LMFDB - Embedded newform 29.16.a.b.1.8

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			1.8
Root			$-101.235$ 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)

$f(q)$	$=$	$q-101.235 q^{2} +2276.05 q^{3} -22519.5 q^{4} +12349.2 q^{5} -230415. q^{6} -3.54158e6 q^{7} +5.59702e6 q^{8} -9.16851e6 q^{9} +O(q^{10})$	\(q-101.235 q^{2} +2276.05 q^{3} -22519.5 q^{4} +12349.2 q^{5} -230415. q^{6} -3.54158e6 q^{7} +5.59702e6 q^{8} -9.16851e6 q^{9} -1.25017e6 q^{10} -3.57168e7 q^{11} -5.12555e7 q^{12} +4.03767e7 q^{13} +3.58531e8 q^{14} +2.81074e7 q^{15} +1.71308e8 q^{16} -8.98386e8 q^{17} +9.28172e8 q^{18} -1.45638e9 q^{19} -2.78098e8 q^{20} -8.06081e9 q^{21} +3.61578e9 q^{22} +2.79170e10 q^{23} +1.27391e10 q^{24} -3.03651e10 q^{25} -4.08752e9 q^{26} -5.35268e10 q^{27} +7.97548e10 q^{28} -1.72499e10 q^{29} -2.84544e9 q^{30} -2.62570e11 q^{31} -2.00745e11 q^{32} -8.12932e10 q^{33} +9.09479e10 q^{34} -4.37357e10 q^{35} +2.06471e11 q^{36} +8.36528e11 q^{37} +1.47437e11 q^{38} +9.18993e10 q^{39} +6.91187e10 q^{40} +1.74578e12 q^{41} +8.16034e11 q^{42} +3.84764e11 q^{43} +8.04327e11 q^{44} -1.13224e11 q^{45} -2.82617e12 q^{46} +4.15714e12 q^{47} +3.89905e11 q^{48} +7.79525e12 q^{49} +3.07400e12 q^{50} -2.04477e12 q^{51} -9.09265e11 q^{52} +1.39488e13 q^{53} +5.41877e12 q^{54} -4.41074e11 q^{55} -1.98223e13 q^{56} -3.31480e12 q^{57} +1.74629e12 q^{58} +2.30895e13 q^{59} -6.32965e11 q^{60} -4.20790e13 q^{61} +2.65812e13 q^{62} +3.24711e13 q^{63} +1.47090e13 q^{64} +4.98620e11 q^{65} +8.22970e12 q^{66} +3.64110e13 q^{67} +2.02312e13 q^{68} +6.35404e13 q^{69} +4.42757e12 q^{70} +7.05417e13 q^{71} -5.13163e13 q^{72} -1.43595e14 q^{73} -8.46857e13 q^{74} -6.91124e13 q^{75} +3.27971e13 q^{76} +1.26494e14 q^{77} -9.30340e12 q^{78} -2.35839e14 q^{79} +2.11551e12 q^{80} +9.72867e12 q^{81} -1.76734e14 q^{82} +3.48349e14 q^{83} +1.81526e14 q^{84} -1.10944e13 q^{85} -3.89515e13 q^{86} -3.92615e13 q^{87} -1.99908e14 q^{88} +1.92866e14 q^{89} +1.14622e13 q^{90} -1.42997e14 q^{91} -6.28677e14 q^{92} -5.97623e14 q^{93} -4.20847e14 q^{94} -1.79852e13 q^{95} -4.56906e14 q^{96} +2.89831e14 q^{97} -7.89150e14 q^{98} +3.27470e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−101.235	−0.559248	−0.279624	−	0.960110i	$-0.590210\pi$
$2$	−101.235	−0.559248	−0.279624	+	0.960110i	$0.590210\pi$
$3$	2276.05	0.600858	0.300429	−	0.953804i	$-0.402870\pi$
$3$	2276.05	0.600858	0.300429	+	0.953804i	$0.402870\pi$
$4$	−22519.5	−0.687242
$5$	12349.2	0.0706909	0.0353455	−	0.999375i	$-0.488747\pi$
$5$	12349.2	0.0706909	0.0353455	+	0.999375i	$0.488747\pi$
$6$	−230415.	−0.336029
$7$	−3.54158e6	−1.62541	−0.812703	−	0.582677i	$-0.802005\pi$
$7$	−3.54158e6	−1.62541	−0.812703	+	0.582677i	$0.802005\pi$
$8$	5.59702e6	0.943587
$9$	−9.16851e6	−0.638969
$10$	−1.25017e6	−0.0395338
$11$	−3.57168e7	−0.552622	−0.276311	−	0.961068i	$-0.589112\pi$
$11$	−3.57168e7	−0.552622	−0.276311	+	0.961068i	$0.589112\pi$
$12$	−5.12555e7	−0.412935
$13$	4.03767e7	0.178466	0.0892331	−	0.996011i	$-0.471558\pi$
$13$	4.03767e7	0.178466	0.0892331	+	0.996011i	$0.471558\pi$
$14$	3.58531e8	0.909006
$15$	2.81074e7	0.0424752
$16$	1.71308e8	0.159543
$17$	−8.98386e8	−0.531002	−0.265501	−	0.964111i	$-0.585537\pi$
$17$	−8.98386e8	−0.531002	−0.265501	+	0.964111i	$0.585537\pi$
$18$	9.28172e8	0.357342
$19$	−1.45638e9	−0.373787	−0.186893	−	0.982380i	$-0.559842\pi$
$19$	−1.45638e9	−0.373787	−0.186893	+	0.982380i	$0.559842\pi$
$20$	−2.78098e8	−0.0485818
$21$	−8.06081e9	−0.976639
$22$	3.61578e9	0.309053
$23$	2.79170e10	1.70966	0.854830	−	0.518909i	$-0.173662\pi$
$23$	2.79170e10	1.70966	0.854830	+	0.518909i	$0.173662\pi$
$24$	1.27391e10	0.566962
$25$	−3.03651e10	−0.995003
$26$	−4.08752e9	−0.0998068
$27$	−5.35268e10	−0.984788
$28$	7.97548e10	1.11705
$29$	−1.72499e10	−0.185695
$29$	−1.72499e10	−0.185695
$30$	−2.84544e9	−0.0237542
$31$	−2.62570e11	−1.71409	−0.857044	−	0.515243i	$-0.827702\pi$
$31$	−2.62570e11	−1.71409	−0.857044	+	0.515243i	$0.827702\pi$
$32$	−2.00745e11	−1.03281
$33$	−8.12932e10	−0.332047
$34$	9.09479e10	0.296962
$35$	−4.37357e10	−0.114902
$36$	2.06471e11	0.439126
$37$	8.36528e11	1.44866	0.724332	−	0.689452i	$-0.242148\pi$
$37$	8.36528e11	1.44866	0.724332	+	0.689452i	$0.242148\pi$
$38$	1.47437e11	0.209039
$39$	9.18993e10	0.107233
$40$	6.91187e10	0.0667030
$41$	1.74578e12	1.39995	0.699973	−	0.714169i	$-0.253195\pi$
$41$	1.74578e12	1.39995	0.699973	+	0.714169i	$0.253195\pi$
$42$	8.16034e11	0.546183
$43$	3.84764e11	0.215865	0.107932	−	0.994158i	$-0.465577\pi$
$43$	3.84764e11	0.215865	0.107932	+	0.994158i	$0.465577\pi$
$44$	8.04327e11	0.379785
$45$	−1.13224e11	−0.0451694
$46$	−2.82617e12	−0.956124
$47$	4.15714e12	1.19691	0.598454	−	0.801158i	$-0.295782\pi$
$47$	4.15714e12	1.19691	0.598454	+	0.801158i	$0.295782\pi$
$48$	3.89905e11	0.0958626
$49$	7.79525e12	1.64195
$50$	3.07400e12	0.556453
$51$	−2.04477e12	−0.319057
$52$	−9.09265e11	−0.122649
$53$	1.39488e13	1.63105	0.815526	−	0.578721i	$-0.196448\pi$
$53$	1.39488e13	1.63105	0.815526	+	0.578721i	$0.196448\pi$
$54$	5.41877e12	0.550741
$55$	−4.41074e11	−0.0390653
$56$	−1.98223e13	−1.53371
$57$	−3.31480e12	−0.224593
$58$	1.74629e12	0.103850
$59$	2.30895e13	1.20788	0.603941	−	0.797029i	$-0.293596\pi$
$59$	2.30895e13	1.20788	0.603941	+	0.797029i	$0.293596\pi$
$60$	−6.32965e11	−0.0291907
$61$	−4.20790e13	−1.71432	−0.857160	−	0.515050i	$-0.827773\pi$
$61$	−4.20790e13	−1.71432	−0.857160	+	0.515050i	$0.827773\pi$
$62$	2.65812e13	0.958601
$63$	3.24711e13	1.03859
$64$	1.47090e13	0.418054
$65$	4.98620e11	0.0126159
$66$	8.22970e12	0.185697
$67$	3.64110e13	0.733958	0.366979	−	0.930229i	$-0.380392\pi$
$67$	3.64110e13	0.733958	0.366979	+	0.930229i	$0.380392\pi$
$68$	2.02312e13	0.364927
$69$	6.35404e13	1.02726
$70$	4.42757e12	0.0642585
$71$	7.05417e13	0.920468	0.460234	−	0.887798i	$-0.347766\pi$
$71$	7.05417e13	0.920468	0.460234	+	0.887798i	$0.347766\pi$
$72$	−5.13163e13	−0.602923
$73$	−1.43595e14	−1.52131	−0.760654	−	0.649157i	$-0.775122\pi$
$73$	−1.43595e14	−1.52131	−0.760654	+	0.649157i	$0.775122\pi$
$74$	−8.46857e13	−0.810162
$75$	−6.91124e13	−0.597856
$76$	3.27971e13	0.256882
$77$	1.26494e14	0.898235
$78$	−9.30340e12	−0.0599698
$79$	−2.35839e14	−1.38170	−0.690848	−	0.723000i	$-0.742763\pi$
$79$	−2.35839e14	−1.38170	−0.690848	+	0.723000i	$0.742763\pi$
$80$	2.11551e12	0.0112782
$81$	9.72867e12	0.0472515
$82$	−1.76734e14	−0.782917
$83$	3.48349e14	1.40906	0.704529	−	0.709675i	$-0.251158\pi$
$83$	3.48349e14	1.40906	0.704529	+	0.709675i	$0.251158\pi$
$84$	1.81526e14	0.671187
$85$	−1.10944e13	−0.0375370
$86$	−3.89515e13	−0.120722
$87$	−3.92615e13	−0.111577
$88$	−1.99908e14	−0.521446
$89$	1.92866e14	0.462202	0.231101	−	0.972930i	$-0.425767\pi$
$89$	1.92866e14	0.462202	0.231101	+	0.972930i	$0.425767\pi$
$90$	1.14622e13	0.0252609
$91$	−1.42997e14	−0.290080
$92$	−6.28677e14	−1.17495
$93$	−5.97623e14	−1.02992
$94$	−4.20847e14	−0.669368
$95$	−1.79852e13	−0.0264233
$96$	−4.56906e14	−0.620573
$97$	2.89831e14	0.364214	0.182107	−	0.983279i	$-0.441708\pi$
$97$	2.89831e14	0.364214	0.182107	+	0.983279i	$0.441708\pi$
$98$	−7.89150e14	−0.918256
$99$	3.27470e14	0.353108
$100$	6.83807e14	0.683807
$101$	−4.44543e14	−0.412576	−0.206288	−	0.978491i	$-0.566138\pi$
$101$	−4.44543e14	−0.412576	−0.206288	+	0.978491i	$0.566138\pi$
$102$	2.07002e14	0.178432
$103$	5.99837e14	0.480567	0.240283	−	0.970703i	$-0.422760\pi$
$103$	5.99837e14	0.480567	0.240283	+	0.970703i	$0.422760\pi$
$104$	2.25989e14	0.168398
$105$	−9.95446e13	−0.0690395
$106$	−1.41210e15	−0.912162
$107$	−2.70993e15	−1.63147	−0.815736	−	0.578424i	$-0.803668\pi$
$107$	−2.70993e15	−1.63147	−0.815736	+	0.578424i	$0.803668\pi$
$108$	1.20540e15	0.676787
$109$	1.02684e15	0.538029	0.269014	−	0.963136i	$-0.413302\pi$
$109$	1.02684e15	0.538029	0.269014	+	0.963136i	$0.413302\pi$
$110$	4.46520e13	0.0218472
$111$	1.90398e15	0.870441
$112$	−6.06701e14	−0.259322
$113$	−2.39668e15	−0.958343	−0.479172	−	0.877721i	$-0.659063\pi$
$113$	−2.39668e15	−0.958343	−0.479172	+	0.877721i	$0.659063\pi$
$114$	3.35573e14	0.125603
$115$	3.44752e14	0.120857
$116$	3.88459e14	0.127618
$117$	−3.70194e14	−0.114034
$118$	−2.33746e15	−0.675505
$119$	3.18171e15	0.863095
$120$	1.57317e14	0.0400790
$121$	−2.90156e15	−0.694609
$122$	4.25986e15	0.958730
$123$	3.97349e15	0.841169
$124$	5.91297e15	1.17799
$125$	−7.51852e14	−0.141029
$126$	−3.28720e15	−0.580827
$127$	9.65707e15	1.60812	0.804058	−	0.594551i	$-0.202670\pi$
$127$	9.65707e15	1.60812	0.804058	+	0.594551i	$0.202670\pi$
$128$	5.08896e15	0.799014
$129$	8.75742e14	0.129704
$130$	−5.04777e13	−0.00705544
$131$	7.88936e14	0.104114	0.0520568	−	0.998644i	$-0.483422\pi$
$131$	7.88936e14	0.104114	0.0520568	+	0.998644i	$0.483422\pi$
$132$	1.83069e15	0.228197
$133$	5.15790e15	0.607555
$134$	−3.68605e15	−0.410465
$135$	−6.61013e14	−0.0696156
$136$	−5.02828e15	−0.501046
$137$	6.39737e15	0.603388	0.301694	−	0.953405i	$-0.402448\pi$
$137$	6.39737e15	0.603388	0.301694	+	0.953405i	$0.402448\pi$
$138$	−6.43249e15	−0.574495
$139$	1.42045e15	0.120175	0.0600875	−	0.998193i	$-0.480862\pi$
$139$	1.42045e15	0.120175	0.0600875	+	0.998193i	$0.480862\pi$
$140$	9.84908e14	0.0789651
$141$	9.46184e15	0.719171
$142$	−7.14127e15	−0.514770
$143$	−1.44213e15	−0.0986243
$144$	−1.57064e15	−0.101943
$145$	−2.13022e14	−0.0131270
$146$	1.45368e16	0.850789
$147$	1.77424e16	0.986578
$148$	−1.88382e16	−0.995582
$149$	7.53260e15	0.378484	0.189242	−	0.981930i	$-0.439397\pi$
$149$	7.53260e15	0.378484	0.189242	+	0.981930i	$0.439397\pi$
$150$	6.99657e15	0.334350
$151$	−3.76018e16	−1.70955	−0.854774	−	0.519000i	$-0.826304\pi$
$151$	−3.76018e16	−1.70955	−0.854774	+	0.519000i	$0.826304\pi$
$152$	−8.15141e15	−0.352700
$153$	8.23687e15	0.339294
$154$	−1.28056e16	−0.502336
$155$	−3.24253e15	−0.121171
$156$	−2.06953e15	−0.0736949
$157$	−9.38127e15	−0.318430	−0.159215	−	0.987244i	$-0.550896\pi$
$157$	−9.38127e15	−0.318430	−0.159215	+	0.987244i	$0.550896\pi$
$158$	2.38751e16	0.772711
$159$	3.17481e16	0.980031
$160$	−2.47904e15	−0.0730103
$161$	−9.88703e16	−2.77889
$162$	−9.84879e14	−0.0264253
$163$	3.30076e15	0.0845681	0.0422841	−	0.999106i	$-0.486537\pi$
$163$	3.30076e15	0.0845681	0.0422841	+	0.999106i	$0.486537\pi$
$164$	−3.93142e16	−0.962101
$165$	−1.00391e15	−0.0234727
$166$	−3.52650e16	−0.788013
$167$	1.90311e16	0.406528	0.203264	−	0.979124i	$-0.434845\pi$
$167$	1.90311e16	0.406528	0.203264	+	0.979124i	$0.434845\pi$
$168$	−4.51165e16	−0.921543
$169$	−4.95556e16	−0.968150
$170$	1.12313e15	0.0209925
$171$	1.33529e16	0.238838
$172$	−8.66471e15	−0.148351
$173$	6.36420e15	0.104327	0.0521636	−	0.998639i	$-0.483388\pi$
$173$	6.36420e15	0.104327	0.0521636	+	0.998639i	$0.483388\pi$
$174$	3.97463e15	0.0623990
$175$	1.07540e17	1.61728
$176$	−6.11857e15	−0.0881668
$177$	5.25528e16	0.725765
$178$	−1.95248e16	−0.258485
$179$	−4.41723e16	−0.560729	−0.280364	−	0.959894i	$-0.590455\pi$
$179$	−4.41723e16	−0.560729	−0.280364	+	0.959894i	$0.590455\pi$
$180$	2.54975e15	0.0310423
$181$	1.49904e16	0.175075	0.0875373	−	0.996161i	$-0.472100\pi$
$181$	1.49904e16	0.175075	0.0875373	+	0.996161i	$0.472100\pi$
$182$	1.44763e16	0.162227
$183$	−9.57739e16	−1.03006
$184$	1.56252e17	1.61321
$185$	1.03304e16	0.102407
$186$	6.05002e16	0.575983
$187$	3.20875e16	0.293443
$188$	−9.36168e16	−0.822564
$189$	1.89570e17	1.60068
$190$	1.82072e15	0.0147772
$191$	−1.00027e17	−0.780491	−0.390245	−	0.920711i	$-0.627610\pi$
$191$	−1.00027e17	−0.780491	−0.390245	+	0.920711i	$0.627610\pi$
$192$	3.34783e16	0.251191
$193$	−2.32499e17	−1.67781	−0.838904	−	0.544280i	$-0.816803\pi$
$193$	−2.32499e17	−1.67781	−0.838904	+	0.544280i	$0.816803\pi$
$194$	−2.93410e16	−0.203686
$195$	1.13488e15	0.00758039
$196$	−1.75545e17	−1.12841
$197$	2.72207e17	1.68423	0.842117	−	0.539295i	$-0.181309\pi$
$197$	2.72207e17	1.68423	0.842117	+	0.539295i	$0.181309\pi$
$198$	−3.31514e16	−0.197475
$199$	1.00106e17	0.574199	0.287099	−	0.957901i	$-0.407309\pi$
$199$	1.00106e17	0.574199	0.287099	+	0.957901i	$0.407309\pi$
$200$	−1.69954e17	−0.938871
$201$	8.28731e16	0.441005
$202$	4.50032e16	0.230732
$203$	6.10919e16	0.301830
$204$	4.60473e16	0.219269
$205$	2.15590e16	0.0989635
$206$	−6.07243e16	−0.268756
$207$	−2.55957e17	−1.09242
$208$	6.91684e15	0.0284730
$209$	5.20174e16	0.206563
$210$	1.00774e16	0.0386102
$211$	4.02935e17	1.48976	0.744880	−	0.667198i	$-0.232507\pi$
$211$	4.02935e17	1.48976	0.744880	+	0.667198i	$0.232507\pi$
$212$	−3.14120e17	−1.12093
$213$	1.60556e17	0.553071
$214$	2.74339e17	0.912397
$215$	4.75153e15	0.0152597
$216$	−2.99590e17	−0.929233
$217$	9.29915e17	2.78609
$218$	−1.03952e17	−0.300892
$219$	−3.26829e17	−0.914090
$220$	9.93279e15	0.0268473
$221$	−3.62739e16	−0.0947659
$222$	−1.92749e17	−0.486793
$223$	2.13538e16	0.0521421	0.0260710	−	0.999660i	$-0.491700\pi$
$223$	2.13538e16	0.0521421	0.0260710	+	0.999660i	$0.491700\pi$
$224$	7.10956e17	1.67874
$225$	2.78403e17	0.635776
$226$	2.42627e17	0.535952
$227$	−7.80710e17	−1.66838	−0.834192	−	0.551475i	$-0.814065\pi$
$227$	−7.80710e17	−1.66838	−0.834192	+	0.551475i	$0.814065\pi$
$228$	7.46477e16	0.154350
$229$	9.68880e16	0.193867	0.0969335	−	0.995291i	$-0.469097\pi$
$229$	9.68880e16	0.193867	0.0969335	+	0.995291i	$0.469097\pi$
$230$	−3.49009e16	−0.0675893
$231$	2.87907e17	0.539712
$232$	−9.65479e16	−0.175220
$233$	5.83094e17	1.02463	0.512317	−	0.858796i	$-0.328787\pi$
$233$	5.83094e17	1.02463	0.512317	+	0.858796i	$0.328787\pi$
$234$	3.74765e16	0.0637735
$235$	5.13373e16	0.0846105
$236$	−5.19965e17	−0.830106
$237$	−5.36781e17	−0.830204
$238$	−3.22099e17	−0.482684
$239$	1.88079e16	0.0273122	0.0136561	−	0.999907i	$-0.495653\pi$
$239$	1.88079e16	0.0273122	0.0136561	+	0.999907i	$0.495653\pi$
$240$	4.81501e15	0.00677661
$241$	−6.17405e17	−0.842252	−0.421126	−	0.907002i	$-0.638365\pi$
$241$	−6.17405e17	−0.842252	−0.421126	+	0.907002i	$0.638365\pi$
$242$	2.93738e17	0.388459
$243$	7.90194e17	1.01318
$244$	9.47600e17	1.17815
$245$	9.62651e16	0.116071
$246$	−4.02255e17	−0.470422
$247$	−5.88040e16	−0.0667083
$248$	−1.46961e18	−1.61739
$249$	7.92859e17	0.846644
$250$	7.61135e16	0.0788700
$251$	−7.67568e17	−0.771905	−0.385952	−	0.922519i	$-0.626127\pi$
$251$	−7.67568e17	−0.771905	−0.385952	+	0.922519i	$0.626127\pi$
$252$	−7.31233e17	−0.713759
$253$	−9.97106e17	−0.944795
$254$	−9.77630e17	−0.899336
$255$	−2.52513e16	−0.0225544
$256$	−9.97164e17	−0.864902
$257$	4.60195e17	0.387653	0.193827	−	0.981036i	$-0.437910\pi$
$257$	4.60195e17	0.387653	0.193827	+	0.981036i	$0.437910\pi$
$258$	−8.86555e16	−0.0725367
$259$	−2.96263e18	−2.35467
$260$	−1.12287e16	−0.00867020
$261$	1.58156e17	0.118654
$262$	−7.98677e16	−0.0582253
$263$	1.65032e18	1.16923	0.584617	−	0.811310i	$-0.301245\pi$
$263$	1.65032e18	1.16923	0.584617	+	0.811310i	$0.301245\pi$
$264$	−4.55000e17	−0.313315
$265$	1.72256e17	0.115301
$266$	−5.22159e17	−0.339774
$267$	4.38973e17	0.277718
$268$	−8.19958e17	−0.504407
$269$	3.73117e17	0.223205	0.111602	−	0.993753i	$-0.464402\pi$
$269$	3.73117e17	0.223205	0.111602	+	0.993753i	$0.464402\pi$
$270$	6.69174e16	0.0389324
$271$	2.61251e18	1.47839	0.739195	−	0.673491i	$-0.235206\pi$
$271$	2.61251e18	1.47839	0.739195	+	0.673491i	$0.235206\pi$
$272$	−1.53901e17	−0.0847175
$273$	−3.25469e17	−0.174297
$274$	−6.47636e17	−0.337444
$275$	1.08454e18	0.549860
$276$	−1.43090e18	−0.705978
$277$	1.75080e18	0.840695	0.420348	−	0.907363i	$-0.361908\pi$
$277$	1.75080e18	0.840695	0.420348	+	0.907363i	$0.361908\pi$
$278$	−1.43799e17	−0.0672076
$279$	2.40738e18	1.09525
$280$	−2.44790e17	−0.108420
$281$	1.26881e18	0.547141	0.273570	−	0.961852i	$-0.411795\pi$
$281$	1.26881e18	0.547141	0.273570	+	0.961852i	$0.411795\pi$
$282$	−9.57867e17	−0.402195
$283$	2.13849e18	0.874397	0.437198	−	0.899365i	$-0.355971\pi$
$283$	2.13849e18	0.874397	0.437198	+	0.899365i	$0.355971\pi$
$284$	−1.58857e18	−0.632584
$285$	−4.09351e16	−0.0158767
$286$	1.45993e17	0.0551554
$287$	−6.18284e18	−2.27548
$288$	1.84054e18	0.659934
$289$	−2.05533e18	−0.718037
$290$	2.15652e16	0.00734124
$291$	6.59669e17	0.218841
$292$	3.23369e18	1.04551
$293$	−8.35652e17	−0.263341	−0.131670	−	0.991294i	$-0.542034\pi$
$293$	−8.35652e17	−0.263341	−0.131670	+	0.991294i	$0.542034\pi$
$294$	−1.79614e18	−0.551742
$295$	2.85137e17	0.0853863
$296$	4.68206e18	1.36694
$297$	1.91181e18	0.544215
$298$	−7.62560e17	−0.211667
$299$	1.12720e18	0.305116
$300$	1.55638e18	0.410871
$301$	−1.36267e18	−0.350868
$302$	3.80661e18	0.956061
$303$	−1.01180e18	−0.247899
$304$	−2.49490e17	−0.0596350
$305$	−5.19642e17	−0.121187
$306$	−8.33857e17	−0.189750
$307$	1.97584e18	0.438748	0.219374	−	0.975641i	$-0.429599\pi$
$307$	1.97584e18	0.438748	0.219374	+	0.975641i	$0.429599\pi$
$308$	−2.84859e18	−0.617305
$309$	1.36526e18	0.288753
$310$	3.28257e17	0.0677644
$311$	3.09600e18	0.623875	0.311937	−	0.950103i	$-0.399022\pi$
$311$	3.09600e18	0.623875	0.311937	+	0.950103i	$0.399022\pi$
$312$	5.14362e17	0.101183
$313$	6.02241e18	1.15661	0.578306	−	0.815820i	$-0.303714\pi$
$313$	6.02241e18	1.15661	0.578306	+	0.815820i	$0.303714\pi$
$314$	9.49710e17	0.178081
$315$	4.00991e17	0.0734186
$316$	5.31099e18	0.949560
$317$	2.67262e18	0.466651	0.233326	−	0.972399i	$-0.425039\pi$
$317$	2.67262e18	0.466651	0.233326	+	0.972399i	$0.425039\pi$
$318$	−3.21401e18	−0.548080
$319$	6.16111e17	0.102619
$320$	1.81644e17	0.0295527
$321$	−6.16793e18	−0.980283
$322$	1.00091e19	1.55409
$323$	1.30840e18	0.198482
$324$	−2.19085e17	−0.0324732
$325$	−1.22604e18	−0.177574
$326$	−3.34151e17	−0.0472945
$327$	2.33714e18	0.323279
$328$	9.77118e18	1.32097
$329$	−1.47228e19	−1.94546
$330$	1.01630e17	0.0131271
$331$	−6.87944e18	−0.868646	−0.434323	−	0.900757i	$-0.643012\pi$
$331$	−6.87944e18	−0.868646	−0.434323	+	0.900757i	$0.643012\pi$
$332$	−7.84466e18	−0.968363
$333$	−7.66972e18	−0.925652
$334$	−1.92661e18	−0.227350
$335$	4.49646e17	0.0518842
$336$	−1.38088e18	−0.155816
$337$	7.90717e17	0.0872563	0.0436281	−	0.999048i	$-0.486108\pi$
$337$	7.90717e17	0.0872563	0.0436281	+	0.999048i	$0.486108\pi$
$338$	5.01675e18	0.541436
$339$	−5.45495e18	−0.575828
$340$	2.49840e17	0.0257970
$341$	9.37819e18	0.947243
$342$	−1.35177e18	−0.133570
$343$	−1.07936e19	−1.04343
$344$	2.15353e18	0.203687
$345$	7.84673e17	0.0726182
$346$	−6.44278e17	−0.0583448
$347$	−1.17729e19	−1.04331	−0.521654	−	0.853157i	$-0.674685\pi$
$347$	−1.17729e19	−1.04331	−0.521654	+	0.853157i	$0.674685\pi$
$348$	8.84152e17	0.0766801
$349$	−1.52602e19	−1.29530	−0.647651	−	0.761937i	$-0.724248\pi$
$349$	−1.52602e19	−1.29530	−0.647651	+	0.761937i	$0.724248\pi$
$350$	−1.08868e19	−0.904463
$351$	−2.16124e18	−0.175751
$352$	7.16999e18	0.570754
$353$	1.93141e19	1.50510	0.752548	−	0.658538i	$-0.228825\pi$
$353$	1.93141e19	1.50510	0.752548	+	0.658538i	$0.228825\pi$
$354$	−5.32017e18	−0.405883
$355$	8.71134e17	0.0650687
$356$	−4.34326e18	−0.317644
$357$	7.24172e18	0.518597
$358$	4.47177e18	0.313586
$359$	−1.20952e19	−0.830621	−0.415311	−	0.909680i	$-0.636327\pi$
$359$	−1.20952e19	−0.830621	−0.415311	+	0.909680i	$0.636327\pi$
$360$	−6.33716e17	−0.0426212
$361$	−1.30601e19	−0.860284
$362$	−1.51755e18	−0.0979101
$363$	−6.60408e18	−0.417362
$364$	3.22024e18	0.199355
$365$	−1.77328e18	−0.107543
$366$	9.69564e18	0.576061
$367$	2.02873e19	1.18094	0.590472	−	0.807058i	$-0.298941\pi$
$367$	2.02873e19	1.18094	0.590472	+	0.807058i	$0.298941\pi$
$368$	4.78239e18	0.272764
$369$	−1.60062e19	−0.894523
$370$	−1.04580e18	−0.0572711
$371$	−4.94008e19	−2.65112
$372$	1.34582e19	0.707807
$373$	2.97839e17	0.0153520	0.00767601	−	0.999971i	$-0.497557\pi$
$373$	2.97839e17	0.0153520	0.00767601	+	0.999971i	$0.497557\pi$
$374$	−3.24837e18	−0.164108
$375$	−1.71125e18	−0.0847382
$376$	2.32676e19	1.12939
$377$	−6.96493e17	−0.0331403
$378$	−1.91910e19	−0.895178
$379$	−3.21179e18	−0.146877	−0.0734383	−	0.997300i	$-0.523397\pi$
$379$	−3.21179e18	−0.146877	−0.0734383	+	0.997300i	$0.523397\pi$
$380$	4.05018e17	0.0181592
$381$	2.19799e19	0.966249
$382$	1.01262e19	0.436488
$383$	5.68072e18	0.240111	0.120056	−	0.992767i	$-0.461693\pi$
$383$	5.68072e18	0.240111	0.120056	+	0.992767i	$0.461693\pi$
$384$	1.15827e19	0.480094
$385$	1.56210e18	0.0634971
$386$	2.35370e19	0.938310
$387$	−3.52772e18	−0.137931
$388$	−6.52686e18	−0.250303
$389$	1.56159e19	0.587414	0.293707	−	0.955895i	$-0.405111\pi$
$389$	1.56159e19	0.587414	0.293707	+	0.955895i	$0.405111\pi$
$390$	−1.14890e17	−0.00423932
$391$	−2.50802e19	−0.907833
$392$	4.36301e19	1.54932
$393$	1.79566e18	0.0625574
$394$	−2.75568e19	−0.941905
$395$	−2.91242e18	−0.0976734
$396$	−7.37448e18	−0.242671
$397$	4.00736e19	1.29399	0.646993	−	0.762496i	$-0.276026\pi$
$397$	4.00736e19	1.29399	0.646993	+	0.762496i	$0.276026\pi$
$398$	−1.01342e19	−0.321120
$399$	1.17396e19	0.365055
$400$	−5.20177e18	−0.158745
$401$	1.91888e19	0.574732	0.287366	−	0.957821i	$-0.407220\pi$
$401$	1.91888e19	0.574732	0.287366	+	0.957821i	$0.407220\pi$
$402$	−8.38964e18	−0.246631
$403$	−1.06017e19	−0.305907
$404$	1.00109e19	0.283539
$405$	1.20141e17	0.00334025
$406$	−6.18462e18	−0.168798
$407$	−2.98781e19	−0.800563
$408$	−1.14446e19	−0.301058
$409$	5.50762e19	1.42246	0.711229	−	0.702961i	$-0.248139\pi$
$409$	5.50762e19	1.42246	0.711229	+	0.702961i	$0.248139\pi$
$410$	−2.18252e18	−0.0553451
$411$	1.45607e19	0.362551
$412$	−1.35080e19	−0.330266
$413$	−8.17733e19	−1.96330
$414$	2.59117e19	0.610934
$415$	4.30183e18	0.0996076
$416$	−8.10544e18	−0.184322
$417$	3.23301e18	0.0722081
$418$	−5.26597e18	−0.115520
$419$	7.09771e19	1.52937	0.764686	−	0.644404i	$-0.222894\pi$
$419$	7.09771e19	1.52937	0.764686	+	0.644404i	$0.222894\pi$
$420$	2.24170e18	0.0474468
$421$	−7.26651e19	−1.51081	−0.755405	−	0.655258i	$-0.772560\pi$
$421$	−7.26651e19	−1.51081	−0.755405	+	0.655258i	$0.772560\pi$
$422$	−4.07910e19	−0.833145
$423$	−3.81148e19	−0.764787
$424$	7.80716e19	1.53904
$425$	2.72796e19	0.528349
$426$	−1.62539e19	−0.309304
$427$	1.49026e20	2.78647
$428$	6.10263e19	1.12122
$429$	−3.28235e18	−0.0592592
$430$	−4.81020e17	−0.00853394
$431$	4.14112e19	0.722001	0.361001	−	0.932566i	$-0.382435\pi$
$431$	4.14112e19	0.722001	0.361001	+	0.932566i	$0.382435\pi$
$432$	−9.16955e18	−0.157116
$433$	7.34233e19	1.23644	0.618222	−	0.786004i	$-0.287853\pi$
$433$	7.34233e19	1.23644	0.618222	+	0.786004i	$0.287853\pi$
$434$	−9.41397e19	−1.55812
$435$	−4.84849e17	−0.00788745
$436$	−2.31240e19	−0.369756
$437$	−4.06578e19	−0.639048
$438$	3.30864e19	0.511203
$439$	−4.98444e18	−0.0757064	−0.0378532	−	0.999283i	$-0.512052\pi$
$439$	−4.98444e18	−0.0757064	−0.0378532	+	0.999283i	$0.512052\pi$
$440$	−2.46870e18	−0.0368615
$441$	−7.14708e19	−1.04915
$442$	3.67218e18	0.0529976
$443$	−3.06774e19	−0.435302	−0.217651	−	0.976027i	$-0.569839\pi$
$443$	−3.06774e19	−0.435302	−0.217651	+	0.976027i	$0.569839\pi$
$444$	−4.28767e19	−0.598203
$445$	2.38174e18	0.0326735
$446$	−2.16174e18	−0.0291604
$447$	1.71446e19	0.227415
$448$	−5.20931e19	−0.679509
$449$	6.10487e19	0.783121	0.391560	−	0.920152i	$-0.371935\pi$
$449$	6.10487e19	0.783121	0.391560	+	0.920152i	$0.371935\pi$
$450$	−2.81840e19	−0.355557
$451$	−6.23539e19	−0.773641
$452$	5.39720e19	0.658613
$453$	−8.55835e19	−1.02720
$454$	7.90349e19	0.933040
$455$	−1.76590e18	−0.0205060
$456$	−1.85530e19	−0.211923
$457$	4.23802e19	0.476202	0.238101	−	0.971240i	$-0.423475\pi$
$457$	4.23802e19	0.476202	0.238101	+	0.971240i	$0.423475\pi$
$458$	−9.80843e18	−0.108420
$459$	4.80877e19	0.522925
$460$	−7.76366e18	−0.0830583
$461$	−9.41450e19	−0.990924	−0.495462	−	0.868630i	$-0.665001\pi$
$461$	−9.41450e19	−0.990924	−0.495462	+	0.868630i	$0.665001\pi$
$462$	−2.91462e19	−0.301833
$463$	1.29135e20	1.31579	0.657896	−	0.753109i	$-0.271447\pi$
$463$	1.29135e20	1.31579	0.657896	+	0.753109i	$0.271447\pi$
$464$	−2.95504e18	−0.0296263
$465$	−7.38016e18	−0.0728063
$466$	−5.90293e19	−0.573025
$467$	2.85132e19	0.272376	0.136188	−	0.990683i	$-0.456515\pi$
$467$	2.85132e19	0.272376	0.136188	+	0.990683i	$0.456515\pi$
$468$	8.33661e18	0.0783692
$469$	−1.28952e20	−1.19298
$470$	−5.19712e18	−0.0473182
$471$	−2.13522e19	−0.191331
$472$	1.29232e20	1.13974
$473$	−1.37426e19	−0.119291
$474$	5.43409e19	0.464290
$475$	4.42232e19	0.371919
$476$	−7.16506e19	−0.593154
$477$	−1.27890e20	−1.04219
$478$	−1.90401e18	−0.0152743
$479$	1.47492e20	1.16480	0.582402	−	0.812901i	$-0.302113\pi$
$479$	1.47492e20	1.16480	0.582402	+	0.812901i	$0.302113\pi$
$480$	−5.64242e18	−0.0438689
$481$	3.37762e19	0.258537
$482$	6.25028e19	0.471028
$483$	−2.25033e20	−1.66972
$484$	6.53417e19	0.477364
$485$	3.57918e18	0.0257466
$486$	−7.99950e19	−0.566619
$487$	−1.32888e20	−0.926871	−0.463436	−	0.886131i	$-0.653383\pi$
$487$	−1.32888e20	−0.926871	−0.463436	+	0.886131i	$0.653383\pi$
$488$	−2.35517e20	−1.61761
$489$	7.51268e18	0.0508134
$490$	−9.74537e18	−0.0649124
$491$	−1.06208e20	−0.696703	−0.348351	−	0.937364i	$-0.613258\pi$
$491$	−1.06208e20	−0.696703	−0.348351	+	0.937364i	$0.613258\pi$
$492$	−8.94810e19	−0.578086
$493$	1.54971e19	0.0986046
$494$	5.95300e18	0.0373065
$495$	4.04400e18	0.0249616
$496$	−4.49804e19	−0.273470
$497$	−2.49829e20	−1.49613
$498$	−8.02648e19	−0.473484
$499$	1.30739e20	0.759714	0.379857	−	0.925045i	$-0.375973\pi$
$499$	1.30739e20	0.759714	0.379857	+	0.925045i	$0.375973\pi$
$500$	1.69314e19	0.0969207
$501$	4.33157e19	0.244265
$502$	7.77045e19	0.431686
$503$	7.31918e19	0.400592	0.200296	−	0.979735i	$-0.435810\pi$
$503$	7.31918e19	0.400592	0.200296	+	0.979735i	$0.435810\pi$
$504$	1.81741e20	0.979995
$505$	−5.48975e18	−0.0291654
$506$	1.00942e20	0.528375
$507$	−1.12791e20	−0.581721
$508$	−2.17473e20	−1.10516
$509$	−2.53305e20	−1.26841	−0.634205	−	0.773165i	$-0.718673\pi$
$509$	−2.53305e20	−1.26841	−0.634205	+	0.773165i	$0.718673\pi$
$510$	2.55631e18	0.0126135
$511$	5.08553e20	2.47274
$512$	−6.58076e19	−0.315320
$513$	7.79555e19	0.368101
$514$	−4.65877e19	−0.216794
$515$	7.40750e18	0.0339717
$516$	−1.97213e19	−0.0891380
$517$	−1.48480e20	−0.661437
$518$	2.99921e20	1.31684
$519$	1.44852e19	0.0626859
$520$	2.79079e18	0.0119042
$521$	2.12161e20	0.892039	0.446019	−	0.895023i	$-0.352841\pi$
$521$	2.12161e20	0.892039	0.446019	+	0.895023i	$0.352841\pi$
$522$	−1.60108e19	−0.0663568
$523$	4.74586e20	1.93889	0.969443	−	0.245319i	$-0.0788926\pi$
$523$	4.74586e20	1.93889	0.969443	+	0.245319i	$0.0788926\pi$
$524$	−1.77665e19	−0.0715511
$525$	2.44767e20	0.971759
$526$	−1.67070e20	−0.653892
$527$	2.35890e20	0.910185
$528$	−1.39262e19	−0.0529757
$529$	5.12722e20	1.92293
$530$	−1.74383e19	−0.0644816
$531$	−2.11696e20	−0.771799
$532$	−1.16154e20	−0.417537
$533$	7.04890e19	0.249843
$534$	−4.44393e19	−0.155313
$535$	−3.34655e19	−0.115330
$536$	2.03793e20	0.692553
$537$	−1.00538e20	−0.336918
$538$	−3.77724e19	−0.124827
$539$	−2.78422e20	−0.907376
$540$	1.48857e19	0.0478427
$541$	−2.32906e20	−0.738246	−0.369123	−	0.929380i	$-0.620342\pi$
$541$	−2.32906e20	−0.738246	−0.369123	+	0.929380i	$0.620342\pi$
$542$	−2.64477e20	−0.826787
$543$	3.41188e19	0.105195
$544$	1.80347e20	0.548425
$545$	1.26807e19	0.0380338
$546$	3.29488e19	0.0974752
$547$	2.77958e20	0.811101	0.405550	−	0.914073i	$-0.367080\pi$
$547$	2.77958e20	0.811101	0.405550	+	0.914073i	$0.367080\pi$
$548$	−1.44066e20	−0.414674
$549$	3.85802e20	1.09540
$550$	−1.09794e20	−0.307508
$551$	2.51224e19	0.0694104
$552$	3.55637e20	0.969311
$553$	8.35244e20	2.24582
$554$	−1.77242e20	−0.470157
$555$	2.35126e19	0.0615323
$556$	−3.19878e19	−0.0825893
$557$	4.31286e20	1.09863	0.549314	−	0.835616i	$-0.314889\pi$
$557$	4.31286e20	1.09863	0.549314	+	0.835616i	$0.314889\pi$
$558$	−2.43711e20	−0.612516
$559$	1.55355e19	0.0385245
$560$	−7.49227e18	−0.0183317
$561$	7.30327e19	0.176318
$562$	−1.28448e20	−0.305988
$563$	−2.05494e20	−0.483045	−0.241522	−	0.970395i	$-0.577647\pi$
$563$	−2.05494e20	−0.483045	−0.241522	+	0.970395i	$0.577647\pi$
$564$	−2.13076e20	−0.494245
$565$	−2.95970e19	−0.0677462
$566$	−2.16489e20	−0.489005
$567$	−3.44549e19	−0.0768029
$568$	3.94823e20	0.868541
$569$	−4.19495e20	−0.910720	−0.455360	−	0.890307i	$-0.650489\pi$
$569$	−4.19495e20	−0.910720	−0.455360	+	0.890307i	$0.650489\pi$
$570$	4.14405e18	0.00887900
$571$	6.19134e20	1.30922	0.654612	−	0.755965i	$-0.272832\pi$
$571$	6.19134e20	1.30922	0.654612	+	0.755965i	$0.272832\pi$
$572$	3.24761e19	0.0677787
$573$	−2.27667e20	−0.468964
$574$	6.25918e20	1.27256
$575$	−8.47701e20	−1.70112
$576$	−1.34860e20	−0.267124
$577$	−8.26848e20	−1.61662	−0.808308	−	0.588759i	$-0.799617\pi$
$577$	−8.26848e20	−1.61662	−0.808308	+	0.588759i	$0.799617\pi$
$578$	2.08070e20	0.401561
$579$	−5.29180e20	−1.00812
$580$	4.79716e18	0.00902141
$581$	−1.23371e21	−2.29029
$582$	−6.67814e19	−0.122386
$583$	−4.98207e20	−0.901355
$584$	−8.03702e20	−1.43549
$585$	−4.57160e18	−0.00806120
$586$	8.45969e19	0.147273
$587$	2.35323e20	0.404462	0.202231	−	0.979338i	$-0.435181\pi$
$587$	2.35323e20	0.404462	0.202231	+	0.979338i	$0.435181\pi$
$588$	−3.99550e20	−0.678017
$589$	3.82403e20	0.640703
$590$	−2.88657e19	−0.0477521
$591$	6.19556e20	1.01199
$592$	1.43304e20	0.231124
$593$	−5.72822e19	−0.0912241	−0.0456121	−	0.998959i	$-0.514524\pi$
$593$	−5.72822e19	−0.0912241	−0.0456121	+	0.998959i	$0.514524\pi$
$594$	−1.93541e20	−0.304351
$595$	3.92916e19	0.0610130
$596$	−1.69631e20	−0.260110
$597$	2.27846e20	0.345012
$598$	−1.14111e20	−0.170636
$599$	5.94122e20	0.877354	0.438677	−	0.898645i	$-0.355447\pi$
$599$	5.94122e20	0.877354	0.438677	+	0.898645i	$0.355447\pi$
$600$	−3.86823e20	−0.564128
$601$	5.56299e19	0.0801216	0.0400608	−	0.999197i	$-0.487245\pi$
$601$	5.56299e19	0.0801216	0.0400608	+	0.999197i	$0.487245\pi$
$602$	1.37950e20	0.196222
$603$	−3.33835e20	−0.468977
$604$	8.46775e20	1.17487
$605$	−3.58319e19	−0.0491026
$606$	1.02429e20	0.138637
$607$	1.54728e20	0.206848	0.103424	−	0.994637i	$-0.467020\pi$
$607$	1.54728e20	0.206848	0.103424	+	0.994637i	$0.467020\pi$
$608$	2.92362e20	0.386051
$609$	1.39048e20	0.181357
$610$	5.26058e19	0.0677735
$611$	1.67852e20	0.213607
$612$	−1.85490e20	−0.233177
$613$	−1.03562e21	−1.28602	−0.643012	−	0.765856i	$-0.722315\pi$
$613$	−1.03562e21	−1.28602	−0.643012	+	0.765856i	$0.722315\pi$
$614$	−2.00024e20	−0.245369
$615$	4.90694e19	0.0594630
$616$	7.07990e20	0.847563
$617$	1.07157e21	1.26731	0.633655	−	0.773616i	$-0.281554\pi$
$617$	1.07157e21	1.26731	0.633655	+	0.773616i	$0.281554\pi$
$618$	−1.38211e20	−0.161484
$619$	1.20552e20	0.139153	0.0695765	−	0.997577i	$-0.477835\pi$
$619$	1.20552e20	0.139153	0.0695765	+	0.997577i	$0.477835\pi$
$620$	7.30204e19	0.0832734
$621$	−1.49431e21	−1.68365
$622$	−3.13422e20	−0.348901
$623$	−6.83052e20	−0.751266
$624$	1.57431e19	0.0171082
$625$	9.17384e20	0.985033
$626$	−6.09677e20	−0.646833
$627$	1.18394e20	0.124115
$628$	2.11262e20	0.218838
$629$	−7.51525e20	−0.769243
$630$	−4.05943e19	−0.0410592
$631$	−3.42875e19	−0.0342701	−0.0171351	−	0.999853i	$-0.505455\pi$
$631$	−3.42875e19	−0.0342701	−0.0171351	+	0.999853i	$0.505455\pi$
$632$	−1.32000e21	−1.30375
$633$	9.17099e20	0.895134
$634$	−2.70562e20	−0.260974
$635$	1.19257e20	0.113679
$636$	−7.14953e20	−0.673518
$637$	3.14747e20	0.293032
$638$	−6.23718e19	−0.0573896
$639$	−6.46763e20	−0.588151
$640$	6.28446e19	0.0564831
$641$	−5.58491e20	−0.496113	−0.248057	−	0.968746i	$-0.579792\pi$
$641$	−5.58491e20	−0.496113	−0.248057	+	0.968746i	$0.579792\pi$
$642$	6.24408e20	0.548221
$643$	−4.28570e20	−0.371911	−0.185956	−	0.982558i	$-0.559538\pi$
$643$	−4.28570e20	−0.371911	−0.185956	+	0.982558i	$0.559538\pi$
$644$	2.22651e21	1.90977
$645$	1.08147e19	0.00916889
$646$	−1.32455e20	−0.111000
$647$	−1.89150e21	−1.56684	−0.783419	−	0.621494i	$-0.786526\pi$
$647$	−1.89150e21	−1.56684	−0.783419	+	0.621494i	$0.786526\pi$
$648$	5.44515e19	0.0445859
$649$	−8.24684e20	−0.667502
$650$	1.24118e20	0.0993081
$651$	2.11653e21	1.67405
$652$	−7.43315e19	−0.0581187
$653$	1.26709e21	0.979394	0.489697	−	0.871893i	$-0.337107\pi$
$653$	1.26709e21	0.979394	0.489697	+	0.871893i	$0.337107\pi$
$654$	−2.36600e20	−0.180793
$655$	9.74273e18	0.00735988
$656$	2.99066e20	0.223351
$657$	1.31655e21	0.972070
$658$	1.49046e21	1.08800
$659$	4.08994e20	0.295173	0.147586	−	0.989049i	$-0.452850\pi$
$659$	4.08994e20	0.295173	0.147586	+	0.989049i	$0.452850\pi$
$660$	2.26075e19	0.0161314
$661$	−1.63413e21	−1.15286	−0.576428	−	0.817148i	$-0.695554\pi$
$661$	−1.63413e21	−1.15286	−0.576428	+	0.817148i	$0.695554\pi$
$662$	6.96438e20	0.485789
$663$	−8.25611e19	−0.0569409
$664$	1.94972e21	1.32957
$665$	6.36960e19	0.0429487
$666$	7.76442e20	0.517669
$667$	−4.81564e20	−0.317476
$668$	−4.28571e20	−0.279383
$669$	4.86022e19	0.0313300
$670$	−4.55198e19	−0.0290161
$671$	1.50293e21	0.947371
$672$	1.61817e21	1.00868
$673$	−7.15650e20	−0.441151	−0.220576	−	0.975370i	$-0.570794\pi$
$673$	−7.15650e20	−0.441151	−0.220576	+	0.975370i	$0.570794\pi$
$674$	−8.00480e19	−0.0487979
$675$	1.62534e21	0.979867
$676$	1.11597e21	0.665353
$677$	−2.40573e21	−1.41851	−0.709255	−	0.704952i	$-0.750968\pi$
$677$	−2.40573e21	−1.41851	−0.709255	+	0.704952i	$0.750968\pi$
$678$	5.52230e20	0.322031
$679$	−1.02646e21	−0.591996
$680$	−6.20953e19	−0.0354194
$681$	−1.77693e21	−1.00246
$682$	−9.49398e20	−0.529743
$683$	4.69312e20	0.259004	0.129502	−	0.991579i	$-0.458662\pi$
$683$	4.69312e20	0.259004	0.129502	+	0.991579i	$0.458662\pi$
$684$	−3.00701e20	−0.164140
$685$	7.90024e19	0.0426541
$686$	1.09269e21	0.583534
$687$	2.20522e20	0.116487
$688$	6.59131e19	0.0344396
$689$	5.63207e20	0.291087
$690$	−7.94361e19	−0.0406116
$691$	5.71662e20	0.289104	0.144552	−	0.989497i	$-0.453826\pi$
$691$	5.71662e20	0.289104	0.144552	+	0.989497i	$0.453826\pi$
$692$	−1.43319e20	−0.0716981
$693$	−1.15976e21	−0.573945
$694$	1.19183e21	0.583468
$695$	1.75414e19	0.00849528
$696$	−2.19748e20	−0.105282
$697$	−1.56839e21	−0.743374
$698$	1.54487e21	0.724395
$699$	1.32715e21	0.615660
$700$	−2.42176e21	−1.11147
$701$	2.14931e21	0.975921	0.487960	−	0.872866i	$-0.337741\pi$
$701$	2.14931e21	0.975921	0.487960	+	0.872866i	$0.337741\pi$
$702$	2.18792e20	0.0982886
$703$	−1.21831e21	−0.541491
$704$	−5.25359e20	−0.231026
$705$	1.16846e20	0.0508389
$706$	−1.95526e21	−0.841722
$707$	1.57439e21	0.670603
$708$	−1.18346e21	−0.498776
$709$	1.66502e21	0.694340	0.347170	−	0.937802i	$-0.387143\pi$
$709$	1.66502e21	0.694340	0.347170	+	0.937802i	$0.387143\pi$
$710$	−8.81890e19	−0.0363896
$711$	2.16229e21	0.882862
$712$	1.07948e21	0.436127
$713$	−7.33017e21	−2.93051
$714$	−7.33114e20	−0.290025
$715$	−1.78091e19	−0.00697184
$716$	9.94741e20	0.385356
$717$	4.28077e19	0.0164107
$718$	1.22445e21	0.464523
$719$	3.47409e21	1.30429	0.652145	−	0.758094i	$-0.273869\pi$
$719$	3.47409e21	1.30429	0.652145	+	0.758094i	$0.273869\pi$
$720$	−1.93961e19	−0.00720644
$721$	−2.12437e21	−0.781117
$722$	1.32213e21	0.481112
$723$	−1.40524e21	−0.506074
$724$	−3.37576e20	−0.120319
$725$	5.23794e20	0.184767
$726$	6.68562e20	0.233409
$727$	−4.80467e21	−1.66018	−0.830090	−	0.557629i	$-0.811711\pi$
$727$	−4.80467e21	−1.66018	−0.830090	+	0.557629i	$0.811711\pi$
$728$	−8.00359e20	−0.273716
$729$	1.65892e21	0.561526
$730$	1.79518e20	0.0601430
$731$	−3.45667e20	−0.114625
$732$	2.15678e21	0.707902
$733$	−2.24746e21	−0.730150	−0.365075	−	0.930978i	$-0.618957\pi$
$733$	−2.24746e21	−0.730150	−0.365075	+	0.930978i	$0.618957\pi$
$734$	−2.05378e21	−0.660441
$735$	2.19104e20	0.0697421
$736$	−5.60420e21	−1.76575
$737$	−1.30049e21	−0.405601
$738$	1.62039e21	0.500260
$739$	−1.08384e21	−0.331232	−0.165616	−	0.986190i	$-0.552961\pi$
$739$	−1.08384e21	−0.331232	−0.165616	+	0.986190i	$0.552961\pi$
$740$	−2.32637e20	−0.0703786
$741$	−1.33841e20	−0.0400822
$742$	5.00108e21	1.48263
$743$	2.54592e21	0.747186	0.373593	−	0.927593i	$-0.378126\pi$
$743$	2.54592e21	0.747186	0.373593	+	0.927593i	$0.378126\pi$
$744$	−3.34491e21	−0.971822
$745$	9.30215e19	0.0267554
$746$	−3.01517e19	−0.00858559
$747$	−3.19384e21	−0.900345
$748$	−7.22596e20	−0.201666
$749$	9.59744e21	2.65181
$750$	1.73238e20	0.0473897
$751$	4.93399e20	0.133628	0.0668142	−	0.997765i	$-0.478717\pi$
$751$	4.93399e20	0.133628	0.0668142	+	0.997765i	$0.478717\pi$
$752$	7.12150e20	0.190958
$753$	−1.74702e21	−0.463805
$754$	7.05093e19	0.0185337
$755$	−4.64352e20	−0.120850
$756$	−4.26902e21	−1.10006
$757$	−3.47424e21	−0.886423	−0.443212	−	0.896417i	$-0.646161\pi$
$757$	−3.47424e21	−0.886423	−0.443212	+	0.896417i	$0.646161\pi$
$758$	3.25144e20	0.0821404
$759$	−2.26946e21	−0.567688
$760$	−1.00663e20	−0.0249327
$761$	3.37203e21	0.827002	0.413501	−	0.910504i	$-0.364306\pi$
$761$	3.37203e21	0.827002	0.413501	+	0.910504i	$0.364306\pi$
$762$	−2.22513e21	−0.540373
$763$	−3.63665e21	−0.874516
$764$	2.25257e21	0.536386
$765$	1.01719e20	0.0239850
$766$	−5.75086e20	−0.134282
$767$	9.32278e20	0.215566
$768$	−2.26959e21	−0.519683
$769$	5.83431e21	1.32295	0.661473	−	0.749969i	$-0.269932\pi$
$769$	5.83431e21	1.32295	0.661473	+	0.749969i	$0.269932\pi$
$770$	−1.58139e20	−0.0355106
$771$	1.04743e21	0.232925
$772$	5.23578e21	1.15306
$773$	−7.43796e21	−1.62221	−0.811106	−	0.584899i	$-0.801134\pi$
$773$	−7.43796e21	−1.62221	−0.811106	+	0.584899i	$0.801134\pi$
$774$	3.57127e20	0.0771375
$775$	7.97297e21	1.70552
$776$	1.62219e21	0.343668
$777$	−6.74309e21	−1.41482
$778$	−1.58087e21	−0.328510
$779$	−2.54253e21	−0.523281
$780$	−2.55570e19	−0.00520956
$781$	−2.51953e21	−0.508670
$782$	2.53899e21	0.507704
$783$	9.23330e20	0.182871
$784$	1.33539e21	0.261961
$785$	−1.15851e20	−0.0225101
$786$	−1.81783e20	−0.0349851
$787$	−7.06696e21	−1.34717	−0.673584	−	0.739110i	$-0.735246\pi$
$787$	−7.06696e21	−1.34717	−0.673584	+	0.739110i	$0.735246\pi$
$788$	−6.12997e21	−1.15748
$789$	3.75622e21	0.702544
$790$	2.94838e20	0.0546237
$791$	8.48803e21	1.55770
$792$	1.83286e21	0.333188
$793$	−1.69901e21	−0.305948
$794$	−4.05684e21	−0.723659
$795$	3.92064e20	0.0692793
$796$	−2.25434e21	−0.394613
$797$	−3.73122e21	−0.647014	−0.323507	−	0.946226i	$-0.604862\pi$
$797$	−3.73122e21	−0.647014	−0.323507	+	0.946226i	$0.604862\pi$
$798$	−1.18846e21	−0.204156
$799$	−3.73472e21	−0.635560
$800$	6.09565e21	1.02765
$801$	−1.76830e21	−0.295333
$802$	−1.94257e21	−0.321418
$803$	5.12875e21	0.840708
$804$	−1.86626e21	−0.303077
$805$	−1.22097e21	−0.196442
$806$	1.07326e21	0.171078
$807$	8.49233e20	0.134114
$808$	−2.48812e21	−0.389301
$809$	−6.43094e21	−0.996920	−0.498460	−	0.866913i	$-0.666101\pi$
$809$	−6.43094e21	−0.996920	−0.498460	+	0.866913i	$0.666101\pi$
$810$	−1.21625e19	−0.00186803
$811$	6.21991e21	0.946516	0.473258	−	0.880924i	$-0.343078\pi$
$811$	6.21991e21	0.946516	0.473258	+	0.880924i	$0.343078\pi$
$812$	−1.37576e21	−0.207430
$813$	5.94621e21	0.888303
$814$	3.02470e21	0.447713
$815$	4.07617e19	0.00597820
$816$	−3.50285e20	−0.0509032
$817$	−5.60364e20	−0.0806873
$818$	−5.57562e21	−0.795506
$819$	1.31107e21	0.185352
$820$	−4.85499e20	−0.0680118
$821$	1.05776e22	1.46830	0.734151	−	0.678986i	$-0.237580\pi$
$821$	1.05776e22	1.46830	0.734151	+	0.678986i	$0.237580\pi$
$822$	−1.47405e21	−0.202756
$823$	1.13709e22	1.54987	0.774934	−	0.632042i	$-0.217783\pi$
$823$	1.13709e22	1.54987	0.774934	+	0.632042i	$0.217783\pi$
$824$	3.35730e21	0.453457
$825$	2.46848e21	0.330388
$826$	8.27830e21	1.09797
$827$	5.96681e21	0.784244	0.392122	−	0.919913i	$-0.371741\pi$
$827$	5.96681e21	0.784244	0.392122	+	0.919913i	$0.371741\pi$
$828$	5.76404e21	0.750757
$829$	−6.39066e21	−0.824872	−0.412436	−	0.910986i	$-0.635322\pi$
$829$	−6.39066e21	−0.824872	−0.412436	+	0.910986i	$0.635322\pi$
$830$	−4.35495e20	−0.0557054
$831$	3.98491e21	0.505139
$832$	5.93900e20	0.0746086
$833$	−7.00314e21	−0.871878
$834$	−3.27292e20	−0.0403823
$835$	2.35019e20	0.0287378
$836$	−1.17141e21	−0.141958
$837$	1.40546e22	1.68801
$838$	−7.18534e21	−0.855298
$839$	−6.70071e20	−0.0790508	−0.0395254	−	0.999219i	$-0.512585\pi$
$839$	−6.70071e20	−0.0790508	−0.0395254	+	0.999219i	$0.512585\pi$
$840$	−5.57153e20	−0.0651448
$841$	2.97558e20	0.0344828
$842$	7.35623e21	0.844918
$843$	2.88787e21	0.328754
$844$	−9.07390e21	−1.02383
$845$	−6.11972e20	−0.0684394
$846$	3.85854e21	0.427706
$847$	1.02761e22	1.12902
$848$	2.38954e21	0.260222
$849$	4.86730e21	0.525388
$850$	−2.76164e21	−0.295478
$851$	2.33533e22	2.47672
$852$	−3.61565e21	−0.380093
$853$	8.72257e21	0.908922	0.454461	−	0.890767i	$-0.349832\pi$
$853$	8.72257e21	0.908922	0.454461	+	0.890767i	$0.349832\pi$
$854$	−1.50866e22	−1.55833
$855$	1.64897e20	0.0168837
$856$	−1.51675e22	−1.53944
$857$	5.97158e21	0.600805	0.300402	−	0.953813i	$-0.402879\pi$
$857$	5.97158e21	0.600805	0.300402	+	0.953813i	$0.402879\pi$
$858$	3.32288e20	0.0331406
$859$	4.69572e21	0.464251	0.232126	−	0.972686i	$-0.425432\pi$
$859$	4.69572e21	0.464251	0.232126	+	0.972686i	$0.425432\pi$
$860$	−1.07002e20	−0.0104871
$861$	−1.40724e22	−1.36724
$862$	−4.19225e21	−0.403778
$863$	−1.81721e22	−1.73510	−0.867551	−	0.497348i	$-0.834307\pi$
$863$	−1.81721e22	−1.73510	−0.867551	+	0.497348i	$0.834307\pi$
$864$	1.07453e22	1.01710
$865$	7.85927e19	0.00737499
$866$	−7.43298e21	−0.691479
$867$	−4.67802e21	−0.431438
$868$	−2.09413e22	−1.91472
$869$	8.42343e21	0.763556
$870$	4.90835e19	0.00441104
$871$	1.47016e21	0.130987
$872$	5.74726e21	0.507677
$873$	−2.65732e21	−0.232722
$874$	4.11598e21	0.357386
$875$	2.66275e21	0.229229
$876$	7.36003e21	0.628201
$877$	−1.90665e22	−1.61352	−0.806758	−	0.590882i	$-0.798780\pi$
$877$	−1.90665e22	−1.61352	−0.806758	+	0.590882i	$0.798780\pi$
$878$	5.04598e20	0.0423386
$879$	−1.90198e21	−0.158230
$880$	−7.55595e19	−0.00623259
$881$	7.45363e21	0.609605	0.304803	−	0.952416i	$-0.401409\pi$
$881$	7.45363e21	0.609605	0.304803	+	0.952416i	$0.401409\pi$
$882$	7.23533e21	0.586738
$883$	−2.03471e21	−0.163605	−0.0818026	−	0.996649i	$-0.526068\pi$
$883$	−2.03471e21	−0.163605	−0.0818026	+	0.996649i	$0.526068\pi$
$884$	8.16871e20	0.0651271
$885$	6.48985e20	0.0513050
$886$	3.10562e21	0.243442
$887$	6.85137e21	0.532538	0.266269	−	0.963899i	$-0.414209\pi$
$887$	6.85137e21	0.532538	0.266269	+	0.963899i	$0.414209\pi$
$888$	1.06566e22	0.821337
$889$	−3.42013e22	−2.61384
$890$	−2.41115e20	−0.0182726
$891$	−3.47477e20	−0.0261122
$892$	−4.80877e20	−0.0358342
$893$	−6.05439e21	−0.447388
$894$	−1.73562e21	−0.127182
$895$	−5.45493e20	−0.0396384
$896$	−1.80230e22	−1.29872
$897$	2.56555e21	0.183332
$898$	−6.18025e21	−0.437959
$899$	4.52931e21	0.318298
$900$	−6.26950e21	−0.436932
$901$	−1.25314e22	−0.866092
$902$	6.31238e21	0.432657
$903$	−3.10151e21	−0.210822
$904$	−1.34142e22	−0.904280
$905$	1.85119e20	0.0123762
$906$	8.66402e21	0.574457
$907$	5.73970e21	0.377428	0.188714	−	0.982032i	$-0.439568\pi$
$907$	5.73970e21	0.377428	0.188714	+	0.982032i	$0.439568\pi$
$908$	1.75812e22	1.14658
$909$	4.07580e21	0.263623
$910$	1.78771e20	0.0114680
$911$	−1.24831e22	−0.794208	−0.397104	−	0.917774i	$-0.629985\pi$
$911$	−1.24831e22	−0.794208	−0.397104	+	0.917774i	$0.629985\pi$
$912$	−5.67851e20	−0.0358322
$913$	−1.24419e22	−0.778676
$914$	−4.29035e21	−0.266315
$915$	−1.18273e21	−0.0728161
$916$	−2.18187e21	−0.133233
$917$	−2.79408e21	−0.169227
$918$	−4.86815e21	−0.292445
$919$	1.87727e22	1.11857	0.559283	−	0.828977i	$-0.311077\pi$
$919$	1.87727e22	1.11857	0.559283	+	0.828977i	$0.311077\pi$
$920$	1.92958e21	0.114039
$921$	4.49712e21	0.263625
$922$	9.53074e21	0.554172
$923$	2.84824e21	0.164272
$924$	−6.48353e21	−0.370913
$925$	−2.54012e22	−1.44142
$926$	−1.30730e22	−0.735854
$927$	−5.49961e21	−0.307068
$928$	3.46283e21	0.191788
$929$	−2.16225e22	−1.18792	−0.593962	−	0.804493i	$-0.702437\pi$
$929$	−2.16225e22	−1.18792	−0.593962	+	0.804493i	$0.702437\pi$
$930$	7.47129e20	0.0407168
$931$	−1.13529e22	−0.613738
$932$	−1.31310e22	−0.704171
$933$	7.04663e21	0.374860
$934$	−2.88652e21	−0.152326
$935$	3.96255e20	0.0207438
$936$	−2.07198e21	−0.107601
$937$	−3.22191e22	−1.65984	−0.829921	−	0.557880i	$-0.811615\pi$
$937$	−3.22191e22	−1.65984	−0.829921	+	0.557880i	$0.811615\pi$
$938$	1.30545e22	0.667172
$939$	1.37073e22	0.694960
$940$	−1.15609e21	−0.0581478
$941$	−4.54403e21	−0.226735	−0.113368	−	0.993553i	$-0.536164\pi$
$941$	−4.54403e21	−0.226735	−0.113368	+	0.993553i	$0.536164\pi$
$942$	2.16158e21	0.107002
$943$	4.87370e22	2.39343
$944$	3.95541e21	0.192709
$945$	2.34103e21	0.113154
$946$	1.39122e21	0.0667135
$947$	1.37329e22	0.653339	0.326669	−	0.945139i	$-0.394074\pi$
$947$	1.37329e22	0.653339	0.326669	+	0.945139i	$0.394074\pi$
$948$	1.20881e22	0.570551
$949$	−5.79789e21	−0.271502
$950$	−4.47692e21	−0.207995
$951$	6.08300e21	0.280391
$952$	1.78081e22	0.814404
$953$	−4.99969e21	−0.226854	−0.113427	−	0.993546i	$-0.536183\pi$
$953$	−4.99969e21	−0.226854	−0.113427	+	0.993546i	$0.536183\pi$
$954$	1.29469e22	0.582844
$955$	−1.23526e21	−0.0551736
$956$	−4.23545e20	−0.0187701
$957$	1.40230e21	0.0616596
$958$	−1.49313e22	−0.651414
$959$	−2.26568e22	−0.980752
$960$	4.13431e20	0.0177570
$961$	4.54780e22	1.93810
$962$	−3.41933e21	−0.144587
$963$	2.48460e22	1.04246
$964$	1.39037e22	0.578831
$965$	−2.87118e21	−0.118606
$966$	2.27812e22	0.933788
$967$	3.30245e22	1.34319	0.671594	−	0.740919i	$-0.265610\pi$
$967$	3.30245e22	1.34319	0.671594	+	0.740919i	$0.265610\pi$
$968$	−1.62401e22	−0.655424
$969$	2.97797e21	0.119259
$970$	−3.62337e20	−0.0143988
$971$	1.84866e21	0.0728977	0.0364489	−	0.999336i	$-0.488395\pi$
$971$	1.84866e21	0.0728977	0.0364489	+	0.999336i	$0.488395\pi$
$972$	−1.77948e22	−0.696299
$973$	−5.03063e21	−0.195333
$974$	1.34529e22	0.518351
$975$	−2.79053e21	−0.106697
$976$	−7.20846e21	−0.273507
$977$	−1.35682e22	−0.510875	−0.255437	−	0.966826i	$-0.582219\pi$
$977$	−1.35682e22	−0.510875	−0.255437	+	0.966826i	$0.582219\pi$
$978$	−7.60544e20	−0.0284173
$979$	−6.88858e21	−0.255423
$980$	−2.16784e21	−0.0797687
$981$	−9.41463e21	−0.343784
$982$	1.07520e22	0.389630
$983$	1.63628e22	0.588445	0.294223	−	0.955737i	$-0.404939\pi$
$983$	1.63628e22	0.588445	0.294223	+	0.955737i	$0.404939\pi$
$984$	2.22397e22	0.793716
$985$	3.36154e21	0.119060
$986$	−1.56884e21	−0.0551444
$987$	−3.35099e22	−1.16895
$988$	1.32424e21	0.0458447
$989$	1.07415e22	0.369055
$990$	−4.09393e20	−0.0139597
$991$	5.16699e22	1.74858	0.874290	−	0.485405i	$-0.161328\pi$
$991$	5.16699e22	1.74858	0.874290	+	0.485405i	$0.161328\pi$
$992$	5.27098e22	1.77033
$993$	−1.56579e22	−0.521933
$994$	2.52914e22	0.836710
$995$	1.23623e21	0.0405907
$996$	−1.78548e22	−0.581849
$997$	−2.98524e22	−0.965528	−0.482764	−	0.875750i	$-0.660367\pi$
$997$	−2.98524e22	−0.965528	−0.482764	+	0.875750i	$0.660367\pi$
$998$	−1.32353e22	−0.424868
$999$	−4.47766e22	−1.42663

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.16.a.b.1.8	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.16.a.b.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-101.235 q^{2} +2276.05 q^{3} -22519.5 q^{4} +12349.2 q^{5} -230415. q^{6} -3.54158e6 q^{7} +5.59702e6 q^{8} -9.16851e6 q^{9} +O(q^{10})\)	\(q-101.235 q^{2} +2276.05 q^{3} -22519.5 q^{4} +12349.2 q^{5} -230415. q^{6} -3.54158e6 q^{7} +5.59702e6 q^{8} -9.16851e6 q^{9} -1.25017e6 q^{10} -3.57168e7 q^{11} -5.12555e7 q^{12} +4.03767e7 q^{13} +3.58531e8 q^{14} +2.81074e7 q^{15} +1.71308e8 q^{16} -8.98386e8 q^{17} +9.28172e8 q^{18} -1.45638e9 q^{19} -2.78098e8 q^{20} -8.06081e9 q^{21} +3.61578e9 q^{22} +2.79170e10 q^{23} +1.27391e10 q^{24} -3.03651e10 q^{25} -4.08752e9 q^{26} -5.35268e10 q^{27} +7.97548e10 q^{28} -1.72499e10 q^{29} -2.84544e9 q^{30} -2.62570e11 q^{31} -2.00745e11 q^{32} -8.12932e10 q^{33} +9.09479e10 q^{34} -4.37357e10 q^{35} +2.06471e11 q^{36} +8.36528e11 q^{37} +1.47437e11 q^{38} +9.18993e10 q^{39} +6.91187e10 q^{40} +1.74578e12 q^{41} +8.16034e11 q^{42} +3.84764e11 q^{43} +8.04327e11 q^{44} -1.13224e11 q^{45} -2.82617e12 q^{46} +4.15714e12 q^{47} +3.89905e11 q^{48} +7.79525e12 q^{49} +3.07400e12 q^{50} -2.04477e12 q^{51} -9.09265e11 q^{52} +1.39488e13 q^{53} +5.41877e12 q^{54} -4.41074e11 q^{55} -1.98223e13 q^{56} -3.31480e12 q^{57} +1.74629e12 q^{58} +2.30895e13 q^{59} -6.32965e11 q^{60} -4.20790e13 q^{61} +2.65812e13 q^{62} +3.24711e13 q^{63} +1.47090e13 q^{64} +4.98620e11 q^{65} +8.22970e12 q^{66} +3.64110e13 q^{67} +2.02312e13 q^{68} +6.35404e13 q^{69} +4.42757e12 q^{70} +7.05417e13 q^{71} -5.13163e13 q^{72} -1.43595e14 q^{73} -8.46857e13 q^{74} -6.91124e13 q^{75} +3.27971e13 q^{76} +1.26494e14 q^{77} -9.30340e12 q^{78} -2.35839e14 q^{79} +2.11551e12 q^{80} +9.72867e12 q^{81} -1.76734e14 q^{82} +3.48349e14 q^{83} +1.81526e14 q^{84} -1.10944e13 q^{85} -3.89515e13 q^{86} -3.92615e13 q^{87} -1.99908e14 q^{88} +1.92866e14 q^{89} +1.14622e13 q^{90} -1.42997e14 q^{91} -6.28677e14 q^{92} -5.97623e14 q^{93} -4.20847e14 q^{94} -1.79852e13 q^{95} -4.56906e14 q^{96} +2.89831e14 q^{97} -7.89150e14 q^{98} +3.27470e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 9908 q^{3} + 387418 q^{4} + 230490 q^{5} + 1566838 q^{6} + 2882024 q^{7} + 26209092 q^{8} + 93022899 q^{9}+O(q^{10}) \) 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

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