LMFDB - Embedded newform 10.12.a.d.1.1

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			1.1
Root			$22.6867$ 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)

$f(q)$	$=$	\(q+32.0000 q^{2} -141.734 q^{3} +1024.00 q^{4} +3125.00 q^{5} -4535.49 q^{6} +85586.9 q^{7} +32768.0 q^{8} -157058. q^{9} +100000. q^{10} +767235. q^{11} -145136. q^{12} +220960. q^{13} +2.73878e6 q^{14} -442919. q^{15} +1.04858e6 q^{16} -930719. q^{17} -5.02587e6 q^{18} -1.77341e7 q^{19} +3.20000e6 q^{20} -1.21306e7 q^{21} +2.45515e7 q^{22} -3.99596e7 q^{23} -4.64434e6 q^{24} +9.76562e6 q^{25} +7.07072e6 q^{26} +4.73683e7 q^{27} +8.76410e7 q^{28} +7.68554e7 q^{29} -1.41734e7 q^{30} -2.96314e7 q^{31} +3.35544e7 q^{32} -1.08743e8 q^{33} -2.97830e7 q^{34} +2.67459e8 q^{35} -1.60828e8 q^{36} +5.40911e7 q^{37} -5.67491e8 q^{38} -3.13176e7 q^{39} +1.02400e8 q^{40} +1.26006e8 q^{41} -3.88179e8 q^{42} -2.88676e8 q^{43} +7.85648e8 q^{44} -4.90808e8 q^{45} -1.27871e9 q^{46} -1.57008e9 q^{47} -1.48619e8 q^{48} +5.34780e9 q^{49} +3.12500e8 q^{50} +1.31915e8 q^{51} +2.26263e8 q^{52} -4.09006e9 q^{53} +1.51579e9 q^{54} +2.39761e9 q^{55} +2.80451e9 q^{56} +2.51353e9 q^{57} +2.45937e9 q^{58} +3.77882e9 q^{59} -4.53549e8 q^{60} -9.64103e9 q^{61} -9.48205e8 q^{62} -1.34422e10 q^{63} +1.07374e9 q^{64} +6.90500e8 q^{65} -3.47979e9 q^{66} -1.63819e10 q^{67} -9.53056e8 q^{68} +5.66364e9 q^{69} +8.55869e9 q^{70} +1.03471e10 q^{71} -5.14649e9 q^{72} +4.27149e9 q^{73} +1.73091e9 q^{74} -1.38412e9 q^{75} -1.81597e10 q^{76} +6.56653e10 q^{77} -1.00216e9 q^{78} -1.96636e10 q^{79} +3.27680e9 q^{80} +2.11087e10 q^{81} +4.03220e9 q^{82} -1.35791e10 q^{83} -1.24217e10 q^{84} -2.90850e9 q^{85} -9.23762e9 q^{86} -1.08930e10 q^{87} +2.51407e10 q^{88} +2.25058e10 q^{89} -1.57058e10 q^{90} +1.89113e10 q^{91} -4.09186e10 q^{92} +4.19978e9 q^{93} -5.02424e10 q^{94} -5.54191e10 q^{95} -4.75581e9 q^{96} -1.08976e11 q^{97} +1.71130e11 q^{98} -1.20501e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 200000 q^{10} + 421584 q^{11} + 618496 q^{12} + 1730524 q^{13} + 450944 q^{14} + 1887500 q^{15}+ \cdots - 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

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
$3$	−141.734	−0.336750	−0.168375	−	0.985723i	$-0.553852\pi$
$3$	−141.734	−0.336750	−0.168375	+	0.985723i	$0.553852\pi$
$4$	1024.00	0.500000
$5$	3125.00	0.447214
$5$	3125.00	0.447214
$6$	−4535.49	−0.238118
$7$	85586.9	1.92472	0.962362	−	0.271772i	$-0.0876097\pi$
$7$	85586.9	1.92472	0.962362	+	0.271772i	$0.0876097\pi$
$8$	32768.0	0.353553
$9$	−157058.	−0.886599
$10$	100000.	0.316228
$11$	767235.	1.43638	0.718188	−	0.695849i	$-0.244972\pi$
$11$	767235.	1.43638	0.718188	+	0.695849i	$0.244972\pi$
$12$	−145136.	−0.168375
$13$	220960.	0.165054	0.0825268	−	0.996589i	$-0.473701\pi$
$13$	220960.	0.165054	0.0825268	+	0.996589i	$0.473701\pi$
$14$	2.73878e6	1.36098
$15$	−442919.	−0.150599
$16$	1.04858e6	0.250000
$17$	−930719.	−0.158983	−0.0794913	−	0.996836i	$-0.525330\pi$
$17$	−930719.	−0.158983	−0.0794913	+	0.996836i	$0.525330\pi$
$18$	−5.02587e6	−0.626920
$19$	−1.77341e7	−1.64310	−0.821551	−	0.570135i	$-0.806891\pi$
$19$	−1.77341e7	−1.64310	−0.821551	+	0.570135i	$0.806891\pi$
$20$	3.20000e6	0.223607
$21$	−1.21306e7	−0.648151
$22$	2.45515e7	1.01567
$23$	−3.99596e7	−1.29455	−0.647274	−	0.762257i	$-0.724091\pi$
$23$	−3.99596e7	−1.29455	−0.647274	+	0.762257i	$0.724091\pi$
$24$	−4.64434e6	−0.119059
$25$	9.76562e6	0.200000
$26$	7.07072e6	0.116711
$27$	4.73683e7	0.635312
$28$	8.76410e7	0.962362
$29$	7.68554e7	0.695801	0.347901	−	0.937531i	$-0.386895\pi$
$29$	7.68554e7	0.695801	0.347901	+	0.937531i	$0.386895\pi$
$30$	−1.41734e7	−0.106490
$31$	−2.96314e7	−0.185893	−0.0929465	−	0.995671i	$-0.529629\pi$
$31$	−2.96314e7	−0.185893	−0.0929465	+	0.995671i	$0.529629\pi$
$32$	3.35544e7	0.176777
$33$	−1.08743e8	−0.483700
$34$	−2.97830e7	−0.112418
$35$	2.67459e8	0.860762
$36$	−1.60828e8	−0.443300
$37$	5.40911e7	0.128238	0.0641189	−	0.997942i	$-0.479576\pi$
$37$	5.40911e7	0.128238	0.0641189	+	0.997942i	$0.479576\pi$
$38$	−5.67491e8	−1.16185
$39$	−3.13176e7	−0.0555818
$40$	1.02400e8	0.158114
$41$	1.26006e8	0.169856	0.0849280	−	0.996387i	$-0.472934\pi$
$41$	1.26006e8	0.169856	0.0849280	+	0.996387i	$0.472934\pi$
$42$	−3.88179e8	−0.458312
$43$	−2.88676e8	−0.299457	−0.149728	−	0.988727i	$-0.547840\pi$
$43$	−2.88676e8	−0.299457	−0.149728	+	0.988727i	$0.547840\pi$
$44$	7.85648e8	0.718188
$45$	−4.90808e8	−0.396499
$46$	−1.27871e9	−0.915384
$47$	−1.57008e9	−0.998579	−0.499290	−	0.866435i	$-0.666406\pi$
$47$	−1.57008e9	−0.998579	−0.499290	+	0.866435i	$0.666406\pi$
$48$	−1.48619e8	−0.0841875
$49$	5.34780e9	2.70456
$50$	3.12500e8	0.141421
$51$	1.31915e8	0.0535374
$52$	2.26263e8	0.0825268
$53$	−4.09006e9	−1.34342	−0.671711	−	0.740813i	$-0.734440\pi$
$53$	−4.09006e9	−1.34342	−0.671711	+	0.740813i	$0.734440\pi$
$54$	1.51579e9	0.449234
$55$	2.39761e9	0.642367
$56$	2.80451e9	0.680492
$57$	2.51353e9	0.553315
$58$	2.45937e9	0.492006
$59$	3.77882e9	0.688129	0.344065	−	0.938946i	$-0.388196\pi$
$59$	3.77882e9	0.688129	0.344065	+	0.938946i	$0.388196\pi$
$60$	−4.53549e8	−0.0752996
$61$	−9.64103e9	−1.46154	−0.730768	−	0.682626i	$-0.760838\pi$
$61$	−9.64103e9	−1.46154	−0.730768	+	0.682626i	$0.760838\pi$
$62$	−9.48205e8	−0.131446
$63$	−1.34422e10	−1.70646
$64$	1.07374e9	0.125000
$65$	6.90500e8	0.0738143
$66$	−3.47979e9	−0.342028
$67$	−1.63819e10	−1.48236	−0.741178	−	0.671308i	$-0.765733\pi$
$67$	−1.63819e10	−1.48236	−0.741178	+	0.671308i	$0.765733\pi$
$68$	−9.53056e8	−0.0794913
$69$	5.66364e9	0.435939
$70$	8.55869e9	0.608651
$71$	1.03471e10	0.680609	0.340304	−	0.940315i	$-0.389470\pi$
$71$	1.03471e10	0.680609	0.340304	+	0.940315i	$0.389470\pi$
$72$	−5.14649e9	−0.313460
$73$	4.27149e9	0.241159	0.120580	−	0.992704i	$-0.461525\pi$
$73$	4.27149e9	0.241159	0.120580	+	0.992704i	$0.461525\pi$
$74$	1.73091e9	0.0906778
$75$	−1.38412e9	−0.0673500
$76$	−1.81597e10	−0.821551
$77$	6.56653e10	2.76463
$78$	−1.00216e9	−0.0393023
$79$	−1.96636e10	−0.718977	−0.359489	−	0.933149i	$-0.617049\pi$
$79$	−1.96636e10	−0.718977	−0.359489	+	0.933149i	$0.617049\pi$
$80$	3.27680e9	0.111803
$81$	2.11087e10	0.672658
$82$	4.03220e9	0.120106
$83$	−1.35791e10	−0.378391	−0.189196	−	0.981939i	$-0.560588\pi$
$83$	−1.35791e10	−0.378391	−0.189196	+	0.981939i	$0.560588\pi$
$84$	−1.24217e10	−0.324075
$85$	−2.90850e9	−0.0710991
$86$	−9.23762e9	−0.211748
$87$	−1.08930e10	−0.234311
$88$	2.51407e10	0.507836
$89$	2.25058e10	0.427218	0.213609	−	0.976919i	$-0.431478\pi$
$89$	2.25058e10	0.427218	0.213609	+	0.976919i	$0.431478\pi$
$90$	−1.57058e10	−0.280367
$91$	1.89113e10	0.317683
$92$	−4.09186e10	−0.647274
$93$	4.19978e9	0.0625994
$94$	−5.02424e10	−0.706102
$95$	−5.54191e10	−0.734818
$96$	−4.75581e9	−0.0595296
$97$	−1.08976e11	−1.28851	−0.644255	−	0.764811i	$-0.722832\pi$
$97$	−1.08976e11	−1.28851	−0.644255	+	0.764811i	$0.722832\pi$
$98$	1.71130e11	1.91241
$99$	−1.20501e11	−1.27349
$100$	1.00000e10	0.100000
$101$	1.63516e11	1.54807	0.774037	−	0.633140i	$-0.218234\pi$
$101$	1.63516e11	1.54807	0.774037	+	0.633140i	$0.218234\pi$
$102$	4.22127e9	0.0378566
$103$	−7.69876e10	−0.654359	−0.327180	−	0.944962i	$-0.606098\pi$
$103$	−7.69876e10	−0.654359	−0.327180	+	0.944962i	$0.606098\pi$
$104$	7.24042e9	0.0583553
$105$	−3.79081e10	−0.289862
$106$	−1.30882e11	−0.949943
$107$	1.19891e11	0.826376	0.413188	−	0.910646i	$-0.364415\pi$
$107$	1.19891e11	0.826376	0.413188	+	0.910646i	$0.364415\pi$
$108$	4.85052e10	0.317656
$109$	−7.33426e10	−0.456573	−0.228287	−	0.973594i	$-0.573312\pi$
$109$	−7.33426e10	−0.456573	−0.228287	+	0.973594i	$0.573312\pi$
$110$	7.67235e10	0.454222
$111$	−7.66655e9	−0.0431841
$112$	8.97444e10	0.481181
$113$	2.18835e11	1.11734	0.558669	−	0.829391i	$-0.311312\pi$
$113$	2.18835e11	1.11734	0.558669	+	0.829391i	$0.311312\pi$
$114$	8.04329e10	0.391253
$115$	−1.24874e11	−0.578939
$116$	7.86999e10	0.347901
$117$	−3.47036e10	−0.146337
$118$	1.20922e11	0.486581
$119$	−7.96574e10	−0.305997
$120$	−1.45136e10	−0.0532449
$121$	3.03337e11	1.06318
$122$	−3.08513e11	−1.03346
$123$	−1.78594e10	−0.0571990
$124$	−3.03426e10	−0.0929465
$125$	3.05176e10	0.0894427
$126$	−4.30149e11	−1.20665
$127$	3.93053e11	1.05568	0.527838	−	0.849345i	$-0.323003\pi$
$127$	3.93053e11	1.05568	0.527838	+	0.849345i	$0.323003\pi$
$128$	3.43597e10	0.0883883
$129$	4.09152e10	0.100842
$130$	2.20960e10	0.0521946
$131$	−2.63175e11	−0.596008	−0.298004	−	0.954565i	$-0.596321\pi$
$131$	−2.63175e11	−0.596008	−0.298004	+	0.954565i	$0.596321\pi$
$132$	−1.11353e11	−0.241850
$133$	−1.51781e12	−3.16252
$134$	−5.24220e11	−1.04818
$135$	1.48026e11	0.284120
$136$	−3.04978e10	−0.0562088
$137$	5.20521e11	0.921457	0.460728	−	0.887541i	$-0.347588\pi$
$137$	5.20521e11	0.921457	0.460728	+	0.887541i	$0.347588\pi$
$138$	1.81237e11	0.308255
$139$	6.82675e11	1.11592	0.557960	−	0.829868i	$-0.311584\pi$
$139$	6.82675e11	1.11592	0.557960	+	0.829868i	$0.311584\pi$
$140$	2.73878e11	0.430381
$141$	2.22533e11	0.336272
$142$	3.31107e11	0.481263
$143$	1.69528e11	0.237079
$144$	−1.64688e11	−0.221650
$145$	2.40173e11	0.311172
$146$	1.36688e11	0.170525
$147$	−7.57966e11	−0.910761
$148$	5.53893e10	0.0641189
$149$	1.01566e12	1.13299	0.566493	−	0.824066i	$-0.308300\pi$
$149$	1.01566e12	1.13299	0.566493	+	0.824066i	$0.308300\pi$
$150$	−4.42919e10	−0.0476236
$151$	5.34040e11	0.553605	0.276803	−	0.960927i	$-0.410725\pi$
$151$	5.34040e11	0.553605	0.276803	+	0.960927i	$0.410725\pi$
$152$	−5.81111e11	−0.580924
$153$	1.46177e11	0.140954
$154$	2.10129e12	1.95489
$155$	−9.25981e10	−0.0831338
$156$	−3.20692e10	−0.0277909
$157$	−7.29675e11	−0.610494	−0.305247	−	0.952273i	$-0.598739\pi$
$157$	−7.29675e11	−0.610494	−0.305247	+	0.952273i	$0.598739\pi$
$158$	−6.29237e11	−0.508394
$159$	5.79701e11	0.452397
$160$	1.04858e11	0.0790569
$161$	−3.42002e12	−2.49165
$162$	6.75479e11	0.475641
$163$	−2.12171e11	−0.144429	−0.0722143	−	0.997389i	$-0.523007\pi$
$163$	−2.12171e11	−0.144429	−0.0722143	+	0.997389i	$0.523007\pi$
$164$	1.29030e11	0.0849280
$165$	−3.39823e11	−0.216317
$166$	−4.34531e11	−0.267563
$167$	−2.36613e11	−0.140961	−0.0704804	−	0.997513i	$-0.522453\pi$
$167$	−2.36613e11	−0.140961	−0.0704804	+	0.997513i	$0.522453\pi$
$168$	−3.97495e11	−0.229156
$169$	−1.74334e12	−0.972757
$170$	−9.30719e10	−0.0502747
$171$	2.78529e12	1.45677
$172$	−2.95604e11	−0.149728
$173$	−7.36983e11	−0.361579	−0.180790	−	0.983522i	$-0.557865\pi$
$173$	−7.36983e11	−0.361579	−0.180790	+	0.983522i	$0.557865\pi$
$174$	−3.48577e11	−0.165683
$175$	8.35810e11	0.384945
$176$	8.04504e11	0.359094
$177$	−5.35588e11	−0.231727
$178$	7.20185e11	0.302089
$179$	1.35344e11	0.0550487	0.0275244	−	0.999621i	$-0.491238\pi$
$179$	1.35344e11	0.0550487	0.0275244	+	0.999621i	$0.491238\pi$
$180$	−5.02587e11	−0.198250
$181$	−1.35881e12	−0.519907	−0.259953	−	0.965621i	$-0.583707\pi$
$181$	−1.35881e12	−0.519907	−0.259953	+	0.965621i	$0.583707\pi$
$182$	6.05161e11	0.224636
$183$	1.36646e12	0.492172
$184$	−1.30940e12	−0.457692
$185$	1.69035e11	0.0573497
$186$	1.34393e11	0.0442645
$187$	−7.14080e11	−0.228359
$188$	−1.60776e12	−0.499290
$189$	4.05411e12	1.22280
$190$	−1.77341e12	−0.519594
$191$	1.10648e12	0.314964	0.157482	−	0.987522i	$-0.449662\pi$
$191$	1.10648e12	0.314964	0.157482	+	0.987522i	$0.449662\pi$
$192$	−1.52186e11	−0.0420938
$193$	6.17025e12	1.65858	0.829292	−	0.558816i	$-0.188744\pi$
$193$	6.17025e12	1.65858	0.829292	+	0.558816i	$0.188744\pi$
$194$	−3.48724e12	−0.911114
$195$	−9.78674e10	−0.0248570
$196$	5.47615e12	1.35228
$197$	2.00333e12	0.481047	0.240523	−	0.970643i	$-0.422681\pi$
$197$	2.00333e12	0.481047	0.240523	+	0.970643i	$0.422681\pi$
$198$	−3.85602e12	−0.900494
$199$	−7.73897e12	−1.75789	−0.878944	−	0.476925i	$-0.841751\pi$
$199$	−7.73897e12	−1.75789	−0.878944	+	0.476925i	$0.841751\pi$
$200$	3.20000e11	0.0707107
$201$	2.32187e12	0.499183
$202$	5.23250e12	1.09465
$203$	6.57782e12	1.33922
$204$	1.35081e11	0.0267687
$205$	3.93770e11	0.0759619
$206$	−2.46360e12	−0.462702
$207$	6.27599e12	1.14775
$208$	2.31693e11	0.0412634
$209$	−1.36062e13	−2.36011
$210$	−1.21306e12	−0.204963
$211$	−9.01879e12	−1.48455	−0.742275	−	0.670096i	$-0.766253\pi$
$211$	−9.01879e12	−1.48455	−0.742275	+	0.670096i	$0.766253\pi$
$212$	−4.18822e12	−0.671711
$213$	−1.46654e12	−0.229195
$214$	3.83653e12	0.584336
$215$	−9.02112e11	−0.133921
$216$	1.55217e12	0.224617
$217$	−2.53606e12	−0.357792
$218$	−2.34696e12	−0.322846
$219$	−6.05416e11	−0.0812103
$220$	2.45515e12	0.321184
$221$	−2.05652e11	−0.0262407
$222$	−2.45330e11	−0.0305358
$223$	2.06620e12	0.250897	0.125448	−	0.992100i	$-0.459963\pi$
$223$	2.06620e12	0.250897	0.125448	+	0.992100i	$0.459963\pi$
$224$	2.87182e12	0.340246
$225$	−1.53377e12	−0.177320
$226$	7.00271e12	0.790077
$227$	−1.56806e13	−1.72672	−0.863359	−	0.504591i	$-0.831643\pi$
$227$	−1.56806e13	−1.72672	−0.863359	+	0.504591i	$0.831643\pi$
$228$	2.57385e12	0.276657
$229$	6.02309e12	0.632010	0.316005	−	0.948758i	$-0.397658\pi$
$229$	6.02309e12	0.632010	0.316005	+	0.948758i	$0.397658\pi$
$230$	−3.99596e12	−0.409372
$231$	−9.30701e12	−0.930989
$232$	2.51840e12	0.246003
$233$	1.43129e13	1.36544	0.682718	−	0.730682i	$-0.260798\pi$
$233$	1.43129e13	1.36544	0.682718	+	0.730682i	$0.260798\pi$
$234$	−1.11052e12	−0.103476
$235$	−4.90649e12	−0.446578
$236$	3.86951e12	0.344065
$237$	2.78701e12	0.242116
$238$	−2.54904e12	−0.216373
$239$	2.22886e13	1.84881	0.924407	−	0.381407i	$-0.124560\pi$
$239$	2.22886e13	1.84881	0.924407	+	0.381407i	$0.124560\pi$
$240$	−4.64434e11	−0.0376498
$241$	2.06638e13	1.63726	0.818629	−	0.574323i	$-0.194735\pi$
$241$	2.06638e13	1.63726	0.818629	+	0.574323i	$0.194735\pi$
$242$	9.70679e12	0.751781
$243$	−1.13830e13	−0.861830
$244$	−9.87241e12	−0.730768
$245$	1.67119e13	1.20952
$246$	−5.71501e11	−0.0404458
$247$	−3.91853e12	−0.271200
$248$	−9.70962e11	−0.0657231
$249$	1.92462e12	0.127423
$250$	9.76562e11	0.0632456
$251$	−1.23384e13	−0.781721	−0.390861	−	0.920450i	$-0.627823\pi$
$251$	−1.23384e13	−0.781721	−0.390861	+	0.920450i	$0.627823\pi$
$252$	−1.37648e13	−0.853229
$253$	−3.06584e13	−1.85946
$254$	1.25777e13	0.746475
$255$	4.12233e11	0.0239426
$256$	1.09951e12	0.0625000
$257$	1.19160e13	0.662975	0.331487	−	0.943460i	$-0.392450\pi$
$257$	1.19160e13	0.662975	0.331487	+	0.943460i	$0.392450\pi$
$258$	1.30929e12	0.0713061
$259$	4.62949e12	0.246822
$260$	7.07072e11	0.0369071
$261$	−1.20708e13	−0.616897
$262$	−8.42159e12	−0.421441
$263$	1.54645e12	0.0757845	0.0378923	−	0.999282i	$-0.487936\pi$
$263$	1.54645e12	0.0757845	0.0378923	+	0.999282i	$0.487936\pi$
$264$	−3.56330e12	−0.171014
$265$	−1.27814e13	−0.600797
$266$	−4.85699e13	−2.23624
$267$	−3.18984e12	−0.143866
$268$	−1.67751e13	−0.741178
$269$	1.43195e13	0.619855	0.309927	−	0.950760i	$-0.399695\pi$
$269$	1.43195e13	0.619855	0.309927	+	0.950760i	$0.399695\pi$
$270$	4.73683e12	0.200903
$271$	2.26776e13	0.942468	0.471234	−	0.882008i	$-0.343809\pi$
$271$	2.26776e13	0.942468	0.471234	+	0.882008i	$0.343809\pi$
$272$	−9.75929e11	−0.0397456
$273$	−2.68038e12	−0.106980
$274$	1.66567e13	0.651568
$275$	7.49253e12	0.287275
$276$	5.79957e12	0.217970
$277$	9.25283e12	0.340907	0.170454	−	0.985366i	$-0.445477\pi$
$277$	9.25283e12	0.340907	0.170454	+	0.985366i	$0.445477\pi$
$278$	2.18456e13	0.789074
$279$	4.65386e12	0.164813
$280$	8.76410e12	0.304325
$281$	−2.26511e12	−0.0771265	−0.0385633	−	0.999256i	$-0.512278\pi$
$281$	−2.26511e12	−0.0771265	−0.0385633	+	0.999256i	$0.512278\pi$
$282$	7.12107e12	0.237780
$283$	−3.60409e13	−1.18024	−0.590121	−	0.807315i	$-0.700920\pi$
$283$	−3.60409e13	−1.18024	−0.590121	+	0.807315i	$0.700920\pi$
$284$	1.05954e13	0.340304
$285$	7.85478e12	0.247450
$286$	5.42490e12	0.167640
$287$	1.07845e13	0.326926
$288$	−5.27001e12	−0.156730
$289$	−3.34057e13	−0.974725
$290$	7.68554e12	0.220032
$291$	1.54457e13	0.433905
$292$	4.37401e12	0.120580
$293$	1.63348e13	0.441918	0.220959	−	0.975283i	$-0.429081\pi$
$293$	1.63348e13	0.441918	0.220959	+	0.975283i	$0.429081\pi$
$294$	−2.42549e13	−0.644005
$295$	1.18088e13	0.307741
$296$	1.77246e12	0.0453389
$297$	3.63426e13	0.912548
$298$	3.25012e13	0.801142
$299$	−8.82948e12	−0.213670
$300$	−1.41734e12	−0.0336750
$301$	−2.47069e13	−0.576371
$302$	1.70893e13	0.391458
$303$	−2.31758e13	−0.521314
$304$	−1.85956e13	−0.410776
$305$	−3.01282e13	−0.653618
$306$	4.67767e12	0.0996694
$307$	−5.61322e13	−1.17476	−0.587382	−	0.809310i	$-0.699842\pi$
$307$	−5.61322e13	−1.17476	−0.587382	+	0.809310i	$0.699842\pi$
$308$	6.72412e13	1.38231
$309$	1.09118e13	0.220355
$310$	−2.96314e12	−0.0587845
$311$	6.92340e13	1.34939	0.674694	−	0.738097i	$-0.264275\pi$
$311$	6.92340e13	1.34939	0.674694	+	0.738097i	$0.264275\pi$
$312$	−1.02621e12	−0.0196511
$313$	−3.23822e13	−0.609273	−0.304637	−	0.952469i	$-0.598535\pi$
$313$	−3.23822e13	−0.609273	−0.304637	+	0.952469i	$0.598535\pi$
$314$	−2.33496e13	−0.431684
$315$	−4.20067e13	−0.763151
$316$	−2.01356e13	−0.359489
$317$	−1.84023e13	−0.322885	−0.161442	−	0.986882i	$-0.551615\pi$
$317$	−1.84023e13	−0.322885	−0.161442	+	0.986882i	$0.551615\pi$
$318$	1.85504e13	0.319893
$319$	5.89661e13	0.999433
$320$	3.35544e12	0.0559017
$321$	−1.69927e13	−0.278282
$322$	−1.09441e14	−1.76186
$323$	1.65055e13	0.261224
$324$	2.16153e13	0.336329
$325$	2.15781e12	0.0330107
$326$	−6.78946e12	−0.102126
$327$	1.03951e13	0.153751
$328$	4.12897e12	0.0600532
$329$	−1.34378e14	−1.92199
$330$	−1.08743e13	−0.152959
$331$	6.74629e13	0.933277	0.466639	−	0.884448i	$-0.345465\pi$
$331$	6.74629e13	0.933277	0.466639	+	0.884448i	$0.345465\pi$
$332$	−1.39050e13	−0.189196
$333$	−8.49546e12	−0.113696
$334$	−7.57163e12	−0.0996744
$335$	−5.11934e13	−0.662930
$336$	−1.27198e13	−0.162038
$337$	1.07897e14	1.35222	0.676109	−	0.736802i	$-0.263665\pi$
$337$	1.07897e14	1.35222	0.676109	+	0.736802i	$0.263665\pi$
$338$	−5.57868e13	−0.687843
$339$	−3.10163e13	−0.376264
$340$	−2.97830e12	−0.0355496
$341$	−2.27342e13	−0.267012
$342$	8.91293e13	1.03009
$343$	2.88468e14	3.28081
$344$	−9.45933e12	−0.105874
$345$	1.76989e13	0.194958
$346$	−2.35834e13	−0.255675
$347$	−1.29756e13	−0.138458	−0.0692288	−	0.997601i	$-0.522054\pi$
$347$	−1.29756e13	−0.138458	−0.0692288	+	0.997601i	$0.522054\pi$
$348$	−1.11545e13	−0.117156
$349$	−7.76358e13	−0.802643	−0.401321	−	0.915937i	$-0.631449\pi$
$349$	−7.76358e13	−0.802643	−0.401321	+	0.915937i	$0.631449\pi$
$350$	2.67459e13	0.272197
$351$	1.04665e13	0.104861
$352$	2.57441e13	0.253918
$353$	−4.21031e13	−0.408839	−0.204420	−	0.978883i	$-0.565531\pi$
$353$	−4.21031e13	−0.408839	−0.204420	+	0.978883i	$0.565531\pi$
$354$	−1.71388e13	−0.163856
$355$	3.23347e13	0.304377
$356$	2.30459e13	0.213609
$357$	1.12902e13	0.103045
$358$	4.33101e12	0.0389253
$359$	1.84963e14	1.63707	0.818533	−	0.574460i	$-0.194788\pi$
$359$	1.84963e14	1.63707	0.818533	+	0.574460i	$0.194788\pi$
$360$	−1.60828e13	−0.140184
$361$	1.98008e14	1.69978
$362$	−4.34818e13	−0.367630
$363$	−4.29933e13	−0.358025
$364$	1.93652e13	0.158841
$365$	1.33484e13	0.107850
$366$	4.37268e13	0.348018
$367$	−1.68959e14	−1.32470	−0.662351	−	0.749194i	$-0.730441\pi$
$367$	−1.68959e14	−1.32470	−0.662351	+	0.749194i	$0.730441\pi$
$368$	−4.19007e13	−0.323637
$369$	−1.97903e13	−0.150594
$370$	5.40911e12	0.0405524
$371$	−3.50056e14	−2.58572
$372$	4.30058e12	0.0312997
$373$	−1.87187e14	−1.34238	−0.671191	−	0.741284i	$-0.734217\pi$
$373$	−1.87187e14	−1.34238	−0.671191	+	0.741284i	$0.734217\pi$
$374$	−2.28505e13	−0.161474
$375$	−4.32538e12	−0.0301198
$376$	−5.14483e13	−0.353051
$377$	1.69820e13	0.114845
$378$	1.29732e14	0.864651
$379$	−7.47613e13	−0.491090	−0.245545	−	0.969385i	$-0.578967\pi$
$379$	−7.47613e13	−0.491090	−0.245545	+	0.969385i	$0.578967\pi$
$380$	−5.67491e13	−0.367409
$381$	−5.57090e13	−0.355499
$382$	3.54074e13	0.222713
$383$	−1.55521e14	−0.964264	−0.482132	−	0.876099i	$-0.660137\pi$
$383$	−1.55521e14	−0.964264	−0.482132	+	0.876099i	$0.660137\pi$
$384$	−4.86995e12	−0.0297648
$385$	2.05204e14	1.23638
$386$	1.97448e14	1.17280
$387$	4.53390e13	0.265498
$388$	−1.11592e14	−0.644255
$389$	−8.76448e13	−0.498889	−0.249444	−	0.968389i	$-0.580248\pi$
$389$	−8.76448e13	−0.498889	−0.249444	+	0.968389i	$0.580248\pi$
$390$	−3.13176e12	−0.0175765
$391$	3.71912e13	0.205811
$392$	1.75237e14	0.956206
$393$	3.73009e13	0.200706
$394$	6.41064e13	0.340151
$395$	−6.14489e13	−0.321536
$396$	−1.23393e14	−0.636745
$397$	5.19767e13	0.264521	0.132261	−	0.991215i	$-0.457776\pi$
$397$	5.19767e13	0.264521	0.132261	+	0.991215i	$0.457776\pi$
$398$	−2.47647e14	−1.24301
$399$	2.15125e14	1.06498
$400$	1.02400e13	0.0500000
$401$	−3.40753e14	−1.64114	−0.820570	−	0.571546i	$-0.806344\pi$
$401$	−3.40753e14	−1.64114	−0.820570	+	0.571546i	$0.806344\pi$
$402$	7.42999e13	0.352976
$403$	−6.54735e12	−0.0306823
$404$	1.67440e14	0.774037
$405$	6.59648e13	0.300822
$406$	2.10490e14	0.946975
$407$	4.15005e13	0.184198
$408$	4.32258e12	0.0189283
$409$	3.34635e14	1.44575	0.722875	−	0.690979i	$-0.242820\pi$
$409$	3.34635e14	1.44575	0.722875	+	0.690979i	$0.242820\pi$
$410$	1.26006e13	0.0537132
$411$	−7.37756e13	−0.310301
$412$	−7.88353e13	−0.327180
$413$	3.23417e14	1.32446
$414$	2.00832e14	0.811579
$415$	−4.24347e13	−0.169222
$416$	7.41419e12	0.0291776
$417$	−9.67584e13	−0.375786
$418$	−4.35399e14	−1.66885
$419$	1.37830e14	0.521396	0.260698	−	0.965420i	$-0.416047\pi$
$419$	1.37830e14	0.521396	0.260698	+	0.965420i	$0.416047\pi$
$420$	−3.88179e13	−0.144931
$421$	4.35453e14	1.60468	0.802342	−	0.596864i	$-0.203587\pi$
$421$	4.35453e14	1.60468	0.802342	+	0.596864i	$0.203587\pi$
$422$	−2.88601e14	−1.04974
$423$	2.46594e14	0.885340
$424$	−1.34023e14	−0.474972
$425$	−9.08905e12	−0.0317965
$426$	−4.69292e13	−0.162065
$427$	−8.25146e14	−2.81305
$428$	1.22769e14	0.413188
$429$	−2.40279e13	−0.0798365
$430$	−2.88676e13	−0.0946965
$431$	1.51185e14	0.489647	0.244824	−	0.969568i	$-0.421270\pi$
$431$	1.51185e14	0.489647	0.244824	+	0.969568i	$0.421270\pi$
$432$	4.96693e13	0.158828
$433$	−3.75044e13	−0.118413	−0.0592065	−	0.998246i	$-0.518857\pi$
$433$	−3.75044e13	−0.118413	−0.0592065	+	0.998246i	$0.518857\pi$
$434$	−8.11539e13	−0.252997
$435$	−3.40407e13	−0.104787
$436$	−7.51028e13	−0.228287
$437$	7.08648e14	2.12707
$438$	−1.93733e13	−0.0574244
$439$	−1.61934e14	−0.474004	−0.237002	−	0.971509i	$-0.576165\pi$
$439$	−1.61934e14	−0.474004	−0.237002	+	0.971509i	$0.576165\pi$
$440$	7.85648e13	0.227111
$441$	−8.39917e14	−2.39786
$442$	−6.58085e12	−0.0185549
$443$	−1.29342e14	−0.360179	−0.180090	−	0.983650i	$-0.557639\pi$
$443$	−1.29342e14	−0.360179	−0.180090	+	0.983650i	$0.557639\pi$
$444$	−7.85055e12	−0.0215920
$445$	7.03306e13	0.191058
$446$	6.61183e13	0.177411
$447$	−1.43954e14	−0.381533
$448$	9.18983e13	0.240590
$449$	1.30255e13	0.0336852	0.0168426	−	0.999858i	$-0.494639\pi$
$449$	1.30255e13	0.0336852	0.0168426	+	0.999858i	$0.494639\pi$
$450$	−4.90808e13	−0.125384
$451$	9.66764e13	0.243977
$452$	2.24087e14	0.558669
$453$	−7.56916e13	−0.186427
$454$	−5.01780e14	−1.22097
$455$	5.90978e13	0.142072
$456$	8.23633e13	0.195626
$457$	3.45724e14	0.811318	0.405659	−	0.914025i	$-0.367042\pi$
$457$	3.45724e14	0.811318	0.405659	+	0.914025i	$0.367042\pi$
$458$	1.92739e14	0.446899
$459$	−4.40866e13	−0.101004
$460$	−1.27871e14	−0.289470
$461$	2.96945e14	0.664234	0.332117	−	0.943238i	$-0.392237\pi$
$461$	2.96945e14	0.664234	0.332117	+	0.943238i	$0.392237\pi$
$462$	−2.97824e14	−0.658308
$463$	4.55258e14	0.994402	0.497201	−	0.867635i	$-0.334361\pi$
$463$	4.55258e14	0.994402	0.497201	+	0.867635i	$0.334361\pi$
$464$	8.05887e13	0.173950
$465$	1.31243e13	0.0279953
$466$	4.58014e14	0.965509
$467$	−3.66499e14	−0.763537	−0.381768	−	0.924258i	$-0.624685\pi$
$467$	−3.66499e14	−0.763537	−0.381768	+	0.924258i	$0.624685\pi$
$468$	−3.55365e13	−0.0731683
$469$	−1.40208e15	−2.85313
$470$	−1.57008e14	−0.315778
$471$	1.03420e14	0.205584
$472$	1.23824e14	0.243290
$473$	−2.21482e14	−0.430132
$474$	8.91843e13	0.171202
$475$	−1.73185e14	−0.328620
$476$	−8.15691e13	−0.152999
$477$	6.42379e14	1.19108
$478$	7.13234e14	1.30731
$479$	5.78377e14	1.04801	0.524005	−	0.851715i	$-0.324437\pi$
$479$	5.78377e14	1.04801	0.524005	+	0.851715i	$0.324437\pi$
$480$	−1.48619e13	−0.0266224
$481$	1.19520e13	0.0211661
$482$	6.61242e14	1.15772
$483$	4.84734e14	0.839062
$484$	3.10617e14	0.531589
$485$	−3.40551e14	−0.576239
$486$	−3.64255e14	−0.609406
$487$	−4.75203e14	−0.786086	−0.393043	−	0.919520i	$-0.628578\pi$
$487$	−4.75203e14	−0.786086	−0.393043	+	0.919520i	$0.628578\pi$
$488$	−3.15917e14	−0.516731
$489$	3.00718e13	0.0486363
$490$	5.34780e14	0.855257
$491$	7.59641e14	1.20132	0.600662	−	0.799503i	$-0.294904\pi$
$491$	7.59641e14	1.20132	0.600662	+	0.799503i	$0.294904\pi$
$492$	−1.82880e13	−0.0285995
$493$	−7.15307e13	−0.110620
$494$	−1.25393e14	−0.191767
$495$	−3.76565e14	−0.569522
$496$	−3.10708e13	−0.0464732
$497$	8.85576e14	1.30998
$498$	6.15879e13	0.0901019
$499$	−4.91039e14	−0.710499	−0.355249	−	0.934772i	$-0.615604\pi$
$499$	−4.91039e14	−0.710499	−0.355249	+	0.934772i	$0.615604\pi$
$500$	3.12500e13	0.0447214
$501$	3.35362e13	0.0474686
$502$	−3.94828e14	−0.552760
$503$	−4.25544e14	−0.589278	−0.294639	−	0.955609i	$-0.595199\pi$
$503$	−4.25544e14	−0.589278	−0.294639	+	0.955609i	$0.595199\pi$
$504$	−4.40472e14	−0.603324
$505$	5.10987e14	0.692320
$506$	−9.81069e14	−1.31484
$507$	2.47090e14	0.327576
$508$	4.02486e14	0.527838
$509$	−1.41466e15	−1.83529	−0.917644	−	0.397404i	$-0.869911\pi$
$509$	−1.41466e15	−1.83529	−0.917644	+	0.397404i	$0.869911\pi$
$510$	1.31915e13	0.0169300
$511$	3.65584e14	0.464165
$512$	3.51844e13	0.0441942
$513$	−8.40035e14	−1.04388
$514$	3.81311e14	0.468794
$515$	−2.40586e14	−0.292638
$516$	4.18972e13	0.0504210
$517$	−1.20462e15	−1.43434
$518$	1.48144e14	0.174530
$519$	1.04456e14	0.121762
$520$	2.26263e13	0.0260973
$521$	6.27267e14	0.715888	0.357944	−	0.933743i	$-0.383478\pi$
$521$	6.27267e14	0.715888	0.357944	+	0.933743i	$0.383478\pi$
$522$	−3.86265e14	−0.436212
$523$	2.23774e14	0.250063	0.125032	−	0.992153i	$-0.460097\pi$
$523$	2.23774e14	0.250063	0.125032	+	0.992153i	$0.460097\pi$
$524$	−2.69491e14	−0.298004
$525$	−1.18463e14	−0.129630
$526$	4.94865e13	0.0535877
$527$	2.75785e13	0.0295537
$528$	−1.14026e14	−0.120925
$529$	6.43961e14	0.675855
$530$	−4.09006e14	−0.424827
$531$	−5.93495e14	−0.610095
$532$	−1.55424e15	−1.58126
$533$	2.78424e13	0.0280354
$534$	−1.02075e14	−0.101728
$535$	3.74661e14	0.369566
$536$	−5.36802e14	−0.524092
$537$	−1.91829e13	−0.0185377
$538$	4.58224e14	0.438303
$539$	4.10302e15	3.88477
$540$	1.51579e14	0.142060
$541$	5.47756e14	0.508162	0.254081	−	0.967183i	$-0.418227\pi$
$541$	5.47756e14	0.508162	0.254081	+	0.967183i	$0.418227\pi$
$542$	7.25684e14	0.666425
$543$	1.92589e14	0.175079
$544$	−3.12297e13	−0.0281044
$545$	−2.29196e14	−0.204186
$546$	−8.57720e13	−0.0756460
$547$	4.33518e14	0.378509	0.189255	−	0.981928i	$-0.439393\pi$
$547$	4.33518e14	0.378509	0.189255	+	0.981928i	$0.439393\pi$
$548$	5.33013e14	0.460728
$549$	1.51420e15	1.29580
$550$	2.39761e14	0.203134
$551$	−1.36296e15	−1.14327
$552$	1.85586e14	0.154128
$553$	−1.68295e15	−1.38383
$554$	2.96091e14	0.241058
$555$	−2.39580e13	−0.0193125
$556$	6.99060e14	0.557960
$557$	−7.36061e14	−0.581715	−0.290857	−	0.956766i	$-0.593941\pi$
$557$	−7.36061e14	−0.581715	−0.290857	+	0.956766i	$0.593941\pi$
$558$	1.48924e14	0.116540
$559$	−6.37858e13	−0.0494264
$560$	2.80451e14	0.215191
$561$	1.01209e14	0.0768998
$562$	−7.24834e13	−0.0545367
$563$	−9.03199e14	−0.672957	−0.336478	−	0.941691i	$-0.609236\pi$
$563$	−9.03199e14	−0.672957	−0.336478	+	0.941691i	$0.609236\pi$
$564$	2.27874e14	0.168136
$565$	6.83858e14	0.499689
$566$	−1.15331e15	−0.834557
$567$	1.80663e15	1.29468
$568$	3.39054e14	0.240632
$569$	−2.25786e15	−1.58701	−0.793503	−	0.608566i	$-0.791745\pi$
$569$	−2.25786e15	−1.58701	−0.793503	+	0.608566i	$0.791745\pi$
$570$	2.51353e14	0.174973
$571$	9.15100e14	0.630913	0.315457	−	0.948940i	$-0.397842\pi$
$571$	9.15100e14	0.630913	0.315457	+	0.948940i	$0.397842\pi$
$572$	1.73597e14	0.118540
$573$	−1.56826e14	−0.106064
$574$	3.45104e14	0.231172
$575$	−3.90231e14	−0.258910
$576$	−1.68640e14	−0.110825
$577$	2.84484e14	0.185179	0.0925893	−	0.995704i	$-0.470486\pi$
$577$	2.84484e14	0.185179	0.0925893	+	0.995704i	$0.470486\pi$
$578$	−1.06898e15	−0.689234
$579$	−8.74535e14	−0.558528
$580$	2.45937e14	0.155586
$581$	−1.16219e15	−0.728299
$582$	4.94261e14	0.306817
$583$	−3.13804e15	−1.92966
$584$	1.39968e14	0.0852626
$585$	−1.08449e14	−0.0654437
$586$	5.22714e14	0.312484
$587$	−1.99879e15	−1.18374	−0.591871	−	0.806032i	$-0.701611\pi$
$587$	−1.99879e15	−1.18374	−0.591871	+	0.806032i	$0.701611\pi$
$588$	−7.76157e14	−0.455380
$589$	5.25486e14	0.305441
$590$	3.77882e14	0.217606
$591$	−2.83940e14	−0.161992
$592$	5.67186e13	0.0320595
$593$	8.52303e14	0.477302	0.238651	−	0.971105i	$-0.423295\pi$
$593$	8.52303e14	0.477302	0.238651	+	0.971105i	$0.423295\pi$
$594$	1.16296e15	0.645269
$595$	−2.48929e14	−0.136846
$596$	1.04004e15	0.566493
$597$	1.09688e15	0.591969
$598$	−2.82543e14	−0.151087
$599$	1.08984e14	0.0577449	0.0288725	−	0.999583i	$-0.490808\pi$
$599$	1.08984e14	0.0577449	0.0288725	+	0.999583i	$0.490808\pi$
$600$	−4.53549e13	−0.0238118
$601$	3.21315e14	0.167156	0.0835778	−	0.996501i	$-0.473365\pi$
$601$	3.21315e14	0.167156	0.0835778	+	0.996501i	$0.473365\pi$
$602$	−7.90620e14	−0.407556
$603$	2.57291e15	1.31426
$604$	5.46856e14	0.276803
$605$	9.47929e14	0.475468
$606$	−7.41624e14	−0.368625
$607$	−3.08680e15	−1.52044	−0.760222	−	0.649664i	$-0.774910\pi$
$607$	−3.08680e15	−1.52044	−0.760222	+	0.649664i	$0.774910\pi$
$608$	−5.95058e14	−0.290462
$609$	−9.32301e14	−0.450984
$610$	−9.64103e14	−0.462178
$611$	−3.46924e14	−0.164819
$612$	1.49685e14	0.0704769
$613$	8.70867e14	0.406368	0.203184	−	0.979141i	$-0.434871\pi$
$613$	8.70867e14	0.406368	0.203184	+	0.979141i	$0.434871\pi$
$614$	−1.79623e15	−0.830684
$615$	−5.58106e13	−0.0255802
$616$	2.15172e15	0.977444
$617$	3.06108e15	1.37818	0.689091	−	0.724675i	$-0.258010\pi$
$617$	3.06108e15	1.37818	0.689091	+	0.724675i	$0.258010\pi$
$618$	3.49177e14	0.155815
$619$	−1.21317e15	−0.536566	−0.268283	−	0.963340i	$-0.586456\pi$
$619$	−1.21317e15	−0.536566	−0.268283	+	0.963340i	$0.586456\pi$
$620$	−9.48205e13	−0.0415669
$621$	−1.89282e15	−0.822442
$622$	2.21549e15	0.954162
$623$	1.92620e15	0.822276
$624$	−3.28389e13	−0.0138955
$625$	9.53674e13	0.0400000
$626$	−1.03623e15	−0.430821
$627$	1.92847e15	0.794768
$628$	−7.47187e14	−0.305247
$629$	−5.03436e13	−0.0203876
$630$	−1.34422e15	−0.539630
$631$	2.95354e15	1.17539	0.587693	−	0.809084i	$-0.300036\pi$
$631$	2.95354e15	1.17539	0.587693	+	0.809084i	$0.300036\pi$
$632$	−6.44338e14	−0.254197
$633$	1.27827e15	0.499922
$634$	−5.88875e14	−0.228314
$635$	1.22829e15	0.472112
$636$	5.93614e14	0.226199
$637$	1.18165e15	0.446398
$638$	1.88691e15	0.706706
$639$	−1.62510e15	−0.603427
$640$	1.07374e14	0.0395285
$641$	−1.24519e15	−0.454483	−0.227241	−	0.973838i	$-0.572971\pi$
$641$	−1.24519e15	−0.454483	−0.227241	+	0.973838i	$0.572971\pi$
$642$	−5.43767e14	−0.196775
$643$	2.82493e14	0.101356	0.0506778	−	0.998715i	$-0.483862\pi$
$643$	2.82493e14	0.101356	0.0506778	+	0.998715i	$0.483862\pi$
$644$	−3.50210e15	−1.24582
$645$	1.27860e14	0.0450979
$646$	5.28175e14	0.184714
$647$	−3.45042e15	−1.19646	−0.598230	−	0.801324i	$-0.704129\pi$
$647$	−3.45042e15	−1.19646	−0.598230	+	0.801324i	$0.704129\pi$
$648$	6.91691e14	0.237821
$649$	2.89924e15	0.988413
$650$	6.90500e13	0.0233421
$651$	3.59446e14	0.120487
$652$	−2.17263e14	−0.0722143
$653$	3.55303e15	1.17105	0.585527	−	0.810653i	$-0.300888\pi$
$653$	3.55303e15	1.17105	0.585527	+	0.810653i	$0.300888\pi$
$654$	3.32645e14	0.108718
$655$	−8.22421e14	−0.266543
$656$	1.32127e14	0.0424640
$657$	−6.70874e14	−0.213812
$658$	−4.30010e15	−1.35905
$659$	1.76602e14	0.0553511	0.0276756	−	0.999617i	$-0.491189\pi$
$659$	1.76602e14	0.0553511	0.0276756	+	0.999617i	$0.491189\pi$
$660$	−3.47979e14	−0.108159
$661$	3.46137e15	1.06694	0.533470	−	0.845819i	$-0.320888\pi$
$661$	3.46137e15	1.06694	0.533470	+	0.845819i	$0.320888\pi$
$662$	2.15881e15	0.659927
$663$	2.91479e13	0.00883654
$664$	−4.44960e14	−0.133782
$665$	−4.74315e15	−1.41432
$666$	−2.71855e14	−0.0803949
$667$	−3.07111e15	−0.900748
$668$	−2.42292e14	−0.0704804
$669$	−2.92851e14	−0.0844895
$670$	−1.63819e15	−0.468762
$671$	−7.39693e15	−2.09932
$672$	−4.07035e14	−0.114578
$673$	6.92295e15	1.93290	0.966448	−	0.256864i	$-0.0826893\pi$
$673$	6.92295e15	1.93290	0.966448	+	0.256864i	$0.0826893\pi$
$674$	3.45272e15	0.956162
$675$	4.62581e14	0.127062
$676$	−1.78518e15	−0.486379
$677$	−3.89173e15	−1.05173	−0.525865	−	0.850568i	$-0.676258\pi$
$677$	−3.89173e15	−1.05173	−0.525865	+	0.850568i	$0.676258\pi$
$678$	−9.92523e14	−0.266058
$679$	−9.32695e15	−2.48002
$680$	−9.53056e13	−0.0251373
$681$	2.22248e15	0.581472
$682$	−7.27496e14	−0.188806
$683$	4.79007e15	1.23318	0.616592	−	0.787283i	$-0.288513\pi$
$683$	4.79007e15	1.23318	0.616592	+	0.787283i	$0.288513\pi$
$684$	2.85214e15	0.728387
$685$	1.62663e15	0.412088
$686$	9.23099e15	2.31988
$687$	−8.53677e14	−0.212829
$688$	−3.02698e14	−0.0748641
$689$	−9.03740e14	−0.221737
$690$	5.66364e14	0.137856
$691$	1.60990e15	0.388749	0.194374	−	0.980927i	$-0.437732\pi$
$691$	1.60990e15	0.388749	0.194374	+	0.980927i	$0.437732\pi$
$692$	−7.54670e14	−0.180790
$693$	−1.03133e16	−2.45112
$694$	−4.15220e14	−0.0979043
$695$	2.13336e15	0.499054
$696$	−3.56943e14	−0.0828415
$697$	−1.17276e14	−0.0270041
$698$	−2.48435e15	−0.567554
$699$	−2.02863e15	−0.459810
$700$	8.55869e14	0.192472
$701$	−2.46356e15	−0.549686	−0.274843	−	0.961489i	$-0.588626\pi$
$701$	−2.46356e15	−0.549686	−0.274843	+	0.961489i	$0.588626\pi$
$702$	3.34928e14	0.0741477
$703$	−9.59257e14	−0.210708
$704$	8.23812e14	0.179547
$705$	6.95417e14	0.150385
$706$	−1.34730e15	−0.289093
$707$	1.39948e16	2.97962
$708$	−5.48442e14	−0.115864
$709$	6.21323e15	1.30246	0.651228	−	0.758882i	$-0.274254\pi$
$709$	6.21323e15	1.30246	0.651228	+	0.758882i	$0.274254\pi$
$710$	1.03471e15	0.215227
$711$	3.08834e15	0.637445
$712$	7.37470e14	0.151044
$713$	1.18406e15	0.240647
$714$	3.61285e14	0.0728635
$715$	5.29776e14	0.106025
$716$	1.38592e14	0.0275244
$717$	−3.15905e15	−0.622588
$718$	5.91883e15	1.15758
$719$	7.12825e15	1.38348	0.691742	−	0.722145i	$-0.256844\pi$
$719$	7.12825e15	1.38348	0.691742	+	0.722145i	$0.256844\pi$
$720$	−5.14649e14	−0.0991248
$721$	−6.58914e15	−1.25946
$722$	6.33627e15	1.20193
$723$	−2.92877e15	−0.551346
$724$	−1.39142e15	−0.259953
$725$	7.50541e14	0.139160
$726$	−1.37578e15	−0.253162
$727$	5.59273e15	1.02137	0.510686	−	0.859767i	$-0.329391\pi$
$727$	5.59273e15	1.02137	0.510686	+	0.859767i	$0.329391\pi$
$728$	6.19685e14	0.112318
$729$	−2.12599e15	−0.382437
$730$	4.27149e14	0.0762612
$731$	2.68676e14	0.0476084
$732$	1.39926e15	0.246086
$733$	−2.75558e15	−0.480995	−0.240498	−	0.970650i	$-0.577311\pi$
$733$	−2.75558e15	−0.480995	−0.240498	+	0.970650i	$0.577311\pi$
$734$	−5.40669e15	−0.936705
$735$	−2.36864e15	−0.407304
$736$	−1.34082e15	−0.228846
$737$	−1.25688e16	−2.12922
$738$	−6.33291e14	−0.106486
$739$	1.99004e15	0.332138	0.166069	−	0.986114i	$-0.446893\pi$
$739$	1.99004e15	0.332138	0.166069	+	0.986114i	$0.446893\pi$
$740$	1.73091e14	0.0286749
$741$	5.55389e14	0.0913266
$742$	−1.12018e16	−1.82838
$743$	−7.01045e15	−1.13581	−0.567907	−	0.823093i	$-0.692247\pi$
$743$	−7.01045e15	−1.13581	−0.567907	+	0.823093i	$0.692247\pi$
$744$	1.37618e14	0.0221322
$745$	3.17394e15	0.506687
$746$	−5.98997e15	−0.949208
$747$	2.13271e15	0.335481
$748$	−7.31218e14	−0.114179
$749$	1.02611e16	1.59054
$750$	−1.38412e14	−0.0212979
$751$	−9.37589e15	−1.43216	−0.716082	−	0.698016i	$-0.754066\pi$
$751$	−9.37589e15	−1.43216	−0.716082	+	0.698016i	$0.754066\pi$
$752$	−1.64634e15	−0.249645
$753$	1.74877e15	0.263245
$754$	5.43423e14	0.0812074
$755$	1.66887e15	0.247580
$756$	4.15141e15	0.611400
$757$	1.88289e15	0.275294	0.137647	−	0.990481i	$-0.456046\pi$
$757$	1.88289e15	0.275294	0.137647	+	0.990481i	$0.456046\pi$
$758$	−2.39236e15	−0.347253
$759$	4.34534e15	0.626173
$760$	−1.81597e15	−0.259797
$761$	6.71695e15	0.954018	0.477009	−	0.878898i	$-0.341721\pi$
$761$	6.71695e15	0.954018	0.477009	+	0.878898i	$0.341721\pi$
$762$	−1.78269e15	−0.251375
$763$	−6.27717e15	−0.878777
$764$	1.13304e15	0.157482
$765$	4.56804e14	0.0630365
$766$	−4.97667e15	−0.681837
$767$	8.34968e14	0.113578
$768$	−1.55838e14	−0.0210469
$769$	−5.72271e15	−0.767374	−0.383687	−	0.923463i	$-0.625346\pi$
$769$	−5.72271e15	−0.767374	−0.383687	+	0.923463i	$0.625346\pi$
$770$	6.56653e15	0.874252
$771$	−1.68890e15	−0.223257
$772$	6.31833e15	0.829292
$773$	−3.24936e15	−0.423458	−0.211729	−	0.977328i	$-0.567909\pi$
$773$	−3.24936e15	−0.423458	−0.211729	+	0.977328i	$0.567909\pi$
$774$	1.45085e15	0.187735
$775$	−2.89369e14	−0.0371786
$776$	−3.57094e15	−0.455557
$777$	−6.56157e14	−0.0831174
$778$	−2.80463e15	−0.352767
$779$	−2.23461e15	−0.279091
$780$	−1.00216e14	−0.0124285
$781$	7.93865e15	0.977611
$782$	1.19012e15	0.145530
$783$	3.64051e15	0.442051
$784$	5.60757e15	0.676140
$785$	−2.28023e15	−0.273021
$786$	1.19363e15	0.141920
$787$	1.29754e16	1.53201	0.766003	−	0.642838i	$-0.222243\pi$
$787$	1.29754e16	1.53201	0.766003	+	0.642838i	$0.222243\pi$
$788$	2.05140e15	0.240523
$789$	−2.19185e14	−0.0255204
$790$	−1.96636e15	−0.227361
$791$	1.87294e16	2.15057
$792$	−3.94857e15	−0.450247
$793$	−2.13028e15	−0.241232
$794$	1.66325e15	0.187045
$795$	1.81157e15	0.202318
$796$	−7.92470e15	−0.878944
$797$	−1.21467e16	−1.33795	−0.668974	−	0.743286i	$-0.733266\pi$
$797$	−1.21467e16	−1.33795	−0.668974	+	0.743286i	$0.733266\pi$
$798$	6.88401e15	0.753053
$799$	1.46130e15	0.158757
$800$	3.27680e14	0.0353553
$801$	−3.53473e15	−0.378771
$802$	−1.09041e16	−1.16046
$803$	3.27724e15	0.346395
$804$	2.37760e15	0.249592
$805$	−1.06876e16	−1.11430
$806$	−2.09515e14	−0.0216957
$807$	−2.02956e15	−0.208736
$808$	5.35808e15	0.547327
$809$	3.06008e15	0.310468	0.155234	−	0.987878i	$-0.450387\pi$
$809$	3.06008e15	0.310468	0.155234	+	0.987878i	$0.450387\pi$
$810$	2.11087e15	0.212713
$811$	1.63765e15	0.163910	0.0819552	−	0.996636i	$-0.473884\pi$
$811$	1.63765e15	0.163910	0.0819552	+	0.996636i	$0.473884\pi$
$812$	6.73568e15	0.669612
$813$	−3.21419e15	−0.317376
$814$	1.32802e15	0.130248
$815$	−6.63033e14	−0.0645904
$816$	1.38323e14	0.0133843
$817$	5.11941e15	0.492038
$818$	1.07083e16	1.02230
$819$	−2.97018e15	−0.281657
$820$	4.03220e14	0.0379810
$821$	1.07044e15	0.100156	0.0500778	−	0.998745i	$-0.484053\pi$
$821$	1.07044e15	0.100156	0.0500778	+	0.998745i	$0.484053\pi$
$822$	−2.36082e15	−0.219416
$823$	−3.24575e15	−0.299651	−0.149825	−	0.988712i	$-0.547871\pi$
$823$	−3.24575e15	−0.299651	−0.149825	+	0.988712i	$0.547871\pi$
$824$	−2.52273e15	−0.231351
$825$	−1.06195e15	−0.0967400
$826$	1.03494e16	0.936533
$827$	−2.05440e16	−1.84674	−0.923369	−	0.383913i	$-0.874576\pi$
$827$	−2.05440e16	−1.84674	−0.923369	+	0.383913i	$0.874576\pi$
$828$	6.42662e15	0.573873
$829$	5.85872e15	0.519700	0.259850	−	0.965649i	$-0.416327\pi$
$829$	5.85872e15	0.519700	0.259850	+	0.965649i	$0.416327\pi$
$830$	−1.35791e15	−0.119658
$831$	−1.31144e15	−0.114800
$832$	2.37254e14	0.0206317
$833$	−4.97730e15	−0.429978
$834$	−3.09627e15	−0.265721
$835$	−7.39417e14	−0.0630396
$836$	−1.39328e16	−1.18006
$837$	−1.40359e15	−0.118100
$838$	4.41057e15	0.368683
$839$	−2.25383e16	−1.87168	−0.935838	−	0.352430i	$-0.885355\pi$
$839$	−2.25383e16	−1.87168	−0.935838	+	0.352430i	$0.885355\pi$
$840$	−1.24217e15	−0.102482
$841$	−6.29376e15	−0.515861
$842$	1.39345e16	1.13468
$843$	3.21043e14	0.0259724
$844$	−9.23524e15	−0.742275
$845$	−5.44793e15	−0.435030
$846$	7.89100e15	0.626030
$847$	2.59617e16	2.04632
$848$	−4.28874e15	−0.335856
$849$	5.10823e15	0.397446
$850$	−2.90850e14	−0.0224835
$851$	−2.16146e15	−0.166010
$852$	−1.50173e15	−0.114597
$853$	1.84471e16	1.39865	0.699326	−	0.714803i	$-0.253484\pi$
$853$	1.84471e16	1.39865	0.699326	+	0.714803i	$0.253484\pi$
$854$	−2.64047e16	−1.98913
$855$	8.70403e15	0.651489
$856$	3.92860e15	0.292168
$857$	−1.53957e15	−0.113764	−0.0568820	−	0.998381i	$-0.518116\pi$
$857$	−1.53957e15	−0.113764	−0.0568820	+	0.998381i	$0.518116\pi$
$858$	−7.68894e14	−0.0564529
$859$	−2.14973e16	−1.56827	−0.784136	−	0.620589i	$-0.786893\pi$
$859$	−2.14973e16	−1.56827	−0.784136	+	0.620589i	$0.786893\pi$
$860$	−9.23762e14	−0.0669605
$861$	−1.52853e15	−0.110092
$862$	4.83792e15	0.346233
$863$	−1.16923e16	−0.831462	−0.415731	−	0.909488i	$-0.636474\pi$
$863$	−1.16923e16	−0.831462	−0.415731	+	0.909488i	$0.636474\pi$
$864$	1.58942e15	0.112308
$865$	−2.30307e15	−0.161703
$866$	−1.20014e15	−0.0837306
$867$	4.73472e15	0.328239
$868$	−2.59693e15	−0.178896
$869$	−1.50866e16	−1.03272
$870$	−1.08930e15	−0.0740957
$871$	−3.61974e15	−0.244668
$872$	−2.40329e15	−0.161423
$873$	1.71156e16	1.14239
$874$	2.26767e16	1.50407
$875$	2.61191e15	0.172152
$876$	−6.19946e14	−0.0406052
$877$	1.13573e16	0.739225	0.369613	−	0.929186i	$-0.379490\pi$
$877$	1.13573e16	0.739225	0.369613	+	0.929186i	$0.379490\pi$
$878$	−5.18188e15	−0.335172
$879$	−2.31520e15	−0.148816
$880$	2.51407e15	0.160592
$881$	1.12847e16	0.716346	0.358173	−	0.933655i	$-0.383400\pi$
$881$	1.12847e16	0.716346	0.358173	+	0.933655i	$0.383400\pi$
$882$	−2.68773e16	−1.69554
$883$	−5.36286e15	−0.336211	−0.168106	−	0.985769i	$-0.553765\pi$
$883$	−5.36286e15	−0.336211	−0.168106	+	0.985769i	$0.553765\pi$
$884$	−2.10587e14	−0.0131203
$885$	−1.67371e15	−0.103632
$886$	−4.13894e15	−0.254685
$887$	8.12685e15	0.496984	0.248492	−	0.968634i	$-0.420065\pi$
$887$	8.12685e15	0.496984	0.248492	+	0.968634i	$0.420065\pi$
$888$	−2.51218e14	−0.0152679
$889$	3.36402e16	2.03188
$890$	2.25058e15	0.135098
$891$	1.61953e16	0.966190
$892$	2.11579e15	0.125448
$893$	2.78439e16	1.64077
$894$	−4.60653e15	−0.269785
$895$	4.22950e14	0.0246185
$896$	2.94075e15	0.170123
$897$	1.25144e15	0.0719534
$898$	4.16815e14	0.0238190
$899$	−2.27733e15	−0.129345
$900$	−1.57058e15	−0.0886599
$901$	3.80670e15	0.213581
$902$	3.09364e15	0.172518
$903$	3.50181e15	0.194093
$904$	7.17077e15	0.395039
$905$	−4.24627e15	−0.232509
$906$	−2.42213e15	−0.131823
$907$	−1.18191e16	−0.639361	−0.319680	−	0.947525i	$-0.603576\pi$
$907$	−1.18191e16	−0.639361	−0.319680	+	0.947525i	$0.603576\pi$
$908$	−1.60570e16	−0.863359
$909$	−2.56815e16	−1.37252
$910$	1.89113e15	0.100460
$911$	1.50443e16	0.794366	0.397183	−	0.917739i	$-0.369988\pi$
$911$	1.50443e16	0.794366	0.397183	+	0.917739i	$0.369988\pi$
$912$	2.63563e15	0.138329
$913$	−1.04183e16	−0.543513
$914$	1.10632e16	0.573688
$915$	4.27020e15	0.220106
$916$	6.16764e15	0.316005
$917$	−2.25243e16	−1.14715
$918$	−1.41077e15	−0.0714203
$919$	−3.98208e15	−0.200389	−0.100195	−	0.994968i	$-0.531947\pi$
$919$	−3.98208e15	−0.200389	−0.100195	+	0.994968i	$0.531947\pi$
$920$	−4.09186e15	−0.204686
$921$	7.95585e15	0.395602
$922$	9.50225e15	0.469685
$923$	2.28629e15	0.112337
$924$	−9.53038e15	−0.465494
$925$	5.28233e14	0.0256476
$926$	1.45682e16	0.703148
$927$	1.20916e16	0.580154
$928$	2.57884e15	0.123001
$929$	4.06546e16	1.92763	0.963814	−	0.266575i	$-0.0858919\pi$
$929$	4.06546e16	1.92763	0.963814	+	0.266575i	$0.0858919\pi$
$930$	4.19978e14	0.0197957
$931$	−9.48384e16	−4.44387
$932$	1.46564e16	0.682718
$933$	−9.81282e15	−0.454407
$934$	−1.17280e16	−0.539902
$935$	−2.23150e15	−0.102125
$936$	−1.13717e15	−0.0517378
$937$	−1.18458e15	−0.0535792	−0.0267896	−	0.999641i	$-0.508528\pi$
$937$	−1.18458e15	−0.0535792	−0.0267896	+	0.999641i	$0.508528\pi$
$938$	−4.48664e16	−2.01746
$939$	4.58966e15	0.205173
$940$	−5.02424e15	−0.223289
$941$	−1.02223e16	−0.451652	−0.225826	−	0.974168i	$-0.572508\pi$
$941$	−1.02223e16	−0.451652	−0.225826	+	0.974168i	$0.572508\pi$
$942$	3.30944e15	0.145370
$943$	−5.03516e15	−0.219887
$944$	3.96238e15	0.172032
$945$	1.26691e16	0.546853
$946$	−7.08743e15	−0.304150
$947$	−1.68932e16	−0.720755	−0.360378	−	0.932807i	$-0.617352\pi$
$947$	−1.68932e16	−0.720755	−0.360378	+	0.932807i	$0.617352\pi$
$948$	2.85390e15	0.121058
$949$	9.43829e14	0.0398042
$950$	−5.54191e15	−0.232370
$951$	2.60824e15	0.108731
$952$	−2.61021e15	−0.108186
$953$	−3.76078e16	−1.54977	−0.774884	−	0.632103i	$-0.782192\pi$
$953$	−3.76078e16	−1.54977	−0.774884	+	0.632103i	$0.782192\pi$
$954$	2.05561e16	0.842219
$955$	3.45775e15	0.140856
$956$	2.28235e16	0.924407
$957$	−8.35751e15	−0.336559
$958$	1.85081e16	0.741055
$959$	4.45498e16	1.77355
$960$	−4.75581e14	−0.0188249
$961$	−2.45305e16	−0.965444
$962$	3.82463e14	0.0149667
$963$	−1.88300e16	−0.732664
$964$	2.11598e16	0.818629
$965$	1.92820e16	0.741741
$966$	1.55115e16	0.593306
$967$	−3.52262e16	−1.33974	−0.669869	−	0.742479i	$-0.733650\pi$
$967$	−3.52262e16	−1.33974	−0.669869	+	0.742479i	$0.733650\pi$
$968$	9.93976e15	0.375890
$969$	−2.33939e15	−0.0879674
$970$	−1.08976e16	−0.407462
$971$	3.56726e16	1.32626	0.663131	−	0.748504i	$-0.269227\pi$
$971$	3.56726e16	1.32626	0.663131	+	0.748504i	$0.269227\pi$
$972$	−1.16562e16	−0.430915
$973$	5.84281e16	2.14784
$974$	−1.52065e16	−0.555847
$975$	−3.05836e14	−0.0111164
$976$	−1.01094e16	−0.365384
$977$	−4.79343e16	−1.72277	−0.861383	−	0.507957i	$-0.830401\pi$
$977$	−4.79343e16	−1.72277	−0.861383	+	0.507957i	$0.830401\pi$
$978$	9.62298e14	0.0343911
$979$	1.72672e16	0.613646
$980$	1.71130e16	0.604758
$981$	1.15191e16	0.404798
$982$	2.43085e16	0.849464
$983$	2.05131e16	0.712833	0.356416	−	0.934327i	$-0.383998\pi$
$983$	2.05131e16	0.712833	0.356416	+	0.934327i	$0.383998\pi$
$984$	−5.85217e14	−0.0202229
$985$	6.26039e15	0.215131
$986$	−2.28898e15	−0.0782203
$987$	1.90460e16	0.647230
$988$	−4.01257e15	−0.135600
$989$	1.15354e16	0.387661
$990$	−1.20501e16	−0.402713
$991$	−2.11314e16	−0.702301	−0.351150	−	0.936319i	$-0.614209\pi$
$991$	−2.11314e16	−0.702301	−0.351150	+	0.936319i	$0.614209\pi$
$992$	−9.94265e14	−0.0328615
$993$	−9.56179e15	−0.314281
$994$	2.83384e16	0.926298
$995$	−2.41843e16	−0.786151
$996$	1.97081e15	0.0637116
$997$	4.57566e16	1.47106	0.735531	−	0.677491i	$-0.236933\pi$
$997$	4.57566e16	1.47106	0.735531	+	0.677491i	$0.236933\pi$
$998$	−1.57133e16	−0.502398
$999$	2.56220e15	0.0814711

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.12.a.d.1.1	✓	2
3.2	odd	2		90.12.a.l.1.2		2
4.3	odd	2		80.12.a.g.1.2		2
5.2	odd	4		50.12.b.f.49.4		4
5.3	odd	4		50.12.b.f.49.1		4
5.4	even	2		50.12.a.f.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.12.a.d.1.1	✓	2	1.1	even	1	trivial
50.12.a.f.1.2		2	5.4	even	2
50.12.b.f.49.1		4	5.3	odd	4
50.12.b.f.49.4		4	5.2	odd	4
80.12.a.g.1.2		2	4.3	odd	2
90.12.a.l.1.2		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)

\(f(q)\)	\(=\)	\(q+32.0000 q^{2} -141.734 q^{3} +1024.00 q^{4} +3125.00 q^{5} -4535.49 q^{6} +85586.9 q^{7} +32768.0 q^{8} -157058. q^{9} +100000. q^{10} +767235. q^{11} -145136. q^{12} +220960. q^{13} +2.73878e6 q^{14} -442919. q^{15} +1.04858e6 q^{16} -930719. q^{17} -5.02587e6 q^{18} -1.77341e7 q^{19} +3.20000e6 q^{20} -1.21306e7 q^{21} +2.45515e7 q^{22} -3.99596e7 q^{23} -4.64434e6 q^{24} +9.76562e6 q^{25} +7.07072e6 q^{26} +4.73683e7 q^{27} +8.76410e7 q^{28} +7.68554e7 q^{29} -1.41734e7 q^{30} -2.96314e7 q^{31} +3.35544e7 q^{32} -1.08743e8 q^{33} -2.97830e7 q^{34} +2.67459e8 q^{35} -1.60828e8 q^{36} +5.40911e7 q^{37} -5.67491e8 q^{38} -3.13176e7 q^{39} +1.02400e8 q^{40} +1.26006e8 q^{41} -3.88179e8 q^{42} -2.88676e8 q^{43} +7.85648e8 q^{44} -4.90808e8 q^{45} -1.27871e9 q^{46} -1.57008e9 q^{47} -1.48619e8 q^{48} +5.34780e9 q^{49} +3.12500e8 q^{50} +1.31915e8 q^{51} +2.26263e8 q^{52} -4.09006e9 q^{53} +1.51579e9 q^{54} +2.39761e9 q^{55} +2.80451e9 q^{56} +2.51353e9 q^{57} +2.45937e9 q^{58} +3.77882e9 q^{59} -4.53549e8 q^{60} -9.64103e9 q^{61} -9.48205e8 q^{62} -1.34422e10 q^{63} +1.07374e9 q^{64} +6.90500e8 q^{65} -3.47979e9 q^{66} -1.63819e10 q^{67} -9.53056e8 q^{68} +5.66364e9 q^{69} +8.55869e9 q^{70} +1.03471e10 q^{71} -5.14649e9 q^{72} +4.27149e9 q^{73} +1.73091e9 q^{74} -1.38412e9 q^{75} -1.81597e10 q^{76} +6.56653e10 q^{77} -1.00216e9 q^{78} -1.96636e10 q^{79} +3.27680e9 q^{80} +2.11087e10 q^{81} +4.03220e9 q^{82} -1.35791e10 q^{83} -1.24217e10 q^{84} -2.90850e9 q^{85} -9.23762e9 q^{86} -1.08930e10 q^{87} +2.51407e10 q^{88} +2.25058e10 q^{89} -1.57058e10 q^{90} +1.89113e10 q^{91} -4.09186e10 q^{92} +4.19978e9 q^{93} -5.02424e10 q^{94} -5.54191e10 q^{95} -4.75581e9 q^{96} -1.08976e11 q^{97} +1.71130e11 q^{98} -1.20501e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 64 q^{2} + 604 q^{3} + 2048 q^{4} + 6250 q^{5} + 19328 q^{6} + 14092 q^{7} + 65536 q^{8} + 221914 q^{9} + 200000 q^{10} + 421584 q^{11} + 618496 q^{12} + 1730524 q^{13} + 450944 q^{14} + 1887500 q^{15}+ \cdots - 251492724912 q^{99}+O(q^{100}) \) 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

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Representations

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Database

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