LMFDB - Embedded newform 29.8.a.b.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,8,Mod(1,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	29.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:	$9.05916573904$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 1101 x^{8} - 1540 x^{7} + 405148 x^{6} + 870160 x^{5} - 54569376 x^{4} - 87078400 x^{3} + \cdots - 9372051456 $ x^10 - 1101x^8 - 1540x^7 + 405148x^6 + 870160x^5 - 54569376x^4 - 87078400x^3 + 2140673280x^2 - 1918315520x - 9372051456
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{11} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-19.0438$ of defining polynomial
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+19.0438 q^{2} +0.836957 q^{3} +234.668 q^{4} +287.010 q^{5} +15.9389 q^{6} -124.374 q^{7} +2031.37 q^{8} -2186.30 q^{9} +O(q^{10})$	\(q+19.0438 q^{2} +0.836957 q^{3} +234.668 q^{4} +287.010 q^{5} +15.9389 q^{6} -124.374 q^{7} +2031.37 q^{8} -2186.30 q^{9} +5465.77 q^{10} +5429.60 q^{11} +196.407 q^{12} +3568.37 q^{13} -2368.55 q^{14} +240.215 q^{15} +8647.53 q^{16} -1040.46 q^{17} -41635.5 q^{18} -50653.1 q^{19} +67352.0 q^{20} -104.095 q^{21} +103401. q^{22} -14861.2 q^{23} +1700.17 q^{24} +4249.65 q^{25} +67955.4 q^{26} -3660.26 q^{27} -29186.5 q^{28} -24389.0 q^{29} +4574.61 q^{30} -116764. q^{31} -95332.8 q^{32} +4544.34 q^{33} -19814.3 q^{34} -35696.4 q^{35} -513054. q^{36} -62770.9 q^{37} -964630. q^{38} +2986.57 q^{39} +583022. q^{40} -56748.3 q^{41} -1982.37 q^{42} +605447. q^{43} +1.27415e6 q^{44} -627489. q^{45} -283013. q^{46} +987536. q^{47} +7237.61 q^{48} -808074. q^{49} +80929.7 q^{50} -870.816 q^{51} +837382. q^{52} +1.67863e6 q^{53} -69705.5 q^{54} +1.55835e6 q^{55} -252648. q^{56} -42394.5 q^{57} -464460. q^{58} +1.60050e6 q^{59} +56370.7 q^{60} +105261. q^{61} -2.22363e6 q^{62} +271918. q^{63} -2.92239e6 q^{64} +1.02416e6 q^{65} +86541.8 q^{66} -3.78326e6 q^{67} -244162. q^{68} -12438.1 q^{69} -679797. q^{70} +3.67796e6 q^{71} -4.44118e6 q^{72} +719137. q^{73} -1.19540e6 q^{74} +3556.78 q^{75} -1.18867e7 q^{76} -675299. q^{77} +56875.8 q^{78} +1.69002e6 q^{79} +2.48193e6 q^{80} +4.77837e6 q^{81} -1.08071e6 q^{82} +2.75859e6 q^{83} -24427.8 q^{84} -298621. q^{85} +1.15300e7 q^{86} -20412.5 q^{87} +1.10295e7 q^{88} +1.13447e7 q^{89} -1.19498e7 q^{90} -443811. q^{91} -3.48744e6 q^{92} -97726.3 q^{93} +1.88065e7 q^{94} -1.45379e7 q^{95} -79789.4 q^{96} -1.45314e7 q^{97} -1.53888e7 q^{98} -1.18707e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 80 q^{3} + 922 q^{4} + 180 q^{5} + 358 q^{6} + 1040 q^{7} - 4620 q^{8} + 10986 q^{9}+O(q^{10}) $ 10 * q + 80 * q^3 + 922 * q^4 + 180 * q^5 + 358 * q^6 + 1040 * q^7 - 4620 * q^8 + 10986 * q^9	\( 10 q + 80 q^{3} + 922 q^{4} + 180 q^{5} + 358 q^{6} + 1040 q^{7} - 4620 q^{8} + 10986 q^{9} + 8496 q^{10} + 7384 q^{11} + 49720 q^{12} + 20820 q^{13} + 50976 q^{14} + 43516 q^{15} + 122082 q^{16} - 11620 q^{17} + 66060 q^{18} + 75068 q^{19} - 42914 q^{20} + 51480 q^{21} - 36950 q^{22} + 62040 q^{23} - 205942 q^{24} + 261022 q^{25} - 201528 q^{26} - 28060 q^{27} - 24980 q^{28} - 243890 q^{29} - 1284894 q^{30} + 200600 q^{31} - 1761460 q^{32} - 1068000 q^{33} - 503932 q^{34} + 107528 q^{35} - 26300 q^{36} - 367740 q^{37} + 766880 q^{38} + 392692 q^{39} - 865000 q^{40} + 932764 q^{41} - 2058060 q^{42} + 1443560 q^{43} - 1325912 q^{44} + 4245684 q^{45} + 1760460 q^{46} - 286960 q^{47} + 3187120 q^{48} + 4713194 q^{49} - 3682652 q^{50} + 1451016 q^{51} + 2560210 q^{52} + 3953220 q^{53} - 3147534 q^{54} + 3981316 q^{55} + 2082464 q^{56} + 2050640 q^{57} + 6712320 q^{59} + 7476756 q^{60} + 1905196 q^{61} - 8048490 q^{62} + 3643800 q^{63} + 8445458 q^{64} + 4667544 q^{65} - 12425580 q^{66} - 2718200 q^{67} - 17699740 q^{68} + 1109064 q^{69} - 30441624 q^{70} + 3447736 q^{71} - 22466840 q^{72} - 2554460 q^{73} - 4214584 q^{74} + 1088084 q^{75} - 8294848 q^{76} - 3967800 q^{77} - 24809970 q^{78} + 4187744 q^{79} - 17715290 q^{80} + 5161402 q^{81} + 7020500 q^{82} + 3498720 q^{83} + 22947224 q^{84} + 1817072 q^{85} - 361638 q^{86} - 1951120 q^{87} + 15118470 q^{88} - 303268 q^{89} - 28959160 q^{90} + 27215080 q^{91} - 10783380 q^{92} + 1097360 q^{93} + 55641726 q^{94} - 8810536 q^{95} - 53327238 q^{96} + 4908620 q^{97} + 40120080 q^{98} - 14408716 q^{99}+O(q^{100}) \) 10 * q + 80 * q^3 + 922 * q^4 + 180 * q^5 + 358 * q^6 + 1040 * q^7 - 4620 * q^8 + 10986 * q^9 + 8496 * q^10 + 7384 * q^11 + 49720 * q^12 + 20820 * q^13 + 50976 * q^14 + 43516 * q^15 + 122082 * q^16 - 11620 * q^17 + 66060 * q^18 + 75068 * q^19 - 42914 * q^20 + 51480 * q^21 - 36950 * q^22 + 62040 * q^23 - 205942 * q^24 + 261022 * q^25 - 201528 * q^26 - 28060 * q^27 - 24980 * q^28 - 243890 * q^29 - 1284894 * q^30 + 200600 * q^31 - 1761460 * q^32 - 1068000 * q^33 - 503932 * q^34 + 107528 * q^35 - 26300 * q^36 - 367740 * q^37 + 766880 * q^38 + 392692 * q^39 - 865000 * q^40 + 932764 * q^41 - 2058060 * q^42 + 1443560 * q^43 - 1325912 * q^44 + 4245684 * q^45 + 1760460 * q^46 - 286960 * q^47 + 3187120 * q^48 + 4713194 * q^49 - 3682652 * q^50 + 1451016 * q^51 + 2560210 * q^52 + 3953220 * q^53 - 3147534 * q^54 + 3981316 * q^55 + 2082464 * q^56 + 2050640 * q^57 + 6712320 * q^59 + 7476756 * q^60 + 1905196 * q^61 - 8048490 * q^62 + 3643800 * q^63 + 8445458 * q^64 + 4667544 * q^65 - 12425580 * q^66 - 2718200 * q^67 - 17699740 * q^68 + 1109064 * q^69 - 30441624 * q^70 + 3447736 * q^71 - 22466840 * q^72 - 2554460 * q^73 - 4214584 * q^74 + 1088084 * q^75 - 8294848 * q^76 - 3967800 * q^77 - 24809970 * q^78 + 4187744 * q^79 - 17715290 * q^80 + 5161402 * q^81 + 7020500 * q^82 + 3498720 * q^83 + 22947224 * q^84 + 1817072 * q^85 - 361638 * q^86 - 1951120 * q^87 + 15118470 * q^88 - 303268 * q^89 - 28959160 * q^90 + 27215080 * q^91 - 10783380 * q^92 + 1097360 * q^93 + 55641726 * q^94 - 8810536 * q^95 - 53327238 * q^96 + 4908620 * q^97 + 40120080 * q^98 - 14408716 * 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 $

$2$	19.0438	1.68325	0.841627	−	0.540060i	$-0.181598\pi$
$2$	19.0438	1.68325	0.841627	+	0.540060i	$0.181598\pi$
$3$	0.836957	0.0178969	0.00894847	−	0.999960i	$-0.497152\pi$
$3$	0.836957	0.0178969	0.00894847	+	0.999960i	$0.497152\pi$
$4$	234.668	1.83334
$5$	287.010	1.02684	0.513419	−	0.858138i	$-0.328379\pi$
$5$	287.010	1.02684	0.513419	+	0.858138i	$0.328379\pi$
$6$	15.9389	0.0301251
$7$	−124.374	−0.137052	−0.0685259	−	0.997649i	$-0.521830\pi$
$7$	−124.374	−0.137052	−0.0685259	+	0.997649i	$0.521830\pi$
$8$	2031.37	1.40273
$9$	−2186.30	−0.999680
$10$	5465.77	1.72843
$11$	5429.60	1.22997	0.614984	−	0.788540i	$-0.289162\pi$
$11$	5429.60	1.22997	0.614984	+	0.788540i	$0.289162\pi$
$12$	196.407	0.0328112
$13$	3568.37	0.450472	0.225236	−	0.974304i	$-0.427685\pi$
$13$	3568.37	0.450472	0.225236	+	0.974304i	$0.427685\pi$
$14$	−2368.55	−0.230693
$15$	240.215	0.0183772
$16$	8647.53	0.527803
$17$	−1040.46	−0.0513632	−0.0256816	−	0.999670i	$-0.508176\pi$
$17$	−1040.46	−0.0513632	−0.0256816	+	0.999670i	$0.508176\pi$
$18$	−41635.5	−1.68271
$19$	−50653.1	−1.69422	−0.847108	−	0.531421i	$-0.821658\pi$
$19$	−50653.1	−1.69422	−0.847108	+	0.531421i	$0.821658\pi$
$20$	67352.0	1.88255
$21$	−104.095	−0.00245281
$22$	103401.	2.07035
$23$	−14861.2	−0.254686	−0.127343	−	0.991859i	$-0.540645\pi$
$23$	−14861.2	−0.254686	−0.127343	+	0.991859i	$0.540645\pi$
$24$	1700.17	0.0251045
$25$	4249.65	0.0543955
$26$	67955.4	0.758259
$27$	−3660.26	−0.0357881
$28$	−29186.5	−0.251263
$29$	−24389.0	−0.185695
$29$	−24389.0	−0.185695
$30$	4574.61	0.0309336
$31$	−116764.	−0.703951	−0.351976	−	0.936009i	$-0.614490\pi$
$31$	−116764.	−0.703951	−0.351976	+	0.936009i	$0.614490\pi$
$32$	−95332.8	−0.514301
$33$	4544.34	0.0220127
$34$	−19814.3	−0.0864574
$35$	−35696.4	−0.140730
$36$	−513054.	−1.83276
$37$	−62770.9	−0.203729	−0.101864	−	0.994798i	$-0.532481\pi$
$37$	−62770.9	−0.203729	−0.101864	+	0.994798i	$0.532481\pi$
$38$	−964630.	−2.85179
$39$	2986.57	0.00806207
$40$	583022.	1.44037
$41$	−56748.3	−0.128591	−0.0642954	−	0.997931i	$-0.520480\pi$
$41$	−56748.3	−0.128591	−0.0642954	+	0.997931i	$0.520480\pi$
$42$	−1982.37	−0.00412870
$43$	605447.	1.16128	0.580640	−	0.814161i	$-0.302803\pi$
$43$	605447.	1.16128	0.580640	+	0.814161i	$0.302803\pi$
$44$	1.27415e6	2.25495
$45$	−627489.	−1.02651
$46$	−283013.	−0.428701
$47$	987536.	1.38743	0.693714	−	0.720250i	$-0.255973\pi$
$47$	987536.	1.38743	0.693714	+	0.720250i	$0.255973\pi$
$48$	7237.61	0.00944606
$49$	−808074.	−0.981217
$50$	80929.7	0.0915615
$51$	−870.816	−0.000919244 0
$52$	837382.	0.825870
$53$	1.67863e6	1.54878	0.774388	−	0.632711i	$-0.218058\pi$
$53$	1.67863e6	1.54878	0.774388	+	0.632711i	$0.218058\pi$
$54$	−69705.5	−0.0602405
$55$	1.55835e6	1.26298
$56$	−252648.	−0.192246
$57$	−42394.5	−0.0303213
$58$	−464460.	−0.312572
$59$	1.60050e6	1.01455	0.507276	−	0.861784i	$-0.330652\pi$
$59$	1.60050e6	1.01455	0.507276	+	0.861784i	$0.330652\pi$
$60$	56370.7	0.0336918
$61$	105261.	0.0593762	0.0296881	−	0.999559i	$-0.490549\pi$
$61$	105261.	0.0593762	0.0296881	+	0.999559i	$0.490549\pi$
$62$	−2.22363e6	−1.18493
$63$	271918.	0.137008
$64$	−2.92239e6	−1.39350
$65$	1.02416e6	0.462562
$66$	86541.8	0.0370529
$67$	−3.78326e6	−1.53676	−0.768378	−	0.639996i	$-0.778936\pi$
$67$	−3.78326e6	−1.53676	−0.768378	+	0.639996i	$0.778936\pi$
$68$	−244162.	−0.0941664
$69$	−12438.1	−0.00455810
$70$	−679797.	−0.236884
$71$	3.67796e6	1.21956	0.609779	−	0.792572i	$-0.291258\pi$
$71$	3.67796e6	1.21956	0.609779	+	0.792572i	$0.291258\pi$
$72$	−4.44118e6	−1.40228
$73$	719137.	0.216362	0.108181	−	0.994131i	$-0.465497\pi$
$73$	719137.	0.216362	0.108181	+	0.994131i	$0.465497\pi$
$74$	−1.19540e6	−0.342927
$75$	3556.78	0.000973514 0
$76$	−1.18867e7	−3.10608
$77$	−675299.	−0.168569
$78$	56875.8	0.0135705
$79$	1.69002e6	0.385654	0.192827	−	0.981233i	$-0.438234\pi$
$79$	1.69002e6	0.385654	0.192827	+	0.981233i	$0.438234\pi$
$80$	2.48193e6	0.541968
$81$	4.77837e6	0.999039
$82$	−1.08071e6	−0.216451
$83$	2.75859e6	0.529558	0.264779	−	0.964309i	$-0.414701\pi$
$83$	2.75859e6	0.529558	0.264779	+	0.964309i	$0.414701\pi$
$84$	−24427.8	−0.00449684
$85$	−298621.	−0.0527417
$86$	1.15300e7	1.95473
$87$	−20412.5	−0.00332338
$88$	1.10295e7	1.72531
$89$	1.13447e7	1.70580	0.852898	−	0.522077i	$-0.174843\pi$
$89$	1.13447e7	1.70580	0.852898	+	0.522077i	$0.174843\pi$
$90$	−1.19498e7	−1.72787
$91$	−443811.	−0.0617380
$92$	−3.48744e6	−0.466927
$93$	−97726.3	−0.0125986
$94$	1.88065e7	2.33539
$95$	−1.45379e7	−1.73968
$96$	−79789.4	−0.00920441
$97$	−1.45314e7	−1.61661	−0.808304	−	0.588765i	$-0.799614\pi$
$97$	−1.45314e7	−1.61661	−0.808304	+	0.588765i	$0.799614\pi$
$98$	−1.53888e7	−1.65164
$99$	−1.18707e7	−1.22957
$100$	997257.	0.0997257
$101$	−7.18921e6	−0.694315	−0.347157	−	0.937807i	$-0.612853\pi$
$101$	−7.18921e6	−0.694315	−0.347157	+	0.937807i	$0.612853\pi$
$102$	−16583.7	−0.00154732
$103$	1.57131e7	1.41687	0.708437	−	0.705774i	$-0.249400\pi$
$103$	1.57131e7	1.41687	0.708437	+	0.705774i	$0.249400\pi$
$104$	7.24866e6	0.631890
$105$	−29876.4	−0.00251863
$106$	3.19675e7	2.60698
$107$	−1.80106e7	−1.42130	−0.710649	−	0.703547i	$-0.751598\pi$
$107$	−1.80106e7	−1.42130	−0.710649	+	0.703547i	$0.751598\pi$
$108$	−858946.	−0.0656119
$109$	−1.74463e7	−1.29036	−0.645178	−	0.764032i	$-0.723217\pi$
$109$	−1.74463e7	−1.29036	−0.645178	+	0.764032i	$0.723217\pi$
$110$	2.96770e7	2.12591
$111$	−52536.5	−0.00364612
$112$	−1.07552e6	−0.0723364
$113$	1.65701e7	1.08031	0.540157	−	0.841564i	$-0.318365\pi$
$113$	1.65701e7	1.08031	0.540157	+	0.841564i	$0.318365\pi$
$114$	−807354.	−0.0510384
$115$	−4.26530e6	−0.261521
$116$	−5.72332e6	−0.340443
$117$	−7.80152e6	−0.450328
$118$	3.04797e7	1.70775
$119$	129405.	0.00703942
$120$	487964.	0.0257783
$121$	9.99343e6	0.512821
$122$	2.00457e6	0.0999452
$123$	−47495.9	−0.00230138
$124$	−2.74007e7	−1.29058
$125$	−2.12030e7	−0.970982
$126$	5.17836e6	0.230619
$127$	3.24510e7	1.40577	0.702886	−	0.711303i	$-0.251894\pi$
$127$	3.24510e7	1.40577	0.702886	+	0.711303i	$0.251894\pi$
$128$	−4.34508e7	−1.83132
$129$	506733.	0.0207833
$130$	1.95039e7	0.778609
$131$	−9.21009e6	−0.357944	−0.178972	−	0.983854i	$-0.557277\pi$
$131$	−9.21009e6	−0.357944	−0.178972	+	0.983854i	$0.557277\pi$
$132$	1.06641e6	0.0403567
$133$	6.29991e6	0.232195
$134$	−7.20479e7	−2.58675
$135$	−1.05053e6	−0.0367486
$136$	−2.11355e6	−0.0720486
$137$	−5.63936e7	−1.87373	−0.936867	−	0.349687i	$-0.886288\pi$
$137$	−5.63936e7	−1.87373	−0.936867	+	0.349687i	$0.886288\pi$
$138$	−236870.	−0.00767244
$139$	3.59342e7	1.13490	0.567448	−	0.823409i	$-0.307931\pi$
$139$	3.59342e7	1.13490	0.567448	+	0.823409i	$0.307931\pi$
$140$	−8.37680e6	−0.258006
$141$	826525.	0.0248307
$142$	7.00424e7	2.05283
$143$	1.93748e7	0.554066
$144$	−1.89061e7	−0.527634
$145$	−6.99988e6	−0.190679
$146$	1.36951e7	0.364193
$147$	−676323.	−0.0175608
$148$	−1.47303e7	−0.373505
$149$	−1.44990e7	−0.359076	−0.179538	−	0.983751i	$-0.557460\pi$
$149$	−1.44990e7	−0.359076	−0.179538	+	0.983751i	$0.557460\pi$
$150$	67734.7	0.00163867
$151$	−6.72088e6	−0.158857	−0.0794286	−	0.996841i	$-0.525310\pi$
$151$	−6.72088e6	−0.158857	−0.0794286	+	0.996841i	$0.525310\pi$
$152$	−1.02895e8	−2.37652
$153$	2.27475e6	0.0513468
$154$	−1.28603e7	−0.283745
$155$	−3.35124e7	−0.722844
$156$	700852.	0.0147805
$157$	5.45966e7	1.12594	0.562972	−	0.826476i	$-0.309658\pi$
$157$	5.45966e7	1.12594	0.562972	+	0.826476i	$0.309658\pi$
$158$	3.21845e7	0.649153
$159$	1.40494e6	0.0277184
$160$	−2.73614e7	−0.528103
$161$	1.84833e6	0.0349052
$162$	9.09986e7	1.68164
$163$	−2.24322e7	−0.405709	−0.202855	−	0.979209i	$-0.565022\pi$
$163$	−2.24322e7	−0.405709	−0.202855	+	0.979209i	$0.565022\pi$
$164$	−1.33170e7	−0.235751
$165$	1.30427e6	0.0226034
$166$	5.25341e7	0.891380
$167$	9.01363e7	1.49759	0.748794	−	0.662803i	$-0.230633\pi$
$167$	9.01363e7	1.49759	0.748794	+	0.662803i	$0.230633\pi$
$168$	−211456.	−0.00344062
$169$	−5.00153e7	−0.797075
$170$	−5.68689e6	−0.0887777
$171$	1.10743e8	1.69367
$172$	1.42079e8	2.12902
$173$	5.38454e7	0.790655	0.395327	−	0.918540i	$-0.370631\pi$
$173$	5.38454e7	0.790655	0.395327	+	0.918540i	$0.370631\pi$
$174$	−388733.	−0.00559409
$175$	−528544.	−0.00745501
$176$	4.69526e7	0.649181
$177$	1.33955e6	0.0181574
$178$	2.16046e8	2.87129
$179$	−1.86781e7	−0.243415	−0.121707	−	0.992566i	$-0.538837\pi$
$179$	−1.86781e7	−0.243415	−0.121707	+	0.992566i	$0.538837\pi$
$180$	−1.47252e8	−1.88194
$181$	−1.29869e8	−1.62790	−0.813952	−	0.580931i	$-0.802688\pi$
$181$	−1.29869e8	−1.62790	−0.813952	+	0.580931i	$0.802688\pi$
$182$	−8.45186e6	−0.103921
$183$	88098.8	0.00106265
$184$	−3.01884e7	−0.357255
$185$	−1.80159e7	−0.209196
$186$	−1.86108e6	−0.0212066
$187$	−5.64926e6	−0.0631751
$188$	2.31743e8	2.54363
$189$	455240.	0.00490483
$190$	−2.76858e8	−2.92833
$191$	−7.18882e7	−0.746519	−0.373259	−	0.927727i	$-0.621760\pi$
$191$	−7.18882e7	−0.746519	−0.373259	+	0.927727i	$0.621760\pi$
$192$	−2.44591e6	−0.0249394
$193$	−7.68746e7	−0.769719	−0.384859	−	0.922975i	$-0.625750\pi$
$193$	−7.68746e7	−0.769719	−0.384859	+	0.922975i	$0.625750\pi$
$194$	−2.76733e8	−2.72116
$195$	857175.	0.00827844
$196$	−1.89629e8	−1.79891
$197$	7.82417e7	0.729132	0.364566	−	0.931177i	$-0.381217\pi$
$197$	7.82417e7	0.729132	0.364566	+	0.931177i	$0.381217\pi$
$198$	−2.26065e8	−2.06968
$199$	1.59291e8	1.43287	0.716435	−	0.697654i	$-0.245773\pi$
$199$	1.59291e8	1.43287	0.716435	+	0.697654i	$0.245773\pi$
$200$	8.63260e6	0.0763021
$201$	−3.16643e6	−0.0275032
$202$	−1.36910e8	−1.16871
$203$	3.03335e6	0.0254499
$204$	−204353.	−0.00168529
$205$	−1.62873e7	−0.132042
$206$	2.99238e8	2.38496
$207$	3.24909e7	0.254604
$208$	3.08576e7	0.237761
$209$	−2.75026e8	−2.08383
$210$	−568961.	−0.00423950
$211$	8.79435e7	0.644488	0.322244	−	0.946657i	$-0.395563\pi$
$211$	8.79435e7	0.644488	0.322244	+	0.946657i	$0.395563\pi$
$212$	3.93920e8	2.83944
$213$	3.07829e6	0.0218263
$214$	−3.42991e8	−2.39240
$215$	1.73769e8	1.19245
$216$	−7.43533e6	−0.0502010
$217$	1.45223e7	0.0964778
$218$	−3.32244e8	−2.17200
$219$	601886.	0.00387222
$220$	3.65695e8	2.31547
$221$	−3.71273e6	−0.0231377
$222$	−1.00050e6	−0.00613734
$223$	1.55197e8	0.937166	0.468583	−	0.883419i	$-0.344765\pi$
$223$	1.55197e8	0.937166	0.468583	+	0.883419i	$0.344765\pi$
$224$	1.18569e7	0.0704859
$225$	−9.29101e6	−0.0543781
$226$	3.15558e8	1.81844
$227$	−2.60816e8	−1.47994	−0.739968	−	0.672642i	$-0.765160\pi$
$227$	−2.60816e8	−1.47994	−0.739968	+	0.672642i	$0.765160\pi$
$228$	−9.94862e6	−0.0555893
$229$	2.08807e7	0.114900	0.0574501	−	0.998348i	$-0.481703\pi$
$229$	2.08807e7	0.114900	0.0574501	+	0.998348i	$0.481703\pi$
$230$	−8.12276e7	−0.440206
$231$	−565196.	−0.00301687
$232$	−4.95430e7	−0.260480
$233$	−3.99218e7	−0.206759	−0.103380	−	0.994642i	$-0.532966\pi$
$233$	−3.99218e7	−0.206759	−0.103380	+	0.994642i	$0.532966\pi$
$234$	−1.48571e8	−0.758016
$235$	2.83433e8	1.42466
$236$	3.75587e8	1.86002
$237$	1.41448e6	0.00690202
$238$	2.46437e6	0.0118491
$239$	−3.19559e8	−1.51411	−0.757057	−	0.653349i	$-0.773363\pi$
$239$	−3.19559e8	−1.51411	−0.757057	+	0.653349i	$0.773363\pi$
$240$	2.07726e6	0.00969957
$241$	2.89494e8	1.33223	0.666117	−	0.745847i	$-0.267955\pi$
$241$	2.89494e8	1.33223	0.666117	+	0.745847i	$0.267955\pi$
$242$	1.90313e8	0.863208
$243$	1.20043e7	0.0536679
$244$	2.47013e7	0.108857
$245$	−2.31925e8	−1.00755
$246$	−904504.	−0.00387381
$247$	−1.80749e8	−0.763197
$248$	−2.37190e8	−0.987452
$249$	2.30882e6	0.00947746
$250$	−4.03786e8	−1.63441
$251$	2.65544e8	1.05993	0.529967	−	0.848018i	$-0.322204\pi$
$251$	2.65544e8	1.05993	0.529967	+	0.848018i	$0.322204\pi$
$252$	6.38104e7	0.251182
$253$	−8.06902e7	−0.313256
$254$	6.17991e8	2.36627
$255$	−249933.	−0.000943915 0
$256$	−4.53406e8	−1.68907
$257$	1.45081e8	0.533145	0.266573	−	0.963815i	$-0.414109\pi$
$257$	1.45081e8	0.533145	0.266573	+	0.963815i	$0.414109\pi$
$258$	9.65015e6	0.0349836
$259$	7.80704e6	0.0279214
$260$	2.40337e8	0.848034
$261$	5.33217e7	0.185636
$262$	−1.75396e8	−0.602510
$263$	3.55310e8	1.20438	0.602189	−	0.798354i	$-0.294296\pi$
$263$	3.55310e8	1.20438	0.602189	+	0.798354i	$0.294296\pi$
$264$	9.23123e6	0.0308778
$265$	4.81783e8	1.59034
$266$	1.19974e8	0.390844
$267$	9.49501e6	0.0305285
$268$	−8.87811e8	−2.81740
$269$	−3.23141e8	−1.01218	−0.506091	−	0.862480i	$-0.668910\pi$
$269$	−3.23141e8	−1.01218	−0.506091	+	0.862480i	$0.668910\pi$
$270$	−2.00062e7	−0.0618572
$271$	3.16979e7	0.0967472	0.0483736	−	0.998829i	$-0.484596\pi$
$271$	3.16979e7	0.0967472	0.0483736	+	0.998829i	$0.484596\pi$
$272$	−8.99737e6	−0.0271097
$273$	−371450.	−0.00110492
$274$	−1.07395e9	−3.15397
$275$	2.30739e7	0.0669048
$276$	−2.91883e6	−0.00835656
$277$	−1.44682e6	−0.00409012	−0.00204506	−	0.999998i	$-0.500651\pi$
$277$	−1.44682e6	−0.00409012	−0.00204506	+	0.999998i	$0.500651\pi$
$278$	6.84325e8	1.91032
$279$	2.55281e8	0.703726
$280$	−7.25125e7	−0.197406
$281$	−4.42261e8	−1.18907	−0.594534	−	0.804070i	$-0.702664\pi$
$281$	−4.42261e8	−1.18907	−0.594534	+	0.804070i	$0.702664\pi$
$282$	1.57402e7	0.0417964
$283$	−2.61084e7	−0.0684743	−0.0342372	−	0.999414i	$-0.510900\pi$
$283$	−2.61084e7	−0.0684743	−0.0342372	+	0.999414i	$0.510900\pi$
$284$	8.63098e8	2.23587
$285$	−1.21676e7	−0.0311350
$286$	3.68971e8	0.932634
$287$	7.05799e6	0.0176236
$288$	2.08426e8	0.514136
$289$	−4.09256e8	−0.997362
$290$	−1.33305e8	−0.320961
$291$	−1.21621e7	−0.0289323
$292$	1.68758e8	0.396666
$293$	−2.70813e8	−0.628974	−0.314487	−	0.949262i	$-0.601833\pi$
$293$	−2.70813e8	−0.628974	−0.314487	+	0.949262i	$0.601833\pi$
$294$	−1.28798e7	−0.0295592
$295$	4.59360e8	1.04178
$296$	−1.27511e8	−0.285776
$297$	−1.98738e7	−0.0440183
$298$	−2.76117e8	−0.604416
$299$	−5.30301e7	−0.114729
$300$	834661.	0.00178478
$301$	−7.53016e7	−0.159155
$302$	−1.27991e8	−0.267397
$303$	−6.01706e6	−0.0124261
$304$	−4.38024e8	−0.894212
$305$	3.02109e7	0.0609697
$306$	4.33199e7	0.0864297
$307$	4.32282e7	0.0852674	0.0426337	−	0.999091i	$-0.486425\pi$
$307$	4.32282e7	0.0852674	0.0426337	+	0.999091i	$0.486425\pi$
$308$	−1.58471e8	−0.309045
$309$	1.31512e7	0.0253577
$310$	−6.38204e8	−1.21673
$311$	−1.47802e8	−0.278624	−0.139312	−	0.990249i	$-0.544489\pi$
$311$	−1.47802e8	−0.278624	−0.139312	+	0.990249i	$0.544489\pi$
$312$	6.06682e6	0.0113089
$313$	−4.47020e8	−0.823990	−0.411995	−	0.911186i	$-0.635168\pi$
$313$	−4.47020e8	−0.823990	−0.411995	+	0.911186i	$0.635168\pi$
$314$	1.03973e9	1.89525
$315$	7.80431e7	0.140685
$316$	3.96594e8	0.707036
$317$	−8.05083e8	−1.41949	−0.709746	−	0.704457i	$-0.751190\pi$
$317$	−8.05083e8	−1.41949	−0.709746	+	0.704457i	$0.751190\pi$
$318$	2.67554e7	0.0466570
$319$	−1.32423e8	−0.228399
$320$	−8.38753e8	−1.43090
$321$	−1.50741e7	−0.0254369
$322$	3.51994e7	0.0587543
$323$	5.27023e7	0.0870204
$324$	1.12133e9	1.83158
$325$	1.51643e7	0.0245037
$326$	−4.27195e8	−0.682912
$327$	−1.46018e7	−0.0230934
$328$	−1.15277e8	−0.180378
$329$	−1.22823e8	−0.190150
$330$	2.48383e7	0.0380473
$331$	−9.07105e8	−1.37486	−0.687432	−	0.726249i	$-0.741262\pi$
$331$	−9.07105e8	−1.37486	−0.687432	+	0.726249i	$0.741262\pi$
$332$	6.47352e8	0.970861
$333$	1.37236e8	0.203663
$334$	1.71654e9	2.52082
$335$	−1.08583e9	−1.57800
$336$	−900167.	−0.00129460
$337$	−8.31707e8	−1.18377	−0.591883	−	0.806024i	$-0.701615\pi$
$337$	−8.31707e8	−1.18377	−0.591883	+	0.806024i	$0.701615\pi$
$338$	−9.52483e8	−1.34168
$339$	1.38684e7	0.0193343
$340$	−7.00768e7	−0.0966936
$341$	−6.33982e8	−0.865837
$342$	2.10897e9	2.85088
$343$	2.02930e8	0.271529
$344$	1.22989e9	1.62896
$345$	−3.56987e6	−0.00468043
$346$	1.02542e9	1.33087
$347$	1.08397e9	1.39272	0.696358	−	0.717694i	$-0.254803\pi$
$347$	1.08397e9	1.39272	0.696358	+	0.717694i	$0.254803\pi$
$348$	−4.79017e6	−0.00609289
$349$	1.48607e9	1.87132	0.935662	−	0.352897i	$-0.114803\pi$
$349$	1.48607e9	1.87132	0.935662	+	0.352897i	$0.114803\pi$
$350$	−1.00655e7	−0.0125487
$351$	−1.30612e7	−0.0161216
$352$	−5.17619e8	−0.632573
$353$	−7.07613e8	−0.856218	−0.428109	−	0.903727i	$-0.640820\pi$
$353$	−7.07613e8	−0.856218	−0.428109	+	0.903727i	$0.640820\pi$
$354$	2.55102e7	0.0305635
$355$	1.05561e9	1.25229
$356$	2.66223e9	3.12731
$357$	108307.	0.000125984 0
$358$	−3.55703e8	−0.409729
$359$	1.63812e8	0.186859	0.0934296	−	0.995626i	$-0.470217\pi$
$359$	1.63812e8	0.186859	0.0934296	+	0.995626i	$0.470217\pi$
$360$	−1.27466e9	−1.43991
$361$	1.67187e9	1.87037
$362$	−2.47320e9	−2.74018
$363$	8.36407e6	0.00917792
$364$	−1.04148e8	−0.113187
$365$	2.06399e8	0.222169
$366$	1.67774e6	0.00178871
$367$	−8.55095e7	−0.0902991	−0.0451495	−	0.998980i	$-0.514376\pi$
$367$	−8.55095e7	−0.0902991	−0.0451495	+	0.998980i	$0.514376\pi$
$368$	−1.28512e8	−0.134424
$369$	1.24069e8	0.128550
$370$	−3.43091e8	−0.352130
$371$	−2.08777e8	−0.212263
$372$	−2.29332e7	−0.0230975
$373$	−1.92616e9	−1.92182	−0.960908	−	0.276869i	$-0.910703\pi$
$373$	−1.92616e9	−1.92182	−0.960908	+	0.276869i	$0.910703\pi$
$374$	−1.07584e8	−0.106340
$375$	−1.77460e7	−0.0173776
$376$	2.00605e9	1.94618
$377$	−8.70289e7	−0.0836506
$378$	8.66951e6	0.00825607
$379$	1.21692e9	1.14822	0.574109	−	0.818779i	$-0.305349\pi$
$379$	1.21692e9	1.14822	0.574109	+	0.818779i	$0.305349\pi$
$380$	−3.41159e9	−3.18944
$381$	2.71601e7	0.0251590
$382$	−1.36903e9	−1.25658
$383$	3.81325e8	0.346817	0.173408	−	0.984850i	$-0.444522\pi$
$383$	3.81325e8	0.346817	0.173408	+	0.984850i	$0.444522\pi$
$384$	−3.63665e7	−0.0327749
$385$	−1.93817e8	−0.173093
$386$	−1.46399e9	−1.29563
$387$	−1.32369e9	−1.16091
$388$	−3.41004e9	−2.96380
$389$	−4.02109e8	−0.346354	−0.173177	−	0.984891i	$-0.555403\pi$
$389$	−4.02109e8	−0.346354	−0.173177	+	0.984891i	$0.555403\pi$
$390$	1.63239e7	0.0139347
$391$	1.54624e7	0.0130815
$392$	−1.64149e9	−1.37638
$393$	−7.70845e6	−0.00640609
$394$	1.49002e9	1.22731
$395$	4.85053e8	0.396004
$396$	−2.78568e9	−2.25423
$397$	1.66353e9	1.33433	0.667166	−	0.744909i	$-0.267507\pi$
$397$	1.66353e9	1.33433	0.667166	+	0.744909i	$0.267507\pi$
$398$	3.03352e9	2.41188
$399$	5.27275e6	0.00415558
$400$	3.67490e7	0.0287101
$401$	1.21705e9	0.942549	0.471274	−	0.881987i	$-0.343794\pi$
$401$	1.21705e9	0.942549	0.471274	+	0.881987i	$0.343794\pi$
$402$	−6.03010e7	−0.0462949
$403$	−4.16656e8	−0.317110
$404$	−1.68708e9	−1.27292
$405$	1.37144e9	1.02585
$406$	5.77666e7	0.0428386
$407$	−3.40821e8	−0.250580
$408$	−1.76895e6	−0.00128945
$409$	−4.54192e8	−0.328253	−0.164126	−	0.986439i	$-0.552480\pi$
$409$	−4.54192e8	−0.328253	−0.164126	+	0.986439i	$0.552480\pi$
$410$	−3.10173e8	−0.222260
$411$	−4.71990e7	−0.0335341
$412$	3.68736e9	2.59762
$413$	−1.99060e8	−0.139046
$414$	6.18752e8	0.428564
$415$	7.91741e8	0.543770
$416$	−3.40182e8	−0.231678
$417$	3.00754e7	0.0203112
$418$	−5.23756e9	−3.50761
$419$	1.37516e9	0.913282	0.456641	−	0.889651i	$-0.349052\pi$
$419$	1.37516e9	0.913282	0.456641	+	0.889651i	$0.349052\pi$
$420$	−7.01102e6	−0.00461752
$421$	2.30644e9	1.50645	0.753227	−	0.657761i	$-0.228496\pi$
$421$	2.30644e9	1.50645	0.753227	+	0.657761i	$0.228496\pi$
$422$	1.67478e9	1.08484
$423$	−2.15905e9	−1.38698
$424$	3.40991e9	2.17251
$425$	−4.42157e6	−0.00279393
$426$	5.86225e7	0.0367393
$427$	−1.30917e7	−0.00813762
$428$	−4.22651e9	−2.60573
$429$	1.62159e7	0.00991609
$430$	3.30924e9	2.00719
$431$	1.16371e9	0.700122	0.350061	−	0.936727i	$-0.386161\pi$
$431$	1.16371e9	0.700122	0.350061	+	0.936727i	$0.386161\pi$
$432$	−3.16522e7	−0.0188891
$433$	−5.10224e8	−0.302032	−0.151016	−	0.988531i	$-0.548255\pi$
$433$	−5.10224e8	−0.302032	−0.151016	+	0.988531i	$0.548255\pi$
$434$	2.76561e8	0.162397
$435$	−5.85860e6	−0.00341257
$436$	−4.09408e9	−2.36567
$437$	7.52764e8	0.431493
$438$	1.14622e7	0.00651793
$439$	−1.85039e9	−1.04385	−0.521925	−	0.852991i	$-0.674786\pi$
$439$	−1.85039e9	−1.04385	−0.521925	+	0.852991i	$0.674786\pi$
$440$	3.16558e9	1.77161
$441$	1.76669e9	0.980903
$442$	−7.07046e7	−0.0389466
$443$	1.32689e9	0.725141	0.362571	−	0.931956i	$-0.381899\pi$
$443$	1.32689e9	0.725141	0.362571	+	0.931956i	$0.381899\pi$
$444$	−1.23286e7	−0.00668459
$445$	3.25603e9	1.75158
$446$	2.95555e9	1.57749
$447$	−1.21350e7	−0.00642636
$448$	3.63467e8	0.190982
$449$	2.32628e8	0.121283	0.0606415	−	0.998160i	$-0.480685\pi$
$449$	2.32628e8	0.121283	0.0606415	+	0.998160i	$0.480685\pi$
$450$	−1.76937e8	−0.0915322
$451$	−3.08121e8	−0.158162
$452$	3.88847e9	1.98059
$453$	−5.62508e6	−0.00284306
$454$	−4.96693e9	−2.49111
$455$	−1.27378e8	−0.0633949
$456$	−8.61187e7	−0.0425325
$457$	2.13977e8	0.104872	0.0524362	−	0.998624i	$-0.483301\pi$
$457$	2.13977e8	0.104872	0.0524362	+	0.998624i	$0.483301\pi$
$458$	3.97649e8	0.193406
$459$	3.80834e6	0.00183819
$460$	−1.00093e9	−0.479458
$461$	−1.08354e9	−0.515102	−0.257551	−	0.966265i	$-0.582916\pi$
$461$	−1.08354e9	−0.515102	−0.257551	+	0.966265i	$0.582916\pi$
$462$	−1.07635e7	−0.00507816
$463$	−1.82247e9	−0.853348	−0.426674	−	0.904405i	$-0.640315\pi$
$463$	−1.82247e9	−0.853348	−0.426674	+	0.904405i	$0.640315\pi$
$464$	−2.10905e8	−0.0980106
$465$	−2.80484e7	−0.0129367
$466$	−7.60265e8	−0.348028
$467$	−2.62038e9	−1.19057	−0.595284	−	0.803515i	$-0.702961\pi$
$467$	−2.62038e9	−1.19057	−0.595284	+	0.803515i	$0.702961\pi$
$468$	−1.83077e9	−0.825605
$469$	4.70538e8	0.210615
$470$	5.39765e9	2.39807
$471$	4.56950e7	0.0201509
$472$	3.25121e9	1.42314
$473$	3.28734e9	1.42834
$474$	2.69371e7	0.0116179
$475$	−2.15258e8	−0.0921578
$476$	3.03672e7	0.0129057
$477$	−3.66998e9	−1.54828
$478$	−6.08563e9	−2.54864
$479$	−2.54441e9	−1.05782	−0.528910	−	0.848678i	$-0.677399\pi$
$479$	−2.54441e9	−1.05782	−0.528910	+	0.848678i	$0.677399\pi$
$480$	−2.29003e7	−0.00945143
$481$	−2.23990e8	−0.0917741
$482$	5.51308e9	2.24249
$483$	1.54698e6	0.000624696 0
$484$	2.34514e9	0.940177
$485$	−4.17064e9	−1.65999
$486$	2.28608e8	0.0903366
$487$	−2.15742e9	−0.846415	−0.423207	−	0.906033i	$-0.639096\pi$
$487$	−2.15742e9	−0.846415	−0.423207	+	0.906033i	$0.639096\pi$
$488$	2.13823e8	0.0832886
$489$	−1.87748e7	−0.00726095
$490$	−4.41675e9	−1.69596
$491$	−1.25122e9	−0.477033	−0.238516	−	0.971138i	$-0.576661\pi$
$491$	−1.25122e9	−0.477033	−0.238516	+	0.971138i	$0.576661\pi$
$492$	−1.11458e7	−0.00421922
$493$	2.53757e7	0.00953791
$494$	−3.44216e9	−1.28465
$495$	−3.40702e9	−1.26257
$496$	−1.00972e9	−0.371548
$497$	−4.57440e8	−0.167143
$498$	4.39688e7	0.0159530
$499$	3.48226e9	1.25461	0.627306	−	0.778773i	$-0.284157\pi$
$499$	3.48226e9	1.25461	0.627306	+	0.778773i	$0.284157\pi$
$500$	−4.97565e9	−1.78014
$501$	7.54402e7	0.0268022
$502$	5.05698e9	1.78414
$503$	−5.73533e8	−0.200942	−0.100471	−	0.994940i	$-0.532035\pi$
$503$	−5.73533e8	−0.200942	−0.100471	+	0.994940i	$0.532035\pi$
$504$	5.52365e8	0.192185
$505$	−2.06337e9	−0.712948
$506$	−1.53665e9	−0.527289
$507$	−4.18606e7	−0.0142652
$508$	7.61520e9	2.57726
$509$	9.51755e8	0.319899	0.159950	−	0.987125i	$-0.448867\pi$
$509$	9.51755e8	0.319899	0.159950	+	0.987125i	$0.448867\pi$
$510$	−4.75968e6	−0.00158885
$511$	−8.94416e7	−0.0296528
$512$	−3.07288e9	−1.01181
$513$	1.85404e8	0.0606328
$514$	2.76291e9	0.897419
$515$	4.50981e9	1.45490
$516$	1.18914e8	0.0381030
$517$	5.36193e9	1.70649
$518$	1.48676e8	0.0469988
$519$	4.50662e7	0.0141503
$520$	2.08044e9	0.648848
$521$	3.07880e9	0.953782	0.476891	−	0.878962i	$-0.341764\pi$
$521$	3.07880e9	0.953782	0.476891	+	0.878962i	$0.341764\pi$
$522$	1.01545e9	0.312472
$523$	−1.47884e9	−0.452029	−0.226014	−	0.974124i	$-0.572570\pi$
$523$	−1.47884e9	−0.452029	−0.226014	+	0.974124i	$0.572570\pi$
$524$	−2.16131e9	−0.656233
$525$	−442369.	−0.000133422 0
$526$	6.76647e9	2.02727
$527$	1.21488e8	0.0361572
$528$	3.92973e7	0.0116183
$529$	−3.18397e9	−0.935135
$530$	9.17499e9	2.67695
$531$	−3.49918e9	−1.01423
$532$	1.47839e9	0.425694
$533$	−2.02499e8	−0.0579265
$534$	1.80821e8	0.0513873
$535$	−5.16922e9	−1.45944
$536$	−7.68520e9	−2.15565
$537$	−1.56328e7	−0.00435638
$538$	−6.15384e9	−1.70376
$539$	−4.38752e9	−1.20687
$540$	−2.46526e8	−0.0673728
$541$	−2.15744e9	−0.585798	−0.292899	−	0.956143i	$-0.594620\pi$
$541$	−2.15744e9	−0.585798	−0.292899	+	0.956143i	$0.594620\pi$
$542$	6.03650e8	0.162850
$543$	−1.08694e8	−0.0291345
$544$	9.91895e7	0.0264162
$545$	−5.00725e9	−1.32499
$546$	−7.07384e6	−0.00185986
$547$	3.53337e9	0.923067	0.461534	−	0.887123i	$-0.347299\pi$
$547$	3.53337e9	0.923067	0.461534	+	0.887123i	$0.347299\pi$
$548$	−1.32338e10	−3.43520
$549$	−2.30132e8	−0.0593572
$550$	4.39416e8	0.112618
$551$	1.23538e9	0.314608
$552$	−2.52664e7	−0.00639377
$553$	−2.10194e8	−0.0528546
$554$	−2.75531e7	−0.00688471
$555$	−1.50785e7	−0.00374397
$556$	8.43260e9	2.08065
$557$	−4.32894e9	−1.06142	−0.530711	−	0.847553i	$-0.678075\pi$
$557$	−4.32894e9	−1.06142	−0.530711	+	0.847553i	$0.678075\pi$
$558$	4.86153e9	1.18455
$559$	2.16046e9	0.523124
$560$	−3.08686e8	−0.0742777
$561$	−4.72819e6	−0.00113064
$562$	−8.42235e9	−2.00150
$563$	3.08897e9	0.729515	0.364758	−	0.931102i	$-0.381152\pi$
$563$	3.08897e9	0.729515	0.364758	+	0.931102i	$0.381152\pi$
$564$	1.93959e8	0.0455232
$565$	4.75578e9	1.10931
$566$	−4.97204e8	−0.115260
$567$	−5.94303e8	−0.136920
$568$	7.47128e9	1.71071
$569$	6.69281e9	1.52305	0.761527	−	0.648133i	$-0.224450\pi$
$569$	6.69281e9	1.52305	0.761527	+	0.648133i	$0.224450\pi$
$570$	−2.31718e8	−0.0524081
$571$	−1.24645e9	−0.280188	−0.140094	−	0.990138i	$-0.544740\pi$
$571$	−1.24645e9	−0.280188	−0.140094	+	0.990138i	$0.544740\pi$
$572$	4.54665e9	1.01579
$573$	−6.01673e7	−0.0133604
$574$	1.34411e8	0.0296650
$575$	−6.31547e7	−0.0138538
$576$	6.38921e9	1.39306
$577$	−1.22638e9	−0.265772	−0.132886	−	0.991131i	$-0.542424\pi$
$577$	−1.22638e9	−0.265772	−0.132886	+	0.991131i	$0.542424\pi$
$578$	−7.79381e9	−1.67881
$579$	−6.43407e7	−0.0137756
$580$	−1.64265e9	−0.349580
$581$	−3.43095e8	−0.0725768
$582$	−2.31613e8	−0.0487005
$583$	9.11428e9	1.90495
$584$	1.46083e9	0.303497
$585$	−2.23911e9	−0.462414
$586$	−5.15732e9	−1.05872
$587$	4.79761e8	0.0979020	0.0489510	−	0.998801i	$-0.484412\pi$
$587$	4.79761e8	0.0979020	0.0489510	+	0.998801i	$0.484412\pi$
$588$	−1.58711e8	−0.0321949
$589$	5.91445e9	1.19264
$590$	8.74798e9	1.75358
$591$	6.54849e7	0.0130492
$592$	−5.42813e8	−0.107529
$593$	3.49156e9	0.687587	0.343794	−	0.939045i	$-0.388288\pi$
$593$	3.49156e9	0.687587	0.343794	+	0.939045i	$0.388288\pi$
$594$	−3.78473e8	−0.0740939
$595$	3.71405e7	0.00722835
$596$	−3.40245e9	−0.658309
$597$	1.33320e8	0.0256440
$598$	−1.00990e9	−0.193118
$599$	−8.43205e9	−1.60302	−0.801511	−	0.597980i	$-0.795970\pi$
$599$	−8.43205e9	−1.60302	−0.801511	+	0.597980i	$0.795970\pi$
$600$	7.22511e6	0.00136557
$601$	9.99881e9	1.87883	0.939415	−	0.342781i	$-0.111369\pi$
$601$	9.99881e9	1.87883	0.939415	+	0.342781i	$0.111369\pi$
$602$	−1.43403e9	−0.267899
$603$	8.27135e9	1.53626
$604$	−1.57717e9	−0.291240
$605$	2.86821e9	0.526584
$606$	−1.14588e8	−0.0209163
$607$	−8.44900e9	−1.53336	−0.766681	−	0.642028i	$-0.778093\pi$
$607$	−8.44900e9	−1.53336	−0.766681	+	0.642028i	$0.778093\pi$
$608$	4.82890e9	0.871336
$609$	2.53878e6	0.000455475 0
$610$	5.75332e8	0.102628
$611$	3.52389e9	0.624998
$612$	5.33810e8	0.0941363
$613$	−7.14246e8	−0.125238	−0.0626190	−	0.998038i	$-0.519945\pi$
$613$	−7.14246e8	−0.125238	−0.0626190	+	0.998038i	$0.519945\pi$
$614$	8.23231e8	0.143527
$615$	−1.36318e7	−0.00236314
$616$	−1.37178e9	−0.236457
$617$	−6.38724e9	−1.09475	−0.547375	−	0.836887i	$-0.684373\pi$
$617$	−6.38724e9	−1.09475	−0.547375	+	0.836887i	$0.684373\pi$
$618$	2.50449e8	0.0426835
$619$	−8.47356e9	−1.43598	−0.717991	−	0.696053i	$-0.754938\pi$
$619$	−8.47356e9	−1.43598	−0.717991	+	0.696053i	$0.754938\pi$
$620$	−7.86428e9	−1.32522
$621$	5.43957e7	0.00911474
$622$	−2.81472e9	−0.468995
$623$	−1.41098e9	−0.233782
$624$	2.58264e7	0.00425519
$625$	−6.41746e9	−1.05144
$626$	−8.51298e9	−1.38698
$627$	−2.30185e8	−0.0372942
$628$	1.28121e10	2.06424
$629$	6.53103e7	0.0104642
$630$	1.48624e9	0.236808
$631$	1.34035e9	0.212381	0.106191	−	0.994346i	$-0.466135\pi$
$631$	1.34035e9	0.212381	0.106191	+	0.994346i	$0.466135\pi$
$632$	3.43305e9	0.540967
$633$	7.36049e7	0.0115344
$634$	−1.53319e10	−2.38937
$635$	9.31375e9	1.44350
$636$	3.29694e8	0.0508172
$637$	−2.88351e9	−0.442011
$638$	−2.52184e9	−0.384454
$639$	−8.04112e9	−1.21917
$640$	−1.24708e10	−1.88046
$641$	9.56239e9	1.43405	0.717023	−	0.697049i	$-0.245504\pi$
$641$	9.56239e9	1.43405	0.717023	+	0.697049i	$0.245504\pi$
$642$	−2.87069e8	−0.0428167
$643$	−7.89728e9	−1.17149	−0.585746	−	0.810495i	$-0.699198\pi$
$643$	−7.89728e9	−1.17149	−0.585746	+	0.810495i	$0.699198\pi$
$644$	4.33745e8	0.0639932
$645$	1.45437e8	0.0213411
$646$	1.00365e9	0.146477
$647$	1.45293e9	0.210901	0.105451	−	0.994425i	$-0.466372\pi$
$647$	1.45293e9	0.210901	0.105451	+	0.994425i	$0.466372\pi$
$648$	9.70663e9	1.40138
$649$	8.69010e9	1.24787
$650$	2.88787e8	0.0412459
$651$	1.21546e7	0.00172666
$652$	−5.26411e9	−0.743804
$653$	4.94004e9	0.694279	0.347140	−	0.937813i	$-0.387153\pi$
$653$	4.94004e9	0.694279	0.347140	+	0.937813i	$0.387153\pi$
$654$	−2.78074e8	−0.0388721
$655$	−2.64339e9	−0.367550
$656$	−4.90733e8	−0.0678706
$657$	−1.57225e9	−0.216293
$658$	−2.33903e9	−0.320070
$659$	−1.42643e10	−1.94157	−0.970784	−	0.239953i	$-0.922868\pi$
$659$	−1.42643e10	−1.94157	−0.970784	+	0.239953i	$0.922868\pi$
$660$	3.06071e8	0.0414398
$661$	8.41697e9	1.13358	0.566788	−	0.823864i	$-0.308186\pi$
$661$	8.41697e9	1.13358	0.566788	+	0.823864i	$0.308186\pi$
$662$	−1.72748e10	−2.31424
$663$	−3.10739e6	−0.000414094 0
$664$	5.60370e9	0.742825
$665$	1.80814e9	0.238427
$666$	2.61350e9	0.342817
$667$	3.62449e8	0.0472940
$668$	2.11521e10	2.74559
$669$	1.29893e8	0.0167724
$670$	−2.06785e10	−2.65617
$671$	5.71525e8	0.0730308
$672$	9.92369e6	0.00126148
$673$	1.60907e9	0.203481	0.101740	−	0.994811i	$-0.467559\pi$
$673$	1.60907e9	0.203481	0.101740	+	0.994811i	$0.467559\pi$
$674$	−1.58389e10	−1.99258
$675$	−1.55548e7	−0.00194672
$676$	−1.17370e10	−1.46131
$677$	−6.26194e9	−0.775620	−0.387810	−	0.921739i	$-0.626768\pi$
$677$	−6.26194e9	−0.775620	−0.387810	+	0.921739i	$0.626768\pi$
$678$	2.64108e8	0.0325445
$679$	1.80732e9	0.221559
$680$	−6.06609e8	−0.0739822
$681$	−2.18291e8	−0.0264863
$682$	−1.20734e10	−1.45742
$683$	8.28070e8	0.0994477	0.0497239	−	0.998763i	$-0.484166\pi$
$683$	8.28070e8	0.0994477	0.0497239	+	0.998763i	$0.484166\pi$
$684$	2.59878e10	3.10508
$685$	−1.61855e10	−1.92402
$686$	3.86457e9	0.457053
$687$	1.74762e7	0.00205636
$688$	5.23562e9	0.612927
$689$	5.98996e9	0.697681
$690$	−6.79840e7	−0.00787835
$691$	9.95391e9	1.14768	0.573839	−	0.818968i	$-0.305453\pi$
$691$	9.95391e9	1.14768	0.573839	+	0.818968i	$0.305453\pi$
$692$	1.26358e10	1.44954
$693$	1.47641e9	0.168515
$694$	2.06429e10	2.34429
$695$	1.03135e10	1.16535
$696$	−4.14653e7	−0.00466179
$697$	5.90441e7	0.00660483
$698$	2.83004e10	3.14991
$699$	−3.34129e7	−0.00370036
$700$	−1.24032e8	−0.0136676
$701$	−1.11577e9	−0.122338	−0.0611692	−	0.998127i	$-0.519483\pi$
$701$	−1.11577e9	−0.122338	−0.0611692	+	0.998127i	$0.519483\pi$
$702$	−2.48735e8	−0.0271367
$703$	3.17954e9	0.345160
$704$	−1.58674e10	−1.71396
$705$	2.37221e8	0.0254971
$706$	−1.34757e10	−1.44123
$707$	8.94147e8	0.0951571
$708$	3.14350e8	0.0332887
$709$	−1.92104e9	−0.202430	−0.101215	−	0.994865i	$-0.532273\pi$
$709$	−1.92104e9	−0.202430	−0.101215	+	0.994865i	$0.532273\pi$
$710$	2.01029e10	2.10792
$711$	−3.69490e9	−0.385530
$712$	2.30452e10	2.39277
$713$	1.73525e9	0.179286
$714$	2.06257e6	0.000212063 0
$715$	5.56077e9	0.568936
$716$	−4.38315e9	−0.446263
$717$	−2.67457e8	−0.0270980
$718$	3.11961e9	0.314532
$719$	8.64628e9	0.867518	0.433759	−	0.901029i	$-0.357187\pi$
$719$	8.64628e9	0.867518	0.433759	+	0.901029i	$0.357187\pi$
$720$	−5.42623e9	−0.541795
$721$	−1.95429e9	−0.194185
$722$	3.18388e10	3.14830
$723$	2.42294e8	0.0238429
$724$	−3.04760e10	−2.98451
$725$	−1.03645e8	−0.0101010
$726$	1.59284e8	0.0154488
$727$	8.59715e9	0.829821	0.414910	−	0.909862i	$-0.363813\pi$
$727$	8.59715e9	0.829821	0.414910	+	0.909862i	$0.363813\pi$
$728$	−9.01542e8	−0.0866016
$729$	−1.04403e10	−0.998079
$730$	3.93064e9	0.373967
$731$	−6.29941e8	−0.0596471
$732$	2.06740e7	0.00194821
$733$	−1.59376e10	−1.49471	−0.747357	−	0.664423i	$-0.768677\pi$
$733$	−1.59376e10	−1.49471	−0.747357	+	0.664423i	$0.768677\pi$
$734$	−1.62843e9	−0.151996
$735$	−1.94111e8	−0.0180321
$736$	1.41675e9	0.130985
$737$	−2.05416e10	−1.89016
$738$	2.36275e9	0.216381
$739$	1.69117e10	1.54146	0.770729	−	0.637163i	$-0.219892\pi$
$739$	1.69117e10	1.54146	0.770729	+	0.637163i	$0.219892\pi$
$740$	−4.22774e9	−0.383529
$741$	−1.51279e8	−0.0136589
$742$	−3.97591e9	−0.357292
$743$	−1.78167e10	−1.59355	−0.796776	−	0.604275i	$-0.793463\pi$
$743$	−1.78167e10	−1.59355	−0.796776	+	0.604275i	$0.793463\pi$
$744$	−1.98518e8	−0.0176724
$745$	−4.16136e9	−0.368713
$746$	−3.66815e10	−3.23490
$747$	−6.03110e9	−0.529388
$748$	−1.32570e9	−0.115822
$749$	2.24004e9	0.194791
$750$	−3.37951e8	−0.0292509
$751$	1.11904e10	0.964067	0.482034	−	0.876153i	$-0.339898\pi$
$751$	1.11904e10	0.964067	0.482034	+	0.876153i	$0.339898\pi$
$752$	8.53975e9	0.732289
$753$	2.22249e8	0.0189696
$754$	−1.65737e9	−0.140805
$755$	−1.92896e9	−0.163120
$756$	1.06830e8	0.00899223
$757$	2.33314e9	0.195482	0.0977408	−	0.995212i	$-0.468838\pi$
$757$	2.33314e9	0.195482	0.0977408	+	0.995212i	$0.468838\pi$
$758$	2.31748e10	1.93274
$759$	−6.75342e7	−0.00560631
$760$	−2.95319e10	−2.44030
$761$	4.76111e9	0.391618	0.195809	−	0.980642i	$-0.437267\pi$
$761$	4.76111e9	0.391618	0.195809	+	0.980642i	$0.437267\pi$
$762$	5.17232e8	0.0423490
$763$	2.16985e9	0.176846
$764$	−1.68698e10	−1.36862
$765$	6.52875e8	0.0527248
$766$	7.26190e9	0.583780
$767$	5.71118e9	0.457027
$768$	−3.79481e8	−0.0302291
$769$	−9.44013e9	−0.748576	−0.374288	−	0.927312i	$-0.622113\pi$
$769$	−9.44013e9	−0.748576	−0.374288	+	0.927312i	$0.622113\pi$
$770$	−3.69103e9	−0.291360
$771$	1.21427e8	0.00954167
$772$	−1.80400e10	−1.41116
$773$	4.76243e9	0.370851	0.185426	−	0.982658i	$-0.440634\pi$
$773$	4.76243e9	0.370851	0.185426	+	0.982658i	$0.440634\pi$
$774$	−2.52081e10	−1.95410
$775$	−4.96206e8	−0.0382918
$776$	−2.95185e10	−2.26766
$777$	6.53415e6	0.000499707 0
$778$	−7.65771e9	−0.583002
$779$	2.87448e9	0.217860
$780$	2.01151e8	0.0151772
$781$	1.99699e10	1.50002
$782$	2.94463e8	0.0220195
$783$	8.92701e7	0.00664569
$784$	−6.98784e9	−0.517889
$785$	1.56698e10	1.15616
$786$	−1.46799e8	−0.0107831
$787$	9.01011e9	0.658899	0.329449	−	0.944173i	$-0.393137\pi$
$787$	9.01011e9	0.658899	0.329449	+	0.944173i	$0.393137\pi$
$788$	1.83608e10	1.33675
$789$	2.97379e8	0.0215547
$790$	9.23727e9	0.666575
$791$	−2.06088e9	−0.148059
$792$	−2.41138e10	−1.72476
$793$	3.75609e8	0.0267473
$794$	3.16800e10	2.24602
$795$	4.03231e8	0.0284623
$796$	3.73806e10	2.62694
$797$	4.47431e9	0.313056	0.156528	−	0.987674i	$-0.449970\pi$
$797$	4.47431e9	0.313056	0.156528	+	0.987674i	$0.449970\pi$
$798$	1.00413e8	0.00699490
$799$	−1.02749e9	−0.0712628
$800$	−4.05131e8	−0.0279757
$801$	−2.48029e10	−1.70525
$802$	2.31773e10	1.58655
$803$	3.90463e9	0.266119
$804$	−7.43059e8	−0.0504228
$805$	5.30490e8	0.0358419
$806$	−7.93474e9	−0.533777
$807$	−2.70455e8	−0.0181150
$808$	−1.46039e10	−0.973934
$809$	−3.59948e9	−0.239012	−0.119506	−	0.992833i	$-0.538131\pi$
$809$	−3.59948e9	−0.239012	−0.119506	+	0.992833i	$0.538131\pi$
$810$	2.61175e10	1.72677
$811$	4.19700e9	0.276290	0.138145	−	0.990412i	$-0.455886\pi$
$811$	4.19700e9	0.276290	0.138145	+	0.990412i	$0.455886\pi$
$812$	7.11829e8	0.0466584
$813$	2.65298e7	0.00173148
$814$	−6.49054e9	−0.421789
$815$	−6.43826e9	−0.416598
$816$	−7.53041e6	−0.000485180 0
$817$	−3.06678e10	−1.96746
$818$	−8.64957e9	−0.552532
$819$	9.70303e8	0.0617183
$820$	−3.82211e9	−0.242078
$821$	2.95484e10	1.86351	0.931756	−	0.363084i	$-0.118276\pi$
$821$	2.95484e10	1.86351	0.931756	+	0.363084i	$0.118276\pi$
$822$	−8.98850e8	−0.0564464
$823$	−1.65648e10	−1.03583	−0.517913	−	0.855433i	$-0.673291\pi$
$823$	−1.65648e10	−1.03583	−0.517913	+	0.855433i	$0.673291\pi$
$824$	3.19190e10	1.98749
$825$	1.93119e7	0.00119739
$826$	−3.79087e9	−0.234050
$827$	1.56492e10	0.962108	0.481054	−	0.876691i	$-0.340254\pi$
$827$	1.56492e10	0.962108	0.481054	+	0.876691i	$0.340254\pi$
$828$	7.62458e9	0.466777
$829$	−1.89289e10	−1.15395	−0.576973	−	0.816763i	$-0.695766\pi$
$829$	−1.89289e10	−1.15395	−0.576973	+	0.816763i	$0.695766\pi$
$830$	1.50778e10	0.915302
$831$	−1.21093e6	−7.32006e−5 0
$832$	−1.04281e10	−0.627734
$833$	8.40765e8	0.0503985
$834$	5.72751e8	0.0341889
$835$	2.58700e10	1.53778
$836$	−6.45399e10	−3.82038
$837$	4.27386e8	0.0251931
$838$	2.61884e10	1.53729
$839$	−3.11150e10	−1.81888	−0.909439	−	0.415838i	$-0.863488\pi$
$839$	−3.11150e10	−1.81888	−0.909439	+	0.415838i	$0.863488\pi$
$840$	−6.06898e7	−0.00353296
$841$	5.94823e8	0.0344828
$842$	4.39236e10	2.53574
$843$	−3.70154e8	−0.0212807
$844$	2.06375e10	1.18157
$845$	−1.43549e10	−0.818466
$846$	−4.11166e10	−2.33465
$847$	−1.24292e9	−0.0702830
$848$	1.45160e10	0.817449
$849$	−2.18516e7	−0.00122548
$850$	−8.42038e7	−0.00470289
$851$	9.32848e8	0.0518869
$852$	7.22376e8	0.0400152
$853$	−1.39347e10	−0.768736	−0.384368	−	0.923180i	$-0.625581\pi$
$853$	−1.39347e10	−0.768736	−0.384368	+	0.923180i	$0.625581\pi$
$854$	−2.49316e8	−0.0136977
$855$	3.17843e10	1.73913
$856$	−3.65861e10	−1.99369
$857$	−3.21238e10	−1.74339	−0.871693	−	0.490052i	$-0.836978\pi$
$857$	−3.21238e10	−1.74339	−0.871693	+	0.490052i	$0.836978\pi$
$858$	3.08813e8	0.0166913
$859$	−8.24123e9	−0.443625	−0.221813	−	0.975089i	$-0.571197\pi$
$859$	−8.24123e9	−0.443625	−0.221813	+	0.975089i	$0.571197\pi$
$860$	4.07781e10	2.18616
$861$	5.90723e6	0.000315408 0
$862$	2.21615e10	1.17848
$863$	1.07922e10	0.571575	0.285788	−	0.958293i	$-0.407745\pi$
$863$	1.07922e10	0.571575	0.285788	+	0.958293i	$0.407745\pi$
$864$	3.48943e8	0.0184059
$865$	1.54541e10	0.811874
$866$	−9.71662e9	−0.508397
$867$	−3.42530e8	−0.0178497
$868$	3.40792e9	0.176877
$869$	9.17615e9	0.474342
$870$	−1.11570e8	−0.00574422
$871$	−1.35001e10	−0.692266
$872$	−3.54398e10	−1.81002
$873$	3.17699e10	1.61609
$874$	1.43355e10	0.726312
$875$	2.63709e9	0.133075
$876$	1.41243e8	0.00709911
$877$	−2.32533e10	−1.16409	−0.582043	−	0.813158i	$-0.697747\pi$
$877$	−2.32533e10	−1.16409	−0.582043	+	0.813158i	$0.697747\pi$
$878$	−3.52386e10	−1.75706
$879$	−2.26659e8	−0.0112567
$880$	1.34759e10	0.666603
$881$	−1.88747e10	−0.929962	−0.464981	−	0.885321i	$-0.653939\pi$
$881$	−1.88747e10	−0.929962	−0.464981	+	0.885321i	$0.653939\pi$
$882$	3.36446e10	1.65111
$883$	−7.37985e9	−0.360732	−0.180366	−	0.983600i	$-0.557728\pi$
$883$	−7.37985e9	−0.360732	−0.180366	+	0.983600i	$0.557728\pi$
$884$	−8.71258e8	−0.0424194
$885$	3.84464e8	0.0186447
$886$	2.52691e10	1.22060
$887$	−2.27600e10	−1.09506	−0.547531	−	0.836785i	$-0.684432\pi$
$887$	−2.27600e10	−1.09506	−0.547531	+	0.836785i	$0.684432\pi$
$888$	−1.06721e8	−0.00511451
$889$	−4.03604e9	−0.192664
$890$	6.20074e10	2.94835
$891$	2.59447e10	1.22879
$892$	3.64198e10	1.71815
$893$	−5.00218e10	−2.35060
$894$	−2.31098e8	−0.0108172
$895$	−5.36080e9	−0.249947
$896$	5.40413e9	0.250985
$897$	−4.43839e7	−0.00205330
$898$	4.43013e9	0.204150
$899$	2.84775e9	0.130720
$900$	−2.18030e9	−0.0996937
$901$	−1.74654e9	−0.0795502
$902$	−5.86781e9	−0.266227
$903$	−6.30242e7	−0.00284839
$904$	3.36599e10	1.51539
$905$	−3.72736e10	−1.67159
$906$	−1.07123e8	−0.00478558
$907$	2.05239e10	0.913345	0.456673	−	0.889635i	$-0.349041\pi$
$907$	2.05239e10	0.913345	0.456673	+	0.889635i	$0.349041\pi$
$908$	−6.12051e10	−2.71323
$909$	1.57178e10	0.694092
$910$	−2.42577e9	−0.106710
$911$	−6.50900e9	−0.285233	−0.142616	−	0.989778i	$-0.545552\pi$
$911$	−6.50900e9	−0.285233	−0.142616	+	0.989778i	$0.545552\pi$
$912$	−3.66607e8	−0.0160037
$913$	1.49780e10	0.651339
$914$	4.07495e9	0.176527
$915$	2.52852e7	0.00109117
$916$	4.90003e9	0.210651
$917$	1.14549e9	0.0490568
$918$	7.25254e7	0.00309415
$919$	−2.04744e10	−0.870174	−0.435087	−	0.900388i	$-0.643282\pi$
$919$	−2.04744e10	−0.870174	−0.435087	+	0.900388i	$0.643282\pi$
$920$	−8.66438e9	−0.366843
$921$	3.61801e7	0.00152602
$922$	−2.06348e10	−0.867047
$923$	1.31243e10	0.549377
$924$	−1.32633e8	−0.00553096
$925$	−2.66754e8	−0.0110819
$926$	−3.47068e10	−1.43640
$927$	−3.43535e10	−1.41642
$928$	2.32507e9	0.0955033
$929$	4.58067e10	1.87445	0.937224	−	0.348727i	$-0.113386\pi$
$929$	4.58067e10	1.87445	0.937224	+	0.348727i	$0.113386\pi$
$930$	−5.34150e8	−0.0217757
$931$	4.09315e10	1.66239
$932$	−9.36837e9	−0.379060
$933$	−1.23704e8	−0.00498652
$934$	−4.99020e10	−2.00403
$935$	−1.62139e9	−0.0648706
$936$	−1.58477e10	−0.631687
$937$	1.88271e10	0.747645	0.373822	−	0.927500i	$-0.378047\pi$
$937$	1.88271e10	0.747645	0.373822	+	0.927500i	$0.378047\pi$
$938$	8.96085e9	0.354519
$939$	−3.74137e8	−0.0147469
$940$	6.65125e10	2.61190
$941$	−2.59965e10	−1.01707	−0.508535	−	0.861041i	$-0.669813\pi$
$941$	−2.59965e10	−1.01707	−0.508535	+	0.861041i	$0.669813\pi$
$942$	8.70208e8	0.0339191
$943$	8.43346e8	0.0327503
$944$	1.38404e10	0.535484
$945$	1.30658e8	0.00503646
$946$	6.26036e10	2.40425
$947$	−2.57319e10	−0.984572	−0.492286	−	0.870434i	$-0.663839\pi$
$947$	−2.57319e10	−0.984572	−0.492286	+	0.870434i	$0.663839\pi$
$948$	3.31932e8	0.0126538
$949$	2.56614e9	0.0974652
$950$	−4.09934e9	−0.155125
$951$	−6.73820e8	−0.0254046
$952$	2.62869e8	0.00987439
$953$	2.08096e10	0.778821	0.389411	−	0.921064i	$-0.372679\pi$
$953$	2.08096e10	0.778821	0.389411	+	0.921064i	$0.372679\pi$
$954$	−6.98906e10	−2.60615
$955$	−2.06326e10	−0.766554
$956$	−7.49902e10	−2.77589
$957$	−1.10832e8	−0.00408765
$958$	−4.84553e10	−1.78058
$959$	7.01387e9	0.256799
$960$	−7.02000e8	−0.0256087
$961$	−1.38788e10	−0.504453
$962$	−4.26562e9	−0.154479
$963$	3.93766e10	1.42084
$964$	6.79350e10	2.44244
$965$	−2.20638e10	−0.790376
$966$	2.94604e7	0.00105152
$967$	9.77904e8	0.0347779	0.0173890	−	0.999849i	$-0.494465\pi$
$967$	9.77904e8	0.0347779	0.0173890	+	0.999849i	$0.494465\pi$
$968$	2.03003e10	0.719348
$969$	4.41096e7	0.00155740
$970$	−7.94250e10	−2.79419
$971$	2.77032e10	0.971096	0.485548	−	0.874210i	$-0.338620\pi$
$971$	2.77032e10	0.971096	0.485548	+	0.874210i	$0.338620\pi$
$972$	2.81702e9	0.0983916
$973$	−4.46926e9	−0.155540
$974$	−4.10856e10	−1.42473
$975$	1.26919e7	0.000438541 0
$976$	9.10246e8	0.0313389
$977$	2.66223e10	0.913302	0.456651	−	0.889646i	$-0.349049\pi$
$977$	2.66223e10	0.913302	0.456651	+	0.889646i	$0.349049\pi$
$978$	−3.57544e8	−0.0122220
$979$	6.15971e10	2.09807
$980$	−5.44254e10	−1.84719
$981$	3.81428e10	1.28994
$982$	−2.38280e10	−0.802967
$983$	−2.14323e10	−0.719666	−0.359833	−	0.933017i	$-0.617166\pi$
$983$	−2.14323e10	−0.719666	−0.359833	+	0.933017i	$0.617166\pi$
$984$	−9.64816e7	−0.00322821
$985$	2.24561e10	0.748701
$986$	4.83250e8	0.0160547
$987$	−1.02798e8	−0.00340309
$988$	−4.24160e10	−1.39920
$989$	−8.99764e9	−0.295762
$990$	−6.48827e10	−2.12523
$991$	−3.33513e10	−1.08857	−0.544283	−	0.838902i	$-0.683198\pi$
$991$	−3.33513e10	−1.08857	−0.544283	+	0.838902i	$0.683198\pi$
$992$	1.11314e10	0.362043
$993$	−7.59208e8	−0.0246058
$994$	−8.71142e9	−0.281343
$995$	4.57182e10	1.47132
$996$	5.41805e8	0.0173754
$997$	5.53807e10	1.76980	0.884902	−	0.465778i	$-0.154225\pi$
$997$	5.53807e10	1.76980	0.884902	+	0.465778i	$0.154225\pi$
$998$	6.63157e10	2.11183
$999$	2.29758e8	0.00729107

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.8.a.b.1.9	✓	10
3.2	odd	2		261.8.a.f.1.2		10
4.3	odd	2		464.8.a.g.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.8.a.b.1.9	✓	10	1.1	even	1	trivial
261.8.a.f.1.2		10	3.2	odd	2
464.8.a.g.1.6		10	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q+19.0438 q^{2} +0.836957 q^{3} +234.668 q^{4} +287.010 q^{5} +15.9389 q^{6} -124.374 q^{7} +2031.37 q^{8} -2186.30 q^{9} +O(q^{10})\)	\(q+19.0438 q^{2} +0.836957 q^{3} +234.668 q^{4} +287.010 q^{5} +15.9389 q^{6} -124.374 q^{7} +2031.37 q^{8} -2186.30 q^{9} +5465.77 q^{10} +5429.60 q^{11} +196.407 q^{12} +3568.37 q^{13} -2368.55 q^{14} +240.215 q^{15} +8647.53 q^{16} -1040.46 q^{17} -41635.5 q^{18} -50653.1 q^{19} +67352.0 q^{20} -104.095 q^{21} +103401. q^{22} -14861.2 q^{23} +1700.17 q^{24} +4249.65 q^{25} +67955.4 q^{26} -3660.26 q^{27} -29186.5 q^{28} -24389.0 q^{29} +4574.61 q^{30} -116764. q^{31} -95332.8 q^{32} +4544.34 q^{33} -19814.3 q^{34} -35696.4 q^{35} -513054. q^{36} -62770.9 q^{37} -964630. q^{38} +2986.57 q^{39} +583022. q^{40} -56748.3 q^{41} -1982.37 q^{42} +605447. q^{43} +1.27415e6 q^{44} -627489. q^{45} -283013. q^{46} +987536. q^{47} +7237.61 q^{48} -808074. q^{49} +80929.7 q^{50} -870.816 q^{51} +837382. q^{52} +1.67863e6 q^{53} -69705.5 q^{54} +1.55835e6 q^{55} -252648. q^{56} -42394.5 q^{57} -464460. q^{58} +1.60050e6 q^{59} +56370.7 q^{60} +105261. q^{61} -2.22363e6 q^{62} +271918. q^{63} -2.92239e6 q^{64} +1.02416e6 q^{65} +86541.8 q^{66} -3.78326e6 q^{67} -244162. q^{68} -12438.1 q^{69} -679797. q^{70} +3.67796e6 q^{71} -4.44118e6 q^{72} +719137. q^{73} -1.19540e6 q^{74} +3556.78 q^{75} -1.18867e7 q^{76} -675299. q^{77} +56875.8 q^{78} +1.69002e6 q^{79} +2.48193e6 q^{80} +4.77837e6 q^{81} -1.08071e6 q^{82} +2.75859e6 q^{83} -24427.8 q^{84} -298621. q^{85} +1.15300e7 q^{86} -20412.5 q^{87} +1.10295e7 q^{88} +1.13447e7 q^{89} -1.19498e7 q^{90} -443811. q^{91} -3.48744e6 q^{92} -97726.3 q^{93} +1.88065e7 q^{94} -1.45379e7 q^{95} -79789.4 q^{96} -1.45314e7 q^{97} -1.53888e7 q^{98} -1.18707e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 80 q^{3} + 922 q^{4} + 180 q^{5} + 358 q^{6} + 1040 q^{7} - 4620 q^{8} + 10986 q^{9}+O(q^{10}) \) 10 * q + 80 * q^3 + 922 * q^4 + 180 * q^5 + 358 * q^6 + 1040 * q^7 - 4620 * q^8 + 10986 * q^9	\( 10 q + 80 q^{3} + 922 q^{4} + 180 q^{5} + 358 q^{6} + 1040 q^{7} - 4620 q^{8} + 10986 q^{9} + 8496 q^{10} + 7384 q^{11} + 49720 q^{12} + 20820 q^{13} + 50976 q^{14} + 43516 q^{15} + 122082 q^{16} - 11620 q^{17} + 66060 q^{18} + 75068 q^{19} - 42914 q^{20} + 51480 q^{21} - 36950 q^{22} + 62040 q^{23} - 205942 q^{24} + 261022 q^{25} - 201528 q^{26} - 28060 q^{27} - 24980 q^{28} - 243890 q^{29} - 1284894 q^{30} + 200600 q^{31} - 1761460 q^{32} - 1068000 q^{33} - 503932 q^{34} + 107528 q^{35} - 26300 q^{36} - 367740 q^{37} + 766880 q^{38} + 392692 q^{39} - 865000 q^{40} + 932764 q^{41} - 2058060 q^{42} + 1443560 q^{43} - 1325912 q^{44} + 4245684 q^{45} + 1760460 q^{46} - 286960 q^{47} + 3187120 q^{48} + 4713194 q^{49} - 3682652 q^{50} + 1451016 q^{51} + 2560210 q^{52} + 3953220 q^{53} - 3147534 q^{54} + 3981316 q^{55} + 2082464 q^{56} + 2050640 q^{57} + 6712320 q^{59} + 7476756 q^{60} + 1905196 q^{61} - 8048490 q^{62} + 3643800 q^{63} + 8445458 q^{64} + 4667544 q^{65} - 12425580 q^{66} - 2718200 q^{67} - 17699740 q^{68} + 1109064 q^{69} - 30441624 q^{70} + 3447736 q^{71} - 22466840 q^{72} - 2554460 q^{73} - 4214584 q^{74} + 1088084 q^{75} - 8294848 q^{76} - 3967800 q^{77} - 24809970 q^{78} + 4187744 q^{79} - 17715290 q^{80} + 5161402 q^{81} + 7020500 q^{82} + 3498720 q^{83} + 22947224 q^{84} + 1817072 q^{85} - 361638 q^{86} - 1951120 q^{87} + 15118470 q^{88} - 303268 q^{89} - 28959160 q^{90} + 27215080 q^{91} - 10783380 q^{92} + 1097360 q^{93} + 55641726 q^{94} - 8810536 q^{95} - 53327238 q^{96} + 4908620 q^{97} + 40120080 q^{98} - 14408716 q^{99}+O(q^{100}) \) 10 * q + 80 * q^3 + 922 * q^4 + 180 * q^5 + 358 * q^6 + 1040 * q^7 - 4620 * q^8 + 10986 * q^9 + 8496 * q^10 + 7384 * q^11 + 49720 * q^12 + 20820 * q^13 + 50976 * q^14 + 43516 * q^15 + 122082 * q^16 - 11620 * q^17 + 66060 * q^18 + 75068 * q^19 - 42914 * q^20 + 51480 * q^21 - 36950 * q^22 + 62040 * q^23 - 205942 * q^24 + 261022 * q^25 - 201528 * q^26 - 28060 * q^27 - 24980 * q^28 - 243890 * q^29 - 1284894 * q^30 + 200600 * q^31 - 1761460 * q^32 - 1068000 * q^33 - 503932 * q^34 + 107528 * q^35 - 26300 * q^36 - 367740 * q^37 + 766880 * q^38 + 392692 * q^39 - 865000 * q^40 + 932764 * q^41 - 2058060 * q^42 + 1443560 * q^43 - 1325912 * q^44 + 4245684 * q^45 + 1760460 * q^46 - 286960 * q^47 + 3187120 * q^48 + 4713194 * q^49 - 3682652 * q^50 + 1451016 * q^51 + 2560210 * q^52 + 3953220 * q^53 - 3147534 * q^54 + 3981316 * q^55 + 2082464 * q^56 + 2050640 * q^57 + 6712320 * q^59 + 7476756 * q^60 + 1905196 * q^61 - 8048490 * q^62 + 3643800 * q^63 + 8445458 * q^64 + 4667544 * q^65 - 12425580 * q^66 - 2718200 * q^67 - 17699740 * q^68 + 1109064 * q^69 - 30441624 * q^70 + 3447736 * q^71 - 22466840 * q^72 - 2554460 * q^73 - 4214584 * q^74 + 1088084 * q^75 - 8294848 * q^76 - 3967800 * q^77 - 24809970 * q^78 + 4187744 * q^79 - 17715290 * q^80 + 5161402 * q^81 + 7020500 * q^82 + 3498720 * q^83 + 22947224 * q^84 + 1817072 * q^85 - 361638 * q^86 - 1951120 * q^87 + 15118470 * q^88 - 303268 * q^89 - 28959160 * q^90 + 27215080 * q^91 - 10783380 * q^92 + 1097360 * q^93 + 55641726 * q^94 - 8810536 * q^95 - 53327238 * q^96 + 4908620 * q^97 + 40120080 * q^98 - 14408716 * q^99

Introduction

L-functions

Modular forms

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