LMFDB - Embedded newform 242.10.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [242,10,Mod(1,242)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(242, 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("242.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 242 = 2 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	242.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:	$124.638672352$
Analytic rank:	$1$
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} - 1503x + 9963 $ x^3 - x^2 - 1503*x + 9963
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 11 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-41.2692$ of defining polynomial
Character	$\chi$	$=$	242.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+16.0000 q^{2} -24.5710 q^{3} +256.000 q^{4} +1002.27 q^{5} -393.136 q^{6} -4370.69 q^{7} +4096.00 q^{8} -19079.3 q^{9} +O(q^{10})$	\(q+16.0000 q^{2} -24.5710 q^{3} +256.000 q^{4} +1002.27 q^{5} -393.136 q^{6} -4370.69 q^{7} +4096.00 q^{8} -19079.3 q^{9} +16036.4 q^{10} -6290.18 q^{12} +13481.5 q^{13} -69931.0 q^{14} -24626.9 q^{15} +65536.0 q^{16} +177624. q^{17} -305268. q^{18} +656570. q^{19} +256582. q^{20} +107392. q^{21} +502956. q^{23} -100643. q^{24} -948573. q^{25} +215705. q^{26} +952429. q^{27} -1.11890e6 q^{28} -4.33373e6 q^{29} -394030. q^{30} -2.80982e6 q^{31} +1.04858e6 q^{32} +2.84198e6 q^{34} -4.38062e6 q^{35} -4.88429e6 q^{36} +1.11774e7 q^{37} +1.05051e7 q^{38} -331255. q^{39} +4.10531e6 q^{40} -1.10232e7 q^{41} +1.71828e6 q^{42} -3.94654e7 q^{43} -1.91226e7 q^{45} +8.04730e6 q^{46} -8.77635e6 q^{47} -1.61029e6 q^{48} -2.12507e7 q^{49} -1.51772e7 q^{50} -4.36441e6 q^{51} +3.45127e6 q^{52} +4.72696e6 q^{53} +1.52389e7 q^{54} -1.79023e7 q^{56} -1.61326e7 q^{57} -6.93397e7 q^{58} -8.93693e6 q^{59} -6.30448e6 q^{60} +4771.56 q^{61} -4.49570e7 q^{62} +8.33895e7 q^{63} +1.67772e7 q^{64} +1.35122e7 q^{65} -1.72224e8 q^{67} +4.54718e7 q^{68} -1.23581e7 q^{69} -7.00900e7 q^{70} +5.15281e7 q^{71} -7.81487e7 q^{72} +3.15769e8 q^{73} +1.78839e8 q^{74} +2.33074e7 q^{75} +1.68082e8 q^{76} -5.30008e6 q^{78} -2.77760e8 q^{79} +6.56850e7 q^{80} +3.52135e8 q^{81} -1.76372e8 q^{82} -4.29761e8 q^{83} +2.74924e7 q^{84} +1.78028e8 q^{85} -6.31446e8 q^{86} +1.06484e8 q^{87} -9.67713e7 q^{89} -3.05962e8 q^{90} -5.89236e7 q^{91} +1.28757e8 q^{92} +6.90400e7 q^{93} -1.40422e8 q^{94} +6.58062e8 q^{95} -2.57646e7 q^{96} +6.20651e7 q^{97} -3.40011e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 48 q^{2} - 78 q^{3} + 768 q^{4} - 2489 q^{5} - 1248 q^{6} - 7762 q^{7} + 12288 q^{8} + 14195 q^{9}+O(q^{10}) $ 3 * q + 48 * q^2 - 78 * q^3 + 768 * q^4 - 2489 * q^5 - 1248 * q^6 - 7762 * q^7 + 12288 * q^8 + 14195 * q^9	\( 3 q + 48 q^{2} - 78 q^{3} + 768 q^{4} - 2489 q^{5} - 1248 q^{6} - 7762 q^{7} + 12288 q^{8} + 14195 q^{9} - 39824 q^{10} - 19968 q^{12} + 74607 q^{13} - 124192 q^{14} + 377754 q^{15} + 196608 q^{16} - 636327 q^{17} + 227120 q^{18} - 560130 q^{19} - 637184 q^{20} + 2310116 q^{21} + 123322 q^{23} - 319488 q^{24} + 2581436 q^{25} + 1193712 q^{26} - 2689668 q^{27} - 1987072 q^{28} - 3359849 q^{29} + 6044064 q^{30} + 3513870 q^{31} + 3145728 q^{32} - 10181232 q^{34} + 10707462 q^{35} + 3633920 q^{36} + 22954923 q^{37} - 8962080 q^{38} - 23544854 q^{39} - 10194944 q^{40} + 10760009 q^{41} + 36961856 q^{42} + 7649128 q^{43} - 93723017 q^{45} + 1973152 q^{46} - 27844070 q^{47} - 5111808 q^{48} - 33563193 q^{49} + 41302976 q^{50} + 59791958 q^{51} + 19099392 q^{52} - 954201 q^{53} - 43034688 q^{54} - 31793152 q^{56} + 5859812 q^{57} - 53757584 q^{58} + 50239440 q^{59} + 96705024 q^{60} - 306912734 q^{61} + 56221920 q^{62} - 85880946 q^{63} + 50331648 q^{64} - 186865645 q^{65} - 112012374 q^{67} - 162899712 q^{68} - 551251156 q^{69} + 171319392 q^{70} + 72167396 q^{71} + 58142720 q^{72} - 204193414 q^{73} + 367278768 q^{74} - 1150193976 q^{75} - 143393280 q^{76} - 376717664 q^{78} - 717133858 q^{79} - 163119104 q^{80} - 320766577 q^{81} + 172160144 q^{82} - 214696882 q^{83} + 591389696 q^{84} + 1782988293 q^{85} + 122386048 q^{86} + 56353690 q^{87} + 201942773 q^{89} - 1499568272 q^{90} - 802638922 q^{91} + 31570432 q^{92} - 58664924 q^{93} - 445505120 q^{94} + 2736352118 q^{95} - 81788928 q^{96} - 31860047 q^{97} - 537011088 q^{98}+O(q^{100}) \) 3 * q + 48 * q^2 - 78 * q^3 + 768 * q^4 - 2489 * q^5 - 1248 * q^6 - 7762 * q^7 + 12288 * q^8 + 14195 * q^9 - 39824 * q^10 - 19968 * q^12 + 74607 * q^13 - 124192 * q^14 + 377754 * q^15 + 196608 * q^16 - 636327 * q^17 + 227120 * q^18 - 560130 * q^19 - 637184 * q^20 + 2310116 * q^21 + 123322 * q^23 - 319488 * q^24 + 2581436 * q^25 + 1193712 * q^26 - 2689668 * q^27 - 1987072 * q^28 - 3359849 * q^29 + 6044064 * q^30 + 3513870 * q^31 + 3145728 * q^32 - 10181232 * q^34 + 10707462 * q^35 + 3633920 * q^36 + 22954923 * q^37 - 8962080 * q^38 - 23544854 * q^39 - 10194944 * q^40 + 10760009 * q^41 + 36961856 * q^42 + 7649128 * q^43 - 93723017 * q^45 + 1973152 * q^46 - 27844070 * q^47 - 5111808 * q^48 - 33563193 * q^49 + 41302976 * q^50 + 59791958 * q^51 + 19099392 * q^52 - 954201 * q^53 - 43034688 * q^54 - 31793152 * q^56 + 5859812 * q^57 - 53757584 * q^58 + 50239440 * q^59 + 96705024 * q^60 - 306912734 * q^61 + 56221920 * q^62 - 85880946 * q^63 + 50331648 * q^64 - 186865645 * q^65 - 112012374 * q^67 - 162899712 * q^68 - 551251156 * q^69 + 171319392 * q^70 + 72167396 * q^71 + 58142720 * q^72 - 204193414 * q^73 + 367278768 * q^74 - 1150193976 * q^75 - 143393280 * q^76 - 376717664 * q^78 - 717133858 * q^79 - 163119104 * q^80 - 320766577 * q^81 + 172160144 * q^82 - 214696882 * q^83 + 591389696 * q^84 + 1782988293 * q^85 + 122386048 * q^86 + 56353690 * q^87 + 201942773 * q^89 - 1499568272 * q^90 - 802638922 * q^91 + 31570432 * q^92 - 58664924 * q^93 - 445505120 * q^94 + 2736352118 * q^95 - 81788928 * q^96 - 31860047 * q^97 - 537011088 * q^98

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 $

$2$	16.0000	0.707107
$2$	16.0000	0.707107
$3$	−24.5710	−0.175137	−0.0875684	−	0.996159i	$-0.527910\pi$
$3$	−24.5710	−0.175137	−0.0875684	+	0.996159i	$0.527910\pi$
$4$	256.000	0.500000
$5$	1002.27	0.717168	0.358584	−	0.933497i	$-0.383260\pi$
$5$	1002.27	0.717168	0.358584	+	0.933497i	$0.383260\pi$
$6$	−393.136	−0.123840
$7$	−4370.69	−0.688032	−0.344016	−	0.938964i	$-0.611787\pi$
$7$	−4370.69	−0.688032	−0.344016	+	0.938964i	$0.611787\pi$
$8$	4096.00	0.353553
$9$	−19079.3	−0.969327
$10$	16036.4	0.507115
$11$	0	0
$11$	0	0
$12$	−6290.18	−0.0875684
$13$	13481.5	0.130916	0.0654582	−	0.997855i	$-0.479149\pi$
$13$	13481.5	0.130916	0.0654582	+	0.997855i	$0.479149\pi$
$14$	−69931.0	−0.486512
$15$	−24626.9	−0.125603
$16$	65536.0	0.250000
$17$	177624.	0.515800	0.257900	−	0.966172i	$-0.416969\pi$
$17$	177624.	0.515800	0.257900	+	0.966172i	$0.416969\pi$
$18$	−305268.	−0.685418
$19$	656570.	1.15582	0.577909	−	0.816101i	$-0.303869\pi$
$19$	656570.	1.15582	0.577909	+	0.816101i	$0.303869\pi$
$20$	256582.	0.358584
$21$	107392.	0.120500
$22$	0	0
$23$	502956.	0.374761	0.187381	−	0.982287i	$-0.440000\pi$
$23$	502956.	0.374761	0.187381	+	0.982287i	$0.440000\pi$
$24$	−100643.	−0.0619202
$25$	−948573.	−0.485670
$26$	215705.	0.0925719
$27$	952429.	0.344902
$28$	−1.11890e6	−0.344016
$29$	−4.33373e6	−1.13781	−0.568907	−	0.822402i	$-0.692633\pi$
$29$	−4.33373e6	−1.13781	−0.568907	+	0.822402i	$0.692633\pi$
$30$	−394030.	−0.0888145
$31$	−2.80982e6	−0.546450	−0.273225	−	0.961950i	$-0.588090\pi$
$31$	−2.80982e6	−0.546450	−0.273225	+	0.961950i	$0.588090\pi$
$32$	1.04858e6	0.176777
$33$	0	0
$34$	2.84198e6	0.364726
$35$	−4.38062e6	−0.493435
$36$	−4.88429e6	−0.484664
$37$	1.11774e7	0.980471	0.490235	−	0.871590i	$-0.336911\pi$
$37$	1.11774e7	0.980471	0.490235	+	0.871590i	$0.336911\pi$
$38$	1.05051e7	0.817287
$39$	−331255.	−0.0229283
$40$	4.10531e6	0.253557
$41$	−1.10232e7	−0.609230	−0.304615	−	0.952476i	$-0.598528\pi$
$41$	−1.10232e7	−0.609230	−0.304615	+	0.952476i	$0.598528\pi$
$42$	1.71828e6	0.0852062
$43$	−3.94654e7	−1.76039	−0.880193	−	0.474615i	$-0.842587\pi$
$43$	−3.94654e7	−1.76039	−0.880193	+	0.474615i	$0.842587\pi$
$44$	0	0
$45$	−1.91226e7	−0.695171
$46$	8.04730e6	0.264996
$47$	−8.77635e6	−0.262345	−0.131173	−	0.991360i	$-0.541874\pi$
$47$	−8.77635e6	−0.262345	−0.131173	+	0.991360i	$0.541874\pi$
$48$	−1.61029e6	−0.0437842
$49$	−2.12507e7	−0.526612
$50$	−1.51772e7	−0.343420
$51$	−4.36441e6	−0.0903357
$52$	3.45127e6	0.0654582
$53$	4.72696e6	0.0822887	0.0411444	−	0.999153i	$-0.486900\pi$
$53$	4.72696e6	0.0822887	0.0411444	+	0.999153i	$0.486900\pi$
$54$	1.52389e7	0.243882
$55$	0	0
$56$	−1.79023e7	−0.243256
$57$	−1.61326e7	−0.202426
$58$	−6.93397e7	−0.804555
$59$	−8.93693e6	−0.0960184	−0.0480092	−	0.998847i	$-0.515288\pi$
$59$	−8.93693e6	−0.0960184	−0.0480092	+	0.998847i	$0.515288\pi$
$60$	−6.30448e6	−0.0628013
$61$	4771.56	4.41241e−5 0	2.20620e−5	−	1.00000i	$-0.499993\pi$
$61$	4771.56	4.41241e−5 0	2.20620e−5		1.00000i	$0.499993\pi$
$62$	−4.49570e7	−0.386398
$63$	8.33895e7	0.666928
$64$	1.67772e7	0.125000
$65$	1.35122e7	0.0938891
$66$	0	0
$67$	−1.72224e8	−1.04414	−0.522069	−	0.852904i	$-0.674839\pi$
$67$	−1.72224e8	−1.04414	−0.522069	+	0.852904i	$0.674839\pi$
$68$	4.54718e7	0.257900
$69$	−1.23581e7	−0.0656346
$70$	−7.00900e7	−0.348911
$71$	5.15281e7	0.240648	0.120324	−	0.992735i	$-0.461607\pi$
$71$	5.15281e7	0.240648	0.120324	+	0.992735i	$0.461607\pi$
$72$	−7.81487e7	−0.342709
$73$	3.15769e8	1.30142	0.650708	−	0.759328i	$-0.274472\pi$
$73$	3.15769e8	1.30142	0.650708	+	0.759328i	$0.274472\pi$
$74$	1.78839e8	0.693298
$75$	2.33074e7	0.0850587
$76$	1.68082e8	0.577909
$77$	0	0
$78$	−5.30008e6	−0.0162128
$79$	−2.77760e8	−0.802321	−0.401161	−	0.916008i	$-0.631393\pi$
$79$	−2.77760e8	−0.802321	−0.401161	+	0.916008i	$0.631393\pi$
$80$	6.56850e7	0.179292
$81$	3.52135e8	0.908922
$82$	−1.76372e8	−0.430791
$83$	−4.29761e8	−0.993975	−0.496988	−	0.867758i	$-0.665561\pi$
$83$	−4.29761e8	−0.993975	−0.496988	+	0.867758i	$0.665561\pi$
$84$	2.74924e7	0.0602499
$85$	1.78028e8	0.369916
$86$	−6.31446e8	−1.24478
$87$	1.06484e8	0.199273
$88$	0	0
$89$	−9.67713e7	−0.163490	−0.0817451	−	0.996653i	$-0.526049\pi$
$89$	−9.67713e7	−0.163490	−0.0817451	+	0.996653i	$0.526049\pi$
$90$	−3.05962e8	−0.491560
$91$	−5.89236e7	−0.0900747
$92$	1.28757e8	0.187381
$93$	6.90400e7	0.0957035
$94$	−1.40422e8	−0.185506
$95$	6.58062e8	0.828916
$96$	−2.57646e7	−0.0309601
$97$	6.20651e7	0.0711827	0.0355914	−	0.999366i	$-0.488669\pi$
$97$	6.20651e7	0.0711827	0.0355914	+	0.999366i	$0.488669\pi$
$98$	−3.40011e8	−0.372371
$99$	0	0
$100$	−2.42835e8	−0.242835
$101$	−1.41760e9	−1.35552	−0.677762	−	0.735281i	$-0.737050\pi$
$101$	−1.41760e9	−1.35552	−0.677762	+	0.735281i	$0.737050\pi$
$102$	−6.98305e7	−0.0638770
$103$	−1.37833e9	−1.20666	−0.603330	−	0.797492i	$-0.706160\pi$
$103$	−1.37833e9	−1.20666	−0.603330	+	0.797492i	$0.706160\pi$
$104$	5.52204e7	0.0462860
$105$	1.07636e8	0.0864186
$106$	7.56313e7	0.0581869
$107$	1.54376e9	1.13855	0.569274	−	0.822148i	$-0.307224\pi$
$107$	1.54376e9	1.13855	0.569274	+	0.822148i	$0.307224\pi$
$108$	2.43822e8	0.172451
$109$	−1.84850e9	−1.25430	−0.627149	−	0.778899i	$-0.715778\pi$
$109$	−1.84850e9	−1.25430	−0.627149	+	0.778899i	$0.715778\pi$
$110$	0	0
$111$	−2.74641e8	−0.171717
$112$	−2.86437e8	−0.172008
$113$	−1.40191e9	−0.808850	−0.404425	−	0.914571i	$-0.632528\pi$
$113$	−1.40191e9	−0.808850	−0.404425	+	0.914571i	$0.632528\pi$
$114$	−2.58121e8	−0.143137
$115$	5.04100e8	0.268767
$116$	−1.10944e9	−0.568907
$117$	−2.57218e8	−0.126901
$118$	−1.42991e8	−0.0678953
$119$	−7.76339e8	−0.354887
$120$	−1.00872e8	−0.0444072
$121$	0	0
$122$	76344.9	3.12004e−5 0
$123$	2.70852e8	0.106699
$124$	−7.19313e8	−0.273225
$125$	−2.90829e9	−1.06548
$126$	1.33423e9	0.471589
$127$	−4.12502e9	−1.40705	−0.703524	−	0.710671i	$-0.748391\pi$
$127$	−4.12502e9	−1.40705	−0.703524	+	0.710671i	$0.748391\pi$
$128$	2.68435e8	0.0883883
$129$	9.69705e8	0.308309
$130$	2.16195e8	0.0663896
$131$	3.15291e8	0.0935384	0.0467692	−	0.998906i	$-0.485107\pi$
$131$	3.15291e8	0.0935384	0.0467692	+	0.998906i	$0.485107\pi$
$132$	0	0
$133$	−2.86966e9	−0.795240
$134$	−2.75559e9	−0.738316
$135$	9.54594e8	0.247353
$136$	7.27548e8	0.182363
$137$	1.42653e9	0.345969	0.172985	−	0.984925i	$-0.444659\pi$
$137$	1.42653e9	0.345969	0.172985	+	0.984925i	$0.444659\pi$
$138$	−1.97730e8	−0.0464106
$139$	−4.98898e9	−1.13356	−0.566781	−	0.823868i	$-0.691812\pi$
$139$	−4.98898e9	−1.13356	−0.566781	+	0.823868i	$0.691812\pi$
$140$	−1.12144e9	−0.246717
$141$	2.15644e8	0.0459464
$142$	8.24449e8	0.170164
$143$	0	0
$144$	−1.25038e9	−0.242332
$145$	−4.34358e9	−0.816004
$146$	5.05230e9	0.920241
$147$	5.22151e8	0.0922292
$148$	2.86143e9	0.490235
$149$	−9.15365e9	−1.52144	−0.760722	−	0.649078i	$-0.775155\pi$
$149$	−9.15365e9	−1.52144	−0.760722	+	0.649078i	$0.775155\pi$
$150$	3.72919e8	0.0601456
$151$	−3.06442e9	−0.479680	−0.239840	−	0.970812i	$-0.577095\pi$
$151$	−3.06442e9	−0.479680	−0.239840	+	0.970812i	$0.577095\pi$
$152$	2.68931e9	0.408644
$153$	−3.38894e9	−0.499979
$154$	0	0
$155$	−2.81620e9	−0.391896
$156$	−8.48013e7	−0.0114642
$157$	1.47984e10	1.94386	0.971930	−	0.235270i	$-0.0755974\pi$
$157$	1.47984e10	1.94386	0.971930	+	0.235270i	$0.0755974\pi$
$158$	−4.44417e9	−0.567327
$159$	−1.16146e8	−0.0144118
$160$	1.05096e9	0.126779
$161$	−2.19826e9	−0.257848
$162$	5.63416e9	0.642705
$163$	−4.05208e9	−0.449607	−0.224804	−	0.974404i	$-0.572174\pi$
$163$	−4.05208e9	−0.449607	−0.224804	+	0.974404i	$0.572174\pi$
$164$	−2.82195e9	−0.304615
$165$	0	0
$166$	−6.87617e9	−0.702847
$167$	6.21034e9	0.617862	0.308931	−	0.951084i	$-0.400029\pi$
$167$	6.21034e9	0.617862	0.308931	+	0.951084i	$0.400029\pi$
$168$	4.39879e8	0.0426031
$169$	−1.04227e10	−0.982861
$170$	2.84845e9	0.261570
$171$	−1.25269e10	−1.12037
$172$	−1.01031e10	−0.880193
$173$	6.19239e9	0.525594	0.262797	−	0.964851i	$-0.415355\pi$
$173$	6.19239e9	0.525594	0.262797	+	0.964851i	$0.415355\pi$
$174$	1.70375e9	0.140907
$175$	4.14592e9	0.334156
$176$	0	0
$177$	2.19590e8	0.0168164
$178$	−1.54834e9	−0.115605
$179$	1.99673e10	1.45372	0.726858	−	0.686788i	$-0.240980\pi$
$179$	1.99673e10	1.45372	0.726858	+	0.686788i	$0.240980\pi$
$180$	−4.89539e9	−0.347585
$181$	2.78227e10	1.92684	0.963421	−	0.267994i	$-0.0863608\pi$
$181$	2.78227e10	1.92684	0.963421	+	0.267994i	$0.0863608\pi$
$182$	−9.42777e8	−0.0636924
$183$	−117242.	−7.72776e−6 0
$184$	2.06011e9	0.132498
$185$	1.12029e10	0.703163
$186$	1.10464e9	0.0676726
$187$	0	0
$188$	−2.24675e9	−0.131173
$189$	−4.16277e9	−0.237303
$190$	1.05290e10	0.586132
$191$	−3.53379e10	−1.92128	−0.960641	−	0.277793i	$-0.910397\pi$
$191$	−3.53379e10	−1.92128	−0.960641	+	0.277793i	$0.910397\pi$
$192$	−4.12233e8	−0.0218921
$193$	−8.95212e9	−0.464427	−0.232214	−	0.972665i	$-0.574597\pi$
$193$	−8.95212e9	−0.464427	−0.232214	+	0.972665i	$0.574597\pi$
$194$	9.93041e8	0.0503338
$195$	−3.32008e8	−0.0164435
$196$	−5.44018e9	−0.263306
$197$	−3.36045e10	−1.58964	−0.794821	−	0.606844i	$-0.792435\pi$
$197$	−3.36045e10	−1.58964	−0.794821	+	0.606844i	$0.792435\pi$
$198$	0	0
$199$	6.62710e9	0.299560	0.149780	−	0.988719i	$-0.452143\pi$
$199$	6.62710e9	0.299560	0.149780	+	0.988719i	$0.452143\pi$
$200$	−3.88536e9	−0.171710
$201$	4.23172e9	0.182867
$202$	−2.26816e10	−0.958500
$203$	1.89414e10	0.782852
$204$	−1.11729e9	−0.0451678
$205$	−1.10483e10	−0.436921
$206$	−2.20532e10	−0.853237
$207$	−9.59603e9	−0.363266
$208$	8.83526e8	0.0327291
$209$	0	0
$210$	1.72218e9	0.0611072
$211$	6.86072e9	0.238286	0.119143	−	0.992877i	$-0.461985\pi$
$211$	6.86072e9	0.238286	0.119143	+	0.992877i	$0.461985\pi$
$212$	1.21010e9	0.0411444
$213$	−1.26610e9	−0.0421463
$214$	2.47001e10	0.805075
$215$	−3.95551e10	−1.26249
$216$	3.90115e9	0.121941
$217$	1.22808e10	0.375975
$218$	−2.95760e10	−0.886922
$219$	−7.75876e9	−0.227926
$220$	0	0
$221$	2.39464e9	0.0675268
$222$	−4.39426e9	−0.121422
$223$	7.16412e10	1.93995	0.969975	−	0.243203i	$-0.0781982\pi$
$223$	7.16412e10	1.93995	0.969975	+	0.243203i	$0.0781982\pi$
$224$	−4.58300e9	−0.121628
$225$	1.80981e10	0.470773
$226$	−2.24306e10	−0.571943
$227$	−3.80320e10	−0.950677	−0.475338	−	0.879803i	$-0.657674\pi$
$227$	−3.80320e10	−0.950677	−0.475338	+	0.879803i	$0.657674\pi$
$228$	−4.12994e9	−0.101213
$229$	−1.76927e10	−0.425141	−0.212571	−	0.977146i	$-0.568184\pi$
$229$	−1.76927e10	−0.425141	−0.212571	+	0.977146i	$0.568184\pi$
$230$	8.06559e9	0.190047
$231$	0	0
$232$	−1.77510e10	−0.402278
$233$	−7.00235e10	−1.55647	−0.778237	−	0.627971i	$-0.783886\pi$
$233$	−7.00235e10	−1.55647	−0.778237	+	0.627971i	$0.783886\pi$
$234$	−4.11548e9	−0.0897325
$235$	−8.79630e9	−0.188146
$236$	−2.28785e9	−0.0480092
$237$	6.82486e9	0.140516
$238$	−1.24214e10	−0.250943
$239$	5.52542e10	1.09541	0.547703	−	0.836673i	$-0.315503\pi$
$239$	5.52542e10	1.09541	0.547703	+	0.836673i	$0.315503\pi$
$240$	−1.61395e9	−0.0314007
$241$	−3.62192e10	−0.691611	−0.345805	−	0.938306i	$-0.612394\pi$
$241$	−3.62192e10	−0.691611	−0.345805	+	0.938306i	$0.612394\pi$
$242$	0	0
$243$	−2.73990e10	−0.504088
$244$	1.22152e6	2.20620e−5 0
$245$	−2.12990e10	−0.377669
$246$	4.33363e9	0.0754473
$247$	8.85157e9	0.151316
$248$	−1.15090e10	−0.193199
$249$	1.05597e10	0.174082
$250$	−4.65327e10	−0.753405
$251$	9.20708e10	1.46416	0.732082	−	0.681216i	$-0.238549\pi$
$251$	9.20708e10	1.46416	0.732082	+	0.681216i	$0.238549\pi$
$252$	2.13477e10	0.333464
$253$	0	0
$254$	−6.60003e10	−0.994934
$255$	−4.37433e9	−0.0647859
$256$	4.29497e9	0.0625000
$257$	−4.34006e9	−0.0620579	−0.0310289	−	0.999518i	$-0.509878\pi$
$257$	−4.34006e9	−0.0620579	−0.0310289	+	0.999518i	$0.509878\pi$
$258$	1.55153e10	0.218007
$259$	−4.88531e10	−0.674595
$260$	3.45912e9	0.0469446
$261$	8.26844e10	1.10291
$262$	5.04465e9	0.0661417
$263$	1.68107e10	0.216664	0.108332	−	0.994115i	$-0.465449\pi$
$263$	1.68107e10	0.216664	0.108332	+	0.994115i	$0.465449\pi$
$264$	0	0
$265$	4.73770e9	0.0590149
$266$	−4.59146e10	−0.562320
$267$	2.37777e9	0.0286332
$268$	−4.40894e10	−0.522069
$269$	−8.12659e10	−0.946287	−0.473144	−	0.880985i	$-0.656881\pi$
$269$	−8.12659e10	−0.946287	−0.473144	+	0.880985i	$0.656881\pi$
$270$	1.52735e10	0.174905
$271$	3.42501e10	0.385745	0.192872	−	0.981224i	$-0.438220\pi$
$271$	3.42501e10	0.385745	0.192872	+	0.981224i	$0.438220\pi$
$272$	1.16408e10	0.128950
$273$	1.44781e9	0.0157754
$274$	2.28244e10	0.244637
$275$	0	0
$276$	−3.16369e9	−0.0328173
$277$	6.13134e10	0.625743	0.312872	−	0.949795i	$-0.398709\pi$
$277$	6.13134e10	0.625743	0.312872	+	0.949795i	$0.398709\pi$
$278$	−7.98237e10	−0.801550
$279$	5.36092e10	0.529688
$280$	−1.79430e10	−0.174456
$281$	−1.91026e11	−1.82774	−0.913869	−	0.406010i	$-0.866920\pi$
$281$	−1.91026e11	−1.82774	−0.913869	+	0.406010i	$0.866920\pi$
$282$	3.45030e9	0.0324890
$283$	−2.01298e10	−0.186552	−0.0932762	−	0.995640i	$-0.529734\pi$
$283$	−2.01298e10	−0.186552	−0.0932762	+	0.995640i	$0.529734\pi$
$284$	1.31912e10	0.120324
$285$	−1.61693e10	−0.145174
$286$	0	0
$287$	4.81791e10	0.419170
$288$	−2.00061e10	−0.171354
$289$	−8.70376e10	−0.733950
$290$	−6.94973e10	−0.577002
$291$	−1.52500e9	−0.0124667
$292$	8.08368e10	0.650708
$293$	8.10535e10	0.642492	0.321246	−	0.946996i	$-0.395898\pi$
$293$	8.10535e10	0.642492	0.321246	+	0.946996i	$0.395898\pi$
$294$	8.35442e9	0.0652159
$295$	−8.95725e9	−0.0688614
$296$	4.57828e10	0.346649
$297$	0	0
$298$	−1.46458e11	−1.07582
$299$	6.78062e9	0.0490624
$300$	5.96670e9	0.0425293
$301$	1.72491e11	1.21120
$302$	−4.90307e10	−0.339185
$303$	3.48319e10	0.237402
$304$	4.30289e10	0.288955
$305$	4.78240e6	3.16444e−5 0
$306$	−5.42230e10	−0.353539
$307$	−1.10840e11	−0.712153	−0.356077	−	0.934457i	$-0.615886\pi$
$307$	−1.10840e11	−0.712153	−0.356077	+	0.934457i	$0.615886\pi$
$308$	0	0
$309$	3.38669e10	0.211331
$310$	−4.50592e10	−0.277113
$311$	−3.45795e10	−0.209603	−0.104801	−	0.994493i	$-0.533421\pi$
$311$	−3.45795e10	−0.209603	−0.104801	+	0.994493i	$0.533421\pi$
$312$	−1.35682e9	−0.00810638
$313$	−1.28799e11	−0.758511	−0.379256	−	0.925292i	$-0.623820\pi$
$313$	−1.28799e11	−0.758511	−0.379256	+	0.925292i	$0.623820\pi$
$314$	2.36774e11	1.37452
$315$	8.35791e10	0.478300
$316$	−7.11066e10	−0.401161
$317$	−1.76424e11	−0.981277	−0.490639	−	0.871363i	$-0.663236\pi$
$317$	−1.76424e11	−0.981277	−0.490639	+	0.871363i	$0.663236\pi$
$318$	−1.85834e9	−0.0101907
$319$	0	0
$320$	1.68154e10	0.0896460
$321$	−3.79317e10	−0.199402
$322$	−3.51722e10	−0.182326
$323$	1.16623e11	0.596172
$324$	9.01466e10	0.454461
$325$	−1.27882e10	−0.0635821
$326$	−6.48332e10	−0.317920
$327$	4.54196e10	0.219674
$328$	−4.51511e10	−0.215395
$329$	3.83587e10	0.180502
$330$	0	0
$331$	4.19841e11	1.92247	0.961234	−	0.275733i	$-0.0889206\pi$
$331$	4.19841e11	1.92247	0.961234	+	0.275733i	$0.0889206\pi$
$332$	−1.10019e11	−0.496988
$333$	−2.13257e11	−0.950397
$334$	9.93654e10	0.436894
$335$	−1.72616e11	−0.748822
$336$	7.03806e9	0.0301249
$337$	1.31045e10	0.0553460	0.0276730	−	0.999617i	$-0.491190\pi$
$337$	1.31045e10	0.0553460	0.0276730	+	0.999617i	$0.491190\pi$
$338$	−1.66764e11	−0.694988
$339$	3.44464e10	0.141659
$340$	4.55751e10	0.184958
$341$	0	0
$342$	−2.00430e11	−0.792218
$343$	2.69253e11	1.05036
$344$	−1.61650e11	−0.622391
$345$	−1.23862e10	−0.0470710
$346$	9.90782e10	0.371651
$347$	4.03926e11	1.49561	0.747806	−	0.663917i	$-0.231107\pi$
$347$	4.03926e11	1.49561	0.747806	+	0.663917i	$0.231107\pi$
$348$	2.72600e10	0.0996365
$349$	2.85481e11	1.03006	0.515030	−	0.857172i	$-0.327781\pi$
$349$	2.85481e11	1.03006	0.515030	+	0.857172i	$0.327781\pi$
$350$	6.63347e10	0.236284
$351$	1.28402e10	0.0451533
$352$	0	0
$353$	4.11243e11	1.40965	0.704827	−	0.709379i	$-0.251025\pi$
$353$	4.11243e11	1.40965	0.704827	+	0.709379i	$0.251025\pi$
$354$	3.51343e9	0.0118910
$355$	5.16452e10	0.172585
$356$	−2.47735e10	−0.0817451
$357$	1.90755e10	0.0621538
$358$	3.19476e11	1.02793
$359$	−5.29892e10	−0.168369	−0.0841846	−	0.996450i	$-0.526829\pi$
$359$	−5.29892e10	−0.168369	−0.0841846	+	0.996450i	$0.526829\pi$
$360$	−7.83263e10	−0.245780
$361$	1.08396e11	0.335916
$362$	4.45163e11	1.36248
$363$	0	0
$364$	−1.50844e10	−0.0450374
$365$	3.16487e11	0.933335
$366$	−1.87587e6	−5.46435e−6 0
$367$	5.65540e11	1.62729	0.813647	−	0.581359i	$-0.197479\pi$
$367$	5.65540e11	1.62729	0.813647	+	0.581359i	$0.197479\pi$
$368$	3.29617e10	0.0936904
$369$	2.10315e11	0.590543
$370$	1.79246e11	0.497211
$371$	−2.06601e10	−0.0566173
$372$	1.76743e10	0.0478517
$373$	1.51400e10	0.0404983	0.0202491	−	0.999795i	$-0.493554\pi$
$373$	1.51400e10	0.0404983	0.0202491	+	0.999795i	$0.493554\pi$
$374$	0	0
$375$	7.14598e10	0.186604
$376$	−3.59479e10	−0.0927531
$377$	−5.84253e10	−0.148958
$378$	−6.66043e10	−0.167799
$379$	−1.70771e11	−0.425145	−0.212572	−	0.977145i	$-0.568184\pi$
$379$	−1.70771e11	−0.425145	−0.212572	+	0.977145i	$0.568184\pi$
$380$	1.68464e11	0.414458
$381$	1.01356e11	0.246426
$382$	−5.65407e11	−1.35855
$383$	5.16645e11	1.22687	0.613434	−	0.789746i	$-0.289788\pi$
$383$	5.16645e11	1.22687	0.613434	+	0.789746i	$0.289788\pi$
$384$	−6.59573e9	−0.0154801
$385$	0	0
$386$	−1.43234e11	−0.328400
$387$	7.52970e11	1.70639
$388$	1.58887e10	0.0355914
$389$	1.80796e11	0.400329	0.200164	−	0.979762i	$-0.435852\pi$
$389$	1.80796e11	0.400329	0.200164	+	0.979762i	$0.435852\pi$
$390$	−5.31213e9	−0.0116273
$391$	8.93371e10	0.193302
$392$	−8.70428e10	−0.186185
$393$	−7.74701e9	−0.0163820
$394$	−5.37672e11	−1.12405
$395$	−2.78392e11	−0.575399
$396$	0	0
$397$	7.40572e10	0.149627	0.0748135	−	0.997198i	$-0.476164\pi$
$397$	7.40572e10	0.149627	0.0748135	+	0.997198i	$0.476164\pi$
$398$	1.06034e11	0.211821
$399$	7.05105e10	0.139276
$400$	−6.21657e10	−0.121417
$401$	−1.00691e12	−1.94464	−0.972321	−	0.233648i	$-0.924934\pi$
$401$	−1.00691e12	−1.94464	−0.972321	+	0.233648i	$0.924934\pi$
$402$	6.77076e10	0.129306
$403$	−3.78806e10	−0.0715393
$404$	−3.62905e11	−0.677762
$405$	3.52935e11	0.651850
$406$	3.03062e11	0.553560
$407$	0	0
$408$	−1.78766e10	−0.0319385
$409$	6.38241e11	1.12779	0.563897	−	0.825845i	$-0.309302\pi$
$409$	6.38241e11	1.12779	0.563897	+	0.825845i	$0.309302\pi$
$410$	−1.76773e11	−0.308949
$411$	−3.50512e10	−0.0605920
$412$	−3.52852e11	−0.603330
$413$	3.90605e10	0.0660637
$414$	−1.53537e11	−0.256868
$415$	−4.30738e11	−0.712847
$416$	1.41364e10	0.0231430
$417$	1.22584e11	0.198529
$418$	0	0
$419$	8.57640e11	1.35938	0.679692	−	0.733498i	$-0.262114\pi$
$419$	8.57640e11	1.35938	0.679692	+	0.733498i	$0.262114\pi$
$420$	2.75549e10	0.0432093
$421$	2.35811e11	0.365843	0.182921	−	0.983128i	$-0.441445\pi$
$421$	2.35811e11	0.365843	0.182921	+	0.983128i	$0.441445\pi$
$422$	1.09771e11	0.168494
$423$	1.67446e11	0.254299
$424$	1.93616e10	0.0290935
$425$	−1.68489e11	−0.250509
$426$	−2.02576e10	−0.0298019
$427$	−2.08550e7	−3.03588e−5 0
$428$	3.95201e11	0.569274
$429$	0	0
$430$	−6.32881e11	−0.892718
$431$	−3.86838e11	−0.539985	−0.269992	−	0.962862i	$-0.587021\pi$
$431$	−3.86838e11	−0.539985	−0.269992	+	0.962862i	$0.587021\pi$
$432$	6.24184e10	0.0862255
$433$	1.14566e12	1.56624	0.783121	−	0.621869i	$-0.213626\pi$
$433$	1.14566e12	1.56624	0.783121	+	0.621869i	$0.213626\pi$
$434$	1.96493e11	0.265854
$435$	1.06726e11	0.142912
$436$	−4.73216e11	−0.627149
$437$	3.30226e11	0.433156
$438$	−1.24140e11	−0.161168
$439$	−2.94193e11	−0.378043	−0.189022	−	0.981973i	$-0.560532\pi$
$439$	−2.94193e11	−0.378043	−0.189022	+	0.981973i	$0.560532\pi$
$440$	0	0
$441$	4.05448e11	0.510459
$442$	3.83143e10	0.0477486
$443$	1.46706e11	0.180980	0.0904900	−	0.995897i	$-0.471157\pi$
$443$	1.46706e11	0.180980	0.0904900	+	0.995897i	$0.471157\pi$
$444$	−7.03082e10	−0.0858583
$445$	−9.69913e10	−0.117250
$446$	1.14626e12	1.37175
$447$	2.24914e11	0.266461
$448$	−7.33280e10	−0.0860040
$449$	8.53061e11	0.990538	0.495269	−	0.868740i	$-0.335069\pi$
$449$	8.53061e11	0.990538	0.495269	+	0.868740i	$0.335069\pi$
$450$	2.89569e11	0.332887
$451$	0	0
$452$	−3.58890e11	−0.404425
$453$	7.52959e10	0.0840097
$454$	−6.08512e11	−0.672230
$455$	−5.90575e10	−0.0645987
$456$	−6.60791e10	−0.0715686
$457$	1.78245e11	0.191158	0.0955792	−	0.995422i	$-0.469530\pi$
$457$	1.78245e11	0.191158	0.0955792	+	0.995422i	$0.469530\pi$
$458$	−2.83083e11	−0.300620
$459$	1.69174e11	0.177900
$460$	1.29049e11	0.134384
$461$	−2.92938e11	−0.302079	−0.151040	−	0.988528i	$-0.548262\pi$
$461$	−2.92938e11	−0.302079	−0.151040	+	0.988528i	$0.548262\pi$
$462$	0	0
$463$	5.54852e11	0.561128	0.280564	−	0.959835i	$-0.409478\pi$
$463$	5.54852e11	0.561128	0.280564	+	0.959835i	$0.409478\pi$
$464$	−2.84015e11	−0.284453
$465$	6.91970e10	0.0686355
$466$	−1.12038e12	−1.10059
$467$	1.12340e12	1.09297	0.546485	−	0.837469i	$-0.315966\pi$
$467$	1.12340e12	1.09297	0.546485	+	0.837469i	$0.315966\pi$
$468$	−6.58477e10	−0.0634504
$469$	7.52738e11	0.718400
$470$	−1.40741e11	−0.133039
$471$	−3.63611e11	−0.340442
$472$	−3.66057e10	−0.0339476
$473$	0	0
$474$	1.09198e11	0.0993599
$475$	−6.22805e11	−0.561346
$476$	−1.98743e11	−0.177444
$477$	−9.01869e10	−0.0797647
$478$	8.84067e11	0.774568
$479$	−1.27163e12	−1.10370	−0.551849	−	0.833944i	$-0.686078\pi$
$479$	−1.27163e12	−1.10370	−0.551849	+	0.833944i	$0.686078\pi$
$480$	−2.58232e10	−0.0222036
$481$	1.50689e11	0.128360
$482$	−5.79506e11	−0.489042
$483$	5.40136e10	0.0451587
$484$	0	0
$485$	6.22062e10	0.0510500
$486$	−4.38384e11	−0.356444
$487$	−1.34342e12	−1.08226	−0.541128	−	0.840940i	$-0.682003\pi$
$487$	−1.34342e12	−1.08226	−0.541128	+	0.840940i	$0.682003\pi$
$488$	1.95443e7	1.56002e−5 0
$489$	9.95637e10	0.0787428
$490$	−3.40784e11	−0.267053
$491$	−1.22830e12	−0.953757	−0.476879	−	0.878969i	$-0.658232\pi$
$491$	−1.22830e12	−0.953757	−0.476879	+	0.878969i	$0.658232\pi$
$492$	6.93381e10	0.0533493
$493$	−7.69775e11	−0.586884
$494$	1.41625e11	0.106996
$495$	0	0
$496$	−1.84144e11	−0.136612
$497$	−2.25213e11	−0.165573
$498$	1.68955e11	0.123094
$499$	2.46359e11	0.177876	0.0889379	−	0.996037i	$-0.471653\pi$
$499$	2.46359e11	0.177876	0.0889379	+	0.996037i	$0.471653\pi$
$500$	−7.44523e11	−0.532738
$501$	−1.52594e11	−0.108210
$502$	1.47313e12	1.03532
$503$	1.80748e12	1.25897	0.629487	−	0.777011i	$-0.283265\pi$
$503$	1.80748e12	1.25897	0.629487	+	0.777011i	$0.283265\pi$
$504$	3.41563e11	0.235795
$505$	−1.42082e12	−0.972139
$506$	0	0
$507$	2.56098e11	0.172135
$508$	−1.05600e12	−0.703524
$509$	1.61948e12	1.06941	0.534706	−	0.845038i	$-0.320422\pi$
$509$	1.61948e12	1.06941	0.534706	+	0.845038i	$0.320422\pi$
$510$	−6.99892e10	−0.0458105
$511$	−1.38013e12	−0.895416
$512$	6.87195e10	0.0441942
$513$	6.25336e11	0.398644
$514$	−6.94410e10	−0.0438815
$515$	−1.38146e12	−0.865378
$516$	2.48244e11	0.154154
$517$	0	0
$518$	−7.81650e11	−0.477011
$519$	−1.52153e11	−0.0920509
$520$	5.53459e10	0.0331948
$521$	−1.90249e12	−1.13123	−0.565616	−	0.824669i	$-0.691362\pi$
$521$	−1.90249e12	−1.13123	−0.565616	+	0.824669i	$0.691362\pi$
$522$	1.32295e12	0.779877
$523$	−2.47948e12	−1.44912	−0.724558	−	0.689214i	$-0.757956\pi$
$523$	−2.47948e12	−1.44912	−0.724558	+	0.689214i	$0.757956\pi$
$524$	8.07144e10	0.0467692
$525$	−1.01869e11	−0.0585231
$526$	2.68972e11	0.153204
$527$	−4.99091e11	−0.281859
$528$	0	0
$529$	−1.54819e12	−0.859554
$530$	7.58032e10	0.0417298
$531$	1.70510e11	0.0930732
$532$	−7.34633e11	−0.397620
$533$	−1.48610e11	−0.0797582
$534$	3.80443e10	0.0202467
$535$	1.54726e12	0.816531
$536$	−7.05430e11	−0.369158
$537$	−4.90616e11	−0.254599
$538$	−1.30025e12	−0.669126
$539$	0	0
$540$	2.44376e11	0.123676
$541$	−2.19882e12	−1.10358	−0.551789	−	0.833984i	$-0.686055\pi$
$541$	−2.19882e12	−1.10358	−0.551789	+	0.833984i	$0.686055\pi$
$542$	5.48002e11	0.272763
$543$	−6.83633e11	−0.337461
$544$	1.86252e11	0.0911815
$545$	−1.85270e12	−0.899543
$546$	2.31650e10	0.0111549
$547$	1.08995e12	0.520549	0.260275	−	0.965535i	$-0.416187\pi$
$547$	1.08995e12	0.520549	0.260275	+	0.965535i	$0.416187\pi$
$548$	3.65191e11	0.172985
$549$	−9.10378e7	−4.27707e−5 0
$550$	0	0
$551$	−2.84540e12	−1.31511
$552$	−5.06190e10	−0.0232053
$553$	1.21400e12	0.552023
$554$	9.81014e11	0.442467
$555$	−2.75266e11	−0.123150
$556$	−1.27718e12	−0.566781
$557$	−1.56726e12	−0.689909	−0.344954	−	0.938619i	$-0.612106\pi$
$557$	−1.56726e12	−0.689909	−0.344954	+	0.938619i	$0.612106\pi$
$558$	8.57747e11	0.374546
$559$	−5.32054e11	−0.230464
$560$	−2.87089e11	−0.123359
$561$	0	0
$562$	−3.05641e12	−1.29241
$563$	1.08339e12	0.454460	0.227230	−	0.973841i	$-0.427033\pi$
$563$	1.08339e12	0.454460	0.227230	+	0.973841i	$0.427033\pi$
$564$	5.52048e10	0.0229732
$565$	−1.40510e12	−0.580082
$566$	−3.22077e11	−0.131912
$567$	−1.53907e12	−0.625367
$568$	2.11059e11	0.0850818
$569$	3.23416e12	1.29347	0.646735	−	0.762715i	$-0.276134\pi$
$569$	3.23416e12	1.29347	0.646735	+	0.762715i	$0.276134\pi$
$570$	−2.58708e11	−0.102653
$571$	2.69057e12	1.05921	0.529606	−	0.848244i	$-0.322340\pi$
$571$	2.69057e12	1.05921	0.529606	+	0.848244i	$0.322340\pi$
$572$	0	0
$573$	8.68290e11	0.336487
$574$	7.70865e11	0.296398
$575$	−4.77091e11	−0.182010
$576$	−3.20097e11	−0.121166
$577$	4.91056e12	1.84434	0.922168	−	0.386790i	$-0.126416\pi$
$577$	4.91056e12	1.84434	0.922168	+	0.386790i	$0.126416\pi$
$578$	−1.39260e12	−0.518981
$579$	2.19963e11	0.0813384
$580$	−1.11196e12	−0.408002
$581$	1.87835e12	0.683887
$582$	−2.44000e10	−0.00881530
$583$	0	0
$584$	1.29339e12	0.460120
$585$	−2.57802e11	−0.0910093
$586$	1.29686e12	0.454310
$587$	−1.39304e12	−0.484274	−0.242137	−	0.970242i	$-0.577848\pi$
$587$	−1.39304e12	−0.484274	−0.242137	+	0.970242i	$0.577848\pi$
$588$	1.33671e11	0.0461146
$589$	−1.84484e12	−0.631597
$590$	−1.43316e11	−0.0486923
$591$	8.25697e11	0.278405
$592$	7.32525e11	0.245118
$593$	−1.79590e12	−0.596397	−0.298199	−	0.954504i	$-0.596386\pi$
$593$	−1.79590e12	−0.596397	−0.298199	+	0.954504i	$0.596386\pi$
$594$	0	0
$595$	−7.78104e11	−0.254514
$596$	−2.34333e12	−0.760722
$597$	−1.62835e11	−0.0524641
$598$	1.08490e11	0.0346924
$599$	2.54337e12	0.807214	0.403607	−	0.914932i	$-0.367756\pi$
$599$	2.54337e12	0.807214	0.403607	+	0.914932i	$0.367756\pi$
$600$	9.54672e10	0.0300728
$601$	−4.53476e12	−1.41781	−0.708906	−	0.705303i	$-0.750811\pi$
$601$	−4.53476e12	−1.41781	−0.708906	+	0.705303i	$0.750811\pi$
$602$	2.75985e12	0.856450
$603$	3.28591e12	1.01211
$604$	−7.84491e11	−0.239840
$605$	0	0
$606$	5.57310e11	0.167869
$607$	−5.33124e12	−1.59397	−0.796983	−	0.604002i	$-0.793572\pi$
$607$	−5.33124e12	−1.59397	−0.796983	+	0.604002i	$0.793572\pi$
$608$	6.88463e11	0.204322
$609$	−4.65409e11	−0.137106
$610$	7.65184e7	2.23760e−5 0
$611$	−1.18319e11	−0.0343453
$612$	−8.67568e11	−0.249990
$613$	−3.16926e12	−0.906538	−0.453269	−	0.891374i	$-0.649742\pi$
$613$	−3.16926e12	−0.906538	−0.453269	+	0.891374i	$0.649742\pi$
$614$	−1.77344e12	−0.503568
$615$	2.71468e11	0.0765209
$616$	0	0
$617$	−5.03854e12	−1.39966	−0.699829	−	0.714311i	$-0.746740\pi$
$617$	−5.03854e12	−1.39966	−0.699829	+	0.714311i	$0.746740\pi$
$618$	5.41871e11	0.149433
$619$	3.47906e12	0.952476	0.476238	−	0.879316i	$-0.342000\pi$
$619$	3.47906e12	0.952476	0.476238	+	0.879316i	$0.342000\pi$
$620$	−7.20948e11	−0.195948
$621$	4.79030e11	0.129256
$622$	−5.53272e11	−0.148212
$623$	4.22957e11	0.112486
$624$	−2.17091e10	−0.00573208
$625$	−1.06222e12	−0.278455
$626$	−2.06078e12	−0.536348
$627$	0	0
$628$	3.78838e12	0.971930
$629$	1.98538e12	0.505727
$630$	1.33727e12	0.338209
$631$	9.09586e11	0.228408	0.114204	−	0.993457i	$-0.463568\pi$
$631$	9.09586e11	0.228408	0.114204	+	0.993457i	$0.463568\pi$
$632$	−1.13771e12	−0.283663
$633$	−1.68575e11	−0.0417327
$634$	−2.82279e12	−0.693868
$635$	−4.13440e12	−1.00909
$636$	−2.97334e10	−0.00720589
$637$	−2.86492e11	−0.0689422
$638$	0	0
$639$	−9.83118e11	−0.233266
$640$	2.69046e11	0.0633893
$641$	1.46888e12	0.343658	0.171829	−	0.985127i	$-0.445032\pi$
$641$	1.46888e12	0.343658	0.171829	+	0.985127i	$0.445032\pi$
$642$	−6.06906e11	−0.140998
$643$	3.37801e12	0.779313	0.389656	−	0.920960i	$-0.372594\pi$
$643$	3.37801e12	0.779313	0.389656	+	0.920960i	$0.372594\pi$
$644$	−5.62756e11	−0.128924
$645$	9.71909e11	0.221109
$646$	1.86596e12	0.421557
$647$	−5.57282e12	−1.25027	−0.625137	−	0.780515i	$-0.714957\pi$
$647$	−5.57282e12	−1.25027	−0.625137	+	0.780515i	$0.714957\pi$
$648$	1.44235e12	0.321352
$649$	0	0
$650$	−2.04612e11	−0.0449594
$651$	−3.01753e11	−0.0658471
$652$	−1.03733e12	−0.224804
$653$	−6.31010e12	−1.35809	−0.679043	−	0.734099i	$-0.737605\pi$
$653$	−6.31010e12	−1.35809	−0.679043	+	0.734099i	$0.737605\pi$
$654$	7.26713e11	0.155333
$655$	3.16007e11	0.0670828
$656$	−7.22418e11	−0.152308
$657$	−6.02464e12	−1.26150
$658$	6.13739e11	0.127634
$659$	−5.14649e12	−1.06298	−0.531492	−	0.847064i	$-0.678368\pi$
$659$	−5.14649e12	−1.06298	−0.531492	+	0.847064i	$0.678368\pi$
$660$	0	0
$661$	6.79740e12	1.38496	0.692479	−	0.721438i	$-0.256519\pi$
$661$	6.79740e12	1.38496	0.692479	+	0.721438i	$0.256519\pi$
$662$	6.71746e12	1.35939
$663$	−5.88389e10	−0.0118264
$664$	−1.76030e12	−0.351423
$665$	−2.87618e12	−0.570321
$666$	−3.41212e12	−0.672032
$667$	−2.17968e12	−0.426409
$668$	1.58985e12	0.308931
$669$	−1.76030e12	−0.339757
$670$	−2.76185e12	−0.529497
$671$	0	0
$672$	1.12609e11	0.0213016
$673$	3.25760e12	0.612110	0.306055	−	0.952014i	$-0.400991\pi$
$673$	3.25760e12	0.612110	0.306055	+	0.952014i	$0.400991\pi$
$674$	2.09672e11	0.0391356
$675$	−9.03448e11	−0.167508
$676$	−2.66822e12	−0.491430
$677$	8.68452e12	1.58890	0.794450	−	0.607329i	$-0.207759\pi$
$677$	8.68452e12	1.58890	0.794450	+	0.607329i	$0.207759\pi$
$678$	5.51143e11	0.100168
$679$	−2.71267e11	−0.0489760
$680$	7.29202e11	0.130785
$681$	9.34485e11	0.166499
$682$	0	0
$683$	−2.72809e12	−0.479696	−0.239848	−	0.970810i	$-0.577098\pi$
$683$	−2.72809e12	−0.479696	−0.239848	+	0.970810i	$0.577098\pi$
$684$	−3.20688e12	−0.560183
$685$	1.42977e12	0.248118
$686$	4.30805e12	0.742715
$687$	4.34727e11	0.0744580
$688$	−2.58640e12	−0.440097
$689$	6.37266e10	0.0107729
$690$	−1.98180e11	−0.0332842
$691$	6.95354e12	1.16026	0.580129	−	0.814525i	$-0.303002\pi$
$691$	6.95354e12	1.16026	0.580129	+	0.814525i	$0.303002\pi$
$692$	1.58525e12	0.262797
$693$	0	0
$694$	6.46281e12	1.05756
$695$	−5.00032e12	−0.812955
$696$	4.36159e11	0.0704537
$697$	−1.95799e12	−0.314241
$698$	4.56769e12	0.728362
$699$	1.72055e12	0.272596
$700$	1.06136e12	0.167078
$701$	−6.17500e11	−0.0965841	−0.0482921	−	0.998833i	$-0.515378\pi$
$701$	−6.17500e11	−0.0965841	−0.0482921	+	0.998833i	$0.515378\pi$
$702$	2.05443e11	0.0319282
$703$	7.33877e12	1.13325
$704$	0	0
$705$	2.16134e11	0.0329513
$706$	6.57989e12	0.996776
$707$	6.19588e12	0.932644
$708$	5.62149e10	0.00840818
$709$	5.11270e11	0.0759875	0.0379938	−	0.999278i	$-0.487903\pi$
$709$	5.11270e11	0.0759875	0.0379938	+	0.999278i	$0.487903\pi$
$710$	8.26323e11	0.122036
$711$	5.29946e12	0.777712
$712$	−3.96375e11	−0.0578025
$713$	−1.41321e12	−0.204788
$714$	3.05207e11	0.0439494
$715$	0	0
$716$	5.11162e12	0.726858
$717$	−1.35765e12	−0.191846
$718$	−8.47828e11	−0.119055
$719$	7.98593e11	0.111441	0.0557206	−	0.998446i	$-0.482254\pi$
$719$	7.98593e11	0.111441	0.0557206	+	0.998446i	$0.482254\pi$
$720$	−1.25322e12	−0.173793
$721$	6.02424e12	0.830221
$722$	1.73434e12	0.237529
$723$	8.89942e11	0.121127
$724$	7.12261e12	0.963421
$725$	4.11086e12	0.552601
$726$	0	0
$727$	−4.49501e12	−0.596796	−0.298398	−	0.954442i	$-0.596452\pi$
$727$	−4.49501e12	−0.596796	−0.298398	+	0.954442i	$0.596452\pi$
$728$	−2.41351e11	−0.0318462
$729$	−6.25785e12	−0.820638
$730$	5.06379e12	0.659967
$731$	−7.01000e12	−0.908008
$732$	−3.00140e7	−3.86388e−6 0
$733$	−7.07645e11	−0.0905415	−0.0452707	−	0.998975i	$-0.514415\pi$
$733$	−7.07645e11	−0.0905415	−0.0452707	+	0.998975i	$0.514415\pi$
$734$	9.04864e12	1.15067
$735$	5.23338e11	0.0661439
$736$	5.27388e11	0.0662491
$737$	0	0
$738$	3.36504e12	0.417577
$739$	5.88373e12	0.725693	0.362847	−	0.931849i	$-0.381805\pi$
$739$	5.88373e12	0.725693	0.362847	+	0.931849i	$0.381805\pi$
$740$	2.86793e12	0.351581
$741$	−2.17492e11	−0.0265010
$742$	−3.30561e11	−0.0400345
$743$	1.07583e13	1.29507	0.647537	−	0.762034i	$-0.275799\pi$
$743$	1.07583e13	1.29507	0.647537	+	0.762034i	$0.275799\pi$
$744$	2.82788e11	0.0338363
$745$	−9.17445e12	−1.09113
$746$	2.42240e11	0.0286366
$747$	8.19952e12	0.963487
$748$	0	0
$749$	−6.74727e12	−0.783358
$750$	1.14336e12	0.131949
$751$	−8.95006e12	−1.02671	−0.513353	−	0.858177i	$-0.671597\pi$
$751$	−8.95006e12	−1.02671	−0.513353	+	0.858177i	$0.671597\pi$
$752$	−5.75167e11	−0.0655864
$753$	−2.26227e12	−0.256429
$754$	−9.34806e11	−0.105330
$755$	−3.07138e12	−0.344011
$756$	−1.06567e12	−0.118652
$757$	−3.91280e12	−0.433068	−0.216534	−	0.976275i	$-0.569475\pi$
$757$	−3.91280e12	−0.433068	−0.216534	+	0.976275i	$0.569475\pi$
$758$	−2.73233e12	−0.300623
$759$	0	0
$760$	2.69542e12	0.293066
$761$	7.52171e12	0.812991	0.406495	−	0.913653i	$-0.366751\pi$
$761$	7.52171e12	0.812991	0.406495	+	0.913653i	$0.366751\pi$
$762$	1.62170e12	0.174250
$763$	8.07922e12	0.862997
$764$	−9.04651e12	−0.960641
$765$	−3.39664e12	−0.358569
$766$	8.26632e12	0.867526
$767$	−1.20484e11	−0.0125704
$768$	−1.05532e11	−0.0109461
$769$	3.18865e12	0.328805	0.164403	−	0.986393i	$-0.447430\pi$
$769$	3.18865e12	0.328805	0.164403	+	0.986393i	$0.447430\pi$
$770$	0	0
$771$	1.06640e11	0.0108686
$772$	−2.29174e12	−0.232214
$773$	−8.32320e12	−0.838461	−0.419230	−	0.907880i	$-0.637700\pi$
$773$	−8.32320e12	−0.838461	−0.419230	+	0.907880i	$0.637700\pi$
$774$	1.20475e13	1.20660
$775$	2.66532e12	0.265394
$776$	2.54219e11	0.0251669
$777$	1.20037e12	0.118147
$778$	2.89274e12	0.283075
$779$	−7.23752e12	−0.704159
$780$	−8.49941e10	−0.00822173
$781$	0	0
$782$	1.42939e12	0.136685
$783$	−4.12757e12	−0.392434
$784$	−1.39269e12	−0.131653
$785$	1.48320e13	1.39407
$786$	−1.23952e11	−0.0115838
$787$	1.50483e13	1.39830	0.699151	−	0.714974i	$-0.253561\pi$
$787$	1.50483e13	1.39830	0.699151	+	0.714974i	$0.253561\pi$
$788$	−8.60275e12	−0.794821
$789$	−4.13057e11	−0.0379458
$790$	−4.45427e12	−0.406869
$791$	6.12732e12	0.556515
$792$	0	0
$793$	6.43279e7	5.77657e−6 0
$794$	1.18492e12	0.105802
$795$	−1.16410e11	−0.0103357
$796$	1.69654e12	0.149780
$797$	−1.19561e13	−1.04961	−0.524803	−	0.851224i	$-0.675861\pi$
$797$	−1.19561e13	−1.04961	−0.524803	+	0.851224i	$0.675861\pi$
$798$	1.12817e12	0.0984829
$799$	−1.55889e12	−0.135318
$800$	−9.94651e11	−0.0858551
$801$	1.84633e12	0.158475
$802$	−1.61105e13	−1.37507
$803$	0	0
$804$	1.08332e12	0.0914335
$805$	−2.20326e12	−0.184920
$806$	−6.06090e11	−0.0505859
$807$	1.99679e12	0.165730
$808$	−5.80648e12	−0.479250
$809$	1.75894e12	0.144372	0.0721860	−	0.997391i	$-0.477002\pi$
$809$	1.75894e12	0.144372	0.0721860	+	0.997391i	$0.477002\pi$
$810$	5.64697e12	0.460928
$811$	−6.36181e12	−0.516401	−0.258200	−	0.966091i	$-0.583129\pi$
$811$	−6.36181e12	−0.516401	−0.258200	+	0.966091i	$0.583129\pi$
$812$	4.84899e12	0.391426
$813$	−8.41561e11	−0.0675582
$814$	0	0
$815$	−4.06129e12	−0.322444
$816$	−2.86026e11	−0.0225839
$817$	−2.59118e13	−2.03469
$818$	1.02119e13	0.797471
$819$	1.12422e12	0.0873119
$820$	−2.82836e12	−0.218460
$821$	1.43506e13	1.10236	0.551182	−	0.834385i	$-0.314177\pi$
$821$	1.43506e13	1.10236	0.551182	+	0.834385i	$0.314177\pi$
$822$	−5.60820e11	−0.0428450
$823$	1.32810e12	0.100909	0.0504546	−	0.998726i	$-0.483933\pi$
$823$	1.32810e12	0.100909	0.0504546	+	0.998726i	$0.483933\pi$
$824$	−5.64563e12	−0.426619
$825$	0	0
$826$	6.24969e11	0.0467141
$827$	1.96089e12	0.145774	0.0728868	−	0.997340i	$-0.476779\pi$
$827$	1.96089e12	0.145774	0.0728868	+	0.997340i	$0.476779\pi$
$828$	−2.45658e12	−0.181633
$829$	−1.02850e13	−0.756328	−0.378164	−	0.925739i	$-0.623445\pi$
$829$	−1.02850e13	−0.756328	−0.378164	+	0.925739i	$0.623445\pi$
$830$	−6.89181e12	−0.504059
$831$	−1.50653e12	−0.109591
$832$	2.26183e11	0.0163646
$833$	−3.77463e12	−0.271627
$834$	1.96135e12	0.140381
$835$	6.22446e12	0.443111
$836$	0	0
$837$	−2.67615e12	−0.188471
$838$	1.37222e13	0.961229
$839$	−2.71032e13	−1.88839	−0.944195	−	0.329388i	$-0.893158\pi$
$839$	−2.71032e13	−1.88839	−0.944195	+	0.329388i	$0.893158\pi$
$840$	4.40879e11	0.0305536
$841$	4.27408e12	0.294619
$842$	3.77297e12	0.258690
$843$	4.69370e12	0.320104
$844$	1.75634e12	0.119143
$845$	−1.04464e13	−0.704877
$846$	2.67914e12	0.179816
$847$	0	0
$848$	3.09786e11	0.0205722
$849$	4.94610e11	0.0326722
$850$	−2.69583e12	−0.177136
$851$	5.62176e12	0.367443
$852$	−3.24121e11	−0.0210731
$853$	5.71261e12	0.369457	0.184728	−	0.982790i	$-0.440859\pi$
$853$	5.71261e12	0.369457	0.184728	+	0.982790i	$0.440859\pi$
$854$	−3.33680e8	−2.14669e−5 0
$855$	−1.25553e13	−0.803491
$856$	6.32322e12	0.402538
$857$	3.25145e12	0.205904	0.102952	−	0.994686i	$-0.467171\pi$
$857$	3.25145e12	0.205904	0.102952	+	0.994686i	$0.467171\pi$
$858$	0	0
$859$	2.23819e13	1.40258	0.701289	−	0.712877i	$-0.252608\pi$
$859$	2.23819e13	1.40258	0.701289	+	0.712877i	$0.252608\pi$
$860$	−1.01261e13	−0.631247
$861$	−1.18381e12	−0.0734121
$862$	−6.18941e12	−0.381827
$863$	−1.11962e13	−0.687104	−0.343552	−	0.939134i	$-0.611630\pi$
$863$	−1.11962e13	−0.687104	−0.343552	+	0.939134i	$0.611630\pi$
$864$	9.98694e11	0.0609706
$865$	6.20646e12	0.376940
$866$	1.83305e13	1.10750
$867$	2.13860e12	0.128542
$868$	3.14389e12	0.187987
$869$	0	0
$870$	1.70762e12	0.101054
$871$	−2.32185e12	−0.136695
$872$	−7.57146e12	−0.443461
$873$	−1.18416e12	−0.0689993
$874$	5.28361e12	0.306288
$875$	1.27112e13	0.733081
$876$	−1.98624e12	−0.113963
$877$	9.15185e12	0.522409	0.261204	−	0.965283i	$-0.415880\pi$
$877$	9.15185e12	0.522409	0.261204	+	0.965283i	$0.415880\pi$
$878$	−4.70708e12	−0.267317
$879$	−1.99157e12	−0.112524
$880$	0	0
$881$	−1.95763e13	−1.09481	−0.547404	−	0.836868i	$-0.684384\pi$
$881$	−1.95763e13	−1.09481	−0.547404	+	0.836868i	$0.684384\pi$
$882$	6.48716e12	0.360949
$883$	−3.73713e12	−0.206878	−0.103439	−	0.994636i	$-0.532985\pi$
$883$	−3.73713e12	−0.206878	−0.103439	+	0.994636i	$0.532985\pi$
$884$	6.13029e11	0.0337634
$885$	2.20089e11	0.0120602
$886$	2.34729e12	0.127972
$887$	−2.31928e13	−1.25805	−0.629023	−	0.777387i	$-0.716545\pi$
$887$	−2.31928e13	−1.25805	−0.629023	+	0.777387i	$0.716545\pi$
$888$	−1.12493e12	−0.0607110
$889$	1.80292e13	0.968095
$890$	−1.55186e12	−0.0829083
$891$	0	0
$892$	1.83401e13	0.969975
$893$	−5.76228e12	−0.303224
$894$	3.59863e12	0.188416
$895$	2.00126e13	1.04256
$896$	−1.17325e12	−0.0608140
$897$	−1.66607e11	−0.00859264
$898$	1.36490e13	0.700416
$899$	1.21770e13	0.621758
$900$	4.63311e12	0.235386
$901$	8.39621e11	0.0424445
$902$	0	0
$903$	−4.23828e12	−0.212126
$904$	−5.74224e12	−0.285972
$905$	2.78860e13	1.38187
$906$	1.20473e12	0.0594038
$907$	1.82220e13	0.894051	0.447026	−	0.894521i	$-0.352483\pi$
$907$	1.82220e13	0.894051	0.447026	+	0.894521i	$0.352483\pi$
$908$	−9.73619e12	−0.475338
$909$	2.70467e13	1.31395
$910$	−9.44920e11	−0.0456782
$911$	−1.51148e13	−0.727061	−0.363530	−	0.931582i	$-0.618429\pi$
$911$	−1.51148e13	−0.727061	−0.363530	+	0.931582i	$0.618429\pi$
$912$	−1.05727e12	−0.0506066
$913$	0	0
$914$	2.85191e12	0.135169
$915$	−1.17509e8	−5.54210e−6 0
$916$	−4.52932e12	−0.212571
$917$	−1.37804e12	−0.0643574
$918$	2.70679e12	0.125795
$919$	4.01201e12	0.185542	0.0927710	−	0.995687i	$-0.470428\pi$
$919$	4.01201e12	0.185542	0.0927710	+	0.995687i	$0.470428\pi$
$920$	2.06479e12	0.0950235
$921$	2.72345e12	0.124724
$922$	−4.68700e12	−0.213602
$923$	6.94678e11	0.0315047
$924$	0	0
$925$	−1.06026e13	−0.476185
$926$	8.87762e12	0.396778
$927$	2.62975e13	1.16965
$928$	−4.54425e12	−0.201139
$929$	−3.81724e13	−1.68143	−0.840715	−	0.541479i	$-0.817865\pi$
$929$	−3.81724e13	−1.68143	−0.840715	+	0.541479i	$0.817865\pi$
$930$	1.10715e12	0.0485326
$931$	−1.39526e13	−0.608668
$932$	−1.79260e13	−0.778237
$933$	8.49654e11	0.0367092
$934$	1.79744e13	0.772846
$935$	0	0
$936$	−1.05356e12	−0.0448662
$937$	−2.28156e13	−0.966949	−0.483474	−	0.875359i	$-0.660625\pi$
$937$	−2.28156e13	−0.966949	−0.483474	+	0.875359i	$0.660625\pi$
$938$	1.20438e13	0.507985
$939$	3.16472e12	0.132843
$940$	−2.25185e12	−0.0940729
$941$	1.66829e13	0.693614	0.346807	−	0.937936i	$-0.387266\pi$
$941$	1.66829e13	0.693614	0.346807	+	0.937936i	$0.387266\pi$
$942$	−5.81777e12	−0.240729
$943$	−5.54420e12	−0.228316
$944$	−5.85691e11	−0.0240046
$945$	−4.17223e12	−0.170187
$946$	0	0
$947$	3.05001e13	1.23233	0.616163	−	0.787618i	$-0.288686\pi$
$947$	3.05001e13	1.23233	0.616163	+	0.787618i	$0.288686\pi$
$948$	1.74716e12	0.0702580
$949$	4.25705e12	0.170377
$950$	−9.96487e12	−0.396931
$951$	4.33493e12	0.171858
$952$	−3.17989e12	−0.125472
$953$	−1.15261e13	−0.452650	−0.226325	−	0.974052i	$-0.572671\pi$
$953$	−1.15261e13	−0.452650	−0.226325	+	0.974052i	$0.572671\pi$
$954$	−1.44299e12	−0.0564021
$955$	−3.54183e13	−1.37788
$956$	1.41451e13	0.547703
$957$	0	0
$958$	−2.03461e13	−0.780433
$959$	−6.23490e12	−0.238038
$960$	−4.13170e11	−0.0157003
$961$	−1.85446e13	−0.701393
$962$	2.41103e12	0.0907641
$963$	−2.94537e13	−1.10363
$964$	−9.27210e12	−0.345805
$965$	−8.97247e12	−0.333073
$966$	8.64218e11	0.0319320
$967$	1.06987e13	0.393469	0.196734	−	0.980457i	$-0.436966\pi$
$967$	1.06987e13	0.393469	0.196734	+	0.980457i	$0.436966\pi$
$968$	0	0
$969$	−2.86554e12	−0.104412
$970$	9.95299e11	0.0360978
$971$	4.98064e13	1.79804	0.899018	−	0.437911i	$-0.144282\pi$
$971$	4.98064e13	1.79804	0.899018	+	0.437911i	$0.144282\pi$
$972$	−7.01414e12	−0.252044
$973$	2.18053e13	0.779927
$974$	−2.14947e13	−0.765271
$975$	3.14220e11	0.0111356
$976$	3.12709e8	1.10310e−5 0
$977$	4.24325e13	1.48995	0.744977	−	0.667090i	$-0.232460\pi$
$977$	4.24325e13	1.48995	0.744977	+	0.667090i	$0.232460\pi$
$978$	1.59302e12	0.0556796
$979$	0	0
$980$	−5.45254e12	−0.188835
$981$	3.52681e13	1.21582
$982$	−1.96528e13	−0.674408
$983$	−3.95050e13	−1.34946	−0.674731	−	0.738063i	$-0.735741\pi$
$983$	−3.95050e13	−1.34946	−0.674731	+	0.738063i	$0.735741\pi$
$984$	1.10941e12	0.0377237
$985$	−3.36809e13	−1.14004
$986$	−1.23164e13	−0.414990
$987$	−9.42512e11	−0.0316126
$988$	2.26600e12	0.0756578
$989$	−1.98494e13	−0.659725
$990$	0	0
$991$	−1.65206e13	−0.544120	−0.272060	−	0.962280i	$-0.587705\pi$
$991$	−1.65206e13	−0.544120	−0.272060	+	0.962280i	$0.587705\pi$
$992$	−2.94630e12	−0.0965996
$993$	−1.03159e13	−0.336695
$994$	−3.60341e12	−0.117078
$995$	6.64216e12	0.214835
$996$	2.70327e12	0.0870409
$997$	2.07713e13	0.665788	0.332894	−	0.942964i	$-0.391975\pi$
$997$	2.07713e13	0.665788	0.332894	+	0.942964i	$0.391975\pi$
$998$	3.94175e12	0.125777
$999$	1.06457e13	0.338166

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	242.10.a.h.1.2	yes	3
11.10	odd	2		242.10.a.g.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
242.10.a.g.1.2	✓	3	11.10	odd	2
242.10.a.h.1.2	yes	3	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	242.a (trivial)

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} -24.5710 q^{3} +256.000 q^{4} +1002.27 q^{5} -393.136 q^{6} -4370.69 q^{7} +4096.00 q^{8} -19079.3 q^{9} +O(q^{10})\)	\(q+16.0000 q^{2} -24.5710 q^{3} +256.000 q^{4} +1002.27 q^{5} -393.136 q^{6} -4370.69 q^{7} +4096.00 q^{8} -19079.3 q^{9} +16036.4 q^{10} -6290.18 q^{12} +13481.5 q^{13} -69931.0 q^{14} -24626.9 q^{15} +65536.0 q^{16} +177624. q^{17} -305268. q^{18} +656570. q^{19} +256582. q^{20} +107392. q^{21} +502956. q^{23} -100643. q^{24} -948573. q^{25} +215705. q^{26} +952429. q^{27} -1.11890e6 q^{28} -4.33373e6 q^{29} -394030. q^{30} -2.80982e6 q^{31} +1.04858e6 q^{32} +2.84198e6 q^{34} -4.38062e6 q^{35} -4.88429e6 q^{36} +1.11774e7 q^{37} +1.05051e7 q^{38} -331255. q^{39} +4.10531e6 q^{40} -1.10232e7 q^{41} +1.71828e6 q^{42} -3.94654e7 q^{43} -1.91226e7 q^{45} +8.04730e6 q^{46} -8.77635e6 q^{47} -1.61029e6 q^{48} -2.12507e7 q^{49} -1.51772e7 q^{50} -4.36441e6 q^{51} +3.45127e6 q^{52} +4.72696e6 q^{53} +1.52389e7 q^{54} -1.79023e7 q^{56} -1.61326e7 q^{57} -6.93397e7 q^{58} -8.93693e6 q^{59} -6.30448e6 q^{60} +4771.56 q^{61} -4.49570e7 q^{62} +8.33895e7 q^{63} +1.67772e7 q^{64} +1.35122e7 q^{65} -1.72224e8 q^{67} +4.54718e7 q^{68} -1.23581e7 q^{69} -7.00900e7 q^{70} +5.15281e7 q^{71} -7.81487e7 q^{72} +3.15769e8 q^{73} +1.78839e8 q^{74} +2.33074e7 q^{75} +1.68082e8 q^{76} -5.30008e6 q^{78} -2.77760e8 q^{79} +6.56850e7 q^{80} +3.52135e8 q^{81} -1.76372e8 q^{82} -4.29761e8 q^{83} +2.74924e7 q^{84} +1.78028e8 q^{85} -6.31446e8 q^{86} +1.06484e8 q^{87} -9.67713e7 q^{89} -3.05962e8 q^{90} -5.89236e7 q^{91} +1.28757e8 q^{92} +6.90400e7 q^{93} -1.40422e8 q^{94} +6.58062e8 q^{95} -2.57646e7 q^{96} +6.20651e7 q^{97} -3.40011e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 48 q^{2} - 78 q^{3} + 768 q^{4} - 2489 q^{5} - 1248 q^{6} - 7762 q^{7} + 12288 q^{8} + 14195 q^{9}+O(q^{10}) \) 3 * q + 48 * q^2 - 78 * q^3 + 768 * q^4 - 2489 * q^5 - 1248 * q^6 - 7762 * q^7 + 12288 * q^8 + 14195 * q^9	\( 3 q + 48 q^{2} - 78 q^{3} + 768 q^{4} - 2489 q^{5} - 1248 q^{6} - 7762 q^{7} + 12288 q^{8} + 14195 q^{9} - 39824 q^{10} - 19968 q^{12} + 74607 q^{13} - 124192 q^{14} + 377754 q^{15} + 196608 q^{16} - 636327 q^{17} + 227120 q^{18} - 560130 q^{19} - 637184 q^{20} + 2310116 q^{21} + 123322 q^{23} - 319488 q^{24} + 2581436 q^{25} + 1193712 q^{26} - 2689668 q^{27} - 1987072 q^{28} - 3359849 q^{29} + 6044064 q^{30} + 3513870 q^{31} + 3145728 q^{32} - 10181232 q^{34} + 10707462 q^{35} + 3633920 q^{36} + 22954923 q^{37} - 8962080 q^{38} - 23544854 q^{39} - 10194944 q^{40} + 10760009 q^{41} + 36961856 q^{42} + 7649128 q^{43} - 93723017 q^{45} + 1973152 q^{46} - 27844070 q^{47} - 5111808 q^{48} - 33563193 q^{49} + 41302976 q^{50} + 59791958 q^{51} + 19099392 q^{52} - 954201 q^{53} - 43034688 q^{54} - 31793152 q^{56} + 5859812 q^{57} - 53757584 q^{58} + 50239440 q^{59} + 96705024 q^{60} - 306912734 q^{61} + 56221920 q^{62} - 85880946 q^{63} + 50331648 q^{64} - 186865645 q^{65} - 112012374 q^{67} - 162899712 q^{68} - 551251156 q^{69} + 171319392 q^{70} + 72167396 q^{71} + 58142720 q^{72} - 204193414 q^{73} + 367278768 q^{74} - 1150193976 q^{75} - 143393280 q^{76} - 376717664 q^{78} - 717133858 q^{79} - 163119104 q^{80} - 320766577 q^{81} + 172160144 q^{82} - 214696882 q^{83} + 591389696 q^{84} + 1782988293 q^{85} + 122386048 q^{86} + 56353690 q^{87} + 201942773 q^{89} - 1499568272 q^{90} - 802638922 q^{91} + 31570432 q^{92} - 58664924 q^{93} - 445505120 q^{94} + 2736352118 q^{95} - 81788928 q^{96} - 31860047 q^{97} - 537011088 q^{98}+O(q^{100}) \) 3 * q + 48 * q^2 - 78 * q^3 + 768 * q^4 - 2489 * q^5 - 1248 * q^6 - 7762 * q^7 + 12288 * q^8 + 14195 * q^9 - 39824 * q^10 - 19968 * q^12 + 74607 * q^13 - 124192 * q^14 + 377754 * q^15 + 196608 * q^16 - 636327 * q^17 + 227120 * q^18 - 560130 * q^19 - 637184 * q^20 + 2310116 * q^21 + 123322 * q^23 - 319488 * q^24 + 2581436 * q^25 + 1193712 * q^26 - 2689668 * q^27 - 1987072 * q^28 - 3359849 * q^29 + 6044064 * q^30 + 3513870 * q^31 + 3145728 * q^32 - 10181232 * q^34 + 10707462 * q^35 + 3633920 * q^36 + 22954923 * q^37 - 8962080 * q^38 - 23544854 * q^39 - 10194944 * q^40 + 10760009 * q^41 + 36961856 * q^42 + 7649128 * q^43 - 93723017 * q^45 + 1973152 * q^46 - 27844070 * q^47 - 5111808 * q^48 - 33563193 * q^49 + 41302976 * q^50 + 59791958 * q^51 + 19099392 * q^52 - 954201 * q^53 - 43034688 * q^54 - 31793152 * q^56 + 5859812 * q^57 - 53757584 * q^58 + 50239440 * q^59 + 96705024 * q^60 - 306912734 * q^61 + 56221920 * q^62 - 85880946 * q^63 + 50331648 * q^64 - 186865645 * q^65 - 112012374 * q^67 - 162899712 * q^68 - 551251156 * q^69 + 171319392 * q^70 + 72167396 * q^71 + 58142720 * q^72 - 204193414 * q^73 + 367278768 * q^74 - 1150193976 * q^75 - 143393280 * q^76 - 376717664 * q^78 - 717133858 * q^79 - 163119104 * q^80 - 320766577 * q^81 + 172160144 * q^82 - 214696882 * q^83 + 591389696 * q^84 + 1782988293 * q^85 + 122386048 * q^86 + 56353690 * q^87 + 201942773 * q^89 - 1499568272 * q^90 - 802638922 * q^91 + 31570432 * q^92 - 58664924 * q^93 - 445505120 * q^94 + 2736352118 * q^95 - 81788928 * q^96 - 31860047 * q^97 - 537011088 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more