LMFDB - Embedded newform 49.10.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,10,Mod(1,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("49.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	49.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$25.2367559720$
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:	no (minimal twist has level 7)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$4.96128$ of defining polynomial
Character	$\chi$	$=$	49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+41.8019 q^{2} -0.232339 q^{3} +1235.40 q^{4} +1791.89 q^{5} -9.71222 q^{6} +30239.6 q^{8} -19682.9 q^{9} +O(q^{10})$	\(q+41.8019 q^{2} -0.232339 q^{3} +1235.40 q^{4} +1791.89 q^{5} -9.71222 q^{6} +30239.6 q^{8} -19682.9 q^{9} +74904.4 q^{10} +17401.5 q^{11} -287.032 q^{12} +122541. q^{13} -416.326 q^{15} +631550. q^{16} -331933. q^{17} -822785. q^{18} -761707. q^{19} +2.21370e6 q^{20} +727418. q^{22} +1.23249e6 q^{23} -7025.85 q^{24} +1.25774e6 q^{25} +5.12246e6 q^{26} +9146.25 q^{27} +634604. q^{29} -17403.2 q^{30} +5.38069e6 q^{31} +1.09173e7 q^{32} -4043.06 q^{33} -1.38754e7 q^{34} -2.43164e7 q^{36} -3.03611e6 q^{37} -3.18408e7 q^{38} -28471.1 q^{39} +5.41861e7 q^{40} +7.37009e6 q^{41} -2.06990e7 q^{43} +2.14979e7 q^{44} -3.52696e7 q^{45} +5.15203e7 q^{46} -2.03632e7 q^{47} -146734. q^{48} +5.25760e7 q^{50} +77120.9 q^{51} +1.51388e8 q^{52} -5.97380e7 q^{53} +382331. q^{54} +3.11816e7 q^{55} +176974. q^{57} +2.65277e7 q^{58} -6.03461e7 q^{59} -514330. q^{60} +9.44357e6 q^{61} +2.24923e8 q^{62} +1.33012e8 q^{64} +2.19580e8 q^{65} -169008. q^{66} -2.19187e8 q^{67} -4.10071e8 q^{68} -286355. q^{69} -5.58741e7 q^{71} -5.95205e8 q^{72} -4.54332e8 q^{73} -1.26915e8 q^{74} -292222. q^{75} -9.41015e8 q^{76} -1.19015e6 q^{78} +4.51057e7 q^{79} +1.13167e9 q^{80} +3.87417e8 q^{81} +3.08084e8 q^{82} +3.34665e8 q^{83} -5.94786e8 q^{85} -8.65259e8 q^{86} -147443. q^{87} +5.26216e8 q^{88} -6.51886e8 q^{89} -1.47434e9 q^{90} +1.52262e9 q^{92} -1.25014e6 q^{93} -8.51220e8 q^{94} -1.36489e9 q^{95} -2.53652e6 q^{96} +1.42804e9 q^{97} -3.42514e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 21 q^{2} - 84 q^{3} + 1557 q^{4} - 1554 q^{5} - 4914 q^{6} + 14055 q^{8} - 26001 q^{9}+O(q^{10}) $ 3 * q + 21 * q^2 - 84 * q^3 + 1557 * q^4 - 1554 * q^5 - 4914 * q^6 + 14055 * q^8 - 26001 * q^9	\( 3 q + 21 q^{2} - 84 q^{3} + 1557 q^{4} - 1554 q^{5} - 4914 q^{6} + 14055 q^{8} - 26001 q^{9} + 97860 q^{10} - 3444 q^{11} + 106386 q^{12} + 19782 q^{13} + 200304 q^{15} + 482961 q^{16} - 1016694 q^{17} - 273267 q^{18} - 222852 q^{19} + 1922088 q^{20} - 2847048 q^{22} + 1885632 q^{23} + 1449630 q^{24} + 3073221 q^{25} + 8785056 q^{26} - 551880 q^{27} + 4081818 q^{29} + 8053200 q^{30} - 2869440 q^{31} + 25221951 q^{32} + 20259792 q^{33} + 3981642 q^{34} - 35396379 q^{36} + 1395618 q^{37} - 43479870 q^{38} - 8990688 q^{39} + 82859280 q^{40} + 14420658 q^{41} - 61631172 q^{43} + 97011984 q^{44} - 29774682 q^{45} + 89747664 q^{46} + 10368960 q^{47} - 16798782 q^{48} + 73325055 q^{50} - 26146728 q^{51} + 80908044 q^{52} + 67502610 q^{53} + 117879300 q^{54} + 105823032 q^{55} + 8471112 q^{57} - 159163830 q^{58} + 42590100 q^{59} - 179551008 q^{60} - 191746842 q^{61} + 46983468 q^{62} + 7852161 q^{64} + 364283220 q^{65} + 8057952 q^{66} - 255175788 q^{67} - 743485806 q^{68} - 257903856 q^{69} + 296514504 q^{71} - 609314265 q^{72} - 344213310 q^{73} - 690696462 q^{74} - 279031116 q^{75} - 728839986 q^{76} + 280132776 q^{78} - 960412656 q^{79} + 1333333344 q^{80} - 35827677 q^{81} - 562675302 q^{82} + 1100517180 q^{83} + 438179412 q^{85} - 880982256 q^{86} + 621821592 q^{87} + 1206124800 q^{88} - 506816478 q^{89} - 2303452620 q^{90} + 691123488 q^{92} + 1693258512 q^{93} - 1388004828 q^{94} - 2203071072 q^{95} - 333385794 q^{96} + 647498250 q^{97} - 1900979172 q^{99}+O(q^{100}) \) 3 * q + 21 * q^2 - 84 * q^3 + 1557 * q^4 - 1554 * q^5 - 4914 * q^6 + 14055 * q^8 - 26001 * q^9 + 97860 * q^10 - 3444 * q^11 + 106386 * q^12 + 19782 * q^13 + 200304 * q^15 + 482961 * q^16 - 1016694 * q^17 - 273267 * q^18 - 222852 * q^19 + 1922088 * q^20 - 2847048 * q^22 + 1885632 * q^23 + 1449630 * q^24 + 3073221 * q^25 + 8785056 * q^26 - 551880 * q^27 + 4081818 * q^29 + 8053200 * q^30 - 2869440 * q^31 + 25221951 * q^32 + 20259792 * q^33 + 3981642 * q^34 - 35396379 * q^36 + 1395618 * q^37 - 43479870 * q^38 - 8990688 * q^39 + 82859280 * q^40 + 14420658 * q^41 - 61631172 * q^43 + 97011984 * q^44 - 29774682 * q^45 + 89747664 * q^46 + 10368960 * q^47 - 16798782 * q^48 + 73325055 * q^50 - 26146728 * q^51 + 80908044 * q^52 + 67502610 * q^53 + 117879300 * q^54 + 105823032 * q^55 + 8471112 * q^57 - 159163830 * q^58 + 42590100 * q^59 - 179551008 * q^60 - 191746842 * q^61 + 46983468 * q^62 + 7852161 * q^64 + 364283220 * q^65 + 8057952 * q^66 - 255175788 * q^67 - 743485806 * q^68 - 257903856 * q^69 + 296514504 * q^71 - 609314265 * q^72 - 344213310 * q^73 - 690696462 * q^74 - 279031116 * q^75 - 728839986 * q^76 + 280132776 * q^78 - 960412656 * q^79 + 1333333344 * q^80 - 35827677 * q^81 - 562675302 * q^82 + 1100517180 * q^83 + 438179412 * q^85 - 880982256 * q^86 + 621821592 * q^87 + 1206124800 * q^88 - 506816478 * q^89 - 2303452620 * q^90 + 691123488 * q^92 + 1693258512 * q^93 - 1388004828 * q^94 - 2203071072 * q^95 - 333385794 * q^96 + 647498250 * q^97 - 1900979172 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	41.8019	1.84740	0.923701	−	0.383114i	$-0.125148\pi$
$2$	41.8019	1.84740	0.923701	+	0.383114i	$0.125148\pi$
$3$	−0.232339	−0.00165606	−0.000828031	−	1.00000i	$-0.500264\pi$
$3$	−0.232339	−0.00165606	−0.000828031		1.00000i	$0.500264\pi$
$4$	1235.40	2.41290
$5$	1791.89	1.28217	0.641086	−	0.767469i	$-0.278484\pi$
$5$	1791.89	1.28217	0.641086	+	0.767469i	$0.278484\pi$
$6$	−9.71222	−0.00305941
$7$	0	0
$7$	0	0
$8$	30239.6	2.61019
$9$	−19682.9	−0.999997
$10$	74904.4	2.36869
$11$	17401.5	0.358361	0.179180	−	0.983816i	$-0.442655\pi$
$11$	17401.5	0.358361	0.179180	+	0.983816i	$0.442655\pi$
$12$	−287.032	−0.00399591
$13$	122541.	1.18997	0.594986	−	0.803736i	$-0.297158\pi$
$13$	122541.	1.18997	0.594986	+	0.803736i	$0.297158\pi$
$14$	0	0
$15$	−416.326	−0.00212335
$16$	631550.	2.40917
$17$	−331933.	−0.963895	−0.481948	−	0.876200i	$-0.660070\pi$
$17$	−331933.	−0.963895	−0.481948	+	0.876200i	$0.660070\pi$
$18$	−822785.	−1.84740
$19$	−761707.	−1.34090	−0.670450	−	0.741954i	$-0.733899\pi$
$19$	−761707.	−1.34090	−0.670450	+	0.741954i	$0.733899\pi$
$20$	2.21370e6	3.09375
$21$	0	0
$22$	727418.	0.662037
$23$	1.23249e6	0.918347	0.459173	−	0.888347i	$-0.348146\pi$
$23$	1.23249e6	0.918347	0.459173	+	0.888347i	$0.348146\pi$
$24$	−7025.85	−0.00432263
$25$	1.25774e6	0.643963
$26$	5.12246e6	2.19836
$27$	9146.25	0.00331212
$28$	0	0
$29$	634604.	0.166614	0.0833071	−	0.996524i	$-0.473452\pi$
$29$	634604.	0.166614	0.0833071	+	0.996524i	$0.473452\pi$
$30$	−17403.2	−0.00392269
$31$	5.38069e6	1.04643	0.523215	−	0.852201i	$-0.324732\pi$
$31$	5.38069e6	1.04643	0.523215	+	0.852201i	$0.324732\pi$
$32$	1.09173e7	1.84052
$33$	−4043.06	−0.000593468 0
$34$	−1.38754e7	−1.78070
$35$	0	0
$36$	−2.43164e7	−2.41289
$37$	−3.03611e6	−0.266324	−0.133162	−	0.991094i	$-0.542513\pi$
$37$	−3.03611e6	−0.266324	−0.133162	+	0.991094i	$0.542513\pi$
$38$	−3.18408e7	−2.47718
$39$	−28471.1	−0.00197067
$40$	5.41861e7	3.34671
$41$	7.37009e6	0.407329	0.203665	−	0.979041i	$-0.434715\pi$
$41$	7.37009e6	0.407329	0.203665	+	0.979041i	$0.434715\pi$
$42$	0	0
$43$	−2.06990e7	−0.923297	−0.461649	−	0.887063i	$-0.652742\pi$
$43$	−2.06990e7	−0.923297	−0.461649	+	0.887063i	$0.652742\pi$
$44$	2.14979e7	0.864687
$45$	−3.52696e7	−1.28217
$46$	5.15203e7	1.69656
$47$	−2.03632e7	−0.608702	−0.304351	−	0.952560i	$-0.598440\pi$
$47$	−2.03632e7	−0.608702	−0.304351	+	0.952560i	$0.598440\pi$
$48$	−146734.	−0.00398974
$49$	0	0
$50$	5.25760e7	1.18966
$51$	77120.9	0.00159627
$52$	1.51388e8	2.87128
$53$	−5.97380e7	−1.03994	−0.519971	−	0.854184i	$-0.674057\pi$
$53$	−5.97380e7	−1.03994	−0.519971	+	0.854184i	$0.674057\pi$
$54$	382331.	0.00611882
$55$	3.11816e7	0.459480
$56$	0	0
$57$	176974.	0.00222061
$58$	2.65277e7	0.307803
$59$	−6.03461e7	−0.648358	−0.324179	−	0.945996i	$-0.605088\pi$
$59$	−6.03461e7	−0.648358	−0.324179	+	0.945996i	$0.605088\pi$
$60$	−514330.	−0.00512343
$61$	9.44357e6	0.0873277	0.0436639	−	0.999046i	$-0.486097\pi$
$61$	9.44357e6	0.0873277	0.0436639	+	0.999046i	$0.486097\pi$
$62$	2.24923e8	1.93318
$63$	0	0
$64$	1.33012e8	0.991013
$65$	2.19580e8	1.52575
$66$	−169008.	−0.00109637
$67$	−2.19187e8	−1.32885	−0.664427	−	0.747353i	$-0.731324\pi$
$67$	−2.19187e8	−1.32885	−0.664427	+	0.747353i	$0.731324\pi$
$68$	−4.10071e8	−2.32578
$69$	−286355.	−0.00152084
$70$	0	0
$71$	−5.58741e7	−0.260944	−0.130472	−	0.991452i	$-0.541649\pi$
$71$	−5.58741e7	−0.260944	−0.130472	+	0.991452i	$0.541649\pi$
$72$	−5.95205e8	−2.61018
$73$	−4.54332e8	−1.87250	−0.936248	−	0.351340i	$-0.885726\pi$
$73$	−4.54332e8	−1.87250	−0.936248	+	0.351340i	$0.885726\pi$
$74$	−1.26915e8	−0.492007
$75$	−292222.	−0.00106644
$76$	−9.41015e8	−3.23545
$77$	0	0
$78$	−1.19015e6	−0.00364062
$79$	4.51057e7	0.130289	0.0651447	−	0.997876i	$-0.479249\pi$
$79$	4.51057e7	0.130289	0.0651447	+	0.997876i	$0.479249\pi$
$80$	1.13167e9	3.08897
$81$	3.87417e8	0.999992
$82$	3.08084e8	0.752501
$83$	3.34665e8	0.774031	0.387016	−	0.922073i	$-0.373506\pi$
$83$	3.34665e8	0.774031	0.387016	+	0.922073i	$0.373506\pi$
$84$	0	0
$85$	−5.94786e8	−1.23588
$86$	−8.65259e8	−1.70570
$87$	−147443.	−0.000275923 0
$88$	5.26216e8	0.935389
$89$	−6.51886e8	−1.10133	−0.550664	−	0.834727i	$-0.685625\pi$
$89$	−6.51886e8	−1.10133	−0.550664	+	0.834727i	$0.685625\pi$
$90$	−1.47434e9	−2.36868
$91$	0	0
$92$	1.52262e9	2.21588
$93$	−1.25014e6	−0.00173295
$94$	−8.51220e8	−1.12452
$95$	−1.36489e9	−1.71926
$96$	−2.53652e6	−0.00304802
$97$	1.42804e9	1.63783	0.818914	−	0.573916i	$-0.194576\pi$
$97$	1.42804e9	1.63783	0.818914	+	0.573916i	$0.194576\pi$
$98$	0	0
$99$	−3.42514e8	−0.358360
$100$	1.55382e9	1.55382
$101$	−8.91532e8	−0.852493	−0.426247	−	0.904607i	$-0.640164\pi$
$101$	−8.91532e8	−0.852493	−0.426247	+	0.904607i	$0.640164\pi$
$102$	3.22380e6	0.00294895
$103$	7.12000e8	0.623322	0.311661	−	0.950193i	$-0.399115\pi$
$103$	7.12000e8	0.623322	0.311661	+	0.950193i	$0.399115\pi$
$104$	3.70560e9	3.10605
$105$	0	0
$106$	−2.49716e9	−1.92119
$107$	2.48598e9	1.83346	0.916729	−	0.399510i	$-0.130820\pi$
$107$	2.48598e9	1.83346	0.916729	+	0.399510i	$0.130820\pi$
$108$	1.12993e7	0.00799180
$109$	3.83455e8	0.260193	0.130096	−	0.991501i	$-0.458471\pi$
$109$	3.83455e8	0.260193	0.130096	+	0.991501i	$0.458471\pi$
$110$	1.30345e9	0.848844
$111$	705407.	0.000441048 0
$112$	0	0
$113$	2.39582e9	1.38230	0.691148	−	0.722713i	$-0.257105\pi$
$113$	2.39582e9	1.38230	0.691148	+	0.722713i	$0.257105\pi$
$114$	7.39787e6	0.00410237
$115$	2.20848e9	1.17748
$116$	7.83991e8	0.402023
$117$	−2.41197e9	−1.18997
$118$	−2.52258e9	−1.19778
$119$	0	0
$120$	−1.25895e7	−0.00554235
$121$	−2.05513e9	−0.871578
$122$	3.94760e8	0.161329
$123$	−1.71236e6	−0.000674562 0
$124$	6.64732e9	2.52493
$125$	−1.24605e9	−0.456501
$126$	0	0
$127$	1.88261e9	0.642161	0.321080	−	0.947052i	$-0.395954\pi$
$127$	1.88261e9	0.642161	0.321080	+	0.947052i	$0.395954\pi$
$128$	−2.95237e7	−0.00972134
$129$	4.80919e6	0.00152904
$130$	9.17888e9	2.81867
$131$	1.49241e9	0.442760	0.221380	−	0.975188i	$-0.428944\pi$
$131$	1.49241e9	0.442760	0.221380	+	0.975188i	$0.428944\pi$
$132$	−4.99480e6	−0.00143198
$133$	0	0
$134$	−9.16242e9	−2.45493
$135$	1.63891e7	0.00424670
$136$	−1.00375e10	−2.51595
$137$	−3.21118e9	−0.778792	−0.389396	−	0.921070i	$-0.627316\pi$
$137$	−3.21118e9	−0.778792	−0.389396	+	0.921070i	$0.627316\pi$
$138$	−1.19702e7	−0.00280960
$139$	3.03934e9	0.690577	0.345289	−	0.938497i	$-0.387781\pi$
$139$	3.03934e9	0.690577	0.345289	+	0.938497i	$0.387781\pi$
$140$	0	0
$141$	4.73116e6	0.00100805
$142$	−2.33565e9	−0.482070
$143$	2.13240e9	0.426439
$144$	−1.24308e10	−2.40917
$145$	1.13714e9	0.213628
$146$	−1.89920e10	−3.45925
$147$	0	0
$148$	−3.75082e9	−0.642611
$149$	−3.64286e9	−0.605487	−0.302743	−	0.953072i	$-0.597902\pi$
$149$	−3.64286e9	−0.605487	−0.302743	+	0.953072i	$0.597902\pi$
$150$	−1.22155e7	−0.00197015
$151$	5.05862e9	0.791837	0.395919	−	0.918286i	$-0.370426\pi$
$151$	5.05862e9	0.791837	0.395919	+	0.918286i	$0.370426\pi$
$152$	−2.30337e10	−3.50000
$153$	6.53341e9	0.963893
$154$	0	0
$155$	9.64159e9	1.34170
$156$	−3.51733e7	−0.00475502
$157$	1.19687e10	1.57216	0.786082	−	0.618122i	$-0.212106\pi$
$157$	1.19687e10	1.57216	0.786082	+	0.618122i	$0.212106\pi$
$158$	1.88551e9	0.240697
$159$	1.38795e7	0.00172221
$160$	1.95626e10	2.35986
$161$	0	0
$162$	1.61948e10	1.84739
$163$	1.40960e10	1.56405	0.782027	−	0.623245i	$-0.214186\pi$
$163$	1.40960e10	1.56405	0.782027	+	0.623245i	$0.214186\pi$
$164$	9.10503e9	0.982843
$165$	−7.24471e6	−0.000760927 0
$166$	1.39896e10	1.42995
$167$	−3.56028e9	−0.354210	−0.177105	−	0.984192i	$-0.556673\pi$
$167$	−3.56028e9	−0.354210	−0.177105	+	0.984192i	$0.556673\pi$
$168$	0	0
$169$	4.41184e9	0.416034
$170$	−2.48632e10	−2.28317
$171$	1.49926e10	1.34090
$172$	−2.55716e10	−2.22782
$173$	−2.64068e9	−0.224134	−0.112067	−	0.993701i	$-0.535747\pi$
$173$	−2.64068e9	−0.224134	−0.112067	+	0.993701i	$0.535747\pi$
$174$	−6.16342e6	−0.000509741 0
$175$	0	0
$176$	1.09899e10	0.863353
$177$	1.40208e7	0.00107372
$178$	−2.72501e10	−2.03459
$179$	1.26973e9	0.0924430	0.0462215	−	0.998931i	$-0.485282\pi$
$179$	1.26973e9	0.0924430	0.0462215	+	0.998931i	$0.485282\pi$
$180$	−4.35722e10	−3.09374
$181$	2.17242e10	1.50449	0.752247	−	0.658881i	$-0.228970\pi$
$181$	2.17242e10	1.50449	0.752247	+	0.658881i	$0.228970\pi$
$182$	0	0
$183$	−2.19411e6	−0.000144620 0
$184$	3.72699e10	2.39706
$185$	−5.44037e9	−0.341473
$186$	−5.22584e7	−0.00320146
$187$	−5.77614e9	−0.345422
$188$	−2.51567e10	−1.46874
$189$	0	0
$190$	−5.70552e10	−3.17617
$191$	−1.07035e10	−0.581937	−0.290968	−	0.956733i	$-0.593977\pi$
$191$	−1.07035e10	−0.581937	−0.290968	+	0.956733i	$0.593977\pi$
$192$	−3.09038e7	−0.00164118
$193$	7.66063e9	0.397426	0.198713	−	0.980058i	$-0.436324\pi$
$193$	7.66063e9	0.397426	0.198713	+	0.980058i	$0.436324\pi$
$194$	5.96950e10	3.02573
$195$	−5.10170e7	−0.00252673
$196$	0	0
$197$	−4.26160e9	−0.201592	−0.100796	−	0.994907i	$-0.532139\pi$
$197$	−4.26160e9	−0.201592	−0.100796	+	0.994907i	$0.532139\pi$
$198$	−1.43177e10	−0.662035
$199$	−3.16291e10	−1.42971	−0.714856	−	0.699272i	$-0.753508\pi$
$199$	−3.16291e10	−1.42971	−0.714856	+	0.699272i	$0.753508\pi$
$200$	3.80336e10	1.68086
$201$	5.09256e7	0.00220066
$202$	−3.72678e10	−1.57490
$203$	0	0
$204$	9.52754e7	0.00385163
$205$	1.32064e10	0.522266
$206$	2.97630e10	1.15153
$207$	−2.42590e10	−0.918344
$208$	7.73909e10	2.86685
$209$	−1.32549e10	−0.480526
$210$	0	0
$211$	1.76561e10	0.613229	0.306615	−	0.951834i	$-0.400804\pi$
$211$	1.76561e10	0.613229	0.306615	+	0.951834i	$0.400804\pi$
$212$	−7.38005e10	−2.50927
$213$	1.29817e7	0.000432140 0
$214$	1.03919e11	3.38713
$215$	−3.70903e10	−1.18383
$216$	2.76579e8	0.00864525
$217$	0	0
$218$	1.60292e10	0.480681
$219$	1.05559e8	0.00310097
$220$	3.85219e10	1.10868
$221$	−4.06754e10	−1.14701
$222$	2.94874e7	0.000814794 0
$223$	1.04686e10	0.283476	0.141738	−	0.989904i	$-0.454731\pi$
$223$	1.04686e10	0.283476	0.141738	+	0.989904i	$0.454731\pi$
$224$	0	0
$225$	−2.47560e10	−0.643961
$226$	1.00150e11	2.55366
$227$	−1.95043e10	−0.487543	−0.243772	−	0.969833i	$-0.578385\pi$
$227$	−1.95043e10	−0.487543	−0.243772	+	0.969833i	$0.578385\pi$
$228$	2.18634e8	0.00535811
$229$	5.96135e10	1.43247	0.716234	−	0.697860i	$-0.245864\pi$
$229$	5.96135e10	1.43247	0.716234	+	0.697860i	$0.245864\pi$
$230$	9.23187e10	2.17528
$231$	0	0
$232$	1.91902e10	0.434894
$233$	8.42619e10	1.87296	0.936482	−	0.350716i	$-0.114062\pi$
$233$	8.42619e10	1.87296	0.936482	+	0.350716i	$0.114062\pi$
$234$	−1.00825e11	−2.19835
$235$	−3.64885e10	−0.780460
$236$	−7.45517e10	−1.56442
$237$	−1.04798e7	−0.000215767 0
$238$	0	0
$239$	−7.28353e10	−1.44395	−0.721974	−	0.691920i	$-0.756765\pi$
$239$	−7.28353e10	−1.44395	−0.721974	+	0.691920i	$0.756765\pi$
$240$	−2.62930e8	−0.00511553
$241$	−4.45555e10	−0.850795	−0.425397	−	0.905007i	$-0.639866\pi$
$241$	−4.45555e10	−0.850795	−0.425397	+	0.905007i	$0.639866\pi$
$242$	−8.59086e10	−1.61015
$243$	−2.70038e8	−0.00496817
$244$	1.16666e10	0.210713
$245$	0	0
$246$	−7.15800e7	−0.00124619
$247$	−9.33404e10	−1.59564
$248$	1.62710e11	2.73138
$249$	−7.77557e7	−0.00128184
$250$	−5.20874e10	−0.843340
$251$	9.55068e10	1.51881	0.759404	−	0.650620i	$-0.225491\pi$
$251$	9.55068e10	1.51881	0.759404	+	0.650620i	$0.225491\pi$
$252$	0	0
$253$	2.14472e10	0.329100
$254$	7.86968e10	1.18633
$255$	1.38192e8	0.00204669
$256$	−6.93361e10	−1.00897
$257$	−9.12794e10	−1.30519	−0.652595	−	0.757707i	$-0.726320\pi$
$257$	−9.12794e10	−1.30519	−0.652595	+	0.757707i	$0.726320\pi$
$258$	2.01033e8	0.00282475
$259$	0	0
$260$	2.71270e11	3.68147
$261$	−1.24909e10	−0.166614
$262$	6.23858e10	0.817956
$263$	1.50976e11	1.94584	0.972921	−	0.231138i	$-0.0742449\pi$
$263$	1.50976e11	1.94584	0.972921	+	0.231138i	$0.0742449\pi$
$264$	−1.22261e8	−0.00154906
$265$	−1.07044e11	−1.33338
$266$	0	0
$267$	1.51458e8	0.00182387
$268$	−2.70784e11	−3.20639
$269$	−2.39622e10	−0.279024	−0.139512	−	0.990220i	$-0.544553\pi$
$269$	−2.39622e10	−0.279024	−0.139512	+	0.990220i	$0.544553\pi$
$270$	6.85094e8	0.00784537
$271$	5.51248e10	0.620848	0.310424	−	0.950598i	$-0.399529\pi$
$271$	5.51248e10	0.620848	0.310424	+	0.950598i	$0.399529\pi$
$272$	−2.09632e11	−2.32219
$273$	0	0
$274$	−1.34233e11	−1.43874
$275$	2.18866e10	0.230771
$276$	−3.53763e8	−0.00366963
$277$	2.19632e10	0.224149	0.112074	−	0.993700i	$-0.464251\pi$
$277$	2.19632e10	0.224149	0.112074	+	0.993700i	$0.464251\pi$
$278$	1.27050e11	1.27577
$279$	−1.05908e11	−1.04643
$280$	0	0
$281$	−1.62670e10	−0.155643	−0.0778213	−	0.996967i	$-0.524796\pi$
$281$	−1.62670e10	−0.155643	−0.0778213	+	0.996967i	$0.524796\pi$
$282$	1.97772e8	0.00186227
$283$	−1.35590e10	−0.125657	−0.0628287	−	0.998024i	$-0.520012\pi$
$283$	−1.35590e10	−0.125657	−0.0628287	+	0.998024i	$0.520012\pi$
$284$	−6.90270e10	−0.629632
$285$	3.17118e8	0.00284721
$286$	8.91387e10	0.787805
$287$	0	0
$288$	−2.14885e11	−1.84052
$289$	−8.40858e9	−0.0709059
$290$	4.75346e10	0.394657
$291$	−3.31790e8	−0.00271235
$292$	−5.61284e11	−4.51814
$293$	−5.41900e10	−0.429551	−0.214776	−	0.976663i	$-0.568902\pi$
$293$	−5.41900e10	−0.429551	−0.214776	+	0.976663i	$0.568902\pi$
$294$	0	0
$295$	−1.08133e11	−0.831306
$296$	−9.18109e10	−0.695155
$297$	1.59159e8	0.00118693
$298$	−1.52279e11	−1.11858
$299$	1.51030e11	1.09281
$300$	−3.61012e8	−0.00257321
$301$	0	0
$302$	2.11460e11	1.46284
$303$	2.07138e8	0.00141178
$304$	−4.81056e11	−3.23046
$305$	1.69218e10	0.111969
$306$	2.73109e11	1.78070
$307$	−7.32498e10	−0.470634	−0.235317	−	0.971919i	$-0.575613\pi$
$307$	−7.32498e10	−0.470634	−0.235317	+	0.971919i	$0.575613\pi$
$308$	0	0
$309$	−1.65425e8	−0.00103226
$310$	4.03037e11	2.47866
$311$	2.44502e11	1.48204	0.741021	−	0.671482i	$-0.234342\pi$
$311$	2.44502e11	1.48204	0.741021	+	0.671482i	$0.234342\pi$
$312$	−8.60956e8	−0.00514381
$313$	4.39895e10	0.259060	0.129530	−	0.991576i	$-0.458653\pi$
$313$	4.39895e10	0.259060	0.129530	+	0.991576i	$0.458653\pi$
$314$	5.00314e11	2.90442
$315$	0	0
$316$	5.57237e10	0.314375
$317$	−2.17653e11	−1.21059	−0.605297	−	0.795999i	$-0.706946\pi$
$317$	−2.17653e11	−1.21059	−0.605297	+	0.795999i	$0.706946\pi$
$318$	5.80189e8	0.00318161
$319$	1.10431e10	0.0597080
$320$	2.38342e11	1.27065
$321$	−5.77591e8	−0.00303632
$322$	0	0
$323$	2.52835e11	1.29249
$324$	4.78616e11	2.41288
$325$	1.54125e11	0.766298
$326$	5.89240e11	2.88944
$327$	−8.90917e7	−0.000430896 0
$328$	2.22869e11	1.06321
$329$	0	0
$330$	−3.02843e8	−0.00140574
$331$	−3.66945e11	−1.68026	−0.840128	−	0.542389i	$-0.817520\pi$
$331$	−3.66945e11	−1.68026	−0.840128	+	0.542389i	$0.817520\pi$
$332$	4.13446e11	1.86766
$333$	5.97596e10	0.266323
$334$	−1.48827e11	−0.654368
$335$	−3.92758e11	−1.70382
$336$	0	0
$337$	1.99451e11	0.842367	0.421183	−	0.906976i	$-0.361615\pi$
$337$	1.99451e11	0.842367	0.421183	+	0.906976i	$0.361615\pi$
$338$	1.84423e11	0.768583
$339$	−5.56642e8	−0.00228917
$340$	−7.34801e11	−2.98205
$341$	9.36322e10	0.374999
$342$	6.26721e11	2.47718
$343$	0	0
$344$	−6.25931e11	−2.40998
$345$	−5.13116e8	−0.00194998
$346$	−1.10385e11	−0.414066
$347$	6.63180e10	0.245555	0.122777	−	0.992434i	$-0.460820\pi$
$347$	6.63180e10	0.245555	0.122777	+	0.992434i	$0.460820\pi$
$348$	−1.82152e8	−0.000665774 0
$349$	1.20301e11	0.434065	0.217033	−	0.976164i	$-0.430362\pi$
$349$	1.20301e11	0.434065	0.217033	+	0.976164i	$0.430362\pi$
$350$	0	0
$351$	1.12079e9	0.00394133
$352$	1.89978e11	0.659571
$353$	−2.43060e11	−0.833159	−0.416580	−	0.909099i	$-0.636771\pi$
$353$	−2.43060e11	−0.833159	−0.416580	+	0.909099i	$0.636771\pi$
$354$	5.86095e8	0.00198360
$355$	−1.00120e11	−0.334575
$356$	−8.05341e11	−2.65739
$357$	0	0
$358$	5.30773e10	0.170779
$359$	2.81654e11	0.894933	0.447466	−	0.894301i	$-0.352326\pi$
$359$	2.81654e11	0.894933	0.447466	+	0.894301i	$0.352326\pi$
$360$	−1.06654e12	−3.34670
$361$	2.57510e11	0.798015
$362$	9.08115e11	2.77941
$363$	4.77488e8	0.00144339
$364$	0	0
$365$	−8.14113e11	−2.40086
$366$	−9.17181e7	−0.000267172 0
$367$	2.41000e11	0.693458	0.346729	−	0.937965i	$-0.387292\pi$
$367$	2.41000e11	0.693458	0.346729	+	0.937965i	$0.387292\pi$
$368$	7.78376e11	2.21246
$369$	−1.45065e11	−0.407328
$370$	−2.27418e11	−0.630837
$371$	0	0
$372$	−1.54443e9	−0.00418143
$373$	−1.33921e11	−0.358227	−0.179114	−	0.983828i	$-0.557323\pi$
$373$	−1.33921e11	−0.358227	−0.179114	+	0.983828i	$0.557323\pi$
$374$	−2.41454e11	−0.638134
$375$	2.89507e8	0.000755993 0
$376$	−6.15775e11	−1.58883
$377$	7.77651e10	0.198266
$378$	0	0
$379$	5.67201e11	1.41208	0.706042	−	0.708170i	$-0.250479\pi$
$379$	5.67201e11	1.41208	0.706042	+	0.708170i	$0.250479\pi$
$380$	−1.68619e12	−4.14841
$381$	−4.37404e8	−0.00106346
$382$	−4.47427e11	−1.07507
$383$	1.03509e11	0.245800	0.122900	−	0.992419i	$-0.460781\pi$
$383$	1.03509e11	0.245800	0.122900	+	0.992419i	$0.460781\pi$
$384$	6.85951e6	1.60991e−5 0
$385$	0	0
$386$	3.20229e11	0.734206
$387$	4.07417e11	0.923295
$388$	1.76421e12	3.95191
$389$	−5.83600e11	−1.29224	−0.646119	−	0.763237i	$-0.723609\pi$
$389$	−5.83600e11	−1.29224	−0.646119	+	0.763237i	$0.723609\pi$
$390$	−2.13261e9	−0.00466789
$391$	−4.09102e11	−0.885190
$392$	0	0
$393$	−3.46746e8	−0.000733238 0
$394$	−1.78143e11	−0.372422
$395$	8.08243e10	0.167053
$396$	−4.23142e11	−0.864685
$397$	6.54542e10	0.132245	0.0661226	−	0.997812i	$-0.478937\pi$
$397$	6.54542e10	0.132245	0.0661226	+	0.997812i	$0.478937\pi$
$398$	−1.32216e12	−2.64125
$399$	0	0
$400$	7.94326e11	1.55142
$401$	4.06647e10	0.0785359	0.0392679	−	0.999229i	$-0.487497\pi$
$401$	4.06647e10	0.0785359	0.0392679	+	0.999229i	$0.487497\pi$
$402$	2.12879e9	0.00406551
$403$	6.59356e11	1.24522
$404$	−1.10140e12	−2.05698
$405$	6.94209e11	1.28216
$406$	0	0
$407$	−5.28330e10	−0.0954400
$408$	2.33211e9	0.00416657
$409$	−1.06163e12	−1.87594	−0.937970	−	0.346716i	$-0.887297\pi$
$409$	−1.06163e12	−1.87594	−0.937970	+	0.346716i	$0.887297\pi$
$410$	5.52052e11	0.964835
$411$	7.46081e8	0.00128973
$412$	8.79607e11	1.50401
$413$	0	0
$414$	−1.01407e12	−1.69655
$415$	5.99682e11	0.992441
$416$	1.33782e12	2.19017
$417$	−7.06157e8	−0.00114364
$418$	−5.54079e11	−0.887726
$419$	1.19335e12	1.89149	0.945744	−	0.324912i	$-0.105335\pi$
$419$	1.19335e12	1.89149	0.945744	+	0.324912i	$0.105335\pi$
$420$	0	0
$421$	−5.88397e11	−0.912853	−0.456427	−	0.889761i	$-0.650871\pi$
$421$	−5.88397e11	−0.912853	−0.456427	+	0.889761i	$0.650871\pi$
$422$	7.38058e11	1.13288
$423$	4.00807e11	0.608701
$424$	−1.80646e12	−2.71444
$425$	−4.17485e11	−0.620713
$426$	5.42662e8	0.000798337 0
$427$	0	0
$428$	3.07119e12	4.42394
$429$	−4.95441e8	−0.000706210 0
$430$	−1.55045e12	−2.18700
$431$	−1.22932e12	−1.71599	−0.857997	−	0.513655i	$-0.828291\pi$
$431$	−1.22932e12	−1.71599	−0.857997	+	0.513655i	$0.828291\pi$
$432$	5.77631e9	0.00797946
$433$	4.73819e10	0.0647764	0.0323882	−	0.999475i	$-0.489689\pi$
$433$	4.73819e10	0.0647764	0.0323882	+	0.999475i	$0.489689\pi$
$434$	0	0
$435$	−2.64202e8	−0.000353781 0
$436$	4.73722e11	0.627819
$437$	−9.38793e11	−1.23141
$438$	4.41258e9	0.00572874
$439$	−6.14236e11	−0.789305	−0.394652	−	0.918830i	$-0.629135\pi$
$439$	−6.14236e11	−0.789305	−0.394652	+	0.918830i	$0.629135\pi$
$440$	9.42921e11	1.19933
$441$	0	0
$442$	−1.70031e12	−2.11899
$443$	−8.19199e11	−1.01058	−0.505292	−	0.862948i	$-0.668615\pi$
$443$	−8.19199e11	−1.01058	−0.505292	+	0.862948i	$0.668615\pi$
$444$	8.71462e8	0.00106420
$445$	−1.16811e12	−1.41209
$446$	4.37607e11	0.523694
$447$	8.46379e8	0.00100272
$448$	0	0
$449$	4.81029e11	0.558551	0.279276	−	0.960211i	$-0.409906\pi$
$449$	4.81029e11	0.558551	0.279276	+	0.960211i	$0.409906\pi$
$450$	−1.03485e12	−1.18966
$451$	1.28251e11	0.145971
$452$	2.95980e12	3.33534
$453$	−1.17532e9	−0.00131133
$454$	−8.15316e11	−0.900689
$455$	0	0
$456$	5.35164e9	0.00579622
$457$	1.15328e12	1.23684	0.618419	−	0.785849i	$-0.287774\pi$
$457$	1.15328e12	1.23684	0.618419	+	0.785849i	$0.287774\pi$
$458$	2.49196e12	2.64635
$459$	−3.03594e9	−0.00319254
$460$	2.72836e12	2.84113
$461$	6.06986e11	0.625928	0.312964	−	0.949765i	$-0.398678\pi$
$461$	6.06986e11	0.625928	0.312964	+	0.949765i	$0.398678\pi$
$462$	0	0
$463$	−8.87758e11	−0.897801	−0.448900	−	0.893582i	$-0.648184\pi$
$463$	−8.87758e11	−0.897801	−0.448900	+	0.893582i	$0.648184\pi$
$464$	4.00784e11	0.401402
$465$	−2.24012e9	−0.00222194
$466$	3.52231e12	3.46012
$467$	1.09779e12	1.06806	0.534029	−	0.845466i	$-0.320677\pi$
$467$	1.09779e12	1.06806	0.534029	+	0.845466i	$0.320677\pi$
$468$	−2.97976e12	−2.87127
$469$	0	0
$470$	−1.52529e12	−1.44182
$471$	−2.78079e9	−0.00260360
$472$	−1.82484e12	−1.69234
$473$	−3.60195e11	−0.330874
$474$	−4.38076e8	−0.000398609 0
$475$	−9.58029e11	−0.863490
$476$	0	0
$477$	1.17582e12	1.03994
$478$	−3.04466e12	−2.66755
$479$	3.12229e11	0.270996	0.135498	−	0.990778i	$-0.456737\pi$
$479$	3.12229e11	0.270996	0.135498	+	0.990778i	$0.456737\pi$
$480$	−4.54516e9	−0.00390808
$481$	−3.72048e11	−0.316918
$482$	−1.86251e12	−1.57176
$483$	0	0
$484$	−2.53892e12	−2.10303
$485$	2.55889e12	2.09998
$486$	−1.12881e10	−0.00917820
$487$	1.08377e12	0.873088	0.436544	−	0.899683i	$-0.356202\pi$
$487$	1.08377e12	0.873088	0.436544	+	0.899683i	$0.356202\pi$
$488$	2.85570e11	0.227942
$489$	−3.27505e9	−0.00259017
$490$	0	0
$491$	2.14702e12	1.66713	0.833567	−	0.552419i	$-0.186295\pi$
$491$	2.14702e12	1.66713	0.833567	+	0.552419i	$0.186295\pi$
$492$	−2.11545e9	−0.00162765
$493$	−2.10646e11	−0.160599
$494$	−3.90181e12	−2.94778
$495$	−6.13746e11	−0.459479
$496$	3.39817e12	2.52103
$497$	0	0
$498$	−3.25034e9	−0.00236808
$499$	−1.85705e12	−1.34082	−0.670411	−	0.741990i	$-0.733882\pi$
$499$	−1.85705e12	−1.34082	−0.670411	+	0.741990i	$0.733882\pi$
$500$	−1.53938e12	−1.10149
$501$	8.27193e8	0.000586593 0
$502$	3.99237e12	2.80585
$503$	1.59040e12	1.10777	0.553885	−	0.832593i	$-0.313145\pi$
$503$	1.59040e12	1.10777	0.553885	+	0.832593i	$0.313145\pi$
$504$	0	0
$505$	−1.59753e12	−1.09304
$506$	8.96533e11	0.607979
$507$	−1.02504e9	−0.000688979 0
$508$	2.32578e12	1.54947
$509$	−2.32864e12	−1.53771	−0.768853	−	0.639426i	$-0.779172\pi$
$509$	−2.32864e12	−1.53771	−0.768853	+	0.639426i	$0.779172\pi$
$510$	5.77670e9	0.00378106
$511$	0	0
$512$	−2.88327e12	−1.85426
$513$	−6.96676e9	−0.00444122
$514$	−3.81566e12	−2.41121
$515$	1.27582e12	0.799205
$516$	5.94128e9	0.00368941
$517$	−3.54350e11	−0.218135
$518$	0	0
$519$	6.13532e8	0.000371180 0
$520$	6.64003e12	3.98249
$521$	1.48366e12	0.882197	0.441099	−	0.897459i	$-0.354589\pi$
$521$	1.48366e12	0.882197	0.441099	+	0.897459i	$0.354589\pi$
$522$	−5.22143e11	−0.307802
$523$	1.95584e12	1.14308	0.571540	−	0.820574i	$-0.306346\pi$
$523$	1.95584e12	1.14308	0.571540	+	0.820574i	$0.306346\pi$
$524$	1.84373e12	1.06833
$525$	0	0
$526$	6.31110e12	3.59475
$527$	−1.78603e12	−1.00865
$528$	−2.55339e9	−0.00142977
$529$	−2.82131e11	−0.156639
$530$	−4.47464e12	−2.46330
$531$	1.18779e12	0.648357
$532$	0	0
$533$	9.03139e11	0.484710
$534$	6.33126e9	0.00336941
$535$	4.45460e12	2.35081
$536$	−6.62812e12	−3.46856
$537$	−2.95009e8	−0.000153091 0
$538$	−1.00167e12	−0.515470
$539$	0	0
$540$	2.02471e10	0.0102469
$541$	−1.34802e12	−0.676563	−0.338281	−	0.941045i	$-0.609846\pi$
$541$	−1.34802e12	−0.676563	−0.338281	+	0.941045i	$0.609846\pi$
$542$	2.30433e12	1.14696
$543$	−5.04738e9	−0.00249154
$544$	−3.62381e12	−1.77407
$545$	6.87109e11	0.333612
$546$	0	0
$547$	1.02503e12	0.489548	0.244774	−	0.969580i	$-0.421286\pi$
$547$	1.02503e12	0.489548	0.244774	+	0.969580i	$0.421286\pi$
$548$	−3.96710e12	−1.87914
$549$	−1.85877e11	−0.0873275
$550$	9.14903e11	0.426327
$551$	−4.83382e11	−0.223413
$552$	−8.65926e9	−0.00396968
$553$	0	0
$554$	9.18103e11	0.414093
$555$	1.26401e9	0.000565500 0
$556$	3.75481e12	1.66629
$557$	1.75343e12	0.771864	0.385932	−	0.922527i	$-0.373880\pi$
$557$	1.75343e12	0.771864	0.385932	+	0.922527i	$0.373880\pi$
$558$	−4.42715e12	−1.93317
$559$	−2.53648e12	−1.09870
$560$	0	0
$561$	1.34202e9	0.000572041 0
$562$	−6.79991e11	−0.287535
$563$	2.17456e12	0.912185	0.456092	−	0.889932i	$-0.349249\pi$
$563$	2.17456e12	0.912185	0.456092	+	0.889932i	$0.349249\pi$
$564$	5.84489e9	0.00243232
$565$	4.29304e12	1.77234
$566$	−5.66792e11	−0.232140
$567$	0	0
$568$	−1.68961e12	−0.681114
$569$	3.13812e12	1.25506	0.627531	−	0.778592i	$-0.284066\pi$
$569$	3.13812e12	1.25506	0.627531	+	0.778592i	$0.284066\pi$
$570$	1.32562e10	0.00525994
$571$	2.05979e12	0.810887	0.405444	−	0.914120i	$-0.367117\pi$
$571$	2.05979e12	0.810887	0.405444	+	0.914120i	$0.367117\pi$
$572$	2.63438e12	1.02895
$573$	2.48684e9	0.000963723 0
$574$	0	0
$575$	1.55015e12	0.591381
$576$	−2.61806e12	−0.991011
$577$	−3.94380e12	−1.48123	−0.740617	−	0.671927i	$-0.765467\pi$
$577$	−3.94380e12	−1.48123	−0.740617	+	0.671927i	$0.765467\pi$
$578$	−3.51495e11	−0.130992
$579$	−1.77986e9	−0.000658162 0
$580$	1.40483e12	0.515462
$581$	0	0
$582$	−1.38695e10	−0.00501079
$583$	−1.03953e12	−0.372675
$584$	−1.37389e13	−4.88757
$585$	−4.32198e12	−1.52574
$586$	−2.26525e12	−0.793555
$587$	−3.68239e12	−1.28014	−0.640071	−	0.768315i	$-0.721095\pi$
$587$	−3.68239e12	−1.28014	−0.640071	+	0.768315i	$0.721095\pi$
$588$	0	0
$589$	−4.09851e12	−1.40316
$590$	−4.52019e12	−1.53576
$591$	9.90135e8	0.000333850 0
$592$	−1.91746e12	−0.641620
$593$	1.17114e12	0.388921	0.194460	−	0.980910i	$-0.437704\pi$
$593$	1.17114e12	0.388921	0.194460	+	0.980910i	$0.437704\pi$
$594$	6.65315e9	0.00219274
$595$	0	0
$596$	−4.50040e12	−1.46098
$597$	7.34868e9	0.00236769
$598$	6.31336e12	2.01886
$599$	2.83757e12	0.900586	0.450293	−	0.892881i	$-0.351319\pi$
$599$	2.83757e12	0.900586	0.450293	+	0.892881i	$0.351319\pi$
$600$	−8.83669e9	−0.00278361
$601$	−2.37066e12	−0.741198	−0.370599	−	0.928793i	$-0.620848\pi$
$601$	−2.37066e12	−0.741198	−0.370599	+	0.928793i	$0.620848\pi$
$602$	0	0
$603$	4.31424e12	1.32885
$604$	6.24943e12	1.91062
$605$	−3.68257e12	−1.11751
$606$	8.65876e9	0.00260813
$607$	−4.40080e12	−1.31578	−0.657889	−	0.753115i	$-0.728550\pi$
$607$	−4.40080e12	−1.31578	−0.657889	+	0.753115i	$0.728550\pi$
$608$	−8.31580e12	−2.46796
$609$	0	0
$610$	7.07366e11	0.206852
$611$	−2.49533e12	−0.724339
$612$	8.07140e12	2.32577
$613$	−1.87570e12	−0.536527	−0.268264	−	0.963346i	$-0.586450\pi$
$613$	−1.87570e12	−0.536527	−0.268264	+	0.963346i	$0.586450\pi$
$614$	−3.06198e12	−0.869451
$615$	−3.06836e9	−0.000864904 0
$616$	0	0
$617$	−3.18170e12	−0.883845	−0.441922	−	0.897053i	$-0.645703\pi$
$617$	−3.18170e12	−0.883845	−0.441922	+	0.897053i	$0.645703\pi$
$618$	−6.91510e9	−0.00190700
$619$	1.16476e11	0.0318880	0.0159440	−	0.999873i	$-0.494925\pi$
$619$	1.16476e11	0.0318880	0.0159440	+	0.999873i	$0.494925\pi$
$620$	1.19113e13	3.23739
$621$	1.12726e10	0.00304167
$622$	1.02207e13	2.73793
$623$	0	0
$624$	−1.79809e10	−0.00474768
$625$	−4.68931e12	−1.22927
$626$	1.83885e12	0.478587
$627$	3.07962e9	0.000795781 0
$628$	1.47861e13	3.79347
$629$	1.00778e12	0.256708
$630$	0	0
$631$	−3.71283e12	−0.932338	−0.466169	−	0.884696i	$-0.654366\pi$
$631$	−3.71283e12	−0.932338	−0.466169	+	0.884696i	$0.654366\pi$
$632$	1.36398e12	0.340080
$633$	−4.10219e9	−0.00101555
$634$	−9.09834e12	−2.23646
$635$	3.37343e12	0.823360
$636$	1.71467e10	0.00415551
$637$	0	0
$638$	4.61622e11	0.110305
$639$	1.09977e12	0.260944
$640$	−5.29032e10	−0.0124644
$641$	2.93764e11	0.0687285	0.0343642	−	0.999409i	$-0.489059\pi$
$641$	2.93764e11	0.0687285	0.0343642	+	0.999409i	$0.489059\pi$
$642$	−2.41444e10	−0.00560930
$643$	−5.27980e12	−1.21806	−0.609029	−	0.793148i	$-0.708441\pi$
$643$	−5.27980e12	−1.21806	−0.609029	+	0.793148i	$0.708441\pi$
$644$	0	0
$645$	8.61753e9	0.00196049
$646$	1.05690e13	2.38775
$647$	2.62000e12	0.587804	0.293902	−	0.955836i	$-0.405046\pi$
$647$	2.62000e12	0.587804	0.293902	+	0.955836i	$0.405046\pi$
$648$	1.17154e13	2.61017
$649$	−1.05011e12	−0.232346
$650$	6.44272e12	1.41566
$651$	0	0
$652$	1.74142e13	3.77390
$653$	3.15918e12	0.679931	0.339965	−	0.940438i	$-0.389585\pi$
$653$	3.15918e12	0.679931	0.339965	+	0.940438i	$0.389585\pi$
$654$	−3.72420e9	−0.000796038 0
$655$	2.67424e12	0.567694
$656$	4.65458e12	0.981326
$657$	8.94260e12	1.87249
$658$	0	0
$659$	8.77292e11	0.181201	0.0906004	−	0.995887i	$-0.471121\pi$
$659$	8.77292e11	0.181201	0.0906004	+	0.995887i	$0.471121\pi$
$660$	−8.95013e9	−0.00183604
$661$	−8.22108e12	−1.67503	−0.837514	−	0.546416i	$-0.815992\pi$
$661$	−8.22108e12	−1.67503	−0.837514	+	0.546416i	$0.815992\pi$
$662$	−1.53390e13	−3.10411
$663$	9.45049e9	0.00189952
$664$	1.01201e13	2.02037
$665$	0	0
$666$	2.49807e12	0.492006
$667$	7.82140e11	0.153010
$668$	−4.39838e12	−0.854671
$669$	−2.43226e9	−0.000469454 0
$670$	−1.64180e13	−3.14764
$671$	1.64333e11	0.0312948
$672$	0	0
$673$	−7.47304e12	−1.40420	−0.702101	−	0.712077i	$-0.747754\pi$
$673$	−7.47304e12	−1.40420	−0.702101	+	0.712077i	$0.747754\pi$
$674$	8.33743e12	1.55619
$675$	1.15036e10	0.00213288
$676$	5.45039e12	1.00385
$677$	−8.71309e12	−1.59413	−0.797064	−	0.603895i	$-0.793614\pi$
$677$	−8.71309e12	−1.59413	−0.797064	+	0.603895i	$0.793614\pi$
$678$	−2.32687e10	−0.00422901
$679$	0	0
$680$	−1.79861e13	−3.22588
$681$	4.53160e9	0.000807402 0
$682$	3.91401e12	0.692775
$683$	−3.73903e12	−0.657455	−0.328727	−	0.944425i	$-0.606620\pi$
$683$	−3.73903e12	−0.657455	−0.328727	+	0.944425i	$0.606620\pi$
$684$	1.85219e13	3.23545
$685$	−5.75407e12	−0.998545
$686$	0	0
$687$	−1.38505e10	−0.00237226
$688$	−1.30725e13	−2.22438
$689$	−7.32036e12	−1.23750
$690$	−2.14492e10	−0.00360239
$691$	6.26971e12	1.04616	0.523078	−	0.852285i	$-0.324784\pi$
$691$	6.26971e12	1.04616	0.523078	+	0.852285i	$0.324784\pi$
$692$	−3.26230e12	−0.540812
$693$	0	0
$694$	2.77222e12	0.453639
$695$	5.44616e12	0.885439
$696$	−4.45863e9	−0.000720212 0
$697$	−2.44637e12	−0.392623
$698$	5.02882e12	0.801893
$699$	−1.95773e10	−0.00310174
$700$	0	0
$701$	−5.13904e12	−0.803805	−0.401903	−	0.915682i	$-0.631651\pi$
$701$	−5.13904e12	−0.803805	−0.401903	+	0.915682i	$0.631651\pi$
$702$	4.68513e10	0.00728122
$703$	2.31263e12	0.357114
$704$	2.31461e12	0.355140
$705$	8.47771e9	0.00129249
$706$	−1.01604e13	−1.53918
$707$	0	0
$708$	1.73213e10	0.00259078
$709$	−2.95438e12	−0.439094	−0.219547	−	0.975602i	$-0.570458\pi$
$709$	−2.95438e12	−0.439094	−0.219547	+	0.975602i	$0.570458\pi$
$710$	−4.18522e12	−0.618096
$711$	−8.87813e11	−0.130289
$712$	−1.97128e13	−2.87467
$713$	6.63162e12	0.960986
$714$	0	0
$715$	3.82103e12	0.546768
$716$	1.56863e12	0.223055
$717$	1.69225e10	0.00239127
$718$	1.17737e13	1.65330
$719$	1.21819e13	1.69994	0.849971	−	0.526829i	$-0.176619\pi$
$719$	1.21819e13	1.69994	0.849971	+	0.526829i	$0.176619\pi$
$720$	−2.22745e13	−3.08896
$721$	0	0
$722$	1.07644e13	1.47426
$723$	1.03520e10	0.00140897
$724$	2.68382e13	3.63019
$725$	7.98167e11	0.107293
$726$	1.99599e10	0.00266652
$727$	−1.26291e13	−1.67675	−0.838376	−	0.545093i	$-0.816494\pi$
$727$	−1.26291e13	−1.67675	−0.838376	+	0.545093i	$0.816494\pi$
$728$	0	0
$729$	−7.62547e12	−0.999984
$730$	−3.40315e13	−4.43536
$731$	6.87068e12	0.889962
$732$	−2.71061e9	−0.000348953 0
$733$	−9.16594e12	−1.17276	−0.586380	−	0.810036i	$-0.699447\pi$
$733$	−9.16594e12	−1.17276	−0.586380	+	0.810036i	$0.699447\pi$
$734$	1.00743e13	1.28110
$735$	0	0
$736$	1.34554e13	1.69024
$737$	−3.81418e12	−0.476209
$738$	−6.06400e12	−0.752499
$739$	1.10658e13	1.36484	0.682420	−	0.730960i	$-0.260927\pi$
$739$	1.10658e13	1.36484	0.682420	+	0.730960i	$0.260927\pi$
$740$	−6.72105e12	−0.823938
$741$	2.16866e10	0.00264247
$742$	0	0
$743$	1.84642e12	0.222270	0.111135	−	0.993805i	$-0.464551\pi$
$743$	1.84642e12	0.222270	0.111135	+	0.993805i	$0.464551\pi$
$744$	−3.78039e10	−0.00452333
$745$	−6.52760e12	−0.776337
$746$	−5.59816e12	−0.661790
$747$	−6.58719e12	−0.774029
$748$	−7.13586e12	−0.833468
$749$	0	0
$750$	1.21019e10	0.00139662
$751$	−9.19672e12	−1.05500	−0.527501	−	0.849555i	$-0.676871\pi$
$751$	−9.19672e12	−1.05500	−0.527501	+	0.849555i	$0.676871\pi$
$752$	−1.28604e13	−1.46647
$753$	−2.21900e10	−0.00251524
$754$	3.25073e12	0.366277
$755$	9.06449e12	1.01527
$756$	0	0
$757$	8.81778e12	0.975950	0.487975	−	0.872858i	$-0.337736\pi$
$757$	8.81778e12	0.975950	0.487975	+	0.872858i	$0.337736\pi$
$758$	2.37101e13	2.60869
$759$	−4.98301e9	−0.000545009 0
$760$	−4.12739e13	−4.48760
$761$	2.42043e12	0.261614	0.130807	−	0.991408i	$-0.458243\pi$
$761$	2.42043e12	0.261614	0.130807	+	0.991408i	$0.458243\pi$
$762$	−1.82843e10	−0.00196464
$763$	0	0
$764$	−1.32231e13	−1.40415
$765$	1.17071e13	1.23588
$766$	4.32686e12	0.454092
$767$	−7.39488e12	−0.771528
$768$	1.61095e10	0.00167092
$769$	−7.67945e12	−0.791885	−0.395942	−	0.918275i	$-0.629582\pi$
$769$	−7.67945e12	−0.791885	−0.395942	+	0.918275i	$0.629582\pi$
$770$	0	0
$771$	2.12078e10	0.00216148
$772$	9.46396e12	0.958948
$773$	−1.04693e13	−1.05466	−0.527328	−	0.849662i	$-0.676806\pi$
$773$	−1.04693e13	−1.05466	−0.527328	+	0.849662i	$0.676806\pi$
$774$	1.70308e13	1.70570
$775$	6.76751e12	0.673862
$776$	4.31835e13	4.27504
$777$	0	0
$778$	−2.43956e13	−2.38728
$779$	−5.61385e12	−0.546188
$780$	−6.30266e10	−0.00609675
$781$	−9.72296e11	−0.0935123
$782$	−1.71013e13	−1.63530
$783$	5.80424e9	0.000551846 0
$784$	0	0
$785$	2.14465e13	2.01578
$786$	−1.44947e10	−0.00135459
$787$	1.26490e13	1.17535	0.587677	−	0.809095i	$-0.300042\pi$
$787$	1.26490e13	1.17535	0.587677	+	0.809095i	$0.300042\pi$
$788$	−5.26479e12	−0.486422
$789$	−3.50777e10	−0.00322243
$790$	3.37862e12	0.308615
$791$	0	0
$792$	−1.03575e13	−0.935387
$793$	1.15723e12	0.103918
$794$	2.73611e12	0.244310
$795$	2.48705e10	0.00220817
$796$	−3.90747e13	−3.44975
$797$	6.02337e11	0.0528782	0.0264391	−	0.999650i	$-0.491583\pi$
$797$	6.02337e11	0.0528782	0.0264391	+	0.999650i	$0.491583\pi$
$798$	0	0
$799$	6.75920e12	0.586725
$800$	1.37311e13	1.18523
$801$	1.28310e13	1.10132
$802$	1.69986e12	0.145087
$803$	−7.90608e12	−0.671029
$804$	6.29136e10	0.00530997
$805$	0	0
$806$	2.75624e13	2.30043
$807$	5.56736e9	0.000462081 0
$808$	−2.69596e13	−2.22517
$809$	−7.72967e12	−0.634443	−0.317222	−	0.948351i	$-0.602750\pi$
$809$	−7.72967e12	−0.634443	−0.317222	+	0.948351i	$0.602750\pi$
$810$	2.90193e13	2.36867
$811$	1.20157e13	0.975335	0.487668	−	0.873029i	$-0.337848\pi$
$811$	1.20157e13	0.975335	0.487668	+	0.873029i	$0.337848\pi$
$812$	0	0
$813$	−1.28077e10	−0.00102816
$814$	−2.20852e12	−0.176316
$815$	2.52585e13	2.00538
$816$	4.87057e10	0.00384569
$817$	1.57666e13	1.23805
$818$	−4.43783e13	−3.46562
$819$	0	0
$820$	1.63152e13	1.26017
$821$	1.39952e13	1.07507	0.537533	−	0.843243i	$-0.319356\pi$
$821$	1.39952e13	1.07507	0.537533	+	0.843243i	$0.319356\pi$
$822$	3.11877e10	0.00238265
$823$	1.61982e13	1.23074	0.615371	−	0.788238i	$-0.289006\pi$
$823$	1.61982e13	1.23074	0.615371	+	0.788238i	$0.289006\pi$
$824$	2.15306e13	1.62699
$825$	−5.08511e9	−0.000382171 0
$826$	0	0
$827$	−1.30127e13	−0.967374	−0.483687	−	0.875241i	$-0.660703\pi$
$827$	−1.30127e13	−0.967374	−0.483687	+	0.875241i	$0.660703\pi$
$828$	−2.99696e13	−2.21587
$829$	1.31364e13	0.966007	0.483004	−	0.875618i	$-0.339546\pi$
$829$	1.31364e13	0.966007	0.483004	+	0.875618i	$0.339546\pi$
$830$	2.50679e13	1.83344
$831$	−5.10290e9	−0.000371204 0
$832$	1.62994e13	1.17928
$833$	0	0
$834$	−2.95187e10	−0.00211276
$835$	−6.37963e12	−0.454157
$836$	−1.63751e13	−1.15946
$837$	4.92131e10	0.00346590
$838$	4.98842e13	3.49434
$839$	5.22420e12	0.363991	0.181996	−	0.983299i	$-0.441744\pi$
$839$	5.22420e12	0.363991	0.181996	+	0.983299i	$0.441744\pi$
$840$	0	0
$841$	−1.41044e13	−0.972240
$842$	−2.45961e13	−1.68641
$843$	3.77945e9	0.000257754 0
$844$	2.18124e13	1.47966
$845$	7.90552e12	0.533427
$846$	1.67545e13	1.12452
$847$	0	0
$848$	−3.77275e13	−2.50540
$849$	3.15028e9	0.000208096 0
$850$	−1.74517e13	−1.14671
$851$	−3.74196e12	−0.244578
$852$	1.60377e10	0.00104271
$853$	5.65076e12	0.365457	0.182728	−	0.983163i	$-0.441507\pi$
$853$	5.65076e12	0.365457	0.182728	+	0.983163i	$0.441507\pi$
$854$	0	0
$855$	2.68651e13	1.71926
$856$	7.51752e13	4.78567
$857$	−1.42516e12	−0.0902503	−0.0451251	−	0.998981i	$-0.514369\pi$
$857$	−1.42516e12	−0.0902503	−0.0451251	+	0.998981i	$0.514369\pi$
$858$	−2.07104e10	−0.00130465
$859$	−2.77961e13	−1.74186	−0.870932	−	0.491404i	$-0.836484\pi$
$859$	−2.77961e13	−1.74186	−0.870932	+	0.491404i	$0.836484\pi$
$860$	−4.58215e13	−2.85645
$861$	0	0
$862$	−5.13878e13	−3.17013
$863$	−1.14117e13	−0.700326	−0.350163	−	0.936689i	$-0.613874\pi$
$863$	−1.14117e13	−0.700326	−0.350163	+	0.936689i	$0.613874\pi$
$864$	9.98525e10	0.00609603
$865$	−4.73180e12	−0.287378
$866$	1.98066e12	0.119668
$867$	1.95364e9	0.000117425 0
$868$	0	0
$869$	7.84908e11	0.0466906
$870$	−1.10442e10	−0.000653576 0
$871$	−2.68594e13	−1.58130
$872$	1.15956e13	0.679153
$873$	−2.81081e13	−1.63782
$874$	−3.92434e13	−2.27491
$875$	0	0
$876$	1.30408e11	0.00748232
$877$	−1.21188e13	−0.691769	−0.345884	−	0.938277i	$-0.612421\pi$
$877$	−1.21188e13	−0.691769	−0.345884	+	0.938277i	$0.612421\pi$
$878$	−2.56763e13	−1.45816
$879$	1.25905e10	0.000711364 0
$880$	1.96927e13	1.10697
$881$	4.60741e12	0.257671	0.128836	−	0.991666i	$-0.458876\pi$
$881$	4.60741e12	0.257671	0.128836	+	0.991666i	$0.458876\pi$
$882$	0	0
$883$	1.04709e13	0.579642	0.289821	−	0.957081i	$-0.406404\pi$
$883$	1.04709e13	0.579642	0.289821	+	0.957081i	$0.406404\pi$
$884$	−5.02505e13	−2.76761
$885$	2.51236e10	0.00137669
$886$	−3.42441e13	−1.86696
$887$	3.68711e12	0.200000	0.0999999	−	0.994987i	$-0.468116\pi$
$887$	3.68711e12	0.200000	0.0999999	+	0.994987i	$0.468116\pi$
$888$	2.13313e10	0.00115122
$889$	0	0
$890$	−4.88291e13	−2.60870
$891$	6.74166e12	0.358358
$892$	1.29329e13	0.683998
$893$	1.55108e13	0.816209
$894$	3.53803e10	0.00185243
$895$	2.27522e12	0.118528
$896$	0	0
$897$	−3.50902e10	−0.00180976
$898$	2.01080e13	1.03187
$899$	3.41461e12	0.174350
$900$	−3.05837e13	−1.55381
$901$	1.98290e13	1.00240
$902$	5.36114e12	0.269667
$903$	0	0
$904$	7.24487e13	3.60805
$905$	3.89274e13	1.92902
$906$	−4.91305e10	−0.00242256
$907$	−6.05209e11	−0.0296943	−0.0148471	−	0.999890i	$-0.504726\pi$
$907$	−6.05209e11	−0.0296943	−0.0148471	+	0.999890i	$0.504726\pi$
$908$	−2.40956e13	−1.17639
$909$	1.75480e13	0.852491
$910$	0	0
$911$	−3.27450e12	−0.157512	−0.0787559	−	0.996894i	$-0.525095\pi$
$911$	−3.27450e12	−0.157512	−0.0787559	+	0.996894i	$0.525095\pi$
$912$	1.11768e11	0.00534984
$913$	5.82368e12	0.277383
$914$	4.82094e13	2.28494
$915$	−3.93160e9	−0.000185428 0
$916$	7.36467e13	3.45640
$917$	0	0
$918$	−1.26908e11	−0.00589790
$919$	2.21117e11	0.0102259	0.00511295	−	0.999987i	$-0.498372\pi$
$919$	2.21117e11	0.0102259	0.00511295	+	0.999987i	$0.498372\pi$
$920$	6.67836e13	3.07344
$921$	1.70188e10	0.000779400 0
$922$	2.53732e13	1.15634
$923$	−6.84688e12	−0.310517
$924$	0	0
$925$	−3.81864e12	−0.171503
$926$	−3.71100e13	−1.65860
$927$	−1.40143e13	−0.623320
$928$	6.92817e12	0.306657
$929$	4.00147e12	0.176258	0.0881290	−	0.996109i	$-0.471911\pi$
$929$	4.00147e12	0.176258	0.0881290	+	0.996109i	$0.471911\pi$
$930$	−9.36413e10	−0.00410482
$931$	0	0
$932$	1.04097e14	4.51927
$933$	−5.68073e10	−0.00245435
$934$	4.58899e13	1.97313
$935$	−1.03502e13	−0.442890
$936$	−7.29372e13	−3.10604
$937$	3.76138e10	0.00159411	0.000797056	−	1.00000i	$-0.499746\pi$
$937$	3.76138e10	0.00159411	0.000797056		1.00000i	$0.499746\pi$
$938$	0	0
$939$	−1.02205e10	−0.000429019 0
$940$	−4.50780e13	−1.88317
$941$	2.21494e12	0.0920894	0.0460447	−	0.998939i	$-0.485338\pi$
$941$	2.21494e12	0.0920894	0.0460447	+	0.998939i	$0.485338\pi$
$942$	−1.16242e11	−0.00480990
$943$	9.08353e12	0.374069
$944$	−3.81116e13	−1.56201
$945$	0	0
$946$	−1.50568e13	−0.611257
$947$	2.36266e13	0.954610	0.477305	−	0.878738i	$-0.341614\pi$
$947$	2.36266e13	0.954610	0.477305	+	0.878738i	$0.341614\pi$
$948$	−1.29468e10	−0.000520624 0
$949$	−5.56744e13	−2.22822
$950$	−4.00475e13	−1.59521
$951$	5.05694e10	0.00200482
$952$	0	0
$953$	−1.15037e13	−0.451771	−0.225885	−	0.974154i	$-0.572527\pi$
$953$	−1.15037e13	−0.451771	−0.225885	+	0.974154i	$0.572527\pi$
$954$	4.91516e13	1.92119
$955$	−1.91795e13	−0.746142
$956$	−8.99810e13	−3.48410
$957$	−2.56574e9	−9.88801e−5 0
$958$	1.30518e13	0.500639
$959$	0	0
$960$	−5.53761e10	−0.00210427
$961$	2.51218e12	0.0950156
$962$	−1.55524e13	−0.585475
$963$	−4.89314e13	−1.83345
$964$	−5.50440e13	−2.05288
$965$	1.37270e13	0.509568
$966$	0	0
$967$	−1.36863e13	−0.503346	−0.251673	−	0.967812i	$-0.580981\pi$
$967$	−1.36863e13	−0.503346	−0.251673	+	0.967812i	$0.580981\pi$
$968$	−6.21465e13	−2.27498
$969$	−5.87435e10	−0.00214044
$970$	1.06967e14	3.87950
$971$	−9.95259e12	−0.359294	−0.179647	−	0.983731i	$-0.557496\pi$
$971$	−9.95259e12	−0.359294	−0.179647	+	0.983731i	$0.557496\pi$
$972$	−3.33605e11	−0.0119877
$973$	0	0
$974$	4.53038e13	1.61295
$975$	−3.58092e10	−0.00126904
$976$	5.96409e12	0.210387
$977$	1.51387e13	0.531575	0.265787	−	0.964032i	$-0.414368\pi$
$977$	1.51387e13	0.531575	0.265787	+	0.964032i	$0.414368\pi$
$978$	−1.36903e11	−0.00478508
$979$	−1.13438e13	−0.394673
$980$	0	0
$981$	−7.54753e12	−0.260192
$982$	8.97498e13	3.07987
$983$	−5.47141e13	−1.86899	−0.934497	−	0.355970i	$-0.884151\pi$
$983$	−5.47141e13	−1.86899	−0.934497	+	0.355970i	$0.884151\pi$
$984$	−5.17811e10	−0.00176073
$985$	−7.63631e12	−0.258476
$986$	−8.80540e12	−0.296690
$987$	0	0
$988$	−1.15313e14	−3.85010
$989$	−2.55112e13	−0.847907
$990$	−2.56558e13	−0.848842
$991$	4.86384e13	1.60195	0.800974	−	0.598699i	$-0.204316\pi$
$991$	4.86384e13	1.60195	0.800974	+	0.598699i	$0.204316\pi$
$992$	5.87427e13	1.92598
$993$	8.52557e10	0.00278261
$994$	0	0
$995$	−5.66759e13	−1.83314
$996$	−9.60596e10	−0.00309296
$997$	−2.77758e13	−0.890304	−0.445152	−	0.895455i	$-0.646850\pi$
$997$	−2.77758e13	−0.890304	−0.445152	+	0.895455i	$0.646850\pi$
$998$	−7.76283e13	−2.47704
$999$	−2.77690e10	−0.000882096 0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.10.a.c.1.3		3
7.2	even	3		49.10.c.e.18.1		6
7.3	odd	6		49.10.c.d.30.1		6
7.4	even	3		49.10.c.e.30.1		6
7.5	odd	6		49.10.c.d.18.1		6
7.6	odd	2		7.10.a.b.1.3	✓	3
21.20	even	2		63.10.a.e.1.1		3
28.27	even	2		112.10.a.h.1.2		3
35.13	even	4		175.10.b.d.99.1		6
35.27	even	4		175.10.b.d.99.6		6
35.34	odd	2		175.10.a.d.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.a.b.1.3	✓	3	7.6	odd	2
49.10.a.c.1.3		3	1.1	even	1	trivial
49.10.c.d.18.1		6	7.5	odd	6
49.10.c.d.30.1		6	7.3	odd	6
49.10.c.e.18.1		6	7.2	even	3
49.10.c.e.30.1		6	7.4	even	3
63.10.a.e.1.1		3	21.20	even	2
112.10.a.h.1.2		3	28.27	even	2
175.10.a.d.1.1		3	35.34	odd	2
175.10.b.d.99.1		6	35.13	even	4
175.10.b.d.99.6		6	35.27	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	49.a (trivial)

\(f(q)\)	\(=\)	\(q+41.8019 q^{2} -0.232339 q^{3} +1235.40 q^{4} +1791.89 q^{5} -9.71222 q^{6} +30239.6 q^{8} -19682.9 q^{9} +O(q^{10})\)	\(q+41.8019 q^{2} -0.232339 q^{3} +1235.40 q^{4} +1791.89 q^{5} -9.71222 q^{6} +30239.6 q^{8} -19682.9 q^{9} +74904.4 q^{10} +17401.5 q^{11} -287.032 q^{12} +122541. q^{13} -416.326 q^{15} +631550. q^{16} -331933. q^{17} -822785. q^{18} -761707. q^{19} +2.21370e6 q^{20} +727418. q^{22} +1.23249e6 q^{23} -7025.85 q^{24} +1.25774e6 q^{25} +5.12246e6 q^{26} +9146.25 q^{27} +634604. q^{29} -17403.2 q^{30} +5.38069e6 q^{31} +1.09173e7 q^{32} -4043.06 q^{33} -1.38754e7 q^{34} -2.43164e7 q^{36} -3.03611e6 q^{37} -3.18408e7 q^{38} -28471.1 q^{39} +5.41861e7 q^{40} +7.37009e6 q^{41} -2.06990e7 q^{43} +2.14979e7 q^{44} -3.52696e7 q^{45} +5.15203e7 q^{46} -2.03632e7 q^{47} -146734. q^{48} +5.25760e7 q^{50} +77120.9 q^{51} +1.51388e8 q^{52} -5.97380e7 q^{53} +382331. q^{54} +3.11816e7 q^{55} +176974. q^{57} +2.65277e7 q^{58} -6.03461e7 q^{59} -514330. q^{60} +9.44357e6 q^{61} +2.24923e8 q^{62} +1.33012e8 q^{64} +2.19580e8 q^{65} -169008. q^{66} -2.19187e8 q^{67} -4.10071e8 q^{68} -286355. q^{69} -5.58741e7 q^{71} -5.95205e8 q^{72} -4.54332e8 q^{73} -1.26915e8 q^{74} -292222. q^{75} -9.41015e8 q^{76} -1.19015e6 q^{78} +4.51057e7 q^{79} +1.13167e9 q^{80} +3.87417e8 q^{81} +3.08084e8 q^{82} +3.34665e8 q^{83} -5.94786e8 q^{85} -8.65259e8 q^{86} -147443. q^{87} +5.26216e8 q^{88} -6.51886e8 q^{89} -1.47434e9 q^{90} +1.52262e9 q^{92} -1.25014e6 q^{93} -8.51220e8 q^{94} -1.36489e9 q^{95} -2.53652e6 q^{96} +1.42804e9 q^{97} -3.42514e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 21 q^{2} - 84 q^{3} + 1557 q^{4} - 1554 q^{5} - 4914 q^{6} + 14055 q^{8} - 26001 q^{9}+O(q^{10}) \) 3 * q + 21 * q^2 - 84 * q^3 + 1557 * q^4 - 1554 * q^5 - 4914 * q^6 + 14055 * q^8 - 26001 * q^9	\( 3 q + 21 q^{2} - 84 q^{3} + 1557 q^{4} - 1554 q^{5} - 4914 q^{6} + 14055 q^{8} - 26001 q^{9} + 97860 q^{10} - 3444 q^{11} + 106386 q^{12} + 19782 q^{13} + 200304 q^{15} + 482961 q^{16} - 1016694 q^{17} - 273267 q^{18} - 222852 q^{19} + 1922088 q^{20} - 2847048 q^{22} + 1885632 q^{23} + 1449630 q^{24} + 3073221 q^{25} + 8785056 q^{26} - 551880 q^{27} + 4081818 q^{29} + 8053200 q^{30} - 2869440 q^{31} + 25221951 q^{32} + 20259792 q^{33} + 3981642 q^{34} - 35396379 q^{36} + 1395618 q^{37} - 43479870 q^{38} - 8990688 q^{39} + 82859280 q^{40} + 14420658 q^{41} - 61631172 q^{43} + 97011984 q^{44} - 29774682 q^{45} + 89747664 q^{46} + 10368960 q^{47} - 16798782 q^{48} + 73325055 q^{50} - 26146728 q^{51} + 80908044 q^{52} + 67502610 q^{53} + 117879300 q^{54} + 105823032 q^{55} + 8471112 q^{57} - 159163830 q^{58} + 42590100 q^{59} - 179551008 q^{60} - 191746842 q^{61} + 46983468 q^{62} + 7852161 q^{64} + 364283220 q^{65} + 8057952 q^{66} - 255175788 q^{67} - 743485806 q^{68} - 257903856 q^{69} + 296514504 q^{71} - 609314265 q^{72} - 344213310 q^{73} - 690696462 q^{74} - 279031116 q^{75} - 728839986 q^{76} + 280132776 q^{78} - 960412656 q^{79} + 1333333344 q^{80} - 35827677 q^{81} - 562675302 q^{82} + 1100517180 q^{83} + 438179412 q^{85} - 880982256 q^{86} + 621821592 q^{87} + 1206124800 q^{88} - 506816478 q^{89} - 2303452620 q^{90} + 691123488 q^{92} + 1693258512 q^{93} - 1388004828 q^{94} - 2203071072 q^{95} - 333385794 q^{96} + 647498250 q^{97} - 1900979172 q^{99}+O(q^{100}) \) 3 * q + 21 * q^2 - 84 * q^3 + 1557 * q^4 - 1554 * q^5 - 4914 * q^6 + 14055 * q^8 - 26001 * q^9 + 97860 * q^10 - 3444 * q^11 + 106386 * q^12 + 19782 * q^13 + 200304 * q^15 + 482961 * q^16 - 1016694 * q^17 - 273267 * q^18 - 222852 * q^19 + 1922088 * q^20 - 2847048 * q^22 + 1885632 * q^23 + 1449630 * q^24 + 3073221 * q^25 + 8785056 * q^26 - 551880 * q^27 + 4081818 * q^29 + 8053200 * q^30 - 2869440 * q^31 + 25221951 * q^32 + 20259792 * q^33 + 3981642 * q^34 - 35396379 * q^36 + 1395618 * q^37 - 43479870 * q^38 - 8990688 * q^39 + 82859280 * q^40 + 14420658 * q^41 - 61631172 * q^43 + 97011984 * q^44 - 29774682 * q^45 + 89747664 * q^46 + 10368960 * q^47 - 16798782 * q^48 + 73325055 * q^50 - 26146728 * q^51 + 80908044 * q^52 + 67502610 * q^53 + 117879300 * q^54 + 105823032 * q^55 + 8471112 * q^57 - 159163830 * q^58 + 42590100 * q^59 - 179551008 * q^60 - 191746842 * q^61 + 46983468 * q^62 + 7852161 * q^64 + 364283220 * q^65 + 8057952 * q^66 - 255175788 * q^67 - 743485806 * q^68 - 257903856 * q^69 + 296514504 * q^71 - 609314265 * q^72 - 344213310 * q^73 - 690696462 * q^74 - 279031116 * q^75 - 728839986 * q^76 + 280132776 * q^78 - 960412656 * q^79 + 1333333344 * q^80 - 35827677 * q^81 - 562675302 * q^82 + 1100517180 * q^83 + 438179412 * q^85 - 880982256 * q^86 + 621821592 * q^87 + 1206124800 * q^88 - 506816478 * q^89 - 2303452620 * q^90 + 691123488 * q^92 + 1693258512 * q^93 - 1388004828 * q^94 - 2203071072 * q^95 - 333385794 * q^96 + 647498250 * q^97 - 1900979172 * q^99

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