LMFDB - Embedded newform 29.16.a.b.1.15

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			1.15
Root			$207.928$ 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)

$f(q)$	$=$	$q+207.928 q^{2} +6078.50 q^{3} +10466.0 q^{4} +181747. q^{5} +1.26389e6 q^{6} +3.03379e6 q^{7} -4.63720e6 q^{8} +2.25992e7 q^{9} +O(q^{10})$	\(q+207.928 q^{2} +6078.50 q^{3} +10466.0 q^{4} +181747. q^{5} +1.26389e6 q^{6} +3.03379e6 q^{7} -4.63720e6 q^{8} +2.25992e7 q^{9} +3.77902e7 q^{10} +6.06771e7 q^{11} +6.36178e7 q^{12} -2.26587e8 q^{13} +6.30809e8 q^{14} +1.10475e9 q^{15} -1.30716e9 q^{16} -3.31389e9 q^{17} +4.69901e9 q^{18} +4.36731e9 q^{19} +1.90217e9 q^{20} +1.84409e10 q^{21} +1.26165e10 q^{22} +1.88583e10 q^{23} -2.81872e10 q^{24} +2.51430e9 q^{25} -4.71138e10 q^{26} +5.01495e10 q^{27} +3.17517e10 q^{28} -1.72499e10 q^{29} +2.29708e11 q^{30} -2.03364e11 q^{31} -1.19842e11 q^{32} +3.68825e11 q^{33} -6.89051e11 q^{34} +5.51381e11 q^{35} +2.36524e11 q^{36} +7.00824e11 q^{37} +9.08087e11 q^{38} -1.37731e12 q^{39} -8.42796e11 q^{40} -1.99287e12 q^{41} +3.83437e12 q^{42} -5.72940e11 q^{43} +6.35049e11 q^{44} +4.10733e12 q^{45} +3.92118e12 q^{46} +3.17229e12 q^{47} -7.94554e12 q^{48} +4.45630e12 q^{49} +5.22793e11 q^{50} -2.01435e13 q^{51} -2.37147e12 q^{52} +7.26168e12 q^{53} +1.04275e13 q^{54} +1.10279e13 q^{55} -1.40683e13 q^{56} +2.65467e13 q^{57} -3.58673e12 q^{58} -8.59920e12 q^{59} +1.15623e13 q^{60} +4.16060e13 q^{61} -4.22852e13 q^{62} +6.85612e13 q^{63} +1.79143e13 q^{64} -4.11814e13 q^{65} +7.66891e13 q^{66} -4.03376e12 q^{67} -3.46834e13 q^{68} +1.14630e14 q^{69} +1.14647e14 q^{70} -6.94992e13 q^{71} -1.04797e14 q^{72} +4.04275e13 q^{73} +1.45721e14 q^{74} +1.52832e13 q^{75} +4.57085e13 q^{76} +1.84081e14 q^{77} -2.86381e14 q^{78} -1.83706e14 q^{79} -2.37571e14 q^{80} -1.94405e13 q^{81} -4.14374e14 q^{82} +2.69840e13 q^{83} +1.93003e14 q^{84} -6.02290e14 q^{85} -1.19130e14 q^{86} -1.04853e14 q^{87} -2.81372e14 q^{88} -4.90285e14 q^{89} +8.54030e14 q^{90} -6.87416e14 q^{91} +1.97372e14 q^{92} -1.23615e15 q^{93} +6.59608e14 q^{94} +7.93745e14 q^{95} -7.28461e14 q^{96} +1.34082e14 q^{97} +9.26589e14 q^{98} +1.37125e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	207.928	1.14865	0.574325	−	0.818627i	$-0.305264\pi$
$2$	207.928	1.14865	0.574325	+	0.818627i	$0.305264\pi$
$3$	6078.50	1.60467	0.802337	−	0.596871i	$-0.203590\pi$
$3$	6078.50	1.60467	0.802337	+	0.596871i	$0.203590\pi$
$4$	10466.0	0.319398
$5$	181747.	1.04038	0.520190	−	0.854051i	$-0.325861\pi$
$5$	181747.	1.04038	0.520190	+	0.854051i	$0.325861\pi$
$6$	1.26389e6	1.84321
$7$	3.03379e6	1.39235	0.696177	−	0.717870i	$-0.254883\pi$
$7$	3.03379e6	1.39235	0.696177	+	0.717870i	$0.254883\pi$
$8$	−4.63720e6	−0.781774
$9$	2.25992e7	1.57498
$10$	3.77902e7	1.19503
$11$	6.06771e7	0.938814	0.469407	−	0.882982i	$-0.344468\pi$
$11$	6.06771e7	0.938814	0.469407	+	0.882982i	$0.344468\pi$
$12$	6.36178e7	0.512530
$13$	−2.26587e8	−1.00152	−0.500760	−	0.865586i	$-0.666946\pi$
$13$	−2.26587e8	−1.00152	−0.500760	+	0.865586i	$0.666946\pi$
$14$	6.30809e8	1.59933
$15$	1.10475e9	1.66947
$16$	−1.30716e9	−1.21738
$17$	−3.31389e9	−1.95872	−0.979359	−	0.202130i	$-0.935214\pi$
$17$	−3.31389e9	−1.95872	−0.979359	+	0.202130i	$0.935214\pi$
$18$	4.69901e9	1.80910
$19$	4.36731e9	1.12089	0.560444	−	0.828192i	$-0.310630\pi$
$19$	4.36731e9	1.12089	0.560444	+	0.828192i	$0.310630\pi$
$20$	1.90217e9	0.332295
$21$	1.84409e10	2.23427
$22$	1.26165e10	1.07837
$23$	1.88583e10	1.15490	0.577450	−	0.816426i	$-0.304048\pi$
$23$	1.88583e10	1.15490	0.577450	+	0.816426i	$0.304048\pi$
$24$	−2.81872e10	−1.25449
$25$	2.51430e9	0.0823886
$26$	−4.71138e10	−1.15040
$27$	5.01495e10	0.922653
$28$	3.17517e10	0.444716
$29$	−1.72499e10	−0.185695
$29$	−1.72499e10	−0.185695
$30$	2.29708e11	1.91764
$31$	−2.03364e11	−1.32758	−0.663792	−	0.747917i	$-0.731054\pi$
$31$	−2.03364e11	−1.32758	−0.663792	+	0.747917i	$0.731054\pi$
$32$	−1.19842e11	−0.616574
$33$	3.68825e11	1.50649
$34$	−6.89051e11	−2.24988
$35$	5.51381e11	1.44858
$36$	2.36524e11	0.503046
$37$	7.00824e11	1.21366	0.606829	−	0.794832i	$-0.292441\pi$
$37$	7.00824e11	1.21366	0.606829	+	0.794832i	$0.292441\pi$
$38$	9.08087e11	1.28751
$39$	−1.37731e12	−1.60711
$40$	−8.42796e11	−0.813341
$41$	−1.99287e12	−1.59809	−0.799043	−	0.601273i	$-0.794660\pi$
$41$	−1.99287e12	−1.59809	−0.799043	+	0.601273i	$0.794660\pi$
$42$	3.83437e12	2.56640
$43$	−5.72940e11	−0.321437	−0.160718	−	0.987000i	$-0.551381\pi$
$43$	−5.72940e11	−0.321437	−0.160718	+	0.987000i	$0.551381\pi$
$44$	6.35049e11	0.299855
$45$	4.10733e12	1.63857
$46$	3.92118e12	1.32658
$47$	3.17229e12	0.913354	0.456677	−	0.889633i	$-0.349040\pi$
$47$	3.17229e12	0.913354	0.456677	+	0.889633i	$0.349040\pi$
$48$	−7.94554e12	−1.95350
$49$	4.45630e12	0.938650
$50$	5.22793e11	0.0946357
$51$	−2.01435e13	−3.14310
$52$	−2.37147e12	−0.319884
$53$	7.26168e12	0.849119	0.424559	−	0.905400i	$-0.360429\pi$
$53$	7.26168e12	0.849119	0.424559	+	0.905400i	$0.360429\pi$
$54$	1.04275e13	1.05981
$55$	1.10279e13	0.976722
$56$	−1.40683e13	−1.08851
$57$	2.65467e13	1.79866
$58$	−3.58673e12	−0.213299
$59$	−8.59920e12	−0.449850	−0.224925	−	0.974376i	$-0.572214\pi$
$59$	−8.59920e12	−0.449850	−0.224925	+	0.974376i	$0.572214\pi$
$60$	1.15623e13	0.533226
$61$	4.16060e13	1.69505	0.847525	−	0.530756i	$-0.178092\pi$
$61$	4.16060e13	1.69505	0.847525	+	0.530756i	$0.178092\pi$
$62$	−4.22852e13	−1.52493
$63$	6.85612e13	2.19293
$64$	1.79143e13	0.509155
$65$	−4.11814e13	−1.04196
$66$	7.66891e13	1.73043
$67$	−4.03376e12	−0.0813110	−0.0406555	−	0.999173i	$-0.512945\pi$
$67$	−4.03376e12	−0.0813110	−0.0406555	+	0.999173i	$0.512945\pi$
$68$	−3.46834e13	−0.625611
$69$	1.14630e14	1.85324
$70$	1.14647e14	1.66391
$71$	−6.94992e13	−0.906864	−0.453432	−	0.891291i	$-0.649801\pi$
$71$	−6.94992e13	−0.906864	−0.453432	+	0.891291i	$0.649801\pi$
$72$	−1.04797e14	−1.23128
$73$	4.04275e13	0.428307	0.214154	−	0.976800i	$-0.431301\pi$
$73$	4.04275e13	0.428307	0.214154	+	0.976800i	$0.431301\pi$
$74$	1.45721e14	1.39407
$75$	1.52832e13	0.132207
$76$	4.57085e13	0.358010
$77$	1.84081e14	1.30716
$78$	−2.86381e14	−1.84601
$79$	−1.83706e14	−1.07627	−0.538135	−	0.842859i	$-0.680871\pi$
$79$	−1.83706e14	−1.07627	−0.538135	+	0.842859i	$0.680871\pi$
$80$	−2.37571e14	−1.26654
$81$	−1.94405e13	−0.0944211
$82$	−4.14374e14	−1.83564
$83$	2.69840e13	0.109149	0.0545745	−	0.998510i	$-0.482620\pi$
$83$	2.69840e13	0.109149	0.0545745	+	0.998510i	$0.482620\pi$
$84$	1.93003e14	0.713623
$85$	−6.02290e14	−2.03781
$86$	−1.19130e14	−0.369218
$87$	−1.04853e14	−0.297980
$88$	−2.81372e14	−0.733940
$89$	−4.90285e14	−1.17496	−0.587480	−	0.809239i	$-0.699880\pi$
$89$	−4.90285e14	−1.17496	−0.587480	+	0.809239i	$0.699880\pi$
$90$	8.54030e14	1.88215
$91$	−6.87416e14	−1.39447
$92$	1.97372e14	0.368873
$93$	−1.23615e15	−2.13034
$94$	6.59608e14	1.04912
$95$	7.93745e14	1.16615
$96$	−7.28461e14	−0.989401
$97$	1.34082e14	0.168493	0.0842466	−	0.996445i	$-0.473152\pi$
$97$	1.34082e14	0.168493	0.0842466	+	0.996445i	$0.473152\pi$
$98$	9.26589e14	1.07818
$99$	1.37125e15	1.47861
$100$	2.63148e13	0.0263148
$101$	−1.15870e15	−1.07538	−0.537689	−	0.843143i	$-0.680703\pi$
$101$	−1.15870e15	−1.07538	−0.537689	+	0.843143i	$0.680703\pi$
$102$	−4.18840e15	−3.61033
$103$	1.32046e15	1.05790	0.528951	−	0.848653i	$-0.322586\pi$
$103$	1.32046e15	1.05790	0.528951	+	0.848653i	$0.322586\pi$
$104$	1.05073e15	0.782962
$105$	3.35157e15	2.32449
$106$	1.50991e15	0.975341
$107$	−2.23134e15	−1.34335	−0.671673	−	0.740848i	$-0.734424\pi$
$107$	−2.23134e15	−1.34335	−0.671673	+	0.740848i	$0.734424\pi$
$108$	5.24867e14	0.294694
$109$	−2.66638e15	−1.39708	−0.698542	−	0.715569i	$-0.746168\pi$
$109$	−2.66638e15	−1.39708	−0.698542	+	0.715569i	$0.746168\pi$
$110$	2.29300e15	1.12191
$111$	4.25996e15	1.94753
$112$	−3.96563e15	−1.69503
$113$	3.61134e15	1.44404	0.722021	−	0.691872i	$-0.243214\pi$
$113$	3.61134e15	1.44404	0.722021	+	0.691872i	$0.243214\pi$
$114$	5.51980e15	2.06603
$115$	3.42744e15	1.20153
$116$	−1.80538e14	−0.0593108
$117$	−5.12069e15	−1.57737
$118$	−1.78801e15	−0.516721
$119$	−1.00536e16	−2.72723
$120$	−5.12293e15	−1.30515
$121$	−4.95543e14	−0.118629
$122$	8.65106e15	1.94702
$123$	−1.21137e16	−2.56441
$124$	−2.12842e15	−0.424028
$125$	−5.08950e15	−0.954664
$126$	1.42558e16	2.51891
$127$	−3.65135e15	−0.608030	−0.304015	−	0.952667i	$-0.598327\pi$
$127$	−3.65135e15	−0.608030	−0.304015	+	0.952667i	$0.598327\pi$
$128$	7.65187e15	1.20142
$129$	−3.48261e15	−0.515801
$130$	−8.56277e15	−1.19685
$131$	3.88259e14	0.0512374	0.0256187	−	0.999672i	$-0.491844\pi$
$131$	3.88259e14	0.0512374	0.0256187	+	0.999672i	$0.491844\pi$
$132$	3.86014e15	0.481170
$133$	1.32495e16	1.56067
$134$	−8.38732e14	−0.0933980
$135$	9.11451e15	0.959909
$136$	1.53672e16	1.53127
$137$	9.23143e15	0.870692	0.435346	−	0.900263i	$-0.356626\pi$
$137$	9.23143e15	0.870692	0.435346	+	0.900263i	$0.356626\pi$
$138$	2.38349e16	2.12872
$139$	−6.21856e15	−0.526113	−0.263056	−	0.964780i	$-0.584731\pi$
$139$	−6.21856e15	−0.526113	−0.263056	+	0.964780i	$0.584731\pi$
$140$	5.77078e15	0.462673
$141$	1.92828e16	1.46564
$142$	−1.44508e16	−1.04167
$143$	−1.37486e16	−0.940241
$144$	−2.95407e16	−1.91735
$145$	−3.13511e15	−0.193194
$146$	8.40601e15	0.491976
$147$	2.70876e16	1.50623
$148$	7.33486e15	0.387640
$149$	−3.12181e15	−0.156859	−0.0784294	−	0.996920i	$-0.524991\pi$
$149$	−3.12181e15	−0.156859	−0.0784294	+	0.996920i	$0.524991\pi$
$150$	3.17780e15	0.151859
$151$	−3.26036e15	−0.148231	−0.0741154	−	0.997250i	$-0.523613\pi$
$151$	−3.26036e15	−0.148231	−0.0741154	+	0.997250i	$0.523613\pi$
$152$	−2.02521e16	−0.876281
$153$	−7.48914e16	−3.08494
$154$	3.82756e16	1.50147
$155$	−3.69608e16	−1.38119
$156$	−1.44150e16	−0.513309
$157$	−1.89271e15	−0.0642445	−0.0321223	−	0.999484i	$-0.510227\pi$
$157$	−1.89271e15	−0.0642445	−0.0321223	+	0.999484i	$0.510227\pi$
$158$	−3.81977e16	−1.23626
$159$	4.41401e16	1.36256
$160$	−2.17810e16	−0.641471
$161$	5.72122e16	1.60803
$162$	−4.04221e15	−0.108457
$163$	−5.56850e15	−0.142670	−0.0713348	−	0.997452i	$-0.522726\pi$
$163$	−5.56850e15	−0.142670	−0.0713348	+	0.997452i	$0.522726\pi$
$164$	−2.08575e16	−0.510426
$165$	6.70328e16	1.56732
$166$	5.61072e15	0.125374
$167$	3.00244e16	0.641357	0.320679	−	0.947188i	$-0.396089\pi$
$167$	3.00244e16	0.641357	0.320679	+	0.947188i	$0.396089\pi$
$168$	−8.55140e16	−1.74670
$169$	1.55740e14	0.00304264
$170$	−1.25233e17	−2.34073
$171$	9.86979e16	1.76537
$172$	−5.99641e15	−0.102666
$173$	6.05281e16	0.992227	0.496113	−	0.868258i	$-0.334760\pi$
$173$	6.05281e16	0.992227	0.496113	+	0.868258i	$0.334760\pi$
$174$	−2.18019e16	−0.342275
$175$	7.62785e15	0.114714
$176$	−7.93143e16	−1.14290
$177$	−5.22702e16	−0.721863
$178$	−1.01944e17	−1.34962
$179$	−5.66169e16	−0.718702	−0.359351	−	0.933203i	$-0.617002\pi$
$179$	−5.66169e16	−0.718702	−0.359351	+	0.933203i	$0.617002\pi$
$180$	4.29875e16	0.523358
$181$	−1.89006e16	−0.220742	−0.110371	−	0.993890i	$-0.535204\pi$
$181$	−1.89006e16	−0.220742	−0.110371	+	0.993890i	$0.535204\pi$
$182$	−1.42933e17	−1.60176
$183$	2.52902e17	2.72000
$184$	−8.74499e16	−0.902871
$185$	1.27373e17	1.26266
$186$	−2.57030e17	−2.44702
$187$	−2.01077e17	−1.83887
$188$	3.32013e16	0.291724
$189$	1.52143e17	1.28466
$190$	1.65042e17	1.33950
$191$	1.08500e16	0.0846603	0.0423302	−	0.999104i	$-0.486522\pi$
$191$	1.08500e16	0.0846603	0.0423302	+	0.999104i	$0.486522\pi$
$192$	1.08892e17	0.817027
$193$	−2.51392e16	−0.181415	−0.0907073	−	0.995878i	$-0.528913\pi$
$193$	−2.51392e16	−0.181415	−0.0907073	+	0.995878i	$0.528913\pi$
$194$	2.78794e16	0.193540
$195$	−2.50321e17	−1.67201
$196$	4.66398e16	0.299803
$197$	2.33412e17	1.44420	0.722098	−	0.691791i	$-0.243178\pi$
$197$	2.33412e17	1.44420	0.722098	+	0.691791i	$0.243178\pi$
$198$	2.85122e17	1.69841
$199$	2.56367e17	1.47050	0.735249	−	0.677797i	$-0.237065\pi$
$199$	2.56367e17	1.47050	0.735249	+	0.677797i	$0.237065\pi$
$200$	−1.16593e16	−0.0644092
$201$	−2.45192e16	−0.130478
$202$	−2.40926e17	−1.23523
$203$	−5.23324e16	−0.258554
$204$	−2.10823e17	−1.00390
$205$	−3.62198e17	−1.66262
$206$	2.74560e17	1.21516
$207$	4.26184e17	1.81894
$208$	2.96184e17	1.21923
$209$	2.64996e17	1.05231
$210$	6.96884e17	2.67003
$211$	−1.17264e17	−0.433558	−0.216779	−	0.976221i	$-0.569555\pi$
$211$	−1.17264e17	−0.433558	−0.216779	+	0.976221i	$0.569555\pi$
$212$	7.60011e16	0.271207
$213$	−4.22451e17	−1.45522
$214$	−4.63959e17	−1.54304
$215$	−1.04130e17	−0.334416
$216$	−2.32553e17	−0.721306
$217$	−6.16964e17	−1.84847
$218$	−5.54414e17	−1.60476
$219$	2.45739e17	0.687294
$220$	1.15418e17	0.311963
$221$	7.50885e17	1.96170
$222$	8.85765e17	2.23703
$223$	8.28746e16	0.202365	0.101182	−	0.994868i	$-0.467737\pi$
$223$	8.28746e16	0.202365	0.101182	+	0.994868i	$0.467737\pi$
$224$	−3.63576e17	−0.858490
$225$	5.68212e16	0.129760
$226$	7.50898e17	1.65870
$227$	4.82583e17	1.03128	0.515642	−	0.856804i	$-0.327553\pi$
$227$	4.82583e17	1.03128	0.515642	+	0.856804i	$0.327553\pi$
$228$	2.77839e17	0.574489
$229$	−4.11358e17	−0.823103	−0.411552	−	0.911386i	$-0.635013\pi$
$229$	−4.11358e17	−0.823103	−0.411552	+	0.911386i	$0.635013\pi$
$230$	7.12661e17	1.38014
$231$	1.11894e18	2.09757
$232$	7.99911e16	0.145172
$233$	4.58461e17	0.805625	0.402813	−	0.915282i	$-0.368033\pi$
$233$	4.58461e17	0.805625	0.402813	+	0.915282i	$0.368033\pi$
$234$	−1.06473e18	−1.81185
$235$	5.76554e17	0.950234
$236$	−8.99996e16	−0.143681
$237$	−1.11666e18	−1.72706
$238$	−2.09043e18	−3.13263
$239$	−1.09470e18	−1.58969	−0.794846	−	0.606812i	$-0.792448\pi$
$239$	−1.09470e18	−1.58969	−0.794846	+	0.606812i	$0.792448\pi$
$240$	−1.44408e18	−2.03238
$241$	−1.13377e17	−0.154666	−0.0773332	−	0.997005i	$-0.524641\pi$
$241$	−1.13377e17	−0.154666	−0.0773332	+	0.997005i	$0.524641\pi$
$242$	−1.03037e17	−0.136263
$243$	−8.37759e17	−1.07417
$244$	4.35451e17	0.541396
$245$	8.09917e17	0.976551
$246$	−2.51877e18	−2.94561
$247$	−9.89576e17	−1.12259
$248$	9.43042e17	1.03787
$249$	1.64022e17	0.175149
$250$	−1.05825e18	−1.09658
$251$	1.79819e18	1.80835	0.904174	−	0.427165i	$-0.140488\pi$
$251$	1.79819e18	1.80835	0.904174	+	0.427165i	$0.140488\pi$
$252$	7.17565e17	0.700417
$253$	1.14427e18	1.08424
$254$	−7.59217e17	−0.698414
$255$	−3.66102e18	−3.27002
$256$	1.00402e18	0.870852
$257$	1.35799e18	1.14393	0.571963	−	0.820279i	$-0.306182\pi$
$257$	1.35799e18	1.14393	0.571963	+	0.820279i	$0.306182\pi$
$258$	−7.24132e17	−0.592475
$259$	2.12615e18	1.68984
$260$	−4.31007e17	−0.332800
$261$	−3.89834e17	−0.292466
$262$	8.07300e16	0.0588539
$263$	1.95140e17	0.138254	0.0691270	−	0.997608i	$-0.477979\pi$
$263$	1.95140e17	0.138254	0.0691270	+	0.997608i	$0.477979\pi$
$264$	−1.71032e18	−1.17773
$265$	1.31979e18	0.883405
$266$	2.75494e18	1.79267
$267$	−2.98019e18	−1.88543
$268$	−4.22176e16	−0.0259706
$269$	−1.83326e17	−0.109669	−0.0548343	−	0.998495i	$-0.517463\pi$
$269$	−1.83326e17	−0.109669	−0.0548343	+	0.998495i	$0.517463\pi$
$270$	1.89516e18	1.10260
$271$	1.01016e18	0.571636	0.285818	−	0.958284i	$-0.407735\pi$
$271$	1.01016e18	0.571636	0.285818	+	0.958284i	$0.407735\pi$
$272$	4.33177e18	2.38451
$273$	−4.17846e18	−2.23767
$274$	1.91947e18	1.00012
$275$	1.52560e17	0.0773475
$276$	1.19973e18	0.591922
$277$	3.75762e18	1.80432	0.902162	−	0.431398i	$-0.141980\pi$
$277$	3.75762e18	1.80432	0.902162	+	0.431398i	$0.141980\pi$
$278$	−1.29301e18	−0.604320
$279$	−4.59588e18	−2.09092
$280$	−2.55686e18	−1.13246
$281$	−8.16517e16	−0.0352101	−0.0176051	−	0.999845i	$-0.505604\pi$
$281$	−8.16517e16	−0.0352101	−0.0176051	+	0.999845i	$0.505604\pi$
$282$	4.00943e18	1.68350
$283$	−5.10299e17	−0.208654	−0.104327	−	0.994543i	$-0.533269\pi$
$283$	−5.10299e17	−0.208654	−0.104327	+	0.994543i	$0.533269\pi$
$284$	−7.27382e17	−0.289651
$285$	4.82478e18	1.87129
$286$	−2.85872e18	−1.08001
$287$	−6.04595e18	−2.22510
$288$	−2.70834e18	−0.971091
$289$	8.11948e18	2.83657
$290$	−6.51877e17	−0.221912
$291$	8.15017e17	0.270377
$292$	4.23116e17	0.136801
$293$	2.00939e18	0.633223	0.316611	−	0.948555i	$-0.397455\pi$
$293$	2.00939e18	0.633223	0.316611	+	0.948555i	$0.397455\pi$
$294$	5.63227e18	1.73013
$295$	−1.56288e18	−0.468015
$296$	−3.24986e18	−0.948806
$297$	3.04292e18	0.866199
$298$	−6.49111e17	−0.180176
$299$	−4.27305e18	−1.15666
$300$	1.59954e17	0.0422266
$301$	−1.73818e18	−0.447554
$302$	−6.77920e17	−0.170265
$303$	−7.04316e18	−1.72563
$304$	−5.70876e18	−1.36455
$305$	7.56176e18	1.76349
$306$	−1.55720e19	−3.54352
$307$	1.68682e18	0.374567	0.187284	−	0.982306i	$-0.440032\pi$
$307$	1.68682e18	0.374567	0.187284	+	0.982306i	$0.440032\pi$
$308$	1.92660e18	0.417505
$309$	8.02640e18	1.69759
$310$	−7.68519e18	−1.58651
$311$	5.73750e18	1.15616	0.578082	−	0.815979i	$-0.303801\pi$
$311$	5.73750e18	1.15616	0.578082	+	0.815979i	$0.303801\pi$
$312$	6.38685e18	1.25640
$313$	−6.48786e17	−0.124600	−0.0623001	−	0.998057i	$-0.519844\pi$
$313$	−6.48786e17	−0.124600	−0.0623001	+	0.998057i	$0.519844\pi$
$314$	−3.93547e17	−0.0737945
$315$	1.24608e19	2.28148
$316$	−1.92268e18	−0.343759
$317$	4.21870e18	0.736604	0.368302	−	0.929706i	$-0.379939\pi$
$317$	4.21870e18	0.736604	0.368302	+	0.929706i	$0.379939\pi$
$318$	9.17797e18	1.56510
$319$	−1.04667e18	−0.174333
$320$	3.25586e18	0.529714
$321$	−1.35632e19	−2.15563
$322$	1.18960e19	1.84707
$323$	−1.44728e19	−2.19550
$324$	−2.03465e17	−0.0301579
$325$	−5.69707e17	−0.0825138
$326$	−1.15785e18	−0.163877
$327$	−1.62076e19	−2.24186
$328$	9.24134e18	1.24934
$329$	9.62405e18	1.27171
$330$	1.39380e19	1.80030
$331$	−2.86482e18	−0.361732	−0.180866	−	0.983508i	$-0.557890\pi$
$331$	−2.86482e18	−0.361732	−0.180866	+	0.983508i	$0.557890\pi$
$332$	2.82415e17	0.0348620
$333$	1.58381e19	1.91149
$334$	6.24290e18	0.736696
$335$	−7.33123e17	−0.0845943
$336$	−2.41051e19	−2.71997
$337$	−6.73323e18	−0.743018	−0.371509	−	0.928429i	$-0.621160\pi$
$337$	−6.73323e18	−0.743018	−0.371509	+	0.928429i	$0.621160\pi$
$338$	3.23828e16	0.00349493
$339$	2.19515e19	2.31722
$340$	−6.30359e18	−0.650873
$341$	−1.23396e19	−1.24635
$342$	2.05220e19	2.02780
$343$	−8.83634e17	−0.0854214
$344$	2.65684e18	0.251291
$345$	2.08337e19	1.92807
$346$	1.25855e19	1.13972
$347$	−8.58396e18	−0.760705	−0.380353	−	0.924842i	$-0.624197\pi$
$347$	−8.58396e18	−0.760705	−0.380353	+	0.924842i	$0.624197\pi$
$348$	−1.09740e18	−0.0951745
$349$	−1.40302e18	−0.119090	−0.0595449	−	0.998226i	$-0.518965\pi$
$349$	−1.40302e18	−0.119090	−0.0595449	+	0.998226i	$0.518965\pi$
$350$	1.58604e18	0.131766
$351$	−1.13632e19	−0.924056
$352$	−7.27168e18	−0.578848
$353$	−8.63754e18	−0.673100	−0.336550	−	0.941666i	$-0.609260\pi$
$353$	−8.63754e18	−0.673100	−0.336550	+	0.941666i	$0.609260\pi$
$354$	−1.08684e19	−0.829169
$355$	−1.26313e19	−0.943483
$356$	−5.13134e18	−0.375280
$357$	−6.11111e19	−4.37631
$358$	−1.17722e19	−0.825537
$359$	7.62937e18	0.523938	0.261969	−	0.965076i	$-0.415628\pi$
$359$	7.62937e18	0.523938	0.261969	+	0.965076i	$0.415628\pi$
$360$	−1.90465e19	−1.28099
$361$	3.89229e18	0.256390
$362$	−3.92996e18	−0.253556
$363$	−3.01216e18	−0.190361
$364$	−7.19453e18	−0.445392
$365$	7.34757e18	0.445602
$366$	5.25854e19	3.12433
$367$	−1.14570e19	−0.666925	−0.333463	−	0.942763i	$-0.608217\pi$
$367$	−1.14570e19	−0.666925	−0.333463	+	0.942763i	$0.608217\pi$
$368$	−2.46508e19	−1.40596
$369$	−4.50373e19	−2.51695
$370$	2.64843e19	1.45036
$371$	2.20304e19	1.18227
$372$	−1.29376e19	−0.680427
$373$	3.03930e19	1.56660	0.783298	−	0.621647i	$-0.213536\pi$
$373$	3.03930e19	1.56660	0.783298	+	0.621647i	$0.213536\pi$
$374$	−4.18096e19	−2.11222
$375$	−3.09365e19	−1.53192
$376$	−1.47105e19	−0.714036
$377$	3.90860e18	0.185978
$378$	3.16348e19	1.47563
$379$	3.02815e19	1.38479	0.692395	−	0.721519i	$-0.256556\pi$
$379$	3.02815e19	1.38479	0.692395	+	0.721519i	$0.256556\pi$
$380$	8.30737e18	0.372466
$381$	−2.21947e19	−0.975691
$382$	2.25602e18	0.0972451
$383$	1.82464e19	0.771236	0.385618	−	0.922658i	$-0.373988\pi$
$383$	1.82464e19	0.771236	0.385618	+	0.922658i	$0.373988\pi$
$384$	4.65119e19	1.92788
$385$	3.34562e19	1.35994
$386$	−5.22715e18	−0.208382
$387$	−1.29480e19	−0.506256
$388$	1.40331e18	0.0538164
$389$	−4.16177e18	−0.156551	−0.0782755	−	0.996932i	$-0.524941\pi$
$389$	−4.16177e18	−0.156551	−0.0782755	+	0.996932i	$0.524941\pi$
$390$	−5.20488e19	−1.92055
$391$	−6.24946e19	−2.26212
$392$	−2.06647e19	−0.733811
$393$	2.36003e18	0.0822193
$394$	4.85328e19	1.65888
$395$	−3.33880e19	−1.11973
$396$	1.43516e19	0.472266
$397$	5.64002e19	1.82117	0.910587	−	0.413317i	$-0.135630\pi$
$397$	5.64002e19	1.82117	0.910587	+	0.413317i	$0.135630\pi$
$398$	5.33059e19	1.68909
$399$	8.05370e19	2.50437
$400$	−3.28658e18	−0.100298
$401$	−5.61727e19	−1.68245	−0.841225	−	0.540685i	$-0.818165\pi$
$401$	−5.61727e19	−1.68245	−0.841225	+	0.540685i	$0.818165\pi$
$402$	−5.09823e18	−0.149873
$403$	4.60797e19	1.32960
$404$	−1.21270e19	−0.343474
$405$	−3.53324e18	−0.0982337
$406$	−1.08814e19	−0.296988
$407$	4.25240e19	1.13940
$408$	9.34094e19	2.45719
$409$	−4.41689e19	−1.14075	−0.570376	−	0.821384i	$-0.693203\pi$
$409$	−4.41689e19	−1.14075	−0.570376	+	0.821384i	$0.693203\pi$
$410$	−7.53111e19	−1.90976
$411$	5.61132e19	1.39718
$412$	1.38200e19	0.337892
$413$	−2.60881e19	−0.626351
$414$	8.86155e19	2.08933
$415$	4.90425e18	0.113556
$416$	2.71547e19	0.617512
$417$	−3.77995e19	−0.844240
$418$	5.51000e19	1.20873
$419$	1.00607e18	0.0216783	0.0108391	−	0.999941i	$-0.496550\pi$
$419$	1.00607e18	0.0216783	0.0108391	+	0.999941i	$0.496550\pi$
$420$	3.50776e19	0.742439
$421$	−7.33823e19	−1.52572	−0.762862	−	0.646562i	$-0.776206\pi$
$421$	−7.33823e19	−1.52572	−0.762862	+	0.646562i	$0.776206\pi$
$422$	−2.43825e19	−0.498007
$423$	7.16913e19	1.43851
$424$	−3.36739e19	−0.663818
$425$	−8.33212e18	−0.161376
$426$	−8.78394e19	−1.67154
$427$	1.26224e20	2.36011
$428$	−2.33533e19	−0.429063
$429$	−8.35710e19	−1.50878
$430$	−2.16515e19	−0.384127
$431$	5.30892e18	0.0925607	0.0462804	−	0.998928i	$-0.485263\pi$
$431$	5.30892e18	0.0925607	0.0462804	+	0.998928i	$0.485263\pi$
$432$	−6.55532e19	−1.12322
$433$	8.56835e18	0.144291	0.0721453	−	0.997394i	$-0.477015\pi$
$433$	8.56835e18	0.144291	0.0721453	+	0.997394i	$0.477015\pi$
$434$	−1.28284e20	−2.12324
$435$	−1.90567e19	−0.310013
$436$	−2.79064e19	−0.446226
$437$	8.23603e19	1.29451
$438$	5.10959e19	0.789461
$439$	−5.43051e19	−0.824815	−0.412408	−	0.910999i	$-0.635312\pi$
$439$	−5.43051e19	−0.824815	−0.412408	+	0.910999i	$0.635312\pi$
$440$	−5.11384e19	−0.763575
$441$	1.00709e20	1.47835
$442$	1.56130e20	2.25330
$443$	−1.28026e20	−1.81665	−0.908323	−	0.418270i	$-0.862637\pi$
$443$	−1.28026e20	−1.81665	−0.908323	+	0.418270i	$0.862637\pi$
$444$	4.45849e19	0.622036
$445$	−8.91076e19	−1.22240
$446$	1.72320e19	0.232447
$447$	−1.89759e19	−0.251707
$448$	5.43481e19	0.708923
$449$	1.39143e20	1.78490	0.892452	−	0.451142i	$-0.148983\pi$
$449$	1.39143e20	1.78490	0.892452	+	0.451142i	$0.148983\pi$
$450$	1.18147e19	0.149049
$451$	−1.20922e20	−1.50031
$452$	3.77964e19	0.461224
$453$	−1.98181e19	−0.237862
$454$	1.00343e20	1.18459
$455$	−1.24936e20	−1.45078
$456$	−1.23102e20	−1.40614
$457$	1.24345e20	1.39719	0.698597	−	0.715516i	$-0.253808\pi$
$457$	1.24345e20	1.39719	0.698597	+	0.715516i	$0.253808\pi$
$458$	−8.55329e19	−0.945458
$459$	−1.66190e20	−1.80722
$460$	3.58718e19	0.383768
$461$	3.63216e19	0.382303	0.191152	−	0.981561i	$-0.438778\pi$
$461$	3.63216e19	0.382303	0.191152	+	0.981561i	$0.438778\pi$
$462$	2.32658e20	2.40937
$463$	3.57104e19	0.363863	0.181931	−	0.983311i	$-0.441765\pi$
$463$	3.57104e19	0.363863	0.181931	+	0.983311i	$0.441765\pi$
$464$	2.25483e19	0.226062
$465$	−2.24666e20	−2.21636
$466$	9.53269e19	0.925382
$467$	−8.13918e19	−0.777507	−0.388753	−	0.921342i	$-0.627094\pi$
$467$	−8.13918e19	−0.777507	−0.388753	+	0.921342i	$0.627094\pi$
$468$	−5.35933e19	−0.503810
$469$	−1.22376e19	−0.113214
$470$	1.19882e20	1.09149
$471$	−1.15048e19	−0.103092
$472$	3.98762e19	0.351681
$473$	−3.47643e19	−0.301769
$474$	−2.32185e20	−1.98379
$475$	1.09807e19	0.0923484
$476$	−1.05222e20	−0.871072
$477$	1.64108e20	1.33734
$478$	−2.27620e20	−1.82600
$479$	−1.04531e20	−0.825521	−0.412760	−	0.910840i	$-0.635435\pi$
$479$	−1.04531e20	−0.825521	−0.412760	+	0.910840i	$0.635435\pi$
$480$	−1.32395e20	−1.02935
$481$	−1.58798e20	−1.21550
$482$	−2.35742e19	−0.177658
$483$	3.47764e20	2.58037
$484$	−5.18638e18	−0.0378899
$485$	2.43690e19	0.175297
$486$	−1.74194e20	−1.23384
$487$	2.20908e20	1.54079	0.770396	−	0.637566i	$-0.220059\pi$
$487$	2.20908e20	1.54079	0.770396	+	0.637566i	$0.220059\pi$
$488$	−1.92935e20	−1.32515
$489$	−3.38481e19	−0.228938
$490$	1.68405e20	1.12172
$491$	−9.63040e19	−0.631733	−0.315866	−	0.948804i	$-0.602295\pi$
$491$	−9.63040e19	−0.631733	−0.315866	+	0.948804i	$0.602295\pi$
$492$	−1.26782e20	−0.819068
$493$	5.71643e19	0.363725
$494$	−2.05761e20	−1.28947
$495$	2.49221e20	1.53832
$496$	2.65829e20	1.61618
$497$	−2.10846e20	−1.26268
$498$	3.41047e19	0.201185
$499$	1.77788e20	1.03311	0.516557	−	0.856253i	$-0.327213\pi$
$499$	1.77788e20	1.03311	0.516557	+	0.856253i	$0.327213\pi$
$500$	−5.32670e19	−0.304918
$501$	1.82503e20	1.02917
$502$	3.73893e20	2.07716
$503$	1.30548e19	0.0714513	0.0357257	−	0.999362i	$-0.488626\pi$
$503$	1.30548e19	0.0714513	0.0357257	+	0.999362i	$0.488626\pi$
$504$	−3.17932e20	−1.71437
$505$	−2.10590e20	−1.11880
$506$	2.37925e20	1.24541
$507$	9.46667e17	0.00488245
$508$	−3.82152e19	−0.194204
$509$	−3.59439e20	−1.79987	−0.899936	−	0.436022i	$-0.856387\pi$
$509$	−3.59439e20	−1.79987	−0.899936	+	0.436022i	$0.856387\pi$
$510$	−7.61228e20	−3.75611
$511$	1.22648e20	0.596356
$512$	−4.19720e19	−0.201111
$513$	2.19019e20	1.03419
$514$	2.82364e20	1.31397
$515$	2.39989e20	1.10062
$516$	−3.64492e19	−0.164746
$517$	1.92485e20	0.857469
$518$	4.42086e20	1.94104
$519$	3.67920e20	1.59220
$520$	1.90967e20	0.814577
$521$	2.02584e20	0.851772	0.425886	−	0.904777i	$-0.359963\pi$
$521$	2.02584e20	0.851772	0.425886	+	0.904777i	$0.359963\pi$
$522$	−8.10573e19	−0.335941
$523$	−1.47875e20	−0.604132	−0.302066	−	0.953287i	$-0.597676\pi$
$523$	−1.47875e20	−0.604132	−0.302066	+	0.953287i	$0.597676\pi$
$524$	4.06354e18	0.0163651
$525$	4.63658e19	0.184079
$526$	4.05750e19	0.158806
$527$	6.73928e20	2.60036
$528$	−4.82112e20	−1.83398
$529$	8.90018e19	0.333796
$530$	2.74421e20	1.01472
$531$	−1.94335e20	−0.708505
$532$	1.38670e20	0.498476
$533$	4.51559e20	1.60052
$534$	−6.19666e20	−2.16570
$535$	−4.05539e20	−1.39759
$536$	1.87054e19	0.0635668
$537$	−3.44146e20	−1.15328
$538$	−3.81187e19	−0.125971
$539$	2.70395e20	0.881217
$540$	9.53929e19	0.306593
$541$	−1.31497e19	−0.0416807	−0.0208404	−	0.999783i	$-0.506634\pi$
$541$	−1.31497e19	−0.0416807	−0.0208404	+	0.999783i	$0.506634\pi$
$542$	2.10040e20	0.656610
$543$	−1.14887e20	−0.354219
$544$	3.97145e20	1.20769
$545$	−4.84605e20	−1.45350
$546$	−8.68818e20	−2.57030
$547$	−9.12912e19	−0.266394	−0.133197	−	0.991090i	$-0.542524\pi$
$547$	−9.12912e19	−0.266394	−0.133197	+	0.991090i	$0.542524\pi$
$548$	9.66166e19	0.278098
$549$	9.40264e20	2.66967
$550$	3.17216e19	0.0888453
$551$	−7.53356e19	−0.208144
$552$	−5.31564e20	−1.44881
$553$	−5.57326e20	−1.49855
$554$	7.81314e20	2.07254
$555$	7.74234e20	2.02616
$556$	−6.50837e19	−0.168040
$557$	−2.88740e20	−0.735518	−0.367759	−	0.929921i	$-0.619875\pi$
$557$	−2.88740e20	−0.735518	−0.367759	+	0.929921i	$0.619875\pi$
$558$	−9.55612e20	−2.40173
$559$	1.29821e20	0.321925
$560$	−7.20740e20	−1.76347
$561$	−1.22225e21	−2.95079
$562$	−1.69777e19	−0.0404442
$563$	−3.70460e20	−0.870820	−0.435410	−	0.900232i	$-0.643397\pi$
$563$	−3.70460e20	−0.870820	−0.435410	+	0.900232i	$0.643397\pi$
$564$	2.01814e20	0.468121
$565$	6.56349e20	1.50235
$566$	−1.06105e20	−0.239670
$567$	−5.89782e19	−0.131468
$568$	3.22282e20	0.708963
$569$	−5.08795e19	−0.110459	−0.0552295	−	0.998474i	$-0.517589\pi$
$569$	−5.08795e19	−0.110459	−0.0552295	+	0.998474i	$0.517589\pi$
$570$	1.00321e21	2.14946
$571$	6.80324e20	1.43862	0.719308	−	0.694691i	$-0.244459\pi$
$571$	6.80324e20	1.43862	0.719308	+	0.694691i	$0.244459\pi$
$572$	−1.43894e20	−0.300311
$573$	6.59518e19	0.135852
$574$	−1.25712e21	−2.55587
$575$	4.74155e19	0.0951506
$576$	4.04849e20	0.801908
$577$	6.43749e20	1.25863	0.629315	−	0.777150i	$-0.283335\pi$
$577$	6.43749e20	1.25863	0.629315	+	0.777150i	$0.283335\pi$
$578$	1.68827e21	3.25823
$579$	−1.52809e20	−0.291111
$580$	−3.28122e19	−0.0617057
$581$	8.18636e19	0.151974
$582$	1.69465e20	0.310568
$583$	4.40618e20	0.797164
$584$	−1.87471e20	−0.334839
$585$	−9.30668e20	−1.64107
$586$	4.17808e20	0.727351
$587$	3.40849e20	0.585837	0.292918	−	0.956137i	$-0.405374\pi$
$587$	3.40849e20	0.585837	0.292918	+	0.956137i	$0.405374\pi$
$588$	2.83500e20	0.481086
$589$	−8.88156e20	−1.48807
$590$	−3.24966e20	−0.537586
$591$	1.41879e21	2.31746
$592$	−9.16086e20	−1.47749
$593$	4.36578e20	0.695268	0.347634	−	0.937630i	$-0.386985\pi$
$593$	4.36578e20	0.695268	0.347634	+	0.937630i	$0.386985\pi$
$594$	6.32709e20	0.994960
$595$	−1.82722e21	−2.83735
$596$	−3.26730e19	−0.0501004
$597$	1.55833e21	2.35967
$598$	−8.88487e20	−1.32859
$599$	−6.92399e20	−1.02248	−0.511240	−	0.859438i	$-0.670814\pi$
$599$	−6.92399e20	−1.02248	−0.511240	+	0.859438i	$0.670814\pi$
$600$	−7.08711e19	−0.103356
$601$	4.38273e20	0.631228	0.315614	−	0.948888i	$-0.397789\pi$
$601$	4.38273e20	0.631228	0.315614	+	0.948888i	$0.397789\pi$
$602$	−3.61415e20	−0.514083
$603$	−9.11599e19	−0.128063
$604$	−3.41231e19	−0.0473447
$605$	−9.00633e19	−0.123419
$606$	−1.46447e21	−1.98215
$607$	−3.34920e19	−0.0447740	−0.0223870	−	0.999749i	$-0.507127\pi$
$607$	−3.34920e19	−0.0447740	−0.0223870	+	0.999749i	$0.507127\pi$
$608$	−5.23389e20	−0.691111
$609$	−3.18103e20	−0.414894
$610$	1.57230e21	2.02564
$611$	−7.18800e20	−0.914742
$612$	−7.83817e20	−0.985324
$613$	−3.88807e20	−0.482814	−0.241407	−	0.970424i	$-0.577609\pi$
$613$	−3.88807e20	−0.482814	−0.241407	+	0.970424i	$0.577609\pi$
$614$	3.50736e20	0.430247
$615$	−2.20162e21	−2.66796
$616$	−8.53622e20	−1.02190
$617$	−1.28188e21	−1.51603	−0.758016	−	0.652236i	$-0.773831\pi$
$617$	−1.28188e21	−1.51603	−0.758016	+	0.652236i	$0.773831\pi$
$618$	1.66891e21	1.94993
$619$	9.13699e20	1.05469	0.527343	−	0.849652i	$-0.323188\pi$
$619$	9.13699e20	1.05469	0.527343	+	0.849652i	$0.323188\pi$
$620$	−3.86834e20	−0.441150
$621$	9.45737e20	1.06557
$622$	1.19299e21	1.32803
$623$	−1.48742e21	−1.63596
$624$	1.80036e21	1.95647
$625$	−1.00173e21	−1.07560
$626$	−1.34901e20	−0.143122
$627$	1.61078e21	1.68861
$628$	−1.98092e19	−0.0205196
$629$	−2.32246e21	−2.37721
$630$	2.59094e21	2.62062
$631$	1.35842e21	1.35773	0.678866	−	0.734262i	$-0.262472\pi$
$631$	1.35842e21	1.35773	0.678866	+	0.734262i	$0.262472\pi$
$632$	8.51883e20	0.841399
$633$	−7.12791e20	−0.695720
$634$	8.77186e20	0.846101
$635$	−6.63621e20	−0.632582
$636$	4.61973e20	0.435199
$637$	−1.00974e21	−0.940077
$638$	−2.17632e20	−0.200248
$639$	−1.57063e21	−1.42829
$640$	1.39070e21	1.24993
$641$	1.12998e21	1.00377	0.501887	−	0.864933i	$-0.332639\pi$
$641$	1.12998e21	1.00377	0.501887	+	0.864933i	$0.332639\pi$
$642$	−2.82017e21	−2.47607
$643$	−8.23519e20	−0.714647	−0.357323	−	0.933981i	$-0.616311\pi$
$643$	−8.23519e20	−0.714647	−0.357323	+	0.933981i	$0.616311\pi$
$644$	5.98785e20	0.513602
$645$	−6.32953e20	−0.536629
$646$	−3.00930e21	−2.52187
$647$	2.25939e21	1.87158	0.935791	−	0.352556i	$-0.114687\pi$
$647$	2.25939e21	1.87158	0.935791	+	0.352556i	$0.114687\pi$
$648$	9.01493e19	0.0738159
$649$	−5.21774e20	−0.422326
$650$	−1.18458e20	−0.0947795
$651$	−3.75022e21	−2.96619
$652$	−5.82802e19	−0.0455684
$653$	−2.01292e21	−1.55589	−0.777944	−	0.628333i	$-0.783737\pi$
$653$	−2.01292e21	−1.55589	−0.777944	+	0.628333i	$0.783737\pi$
$654$	−3.37000e21	−2.57512
$655$	7.05649e19	0.0533063
$656$	2.60499e21	1.94548
$657$	9.13630e20	0.674575
$658$	2.00111e21	1.46075
$659$	−2.34491e21	−1.69233	−0.846165	−	0.532921i	$-0.821094\pi$
$659$	−2.34491e21	−1.69233	−0.846165	+	0.532921i	$0.821094\pi$
$660$	7.01568e20	0.500600
$661$	1.18629e21	0.836911	0.418455	−	0.908237i	$-0.362572\pi$
$661$	1.18629e21	0.836911	0.418455	+	0.908237i	$0.362572\pi$
$662$	−5.95675e20	−0.415504
$663$	4.56425e21	3.14788
$664$	−1.25130e20	−0.0853298
$665$	2.40805e21	1.62369
$666$	3.29318e21	2.19563
$667$	−3.25304e20	−0.214460
$668$	3.14236e20	0.204848
$669$	5.03753e20	0.324730
$670$	−1.52437e20	−0.0971693
$671$	2.52453e21	1.59134
$672$	−2.21000e21	−1.37760
$673$	−2.11153e21	−1.30162	−0.650812	−	0.759239i	$-0.725571\pi$
$673$	−2.11153e21	−1.30162	−0.650812	+	0.759239i	$0.725571\pi$
$674$	−1.40003e21	−0.853468
$675$	1.26091e20	0.0760161
$676$	1.62998e18	0.000971814 0
$677$	−8.30115e18	−0.00489467	−0.00244733	−	0.999997i	$-0.500779\pi$
$677$	−8.30115e18	−0.00489467	−0.00244733	+	0.999997i	$0.500779\pi$
$678$	4.56433e21	2.66167
$679$	4.06776e20	0.234602
$680$	2.79294e21	1.59310
$681$	2.93338e21	1.65488
$682$	−2.56574e21	−1.43163
$683$	1.15101e21	0.635220	0.317610	−	0.948221i	$-0.397120\pi$
$683$	1.15101e21	0.635220	0.317610	+	0.948221i	$0.397120\pi$
$684$	1.03298e21	0.563858
$685$	1.67778e21	0.905850
$686$	−1.83732e20	−0.0981193
$687$	−2.50044e21	−1.32081
$688$	7.48921e20	0.391312
$689$	−1.64540e21	−0.850409
$690$	4.33191e21	2.21468
$691$	−6.14511e20	−0.310773	−0.155387	−	0.987854i	$-0.549662\pi$
$691$	−6.14511e20	−0.310773	−0.155387	+	0.987854i	$0.549662\pi$
$692$	6.33489e20	0.316916
$693$	4.16009e21	2.05875
$694$	−1.78484e21	−0.873785
$695$	−1.13020e21	−0.547357
$696$	4.86226e20	0.232953
$697$	6.60417e21	3.13020
$698$	−2.91728e20	−0.136793
$699$	2.78675e21	1.29277
$700$	7.98334e19	0.0366395
$701$	6.13112e20	0.278391	0.139195	−	0.990265i	$-0.455548\pi$
$701$	6.13112e20	0.278391	0.139195	+	0.990265i	$0.455548\pi$
$702$	−2.36273e21	−1.06142
$703$	3.06072e21	1.36037
$704$	1.08699e21	0.478001
$705$	3.50458e21	1.52482
$706$	−1.79599e21	−0.773157
$707$	−3.51525e21	−1.49731
$708$	−5.47063e20	−0.230562
$709$	−4.20918e21	−1.75530	−0.877650	−	0.479303i	$-0.840890\pi$
$709$	−4.20918e21	−1.75530	−0.877650	+	0.479303i	$0.840890\pi$
$710$	−2.62639e21	−1.08373
$711$	−4.15162e21	−1.69510
$712$	2.27355e21	0.918553
$713$	−3.83512e21	−1.53323
$714$	−1.27067e22	−5.02685
$715$	−2.49877e21	−0.978207
$716$	−5.92555e20	−0.229552
$717$	−6.65416e21	−2.55094
$718$	1.58636e21	0.601822
$719$	9.68168e19	0.0363483	0.0181742	−	0.999835i	$-0.494215\pi$
$719$	9.68168e19	0.0363483	0.0181742	+	0.999835i	$0.494215\pi$
$720$	−5.36892e21	−1.99477
$721$	4.00599e21	1.47297
$722$	8.09317e20	0.294503
$723$	−6.89160e20	−0.248189
$724$	−1.97814e20	−0.0705047
$725$	−4.33714e19	−0.0152992
$726$	−6.26312e20	−0.218658
$727$	3.78937e21	1.30936	0.654680	−	0.755906i	$-0.272803\pi$
$727$	3.78937e21	1.30936	0.654680	+	0.755906i	$0.272803\pi$
$728$	3.18769e21	1.09016
$729$	−4.81337e21	−1.62927
$730$	1.52777e21	0.511841
$731$	1.89866e21	0.629604
$732$	2.64688e21	0.868764
$733$	−2.22276e21	−0.722126	−0.361063	−	0.932542i	$-0.617586\pi$
$733$	−2.22276e21	−0.722126	−0.361063	+	0.932542i	$0.617586\pi$
$734$	−2.38224e21	−0.766064
$735$	4.92308e21	1.56705
$736$	−2.26003e21	−0.712082
$737$	−2.44757e20	−0.0763359
$738$	−9.36452e21	−2.89110
$739$	2.81543e21	0.860421	0.430210	−	0.902729i	$-0.358439\pi$
$739$	2.81543e21	0.860421	0.430210	+	0.902729i	$0.358439\pi$
$740$	1.33309e21	0.403293
$741$	−6.01513e21	−1.80139
$742$	4.58074e21	1.35802
$743$	−1.76467e21	−0.517902	−0.258951	−	0.965890i	$-0.583377\pi$
$743$	−1.76467e21	−0.517902	−0.258951	+	0.965890i	$0.583377\pi$
$744$	5.73228e21	1.66544
$745$	−5.67378e20	−0.163193
$746$	6.31955e21	1.79947
$747$	6.09816e20	0.171907
$748$	−2.10448e21	−0.587332
$749$	−6.76942e21	−1.87041
$750$	−6.43257e21	−1.75965
$751$	−1.38229e21	−0.374370	−0.187185	−	0.982325i	$-0.559936\pi$
$751$	−1.38229e21	−0.374370	−0.187185	+	0.982325i	$0.559936\pi$
$752$	−4.14668e21	−1.11190
$753$	1.09303e22	2.90181
$754$	8.12707e20	0.213623
$755$	−5.92560e20	−0.154216
$756$	1.59233e21	0.410318
$757$	−2.86614e21	−0.731272	−0.365636	−	0.930758i	$-0.619148\pi$
$757$	−2.86614e21	−0.731272	−0.365636	+	0.930758i	$0.619148\pi$
$758$	6.29638e21	1.59064
$759$	6.95543e21	1.73985
$760$	−3.68075e21	−0.911664
$761$	−7.15579e20	−0.175498	−0.0877492	−	0.996143i	$-0.527967\pi$
$761$	−7.15579e20	−0.175498	−0.0877492	+	0.996143i	$0.527967\pi$
$762$	−4.61490e21	−1.12073
$763$	−8.08921e21	−1.94524
$764$	1.13557e20	0.0270404
$765$	−1.36113e22	−3.20950
$766$	3.79395e21	0.885881
$767$	1.94847e21	0.450534
$768$	6.10295e21	1.39743
$769$	4.80397e21	1.08931	0.544656	−	0.838659i	$-0.316660\pi$
$769$	4.80397e21	1.08931	0.544656	+	0.838659i	$0.316660\pi$
$770$	6.95647e21	1.56210
$771$	8.25454e21	1.83563
$772$	−2.63108e20	−0.0579435
$773$	8.45805e21	1.84469	0.922346	−	0.386365i	$-0.126270\pi$
$773$	8.45805e21	1.84469	0.922346	+	0.386365i	$0.126270\pi$
$774$	−2.69225e21	−0.581511
$775$	−5.11319e20	−0.109378
$776$	−6.21765e20	−0.131724
$777$	1.29238e22	2.71164
$778$	−8.65348e20	−0.179822
$779$	−8.70349e21	−1.79128
$780$	−2.61987e21	−0.534036
$781$	−4.21701e21	−0.851377
$782$	−1.29944e22	−2.59839
$783$	−8.65073e20	−0.171332
$784$	−5.82507e21	−1.14270
$785$	−3.43993e20	−0.0668387
$786$	4.90717e20	0.0944413
$787$	9.07742e21	1.73042	0.865211	−	0.501409i	$-0.167185\pi$
$787$	9.07742e21	1.73042	0.865211	+	0.501409i	$0.167185\pi$
$788$	2.44290e21	0.461274
$789$	1.18616e21	0.221853
$790$	−6.94230e21	−1.28618
$791$	1.09560e22	2.01062
$792$	−6.35878e21	−1.15594
$793$	−9.42738e21	−1.69763
$794$	1.17272e22	2.09189
$795$	8.02232e21	1.41758
$796$	2.68315e21	0.469675
$797$	−7.01384e21	−1.21624	−0.608119	−	0.793846i	$-0.708076\pi$
$797$	−7.01384e21	−1.21624	−0.608119	+	0.793846i	$0.708076\pi$
$798$	1.67459e22	2.87665
$799$	−1.05126e22	−1.78900
$800$	−3.01319e20	−0.0507987
$801$	−1.10801e22	−1.85054
$802$	−1.16799e22	−1.93255
$803$	2.45302e21	0.402101
$804$	−2.56619e20	−0.0416744
$805$	1.03981e22	1.67296
$806$	9.58126e21	1.52725
$807$	−1.11435e21	−0.175982
$808$	5.37313e21	0.840702
$809$	2.62121e21	0.406338	0.203169	−	0.979144i	$-0.434876\pi$
$809$	2.62121e21	0.406338	0.203169	+	0.979144i	$0.434876\pi$
$810$	−7.34659e20	−0.112836
$811$	−7.52299e21	−1.14481	−0.572405	−	0.819971i	$-0.693990\pi$
$811$	−7.52299e21	−1.14481	−0.572405	+	0.819971i	$0.693990\pi$
$812$	−5.47714e20	−0.0825816
$813$	6.14024e21	0.917290
$814$	8.84192e21	1.30877
$815$	−1.01206e21	−0.148430
$816$	2.63307e22	3.82636
$817$	−2.50221e21	−0.360295
$818$	−9.18394e21	−1.31033
$819$	−1.55351e22	−2.19626
$820$	−3.79078e21	−0.531037
$821$	8.31296e21	1.15394	0.576969	−	0.816766i	$-0.304235\pi$
$821$	8.31296e21	1.15394	0.576969	+	0.816766i	$0.304235\pi$
$822$	1.16675e22	1.60487
$823$	−4.82095e21	−0.657104	−0.328552	−	0.944486i	$-0.606561\pi$
$823$	−4.82095e21	−0.657104	−0.328552	+	0.944486i	$0.606561\pi$
$824$	−6.12323e21	−0.827039
$825$	9.27337e20	0.124118
$826$	−5.42445e21	−0.719458
$827$	−1.13083e22	−1.48629	−0.743147	−	0.669128i	$-0.766668\pi$
$827$	−1.13083e22	−1.48629	−0.743147	+	0.669128i	$0.766668\pi$
$828$	4.46046e21	0.580968
$829$	3.54282e21	0.457289	0.228644	−	0.973510i	$-0.426571\pi$
$829$	3.54282e21	0.457289	0.228644	+	0.973510i	$0.426571\pi$
$830$	1.01973e21	0.130437
$831$	2.28407e22	2.89535
$832$	−4.05914e21	−0.509929
$833$	−1.47677e22	−1.83855
$834$	−7.85958e21	−0.969736
$835$	5.45683e21	0.667255
$836$	2.77346e21	0.336104
$837$	−1.01986e22	−1.22490
$838$	2.09191e20	0.0249008
$839$	2.57132e21	0.303348	0.151674	−	0.988431i	$-0.451534\pi$
$839$	2.57132e21	0.303348	0.151674	+	0.988431i	$0.451534\pi$
$840$	−1.55419e22	−1.81723
$841$	2.97558e20	0.0344828
$842$	−1.52582e22	−1.75252
$843$	−4.96320e20	−0.0565008
$844$	−1.22729e21	−0.138478
$845$	2.83053e19	0.00316550
$846$	1.49066e22	1.65235
$847$	−1.50337e21	−0.165174
$848$	−9.49215e21	−1.03370
$849$	−3.10185e21	−0.334821
$850$	−1.73248e21	−0.185365
$851$	1.32164e22	1.40165
$852$	−4.42139e21	−0.464795
$853$	1.45537e22	1.51654	0.758272	−	0.651939i	$-0.226044\pi$
$853$	1.45537e22	1.51654	0.758272	+	0.651939i	$0.226044\pi$
$854$	2.62455e22	2.71094
$855$	1.79380e22	1.83666
$856$	1.03472e22	1.05019
$857$	1.17842e22	1.18562	0.592808	−	0.805344i	$-0.298019\pi$
$857$	1.17842e22	1.18562	0.592808	+	0.805344i	$0.298019\pi$
$858$	−1.73767e22	−1.73306
$859$	−1.42222e22	−1.40610	−0.703052	−	0.711139i	$-0.748180\pi$
$859$	−1.42222e22	−1.40610	−0.703052	+	0.711139i	$0.748180\pi$
$860$	−1.08983e21	−0.106812
$861$	−3.67503e22	−3.57056
$862$	1.10387e21	0.106320
$863$	−1.12982e22	−1.07877	−0.539384	−	0.842060i	$-0.681343\pi$
$863$	−1.12982e22	−1.07877	−0.539384	+	0.842060i	$0.681343\pi$
$864$	−6.01003e21	−0.568884
$865$	1.10008e22	1.03229
$866$	1.78160e21	0.165739
$867$	4.93542e22	4.55178
$868$	−6.45717e21	−0.590398
$869$	−1.11468e22	−1.01042
$870$	−3.96243e21	−0.356096
$871$	9.13998e20	0.0814346
$872$	1.23645e22	1.09220
$873$	3.03015e21	0.265373
$874$	1.71250e22	1.48695
$875$	−1.54405e22	−1.32923
$876$	2.57191e21	0.219521
$877$	1.38964e21	0.117600	0.0587998	−	0.998270i	$-0.481273\pi$
$877$	1.38964e21	0.117600	0.0587998	+	0.998270i	$0.481273\pi$
$878$	−1.12915e22	−0.947424
$879$	1.22141e22	1.01612
$880$	−1.44151e22	−1.18904
$881$	−4.03845e21	−0.330290	−0.165145	−	0.986269i	$-0.552809\pi$
$881$	−4.03845e21	−0.330290	−0.165145	+	0.986269i	$0.552809\pi$
$882$	2.09402e22	1.69811
$883$	1.15866e22	0.931646	0.465823	−	0.884878i	$-0.345758\pi$
$883$	1.15866e22	0.931646	0.465823	+	0.884878i	$0.345758\pi$
$884$	7.85880e21	0.626562
$885$	−9.49994e21	−0.751011
$886$	−2.66202e22	−2.08669
$887$	1.58422e22	1.23137	0.615685	−	0.787992i	$-0.288879\pi$
$887$	1.58422e22	1.23137	0.615685	+	0.787992i	$0.288879\pi$
$888$	−1.97543e22	−1.52252
$889$	−1.10774e22	−0.846594
$890$	−1.85280e22	−1.40412
$891$	−1.17959e21	−0.0886438
$892$	8.67370e20	0.0646350
$893$	1.38544e22	1.02377
$894$	−3.94562e21	−0.289124
$895$	−1.02899e22	−0.747722
$896$	2.32142e22	1.67280
$897$	−2.59737e22	−1.85606
$898$	2.89318e22	2.05023
$899$	3.50801e21	0.246526
$900$	5.94693e20	0.0414452
$901$	−2.40645e22	−1.66318
$902$	−2.51430e22	−1.72333
$903$	−1.05655e22	−0.718178
$904$	−1.67465e22	−1.12891
$905$	−3.43512e21	−0.229656
$906$	−4.12074e21	−0.273221
$907$	−9.77034e21	−0.642473	−0.321236	−	0.946999i	$-0.604098\pi$
$907$	−9.77034e21	−0.642473	−0.321236	+	0.946999i	$0.604098\pi$
$908$	5.05074e21	0.329391
$909$	−2.61857e22	−1.69370
$910$	−2.59776e22	−1.66644
$911$	1.75453e22	1.11628	0.558139	−	0.829747i	$-0.311516\pi$
$911$	1.75453e22	1.11628	0.558139	+	0.829747i	$0.311516\pi$
$912$	−3.47007e22	−2.18966
$913$	1.63731e21	0.102471
$914$	2.58548e22	1.60489
$915$	4.59641e22	2.82983
$916$	−4.30529e21	−0.262898
$917$	1.17790e21	0.0713406
$918$	−3.45556e22	−2.07586
$919$	2.37729e22	1.41650	0.708248	−	0.705963i	$-0.249486\pi$
$919$	2.37729e22	1.41650	0.708248	+	0.705963i	$0.249486\pi$
$920$	−1.58937e22	−0.939328
$921$	1.02533e22	0.601058
$922$	7.55227e21	0.439133
$923$	1.57476e22	0.908243
$924$	1.17108e22	0.669959
$925$	1.76208e21	0.0999915
$926$	7.42520e21	0.417951
$927$	2.98413e22	1.66617
$928$	2.06727e21	0.114495
$929$	3.23678e22	1.77826	0.889130	−	0.457655i	$-0.151311\pi$
$929$	3.23678e22	1.77826	0.889130	+	0.457655i	$0.151311\pi$
$930$	−4.67144e22	−2.54583
$931$	1.94620e22	1.05212
$932$	4.79827e21	0.257315
$933$	3.48753e22	1.85527
$934$	−1.69236e22	−0.893084
$935$	−3.65452e22	−1.91312
$936$	2.37457e22	1.23315
$937$	−2.23867e22	−1.15330	−0.576651	−	0.816990i	$-0.695641\pi$
$937$	−2.23867e22	−1.15330	−0.576651	+	0.816990i	$0.695641\pi$
$938$	−2.54453e21	−0.130043
$939$	−3.94364e21	−0.199943
$940$	6.03424e21	0.303503
$941$	−2.38895e22	−1.19203	−0.596013	−	0.802975i	$-0.703249\pi$
$941$	−2.38895e22	−1.19203	−0.596013	+	0.802975i	$0.703249\pi$
$942$	−2.39217e21	−0.118416
$943$	−3.75822e22	−1.84563
$944$	1.12405e22	0.547640
$945$	2.76515e22	1.33653
$946$	−7.22847e21	−0.346627
$947$	−8.20240e21	−0.390226	−0.195113	−	0.980781i	$-0.562507\pi$
$947$	−8.20240e21	−0.390226	−0.195113	+	0.980781i	$0.562507\pi$
$948$	−1.16870e22	−0.551621
$949$	−9.16035e21	−0.428959
$950$	2.28320e21	0.106076
$951$	2.56433e22	1.18201
$952$	4.66208e22	2.13207
$953$	−1.43822e22	−0.652571	−0.326286	−	0.945271i	$-0.605797\pi$
$953$	−1.43822e22	−0.652571	−0.326286	+	0.945271i	$0.605797\pi$
$954$	3.41227e22	1.53614
$955$	1.97195e21	0.0880788
$956$	−1.14572e22	−0.507745
$957$	−6.36219e21	−0.279748
$958$	−2.17349e22	−0.948235
$959$	2.80062e22	1.21231
$960$	1.97908e22	0.850018
$961$	1.78918e22	0.762482
$962$	−3.30185e22	−1.39619
$963$	−5.04266e22	−2.11574
$964$	−1.18661e21	−0.0494002
$965$	−4.56898e21	−0.188740
$966$	7.23099e22	2.96394
$967$	1.40210e20	0.00570269	0.00285135	−	0.999996i	$-0.499092\pi$
$967$	1.40210e20	0.00570269	0.00285135	+	0.999996i	$0.499092\pi$
$968$	2.29793e21	0.0927411
$969$	−8.79730e22	−3.52307
$970$	5.06699e21	0.201355
$971$	2.44982e22	0.966029	0.483015	−	0.875612i	$-0.339542\pi$
$971$	2.44982e22	0.966029	0.483015	+	0.875612i	$0.339542\pi$
$972$	−8.76803e21	−0.343088
$973$	−1.88658e22	−0.732535
$974$	4.59329e22	1.76983
$975$	−3.46296e21	−0.132408
$976$	−5.43855e22	−2.06352
$977$	3.43793e22	1.29446	0.647229	−	0.762296i	$-0.275928\pi$
$977$	3.43793e22	1.29446	0.647229	+	0.762296i	$0.275928\pi$
$978$	−7.03797e21	−0.262970
$979$	−2.97490e22	−1.10307
$980$	8.47663e21	0.311909
$981$	−6.02580e22	−2.20038
$982$	−2.00243e22	−0.725640
$983$	−3.79088e22	−1.36329	−0.681645	−	0.731683i	$-0.738735\pi$
$983$	−3.79088e22	−1.36329	−0.681645	+	0.731683i	$0.738735\pi$
$984$	5.61735e22	2.00479
$985$	4.24218e22	1.50251
$986$	1.18861e22	0.417793
$987$	5.84998e22	2.04068
$988$	−1.03569e22	−0.358554
$989$	−1.08047e22	−0.371227
$990$	5.18200e22	1.76699
$991$	−2.65605e21	−0.0898844	−0.0449422	−	0.998990i	$-0.514310\pi$
$991$	−2.65605e21	−0.0898844	−0.0449422	+	0.998990i	$0.514310\pi$
$992$	2.43717e22	0.818555
$993$	−1.74138e22	−0.580462
$994$	−4.38407e22	−1.45037
$995$	4.65939e22	1.52988
$996$	1.71666e21	0.0559422
$997$	−4.53274e22	−1.46605	−0.733023	−	0.680204i	$-0.761891\pi$
$997$	−4.53274e22	−1.46605	−0.733023	+	0.680204i	$0.761891\pi$
$998$	3.69671e22	1.18669
$999$	3.51460e22	1.11979

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.16.a.b.1.15	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.16.a.b.1.15	✓	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)

\(f(q)\)	\(=\)	\(q+207.928 q^{2} +6078.50 q^{3} +10466.0 q^{4} +181747. q^{5} +1.26389e6 q^{6} +3.03379e6 q^{7} -4.63720e6 q^{8} +2.25992e7 q^{9} +O(q^{10})\)	\(q+207.928 q^{2} +6078.50 q^{3} +10466.0 q^{4} +181747. q^{5} +1.26389e6 q^{6} +3.03379e6 q^{7} -4.63720e6 q^{8} +2.25992e7 q^{9} +3.77902e7 q^{10} +6.06771e7 q^{11} +6.36178e7 q^{12} -2.26587e8 q^{13} +6.30809e8 q^{14} +1.10475e9 q^{15} -1.30716e9 q^{16} -3.31389e9 q^{17} +4.69901e9 q^{18} +4.36731e9 q^{19} +1.90217e9 q^{20} +1.84409e10 q^{21} +1.26165e10 q^{22} +1.88583e10 q^{23} -2.81872e10 q^{24} +2.51430e9 q^{25} -4.71138e10 q^{26} +5.01495e10 q^{27} +3.17517e10 q^{28} -1.72499e10 q^{29} +2.29708e11 q^{30} -2.03364e11 q^{31} -1.19842e11 q^{32} +3.68825e11 q^{33} -6.89051e11 q^{34} +5.51381e11 q^{35} +2.36524e11 q^{36} +7.00824e11 q^{37} +9.08087e11 q^{38} -1.37731e12 q^{39} -8.42796e11 q^{40} -1.99287e12 q^{41} +3.83437e12 q^{42} -5.72940e11 q^{43} +6.35049e11 q^{44} +4.10733e12 q^{45} +3.92118e12 q^{46} +3.17229e12 q^{47} -7.94554e12 q^{48} +4.45630e12 q^{49} +5.22793e11 q^{50} -2.01435e13 q^{51} -2.37147e12 q^{52} +7.26168e12 q^{53} +1.04275e13 q^{54} +1.10279e13 q^{55} -1.40683e13 q^{56} +2.65467e13 q^{57} -3.58673e12 q^{58} -8.59920e12 q^{59} +1.15623e13 q^{60} +4.16060e13 q^{61} -4.22852e13 q^{62} +6.85612e13 q^{63} +1.79143e13 q^{64} -4.11814e13 q^{65} +7.66891e13 q^{66} -4.03376e12 q^{67} -3.46834e13 q^{68} +1.14630e14 q^{69} +1.14647e14 q^{70} -6.94992e13 q^{71} -1.04797e14 q^{72} +4.04275e13 q^{73} +1.45721e14 q^{74} +1.52832e13 q^{75} +4.57085e13 q^{76} +1.84081e14 q^{77} -2.86381e14 q^{78} -1.83706e14 q^{79} -2.37571e14 q^{80} -1.94405e13 q^{81} -4.14374e14 q^{82} +2.69840e13 q^{83} +1.93003e14 q^{84} -6.02290e14 q^{85} -1.19130e14 q^{86} -1.04853e14 q^{87} -2.81372e14 q^{88} -4.90285e14 q^{89} +8.54030e14 q^{90} -6.87416e14 q^{91} +1.97372e14 q^{92} -1.23615e15 q^{93} +6.59608e14 q^{94} +7.93745e14 q^{95} -7.28461e14 q^{96} +1.34082e14 q^{97} +9.26589e14 q^{98} +1.37125e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 9908 q^{3} + 387418 q^{4} + 230490 q^{5} + 1566838 q^{6} + 2882024 q^{7} + 26209092 q^{8} + 93022899 q^{9}+O(q^{10}) \) 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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