LMFDB - Embedded newform 29.8.a.b.1.5

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			1.5
Root			$3.85204$ 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)

$f(q)$	$=$	$q-3.85204 q^{2} -70.5970 q^{3} -113.162 q^{4} -69.8627 q^{5} +271.943 q^{6} -1359.73 q^{7} +928.965 q^{8} +2796.94 q^{9} +O(q^{10})$	\(q-3.85204 q^{2} -70.5970 q^{3} -113.162 q^{4} -69.8627 q^{5} +271.943 q^{6} -1359.73 q^{7} +928.965 q^{8} +2796.94 q^{9} +269.114 q^{10} +6504.11 q^{11} +7988.88 q^{12} -13921.7 q^{13} +5237.74 q^{14} +4932.10 q^{15} +10906.3 q^{16} +10947.7 q^{17} -10773.9 q^{18} -5012.48 q^{19} +7905.79 q^{20} +95993.0 q^{21} -25054.1 q^{22} -30890.7 q^{23} -65582.2 q^{24} -73244.2 q^{25} +53627.0 q^{26} -43059.9 q^{27} +153870. q^{28} -24389.0 q^{29} -18998.6 q^{30} +50351.6 q^{31} -160919. q^{32} -459171. q^{33} -42171.0 q^{34} +94994.5 q^{35} -316507. q^{36} -425073. q^{37} +19308.3 q^{38} +982831. q^{39} -64900.0 q^{40} +520165. q^{41} -369769. q^{42} +644901. q^{43} -736017. q^{44} -195402. q^{45} +118992. q^{46} +1.07914e6 q^{47} -769952. q^{48} +1.02533e6 q^{49} +282140. q^{50} -772876. q^{51} +1.57540e6 q^{52} -679314. q^{53} +165868. q^{54} -454395. q^{55} -1.26314e6 q^{56} +353866. q^{57} +93947.4 q^{58} +2.49465e6 q^{59} -558125. q^{60} +876441. q^{61} -193956. q^{62} -3.80309e6 q^{63} -776140. q^{64} +972608. q^{65} +1.76875e6 q^{66} +45251.1 q^{67} -1.23886e6 q^{68} +2.18079e6 q^{69} -365923. q^{70} -2.43395e6 q^{71} +2.59826e6 q^{72} +1.33864e6 q^{73} +1.63740e6 q^{74} +5.17082e6 q^{75} +567221. q^{76} -8.84385e6 q^{77} -3.78590e6 q^{78} -5.97610e6 q^{79} -761943. q^{80} -3.07701e6 q^{81} -2.00370e6 q^{82} +2.50894e6 q^{83} -1.08627e7 q^{84} -764836. q^{85} -2.48418e6 q^{86} +1.72179e6 q^{87} +6.04209e6 q^{88} -7.88908e6 q^{89} +752695. q^{90} +1.89298e7 q^{91} +3.49564e6 q^{92} -3.55467e6 q^{93} -4.15688e6 q^{94} +350185. q^{95} +1.13604e7 q^{96} +1.51241e7 q^{97} -3.94960e6 q^{98} +1.81916e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.85204	−0.340475	−0.170238	−	0.985403i	$-0.554454\pi$
$2$	−3.85204	−0.340475	−0.170238	+	0.985403i	$0.554454\pi$
$3$	−70.5970	−1.50960	−0.754800	−	0.655955i	$-0.772266\pi$
$3$	−70.5970	−1.50960	−0.754800	+	0.655955i	$0.772266\pi$
$4$	−113.162	−0.884076
$5$	−69.8627	−0.249948	−0.124974	−	0.992160i	$-0.539885\pi$
$5$	−69.8627	−0.249948	−0.124974	+	0.992160i	$0.539885\pi$
$6$	271.943	0.513982
$7$	−1359.73	−1.49834	−0.749170	−	0.662378i	$-0.769547\pi$
$7$	−1359.73	−1.49834	−0.749170	+	0.662378i	$0.769547\pi$
$8$	928.965	0.641482
$9$	2796.94	1.27889
$10$	269.114	0.0851013
$11$	6504.11	1.47338	0.736688	−	0.676233i	$-0.236389\pi$
$11$	6504.11	1.47338	0.736688	+	0.676233i	$0.236389\pi$
$12$	7988.88	1.33460
$13$	−13921.7	−1.75748	−0.878740	−	0.477300i	$-0.841616\pi$
$13$	−13921.7	−1.75748	−0.878740	+	0.477300i	$0.841616\pi$
$14$	5237.74	0.510148
$15$	4932.10	0.377322
$16$	10906.3	0.665668
$17$	10947.7	0.540446	0.270223	−	0.962798i	$-0.412903\pi$
$17$	10947.7	0.540446	0.270223	+	0.962798i	$0.412903\pi$
$18$	−10773.9	−0.435432
$19$	−5012.48	−0.167654	−0.0838272	−	0.996480i	$-0.526714\pi$
$19$	−5012.48	−0.167654	−0.0838272	+	0.996480i	$0.526714\pi$
$20$	7905.79	0.220973
$21$	95993.0	2.26189
$22$	−25054.1	−0.501649
$23$	−30890.7	−0.529395	−0.264698	−	0.964331i	$-0.585272\pi$
$23$	−30890.7	−0.529395	−0.264698	+	0.964331i	$0.585272\pi$
$24$	−65582.2	−0.968381
$25$	−73244.2	−0.937526
$26$	53627.0	0.598379
$27$	−43059.9	−0.421017
$28$	153870.	1.32465
$29$	−24389.0	−0.185695
$29$	−24389.0	−0.185695
$30$	−18998.6	−0.128469
$31$	50351.6	0.303562	0.151781	−	0.988414i	$-0.451499\pi$
$31$	50351.6	0.303562	0.151781	+	0.988414i	$0.451499\pi$
$32$	−160919.	−0.868125
$33$	−459171.	−2.22421
$34$	−42171.0	−0.184008
$35$	94994.5	0.374507
$36$	−316507.	−1.13064
$37$	−425073.	−1.37961	−0.689806	−	0.723994i	$-0.742304\pi$
$37$	−425073.	−1.37961	−0.689806	+	0.723994i	$0.742304\pi$
$38$	19308.3	0.0570822
$39$	982831.	2.65309
$40$	−64900.0	−0.160337
$41$	520165.	1.17869	0.589343	−	0.807883i	$-0.299387\pi$
$41$	520165.	1.17869	0.589343	+	0.807883i	$0.299387\pi$
$42$	−369769.	−0.770119
$43$	644901.	1.23695	0.618477	−	0.785803i	$-0.287750\pi$
$43$	644901.	1.23695	0.618477	+	0.785803i	$0.287750\pi$
$44$	−736017.	−1.30258
$45$	−195402.	−0.319657
$46$	118992.	0.180246
$47$	1.07914e6	1.51612	0.758061	−	0.652184i	$-0.226147\pi$
$47$	1.07914e6	1.51612	0.758061	+	0.652184i	$0.226147\pi$
$48$	−769952.	−1.00489
$49$	1.02533e6	1.24502
$50$	282140.	0.319205
$51$	−772876.	−0.815857
$52$	1.57540e6	1.55375
$53$	−679314.	−0.626765	−0.313383	−	0.949627i	$-0.601462\pi$
$53$	−679314.	−0.626765	−0.313383	+	0.949627i	$0.601462\pi$
$54$	165868.	0.143346
$55$	−454395.	−0.368268
$56$	−1.26314e6	−0.961157
$57$	353866.	0.253091
$58$	93947.4	0.0632247
$59$	2.49465e6	1.58135	0.790674	−	0.612237i	$-0.209730\pi$
$59$	2.49465e6	1.58135	0.790674	+	0.612237i	$0.209730\pi$
$60$	−558125.	−0.333582
$61$	876441.	0.494389	0.247194	−	0.968966i	$-0.420491\pi$
$61$	876441.	0.494389	0.247194	+	0.968966i	$0.420491\pi$
$62$	−193956.	−0.103355
$63$	−3.80309e6	−1.91622
$64$	−776140.	−0.370092
$65$	972608.	0.439279
$66$	1.76875e6	0.757289
$67$	45251.1	0.0183809	0.00919047	−	0.999958i	$-0.497075\pi$
$67$	45251.1	0.0183809	0.00919047	+	0.999958i	$0.497075\pi$
$68$	−1.23886e6	−0.477795
$69$	2.18079e6	0.799175
$70$	−365923.	−0.127511
$71$	−2.43395e6	−0.807064	−0.403532	−	0.914965i	$-0.632218\pi$
$71$	−2.43395e6	−0.807064	−0.403532	+	0.914965i	$0.632218\pi$
$72$	2.59826e6	0.820387
$73$	1.33864e6	0.402748	0.201374	−	0.979514i	$-0.435459\pi$
$73$	1.33864e6	0.402748	0.201374	+	0.979514i	$0.435459\pi$
$74$	1.63740e6	0.469724
$75$	5.17082e6	1.41529
$76$	567221.	0.148219
$77$	−8.84385e6	−2.20762
$78$	−3.78590e6	−0.903313
$79$	−5.97610e6	−1.36371	−0.681856	−	0.731486i	$-0.738827\pi$
$79$	−5.97610e6	−1.36371	−0.681856	+	0.731486i	$0.738827\pi$
$80$	−761943.	−0.166383
$81$	−3.07701e6	−0.643326
$82$	−2.00370e6	−0.401314
$83$	2.50894e6	0.481634	0.240817	−	0.970571i	$-0.422585\pi$
$83$	2.50894e6	0.481634	0.240817	+	0.970571i	$0.422585\pi$
$84$	−1.08627e7	−1.99969
$85$	−764836.	−0.135083
$86$	−2.48418e6	−0.421152
$87$	1.72179e6	0.280326
$88$	6.04209e6	0.945144
$89$	−7.88908e6	−1.18621	−0.593105	−	0.805125i	$-0.702098\pi$
$89$	−7.88908e6	−1.18621	−0.593105	+	0.805125i	$0.702098\pi$
$90$	752695.	0.108835
$91$	1.89298e7	2.63330
$92$	3.49564e6	0.468026
$93$	−3.55467e6	−0.458257
$94$	−4.15688e6	−0.516202
$95$	350185.	0.0419049
$96$	1.13604e7	1.31052
$97$	1.51241e7	1.68255	0.841276	−	0.540606i	$-0.181805\pi$
$97$	1.51241e7	1.68255	0.841276	+	0.540606i	$0.181805\pi$
$98$	−3.94960e6	−0.423899
$99$	1.81916e7	1.88429
$100$	8.28844e6	0.828844
$101$	−4.52175e6	−0.436698	−0.218349	−	0.975871i	$-0.570067\pi$
$101$	−4.52175e6	−0.436698	−0.218349	+	0.975871i	$0.570067\pi$
$102$	2.97715e6	0.277779
$103$	−1.07150e6	−0.0966191	−0.0483095	−	0.998832i	$-0.515383\pi$
$103$	−1.07150e6	−0.0966191	−0.0483095	+	0.998832i	$0.515383\pi$
$104$	−1.29328e7	−1.12739
$105$	−6.70633e6	−0.565356
$106$	2.61674e6	0.213398
$107$	−2.01609e6	−0.159098	−0.0795492	−	0.996831i	$-0.525348\pi$
$107$	−2.01609e6	−0.159098	−0.0795492	+	0.996831i	$0.525348\pi$
$108$	4.87273e6	0.372211
$109$	−1.65666e7	−1.22530	−0.612648	−	0.790356i	$-0.709896\pi$
$109$	−1.65666e7	−1.22530	−0.612648	+	0.790356i	$0.709896\pi$
$110$	1.75035e6	0.125386
$111$	3.00089e7	2.08266
$112$	−1.48296e7	−0.997396
$113$	1.42539e7	0.929304	0.464652	−	0.885493i	$-0.346179\pi$
$113$	1.42539e7	0.929304	0.464652	+	0.885493i	$0.346179\pi$
$114$	−1.36311e6	−0.0861713
$115$	2.15811e6	0.132321
$116$	2.75990e6	0.164169
$117$	−3.89382e7	−2.24763
$118$	−9.60950e6	−0.538411
$119$	−1.48859e7	−0.809771
$120$	4.58175e6	0.242045
$121$	2.28163e7	1.17084
$122$	−3.37609e6	−0.168327
$123$	−3.67221e7	−1.77934
$124$	−5.69787e6	−0.268372
$125$	1.05751e7	0.484281
$126$	1.46496e7	0.652424
$127$	−7.83768e6	−0.339527	−0.169764	−	0.985485i	$-0.554300\pi$
$127$	−7.83768e6	−0.339527	−0.169764	+	0.985485i	$0.554300\pi$
$128$	2.35874e7	0.994133
$129$	−4.55281e7	−1.86730
$130$	−3.74652e6	−0.149564
$131$	3.16847e7	1.23140	0.615701	−	0.787980i	$-0.288873\pi$
$131$	3.16847e7	1.23140	0.615701	+	0.787980i	$0.288873\pi$
$132$	5.19606e7	1.96637
$133$	6.81562e6	0.251203
$134$	−174309.	−0.00625826
$135$	3.00828e6	0.105233
$136$	1.01700e7	0.346686
$137$	−1.95228e7	−0.648665	−0.324332	−	0.945943i	$-0.605140\pi$
$137$	−1.95228e7	−0.648665	−0.324332	+	0.945943i	$0.605140\pi$
$138$	−8.40049e6	−0.272099
$139$	−8.95066e6	−0.282685	−0.141343	−	0.989961i	$-0.545142\pi$
$139$	−8.95066e6	−0.282685	−0.141343	+	0.989961i	$0.545142\pi$
$140$	−1.07497e7	−0.331093
$141$	−7.61838e7	−2.28874
$142$	9.37569e6	0.274786
$143$	−9.05483e7	−2.58943
$144$	3.05043e7	0.851318
$145$	1.70388e6	0.0464142
$146$	−5.15650e6	−0.137126
$147$	−7.23851e7	−1.87948
$148$	4.81020e7	1.21968
$149$	7.35481e7	1.82146	0.910730	−	0.413003i	$-0.135520\pi$
$149$	7.35481e7	1.82146	0.910730	+	0.413003i	$0.135520\pi$
$150$	−1.99182e7	−0.481871
$151$	3.16126e7	0.747207	0.373603	−	0.927589i	$-0.378122\pi$
$151$	3.16126e7	0.747207	0.373603	+	0.927589i	$0.378122\pi$
$152$	−4.65641e6	−0.107547
$153$	3.06201e7	0.691172
$154$	3.40669e7	0.751640
$155$	−3.51770e6	−0.0758748
$156$	−1.11219e8	−2.34554
$157$	2.97255e7	0.613029	0.306514	−	0.951866i	$-0.400837\pi$
$157$	2.97255e7	0.613029	0.306514	+	0.951866i	$0.400837\pi$
$158$	2.30202e7	0.464311
$159$	4.79575e7	0.946165
$160$	1.12422e7	0.216987
$161$	4.20030e7	0.793213
$162$	1.18528e7	0.219037
$163$	1.06341e7	0.192329	0.0961643	−	0.995365i	$-0.469343\pi$
$163$	1.06341e7	0.192329	0.0961643	+	0.995365i	$0.469343\pi$
$164$	−5.88629e7	−1.04205
$165$	3.20789e7	0.555938
$166$	−9.66454e6	−0.163984
$167$	3.41266e7	0.567003	0.283501	−	0.958972i	$-0.408504\pi$
$167$	3.41266e7	0.567003	0.283501	+	0.958972i	$0.408504\pi$
$168$	8.91741e7	1.45096
$169$	1.31065e8	2.08874
$170$	2.94618e6	0.0459926
$171$	−1.40196e7	−0.214412
$172$	−7.29781e7	−1.09356
$173$	−9.93329e7	−1.45859	−0.729293	−	0.684202i	$-0.760151\pi$
$173$	−9.93329e7	−1.45859	−0.729293	+	0.684202i	$0.760151\pi$
$174$	−6.63241e6	−0.0954440
$175$	9.95925e7	1.40473
$176$	7.09358e7	0.980779
$177$	−1.76115e8	−2.38720
$178$	3.03891e7	0.403875
$179$	−1.45905e7	−0.190145	−0.0950724	−	0.995470i	$-0.530308\pi$
$179$	−1.45905e7	−0.190145	−0.0950724	+	0.995470i	$0.530308\pi$
$180$	2.21120e7	0.282601
$181$	7.70405e7	0.965704	0.482852	−	0.875702i	$-0.339601\pi$
$181$	7.70405e7	0.965704	0.482852	+	0.875702i	$0.339601\pi$
$182$	−7.29183e7	−0.896575
$183$	−6.18741e7	−0.746329
$184$	−2.86963e7	−0.339597
$185$	2.96967e7	0.344832
$186$	1.36927e7	0.156025
$187$	7.12051e7	0.796280
$188$	−1.22117e8	−1.34037
$189$	5.85499e7	0.630826
$190$	−1.34893e6	−0.0142676
$191$	8.54538e7	0.887390	0.443695	−	0.896178i	$-0.353667\pi$
$191$	8.54538e7	0.887390	0.443695	+	0.896178i	$0.353667\pi$
$192$	5.47931e7	0.558691
$193$	−1.64103e8	−1.64310	−0.821552	−	0.570133i	$-0.806892\pi$
$193$	−1.64103e8	−1.64310	−0.821552	+	0.570133i	$0.806892\pi$
$194$	−5.82587e7	−0.572868
$195$	−6.86632e7	−0.663136
$196$	−1.16028e8	−1.10069
$197$	8.78529e7	0.818699	0.409349	−	0.912378i	$-0.365756\pi$
$197$	8.78529e7	0.818699	0.409349	+	0.912378i	$0.365756\pi$
$198$	−7.00748e7	−0.641555
$199$	6.20987e7	0.558595	0.279297	−	0.960205i	$-0.409899\pi$
$199$	6.20987e7	0.558595	0.279297	+	0.960205i	$0.409899\pi$
$200$	−6.80413e7	−0.601406
$201$	−3.19459e6	−0.0277479
$202$	1.74180e7	0.148685
$203$	3.31625e7	0.278235
$204$	8.74600e7	0.721280
$205$	−3.63402e7	−0.294611
$206$	4.12747e6	0.0328964
$207$	−8.63993e7	−0.677040
$208$	−1.51834e8	−1.16990
$209$	−3.26017e7	−0.247018
$210$	2.58331e7	0.192490
$211$	1.63014e8	1.19464	0.597319	−	0.802004i	$-0.296233\pi$
$211$	1.63014e8	1.19464	0.597319	+	0.802004i	$0.296233\pi$
$212$	7.68724e7	0.554108
$213$	1.71830e8	1.21834
$214$	7.76605e6	0.0541691
$215$	−4.50545e7	−0.309174
$216$	−4.00011e7	−0.270075
$217$	−6.84646e7	−0.454838
$218$	6.38153e7	0.417183
$219$	−9.45040e7	−0.607989
$220$	5.14201e7	0.325577
$221$	−1.52411e8	−0.949823
$222$	−1.15595e8	−0.709096
$223$	−3.19127e8	−1.92706	−0.963532	−	0.267592i	$-0.913772\pi$
$223$	−3.19127e8	−1.92706	−0.963532	+	0.267592i	$0.913772\pi$
$224$	2.18807e8	1.30075
$225$	−2.04860e8	−1.19900
$226$	−5.49065e7	−0.316405
$227$	1.46494e8	0.831243	0.415622	−	0.909538i	$-0.363564\pi$
$227$	1.46494e8	0.831243	0.415622	+	0.909538i	$0.363564\pi$
$228$	−4.00441e7	−0.223752
$229$	−2.10628e7	−0.115902	−0.0579510	−	0.998319i	$-0.518457\pi$
$229$	−2.10628e7	−0.115902	−0.0579510	+	0.998319i	$0.518457\pi$
$230$	−8.31311e6	−0.0450522
$231$	6.24349e8	3.33262
$232$	−2.26565e7	−0.119120
$233$	−5.92467e7	−0.306845	−0.153422	−	0.988161i	$-0.549029\pi$
$233$	−5.92467e7	−0.306845	−0.153422	+	0.988161i	$0.549029\pi$
$234$	1.49991e8	0.765263
$235$	−7.53914e7	−0.378952
$236$	−2.82299e8	−1.39803
$237$	4.21895e8	2.05866
$238$	5.73413e7	0.275707
$239$	−1.81309e8	−0.859067	−0.429533	−	0.903051i	$-0.641322\pi$
$239$	−1.81309e8	−0.859067	−0.429533	+	0.903051i	$0.641322\pi$
$240$	5.37909e7	0.251171
$241$	−3.09095e8	−1.42244	−0.711218	−	0.702972i	$-0.751856\pi$
$241$	−3.09095e8	−1.42244	−0.711218	+	0.702972i	$0.751856\pi$
$242$	−8.78894e7	−0.398642
$243$	3.11399e8	1.39218
$244$	−9.91797e7	−0.437077
$245$	−7.16321e7	−0.311191
$246$	1.41455e8	0.605823
$247$	6.97822e7	0.294649
$248$	4.67748e7	0.194729
$249$	−1.77124e8	−0.727074
$250$	−4.07356e7	−0.164886
$251$	1.15888e8	0.462571	0.231286	−	0.972886i	$-0.425707\pi$
$251$	1.15888e8	0.462571	0.231286	+	0.972886i	$0.425707\pi$
$252$	4.30364e8	1.69408
$253$	−2.00916e8	−0.779998
$254$	3.01911e7	0.115601
$255$	5.39952e7	0.203922
$256$	8.48642e6	0.0316144
$257$	1.57386e8	0.578362	0.289181	−	0.957274i	$-0.406617\pi$
$257$	1.57386e8	0.578362	0.289181	+	0.957274i	$0.406617\pi$
$258$	1.75376e8	0.635771
$259$	5.77985e8	2.06713
$260$	−1.10062e8	−0.388357
$261$	−6.82145e7	−0.237484
$262$	−1.22051e8	−0.419262
$263$	2.28632e8	0.774982	0.387491	−	0.921874i	$-0.373342\pi$
$263$	2.28632e8	0.774982	0.387491	+	0.921874i	$0.373342\pi$
$264$	−4.26554e8	−1.42679
$265$	4.74587e7	0.156659
$266$	−2.62541e7	−0.0855285
$267$	5.56946e8	1.79070
$268$	−5.12070e6	−0.0162501
$269$	1.78157e8	0.558045	0.279023	−	0.960285i	$-0.409990\pi$
$269$	1.78157e8	0.558045	0.279023	+	0.960285i	$0.409990\pi$
$270$	−1.15880e7	−0.0358291
$271$	1.96609e8	0.600084	0.300042	−	0.953926i	$-0.402999\pi$
$271$	1.96609e8	0.600084	0.300042	+	0.953926i	$0.402999\pi$
$272$	1.19399e8	0.359757
$273$	−1.33639e9	−3.97523
$274$	7.52026e7	0.220854
$275$	−4.76389e8	−1.38133
$276$	−2.46782e8	−0.706532
$277$	−4.44045e8	−1.25530	−0.627650	−	0.778496i	$-0.715983\pi$
$277$	−4.44045e8	−1.25530	−0.627650	+	0.778496i	$0.715983\pi$
$278$	3.44783e7	0.0962475
$279$	1.40830e8	0.388223
$280$	8.82466e7	0.240240
$281$	3.99424e8	1.07389	0.536947	−	0.843616i	$-0.319577\pi$
$281$	3.99424e8	1.07389	0.536947	+	0.843616i	$0.319577\pi$
$282$	2.93463e8	0.779259
$283$	6.41949e7	0.168364	0.0841818	−	0.996450i	$-0.473172\pi$
$283$	6.41949e7	0.168364	0.0841818	+	0.996450i	$0.473172\pi$
$284$	2.75431e8	0.713507
$285$	−2.47220e7	−0.0632597
$286$	3.48796e8	0.881638
$287$	−7.07285e8	−1.76607
$288$	−4.50081e8	−1.11024
$289$	−2.90486e8	−0.707919
$290$	−6.56342e6	−0.0158029
$291$	−1.06772e9	−2.53998
$292$	−1.51483e8	−0.356060
$293$	6.99540e8	1.62471	0.812355	−	0.583163i	$-0.198185\pi$
$293$	6.99540e8	1.62471	0.812355	+	0.583163i	$0.198185\pi$
$294$	2.78830e8	0.639918
$295$	−1.74283e8	−0.395256
$296$	−3.94878e8	−0.884997
$297$	−2.80066e8	−0.620317
$298$	−2.83310e8	−0.620162
$299$	4.30051e8	0.930402
$300$	−5.85140e8	−1.25122
$301$	−8.76892e8	−1.85338
$302$	−1.21773e8	−0.254406
$303$	3.19222e8	0.659240
$304$	−5.46676e7	−0.111602
$305$	−6.12306e7	−0.123572
$306$	−1.17950e8	−0.235327
$307$	3.74818e8	0.739326	0.369663	−	0.929166i	$-0.379473\pi$
$307$	3.74818e8	0.739326	0.369663	+	0.929166i	$0.379473\pi$
$308$	1.00079e9	1.95170
$309$	7.56449e7	0.145856
$310$	1.35503e7	0.0258335
$311$	4.26392e8	0.803799	0.401900	−	0.915684i	$-0.368350\pi$
$311$	4.26392e8	0.803799	0.401900	+	0.915684i	$0.368350\pi$
$312$	9.13015e8	1.70191
$313$	−5.61937e8	−1.03582	−0.517908	−	0.855437i	$-0.673289\pi$
$313$	−5.61937e8	−1.03582	−0.517908	+	0.855437i	$0.673289\pi$
$314$	−1.14504e8	−0.208721
$315$	2.65694e8	0.478955
$316$	6.76266e8	1.20563
$317$	5.91476e8	1.04287	0.521434	−	0.853291i	$-0.325397\pi$
$317$	5.91476e8	1.04287	0.521434	+	0.853291i	$0.325397\pi$
$318$	−1.84734e8	−0.322146
$319$	−1.58629e8	−0.273599
$320$	5.42232e7	0.0925039
$321$	1.42330e8	0.240175
$322$	−1.61797e8	−0.270070
$323$	−5.48751e7	−0.0906080
$324$	3.48200e8	0.568749
$325$	1.01968e9	1.64768
$326$	−4.09629e7	−0.0654832
$327$	1.16955e9	1.84971
$328$	4.83215e8	0.756105
$329$	−1.46734e9	−2.27166
$330$	−1.23569e8	−0.189283
$331$	−5.39249e8	−0.817319	−0.408659	−	0.912687i	$-0.634004\pi$
$331$	−5.39249e8	−0.817319	−0.408659	+	0.912687i	$0.634004\pi$
$332$	−2.83916e8	−0.425801
$333$	−1.18890e9	−1.76438
$334$	−1.31457e8	−0.193051
$335$	−3.16136e6	−0.00459428
$336$	1.04693e9	1.50567
$337$	6.27905e7	0.0893695	0.0446847	−	0.999001i	$-0.485772\pi$
$337$	6.27905e7	0.0893695	0.0446847	+	0.999001i	$0.485772\pi$
$338$	−5.04869e8	−0.711164
$339$	−1.00628e9	−1.40288
$340$	8.65502e7	0.119424
$341$	3.27492e8	0.447261
$342$	5.40040e7	0.0730020
$343$	−2.74373e8	−0.367123
$344$	5.99090e8	0.793483
$345$	−1.52356e8	−0.199752
$346$	3.82634e8	0.496613
$347$	3.52789e8	0.453275	0.226637	−	0.973979i	$-0.427227\pi$
$347$	3.52789e8	0.453275	0.226637	+	0.973979i	$0.427227\pi$
$348$	−1.94841e8	−0.247829
$349$	1.34072e8	0.168830	0.0844152	−	0.996431i	$-0.473098\pi$
$349$	1.34072e8	0.168830	0.0844152	+	0.996431i	$0.473098\pi$
$350$	−3.83634e8	−0.478277
$351$	5.99467e8	0.739929
$352$	−1.04664e9	−1.27908
$353$	1.31528e9	1.59149	0.795747	−	0.605629i	$-0.207078\pi$
$353$	1.31528e9	1.59149	0.795747	+	0.605629i	$0.207078\pi$
$354$	6.78402e8	0.812785
$355$	1.70043e8	0.201724
$356$	8.92743e8	1.04870
$357$	1.05090e9	1.22243
$358$	5.62032e7	0.0647396
$359$	−2.34254e8	−0.267213	−0.133606	−	0.991034i	$-0.542656\pi$
$359$	−2.34254e8	−0.267213	−0.133606	+	0.991034i	$0.542656\pi$
$360$	−1.81521e8	−0.205054
$361$	−8.68747e8	−0.971892
$362$	−2.96763e8	−0.328799
$363$	−1.61076e9	−1.76750
$364$	−2.14213e9	−2.32804
$365$	−9.35210e7	−0.100666
$366$	2.38342e8	0.254107
$367$	−3.82702e8	−0.404138	−0.202069	−	0.979371i	$-0.564766\pi$
$367$	−3.82702e8	−0.404138	−0.202069	+	0.979371i	$0.564766\pi$
$368$	−3.36903e8	−0.352401
$369$	1.45487e9	1.50741
$370$	−1.14393e8	−0.117407
$371$	9.23685e8	0.939107
$372$	4.02253e8	0.405134
$373$	6.38932e8	0.637490	0.318745	−	0.947840i	$-0.396739\pi$
$373$	6.38932e8	0.637490	0.318745	+	0.947840i	$0.396739\pi$
$374$	−2.74285e8	−0.271114
$375$	−7.46568e8	−0.731071
$376$	1.00248e9	0.972564
$377$	3.39536e8	0.326356
$378$	−2.25537e8	−0.214781
$379$	1.90014e9	1.79287	0.896436	−	0.443174i	$-0.146148\pi$
$379$	1.90014e9	1.79287	0.896436	+	0.443174i	$0.146148\pi$
$380$	−3.96276e7	−0.0370472
$381$	5.53317e8	0.512550
$382$	−3.29171e8	−0.302135
$383$	−1.94395e9	−1.76803	−0.884016	−	0.467457i	$-0.845170\pi$
$383$	−1.94395e9	−1.76803	−0.884016	+	0.467457i	$0.845170\pi$
$384$	−1.66520e9	−1.50074
$385$	6.17855e8	0.551790
$386$	6.32130e8	0.559437
$387$	1.80375e9	1.58193
$388$	−1.71147e9	−1.48750
$389$	6.82979e8	0.588279	0.294140	−	0.955762i	$-0.404967\pi$
$389$	6.82979e8	0.588279	0.294140	+	0.955762i	$0.404967\pi$
$390$	2.64493e8	0.225782
$391$	−3.38182e8	−0.286109
$392$	9.52493e8	0.798658
$393$	−2.23684e9	−1.85892
$394$	−3.38413e8	−0.278747
$395$	4.17506e8	0.340858
$396$	−2.05860e9	−1.66586
$397$	1.40470e9	1.12672	0.563360	−	0.826211i	$-0.309508\pi$
$397$	1.40470e9	1.12672	0.563360	+	0.826211i	$0.309508\pi$
$398$	−2.39207e8	−0.190188
$399$	−4.81163e8	−0.379216
$400$	−7.98823e8	−0.624081
$401$	−1.30325e9	−1.00931	−0.504653	−	0.863322i	$-0.668380\pi$
$401$	−1.30325e9	−1.00931	−0.504653	+	0.863322i	$0.668380\pi$
$402$	1.23057e7	0.00944747
$403$	−7.00980e8	−0.533504
$404$	5.11689e8	0.386075
$405$	2.14968e8	0.160798
$406$	−1.27743e8	−0.0947321
$407$	−2.76472e9	−2.03269
$408$	−7.17974e8	−0.523357
$409$	−1.27972e9	−0.924877	−0.462439	−	0.886651i	$-0.653025\pi$
$409$	−1.27972e9	−0.924877	−0.462439	+	0.886651i	$0.653025\pi$
$410$	1.39984e8	0.100308
$411$	1.37825e9	0.979224
$412$	1.21253e8	0.0854186
$413$	−3.39206e9	−2.36940
$414$	3.32814e8	0.230515
$415$	−1.75281e8	−0.120384
$416$	2.24027e9	1.52571
$417$	6.31890e8	0.426742
$418$	1.25583e8	0.0841035
$419$	−2.33612e9	−1.55148	−0.775738	−	0.631055i	$-0.782622\pi$
$419$	−2.33612e9	−1.55148	−0.775738	+	0.631055i	$0.782622\pi$
$420$	7.58900e8	0.499818
$421$	2.84462e9	1.85797	0.928983	−	0.370123i	$-0.120684\pi$
$421$	2.84462e9	1.85797	0.928983	+	0.370123i	$0.120684\pi$
$422$	−6.27936e8	−0.406745
$423$	3.01828e9	1.93896
$424$	−6.31059e8	−0.402059
$425$	−8.01856e8	−0.506682
$426$	−6.61896e8	−0.414817
$427$	−1.19173e9	−0.740762
$428$	2.28144e8	0.140655
$429$	6.39244e9	3.90901
$430$	1.73552e8	0.105266
$431$	1.52129e9	0.915254	0.457627	−	0.889144i	$-0.348700\pi$
$431$	1.52129e9	0.915254	0.457627	+	0.889144i	$0.348700\pi$
$432$	−4.69624e8	−0.280257
$433$	−8.15595e8	−0.482799	−0.241400	−	0.970426i	$-0.577606\pi$
$433$	−8.15595e8	−0.482799	−0.241400	+	0.970426i	$0.577606\pi$
$434$	2.63729e8	0.154861
$435$	−1.20289e8	−0.0700670
$436$	1.87471e9	1.08326
$437$	1.54839e8	0.0887554
$438$	3.64033e8	0.207005
$439$	2.65445e9	1.49744	0.748719	−	0.662887i	$-0.230669\pi$
$439$	2.65445e9	1.49744	0.748719	+	0.662887i	$0.230669\pi$
$440$	−4.22117e8	−0.236237
$441$	2.86778e9	1.59225
$442$	5.87092e8	0.323391
$443$	6.06287e8	0.331334	0.165667	−	0.986182i	$-0.447022\pi$
$443$	6.06287e8	0.331334	0.165667	+	0.986182i	$0.447022\pi$
$444$	−3.39586e9	−1.84123
$445$	5.51152e8	0.296491
$446$	1.22929e9	0.656118
$447$	−5.19228e9	−2.74968
$448$	1.05534e9	0.554524
$449$	1.17328e9	0.611700	0.305850	−	0.952080i	$-0.401059\pi$
$449$	1.17328e9	0.611700	0.305850	+	0.952080i	$0.401059\pi$
$450$	7.89127e8	0.408229
$451$	3.38322e9	1.73665
$452$	−1.61299e9	−0.821576
$453$	−2.23175e9	−1.12798
$454$	−5.64299e8	−0.283018
$455$	−1.32249e9	−0.658190
$456$	3.28729e8	0.162353
$457$	−2.98827e9	−1.46458	−0.732290	−	0.680993i	$-0.761549\pi$
$457$	−2.98827e9	−1.46458	−0.732290	+	0.680993i	$0.761549\pi$
$458$	8.11346e7	0.0394618
$459$	−4.71407e8	−0.227537
$460$	−2.44215e8	−0.116982
$461$	−1.96686e9	−0.935020	−0.467510	−	0.883988i	$-0.654849\pi$
$461$	−1.96686e9	−0.935020	−0.467510	+	0.883988i	$0.654849\pi$
$462$	−2.40502e9	−1.13468
$463$	1.82287e9	0.853537	0.426769	−	0.904361i	$-0.359652\pi$
$463$	1.82287e9	0.853537	0.426769	+	0.904361i	$0.359652\pi$
$464$	−2.65994e8	−0.123611
$465$	2.48339e8	0.114541
$466$	2.28221e8	0.104473
$467$	−1.22594e9	−0.557007	−0.278503	−	0.960435i	$-0.589838\pi$
$467$	−1.22594e9	−0.557007	−0.278503	+	0.960435i	$0.589838\pi$
$468$	4.40631e9	1.98708
$469$	−6.15294e7	−0.0275409
$470$	2.90411e8	0.129024
$471$	−2.09853e9	−0.925429
$472$	2.31744e9	1.01441
$473$	4.19451e9	1.82250
$474$	−1.62516e9	−0.700923
$475$	3.67135e8	0.157180
$476$	1.68452e9	0.715899
$477$	−1.90000e9	−0.801566
$478$	6.98410e8	0.292491
$479$	−2.30108e9	−0.956660	−0.478330	−	0.878180i	$-0.658758\pi$
$479$	−2.30108e9	−0.956660	−0.478330	+	0.878180i	$0.658758\pi$
$480$	−7.93668e8	−0.327563
$481$	5.91774e9	2.42464
$482$	1.19065e9	0.484304
$483$	−2.96529e9	−1.19743
$484$	−2.58194e9	−1.03511
$485$	−1.05661e9	−0.420551
$486$	−1.19952e9	−0.474004
$487$	1.09786e9	0.430721	0.215361	−	0.976535i	$-0.430907\pi$
$487$	1.09786e9	0.430721	0.215361	+	0.976535i	$0.430907\pi$
$488$	8.14183e8	0.317141
$489$	−7.50735e8	−0.290339
$490$	2.75930e8	0.105953
$491$	−3.39538e9	−1.29450	−0.647252	−	0.762276i	$-0.724082\pi$
$491$	−3.39538e9	−1.29450	−0.647252	+	0.762276i	$0.724082\pi$
$492$	4.15554e9	1.57308
$493$	−2.67004e8	−0.100358
$494$	−2.68804e8	−0.100321
$495$	−1.27091e9	−0.470975
$496$	5.49149e8	0.202071
$497$	3.30952e9	1.20926
$498$	6.82287e8	0.247551
$499$	−3.73693e8	−0.134637	−0.0673183	−	0.997732i	$-0.521444\pi$
$499$	−3.73693e8	−0.134637	−0.0673183	+	0.997732i	$0.521444\pi$
$500$	−1.19669e9	−0.428142
$501$	−2.40923e9	−0.855947
$502$	−4.46403e8	−0.157494
$503$	8.48398e8	0.297243	0.148622	−	0.988894i	$-0.452516\pi$
$503$	8.48398e8	0.297243	0.148622	+	0.988894i	$0.452516\pi$
$504$	−3.53293e9	−1.22922
$505$	3.15902e8	0.109152
$506$	7.73938e8	0.265570
$507$	−9.25282e9	−3.15316
$508$	8.86926e8	0.300168
$509$	3.50938e9	1.17955	0.589777	−	0.807566i	$-0.299216\pi$
$509$	3.50938e9	1.17955	0.589777	+	0.807566i	$0.299216\pi$
$510$	−2.07992e8	−0.0694305
$511$	−1.82019e9	−0.603454
$512$	−3.05187e9	−1.00490
$513$	2.15837e8	0.0705853
$514$	−6.06257e8	−0.196918
$515$	7.48580e7	0.0241498
$516$	5.15204e9	1.65084
$517$	7.01883e9	2.23382
$518$	−2.22642e9	−0.703806
$519$	7.01261e9	2.20188
$520$	9.03518e8	0.281790
$521$	−5.58236e9	−1.72936	−0.864681	−	0.502322i	$-0.832479\pi$
$521$	−5.58236e9	−1.72936	−0.864681	+	0.502322i	$0.832479\pi$
$522$	2.62765e8	0.0808576
$523$	−7.06276e7	−0.0215883	−0.0107942	−	0.999942i	$-0.503436\pi$
$523$	−7.06276e7	−0.0215883	−0.0107942	+	0.999942i	$0.503436\pi$
$524$	−3.58550e9	−1.08865
$525$	−7.03093e9	−2.12058
$526$	−8.80699e8	−0.263862
$527$	5.51234e8	0.164059
$528$	−5.00786e9	−1.48058
$529$	−2.45059e9	−0.719741
$530$	−1.82813e8	−0.0533385
$531$	6.97739e9	2.02238
$532$	−7.71268e8	−0.222083
$533$	−7.24159e9	−2.07152
$534$	−2.14538e9	−0.609690
$535$	1.40849e8	0.0397664
$536$	4.20367e7	0.0117910
$537$	1.03005e9	0.287043
$538$	−6.86267e8	−0.190001
$539$	6.66885e9	1.83438
$540$	−3.40422e8	−0.0930336
$541$	−4.71756e8	−0.128093	−0.0640467	−	0.997947i	$-0.520401\pi$
$541$	−4.71756e8	−0.128093	−0.0640467	+	0.997947i	$0.520401\pi$
$542$	−7.57347e8	−0.204314
$543$	−5.43883e9	−1.45783
$544$	−1.76169e9	−0.469175
$545$	1.15739e9	0.306261
$546$	5.14781e9	1.35347
$547$	2.11698e8	0.0553047	0.0276523	−	0.999618i	$-0.491197\pi$
$547$	2.11698e8	0.0553047	0.0276523	+	0.999618i	$0.491197\pi$
$548$	2.20924e9	0.573469
$549$	2.45135e9	0.632270
$550$	1.83507e9	0.470308
$551$	1.22249e8	0.0311326
$552$	2.02588e9	0.512656
$553$	8.12589e9	2.04330
$554$	1.71048e9	0.427399
$555$	−2.09650e9	−0.520558
$556$	1.01287e9	0.249916
$557$	7.03624e9	1.72523	0.862615	−	0.505860i	$-0.168825\pi$
$557$	7.03624e9	1.72523	0.862615	+	0.505860i	$0.168825\pi$
$558$	−5.42484e8	−0.132180
$559$	−8.97811e9	−2.17392
$560$	1.03604e9	0.249297
$561$	−5.02687e9	−1.20206
$562$	−1.53860e9	−0.365635
$563$	2.83983e9	0.670677	0.335339	−	0.942098i	$-0.391149\pi$
$563$	2.83983e9	0.670677	0.335339	+	0.942098i	$0.391149\pi$
$564$	8.62110e9	2.02342
$565$	−9.95813e8	−0.232278
$566$	−2.47281e8	−0.0573237
$567$	4.18390e9	0.963920
$568$	−2.26106e9	−0.517717
$569$	−1.58570e9	−0.360850	−0.180425	−	0.983589i	$-0.557747\pi$
$569$	−1.58570e9	−0.360850	−0.180425	+	0.983589i	$0.557747\pi$
$570$	9.52302e7	0.0215384
$571$	−1.80154e9	−0.404964	−0.202482	−	0.979286i	$-0.564901\pi$
$571$	−1.80154e9	−0.404964	−0.202482	+	0.979286i	$0.564901\pi$
$572$	1.02466e10	2.28925
$573$	−6.03278e9	−1.33960
$574$	2.72449e9	0.601304
$575$	2.26256e9	0.496322
$576$	−2.17082e9	−0.473308
$577$	9.47117e8	0.205253	0.102626	−	0.994720i	$-0.467275\pi$
$577$	9.47117e8	0.205253	0.102626	+	0.994720i	$0.467275\pi$
$578$	1.11897e9	0.241029
$579$	1.15852e10	2.48043
$580$	−1.92814e8	−0.0410337
$581$	−3.41148e9	−0.721650
$582$	4.11289e9	0.864801
$583$	−4.41834e9	−0.923461
$584$	1.24355e9	0.258356
$585$	2.72032e9	0.561791
$586$	−2.69466e9	−0.553174
$587$	3.36418e9	0.686509	0.343255	−	0.939242i	$-0.388471\pi$
$587$	3.36418e9	0.686509	0.343255	+	0.939242i	$0.388471\pi$
$588$	8.19122e9	1.66161
$589$	−2.52386e8	−0.0508934
$590$	6.71345e8	0.134575
$591$	−6.20215e9	−1.23591
$592$	−4.63597e9	−0.918364
$593$	−7.19523e9	−1.41695	−0.708473	−	0.705738i	$-0.750616\pi$
$593$	−7.19523e9	−1.41695	−0.708473	+	0.705738i	$0.750616\pi$
$594$	1.07883e9	0.211203
$595$	1.03997e9	0.202401
$596$	−8.32284e9	−1.61031
$597$	−4.38398e9	−0.843254
$598$	−1.65657e9	−0.316779
$599$	−1.93743e9	−0.368326	−0.184163	−	0.982896i	$-0.558957\pi$
$599$	−1.93743e9	−0.368326	−0.184163	+	0.982896i	$0.558957\pi$
$600$	4.80351e9	0.907882
$601$	7.98811e8	0.150101	0.0750505	−	0.997180i	$-0.476088\pi$
$601$	7.98811e8	0.150101	0.0750505	+	0.997180i	$0.476088\pi$
$602$	3.37782e9	0.631029
$603$	1.26565e8	0.0235072
$604$	−3.57734e9	−0.660588
$605$	−1.59401e9	−0.292649
$606$	−1.22966e9	−0.224455
$607$	−9.35100e8	−0.169706	−0.0848531	−	0.996393i	$-0.527042\pi$
$607$	−9.35100e8	−0.169706	−0.0848531	+	0.996393i	$0.527042\pi$
$608$	8.06603e8	0.145545
$609$	−2.34117e9	−0.420023
$610$	2.35863e8	0.0420731
$611$	−1.50234e10	−2.66455
$612$	−3.46502e9	−0.611049
$613$	5.41673e8	0.0949786	0.0474893	−	0.998872i	$-0.484878\pi$
$613$	5.41673e8	0.0949786	0.0474893	+	0.998872i	$0.484878\pi$
$614$	−1.44381e9	−0.251722
$615$	2.56551e9	0.444744
$616$	−8.21563e9	−1.41615
$617$	1.15613e10	1.98157	0.990785	−	0.135446i	$-0.0432469\pi$
$617$	1.15613e10	1.98157	0.990785	+	0.135446i	$0.0432469\pi$
$618$	−2.91387e8	−0.0496605
$619$	9.62209e8	0.163062	0.0815309	−	0.996671i	$-0.474019\pi$
$619$	9.62209e8	0.163062	0.0815309	+	0.996671i	$0.474019\pi$
$620$	3.98069e8	0.0670791
$621$	1.33015e9	0.222884
$622$	−1.64248e9	−0.273674
$623$	1.07270e10	1.77734
$624$	1.07190e10	1.76608
$625$	4.98340e9	0.816480
$626$	2.16460e9	0.352670
$627$	2.30158e9	0.372898
$628$	−3.36379e9	−0.541964
$629$	−4.65357e9	−0.745606
$630$	−1.02346e9	−0.163072
$631$	4.10539e9	0.650507	0.325253	−	0.945627i	$-0.394550\pi$
$631$	4.10539e9	0.650507	0.325253	+	0.945627i	$0.394550\pi$
$632$	−5.55158e9	−0.874797
$633$	−1.15083e10	−1.80342
$634$	−2.27839e9	−0.355071
$635$	5.47562e8	0.0848643
$636$	−5.42696e9	−0.836482
$637$	−1.42743e10	−2.18810
$638$	6.11045e8	0.0931538
$639$	−6.80762e9	−1.03215
$640$	−1.64788e9	−0.248482
$641$	8.12719e9	1.21881	0.609407	−	0.792857i	$-0.291408\pi$
$641$	8.12719e9	1.21881	0.609407	+	0.792857i	$0.291408\pi$
$642$	−5.48260e8	−0.0817738
$643$	5.87471e9	0.871461	0.435731	−	0.900077i	$-0.356490\pi$
$643$	5.87471e9	0.871461	0.435731	+	0.900077i	$0.356490\pi$
$644$	−4.75314e9	−0.701261
$645$	3.18071e9	0.466730
$646$	2.11381e8	0.0308498
$647$	−9.84819e9	−1.42952	−0.714762	−	0.699368i	$-0.753465\pi$
$647$	−9.84819e9	−1.42952	−0.714762	+	0.699368i	$0.753465\pi$
$648$	−2.85843e9	−0.412682
$649$	1.62255e10	2.32992
$650$	−3.92786e9	−0.560996
$651$	4.83340e9	0.686624
$652$	−1.20337e9	−0.170033
$653$	−6.25022e9	−0.878413	−0.439207	−	0.898386i	$-0.644740\pi$
$653$	−6.25022e9	−0.878413	−0.439207	+	0.898386i	$0.644740\pi$
$654$	−4.50517e9	−0.629780
$655$	−2.21358e9	−0.307787
$656$	5.67308e9	0.784613
$657$	3.74410e9	0.515072
$658$	5.65224e9	0.773446
$659$	−9.83697e9	−1.33894	−0.669472	−	0.742837i	$-0.733480\pi$
$659$	−9.83697e9	−1.33894	−0.669472	+	0.742837i	$0.733480\pi$
$660$	−3.63011e9	−0.491491
$661$	3.62871e9	0.488705	0.244353	−	0.969686i	$-0.421425\pi$
$661$	3.62871e9	0.488705	0.244353	+	0.969686i	$0.421425\pi$
$662$	2.07721e9	0.278277
$663$	1.07597e10	1.43385
$664$	2.33072e9	0.308959
$665$	−4.76158e8	−0.0627878
$666$	4.57970e9	0.600727
$667$	7.53392e8	0.0983062
$668$	−3.86182e9	−0.501274
$669$	2.25294e10	2.90910
$670$	1.21777e7	0.00156424
$671$	5.70047e9	0.728421
$672$	−1.54471e10	−1.96361
$673$	1.23685e10	1.56410	0.782051	−	0.623215i	$-0.214174\pi$
$673$	1.23685e10	1.56410	0.782051	+	0.623215i	$0.214174\pi$
$674$	−2.41871e8	−0.0304281
$675$	3.15389e9	0.394714
$676$	−1.48316e10	−1.84661
$677$	1.46924e10	1.81983	0.909916	−	0.414793i	$-0.136146\pi$
$677$	1.46924e10	1.81983	0.909916	+	0.414793i	$0.136146\pi$
$678$	3.87623e9	0.477646
$679$	−2.05647e10	−2.52103
$680$	−7.10506e8	−0.0866536
$681$	−1.03420e10	−1.25485
$682$	−1.26151e9	−0.152281
$683$	−1.07348e10	−1.28920	−0.644602	−	0.764518i	$-0.722977\pi$
$683$	−1.07348e10	−1.28920	−0.644602	+	0.764518i	$0.722977\pi$
$684$	1.58648e9	0.189557
$685$	1.36392e9	0.162133
$686$	1.05689e9	0.124996
$687$	1.48697e9	0.174966
$688$	7.03348e9	0.823400
$689$	9.45721e9	1.10153
$690$	5.86881e8	0.0680108
$691$	−8.04700e9	−0.927814	−0.463907	−	0.885884i	$-0.653553\pi$
$691$	−8.04700e9	−0.927814	−0.463907	+	0.885884i	$0.653553\pi$
$692$	1.12407e10	1.28950
$693$	−2.47357e10	−2.82331
$694$	−1.35896e9	−0.154329
$695$	6.25317e8	0.0706568
$696$	1.59948e9	0.179824
$697$	5.69462e9	0.637016
$698$	−5.16453e8	−0.0574826
$699$	4.18264e9	0.463213
$700$	−1.12701e10	−1.24189
$701$	7.19522e9	0.788917	0.394458	−	0.918914i	$-0.370932\pi$
$701$	7.19522e9	0.788917	0.394458	+	0.918914i	$0.370932\pi$
$702$	−2.30917e9	−0.251928
$703$	2.13067e9	0.231298
$704$	−5.04810e9	−0.545285
$705$	5.32241e9	0.572066
$706$	−5.06649e9	−0.541865
$707$	6.14837e9	0.654322
$708$	1.99295e10	2.11047
$709$	6.99475e9	0.737072	0.368536	−	0.929613i	$-0.379859\pi$
$709$	6.99475e9	0.737072	0.368536	+	0.929613i	$0.379859\pi$
$710$	−6.55011e8	−0.0686822
$711$	−1.67148e10	−1.74404
$712$	−7.32868e9	−0.760932
$713$	−1.55539e9	−0.160704
$714$	−4.04812e9	−0.416208
$715$	6.32595e9	0.647224
$716$	1.65109e9	0.168103
$717$	1.27999e10	1.29685
$718$	9.02357e8	0.0909793
$719$	−7.35872e9	−0.738331	−0.369166	−	0.929364i	$-0.620356\pi$
$719$	−7.35872e9	−0.738331	−0.369166	+	0.929364i	$0.620356\pi$
$720$	−2.13111e9	−0.212785
$721$	1.45696e9	0.144768
$722$	3.34645e9	0.330905
$723$	2.18212e10	2.14731
$724$	−8.71804e9	−0.853756
$725$	1.78635e9	0.174094
$726$	6.20473e9	0.601790
$727$	−3.31903e9	−0.320362	−0.160181	−	0.987088i	$-0.551208\pi$
$727$	−3.31903e9	−0.320362	−0.160181	+	0.987088i	$0.551208\pi$
$728$	1.75851e10	1.68922
$729$	−1.52545e10	−1.45831
$730$	3.60247e8	0.0342744
$731$	7.06018e9	0.668506
$732$	7.00179e9	0.659812
$733$	3.23274e9	0.303185	0.151592	−	0.988443i	$-0.451560\pi$
$733$	3.23274e9	0.303185	0.151592	+	0.988443i	$0.451560\pi$
$734$	1.47418e9	0.137599
$735$	5.05701e9	0.469774
$736$	4.97090e9	0.459581
$737$	2.94318e8	0.0270820
$738$	−5.60422e9	−0.513237
$739$	7.82881e8	0.0713576	0.0356788	−	0.999363i	$-0.488641\pi$
$739$	7.82881e8	0.0713576	0.0356788	+	0.999363i	$0.488641\pi$
$740$	−3.36053e9	−0.304858
$741$	−4.92642e9	−0.444803
$742$	−3.55807e9	−0.319743
$743$	1.40090e10	1.25298	0.626491	−	0.779428i	$-0.284490\pi$
$743$	1.40090e10	1.25298	0.626491	+	0.779428i	$0.284490\pi$
$744$	−3.30216e9	−0.293964
$745$	−5.13827e9	−0.455271
$746$	−2.46119e9	−0.217050
$747$	7.01735e9	0.615958
$748$	−8.05770e9	−0.703972
$749$	2.74134e9	0.238383
$750$	2.87581e9	0.248912
$751$	−1.35848e10	−1.17035	−0.585174	−	0.810908i	$-0.698974\pi$
$751$	−1.35848e10	−1.17035	−0.585174	+	0.810908i	$0.698974\pi$
$752$	1.17694e10	1.00923
$753$	−8.18131e9	−0.698298
$754$	−1.30791e9	−0.111116
$755$	−2.20854e9	−0.186763
$756$	−6.62561e9	−0.557699
$757$	−8.32623e9	−0.697610	−0.348805	−	0.937195i	$-0.613413\pi$
$757$	−8.32623e9	−0.697610	−0.348805	+	0.937195i	$0.613413\pi$
$758$	−7.31943e9	−0.610429
$759$	1.41841e10	1.17749
$760$	3.25310e8	0.0268812
$761$	3.46947e9	0.285375	0.142688	−	0.989768i	$-0.454426\pi$
$761$	3.46947e9	0.285375	0.142688	+	0.989768i	$0.454426\pi$
$762$	−2.13140e9	−0.174511
$763$	2.25262e10	1.83591
$764$	−9.67010e9	−0.784521
$765$	−2.13920e9	−0.172757
$766$	7.48818e9	0.601971
$767$	−3.47298e10	−2.77919
$768$	−5.99116e8	−0.0477250
$769$	−1.32653e9	−0.105190	−0.0525950	−	0.998616i	$-0.516749\pi$
$769$	−1.32653e9	−0.105190	−0.0525950	+	0.998616i	$0.516749\pi$
$770$	−2.38000e9	−0.187871
$771$	−1.11110e10	−0.873095
$772$	1.85702e10	1.45263
$773$	7.83233e9	0.609906	0.304953	−	0.952367i	$-0.401359\pi$
$773$	7.83233e9	0.609906	0.304953	+	0.952367i	$0.401359\pi$
$774$	−6.94811e9	−0.538609
$775$	−3.68796e9	−0.284597
$776$	1.40498e10	1.07933
$777$	−4.08040e10	−3.12054
$778$	−2.63086e9	−0.200295
$779$	−2.60732e9	−0.197612
$780$	7.77005e9	0.586263
$781$	−1.58307e10	−1.18911
$782$	1.30269e9	0.0974132
$783$	1.05019e9	0.0781809
$784$	1.11825e10	0.828769
$785$	−2.07671e9	−0.153226
$786$	8.61641e9	0.632918
$787$	−7.58938e9	−0.555002	−0.277501	−	0.960725i	$-0.589506\pi$
$787$	−7.58938e9	−0.555002	−0.277501	+	0.960725i	$0.589506\pi$
$788$	−9.94159e9	−0.723792
$789$	−1.61407e10	−1.16991
$790$	−1.60825e9	−0.116054
$791$	−1.93814e10	−1.39241
$792$	1.68994e10	1.20874
$793$	−1.22016e10	−0.868879
$794$	−5.41095e9	−0.383621
$795$	−3.35044e9	−0.236492
$796$	−7.02720e9	−0.493840
$797$	−6.97607e9	−0.488098	−0.244049	−	0.969763i	$-0.578476\pi$
$797$	−6.97607e9	−0.488098	−0.244049	+	0.969763i	$0.578476\pi$
$798$	1.85346e9	0.129114
$799$	1.18141e10	0.819381
$800$	1.17864e10	0.813890
$801$	−2.20653e10	−1.51704
$802$	5.02018e9	0.343644
$803$	8.70667e9	0.593400
$804$	3.61506e8	0.0245312
$805$	−2.93444e9	−0.198262
$806$	2.70020e9	0.181645
$807$	−1.25773e10	−0.842425
$808$	−4.20055e9	−0.280134
$809$	−3.58512e9	−0.238058	−0.119029	−	0.992891i	$-0.537978\pi$
$809$	−3.58512e9	−0.238058	−0.119029	+	0.992891i	$0.537978\pi$
$810$	−8.28065e8	−0.0547478
$811$	2.02030e10	1.32998	0.664988	−	0.746854i	$-0.268437\pi$
$811$	2.02030e10	1.32998	0.664988	+	0.746854i	$0.268437\pi$
$812$	−3.75273e9	−0.245981
$813$	−1.38800e10	−0.905887
$814$	1.06498e10	0.692081
$815$	−7.42926e8	−0.0480722
$816$	−8.42921e9	−0.543089
$817$	−3.23255e9	−0.207381
$818$	4.92954e9	0.314898
$819$	5.29454e10	3.36771
$820$	4.11232e9	0.260458
$821$	−1.00041e10	−0.630925	−0.315462	−	0.948938i	$-0.602160\pi$
$821$	−1.00041e10	−0.630925	−0.315462	+	0.948938i	$0.602160\pi$
$822$	−5.30908e9	−0.333402
$823$	1.13158e10	0.707594	0.353797	−	0.935322i	$-0.384890\pi$
$823$	1.13158e10	0.707594	0.353797	+	0.935322i	$0.384890\pi$
$824$	−9.95388e8	−0.0619794
$825$	3.36316e10	2.08525
$826$	1.30663e10	0.806722
$827$	1.06478e9	0.0654622	0.0327311	−	0.999464i	$-0.489580\pi$
$827$	1.06478e9	0.0654622	0.0327311	+	0.999464i	$0.489580\pi$
$828$	9.77710e9	0.598555
$829$	−1.73341e10	−1.05672	−0.528360	−	0.849020i	$-0.677193\pi$
$829$	−1.73341e10	−1.05672	−0.528360	+	0.849020i	$0.677193\pi$
$830$	6.75190e8	0.0409876
$831$	3.13482e10	1.89500
$832$	1.08052e10	0.650430
$833$	1.12250e10	0.672866
$834$	−2.43407e9	−0.145295
$835$	−2.38417e9	−0.141721
$836$	3.68927e9	0.218383
$837$	−2.16813e9	−0.127805
$838$	8.99881e9	0.528240
$839$	1.85936e10	1.08691	0.543457	−	0.839437i	$-0.317115\pi$
$839$	1.85936e10	1.08691	0.543457	+	0.839437i	$0.317115\pi$
$840$	−6.22995e9	−0.362666
$841$	5.94823e8	0.0344828
$842$	−1.09576e10	−0.632592
$843$	−2.81981e10	−1.62115
$844$	−1.84469e10	−1.05615
$845$	−9.15657e9	−0.522077
$846$	−1.16265e10	−0.660167
$847$	−3.10241e10	−1.75431
$848$	−7.40880e9	−0.417217
$849$	−4.53197e9	−0.254162
$850$	3.08878e9	0.172513
$851$	1.31308e10	0.730360
$852$	−1.94446e10	−1.07711
$853$	2.25605e10	1.24459	0.622297	−	0.782782i	$-0.286200\pi$
$853$	2.25605e10	1.24459	0.622297	+	0.782782i	$0.286200\pi$
$854$	4.59057e9	0.252211
$855$	9.79446e8	0.0535919
$856$	−1.87287e9	−0.102059
$857$	2.91881e10	1.58406	0.792032	−	0.610480i	$-0.209023\pi$
$857$	2.91881e10	1.58406	0.792032	+	0.610480i	$0.209023\pi$
$858$	−2.46239e10	−1.33092
$859$	1.24668e10	0.671086	0.335543	−	0.942025i	$-0.391080\pi$
$859$	1.24668e10	0.671086	0.335543	+	0.942025i	$0.391080\pi$
$860$	5.09845e9	0.273334
$861$	4.99322e10	2.66606
$862$	−5.86007e9	−0.311621
$863$	−8.36290e9	−0.442914	−0.221457	−	0.975170i	$-0.571081\pi$
$863$	−8.36290e9	−0.442914	−0.221457	+	0.975170i	$0.571081\pi$
$864$	6.92915e9	0.365496
$865$	6.93967e9	0.364571
$866$	3.14170e9	0.164381
$867$	2.05075e10	1.06867
$868$	7.74758e9	0.402112
$869$	−3.88692e10	−2.00926
$870$	4.63358e8	0.0238561
$871$	−6.29973e8	−0.0323041
$872$	−1.53898e10	−0.786006
$873$	4.23012e10	2.15180
$874$	−5.96445e8	−0.0302190
$875$	−1.43792e10	−0.725618
$876$	1.06942e10	0.537509
$877$	−3.04696e10	−1.52534	−0.762672	−	0.646786i	$-0.776113\pi$
$877$	−3.04696e10	−1.52534	−0.762672	+	0.646786i	$0.776113\pi$
$878$	−1.02251e10	−0.509841
$879$	−4.93854e10	−2.45266
$880$	−4.95577e9	−0.245144
$881$	−1.45374e9	−0.0716262	−0.0358131	−	0.999359i	$-0.511402\pi$
$881$	−1.45374e9	−0.0716262	−0.0358131	+	0.999359i	$0.511402\pi$
$882$	−1.10468e10	−0.542121
$883$	2.24113e10	1.09548	0.547740	−	0.836649i	$-0.315488\pi$
$883$	2.24113e10	1.09548	0.547740	+	0.836649i	$0.315488\pi$
$884$	1.72471e10	0.839716
$885$	1.23039e10	0.596678
$886$	−2.33544e9	−0.112811
$887$	−1.73602e10	−0.835261	−0.417630	−	0.908617i	$-0.637139\pi$
$887$	−1.73602e10	−0.835261	−0.417630	+	0.908617i	$0.637139\pi$
$888$	2.78772e10	1.33599
$889$	1.06571e10	0.508727
$890$	−2.12306e9	−0.100948
$891$	−2.00132e10	−0.947861
$892$	3.61130e10	1.70367
$893$	−5.40915e9	−0.254184
$894$	2.00009e10	0.936197
$895$	1.01933e9	0.0475264
$896$	−3.20725e10	−1.48955
$897$	−3.03603e10	−1.40453
$898$	−4.51951e9	−0.208269
$899$	−1.22802e9	−0.0563700
$900$	2.31823e10	1.06000
$901$	−7.43693e9	−0.338733
$902$	−1.30323e10	−0.591286
$903$	6.19060e10	2.79786
$904$	1.32413e10	0.596132
$905$	−5.38226e9	−0.241376
$906$	8.59681e9	0.384051
$907$	1.79590e9	0.0799204	0.0399602	−	0.999201i	$-0.487277\pi$
$907$	1.79590e9	0.0799204	0.0399602	+	0.999201i	$0.487277\pi$
$908$	−1.65775e10	−0.734883
$909$	−1.26471e10	−0.558491
$910$	5.09427e9	0.224097
$911$	3.30449e10	1.44807	0.724035	−	0.689763i	$-0.242285\pi$
$911$	3.30449e10	1.44807	0.724035	+	0.689763i	$0.242285\pi$
$912$	3.85937e9	0.168474
$913$	1.63184e10	0.709628
$914$	1.15109e10	0.498654
$915$	4.32269e9	0.186544
$916$	2.38350e9	0.102466
$917$	−4.30827e10	−1.84506
$918$	1.81588e9	0.0774707
$919$	−1.81059e10	−0.769515	−0.384757	−	0.923018i	$-0.625715\pi$
$919$	−1.81059e10	−0.769515	−0.384757	+	0.923018i	$0.625715\pi$
$920$	2.00480e9	0.0848818
$921$	−2.64610e10	−1.11609
$922$	7.57644e9	0.318351
$923$	3.38848e10	1.41840
$924$	−7.06525e10	−2.94629
$925$	3.11341e10	1.29342
$926$	−7.02177e9	−0.290609
$927$	−2.99693e9	−0.123565
$928$	3.92465e9	0.161207
$929$	−4.28748e9	−0.175447	−0.0877237	−	0.996145i	$-0.527959\pi$
$929$	−4.28748e9	−0.175447	−0.0877237	+	0.996145i	$0.527959\pi$
$930$	−9.56611e8	−0.0389983
$931$	−5.13943e9	−0.208733
$932$	6.70446e9	0.271274
$933$	−3.01020e10	−1.21342
$934$	4.72237e9	0.189647
$935$	−4.97458e9	−0.199029
$936$	−3.61722e10	−1.44181
$937$	−3.61635e10	−1.43609	−0.718045	−	0.695997i	$-0.754963\pi$
$937$	−3.61635e10	−1.43609	−0.718045	+	0.695997i	$0.754963\pi$
$938$	2.37014e8	0.00937699
$939$	3.96711e10	1.56367
$940$	8.53142e9	0.335023
$941$	1.69964e10	0.664958	0.332479	−	0.943111i	$-0.392115\pi$
$941$	1.69964e10	0.664958	0.332479	+	0.943111i	$0.392115\pi$
$942$	8.08364e9	0.315086
$943$	−1.60683e10	−0.623990
$944$	2.72074e10	1.05265
$945$	−4.09045e9	−0.157674
$946$	−1.61574e10	−0.620516
$947$	−9.88265e9	−0.378136	−0.189068	−	0.981964i	$-0.560547\pi$
$947$	−9.88265e9	−0.378136	−0.189068	+	0.981964i	$0.560547\pi$
$948$	−4.77423e10	−1.82001
$949$	−1.86362e10	−0.707823
$950$	−1.41422e9	−0.0535160
$951$	−4.17564e10	−1.57432
$952$	−1.38285e10	−0.519453
$953$	−3.58714e10	−1.34253	−0.671264	−	0.741218i	$-0.734248\pi$
$953$	−3.58714e10	−1.34253	−0.671264	+	0.741218i	$0.734248\pi$
$954$	7.31888e9	0.272914
$955$	−5.97003e9	−0.221802
$956$	2.05173e10	0.759481
$957$	1.11987e10	0.413025
$958$	8.86386e9	0.325719
$959$	2.65458e10	0.971920
$960$	−3.82800e9	−0.139644
$961$	−2.49773e10	−0.907850
$962$	−2.27954e10	−0.825532
$963$	−5.63887e9	−0.203470
$964$	3.49778e10	1.25754
$965$	1.14647e10	0.410691
$966$	1.14224e10	0.407697
$967$	4.25013e10	1.51150	0.755752	−	0.654858i	$-0.227272\pi$
$967$	4.25013e10	1.51150	0.755752	+	0.654858i	$0.227272\pi$
$968$	2.11956e10	0.751071
$969$	3.87402e9	0.136782
$970$	4.07011e9	0.143187
$971$	8.55456e9	0.299868	0.149934	−	0.988696i	$-0.452094\pi$
$971$	8.55456e9	0.299868	0.149934	+	0.988696i	$0.452094\pi$
$972$	−3.52385e10	−1.23079
$973$	1.21705e10	0.423559
$974$	−4.22901e9	−0.146650
$975$	−7.19867e10	−2.48734
$976$	9.55873e9	0.329098
$977$	−2.72557e10	−0.935032	−0.467516	−	0.883985i	$-0.654851\pi$
$977$	−2.72557e10	−0.935032	−0.467516	+	0.883985i	$0.654851\pi$
$978$	2.89186e9	0.0988534
$979$	−5.13115e10	−1.74773
$980$	8.10602e9	0.275116
$981$	−4.63358e10	−1.56702
$982$	1.30792e10	0.440747
$983$	4.31580e10	1.44919	0.724593	−	0.689177i	$-0.242028\pi$
$983$	4.31580e10	1.44919	0.724593	+	0.689177i	$0.242028\pi$
$984$	−3.41136e10	−1.14142
$985$	−6.13764e9	−0.204632
$986$	1.02851e9	0.0341695
$987$	1.03590e11	3.42930
$988$	−7.89668e9	−0.260492
$989$	−1.99214e10	−0.654837
$990$	4.89562e9	0.160356
$991$	2.30316e10	0.751737	0.375869	−	0.926673i	$-0.377344\pi$
$991$	2.30316e10	0.751737	0.375869	+	0.926673i	$0.377344\pi$
$992$	−8.10252e9	−0.263530
$993$	3.80694e10	1.23382
$994$	−1.27484e10	−0.411722
$995$	−4.33838e9	−0.139620
$996$	2.00436e10	0.642789
$997$	1.34227e10	0.428949	0.214475	−	0.976730i	$-0.431196\pi$
$997$	1.34227e10	0.428949	0.214475	+	0.976730i	$0.431196\pi$
$998$	1.43948e9	0.0458404
$999$	1.83036e10	0.580841

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.8.a.b.1.5	✓	10
3.2	odd	2		261.8.a.f.1.6		10
4.3	odd	2		464.8.a.g.1.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.8.a.b.1.5	✓	10	1.1	even	1	trivial
261.8.a.f.1.6		10	3.2	odd	2
464.8.a.g.1.9		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)

\(f(q)\)	\(=\)	\(q-3.85204 q^{2} -70.5970 q^{3} -113.162 q^{4} -69.8627 q^{5} +271.943 q^{6} -1359.73 q^{7} +928.965 q^{8} +2796.94 q^{9} +O(q^{10})\)	\(q-3.85204 q^{2} -70.5970 q^{3} -113.162 q^{4} -69.8627 q^{5} +271.943 q^{6} -1359.73 q^{7} +928.965 q^{8} +2796.94 q^{9} +269.114 q^{10} +6504.11 q^{11} +7988.88 q^{12} -13921.7 q^{13} +5237.74 q^{14} +4932.10 q^{15} +10906.3 q^{16} +10947.7 q^{17} -10773.9 q^{18} -5012.48 q^{19} +7905.79 q^{20} +95993.0 q^{21} -25054.1 q^{22} -30890.7 q^{23} -65582.2 q^{24} -73244.2 q^{25} +53627.0 q^{26} -43059.9 q^{27} +153870. q^{28} -24389.0 q^{29} -18998.6 q^{30} +50351.6 q^{31} -160919. q^{32} -459171. q^{33} -42171.0 q^{34} +94994.5 q^{35} -316507. q^{36} -425073. q^{37} +19308.3 q^{38} +982831. q^{39} -64900.0 q^{40} +520165. q^{41} -369769. q^{42} +644901. q^{43} -736017. q^{44} -195402. q^{45} +118992. q^{46} +1.07914e6 q^{47} -769952. q^{48} +1.02533e6 q^{49} +282140. q^{50} -772876. q^{51} +1.57540e6 q^{52} -679314. q^{53} +165868. q^{54} -454395. q^{55} -1.26314e6 q^{56} +353866. q^{57} +93947.4 q^{58} +2.49465e6 q^{59} -558125. q^{60} +876441. q^{61} -193956. q^{62} -3.80309e6 q^{63} -776140. q^{64} +972608. q^{65} +1.76875e6 q^{66} +45251.1 q^{67} -1.23886e6 q^{68} +2.18079e6 q^{69} -365923. q^{70} -2.43395e6 q^{71} +2.59826e6 q^{72} +1.33864e6 q^{73} +1.63740e6 q^{74} +5.17082e6 q^{75} +567221. q^{76} -8.84385e6 q^{77} -3.78590e6 q^{78} -5.97610e6 q^{79} -761943. q^{80} -3.07701e6 q^{81} -2.00370e6 q^{82} +2.50894e6 q^{83} -1.08627e7 q^{84} -764836. q^{85} -2.48418e6 q^{86} +1.72179e6 q^{87} +6.04209e6 q^{88} -7.88908e6 q^{89} +752695. q^{90} +1.89298e7 q^{91} +3.49564e6 q^{92} -3.55467e6 q^{93} -4.15688e6 q^{94} +350185. q^{95} +1.13604e7 q^{96} +1.51241e7 q^{97} -3.94960e6 q^{98} +1.81916e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 80 q^{3} + 922 q^{4} + 180 q^{5} + 358 q^{6} + 1040 q^{7} - 4620 q^{8} + 10986 q^{9}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

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