LMFDB - Embedded newform 1.24.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,24,Mod(1,1)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 24, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	1.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:	$3.35204037345$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{144169}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 36042 $ x^2 - x - 36042
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-189.348$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5096.35 q^{2} -48964.9 q^{3} +1.75842e7 q^{4} -3.19930e7 q^{5} -2.49542e8 q^{6} -5.17135e9 q^{7} +4.68639e10 q^{8} -9.17456e10 q^{9} +O(q^{10})$	\(q+5096.35 q^{2} -48964.9 q^{3} +1.75842e7 q^{4} -3.19930e7 q^{5} -2.49542e8 q^{6} -5.17135e9 q^{7} +4.68639e10 q^{8} -9.17456e10 q^{9} -1.63048e11 q^{10} +6.04602e11 q^{11} -8.61007e11 q^{12} +7.96710e12 q^{13} -2.63550e13 q^{14} +1.56653e12 q^{15} +9.13280e13 q^{16} +1.98385e13 q^{17} -4.67568e14 q^{18} +6.27346e14 q^{19} -5.62571e14 q^{20} +2.53215e14 q^{21} +3.08127e15 q^{22} -4.55685e15 q^{23} -2.29468e15 q^{24} -1.08974e16 q^{25} +4.06032e16 q^{26} +9.10202e15 q^{27} -9.09340e16 q^{28} +4.14107e16 q^{29} +7.98360e15 q^{30} +1.35683e15 q^{31} +7.23169e16 q^{32} -2.96043e16 q^{33} +1.01104e17 q^{34} +1.65447e17 q^{35} -1.61327e18 q^{36} +3.41258e17 q^{37} +3.19718e18 q^{38} -3.90108e17 q^{39} -1.49932e18 q^{40} -3.69518e18 q^{41} +1.29047e18 q^{42} -1.96955e18 q^{43} +1.06314e19 q^{44} +2.93522e18 q^{45} -2.32233e19 q^{46} +2.44381e19 q^{47} -4.47186e18 q^{48} -6.25860e17 q^{49} -5.55369e19 q^{50} -9.71391e17 q^{51} +1.40095e20 q^{52} -6.39437e19 q^{53} +4.63871e19 q^{54} -1.93431e19 q^{55} -2.42350e20 q^{56} -3.07179e19 q^{57} +2.11044e20 q^{58} +2.81892e20 q^{59} +2.75462e19 q^{60} -4.67790e20 q^{61} +6.91488e18 q^{62} +4.74449e20 q^{63} -3.97563e20 q^{64} -2.54892e20 q^{65} -1.50874e20 q^{66} +2.77406e20 q^{67} +3.48844e20 q^{68} +2.23126e20 q^{69} +8.43177e20 q^{70} +2.29069e21 q^{71} -4.29956e21 q^{72} -4.56908e21 q^{73} +1.73917e21 q^{74} +5.33588e20 q^{75} +1.10314e22 q^{76} -3.12661e21 q^{77} -1.98813e21 q^{78} -3.99005e21 q^{79} -2.92186e21 q^{80} +8.19155e21 q^{81} -1.88319e22 q^{82} +1.45920e22 q^{83} +4.45257e21 q^{84} -6.34694e20 q^{85} -1.00375e22 q^{86} -2.02767e21 q^{87} +2.83340e22 q^{88} +1.80991e21 q^{89} +1.49589e22 q^{90} -4.12007e22 q^{91} -8.01285e22 q^{92} -6.64369e19 q^{93} +1.24545e23 q^{94} -2.00707e22 q^{95} -3.54099e21 q^{96} +8.25561e22 q^{97} -3.18960e21 q^{98} -5.54696e22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 1080 q^{2} + 339480 q^{3} + 25326656 q^{4} + 73069020 q^{5} - 1809673056 q^{6} - 1359184400 q^{7} + 49459023360 q^{8} - 34999394166 q^{9}+O(q^{10}) $ 2 * q + 1080 * q^2 + 339480 * q^3 + 25326656 * q^4 + 73069020 * q^5 - 1809673056 * q^6 - 1359184400 * q^7 + 49459023360 * q^8 - 34999394166 * q^9	$ 2 q + 1080 q^{2} + 339480 q^{3} + 25326656 q^{4} + 73069020 q^{5} - 1809673056 q^{6} - 1359184400 q^{7} + 49459023360 q^{8} - 34999394166 q^{9} - 585013636080 q^{10} + 856801968264 q^{11} + 2146514952960 q^{12} + 4376109322060 q^{13} - 41666034529728 q^{14} + 42377338985040 q^{15} + 15956586401792 q^{16} + 254028147597540 q^{17} - 695480683916520 q^{18} + 4260600979960 q^{19} + 250868387468160 q^{20} + 17\!\cdots\!44 q^{21}+ \cdots - 41\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q + 1080 * q^2 + 339480 * q^3 + 25326656 * q^4 + 73069020 * q^5 - 1809673056 * q^6 - 1359184400 * q^7 + 49459023360 * q^8 - 34999394166 * q^9 - 585013636080 * q^10 + 856801968264 * q^11 + 2146514952960 * q^12 + 4376109322060 * q^13 - 41666034529728 * q^14 + 42377338985040 * q^15 + 15956586401792 * q^16 + 254028147597540 * q^17 - 695480683916520 * q^18 + 4260600979960 * q^19 + 250868387468160 * q^20 + 1734031637722944 * q^21 + 2068343882177760 * q^22 - 8144713079008560 * q^23 - 1286622315141120 * q^24 - 11780274628800850 * q^25 + 55025854658735184 * q^26 - 5424634982716560 * q^27 - 61418438819709440 * q^28 + 20818433601623340 * q^29 - 155926924188644160 * q^30 + 137714017177000384 * q^31 + 353265663781601280 * q^32 + 68361366766001760 * q^33 - 839483655961325328 * q^34 + 565961271250425120 * q^35 - 1173916300077574848 * q^36 - 897721264408967780 * q^37 + 5699708971590961440 * q^38 - 1785011473665029232 * q^39 - 1226668524414336000 * q^40 - 2294435477168314956 * q^41 - 4657011326437397760 * q^42 - 1750760768619855800 * q^43 + 12584088840033038592 * q^44 + 8897092690294206540 * q^45 - 8813206018050221376 * q^46 + 15759744217656780960 * q^47 - 33749519399576616960 * q^48 - 13461981704376200814 * q^49 - 51990825483785316600 * q^50 + 89998362845078292144 * q^51 + 112291883783912022400 * q^52 - 140287253401646796420 * q^53 + 104731223417039799360 * q^54 + 7153550955060182640 * q^55 - 232456712054288117760 * q^56 - 272752401448627175520 * q^57 + 293749486923568689360 * q^58 + 280872989971340771880 * q^59 + 343522601114937592320 * q^60 - 180452892516502223636 * q^61 - 540743475843874103040 * q^62 + 690775113933935014320 * q^63 - 893690254469352914944 * q^64 - 632168834809440380760 * q^65 - 544338140913651883392 * q^66 + 1754233163431557625240 * q^67 + 2162050190142944330880 * q^68 - 1170560672172404223552 * q^69 - 765428657799921252480 * q^70 + 3055033510194143328624 * q^71 - 4152294352103038548480 * q^72 - 8063408253877606149260 * q^73 + 6715344283148807757072 * q^74 + 190631089350520885800 * q^75 + 6207154294513080590080 * q^76 - 2165184764357449665600 * q^77 + 3614293948840808587200 * q^78 + 6244916814559639980640 * q^79 - 10840537585501794017280 * q^80 - 2793528580929833975598 * q^81 - 24457792891615712450640 * q^82 + 6875994082418498976120 * q^83 + 15917751907190402476032 * q^84 + 23969743087870314902520 * q^85 - 10916288812918999243296 * q^86 - 10026640653837674384880 * q^87 + 28988514668199273707520 * q^88 + 6395093086173070004820 * q^89 - 8986073954327865866160 * q^90 - 54890178162704560146016 * q^91 - 107907439017191756981760 * q^92 + 52900811441357852079360 * q^93 + 159400518006534931827072 * q^94 - 85533361066700858502000 * q^95 + 105592121669584394256384 * q^96 - 31147288846254030500540 * q^97 + 48364767616374671003640 * q^98 - 41158245132312135981912 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	5096.35	1.75960	0.879801	−	0.475342i	$-0.157676\pi$
$2$	5096.35	1.75960	0.879801	+	0.475342i	$0.157676\pi$
$3$	−48964.9	−0.159584	−0.0797921	−	0.996812i	$-0.525426\pi$
$3$	−48964.9	−0.159584	−0.0797921	+	0.996812i	$0.525426\pi$
$4$	1.75842e7	2.09620
$5$	−3.19930e7	−0.293022	−0.146511	−	0.989209i	$-0.546804\pi$
$5$	−3.19930e7	−0.293022	−0.146511	+	0.989209i	$0.546804\pi$
$6$	−2.49542e8	−0.280805
$7$	−5.17135e9	−0.988500	−0.494250	−	0.869320i	$-0.664557\pi$
$7$	−5.17135e9	−0.988500	−0.494250	+	0.869320i	$0.664557\pi$
$8$	4.68639e10	1.92887
$9$	−9.17456e10	−0.974533
$10$	−1.63048e11	−0.515602
$11$	6.04602e11	0.638931	0.319466	−	0.947598i	$-0.396497\pi$
$11$	6.04602e11	0.638931	0.319466	+	0.947598i	$0.396497\pi$
$12$	−8.61007e11	−0.334520
$13$	7.96710e12	1.23297	0.616484	−	0.787367i	$-0.288556\pi$
$13$	7.96710e12	1.23297	0.616484	+	0.787367i	$0.288556\pi$
$14$	−2.63550e13	−1.73937
$15$	1.56653e12	0.0467617
$16$	9.13280e13	1.29785
$17$	1.98385e13	0.140393	0.0701967	−	0.997533i	$-0.477637\pi$
$17$	1.98385e13	0.140393	0.0701967	+	0.997533i	$0.477637\pi$
$18$	−4.67568e14	−1.71479
$19$	6.27346e14	1.23550	0.617748	−	0.786377i	$-0.288045\pi$
$19$	6.27346e14	1.23550	0.617748	+	0.786377i	$0.288045\pi$
$20$	−5.62571e14	−0.614232
$21$	2.53215e14	0.157749
$22$	3.08127e15	1.12426
$23$	−4.55685e15	−0.997229	−0.498614	−	0.866824i	$-0.666158\pi$
$23$	−4.55685e15	−0.997229	−0.498614	+	0.866824i	$0.666158\pi$
$24$	−2.29468e15	−0.307818
$25$	−1.08974e16	−0.914138
$26$	4.06032e16	2.16953
$27$	9.10202e15	0.315104
$28$	−9.09340e16	−2.07209
$29$	4.14107e16	0.630283	0.315142	−	0.949045i	$-0.397948\pi$
$29$	4.14107e16	0.630283	0.315142	+	0.949045i	$0.397948\pi$
$30$	7.98360e15	0.0822819
$31$	1.35683e15	0.00959104	0.00479552	−	0.999989i	$-0.498474\pi$
$31$	1.35683e15	0.00959104	0.00479552	+	0.999989i	$0.498474\pi$
$32$	7.23169e16	0.354826
$33$	−2.96043e16	−0.101963
$34$	1.01104e17	0.247037
$35$	1.65447e17	0.289652
$36$	−1.61327e18	−2.04281
$37$	3.41258e17	0.315328	0.157664	−	0.987493i	$-0.449604\pi$
$37$	3.41258e17	0.315328	0.157664	+	0.987493i	$0.449604\pi$
$38$	3.19718e18	2.17398
$39$	−3.90108e17	−0.196762
$40$	−1.49932e18	−0.565202
$41$	−3.69518e18	−1.04863	−0.524313	−	0.851525i	$-0.675678\pi$
$41$	−3.69518e18	−1.04863	−0.524313	+	0.851525i	$0.675678\pi$
$42$	1.29047e18	0.277576
$43$	−1.96955e18	−0.323207	−0.161603	−	0.986856i	$-0.551667\pi$
$43$	−1.96955e18	−0.323207	−0.161603	+	0.986856i	$0.551667\pi$
$44$	1.06314e19	1.33933
$45$	2.93522e18	0.285559
$46$	−2.32233e19	−1.75473
$47$	2.44381e19	1.44192	0.720962	−	0.692975i	$-0.243700\pi$
$47$	2.44381e19	1.44192	0.720962	+	0.692975i	$0.243700\pi$
$48$	−4.47186e18	−0.207116
$49$	−6.25860e17	−0.0228677
$50$	−5.55369e19	−1.60852
$51$	−9.71391e17	−0.0224046
$52$	1.40095e20	2.58455
$53$	−6.39437e19	−0.947600	−0.473800	−	0.880632i	$-0.657118\pi$
$53$	−6.39437e19	−0.947600	−0.473800	+	0.880632i	$0.657118\pi$
$54$	4.63871e19	0.554458
$55$	−1.93431e19	−0.187221
$56$	−2.42350e20	−1.90669
$57$	−3.07179e19	−0.197166
$58$	2.11044e20	1.10905
$59$	2.81892e20	1.21698	0.608491	−	0.793561i	$-0.291775\pi$
$59$	2.81892e20	1.21698	0.608491	+	0.793561i	$0.291775\pi$
$60$	2.75462e19	0.0980218
$61$	−4.67790e20	−1.37644	−0.688221	−	0.725501i	$-0.741608\pi$
$61$	−4.67790e20	−1.37644	−0.688221	+	0.725501i	$0.741608\pi$
$62$	6.91488e18	0.0168764
$63$	4.74449e20	0.963326
$64$	−3.97563e20	−0.673498
$65$	−2.54892e20	−0.361287
$66$	−1.50874e20	−0.179415
$67$	2.77406e20	0.277495	0.138747	−	0.990328i	$-0.455692\pi$
$67$	2.77406e20	0.277495	0.138747	+	0.990328i	$0.455692\pi$
$68$	3.48844e20	0.294293
$69$	2.23126e20	0.159142
$70$	8.43177e20	0.509672
$71$	2.29069e21	1.17624	0.588119	−	0.808775i	$-0.299869\pi$
$71$	2.29069e21	1.17624	0.588119	+	0.808775i	$0.299869\pi$
$72$	−4.29956e21	−1.87975
$73$	−4.56908e21	−1.70457	−0.852286	−	0.523075i	$-0.824785\pi$
$73$	−4.56908e21	−1.70457	−0.852286	+	0.523075i	$0.824785\pi$
$74$	1.73917e21	0.554852
$75$	5.33588e20	0.145882
$76$	1.10314e22	2.58984
$77$	−3.12661e21	−0.631583
$78$	−1.98813e21	−0.346223
$79$	−3.99005e21	−0.600160	−0.300080	−	0.953914i	$-0.597013\pi$
$79$	−3.99005e21	−0.600160	−0.300080	+	0.953914i	$0.597013\pi$
$80$	−2.92186e21	−0.380298
$81$	8.19155e21	0.924247
$82$	−1.88319e22	−1.84517
$83$	1.45920e22	1.24370	0.621850	−	0.783136i	$-0.286381\pi$
$83$	1.45920e22	1.24370	0.621850	+	0.783136i	$0.286381\pi$
$84$	4.45257e21	0.330673
$85$	−6.34694e20	−0.0411384
$86$	−1.00375e22	−0.568715
$87$	−2.02767e21	−0.100583
$88$	2.83340e22	1.23242
$89$	1.80991e21	0.0691310	0.0345655	−	0.999402i	$-0.488995\pi$
$89$	1.80991e21	0.0691310	0.0345655	+	0.999402i	$0.488995\pi$
$90$	1.49589e22	0.502471
$91$	−4.12007e22	−1.21879
$92$	−8.01285e22	−2.09039
$93$	−6.64369e19	−0.00153058
$94$	1.24545e23	2.53721
$95$	−2.00707e22	−0.362027
$96$	−3.54099e21	−0.0566246
$97$	8.25561e22	1.17186	0.585928	−	0.810363i	$-0.300730\pi$
$97$	8.25561e22	1.17186	0.585928	+	0.810363i	$0.300730\pi$
$98$	−3.18960e21	−0.0402380
$99$	−5.54696e22	−0.622659
$100$	−1.91622e23	−1.91622
$101$	4.84234e22	0.431877	0.215938	−	0.976407i	$-0.430719\pi$
$101$	4.84234e22	0.431877	0.215938	+	0.976407i	$0.430719\pi$
$102$	−4.95055e21	−0.0394231
$103$	−3.23687e22	−0.230408	−0.115204	−	0.993342i	$-0.536752\pi$
$103$	−3.23687e22	−0.230408	−0.115204	+	0.993342i	$0.536752\pi$
$104$	3.73370e23	2.37824
$105$	−8.10110e21	−0.0462239
$106$	−3.25880e23	−1.66740
$107$	−5.92757e22	−0.272247	−0.136124	−	0.990692i	$-0.543464\pi$
$107$	−5.92757e22	−0.272247	−0.136124	+	0.990692i	$0.543464\pi$
$108$	1.60052e23	0.660521
$109$	2.86887e23	1.06490	0.532448	−	0.846463i	$-0.321272\pi$
$109$	2.86887e23	1.06490	0.532448	+	0.846463i	$0.321272\pi$
$110$	−9.85790e22	−0.329434
$111$	−1.67096e22	−0.0503214
$112$	−4.72290e23	−1.28292
$113$	−4.87844e22	−0.119641	−0.0598204	−	0.998209i	$-0.519053\pi$
$113$	−4.87844e22	−0.119641	−0.0598204	+	0.998209i	$0.519053\pi$
$114$	−1.56549e23	−0.346933
$115$	1.45787e23	0.292210
$116$	7.28174e23	1.32120
$117$	−7.30947e23	−1.20157
$118$	1.43662e24	2.14140
$119$	−1.02592e23	−0.138779
$120$	7.34139e22	0.0901973
$121$	−5.29886e23	−0.591767
$122$	−2.38402e24	−2.42199
$123$	1.80934e23	0.167344
$124$	2.38587e22	0.0201047
$125$	7.30026e23	0.560884
$126$	2.41796e24	1.69507
$127$	1.36871e24	0.876131	0.438065	−	0.898943i	$-0.355664\pi$
$127$	1.36871e24	0.876131	0.438065	+	0.898943i	$0.355664\pi$
$128$	−2.63276e24	−1.53991
$129$	9.64389e22	0.0515787
$130$	−1.29902e24	−0.635721
$131$	2.63272e24	1.17974	0.589869	−	0.807499i	$-0.299180\pi$
$131$	2.63272e24	1.17974	0.589869	+	0.807499i	$0.299180\pi$
$132$	−5.20567e23	−0.213735
$133$	−3.24423e24	−1.22129
$134$	1.41376e24	0.488280
$135$	−2.91201e23	−0.0923325
$136$	9.29711e23	0.270801
$137$	−1.21837e24	−0.326207	−0.163103	−	0.986609i	$-0.552150\pi$
$137$	−1.21837e24	−0.326207	−0.163103	+	0.986609i	$0.552150\pi$
$138$	1.13713e24	0.280027
$139$	−3.72223e24	−0.843593	−0.421797	−	0.906690i	$-0.638600\pi$
$139$	−3.72223e24	−0.843593	−0.421797	+	0.906690i	$0.638600\pi$
$140$	2.90925e24	0.607168
$141$	−1.19661e24	−0.230108
$142$	1.16741e25	2.06971
$143$	4.81693e24	0.787782
$144$	−8.37895e24	−1.26480
$145$	−1.32485e24	−0.184687
$146$	−2.32856e25	−2.99937
$147$	3.06452e22	0.00364932
$148$	6.00074e24	0.660990
$149$	1.53044e25	1.56018	0.780088	−	0.625670i	$-0.215174\pi$
$149$	1.53044e25	1.56018	0.780088	+	0.625670i	$0.215174\pi$
$150$	2.71935e24	0.256694
$151$	−1.25232e25	−1.09516	−0.547582	−	0.836752i	$-0.684452\pi$
$151$	−1.25232e25	−1.09516	−0.547582	+	0.836752i	$0.684452\pi$
$152$	2.93999e25	2.38311
$153$	−1.82010e24	−0.136818
$154$	−1.59343e25	−1.11134
$155$	−4.34090e22	−0.00281038
$156$	−6.85973e24	−0.412453
$157$	1.92166e23	0.0107357	0.00536785	−	0.999986i	$-0.498291\pi$
$157$	1.92166e23	0.0107357	0.00536785	+	0.999986i	$0.498291\pi$
$158$	−2.03347e25	−1.05604
$159$	3.13099e24	0.151222
$160$	−2.31363e24	−0.103972
$161$	2.35651e25	0.985761
$162$	4.17470e25	1.62631
$163$	−2.27639e25	−0.826206	−0.413103	−	0.910684i	$-0.635555\pi$
$163$	−2.27639e25	−0.826206	−0.413103	+	0.910684i	$0.635555\pi$
$164$	−6.49767e25	−2.19813
$165$	9.47130e23	0.0298775
$166$	7.43657e25	2.18842
$167$	−1.17984e25	−0.324029	−0.162015	−	0.986788i	$-0.551799\pi$
$167$	−1.17984e25	−0.324029	−0.162015	+	0.986788i	$0.551799\pi$
$168$	1.18666e25	0.304278
$169$	2.17208e25	0.520211
$170$	−3.23462e24	−0.0723871
$171$	−5.75563e25	−1.20403
$172$	−3.46330e25	−0.677506
$173$	−4.75865e25	−0.870871	−0.435435	−	0.900220i	$-0.643406\pi$
$173$	−4.75865e25	−0.870871	−0.435435	+	0.900220i	$0.643406\pi$
$174$	−1.03337e25	−0.176987
$175$	5.63542e25	0.903626
$176$	5.52172e25	0.829236
$177$	−1.38028e25	−0.194211
$178$	9.22395e24	0.121643
$179$	9.84804e25	1.21770	0.608850	−	0.793286i	$-0.291631\pi$
$179$	9.84804e25	1.21770	0.608850	+	0.793286i	$0.291631\pi$
$180$	5.16134e25	0.598589
$181$	4.76456e25	0.518465	0.259233	−	0.965815i	$-0.416530\pi$
$181$	4.76456e25	0.518465	0.259233	+	0.965815i	$0.416530\pi$
$182$	−2.09973e26	−2.14458
$183$	2.29053e25	0.219659
$184$	−2.13552e26	−1.92353
$185$	−1.09179e25	−0.0923980
$186$	−3.38586e23	−0.00269321
$187$	1.19944e25	0.0897017
$188$	4.29724e26	3.02256
$189$	−4.70697e25	−0.311481
$190$	−1.02287e26	−0.637024
$191$	−8.54117e25	−0.500765	−0.250382	−	0.968147i	$-0.580556\pi$
$191$	−8.54117e25	−0.500765	−0.250382	+	0.968147i	$0.580556\pi$
$192$	1.94666e25	0.107480
$193$	−2.66797e26	−1.38762	−0.693812	−	0.720156i	$-0.744070\pi$
$193$	−2.66797e26	−1.38762	−0.693812	+	0.720156i	$0.744070\pi$
$194$	4.20735e26	2.06200
$195$	1.24807e25	0.0576557
$196$	−1.10052e25	−0.0479352
$197$	−1.00070e26	−0.411095	−0.205547	−	0.978647i	$-0.565897\pi$
$197$	−1.00070e26	−0.411095	−0.205547	+	0.978647i	$0.565897\pi$
$198$	−2.82693e26	−1.09563
$199$	4.46897e26	1.63454	0.817272	−	0.576251i	$-0.195485\pi$
$199$	4.46897e26	1.63454	0.817272	+	0.576251i	$0.195485\pi$
$200$	−5.10694e26	−1.76326
$201$	−1.35831e25	−0.0442838
$202$	2.46783e26	0.759931
$203$	−2.14149e26	−0.623035
$204$	−1.70811e25	−0.0469645
$205$	1.18220e26	0.307271
$206$	−1.64962e26	−0.405426
$207$	4.18071e26	0.971832
$208$	7.27620e26	1.60021
$209$	3.79295e26	0.789396
$210$	−4.12860e25	−0.0813357
$211$	−7.96987e26	−1.48663	−0.743315	−	0.668941i	$-0.766748\pi$
$211$	−7.96987e26	−1.48663	−0.743315	+	0.668941i	$0.766748\pi$
$212$	−1.12440e27	−1.98636
$213$	−1.12163e26	−0.187709
$214$	−3.02090e26	−0.479047
$215$	6.30120e25	0.0947067
$216$	4.26556e26	0.607796
$217$	−7.01664e24	−0.00948074
$218$	1.46208e27	1.87379
$219$	2.23724e26	0.272023
$220$	−3.40132e26	−0.392452
$221$	1.58056e26	0.173101
$222$	−8.51582e25	−0.0885456
$223$	−5.69004e26	−0.561836	−0.280918	−	0.959732i	$-0.590639\pi$
$223$	−5.69004e26	−0.561836	−0.280918	+	0.959732i	$0.590639\pi$
$224$	−3.73976e26	−0.350745
$225$	9.99787e26	0.890858
$226$	−2.48623e26	−0.210520
$227$	−1.82165e27	−1.46611	−0.733056	−	0.680168i	$-0.761907\pi$
$227$	−1.82165e27	−1.46611	−0.733056	+	0.680168i	$0.761907\pi$
$228$	−5.40150e26	−0.413298
$229$	1.11330e27	0.810032	0.405016	−	0.914310i	$-0.367266\pi$
$229$	1.11330e27	0.810032	0.405016	+	0.914310i	$0.367266\pi$
$230$	7.42984e26	0.514173
$231$	1.53094e26	0.100791
$232$	1.94067e27	1.21574
$233$	−1.63214e27	−0.973118	−0.486559	−	0.873648i	$-0.661748\pi$
$233$	−1.63214e27	−0.973118	−0.486559	+	0.873648i	$0.661748\pi$
$234$	−3.72516e27	−2.11428
$235$	−7.81849e26	−0.422515
$236$	4.95683e27	2.55104
$237$	1.95372e26	0.0957761
$238$	−5.22845e26	−0.244196
$239$	2.58550e27	1.15072	0.575358	−	0.817902i	$-0.304863\pi$
$239$	2.58550e27	1.15072	0.575358	+	0.817902i	$0.304863\pi$
$240$	1.43068e26	0.0606896
$241$	1.86784e27	0.755340	0.377670	−	0.925940i	$-0.376725\pi$
$241$	1.86784e27	0.755340	0.377670	+	0.925940i	$0.376725\pi$
$242$	−2.70049e27	−1.04127
$243$	−1.25799e27	−0.462600
$244$	−8.22571e27	−2.88530
$245$	2.00232e25	0.00670074
$246$	9.22102e26	0.294459
$247$	4.99813e27	1.52333
$248$	6.35863e25	0.0184999
$249$	−7.14493e26	−0.198475
$250$	3.72047e27	0.986933
$251$	−4.11170e27	−1.04177	−0.520887	−	0.853626i	$-0.674399\pi$
$251$	−4.11170e27	−1.04177	−0.520887	+	0.853626i	$0.674399\pi$
$252$	8.34280e27	2.01932
$253$	−2.75508e27	−0.637160
$254$	6.97543e27	1.54164
$255$	3.10777e25	0.00656503
$256$	−1.00825e28	−2.03614
$257$	−5.10426e27	−0.985603	−0.492802	−	0.870142i	$-0.664027\pi$
$257$	−5.10426e27	−0.985603	−0.492802	+	0.870142i	$0.664027\pi$
$258$	4.91487e26	0.0907580
$259$	−1.76476e27	−0.311702
$260$	−4.48206e27	−0.757329
$261$	−3.79925e27	−0.614232
$262$	1.34173e28	2.07587
$263$	9.95433e27	1.47408	0.737040	−	0.675849i	$-0.236223\pi$
$263$	9.95433e27	1.47408	0.737040	+	0.675849i	$0.236223\pi$
$264$	−1.38737e27	−0.196674
$265$	2.04575e27	0.277668
$266$	−1.65337e28	−2.14898
$267$	−8.86222e25	−0.0110322
$268$	4.87795e27	0.581684
$269$	6.42524e26	0.0734071	0.0367036	−	0.999326i	$-0.488314\pi$
$269$	6.42524e26	0.0734071	0.0367036	+	0.999326i	$0.488314\pi$
$270$	−1.48406e27	−0.162468
$271$	1.19246e28	1.25111	0.625557	−	0.780178i	$-0.284872\pi$
$271$	1.19246e28	1.25111	0.625557	+	0.780178i	$0.284872\pi$
$272$	1.81181e27	0.182210
$273$	2.01739e27	0.194500
$274$	−6.20925e27	−0.573994
$275$	−6.58858e27	−0.584071
$276$	3.92348e27	0.333593
$277$	−5.29510e27	−0.431874	−0.215937	−	0.976407i	$-0.569281\pi$
$277$	−5.29510e27	−0.431874	−0.215937	+	0.976407i	$0.569281\pi$
$278$	−1.89698e28	−1.48439
$279$	−1.24483e26	−0.00934678
$280$	7.75350e27	0.558702
$281$	9.67433e27	0.669111	0.334556	−	0.942376i	$-0.391414\pi$
$281$	9.67433e27	0.669111	0.334556	+	0.942376i	$0.391414\pi$
$282$	−6.09834e27	−0.404899
$283$	−2.62436e28	−1.67294	−0.836468	−	0.548016i	$-0.815383\pi$
$283$	−2.62436e28	−1.67294	−0.836468	+	0.548016i	$0.815383\pi$
$284$	4.02799e28	2.46563
$285$	9.82759e26	0.0577738
$286$	2.45488e28	1.38618
$287$	1.91091e28	1.03657
$288$	−6.63476e27	−0.345789
$289$	−1.95740e28	−0.980290
$290$	−6.75192e27	−0.324975
$291$	−4.04235e27	−0.187010
$292$	−8.03435e28	−3.57312
$293$	3.20151e28	1.36892	0.684458	−	0.729052i	$-0.260039\pi$
$293$	3.20151e28	1.36892	0.684458	+	0.729052i	$0.260039\pi$
$294$	1.56178e26	0.00642136
$295$	−9.01856e27	−0.356602
$296$	1.59927e28	0.608228
$297$	5.50310e27	0.201330
$298$	7.79965e28	2.74529
$299$	−3.63049e28	−1.22955
$300$	9.38272e27	0.305798
$301$	1.01853e28	0.319490
$302$	−6.38225e28	−1.92705
$303$	−2.37105e27	−0.0689207
$304$	5.72943e28	1.60349
$305$	1.49660e28	0.403328
$306$	−9.27586e27	−0.240745
$307$	−1.15407e28	−0.288496	−0.144248	−	0.989542i	$-0.546076\pi$
$307$	−1.15407e28	−0.288496	−0.144248	+	0.989542i	$0.546076\pi$
$308$	−5.49789e28	−1.32392
$309$	1.58493e27	0.0367695
$310$	−2.21228e26	−0.00494516
$311$	3.62817e28	0.781525	0.390763	−	0.920491i	$-0.372211\pi$
$311$	3.62817e28	0.781525	0.390763	+	0.920491i	$0.372211\pi$
$312$	−1.82820e28	−0.379530
$313$	2.56117e28	0.512481	0.256241	−	0.966613i	$-0.417516\pi$
$313$	2.56117e28	0.512481	0.256241	+	0.966613i	$0.417516\pi$
$314$	9.79346e26	0.0188906
$315$	−1.51791e28	−0.282276
$316$	−7.01618e28	−1.25805
$317$	−2.91424e27	−0.0503899	−0.0251950	−	0.999683i	$-0.508021\pi$
$317$	−2.91424e27	−0.0503899	−0.0251950	+	0.999683i	$0.508021\pi$
$318$	1.59566e28	0.266091
$319$	2.50370e28	0.402708
$320$	1.27192e28	0.197350
$321$	2.90243e27	0.0434464
$322$	1.20096e29	1.73455
$323$	1.24456e28	0.173455
$324$	1.44042e29	1.93741
$325$	−8.68205e28	−1.12710
$326$	−1.16013e29	−1.45379
$327$	−1.40474e28	−0.169940
$328$	−1.73170e29	−2.02267
$329$	−1.26378e29	−1.42534
$330$	4.82691e27	0.0525725
$331$	4.00537e28	0.421328	0.210664	−	0.977558i	$-0.432437\pi$
$331$	4.00537e28	0.421328	0.210664	+	0.977558i	$0.432437\pi$
$332$	2.56588e29	2.60704
$333$	−3.13089e28	−0.307298
$334$	−6.01289e28	−0.570163
$335$	−8.87504e27	−0.0813121
$336$	2.31256e28	0.204735
$337$	1.31131e29	1.12192	0.560959	−	0.827843i	$-0.310432\pi$
$337$	1.31131e29	1.12192	0.560959	+	0.827843i	$0.310432\pi$
$338$	1.10697e29	0.915364
$339$	2.38872e27	0.0190928
$340$	−1.11606e28	−0.0862342
$341$	8.20342e26	0.00612801
$342$	−2.93327e29	−2.11861
$343$	1.44770e29	1.01110
$344$	−9.23010e28	−0.623425
$345$	−7.13846e27	−0.0466321
$346$	−2.42518e29	−1.53239
$347$	1.14051e29	0.697126	0.348563	−	0.937285i	$-0.386670\pi$
$347$	1.14051e29	0.697126	0.348563	+	0.937285i	$0.386670\pi$
$348$	−3.56549e28	−0.210843
$349$	7.28518e28	0.416820	0.208410	−	0.978042i	$-0.433171\pi$
$349$	7.28518e28	0.416820	0.208410	+	0.978042i	$0.433171\pi$
$350$	2.87201e29	1.59002
$351$	7.25167e28	0.388514
$352$	4.37230e28	0.226709
$353$	−3.68425e29	−1.84902	−0.924508	−	0.381164i	$-0.875523\pi$
$353$	−3.68425e29	−1.84902	−0.924508	+	0.381164i	$0.875523\pi$
$354$	−7.03438e28	−0.341734
$355$	−7.32860e28	−0.344663
$356$	3.18259e28	0.144912
$357$	5.02340e27	0.0221469
$358$	5.01891e29	2.14267
$359$	−2.45802e29	−1.01625	−0.508123	−	0.861284i	$-0.669661\pi$
$359$	−2.45802e29	−1.01625	−0.508123	+	0.861284i	$0.669661\pi$
$360$	1.37556e29	0.550808
$361$	1.35734e29	0.526448
$362$	2.42819e29	0.912292
$363$	2.59458e28	0.0944367
$364$	−7.24481e29	−2.55482
$365$	1.46179e29	0.499477
$366$	1.16733e29	0.386512
$367$	−4.73025e29	−1.51783	−0.758917	−	0.651187i	$-0.774271\pi$
$367$	−4.73025e29	−1.51783	−0.758917	+	0.651187i	$0.774271\pi$
$368$	−4.16168e29	−1.29425
$369$	3.39016e29	1.02192
$370$	−5.56413e28	−0.162584
$371$	3.30675e29	0.936703
$372$	−1.16824e27	−0.00320840
$373$	−2.90241e29	−0.772872	−0.386436	−	0.922316i	$-0.626294\pi$
$373$	−2.90241e29	−0.772872	−0.386436	+	0.922316i	$0.626294\pi$
$374$	6.11278e28	0.157839
$375$	−3.57456e28	−0.0895083
$376$	1.14526e30	2.78129
$377$	3.29924e29	0.777120
$378$	−2.39884e29	−0.548082
$379$	2.72591e29	0.604172	0.302086	−	0.953281i	$-0.402317\pi$
$379$	2.72591e29	0.604172	0.302086	+	0.953281i	$0.402317\pi$
$380$	−3.52927e29	−0.758881
$381$	−6.70187e28	−0.139817
$382$	−4.35288e29	−0.881147
$383$	−9.91721e29	−1.94806	−0.974032	−	0.226408i	$-0.927302\pi$
$383$	−9.91721e29	−1.94806	−0.974032	+	0.226408i	$0.927302\pi$
$384$	1.28913e29	0.245746
$385$	1.00030e29	0.185068
$386$	−1.35969e30	−2.44166
$387$	1.80698e29	0.314976
$388$	1.45168e30	2.45644
$389$	8.39840e29	1.37967	0.689836	−	0.723966i	$-0.257683\pi$
$389$	8.39840e29	1.37967	0.689836	+	0.723966i	$0.257683\pi$
$390$	6.36062e28	0.101451
$391$	−9.04012e28	−0.140004
$392$	−2.93303e28	−0.0441089
$393$	−1.28911e29	−0.188268
$394$	−5.09992e29	−0.723363
$395$	1.27654e29	0.175860
$396$	−9.75388e29	−1.30522
$397$	9.94808e27	0.0129315	0.00646574	−	0.999979i	$-0.497942\pi$
$397$	9.94808e27	0.0129315	0.00646574	+	0.999979i	$0.497942\pi$
$398$	2.27754e30	2.87615
$399$	1.58853e29	0.194898
$400$	−9.95236e29	−1.18641
$401$	−4.81480e29	−0.557723	−0.278861	−	0.960331i	$-0.589957\pi$
$401$	−4.81480e29	−0.557723	−0.278861	+	0.960331i	$0.589957\pi$
$402$	−6.92244e28	−0.0779219
$403$	1.08100e28	0.0118254
$404$	8.51487e29	0.905299
$405$	−2.62072e29	−0.270825
$406$	−1.09138e30	−1.09629
$407$	2.06325e29	0.201473
$408$	−4.55232e28	−0.0432156
$409$	−8.22531e29	−0.759162	−0.379581	−	0.925159i	$-0.623932\pi$
$409$	−8.22531e29	−0.759162	−0.379581	+	0.925159i	$0.623932\pi$
$410$	6.02490e29	0.540674
$411$	5.96573e28	0.0520575
$412$	−5.69178e29	−0.482981
$413$	−1.45776e30	−1.20299
$414$	2.13064e30	1.71004
$415$	−4.66841e29	−0.364431
$416$	5.76156e29	0.437489
$417$	1.82259e29	0.134624
$418$	1.93302e30	1.38902
$419$	2.72055e30	1.90194	0.950969	−	0.309287i	$-0.100090\pi$
$419$	2.72055e30	1.90194	0.950969	+	0.309287i	$0.100090\pi$
$420$	−1.42451e29	−0.0968945
$421$	1.73534e30	1.14852	0.574261	−	0.818672i	$-0.305289\pi$
$421$	1.73534e30	1.14852	0.574261	+	0.818672i	$0.305289\pi$
$422$	−4.06173e30	−2.61588
$423$	−2.24209e30	−1.40520
$424$	−2.99665e30	−1.82780
$425$	−2.16188e29	−0.128339
$426$	−5.71623e29	−0.330293
$427$	2.41911e30	1.36061
$428$	−1.04232e30	−0.570684
$429$	−2.35860e29	−0.125718
$430$	3.21131e29	0.166646
$431$	2.30954e30	1.16691	0.583455	−	0.812146i	$-0.301701\pi$
$431$	2.30954e30	1.16691	0.583455	+	0.812146i	$0.301701\pi$
$432$	8.31270e29	0.408958
$433$	−4.49441e29	−0.215309	−0.107655	−	0.994188i	$-0.534334\pi$
$433$	−4.49441e29	−0.215309	−0.107655	+	0.994188i	$0.534334\pi$
$434$	−3.57593e28	−0.0166823
$435$	6.48713e28	0.0294731
$436$	5.04468e30	2.23223
$437$	−2.85872e30	−1.23207
$438$	1.14018e30	0.478652
$439$	−1.98640e30	−0.812315	−0.406157	−	0.913803i	$-0.633132\pi$
$439$	−1.98640e30	−0.812315	−0.406157	+	0.913803i	$0.633132\pi$
$440$	−9.06491e29	−0.361125
$441$	5.74199e28	0.0222853
$442$	8.05507e29	0.304588
$443$	−2.09074e30	−0.770294	−0.385147	−	0.922855i	$-0.625849\pi$
$443$	−2.09074e30	−0.770294	−0.385147	+	0.922855i	$0.625849\pi$
$444$	−2.93825e29	−0.105484
$445$	−5.79046e28	−0.0202569
$446$	−2.89984e30	−0.988607
$447$	−7.49376e29	−0.248979
$448$	2.05594e30	0.665753
$449$	2.38796e30	0.753694	0.376847	−	0.926276i	$-0.377008\pi$
$449$	2.38796e30	0.753694	0.376847	+	0.926276i	$0.377008\pi$
$450$	5.09526e30	1.56755
$451$	−2.23411e30	−0.670000
$452$	−8.57834e29	−0.250791
$453$	6.13195e29	0.174771
$454$	−9.28376e30	−2.57977
$455$	1.31813e30	0.357132
$456$	−1.43956e30	−0.380307
$457$	1.54921e30	0.399093	0.199547	−	0.979888i	$-0.436053\pi$
$457$	1.54921e30	0.399093	0.199547	+	0.979888i	$0.436053\pi$
$458$	5.67374e30	1.42533
$459$	1.80571e29	0.0442386
$460$	2.56355e30	0.612530
$461$	4.06665e30	0.947711	0.473855	−	0.880603i	$-0.342862\pi$
$461$	4.06665e30	0.947711	0.473855	+	0.880603i	$0.342862\pi$
$462$	7.80221e29	0.177352
$463$	−6.37975e29	−0.141456	−0.0707282	−	0.997496i	$-0.522532\pi$
$463$	−6.37975e29	−0.141456	−0.0707282	+	0.997496i	$0.522532\pi$
$464$	3.78196e30	0.818013
$465$	2.12552e27	0.000448493 0
$466$	−8.31798e30	−1.71230
$467$	1.15365e30	0.231701	0.115851	−	0.993267i	$-0.463041\pi$
$467$	1.15365e30	0.231701	0.115851	+	0.993267i	$0.463041\pi$
$468$	−1.28531e31	−2.51873
$469$	−1.43456e30	−0.274304
$470$	−3.98458e30	−0.743458
$471$	−9.40938e27	−0.00171325
$472$	1.32105e31	2.34740
$473$	−1.19080e30	−0.206507
$474$	9.95686e29	0.168528
$475$	−6.83643e30	−1.12941
$476$	−1.80400e30	−0.290908
$477$	5.86655e30	0.923468
$478$	1.31766e31	2.02480
$479$	−2.12936e30	−0.319441	−0.159721	−	0.987162i	$-0.551059\pi$
$479$	−2.12936e30	−0.319441	−0.159721	+	0.987162i	$0.551059\pi$
$480$	1.13287e29	0.0165922
$481$	2.71884e30	0.388790
$482$	9.51914e30	1.32910
$483$	−1.15386e30	−0.157312
$484$	−9.31762e30	−1.24046
$485$	−2.64122e30	−0.343380
$486$	−6.41116e30	−0.813991
$487$	4.84200e30	0.600401	0.300201	−	0.953876i	$-0.402946\pi$
$487$	4.84200e30	0.600401	0.300201	+	0.953876i	$0.402946\pi$
$488$	−2.19225e31	−2.65498
$489$	1.11463e30	0.131849
$490$	1.02045e29	0.0117906
$491$	−3.44338e29	−0.0388640	−0.0194320	−	0.999811i	$-0.506186\pi$
$491$	−3.44338e29	−0.0388640	−0.0194320	+	0.999811i	$0.506186\pi$
$492$	3.18157e30	0.350787
$493$	8.21528e29	0.0884877
$494$	2.54722e31	2.68045
$495$	1.77464e30	0.182453
$496$	1.23917e29	0.0124477
$497$	−1.18460e31	−1.16271
$498$	−3.64131e30	−0.349237
$499$	−1.27549e31	−1.19542	−0.597711	−	0.801711i	$-0.703923\pi$
$499$	−1.27549e31	−1.19542	−0.597711	+	0.801711i	$0.703923\pi$
$500$	1.28369e31	1.17573
$501$	5.77708e29	0.0517100
$502$	−2.09546e31	−1.83311
$503$	1.67840e31	1.43504	0.717520	−	0.696538i	$-0.245277\pi$
$503$	1.67840e31	1.43504	0.717520	+	0.696538i	$0.245277\pi$
$504$	2.22345e31	1.85813
$505$	−1.54921e30	−0.126549
$506$	−1.40409e31	−1.12115
$507$	−1.06356e30	−0.0830175
$508$	2.40677e31	1.83654
$509$	−2.11935e31	−1.58106	−0.790529	−	0.612425i	$-0.790194\pi$
$509$	−2.11935e31	−1.58106	−0.790529	+	0.612425i	$0.790194\pi$
$510$	1.58383e29	0.0115518
$511$	2.36283e31	1.68497
$512$	−2.92986e31	−2.04288
$513$	5.71012e30	0.389310
$514$	−2.60131e31	−1.73427
$515$	1.03557e30	0.0675146
$516$	1.69580e30	0.108119
$517$	1.47753e31	0.921290
$518$	−8.99386e30	−0.548471
$519$	2.33007e30	0.138977
$520$	−1.19452e31	−0.696876
$521$	−1.22820e30	−0.0700869	−0.0350434	−	0.999386i	$-0.511157\pi$
$521$	−1.22820e30	−0.0700869	−0.0350434	+	0.999386i	$0.511157\pi$
$522$	−1.93623e31	−1.08080
$523$	7.24558e30	0.395643	0.197821	−	0.980238i	$-0.436613\pi$
$523$	7.24558e30	0.395643	0.197821	+	0.980238i	$0.436613\pi$
$524$	4.62943e31	2.47296
$525$	−2.75937e30	−0.144204
$526$	5.07308e31	2.59379
$527$	2.69175e28	0.00134652
$528$	−2.70370e30	−0.132333
$529$	−1.15570e29	−0.00553483
$530$	1.04259e31	0.488585
$531$	−2.58623e31	−1.18599
$532$	−5.70471e31	−2.56006
$533$	−2.94399e31	−1.29292
$534$	−4.51650e29	−0.0194123
$535$	1.89641e30	0.0797744
$536$	1.30003e31	0.535252
$537$	−4.82208e30	−0.194326
$538$	3.27453e30	0.129167
$539$	−3.78397e29	−0.0146109
$540$	−5.12053e30	−0.193547
$541$	9.30820e30	0.344427	0.172214	−	0.985060i	$-0.444908\pi$
$541$	9.30820e30	0.344427	0.172214	+	0.985060i	$0.444908\pi$
$542$	6.07719e31	2.20146
$543$	−2.33296e30	−0.0827389
$544$	1.43466e30	0.0498152
$545$	−9.17839e30	−0.312038
$546$	1.02813e31	0.342242
$547$	−2.67466e31	−0.871796	−0.435898	−	0.899996i	$-0.643569\pi$
$547$	−2.67466e31	−0.871796	−0.435898	+	0.899996i	$0.643569\pi$
$548$	−2.14241e31	−0.683794
$549$	4.29177e31	1.34139
$550$	−3.35777e31	−1.02773
$551$	2.59789e31	0.778712
$552$	1.04565e31	0.306965
$553$	2.06340e31	0.593258
$554$	−2.69857e31	−0.759926
$555$	5.34592e29	0.0147453
$556$	−6.54524e31	−1.76834
$557$	2.40510e31	0.636501	0.318250	−	0.948007i	$-0.396905\pi$
$557$	2.40510e31	0.636501	0.318250	+	0.948007i	$0.396905\pi$
$558$	−6.34410e29	−0.0164466
$559$	−1.56916e31	−0.398504
$560$	1.51100e31	0.375925
$561$	−5.87305e29	−0.0143150
$562$	4.93038e31	1.17737
$563$	2.15437e31	0.504049	0.252025	−	0.967721i	$-0.418904\pi$
$563$	2.15437e31	0.504049	0.252025	+	0.967721i	$0.418904\pi$
$564$	−2.10414e31	−0.482353
$565$	1.56076e30	0.0350574
$566$	−1.33747e32	−2.94370
$567$	−4.23614e31	−0.913618
$568$	1.07351e32	2.26881
$569$	1.70978e31	0.354120	0.177060	−	0.984200i	$-0.443341\pi$
$569$	1.70978e31	0.354120	0.177060	+	0.984200i	$0.443341\pi$
$570$	5.00848e30	0.101659
$571$	−8.69138e31	−1.72891	−0.864457	−	0.502707i	$-0.832337\pi$
$571$	−8.69138e31	−1.72891	−0.864457	+	0.502707i	$0.832337\pi$
$572$	8.47018e31	1.65135
$573$	4.18217e30	0.0799142
$574$	9.73865e31	1.82395
$575$	4.96577e31	0.911605
$576$	3.64747e31	0.656346
$577$	1.59167e31	0.280757	0.140378	−	0.990098i	$-0.455168\pi$
$577$	1.59167e31	0.280757	0.140378	+	0.990098i	$0.455168\pi$
$578$	−9.97560e31	−1.72492
$579$	1.30637e31	0.221443
$580$	−2.32965e31	−0.387140
$581$	−7.54602e31	−1.22940
$582$	−2.06012e31	−0.329063
$583$	−3.86605e31	−0.605451
$584$	−2.14125e32	−3.28790
$585$	2.33852e31	0.352086
$586$	1.63160e32	2.40875
$587$	5.71080e31	0.826721	0.413361	−	0.910567i	$-0.364355\pi$
$587$	5.71080e31	0.826721	0.413361	+	0.910567i	$0.364355\pi$
$588$	5.38870e29	0.00764971
$589$	8.51202e29	0.0118497
$590$	−4.59618e31	−0.627478
$591$	4.89991e30	0.0656043
$592$	3.11664e31	0.409248
$593$	2.68653e31	0.345989	0.172995	−	0.984923i	$-0.444656\pi$
$593$	2.68653e31	0.345989	0.172995	+	0.984923i	$0.444656\pi$
$594$	2.80457e31	0.354261
$595$	3.28223e30	0.0406653
$596$	2.69115e32	3.27044
$597$	−2.18822e31	−0.260848
$598$	−1.85023e32	−2.16352
$599$	1.35452e30	0.0155373	0.00776867	−	0.999970i	$-0.497527\pi$
$599$	1.35452e30	0.0155373	0.00776867	+	0.999970i	$0.497527\pi$
$600$	2.50060e31	0.281388
$601$	−7.37959e31	−0.814659	−0.407329	−	0.913281i	$-0.633540\pi$
$601$	−7.37959e31	−0.814659	−0.407329	+	0.913281i	$0.633540\pi$
$602$	5.19077e31	0.562175
$603$	−2.54507e31	−0.270428
$604$	−2.20210e32	−2.29568
$605$	1.69527e31	0.173401
$606$	−1.20837e31	−0.121273
$607$	−3.23323e31	−0.318395	−0.159198	−	0.987247i	$-0.550891\pi$
$607$	−3.23323e31	−0.318395	−0.159198	+	0.987247i	$0.550891\pi$
$608$	4.53677e31	0.438385
$609$	1.04858e31	0.0994266
$610$	7.62721e31	0.709696
$611$	1.94701e32	1.77785
$612$	−3.20049e31	−0.286798
$613$	4.35574e31	0.383059	0.191530	−	0.981487i	$-0.438655\pi$
$613$	4.35574e31	0.383059	0.191530	+	0.981487i	$0.438655\pi$
$614$	−5.88154e31	−0.507639
$615$	−5.78862e30	−0.0490356
$616$	−1.46525e32	−1.21824
$617$	−2.29127e32	−1.86981	−0.934904	−	0.354902i	$-0.884514\pi$
$617$	−2.29127e32	−1.86981	−0.934904	+	0.354902i	$0.884514\pi$
$618$	8.07736e30	0.0646997
$619$	2.32366e32	1.82697	0.913484	−	0.406875i	$-0.133382\pi$
$619$	2.32366e32	1.82697	0.913484	+	0.406875i	$0.133382\pi$
$620$	−7.63313e29	−0.00589112
$621$	−4.14765e31	−0.314231
$622$	1.84904e32	1.37517
$623$	−9.35970e30	−0.0683360
$624$	−3.56278e31	−0.255368
$625$	1.06551e32	0.749787
$626$	1.30526e32	0.901763
$627$	−1.85721e31	−0.125975
$628$	3.37908e30	0.0225042
$629$	6.77005e30	0.0442700
$630$	−7.73578e31	−0.496693
$631$	−2.22944e32	−1.40559	−0.702793	−	0.711394i	$-0.748064\pi$
$631$	−2.22944e32	−1.40559	−0.702793	+	0.711394i	$0.748064\pi$
$632$	−1.86989e32	−1.15763
$633$	3.90244e31	0.237243
$634$	−1.48520e31	−0.0886662
$635$	−4.37892e31	−0.256726
$636$	5.50560e31	0.316992
$637$	−4.98629e30	−0.0281951
$638$	1.27597e32	0.708605
$639$	−2.10161e32	−1.14628
$640$	8.42299e31	0.451228
$641$	−2.75021e32	−1.44710	−0.723550	−	0.690272i	$-0.757491\pi$
$641$	−2.75021e32	−1.44710	−0.723550	+	0.690272i	$0.757491\pi$
$642$	1.47918e31	0.0764483
$643$	1.47614e32	0.749377	0.374689	−	0.927151i	$-0.377750\pi$
$643$	1.47614e32	0.749377	0.374689	+	0.927151i	$0.377750\pi$
$644$	4.14373e32	2.06635
$645$	−3.08537e30	−0.0151137
$646$	6.34273e31	0.305212
$647$	1.82358e32	0.862036	0.431018	−	0.902343i	$-0.358154\pi$
$647$	1.82358e32	0.862036	0.431018	+	0.902343i	$0.358154\pi$
$648$	3.83888e32	1.78276
$649$	1.70432e32	0.777567
$650$	−4.42468e32	−1.98325
$651$	3.43569e29	0.00151298
$652$	−4.00284e32	−1.73189
$653$	−4.35899e31	−0.185304	−0.0926519	−	0.995699i	$-0.529534\pi$
$653$	−4.35899e31	−0.185304	−0.0926519	+	0.995699i	$0.529534\pi$
$654$	−7.15905e31	−0.299028
$655$	−8.42287e31	−0.345689
$656$	−3.37473e32	−1.36096
$657$	4.19193e32	1.66116
$658$	−6.44067e32	−2.50803
$659$	−3.58880e31	−0.137331	−0.0686653	−	0.997640i	$-0.521874\pi$
$659$	−3.58880e31	−0.137331	−0.0686653	+	0.997640i	$0.521874\pi$
$660$	1.66545e31	0.0626291
$661$	2.78803e32	1.03034	0.515171	−	0.857088i	$-0.327729\pi$
$661$	2.78803e32	1.03034	0.515171	+	0.857088i	$0.327729\pi$
$662$	2.04128e32	0.741370
$663$	−7.73917e30	−0.0276241
$664$	6.83836e32	2.39894
$665$	1.03793e32	0.357864
$666$	−1.59561e32	−0.540721
$667$	−1.88703e32	−0.628537
$668$	−2.07466e32	−0.679230
$669$	2.78612e31	0.0896601
$670$	−4.52303e31	−0.143077
$671$	−2.82827e32	−0.879452
$672$	1.83117e31	0.0559734
$673$	1.90131e31	0.0571320	0.0285660	−	0.999592i	$-0.490906\pi$
$673$	1.90131e31	0.0571320	0.0285660	+	0.999592i	$0.490906\pi$
$674$	6.68289e32	1.97413
$675$	−9.91881e31	−0.288049
$676$	3.81943e32	1.09047
$677$	−3.87840e32	−1.08864	−0.544318	−	0.838879i	$-0.683212\pi$
$677$	−3.87840e32	−1.08864	−0.544318	+	0.838879i	$0.683212\pi$
$678$	1.21738e31	0.0335957
$679$	−4.26927e32	−1.15838
$680$	−2.97442e31	−0.0793507
$681$	8.91968e31	0.233969
$682$	4.18075e30	0.0107829
$683$	6.51681e32	1.65271	0.826356	−	0.563148i	$-0.190410\pi$
$683$	6.51681e32	1.65271	0.826356	+	0.563148i	$0.190410\pi$
$684$	−1.01208e33	−2.52389
$685$	3.89794e31	0.0955857
$686$	7.37799e32	1.77914
$687$	−5.45123e31	−0.129268
$688$	−1.79876e32	−0.419474
$689$	−5.09446e32	−1.16836
$690$	−3.63801e31	−0.0820539
$691$	−6.18205e31	−0.137131	−0.0685654	−	0.997647i	$-0.521842\pi$
$691$	−6.18205e31	−0.137131	−0.0685654	+	0.997647i	$0.521842\pi$
$692$	−8.36770e32	−1.82552
$693$	2.86853e32	0.615499
$694$	5.81246e32	1.22666
$695$	1.19085e32	0.247191
$696$	−9.50245e31	−0.194012
$697$	−7.33069e31	−0.147220
$698$	3.71278e32	0.733436
$699$	7.99177e31	0.155294
$700$	9.90942e32	1.89418
$701$	5.26483e32	0.989982	0.494991	−	0.868898i	$-0.335171\pi$
$701$	5.26483e32	0.989982	0.494991	+	0.868898i	$0.335171\pi$
$702$	3.69571e32	0.683629
$703$	2.14087e32	0.389586
$704$	−2.40367e32	−0.430319
$705$	3.82831e31	0.0674268
$706$	−1.87763e33	−3.25353
$707$	−2.50415e32	−0.426910
$708$	−2.42711e32	−0.407105
$709$	−7.09958e32	−1.17166	−0.585829	−	0.810435i	$-0.699231\pi$
$709$	−7.09958e32	−1.17166	−0.585829	+	0.810435i	$0.699231\pi$
$710$	−3.73491e32	−0.606470
$711$	3.66070e32	0.584876
$712$	8.48196e31	0.133345
$713$	−6.18287e30	−0.00956446
$714$	2.56010e31	0.0389698
$715$	−1.54108e32	−0.230837
$716$	1.73170e33	2.55254
$717$	−1.26598e32	−0.183636
$718$	−1.25269e33	−1.78819
$719$	4.58875e32	0.644633	0.322316	−	0.946632i	$-0.395539\pi$
$719$	4.58875e32	0.644633	0.322316	+	0.946632i	$0.395539\pi$
$720$	2.68068e32	0.370613
$721$	1.67390e32	0.227758
$722$	6.91748e32	0.926339
$723$	−9.14583e31	−0.120540
$724$	8.37810e32	1.08681
$725$	−4.51268e32	−0.576166
$726$	1.32229e32	0.166171
$727$	1.25284e33	1.54970	0.774851	−	0.632144i	$-0.217825\pi$
$727$	1.25284e33	1.54970	0.774851	+	0.632144i	$0.217825\pi$
$728$	−1.93083e33	−2.35089
$729$	−7.09581e32	−0.850424
$730$	7.44977e32	0.878881
$731$	−3.90730e31	−0.0453761
$732$	4.02771e32	0.460448
$733$	−1.67809e30	−0.00188852	−0.000944258	−	1.00000i	$-0.500301\pi$
$733$	−1.67809e30	−0.00188852	−0.000944258		1.00000i	$0.500301\pi$
$734$	−2.41070e33	−2.67078
$735$	−9.80431e29	−0.00106933
$736$	−3.29537e32	−0.353842
$737$	1.67720e32	0.177300
$738$	1.72775e33	1.79817
$739$	2.96573e32	0.303893	0.151946	−	0.988389i	$-0.451446\pi$
$739$	2.96573e32	0.303893	0.151946	+	0.988389i	$0.451446\pi$
$740$	−1.91982e32	−0.193685
$741$	−2.44733e32	−0.243099
$742$	1.68524e33	1.64822
$743$	−4.48312e32	−0.431727	−0.215863	−	0.976424i	$-0.569257\pi$
$743$	−4.48312e32	−0.431727	−0.215863	+	0.976424i	$0.569257\pi$
$744$	−3.11349e30	−0.00295229
$745$	−4.89633e32	−0.457166
$746$	−1.47917e33	−1.35995
$747$	−1.33875e33	−1.21203
$748$	2.10912e32	0.188033
$749$	3.06536e32	0.269116
$750$	−1.82172e32	−0.157499
$751$	−3.50465e32	−0.298391	−0.149195	−	0.988808i	$-0.547668\pi$
$751$	−3.50465e32	−0.298391	−0.149195	+	0.988808i	$0.547668\pi$
$752$	2.23188e33	1.87140
$753$	2.01329e32	0.166251
$754$	1.68141e33	1.36742
$755$	4.00654e32	0.320907
$756$	−8.27683e32	−0.652925
$757$	4.37490e32	0.339911	0.169956	−	0.985452i	$-0.445638\pi$
$757$	4.37490e32	0.339911	0.169956	+	0.985452i	$0.445638\pi$
$758$	1.38922e33	1.06310
$759$	1.34902e32	0.101681
$760$	−9.40591e32	−0.698304
$761$	−1.53089e31	−0.0111949	−0.00559744	−	0.999984i	$-0.501782\pi$
$761$	−1.53089e31	−0.0111949	−0.00559744	+	0.999984i	$0.501782\pi$
$762$	−3.41551e32	−0.246022
$763$	−1.48360e33	−1.05265
$764$	−1.50190e33	−1.04970
$765$	5.82304e31	0.0400907
$766$	−5.05416e33	−3.42782
$767$	2.24586e33	1.50050
$768$	4.93686e32	0.324935
$769$	2.67481e33	1.73436	0.867180	−	0.497995i	$-0.165930\pi$
$769$	2.67481e33	1.73436	0.867180	+	0.497995i	$0.165930\pi$
$770$	5.09787e32	0.325646
$771$	2.49929e32	0.157287
$772$	−4.69141e33	−2.90873
$773$	8.38808e31	0.0512387	0.0256194	−	0.999672i	$-0.491844\pi$
$773$	8.38808e31	0.0512387	0.0256194	+	0.999672i	$0.491844\pi$
$774$	9.20900e32	0.554232
$775$	−1.47859e31	−0.00876753
$776$	3.86890e33	2.26036
$777$	8.64114e31	0.0497427
$778$	4.28012e33	2.42767
$779$	−2.31816e33	−1.29557
$780$	2.19464e32	0.120858
$781$	1.38496e33	0.751534
$782$	−4.60716e32	−0.246352
$783$	3.76921e32	0.198605
$784$	−5.71586e31	−0.0296788
$785$	−6.14797e30	−0.00314580
$786$	−6.56975e32	−0.331276
$787$	−3.07440e33	−1.52775	−0.763874	−	0.645366i	$-0.776705\pi$
$787$	−3.07440e33	−1.52775	−0.763874	+	0.645366i	$0.776705\pi$
$788$	−1.75965e33	−0.861737
$789$	−4.87412e32	−0.235240
$790$	6.50569e32	0.309444
$791$	2.52281e32	0.118265
$792$	−2.59952e33	−1.20103
$793$	−3.72693e33	−1.69711
$794$	5.06989e31	0.0227543
$795$	−1.00170e32	−0.0443114
$796$	7.85832e33	3.42633
$797$	2.31415e33	0.994535	0.497268	−	0.867597i	$-0.334337\pi$
$797$	2.31415e33	0.994535	0.497268	+	0.867597i	$0.334337\pi$
$798$	8.09572e32	0.342943
$799$	4.84816e32	0.202437
$800$	−7.88064e32	−0.324360
$801$	−1.66052e32	−0.0673704
$802$	−2.45379e33	−0.981370
$803$	−2.76247e33	−1.08910
$804$	−2.38848e32	−0.0928276
$805$	−7.53918e32	−0.288849
$806$	5.50915e31	0.0208081
$807$	−3.14611e31	−0.0117146
$808$	2.26931e33	0.833035
$809$	3.80662e33	1.37763	0.688814	−	0.724938i	$-0.258132\pi$
$809$	3.80662e33	1.37763	0.688814	+	0.724938i	$0.258132\pi$
$810$	−1.33561e33	−0.476544
$811$	4.24454e33	1.49311	0.746554	−	0.665325i	$-0.231707\pi$
$811$	4.24454e33	1.49311	0.746554	+	0.665325i	$0.231707\pi$
$812$	−3.76564e33	−1.30601
$813$	−5.83886e32	−0.199658
$814$	1.05151e33	0.354512
$815$	7.28284e32	0.242096
$816$	−8.87152e31	−0.0290778
$817$	−1.23559e33	−0.399321
$818$	−4.19191e33	−1.33582
$819$	3.77998e33	1.18775
$820$	2.07880e33	0.644100
$821$	−2.99736e33	−0.915784	−0.457892	−	0.889008i	$-0.651395\pi$
$821$	−2.99736e33	−0.915784	−0.457892	+	0.889008i	$0.651395\pi$
$822$	3.04035e32	0.0916004
$823$	−5.19319e32	−0.154289	−0.0771447	−	0.997020i	$-0.524580\pi$
$823$	−5.19319e32	−0.154289	−0.0771447	+	0.997020i	$0.524580\pi$
$824$	−1.51692e33	−0.444428
$825$	3.22609e32	0.0932086
$826$	−7.42926e33	−2.11678
$827$	4.81781e32	0.135374	0.0676872	−	0.997707i	$-0.478438\pi$
$827$	4.81781e32	0.135374	0.0676872	+	0.997707i	$0.478438\pi$
$828$	7.35144e33	2.03715
$829$	−2.15627e33	−0.589287	−0.294644	−	0.955607i	$-0.595201\pi$
$829$	−2.15627e33	−0.589287	−0.294644	+	0.955607i	$0.595201\pi$
$830$	−2.37918e33	−0.641254
$831$	2.59274e32	0.0689202
$832$	−3.16743e33	−0.830401
$833$	−1.24161e31	−0.00321048
$834$	9.28853e32	0.236885
$835$	3.77467e32	0.0949477
$836$	6.66960e33	1.65473
$837$	1.23499e31	0.00302218
$838$	1.38649e34	3.34665
$839$	−2.38371e32	−0.0567532	−0.0283766	−	0.999597i	$-0.509034\pi$
$839$	−2.38371e32	−0.0567532	−0.0283766	+	0.999597i	$0.509034\pi$
$840$	−3.79649e32	−0.0891601
$841$	−2.60187e33	−0.602743
$842$	8.84388e33	2.02094
$843$	−4.73702e32	−0.106780
$844$	−1.40144e34	−3.11627
$845$	−6.94915e32	−0.152433
$846$	−1.14265e34	−2.47260
$847$	2.74023e33	0.584962
$848$	−5.83985e33	−1.22984
$849$	1.28501e33	0.266974
$850$	−1.10177e33	−0.225826
$851$	−1.55506e33	−0.314454
$852$	−1.97230e33	−0.393475
$853$	−1.94872e32	−0.0383563	−0.0191781	−	0.999816i	$-0.506105\pi$
$853$	−1.94872e32	−0.0383563	−0.0191781	+	0.999816i	$0.506105\pi$
$854$	1.23286e34	2.39414
$855$	1.84140e33	0.352807
$856$	−2.77789e33	−0.525130
$857$	−1.87495e33	−0.349711	−0.174855	−	0.984594i	$-0.555946\pi$
$857$	−1.87495e33	−0.349711	−0.174855	+	0.984594i	$0.555946\pi$
$858$	−1.20203e33	−0.221213
$859$	6.46779e33	1.17445	0.587225	−	0.809424i	$-0.300220\pi$
$859$	6.46779e33	1.17445	0.587225	+	0.809424i	$0.300220\pi$
$860$	1.10801e33	0.198524
$861$	−9.35673e32	−0.165420
$862$	1.17702e34	2.05330
$863$	−1.04050e34	−1.79110	−0.895550	−	0.444961i	$-0.853218\pi$
$863$	−1.04050e34	−1.79110	−0.895550	+	0.444961i	$0.853218\pi$
$864$	6.58230e32	0.111807
$865$	1.52244e33	0.255184
$866$	−2.29051e33	−0.378858
$867$	9.58438e32	0.156439
$868$	−1.23382e32	−0.0198735
$869$	−2.41239e33	−0.383461
$870$	3.30607e32	0.0518609
$871$	2.21012e33	0.342142
$872$	1.34447e34	2.05405
$873$	−7.57417e33	−1.14201
$874$	−1.45691e34	−2.16795
$875$	−3.77522e33	−0.554434
$876$	3.93401e33	0.570214
$877$	8.52438e33	1.21946	0.609730	−	0.792609i	$-0.291278\pi$
$877$	8.52438e33	1.21946	0.609730	+	0.792609i	$0.291278\pi$
$878$	−1.01234e34	−1.42935
$879$	−1.56761e33	−0.218457
$880$	−1.76656e33	−0.242984
$881$	1.20706e34	1.63872	0.819362	−	0.573276i	$-0.194328\pi$
$881$	1.20706e34	1.63872	0.819362	+	0.573276i	$0.194328\pi$
$882$	2.92632e32	0.0392133
$883$	4.60310e33	0.608839	0.304420	−	0.952538i	$-0.401538\pi$
$883$	4.60310e33	0.608839	0.304420	+	0.952538i	$0.401538\pi$
$884$	2.77928e33	0.362853
$885$	4.41593e32	0.0569081
$886$	−1.06551e34	−1.35541
$887$	−7.25037e33	−0.910413	−0.455207	−	0.890386i	$-0.650435\pi$
$887$	−7.25037e33	−0.910413	−0.455207	+	0.890386i	$0.650435\pi$
$888$	−7.83079e32	−0.0970636
$889$	−7.07809e33	−0.866055
$890$	−2.95102e32	−0.0356441
$891$	4.95263e33	0.590530
$892$	−1.00055e34	−1.17772
$893$	1.53312e34	1.78149
$894$	−3.81909e33	−0.438105
$895$	−3.15069e33	−0.356813
$896$	1.36149e34	1.52220
$897$	1.77766e33	0.196217
$898$	1.21699e34	1.32620
$899$	5.61873e31	0.00604507
$900$	1.75804e34	1.86741
$901$	−1.26855e33	−0.133037
$902$	−1.13858e34	−1.17893
$903$	−4.98720e32	−0.0509856
$904$	−2.28623e33	−0.230772
$905$	−1.52433e33	−0.151922
$906$	3.12506e33	0.307528
$907$	−3.03876e33	−0.295266	−0.147633	−	0.989042i	$-0.547165\pi$
$907$	−3.03876e33	−0.295266	−0.147633	+	0.989042i	$0.547165\pi$
$908$	−3.20322e34	−3.07326
$909$	−4.44264e33	−0.420878
$910$	6.71768e33	0.628410
$911$	−1.60065e34	−1.47855	−0.739273	−	0.673406i	$-0.764831\pi$
$911$	−1.60065e34	−1.47855	−0.739273	+	0.673406i	$0.764831\pi$
$912$	−2.80541e33	−0.255891
$913$	8.82233e33	0.794638
$914$	7.89533e33	0.702245
$915$	−7.32809e32	−0.0643648
$916$	1.95764e34	1.69799
$917$	−1.36147e34	−1.16617
$918$	9.20251e32	0.0778423
$919$	−1.54454e34	−1.29024	−0.645120	−	0.764081i	$-0.723193\pi$
$919$	−1.54454e34	−1.29024	−0.645120	+	0.764081i	$0.723193\pi$
$920$	6.83217e33	0.563636
$921$	5.65088e32	0.0460395
$922$	2.07251e34	1.66759
$923$	1.82501e34	1.45026
$924$	2.69204e33	0.211277
$925$	−3.71881e33	−0.288253
$926$	−3.25135e33	−0.248907
$927$	2.96969e33	0.224540
$928$	2.99469e33	0.223641
$929$	1.19786e34	0.883535	0.441768	−	0.897129i	$-0.354352\pi$
$929$	1.19786e34	0.883535	0.441768	+	0.897129i	$0.354352\pi$
$930$	1.08324e31	0.000789169 0
$931$	−3.92631e32	−0.0282529
$932$	−2.86999e34	−2.03985
$933$	−1.77653e33	−0.124719
$934$	5.87939e33	0.407702
$935$	−3.83738e32	−0.0262846
$936$	−3.42550e34	−2.31767
$937$	−2.83646e33	−0.189570	−0.0947852	−	0.995498i	$-0.530216\pi$
$937$	−2.83646e33	−0.189570	−0.0947852	+	0.995498i	$0.530216\pi$
$938$	−7.31103e33	−0.482665
$939$	−1.25407e33	−0.0817839
$940$	−1.37482e34	−0.885676
$941$	2.88589e34	1.83653	0.918267	−	0.395961i	$-0.129588\pi$
$941$	2.88589e34	1.83653	0.918267	+	0.395961i	$0.129588\pi$
$942$	−4.79535e31	−0.00301464
$943$	1.68384e34	1.04572
$944$	2.57446e34	1.57946
$945$	1.50590e33	0.0912707
$946$	−6.06872e33	−0.363370
$947$	2.29990e34	1.36045	0.680226	−	0.733002i	$-0.261882\pi$
$947$	2.29990e34	1.36045	0.680226	+	0.733002i	$0.261882\pi$
$948$	3.43546e33	0.200766
$949$	−3.64023e34	−2.10168
$950$	−3.48408e34	−1.98732
$951$	1.42695e32	0.00804144
$952$	−4.80786e33	−0.267687
$953$	−2.39769e34	−1.31894	−0.659470	−	0.751731i	$-0.729219\pi$
$953$	−2.39769e34	−1.31894	−0.659470	+	0.751731i	$0.729219\pi$
$954$	2.98980e34	1.62494
$955$	2.73258e33	0.146735
$956$	4.54638e34	2.41213
$957$	−1.22593e33	−0.0642658
$958$	−1.08520e34	−0.562090
$959$	6.30062e33	0.322455
$960$	−6.22796e32	−0.0314939
$961$	−2.00115e34	−0.999908
$962$	1.38561e34	0.684115
$963$	5.43829e33	0.265314
$964$	3.28444e34	1.58334
$965$	8.53563e33	0.406604
$966$	−5.88048e33	−0.276806
$967$	−6.66196e33	−0.309883	−0.154942	−	0.987924i	$-0.549519\pi$
$967$	−6.66196e33	−0.309883	−0.154942	+	0.987924i	$0.549519\pi$
$968$	−2.48325e34	−1.14144
$969$	−6.09398e32	−0.0276808
$970$	−1.34606e34	−0.604211
$971$	−3.35172e34	−1.48678	−0.743390	−	0.668858i	$-0.766783\pi$
$971$	−3.35172e34	−1.48678	−0.743390	+	0.668858i	$0.766783\pi$
$972$	−2.21207e34	−0.969701
$973$	1.92490e34	0.833892
$974$	2.46765e34	1.05647
$975$	4.25115e33	0.179868
$976$	−4.27224e34	−1.78642
$977$	1.17263e34	0.484590	0.242295	−	0.970203i	$-0.422100\pi$
$977$	1.17263e34	0.484590	0.242295	+	0.970203i	$0.422100\pi$
$978$	5.68054e33	0.232003
$979$	1.09428e33	0.0441699
$980$	3.52091e32	0.0140461
$981$	−2.63207e34	−1.03778
$982$	−1.75487e33	−0.0683851
$983$	1.51439e34	0.583274	0.291637	−	0.956529i	$-0.405800\pi$
$983$	1.51439e34	0.583274	0.291637	+	0.956529i	$0.405800\pi$
$984$	8.47927e33	0.322786
$985$	3.20154e33	0.120460
$986$	4.18679e33	0.155703
$987$	6.18808e33	0.227462
$988$	8.78881e34	3.19319
$989$	8.97497e33	0.322311
$990$	9.04419e33	0.321044
$991$	2.60260e34	0.913187	0.456593	−	0.889675i	$-0.349069\pi$
$991$	2.60260e34	0.913187	0.456593	+	0.889675i	$0.349069\pi$
$992$	9.81216e31	0.00340315
$993$	−1.96122e33	−0.0672374
$994$	−6.03711e34	−2.04591
$995$	−1.42976e34	−0.478957
$996$	−1.25638e34	−0.416043
$997$	−1.96863e34	−0.644422	−0.322211	−	0.946668i	$-0.604426\pi$
$997$	−1.96863e34	−0.644422	−0.322211	+	0.946668i	$0.604426\pi$
$998$	−6.50036e34	−2.10347
$999$	3.10613e33	0.0993613

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.24.a.a.1.2	✓	2
3.2	odd	2		9.24.a.b.1.1		2
4.3	odd	2		16.24.a.b.1.2		2
5.2	odd	4		25.24.b.a.24.4		4
5.3	odd	4		25.24.b.a.24.1		4
5.4	even	2		25.24.a.a.1.1		2
7.6	odd	2		49.24.a.b.1.2		2
8.3	odd	2		64.24.a.g.1.1		2
8.5	even	2		64.24.a.d.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.24.a.a.1.2	✓	2	1.1	even	1	trivial
9.24.a.b.1.1		2	3.2	odd	2
16.24.a.b.1.2		2	4.3	odd	2
25.24.a.a.1.1		2	5.4	even	2
25.24.b.a.24.1		4	5.3	odd	4
25.24.b.a.24.4		4	5.2	odd	4
49.24.a.b.1.2		2	7.6	odd	2
64.24.a.d.1.2		2	8.5	even	2
64.24.a.g.1.1		2	8.3	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:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+5096.35 q^{2} -48964.9 q^{3} +1.75842e7 q^{4} -3.19930e7 q^{5} -2.49542e8 q^{6} -5.17135e9 q^{7} +4.68639e10 q^{8} -9.17456e10 q^{9} +O(q^{10})\)	\(q+5096.35 q^{2} -48964.9 q^{3} +1.75842e7 q^{4} -3.19930e7 q^{5} -2.49542e8 q^{6} -5.17135e9 q^{7} +4.68639e10 q^{8} -9.17456e10 q^{9} -1.63048e11 q^{10} +6.04602e11 q^{11} -8.61007e11 q^{12} +7.96710e12 q^{13} -2.63550e13 q^{14} +1.56653e12 q^{15} +9.13280e13 q^{16} +1.98385e13 q^{17} -4.67568e14 q^{18} +6.27346e14 q^{19} -5.62571e14 q^{20} +2.53215e14 q^{21} +3.08127e15 q^{22} -4.55685e15 q^{23} -2.29468e15 q^{24} -1.08974e16 q^{25} +4.06032e16 q^{26} +9.10202e15 q^{27} -9.09340e16 q^{28} +4.14107e16 q^{29} +7.98360e15 q^{30} +1.35683e15 q^{31} +7.23169e16 q^{32} -2.96043e16 q^{33} +1.01104e17 q^{34} +1.65447e17 q^{35} -1.61327e18 q^{36} +3.41258e17 q^{37} +3.19718e18 q^{38} -3.90108e17 q^{39} -1.49932e18 q^{40} -3.69518e18 q^{41} +1.29047e18 q^{42} -1.96955e18 q^{43} +1.06314e19 q^{44} +2.93522e18 q^{45} -2.32233e19 q^{46} +2.44381e19 q^{47} -4.47186e18 q^{48} -6.25860e17 q^{49} -5.55369e19 q^{50} -9.71391e17 q^{51} +1.40095e20 q^{52} -6.39437e19 q^{53} +4.63871e19 q^{54} -1.93431e19 q^{55} -2.42350e20 q^{56} -3.07179e19 q^{57} +2.11044e20 q^{58} +2.81892e20 q^{59} +2.75462e19 q^{60} -4.67790e20 q^{61} +6.91488e18 q^{62} +4.74449e20 q^{63} -3.97563e20 q^{64} -2.54892e20 q^{65} -1.50874e20 q^{66} +2.77406e20 q^{67} +3.48844e20 q^{68} +2.23126e20 q^{69} +8.43177e20 q^{70} +2.29069e21 q^{71} -4.29956e21 q^{72} -4.56908e21 q^{73} +1.73917e21 q^{74} +5.33588e20 q^{75} +1.10314e22 q^{76} -3.12661e21 q^{77} -1.98813e21 q^{78} -3.99005e21 q^{79} -2.92186e21 q^{80} +8.19155e21 q^{81} -1.88319e22 q^{82} +1.45920e22 q^{83} +4.45257e21 q^{84} -6.34694e20 q^{85} -1.00375e22 q^{86} -2.02767e21 q^{87} +2.83340e22 q^{88} +1.80991e21 q^{89} +1.49589e22 q^{90} -4.12007e22 q^{91} -8.01285e22 q^{92} -6.64369e19 q^{93} +1.24545e23 q^{94} -2.00707e22 q^{95} -3.54099e21 q^{96} +8.25561e22 q^{97} -3.18960e21 q^{98} -5.54696e22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 1080 q^{2} + 339480 q^{3} + 25326656 q^{4} + 73069020 q^{5} - 1809673056 q^{6} - 1359184400 q^{7} + 49459023360 q^{8} - 34999394166 q^{9}+O(q^{10}) \) 2 * q + 1080 * q^2 + 339480 * q^3 + 25326656 * q^4 + 73069020 * q^5 - 1809673056 * q^6 - 1359184400 * q^7 + 49459023360 * q^8 - 34999394166 * q^9	\( 2 q + 1080 q^{2} + 339480 q^{3} + 25326656 q^{4} + 73069020 q^{5} - 1809673056 q^{6} - 1359184400 q^{7} + 49459023360 q^{8} - 34999394166 q^{9} - 585013636080 q^{10} + 856801968264 q^{11} + 2146514952960 q^{12} + 4376109322060 q^{13} - 41666034529728 q^{14} + 42377338985040 q^{15} + 15956586401792 q^{16} + 254028147597540 q^{17} - 695480683916520 q^{18} + 4260600979960 q^{19} + 250868387468160 q^{20} + 17\!\cdots\!44 q^{21}+ \cdots - 41\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q + 1080 * q^2 + 339480 * q^3 + 25326656 * q^4 + 73069020 * q^5 - 1809673056 * q^6 - 1359184400 * q^7 + 49459023360 * q^8 - 34999394166 * q^9 - 585013636080 * q^10 + 856801968264 * q^11 + 2146514952960 * q^12 + 4376109322060 * q^13 - 41666034529728 * q^14 + 42377338985040 * q^15 + 15956586401792 * q^16 + 254028147597540 * q^17 - 695480683916520 * q^18 + 4260600979960 * q^19 + 250868387468160 * q^20 + 1734031637722944 * q^21 + 2068343882177760 * q^22 - 8144713079008560 * q^23 - 1286622315141120 * q^24 - 11780274628800850 * q^25 + 55025854658735184 * q^26 - 5424634982716560 * q^27 - 61418438819709440 * q^28 + 20818433601623340 * q^29 - 155926924188644160 * q^30 + 137714017177000384 * q^31 + 353265663781601280 * q^32 + 68361366766001760 * q^33 - 839483655961325328 * q^34 + 565961271250425120 * q^35 - 1173916300077574848 * q^36 - 897721264408967780 * q^37 + 5699708971590961440 * q^38 - 1785011473665029232 * q^39 - 1226668524414336000 * q^40 - 2294435477168314956 * q^41 - 4657011326437397760 * q^42 - 1750760768619855800 * q^43 + 12584088840033038592 * q^44 + 8897092690294206540 * q^45 - 8813206018050221376 * q^46 + 15759744217656780960 * q^47 - 33749519399576616960 * q^48 - 13461981704376200814 * q^49 - 51990825483785316600 * q^50 + 89998362845078292144 * q^51 + 112291883783912022400 * q^52 - 140287253401646796420 * q^53 + 104731223417039799360 * q^54 + 7153550955060182640 * q^55 - 232456712054288117760 * q^56 - 272752401448627175520 * q^57 + 293749486923568689360 * q^58 + 280872989971340771880 * q^59 + 343522601114937592320 * q^60 - 180452892516502223636 * q^61 - 540743475843874103040 * q^62 + 690775113933935014320 * q^63 - 893690254469352914944 * q^64 - 632168834809440380760 * q^65 - 544338140913651883392 * q^66 + 1754233163431557625240 * q^67 + 2162050190142944330880 * q^68 - 1170560672172404223552 * q^69 - 765428657799921252480 * q^70 + 3055033510194143328624 * q^71 - 4152294352103038548480 * q^72 - 8063408253877606149260 * q^73 + 6715344283148807757072 * q^74 + 190631089350520885800 * q^75 + 6207154294513080590080 * q^76 - 2165184764357449665600 * q^77 + 3614293948840808587200 * q^78 + 6244916814559639980640 * q^79 - 10840537585501794017280 * q^80 - 2793528580929833975598 * q^81 - 24457792891615712450640 * q^82 + 6875994082418498976120 * q^83 + 15917751907190402476032 * q^84 + 23969743087870314902520 * q^85 - 10916288812918999243296 * q^86 - 10026640653837674384880 * q^87 + 28988514668199273707520 * q^88 + 6395093086173070004820 * q^89 - 8986073954327865866160 * q^90 - 54890178162704560146016 * q^91 - 107907439017191756981760 * q^92 + 52900811441357852079360 * q^93 + 159400518006534931827072 * q^94 - 85533361066700858502000 * q^95 + 105592121669584394256384 * q^96 - 31147288846254030500540 * q^97 + 48364767616374671003640 * q^98 - 41158245132312135981912 * q^99

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