LMFDB - Embedded newform 10.30.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,30,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, 30, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 30);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 30 $
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:	$53.2780423830$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 2788867122 $ x^2 - x - 2788867122
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-52809.2$ 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)

$f(q)$	$=$	\(q+16384.0 q^{2} +7.68338e6 q^{3} +2.68435e8 q^{4} +6.10352e9 q^{5} +1.25884e11 q^{6} -1.48072e12 q^{7} +4.39805e12 q^{8} -9.59610e12 q^{9} +1.00000e14 q^{10} -1.49204e15 q^{11} +2.06249e15 q^{12} -1.87567e16 q^{13} -2.42601e16 q^{14} +4.68956e16 q^{15} +7.20576e16 q^{16} -5.52201e17 q^{17} -1.57223e17 q^{18} -3.63993e18 q^{19} +1.63840e18 q^{20} -1.13769e19 q^{21} -2.44455e19 q^{22} +1.19154e19 q^{23} +3.37918e19 q^{24} +3.72529e19 q^{25} -3.07309e20 q^{26} -6.01043e20 q^{27} -3.97477e20 q^{28} +1.49220e21 q^{29} +7.68338e20 q^{30} +2.12272e20 q^{31} +1.18059e21 q^{32} -1.14639e22 q^{33} -9.04727e21 q^{34} -9.03758e21 q^{35} -2.57593e21 q^{36} +4.36693e22 q^{37} -5.96365e22 q^{38} -1.44114e23 q^{39} +2.68435e22 q^{40} +1.24529e23 q^{41} -1.86399e23 q^{42} +4.89124e23 q^{43} -4.00515e23 q^{44} -5.85700e22 q^{45} +1.95221e23 q^{46} +3.20595e24 q^{47} +5.53646e23 q^{48} -1.02738e24 q^{49} +6.10352e23 q^{50} -4.24277e24 q^{51} -5.03495e24 q^{52} -1.61509e25 q^{53} -9.84750e24 q^{54} -9.10667e24 q^{55} -6.51226e24 q^{56} -2.79669e25 q^{57} +2.44481e25 q^{58} -6.74135e25 q^{59} +1.25884e25 q^{60} -4.59568e25 q^{61} +3.47787e24 q^{62} +1.42091e25 q^{63} +1.93428e25 q^{64} -1.14482e26 q^{65} -1.87824e26 q^{66} -3.04003e26 q^{67} -1.48230e26 q^{68} +9.15502e25 q^{69} -1.48072e26 q^{70} +8.77630e25 q^{71} -4.22041e25 q^{72} -1.54604e27 q^{73} +7.15478e26 q^{74} +2.86228e26 q^{75} -9.77085e26 q^{76} +2.20928e27 q^{77} -2.36117e27 q^{78} +8.64681e25 q^{79} +4.39805e26 q^{80} -3.95946e27 q^{81} +2.04028e27 q^{82} +8.92312e27 q^{83} -3.05396e27 q^{84} -3.37037e27 q^{85} +8.01381e27 q^{86} +1.14651e28 q^{87} -6.56204e27 q^{88} +4.85579e27 q^{89} -9.59610e26 q^{90} +2.77733e28 q^{91} +3.19851e27 q^{92} +1.63097e27 q^{93} +5.25263e28 q^{94} -2.22163e28 q^{95} +9.07093e27 q^{96} +6.50601e28 q^{97} -1.68327e28 q^{98} +1.43177e28 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 32768 q^{2} - 3644748 q^{3} + 536870912 q^{4} + 12207031250 q^{5} - 59715551232 q^{6} - 2619992530316 q^{7} + 8796093022208 q^{8} + 50099928783786 q^{9} + 200000000000000 q^{10} - 609601386608016 q^{11}+ \cdots + 66\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q + 32768 * q^2 - 3644748 * q^3 + 536870912 * q^4 + 12207031250 * q^5 - 59715551232 * q^6 - 2619992530316 * q^7 + 8796093022208 * q^8 + 50099928783786 * q^9 + 200000000000000 * q^10 - 609601386608016 * q^11 - 978379591385088 * q^12 - 23082045945895508 * q^13 - 42925957616697344 * q^14 - 22245776367187500 * q^15 + 144115188075855872 * q^16 - 212788505698107756 * q^17 + 820837233193549824 * q^18 - 1552916806248440360 * q^19 + 3276800000000000000 * q^20 + 1528960639160402784 * q^21 - 9987709118185734144 * q^22 + 48569213108206117932 * q^23 - 16029771225253281792 * q^24 + 74505805969238281250 * q^25 - 378176240777552003072 * q^26 - 499834094699922149880 * q^27 - 703298889591969284096 * q^28 - 956704614090527918340 * q^29 - 364474800000000000000 * q^30 - 6511575098724600253256 * q^31 + 2361183241434822606848 * q^32 - 21460205670988095790416 * q^33 - 3486326877357797474304 * q^34 - 15991165346166992187500 * q^35 + 13448597228643120316416 * q^36 + 66439751853531567521164 * q^37 - 25442988953574446858240 * q^38 - 95115872074782751314408 * q^39 + 53687091200000000000000 * q^40 - 91892384814903461498076 * q^41 + 25050491112004039213056 * q^42 - 238995461328392693017388 * q^43 - 163638626192355068215296 * q^44 + 305785698143225097656250 * q^45 + 795757987564849036197888 * q^46 + 3194171921256703883825124 * q^47 - 262631771754549768880128 * q^48 - 2949340368568478352337086 * q^49 + 1220703125000000000000000 * q^50 - 8087681914959142709504856 * q^51 - 6196039528899412018331648 * q^52 - 20940542608549012866299748 * q^53 - 8189281807563524503633920 * q^54 - 3720711588183691406250000 * q^55 - 11522849007074824750628864 * q^56 - 51608811383891390387075760 * q^57 - 15674648397259209414082560 * q^58 - 56386542314605437066955080 * q^59 - 5971555123200000000000000 * q^60 - 196473830091215280192586916 * q^61 - 106685646417503850549346304 * q^62 - 53801159179053017719352988 * q^63 + 38685626227668133590597632 * q^64 - 140881628087741137695312500 * q^65 - 351604009713468961430175744 * q^66 - 197664660356478435334723556 * q^67 - 57119979558630153818996736 * q^68 - 323669150960022130439724768 * q^69 - 261999253031600000000000000 * q^70 + 88675798275412809064073064 * q^71 + 220341816994088883264159744 * q^72 - 1207143104281105009657980668 * q^73 + 1088548894368261202266750976 * q^74 - 135777443647384643554687500 * q^75 - 416857931015363737325404160 * q^76 + 1203945463876494165080443728 * q^77 - 1558378448073240597535260672 * q^78 - 5568328716406737078915459440 * q^79 + 879609302220800000000000000 * q^80 - 9202933265485984731362760318 * q^81 - 1505564832807378313184477184 * q^82 + 14501131796523133613084409972 * q^83 + 410427246379074178466709504 * q^84 - 1298757969348802221679687500 * q^85 - 3915701638404385882396884992 * q^86 + 39206560880287419756561414360 * q^87 - 2681055251535545437639409664 * q^88 + 37316392549473006147343615380 * q^89 + 5009992878378600000000000000 * q^90 + 32701100919486363870999957464 * q^91 + 13037698868262486609066196992 * q^92 + 77799548305316321338678930944 * q^93 + 52333312757869836432590831616 * q^94 - 9478251991262453369140625000 * q^95 - 4302958948426543413332017152 * q^96 - 23376807728262299973955852076 * q^97 - 48321992598625949324690817024 * q^98 + 66995578378495912231289004912 * 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 $

$2$	16384.0	0.707107
$2$	16384.0	0.707107
$3$	7.68338e6	0.927457	0.463729	−	0.885977i	$-0.346511\pi$
$3$	7.68338e6	0.927457	0.463729	+	0.885977i	$0.346511\pi$
$4$	2.68435e8	0.500000
$5$	6.10352e9	0.447214
$5$	6.10352e9	0.447214
$6$	1.25884e11	0.655811
$7$	−1.48072e12	−0.825183	−0.412592	−	0.910916i	$-0.635376\pi$
$7$	−1.48072e12	−0.825183	−0.412592	+	0.910916i	$0.635376\pi$
$8$	4.39805e12	0.353553
$9$	−9.59610e12	−0.139823
$10$	1.00000e14	0.316228
$11$	−1.49204e15	−1.18464	−0.592319	−	0.805704i	$-0.701787\pi$
$11$	−1.49204e15	−1.18464	−0.592319	+	0.805704i	$0.701787\pi$
$12$	2.06249e15	0.463729
$13$	−1.87567e16	−1.32122	−0.660612	−	0.750727i	$-0.729703\pi$
$13$	−1.87567e16	−1.32122	−0.660612	+	0.750727i	$0.729703\pi$
$14$	−2.42601e16	−0.583493
$15$	4.68956e16	0.414772
$16$	7.20576e16	0.250000
$17$	−5.52201e17	−0.795405	−0.397702	−	0.917515i	$-0.630192\pi$
$17$	−5.52201e17	−0.795405	−0.397702	+	0.917515i	$0.630192\pi$
$18$	−1.57223e17	−0.0988697
$19$	−3.63993e18	−1.04512	−0.522559	−	0.852603i	$-0.675023\pi$
$19$	−3.63993e18	−1.04512	−0.522559	+	0.852603i	$0.675023\pi$
$20$	1.63840e18	0.223607
$21$	−1.13769e19	−0.765322
$22$	−2.44455e19	−0.837665
$23$	1.19154e19	0.214316	0.107158	−	0.994242i	$-0.465825\pi$
$23$	1.19154e19	0.214316	0.107158	+	0.994242i	$0.465825\pi$
$24$	3.37918e19	0.327906
$25$	3.72529e19	0.200000
$26$	−3.07309e20	−0.934247
$27$	−6.01043e20	−1.05714
$28$	−3.97477e20	−0.412592
$29$	1.49220e21	0.931226	0.465613	−	0.884988i	$-0.345834\pi$
$29$	1.49220e21	0.931226	0.465613	+	0.884988i	$0.345834\pi$
$30$	7.68338e20	0.293288
$31$	2.12272e20	0.0503673	0.0251836	−	0.999683i	$-0.491983\pi$
$31$	2.12272e20	0.0503673	0.0251836	+	0.999683i	$0.491983\pi$
$32$	1.18059e21	0.176777
$33$	−1.14639e22	−1.09870
$34$	−9.04727e21	−0.562436
$35$	−9.03758e21	−0.369033
$36$	−2.57593e21	−0.0699115
$37$	4.36693e22	0.796620	0.398310	−	0.917251i	$-0.369597\pi$
$37$	4.36693e22	0.796620	0.398310	+	0.917251i	$0.369597\pi$
$38$	−5.96365e22	−0.739010
$39$	−1.44114e23	−1.22538
$40$	2.68435e22	0.158114
$41$	1.24529e23	0.512749	0.256375	−	0.966578i	$-0.417472\pi$
$41$	1.24529e23	0.512749	0.256375	+	0.966578i	$0.417472\pi$
$42$	−1.86399e23	−0.541164
$43$	4.89124e23	1.00955	0.504774	−	0.863252i	$-0.331576\pi$
$43$	4.89124e23	1.00955	0.504774	+	0.863252i	$0.331576\pi$
$44$	−4.00515e23	−0.592319
$45$	−5.85700e22	−0.0625307
$46$	1.95221e23	0.151544
$47$	3.20595e24	1.82195	0.910977	−	0.412456i	$-0.135329\pi$
$47$	3.20595e24	1.82195	0.910977	+	0.412456i	$0.135329\pi$
$48$	5.53646e23	0.231864
$49$	−1.02738e24	−0.319073
$50$	6.10352e23	0.141421
$51$	−4.24277e24	−0.737704
$52$	−5.03495e24	−0.660612
$53$	−1.61509e25	−1.60767	−0.803834	−	0.594854i	$-0.797210\pi$
$53$	−1.61509e25	−1.60767	−0.803834	+	0.594854i	$0.797210\pi$
$54$	−9.84750e24	−0.747509
$55$	−9.10667e24	−0.529786
$56$	−6.51226e24	−0.291746
$57$	−2.79669e25	−0.969302
$58$	2.44481e25	0.658476
$59$	−6.74135e25	−1.41708	−0.708538	−	0.705673i	$-0.750645\pi$
$59$	−6.74135e25	−1.41708	−0.708538	+	0.705673i	$0.750645\pi$
$60$	1.25884e25	0.207386
$61$	−4.59568e25	−0.595755	−0.297877	−	0.954604i	$-0.596279\pi$
$61$	−4.59568e25	−0.595755	−0.297877	+	0.954604i	$0.596279\pi$
$62$	3.47787e24	0.0356151
$63$	1.42091e25	0.115380
$64$	1.93428e25	0.125000
$65$	−1.14482e26	−0.590870
$66$	−1.87824e26	−0.776899
$67$	−3.04003e26	−1.01110	−0.505548	−	0.862798i	$-0.668710\pi$
$67$	−3.04003e26	−1.01110	−0.505548	+	0.862798i	$0.668710\pi$
$68$	−1.48230e26	−0.397702
$69$	9.15502e25	0.198769
$70$	−1.48072e26	−0.260946
$71$	8.77630e25	0.125912	0.0629558	−	0.998016i	$-0.479947\pi$
$71$	8.77630e25	0.125912	0.0629558	+	0.998016i	$0.479947\pi$
$72$	−4.22041e25	−0.0494349
$73$	−1.54604e27	−1.48265	−0.741327	−	0.671144i	$-0.765803\pi$
$73$	−1.54604e27	−1.48265	−0.741327	+	0.671144i	$0.765803\pi$
$74$	7.15478e26	0.563295
$75$	2.86228e26	0.185491
$76$	−9.77085e26	−0.522559
$77$	2.20928e27	0.977543
$78$	−2.36117e27	−0.866474
$79$	8.64681e25	0.0263793	0.0131896	−	0.999913i	$-0.495801\pi$
$79$	8.64681e25	0.0263793	0.0131896	+	0.999913i	$0.495801\pi$
$80$	4.39805e26	0.111803
$81$	−3.95946e27	−0.840627
$82$	2.04028e27	0.362568
$83$	8.92312e27	1.33010	0.665051	−	0.746798i	$-0.268410\pi$
$83$	8.92312e27	1.33010	0.665051	+	0.746798i	$0.268410\pi$
$84$	−3.05396e27	−0.382661
$85$	−3.37037e27	−0.355716
$86$	8.01381e27	0.713858
$87$	1.14651e28	0.863672
$88$	−6.56204e27	−0.418833
$89$	4.85579e27	0.263090	0.131545	−	0.991310i	$-0.458006\pi$
$89$	4.85579e27	0.263090	0.131545	+	0.991310i	$0.458006\pi$
$90$	−9.59610e26	−0.0442159
$91$	2.77733e28	1.09025
$92$	3.19851e27	0.107158
$93$	1.63097e27	0.0467135
$94$	5.25263e28	1.28832
$95$	−2.22163e28	−0.467391
$96$	9.07093e27	0.163953
$97$	6.50601e28	1.01187	0.505934	−	0.862572i	$-0.331148\pi$
$97$	6.50601e28	1.01187	0.505934	+	0.862572i	$0.331148\pi$
$98$	−1.68327e28	−0.225619
$99$	1.43177e28	0.165639
$100$	1.00000e28	0.100000
$101$	2.13267e29	1.84614	0.923068	−	0.384638i	$-0.125674\pi$
$101$	2.13267e29	1.84614	0.923068	+	0.384638i	$0.125674\pi$
$102$	−6.95136e28	−0.521635
$103$	−8.52648e28	−0.555431	−0.277715	−	0.960663i	$-0.589577\pi$
$103$	−8.52648e28	−0.555431	−0.277715	+	0.960663i	$0.589577\pi$
$104$	−8.24926e28	−0.467124
$105$	−6.94391e28	−0.342262
$106$	−2.64616e29	−1.13679
$107$	−1.53318e29	−0.574814	−0.287407	−	0.957809i	$-0.592793\pi$
$107$	−1.53318e29	−0.574814	−0.287407	+	0.957809i	$0.592793\pi$
$108$	−1.61341e29	−0.528569
$109$	−4.55386e28	−0.130525	−0.0652627	−	0.997868i	$-0.520789\pi$
$109$	−4.55386e28	−0.130525	−0.0652627	+	0.997868i	$0.520789\pi$
$110$	−1.49204e29	−0.374615
$111$	3.35528e29	0.738831
$112$	−1.06697e29	−0.206296
$113$	−9.49638e29	−1.61406	−0.807031	−	0.590508i	$-0.798927\pi$
$113$	−9.49638e29	−1.61406	−0.807031	+	0.590508i	$0.798927\pi$
$114$	−4.58210e29	−0.685400
$115$	7.27256e28	0.0958448
$116$	4.00558e29	0.465613
$117$	1.79991e29	0.184738
$118$	−1.10450e30	−1.00202
$119$	8.17654e29	0.656354
$120$	2.06249e29	0.146644
$121$	6.39862e29	0.403365
$122$	−7.52957e29	−0.421262
$123$	9.56804e29	0.475553
$124$	5.69814e28	0.0251836
$125$	2.27374e29	0.0894427
$126$	2.32802e29	0.0815856
$127$	−6.99268e28	−0.0218519	−0.0109260	−	0.999940i	$-0.503478\pi$
$127$	−6.99268e28	−0.0218519	−0.0109260	+	0.999940i	$0.503478\pi$
$128$	3.16913e29	0.0883883
$129$	3.75813e30	0.936312
$130$	−1.87567e30	−0.417808
$131$	−1.54928e30	−0.308814	−0.154407	−	0.988007i	$-0.549347\pi$
$131$	−1.54928e30	−0.308814	−0.154407	+	0.988007i	$0.549347\pi$
$132$	−3.07731e30	−0.549350
$133$	5.38970e30	0.862414
$134$	−4.98078e30	−0.714953
$135$	−3.66848e30	−0.472766
$136$	−2.42861e30	−0.281218
$137$	−5.90514e29	−0.0614868	−0.0307434	−	0.999527i	$-0.509787\pi$
$137$	−5.90514e29	−0.0614868	−0.0307434	+	0.999527i	$0.509787\pi$
$138$	1.49996e30	0.140551
$139$	1.35271e31	1.14154	0.570769	−	0.821111i	$-0.306645\pi$
$139$	1.35271e31	1.14154	0.570769	+	0.821111i	$0.306645\pi$
$140$	−2.42601e30	−0.184517
$141$	2.46325e31	1.68979
$142$	1.43791e30	0.0890329
$143$	2.79856e31	1.56517
$144$	−6.91472e29	−0.0349557
$145$	9.10764e30	0.416457
$146$	−2.53304e31	−1.04839
$147$	−7.89378e30	−0.295927
$148$	1.17224e31	0.398310
$149$	3.78242e31	1.16565	0.582826	−	0.812597i	$-0.301947\pi$
$149$	3.78242e31	1.16565	0.582826	+	0.812597i	$0.301947\pi$
$150$	4.68956e30	0.131162
$151$	−5.96443e31	−1.51497	−0.757483	−	0.652854i	$-0.773571\pi$
$151$	−5.96443e31	−1.51497	−0.757483	+	0.652854i	$0.773571\pi$
$152$	−1.60086e31	−0.369505
$153$	5.29898e30	0.111216
$154$	3.61969e31	0.691227
$155$	1.29561e30	0.0225249
$156$	−3.86854e31	−0.612690
$157$	−6.30671e31	−0.910454	−0.455227	−	0.890375i	$-0.650442\pi$
$157$	−6.30671e31	−0.910454	−0.455227	+	0.890375i	$0.650442\pi$
$158$	1.41669e30	0.0186530
$159$	−1.24093e32	−1.49104
$160$	7.20576e30	0.0790569
$161$	−1.76433e31	−0.176850
$162$	−6.48718e31	−0.594413
$163$	−1.15204e29	−0.000965486 0	−0.000482743	−	1.00000i	$-0.500154\pi$
$163$	−1.15204e29	−0.000965486 0	−0.000482743		1.00000i	$0.500154\pi$
$164$	3.34280e31	0.256375
$165$	−6.99699e31	−0.491354
$166$	1.46196e32	0.940523
$167$	−3.21378e32	−1.89508	−0.947539	−	0.319641i	$-0.896438\pi$
$167$	−3.21378e32	−1.89508	−0.947539	+	0.319641i	$0.896438\pi$
$168$	−5.00361e31	−0.270582
$169$	1.50274e32	0.745635
$170$	−5.52201e31	−0.251529
$171$	3.49291e31	0.146131
$172$	1.31298e32	0.504774
$173$	2.25727e32	0.797840	0.398920	−	0.916986i	$-0.369385\pi$
$173$	2.25727e32	0.797840	0.398920	+	0.916986i	$0.369385\pi$
$174$	1.87844e32	0.610708
$175$	−5.51610e31	−0.165037
$176$	−1.07513e32	−0.296159
$177$	−5.17964e32	−1.31428
$178$	7.95572e31	0.186033
$179$	−1.67639e32	−0.361415	−0.180707	−	0.983537i	$-0.557839\pi$
$179$	−1.67639e32	−0.361415	−0.180707	+	0.983537i	$0.557839\pi$
$180$	−1.57223e31	−0.0312654
$181$	5.21905e32	0.957751	0.478875	−	0.877883i	$-0.341045\pi$
$181$	5.21905e32	0.957751	0.478875	+	0.877883i	$0.341045\pi$
$182$	4.55038e32	0.770925
$183$	−3.53104e32	−0.552537
$184$	5.24043e31	0.0757720
$185$	2.66536e32	0.356259
$186$	2.67218e31	0.0330314
$187$	8.23904e32	0.942266
$188$	8.60590e32	0.910977
$189$	8.89975e32	0.872332
$190$	−3.63993e32	−0.330495
$191$	2.11179e33	1.77692	0.888460	−	0.458955i	$-0.151776\pi$
$191$	2.11179e33	1.77692	0.888460	+	0.458955i	$0.151776\pi$
$192$	1.48618e32	0.115932
$193$	−1.46578e33	−1.06045	−0.530224	−	0.847858i	$-0.677892\pi$
$193$	−1.46578e33	−1.06045	−0.530224	+	0.847858i	$0.677892\pi$
$194$	1.06594e33	0.715499
$195$	−8.79605e32	−0.548006
$196$	−2.75786e32	−0.159536
$197$	−8.00038e32	−0.429883	−0.214942	−	0.976627i	$-0.568956\pi$
$197$	−8.00038e32	−0.429883	−0.214942	+	0.976627i	$0.568956\pi$
$198$	2.34582e32	0.117125
$199$	−3.40186e33	−1.57887	−0.789436	−	0.613833i	$-0.789627\pi$
$199$	−3.40186e33	−1.57887	−0.789436	+	0.613833i	$0.789627\pi$
$200$	1.63840e32	0.0707107
$201$	−2.33577e33	−0.937749
$202$	3.49416e33	1.30541
$203$	−2.20952e33	−0.768432
$204$	−1.13891e33	−0.368852
$205$	7.60065e32	0.229308
$206$	−1.39698e33	−0.392749
$207$	−1.14341e32	−0.0299662
$208$	−1.35156e33	−0.330306
$209$	5.43090e33	1.23809
$210$	−1.13769e33	−0.242016
$211$	−1.67250e33	−0.332102	−0.166051	−	0.986117i	$-0.553102\pi$
$211$	−1.67250e33	−0.332102	−0.166051	+	0.986117i	$0.553102\pi$
$212$	−4.33547e33	−0.803834
$213$	6.74316e32	0.116778
$214$	−2.51196e33	−0.406455
$215$	2.98538e33	0.451483
$216$	−2.64342e33	−0.373754
$217$	−3.14315e32	−0.0415622
$218$	−7.46104e32	−0.0922954
$219$	−1.18788e34	−1.37510
$220$	−2.44455e33	−0.264893
$221$	1.03575e34	1.05091
$222$	5.49729e33	0.522432
$223$	1.89519e34	1.68745	0.843726	−	0.536775i	$-0.180357\pi$
$223$	1.89519e34	1.68745	0.843726	+	0.536775i	$0.180357\pi$
$224$	−1.74812e33	−0.145873
$225$	−3.57483e32	−0.0279646
$226$	−1.55589e34	−1.14131
$227$	2.37544e33	0.163444	0.0817222	−	0.996655i	$-0.473958\pi$
$227$	2.37544e33	0.163444	0.0817222	+	0.996655i	$0.473958\pi$
$228$	−7.50731e33	−0.484651
$229$	−3.16033e34	−1.91478	−0.957388	−	0.288804i	$-0.906742\pi$
$229$	−3.16033e34	−1.91478	−0.957388	+	0.288804i	$0.906742\pi$
$230$	1.19154e33	0.0677725
$231$	1.69747e34	0.906629
$232$	6.56275e33	0.329238
$233$	1.58340e34	0.746328	0.373164	−	0.927765i	$-0.378273\pi$
$233$	1.58340e34	0.746328	0.373164	+	0.927765i	$0.378273\pi$
$234$	2.94897e33	0.130629
$235$	1.95676e34	0.814803
$236$	−1.80962e34	−0.708538
$237$	6.64367e32	0.0244657
$238$	1.33964e34	0.464113
$239$	−1.69580e34	−0.552849	−0.276424	−	0.961036i	$-0.589150\pi$
$239$	−1.69580e34	−0.552849	−0.276424	+	0.961036i	$0.589150\pi$
$240$	3.37918e33	0.103693
$241$	−6.52685e33	−0.188563	−0.0942815	−	0.995546i	$-0.530055\pi$
$241$	−6.52685e33	−0.188563	−0.0942815	+	0.995546i	$0.530055\pi$
$242$	1.04835e34	0.285222
$243$	1.08278e34	0.277492
$244$	−1.23364e34	−0.297877
$245$	−6.27066e33	−0.142694
$246$	1.56763e34	0.336267
$247$	6.82728e34	1.38084
$248$	9.33583e32	0.0178075
$249$	6.85597e34	1.23361
$250$	3.72529e33	0.0632456
$251$	8.19176e34	1.31253	0.656264	−	0.754532i	$-0.272136\pi$
$251$	8.19176e34	1.31253	0.656264	+	0.754532i	$0.272136\pi$
$252$	3.81423e33	0.0576898
$253$	−1.77782e34	−0.253886
$254$	−1.14568e33	−0.0154516
$255$	−2.58958e34	−0.329911
$256$	5.19230e33	0.0625000
$257$	−1.00126e35	−1.13899	−0.569493	−	0.821996i	$-0.692861\pi$
$257$	−1.00126e35	−1.13899	−0.569493	+	0.821996i	$0.692861\pi$
$258$	6.15731e34	0.662073
$259$	−6.46618e34	−0.657357
$260$	−3.07309e34	−0.295435
$261$	−1.43193e34	−0.130207
$262$	−2.53835e34	−0.218365
$263$	−3.41235e34	−0.277776	−0.138888	−	0.990308i	$-0.544353\pi$
$263$	−3.41235e34	−0.277776	−0.138888	+	0.990308i	$0.544353\pi$
$264$	−5.04187e34	−0.388449
$265$	−9.85772e34	−0.718971
$266$	8.83048e34	0.609818
$267$	3.73088e34	0.244005
$268$	−8.16051e34	−0.505548
$269$	−3.29203e35	−1.93222	−0.966109	−	0.258133i	$-0.916893\pi$
$269$	−3.29203e35	−1.93222	−0.966109	+	0.258133i	$0.916893\pi$
$270$	−6.01043e34	−0.334296
$271$	−2.96956e35	−1.56544	−0.782721	−	0.622373i	$-0.786169\pi$
$271$	−2.96956e35	−1.56544	−0.782721	+	0.622373i	$0.786169\pi$
$272$	−3.97903e34	−0.198851
$273$	2.13393e35	1.01116
$274$	−9.67498e33	−0.0434778
$275$	−5.55827e34	−0.236927
$276$	2.45753e34	0.0993843
$277$	−1.65686e35	−0.635813	−0.317906	−	0.948122i	$-0.602980\pi$
$277$	−1.65686e35	−0.635813	−0.317906	+	0.948122i	$0.602980\pi$
$278$	2.21628e35	0.807189
$279$	−2.03699e33	−0.00704250
$280$	−3.97477e34	−0.130473
$281$	3.67502e35	1.14556	0.572781	−	0.819708i	$-0.305865\pi$
$281$	3.67502e35	1.14556	0.572781	+	0.819708i	$0.305865\pi$
$282$	4.03579e35	1.19486
$283$	−2.61559e35	−0.735641	−0.367820	−	0.929897i	$-0.619896\pi$
$283$	−2.61559e35	−0.735641	−0.367820	+	0.929897i	$0.619896\pi$
$284$	2.35587e34	0.0629558
$285$	−1.70697e35	−0.433485
$286$	4.58516e35	1.10674
$287$	−1.84392e35	−0.423112
$288$	−1.13291e34	−0.0247174
$289$	−1.77042e35	−0.367332
$290$	1.49220e35	0.294479
$291$	4.99881e35	0.938465
$292$	−4.15013e35	−0.741327
$293$	8.43142e35	1.43324	0.716622	−	0.697462i	$-0.245687\pi$
$293$	8.43142e35	1.43324	0.716622	+	0.697462i	$0.245687\pi$
$294$	−1.29332e35	−0.209252
$295$	−4.11460e35	−0.633735
$296$	1.92060e35	0.281648
$297$	8.96779e35	1.25232
$298$	6.19712e35	0.824240
$299$	−2.23492e35	−0.283159
$300$	7.68338e34	0.0927457
$301$	−7.24254e35	−0.833061
$302$	−9.77212e35	−1.07124
$303$	1.63861e36	1.71221
$304$	−2.62284e35	−0.261279
$305$	−2.80498e35	−0.266430
$306$	8.68185e34	0.0786415
$307$	−1.18090e36	−1.02025	−0.510124	−	0.860101i	$-0.670400\pi$
$307$	−1.18090e36	−1.02025	−0.510124	+	0.860101i	$0.670400\pi$
$308$	5.93050e35	0.488771
$309$	−6.55121e35	−0.515138
$310$	2.12272e34	0.0159275
$311$	1.04336e36	0.747149	0.373574	−	0.927600i	$-0.378132\pi$
$311$	1.04336e36	0.747149	0.373574	+	0.927600i	$0.378132\pi$
$312$	−6.33822e35	−0.433237
$313$	2.76507e36	1.80432	0.902161	−	0.431400i	$-0.141980\pi$
$313$	2.76507e36	1.80432	0.902161	+	0.431400i	$0.141980\pi$
$314$	−1.03329e36	−0.643788
$315$	8.67255e34	0.0515993
$316$	2.32111e34	0.0131896
$317$	2.19277e36	1.19024	0.595119	−	0.803638i	$-0.297105\pi$
$317$	2.19277e36	1.19024	0.595119	+	0.803638i	$0.297105\pi$
$318$	−2.03315e36	−1.05433
$319$	−2.22641e36	−1.10316
$320$	1.18059e35	0.0559017
$321$	−1.17800e36	−0.533116
$322$	−2.89067e35	−0.125052
$323$	2.00997e36	0.831292
$324$	−1.06286e36	−0.420313
$325$	−6.98740e35	−0.264245
$326$	−1.88750e33	−0.000682702 0
$327$	−3.49890e35	−0.121057
$328$	5.47685e35	0.181284
$329$	−4.74710e36	−1.50345
$330$	−1.14639e36	−0.347440
$331$	3.32856e35	0.0965496	0.0482748	−	0.998834i	$-0.484628\pi$
$331$	3.32856e35	0.0965496	0.0482748	+	0.998834i	$0.484628\pi$
$332$	2.39528e36	0.665051
$333$	−4.19055e35	−0.111386
$334$	−5.26545e36	−1.34002
$335$	−1.85548e36	−0.452176
$336$	−8.19792e35	−0.191331
$337$	4.57852e36	1.02351	0.511755	−	0.859132i	$-0.328996\pi$
$337$	4.57852e36	1.02351	0.511755	+	0.859132i	$0.328996\pi$
$338$	2.46209e36	0.527244
$339$	−7.29642e36	−1.49697
$340$	−9.04727e35	−0.177858
$341$	−3.16718e35	−0.0596670
$342$	5.72278e35	0.103331
$343$	6.28903e36	1.08848
$344$	2.15119e36	0.356929
$345$	5.58778e35	0.0888920
$346$	3.69832e36	0.564158
$347$	3.69118e36	0.539993	0.269997	−	0.962861i	$-0.412977\pi$
$347$	3.69118e36	0.539993	0.269997	+	0.962861i	$0.412977\pi$
$348$	3.07764e36	0.431836
$349$	−2.78937e36	−0.375438	−0.187719	−	0.982223i	$-0.560109\pi$
$349$	−2.78937e36	−0.375438	−0.187719	+	0.982223i	$0.560109\pi$
$350$	−9.03758e35	−0.116699
$351$	1.12736e37	1.39672
$352$	−1.76149e36	−0.209416
$353$	−1.23430e37	−1.40827	−0.704135	−	0.710066i	$-0.748665\pi$
$353$	−1.23430e37	−1.40827	−0.704135	+	0.710066i	$0.748665\pi$
$354$	−8.48631e36	−0.929334
$355$	5.35663e35	0.0563093
$356$	1.30347e36	0.131545
$357$	6.28234e36	0.608741
$358$	−2.74660e36	−0.255559
$359$	1.60585e36	0.143494	0.0717472	−	0.997423i	$-0.477143\pi$
$359$	1.60585e36	0.143494	0.0717472	+	0.997423i	$0.477143\pi$
$360$	−2.57593e35	−0.0221079
$361$	1.11924e36	0.0922713
$362$	8.55090e36	0.677232
$363$	4.91630e36	0.374104
$364$	7.45533e36	0.545126
$365$	−9.43629e36	−0.663063
$366$	−5.78525e36	−0.390703
$367$	−3.15301e36	−0.204677	−0.102338	−	0.994750i	$-0.532632\pi$
$367$	−3.15301e36	−0.204677	−0.102338	+	0.994750i	$0.532632\pi$
$368$	8.58592e35	0.0535789
$369$	−1.19499e36	−0.0716941
$370$	4.36693e36	0.251913
$371$	2.39149e37	1.32662
$372$	4.37810e35	0.0233568
$373$	1.47949e37	0.759162	0.379581	−	0.925158i	$-0.376068\pi$
$373$	1.47949e37	0.759162	0.379581	+	0.925158i	$0.376068\pi$
$374$	1.34988e37	0.666283
$375$	1.74700e36	0.0829543
$376$	1.40999e37	0.644158
$377$	−2.79886e37	−1.23036
$378$	1.45813e37	0.616832
$379$	−3.91070e37	−1.59216	−0.796079	−	0.605193i	$-0.793096\pi$
$379$	−3.91070e37	−1.59216	−0.796079	+	0.605193i	$0.793096\pi$
$380$	−5.96365e36	−0.233695
$381$	−5.37274e35	−0.0202667
$382$	3.45996e37	1.25647
$383$	1.25775e37	0.439757	0.219879	−	0.975527i	$-0.429434\pi$
$383$	1.25775e37	0.439757	0.219879	+	0.975527i	$0.429434\pi$
$384$	2.43496e36	0.0819764
$385$	1.34844e37	0.437170
$386$	−2.40154e37	−0.749850
$387$	−4.69369e36	−0.141158
$388$	1.74644e37	0.505934
$389$	−5.78321e37	−1.61398	−0.806992	−	0.590562i	$-0.798906\pi$
$389$	−5.78321e37	−1.61398	−0.806992	+	0.590562i	$0.798906\pi$
$390$	−1.44114e37	−0.387499
$391$	−6.57968e36	−0.170468
$392$	−4.51849e36	−0.112809
$393$	−1.19037e37	−0.286412
$394$	−1.31078e37	−0.303973
$395$	5.27759e35	0.0117972
$396$	3.84339e36	0.0828197
$397$	−6.66269e37	−1.38416	−0.692081	−	0.721820i	$-0.743306\pi$
$397$	−6.66269e37	−1.38416	−0.692081	+	0.721820i	$0.743306\pi$
$398$	−5.57361e37	−1.11643
$399$	4.14111e37	0.799852
$400$	2.68435e36	0.0500000
$401$	−8.06663e37	−1.44910	−0.724551	−	0.689221i	$-0.757953\pi$
$401$	−8.06663e37	−1.44910	−0.724551	+	0.689221i	$0.757953\pi$
$402$	−3.82692e37	−0.663088
$403$	−3.98152e36	−0.0665465
$404$	5.72484e37	0.923068
$405$	−2.41666e37	−0.375940
$406$	−3.62008e37	−0.543363
$407$	−6.51562e37	−0.943706
$408$	−1.86599e37	−0.260818
$409$	1.28165e38	1.72895	0.864473	−	0.502679i	$-0.167652\pi$
$409$	1.28165e38	1.72895	0.864473	+	0.502679i	$0.167652\pi$
$410$	1.24529e37	0.162145
$411$	−4.53714e36	−0.0570264
$412$	−2.28881e37	−0.277715
$413$	9.98203e37	1.16935
$414$	−1.87336e36	−0.0211893
$415$	5.44624e37	0.594839
$416$	−2.21439e37	−0.233562
$417$	1.03934e38	1.05873
$418$	8.89799e37	0.875459
$419$	1.46843e38	1.39556	0.697780	−	0.716312i	$-0.254171\pi$
$419$	1.46843e38	1.39556	0.697780	+	0.716312i	$0.254171\pi$
$420$	−1.86399e37	−0.171131
$421$	2.12573e36	0.0188546	0.00942732	−	0.999956i	$-0.496999\pi$
$421$	2.12573e36	0.0188546	0.00942732	+	0.999956i	$0.496999\pi$
$422$	−2.74023e37	−0.234832
$423$	−3.07646e37	−0.254751
$424$	−7.10324e37	−0.568396
$425$	−2.05711e37	−0.159081
$426$	1.10480e37	0.0825742
$427$	6.80490e37	0.491607
$428$	−4.11559e37	−0.287407
$429$	2.15024e38	1.45163
$430$	4.89124e37	0.319247
$431$	8.37130e37	0.528290	0.264145	−	0.964483i	$-0.414910\pi$
$431$	8.37130e37	0.528290	0.264145	+	0.964483i	$0.414910\pi$
$432$	−4.33097e37	−0.264284
$433$	−1.09694e38	−0.647305	−0.323652	−	0.946176i	$-0.604911\pi$
$433$	−1.09694e38	−0.647305	−0.323652	+	0.946176i	$0.604911\pi$
$434$	−5.14974e36	−0.0293889
$435$	6.99775e37	0.386246
$436$	−1.22242e37	−0.0652627
$437$	−4.33710e37	−0.223985
$438$	−1.94623e38	−0.972341
$439$	1.66935e38	0.806885	0.403442	−	0.915005i	$-0.367814\pi$
$439$	1.66935e38	0.806885	0.403442	+	0.915005i	$0.367814\pi$
$440$	−4.00515e37	−0.187308
$441$	9.85889e36	0.0446137
$442$	1.69696e38	0.743104
$443$	−3.71165e38	−1.57294	−0.786472	−	0.617626i	$-0.788094\pi$
$443$	−3.71165e38	−1.57294	−0.786472	+	0.617626i	$0.788094\pi$
$444$	9.00675e37	0.369416
$445$	2.96374e37	0.117657
$446$	3.10507e38	1.19321
$447$	2.90618e38	1.08109
$448$	−2.86412e37	−0.103148
$449$	−3.75572e38	−1.30955	−0.654774	−	0.755825i	$-0.727236\pi$
$449$	−3.75572e38	−1.30955	−0.654774	+	0.755825i	$0.727236\pi$
$450$	−5.85700e36	−0.0197739
$451$	−1.85802e38	−0.607422
$452$	−2.54916e38	−0.807031
$453$	−4.58270e38	−1.40507
$454$	3.89193e37	0.115573
$455$	1.69515e38	0.487576
$456$	−1.23000e38	−0.342700
$457$	−2.86202e38	−0.772482	−0.386241	−	0.922398i	$-0.626227\pi$
$457$	−2.86202e38	−0.772482	−0.386241	+	0.922398i	$0.626227\pi$
$458$	−5.17789e38	−1.35395
$459$	3.31897e38	0.840852
$460$	1.95221e37	0.0479224
$461$	−3.46285e38	−0.823703	−0.411851	−	0.911251i	$-0.635118\pi$
$461$	−3.46285e38	−0.823703	−0.411851	+	0.911251i	$0.635118\pi$
$462$	2.78114e38	0.641084
$463$	5.93445e38	1.32573	0.662867	−	0.748738i	$-0.269340\pi$
$463$	5.93445e38	1.32573	0.662867	+	0.748738i	$0.269340\pi$
$464$	1.07524e38	0.232806
$465$	9.95464e36	0.0208909
$466$	2.59424e38	0.527734
$467$	9.62200e37	0.189745	0.0948725	−	0.995489i	$-0.469756\pi$
$467$	9.62200e37	0.189745	0.0948725	+	0.995489i	$0.469756\pi$
$468$	4.83159e37	0.0923688
$469$	4.50141e38	0.834340
$470$	3.20595e38	0.576153
$471$	−4.84569e38	−0.844408
$472$	−2.96488e38	−0.501012
$473$	−7.29791e38	−1.19595
$474$	1.08850e37	0.0172998
$475$	−1.35598e38	−0.209024
$476$	2.19487e38	0.328177
$477$	1.54986e38	0.224789
$478$	−2.77841e38	−0.390923
$479$	−4.88061e38	−0.666207	−0.333104	−	0.942890i	$-0.608096\pi$
$479$	−4.88061e38	−0.666207	−0.333104	+	0.942890i	$0.608096\pi$
$480$	5.53646e37	0.0733219
$481$	−8.19090e38	−1.05251
$482$	−1.06936e38	−0.133334
$483$	−1.35560e38	−0.164020
$484$	1.71762e38	0.201683
$485$	3.97095e38	0.452522
$486$	1.77403e38	0.196216
$487$	1.54915e38	0.166312	0.0831558	−	0.996537i	$-0.473500\pi$
$487$	1.54915e38	0.166312	0.0831558	+	0.996537i	$0.473500\pi$
$488$	−2.02120e38	−0.210631
$489$	−8.85153e35	−0.000895447 0
$490$	−1.02738e38	−0.100900
$491$	−8.20640e37	−0.0782476	−0.0391238	−	0.999234i	$-0.512457\pi$
$491$	−8.20640e37	−0.0782476	−0.0391238	+	0.999234i	$0.512457\pi$
$492$	2.56840e38	0.237776
$493$	−8.23993e38	−0.740701
$494$	1.11858e39	0.976398
$495$	8.73885e37	0.0740762
$496$	1.52958e37	0.0125918
$497$	−1.29952e38	−0.103900
$498$	1.12328e39	0.872295
$499$	2.36296e39	1.78237	0.891187	−	0.453637i	$-0.149874\pi$
$499$	2.36296e39	1.78237	0.891187	+	0.453637i	$0.149874\pi$
$500$	6.10352e37	0.0447214
$501$	−2.46927e39	−1.75760
$502$	1.34214e39	0.928097
$503$	1.38727e39	0.932023	0.466011	−	0.884779i	$-0.345691\pi$
$503$	1.38727e39	0.932023	0.466011	+	0.884779i	$0.345691\pi$
$504$	6.24923e37	0.0407928
$505$	1.30168e39	0.825617
$506$	−2.91277e38	−0.179525
$507$	1.15461e39	0.691545
$508$	−1.87708e37	−0.0109260
$509$	−2.30259e39	−1.30259	−0.651297	−	0.758823i	$-0.725775\pi$
$509$	−2.30259e39	−1.30259	−0.651297	+	0.758823i	$0.725775\pi$
$510$	−4.24277e38	−0.233282
$511$	2.28925e39	1.22346
$512$	8.50706e37	0.0441942
$513$	2.18775e39	1.10483
$514$	−1.64047e39	−0.805385
$515$	−5.20415e38	−0.248396
$516$	1.00881e39	0.468156
$517$	−4.78339e39	−2.15836
$518$	−1.05942e39	−0.464822
$519$	1.73435e39	0.739962
$520$	−5.03495e38	−0.208904
$521$	1.16195e39	0.468857	0.234429	−	0.972133i	$-0.424678\pi$
$521$	1.16195e39	0.468857	0.234429	+	0.972133i	$0.424678\pi$
$522$	−2.34607e38	−0.0920701
$523$	4.58242e39	1.74912	0.874561	−	0.484915i	$-0.161149\pi$
$523$	4.58242e39	1.74912	0.874561	+	0.484915i	$0.161149\pi$
$524$	−4.15883e38	−0.154407
$525$	−4.23823e38	−0.153064
$526$	−5.59080e38	−0.196418
$527$	−1.17217e38	−0.0400624
$528$	−8.26059e38	−0.274675
$529$	−2.94908e39	−0.954069
$530$	−1.61509e39	−0.508389
$531$	6.46907e38	0.198140
$532$	1.44679e39	0.431207
$533$	−2.33575e39	−0.677457
$534$	6.11268e38	0.172537
$535$	−9.35777e38	−0.257065
$536$	−1.33702e39	−0.357477
$537$	−1.28803e39	−0.335197
$538$	−5.39367e39	−1.36628
$539$	1.53290e39	0.377986
$540$	−9.84750e38	−0.236383
$541$	3.15300e39	0.736824	0.368412	−	0.929663i	$-0.379902\pi$
$541$	3.15300e39	0.736824	0.368412	+	0.929663i	$0.379902\pi$
$542$	−4.86532e39	−1.10693
$543$	4.01000e39	0.888273
$544$	−6.51924e38	−0.140609
$545$	−2.77945e38	−0.0583728
$546$	3.49622e39	0.715000
$547$	−1.24403e39	−0.247750	−0.123875	−	0.992298i	$-0.539532\pi$
$547$	−1.24403e39	−0.247750	−0.123875	+	0.992298i	$0.539532\pi$
$548$	−1.58515e38	−0.0307434
$549$	4.41006e38	0.0833002
$550$	−9.10667e38	−0.167533
$551$	−5.43148e39	−0.973241
$552$	4.02642e38	0.0702753
$553$	−1.28035e38	−0.0217677
$554$	−2.71460e39	−0.449588
$555$	2.04790e39	0.330415
$556$	3.63116e39	0.570769
$557$	−7.59373e39	−1.16293	−0.581467	−	0.813570i	$-0.697521\pi$
$557$	−7.59373e39	−1.16293	−0.581467	+	0.813570i	$0.697521\pi$
$558$	−3.33740e37	−0.00497980
$559$	−9.17434e39	−1.33384
$560$	−6.51226e38	−0.0922583
$561$	6.33037e39	0.873911
$562$	6.02116e39	0.810035
$563$	−8.33986e38	−0.109342	−0.0546710	−	0.998504i	$-0.517411\pi$
$563$	−8.33986e38	−0.109342	−0.0546710	+	0.998504i	$0.517411\pi$
$564$	6.61224e39	0.844893
$565$	−5.79613e39	−0.721831
$566$	−4.28538e39	−0.520177
$567$	5.86284e39	0.693671
$568$	3.85986e38	0.0445164
$569$	−1.07248e40	−1.20576	−0.602879	−	0.797833i	$-0.705980\pi$
$569$	−1.07248e40	−1.20576	−0.602879	+	0.797833i	$0.705980\pi$
$570$	−2.79669e39	−0.306520
$571$	1.45529e40	1.55498	0.777490	−	0.628895i	$-0.216493\pi$
$571$	1.45529e40	1.55498	0.777490	+	0.628895i	$0.216493\pi$
$572$	7.51233e39	0.782586
$573$	1.62257e40	1.64802
$574$	−3.02108e39	−0.299185
$575$	4.43882e38	0.0428631
$576$	−1.85616e38	−0.0174779
$577$	1.89246e40	1.73771	0.868855	−	0.495067i	$-0.164856\pi$
$577$	1.89246e40	1.73771	0.868855	+	0.495067i	$0.164856\pi$
$578$	−2.90066e39	−0.259743
$579$	−1.12622e40	−0.983520
$580$	2.44481e39	0.208228
$581$	−1.32126e40	−1.09758
$582$	8.19005e39	0.663595
$583$	2.40977e40	1.90450
$584$	−6.79956e39	−0.524197
$585$	1.09858e39	0.0826171
$586$	1.38140e40	1.01346
$587$	1.86692e39	0.133621	0.0668104	−	0.997766i	$-0.478718\pi$
$587$	1.86692e39	0.133621	0.0668104	+	0.997766i	$0.478718\pi$
$588$	−2.11897e39	−0.147963
$589$	−7.72655e38	−0.0526398
$590$	−6.74135e39	−0.448119
$591$	−6.14700e39	−0.398698
$592$	3.14670e39	0.199155
$593$	2.24511e40	1.38658	0.693289	−	0.720659i	$-0.256161\pi$
$593$	2.24511e40	1.38658	0.693289	+	0.720659i	$0.256161\pi$
$594$	1.46928e40	0.885527
$595$	4.99056e39	0.293531
$596$	1.01534e40	0.582826
$597$	−2.61378e40	−1.46434
$598$	−3.66170e39	−0.200224
$599$	−1.43934e40	−0.768198	−0.384099	−	0.923292i	$-0.625488\pi$
$599$	−1.43934e40	−0.768198	−0.384099	+	0.923292i	$0.625488\pi$
$600$	1.25884e39	0.0655811
$601$	−3.10527e40	−1.57914	−0.789569	−	0.613662i	$-0.789696\pi$
$601$	−3.10527e40	−1.57914	−0.789569	+	0.613662i	$0.789696\pi$
$602$	−1.18662e40	−0.589063
$603$	2.91724e39	0.141374
$604$	−1.60106e40	−0.757483
$605$	3.90541e39	0.180391
$606$	2.68470e40	1.21072
$607$	−3.10127e39	−0.136554	−0.0682769	−	0.997666i	$-0.521750\pi$
$607$	−3.10127e39	−0.136554	−0.0682769	+	0.997666i	$0.521750\pi$
$608$	−4.29727e39	−0.184752
$609$	−1.69766e40	−0.712688
$610$	−4.59568e39	−0.188394
$611$	−6.01329e40	−2.40721
$612$	1.42243e39	0.0556079
$613$	−3.61509e38	−0.0138020	−0.00690101	−	0.999976i	$-0.502197\pi$
$613$	−3.61509e38	−0.0138020	−0.00690101	+	0.999976i	$0.502197\pi$
$614$	−1.93478e40	−0.721424
$615$	5.83987e39	0.212674
$616$	9.71653e39	0.345614
$617$	−1.26407e40	−0.439173	−0.219586	−	0.975593i	$-0.570471\pi$
$617$	−1.26407e40	−0.439173	−0.219586	+	0.975593i	$0.570471\pi$
$618$	−1.07335e40	−0.364258
$619$	8.23888e39	0.273120	0.136560	−	0.990632i	$-0.456395\pi$
$619$	8.23888e39	0.273120	0.136560	+	0.990632i	$0.456395\pi$
$620$	3.47787e38	0.0112625
$621$	−7.16165e39	−0.226561
$622$	1.70944e40	0.528314
$623$	−7.19004e39	−0.217097
$624$	−1.03845e40	−0.306345
$625$	1.38778e39	0.0400000
$626$	4.53030e40	1.27585
$627$	4.17277e40	1.14827
$628$	−1.69295e40	−0.455227
$629$	−2.41142e40	−0.633635
$630$	1.42091e39	0.0364862
$631$	5.22318e40	1.31072	0.655359	−	0.755317i	$-0.272517\pi$
$631$	5.22318e40	1.31072	0.655359	+	0.755317i	$0.272517\pi$
$632$	3.80291e38	0.00932648
$633$	−1.28505e40	−0.308011
$634$	3.59263e40	0.841625
$635$	−4.26799e38	−0.00977247
$636$	−3.33111e40	−0.745522
$637$	1.92703e40	0.421567
$638$	−3.64775e40	−0.780055
$639$	−8.42183e38	−0.0176053
$640$	1.93428e39	0.0395285
$641$	−4.31938e40	−0.862940	−0.431470	−	0.902127i	$-0.642005\pi$
$641$	−4.31938e40	−0.862940	−0.431470	+	0.902127i	$0.642005\pi$
$642$	−1.93003e40	−0.376970
$643$	8.02353e40	1.53217	0.766084	−	0.642740i	$-0.222202\pi$
$643$	8.02353e40	1.53217	0.766084	+	0.642740i	$0.222202\pi$
$644$	−4.73608e39	−0.0884248
$645$	2.29378e40	0.418731
$646$	3.29314e40	0.587812
$647$	−8.30129e40	−1.44888	−0.724442	−	0.689336i	$-0.757902\pi$
$647$	−8.30129e40	−1.44888	−0.724442	+	0.689336i	$0.757902\pi$
$648$	−1.74139e40	−0.297206
$649$	1.00583e41	1.67872
$650$	−1.14482e40	−0.186849
$651$	−2.41500e39	−0.0385472
$652$	−3.09247e37	−0.000482743 0
$653$	−6.89266e40	−1.05232	−0.526158	−	0.850387i	$-0.676368\pi$
$653$	−6.89266e40	−1.05232	−0.526158	+	0.850387i	$0.676368\pi$
$654$	−5.73260e39	−0.0856001
$655$	−9.45608e39	−0.138106
$656$	8.97327e39	0.128187
$657$	1.48360e40	0.207309
$658$	−7.77765e40	−1.06310
$659$	4.28089e40	0.572395	0.286198	−	0.958171i	$-0.407609\pi$
$659$	4.28089e40	0.572395	0.286198	+	0.958171i	$0.407609\pi$
$660$	−1.87824e40	−0.245677
$661$	−3.05389e40	−0.390780	−0.195390	−	0.980726i	$-0.562597\pi$
$661$	−3.05389e40	−0.390780	−0.195390	+	0.980726i	$0.562597\pi$
$662$	5.45351e39	0.0682709
$663$	7.95802e40	0.974673
$664$	3.92443e40	0.470262
$665$	3.28961e40	0.385683
$666$	−6.86580e39	−0.0787616
$667$	1.77801e40	0.199576
$668$	−8.62692e40	−0.947539
$669$	1.45614e41	1.56504
$670$	−3.04003e40	−0.319737
$671$	6.85692e40	0.705753
$672$	−1.34315e40	−0.135291
$673$	1.17559e41	1.15887	0.579437	−	0.815017i	$-0.303273\pi$
$673$	1.17559e41	1.15887	0.579437	+	0.815017i	$0.303273\pi$
$674$	7.50145e40	0.723730
$675$	−2.23906e40	−0.211427
$676$	4.03389e40	0.372818
$677$	8.31378e40	0.752078	0.376039	−	0.926604i	$-0.377286\pi$
$677$	8.31378e40	0.752078	0.376039	+	0.926604i	$0.377286\pi$
$678$	−1.19545e41	−1.05852
$679$	−9.63355e40	−0.834977
$680$	−1.48230e40	−0.125765
$681$	1.82514e40	0.151588
$682$	−5.18911e39	−0.0421909
$683$	−6.88330e40	−0.547894	−0.273947	−	0.961745i	$-0.588329\pi$
$683$	−6.88330e40	−0.547894	−0.273947	+	0.961745i	$0.588329\pi$
$684$	9.37621e39	0.0730657
$685$	−3.60421e39	−0.0274977
$686$	1.03040e41	0.769669
$687$	−2.42820e41	−1.77587
$688$	3.52451e40	0.252387
$689$	3.02937e41	2.12409
$690$	9.15502e39	0.0628561
$691$	−2.86827e41	−1.92836	−0.964182	−	0.265243i	$-0.914548\pi$
$691$	−2.86827e41	−1.92836	−0.964182	+	0.265243i	$0.914548\pi$
$692$	6.05932e40	0.398920
$693$	−2.12005e40	−0.136683
$694$	6.04764e40	0.381833
$695$	8.25629e40	0.510511
$696$	5.04241e40	0.305354
$697$	−6.87651e40	−0.407843
$698$	−4.57011e40	−0.265475
$699$	1.21659e41	0.692188
$700$	−1.48072e40	−0.0825183
$701$	−3.31493e41	−1.80952	−0.904759	−	0.425923i	$-0.859949\pi$
$701$	−3.31493e41	−1.80952	−0.904759	+	0.425923i	$0.859949\pi$
$702$	1.84706e41	0.987627
$703$	−1.58953e41	−0.832562
$704$	−2.88602e40	−0.148080
$705$	1.50345e41	0.755695
$706$	−2.02227e41	−0.995797
$707$	−3.15788e41	−1.52340
$708$	−1.39040e41	−0.657138
$709$	−3.21463e41	−1.48854	−0.744271	−	0.667878i	$-0.767203\pi$
$709$	−3.21463e41	−1.48854	−0.744271	+	0.667878i	$0.767203\pi$
$710$	8.77630e39	0.0398167
$711$	−8.29756e38	−0.00368843
$712$	2.13560e40	0.0930164
$713$	2.52930e39	0.0107945
$714$	1.02930e41	0.430445
$715$	1.70811e41	0.699966
$716$	−4.50002e40	−0.180707
$717$	−1.30295e41	−0.512743
$718$	2.63102e40	0.101466
$719$	−1.53997e41	−0.582029	−0.291015	−	0.956719i	$-0.593993\pi$
$719$	−1.53997e41	−0.582029	−0.291015	+	0.956719i	$0.593993\pi$
$720$	−4.22041e39	−0.0156327
$721$	1.26253e41	0.458332
$722$	1.83375e40	0.0652457
$723$	−5.01482e40	−0.174884
$724$	1.40098e41	0.478875
$725$	5.55886e40	0.186245
$726$	8.05487e40	0.264532
$727$	−2.73405e40	−0.0880153	−0.0440076	−	0.999031i	$-0.514013\pi$
$727$	−2.73405e40	−0.0880153	−0.0440076	+	0.999031i	$0.514013\pi$
$728$	1.22148e41	0.385462
$729$	3.54933e41	1.09799
$730$	−1.54604e41	−0.468856
$731$	−2.70095e41	−0.802999
$732$	−9.47855e40	−0.276269
$733$	−7.89799e40	−0.225688	−0.112844	−	0.993613i	$-0.535996\pi$
$733$	−7.89799e40	−0.225688	−0.112844	+	0.993613i	$0.535996\pi$
$734$	−5.16590e40	−0.144728
$735$	−4.81798e40	−0.132342
$736$	1.40672e40	0.0378860
$737$	4.53583e41	1.19778
$738$	−1.95788e40	−0.0506954
$739$	−4.82157e41	−1.22418	−0.612088	−	0.790789i	$-0.709670\pi$
$739$	−4.82157e41	−1.22418	−0.612088	+	0.790789i	$0.709670\pi$
$740$	7.15478e40	0.178130
$741$	5.24566e41	1.28067
$742$	3.91822e41	0.938062
$743$	2.55089e41	0.598900	0.299450	−	0.954112i	$-0.403197\pi$
$743$	2.55089e41	0.598900	0.299450	+	0.954112i	$0.403197\pi$
$744$	7.17307e39	0.0165157
$745$	2.30861e41	0.521295
$746$	2.42400e41	0.536809
$747$	−8.56272e40	−0.185979
$748$	2.21165e41	0.471133
$749$	2.27020e41	0.474327
$750$	2.86228e40	0.0586576
$751$	−4.47925e40	−0.0900380	−0.0450190	−	0.998986i	$-0.514335\pi$
$751$	−4.47925e40	−0.0900380	−0.0450190	+	0.998986i	$0.514335\pi$
$752$	2.31013e41	0.455489
$753$	6.29404e41	1.21731
$754$	−4.58565e41	−0.869995
$755$	−3.64040e41	−0.677514
$756$	2.38901e41	0.436166
$757$	−1.78881e41	−0.320387	−0.160194	−	0.987086i	$-0.551212\pi$
$757$	−1.78881e41	−0.320387	−0.160194	+	0.987086i	$0.551212\pi$
$758$	−6.40729e41	−1.12583
$759$	−1.36596e41	−0.235469
$760$	−9.77085e40	−0.165248
$761$	4.40276e40	0.0730546	0.0365273	−	0.999333i	$-0.488370\pi$
$761$	4.40276e40	0.0730546	0.0365273	+	0.999333i	$0.488370\pi$
$762$	−8.80269e39	−0.0143307
$763$	6.74297e40	0.107707
$764$	5.66880e41	0.888460
$765$	3.23424e40	0.0497372
$766$	2.06070e41	0.310955
$767$	1.26445e42	1.87228
$768$	3.98944e40	0.0579661
$769$	−1.76688e41	−0.251927	−0.125964	−	0.992035i	$-0.540202\pi$
$769$	−1.76688e41	−0.251927	−0.125964	+	0.992035i	$0.540202\pi$
$770$	2.20928e41	0.309126
$771$	−7.69309e41	−1.05636
$772$	−3.93469e41	−0.530224
$773$	−1.91963e41	−0.253873	−0.126936	−	0.991911i	$-0.540514\pi$
$773$	−1.91963e41	−0.253873	−0.126936	+	0.991911i	$0.540514\pi$
$774$	−7.69014e40	−0.0998137
$775$	7.90776e39	0.0100735
$776$	2.86137e41	0.357750
$777$	−4.96821e41	−0.609671
$778$	−9.47521e41	−1.14126
$779$	−4.53277e41	−0.535883
$780$	−2.36117e41	−0.274003
$781$	−1.30946e41	−0.149159
$782$	−1.07801e41	−0.120539
$783$	−8.96875e41	−0.984433
$784$	−7.40309e40	−0.0797682
$785$	−3.84931e41	−0.407168
$786$	−1.95031e41	−0.202524
$787$	1.48600e42	1.51491	0.757454	−	0.652888i	$-0.226443\pi$
$787$	1.48600e42	1.51491	0.757454	+	0.652888i	$0.226443\pi$
$788$	−2.14759e41	−0.214942
$789$	−2.62184e41	−0.257626
$790$	8.64681e39	0.00834186
$791$	1.40614e42	1.33190
$792$	6.29700e40	0.0585624
$793$	8.61996e41	0.787126
$794$	−1.09161e42	−0.978751
$795$	−7.57406e41	−0.666815
$796$	−9.13180e41	−0.789436
$797$	6.29245e41	0.534163	0.267082	−	0.963674i	$-0.413941\pi$
$797$	6.29245e41	0.534163	0.267082	+	0.963674i	$0.413941\pi$
$798$	6.78479e41	0.565581
$799$	−1.77033e42	−1.44919
$800$	4.39805e40	0.0353553
$801$	−4.65966e40	−0.0367860
$802$	−1.32164e42	−1.02467
$803$	2.30675e42	1.75641
$804$	−6.27002e41	−0.468874
$805$	−1.07686e41	−0.0790895
$806$	−6.52332e40	−0.0470555
$807$	−2.52939e42	−1.79205
$808$	9.37958e41	0.652707
$809$	8.35891e41	0.571342	0.285671	−	0.958328i	$-0.407784\pi$
$809$	8.35891e41	0.571342	0.285671	+	0.958328i	$0.407784\pi$
$810$	−3.95946e41	−0.265829
$811$	8.80958e41	0.580969	0.290484	−	0.956880i	$-0.406184\pi$
$811$	8.80958e41	0.580969	0.290484	+	0.956880i	$0.406184\pi$
$812$	−5.93113e41	−0.384216
$813$	−2.28162e42	−1.45188
$814$	−1.06752e42	−0.667301
$815$	−7.03147e38	−0.000431779 0
$816$	−3.05724e41	−0.184426
$817$	−1.78038e42	−1.05510
$818$	2.09985e42	1.22255
$819$	−2.66515e41	−0.152442
$820$	2.04028e41	0.114654
$821$	1.16383e42	0.642559	0.321280	−	0.946984i	$-0.395887\pi$
$821$	1.16383e42	0.642559	0.321280	+	0.946984i	$0.395887\pi$
$822$	−7.43365e40	−0.0403238
$823$	3.33222e42	1.77597	0.887987	−	0.459869i	$-0.152103\pi$
$823$	3.33222e42	1.77597	0.887987	+	0.459869i	$0.152103\pi$
$824$	−3.74998e41	−0.196374
$825$	−4.27063e41	−0.219740
$826$	1.63546e42	0.826853
$827$	2.56265e42	1.27309	0.636545	−	0.771239i	$-0.280363\pi$
$827$	2.56265e42	1.27309	0.636545	+	0.771239i	$0.280363\pi$
$828$	−3.06932e40	−0.0149831
$829$	3.15692e42	1.51434	0.757169	−	0.653219i	$-0.226582\pi$
$829$	3.15692e42	1.51434	0.757169	+	0.653219i	$0.226582\pi$
$830$	8.92312e41	0.420615
$831$	−1.27303e42	−0.589689
$832$	−3.62806e41	−0.165153
$833$	5.67323e41	0.253792
$834$	1.70285e42	0.748634
$835$	−1.96153e42	−0.847504
$836$	1.45785e42	0.619043
$837$	−1.27585e41	−0.0532451
$838$	2.40587e42	0.986810
$839$	−2.03367e42	−0.819846	−0.409923	−	0.912120i	$-0.634444\pi$
$839$	−2.03367e42	−0.819846	−0.409923	+	0.912120i	$0.634444\pi$
$840$	−3.05396e41	−0.121008
$841$	−3.41036e41	−0.132819
$842$	3.48280e40	0.0133322
$843$	2.82366e42	1.06246
$844$	−4.48959e41	−0.166051
$845$	9.17200e41	0.333458
$846$	−5.04047e41	−0.180136
$847$	−9.47455e41	−0.332850
$848$	−1.16379e42	−0.401917
$849$	−2.00965e42	−0.682275
$850$	−3.37037e41	−0.112487
$851$	5.20336e41	0.170728
$852$	1.81010e41	0.0583888
$853$	−4.30318e42	−1.36467	−0.682337	−	0.731038i	$-0.739036\pi$
$853$	−4.30318e42	−1.36467	−0.682337	+	0.731038i	$0.739036\pi$
$854$	1.11492e42	0.347618
$855$	2.13190e41	0.0653520
$856$	−6.74298e41	−0.203228
$857$	1.85145e40	0.00548642	0.00274321	−	0.999996i	$-0.499127\pi$
$857$	1.85145e40	0.00548642	0.00274321	+	0.999996i	$0.499127\pi$
$858$	3.52295e42	1.02646
$859$	−4.76577e42	−1.36531	−0.682656	−	0.730740i	$-0.739175\pi$
$859$	−4.76577e42	−1.36531	−0.682656	+	0.730740i	$0.739175\pi$
$860$	8.01381e41	0.225742
$861$	−1.41676e42	−0.392418
$862$	1.37155e42	0.373558
$863$	5.09150e40	0.0136361	0.00681804	−	0.999977i	$-0.497830\pi$
$863$	5.09150e40	0.0136361	0.00681804	+	0.999977i	$0.497830\pi$
$864$	−7.09587e41	−0.186877
$865$	1.37773e42	0.356805
$866$	−1.79723e42	−0.457713
$867$	−1.36028e42	−0.340684
$868$	−8.43733e40	−0.0207811
$869$	−1.29013e41	−0.0312499
$870$	1.14651e42	0.273117
$871$	5.70207e42	1.33589
$872$	−2.00281e41	−0.0461477
$873$	−6.24323e41	−0.141482
$874$	−7.10591e41	−0.158381
$875$	−3.36676e41	−0.0738066
$876$	−3.18870e42	−0.687549
$877$	5.73938e42	1.21722	0.608612	−	0.793468i	$-0.291727\pi$
$877$	5.73938e42	1.21722	0.608612	+	0.793468i	$0.291727\pi$
$878$	2.73506e42	0.570554
$879$	6.47818e42	1.32927
$880$	−6.56204e41	−0.132446
$881$	−4.61884e42	−0.917028	−0.458514	−	0.888687i	$-0.651618\pi$
$881$	−4.61884e42	−0.917028	−0.458514	+	0.888687i	$0.651618\pi$
$882$	1.61528e41	0.0315467
$883$	−6.74072e42	−1.29502	−0.647509	−	0.762058i	$-0.724189\pi$
$883$	−6.74072e42	−1.29502	−0.647509	+	0.762058i	$0.724189\pi$
$884$	2.78031e42	0.525454
$885$	−3.16140e42	−0.587762
$886$	−6.08117e42	−1.11224
$887$	−3.54607e42	−0.638050	−0.319025	−	0.947746i	$-0.603355\pi$
$887$	−3.54607e42	−0.638050	−0.319025	+	0.947746i	$0.603355\pi$
$888$	1.47567e42	0.261216
$889$	1.03542e41	0.0180318
$890$	4.85579e41	0.0831964
$891$	5.90766e42	0.995838
$892$	5.08735e42	0.843726
$893$	−1.16694e43	−1.90416
$894$	4.76148e42	0.764448
$895$	−1.02319e42	−0.161630
$896$	−4.69258e41	−0.0729366
$897$	−1.71718e42	−0.262618
$898$	−6.15337e42	−0.925990
$899$	3.16752e41	0.0469033
$900$	−9.59610e40	−0.0139823
$901$	8.91854e42	1.27875
$902$	−3.04418e42	−0.429512
$903$	−5.56472e42	−0.772629
$904$	−4.17655e42	−0.570657
$905$	3.18546e42	0.428319
$906$	−7.50829e42	−0.993532
$907$	8.10190e42	1.05507	0.527535	−	0.849533i	$-0.323116\pi$
$907$	8.10190e42	1.05507	0.527535	+	0.849533i	$0.323116\pi$
$908$	6.37654e41	0.0817222
$909$	−2.04653e42	−0.258132
$910$	2.77733e42	0.344768
$911$	7.96842e42	0.973544	0.486772	−	0.873529i	$-0.338174\pi$
$911$	7.96842e42	0.973544	0.486772	+	0.873529i	$0.338174\pi$
$912$	−2.01523e42	−0.242326
$913$	−1.33136e43	−1.57569
$914$	−4.68914e42	−0.546227
$915$	−2.15517e42	−0.247102
$916$	−8.48345e42	−0.957388
$917$	2.29405e42	0.254828
$918$	5.43780e42	0.594572
$919$	−2.53647e42	−0.272995	−0.136497	−	0.990640i	$-0.543585\pi$
$919$	−2.53647e42	−0.272995	−0.136497	+	0.990640i	$0.543585\pi$
$920$	3.19851e41	0.0338863
$921$	−9.07328e42	−0.946236
$922$	−5.67354e42	−0.582446
$923$	−1.64614e42	−0.166357
$924$	4.55662e42	0.453315
$925$	1.62681e42	0.159324
$926$	9.72300e42	0.937435
$927$	8.18209e41	0.0776619
$928$	1.76167e42	0.164619
$929$	3.99948e42	0.367939	0.183970	−	0.982932i	$-0.441105\pi$
$929$	3.99948e42	0.367939	0.183970	+	0.982932i	$0.441105\pi$
$930$	1.63097e41	0.0147721
$931$	3.73960e42	0.333469
$932$	4.25041e42	0.373164
$933$	8.01650e42	0.692949
$934$	1.57647e42	0.134170
$935$	5.02871e42	0.421394
$936$	7.91608e41	0.0653146
$937$	1.52825e42	0.124157	0.0620784	−	0.998071i	$-0.480227\pi$
$937$	1.52825e42	0.124157	0.0620784	+	0.998071i	$0.480227\pi$
$938$	7.37512e42	0.589967
$939$	2.12451e43	1.67343
$940$	5.25263e42	0.407401
$941$	1.35671e42	0.103619	0.0518093	−	0.998657i	$-0.483501\pi$
$941$	1.35671e42	0.103619	0.0518093	+	0.998657i	$0.483501\pi$
$942$	−7.93917e42	−0.597086
$943$	1.48381e42	0.109890
$944$	−4.85766e42	−0.354269
$945$	5.43198e42	0.390119
$946$	−1.19569e43	−0.845662
$947$	2.29402e43	1.59780	0.798901	−	0.601463i	$-0.205415\pi$
$947$	2.29402e43	1.59780	0.798901	+	0.601463i	$0.205415\pi$
$948$	1.78340e41	0.0122328
$949$	2.89986e43	1.95892
$950$	−2.22163e42	−0.147802
$951$	1.68479e43	1.10389
$952$	3.59608e42	0.232056
$953$	−1.86788e43	−1.18714	−0.593570	−	0.804782i	$-0.702282\pi$
$953$	−1.86788e43	−1.18714	−0.593570	+	0.804782i	$0.702282\pi$
$954$	2.53928e42	0.158950
$955$	1.28894e43	0.794663
$956$	−4.55214e42	−0.276424
$957$	−1.71064e43	−1.02314
$958$	−7.99639e42	−0.471080
$959$	8.74384e41	0.0507379
$960$	9.07093e41	0.0518464
$961$	−1.77168e43	−0.997463
$962$	−1.34200e43	−0.744240
$963$	1.47125e42	0.0803722
$964$	−1.75204e42	−0.0942815
$965$	−8.94644e42	−0.474247
$966$	−2.22101e42	−0.115980
$967$	−4.98614e42	−0.256496	−0.128248	−	0.991742i	$-0.540935\pi$
$967$	−4.98614e42	−0.256496	−0.128248	+	0.991742i	$0.540935\pi$
$968$	2.81414e42	0.142611
$969$	1.54434e43	0.770987
$970$	6.50601e42	0.319981
$971$	−1.80120e43	−0.872735	−0.436368	−	0.899768i	$-0.643735\pi$
$971$	−1.80120e43	−0.872735	−0.436368	+	0.899768i	$0.643735\pi$
$972$	2.90657e42	0.138746
$973$	−2.00298e43	−0.941978
$974$	2.53812e42	0.117600
$975$	−5.36868e42	−0.245076
$976$	−3.31154e42	−0.148939
$977$	−2.15005e43	−0.952747	−0.476373	−	0.879243i	$-0.658049\pi$
$977$	−2.15005e43	−0.952747	−0.476373	+	0.879243i	$0.658049\pi$
$978$	−1.45023e40	−0.000633177 0
$979$	−7.24501e42	−0.311666
$980$	−1.68327e42	−0.0713469
$981$	4.36993e41	0.0182505
$982$	−1.34454e42	−0.0553294
$983$	2.69873e42	0.109429	0.0547146	−	0.998502i	$-0.482575\pi$
$983$	2.69873e42	0.109429	0.0547146	+	0.998502i	$0.482575\pi$
$984$	4.20807e42	0.168133
$985$	−4.88305e42	−0.192250
$986$	−1.35003e43	−0.523755
$987$	−3.64738e43	−1.39438
$988$	1.83268e43	0.690418
$989$	5.82809e42	0.216362
$990$	1.43177e42	0.0523798
$991$	−1.68950e43	−0.609101	−0.304551	−	0.952496i	$-0.598506\pi$
$991$	−1.68950e43	−0.609101	−0.304551	+	0.952496i	$0.598506\pi$
$992$	2.50607e41	0.00890376
$993$	2.55746e42	0.0895456
$994$	−2.12914e42	−0.0734684
$995$	−2.07633e43	−0.706093
$996$	1.84039e43	0.616806
$997$	2.21106e41	0.00730333	0.00365167	−	0.999993i	$-0.498838\pi$
$997$	2.21106e41	0.00730333	0.00365167	+	0.999993i	$0.498838\pi$
$998$	3.87148e43	1.26033
$999$	−2.62471e43	−0.842137

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.30.a.a.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.30.a.a.1.2	✓	2	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q+16384.0 q^{2} +7.68338e6 q^{3} +2.68435e8 q^{4} +6.10352e9 q^{5} +1.25884e11 q^{6} -1.48072e12 q^{7} +4.39805e12 q^{8} -9.59610e12 q^{9} +1.00000e14 q^{10} -1.49204e15 q^{11} +2.06249e15 q^{12} -1.87567e16 q^{13} -2.42601e16 q^{14} +4.68956e16 q^{15} +7.20576e16 q^{16} -5.52201e17 q^{17} -1.57223e17 q^{18} -3.63993e18 q^{19} +1.63840e18 q^{20} -1.13769e19 q^{21} -2.44455e19 q^{22} +1.19154e19 q^{23} +3.37918e19 q^{24} +3.72529e19 q^{25} -3.07309e20 q^{26} -6.01043e20 q^{27} -3.97477e20 q^{28} +1.49220e21 q^{29} +7.68338e20 q^{30} +2.12272e20 q^{31} +1.18059e21 q^{32} -1.14639e22 q^{33} -9.04727e21 q^{34} -9.03758e21 q^{35} -2.57593e21 q^{36} +4.36693e22 q^{37} -5.96365e22 q^{38} -1.44114e23 q^{39} +2.68435e22 q^{40} +1.24529e23 q^{41} -1.86399e23 q^{42} +4.89124e23 q^{43} -4.00515e23 q^{44} -5.85700e22 q^{45} +1.95221e23 q^{46} +3.20595e24 q^{47} +5.53646e23 q^{48} -1.02738e24 q^{49} +6.10352e23 q^{50} -4.24277e24 q^{51} -5.03495e24 q^{52} -1.61509e25 q^{53} -9.84750e24 q^{54} -9.10667e24 q^{55} -6.51226e24 q^{56} -2.79669e25 q^{57} +2.44481e25 q^{58} -6.74135e25 q^{59} +1.25884e25 q^{60} -4.59568e25 q^{61} +3.47787e24 q^{62} +1.42091e25 q^{63} +1.93428e25 q^{64} -1.14482e26 q^{65} -1.87824e26 q^{66} -3.04003e26 q^{67} -1.48230e26 q^{68} +9.15502e25 q^{69} -1.48072e26 q^{70} +8.77630e25 q^{71} -4.22041e25 q^{72} -1.54604e27 q^{73} +7.15478e26 q^{74} +2.86228e26 q^{75} -9.77085e26 q^{76} +2.20928e27 q^{77} -2.36117e27 q^{78} +8.64681e25 q^{79} +4.39805e26 q^{80} -3.95946e27 q^{81} +2.04028e27 q^{82} +8.92312e27 q^{83} -3.05396e27 q^{84} -3.37037e27 q^{85} +8.01381e27 q^{86} +1.14651e28 q^{87} -6.56204e27 q^{88} +4.85579e27 q^{89} -9.59610e26 q^{90} +2.77733e28 q^{91} +3.19851e27 q^{92} +1.63097e27 q^{93} +5.25263e28 q^{94} -2.22163e28 q^{95} +9.07093e27 q^{96} +6.50601e28 q^{97} -1.68327e28 q^{98} +1.43177e28 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 32768 q^{2} - 3644748 q^{3} + 536870912 q^{4} + 12207031250 q^{5} - 59715551232 q^{6} - 2619992530316 q^{7} + 8796093022208 q^{8} + 50099928783786 q^{9} + 200000000000000 q^{10} - 609601386608016 q^{11}+ \cdots + 66\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q + 32768 * q^2 - 3644748 * q^3 + 536870912 * q^4 + 12207031250 * q^5 - 59715551232 * q^6 - 2619992530316 * q^7 + 8796093022208 * q^8 + 50099928783786 * q^9 + 200000000000000 * q^10 - 609601386608016 * q^11 - 978379591385088 * q^12 - 23082045945895508 * q^13 - 42925957616697344 * q^14 - 22245776367187500 * q^15 + 144115188075855872 * q^16 - 212788505698107756 * q^17 + 820837233193549824 * q^18 - 1552916806248440360 * q^19 + 3276800000000000000 * q^20 + 1528960639160402784 * q^21 - 9987709118185734144 * q^22 + 48569213108206117932 * q^23 - 16029771225253281792 * q^24 + 74505805969238281250 * q^25 - 378176240777552003072 * q^26 - 499834094699922149880 * q^27 - 703298889591969284096 * q^28 - 956704614090527918340 * q^29 - 364474800000000000000 * q^30 - 6511575098724600253256 * q^31 + 2361183241434822606848 * q^32 - 21460205670988095790416 * q^33 - 3486326877357797474304 * q^34 - 15991165346166992187500 * q^35 + 13448597228643120316416 * q^36 + 66439751853531567521164 * q^37 - 25442988953574446858240 * q^38 - 95115872074782751314408 * q^39 + 53687091200000000000000 * q^40 - 91892384814903461498076 * q^41 + 25050491112004039213056 * q^42 - 238995461328392693017388 * q^43 - 163638626192355068215296 * q^44 + 305785698143225097656250 * q^45 + 795757987564849036197888 * q^46 + 3194171921256703883825124 * q^47 - 262631771754549768880128 * q^48 - 2949340368568478352337086 * q^49 + 1220703125000000000000000 * q^50 - 8087681914959142709504856 * q^51 - 6196039528899412018331648 * q^52 - 20940542608549012866299748 * q^53 - 8189281807563524503633920 * q^54 - 3720711588183691406250000 * q^55 - 11522849007074824750628864 * q^56 - 51608811383891390387075760 * q^57 - 15674648397259209414082560 * q^58 - 56386542314605437066955080 * q^59 - 5971555123200000000000000 * q^60 - 196473830091215280192586916 * q^61 - 106685646417503850549346304 * q^62 - 53801159179053017719352988 * q^63 + 38685626227668133590597632 * q^64 - 140881628087741137695312500 * q^65 - 351604009713468961430175744 * q^66 - 197664660356478435334723556 * q^67 - 57119979558630153818996736 * q^68 - 323669150960022130439724768 * q^69 - 261999253031600000000000000 * q^70 + 88675798275412809064073064 * q^71 + 220341816994088883264159744 * q^72 - 1207143104281105009657980668 * q^73 + 1088548894368261202266750976 * q^74 - 135777443647384643554687500 * q^75 - 416857931015363737325404160 * q^76 + 1203945463876494165080443728 * q^77 - 1558378448073240597535260672 * q^78 - 5568328716406737078915459440 * q^79 + 879609302220800000000000000 * q^80 - 9202933265485984731362760318 * q^81 - 1505564832807378313184477184 * q^82 + 14501131796523133613084409972 * q^83 + 410427246379074178466709504 * q^84 - 1298757969348802221679687500 * q^85 - 3915701638404385882396884992 * q^86 + 39206560880287419756561414360 * q^87 - 2681055251535545437639409664 * q^88 + 37316392549473006147343615380 * q^89 + 5009992878378600000000000000 * q^90 + 32701100919486363870999957464 * q^91 + 13037698868262486609066196992 * q^92 + 77799548305316321338678930944 * q^93 + 52333312757869836432590831616 * q^94 - 9478251991262453369140625000 * q^95 - 4302958948426543413332017152 * q^96 - 23376807728262299973955852076 * q^97 - 48321992598625949324690817024 * q^98 + 66995578378495912231289004912 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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