LMFDB - Embedded newform 42.12.a.g.1.2

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			1.2
Root			$-1067.55$ 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)

$f(q)$	$=$	\(q+32.0000 q^{2} -243.000 q^{3} +1024.00 q^{4} +12300.5 q^{5} -7776.00 q^{6} +16807.0 q^{7} +32768.0 q^{8} +59049.0 q^{9} +393617. q^{10} -352614. q^{11} -248832. q^{12} +1.58019e6 q^{13} +537824. q^{14} -2.98903e6 q^{15} +1.04858e6 q^{16} -2.48947e6 q^{17} +1.88957e6 q^{18} -1.61491e7 q^{19} +1.25958e7 q^{20} -4.08410e6 q^{21} -1.12836e7 q^{22} +4.52807e7 q^{23} -7.96262e6 q^{24} +1.02475e8 q^{25} +5.05660e7 q^{26} -1.43489e7 q^{27} +1.72104e7 q^{28} +1.70228e8 q^{29} -9.56490e7 q^{30} -1.42185e7 q^{31} +3.35544e7 q^{32} +8.56851e7 q^{33} -7.96630e7 q^{34} +2.06735e8 q^{35} +6.04662e7 q^{36} +1.89882e8 q^{37} -5.16772e8 q^{38} -3.83985e8 q^{39} +4.03064e8 q^{40} +2.36187e8 q^{41} -1.30691e8 q^{42} -2.90280e8 q^{43} -3.61076e8 q^{44} +7.26335e8 q^{45} +1.44898e9 q^{46} +2.17855e9 q^{47} -2.54804e8 q^{48} +2.82475e8 q^{49} +3.27921e9 q^{50} +6.04941e8 q^{51} +1.61811e9 q^{52} -6.05457e9 q^{53} -4.59165e8 q^{54} -4.33734e9 q^{55} +5.50732e8 q^{56} +3.92424e9 q^{57} +5.44731e9 q^{58} +3.82911e9 q^{59} -3.06077e9 q^{60} +1.02849e10 q^{61} -4.54992e8 q^{62} +9.92437e8 q^{63} +1.07374e9 q^{64} +1.94372e10 q^{65} +2.74192e9 q^{66} -1.64714e10 q^{67} -2.54922e9 q^{68} -1.10032e10 q^{69} +6.61553e9 q^{70} +6.23066e9 q^{71} +1.93492e9 q^{72} -1.55471e10 q^{73} +6.07621e9 q^{74} -2.49015e10 q^{75} -1.65367e10 q^{76} -5.92638e9 q^{77} -1.22875e10 q^{78} -3.48390e10 q^{79} +1.28981e10 q^{80} +3.48678e9 q^{81} +7.55798e9 q^{82} -4.20883e10 q^{83} -4.18212e9 q^{84} -3.06218e10 q^{85} -9.28897e9 q^{86} -4.13655e10 q^{87} -1.15544e10 q^{88} +2.22750e10 q^{89} +2.32427e10 q^{90} +2.65582e10 q^{91} +4.63674e10 q^{92} +3.45509e9 q^{93} +6.97136e10 q^{94} -1.98643e11 q^{95} -8.15373e9 q^{96} +8.88715e10 q^{97} +9.03921e9 q^{98} -2.08215e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	12300.5	1.76031	0.880155	−	0.474686i	$-0.157438\pi$
$5$	12300.5	1.76031	0.880155	+	0.474686i	$0.157438\pi$
$6$	−7776.00	−0.408248
$7$	16807.0	0.377964
$7$	16807.0	0.377964
$8$	32768.0	0.353553
$9$	59049.0	0.333333
$10$	393617.	1.24473
$11$	−352614.	−0.660145	−0.330072	−	0.943956i	$-0.607073\pi$
$11$	−352614.	−0.660145	−0.330072	+	0.943956i	$0.607073\pi$
$12$	−248832.	−0.288675
$13$	1.58019e6	1.18038	0.590188	−	0.807266i	$-0.299054\pi$
$13$	1.58019e6	1.18038	0.590188	+	0.807266i	$0.299054\pi$
$14$	537824.	0.267261
$15$	−2.98903e6	−1.01632
$16$	1.04858e6	0.250000
$17$	−2.48947e6	−0.425243	−0.212622	−	0.977135i	$-0.568200\pi$
$17$	−2.48947e6	−0.425243	−0.212622	+	0.977135i	$0.568200\pi$
$18$	1.88957e6	0.235702
$19$	−1.61491e7	−1.49625	−0.748125	−	0.663558i	$-0.769046\pi$
$19$	−1.61491e7	−1.49625	−0.748125	+	0.663558i	$0.769046\pi$
$20$	1.25958e7	0.880155
$21$	−4.08410e6	−0.218218
$22$	−1.12836e7	−0.466793
$23$	4.52807e7	1.46693	0.733466	−	0.679727i	$-0.237902\pi$
$23$	4.52807e7	1.46693	0.733466	+	0.679727i	$0.237902\pi$
$24$	−7.96262e6	−0.204124
$25$	1.02475e8	2.09869
$26$	5.05660e7	0.834651
$27$	−1.43489e7	−0.192450
$28$	1.72104e7	0.188982
$29$	1.70228e8	1.54114	0.770572	−	0.637353i	$-0.219971\pi$
$29$	1.70228e8	1.54114	0.770572	+	0.637353i	$0.219971\pi$
$30$	−9.56490e7	−0.718644
$31$	−1.42185e7	−0.0891999	−0.0445999	−	0.999005i	$-0.514201\pi$
$31$	−1.42185e7	−0.0891999	−0.0445999	+	0.999005i	$0.514201\pi$
$32$	3.35544e7	0.176777
$33$	8.56851e7	0.381135
$34$	−7.96630e7	−0.300692
$35$	2.06735e8	0.665335
$36$	6.04662e7	0.166667
$37$	1.89882e8	0.450167	0.225083	−	0.974340i	$-0.427735\pi$
$37$	1.89882e8	0.450167	0.225083	+	0.974340i	$0.427735\pi$
$38$	−5.16772e8	−1.05801
$39$	−3.83985e8	−0.681490
$40$	4.03064e8	0.622364
$41$	2.36187e8	0.318379	0.159190	−	0.987248i	$-0.449112\pi$
$41$	2.36187e8	0.318379	0.159190	+	0.987248i	$0.449112\pi$
$42$	−1.30691e8	−0.154303
$43$	−2.90280e8	−0.301121	−0.150560	−	0.988601i	$-0.548108\pi$
$43$	−2.90280e8	−0.301121	−0.150560	+	0.988601i	$0.548108\pi$
$44$	−3.61076e8	−0.330072
$45$	7.26335e8	0.586770
$46$	1.44898e9	1.03728
$47$	2.17855e9	1.38557	0.692786	−	0.721143i	$-0.256383\pi$
$47$	2.17855e9	1.38557	0.692786	+	0.721143i	$0.256383\pi$
$48$	−2.54804e8	−0.144338
$49$	2.82475e8	0.142857
$50$	3.27921e9	1.48400
$51$	6.04941e8	0.245514
$52$	1.61811e9	0.590188
$53$	−6.05457e9	−1.98868	−0.994342	−	0.106224i	$-0.966124\pi$
$53$	−6.05457e9	−1.98868	−0.994342	+	0.106224i	$0.966124\pi$
$54$	−4.59165e8	−0.136083
$55$	−4.33734e9	−1.16206
$56$	5.50732e8	0.133631
$57$	3.92424e9	0.863860
$58$	5.44731e9	1.08975
$59$	3.82911e9	0.697287	0.348643	−	0.937256i	$-0.386642\pi$
$59$	3.82911e9	0.697287	0.348643	+	0.937256i	$0.386642\pi$
$60$	−3.06077e9	−0.508158
$61$	1.02849e10	1.55914	0.779571	−	0.626314i	$-0.215437\pi$
$61$	1.02849e10	1.55914	0.779571	+	0.626314i	$0.215437\pi$
$62$	−4.54992e8	−0.0630738
$63$	9.92437e8	0.125988
$64$	1.07374e9	0.125000
$65$	1.94372e10	2.07783
$66$	2.74192e9	0.269503
$67$	−1.64714e10	−1.49045	−0.745227	−	0.666811i	$-0.767659\pi$
$67$	−1.64714e10	−1.49045	−0.745227	+	0.666811i	$0.767659\pi$
$68$	−2.54922e9	−0.212622
$69$	−1.10032e10	−0.846933
$70$	6.61553e9	0.470463
$71$	6.23066e9	0.409839	0.204919	−	0.978779i	$-0.434307\pi$
$71$	6.23066e9	0.409839	0.204919	+	0.978779i	$0.434307\pi$
$72$	1.93492e9	0.117851
$73$	−1.55471e10	−0.877756	−0.438878	−	0.898547i	$-0.644624\pi$
$73$	−1.55471e10	−0.877756	−0.438878	+	0.898547i	$0.644624\pi$
$74$	6.07621e9	0.318316
$75$	−2.49015e10	−1.21168
$76$	−1.65367e10	−0.748125
$77$	−5.92638e9	−0.249511
$78$	−1.22875e10	−0.481886
$79$	−3.48390e10	−1.27385	−0.636923	−	0.770927i	$-0.719793\pi$
$79$	−3.48390e10	−1.27385	−0.636923	+	0.770927i	$0.719793\pi$
$80$	1.28981e10	0.440078
$81$	3.48678e9	0.111111
$82$	7.55798e9	0.225128
$83$	−4.20883e10	−1.17282	−0.586410	−	0.810014i	$-0.699459\pi$
$83$	−4.20883e10	−1.17282	−0.586410	+	0.810014i	$0.699459\pi$
$84$	−4.18212e9	−0.109109
$85$	−3.06218e10	−0.748560
$86$	−9.28897e9	−0.212925
$87$	−4.13655e10	−0.889779
$88$	−1.15544e10	−0.233396
$89$	2.22750e10	0.422837	0.211419	−	0.977396i	$-0.432192\pi$
$89$	2.22750e10	0.422837	0.211419	+	0.977396i	$0.432192\pi$
$90$	2.32427e10	0.414909
$91$	2.65582e10	0.446140
$92$	4.63674e10	0.733466
$93$	3.45509e9	0.0514996
$94$	6.97136e10	0.979748
$95$	−1.98643e11	−2.63386
$96$	−8.15373e9	−0.102062
$97$	8.88715e10	1.05079	0.525397	−	0.850857i	$-0.323917\pi$
$97$	8.88715e10	1.05079	0.525397	+	0.850857i	$0.323917\pi$
$98$	9.03921e9	0.101015
$99$	−2.08215e10	−0.220048
$100$	1.04935e11	1.04935
$101$	−8.59718e10	−0.813933	−0.406966	−	0.913443i	$-0.633413\pi$
$101$	−8.59718e10	−0.813933	−0.406966	+	0.913443i	$0.633413\pi$
$102$	1.93581e10	0.173605
$103$	3.94424e10	0.335242	0.167621	−	0.985851i	$-0.446391\pi$
$103$	3.94424e10	0.335242	0.167621	+	0.985851i	$0.446391\pi$
$104$	5.17796e10	0.417326
$105$	−5.02367e10	−0.384131
$106$	−1.93746e11	−1.40621
$107$	−9.39997e10	−0.647912	−0.323956	−	0.946072i	$-0.605013\pi$
$107$	−9.39997e10	−0.647912	−0.323956	+	0.946072i	$0.605013\pi$
$108$	−1.46933e10	−0.0962250
$109$	1.66863e11	1.03876	0.519378	−	0.854544i	$-0.326164\pi$
$109$	1.66863e11	1.03876	0.519378	+	0.854544i	$0.326164\pi$
$110$	−1.38795e11	−0.821700
$111$	−4.61412e10	−0.259904
$112$	1.76234e10	0.0944911
$113$	−2.38994e11	−1.22027	−0.610136	−	0.792297i	$-0.708885\pi$
$113$	−2.38994e11	−1.22027	−0.610136	+	0.792297i	$0.708885\pi$
$114$	1.25576e11	0.610841
$115$	5.56977e11	2.58225
$116$	1.74314e11	0.770572
$117$	9.33085e10	0.393458
$118$	1.22531e11	0.493056
$119$	−4.18405e10	−0.160727
$120$	−9.79446e10	−0.359322
$121$	−1.60975e11	−0.564209
$122$	3.29116e11	1.10248
$123$	−5.73934e10	−0.183816
$124$	−1.45597e10	−0.0445999
$125$	6.59888e11	1.93404
$126$	3.17580e10	0.0890871
$127$	5.85931e10	0.157371	0.0786857	−	0.996899i	$-0.474928\pi$
$127$	5.85931e10	0.157371	0.0786857	+	0.996899i	$0.474928\pi$
$128$	3.43597e10	0.0883883
$129$	7.05381e10	0.173852
$130$	6.21989e11	1.46925
$131$	3.06164e11	0.693366	0.346683	−	0.937982i	$-0.387308\pi$
$131$	3.06164e11	0.693366	0.346683	+	0.937982i	$0.387308\pi$
$132$	8.77415e10	0.190567
$133$	−2.71418e11	−0.565529
$134$	−5.27084e11	−1.05391
$135$	−1.76499e11	−0.338772
$136$	−8.15749e10	−0.150346
$137$	−9.61170e11	−1.70152	−0.850760	−	0.525554i	$-0.823858\pi$
$137$	−9.61170e11	−1.70152	−0.850760	+	0.525554i	$0.823858\pi$
$138$	−3.52103e11	−0.598872
$139$	−6.50219e10	−0.106287	−0.0531433	−	0.998587i	$-0.516924\pi$
$139$	−6.50219e10	−0.106287	−0.0531433	+	0.998587i	$0.516924\pi$
$140$	2.11697e11	0.332667
$141$	−5.29387e11	−0.799960
$142$	1.99381e11	0.289800
$143$	−5.57195e11	−0.779219
$144$	6.19174e10	0.0833333
$145$	2.09390e12	2.71289
$146$	−4.97507e11	−0.620667
$147$	−6.86415e10	−0.0824786
$148$	1.94439e11	0.225083
$149$	1.48114e11	0.165223	0.0826116	−	0.996582i	$-0.473674\pi$
$149$	1.48114e11	0.165223	0.0826116	+	0.996582i	$0.473674\pi$
$150$	−7.96847e11	−0.856787
$151$	9.65401e11	1.00077	0.500385	−	0.865803i	$-0.333192\pi$
$151$	9.65401e11	1.00077	0.500385	+	0.865803i	$0.333192\pi$
$152$	−5.29174e11	−0.529004
$153$	−1.47001e11	−0.141748
$154$	−1.89644e11	−0.176431
$155$	−1.74895e11	−0.157019
$156$	−3.93201e11	−0.340745
$157$	−2.17938e12	−1.82341	−0.911704	−	0.410847i	$-0.865233\pi$
$157$	−2.17938e12	−1.82341	−0.911704	+	0.410847i	$0.865233\pi$
$158$	−1.11485e12	−0.900746
$159$	1.47126e12	1.14817
$160$	4.12738e11	0.311182
$161$	7.61032e11	0.554448
$162$	1.11577e11	0.0785674
$163$	1.99515e12	1.35814	0.679069	−	0.734074i	$-0.262384\pi$
$163$	1.99515e12	1.35814	0.679069	+	0.734074i	$0.262384\pi$
$164$	2.41855e11	0.159190
$165$	1.05397e12	0.670915
$166$	−1.34682e12	−0.829309
$167$	−9.20263e11	−0.548241	−0.274121	−	0.961695i	$-0.588387\pi$
$167$	−9.20263e11	−0.548241	−0.274121	+	0.961695i	$0.588387\pi$
$168$	−1.33828e11	−0.0771517
$169$	7.04830e11	0.393285
$170$	−9.79898e11	−0.529312
$171$	−9.53589e11	−0.498750
$172$	−2.97247e11	−0.150560
$173$	−6.31837e11	−0.309993	−0.154996	−	0.987915i	$-0.549537\pi$
$173$	−6.31837e11	−0.309993	−0.154996	+	0.987915i	$0.549537\pi$
$174$	−1.32370e12	−0.629169
$175$	1.72230e12	0.793231
$176$	−3.69742e11	−0.165036
$177$	−9.30473e11	−0.402579
$178$	7.12801e11	0.298991
$179$	−4.39711e12	−1.78845	−0.894223	−	0.447622i	$-0.852271\pi$
$179$	−4.39711e12	−1.78845	−0.894223	+	0.447622i	$0.852271\pi$
$180$	7.43767e11	0.293385
$181$	−1.65348e12	−0.632654	−0.316327	−	0.948650i	$-0.602450\pi$
$181$	−1.65348e12	−0.632654	−0.316327	+	0.948650i	$0.602450\pi$
$182$	8.49862e11	0.315469
$183$	−2.49923e12	−0.900170
$184$	1.48376e12	0.518639
$185$	2.33565e12	0.792433
$186$	1.10563e11	0.0364157
$187$	8.77820e11	0.280722
$188$	2.23083e12	0.692786
$189$	−2.41162e11	−0.0727393
$190$	−6.35657e12	−1.86242
$191$	−2.48628e12	−0.707727	−0.353864	−	0.935297i	$-0.615132\pi$
$191$	−2.48628e12	−0.707727	−0.353864	+	0.935297i	$0.615132\pi$
$192$	−2.60919e11	−0.0721688
$193$	1.42880e12	0.384067	0.192034	−	0.981388i	$-0.438492\pi$
$193$	1.42880e12	0.384067	0.192034	+	0.981388i	$0.438492\pi$
$194$	2.84389e12	0.743024
$195$	−4.72323e12	−1.19963
$196$	2.89255e11	0.0714286
$197$	5.05550e12	1.21395	0.606974	−	0.794722i	$-0.292383\pi$
$197$	5.05550e12	1.21395	0.606974	+	0.794722i	$0.292383\pi$
$198$	−6.66287e11	−0.155598
$199$	−1.59942e12	−0.363304	−0.181652	−	0.983363i	$-0.558144\pi$
$199$	−1.59942e12	−0.363304	−0.181652	+	0.983363i	$0.558144\pi$
$200$	3.35791e12	0.742000
$201$	4.00254e12	0.860514
$202$	−2.75110e12	−0.575538
$203$	2.86103e12	0.582497
$204$	6.19459e11	0.122757
$205$	2.90523e12	0.560446
$206$	1.26216e12	0.237052
$207$	2.67378e12	0.488977
$208$	1.65695e12	0.295094
$209$	5.69440e12	0.987741
$210$	−1.60757e12	−0.271622
$211$	−4.36281e12	−0.718146	−0.359073	−	0.933309i	$-0.616907\pi$
$211$	−4.36281e12	−0.718146	−0.359073	+	0.933309i	$0.616907\pi$
$212$	−6.19988e12	−0.994342
$213$	−1.51405e12	−0.236621
$214$	−3.00799e12	−0.458143
$215$	−3.57060e12	−0.530066
$216$	−4.70185e11	−0.0680414
$217$	−2.38970e11	−0.0337144
$218$	5.33961e12	0.734512
$219$	3.77795e12	0.506773
$220$	−4.44143e12	−0.581030
$221$	−3.93382e12	−0.501947
$222$	−1.47652e12	−0.183780
$223$	3.03894e12	0.369016	0.184508	−	0.982831i	$-0.440931\pi$
$223$	3.03894e12	0.369016	0.184508	+	0.982831i	$0.440931\pi$
$224$	5.63949e11	0.0668153
$225$	6.05106e12	0.699564
$226$	−7.64782e12	−0.862862
$227$	1.01313e13	1.11564	0.557819	−	0.829963i	$-0.311638\pi$
$227$	1.01313e13	1.11564	0.557819	+	0.829963i	$0.311638\pi$
$228$	4.01842e12	0.431930
$229$	−6.06368e12	−0.636270	−0.318135	−	0.948045i	$-0.603056\pi$
$229$	−6.06368e12	−0.636270	−0.318135	+	0.948045i	$0.603056\pi$
$230$	1.78233e13	1.82593
$231$	1.44011e12	0.144055
$232$	5.57804e12	0.544876
$233$	−1.45930e13	−1.39215	−0.696074	−	0.717970i	$-0.745072\pi$
$233$	−1.45930e13	−1.39215	−0.696074	+	0.717970i	$0.745072\pi$
$234$	2.98587e12	0.278217
$235$	2.67973e13	2.43904
$236$	3.92100e12	0.348643
$237$	8.46589e12	0.735456
$238$	−1.33890e12	−0.113651
$239$	−1.33839e13	−1.11019	−0.555093	−	0.831788i	$-0.687317\pi$
$239$	−1.33839e13	−1.11019	−0.555093	+	0.831788i	$0.687317\pi$
$240$	−3.13423e12	−0.254079
$241$	1.06473e13	0.843615	0.421807	−	0.906686i	$-0.361396\pi$
$241$	1.06473e13	0.843615	0.421807	+	0.906686i	$0.361396\pi$
$242$	−5.15121e12	−0.398956
$243$	−8.47289e11	−0.0641500
$244$	1.05317e13	0.779571
$245$	3.47460e12	0.251473
$246$	−1.83659e12	−0.129978
$247$	−2.55186e13	−1.76614
$248$	−4.65912e11	−0.0315369
$249$	1.02274e13	0.677128
$250$	2.11164e13	1.36757
$251$	−3.33900e12	−0.211549	−0.105775	−	0.994390i	$-0.533732\pi$
$251$	−3.33900e12	−0.211549	−0.105775	+	0.994390i	$0.533732\pi$
$252$	1.01626e12	0.0629941
$253$	−1.59666e13	−0.968387
$254$	1.87498e12	0.111278
$255$	7.44110e12	0.432181
$256$	1.09951e12	0.0625000
$257$	−1.69762e12	−0.0944511	−0.0472256	−	0.998884i	$-0.515038\pi$
$257$	−1.69762e12	−0.0944511	−0.0472256	+	0.998884i	$0.515038\pi$
$258$	2.25722e12	0.122932
$259$	3.19134e12	0.170147
$260$	1.99036e13	1.03891
$261$	1.00518e13	0.513714
$262$	9.79726e12	0.490284
$263$	−2.71445e13	−1.33022	−0.665112	−	0.746744i	$-0.731616\pi$
$263$	−2.71445e13	−1.33022	−0.665112	+	0.746744i	$0.731616\pi$
$264$	2.80773e12	0.134752
$265$	−7.44745e13	−3.50070
$266$	−8.68538e12	−0.399889
$267$	−5.41283e12	−0.244125
$268$	−1.68667e13	−0.745227
$269$	−1.75965e12	−0.0761707	−0.0380853	−	0.999274i	$-0.512126\pi$
$269$	−1.75965e12	−0.0761707	−0.0380853	+	0.999274i	$0.512126\pi$
$270$	−5.64798e12	−0.239548
$271$	−4.05461e13	−1.68507	−0.842535	−	0.538641i	$-0.818938\pi$
$271$	−4.05461e13	−1.68507	−0.842535	+	0.538641i	$0.818938\pi$
$272$	−2.61040e12	−0.106311
$273$	−6.45364e12	−0.257579
$274$	−3.07575e13	−1.20316
$275$	−3.61341e13	−1.38544
$276$	−1.12673e13	−0.423467
$277$	9.72793e11	0.0358411	0.0179206	−	0.999839i	$-0.494295\pi$
$277$	9.72793e11	0.0358411	0.0179206	+	0.999839i	$0.494295\pi$
$278$	−2.08070e12	−0.0751559
$279$	−8.39588e11	−0.0297333
$280$	6.77430e12	0.235231
$281$	−1.71930e13	−0.585420	−0.292710	−	0.956201i	$-0.594557\pi$
$281$	−1.71930e13	−0.585420	−0.292710	+	0.956201i	$0.594557\pi$
$282$	−1.69404e13	−0.565657
$283$	4.73764e13	1.55145	0.775723	−	0.631073i	$-0.217385\pi$
$283$	4.73764e13	1.55145	0.775723	+	0.631073i	$0.217385\pi$
$284$	6.38020e12	0.204919
$285$	4.82702e13	1.52066
$286$	−1.78303e13	−0.550991
$287$	3.96959e12	0.120336
$288$	1.98136e12	0.0589256
$289$	−2.80744e13	−0.819168
$290$	6.70048e13	1.91830
$291$	−2.15958e13	−0.606677
$292$	−1.59202e13	−0.438878
$293$	−3.38242e13	−0.915072	−0.457536	−	0.889191i	$-0.651268\pi$
$293$	−3.38242e13	−0.915072	−0.457536	+	0.889191i	$0.651268\pi$
$294$	−2.19653e12	−0.0583212
$295$	4.71001e13	1.22744
$296$	6.22204e12	0.159158
$297$	5.05962e12	0.127045
$298$	4.73964e12	0.116830
$299$	7.15519e13	1.73153
$300$	−2.54991e13	−0.605840
$301$	−4.87874e12	−0.113813
$302$	3.08928e13	0.707652
$303$	2.08912e13	0.469924
$304$	−1.69336e13	−0.374062
$305$	1.26510e14	2.74457
$306$	−4.70402e12	−0.100231
$307$	−5.70211e13	−1.19337	−0.596684	−	0.802476i	$-0.703515\pi$
$307$	−5.70211e13	−1.19337	−0.596684	+	0.802476i	$0.703515\pi$
$308$	−6.06861e12	−0.124756
$309$	−9.58451e12	−0.193552
$310$	−5.59665e12	−0.111030
$311$	−8.45075e13	−1.64707	−0.823537	−	0.567262i	$-0.808003\pi$
$311$	−8.45075e13	−1.64707	−0.823537	+	0.567262i	$0.808003\pi$
$312$	−1.25824e13	−0.240943
$313$	7.84140e13	1.47537	0.737683	−	0.675148i	$-0.235920\pi$
$313$	7.84140e13	1.47537	0.737683	+	0.675148i	$0.235920\pi$
$314$	−6.97400e13	−1.28934
$315$	1.22075e13	0.221778
$316$	−3.56752e13	−0.636923
$317$	−3.21958e13	−0.564901	−0.282451	−	0.959282i	$-0.591147\pi$
$317$	−3.21958e13	−0.564901	−0.282451	+	0.959282i	$0.591147\pi$
$318$	4.70803e13	0.811877
$319$	−6.00248e13	−1.01738
$320$	1.32076e13	0.220039
$321$	2.28419e13	0.374072
$322$	2.43530e13	0.392054
$323$	4.02027e13	0.636270
$324$	3.57047e12	0.0555556
$325$	1.61930e14	2.47724
$326$	6.38448e13	0.960349
$327$	−4.05477e13	−0.599726
$328$	7.73937e12	0.112564
$329$	3.66149e13	0.523697
$330$	3.37271e13	0.474409
$331$	−2.34609e13	−0.324557	−0.162278	−	0.986745i	$-0.551884\pi$
$331$	−2.34609e13	−0.324557	−0.162278	+	0.986745i	$0.551884\pi$
$332$	−4.30984e13	−0.586410
$333$	1.12123e13	0.150056
$334$	−2.94484e13	−0.387665
$335$	−2.02607e14	−2.62366
$336$	−4.28249e12	−0.0545545
$337$	1.56302e14	1.95884	0.979422	−	0.201822i	$-0.0646863\pi$
$337$	1.56302e14	1.95884	0.979422	+	0.201822i	$0.0646863\pi$
$338$	2.25546e13	0.278095
$339$	5.80757e13	0.704524
$340$	−3.13567e13	−0.374280
$341$	5.01363e12	0.0588849
$342$	−3.05149e13	−0.352669
$343$	4.74756e12	0.0539949
$344$	−9.51190e12	−0.106462
$345$	−1.35345e14	−1.49087
$346$	−2.02188e13	−0.219198
$347$	9.55696e13	1.01978	0.509892	−	0.860239i	$-0.329686\pi$
$347$	9.55696e13	1.01978	0.509892	+	0.860239i	$0.329686\pi$
$348$	−4.23583e13	−0.444890
$349$	1.66681e14	1.72325	0.861623	−	0.507548i	$-0.169448\pi$
$349$	1.66681e14	1.72325	0.861623	+	0.507548i	$0.169448\pi$
$350$	5.51136e13	0.560899
$351$	−2.26740e13	−0.227163
$352$	−1.18317e13	−0.116698
$353$	1.56526e14	1.51994	0.759968	−	0.649960i	$-0.225214\pi$
$353$	1.56526e14	1.51994	0.759968	+	0.649960i	$0.225214\pi$
$354$	−2.97751e13	−0.284666
$355$	7.66405e13	0.721444
$356$	2.28096e13	0.211419
$357$	1.01672e13	0.0927957
$358$	−1.40708e14	−1.26462
$359$	−1.20856e14	−1.06967	−0.534834	−	0.844957i	$-0.679626\pi$
$359$	−1.20856e14	−1.06967	−0.534834	+	0.844957i	$0.679626\pi$
$360$	2.38005e13	0.207455
$361$	1.44304e14	1.23876
$362$	−5.29113e13	−0.447354
$363$	3.91170e13	0.325746
$364$	2.71956e13	0.223070
$365$	−1.91238e14	−1.54512
$366$	−7.99753e13	−0.636517
$367$	−7.27031e13	−0.570020	−0.285010	−	0.958525i	$-0.591997\pi$
$367$	−7.27031e13	−0.570020	−0.285010	+	0.958525i	$0.591997\pi$
$368$	4.74802e13	0.366733
$369$	1.39466e13	0.106126
$370$	7.47407e13	0.560335
$371$	−1.01759e14	−0.751652
$372$	3.53802e12	0.0257498
$373$	−4.65924e13	−0.334131	−0.167065	−	0.985946i	$-0.553429\pi$
$373$	−4.65924e13	−0.334131	−0.167065	+	0.985946i	$0.553429\pi$
$374$	2.80902e13	0.198501
$375$	−1.60353e14	−1.11662
$376$	7.13867e13	0.489874
$377$	2.68993e14	1.81913
$378$	−7.71719e12	−0.0514344
$379$	−1.00792e14	−0.662081	−0.331041	−	0.943616i	$-0.607400\pi$
$379$	−1.00792e14	−0.662081	−0.331041	+	0.943616i	$0.607400\pi$
$380$	−2.03410e14	−1.31693
$381$	−1.42381e13	−0.0908584
$382$	−7.95609e13	−0.500439
$383$	2.84945e14	1.76672	0.883360	−	0.468694i	$-0.155275\pi$
$383$	2.84945e14	1.76672	0.883360	+	0.468694i	$0.155275\pi$
$384$	−8.34942e12	−0.0510310
$385$	−7.28976e13	−0.439217
$386$	4.57217e13	0.271577
$387$	−1.71408e13	−0.100374
$388$	9.10044e13	0.525397
$389$	7.33825e13	0.417705	0.208852	−	0.977947i	$-0.433027\pi$
$389$	7.33825e13	0.417705	0.208852	+	0.977947i	$0.433027\pi$
$390$	−1.51143e14	−0.848269
$391$	−1.12725e14	−0.623803
$392$	9.25615e12	0.0505076
$393$	−7.43979e13	−0.400315
$394$	1.61776e14	0.858391
$395$	−4.28539e14	−2.24237
$396$	−2.13212e13	−0.110024
$397$	−6.07382e13	−0.309111	−0.154555	−	0.987984i	$-0.549395\pi$
$397$	−6.07382e13	−0.309111	−0.154555	+	0.987984i	$0.549395\pi$
$398$	−5.11813e13	−0.256894
$399$	6.59546e13	0.326508
$400$	1.07453e14	0.524673
$401$	−4.03753e14	−1.94456	−0.972281	−	0.233816i	$-0.924879\pi$
$401$	−4.03753e14	−1.94456	−0.972281	+	0.233816i	$0.924879\pi$
$402$	1.28081e14	0.608475
$403$	−2.24679e13	−0.105289
$404$	−8.80352e13	−0.406966
$405$	4.28893e13	0.195590
$406$	9.15529e13	0.411888
$407$	−6.69548e13	−0.297175
$408$	1.98227e13	0.0868024
$409$	4.28688e14	1.85210	0.926048	−	0.377406i	$-0.123184\pi$
$409$	4.28688e14	1.85210	0.926048	+	0.377406i	$0.123184\pi$
$410$	9.29672e13	0.396295
$411$	2.33564e14	0.982373
$412$	4.03890e13	0.167621
$413$	6.43558e13	0.263550
$414$	8.55609e13	0.345759
$415$	−5.17708e14	−2.06453
$416$	5.30223e13	0.208663
$417$	1.58003e13	0.0613646
$418$	1.82221e14	0.698439
$419$	−2.15064e14	−0.813564	−0.406782	−	0.913525i	$-0.633349\pi$
$419$	−2.15064e14	−0.813564	−0.406782	+	0.913525i	$0.633349\pi$
$420$	−5.14423e13	−0.192066
$421$	−4.34512e13	−0.160122	−0.0800608	−	0.996790i	$-0.525511\pi$
$421$	−4.34512e13	−0.160122	−0.0800608	+	0.996790i	$0.525511\pi$
$422$	−1.39610e14	−0.507806
$423$	1.28641e14	0.461857
$424$	−1.98396e14	−0.703106
$425$	−2.55109e14	−0.892455
$426$	−4.84496e13	−0.167316
$427$	1.72858e14	0.589300
$428$	−9.62557e13	−0.323956
$429$	1.35398e14	0.449882
$430$	−1.14259e14	−0.374813
$431$	3.93813e14	1.27546	0.637728	−	0.770262i	$-0.279875\pi$
$431$	3.93813e14	1.27546	0.637728	+	0.770262i	$0.279875\pi$
$432$	−1.50459e13	−0.0481125
$433$	3.41565e13	0.107842	0.0539212	−	0.998545i	$-0.482828\pi$
$433$	3.41565e13	0.107842	0.0539212	+	0.998545i	$0.482828\pi$
$434$	−7.64705e12	−0.0238397
$435$	−5.08818e14	−1.56629
$436$	1.70867e14	0.519378
$437$	−7.31243e14	−2.19489
$438$	1.20894e14	0.358342
$439$	4.05695e13	0.118753	0.0593766	−	0.998236i	$-0.481089\pi$
$439$	4.05695e13	0.118753	0.0593766	+	0.998236i	$0.481089\pi$
$440$	−1.42126e14	−0.410850
$441$	1.66799e13	0.0476190
$442$	−1.25882e14	−0.354930
$443$	3.75177e14	1.04476	0.522379	−	0.852713i	$-0.325045\pi$
$443$	3.75177e14	1.04476	0.522379	+	0.852713i	$0.325045\pi$
$444$	−4.72486e13	−0.129952
$445$	2.73995e14	0.744325
$446$	9.72460e13	0.260934
$447$	−3.59917e13	−0.0953917
$448$	1.80464e13	0.0472456
$449$	−1.23670e14	−0.319824	−0.159912	−	0.987131i	$-0.551121\pi$
$449$	−1.23670e14	−0.319824	−0.159912	+	0.987131i	$0.551121\pi$
$450$	1.93634e14	0.494666
$451$	−8.32827e13	−0.210176
$452$	−2.44730e14	−0.610136
$453$	−2.34592e14	−0.577795
$454$	3.24202e14	0.788875
$455$	3.26680e14	0.785344
$456$	1.28589e14	0.305421
$457$	5.07330e13	0.119056	0.0595280	−	0.998227i	$-0.481040\pi$
$457$	5.07330e13	0.119056	0.0595280	+	0.998227i	$0.481040\pi$
$458$	−1.94038e14	−0.449911
$459$	3.57211e13	0.0818381
$460$	5.70344e14	1.29113
$461$	7.12205e14	1.59313	0.796563	−	0.604556i	$-0.206649\pi$
$461$	7.12205e14	1.59313	0.796563	+	0.604556i	$0.206649\pi$
$462$	4.60835e13	0.101863
$463$	5.87785e14	1.28388	0.641938	−	0.766757i	$-0.278131\pi$
$463$	5.87785e14	1.28388	0.641938	+	0.766757i	$0.278131\pi$
$464$	1.78497e14	0.385286
$465$	4.24995e13	0.0906552
$466$	−4.66975e14	−0.984398
$467$	−1.30452e14	−0.271775	−0.135887	−	0.990724i	$-0.543389\pi$
$467$	−1.30452e14	−0.271775	−0.135887	+	0.990724i	$0.543389\pi$
$468$	9.55479e13	0.196729
$469$	−2.76834e14	−0.563338
$470$	8.57515e14	1.72466
$471$	5.29588e14	1.05275
$472$	1.25472e14	0.246528
$473$	1.02357e14	0.198783
$474$	2.70908e14	0.520046
$475$	−1.65488e15	−3.14017
$476$	−4.28447e13	−0.0803634
$477$	−3.57516e14	−0.662895
$478$	−4.28286e14	−0.785020
$479$	3.81190e14	0.690711	0.345356	−	0.938472i	$-0.387758\pi$
$479$	3.81190e14	0.690711	0.345356	+	0.938472i	$0.387758\pi$
$480$	−1.00295e14	−0.179661
$481$	3.00048e14	0.531366
$482$	3.40712e14	0.596526
$483$	−1.84931e14	−0.320111
$484$	−1.64839e14	−0.282104
$485$	1.09317e15	1.84972
$486$	−2.71132e13	−0.0453609
$487$	−4.47699e14	−0.740588	−0.370294	−	0.928915i	$-0.620743\pi$
$487$	−4.47699e14	−0.740588	−0.370294	+	0.928915i	$0.620743\pi$
$488$	3.37015e14	0.551240
$489$	−4.84822e14	−0.784122
$490$	1.11187e14	0.177818
$491$	−3.06675e14	−0.484987	−0.242494	−	0.970153i	$-0.577965\pi$
$491$	−3.06675e14	−0.484987	−0.242494	+	0.970153i	$0.577965\pi$
$492$	−5.87708e13	−0.0919081
$493$	−4.23778e14	−0.655361
$494$	−8.16596e14	−1.24885
$495$	−2.56115e14	−0.387353
$496$	−1.49092e13	−0.0223000
$497$	1.04719e14	0.154905
$498$	3.27278e14	0.478802
$499$	1.19798e15	1.73338	0.866692	−	0.498843i	$-0.166242\pi$
$499$	1.19798e15	1.73338	0.866692	+	0.498843i	$0.166242\pi$
$500$	6.75725e14	0.967019
$501$	2.23624e14	0.316527
$502$	−1.06848e14	−0.149588
$503$	2.27154e14	0.314556	0.157278	−	0.987554i	$-0.449728\pi$
$503$	2.27154e14	0.314556	0.157278	+	0.987554i	$0.449728\pi$
$504$	3.25202e13	0.0445435
$505$	−1.05750e15	−1.43277
$506$	−5.10931e14	−0.684753
$507$	−1.71274e14	−0.227063
$508$	5.99993e13	0.0786857
$509$	8.08801e14	1.04929	0.524643	−	0.851322i	$-0.324199\pi$
$509$	8.08801e14	1.04929	0.524643	+	0.851322i	$0.324199\pi$
$510$	2.38115e14	0.305598
$511$	−2.61300e14	−0.331761
$512$	3.51844e13	0.0441942
$513$	2.31722e14	0.287953
$514$	−5.43237e13	−0.0667870
$515$	4.85163e14	0.590131
$516$	7.22310e13	0.0869261
$517$	−7.68186e14	−0.914678
$518$	1.02123e14	0.120312
$519$	1.53536e14	0.178974
$520$	6.36917e14	0.734623
$521$	8.85649e14	1.01077	0.505387	−	0.862893i	$-0.331350\pi$
$521$	8.85649e14	1.01077	0.505387	+	0.862893i	$0.331350\pi$
$522$	3.21658e14	0.363251
$523$	4.08540e14	0.456537	0.228268	−	0.973598i	$-0.426694\pi$
$523$	4.08540e14	0.456537	0.228268	+	0.973598i	$0.426694\pi$
$524$	3.13512e14	0.346683
$525$	−4.18519e14	−0.457972
$526$	−8.68623e14	−0.940610
$527$	3.53965e13	0.0379317
$528$	8.98473e13	0.0952837
$529$	1.09753e15	1.15189
$530$	−2.38318e15	−2.47537
$531$	2.26105e14	0.232429
$532$	−2.77932e14	−0.282765
$533$	3.73219e14	0.375807
$534$	−1.73211e14	−0.172623
$535$	−1.15625e15	−1.14053
$536$	−5.39734e14	−0.526955
$537$	1.06850e15	1.03256
$538$	−5.63087e13	−0.0538608
$539$	−9.96046e13	−0.0943064
$540$	−1.80735e14	−0.169386
$541$	3.64170e14	0.337846	0.168923	−	0.985629i	$-0.445971\pi$
$541$	3.64170e14	0.337846	0.168923	+	0.985629i	$0.445971\pi$
$542$	−1.29748e15	−1.19152
$543$	4.01795e14	0.365263
$544$	−8.35327e13	−0.0751731
$545$	2.05250e15	1.82853
$546$	−2.06517e14	−0.182136
$547$	−1.61653e14	−0.141141	−0.0705706	−	0.997507i	$-0.522482\pi$
$547$	−1.61653e14	−0.141141	−0.0705706	+	0.997507i	$0.522482\pi$
$548$	−9.84238e14	−0.850760
$549$	6.07312e14	0.519714
$550$	−1.15629e15	−0.979654
$551$	−2.74904e15	−2.30593
$552$	−3.60553e14	−0.299436
$553$	−5.85540e14	−0.481469
$554$	3.11294e13	0.0253435
$555$	−5.67562e14	−0.457511
$556$	−6.65824e13	−0.0531433
$557$	−8.84208e14	−0.698797	−0.349398	−	0.936974i	$-0.613614\pi$
$557$	−8.84208e14	−0.698797	−0.349398	+	0.936974i	$0.613614\pi$
$558$	−2.68668e13	−0.0210246
$559$	−4.58697e14	−0.355436
$560$	2.16778e14	0.166334
$561$	−2.13310e14	−0.162075
$562$	−5.50177e14	−0.413954
$563$	−7.41363e14	−0.552376	−0.276188	−	0.961104i	$-0.589071\pi$
$563$	−7.41363e14	−0.552376	−0.276188	+	0.961104i	$0.589071\pi$
$564$	−5.42093e14	−0.399980
$565$	−2.93976e15	−2.14806
$566$	1.51605e15	1.09704
$567$	5.86024e13	0.0419961
$568$	2.04166e14	0.144900
$569$	−2.33591e15	−1.64187	−0.820935	−	0.571021i	$-0.806547\pi$
$569$	−2.33591e15	−1.64187	−0.820935	+	0.571021i	$0.806547\pi$
$570$	1.54465e15	1.07527
$571$	−1.60881e15	−1.10919	−0.554596	−	0.832120i	$-0.687127\pi$
$571$	−1.60881e15	−1.10919	−0.554596	+	0.832120i	$0.687127\pi$
$572$	−5.70568e14	−0.389609
$573$	6.04165e14	0.408607
$574$	1.27027e14	0.0850904
$575$	4.64014e15	3.07864
$576$	6.34034e13	0.0416667
$577$	−1.26443e15	−0.823051	−0.411525	−	0.911398i	$-0.635004\pi$
$577$	−1.26443e15	−0.823051	−0.411525	+	0.911398i	$0.635004\pi$
$578$	−8.98382e14	−0.579239
$579$	−3.47199e14	−0.221741
$580$	2.14415e15	1.35645
$581$	−7.07377e14	−0.443284
$582$	−6.91065e14	−0.428985
$583$	2.13492e15	1.31282
$584$	−5.09447e14	−0.310334
$585$	1.14774e15	0.692609
$586$	−1.08237e15	−0.647053
$587$	−1.24119e15	−0.735069	−0.367535	−	0.930010i	$-0.619798\pi$
$587$	−1.24119e15	−0.735069	−0.367535	+	0.930010i	$0.619798\pi$
$588$	−7.02889e13	−0.0412393
$589$	2.29616e14	0.133465
$590$	1.50720e15	0.867931
$591$	−1.22849e15	−0.700873
$592$	1.99105e14	0.112542
$593$	1.71268e15	0.959125	0.479562	−	0.877508i	$-0.340795\pi$
$593$	1.71268e15	0.959125	0.479562	+	0.877508i	$0.340795\pi$
$594$	1.61908e14	0.0898343
$595$	−5.14661e14	−0.282929
$596$	1.51669e14	0.0826116
$597$	3.88658e14	0.209753
$598$	2.28966e15	1.22438
$599$	2.24071e15	1.18724	0.593620	−	0.804746i	$-0.297698\pi$
$599$	2.24071e15	1.18724	0.593620	+	0.804746i	$0.297698\pi$
$600$	−8.15971e14	−0.428394
$601$	3.50618e15	1.82400	0.911999	−	0.410193i	$-0.134539\pi$
$601$	3.50618e15	1.82400	0.911999	+	0.410193i	$0.134539\pi$
$602$	−1.56120e14	−0.0804780
$603$	−9.72618e14	−0.496818
$604$	9.88571e14	0.500385
$605$	−1.98008e15	−0.993182
$606$	6.68517e14	0.332287
$607$	3.76699e15	1.85548	0.927740	−	0.373226i	$-0.121748\pi$
$607$	3.76699e15	1.85548	0.927740	+	0.373226i	$0.121748\pi$
$608$	−5.41874e14	−0.264502
$609$	−6.95230e14	−0.336305
$610$	4.04831e15	1.94071
$611$	3.44252e15	1.63549
$612$	−1.50529e14	−0.0708739
$613$	−6.39672e14	−0.298487	−0.149243	−	0.988801i	$-0.547684\pi$
$613$	−6.39672e14	−0.298487	−0.149243	+	0.988801i	$0.547684\pi$
$614$	−1.82468e15	−0.843839
$615$	−7.05970e14	−0.323574
$616$	−1.94195e14	−0.0882156
$617$	−1.76213e15	−0.793358	−0.396679	−	0.917957i	$-0.629837\pi$
$617$	−1.76213e15	−0.793358	−0.396679	+	0.917957i	$0.629837\pi$
$618$	−3.06704e14	−0.136862
$619$	−5.99081e14	−0.264964	−0.132482	−	0.991185i	$-0.542295\pi$
$619$	−5.99081e14	−0.264964	−0.132482	+	0.991185i	$0.542295\pi$
$620$	−1.79093e14	−0.0785097
$621$	−6.49728e14	−0.282311
$622$	−2.70424e15	−1.16466
$623$	3.74376e14	0.159817
$624$	−4.02638e14	−0.170372
$625$	3.11331e15	1.30581
$626$	2.50925e15	1.04324
$627$	−1.38374e15	−0.570273
$628$	−2.23168e15	−0.911704
$629$	−4.72704e14	−0.191430
$630$	3.90640e14	0.156821
$631$	3.31823e15	1.32052	0.660260	−	0.751037i	$-0.270446\pi$
$631$	3.31823e15	1.32052	0.660260	+	0.751037i	$0.270446\pi$
$632$	−1.14161e15	−0.450373
$633$	1.06016e15	0.414622
$634$	−1.03026e15	−0.399446
$635$	7.20726e14	0.277022
$636$	1.50657e15	0.574084
$637$	4.46364e14	0.168625
$638$	−1.92079e15	−0.719395
$639$	3.67914e14	0.136613
$640$	4.22643e14	0.155591
$641$	−8.35966e14	−0.305119	−0.152560	−	0.988294i	$-0.548752\pi$
$641$	−8.35966e14	−0.305119	−0.152560	+	0.988294i	$0.548752\pi$
$642$	7.30942e14	0.264509
$643$	−2.95306e15	−1.05953	−0.529764	−	0.848145i	$-0.677719\pi$
$643$	−2.95306e15	−1.05953	−0.529764	+	0.848145i	$0.677719\pi$
$644$	7.79297e14	0.277224
$645$	8.67657e14	0.306034
$646$	1.28649e15	0.449911
$647$	−4.12522e15	−1.43045	−0.715226	−	0.698893i	$-0.753676\pi$
$647$	−4.12522e15	−1.43045	−0.715226	+	0.698893i	$0.753676\pi$
$648$	1.14255e14	0.0392837
$649$	−1.35019e15	−0.460310
$650$	5.18176e15	1.75168
$651$	5.80698e13	0.0194650
$652$	2.04303e15	0.679069
$653$	−1.85337e15	−0.610857	−0.305428	−	0.952215i	$-0.598800\pi$
$653$	−1.85337e15	−0.610857	−0.305428	+	0.952215i	$0.598800\pi$
$654$	−1.29752e15	−0.424071
$655$	3.76599e15	1.22054
$656$	2.47660e14	0.0795948
$657$	−9.18041e14	−0.292585
$658$	1.17168e15	0.370310
$659$	3.29701e15	1.03336	0.516679	−	0.856179i	$-0.327168\pi$
$659$	3.29701e15	1.03336	0.516679	+	0.856179i	$0.327168\pi$
$660$	1.07927e15	0.335458
$661$	3.10628e14	0.0957486	0.0478743	−	0.998853i	$-0.484755\pi$
$661$	3.10628e14	0.0957486	0.0478743	+	0.998853i	$0.484755\pi$
$662$	−7.50748e14	−0.229496
$663$	9.55919e14	0.289799
$664$	−1.37915e15	−0.414654
$665$	−3.33859e15	−0.995507
$666$	3.58794e14	0.106105
$667$	7.70806e15	2.26075
$668$	−9.42350e14	−0.274121
$669$	−7.38462e14	−0.213051
$670$	−6.48342e15	−1.85521
$671$	−3.62659e15	−1.02926
$672$	−1.37040e14	−0.0385758
$673$	8.84198e14	0.246869	0.123435	−	0.992353i	$-0.460609\pi$
$673$	8.84198e14	0.246869	0.123435	+	0.992353i	$0.460609\pi$
$674$	5.00166e15	1.38511
$675$	−1.47041e15	−0.403893
$676$	7.21746e14	0.196643
$677$	−1.49489e15	−0.403992	−0.201996	−	0.979386i	$-0.564743\pi$
$677$	−1.49489e15	−0.403992	−0.201996	+	0.979386i	$0.564743\pi$
$678$	1.85842e15	0.498174
$679$	1.49366e15	0.397163
$680$	−1.00342e15	−0.264656
$681$	−2.46191e15	−0.644113
$682$	1.60436e14	0.0416379
$683$	−3.65655e14	−0.0941364	−0.0470682	−	0.998892i	$-0.514988\pi$
$683$	−3.65655e14	−0.0941364	−0.0470682	+	0.998892i	$0.514988\pi$
$684$	−9.76475e14	−0.249375
$685$	−1.18229e16	−2.99520
$686$	1.51922e14	0.0381802
$687$	1.47347e15	0.367350
$688$	−3.04381e14	−0.0752802
$689$	−9.56735e15	−2.34739
$690$	−4.33105e15	−1.05420
$691$	5.51737e15	1.33230	0.666151	−	0.745817i	$-0.267941\pi$
$691$	5.51737e15	1.33230	0.666151	+	0.745817i	$0.267941\pi$
$692$	−6.47001e14	−0.154996
$693$	−3.49947e14	−0.0831704
$694$	3.05823e15	0.721096
$695$	−7.99805e14	−0.187097
$696$	−1.35546e15	−0.314585
$697$	−5.87979e14	−0.135389
$698$	5.33381e15	1.21852
$699$	3.54609e15	0.803757
$700$	1.76364e15	0.396615
$701$	−5.84171e15	−1.30344	−0.651719	−	0.758460i	$-0.725952\pi$
$701$	−5.84171e15	−1.30344	−0.651719	+	0.758460i	$0.725952\pi$
$702$	−7.25567e14	−0.160629
$703$	−3.06642e15	−0.673562
$704$	−3.78616e14	−0.0825181
$705$	−6.51175e15	−1.40818
$706$	5.00883e15	1.07476
$707$	−1.44493e15	−0.307638
$708$	−9.52804e14	−0.201289
$709$	−2.22339e15	−0.466081	−0.233040	−	0.972467i	$-0.574867\pi$
$709$	−2.22339e15	−0.466081	−0.233040	+	0.972467i	$0.574867\pi$
$710$	2.45250e15	0.510138
$711$	−2.05721e15	−0.424616
$712$	7.29908e14	0.149496
$713$	−6.43823e14	−0.130850
$714$	3.25352e14	0.0656165
$715$	−6.85380e15	−1.37167
$716$	−4.50264e15	−0.894223
$717$	3.25230e15	0.640966
$718$	−3.86740e15	−0.756370
$719$	−7.51446e14	−0.145844	−0.0729220	−	0.997338i	$-0.523232\pi$
$719$	−7.51446e14	−0.145844	−0.0729220	+	0.997338i	$0.523232\pi$
$720$	7.61617e14	0.146693
$721$	6.62909e14	0.126710
$722$	4.61772e15	0.875937
$723$	−2.58728e15	−0.487061
$724$	−1.69316e15	−0.316327
$725$	1.74442e16	3.23438
$726$	1.25174e15	0.230337
$727$	4.17850e15	0.763099	0.381549	−	0.924348i	$-0.375391\pi$
$727$	4.17850e15	0.763099	0.381549	+	0.924348i	$0.375391\pi$
$728$	8.70259e14	0.157734
$729$	2.05891e14	0.0370370
$730$	−6.11961e15	−1.09257
$731$	7.22643e14	0.128050
$732$	−2.55921e15	−0.450085
$733$	5.38066e15	0.939213	0.469606	−	0.882876i	$-0.344396\pi$
$733$	5.38066e15	0.939213	0.469606	+	0.882876i	$0.344396\pi$
$734$	−2.32650e15	−0.403065
$735$	−8.44327e14	−0.145188
$736$	1.51937e15	0.259319
$737$	5.80803e15	0.983915
$738$	4.46291e14	0.0750427
$739$	−5.23037e15	−0.872947	−0.436474	−	0.899717i	$-0.643773\pi$
$739$	−5.23037e15	−0.872947	−0.436474	+	0.899717i	$0.643773\pi$
$740$	2.39170e15	0.396217
$741$	6.20103e15	1.01968
$742$	−3.25629e15	−0.531498
$743$	−3.29420e15	−0.533718	−0.266859	−	0.963736i	$-0.585986\pi$
$743$	−3.29420e15	−0.533718	−0.266859	+	0.963736i	$0.585986\pi$
$744$	1.13217e14	0.0182079
$745$	1.82188e15	0.290844
$746$	−1.49096e15	−0.236266
$747$	−2.48527e15	−0.390940
$748$	8.98888e14	0.140361
$749$	−1.57985e15	−0.244888
$750$	−5.13129e15	−0.789568
$751$	−2.78992e15	−0.426159	−0.213079	−	0.977035i	$-0.568349\pi$
$751$	−2.78992e15	−0.426159	−0.213079	+	0.977035i	$0.568349\pi$
$752$	2.28437e15	0.346393
$753$	8.11378e14	0.122138
$754$	8.60777e15	1.28632
$755$	1.18750e16	1.76167
$756$	−2.46950e14	−0.0363696
$757$	−7.32965e15	−1.07166	−0.535829	−	0.844327i	$-0.680001\pi$
$757$	−7.32965e15	−1.07166	−0.535829	+	0.844327i	$0.680001\pi$
$758$	−3.22535e15	−0.468162
$759$	3.87988e15	0.559099
$760$	−6.50913e15	−0.931211
$761$	−3.38693e15	−0.481051	−0.240525	−	0.970643i	$-0.577320\pi$
$761$	−3.38693e15	−0.481051	−0.240525	+	0.970643i	$0.577320\pi$
$762$	−4.55620e14	−0.0642466
$763$	2.80446e15	0.392613
$764$	−2.54595e15	−0.353864
$765$	−1.80819e15	−0.249520
$766$	9.11824e15	1.24926
$767$	6.05070e15	0.823060
$768$	−2.67181e14	−0.0360844
$769$	3.45885e15	0.463806	0.231903	−	0.972739i	$-0.425505\pi$
$769$	3.45885e15	0.463806	0.231903	+	0.972739i	$0.425505\pi$
$770$	−2.33272e15	−0.310574
$771$	4.12521e14	0.0545314
$772$	1.46309e15	0.192034
$773$	6.36654e15	0.829691	0.414845	−	0.909892i	$-0.363836\pi$
$773$	6.36654e15	0.829691	0.414845	+	0.909892i	$0.363836\pi$
$774$	−5.48504e14	−0.0709749
$775$	−1.45704e15	−0.187203
$776$	2.91214e15	0.371512
$777$	−7.75496e14	−0.0982344
$778$	2.34824e15	0.295362
$779$	−3.81421e15	−0.476374
$780$	−4.83659e15	−0.599817
$781$	−2.19702e15	−0.270553
$782$	−3.60719e15	−0.441095
$783$	−2.44259e15	−0.296593
$784$	2.96197e14	0.0357143
$785$	−2.68075e16	−3.20976
$786$	−2.38073e15	−0.283065
$787$	−7.04233e15	−0.831487	−0.415743	−	0.909482i	$-0.636479\pi$
$787$	−7.04233e15	−0.831487	−0.415743	+	0.909482i	$0.636479\pi$
$788$	5.17683e15	0.606974
$789$	6.59610e15	0.768005
$790$	−1.37132e16	−1.58559
$791$	−4.01678e15	−0.461219
$792$	−6.82278e14	−0.0777988
$793$	1.62520e16	1.84037
$794$	−1.94362e15	−0.218574
$795$	1.80973e16	2.02113
$796$	−1.63780e15	−0.181652
$797$	−1.60655e16	−1.76959	−0.884794	−	0.465982i	$-0.845701\pi$
$797$	−1.60655e16	−1.76959	−0.884794	+	0.465982i	$0.845701\pi$
$798$	2.11055e15	0.230876
$799$	−5.42343e15	−0.589205
$800$	3.43850e15	0.371000
$801$	1.31532e15	0.140946
$802$	−1.29201e16	−1.37501
$803$	5.48212e15	0.579446
$804$	4.09860e15	0.430257
$805$	9.36111e15	0.976000
$806$	−7.18972e14	−0.0744508
$807$	4.27594e14	0.0439772
$808$	−2.81712e15	−0.287769
$809$	−7.04385e15	−0.714650	−0.357325	−	0.933980i	$-0.616311\pi$
$809$	−7.04385e15	−0.714650	−0.357325	+	0.933980i	$0.616311\pi$
$810$	1.37246e15	0.138303
$811$	1.98580e15	0.198756	0.0993782	−	0.995050i	$-0.468315\pi$
$811$	1.98580e15	0.198756	0.0993782	+	0.995050i	$0.468315\pi$
$812$	2.92969e15	0.291249
$813$	9.85271e15	0.972876
$814$	−2.14255e15	−0.210135
$815$	2.45414e16	2.39074
$816$	6.34326e14	0.0613786
$817$	4.68777e15	0.450552
$818$	1.37180e16	1.30963
$819$	1.56824e15	0.148713
$820$	2.97495e15	0.280223
$821$	5.14306e14	0.0481210	0.0240605	−	0.999711i	$-0.492341\pi$
$821$	5.14306e14	0.0481210	0.0240605	+	0.999711i	$0.492341\pi$
$822$	7.47406e15	0.694643
$823$	1.34737e16	1.24391	0.621955	−	0.783053i	$-0.286338\pi$
$823$	1.34737e16	1.24391	0.621955	+	0.783053i	$0.286338\pi$
$824$	1.29245e15	0.118526
$825$	8.78060e15	0.799884
$826$	2.05938e15	0.186358
$827$	4.12894e14	0.0371158	0.0185579	−	0.999828i	$-0.494093\pi$
$827$	4.12894e14	0.0371158	0.0185579	+	0.999828i	$0.494093\pi$
$828$	2.73795e15	0.244489
$829$	−2.60570e14	−0.0231139	−0.0115570	−	0.999933i	$-0.503679\pi$
$829$	−2.60570e14	−0.0231139	−0.0115570	+	0.999933i	$0.503679\pi$
$830$	−1.65667e16	−1.45984
$831$	−2.36389e14	−0.0206929
$832$	1.69671e15	0.147547
$833$	−7.03213e14	−0.0607490
$834$	5.05610e14	0.0433913
$835$	−1.13197e16	−0.965074
$836$	5.83106e15	0.493871
$837$	2.04020e14	0.0171665
$838$	−6.88206e15	−0.575276
$839$	7.52155e15	0.624621	0.312311	−	0.949980i	$-0.398897\pi$
$839$	7.52155e15	0.624621	0.312311	+	0.949980i	$0.398897\pi$
$840$	−1.64615e15	−0.135811
$841$	1.67772e16	1.37512
$842$	−1.39044e15	−0.113223
$843$	4.17790e15	0.337992
$844$	−4.46752e15	−0.359073
$845$	8.66980e15	0.692304
$846$	4.11652e15	0.326583
$847$	−2.70551e15	−0.213251
$848$	−6.34867e15	−0.497171
$849$	−1.15125e16	−0.895728
$850$	−8.16348e15	−0.631061
$851$	8.59797e15	0.660364
$852$	−1.55039e15	−0.118310
$853$	−2.01491e16	−1.52769	−0.763845	−	0.645399i	$-0.776691\pi$
$853$	−2.01491e16	−1.52769	−0.763845	+	0.645399i	$0.776691\pi$
$854$	5.53146e15	0.416698
$855$	−1.17297e16	−0.877954
$856$	−3.08018e15	−0.229071
$857$	1.66555e16	1.23073	0.615365	−	0.788242i	$-0.289009\pi$
$857$	1.66555e16	1.23073	0.615365	+	0.788242i	$0.289009\pi$
$858$	4.33275e15	0.318115
$859$	6.98089e15	0.509271	0.254635	−	0.967037i	$-0.418045\pi$
$859$	6.98089e15	0.509271	0.254635	+	0.967037i	$0.418045\pi$
$860$	−3.65630e15	−0.265033
$861$	−9.64611e14	−0.0694760
$862$	1.26020e16	0.901883
$863$	−2.65782e16	−1.89002	−0.945009	−	0.327044i	$-0.893947\pi$
$863$	−2.65782e16	−1.89002	−0.945009	+	0.327044i	$0.893947\pi$
$864$	−4.81469e14	−0.0340207
$865$	−7.77193e15	−0.545683
$866$	1.09301e15	0.0762561
$867$	6.82209e15	0.472947
$868$	−2.44706e14	−0.0168572
$869$	1.22847e16	0.840923
$870$	−1.62822e16	−1.10753
$871$	−2.60278e16	−1.75929
$872$	5.46776e15	0.367256
$873$	5.24777e15	0.350265
$874$	−2.33998e16	−1.55203
$875$	1.10907e16	0.730998
$876$	3.86862e15	0.253386
$877$	9.98093e15	0.649640	0.324820	−	0.945776i	$-0.394696\pi$
$877$	9.98093e15	0.649640	0.324820	+	0.945776i	$0.394696\pi$
$878$	1.29822e15	0.0839711
$879$	8.21927e15	0.528317
$880$	−4.54803e15	−0.290515
$881$	−1.46967e16	−0.932935	−0.466467	−	0.884538i	$-0.654473\pi$
$881$	−1.46967e16	−0.932935	−0.466467	+	0.884538i	$0.654473\pi$
$882$	5.33756e14	0.0336718
$883$	8.36920e15	0.524687	0.262343	−	0.964975i	$-0.415505\pi$
$883$	8.36920e15	0.524687	0.262343	+	0.964975i	$0.415505\pi$
$884$	−4.02824e15	−0.250973
$885$	−1.14453e16	−0.708663
$886$	1.20057e16	0.738755
$887$	1.88849e16	1.15487	0.577437	−	0.816435i	$-0.304053\pi$
$887$	1.88849e16	1.15487	0.577437	+	0.816435i	$0.304053\pi$
$888$	−1.51196e15	−0.0918899
$889$	9.84774e14	0.0594808
$890$	8.76784e15	0.526317
$891$	−1.22949e15	−0.0733494
$892$	3.11187e15	0.184508
$893$	−3.51816e16	−2.07316
$894$	−1.15173e15	−0.0674521
$895$	−5.40868e16	−3.14822
$896$	5.77484e14	0.0334077
$897$	−1.73871e16	−0.999699
$898$	−3.95745e15	−0.226150
$899$	−2.42039e15	−0.137470
$900$	6.19628e15	0.349782
$901$	1.50727e16	0.845675
$902$	−2.66505e15	−0.148617
$903$	1.18553e15	0.0657100
$904$	−7.83137e15	−0.431431
$905$	−2.03387e16	−1.11367
$906$	−7.50696e15	−0.408563
$907$	2.16556e15	0.117147	0.0585735	−	0.998283i	$-0.481345\pi$
$907$	2.16556e15	0.117147	0.0585735	+	0.998283i	$0.481345\pi$
$908$	1.03745e16	0.557819
$909$	−5.07655e15	−0.271311
$910$	1.04538e16	0.555322
$911$	−9.43108e15	−0.497978	−0.248989	−	0.968506i	$-0.580098\pi$
$911$	−9.43108e15	−0.497978	−0.248989	+	0.968506i	$0.580098\pi$
$912$	4.11486e15	0.215965
$913$	1.48409e16	0.774231
$914$	1.62346e15	0.0841853
$915$	−3.07418e16	−1.58458
$916$	−6.20921e15	−0.318135
$917$	5.14570e15	0.262068
$918$	1.14308e15	0.0578683
$919$	−2.02685e16	−1.01997	−0.509984	−	0.860184i	$-0.670349\pi$
$919$	−2.02685e16	−1.01997	−0.509984	+	0.860184i	$0.670349\pi$
$920$	1.82510e16	0.912965
$921$	1.38561e16	0.688991
$922$	2.27906e16	1.12651
$923$	9.84561e15	0.483764
$924$	1.47467e15	0.0720277
$925$	1.94581e16	0.944761
$926$	1.88091e16	0.907837
$927$	2.32904e15	0.111747
$928$	5.71192e15	0.272438
$929$	−2.62415e16	−1.24423	−0.622117	−	0.782924i	$-0.713727\pi$
$929$	−2.62415e16	−1.24423	−0.622117	+	0.782924i	$0.713727\pi$
$930$	1.35998e15	0.0641029
$931$	−4.56173e15	−0.213750
$932$	−1.49432e16	−0.696074
$933$	2.05353e16	0.950939
$934$	−4.17448e15	−0.192174
$935$	1.07977e16	0.494158
$936$	3.05753e15	0.139109
$937$	−1.86612e16	−0.844055	−0.422028	−	0.906583i	$-0.638681\pi$
$937$	−1.86612e16	−0.844055	−0.422028	+	0.906583i	$0.638681\pi$
$938$	−8.85870e15	−0.398340
$939$	−1.90546e16	−0.851802
$940$	2.74405e16	1.21952
$941$	8.07038e15	0.356575	0.178288	−	0.983978i	$-0.442944\pi$
$941$	8.07038e15	0.356575	0.178288	+	0.983978i	$0.442944\pi$
$942$	1.69468e16	0.744404
$943$	1.06947e16	0.467040
$944$	4.01511e15	0.174322
$945$	−2.96642e15	−0.128044
$946$	3.27542e15	0.140561
$947$	−2.41583e16	−1.03072	−0.515361	−	0.856973i	$-0.672342\pi$
$947$	−2.41583e16	−1.03072	−0.515361	+	0.856973i	$0.672342\pi$
$948$	8.66907e15	0.367728
$949$	−2.45673e16	−1.03608
$950$	−5.29563e16	−2.22043
$951$	7.82357e15	0.326146
$952$	−1.37103e15	−0.0568255
$953$	3.30289e16	1.36108	0.680538	−	0.732712i	$-0.261746\pi$
$953$	3.30289e16	1.36108	0.680538	+	0.732712i	$0.261746\pi$
$954$	−1.14405e16	−0.468737
$955$	−3.05826e16	−1.24582
$956$	−1.37052e16	−0.555093
$957$	1.45860e16	0.587383
$958$	1.21981e16	0.488407
$959$	−1.61544e16	−0.643114
$960$	−3.20945e15	−0.127039
$961$	−2.52063e16	−0.992043
$962$	9.60155e15	0.375732
$963$	−5.55059e15	−0.215971
$964$	1.09028e16	0.421807
$965$	1.75751e16	0.676077
$966$	−5.91779e15	−0.226352
$967$	2.53065e16	0.962468	0.481234	−	0.876592i	$-0.340189\pi$
$967$	2.53065e16	0.962468	0.481234	+	0.876592i	$0.340189\pi$
$968$	−5.27484e15	−0.199478
$969$	−9.76926e15	−0.367351
$970$	3.49813e16	1.30795
$971$	−1.40760e16	−0.523327	−0.261664	−	0.965159i	$-0.584271\pi$
$971$	−1.40760e16	−0.523327	−0.261664	+	0.965159i	$0.584271\pi$
$972$	−8.67624e14	−0.0320750
$973$	−1.09282e15	−0.0401725
$974$	−1.43264e16	−0.523675
$975$	−3.93490e16	−1.43024
$976$	1.07845e16	0.389785
$977$	1.38102e16	0.496339	0.248170	−	0.968717i	$-0.420171\pi$
$977$	1.38102e16	0.496339	0.248170	+	0.968717i	$0.420171\pi$
$978$	−1.55143e16	−0.554458
$979$	−7.85448e15	−0.279134
$980$	3.55799e15	0.125736
$981$	9.85308e15	0.346252
$982$	−9.81361e15	−0.342938
$983$	4.36384e16	1.51644	0.758219	−	0.652000i	$-0.226070\pi$
$983$	4.36384e16	1.51644	0.758219	+	0.652000i	$0.226070\pi$
$984$	−1.88067e15	−0.0649888
$985$	6.21854e16	2.13692
$986$	−1.35609e16	−0.463410
$987$	−8.89742e15	−0.302357
$988$	−2.61311e16	−0.883068
$989$	−1.31441e16	−0.441724
$990$	−8.19569e15	−0.273900
$991$	4.52989e16	1.50551	0.752754	−	0.658302i	$-0.228725\pi$
$991$	4.52989e16	1.50551	0.752754	+	0.658302i	$0.228725\pi$
$992$	−4.77094e14	−0.0157685
$993$	5.70099e15	0.187383
$994$	3.35100e15	0.109534
$995$	−1.96737e16	−0.639527
$996$	1.04729e16	0.338564
$997$	1.58537e16	0.509692	0.254846	−	0.966982i	$-0.417975\pi$
$997$	1.58537e16	0.509692	0.254846	+	0.966982i	$0.417975\pi$
$998$	3.83352e16	1.22569
$999$	−2.72459e15	−0.0866346

Twists

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

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

\(f(q)\)	\(=\)	\(q+32.0000 q^{2} -243.000 q^{3} +1024.00 q^{4} +12300.5 q^{5} -7776.00 q^{6} +16807.0 q^{7} +32768.0 q^{8} +59049.0 q^{9} +393617. q^{10} -352614. q^{11} -248832. q^{12} +1.58019e6 q^{13} +537824. q^{14} -2.98903e6 q^{15} +1.04858e6 q^{16} -2.48947e6 q^{17} +1.88957e6 q^{18} -1.61491e7 q^{19} +1.25958e7 q^{20} -4.08410e6 q^{21} -1.12836e7 q^{22} +4.52807e7 q^{23} -7.96262e6 q^{24} +1.02475e8 q^{25} +5.05660e7 q^{26} -1.43489e7 q^{27} +1.72104e7 q^{28} +1.70228e8 q^{29} -9.56490e7 q^{30} -1.42185e7 q^{31} +3.35544e7 q^{32} +8.56851e7 q^{33} -7.96630e7 q^{34} +2.06735e8 q^{35} +6.04662e7 q^{36} +1.89882e8 q^{37} -5.16772e8 q^{38} -3.83985e8 q^{39} +4.03064e8 q^{40} +2.36187e8 q^{41} -1.30691e8 q^{42} -2.90280e8 q^{43} -3.61076e8 q^{44} +7.26335e8 q^{45} +1.44898e9 q^{46} +2.17855e9 q^{47} -2.54804e8 q^{48} +2.82475e8 q^{49} +3.27921e9 q^{50} +6.04941e8 q^{51} +1.61811e9 q^{52} -6.05457e9 q^{53} -4.59165e8 q^{54} -4.33734e9 q^{55} +5.50732e8 q^{56} +3.92424e9 q^{57} +5.44731e9 q^{58} +3.82911e9 q^{59} -3.06077e9 q^{60} +1.02849e10 q^{61} -4.54992e8 q^{62} +9.92437e8 q^{63} +1.07374e9 q^{64} +1.94372e10 q^{65} +2.74192e9 q^{66} -1.64714e10 q^{67} -2.54922e9 q^{68} -1.10032e10 q^{69} +6.61553e9 q^{70} +6.23066e9 q^{71} +1.93492e9 q^{72} -1.55471e10 q^{73} +6.07621e9 q^{74} -2.49015e10 q^{75} -1.65367e10 q^{76} -5.92638e9 q^{77} -1.22875e10 q^{78} -3.48390e10 q^{79} +1.28981e10 q^{80} +3.48678e9 q^{81} +7.55798e9 q^{82} -4.20883e10 q^{83} -4.18212e9 q^{84} -3.06218e10 q^{85} -9.28897e9 q^{86} -4.13655e10 q^{87} -1.15544e10 q^{88} +2.22750e10 q^{89} +2.32427e10 q^{90} +2.65582e10 q^{91} +4.63674e10 q^{92} +3.45509e9 q^{93} +6.97136e10 q^{94} -1.98643e11 q^{95} -8.15373e9 q^{96} +8.88715e10 q^{97} +9.03921e9 q^{98} -2.08215e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 64 q^{2} - 486 q^{3} + 2048 q^{4} - 1032 q^{5} - 15552 q^{6} + 33614 q^{7} + 65536 q^{8} + 118098 q^{9} - 33024 q^{10} - 1294788 q^{11} - 497664 q^{12} + 2545180 q^{13} + 1075648 q^{14} + 250776 q^{15}+ \cdots - 76455936612 q^{99}+O(q^{100}) \) 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

Fields

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Database

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