LMFDB - Embedded newform 42.12.a.g.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [42,12,Mod(1,42)] 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("42.1"); S:= CuspForms(chi, 12); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 12, names="a")

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	42.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,64,-486,2048,-1032] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$32.2704135835$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1140720 $ x^2 - x - 1140720
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1068.55$ of defining polynomial
Character	$\chi$	$=$	42.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+32.0000 q^{2} -243.000 q^{3} +1024.00 q^{4} -13332.5 q^{5} -7776.00 q^{6} +16807.0 q^{7} +32768.0 q^{8} +59049.0 q^{9} -426641. q^{10} -942174. q^{11} -248832. q^{12} +964993. q^{13} +537824. q^{14} +3.23981e6 q^{15} +1.04858e6 q^{16} +4.71343e6 q^{17} +1.88957e6 q^{18} +1.13808e7 q^{19} -1.36525e7 q^{20} -4.08410e6 q^{21} -3.01496e7 q^{22} -8.11304e6 q^{23} -7.96262e6 q^{24} +1.28929e8 q^{25} +3.08798e7 q^{26} -1.43489e7 q^{27} +1.72104e7 q^{28} -1.19784e8 q^{29} +1.03674e8 q^{30} +2.54467e8 q^{31} +3.35544e7 q^{32} +2.28948e8 q^{33} +1.50830e8 q^{34} -2.24080e8 q^{35} +6.04662e7 q^{36} +2.92927e8 q^{37} +3.64186e8 q^{38} -2.34493e8 q^{39} -4.36881e8 q^{40} +5.90103e8 q^{41} -1.30691e8 q^{42} -1.12848e9 q^{43} -9.64787e8 q^{44} -7.87273e8 q^{45} -2.59617e8 q^{46} +2.37956e9 q^{47} -2.54804e8 q^{48} +2.82475e8 q^{49} +4.12571e9 q^{50} -1.14536e9 q^{51} +9.88153e8 q^{52} +1.35257e9 q^{53} -4.59165e8 q^{54} +1.25616e10 q^{55} +5.50732e8 q^{56} -2.76554e9 q^{57} -3.83310e9 q^{58} +8.14638e9 q^{59} +3.31756e9 q^{60} -9.13202e9 q^{61} +8.14296e9 q^{62} +9.92437e8 q^{63} +1.07374e9 q^{64} -1.28658e10 q^{65} +7.32635e9 q^{66} -4.54261e9 q^{67} +4.82655e9 q^{68} +1.97147e9 q^{69} -7.17056e9 q^{70} -1.62398e10 q^{71} +1.93492e9 q^{72} -1.46180e10 q^{73} +9.37365e9 q^{74} -3.13296e10 q^{75} +1.16540e10 q^{76} -1.58351e10 q^{77} -7.50379e9 q^{78} +2.98983e10 q^{79} -1.39802e10 q^{80} +3.48678e9 q^{81} +1.88833e10 q^{82} +2.00567e9 q^{83} -4.18212e9 q^{84} -6.28420e10 q^{85} -3.61114e10 q^{86} +2.91076e10 q^{87} -3.08732e10 q^{88} +2.27403e10 q^{89} -2.51927e10 q^{90} +1.62186e10 q^{91} -8.30775e9 q^{92} -6.18356e10 q^{93} +7.61460e10 q^{94} -1.51735e11 q^{95} -8.15373e9 q^{96} -4.69241e10 q^{97} +9.03921e9 q^{98} -5.56345e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 64 q^{2} - 486 q^{3} + 2048 q^{4} - 1032 q^{5} - 15552 q^{6} + 33614 q^{7} + 65536 q^{8} + 118098 q^{9} - 33024 q^{10} - 1294788 q^{11} - 497664 q^{12} + 2545180 q^{13} + 1075648 q^{14} + 250776 q^{15}+ \cdots - 76455936612 q^{99}+O(q^{100}) $ 2 * q + 64 * q^2 - 486 * q^3 + 2048 * q^4 - 1032 * q^5 - 15552 * q^6 + 33614 * q^7 + 65536 * q^8 + 118098 * q^9 - 33024 * q^10 - 1294788 * q^11 - 497664 * q^12 + 2545180 * q^13 + 1075648 * q^14 + 250776 * q^15 + 2097152 * q^16 + 2223960 * q^17 + 3779136 * q^18 - 4768304 * q^19 - 1056768 * q^20 - 8168202 * q^21 - 41433216 * q^22 + 37167636 * q^23 - 15925248 * q^24 + 231403694 * q^25 + 81445760 * q^26 - 28697814 * q^27 + 34420736 * q^28 + 50444100 * q^29 + 8024832 * q^30 + 240248968 * q^31 + 67108864 * q^32 + 314633484 * q^33 + 71166720 * q^34 - 17344824 * q^35 + 120932352 * q^36 + 482808172 * q^37 - 152585728 * q^38 - 618478740 * q^39 - 33816576 * q^40 + 826289568 * q^41 - 261382464 * q^42 - 1418762312 * q^43 - 1325862912 * q^44 - 60938568 * q^45 + 1189364352 * q^46 + 4558113192 * q^47 - 509607936 * q^48 + 564950498 * q^49 + 7404918208 * q^50 - 540422280 * q^51 + 2606264320 * q^52 - 4701996228 * q^53 - 918330048 * q^54 + 8224241544 * q^55 + 1101463552 * q^56 + 1158697872 * q^57 + 1614211200 * q^58 + 11975488224 * q^59 + 256794624 * q^60 + 1152867268 * q^61 + 7687966976 * q^62 + 1984873086 * q^63 + 2147483648 * q^64 + 6571345488 * q^65 + 10068271488 * q^66 - 21013981040 * q^67 + 2277335040 * q^68 - 9031735548 * q^69 - 555034368 * q^70 - 10009175796 * q^71 + 3869835264 * q^72 - 30165108692 * q^73 + 15449861504 * q^74 - 56231097642 * q^75 - 4882743296 * q^76 - 21761501916 * q^77 - 19791319680 * q^78 - 4940763704 * q^79 - 1082130432 * q^80 + 6973568802 * q^81 + 26441266176 * q^82 - 40082578056 * q^83 - 8364238848 * q^84 - 93463771752 * q^85 - 45400393984 * q^86 - 12257916300 * q^87 - 42427613184 * q^88 + 45015319488 * q^89 - 1950034176 * q^90 + 42776840260 * q^91 + 38059659264 * q^92 - 58380499224 * q^93 + 145859622144 * q^94 - 350378017104 * q^95 - 16307453952 * q^96 + 41947334380 * q^97 + 18078415936 * q^98 - 76455936612 * q^99

Coefficient data

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

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

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

$2$	32.0000	0.707107
$2$	32.0000	0.707107
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	1024.00	0.500000
$5$	−13332.5	−1.90800	−0.953999	−	0.299810i	$-0.903077\pi$
$5$	−13332.5	−1.90800	−0.953999	+	0.299810i	$0.903077\pi$
$6$	−7776.00	−0.408248
$7$	16807.0	0.377964
$7$	16807.0	0.377964
$8$	32768.0	0.353553
$9$	59049.0	0.333333
$10$	−426641.	−1.34916
$11$	−942174.	−1.76389	−0.881945	−	0.471352i	$-0.843766\pi$
$11$	−942174.	−1.76389	−0.881945	+	0.471352i	$0.843766\pi$
$12$	−248832.	−0.288675
$13$	964993.	0.720835	0.360417	−	0.932791i	$-0.382634\pi$
$13$	964993.	0.720835	0.360417	+	0.932791i	$0.382634\pi$
$14$	537824.	0.267261
$15$	3.23981e6	1.10158
$16$	1.04858e6	0.250000
$17$	4.71343e6	0.805133	0.402567	−	0.915391i	$-0.368118\pi$
$17$	4.71343e6	0.805133	0.402567	+	0.915391i	$0.368118\pi$
$18$	1.88957e6	0.235702
$19$	1.13808e7	1.05446	0.527228	−	0.849724i	$-0.323231\pi$
$19$	1.13808e7	1.05446	0.527228	+	0.849724i	$0.323231\pi$
$20$	−1.36525e7	−0.953999
$21$	−4.08410e6	−0.218218
$22$	−3.01496e7	−1.24726
$23$	−8.11304e6	−0.262833	−0.131417	−	0.991327i	$-0.541953\pi$
$23$	−8.11304e6	−0.262833	−0.131417	+	0.991327i	$0.541953\pi$
$24$	−7.96262e6	−0.204124
$25$	1.28929e8	2.64046
$26$	3.08798e7	0.509707
$27$	−1.43489e7	−0.192450
$28$	1.72104e7	0.188982
$29$	−1.19784e8	−1.08445	−0.542227	−	0.840232i	$-0.682419\pi$
$29$	−1.19784e8	−1.08445	−0.542227	+	0.840232i	$0.682419\pi$
$30$	1.03674e8	0.778937
$31$	2.54467e8	1.59640	0.798202	−	0.602390i	$-0.205785\pi$
$31$	2.54467e8	1.59640	0.798202	+	0.602390i	$0.205785\pi$
$32$	3.35544e7	0.176777
$33$	2.28948e8	1.01838
$34$	1.50830e8	0.569315
$35$	−2.24080e8	−0.721155
$36$	6.04662e7	0.166667
$37$	2.92927e8	0.694463	0.347232	−	0.937779i	$-0.387122\pi$
$37$	2.92927e8	0.694463	0.347232	+	0.937779i	$0.387122\pi$
$38$	3.64186e8	0.745613
$39$	−2.34493e8	−0.416174
$40$	−4.36881e8	−0.674579
$41$	5.90103e8	0.795457	0.397728	−	0.917503i	$-0.369799\pi$
$41$	5.90103e8	0.795457	0.397728	+	0.917503i	$0.369799\pi$
$42$	−1.30691e8	−0.154303
$43$	−1.12848e9	−1.17063	−0.585313	−	0.810807i	$-0.699028\pi$
$43$	−1.12848e9	−1.17063	−0.585313	+	0.810807i	$0.699028\pi$
$44$	−9.64787e8	−0.881945
$45$	−7.87273e8	−0.635999
$46$	−2.59617e8	−0.185851
$47$	2.37956e9	1.51342	0.756709	−	0.653751i	$-0.226806\pi$
$47$	2.37956e9	1.51342	0.756709	+	0.653751i	$0.226806\pi$
$48$	−2.54804e8	−0.144338
$49$	2.82475e8	0.142857
$50$	4.12571e9	1.86708
$51$	−1.14536e9	−0.464844
$52$	9.88153e8	0.360417
$53$	1.35257e9	0.444266	0.222133	−	0.975016i	$-0.428698\pi$
$53$	1.35257e9	0.444266	0.222133	+	0.975016i	$0.428698\pi$
$54$	−4.59165e8	−0.136083
$55$	1.25616e10	3.36550
$56$	5.50732e8	0.133631
$57$	−2.76554e9	−0.608790
$58$	−3.83310e9	−0.766824
$59$	8.14638e9	1.48347	0.741735	−	0.670693i	$-0.234003\pi$
$59$	8.14638e9	1.48347	0.741735	+	0.670693i	$0.234003\pi$
$60$	3.31756e9	0.550792
$61$	−9.13202e9	−1.38437	−0.692186	−	0.721719i	$-0.743352\pi$
$61$	−9.13202e9	−1.38437	−0.692186	+	0.721719i	$0.743352\pi$
$62$	8.14296e9	1.12883
$63$	9.92437e8	0.125988
$64$	1.07374e9	0.125000
$65$	−1.28658e10	−1.37535
$66$	7.32635e9	0.720105
$67$	−4.54261e9	−0.411049	−0.205525	−	0.978652i	$-0.565890\pi$
$67$	−4.54261e9	−0.411049	−0.205525	+	0.978652i	$0.565890\pi$
$68$	4.82655e9	0.402567
$69$	1.97147e9	0.151747
$70$	−7.17056e9	−0.509934
$71$	−1.62398e10	−1.06822	−0.534110	−	0.845415i	$-0.679353\pi$
$71$	−1.62398e10	−1.06822	−0.534110	+	0.845415i	$0.679353\pi$
$72$	1.93492e9	0.117851
$73$	−1.46180e10	−0.825301	−0.412651	−	0.910889i	$-0.635397\pi$
$73$	−1.46180e10	−0.825301	−0.412651	+	0.910889i	$0.635397\pi$
$74$	9.37365e9	0.491060
$75$	−3.13296e10	−1.52447
$76$	1.16540e10	0.527228
$77$	−1.58351e10	−0.666688
$78$	−7.50379e9	−0.294280
$79$	2.98983e10	1.09319	0.546597	−	0.837396i	$-0.315923\pi$
$79$	2.98983e10	1.09319	0.546597	+	0.837396i	$0.315923\pi$
$80$	−1.39802e10	−0.476999
$81$	3.48678e9	0.111111
$82$	1.88833e10	0.562473
$83$	2.00567e9	0.0558896	0.0279448	−	0.999609i	$-0.491104\pi$
$83$	2.00567e9	0.0558896	0.0279448	+	0.999609i	$0.491104\pi$
$84$	−4.18212e9	−0.109109
$85$	−6.28420e10	−1.53619
$86$	−3.61114e10	−0.827758
$87$	2.91076e10	0.626109
$88$	−3.08732e10	−0.623629
$89$	2.27403e10	0.431669	0.215835	−	0.976430i	$-0.430753\pi$
$89$	2.27403e10	0.431669	0.215835	+	0.976430i	$0.430753\pi$
$90$	−2.51927e10	−0.449719
$91$	1.62186e10	0.272450
$92$	−8.30775e9	−0.131417
$93$	−6.18356e10	−0.921685
$94$	7.61460e10	1.07015
$95$	−1.51735e11	−2.01190
$96$	−8.15373e9	−0.102062
$97$	−4.69241e10	−0.554820	−0.277410	−	0.960752i	$-0.589476\pi$
$97$	−4.69241e10	−0.554820	−0.277410	+	0.960752i	$0.589476\pi$
$98$	9.03921e9	0.101015
$99$	−5.56345e10	−0.587963
$100$	1.32023e11	1.32023
$101$	3.96225e10	0.375124	0.187562	−	0.982253i	$-0.439942\pi$
$101$	3.96225e10	0.375124	0.187562	+	0.982253i	$0.439942\pi$
$102$	−3.66516e10	−0.328694
$103$	−1.95869e11	−1.66479	−0.832397	−	0.554180i	$-0.813032\pi$
$103$	−1.95869e11	−1.66479	−0.832397	+	0.554180i	$0.813032\pi$
$104$	3.16209e10	0.254854
$105$	5.44514e10	0.416359
$106$	4.32823e10	0.314144
$107$	5.96238e10	0.410969	0.205484	−	0.978660i	$-0.434123\pi$
$107$	5.96238e10	0.410969	0.205484	+	0.978660i	$0.434123\pi$
$108$	−1.46933e10	−0.0962250
$109$	1.37704e11	0.857240	0.428620	−	0.903485i	$-0.359000\pi$
$109$	1.37704e11	0.857240	0.428620	+	0.903485i	$0.359000\pi$
$110$	4.01971e11	2.37977
$111$	−7.11812e10	−0.400949
$112$	1.76234e10	0.0944911
$113$	5.37389e9	0.0274383	0.0137192	−	0.999906i	$-0.495633\pi$
$113$	5.37389e9	0.0274383	0.0137192	+	0.999906i	$0.495633\pi$
$114$	−8.84972e10	−0.430480
$115$	1.08167e11	0.501485
$116$	−1.22659e11	−0.542227
$117$	5.69819e10	0.240278
$118$	2.60684e11	1.04897
$119$	7.92186e10	0.304312
$120$	1.06162e11	0.389468
$121$	6.02381e11	2.11131
$122$	−2.92225e11	−0.978899
$123$	−1.43395e11	−0.459257
$124$	2.60575e11	0.798202
$125$	−1.06794e12	−3.12999
$126$	3.17580e10	0.0890871
$127$	2.45584e11	0.659598	0.329799	−	0.944051i	$-0.393019\pi$
$127$	2.45584e11	0.659598	0.329799	+	0.944051i	$0.393019\pi$
$128$	3.43597e10	0.0883883
$129$	2.74221e11	0.675861
$130$	−4.11706e11	−0.972520
$131$	−1.94455e11	−0.440379	−0.220190	−	0.975457i	$-0.570668\pi$
$131$	−1.94455e11	−0.440379	−0.220190	+	0.975457i	$0.570668\pi$
$132$	2.34443e11	0.509191
$133$	1.91277e11	0.398547
$134$	−1.45363e11	−0.290656
$135$	1.91307e11	0.367194
$136$	1.54450e11	0.284658
$137$	9.24556e11	1.63670	0.818352	−	0.574718i	$-0.194888\pi$
$137$	9.24556e11	1.63670	0.818352	+	0.574718i	$0.194888\pi$
$138$	6.30870e10	0.107301
$139$	5.91668e11	0.967156	0.483578	−	0.875301i	$-0.339337\pi$
$139$	5.91668e11	0.967156	0.483578	+	0.875301i	$0.339337\pi$
$140$	−2.29458e11	−0.360578
$141$	−5.78234e11	−0.873773
$142$	−5.19675e11	−0.755346
$143$	−9.09192e11	−1.27147
$144$	6.19174e10	0.0833333
$145$	1.59703e12	2.06913
$146$	−4.67776e11	−0.583576
$147$	−6.86415e10	−0.0824786
$148$	2.99957e11	0.347232
$149$	1.19926e12	1.33780	0.668899	−	0.743354i	$-0.266766\pi$
$149$	1.19926e12	1.33780	0.668899	+	0.743354i	$0.266766\pi$
$150$	−1.00255e12	−1.07796
$151$	1.33922e11	0.138829	0.0694143	−	0.997588i	$-0.477887\pi$
$151$	1.33922e11	0.138829	0.0694143	+	0.997588i	$0.477887\pi$
$152$	3.72926e11	0.372807
$153$	2.78323e11	0.268378
$154$	−5.06724e11	−0.471419
$155$	−3.39270e12	−3.04594
$156$	−2.40121e11	−0.208087
$157$	1.13054e12	0.945888	0.472944	−	0.881093i	$-0.343191\pi$
$157$	1.13054e12	0.945888	0.472944	+	0.881093i	$0.343191\pi$
$158$	9.56745e11	0.773005
$159$	−3.28675e11	−0.256497
$160$	−4.47366e11	−0.337290
$161$	−1.36356e11	−0.0993416
$162$	1.11577e11	0.0785674
$163$	−1.16531e12	−0.793248	−0.396624	−	0.917981i	$-0.629818\pi$
$163$	−1.16531e12	−0.793248	−0.396624	+	0.917981i	$0.629818\pi$
$164$	6.04265e11	0.397728
$165$	−3.05246e12	−1.94307
$166$	6.41815e10	0.0395199
$167$	1.18497e12	0.705939	0.352970	−	0.935635i	$-0.385172\pi$
$167$	1.18497e12	0.705939	0.352970	+	0.935635i	$0.385172\pi$
$168$	−1.33828e11	−0.0771517
$169$	−8.60949e11	−0.480397
$170$	−2.01094e12	−1.08625
$171$	6.72026e11	0.351485
$172$	−1.15557e12	−0.585313
$173$	7.17811e11	0.352173	0.176087	−	0.984375i	$-0.443656\pi$
$173$	7.17811e11	0.352173	0.176087	+	0.984375i	$0.443656\pi$
$174$	9.31443e11	0.442726
$175$	2.16690e12	0.997999
$176$	−9.87942e11	−0.440973
$177$	−1.97957e12	−0.856482
$178$	7.27689e11	0.305236
$179$	3.92102e12	1.59480	0.797402	−	0.603449i	$-0.206207\pi$
$179$	3.92102e12	1.59480	0.797402	+	0.603449i	$0.206207\pi$
$180$	−8.06168e11	−0.318000
$181$	3.93765e12	1.50663	0.753313	−	0.657662i	$-0.228455\pi$
$181$	3.93765e12	1.50663	0.753313	+	0.657662i	$0.228455\pi$
$182$	5.18996e11	0.192651
$183$	2.21908e12	0.799267
$184$	−2.65848e11	−0.0929256
$185$	−3.90546e12	−1.32503
$186$	−1.97874e12	−0.651729
$187$	−4.44087e12	−1.42017
$188$	2.43667e12	0.756709
$189$	−2.41162e11	−0.0727393
$190$	−4.85552e12	−1.42263
$191$	8.47221e11	0.241164	0.120582	−	0.992703i	$-0.461524\pi$
$191$	8.47221e11	0.241164	0.120582	+	0.992703i	$0.461524\pi$
$192$	−2.60919e11	−0.0721688
$193$	4.75627e12	1.27850	0.639251	−	0.768998i	$-0.279244\pi$
$193$	4.75627e12	1.27850	0.639251	+	0.768998i	$0.279244\pi$
$194$	−1.50157e12	−0.392317
$195$	3.12639e12	0.794059
$196$	2.89255e11	0.0714286
$197$	−1.89245e12	−0.454424	−0.227212	−	0.973845i	$-0.572961\pi$
$197$	−1.89245e12	−0.454424	−0.227212	+	0.973845i	$0.572961\pi$
$198$	−1.78030e12	−0.415753
$199$	−2.65469e12	−0.603007	−0.301504	−	0.953465i	$-0.597489\pi$
$199$	−2.65469e12	−0.603007	−0.301504	+	0.953465i	$0.597489\pi$
$200$	4.22473e12	0.933542
$201$	1.10385e12	0.237319
$202$	1.26792e12	0.265252
$203$	−2.01321e12	−0.409885
$204$	−1.17285e12	−0.232422
$205$	−7.86757e12	−1.51773
$206$	−6.26780e12	−1.17719
$207$	−4.79067e11	−0.0876111
$208$	1.01187e12	0.180209
$209$	−1.07227e13	−1.85994
$210$	1.74245e12	0.294410
$211$	1.84201e12	0.303206	0.151603	−	0.988441i	$-0.451556\pi$
$211$	1.84201e12	0.303206	0.151603	+	0.988441i	$0.451556\pi$
$212$	1.38503e12	0.222133
$213$	3.94628e12	0.616737
$214$	1.90796e12	0.290599
$215$	1.50455e13	2.23355
$216$	−4.70185e11	−0.0680414
$217$	4.27683e12	0.603384
$218$	4.40654e12	0.606160
$219$	3.55218e12	0.476488
$220$	1.28631e13	1.68275
$221$	4.54843e12	0.580368
$222$	−2.27780e12	−0.283513
$223$	−5.87674e12	−0.713608	−0.356804	−	0.934179i	$-0.616134\pi$
$223$	−5.87674e12	−0.713608	−0.356804	+	0.934179i	$0.616134\pi$
$224$	5.63949e11	0.0668153
$225$	7.61310e12	0.880152
$226$	1.71964e11	0.0194018
$227$	3.50365e12	0.385815	0.192907	−	0.981217i	$-0.438208\pi$
$227$	3.50365e12	0.385815	0.192907	+	0.981217i	$0.438208\pi$
$228$	−2.83191e12	−0.304395
$229$	1.36835e13	1.43583	0.717915	−	0.696131i	$-0.245097\pi$
$229$	1.36835e13	1.43583	0.717915	+	0.696131i	$0.245097\pi$
$230$	3.46136e12	0.354604
$231$	3.84794e12	0.384912
$232$	−3.92509e12	−0.383412
$233$	−5.97100e12	−0.569626	−0.284813	−	0.958583i	$-0.591931\pi$
$233$	−5.97100e12	−0.569626	−0.284813	+	0.958583i	$0.591931\pi$
$234$	1.82342e12	0.169902
$235$	−3.17256e13	−2.88760
$236$	8.34190e12	0.741735
$237$	−7.26528e12	−0.631156
$238$	2.53499e12	0.215181
$239$	1.32284e13	1.09728	0.548640	−	0.836059i	$-0.315146\pi$
$239$	1.32284e13	1.09728	0.548640	+	0.836059i	$0.315146\pi$
$240$	3.39718e12	0.275396
$241$	2.01903e12	0.159974	0.0799868	−	0.996796i	$-0.474512\pi$
$241$	2.01903e12	0.159974	0.0799868	+	0.996796i	$0.474512\pi$
$242$	1.92762e13	1.49292
$243$	−8.47289e11	−0.0641500
$244$	−9.35119e12	−0.692186
$245$	−3.76611e12	−0.272571
$246$	−4.58864e12	−0.324744
$247$	1.09824e13	0.760089
$248$	8.33839e12	0.564414
$249$	−4.87379e11	−0.0322678
$250$	−3.41741e13	−2.21323
$251$	−1.98605e13	−1.25830	−0.629149	−	0.777284i	$-0.716597\pi$
$251$	−1.98605e13	−1.25830	−0.629149	+	0.777284i	$0.716597\pi$
$252$	1.01626e12	0.0629941
$253$	7.64390e12	0.463609
$254$	7.85868e12	0.466406
$255$	1.52706e13	0.886921
$256$	1.09951e12	0.0625000
$257$	1.93132e13	1.07454	0.537269	−	0.843411i	$-0.319456\pi$
$257$	1.93132e13	1.07454	0.537269	+	0.843411i	$0.319456\pi$
$258$	8.77508e12	0.477906
$259$	4.92322e12	0.262482
$260$	−1.31746e13	−0.687676
$261$	−7.07314e12	−0.361484
$262$	−6.22256e12	−0.311395
$263$	−2.28701e13	−1.12076	−0.560378	−	0.828237i	$-0.689344\pi$
$263$	−2.28701e13	−1.12076	−0.560378	+	0.828237i	$0.689344\pi$
$264$	7.50218e12	0.360053
$265$	−1.80332e13	−0.847659
$266$	6.12087e12	0.281815
$267$	−5.52589e12	−0.249224
$268$	−4.65163e12	−0.205525
$269$	−2.72360e13	−1.17898	−0.589488	−	0.807777i	$-0.700671\pi$
$269$	−2.72360e13	−1.17898	−0.589488	+	0.807777i	$0.700671\pi$
$270$	6.12184e12	0.259646
$271$	−2.44294e13	−1.01527	−0.507634	−	0.861573i	$-0.669480\pi$
$271$	−2.44294e13	−1.01527	−0.507634	+	0.861573i	$0.669480\pi$
$272$	4.94239e12	0.201283
$273$	−3.94113e12	−0.157299
$274$	2.95858e13	1.15732
$275$	−1.21473e14	−4.65747
$276$	2.01878e12	0.0758734
$277$	2.35739e13	0.868545	0.434272	−	0.900782i	$-0.357006\pi$
$277$	2.35739e13	0.868545	0.434272	+	0.900782i	$0.357006\pi$
$278$	1.89334e13	0.683883
$279$	1.50260e13	0.532135
$280$	−7.34265e12	−0.254967
$281$	−1.32102e13	−0.449805	−0.224902	−	0.974381i	$-0.572206\pi$
$281$	−1.32102e13	−0.449805	−0.224902	+	0.974381i	$0.572206\pi$
$282$	−1.85035e13	−0.617851
$283$	1.65738e13	0.542746	0.271373	−	0.962474i	$-0.412522\pi$
$283$	1.65738e13	0.542746	0.271373	+	0.962474i	$0.412522\pi$
$284$	−1.66296e13	−0.534110
$285$	3.68716e13	1.16157
$286$	−2.90941e13	−0.899067
$287$	9.91786e12	0.300654
$288$	1.98136e12	0.0589256
$289$	−1.20555e13	−0.351760
$290$	5.11049e13	1.46310
$291$	1.14026e13	0.320325
$292$	−1.49688e13	−0.412651
$293$	−3.74363e13	−1.01279	−0.506397	−	0.862300i	$-0.669023\pi$
$293$	−3.74363e13	−1.01279	−0.506397	+	0.862300i	$0.669023\pi$
$294$	−2.19653e12	−0.0583212
$295$	−1.08612e14	−2.83046
$296$	9.59862e12	0.245530
$297$	1.35192e13	0.339461
$298$	3.83764e13	0.945965
$299$	−7.82902e12	−0.189459
$300$	−3.20815e13	−0.762234
$301$	−1.89664e13	−0.442455
$302$	4.28550e12	0.0981666
$303$	−9.62827e12	−0.216578
$304$	1.19336e13	0.263614
$305$	1.21753e14	2.64138
$306$	8.90634e12	0.189772
$307$	−2.13132e13	−0.446055	−0.223027	−	0.974812i	$-0.571594\pi$
$307$	−2.13132e13	−0.446055	−0.223027	+	0.974812i	$0.571594\pi$
$308$	−1.62152e13	−0.333344
$309$	4.75961e13	0.961169
$310$	−1.08566e14	−2.15380
$311$	8.59687e13	1.67555	0.837777	−	0.546013i	$-0.183855\pi$
$311$	8.59687e13	1.67555	0.837777	+	0.546013i	$0.183855\pi$
$312$	−7.68388e12	−0.147140
$313$	7.93853e13	1.49364	0.746821	−	0.665026i	$-0.231579\pi$
$313$	7.93853e13	1.49364	0.746821	+	0.665026i	$0.231579\pi$
$314$	3.61774e13	0.668844
$315$	−1.32317e13	−0.240385
$316$	3.06158e13	0.546597
$317$	6.76251e13	1.18654	0.593269	−	0.805004i	$-0.297837\pi$
$317$	6.76251e13	1.18654	0.593269	+	0.805004i	$0.297837\pi$
$318$	−1.05176e13	−0.181371
$319$	1.12858e14	1.91286
$320$	−1.43157e13	−0.238500
$321$	−1.44886e13	−0.237273
$322$	−4.36339e12	−0.0702451
$323$	5.36426e13	0.848978
$324$	3.57047e12	0.0555556
$325$	1.24415e14	1.90333
$326$	−3.72899e13	−0.560911
$327$	−3.34622e13	−0.494927
$328$	1.93365e13	0.281236
$329$	3.99933e13	0.572019
$330$	−9.76788e13	−1.37396
$331$	−6.70678e13	−0.927813	−0.463906	−	0.885884i	$-0.653553\pi$
$331$	−6.70678e13	−0.927813	−0.463906	+	0.885884i	$0.653553\pi$
$332$	2.05381e12	0.0279448
$333$	1.72970e13	0.231488
$334$	3.79191e13	0.499175
$335$	6.05645e13	0.784281
$336$	−4.28249e12	−0.0545545
$337$	−3.74847e13	−0.469775	−0.234887	−	0.972023i	$-0.575472\pi$
$337$	−3.74847e13	−0.469775	−0.234887	+	0.972023i	$0.575472\pi$
$338$	−2.75504e13	−0.339692
$339$	−1.30586e12	−0.0158415
$340$	−6.43502e13	−0.768096
$341$	−2.39753e14	−2.81588
$342$	2.15048e13	0.248538
$343$	4.74756e12	0.0539949
$344$	−3.69781e13	−0.413879
$345$	−2.62847e13	−0.289533
$346$	2.29699e13	0.249024
$347$	−8.68785e13	−0.927044	−0.463522	−	0.886085i	$-0.653414\pi$
$347$	−8.68785e13	−0.927044	−0.463522	+	0.886085i	$0.653414\pi$
$348$	2.98062e13	0.313055
$349$	−3.59701e13	−0.371879	−0.185939	−	0.982561i	$-0.559533\pi$
$349$	−3.59701e13	−0.371879	−0.185939	+	0.982561i	$0.559533\pi$
$350$	6.93409e13	0.705692
$351$	−1.38466e13	−0.138725
$352$	−3.16141e13	−0.311815
$353$	1.74098e14	1.69057	0.845287	−	0.534313i	$-0.179430\pi$
$353$	1.74098e14	1.69057	0.845287	+	0.534313i	$0.179430\pi$
$354$	−6.33463e13	−0.605624
$355$	2.16518e14	2.03816
$356$	2.32861e13	0.215835
$357$	−1.92501e13	−0.175694
$358$	1.25473e14	1.12770
$359$	−2.02507e14	−1.79234	−0.896171	−	0.443709i	$-0.853662\pi$
$359$	−2.02507e14	−1.79234	−0.896171	+	0.443709i	$0.853662\pi$
$360$	−2.57974e13	−0.224860
$361$	1.30326e13	0.111878
$362$	1.26005e14	1.06535
$363$	−1.46379e14	−1.21896
$364$	1.66079e13	0.136225
$365$	1.94895e14	1.57467
$366$	7.10106e13	0.565167
$367$	4.73835e13	0.371504	0.185752	−	0.982597i	$-0.440528\pi$
$367$	4.73835e13	0.371504	0.185752	+	0.982597i	$0.440528\pi$
$368$	−8.50714e12	−0.0657083
$369$	3.48450e13	0.265152
$370$	−1.24975e14	−0.936941
$371$	2.27327e13	0.167917
$372$	−6.33196e13	−0.460842
$373$	1.10001e14	0.788853	0.394427	−	0.918927i	$-0.370943\pi$
$373$	1.10001e14	0.788853	0.394427	+	0.918927i	$0.370943\pi$
$374$	−1.42108e14	−1.00421
$375$	2.59510e14	1.80710
$376$	7.79736e13	0.535074
$377$	−1.15591e14	−0.781712
$378$	−7.71719e12	−0.0514344
$379$	−1.87150e14	−1.22934	−0.614672	−	0.788783i	$-0.710712\pi$
$379$	−1.87150e14	−1.22934	−0.614672	+	0.788783i	$0.710712\pi$
$380$	−1.55377e14	−1.00595
$381$	−5.96769e13	−0.380819
$382$	2.71111e13	0.170529
$383$	−7.14818e13	−0.443202	−0.221601	−	0.975137i	$-0.571128\pi$
$383$	−7.14818e13	−0.443202	−0.221601	+	0.975137i	$0.571128\pi$
$384$	−8.34942e12	−0.0510310
$385$	2.11122e14	1.27204
$386$	1.52201e14	0.904037
$387$	−6.66357e13	−0.390209
$388$	−4.80503e13	−0.277410
$389$	−2.21859e14	−1.26285	−0.631427	−	0.775435i	$-0.717531\pi$
$389$	−2.21859e14	−1.26285	−0.631427	+	0.775435i	$0.717531\pi$
$390$	1.00045e14	0.561485
$391$	−3.82402e13	−0.211616
$392$	9.25615e12	0.0505076
$393$	4.72525e13	0.254253
$394$	−6.05586e13	−0.321326
$395$	−3.98620e14	−2.08581
$396$	−5.69697e13	−0.293982
$397$	1.93118e14	0.982823	0.491411	−	0.870928i	$-0.336481\pi$
$397$	1.93118e14	0.982823	0.491411	+	0.870928i	$0.336481\pi$
$398$	−8.49502e13	−0.426391
$399$	−4.64804e13	−0.230101
$400$	1.35191e14	0.660114
$401$	−2.35185e14	−1.13270	−0.566351	−	0.824164i	$-0.691645\pi$
$401$	−2.35185e14	−1.13270	−0.566351	+	0.824164i	$0.691645\pi$
$402$	3.53233e13	0.167810
$403$	2.45559e14	1.15074
$404$	4.05734e13	0.187562
$405$	−4.64877e13	−0.212000
$406$	−6.44229e13	−0.289832
$407$	−2.75988e14	−1.22496
$408$	−3.75313e13	−0.164347
$409$	−6.53420e13	−0.282302	−0.141151	−	0.989988i	$-0.545080\pi$
$409$	−6.53420e13	−0.282302	−0.141151	+	0.989988i	$0.545080\pi$
$410$	−2.51762e14	−1.07320
$411$	−2.24667e14	−0.944951
$412$	−2.00570e14	−0.832397
$413$	1.36916e14	0.560699
$414$	−1.53301e13	−0.0619504
$415$	−2.67407e13	−0.106637
$416$	3.23798e13	0.127427
$417$	−1.43775e14	−0.558388
$418$	−3.43127e14	−1.31518
$419$	2.10835e14	0.797564	0.398782	−	0.917046i	$-0.369433\pi$
$419$	2.10835e14	0.797564	0.398782	+	0.917046i	$0.369433\pi$
$420$	5.57583e13	0.208180
$421$	−1.07833e14	−0.397374	−0.198687	−	0.980063i	$-0.563668\pi$
$421$	−1.07833e14	−0.397374	−0.198687	+	0.980063i	$0.563668\pi$
$422$	5.89443e13	0.214399
$423$	1.40511e14	0.504473
$424$	4.43211e13	0.157072
$425$	6.07695e14	2.12592
$426$	1.26281e14	0.436099
$427$	−1.53482e14	−0.523243
$428$	6.10547e13	0.205484
$429$	2.20934e14	0.734086
$430$	4.81457e14	1.57936
$431$	3.46201e14	1.12125	0.560626	−	0.828069i	$-0.310561\pi$
$431$	3.46201e14	1.12125	0.560626	+	0.828069i	$0.310561\pi$
$432$	−1.50459e13	−0.0481125
$433$	−1.25487e14	−0.396201	−0.198100	−	0.980182i	$-0.563477\pi$
$433$	−1.25487e14	−0.396201	−0.198100	+	0.980182i	$0.563477\pi$
$434$	1.36859e14	0.426657
$435$	−3.88078e14	−1.19462
$436$	1.41009e14	0.428620
$437$	−9.23329e13	−0.277146
$438$	1.13670e14	0.336928
$439$	3.02031e14	0.884091	0.442046	−	0.896993i	$-0.354253\pi$
$439$	3.02031e14	0.884091	0.442046	+	0.896993i	$0.354253\pi$
$440$	4.11618e14	1.18988
$441$	1.66799e13	0.0476190
$442$	1.45550e14	0.410382
$443$	−4.84691e14	−1.34972	−0.674861	−	0.737945i	$-0.735796\pi$
$443$	−4.84691e14	−1.34972	−0.674861	+	0.737945i	$0.735796\pi$
$444$	−7.28895e13	−0.200474
$445$	−3.03186e14	−0.823624
$446$	−1.88056e14	−0.504597
$447$	−2.91421e14	−0.772378
$448$	1.80464e13	0.0472456
$449$	−2.87545e13	−0.0743620	−0.0371810	−	0.999309i	$-0.511838\pi$
$449$	−2.87545e13	−0.0743620	−0.0371810	+	0.999309i	$0.511838\pi$
$450$	2.43619e14	0.622361
$451$	−5.55980e14	−1.40310
$452$	5.50286e12	0.0137192
$453$	−3.25430e13	−0.0801527
$454$	1.12117e14	0.272812
$455$	−2.16236e14	−0.519834
$456$	−9.06211e13	−0.215240
$457$	−9.40665e13	−0.220748	−0.110374	−	0.993890i	$-0.535205\pi$
$457$	−9.40665e13	−0.220748	−0.110374	+	0.993890i	$0.535205\pi$
$458$	4.37873e14	1.01529
$459$	−6.76325e13	−0.154948
$460$	1.10763e14	0.250743
$461$	2.11386e14	0.472847	0.236423	−	0.971650i	$-0.424025\pi$
$461$	2.11386e14	0.472847	0.236423	+	0.971650i	$0.424025\pi$
$462$	1.23134e14	0.272174
$463$	−6.35953e14	−1.38909	−0.694543	−	0.719451i	$-0.744394\pi$
$463$	−6.35953e14	−1.38909	−0.694543	+	0.719451i	$0.744394\pi$
$464$	−1.25603e14	−0.271113
$465$	8.24426e14	1.75857
$466$	−1.91072e14	−0.402786
$467$	−5.78281e14	−1.20475	−0.602374	−	0.798214i	$-0.705778\pi$
$467$	−5.78281e14	−1.20475	−0.602374	+	0.798214i	$0.705778\pi$
$468$	5.83494e13	0.120139
$469$	−7.63476e13	−0.155362
$470$	−1.01522e15	−2.04184
$471$	−2.74722e14	−0.546109
$472$	2.66941e14	0.524486
$473$	1.06323e15	2.06486
$474$	−2.32489e14	−0.446295
$475$	1.46731e15	2.78424
$476$	8.11198e13	0.152156
$477$	7.98680e13	0.148089
$478$	4.23307e14	0.775894
$479$	−2.32548e14	−0.421374	−0.210687	−	0.977554i	$-0.567570\pi$
$479$	−2.32548e14	−0.421374	−0.210687	+	0.977554i	$0.567570\pi$
$480$	1.08710e14	0.194734
$481$	2.82672e14	0.500593
$482$	6.46088e13	0.113118
$483$	3.31345e13	0.0573549
$484$	6.16838e14	1.05565
$485$	6.25618e14	1.05859
$486$	−2.71132e13	−0.0453609
$487$	−8.73747e14	−1.44536	−0.722681	−	0.691182i	$-0.757090\pi$
$487$	−8.73747e14	−1.44536	−0.722681	+	0.691182i	$0.757090\pi$
$488$	−2.99238e14	−0.489449
$489$	2.83170e14	0.457982
$490$	−1.20516e14	−0.192737
$491$	7.48940e14	1.18440	0.592200	−	0.805791i	$-0.298259\pi$
$491$	7.48940e14	1.18440	0.592200	+	0.805791i	$0.298259\pi$
$492$	−1.46836e14	−0.229629
$493$	−5.64595e14	−0.873130
$494$	3.51437e14	0.537464
$495$	7.41749e14	1.12183
$496$	2.66828e14	0.399101
$497$	−2.72943e14	−0.403749
$498$	−1.55961e13	−0.0228168
$499$	9.82984e13	0.142231	0.0711154	−	0.997468i	$-0.477344\pi$
$499$	9.82984e13	0.142231	0.0711154	+	0.997468i	$0.477344\pi$
$500$	−1.09357e15	−1.56499
$501$	−2.87948e14	−0.407574
$502$	−6.35535e14	−0.889752
$503$	2.00714e14	0.277942	0.138971	−	0.990296i	$-0.455620\pi$
$503$	2.00714e14	0.277942	0.138971	+	0.990296i	$0.455620\pi$
$504$	3.25202e13	0.0445435
$505$	−5.28269e14	−0.715735
$506$	2.44605e14	0.327821
$507$	2.09211e14	0.277357
$508$	2.51478e14	0.329799
$509$	1.35293e15	1.75521	0.877605	−	0.479385i	$-0.159140\pi$
$509$	1.35293e15	1.75521	0.877605	+	0.479385i	$0.159140\pi$
$510$	4.88659e14	0.627148
$511$	−2.45685e14	−0.311934
$512$	3.51844e13	0.0441942
$513$	−1.63302e14	−0.202930
$514$	6.18022e14	0.759814
$515$	2.61143e15	3.17642
$516$	2.80802e14	0.337931
$517$	−2.24196e15	−2.66950
$518$	1.57543e14	0.185603
$519$	−1.74428e14	−0.203327
$520$	−4.21587e14	−0.486260
$521$	−1.09487e15	−1.24956	−0.624778	−	0.780803i	$-0.714810\pi$
$521$	−1.09487e15	−1.24956	−0.624778	+	0.780803i	$0.714810\pi$
$522$	−2.26341e14	−0.255608
$523$	−3.36352e14	−0.375868	−0.187934	−	0.982182i	$-0.560179\pi$
$523$	−3.36352e14	−0.375868	−0.187934	+	0.982182i	$0.560179\pi$
$524$	−1.99122e14	−0.220190
$525$	−5.26557e14	−0.576195
$526$	−7.31842e14	−0.792494
$527$	1.19941e15	1.28532
$528$	2.40070e14	0.254596
$529$	−8.86988e14	−0.930919
$530$	−5.77063e14	−0.599385
$531$	4.81036e14	0.494490
$532$	1.95868e14	0.199273
$533$	5.69445e14	0.573393
$534$	−1.76829e14	−0.176228
$535$	−7.94936e14	−0.784127
$536$	−1.48852e14	−0.145328
$537$	−9.52807e14	−0.920760
$538$	−8.71551e14	−0.833663
$539$	−2.66141e14	−0.251984
$540$	1.95899e14	0.183597
$541$	1.87131e15	1.73604	0.868022	−	0.496526i	$-0.165391\pi$
$541$	1.87131e15	1.73604	0.868022	+	0.496526i	$0.165391\pi$
$542$	−7.81739e14	−0.717903
$543$	−9.56850e14	−0.869851
$544$	1.58156e14	0.142329
$545$	−1.83595e15	−1.63561
$546$	−1.26116e14	−0.111227
$547$	9.92908e14	0.866919	0.433459	−	0.901173i	$-0.357293\pi$
$547$	9.92908e14	0.866919	0.433459	+	0.901173i	$0.357293\pi$
$548$	9.46745e14	0.818352
$549$	−5.39237e14	−0.461457
$550$	−3.88714e15	−3.29333
$551$	−1.36324e15	−1.14351
$552$	6.46011e13	0.0536506
$553$	5.02500e14	0.413188
$554$	7.54364e14	0.614154
$555$	9.49026e14	0.765009
$556$	6.05868e14	0.483578
$557$	−1.46331e15	−1.15647	−0.578234	−	0.815871i	$-0.696258\pi$
$557$	−1.46331e15	−1.15647	−0.578234	+	0.815871i	$0.696258\pi$
$558$	4.80834e14	0.376276
$559$	−1.08898e15	−0.843828
$560$	−2.34965e14	−0.180289
$561$	1.07913e15	0.819934
$562$	−4.22726e14	−0.318060
$563$	1.97309e15	1.47011	0.735056	−	0.678006i	$-0.237156\pi$
$563$	1.97309e15	1.47011	0.735056	+	0.678006i	$0.237156\pi$
$564$	−5.92112e14	−0.436886
$565$	−7.16476e13	−0.0523522
$566$	5.30361e14	0.383779
$567$	5.86024e13	0.0419961
$568$	−5.32147e14	−0.377673
$569$	1.47960e15	1.03999	0.519993	−	0.854170i	$-0.325934\pi$
$569$	1.47960e15	1.03999	0.519993	+	0.854170i	$0.325934\pi$
$570$	1.17989e15	0.821355
$571$	−5.01296e14	−0.345617	−0.172809	−	0.984955i	$-0.555284\pi$
$571$	−5.01296e14	−0.345617	−0.172809	+	0.984955i	$0.555284\pi$
$572$	−9.31012e14	−0.635737
$573$	−2.05875e14	−0.139236
$574$	3.17371e14	0.212595
$575$	−1.04600e15	−0.694000
$576$	6.34034e13	0.0416667
$577$	1.47089e15	0.957446	0.478723	−	0.877966i	$-0.341100\pi$
$577$	1.47089e15	0.957446	0.478723	+	0.877966i	$0.341100\pi$
$578$	−3.85776e14	−0.248732
$579$	−1.15577e15	−0.738143
$580$	1.63536e15	1.03457
$581$	3.37093e13	0.0211243
$582$	3.64882e14	0.226504
$583$	−1.27436e15	−0.783637
$584$	−4.79003e14	−0.291788
$585$	−7.59713e14	−0.458450
$586$	−1.19796e15	−0.716154
$587$	−4.07703e12	−0.00241454	−0.00120727	−	0.999999i	$-0.500384\pi$
$587$	−4.07703e12	−0.00241454	−0.00120727	+	0.999999i	$0.500384\pi$
$588$	−7.02889e13	−0.0412393
$589$	2.89605e15	1.68334
$590$	−3.47558e15	−2.00144
$591$	4.59867e14	0.262362
$592$	3.07156e14	0.173616
$593$	1.27454e15	0.713760	0.356880	−	0.934150i	$-0.383841\pi$
$593$	1.27454e15	0.713760	0.356880	+	0.934150i	$0.383841\pi$
$594$	4.32614e14	0.240035
$595$	−1.05618e15	−0.580626
$596$	1.22805e15	0.668899
$597$	6.45091e14	0.348146
$598$	−2.50529e14	−0.133968
$599$	2.17309e15	1.15141	0.575706	−	0.817657i	$-0.304727\pi$
$599$	2.17309e15	1.15141	0.575706	+	0.817657i	$0.304727\pi$
$600$	−1.02661e15	−0.538981
$601$	−7.15146e14	−0.372036	−0.186018	−	0.982546i	$-0.559558\pi$
$601$	−7.15146e14	−0.372036	−0.186018	+	0.982546i	$0.559558\pi$
$602$	−6.06925e14	−0.312863
$603$	−2.68236e14	−0.137016
$604$	1.37136e14	0.0694143
$605$	−8.03127e15	−4.02837
$606$	−3.08105e14	−0.153144
$607$	1.32744e15	0.653848	0.326924	−	0.945051i	$-0.393988\pi$
$607$	1.32744e15	0.653848	0.326924	+	0.945051i	$0.393988\pi$
$608$	3.81877e14	0.186403
$609$	4.89211e14	0.236647
$610$	3.89610e15	1.86774
$611$	2.29626e15	1.09092
$612$	2.85003e14	0.134189
$613$	3.33889e15	1.55801	0.779003	−	0.627021i	$-0.215726\pi$
$613$	3.33889e15	1.55801	0.779003	+	0.627021i	$0.215726\pi$
$614$	−6.82023e14	−0.315408
$615$	1.91182e15	0.876261
$616$	−5.18885e14	−0.235710
$617$	1.01248e15	0.455845	0.227922	−	0.973679i	$-0.426807\pi$
$617$	1.01248e15	0.455845	0.227922	+	0.973679i	$0.426807\pi$
$618$	1.52308e15	0.679649
$619$	−1.74701e15	−0.772677	−0.386338	−	0.922357i	$-0.626260\pi$
$619$	−1.74701e15	−0.772677	−0.386338	+	0.922357i	$0.626260\pi$
$620$	−3.47412e15	−1.52297
$621$	1.16413e14	0.0505823
$622$	2.75100e15	1.18480
$623$	3.82196e14	0.163156
$624$	−2.45884e14	−0.104044
$625$	7.94304e15	3.33155
$626$	2.54033e15	1.05616
$627$	2.60562e15	1.07384
$628$	1.15768e15	0.472944
$629$	1.38069e15	0.559136
$630$	−4.23414e14	−0.169978
$631$	−1.02070e15	−0.406196	−0.203098	−	0.979158i	$-0.565101\pi$
$631$	−1.02070e15	−0.406196	−0.203098	+	0.979158i	$0.565101\pi$
$632$	9.79707e14	0.386502
$633$	−4.47608e14	−0.175056
$634$	2.16400e15	0.839009
$635$	−3.27426e15	−1.25851
$636$	−3.36563e14	−0.128249
$637$	2.72587e14	0.102976
$638$	3.61145e15	1.35259
$639$	−9.58946e14	−0.356073
$640$	−4.58103e14	−0.168645
$641$	1.04132e15	0.380071	0.190035	−	0.981777i	$-0.439140\pi$
$641$	1.04132e15	0.380071	0.190035	+	0.981777i	$0.439140\pi$
$642$	−4.63634e14	−0.167777
$643$	−2.11500e14	−0.0758838	−0.0379419	−	0.999280i	$-0.512080\pi$
$643$	−2.11500e14	−0.0758838	−0.0379419	+	0.999280i	$0.512080\pi$
$644$	−1.39628e14	−0.0496708
$645$	−3.65606e15	−1.28954
$646$	1.71656e15	0.600318
$647$	−1.73431e15	−0.601387	−0.300693	−	0.953721i	$-0.597218\pi$
$647$	−1.73431e15	−0.601387	−0.300693	+	0.953721i	$0.597218\pi$
$648$	1.14255e14	0.0392837
$649$	−7.67531e15	−2.61668
$650$	3.98128e15	1.34586
$651$	−1.03927e15	−0.348364
$652$	−1.19328e15	−0.396624
$653$	−3.27517e15	−1.07947	−0.539735	−	0.841835i	$-0.681476\pi$
$653$	−3.27517e15	−1.07947	−0.539735	+	0.841835i	$0.681476\pi$
$654$	−1.07079e15	−0.349967
$655$	2.59258e15	0.840242
$656$	6.18768e14	0.198864
$657$	−8.63179e14	−0.275100
$658$	1.27979e15	0.404478
$659$	1.56825e15	0.491525	0.245763	−	0.969330i	$-0.420962\pi$
$659$	1.56825e15	0.491525	0.245763	+	0.969330i	$0.420962\pi$
$660$	−3.12572e15	−0.971536
$661$	3.82080e15	1.17773	0.588865	−	0.808231i	$-0.299575\pi$
$661$	3.82080e15	1.17773	0.588865	+	0.808231i	$0.299575\pi$
$662$	−2.14617e15	−0.656063
$663$	−1.10527e15	−0.335076
$664$	6.57219e13	0.0197599
$665$	−2.55021e15	−0.760427
$666$	5.53505e14	0.163687
$667$	9.71814e14	0.285030
$668$	1.21341e15	0.352970
$669$	1.42805e15	0.412002
$670$	1.93806e15	0.554571
$671$	8.60395e15	2.44188
$672$	−1.37040e14	−0.0385758
$673$	−1.86527e15	−0.520784	−0.260392	−	0.965503i	$-0.583852\pi$
$673$	−1.86527e15	−0.520784	−0.260392	+	0.965503i	$0.583852\pi$
$674$	−1.19951e15	−0.332181
$675$	−1.84998e15	−0.508156
$676$	−8.81612e14	−0.240199
$677$	−7.74999e14	−0.209442	−0.104721	−	0.994502i	$-0.533395\pi$
$677$	−7.74999e14	−0.209442	−0.104721	+	0.994502i	$0.533395\pi$
$678$	−4.17874e13	−0.0112016
$679$	−7.88654e14	−0.209702
$680$	−2.05921e15	−0.543126
$681$	−8.51387e14	−0.222750
$682$	−7.67209e15	−1.99113
$683$	2.01384e15	0.518454	0.259227	−	0.965816i	$-0.416532\pi$
$683$	2.01384e15	0.518454	0.259227	+	0.965816i	$0.416532\pi$
$684$	6.88154e14	0.175743
$685$	−1.23267e16	−3.12283
$686$	1.51922e14	0.0381802
$687$	−3.32510e15	−0.828977
$688$	−1.18330e15	−0.292656
$689$	1.30522e15	0.320242
$690$	−8.41110e14	−0.204731
$691$	−3.69003e15	−0.891048	−0.445524	−	0.895270i	$-0.646983\pi$
$691$	−3.69003e15	−0.891048	−0.445524	+	0.895270i	$0.646983\pi$
$692$	7.35038e14	0.176087
$693$	−9.35048e14	−0.222229
$694$	−2.78011e15	−0.655519
$695$	−7.88843e15	−1.84533
$696$	9.53797e14	0.221363
$697$	2.78141e15	0.640449
$698$	−1.15104e15	−0.262958
$699$	1.45095e15	0.328873
$700$	2.21891e15	0.498999
$701$	−3.75954e15	−0.838853	−0.419427	−	0.907789i	$-0.637769\pi$
$701$	−3.75954e15	−0.838853	−0.419427	+	0.907789i	$0.637769\pi$
$702$	−4.43091e14	−0.0980932
$703$	3.33374e15	0.732281
$704$	−1.01165e15	−0.220486
$705$	7.70933e15	1.66716
$706$	5.57115e15	1.19542
$707$	6.65935e14	0.141783
$708$	−2.02708e15	−0.428241
$709$	3.70373e15	0.776398	0.388199	−	0.921575i	$-0.373097\pi$
$709$	3.70373e15	0.776398	0.388199	+	0.921575i	$0.373097\pi$
$710$	6.92859e15	1.44120
$711$	1.76546e15	0.364398
$712$	7.45154e14	0.152618
$713$	−2.06450e15	−0.419588
$714$	−6.16004e14	−0.124235
$715$	1.21218e16	2.42597
$716$	4.01512e15	0.797402
$717$	−3.21449e15	−0.633515
$718$	−6.48023e15	−1.26738
$719$	2.83631e15	0.550485	0.275242	−	0.961375i	$-0.411242\pi$
$719$	2.83631e15	0.550485	0.275242	+	0.961375i	$0.411242\pi$
$720$	−8.25516e14	−0.159000
$721$	−3.29197e15	−0.629233
$722$	4.17044e14	0.0791093
$723$	−4.90623e14	−0.0923608
$724$	4.03216e15	0.753313
$725$	−1.54436e16	−2.86345
$726$	−4.68411e15	−0.861938
$727$	1.93703e15	0.353751	0.176875	−	0.984233i	$-0.443401\pi$
$727$	1.93703e15	0.353751	0.176875	+	0.984233i	$0.443401\pi$
$728$	5.31452e14	0.0963256
$729$	2.05891e14	0.0370370
$730$	6.23665e15	1.11346
$731$	−5.31902e15	−0.942510
$732$	2.27234e15	0.399634
$733$	1.06583e16	1.86044	0.930222	−	0.366997i	$-0.119614\pi$
$733$	1.06583e16	1.86044	0.930222	+	0.366997i	$0.119614\pi$
$734$	1.51627e15	0.262693
$735$	9.15165e14	0.157369
$736$	−2.72228e14	−0.0464628
$737$	4.27993e15	0.725046
$738$	1.11504e15	0.187491
$739$	−7.46006e15	−1.24508	−0.622541	−	0.782588i	$-0.713899\pi$
$739$	−7.46006e15	−1.24508	−0.622541	+	0.782588i	$0.713899\pi$
$740$	−3.99919e15	−0.662517
$741$	−2.66872e15	−0.438837
$742$	7.27446e14	0.118735
$743$	−5.09128e15	−0.824876	−0.412438	−	0.910986i	$-0.635323\pi$
$743$	−5.09128e15	−0.824876	−0.412438	+	0.910986i	$0.635323\pi$
$744$	−2.02623e15	−0.325865
$745$	−1.59892e16	−2.55251
$746$	3.52002e15	0.557803
$747$	1.18433e14	0.0186299
$748$	−4.54745e15	−0.710083
$749$	1.00210e15	0.155332
$750$	8.30431e15	1.27781
$751$	7.54756e15	1.15289	0.576444	−	0.817137i	$-0.304440\pi$
$751$	7.54756e15	1.15289	0.576444	+	0.817137i	$0.304440\pi$
$752$	2.49515e15	0.378355
$753$	4.82609e15	0.726479
$754$	−3.69891e15	−0.552754
$755$	−1.78552e15	−0.264885
$756$	−2.46950e14	−0.0363696
$757$	−5.56380e15	−0.813475	−0.406737	−	0.913545i	$-0.633334\pi$
$757$	−5.56380e15	−0.813475	−0.406737	+	0.913545i	$0.633334\pi$
$758$	−5.98879e15	−0.869277
$759$	−1.85747e15	−0.267665
$760$	−4.97206e15	−0.711314
$761$	−6.47250e15	−0.919298	−0.459649	−	0.888101i	$-0.652025\pi$
$761$	−6.47250e15	−0.919298	−0.459649	+	0.888101i	$0.652025\pi$
$762$	−1.90966e15	−0.269280
$763$	2.31440e15	0.324006
$764$	8.67554e14	0.120582
$765$	−3.71076e15	−0.512064
$766$	−2.28742e15	−0.313391
$767$	7.86120e15	1.06934
$768$	−2.67181e14	−0.0360844
$769$	−1.11739e16	−1.49834	−0.749169	−	0.662379i	$-0.769547\pi$
$769$	−1.11739e16	−1.49834	−0.749169	+	0.662379i	$0.769547\pi$
$770$	6.75592e15	0.899467
$771$	−4.69311e15	−0.620385
$772$	4.87042e15	0.639251
$773$	1.18139e16	1.53960	0.769799	−	0.638286i	$-0.220356\pi$
$773$	1.18139e16	1.53960	0.769799	+	0.638286i	$0.220356\pi$
$774$	−2.13234e15	−0.275919
$775$	3.28081e16	4.21524
$776$	−1.53761e15	−0.196158
$777$	−1.19634e15	−0.151544
$778$	−7.09947e15	−0.892973
$779$	6.71585e15	0.838774
$780$	3.20142e15	0.397030
$781$	1.53008e16	1.88422
$782$	−1.22369e15	−0.149635
$783$	1.71877e15	0.208703
$784$	2.96197e14	0.0357143
$785$	−1.50730e16	−1.80475
$786$	1.51208e15	0.179784
$787$	−1.37519e16	−1.62368	−0.811841	−	0.583879i	$-0.801534\pi$
$787$	−1.37519e16	−1.62368	−0.811841	+	0.583879i	$0.801534\pi$
$788$	−1.93787e15	−0.227212
$789$	5.55743e15	0.647068
$790$	−1.27558e16	−1.47489
$791$	9.03190e13	0.0103707
$792$	−1.82303e15	−0.207876
$793$	−8.81233e15	−0.997903
$794$	6.17978e15	0.694961
$795$	4.38207e15	0.489396
$796$	−2.71841e15	−0.301504
$797$	8.06181e15	0.887998	0.443999	−	0.896027i	$-0.353559\pi$
$797$	8.06181e15	0.887998	0.443999	+	0.896027i	$0.353559\pi$
$798$	−1.48737e15	−0.162706
$799$	1.12159e16	1.21850
$800$	4.32612e15	0.466771
$801$	1.34279e15	0.143890
$802$	−7.52593e15	−0.800942
$803$	1.37727e16	1.45574
$804$	1.13035e15	0.118660
$805$	1.81797e15	0.189544
$806$	7.85790e15	0.813699
$807$	6.61834e15	0.680683
$808$	1.29835e15	0.132626
$809$	−1.17570e15	−0.119283	−0.0596414	−	0.998220i	$-0.518996\pi$
$809$	−1.17570e15	−0.119283	−0.0596414	+	0.998220i	$0.518996\pi$
$810$	−1.48761e15	−0.149906
$811$	−9.38568e15	−0.939401	−0.469700	−	0.882826i	$-0.655638\pi$
$811$	−9.38568e15	−0.939401	−0.469700	+	0.882826i	$0.655638\pi$
$812$	−2.06153e15	−0.204942
$813$	5.93633e15	0.586165
$814$	−8.83161e15	−0.866175
$815$	1.55365e16	1.51352
$816$	−1.20100e15	−0.116211
$817$	−1.28430e16	−1.23437
$818$	−2.09094e15	−0.199618
$819$	9.57694e14	0.0908166
$820$	−8.05639e15	−0.758865
$821$	−6.18260e15	−0.578474	−0.289237	−	0.957257i	$-0.593402\pi$
$821$	−6.18260e15	−0.578474	−0.289237	+	0.957257i	$0.593402\pi$
$822$	−7.18934e15	−0.668181
$823$	−4.01768e15	−0.370917	−0.185458	−	0.982652i	$-0.559377\pi$
$823$	−4.01768e15	−0.370917	−0.185458	+	0.982652i	$0.559377\pi$
$824$	−6.41823e15	−0.588594
$825$	2.95180e16	2.68899
$826$	4.38132e15	0.396474
$827$	7.52839e14	0.0676740	0.0338370	−	0.999427i	$-0.489227\pi$
$827$	7.52839e14	0.0676740	0.0338370	+	0.999427i	$0.489227\pi$
$828$	−4.90564e14	−0.0438055
$829$	2.04085e16	1.81035	0.905173	−	0.425044i	$-0.139741\pi$
$829$	2.04085e16	1.81035	0.905173	+	0.425044i	$0.139741\pi$
$830$	−8.55703e14	−0.0754039
$831$	−5.72845e15	−0.501455
$832$	1.03615e15	0.0901043
$833$	1.33143e15	0.115019
$834$	−4.60081e15	−0.394840
$835$	−1.57987e16	−1.34693
$836$	−1.09801e16	−0.929972
$837$	−3.65133e15	−0.307228
$838$	6.74672e15	0.563963
$839$	−1.04297e16	−0.866128	−0.433064	−	0.901363i	$-0.642568\pi$
$839$	−1.04297e16	−0.866128	−0.433064	+	0.901363i	$0.642568\pi$
$840$	1.78426e15	0.147205
$841$	2.14777e15	0.176039
$842$	−3.45065e15	−0.280986
$843$	3.21007e15	0.259695
$844$	1.88622e15	0.151603
$845$	1.14786e16	0.916597
$846$	4.49635e15	0.356716
$847$	1.01242e16	0.798000
$848$	1.41827e15	0.111067
$849$	−4.02743e15	−0.313355
$850$	1.94462e16	1.50325
$851$	−2.37652e15	−0.182528
$852$	4.04099e15	0.308369
$853$	4.62836e15	0.350920	0.175460	−	0.984487i	$-0.443859\pi$
$853$	4.62836e15	0.350920	0.175460	+	0.984487i	$0.443859\pi$
$854$	−4.91142e15	−0.369989
$855$	−8.95981e15	−0.670633
$856$	1.95375e15	0.145299
$857$	1.98113e16	1.46392	0.731962	−	0.681346i	$-0.238605\pi$
$857$	1.98113e16	1.46392	0.731962	+	0.681346i	$0.238605\pi$
$858$	7.06988e15	0.519077
$859$	−1.62985e16	−1.18901	−0.594504	−	0.804092i	$-0.702652\pi$
$859$	−1.62985e16	−1.18901	−0.594504	+	0.804092i	$0.702652\pi$
$860$	1.54066e16	1.11678
$861$	−2.41004e15	−0.173583
$862$	1.10784e16	0.792844
$863$	−5.19049e15	−0.369104	−0.184552	−	0.982823i	$-0.559083\pi$
$863$	−5.19049e15	−0.369104	−0.184552	+	0.982823i	$0.559083\pi$
$864$	−4.81469e14	−0.0340207
$865$	−9.57024e15	−0.671946
$866$	−4.01559e15	−0.280156
$867$	2.92948e15	0.203089
$868$	4.37948e15	0.301692
$869$	−2.81694e16	−1.92827
$870$	−1.24185e16	−0.844721
$871$	−4.38359e15	−0.296299
$872$	4.51230e15	0.303080
$873$	−2.77082e15	−0.184940
$874$	−2.95465e15	−0.195972
$875$	−1.79489e16	−1.18302
$876$	3.63743e15	0.238244
$877$	−1.19437e16	−0.777391	−0.388696	−	0.921366i	$-0.627074\pi$
$877$	−1.19437e16	−0.777391	−0.388696	+	0.921366i	$0.627074\pi$
$878$	9.66500e15	0.625147
$879$	9.09702e15	0.584737
$880$	1.31718e16	0.841375
$881$	2.05626e16	1.30530	0.652652	−	0.757658i	$-0.273656\pi$
$881$	2.05626e16	1.30530	0.652652	+	0.757658i	$0.273656\pi$
$882$	5.33756e14	0.0336718
$883$	−9.10836e15	−0.571026	−0.285513	−	0.958375i	$-0.592164\pi$
$883$	−9.10836e15	−0.571026	−0.285513	+	0.958375i	$0.592164\pi$
$884$	4.65759e15	0.290184
$885$	2.63927e16	1.63417
$886$	−1.55101e16	−0.954397
$887$	9.02318e15	0.551797	0.275899	−	0.961187i	$-0.411025\pi$
$887$	9.02318e15	0.551797	0.275899	+	0.961187i	$0.411025\pi$
$888$	−2.33246e15	−0.141757
$889$	4.12753e15	0.249305
$890$	−9.70195e15	−0.582390
$891$	−3.28516e15	−0.195988
$892$	−6.01778e15	−0.356804
$893$	2.70814e16	1.59583
$894$	−9.32548e15	−0.546153
$895$	−5.22771e16	−3.04288
$896$	5.77484e14	0.0334077
$897$	1.90245e15	0.109384
$898$	−9.20144e14	−0.0525819
$899$	−3.04812e16	−1.73123
$900$	7.79581e15	0.440076
$901$	6.37525e15	0.357693
$902$	−1.77914e16	−0.992140
$903$	4.60883e15	0.255452
$904$	1.76092e14	0.00970091
$905$	−5.24989e16	−2.87464
$906$	−1.04138e15	−0.0566765
$907$	1.07100e16	0.579360	0.289680	−	0.957124i	$-0.406451\pi$
$907$	1.07100e16	0.579360	0.289680	+	0.957124i	$0.406451\pi$
$908$	3.58774e15	0.192907
$909$	2.33967e15	0.125041
$910$	−6.91954e15	−0.367578
$911$	−1.40721e16	−0.743030	−0.371515	−	0.928427i	$-0.621162\pi$
$911$	−1.40721e16	−0.743030	−0.371515	+	0.928427i	$0.621162\pi$
$912$	−2.89988e15	−0.152198
$913$	−1.88969e15	−0.0985830
$914$	−3.01013e15	−0.156092
$915$	−2.95860e16	−1.52500
$916$	1.40119e16	0.717915
$917$	−3.26820e15	−0.166448
$918$	−2.16424e15	−0.109565
$919$	−1.80497e16	−0.908311	−0.454156	−	0.890922i	$-0.650059\pi$
$919$	−1.80497e16	−0.908311	−0.454156	+	0.890922i	$0.650059\pi$
$920$	3.54443e15	0.177302
$921$	5.17911e15	0.257530
$922$	6.76434e15	0.334353
$923$	−1.56713e16	−0.770010
$924$	3.94029e15	0.192456
$925$	3.77666e16	1.83370
$926$	−2.03505e16	−0.982233
$927$	−1.15659e16	−0.554931
$928$	−4.01929e15	−0.191706
$929$	−4.98042e15	−0.236145	−0.118073	−	0.993005i	$-0.537672\pi$
$929$	−4.98042e15	−0.236145	−0.118073	+	0.993005i	$0.537672\pi$
$930$	2.63816e16	1.24350
$931$	3.21480e15	0.150637
$932$	−6.11430e15	−0.284813
$933$	−2.08904e16	−0.967382
$934$	−1.85050e16	−0.851885
$935$	5.92081e16	2.70968
$936$	1.86718e15	0.0849512
$937$	7.40349e15	0.334864	0.167432	−	0.985884i	$-0.446452\pi$
$937$	7.40349e15	0.334864	0.167432	+	0.985884i	$0.446452\pi$
$938$	−2.44312e15	−0.109858
$939$	−1.92906e16	−0.862354
$940$	−3.24870e16	−1.44380
$941$	4.67123e15	0.206390	0.103195	−	0.994661i	$-0.467093\pi$
$941$	4.67123e15	0.206390	0.103195	+	0.994661i	$0.467093\pi$
$942$	−8.79112e15	−0.386157
$943$	−4.78753e15	−0.209072
$944$	8.54210e15	0.370867
$945$	3.21530e15	0.138786
$946$	3.40233e16	1.46007
$947$	3.17364e16	1.35404	0.677021	−	0.735963i	$-0.263270\pi$
$947$	3.17364e16	1.35404	0.677021	+	0.735963i	$0.263270\pi$
$948$	−7.43965e15	−0.315578
$949$	−1.41063e16	−0.594906
$950$	4.69540e16	1.96876
$951$	−1.64329e16	−0.685048
$952$	2.59583e15	0.107590
$953$	2.11673e16	0.872279	0.436139	−	0.899879i	$-0.356345\pi$
$953$	2.11673e16	0.872279	0.436139	+	0.899879i	$0.356345\pi$
$954$	2.55578e15	0.104715
$955$	−1.12956e16	−0.460141
$956$	1.35458e16	0.548640
$957$	−2.74244e16	−1.10439
$958$	−7.44155e15	−0.297957
$959$	1.55390e16	0.618616
$960$	3.47872e15	0.137698
$961$	3.93452e16	1.54851
$962$	9.04551e15	0.353973
$963$	3.52072e15	0.136990
$964$	2.06748e15	0.0799868
$965$	−6.34132e16	−2.43938
$966$	1.06030e15	0.0405561
$967$	3.50734e16	1.33393	0.666963	−	0.745091i	$-0.267594\pi$
$967$	3.50734e16	1.33393	0.666963	+	0.745091i	$0.267594\pi$
$968$	1.97388e16	0.746460
$969$	−1.30352e16	−0.490157
$970$	2.00198e16	0.748539
$971$	1.54954e16	0.576099	0.288049	−	0.957616i	$-0.406993\pi$
$971$	1.54954e16	0.576099	0.288049	+	0.957616i	$0.406993\pi$
$972$	−8.67624e14	−0.0320750
$973$	9.94416e15	0.365551
$974$	−2.79599e16	−1.02203
$975$	−3.02329e16	−1.09889
$976$	−9.57562e15	−0.346093
$977$	6.90269e15	0.248084	0.124042	−	0.992277i	$-0.460414\pi$
$977$	6.90269e15	0.248084	0.124042	+	0.992277i	$0.460414\pi$
$978$	9.06144e15	0.323842
$979$	−2.14253e16	−0.761417
$980$	−3.85650e15	−0.136286
$981$	8.13131e15	0.285747
$982$	2.39661e16	0.837498
$983$	2.01691e16	0.700877	0.350438	−	0.936586i	$-0.386033\pi$
$983$	2.01691e16	0.700877	0.350438	+	0.936586i	$0.386033\pi$
$984$	−4.69877e15	−0.162372
$985$	2.52312e16	0.867040
$986$	−1.80670e16	−0.617396
$987$	−9.71838e15	−0.330255
$988$	1.12460e16	0.380044
$989$	9.15542e15	0.307679
$990$	2.37360e16	0.793256
$991$	−3.76304e16	−1.25064	−0.625322	−	0.780367i	$-0.715032\pi$
$991$	−3.76304e16	−1.25064	−0.625322	+	0.780367i	$0.715032\pi$
$992$	8.53851e15	0.282207
$993$	1.62975e16	0.535673
$994$	−8.73417e15	−0.285494
$995$	3.53938e16	1.15054
$996$	−4.99076e14	−0.0161339
$997$	−1.38219e16	−0.444371	−0.222185	−	0.975004i	$-0.571319\pi$
$997$	−1.38219e16	−0.444371	−0.222185	+	0.975004i	$0.571319\pi$
$998$	3.14555e15	0.100572
$999$	−4.20318e15	−0.133650

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.12.a.g.1.1	✓	2
3.2	odd	2		126.12.a.k.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.12.a.g.1.1	✓	2	1.1	even	1	trivial
126.12.a.k.1.2		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	42.a (trivial)

\(f(q)\)	\(=\)	\(q+32.0000 q^{2} -243.000 q^{3} +1024.00 q^{4} -13332.5 q^{5} -7776.00 q^{6} +16807.0 q^{7} +32768.0 q^{8} +59049.0 q^{9} -426641. q^{10} -942174. q^{11} -248832. q^{12} +964993. q^{13} +537824. q^{14} +3.23981e6 q^{15} +1.04858e6 q^{16} +4.71343e6 q^{17} +1.88957e6 q^{18} +1.13808e7 q^{19} -1.36525e7 q^{20} -4.08410e6 q^{21} -3.01496e7 q^{22} -8.11304e6 q^{23} -7.96262e6 q^{24} +1.28929e8 q^{25} +3.08798e7 q^{26} -1.43489e7 q^{27} +1.72104e7 q^{28} -1.19784e8 q^{29} +1.03674e8 q^{30} +2.54467e8 q^{31} +3.35544e7 q^{32} +2.28948e8 q^{33} +1.50830e8 q^{34} -2.24080e8 q^{35} +6.04662e7 q^{36} +2.92927e8 q^{37} +3.64186e8 q^{38} -2.34493e8 q^{39} -4.36881e8 q^{40} +5.90103e8 q^{41} -1.30691e8 q^{42} -1.12848e9 q^{43} -9.64787e8 q^{44} -7.87273e8 q^{45} -2.59617e8 q^{46} +2.37956e9 q^{47} -2.54804e8 q^{48} +2.82475e8 q^{49} +4.12571e9 q^{50} -1.14536e9 q^{51} +9.88153e8 q^{52} +1.35257e9 q^{53} -4.59165e8 q^{54} +1.25616e10 q^{55} +5.50732e8 q^{56} -2.76554e9 q^{57} -3.83310e9 q^{58} +8.14638e9 q^{59} +3.31756e9 q^{60} -9.13202e9 q^{61} +8.14296e9 q^{62} +9.92437e8 q^{63} +1.07374e9 q^{64} -1.28658e10 q^{65} +7.32635e9 q^{66} -4.54261e9 q^{67} +4.82655e9 q^{68} +1.97147e9 q^{69} -7.17056e9 q^{70} -1.62398e10 q^{71} +1.93492e9 q^{72} -1.46180e10 q^{73} +9.37365e9 q^{74} -3.13296e10 q^{75} +1.16540e10 q^{76} -1.58351e10 q^{77} -7.50379e9 q^{78} +2.98983e10 q^{79} -1.39802e10 q^{80} +3.48678e9 q^{81} +1.88833e10 q^{82} +2.00567e9 q^{83} -4.18212e9 q^{84} -6.28420e10 q^{85} -3.61114e10 q^{86} +2.91076e10 q^{87} -3.08732e10 q^{88} +2.27403e10 q^{89} -2.51927e10 q^{90} +1.62186e10 q^{91} -8.30775e9 q^{92} -6.18356e10 q^{93} +7.61460e10 q^{94} -1.51735e11 q^{95} -8.15373e9 q^{96} -4.69241e10 q^{97} +9.03921e9 q^{98} -5.56345e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 64 q^{2} - 486 q^{3} + 2048 q^{4} - 1032 q^{5} - 15552 q^{6} + 33614 q^{7} + 65536 q^{8} + 118098 q^{9} - 33024 q^{10} - 1294788 q^{11} - 497664 q^{12} + 2545180 q^{13} + 1075648 q^{14} + 250776 q^{15}+ \cdots - 76455936612 q^{99}+O(q^{100}) \) 2 * q + 64 * q^2 - 486 * q^3 + 2048 * q^4 - 1032 * q^5 - 15552 * q^6 + 33614 * q^7 + 65536 * q^8 + 118098 * q^9 - 33024 * q^10 - 1294788 * q^11 - 497664 * q^12 + 2545180 * q^13 + 1075648 * q^14 + 250776 * q^15 + 2097152 * q^16 + 2223960 * q^17 + 3779136 * q^18 - 4768304 * q^19 - 1056768 * q^20 - 8168202 * q^21 - 41433216 * q^22 + 37167636 * q^23 - 15925248 * q^24 + 231403694 * q^25 + 81445760 * q^26 - 28697814 * q^27 + 34420736 * q^28 + 50444100 * q^29 + 8024832 * q^30 + 240248968 * q^31 + 67108864 * q^32 + 314633484 * q^33 + 71166720 * q^34 - 17344824 * q^35 + 120932352 * q^36 + 482808172 * q^37 - 152585728 * q^38 - 618478740 * q^39 - 33816576 * q^40 + 826289568 * q^41 - 261382464 * q^42 - 1418762312 * q^43 - 1325862912 * q^44 - 60938568 * q^45 + 1189364352 * q^46 + 4558113192 * q^47 - 509607936 * q^48 + 564950498 * q^49 + 7404918208 * q^50 - 540422280 * q^51 + 2606264320 * q^52 - 4701996228 * q^53 - 918330048 * q^54 + 8224241544 * q^55 + 1101463552 * q^56 + 1158697872 * q^57 + 1614211200 * q^58 + 11975488224 * q^59 + 256794624 * q^60 + 1152867268 * q^61 + 7687966976 * q^62 + 1984873086 * q^63 + 2147483648 * q^64 + 6571345488 * q^65 + 10068271488 * q^66 - 21013981040 * q^67 + 2277335040 * q^68 - 9031735548 * q^69 - 555034368 * q^70 - 10009175796 * q^71 + 3869835264 * q^72 - 30165108692 * q^73 + 15449861504 * q^74 - 56231097642 * q^75 - 4882743296 * q^76 - 21761501916 * q^77 - 19791319680 * q^78 - 4940763704 * q^79 - 1082130432 * q^80 + 6973568802 * q^81 + 26441266176 * q^82 - 40082578056 * q^83 - 8364238848 * q^84 - 93463771752 * q^85 - 45400393984 * q^86 - 12257916300 * q^87 - 42427613184 * q^88 + 45015319488 * q^89 - 1950034176 * q^90 + 42776840260 * q^91 + 38059659264 * q^92 - 58380499224 * q^93 + 145859622144 * q^94 - 350378017104 * q^95 - 16307453952 * q^96 + 41947334380 * q^97 + 18078415936 * q^98 - 76455936612 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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