LMFDB - Embedded newform 105.10.a.a.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [105,10,Mod(1,105)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("105.1"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(105, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	105.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,-41] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$54.0787627972$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 988x^{2} - 844x + 192256 $ x^4 - x^3 - 988x^2 - 844x + 192256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$28.4297$ of defining polynomial
Character	$\chi$	$=$	105.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-27.3730 q^{2} -81.0000 q^{3} +237.282 q^{4} +625.000 q^{5} +2217.21 q^{6} +2401.00 q^{7} +7519.86 q^{8} +6561.00 q^{9} -17108.1 q^{10} -91461.8 q^{11} -19219.8 q^{12} -73323.1 q^{13} -65722.6 q^{14} -50625.0 q^{15} -327330. q^{16} +445465. q^{17} -179594. q^{18} +498900. q^{19} +148301. q^{20} -194481. q^{21} +2.50359e6 q^{22} -1.05133e6 q^{23} -609109. q^{24} +390625. q^{25} +2.00708e6 q^{26} -531441. q^{27} +569714. q^{28} +3.98954e6 q^{29} +1.38576e6 q^{30} -4.43733e6 q^{31} +5.10983e6 q^{32} +7.40841e6 q^{33} -1.21937e7 q^{34} +1.50062e6 q^{35} +1.55681e6 q^{36} +1.75400e7 q^{37} -1.36564e7 q^{38} +5.93917e6 q^{39} +4.69991e6 q^{40} +2.70662e7 q^{41} +5.32353e6 q^{42} +1.43890e7 q^{43} -2.17022e7 q^{44} +4.10062e6 q^{45} +2.87780e7 q^{46} -4.43952e7 q^{47} +2.65137e7 q^{48} +5.76480e6 q^{49} -1.06926e7 q^{50} -3.60827e7 q^{51} -1.73983e7 q^{52} -9.63440e6 q^{53} +1.45471e7 q^{54} -5.71637e7 q^{55} +1.80552e7 q^{56} -4.04109e7 q^{57} -1.09206e8 q^{58} +4.64040e7 q^{59} -1.20124e7 q^{60} -1.16367e8 q^{61} +1.21463e8 q^{62} +1.57530e7 q^{63} +2.77213e7 q^{64} -4.58270e7 q^{65} -2.02791e8 q^{66} -1.96041e8 q^{67} +1.05701e8 q^{68} +8.51575e7 q^{69} -4.10766e7 q^{70} +1.54697e8 q^{71} +4.93378e7 q^{72} -1.59429e8 q^{73} -4.80122e8 q^{74} -3.16406e7 q^{75} +1.18380e8 q^{76} -2.19600e8 q^{77} -1.62573e8 q^{78} -6.61142e7 q^{79} -2.04581e8 q^{80} +4.30467e7 q^{81} -7.40883e8 q^{82} -1.58832e8 q^{83} -4.61468e7 q^{84} +2.78416e8 q^{85} -3.93871e8 q^{86} -3.23153e8 q^{87} -6.87780e8 q^{88} +7.27453e8 q^{89} -1.12246e8 q^{90} -1.76049e8 q^{91} -2.49461e8 q^{92} +3.59424e8 q^{93} +1.21523e9 q^{94} +3.11812e8 q^{95} -4.13896e8 q^{96} -1.07704e9 q^{97} -1.57800e8 q^{98} -6.00081e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 41 q^{2} - 324 q^{3} + 501 q^{4} + 2500 q^{5} + 3321 q^{6} + 9604 q^{7} - 29367 q^{8} + 26244 q^{9} - 25625 q^{10} - 32854 q^{11} - 40581 q^{12} - 133882 q^{13} - 98441 q^{14} - 202500 q^{15} - 90479 q^{16}+ \cdots - 215555094 q^{99}+O(q^{100}) $ 4 * q - 41 * q^2 - 324 * q^3 + 501 * q^4 + 2500 * q^5 + 3321 * q^6 + 9604 * q^7 - 29367 * q^8 + 26244 * q^9 - 25625 * q^10 - 32854 * q^11 - 40581 * q^12 - 133882 * q^13 - 98441 * q^14 - 202500 * q^15 - 90479 * q^16 + 334344 * q^17 - 269001 * q^18 + 72046 * q^19 + 313125 * q^20 - 777924 * q^21 + 990556 * q^22 + 47460 * q^23 + 2378727 * q^24 + 1562500 * q^25 + 4203458 * q^26 - 2125764 * q^27 + 1202901 * q^28 + 7010312 * q^29 + 2075625 * q^30 - 3711690 * q^31 + 18115265 * q^32 + 2661174 * q^33 + 12757214 * q^34 + 6002500 * q^35 + 3287061 * q^36 + 5222716 * q^37 - 759964 * q^38 + 10844442 * q^39 - 18354375 * q^40 - 5689292 * q^41 + 7973721 * q^42 - 71286384 * q^43 + 6098004 * q^44 + 16402500 * q^45 + 13833560 * q^46 - 100832160 * q^47 + 7328799 * q^48 + 23059204 * q^49 - 16015625 * q^50 - 27081864 * q^51 - 7238698 * q^52 - 149250454 * q^53 + 21789081 * q^54 - 20533750 * q^55 - 70510167 * q^56 - 5835726 * q^57 - 191838758 * q^58 + 24779068 * q^59 - 25363125 * q^60 - 301336048 * q^61 - 107946280 * q^62 + 63011844 * q^63 - 71492607 * q^64 - 83676250 * q^65 - 80235036 * q^66 - 10978016 * q^67 - 527886134 * q^68 - 3844260 * q^69 - 61525625 * q^70 - 507837170 * q^71 - 192676887 * q^72 - 158796526 * q^73 - 252589374 * q^74 - 126562500 * q^75 - 604814036 * q^76 - 78882454 * q^77 - 340480098 * q^78 - 36676584 * q^79 - 56549375 * q^80 + 172186884 * q^81 - 1841487282 * q^82 + 201009048 * q^83 - 97434981 * q^84 + 208965000 * q^85 + 162200156 * q^86 - 567835272 * q^87 - 1446483548 * q^88 + 161323024 * q^89 - 168125625 * q^90 - 321450682 * q^91 + 563662840 * q^92 + 300646890 * q^93 - 918128840 * q^94 + 45028750 * q^95 - 1467336465 * q^96 - 1913030882 * q^97 - 236356841 * q^98 - 215555094 * 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 $

$2$	−27.3730	−1.20973	−0.604864	−	0.796329i	$-0.706772\pi$
$2$	−27.3730	−1.20973	−0.604864	+	0.796329i	$0.706772\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	237.282	0.463441
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	2217.21	0.698437
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	7519.86	0.649090
$9$	6561.00	0.333333
$10$	−17108.1	−0.541007
$11$	−91461.8	−1.88353	−0.941766	−	0.336270i	$-0.890835\pi$
$11$	−91461.8	−1.88353	−0.941766	+	0.336270i	$0.890835\pi$
$12$	−19219.8	−0.267568
$13$	−73323.1	−0.712026	−0.356013	−	0.934481i	$-0.615864\pi$
$13$	−73323.1	−0.712026	−0.356013	+	0.934481i	$0.615864\pi$
$14$	−65722.6	−0.457234
$15$	−50625.0	−0.258199
$16$	−327330.	−1.24866
$17$	445465.	1.29358	0.646790	−	0.762668i	$-0.276111\pi$
$17$	445465.	1.29358	0.646790	+	0.762668i	$0.276111\pi$
$18$	−179594.	−0.403243
$19$	498900.	0.878258	0.439129	−	0.898424i	$-0.355287\pi$
$19$	498900.	0.878258	0.439129	+	0.898424i	$0.355287\pi$
$20$	148301.	0.207257
$21$	−194481.	−0.218218
$22$	2.50359e6	2.27856
$23$	−1.05133e6	−0.783362	−0.391681	−	0.920101i	$-0.628106\pi$
$23$	−1.05133e6	−0.783362	−0.391681	+	0.920101i	$0.628106\pi$
$24$	−609109.	−0.374752
$25$	390625.	0.200000
$26$	2.00708e6	0.861358
$27$	−531441.	−0.192450
$28$	569714.	0.175164
$29$	3.98954e6	1.04745	0.523724	−	0.851888i	$-0.324542\pi$
$29$	3.98954e6	1.04745	0.523724	+	0.851888i	$0.324542\pi$
$30$	1.38576e6	0.312350
$31$	−4.43733e6	−0.862967	−0.431483	−	0.902121i	$-0.642010\pi$
$31$	−4.43733e6	−0.862967	−0.431483	+	0.902121i	$0.642010\pi$
$32$	5.10983e6	0.861453
$33$	7.40841e6	1.08746
$34$	−1.21937e7	−1.56488
$35$	1.50062e6	0.169031
$36$	1.55681e6	0.154480
$37$	1.75400e7	1.53858	0.769292	−	0.638897i	$-0.220609\pi$
$37$	1.75400e7	1.53858	0.769292	+	0.638897i	$0.220609\pi$
$38$	−1.36564e7	−1.06245
$39$	5.93917e6	0.411089
$40$	4.69991e6	0.290282
$41$	2.70662e7	1.49589	0.747945	−	0.663761i	$-0.231041\pi$
$41$	2.70662e7	1.49589	0.747945	+	0.663761i	$0.231041\pi$
$42$	5.32353e6	0.263984
$43$	1.43890e7	0.641835	0.320917	−	0.947107i	$-0.396009\pi$
$43$	1.43890e7	0.641835	0.320917	+	0.947107i	$0.396009\pi$
$44$	−2.17022e7	−0.872906
$45$	4.10062e6	0.149071
$46$	2.87780e7	0.947655
$47$	−4.43952e7	−1.32707	−0.663537	−	0.748143i	$-0.730946\pi$
$47$	−4.43952e7	−1.32707	−0.663537	+	0.748143i	$0.730946\pi$
$48$	2.65137e7	0.720916
$49$	5.76480e6	0.142857
$50$	−1.06926e7	−0.241946
$51$	−3.60827e7	−0.746849
$52$	−1.73983e7	−0.329982
$53$	−9.63440e6	−0.167719	−0.0838597	−	0.996478i	$-0.526725\pi$
$53$	−9.63440e6	−0.167719	−0.0838597	+	0.996478i	$0.526725\pi$
$54$	1.45471e7	0.232812
$55$	−5.71637e7	−0.842341
$56$	1.80552e7	0.245333
$57$	−4.04109e7	−0.507063
$58$	−1.09206e8	−1.26713
$59$	4.64040e7	0.498564	0.249282	−	0.968431i	$-0.419805\pi$
$59$	4.64040e7	0.498564	0.249282	+	0.968431i	$0.419805\pi$
$60$	−1.20124e7	−0.119660
$61$	−1.16367e8	−1.07608	−0.538042	−	0.842918i	$-0.680836\pi$
$61$	−1.16367e8	−1.07608	−0.538042	+	0.842918i	$0.680836\pi$
$62$	1.21463e8	1.04395
$63$	1.57530e7	0.125988
$64$	2.77213e7	0.206540
$65$	−4.58270e7	−0.318428
$66$	−2.02791e8	−1.31553
$67$	−1.96041e8	−1.18853	−0.594265	−	0.804270i	$-0.702557\pi$
$67$	−1.96041e8	−1.18853	−0.594265	+	0.804270i	$0.702557\pi$
$68$	1.05701e8	0.599499
$69$	8.51575e7	0.452274
$70$	−4.10766e7	−0.204481
$71$	1.54697e8	0.722468	0.361234	−	0.932475i	$-0.382356\pi$
$71$	1.54697e8	0.722468	0.361234	+	0.932475i	$0.382356\pi$
$72$	4.93378e7	0.216363
$73$	−1.59429e8	−0.657073	−0.328536	−	0.944491i	$-0.606555\pi$
$73$	−1.59429e8	−0.657073	−0.328536	+	0.944491i	$0.606555\pi$
$74$	−4.80122e8	−1.86127
$75$	−3.16406e7	−0.115470
$76$	1.18380e8	0.407021
$77$	−2.19600e8	−0.711908
$78$	−1.62573e8	−0.497305
$79$	−6.61142e7	−0.190973	−0.0954867	−	0.995431i	$-0.530441\pi$
$79$	−6.61142e7	−0.190973	−0.0954867	+	0.995431i	$0.530441\pi$
$80$	−2.04581e8	−0.558419
$81$	4.30467e7	0.111111
$82$	−7.40883e8	−1.80962
$83$	−1.58832e8	−0.367356	−0.183678	−	0.982986i	$-0.558800\pi$
$83$	−1.58832e8	−0.367356	−0.183678	+	0.982986i	$0.558800\pi$
$84$	−4.61468e7	−0.101131
$85$	2.78416e8	0.578507
$86$	−3.93871e8	−0.776445
$87$	−3.23153e8	−0.604744
$88$	−6.87780e8	−1.22258
$89$	7.27453e8	1.22899	0.614497	−	0.788919i	$-0.289359\pi$
$89$	7.27453e8	1.22899	0.614497	+	0.788919i	$0.289359\pi$
$90$	−1.12246e8	−0.180336
$91$	−1.76049e8	−0.269121
$92$	−2.49461e8	−0.363042
$93$	3.59424e8	0.498234
$94$	1.21523e9	1.60540
$95$	3.11812e8	0.392769
$96$	−4.13896e8	−0.497360
$97$	−1.07704e9	−1.23526	−0.617629	−	0.786470i	$-0.711907\pi$
$97$	−1.07704e9	−1.23526	−0.617629	+	0.786470i	$0.711907\pi$
$98$	−1.57800e8	−0.172818
$99$	−6.00081e8	−0.627844
$100$	9.26883e7	0.0926883
$101$	−1.39474e7	−0.0133366	−0.00666831	−	0.999978i	$-0.502123\pi$
$101$	−1.39474e7	−0.0133366	−0.00666831	+	0.999978i	$0.502123\pi$
$102$	9.87691e8	0.903484
$103$	−1.53422e9	−1.34314	−0.671568	−	0.740943i	$-0.734379\pi$
$103$	−1.53422e9	−1.34314	−0.671568	+	0.740943i	$0.734379\pi$
$104$	−5.51380e8	−0.462169
$105$	−1.21551e8	−0.0975900
$106$	2.63722e8	0.202895
$107$	1.05757e9	0.779976	0.389988	−	0.920820i	$-0.372479\pi$
$107$	1.05757e9	0.779976	0.389988	+	0.920820i	$0.372479\pi$
$108$	−1.26101e8	−0.0891893
$109$	−2.51108e9	−1.70389	−0.851945	−	0.523632i	$-0.824577\pi$
$109$	−2.51108e9	−1.70389	−0.851945	+	0.523632i	$0.824577\pi$
$110$	1.56474e9	1.01900
$111$	−1.42074e9	−0.888302
$112$	−7.85918e8	−0.471950
$113$	5.54494e7	0.0319922	0.0159961	−	0.999872i	$-0.494908\pi$
$113$	5.54494e7	0.0319922	0.0159961	+	0.999872i	$0.494908\pi$
$114$	1.10617e9	0.613408
$115$	−6.57080e8	−0.350330
$116$	9.46647e8	0.485431
$117$	−4.81073e8	−0.237342
$118$	−1.27022e9	−0.603127
$119$	1.06956e9	0.488927
$120$	−3.80693e8	−0.167594
$121$	6.00732e9	2.54769
$122$	3.18532e9	1.30177
$123$	−2.19236e9	−0.863652
$124$	−1.05290e9	−0.399934
$125$	2.44141e8	0.0894427
$126$	−4.31206e8	−0.152411
$127$	−2.32928e9	−0.794519	−0.397259	−	0.917706i	$-0.630039\pi$
$127$	−2.32928e9	−0.794519	−0.397259	+	0.917706i	$0.630039\pi$
$128$	−3.37505e9	−1.11131
$129$	−1.16551e9	−0.370563
$130$	1.25442e9	0.385211
$131$	1.79240e9	0.531758	0.265879	−	0.964006i	$-0.414338\pi$
$131$	1.79240e9	0.531758	0.265879	+	0.964006i	$0.414338\pi$
$132$	1.75788e9	0.503973
$133$	1.19786e9	0.331950
$134$	5.36623e9	1.43780
$135$	−3.32151e8	−0.0860663
$136$	3.34983e9	0.839650
$137$	4.30721e9	1.04461	0.522304	−	0.852759i	$-0.325073\pi$
$137$	4.30721e9	1.04461	0.522304	+	0.852759i	$0.325073\pi$
$138$	−2.33102e9	−0.547129
$139$	5.48252e7	0.0124570	0.00622851	−	0.999981i	$-0.498017\pi$
$139$	5.48252e7	0.0124570	0.00622851	+	0.999981i	$0.498017\pi$
$140$	3.56071e8	0.0783359
$141$	3.59601e9	0.766187
$142$	−4.23452e9	−0.873990
$143$	6.70627e9	1.34112
$144$	−2.14761e9	−0.416221
$145$	2.49347e9	0.468433
$146$	4.36404e9	0.794879
$147$	−4.66949e8	−0.0824786
$148$	4.16192e9	0.713043
$149$	−1.55903e9	−0.259129	−0.129564	−	0.991571i	$-0.541358\pi$
$149$	−1.55903e9	−0.259129	−0.129564	+	0.991571i	$0.541358\pi$
$150$	8.66099e8	0.139687
$151$	−1.09620e10	−1.71590	−0.857950	−	0.513734i	$-0.828262\pi$
$151$	−1.09620e10	−1.71590	−0.857950	+	0.513734i	$0.828262\pi$
$152$	3.75166e9	0.570068
$153$	2.92270e9	0.431193
$154$	6.01111e9	0.861215
$155$	−2.77333e9	−0.385930
$156$	1.40926e9	0.190515
$157$	−8.73982e9	−1.14803	−0.574016	−	0.818844i	$-0.694615\pi$
$157$	−8.73982e9	−1.14803	−0.574016	+	0.818844i	$0.694615\pi$
$158$	1.80974e9	0.231026
$159$	7.80386e8	0.0968328
$160$	3.19364e9	0.385254
$161$	−2.52424e9	−0.296083
$162$	−1.17832e9	−0.134414
$163$	1.07177e10	1.18921	0.594606	−	0.804017i	$-0.297308\pi$
$163$	1.07177e10	1.18921	0.594606	+	0.804017i	$0.297308\pi$
$164$	6.42231e9	0.693257
$165$	4.63026e9	0.486326
$166$	4.34772e9	0.444401
$167$	−1.18586e10	−1.17980	−0.589902	−	0.807475i	$-0.700834\pi$
$167$	−1.18586e10	−1.17980	−0.589902	+	0.807475i	$0.700834\pi$
$168$	−1.46247e9	−0.141643
$169$	−5.22822e9	−0.493019
$170$	−7.62107e9	−0.699836
$171$	3.27328e9	0.292753
$172$	3.41426e9	0.297453
$173$	−1.08319e10	−0.919388	−0.459694	−	0.888077i	$-0.652041\pi$
$173$	−1.08319e10	−0.919388	−0.459694	+	0.888077i	$0.652041\pi$
$174$	8.84567e9	0.731576
$175$	9.37891e8	0.0755929
$176$	2.99382e10	2.35190
$177$	−3.75872e9	−0.287846
$178$	−1.99126e10	−1.48675
$179$	−5.00228e9	−0.364191	−0.182095	−	0.983281i	$-0.558288\pi$
$179$	−5.00228e9	−0.364191	−0.182095	+	0.983281i	$0.558288\pi$
$180$	9.73004e8	0.0690858
$181$	−4.85086e9	−0.335942	−0.167971	−	0.985792i	$-0.553722\pi$
$181$	−4.85086e9	−0.335942	−0.167971	+	0.985792i	$0.553722\pi$
$182$	4.81899e9	0.325563
$183$	9.42575e9	0.621278
$184$	−7.90583e9	−0.508473
$185$	1.09625e10	0.688076
$186$	−9.83851e9	−0.602728
$187$	−4.07430e10	−2.43650
$188$	−1.05342e10	−0.615021
$189$	−1.27599e9	−0.0727393
$190$	−8.53525e9	−0.475144
$191$	3.59595e9	0.195507	0.0977537	−	0.995211i	$-0.468834\pi$
$191$	3.59595e9	0.195507	0.0977537	+	0.995211i	$0.468834\pi$
$192$	−2.24542e9	−0.119246
$193$	−8.46074e9	−0.438935	−0.219468	−	0.975620i	$-0.570432\pi$
$193$	−8.46074e9	−0.438935	−0.219468	+	0.975620i	$0.570432\pi$
$194$	2.94817e10	1.49433
$195$	3.71198e9	0.183844
$196$	1.36788e9	0.0662059
$197$	−3.34522e10	−1.58244	−0.791220	−	0.611532i	$-0.790554\pi$
$197$	−3.34522e10	−1.58244	−0.791220	+	0.611532i	$0.790554\pi$
$198$	1.64260e10	0.759520
$199$	6.65820e9	0.300966	0.150483	−	0.988613i	$-0.451917\pi$
$199$	6.65820e9	0.300966	0.150483	+	0.988613i	$0.451917\pi$
$200$	2.93745e9	0.129818
$201$	1.58793e10	0.686198
$202$	3.81781e8	0.0161337
$203$	9.57890e9	0.395898
$204$	−8.56177e9	−0.346121
$205$	1.69164e10	0.668982
$206$	4.19962e10	1.62483
$207$	−6.89776e9	−0.261121
$208$	2.40008e10	0.889081
$209$	−4.56303e10	−1.65423
$210$	3.32721e9	0.118057
$211$	−1.17806e10	−0.409162	−0.204581	−	0.978850i	$-0.565583\pi$
$211$	−1.17806e10	−0.409162	−0.204581	+	0.978850i	$0.565583\pi$
$212$	−2.28607e9	−0.0777281
$213$	−1.25304e10	−0.417117
$214$	−2.89488e10	−0.943559
$215$	8.99314e9	0.287037
$216$	−3.99636e9	−0.124917
$217$	−1.06540e10	−0.326171
$218$	6.87359e10	2.06124
$219$	1.29137e10	0.379361
$220$	−1.35639e10	−0.390376
$221$	−3.26629e10	−0.921063
$222$	3.88899e10	1.07460
$223$	−4.58580e10	−1.24178	−0.620888	−	0.783899i	$-0.713228\pi$
$223$	−4.58580e10	−1.24178	−0.620888	+	0.783899i	$0.713228\pi$
$224$	1.22687e10	0.325599
$225$	2.56289e9	0.0666667
$226$	−1.51782e9	−0.0387018
$227$	2.58329e10	0.645739	0.322869	−	0.946444i	$-0.395353\pi$
$227$	2.58329e10	0.645739	0.322869	+	0.946444i	$0.395353\pi$
$228$	−9.58878e9	−0.234994
$229$	5.99178e10	1.43978	0.719890	−	0.694089i	$-0.244192\pi$
$229$	5.99178e10	1.43978	0.719890	+	0.694089i	$0.244192\pi$
$230$	1.79862e10	0.423804
$231$	1.77876e10	0.411020
$232$	3.00008e10	0.679888
$233$	−1.45538e10	−0.323501	−0.161751	−	0.986832i	$-0.551714\pi$
$233$	−1.45538e10	−0.323501	−0.161751	+	0.986832i	$0.551714\pi$
$234$	1.31684e10	0.287119
$235$	−2.77470e10	−0.593486
$236$	1.10108e10	0.231055
$237$	5.35525e9	0.110259
$238$	−2.92771e10	−0.591469
$239$	−9.82911e10	−1.94860	−0.974302	−	0.225247i	$-0.927681\pi$
$239$	−9.82911e10	−1.94860	−0.974302	+	0.225247i	$0.927681\pi$
$240$	1.65711e10	0.322404
$241$	−1.53016e9	−0.0292187	−0.0146093	−	0.999893i	$-0.504650\pi$
$241$	−1.53016e9	−0.0292187	−0.0146093	+	0.999893i	$0.504650\pi$
$242$	−1.64439e11	−3.08201
$243$	−3.48678e9	−0.0641500
$244$	−2.76119e10	−0.498702
$245$	3.60300e9	0.0638877
$246$	6.00115e10	1.04478
$247$	−3.65809e10	−0.625343
$248$	−3.33681e10	−0.560143
$249$	1.28654e10	0.212093
$250$	−6.68287e9	−0.108201
$251$	7.64864e10	1.21633	0.608166	−	0.793810i	$-0.291905\pi$
$251$	7.64864e10	1.21633	0.608166	+	0.793810i	$0.291905\pi$
$252$	3.73789e9	0.0583881
$253$	9.61563e10	1.47549
$254$	6.37593e10	0.961151
$255$	−2.25517e10	−0.334001
$256$	7.81920e10	1.13784
$257$	−8.13789e10	−1.16362	−0.581812	−	0.813323i	$-0.697656\pi$
$257$	−8.13789e10	−1.16362	−0.581812	+	0.813323i	$0.697656\pi$
$258$	3.19035e10	0.448281
$259$	4.21135e10	0.581530
$260$	−1.08739e10	−0.147573
$261$	2.61754e10	0.349149
$262$	−4.90634e10	−0.643283
$263$	8.69551e10	1.12071	0.560356	−	0.828252i	$-0.310664\pi$
$263$	8.69551e10	1.12071	0.560356	+	0.828252i	$0.310664\pi$
$264$	5.57102e10	0.705858
$265$	−6.02150e9	−0.0750064
$266$	−3.27890e10	−0.401570
$267$	−5.89237e10	−0.709560
$268$	−4.65170e10	−0.550814
$269$	−1.68056e11	−1.95690	−0.978450	−	0.206484i	$-0.933798\pi$
$269$	−1.68056e11	−1.95690	−0.978450	+	0.206484i	$0.933798\pi$
$270$	9.09196e9	0.104117
$271$	−8.59837e10	−0.968399	−0.484199	−	0.874958i	$-0.660889\pi$
$271$	−8.59837e10	−0.968399	−0.484199	+	0.874958i	$0.660889\pi$
$272$	−1.45814e11	−1.61525
$273$	1.42600e10	0.155377
$274$	−1.17901e11	−1.26369
$275$	−3.57273e10	−0.376706
$276$	2.02063e10	0.209603
$277$	−1.53432e11	−1.56587	−0.782936	−	0.622102i	$-0.786279\pi$
$277$	−1.53432e11	−1.56587	−0.782936	+	0.622102i	$0.786279\pi$
$278$	−1.50073e9	−0.0150696
$279$	−2.91133e10	−0.287656
$280$	1.12845e10	0.109716
$281$	1.36314e11	1.30425	0.652125	−	0.758112i	$-0.273878\pi$
$281$	1.36314e11	1.30425	0.652125	+	0.758112i	$0.273878\pi$
$282$	−9.84336e10	−0.926878
$283$	−8.21276e10	−0.761115	−0.380557	−	0.924757i	$-0.624268\pi$
$283$	−8.21276e10	−0.761115	−0.380557	+	0.924757i	$0.624268\pi$
$284$	3.67068e10	0.334822
$285$	−2.52568e10	−0.226765
$286$	−1.83571e11	−1.62239
$287$	6.49859e10	0.565393
$288$	3.35256e10	0.287151
$289$	7.98511e10	0.673350
$290$	−6.82537e10	−0.566676
$291$	8.72399e10	0.713176
$292$	−3.78296e10	−0.304515
$293$	−2.32388e11	−1.84208	−0.921042	−	0.389464i	$-0.872660\pi$
$293$	−2.32388e11	−1.84208	−0.921042	+	0.389464i	$0.872660\pi$
$294$	1.27818e10	0.0997767
$295$	2.90025e10	0.222965
$296$	1.31898e11	0.998679
$297$	4.86066e10	0.362486
$298$	4.26753e10	0.313475
$299$	7.70866e10	0.557774
$300$	−7.50775e9	−0.0535136
$301$	3.45480e10	0.242591
$302$	3.00062e11	2.07577
$303$	1.12974e9	0.00769991
$304$	−1.63305e11	−1.09665
$305$	−7.27295e10	−0.481240
$306$	−8.00030e10	−0.521627
$307$	−1.00777e11	−0.647499	−0.323750	−	0.946143i	$-0.604944\pi$
$307$	−1.00777e11	−0.647499	−0.323750	+	0.946143i	$0.604944\pi$
$308$	−5.21071e10	−0.329928
$309$	1.24272e11	0.775460
$310$	7.59144e10	0.466871
$311$	−2.48144e11	−1.50412	−0.752059	−	0.659095i	$-0.770939\pi$
$311$	−2.48144e11	−1.50412	−0.752059	+	0.659095i	$0.770939\pi$
$312$	4.46618e10	0.266833
$313$	1.65974e10	0.0977442	0.0488721	−	0.998805i	$-0.484437\pi$
$313$	1.65974e10	0.0977442	0.0488721	+	0.998805i	$0.484437\pi$
$314$	2.39235e11	1.38881
$315$	9.84560e9	0.0563436
$316$	−1.56877e10	−0.0885049
$317$	2.55054e11	1.41862	0.709309	−	0.704897i	$-0.249007\pi$
$317$	2.55054e11	1.41862	0.709309	+	0.704897i	$0.249007\pi$
$318$	−2.13615e10	−0.117141
$319$	−3.64891e11	−1.97290
$320$	1.73258e10	0.0923674
$321$	−8.56630e10	−0.450320
$322$	6.90960e10	0.358180
$323$	2.22242e11	1.13610
$324$	1.02142e10	0.0514935
$325$	−2.86419e10	−0.142405
$326$	−2.93377e11	−1.43862
$327$	2.03398e11	0.983741
$328$	2.03534e11	0.970967
$329$	−1.06593e11	−0.501587
$330$	−1.26744e11	−0.588322
$331$	1.79574e11	0.822274	0.411137	−	0.911574i	$-0.365132\pi$
$331$	1.79574e11	0.822274	0.411137	+	0.911574i	$0.365132\pi$
$332$	−3.76880e10	−0.170248
$333$	1.15080e11	0.512861
$334$	3.24606e11	1.42724
$335$	−1.22526e11	−0.531526
$336$	6.36594e10	0.272481
$337$	7.28949e10	0.307867	0.153933	−	0.988081i	$-0.450806\pi$
$337$	7.28949e10	0.307867	0.153933	+	0.988081i	$0.450806\pi$
$338$	1.43112e11	0.596418
$339$	−4.49140e9	−0.0184707
$340$	6.60630e10	0.268104
$341$	4.05846e11	1.62542
$342$	−8.95996e10	−0.354151
$343$	1.38413e10	0.0539949
$344$	1.08203e11	0.416608
$345$	5.32234e10	0.202263
$346$	2.96503e11	1.11221
$347$	1.22750e11	0.454504	0.227252	−	0.973836i	$-0.427026\pi$
$347$	1.22750e11	0.454504	0.227252	+	0.973836i	$0.427026\pi$
$348$	−7.66784e10	−0.280263
$349$	2.94669e11	1.06321	0.531606	−	0.846992i	$-0.321589\pi$
$349$	2.94669e11	1.06321	0.531606	+	0.846992i	$0.321589\pi$
$350$	−2.56729e10	−0.0914468
$351$	3.89669e10	0.137030
$352$	−4.67355e11	−1.62257
$353$	5.01891e11	1.72038	0.860188	−	0.509976i	$-0.170346\pi$
$353$	5.01891e11	1.72038	0.860188	+	0.509976i	$0.170346\pi$
$354$	1.02888e11	0.348215
$355$	9.66855e10	0.323098
$356$	1.72611e11	0.569567
$357$	−8.66345e10	−0.282282
$358$	1.36927e11	0.440572
$359$	2.55587e11	0.812109	0.406054	−	0.913849i	$-0.366904\pi$
$359$	2.55587e11	0.812109	0.406054	+	0.913849i	$0.366904\pi$
$360$	3.08361e10	0.0967606
$361$	−7.37866e10	−0.228663
$362$	1.32783e11	0.406399
$363$	−4.86593e11	−1.47091
$364$	−4.17732e10	−0.124722
$365$	−9.96429e10	−0.293852
$366$	−2.58011e11	−0.751577
$367$	−4.92287e11	−1.41651	−0.708257	−	0.705955i	$-0.750518\pi$
$367$	−4.92287e11	−1.41651	−0.708257	+	0.705955i	$0.750518\pi$
$368$	3.44131e11	0.978156
$369$	1.77581e11	0.498630
$370$	−3.00076e11	−0.832384
$371$	−2.31322e10	−0.0633919
$372$	8.52848e10	0.230902
$373$	−2.80142e11	−0.749356	−0.374678	−	0.927155i	$-0.622247\pi$
$373$	−2.80142e11	−0.749356	−0.374678	+	0.927155i	$0.622247\pi$
$374$	1.11526e12	2.94750
$375$	−1.97754e10	−0.0516398
$376$	−3.33845e11	−0.861391
$377$	−2.92526e11	−0.745810
$378$	3.49277e10	0.0879948
$379$	5.28234e11	1.31507	0.657536	−	0.753423i	$-0.271599\pi$
$379$	5.28234e11	1.31507	0.657536	+	0.753423i	$0.271599\pi$
$380$	7.39875e10	0.182025
$381$	1.88671e11	0.458716
$382$	−9.84320e10	−0.236511
$383$	3.71762e11	0.882817	0.441408	−	0.897306i	$-0.354479\pi$
$383$	3.71762e11	0.882817	0.441408	+	0.897306i	$0.354479\pi$
$384$	2.73379e11	0.641615
$385$	−1.37250e11	−0.318375
$386$	2.31596e11	0.530992
$387$	9.44064e10	0.213945
$388$	−2.55561e11	−0.572470
$389$	1.35616e11	0.300288	0.150144	−	0.988664i	$-0.452026\pi$
$389$	1.35616e11	0.300288	0.150144	+	0.988664i	$0.452026\pi$
$390$	−1.01608e11	−0.222402
$391$	−4.68329e11	−1.01334
$392$	4.33505e10	0.0927271
$393$	−1.45184e11	−0.307011
$394$	9.15689e11	1.91432
$395$	−4.13214e10	−0.0854059
$396$	−1.42388e11	−0.290969
$397$	6.39520e11	1.29210	0.646051	−	0.763294i	$-0.276419\pi$
$397$	6.39520e11	1.29210	0.646051	+	0.763294i	$0.276419\pi$
$398$	−1.82255e11	−0.364087
$399$	−9.70265e10	−0.191652
$400$	−1.27863e11	−0.249733
$401$	−8.56256e11	−1.65369	−0.826845	−	0.562430i	$-0.809866\pi$
$401$	−8.56256e11	−1.65369	−0.826845	+	0.562430i	$0.809866\pi$
$402$	−4.34665e11	−0.830112
$403$	3.25359e11	0.614455
$404$	−3.30946e9	−0.00618074
$405$	2.69042e10	0.0496904
$406$	−2.62203e11	−0.478929
$407$	−1.60424e12	−2.89797
$408$	−2.71337e11	−0.484772
$409$	2.76777e11	0.489075	0.244537	−	0.969640i	$-0.421364\pi$
$409$	2.76777e11	0.489075	0.244537	+	0.969640i	$0.421364\pi$
$410$	−4.63052e11	−0.809286
$411$	−3.48884e11	−0.603105
$412$	−3.64043e11	−0.622465
$413$	1.11416e11	0.188439
$414$	1.88812e11	0.315885
$415$	−9.92701e10	−0.164287
$416$	−3.74669e11	−0.613377
$417$	−4.44084e9	−0.00719206
$418$	1.24904e12	2.00116
$419$	2.40675e11	0.381476	0.190738	−	0.981641i	$-0.438912\pi$
$419$	2.40675e11	0.381476	0.190738	+	0.981641i	$0.438912\pi$
$420$	−2.88418e10	−0.0452272
$421$	5.38916e11	0.836088	0.418044	−	0.908427i	$-0.362716\pi$
$421$	5.38916e11	0.836088	0.418044	+	0.908427i	$0.362716\pi$
$422$	3.22470e11	0.494975
$423$	−2.91277e11	−0.442358
$424$	−7.24493e10	−0.108865
$425$	1.74010e11	0.258716
$426$	3.42996e11	0.504598
$427$	−2.79398e11	−0.406722
$428$	2.50942e11	0.361473
$429$	−5.43208e11	−0.774298
$430$	−2.46169e11	−0.347237
$431$	−1.36692e12	−1.90808	−0.954039	−	0.299682i	$-0.903119\pi$
$431$	−1.36692e12	−1.90808	−0.954039	+	0.299682i	$0.903119\pi$
$432$	1.73956e11	0.240305
$433$	5.96620e10	0.0815647	0.0407823	−	0.999168i	$-0.487015\pi$
$433$	5.96620e10	0.0815647	0.0407823	+	0.999168i	$0.487015\pi$
$434$	2.91633e11	0.394578
$435$	−2.01971e11	−0.270450
$436$	−5.95834e11	−0.789653
$437$	−5.24507e11	−0.687994
$438$	−3.53488e11	−0.458924
$439$	6.16423e11	0.792116	0.396058	−	0.918226i	$-0.370378\pi$
$439$	6.16423e11	0.792116	0.396058	+	0.918226i	$0.370378\pi$
$440$	−4.29863e11	−0.546755
$441$	3.78229e10	0.0476190
$442$	8.94082e11	1.11424
$443$	−8.28982e11	−1.02265	−0.511326	−	0.859387i	$-0.670846\pi$
$443$	−8.28982e11	−1.02265	−0.511326	+	0.859387i	$0.670846\pi$
$444$	−3.37115e11	−0.411676
$445$	4.54658e11	0.549623
$446$	1.25527e12	1.50221
$447$	1.26281e11	0.149608
$448$	6.65588e10	0.0780647
$449$	−1.17455e12	−1.36384	−0.681918	−	0.731428i	$-0.738854\pi$
$449$	−1.17455e12	−1.36384	−0.681918	+	0.731428i	$0.738854\pi$
$450$	−7.01540e10	−0.0806485
$451$	−2.47552e12	−2.81755
$452$	1.31571e10	0.0148265
$453$	8.87919e11	0.990675
$454$	−7.07124e11	−0.781168
$455$	−1.10031e11	−0.120354
$456$	−3.03884e11	−0.329129
$457$	−1.01703e12	−1.09072	−0.545358	−	0.838203i	$-0.683606\pi$
$457$	−1.01703e12	−1.09072	−0.545358	+	0.838203i	$0.683606\pi$
$458$	−1.64013e12	−1.74174
$459$	−2.36738e11	−0.248950
$460$	−1.55913e11	−0.162358
$461$	6.49859e11	0.670140	0.335070	−	0.942193i	$-0.391240\pi$
$461$	6.49859e11	0.670140	0.335070	+	0.942193i	$0.391240\pi$
$462$	−4.86900e11	−0.497223
$463$	−4.14476e11	−0.419165	−0.209583	−	0.977791i	$-0.567211\pi$
$463$	−4.14476e11	−0.419165	−0.209583	+	0.977791i	$0.567211\pi$
$464$	−1.30590e12	−1.30791
$465$	2.24640e11	0.222817
$466$	3.98383e11	0.391349
$467$	7.81559e10	0.0760389	0.0380195	−	0.999277i	$-0.487895\pi$
$467$	7.81559e10	0.0760389	0.0380195	+	0.999277i	$0.487895\pi$
$468$	−1.14150e11	−0.109994
$469$	−4.70694e11	−0.449222
$470$	7.59519e11	0.717956
$471$	7.07925e11	0.662816
$472$	3.48951e11	0.323613
$473$	−1.31605e12	−1.20892
$474$	−1.46589e11	−0.133383
$475$	1.94883e11	0.175652
$476$	2.53788e11	0.226589
$477$	−6.32113e10	−0.0559064
$478$	2.69052e12	2.35728
$479$	1.01714e12	0.882820	0.441410	−	0.897306i	$-0.354478\pi$
$479$	1.01714e12	0.882820	0.441410	+	0.897306i	$0.354478\pi$
$480$	−2.58685e11	−0.222426
$481$	−1.28609e12	−1.09551
$482$	4.18852e10	0.0353467
$483$	2.04463e11	0.170944
$484$	1.42543e12	1.18071
$485$	−6.73148e11	−0.552424
$486$	9.54438e10	0.0776041
$487$	−5.75670e11	−0.463760	−0.231880	−	0.972744i	$-0.574488\pi$
$487$	−5.75670e11	−0.463760	−0.231880	+	0.972744i	$0.574488\pi$
$488$	−8.75066e11	−0.698476
$489$	−8.68137e11	−0.686592
$490$	−9.86250e10	−0.0772867
$491$	7.05967e11	0.548173	0.274087	−	0.961705i	$-0.411625\pi$
$491$	7.05967e11	0.548173	0.274087	+	0.961705i	$0.411625\pi$
$492$	−5.20207e11	−0.400252
$493$	1.77720e12	1.35496
$494$	1.00133e12	0.756495
$495$	−3.75051e11	−0.280780
$496$	1.45247e12	1.07755
$497$	3.71427e11	0.273067
$498$	−3.52165e11	−0.256575
$499$	1.61624e12	1.16695	0.583476	−	0.812131i	$-0.301692\pi$
$499$	1.61624e12	1.16695	0.583476	+	0.812131i	$0.301692\pi$
$500$	5.79302e10	0.0414515
$501$	9.60548e11	0.681160
$502$	−2.09366e12	−1.47143
$503$	2.38722e12	1.66279	0.831393	−	0.555684i	$-0.187544\pi$
$503$	2.38722e12	1.66279	0.831393	+	0.555684i	$0.187544\pi$
$504$	1.18460e11	0.0817776
$505$	−8.71710e9	−0.00596432
$506$	−2.63209e12	−1.78494
$507$	4.23486e11	0.284644
$508$	−5.52695e11	−0.368213
$509$	−4.00271e11	−0.264316	−0.132158	−	0.991229i	$-0.542191\pi$
$509$	−4.00271e11	−0.264316	−0.132158	+	0.991229i	$0.542191\pi$
$510$	6.17307e11	0.404050
$511$	−3.82788e11	−0.248350
$512$	−4.12325e11	−0.265170
$513$	−2.65136e11	−0.169021
$514$	2.22759e12	1.40767
$515$	−9.58888e11	−0.600669
$516$	−2.76555e11	−0.171734
$517$	4.06046e12	2.49959
$518$	−1.15277e12	−0.703493
$519$	8.77388e11	0.530809
$520$	−3.44612e11	−0.206688
$521$	1.48907e12	0.885412	0.442706	−	0.896667i	$-0.354019\pi$
$521$	1.48907e12	0.885412	0.442706	+	0.896667i	$0.354019\pi$
$522$	−7.16500e11	−0.422376
$523$	2.26235e12	1.32222	0.661108	−	0.750290i	$-0.270086\pi$
$523$	2.26235e12	1.32222	0.661108	+	0.750290i	$0.270086\pi$
$524$	4.25305e11	0.246439
$525$	−7.59691e10	−0.0436436
$526$	−2.38022e12	−1.35576
$527$	−1.97667e12	−1.11632
$528$	−2.42499e12	−1.35787
$529$	−6.95864e11	−0.386344
$530$	1.64827e11	0.0907373
$531$	3.04456e11	0.166188
$532$	2.84230e11	0.153840
$533$	−1.98458e12	−1.06511
$534$	1.61292e12	0.858374
$535$	6.60980e11	0.348816
$536$	−1.47420e12	−0.771462
$537$	4.05184e11	0.210266
$538$	4.60020e12	2.36732
$539$	−5.27259e11	−0.269076
$540$	−7.88134e10	−0.0398867
$541$	2.40018e11	0.120464	0.0602318	−	0.998184i	$-0.480816\pi$
$541$	2.40018e11	0.120464	0.0602318	+	0.998184i	$0.480816\pi$
$542$	2.35363e12	1.17150
$543$	3.92919e11	0.193956
$544$	2.27625e12	1.11436
$545$	−1.56943e12	−0.762003
$546$	−3.90338e11	−0.187964
$547$	−1.62185e12	−0.774582	−0.387291	−	0.921957i	$-0.626589\pi$
$547$	−1.62185e12	−0.774582	−0.387291	+	0.921957i	$0.626589\pi$
$548$	1.02202e12	0.484115
$549$	−7.63486e11	−0.358695
$550$	9.77963e11	0.455712
$551$	1.99038e12	0.919929
$552$	6.40373e11	0.293567
$553$	−1.58740e11	−0.0721811
$554$	4.19989e12	1.89428
$555$	−8.87961e11	−0.397261
$556$	1.30090e10	0.00577310
$557$	−1.91466e12	−0.842835	−0.421418	−	0.906867i	$-0.638467\pi$
$557$	−1.91466e12	−0.842835	−0.421418	+	0.906867i	$0.638467\pi$
$558$	7.96919e11	0.347985
$559$	−1.05505e12	−0.457003
$560$	−4.91199e11	−0.211063
$561$	3.30019e12	1.40671
$562$	−3.73131e12	−1.57779
$563$	−3.47969e12	−1.45966	−0.729832	−	0.683626i	$-0.760402\pi$
$563$	−3.47969e12	−1.45966	−0.729832	+	0.683626i	$0.760402\pi$
$564$	8.53268e11	0.355083
$565$	3.46559e10	0.0143073
$566$	2.24808e12	0.920742
$567$	1.03355e11	0.0419961
$568$	1.16330e12	0.468947
$569$	−4.35637e12	−1.74229	−0.871143	−	0.491030i	$-0.836621\pi$
$569$	−4.35637e12	−1.74229	−0.871143	+	0.491030i	$0.836621\pi$
$570$	6.91355e11	0.274324
$571$	4.36816e12	1.71963	0.859817	−	0.510603i	$-0.170578\pi$
$571$	4.36816e12	1.71963	0.859817	+	0.510603i	$0.170578\pi$
$572$	1.59128e12	0.621532
$573$	−2.91272e11	−0.112876
$574$	−1.77886e12	−0.683972
$575$	−4.10675e11	−0.156672
$576$	1.81879e11	0.0688466
$577$	−4.00857e12	−1.50556	−0.752781	−	0.658271i	$-0.771288\pi$
$577$	−4.00857e12	−1.50556	−0.752781	+	0.658271i	$0.771288\pi$
$578$	−2.18577e12	−0.814570
$579$	6.85320e11	0.253419
$580$	5.91654e11	0.217091
$581$	−3.81356e11	−0.138848
$582$	−2.38802e12	−0.862749
$583$	8.81180e11	0.315905
$584$	−1.19888e12	−0.426499
$585$	−3.00671e11	−0.106143
$586$	6.36116e12	2.22842
$587$	1.98385e11	0.0689665	0.0344832	−	0.999405i	$-0.489021\pi$
$587$	1.98385e11	0.0689665	0.0344832	+	0.999405i	$0.489021\pi$
$588$	−1.10799e11	−0.0382240
$589$	−2.21378e12	−0.757908
$590$	−7.93885e11	−0.269727
$591$	2.70963e12	0.913622
$592$	−5.74135e12	−1.92117
$593$	−2.01791e11	−0.0670124	−0.0335062	−	0.999439i	$-0.510667\pi$
$593$	−2.01791e11	−0.0670124	−0.0335062	+	0.999439i	$0.510667\pi$
$594$	−1.33051e12	−0.438509
$595$	6.68476e11	0.218655
$596$	−3.69929e11	−0.120091
$597$	−5.39314e11	−0.173763
$598$	−2.11009e12	−0.674755
$599$	−8.67600e11	−0.275359	−0.137679	−	0.990477i	$-0.543964\pi$
$599$	−8.67600e11	−0.275359	−0.137679	+	0.990477i	$0.543964\pi$
$600$	−2.37933e11	−0.0749504
$601$	8.98605e11	0.280953	0.140477	−	0.990084i	$-0.455137\pi$
$601$	8.98605e11	0.280953	0.140477	+	0.990084i	$0.455137\pi$
$602$	−9.45684e11	−0.293469
$603$	−1.28622e12	−0.396176
$604$	−2.60107e12	−0.795219
$605$	3.75458e12	1.13936
$606$	−3.09243e10	−0.00931479
$607$	−6.20037e11	−0.185382	−0.0926912	−	0.995695i	$-0.529547\pi$
$607$	−6.20037e11	−0.185382	−0.0926912	+	0.995695i	$0.529547\pi$
$608$	2.54929e12	0.756578
$609$	−7.75891e11	−0.228572
$610$	1.99083e12	0.582169
$611$	3.25519e12	0.944912
$612$	6.93503e11	0.199833
$613$	5.06850e12	1.44980	0.724899	−	0.688855i	$-0.241886\pi$
$613$	5.06850e12	1.44980	0.724899	+	0.688855i	$0.241886\pi$
$614$	2.75857e12	0.783298
$615$	−1.37022e12	−0.386237
$616$	−1.65136e12	−0.462092
$617$	3.37674e12	0.938024	0.469012	−	0.883192i	$-0.344610\pi$
$617$	3.37674e12	0.938024	0.469012	+	0.883192i	$0.344610\pi$
$618$	−3.40170e12	−0.938096
$619$	2.55882e12	0.700537	0.350269	−	0.936649i	$-0.386090\pi$
$619$	2.55882e12	0.700537	0.350269	+	0.936649i	$0.386090\pi$
$620$	−6.58061e11	−0.178856
$621$	5.58718e11	0.150758
$622$	6.79245e12	1.81957
$623$	1.74661e12	0.464516
$624$	−1.94407e12	−0.513311
$625$	1.52588e11	0.0400000
$626$	−4.54321e11	−0.118244
$627$	3.69605e12	0.955068
$628$	−2.07380e12	−0.532045
$629$	7.81344e12	1.99028
$630$	−2.69504e11	−0.0681604
$631$	4.06262e12	1.02017	0.510087	−	0.860123i	$-0.329613\pi$
$631$	4.06262e12	1.02017	0.510087	+	0.860123i	$0.329613\pi$
$632$	−4.97169e11	−0.123959
$633$	9.54227e11	0.236230
$634$	−6.98160e12	−1.71614
$635$	−1.45580e12	−0.355320
$636$	1.85172e11	0.0448763
$637$	−4.22693e11	−0.101718
$638$	9.98817e12	2.38667
$639$	1.01497e12	0.240823
$640$	−2.10941e12	−0.496993
$641$	9.18637e11	0.214923	0.107461	−	0.994209i	$-0.465728\pi$
$641$	9.18637e11	0.214923	0.107461	+	0.994209i	$0.465728\pi$
$642$	2.34486e12	0.544764
$643$	−6.19972e12	−1.43029	−0.715143	−	0.698979i	$-0.753638\pi$
$643$	−6.19972e12	−1.43029	−0.715143	+	0.698979i	$0.753638\pi$
$644$	−5.98956e11	−0.137217
$645$	−7.28444e11	−0.165721
$646$	−6.08344e12	−1.37437
$647$	−4.27995e12	−0.960216	−0.480108	−	0.877209i	$-0.659403\pi$
$647$	−4.27995e12	−0.960216	−0.480108	+	0.877209i	$0.659403\pi$
$648$	3.23705e11	0.0721211
$649$	−4.24419e12	−0.939061
$650$	7.84014e11	0.172272
$651$	8.62976e11	0.188315
$652$	2.54313e12	0.551130
$653$	−3.75302e12	−0.807739	−0.403870	−	0.914817i	$-0.632335\pi$
$653$	−3.75302e12	−0.807739	−0.403870	+	0.914817i	$0.632335\pi$
$654$	−5.56760e12	−1.19006
$655$	1.12025e12	0.237810
$656$	−8.85956e12	−1.86786
$657$	−1.04601e12	−0.219024
$658$	2.91777e12	0.606784
$659$	−3.31422e12	−0.684536	−0.342268	−	0.939602i	$-0.611195\pi$
$659$	−3.31422e12	−0.684536	−0.342268	+	0.939602i	$0.611195\pi$
$660$	1.09868e12	0.225383
$661$	3.52615e12	0.718447	0.359223	−	0.933252i	$-0.383042\pi$
$661$	3.52615e12	0.718447	0.359223	+	0.933252i	$0.383042\pi$
$662$	−4.91547e12	−0.994728
$663$	2.64569e12	0.531776
$664$	−1.19440e12	−0.238447
$665$	7.48662e11	0.148453
$666$	−3.15008e12	−0.620423
$667$	−4.19432e12	−0.820531
$668$	−2.81384e12	−0.546770
$669$	3.71450e12	0.716940
$670$	3.35389e12	0.643002
$671$	1.06432e13	2.02684
$672$	−9.93765e11	−0.187984
$673$	5.54236e12	1.04142	0.520711	−	0.853733i	$-0.325667\pi$
$673$	5.54236e12	1.04142	0.520711	+	0.853733i	$0.325667\pi$
$674$	−1.99535e12	−0.372435
$675$	−2.07594e11	−0.0384900
$676$	−1.24056e12	−0.228485
$677$	9.17822e12	1.67923	0.839613	−	0.543185i	$-0.182782\pi$
$677$	9.17822e12	1.67923	0.839613	+	0.543185i	$0.182782\pi$
$678$	1.22943e11	0.0223445
$679$	−2.58596e12	−0.466883
$680$	2.09365e12	0.375503
$681$	−2.09247e12	−0.372817
$682$	−1.11092e13	−1.96632
$683$	−8.26632e12	−1.45351	−0.726757	−	0.686895i	$-0.758973\pi$
$683$	−8.26632e12	−1.45351	−0.726757	+	0.686895i	$0.758973\pi$
$684$	7.76691e11	0.135674
$685$	2.69201e12	0.467163
$686$	−3.78878e11	−0.0653192
$687$	−4.85334e12	−0.831257
$688$	−4.70995e12	−0.801436
$689$	7.06424e11	0.119421
$690$	−1.45689e12	−0.244683
$691$	−3.87899e11	−0.0647244	−0.0323622	−	0.999476i	$-0.510303\pi$
$691$	−3.87899e11	−0.0647244	−0.0323622	+	0.999476i	$0.510303\pi$
$692$	−2.57023e12	−0.426083
$693$	−1.44079e12	−0.237303
$694$	−3.36003e12	−0.549826
$695$	3.42658e10	0.00557095
$696$	−2.43007e12	−0.392533
$697$	1.20570e13	1.93505
$698$	−8.06598e12	−1.28620
$699$	1.17886e12	0.186774
$700$	2.22545e11	0.0350329
$701$	7.25354e12	1.13454	0.567269	−	0.823533i	$-0.308000\pi$
$701$	7.25354e12	1.13454	0.567269	+	0.823533i	$0.308000\pi$
$702$	−1.06664e12	−0.165768
$703$	8.75069e12	1.35127
$704$	−2.53544e12	−0.389024
$705$	2.24751e12	0.342649
$706$	−1.37383e13	−2.08119
$707$	−3.34876e10	−0.00504077
$708$	−8.91877e11	−0.133400
$709$	−1.10388e13	−1.64064	−0.820322	−	0.571901i	$-0.806206\pi$
$709$	−1.10388e13	−1.64064	−0.820322	+	0.571901i	$0.806206\pi$
$710$	−2.64657e12	−0.390860
$711$	−4.33775e11	−0.0636578
$712$	5.47034e12	0.797727
$713$	4.66509e12	0.676016
$714$	2.37145e12	0.341485
$715$	4.19142e12	0.599769
$716$	−1.18695e12	−0.168781
$717$	7.96158e12	1.12503
$718$	−6.99620e12	−0.982431
$719$	2.47662e12	0.345604	0.172802	−	0.984957i	$-0.444718\pi$
$719$	2.47662e12	0.345604	0.172802	+	0.984957i	$0.444718\pi$
$720$	−1.34226e12	−0.186140
$721$	−3.68366e12	−0.507658
$722$	2.01976e12	0.276620
$723$	1.23943e11	0.0168694
$724$	−1.15102e12	−0.155690
$725$	1.55842e12	0.209490
$726$	1.33195e13	1.77940
$727$	−1.28405e13	−1.70481	−0.852404	−	0.522884i	$-0.824856\pi$
$727$	−1.28405e13	−1.70481	−0.852404	+	0.522884i	$0.824856\pi$
$728$	−1.32386e12	−0.174683
$729$	2.82430e11	0.0370370
$730$	2.72753e12	0.355481
$731$	6.40980e12	0.830265
$732$	2.23656e12	0.287926
$733$	1.17838e13	1.50771	0.753856	−	0.657039i	$-0.228191\pi$
$733$	1.17838e13	1.50771	0.753856	+	0.657039i	$0.228191\pi$
$734$	1.34754e13	1.71360
$735$	−2.91843e11	−0.0368856
$736$	−5.37210e12	−0.674830
$737$	1.79303e13	2.23863
$738$	−4.86093e12	−0.603206
$739$	−8.32717e12	−1.02706	−0.513532	−	0.858070i	$-0.671663\pi$
$739$	−8.32717e12	−1.02706	−0.513532	+	0.858070i	$0.671663\pi$
$740$	2.60120e12	0.318883
$741$	2.96305e12	0.361042
$742$	6.33198e11	0.0766870
$743$	5.75163e11	0.0692375	0.0346188	−	0.999401i	$-0.488978\pi$
$743$	5.75163e11	0.0692375	0.0346188	+	0.999401i	$0.488978\pi$
$744$	2.70282e12	0.323399
$745$	−9.74392e11	−0.115886
$746$	7.66832e12	0.906516
$747$	−1.04210e12	−0.122452
$748$	−9.66759e12	−1.12917
$749$	2.53922e12	0.294803
$750$	5.41312e11	0.0624701
$751$	−6.99828e12	−0.802808	−0.401404	−	0.915901i	$-0.631478\pi$
$751$	−6.99828e12	−0.802808	−0.401404	+	0.915901i	$0.631478\pi$
$752$	1.45319e13	1.65707
$753$	−6.19540e12	−0.702250
$754$	8.00732e12	0.902227
$755$	−6.85122e12	−0.767374
$756$	−3.02769e11	−0.0337104
$757$	−1.61915e13	−1.79207	−0.896035	−	0.443983i	$-0.853565\pi$
$757$	−1.61915e13	−1.79207	−0.896035	+	0.443983i	$0.853565\pi$
$758$	−1.44594e13	−1.59088
$759$	−7.78866e12	−0.851873
$760$	2.34479e12	0.254942
$761$	−1.81964e13	−1.96677	−0.983386	−	0.181527i	$-0.941896\pi$
$761$	−1.81964e13	−1.96677	−0.983386	+	0.181527i	$0.941896\pi$
$762$	−5.16450e12	−0.554921
$763$	−6.02910e12	−0.644010
$764$	8.53254e11	0.0906063
$765$	1.82668e12	0.192836
$766$	−1.01763e13	−1.06797
$767$	−3.40248e12	−0.354991
$768$	−6.33355e12	−0.656934
$769$	1.73618e12	0.179030	0.0895148	−	0.995985i	$-0.471468\pi$
$769$	1.73618e12	0.179030	0.0895148	+	0.995985i	$0.471468\pi$
$770$	3.75694e12	0.385147
$771$	6.59169e12	0.671819
$772$	−2.00758e12	−0.203421
$773$	1.12087e13	1.12914	0.564568	−	0.825387i	$-0.309043\pi$
$773$	1.12087e13	1.12914	0.564568	+	0.825387i	$0.309043\pi$
$774$	−2.58419e12	−0.258815
$775$	−1.73333e12	−0.172593
$776$	−8.09916e12	−0.801793
$777$	−3.41119e12	−0.335747
$778$	−3.71222e12	−0.363266
$779$	1.35033e13	1.31378
$780$	8.80787e11	0.0852011
$781$	−1.41489e13	−1.36079
$782$	1.28196e13	1.22587
$783$	−2.12021e12	−0.201581
$784$	−1.88699e12	−0.178380
$785$	−5.46238e12	−0.513415
$786$	3.97414e12	0.371400
$787$	−3.06316e12	−0.284632	−0.142316	−	0.989821i	$-0.545455\pi$
$787$	−3.06316e12	−0.284632	−0.142316	+	0.989821i	$0.545455\pi$
$788$	−7.93761e12	−0.733368
$789$	−7.04337e12	−0.647044
$790$	1.13109e12	0.103318
$791$	1.33134e11	0.0120919
$792$	−4.51253e12	−0.407527
$793$	8.53241e12	0.766201
$794$	−1.75056e13	−1.56309
$795$	4.87741e11	0.0433049
$796$	1.57987e12	0.139480
$797$	2.48451e12	0.218112	0.109056	−	0.994036i	$-0.465217\pi$
$797$	2.48451e12	0.218112	0.109056	+	0.994036i	$0.465217\pi$
$798$	2.65591e12	0.231846
$799$	−1.97765e13	−1.71668
$800$	1.99603e12	0.172291
$801$	4.77282e12	0.409665
$802$	2.34383e13	2.00051
$803$	1.45816e13	1.23762
$804$	3.76787e12	0.318012
$805$	−1.57765e12	−0.132412
$806$	−8.90606e12	−0.743323
$807$	1.36125e13	1.12982
$808$	−1.04882e11	−0.00865667
$809$	−1.93379e13	−1.58724	−0.793619	−	0.608415i	$-0.791806\pi$
$809$	−1.93379e13	−1.58724	−0.793619	+	0.608415i	$0.791806\pi$
$810$	−7.36449e11	−0.0601119
$811$	−1.69150e13	−1.37302	−0.686512	−	0.727119i	$-0.740859\pi$
$811$	−1.69150e13	−1.37302	−0.686512	+	0.727119i	$0.740859\pi$
$812$	2.27290e12	0.183476
$813$	6.96468e12	0.559105
$814$	4.39128e13	3.50576
$815$	6.69859e12	0.531832
$816$	1.18109e13	0.932563
$817$	7.17868e12	0.563697
$818$	−7.57623e12	−0.591648
$819$	−1.15506e12	−0.0897069
$820$	4.01395e12	0.310034
$821$	−1.58862e13	−1.22033	−0.610164	−	0.792276i	$-0.708896\pi$
$821$	−1.58862e13	−1.22033	−0.610164	+	0.792276i	$0.708896\pi$
$822$	9.55001e12	0.729593
$823$	−5.71421e12	−0.434167	−0.217084	−	0.976153i	$-0.569654\pi$
$823$	−5.71421e12	−0.434167	−0.217084	+	0.976153i	$0.569654\pi$
$824$	−1.15371e13	−0.871816
$825$	2.89391e12	0.217491
$826$	−3.04979e12	−0.227961
$827$	1.75518e13	1.30481	0.652404	−	0.757872i	$-0.273761\pi$
$827$	1.75518e13	1.30481	0.652404	+	0.757872i	$0.273761\pi$
$828$	−1.63671e12	−0.121014
$829$	−1.59895e13	−1.17582	−0.587908	−	0.808928i	$-0.700048\pi$
$829$	−1.59895e13	−1.17582	−0.587908	+	0.808928i	$0.700048\pi$
$830$	2.71732e12	0.198742
$831$	1.24280e13	0.904057
$832$	−2.03261e12	−0.147062
$833$	2.56802e12	0.184797
$834$	1.21559e11	0.00870044
$835$	−7.41163e12	−0.527624
$836$	−1.08272e13	−0.766637
$837$	2.35818e12	0.166078
$838$	−6.58800e12	−0.461483
$839$	−2.08466e13	−1.45247	−0.726235	−	0.687447i	$-0.758732\pi$
$839$	−2.08466e13	−1.45247	−0.726235	+	0.687447i	$0.758732\pi$
$840$	−9.14044e11	−0.0633447
$841$	1.40932e12	0.0971465
$842$	−1.47518e13	−1.01144
$843$	−1.10414e13	−0.753009
$844$	−2.79532e12	−0.189623
$845$	−3.26764e12	−0.220485
$846$	7.97312e12	0.535133
$847$	1.44236e13	0.962937
$848$	3.15362e12	0.209425
$849$	6.65233e12	0.439430
$850$	−4.76317e12	−0.312976
$851$	−1.84403e13	−1.20527
$852$	−2.97325e12	−0.193309
$853$	−1.59460e13	−1.03129	−0.515645	−	0.856802i	$-0.672448\pi$
$853$	−1.59460e13	−1.03129	−0.515645	+	0.856802i	$0.672448\pi$
$854$	7.64796e12	0.492023
$855$	2.04580e12	0.130923
$856$	7.95277e12	0.506275
$857$	2.40044e13	1.52012	0.760058	−	0.649855i	$-0.225170\pi$
$857$	2.40044e13	1.52012	0.760058	+	0.649855i	$0.225170\pi$
$858$	1.48692e13	0.936690
$859$	7.99453e12	0.500984	0.250492	−	0.968119i	$-0.419408\pi$
$859$	7.99453e12	0.500984	0.250492	+	0.968119i	$0.419408\pi$
$860$	2.13391e12	0.133025
$861$	−5.26386e12	−0.326430
$862$	3.74168e13	2.30826
$863$	2.19924e13	1.34966	0.674831	−	0.737972i	$-0.264217\pi$
$863$	2.19924e13	1.34966	0.674831	+	0.737972i	$0.264217\pi$
$864$	−2.71557e12	−0.165787
$865$	−6.76997e12	−0.411163
$866$	−1.63313e12	−0.0986711
$867$	−6.46794e12	−0.388759
$868$	−2.52801e12	−0.151161
$869$	6.04693e12	0.359704
$870$	5.52855e12	0.327171
$871$	1.43743e13	0.846264
$872$	−1.88830e13	−1.10598
$873$	−7.06644e12	−0.411753
$874$	1.43573e13	0.832286
$875$	5.86182e11	0.0338062
$876$	3.06419e12	0.175812
$877$	−1.38835e13	−0.792500	−0.396250	−	0.918143i	$-0.629689\pi$
$877$	−1.38835e13	−0.792500	−0.396250	+	0.918143i	$0.629689\pi$
$878$	−1.68734e13	−0.958244
$879$	1.88234e13	1.06353
$880$	1.87114e13	1.05180
$881$	1.28492e11	0.00718596	0.00359298	−	0.999994i	$-0.498856\pi$
$881$	1.28492e11	0.00718596	0.00359298	+	0.999994i	$0.498856\pi$
$882$	−1.03533e12	−0.0576061
$883$	2.08112e13	1.15206	0.576029	−	0.817429i	$-0.304602\pi$
$883$	2.08112e13	1.15206	0.576029	+	0.817429i	$0.304602\pi$
$884$	−7.75032e12	−0.426859
$885$	−2.34920e12	−0.128729
$886$	2.26917e13	1.23713
$887$	2.18553e13	1.18549	0.592747	−	0.805389i	$-0.298043\pi$
$887$	2.18553e13	1.18549	0.592747	+	0.805389i	$0.298043\pi$
$888$	−1.06837e13	−0.576588
$889$	−5.59259e12	−0.300300
$890$	−1.24454e13	−0.664894
$891$	−3.93713e12	−0.209281
$892$	−1.08813e13	−0.575490
$893$	−2.21487e13	−1.16551
$894$	−3.45670e12	−0.180985
$895$	−3.12642e12	−0.162871
$896$	−8.10349e12	−0.420036
$897$	−6.24402e12	−0.322031
$898$	3.21509e13	1.64987
$899$	−1.77029e13	−0.903912
$900$	6.08128e11	0.0308961
$901$	−4.29179e12	−0.216958
$902$	6.77625e13	3.40847
$903$	−2.79839e12	−0.140060
$904$	4.16972e11	0.0207658
$905$	−3.03178e12	−0.150238
$906$	−2.43050e13	−1.19845
$907$	2.50979e13	1.23142	0.615709	−	0.787974i	$-0.288870\pi$
$907$	2.50979e13	1.23142	0.615709	+	0.787974i	$0.288870\pi$
$908$	6.12968e12	0.299262
$909$	−9.15087e10	−0.00444554
$910$	3.01187e12	0.145596
$911$	8.37468e12	0.402843	0.201421	−	0.979505i	$-0.435444\pi$
$911$	8.37468e12	0.402843	0.201421	+	0.979505i	$0.435444\pi$
$912$	1.32277e13	0.633151
$913$	1.45271e13	0.691927
$914$	2.78392e13	1.31947
$915$	5.89109e12	0.277844
$916$	1.42174e13	0.667253
$917$	4.30356e12	0.200986
$918$	6.48024e12	0.301161
$919$	−8.54510e12	−0.395182	−0.197591	−	0.980285i	$-0.563312\pi$
$919$	−8.54510e12	−0.395182	−0.197591	+	0.980285i	$0.563312\pi$
$920$	−4.94115e12	−0.227396
$921$	8.16295e12	0.373834
$922$	−1.77886e13	−0.810687
$923$	−1.13429e13	−0.514416
$924$	4.22068e12	0.190484
$925$	6.85155e12	0.307717
$926$	1.13455e13	0.507076
$927$	−1.00660e13	−0.447712
$928$	2.03859e13	0.902327
$929$	3.63140e13	1.59957	0.799786	−	0.600285i	$-0.204946\pi$
$929$	3.63140e13	1.59957	0.799786	+	0.600285i	$0.204946\pi$
$930$	−6.14907e12	−0.269548
$931$	2.87606e12	0.125465
$932$	−3.45337e12	−0.149924
$933$	2.00997e13	0.868403
$934$	−2.13936e12	−0.0919864
$935$	−2.54644e13	−1.08964
$936$	−3.61760e12	−0.154056
$937$	−1.31500e12	−0.0557312	−0.0278656	−	0.999612i	$-0.508871\pi$
$937$	−1.31500e12	−0.0557312	−0.0278656	+	0.999612i	$0.508871\pi$
$938$	1.28843e13	0.543436
$939$	−1.34439e12	−0.0564326
$940$	−6.58386e12	−0.275046
$941$	1.02788e13	0.427354	0.213677	−	0.976904i	$-0.431456\pi$
$941$	1.02788e13	0.427354	0.213677	+	0.976904i	$0.431456\pi$
$942$	−1.93780e13	−0.801827
$943$	−2.84554e13	−1.17182
$944$	−1.51894e13	−0.622539
$945$	−7.97494e11	−0.0325300
$946$	3.60242e13	1.46246
$947$	−3.61307e13	−1.45983	−0.729913	−	0.683540i	$-0.760440\pi$
$947$	−3.61307e13	−1.45983	−0.729913	+	0.683540i	$0.760440\pi$
$948$	1.27070e12	0.0510984
$949$	1.16898e13	0.467853
$950$	−5.33453e12	−0.212491
$951$	−2.06594e13	−0.819040
$952$	8.04295e12	0.317358
$953$	−1.52995e13	−0.600839	−0.300420	−	0.953807i	$-0.597127\pi$
$953$	−1.52995e13	−0.600839	−0.300420	+	0.953807i	$0.597127\pi$
$954$	1.73028e12	0.0676316
$955$	2.24747e12	0.0874336
$956$	−2.33227e13	−0.903063
$957$	2.95562e13	1.13905
$958$	−2.78423e13	−1.06797
$959$	1.03416e13	0.394825
$960$	−1.40339e12	−0.0533283
$961$	−6.74973e12	−0.255288
$962$	3.52041e13	1.32527
$963$	6.93871e12	0.259992
$964$	−3.63080e11	−0.0135412
$965$	−5.28796e12	−0.196298
$966$	−5.59677e12	−0.206795
$967$	−2.38383e13	−0.876711	−0.438355	−	0.898802i	$-0.644439\pi$
$967$	−2.38383e13	−0.876711	−0.438355	+	0.898802i	$0.644439\pi$
$968$	4.51742e13	1.65368
$969$	−1.80016e13	−0.655926
$970$	1.84261e13	0.668283
$971$	−1.75814e13	−0.634699	−0.317350	−	0.948309i	$-0.602793\pi$
$971$	−1.75814e13	−0.634699	−0.317350	+	0.948309i	$0.602793\pi$
$972$	−8.27351e11	−0.0297298
$973$	1.31635e11	0.00470831
$974$	1.57578e13	0.561023
$975$	2.31999e12	0.0822177
$976$	3.80905e13	1.34367
$977$	1.73590e13	0.609535	0.304768	−	0.952427i	$-0.401421\pi$
$977$	1.73590e13	0.609535	0.304768	+	0.952427i	$0.401421\pi$
$978$	2.37635e13	0.830589
$979$	−6.65342e13	−2.31485
$980$	8.54927e11	0.0296082
$981$	−1.64752e13	−0.567963
$982$	−1.93245e13	−0.663140
$983$	4.80777e12	0.164230	0.0821151	−	0.996623i	$-0.473832\pi$
$983$	4.80777e12	0.164230	0.0821151	+	0.996623i	$0.473832\pi$
$984$	−1.64862e13	−0.560588
$985$	−2.09077e13	−0.707689
$986$	−4.86474e13	−1.63913
$987$	8.63402e12	0.289591
$988$	−8.67999e12	−0.289810
$989$	−1.51276e13	−0.502789
$990$	1.02663e13	0.339668
$991$	−4.17011e12	−0.137346	−0.0686729	−	0.997639i	$-0.521876\pi$
$991$	−4.17011e12	−0.137346	−0.0686729	+	0.997639i	$0.521876\pi$
$992$	−2.26740e13	−0.743405
$993$	−1.45455e13	−0.474740
$994$	−1.01671e13	−0.330337
$995$	4.16137e12	0.134596
$996$	3.05273e12	0.0982927
$997$	2.43167e13	0.779429	0.389714	−	0.920936i	$-0.372574\pi$
$997$	2.43167e13	0.779429	0.389714	+	0.920936i	$0.372574\pi$
$998$	−4.42413e13	−1.41169
$999$	−9.32146e12	−0.296101

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.10.a.a.1.2	✓	4
3.2	odd	2		315.10.a.i.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.10.a.a.1.2	✓	4	1.1	even	1	trivial
315.10.a.i.1.3		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	105.a (trivial)

\(f(q)\)	\(=\)	\(q-27.3730 q^{2} -81.0000 q^{3} +237.282 q^{4} +625.000 q^{5} +2217.21 q^{6} +2401.00 q^{7} +7519.86 q^{8} +6561.00 q^{9} -17108.1 q^{10} -91461.8 q^{11} -19219.8 q^{12} -73323.1 q^{13} -65722.6 q^{14} -50625.0 q^{15} -327330. q^{16} +445465. q^{17} -179594. q^{18} +498900. q^{19} +148301. q^{20} -194481. q^{21} +2.50359e6 q^{22} -1.05133e6 q^{23} -609109. q^{24} +390625. q^{25} +2.00708e6 q^{26} -531441. q^{27} +569714. q^{28} +3.98954e6 q^{29} +1.38576e6 q^{30} -4.43733e6 q^{31} +5.10983e6 q^{32} +7.40841e6 q^{33} -1.21937e7 q^{34} +1.50062e6 q^{35} +1.55681e6 q^{36} +1.75400e7 q^{37} -1.36564e7 q^{38} +5.93917e6 q^{39} +4.69991e6 q^{40} +2.70662e7 q^{41} +5.32353e6 q^{42} +1.43890e7 q^{43} -2.17022e7 q^{44} +4.10062e6 q^{45} +2.87780e7 q^{46} -4.43952e7 q^{47} +2.65137e7 q^{48} +5.76480e6 q^{49} -1.06926e7 q^{50} -3.60827e7 q^{51} -1.73983e7 q^{52} -9.63440e6 q^{53} +1.45471e7 q^{54} -5.71637e7 q^{55} +1.80552e7 q^{56} -4.04109e7 q^{57} -1.09206e8 q^{58} +4.64040e7 q^{59} -1.20124e7 q^{60} -1.16367e8 q^{61} +1.21463e8 q^{62} +1.57530e7 q^{63} +2.77213e7 q^{64} -4.58270e7 q^{65} -2.02791e8 q^{66} -1.96041e8 q^{67} +1.05701e8 q^{68} +8.51575e7 q^{69} -4.10766e7 q^{70} +1.54697e8 q^{71} +4.93378e7 q^{72} -1.59429e8 q^{73} -4.80122e8 q^{74} -3.16406e7 q^{75} +1.18380e8 q^{76} -2.19600e8 q^{77} -1.62573e8 q^{78} -6.61142e7 q^{79} -2.04581e8 q^{80} +4.30467e7 q^{81} -7.40883e8 q^{82} -1.58832e8 q^{83} -4.61468e7 q^{84} +2.78416e8 q^{85} -3.93871e8 q^{86} -3.23153e8 q^{87} -6.87780e8 q^{88} +7.27453e8 q^{89} -1.12246e8 q^{90} -1.76049e8 q^{91} -2.49461e8 q^{92} +3.59424e8 q^{93} +1.21523e9 q^{94} +3.11812e8 q^{95} -4.13896e8 q^{96} -1.07704e9 q^{97} -1.57800e8 q^{98} -6.00081e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 41 q^{2} - 324 q^{3} + 501 q^{4} + 2500 q^{5} + 3321 q^{6} + 9604 q^{7} - 29367 q^{8} + 26244 q^{9} - 25625 q^{10} - 32854 q^{11} - 40581 q^{12} - 133882 q^{13} - 98441 q^{14} - 202500 q^{15} - 90479 q^{16}+ \cdots - 215555094 q^{99}+O(q^{100}) \) 4 * q - 41 * q^2 - 324 * q^3 + 501 * q^4 + 2500 * q^5 + 3321 * q^6 + 9604 * q^7 - 29367 * q^8 + 26244 * q^9 - 25625 * q^10 - 32854 * q^11 - 40581 * q^12 - 133882 * q^13 - 98441 * q^14 - 202500 * q^15 - 90479 * q^16 + 334344 * q^17 - 269001 * q^18 + 72046 * q^19 + 313125 * q^20 - 777924 * q^21 + 990556 * q^22 + 47460 * q^23 + 2378727 * q^24 + 1562500 * q^25 + 4203458 * q^26 - 2125764 * q^27 + 1202901 * q^28 + 7010312 * q^29 + 2075625 * q^30 - 3711690 * q^31 + 18115265 * q^32 + 2661174 * q^33 + 12757214 * q^34 + 6002500 * q^35 + 3287061 * q^36 + 5222716 * q^37 - 759964 * q^38 + 10844442 * q^39 - 18354375 * q^40 - 5689292 * q^41 + 7973721 * q^42 - 71286384 * q^43 + 6098004 * q^44 + 16402500 * q^45 + 13833560 * q^46 - 100832160 * q^47 + 7328799 * q^48 + 23059204 * q^49 - 16015625 * q^50 - 27081864 * q^51 - 7238698 * q^52 - 149250454 * q^53 + 21789081 * q^54 - 20533750 * q^55 - 70510167 * q^56 - 5835726 * q^57 - 191838758 * q^58 + 24779068 * q^59 - 25363125 * q^60 - 301336048 * q^61 - 107946280 * q^62 + 63011844 * q^63 - 71492607 * q^64 - 83676250 * q^65 - 80235036 * q^66 - 10978016 * q^67 - 527886134 * q^68 - 3844260 * q^69 - 61525625 * q^70 - 507837170 * q^71 - 192676887 * q^72 - 158796526 * q^73 - 252589374 * q^74 - 126562500 * q^75 - 604814036 * q^76 - 78882454 * q^77 - 340480098 * q^78 - 36676584 * q^79 - 56549375 * q^80 + 172186884 * q^81 - 1841487282 * q^82 + 201009048 * q^83 - 97434981 * q^84 + 208965000 * q^85 + 162200156 * q^86 - 567835272 * q^87 - 1446483548 * q^88 + 161323024 * q^89 - 168125625 * q^90 - 321450682 * q^91 + 563662840 * q^92 + 300646890 * q^93 - 918128840 * q^94 + 45028750 * q^95 - 1467336465 * q^96 - 1913030882 * q^97 - 236356841 * q^98 - 215555094 * q^99

Introduction

L-functions

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