LMFDB - Embedded newform 7.10.a.b.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7,10,Mod(1,7)] 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("7.1"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 10, names="a")

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

Newform invariants

comment:select newform

sage:traces = [3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$3.60525085315$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 426x + 2016 $ x^3 - x^2 - 426*x + 2016
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-22.2358$ of defining polynomial
Character	$\chi$	$=$	7.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+13.3607 q^{2} +163.415 q^{3} -333.491 q^{4} +1922.19 q^{5} +2183.34 q^{6} +2401.00 q^{7} -11296.4 q^{8} +7021.32 q^{9} +25681.8 q^{10} -90199.9 q^{11} -54497.3 q^{12} -3199.89 q^{13} +32079.1 q^{14} +314114. q^{15} +19819.7 q^{16} +116494. q^{17} +93809.9 q^{18} -142449. q^{19} -641033. q^{20} +392358. q^{21} -1.20514e6 q^{22} +1.27391e6 q^{23} -1.84599e6 q^{24} +1.74168e6 q^{25} -42752.8 q^{26} -2.06910e6 q^{27} -800712. q^{28} -1.42931e6 q^{29} +4.19679e6 q^{30} +9.67494e6 q^{31} +6.04855e6 q^{32} -1.47400e7 q^{33} +1.55645e6 q^{34} +4.61518e6 q^{35} -2.34155e6 q^{36} -8.67744e6 q^{37} -1.90323e6 q^{38} -522908. q^{39} -2.17138e7 q^{40} +1.32544e7 q^{41} +5.24219e6 q^{42} -2.97554e7 q^{43} +3.00809e7 q^{44} +1.34963e7 q^{45} +1.70204e7 q^{46} -1.07969e7 q^{47} +3.23882e6 q^{48} +5.76480e6 q^{49} +2.32702e7 q^{50} +1.90369e7 q^{51} +1.06713e6 q^{52} +7.07399e7 q^{53} -2.76447e7 q^{54} -1.73381e8 q^{55} -2.71226e7 q^{56} -2.32783e7 q^{57} -1.90966e7 q^{58} +6.40400e6 q^{59} -1.04754e8 q^{60} +1.69190e8 q^{61} +1.29264e8 q^{62} +1.68582e7 q^{63} +7.06653e7 q^{64} -6.15078e6 q^{65} -1.96937e8 q^{66} -1.16276e8 q^{67} -3.88498e7 q^{68} +2.08176e8 q^{69} +6.16621e7 q^{70} +1.44496e8 q^{71} -7.93154e7 q^{72} +1.60155e8 q^{73} -1.15937e8 q^{74} +2.84617e8 q^{75} +4.75056e7 q^{76} -2.16570e8 q^{77} -6.98643e6 q^{78} -4.89322e8 q^{79} +3.80972e7 q^{80} -4.76322e8 q^{81} +1.77088e8 q^{82} -8.31590e7 q^{83} -1.30848e8 q^{84} +2.23924e8 q^{85} -3.97553e8 q^{86} -2.33569e8 q^{87} +1.01893e9 q^{88} +2.08083e6 q^{89} +1.80320e8 q^{90} -7.68292e6 q^{91} -4.24838e8 q^{92} +1.58103e9 q^{93} -1.44255e8 q^{94} -2.73815e8 q^{95} +9.88421e8 q^{96} -3.15885e8 q^{97} +7.70219e7 q^{98} -6.33322e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 21 q^{2} + 84 q^{3} + 1557 q^{4} + 1554 q^{5} + 4914 q^{6} + 7203 q^{7} + 14055 q^{8} - 26001 q^{9} - 97860 q^{10} - 3444 q^{11} - 106386 q^{12} - 19782 q^{13} + 50421 q^{14} + 200304 q^{15} + 482961 q^{16}+ \cdots - 1900979172 q^{99}+O(q^{100}) $ 3 * q + 21 * q^2 + 84 * q^3 + 1557 * q^4 + 1554 * q^5 + 4914 * q^6 + 7203 * q^7 + 14055 * q^8 - 26001 * q^9 - 97860 * q^10 - 3444 * q^11 - 106386 * q^12 - 19782 * q^13 + 50421 * q^14 + 200304 * q^15 + 482961 * q^16 + 1016694 * q^17 - 273267 * q^18 + 222852 * q^19 - 1922088 * q^20 + 201684 * q^21 - 2847048 * q^22 + 1885632 * q^23 - 1449630 * q^24 + 3073221 * q^25 - 8785056 * q^26 + 551880 * q^27 + 3738357 * q^28 + 4081818 * q^29 + 8053200 * q^30 + 2869440 * q^31 + 25221951 * q^32 - 20259792 * q^33 - 3981642 * q^34 + 3731154 * q^35 - 35396379 * q^36 + 1395618 * q^37 + 43479870 * q^38 - 8990688 * q^39 - 82859280 * q^40 - 14420658 * q^41 + 11798514 * q^42 - 61631172 * q^43 + 97011984 * q^44 + 29774682 * q^45 + 89747664 * q^46 - 10368960 * q^47 + 16798782 * q^48 + 17294403 * q^49 + 73325055 * q^50 - 26146728 * q^51 - 80908044 * q^52 + 67502610 * q^53 - 117879300 * q^54 - 105823032 * q^55 + 33746055 * q^56 + 8471112 * q^57 - 159163830 * q^58 - 42590100 * q^59 - 179551008 * q^60 + 191746842 * q^61 - 46983468 * q^62 - 62428401 * q^63 + 7852161 * q^64 + 364283220 * q^65 - 8057952 * q^66 - 255175788 * q^67 + 743485806 * q^68 + 257903856 * q^69 - 234961860 * q^70 + 296514504 * q^71 - 609314265 * q^72 + 344213310 * q^73 - 690696462 * q^74 + 279031116 * q^75 + 728839986 * q^76 - 8269044 * q^77 + 280132776 * q^78 - 960412656 * q^79 - 1333333344 * q^80 - 35827677 * q^81 + 562675302 * q^82 - 1100517180 * q^83 - 255432786 * q^84 + 438179412 * q^85 - 880982256 * q^86 - 621821592 * q^87 + 1206124800 * q^88 + 506816478 * q^89 + 2303452620 * q^90 - 47496582 * q^91 + 691123488 * q^92 + 1693258512 * q^93 + 1388004828 * q^94 - 2203071072 * q^95 + 333385794 * q^96 - 647498250 * q^97 + 121060821 * q^98 - 1900979172 * 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 $

$2$	13.3607	0.590466	0.295233	−	0.955425i	$-0.404603\pi$
$2$	13.3607	0.590466	0.295233	+	0.955425i	$0.404603\pi$
$3$	163.415	1.16478	0.582392	−	0.812908i	$-0.302117\pi$
$3$	163.415	1.16478	0.582392	+	0.812908i	$0.302117\pi$
$4$	−333.491	−0.651350
$5$	1922.19	1.37541	0.687703	−	0.725992i	$-0.258619\pi$
$5$	1922.19	1.37541	0.687703	+	0.725992i	$0.258619\pi$
$6$	2183.34	0.687765
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	−11296.4	−0.975066
$9$	7021.32	0.356720
$10$	25681.8	0.812131
$11$	−90199.9	−1.85754	−0.928772	−	0.370652i	$-0.879134\pi$
$11$	−90199.9	−1.85754	−0.928772	+	0.370652i	$0.879134\pi$
$12$	−54497.3	−0.758681
$13$	−3199.89	−0.0310734	−0.0155367	−	0.999879i	$-0.504946\pi$
$13$	−3199.89	−0.0310734	−0.0155367	+	0.999879i	$0.504946\pi$
$14$	32079.1	0.223175
$15$	314114.	1.60205
$16$	19819.7	0.0756061
$17$	116494.	0.338286	0.169143	−	0.985591i	$-0.445900\pi$
$17$	116494.	0.338286	0.169143	+	0.985591i	$0.445900\pi$
$18$	93809.9	0.210631
$19$	−142449.	−0.250767	−0.125383	−	0.992108i	$-0.540016\pi$
$19$	−142449.	−0.250767	−0.125383	+	0.992108i	$0.540016\pi$
$20$	−641033.	−0.895870
$21$	392358.	0.440247
$22$	−1.20514e6	−1.09682
$23$	1.27391e6	0.949213	0.474606	−	0.880198i	$-0.342590\pi$
$23$	1.27391e6	0.949213	0.474606	+	0.880198i	$0.342590\pi$
$24$	−1.84599e6	−1.13574
$25$	1.74168e6	0.891742
$26$	−42752.8	−0.0183478
$27$	−2.06910e6	−0.749282
$28$	−800712.	−0.246187
$29$	−1.42931e6	−0.375262	−0.187631	−	0.982240i	$-0.560081\pi$
$29$	−1.42931e6	−0.375262	−0.187631	+	0.982240i	$0.560081\pi$
$30$	4.19679e6	0.945956
$31$	9.67494e6	1.88157	0.940786	−	0.339001i	$-0.110089\pi$
$31$	9.67494e6	1.88157	0.940786	+	0.339001i	$0.110089\pi$
$32$	6.04855e6	1.01971
$33$	−1.47400e7	−2.16364
$34$	1.55645e6	0.199747
$35$	4.61518e6	0.519855
$36$	−2.34155e6	−0.232349
$37$	−8.67744e6	−0.761174	−0.380587	−	0.924745i	$-0.624278\pi$
$37$	−8.67744e6	−0.761174	−0.380587	+	0.924745i	$0.624278\pi$
$38$	−1.90323e6	−0.148069
$39$	−522908.	−0.0361938
$40$	−2.17138e7	−1.34111
$41$	1.32544e7	0.732541	0.366271	−	0.930508i	$-0.380634\pi$
$41$	1.32544e7	0.732541	0.366271	+	0.930508i	$0.380634\pi$
$42$	5.24219e6	0.259951
$43$	−2.97554e7	−1.32726	−0.663632	−	0.748060i	$-0.730986\pi$
$43$	−2.97554e7	−1.32726	−0.663632	+	0.748060i	$0.730986\pi$
$44$	3.00809e7	1.20991
$45$	1.34963e7	0.490635
$46$	1.70204e7	0.560478
$47$	−1.07969e7	−0.322745	−0.161373	−	0.986894i	$-0.551592\pi$
$47$	−1.07969e7	−0.322745	−0.161373	+	0.986894i	$0.551592\pi$
$48$	3.23882e6	0.0880647
$49$	5.76480e6	0.142857
$50$	2.32702e7	0.526544
$51$	1.90369e7	0.394030
$52$	1.06713e6	0.0202397
$53$	7.07399e7	1.23147	0.615734	−	0.787954i	$-0.288860\pi$
$53$	7.07399e7	1.23147	0.615734	+	0.787954i	$0.288860\pi$
$54$	−2.76447e7	−0.442426
$55$	−1.73381e8	−2.55488
$56$	−2.71226e7	−0.368540
$57$	−2.32783e7	−0.292089
$58$	−1.90966e7	−0.221579
$59$	6.40400e6	0.0688046	0.0344023	−	0.999408i	$-0.489047\pi$
$59$	6.40400e6	0.0688046	0.0344023	+	0.999408i	$0.489047\pi$
$60$	−1.04754e8	−1.04349
$61$	1.69190e8	1.56455	0.782275	−	0.622933i	$-0.214059\pi$
$61$	1.69190e8	1.56455	0.782275	+	0.622933i	$0.214059\pi$
$62$	1.29264e8	1.11100
$63$	1.68582e7	0.134827
$64$	7.06653e7	0.526498
$65$	−6.15078e6	−0.0427386
$66$	−1.96937e8	−1.27755
$67$	−1.16276e8	−0.704943	−0.352471	−	0.935823i	$-0.614659\pi$
$67$	−1.16276e8	−0.704943	−0.352471	+	0.935823i	$0.614659\pi$
$68$	−3.88498e7	−0.220343
$69$	2.08176e8	1.10563
$70$	6.16621e7	0.306957
$71$	1.44496e8	0.674826	0.337413	−	0.941357i	$-0.390448\pi$
$71$	1.44496e8	0.674826	0.337413	+	0.941357i	$0.390448\pi$
$72$	−7.93154e7	−0.347825
$73$	1.60155e8	0.660066	0.330033	−	0.943969i	$-0.392940\pi$
$73$	1.60155e8	0.660066	0.330033	+	0.943969i	$0.392940\pi$
$74$	−1.15937e8	−0.449447
$75$	2.84617e8	1.03869
$76$	4.75056e7	0.163337
$77$	−2.16570e8	−0.702085
$78$	−6.98643e6	−0.0213712
$79$	−4.89322e8	−1.41343	−0.706713	−	0.707500i	$-0.749823\pi$
$79$	−4.89322e8	−1.41343	−0.706713	+	0.707500i	$0.749823\pi$
$80$	3.80972e7	0.103989
$81$	−4.76322e8	−1.22947
$82$	1.77088e8	0.432541
$83$	−8.31590e7	−0.192335	−0.0961674	−	0.995365i	$-0.530658\pi$
$83$	−8.31590e7	−0.192335	−0.0961674	+	0.995365i	$0.530658\pi$
$84$	−1.30848e8	−0.286755
$85$	2.23924e8	0.465281
$86$	−3.97553e8	−0.783704
$87$	−2.33569e8	−0.437098
$88$	1.01893e9	1.81123
$89$	2.08083e6	0.00351546	0.00175773	−	0.999998i	$-0.499440\pi$
$89$	2.08083e6	0.00351546	0.00175773	+	0.999998i	$0.499440\pi$
$90$	1.80320e8	0.289703
$91$	−7.68292e6	−0.0117447
$92$	−4.24838e8	−0.618270
$93$	1.58103e9	2.19162
$94$	−1.44255e8	−0.190570
$95$	−2.73815e8	−0.344906
$96$	9.88421e8	1.18774
$97$	−3.15885e8	−0.362290	−0.181145	−	0.983456i	$-0.557980\pi$
$97$	−3.15885e8	−0.362290	−0.181145	+	0.983456i	$0.557980\pi$
$98$	7.70219e7	0.0843523
$99$	−6.33322e8	−0.662623
$100$	−5.80836e8	−0.580836
$101$	−5.74841e8	−0.549669	−0.274835	−	0.961492i	$-0.588623\pi$
$101$	−5.74841e8	−0.549669	−0.274835	+	0.961492i	$0.588623\pi$
$102$	2.54346e8	0.232662
$103$	−1.51870e9	−1.32955	−0.664775	−	0.747044i	$-0.731473\pi$
$103$	−1.51870e9	−1.32955	−0.664775	+	0.747044i	$0.731473\pi$
$104$	3.61471e7	0.0302987
$105$	7.54187e8	0.605518
$106$	9.45137e8	0.727140
$107$	−2.01863e8	−0.148878	−0.0744390	−	0.997226i	$-0.523717\pi$
$107$	−2.01863e8	−0.148878	−0.0744390	+	0.997226i	$0.523717\pi$
$108$	6.90027e8	0.488044
$109$	−8.73952e8	−0.593019	−0.296509	−	0.955030i	$-0.595823\pi$
$109$	−8.73952e8	−0.593019	−0.296509	+	0.955030i	$0.595823\pi$
$110$	−2.31650e9	−1.50857
$111$	−1.41802e9	−0.886603
$112$	4.75871e7	0.0285764
$113$	1.52955e9	0.882491	0.441245	−	0.897386i	$-0.354537\pi$
$113$	1.52955e9	0.882491	0.441245	+	0.897386i	$0.354537\pi$
$114$	−3.11015e8	−0.172469
$115$	2.44870e9	1.30555
$116$	4.76661e8	0.244427
$117$	−2.24674e7	−0.0110845
$118$	8.55621e7	0.0406268
$119$	2.79703e8	0.127860
$120$	−3.54834e9	−1.56210
$121$	5.77807e9	2.45047
$122$	2.26050e9	0.923814
$123$	2.16596e9	0.853252
$124$	−3.22651e9	−1.22556
$125$	−4.06429e8	−0.148898
$126$	2.25238e8	0.0796110
$127$	−8.71958e8	−0.297426	−0.148713	−	0.988880i	$-0.547513\pi$
$127$	−8.71958e8	−0.297426	−0.148713	+	0.988880i	$0.547513\pi$
$128$	−2.15272e9	−0.708830
$129$	−4.86246e9	−1.54597
$130$	−8.21789e7	−0.0252357
$131$	2.24404e9	0.665747	0.332874	−	0.942971i	$-0.391982\pi$
$131$	2.24404e9	0.665747	0.332874	+	0.942971i	$0.391982\pi$
$132$	4.91565e9	1.40928
$133$	−3.42021e8	−0.0947809
$134$	−1.55353e9	−0.416245
$135$	−3.97721e9	−1.03057
$136$	−1.31596e9	−0.329852
$137$	4.16141e9	1.00925	0.504624	−	0.863339i	$-0.331631\pi$
$137$	4.16141e9	1.00925	0.504624	+	0.863339i	$0.331631\pi$
$138$	2.78138e9	0.652836
$139$	−6.03383e9	−1.37097	−0.685483	−	0.728089i	$-0.740409\pi$
$139$	−6.03383e9	−1.37097	−0.685483	+	0.728089i	$0.740409\pi$
$140$	−1.53912e9	−0.338607
$141$	−1.76438e9	−0.375928
$142$	1.93057e9	0.398462
$143$	2.88629e8	0.0577203
$144$	1.39160e8	0.0269702
$145$	−2.74740e9	−0.516137
$146$	2.13979e9	0.389747
$147$	9.42052e8	0.166398
$148$	2.89385e9	0.495790
$149$	−4.37832e9	−0.727728	−0.363864	−	0.931452i	$-0.618543\pi$
$149$	−4.37832e9	−0.727728	−0.363864	+	0.931452i	$0.618543\pi$
$150$	3.80268e9	0.613309
$151$	−2.69365e9	−0.421642	−0.210821	−	0.977525i	$-0.567614\pi$
$151$	−2.69365e9	−0.421642	−0.210821	+	0.977525i	$0.567614\pi$
$152$	1.60916e9	0.244514
$153$	8.17943e8	0.120673
$154$	−2.89353e9	−0.414558
$155$	1.85971e10	2.58793
$156$	1.74385e8	0.0235748
$157$	−1.33044e9	−0.174762	−0.0873810	−	0.996175i	$-0.527850\pi$
$157$	−1.33044e9	−0.174762	−0.0873810	+	0.996175i	$0.527850\pi$
$158$	−6.53770e9	−0.834580
$159$	1.15599e10	1.43439
$160$	1.16265e10	1.40251
$161$	3.05866e9	0.358769
$162$	−6.36401e9	−0.725961
$163$	−3.56094e9	−0.395112	−0.197556	−	0.980292i	$-0.563301\pi$
$163$	−3.56094e9	−0.395112	−0.197556	+	0.980292i	$0.563301\pi$
$164$	−4.42022e9	−0.477140
$165$	−2.83330e10	−2.97588
$166$	−1.11106e9	−0.113567
$167$	−1.04285e10	−1.03752	−0.518762	−	0.854919i	$-0.673607\pi$
$167$	−1.04285e10	−1.03752	−0.518762	+	0.854919i	$0.673607\pi$
$168$	−4.43223e9	−0.429270
$169$	−1.05943e10	−0.999034
$170$	2.99179e9	0.274733
$171$	−1.00018e9	−0.0894534
$172$	9.92314e9	0.864512
$173$	2.04717e10	1.73759	0.868793	−	0.495176i	$-0.164896\pi$
$173$	2.04717e10	1.73759	0.868793	+	0.495176i	$0.164896\pi$
$174$	−3.12066e9	−0.258092
$175$	4.18178e9	0.337047
$176$	−1.78773e9	−0.140442
$177$	1.04651e9	0.0801424
$178$	2.78014e7	0.00207576
$179$	5.46705e9	0.398029	0.199014	−	0.979997i	$-0.436226\pi$
$179$	5.46705e9	0.398029	0.199014	+	0.979997i	$0.436226\pi$
$180$	−4.50089e9	−0.319575
$181$	−2.11628e9	−0.146561	−0.0732807	−	0.997311i	$-0.523347\pi$
$181$	−2.11628e9	−0.146561	−0.0732807	+	0.997311i	$0.523347\pi$
$182$	−1.02649e8	−0.00693482
$183$	2.76481e10	1.82236
$184$	−1.43906e10	−0.925545
$185$	−1.66797e10	−1.04692
$186$	2.11237e10	1.29408
$187$	−1.05078e10	−0.628381
$188$	3.60068e9	0.210220
$189$	−4.96792e9	−0.283202
$190$	−3.65836e9	−0.203655
$191$	1.72421e10	0.937431	0.468715	−	0.883349i	$-0.344717\pi$
$191$	1.72421e10	0.937431	0.468715	+	0.883349i	$0.344717\pi$
$192$	1.15477e10	0.613256
$193$	2.02030e10	1.04811	0.524055	−	0.851684i	$-0.324418\pi$
$193$	2.02030e10	1.04811	0.524055	+	0.851684i	$0.324418\pi$
$194$	−4.22045e9	−0.213920
$195$	−1.00513e9	−0.0497812
$196$	−1.92251e9	−0.0930500
$197$	−2.22592e10	−1.05296	−0.526481	−	0.850187i	$-0.676489\pi$
$197$	−2.22592e10	−1.05296	−0.526481	+	0.850187i	$0.676489\pi$
$198$	−8.46164e9	−0.391256
$199$	1.70588e10	0.771098	0.385549	−	0.922687i	$-0.374012\pi$
$199$	1.70588e10	0.771098	0.385549	+	0.922687i	$0.374012\pi$
$200$	−1.96747e10	−0.869508
$201$	−1.90012e10	−0.821105
$202$	−7.68029e9	−0.324561
$203$	−3.43176e9	−0.141836
$204$	−6.34862e9	−0.256651
$205$	2.54774e10	1.00754
$206$	−2.02909e10	−0.785054
$207$	8.94453e9	0.338603
$208$	−6.34207e7	−0.00234934
$209$	1.28489e10	0.465810
$210$	1.00765e10	0.357538
$211$	−3.19873e10	−1.11098	−0.555490	−	0.831523i	$-0.687469\pi$
$211$	−3.19873e10	−1.11098	−0.555490	+	0.831523i	$0.687469\pi$
$212$	−2.35911e10	−0.802116
$213$	2.36127e10	0.786026
$214$	−2.69704e9	−0.0879074
$215$	−5.71954e10	−1.82553
$216$	2.33734e10	0.730599
$217$	2.32295e10	0.711167
$218$	−1.16766e10	−0.350157
$219$	2.61717e10	0.768834
$220$	5.78211e10	1.66412
$221$	−3.72768e8	−0.0105117
$222$	−1.89458e10	−0.523509
$223$	−2.30967e10	−0.625428	−0.312714	−	0.949847i	$-0.601238\pi$
$223$	−2.30967e10	−0.625428	−0.312714	+	0.949847i	$0.601238\pi$
$224$	1.45226e10	0.385414
$225$	1.22289e10	0.318102
$226$	2.04359e10	0.521081
$227$	−2.30894e10	−0.577160	−0.288580	−	0.957456i	$-0.593183\pi$
$227$	−2.30894e10	−0.577160	−0.288580	+	0.957456i	$0.593183\pi$
$228$	7.76311e9	0.190252
$229$	4.25496e10	1.02244	0.511218	−	0.859451i	$-0.329195\pi$
$229$	4.25496e10	1.02244	0.511218	+	0.859451i	$0.329195\pi$
$230$	3.27164e10	0.770885
$231$	−3.53907e10	−0.817777
$232$	1.61460e10	0.365905
$233$	−1.26679e10	−0.281582	−0.140791	−	0.990039i	$-0.544964\pi$
$233$	−1.26679e10	−0.281582	−0.140791	+	0.990039i	$0.544964\pi$
$234$	−3.00181e8	−0.00654503
$235$	−2.07537e10	−0.443906
$236$	−2.13568e9	−0.0448158
$237$	−7.99624e10	−1.64633
$238$	3.73703e9	0.0754971
$239$	6.37875e10	1.26458	0.632289	−	0.774733i	$-0.282116\pi$
$239$	6.37875e10	1.26458	0.632289	+	0.774733i	$0.282116\pi$
$240$	6.22563e9	0.121125
$241$	−2.91604e10	−0.556823	−0.278412	−	0.960462i	$-0.589808\pi$
$241$	−2.91604e10	−0.556823	−0.278412	+	0.960462i	$0.589808\pi$
$242$	7.71992e10	1.44692
$243$	−3.71118e10	−0.682785
$244$	−5.64232e10	−1.01907
$245$	1.10810e10	0.196487
$246$	2.89388e10	0.503816
$247$	4.55822e8	0.00779218
$248$	−1.09292e11	−1.83466
$249$	−1.35894e10	−0.224028
$250$	−5.43018e9	−0.0879194
$251$	6.28939e10	1.00018	0.500088	−	0.865974i	$-0.333301\pi$
$251$	6.28939e10	1.00018	0.500088	+	0.865974i	$0.333301\pi$
$252$	−5.62205e9	−0.0878198
$253$	−1.14907e11	−1.76320
$254$	−1.16500e10	−0.175620
$255$	3.65924e10	0.541952
$256$	−6.49425e10	−0.945038
$257$	1.14480e11	1.63694	0.818469	−	0.574551i	$-0.194823\pi$
$257$	1.14480e11	1.63694	0.818469	+	0.574551i	$0.194823\pi$
$258$	−6.49660e10	−0.912845
$259$	−2.08345e10	−0.287697
$260$	2.05123e9	0.0278378
$261$	−1.00356e10	−0.133863
$262$	2.99820e10	0.393101
$263$	1.40705e10	0.181346	0.0906728	−	0.995881i	$-0.471098\pi$
$263$	1.40705e10	0.181346	0.0906728	+	0.995881i	$0.471098\pi$
$264$	1.66508e11	2.10969
$265$	1.35975e11	1.69377
$266$	−4.56965e9	−0.0559649
$267$	3.40038e8	0.00409475
$268$	3.87770e10	0.459164
$269$	8.39143e10	0.977127	0.488563	−	0.872528i	$-0.337521\pi$
$269$	8.39143e10	0.977127	0.488563	+	0.872528i	$0.337521\pi$
$270$	−5.31384e10	−0.608515
$271$	1.98401e10	0.223451	0.111726	−	0.993739i	$-0.464362\pi$
$271$	1.98401e10	0.223451	0.111726	+	0.993739i	$0.464362\pi$
$272$	2.30888e9	0.0255765
$273$	−1.25550e9	−0.0136800
$274$	5.55995e10	0.595927
$275$	−1.57100e11	−1.65645
$276$	−6.94247e10	−0.720150
$277$	−7.17911e10	−0.732675	−0.366338	−	0.930482i	$-0.619389\pi$
$277$	−7.17911e10	−0.732675	−0.366338	+	0.930482i	$0.619389\pi$
$278$	−8.06163e10	−0.809508
$279$	6.79308e10	0.671194
$280$	−5.21347e10	−0.506893
$281$	1.02853e11	0.984101	0.492050	−	0.870567i	$-0.336248\pi$
$281$	1.02853e11	0.984101	0.492050	+	0.870567i	$0.336248\pi$
$282$	−2.35733e10	−0.221973
$283$	−5.52883e10	−0.512382	−0.256191	−	0.966626i	$-0.582468\pi$
$283$	−5.52883e10	−0.512382	−0.256191	+	0.966626i	$0.582468\pi$
$284$	−4.81880e10	−0.439548
$285$	−4.47453e10	−0.401741
$286$	3.85630e9	0.0340819
$287$	3.18238e10	0.276875
$288$	4.24688e10	0.363750
$289$	−1.05017e11	−0.885562
$290$	−3.67072e10	−0.304762
$291$	−5.16202e10	−0.421989
$292$	−5.34102e10	−0.429934
$293$	1.05721e11	0.838028	0.419014	−	0.907980i	$-0.362376\pi$
$293$	1.05721e11	0.838028	0.419014	+	0.907980i	$0.362376\pi$
$294$	1.25865e10	0.0982522
$295$	1.23097e10	0.0946343
$296$	9.80236e10	0.742195
$297$	1.86633e11	1.39182
$298$	−5.84975e10	−0.429699
$299$	−4.07637e9	−0.0294953
$300$	−9.49171e10	−0.676548
$301$	−7.14426e10	−0.501658
$302$	−3.59891e10	−0.248966
$303$	−9.39374e10	−0.640246
$304$	−2.82330e9	−0.0189595
$305$	3.25214e11	2.15189
$306$	1.09283e10	0.0712536
$307$	−8.10064e10	−0.520471	−0.260236	−	0.965545i	$-0.583800\pi$
$307$	−8.10064e10	−0.520471	−0.260236	+	0.965545i	$0.583800\pi$
$308$	7.22241e10	0.457303
$309$	−2.48178e11	−1.54864
$310$	2.48470e11	1.52808
$311$	−3.18435e11	−1.93018	−0.965091	−	0.261913i	$-0.915647\pi$
$311$	−3.18435e11	−1.93018	−0.965091	+	0.261913i	$0.915647\pi$
$312$	5.90696e9	0.0352914
$313$	1.28876e11	0.758965	0.379483	−	0.925199i	$-0.376102\pi$
$313$	1.28876e11	0.758965	0.379483	+	0.925199i	$0.376102\pi$
$314$	−1.77757e10	−0.103191
$315$	3.24046e10	0.185443
$316$	1.63185e11	0.920635
$317$	−7.44722e10	−0.414217	−0.207108	−	0.978318i	$-0.566405\pi$
$317$	−7.44722e10	−0.414217	−0.207108	+	0.978318i	$0.566405\pi$
$318$	1.54449e11	0.846961
$319$	1.28923e11	0.697065
$320$	1.35832e11	0.724148
$321$	−3.29874e10	−0.173411
$322$	4.08659e10	0.211841
$323$	−1.65945e10	−0.0848309
$324$	1.58849e11	0.800815
$325$	−5.57319e9	−0.0277095
$326$	−4.75768e10	−0.233301
$327$	−1.42816e11	−0.690738
$328$	−1.49726e11	−0.714276
$329$	−2.59234e10	−0.121986
$330$	−3.78550e11	−1.75715
$331$	2.83840e11	1.29971	0.649857	−	0.760057i	$-0.274829\pi$
$331$	2.83840e11	1.29971	0.649857	+	0.760057i	$0.274829\pi$
$332$	2.77328e10	0.125277
$333$	−6.09271e10	−0.271526
$334$	−1.39332e11	−0.612623
$335$	−2.23505e11	−0.969583
$336$	7.77642e9	0.0332853
$337$	−5.61414e9	−0.0237109	−0.0118555	−	0.999930i	$-0.503774\pi$
$337$	−5.61414e9	−0.0237109	−0.0118555	+	0.999930i	$0.503774\pi$
$338$	−1.41547e11	−0.589896
$339$	2.49950e11	1.02791
$340$	−7.46766e10	−0.303061
$341$	−8.72679e11	−3.49510
$342$	−1.33632e10	−0.0528192
$343$	1.38413e10	0.0539949
$344$	3.36128e11	1.29417
$345$	4.00153e11	1.52069
$346$	2.73517e11	1.02599
$347$	3.39846e11	1.25834	0.629171	−	0.777267i	$-0.283394\pi$
$347$	3.39846e11	1.25834	0.629171	+	0.777267i	$0.283394\pi$
$348$	7.78933e10	0.284704
$349$	3.46718e10	0.125101	0.0625506	−	0.998042i	$-0.480077\pi$
$349$	3.46718e10	0.125101	0.0625506	+	0.998042i	$0.480077\pi$
$350$	5.58717e10	0.199015
$351$	6.62089e9	0.0232828
$352$	−5.45578e11	−1.89415
$353$	−3.46900e11	−1.18910	−0.594550	−	0.804059i	$-0.702670\pi$
$353$	−3.46900e11	−1.18910	−0.594550	+	0.804059i	$0.702670\pi$
$354$	1.39821e10	0.0473214
$355$	2.77748e11	0.928160
$356$	−6.93939e8	−0.00228979
$357$	4.57075e10	0.148929
$358$	7.30438e10	0.235023
$359$	−2.51011e11	−0.797569	−0.398785	−	0.917045i	$-0.630568\pi$
$359$	−2.51011e11	−0.797569	−0.398785	+	0.917045i	$0.630568\pi$
$360$	−1.52459e11	−0.478401
$361$	−3.02396e11	−0.937116
$362$	−2.82750e10	−0.0865396
$363$	9.44221e11	2.85426
$364$	2.56219e9	0.00764988
$365$	3.07848e11	0.907859
$366$	3.69398e11	1.07604
$367$	4.79871e11	1.38079	0.690394	−	0.723433i	$-0.257437\pi$
$367$	4.79871e11	1.38079	0.690394	+	0.723433i	$0.257437\pi$
$368$	2.52485e10	0.0717663
$369$	9.30632e10	0.261312
$370$	−2.22853e11	−0.618173
$371$	1.69847e11	0.465451
$372$	−5.27258e11	−1.42751
$373$	−1.84794e11	−0.494308	−0.247154	−	0.968976i	$-0.579495\pi$
$373$	−1.84794e11	−0.494308	−0.247154	+	0.968976i	$0.579495\pi$
$374$	−1.40391e11	−0.371038
$375$	−6.64164e10	−0.173434
$376$	1.21966e11	0.314698
$377$	4.57361e9	0.0116607
$378$	−6.63750e10	−0.167221
$379$	−7.08908e11	−1.76487	−0.882437	−	0.470431i	$-0.844098\pi$
$379$	−7.08908e11	−1.76487	−0.882437	+	0.470431i	$0.844098\pi$
$380$	9.13148e10	0.224654
$381$	−1.42491e11	−0.346437
$382$	2.30367e11	0.553521
$383$	1.23789e11	0.293959	0.146980	−	0.989140i	$-0.453045\pi$
$383$	1.23789e11	0.293959	0.146980	+	0.989140i	$0.453045\pi$
$384$	−3.51785e11	−0.825633
$385$	−4.16288e11	−0.965653
$386$	2.69926e11	0.618874
$387$	−2.08922e11	−0.473461
$388$	1.05345e11	0.235977
$389$	−2.97971e11	−0.659782	−0.329891	−	0.944019i	$-0.607012\pi$
$389$	−2.97971e11	−0.659782	−0.329891	+	0.944019i	$0.607012\pi$
$390$	−1.34292e10	−0.0293941
$391$	1.48403e11	0.321106
$392$	−6.51213e10	−0.139295
$393$	3.66708e11	0.775451
$394$	−2.97400e11	−0.621738
$395$	−9.40570e11	−1.94404
$396$	2.11207e11	0.431599
$397$	5.33426e11	1.07775	0.538873	−	0.842387i	$-0.318850\pi$
$397$	5.33426e11	1.07775	0.538873	+	0.842387i	$0.318850\pi$
$398$	2.27918e11	0.455307
$399$	−5.58912e10	−0.110399
$400$	3.45196e10	0.0674212
$401$	4.15640e11	0.802726	0.401363	−	0.915919i	$-0.368537\pi$
$401$	4.15640e11	0.802726	0.401363	+	0.915919i	$0.368537\pi$
$402$	−2.53870e11	−0.484835
$403$	−3.09587e10	−0.0584669
$404$	1.91704e11	0.358027
$405$	−9.15581e11	−1.69102
$406$	−4.58508e10	−0.0837491
$407$	7.82704e11	1.41391
$408$	−2.15047e11	−0.384206
$409$	1.07978e12	1.90801	0.954006	−	0.299788i	$-0.0969159\pi$
$409$	1.07978e12	1.90801	0.954006	+	0.299788i	$0.0969159\pi$
$410$	3.40397e11	0.594919
$411$	6.80035e11	1.17556
$412$	5.06473e11	0.866002
$413$	1.53760e10	0.0260057
$414$	1.19505e11	0.199934
$415$	−1.59847e11	−0.264539
$416$	−1.93547e10	−0.0316859
$417$	−9.86015e11	−1.59688
$418$	1.71671e11	0.275045
$419$	−2.20998e11	−0.350289	−0.175144	−	0.984543i	$-0.556039\pi$
$419$	−2.20998e11	−0.350289	−0.175144	+	0.984543i	$0.556039\pi$
$420$	−2.51515e11	−0.394404
$421$	3.47478e11	0.539086	0.269543	−	0.962988i	$-0.413127\pi$
$421$	3.47478e11	0.539086	0.269543	+	0.962988i	$0.413127\pi$
$422$	−4.27373e11	−0.655996
$423$	−7.58087e10	−0.115130
$424$	−7.99105e11	−1.20076
$425$	2.02896e11	0.301664
$426$	3.15483e11	0.464122
$427$	4.06224e11	0.591344
$428$	6.73196e10	0.0969716
$429$	4.71662e10	0.0672316
$430$	−7.64172e11	−1.07791
$431$	1.23574e11	0.172496	0.0862479	−	0.996274i	$-0.472512\pi$
$431$	1.23574e11	0.172496	0.0862479	+	0.996274i	$0.472512\pi$
$432$	−4.10090e10	−0.0566503
$433$	−7.27679e11	−0.994820	−0.497410	−	0.867516i	$-0.665716\pi$
$433$	−7.27679e11	−0.994820	−0.497410	+	0.867516i	$0.665716\pi$
$434$	3.10363e11	0.419920
$435$	−4.48964e11	−0.601188
$436$	2.91455e11	0.386262
$437$	−1.81468e11	−0.238031
$438$	3.49672e11	0.453970
$439$	−5.85966e11	−0.752977	−0.376489	−	0.926421i	$-0.622869\pi$
$439$	−5.85966e11	−0.752977	−0.376489	+	0.926421i	$0.622869\pi$
$440$	1.95858e12	2.49117
$441$	4.04765e10	0.0509600
$442$	−4.98045e9	−0.00620681
$443$	−2.11546e11	−0.260969	−0.130484	−	0.991450i	$-0.541653\pi$
$443$	−2.11546e11	−0.260969	−0.130484	+	0.991450i	$0.541653\pi$
$444$	4.72897e11	0.577488
$445$	3.99975e9	0.00483519
$446$	−3.08588e11	−0.369294
$447$	−7.15480e11	−0.847645
$448$	1.69667e11	0.198997
$449$	−9.21048e11	−1.06948	−0.534741	−	0.845016i	$-0.679591\pi$
$449$	−9.21048e11	−1.06948	−0.534741	+	0.845016i	$0.679591\pi$
$450$	1.63387e11	0.187829
$451$	−1.19554e12	−1.36073
$452$	−5.10091e11	−0.574810
$453$	−4.40181e11	−0.491122
$454$	−3.08491e11	−0.340794
$455$	−1.47680e10	−0.0161537
$456$	2.62961e11	0.284806
$457$	8.11185e11	0.869955	0.434977	−	0.900441i	$-0.356756\pi$
$457$	8.11185e11	0.869955	0.434977	+	0.900441i	$0.356756\pi$
$458$	5.68493e11	0.603713
$459$	−2.41039e11	−0.253472
$460$	−8.16618e11	−0.850372
$461$	−1.90069e11	−0.196001	−0.0980004	−	0.995186i	$-0.531245\pi$
$461$	−1.90069e11	−0.196001	−0.0980004	+	0.995186i	$0.531245\pi$
$462$	−4.72845e11	−0.482870
$463$	4.76945e11	0.482341	0.241170	−	0.970483i	$-0.422469\pi$
$463$	4.76945e11	0.482341	0.241170	+	0.970483i	$0.422469\pi$
$464$	−2.83284e10	−0.0283721
$465$	3.03903e12	3.01437
$466$	−1.69253e11	−0.166264
$467$	1.06392e12	1.03510	0.517549	−	0.855653i	$-0.326844\pi$
$467$	1.06392e12	1.03510	0.517549	+	0.855653i	$0.326844\pi$
$468$	7.49268e9	0.00721990
$469$	−2.79179e11	−0.266443
$470$	−2.77285e11	−0.262111
$471$	−2.17413e11	−0.203560
$472$	−7.23420e10	−0.0670890
$473$	2.68393e12	2.46545
$474$	−1.06836e12	−0.972105
$475$	−2.48102e11	−0.223619
$476$	−9.32784e10	−0.0832817
$477$	4.96687e11	0.439289
$478$	8.52248e11	0.746690
$479$	−8.43415e11	−0.732034	−0.366017	−	0.930608i	$-0.619279\pi$
$479$	−8.43415e11	−0.732034	−0.366017	+	0.930608i	$0.619279\pi$
$480$	1.89993e12	1.63362
$481$	2.77668e10	0.0236523
$482$	−3.89605e11	−0.328785
$483$	4.99829e11	0.417888
$484$	−1.92694e12	−1.59611
$485$	−6.07191e11	−0.498296
$486$	−4.95841e11	−0.403162
$487$	1.15202e12	0.928065	0.464032	−	0.885818i	$-0.346402\pi$
$487$	1.15202e12	0.928065	0.464032	+	0.885818i	$0.346402\pi$
$488$	−1.91123e12	−1.52554
$489$	−5.81910e11	−0.460220
$490$	1.48051e11	0.116019
$491$	−9.68703e11	−0.752184	−0.376092	−	0.926582i	$-0.622732\pi$
$491$	−9.68703e11	−0.752184	−0.376092	+	0.926582i	$0.622732\pi$
$492$	−7.22328e11	−0.555765
$493$	−1.66506e11	−0.126946
$494$	6.09011e9	0.00460102
$495$	−1.21736e12	−0.911375
$496$	1.91754e11	0.142258
$497$	3.46934e11	0.255060
$498$	−1.81564e11	−0.132281
$499$	2.62821e12	1.89761	0.948805	−	0.315863i	$-0.102294\pi$
$499$	2.62821e12	1.89761	0.948805	+	0.315863i	$0.102294\pi$
$500$	1.35540e11	0.0969848
$501$	−1.70417e12	−1.20849
$502$	8.40308e11	0.590570
$503$	3.95070e11	0.275181	0.137590	−	0.990489i	$-0.456064\pi$
$503$	3.95070e11	0.275181	0.137590	+	0.990489i	$0.456064\pi$
$504$	−1.90436e11	−0.131466
$505$	−1.10495e12	−0.756019
$506$	−1.53524e12	−1.04111
$507$	−1.73126e12	−1.16366
$508$	2.90790e11	0.193728
$509$	6.64157e11	0.438572	0.219286	−	0.975661i	$-0.429627\pi$
$509$	6.64157e11	0.438572	0.219286	+	0.975661i	$0.429627\pi$
$510$	4.88901e11	0.320004
$511$	3.84532e11	0.249482
$512$	2.34512e11	0.150817
$513$	2.94743e11	0.187895
$514$	1.52954e12	0.966556
$515$	−2.91923e12	−1.82867
$516$	1.62159e12	1.00697
$517$	9.73882e11	0.599513
$518$	−2.78364e11	−0.169875
$519$	3.34537e12	2.02391
$520$	6.94815e10	0.0416730
$521$	5.22766e11	0.310841	0.155420	−	0.987848i	$-0.450327\pi$
$521$	5.22766e11	0.310841	0.155420	+	0.987848i	$0.450327\pi$
$522$	−1.34083e11	−0.0790417
$523$	−3.09135e12	−1.80672	−0.903360	−	0.428882i	$-0.858907\pi$
$523$	−3.09135e12	−1.80672	−0.903360	+	0.428882i	$0.858907\pi$
$524$	−7.48366e11	−0.433634
$525$	6.83364e11	0.392587
$526$	1.87991e11	0.107078
$527$	1.12708e12	0.636510
$528$	−2.92142e11	−0.163584
$529$	−1.78305e11	−0.0989947
$530$	1.81673e12	1.00011
$531$	4.49645e10	0.0245440
$532$	1.14061e11	0.0617355
$533$	−4.24125e10	−0.0227626
$534$	4.54316e9	0.00241781
$535$	−3.88019e11	−0.204768
$536$	1.31350e12	0.687366
$537$	8.93396e11	0.463617
$538$	1.12116e12	0.576960
$539$	−5.19984e11	−0.265363
$540$	1.32636e12	0.671259
$541$	−1.47490e12	−0.740243	−0.370121	−	0.928983i	$-0.620684\pi$
$541$	−1.47490e12	−0.740243	−0.370121	+	0.928983i	$0.620684\pi$
$542$	2.65079e11	0.131940
$543$	−3.45831e11	−0.170712
$544$	7.04621e11	0.344954
$545$	−1.67990e12	−0.815642
$546$	−1.67744e10	−0.00807756
$547$	2.12294e12	1.01390	0.506949	−	0.861976i	$-0.330773\pi$
$547$	2.12294e12	1.01390	0.506949	+	0.861976i	$0.330773\pi$
$548$	−1.38779e12	−0.657374
$549$	1.18793e12	0.558106
$550$	−2.09897e12	−0.978078
$551$	2.03604e11	0.0941031
$552$	−2.35163e12	−1.07806
$553$	−1.17486e12	−0.534225
$554$	−9.59181e11	−0.432620
$555$	−2.72570e12	−1.21944
$556$	2.01223e12	0.892978
$557$	−3.52857e12	−1.55328	−0.776641	−	0.629943i	$-0.783078\pi$
$557$	−3.52857e12	−1.55328	−0.776641	+	0.629943i	$0.783078\pi$
$558$	9.07605e11	0.396317
$559$	9.52137e10	0.0412426
$560$	9.14713e10	0.0393042
$561$	−1.71712e12	−0.731928
$562$	1.37419e12	0.581078
$563$	−3.35280e12	−1.40644	−0.703218	−	0.710974i	$-0.748254\pi$
$563$	−3.35280e12	−1.40644	−0.703218	+	0.710974i	$0.748254\pi$
$564$	5.88403e11	0.244861
$565$	2.94008e12	1.21378
$566$	−7.38691e11	−0.302544
$567$	−1.14365e12	−0.464696
$568$	−1.63228e12	−0.658000
$569$	2.99364e12	1.19727	0.598637	−	0.801020i	$-0.295709\pi$
$569$	2.99364e12	1.19727	0.598637	+	0.801020i	$0.295709\pi$
$570$	−5.97830e11	−0.237214
$571$	4.67267e12	1.83951	0.919756	−	0.392490i	$-0.128386\pi$
$571$	4.67267e12	1.83951	0.919756	+	0.392490i	$0.128386\pi$
$572$	−9.62553e10	−0.0375961
$573$	2.81761e12	1.09190
$574$	4.25189e11	0.163485
$575$	2.21875e12	0.846453
$576$	4.96164e11	0.187812
$577$	−3.62799e12	−1.36262	−0.681310	−	0.731995i	$-0.738589\pi$
$577$	−3.62799e12	−1.36262	−0.681310	+	0.731995i	$0.738589\pi$
$578$	−1.40310e12	−0.522895
$579$	3.30146e12	1.22082
$580$	9.16232e11	0.336186
$581$	−1.99665e11	−0.0726957
$582$	−6.89683e11	−0.249170
$583$	−6.38073e12	−2.28751
$584$	−1.80917e12	−0.643608
$585$	−4.31866e10	−0.0152457
$586$	1.41252e12	0.494827
$587$	3.97200e12	1.38082	0.690411	−	0.723417i	$-0.257430\pi$
$587$	3.97200e12	1.38082	0.690411	+	0.723417i	$0.257430\pi$
$588$	−3.14166e11	−0.108383
$589$	−1.37819e12	−0.471835
$590$	1.64466e11	0.0558783
$591$	−3.63748e12	−1.22647
$592$	−1.71984e11	−0.0575494
$593$	2.67436e12	0.888123	0.444061	−	0.895996i	$-0.353537\pi$
$593$	2.67436e12	0.888123	0.444061	+	0.895996i	$0.353537\pi$
$594$	2.49355e12	0.821825
$595$	5.37641e11	0.175860
$596$	1.46013e12	0.474005
$597$	2.78765e12	0.898162
$598$	−5.44632e10	−0.0174160
$599$	4.84522e12	1.53777	0.768887	−	0.639384i	$-0.220811\pi$
$599$	4.84522e12	1.53777	0.768887	+	0.639384i	$0.220811\pi$
$600$	−3.21513e12	−1.01279
$601$	−4.64764e12	−1.45311	−0.726553	−	0.687110i	$-0.758879\pi$
$601$	−4.64764e12	−1.45311	−0.726553	+	0.687110i	$0.758879\pi$
$602$	−9.54525e11	−0.296212
$603$	−8.16411e11	−0.251467
$604$	8.98307e11	0.274637
$605$	1.11065e13	3.37039
$606$	−1.25507e12	−0.378043
$607$	−6.52447e12	−1.95073	−0.975363	−	0.220604i	$-0.929197\pi$
$607$	−6.52447e12	−1.95073	−0.975363	+	0.220604i	$0.929197\pi$
$608$	−8.61613e11	−0.255709
$609$	−5.60800e11	−0.165208
$610$	4.34510e12	1.27062
$611$	3.45489e10	0.0100288
$612$	−2.72777e11	−0.0786006
$613$	−9.54536e11	−0.273036	−0.136518	−	0.990638i	$-0.543591\pi$
$613$	−9.54536e11	−0.273036	−0.136518	+	0.990638i	$0.543591\pi$
$614$	−1.08230e12	−0.307321
$615$	4.16338e12	1.17357
$616$	2.44645e12	0.684580
$617$	−4.50764e12	−1.25218	−0.626088	−	0.779752i	$-0.715345\pi$
$617$	−4.50764e12	−1.25218	−0.626088	+	0.779752i	$0.715345\pi$
$618$	−3.31583e12	−0.914418
$619$	3.64346e12	0.997484	0.498742	−	0.866750i	$-0.333796\pi$
$619$	3.64346e12	0.997484	0.498742	+	0.866750i	$0.333796\pi$
$620$	−6.20195e12	−1.68564
$621$	−2.63585e12	−0.711228
$622$	−4.25452e12	−1.13971
$623$	4.99608e9	0.00132872
$624$	−1.03639e10	−0.00273647
$625$	−4.18296e12	−1.09654
$626$	1.72187e12	0.448143
$627$	2.09970e12	0.542567
$628$	4.43690e11	0.113831
$629$	−1.01087e12	−0.257495
$630$	4.32949e11	0.109498
$631$	3.61498e12	0.907766	0.453883	−	0.891061i	$-0.350038\pi$
$631$	3.61498e12	0.907766	0.453883	+	0.891061i	$0.350038\pi$
$632$	5.52757e12	1.37818
$633$	−5.22718e12	−1.29405
$634$	−9.95003e11	−0.244581
$635$	−1.67607e12	−0.409081
$636$	−3.85513e12	−0.934292
$637$	−1.84467e10	−0.00443906
$638$	1.72251e12	0.411593
$639$	1.01455e12	0.240724
$640$	−4.13793e12	−0.974929
$641$	−2.66304e12	−0.623041	−0.311521	−	0.950239i	$-0.600838\pi$
$641$	−2.66304e12	−0.623041	−0.311521	+	0.950239i	$0.600838\pi$
$642$	−4.40736e11	−0.102393
$643$	4.09899e12	0.945644	0.472822	−	0.881158i	$-0.343235\pi$
$643$	4.09899e12	0.945644	0.472822	+	0.881158i	$0.343235\pi$
$644$	−1.02004e12	−0.233684
$645$	−9.34656e12	−2.12634
$646$	−2.21715e11	−0.0500898
$647$	6.11325e12	1.37152	0.685761	−	0.727827i	$-0.259469\pi$
$647$	6.11325e12	1.37152	0.685761	+	0.727827i	$0.259469\pi$
$648$	5.38071e12	1.19882
$649$	−5.77640e11	−0.127807
$650$	−7.44619e10	−0.0163615
$651$	3.79604e12	0.828356
$652$	1.18754e12	0.257356
$653$	7.66270e12	1.64920	0.824598	−	0.565719i	$-0.191401\pi$
$653$	7.66270e12	1.64920	0.824598	+	0.565719i	$0.191401\pi$
$654$	−1.90813e12	−0.407858
$655$	4.31346e12	0.915673
$656$	2.62698e11	0.0553846
$657$	1.12450e12	0.235459
$658$	−3.46356e11	−0.0720287
$659$	−8.20110e9	−0.00169390	−0.000846950	−	1.00000i	$-0.500270\pi$
$659$	−8.20110e9	−0.00169390	−0.000846950		1.00000i	$0.500270\pi$
$660$	9.44881e12	1.93834
$661$	3.20922e12	0.653872	0.326936	−	0.945046i	$-0.393984\pi$
$661$	3.20922e12	0.653872	0.326936	+	0.945046i	$0.393984\pi$
$662$	3.79231e12	0.767437
$663$	−6.09158e10	−0.0122439
$664$	9.39395e11	0.187539
$665$	−6.57429e11	−0.130362
$666$	−8.14030e11	−0.160327
$667$	−1.82081e12	−0.356203
$668$	3.47781e12	0.675791
$669$	−3.77433e12	−0.728488
$670$	−2.98618e12	−0.572506
$671$	−1.52609e13	−2.90622
$672$	2.37320e12	0.448923
$673$	−4.91229e12	−0.923031	−0.461515	−	0.887132i	$-0.652694\pi$
$673$	−4.91229e12	−0.923031	−0.461515	+	0.887132i	$0.652694\pi$
$674$	−7.50089e10	−0.0140005
$675$	−3.60372e12	−0.668166
$676$	3.53309e12	0.650721
$677$	−3.11910e12	−0.570664	−0.285332	−	0.958429i	$-0.592104\pi$
$677$	−3.11910e12	−0.570664	−0.285332	+	0.958429i	$0.592104\pi$
$678$	3.33952e12	0.606946
$679$	−7.58440e11	−0.136933
$680$	−2.52953e12	−0.453680
$681$	−3.77315e12	−0.672267
$682$	−1.16596e13	−2.06374
$683$	2.91806e12	0.513099	0.256550	−	0.966531i	$-0.417414\pi$
$683$	2.91806e12	0.513099	0.256550	+	0.966531i	$0.417414\pi$
$684$	3.33552e11	0.0582655
$685$	7.99902e12	1.38813
$686$	1.84930e11	0.0318822
$687$	6.95322e12	1.19092
$688$	−5.89742e11	−0.100349
$689$	−2.26360e11	−0.0382660
$690$	5.34633e12	0.897914
$691$	4.74697e12	0.792073	0.396037	−	0.918235i	$-0.370385\pi$
$691$	4.74697e12	0.792073	0.396037	+	0.918235i	$0.370385\pi$
$692$	−6.82712e12	−1.13178
$693$	−1.52061e12	−0.250448
$694$	4.54058e12	0.743009
$695$	−1.15982e13	−1.88563
$696$	2.63849e12	0.426200
$697$	1.54406e12	0.247809
$698$	4.63240e11	0.0738680
$699$	−2.07013e12	−0.327981
$700$	−1.39459e12	−0.219535
$701$	−2.24423e11	−0.0351023	−0.0175512	−	0.999846i	$-0.505587\pi$
$701$	−2.24423e11	−0.0351023	−0.0175512	+	0.999846i	$0.505587\pi$
$702$	8.84599e10	0.0137477
$703$	1.23610e12	0.190877
$704$	−6.37400e12	−0.977992
$705$	−3.39146e12	−0.517054
$706$	−4.63484e12	−0.702123
$707$	−1.38019e12	−0.207755
$708$	−3.49001e11	−0.0522007
$709$	4.25463e12	0.632344	0.316172	−	0.948702i	$-0.397602\pi$
$709$	4.25463e12	0.632344	0.316172	+	0.948702i	$0.397602\pi$
$710$	3.71091e12	0.548047
$711$	−3.43569e12	−0.504197
$712$	−2.35059e10	−0.00342781
$713$	1.23250e13	1.78601
$714$	6.10685e11	0.0879378
$715$	5.54800e11	0.0793888
$716$	−1.82321e12	−0.259256
$717$	1.04238e13	1.47296
$718$	−3.35369e12	−0.470938
$719$	−4.28931e12	−0.598559	−0.299280	−	0.954165i	$-0.596746\pi$
$719$	−4.28931e12	−0.598559	−0.299280	+	0.954165i	$0.596746\pi$
$720$	2.67492e11	0.0370950
$721$	−3.64640e12	−0.502523
$722$	−4.04023e12	−0.553335
$723$	−4.76524e12	−0.648578
$724$	7.05761e11	0.0954627
$725$	−2.48940e12	−0.334637
$726$	1.26155e13	1.68535
$727$	1.28935e13	1.71185	0.855926	−	0.517098i	$-0.172988\pi$
$727$	1.28935e13	1.71185	0.855926	+	0.517098i	$0.172988\pi$
$728$	8.67892e10	0.0114518
$729$	3.31084e12	0.434174
$730$	4.11307e12	0.536060
$731$	−3.46633e12	−0.448995
$732$	−9.22038e12	−1.18699
$733$	2.71447e12	0.347310	0.173655	−	0.984807i	$-0.444442\pi$
$733$	2.71447e12	0.347310	0.173655	+	0.984807i	$0.444442\pi$
$734$	6.41143e12	0.815309
$735$	1.81080e12	0.228864
$736$	7.70531e12	0.967921
$737$	1.04881e13	1.30946
$738$	1.24339e12	0.154296
$739$	−9.62579e12	−1.18723	−0.593617	−	0.804747i	$-0.702301\pi$
$739$	−9.62579e12	−1.18723	−0.593617	+	0.804747i	$0.702301\pi$
$740$	5.56252e12	0.681913
$741$	7.44880e10	0.00907620
$742$	2.26927e12	0.274833
$743$	−1.24362e13	−1.49706	−0.748529	−	0.663103i	$-0.769239\pi$
$743$	−1.24362e13	−1.49706	−0.748529	+	0.663103i	$0.769239\pi$
$744$	−1.78599e13	−2.13698
$745$	−8.41595e12	−1.00092
$746$	−2.46898e12	−0.291872
$747$	−5.83886e11	−0.0686097
$748$	3.50425e12	0.409296
$749$	−4.84674e11	−0.0562706
$750$	−8.87371e11	−0.102407
$751$	4.26959e12	0.489786	0.244893	−	0.969550i	$-0.421247\pi$
$751$	4.26959e12	0.489786	0.244893	+	0.969550i	$0.421247\pi$
$752$	−2.13992e11	−0.0244015
$753$	1.02778e13	1.16499
$754$	6.11068e10	0.00688523
$755$	−5.17770e12	−0.579930
$756$	1.65676e12	0.184463
$757$	9.76840e12	1.08116	0.540582	−	0.841291i	$-0.318204\pi$
$757$	9.76840e12	1.08116	0.540582	+	0.841291i	$0.318204\pi$
$758$	−9.47153e12	−1.04210
$759$	−1.87774e13	−2.05375
$760$	3.09311e12	0.336306
$761$	1.23336e13	1.33309	0.666543	−	0.745466i	$-0.267773\pi$
$761$	1.23336e13	1.33309	0.666543	+	0.745466i	$0.267773\pi$
$762$	−1.90378e12	−0.204559
$763$	−2.09836e12	−0.224140
$764$	−5.75008e12	−0.610595
$765$	1.57224e12	0.165975
$766$	1.65391e12	0.173573
$767$	−2.04921e10	−0.00213800
$768$	−1.06125e13	−1.10076
$769$	−1.68919e13	−1.74185	−0.870926	−	0.491415i	$-0.836480\pi$
$769$	−1.68919e13	−1.74185	−0.870926	+	0.491415i	$0.836480\pi$
$770$	−5.56191e12	−0.570185
$771$	1.87078e13	1.90668
$772$	−6.73751e12	−0.682687
$773$	1.47186e13	1.48272	0.741359	−	0.671109i	$-0.234182\pi$
$773$	1.47186e13	1.48272	0.741359	+	0.671109i	$0.234182\pi$
$774$	−2.79135e12	−0.279563
$775$	1.68507e13	1.67788
$776$	3.56835e12	0.353257
$777$	−3.40467e12	−0.335104
$778$	−3.98111e12	−0.389579
$779$	−1.88808e12	−0.183697
$780$	3.35201e11	0.0324250
$781$	−1.30335e13	−1.25352
$782$	1.98278e12	0.189602
$783$	2.95738e12	0.281177
$784$	1.14257e11	0.0108009
$785$	−2.55736e12	−0.240369
$786$	4.89949e12	0.457878
$787$	−1.82466e13	−1.69549	−0.847744	−	0.530406i	$-0.822040\pi$
$787$	−1.82466e13	−1.69549	−0.847744	+	0.530406i	$0.822040\pi$
$788$	7.42326e12	0.685846
$789$	2.29932e12	0.211228
$790$	−1.25667e13	−1.14789
$791$	3.67245e12	0.333550
$792$	7.15424e12	0.646101
$793$	−5.41388e11	−0.0486160
$794$	7.12695e12	0.636373
$795$	2.22204e13	1.97287
$796$	−5.68895e12	−0.502254
$797$	−1.21558e13	−1.06714	−0.533568	−	0.845757i	$-0.679149\pi$
$797$	−1.21558e13	−1.06714	−0.533568	+	0.845757i	$0.679149\pi$
$798$	−7.46748e11	−0.0651870
$799$	−1.25778e12	−0.109180
$800$	1.05347e13	0.909318
$801$	1.46102e10	0.00125403
$802$	5.55325e12	0.473982
$803$	−1.44460e13	−1.22610
$804$	6.33673e12	0.534827
$805$	5.87932e12	0.493453
$806$	−4.13631e11	−0.0345227
$807$	1.37128e13	1.13814
$808$	6.49362e12	0.535964
$809$	−2.61893e12	−0.214959	−0.107479	−	0.994207i	$-0.534278\pi$
$809$	−2.61893e12	−0.214959	−0.107479	+	0.994207i	$0.534278\pi$
$810$	−1.22328e13	−0.998491
$811$	1.16994e13	0.949662	0.474831	−	0.880077i	$-0.342509\pi$
$811$	1.16994e13	0.949662	0.474831	+	0.880077i	$0.342509\pi$
$812$	1.14446e12	0.0923845
$813$	3.24217e12	0.260272
$814$	1.04575e13	0.834868
$815$	−6.84480e12	−0.543440
$816$	3.77305e11	0.0297911
$817$	4.23863e12	0.332833
$818$	1.44267e13	1.12662
$819$	−5.39443e10	−0.00418955
$820$	−8.49649e12	−0.656262
$821$	5.17673e12	0.397659	0.198830	−	0.980034i	$-0.436286\pi$
$821$	5.17673e12	0.397659	0.198830	+	0.980034i	$0.436286\pi$
$822$	9.08577e12	0.694126
$823$	−7.84017e12	−0.595698	−0.297849	−	0.954613i	$-0.596269\pi$
$823$	−7.84017e12	−0.595698	−0.297849	+	0.954613i	$0.596269\pi$
$824$	1.71558e13	1.29640
$825$	−2.56724e13	−1.92941
$826$	2.05435e11	0.0153555
$827$	−1.43263e13	−1.06502	−0.532512	−	0.846422i	$-0.678752\pi$
$827$	−1.43263e13	−1.06502	−0.532512	+	0.846422i	$0.678752\pi$
$828$	−2.98292e12	−0.220549
$829$	4.95546e12	0.364408	0.182204	−	0.983261i	$-0.441677\pi$
$829$	4.95546e12	0.364408	0.182204	+	0.983261i	$0.441677\pi$
$830$	−2.13568e12	−0.156201
$831$	−1.17317e13	−0.853408
$832$	−2.26121e11	−0.0163601
$833$	6.71566e11	0.0483266
$834$	−1.31739e13	−0.942902
$835$	−2.00456e13	−1.42702
$836$	−4.28500e12	−0.303405
$837$	−2.00185e13	−1.40983
$838$	−2.95270e12	−0.206834
$839$	7.38235e12	0.514358	0.257179	−	0.966364i	$-0.417207\pi$
$839$	7.38235e12	0.514358	0.257179	+	0.966364i	$0.417207\pi$
$840$	−8.51958e12	−0.590420
$841$	−1.24642e13	−0.859179
$842$	4.64256e12	0.318312
$843$	1.68077e13	1.14626
$844$	1.06675e13	0.723636
$845$	−2.03642e13	−1.37408
$846$	−1.01286e12	−0.0679802
$847$	1.38732e13	0.926189
$848$	1.40204e12	0.0931065
$849$	−9.03491e12	−0.596814
$850$	2.71084e12	0.178123
$851$	−1.10543e13	−0.722516
$852$	−7.87462e12	−0.511978
$853$	2.13356e13	1.37985	0.689927	−	0.723879i	$-0.257643\pi$
$853$	2.13356e13	1.37985	0.689927	+	0.723879i	$0.257643\pi$
$854$	5.42745e12	0.349169
$855$	−1.92254e12	−0.123035
$856$	2.28032e12	0.145166
$857$	1.65008e13	1.04494	0.522468	−	0.852659i	$-0.325011\pi$
$857$	1.65008e13	1.04494	0.522468	+	0.852659i	$0.325011\pi$
$858$	6.30175e11	0.0396980
$859$	−1.94817e13	−1.22083	−0.610417	−	0.792080i	$-0.708998\pi$
$859$	−1.94817e13	−1.22083	−0.610417	+	0.792080i	$0.708998\pi$
$860$	1.90742e13	1.18906
$861$	5.20047e12	0.322499
$862$	1.65103e12	0.101853
$863$	1.61059e13	0.988411	0.494205	−	0.869345i	$-0.335459\pi$
$863$	1.61059e13	0.988411	0.494205	+	0.869345i	$0.335459\pi$
$864$	−1.25151e13	−0.764049
$865$	3.93504e13	2.38989
$866$	−9.72232e12	−0.587408
$867$	−1.71613e13	−1.03149
$868$	−7.74684e12	−0.463219
$869$	4.41368e13	2.62550
$870$	−5.99849e12	−0.354981
$871$	3.72070e11	0.0219050
$872$	9.87249e12	0.578232
$873$	−2.21793e12	−0.129236
$874$	−2.42454e12	−0.140549
$875$	−9.75836e11	−0.0562782
$876$	−8.72801e12	−0.500780
$877$	−1.84919e13	−1.05556	−0.527780	−	0.849381i	$-0.676975\pi$
$877$	−1.84919e13	−1.05556	−0.527780	+	0.849381i	$0.676975\pi$
$878$	−7.82892e12	−0.444607
$879$	1.72764e13	0.976121
$880$	−3.43636e12	−0.193164
$881$	−2.83078e13	−1.58312	−0.791562	−	0.611089i	$-0.790732\pi$
$881$	−2.83078e13	−1.58312	−0.791562	+	0.611089i	$0.790732\pi$
$882$	5.40795e11	0.0300901
$883$	−7.32328e12	−0.405399	−0.202700	−	0.979241i	$-0.564971\pi$
$883$	−7.32328e12	−0.405399	−0.202700	+	0.979241i	$0.564971\pi$
$884$	1.24315e11	0.00684681
$885$	2.01158e12	0.110228
$886$	−2.82641e12	−0.154093
$887$	1.51372e13	0.821087	0.410544	−	0.911841i	$-0.365339\pi$
$887$	1.51372e13	0.821087	0.410544	+	0.911841i	$0.365339\pi$
$888$	1.60185e13	0.864496
$889$	−2.09357e12	−0.112416
$890$	5.34396e10	0.00285501
$891$	4.29642e13	2.28380
$892$	7.70253e12	0.407372
$893$	1.53802e12	0.0809337
$894$	−9.55934e12	−0.500506
$895$	1.05087e13	0.547451
$896$	−5.16867e12	−0.267913
$897$	−6.66138e11	−0.0343556
$898$	−1.23059e13	−0.631493
$899$	−1.38285e13	−0.706082
$900$	−4.07823e12	−0.207196
$901$	8.24080e12	0.416589
$902$	−1.59733e13	−0.803463
$903$	−1.16748e13	−0.584323
$904$	−1.72783e13	−0.860487
$905$	−4.06789e12	−0.201582
$906$	−5.88114e12	−0.289991
$907$	−2.24337e13	−1.10070	−0.550349	−	0.834935i	$-0.685505\pi$
$907$	−2.24337e13	−1.10070	−0.550349	+	0.834935i	$0.685505\pi$
$908$	7.70011e12	0.375933
$909$	−4.03614e12	−0.196078
$910$	−1.97312e11	−0.00953820
$911$	−6.34178e12	−0.305055	−0.152528	−	0.988299i	$-0.548741\pi$
$911$	−6.34178e12	−0.305055	−0.152528	+	0.988299i	$0.548741\pi$
$912$	−4.61369e11	−0.0220837
$913$	7.50094e12	0.357270
$914$	1.08380e13	0.513679
$915$	5.31448e13	2.50649
$916$	−1.41899e13	−0.665963
$917$	5.38793e12	0.251629
$918$	−3.22045e12	−0.149667
$919$	9.04471e12	0.418288	0.209144	−	0.977885i	$-0.432932\pi$
$919$	9.04471e12	0.418288	0.209144	+	0.977885i	$0.432932\pi$
$920$	−2.76614e13	−1.27300
$921$	−1.32376e13	−0.606236
$922$	−2.53946e12	−0.115732
$923$	−4.62369e11	−0.0209692
$924$	1.18025e13	0.532659
$925$	−1.51134e13	−0.678771
$926$	6.37233e12	0.284806
$927$	−1.06633e13	−0.474277
$928$	−8.64522e12	−0.382658
$929$	8.50641e12	0.374693	0.187346	−	0.982294i	$-0.440011\pi$
$929$	8.50641e12	0.374693	0.187346	+	0.982294i	$0.440011\pi$
$930$	4.06037e13	1.77988
$931$	−8.21193e11	−0.0358238
$932$	4.22464e12	0.183408
$933$	−5.20368e13	−2.24824
$934$	1.42147e13	0.611191
$935$	−2.01979e13	−0.864280
$936$	2.53800e11	0.0108081
$937$	−3.00276e13	−1.27260	−0.636300	−	0.771442i	$-0.719536\pi$
$937$	−3.00276e13	−1.27260	−0.636300	+	0.771442i	$0.719536\pi$
$938$	−3.73003e12	−0.157326
$939$	2.10602e13	0.884030
$940$	6.92118e12	0.289138
$941$	−3.15982e13	−1.31374	−0.656870	−	0.754004i	$-0.728120\pi$
$941$	−3.15982e13	−1.31374	−0.656870	+	0.754004i	$0.728120\pi$
$942$	−2.90480e12	−0.120195
$943$	1.68849e13	0.695338
$944$	1.26925e11	0.00520205
$945$	−9.54927e12	−0.389518
$946$	3.58592e13	1.45576
$947$	−8.84885e12	−0.357529	−0.178765	−	0.983892i	$-0.557210\pi$
$947$	−8.84885e12	−0.357529	−0.178765	+	0.983892i	$0.557210\pi$
$948$	2.66667e13	1.07234
$949$	−5.12477e11	−0.0205105
$950$	−3.31482e12	−0.132040
$951$	−1.21698e13	−0.482473
$952$	−3.15963e12	−0.124672
$953$	−4.90260e12	−0.192534	−0.0962672	−	0.995356i	$-0.530690\pi$
$953$	−4.90260e12	−0.192534	−0.0962672	+	0.995356i	$0.530690\pi$
$954$	6.63610e12	0.259385
$955$	3.31425e13	1.28935
$956$	−2.12726e13	−0.823682
$957$	2.10679e13	0.811929
$958$	−1.12686e13	−0.432241
$959$	9.99155e12	0.381460
$960$	2.21969e13	0.843476
$961$	6.71649e13	2.54031
$962$	3.70985e11	0.0139659
$963$	−1.41735e12	−0.0531077
$964$	9.72475e12	0.362687
$965$	3.88339e13	1.44158
$966$	6.67808e12	0.246749
$967$	1.55633e13	0.572378	0.286189	−	0.958173i	$-0.407612\pi$
$967$	1.55633e13	0.572378	0.286189	+	0.958173i	$0.407612\pi$
$968$	−6.52713e13	−2.38937
$969$	−2.71179e12	−0.0988096
$970$	−8.11251e12	−0.294227
$971$	−2.49197e13	−0.899613	−0.449806	−	0.893126i	$-0.648507\pi$
$971$	−2.49197e13	−0.899613	−0.449806	+	0.893126i	$0.648507\pi$
$972$	1.23765e13	0.444732
$973$	−1.44872e13	−0.518176
$974$	1.53918e13	0.547991
$975$	−9.10740e11	−0.0322756
$976$	3.35329e12	0.118290
$977$	4.47898e12	0.157273	0.0786364	−	0.996903i	$-0.474943\pi$
$977$	4.47898e12	0.157273	0.0786364	+	0.996903i	$0.474943\pi$
$978$	−7.77474e12	−0.271745
$979$	−1.87691e11	−0.00653012
$980$	−3.69543e12	−0.127981
$981$	−6.13629e12	−0.211542
$982$	−1.29426e13	−0.444139
$983$	−1.43233e13	−0.489275	−0.244637	−	0.969615i	$-0.578669\pi$
$983$	−1.43233e13	−0.489275	−0.244637	+	0.969615i	$0.578669\pi$
$984$	−2.44675e13	−0.831977
$985$	−4.27865e13	−1.44825
$986$	−2.22464e12	−0.0749572
$987$	−4.23626e12	−0.142088
$988$	−1.52013e11	−0.00507543
$989$	−3.79057e13	−1.25986
$990$	−1.62649e13	−0.538136
$991$	−2.28575e13	−0.752829	−0.376415	−	0.926451i	$-0.622843\pi$
$991$	−2.28575e13	−0.752829	−0.376415	+	0.926451i	$0.622843\pi$
$992$	5.85194e13	1.91866
$993$	4.63836e13	1.51388
$994$	4.63529e12	0.150605
$995$	3.27902e13	1.06057
$996$	4.53194e12	0.145921
$997$	−2.67132e13	−0.856243	−0.428121	−	0.903721i	$-0.640824\pi$
$997$	−2.67132e13	−0.856243	−0.428121	+	0.903721i	$0.640824\pi$
$998$	3.51147e13	1.12047
$999$	1.79545e13	0.570334

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.10.a.b.1.2	✓	3
3.2	odd	2		63.10.a.e.1.2		3
4.3	odd	2		112.10.a.h.1.1		3
5.2	odd	4		175.10.b.d.99.4		6
5.3	odd	4		175.10.b.d.99.3		6
5.4	even	2		175.10.a.d.1.2		3
7.2	even	3		49.10.c.d.18.2		6
7.3	odd	6		49.10.c.e.30.2		6
7.4	even	3		49.10.c.d.30.2		6
7.5	odd	6		49.10.c.e.18.2		6
7.6	odd	2		49.10.a.c.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.a.b.1.2	✓	3	1.1	even	1	trivial
49.10.a.c.1.2		3	7.6	odd	2
49.10.c.d.18.2		6	7.2	even	3
49.10.c.d.30.2		6	7.4	even	3
49.10.c.e.18.2		6	7.5	odd	6
49.10.c.e.30.2		6	7.3	odd	6
63.10.a.e.1.2		3	3.2	odd	2
112.10.a.h.1.1		3	4.3	odd	2
175.10.a.d.1.2		3	5.4	even	2
175.10.b.d.99.3		6	5.3	odd	4
175.10.b.d.99.4		6	5.2	odd	4

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:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	7.a (trivial)

\(f(q)\)	\(=\)	\(q+13.3607 q^{2} +163.415 q^{3} -333.491 q^{4} +1922.19 q^{5} +2183.34 q^{6} +2401.00 q^{7} -11296.4 q^{8} +7021.32 q^{9} +25681.8 q^{10} -90199.9 q^{11} -54497.3 q^{12} -3199.89 q^{13} +32079.1 q^{14} +314114. q^{15} +19819.7 q^{16} +116494. q^{17} +93809.9 q^{18} -142449. q^{19} -641033. q^{20} +392358. q^{21} -1.20514e6 q^{22} +1.27391e6 q^{23} -1.84599e6 q^{24} +1.74168e6 q^{25} -42752.8 q^{26} -2.06910e6 q^{27} -800712. q^{28} -1.42931e6 q^{29} +4.19679e6 q^{30} +9.67494e6 q^{31} +6.04855e6 q^{32} -1.47400e7 q^{33} +1.55645e6 q^{34} +4.61518e6 q^{35} -2.34155e6 q^{36} -8.67744e6 q^{37} -1.90323e6 q^{38} -522908. q^{39} -2.17138e7 q^{40} +1.32544e7 q^{41} +5.24219e6 q^{42} -2.97554e7 q^{43} +3.00809e7 q^{44} +1.34963e7 q^{45} +1.70204e7 q^{46} -1.07969e7 q^{47} +3.23882e6 q^{48} +5.76480e6 q^{49} +2.32702e7 q^{50} +1.90369e7 q^{51} +1.06713e6 q^{52} +7.07399e7 q^{53} -2.76447e7 q^{54} -1.73381e8 q^{55} -2.71226e7 q^{56} -2.32783e7 q^{57} -1.90966e7 q^{58} +6.40400e6 q^{59} -1.04754e8 q^{60} +1.69190e8 q^{61} +1.29264e8 q^{62} +1.68582e7 q^{63} +7.06653e7 q^{64} -6.15078e6 q^{65} -1.96937e8 q^{66} -1.16276e8 q^{67} -3.88498e7 q^{68} +2.08176e8 q^{69} +6.16621e7 q^{70} +1.44496e8 q^{71} -7.93154e7 q^{72} +1.60155e8 q^{73} -1.15937e8 q^{74} +2.84617e8 q^{75} +4.75056e7 q^{76} -2.16570e8 q^{77} -6.98643e6 q^{78} -4.89322e8 q^{79} +3.80972e7 q^{80} -4.76322e8 q^{81} +1.77088e8 q^{82} -8.31590e7 q^{83} -1.30848e8 q^{84} +2.23924e8 q^{85} -3.97553e8 q^{86} -2.33569e8 q^{87} +1.01893e9 q^{88} +2.08083e6 q^{89} +1.80320e8 q^{90} -7.68292e6 q^{91} -4.24838e8 q^{92} +1.58103e9 q^{93} -1.44255e8 q^{94} -2.73815e8 q^{95} +9.88421e8 q^{96} -3.15885e8 q^{97} +7.70219e7 q^{98} -6.33322e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 21 q^{2} + 84 q^{3} + 1557 q^{4} + 1554 q^{5} + 4914 q^{6} + 7203 q^{7} + 14055 q^{8} - 26001 q^{9} - 97860 q^{10} - 3444 q^{11} - 106386 q^{12} - 19782 q^{13} + 50421 q^{14} + 200304 q^{15} + 482961 q^{16}+ \cdots - 1900979172 q^{99}+O(q^{100}) \) 3 * q + 21 * q^2 + 84 * q^3 + 1557 * q^4 + 1554 * q^5 + 4914 * q^6 + 7203 * q^7 + 14055 * q^8 - 26001 * q^9 - 97860 * q^10 - 3444 * q^11 - 106386 * q^12 - 19782 * q^13 + 50421 * q^14 + 200304 * q^15 + 482961 * q^16 + 1016694 * q^17 - 273267 * q^18 + 222852 * q^19 - 1922088 * q^20 + 201684 * q^21 - 2847048 * q^22 + 1885632 * q^23 - 1449630 * q^24 + 3073221 * q^25 - 8785056 * q^26 + 551880 * q^27 + 3738357 * q^28 + 4081818 * q^29 + 8053200 * q^30 + 2869440 * q^31 + 25221951 * q^32 - 20259792 * q^33 - 3981642 * q^34 + 3731154 * q^35 - 35396379 * q^36 + 1395618 * q^37 + 43479870 * q^38 - 8990688 * q^39 - 82859280 * q^40 - 14420658 * q^41 + 11798514 * q^42 - 61631172 * q^43 + 97011984 * q^44 + 29774682 * q^45 + 89747664 * q^46 - 10368960 * q^47 + 16798782 * q^48 + 17294403 * q^49 + 73325055 * q^50 - 26146728 * q^51 - 80908044 * q^52 + 67502610 * q^53 - 117879300 * q^54 - 105823032 * q^55 + 33746055 * q^56 + 8471112 * q^57 - 159163830 * q^58 - 42590100 * q^59 - 179551008 * q^60 + 191746842 * q^61 - 46983468 * q^62 - 62428401 * q^63 + 7852161 * q^64 + 364283220 * q^65 - 8057952 * q^66 - 255175788 * q^67 + 743485806 * q^68 + 257903856 * q^69 - 234961860 * q^70 + 296514504 * q^71 - 609314265 * q^72 + 344213310 * q^73 - 690696462 * q^74 + 279031116 * q^75 + 728839986 * q^76 - 8269044 * q^77 + 280132776 * q^78 - 960412656 * q^79 - 1333333344 * q^80 - 35827677 * q^81 + 562675302 * q^82 - 1100517180 * q^83 - 255432786 * q^84 + 438179412 * q^85 - 880982256 * q^86 - 621821592 * q^87 + 1206124800 * q^88 + 506816478 * q^89 + 2303452620 * q^90 - 47496582 * q^91 + 691123488 * q^92 + 1693258512 * q^93 + 1388004828 * q^94 - 2203071072 * q^95 + 333385794 * q^96 - 647498250 * q^97 + 121060821 * q^98 - 1900979172 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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