LMFDB - Embedded newform 7.10.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,10,Mod(1,7)]

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

lf = mfeigenbasis(mf)

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")

//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);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	7.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:	$3.60525085315$
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			1.3
Root			$4.96128$ 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)

$f(q)$	$=$	$q+41.8019 q^{2} +0.232339 q^{3} +1235.40 q^{4} -1791.89 q^{5} +9.71222 q^{6} +2401.00 q^{7} +30239.6 q^{8} -19682.9 q^{9} +O(q^{10})$	\(q+41.8019 q^{2} +0.232339 q^{3} +1235.40 q^{4} -1791.89 q^{5} +9.71222 q^{6} +2401.00 q^{7} +30239.6 q^{8} -19682.9 q^{9} -74904.4 q^{10} +17401.5 q^{11} +287.032 q^{12} -122541. q^{13} +100366. q^{14} -416.326 q^{15} +631550. q^{16} +331933. q^{17} -822785. q^{18} +761707. q^{19} -2.21370e6 q^{20} +557.846 q^{21} +727418. q^{22} +1.23249e6 q^{23} +7025.85 q^{24} +1.25774e6 q^{25} -5.12246e6 q^{26} -9146.25 q^{27} +2.96620e6 q^{28} +634604. q^{29} -17403.2 q^{30} -5.38069e6 q^{31} +1.09173e7 q^{32} +4043.06 q^{33} +1.38754e7 q^{34} -4.30232e6 q^{35} -2.43164e7 q^{36} -3.03611e6 q^{37} +3.18408e7 q^{38} -28471.1 q^{39} -5.41861e7 q^{40} -7.37009e6 q^{41} +23319.1 q^{42} -2.06990e7 q^{43} +2.14979e7 q^{44} +3.52696e7 q^{45} +5.15203e7 q^{46} +2.03632e7 q^{47} +146734. q^{48} +5.76480e6 q^{49} +5.25760e7 q^{50} +77120.9 q^{51} -1.51388e8 q^{52} -5.97380e7 q^{53} -382331. q^{54} -3.11816e7 q^{55} +7.26054e7 q^{56} +176974. q^{57} +2.65277e7 q^{58} +6.03461e7 q^{59} -514330. q^{60} -9.44357e6 q^{61} -2.24923e8 q^{62} -4.72588e7 q^{63} +1.33012e8 q^{64} +2.19580e8 q^{65} +169008. q^{66} -2.19187e8 q^{67} +4.10071e8 q^{68} +286355. q^{69} -1.79846e8 q^{70} -5.58741e7 q^{71} -5.95205e8 q^{72} +4.54332e8 q^{73} -1.26915e8 q^{74} +292222. q^{75} +9.41015e8 q^{76} +4.17811e7 q^{77} -1.19015e6 q^{78} +4.51057e7 q^{79} -1.13167e9 q^{80} +3.87417e8 q^{81} -3.08084e8 q^{82} -3.34665e8 q^{83} +689165. q^{84} -5.94786e8 q^{85} -8.65259e8 q^{86} +147443. q^{87} +5.26216e8 q^{88} +6.51886e8 q^{89} +1.47434e9 q^{90} -2.94221e8 q^{91} +1.52262e9 q^{92} -1.25014e6 q^{93} +8.51220e8 q^{94} -1.36489e9 q^{95} +2.53652e6 q^{96} -1.42804e9 q^{97} +2.40980e8 q^{98} -3.42514e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 21 q^{2} + 84 q^{3} + 1557 q^{4} + 1554 q^{5} + 4914 q^{6} + 7203 q^{7} + 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 + 7203 * q^7 + 14055 * q^8 - 26001 * q^9	\( 3 q + 21 q^{2} + 84 q^{3} + 1557 q^{4} + 1554 q^{5} + 4914 q^{6} + 7203 q^{7} + 14055 q^{8} - 26001 q^{9} - 97860 q^{10} - 3444 q^{11} - 106386 q^{12} - 19782 q^{13} + 50421 q^{14} + 200304 q^{15} + 482961 q^{16} + 1016694 q^{17} - 273267 q^{18} + 222852 q^{19} - 1922088 q^{20} + 201684 q^{21} - 2847048 q^{22} + 1885632 q^{23} - 1449630 q^{24} + 3073221 q^{25} - 8785056 q^{26} + 551880 q^{27} + 3738357 q^{28} + 4081818 q^{29} + 8053200 q^{30} + 2869440 q^{31} + 25221951 q^{32} - 20259792 q^{33} - 3981642 q^{34} + 3731154 q^{35} - 35396379 q^{36} + 1395618 q^{37} + 43479870 q^{38} - 8990688 q^{39} - 82859280 q^{40} - 14420658 q^{41} + 11798514 q^{42} - 61631172 q^{43} + 97011984 q^{44} + 29774682 q^{45} + 89747664 q^{46} - 10368960 q^{47} + 16798782 q^{48} + 17294403 q^{49} + 73325055 q^{50} - 26146728 q^{51} - 80908044 q^{52} + 67502610 q^{53} - 117879300 q^{54} - 105823032 q^{55} + 33746055 q^{56} + 8471112 q^{57} - 159163830 q^{58} - 42590100 q^{59} - 179551008 q^{60} + 191746842 q^{61} - 46983468 q^{62} - 62428401 q^{63} + 7852161 q^{64} + 364283220 q^{65} - 8057952 q^{66} - 255175788 q^{67} + 743485806 q^{68} + 257903856 q^{69} - 234961860 q^{70} + 296514504 q^{71} - 609314265 q^{72} + 344213310 q^{73} - 690696462 q^{74} + 279031116 q^{75} + 728839986 q^{76} - 8269044 q^{77} + 280132776 q^{78} - 960412656 q^{79} - 1333333344 q^{80} - 35827677 q^{81} + 562675302 q^{82} - 1100517180 q^{83} - 255432786 q^{84} + 438179412 q^{85} - 880982256 q^{86} - 621821592 q^{87} + 1206124800 q^{88} + 506816478 q^{89} + 2303452620 q^{90} - 47496582 q^{91} + 691123488 q^{92} + 1693258512 q^{93} + 1388004828 q^{94} - 2203071072 q^{95} + 333385794 q^{96} - 647498250 q^{97} + 121060821 q^{98} - 1900979172 q^{99}+O(q^{100}) \) 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

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	$-0.499736\pi$
$3$	0.232339	0.00165606	0.000828031		1.00000i	$0.499736\pi$
$4$	1235.40	2.41290
$5$	−1791.89	−1.28217	−0.641086	−	0.767469i	$-0.721516\pi$
$5$	−1791.89	−1.28217	−0.641086	+	0.767469i	$0.721516\pi$
$6$	9.71222	0.00305941
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	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	$-0.702842\pi$
$13$	−122541.	−1.18997	−0.594986	+	0.803736i	$0.702842\pi$
$14$	100366.	0.698253
$15$	−416.326	−0.00212335
$16$	631550.	2.40917
$17$	331933.	0.963895	0.481948	−	0.876200i	$-0.339930\pi$
$17$	331933.	0.963895	0.481948	+	0.876200i	$0.339930\pi$
$18$	−822785.	−1.84740
$19$	761707.	1.34090	0.670450	−	0.741954i	$-0.266101\pi$
$19$	761707.	1.34090	0.670450	+	0.741954i	$0.266101\pi$
$20$	−2.21370e6	−3.09375
$21$	557.846	0.000625933 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
$28$	2.96620e6	0.911989
$29$	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	$-0.675268\pi$
$31$	−5.38069e6	−1.04643	−0.523215	+	0.852201i	$0.675268\pi$
$32$	1.09173e7	1.84052
$33$	4043.06	0.000593468 0
$34$	1.38754e7	1.78070
$35$	−4.30232e6	−0.484615
$36$	−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	$-0.565285\pi$
$41$	−7.37009e6	−0.407329	−0.203665	+	0.979041i	$0.565285\pi$
$42$	23319.1	0.00115635
$43$	−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	$-0.401560\pi$
$47$	2.03632e7	0.608702	0.304351	+	0.952560i	$0.401560\pi$
$48$	146734.	0.00398974
$49$	5.76480e6	0.142857
$50$	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
$56$	7.26054e7	0.986558
$57$	176974.	0.00222061
$58$	2.65277e7	0.307803
$59$	6.03461e7	0.648358	0.324179	−	0.945996i	$-0.394912\pi$
$59$	6.03461e7	0.648358	0.324179	+	0.945996i	$0.394912\pi$
$60$	−514330.	−0.00512343
$61$	−9.44357e6	−0.0873277	−0.0436639	−	0.999046i	$-0.513903\pi$
$61$	−9.44357e6	−0.0873277	−0.0436639	+	0.999046i	$0.513903\pi$
$62$	−2.24923e8	−1.93318
$63$	−4.72588e7	−0.377963
$64$	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
$70$	−1.79846e8	−0.895279
$71$	−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	$-0.114274\pi$
$73$	4.54332e8	1.87250	0.936248	+	0.351340i	$0.114274\pi$
$74$	−1.26915e8	−0.492007
$75$	292222.	0.00106644
$76$	9.41015e8	3.23545
$77$	4.17811e7	0.135448
$78$	−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	$-0.626494\pi$
$83$	−3.34665e8	−0.774031	−0.387016	+	0.922073i	$0.626494\pi$
$84$	689165.	0.00151031
$85$	−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	$-0.314375\pi$
$89$	6.51886e8	1.10133	0.550664	+	0.834727i	$0.314375\pi$
$90$	1.47434e9	2.36868
$91$	−2.94221e8	−0.449767
$92$	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	$-0.805424\pi$
$97$	−1.42804e9	−1.63783	−0.818914	+	0.573916i	$0.805424\pi$
$98$	2.40980e8	0.263915
$99$	−3.42514e8	−0.358360
$100$	1.55382e9	1.55382
$101$	8.91532e8	0.852493	0.426247	−	0.904607i	$-0.359836\pi$
$101$	8.91532e8	0.852493	0.426247	+	0.904607i	$0.359836\pi$
$102$	3.22380e6	0.00294895
$103$	−7.12000e8	−0.623322	−0.311661	−	0.950193i	$-0.600885\pi$
$103$	−7.12000e8	−0.623322	−0.311661	+	0.950193i	$0.600885\pi$
$104$	−3.70560e9	−3.10605
$105$	−999598.	−0.000802553 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
$112$	1.51635e9	0.910581
$113$	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
$119$	7.96970e8	0.364318
$120$	−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
$126$	−1.97551e9	−0.698251
$127$	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	$-0.571056\pi$
$131$	−1.49241e9	−0.442760	−0.221380	+	0.975188i	$0.571056\pi$
$132$	4.99480e6	0.00143198
$133$	1.82886e9	0.506813
$134$	−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	$-0.612219\pi$
$139$	−3.03934e9	−0.690577	−0.345289	+	0.938497i	$0.612219\pi$
$140$	−5.31510e9	−1.16933
$141$	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
$147$	1.33939e6	0.000236580 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
$154$	1.74653e9	0.250226
$155$	9.64159e9	1.34170
$156$	−3.51733e7	−0.00475502
$157$	−1.19687e10	−1.57216	−0.786082	−	0.618122i	$-0.787894\pi$
$157$	−1.19687e10	−1.57216	−0.786082	+	0.618122i	$0.787894\pi$
$158$	1.88551e9	0.240697
$159$	−1.38795e7	−0.00172221
$160$	−1.95626e10	−2.35986
$161$	2.95920e9	0.347102
$162$	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	$-0.443327\pi$
$167$	3.56028e9	0.354210	0.177105	+	0.984192i	$0.443327\pi$
$168$	1.68691e7	0.00163380
$169$	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	$-0.464253\pi$
$173$	2.64068e9	0.224134	0.112067	+	0.993701i	$0.464253\pi$
$174$	6.16342e6	0.000509741 0
$175$	3.01983e9	0.243395
$176$	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	$-0.771030\pi$
$181$	−2.17242e10	−1.50449	−0.752247	+	0.658881i	$0.771030\pi$
$182$	−1.22990e10	−0.830901
$183$	−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
$189$	−2.19601e7	−0.00125186
$190$	−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
$196$	7.12185e9	0.344699
$197$	−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	$-0.246492\pi$
$199$	3.16291e10	1.42971	0.714856	+	0.699272i	$0.246492\pi$
$200$	3.80336e10	1.68086
$201$	−5.09256e7	−0.00220066
$202$	3.72678e10	1.57490
$203$	1.52368e9	0.0629742
$204$	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
$210$	−4.17851e7	−0.00148264
$211$	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
$217$	−1.29190e10	−0.395513
$218$	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	$-0.545269\pi$
$223$	−1.04686e10	−0.283476	−0.141738	+	0.989904i	$0.545269\pi$
$224$	2.62125e10	0.695652
$225$	−2.47560e10	−0.643961
$226$	1.00150e11	2.55366
$227$	1.95043e10	0.487543	0.243772	−	0.969833i	$-0.421615\pi$
$227$	1.95043e10	0.487543	0.243772	+	0.969833i	$0.421615\pi$
$228$	2.18634e8	0.00535811
$229$	−5.96135e10	−1.43247	−0.716234	−	0.697860i	$-0.754136\pi$
$229$	−5.96135e10	−1.43247	−0.716234	+	0.697860i	$0.754136\pi$
$230$	−9.23187e10	−2.17528
$231$	9.70738e6	0.000224310 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
$238$	3.33149e10	0.673042
$239$	−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	$-0.360134\pi$
$241$	4.45555e10	0.850795	0.425397	+	0.905007i	$0.360134\pi$
$242$	−8.59086e10	−1.61015
$243$	2.70038e8	0.00496817
$244$	−1.16666e10	−0.210713
$245$	−1.03299e10	−0.183167
$246$	−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	$-0.774509\pi$
$251$	−9.55068e10	−1.51881	−0.759404	+	0.650620i	$0.774509\pi$
$252$	−5.83836e10	−0.911987
$253$	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	$-0.273680\pi$
$257$	9.12794e10	1.30519	0.652595	+	0.757707i	$0.273680\pi$
$258$	−2.01033e8	−0.00282475
$259$	−7.28970e9	−0.100661
$260$	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
$266$	7.64498e10	0.936287
$267$	1.51458e8	0.00182387
$268$	−2.70784e11	−3.20639
$269$	2.39622e10	0.279024	0.139512	−	0.990220i	$-0.455447\pi$
$269$	2.39622e10	0.279024	0.139512	+	0.990220i	$0.455447\pi$
$270$	6.85094e8	0.00784537
$271$	−5.51248e10	−0.620848	−0.310424	−	0.950598i	$-0.600471\pi$
$271$	−5.51248e10	−0.620848	−0.310424	+	0.950598i	$0.600471\pi$
$272$	2.09632e11	2.32219
$273$	−6.83591e7	−0.000744842 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
$280$	−1.30101e11	−1.26494
$281$	−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	$-0.479988\pi$
$283$	1.35590e10	0.125657	0.0628287	+	0.998024i	$0.479988\pi$
$284$	−6.90270e10	−0.629632
$285$	−3.17118e8	−0.00284721
$286$	−8.91387e10	−0.787805
$287$	−1.76956e10	−0.153956
$288$	−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	$-0.431098\pi$
$293$	5.41900e10	0.429551	0.214776	+	0.976663i	$0.431098\pi$
$294$	5.59890e7	0.000437059 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
$301$	−4.96983e10	−0.348974
$302$	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	$-0.424387\pi$
$307$	7.32498e10	0.470634	0.235317	+	0.971919i	$0.424387\pi$
$308$	5.16165e10	0.326821
$309$	−1.65425e8	−0.00103226
$310$	4.03037e11	2.47866
$311$	−2.44502e11	−1.48204	−0.741021	−	0.671482i	$-0.765658\pi$
$311$	−2.44502e11	−1.48204	−0.741021	+	0.671482i	$0.765658\pi$
$312$	−8.60956e8	−0.00514381
$313$	−4.39895e10	−0.259060	−0.129530	−	0.991576i	$-0.541347\pi$
$313$	−4.39895e10	−0.259060	−0.129530	+	0.991576i	$0.541347\pi$
$314$	−5.00314e11	−2.90442
$315$	8.46824e10	0.484614
$316$	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
$322$	1.23700e11	0.641238
$323$	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
$329$	4.88920e10	0.230068
$330$	−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
$336$	3.52308e8	0.00150798
$337$	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
$343$	1.38413e10	0.0539949
$344$	−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	$-0.569638\pi$
$349$	−1.20301e11	−0.434065	−0.217033	+	0.976164i	$0.569638\pi$
$350$	1.26235e11	0.449649
$351$	1.12079e9	0.00394133
$352$	1.89978e11	0.659571
$353$	2.43060e11	0.833159	0.416580	−	0.909099i	$-0.363229\pi$
$353$	2.43060e11	0.833159	0.416580	+	0.909099i	$0.363229\pi$
$354$	5.86095e8	0.00198360
$355$	1.00120e11	0.334575
$356$	8.05341e11	2.65739
$357$	1.85167e8	0.000603333 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
$364$	−3.63482e11	−1.08524
$365$	−8.14113e11	−2.40086
$366$	−9.17181e7	−0.000267172 0
$367$	−2.41000e11	−0.693458	−0.346729	−	0.937965i	$-0.612708\pi$
$367$	−2.41000e11	−0.693458	−0.346729	+	0.937965i	$0.612708\pi$
$368$	7.78376e11	2.21246
$369$	1.45065e11	0.407328
$370$	2.27418e11	0.630837
$371$	−1.43431e11	−0.393061
$372$	−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
$378$	−9.17976e8	−0.00231270
$379$	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	$-0.539219\pi$
$383$	−1.03509e11	−0.245800	−0.122900	+	0.992419i	$0.539219\pi$
$384$	−6.85951e6	−1.60991e−5 0
$385$	−7.48671e10	−0.173667
$386$	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
$392$	1.74326e11	0.372884
$393$	−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	$-0.521063\pi$
$397$	−6.54542e10	−0.132245	−0.0661226	+	0.997812i	$0.521063\pi$
$398$	1.32216e12	2.64125
$399$	4.24915e8	0.000839313 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
$406$	6.36930e10	0.116339
$407$	−5.28330e10	−0.0954400
$408$	2.33211e9	0.00416657
$409$	1.06163e12	1.87594	0.937970	−	0.346716i	$-0.112703\pi$
$409$	1.06163e12	1.87594	0.937970	+	0.346716i	$0.112703\pi$
$410$	5.52052e11	0.964835
$411$	−7.46081e8	−0.00128973
$412$	−8.79607e11	−1.50401
$413$	1.44891e11	0.245056
$414$	−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	$-0.894665\pi$
$419$	−1.19335e12	−1.89149	−0.945744	+	0.324912i	$0.894665\pi$
$420$	−1.23491e9	−0.00193648
$421$	−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
$427$	−2.26740e10	−0.0330068
$428$	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	$-0.510311\pi$
$433$	−4.73819e10	−0.0647764	−0.0323882	+	0.999475i	$0.510311\pi$
$434$	−5.40041e11	−0.730672
$435$	−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	$-0.370865\pi$
$439$	6.14236e11	0.789305	0.394652	+	0.918830i	$0.370865\pi$
$440$	−9.42921e11	−1.19933
$441$	−1.13468e11	−0.142857
$442$	−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
$448$	3.19361e11	0.374568
$449$	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
$455$	5.27212e11	0.576679
$456$	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	$-0.601322\pi$
$461$	−6.06986e11	−0.625928	−0.312964	+	0.949765i	$0.601322\pi$
$462$	4.05787e8	0.000414390 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	$-0.679323\pi$
$467$	−1.09779e12	−1.06806	−0.534029	+	0.845466i	$0.679323\pi$
$468$	2.97976e12	2.87127
$469$	−5.26267e11	−0.502260
$470$	−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
$476$	9.84579e11	0.879062
$477$	1.17582e12	1.03994
$478$	−3.04466e12	−2.66755
$479$	−3.12229e11	−0.270996	−0.135498	−	0.990778i	$-0.543263\pi$
$479$	−3.12229e11	−0.270996	−0.135498	+	0.990778i	$0.543263\pi$
$480$	−4.54516e9	−0.00390808
$481$	3.72048e11	0.316918
$482$	1.86251e12	1.57176
$483$	6.87537e8	0.000574823 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
$490$	−4.31809e11	−0.338384
$491$	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
$497$	−1.34154e11	−0.0986277
$498$	−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	$-0.686855\pi$
$503$	−1.59040e12	−1.10777	−0.553885	+	0.832593i	$0.686855\pi$
$504$	−1.42909e12	−0.986556
$505$	−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	$-0.220828\pi$
$509$	2.32864e12	1.53771	0.768853	+	0.639426i	$0.220828\pi$
$510$	−5.77670e9	−0.00378106
$511$	1.09085e12	0.707737
$512$	−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
$518$	−3.04724e11	−0.185961
$519$	6.13532e8	0.000371180 0
$520$	6.64003e12	3.98249
$521$	−1.48366e12	−0.882197	−0.441099	−	0.897459i	$-0.645411\pi$
$521$	−1.48366e12	−0.882197	−0.441099	+	0.897459i	$0.645411\pi$
$522$	−5.22143e11	−0.307802
$523$	−1.95584e12	−1.14308	−0.571540	−	0.820574i	$-0.693654\pi$
$523$	−1.95584e12	−1.14308	−0.571540	+	0.820574i	$0.693654\pi$
$524$	−1.84373e12	−1.06833
$525$	7.01625e8	0.000403077 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
$532$	2.25938e12	1.22289
$533$	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
$539$	1.00316e11	0.0511944
$540$	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
$546$	−2.85754e9	−0.00137602
$547$	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
$553$	1.08299e11	0.0492448
$554$	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
$560$	−2.71713e12	−1.16752
$561$	1.34202e9	0.000572041 0
$562$	−6.79991e11	−0.287535
$563$	−2.17456e12	−0.912185	−0.456092	−	0.889932i	$-0.650751\pi$
$563$	−2.17456e12	−0.912185	−0.456092	+	0.889932i	$0.650751\pi$
$564$	5.84489e9	0.00243232
$565$	−4.29304e12	−1.77234
$566$	5.66792e11	0.232140
$567$	9.30189e11	0.377961
$568$	−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
$574$	−7.39710e11	−0.284419
$575$	1.55015e12	0.591381
$576$	−2.61806e12	−0.991011
$577$	3.94380e12	1.48123	0.740617	−	0.671927i	$-0.234533\pi$
$577$	3.94380e12	1.48123	0.740617	+	0.671927i	$0.234533\pi$
$578$	−3.51495e11	−0.130992
$579$	1.77986e9	0.000658162 0
$580$	−1.40483e12	−0.515462
$581$	−8.03530e11	−0.292556
$582$	−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	$-0.278905\pi$
$587$	3.68239e12	1.28014	0.640071	+	0.768315i	$0.278905\pi$
$588$	1.65468e9	0.000570844 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	$-0.562296\pi$
$593$	−1.17114e12	−0.388921	−0.194460	+	0.980910i	$0.562296\pi$
$594$	−6.65315e9	−0.00219274
$595$	−1.42808e12	−0.467118
$596$	−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	$-0.379152\pi$
$601$	2.37066e12	0.741198	0.370599	+	0.928793i	$0.379152\pi$
$602$	−2.07749e12	−0.644695
$603$	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	$-0.271450\pi$
$607$	4.40080e12	1.31578	0.657889	+	0.753115i	$0.271450\pi$
$608$	8.31580e12	2.46796
$609$	3.54011e8	0.000104289 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
$616$	1.26345e12	0.353544
$617$	−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	$-0.505075\pi$
$619$	−1.16476e11	−0.0318880	−0.0159440	+	0.999873i	$0.505075\pi$
$620$	1.19113e13	3.23739
$621$	−1.12726e10	−0.00304167
$622$	−1.02207e13	−2.73793
$623$	1.56518e12	0.416263
$624$	−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
$630$	3.53989e12	0.895277
$631$	−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
$637$	−7.06425e11	−0.169996
$638$	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	$-0.291559\pi$
$643$	5.27980e12	1.21806	0.609029	+	0.793148i	$0.291559\pi$
$644$	3.65580e12	0.837522
$645$	8.61753e9	0.00196049
$646$	1.05690e13	2.38775
$647$	−2.62000e12	−0.587804	−0.293902	−	0.955836i	$-0.594954\pi$
$647$	−2.62000e12	−0.587804	−0.293902	+	0.955836i	$0.594954\pi$
$648$	1.17154e13	2.61017
$649$	1.05011e12	0.232346
$650$	−6.44272e12	−1.41566
$651$	−3.00160e9	−0.000654995 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
$658$	2.04378e12	0.425028
$659$	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	$-0.184008\pi$
$661$	8.22108e12	1.67503	0.837514	+	0.546416i	$0.184008\pi$
$662$	−1.53390e13	−3.10411
$663$	−9.45049e9	−0.00189952
$664$	−1.01201e13	−2.02037
$665$	−3.27711e12	−0.649821
$666$	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
$672$	6.09018e9	0.00115204
$673$	−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	$-0.206386\pi$
$677$	8.71309e12	1.59413	0.797064	+	0.603895i	$0.206386\pi$
$678$	2.32687e10	0.00422901
$679$	−3.42873e12	−0.619041
$680$	−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
$686$	5.78593e11	0.0997504
$687$	−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	$-0.675216\pi$
$691$	−6.26971e12	−1.04616	−0.523078	+	0.852285i	$0.675216\pi$
$692$	3.26230e12	0.540812
$693$	−8.22375e11	−0.135447
$694$	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
$700$	3.73071e12	0.587287
$701$	−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
$707$	2.14057e12	0.322212
$708$	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
$714$	7.74035e9	0.00111460
$715$	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	$-0.823381\pi$
$719$	−1.21819e13	−1.69994	−0.849971	+	0.526829i	$0.823381\pi$
$720$	2.22745e13	3.08896
$721$	−1.70951e12	−0.235594
$722$	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	$-0.183506\pi$
$727$	1.26291e13	1.67675	0.838376	+	0.545093i	$0.183506\pi$
$728$	−8.89715e12	−1.17398
$729$	−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	$-0.300553\pi$
$733$	9.16594e12	1.17276	0.586380	+	0.810036i	$0.300553\pi$
$734$	−1.00743e13	−1.28110
$735$	−2.40003e9	−0.000303336 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
$742$	−5.99569e12	−0.726142
$743$	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
$749$	5.96884e12	0.692982
$750$	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
$756$	−2.71296e10	−0.00302062
$757$	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	$-0.541757\pi$
$761$	−2.42043e12	−0.261614	−0.130807	+	0.991408i	$0.541757\pi$
$762$	1.82843e10	0.00196464
$763$	9.20676e11	0.0983437
$764$	−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	$-0.370418\pi$
$769$	7.67945e12	0.791885	0.395942	+	0.918275i	$0.370418\pi$
$770$	−3.12959e12	−0.320833
$771$	2.12078e10	0.00216148
$772$	9.46396e12	0.958948
$773$	1.04693e13	1.05466	0.527328	−	0.849662i	$-0.323194\pi$
$773$	1.04693e13	1.05466	0.527328	+	0.849662i	$0.323194\pi$
$774$	1.70308e13	1.70570
$775$	−6.76751e12	−0.673862
$776$	−4.31835e13	−4.27504
$777$	−1.69368e9	−0.000166701 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
$784$	3.64076e12	0.344167
$785$	2.14465e13	2.01578
$786$	−1.44947e10	−0.00135459
$787$	−1.26490e13	−1.17535	−0.587677	−	0.809095i	$-0.699958\pi$
$787$	−1.26490e13	−1.17535	−0.587677	+	0.809095i	$0.699958\pi$
$788$	−5.26479e12	−0.486422
$789$	3.50777e10	0.00322243
$790$	−3.37862e12	−0.308615
$791$	5.75236e12	0.522459
$792$	−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	$-0.508417\pi$
$797$	−6.02337e11	−0.0528782	−0.0264391	+	0.999650i	$0.508417\pi$
$798$	1.77623e10	0.00155055
$799$	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
$805$	−5.30256e12	−0.445045
$806$	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	$-0.662152\pi$
$811$	−1.20157e13	−0.975335	−0.487668	+	0.873029i	$0.662152\pi$
$812$	1.88236e12	0.151950
$813$	−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
$819$	5.79114e12	0.449766
$820$	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
$826$	6.05672e12	0.452718
$827$	−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	$-0.660454\pi$
$829$	−1.31364e13	−0.966007	−0.483004	+	0.875618i	$0.660454\pi$
$830$	2.50679e13	1.83344
$831$	5.10290e9	0.000371204 0
$832$	−1.62994e13	−1.17928
$833$	1.91353e12	0.137699
$834$	−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	$-0.558256\pi$
$839$	−5.22420e12	−0.363991	−0.181996	+	0.983299i	$0.558256\pi$
$840$	−3.02275e10	−0.00209481
$841$	−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
$847$	−4.93438e12	−0.329425
$848$	−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	$-0.558493\pi$
$853$	−5.65076e12	−0.365457	−0.182728	+	0.983163i	$0.558493\pi$
$854$	−9.47818e11	−0.0609768
$855$	2.68651e13	1.71926
$856$	7.51752e13	4.78567
$857$	1.42516e12	0.0902503	0.0451251	−	0.998981i	$-0.485631\pi$
$857$	1.42516e12	0.0902503	0.0451251	+	0.998981i	$0.485631\pi$
$858$	−2.07104e10	−0.00130465
$859$	2.77961e13	1.74186	0.870932	−	0.491404i	$-0.163516\pi$
$859$	2.77961e13	1.74186	0.870932	+	0.491404i	$0.163516\pi$
$860$	4.58215e13	2.85645
$861$	−4.11137e9	−0.000254960 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
$868$	−1.59602e13	−0.954333
$869$	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
$875$	2.99177e12	0.172541
$876$	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	$-0.541124\pi$
$881$	−4.60741e12	−0.257671	−0.128836	+	0.991666i	$0.541124\pi$
$882$	−4.74319e12	−0.263914
$883$	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	$-0.531884\pi$
$887$	−3.68711e12	−0.200000	−0.0999999	+	0.994987i	$0.531884\pi$
$888$	−2.13313e10	−0.00115122
$889$	4.52015e12	0.242714
$890$	−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
$896$	−7.08864e10	−0.00367432
$897$	−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
$903$	−1.15469e10	−0.000577922 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
$910$	2.20385e13	1.06536
$911$	−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
$917$	−3.58329e12	−0.167348
$918$	−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
$924$	1.19925e10	0.000541236 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	$-0.528089\pi$
$929$	−4.00147e12	−0.176258	−0.0881290	+	0.996109i	$0.528089\pi$
$930$	9.36413e10	0.00410482
$931$	4.39109e12	0.191557
$932$	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	$-0.500254\pi$
$937$	−3.76138e10	−0.00159411	−0.000797056		1.00000i	$0.500254\pi$
$938$	−2.19990e13	−0.927876
$939$	−1.02205e10	−0.000429019 0
$940$	−4.50780e13	−1.88317
$941$	−2.21494e12	−0.0920894	−0.0460447	−	0.998939i	$-0.514662\pi$
$941$	−2.21494e12	−0.0920894	−0.0460447	+	0.998939i	$0.514662\pi$
$942$	−1.16242e11	−0.00480990
$943$	−9.08353e12	−0.374069
$944$	3.81116e13	1.56201
$945$	3.93501e10	0.00160510
$946$	−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
$952$	2.41001e13	0.950939
$953$	−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
$959$	−7.71003e12	−0.294356
$960$	−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
$966$	2.87404e10	0.00106193
$967$	−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	$-0.442504\pi$
$971$	9.95259e12	0.359294	0.179647	+	0.983731i	$0.442504\pi$
$972$	3.33605e11	0.0119877
$973$	−7.29745e12	−0.261014
$974$	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
$980$	−1.27616e13	−0.441964
$981$	−7.54753e12	−0.260192
$982$	8.97498e13	3.07987
$983$	5.47141e13	1.86899	0.934497	−	0.355970i	$-0.115849\pi$
$983$	5.47141e13	1.86899	0.934497	+	0.355970i	$0.115849\pi$
$984$	−5.17811e10	−0.00176073
$985$	7.63631e12	0.258476
$986$	8.80540e12	0.296690
$987$	1.13595e10	0.000381007 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
$994$	−5.60789e12	−0.182205
$995$	−5.66759e13	−1.83314
$996$	−9.60596e10	−0.00309296
$997$	2.77758e13	0.890304	0.445152	−	0.895455i	$-0.353150\pi$
$997$	2.77758e13	0.890304	0.445152	+	0.895455i	$0.353150\pi$
$998$	−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	7.10.a.b.1.3	✓	3
3.2	odd	2		63.10.a.e.1.1		3
4.3	odd	2		112.10.a.h.1.2		3
5.2	odd	4		175.10.b.d.99.6		6
5.3	odd	4		175.10.b.d.99.1		6
5.4	even	2		175.10.a.d.1.1		3
7.2	even	3		49.10.c.d.18.1		6
7.3	odd	6		49.10.c.e.30.1		6
7.4	even	3		49.10.c.d.30.1		6
7.5	odd	6		49.10.c.e.18.1		6
7.6	odd	2		49.10.a.c.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.a.b.1.3	✓	3	1.1	even	1	trivial
49.10.a.c.1.3		3	7.6	odd	2
49.10.c.d.18.1		6	7.2	even	3
49.10.c.d.30.1		6	7.4	even	3
49.10.c.e.18.1		6	7.5	odd	6
49.10.c.e.30.1		6	7.3	odd	6
63.10.a.e.1.1		3	3.2	odd	2
112.10.a.h.1.2		3	4.3	odd	2
175.10.a.d.1.1		3	5.4	even	2
175.10.b.d.99.1		6	5.3	odd	4
175.10.b.d.99.6		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+41.8019 q^{2} +0.232339 q^{3} +1235.40 q^{4} -1791.89 q^{5} +9.71222 q^{6} +2401.00 q^{7} +30239.6 q^{8} -19682.9 q^{9} +O(q^{10})\)	\(q+41.8019 q^{2} +0.232339 q^{3} +1235.40 q^{4} -1791.89 q^{5} +9.71222 q^{6} +2401.00 q^{7} +30239.6 q^{8} -19682.9 q^{9} -74904.4 q^{10} +17401.5 q^{11} +287.032 q^{12} -122541. q^{13} +100366. q^{14} -416.326 q^{15} +631550. q^{16} +331933. q^{17} -822785. q^{18} +761707. q^{19} -2.21370e6 q^{20} +557.846 q^{21} +727418. q^{22} +1.23249e6 q^{23} +7025.85 q^{24} +1.25774e6 q^{25} -5.12246e6 q^{26} -9146.25 q^{27} +2.96620e6 q^{28} +634604. q^{29} -17403.2 q^{30} -5.38069e6 q^{31} +1.09173e7 q^{32} +4043.06 q^{33} +1.38754e7 q^{34} -4.30232e6 q^{35} -2.43164e7 q^{36} -3.03611e6 q^{37} +3.18408e7 q^{38} -28471.1 q^{39} -5.41861e7 q^{40} -7.37009e6 q^{41} +23319.1 q^{42} -2.06990e7 q^{43} +2.14979e7 q^{44} +3.52696e7 q^{45} +5.15203e7 q^{46} +2.03632e7 q^{47} +146734. q^{48} +5.76480e6 q^{49} +5.25760e7 q^{50} +77120.9 q^{51} -1.51388e8 q^{52} -5.97380e7 q^{53} -382331. q^{54} -3.11816e7 q^{55} +7.26054e7 q^{56} +176974. q^{57} +2.65277e7 q^{58} +6.03461e7 q^{59} -514330. q^{60} -9.44357e6 q^{61} -2.24923e8 q^{62} -4.72588e7 q^{63} +1.33012e8 q^{64} +2.19580e8 q^{65} +169008. q^{66} -2.19187e8 q^{67} +4.10071e8 q^{68} +286355. q^{69} -1.79846e8 q^{70} -5.58741e7 q^{71} -5.95205e8 q^{72} +4.54332e8 q^{73} -1.26915e8 q^{74} +292222. q^{75} +9.41015e8 q^{76} +4.17811e7 q^{77} -1.19015e6 q^{78} +4.51057e7 q^{79} -1.13167e9 q^{80} +3.87417e8 q^{81} -3.08084e8 q^{82} -3.34665e8 q^{83} +689165. q^{84} -5.94786e8 q^{85} -8.65259e8 q^{86} +147443. q^{87} +5.26216e8 q^{88} +6.51886e8 q^{89} +1.47434e9 q^{90} -2.94221e8 q^{91} +1.52262e9 q^{92} -1.25014e6 q^{93} +8.51220e8 q^{94} -1.36489e9 q^{95} +2.53652e6 q^{96} -1.42804e9 q^{97} +2.40980e8 q^{98} -3.42514e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 21 q^{2} + 84 q^{3} + 1557 q^{4} + 1554 q^{5} + 4914 q^{6} + 7203 q^{7} + 14055 q^{8} - 26001 q^{9}+O(q^{10}) \) 3 * q + 21 * q^2 + 84 * q^3 + 1557 * q^4 + 1554 * q^5 + 4914 * q^6 + 7203 * q^7 + 14055 * q^8 - 26001 * q^9	\( 3 q + 21 q^{2} + 84 q^{3} + 1557 q^{4} + 1554 q^{5} + 4914 q^{6} + 7203 q^{7} + 14055 q^{8} - 26001 q^{9} - 97860 q^{10} - 3444 q^{11} - 106386 q^{12} - 19782 q^{13} + 50421 q^{14} + 200304 q^{15} + 482961 q^{16} + 1016694 q^{17} - 273267 q^{18} + 222852 q^{19} - 1922088 q^{20} + 201684 q^{21} - 2847048 q^{22} + 1885632 q^{23} - 1449630 q^{24} + 3073221 q^{25} - 8785056 q^{26} + 551880 q^{27} + 3738357 q^{28} + 4081818 q^{29} + 8053200 q^{30} + 2869440 q^{31} + 25221951 q^{32} - 20259792 q^{33} - 3981642 q^{34} + 3731154 q^{35} - 35396379 q^{36} + 1395618 q^{37} + 43479870 q^{38} - 8990688 q^{39} - 82859280 q^{40} - 14420658 q^{41} + 11798514 q^{42} - 61631172 q^{43} + 97011984 q^{44} + 29774682 q^{45} + 89747664 q^{46} - 10368960 q^{47} + 16798782 q^{48} + 17294403 q^{49} + 73325055 q^{50} - 26146728 q^{51} - 80908044 q^{52} + 67502610 q^{53} - 117879300 q^{54} - 105823032 q^{55} + 33746055 q^{56} + 8471112 q^{57} - 159163830 q^{58} - 42590100 q^{59} - 179551008 q^{60} + 191746842 q^{61} - 46983468 q^{62} - 62428401 q^{63} + 7852161 q^{64} + 364283220 q^{65} - 8057952 q^{66} - 255175788 q^{67} + 743485806 q^{68} + 257903856 q^{69} - 234961860 q^{70} + 296514504 q^{71} - 609314265 q^{72} + 344213310 q^{73} - 690696462 q^{74} + 279031116 q^{75} + 728839986 q^{76} - 8269044 q^{77} + 280132776 q^{78} - 960412656 q^{79} - 1333333344 q^{80} - 35827677 q^{81} + 562675302 q^{82} - 1100517180 q^{83} - 255432786 q^{84} + 438179412 q^{85} - 880982256 q^{86} - 621821592 q^{87} + 1206124800 q^{88} + 506816478 q^{89} + 2303452620 q^{90} - 47496582 q^{91} + 691123488 q^{92} + 1693258512 q^{93} + 1388004828 q^{94} - 2203071072 q^{95} + 333385794 q^{96} - 647498250 q^{97} + 121060821 q^{98} - 1900979172 q^{99}+O(q^{100}) \) 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

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