15	−0.420105	−0.210053	−	0.977690i	$-0.567364\pi$
$709$	−2.00407e15	−0.420105	−0.210053	+	0.977690i	$0.567364\pi$
$710$	3.45274e14	0.0718196
$711$	2.66293e15	0.549639
$712$	−3.04646e14	−0.0623958
$713$	−3.74865e14	−0.0761873
$714$	9.20095e15	1.85563
$715$	−1.63057e15	−0.326329
$716$	3.59582e14	0.0714128
$717$	5.00406e15	0.986205
$718$	−3.73303e15	−0.730092
$719$	−6.94101e15	−1.34714	−0.673571	−	0.739122i	$-0.735241\pi$
$719$	−6.94101e15	−1.34714	−0.673571	+	0.739122i	$0.735241\pi$
$720$	1.24182e15	0.239182
$721$	1.32679e16	2.53606
$722$	2.60123e14	0.0493428
$723$	−8.97336e15	−1.68925
$724$	6.49324e14	0.121311
$725$	−1.81925e14	−0.0337313
$726$	−3.95746e15	−0.728224
$727$	−8.96895e14	−0.163796	−0.0818978	−	0.996641i	$-0.526098\pi$
$727$	−8.96895e14	−0.163796	−0.0818978	+	0.996641i	$0.526098\pi$
$728$	−3.53653e15	−0.640994
$729$	−2.78918e15	−0.501735
$730$	−2.21136e15	−0.394805
$731$	6.27903e15	1.11262
$732$	8.21403e15	1.44459
$733$	−1.11078e16	−1.93890	−0.969451	−	0.245286i	$-0.921118\pi$
$733$	−1.11078e16	−1.93890	−0.969451	+	0.245286i	$0.921118\pi$
$734$	4.60985e15	0.798653
$735$	7.30400e15	1.25597
$736$	−1.77049e14	−0.0302179
$737$	−1.28171e15	−0.217130
$738$	−1.10512e16	−1.85822
$739$	5.03625e15	0.840548	0.420274	−	0.907397i	$-0.361934\pi$
$739$	5.03625e15	0.840548	0.420274	+	0.907397i	$0.361934\pi$
$740$	1.03413e15	0.171316
$741$	−1.25669e16	−2.06646
$742$	−9.28764e15	−1.51595
$743$	1.36645e15	0.221389	0.110695	−	0.993854i	$-0.464692\pi$
$743$	1.36645e15	0.221389	0.110695	+	0.993854i	$0.464692\pi$
$744$	1.73607e15	0.279200
$745$	−7.45643e14	−0.119034
$746$	2.20990e15	0.350194
$747$	2.10578e16	3.31246
$748$	1.90880e15	0.298059
$749$	3.90225e15	0.604874
$750$	7.28256e14	0.112059
$751$	−9.78301e15	−1.49435	−0.747176	−	0.664627i	$-0.768591\pi$
$751$	−9.78301e15	−1.49435	−0.747176	+	0.664627i	$0.768591\pi$
$752$	2.95644e14	0.0448303
$753$	−1.66456e16	−2.50570
$754$	−8.99900e14	−0.134478
$755$	−2.99159e14	−0.0443807
$756$	−1.10188e16	−1.62280
$757$	−1.39502e15	−0.203964	−0.101982	−	0.994786i	$-0.532518\pi$
$757$	−1.39502e15	−0.203964	−0.101982	+	0.994786i	$0.532518\pi$
$758$	7.31454e15	1.06171
$759$	1.36008e15	0.195990
$760$	−1.14312e15	−0.163538
$761$	6.09995e15	0.866385	0.433192	−	0.901301i	$-0.357387\pi$
$761$	6.09995e15	0.866385	0.433192	+	0.901301i	$0.357387\pi$
$762$	−1.33799e16	−1.88670
$763$	2.53117e15	0.354353
$764$	−2.67862e15	−0.372304
$765$	−6.38676e15	−0.881339
$766$	−2.29352e15	−0.314228
$767$	7.39427e15	1.00582
$768$	8.19943e14	0.110738
$769$	6.60626e15	0.885851	0.442925	−	0.896558i	$-0.353941\pi$
$769$	6.60626e15	0.885851	0.442925	+	0.896558i	$0.353941\pi$
$770$	2.47123e15	0.329013
$771$	1.34273e16	1.77496
$772$	1.63654e15	0.214799
$773$	3.74520e15	0.488076	0.244038	−	0.969766i	$-0.421528\pi$
$773$	3.74520e15	0.488076	0.244038	+	0.969766i	$0.421528\pi$
$774$	−1.41197e16	−1.82705
$775$	6.93797e14	0.0891400
$776$	1.54628e15	0.197265
$777$	−1.72299e16	−2.18257
$778$	1.69977e15	0.213798
$779$	1.01729e16	1.27054
$780$	3.60235e15	0.446751
$781$	−1.19344e15	−0.146967
$782$	9.10576e14	0.111347
$783$	−2.80384e15	−0.340458
$784$	3.28645e15	0.396267
$785$	−5.62297e15	−0.673259
$786$	9.83174e15	1.16898
$787$	−1.01107e16	−1.19377	−0.596885	−	0.802326i	$-0.703595\pi$
$787$	−1.01107e16	−1.19377	−0.596885	+	0.802326i	$0.703595\pi$
$788$	−6.31072e13	−0.00739920
$789$	1.03578e16	1.20599
$790$	7.02672e14	0.0812463
$791$	−8.60188e15	−0.987694
$792$	−4.29235e15	−0.489448
$793$	1.62377e16	1.83874
$794$	3.00711e14	0.0338171
$795$	9.46050e15	1.05656
$796$	2.42221e15	0.268652
$797$	−1.40032e16	−1.54244	−0.771219	−	0.636570i	$-0.780353\pi$
$797$	−1.40032e16	−1.54244	−0.771219	+	0.636570i	$0.780353\pi$
$798$	1.90459e16	2.08346
$799$	−1.52052e15	−0.165191
$800$	3.27680e14	0.0353553
$801$	−3.52333e15	−0.377550
$802$	7.04691e15	0.749962
$803$	7.64357e15	0.807906
$804$	2.83164e15	0.297255
$805$	1.17888e15	0.122911
$806$	3.43189e15	0.355378
$807$	2.02550e16	2.08318
$808$	5.28313e15	0.539671
$809$	2.05016e15	0.208004	0.104002	−	0.994577i	$-0.466835\pi$
$809$	2.05016e15	0.208004	0.104002	+	0.994577i	$0.466835\pi$
$810$	4.51052e15	0.454526
$811$	−1.45631e16	−1.45760	−0.728801	−	0.684725i	$-0.759922\pi$
$811$	−1.45631e16	−1.45760	−0.728801	+	0.684725i	$0.759922\pi$
$812$	1.36385e15	0.135584
$813$	−5.40316e15	−0.533519
$814$	−3.57446e15	−0.350571
$815$	−7.83183e15	−0.762951
$816$	−4.21703e15	−0.408048
$817$	1.29975e16	1.24922
$818$	−9.76330e15	−0.932080
$819$	−4.09011e16	−3.87858
$820$	−2.91609e15	−0.274678
$821$	−5.13429e15	−0.480389	−0.240195	−	0.970725i	$-0.577211\pi$
$821$	−5.13429e15	−0.480389	−0.240195	+	0.970725i	$0.577211\pi$
$822$	−1.87629e16	−1.74383
$823$	−6.16638e15	−0.569287	−0.284643	−	0.958633i	$-0.591875\pi$
$823$	−6.16638e15	−0.569287	−0.284643	+	0.958633i	$0.591875\pi$
$824$	−6.08104e15	−0.557671
$825$	−2.51722e15	−0.229311
$826$	−1.12065e16	−1.01410
$827$	−2.77673e15	−0.249605	−0.124803	−	0.992182i	$-0.539830\pi$
$827$	−2.77673e15	−0.249605	−0.124803	+	0.992182i	$0.539830\pi$
$828$	−2.04763e15	−0.182845
$829$	1.33865e16	1.18745	0.593726	−	0.804667i	$-0.297656\pi$
$829$	1.33865e16	1.18745	0.593726	+	0.804667i	$0.297656\pi$
$830$	5.55656e15	0.489639
$831$	2.96281e16	2.59357
$832$	1.62088e15	0.140953
$833$	−1.69025e16	−1.46017
$834$	2.04546e16	1.75541
$835$	−8.43296e15	−0.718960
$836$	3.95121e15	0.334653
$837$	1.06928e16	0.899709
$838$	1.34861e16	1.12731
$839$	1.47887e16	1.22812	0.614059	−	0.789260i	$-0.289536\pi$
$839$	1.47887e16	1.22812	0.614059	+	0.789260i	$0.289536\pi$
$840$	−5.45958e15	−0.450426
$841$	−1.18535e16	−0.971555
$842$	3.55584e13	0.00289551
$843$	4.43902e15	0.359116
$844$	5.52687e15	0.444218
$845$	1.52070e15	0.121431
$846$	3.41922e15	0.271263
$847$	1.18565e16	0.934542
$848$	4.25677e15	0.333352
$849$	−2.87691e16	−2.23838
$850$	−1.68528e15	−0.130277
$851$	−1.70517e15	−0.130965
$852$	2.63662e15	0.201201
$853$	1.97554e16	1.49784	0.748922	−	0.662658i	$-0.230572\pi$
$853$	1.97554e16	1.49784	0.748922	+	0.662658i	$0.230572\pi$
$854$	−2.46092e16	−1.85387
$855$	−1.32206e16	−0.989547
$856$	−1.78850e15	−0.133010
$857$	−2.32233e16	−1.71605	−0.858023	−	0.513612i	$-0.828307\pi$
$857$	−2.32233e16	−1.71605	−0.858023	+	0.513612i	$0.828307\pi$
$858$	−1.24515e16	−0.914203
$859$	−1.67344e16	−1.22081	−0.610405	−	0.792089i	$-0.708993\pi$
$859$	−1.67344e16	−1.22081	−0.610405	+	0.792089i	$0.708993\pi$
$860$	−3.72580e15	−0.270071
$861$	4.85859e16	3.49939
$862$	7.33454e15	0.524908
$863$	−2.46024e16	−1.74951	−0.874757	−	0.484563i	$-0.838979\pi$
$863$	−2.46024e16	−1.74951	−0.874757	+	0.484563i	$0.838979\pi$
$864$	5.05021e15	0.356849
$865$	9.61864e15	0.675344
$866$	4.92901e15	0.343883
$867$	−3.86919e15	−0.268234
$868$	−5.20125e15	−0.358302
$869$	−2.42879e15	−0.166257
$870$	−1.38924e15	−0.0944976
$871$	5.59764e15	0.378360
$872$	−1.16010e15	−0.0779211
$873$	1.78833e16	1.19363
$874$	1.88489e15	0.125018
$875$	−2.18185e15	−0.143807
$876$	−1.68866e16	−1.10604
$877$	−4.55865e15	−0.296714	−0.148357	−	0.988934i	$-0.547399\pi$
$877$	−4.55865e15	−0.296714	−0.148357	+	0.988934i	$0.547399\pi$
$878$	−4.02551e15	−0.260376
$879$	−3.97125e16	−2.55263
$880$	−1.13263e15	−0.0723490
$881$	1.67834e16	1.06540	0.532701	−	0.846304i	$-0.321177\pi$
$881$	1.67834e16	1.06540	0.532701	+	0.846304i	$0.321177\pi$
$882$	3.80088e16	2.39777
$883$	−1.13628e16	−0.712362	−0.356181	−	0.934417i	$-0.615921\pi$
$883$	−1.13628e16	−0.712362	−0.356181	+	0.934417i	$0.615921\pi$
$884$	−8.33632e15	−0.519382
$885$	1.14151e16	0.706789
$886$	−4.30793e15	−0.265084
$887$	1.55603e16	0.951563	0.475782	−	0.879563i	$-0.342165\pi$
$887$	1.55603e16	0.951563	0.475782	+	0.879563i	$0.342165\pi$
$888$	7.89691e15	0.479939
$889$	4.00863e16	2.42123
$890$	−9.29706e14	−0.0558085
$891$	−1.55906e16	−0.930115
$892$	−9.59615e15	−0.568971
$893$	−3.14747e15	−0.185472
$894$	−5.69397e15	−0.333471
$895$	1.09736e15	0.0638736
$896$	−2.45655e15	−0.142112
$897$	−5.93989e15	−0.341523
$898$	1.37271e16	0.784440
$899$	−1.32350e15	−0.0751704
$900$	3.78972e15	0.213931
$901$	−2.18929e16	−1.22834
$902$	1.00795e16	0.562085
$903$	6.20767e16	3.44069
$904$	3.94246e15	0.217191
$905$	1.98158e15	0.108504
$906$	−2.28447e15	−0.124331
$907$	3.40764e16	1.84338	0.921688	−	0.387932i	$-0.126811\pi$
$907$	3.40764e16	1.84338	0.921688	+	0.387932i	$0.126811\pi$
$908$	−6.67198e15	−0.358742
$909$	6.11011e16	3.26548
$910$	−1.07926e16	−0.573323
$911$	1.60732e16	0.848697	0.424348	−	0.905499i	$-0.360503\pi$
$911$	1.60732e16	0.848697	0.424348	+	0.905499i	$0.360503\pi$
$912$	−8.72924e15	−0.458147
$913$	−1.92063e16	−1.00197
$914$	−2.52543e16	−1.30958
$915$	2.50672e16	1.29208
$916$	−1.79004e15	−0.0917144
$917$	−2.94559e16	−1.50017
$918$	−2.59737e16	−1.31492
$919$	−7.32080e15	−0.368403	−0.184201	−	0.982889i	$-0.558970\pi$
$919$	−7.32080e15	−0.368403	−0.184201	+	0.982889i	$0.558970\pi$
$920$	−5.40310e14	−0.0270277
$921$	−4.28302e16	−2.12972
$922$	−1.92556e16	−0.951783
$923$	5.21213e15	0.256098
$924$	1.88711e16	0.921724
$925$	3.15590e15	0.153230
$926$	7.57994e15	0.365852
$927$	−7.03292e16	−3.37440
$928$	−6.25090e14	−0.0298146
$929$	−1.41658e16	−0.671666	−0.335833	−	0.941922i	$-0.609018\pi$
$929$	−1.41658e16	−0.671666	−0.335833	+	0.941922i	$0.609018\pi$
$930$	5.29805e15	0.249724
$931$	−3.49880e16	−1.63944
$932$	8.85241e15	0.412358
$933$	−1.92859e16	−0.893081
$934$	2.61459e16	1.20364
$935$	5.82520e15	0.266592
$936$	1.87460e16	0.852888
$937$	1.51385e16	0.684721	0.342361	−	0.939569i	$-0.388774\pi$
$937$	1.51385e16	0.684721	0.342361	+	0.939569i	$0.388774\pi$
$938$	−8.48358e15	−0.381473
$939$	−2.66456e16	−1.19115
$940$	9.02235e14	0.0400974
$941$	8.81297e15	0.389385	0.194693	−	0.980864i	$-0.437629\pi$
$941$	8.81297e15	0.389385	0.194693	+	0.980864i	$0.437629\pi$
$942$	−4.29388e16	−1.88612
$943$	4.80832e15	0.209981
$944$	5.13622e15	0.222996
$945$	−3.36268e16	−1.45148
$946$	1.28782e16	0.552656
$947$	6.85225e15	0.292353	0.146177	−	0.989258i	$-0.453303\pi$
$947$	6.85225e15	0.292353	0.146177	+	0.989258i	$0.453303\pi$
$948$	5.36582e15	0.227610
$949$	−3.33818e16	−1.40782
$950$	−3.48853e15	−0.146272
$951$	−1.33211e16	−0.555325
$952$	1.26342e16	0.523655
$953$	3.21185e16	1.32356	0.661781	−	0.749697i	$-0.269801\pi$
$953$	3.21185e16	1.32356	0.661781	+	0.749697i	$0.269801\pi$
$954$	4.92309e16	2.01707
$955$	−8.17451e15	−0.332999
$956$	6.87129e15	0.278304
$957$	4.80191e15	0.193374
$958$	8.98935e15	0.359930
$959$	5.62135e16	2.23789
$960$	2.50227e15	0.0990472
$961$	−2.03611e16	−0.801351
$962$	1.56108e16	0.610889
$963$	−2.06846e16	−0.804827
$964$	−1.23217e16	−0.476702
$965$	4.99433e15	0.192122
$966$	9.00228e15	0.344333
$967$	2.01801e16	0.767500	0.383750	−	0.923437i	$-0.374633\pi$
$967$	2.01801e16	0.767500	0.383750	+	0.923437i	$0.374633\pi$
$968$	−5.43416e15	−0.205503
$969$	4.48952e16	1.68818
$970$	4.71888e15	0.176439
$971$	7.19924e15	0.267658	0.133829	−	0.991004i	$-0.457273\pi$
$971$	7.19924e15	0.267658	0.133829	+	0.991004i	$0.457273\pi$
$972$	7.14182e15	0.264025
$973$	−6.12821e16	−2.25275
$974$	−1.30052e16	−0.475383
$975$	1.09935e16	0.399586
$976$	1.12790e16	0.407660
$977$	3.14860e16	1.13161	0.565806	−	0.824538i	$-0.308565\pi$
$977$	3.14860e16	1.13161	0.565806	+	0.824538i	$0.308565\pi$
$978$	−5.98064e16	−2.13739
$979$	3.21353e15	0.114203
$980$	1.00294e16	0.354432
$981$	−1.34169e16	−0.471491
$982$	3.27934e16	1.14597
$983$	−1.68059e15	−0.0584006	−0.0292003	−	0.999574i	$-0.509296\pi$
$983$	−1.68059e15	−0.0584006	−0.0292003	+	0.999574i	$0.509296\pi$
$984$	−2.22682e16	−0.769505
$985$	−1.92588e14	−0.00661805
$986$	3.21489e15	0.109861
$987$	−1.50324e16	−0.510840
$988$	−1.72561e16	−0.583150
$989$	6.14345e15	0.206458
$990$	−1.30992e16	−0.437775
$991$	−2.21678e15	−0.0736746	−0.0368373	−	0.999321i	$-0.511728\pi$
$991$	−2.21678e15	−0.0736746	−0.0368373	+	0.999321i	$0.511728\pi$
$992$	2.38387e15	0.0787894
$993$	5.80389e16	1.90765
$994$	−7.89931e15	−0.258205
$995$	7.39199e15	0.240289
$996$	4.24316e16	1.37171
$997$	2.59411e14	0.00833999	0.00416999	−	0.999991i	$-0.498673\pi$
$997$	2.59411e14	0.00833999	0.00416999	+	0.999991i	$0.498673\pi$
$998$	3.25097e15	0.103943
$999$	4.86389e16	1.54658

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.12.a.d.1.2	✓	2
3.2	odd	2		90.12.a.l.1.1		2
4.3	odd	2		80.12.a.g.1.1		2
5.2	odd	4		50.12.b.f.49.3		4
5.3	odd	4		50.12.b.f.49.2		4
5.4	even	2		50.12.a.f.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.12.a.d.1.2	✓	2	1.1	even	1	trivial
50.12.a.f.1.1		2	5.4	even	2
50.12.b.f.49.2		4	5.3	odd	4
50.12.b.f.49.3		4	5.2	odd	4
80.12.a.g.1.1		2	4.3	odd	2
90.12.a.l.1.1		2	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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q+32.0000 q^{2} +745.734 q^{3} +1024.00 q^{4} +3125.00 q^{5} +23863.5 q^{6} -71494.9 q^{7} +32768.0 q^{8} +378972. q^{9} +O(q^{10})\)	\(q+32.0000 q^{2} +745.734 q^{3} +1024.00 q^{4} +3125.00 q^{5} +23863.5 q^{6} -71494.9 q^{7} +32768.0 q^{8} +378972. q^{9} +100000. q^{10} -345651. q^{11} +763632. q^{12} +1.50956e6 q^{13} -2.28784e6 q^{14} +2.33042e6 q^{15} +1.04858e6 q^{16} -5.39291e6 q^{17} +1.21271e7 q^{18} -1.11633e7 q^{19} +3.20000e6 q^{20} -5.33162e7 q^{21} -1.10608e7 q^{22} -5.27646e6 q^{23} +2.44362e7 q^{24} +9.76562e6 q^{25} +4.83060e7 q^{26} +1.50508e8 q^{27} -7.32108e7 q^{28} -1.86291e7 q^{29} +7.45734e7 q^{30} +7.10448e7 q^{31} +3.35544e7 q^{32} -2.57763e8 q^{33} -1.72573e8 q^{34} -2.23422e8 q^{35} +3.88068e8 q^{36} +3.23164e8 q^{37} -3.57225e8 q^{38} +1.12573e9 q^{39} +1.02400e8 q^{40} -9.11277e8 q^{41} -1.70612e9 q^{42} -1.16431e9 q^{43} -3.53946e8 q^{44} +1.18429e9 q^{45} -1.68847e8 q^{46} +2.81949e8 q^{47} +7.81959e8 q^{48} +3.13420e9 q^{49} +3.12500e8 q^{50} -4.02168e9 q^{51} +1.54579e9 q^{52} +4.05957e9 q^{53} +4.81626e9 q^{54} -1.08016e9 q^{55} -2.34275e9 q^{56} -8.32485e9 q^{57} -5.96132e8 q^{58} +4.89828e9 q^{59} +2.38635e9 q^{60} +1.07565e10 q^{61} +2.27343e9 q^{62} -2.70946e10 q^{63} +1.07374e9 q^{64} +4.71739e9 q^{65} -8.24843e9 q^{66} +3.70812e9 q^{67} -5.52234e9 q^{68} -3.93484e9 q^{69} -7.14949e9 q^{70} +3.45274e9 q^{71} +1.24182e10 q^{72} -2.21136e10 q^{73} +1.03413e10 q^{74} +7.28256e9 q^{75} -1.14312e10 q^{76} +2.47123e10 q^{77} +3.60235e10 q^{78} +7.02672e9 q^{79} +3.27680e9 q^{80} +4.51052e10 q^{81} -2.91609e10 q^{82} +5.55656e10 q^{83} -5.45958e10 q^{84} -1.68528e10 q^{85} -3.72580e10 q^{86} -1.38924e10 q^{87} -1.13263e10 q^{88} -9.29706e9 q^{89} +3.78972e10 q^{90} -1.07926e11 q^{91} -5.40310e9 q^{92} +5.29805e10 q^{93} +9.02235e9 q^{94} -3.48853e10 q^{95} +2.50227e10 q^{96} +4.71888e10 q^{97} +1.00294e11 q^{98} -1.30992e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 64 q^{2} + 604 q^{3} + 2048 q^{4} + 6250 q^{5} + 19328 q^{6} + 14092 q^{7} + 65536 q^{8} + 221914 q^{9}+O(q^{10}) \) 2 * q + 64 * q^2 + 604 * q^3 + 2048 * q^4 + 6250 * q^5 + 19328 * q^6 + 14092 * q^7 + 65536 * q^8 + 221914 * q^9	\( 2 q + 64 q^{2} + 604 q^{3} + 2048 q^{4} + 6250 q^{5} + 19328 q^{6} + 14092 q^{7} + 65536 q^{8} + 221914 q^{9} + 200000 q^{10} + 421584 q^{11} + 618496 q^{12} + 1730524 q^{13} + 450944 q^{14} + 1887500 q^{15} + 2097152 q^{16} - 6323628 q^{17} + 7101248 q^{18} - 28897400 q^{19} + 6400000 q^{20} - 65446816 q^{21} + 13490688 q^{22} - 45236076 q^{23} + 19791872 q^{24} + 19531250 q^{25} + 55376768 q^{26} + 197876440 q^{27} + 14430208 q^{28} + 58226220 q^{29} + 60400000 q^{30} + 41413384 q^{31} + 67108864 q^{32} - 366506832 q^{33} - 202356096 q^{34} + 44037500 q^{35} + 227239936 q^{36} + 377255452 q^{37} - 924716800 q^{38} + 1094415848 q^{39} + 204800000 q^{40} - 785271036 q^{41} - 2094298112 q^{42} - 1452987236 q^{43} + 431702016 q^{44} + 693481250 q^{45} - 1447554432 q^{46} - 1288127748 q^{47} + 633339904 q^{48} + 8481998946 q^{49} + 625000000 q^{50} - 3889762056 q^{51} + 1772056576 q^{52} - 30490836 q^{53} + 6332046080 q^{54} + 1317450000 q^{55} + 461766656 q^{56} - 5811319600 q^{57} + 1863239040 q^{58} + 8677102440 q^{59} + 1932800000 q^{60} + 1115498764 q^{61} + 1325228288 q^{62} - 40536764356 q^{63} + 2147483648 q^{64} + 5407887500 q^{65} - 11728218624 q^{66} - 12673769708 q^{67} - 6475395072 q^{68} + 1728802848 q^{69} + 1409200000 q^{70} + 13799832984 q^{71} + 7271677952 q^{72} - 17842079516 q^{73} + 12072174464 q^{74} + 5898437500 q^{75} - 29590937600 q^{76} + 90377541264 q^{77} + 35021307136 q^{78} - 12636930320 q^{79} + 6553600000 q^{80} + 66213933922 q^{81} - 25128673152 q^{82} + 41986488924 q^{83} - 67017539584 q^{84} - 19761337500 q^{85} - 46495591552 q^{86} - 24785411160 q^{87} + 13814464512 q^{88} + 13208740020 q^{89} + 22191400000 q^{90} - 89014903096 q^{91} - 46321741824 q^{92} + 57180301568 q^{93} - 41220087936 q^{94} - 90304375000 q^{95} + 20266876928 q^{96} - 61787462828 q^{97} + 271423966272 q^{98} - 251492724912 q^{99}+O(q^{100}) \) 2 * q + 64 * q^2 + 604 * q^3 + 2048 * q^4 + 6250 * q^5 + 19328 * q^6 + 14092 * q^7 + 65536 * q^8 + 221914 * q^9 + 200000 * q^10 + 421584 * q^11 + 618496 * q^12 + 1730524 * q^13 + 450944 * q^14 + 1887500 * q^15 + 2097152 * q^16 - 6323628 * q^17 + 7101248 * q^18 - 28897400 * q^19 + 6400000 * q^20 - 65446816 * q^21 + 13490688 * q^22 - 45236076 * q^23 + 19791872 * q^24 + 19531250 * q^25 + 55376768 * q^26 + 197876440 * q^27 + 14430208 * q^28 + 58226220 * q^29 + 60400000 * q^30 + 41413384 * q^31 + 67108864 * q^32 - 366506832 * q^33 - 202356096 * q^34 + 44037500 * q^35 + 227239936 * q^36 + 377255452 * q^37 - 924716800 * q^38 + 1094415848 * q^39 + 204800000 * q^40 - 785271036 * q^41 - 2094298112 * q^42 - 1452987236 * q^43 + 431702016 * q^44 + 693481250 * q^45 - 1447554432 * q^46 - 1288127748 * q^47 + 633339904 * q^48 + 8481998946 * q^49 + 625000000 * q^50 - 3889762056 * q^51 + 1772056576 * q^52 - 30490836 * q^53 + 6332046080 * q^54 + 1317450000 * q^55 + 461766656 * q^56 - 5811319600 * q^57 + 1863239040 * q^58 + 8677102440 * q^59 + 1932800000 * q^60 + 1115498764 * q^61 + 1325228288 * q^62 - 40536764356 * q^63 + 2147483648 * q^64 + 5407887500 * q^65 - 11728218624 * q^66 - 12673769708 * q^67 - 6475395072 * q^68 + 1728802848 * q^69 + 1409200000 * q^70 + 13799832984 * q^71 + 7271677952 * q^72 - 17842079516 * q^73 + 12072174464 * q^74 + 5898437500 * q^75 - 29590937600 * q^76 + 90377541264 * q^77 + 35021307136 * q^78 - 12636930320 * q^79 + 6553600000 * q^80 + 66213933922 * q^81 - 25128673152 * q^82 + 41986488924 * q^83 - 67017539584 * q^84 - 19761337500 * q^85 - 46495591552 * q^86 - 24785411160 * q^87 + 13814464512 * q^88 + 13208740020 * q^89 + 22191400000 * q^90 - 89014903096 * q^91 - 46321741824 * q^92 + 57180301568 * q^93 - 41220087936 * q^94 - 90304375000 * q^95 + 20266876928 * q^96 - 61787462828 * q^97 + 271423966272 * q^98 - 251492724912 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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