LMFDB - Embedded newform 29.10.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,10,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, 10, names="a")

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

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 10 $
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:	$14.9360392488$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 2901 x^{7} - 4592 x^{6} + 2830996 x^{5} + 7409504 x^{4} - 1038861888 x^{3} - 2974719488 x^{2} + \cdots + 456378417152 $ x^9 - 2901x^7 - 4592x^6 + 2830996x^5 + 7409504x^4 - 1038861888x^3 - 2974719488x^2 + 115773751296*x + 456378417152
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{2}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$35.6552$ 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)

$f(q)$	$=$	$q-35.6552 q^{2} +190.523 q^{3} +759.292 q^{4} -886.258 q^{5} -6793.13 q^{6} -3878.27 q^{7} -8817.24 q^{8} +16616.0 q^{9} +O(q^{10})$	\(q-35.6552 q^{2} +190.523 q^{3} +759.292 q^{4} -886.258 q^{5} -6793.13 q^{6} -3878.27 q^{7} -8817.24 q^{8} +16616.0 q^{9} +31599.7 q^{10} +26057.4 q^{11} +144663. q^{12} -6571.28 q^{13} +138280. q^{14} -168852. q^{15} -74377.2 q^{16} -149426. q^{17} -592447. q^{18} -143380. q^{19} -672928. q^{20} -738899. q^{21} -929083. q^{22} -328036. q^{23} -1.67989e6 q^{24} -1.16767e6 q^{25} +234300. q^{26} -584334. q^{27} -2.94474e6 q^{28} -707281. q^{29} +6.02046e6 q^{30} -8.83943e6 q^{31} +7.16636e6 q^{32} +4.96454e6 q^{33} +5.32781e6 q^{34} +3.43714e6 q^{35} +1.26164e7 q^{36} +3.11425e6 q^{37} +5.11223e6 q^{38} -1.25198e6 q^{39} +7.81435e6 q^{40} -2.46535e7 q^{41} +2.63456e7 q^{42} -4.11528e7 q^{43} +1.97852e7 q^{44} -1.47261e7 q^{45} +1.16962e7 q^{46} +1.85830e7 q^{47} -1.41706e7 q^{48} -2.53127e7 q^{49} +4.16336e7 q^{50} -2.84691e7 q^{51} -4.98952e6 q^{52} -1.68326e7 q^{53} +2.08345e7 q^{54} -2.30936e7 q^{55} +3.41956e7 q^{56} -2.73172e7 q^{57} +2.52182e7 q^{58} +1.55526e8 q^{59} -1.28208e8 q^{60} +1.48523e8 q^{61} +3.15172e8 q^{62} -6.44413e7 q^{63} -2.17437e8 q^{64} +5.82385e6 q^{65} -1.77012e8 q^{66} -1.13774e8 q^{67} -1.13458e8 q^{68} -6.24985e7 q^{69} -1.22552e8 q^{70} +1.60972e8 q^{71} -1.46507e8 q^{72} -1.93160e8 q^{73} -1.11039e8 q^{74} -2.22468e8 q^{75} -1.08867e8 q^{76} -1.01058e8 q^{77} +4.46396e7 q^{78} +2.95627e8 q^{79} +6.59173e7 q^{80} -4.38382e8 q^{81} +8.79024e8 q^{82} +3.45236e8 q^{83} -5.61040e8 q^{84} +1.32430e8 q^{85} +1.46731e9 q^{86} -1.34753e8 q^{87} -2.29755e8 q^{88} -9.93415e8 q^{89} +5.25060e8 q^{90} +2.54852e7 q^{91} -2.49075e8 q^{92} -1.68411e9 q^{93} -6.62581e8 q^{94} +1.27071e8 q^{95} +1.36536e9 q^{96} +1.17922e9 q^{97} +9.02528e8 q^{98} +4.32971e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 244 q^{3} + 1194 q^{4} - 738 q^{5} - 2330 q^{6} - 7128 q^{7} - 13776 q^{8} + 33017 q^{9}+O(q^{10}) $ 9 * q - 244 * q^3 + 1194 * q^4 - 738 * q^5 - 2330 * q^6 - 7128 * q^7 - 13776 * q^8 + 33017 * q^9	\( 9 q - 244 q^{3} + 1194 q^{4} - 738 q^{5} - 2330 q^{6} - 7128 q^{7} - 13776 q^{8} + 33017 q^{9} + 37812 q^{10} - 59512 q^{11} - 127348 q^{12} - 165758 q^{13} - 406080 q^{14} - 693178 q^{15} - 1044958 q^{16} - 394814 q^{17} - 1676576 q^{18} - 2256606 q^{19} - 2237578 q^{20} - 1750168 q^{21} - 5311718 q^{22} - 1699500 q^{23} - 4446318 q^{24} - 983481 q^{25} - 4264740 q^{26} - 6987958 q^{27} - 8491636 q^{28} - 6365529 q^{29} - 16907854 q^{30} - 11929632 q^{31} - 1346192 q^{32} + 1750252 q^{33} + 8655764 q^{34} - 3275324 q^{35} + 29848532 q^{36} + 14454898 q^{37} + 14709736 q^{38} + 41155042 q^{39} + 45167060 q^{40} + 52495202 q^{41} + 103102340 q^{42} + 21819888 q^{43} + 70837004 q^{44} + 61248326 q^{45} + 20628012 q^{46} + 44968948 q^{47} + 122982540 q^{48} - 26826775 q^{49} + 155997680 q^{50} - 28882428 q^{51} + 29562122 q^{52} - 111394302 q^{53} + 70575802 q^{54} - 173560742 q^{55} + 67419136 q^{56} + 85769252 q^{57} - 236142720 q^{59} - 47991000 q^{60} - 241129054 q^{61} + 261343278 q^{62} - 328513060 q^{63} - 333112958 q^{64} - 625660884 q^{65} + 223958776 q^{66} - 672046492 q^{67} - 63179948 q^{68} - 705827600 q^{69} - 366389016 q^{70} - 475841956 q^{71} - 18937608 q^{72} - 424813822 q^{73} - 532689728 q^{74} - 913708498 q^{75} - 552478056 q^{76} - 182224776 q^{77} + 928127886 q^{78} - 170801148 q^{79} + 562655678 q^{80} - 914585851 q^{81} + 1468192652 q^{82} - 468898296 q^{83} + 952386216 q^{84} - 271552972 q^{85} + 1462277802 q^{86} + 172576564 q^{87} + 1176890862 q^{88} - 676036598 q^{89} + 4017858752 q^{90} + 9763884 q^{91} + 2724990708 q^{92} - 858755220 q^{93} + 2429128614 q^{94} + 69331732 q^{95} + 3111862050 q^{96} + 170708754 q^{97} + 3278517600 q^{98} + 305494078 q^{99}+O(q^{100}) \) 9 * q - 244 * q^3 + 1194 * q^4 - 738 * q^5 - 2330 * q^6 - 7128 * q^7 - 13776 * q^8 + 33017 * q^9 + 37812 * q^10 - 59512 * q^11 - 127348 * q^12 - 165758 * q^13 - 406080 * q^14 - 693178 * q^15 - 1044958 * q^16 - 394814 * q^17 - 1676576 * q^18 - 2256606 * q^19 - 2237578 * q^20 - 1750168 * q^21 - 5311718 * q^22 - 1699500 * q^23 - 4446318 * q^24 - 983481 * q^25 - 4264740 * q^26 - 6987958 * q^27 - 8491636 * q^28 - 6365529 * q^29 - 16907854 * q^30 - 11929632 * q^31 - 1346192 * q^32 + 1750252 * q^33 + 8655764 * q^34 - 3275324 * q^35 + 29848532 * q^36 + 14454898 * q^37 + 14709736 * q^38 + 41155042 * q^39 + 45167060 * q^40 + 52495202 * q^41 + 103102340 * q^42 + 21819888 * q^43 + 70837004 * q^44 + 61248326 * q^45 + 20628012 * q^46 + 44968948 * q^47 + 122982540 * q^48 - 26826775 * q^49 + 155997680 * q^50 - 28882428 * q^51 + 29562122 * q^52 - 111394302 * q^53 + 70575802 * q^54 - 173560742 * q^55 + 67419136 * q^56 + 85769252 * q^57 - 236142720 * q^59 - 47991000 * q^60 - 241129054 * q^61 + 261343278 * q^62 - 328513060 * q^63 - 333112958 * q^64 - 625660884 * q^65 + 223958776 * q^66 - 672046492 * q^67 - 63179948 * q^68 - 705827600 * q^69 - 366389016 * q^70 - 475841956 * q^71 - 18937608 * q^72 - 424813822 * q^73 - 532689728 * q^74 - 913708498 * q^75 - 552478056 * q^76 - 182224776 * q^77 + 928127886 * q^78 - 170801148 * q^79 + 562655678 * q^80 - 914585851 * q^81 + 1468192652 * q^82 - 468898296 * q^83 + 952386216 * q^84 - 271552972 * q^85 + 1462277802 * q^86 + 172576564 * q^87 + 1176890862 * q^88 - 676036598 * q^89 + 4017858752 * q^90 + 9763884 * q^91 + 2724990708 * q^92 - 858755220 * q^93 + 2429128614 * q^94 + 69331732 * q^95 + 3111862050 * q^96 + 170708754 * q^97 + 3278517600 * q^98 + 305494078 * 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 $

$2$	−35.6552	−1.57575	−0.787876	−	0.615834i	$-0.788819\pi$
$2$	−35.6552	−1.57575	−0.787876	+	0.615834i	$0.788819\pi$
$3$	190.523	1.35801	0.679003	−	0.734135i	$-0.262412\pi$
$3$	190.523	1.35801	0.679003	+	0.734135i	$0.262412\pi$
$4$	759.292	1.48299
$5$	−886.258	−0.634154	−0.317077	−	0.948400i	$-0.602701\pi$
$5$	−886.258	−0.634154	−0.317077	+	0.948400i	$0.602701\pi$
$6$	−6793.13	−2.13988
$7$	−3878.27	−0.610515	−0.305257	−	0.952270i	$-0.598743\pi$
$7$	−3878.27	−0.610515	−0.305257	+	0.952270i	$0.598743\pi$
$8$	−8817.24	−0.761076
$9$	16616.0	0.844180
$10$	31599.7	0.999270
$11$	26057.4	0.536617	0.268309	−	0.963333i	$-0.413535\pi$
$11$	26057.4	0.536617	0.268309	+	0.963333i	$0.413535\pi$
$12$	144663.	2.01391
$13$	−6571.28	−0.0638124	−0.0319062	−	0.999491i	$-0.510158\pi$
$13$	−6571.28	−0.0638124	−0.0319062	+	0.999491i	$0.510158\pi$
$14$	138280.	0.962020
$15$	−168852.	−0.861185
$16$	−74377.2	−0.283726
$17$	−149426.	−0.433916	−0.216958	−	0.976181i	$-0.569613\pi$
$17$	−149426.	−0.433916	−0.216958	+	0.976181i	$0.569613\pi$
$18$	−592447.	−1.33022
$19$	−143380.	−0.252404	−0.126202	−	0.992005i	$-0.540279\pi$
$19$	−143380.	−0.252404	−0.126202	+	0.992005i	$0.540279\pi$
$20$	−672928.	−0.940446
$21$	−738899.	−0.829083
$22$	−929083.	−0.845575
$23$	−328036.	−0.244426	−0.122213	−	0.992504i	$-0.538999\pi$
$23$	−328036.	−0.244426	−0.122213	+	0.992504i	$0.538999\pi$
$24$	−1.67989e6	−1.03355
$25$	−1.16767e6	−0.597848
$26$	234300.	0.100552
$27$	−584334.	−0.211604
$28$	−2.94474e6	−0.905389
$29$	−707281.	−0.185695
$29$	−707281.	−0.185695
$30$	6.02046e6	1.35701
$31$	−8.83943e6	−1.71908	−0.859541	−	0.511066i	$-0.829251\pi$
$31$	−8.83943e6	−1.71908	−0.859541	+	0.511066i	$0.829251\pi$
$32$	7.16636e6	1.20816
$33$	4.96454e6	0.728730
$34$	5.32781e6	0.683744
$35$	3.43714e6	0.387161
$36$	1.26164e7	1.25191
$37$	3.11425e6	0.273178	0.136589	−	0.990628i	$-0.456386\pi$
$37$	3.11425e6	0.273178	0.136589	+	0.990628i	$0.456386\pi$
$38$	5.11223e6	0.397727
$39$	−1.25198e6	−0.0866576
$40$	7.81435e6	0.482639
$41$	−2.46535e7	−1.36255	−0.681273	−	0.732030i	$-0.738573\pi$
$41$	−2.46535e7	−1.36255	−0.681273	+	0.732030i	$0.738573\pi$
$42$	2.63456e7	1.30643
$43$	−4.11528e7	−1.83566	−0.917829	−	0.396976i	$-0.870060\pi$
$43$	−4.11528e7	−1.83566	−0.917829	+	0.396976i	$0.870060\pi$
$44$	1.97852e7	0.795799
$45$	−1.47261e7	−0.535341
$46$	1.16962e7	0.385154
$47$	1.85830e7	0.555490	0.277745	−	0.960655i	$-0.410413\pi$
$47$	1.85830e7	0.555490	0.277745	+	0.960655i	$0.410413\pi$
$48$	−1.41706e7	−0.385302
$49$	−2.53127e7	−0.627271
$50$	4.16336e7	0.942060
$51$	−2.84691e7	−0.589260
$52$	−4.98952e6	−0.0946333
$53$	−1.68326e7	−0.293028	−0.146514	−	0.989209i	$-0.546805\pi$
$53$	−1.68326e7	−0.293028	−0.146514	+	0.989209i	$0.546805\pi$
$54$	2.08345e7	0.333435
$55$	−2.30936e7	−0.340298
$56$	3.41956e7	0.464648
$57$	−2.73172e7	−0.342767
$58$	2.52182e7	0.292610
$59$	1.55526e8	1.67097	0.835485	−	0.549514i	$-0.185187\pi$
$59$	1.55526e8	1.67097	0.835485	+	0.549514i	$0.185187\pi$
$60$	−1.28208e8	−1.27713
$61$	1.48523e8	1.37344	0.686721	−	0.726921i	$-0.259050\pi$
$61$	1.48523e8	1.37344	0.686721	+	0.726921i	$0.259050\pi$
$62$	3.15172e8	2.70885
$63$	−6.44413e7	−0.515385
$64$	−2.17437e8	−1.62003
$65$	5.82385e6	0.0404669
$66$	−1.77012e8	−1.14830
$67$	−1.13774e8	−0.689770	−0.344885	−	0.938645i	$-0.612082\pi$
$67$	−1.13774e8	−0.689770	−0.344885	+	0.938645i	$0.612082\pi$
$68$	−1.13458e8	−0.643494
$69$	−6.24985e7	−0.331931
$70$	−1.22552e8	−0.610069
$71$	1.60972e8	0.751774	0.375887	−	0.926665i	$-0.377338\pi$
$71$	1.60972e8	0.751774	0.375887	+	0.926665i	$0.377338\pi$
$72$	−1.46507e8	−0.642485
$73$	−1.93160e8	−0.796092	−0.398046	−	0.917365i	$-0.630312\pi$
$73$	−1.93160e8	−0.796092	−0.398046	+	0.917365i	$0.630312\pi$
$74$	−1.11039e8	−0.430460
$75$	−2.22468e8	−0.811882
$76$	−1.08867e8	−0.374314
$77$	−1.01058e8	−0.327613
$78$	4.46396e7	0.136551
$79$	2.95627e8	0.853928	0.426964	−	0.904269i	$-0.359583\pi$
$79$	2.95627e8	0.853928	0.426964	+	0.904269i	$0.359583\pi$
$80$	6.59173e7	0.179926
$81$	−4.38382e8	−1.13154
$82$	8.79024e8	2.14703
$83$	3.45236e8	0.798480	0.399240	−	0.916846i	$-0.369274\pi$
$83$	3.45236e8	0.798480	0.399240	+	0.916846i	$0.369274\pi$
$84$	−5.61040e8	−1.22952
$85$	1.32430e8	0.275170
$86$	1.46731e9	2.89254
$87$	−1.34753e8	−0.252175
$88$	−2.29755e8	−0.408406
$89$	−9.93415e8	−1.67832	−0.839162	−	0.543881i	$-0.816954\pi$
$89$	−9.93415e8	−1.67832	−0.839162	+	0.543881i	$0.816954\pi$
$90$	5.25060e8	0.843564
$91$	2.54852e7	0.0389584
$92$	−2.49075e8	−0.362481
$93$	−1.68411e9	−2.33452
$94$	−6.62581e8	−0.875314
$95$	1.27071e8	0.160063
$96$	1.36536e9	1.64069
$97$	1.17922e9	1.35245	0.676225	−	0.736695i	$-0.263615\pi$
$97$	1.17922e9	1.35245	0.676225	+	0.736695i	$0.263615\pi$
$98$	9.02528e8	0.988424
$99$	4.32971e8	0.453002
$100$	−8.86604e8	−0.886604
$101$	4.84146e8	0.462945	0.231473	−	0.972841i	$-0.425646\pi$
$101$	4.84146e8	0.462945	0.231473	+	0.972841i	$0.425646\pi$
$102$	1.01507e9	0.928528
$103$	6.26100e8	0.548121	0.274060	−	0.961712i	$-0.411633\pi$
$103$	6.26100e8	0.548121	0.274060	+	0.961712i	$0.411633\pi$
$104$	5.79406e7	0.0485660
$105$	6.54855e8	0.525767
$106$	6.00168e8	0.461739
$107$	1.64986e9	1.21680	0.608402	−	0.793629i	$-0.291811\pi$
$107$	1.64986e9	1.21680	0.608402	+	0.793629i	$0.291811\pi$
$108$	−4.43680e8	−0.313807
$109$	−1.20280e9	−0.816160	−0.408080	−	0.912946i	$-0.633802\pi$
$109$	−1.20280e9	−0.816160	−0.408080	+	0.912946i	$0.633802\pi$
$110$	8.23407e8	0.536225
$111$	5.93336e8	0.370977
$112$	2.88454e8	0.173219
$113$	−1.39546e9	−0.805127	−0.402564	−	0.915392i	$-0.631881\pi$
$113$	−1.39546e9	−0.805127	−0.402564	+	0.915392i	$0.631881\pi$
$114$	9.73998e8	0.540115
$115$	2.90725e8	0.155004
$116$	−5.37033e8	−0.275385
$117$	−1.09188e8	−0.0538692
$118$	−5.54530e9	−2.63303
$119$	5.79513e8	0.264912
$120$	1.48881e9	0.655427
$121$	−1.67896e9	−0.712042
$122$	−5.29562e9	−2.16420
$123$	−4.69706e9	−1.85034
$124$	−6.71171e9	−2.54939
$125$	2.76583e9	1.01328
$126$	2.29767e9	0.812118
$127$	−8.91835e8	−0.304206	−0.152103	−	0.988365i	$-0.548605\pi$
$127$	−8.91835e8	−0.304206	−0.152103	+	0.988365i	$0.548605\pi$
$128$	4.08357e9	1.34461
$129$	−7.84056e9	−2.49283
$130$	−2.07650e8	−0.0637658
$131$	−3.38258e8	−0.100352	−0.0501761	−	0.998740i	$-0.515978\pi$
$131$	−3.38258e8	−0.100352	−0.0501761	+	0.998740i	$0.515978\pi$
$132$	3.76954e9	1.08070
$133$	5.56065e8	0.154097
$134$	4.05662e9	1.08691
$135$	5.17870e8	0.134190
$136$	1.31752e9	0.330243
$137$	−6.17258e7	−0.0149701	−0.00748504	−	0.999972i	$-0.502383\pi$
$137$	−6.17258e7	−0.0149701	−0.00748504	+	0.999972i	$0.502383\pi$
$138$	2.22839e9	0.523041
$139$	−8.60173e8	−0.195443	−0.0977213	−	0.995214i	$-0.531155\pi$
$139$	−8.60173e8	−0.195443	−0.0977213	+	0.995214i	$0.531155\pi$
$140$	2.60979e9	0.574156
$141$	3.54049e9	0.754359
$142$	−5.73948e9	−1.18461
$143$	−1.71231e8	−0.0342428
$144$	−1.23585e9	−0.239516
$145$	6.26833e8	0.117760
$146$	6.88714e9	1.25444
$147$	−4.82264e9	−0.851838
$148$	2.36462e9	0.405120
$149$	9.65419e9	1.60464	0.802320	−	0.596895i	$-0.203599\pi$
$149$	9.65419e9	1.60464	0.802320	+	0.596895i	$0.203599\pi$
$150$	7.93215e9	1.27932
$151$	3.81866e9	0.597744	0.298872	−	0.954293i	$-0.403390\pi$
$151$	3.81866e9	0.597744	0.298872	+	0.954293i	$0.403390\pi$
$152$	1.26421e9	0.192099
$153$	−2.48286e9	−0.366303
$154$	3.60323e9	0.516236
$155$	7.83401e9	1.09016
$156$	−9.50619e8	−0.128513
$157$	2.26506e8	0.0297530	0.0148765	−	0.999889i	$-0.495264\pi$
$157$	2.26506e8	0.0297530	0.0148765	+	0.999889i	$0.495264\pi$
$158$	−1.05406e10	−1.34558
$159$	−3.20699e9	−0.397934
$160$	−6.35124e9	−0.766159
$161$	1.27221e9	0.149225
$162$	1.56306e10	1.78303
$163$	−3.22539e7	−0.00357881	−0.00178940	−	0.999998i	$-0.500570\pi$
$163$	−3.22539e7	−0.00357881	−0.00178940	+	0.999998i	$0.500570\pi$
$164$	−1.87192e10	−2.02064
$165$	−4.39986e9	−0.462127
$166$	−1.23094e10	−1.25821
$167$	9.37015e9	0.932229	0.466114	−	0.884724i	$-0.345654\pi$
$167$	9.37015e9	0.932229	0.466114	+	0.884724i	$0.345654\pi$
$168$	6.51505e9	0.630995
$169$	−1.05613e10	−0.995928
$170$	−4.72181e9	−0.433599
$171$	−2.38240e9	−0.213075
$172$	−3.12470e10	−2.72227
$173$	−1.09382e10	−0.928411	−0.464205	−	0.885728i	$-0.653660\pi$
$173$	−1.09382e10	−0.928411	−0.464205	+	0.885728i	$0.653660\pi$
$174$	4.80465e9	0.397366
$175$	4.52854e9	0.364995
$176$	−1.93808e9	−0.152253
$177$	2.96312e10	2.26919
$178$	3.54204e10	2.64462
$179$	−1.10259e10	−0.802744	−0.401372	−	0.915915i	$-0.631467\pi$
$179$	−1.10259e10	−0.802744	−0.401372	+	0.915915i	$0.631467\pi$
$180$	−1.11814e10	−0.793906
$181$	−1.12308e10	−0.777781	−0.388890	−	0.921284i	$-0.627142\pi$
$181$	−1.12308e10	−0.777781	−0.388890	+	0.921284i	$0.627142\pi$
$182$	−9.08679e8	−0.0613888
$183$	2.82971e10	1.86514
$184$	2.89238e9	0.186026
$185$	−2.76002e9	−0.173237
$186$	6.00474e10	3.67863
$187$	−3.89366e9	−0.232847
$188$	1.41099e10	0.823787
$189$	2.26620e9	0.129187
$190$	−4.53076e9	−0.252220
$191$	−8.77610e9	−0.477146	−0.238573	−	0.971125i	$-0.576680\pi$
$191$	−8.77610e9	−0.477146	−0.238573	+	0.971125i	$0.576680\pi$
$192$	−4.14267e10	−2.20001
$193$	2.97381e10	1.54278	0.771391	−	0.636361i	$-0.219561\pi$
$193$	2.97381e10	1.54278	0.771391	+	0.636361i	$0.219561\pi$
$194$	−4.20452e10	−2.13112
$195$	1.10958e9	0.0549543
$196$	−1.92197e10	−0.930239
$197$	2.02885e10	0.959734	0.479867	−	0.877341i	$-0.340685\pi$
$197$	2.02885e10	0.959734	0.479867	+	0.877341i	$0.340685\pi$
$198$	−1.54376e10	−0.713818
$199$	−2.34387e10	−1.05948	−0.529742	−	0.848159i	$-0.677711\pi$
$199$	−2.34387e10	−1.05948	−0.529742	+	0.848159i	$0.677711\pi$
$200$	1.02956e10	0.455008
$201$	−2.16765e10	−0.936712
$202$	−1.72623e10	−0.729487
$203$	2.74302e9	0.113370
$204$	−2.16163e10	−0.873869
$205$	2.18493e10	0.864064
$206$	−2.23237e10	−0.863702
$207$	−5.45065e9	−0.206339
$208$	4.88753e8	0.0181053
$209$	−3.73611e9	−0.135445
$210$	−2.33490e10	−0.828477
$211$	4.60471e10	1.59930	0.799652	−	0.600463i	$-0.205017\pi$
$211$	4.60471e10	1.59930	0.799652	+	0.600463i	$0.205017\pi$
$212$	−1.27808e10	−0.434558
$213$	3.06688e10	1.02091
$214$	−5.88261e10	−1.91738
$215$	3.64720e10	1.16409
$216$	5.15221e9	0.161047
$217$	3.42817e10	1.04953
$218$	4.28862e10	1.28607
$219$	−3.68013e10	−1.08110
$220$	−1.75348e10	−0.504660
$221$	9.81919e8	0.0276892
$222$	−2.11555e10	−0.584567
$223$	4.43720e9	0.120154	0.0600769	−	0.998194i	$-0.480865\pi$
$223$	4.43720e9	0.120154	0.0600769	+	0.998194i	$0.480865\pi$
$224$	−2.77930e10	−0.737598
$225$	−1.94020e10	−0.504692
$226$	4.97554e10	1.26868
$227$	−5.17338e10	−1.29318	−0.646589	−	0.762839i	$-0.723805\pi$
$227$	−5.17338e10	−1.29318	−0.646589	+	0.762839i	$0.723805\pi$
$228$	−2.07417e10	−0.508320
$229$	1.44607e10	0.347479	0.173739	−	0.984792i	$-0.444415\pi$
$229$	1.44607e10	0.347479	0.173739	+	0.984792i	$0.444415\pi$
$230$	−1.03658e10	−0.244247
$231$	−1.92538e10	−0.444900
$232$	6.23627e9	0.141328
$233$	−8.28487e9	−0.184155	−0.0920776	−	0.995752i	$-0.529351\pi$
$233$	−8.28487e9	−0.184155	−0.0920776	+	0.995752i	$0.529351\pi$
$234$	3.89313e9	0.0848844
$235$	−1.64694e10	−0.352266
$236$	1.18090e11	2.47803
$237$	5.63236e10	1.15964
$238$	−2.06626e10	−0.417436
$239$	−5.28899e10	−1.04853	−0.524267	−	0.851554i	$-0.675661\pi$
$239$	−5.28899e10	−1.04853	−0.524267	+	0.851554i	$0.675661\pi$
$240$	1.25588e10	0.244341
$241$	−2.23304e10	−0.426403	−0.213201	−	0.977008i	$-0.568389\pi$
$241$	−2.23304e10	−0.426403	−0.213201	+	0.977008i	$0.568389\pi$
$242$	5.98635e10	1.12200
$243$	−7.20204e10	−1.32503
$244$	1.12772e11	2.03680
$245$	2.24335e10	0.397787
$246$	1.67474e11	2.91568
$247$	9.42189e8	0.0161065
$248$	7.79394e10	1.30835
$249$	6.57753e10	1.08434
$250$	−9.86162e10	−1.59668
$251$	−1.06761e10	−0.169777	−0.0848886	−	0.996390i	$-0.527053\pi$
$251$	−1.06761e10	−0.169777	−0.0848886	+	0.996390i	$0.527053\pi$
$252$	−4.89297e10	−0.764312
$253$	−8.54779e9	−0.131163
$254$	3.17985e10	0.479353
$255$	2.52309e10	0.373682
$256$	−3.42728e10	−0.498735
$257$	−1.05661e11	−1.51082	−0.755412	−	0.655250i	$-0.772563\pi$
$257$	−1.05661e11	−1.51082	−0.755412	+	0.655250i	$0.772563\pi$
$258$	2.79557e11	3.92809
$259$	−1.20779e10	−0.166779
$260$	4.42200e9	0.0600121
$261$	−1.17522e10	−0.156760
$262$	1.20606e10	0.158130
$263$	3.78997e10	0.488466	0.244233	−	0.969717i	$-0.421464\pi$
$263$	3.78997e10	0.488466	0.244233	+	0.969717i	$0.421464\pi$
$264$	−4.37736e10	−0.554618
$265$	1.49180e10	0.185825
$266$	−1.98266e10	−0.242818
$267$	−1.89268e11	−2.27917
$268$	−8.63873e10	−1.02292
$269$	−1.23676e11	−1.44012	−0.720060	−	0.693912i	$-0.755886\pi$
$269$	−1.23676e11	−1.44012	−0.720060	+	0.693912i	$0.755886\pi$
$270$	−1.84648e10	−0.211449
$271$	−1.60313e11	−1.80554	−0.902770	−	0.430124i	$-0.858470\pi$
$271$	−1.60313e11	−1.80554	−0.902770	+	0.430124i	$0.858470\pi$
$272$	1.11139e10	0.123113
$273$	4.85551e9	0.0529058
$274$	2.20085e9	0.0235891
$275$	−3.04266e10	−0.320816
$276$	−4.74546e10	−0.492252
$277$	3.56861e10	0.364201	0.182100	−	0.983280i	$-0.441710\pi$
$277$	3.56861e10	0.364201	0.182100	+	0.983280i	$0.441710\pi$
$278$	3.06696e10	0.307969
$279$	−1.46876e11	−1.45122
$280$	−3.03061e10	−0.294659
$281$	5.18376e10	0.495983	0.247991	−	0.968762i	$-0.420230\pi$
$281$	5.18376e10	0.495983	0.247991	+	0.968762i	$0.420230\pi$
$282$	−1.26237e11	−1.18868
$283$	−1.10964e11	−1.02836	−0.514179	−	0.857683i	$-0.671903\pi$
$283$	−1.10964e11	−1.02836	−0.514179	+	0.857683i	$0.671903\pi$
$284$	1.22225e11	1.11488
$285$	2.42100e10	0.217367
$286$	6.10527e9	0.0539582
$287$	9.56128e10	0.831854
$288$	1.19076e11	1.01990
$289$	−9.62598e10	−0.811717
$290$	−2.23499e10	−0.185560
$291$	2.24668e11	1.83663
$292$	−1.46664e11	−1.18060
$293$	1.73114e11	1.37223	0.686115	−	0.727493i	$-0.259315\pi$
$293$	1.73114e11	1.37223	0.686115	+	0.727493i	$0.259315\pi$
$294$	1.71952e11	1.34229
$295$	−1.37836e11	−1.05965
$296$	−2.74591e10	−0.207909
$297$	−1.52262e10	−0.113550
$298$	−3.44222e11	−2.52851
$299$	2.15562e9	0.0155974
$300$	−1.68918e11	−1.20401
$301$	1.59602e11	1.12070
$302$	−1.36155e11	−0.941895
$303$	9.22409e10	0.628683
$304$	1.06642e10	0.0716138
$305$	−1.31630e11	−0.870974
$306$	8.85268e10	0.577203
$307$	2.06532e11	1.32698	0.663490	−	0.748185i	$-0.269075\pi$
$307$	2.06532e11	1.32698	0.663490	+	0.748185i	$0.269075\pi$
$308$	−7.67323e10	−0.485847
$309$	1.19286e11	0.744352
$310$	−2.79323e11	−1.71783
$311$	−1.10271e11	−0.668408	−0.334204	−	0.942501i	$-0.608467\pi$
$311$	−1.10271e11	−0.668408	−0.334204	+	0.942501i	$0.608467\pi$
$312$	1.10390e10	0.0659530
$313$	2.41091e11	1.41982	0.709908	−	0.704294i	$-0.248736\pi$
$313$	2.41091e11	1.41982	0.709908	+	0.704294i	$0.248736\pi$
$314$	−8.07610e9	−0.0468833
$315$	5.71116e10	0.326833
$316$	2.24467e11	1.26637
$317$	1.52508e11	0.848256	0.424128	−	0.905602i	$-0.360581\pi$
$317$	1.52508e11	0.848256	0.424128	+	0.905602i	$0.360581\pi$
$318$	1.14346e11	0.627045
$319$	−1.84299e10	−0.0996473
$320$	1.92705e11	1.02735
$321$	3.14337e11	1.65243
$322$	−4.53609e10	−0.235142
$323$	2.14247e10	0.109522
$324$	−3.32860e11	−1.67806
$325$	7.67310e9	0.0381501
$326$	1.15002e9	0.00563931
$327$	−2.29162e11	−1.10835
$328$	2.17376e11	1.03700
$329$	−7.20699e10	−0.339135
$330$	1.56878e11	0.728197
$331$	−2.95917e11	−1.35501	−0.677507	−	0.735516i	$-0.736940\pi$
$331$	−2.95917e11	−1.35501	−0.677507	+	0.735516i	$0.736940\pi$
$332$	2.62135e11	1.18414
$333$	5.17463e10	0.230611
$334$	−3.34094e11	−1.46896
$335$	1.00833e11	0.437421
$336$	5.49572e10	0.235233
$337$	−1.06720e11	−0.450724	−0.225362	−	0.974275i	$-0.572356\pi$
$337$	−1.06720e11	−0.450724	−0.225362	+	0.974275i	$0.572356\pi$
$338$	3.76566e11	1.56933
$339$	−2.65867e11	−1.09337
$340$	1.00553e11	0.408074
$341$	−2.30333e11	−0.922489
$342$	8.49449e10	0.335753
$343$	2.54671e11	0.993474
$344$	3.62854e11	1.39707
$345$	5.53897e10	0.210496
$346$	3.90005e11	1.46294
$347$	3.34743e11	1.23945	0.619725	−	0.784819i	$-0.287244\pi$
$347$	3.34743e11	1.23945	0.619725	+	0.784819i	$0.287244\pi$
$348$	−1.02317e11	−0.373974
$349$	2.25853e11	0.814912	0.407456	−	0.913225i	$-0.366416\pi$
$349$	2.25853e11	0.814912	0.407456	+	0.913225i	$0.366416\pi$
$350$	−1.61466e11	−0.575142
$351$	3.83982e9	0.0135030
$352$	1.86737e11	0.648318
$353$	8.14130e10	0.279067	0.139533	−	0.990217i	$-0.455440\pi$
$353$	8.14130e10	0.279067	0.139533	+	0.990217i	$0.455440\pi$
$354$	−1.05651e12	−3.57567
$355$	−1.42663e11	−0.476741
$356$	−7.54292e11	−2.48894
$357$	1.10411e11	0.359752
$358$	3.93132e11	1.26493
$359$	−3.48035e11	−1.10585	−0.552927	−	0.833230i	$-0.686489\pi$
$359$	−3.48035e11	−1.10585	−0.552927	+	0.833230i	$0.686489\pi$
$360$	1.29843e11	0.407435
$361$	−3.02130e11	−0.936292
$362$	4.00436e11	1.22559
$363$	−3.19880e11	−0.966957
$364$	1.93507e10	0.0577750
$365$	1.71189e11	0.504845
$366$	−1.00894e12	−2.93900
$367$	6.56011e11	1.88762	0.943808	−	0.330493i	$-0.107215\pi$
$367$	6.56011e11	1.88762	0.943808	+	0.330493i	$0.107215\pi$
$368$	2.43984e10	0.0693500
$369$	−4.09642e11	−1.15023
$370$	9.84092e10	0.272978
$371$	6.52812e10	0.178898
$372$	−1.27873e12	−3.46208
$373$	3.51915e10	0.0941344	0.0470672	−	0.998892i	$-0.485013\pi$
$373$	3.51915e10	0.0941344	0.0470672	+	0.998892i	$0.485013\pi$
$374$	1.38829e11	0.366909
$375$	5.26954e11	1.37604
$376$	−1.63851e11	−0.422770
$377$	4.64774e9	0.0118497
$378$	−8.08018e10	−0.203567
$379$	7.63955e11	1.90192	0.950958	−	0.309319i	$-0.100101\pi$
$379$	7.63955e11	1.90192	0.950958	+	0.309319i	$0.100101\pi$
$380$	9.64844e10	0.237373
$381$	−1.69915e11	−0.413113
$382$	3.12914e11	0.751864
$383$	−5.75234e11	−1.36600	−0.682999	−	0.730420i	$-0.739325\pi$
$383$	−5.75234e11	−1.36600	−0.682999	+	0.730420i	$0.739325\pi$
$384$	7.78014e11	1.82598
$385$	8.95631e10	0.207757
$386$	−1.06032e12	−2.43104
$387$	−6.83796e11	−1.54963
$388$	8.95370e11	2.00567
$389$	−1.46431e11	−0.324235	−0.162118	−	0.986771i	$-0.551832\pi$
$389$	−1.46431e11	−0.324235	−0.162118	+	0.986771i	$0.551832\pi$
$390$	−3.95622e10	−0.0865943
$391$	4.90171e10	0.106060
$392$	2.23188e11	0.477401
$393$	−6.44459e10	−0.136279
$394$	−7.23388e11	−1.51230
$395$	−2.62001e11	−0.541522
$396$	3.28751e11	0.671798
$397$	8.92153e11	1.80253	0.901264	−	0.433271i	$-0.142641\pi$
$397$	8.92153e11	1.80253	0.901264	+	0.433271i	$0.142641\pi$
$398$	8.35710e11	1.66948
$399$	1.05943e11	0.209264
$400$	8.68482e10	0.169625
$401$	−5.12731e11	−0.990238	−0.495119	−	0.868825i	$-0.664876\pi$
$401$	−5.12731e11	−0.990238	−0.495119	+	0.868825i	$0.664876\pi$
$402$	7.72878e11	1.47603
$403$	5.80864e10	0.109699
$404$	3.67608e11	0.686545
$405$	3.88519e11	0.717571
$406$	−9.78030e10	−0.178643
$407$	8.11493e10	0.146592
$408$	2.51019e11	0.448472
$409$	3.16870e11	0.559921	0.279960	−	0.960012i	$-0.409679\pi$
$409$	3.16870e11	0.559921	0.279960	+	0.960012i	$0.409679\pi$
$410$	−7.79042e11	−1.36155
$411$	−1.17602e10	−0.0203295
$412$	4.75393e11	0.812859
$413$	−6.03170e11	−1.02015
$414$	1.94344e11	0.325139
$415$	−3.05968e11	−0.506360
$416$	−4.70922e10	−0.0770954
$417$	−1.63883e11	−0.265412
$418$	1.33212e11	0.213427
$419$	−6.79671e11	−1.07730	−0.538649	−	0.842530i	$-0.681065\pi$
$419$	−6.79671e11	−1.07730	−0.538649	+	0.842530i	$0.681065\pi$
$420$	4.97226e11	0.779708
$421$	−3.43573e11	−0.533027	−0.266514	−	0.963831i	$-0.585872\pi$
$421$	−3.43573e11	−0.533027	−0.266514	+	0.963831i	$0.585872\pi$
$422$	−1.64182e12	−2.52011
$423$	3.08776e11	0.468934
$424$	1.48417e11	0.223016
$425$	1.74480e11	0.259416
$426$	−1.09350e12	−1.60871
$427$	−5.76012e11	−0.838506
$428$	1.25273e12	1.80451
$429$	−3.26234e10	−0.0465020
$430$	−1.30042e12	−1.83432
$431$	−6.22721e11	−0.869252	−0.434626	−	0.900611i	$-0.643119\pi$
$431$	−6.22721e11	−0.869252	−0.434626	+	0.900611i	$0.643119\pi$
$432$	4.34611e10	0.0600376
$433$	−4.13507e11	−0.565311	−0.282655	−	0.959221i	$-0.591215\pi$
$433$	−4.13507e11	−0.565311	−0.282655	+	0.959221i	$0.591215\pi$
$434$	−1.22232e12	−1.65379
$435$	1.19426e11	0.159918
$436$	−9.13279e11	−1.21036
$437$	4.70338e10	0.0616941
$438$	1.31216e12	1.70354
$439$	4.94612e10	0.0635585	0.0317793	−	0.999495i	$-0.489883\pi$
$439$	4.94612e10	0.0635585	0.0317793	+	0.999495i	$0.489883\pi$
$440$	2.03622e11	0.258993
$441$	−4.20595e11	−0.529530
$442$	−3.50105e10	−0.0436313
$443$	7.94804e11	0.980491	0.490245	−	0.871584i	$-0.336907\pi$
$443$	7.94804e11	0.980491	0.490245	+	0.871584i	$0.336907\pi$
$444$	4.50515e11	0.550156
$445$	8.80422e11	1.06432
$446$	−1.58209e11	−0.189332
$447$	1.83934e12	2.17911
$448$	8.43277e11	0.989052
$449$	1.63236e11	0.189543	0.0947713	−	0.995499i	$-0.469788\pi$
$449$	1.63236e11	0.189543	0.0947713	+	0.995499i	$0.469788\pi$
$450$	6.91784e11	0.795269
$451$	−6.42407e11	−0.731165
$452$	−1.05956e12	−1.19400
$453$	7.27543e11	0.811740
$454$	1.84458e12	2.03773
$455$	−2.25864e10	−0.0247057
$456$	2.40862e11	0.260871
$457$	1.52036e12	1.63051	0.815254	−	0.579104i	$-0.196598\pi$
$457$	1.52036e12	1.63051	0.815254	+	0.579104i	$0.196598\pi$
$458$	−5.15598e11	−0.547540
$459$	8.73145e10	0.0918183
$460$	2.20745e11	0.229869
$461$	1.85531e12	1.91321	0.956605	−	0.291389i	$-0.0941175\pi$
$461$	1.85531e12	1.91321	0.956605	+	0.291389i	$0.0941175\pi$
$462$	6.86498e11	0.701052
$463$	−1.89279e12	−1.91421	−0.957103	−	0.289748i	$-0.906429\pi$
$463$	−1.89279e12	−1.91421	−0.957103	+	0.289748i	$0.906429\pi$
$464$	5.26056e10	0.0526867
$465$	1.49256e12	1.48045
$466$	2.95399e11	0.290183
$467$	1.42261e12	1.38407	0.692037	−	0.721862i	$-0.256713\pi$
$467$	1.42261e12	1.38407	0.692037	+	0.721862i	$0.256713\pi$
$468$	−8.29059e10	−0.0798876
$469$	4.41244e11	0.421115
$470$	5.87218e11	0.555084
$471$	4.31545e10	0.0404047
$472$	−1.37131e12	−1.27173
$473$	−1.07234e12	−0.985046
$474$	−2.00823e12	−1.82730
$475$	1.67421e11	0.150900
$476$	4.40020e11	0.392863
$477$	−2.79690e11	−0.247368
$478$	1.88580e12	1.65223
$479$	−1.69172e12	−1.46831	−0.734156	−	0.678981i	$-0.762422\pi$
$479$	−1.69172e12	−1.46831	−0.734156	+	0.678981i	$0.762422\pi$
$480$	−1.21006e12	−1.04045
$481$	−2.04646e10	−0.0174321
$482$	7.96195e11	0.671904
$483$	2.42386e11	0.202649
$484$	−1.27482e12	−1.05595
$485$	−1.04509e12	−0.857662
$486$	2.56790e12	2.08792
$487$	−1.17201e12	−0.944170	−0.472085	−	0.881553i	$-0.656499\pi$
$487$	−1.17201e12	−0.944170	−0.472085	+	0.881553i	$0.656499\pi$
$488$	−1.30956e12	−1.04529
$489$	−6.14512e9	−0.00486004
$490$	−7.99872e11	−0.626813
$491$	−2.30362e12	−1.78872	−0.894362	−	0.447344i	$-0.852370\pi$
$491$	−2.30362e12	−1.78872	−0.894362	+	0.447344i	$0.852370\pi$
$492$	−3.56644e12	−2.74405
$493$	1.05686e11	0.0805762
$494$	−3.35939e10	−0.0253799
$495$	−3.83723e11	−0.287273
$496$	6.57452e11	0.487749
$497$	−6.24292e11	−0.458969
$498$	−2.34523e12	−1.70865
$499$	5.43725e11	0.392579	0.196290	−	0.980546i	$-0.437111\pi$
$499$	5.43725e11	0.392579	0.196290	+	0.980546i	$0.437111\pi$
$500$	2.10007e12	1.50269
$501$	1.78523e12	1.26597
$502$	3.80657e11	0.267527
$503$	2.27789e11	0.158663	0.0793316	−	0.996848i	$-0.474721\pi$
$503$	2.27789e11	0.158663	0.0793316	+	0.996848i	$0.474721\pi$
$504$	5.68194e11	0.392247
$505$	−4.29078e11	−0.293579
$506$	3.04773e11	0.206680
$507$	−2.01217e12	−1.35248
$508$	−6.77163e11	−0.451135
$509$	−1.91056e9	−0.00126163	−0.000630813	−	1.00000i	$-0.500201\pi$
$509$	−1.91056e9	−0.00126163	−0.000630813		1.00000i	$0.500201\pi$
$510$	−8.99613e11	−0.588830
$511$	7.49124e11	0.486026
$512$	−8.68784e11	−0.558723
$513$	8.37816e10	0.0534098
$514$	3.76735e12	2.38068
$515$	−5.54886e11	−0.347593
$516$	−5.95327e12	−3.69685
$517$	4.84226e11	0.298086
$518$	4.30639e11	0.262802
$519$	−2.08399e12	−1.26079
$520$	−5.13503e10	−0.0307984
$521$	−4.68965e10	−0.0278850	−0.0139425	−	0.999903i	$-0.504438\pi$
$521$	−4.68965e10	−0.0278850	−0.0139425	+	0.999903i	$0.504438\pi$
$522$	4.19026e11	0.247015
$523$	−2.21117e12	−1.29231	−0.646153	−	0.763208i	$-0.723623\pi$
$523$	−2.21117e12	−1.29231	−0.646153	+	0.763208i	$0.723623\pi$
$524$	−2.56837e11	−0.148822
$525$	8.62792e11	0.495666
$526$	−1.35132e12	−0.769701
$527$	1.32084e12	0.745937
$528$	−3.69249e11	−0.206760
$529$	−1.69354e12	−0.940256
$530$	−5.31904e11	−0.292814
$531$	2.58422e12	1.41060
$532$	4.22216e11	0.228524
$533$	1.62005e11	0.0869473
$534$	6.74840e12	3.59141
$535$	−1.46220e12	−0.771641
$536$	1.00317e12	0.524967
$537$	−2.10070e12	−1.09013
$538$	4.40967e12	2.26927
$539$	−6.59583e11	−0.336605
$540$	3.93215e11	0.199002
$541$	1.48254e12	0.744080	0.372040	−	0.928217i	$-0.378658\pi$
$541$	1.48254e12	0.744080	0.372040	+	0.928217i	$0.378658\pi$
$542$	5.71599e12	2.84508
$543$	−2.13973e12	−1.05623
$544$	−1.07084e12	−0.524239
$545$	1.06599e12	0.517571
$546$	−1.73124e11	−0.0833663
$547$	−2.33816e12	−1.11668	−0.558342	−	0.829611i	$-0.688562\pi$
$547$	−2.33816e12	−1.11668	−0.558342	+	0.829611i	$0.688562\pi$
$548$	−4.68679e10	−0.0222005
$549$	2.46786e12	1.15943
$550$	1.08486e12	0.505526
$551$	1.01410e11	0.0468703
$552$	5.51064e11	0.252625
$553$	−1.14652e12	−0.521336
$554$	−1.27240e12	−0.573890
$555$	−5.25848e11	−0.235257
$556$	−6.53123e11	−0.289840
$557$	1.08836e12	0.479096	0.239548	−	0.970885i	$-0.423001\pi$
$557$	1.08836e12	0.479096	0.239548	+	0.970885i	$0.423001\pi$
$558$	5.23689e12	2.28675
$559$	2.70427e11	0.117138
$560$	−2.55645e11	−0.109848
$561$	−7.41831e11	−0.316207
$562$	−1.84828e12	−0.781546
$563$	−2.10172e12	−0.881632	−0.440816	−	0.897598i	$-0.645311\pi$
$563$	−2.10172e12	−0.881632	−0.440816	+	0.897598i	$0.645311\pi$
$564$	2.68827e12	1.11871
$565$	1.23674e12	0.510575
$566$	3.95645e12	1.62044
$567$	1.70016e12	0.690822
$568$	−1.41933e12	−0.572157
$569$	2.38868e12	0.955329	0.477664	−	0.878542i	$-0.341484\pi$
$569$	2.38868e12	0.955329	0.477664	+	0.878542i	$0.341484\pi$
$570$	−8.63213e11	−0.342516
$571$	1.59595e12	0.628284	0.314142	−	0.949376i	$-0.398283\pi$
$571$	1.59595e12	0.628284	0.314142	+	0.949376i	$0.398283\pi$
$572$	−1.30014e11	−0.0507819
$573$	−1.67205e12	−0.647967
$574$	−3.40909e12	−1.31080
$575$	3.83039e11	0.146129
$576$	−3.61293e12	−1.36760
$577$	−3.54204e12	−1.33034	−0.665170	−	0.746692i	$-0.731641\pi$
$577$	−3.54204e12	−1.33034	−0.665170	+	0.746692i	$0.731641\pi$
$578$	3.43216e12	1.27906
$579$	5.66578e12	2.09511
$580$	4.75949e11	0.174636
$581$	−1.33892e12	−0.487484
$582$	−8.01058e12	−2.89408
$583$	−4.38614e11	−0.157244
$584$	1.70313e12	0.605886
$585$	9.67691e10	0.0341614
$586$	−6.17240e12	−2.16229
$587$	2.45844e12	0.854650	0.427325	−	0.904098i	$-0.359456\pi$
$587$	2.45844e12	0.854650	0.427325	+	0.904098i	$0.359456\pi$
$588$	−3.66180e12	−1.26327
$589$	1.26740e12	0.433904
$590$	4.91457e12	1.66975
$591$	3.86542e12	1.30332
$592$	−2.31629e11	−0.0775077
$593$	−4.11817e12	−1.36760	−0.683799	−	0.729671i	$-0.739673\pi$
$593$	−4.11817e12	−1.36760	−0.683799	+	0.729671i	$0.739673\pi$
$594$	5.42894e11	0.178927
$595$	−5.13598e11	−0.167995
$596$	7.33035e12	2.37967
$597$	−4.46561e12	−1.43878
$598$	−7.68590e10	−0.0245776
$599$	4.58964e12	1.45666	0.728329	−	0.685228i	$-0.240297\pi$
$599$	4.58964e12	1.45666	0.728329	+	0.685228i	$0.240297\pi$
$600$	1.96156e12	0.617903
$601$	−4.93141e12	−1.54183	−0.770915	−	0.636938i	$-0.780201\pi$
$601$	−4.93141e12	−1.54183	−0.770915	+	0.636938i	$0.780201\pi$
$602$	−5.69062e12	−1.76594
$603$	−1.89046e12	−0.582291
$604$	2.89948e12	0.886449
$605$	1.48799e12	0.451544
$606$	−3.28886e12	−0.990648
$607$	−2.61891e12	−0.783018	−0.391509	−	0.920174i	$-0.628047\pi$
$607$	−2.61891e12	−0.783018	−0.391509	+	0.920174i	$0.628047\pi$
$608$	−1.02751e12	−0.304944
$609$	5.22609e11	0.153957
$610$	4.69329e12	1.37244
$611$	−1.22114e11	−0.0354471
$612$	−1.88522e12	−0.543225
$613$	−4.59245e11	−0.131363	−0.0656814	−	0.997841i	$-0.520922\pi$
$613$	−4.59245e11	−0.131363	−0.0656814	+	0.997841i	$0.520922\pi$
$614$	−7.36393e12	−2.09099
$615$	4.16280e12	1.17340
$616$	8.91050e11	0.249338
$617$	−4.89895e12	−1.36088	−0.680440	−	0.732804i	$-0.738211\pi$
$617$	−4.89895e12	−1.36088	−0.680440	+	0.732804i	$0.738211\pi$
$618$	−4.25318e12	−1.17291
$619$	2.85637e12	0.781999	0.391000	−	0.920391i	$-0.372129\pi$
$619$	2.85637e12	0.781999	0.391000	+	0.920391i	$0.372129\pi$
$620$	5.94830e12	1.61670
$621$	1.91683e11	0.0517214
$622$	3.93175e12	1.05324
$623$	3.85273e12	1.02464
$624$	9.31187e10	0.0245871
$625$	−1.70628e11	−0.0447292
$626$	−8.59616e12	−2.23728
$627$	−7.11815e11	−0.183935
$628$	1.71984e11	0.0441235
$629$	−4.65349e11	−0.118536
$630$	−2.03632e12	−0.515008
$631$	−5.11822e12	−1.28525	−0.642623	−	0.766182i	$-0.722154\pi$
$631$	−5.11822e12	−1.28525	−0.642623	+	0.766182i	$0.722154\pi$
$632$	−2.60661e12	−0.649904
$633$	8.77303e12	2.17187
$634$	−5.43771e12	−1.33664
$635$	7.90395e11	0.192914
$636$	−2.43504e12	−0.590133
$637$	1.66337e11	0.0400277
$638$	6.57123e11	0.157019
$639$	2.67471e12	0.634633
$640$	−3.61910e12	−0.852688
$641$	−2.90440e12	−0.679508	−0.339754	−	0.940514i	$-0.610344\pi$
$641$	−2.90440e12	−0.679508	−0.339754	+	0.940514i	$0.610344\pi$
$642$	−1.12077e13	−2.60381
$643$	−1.38980e12	−0.320628	−0.160314	−	0.987066i	$-0.551251\pi$
$643$	−1.38980e12	−0.320628	−0.160314	+	0.987066i	$0.551251\pi$
$644$	9.65980e11	0.221300
$645$	6.94876e12	1.58084
$646$	−7.63900e11	−0.172580
$647$	−2.95103e12	−0.662070	−0.331035	−	0.943618i	$-0.607398\pi$
$647$	−2.95103e12	−0.662070	−0.331035	+	0.943618i	$0.607398\pi$
$648$	3.86532e12	0.861187
$649$	4.05261e12	0.896671
$650$	−2.73586e11	−0.0601151
$651$	6.53144e12	1.42526
$652$	−2.44902e10	−0.00530735
$653$	4.53520e12	0.976084	0.488042	−	0.872820i	$-0.337711\pi$
$653$	4.53520e12	0.976084	0.488042	+	0.872820i	$0.337711\pi$
$654$	8.17080e12	1.74648
$655$	2.99784e11	0.0636388
$656$	1.83366e12	0.386590
$657$	−3.20954e12	−0.672045
$658$	2.56967e12	0.534392
$659$	2.76745e12	0.571605	0.285802	−	0.958289i	$-0.407740\pi$
$659$	2.76745e12	0.571605	0.285802	+	0.958289i	$0.407740\pi$
$660$	−3.34078e12	−0.685331
$661$	−7.35152e12	−1.49786	−0.748929	−	0.662650i	$-0.769432\pi$
$661$	−7.35152e12	−1.49786	−0.748929	+	0.662650i	$0.769432\pi$
$662$	1.05510e13	2.13517
$663$	1.87078e11	0.0376021
$664$	−3.04403e12	−0.607704
$665$	−4.92817e11	−0.0977211
$666$	−1.84502e12	−0.363386
$667$	2.32014e11	0.0453887
$668$	7.11468e12	1.38249
$669$	8.45389e11	0.163170
$670$	−3.59521e12	−0.689267
$671$	3.87013e12	0.737012
$672$	−5.29521e12	−1.00166
$673$	2.94059e12	0.552544	0.276272	−	0.961080i	$-0.410901\pi$
$673$	2.94059e12	0.552544	0.276272	+	0.961080i	$0.410901\pi$
$674$	3.80512e12	0.710229
$675$	6.82310e11	0.126507
$676$	−8.01912e12	−1.47695
$677$	−5.57737e12	−1.02042	−0.510211	−	0.860049i	$-0.670433\pi$
$677$	−5.57737e12	−1.02042	−0.510211	+	0.860049i	$0.670433\pi$
$678$	9.47955e12	1.72288
$679$	−4.57332e12	−0.825691
$680$	−1.16767e12	−0.209425
$681$	−9.85648e12	−1.75614
$682$	8.21256e12	1.45361
$683$	8.18245e12	1.43877	0.719383	−	0.694614i	$-0.244425\pi$
$683$	8.18245e12	1.43877	0.719383	+	0.694614i	$0.244425\pi$
$684$	−1.80894e12	−0.315988
$685$	5.47050e10	0.00949334
$686$	−9.08035e12	−1.56547
$687$	2.75509e12	0.471879
$688$	3.06083e12	0.520825
$689$	1.10612e11	0.0186988
$690$	−1.97493e12	−0.331689
$691$	5.96962e12	0.996083	0.498042	−	0.867153i	$-0.334053\pi$
$691$	5.96962e12	0.996083	0.498042	+	0.867153i	$0.334053\pi$
$692$	−8.30532e12	−1.37683
$693$	−1.67917e12	−0.276564
$694$	−1.19353e13	−1.95307
$695$	7.62335e11	0.123941
$696$	1.18815e12	0.191925
$697$	3.68387e12	0.591230
$698$	−8.05281e12	−1.28410
$699$	−1.57846e12	−0.250084
$700$	3.43849e12	0.541285
$701$	3.47393e11	0.0543362	0.0271681	−	0.999631i	$-0.491351\pi$
$701$	3.47393e11	0.0543362	0.0271681	+	0.999631i	$0.491351\pi$
$702$	−1.36909e11	−0.0212773
$703$	−4.46520e11	−0.0689512
$704$	−5.66584e12	−0.869336
$705$	−3.13779e12	−0.478380
$706$	−2.90280e12	−0.439739
$707$	−1.87765e12	−0.282635
$708$	2.24988e13	3.36519
$709$	4.96767e12	0.738320	0.369160	−	0.929366i	$-0.379645\pi$
$709$	4.96767e12	0.738320	0.369160	+	0.929366i	$0.379645\pi$
$710$	5.08666e12	0.751225
$711$	4.91213e12	0.720870
$712$	8.75918e12	1.27733
$713$	2.89965e12	0.420188
$714$	−3.93671e12	−0.566880
$715$	1.51755e11	0.0217152
$716$	−8.37191e12	−1.19046
$717$	−1.00767e13	−1.42392
$718$	1.24093e13	1.74255
$719$	5.99605e11	0.0836730	0.0418365	−	0.999124i	$-0.486679\pi$
$719$	5.99605e11	0.0836730	0.0418365	+	0.999124i	$0.486679\pi$
$720$	1.09528e12	0.151890
$721$	−2.42818e12	−0.334636
$722$	1.07725e13	1.47536
$723$	−4.25445e12	−0.579057
$724$	−8.52746e12	−1.15344
$725$	8.25872e11	0.111018
$726$	1.14054e13	1.52368
$727$	1.18716e13	1.57618	0.788090	−	0.615560i	$-0.211070\pi$
$727$	1.18716e13	1.57618	0.788090	+	0.615560i	$0.211070\pi$
$728$	−2.24709e11	−0.0296503
$729$	−5.09286e12	−0.667864
$730$	−6.10378e12	−0.795510
$731$	6.14930e12	0.796521
$732$	2.14857e13	2.76599
$733$	−5.82970e12	−0.745896	−0.372948	−	0.927852i	$-0.621653\pi$
$733$	−5.82970e12	−0.745896	−0.372948	+	0.927852i	$0.621653\pi$
$734$	−2.33902e13	−2.97441
$735$	4.27411e12	0.540197
$736$	−2.35083e12	−0.295305
$737$	−2.96465e12	−0.370143
$738$	1.46059e13	1.81248
$739$	2.95218e12	0.364119	0.182059	−	0.983288i	$-0.441724\pi$
$739$	2.95218e12	0.364119	0.182059	+	0.983288i	$0.441724\pi$
$740$	−2.09566e12	−0.256909
$741$	1.79509e11	0.0218728
$742$	−2.32761e12	−0.281899
$743$	−8.88573e12	−1.06965	−0.534827	−	0.844962i	$-0.679623\pi$
$743$	−8.88573e12	−1.06965	−0.534827	+	0.844962i	$0.679623\pi$
$744$	1.48492e13	1.77675
$745$	−8.55610e12	−1.01759
$746$	−1.25476e12	−0.148332
$747$	5.73644e12	0.674061
$748$	−2.95642e12	−0.345310
$749$	−6.39860e12	−0.742877
$750$	−1.87886e13	−2.16830
$751$	−8.08516e11	−0.0927489	−0.0463745	−	0.998924i	$-0.514767\pi$
$751$	−8.08516e11	−0.0927489	−0.0463745	+	0.998924i	$0.514767\pi$
$752$	−1.38215e12	−0.157607
$753$	−2.03404e12	−0.230558
$754$	−1.65716e11	−0.0186721
$755$	−3.38432e12	−0.379062
$756$	1.72071e12	0.191584
$757$	−1.74173e13	−1.92774	−0.963872	−	0.266366i	$-0.914177\pi$
$757$	−1.74173e13	−1.92774	−0.963872	+	0.266366i	$0.914177\pi$
$758$	−2.72390e13	−2.99695
$759$	−1.62855e12	−0.178120
$760$	−1.12042e12	−0.121820
$761$	1.08775e13	1.17571	0.587854	−	0.808967i	$-0.299973\pi$
$761$	1.08775e13	1.17571	0.587854	+	0.808967i	$0.299973\pi$
$762$	6.05835e12	0.650964
$763$	4.66479e12	0.498278
$764$	−6.66362e12	−0.707604
$765$	2.20045e12	0.232293
$766$	2.05101e13	2.15247
$767$	−1.02200e12	−0.106629
$768$	−6.52976e12	−0.677286
$769$	4.86867e12	0.502045	0.251022	−	0.967981i	$-0.419233\pi$
$769$	4.86867e12	0.502045	0.251022	+	0.967981i	$0.419233\pi$
$770$	−3.19339e12	−0.327374
$771$	−2.01308e13	−2.05171
$772$	2.25799e13	2.28793
$773$	1.59140e12	0.160314	0.0801572	−	0.996782i	$-0.474458\pi$
$773$	1.59140e12	0.160314	0.0801572	+	0.996782i	$0.474458\pi$
$774$	2.43809e13	2.44183
$775$	1.03216e13	1.02775
$776$	−1.03974e13	−1.02932
$777$	−2.30111e12	−0.226487
$778$	5.22103e12	0.510914
$779$	3.53481e12	0.343912
$780$	8.42493e11	0.0814968
$781$	4.19451e12	0.403415
$782$	−1.74771e12	−0.167124
$783$	4.13288e11	0.0392939
$784$	1.88268e12	0.177973
$785$	−2.00742e11	−0.0188680
$786$	2.29783e12	0.214742
$787$	−5.01064e12	−0.465593	−0.232797	−	0.972525i	$-0.574788\pi$
$787$	−5.01064e12	−0.465593	−0.232797	+	0.972525i	$0.574788\pi$
$788$	1.54049e13	1.42328
$789$	7.22076e12	0.663340
$790$	9.34170e12	0.853305
$791$	5.41197e12	0.491542
$792$	−3.81761e12	−0.344769
$793$	−9.75988e11	−0.0876426
$794$	−3.18099e13	−2.84034
$795$	2.84222e12	0.252351
$796$	−1.77968e13	−1.57121
$797$	6.92926e12	0.608309	0.304155	−	0.952623i	$-0.401626\pi$
$797$	6.92926e12	0.608309	0.304155	+	0.952623i	$0.401626\pi$
$798$	−3.77742e12	−0.329748
$799$	−2.77679e12	−0.241036
$800$	−8.36796e12	−0.722295
$801$	−1.65066e13	−1.41681
$802$	1.82815e13	1.56037
$803$	−5.03324e12	−0.427197
$804$	−1.64588e13	−1.38914
$805$	−1.12751e12	−0.0946320
$806$	−2.07108e12	−0.172858
$807$	−2.35630e13	−1.95569
$808$	−4.26883e12	−0.352336
$809$	−3.17263e12	−0.260406	−0.130203	−	0.991487i	$-0.541563\pi$
$809$	−3.17263e12	−0.260406	−0.130203	+	0.991487i	$0.541563\pi$
$810$	−1.38527e13	−1.13071
$811$	−1.70748e13	−1.38600	−0.692998	−	0.720940i	$-0.743710\pi$
$811$	−1.70748e13	−1.38600	−0.692998	+	0.720940i	$0.743710\pi$
$812$	2.08276e12	0.168127
$813$	−3.05433e13	−2.45193
$814$	−2.89339e12	−0.230992
$815$	2.85853e10	0.00226952
$816$	2.11745e12	0.167189
$817$	5.90049e12	0.463328
$818$	−1.12981e13	−0.882295
$819$	4.23462e11	0.0328879
$820$	1.65900e13	1.28140
$821$	2.29149e13	1.76025	0.880123	−	0.474746i	$-0.157460\pi$
$821$	2.29149e13	1.76025	0.880123	+	0.474746i	$0.157460\pi$
$822$	4.19312e11	0.0320342
$823$	−1.20135e13	−0.912792	−0.456396	−	0.889777i	$-0.650860\pi$
$823$	−1.20135e13	−0.912792	−0.456396	+	0.889777i	$0.650860\pi$
$824$	−5.52048e12	−0.417161
$825$	−5.79696e12	−0.435670
$826$	2.15062e13	1.60751
$827$	1.46620e13	1.08998	0.544991	−	0.838442i	$-0.316533\pi$
$827$	1.46620e13	1.08998	0.544991	+	0.838442i	$0.316533\pi$
$828$	−4.13864e12	−0.306000
$829$	−1.23368e13	−0.907206	−0.453603	−	0.891204i	$-0.649862\pi$
$829$	−1.23368e13	−0.907206	−0.453603	+	0.891204i	$0.649862\pi$
$830$	1.09093e13	0.797897
$831$	6.79903e12	0.494587
$832$	1.42884e12	0.103378
$833$	3.78237e12	0.272183
$834$	5.84327e12	0.418224
$835$	−8.30437e12	−0.591177
$836$	−2.83680e12	−0.200863
$837$	5.16518e12	0.363765
$838$	2.42338e13	1.69755
$839$	6.64167e11	0.0462752	0.0231376	−	0.999732i	$-0.492634\pi$
$839$	6.64167e11	0.0462752	0.0231376	+	0.999732i	$0.492634\pi$
$840$	−5.77401e12	−0.400148
$841$	5.00246e11	0.0344828
$842$	1.22502e13	0.839918
$843$	9.87626e12	0.673548
$844$	3.49632e13	2.37176
$845$	9.36005e12	0.631572
$846$	−1.10095e13	−0.738923
$847$	6.51144e12	0.434712
$848$	1.25196e12	0.0831398
$849$	−2.11412e13	−1.39652
$850$	−6.22113e12	−0.408775
$851$	−1.02159e12	−0.0667716
$852$	2.32866e13	1.51401
$853$	−2.70466e12	−0.174921	−0.0874604	−	0.996168i	$-0.527875\pi$
$853$	−2.70466e12	−0.174921	−0.0874604	+	0.996168i	$0.527875\pi$
$854$	2.05378e13	1.32128
$855$	2.11142e12	0.135122
$856$	−1.45472e13	−0.926080
$857$	2.04733e13	1.29651	0.648253	−	0.761425i	$-0.275500\pi$
$857$	2.04733e13	1.29651	0.648253	+	0.761425i	$0.275500\pi$
$858$	1.16319e12	0.0732755
$859$	−2.27502e13	−1.42566	−0.712831	−	0.701335i	$-0.752588\pi$
$859$	−2.27502e13	−1.42566	−0.712831	+	0.701335i	$0.752588\pi$
$860$	2.76929e13	1.72634
$861$	1.82164e13	1.12966
$862$	2.22032e13	1.36972
$863$	1.85412e13	1.13786	0.568930	−	0.822386i	$-0.307358\pi$
$863$	1.85412e13	1.13786	0.568930	+	0.822386i	$0.307358\pi$
$864$	−4.18754e12	−0.255651
$865$	9.69411e12	0.588756
$866$	1.47437e13	0.890789
$867$	−1.83397e13	−1.10232
$868$	2.60298e13	1.55644
$869$	7.70327e12	0.458233
$870$	−4.25816e12	−0.251991
$871$	7.47638e11	0.0440159
$872$	1.06054e13	0.621159
$873$	1.95939e13	1.14171
$874$	−1.67700e12	−0.0972145
$875$	−1.07266e13	−0.618624
$876$	−2.79430e13	−1.60326
$877$	−2.17390e13	−1.24091	−0.620456	−	0.784242i	$-0.713052\pi$
$877$	−2.17390e13	−1.24091	−0.620456	+	0.784242i	$0.713052\pi$
$878$	−1.76355e12	−0.100152
$879$	3.29821e13	1.86350
$880$	1.71764e12	0.0965516
$881$	3.38989e13	1.89581	0.947903	−	0.318560i	$-0.103199\pi$
$881$	3.38989e13	1.89581	0.947903	+	0.318560i	$0.103199\pi$
$882$	1.49964e13	0.834408
$883$	−1.97035e13	−1.09074	−0.545368	−	0.838197i	$-0.683610\pi$
$883$	−1.97035e13	−1.09074	−0.545368	+	0.838197i	$0.683610\pi$
$884$	7.45564e11	0.0410629
$885$	−2.62609e13	−1.43901
$886$	−2.83389e13	−1.54501
$887$	1.54246e13	0.836676	0.418338	−	0.908292i	$-0.362613\pi$
$887$	1.54246e13	0.836676	0.418338	+	0.908292i	$0.362613\pi$
$888$	−5.23158e12	−0.282341
$889$	3.45877e12	0.185722
$890$	−3.13916e13	−1.67710
$891$	−1.14231e13	−0.607204
$892$	3.36913e12	0.178187
$893$	−2.66443e12	−0.140208
$894$	−6.55821e13	−3.43374
$895$	9.77183e12	0.509064
$896$	−1.58372e13	−0.820902
$897$	4.10695e11	0.0211813
$898$	−5.82020e12	−0.298672
$899$	6.25196e12	0.319226
$900$	−1.47318e13	−0.748454
$901$	2.51522e12	0.127149
$902$	2.29051e13	1.15213
$903$	3.04078e13	1.52191
$904$	1.23041e13	0.612763
$905$	9.95339e12	0.493233
$906$	−2.59407e13	−1.27910
$907$	−3.06923e13	−1.50590	−0.752951	−	0.658076i	$-0.771371\pi$
$907$	−3.06923e13	−1.50590	−0.752951	+	0.658076i	$0.771371\pi$
$908$	−3.92811e13	−1.91777
$909$	8.04457e12	0.390810
$910$	8.05323e11	0.0389300
$911$	−1.00808e13	−0.484912	−0.242456	−	0.970162i	$-0.577953\pi$
$911$	−1.00808e13	−0.484912	−0.242456	+	0.970162i	$0.577953\pi$
$912$	2.03177e12	0.0972520
$913$	8.99596e12	0.428478
$914$	−5.42086e13	−2.56927
$915$	−2.50785e13	−1.18279
$916$	1.09799e13	0.515309
$917$	1.31185e12	0.0612666
$918$	−3.11322e12	−0.144683
$919$	−1.30756e13	−0.604701	−0.302351	−	0.953197i	$-0.597771\pi$
$919$	−1.30756e13	−0.604701	−0.302351	+	0.953197i	$0.597771\pi$
$920$	−2.56339e12	−0.117969
$921$	3.93491e13	1.80205
$922$	−6.61514e13	−3.01474
$923$	−1.05779e12	−0.0479725
$924$	−1.46193e13	−0.659784
$925$	−3.63642e12	−0.163319
$926$	6.74879e13	3.01631
$927$	1.04033e13	0.462713
$928$	−5.06863e12	−0.224349
$929$	−1.55091e13	−0.683149	−0.341575	−	0.939855i	$-0.610960\pi$
$929$	−1.55091e13	−0.683149	−0.341575	+	0.939855i	$0.610960\pi$
$930$	−5.32175e13	−2.33282
$931$	3.62933e12	0.158326
$932$	−6.29063e12	−0.273101
$933$	−2.10092e13	−0.907701
$934$	−5.07234e13	−2.18096
$935$	3.45078e12	0.147661
$936$	9.62741e11	0.0409985
$937$	2.89746e13	1.22798	0.613988	−	0.789316i	$-0.289564\pi$
$937$	2.89746e13	1.22798	0.613988	+	0.789316i	$0.289564\pi$
$938$	−1.57326e13	−0.663573
$939$	4.59334e13	1.92812
$940$	−1.25051e13	−0.522408
$941$	−3.19379e13	−1.32786	−0.663932	−	0.747793i	$-0.731114\pi$
$941$	−3.19379e13	−1.32786	−0.663932	+	0.747793i	$0.731114\pi$
$942$	−1.53868e12	−0.0636678
$943$	8.08724e12	0.333041
$944$	−1.15676e13	−0.474098
$945$	−2.00844e12	−0.0819248
$946$	3.82344e13	1.55219
$947$	−7.66503e12	−0.309698	−0.154849	−	0.987938i	$-0.549489\pi$
$947$	−7.66503e12	−0.309698	−0.154849	+	0.987938i	$0.549489\pi$
$948$	4.27661e13	1.71974
$949$	1.26931e12	0.0508005
$950$	−5.96941e12	−0.237780
$951$	2.90563e13	1.15194
$952$	−5.10971e12	−0.201618
$953$	4.64396e13	1.82377	0.911886	−	0.410444i	$-0.134626\pi$
$953$	4.64396e13	1.82377	0.911886	+	0.410444i	$0.134626\pi$
$954$	9.97240e12	0.389791
$955$	7.77789e12	0.302584
$956$	−4.01589e13	−1.55497
$957$	−3.51133e12	−0.135322
$958$	6.03185e13	2.31369
$959$	2.39389e11	0.00913946
$960$	3.67147e13	1.39515
$961$	5.16959e13	1.95524
$962$	7.29669e11	0.0274687
$963$	2.74141e13	1.02720
$964$	−1.69553e13	−0.632352
$965$	−2.63556e13	−0.978362
$966$	−8.64230e12	−0.319325
$967$	−3.23884e13	−1.19116	−0.595580	−	0.803296i	$-0.703078\pi$
$967$	−3.23884e13	−1.19116	−0.595580	+	0.803296i	$0.703078\pi$
$968$	1.48038e13	0.541918
$969$	4.08189e12	0.148732
$970$	3.72629e13	1.35146
$971$	1.27609e13	0.460676	0.230338	−	0.973111i	$-0.426017\pi$
$971$	1.27609e13	0.460676	0.230338	+	0.973111i	$0.426017\pi$
$972$	−5.46845e13	−1.96501
$973$	3.33598e12	0.119321
$974$	4.17882e13	1.48778
$975$	1.46190e12	0.0518081
$976$	−1.10467e13	−0.389682
$977$	−4.26725e13	−1.49838	−0.749190	−	0.662355i	$-0.769557\pi$
$977$	−4.26725e13	−1.49838	−0.749190	+	0.662355i	$0.769557\pi$
$978$	2.19105e11	0.00765822
$979$	−2.58859e13	−0.900618
$980$	1.70336e13	0.589915
$981$	−1.99858e13	−0.688986
$982$	8.21358e13	2.81858
$983$	7.88375e12	0.269304	0.134652	−	0.990893i	$-0.457008\pi$
$983$	7.88375e12	0.269304	0.134652	+	0.990893i	$0.457008\pi$
$984$	4.14151e13	1.40825
$985$	−1.79808e13	−0.608620
$986$	−3.76826e12	−0.126968
$987$	−1.37310e13	−0.460547
$988$	7.15397e11	0.0238859
$989$	1.34996e13	0.448682
$990$	1.36817e13	0.452671
$991$	−5.57511e11	−0.0183621	−0.00918105	−	0.999958i	$-0.502922\pi$
$991$	−5.57511e11	−0.0183621	−0.00918105	+	0.999958i	$0.502922\pi$
$992$	−6.33465e13	−2.07692
$993$	−5.63790e13	−1.84012
$994$	2.22592e13	0.723222
$995$	2.07727e13	0.671876
$996$	4.99427e13	1.60807
$997$	−7.68901e12	−0.246458	−0.123229	−	0.992378i	$-0.539325\pi$
$997$	−7.68901e12	−0.246458	−0.123229	+	0.992378i	$0.539325\pi$
$998$	−1.93866e13	−0.618607
$999$	−1.81976e12	−0.0578055

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.10.a.a.1.1	✓	9
3.2	odd	2		261.10.a.b.1.9		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.10.a.a.1.1	✓	9	1.1	even	1	trivial
261.10.a.b.1.9		9	3.2	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q-35.6552 q^{2} +190.523 q^{3} +759.292 q^{4} -886.258 q^{5} -6793.13 q^{6} -3878.27 q^{7} -8817.24 q^{8} +16616.0 q^{9} +O(q^{10})\)	\(q-35.6552 q^{2} +190.523 q^{3} +759.292 q^{4} -886.258 q^{5} -6793.13 q^{6} -3878.27 q^{7} -8817.24 q^{8} +16616.0 q^{9} +31599.7 q^{10} +26057.4 q^{11} +144663. q^{12} -6571.28 q^{13} +138280. q^{14} -168852. q^{15} -74377.2 q^{16} -149426. q^{17} -592447. q^{18} -143380. q^{19} -672928. q^{20} -738899. q^{21} -929083. q^{22} -328036. q^{23} -1.67989e6 q^{24} -1.16767e6 q^{25} +234300. q^{26} -584334. q^{27} -2.94474e6 q^{28} -707281. q^{29} +6.02046e6 q^{30} -8.83943e6 q^{31} +7.16636e6 q^{32} +4.96454e6 q^{33} +5.32781e6 q^{34} +3.43714e6 q^{35} +1.26164e7 q^{36} +3.11425e6 q^{37} +5.11223e6 q^{38} -1.25198e6 q^{39} +7.81435e6 q^{40} -2.46535e7 q^{41} +2.63456e7 q^{42} -4.11528e7 q^{43} +1.97852e7 q^{44} -1.47261e7 q^{45} +1.16962e7 q^{46} +1.85830e7 q^{47} -1.41706e7 q^{48} -2.53127e7 q^{49} +4.16336e7 q^{50} -2.84691e7 q^{51} -4.98952e6 q^{52} -1.68326e7 q^{53} +2.08345e7 q^{54} -2.30936e7 q^{55} +3.41956e7 q^{56} -2.73172e7 q^{57} +2.52182e7 q^{58} +1.55526e8 q^{59} -1.28208e8 q^{60} +1.48523e8 q^{61} +3.15172e8 q^{62} -6.44413e7 q^{63} -2.17437e8 q^{64} +5.82385e6 q^{65} -1.77012e8 q^{66} -1.13774e8 q^{67} -1.13458e8 q^{68} -6.24985e7 q^{69} -1.22552e8 q^{70} +1.60972e8 q^{71} -1.46507e8 q^{72} -1.93160e8 q^{73} -1.11039e8 q^{74} -2.22468e8 q^{75} -1.08867e8 q^{76} -1.01058e8 q^{77} +4.46396e7 q^{78} +2.95627e8 q^{79} +6.59173e7 q^{80} -4.38382e8 q^{81} +8.79024e8 q^{82} +3.45236e8 q^{83} -5.61040e8 q^{84} +1.32430e8 q^{85} +1.46731e9 q^{86} -1.34753e8 q^{87} -2.29755e8 q^{88} -9.93415e8 q^{89} +5.25060e8 q^{90} +2.54852e7 q^{91} -2.49075e8 q^{92} -1.68411e9 q^{93} -6.62581e8 q^{94} +1.27071e8 q^{95} +1.36536e9 q^{96} +1.17922e9 q^{97} +9.02528e8 q^{98} +4.32971e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 244 q^{3} + 1194 q^{4} - 738 q^{5} - 2330 q^{6} - 7128 q^{7} - 13776 q^{8} + 33017 q^{9}+O(q^{10}) \) 9 * q - 244 * q^3 + 1194 * q^4 - 738 * q^5 - 2330 * q^6 - 7128 * q^7 - 13776 * q^8 + 33017 * q^9	\( 9 q - 244 q^{3} + 1194 q^{4} - 738 q^{5} - 2330 q^{6} - 7128 q^{7} - 13776 q^{8} + 33017 q^{9} + 37812 q^{10} - 59512 q^{11} - 127348 q^{12} - 165758 q^{13} - 406080 q^{14} - 693178 q^{15} - 1044958 q^{16} - 394814 q^{17} - 1676576 q^{18} - 2256606 q^{19} - 2237578 q^{20} - 1750168 q^{21} - 5311718 q^{22} - 1699500 q^{23} - 4446318 q^{24} - 983481 q^{25} - 4264740 q^{26} - 6987958 q^{27} - 8491636 q^{28} - 6365529 q^{29} - 16907854 q^{30} - 11929632 q^{31} - 1346192 q^{32} + 1750252 q^{33} + 8655764 q^{34} - 3275324 q^{35} + 29848532 q^{36} + 14454898 q^{37} + 14709736 q^{38} + 41155042 q^{39} + 45167060 q^{40} + 52495202 q^{41} + 103102340 q^{42} + 21819888 q^{43} + 70837004 q^{44} + 61248326 q^{45} + 20628012 q^{46} + 44968948 q^{47} + 122982540 q^{48} - 26826775 q^{49} + 155997680 q^{50} - 28882428 q^{51} + 29562122 q^{52} - 111394302 q^{53} + 70575802 q^{54} - 173560742 q^{55} + 67419136 q^{56} + 85769252 q^{57} - 236142720 q^{59} - 47991000 q^{60} - 241129054 q^{61} + 261343278 q^{62} - 328513060 q^{63} - 333112958 q^{64} - 625660884 q^{65} + 223958776 q^{66} - 672046492 q^{67} - 63179948 q^{68} - 705827600 q^{69} - 366389016 q^{70} - 475841956 q^{71} - 18937608 q^{72} - 424813822 q^{73} - 532689728 q^{74} - 913708498 q^{75} - 552478056 q^{76} - 182224776 q^{77} + 928127886 q^{78} - 170801148 q^{79} + 562655678 q^{80} - 914585851 q^{81} + 1468192652 q^{82} - 468898296 q^{83} + 952386216 q^{84} - 271552972 q^{85} + 1462277802 q^{86} + 172576564 q^{87} + 1176890862 q^{88} - 676036598 q^{89} + 4017858752 q^{90} + 9763884 q^{91} + 2724990708 q^{92} - 858755220 q^{93} + 2429128614 q^{94} + 69331732 q^{95} + 3111862050 q^{96} + 170708754 q^{97} + 3278517600 q^{98} + 305494078 q^{99}+O(q^{100}) \) 9 * q - 244 * q^3 + 1194 * q^4 - 738 * q^5 - 2330 * q^6 - 7128 * q^7 - 13776 * q^8 + 33017 * q^9 + 37812 * q^10 - 59512 * q^11 - 127348 * q^12 - 165758 * q^13 - 406080 * q^14 - 693178 * q^15 - 1044958 * q^16 - 394814 * q^17 - 1676576 * q^18 - 2256606 * q^19 - 2237578 * q^20 - 1750168 * q^21 - 5311718 * q^22 - 1699500 * q^23 - 4446318 * q^24 - 983481 * q^25 - 4264740 * q^26 - 6987958 * q^27 - 8491636 * q^28 - 6365529 * q^29 - 16907854 * q^30 - 11929632 * q^31 - 1346192 * q^32 + 1750252 * q^33 + 8655764 * q^34 - 3275324 * q^35 + 29848532 * q^36 + 14454898 * q^37 + 14709736 * q^38 + 41155042 * q^39 + 45167060 * q^40 + 52495202 * q^41 + 103102340 * q^42 + 21819888 * q^43 + 70837004 * q^44 + 61248326 * q^45 + 20628012 * q^46 + 44968948 * q^47 + 122982540 * q^48 - 26826775 * q^49 + 155997680 * q^50 - 28882428 * q^51 + 29562122 * q^52 - 111394302 * q^53 + 70575802 * q^54 - 173560742 * q^55 + 67419136 * q^56 + 85769252 * q^57 - 236142720 * q^59 - 47991000 * q^60 - 241129054 * q^61 + 261343278 * q^62 - 328513060 * q^63 - 333112958 * q^64 - 625660884 * q^65 + 223958776 * q^66 - 672046492 * q^67 - 63179948 * q^68 - 705827600 * q^69 - 366389016 * q^70 - 475841956 * q^71 - 18937608 * q^72 - 424813822 * q^73 - 532689728 * q^74 - 913708498 * q^75 - 552478056 * q^76 - 182224776 * q^77 + 928127886 * q^78 - 170801148 * q^79 + 562655678 * q^80 - 914585851 * q^81 + 1468192652 * q^82 - 468898296 * q^83 + 952386216 * q^84 - 271552972 * q^85 + 1462277802 * q^86 + 172576564 * q^87 + 1176890862 * q^88 - 676036598 * q^89 + 4017858752 * q^90 + 9763884 * q^91 + 2724990708 * q^92 - 858755220 * q^93 + 2429128614 * q^94 + 69331732 * q^95 + 3111862050 * q^96 + 170708754 * q^97 + 3278517600 * q^98 + 305494078 * q^99

Introduction

L-functions

Modular forms

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