LMFDB - Embedded newform 29.16.a.b.1.18

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			1.18
Root			$345.887$ 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)

$f(q)$	$=$	$q+345.887 q^{2} -415.807 q^{3} +86869.8 q^{4} +271690. q^{5} -143822. q^{6} +3.51139e6 q^{7} +1.87131e7 q^{8} -1.41760e7 q^{9} +O(q^{10})$	\(q+345.887 q^{2} -415.807 q^{3} +86869.8 q^{4} +271690. q^{5} -143822. q^{6} +3.51139e6 q^{7} +1.87131e7 q^{8} -1.41760e7 q^{9} +9.39741e7 q^{10} -7.42451e7 q^{11} -3.61211e7 q^{12} +1.30190e8 q^{13} +1.21454e9 q^{14} -1.12971e8 q^{15} +3.62607e9 q^{16} -1.89231e9 q^{17} -4.90330e9 q^{18} -4.37257e9 q^{19} +2.36017e10 q^{20} -1.46006e9 q^{21} -2.56804e10 q^{22} -2.01671e10 q^{23} -7.78104e9 q^{24} +4.32981e10 q^{25} +4.50310e10 q^{26} +1.18609e10 q^{27} +3.05034e11 q^{28} -1.72499e10 q^{29} -3.90751e10 q^{30} +9.47409e10 q^{31} +6.41018e11 q^{32} +3.08717e10 q^{33} -6.54524e11 q^{34} +9.54010e11 q^{35} -1.23147e12 q^{36} +2.77947e11 q^{37} -1.51241e12 q^{38} -5.41340e10 q^{39} +5.08417e12 q^{40} -6.78004e11 q^{41} -5.05016e11 q^{42} +2.60715e12 q^{43} -6.44966e12 q^{44} -3.85149e12 q^{45} -6.97553e12 q^{46} -2.12509e12 q^{47} -1.50775e12 q^{48} +7.58229e12 q^{49} +1.49762e13 q^{50} +7.86835e11 q^{51} +1.13096e13 q^{52} -1.06769e13 q^{53} +4.10252e12 q^{54} -2.01717e13 q^{55} +6.57089e13 q^{56} +1.81815e12 q^{57} -5.96651e12 q^{58} +1.19362e13 q^{59} -9.81375e12 q^{60} -2.07875e13 q^{61} +3.27696e13 q^{62} -4.97775e13 q^{63} +1.02901e14 q^{64} +3.53714e13 q^{65} +1.06781e13 q^{66} +4.31845e13 q^{67} -1.64384e14 q^{68} +8.38562e12 q^{69} +3.29980e14 q^{70} +4.28784e13 q^{71} -2.65277e14 q^{72} +5.58039e13 q^{73} +9.61383e13 q^{74} -1.80037e13 q^{75} -3.79844e14 q^{76} -2.60704e14 q^{77} -1.87242e13 q^{78} -1.19078e13 q^{79} +9.85167e14 q^{80} +1.98478e14 q^{81} -2.34513e14 q^{82} -3.55383e14 q^{83} -1.26835e14 q^{84} -5.14122e14 q^{85} +9.01779e14 q^{86} +7.17263e12 q^{87} -1.38936e15 q^{88} -6.42265e14 q^{89} -1.33218e15 q^{90} +4.57148e14 q^{91} -1.75191e15 q^{92} -3.93940e13 q^{93} -7.35041e14 q^{94} -1.18798e15 q^{95} -2.66540e14 q^{96} +1.38711e15 q^{97} +2.62261e15 q^{98} +1.05250e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	345.887	1.91077	0.955387	−	0.295358i	$-0.0954389\pi$
$2$	345.887	1.91077	0.955387	+	0.295358i	$0.0954389\pi$
$3$	−415.807	−0.109770	−0.0548849	−	0.998493i	$-0.517479\pi$
$3$	−415.807	−0.109770	−0.0548849	+	0.998493i	$0.517479\pi$
$4$	86869.8	2.65105
$5$	271690.	1.55525	0.777623	−	0.628731i	$-0.216425\pi$
$5$	271690.	1.55525	0.777623	+	0.628731i	$0.216425\pi$
$6$	−143822.	−0.209745
$7$	3.51139e6	1.61155	0.805775	−	0.592222i	$-0.201749\pi$
$7$	3.51139e6	1.61155	0.805775	+	0.592222i	$0.201749\pi$
$8$	1.87131e7	3.15479
$9$	−1.41760e7	−0.987951
$10$	9.39741e7	2.97172
$11$	−7.42451e7	−1.14874	−0.574372	−	0.818595i	$-0.694754\pi$
$11$	−7.42451e7	−1.14874	−0.574372	+	0.818595i	$0.694754\pi$
$12$	−3.61211e7	−0.291006
$13$	1.30190e8	0.575443	0.287722	−	0.957714i	$-0.407102\pi$
$13$	1.30190e8	0.575443	0.287722	+	0.957714i	$0.407102\pi$
$14$	1.21454e9	3.07931
$15$	−1.12971e8	−0.170719
$16$	3.62607e9	3.37704
$17$	−1.89231e9	−1.11847	−0.559236	−	0.829009i	$-0.688905\pi$
$17$	−1.89231e9	−1.11847	−0.559236	+	0.829009i	$0.688905\pi$
$18$	−4.90330e9	−1.88775
$19$	−4.37257e9	−1.12224	−0.561118	−	0.827736i	$-0.689629\pi$
$19$	−4.37257e9	−1.12224	−0.561118	+	0.827736i	$0.689629\pi$
$20$	2.36017e10	4.12304
$21$	−1.46006e9	−0.176899
$22$	−2.56804e10	−2.19499
$23$	−2.01671e10	−1.23505	−0.617524	−	0.786552i	$-0.711864\pi$
$23$	−2.01671e10	−1.23505	−0.617524	+	0.786552i	$0.711864\pi$
$24$	−7.78104e9	−0.346301
$25$	4.32981e10	1.41879
$26$	4.50310e10	1.09954
$27$	1.18609e10	0.218217
$28$	3.05034e11	4.27231
$29$	−1.72499e10	−0.185695
$29$	−1.72499e10	−0.185695
$30$	−3.90751e10	−0.326205
$31$	9.47409e10	0.618479	0.309239	−	0.950984i	$-0.399926\pi$
$31$	9.47409e10	0.618479	0.309239	+	0.950984i	$0.399926\pi$
$32$	6.41018e11	3.29796
$33$	3.08717e10	0.126097
$34$	−6.54524e11	−2.13715
$35$	9.54010e11	2.50636
$36$	−1.23147e12	−2.61911
$37$	2.77947e11	0.481337	0.240669	−	0.970607i	$-0.422633\pi$
$37$	2.77947e11	0.481337	0.240669	+	0.970607i	$0.422633\pi$
$38$	−1.51241e12	−2.14434
$39$	−5.41340e10	−0.0631663
$40$	5.08417e12	4.90648
$41$	−6.78004e11	−0.543692	−0.271846	−	0.962341i	$-0.587634\pi$
$41$	−6.78004e11	−0.543692	−0.271846	+	0.962341i	$0.587634\pi$
$42$	−5.05016e11	−0.338015
$43$	2.60715e12	1.46269	0.731345	−	0.682007i	$-0.238893\pi$
$43$	2.60715e12	1.46269	0.731345	+	0.682007i	$0.238893\pi$
$44$	−6.44966e12	−3.04538
$45$	−3.85149e12	−1.53651
$46$	−6.97553e12	−2.35990
$47$	−2.12509e12	−0.611848	−0.305924	−	0.952056i	$-0.598965\pi$
$47$	−2.12509e12	−0.611848	−0.305924	+	0.952056i	$0.598965\pi$
$48$	−1.50775e12	−0.370697
$49$	7.58229e12	1.59709
$50$	1.49762e13	2.71099
$51$	7.86835e11	0.122774
$52$	1.13096e13	1.52553
$53$	−1.06769e13	−1.24847	−0.624233	−	0.781238i	$-0.714588\pi$
$53$	−1.06769e13	−1.24847	−0.624233	+	0.781238i	$0.714588\pi$
$54$	4.10252e12	0.416963
$55$	−2.01717e13	−1.78658
$56$	6.57089e13	5.08410
$57$	1.81815e12	0.123188
$58$	−5.96651e12	−0.354822
$59$	1.19362e13	0.624420	0.312210	−	0.950013i	$-0.398931\pi$
$59$	1.19362e13	0.624420	0.312210	+	0.950013i	$0.398931\pi$
$60$	−9.81375e12	−0.452586
$61$	−2.07875e13	−0.846893	−0.423447	−	0.905921i	$-0.639180\pi$
$61$	−2.07875e13	−0.846893	−0.423447	+	0.905921i	$0.639180\pi$
$62$	3.27696e13	1.18177
$63$	−4.97775e13	−1.59213
$64$	1.02901e14	2.92462
$65$	3.53714e13	0.894956
$66$	1.06781e13	0.240943
$67$	4.31845e13	0.870496	0.435248	−	0.900311i	$-0.356661\pi$
$67$	4.31845e13	0.870496	0.435248	+	0.900311i	$0.356661\pi$
$68$	−1.64384e14	−2.96513
$69$	8.38562e12	0.135571
$70$	3.29980e14	4.78908
$71$	4.28784e13	0.559501	0.279750	−	0.960073i	$-0.409748\pi$
$71$	4.28784e13	0.559501	0.279750	+	0.960073i	$0.409748\pi$
$72$	−2.65277e14	−3.11678
$73$	5.58039e13	0.591212	0.295606	−	0.955310i	$-0.404478\pi$
$73$	5.58039e13	0.591212	0.295606	+	0.955310i	$0.404478\pi$
$74$	9.61383e13	0.919726
$75$	−1.80037e13	−0.155740
$76$	−3.79844e14	−2.97511
$77$	−2.60704e14	−1.85126
$78$	−1.87242e13	−0.120696
$79$	−1.19078e13	−0.0697633	−0.0348816	−	0.999391i	$-0.511105\pi$
$79$	−1.19078e13	−0.0697633	−0.0348816	+	0.999391i	$0.511105\pi$
$80$	9.85167e14	5.25212
$81$	1.98478e14	0.963997
$82$	−2.34513e14	−1.03887
$83$	−3.55383e14	−1.43751	−0.718755	−	0.695264i	$-0.755287\pi$
$83$	−3.55383e14	−1.43751	−0.718755	+	0.695264i	$0.755287\pi$
$84$	−1.26835e14	−0.468970
$85$	−5.14122e14	−1.73950
$86$	9.01779e14	2.79487
$87$	7.17263e12	0.0203837
$88$	−1.38936e15	−3.62405
$89$	−6.42265e14	−1.53918	−0.769589	−	0.638539i	$-0.779539\pi$
$89$	−6.42265e14	−1.53918	−0.769589	+	0.638539i	$0.779539\pi$
$90$	−1.33218e15	−2.93592
$91$	4.57148e14	0.927355
$92$	−1.75191e15	−3.27418
$93$	−3.93940e13	−0.0678903
$94$	−7.35041e14	−1.16910
$95$	−1.18798e15	−1.74535
$96$	−2.66540e14	−0.362016
$97$	1.38711e15	1.74310	0.871551	−	0.490305i	$-0.163115\pi$
$97$	1.38711e15	1.74310	0.871551	+	0.490305i	$0.163115\pi$
$98$	2.62261e15	3.05168
$99$	1.05250e15	1.13490
$100$	3.76129e15	3.76129
$101$	2.87421e13	0.0266752	0.0133376	−	0.999911i	$-0.495754\pi$
$101$	2.87421e13	0.0266752	0.0133376	+	0.999911i	$0.495754\pi$
$102$	2.72156e14	0.234594
$103$	4.84407e14	0.388089	0.194045	−	0.980993i	$-0.437839\pi$
$103$	4.84407e14	0.388089	0.194045	+	0.980993i	$0.437839\pi$
$104$	2.43626e15	1.81540
$105$	−3.96685e14	−0.275122
$106$	−3.69300e15	−2.38554
$107$	−2.64825e15	−1.59434	−0.797170	−	0.603755i	$-0.793671\pi$
$107$	−2.64825e15	−1.59434	−0.797170	+	0.603755i	$0.793671\pi$
$108$	1.03035e15	0.578505
$109$	3.13530e15	1.64278	0.821392	−	0.570365i	$-0.193198\pi$
$109$	3.13530e15	1.64278	0.821392	+	0.570365i	$0.193198\pi$
$110$	−6.97712e15	−3.41375
$111$	−1.15573e14	−0.0528363
$112$	1.27325e16	5.44226
$113$	−1.73825e14	−0.0695064	−0.0347532	−	0.999396i	$-0.511065\pi$
$113$	−1.73825e14	−0.0695064	−0.0347532	+	0.999396i	$0.511065\pi$
$114$	6.28873e14	0.235384
$115$	−5.47920e15	−1.92081
$116$	−1.49849e15	−0.492289
$117$	−1.84558e15	−0.568510
$118$	4.12859e15	1.19313
$119$	−6.64463e15	−1.80247
$120$	−2.11403e15	−0.538583
$121$	1.33509e15	0.319611
$122$	−7.19013e15	−1.61822
$123$	2.81919e14	0.0596810
$124$	8.23012e15	1.63962
$125$	3.47233e15	0.651323
$126$	−1.72174e16	−3.04220
$127$	1.32942e15	0.221378	0.110689	−	0.993855i	$-0.464694\pi$
$127$	1.32942e15	0.221378	0.110689	+	0.993855i	$0.464694\pi$
$128$	1.45872e16	2.29032
$129$	−1.08407e15	−0.160559
$130$	1.22345e16	1.71006
$131$	−6.59231e15	−0.869967	−0.434984	−	0.900438i	$-0.643246\pi$
$131$	−6.59231e15	−0.869967	−0.434984	+	0.900438i	$0.643246\pi$
$132$	2.68182e15	0.334291
$133$	−1.53538e16	−1.80854
$134$	1.49370e16	1.66332
$135$	3.22248e15	0.339381
$136$	−3.54109e16	−3.52854
$137$	7.39786e15	0.697753	0.348877	−	0.937169i	$-0.386563\pi$
$137$	7.39786e15	0.697753	0.348877	+	0.937169i	$0.386563\pi$
$138$	2.90048e15	0.259046
$139$	6.32147e15	0.534820	0.267410	−	0.963583i	$-0.413832\pi$
$139$	6.32147e15	0.534820	0.267410	+	0.963583i	$0.413832\pi$
$140$	8.28747e16	6.64449
$141$	8.83628e14	0.0671624
$142$	1.48311e16	1.06908
$143$	−9.66598e15	−0.661037
$144$	−5.14032e16	−3.33635
$145$	−4.68662e15	−0.288802
$146$	1.93018e16	1.12967
$147$	−3.15277e15	−0.175312
$148$	2.41452e16	1.27605
$149$	−1.64168e15	−0.0824884	−0.0412442	−	0.999149i	$-0.513132\pi$
$149$	−1.64168e15	−0.0824884	−0.0412442	+	0.999149i	$0.513132\pi$
$150$	−6.22723e15	−0.297584
$151$	−1.33379e16	−0.606403	−0.303201	−	0.952927i	$-0.598055\pi$
$151$	−1.33379e16	−0.606403	−0.303201	+	0.952927i	$0.598055\pi$
$152$	−8.18242e16	−3.54042
$153$	2.68254e16	1.10499
$154$	−9.01740e16	−3.53733
$155$	2.57402e16	0.961886
$156$	−4.70261e15	−0.167457
$157$	1.25462e16	0.425857	0.212929	−	0.977068i	$-0.431700\pi$
$157$	1.25462e16	0.425857	0.212929	+	0.977068i	$0.431700\pi$
$158$	−4.11874e15	−0.133302
$159$	4.43954e15	0.137044
$160$	1.74158e17	5.12914
$161$	−7.08144e16	−1.99034
$162$	6.86511e16	1.84198
$163$	7.52803e16	1.92874	0.964372	−	0.264550i	$-0.0852234\pi$
$163$	7.52803e16	1.92874	0.964372	+	0.264550i	$0.0852234\pi$
$164$	−5.88980e16	−1.44136
$165$	8.38754e15	0.196112
$166$	−1.22922e17	−2.74675
$167$	3.79389e16	0.810422	0.405211	−	0.914223i	$-0.367198\pi$
$167$	3.79389e16	0.810422	0.405211	+	0.914223i	$0.367198\pi$
$168$	−2.73223e16	−0.558081
$169$	−3.42364e16	−0.668865
$170$	−1.77828e17	−3.32379
$171$	6.19855e16	1.10871
$172$	2.26482e17	3.87767
$173$	6.30895e16	1.03422	0.517108	−	0.855920i	$-0.327008\pi$
$173$	6.30895e16	1.03422	0.517108	+	0.855920i	$0.327008\pi$
$174$	2.48092e15	0.0389487
$175$	1.52036e17	2.28645
$176$	−2.69218e17	−3.87935
$177$	−4.96317e15	−0.0685425
$178$	−2.22151e17	−2.94102
$179$	2.27355e16	0.288608	0.144304	−	0.989533i	$-0.453906\pi$
$179$	2.27355e16	0.288608	0.144304	+	0.989533i	$0.453906\pi$
$180$	−3.34578e17	−4.07336
$181$	−8.70431e15	−0.101659	−0.0508294	−	0.998707i	$-0.516186\pi$
$181$	−8.70431e15	−0.101659	−0.0508294	+	0.998707i	$0.516186\pi$
$182$	1.58121e17	1.77197
$183$	8.64360e15	0.0929633
$184$	−3.77388e17	−3.89632
$185$	7.55156e16	0.748598
$186$	−1.36259e16	−0.129723
$187$	1.40495e17	1.28484
$188$	−1.84606e17	−1.62204
$189$	4.16481e16	0.351667
$190$	−4.10908e17	−3.33498
$191$	4.57869e16	0.357265	0.178633	−	0.983916i	$-0.442833\pi$
$191$	4.57869e16	0.357265	0.178633	+	0.983916i	$0.442833\pi$
$192$	−4.27869e16	−0.321035
$193$	−2.71759e17	−1.96112	−0.980560	−	0.196220i	$-0.937133\pi$
$193$	−2.71759e17	−1.96112	−0.980560	+	0.196220i	$0.937133\pi$
$194$	4.79783e17	3.33067
$195$	−1.47077e16	−0.0982391
$196$	6.58672e17	4.23398
$197$	−4.06490e16	−0.251509	−0.125754	−	0.992061i	$-0.540135\pi$
$197$	−4.06490e16	−0.251509	−0.125754	+	0.992061i	$0.540135\pi$
$198$	3.64046e17	2.16854
$199$	9.92357e16	0.569207	0.284603	−	0.958645i	$-0.408138\pi$
$199$	9.92357e16	0.569207	0.284603	+	0.958645i	$0.408138\pi$
$200$	8.10241e17	4.47599
$201$	−1.79564e16	−0.0955542
$202$	9.94151e15	0.0509703
$203$	−6.05710e16	−0.299257
$204$	6.83522e16	0.325482
$205$	−1.84207e17	−0.845575
$206$	1.67550e17	0.741551
$207$	2.85889e17	1.22017
$208$	4.72078e17	1.94329
$209$	3.24642e17	1.28916
$210$	−1.37208e17	−0.525696
$211$	−3.10468e17	−1.14789	−0.573943	−	0.818895i	$-0.694587\pi$
$211$	−3.10468e17	−1.14789	−0.573943	+	0.818895i	$0.694587\pi$
$212$	−9.27501e17	−3.30975
$213$	−1.78292e16	−0.0614163
$214$	−9.15996e17	−3.04642
$215$	7.08337e17	2.27484
$216$	2.21954e17	0.688429
$217$	3.32672e17	0.996709
$218$	1.08446e18	3.13899
$219$	−2.32037e16	−0.0648972
$220$	−1.75231e18	−4.73632
$221$	−2.46360e17	−0.643617
$222$	−3.99750e16	−0.100958
$223$	2.72030e17	0.664249	0.332124	−	0.943236i	$-0.392235\pi$
$223$	2.72030e17	0.664249	0.332124	+	0.943236i	$0.392235\pi$
$224$	2.25086e18	5.31483
$225$	−6.13794e17	−1.40170
$226$	−6.01239e16	−0.132811
$227$	−5.08117e16	−0.108585	−0.0542925	−	0.998525i	$-0.517290\pi$
$227$	−5.08117e16	−0.108585	−0.0542925	+	0.998525i	$0.517290\pi$
$228$	1.57942e17	0.326577
$229$	1.29005e17	0.258130	0.129065	−	0.991636i	$-0.458802\pi$
$229$	1.29005e17	0.258130	0.129065	+	0.991636i	$0.458802\pi$
$230$	−1.89518e18	−3.67022
$231$	1.08402e17	0.203212
$232$	−3.22799e17	−0.585830
$233$	3.99283e16	0.0701636	0.0350818	−	0.999384i	$-0.488831\pi$
$233$	3.99283e16	0.0701636	0.0350818	+	0.999384i	$0.488831\pi$
$234$	−6.38360e17	−1.08629
$235$	−5.77366e17	−0.951574
$236$	1.03690e18	1.65537
$237$	4.95133e15	0.00765790
$238$	−2.29829e18	−3.44411
$239$	3.94908e17	0.573471	0.286736	−	0.958010i	$-0.407430\pi$
$239$	3.94908e17	0.573471	0.286736	+	0.958010i	$0.407430\pi$
$240$	−4.09640e17	−0.576525
$241$	−3.30070e17	−0.450275	−0.225137	−	0.974327i	$-0.572283\pi$
$241$	−3.30070e17	−0.450275	−0.225137	+	0.974327i	$0.572283\pi$
$242$	4.61792e17	0.610704
$243$	−2.52719e17	−0.324035
$244$	−1.80581e18	−2.24516
$245$	2.06003e18	2.48387
$246$	9.75121e16	0.114037
$247$	−5.69265e17	−0.645784
$248$	1.77289e18	1.95117
$249$	1.47771e17	0.157795
$250$	1.20103e18	1.24453
$251$	−7.28617e17	−0.732734	−0.366367	−	0.930470i	$-0.619399\pi$
$251$	−7.28617e17	−0.732734	−0.366367	+	0.930470i	$0.619399\pi$
$252$	−4.32416e18	−4.22083
$253$	1.49731e18	1.41875
$254$	4.59829e17	0.423003
$255$	2.13776e17	0.190944
$256$	1.67366e18	1.45167
$257$	2.00802e17	0.169149	0.0845746	−	0.996417i	$-0.473047\pi$
$257$	2.00802e17	0.169149	0.0845746	+	0.996417i	$0.473047\pi$
$258$	−3.74966e17	−0.306792
$259$	9.75981e17	0.775699
$260$	3.07270e18	2.37258
$261$	2.44534e17	0.183458
$262$	−2.28019e18	−1.66231
$263$	1.95124e18	1.38243	0.691215	−	0.722649i	$-0.257076\pi$
$263$	1.95124e18	1.38243	0.691215	+	0.722649i	$0.257076\pi$
$264$	5.77705e17	0.397811
$265$	−2.90081e18	−1.94167
$266$	−5.31067e18	−3.45571
$267$	2.67058e17	0.168955
$268$	3.75143e18	2.30773
$269$	−1.04319e18	−0.624054	−0.312027	−	0.950073i	$-0.601008\pi$
$269$	−1.04319e18	−0.624054	−0.312027	+	0.950073i	$0.601008\pi$
$270$	1.11462e18	0.648480
$271$	−2.13559e18	−1.20851	−0.604253	−	0.796792i	$-0.706528\pi$
$271$	−2.13559e18	−1.20851	−0.604253	+	0.796792i	$0.706528\pi$
$272$	−6.86163e18	−3.77712
$273$	−1.90085e17	−0.101796
$274$	2.55882e18	1.33325
$275$	−3.21467e18	−1.62983
$276$	7.28457e17	0.359406
$277$	−3.78711e18	−1.81849	−0.909243	−	0.416265i	$-0.863339\pi$
$277$	−3.78711e18	−1.81849	−0.909243	+	0.416265i	$0.863339\pi$
$278$	2.18652e18	1.02192
$279$	−1.34305e18	−0.611026
$280$	1.78525e19	7.90703
$281$	2.32972e18	1.00463	0.502315	−	0.864685i	$-0.332482\pi$
$281$	2.32972e18	1.00463	0.502315	+	0.864685i	$0.332482\pi$
$282$	3.05635e17	0.128332
$283$	2.92306e17	0.119520	0.0597598	−	0.998213i	$-0.480967\pi$
$283$	2.92306e17	0.119520	0.0597598	+	0.998213i	$0.480967\pi$
$284$	3.72484e18	1.48327
$285$	4.93972e17	0.191587
$286$	−3.34334e18	−1.26309
$287$	−2.38073e18	−0.876187
$288$	−9.08708e18	−3.25822
$289$	7.18405e17	0.250978
$290$	−1.62104e18	−0.551835
$291$	−5.76770e17	−0.191340
$292$	4.84767e18	1.56734
$293$	4.55664e18	1.43594	0.717972	−	0.696072i	$-0.245071\pi$
$293$	4.55664e18	1.43594	0.717972	+	0.696072i	$0.245071\pi$
$294$	−1.09050e18	−0.334982
$295$	3.24296e18	0.971128
$296$	5.20125e18	1.51852
$297$	−8.80612e17	−0.250675
$298$	−5.67837e17	−0.157617
$299$	−2.62555e18	−0.710701
$300$	−1.56397e18	−0.412876
$301$	9.15471e18	2.35720
$302$	−4.61341e18	−1.15870
$303$	−1.19512e16	−0.00292813
$304$	−1.58552e19	−3.78983
$305$	−5.64776e18	−1.31713
$306$	9.27855e18	2.11139
$307$	3.52558e18	0.782875	0.391437	−	0.920205i	$-0.371978\pi$
$307$	3.52558e18	0.782875	0.391437	+	0.920205i	$0.371978\pi$
$308$	−2.26473e19	−4.90778
$309$	−2.01420e17	−0.0426005
$310$	8.90319e18	1.83795
$311$	−6.21055e18	−1.25149	−0.625745	−	0.780028i	$-0.715205\pi$
$311$	−6.21055e18	−1.25149	−0.625745	+	0.780028i	$0.715205\pi$
$312$	−1.01301e18	−0.199277
$313$	1.01087e19	1.94139	0.970696	−	0.240312i	$-0.0772496\pi$
$313$	1.01087e19	1.94139	0.970696	+	0.240312i	$0.0772496\pi$
$314$	4.33956e18	0.813717
$315$	−1.35241e19	−2.47616
$316$	−1.03442e18	−0.184946
$317$	3.08669e18	0.538950	0.269475	−	0.963007i	$-0.413150\pi$
$317$	3.08669e18	0.538950	0.269475	+	0.963007i	$0.413150\pi$
$318$	1.53558e18	0.261860
$319$	1.28072e18	0.213316
$320$	2.79572e19	4.54850
$321$	1.10116e18	0.175010
$322$	−2.44938e19	−3.80309
$323$	8.27424e18	1.25519
$324$	1.72418e19	2.55561
$325$	5.63698e18	0.816434
$326$	2.60385e19	3.68539
$327$	−1.30368e18	−0.180328
$328$	−1.26875e19	−1.71524
$329$	−7.46201e18	−0.986023
$330$	2.90114e18	0.374726
$331$	3.44603e18	0.435120	0.217560	−	0.976047i	$-0.430190\pi$
$331$	3.44603e18	0.435120	0.217560	+	0.976047i	$0.430190\pi$
$332$	−3.08720e19	−3.81092
$333$	−3.94018e18	−0.475537
$334$	1.31226e19	1.54853
$335$	1.17328e19	1.35384
$336$	−5.29428e18	−0.597396
$337$	−9.18644e18	−1.01373	−0.506866	−	0.862025i	$-0.669196\pi$
$337$	−9.18644e18	−1.01373	−0.506866	+	0.862025i	$0.669196\pi$
$338$	−1.18419e19	−1.27805
$339$	7.22779e16	0.00762970
$340$	−4.46616e19	−4.61150
$341$	−7.03405e18	−0.710473
$342$	2.14400e19	2.11850
$343$	9.95383e18	0.962242
$344$	4.87878e19	4.61448
$345$	2.27829e18	0.210846
$346$	2.18218e19	1.97615
$347$	7.43332e18	0.658736	0.329368	−	0.944202i	$-0.393164\pi$
$347$	7.43332e18	0.658736	0.329368	+	0.944202i	$0.393164\pi$
$348$	6.23084e17	0.0540384
$349$	−1.12452e19	−0.954498	−0.477249	−	0.878768i	$-0.658366\pi$
$349$	−1.12452e19	−0.954498	−0.477249	+	0.878768i	$0.658366\pi$
$350$	5.25874e19	4.36889
$351$	1.54417e18	0.125571
$352$	−4.75925e19	−3.78851
$353$	8.41372e18	0.655659	0.327829	−	0.944737i	$-0.393683\pi$
$353$	8.41372e18	0.655659	0.327829	+	0.944737i	$0.393683\pi$
$354$	−1.71670e18	−0.130969
$355$	1.16496e19	0.870162
$356$	−5.57934e19	−4.08045
$357$	2.76289e18	0.197857
$358$	7.86393e18	0.551464
$359$	−1.16406e19	−0.799403	−0.399701	−	0.916645i	$-0.630886\pi$
$359$	−1.16406e19	−0.799403	−0.399701	+	0.916645i	$0.630886\pi$
$360$	−7.20732e19	−4.84736
$361$	3.93821e18	0.259415
$362$	−3.01071e18	−0.194247
$363$	−5.55142e17	−0.0350836
$364$	3.97123e19	2.45847
$365$	1.51614e19	0.919480
$366$	2.98971e18	0.177632
$367$	−1.43239e19	−0.833807	−0.416904	−	0.908951i	$-0.636885\pi$
$367$	−1.43239e19	−0.833807	−0.416904	+	0.908951i	$0.636885\pi$
$368$	−7.31272e19	−4.17081
$369$	9.61139e18	0.537141
$370$	2.61198e19	1.43040
$371$	−3.74908e19	−2.01196
$372$	−3.42214e18	−0.179981
$373$	−2.87041e17	−0.0147955	−0.00739773	−	0.999973i	$-0.502355\pi$
$373$	−2.87041e17	−0.0147955	−0.00739773	+	0.999973i	$0.502355\pi$
$374$	4.85953e19	2.45503
$375$	−1.44382e18	−0.0714955
$376$	−3.97670e19	−1.93025
$377$	−2.24576e18	−0.106857
$378$	1.44055e19	0.671957
$379$	3.05814e18	0.139850	0.0699251	−	0.997552i	$-0.477724\pi$
$379$	3.05814e18	0.139850	0.0699251	+	0.997552i	$0.477724\pi$
$380$	−1.03200e20	−4.62703
$381$	−5.52783e17	−0.0243006
$382$	1.58371e19	0.682653
$383$	2.75582e19	1.16483	0.582413	−	0.812893i	$-0.302109\pi$
$383$	2.75582e19	1.16483	0.582413	+	0.812893i	$0.302109\pi$
$384$	−6.06546e18	−0.251408
$385$	−7.08306e19	−2.87916
$386$	−9.39979e19	−3.74726
$387$	−3.69590e19	−1.44507
$388$	1.20498e20	4.62106
$389$	−2.45123e19	−0.922067	−0.461033	−	0.887383i	$-0.652521\pi$
$389$	−2.45123e19	−0.922067	−0.461033	+	0.887383i	$0.652521\pi$
$390$	−5.08719e18	−0.187713
$391$	3.81623e19	1.38137
$392$	1.41888e20	5.03849
$393$	2.74113e18	0.0954961
$394$	−1.40600e19	−0.480577
$395$	−3.23522e18	−0.108499
$396$	9.14304e19	3.00869
$397$	−2.70280e19	−0.872741	−0.436370	−	0.899767i	$-0.643736\pi$
$397$	−2.70280e19	−0.872741	−0.436370	+	0.899767i	$0.643736\pi$
$398$	3.43243e19	1.08762
$399$	6.38421e18	0.198523
$400$	1.57002e20	4.79131
$401$	−3.52364e19	−1.05538	−0.527691	−	0.849437i	$-0.676942\pi$
$401$	−3.52364e19	−1.05538	−0.527691	+	0.849437i	$0.676942\pi$
$402$	−6.21090e18	−0.182582
$403$	1.23343e19	0.355899
$404$	2.49682e18	0.0707174
$405$	5.39247e19	1.49925
$406$	−2.09507e19	−0.571813
$407$	−2.06362e19	−0.552933
$408$	1.47241e19	0.387327
$409$	−4.21461e19	−1.08851	−0.544256	−	0.838919i	$-0.683188\pi$
$409$	−4.21461e19	−1.08851	−0.544256	+	0.838919i	$0.683188\pi$
$410$	−6.37148e19	−1.61570
$411$	−3.07608e18	−0.0765922
$412$	4.20804e19	1.02885
$413$	4.19127e19	1.00628
$414$	9.88852e19	2.33146
$415$	−9.65540e19	−2.23568
$416$	8.34542e19	1.89779
$417$	−2.62852e18	−0.0587070
$418$	1.12289e20	2.46330
$419$	8.42242e19	1.81481	0.907406	−	0.420256i	$-0.138060\pi$
$419$	8.42242e19	1.81481	0.907406	+	0.420256i	$0.138060\pi$
$420$	−3.44599e19	−0.729364
$421$	−3.48619e19	−0.724829	−0.362414	−	0.932017i	$-0.618047\pi$
$421$	−3.48619e19	−0.724829	−0.362414	+	0.932017i	$0.618047\pi$
$422$	−1.07387e20	−2.19335
$423$	3.01253e19	0.604475
$424$	−1.99798e20	−3.93865
$425$	−8.19332e19	−1.58688
$426$	−6.16687e18	−0.117353
$427$	−7.29930e19	−1.36481
$428$	−2.30053e20	−4.22668
$429$	4.01919e18	0.0725619
$430$	2.45005e20	4.34671
$431$	8.12750e19	1.41702	0.708512	−	0.705698i	$-0.249367\pi$
$431$	8.12750e19	1.41702	0.708512	+	0.705698i	$0.249367\pi$
$432$	4.30083e19	0.736927
$433$	−9.44230e18	−0.159008	−0.0795039	−	0.996835i	$-0.525334\pi$
$433$	−9.44230e18	−0.159008	−0.0795039	+	0.996835i	$0.525334\pi$
$434$	1.15067e20	1.90448
$435$	1.94873e18	0.0317017
$436$	2.72363e20	4.35511
$437$	8.81819e19	1.38602
$438$	−8.02585e18	−0.124004
$439$	1.14566e19	0.174009	0.0870046	−	0.996208i	$-0.472271\pi$
$439$	1.14566e19	0.174009	0.0870046	+	0.996208i	$0.472271\pi$
$440$	−3.77475e20	−5.63628
$441$	−1.07487e20	−1.57785
$442$	−8.52126e19	−1.22981
$443$	−9.08945e18	−0.128976	−0.0644881	−	0.997918i	$-0.520541\pi$
$443$	−9.08945e18	−0.128976	−0.0644881	+	0.997918i	$0.520541\pi$
$444$	−1.00398e19	−0.140072
$445$	−1.74497e20	−2.39380
$446$	9.40917e19	1.26923
$447$	6.82625e17	0.00905473
$448$	3.61325e20	4.71317
$449$	−3.02050e19	−0.387463	−0.193732	−	0.981055i	$-0.562059\pi$
$449$	−3.02050e19	−0.387463	−0.193732	+	0.981055i	$0.562059\pi$
$450$	−2.12303e20	−2.67832
$451$	5.03385e19	0.624563
$452$	−1.51002e19	−0.184265
$453$	5.54601e18	0.0665647
$454$	−1.75751e19	−0.207481
$455$	1.24203e20	1.44227
$456$	3.40231e19	0.388631
$457$	8.24369e19	0.926296	0.463148	−	0.886281i	$-0.346720\pi$
$457$	8.24369e19	0.926296	0.463148	+	0.886281i	$0.346720\pi$
$458$	4.46210e19	0.493229
$459$	−2.24444e19	−0.244069
$460$	−4.75977e20	−5.09216
$461$	−1.67353e19	−0.176147	−0.0880736	−	0.996114i	$-0.528071\pi$
$461$	−1.67353e19	−0.176147	−0.0880736	+	0.996114i	$0.528071\pi$
$462$	3.74950e19	0.388292
$463$	1.47337e20	1.50126	0.750630	−	0.660723i	$-0.229750\pi$
$463$	1.47337e20	1.50126	0.750630	+	0.660723i	$0.229750\pi$
$464$	−6.25492e19	−0.627100
$465$	−1.07030e19	−0.105586
$466$	1.38107e19	0.134067
$467$	1.08631e19	0.103772	0.0518858	−	0.998653i	$-0.483477\pi$
$467$	1.08631e19	0.103772	0.0518858	+	0.998653i	$0.483477\pi$
$468$	−1.60325e20	−1.50715
$469$	1.51638e20	1.40285
$470$	−1.99703e20	−1.81824
$471$	−5.21680e18	−0.0467463
$472$	2.23364e20	1.96992
$473$	−1.93568e20	−1.68026
$474$	1.71260e18	0.0146325
$475$	−1.89324e20	−1.59222
$476$	−5.77217e20	−4.77845
$477$	1.51356e20	1.23342
$478$	1.36593e20	1.09577
$479$	−7.23355e19	−0.571262	−0.285631	−	0.958340i	$-0.592203\pi$
$479$	−7.23355e19	−0.571262	−0.285631	+	0.958340i	$0.592203\pi$
$480$	−7.24164e19	−0.563025
$481$	3.61860e19	0.276982
$482$	−1.14167e20	−0.860373
$483$	2.94452e19	0.218479
$484$	1.15979e20	0.847306
$485$	3.76864e20	2.71095
$486$	−8.74123e19	−0.619157
$487$	−5.21175e19	−0.363510	−0.181755	−	0.983344i	$-0.558178\pi$
$487$	−5.21175e19	−0.363510	−0.181755	+	0.983344i	$0.558178\pi$
$488$	−3.88999e20	−2.67177
$489$	−3.13021e19	−0.211718
$490$	7.12539e20	4.74611
$491$	−2.01495e20	−1.32176	−0.660880	−	0.750492i	$-0.729817\pi$
$491$	−2.01495e20	−1.32176	−0.660880	+	0.750492i	$0.729817\pi$
$492$	2.44902e19	0.158218
$493$	3.26421e19	0.207695
$494$	−1.96901e20	−1.23395
$495$	2.85954e20	1.76505
$496$	3.43537e20	2.08863
$497$	1.50563e20	0.901663
$498$	5.11120e19	0.301511
$499$	−2.71056e20	−1.57509	−0.787544	−	0.616258i	$-0.788648\pi$
$499$	−2.71056e20	−1.57509	−0.787544	+	0.616258i	$0.788648\pi$
$500$	3.01641e20	1.72669
$501$	−1.57753e19	−0.0889598
$502$	−2.52019e20	−1.40009
$503$	1.11659e20	0.611130	0.305565	−	0.952171i	$-0.401155\pi$
$503$	1.11659e20	0.611130	0.305565	+	0.952171i	$0.401155\pi$
$504$	−9.31491e20	−5.02284
$505$	7.80894e18	0.0414865
$506$	5.17899e20	2.71092
$507$	1.42358e19	0.0734212
$508$	1.15486e20	0.586885
$509$	2.93815e20	1.47126	0.735631	−	0.677382i	$-0.236886\pi$
$509$	2.93815e20	1.47126	0.735631	+	0.677382i	$0.236886\pi$
$510$	7.39422e19	0.364851
$511$	1.95949e20	0.952767
$512$	1.00904e20	0.483487
$513$	−5.18624e19	−0.244891
$514$	6.94549e19	0.323206
$515$	1.31609e20	0.603574
$516$	−9.41731e19	−0.425651
$517$	1.57778e20	0.702856
$518$	3.37579e20	1.48218
$519$	−2.62331e19	−0.113526
$520$	6.61908e20	2.82340
$521$	3.39312e20	1.42665	0.713323	−	0.700836i	$-0.247189\pi$
$521$	3.39312e20	1.42665	0.713323	+	0.700836i	$0.247189\pi$
$522$	8.45813e19	0.350546
$523$	2.63463e20	1.07636	0.538179	−	0.842831i	$-0.319112\pi$
$523$	2.63463e20	1.07636	0.538179	+	0.842831i	$0.319112\pi$
$524$	−5.72672e20	−2.30633
$525$	−6.32178e19	−0.250983
$526$	6.74910e20	2.64151
$527$	−1.79279e20	−0.691751
$528$	1.11943e20	0.425835
$529$	1.40076e20	0.525346
$530$	−1.00335e21	−3.71009
$531$	−1.69208e20	−0.616897
$532$	−1.33378e21	−4.79454
$533$	−8.82693e19	−0.312864
$534$	9.23720e19	0.322835
$535$	−7.19504e20	−2.47959
$536$	8.08116e20	2.74623
$537$	−9.45361e18	−0.0316804
$538$	−3.60826e20	−1.19243
$539$	−5.62948e20	−1.83465
$540$	2.79936e20	0.899718
$541$	−5.29811e20	−1.67935	−0.839676	−	0.543088i	$-0.817255\pi$
$541$	−5.29811e20	−1.67935	−0.839676	+	0.543088i	$0.817255\pi$
$542$	−7.38674e20	−2.30918
$543$	3.61932e18	0.0111591
$544$	−1.21300e21	−3.68867
$545$	8.51830e20	2.55493
$546$	−6.57481e19	−0.194508
$547$	6.36693e20	1.85791	0.928956	−	0.370191i	$-0.120708\pi$
$547$	6.36693e20	1.85791	0.928956	+	0.370191i	$0.120708\pi$
$548$	6.42650e20	1.84978
$549$	2.94684e20	0.836689
$550$	−1.11191e21	−3.11423
$551$	7.54262e19	0.208394
$552$	1.56921e20	0.427698
$553$	−4.18128e19	−0.112427
$554$	−1.30991e21	−3.47472
$555$	−3.13999e19	−0.0821734
$556$	5.49145e20	1.41784
$557$	8.82362e19	0.224767	0.112384	−	0.993665i	$-0.464151\pi$
$557$	8.82362e19	0.224767	0.112384	+	0.993665i	$0.464151\pi$
$558$	−4.64543e20	−1.16753
$559$	3.39425e20	0.841696
$560$	3.45930e21	8.46406
$561$	−5.84187e19	−0.141036
$562$	8.05820e20	1.91962
$563$	5.14798e20	1.21011	0.605053	−	0.796185i	$-0.293152\pi$
$563$	5.14798e20	1.21011	0.605053	+	0.796185i	$0.293152\pi$
$564$	7.67605e19	0.178051
$565$	−4.72267e19	−0.108100
$566$	1.01105e20	0.228375
$567$	6.96935e20	1.55353
$568$	8.02387e20	1.76511
$569$	−4.39293e20	−0.953701	−0.476851	−	0.878984i	$-0.658222\pi$
$569$	−4.39293e20	−0.953701	−0.476851	+	0.878984i	$0.658222\pi$
$570$	1.70859e20	0.366080
$571$	6.05701e20	1.28082	0.640409	−	0.768034i	$-0.278765\pi$
$571$	6.05701e20	1.28082	0.640409	+	0.768034i	$0.278765\pi$
$572$	−8.39681e20	−1.75244
$573$	−1.90385e19	−0.0392169
$574$	−8.23465e20	−1.67419
$575$	−8.73195e20	−1.75228
$576$	−1.45872e21	−2.88938
$577$	1.93233e20	0.377801	0.188901	−	0.981996i	$-0.439508\pi$
$577$	1.93233e20	0.377801	0.188901	+	0.981996i	$0.439508\pi$
$578$	2.48487e20	0.479562
$579$	1.12999e20	0.215272
$580$	−4.07126e20	−0.765630
$581$	−1.24789e21	−2.31662
$582$	−1.99497e20	−0.365607
$583$	7.92709e20	1.43417
$584$	1.04426e21	1.86515
$585$	−5.01425e20	−0.884172
$586$	1.57608e21	2.74376
$587$	4.14803e19	0.0712946	0.0356473	−	0.999364i	$-0.488651\pi$
$587$	4.14803e19	0.0712946	0.0356473	+	0.999364i	$0.488651\pi$
$588$	−2.73881e20	−0.464763
$589$	−4.14261e20	−0.694079
$590$	1.12170e21	1.85560
$591$	1.69022e19	0.0276081
$592$	1.00785e21	1.62549
$593$	−2.91309e20	−0.463920	−0.231960	−	0.972725i	$-0.574514\pi$
$593$	−2.91309e20	−0.463920	−0.231960	+	0.972725i	$0.574514\pi$
$594$	−3.04592e20	−0.478983
$595$	−1.80528e21	−2.80329
$596$	−1.42613e20	−0.218681
$597$	−4.12629e19	−0.0624817
$598$	−9.08144e20	−1.35799
$599$	1.02776e21	1.51772	0.758859	−	0.651254i	$-0.225757\pi$
$599$	1.02776e21	1.51772	0.758859	+	0.651254i	$0.225757\pi$
$600$	−3.36904e20	−0.491328
$601$	−6.81991e20	−0.982246	−0.491123	−	0.871090i	$-0.663413\pi$
$601$	−6.81991e20	−0.982246	−0.491123	+	0.871090i	$0.663413\pi$
$602$	3.16650e21	4.50407
$603$	−6.12184e20	−0.860007
$604$	−1.15866e21	−1.60761
$605$	3.62732e20	0.497074
$606$	−4.13375e18	−0.00559500
$607$	1.01755e21	1.36032	0.680161	−	0.733062i	$-0.261910\pi$
$607$	1.01755e21	1.36032	0.680161	+	0.733062i	$0.261910\pi$
$608$	−2.80289e21	−3.70109
$609$	2.51859e19	0.0328494
$610$	−1.95349e21	−2.51673
$611$	−2.76665e20	−0.352084
$612$	2.33031e21	2.92940
$613$	−5.20837e20	−0.646768	−0.323384	−	0.946268i	$-0.604821\pi$
$613$	−5.20837e20	−0.646768	−0.323384	+	0.946268i	$0.604821\pi$
$614$	1.21945e21	1.49590
$615$	7.65946e19	0.0928186
$616$	−4.87857e21	−5.84033
$617$	−5.52611e20	−0.653552	−0.326776	−	0.945102i	$-0.605962\pi$
$617$	−5.52611e20	−0.653552	−0.326776	+	0.945102i	$0.605962\pi$
$618$	−6.96686e19	−0.0813998
$619$	2.10164e20	0.242593	0.121297	−	0.992616i	$-0.461295\pi$
$619$	2.10164e20	0.242593	0.121297	+	0.992616i	$0.461295\pi$
$620$	2.23604e21	2.55001
$621$	−2.39199e20	−0.269509
$622$	−2.14815e21	−2.39131
$623$	−2.25524e21	−2.48046
$624$	−1.96293e20	−0.213315
$625$	−3.77953e20	−0.405824
$626$	3.49647e21	3.70956
$627$	−1.34988e20	−0.141511
$628$	1.08988e21	1.12897
$629$	−5.25962e20	−0.538362
$630$	−4.67780e21	−4.73137
$631$	4.52262e20	0.452032	0.226016	−	0.974124i	$-0.427430\pi$
$631$	4.52262e20	0.452032	0.226016	+	0.974124i	$0.427430\pi$
$632$	−2.22831e20	−0.220089
$633$	1.29095e20	0.126003
$634$	1.06765e21	1.02981
$635$	3.61191e20	0.344297
$636$	3.85662e20	0.363311
$637$	9.87139e20	0.919036
$638$	4.42984e20	0.407599
$639$	−6.07844e20	−0.552759
$640$	3.96320e21	3.56202
$641$	−1.71222e20	−0.152098	−0.0760490	−	0.997104i	$-0.524231\pi$
$641$	−1.71222e20	−0.152098	−0.0760490	+	0.997104i	$0.524231\pi$
$642$	3.80878e20	0.334405
$643$	1.08788e21	0.944061	0.472031	−	0.881582i	$-0.343521\pi$
$643$	1.08788e21	0.944061	0.472031	+	0.881582i	$0.343521\pi$
$644$	−6.15163e21	−5.27651
$645$	−2.94532e20	−0.249709
$646$	2.86195e21	2.39838
$647$	2.16370e21	1.79232	0.896161	−	0.443730i	$-0.146345\pi$
$647$	2.16370e21	1.79232	0.896161	+	0.443730i	$0.146345\pi$
$648$	3.71415e21	3.04121
$649$	−8.86207e20	−0.717299
$650$	1.94976e21	1.56002
$651$	−1.38327e20	−0.109409
$652$	6.53959e21	5.11321
$653$	−1.66745e21	−1.28885	−0.644427	−	0.764666i	$-0.722904\pi$
$653$	−1.66745e21	−1.28885	−0.644427	+	0.764666i	$0.722904\pi$
$654$	−4.50926e20	−0.344566
$655$	−1.79107e21	−1.35301
$656$	−2.45849e21	−1.83607
$657$	−7.91077e20	−0.584088
$658$	−2.58101e21	−1.88407
$659$	−1.06178e20	−0.0766291	−0.0383146	−	0.999266i	$-0.512199\pi$
$659$	−1.06178e20	−0.0766291	−0.0383146	+	0.999266i	$0.512199\pi$
$660$	7.28623e20	0.519905
$661$	2.59715e21	1.83226	0.916128	−	0.400886i	$-0.131298\pi$
$661$	2.59715e21	1.83226	0.916128	+	0.400886i	$0.131298\pi$
$662$	1.19194e21	0.831415
$663$	1.02438e20	0.0706497
$664$	−6.65031e21	−4.53504
$665$	−4.17147e21	−2.81272
$666$	−1.36286e21	−0.908644
$667$	3.47880e20	0.229343
$668$	3.29574e21	2.14847
$669$	−1.13112e20	−0.0729144
$670$	4.05823e21	2.58687
$671$	1.54337e21	0.972863
$672$	−9.35926e20	−0.583407
$673$	6.11624e20	0.377026	0.188513	−	0.982071i	$-0.439633\pi$
$673$	6.11624e20	0.377026	0.188513	+	0.982071i	$0.439633\pi$
$674$	−3.17747e21	−1.93701
$675$	5.13553e20	0.309604
$676$	−2.97411e21	−1.77320
$677$	−1.62933e21	−0.960711	−0.480356	−	0.877074i	$-0.659492\pi$
$677$	−1.62933e21	−0.960711	−0.480356	+	0.877074i	$0.659492\pi$
$678$	2.50000e19	0.0145786
$679$	4.87068e21	2.80909
$680$	−9.62081e21	−5.48775
$681$	2.11279e19	0.0119193
$682$	−2.43299e21	−1.35755
$683$	1.50581e21	0.831025	0.415512	−	0.909588i	$-0.363602\pi$
$683$	1.50581e21	0.831025	0.415512	+	0.909588i	$0.363602\pi$
$684$	5.38467e21	2.93926
$685$	2.00993e21	1.08518
$686$	3.44290e21	1.83863
$687$	−5.36411e19	−0.0283349
$688$	9.45369e21	4.93956
$689$	−1.39003e21	−0.718421
$690$	7.88031e20	0.402880
$691$	−3.06868e21	−1.55191	−0.775955	−	0.630788i	$-0.782732\pi$
$691$	−3.06868e21	−1.55191	−0.775955	+	0.630788i	$0.782732\pi$
$692$	5.48057e21	2.74176
$693$	3.69574e21	1.82895
$694$	2.57109e21	1.25870
$695$	1.71748e21	0.831776
$696$	1.34222e20	0.0643064
$697$	1.28299e21	0.608104
$698$	−3.88956e21	−1.82383
$699$	−1.66025e19	−0.00770184
$700$	1.32074e22	6.06151
$701$	−2.07847e21	−0.943751	−0.471876	−	0.881665i	$-0.656423\pi$
$701$	−2.07847e21	−0.943751	−0.471876	+	0.881665i	$0.656423\pi$
$702$	5.34107e20	0.239939
$703$	−1.21534e21	−0.540174
$704$	−7.63989e21	−3.35964
$705$	2.40073e20	0.104454
$706$	2.91020e21	1.25282
$707$	1.00925e20	0.0429884
$708$	−4.31150e20	−0.181710
$709$	5.47042e20	0.228126	0.114063	−	0.993474i	$-0.463614\pi$
$709$	5.47042e20	0.228126	0.114063	+	0.993474i	$0.463614\pi$
$710$	4.02946e21	1.66268
$711$	1.68805e20	0.0689227
$712$	−1.20188e22	−4.85579
$713$	−1.91065e21	−0.763851
$714$	9.55646e20	0.378060
$715$	−2.62615e21	−1.02807
$716$	1.97503e21	0.765115
$717$	−1.64206e20	−0.0629498
$718$	−4.02632e21	−1.52748
$719$	2.27424e21	0.853825	0.426913	−	0.904293i	$-0.359601\pi$
$719$	2.27424e21	0.853825	0.426913	+	0.904293i	$0.359601\pi$
$720$	−1.39657e22	−5.18884
$721$	1.70094e21	0.625425
$722$	1.36217e21	0.495682
$723$	1.37245e20	0.0494266
$724$	−7.56141e20	−0.269503
$725$	−7.46886e20	−0.263463
$726$	−1.92016e20	−0.0670368
$727$	−5.65774e21	−1.95495	−0.977474	−	0.211057i	$-0.932309\pi$
$727$	−5.65774e21	−1.95495	−0.977474	+	0.211057i	$0.932309\pi$
$728$	8.55465e21	2.92561
$729$	−2.74287e21	−0.928428
$730$	5.24412e21	1.75692
$731$	−4.93353e21	−1.63598
$732$	7.50867e20	0.246451
$733$	7.72112e20	0.250842	0.125421	−	0.992104i	$-0.459972\pi$
$733$	7.72112e20	0.250842	0.125421	+	0.992104i	$0.459972\pi$
$734$	−4.95445e21	−1.59322
$735$	−8.56578e20	−0.272654
$736$	−1.29275e22	−4.07314
$737$	−3.20624e21	−0.999977
$738$	3.32445e21	1.02635
$739$	−1.18865e21	−0.363262	−0.181631	−	0.983367i	$-0.558138\pi$
$739$	−1.18865e21	−0.363262	−0.181631	+	0.983367i	$0.558138\pi$
$740$	6.56002e21	1.98457
$741$	2.36704e20	0.0708875
$742$	−1.29676e22	−3.84441
$743$	5.05257e21	1.48285	0.741424	−	0.671037i	$-0.234151\pi$
$743$	5.05257e21	1.48285	0.741424	+	0.671037i	$0.234151\pi$
$744$	−7.37183e20	−0.214180
$745$	−4.46030e20	−0.128290
$746$	−9.92839e19	−0.0282708
$747$	5.03791e21	1.42019
$748$	1.22047e22	3.40617
$749$	−9.29904e21	−2.56936
$750$	−4.99399e20	−0.136612
$751$	2.87339e21	0.778207	0.389103	−	0.921194i	$-0.372785\pi$
$751$	2.87339e21	0.778207	0.389103	+	0.921194i	$0.372785\pi$
$752$	−7.70571e21	−2.06623
$753$	3.02964e20	0.0804321
$754$	−7.76780e20	−0.204180
$755$	−3.62379e21	−0.943106
$756$	3.61796e21	0.932289
$757$	3.92223e21	1.00072	0.500361	−	0.865817i	$-0.333201\pi$
$757$	3.92223e21	1.00072	0.500361	+	0.865817i	$0.333201\pi$
$758$	1.05777e21	0.267222
$759$	−6.22592e20	−0.155736
$760$	−2.22309e22	−5.50623
$761$	7.63530e21	1.87258	0.936292	−	0.351223i	$-0.114234\pi$
$761$	7.63530e21	1.87258	0.936292	+	0.351223i	$0.114234\pi$
$762$	−1.91200e20	−0.0464330
$763$	1.10093e22	2.64743
$764$	3.97750e21	0.947130
$765$	7.28819e21	1.71854
$766$	9.53204e21	2.22572
$767$	1.55398e21	0.359319
$768$	−6.95920e20	−0.159349
$769$	6.63246e20	0.150393	0.0751965	−	0.997169i	$-0.476042\pi$
$769$	6.63246e20	0.150393	0.0751965	+	0.997169i	$0.476042\pi$
$770$	−2.44994e22	−5.50142
$771$	−8.34950e19	−0.0185675
$772$	−2.36076e22	−5.19904
$773$	3.79539e21	0.827772	0.413886	−	0.910329i	$-0.364171\pi$
$773$	3.79539e21	0.827772	0.413886	+	0.910329i	$0.364171\pi$
$774$	−1.27836e22	−2.76119
$775$	4.10210e21	0.877492
$776$	2.59571e22	5.49912
$777$	−4.05820e20	−0.0851483
$778$	−8.47849e21	−1.76186
$779$	2.96462e21	0.610151
$780$	−1.27765e21	−0.260437
$781$	−3.18351e21	−0.642723
$782$	1.31998e22	2.63948
$783$	−2.04599e20	−0.0405219
$784$	2.74939e22	5.39344
$785$	3.40868e21	0.662313
$786$	9.48121e20	0.182471
$787$	−7.65143e20	−0.145859	−0.0729293	−	0.997337i	$-0.523235\pi$
$787$	−7.65143e20	−0.145859	−0.0729293	+	0.997337i	$0.523235\pi$
$788$	−3.53117e21	−0.666764
$789$	−8.11342e20	−0.151749
$790$	−1.11902e21	−0.207317
$791$	−6.10368e20	−0.112013
$792$	1.96955e22	3.58038
$793$	−2.70633e21	−0.487339
$794$	−9.34863e21	−1.66761
$795$	1.20618e21	0.213137
$796$	8.62058e21	1.50900
$797$	−9.62784e21	−1.66952	−0.834760	−	0.550614i	$-0.814393\pi$
$797$	−9.62784e21	−1.66952	−0.834760	+	0.550614i	$0.814393\pi$
$798$	2.20822e21	0.379332
$799$	4.02132e21	0.684334
$800$	2.77548e22	4.67912
$801$	9.10475e21	1.52063
$802$	−1.21878e22	−2.01659
$803$	−4.14317e21	−0.679151
$804$	−1.55987e21	−0.253319
$805$	−1.92396e22	−3.09547
$806$	4.26628e21	0.680043
$807$	4.33767e20	0.0685022
$808$	5.37853e20	0.0841547
$809$	5.36074e21	0.831018	0.415509	−	0.909589i	$-0.363603\pi$
$809$	5.36074e21	0.831018	0.415509	+	0.909589i	$0.363603\pi$
$810$	1.86518e22	2.86473
$811$	−1.07967e22	−1.64299	−0.821495	−	0.570216i	$-0.806860\pi$
$811$	−1.07967e22	−1.64299	−0.821495	+	0.570216i	$0.806860\pi$
$812$	−5.26179e21	−0.793347
$813$	8.87996e20	0.132658
$814$	−7.13780e21	−1.05653
$815$	2.04529e22	2.99967
$816$	2.85312e21	0.414614
$817$	−1.13999e22	−1.64148
$818$	−1.45778e22	−2.07990
$819$	−6.48053e21	−0.916181
$820$	−1.60020e22	−2.24167
$821$	−1.11384e22	−1.54614	−0.773069	−	0.634321i	$-0.781280\pi$
$821$	−1.11384e22	−1.54614	−0.773069	+	0.634321i	$0.781280\pi$
$822$	−1.06398e21	−0.146350
$823$	−6.46041e21	−0.880565	−0.440282	−	0.897859i	$-0.645122\pi$
$823$	−6.46041e21	−0.880565	−0.440282	+	0.897859i	$0.645122\pi$
$824$	9.06476e21	1.22434
$825$	1.33668e21	0.178906
$826$	1.44971e22	1.92278
$827$	−4.38568e21	−0.576428	−0.288214	−	0.957566i	$-0.593061\pi$
$827$	−4.38568e21	−0.576428	−0.288214	+	0.957566i	$0.593061\pi$
$828$	2.48351e22	3.23473
$829$	4.99220e21	0.644366	0.322183	−	0.946677i	$-0.395583\pi$
$829$	4.99220e21	0.644366	0.322183	+	0.946677i	$0.395583\pi$
$830$	−3.33968e22	−4.27188
$831$	1.57471e21	0.199615
$832$	1.33967e22	1.68295
$833$	−1.43480e22	−1.78630
$834$	−9.09169e20	−0.112176
$835$	1.03076e22	1.26041
$836$	2.82016e22	3.41764
$837$	1.12371e21	0.134962
$838$	2.91320e22	3.46769
$839$	−9.89573e21	−1.16744	−0.583718	−	0.811956i	$-0.698403\pi$
$839$	−9.89573e21	−1.16744	−0.583718	+	0.811956i	$0.698403\pi$
$840$	−7.42320e21	−0.867953
$841$	2.97558e20	0.0344828
$842$	−1.20583e22	−1.38498
$843$	−9.68715e20	−0.110278
$844$	−2.69703e22	−3.04311
$845$	−9.30171e21	−1.04025
$846$	1.04199e22	1.15502
$847$	4.68803e21	0.515069
$848$	−3.87152e22	−4.21612
$849$	−1.21543e20	−0.0131196
$850$	−2.83396e22	−3.03216
$851$	−5.60538e21	−0.594475
$852$	−1.54881e21	−0.162818
$853$	4.41757e21	0.460327	0.230163	−	0.973152i	$-0.426074\pi$
$853$	4.41757e21	0.460327	0.230163	+	0.973152i	$0.426074\pi$
$854$	−2.52473e22	−2.60784
$855$	1.68409e22	1.72432
$856$	−4.95570e22	−5.02981
$857$	2.09169e21	0.210446	0.105223	−	0.994449i	$-0.466444\pi$
$857$	2.09169e21	0.210446	0.105223	+	0.994449i	$0.466444\pi$
$858$	1.39018e21	0.138649
$859$	1.60393e22	1.58576	0.792881	−	0.609377i	$-0.208580\pi$
$859$	1.60393e22	1.58576	0.792881	+	0.609377i	$0.208580\pi$
$860$	6.15331e22	6.03074
$861$	9.89927e20	0.0961788
$862$	2.81120e22	2.70761
$863$	−2.84865e21	−0.271993	−0.135997	−	0.990709i	$-0.543424\pi$
$863$	−2.84865e21	−0.271993	−0.135997	+	0.990709i	$0.543424\pi$
$864$	7.60303e21	0.719671
$865$	1.71408e22	1.60846
$866$	−3.26597e21	−0.303828
$867$	−2.98718e20	−0.0275498
$868$	2.88991e22	2.64233
$869$	8.84093e20	0.0801401
$870$	6.74041e20	0.0605748
$871$	5.62219e21	0.500921
$872$	5.86711e22	5.18264
$873$	−1.96637e22	−1.72210
$874$	3.05010e22	2.64836
$875$	1.21927e22	1.04964
$876$	−2.01570e21	−0.172046
$877$	−1.62471e22	−1.37493	−0.687463	−	0.726219i	$-0.741276\pi$
$877$	−1.62471e22	−1.37493	−0.687463	+	0.726219i	$0.741276\pi$
$878$	3.96269e21	0.332492
$879$	−1.89468e21	−0.157623
$880$	−7.31439e22	−6.03334
$881$	−8.10619e21	−0.662975	−0.331488	−	0.943460i	$-0.607550\pi$
$881$	−8.10619e21	−0.662975	−0.331488	+	0.943460i	$0.607550\pi$
$882$	−3.71782e22	−3.01491
$883$	1.06965e21	0.0860076	0.0430038	−	0.999075i	$-0.486307\pi$
$883$	1.06965e21	0.0860076	0.0430038	+	0.999075i	$0.486307\pi$
$884$	−2.14012e22	−1.70626
$885$	−1.34845e21	−0.106600
$886$	−3.14392e21	−0.246444
$887$	1.99410e22	1.54996	0.774980	−	0.631986i	$-0.217760\pi$
$887$	1.99410e22	1.54996	0.774980	+	0.631986i	$0.217760\pi$
$888$	−2.16272e21	−0.166687
$889$	4.66811e21	0.356762
$890$	−6.03563e22	−4.57401
$891$	−1.47361e22	−1.10738
$892$	2.36312e22	1.76096
$893$	9.29209e21	0.686638
$894$	2.36111e20	0.0173015
$895$	6.17703e21	0.448856
$896$	5.12213e22	3.69097
$897$	1.09172e21	0.0780135
$898$	−1.04475e22	−0.740355
$899$	−1.63427e21	−0.114849
$900$	−5.33201e22	−3.71597
$901$	2.02040e22	1.39637
$902$	1.74114e22	1.19340
$903$	−3.80660e21	−0.258749
$904$	−3.25281e21	−0.219278
$905$	−2.36488e21	−0.158104
$906$	1.91829e21	0.127190
$907$	−1.56642e22	−1.03004	−0.515018	−	0.857179i	$-0.672215\pi$
$907$	−1.56642e22	−1.03004	−0.515018	+	0.857179i	$0.672215\pi$
$908$	−4.41400e21	−0.287865
$909$	−4.07448e20	−0.0263538
$910$	4.29601e22	2.75584
$911$	−5.77920e21	−0.367688	−0.183844	−	0.982955i	$-0.558854\pi$
$911$	−5.77920e21	−0.367688	−0.183844	+	0.982955i	$0.558854\pi$
$912$	6.59271e21	0.416009
$913$	2.63854e22	1.65133
$914$	2.85138e22	1.76994
$915$	2.34838e21	0.144581
$916$	1.12066e22	0.684318
$917$	−2.31482e22	−1.40199
$918$	−7.76323e21	−0.466361
$919$	−5.57702e21	−0.332304	−0.166152	−	0.986100i	$-0.553134\pi$
$919$	−5.57702e21	−0.332304	−0.166152	+	0.986100i	$0.553134\pi$
$920$	−1.02533e23	−6.05974
$921$	−1.46596e21	−0.0859360
$922$	−5.78851e21	−0.336577
$923$	5.58234e21	0.321961
$924$	9.41690e21	0.538726
$925$	1.20346e22	0.682917
$926$	5.09621e22	2.86857
$927$	−6.86696e21	−0.383413
$928$	−1.10575e22	−0.612416
$929$	2.61820e22	1.43842	0.719210	−	0.694793i	$-0.244504\pi$
$929$	2.61820e22	1.43842	0.719210	+	0.694793i	$0.244504\pi$
$930$	−3.70201e21	−0.201751
$931$	−3.31541e22	−1.79231
$932$	3.46856e21	0.186007
$933$	2.58239e21	0.137376
$934$	3.75741e21	0.198284
$935$	3.81710e22	1.99824
$936$	−3.45364e22	−1.79353
$937$	1.88525e22	0.971228	0.485614	−	0.874173i	$-0.338596\pi$
$937$	1.88525e22	0.971228	0.485614	+	0.874173i	$0.338596\pi$
$938$	5.24495e22	2.68052
$939$	−4.20328e21	−0.213106
$940$	−5.01557e22	−2.52267
$941$	−1.22356e22	−0.610526	−0.305263	−	0.952268i	$-0.598744\pi$
$941$	−1.22356e22	−0.610526	−0.305263	+	0.952268i	$0.598744\pi$
$942$	−1.80442e21	−0.0893215
$943$	1.36734e22	0.671486
$944$	4.32816e22	2.10869
$945$	1.13154e22	0.546929
$946$	−6.69527e22	−3.21059
$947$	2.27969e22	1.08455	0.542277	−	0.840200i	$-0.317562\pi$
$947$	2.27969e22	1.08455	0.542277	+	0.840200i	$0.317562\pi$
$948$	4.30121e20	0.0203015
$949$	7.26511e21	0.340209
$950$	−6.54846e22	−3.04237
$951$	−1.28347e21	−0.0591604
$952$	−1.24342e23	−5.68642
$953$	2.64864e21	0.120178	0.0600892	−	0.998193i	$-0.480861\pi$
$953$	2.64864e21	0.120178	0.0600892	+	0.998193i	$0.480861\pi$
$954$	5.23521e22	2.35679
$955$	1.24399e22	0.555636
$956$	3.43056e22	1.52030
$957$	−5.32533e20	−0.0234157
$958$	−2.50199e22	−1.09155
$959$	2.59768e22	1.12446
$960$	−1.16248e22	−0.499288
$961$	−1.44894e22	−0.617484
$962$	1.25163e22	0.529250
$963$	3.75416e22	1.57513
$964$	−2.86731e22	−1.19370
$965$	−7.38343e22	−3.05002
$966$	1.01847e22	0.417465
$967$	−1.54659e22	−0.629038	−0.314519	−	0.949251i	$-0.601843\pi$
$967$	−1.54659e22	−0.629038	−0.314519	+	0.949251i	$0.601843\pi$
$968$	2.49837e22	1.00831
$969$	−3.44049e21	−0.137782
$970$	1.30352e23	5.18001
$971$	−2.64706e22	−1.04381	−0.521903	−	0.853005i	$-0.674778\pi$
$971$	−2.64706e22	−1.04381	−0.521903	+	0.853005i	$0.674778\pi$
$972$	−2.19537e22	−0.859034
$973$	2.21972e22	0.861888
$974$	−1.80268e22	−0.694586
$975$	−2.34390e21	−0.0896198
$976$	−7.53769e22	−2.85999
$977$	1.99440e22	0.750936	0.375468	−	0.926835i	$-0.377482\pi$
$977$	1.99440e22	0.750936	0.375468	+	0.926835i	$0.377482\pi$
$978$	−1.08270e22	−0.404545
$979$	4.76850e22	1.76812
$980$	1.78955e23	6.58488
$981$	−4.44460e22	−1.62299
$982$	−6.96944e22	−2.52558
$983$	−3.30238e22	−1.18762	−0.593808	−	0.804607i	$-0.702376\pi$
$983$	−3.30238e22	−1.18762	−0.593808	+	0.804607i	$0.702376\pi$
$984$	5.27558e21	0.188281
$985$	−1.10439e22	−0.391158
$986$	1.12905e22	0.396858
$987$	3.10276e21	0.108235
$988$	−4.94519e22	−1.71201
$989$	−5.25786e22	−1.80649
$990$	9.89078e22	3.37261
$991$	1.55481e22	0.526167	0.263084	−	0.964773i	$-0.415260\pi$
$991$	1.55481e22	0.526167	0.263084	+	0.964773i	$0.415260\pi$
$992$	6.07306e22	2.03972
$993$	−1.43288e21	−0.0477630
$994$	5.20777e22	1.72287
$995$	2.69614e22	0.885256
$996$	1.28368e22	0.418323
$997$	1.80809e22	0.584800	0.292400	−	0.956296i	$-0.405546\pi$
$997$	1.80809e22	0.584800	0.292400	+	0.956296i	$0.405546\pi$
$998$	−9.37548e22	−3.00964
$999$	3.29670e21	0.105036

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.16.a.b.1.18	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.16.a.b.1.18	✓	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)

\(f(q)\)	\(=\)	\(q+345.887 q^{2} -415.807 q^{3} +86869.8 q^{4} +271690. q^{5} -143822. q^{6} +3.51139e6 q^{7} +1.87131e7 q^{8} -1.41760e7 q^{9} +O(q^{10})\)	\(q+345.887 q^{2} -415.807 q^{3} +86869.8 q^{4} +271690. q^{5} -143822. q^{6} +3.51139e6 q^{7} +1.87131e7 q^{8} -1.41760e7 q^{9} +9.39741e7 q^{10} -7.42451e7 q^{11} -3.61211e7 q^{12} +1.30190e8 q^{13} +1.21454e9 q^{14} -1.12971e8 q^{15} +3.62607e9 q^{16} -1.89231e9 q^{17} -4.90330e9 q^{18} -4.37257e9 q^{19} +2.36017e10 q^{20} -1.46006e9 q^{21} -2.56804e10 q^{22} -2.01671e10 q^{23} -7.78104e9 q^{24} +4.32981e10 q^{25} +4.50310e10 q^{26} +1.18609e10 q^{27} +3.05034e11 q^{28} -1.72499e10 q^{29} -3.90751e10 q^{30} +9.47409e10 q^{31} +6.41018e11 q^{32} +3.08717e10 q^{33} -6.54524e11 q^{34} +9.54010e11 q^{35} -1.23147e12 q^{36} +2.77947e11 q^{37} -1.51241e12 q^{38} -5.41340e10 q^{39} +5.08417e12 q^{40} -6.78004e11 q^{41} -5.05016e11 q^{42} +2.60715e12 q^{43} -6.44966e12 q^{44} -3.85149e12 q^{45} -6.97553e12 q^{46} -2.12509e12 q^{47} -1.50775e12 q^{48} +7.58229e12 q^{49} +1.49762e13 q^{50} +7.86835e11 q^{51} +1.13096e13 q^{52} -1.06769e13 q^{53} +4.10252e12 q^{54} -2.01717e13 q^{55} +6.57089e13 q^{56} +1.81815e12 q^{57} -5.96651e12 q^{58} +1.19362e13 q^{59} -9.81375e12 q^{60} -2.07875e13 q^{61} +3.27696e13 q^{62} -4.97775e13 q^{63} +1.02901e14 q^{64} +3.53714e13 q^{65} +1.06781e13 q^{66} +4.31845e13 q^{67} -1.64384e14 q^{68} +8.38562e12 q^{69} +3.29980e14 q^{70} +4.28784e13 q^{71} -2.65277e14 q^{72} +5.58039e13 q^{73} +9.61383e13 q^{74} -1.80037e13 q^{75} -3.79844e14 q^{76} -2.60704e14 q^{77} -1.87242e13 q^{78} -1.19078e13 q^{79} +9.85167e14 q^{80} +1.98478e14 q^{81} -2.34513e14 q^{82} -3.55383e14 q^{83} -1.26835e14 q^{84} -5.14122e14 q^{85} +9.01779e14 q^{86} +7.17263e12 q^{87} -1.38936e15 q^{88} -6.42265e14 q^{89} -1.33218e15 q^{90} +4.57148e14 q^{91} -1.75191e15 q^{92} -3.93940e13 q^{93} -7.35041e14 q^{94} -1.18798e15 q^{95} -2.66540e14 q^{96} +1.38711e15 q^{97} +2.62261e15 q^{98} +1.05250e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 9908 q^{3} + 387418 q^{4} + 230490 q^{5} + 1566838 q^{6} + 2882024 q^{7} + 26209092 q^{8} + 93022899 q^{9}+O(q^{10}) \) 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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