LMFDB - Embedded newform 29.16.a.b.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,16,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, 16, names="a")

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

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 16 $
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:	$41.3811164790$
Analytic rank:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 505005 x^{17} - 8736364 x^{16} + 105356631548 x^{15} + 3420215362096 x^{14} + \cdots - 44\!\cdots\!16 $ x^19 - 505005x^17 - 8736364x^16 + 105356631548x^15 + 3420215362096x^14 - 11728115084600096x^13 - 526667384321784320x^12 + 752639041053026643200x^11 + 40754151979122502310912x^10 - 28214216503608778938845184x^9 - 1695908354434496093367894016x^8 + 602673095240440629989514543104x^7 + 38350831066057179894641242144768x^6 - 6885716108325545063604182908403712x^5 - 456772325113502009511188321406025728x^4 + 36920835566283148767251922402968338432x^3 + 2536352111314177920131172586486147055616x^2 - 64060563711600166379571072317272711233536*x - 4498782094616840134153644664240655371862016
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{43}\cdot 3^{6}\cdot 5^{5}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$281.041$ 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)

$f(q)$	$=$	$q+281.041 q^{2} +4013.45 q^{3} +46215.9 q^{4} +150501. q^{5} +1.12794e6 q^{6} -1.57306e6 q^{7} +3.77941e6 q^{8} +1.75891e6 q^{9} +O(q^{10})$	\(q+281.041 q^{2} +4013.45 q^{3} +46215.9 q^{4} +150501. q^{5} +1.12794e6 q^{6} -1.57306e6 q^{7} +3.77941e6 q^{8} +1.75891e6 q^{9} +4.22968e7 q^{10} +6.02762e7 q^{11} +1.85485e8 q^{12} +3.83967e8 q^{13} -4.42095e8 q^{14} +6.04027e8 q^{15} -4.52235e8 q^{16} +2.68639e9 q^{17} +4.94325e8 q^{18} -8.88241e8 q^{19} +6.95552e9 q^{20} -6.31342e9 q^{21} +1.69401e10 q^{22} +5.07294e9 q^{23} +1.51685e10 q^{24} -7.86717e9 q^{25} +1.07910e11 q^{26} -5.05294e10 q^{27} -7.27006e10 q^{28} -1.72499e10 q^{29} +1.69756e11 q^{30} +1.27228e11 q^{31} -2.50940e11 q^{32} +2.41916e11 q^{33} +7.54985e11 q^{34} -2.36747e11 q^{35} +8.12895e10 q^{36} -3.08988e11 q^{37} -2.49632e11 q^{38} +1.54103e12 q^{39} +5.68803e11 q^{40} -7.55514e11 q^{41} -1.77433e12 q^{42} -2.74489e12 q^{43} +2.78572e12 q^{44} +2.64717e11 q^{45} +1.42570e12 q^{46} -1.98075e12 q^{47} -1.81502e12 q^{48} -2.27303e12 q^{49} -2.21100e12 q^{50} +1.07817e13 q^{51} +1.77454e13 q^{52} +9.23657e12 q^{53} -1.42008e13 q^{54} +9.07159e12 q^{55} -5.94526e12 q^{56} -3.56491e12 q^{57} -4.84792e12 q^{58} -3.45501e11 q^{59} +2.79157e13 q^{60} -1.67739e13 q^{61} +3.57564e13 q^{62} -2.76688e12 q^{63} -5.57056e13 q^{64} +5.77872e13 q^{65} +6.79882e13 q^{66} +8.34631e13 q^{67} +1.24154e14 q^{68} +2.03600e13 q^{69} -6.65356e13 q^{70} +6.63643e13 q^{71} +6.64763e12 q^{72} -9.40965e13 q^{73} -8.68382e13 q^{74} -3.15745e13 q^{75} -4.10508e13 q^{76} -9.48183e13 q^{77} +4.33093e14 q^{78} -1.50015e14 q^{79} -6.80616e13 q^{80} -2.28036e14 q^{81} -2.12330e14 q^{82} -2.78481e14 q^{83} -2.91781e14 q^{84} +4.04303e14 q^{85} -7.71425e14 q^{86} -6.92316e13 q^{87} +2.27808e14 q^{88} -5.70178e14 q^{89} +7.43962e13 q^{90} -6.04004e14 q^{91} +2.34451e14 q^{92} +5.10625e14 q^{93} -5.56673e14 q^{94} -1.33681e14 q^{95} -1.00714e15 q^{96} -3.76385e14 q^{97} -6.38814e14 q^{98} +1.06020e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 9908 q^{3} + 387418 q^{4} + 230490 q^{5} + 1566838 q^{6} + 2882024 q^{7} + 26209092 q^{8} + 93022899 q^{9}+O(q^{10}) $ 19 * q + 9908 * q^3 + 387418 * q^4 + 230490 * q^5 + 1566838 * q^6 + 2882024 * q^7 + 26209092 * q^8 + 93022899 * q^9	\( 19 q + 9908 q^{3} + 387418 q^{4} + 230490 q^{5} + 1566838 q^{6} + 2882024 q^{7} + 26209092 q^{8} + 93022899 q^{9} - 46518144 q^{10} + 56910992 q^{11} + 907194664 q^{12} + 377780326 q^{13} + 1552762656 q^{14} + 2058712006 q^{15} + 9746645474 q^{16} - 797562458 q^{17} - 2812146948 q^{18} + 5568901154 q^{19} - 6814671874 q^{20} - 19358601528 q^{21} - 43431230566 q^{22} - 22787265900 q^{23} - 32333767894 q^{24} + 113218218877 q^{25} - 60020783208 q^{26} + 115546592594 q^{27} + 171573547692 q^{28} - 327747649871 q^{29} - 152869385454 q^{30} + 190165645448 q^{31} + 1523182591996 q^{32} + 1432316120556 q^{33} + 781895976484 q^{34} + 1076956461508 q^{35} + 4124169333892 q^{36} + 1157558623486 q^{37} + 454200349888 q^{38} - 3276695149790 q^{39} + 1497234313960 q^{40} - 327181726714 q^{41} + 14801498493780 q^{42} + 3969726268184 q^{43} + 9884551144664 q^{44} + 13723027476954 q^{45} + 4360233976812 q^{46} + 17801533447516 q^{47} + 44888708498560 q^{48} + 26274460777219 q^{49} + 49590112735028 q^{50} + 48299925405108 q^{51} + 38417786090034 q^{52} + 42945469924134 q^{53} + 78537259690434 q^{54} + 43646306609786 q^{55} + 153497246476960 q^{56} + 87149617056284 q^{57} + 76276585694640 q^{59} + 137931874827396 q^{60} + 75095043245982 q^{61} + 45115853357766 q^{62} + 77728938376620 q^{63} + 263521279152786 q^{64} + 25707147233724 q^{65} - 97128209185404 q^{66} + 39919578800676 q^{67} + 172949157314596 q^{68} + 61328545437264 q^{69} + 524547167494056 q^{70} + 128037096114140 q^{71} + 307467488440744 q^{72} + 333487363889334 q^{73} + 220493893416424 q^{74} - 68218174510546 q^{75} + 354934779140576 q^{76} - 692163369062472 q^{77} - 818320982346402 q^{78} + 213267241183292 q^{79} - 452775952882810 q^{80} + 48823702443271 q^{81} - 17\!\cdots\!96 q^{82}+ \cdots - 233858833882834 q^{99}+O(q^{100}) \) 19 * q + 9908 * q^3 + 387418 * q^4 + 230490 * q^5 + 1566838 * q^6 + 2882024 * q^7 + 26209092 * q^8 + 93022899 * q^9 - 46518144 * q^10 + 56910992 * q^11 + 907194664 * q^12 + 377780326 * q^13 + 1552762656 * q^14 + 2058712006 * q^15 + 9746645474 * q^16 - 797562458 * q^17 - 2812146948 * q^18 + 5568901154 * q^19 - 6814671874 * q^20 - 19358601528 * q^21 - 43431230566 * q^22 - 22787265900 * q^23 - 32333767894 * q^24 + 113218218877 * q^25 - 60020783208 * q^26 + 115546592594 * q^27 + 171573547692 * q^28 - 327747649871 * q^29 - 152869385454 * q^30 + 190165645448 * q^31 + 1523182591996 * q^32 + 1432316120556 * q^33 + 781895976484 * q^34 + 1076956461508 * q^35 + 4124169333892 * q^36 + 1157558623486 * q^37 + 454200349888 * q^38 - 3276695149790 * q^39 + 1497234313960 * q^40 - 327181726714 * q^41 + 14801498493780 * q^42 + 3969726268184 * q^43 + 9884551144664 * q^44 + 13723027476954 * q^45 + 4360233976812 * q^46 + 17801533447516 * q^47 + 44888708498560 * q^48 + 26274460777219 * q^49 + 49590112735028 * q^50 + 48299925405108 * q^51 + 38417786090034 * q^52 + 42945469924134 * q^53 + 78537259690434 * q^54 + 43646306609786 * q^55 + 153497246476960 * q^56 + 87149617056284 * q^57 + 76276585694640 * q^59 + 137931874827396 * q^60 + 75095043245982 * q^61 + 45115853357766 * q^62 + 77728938376620 * q^63 + 263521279152786 * q^64 + 25707147233724 * q^65 - 97128209185404 * q^66 + 39919578800676 * q^67 + 172949157314596 * q^68 + 61328545437264 * q^69 + 524547167494056 * q^70 + 128037096114140 * q^71 + 307467488440744 * q^72 + 333487363889334 * q^73 + 220493893416424 * q^74 - 68218174510546 * q^75 + 354934779140576 * q^76 - 692163369062472 * q^77 - 818320982346402 * q^78 + 213267241183292 * q^79 - 452775952882810 * q^80 + 48823702443271 * q^81 - 1736995581874796 * q^82 - 66633324408168 * q^83 - 2217716778602152 * q^84 - 1419457827450068 * q^85 - 1364891612086326 * q^86 - 170911774469572 * q^87 - 4325342725143834 * q^88 - 2341312102493090 * q^89 - 6182213358743320 * q^90 + 852022408820524 * q^91 - 3781297333622004 * q^92 - 3548745569232820 * q^93 - 914001881049618 * q^94 - 4053850425835916 * q^95 - 775984072309158 * q^96 - 686179834828282 * q^97 - 5170682580897840 * q^98 - 233858833882834 * 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 $

$2$	281.041	1.55255	0.776273	−	0.630397i	$-0.217108\pi$
$2$	281.041	1.55255	0.776273	+	0.630397i	$0.217108\pi$
$3$	4013.45	1.05952	0.529760	−	0.848148i	$-0.322282\pi$
$3$	4013.45	1.05952	0.529760	+	0.848148i	$0.322282\pi$
$4$	46215.9	1.41040
$5$	150501.	0.861515	0.430758	−	0.902468i	$-0.358246\pi$
$5$	150501.	0.861515	0.430758	+	0.902468i	$0.358246\pi$
$6$	1.12794e6	1.64495
$7$	−1.57306e6	−0.721957	−0.360979	−	0.932574i	$-0.617557\pi$
$7$	−1.57306e6	−0.721957	−0.360979	+	0.932574i	$0.617557\pi$
$8$	3.77941e6	0.637161
$9$	1.75891e6	0.122581
$10$	4.22968e7	1.33754
$11$	6.02762e7	0.932611	0.466305	−	0.884624i	$-0.345585\pi$
$11$	6.02762e7	0.932611	0.466305	+	0.884624i	$0.345585\pi$
$12$	1.85485e8	1.49434
$13$	3.83967e8	1.69714	0.848571	−	0.529081i	$-0.177463\pi$
$13$	3.83967e8	1.69714	0.848571	+	0.529081i	$0.177463\pi$
$14$	−4.42095e8	−1.12087
$15$	6.04027e8	0.912792
$16$	−4.52235e8	−0.421176
$17$	2.68639e9	1.58782	0.793912	−	0.608033i	$-0.208041\pi$
$17$	2.68639e9	1.58782	0.793912	+	0.608033i	$0.208041\pi$
$18$	4.94325e8	0.190313
$19$	−8.88241e8	−0.227970	−0.113985	−	0.993482i	$-0.536362\pi$
$19$	−8.88241e8	−0.227970	−0.113985	+	0.993482i	$0.536362\pi$
$20$	6.95552e9	1.21508
$21$	−6.31342e9	−0.764927
$22$	1.69401e10	1.44792
$23$	5.07294e9	0.310671	0.155336	−	0.987862i	$-0.450354\pi$
$23$	5.07294e9	0.310671	0.155336	+	0.987862i	$0.450354\pi$
$24$	1.51685e10	0.675084
$25$	−7.86717e9	−0.257792
$26$	1.07910e11	2.63489
$27$	−5.05294e10	−0.929642
$28$	−7.27006e10	−1.01825
$29$	−1.72499e10	−0.185695
$29$	−1.72499e10	−0.185695
$30$	1.69756e11	1.41715
$31$	1.27228e11	0.830560	0.415280	−	0.909694i	$-0.363684\pi$
$31$	1.27228e11	0.830560	0.415280	+	0.909694i	$0.363684\pi$
$32$	−2.50940e11	−1.29106
$33$	2.41916e11	0.988119
$34$	7.54985e11	2.46517
$35$	−2.36747e11	−0.621977
$36$	8.12895e10	0.172888
$37$	−3.08988e11	−0.535092	−0.267546	−	0.963545i	$-0.586213\pi$
$37$	−3.08988e11	−0.535092	−0.267546	+	0.963545i	$0.586213\pi$
$38$	−2.49632e11	−0.353935
$39$	1.54103e12	1.79816
$40$	5.68803e11	0.548924
$41$	−7.55514e11	−0.605848	−0.302924	−	0.953015i	$-0.597963\pi$
$41$	−7.55514e11	−0.605848	−0.302924	+	0.953015i	$0.597963\pi$
$42$	−1.77433e12	−1.18758
$43$	−2.74489e12	−1.53996	−0.769982	−	0.638065i	$-0.779735\pi$
$43$	−2.74489e12	−1.53996	−0.769982	+	0.638065i	$0.779735\pi$
$44$	2.78572e12	1.31535
$45$	2.64717e11	0.105606
$46$	1.42570e12	0.482331
$47$	−1.98075e12	−0.570291	−0.285146	−	0.958484i	$-0.592042\pi$
$47$	−1.98075e12	−0.570291	−0.285146	+	0.958484i	$0.592042\pi$
$48$	−1.81502e12	−0.446245
$49$	−2.27303e12	−0.478778
$50$	−2.21100e12	−0.400233
$51$	1.07817e13	1.68233
$52$	1.77454e13	2.39365
$53$	9.23657e12	1.08005	0.540023	−	0.841651i	$-0.318416\pi$
$53$	9.23657e12	1.08005	0.540023	+	0.841651i	$0.318416\pi$
$54$	−1.42008e13	−1.44331
$55$	9.07159e12	0.803459
$56$	−5.94526e12	−0.460003
$57$	−3.56491e12	−0.241539
$58$	−4.84792e12	−0.288300
$59$	−3.45501e11	−0.0180742	−0.00903710	−	0.999959i	$-0.502877\pi$
$59$	−3.45501e11	−0.0180742	−0.00903710	+	0.999959i	$0.502877\pi$
$60$	2.79157e13	1.28740
$61$	−1.67739e13	−0.683378	−0.341689	−	0.939813i	$-0.610999\pi$
$61$	−1.67739e13	−0.683378	−0.341689	+	0.939813i	$0.610999\pi$
$62$	3.57564e13	1.28948
$63$	−2.76688e12	−0.0884985
$64$	−5.57056e13	−1.58325
$65$	5.77872e13	1.46211
$66$	6.79882e13	1.53410
$67$	8.34631e13	1.68242	0.841208	−	0.540711i	$-0.181845\pi$
$67$	8.34631e13	1.68242	0.841208	+	0.540711i	$0.181845\pi$
$68$	1.24154e14	2.23946
$69$	2.03600e13	0.329162
$70$	−6.65356e13	−0.965648
$71$	6.63643e13	0.865958	0.432979	−	0.901404i	$-0.357462\pi$
$71$	6.63643e13	0.865958	0.432979	+	0.901404i	$0.357462\pi$
$72$	6.64763e12	0.0781040
$73$	−9.40965e13	−0.996900	−0.498450	−	0.866918i	$-0.666097\pi$
$73$	−9.40965e13	−0.996900	−0.498450	+	0.866918i	$0.666097\pi$
$74$	−8.68382e13	−0.830755
$75$	−3.15745e13	−0.273135
$76$	−4.10508e13	−0.321529
$77$	−9.48183e13	−0.673305
$78$	4.33093e14	2.79172
$79$	−1.50015e14	−0.878885	−0.439442	−	0.898271i	$-0.644824\pi$
$79$	−1.50015e14	−0.878885	−0.439442	+	0.898271i	$0.644824\pi$
$80$	−6.80616e13	−0.362850
$81$	−2.28036e14	−1.10756
$82$	−2.12330e14	−0.940606
$83$	−2.78481e14	−1.12645	−0.563223	−	0.826305i	$-0.690439\pi$
$83$	−2.78481e14	−1.12645	−0.563223	+	0.826305i	$0.690439\pi$
$84$	−2.91781e14	−1.07885
$85$	4.04303e14	1.36793
$86$	−7.71425e14	−2.39087
$87$	−6.92316e13	−0.196748
$88$	2.27808e14	0.594223
$89$	−5.70178e14	−1.36642	−0.683212	−	0.730220i	$-0.739418\pi$
$89$	−5.70178e14	−1.36642	−0.683212	+	0.730220i	$0.739418\pi$
$90$	7.43962e13	0.163958
$91$	−6.04004e14	−1.22526
$92$	2.34451e14	0.438170
$93$	5.10625e14	0.879995
$94$	−5.56673e14	−0.885403
$95$	−1.33681e14	−0.196400
$96$	−1.00714e15	−1.36790
$97$	−3.76385e14	−0.472982	−0.236491	−	0.971634i	$-0.575997\pi$
$97$	−3.76385e14	−0.472982	−0.236491	+	0.971634i	$0.575997\pi$
$98$	−6.38814e14	−0.743325
$99$	1.06020e14	0.114321
$100$	−3.63589e14	−0.363589
$101$	1.17224e15	1.08794	0.543970	−	0.839105i	$-0.316920\pi$
$101$	1.17224e15	1.08794	0.543970	+	0.839105i	$0.316920\pi$
$102$	3.03010e15	2.61189
$103$	5.35026e14	0.428643	0.214322	−	0.976763i	$-0.431246\pi$
$103$	5.35026e14	0.428643	0.214322	+	0.976763i	$0.431246\pi$
$104$	1.45117e15	1.08135
$105$	−9.50174e14	−0.658997
$106$	2.59585e15	1.67682
$107$	2.96259e15	1.78358	0.891790	−	0.452449i	$-0.149449\pi$
$107$	2.96259e15	1.78358	0.891790	+	0.452449i	$0.149449\pi$
$108$	−2.33526e15	−1.31116
$109$	−5.44448e14	−0.285271	−0.142635	−	0.989775i	$-0.545558\pi$
$109$	−5.44448e14	−0.285271	−0.142635	+	0.989775i	$0.545558\pi$
$110$	2.54949e15	1.24741
$111$	−1.24011e15	−0.566941
$112$	7.11395e14	0.304071
$113$	−3.40475e15	−1.36143	−0.680717	−	0.732546i	$-0.738332\pi$
$113$	−3.40475e15	−1.36143	−0.680717	+	0.732546i	$0.738332\pi$
$114$	−1.00189e15	−0.375001
$115$	7.63480e14	0.267648
$116$	−7.97219e14	−0.261904
$117$	6.75362e14	0.208038
$118$	−9.70998e13	−0.0280610
$119$	−4.22587e15	−1.14634
$120$	2.28286e15	0.581595
$121$	−5.44031e14	−0.130237
$122$	−4.71416e15	−1.06098
$123$	−3.03222e15	−0.641907
$124$	5.87997e15	1.17142
$125$	−5.77692e15	−1.08361
$126$	−7.77605e14	−0.137398
$127$	−5.07419e15	−0.844965	−0.422482	−	0.906371i	$-0.638841\pi$
$127$	−5.07419e15	−0.844965	−0.422482	+	0.906371i	$0.638841\pi$
$128$	−7.43273e15	−1.16701
$129$	−1.10165e16	−1.63162
$130$	1.62405e16	2.27000
$131$	9.69773e15	1.27978	0.639890	−	0.768466i	$-0.278980\pi$
$131$	9.69773e15	1.27978	0.639890	+	0.768466i	$0.278980\pi$
$132$	1.11804e16	1.39364
$133$	1.39726e15	0.164585
$134$	2.34565e16	2.61203
$135$	−7.60470e15	−0.800901
$136$	1.01530e16	1.01170
$137$	6.50537e14	0.0613575	0.0306787	−	0.999529i	$-0.490233\pi$
$137$	6.50537e14	0.0613575	0.0306787	+	0.999529i	$0.490233\pi$
$138$	5.72199e15	0.511039
$139$	8.71552e15	0.737365	0.368682	−	0.929555i	$-0.379809\pi$
$139$	8.71552e15	0.737365	0.368682	+	0.929555i	$0.379809\pi$
$140$	−1.09415e16	−0.877235
$141$	−7.94966e15	−0.604234
$142$	1.86511e16	1.34444
$143$	2.31440e16	1.58277
$144$	−7.95440e14	−0.0516284
$145$	−2.59612e15	−0.159979
$146$	−2.64449e16	−1.54773
$147$	−9.12269e15	−0.507275
$148$	−1.42802e16	−0.754693
$149$	−7.43967e15	−0.373815	−0.186908	−	0.982378i	$-0.559846\pi$
$149$	−7.43967e15	−0.373815	−0.186908	+	0.982378i	$0.559846\pi$
$150$	−8.87373e15	−0.424055
$151$	−1.24996e16	−0.568286	−0.284143	−	0.958782i	$-0.591709\pi$
$151$	−1.24996e16	−0.568286	−0.284143	+	0.958782i	$0.591709\pi$
$152$	−3.35702e15	−0.145254
$153$	4.72512e15	0.194638
$154$	−2.66478e16	−1.04534
$155$	1.91479e16	0.715540
$156$	7.12202e16	2.53611
$157$	1.45576e16	0.494130	0.247065	−	0.968999i	$-0.420534\pi$
$157$	1.45576e16	0.494130	0.247065	+	0.968999i	$0.420534\pi$
$158$	−4.21604e16	−1.36451
$159$	3.70706e16	1.14433
$160$	−3.77666e16	−1.11226
$161$	−7.98007e15	−0.224291
$162$	−6.40873e16	−1.71953
$163$	1.06014e16	0.271617	0.135809	−	0.990735i	$-0.456637\pi$
$163$	1.06014e16	0.271617	0.135809	+	0.990735i	$0.456637\pi$
$164$	−3.49167e16	−0.854486
$165$	3.64084e16	0.851280
$166$	−7.82646e16	−1.74886
$167$	4.55258e16	0.972487	0.486244	−	0.873823i	$-0.338367\pi$
$167$	4.55258e16	0.972487	0.486244	+	0.873823i	$0.338367\pi$
$168$	−2.38610e16	−0.487382
$169$	9.62444e16	1.88029
$170$	1.13626e17	2.12378
$171$	−1.56233e15	−0.0279449
$172$	−1.26857e17	−2.17196
$173$	1.63846e16	0.268590	0.134295	−	0.990941i	$-0.457123\pi$
$173$	1.63846e16	0.268590	0.134295	+	0.990941i	$0.457123\pi$
$174$	−1.94569e16	−0.305460
$175$	1.23756e16	0.186114
$176$	−2.72590e16	−0.392794
$177$	−1.38665e15	−0.0191500
$178$	−1.60243e17	−2.12144
$179$	−3.78830e16	−0.480891	−0.240445	−	0.970663i	$-0.577294\pi$
$179$	−3.78830e16	−0.480891	−0.240445	+	0.970663i	$0.577294\pi$
$180$	1.22341e16	0.148946
$181$	−1.14533e17	−1.33765	−0.668824	−	0.743421i	$-0.733202\pi$
$181$	−1.14533e17	−1.33765	−0.668824	+	0.743421i	$0.733202\pi$
$182$	−1.69750e17	−1.90228
$183$	−6.73214e16	−0.724053
$184$	1.91727e16	0.197948
$185$	−4.65029e16	−0.460990
$186$	1.43506e17	1.36623
$187$	1.61925e17	1.48082
$188$	−9.15423e16	−0.804337
$189$	7.94860e16	0.671162
$190$	−3.75697e16	−0.304920
$191$	2.07295e17	1.61748	0.808739	−	0.588167i	$-0.200150\pi$
$191$	2.07295e17	1.61748	0.808739	+	0.588167i	$0.200150\pi$
$192$	−2.23572e17	−1.67748
$193$	−9.44965e16	−0.681924	−0.340962	−	0.940077i	$-0.610753\pi$
$193$	−9.44965e16	−0.681924	−0.340962	+	0.940077i	$0.610753\pi$
$194$	−1.05780e17	−0.734326
$195$	2.31926e17	1.54914
$196$	−1.05050e17	−0.675267
$197$	2.22969e17	1.37958	0.689792	−	0.724007i	$-0.257702\pi$
$197$	2.22969e17	1.37958	0.689792	+	0.724007i	$0.257702\pi$
$198$	2.97960e16	0.177488
$199$	−7.17407e16	−0.411498	−0.205749	−	0.978605i	$-0.565963\pi$
$199$	−7.17407e16	−0.411498	−0.205749	+	0.978605i	$0.565963\pi$
$200$	−2.97333e16	−0.164255
$201$	3.34975e17	1.78255
$202$	3.29446e17	1.68908
$203$	2.71352e16	0.134064
$204$	4.98286e17	2.37275
$205$	−1.13705e17	−0.521947
$206$	1.50364e17	0.665488
$207$	8.92284e15	0.0380825
$208$	−1.73643e17	−0.714796
$209$	−5.35397e16	−0.212608
$210$	−2.67038e17	−1.02312
$211$	−1.96439e17	−0.726289	−0.363144	−	0.931733i	$-0.618297\pi$
$211$	−1.96439e17	−0.726289	−0.363144	+	0.931733i	$0.618297\pi$
$212$	4.26877e17	1.52329
$213$	2.66350e17	0.917500
$214$	8.32608e17	2.76909
$215$	−4.13107e17	−1.32670
$216$	−1.90971e17	−0.592331
$217$	−2.00138e17	−0.599629
$218$	−1.53012e17	−0.442896
$219$	−3.77652e17	−1.05624
$220$	4.19252e17	1.13320
$221$	1.03148e18	2.69476
$222$	−3.48521e17	−0.880201
$223$	−4.50442e17	−1.09990	−0.549949	−	0.835198i	$-0.685353\pi$
$223$	−4.50442e17	−1.09990	−0.549949	+	0.835198i	$0.685353\pi$
$224$	3.94745e17	0.932087
$225$	−1.38376e16	−0.0316004
$226$	−9.56873e17	−2.11369
$227$	4.29447e17	0.917732	0.458866	−	0.888506i	$-0.348256\pi$
$227$	4.29447e17	0.917732	0.458866	+	0.888506i	$0.348256\pi$
$228$	−1.64756e17	−0.340666
$229$	−1.02203e17	−0.204502	−0.102251	−	0.994759i	$-0.532604\pi$
$229$	−1.02203e17	−0.204502	−0.102251	+	0.994759i	$0.532604\pi$
$230$	2.14569e17	0.415536
$231$	−3.80549e17	−0.713380
$232$	−6.51943e16	−0.118318
$233$	1.05022e18	1.84548	0.922739	−	0.385425i	$-0.125945\pi$
$233$	1.05022e18	1.84548	0.922739	+	0.385425i	$0.125945\pi$
$234$	1.89804e17	0.322988
$235$	−2.98104e17	−0.491314
$236$	−1.59676e16	−0.0254918
$237$	−6.02079e17	−0.931196
$238$	−1.18764e18	−1.77975
$239$	1.14014e18	1.65567	0.827837	−	0.560968i	$-0.189571\pi$
$239$	1.14014e18	1.65567	0.827837	+	0.560968i	$0.189571\pi$
$240$	−2.73162e17	−0.384447
$241$	−6.98269e17	−0.952565	−0.476283	−	0.879292i	$-0.658016\pi$
$241$	−6.98269e17	−0.952565	−0.476283	+	0.879292i	$0.658016\pi$
$242$	−1.52895e17	−0.202199
$243$	−1.90170e17	−0.243834
$244$	−7.75223e17	−0.963835
$245$	−3.42092e17	−0.412475
$246$	−8.52177e17	−0.996590
$247$	−3.41055e17	−0.386898
$248$	4.80848e17	0.529200
$249$	−1.11767e18	−1.19349
$250$	−1.62355e18	−1.68235
$251$	6.97551e17	0.701492	0.350746	−	0.936471i	$-0.385928\pi$
$251$	6.97551e17	0.701492	0.350746	+	0.936471i	$0.385928\pi$
$252$	−1.27874e17	−0.124818
$253$	3.05777e17	0.289735
$254$	−1.42605e18	−1.31185
$255$	1.62265e18	1.44935
$256$	−2.63540e17	−0.228584
$257$	1.65391e18	1.39320	0.696601	−	0.717459i	$-0.254695\pi$
$257$	1.65391e18	1.39320	0.696601	+	0.717459i	$0.254695\pi$
$258$	−3.09608e18	−2.53317
$259$	4.86058e17	0.386314
$260$	2.67069e18	2.06216
$261$	−3.03410e16	−0.0227628
$262$	2.72546e18	1.98692
$263$	−1.16333e18	−0.824203	−0.412101	−	0.911138i	$-0.635205\pi$
$263$	−1.16333e18	−0.824203	−0.412101	+	0.911138i	$0.635205\pi$
$264$	9.14298e17	0.629591
$265$	1.39011e18	0.930475
$266$	3.92687e17	0.255526
$267$	−2.28838e18	−1.44775
$268$	3.85732e18	2.37288
$269$	−2.45964e18	−1.47139	−0.735697	−	0.677311i	$-0.763145\pi$
$269$	−2.45964e18	−1.47139	−0.735697	+	0.677311i	$0.763145\pi$
$270$	−2.13723e18	−1.24343
$271$	3.27801e17	0.185499	0.0927494	−	0.995689i	$-0.470434\pi$
$271$	3.27801e17	0.185499	0.0927494	+	0.995689i	$0.470434\pi$
$272$	−1.21488e18	−0.668754
$273$	−2.42414e18	−1.29819
$274$	1.82827e17	0.0952603
$275$	−4.74203e17	−0.240419
$276$	9.40957e17	0.464250
$277$	1.74271e18	0.836808	0.418404	−	0.908261i	$-0.362590\pi$
$277$	1.74271e18	0.836808	0.418404	+	0.908261i	$0.362590\pi$
$278$	2.44942e18	1.14479
$279$	2.23783e17	0.101811
$280$	−8.94764e17	−0.396299
$281$	3.75876e18	1.62087	0.810434	−	0.585830i	$-0.199231\pi$
$281$	3.75876e18	1.62087	0.810434	+	0.585830i	$0.199231\pi$
$282$	−2.23418e18	−0.938101
$283$	−3.36324e18	−1.37518	−0.687590	−	0.726100i	$-0.741331\pi$
$283$	−3.36324e18	−1.37518	−0.687590	+	0.726100i	$0.741331\pi$
$284$	3.06709e18	1.22135
$285$	−5.36521e17	−0.208090
$286$	6.50442e18	2.45733
$287$	1.18847e18	0.437396
$288$	−4.41381e17	−0.158259
$289$	4.35428e18	1.52119
$290$	−7.29614e17	−0.248375
$291$	−1.51060e18	−0.501133
$292$	−4.34875e18	−1.40603
$293$	−1.44052e18	−0.453955	−0.226978	−	0.973900i	$-0.572884\pi$
$293$	−1.44052e18	−0.453955	−0.226978	+	0.973900i	$0.572884\pi$
$294$	−2.56385e18	−0.787567
$295$	−5.19981e16	−0.0155712
$296$	−1.16779e18	−0.340940
$297$	−3.04572e18	−0.866994
$298$	−2.09085e18	−0.580365
$299$	1.94784e18	0.527253
$300$	−1.45925e18	−0.385229
$301$	4.31788e18	1.11179
$302$	−3.51288e18	−0.882291
$303$	4.70472e18	1.15269
$304$	4.01693e17	0.0960158
$305$	−2.52449e18	−0.588741
$306$	1.32795e18	0.302184
$307$	−6.37862e18	−1.41641	−0.708205	−	0.706007i	$-0.750495\pi$
$307$	−6.37862e18	−1.41641	−0.708205	+	0.706007i	$0.750495\pi$
$308$	−4.38212e18	−0.949628
$309$	2.14730e18	0.454156
$310$	5.38135e18	1.11091
$311$	−5.79461e18	−1.16767	−0.583837	−	0.811871i	$-0.698449\pi$
$311$	−5.79461e18	−1.16767	−0.583837	+	0.811871i	$0.698449\pi$
$312$	5.82419e18	1.14571
$313$	4.17255e18	0.801344	0.400672	−	0.916222i	$-0.368777\pi$
$313$	4.17255e18	0.801344	0.400672	+	0.916222i	$0.368777\pi$
$314$	4.09127e18	0.767159
$315$	−4.16416e17	−0.0762428
$316$	−6.93309e18	−1.23958
$317$	5.95869e18	1.04041	0.520207	−	0.854040i	$-0.325855\pi$
$317$	5.95869e18	1.04041	0.520207	+	0.854040i	$0.325855\pi$
$318$	1.04183e19	1.77662
$319$	−1.03976e18	−0.173182
$320$	−8.38372e18	−1.36399
$321$	1.18902e19	1.88974
$322$	−2.24272e18	−0.348222
$323$	−2.38616e18	−0.361977
$324$	−1.05389e19	−1.56209
$325$	−3.02073e18	−0.437509
$326$	2.97943e18	0.421698
$327$	−2.18512e18	−0.302250
$328$	−2.85540e18	−0.386022
$329$	3.11585e18	0.411726
$330$	1.02323e19	1.32165
$331$	−1.18960e19	−1.50207	−0.751036	−	0.660261i	$-0.770446\pi$
$331$	−1.18960e19	−1.50207	−0.751036	+	0.660261i	$0.770446\pi$
$332$	−1.28703e19	−1.58874
$333$	−5.43482e17	−0.0655924
$334$	1.27946e19	1.50983
$335$	1.25612e19	1.44943
$336$	2.85515e18	0.322169
$337$	−1.30285e18	−0.143770	−0.0718851	−	0.997413i	$-0.522901\pi$
$337$	−1.30285e18	−0.143770	−0.0718851	+	0.997413i	$0.522901\pi$
$338$	2.70486e19	2.91924
$339$	−1.36648e19	−1.44247
$340$	1.86852e19	1.92933
$341$	7.66884e18	0.774590
$342$	−4.39079e17	−0.0433858
$343$	1.10438e19	1.06761
$344$	−1.03740e19	−0.981205
$345$	3.06419e18	0.283578
$346$	4.60474e18	0.416999
$347$	−4.65114e18	−0.412181	−0.206091	−	0.978533i	$-0.566074\pi$
$347$	−4.65114e18	−0.412181	−0.206091	+	0.978533i	$0.566074\pi$
$348$	−3.19960e18	−0.277493
$349$	1.35863e19	1.15321	0.576606	−	0.817022i	$-0.304377\pi$
$349$	1.35863e19	1.15321	0.576606	+	0.817022i	$0.304377\pi$
$350$	3.47804e18	0.288951
$351$	−1.94016e19	−1.57773
$352$	−1.51257e19	−1.20405
$353$	1.29921e18	0.101244	0.0506220	−	0.998718i	$-0.483880\pi$
$353$	1.29921e18	0.101244	0.0506220	+	0.998718i	$0.483880\pi$
$354$	−3.89706e17	−0.0297312
$355$	9.98786e18	0.746036
$356$	−2.63513e19	−1.92720
$357$	−1.69603e19	−1.21457
$358$	−1.06467e19	−0.746605
$359$	3.17591e18	0.218102	0.109051	−	0.994036i	$-0.465219\pi$
$359$	3.17591e18	0.218102	0.109051	+	0.994036i	$0.465219\pi$
$360$	1.00047e18	0.0672878
$361$	−1.43922e19	−0.948029
$362$	−3.21885e19	−2.07676
$363$	−2.18344e18	−0.137988
$364$	−2.79146e19	−1.72811
$365$	−1.41616e19	−0.858845
$366$	−1.89201e19	−1.12412
$367$	4.18609e18	0.243676	0.121838	−	0.992550i	$-0.461121\pi$
$367$	4.18609e18	0.243676	0.121838	+	0.992550i	$0.461121\pi$
$368$	−2.29416e18	−0.130847
$369$	−1.32888e18	−0.0742656
$370$	−1.30692e19	−0.715708
$371$	−1.45297e19	−0.779746
$372$	2.35990e19	1.24114
$373$	−1.82704e19	−0.941741	−0.470871	−	0.882202i	$-0.656060\pi$
$373$	−1.82704e19	−0.941741	−0.470871	+	0.882202i	$0.656060\pi$
$374$	4.55076e19	2.29904
$375$	−2.31854e19	−1.14810
$376$	−7.48608e18	−0.363367
$377$	−6.62338e18	−0.315151
$378$	2.23388e19	1.04201
$379$	2.40287e19	1.09884	0.549422	−	0.835545i	$-0.314848\pi$
$379$	2.40287e19	1.09884	0.549422	+	0.835545i	$0.314848\pi$
$380$	−6.17817e18	−0.277002
$381$	−2.03650e19	−0.895257
$382$	5.82583e19	2.51121
$383$	3.48133e19	1.47148	0.735740	−	0.677264i	$-0.236835\pi$
$383$	3.48133e19	1.47148	0.735740	+	0.677264i	$0.236835\pi$
$384$	−2.98309e19	−1.23647
$385$	−1.42702e19	−0.580063
$386$	−2.65574e19	−1.05872
$387$	−4.82800e18	−0.188771
$388$	−1.73950e19	−0.667092
$389$	−3.58020e19	−1.34675	−0.673373	−	0.739303i	$-0.735155\pi$
$389$	−3.58020e19	−1.34675	−0.673373	+	0.739303i	$0.735155\pi$
$390$	6.51807e19	2.40511
$391$	1.36279e19	0.493291
$392$	−8.59070e18	−0.305059
$393$	3.89214e19	1.35595
$394$	6.26635e19	2.14187
$395$	−2.25774e19	−0.757173
$396$	4.89982e18	0.161238
$397$	−5.34144e19	−1.72476	−0.862382	−	0.506258i	$-0.831028\pi$
$397$	−5.34144e19	−1.72476	−0.862382	+	0.506258i	$0.831028\pi$
$398$	−2.01621e19	−0.638869
$399$	5.60784e18	0.174381
$400$	3.55781e18	0.108576
$401$	2.32577e19	0.696601	0.348301	−	0.937383i	$-0.386759\pi$
$401$	2.32577e19	0.696601	0.348301	+	0.937383i	$0.386759\pi$
$402$	9.41417e19	2.76749
$403$	4.88514e19	1.40958
$404$	5.41760e19	1.53443
$405$	−3.43195e19	−0.954176
$406$	7.62609e18	0.208141
$407$	−1.86246e19	−0.499033
$408$	4.07485e19	1.07191
$409$	4.57579e19	1.18179	0.590896	−	0.806748i	$-0.298774\pi$
$409$	4.57579e19	1.18179	0.590896	+	0.806748i	$0.298774\pi$
$410$	−3.19558e19	−0.810346
$411$	2.61090e18	0.0650094
$412$	2.47267e19	0.604557
$413$	5.43495e17	0.0130488
$414$	2.50768e18	0.0591248
$415$	−4.19116e19	−0.970451
$416$	−9.63526e19	−2.19111
$417$	3.49793e19	0.781252
$418$	−1.50468e19	−0.330083
$419$	4.07064e19	0.877118	0.438559	−	0.898702i	$-0.355489\pi$
$419$	4.07064e19	0.877118	0.438559	+	0.898702i	$0.355489\pi$
$420$	−4.39131e19	−0.929447
$421$	1.35203e19	0.281106	0.140553	−	0.990073i	$-0.455112\pi$
$421$	1.35203e19	0.281106	0.140553	+	0.990073i	$0.455112\pi$
$422$	−5.52074e19	−1.12760
$423$	−3.48396e18	−0.0699070
$424$	3.49088e19	0.688162
$425$	−2.11343e19	−0.409328
$426$	7.48553e19	1.42446
$427$	2.63865e19	0.493370
$428$	1.36919e20	2.51556
$429$	9.28875e19	1.67698
$430$	−1.16100e20	−2.05977
$431$	−1.07360e20	−1.87182	−0.935909	−	0.352242i	$-0.885419\pi$
$431$	−1.07360e20	−1.87182	−0.935909	+	0.352242i	$0.885419\pi$
$432$	2.28511e19	0.391543
$433$	3.59048e19	0.604635	0.302317	−	0.953207i	$-0.402240\pi$
$433$	3.59048e19	0.604635	0.302317	+	0.953207i	$0.402240\pi$
$434$	−5.62471e19	−0.930951
$435$	−1.04194e19	−0.169501
$436$	−2.51621e19	−0.402345
$437$	−4.50599e18	−0.0708239
$438$	−1.06136e20	−1.63985
$439$	−5.28280e19	−0.802381	−0.401190	−	0.915995i	$-0.631403\pi$
$439$	−5.28280e19	−0.802381	−0.401190	+	0.915995i	$0.631403\pi$
$440$	3.42853e19	0.511932
$441$	−3.99805e18	−0.0586893
$442$	2.89889e20	4.18374
$443$	1.30454e20	1.85110	0.925548	−	0.378631i	$-0.123605\pi$
$443$	1.30454e20	1.85110	0.925548	+	0.378631i	$0.123605\pi$
$444$	−5.73128e19	−0.799612
$445$	−8.58121e19	−1.17720
$446$	−1.26593e20	−1.70764
$447$	−2.98588e19	−0.396064
$448$	8.76285e19	1.14304
$449$	−1.50360e20	−1.92878	−0.964392	−	0.264477i	$-0.914801\pi$
$449$	−1.50360e20	−1.92878	−0.964392	+	0.264477i	$0.914801\pi$
$450$	−3.88894e18	−0.0490611
$451$	−4.55395e19	−0.565020
$452$	−1.57354e20	−1.92016
$453$	−5.01664e19	−0.602111
$454$	1.20692e20	1.42482
$455$	−9.09030e19	−1.05558
$456$	−1.34733e19	−0.153899
$457$	−3.81582e19	−0.428762	−0.214381	−	0.976750i	$-0.568773\pi$
$457$	−3.81582e19	−0.428762	−0.214381	+	0.976750i	$0.568773\pi$
$458$	−2.87232e19	−0.317498
$459$	−1.35742e20	−1.47611
$460$	3.52849e19	0.377490
$461$	1.65713e20	1.74421	0.872107	−	0.489316i	$-0.162753\pi$
$461$	1.65713e20	1.74421	0.872107	+	0.489316i	$0.162753\pi$
$462$	−1.06950e20	−1.10755
$463$	1.18646e20	1.20892	0.604459	−	0.796636i	$-0.293389\pi$
$463$	1.18646e20	1.20892	0.604459	+	0.796636i	$0.293389\pi$
$464$	7.80099e18	0.0782105
$465$	7.68494e19	0.758129
$466$	2.95153e20	2.86519
$467$	1.27477e19	0.121774	0.0608871	−	0.998145i	$-0.480607\pi$
$467$	1.27477e19	0.121774	0.0608871	+	0.998145i	$0.480607\pi$
$468$	3.12125e19	0.293416
$469$	−1.31293e20	−1.21463
$470$	−8.37795e19	−0.762788
$471$	5.84261e19	0.523540
$472$	−1.30579e18	−0.0115162
$473$	−1.65451e20	−1.43619
$474$	−1.69209e20	−1.44572
$475$	6.98794e18	0.0587689
$476$	−1.95302e20	−1.61680
$477$	1.62463e19	0.132393
$478$	3.20427e20	2.57051
$479$	2.99111e19	0.236220	0.118110	−	0.993001i	$-0.462317\pi$
$479$	2.99111e19	0.236220	0.118110	+	0.993001i	$0.462317\pi$
$480$	−1.51575e20	−1.17847
$481$	−1.18641e20	−0.908128
$482$	−1.96242e20	−1.47890
$483$	−3.20276e19	−0.237641
$484$	−2.51429e19	−0.183686
$485$	−5.66461e19	−0.407481
$486$	−5.34455e19	−0.378564
$487$	2.65762e20	1.85364	0.926820	−	0.375506i	$-0.122531\pi$
$487$	2.65762e20	1.85364	0.926820	+	0.375506i	$0.122531\pi$
$488$	−6.33956e19	−0.435422
$489$	4.25484e19	0.287784
$490$	−9.61418e19	−0.640385
$491$	2.43981e20	1.60046	0.800229	−	0.599694i	$-0.204711\pi$
$491$	2.43981e20	1.60046	0.800229	+	0.599694i	$0.204711\pi$
$492$	−1.40137e20	−0.905344
$493$	−4.63399e19	−0.294852
$494$	−9.58503e19	−0.600677
$495$	1.59561e19	0.0984890
$496$	−5.75371e19	−0.349812
$497$	−1.04395e20	−0.625185
$498$	−3.14112e20	−1.85295
$499$	2.55123e20	1.48250	0.741250	−	0.671229i	$-0.234233\pi$
$499$	2.55123e20	1.48250	0.741250	+	0.671229i	$0.234233\pi$
$500$	−2.66986e20	−1.52832
$501$	1.82716e20	1.03037
$502$	1.96040e20	1.08910
$503$	−4.11104e18	−0.0225005	−0.0112502	−	0.999937i	$-0.503581\pi$
$503$	−4.11104e18	−0.0225005	−0.0112502	+	0.999937i	$0.503581\pi$
$504$	−1.04572e19	−0.0563877
$505$	1.76422e20	0.937277
$506$	8.59359e19	0.449827
$507$	3.86273e20	1.99221
$508$	−2.34508e20	−1.19174
$509$	−4.58111e18	−0.0229397	−0.0114698	−	0.999934i	$-0.503651\pi$
$509$	−4.58111e18	−0.0229397	−0.0114698	+	0.999934i	$0.503651\pi$
$510$	4.56032e20	2.25019
$511$	1.48020e20	0.719719
$512$	1.69490e20	0.812120
$513$	4.48822e19	0.211931
$514$	4.64817e20	2.16301
$515$	8.05217e19	0.369282
$516$	−5.09136e20	−2.30124
$517$	−1.19392e20	−0.531860
$518$	1.36602e20	0.599770
$519$	6.57589e19	0.284577
$520$	2.18401e20	0.931602
$521$	2.69535e20	1.13327	0.566633	−	0.823970i	$-0.308246\pi$
$521$	2.69535e20	1.13327	0.566633	+	0.823970i	$0.308246\pi$
$522$	−8.52704e18	−0.0353403
$523$	−3.06920e20	−1.25390	−0.626950	−	0.779060i	$-0.715697\pi$
$523$	−3.06920e20	−1.25390	−0.626950	+	0.779060i	$0.715697\pi$
$524$	4.48189e20	1.80500
$525$	4.96688e19	0.197192
$526$	−3.26943e20	−1.27961
$527$	3.41785e20	1.31878
$528$	−1.09403e20	−0.416173
$529$	−2.40901e20	−0.903483
$530$	3.90677e20	1.44461
$531$	−6.07704e17	−0.00221556
$532$	6.45756e19	0.232130
$533$	−2.90092e20	−1.02821
$534$	−6.43129e20	−2.24770
$535$	4.45871e20	1.53658
$536$	3.15441e20	1.07197
$537$	−1.52042e20	−0.509513
$538$	−6.91258e20	−2.28441
$539$	−1.37009e20	−0.446514
$540$	−3.51458e20	−1.12959
$541$	3.78745e20	1.20051	0.600257	−	0.799807i	$-0.295065\pi$
$541$	3.78745e20	1.20051	0.600257	+	0.799807i	$0.295065\pi$
$542$	9.21255e19	0.287995
$543$	−4.59674e20	−1.41726
$544$	−6.74123e20	−2.04997
$545$	−8.19396e19	−0.245765
$546$	−6.81283e20	−2.01550
$547$	4.17975e20	1.21968	0.609839	−	0.792525i	$-0.291234\pi$
$547$	4.17975e20	1.21968	0.609839	+	0.792525i	$0.291234\pi$
$548$	3.00651e19	0.0865384
$549$	−2.95038e19	−0.0837695
$550$	−1.33270e20	−0.373262
$551$	1.53220e19	0.0423331
$552$	7.69488e19	0.209729
$553$	2.35984e20	0.634517
$554$	4.89771e20	1.29918
$555$	−1.86637e20	−0.488428
$556$	4.02796e20	1.03998
$557$	−2.62772e20	−0.669368	−0.334684	−	0.942330i	$-0.608630\pi$
$557$	−2.62772e20	−0.669368	−0.334684	+	0.942330i	$0.608630\pi$
$558$	6.28922e19	0.158067
$559$	−1.05394e21	−2.61354
$560$	1.07065e20	0.261962
$561$	6.49880e20	1.56896
$562$	1.05637e21	2.51647
$563$	2.18082e20	0.512634	0.256317	−	0.966593i	$-0.417491\pi$
$563$	2.18082e20	0.512634	0.256317	+	0.966593i	$0.417491\pi$
$564$	−3.67401e20	−0.852211
$565$	−5.12417e20	−1.17290
$566$	−9.45207e20	−2.13503
$567$	3.58715e20	0.799607
$568$	2.50818e20	0.551755
$569$	3.85389e20	0.836675	0.418338	−	0.908292i	$-0.362613\pi$
$569$	3.85389e20	0.836675	0.418338	+	0.908292i	$0.362613\pi$
$570$	−1.50784e20	−0.323069
$571$	−5.17641e19	−0.109461	−0.0547303	−	0.998501i	$-0.517430\pi$
$571$	−5.17641e19	−0.109461	−0.0547303	+	0.998501i	$0.517430\pi$
$572$	1.06962e21	2.23234
$573$	8.31969e20	1.71375
$574$	3.34009e20	0.679077
$575$	−3.99097e19	−0.0800884
$576$	−9.79810e19	−0.194077
$577$	1.16997e20	0.228747	0.114374	−	0.993438i	$-0.463514\pi$
$577$	1.16997e20	0.228747	0.114374	+	0.993438i	$0.463514\pi$
$578$	1.22373e21	2.36171
$579$	−3.79257e20	−0.722511
$580$	−1.19982e20	−0.225634
$581$	4.38069e20	0.813246
$582$	−4.24541e20	−0.778032
$583$	5.56745e20	1.00726
$584$	−3.55629e20	−0.635186
$585$	1.01642e20	0.179228
$586$	−4.04846e20	−0.704786
$587$	−9.11338e20	−1.56637	−0.783184	−	0.621790i	$-0.786406\pi$
$587$	−9.11338e20	−1.56637	−0.783184	+	0.621790i	$0.786406\pi$
$588$	−4.21614e20	−0.715459
$589$	−1.13009e20	−0.189343
$590$	−1.46136e19	−0.0241750
$591$	8.94877e20	1.46170
$592$	1.39735e20	0.225368
$593$	−7.08912e20	−1.12897	−0.564485	−	0.825443i	$-0.690925\pi$
$593$	−7.08912e20	−1.12897	−0.564485	+	0.825443i	$0.690925\pi$
$594$	−8.55971e20	−1.34605
$595$	−6.35995e20	−0.987590
$596$	−3.43831e20	−0.527228
$597$	−2.87928e20	−0.435990
$598$	5.47422e20	0.818585
$599$	−6.26354e20	−0.924951	−0.462475	−	0.886632i	$-0.653039\pi$
$599$	−6.26354e20	−0.924951	−0.462475	+	0.886632i	$0.653039\pi$
$600$	−1.19333e20	−0.174031
$601$	−1.07383e21	−1.54659	−0.773295	−	0.634046i	$-0.781393\pi$
$601$	−1.07383e21	−1.54659	−0.773295	+	0.634046i	$0.781393\pi$
$602$	1.21350e21	1.72610
$603$	1.46804e20	0.206233
$604$	−5.77678e20	−0.801510
$605$	−8.18770e19	−0.112201
$606$	1.32222e21	1.78961
$607$	1.04998e21	1.40367	0.701837	−	0.712337i	$-0.252363\pi$
$607$	1.04998e21	1.40367	0.701837	+	0.712337i	$0.252363\pi$
$608$	2.22895e20	0.294323
$609$	1.08906e20	0.142043
$610$	−7.09484e20	−0.914047
$611$	−7.60543e20	−0.967865
$612$	2.18376e20	0.274516
$613$	1.46273e21	1.81640	0.908201	−	0.418534i	$-0.137456\pi$
$613$	1.46273e21	1.81640	0.908201	+	0.418534i	$0.137456\pi$
$614$	−1.79265e21	−2.19904
$615$	−4.56351e20	−0.553013
$616$	−3.58357e20	−0.429004
$617$	−3.66757e20	−0.433750	−0.216875	−	0.976199i	$-0.569586\pi$
$617$	−3.66757e20	−0.433750	−0.216875	+	0.976199i	$0.569586\pi$
$618$	6.03480e20	0.705097
$619$	−1.38140e21	−1.59456	−0.797279	−	0.603612i	$-0.793728\pi$
$619$	−1.38140e21	−1.59456	−0.797279	+	0.603612i	$0.793728\pi$
$620$	8.84939e20	1.00920
$621$	−2.56333e20	−0.288813
$622$	−1.62852e21	−1.81287
$623$	8.96927e20	0.986500
$624$	−6.96908e20	−0.757341
$625$	−6.29343e20	−0.675752
$626$	1.17266e21	1.24412
$627$	−2.14879e20	−0.225262
$628$	6.72790e20	0.696919
$629$	−8.30063e20	−0.849633
$630$	−1.17030e20	−0.118370
$631$	−1.54129e21	−1.54051	−0.770255	−	0.637736i	$-0.779871\pi$
$631$	−1.54129e21	−1.54051	−0.770255	+	0.637736i	$0.779871\pi$
$632$	−5.66969e20	−0.559991
$633$	−7.88399e20	−0.769517
$634$	1.67463e21	1.61529
$635$	−7.63668e20	−0.727950
$636$	1.71325e21	1.61396
$637$	−8.72767e20	−0.812554
$638$	−2.92214e20	−0.268872
$639$	1.16729e20	0.106150
$640$	−1.11863e21	−1.00539
$641$	8.09894e20	0.719437	0.359718	−	0.933061i	$-0.382873\pi$
$641$	8.09894e20	0.719437	0.359718	+	0.933061i	$0.382873\pi$
$642$	3.34163e21	2.93391
$643$	1.67797e21	1.45614	0.728070	−	0.685503i	$-0.240418\pi$
$643$	1.67797e21	1.45614	0.728070	+	0.685503i	$0.240418\pi$
$644$	−3.68806e20	−0.316340
$645$	−1.65798e21	−1.40567
$646$	−6.70609e20	−0.561986
$647$	1.08978e21	0.902729	0.451365	−	0.892340i	$-0.350937\pi$
$647$	1.08978e21	0.902729	0.451365	+	0.892340i	$0.350937\pi$
$648$	−8.61841e20	−0.705691
$649$	−2.08255e19	−0.0168562
$650$	−8.48949e20	−0.679253
$651$	−8.03247e20	−0.635319
$652$	4.89955e20	0.383088
$653$	−1.58232e21	−1.22305	−0.611525	−	0.791225i	$-0.709444\pi$
$653$	−1.58232e21	−1.22305	−0.611525	+	0.791225i	$0.709444\pi$
$654$	−6.14107e20	−0.469257
$655$	1.45951e21	1.10255
$656$	3.41670e20	0.255169
$657$	−1.65507e20	−0.122201
$658$	8.75682e20	0.639223
$659$	−2.01204e21	−1.45210	−0.726050	−	0.687642i	$-0.758646\pi$
$659$	−2.01204e21	−1.45210	−0.726050	+	0.687642i	$0.758646\pi$
$660$	1.68265e21	1.20064
$661$	−1.63001e20	−0.114995	−0.0574975	−	0.998346i	$-0.518312\pi$
$661$	−1.63001e20	−0.114995	−0.0574975	+	0.998346i	$0.518312\pi$
$662$	−3.34326e21	−2.33204
$663$	4.13982e21	2.85515
$664$	−1.05250e21	−0.717728
$665$	2.10288e20	0.141792
$666$	−1.52741e20	−0.101835
$667$	−8.75076e19	−0.0576902
$668$	2.10402e21	1.37159
$669$	−1.80783e21	−1.16536
$670$	3.53022e21	2.25030
$671$	−1.01107e21	−0.637326
$672$	1.58429e21	0.987564
$673$	−1.78803e21	−1.10220	−0.551101	−	0.834439i	$-0.685792\pi$
$673$	−1.78803e21	−1.10220	−0.551101	+	0.834439i	$0.685792\pi$
$674$	−3.66153e20	−0.223210
$675$	3.97523e20	0.239654
$676$	4.44802e21	2.65196
$677$	3.87297e20	0.228365	0.114182	−	0.993460i	$-0.463575\pi$
$677$	3.87297e20	0.228365	0.114182	+	0.993460i	$0.463575\pi$
$678$	−3.84037e21	−2.23950
$679$	5.92078e20	0.341472
$680$	1.52803e21	0.871594
$681$	1.72357e21	0.972355
$682$	2.15526e21	1.20259
$683$	−7.05164e20	−0.389166	−0.194583	−	0.980886i	$-0.562335\pi$
$683$	−7.05164e20	−0.389166	−0.194583	+	0.980886i	$0.562335\pi$
$684$	−7.22047e19	−0.0394135
$685$	9.79061e19	0.0528604
$686$	3.10377e21	1.65752
$687$	−4.10187e20	−0.216674
$688$	1.24133e21	0.648597
$689$	3.54654e21	1.83299
$690$	8.61163e20	0.440268
$691$	2.20369e21	1.11446	0.557230	−	0.830358i	$-0.311864\pi$
$691$	2.20369e21	1.11446	0.557230	+	0.830358i	$0.311864\pi$
$692$	7.57229e20	0.378819
$693$	−1.66777e20	−0.0825346
$694$	−1.30716e21	−0.639930
$695$	1.31169e21	0.635251
$696$	−2.61654e20	−0.125360
$697$	−2.02961e21	−0.961979
$698$	3.81829e21	1.79041
$699$	4.21499e21	1.95532
$700$	5.71948e20	0.262495
$701$	−8.41871e20	−0.382262	−0.191131	−	0.981565i	$-0.561215\pi$
$701$	−8.41871e20	−0.382262	−0.191131	+	0.981565i	$0.561215\pi$
$702$	−5.45264e21	−2.44951
$703$	2.74456e20	0.121985
$704$	−3.35772e21	−1.47655
$705$	−1.19643e21	−0.520557
$706$	3.65131e20	0.157186
$707$	−1.84400e21	−0.785446
$708$	−6.40854e19	−0.0270091
$709$	−3.47596e21	−1.44953	−0.724765	−	0.688996i	$-0.758052\pi$
$709$	−3.47596e21	−1.44953	−0.724765	+	0.688996i	$0.758052\pi$
$710$	2.80700e21	1.15826
$711$	−2.63863e20	−0.107735
$712$	−2.15494e21	−0.870632
$713$	6.45422e20	0.258031
$714$	−4.76654e21	−1.88568
$715$	3.48319e21	1.36358
$716$	−1.75080e21	−0.678247
$717$	4.57591e21	1.75422
$718$	8.92560e20	0.338614
$719$	9.74002e20	0.365673	0.182837	−	0.983143i	$-0.441472\pi$
$719$	9.74002e20	0.365673	0.182837	+	0.983143i	$0.441472\pi$
$720$	−1.19714e20	−0.0444786
$721$	−8.41631e20	−0.309462
$722$	−4.04478e21	−1.47186
$723$	−2.80247e21	−1.00926
$724$	−5.29325e21	−1.88662
$725$	1.35708e20	0.0478707
$726$	−6.13637e20	−0.214233
$727$	3.66741e20	0.126722	0.0633609	−	0.997991i	$-0.479818\pi$
$727$	3.66741e20	0.126722	0.0633609	+	0.997991i	$0.479818\pi$
$728$	−2.28278e21	−0.780690
$729$	2.50883e21	0.849208
$730$	−3.97998e21	−1.33340
$731$	−7.37384e21	−2.44519
$732$	−3.11132e21	−1.02120
$733$	4.60442e21	1.49587	0.747937	−	0.663770i	$-0.231045\pi$
$733$	4.60442e21	1.49587	0.747937	+	0.663770i	$0.231045\pi$
$734$	1.17646e21	0.378319
$735$	−1.37297e21	−0.437025
$736$	−1.27300e21	−0.401094
$737$	5.03084e21	1.56904
$738$	−3.73469e20	−0.115301
$739$	−4.03369e20	−0.123273	−0.0616366	−	0.998099i	$-0.519632\pi$
$739$	−4.03369e20	−0.123273	−0.0616366	+	0.998099i	$0.519632\pi$
$740$	−2.14917e21	−0.650180
$741$	−1.36881e21	−0.409926
$742$	−4.08345e21	−1.21059
$743$	−3.61255e21	−1.06022	−0.530112	−	0.847928i	$-0.677850\pi$
$743$	−3.61255e21	−1.06022	−0.530112	+	0.847928i	$0.677850\pi$
$744$	1.92986e21	0.560698
$745$	−1.11967e21	−0.322047
$746$	−5.13472e21	−1.46210
$747$	−4.89823e20	−0.138081
$748$	7.48353e21	2.08855
$749$	−4.66034e21	−1.28767
$750$	−6.51605e21	−1.78248
$751$	6.22201e21	1.68512	0.842561	−	0.538601i	$-0.181047\pi$
$751$	6.22201e21	1.68512	0.842561	+	0.538601i	$0.181047\pi$
$752$	8.95766e20	0.240193
$753$	2.79959e21	0.743245
$754$	−1.86144e21	−0.489287
$755$	−1.88119e21	−0.489587
$756$	3.67352e21	0.946605
$757$	−3.02190e21	−0.771012	−0.385506	−	0.922705i	$-0.625973\pi$
$757$	−3.02190e21	−0.771012	−0.385506	+	0.922705i	$0.625973\pi$
$758$	6.75304e21	1.70601
$759$	1.22722e21	0.306980
$760$	−5.05234e20	−0.125138
$761$	−3.35914e21	−0.823842	−0.411921	−	0.911220i	$-0.635142\pi$
$761$	−3.35914e21	−0.823842	−0.411921	+	0.911220i	$0.635142\pi$
$762$	−5.72340e21	−1.38993
$763$	8.56451e20	0.205953
$764$	9.58032e21	2.28129
$765$	7.11132e20	0.167683
$766$	9.78395e21	2.28454
$767$	−1.32661e20	−0.0306745
$768$	−1.05770e21	−0.242189
$769$	−5.41991e21	−1.22898	−0.614489	−	0.788925i	$-0.710638\pi$
$769$	−5.41991e21	−1.22898	−0.614489	+	0.788925i	$0.710638\pi$
$770$	−4.01051e21	−0.900573
$771$	6.63790e21	1.47612
$772$	−4.36724e21	−0.961784
$773$	−3.43545e21	−0.749268	−0.374634	−	0.927173i	$-0.622232\pi$
$773$	−3.43545e21	−0.749268	−0.374634	+	0.927173i	$0.622232\pi$
$774$	−1.35687e21	−0.293075
$775$	−1.00093e21	−0.214111
$776$	−1.42251e21	−0.301365
$777$	1.95077e21	0.409307
$778$	−1.00618e22	−2.09088
$779$	6.71078e20	0.138115
$780$	1.07187e22	2.18490
$781$	4.00019e21	0.807602
$782$	3.83000e21	0.765857
$783$	8.71626e20	0.172630
$784$	1.02794e21	0.201650
$785$	2.19092e21	0.425700
$786$	1.09385e22	2.10518
$787$	4.26065e21	0.812204	0.406102	−	0.913828i	$-0.366888\pi$
$787$	4.26065e21	0.812204	0.406102	+	0.913828i	$0.366888\pi$
$788$	1.03047e22	1.94576
$789$	−4.66896e21	−0.873259
$790$	−6.34516e21	−1.17555
$791$	5.35589e21	0.982897
$792$	4.00694e20	0.0728407
$793$	−6.44063e21	−1.15979
$794$	−1.50116e22	−2.67777
$795$	5.57914e21	0.985857
$796$	−3.31556e21	−0.580376
$797$	1.26474e21	0.219313	0.109657	−	0.993970i	$-0.465025\pi$
$797$	1.26474e21	0.219313	0.109657	+	0.993970i	$0.465025\pi$
$798$	1.57603e21	0.270734
$799$	−5.32108e21	−0.905522
$800$	1.97419e21	0.332823
$801$	−1.00289e21	−0.167498
$802$	6.53636e21	1.08150
$803$	−5.67177e21	−0.929720
$804$	1.54812e22	2.51411
$805$	−1.20100e21	−0.193230
$806$	1.37292e22	2.18844
$807$	−9.87164e21	−1.55897
$808$	4.43036e21	0.693193
$809$	8.98922e21	1.39350	0.696752	−	0.717312i	$-0.254628\pi$
$809$	8.98922e21	1.39350	0.696752	+	0.717312i	$0.254628\pi$
$810$	−9.64518e21	−1.48140
$811$	2.06240e21	0.313846	0.156923	−	0.987611i	$-0.449843\pi$
$811$	2.06240e21	0.313846	0.156923	+	0.987611i	$0.449843\pi$
$812$	1.25408e21	0.189084
$813$	1.31562e21	0.196540
$814$	−5.23428e21	−0.774772
$815$	1.59552e21	0.234002
$816$	−4.87586e21	−0.708558
$817$	2.43812e21	0.351066
$818$	1.28598e22	1.83478
$819$	−1.06239e21	−0.150194
$820$	−5.25499e21	−0.736153
$821$	−1.35572e22	−1.88190	−0.940949	−	0.338548i	$-0.890064\pi$
$821$	−1.35572e22	−1.88190	−0.940949	+	0.338548i	$0.890064\pi$
$822$	7.33769e20	0.100930
$823$	−4.10603e18	−0.000559659 0	−0.000279830	−	1.00000i	$-0.500089\pi$
$823$	−4.10603e18	−0.000559659 0	−0.000279830		1.00000i	$0.500089\pi$
$824$	2.02208e21	0.273115
$825$	−1.90319e21	−0.254729
$826$	1.52744e20	0.0202588
$827$	1.81727e21	0.238852	0.119426	−	0.992843i	$-0.461895\pi$
$827$	1.81727e21	0.238852	0.119426	+	0.992843i	$0.461895\pi$
$828$	4.12377e20	0.0537115
$829$	5.82601e20	0.0751990	0.0375995	−	0.999293i	$-0.488029\pi$
$829$	5.82601e20	0.0751990	0.0375995	+	0.999293i	$0.488029\pi$
$830$	−1.17789e22	−1.50667
$831$	6.99427e21	0.886614
$832$	−2.13891e22	−2.68700
$833$	−6.10624e21	−0.760215
$834$	9.83062e21	1.21293
$835$	6.85166e21	0.837813
$836$	−2.47439e21	−0.299861
$837$	−6.42877e21	−0.772124
$838$	1.14402e22	1.36177
$839$	−7.04645e21	−0.831296	−0.415648	−	0.909526i	$-0.636445\pi$
$839$	−7.04645e21	−0.831296	−0.415648	+	0.909526i	$0.636445\pi$
$840$	−3.59109e21	−0.419887
$841$	2.97558e20	0.0344828
$842$	3.79975e21	0.436430
$843$	1.50856e22	1.71734
$844$	−9.07860e21	−1.02436
$845$	1.44848e22	1.61990
$846$	−9.79136e20	−0.108534
$847$	8.55797e20	0.0940254
$848$	−4.17710e21	−0.454890
$849$	−1.34982e22	−1.45703
$850$	−5.93960e21	−0.635500
$851$	−1.56748e21	−0.166238
$852$	1.23096e22	1.29404
$853$	−5.26698e21	−0.548838	−0.274419	−	0.961610i	$-0.588485\pi$
$853$	−5.26698e21	−0.548838	−0.274419	+	0.961610i	$0.588485\pi$
$854$	7.41568e21	0.765979
$855$	−2.35132e20	−0.0240750
$856$	1.11968e22	1.13643
$857$	−6.39365e21	−0.643269	−0.321635	−	0.946864i	$-0.604232\pi$
$857$	−6.39365e21	−0.643269	−0.321635	+	0.946864i	$0.604232\pi$
$858$	2.61052e22	2.60359
$859$	−1.46139e22	−1.44483	−0.722417	−	0.691458i	$-0.756969\pi$
$859$	−1.46139e22	−1.44483	−0.722417	+	0.691458i	$0.756969\pi$
$860$	−1.90921e22	−1.87118
$861$	4.76988e21	0.463429
$862$	−3.01726e22	−2.90608
$863$	6.08661e21	0.581158	0.290579	−	0.956851i	$-0.406152\pi$
$863$	6.08661e21	0.581158	0.290579	+	0.956851i	$0.406152\pi$
$864$	1.26798e22	1.20022
$865$	2.46589e21	0.231395
$866$	1.00907e22	0.938723
$867$	1.74757e22	1.61173
$868$	−9.24958e21	−0.845715
$869$	−9.04234e21	−0.819658
$870$	−2.92827e21	−0.263158
$871$	3.20470e22	2.85530
$872$	−2.05769e21	−0.181763
$873$	−6.62027e20	−0.0579787
$874$	−1.26637e21	−0.109957
$875$	9.08748e21	0.782317
$876$	−1.74535e22	−1.48971
$877$	−1.02772e22	−0.869715	−0.434857	−	0.900499i	$-0.643201\pi$
$877$	−1.02772e22	−0.869715	−0.434857	+	0.900499i	$0.643201\pi$
$878$	−1.48468e22	−1.24573
$879$	−5.78147e21	−0.480974
$880$	−4.10249e21	−0.338398
$881$	6.72665e21	0.550148	0.275074	−	0.961423i	$-0.411298\pi$
$881$	6.72665e21	0.550148	0.275074	+	0.961423i	$0.411298\pi$
$882$	−1.12361e21	−0.0911177
$883$	−7.57072e20	−0.0608740	−0.0304370	−	0.999537i	$-0.509690\pi$
$883$	−7.57072e20	−0.0608740	−0.0304370	+	0.999537i	$0.509690\pi$
$884$	4.76710e22	3.80069
$885$	−2.08692e20	−0.0164980
$886$	3.66628e22	2.87391
$887$	−2.68557e21	−0.208742	−0.104371	−	0.994538i	$-0.533283\pi$
$887$	−2.68557e21	−0.208742	−0.104371	+	0.994538i	$0.533283\pi$
$888$	−4.68688e21	−0.361232
$889$	7.98203e21	0.610028
$890$	−2.41167e22	−1.82765
$891$	−1.37451e22	−1.03292
$892$	−2.08176e22	−1.55129
$893$	1.75939e21	0.130010
$894$	−8.39154e21	−0.614908
$895$	−5.70141e21	−0.414295
$896$	1.16922e22	0.842529
$897$	7.81757e21	0.558635
$898$	−4.22572e22	−2.99453
$899$	−2.19467e21	−0.154231
$900$	−6.39519e20	−0.0445692
$901$	2.48131e22	1.71492
$902$	−1.27984e22	−0.877219
$903$	1.73296e22	1.17796
$904$	−1.28679e22	−0.867453
$905$	−1.72373e22	−1.15240
$906$	−1.40988e22	−0.934804
$907$	9.07845e21	0.596976	0.298488	−	0.954413i	$-0.403518\pi$
$907$	9.07845e21	0.596976	0.298488	+	0.954413i	$0.403518\pi$
$908$	1.98473e22	1.29437
$909$	2.06186e21	0.133361
$910$	−2.55474e22	−1.63884
$911$	−1.36257e22	−0.866903	−0.433452	−	0.901177i	$-0.642704\pi$
$911$	−1.36257e22	−0.866903	−0.433452	+	0.901177i	$0.642704\pi$
$912$	1.61218e21	0.101731
$913$	−1.67858e22	−1.05054
$914$	−1.07240e22	−0.665673
$915$	−1.01319e22	−0.623782
$916$	−4.72340e21	−0.288429
$917$	−1.52552e22	−0.923946
$918$	−3.81490e22	−2.29172
$919$	1.56883e22	0.934782	0.467391	−	0.884051i	$-0.345194\pi$
$919$	1.56883e22	0.934782	0.467391	+	0.884051i	$0.345194\pi$
$920$	2.88550e21	0.170535
$921$	−2.56003e22	−1.50071
$922$	4.65721e22	2.70797
$923$	2.54817e22	1.46965
$924$	−1.75874e22	−1.00615
$925$	2.43086e21	0.137942
$926$	3.33445e22	1.87690
$927$	9.41062e20	0.0525436
$928$	4.32869e21	0.239743
$929$	−1.89875e22	−1.04316	−0.521579	−	0.853203i	$-0.674657\pi$
$929$	−1.89875e22	−1.04316	−0.521579	+	0.853203i	$0.674657\pi$
$930$	2.15978e22	1.17703
$931$	2.01900e21	0.109147
$932$	4.85367e22	2.60286
$933$	−2.32564e22	−1.23717
$934$	3.58262e21	0.189060
$935$	2.43699e22	1.27575
$936$	2.55247e21	0.132554
$937$	2.64493e22	1.36260	0.681298	−	0.732006i	$-0.261416\pi$
$937$	2.64493e22	1.36260	0.681298	+	0.732006i	$0.261416\pi$
$938$	−3.68987e22	−1.88577
$939$	1.67463e22	0.849040
$940$	−1.37772e22	−0.692949
$941$	1.84747e22	0.921840	0.460920	−	0.887442i	$-0.347520\pi$
$941$	1.84747e22	0.921840	0.460920	+	0.887442i	$0.347520\pi$
$942$	1.64201e22	0.812820
$943$	−3.83268e21	−0.188219
$944$	1.56248e20	0.00761243
$945$	1.19627e22	0.578216
$946$	−4.64985e22	−2.22975
$947$	1.94258e22	0.924176	0.462088	−	0.886834i	$-0.347100\pi$
$947$	1.94258e22	0.924176	0.462088	+	0.886834i	$0.347100\pi$
$948$	−2.78256e22	−1.31336
$949$	−3.61299e22	−1.69188
$950$	1.96390e21	0.0912413
$951$	2.39149e22	1.10234
$952$	−1.59713e22	−0.730403
$953$	−2.29755e22	−1.04248	−0.521240	−	0.853410i	$-0.674530\pi$
$953$	−2.29755e22	−1.04248	−0.521240	+	0.853410i	$0.674530\pi$
$954$	4.56587e21	0.205547
$955$	3.11980e22	1.39348
$956$	5.26927e22	2.33516
$957$	−4.17302e21	−0.183489
$958$	8.40624e21	0.366742
$959$	−1.02334e21	−0.0442975
$960$	−3.36477e22	−1.44518
$961$	−7.27821e21	−0.310169
$962$	−3.33430e22	−1.40991
$963$	5.21092e21	0.218634
$964$	−3.22711e22	−1.34350
$965$	−1.42218e22	−0.587488
$966$	−9.00107e21	−0.368948
$967$	3.66733e22	1.49160	0.745799	−	0.666171i	$-0.232068\pi$
$967$	3.66733e22	1.49160	0.745799	+	0.666171i	$0.232068\pi$
$968$	−2.05612e21	−0.0829818
$969$	−9.57675e21	−0.383522
$970$	−1.59199e22	−0.632633
$971$	1.84152e21	0.0726161	0.0363080	−	0.999341i	$-0.488440\pi$
$971$	1.84152e21	0.0726161	0.0363080	+	0.999341i	$0.488440\pi$
$972$	−8.78887e21	−0.343903
$973$	−1.37101e22	−0.532346
$974$	7.46899e22	2.87786
$975$	−1.21236e22	−0.463549
$976$	7.58576e21	0.287823
$977$	1.57862e22	0.594387	0.297193	−	0.954817i	$-0.403949\pi$
$977$	1.57862e22	0.594387	0.297193	+	0.954817i	$0.403949\pi$
$978$	1.19578e22	0.446797
$979$	−3.43682e22	−1.27434
$980$	−1.58101e22	−0.581753
$981$	−9.57634e20	−0.0349689
$982$	6.85686e22	2.48479
$983$	1.34794e22	0.484752	0.242376	−	0.970182i	$-0.422073\pi$
$983$	1.34794e22	0.484752	0.242376	+	0.970182i	$0.422073\pi$
$984$	−1.14600e22	−0.408998
$985$	3.35570e22	1.18853
$986$	−1.30234e22	−0.457770
$987$	1.25053e22	0.436231
$988$	−1.57622e22	−0.545680
$989$	−1.39246e22	−0.478423
$990$	4.48432e21	0.152909
$991$	−1.23389e22	−0.417565	−0.208782	−	0.977962i	$-0.566950\pi$
$991$	−1.23389e22	−0.417565	−0.208782	+	0.977962i	$0.566950\pi$
$992$	−3.19267e22	−1.07230
$993$	−4.77440e22	−1.59147
$994$	−2.93394e22	−0.970628
$995$	−1.07970e22	−0.354512
$996$	−5.16543e22	−1.68330
$997$	−2.85169e22	−0.922334	−0.461167	−	0.887313i	$-0.652569\pi$
$997$	−2.85169e22	−0.922334	−0.461167	+	0.887313i	$0.652569\pi$
$998$	7.16999e22	2.30165
$999$	1.56130e22	0.497444

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.16.a.b.1.16	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.16.a.b.1.16	✓	19	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q+281.041 q^{2} +4013.45 q^{3} +46215.9 q^{4} +150501. q^{5} +1.12794e6 q^{6} -1.57306e6 q^{7} +3.77941e6 q^{8} +1.75891e6 q^{9} +O(q^{10})\)	\(q+281.041 q^{2} +4013.45 q^{3} +46215.9 q^{4} +150501. q^{5} +1.12794e6 q^{6} -1.57306e6 q^{7} +3.77941e6 q^{8} +1.75891e6 q^{9} +4.22968e7 q^{10} +6.02762e7 q^{11} +1.85485e8 q^{12} +3.83967e8 q^{13} -4.42095e8 q^{14} +6.04027e8 q^{15} -4.52235e8 q^{16} +2.68639e9 q^{17} +4.94325e8 q^{18} -8.88241e8 q^{19} +6.95552e9 q^{20} -6.31342e9 q^{21} +1.69401e10 q^{22} +5.07294e9 q^{23} +1.51685e10 q^{24} -7.86717e9 q^{25} +1.07910e11 q^{26} -5.05294e10 q^{27} -7.27006e10 q^{28} -1.72499e10 q^{29} +1.69756e11 q^{30} +1.27228e11 q^{31} -2.50940e11 q^{32} +2.41916e11 q^{33} +7.54985e11 q^{34} -2.36747e11 q^{35} +8.12895e10 q^{36} -3.08988e11 q^{37} -2.49632e11 q^{38} +1.54103e12 q^{39} +5.68803e11 q^{40} -7.55514e11 q^{41} -1.77433e12 q^{42} -2.74489e12 q^{43} +2.78572e12 q^{44} +2.64717e11 q^{45} +1.42570e12 q^{46} -1.98075e12 q^{47} -1.81502e12 q^{48} -2.27303e12 q^{49} -2.21100e12 q^{50} +1.07817e13 q^{51} +1.77454e13 q^{52} +9.23657e12 q^{53} -1.42008e13 q^{54} +9.07159e12 q^{55} -5.94526e12 q^{56} -3.56491e12 q^{57} -4.84792e12 q^{58} -3.45501e11 q^{59} +2.79157e13 q^{60} -1.67739e13 q^{61} +3.57564e13 q^{62} -2.76688e12 q^{63} -5.57056e13 q^{64} +5.77872e13 q^{65} +6.79882e13 q^{66} +8.34631e13 q^{67} +1.24154e14 q^{68} +2.03600e13 q^{69} -6.65356e13 q^{70} +6.63643e13 q^{71} +6.64763e12 q^{72} -9.40965e13 q^{73} -8.68382e13 q^{74} -3.15745e13 q^{75} -4.10508e13 q^{76} -9.48183e13 q^{77} +4.33093e14 q^{78} -1.50015e14 q^{79} -6.80616e13 q^{80} -2.28036e14 q^{81} -2.12330e14 q^{82} -2.78481e14 q^{83} -2.91781e14 q^{84} +4.04303e14 q^{85} -7.71425e14 q^{86} -6.92316e13 q^{87} +2.27808e14 q^{88} -5.70178e14 q^{89} +7.43962e13 q^{90} -6.04004e14 q^{91} +2.34451e14 q^{92} +5.10625e14 q^{93} -5.56673e14 q^{94} -1.33681e14 q^{95} -1.00714e15 q^{96} -3.76385e14 q^{97} -6.38814e14 q^{98} +1.06020e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 9908 q^{3} + 387418 q^{4} + 230490 q^{5} + 1566838 q^{6} + 2882024 q^{7} + 26209092 q^{8} + 93022899 q^{9}+O(q^{10}) \) 19 * q + 9908 * q^3 + 387418 * q^4 + 230490 * q^5 + 1566838 * q^6 + 2882024 * q^7 + 26209092 * q^8 + 93022899 * q^9	\( 19 q + 9908 q^{3} + 387418 q^{4} + 230490 q^{5} + 1566838 q^{6} + 2882024 q^{7} + 26209092 q^{8} + 93022899 q^{9} - 46518144 q^{10} + 56910992 q^{11} + 907194664 q^{12} + 377780326 q^{13} + 1552762656 q^{14} + 2058712006 q^{15} + 9746645474 q^{16} - 797562458 q^{17} - 2812146948 q^{18} + 5568901154 q^{19} - 6814671874 q^{20} - 19358601528 q^{21} - 43431230566 q^{22} - 22787265900 q^{23} - 32333767894 q^{24} + 113218218877 q^{25} - 60020783208 q^{26} + 115546592594 q^{27} + 171573547692 q^{28} - 327747649871 q^{29} - 152869385454 q^{30} + 190165645448 q^{31} + 1523182591996 q^{32} + 1432316120556 q^{33} + 781895976484 q^{34} + 1076956461508 q^{35} + 4124169333892 q^{36} + 1157558623486 q^{37} + 454200349888 q^{38} - 3276695149790 q^{39} + 1497234313960 q^{40} - 327181726714 q^{41} + 14801498493780 q^{42} + 3969726268184 q^{43} + 9884551144664 q^{44} + 13723027476954 q^{45} + 4360233976812 q^{46} + 17801533447516 q^{47} + 44888708498560 q^{48} + 26274460777219 q^{49} + 49590112735028 q^{50} + 48299925405108 q^{51} + 38417786090034 q^{52} + 42945469924134 q^{53} + 78537259690434 q^{54} + 43646306609786 q^{55} + 153497246476960 q^{56} + 87149617056284 q^{57} + 76276585694640 q^{59} + 137931874827396 q^{60} + 75095043245982 q^{61} + 45115853357766 q^{62} + 77728938376620 q^{63} + 263521279152786 q^{64} + 25707147233724 q^{65} - 97128209185404 q^{66} + 39919578800676 q^{67} + 172949157314596 q^{68} + 61328545437264 q^{69} + 524547167494056 q^{70} + 128037096114140 q^{71} + 307467488440744 q^{72} + 333487363889334 q^{73} + 220493893416424 q^{74} - 68218174510546 q^{75} + 354934779140576 q^{76} - 692163369062472 q^{77} - 818320982346402 q^{78} + 213267241183292 q^{79} - 452775952882810 q^{80} + 48823702443271 q^{81} - 17\!\cdots\!96 q^{82}+ \cdots - 233858833882834 q^{99}+O(q^{100}) \) 19 * q + 9908 * q^3 + 387418 * q^4 + 230490 * q^5 + 1566838 * q^6 + 2882024 * q^7 + 26209092 * q^8 + 93022899 * q^9 - 46518144 * q^10 + 56910992 * q^11 + 907194664 * q^12 + 377780326 * q^13 + 1552762656 * q^14 + 2058712006 * q^15 + 9746645474 * q^16 - 797562458 * q^17 - 2812146948 * q^18 + 5568901154 * q^19 - 6814671874 * q^20 - 19358601528 * q^21 - 43431230566 * q^22 - 22787265900 * q^23 - 32333767894 * q^24 + 113218218877 * q^25 - 60020783208 * q^26 + 115546592594 * q^27 + 171573547692 * q^28 - 327747649871 * q^29 - 152869385454 * q^30 + 190165645448 * q^31 + 1523182591996 * q^32 + 1432316120556 * q^33 + 781895976484 * q^34 + 1076956461508 * q^35 + 4124169333892 * q^36 + 1157558623486 * q^37 + 454200349888 * q^38 - 3276695149790 * q^39 + 1497234313960 * q^40 - 327181726714 * q^41 + 14801498493780 * q^42 + 3969726268184 * q^43 + 9884551144664 * q^44 + 13723027476954 * q^45 + 4360233976812 * q^46 + 17801533447516 * q^47 + 44888708498560 * q^48 + 26274460777219 * q^49 + 49590112735028 * q^50 + 48299925405108 * q^51 + 38417786090034 * q^52 + 42945469924134 * q^53 + 78537259690434 * q^54 + 43646306609786 * q^55 + 153497246476960 * q^56 + 87149617056284 * q^57 + 76276585694640 * q^59 + 137931874827396 * q^60 + 75095043245982 * q^61 + 45115853357766 * q^62 + 77728938376620 * q^63 + 263521279152786 * q^64 + 25707147233724 * q^65 - 97128209185404 * q^66 + 39919578800676 * q^67 + 172949157314596 * q^68 + 61328545437264 * q^69 + 524547167494056 * q^70 + 128037096114140 * q^71 + 307467488440744 * q^72 + 333487363889334 * q^73 + 220493893416424 * q^74 - 68218174510546 * q^75 + 354934779140576 * q^76 - 692163369062472 * q^77 - 818320982346402 * q^78 + 213267241183292 * q^79 - 452775952882810 * q^80 + 48823702443271 * q^81 - 1736995581874796 * q^82 - 66633324408168 * q^83 - 2217716778602152 * q^84 - 1419457827450068 * q^85 - 1364891612086326 * q^86 - 170911774469572 * q^87 - 4325342725143834 * q^88 - 2341312102493090 * q^89 - 6182213358743320 * q^90 + 852022408820524 * q^91 - 3781297333622004 * q^92 - 3548745569232820 * q^93 - 914001881049618 * q^94 - 4053850425835916 * q^95 - 775984072309158 * q^96 - 686179834828282 * q^97 - 5170682580897840 * q^98 - 233858833882834 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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